Repository: keep-starknet-strange/garaga Branch: main Commit: 307c00af4a7f Files: 465 Total size: 12.8 MB Directory structure: gitextract_6da2_nl2/ ├── .cargo/ │ └── config.toml ├── .claude/ │ ├── commands/ │ │ ├── bump-version.md │ │ └── upgrade-cairo.md │ └── skills/ │ ├── benchmarking-cairo/ │ │ ├── SKILL.md │ │ ├── installation.md │ │ └── profile.py │ └── cairo-coding/ │ ├── SKILL.md │ └── bounded_int_calc.py ├── .github/ │ ├── .all-contributorsrc │ ├── CODEOWNERS │ ├── ISSUE_TEMPLATE/ │ │ ├── 01_BUG_REPORT.md │ │ ├── 02_FEATURE_REQUEST.md │ │ ├── 03_CODEBASE_IMPROVEMENT.md │ │ └── config.yml │ ├── PULL_REQUEST_TEMPLATE.md │ ├── labels.yml │ ├── scripts/ │ │ ├── declare_maintained_contracts.py │ │ └── verify_contracts.py │ └── workflows/ │ ├── cairo.yml │ ├── docs-sync.yml │ ├── e2e.yml │ ├── hydra.yml │ ├── labels.yml │ ├── maturin.yml │ ├── node.yml │ ├── setup.yml │ └── wasm.yml ├── .gitignore ├── .pre-commit-config.yaml ├── .secrets.template ├── .tool-versions ├── CLAUDE.md ├── Cargo.toml ├── LICENSE ├── Makefile ├── README.md ├── Scarb.toml ├── docs/ │ ├── CODE_OF_CONDUCT.md │ ├── CONTRIBUTING.md │ ├── PYPI_README.md │ ├── SECURITY.md │ ├── benchmarks/ │ │ └── test_summary.json │ └── gitbook/ │ ├── README.md │ ├── SUMMARY.md │ ├── building-powerful-applications.md │ ├── developer-setup-and-guides/ │ │ ├── README.md │ │ ├── garaga-rs-crate/ │ │ │ ├── README.md │ │ │ ├── rust-greater-than-python-bindings.md │ │ │ └── rust-greater-than-wasm-bindings.md │ │ └── working-with-auto-generated-cairo-code.md │ ├── installation/ │ │ ├── README.md │ │ ├── cairo-library.md │ │ ├── developer-setup.md │ │ ├── npm-package.md │ │ ├── python-package.md │ │ └── rust-crate.md │ ├── maintained-smart-contracts/ │ │ ├── README.md │ │ ├── drand.md │ │ ├── risczero.md │ │ └── sp1.md │ ├── security.md │ ├── smart-contract-generators/ │ │ ├── README.md │ │ ├── groth16/ │ │ │ ├── README.md │ │ │ ├── generate-and-deploy-your-verifier-contract.md │ │ │ └── generating-calldata-from-a-proof-and-using-your-deployed-contract/ │ │ │ ├── README.md │ │ │ ├── using-python-garaga-cli.md │ │ │ ├── using-rust.md │ │ │ └── using-typescript.md │ │ └── noir.md │ ├── support.md │ ├── updating-these-docs.md │ └── using-garaga-libraries-in-your-cairo-project/ │ ├── README.md │ ├── ec-multi-scalar-multiplication.md │ ├── ec-signatures.md │ ├── hashing-functions.md │ └── rsa-signatures.md ├── hydra/ │ └── garaga/ │ ├── algebra.py │ ├── curves.py │ ├── drand/ │ │ ├── client.py │ │ └── tlock.py │ ├── extension_field_modulo_circuit.py │ ├── hints/ │ │ ├── bls.py │ │ ├── ecip.py │ │ ├── eisenstein.py │ │ ├── extf_mul.py │ │ ├── fake_glv.py │ │ ├── frobenius.py │ │ ├── io.py │ │ ├── keccak256.py │ │ ├── multi_miller_witness.py │ │ ├── neg_3.py │ │ └── tower_backup.py │ ├── modulo_circuit.py │ ├── modulo_circuit_structs.py │ ├── points.py │ ├── poseidon_transcript.py │ ├── precompiled_circuits/ │ │ ├── all_circuits.py │ │ ├── cofactor_clearing.py │ │ ├── compilable_circuits/ │ │ │ ├── apply_isogeny.py │ │ │ ├── base.py │ │ │ ├── cairo1_mpcheck_circuits.py │ │ │ ├── cairo1_tower_pairing.py │ │ │ ├── common_cairo_fustat_circuits.py │ │ │ ├── rsa.py │ │ │ └── ultra_honk.py │ │ ├── ec.py │ │ ├── final_exp.py │ │ ├── fp2.py │ │ ├── isogeny.py │ │ ├── map_to_curve.py │ │ ├── miller_tower.py │ │ ├── multi_miller_loop.py │ │ ├── multi_pairing_check.py │ │ ├── poseidon_bn254.py │ │ └── zk_honk.py │ ├── rsa_rns.py │ ├── signature.py │ └── starknet/ │ ├── cli/ │ │ ├── declare.py │ │ ├── deploy.py │ │ ├── gen.py │ │ ├── smart_contract_project.py │ │ ├── starknet_cli.py │ │ ├── utils.py │ │ └── verify.py │ ├── constants.py │ ├── groth16_contract_generator/ │ │ ├── calldata.py │ │ ├── examples/ │ │ │ ├── gnark_proof_bn254.json │ │ │ ├── gnark_public_bn254.json │ │ │ ├── gnark_vk_bn254.json │ │ │ ├── proof_bls.json │ │ │ ├── proof_bn254.json │ │ │ ├── proof_risc0.json │ │ │ ├── proof_sp1.json │ │ │ ├── snarkjs_proof_bls12381.json │ │ │ ├── snarkjs_proof_bn254.json │ │ │ ├── snarkjs_public_bls12381.json │ │ │ ├── snarkjs_public_bn254.json │ │ │ ├── snarkjs_vk_bls12381.json │ │ │ ├── snarkjs_vk_bn254.json │ │ │ ├── vk_bls.json │ │ │ ├── vk_bn254.json │ │ │ ├── vk_risc0.json │ │ │ └── vk_sp1.json │ │ ├── generator.py │ │ ├── generator_risc0.py │ │ ├── generator_sp1.py │ │ └── parsing_utils.py │ ├── honk_contract_generator/ │ │ ├── calldata.py │ │ └── generator_honk.py │ └── tests_and_calldata_generators/ │ ├── drand_calldata.py │ ├── map_to_curve.py │ ├── mpcheck.py │ ├── msm.py │ ├── signatures.py │ └── test_writer.py ├── pyproject.toml ├── src/ │ ├── .tool-versions │ ├── Scarb.toml │ ├── contracts/ │ │ ├── autogenerated/ │ │ │ ├── groth16_example_bls12_381/ │ │ │ │ ├── .tool-versions │ │ │ │ ├── Scarb.toml │ │ │ │ ├── src/ │ │ │ │ │ ├── groth16_verifier.cairo │ │ │ │ │ ├── groth16_verifier_constants.cairo │ │ │ │ │ └── lib.cairo │ │ │ │ └── tests/ │ │ │ │ ├── proof_calldata.txt │ │ │ │ └── test_contract.cairo │ │ │ ├── groth16_example_bn254/ │ │ │ │ ├── .tool-versions │ │ │ │ ├── Scarb.toml │ │ │ │ ├── src/ │ │ │ │ │ ├── groth16_verifier.cairo │ │ │ │ │ ├── groth16_verifier_constants.cairo │ │ │ │ │ └── lib.cairo │ │ │ │ └── tests/ │ │ │ │ ├── proof_calldata.txt │ │ │ │ └── test_contract.cairo │ │ │ ├── noir_ultra_keccak_zk_honk_example/ │ │ │ │ ├── .tool-versions │ │ │ │ ├── Scarb.toml │ │ │ │ ├── src/ │ │ │ │ │ ├── honk_verifier.cairo │ │ │ │ │ ├── honk_verifier_circuits.cairo │ │ │ │ │ ├── honk_verifier_constants.cairo │ │ │ │ │ └── lib.cairo │ │ │ │ └── tests/ │ │ │ │ ├── proof_calldata.txt │ │ │ │ └── test_contract.cairo │ │ │ ├── risc0_verifier_bn254/ │ │ │ │ ├── .tool-versions │ │ │ │ ├── Scarb.toml │ │ │ │ ├── src/ │ │ │ │ │ ├── groth16_verifier.cairo │ │ │ │ │ ├── groth16_verifier_constants.cairo │ │ │ │ │ └── lib.cairo │ │ │ │ └── tests/ │ │ │ │ ├── proof_calldata.txt │ │ │ │ └── test_contract.cairo │ │ │ └── sp1_verifier_bn254/ │ │ │ ├── .tool-versions │ │ │ ├── Scarb.toml │ │ │ ├── src/ │ │ │ │ ├── groth16_verifier.cairo │ │ │ │ └── lib.cairo │ │ │ └── tests/ │ │ │ ├── proof_calldata.txt │ │ │ └── test_contract.cairo │ │ ├── drand_decrypt_quicknet/ │ │ │ ├── Scarb.toml │ │ │ └── src/ │ │ │ ├── drand_decrypt.cairo │ │ │ ├── drand_decrypt_constants.cairo │ │ │ └── lib.cairo │ │ ├── drand_quicknet/ │ │ │ ├── .tool-versions │ │ │ ├── Scarb.toml │ │ │ └── src/ │ │ │ ├── drand_verifier.cairo │ │ │ ├── drand_verifier_constants.cairo │ │ │ └── lib.cairo │ │ ├── mutator_set/ │ │ │ ├── .tool-versions │ │ │ ├── Makefile │ │ │ ├── Scarb.toml │ │ │ ├── scripts/ │ │ │ │ ├── prover.py │ │ │ │ └── regenerate_verifier.py │ │ │ ├── snfoundry.toml │ │ │ ├── src/ │ │ │ │ ├── lib.cairo │ │ │ │ ├── mutator_set_contract.cairo │ │ │ │ └── zk_verifier/ │ │ │ │ ├── honk_verifier_circuits.cairo │ │ │ │ ├── honk_verifier_constants.cairo │ │ │ │ └── honk_verifier_contract.cairo │ │ │ ├── tests/ │ │ │ │ └── test_contract.cairo │ │ │ └── zk_program/ │ │ │ ├── Nargo.toml │ │ │ ├── Prover.toml │ │ │ └── src/ │ │ │ ├── main.nr │ │ │ ├── mmr.nr │ │ │ └── mmr_tests.nr │ │ ├── risc0_sample_app/ │ │ │ ├── README.md │ │ │ ├── fibonacci_prover/ │ │ │ │ ├── .gitignore │ │ │ │ ├── Cargo.toml │ │ │ │ ├── README.md │ │ │ │ ├── host/ │ │ │ │ │ ├── Cargo.toml │ │ │ │ │ └── src/ │ │ │ │ │ └── main.rs │ │ │ │ ├── methods/ │ │ │ │ │ ├── Cargo.toml │ │ │ │ │ ├── build.rs │ │ │ │ │ ├── guest/ │ │ │ │ │ │ ├── Cargo.toml │ │ │ │ │ │ └── src/ │ │ │ │ │ │ └── main.rs │ │ │ │ │ └── src/ │ │ │ │ │ └── lib.rs │ │ │ │ └── rust-toolchain.toml │ │ │ └── fibonacci_sequencer/ │ │ │ ├── .gitignore │ │ │ ├── Scarb.toml │ │ │ ├── snfoundry.toml │ │ │ ├── src/ │ │ │ │ └── lib.cairo │ │ │ └── tests/ │ │ │ └── test_contract.cairo │ │ └── universal_ecip/ │ │ ├── Scarb.toml │ │ └── src/ │ │ └── lib.cairo │ ├── corelib_imports/ │ │ ├── README.md │ │ ├── Scarb.toml │ │ └── src/ │ │ └── lib.cairo │ └── src/ │ ├── apps/ │ │ ├── drand.cairo │ │ ├── noir/ │ │ │ └── zk_honk_transcript.cairo │ │ ├── noir.cairo │ │ ├── risc0.cairo │ │ ├── sp1.cairo │ │ └── sp1_constants.cairo │ ├── basic_field_ops.cairo │ ├── circuits/ │ │ ├── README.md │ │ ├── dummy.cairo │ │ ├── ec.cairo │ │ ├── extf_mul.cairo │ │ ├── isogeny.cairo │ │ ├── multi_pairing_check.cairo │ │ ├── rsa.cairo │ │ └── tower_circuits.cairo │ ├── core/ │ │ └── circuit.cairo │ ├── crypto/ │ │ └── mmr.cairo │ ├── definitions/ │ │ ├── curves.cairo │ │ └── structs/ │ │ ├── fields.cairo │ │ └── points.cairo │ ├── definitions.cairo │ ├── ec/ │ │ ├── ec_ops.cairo │ │ ├── ec_ops_g2.cairo │ │ ├── generate_selector_code.py │ │ ├── pairing/ │ │ │ ├── groth16.cairo │ │ │ ├── pairing_check.cairo │ │ │ └── single_pairing_tower.cairo │ │ └── selectors.cairo │ ├── hashes/ │ │ ├── poseidon_bn254.cairo │ │ └── sha_512.cairo │ ├── lib.cairo │ ├── signatures/ │ │ ├── ecdsa.cairo │ │ ├── eddsa_25519.cairo │ │ ├── rsa.cairo │ │ └── schnorr.cairo │ ├── tests/ │ │ ├── autogenerated/ │ │ │ ├── ecdsa_tests.cairo │ │ │ ├── eddsa_tests.cairo │ │ │ ├── msm_tests.cairo │ │ │ ├── pairing_tests.cairo │ │ │ ├── rsa_tests.cairo │ │ │ ├── schnorr_tests.cairo │ │ │ └── tower_pairing_tests.cairo │ │ ├── calldata_tests.cairo │ │ ├── proof_calldata.txt │ │ ├── sha512_tests.cairo │ │ └── sp1_groth_16_tests.cairo │ └── utils/ │ ├── calldata.cairo │ ├── hashing.cairo │ └── neg_3.cairo ├── tests/ │ ├── benchmarks_compiled.py │ ├── benchmarks_manual.py │ ├── conftest.py │ ├── contracts_e2e/ │ │ ├── __init__.py │ │ ├── e2e_test.py │ │ ├── fixtures/ │ │ │ ├── __init__.py │ │ │ ├── accounts.py │ │ │ ├── clients.py │ │ │ ├── constants.py │ │ │ └── devnet.py │ │ ├── install_devnet.sh │ │ ├── test-variables.env.template │ │ └── utils.py │ ├── ed25519_test_vectors.json │ └── hydra/ │ ├── algebra/ │ │ ├── test_polynomial.py │ │ ├── test_pyfelt.py │ │ └── test_tower_final_exp.py │ ├── circuits/ │ │ ├── test_ec.py │ │ ├── test_honk.py │ │ └── test_multi_miller_loop.py │ ├── hints/ │ │ ├── test_ecip.py │ │ ├── test_eisenstein.py │ │ ├── test_fake_glv.py │ │ ├── test_final_exp_witness.py │ │ ├── test_frobenius.py │ │ └── test_neg3.py │ ├── starknet/ │ │ ├── test_calldata.py │ │ ├── test_groth16_vk_proof_parsing.py │ │ ├── test_honk_vk_proof_parsing.py │ │ └── test_signatures_calldata.py │ ├── test_bls18_381_map_to_curve.py │ ├── test_cofactor_clearing.py │ ├── test_drand.py │ ├── test_extension_field_modulo_circuit.py │ ├── test_g1_point.py │ ├── test_g2_point.py │ ├── test_isogeny.py │ ├── test_poseidon_hash.py │ └── test_rsa_rns.py └── tools/ ├── addchain/ │ ├── bls12_381_e.acc │ ├── bls12_381_h3_s.acc │ ├── bn254_exp.acc │ ├── bn254_exp0.acc │ ├── bn254_r_m_d_inv.acc │ └── gen_rust_addchain.py ├── garaga_rs/ │ ├── Cargo.toml │ └── src/ │ ├── algebra/ │ │ ├── extf_mul.rs │ │ ├── g1g2pair.rs │ │ ├── g1point.rs │ │ ├── g2point.rs │ │ ├── polynomial.rs │ │ └── rational_function.rs │ ├── calldata/ │ │ ├── drand_calldata.rs │ │ ├── drand_tlock_calldata.rs │ │ ├── full_proof_with_hints/ │ │ │ ├── groth16.rs │ │ │ └── zk_honk.rs │ │ ├── mod.rs │ │ ├── mpc_calldata.rs │ │ ├── msm_calldata.rs │ │ └── signatures.rs │ ├── constants.rs │ ├── crypto/ │ │ ├── digest.rs │ │ ├── merkle_tree.rs │ │ ├── mmr/ │ │ │ ├── mmr_accumulator.rs │ │ │ ├── mmr_membership_proof.rs │ │ │ ├── mmr_successor_proof.rs │ │ │ ├── mmr_trait.rs │ │ │ ├── shared_advanced.rs │ │ │ └── shared_basic.rs │ │ └── poseidon_bn254.rs │ ├── definitions.rs │ ├── ecip/ │ │ ├── core.rs │ │ └── ff.rs │ ├── frobenius.rs │ ├── hints/ │ │ ├── eisenstein.rs │ │ └── fake_glv.rs │ ├── io.rs │ ├── lib.rs │ ├── pairing/ │ │ ├── final_exp_witness/ │ │ │ ├── addchain_pow_generated.rs │ │ │ ├── bls12_381_final_exp_witness.rs │ │ │ ├── bn254_final_exp_witness.rs │ │ │ └── mod.rs │ │ ├── multi_miller_loop.rs │ │ └── multi_pairing_check.rs │ ├── poseidon_transcript.rs │ ├── python_bindings/ │ │ ├── drand_calldata.rs │ │ ├── ecip.rs │ │ ├── extf_mul.rs │ │ ├── final_exp_witness.rs │ │ ├── g2.rs │ │ ├── groth16_calldata.rs │ │ ├── hades_permutation.rs │ │ ├── mod.rs │ │ ├── mpc_calldata.rs │ │ ├── msm.rs │ │ ├── pairing.rs │ │ ├── signatures.rs │ │ └── zk_honk_calldata.rs │ └── wasm_bindings.rs ├── make/ │ ├── bytecode_check.sh │ ├── bytecode_check_max_log_n.sh │ ├── check_sierra_size.py │ ├── ci_cairo.sh │ ├── ci_e2e.sh │ ├── ci_hydra.sh │ ├── ci_wasm.sh │ ├── common.sh │ ├── constants.json │ ├── generate_constants.py │ ├── rewrite.sh │ ├── setup.sh │ ├── steps.sh │ ├── test_contracts.sh │ ├── update_bench_in_readme.py │ ├── update_risc0_class_hash.sh │ ├── wasm-test-gen.sh │ └── wasm.sh ├── noir/ │ ├── Makefile │ ├── hello/ │ │ ├── Nargo.toml │ │ ├── Prover.toml │ │ └── src/ │ │ └── main.nr │ ├── run.sh │ └── transcript.py ├── npm/ │ ├── garaga_ts/ │ │ ├── .gitignore │ │ ├── Dockerfile │ │ ├── README.md │ │ ├── babel.config.cjs │ │ ├── docker-compose.yml │ │ ├── fix-chown.sh │ │ ├── jest.config.ts │ │ ├── patch.wasm.cjs │ │ ├── rollup.config.js │ │ ├── src/ │ │ │ ├── constants.ts │ │ │ ├── node/ │ │ │ │ ├── api.ts │ │ │ │ ├── definitions.ts │ │ │ │ ├── hints/ │ │ │ │ │ └── io.ts │ │ │ │ ├── index.ts │ │ │ │ └── starknet/ │ │ │ │ ├── groth16ContractGenerator/ │ │ │ │ │ └── parsingUtils.ts │ │ │ │ └── honkContractGenerator/ │ │ │ │ └── parsingUtils.ts │ │ │ └── wasm/ │ │ │ └── pkg/ │ │ │ ├── garaga_rs.d.ts │ │ │ ├── garaga_rs.js │ │ │ ├── garaga_rs_bg.wasm.d.ts │ │ │ └── garaga_rs_bg.wasm.js │ │ └── tests/ │ │ └── starknet/ │ │ ├── drandCalldata.test.ts │ │ ├── drandTlockCalldata.test.ts │ │ ├── groth16Calldata.test.ts │ │ ├── groth16VkProofParsing.test.ts │ │ ├── poseidonHash.test.ts │ │ ├── signaturesCalldata.test.ts │ │ └── zkHonkCalldata.test.ts │ └── integration-test-suite/ │ ├── .gitignore │ └── packages/ │ ├── nodejs-ts-cjs-tsc/ │ │ ├── .gitignore │ │ ├── output.txt │ │ └── src/ │ │ ├── examples.ts │ │ └── index.ts │ ├── nodejs-ts-esm-tsc/ │ │ ├── .gitignore │ │ ├── output.txt │ │ └── src/ │ │ ├── examples.ts │ │ └── index.ts │ ├── web-js-esm-react/ │ │ ├── .gitignore │ │ ├── next.config.mjs │ │ ├── output.txt │ │ ├── scrape.cjs │ │ └── src/ │ │ └── app/ │ │ ├── examples.js │ │ ├── layout.js │ │ └── page.js │ └── web-js-esm-webpack/ │ ├── .gitignore │ ├── output.txt │ ├── scrape.cjs │ ├── src/ │ │ ├── bootstrap.js │ │ ├── examples.js │ │ └── index.js │ └── webpack.config.js ├── process_manager.py └── profile_tests.py ================================================ FILE CONTENTS ================================================ ================================================ FILE: .cargo/config.toml ================================================ [build] target-dir = ".cargo/garaga_rs/target" ================================================ FILE: .claude/commands/bump-version.md ================================================ # Bump Garaga Version Bump the garaga version across the entire codebase (Python, Rust, Cairo, TypeScript, docs). ## Arguments The user provides: - **NEW_VERSION**: The new garaga version (e.g. `1.0.2`) ## Procedure ### Step 0: Detect current version Read `tools/make/constants.json` and extract `release_info.garaga_version`. This is the OLD version that will be replaced everywhere. Present the current version to the user and confirm the target version before proceeding. If the user already provided an explicit version number as an argument, skip the proposal and use it directly. ### Step 1: Update `tools/make/constants.json` Update `release_info.garaga_version` to the new version. ### Step 2: Run `generate_constants.py` Run `make constants` from the project root. This auto-regenerates the constants files AND updates version references in: - `hydra/garaga/starknet/constants.py` - `tools/garaga_rs/src/constants.rs` - `tools/npm/garaga_ts/src/constants.ts` - `pyproject.toml` (package version) - `tools/garaga_rs/Cargo.toml` (package version) - `tools/npm/garaga_ts/package.json` (package version) - `docs/PYPI_README.md` (pip install version) - `tools/npm/garaga_ts/README.md` (API doc link) - `docs/gitbook/smart-contract-generators/noir.md` (Garaga CLI version line only) If the script fails, fall back to manually editing each of these files. ### Step 3: Update `src/Scarb.toml` Update the `version = "OLD"` field (line near the top, under `[package]`) to the new version. ### Step 4: Update `Cargo.lock` Run `cargo update -p garaga_rs` from the project root to sync the lock file with the new Cargo.toml version. ### Step 5: Run `make rewrite` Run `make rewrite` from the project root. This regenerates all autogenerated contracts under `src/contracts/autogenerated/` which embed the garaga version in comments and Scarb.toml files. This takes a few minutes. The makefile activates the venv automatically. If it fails, report the error. ### Step 6: Update documentation Replace ALL occurrences of the old garaga version with the new one in these documentation files: - `docs/gitbook/README.md` - `docs/gitbook/installation/README.md` - `docs/gitbook/installation/cairo-library.md` - `docs/gitbook/installation/npm-package.md` - `docs/gitbook/installation/python-package.md` - `docs/gitbook/installation/rust-crate.md` - `docs/gitbook/maintained-smart-contracts/README.md` - `docs/gitbook/maintained-smart-contracts/risczero.md` - `docs/gitbook/security.md` - `docs/gitbook/smart-contract-generators/groth16/generate-and-deploy-your-verifier-contract.md` - `docs/gitbook/using-garaga-libraries-in-your-cairo-project/README.md` - `docs/gitbook/using-garaga-libraries-in-your-cairo-project/ec-multi-scalar-multiplication.md` Version appears in several forms that must ALL be updated: - Bare version: `1.0.1` (in Scarb.toml examples, pip install, npm install, class hash headers) - Prefixed with `v`: `v1.0.1` (in git tags, release links, Cargo.toml git tag references) - Prefixed with `==`: `==1.0.1` (pip install commands) - Prefixed with `@`: `@1.0.1` (npm/scarb add commands) Be thorough: read each file, find all old version occurrences, and replace them. Do NOT change version numbers that belong to other tools (Cairo, Scarb, Noir, Barretenberg, RiscZero, SP1, Starknet Foundry). ### Step 7: Verify Run a grep for the old version across the repo: ``` grep -r "OLD_VERSION" --include="*.toml" --include="*.yml" --include="*.json" --include="*.py" --include="*.rs" --include="*.ts" --include="*.md" --include="*.sh" . ``` Report any remaining references. Some may be intentional (e.g. changelogs, historical references). Flag anything that looks like it should have been updated. ## Notes - The `generate_constants.py` script handles: constants files (Python/Rust/TS), `pyproject.toml`, `Cargo.toml`, `package.json`, `PYPI_README.md`, `npm README.md`, and Noir docs version line. Everything else must be updated manually. - `make rewrite` regenerates everything under `src/contracts/autogenerated/`. Never manually edit those files. - The `src/Scarb.toml` version must be updated manually (Step 3) as `generate_constants.py` does not touch it. - Documentation (Step 6) is the most labor-intensive part. Be careful to only replace the garaga version, not versions of other tools. ================================================ FILE: .claude/commands/upgrade-cairo.md ================================================ # Upgrade Cairo Version Upgrade the Cairo/Scarb version (and optionally the Starknet Foundry version) across the entire codebase. ## Arguments The user provides: - **NEW_CAIRO_VERSION**: The new Cairo/Scarb version (e.g. `2.16.0`) - **NEW_FOUNDRY_VERSION** (optional): The new Starknet Foundry version (e.g. `0.58.0`). If not provided, keep the current Foundry version unchanged. ## Procedure ### Step 0: Detect current versions and propose latest available Read `tools/make/constants.json` to extract the current `cairo_version` and `starknet_foundry_version`. These are the OLD versions that will be replaced everywhere. Then query asdf for the latest available versions: - Run `asdf list all scarb` and pick the latest stable version (no `-rc`, `-alpha`, `-beta`, `-nightly` suffixes). - Run `asdf list all starknet-foundry` and pick the latest stable version. Present the current and latest available versions to the user, e.g.: ``` Current: scarb 2.14.0, starknet-foundry 0.53.0 Latest: scarb 2.16.1, starknet-foundry 0.58.0 ``` Ask the user to confirm the target versions before proceeding. If the user already provided explicit version numbers as arguments, skip the proposal and use those directly. ### Step 1: Update `tools/make/constants.json` Update `release_info.cairo_version` to the new Cairo version. If a new Foundry version was provided, also update `release_info.starknet_foundry_version`. ### Step 2: Run `generate_constants.py` Run `make constants` from the project root (the makefile activates the venv automatically). This auto-regenerates: - `hydra/garaga/starknet/constants.py` (CAIRO_VERSION, STARKNET_FOUNDRY_VERSION) - `tools/garaga_rs/src/constants.rs` - `tools/npm/garaga_ts/src/constants.ts` If the script fails (e.g. missing dependencies), fall back to manually editing `hydra/garaga/starknet/constants.py` to update `CAIRO_VERSION` and `STARKNET_FOUNDRY_VERSION`. ### Step 3: Update root `Scarb.toml` Update `[workspace.dependencies]`: - `cairo_test = "OLD"` → `"NEW_CAIRO_VERSION"` - `starknet = "OLD"` → `"NEW_CAIRO_VERSION"` ### Step 4: Update `src/Scarb.toml` Update: - `starknet = "..."` → `"NEW_CAIRO_VERSION"` (in `[dependencies]`) - `assert_macros = "..."` → `"NEW_CAIRO_VERSION"` (in `[dev-dependencies]`) - `cairo_execute = "..."` → `"NEW_CAIRO_VERSION"` (in `[dev-dependencies]`) - If new Foundry version provided: `snforge_std = "..."` → `"NEW_FOUNDRY_VERSION"` (in `[dev-dependencies]`) ### Step 5: Update `src/corelib_imports/Scarb.toml` Update `cairo_test = "..."` → `"NEW_CAIRO_VERSION"` (in `[dev-dependencies]`). ### Step 6: Update `.tool-versions` files Update the root `.tool-versions`: - `scarb OLD` → `scarb NEW_CAIRO_VERSION` - If new Foundry version: `starknet-foundry OLD` → `starknet-foundry NEW_FOUNDRY_VERSION` Update `src/.tool-versions`: - `scarb OLD` → `scarb NEW_CAIRO_VERSION` - If new Foundry version: `starknet-foundry OLD` → `starknet-foundry NEW_FOUNDRY_VERSION` After updating both `.tool-versions` files, run `asdf install` from the project root to install the new tool versions. Report the output to the user. If asdf is not available or fails, tell the user to manually install the required scarb and starknet-foundry versions. ### Step 7: Update manual (non-autogenerated) contract `Scarb.toml` files The following contract directories are NOT auto-generated by `make rewrite` and must be updated manually: - `src/contracts/drand_quicknet/Scarb.toml` - `src/contracts/drand_decrypt_quicknet/Scarb.toml` - `src/contracts/mutator_set/Scarb.toml` - `src/contracts/universal_ecip/Scarb.toml` - `src/contracts/risc0_sample_app/fibonacci_sequencer/Scarb.toml` In each, update: - `starknet = "OLD_CAIRO"` → `"NEW_CAIRO_VERSION"` - `assert_macros = "OLD_CAIRO"` → `"NEW_CAIRO_VERSION"` (if present) - If new Foundry version: `snforge_std = "OLD_FOUNDRY"` → `"NEW_FOUNDRY_VERSION"` (if present) Also update any `.tool-versions` files in these directories (currently only `src/contracts/drand_quicknet/.tool-versions` and `src/contracts/mutator_set/.tool-versions` exist). **DO NOT** manually edit files under `src/contracts/autogenerated/` — those are regenerated by `make rewrite` in the next step. ### Step 8: Run `make rewrite` Run `make rewrite` from the project root. This regenerates: - All `src/contracts/autogenerated/*/Scarb.toml` (using CAIRO_VERSION from constants.py) - All `src/contracts/autogenerated/*/.tool-versions` (using CAIRO_VERSION and STARKNET_FOUNDRY_VERSION from constants.py) - All Cairo circuit files under `src/src/circuits/` - All autogenerated contract source code and tests This takes a few minutes. The makefile activates the venv automatically. If it fails, report the error — the user may need to run `make setup` first. ### Step 9: Update CI workflows Update `scarb-version: "OLD"` → `"NEW_CAIRO_VERSION"` in: - `.github/workflows/e2e.yml` - `.github/workflows/hydra.yml` - `.github/workflows/maturin.yml` - `.github/workflows/wasm.yml` Only update lines that contain `scarb-version:`. ### Step 10: Update `tools/make/setup.sh` Replace all occurrences of the old Cairo version with the new one in the Scarb version check block near the end of the file (the `grep -q` line and the two echo lines that mention the version). ### Step 11: Update documentation Update the old Cairo/Scarb version string to the new one in: - `README.md` - `docs/gitbook/installation/developer-setup.md` - `docs/gitbook/maintained-smart-contracts/risczero.md` - `docs/CONTRIBUTING.md` Only change lines that reference Scarb version numbers. If new Foundry version provided, also update any Foundry version references in these docs. ### Step 12: Update hardcoded class hashes The Cairo compiler version affects compiled Sierra output, so all hardcoded class hashes must be recomputed. **ECIP class hash** — used by all Groth16 verifier contracts: 1. `cd src/contracts/universal_ecip && scarb build` 2. `sncast utils class-hash --contract-name UniversalECIP` → copy the hash (strip leading zeros after `0x`) 3. Update `ECIP_OPS_CLASS_HASH` in `hydra/garaga/starknet/groth16_contract_generator/generator.py` 4. Re-run `make rewrite` to regenerate autogenerated contracts with the new hash **RISC0 verifier class hash** — used by the fibonacci_sequencer sample app: Run `make update-risc0-class-hash` (this builds, computes, and patches automatically). ### Step 13: Verify Run `grep -r "OLD_CAIRO_VERSION" --include="*.toml" --include="*.yml" --include="*.json" --include="*.py" --include="*.sh" --include="*.md" .` to check for any remaining references to the old version. Report any stragglers found (some may be intentional, e.g. changelogs). ### Step 14: Test compilation Run `cd src && scarb build` to verify the new version compiles. If it fails with type errors on `const` declarations (e.g. `E2126: Constant type must not depend on its value`), the Cairo version may require explicit generic type parameters. Update the Python generators in `hydra/garaga/starknet/groth16_contract_generator/` and `hydra/garaga/starknet/honk_contract_generator/` to emit the required generics (e.g. `Groth16VerifyingKey`, `G2Line`), then fix the generated `.cairo` files and re-run `make rewrite`. ### Step 15: Run black formatting check Run `source venv/bin/activate && black --target-version py310 --check hydra/` to verify Python formatting passes. The pre-commit hook and CI both use `--target-version py310` to avoid formatting differences across Python versions. If files need reformatting, run `black --target-version py310 hydra/` and include the changes. ## Notes - This procedure does NOT modify Cairo source code. If the new Cairo version introduces breaking language changes, those must be handled separately. - The `generate_constants.py` script propagates constants from `constants.json` into Python/Rust/TS constants files — it does NOT touch Scarb.toml or .tool-versions files. - `make rewrite` auto-generates everything under `src/contracts/autogenerated/` and `src/src/circuits/`. Never manually edit those — they will be overwritten. - Manual contracts (`drand_quicknet`, `drand_decrypt_quicknet`, `mutator_set`, `universal_ecip`, `fibonacci_sequencer`) must be updated by hand since they are not regenerated. - The pre-commit hook uses black from `.pre-commit-config.yaml` (must match the version in `tools/make/requirements.txt`). If they diverge, formatting will pass locally but fail in CI. ================================================ FILE: .claude/skills/benchmarking-cairo/SKILL.md ================================================ --- name: benchmarking-cairo description: Use when profiling Cairo functions, measuring step counts, analyzing resource usage, generating call-graph PNGs, or launching pprof to visualize Cairo execution traces --- # Benchmarking Cairo ## Overview Profile Cairo function execution to identify hotspots by steps, calls, range checks, and other builtins. Works with both `scarb execute` (standalone programs) and `snforge test` (Starknet Foundry tests). If tools are missing, see `installation.md` in this skill directory. The CLI script is `profile.py` in this skill directory. ## REQUIRED: Use the CLI **Always use `python3 profile.py profile` (from this skill directory) for profiling.** Do NOT run snforge/cairo-profiler/pprof manually — the CLI handles the full pipeline deterministically (trace generation, profile building, PNG export, naming). ### snforge mode (test functions) ```bash python3 profile.py profile \ --mode snforge \ --package falcon \ --test test_ntt_zknox_vs_felt252 \ --name ntt-zknox-reduced \ --metric steps ``` ### scarb mode (standalone executables) ```bash python3 profile.py profile \ --mode scarb \ --package falcon \ --executable bench_ntt \ --args-file tests/data/ntt_input_512.json \ --name ntt-felt252 \ --metric steps ``` ### CLI arguments | Argument | Required | Description | |----------|----------|-------------| | `--mode` | yes | `snforge` or `scarb` | | `--package` | yes | Scarb package name (e.g. `falcon`) | | `--name` | yes | Human-friendly profile label (e.g. `ntt-zknox-reduced`) | | `--test` | snforge | Test filter passed to `snforge test` | | `--executable` | scarb | Executable name for `scarb execute` | | `--args-file` | no | Arguments file for `scarb execute` | | `--metric` | no | `steps` (default), `rc`, `sierra-gas`, `l2-gas` | | `--output` | no | Output directory (default: `profiles/`) | | `--nodefraction` | no | Hide PNG nodes below this fraction of total (default: `0.005`). Use `0` to show all nodes. | | `--edgefraction` | no | Hide PNG edges below this fraction of total (default: `0.001`). Use `0` to show all edges. | ### CLI exit codes — act on errors | Code | Meaning | What to do | |------|---------|------------| | 0 | Success | Read the PNG path from output | | 1 | Argument error | Fix the CLI invocation | | 2 | snforge/scarb failed | Check compilation errors, test failures | | 3 | Trace file not found | Test must PASS to produce a trace. Check test name matches exactly. | | 4 | cairo-profiler failed | Check trace JSON is valid | | 5 | pprof PNG export failed | Check graphviz is installed (`apt install graphviz`) | | 6 | Missing tool | Install the missing tool (see `installation.md`) | ### Output The CLI produces two files in `profiles/`: ``` profiles/YY-MM-DD-HH:MM____.pb.gz profiles/YY-MM-DD-HH:MM____.png ``` After running the CLI, **always read the PNG** to verify the profile shows the expected functions. ## Pitfalls ### Stale trace files `snfoundry_trace/` keeps old traces. If you change code and re-profile, you MUST re-run `snforge test --save-trace-data` (the CLI does this automatically). **Never build a profile from a trace that predates your code change.** ### Missing functions in the PNG If a function doesn't appear in the PNG, it may be below the `--nodefraction` threshold. Use `--nodefraction 0` to show all nodes. You can also check the text output (printed by the CLI) — functions with 0 flat steps but high cumulative steps are wrappers that delegate all work to callees. ### Timestamp mismatch between pb.gz and png When running steps manually, the pb.gz and png may get different timestamps if they cross a minute boundary. The CLI computes the timestamp once so both files always match. ## Manual profiling (advanced) For interactive exploration beyond what the CLI provides: ```bash # Launch web UI for interactive flame graphs pprof -http=:8080 profiles/.pb.gz # View specific sample in terminal cairo-profiler view profiles/.pb.gz --sample steps --limit 20 # List available samples cairo-profiler view profiles/.pb.gz --list-samples ``` ## Metric reference | `--metric` | tracked-resource | Samples in profile | |------------|------------------|--------------------| | `steps` | `cairo-steps` | steps, calls, range check builtin, memory holes, casm size | | `rc` | `cairo-steps` | (same as steps, PNG shows range check builtin) | | `sierra-gas` | `sierra-gas` | sierra gas, calls, casm size | | `l2-gas` | `sierra-gas` | l2 gas (requires `enable-gas = true` + dispatcher pattern) | ## L2 Gas profiling (snforge) L2 gas requires **all three**: 1. `[cairo] enable-gas = true` in Scarb.toml 2. `--metric l2-gas` (uses sierra-gas tracking) 3. **Dispatcher pattern** — profiled code must run inside a deployed contract ```cairo #[starknet::interface] trait IBench { fn my_function(self: @TContractState) -> felt252; } #[starknet::contract] mod bench { /* ... */ } // Test using dispatcher #[test] fn bench_my_function() { let contract = declare("bench").unwrap().contract_class(); let (addr, _) = contract.deploy(@array![]).unwrap(); let dispatcher = IBenchDispatcher { contract_address: addr }; dispatcher.my_function(); } ``` **Known limitation:** Syscall execution costs (secp256r1, keccak, etc.) are not attributed in the l2 gas profile. Use snforge test output for total gas; use profiler for relative hotspot analysis within Cairo code. ================================================ FILE: .claude/skills/benchmarking-cairo/installation.md ================================================ # Tool Installation for Cairo Benchmarking ## Scarb (Cairo build tool & package manager) ```bash # Via asdf (recommended) asdf plugin add scarb asdf install scarb latest asdf global scarb latest # Or via installer curl --proto '=https' --tlsv1.2 -sSf https://docs.swmansion.com/scarb/install.sh | sh ``` Verify: `scarb --version` ## Starknet Foundry (snforge) ```bash # Via snfoundryup installer curl -L https://raw.githubusercontent.com/foundry-rs/starknet-foundry/master/scripts/install.sh | sh snfoundryup # Or via asdf asdf plugin add starknet-foundry asdf install starknet-foundry latest asdf global starknet-foundry latest ``` Verify: `snforge --version` ## cairo-profiler ```bash # Via curl (Linux/macOS) curl -L https://raw.githubusercontent.com/software-mansion/cairo-profiler/main/scripts/install.sh | sh # Or via asdf asdf plugin add cairo-profiler asdf install cairo-profiler latest asdf global cairo-profiler latest ``` Verify: `cairo-profiler --version` GitHub: https://github.com/software-mansion/cairo-profiler ## pprof (Google profiling visualization) Requires Go toolchain: ```bash # Install Go (if not present) # See https://go.dev/doc/install # Install pprof go install github.com/google/pprof@latest ``` Ensure `$(go env GOPATH)/bin` is in your `PATH`. Verify: `pprof -h` ## Graphviz (required by pprof for PNG/SVG/PDF output) ```bash # Debian/Ubuntu sudo apt-get install graphviz # macOS brew install graphviz # Fedora sudo dnf install graphviz ``` Verify: `dot -V` ================================================ FILE: .claude/skills/benchmarking-cairo/profile.py ================================================ #!/usr/bin/env python3 """ Cairo profiling CLI — deterministic pipeline for generating profiles. Usage: # snforge mode (run test, build profile, export PNG) python3 profile.py profile \ --mode snforge \ --package falcon \ --test test_ntt_zknox_vs_felt252 \ --name ntt-zknox-reduced \ --metric steps # scarb execute mode python3 profile.py profile \ --mode scarb \ --package falcon \ --executable bench_ntt \ --args-file tests/data/ntt_input_512.json \ --name ntt-felt252 \ --metric steps Exit codes: 0 Success 1 Argument error 2 snforge/scarb execution failed 3 Trace file not found after execution 4 cairo-profiler build failed 5 pprof PNG export failed 6 Missing external tool (snforge, scarb, cairo-profiler, pprof) """ import argparse import glob import os import subprocess import sys from datetime import datetime from pathlib import Path # --------------------------------------------------------------------------- # Helpers # --------------------------------------------------------------------------- def _check_tool(name: str) -> str: """Return path to tool or exit with code 6.""" import shutil path = shutil.which(name) if path is None: _fail(6, f"Required tool '{name}' not found on PATH. See installation.md.") return path def _fail(code: int, msg: str) -> None: """Print error and exit.""" print(f"ERROR [{code}]: {msg}", file=sys.stderr) sys.exit(code) def _run( cmd: list[str], cwd: str | None = None, timeout: int = 600 ) -> subprocess.CompletedProcess: """Run a command, printing it first. Returns CompletedProcess.""" print(f" $ {' '.join(cmd)}") return subprocess.run(cmd, cwd=cwd, timeout=timeout, capture_output=False) def _git_short_hash(repo_root: str) -> str: """Return short git hash or 'unknown'.""" try: result = subprocess.run( ["git", "rev-parse", "--short", "HEAD"], cwd=repo_root, capture_output=True, text=True, timeout=5, ) return result.stdout.strip() if result.returncode == 0 else "unknown" except Exception: return "unknown" def _profile_filename( output_dir: str, package: str, name: str, metric: str, commit: str, ext: str ) -> str: """Generate deterministic profile filename.""" ts = datetime.now().strftime("%y-%m-%d-%H:%M") return os.path.join(output_dir, f"{ts}_{package}_{name}_{metric}_{commit}.{ext}") # --------------------------------------------------------------------------- # Metric → sample mapping # --------------------------------------------------------------------------- METRIC_CONFIG = { "steps": { "tracked_resource": "cairo-steps", "sample_name": "steps", "pprof_sample_index": "steps", }, "rc": { "tracked_resource": "cairo-steps", "sample_name": "range check builtin", "pprof_sample_index": "range_check_builtin", }, "sierra-gas": { "tracked_resource": "sierra-gas", "sample_name": "sierra gas", "pprof_sample_index": "sierra_gas", }, "l2-gas": { "tracked_resource": "sierra-gas", "sample_name": "l2 gas", "pprof_sample_index": "l2_gas", }, } # --------------------------------------------------------------------------- # Pipeline steps # --------------------------------------------------------------------------- def _find_package_dir(repo_root: str, package: str) -> str: """Resolve package directory from workspace.""" pkg_dir = os.path.join(repo_root, "packages", package) if os.path.isdir(pkg_dir) and os.path.isfile(os.path.join(pkg_dir, "Scarb.toml")): return pkg_dir # Maybe it's a top-level package if os.path.isfile(os.path.join(repo_root, "Scarb.toml")): return repo_root _fail( 1, f"Cannot find package '{package}'. Looked in packages/{package}/ and repo root.", ) return "" # unreachable def _step_snforge(pkg_dir: str, test_filter: str, tracked_resource: str) -> None: """Run snforge test with trace generation.""" _check_tool("snforge") print( f"\n[1/4] Running snforge test (filter: {test_filter}, resource: {tracked_resource})" ) result = _run( [ "snforge", "test", test_filter, "--save-trace-data", "--tracked-resource", tracked_resource, ], cwd=pkg_dir, timeout=600, ) if result.returncode != 0: _fail(2, f"snforge test failed with exit code {result.returncode}") def _step_scarb(pkg_dir: str, executable: str, args_file: str) -> None: """Run scarb execute with trace generation.""" _check_tool("scarb") print(f"\n[1/4] Running scarb execute (executable: {executable})") cmd = [ "scarb", "execute", "--executable-name", executable, "--print-resource-usage", "--save-profiler-trace-data", ] if args_file: cmd.extend(["--arguments-file", args_file]) result = _run(cmd, cwd=pkg_dir, timeout=600) if result.returncode != 0: _fail(2, f"scarb execute failed with exit code {result.returncode}") def _find_trace_snforge(pkg_dir: str, test_filter: str) -> str: """Find the trace JSON generated by snforge.""" trace_dir = os.path.join(pkg_dir, "snfoundry_trace") if not os.path.isdir(trace_dir): # In workspace setups, snforge may create trace in a member subdir. # Search for snfoundry_trace under pkg_dir. for root, dirs, _files in os.walk(pkg_dir): if "snfoundry_trace" in dirs: trace_dir = os.path.join(root, "snfoundry_trace") break else: _fail( 3, f"Trace directory not found: {os.path.join(pkg_dir, 'snfoundry_trace')}\n" f" Also searched subdirectories of {pkg_dir}\n" f" Did snforge run successfully? Check that the test passed.", ) # snforge names traces like: __.json # It replaces "::" with "_" in filenames, so normalize the filter. filter_normalized = test_filter.replace("::", "_") pattern = os.path.join(trace_dir, f"*{filter_normalized}*.json") matches = sorted(glob.glob(pattern), key=os.path.getmtime, reverse=True) if not matches: # Also try the original filter in case naming convention differs pattern = os.path.join(trace_dir, f"*{test_filter}*.json") matches = sorted(glob.glob(pattern), key=os.path.getmtime, reverse=True) if not matches: # List what IS there for debugging all_traces = glob.glob(os.path.join(trace_dir, "*.json")) available = ( "\n ".join(os.path.basename(f) for f in all_traces) if all_traces else "(none)" ) _fail( 3, f"No trace file matching '*{test_filter}*' in {trace_dir}/\n" f" Available traces:\n {available}\n" f" Hint: The test must PASS to generate a trace. Failing/filtered tests produce no trace.", ) if len(matches) > 1: print(f" Warning: Multiple traces match '{test_filter}', using most recent:") for m in matches: print(f" {os.path.basename(m)}") trace = matches[0] print(f" Trace: {os.path.basename(trace)}") return trace def _find_trace_scarb(pkg_dir: str, package: str) -> str: """Find the trace JSON generated by scarb execute.""" # Standard location: target/execute//execution1/cairo_profiler_trace.json trace = os.path.join( pkg_dir, "target", "execute", package, "execution1", "cairo_profiler_trace.json" ) if not os.path.isfile(trace): _fail( 3, f"Trace file not found: {trace}\n" f" Expected at: target/execute/{package}/execution1/cairo_profiler_trace.json\n" f" Did scarb execute succeed? Check --save-profiler-trace-data was used.", ) print(f" Trace: {trace}") return trace def _step_build_profile(trace_path: str, output_path: str) -> None: """Build pprof profile from trace JSON.""" _check_tool("cairo-profiler") print(f"\n[3/4] Building profile: {os.path.basename(output_path)}") result = _run( [ "cairo-profiler", "build-profile", trace_path, "--show-libfuncs", "--output-path", output_path, ] ) if result.returncode != 0: _fail( 4, f"cairo-profiler build-profile failed with exit code {result.returncode}\n" f" Trace: {trace_path}", ) if not os.path.isfile(output_path): _fail(4, f"cairo-profiler completed but output file not found: {output_path}") def _step_view_profile(profile_path: str, sample_name: str) -> None: """Print top-20 functions by the chosen sample.""" print(f"\n Top functions by {sample_name}:") _run( [ "cairo-profiler", "view", profile_path, "--sample", sample_name, "--limit", "20", ] ) def _step_export_png( profile_path: str, png_path: str, pprof_sample_index: str, nodefraction: float = 0.005, edgefraction: float = 0.001, ) -> None: """Export PNG call graph via pprof.""" _check_tool("pprof") print(f"\n[4/4] Exporting PNG: {os.path.basename(png_path)}") result = _run( [ "pprof", "-png", f"-sample_index={pprof_sample_index}", f"-nodefraction={nodefraction}", f"-edgefraction={edgefraction}", "-output", png_path, profile_path, ] ) if result.returncode != 0: _fail( 5, f"pprof PNG export failed with exit code {result.returncode}\n" f" Profile: {profile_path}\n" f" Hint: Is graphviz (dot) installed? Run: apt install graphviz", ) if not os.path.isfile(png_path): _fail(5, f"pprof completed but PNG not found: {png_path}") # --------------------------------------------------------------------------- # Main # --------------------------------------------------------------------------- def build_parser() -> argparse.ArgumentParser: parser = argparse.ArgumentParser( prog="profile.py", description="Cairo profiling CLI — run tests, build profiles, export PNGs.", ) sub = parser.add_subparsers(dest="command") p = sub.add_parser("profile", help="Full profiling pipeline") p.add_argument( "--mode", required=True, choices=["snforge", "scarb"], help="Execution mode: snforge (test) or scarb (executable)", ) p.add_argument("--package", required=True, help="Scarb package name (e.g. falcon)") p.add_argument( "--name", required=True, help="Human-friendly profile name (e.g. ntt-zknox-reduced)", ) p.add_argument( "--metric", default="steps", choices=list(METRIC_CONFIG.keys()), help="Metric to profile (default: steps)", ) p.add_argument( "--output", default="profiles", help="Output directory (default: profiles/)" ) # snforge-specific p.add_argument( "--test", default=None, help="[snforge] Test filter (e.g. test_ntt_zknox_vs_felt252)", ) # scarb-specific p.add_argument("--executable", default=None, help="[scarb] Executable name") p.add_argument("--args-file", default=None, help="[scarb] Arguments file path") # pprof display options p.add_argument( "--nodefraction", type=float, default=0.005, help="Hide nodes below this fraction of total (default: 0.005). Use 0 to show all.", ) p.add_argument( "--edgefraction", type=float, default=0.001, help="Hide edges below this fraction of total (default: 0.001). Use 0 to show all.", ) return parser def main() -> int: parser = build_parser() args = parser.parse_args() if args.command != "profile": parser.print_help() return 1 # Validate mode-specific args if args.mode == "snforge" and not args.test: _fail( 1, "--test is required for snforge mode.\n" " Example: --test test_ntt_zknox_vs_felt252", ) if args.mode == "scarb" and not args.executable: _fail( 1, "--executable is required for scarb mode.\n" " Example: --executable bench_ntt", ) # Resolve paths repo_root = _find_repo_root() pkg_dir = _find_package_dir(repo_root, args.package) output_dir = os.path.join(repo_root, args.output) os.makedirs(output_dir, exist_ok=True) commit = _git_short_hash(repo_root) metric_cfg = METRIC_CONFIG[args.metric] # Generate output filenames pb_path = _profile_filename( output_dir, args.package, args.name, args.metric, commit, "pb.gz" ) png_path = _profile_filename( output_dir, args.package, args.name, args.metric, commit, "png" ) print(f"Cairo Profiling Pipeline") print(f" Mode: {args.mode}") print(f" Package: {args.package} ({pkg_dir})") print(f" Name: {args.name}") print(f" Metric: {args.metric} (sample: {metric_cfg['sample_name']})") print(f" Commit: {commit}") print(f" Output: {os.path.basename(pb_path)}") sys.stdout.flush() # Step 1: Run test/executable if args.mode == "snforge": _step_snforge(pkg_dir, args.test, metric_cfg["tracked_resource"]) else: _step_scarb(pkg_dir, args.executable, args.args_file) # Step 2: Find trace print(f"\n[2/4] Locating trace file") if args.mode == "snforge": trace_path = _find_trace_snforge(pkg_dir, args.test) else: trace_path = _find_trace_scarb(pkg_dir, args.package) # Step 3: Build profile _step_build_profile(trace_path, pb_path) _step_view_profile(pb_path, metric_cfg["sample_name"]) # Step 4: Export PNG _step_export_png( pb_path, png_path, metric_cfg["pprof_sample_index"], nodefraction=args.nodefraction, edgefraction=args.edgefraction, ) # Summary print(f"\n{'='*60}") print(f"Profile: {pb_path}") print(f"PNG: {png_path}") print(f"{'='*60}") return 0 def _find_repo_root() -> str: """Walk up from cwd to find the git repo root.""" path = Path.cwd() while path != path.parent: if (path / ".git").exists(): return str(path) path = path.parent # Fallback to cwd return str(Path.cwd()) if __name__ == "__main__": sys.exit(main()) ================================================ FILE: .claude/skills/cairo-coding/SKILL.md ================================================ --- name: cairo-coding description: Use when writing or optimizing Cairo functions — fixing slow loops, expensive arithmetic, integer splitting or limb assembly, modular reduction, storage slot packing, or BoundedInt type bounds --- # Coding Cairo Rules and patterns for writing efficient Cairo code. Sourced from audit findings and production profiling. ## When to Use - Implementing arithmetic (modular, parity checks, quotient/remainder) - Optimizing loops (slow iteration, repeated `.len()` calls, index-based access) - Splitting or assembling integer limbs (u256 → u128, u32s → u128, felt252 → u96) - Packing struct fields into storage slots - Using `BoundedInt` for zero-overhead arithmetic with compile-time bounds - Choosing integer types (u128 vs u256, BoundedInt vs native types) **Not for:** Profiling/benchmarking (use benchmarking-cairo) ## Quick Reference — All Rules | # | Rule | Instead of | Use | |---|------|-----------|-----| | 1 | Combined quotient+remainder | `x / m` + `x % m` | `DivRem::div_rem(x, m)` | | 2 | Cheap loop conditions | `while i < n` | `while i != n` | | 3 | Constant powers of 2 | `2_u32.pow(k)` | `match`-based lookup table | | 4 | Pointer-based iteration | `*data.at(i)` in index loop | `pop_front` / `for` / `multi_pop_front` | | 5 | Cache array length | `.len()` in loop condition | `let n = data.len();` before loop | | 6 | Pointer-based slicing | Manual loop extraction | `span.slice(start, length)` | | 7 | Cheap parity/halving | `index & 1`, `index / 2` | `DivRem::div_rem(index, 2)` | | 8 | Smallest integer type | `u256` when range < 2^128 | `u128` (type encodes constraint) | | 9 | Storage slot packing | One slot per field | `StorePacking` trait | | 10 | BoundedInt for limbs | Bitwise ops / raw u128 math | `bounded_int::{div_rem, mul, add}` | | 11 | Fast 2-input Poseidon | `poseidon_hash_span([x,y])` | `hades_permutation(x, y, 2)` | | 12 | Bulk felt252→BoundedInt | `downcast` / `try_into` (4 steps) | `u128s_from_felt252` + `upcast` (2 steps) | ## Always / Never Rules ### 1. Always use `DivRem::div_rem` — never separate `%` and `/` Cairo computes quotient and remainder in a single operation. Using both `%` and `/` on the same value doubles the cost. ```cairo // BAD let q = x / m; let r = x % m; // GOOD let (q, r) = DivRem::div_rem(x, m); ``` ### 2. Never use `<` or `>` in while loop conditions — use `!=` Equality checks are cheaper than comparisons in Cairo. ```cairo // BAD while i < n { ... i += 1; } // GOOD while i != n { ... i += 1; } ``` ### 3. Never compute `2^k` with `pow()` — use a lookup table `u32::pow()` is expensive. Use a `match` lookup for known ranges. ```cairo // BAD let p = 2_u32.pow(depth.into()); // GOOD — match-based lookup fn pow2(n: u32) -> u32 { match n { 0 => 1, 1 => 2, 2 => 4, 3 => 8, 4 => 16, 5 => 32, 6 => 64, 7 => 128, 8 => 256, 9 => 512, 10 => 1024, // extend as needed _ => core::panic_with_felt252('pow2 out of range'), } } ``` ### 4. Always iterate arrays with `pop_front` / `for` / `multi_pop_front` — never index-loop Index-based access (`array.at(i)`) is more expensive than pointer-based iteration. ```cairo // BAD let mut i = 0; while i != data.len() { let val = *data.at(i); i += 1; } // GOOD — pop_front while let Option::Some(val) = data.pop_front() { ... } // GOOD — for loop (equivalent) for val in data { ... } // GOOD — batch iteration while let Option::Some(chunk) = data.multi_pop_front::<4>() { ... } ``` ### 5. Never call `.len()` inside a loop condition — cache it `.len()` recomputes every iteration. Store it once. ```cairo // BAD while i != data.len() { ... i += 1; } // GOOD let n = data.len(); while i != n { ... i += 1; } ``` ### 6. Always use `span.slice()` instead of manual loop extraction `slice()` manipulates pointers directly — no element-by-element copying. ```cairo // BAD let mut result: Array = array![]; let mut i = 0; while i != length { result.append(*data.at(start + i)); i += 1; } // GOOD let result = data.slice(start, length); ``` ### 7. Always use `DivRem` for parity checks — never use bitwise ops Bitwise AND is more expensive than `div_rem` in Cairo. Use `DivRem::div_rem(x, 2)` to get both the halved value and parity in one operation. ```cairo // BAD let is_odd = (index & 1) == 1; index = index / 2; // GOOD let (q, r) = DivRem::div_rem(index, 2); if r == 1 { /* odd branch */ } index = q; ``` ### 8. Always use the smallest integer type that fits the value range `u128` instead of `u256` when the range is known. Adds clarity, prevents intermediate overflow. ```cairo // BAD — u256 for a value known to be < 2^128 fn deposit(value: u256) { assert(value < MAX_U128, '...'); ... } // GOOD — type encodes the constraint fn deposit(value: u128) { ... } ``` ### 9. Always use `StorePacking` to pack small fields into one storage slot Multiple small fields (basis points, flags, bounded amounts) can share a single `felt252` slot. ```cairo use starknet::storage_access::StorePacking; const POW_2_128: felt252 = 0x100000000000000000000000000000000; impl MyStorePacking of StorePacking { fn pack(value: MyStruct) -> felt252 { value.amount.into() + value.fee_bps.into() * POW_2_128 } fn unpack(value: felt252) -> MyStruct { let u256 { low, high } = value.into(); MyStruct { amount: low, fee_bps: high.try_into().unwrap() } } } ``` ### 10. Always use BoundedInt for byte cutting, limb assembly, and type conversions Never use bitwise ops (`&`, `|`, shifts) or raw `u128`/`u256` arithmetic for splitting or combining integer limbs. Use `bounded_int::div_rem` to extract parts and `bounded_int::mul` + `bounded_int::add` to assemble them. BoundedInt tracks bounds at compile time, eliminating overflow checks. **Assembling limbs** (e.g., 4 x u32 → u128): ```cairo // BAD — direct u128 arithmetic (28,340 gas) fn u32s_to_u128(d0: u32, d1: u32, d2: u32, d3: u32) -> u128 { d0.into() + d1.into() * POW_2_32 + d2.into() * POW_2_64 + d3.into() * POW_2_96 } // GOOD — BoundedInt (13,840 gas, 2x faster) fn u32s_to_u128(d0: u32, d1: u32, d2: u32, d3: u32) -> u128 { let d0_bi: u32_bi = upcast(d0); let d1_bi: u32_bi = upcast(d1); let d2_bi: u32_bi = upcast(d2); let d3_bi: u32_bi = upcast(d3); let r: u128_bi = add(add(add(d0_bi, mul(d1_bi, POW_32_UI)), mul(d2_bi, POW_64_UI)), mul(d3_bi, POW_96_UI)); upcast(r) } ``` **Splitting values** (e.g., felt252 → two u96 limbs): ```cairo // GOOD — div_rem to split, mul+add to reassemble fn felt252_to_two_u96(value: felt252) -> (u96, u96) { match u128s_from_felt252(value) { U128sFromFelt252Result::Narrow(low) => { let (hi32, lo96) = bounded_int::div_rem(low, NZ_POW96_TYPED); (lo96, upcast(hi32)) }, U128sFromFelt252Result::Wide((high, low)) => { let (lo_hi32, lo96) = bounded_int::div_rem(low, NZ_POW96_TYPED); let hi64: BoundedInt<0, { POW64 - 1 }> = downcast(high).unwrap(); (lo96, bounded_int::add(bounded_int::mul(hi64, POW32_TYPED), lo_hi32)) }, } } ``` **Extracting bits** (e.g., building a 4-bit selector): ```cairo // GOOD — div_rem by 2 extracts LSB, quotient is right-shifted value let (qu1, bit0) = bounded_int::div_rem(u1, TWO_NZ); // bit0 in {0,1} let (qu2, bit1) = bounded_int::div_rem(u2, TWO_NZ); let selector = add(bit0, mul(bit1, TWO_UI)); // selector in {0..3} ``` See [garaga/selectors.cairo](https://github.com/keep-starknet-strange/garaga/blob/main/src/src/ec/selectors.cairo) and [cairo-perfs-snippets](https://github.com/feltroidprime/cairo-perfs-snippets) for production examples. ## Code Quality - **DRY:** Extract repeated validation into helper functions. If two functions validate-then-write the same struct, extract a shared `_set_config()`. - **`scarb fmt`:** Run before every commit. - **`.tool-versions`:** Pin Scarb and Starknet Foundry versions with ASDF for reproducible builds. - **Keep dependencies updated:** Newer Scarb/Foundry versions include gas optimizations and compiler improvements. --- ## BoundedInt Optimization `BoundedInt` encodes value constraints in the type system, eliminating runtime overflow checks. Use the CLI tool to compute bounds — do NOT calculate manually. ### Critical Architecture Decision: Avoid Downcast **The #1 optimization pitfall:** Converting between `u16`/`u32`/`u64` and `BoundedInt` at function boundaries. #### The Problem If your functions take `u16` and return `u16`, you must: 1. `downcast` input to `BoundedInt` (expensive — requires range check) 2. Do bounded arithmetic (cheap) 3. `upcast` result back to `u16` (cheap but wasteful) The `downcast` operation adds a range check that **dominates the savings** from bounded arithmetic. In profiling: - `downcast`: 161,280 steps (18.86%) - `bounded_int_div_rem`: 204,288 steps (23.89%) - Total bounded approach: worse than original! #### The Solution: BoundedInt Throughout **Use `BoundedInt` types as function inputs AND outputs.** This eliminates downcast entirely. ```cairo // BAD: Converts at every call (downcast overhead kills performance) pub fn add_mod(a: u16, b: u16) -> u16 { let a: Zq = downcast(a).expect('overflow'); // EXPENSIVE let b: Zq = downcast(b).expect('overflow'); // EXPENSIVE let sum: ZqSum = add(a, b); let (_q, rem) = bounded_int_div_rem(sum, nz_q); upcast(rem) } // GOOD: BoundedInt in, BoundedInt out (no downcast) pub fn add_mod(a: Zq, b: Zq) -> Zq { let sum: ZqSum = add(a, b); let (_q, rem) = bounded_int_div_rem(sum, nz_q); rem } ``` #### Refactoring Strategy When optimizing existing code: 1. **Identify the hot path** — profile to find which functions use modular arithmetic heavily 2. **Change signatures** — update function inputs/outputs to use `BoundedInt` types 3. **Propagate types outward** — callers must also use `BoundedInt` 4. **Downcast only at boundaries** — convert from u16/u32 only at system entry points (e.g., deserialization) #### Type Conversion Rules | From | To | Operation | Cost | |------|-----|-----------|------| | `u16` | `BoundedInt<0, 65535>` | `upcast` | Free (superset) | | `u16` | `BoundedInt<0, 12288>` | `downcast` | **Expensive** (range check) | | `BoundedInt<0, 12288>` | `u16` | `upcast` | Free (subset) | | `BoundedInt` | `BoundedInt` where [A,B] ⊆ [C,D] | `upcast` | Free | | `BoundedInt` | `BoundedInt` where [A,B] ⊄ [C,D] | `downcast` | **Expensive** | **Key insight:** `upcast` only works when target range is a **superset** of source range. You cannot upcast `u32` to `BoundedInt<0, 150994944>` because `u32` max (4294967295) > 150994944. ### Prerequisites ```toml # Scarb.toml [dependencies] corelib_imports = "0.1.3" ``` ```cairo // CORRECT imports — copy exactly use corelib_imports::bounded_int::{ BoundedInt, upcast, downcast, bounded_int_div_rem, AddHelper, MulHelper, DivRemHelper, UnitInt, }; use corelib_imports::bounded_int::bounded_int::{SubHelper, add, sub, mul}; ``` ### Copy-Paste Template Working example for modular arithmetic mod 100: ```cairo use corelib_imports::bounded_int::{ BoundedInt, upcast, downcast, bounded_int_div_rem, AddHelper, MulHelper, DivRemHelper, UnitInt, }; use corelib_imports::bounded_int::bounded_int::{SubHelper, add, sub, mul}; type Val = BoundedInt<0, 99>; // [0, 99] type ValSum = BoundedInt<0, 198>; // [0, 198] type ValConst = UnitInt<100>; // singleton {100} impl AddValImpl of AddHelper { type Result = ValSum; } impl DivRemValImpl of DivRemHelper { type DivT = BoundedInt<0, 1>; type RemT = Val; } fn add_mod_100(a: Val, b: Val) -> Val { let sum: ValSum = add(a, b); let nz_100: NonZero = 100; let (_q, rem) = bounded_int_div_rem(sum, nz_100); rem } ``` ### CLI Tool Use `bounded_int_calc.py` in this skill directory. **Always use CLI — never calculate manually.** ```bash # Addition: [a_lo, a_hi] + [b_lo, b_hi] python3 bounded_int_calc.py add 0 12288 0 12288 # -> BoundedInt<0, 24576> # Subtraction: [a_lo, a_hi] - [b_lo, b_hi] python3 bounded_int_calc.py sub 0 12288 0 12288 # -> BoundedInt<-12288, 12288> # Multiplication python3 bounded_int_calc.py mul 0 12288 0 12288 # -> BoundedInt<0, 150994944> # Division: quotient and remainder bounds python3 bounded_int_calc.py div 0 24576 12289 12289 # -> DivT: BoundedInt<0, 1>, RemT: BoundedInt<0, 12288> # Custom impl name python3 bounded_int_calc.py mul 0 12288 0 12288 --name MulZqImpl ``` ### BoundedInt Bounds Quick Reference | Operation | Formula | |-----------|---------| | Add | `[a_lo + b_lo, a_hi + b_hi]` | | Sub | `[a_lo - b_hi, a_hi - b_lo]` | | Mul (unsigned) | `[a_lo * b_lo, a_hi * b_hi]` | | Div quotient | `[a_lo / b_hi, a_hi / b_lo]` | | Div remainder | `[0, b_hi - 1]` | ### Negative Dividends: SHIFT Pattern `bounded_int_div_rem` doesn't support negative lower bounds. When a subtraction produces a negative-bounded result that needs reduction, add a multiple of the modulus first: ```cairo // sub_mod: (a - b) mod Q via SHIFT pub fn sub_mod(a: Zq, b: Zq) -> Zq { let a_plus_q: BoundedInt<12289, 24577> = add(a, Q_CONST); // shift by +Q let diff: BoundedInt<1, 24577> = sub(a_plus_q, b); // now non-negative let (_q, rem) = bounded_int_div_rem(diff, nz_q()); rem } // fused_sub_mul_mod: a - (b*c) mod Q via large SHIFT // OFFSET = 12288 * Q = 151007232 (smallest multiple of Q >= max product) pub fn fused_sub_mul_mod(a: Zq, b: Zq, c: Zq) -> Zq { let prod: ZqProd = mul(b, c); let a_offset: BoundedInt<151007232, 151019520> = add(a, OFFSET_CONST); let diff: BoundedInt<12288, 151019520> = sub(a_offset, prod); let (_q, rem) = bounded_int_div_rem(diff, nz_q()); rem } ``` Rule: SHIFT = `ceil(|min_possible_value| / modulus) * modulus`. Adding SHIFT preserves the result mod Q (since SHIFT ≡ 0 mod Q) while making all values non-negative. ### felt252 → BoundedInt: Prefer u128 Decomposition Over Downcast `u128s_from_felt252` is a native VM operation (2 steps/call). `downcast` (used by `try_into()`) performs a range check (4 steps/call). When converting many felt252 values to BoundedInt, decompose to u128 first, then upcast to `BoundedInt<0, u128_max>`. You lose tight compile-time bounds but save 2 steps per conversion — significant at scale. Benchmarked per-call costs (isolated loop, 512 iterations, varying input): | Libfunc | Steps/call | Source | |---------|-----------|--------| | `u128s_from_felt252` | 2 | 1,024 flat / 512 calls | | `downcast` (try_into) | 4 | 2,048 flat / 512 calls | | `bounded_int_div_rem` | 7 | 3,584 flat / 512 calls (same both) | | Approach | Per-conversion cost | Sierra bloat | Notes | |----------|-------------------|--------------|-------| | `try_into().unwrap()` | 4 steps (downcast) | **O(N^2)** — panic drops all live vars | Never in unrolled code | | `match try_into() { Some/None }` | 4 steps (downcast) | OK | No panic but pays downcast cost | | `u128s_from_felt252` + `upcast` | 2 steps | OK | **Preferred** — native decomposition | End-to-end impact (512-point NTT verify): u128 approach saves 1,024 steps / ~1.6M L2 gas (4.4%) vs match-based downcast. ```cairo use corelib_imports::integer::{U128sFromFelt252Result, u128s_from_felt252}; type U128AsBounded = BoundedInt<0, 340282366920938463463374607431768211455>; #[inline(always)] fn felt252_as_u128(x: felt252) -> u128 { match u128s_from_felt252(x) { U128sFromFelt252Result::Narrow(low) => low, U128sFromFelt252Result::Wide((_, low)) => low, } } // Convert felt252 to BoundedInt via u128 (no range-check overhead) let r: U128AsBounded = upcast(felt252_as_u128(value + SHIFT)); let (_, r) = bounded_int_div_rem(r, NZ_Q); // DivRemHelper ``` **Trade-off:** `U128AsBounded` has max=2^128-1 instead of the tight shifted bound. The `DivRemHelper` quotient type is wider, but `bounded_int_div_rem` cost is the same. Fine for most cases — only matters if downstream code needs tight bounds on the quotient. **When to use which:** - **Bulk conversions (generated/unrolled code):** Always `u128s_from_felt252` + `upcast` - **One-off boundary conversions (deserialization):** `downcast` is fine — per-call overhead negligible - **Never in hot paths:** `try_into().unwrap()` — panic path causes quadratic Sierra bloat ### Common BoundedInt Mistakes - **Downcast at every function call** — the biggest performance killer. Use `BoundedInt` types throughout, not just inside arithmetic functions. - **Trying to upcast to a narrower type** — `upcast(val: u32)` to `BoundedInt<0, 150994944>` fails because u32 max > 150994944. - **Wrong imports** — use exact imports from Prerequisites section above. - **Wrong subtraction bounds** — it's `[a_lo - b_hi, a_hi - b_lo]`, NOT `[a_lo - b_lo, a_hi - b_hi]`. - **Negative dividend in `bounded_int_div_rem`** — div_rem doesn't support negative lower bounds. Add a SHIFT (multiple of modulus) before reducing. See SHIFT pattern above. - **Missing intermediate types** — always annotate: `let sum: ZqSum = add(a, b);` - **Division quotient off-by-one** — integer division floors: `24576 / 12289 = 1`, not 2. - **Using `UnitInt` vs `BoundedInt` for constants** — use `UnitInt` for singleton constants like divisors. - **Using `div_rem` vs `bounded_int_div_rem`** — the function is `bounded_int_div_rem`, not `div_rem`. - **Bounds exceed u128::max** — BoundedInt bounds are hard-capped at 2^128. Larger values crash the Sierra specializer: 'Provided generic argument is unsupported.' - **Using `downcast`/`try_into` for bulk felt252 → BoundedInt** — use `u128s_from_felt252` + `upcast` instead (2 vs 4 steps/call). See "felt252 → BoundedInt" section above. ================================================ FILE: .claude/skills/cairo-coding/bounded_int_calc.py ================================================ #!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Bounded Integer Implementation Calculator Computes exact type bounds for Cairo BoundedInt helper trait implementations. Outputs ready-to-paste Cairo code. Usage: python3 bounded_int_calc.py add [--name NAME] python3 bounded_int_calc.py sub [--name NAME] python3 bounded_int_calc.py mul [--name NAME] python3 bounded_int_calc.py div [--name NAME] """ import argparse import sys # felt252 prime (for validation) FELT252_PRIME = 0x800000000000011000000000000000000000000000000000000000000000001 def validate_felt252(value: int, name: str) -> None: """Warn if value exceeds felt252 range.""" if value < 0: # Negative values are represented as P - |value| in felt252 if abs(value) >= FELT252_PRIME: print(f"WARNING: {name} = {value} exceeds felt252 range!", file=sys.stderr) elif value >= FELT252_PRIME: print(f"WARNING: {name} = {value} exceeds felt252 range!", file=sys.stderr) def format_bound(value: int) -> str: """Format a bound value, handling negatives.""" if value < 0: return str(value) return str(value) def calc_add(a_lo: int, a_hi: int, b_lo: int, b_hi: int) -> tuple[int, int]: """Calculate addition bounds: [a_lo + b_lo, a_hi + b_hi]""" result_lo = a_lo + b_lo result_hi = a_hi + b_hi return result_lo, result_hi def calc_sub(a_lo: int, a_hi: int, b_lo: int, b_hi: int) -> tuple[int, int]: """Calculate subtraction bounds: [a_lo - b_hi, a_hi - b_lo]""" result_lo = a_lo - b_hi result_hi = a_hi - b_lo return result_lo, result_hi def calc_mul(a_lo: int, a_hi: int, b_lo: int, b_hi: int) -> tuple[int, int]: """ Calculate multiplication bounds. For unsigned: [a_lo * b_lo, a_hi * b_hi] For signed/mixed: evaluate all corners. """ corners = [ a_lo * b_lo, a_lo * b_hi, a_hi * b_lo, a_hi * b_hi, ] return min(corners), max(corners) def calc_div( a_lo: int, a_hi: int, b_lo: int, b_hi: int ) -> tuple[tuple[int, int], tuple[int, int]]: """ Calculate division bounds. Quotient: [a_lo // b_hi, a_hi // b_lo] Remainder: [0, b_hi - 1] Note: Cairo's bounded_int_div_rem requires non-negative dividends. """ if b_lo <= 0: print("ERROR: Divisor lower bound must be positive!", file=sys.stderr) sys.exit(1) if a_lo < 0: print( "ERROR: Dividend lower bound must be non-negative! Cairo's bounded_int_div_rem does not support negative dividends.", file=sys.stderr, ) sys.exit(1) quot_lo = a_lo // b_hi quot_hi = a_hi // b_lo rem_lo = 0 rem_hi = b_hi - 1 return (quot_lo, quot_hi), (rem_lo, rem_hi) def generate_add_impl(a_lo: int, a_hi: int, b_lo: int, b_hi: int, name: str) -> str: result_lo, result_hi = calc_add(a_lo, a_hi, b_lo, b_hi) validate_felt252(result_lo, "Result min") validate_felt252(result_hi, "Result max") return f"""impl {name} of AddHelper, BoundedInt<{format_bound(b_lo)}, {format_bound(b_hi)}>> {{ type Result = BoundedInt<{format_bound(result_lo)}, {format_bound(result_hi)}>; }}""" def generate_sub_impl(a_lo: int, a_hi: int, b_lo: int, b_hi: int, name: str) -> str: result_lo, result_hi = calc_sub(a_lo, a_hi, b_lo, b_hi) validate_felt252(result_lo, "Result min") validate_felt252(result_hi, "Result max") return f"""impl {name} of SubHelper, BoundedInt<{format_bound(b_lo)}, {format_bound(b_hi)}>> {{ type Result = BoundedInt<{format_bound(result_lo)}, {format_bound(result_hi)}>; }}""" def generate_mul_impl(a_lo: int, a_hi: int, b_lo: int, b_hi: int, name: str) -> str: result_lo, result_hi = calc_mul(a_lo, a_hi, b_lo, b_hi) validate_felt252(result_lo, "Result min") validate_felt252(result_hi, "Result max") return f"""impl {name} of MulHelper, BoundedInt<{format_bound(b_lo)}, {format_bound(b_hi)}>> {{ type Result = BoundedInt<{format_bound(result_lo)}, {format_bound(result_hi)}>; }}""" def generate_div_impl(a_lo: int, a_hi: int, b_lo: int, b_hi: int, name: str) -> str: (quot_lo, quot_hi), (rem_lo, rem_hi) = calc_div(a_lo, a_hi, b_lo, b_hi) validate_felt252(quot_lo, "Quotient min") validate_felt252(quot_hi, "Quotient max") validate_felt252(rem_lo, "Remainder min") validate_felt252(rem_hi, "Remainder max") return f"""impl {name} of DivRemHelper, BoundedInt<{format_bound(b_lo)}, {format_bound(b_hi)}>> {{ type DivT = BoundedInt<{format_bound(quot_lo)}, {format_bound(quot_hi)}>; type RemT = BoundedInt<{format_bound(rem_lo)}, {format_bound(rem_hi)}>; }}""" def main(): parser = argparse.ArgumentParser( description="Calculate BoundedInt helper trait implementations", formatter_class=argparse.RawDescriptionHelpFormatter, epilog=""" Examples: # Addition: [0, 12288] + [0, 12288] python3 bounded_int_calc.py add 0 12288 0 12288 # Subtraction: [0, 12288] - [0, 12288] python3 bounded_int_calc.py sub 0 12288 0 12288 # Multiplication: [0, 12288] * [0, 12288] python3 bounded_int_calc.py mul 0 12288 0 12288 # Division: [128, 255] / [3, 8] python3 bounded_int_calc.py div 128 255 3 8 # Custom impl name python3 bounded_int_calc.py mul 0 12288 0 12288 --name Zq12289MulHelper """, ) subparsers = parser.add_subparsers(dest="operation", required=True) # Add command add_parser = subparsers.add_parser( "add", help="Addition: [a_lo, a_hi] + [b_lo, b_hi]" ) add_parser.add_argument("a_lo", type=int, help="Lower bound of first operand") add_parser.add_argument("a_hi", type=int, help="Upper bound of first operand") add_parser.add_argument("b_lo", type=int, help="Lower bound of second operand") add_parser.add_argument("b_hi", type=int, help="Upper bound of second operand") add_parser.add_argument("--name", default="AddImpl", help="Name for the impl") # Sub command sub_parser = subparsers.add_parser( "sub", help="Subtraction: [a_lo, a_hi] - [b_lo, b_hi]" ) sub_parser.add_argument("a_lo", type=int, help="Lower bound of first operand") sub_parser.add_argument("a_hi", type=int, help="Upper bound of first operand") sub_parser.add_argument("b_lo", type=int, help="Lower bound of second operand") sub_parser.add_argument("b_hi", type=int, help="Upper bound of second operand") sub_parser.add_argument("--name", default="SubImpl", help="Name for the impl") # Mul command mul_parser = subparsers.add_parser( "mul", help="Multiplication: [a_lo, a_hi] * [b_lo, b_hi]" ) mul_parser.add_argument("a_lo", type=int, help="Lower bound of first operand") mul_parser.add_argument("a_hi", type=int, help="Upper bound of first operand") mul_parser.add_argument("b_lo", type=int, help="Lower bound of second operand") mul_parser.add_argument("b_hi", type=int, help="Upper bound of second operand") mul_parser.add_argument("--name", default="MulImpl", help="Name for the impl") # Div command div_parser = subparsers.add_parser( "div", help="Division: [a_lo, a_hi] / [b_lo, b_hi]" ) div_parser.add_argument("a_lo", type=int, help="Lower bound of dividend") div_parser.add_argument("a_hi", type=int, help="Upper bound of dividend") div_parser.add_argument( "b_lo", type=int, help="Lower bound of divisor (must be > 0)" ) div_parser.add_argument("b_hi", type=int, help="Upper bound of divisor") div_parser.add_argument("--name", default="DivRemImpl", help="Name for the impl") args = parser.parse_args() if args.operation == "add": print(generate_add_impl(args.a_lo, args.a_hi, args.b_lo, args.b_hi, args.name)) elif args.operation == "sub": print(generate_sub_impl(args.a_lo, args.a_hi, args.b_lo, args.b_hi, args.name)) elif args.operation == "mul": print(generate_mul_impl(args.a_lo, args.a_hi, args.b_lo, args.b_hi, args.name)) elif args.operation == "div": print(generate_div_impl(args.a_lo, args.a_hi, args.b_lo, args.b_hi, args.name)) if __name__ == "__main__": main() ================================================ FILE: .github/.all-contributorsrc ================================================ { "projectName": "garaga", "projectOwner": "keep-starknet-strange", "repoType": "github", "repoHost": "https://github.com", "files": [ "README.md" ], "imageSize": 100, "commit": true, "commitConvention": "gitmoji", "contributors": [ { "login": "feltroidprime", "name": "Feltroid Prime", "avatar_url": "https://avatars.githubusercontent.com/u/96737978?v=4", "profile": "https://github.com/feltroidprime", "contributions": [ "code" ] }, { "login": "abdelhamidbakhta", "name": "Abdel @ StarkWare ", "avatar_url": "https://avatars.githubusercontent.com/u/45264458?v=4", "profile": "https://github.com/abdelhamidbakhta", "contributions": [ "code" ] }, { "login": "tekkac", "name": "Tarik K.", "avatar_url": "https://avatars.githubusercontent.com/u/98529704?v=4", "profile": "https://github.com/tekkac", "contributions": [ "code" ] }, { "login": "bacharif", "name": "Bachir Arif", "avatar_url": "https://avatars.githubusercontent.com/u/22233193?v=4", "profile": "https://github.com/bacharif", "contributions": [ "code" ] }, { "login": "rdubois-crypto", "name": "Renaud Dubois", "avatar_url": "https://avatars.githubusercontent.com/u/103030189?v=4", "profile": "https://github.com/rdubois-crypto", "contributions": [ "code" ] }, { "login": "raugfer", "name": "Rodrigo Ferreira", "avatar_url": "https://avatars.githubusercontent.com/u/725060?v=4", "profile": "https://raugfer.com/", "contributions": [ "code" ] }, { "login": "luiz-lvj", "name": "Luiz Vasconcelos Júnior", "avatar_url": "https://avatars.githubusercontent.com/u/64055364?v=4", "profile": "https://github.com/luiz-lvj", "contributions": [ "code" ] }, { "login": "shramee", "name": "Shramee Srivastav", "avatar_url": "https://avatars.githubusercontent.com/u/11048263?v=4", "profile": "http://shramee.me/", "contributions": [ "code" ] }, { "login": "akinovak", "name": "Andrija Novakovic", "avatar_url": "https://avatars.githubusercontent.com/u/28649205?v=4", "profile": "https://github.com/akinovak", "contributions": [ "code" ] }, { "login": "Liam-Eagen", "name": "Liam Eagen", "avatar_url": "https://avatars.githubusercontent.com/u/5618692?v=4", "profile": "https://github.com/Liam-Eagen", "contributions": [ "code" ] }, { "login": "petscheit", "name": "Paul Etscheit", "avatar_url": "https://avatars.githubusercontent.com/u/10947187?v=4", "profile": "https://github.com/petscheit", "contributions": [ "code" ] }, { "login": "stefanMadzharov", "name": "stefanMadzharov", "avatar_url": "https://avatars.githubusercontent.com/u/83451593?v=4", "profile": "https://github.com/stefanMadzharov", "contributions": [ "code" ] } ], "contributorsPerLine": 7, "linkToUsage": true } ================================================ FILE: .github/CODEOWNERS ================================================ * @abdelhamidbakhta @feltroidprime ================================================ FILE: .github/ISSUE_TEMPLATE/01_BUG_REPORT.md ================================================ --- name: Bug Report about: Create a report to help Garaga to improve title: "bug: " labels: "bug" assignees: "" --- # Bug Report **Garaga version:** **Current behavior:** **Expected behavior:** **Steps to reproduce:** **Related code:** ``` insert short code snippets here ``` **Other information:** ================================================ FILE: .github/ISSUE_TEMPLATE/02_FEATURE_REQUEST.md ================================================ --- name: Feature Request about: Suggest an idea for this project title: "feat: " labels: "enhancement" assignees: "" --- # Feature Request **Describe the Feature Request** **Describe Preferred Solution** **Describe Alternatives** **Related Code** **Additional Context** **If the feature request is approved, would you be willing to submit a PR?** _(Help can be provided if you need assistance submitting a PR)_ - [ ] Yes - [ ] No ================================================ FILE: .github/ISSUE_TEMPLATE/03_CODEBASE_IMPROVEMENT.md ================================================ --- name: Codebase improvement about: Provide your feedback for the existing codebase. Suggest a better solution for algorithms, development tools, etc. title: "dev: " labels: "enhancement" assignees: "" --- ================================================ FILE: .github/ISSUE_TEMPLATE/config.yml ================================================ --- blank_issues_enabled: false contact_links: - name: Garaga Community Support url: https://github.com/keep-starknet-strange/garaga/discussions about: Please ask and answer questions here. ================================================ FILE: .github/PULL_REQUEST_TEMPLATE.md ================================================ # Pull Request type Please check the type of change your PR introduces: - [ ] Bugfix - [ ] Feature - [ ] Code style update (formatting, renaming) - [ ] Refactoring (no functional changes, no API changes) - [ ] Build-related changes - [ ] Documentation content changes - [ ] Testing - [ ] Other (please describe): # What is the current behavior? Issue Number: N/A # What is the new behavior? - - - # Does this introduce a breaking change? - [ ] Yes - [ ] No # Other information ================================================ FILE: .github/labels.yml ================================================ --- - name: "breaking-change" color: ee0701 description: "A change that changes the API or breaks backward compatibility for users." - name: "bugfix" color: ee0701 description: "Inconsistencies or issues which will cause a problem for users or implementors." - name: "documentation" color: 0052cc description: "Solely about the documentation of the project." - name: "enhancement" color: 1d76db description: "Enhancement of the code, not introducing new features." - name: "refactor" color: 1d76db description: "Updating the code with simpler, easier to understand or more efficient syntax or methods, but not introducing new features." - name: "performance" color: 1d76db description: "Improving performance of the project, not introducing new features." - name: "new-feature" color: 0e8a16 description: "New features or options." - name: "maintenance" color: 2af79e description: "Generic maintenance tasks." - name: "ci" color: 1d76db description: "Work that improves the continuous integration." - name: "dependencies" color: 1d76db description: "Change in project dependencies." - name: "in-progress" color: fbca04 description: "Issue is currently being worked on by a developer." - name: "stale" color: fef2c0 description: "No activity for quite some time." - name: "no-stale" color: fef2c0 description: "This is exempt from the stale bot." - name: "security" color: ee0701 description: "Addressing a vulnerability or security risk in this project." - name: "incomplete" color: fef2c0 description: "Missing information." - name: "invalid" color: fef2c0 description: "This is off-topic, spam, or otherwise doesn't apply to this project." - name: "beginner-friendly" color: 0e8a16 description: "Good first issue for people wanting to contribute to this project." - name: "help-wanted" color: 0e8a16 description: "We need some extra helping hands or expertise in order to resolve this!" - name: "priority-critical" color: ee0701 description: "Must be addressed as soon as possible." - name: "priority-high" color: b60205 description: "After critical issues are fixed, these should be dealt with before any further issues." - name: "priority-medium" color: 0e8a16 description: "This issue may be useful, and needs some attention." - name: "priority-low" color: e4ea8a description: "Nice addition, maybe... someday..." - name: "major" color: b60205 description: "This PR causes a major bump in the version number." - name: "minor" color: 0e8a16 description: "This PR causes a minor bump in the version number." ================================================ FILE: .github/scripts/declare_maintained_contracts.py ================================================ import asyncio import os from enum import Enum from pathlib import Path import dotenv from starknet_py.net.account.account import Account from starknet_py.net.full_node_client import FullNodeClient from starknet_py.net.models import StarknetChainId from starknet_py.net.signer.stark_curve_signer import KeyPair from garaga.hints.io import to_int from garaga.starknet.cli.smart_contract_project import SmartContractProject from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( generate_drand_decrypt_constants, ) dotenv.load_dotenv(".secrets") CONTRACTS_PATH = Path("src/contracts") class Network(Enum): SEPOLIA = "sepolia" MAINNET = "mainnet" def to_starknet_chain_id(self): if self == Network.SEPOLIA: return StarknetChainId.SEPOLIA elif self == Network.MAINNET: return StarknetChainId.MAINNET else: raise ValueError(f"Unknown network: {self}") def get_account(network: Network): rpc_url = os.getenv(f"{network.value.upper()}_RPC_URL") account_address = os.getenv(f"{network.value.upper()}_ACCOUNT_ADDRESS") account_private_key = os.getenv(f"{network.value.upper()}_ACCOUNT_PRIVATE_KEY") client = FullNodeClient(node_url=rpc_url) account = Account( address=account_address, client=client, key_pair=KeyPair.from_private_key(to_int(account_private_key)), chain=network.to_starknet_chain_id(), ) return account async def declare_contract_from_path(path: Path, network: Network): contract = SmartContractProject(smart_contract_folder=path) account = get_account(network) await contract.declare_class_hash(account=account) async def declare_contract_from_path_both_networks(path: Path): await declare_contract_from_path(path, Network.SEPOLIA) await asyncio.sleep(0.3) await declare_contract_from_path(path, Network.MAINNET) async def main(): await declare_contract_from_path_both_networks(CONTRACTS_PATH / "universal_ecip") await asyncio.sleep(0.3) await declare_contract_from_path_both_networks(CONTRACTS_PATH / "drand_quicknet") await asyncio.sleep(0.3) # Generate verifier class hash into decrypt constants, then declare verifier = SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "drand_quicknet" ) generate_drand_decrypt_constants( verifier.get_sierra_class_hash(), CONTRACTS_PATH / "drand_decrypt_quicknet", ) await declare_contract_from_path_both_networks( CONTRACTS_PATH / "drand_decrypt_quicknet" ) await asyncio.sleep(0.3) await declare_contract_from_path_both_networks( CONTRACTS_PATH / "autogenerated" / "risc0_verifier_bn254" ) await asyncio.sleep(0.3) await declare_contract_from_path_both_networks( CONTRACTS_PATH / "autogenerated" / "sp1_verifier_bn254" ) if __name__ == "__main__": asyncio.run(main()) ================================================ FILE: .github/scripts/verify_contracts.py ================================================ import ast import asyncio import os import sys from enum import Enum from pathlib import Path import dotenv from starknet_py.net.full_node_client import FullNodeClient import garaga.hints.io as io from garaga.starknet.cli.smart_contract_project import SmartContractProject dotenv.load_dotenv(".secrets") class Network(Enum): SEPOLIA = "sepolia" MAINNET = "mainnet" def get_rpc_url(self): return os.getenv(f"{self.value.upper()}_RPC_URL") def get_class_hash_from_generator(): try: with open( "hydra/garaga/starknet/groth16_contract_generator/generator.py", "r" ) as f: tree = ast.parse(f.read()) for node in ast.walk(tree): if isinstance(node, ast.Assign) and len(node.targets) == 1: if getattr(node.targets[0], "id", None) == "ECIP_OPS_CLASS_HASH": return hex(node.value.value) raise ValueError("ECIP_OPS_CLASS_HASH not found in generator.py") except Exception as e: print(f"Error parsing generator.py: {str(e)}", file=sys.stderr) sys.exit(1) async def verify_network(network: Network, class_hash: str): class_hash = io.to_hex_str(class_hash) print(f"\nVerifying class hash {class_hash} on {network.value}...") rpc_url = network.get_rpc_url() print(f"Using RPC URL: {rpc_url}") client = FullNodeClient(rpc_url) try: result = await client.get_class_by_hash(class_hash) if not result: print(f"Error: Contract not declared on {network.value}", file=sys.stderr) sys.exit(1) print(f"✓ Contract verified on {network.value}") except Exception as e: print(f"Error checking {network.value}: {str(e)}", file=sys.stderr) sys.exit(1) async def verify_ecip_contract(): class_hash = get_class_hash_from_generator() print(f"Verifying ECIP contract using class hash: {class_hash}") await verify_network(Network.SEPOLIA, class_hash) await verify_network(Network.MAINNET, class_hash) print("\n✓ Contract verified on both networks") async def verify_contract_from_path(path: Path): contract = SmartContractProject(smart_contract_folder=path) class_hash = contract.get_sierra_class_hash() print(f"Verifying contract {path} with class hash {io.to_hex_str(class_hash)}") await verify_network(Network.SEPOLIA, class_hash) await verify_network(Network.MAINNET, class_hash) if __name__ == "__main__": asyncio.run(verify_ecip_contract()) asyncio.run(verify_contract_from_path(Path("src/contracts/drand_quicknet"))) asyncio.run(verify_contract_from_path(Path("src/contracts/drand_decrypt_quicknet"))) asyncio.run( verify_contract_from_path( Path("src/contracts/autogenerated/risc0_verifier_bn254") ) ) asyncio.run( verify_contract_from_path( Path("src/contracts/autogenerated/sp1_verifier_bn254") ) ) ================================================ FILE: .github/workflows/cairo.yml ================================================ name: Cairo Workflow / publish on: push: branches: [main] pull_request: workflow_dispatch: jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths: '["src/**", ".github/workflows/cairo.yml"]' test-cairo: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest steps: # Checkout the repository - name: Checkout uses: actions/checkout@v3 - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: stable override: true profile: minimal components: rustfmt - name: Setup Starknet Foundry uses: foundry-rs/setup-snfoundry@v4 - name: Setup Scarb uses: software-mansion/setup-scarb@v1 with: scarb-lock: ./src/Scarb.lock - name: Run scarb fmt check in src working-directory: src/ run: scarb fmt --check - name: Run scarb test in src working-directory: src/ run: scarb test - name: Run scarb fmt check in mutator_set working-directory: src/contracts/mutator_set run: scarb fmt --check - name: Run snforge test in mutator_set working-directory: src/contracts/mutator_set run: snforge test - name: Run scarb test for all autogenerated contracts run: ./tools/make/test_contracts.sh - name: Run scarb fmt check in risc0_sample_app working-directory: src/contracts/risc0_sample_app/fibonacci_sequencer run: scarb fmt --check # Conflicting with the e2e test : we don't want to dedeploy the verifier at each commit. # - name: Run snforge test in risc0_sample_app # working-directory: src/contracts/risc0_sample_app/fibonacci_sequencer # run: snforge test - name: Publish to Scarb Registry if: startsWith(github.ref, 'refs/tags/') working-directory: src/ env: SCARB_REGISTRY_AUTH_TOKEN: ${{ secrets.SCARB_REGISTRY_AUTH_TOKEN }} run: scarb publish ================================================ FILE: .github/workflows/docs-sync.yml ================================================ # .github/workflows/docs-sync.yml # # Keep GitBook docs (docs/gitbook) and source code in sync. # ├─ create-docs-pr : docs ➜ main (PR auto-merges if docs-only) # └─ sync-main-to-docs : main ➜ docs (keeps non-docs files identical to main) name: Documentation Sync permissions: contents: write # allow pushing branches / squash-merge pull-requests: write # allow opening / merging PRs issues: write # create & apply labels on: push: branches: [ main, docs ] # run on every push to either branch defaults: run: shell: bash # strict mode added in scripts concurrency: group: docs-sync-${{ github.ref }} cancel-in-progress: true jobs: #─────────────────────────────────────────────────────────────────────────────── # A. docs ➜ main – single rolling PR on branch: docs-sync #─────────────────────────────────────────────────────────────────────────────── create-docs-pr: if: >- github.event.ref == 'refs/heads/docs' && ( github.actor == 'gitbook-com[bot]' || github.actor == 'gitbook-io[bot]' || contains(github.event.head_commit.message, '[gitbook]') ) runs-on: ubuntu-latest steps: # 1️⃣ Check out the latest MAIN in a clean worktree - uses: actions/checkout@v4 with: ref: main fetch-depth: 0 persist-credentials: false - run: | git config user.name "GitBook Docs Bot" git config user.email "docs-bot@garaga.dev" # 2️⃣ Overlay docs/gitbook from the docs branch - name: Sync docs/gitbook from docs branch run: | set -euo pipefail git fetch --quiet origin docs git checkout origin/docs -- docs/gitbook # Exit early if nothing changed (check staged changes since git checkout stages them) if git diff --cached --quiet; then echo "No documentation changes — skipping PR." echo "SKIP_PR=true" >>"$GITHUB_ENV" fi # 3️⃣ Commit the changes (only if any) - name: Commit docs update if: env.SKIP_PR != 'true' run: | set -euo pipefail # Changes are already staged by git checkout, just commit them git commit -m "📚 Sync docs/gitbook @ ${{ github.sha }}" # 4️⃣ Create / update the rolling PR on branch docs-sync - uses: peter-evans/create-pull-request@v7 if: env.SKIP_PR != 'true' id: cpr with: token: ${{ secrets.DOCS_SYNC_PAT }} branch: docs-sync # ← single, reusable branch base: main title: "📚 Update documentation from GitBook" commit-message: "📚 docs(branch=docs) → main @ ${{ github.sha }}" labels: documentation,auto-generated delete-branch: true # auto-delete after you squash-merge # 5️⃣ Add an extra label & comment if non-docs files slipped in - name: Flag mixed-content PRs if: env.SKIP_PR != 'true' env: GH_TOKEN: ${{ secrets.DOCS_SYNC_PAT }} run: | set -euo pipefail # If *any* file outside docs/gitbook changed, add label + comment if git diff --name-only origin/main | grep -vqE '^docs/gitbook/'; then gh pr edit "${{ steps.cpr.outputs.pull-request-number }}" \ --add-label "needs-review" gh pr comment "${{ steps.cpr.outputs.pull-request-number }}" \ --body "⚠️ *Mixed content* – this PR touches files outside \`docs/gitbook\`. Please review." fi #─────────────────────────────────────────────────────────────────────────────── # B. main ➜ docs – keep non-docs files identical to main #─────────────────────────────────────────────────────────────────────────────── sync-main-to-docs: if: >- github.event.ref == 'refs/heads/main' && !contains(github.event.head_commit.message, '[gitbook]') && github.actor != 'gitbook-com[bot]' && github.actor != 'gitbook-io[bot]' runs-on: ubuntu-latest steps: # 1) Check out docs branch (create it if it doesn't exist) - uses: actions/checkout@v4 with: ref: docs fetch-depth: 0 token: ${{ secrets.DOCS_SYNC_PAT }} - name: Configure Git run: | git config user.name "GitHub Docs Sync" git config user.email "docs-sync@garaga.dev" git fetch origin main --tags --prune # 2) Bring EVERYTHING (including docs/gitbook) up to date with main - name: Sync repo from main run: | set -euo pipefail git fetch origin main --tags --prune # Overwrite the working tree with the state of main git checkout origin/main -- . # Stage everything and commit only if something changed git add -A if git diff --cached --quiet; then echo "No updates required – docs branch already matches main." exit 0 fi git commit -m "🔄 Sync all files from main @ ${{ github.sha }}" # ─── 3) Open (or update) a PR towards docs ───────────────────────────── - uses: peter-evans/create-pull-request@v7 id: cpr with: token: ${{ secrets.DOCS_SYNC_PAT }} # the current HEAD contains the commit we just made branch: main-sync-${{ github.sha }}-${{ github.run_id }} base: docs commit-message: "🔄 Sync non-docs files from main @ ${{ github.sha }}" title: "🔄 Sync main → docs (non-docs files)" body: | This PR keeps the **docs** branch in sync with **main**. Source commit: ${{ github.sha }} > 🤖 _docs-sync workflow_ labels: documentation,auto-generated,auto-merge delete-branch: true draft: false # open as a normal PR # ─── 4) Enable auto-merge; will complete when checks are green ───────── - name: Enable auto-merge if: steps.cpr.outputs.pull-request-number env: GH_TOKEN: ${{ secrets.DOCS_SYNC_PAT }} run: | gh pr merge ${{ steps.cpr.outputs.pull-request-number }} \ --auto --squash --delete-branch --repo "$GITHUB_REPOSITORY" || \ echo "Auto-merge pending required checks." ================================================ FILE: .github/workflows/e2e.yml ================================================ name: E2E-devnet on: push: branches: [main] pull_request: jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths_ignore: '["**/README.md", "**/docs/**"]' devnet-test-matrix: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest strategy: matrix: python-version: ['3.10', '3.14'] fail-fast: false steps: - uses: actions/checkout@v3 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: 1.87.0 override: true profile: minimal - name: Setup Scarb uses: software-mansion/setup-scarb@v1 with: scarb-version: "2.16.1" - name: Install dependencies run: make setup env: PYTHON_VERSION: ${{ matrix.python-version }} - name: Install devnet run: ./tests/contracts_e2e/install_devnet.sh - name: Run tests run: source venv/bin/activate && pytest -n auto -s -x tests/contracts_e2e/e2e_test.py # Summary job for branch protection (matrix jobs have version suffix in name) devnet-test: needs: [pre_job, devnet-test-matrix] if: always() runs-on: ubuntu-latest steps: - name: Check matrix job status run: | if [ "${{ needs.pre_job.outputs.should_skip }}" == "true" ]; then echo "Tests skipped" exit 0 fi if [ "${{ needs.devnet-test-matrix.result }}" != "success" ]; then echo "Matrix tests failed" exit 1 fi echo "All tests passed" ================================================ FILE: .github/workflows/hydra.yml ================================================ name: Hydra backend test on: push: branches: [main] pull_request: jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths_ignore: '["**/README.md", "**/docs/**"]' test-hydra-matrix: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest strategy: matrix: python-version: ['3.10', '3.12', '3.14'] fail-fast: false steps: - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: stable override: true profile: minimal components: rustfmt - uses: actions/checkout@v3 - name: Set up Python ${{ matrix.python-version }} uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies run: make setup env: PYTHON_VERSION: ${{ matrix.python-version }} - name: Check Black formatting run: source venv/bin/activate && black --check . - name: Test garaga_rs run: | source venv/bin/activate (cd tools/garaga_rs && cargo fmt --check && cargo test) - name: Run pytest run: | source venv/bin/activate pytest -n auto - name: Set up Scarb uses: software-mansion/setup-scarb@v1 with: scarb-version: "2.16.1" - name: Run make rewrite and check for unstaged changes if: matrix.python-version == '3.14' run: | source venv/bin/activate if ! make rewrite; then echo "Error: 'make rewrite' command failed" exit 1 fi if [[ -n $(git status --porcelain) ]]; then echo "Error: Unstaged changes detected after running 'make rewrite'" git status exit 1 fi - name: Check bytecode size limits if: matrix.python-version == '3.14' run: | source venv/bin/activate make check-max-log-n continue-on-error: false # Summary job for branch protection (matrix jobs have version suffix in name) test-hydra: needs: [pre_job, test-hydra-matrix] if: always() runs-on: ubuntu-latest steps: - name: Check matrix job status run: | if [ "${{ needs.pre_job.outputs.should_skip }}" == "true" ]; then echo "Tests skipped" exit 0 fi if [ "${{ needs.test-hydra-matrix.result }}" != "success" ]; then echo "Matrix tests failed" exit 1 fi echo "All tests passed" ================================================ FILE: .github/workflows/labels.yml ================================================ --- name: Sync labels on: push: branches: - main paths: - .github/labels.yml jobs: labels: name: ♻️ Sync labels runs-on: ubuntu-latest steps: - name: ⤵️ Check out code from GitHub uses: actions/checkout@v2 - name: 🚀 Run Label Syncer uses: micnncim/action-label-syncer@v1.2.0 env: GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} ================================================ FILE: .github/workflows/maturin.yml ================================================ name: Maturin on: push: tags: - '*' workflow_dispatch: permissions: contents: read jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths_ignore: '["**/README.md", "**/docs/**"]' linux: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ${{ matrix.platform.runner }} strategy: matrix: platform: - runner: ubuntu-latest target: x86_64 - runner: ubuntu-latest target: x86 - runner: ubuntu-latest target: aarch64 - runner: ubuntu-latest target: armv7 - runner: ubuntu-latest target: s390x - runner: ubuntu-latest target: ppc64le steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: | 3.10 3.11 3.12 3.13 3.14 - name: Build wheels uses: PyO3/maturin-action@v1 with: target: ${{ matrix.platform.target }} args: --release --out dist --find-interpreter --features python sccache: 'true' manylinux: auto - name: Upload wheels uses: actions/upload-artifact@v4 with: name: wheels-linux-${{ matrix.platform.target }} path: dist musllinux: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ${{ matrix.platform.runner }} strategy: matrix: platform: - runner: ubuntu-latest target: x86_64 - runner: ubuntu-latest target: x86 - runner: ubuntu-latest target: aarch64 - runner: ubuntu-latest target: armv7 steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: | 3.10 3.11 3.12 3.13 3.14 - name: Build wheels uses: PyO3/maturin-action@v1 with: target: ${{ matrix.platform.target }} args: --release --out dist --find-interpreter --features python sccache: 'true' manylinux: musllinux_1_2 - name: Upload wheels uses: actions/upload-artifact@v4 with: name: wheels-musllinux-${{ matrix.platform.target }} path: dist windows: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ${{ matrix.platform.runner }} strategy: matrix: platform: - runner: windows-latest target: x64 - runner: windows-latest target: x86 python-version: ['3.10', '3.11', '3.12', '3.13', '3.14'] steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} architecture: ${{ matrix.platform.target }} - name: Build wheels uses: PyO3/maturin-action@v1 with: target: ${{ matrix.platform.target }} args: --release --out dist --features python sccache: 'true' - name: Upload wheels uses: actions/upload-artifact@v4 with: name: wheels-windows-${{ matrix.platform.target }}-py${{ matrix.python-version }} path: dist macos: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ${{ matrix.platform.runner }} strategy: matrix: platform: - runner: macos-14 target: x86_64 - runner: macos-14 target: aarch64 steps: - uses: actions/checkout@v4 - uses: actions/setup-python@v5 with: python-version: | 3.10 3.11 3.12 3.13 3.14 - name: Build wheels uses: PyO3/maturin-action@v1 with: target: ${{ matrix.platform.target }} args: --release --out dist --find-interpreter --features python sccache: 'true' - name: Upload wheels uses: actions/upload-artifact@v4 with: name: wheels-macos-${{ matrix.platform.target }} path: dist sdist: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - name: Build sdist uses: PyO3/maturin-action@v1 with: command: sdist args: --out dist - name: Upload sdist uses: actions/upload-artifact@v4 with: name: wheels-sdist path: dist release: name: Release runs-on: ubuntu-latest if: "startsWith(github.ref, 'refs/tags/')" # Only run on tag pushes needs: [linux, musllinux, windows, macos, sdist] steps: - uses: actions/checkout@v4 - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: stable override: true profile: minimal components: rustfmt - uses: software-mansion/setup-scarb@v1 with: scarb-version: "2.16.1" - name: Set up Python 3.10 uses: actions/setup-python@v5 with: python-version: "3.10.x" - name: Install dependencies run: make setup - name: Verify Contract Declaration env: SEPOLIA_RPC_URL: ${{ secrets.SEPOLIA_RPC_URL }} MAINNET_RPC_URL: ${{ secrets.MAINNET_RPC_URL }} run: source venv/bin/activate && python .github/scripts/verify_contracts.py - uses: actions/download-artifact@v4 - name: Publish to PyPI uses: PyO3/maturin-action@v1 env: MATURIN_PYPI_TOKEN: ${{ secrets.PYPI_API_TOKEN }} with: command: upload args: --non-interactive --skip-existing wheels-*/* ================================================ FILE: .github/workflows/node.yml ================================================ name: NODE tests on: push: branches: - main - master tags: - '*' pull_request: workflow_dispatch: jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths: '["tools/**"]' npm-test: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' name: NPM Test runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: actions/setup-node@v4 with: node-version: 'lts/*' - name: Run npm test in garaga_ts working-directory: tools/npm/garaga_ts run: | npm ci npm test ================================================ FILE: .github/workflows/setup.yml ================================================ name: Test make setup (cross-platform) on: push: branches: [main] paths: - 'tools/make/setup.sh' - '.github/workflows/setup.yml' pull_request: paths: - 'tools/make/setup.sh' - '.github/workflows/setup.yml' jobs: pre_job: runs-on: ubuntu-latest outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' shellcheck: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - name: Run ShellCheck # SC2016: single-quoted strings intentionally prevent expansion (activate script) # SC1091: sourced files (venv/bin/activate) don't exist at lint time run: shellcheck -s bash -e SC2016,SC1091 tools/make/setup.sh test-setup: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ${{ matrix.os }} strategy: matrix: include: - os: ubuntu-latest name: Linux x86_64 - os: macos-14 name: macOS arm64 fail-fast: false name: setup (${{ matrix.name }}) steps: - uses: actions/checkout@v4 - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: stable override: true profile: minimal - name: Run make setup run: make setup - name: Verify venv run: | source venv/bin/activate python --version test-setup-fedora: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' runs-on: ubuntu-latest container: fedora:latest name: setup (Fedora dnf) steps: - name: Install base tools run: dnf install -y git curl gcc g++ make perl-FindBin - uses: actions/checkout@v4 - name: Mark workspace as safe for git run: git config --global --add safe.directory "$GITHUB_WORKSPACE" - name: Install Rust run: | curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y echo "$HOME/.cargo/bin" >> "$GITHUB_PATH" - name: Run make setup run: | source "$HOME/.cargo/env" make setup - name: Verify venv run: | source "$HOME/.cargo/env" source venv/bin/activate python --version ================================================ FILE: .github/workflows/wasm.yml ================================================ name: WASM npm publish on: push: branches: - main - master tags: - '*' pull_request: workflow_dispatch: jobs: pre_job: # continue-on-error: true # Uncomment once integration is finished runs-on: ubuntu-latest # Map a step output to a job output outputs: should_skip: ${{ steps.skip_check.outputs.should_skip }} steps: - id: skip_check uses: fkirc/skip-duplicate-actions@v5 with: concurrent_skipping: 'never' paths: '["tools/**"]' test-wasm: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' name: test-wasm runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: actions/setup-node@v4 with: node-version: 'lts/*' - uses: dtolnay/rust-toolchain@stable - run: cargo install wasm-pack - name: Run wasm specific tests working-directory: tools/garaga_rs run: RUSTFLAGS='--cfg getrandom_backend="wasm_js"' wasm-pack test --node --release --no-default-features --features wasm build-wasm: needs: pre_job if: needs.pre_job.outputs.should_skip != 'true' name: build-wasm runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - name: Build and check for changes in generated code working-directory: tools/npm/garaga_ts run: | docker compose up --build --exit-code-from app git status --porcelain [[ -z $(git status --porcelain ) ]] - name: Upload package file as artifact uses: actions/upload-artifact@v4 with: name: npm-package path: tools/npm/garaga_ts/*.tgz if-no-files-found: error test-integration: needs: [pre_job, build-wasm] if: needs.pre_job.outputs.should_skip != 'true' name: test-integration runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: actions/setup-node@v4 with: node-version: 'lts/*' - name: Install Puppeteer dependencies run: | sudo apt-get update sudo apt-get install -y \ libnss3 libxss1 libasound2t64 libatk-bridge2.0-0 libatk1.0-0 \ libcups2 libxcomposite1 libxdamage1 libxrandr2 libgbm1 \ libpango-1.0-0 libpangocairo-1.0-0 libpangoft2-1.0-0 libgtk-3-0 - name: Download package file as artifact uses: actions/download-artifact@v4 with: name: npm-package path: tools/npm/garaga_ts - name: Build and tests integration test packages working-directory: tools/npm/integration-test-suite run: | cp ../garaga_ts/garaga-*.tgz garaga.tgz npm i npm run build npx puppeteer browsers install npm run test release: name: Release runs-on: ubuntu-latest if: "startsWith(github.ref, 'refs/tags/')" # Only run on tag pushes needs: [build-wasm, test-wasm, test-integration] steps: - uses: actions/checkout@v4 - name: Set up Rust uses: actions-rs/toolchain@v1 with: toolchain: stable override: true profile: minimal components: rustfmt - uses: software-mansion/setup-scarb@v1 with: scarb-version: "2.16.1" - name: Set up Python uses: actions/setup-python@v5 with: python-version: "3.10" - name: Install dependencies run: make setup - name: Verify Contract Declaration env: SEPOLIA_RPC_URL: ${{ secrets.SEPOLIA_RPC_URL }} MAINNET_RPC_URL: ${{ secrets.MAINNET_RPC_URL }} run: source venv/bin/activate && python .github/scripts/verify_contracts.py - uses: actions/setup-node@v4 with: node-version: 'lts/*' registry-url: 'https://registry.npmjs.org' - name: Download package file as artifact uses: actions/download-artifact@v4 with: name: npm-package - name: Publish to npm run: | npm publish --access=public *.tgz env: NODE_AUTH_TOKEN: ${{ secrets.NPM_API_TOKEN }} ================================================ FILE: .gitignore ================================================ *.json !*_input.json !*Proof.json !frobenius_*.json !*test_vectors.json __pycache__ venv *.env *profiling* *.o *.c *.so *.html *.sage.py *.idea *.secrets *.pb.gz .cargo/hypothesis/ *.go tools/garaga_rs/target/ tools/make/requirements.txt .prev_tests_failed src/cairo/target/ *target* Scarb.lock tests/contracts_e2e/devnet/* # Foundry artifacts for Solidity testing tools/noir/hello/lib/ tools/noir/hello/out/ tools/noir/hello/cache/ tools/noir/hello/test/ tools/noir/hello/foundry.toml !hydra/garaga/starknet/groth16_contract_generator/examples/*.json !docs/benchmarks/test_summary.json *snfoundry_cache !tools/npm/garaga_rs/*.json !tools/make/constants.json # Benchmarks and profiling data .cargo/benchmarks/*/ src/profile/ /profiles/ **/.snfoundry_trace/** # Worktrees .worktrees/ .stignore .claude/worktrees/ ================================================ FILE: .pre-commit-config.yaml ================================================ repos: - repo: https://github.com/PyCQA/autoflake rev: v2.3.1 hooks: - id: autoflake args: ["--in-place", "--remove-all-unused-imports"] files: \.py$ - repo: https://github.com/pycqa/isort rev: 5.13.2 hooks: - id: isort args: ["--profile", "black"] files: \.py$ - repo: https://github.com/pre-commit/pre-commit-hooks rev: v4.4.0 hooks: - id: trailing-whitespace exclude: ^tools/npm/garaga_ts/src/wasm/pkg/ - id: end-of-file-fixer exclude: (\.cairo$|^tools/npm/garaga_ts/src/wasm/pkg/) - id: check-yaml - id: check-toml - repo: https://github.com/psf/black rev: 26.1.0 hooks: - id: black args: ["--target-version", "py310"] files: \.py$ - repo: local hooks: - id: scarb-fmt name: scarb fmt entry: bash -c 'cd src && scarb fmt' language: system files: \.cairo$ pass_filenames: false - id: cargo-fmt name: cargo fmt entry: bash -c 'cd tools/garaga_rs && cargo fmt' language: system files: ^tools/garaga_rs/.*\.rs$ pass_filenames: false ================================================ FILE: .secrets.template ================================================ SEPOLIA_RPC_URL="https://rpc.starknet-testnet.lava.build:443" SEPOLIA_ACCOUNT_PRIVATE_KEY=0x1 SEPOLIA_ACCOUNT_ADDRESS=0x2 MAINNET_RPC_URL="https://" MAINNET_ACCOUNT_PRIVATE_KEY=0x3 MAINNET_ACCOUNT_ADDRESS=0x4 ================================================ FILE: .tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 starknet-devnet 0.5.1 cairo-profiler 0.14.0 ================================================ FILE: CLAUDE.md ================================================ # Garaga ## Project layout - `src/` — Cairo contracts and library (Scarb workspace, `snforge test`) - `tools/garaga_rs/` — Rust core (`cargo test -p garaga_rs`, `cargo clippy`) - `tools/garaga_rs/src/python_bindings/` — PyO3 bindings (`make maturin`) - `tools/garaga_rs/src/wasm_bindings.rs` — WASM bindings (`make wasm`, Docker-based) - `tools/npm/garaga_ts/` — TypeScript wrappers + WASM pkg - `hydra/` — Python calldata builders and helpers - `tests/` — E2E and integration tests ## Build commands | What | Command | |------|---------| | Rust tests | `cargo test -p garaga_rs` | | Rust lint | `cargo clippy --workspace` | | Python bindings | `make maturin` | | WASM + TS + npm | `make wasm` (Docker) | | Cairo tests | `snforge test -p garaga` | | Format | `make fmt` (scarb fmt + cargo fmt) | ## Critical invariants **Rust/Python parity**: Every calldata builder has both a Python and Rust path via `use_rust` flag. Parity is enforced by pytest asserting `calldata_py == calldata_rs` byte-for-byte. Use `fixed_sigma` or equivalent for determinism. **WASM regeneration**: After any change to Rust source in `tools/garaga_rs/src/` (except `python_bindings/`) or `Cargo.toml`, run `make wasm` and commit regenerated files in `tools/npm/garaga_ts/src/wasm/pkg/`. CI will fail if out of sync. **TypeScript coverage**: Every WASM binding needs a typed wrapper in `tools/npm/garaga_ts/src/node/api.ts`, a Jest test, and coverage across all 4 integration suites (Node CJS, Node ESM, Webpack, React). **E2E tests**: Deploy on starknet-devnet via `SmartContractProject.declare_class_hash()`, generate calldata via Python, invoke contract, assert via `wait_for_acceptance()`. **Cairo circuits**: Never include unused values in circuit output tuples (`extend_struct_output`) — each output enlarges the circuit's generic tuple and can trigger CASM `Offset overflow` when the tuple exceeds stdlib `CircuitDefinition` bounds. Prefer `#[inline(always)]` on circuit functions and loops over repeated calls to keep AP offsets scoped per iteration. ================================================ FILE: Cargo.toml ================================================ [workspace] resolver = "2" members = [ "tools/garaga_rs" ] [profile.release] lto = true debug = false opt-level = 3 ================================================ FILE: LICENSE ================================================ MIT License Copyright (c) 2023 Keep StarkNet Strange Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ================================================ FILE: Makefile ================================================ SHELL := /bin/bash ACTIVATE := source venv/bin/activate && .PHONY: build test coverage run run-profile generate-constants profile-test benchmarks update-risc0-class-hash constants: $(ACTIVATE) python tools/make/generate_constants.py setup: ./tools/make/setup.sh bytecode-check: ./tools/make/bytecode_check.sh check-max-log-n: ./tools/make/bytecode_check_max_log_n.sh rewrite: $(ACTIVATE) ./tools/make/rewrite.sh rewrite-no-tests: $(ACTIVATE) ./tools/make/rewrite.sh no-tests regen: cd src/contracts/mutator_set && make regen update-risc0-class-hash: ./tools/make/update_risc0_class_hash.sh steps: ./tools/make/steps.sh fmt: scarb fmt && cargo fmt # Profile a specific test and generate performance visualizations # Usage: make profile-test [TEST=] [JOBS=] # Each job takes ~3GB of ram DEFAULT_JOBS := 8 profile-test: @JOBS_VAL=$${JOBS:-$(DEFAULT_JOBS)}; \ if [ -z "$(TEST)" ]; then \ echo "Running all tests with profiling ($$JOBS_VAL jobs)..."; \ $(ACTIVATE) python tools/profile_tests.py --all --parallel-jobs $$JOBS_VAL --generate-benchmarks; \ else \ echo "Running tests with filter: $(TEST) ($$JOBS_VAL jobs)"; \ $(ACTIVATE) python tools/profile_tests.py $(TEST) --parallel-jobs $$JOBS_VAL --generate-benchmarks; \ fi benchmarks: @echo "Generating Cairo benchmarks from existing test data..." $(ACTIVATE) python tools/profile_tests.py --benchmarks-only ci-e2e: ./tools/make/ci_e2e.sh ci-hydra: ./tools/make/ci_hydra.sh ci-cairo: ./tools/make/ci_cairo.sh ci-wasm: ./tools/make/ci_wasm.sh wasm: ./tools/make/wasm.sh wasm-test-gen: ./tools/make/wasm-test-gen.sh maturin: $(ACTIVATE) maturin develop --release --features python clean: sudo rm -rf build/ mkdir -p build/ ================================================ FILE: README.md ================================================

[![CI Status](https://img.shields.io/github/checks-status/keep-starknet-strange/garaga/main?label=All%20Workflows)](https://github.com/keep-starknet-strange/garaga/actions) [![Project license](https://img.shields.io/github/license/keep-starknet-strange/garaga.svg?style=flat-square)](LICENSE) [![Pull Requests welcome](https://img.shields.io/badge/PRs-welcome-ff69b4.svg?style=flat-square)](https://github.com/keep-starknet-strange/garaga/issues?q=is%3Aissue+is%3Aopen+label%3A%22help+wanted%22) [![Exploration_Team](https://img.shields.io/badge/Exploration_Team-29296E.svg?&style=for-the-badge&logo=data:image/svg%2bxml;base64,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)](https://github.com/keep-starknet-strange)
## About > State-of-the-art Elliptic Curve tooling and SNARKS verification for Cairo & Starknet 🐺. Garaga enables efficient elliptic curve operations on Starknet. It achieves state of the art performance by - using a dedicated builtin made by Starkware for emulated modular arithmetic - using a suite of non-deterministic techniques for extension field multiplication, pairings, and multi scalar multiplication to reduce the number of steps to verify results. Garaga currently supports: - Scalar & Multi-scalar multiplication for any Weirstrass curve, including BN254, BLS12_381, SECP256/R1, and ED25519. You can add the one you need by specifying the curve parameters. - Pairing operations for BN254 and BLS12_381. - Groth16 smart contract verifiers generators for BN254 and BLS12_381. - Noir smart contract verifiers generators for ultra keccak honk flavour. ## Architecture overview ![Architecture Overview](docs/images/architecture_overview.svg) Garaga consists of a Pythonic backend with Rust bindings and CairoZero / Cairo libraries. - The Pythonic backend is here to define emulated modular arithmetic circuits that can be compiled to Cairo or Cairo1 code. It also handles witnesses generation for the non-deterministic computations, smart contract contract generation for a given proof system and elliptic curve, and calldata generation from a given proof. - The CairoZero / Starknet interfaces are responsible for composing and calling the circuits, as well as adding all the extra logic needed to make the algorithms work (Fiat-Shamir heuristic, SNARKS verifiers algorithms, etc). ## Quickstart : deploying a SNARK verifier on Starknet Currently, only Groth16 on BN254 and BLS12_381 is supported with automatic support for json files coming from SnarkJS and Gnark. 1. Create a new directory for you project, and bring the jsons files for verification key, proof file and public inputs inside it. 2. Install the garaga pip package with `pip install garaga`. Python 3.10+ is required and a virtual environment is recommended. Enter `garaga` in your terminal to get started. 3. Run the `garaga gen` command in your terminal to generate the code for the SNARK verifier given your verification key. 4. Edit the generated smart contract to fit the needs of your dapp. 5. Create an environment file `.secrets` following the `.secrets.template` file in the root of this repository, containing the Starkner RPC url, your account address, and the private key. 6. Run the `garaga declare` command in your terminal to declare the smart contract on Starknet and obtain its class hash. Note that this is an expensive operation. 7. Run the `garaga deploy` command in your terminal using the class hash obtained in the previous step to get the contract address. 8. Run the `garaga verify-onchain` command in your terminal using the contract address, the verification key, the proof and the public inputs to verify the proof against the SNARK verifier contract. For more details, please refer to the [documentation](https://garaga.gitbook.io/garaga/). ## Developer setup To get started with Garaga, you'll need to have some tools and dependencies installed. Here's everything you need: ### Prerequisites Ensure you have the following installed: - [Rust](https://www.rust-lang.org/tools/install) - Required for building the `garaga_rs` extension. - [Scarb 2.16.1](https://docs.swmansion.com/scarb/download.html) - The Cairo package manager. Comes with Cairo inside. Python 3.10-3.14 is used for development but does **not** need to be installed manually — `make setup` will auto-install it via [uv](https://docs.astral.sh/uv/) if it's not already available. Make sure you have GMP installed for the `fastecdsa` python package. See [here](https://pypi.org/project/fastecdsa/#installing) for linux and [here](https://github.com/AntonKueltz/fastecdsa/issues/74) for macos. ##### Optionally : - [pprof](https://github.com/google/pprof) - A tool for visualization and analysis of profiling data. Requires [Go](https://go.dev/). - [graphviz](https://graphviz.org/download/) - Necessary for generating graphical representations of profiling data. ### Setup Clone the repository and run the setup command from the root: ```bash make setup ``` This will automatically: - Install [uv](https://docs.astral.sh/uv/) if not present - Install Python 3.14 via uv if no compatible version (3.10-3.14) is found - Create a virtual environment and install all dependencies - Build the Rust extension The setup is idempotent — running it again will update dependencies without recreating the virtual environment. Before proceeding, activate the virtual environment by running `source venv/bin/activate`. ## Cairo Benchmarks 📊 **Click on any section below to expand and view detailed benchmark tables with test performance metrics.** **Note:** Click on the test name to view the profiling image. Resources shown in the table for contracts include extra costs due to the foundry logic. Check the profile file for more details.
contracts
└── groth16_example_bls12_381_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Poseidon | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------------------------------------------|---------|---------------|------------------|------------|-----------|-----------|--------------| | [test_verify_groth16_proof_bls12_381](docs/benchmarks/test_verify_groth16_proof_bls12_381.png) | 353,527 | 10,972 | 90,280 | 586 | 7,506 | 10,868 | 49,754,798 |
└── groth16_example_bn254_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Poseidon | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------|---------|---------------|------------------|------------|-----------|-----------|--------------| | [test_verify_groth16_proof_bn254](docs/benchmarks/test_verify_groth16_proof_bn254.png) | 228,557 | 9,785 | 67,149 | 509 | 5,401 | 8,754 | 34,080,559 |
└── noir_ultra_keccak_honk_example_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Poseidon | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------------------------------------------|-----------|---------------|------------------|-----------|------------|-----------|-----------|--------------| | [test_verify_ultra_keccak_honk_proof](docs/benchmarks/test_verify_ultra_keccak_honk_proof.png) | 1,213,031 | 65,539 | 412,656 | 3,180 | 461 | 45,756 | 43,585 | 187,929,077 |
└── noir_ultra_keccak_zk_honk_example_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Poseidon | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------------------------------------------------|-----------|---------------|------------------|-----------|------------|-----------|-----------|--------------| | [test_verify_ultra_keccak_zk_honk_proof](docs/benchmarks/test_verify_ultra_keccak_zk_honk_proof.png) | 1,306,049 | 70,398 | 451,651 | 3,476 | 461 | 49,914 | 47,993 | 203,546,067 |
└── noir_ultra_starknet_honk_example_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Poseidon | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------------------|-----------|---------------|------------------|------------|-----------|-----------|--------------| | [test_verify_ultra_starknet_honk_proof](docs/benchmarks/test_verify_ultra_starknet_honk_proof.png) | 1,127,871 | 61,433 | 412,522 | 992 | 45,742 | 43,569 | 177,512,050 |
└── noir_ultra_starknet_zk_honk_example_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Poseidon | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------------------------|-----------|---------------|------------------|------------|-----------|-----------|--------------| | [test_verify_ultra_starknet_zk_honk_proof](docs/benchmarks/test_verify_ultra_starknet_zk_honk_proof.png) | 1,221,360 | 66,173 | 451,576 | 1,044 | 49,911 | 47,987 | 193,032,648 |
└── risc0_verifier_bn254_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Poseidon | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------------|---------|---------------|------------------|-----------|------------|-----------|-----------|--------------| | [test_verify_r0_groth16_proof_bn254](docs/benchmarks/test_verify_r0_groth16_proof_bn254.png) | 264,545 | 12,069 | 74,896 | 6,698 | 509 | 6,303 | 9,541 | 42,860,813 |
└── sp1_verifier_bn254_integrationtest::test_contract | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Poseidon | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------------------------------------------|---------|---------------|------------------|-----------|------------|-----------|-----------|--------------| | [test_verify_sp1_groth16_proof_bn254](docs/benchmarks/test_verify_sp1_groth16_proof_bn254.png) | 244,680 | 11,127 | 75,027 | 2,230 | 509 | 6,314 | 9,555 | 38,221,851 |
garaga
└── apps
│ └── drand::tests | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Add Mod | Mul Mod | Sierra Gas | |--------------------------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|-----------|--------------| | [test_decrypt_at_round](docs/benchmarks/test_decrypt_at_round.png) | 289,447 | 3,919 | 385,790 | 14,506 | 57,320 | 28,871 | 89,901,952 | | [test_hash_to_curve](docs/benchmarks/test_hash_to_curve.png) | 26,526 | 971 | 4,559 | 12,289 | 422 | 602 | 10,601,029 | | [test_hash_to_two_bls_felts](docs/benchmarks/test_hash_to_two_bls_felts.png) | 23,557 | 900 | 74 | 12,289 | 2 | 8 | 9,592,623 | | [test_drand_quicknet_public_key](docs/benchmarks/test_drand_quicknet_public_key.png) | 12,861 | 68 | 14,864 | 0 | 1,490 | 1,674 | 3,477,040 | | [test_isogeny](docs/benchmarks/test_isogeny.png) | 1,844 | 58 | 878 | 0 | 51 | 111 | 316,402 | | [test_map_to_curve](docs/benchmarks/test_map_to_curve.png) | 647 | 11 | 264 | 0 | 6 | 39 | 105,190 |
│ └── noir
│ │ └── honk_transcript::tests | Test Name | Steps | Range Check | Bitwise | Poseidon | Sierra Gas | |--------------------------------------------------------------------------|---------|---------------|-----------|------------|--------------| | [test_transcript_keccak](docs/benchmarks/test_transcript_keccak.png) | 71,084 | 5,035 | 3,180 | 1 | 9,315,281 | | [test_transcript_starknet](docs/benchmarks/test_transcript_starknet.png) | 19,758 | 1,103 | 0 | 532 | 2,314,222 |
│ │ └── zk_honk_transcript::tests | Test Name | Steps | Range Check | Bitwise | Poseidon | Sierra Gas | |--------------------------------------------------------------------------------|---------|---------------|-----------|------------|--------------| | [test_zk_transcript_keccak](docs/benchmarks/test_zk_transcript_keccak.png) | 73,392 | 5,241 | 3,476 | 1 | 9,733,069 | | [test_zk_transcript_starknet](docs/benchmarks/test_zk_transcript_starknet.png) | 21,173 | 1,185 | 0 | 584 | 2,486,994 |
│ └── risc0::risc0_utils_tests | Test Name | Steps | Range Check | Bitwise | Sierra Gas | |--------------------------------------------------------------|---------|---------------|-----------|--------------| | [test_receipt_claim](docs/benchmarks/test_receipt_claim.png) | 11,117 | 433 | 5,591 | 4,401,563 | | [test_output_digest](docs/benchmarks/test_output_digest.png) | 4,424 | 171 | 2,230 | 1,754,460 |
│ └── sp1::tests | Test Name | Steps | Range Check | Sierra Gas | |--------------------------------------------------------------------------|---------|---------------|--------------| | [test_convert_u32_to_u128](docs/benchmarks/test_convert_u32_to_u128.png) | 58 | 3 | 6,010 |
└── crypto::mmr::tests | Test Name | Steps | Range Check | Sierra Gas | |--------------------------------------------------------------|---------|---------------|--------------| | [test_trailing_ones](docs/benchmarks/test_trailing_ones.png) | 441 | 51 | 47,670 |
└── ec::ec_ops_g2::tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_ec_mul_g2](docs/benchmarks/test_ec_mul_g2.png) | 105,060 | 1,074 | 87,664 | 8,551 | 9,755 | 23,349,114 |
└── hashes::poseidon_bn254::tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |--------------------------------------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_run_poseidon_grumpkin_circuit_1](docs/benchmarks/test_run_poseidon_grumpkin_circuit_1.png) | 9,913 | 327 | 6,393 | 353 | 919 | 2,008,464 |
└── tests
│ └── autogenerated
│ │ └── ecdsa_tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_ecdsa_SECP256R1](docs/benchmarks/test_ecdsa_SECP256R1.png) | 14,099 | 1,072 | 20,022 | 2,367 | 2,184 | 4,469,718 | | [test_ecdsa_SECP256K1](docs/benchmarks/test_ecdsa_SECP256K1.png) | 18,723 | 2,082 | 15,629 | 1,810 | 1,592 | 4,271,132 |
│ │ └── eddsa_tests | Test Name | Steps | Range Check | Range Check 96 | Bitwise | Add Mod | Mul Mod | Sierra Gas | |------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|-----------|--------------| | [test_eddsa_32_64B](docs/benchmarks/test_eddsa_32_64B.png) | 88,025 | 13,786 | 20,762 | 3,288 | 2,412 | 2,276 | 14,776,560 | | [test_eddsa_16_32B](docs/benchmarks/test_eddsa_16_32B.png) | 52,391 | 7,643 | 20,840 | 1,656 | 2,418 | 2,284 | 9,842,274 | | [test_eddsa_0_0B](docs/benchmarks/test_eddsa_0_0B.png) | 51,814 | 7,549 | 20,865 | 1,656 | 2,419 | 2,286 | 9,780,832 |
│ │ └── msm_tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |--------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_msm_SECP256R1_3P](docs/benchmarks/test_msm_SECP256R1_3P.png) | 20,115 | 1,576 | 29,835 | 3,546 | 3,252 | 6,572,368 | | [test_msm_SECP256K1_3P](docs/benchmarks/test_msm_SECP256K1_3P.png) | 26,954 | 3,087 | 23,194 | 2,707 | 2,359 | 6,257,800 | | [test_msm_SECP256R1_2P](docs/benchmarks/test_msm_SECP256R1_2P.png) | 13,465 | 1,053 | 19,865 | 2,363 | 2,166 | 4,384,404 | | [test_msm_SECP256K1_2P](docs/benchmarks/test_msm_SECP256K1_2P.png) | 17,919 | 2,061 | 15,369 | 1,799 | 1,564 | 4,155,260 | | [test_msm_SECP256R1_1P](docs/benchmarks/test_msm_SECP256R1_1P.png) | 6,991 | 530 | 9,945 | 1,182 | 1,084 | 2,219,716 | | [test_msm_SECP256K1_1P](docs/benchmarks/test_msm_SECP256K1_1P.png) | 9,221 | 1,037 | 7,697 | 900 | 783 | 2,105,654 |
│ │ └── pairing_tests | Test Name | Steps | Range Check | Range Check 96 | Poseidon | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------------------------------------------------------------|---------|---------------|------------------|------------|-----------|-----------|--------------| | [test_BN254_mpcheck_3P_2F_with_extra_miller_loop_result](docs/benchmarks/test_BN254_mpcheck_3P_2F_with_extra_miller_loop_result.png) | 59,916 | 472 | 59,008 | 509 | 4,469 | 7,922 | 15,391,765 | | [test_BLS12_381_mpcheck_3P_2F_with_extra_miller_loop_result](docs/benchmarks/test_BLS12_381_mpcheck_3P_2F_with_extra_miller_loop_result.png) | 54,316 | 356 | 44,885 | 586 | 3,482 | 5,791 | 12,556,430 | | [test_BN254_mpcheck_2P_2F](docs/benchmarks/test_BN254_mpcheck_2P_2F.png) | 47,930 | 393 | 33,047 | 460 | 1,731 | 4,665 | 10,112,792 | | [test_BLS12_381_mpcheck_2P_2F](docs/benchmarks/test_BLS12_381_mpcheck_2P_2F.png) | 45,132 | 308 | 25,250 | 544 | 1,420 | 3,340 | 8,559,824 |
│ │ └── schnorr_tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_schnorr_SECP256K1](docs/benchmarks/test_schnorr_SECP256K1.png) | 18,321 | 2,082 | 15,512 | 1,808 | 1,580 | 4,216,672 |
│ │ └── tower_pairing_tests | Test Name | Steps | Range Check | Range Check 96 | Add Mod | Mul Mod | Sierra Gas | |----------------------------------------------------------------------------------------|---------|---------------|------------------|-----------|-----------|--------------| | [test_tower_pairing_BN254_3P](docs/benchmarks/test_tower_pairing_BN254_3P.png) | 268,869 | 474 | 626,255 | 94,555 | 50,514 | 114,248,466 | | [test_tower_pairing_BLS12_381_3P](docs/benchmarks/test_tower_pairing_BLS12_381_3P.png) | 248,951 | 556 | 538,321 | 86,187 | 37,849 | 97,763,802 | | [test_tower_pairing_BN254_2P](docs/benchmarks/test_tower_pairing_BN254_2P.png) | 219,367 | 398 | 486,548 | 73,494 | 38,661 | 89,466,112 | | [test_tower_pairing_BLS12_381_2P](docs/benchmarks/test_tower_pairing_BLS12_381_2P.png) | 207,121 | 493 | 422,516 | 67,911 | 28,926 | 77,498,340 | | [test_tower_pairing_BN254_1P](docs/benchmarks/test_tower_pairing_BN254_1P.png) | 169,865 | 322 | 346,841 | 52,433 | 26,808 | 64,683,758 | | [test_tower_pairing_BLS12_381_1P](docs/benchmarks/test_tower_pairing_BLS12_381_1P.png) | 165,291 | 430 | 306,711 | 49,635 | 20,003 | 57,232,878 | | [test_tower_final_exp_BN254](docs/benchmarks/test_tower_final_exp_BN254.png) | 120,363 | 246 | 207,134 | 31,372 | 14,955 | 39,901,404 | | [test_tower_final_exp_BLS12_381](docs/benchmarks/test_tower_final_exp_BLS12_381.png) | 123,509 | 367 | 190,906 | 31,359 | 11,080 | 36,972,216 |
│ └── calldata_tests | Test Name | Steps | Range Check | Sierra Gas | |--------------------------------------------------------------------------------------------------------------------------|---------|---------------|--------------| | [test_deserialize_full_proof_with_hints_bls12_381](docs/benchmarks/test_deserialize_full_proof_with_hints_bls12_381.png) | 22,272 | 4,714 | 2,557,180 |
│ └── sha512_tests | Test Name | Steps | Range Check | Bitwise | Sierra Gas | |------------------------------------------------------------------------|---------|---------------|-----------|--------------| | [test_sha512_lorem_ipsum](docs/benchmarks/test_sha512_lorem_ipsum.png) | 102,856 | 18,169 | 4,904 | 14,416,462 | | [test_size_zero](docs/benchmarks/test_size_zero.png) | 37,579 | 6,404 | 1,640 | 5,162,300 | | [test_sha512_size_one](docs/benchmarks/test_sha512_size_one.png) | 37,564 | 6,403 | 1,640 | 5,160,730 |
└── utils::neg_3::tests | Test Name | Steps | Range Check | Sierra Gas | |------------------------------------------------------------------------------|---------|---------------|--------------| | [test_scalar_to_epns](docs/benchmarks/test_scalar_to_epns.png) | 6,103 | 928 | 675,260 | | [test_scalar_to_epns_single](docs/benchmarks/test_scalar_to_epns_single.png) | 1,940 | 297 | 214,790 |
--- 🔄 **To regenerate these benchmarks:** Run `make profile-test` from the project root. ## Support & How to Contribute We warmly welcome contributions and support from the community! Here's how you can help Garaga grow and improve: ### Reporting Issues & Requesting Features - **Spot a bug? Have a feature request?** Check out our [issues page](https://github.com/keep-starknet-strange/garaga/issues) to see if it's already been reported or to open a new issue. ### Contributing to Garaga - **Interested in contributing?** Please take a moment to read our [contribution guidelines](docs/CONTRIBUTING.md) for details on how to get started. Your contributions make the open-source community an incredible place for learning, inspiration, and creation. ### Showing Support - **Love Garaga?** Give us a [star on GitHub](https://github.com/keep-starknet-strange/garaga) to show your support. - **Spread the word:** Share your excitement about Garaga on social platforms like Twitter, [Dev.to](https://dev.to/), [Medium](https://medium.com/), or your personal blog. - **Join the conversation:** Connect with us and other Garaga enthusiasts on our [Telegram group](https://t.me/GaragaPairingCairo). Every contribution, whether it's code, feedback, or spreading the word, greatly benefits everyone and is deeply appreciated. Thank you for being a part of Garaga's journey! ## Security Garaga follows good practices of security, but 100% security cannot be assured. Garaga is provided **"as is"** without any **warranty**. Use at your own risk. _For more information and to report security issues, please refer to our [security documentation](docs/SECURITY.md)._ ## License This project is licensed under the **MIT license**. See [LICENSE](LICENSE) for more information. ## Acknowledgements - Huge props to [tekkac](https://github.com/tekkac) and [feltroidprime](https://github.com/feltroidprime) for their initial work on provable pairing-based cryptography in StarkNet. - Credits to [Nethermind](https://github.com/NethermindEth/) for their [initial work on optimized modular arithmetic](https://github.com/NethermindEth/research-basic-Cairo-operations-big-integers/tree/main/lib). - [Herodotus](https://www.herodotus.dev/) for supporting this project. - [Gnark project](https://github.com/ConsenSys/gnark-crypto) and team, especially [yelhousni](https://github.com/yelhousni) for his amazing knowledge and support. - [OnlyDust](https://www.onlydust.xyz/) and [Starkware](https://starkware.co/). - Liam Eagen and Andrija Novakovic for their support and amazing research. ## Resources - Craig Costello, [Pairing for beginners](https://static1.squarespace.com/static/5fdbb09f31d71c1227082339/t/5ff394720493bd28278889c6/1609798774687/PairingsForBeginners.pdf) - Y. El Housni, "Pairings in Rank-1 Constraint Systems," Cryptology ePrint Archive, Report 2022/1162, 2022. Available: [https://eprint.iacr.org/2022/1162](https://eprint.iacr.org/2022/1162). - feltroidprime. "Faster Extension Field multiplications for Emulated Pairing Circuits." HackMD, [https://hackmd.io/@feltroidprime/B1eyHHXNT](https://hackmd.io/@feltroidprime/B1eyHHXNT). - Liam Eagen, "Zero Knowledge Proofs of Elliptic Curve Inner Products from Principal Divisors and Weil Reciprocity," Cryptology ePrint Archive, Report 2022/596, 2022. Available: [https://eprint.iacr.org/2022/596](https://eprint.iacr.org/2022/596) - Andrija Novakovic and Liam Eagen, "On Proving Pairings," Cryptology ePrint Archive, Paper 2024/640, 2024. Available: [https://eprint.iacr.org/2024/640](https://eprint.iacr.org/2024/640) - Liam Eagen, Youssef El Housni, Simon Masson, and Thomas Piellard, "Fast elliptic curve scalar multiplications in SN(T)ARK circuits," Cryptology ePrint Archive, Paper 2025/933, 2025. Available: [https://eprint.iacr.org/2025/933](https://eprint.iacr.org/2025/933) > **Note:** This list is not exhaustive, and is not intended to be. ## Contributors For a full list of all authors and contributors, see [the contributors page](https://github.com/keep-starknet-strange/garaga/contributors). Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)):
Feltroid Prime
Feltroid Prime
💻		 Abdel @ StarkWare
Abdel @ StarkWare
💻		 Tarik K.
Tarik K.
💻		 Bachir Arif
Bachir Arif
💻		 Renaud Dubois
Renaud Dubois
💻		 Rodrigo Ferreira
Rodrigo Ferreira
💻		 Luiz Vasconcelos Júnior
Luiz Vasconcelos Júnior
💻
Shramee Srivastav
Shramee Srivastav
💻		 Andrija Novakovic
Andrija Novakovic
💻		 Liam Eagen
Liam Eagen
💻		 Paul Etscheit
Paul Etscheit
💻		 stefanMadzharov
stefanMadzharov
💻
Add your contributions
This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome! ================================================ FILE: Scarb.toml ================================================ [workspace] members = [ "src/", "src/corelib_imports", ] [workspace.dependencies] cairo_test = "2.16.1" starknet = "2.16.1" [workspace.scripts] test = "snforge test -p garaga --include-ignored" [cairo] sierra-replace-ids = false ================================================ FILE: docs/CODE_OF_CONDUCT.md ================================================ # Contributor Covenant Code of Conduct ## Our Pledge In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to make participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, sex characteristics, gender identity and expression, level of experience, education, socio-economic status, nationality, personal appearance, race, religion, or sexual identity and orientation. ## Our Standards Examples of behavior that contributes to creating a positive environment include: * Using welcoming and inclusive language * Being respectful of differing viewpoints and experiences * Gracefully accepting constructive criticism * Focusing on what is best for the community * Showing empathy towards other community members Examples of unacceptable behavior by participants include: * The use of sexualized language or imagery and unwelcome sexual attention or advances * Trolling, insulting/derogatory comments, and personal or political attacks * Public or private harassment * Publishing others' private information, such as a physical or electronic address, without explicit permission * Other conduct which could reasonably be considered inappropriate in a professional setting ## Our Responsibilities Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior. Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful. ## Scope This Code of Conduct applies within all project spaces, and it also applies when an individual is representing the project or its community in public spaces. Examples of representing a project or community include using an official project email address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers. ## Enforcement Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project maintainer using any of the [private contact addresses](https://github.com/keep-starknet-strange/garaga#support). All complaints will be reviewed and investigated and will result in a response that is deemed necessary and appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately. Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership. ## Attribution This Code of Conduct is adapted from the [Contributor Covenant](https://www.contributor-covenant.org), version 1.4, available at For answers to common questions about this code of conduct, see ================================================ FILE: docs/CONTRIBUTING.md ================================================ # Contributing When contributing to this repository, please first discuss the change you wish to make via issue, email, or any other method with the owners of this repository before making a change. Please note we have a [code of conduct](CODE_OF_CONDUCT.md), please follow it in all your interactions with the project. ## Development environment setup > **[?]** > Proceed to describe how to setup local development environment. > e.g: To set up a development environment, please follow these steps: 1. Clone the repo and run setup (Python 3.10-3.14 and [uv](https://docs.astral.sh/uv/) are installed automatically if needed): ```sh git clone https://github.com/keep-starknet-strange/garaga cd garaga make setup source venv/bin/activate ``` 2. You also need [Rust](https://www.rust-lang.org/tools/install) and [Scarb 2.16.1](https://docs.swmansion.com/scarb/download.html) installed. ## Issues and feature requests You've found a bug in the source code, a mistake in the documentation or maybe you'd like a new feature?Take a look at [GitHub Discussions](https://github.com/keep-starknet-strange/garaga/discussions) to see if it's already being discussed. You can help us by [submitting an issue on GitHub](https://github.com/keep-starknet-strange/garaga/issues). Before you create an issue, make sure to search the issue archive -- your issue may have already been addressed! Please try to create bug reports that are: - _Reproducible._ Include steps to reproduce the problem. - _Specific._ Include as much detail as possible: which version, what environment, etc. - _Unique._ Do not duplicate existing opened issues. - _Scoped to a Single Bug._ One bug per report. **Even better: Submit a pull request with a fix or new feature!** ### How to submit a Pull Request 1. Search our repository for open or closed [Pull Requests](https://github.com/keep-starknet-strange/garaga/pulls) that relate to your submission. You don't want to duplicate effort. 2. Fork the project 3. Create your feature branch (`git checkout -b feat/amazing_feature`) 4. Commit your changes (`git commit -m 'feat: add amazing_feature'`) 5. Push to the branch (`git push origin feat/amazing_feature`) 6. [Open a Pull Request](https://github.com/keep-starknet-strange/garaga/compare?expand=1) ================================================ FILE: docs/PYPI_README.md ================================================ # Garaga 🐺 State-of-the-art Elliptic Curve operations and SNARKS verification for Cairo & Starknet. ## Quick Start ```bash pip install garaga ``` **Requirements:** Python 3.10 through 3.14 ## What is Garaga? Garaga provides optimized cryptographic primitives for: - **Elliptic Curve Operations** - High-performance curve arithmetic - **SNARK Verification** - Groth16, Honk, and other proof systems - **Pairing-Based Cryptography** - BN254, BLS12-381 curves - **Cairo/Starknet Integration** - Native integration with Starknet ecosystem ## CLI Usage After installation, access the CLI: ```bash garaga --help ``` Generate SNARK verifier contracts: ```bash garaga gen ``` ## Key Features ✅ **Multi-Curve Support** - BN254, BLS12-381, and more ✅ **SNARK Verifiers** - Groth16, Noir Honk proof verification ✅ **Cairo Integration** - Seamless Starknet development ✅ **Rust Performance** - Optimized core operations ## Documentation & Links - 📖 **Documentation**: [garaga.gitbook.io](https://garaga.gitbook.io/) - 🔧 **GitHub**: [github.com/keep-starknet-strange/garaga](https://github.com/keep-starknet-strange/garaga) - 🐛 **Issues**: [Report bugs](https://github.com/keep-starknet-strange/garaga/issues) ## Version Management Install specific version: ```bash pip install garaga==1.1.0 ``` Install from Git commit: ```bash pip install git+https://github.com/keep-starknet-strange/garaga.git@COMMIT_HASH ``` ## License MIT License - see [LICENSE](https://github.com/keep-starknet-strange/garaga/blob/main/LICENSE) ================================================ FILE: docs/SECURITY.md ================================================ # Security Policy ## Reporting a Vulnerability If there are any vulnerabilities in **Garaga**, don't hesitate to _report them_. 1. Use any of the [private contact addresses](https://github.com/keep-starknet-strange/garaga#support). 2. Describe the vulnerability. If you have a fix, that is most welcome -- please attach or summarize it in your message! 3. We will evaluate the vulnerability and, if necessary, release a fix or mitigating steps to address it. We will contact you to let you know the outcome, and will credit you in the report. Please **do not disclose the vulnerability publicly** until a fix is released! 4. Once we have either a) published a fix, or b) declined to address the vulnerability for whatever reason, you are free to publicly disclose it. ================================================ FILE: docs/benchmarks/test_summary.json ================================================ { "test_trailing_ones": { "last_updated": "2025-10-30T15:26:00.944704", "latest_metrics": { "test_name_hierarchical": "garaga::crypto::mmr::tests::test_trailing_ones", "test_name": "test_trailing_ones", "steps": 441, "sierra_gas": 47670, "image_path": "docs/benchmarks/test_trailing_ones.png", "category": "garaga", "range_check": 51, "range_check96": 0, "keccak": 0, "pedersen": 0, "bitwise": 0, "ecop": 0, "poseidon": 0, "add_mod": 0, "mul_mod": 0 } }, "test_receipt_claim": { "last_updated": "2025-10-30T15:26:00.944704", "latest_metrics": { "test_name_hierarchical": "garaga::apps::risc0::risc0_utils_tests::test_receipt_claim", "test_name": "test_receipt_claim", "steps": 11117, "sierra_gas": 4401563, 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"sp1_verifier_bn254_integrationtest::test_contract::test_verify_sp1_groth16_proof_bn254", "test_name": "test_verify_sp1_groth16_proof_bn254", "steps": 244680, "sierra_gas": 38221851, "image_path": "docs/benchmarks/test_verify_sp1_groth16_proof_bn254.png", "category": "contracts", "range_check": 11127, "range_check96": 75027, "keccak": 0, "pedersen": 0, "bitwise": 2230, "ecop": 0, "poseidon": 509, "add_mod": 6314, "mul_mod": 9555 } } } ================================================ FILE: docs/gitbook/README.md ================================================ # Garaga
Garaga Logo
## State-of-the-Art Elliptic Curve Tooling & ZK Proof Verification for Starknet Garaga enables **efficient verification of zero-knowledge proofs** and **cryptographic operations** on Starknet. It achieves state-of-the-art performance through: * A **dedicated builtin** from StarkWare for emulated modular arithmetic * **Non-deterministic techniques** for extension field multiplication, pairings, and multi-scalar multiplication * **Precomputed verification hints** that dramatically reduce on-chain computation *** ## What Can You Build?
🛡️ ZK Proof VerificationVerify Groth16 and Honk proofs on-chain with production-ready verifier contracts.Learn more →
🔗 zkVM IntegrationVerify proofs from RISC Zero and SP1 using maintained, audited contracts.Learn more →
✍️ Signature VerificationECDSA, Schnorr, and EdDSA verification across multiple elliptic curves.Learn more →
🎲 Randomness & Time-Lock EncryptionOn-chain drand verification for provably fair randomness, plus tlock encryption that only decrypts after a future time.Learn more →
🧮 Elliptic Curve OperationsMulti-scalar multiplication on 6 curves, pairing operations for BN254/BLS12-381.Learn more →
🔒 Privacy-Preserving dAppsBuild applications with Noir/Honk circuits for complex privacy logic.Learn more →
*** ## Architecture Overview ``` ┌──────────────────────────────────────────────────────────────────────────────┐ │ YOUR STARKNET DAPP │ ├──────────────────────────────────────────────────────────────────────────────┤ │ │ │ Smart Contract Generators │ Cairo Libraries │ │ ───────────────────────── │ ─────────────── │ │ • Groth16 Verifier (BN254/BLS) │ • EC Operations (MSM) │ │ • Noir/Honk Verifier │ • Signatures (ECDSA/Schnorr) │ │ • Custom circuit verifiers │ • Pairing Checks │ │ │ • Hashing (SHA-512, Poseidon) │ │ │ ├──────────────────────────────────────────────────────────────────────────────┤ │ Maintained Contracts (Declared on Mainnet) │ │ ───────────────────────────────────────────────────────────── │ │ • Universal ECIP (MSM) • RISC Zero • SP1 • Drand Verifier • Drand tlock │ │ │ ├──────────────────────────────────────────────────────────────────────────────┤ │ SDK (Python / Rust / TypeScript) │ │ ───────────────────────────────────────────────────────────── │ │ Calldata generation • Proof preprocessing • Contract generation │ │ │ ├──────────────────────────────────────────────────────────────────────────────┤ │ Supported Curves │ │ ──────────────── │ │ BN254 │ BLS12-381 │ SECP256K1 │ SECP256R1 │ ED25519 │ GRUMPKIN │ │ │ └──────────────────────────────────────────────────────────────────────────────┘ ``` *** ## Performance Garaga achieves remarkable efficiency through optimized Cairo implementations. See the [full benchmark suite](https://github.com/keep-starknet-strange/garaga#cairo-benchmarks) for detailed metrics on all operations including: * Groth16 verification (BN254 & BLS12-381) * Honk/Noir proof verification * RISC Zero & SP1 proof verification * Signature verification (ECDSA, Schnorr, EdDSA) * Multi-scalar multiplication * Pairing operations *** ## Version Compatibility {% hint style="warning" %} **Important:** Garaga SDK versions (Python, Rust, npm) must match across your toolchain to ensure calldata is correctly formatted for on-chain verification. * **For generated contracts** (Groth16, Noir): Use the same SDK version that generated your verifier contract * **For maintained contracts** (RISC Zero, SP1, drand): Use the SDK version matching the Garaga release that declared the contract class hashes All packages are released together with matching version numbers (e.g., `pip install garaga==1.1.0` + `garaga = "1.1.0"` in Scarb.toml + `garaga_rs` tag `v1.1.0` + `npm install garaga@1.1.0`). {% endhint %} *** ## Quick Start ### 1. Install {% tabs %} {% tab title="Python (Recommended)" %} ```bash pip install garaga ``` {% endtab %} {% tab title="Cairo Library" %} ```bash scarb add garaga ``` Or add to `Scarb.toml`: ```toml [dependencies] garaga = "1.1.0" ``` {% endtab %} {% tab title="Rust" %} ```bash cargo add garaga_rs ``` {% endtab %} {% tab title="npm" %} ```bash npm install garaga ``` {% endtab %} {% endtabs %} ### 2. Generate a Verifier Contract ```bash # Generate a Groth16 verifier from your verification key garaga gen --system groth16 --vk your_vk.json # Or generate a Noir/Honk verifier garaga gen --system ultra_keccak_honk --vk target/vk ``` ### 3. Deploy & Verify ```bash # Declare and deploy your contract garaga declare garaga deploy --class-hash # Verify a proof on-chain garaga verify-onchain --address \ --vk your_vk.json --proof proof.json --public-inputs inputs.json ``` *** ## Production Ready Garaga is used in production by teams building: * **Validity rollups** and L2 solutions * **Cross-chain bridges** with ZK verification * **Privacy-preserving applications** * **Verifiable computation** platforms ### Security * ✅ [**Audited**](https://github.com/keep-starknet-strange/garaga/blob/main/docs/Garaga-audit-report-v2.pdf) by [CryptoExperts](https://www.cryptoexperts.com/) * ✅ **Battle-tested** on Starknet mainnet * ✅ **Open source** under MIT license *** ## Resources * **GitHub**: [github.com/keep-starknet-strange/garaga](https://github.com/keep-starknet-strange/garaga) * **Telegram**: [t.me/GaragaPairingCairo](https://t.me/GaragaPairingCairo) * **Academic Papers**: See [References](./#references) below *** ## References Garaga's cryptographic implementations are based on peer-reviewed research: 1. **Groth16**: Groth, J. "On the Size of Pairing-Based Non-interactive Arguments." EUROCRYPT 2016. [ePrint 2016/260](https://eprint.iacr.org/2016/260) 2. **Efficient Pairings**: El Housni, Y. "Pairings in Rank-1 Constraint Systems." [ePrint 2022/1162](https://eprint.iacr.org/2022/1162) 3. **ECIP**: Eagen, L. "Zero Knowledge Proofs of Elliptic Curve Inner Products." [ePrint 2022/596](https://eprint.iacr.org/2022/596) 4. **On Proving Pairings**: Novakovic, A. & Eagen, L. [ePrint 2024/640](https://eprint.iacr.org/2024/640) 5. **Fast EC Scalar Multiplications**: Eagen, L., El Housni, Y., Masson, S., Piellard, T. [ePrint 2025/933](https://eprint.iacr.org/2025/933) ================================================ FILE: docs/gitbook/SUMMARY.md ================================================ # Table of contents * [Garaga](README.md) * [Building Powerful Applications](building-powerful-applications.md) * [Security](security.md) * [Installation](installation/README.md) * [Python package](installation/python-package.md) * [Cairo Library](installation/cairo-library.md) * [Rust Crate](installation/rust-crate.md) * [Npm package](installation/npm-package.md) * [Developer setup & guides](developer-setup-and-guides/README.md) * [Working with auto-generated Cairo Code](developer-setup-and-guides/working-with-auto-generated-cairo-code.md) * [garaga-rs crate](developer-setup-and-guides/garaga-rs-crate/README.md) * [Rust -> Python bindings](developer-setup-and-guides/garaga-rs-crate/rust-greater-than-python-bindings.md) * [Rust -> Wasm bindings](developer-setup-and-guides/garaga-rs-crate/rust-greater-than-wasm-bindings.md) * [Using garaga libraries in your Cairo project](using-garaga-libraries-in-your-cairo-project/README.md) * [EC (Multi)-Scalar Multiplication](using-garaga-libraries-in-your-cairo-project/ec-multi-scalar-multiplication.md) * [ECDSA, Schnorr & EdDSA Signatures](using-garaga-libraries-in-your-cairo-project/ec-signatures.md) * [RSA-2048 Signatures](using-garaga-libraries-in-your-cairo-project/rsa-signatures.md) * [Hashing functions](using-garaga-libraries-in-your-cairo-project/hashing-functions.md) * [Smart Contract Generators](smart-contract-generators/README.md) * [Groth16 Verifier](smart-contract-generators/groth16/README.md) * [Generate and deploy your verifier contract](smart-contract-generators/groth16/generate-and-deploy-your-verifier-contract.md) * [Generating calldata from a proof and using your deployed contract](smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/README.md) * [Using Python/Garaga CLI](smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-python-garaga-cli.md) * [Using Rust](smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-rust.md) * [Using Typescript](smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-typescript.md) * [Noir Verifier](smart-contract-generators/noir.md) * [Maintained Smart Contracts](maintained-smart-contracts/README.md) * [RiscZero](maintained-smart-contracts/risczero.md) * [SP1](maintained-smart-contracts/sp1.md) * [Drand](maintained-smart-contracts/drand.md) * [Support](support.md) * [Updating these docs](updating-these-docs.md) ================================================ FILE: docs/gitbook/building-powerful-applications.md ================================================ --- icon: rocket --- # Building Powerful Applications Garaga's cryptographic primitives enable a wide range of powerful applications on Starknet. This page showcases what you can build and links to production-ready implementations. *** ## Validity Rollups & L2 Solutions Verify SNARK proofs on Starknet to build trustless bridges and rollup solutions. ### How It Works 1. **Off-chain**: Execute computation and generate a ZK proof (Groth16 or Honk) 2. **On-chain**: Verify the proof using Garaga's optimized verifier contracts 3. **Result**: Trustless verification of arbitrary computation ### Example: Cross-Chain Bridge ```rust use garaga::groth16::{Groth16Proof, verify_groth16_proof}; #[starknet::contract] mod Bridge { #[storage] struct Storage { processed_proofs: LegacyMap, } #[external(v0)] fn process_deposit( ref self: ContractState, proof_with_hints: Span, deposit_hash: felt252, ) -> Result<(), felt252> { // Verify the proof that a deposit occurred on the source chain let public_inputs = verify_groth16_proof(proof_with_hints)?; // Check the deposit hash matches assert(*public_inputs.at(0) == deposit_hash, 'Invalid deposit'); // Process the deposit... Result::Ok(()) } } ``` {% hint style="info" %} **Real-world usage**: Teams use Garaga to verify proofs from RISC Zero and SP1 zkVMs, enabling trustless verification of arbitrary Rust programs on Starknet. {% endhint %} *** ## Privacy-Preserving Applications Build applications where users can prove statements without revealing underlying data. ### Use Cases | Application | What's Proven | What's Hidden | | -------------------------- | ------------------------- | ------------------ | | **Private Voting** | Vote is valid and counted | Who voted for whom | | **Anonymous Credentials** | User meets criteria | User's identity | | **Confidential Transfers** | Balance is sufficient | Transfer amount | | **Private Auctions** | Bid is valid | Bid amount | ### Implementation with Noir Noir makes it easy to write privacy-preserving circuits: ```rust // circuit.nr - Private voting circuit fn main( // Private inputs (not revealed on-chain) private_key: Field, vote_choice: Field, // Public inputs (verified on-chain) public_key_hash: pub Field, merkle_root: pub Field, nullifier: pub Field, ) { // Prove ownership of private key let computed_hash = std::hash::pedersen([private_key]); assert(computed_hash == public_key_hash); // Prove membership in voter set (merkle proof) // ... merkle verification ... // Generate unique nullifier to prevent double voting let computed_nullifier = std::hash::pedersen([private_key, vote_choice]); assert(computed_nullifier == nullifier); } ``` Then verify on Starknet with a single function call. *** ## Verifiable Randomness (drand) Generate provably fair random numbers using the [drand](https://drand.love) distributed randomness beacon. ### Why drand? * **Unpredictable**: Random values can't be known before they're generated * **Unbiasable**: No single party can influence the output * **Publicly verifiable**: Anyone can verify the randomness is legitimate ### Example: On-Chain Lottery Use the maintained drand verifier contract via library call: ```rust use starknet::{SyscallResultTrait, syscalls}; const DRAND_QUICKNET_CLASS_HASH: felt252 = 0x1628f8e2d8ad8c26aea873b13703e4421f2c01a57c0c4974e599490ee30677d; #[starknet::contract] mod Lottery { use starknet::storage::{Map, StorageMapReadAccess, StoragePointerReadAccess}; use super::{DRAND_QUICKNET_CLASS_HASH, SyscallResultTrait, syscalls}; #[storage] struct Storage { participants: Map, participant_count: u32, target_round: u64, } #[external(v0)] fn draw_winner( ref self: ContractState, full_proof_with_hints: Span, ) -> ContractAddress { // Serialize calldata for library call let mut call_data: Array = array![]; Serde::serialize(@full_proof_with_hints, ref call_data); // Verify drand signature via library call to maintained contract let mut result = syscalls::library_call_syscall( DRAND_QUICKNET_CLASS_HASH.try_into().unwrap(), selector!("verify_round"), call_data.span(), ).unwrap_syscall(); let round_result: Result = Serde::deserialize(ref result).unwrap(); let verified_round = round_result.unwrap(); // Ensure we're using the correct round assert!(verified_round == self.target_round.read(), "Wrong round"); // Retrieve randomness for the verified round let mut rand_call_data: Array = array![]; Serde::serialize(@verified_round, ref rand_call_data); let mut rand_result = syscalls::library_call_syscall( DRAND_QUICKNET_CLASS_HASH.try_into().unwrap(), selector!("get_randomness_for_round"), rand_call_data.span(), ).unwrap_syscall(); let randomness: Result = Serde::deserialize(ref rand_result).unwrap(); // Use randomness to select winner let count: u256 = self.participant_count.read().into(); let winner_index: u32 = (randomness.unwrap().into() % count).try_into().unwrap(); self.participants.read(winner_index) } } ``` {% hint style="success" %} **Production contract available**: Use the [maintained drand verifier](maintained-smart-contracts/drand.md) via library call - no deployment needed! {% endhint %} *** ## Signature Verification at Scale Verify signatures from external systems (Bitcoin, Ethereum, Solana) on Starknet. ### Supported Signature Schemes | Scheme | Curves | Use Case | | ----------- | -------------------------------------- | ----------------------------- | | **ECDSA** | SECP256K1, SECP256R1, BN254, BLS12-381 | Bitcoin, Ethereum, WebAuthn | | **Schnorr** | All Weierstrass curves | BIP340 (Taproot), general use | | **EdDSA** | Ed25519 | Solana, general use | ### Example: Multi-Chain Message Verification ```rust use garaga::signatures::ecdsa::{ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash}; use garaga::definitions::G1Point; fn verify_ethereum_message( signature_with_hints: ECDSASignatureWithHint, public_key: G1Point, message_hash: u256, ) -> bool { // curve_id 2 = SECP256K1 (Ethereum's curve) is_valid_ecdsa_signature_assuming_hash(signature_with_hints, public_key, 2) } fn verify_webauthn_signature( signature_with_hints: ECDSASignatureWithHint, public_key: G1Point, message_hash: u256, ) -> bool { // curve_id 3 = SECP256R1 (WebAuthn/Passkeys) is_valid_ecdsa_signature_assuming_hash(signature_with_hints, public_key, 3) } ``` *** ## zkVM Proof Verification Verify proofs from zkVMs like RISC Zero and SP1 to enable trustless execution of arbitrary programs. ### Architecture ``` ┌─────────────────────────────────────────────────────────────┐ │ Off-Chain (zkVM) │ │ ┌─────────────────────────────────────────────────────┐ │ │ │ Your Rust Program │ │ │ │ - Complex business logic │ │ │ │ - State transitions │ │ │ │ - Any computation you can write in Rust │ │ │ └─────────────────────────────────────────────────────┘ │ │ ↓ │ │ ┌─────────────────────────────────────────────────────┐ │ │ │ zkVM (RISC Zero / SP1) │ │ │ │ - Executes program │ │ │ │ - Generates Groth16 proof │ │ │ └─────────────────────────────────────────────────────┘ │ └─────────────────────────────────────────────────────────────┘ ↓ proof ┌─────────────────────────────────────────────────────────────┐ │ On-Chain (Starknet) │ │ ┌─────────────────────────────────────────────────────┐ │ │ │ Garaga Verifier Contract │ │ │ │ - Verifies Groth16 proof │ │ │ │ - Returns public outputs │ │ │ └─────────────────────────────────────────────────────┘ │ └─────────────────────────────────────────────────────────────┘ ``` ### Getting Started See the maintained contracts: * [RISC Zero Integration](maintained-smart-contracts/risczero.md) * [SP1 Integration](maintained-smart-contracts/sp1.md) *** ## Time-Lock Encryption (tlock) Encrypt data that can only be decrypted at a specific future time, using drand's distributed randomness beacon. Decryption can happen entirely on-chain. ### How It Works 1. **Encrypt** a 16-byte message for a future drand round `N` using the SDK (Python, Rust, or TypeScript) 2. **Wait** for drand to publish round `N` 3. **Decrypt on-chain** by verifying the drand signature and using it to recover the message ### Use Cases * **Sealed-bid auctions**: Bids are encrypted until the auction ends * **Scheduled reveals**: Information released at a predetermined time * **Fair launches**: Token distributions with time-locked claiming * **Commit-reveal schemes**: Players commit encrypted moves, revealed together ### Example: Encrypt Off-Chain, Decrypt On-Chain {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_encrypt_to_calldata, ) # Encrypt a 16-byte message for a future round message = b"secret message!!" # exactly 16 bytes calldata = drand_encrypt_to_calldata(round_number=100000, message=message) # Submit calldata to the decrypt contract once the round is published ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import * as garaga from 'garaga'; await garaga.init(); const message = new Uint8Array(16); message.set(new TextEncoder().encode('secret message!!')); const randomness = crypto.getRandomValues(new Uint8Array(16)); const calldata = garaga.encryptToDrandRoundAndGetCallData(100000, message, randomness); ``` {% endtab %} {% endtabs %} {% hint style="success" %} **Production contracts available**: Use the [maintained drand decrypt contract](maintained-smart-contracts/drand.md) for on-chain tlock decryption. See the [full tlock documentation](maintained-smart-contracts/drand.md#time-lock-encryption-tlock) for details. {% endhint %} *** ## Build Your Own The primitives above can be combined to create novel applications: | Combination | Application | | -------------------------- | ---------------------------------------------- | | Groth16 + Signatures | Cross-chain asset bridges | | Noir + drand | Private lotteries with verifiable randomness | | tlock + Noir | Sealed-bid auctions with private bid amounts | | zkVM + MSM | Verifiable ML inference | | EdDSA + Groth16 | Solana → Starknet bridges | **Need help?** Join our [Telegram community](https://t.me/GaragaPairingCairo) to discuss your use case. ================================================ FILE: docs/gitbook/developer-setup-and-guides/README.md ================================================ --- icon: wrench --- # Developer setup & guides ### Installation To work with Garaga, you need the following dependencies : * [Rust](https://www.rust-lang.org/tools/install) * [Scarb](https://docs.swmansion.com/scarb/download.html) with the version specified in [https://github.com/keep-starknet-strange/garaga/blob/main/src/.tool-versions](https://github.com/keep-starknet-strange/garaga/blob/main/src/.tool-versions) Python 3.10-3.14 is used for development but does **not** need to be installed manually — `make setup` will auto-install it via [uv](https://docs.astral.sh/uv/) if it's not already available. Simply clone the [repository](https://github.com/keep-starknet-strange/garaga) : Using git: ```bash git clone https://github.com/keep-starknet-strange/garaga.git ``` Using [github cli ](https://cli.github.com/): ```bash gh repo clone keep-starknet-strange/garaga ``` After that, go into the root of the directory and run the command : ```bash make setup ``` This will automatically install [uv](https://docs.astral.sh/uv/) and Python 3.14 if needed, create a virtual environment, install all dependencies, and build the Rust extension. The setup is idempotent — running it again updates dependencies without recreating the venv. Pay attention to any message indicating failure. Contact us on Garaga telegram if you have any trouble at this point. If everything succeeded, you're good to go! {% hint style="info" %} Make sure to activate the virtual environment created with this setup, using `source venv/bin/activate` {% endhint %} --- ## Project Architecture Understanding the Garaga codebase structure: ``` garaga/ ├── hydra/garaga/ # Python SDK and circuit generators │ ├── starknet/cli/ # CLI commands (gen, declare, deploy, verify) │ ├── precompiled_circuits/ # Circuit definitions │ └── hints/ # Cryptographic hints for Cairo ├── src/ # Cairo code │ ├── src/ # Main Cairo library (garaga package) │ └── contracts/ # Example smart contracts ├── tools/ │ ├── garaga_rs/ # Rust crate (Python/WASM bindings) │ ├── npm/garaga_ts/ # TypeScript SDK │ └── make/ # Build scripts └── tests/ # Python and E2E tests ``` ### Key Components | Component | Location | Purpose | |-----------|----------|---------| | Python SDK | `hydra/garaga/` | CLI, circuit generation, proof processing | | Rust Crate | `tools/garaga_rs/` | Performance-critical operations | | Cairo Library | `src/src/` | On-chain verification | | TypeScript SDK | `tools/npm/garaga_ts/` | Browser/Node.js integration | --- ## Common Commands ### Development ```bash # Format code make fmt # Regenerate Cairo code from Python circuits make rewrite # Run Python tests pytest -n auto # Run Cairo tests scarb test # Run Rust tests cargo test -p garaga_rs ``` ### Building ```bash # Build Python package with Rust extension maturin develop --release --features python # Build WASM package make wasm ``` ### Profiling ```bash # Profile a specific test make profile-test TEST= # Generate benchmarks make benchmarks ``` --- ## Next Steps - [Working with auto-generated Cairo Code](working-with-auto-generated-cairo-code.md) - [garaga-rs crate](garaga-rs-crate/) — Rust library and bindings ================================================ FILE: docs/gitbook/developer-setup-and-guides/garaga-rs-crate/README.md ================================================ --- icon: crab --- # garaga-rs crate The `garaga_rs` crate is the performance-critical Rust library that powers Garaga's cryptographic operations. It provides high-performance implementations of elliptic curve operations, pairing computations, and proof serialization, with bindings to both Python (via PyO3) and WebAssembly (via wasm-bindgen). ## Overview The crate serves as the computational backend for Garaga, accelerating operations that would be too slow in pure Python: - **Elliptic curve operations**: Point addition, scalar multiplication, multi-scalar multiplication (MSM) - **Pairing computations**: Miller loop, final exponentiation, multi-pairing checks - **Proof serialization**: Calldata generation for Groth16, Honk, and signature verification - **Cryptographic hints**: GLV decomposition, ECIP protocol, Frobenius maps ## Module Structure ``` tools/garaga_rs/src/ ├── lib.rs # Crate entry point ├── definitions.rs # Curve definitions (6 curves) ├── io.rs # Field element serialization ├── algebra/ # EC operations │ ├── g1point.rs # G1 point arithmetic │ ├── g2point.rs # G2 point arithmetic │ ├── polynomial.rs # Polynomial operations │ └── extf_mul.rs # Extension field multiplication ├── calldata/ # Proof serialization │ ├── msm_calldata.rs # MSM calldata generation │ ├── mpc_calldata.rs # Multi-pairing check calldata │ └── full_proof_with_hints/ │ ├── groth16.rs # Groth16 (+ RISC0, SP1) │ └── zk_honk.rs # ZK Honk calldata ├── pairing/ # Pairing operations │ ├── multi_miller_loop.rs │ └── final_exp_witness/ ├── ecip/ # ECIP protocol │ ├── core.rs # ECIP hint generation │ └── ff.rs # Function field arithmetic ├── hints/ # Cryptographic hints │ ├── fake_glv.rs # GLV decomposition │ └── eisenstein.rs # Eisenstein integers ├── crypto/ # Hash functions │ ├── poseidon_bn254.rs # Poseidon hash │ └── mmr/ # Merkle Mountain Range ├── python_bindings/ # PyO3 bindings └── wasm_bindings.rs # WASM bindings ``` ## Supported Curves | ID | Curve | Use Cases | |----|-------|-----------| | 0 | BN254 | Groth16, Honk, RISC0, SP1 | | 1 | BLS12-381 | Groth16, drand signatures | | 2 | SECP256K1 | Bitcoin/Ethereum ECDSA | | 3 | SECP256R1 | NIST P-256, WebAuthn | | 4 | X25519/ED25519 | EdDSA signatures | | 5 | GRUMPKIN | Noir circuits | ## Feature Flags The crate uses feature flags to control which bindings are compiled: ```toml [features] default = [] # Pure Rust library python = ["pyo3"] # Python bindings via PyO3 wasm = ["wasm-bindgen", "js-sys"] # WASM bindings ``` ## Key Exports ### Python Bindings When compiled with `--features python`, the following functions are available: ```python from garaga import garaga_rs # G2 operations garaga_rs.g2_add(...) garaga_rs.g2_scalar_mul(...) # Pairing operations garaga_rs.multi_pairing(...) garaga_rs.multi_miller_loop(...) garaga_rs.final_exp(...) # Hint generation garaga_rs.get_final_exp_witness(...) garaga_rs.zk_ecip_hint(...) # Calldata builders garaga_rs.msm_calldata_builder(...) garaga_rs.mpc_calldata_builder(...) garaga_rs.get_groth16_calldata(...) garaga_rs.get_zk_honk_calldata(...) # Signatures garaga_rs.schnorr_calldata_builder(...) garaga_rs.ecdsa_calldata_builder(...) garaga_rs.eddsa_calldata_builder(...) # Hashing garaga_rs.poseidon_hash_bn254(...) garaga_rs.hades_permutation(...) # Extension field garaga_rs.nondeterministic_extension_field_mul_divmod(...) # drand garaga_rs.drand_calldata_builder(...) ``` ### WASM Bindings When compiled with `--features wasm`, similar functions are exported for JavaScript/TypeScript use via `wasm-bindgen`. ## Building ### For Python (via maturin) ```bash cd tools/garaga_rs maturin develop --release --features python ``` ### For WASM ```bash cd tools/garaga_rs wasm-pack build --target web --release --no-default-features --features wasm ``` ### Docker build (reproducible) ```bash cd tools/npm/garaga_ts docker compose up --build ``` ## Testing ```bash cd tools/garaga_rs cargo test ``` ## Dependencies Key external crates: - **lambdaworks-math/crypto**: Field arithmetic and cryptographic primitives - **num-bigint**: Arbitrary precision integers - **pyo3**: Python bindings (optional) - **wasm-bindgen**: WASM bindings (optional) - **sha2/sha3**: Hash functions - **rayon**: Parallel computation ## Next Steps - [Rust -> Python bindings](rust-greater-than-python-bindings.md) — Adding new Python bindings - [Rust -> WASM bindings](rust-greater-than-wasm-bindings.md) — Adding new WASM bindings ================================================ FILE: docs/gitbook/developer-setup-and-guides/garaga-rs-crate/rust-greater-than-python-bindings.md ================================================ # Rust -> Python bindings This guide explains how to add new Python bindings for Rust functions in the `garaga_rs` crate. ## Overview The Python bindings are implemented using PyO3, which provides a safe and ergonomic way to create Python extensions in Rust. The bindings are located in the `tools/garaga_rs/src/python_bindings` directory. ## Adding a new binding 1. Create a new file in `tools/garaga_rs/src/python_bindings/` for your binding 2. Add the module to `mod.rs` 3. Implement your binding function 4. Register the function in the `garaga_rs` module ## Type Conversions ### Common Type Conversions 1. **Python Int -> Rust BigUint** ```rust let py_int: &Bound<'_, PyInt> = ...; let biguint: BigUint = py_int.extract()?; ``` 2. **Rust BigUint -> Python Int** ```rust let biguint: BigUint = ...; Ok(biguint.into_pyobject(py)?.into()) ``` 3. **Python List -> Rust Vec** ```rust let py_list: &Bound<'_, PyList> = ...; let values: Vec = py_list .into_iter() .map(|x| x.extract()) .collect::, _>>()?; ``` 4. **Python Bytes -> Rust Bytes** ```rust let py_bytes: &Bound<'_, PyBytes> = ...; let bytes = py_bytes.as_bytes(); ``` 5. **Field Elements** ```rust // Python Int -> Field Element let fe = element_from_biguint::(&biguint); // Field Element -> Python Int let biguint = element_to_biguint(&fe); ``` ### Error Handling 1. **Converting Rust Errors to Python** ```rust // For custom errors .map_err(PyErr::new::)?; // For simple error propagation .map_err(|e| PyErr::new::(e.to_string()))? ``` 2. **Enum Conversion** ```rust let value = YourEnum::try_from(py_value) .map_err(PyErr::new::)?; ``` ### Common Patterns 1. **Function Declaration** ```rust #[pyfunction] #[allow(clippy::too_many_arguments)] // If needed for complex functions pub fn your_function( py: Python, // ... parameters ... ) -> PyResult { // Implementation } ``` 2. **Returning Results** ```rust // For single values Ok(result.into_pyobject(py)?.into()) // For lists let py_list = PyList::new(py, result); Ok(py_list?.into()) // For tuples Ok(PyTuple::new(py, &[x, y]).into()) ``` ## Example Implementation Here's a complete example showing common patterns: ```rust use pyo3::prelude::*; use pyo3::types::{PyInt, PyList, PyBytes}; use num_bigint::BigUint; #[pyfunction] pub fn example_function( py: Python, input_int: &Bound<'_, PyInt>, input_list: &Bound<'_, PyList>, input_bytes: &Bound<'_, PyBytes>, ) -> PyResult { // Convert Python int to BigUint let value: BigUint = input_int.extract()?; // Convert Python list to Vec let values: Vec = input_list .into_iter() .map(|x| x.extract()) .collect::, _>>()?; // Get bytes let bytes = input_bytes.as_bytes(); // Do your computation let result = process_data(&value, &values, bytes) .map_err(PyErr::new::)?; // Return as Python list let py_list = PyList::new(py, result); Ok(py_list?.into()) } ``` ## Registering Your Function Add your function to the `garaga_rs` module in `mod.rs`: ```rust #[pymodule] fn garaga_rs(m: &Bound<'_, PyModule>) -> PyResult<()> { m.add_function(wrap_pyfunction!(your_function, m)?)?; Ok(()) } ``` ## Using the Bindings After implementing and registering your binding, you can use it in Python like this: ```python from garaga import garaga_rs # For simple integer operations result = garaga_rs.example_function( input_int=42, input_list=[1, 2, 3], input_bytes=b"some bytes" ) ``` ## Testing 1. Add Python tests in `tests/hydra/` 2. Test both successful and error cases 3. Test edge cases (empty lists, zero values) ## Common Pitfalls 1. Always use `PyResult` for error handling 2. Remember to propagate errors with `?` 3. Handle edge cases (e.g., zero values, maximum values) 4. Be careful with memory management for large data structures ## Available Utilities The following utilities are available in the codebase: - `element_from_biguint`: Convert BigUint to Field Element - `element_to_biguint`: Convert Field Element to BigUint - `biguint_to_u256`: Convert BigUint to u256 ## Building and Testing 1. Build/Update the Rust extension: ```bash maturin develop --release --features python ``` 2. Run tests: ```bash pytest -xs ``` ## Best Practices 1. Keep bindings simple and focused 2. Use appropriate error handling 3. Test edge cases thoroughly 4. Follow existing patterns in the codebase ================================================ FILE: docs/gitbook/developer-setup-and-guides/garaga-rs-crate/rust-greater-than-wasm-bindings.md ================================================ # Rust -> Wasm bindings This guide explains how to add new WASM bindings for Rust functions in the `garaga_rs` crate. ## Overview The WASM bindings are implemented using `wasm-bindgen`, which provides a way to expose Rust functions to JavaScript/TypeScript. The bindings are located in `tools/garaga_rs/src/wasm_bindings.rs`. ## Adding a New Binding 1. Add your function to `tools/garaga_rs/src/wasm_bindings.rs` 2. Use the `#[wasm_bindgen]` attribute to expose the function 3. Rebuild the WASM package ### Example Implementation ```rust use wasm_bindgen::prelude::*; use num_bigint::BigUint; #[wasm_bindgen] pub fn your_function( input_hex: &str, // Hex string input input_array: Vec, // Array of values ) -> Result { // Parse hex string to BigUint let value = jsvalue_to_biguint(&JsValue::from_str(input_hex))?; // Process array elements let values: Vec = input_array .iter() .map(|v| jsvalue_to_biguint(v)) .collect::, _>>()?; // Perform computation let result = compute_something(&value, &values) .map_err(|e| JsError::new(&e.to_string()))?; // Return result as BigInt string Ok(biguint_to_jsvalue(&result)) } ``` ### Type Conversions Common conversion patterns for WASM bindings: ```rust // JsValue (hex string) -> BigUint let biguint = jsvalue_to_biguint(&js_value)?; // BigUint -> JsValue (string) let js_value = biguint_to_jsvalue(&biguint); // Parse G1 point from JS object let point = parse_g1_point(&js_object)?; // Parse G2 point from JS object let point = parse_g2_point(&js_object)?; ``` ### Error Handling Use `JsError` for errors that should be visible in JavaScript: ```rust .map_err(|e| JsError::new(&e.to_string()))? ``` ## Available Functions The following functions are currently exposed via WASM: | Function | Description | |----------|-------------| | `msm_calldata_builder` | Generate MSM calldata | | `mpc_calldata_builder` | Generate multi-pairing check calldata | | `get_groth16_calldata` | Generate Groth16 proof calldata | | `get_zk_honk_calldata` | Generate ZK Honk proof calldata | | `schnorr_calldata_builder` | Schnorr signature calldata | | `ecdsa_calldata_builder` | ECDSA signature calldata | | `eddsa_calldata_builder` | EdDSA signature calldata | | `drand_calldata_builder` | drand verification calldata | | `poseidon_hash` | Poseidon hash (BN254) | | `to_weirstrass` | Convert Ed25519 to Weierstrass form | | `to_twistededwards` | Convert Weierstrass to Twisted Edwards | ## TypeScript Wrapper The TypeScript API in `tools/npm/garaga_ts/src/node/api.ts` provides a friendlier interface over the raw WASM bindings: ```typescript import { init, msmCalldataBuilder } from 'garaga'; // Initialize WASM module (required once) await init(); // Use the API const calldata = msmCalldataBuilder( points, // Array of {x, y} objects scalars, // Array of bigint or hex strings curveId, // 0=BN254, 1=BLS12-381, etc. { includePointsAndScalars: true } ); ``` ## Development notes The Garaga NPM package is a mixed package. It is implemented in TypeScript but also reuses Rust code targeted to WebAssembly (WASM) with the help of [`wasm-pack`](https://rustwasm.github.io/wasm-pack/). The `src` folder is organized into two subfolders: `node` which contains the implementation in TypeScript; and `wasm` which has the interoperabilty code produced by `wasm-pack`. Changes to the TypeScript library should only be made to files under the `node` subfolder. Changes to the Rust implementation requires regenerating files under the `wasm` subfolder. Onces changes are in place they can be made permanent into the repository by committing the contents of both folders. Here is the bulk of the process: 1. Open your terminal or command prompt. 2. Use `git` to clone the repository: ```bash git clone https://github.com/keep-starknet-strange/garaga.git cd tools/npm/garaga_ts npm ci ``` 3. If you make TypeScript only changes, you can quickly rebuild the package using the `build:node` NPM script: ```bash npm run build:node npm pack ``` 4. If instead you make Rust changes, it is necessary to generate the WASM interoperability code using the `build` NPM script: ```bash npm run build npm pack ``` 5. However, before commiting changes, it is necessary to generate the WASM interoperability code in a reproducible manner using docker: ```bash docker compose up --build git commit . ``` ### How `wasm-pack` is used to achieve interoperability Internaly the `build` NPM script uses `wasm-pack` to produce the WASM interoperability code. This is achieved by running ```` ```bash cd tools/garaga_rs && wasm-pack build --target web --out-dir ../npm/garaga_ts/src/wasm/pkg --release --no-default-features --features wasm cd tools/npm/garaga_ts && node patch.wasm.cjs ``` ```` Let's unpack it. In the Rust source folder we run `wasm-pack` in `--target web` mode. This generates TypeScript code targeting web pages. The `--release` option is required to minimize the size of the WASM module. The `--no-default-features` ensures we start with a clean slate (no bindings), and `--features wasm` explicitly enables only the WASM bindings we need. Once the `wasm-pack` is done, the code is generated under the folder `src/wasm/pkg` of garaga\_ts that houses the TypeScript source code. We then run a custom script `patch.wasm.cjs` which makes minimal changes to the code generated by wasm-pack to facilitate seamless support of the WASM module in both the browser and Node.js. Basically it converts the WASM module to a [Base64](https://en.wikipedia.org/wiki/Base64) string that can be loaded in a portable way in both environments, amongst other minor tweaks. (It is important to note that the use of a custom script is only required so long `wasm-pack` itself does not provide a more portable/universal target mode.) ================================================ FILE: docs/gitbook/developer-setup-and-guides/working-with-auto-generated-cairo-code.md ================================================ --- icon: wand-sparkles --- # Working with auto-generated Cairo Code ### Developer workflow If working with the python - auto generated cairo code, the main script to work with is `make rewrite` \ {% code title="tools/make/rewrite.sh" %} ```bash rm -rf src/src/tests/* rm -rf src/src/circuits/* rm -rf src/contracts/groth16_example_bls12_381/* rm -rf src/contracts/groth16_example_bn254/* rm -rf src/contracts/risc0_verifier_bn254/* set -e # Exit immediately if a command exits with a non-zero status python hydra/garaga/precompiled_circuits/all_circuits.py || { echo "Error in all_circuits.py"; exit 1; } python hydra/garaga/starknet/tests_and_calldata_generators/test_writer.py || { echo "Error in test_writer.py"; exit 1; } python hydra/garaga/starknet/groth16_contract_generator/generator.py || { echo "Error in generator.py"; exit 1; } python hydra/garaga/starknet/groth16_contract_generator/generator_risc0.py || { echo "Error in generator_risc0.py"; exit 1; } ``` {% endcode %} \ As you can see this will : * Rewrite all the auto-generated cairo code in `src/src/circuits/` (with the `all_circuits.py` script) * Rewrite all the auto-generated cairo tests in `src/src/tests/` (with the `test_writer.py` script) * Rewrite the Groth16 verifiers smart contract templates examples in `src/contracts/` (with the `generator.py` and `generator_risc0.py` scripts) ## Creating auto-generated circuits. While it's relatively easy to write Cairo circuits yourself if their size is small, it starts to be quite time consuming if you need to build a large amount of them, parametrize them, and the circuits themselves are quite large. {% hint style="info" %} Examples of small hand-made small circuits can be found in [https://github.com/keep-starknet-strange/garaga/blob/main/src/src/basic\_field\_ops.cairo](https://github.com/keep-starknet-strange/garaga/blob/main/src/src/basic\_field\_ops.cairo) {% endhint %} \ If you want to write a new auto-generated circuit to `src/src/circuits`, you can define them with python code, and register them to the `all_circuits.py` file. \ \ Below we show a basic tutorial for a non-parametrized circuit. ### Simple isolated example 
import garaga.modulo_circuit_structs as structs
from garaga.definitions import CurveID, get_base_field
from garaga.modulo_circuit import PyFelt, ModuloCircuit


curve_id = CurveID.BN254 # BN254
field = get_base_field(curve_id) # Use with field(int) or field.random().

COMPILATION_MODE = 1 # 1 for Cairo, 0 for CairoZero.

circuit = ModuloCircuit(
    name=f"dummy_{curve_id.name.lower()},
    curve_id.value,
    generic_circuit=False,
    compilation_mode=COMPILATION_MODE,
)
# All "structs" expect a name (replicated in the signature) and a list of elements.
x, y = circuit.write_struct(structs.u384Span("xy", [field.random(), field.random()]))
# All "structs" written with write_struct will be expected in the Cairo
# function signature of the given type.
z = circuit.write_struct(structs.u384("z", [field(42)]))

# With this configuration,
# the signature will be fn(xy: Span<u384>, z:u384).
# More structs and arbitrary ones are supported as well.

# To write constants, use set_or_get_constant.
one = circuit.set_or_get_constant(1)

# Here happens the core circuit logic.
# The core operations are add, sub, mul, inv.
# However, more high level methods are available that translate to
# a sequence of the core operations (ex: div <=> inv then mul)
a = circuit.add(x, y)
b = circuit.sub(a, one)
c = circuit.mul(b, z)
d = circuit.inv(c)
f = circuit.div(d, z)

# Define the output of the function using structs as well.
circuit.extend_struct_output(structs.u384Span("abc", [a, b, c]))
circuit.extend_struct_output(structs.u384("f", [f]))

# Compile and print the compiled cairo circuit :
header = compilation_mode_to_file_header(1) # Cairo 1
compiled_code, function_name = circuit.compile_circuit()
# Note: some imports are unused in the header,
# we should make the compiler aware of the structs used ;)
print(header)
print(compiled_code)
To obtain the corresponding Cairo code, you can do it like this The obtained Cairo code will be ```rust use core::circuit::{ RangeCheck96, AddMod, MulMod, u384, u96, CircuitElement, CircuitInput, circuit_add, circuit_sub, circuit_mul, circuit_inverse, EvalCircuitResult, EvalCircuitTrait, CircuitOutputsTrait, CircuitModulus, AddInputResultTrait, CircuitInputs, CircuitDefinition, CircuitData, CircuitInputAccumulator }; use garaga::core::circuit::AddInputResultTrait2; use core::circuit::CircuitElement as CE; use core::circuit::CircuitInput as CI; use garaga::definitions::{get_a, get_b, get_p, get_g, get_min_one, G1Point, G2Point, E12D, u288, G1G2Pair, BNProcessedPair, BLSProcessedPair, MillerLoopResultScalingFactor, G2Line, get_BLS12_381_modulus,get_BN254_modulus}; use garaga::ec_ops::{SlopeInterceptOutput, FunctionFeltEvaluations, FunctionFelt}; use core::option::Option; #[inline(always)] fn run_dummy_bn254_circuit(xy: Span, z: u384) -> (Span, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in1, in2); let t1 = circuit_sub(t0, in0); let t2 = circuit_mul(t1, in3); let t3 = circuit_inverse(t2); let t4 = circuit_inverse(in3); let t5 = circuit_mul(t3, t4); let modulus = get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t0, t1, t2, t5,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in0 // Fill inputs: let mut xy = xy; while let Option::Some(val) = xy.pop_front() { circuit_inputs = circuit_inputs.next_2(*val); }; // in1 - in2 circuit_inputs = circuit_inputs.next_2(z); // in3 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let abc: Span = array![ outputs.get_output(t0), outputs.get_output(t1), outputs.get_output(t2) ] .span(); let f: u384 = outputs.get_output(t5); return (abc, f); } ``` Note that the compiler will adapt the signature of the Cairo function depending on the `generic_circuit` parameter, and retrieve the corresponding modulus inside the function code. {% code title="https://github.com/keep-starknet-strange/garaga/blob/584cad66d067aa6c04447fe06a00c7be99bc2445/hydra/garaga/modulo_circuit.py#L1068-L1071" %} ```python if self.generic_circuit: code = f"#[inline(always)]\nfn {function_name}({signature_input}, curve_index:usize)->{signature_output} {{\n" else: code = f"#[inline(always)]\nfn {function_name}({signature_input})->{signature_output} {{\n" ``` {% endcode %} ### Using parameterization (docs in progress :construction:) #### The base class Currently, the way we deal with parameterization is encapsulating the earlier `ModuloCircuit` class into a [BaseModuloCircuit](https://github.com/keep-starknet-strange/garaga/blob/584cad66d067aa6c04447fe06a00c7be99bc2445/hydra/garaga/precompiled\_circuits/compilable\_circuits/base.py#L12C7-L12C25) class, and adding keyword arguments to the class deriving it. ```python class BaseModuloCircuit(ABC): """ Base class for all modulo circuits that will be compiled to Cairo code. Parameters: - name: str, the name of the circuit - curve_id: int, the id of the curve - auto_run: bool, whether to run the circuit automatically at initialization. When compiling, this flag must be set to true so the ModuloCircuit class inside the ".circuit" member of this class holds the necessary metadata about the operations that will be compiled. For CairoZero, this flag will be set to False in the Python hint, so that BaseModuloCircuit.run_circuit() can be called on a segment parsed from the CairoZero VM. - compilation mode: 0 (CairoZero) or 1 (Cairo) """ def __init__( self, name: str, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ``` All Cairo function must inherit from the base abstract class \ The abstract methods to implement are : \ * `build_input` ```python def build_input(self) -> list[PyFelt]: """ This method is used to create the necessary inputs that will be written to the ModuloCircuit. It works in pair with the _run_circuit_inner function, where the _run_circuit_inner will use the output of the build_input function to "deserialize" the list of elements and "write" them to the ModuloCircuit class. """ ``` * `_run_circuit_inner` ```python def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: """ This method is responsible for - deserializing the input list of elements, - creating a ModuloCircuit class (or class that derives from ModuloCircuit) - "writing" the inputs to the ModuloCircuit class to obtain ModuloCircuitElements - using the methods add, sub, mul, inv (or higher level methods) of the ModuloCircuit class to define the list of operations on the given inputs. - Returning the ModuloCircuit class in a state where the circuit has been run, and therefore holding the metadata so that its instructions can be compiled to Cairo code. """ ``` At initialization, you must choose a name for the circuit. \ Pay attention to the parameter `generic_circuit` passed to the `ModuloCircuit` class inside `_run_circuit_inner` 
import garaga.modulo_circuit_structs as structs
from garaga.definitions import CurveID
from garaga.precompiled_circuits.compilable_circuits.base import BaseModuloCircuit
from garaga.modulo_circuit import PyFelt, ModuloCircuit

class FixedExpCircuit(BaseModuloCircuit):
    def __init__(
        self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, n:int=1

    ) -> None:
        super().__init__(
            name=f"fixed_exp_circuit_{CurveID(curve_id).name.lower()}_{n}",
            curve_id=curve_id,
            auto_run=auto_run,
            compilation_mode=compilation_mode,
        )
        self.n = n

    def build_input(self) -> list[PyFelt]:
        return [self.field.random()]

    def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit:
        circuit = ModuloCircuit(
            self.name,
            self.curve_id,
            generic_circuit=True,
            compilation_mode=self.compilation_mode,
        )

        z = circuit.write_struct(structs.u384("z", [input[2]]), WriteOps.INPUT)
        res = z
        for i in range(n):
            res = circuit.mul(res, z)
        circuit.extend_struct_output(structs.u384("res", [res]))

        return circuit
================================================ FILE: docs/gitbook/installation/README.md ================================================ --- icon: gear --- # Installation Garaga is available in multiple formats for different use cases: | Package | Use Case | Install Command | |---------|----------|-----------------| | [**Python package**](python-package.md) | CLI for generating verifiers, deployment, calldata generation | `pip install garaga` | | [**Cairo Library**](cairo-library.md) | Use Garaga's Cairo primitives in your smart contracts | `scarb add garaga` | | [**Rust Crate**](rust-crate.md) | Rust applications, calldata generation | `cargo add garaga_rs` | | [**npm package**](npm-package.md) | Browser dApps, frontend integration | `npm install garaga` | ## Quick Start {% tabs %} {% tab title="Python" %} ```bash pip install garaga garaga --help ``` {% endtab %} {% tab title="Cairo" %} ```bash scarb add garaga ``` Or in `Scarb.toml`: ```toml [dependencies] garaga = "1.1.0" ``` {% endtab %} {% tab title="Rust" %} ```toml [dependencies] garaga_rs = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0" } ``` {% endtab %} {% tab title="npm" %} ```bash npm install garaga ``` {% endtab %} {% endtabs %} ## Version Compatibility All Garaga packages are released together with matching version numbers. When using multiple packages, ensure they all use the same version to guarantee compatibility. For example, when using version 1.1.0: - Python: `pip install garaga==1.1.0` - Cairo: `garaga = "1.1.0"` in Scarb.toml - Rust: `tag = "v1.1.0"` in Cargo.toml - npm: `npm install garaga@1.1.0` ## Developer Setup For contributing to Garaga or advanced development workflows, see the [Developer Setup & Guides](../developer-setup-and-guides/README.md). ================================================ FILE: docs/gitbook/installation/cairo-library.md ================================================ --- icon: sparkles --- # Cairo Library The Garaga Cairo library is available on the [scarbs.xyz registry](https://scarbs.xyz/packages/garaga), the official package registry for Cairo/Scarb projects. ## Quick Install The recommended way to add Garaga to your Cairo project: ```bash scarb add garaga ``` This will add the latest version to your `Scarb.toml`. ## Manual Installation Alternatively, add Garaga directly to your `Scarb.toml`: ```toml [dependencies] garaga = "1.1.0" [cairo] sierra-replace-ids = false # Required for Garaga ``` {% hint style="warning" %} **Important:** The `sierra-replace-ids = false` setting is required for Garaga to compile correctly. {% endhint %} ## Installing a Specific Version To install a specific version: ```bash scarb add garaga@1.1.0 ``` Or in `Scarb.toml`: ```toml [dependencies] garaga = "=1.1.0" # Exact version ``` ## Installing from Git If you need an unreleased version or a specific commit: ```toml [dependencies] garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0" } ``` Or from a specific branch/commit: ```toml [dependencies] garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", branch = "main" } ``` {% hint style="info" %} For more information on managing dependencies with Scarb, see the [Scarb documentation](https://docs.swmansion.com/scarb/docs/guides/dependencies.html). {% endhint %} ## Version Compatibility {% hint style="warning" %} **Version Matching:** When using Garaga SDKs (Python, Rust, npm) to generate calldata, ensure the Cairo library version matches the SDK version. Mismatched versions may produce incompatible calldata. For example, if using `pip install garaga==1.1.0`, use `garaga = "1.1.0"` in your `Scarb.toml`. {% endhint %} ## Usage After installation, you can import Garaga modules: ```cairo use garaga::definitions::{G1Point, u384}; use garaga::ec_ops::msm_g1; use garaga::signatures::ecdsa::{ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash}; ``` See [Using Garaga Libraries](../using-garaga-libraries-in-your-cairo-project/) for detailed usage documentation. ## Registry Links * **Package Page:** [scarbs.xyz/packages/garaga](https://scarbs.xyz/packages/garaga) * **Source Code:** [github.com/keep-starknet-strange/garaga](https://github.com/keep-starknet-strange/garaga) ================================================ FILE: docs/gitbook/installation/developer-setup.md ================================================ --- icon: wrench --- # Developer setup To work with Garaga, you need the following dependencies : * [Rust](https://www.rust-lang.org/tools/install) * [Scarb](https://docs.swmansion.com/scarb/download.html) v2.16.1 Python 3.10-3.14 is used for development but does **not** need to be installed manually — `make setup` will auto-install it via [uv](https://docs.astral.sh/uv/) if it's not already available. Simply clone the [repository](https://github.com/keep-starknet-strange/garaga) : Using git: ```bash git clone https://github.com/keep-starknet-strange/garaga.git ``` Using [github cli ](https://cli.github.com/) : ```bash gh repo clone keep-starknet-strange/garaga ``` After that, go into the root of the directory and run the command : ```bash make setup ``` This will automatically install [uv](https://docs.astral.sh/uv/) and Python 3.14 if needed, create a virtual environment, install all dependencies, and build the Rust extension. The setup is idempotent — running it again updates dependencies without recreating the venv. Pay attention to any message indicating failure. Contact us on Garaga telegram if you have any trouble at this point. If everything succeeded, you're good to go! {% hint style="info" %} Make sure to activate the virtual environment created with this setup, using `source venv/bin/activate` {% endhint %} ================================================ FILE: docs/gitbook/installation/npm-package.md ================================================ --- icon: js --- # Npm package Garaga is available as an npm package, making it easy to integrate into your Node.js projects. This guide will help you get started with installation and usage. ## Quick Start The recommended way to install Garaga is through the npm registry: ```bash npm install garaga ``` {% hint style="warning" %} **Version Compatibility:** Use the same version as your pip package (`garaga==X.Y.Z` → `garaga@X.Y.Z`) to ensure calldata compatibility with generated verifiers and maintained contracts. {% endhint %} Or if you prefer using Yarn: ```bash yarn add garaga ``` ## Available Functions The package exports several functions that you can use in your project. For a complete list of available functions and their usage, check out the [API Reference](https://github.com/keep-starknet-strange/garaga/blob/v1.1.0/tools/npm/garaga_ts/src/node/api.ts). This file contains all the exported functions and their TypeScript definitions. ## Package Details - **NPM Registry**: [garaga on npmjs.com](https://www.npmjs.com/package/garaga) - **Source Code**: [GitHub Repository](https://github.com/keep-starknet-strange/garaga/tree/main/tools/npm/garaga_ts) ## Building from Source If you need to build the package from source (e.g., for development or custom modifications), follow these steps: ### Prerequisites - [Rust](https://www.rust-lang.org/tools/install) - [Node.js](https://nodejs.org/en/learn/getting-started/how-to-install-nodejs) - [wasm-pack](https://drager.github.io/wasm-pack/installer/) ### Manual Build 1. Clone the repository: ```bash git clone https://github.com/keep-starknet-strange/garaga.git cd tools/npm/garaga_ts ``` 2. Install dependencies and build: ```bash npm ci npm run build npm pack ``` 3. Install the generated package: ```bash npm install ./garaga-.tgz ``` ### Docker Build (Recommended) For reproducible builds, use Docker: 1. Clone the repository: ```bash git clone https://github.com/keep-starknet-strange/garaga.git cd tools/npm/garaga_ts ``` 2. Build using Docker: ```bash docker compose up --build ``` 3. Install the generated package: ```bash npm install ./garaga-.tgz ``` ## Troubleshooting If you encounter any issues during installation: 1. Ensure you have the latest version of Node.js installed 2. Clear your npm cache: `npm cache clean --force` 3. Delete `node_modules` and `package-lock.json`, then run `npm install` again 4. For build issues, make sure you have the latest version of Rust and wasm-pack ## Support For additional help or to report issues: See [support.md](../support.md "mention") ================================================ FILE: docs/gitbook/installation/python-package.md ================================================ --- icon: python --- # Python package ## Install the latest released version of the CLI {% hint style="info" %} PyPi link : [https://pypi.org/project/garaga/](https://pypi.org/project/garaga/) {% endhint %} The easiest way to install Garaga is via `pip`, which will fetch and install the pre-built binary wheels for your platform. 1. Open your terminal or command prompt. 2. (Optional) If you're using a [virtual environment (venv)](https://docs.python.org/3/library/venv.html), simply activate your venv. 3. Run the following command to install latest release version: ```bash pip install garaga ``` 4. Once the package is successfully installed, the CLI will be accessible via the command line: ```bash garaga ``` {% hint style="info" %} **Garaga supports Python 3.10 through 3.14.** If you need to install a specific Python version, you can use [uv](https://docs.astral.sh/uv/): ```bash uv python install 3.14 # or 3.13, 3.12, 3.11, 3.10 ``` {% endhint %} {% hint style="info" %} Please, ensure that the directory containing Python's executable files is included in your system's `PATH` environment variable. If you're using a venv, the necessary paths are automatically managed, so simply activate your venv before running the CLI. {% endhint %} {% hint style="info" %} If your Python installation is not supported by one of the pre-built binary wheels, `pip` will attempt to install Garaga from its source distribution. In that case, please make sure to have [Rust installed](https://www.rust-lang.org/tools/install) and available. {% endhint %} ## Install a specific version or from a specific commit / from source To install a specific version, use : ```bash pip install --force-reinstall garaga==1.1.0 ``` To install a version at specific commit, pick a commit hash from the [github history](https://github.com/keep-starknet-strange/garaga/commits/main/) and use : ```bash pip install git+https://github.com/keep-starknet-strange/garaga.git@COMMIT_HASH ``` {% hint style="warning" %} **Version Compatibility:** When installing from a specific commit, ensure all Garaga components match: - The `garaga` Cairo dependency in `Scarb.toml` should use the same version (e.g., `garaga = "1.1.0"` or the same git tag) - If using Rust/npm SDKs, use the same version for those as well See the [main documentation](../README.md#version-compatibility) for details on why version matching matters. {% endhint %} ## Installation troubleshooting You might have some dependencies issues on Linux or MacOs related to some packages that uses C code. Refer to the installations notes of Starknet.py [https://starknetpy.readthedocs.io/en/latest/installation.html](https://starknetpy.readthedocs.io/en/latest/installation.html) to fix those issues. ================================================ FILE: docs/gitbook/installation/rust-crate.md ================================================ --- icon: rust --- # Rust Crate To use the [`garaga_rs`](https://github.com/keep-starknet-strange/garaga/tree/main/tools/garaga_rs) crate in your project, add the following to your `Cargo.toml` ```toml [dependencies] garaga_rs = { git = "https://github.com/keep-starknet-strange/garaga.git"} ``` {% hint style="warning" %} **Version Compatibility:** Use the latest [release tag](https://github.com/keep-starknet-strange/garaga/releases) (e.g., `v1.1.0`) to match the declared [maintained smart contracts](../maintained-smart-contracts/ "mention") and ensure compatibility with the pip package that generated your verifiers. {% endhint %} ```toml [dependencies] garaga_rs = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0" } ``` ## Features The `garaga_rs` crate provides optional features for different use cases: - **No features (default)**: Pure Rust library without any bindings - **`python` feature**: Enables Python bindings via PyO3 (for use with maturin) - **`wasm` feature**: Enables WebAssembly bindings via wasm-bindgen (for use with wasm-pack) For example, if you're building a Python extension: ```toml [dependencies] garaga_rs = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0", features = ["python"] } ``` ================================================ FILE: docs/gitbook/maintained-smart-contracts/README.md ================================================ --- icon: file-lock --- # Maintained Smart Contracts We declare & maintain Smart Contracts for the community so they can be used as library calls. \ Those contracts: * Are _declared_ **both** Starknet Sepolia **and** Mainnet. * Those contracts are re-deployed at each release, so their code correspond to the release commit. * The source code is always available in the main garaga repository under `src/contracts` * The contracts are only declared and not deployed, their expected usage is through [library syscalls.](https://book.cairo-lang.org/ch15-03-executing-code-from-another-class.html#library-calls), so their usage is done through their class hashes and not their contract address (which don't exist unless you deploy them yourself) ### Class hashes for Garaga v1.1.0. | Contract | Class hash | Description | | -------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------- | | [Universal ECIP](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/universal_ecip) | 0x396d5915ecf475aab117bb25a0272b261e9e25ffe1c0ce05a51a3f77489c89e | A contract allowing to compute elliptic curve multi scalar multiplication for all supported curve identifiers | | [RiscZero Verifier](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/autogenerated/risc0_verifier_bn254) | 0x41d5e111b93acbf1afb531253e0bc64d43f90a8a99290361e851ec0c4968ab1 | A verifier for RiscZero Groth16-wrapped proofs. | | [Drand Quicknet Verifier](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/drand_quicknet) | 0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0 | A contract to verify Drand BLS signatures and store them on-chain for randomness and tlock decryption. | | [Drand Decrypt Quicknet](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/drand_decrypt_quicknet) | 0x68e2381aa99c02aabe2a0fec18d9fb7cde6138b588dc0bcf0135a26d8ae7e22 | A contract for on-chain tlock decryption using drand. Wraps the verifier via library call. | | [SP1 Groth16 Verifier](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/autogenerated/sp1_verifier_bn254) | 0x230d8612bd464979000193e4eaa73489da965a6593fb563dd2244e0b6e0443a | A verifier for SP1 Groth16-wrapped proofs. | {% hint style="warning" %} **Version Compatibility:** When generating calldata for these contracts, use the **same Garaga SDK version** as the release that declared the class hashes. For v1.1.0 contracts above, use `garaga==1.1.0` (pip), `garaga_rs` tag `v1.1.0`, or `garaga@1.1.0` (npm). The SDK generates hints that are specific to each contract version. Mismatched versions will cause verification to fail. {% endhint %} {% hint style="info" %} In case you need to obtain class hashes for different versions of Garaga or declare them yourself if they do not exist, you can checkout the Garaga repo at a particular commit and run `python .github/scripts/declare_maintained_contracts.py` or `python .github/scripts/verify_contracts.py`. At each release tag, the CI ensures all contracts are declared before publishing packages. {% endhint %} ================================================ FILE: docs/gitbook/maintained-smart-contracts/drand.md ================================================ --- icon: dice --- # Drand Garaga provides maintained contracts for the [drand](https://drand.love) distributed randomness beacon. These enable: - **On-chain signature verification** of drand rounds for verifiable randomness - **Time-lock encryption (tlock)**: encrypt data that can only be decrypted after a specific drand round is published ## What is drand? drand is a distributed randomness beacon that provides: - **Unpredictable randomness**: Values cannot be known before generation - **Unbiasable output**: No single party can influence results - **Public verifiability**: Anyone can verify the randomness is legitimate - **Regular intervals**: New randomness every 3 seconds (quicknet) ## What is tlock? Time-lock encryption (tlock) leverages drand's BLS threshold signatures to create an identity-based encryption (IBE) scheme where the "identity" is a future drand round number. A message encrypted for round `N` can only be decrypted once drand publishes the signature for round `N`. No single party can decrypt early. ### Use Cases | Application | How tlock helps | |---|---| | **Sealed-bid auctions** | Bids encrypted until auction close (a specific drand round) | | **Scheduled reveals** | Information released at a predetermined time | | **Fair launches** | Token distributions with time-locked claiming | | **Commit-reveal schemes** | Players commit encrypted moves, revealed together after a round | ## Contracts ### Drand Quicknet Verifier Verifies drand BLS signatures and stores them on-chain. | Network | Class Hash | |---------|------------| | **Mainnet** | `0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0` | | **Sepolia** | `0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0` | ```cairo #[starknet::interface] trait IDrandQuicknet { /// Verify a drand round BLS signature and store it on-chain. fn verify_round( ref self: TContractState, full_proof_with_hints: Span, ) -> Result; /// Look up the stored signature for a previously verified round. fn get_signature_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Look up the randomness (poseidon_hash(signature)) for a previously verified round. fn get_randomness_for_round( self: @TContractState, round_number: u64, ) -> Result; } ``` ### Drand Decrypt Quicknet Wraps the verifier to add on-chain tlock decryption. Deploy this contract yourself and point it at the verifier class hash. ```cairo #[starknet::interface] trait IDrandDecryptQuicknet { /// Verify a drand round BLS signature via library_call to the verifier class. fn verify_round( ref self: TContractState, full_proof_with_hints: Span, ) -> Result; /// Read the stored signature for a previously verified round. fn get_signature_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Get poseidon_hash(signature) for a previously verified round. fn get_randomness_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Decrypt a tlock ciphertext for a given round. /// If the round signature is not yet stored, a DrandHint must follow in the calldata. fn decrypt_cipher_text( ref self: TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } ``` {% hint style="info" %} The verifier contract is designed for **library calls** and does not need to be deployed. The decrypt contract wraps it and **must be deployed** since it stores signatures in its own storage. {% endhint %} ## Quicknet Configuration Both contracts are configured for drand's **quicknet** network: | Parameter | Value | |-----------|-------| | **Chain Hash** | `52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971` | | **Public Key** | G2 point on BLS12-381 (hardcoded in contract) | | **Period** | 3 seconds | | **Genesis** | 1692803367 (Aug 23, 2023) | --- ## Verifiable Randomness ### Fetching drand Randomness First, fetch randomness from drand's HTTP API: ```bash # Get the latest round curl https://api.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971/public/latest # Get a specific round curl https://api.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971/public/12345 ``` Response: ```json { "round": 12345, "randomness": "8b9c...", "signature": "a1b2..." } ``` ### Generating Verification Calldata Use the Garaga SDK to generate the `full_proof_with_hints` calldata from the drand response: {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_round_to_calldata, ) # Generate calldata for a specific round (fetches from drand API automatically) calldata = drand_round_to_calldata(round_number=12345) # Returns list[int] ready for on-chain verification # Use the Rust backend for better performance calldata = drand_round_to_calldata(round_number=12345, use_rust=True) ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import * as garaga from 'garaga'; await garaga.init(); // Fetch drand randomness and build calldata const drandData = await garaga.fetchDrandRandomness(12345); const calldata = garaga.getDrandCallData(drandData); ``` {% endtab %} {% endtabs %} ### On-Chain Verification with Library Call Use `library_call_syscall` to call the drand verifier contract: ```cairo use starknet::{SyscallResultTrait, syscalls}; use garaga::definitions::G1Point; const DRAND_QUICKNET_CLASS_HASH: felt252 = 0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0; fn verify_drand_round(full_proof_with_hints: Span) -> u64 { let mut call_data: Array = array![]; Serde::serialize(@full_proof_with_hints, ref call_data); let mut result = syscalls::library_call_syscall( DRAND_QUICKNET_CLASS_HASH.try_into().unwrap(), selector!("verify_round"), call_data.span(), ).unwrap_syscall(); let round: Result = Serde::deserialize(ref result).unwrap(); round.unwrap() } ``` --- ## Time-Lock Encryption (tlock) ### How It Works ``` ┌─────────────────────────────────────────────────────────────────┐ │ ENCRYPTION (off-chain) │ │ │ │ 1. Choose a future drand round number N │ │ 2. Encrypt 16-byte message using drand's public key + round N │ │ 3. Produces CipherText { U: G2Point, V: [u8;16], W: [u8;16] } │ │ 4. Store ciphertext on-chain or off-chain │ │ │ └──────────────────────────────┬──────────────────────────────────┘ │ time passes... │ ▼ ┌─────────────────────────────────────────────────────────────────┐ │ drand publishes round N signature │ └──────────────────────────────┬──────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────────────────┐ │ DECRYPTION (on-chain) │ │ │ │ 1. Verify the drand signature for round N (BLS pairing check) │ │ 2. Use signature to decrypt: e(signature, U) recovers key │ │ 3. XOR-decrypt to recover the original 16-byte message │ │ 4. Verify ciphertext integrity (U = r·G₂ check) │ │ │ └─────────────────────────────────────────────────────────────────┘ ``` {% hint style="info" %} **Message size**: tlock encrypts a 16-byte (128-bit) message. For larger payloads, encrypt a symmetric key with tlock and use it to encrypt the larger data off-chain. {% endhint %} ### Encrypting a Message (Off-Chain) Use the Garaga SDK to encrypt a message for a future drand round: {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_encrypt_to_calldata, ) # Encrypt a 16-byte message for a future round message = b"secret message!!" # exactly 16 bytes round_number = 100000 # a future drand round # Generate calldata containing the encrypted ciphertext calldata = drand_encrypt_to_calldata(round_number, message) # Use the Rust backend for better performance calldata = drand_encrypt_to_calldata(round_number, message, use_rust=True) ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import * as garaga from 'garaga'; await garaga.init(); // Prepare 16-byte message and randomness const message = new Uint8Array(16); message.set(new TextEncoder().encode('secret message!!')); const randomness = crypto.getRandomValues(new Uint8Array(16)); // Encrypt for a specific future round const calldata = garaga.encryptToDrandRoundAndGetCallData( 100000, // round number message, // 16-byte message randomness, // 16-byte randomness ); ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::drand_tlock_calldata::drand_tlock_encrypt_calldata_builder; use num_bigint::BigUint; let round_number = 100000u64; let message: [u8; 16] = *b"secret message!!"; let randomness: [u8; 16] = rand::random(); let values = vec![ BigUint::from(round_number), BigUint::from_bytes_be(&message), BigUint::from_bytes_be(&randomness), ]; let calldata = drand_tlock_encrypt_calldata_builder(&values).unwrap(); ``` {% endtab %} {% endtabs %} ### Decrypting On-Chain The `decrypt_cipher_text` function on the decrypt contract handles two scenarios: 1. **Round already verified**: If the drand signature for the round is already stored, only the ciphertext calldata is needed. 2. **Round not yet verified**: The ciphertext calldata is followed by the drand verification hint, and both verification and decryption happen in a single transaction. #### Scenario 1: Verify first, then decrypt ```python from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_round_to_calldata, drand_encrypt_to_calldata, ) # Step 1: Verify the round (stores the signature) verify_calldata = drand_round_to_calldata(round_number=12345) # Call contract.verify_round(verify_calldata) # Step 2: Decrypt (uses stored signature) decrypt_calldata = drand_encrypt_to_calldata(12345, message) # Call contract.decrypt_cipher_text(decrypt_calldata) ``` #### Scenario 2: Verify and decrypt in one transaction ```python # Combine encryption calldata + verification calldata encrypt_cd = drand_encrypt_to_calldata(round_number, message) verify_cd = drand_round_to_calldata(round_number) # Strip the length prefix from each, combine, and add new length prefix. # This works because decrypt_cipher_text deserializes the DrandDecryptHint # (round + ciphertext) first, then passes the remaining bytes to verify_round. combined_data = encrypt_cd[1:] + verify_cd[1:] combined_calldata = [len(combined_data)] + combined_data # Call contract.decrypt_cipher_text(combined_calldata) ``` ### Cairo: CipherText Struct The tlock ciphertext is defined in `garaga::apps::drand`: ```cairo use garaga::apps::drand::CipherText; use garaga::definitions::G2Point; /// The result of a timelock encryption over drand quicknet. struct CipherText { U: G2Point, // r·G₂ — the ephemeral public key V: [u8; 16], // sigma XOR H₂(r·e(H(round), pk)) W: [u8; 16], // message XOR H₄(sigma) } ``` ### Cairo: Direct Decryption in Your Contract If you want to call the `decrypt_at_round` function directly from the garaga library: ```cairo use garaga::apps::drand::{CipherText, decrypt_at_round}; use garaga::definitions::G1Point; fn my_decrypt(signature: G1Point, ciphertext: CipherText) -> [u8; 16] { // Performs: miller loop, final exponentiation, XOR decryption, and U = r·G₂ check decrypt_at_round(signature, ciphertext) } ``` {% hint style="warning" %} `decrypt_at_round` verifies ciphertext integrity (`U = r·G₂`) but does **not** verify that the provided signature is a valid drand BLS signature. You must verify the signature separately via `verify_round` or perform your own pairing check before calling this function. {% endhint %} --- ## Example: On-Chain Lottery ```cairo #[starknet::contract] mod Lottery { use starknet::ContractAddress; use starknet::storage::{ Map, StorageMapReadAccess, StorageMapWriteAccess, StoragePointerReadAccess, StoragePointerWriteAccess, }; use starknet::{SyscallResultTrait, syscalls}; const DRAND_QUICKNET_CLASS_HASH: felt252 = 0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0; #[storage] struct Storage { participants: Map, participant_count: u32, target_round: u64, is_open: bool, } #[external(v0)] fn enter_lottery(ref self: ContractState) { assert!(self.is_open.read(), "Lottery closed"); let count = self.participant_count.read(); self.participants.write(count, starknet::get_caller_address()); self.participant_count.write(count + 1); } #[external(v0)] fn draw_winner( ref self: ContractState, full_proof_with_hints: Span, ) -> ContractAddress { let mut call_data: Array = array![]; Serde::serialize(@full_proof_with_hints, ref call_data); let mut result = syscalls::library_call_syscall( DRAND_QUICKNET_CLASS_HASH.try_into().unwrap(), selector!("verify_round"), call_data.span(), ).unwrap_syscall(); let round_result: Result = Serde::deserialize(ref result).unwrap(); let verified_round = round_result.unwrap(); assert!(verified_round == self.target_round.read(), "Wrong round"); let count: u256 = self.participant_count.read().into(); // Retrieve randomness from the verified round let mut rand_call_data: Array = array![]; Serde::serialize(@verified_round, ref rand_call_data); let mut rand_result = syscalls::library_call_syscall( DRAND_QUICKNET_CLASS_HASH.try_into().unwrap(), selector!("get_randomness_for_round"), rand_call_data.span(), ).unwrap_syscall(); let randomness: Result = Serde::deserialize(ref rand_result).unwrap(); let winner_index: u32 = (randomness.unwrap().into() % count).try_into().unwrap(); self.participants.read(winner_index) } } ``` ## Example: Sealed-Bid Auction with tlock A sketch of how tlock enables sealed-bid auctions. Bids are encrypted for a future reveal round. Once drand publishes that round, bids can be decrypted on-chain. ``` 1. Auction opens — bidders encrypt their bids for reveal_round using tlock 2. Bidders submit a hash of their ciphertext on-chain (commitment) 3. Auction closes — no more bids accepted 4. drand publishes reveal_round signature 5. Anyone calls decrypt_cipher_text to reveal each bid on-chain 6. Contract determines the winner from the decrypted bids ``` The ciphertext itself (a `G2Point` + 32 bytes) can be stored off-chain (e.g., IPFS) with only a commitment hash on-chain, or submitted directly in the decryption transaction. ## Helper Functions The `garaga::apps::drand` module provides utilities for working with drand rounds: ```cairo use garaga::apps::drand::{timestamp_to_round, round_to_timestamp}; // Convert a Unix timestamp to a drand round number let round = timestamp_to_round(1692803370); // returns 2 // Convert a drand round number to a Unix timestamp let timestamp = round_to_timestamp(2); // returns 1692803370 ``` ## Security Considerations - **Round timing**: Ensure you're using the correct round for your application's timing requirements. Use `timestamp_to_round` to map wall-clock time to drand rounds. - **Message size**: tlock encrypts exactly 16 bytes. Use it to encrypt a symmetric key for larger payloads. - **Ciphertext integrity**: The `decrypt_at_round` function verifies `U = r·G₂` to ensure the ciphertext was formed correctly. Tampered ciphertexts will be rejected. - **Finality**: Once a drand round is published, the signature is permanent. The ciphertext becomes decryptable by anyone with the round signature. - **Fallback**: Consider implementing fallback mechanisms if drand becomes unavailable. ## Resources - [drand Website](https://drand.love) - [drand API Documentation](https://drand.love/developer/http-api/) - [Quicknet Information](https://drand.love/blog/2023/07/03/quicknet-is-live/) - [tlock Paper](https://eprint.iacr.org/2023/189) — "tlock: Practical Timelock Encryption from Threshold BLS" - [Verifier Source Code](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/drand_quicknet) - [Decrypt Contract Source Code](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/drand_decrypt_quicknet) ================================================ FILE: docs/gitbook/maintained-smart-contracts/risczero.md ================================================ --- icon: microchip --- # RiscZero RiscZero is a Zero-Knowledge Proof system designed to enable efficient and scalable construction of computational proofs based on the RISC-V architecture. It is Groth16-based and works over the BN254 elliptic curve. Garaga provides the tools and makes it possible to verify such proofs on-chain in a Starknet/Cairo smart contract. A Zero-Knowledge proof is a mathematical construct that guarantees that a given value is the output of a predefined computation where some of the inputs are private and must not be disclosed. This is achieved in two steps: 1- A Prover performs the computation and constructs the proof artifact. The proof artifact contains the computational journal which is, in simple terms, the list of public inputs and the output value. The proof artifact attests the integrity of the computation, which means the prover ran the computation properly and the output value registered in the journal corresponds to the result of such computation given the public inputs, also registered in the jornal, an some undisclosed private inputs. Here the Prover is a RiscZero user-defined program that implements the desired computation and is augmented to produce the desired proof artifact. 2- Given the proof artifact, a Verifier must check its integrity before processing the output as valid. Here the Verifier is a Starknet smart contract written in Cairo and Garaga acts as a library to which the verification is delegated to. ### Setting up the development environment Before starting development we need to install all the software prerequisites for building either or both the Prover and Verifier components. Below we provide general installation instructions for a Linux-based system. Depending on your setup you may already have some of the software installed, in which case you can skip the associated sections. But if you need additional help for a specific set up, please follow the links provided.\ \ In order to implement the Prover one needs to install the tooling required by RiscZero: 1. Install Rust/Cargo using [`rustup`](https://rustup.rs/) (default version 1.8.3) ```bash curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y export PATH="$HOME/.cargo/bin:$PATH" ``` 2. Install the RiscZero tool-chain using [`rzup`](https://dev.risczero.com/api/zkvm/install) (default version 1.2.0) ```bash curl -L https://risczero.com/install | bash export PATH="$HOME/.risc0/bin:$PATH" rzup install ``` _Important: Make sure the RiscZero version installed matches the version supported by Garaga. For RiscZero v2.2.2 use Garaga 1.1.0. Check [constants.json](https://github.com/keep-starknet-strange/garaga/blob/main/tools/make/constants.json) for the latest supported versions._ 3. Install RiscZero additional/custom dependencies A C compiler, such as `gcc`, `pkg-config` and OpenSSL development libraries (`libssl-dev)` are necessary to build a RiscZero project. You should refer to your system documentation on how to install those. Here is a quick reference for Debian compatible systems ```bash sudo apt install -y gcc libssl-dev pkg-config ``` Optionally, if you intend to have the Prover generate the contract call data explicitly, Garaga requires that Python is available in your environment. If necessary, check their [documentation](https://docs.python.org/3/using/index.html) for installation instructions for your system. Again, here is a quick reference for Debian compatible systems ```bash sudo apt install -y python3 ``` In order to implement the Verifier one needs to install the tooling for Cairo development and Garaga: 4. Install the Starknet/Cairo bundler tool [`scarb`](https://docs.swmansion.com/scarb/download#install-via-installation-script) (default version 2.16.1) ```bash curl --proto '=https' --tlsv1.2 -sSf https://docs.swmansion.com/scarb/install.sh | bash export PATH="$HOME/.local/bin:$PATH" ``` 5. Install Starknet Foundry using [`snfoundryup`](https://foundry-rs.github.io/starknet-foundry/getting-started/installation.html) (default version 0.57.0) ```bash curl -L https://raw.githubusercontent.com/foundry-rs/starknet-foundry/master/scripts/install.sh | bash export PATH="$HOME/.local/bin:$PATH" snfoundryup ``` ### Create or configure the RiscZero project 1. If you are setting up a new RiscZero project, run the command below, it will create a new project folder and define the Guest program name. The Guest program is the program that is compiled to and will run in the RiscZero VM. The project setup also creates a Host program that runs outside the RiscZero VM and interacts with the Guest, providing inputs and collecting outputs, to produce the ZK proof. Here we set up a sample project called `fibonacci_prover` with a Guest called `fibonacci_guest` (for reference, the complete RiscZero app presented here is available in [Garaga's GitHub repository](https://github.com/keep-starknet-strange/garaga/tree/main/src/contracts/risc0_sample_app)) ``` cargo risczero new fibonacci_prover --guest-name fibonacci_guest ``` If you already have a RiscZero project set up, make sure the RiscZero version configured as dependencies is consistent with the RiscZero toolchain installed in the previous steps. 2. Next we need to modify the RiscZero Host program to output the proof artifact in the desired JSON format. Add the following dependencies to `host/Cargo.toml` ```toml [dependencies] risc0-ethereum-contracts = { version = "1.2.0" } hex = "0.4" ... ``` Optionally, if you intend to explicitly generate and handle the call-data, also add the following dependency to `host/Cargo.toml`. Make sure to use a Garaga version tag that is consistent with your setup. 
[dependencies]
garaga_rs = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0" }
...
Then we modify the Host program `host/src/main.rs` to generate the JSON file containing the proof artifact. We start by adding the required imports ```rust use risc0_zkvm::{ compute_image_id, default_prover, ExecutorEnv, ProverOpts, VerifierContext }; use risc0_ethereum_contracts::encode_seal; ``` Optionally, if you intend to generate the call-data explicitly, add the following imports ```rust use garaga_rs::definitions::CurveID; use garaga_rs::calldata::full_proof_with_hints::groth16::{ get_groth16_calldata, Groth16Proof }; use garaga_rs::calldata::full_proof_with_hints::groth16::risc0_utils::get_risc0_vk; ``` Next we need to modify the Host main function. If you are starting a fresh RiscZero project, you will need to setup the environment for the computation. This is basically the set of inputs that will be used by the Guest program to perform the computation. Below is an example for the `fibonacci_prover`. In this example, we want to compute the number at position `n` of the Fibonacci sequence. However we do not want to reveal `n`, but instead show that `n` lies in a given interval defined by a lower bound `l` and an upper bound `u`. ```rust let l: u32 = 3; // public lower bound for n let u: u32 = 8; // public upper bound for n let n: u32 = 6; // private n for which we will compute fibonacci(n) let env = ExecutorEnv::builder() .write(&l) .unwrap() .write(&u) .unwrap() .write(&n) .unwrap() .build() .unwrap(); ``` _As a note, the sample app provided here exists only to demonstrate how to setup a ZK project using Garaga/RiscZero. It is clear that datatype `u32` is not appropriate datatype to host a secret Fibonacci number as it can be easily discovered by brute force checking all possibilities between the bounds._ Next we modify the default Prover setup to explicitly use Groth16 ```rust let prove_info = prover .prove_with_ctx( env, &VerifierContext::default(), FIBONACCI_GUEST_ELF, &ProverOpts::groth16() ) .unwrap(); ``` Finally, as the last step of the Host program, we extract and print the proof artifact JSON to the standard output 
let receipt = prove_info.receipt;
let seal = to_bytes(encode_seal(&receipt).unwrap());
let image_id = to_bytes(compute_image_id(&FIBONACCI_GUEST_ELF).unwrap());
let journal = to_bytes(receipt.journal);
println!(
    "{{\"seal\": \"0x{}\", \"image_id\": \"0x{}\", \"journal\": \"0x{}\"}}",
    hex::encode(&seal),
    hex::encode(&image_id),
    hex::encode(&journal)
);

// helper function to convert objects to array of bytes
fn to_bytes<T: AsRef<[u8]>>(obj: T) -> Vec<u8> {
    obj.as_ref().to_vec()
}
Optionally, if you also intend to handle the call-data explicitly, it can be computed and output as a JSON as well. This produces a large array that encodes the full RiscZero proof wih hints ```rust let proof = Groth16Proof::from_risc0(seal, image_id, journal); let calldata = get_groth16_calldata(&proof, &get_risc0_vk(), CurveID::BN254).unwrap(); println!("[{}]", calldata.iter().skip(1).map(|v| format!("\"{}\"", v)).collect::>().join(", ")); ``` Now we need to set up the Guest program that performs the computation required by our use case. If you started a fresh RiscZero project, then you will need to write the Guest program that performs the computation. It is done by modifying the main function of the Guest source file at `methods/guest/src/main.rs` In our example, here is what the Guest code looks like for the `fibonacci_guest` ```rust // reads the public bounds and private n provided by the Host let l: u32 = env::read(); let u: u32 = env::read(); let n: u32 = env::read(); // sanity check for the bounds assert!(l <= n && n < u); // performs the computation let fib_n: u32 = fibonacci(n); fn fibonacci(n: u32) -> u32 { let mut a = 0; let mut b = 1; for _ in 0..n { (a, b) = (b, a + b); } a } // writes the public inputs and output to the journal env::commit(&l); env::commit(&u); env::commit(&fib_n); ``` ### RiscZero Proof Generation RiscZero provides some options when it comes to proof generation. Please refer to their [documentation](https://dev.risczero.com/api/generating-proofs/proving-options) in case you need to in depth information on that. The easiest and most convenient way is to use the provided [Bonsai](https://www.bonsai.xyz/) service, which works fine for many purposes. In that case, an API key for the service is required. _It is important to note that, if your computation has private inputs, you should definitely protect them from being exposed to external services like Bonsai by performing the proof generation locally._ Here is the command to run the Prover via Bonsai ``` BONSAI_API_KEY= BONSAI_API_URL= RISC0_DEV_MODE=0 \ cargo run --release ``` ### Developing the RiscZero Verifier smart contract There are different ways one can choose to develop a Cairo smart contract, we recommend using Staknet Foundry. A fresh new project can be created by issuing the following command ```bash snforge new fibonacci_sequencer ``` This will output a template for a smart contract along with the necessary tooling configuration to build and test it. In this case we are creating a contract called `fibonacci_sequencer`, that will process and update its state with a new number in the Fibonacci sequence that is guaranteed to have an index `n` in the sequence that is higher than the last one currently registered by the contract, although that exact index `n` is never revealed publicly. Garaga already provides a smart contract to verify RiscZero proofs. To make use of that functionality, one just has to call a predefined library function from the client smart contract. In order to do that, one needs to declare the interface of the RiscZero verifying library function in `src/lib.cairo`: ```rust #[starknet::interface] trait IRisc0Groth16VerifierBN254 { fn verify_groth16_proof_bn254( self: @TContractState, full_proof_with_hints: Span, ) -> Option>; } ``` The `verify_groth16_proof_bn254` function takes the call data that encodes the proof with hints as a list of integers of type `felt252` and returns the journal (as a list of bytes) on proof verification success, or nothing if the verification fails. Here is how to verify the RiscZero proof and update the smart contract state for our Fibonacci sequencer example: ```rust fn verify_and_submit_fibonacci_number(ref self: ContractState, full_proof_with_hints: Span) { // sets the class hash for the RiscZero verifier already declared on-chain // by the Garaga team let class_hash: ClassHash = RISC_ZERO_VERIFIER_CLASS_HASH.try_into().unwrap(); // instantiate a library dispatcher to perform the library call // to the RiscZero verifier class, given that verifying a proof is // a read-only operation let dispatcher = IRisc0Groth16VerifierBN254LibraryDispatcher { class_hash }; // calls the RiscZero verifier passing along the proof artifact and // checks whether the proof is valid or not, aborting the transaction if not let optional_journal = dispatcher.verify_groth16_proof_bn254(full_proof_with_hints); assert(optional_journal != Option::None, 'Invalid proof'); // parses the public inputs and output from the journal let mut journal = optional_journal.unwrap(); let l = pop_front_u32_le(ref journal); let u = pop_front_u32_le(ref journal); let fib_n = pop_front_u32_le(ref journal); // performs the necessary state update check, updates the state, // and emits an event with the new fibnoacci number submitted // the smart contract invariant guarantees that every fiboacci number // accepted comes later in the fibonacci sequence without revealing // its index, which is trivial for monotonic sequences like fibnacci, // but would also work as expected also for non-monotonic ones let b = self.lower_bound.read(); assert(l >= b, 'Invalid lower bound'); self.lower_bound.write(u); self.emit(FibonnacciNumberSubmitted { n: fib_n }); self.emit(LowerBoundUpdated { n: u }); } ``` Along with the `verify_and_submit_fibonacci_number` contract method, we need to define the RiscZero Verifier class hash, which can be obtained [here](./) ```rust use core::starknet::ClassHash; pub const RISC_ZERO_VERIFIER_CLASS_HASH: felt252 = 0x41d5e111b93acbf1afb531253e0bc64d43f90a8a99290361e851ec0c4968ab1; ``` The contract state which stores the current lower bound which gets updated whenever a new Fibonacci number is submitted ```rust #[storage] struct Storage { lower_bound: u32, } ``` And also the helper function used to decode the journal values ```rust fn pop_front_u32_le(ref bytes: Span) -> u32 { let [b0, b1, b2, b3] = (*bytes.multi_pop_front::<4>().unwrap()).unbox(); let b0: u32 = b0.into(); let b1: u32 = b1.into(); let b2: u32 = b2.into(); let b3: u32 = b3.into(); b0 + 256 * (b1 + 256 * (b2 + 256 * b3)) } ``` For completeness, we also provide the definition of the events emitted by the operation ```rust #[event] #[derive(Drop, starknet::Event)] enum Event { FibonnacciNumberSubmitted: FibonnacciNumberSubmitted, LowerBoundUpdated: LowerBoundUpdated, } #[derive(Drop, starknet::Event)] struct FibonnacciNumberSubmitted { #[key] n: u32, } #[derive(Drop, starknet::Event)] struct LowerBoundUpdated { #[key] n: u32, } ``` It is important to note that the `verify_and_submit_fibonacci_number` function defined in this sample contract has a signature that takes a single argument: the proof artifact. This is useful because we can then submit the transaction to the blockchain directly, simply using the Garaga CLI passing along the JSON file output by the RiscZero Host program. This avoids the need to encode the proof as a customized call data. It also spares us from dealing with the transaction submission details which is handled internally by the Garaga CLI. This is an approach that makes sense when all the information required to validate and update the smart contract state can be extracted from the journal, exempting us from the need of passing additional parameters to the function which would deem it incompatible with the interface expected by the CLI. The CLI also requires the contract method processing the proof (referred to as endpoint) to have the word `verify` as part of it. Once the Cairo smart contract is ready, it can be deployed in three steps: * Declare ```bash sncast --profile declare --contract-name ``` This will declare the smart contract class and return its hash. * Deploy ```bash sncast --profile deploy --class-hash ``` This will deploy the smart contract instance and return its address. * Verify (Optional) ```bash sncast --profile verify \ --network \ --contract-name \ --contract-address ``` This will match the deployed code with the smart contract source code and make it available on Starknet block explorers. Before running any of the commands above, one has to configure foundry to add the desired profile name. That is achieved by editing the `snfoundry.toml` file. Here is a sample configuration as reference ```toml [sncast.sepolia] account = "deployer" accounts-file = "./accounts.json" url = "https://starknet-sepolia.public.blastapi.io/rpc/v0_7" ``` This requires an `accounts.json` file. One such a way to generate it is using the following command ```bash sncast account import \ --name deployer \ --type \ --address \ --private-key ``` One can setup an [ArgentX](https://www.argent.xyz/) or [Braavos](https://braavos.app/) wallet, fund it, and export its private key. ### Submitting the proof to the blockchain using the Garaga CLI Once the smart contract is published on the blockchain network, users can interact with it. In our case, one such interaction would be to perform a computation off-chain with RiscZero and submit it to the smart contract. As mentioned before, the JSON proof artifact generated by the RiscZero execution can be submitted to the blockchain using Garaga CLI: ```bash garaga verify-onchain \ --system risc0_groth16 \ --network \ --contract-address \ --endpoint \ --proof ``` In order to run the Garaga `verify-onchain` command you will need to provide a .`secrets` file in the current folder, or elsewhere using the `--env-file` option. Here is the format for the `.secrets` file ``` SEPOLIA_RPC_URL="https://starknet-sepolia.public.blastapi.io/rpc/v0_7" SEPOLIA_ACCOUNT_PRIVATE_KEY= SEPOLIA_ACCOUNT_ADDRESS= MAINNET_RPC_URL="https://starknet-mainnet.public.blastapi.io/rpc/v0_7" MAINNET_ACCOUNT_PRIVATE_KEY= MAINNET_ACCOUNT_ADDRESS= ``` Please make sure to provide RPC endpoints that supports version 0.7 of the Starknet JSON API ================================================ FILE: docs/gitbook/maintained-smart-contracts/sp1.md ================================================ --- icon: microchip --- # SP1 To use the SP1 Groth16 verifier on Starknet, you can follow code snippets from the [SP1 documentation](https://docs.succinct.xyz/docs/sp1/introduction) to generate a proof.\ \ The version of SP1 expected by Garaga is defined in the file [constants.json](https://github.com/keep-starknet-strange/garaga/blob/main/tools/make/constants.json) .\ \ A template modeled after [Succinct's official one](https://github.com/succinctlabs/sp1-project-template/) for solidity and EVM is available in [this repository](https://github.com/feltroidprime/SP1-starknet-garaga-template/)\ Please follow the instructions there to get you started. ================================================ FILE: docs/gitbook/security.md ================================================ --- icon: shield-check --- # Security Garaga is designed with security as a primary concern. This page documents our security practices, audit history, and important considerations for users. --- ## Audit Status ### ✅ Audited by CryptoExperts Garaga has undergone a comprehensive security audit: | Audit | Auditor | Date | Report | |-------|---------|------|--------| | **Garaga v1.1.0** | [CryptoExperts](https://www.cryptoexperts.com/) | June 27, 2025 | [View Report (PDF)](https://github.com/keep-starknet-strange/garaga/blob/main/docs/Garaga-audit-report-v2.pdf) | {% hint style="success" %} The audit covered core cryptographic operations including pairing checks, multi-scalar multiplication, and the Groth16 verifier implementation. {% endhint %} --- ## Security Considerations ### Signature Verification {% hint style="warning" %} **Hash Computation Responsibility** The functions `is_valid_ecdsa_signature_assuming_hash` and `is_valid_schnorr_signature_assuming_hash` verify signature equations but **do not hash the message**. The caller is responsible for: 1. Correctly computing the message hash 2. Using the appropriate hash function for the signature scheme 3. Ensuring the hash is computed over the correct message **Incorrect hash computation will result in invalid signatures being accepted or valid signatures being rejected.** {% endhint %} ### EdDSA (Ed25519) Specific The EdDSA implementation includes protections against common attacks: - ✅ **Small-order point rejection**: Explicitly rejects points in small subgroups - ✅ **Cofactor handling**: Properly handles the Ed25519 cofactor - ✅ **Canonical encoding**: Enforces canonical point encoding ### Curve Selection When using Garaga's curve-agnostic APIs, ensure you: 1. Use the correct `curve_id` for your application 2. Understand the security properties of your chosen curve 3. Use appropriate key sizes and parameters | Curve | Security Level | Notes | |-------|----------------|-------| | BN254 | ~100 bits | Widely used in Ethereum ecosystem | | BLS12-381 | ~128 bits | Recommended for new applications | | SECP256K1 | ~128 bits | Bitcoin/Ethereum compatibility | | SECP256R1 | ~128 bits | WebAuthn/TLS compatibility | | ED25519 | ~128 bits | High performance EdDSA | --- ## Responsible Disclosure If you discover a security vulnerability in Garaga: 1. **Do NOT** open a public GitHub issue 2. **DO** email the maintainers privately 3. **DO** provide detailed information about the vulnerability 4. **DO** allow reasonable time for a fix before public disclosure See our [Security Policy](https://github.com/keep-starknet-strange/garaga/blob/main/docs/SECURITY.md) for contact information. --- ## Cryptographic References Garaga's implementations are based on peer-reviewed cryptographic research. We recommend understanding these papers if you're building security-critical applications: ### Zero-Knowledge Proofs | Paper | Authors | Reference | |-------|---------|-----------| | **Groth16** | Jens Groth | "On the Size of Pairing-Based Non-interactive Arguments" EUROCRYPT 2016. [ePrint 2016/260](https://eprint.iacr.org/2016/260) | | **PLONK** | Gabizon, Williamson, Ciobotaru | "PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge" [ePrint 2019/953](https://eprint.iacr.org/2019/953) | ### Elliptic Curves & Pairings | Paper | Authors | Reference | |-------|---------|-----------| | **Efficient Pairings** | Youssef El Housni | "Pairings in Rank-1 Constraint Systems" [ePrint 2022/1162](https://eprint.iacr.org/2022/1162) | | **ECIP** | Liam Eagen | "Zero Knowledge Proofs of Elliptic Curve Inner Products from Principal Divisors and Weil Reciprocity" [ePrint 2022/596](https://eprint.iacr.org/2022/596) | | **On Proving Pairings** | Novakovic & Eagen | [ePrint 2024/640](https://eprint.iacr.org/2024/640) | | **Fast EC Scalar Multiplications** | Eagen, El Housni, Masson, Piellard | [ePrint 2025/933](https://eprint.iacr.org/2025/933) | | **Pairing for Beginners** | Craig Costello | [PDF](https://static1.squarespace.com/static/5fdbb09f31d71c1227082339/t/5ff394720493bd28278889c6/1609798774687/PairingsForBeginners.pdf) | ### Signatures | Paper | Authors | Reference | |-------|---------|-----------| | **EdDSA** | Bernstein et al. | "High-speed high-security signatures" [ed25519.cr.yp.to](https://ed25519.cr.yp.to/) | | **Taming EdDSAs** | Chalkias, Garillot, Nikolaenko | "Taming the Many EdDSAs" SSR 2020. [ACM DL](https://dl.acm.org/doi/abs/10.1007/978-3-030-64357-7_4) | | **BIP340** | Wuille, Nick, Towns | "Schnorr Signatures for secp256k1" [BIP340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki) | ### Randomness | Paper | Authors | Reference | |-------|---------|-----------| | **drand** | Syta et al. | "Scalable Bias-Resistant Distributed Randomness" IEEE S&P 2017 | | **Time-Lock Encryption** | Gailly, Melissaris, Romailler | "tlock: Practical Timelock Encryption from Threshold BLS" [ePrint 2023/189](https://eprint.iacr.org/2023/189) | --- ## Disclaimer {% hint style="danger" %} **USE AT YOUR OWN RISK** Garaga is provided "as is" without any warranty. While we strive for correctness and security: - 100% security cannot be assured - Cryptographic software is inherently complex - Always perform your own security review for production use - Consider additional audits for high-value applications See the [MIT License](https://github.com/keep-starknet-strange/garaga/blob/main/LICENSE) for full terms. {% endhint %} --- ## Security Checklist Before deploying to production: - [ ] Understand the cryptographic assumptions - [ ] Test thoroughly on testnet first - [ ] Use the latest stable release - [ ] Monitor for security advisories - [ ] Consider additional application-level audits ================================================ FILE: docs/gitbook/smart-contract-generators/README.md ================================================ --- icon: monero --- # Deploy your own SNARK verifier on Starknet Supported verifiers: * [groth16](groth16/ "mention") * [noir.md](noir.md "mention") ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/README.md ================================================ --- icon: bat --- # Groth16 ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/generate-and-deploy-your-verifier-contract.md ================================================ --- icon: file-lock --- # Generate and deploy your verifier contract ## Prepare your Groth16 verifying key {% hint style="info" %} Pairing operations over BLS12-381 are cheaper than BN254 on Garaga, so if possible, prefer using BLS12-381. The security of this curve is also much closer to 128 bits than BN254. {% endhint %} \ To deploy a groth16 verifier, you need the associated verifying key in `.json` format. Both BN254 and BLS12-381 are supported. [Snarkjs](https://github.com/iden3/snarkjs?tab=readme-ov-file#22-export-the-verification-key) and [Gnark](https://docs.gnark.consensys.io/HowTo/serialize) jsons output are supported out of the box. You can find a bunch of example of verifying keys that will work directly in the [`hydra/garaga/starknet/groth16_contract_generator/examples`](https://github.com/keep-starknet-strange/garaga/tree/main/hydra/garaga/starknet/groth16\_contract\_generator/examples) folder. While Snarkjs jsons export are easy and working well, the gnark documentation is a bit outdated. Below we show a quick example on how to export the verifying key from your Gnark circuit .
Gnark export to json example ```go package main import ( "encoding/json" "os" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark/backend/groth16" "github.com/consensys/gnark/frontend" "github.com/consensys/gnark/frontend/cs/r1cs" ) // CubicCircuit defines a simple circuit // x**3 + x + 5 == y type CubicCircuit struct { // struct tags on a variable is optional // default uses variable name and secret visibility. X frontend.Variable `gnark:"x"` Y frontend.Variable `gnark:",public"` B frontend.Variable A frontend.Variable `gnark:",public"` } // Define declares the circuit constraints // x**3 + x + 5 == y func (circuit *CubicCircuit) Define(api frontend.API) error { x3 := api.Mul(circuit.X, circuit.X, circuit.X) api.AssertIsEqual(circuit.Y, api.Add(x3, circuit.X, 5)) api.AssertIsEqual(circuit.B, circuit.A) return nil } func main() { // compiles our circuit into a R1CS var circuit CubicCircuit ccs, _ := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, &circuit) // groth16 zkSNARK: Setup pk, vk, _ := groth16.Setup(ccs) // witness definition assignment := CubicCircuit{X: 3, Y: 35, A: 3, B: 3} witness, _ := frontend.NewWitness(&assignment, ecc.BN254.ScalarField()) publicWitness, _ := witness.Public() // groth16: Prove & Verify proof, _ := groth16.Prove(ccs, pk, witness) groth16.Verify(proof, vk, publicWitness) vk.ExportSolidity(os.Stdout) // Export to JSON: schema, _ := frontend.NewSchema(&circuit) pubWitnessJSON, _ := publicWitness.ToJSON(schema) SaveToJSON("gnark_vk_bn254.json", vk) SaveToJSON("gnark_proof_bn254.json", proof) os.WriteFile("gnark_public_bn254.json", pubWitnessJSON, 0644) } func SaveToJSON(filePath string, v interface{}) error { jsonData, err := json.MarshalIndent(v, "", " ") if err != nil { return err } err = os.WriteFile(filePath, jsonData, 0644) if err != nil { return err } return nil } ```
## Generate the Smart contract code \ Using the [developer-setup-and-guides](../../developer-setup-and-guides/ "mention") or the [python-package.md](../../installation/python-package.md "mention"), you should now have access to the Garaga CLI from your terminal, using the command `garaga` ```bash garaga ``` Once your verifying key is ready, you can use the following command : ``` garaga gen --system groth16 --vk vk.json ``` You should see an output like this : ```bash (venv) :~/garaga-flow garaga gen --system groth16 --vk vk_bls.json Please enter the name of your project. Press enter for default name. [my_project]: Detected curve: CurveID.BLS12_381 ⠧ Generating Smart Contract project for ProofSystem.Groth16 using vk_bls.json... Done! Smart Contract project created: /home/garaga-flow/my_project/ ├── Scarb.lock ├── Scarb.toml ├── src/ │ ├── groth16_verifier.cairo │ ├── groth16_verifier_constants.cairo │ └── lib.cairo └── target/ └── dev/ ├── groth16_example_bls12_381.starknet_artifacts.json ├── groth16_example_bls12_381_Groth16VerifierBLS12_381.compiled_contract │ _class.json └── groth16_example_bls12_381_Groth16VerifierBLS12_381.contract_class.js on You can now modify the groth16_verifier.cairo file to adapt the verifier to your use case. ``` The curve identifier is automatically detected from the content of your verifying key. ## Build your contract {% hint style="info" %} The generated verifier contract only verifies a proof and returns the public inputs on success. You can extend it to add your dapp logic, or use it as a library call from another contract. {% endhint %} The generated template is as follows. The main endpoint is `verify_groth16_proof_[curve_name]`. The function takes a single `full_proof_with_hints: Span` parameter (generated using the `garaga calldata` command or the SDK) and returns: - `Result::Ok(public_inputs)` if the proof is valid - `Result::Err(error)` if the proof is invalid {% code title="groth16_verifier.cairo" %} ```rust // Generated by Garaga version 1.1.0 use super::groth16_verifier_constants::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; #[starknet::interface] pub trait IGroth16VerifierBLS12_381 { fn verify_groth16_proof_bls12_381( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod Groth16VerifierBLS12_381 { use garaga::definitions::{G1G2Pair, G1Point}; use garaga::ec_ops::{G1PointTrait, ec_safe_add}; use garaga::groth16::{ Groth16ProofRawTrait, multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result, }; use garaga::utils::calldata::deserialize_full_proof_with_hints_bls12_381; use starknet::SyscallResultTrait; use super::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; const ECIP_OPS_CLASS_HASH: felt252 = 0x312d1dd5f967eaf6f86965e3fa7acbc9d0fbd979066a17721dd913736af2f5e; #[storage] struct Storage {} #[abi(embed_v0)] impl IGroth16VerifierBLS12_381 of super::IGroth16VerifierBLS12_381 { fn verify_groth16_proof_bls12_381( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let fph = deserialize_full_proof_with_hints_bls12_381(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.raw.check_proof_points(1); let ic = ic.span(); let vk_x: G1Point = match ic.len() { 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => { // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); Serde::serialize(@groth16_proof.public_inputs, ref msm_calldata); // Complete with the curve indentifier (1 for BLS12_381): msm_calldata.append(1); // Add the hint array. for x in msm_hint { msm_calldata.append(*x); } // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span(), ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), 1, ) }, }; // Perform the pairing check. let check = multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: vk.gamma_g2 }, G1G2Pair { p: groth16_proof.raw.c, q: vk.delta_g2 }, G1G2Pair { p: groth16_proof.raw.a.negate(1), q: groth16_proof.raw.b }, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(groth16_proof.public_inputs), Result::Err(error) => Result::Err(error), } } } } ``` {% endcode %} ## Declare and deploy your contract When you are satisfied with your contract it's time to send it to Starknet! The CLI provides utilities to simplify the process. Otherwise, it is a similar process than for every other contracts, please refer to [Starknet documentation](https://docs.starknet.io/quick-start/declare-a-smart-contract/).\ \ You will to create a file containing the following variables, depending on if you want to declare & deploy on Starknet Sepolia or Starknet Mainnet. \ Create the following file and update its content. {% code title=".secrets" %} ``` SEPOLIA_RPC_URL="https://free-rpc.nethermind.io/sepolia-juno" SEPOLIA_ACCOUNT_PRIVATE_KEY=0x1 SEPOLIA_ACCOUNT_ADDRESS=0x2 MAINNET_RPC_URL="https://" MAINNET_ACCOUNT_PRIVATE_KEY=0x3 MAINNET_ACCOUNT_ADDRESS=0x4 ``` {% endcode %} Then, you can run the command `garaga declare`, which will build the contract and declare it to Starknet. If the class hash is already deployed, it will return it as well. Declaring the contract involves sending all its bytecode and it is quite an expensive operation. Make sure you dapp is properly tested before! ```bash Usage: garaga declare [OPTIONS] Declare your smart contract to Starknet. Obtain its class hash and a explorer link. ╭─ Options ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮ │ --project-path DIRECTORY Path to the Cairo project holding the Scarb.toml file to declare │ │ [default: /home/felt/garaga-flow/my_project/] │ │ --env-file FILE Path to the environment file │ │ [default: /home/felt/garaga-flow/my_project/.secrets] │ │ --network [sepolia|mainnet] Starknet network [default: sepolia] │ │ --fee TEXT Fee token type [eth, strk] [default: eth] │ │ --help -h Show this message and exit. │ ╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯ ``` ```bash garaga declare --project-path my_project/ --env-file .secrets --network sepolia --fee strk ``` This command will return the class hash, used in the next step.\ \ Finally, to deploy the contract, a use `garaga deploy` : ```bash Usage: garaga deploy [OPTIONS] Deploy an instance of a smart contract class hash to Starknet. Obtain its address, the available endpoints and a explorer link. ╭─ Options ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮ │ * --class-hash TEXT Contract class hash to deploy. Can be decimal or hex string [default: None] [required] │ │ --env-file FILE Path to the environment file containing rpc, address, private_key │ │ [default: /home/felt/garaga-flow/my_project/.secrets] │ │ --network [sepolia|mainnet] Starknet network [default: sepolia] │ │ --fee TEXT Fee token type [eth, strk] [default: strk] │ │ --help -h Show this message and exit. │ ╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯ ``` The contract address will be prompted. Be sure to save it! \ ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/README.md ================================================ --- icon: microchip --- # Generating calldata from a proof and using your deployed contract {% hint style="warning" %} **Version Compatibility:** Use the same Garaga SDK version (pip/npm/Rust) that generated your verifier contract. Mismatched versions produce incompatible calldata and cause verification to fail. {% endhint %} Once your groth16 contract is deployed and you have its address, you will need to call its main endpoint `verify_groth16_proof_bn254`, or `verify_groth16_proof_bls12_381`. \ \ The Groth16 proof needs pre-processing and extra computation to allow efficient verification. \ \ The Garaga CLI takes care of converting your proof to the correct calldata and calling your contract.\ To do this, use the garaga `verify-onchain` command. ```bash Usage: garaga verify-onchain [OPTIONS] Invoke a SNARK verifier on Starknet given a contract address, a proof and a verification key. ╭─ Options ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╮ │ * --system [groth16] Proof system [default: None] [required] │ │ * --contract-address TEXT Starknet contract address [default: None] [required] │ │ * --vk FILE Path to the verification key JSON file [default: None] [required] │ │ * --proof FILE Path to the proof JSON file [default: None] [required] │ │ --public-inputs FILE Path to the public inputs JSON file [default: None] │ │ --endpoint TEXT Smart contract function name. If not provided, the default │ │ 'verify_[proof_system]_proof_[curve_name]' will be used. │ │ --env-file FILE Path to the environment file containing rpc, address, private_key │ │ [default: /home/felt/PycharmProjects/garaga-flow/my_project/target/.secrets] │ │ --network [sepolia|mainnet] Starknet network [default: sepolia] │ │ --help -h Show this message and exit. │ ╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯ ``` As for the verifying key, both Snarkjs and Gnark `proof.json` and `public.json` are supported out of the box. See the example in the [generate-and-deploy-your-verifier-contract.md](../generate-and-deploy-your-verifier-contract.md "mention") for Gnark export. Alternatively, the `--public-inputs` parameter can be omitted if your proof include everything at once, as below. 
{
    "eliptic_curve_id": "bn254",
    "proof": {
        "a": {
            "x": "0x2abaae3dd6e4c662f5e071bca525a26d21e2400d01d02c87bce2e8363285990a",
            "y": "0x24211ff0aa742a6dd1651aadce6f72757beb89de2cff83a6162de7c15674c2"
        },
        "b": {
            "x": [
                "0x2335f1564c154d7a2ec5d11faf6d991a205bef2858f1687976d0a46502f5224a",
                "0x223af0bb0912d8ebc535ed489d06cd01fcf4a8ab4596cc28164edf9041d97080"
            ],
            "y": [
                "0x182e8fd86a44983de1d1d9dc4f12f134535b75d39f7aeb21adbf57e1a32ee603",
                "0xecb11668a0dd5d5031b0837e62ba14222b45718dc101c1278f44a9ed823c16b"
            ]
        },
        "c": {
            "x": "0x290243624a4c11868e7cb0c0f7cfd690dac08e4205d19795b0a8f686dddcdfd6",
            "y": "0x15de00cc8af159fbdbdc802592e83e1ac61a8026b97e8889b8c5def59ec50b16"
        }
    },
    "public_inputs": [
        "0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474"
    ]
}
The command should look like this: {% code overflow="wrap" %} ``` garaga verify-onchain --system groth16 --contract-address 0x1234... --vk vk.json --proof proof.json --public-inputs public.json --env-file .secrets --network sepolia ``` {% endcode %} If everything is good, the command will output the transaction hash along with an explorer link. \ Congrats! ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-python-garaga-cli.md ================================================ # Using Python/Garaga CLI Using the `garaga calldata` command from the CLI, you can generate the calldata needed to verify a proof for the `verify_groth16_proof_[curve_name]`. First, ensure that: * Your circuit is compiled and the verification key `verification_key.json` is created * The public input file `public.json` and the associated proof `proof.json` are created The call the following command by replacing the parameters with your data: ```bash garaga calldata --system groth16 --vk verification_key.json --proof proof.json --public-inputs public.json 2789 41983001825546257095993508953 3045291465937026073442547681 1840582864647114302 0 69020349870260156176548317333 16784567729677911275297018120 1865382613176499468 0 51545988015561248414407597558 44248521764831362261757723052 8850086 ... ``` ## `starkli` usage Using the command option `--format starkli`,\ you can directly pipe the generated calldata to `starkli` to invoke a transaction on your deployed contract. The proof must be the last parameter of your contract's method. ```bash garaga calldata --system groth16 --vk verification_key.json --proof proof.json --public-inputs public.json --format starkli | xargs starkli invoke --keystore-password $KEYSTORE_PASSWORD --watch $YOUR_CONTRACT your_verify_method YOUR_PARAMETERS ``` ## Cairo code usage Use the command option `--format array` to generate calldata in array format to be used in your smart-contract tests. ```bash garaga calldata --system groth16 --vk verification_key.json --proof proof.json --public-inputs public.json --format array [2789, 41983001825546257095993508953, 3045291465937026073442547681, 1840582864647114302, 0, 69020349870260156176548317333, 16784567729677911275297018120, 1865382613176499468, 0, 51545988015561248414407597558, 44248521764831362261757723052, 88500861247646845, 0, ... ] ``` ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-rust.md ================================================ # Using Rust Add the [rust-crate.md](../../../installation/rust-crate.md "mention") to your project. ```rust // Version must match the pip package that generated the verifier use garaga_rs::calldata::full_proof_with_hints::groth16::{ get_groth16_calldata, Groth16Proof, Groth16VerifyingKey, }; use garaga_rs::definitions::CurveID; use std::fs; fn main() -> Result<(), String> { // 1. Load and parse verification key from JSON let vk_json = fs::read_to_string("verification_key.json").map_err(|e| e.to_string())?; let vk = Groth16VerifyingKey::from_json(&vk_json)?; // 2. Load and parse proof from JSON let proof_json = fs::read_to_string("proof.json").map_err(|e| e.to_string())?; let public_inputs_json = fs::read_to_string("public.json").map_err(|e| e.to_string())?; let proof = Groth16Proof::from_json(&proof_json, &public_inputs_json)?; // 3. Generate calldata (curve is auto-detected from vk) let calldata = get_groth16_calldata(&proof, &vk, CurveID::BN254)?; println!("Calldata length: {}", calldata.len()); // The calldata can now be used to call your deployed verifier contract Ok(()) } ``` {% hint style="info" %} The `CurveID` should match your verifying key's curve: `CurveID::BN254` or `CurveID::BLS12_381`. {% endhint %} ## Alternative: Using JSON files directly If your proof and public inputs are in separate Snarkjs-style JSON files: ```rust use garaga_rs::calldata::full_proof_with_hints::groth16::{ get_groth16_calldata, Groth16Proof, Groth16VerifyingKey, }; use garaga_rs::definitions::CurveID; // Parse verification key let vk = Groth16VerifyingKey::from_json(&vk_json_string)?; // Parse proof with separate public inputs let proof = Groth16Proof::from_json(&proof_json_string, &public_inputs_json_string)?; // Generate calldata let calldata = get_groth16_calldata(&proof, &vk, CurveID::BN254)?; ``` See the [Rust crate documentation](https://github.com/keep-starknet-strange/garaga/tree/main/tools/garaga_rs) for more details. ================================================ FILE: docs/gitbook/smart-contract-generators/groth16/generating-calldata-from-a-proof-and-using-your-deployed-contract/using-typescript.md ================================================ # Using Typescript Using the `garaga` [npm-package.md](../../../installation/npm-package.md "mention") ## Node.js (with file reading) ```typescript import * as garaga from 'garaga'; import { CurveId } from 'garaga'; import { readFileSync } from 'fs'; await garaga.init(); // Parse from file paths (Node.js only) const vk = garaga.parseGroth16VerifyingKeyFromJson('verification_key.json'); const proof = garaga.parseGroth16ProofFromJson('proof.json', 'public.json'); const calldata = garaga.getGroth16CallData(proof, vk, CurveId.BN254); ``` ## From JSON objects (Node.js and Browser) ```typescript import * as garaga from 'garaga'; import { CurveId } from 'garaga'; await garaga.init(); // Parse from already-loaded JSON objects const vkJson = { /* verification key JSON */ }; const proofJson = { /* proof JSON */ }; const publicInputs = [/* public inputs as bigint[] */]; const vk = garaga.parseGroth16VerifyingKeyFromObject(vkJson); const proof = garaga.parseGroth16ProofFromObject(proofJson, publicInputs); const calldata = garaga.getGroth16CallData(proof, vk, CurveId.BN254); ``` {% hint style="info" %} The `CurveId` should match your verifying key's curve: `CurveId.BN254` or `CurveId.BLS12_381`. {% endhint %} ## Browser Usage Use `parseGroth16*FromObject` functions in the browser (no filesystem access): ```typescript import * as garaga from 'garaga'; import { CurveId } from 'garaga'; async function generateCalldata(vkJson: object, proofJson: object, publicInputs?: bigint[]) { await garaga.init(); const vk = garaga.parseGroth16VerifyingKeyFromObject(vkJson); const proof = garaga.parseGroth16ProofFromObject(proofJson, publicInputs); return garaga.getGroth16CallData(proof, vk, CurveId.BN254); } ``` ================================================ FILE: docs/gitbook/smart-contract-generators/noir.md ================================================ --- icon: octopus --- # Noir ## Requirements (read carefully to avoid 99% of issues!) * Garaga CLI [python-package.md](../installation/python-package.md "mention") version 1.1.0 (install with `pip install garaga==1.1.0`) * Noir 1.0.0-beta.16 (install with `noirup --version 1.0.0-beta.16` or `npm i @noir-lang/noir_js@1.0.0-beta.16`) * Barretenberg 3.0.0-nightly.20251104 (install with `bbup --version 3.0.0-nightly.20251104` or `npm i @aztec/bb.js@3.0.0-nightly.20251104`) To install `noirup` and `bbup`, follow the [quickstart guide from aztec](https://noir-lang.org/docs/getting_started/quick_start). ## Generate a Starknet smart contract for your Noir program First, create a new Noir project and compile it with `nargo build`. ```bash nargo new hello cd hello nargo build ``` This will create a json file in `hello/target/hello.json` Now, generate the corresponding verifying key `vk` using barretenberg: ```bash bb write_vk -s ultra_honk --oracle_hash keccak -b target/hello.json -o target/vk ``` {% hint style="info" %} Note: ZK mode is enabled by default in barretenberg. The verification key is the same whether you generate a ZK proof or not. {% endhint %} Finally, generate a smart contract from the verifying key using the garaga CLI. ```bash garaga gen --system ultra_keccak_zk_honk --vk target/vk ``` This will create a smart contract folder with the following structure. ``` Generating Smart Contract project for ProofSystem.UltraKeccakZKHonk using vk... Done! Smart Contract project created: /noir/hello/my_project/ ├── .tools-versions ├── Scarb.toml └── src/ ├── honk_verifier.cairo ├── honk_verifier_circuits.cairo ├── honk_verifier_constants.cairo └── lib.cairo ``` The main function of interest is located in `honk_verifier.cairo` The contract interface will be ```rust #[starknet::interface] pub trait IUltraKeccakZKHonkVerifier { fn verify_ultra_keccak_zk_honk_proof( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; // Returns Ok(public_inputs) on success, Err on failure. } ``` In order to interact with the endpoint, we need to generate the `full_proof_with_hints` array. To do so, we need a specific proof for your program. But first, Noir requires to specify the inputs of the program in `hello/Prover.toml` ```toml // The "hello" program simply proves that x!=y, with x being private and y public. x = "1" y = "2" ``` Now, generate a proof with barretenberg: ```bash nargo execute witness bb prove -s ultra_honk --oracle_hash keccak -b target/hello.json -w target/witness.gz -o target/ ``` This creates two files in the `target/` directory: - `target/proof` - the ZK proof - `target/public_inputs` - the public inputs {% hint style="info" %} ZK mode is enabled by default. Use `--disable_zk` flag if you want to generate a non-ZK proof (not recommended for production). {% endhint %} ## Generating the calldata (`full_proof_with_hints` array) {% hint style="warning" %} **Version Compatibility:** Use the same Garaga SDK version (pip/npm/Rust) that generated your verifier contract. Mismatched versions produce incompatible calldata and cause verification to fail. {% endhint %} {% tabs %} {% tab title="CLI" %} Finalizing the above CLI example, you can obtain the `full_proof_with_hints` array using the garaga CLI. From within the "hello" directory: ```bash garaga calldata --system ultra_keccak_zk_honk --proof target/proof --vk target/vk --public-inputs target/public_inputs ``` {% hint style="info" %} Using `garaga calldata` with the `--format array` lets you paste this array in cairo code for unit tests by doing `let proof: Array = [...];`. The `--format starkli` has a formatting which is composable with starkli in the command line and also prepends the length of the array so that it can be deserialized by starknet. The `--format snforge` (default) creates a file that can be used with snforge. {% endhint %} {% endtab %} {% tab title="Rust" %} Add the [rust-crate.md](../installation/rust-crate.md "mention") to your project. ```rust // Version must match the pip package that generated the verifier use garaga_rs::calldata::full_proof_with_hints::zk_honk::{ get_zk_honk_calldata, HonkVerificationKey, ZKHonkProof, }; use std::fs; fn main() -> Result<(), String> { // 1. Load your verification key let vk_bytes = fs::read("target/vk").map_err(|e| e.to_string())?; let vk = HonkVerificationKey::from_bytes(&vk_bytes)?; // 2. Load the proof file let proof_bytes = fs::read("target/proof").map_err(|e| e.to_string())?; // 3. Load public inputs file let pub_inputs_bytes = fs::read("target/public_inputs").map_err(|e| e.to_string())?; // 4. Parse the proof (requires log_circuit_size from vk) let proof = ZKHonkProof::from_bytes(&proof_bytes, &pub_inputs_bytes, vk.log_circuit_size)?; // 5. Generate calldata let calldata = get_zk_honk_calldata(&proof, &vk)?; println!("Calldata length: {}", calldata.len()); Ok(()) } ``` {% endtab %} {% tab title="Typescript" %} Using the `garaga` [npm-package.md](../installation/npm-package.md "mention") ```typescript // Version must match the pip package that generated the verifier import * as garaga from 'garaga'; import { readFileSync } from 'fs'; // 1. Initialize the WASM module (required before using any garaga functions) await garaga.init(); // 2. Load your proof, public inputs, and verification key as Uint8Array const vk = new Uint8Array(readFileSync('target/vk')); const proof = new Uint8Array(readFileSync('target/proof')); const publicInputs = new Uint8Array(readFileSync('target/public_inputs')); // 3. Generate calldata for ZK Honk proofs const calldata: bigint[] = garaga.getZKHonkCallData(proof, publicInputs, vk); console.log('Calldata length:', calldata.length); ``` {% endtab %} {% tab title="Python" %} Using the `garaga` [python-package.md](../installation/python-package.md "mention") ```python # Version must match the pip package that generated the verifier from garaga.precompiled_circuits.zk_honk import HonkVk, ZKHonkProof from garaga.starknet.honk_contract_generator.calldata import ( get_ultra_flavor_honk_calldata_from_vk_and_proof ) # 1. Load your verification key vk = HonkVk.from_bytes(open('target/vk', 'rb').read()) # 2. Load proof and public inputs proof_bytes = open('target/proof', 'rb').read() public_inputs_bytes = open('target/public_inputs', 'rb').read() # 3. Parse the proof proof = ZKHonkProof.from_bytes(proof_bytes, public_inputs_bytes, vk) # 4. Generate calldata calldata: list[int] = get_ultra_flavor_honk_calldata_from_vk_and_proof(vk=vk, proof=proof) print(f'Calldata length: {len(calldata)}') ``` {% endtab %} {% endtabs %} ## BB CLI Reference {% hint style="info" %} Use `bb write_vk --help` and `bb prove --help` to see all available options. {% endhint %} **Verification Key Generation:** ```bash bb write_vk -s ultra_honk --oracle_hash keccak -b target/hello.json -o target/vk ``` **Proof Generation (ZK mode is default):** ```bash bb prove -s ultra_honk --oracle_hash keccak -b target/hello.json -w target/witness.gz -o target/ ``` **Proof Verification (optional, for local testing):** ```bash bb verify -s ultra_honk --oracle_hash keccak -p target/proof -k target/vk -i target/public_inputs ``` ## Complete dApp Tutorial Follow the [Scaffold‑Garaga repository](https://github.com/m-kus/scaffold-garaga). This starter kit combines **Noir**, **Garaga**, and **Starknet** with in‑browser proving to help you ship a privacy‑preserving dApp fast. #### What you'll learn 1. **Generate & deploy an UltraHonk proof verifier** to a local Starknet devnet. 2. **Add on‑chain state** to your privacy‑preserving app. 3. **Connect a wallet and deploy to a public testnet**. --- Need [support.md](../support.md "mention") ? ================================================ FILE: docs/gitbook/support.md ================================================ --- icon: message-question --- # Support * Is something unclear ? * Spotted a bug ? * Need help on a specific subject or additional documentation ? Feel free to ask questions on the Garaga telegram [group](https://t.me/GaragaStarknet), or [raise an issue](https://github.com/keep-starknet-strange/garaga/issues/new/choose) on the github repository, it will help us making this documentation better and enhancing Garaga! ================================================ FILE: docs/gitbook/updating-these-docs.md ================================================ --- icon: file-doc --- # Updating these docs ### Overview Gitbook website is synced with the `docs` branch. Documentation updates are handled through an automated bidirectional sync between the `main` and `docs` branches: * **GitBook edits** → `docs` branch → automated PR to `main` * **Code changes** → `main` branch → automated sync to `docs` branch ### Making Documentation Changes #### For Contributors: PR to Main (Recommended) 1. Create a branch from `main` 2. Edit files in `docs/gitbook/` folder 3. PR directly to `main` branch 4. Changes will automatically sync to `docs` branch after merge and reflected on the website. #### For Maintainers: GitBook Interface Repo maintainers and selected contributors can edit directly in GitBook - changes automatically sync to the `docs` branch and create a PR to `main`. ### Automated Workflow * **Documentation-only changes**: Auto-labeled and ready for review * **Mixed changes** (docs + code): Flagged for manual review with `needs-review` label * **Code changes on main**: Non-docs files automatically sync to `docs` branch * All PRs use squash & merge to maintain clean history The GitBook website updates automatically when changes reach the `docs` branch. ================================================ FILE: docs/gitbook/using-garaga-libraries-in-your-cairo-project/README.md ================================================ --- icon: arrow-down-to-bracket --- # Using Garaga Libraries in Your Cairo Project Garaga provides a powerful Cairo library for elliptic curve operations, signature verification, and cryptographic primitives. The library is designed to work **uniformly across all supported curves**—the same functions, the same patterns, just change the curve identifier. ## Installation Garaga is available on the [scarbs.xyz registry](https://scarbs.xyz/packages/garaga). Add it to your project using `scarb add`: ```bash scarb add garaga ``` Or add it manually to your `Scarb.toml`: {% code title="Scarb.toml" %} ```toml [dependencies] garaga = "1.1.0" [cairo] sierra-replace-ids = false # Required to avoid compilation errors ``` {% endcode %} {% hint style="info" %} Using the registry is the recommended approach. For more details on managing dependencies, see the [Scarb documentation](https://docs.swmansion.com/scarb/docs/guides/dependencies.html). {% endhint %} {% hint style="warning" %} **Important**: The `sierra-replace-ids = false` setting is required. See [issue #198](https://github.com/keep-starknet-strange/garaga/issues/198) for details about using Garaga with workspaces. {% endhint %} ### Installing from Git (alternative) If you need a specific commit or unreleased version, you can install from Git: ```toml [dependencies] garaga = { git = "https://github.com/keep-starknet-strange/garaga.git", tag = "v1.1.0" } ``` --- ## Generic Over Any Curve One of Garaga's key architectural decisions is that **all operations work uniformly across any supported curve**. This means: - ✅ The same `msm_g1` function works for BN254, BLS12-381, SECP256K1, and more - ✅ The same signature verification patterns apply to all curves - ✅ Switching curves requires only changing the `curve_id` parameter - ✅ Future curves can be added without changing your code ### Example: Curve-Agnostic MSM ```cairo use garaga::ec_ops::msm_g1; use garaga::definitions::{G1Point, u384}; // This exact same function works for ANY supported curve fn compute_msm( points: Span, scalars: Span, curve_id: usize, // Just change this to switch curves! hints: Span, ) -> G1Point { msm_g1(points, scalars, hints, curve_id) } // Usage: // compute_msm(points, scalars, 0, hints) // BN254 // compute_msm(points, scalars, 2, hints) // SECP256K1 // compute_msm(points, scalars, 3, hints) // SECP256R1 ``` This design enables maximum code reuse and flexibility across your applications. --- ## Supported Elliptic Curves | Curve ID | Curve | Common Use Cases | |----------|-------|------------------| | **0** | BN254 | Ethereum zkSNARKs, Groth16 | | **1** | BLS12-381 | Ethereum 2.0, Zcash, drand | | **2** | SECP256K1 | Bitcoin, Ethereum ECDSA | | **3** | SECP256R1 | WebAuthn, TLS, P-256 | | **4** | ED25519 | Solana, SSH, general EdDSA | | **5** | GRUMPKIN | Noir circuits, Aztec | {% hint style="info" %} These curve identifiers are consistent across **all** Garaga code—Cairo, Python, Rust, and TypeScript. Use the same ID everywhere. {% endhint %} --- ## Available Operations ### Elliptic Curve Operations | Operation | Description | Curves | |-----------|-------------|--------| | **Multi-Scalar Multiplication (MSM)** | Compute `∑ sᵢ·Pᵢ` efficiently | All | | **Scalar Multiplication** | Compute `s·P` for a single point | All | | **Point Addition** | Add two elliptic curve points | All | | **Pairing Check** | Verify pairing equations | BN254, BLS12-381 | [→ EC Operations Documentation](ec-multi-scalar-multiplication.md) ### Signature Verification | Scheme | Description | Curves | |--------|-------------|--------| | **ECDSA** | Standard elliptic curve signatures | SECP256K1, SECP256R1, BN254, BLS12-381 | | **Schnorr** | BIP340-compatible Schnorr signatures | All Weierstrass curves | | **EdDSA** | Edwards-curve signatures | ED25519 | [→ Signatures Documentation](ec-signatures.md) ### Hashing Functions | Function | Description | Use Case | |----------|-------------|----------| | **SHA-512** | Standard SHA-512 | EdDSA, general hashing | | **Poseidon (BN254)** | ZK-friendly hash | Grumpkin circuits | [→ Hashing Documentation](hashing-functions.md) --- ## Performance Characteristics Garaga achieves efficiency through **precomputed hints**. The SDK (Python/Rust/TypeScript) generates these hints off-chain, and the Cairo code verifies them on-chain. This means: 1. **Off-chain**: Complex computations happen in the SDK 2. **On-chain**: Cairo only verifies the results are correct ``` ┌─────────────────────────────────────────────────────────────┐ │ Off-chain (SDK) │ │ - Compute MSM/signature verification │ │ - Generate verification hints │ │ - Serialize as calldata │ └───────────────────────────┬─────────────────────────────────┘ │ calldata with hints ▼ ┌─────────────────────────────────────────────────────────────┐ │ On-chain (Cairo) │ │ - Deserialize calldata │ │ - Verify hints are correct │ │ - Return result (success/failure) │ └─────────────────────────────────────────────────────────────┘ ``` This architecture enables operations that would otherwise be prohibitively expensive on-chain. --- ## Next Steps - [**EC Multi-Scalar Multiplication**](ec-multi-scalar-multiplication.md) — Compute MSMs on any curve - [**Signature Verification**](ec-signatures.md) — ECDSA, Schnorr, and EdDSA - [**Hashing Functions**](hashing-functions.md) — SHA-512 and Poseidon ================================================ FILE: docs/gitbook/using-garaga-libraries-in-your-cairo-project/ec-multi-scalar-multiplication.md ================================================ --- hidden: true icon: florin-sign --- # EC (Multi)-Scalar Multiplication For a given elliptic curve, scalar multiplication consists of adding a point `P` to itself `s` times, where `P` is a point satisfying the curve equation and `s` a scalar.\ \ `k.P = P+P+P+...+P (k times)`\ \ \ Multi scalar multiplication consists of the sum of `n` scalar multiplication with different points and scalars : $$ \sum_{i=1}^{n} k_i \times P_i $$ A single `msm_g1` function in Garaga computes the multi-scalar multiplication for a given set of points and scalars for a given elliptic curve. Since it also works with `n=1`, it is also able to compute a single scalar multiplication. ```toml [package] name = "my_package_that_needs_ec_scalar_mul" version = "0.1.0" edition = "2024_07" [dependencies] garaga = "1.1.0" [cairo] sierra-replace-ids = false ``` {% hint style="info" %} You can also add the dependency using `scarb add garaga`. See the [installation guide](README.md#installation) for more options. {% endhint %} The function will be importable using ```rust use garaga::ec_ops::msm_g1; use garaga::definitions::G1Point; ``` ```rust fn msm_g1( points: Span, scalars: Span, curve_index: usize, msm_hint: Span, ) -> G1Point { ``` As you can see, this function not only needs points and scalars, but also additional information, to perform the computation much more efficiently.\ \ Under `hydra/garaga/starknet/tests_and_calldata_generators/`, you will find in the file [`msm.py`](https://github.com/keep-starknet-strange/garaga/blob/main/hydra/garaga/starknet/tests_and_calldata_generators/msm.py) some tools to generate a cairo test (using `MSMCalldataBuilder.to_cairo_1_test()`) for this function given some points and scalars, or directly the raw calldata for starknet usage (using `MSMCalldataBuilder.serialize_to_calldata()`). ### Generating and using calldata \ An example contract is already [deployed](https://sepolia.voyager.online/contract/0x012686bdb4ca3f22ffc93dfe1e24d72294aac38a4f6b997b456fb4368fb3390b#readContract) on sepolia, solely holding an endpoint to this function.\ The source code to the contract is [here](https://github.com/keep-starknet-strange/garaga/blob/main/src/contracts/universal_ecip/src/lib.cairo) .\ \ You can try this deployed contract on any supported curves modifying the [`msm.py`](https://github.com/keep-starknet-strange/garaga/blob/main/hydra/garaga/starknet/tests_and_calldata_generators/msm.py) script at the end : ```python if __name__ == "__main__": import random c = CurveID.SECP256K1 order = CURVES[c.value].n msm = MSMCalldataBuilder( curve_id=c, points=[G1Point.gen_random_point(c) for _ in range(1)], scalars=[random.randint(0, order) for _ in range(1)], ) cd = msm.serialize_to_calldata( include_points_and_scalars=True, serialize_as_pure_felt252_array=False, ) print(cd) print(len(cd)) ``` The options are : * `include_points_and_scalars` : If set to `False`, the input points, scalars, and `curve_index` will not be part of the calldata. * `serialize_as_pure_felt252_array` : If set to `True`, preprend the total length of the calldata at the beginning. \\ These options are only useful when you want to use points and scalars from another source than the calldata.\ \ For example, checkout the [groth16 verifier contracts](https://github.com/keep-starknet-strange/garaga/blob/main/src/contracts/autogenerated/groth16_example_bn254/src/groth16_verifier.cairo). It makes a delegated call to the endpoint `msm_g1` using the already declared contract's class hash, and pushes the (fixed) points from the hardcoded verifying key, and the scalars from the groth16 proof. : ```rust impl IGroth16VerifierBN254 of super::IGroth16VerifierBN254 { fn verify_groth16_proof_bn254( ref self: ContractState, groth16_proof: Groth16Proof, mpcheck_hint: MPCheckHintBN254, msm_hint: Array, ) -> bool { groth16_proof.a.assert_on_curve(0); groth16_proof.b.assert_on_curve(0); groth16_proof.c.assert_on_curve(0); let ic = ic.span(); let vk_x: G1Point = match ic.len() { 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => { // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = msm_hint; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); Serde::serialize(@groth16_proof.public_inputs, ref msm_calldata); // Complete with the curve indentifier (0 for BN254): msm_calldata.append(0); // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = core::starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span() ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), 0 ) } }; ``` Here the `msm_hint` is used with `include_points_and_scalars=False` and `serialize_as_pure_felt252_array=True`\ \ Then the points from `ic` are pushed to the array, and the scalars from the groth16 proof's public inputs. Finally the curve identifier is pushed as well.\ \ In our example, we'll leave the default parameters that will include everything for a direct endpoint call.\ Simply run : ``` python hydra/garaga/starknet/tests_and_calldata_generators/msm.py ``` And copy paste the array in voyager to see!
================================================ FILE: docs/gitbook/using-garaga-libraries-in-your-cairo-project/ec-signatures.md ================================================ --- icon: pen-field --- # ECDSA, Schnorr & EdDSA Signatures All three signature schemes follow a similar pattern with a Cairo struct containing the signature data and hints for efficient verification. Garaga provides tooling in Python/Rust/JavaScript to generate the full expected Cairo struct given signature information. All signature verification schemes work with all [#supported-elliptic-curves](./#supported-elliptic-curves "mention") in Garaga (except EdDSA which is specific to Ed25519), using the corresponding curve identifier. ## Cairo Verification Functions Verification functions take the public key as a **separate parameter**: - `is_valid_ecdsa_signature_assuming_hash(signature, public_key, curve_id) -> bool` - `is_valid_schnorr_signature_assuming_hash(signature, public_key, curve_id) -> bool` - `is_valid_eddsa_signature(signature, Py_twisted) -> bool` {% hint style="warning" %} **Important:** The ECDSA and Schnorr verification functions assume that the message hash has been correctly computed by the caller. They verify the signature equation but do not hash the message themselves. {% endhint %} ## Public Key Handling The public key is always passed as a **separate parameter** to the verification function. This allows you to: 1. **Hardcode the public key** in your contract if it's known at compile time 2. **Provide the public key dynamically** at runtime When generating calldata with the SDK, use the `prepend_public_key` parameter: - `prepend_public_key=True` (default): The public key is included in the serialized calldata, allowing you to deserialize both the signature and public key from the same array - `prepend_public_key=False`: Only the signature is serialized; you must provide the public key separately (useful when the public key is hardcoded in your contract) --- ## ECDSA Signature Verification ### Cairo Structs ```rust use garaga::signatures::ecdsa::{ECDSASignature, ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash}; use garaga::definitions::{G1Point, u384}; /// Core signature data struct ECDSASignature { rx: u384, // r component (R.x mod n) s: u256, // s component v: bool, // Parity of R.y (false if even, true if odd) z: u256, // Message hash (assumed correctly computed by caller) } /// Signature bundled with verification hints struct ECDSASignatureWithHint { signature: ECDSASignature, msm_hint: Span, } ``` ### Usage Example ```rust use garaga::signatures::ecdsa::{ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash}; use garaga::definitions::{G1Point, u384}; fn verify_ecdsa_signature( serialized_signature: Span, public_key: G1Point, curve_id: usize, ) -> bool { // Deserialize the signature with hints let mut data = serialized_signature; let signature_with_hints = Serde::::deserialize(ref data).unwrap(); // Verify the signature // curve_id: 0=BN254, 1=BLS12_381, 2=SECP256K1, 3=SECP256R1, 5=GRUMPKIN is_valid_ecdsa_signature_assuming_hash(signature_with_hints, public_key, curve_id) } ``` ### Calldata Generation {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.signatures import ECDSASignature from garaga.definitions import CurveID # Create signature object with all required fields sig = ECDSASignature( r=0x..., # r component of signature s=0x..., # s component of signature v=0, # 0 if R.y is even, 1 if odd px=0x..., # Public key x-coordinate py=0x..., # Public key y-coordinate z=0x..., # Message hash curve_id=CurveID.SECP256K1 ) # Generate calldata with public key included (for dynamic public key) calldata = sig.serialize_with_hints(prepend_public_key=True) # Generate calldata without public key (for hardcoded public key in contract) calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False) ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::signatures::ecdsa_calldata_builder; use garaga_rs::definitions::CurveID; // Generate calldata with public key included let calldata = ecdsa_calldata_builder( r, // r component s, // s component v, // recovery parameter (0 or 1) px, // public key x py, // public key y z, // message hash true, // prepend_public_key CurveID::SECP256K1 as usize, )?; // Generate calldata without public key (for hardcoded public key) let calldata_no_pk = ecdsa_calldata_builder(r, s, v, px, py, z, false, CurveID::SECP256K1 as usize)?; ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import { ecdsaCalldataBuilder, CurveId } from 'garaga'; // Generate calldata with public key included const calldata = ecdsaCalldataBuilder( r, // r component (bigint) s, // s component (bigint) v, // recovery parameter (0 or 1) px, // public key x (bigint) py, // public key y (bigint) z, // message hash (bigint) true, // prependPublickey CurveId.SECP256K1 ); // Generate calldata without public key (for hardcoded public key) const calldataNoKey = ecdsaCalldataBuilder(r, s, v, px, py, z, false, CurveId.SECP256K1); ``` {% endtab %} {% endtabs %} --- ## Schnorr Signature Verification ### Cairo Structs ```rust use garaga::signatures::schnorr::{SchnorrSignature, SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash}; use garaga::definitions::{G1Point, u384}; /// Core signature data struct SchnorrSignature { rx: u384, // x-coordinate of R point s: u256, // s component e: u256, // Challenge hash (assumed correctly computed by caller) } /// Signature bundled with verification hints struct SchnorrSignatureWithHint { signature: SchnorrSignature, msm_hint: Span, } ``` {% hint style="info" %} **BIP340 Requirement:** The public key's y-coordinate must be even. The verification function will return `false` if the public key has an odd y-coordinate. {% endhint %} ### Usage Example ```rust use garaga::signatures::schnorr::{SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash}; use garaga::definitions::{G1Point, u384}; fn verify_schnorr_signature( serialized_signature: Span, public_key: G1Point, curve_id: usize, ) -> bool { // Deserialize the signature with hints let mut data = serialized_signature; let signature_with_hints = Serde::::deserialize(ref data).unwrap(); // Verify the signature // Note: public_key.y must be even (BIP340 requirement) is_valid_schnorr_signature_assuming_hash(signature_with_hints, public_key, curve_id) } ``` ### Calldata Generation {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.signatures import SchnorrSignature from garaga.definitions import CurveID # Create signature object (py must be even) sig = SchnorrSignature( rx=0x..., # x-coordinate of R point s=0x..., # s component e=0x..., # Challenge hash px=0x..., # Public key x-coordinate py=0x..., # Public key y-coordinate (must be even!) curve_id=CurveID.BN254 ) # Generate calldata with public key included calldata = sig.serialize_with_hints(prepend_public_key=True) # Generate calldata without public key (for hardcoded public key) calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False) ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::signatures::schnorr_calldata_builder; use garaga_rs::definitions::CurveID; // Generate calldata with public key included let calldata = schnorr_calldata_builder( rx, // R.x coordinate s, // s component e, // challenge hash px, // public key x py, // public key y (must be even!) true, // prepend_public_key CurveID::BN254 as usize, )?; // Generate calldata without public key let calldata_no_pk = schnorr_calldata_builder(rx, s, e, px, py, false, CurveID::BN254 as usize)?; ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import { schnorrCalldataBuilder, CurveId } from 'garaga'; // Generate calldata with public key included const calldata = schnorrCalldataBuilder( rx, // R.x coordinate (bigint) s, // s component (bigint) e, // challenge hash (bigint) px, // public key x (bigint) py, // public key y (bigint, must be even!) true, // prependPublickey CurveId.BN254 ); // Generate calldata without public key const calldataNoKey = schnorrCalldataBuilder(rx, s, e, px, py, false, CurveId.BN254); ``` {% endtab %} {% endtabs %} --- ## EdDSA Signature Verification (Ed25519) EdDSA signatures use the Ed25519 curve following RFC 8032. The implementation explicitly rejects small-order points to prevent key-compromise and signature-malleability attacks. ### Cairo Structs ```rust use garaga::signatures::eddsa_25519::{EdDSASignature, EdDSASignatureWithHint, is_valid_eddsa_signature}; /// Core signature data struct EdDSASignature { Ry_twisted: u256, // Compressed R point y-coordinate (little-endian) s: u256, // Signature scalar msg: Span, // Original message bytes } /// Signature bundled with verification hints struct EdDSASignatureWithHint { signature: EdDSASignature, msm_hint: Span, sqrt_Rx_hint: u256, // Hint for R point decompression sqrt_Px_hint: u256, // Hint for public key decompression } ``` {% hint style="info" %} **Note:** EdDSA takes the raw message bytes, not a hash. The verification function computes `SHA-512(R || A || msg)` internally as per RFC 8032. {% endhint %} ### Usage Example ```rust use garaga::signatures::eddsa_25519::{EdDSASignatureWithHint, is_valid_eddsa_signature}; fn verify_eddsa_signature( serialized_signature: Span, Py_twisted: u256, // Compressed public key y-coordinate (little-endian) ) -> bool { // Deserialize the signature with hints let mut data = serialized_signature; let signature_with_hints = Serde::::deserialize(ref data).unwrap(); // Verify the signature is_valid_eddsa_signature(signature_with_hints, Py_twisted) } ``` ### Calldata Generation {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.signatures import EdDSA25519Signature # Create signature object sig = EdDSA25519Signature( Ry_twisted=0x..., # Compressed R point (little-endian integer) s=0x..., # Signature scalar Py_twisted=0x..., # Compressed public key (little-endian integer) msg=b"Hello, World!" # Raw message bytes ) # Generate calldata with public key included calldata = sig.serialize_with_hints(prepend_public_key=True) # Generate calldata without public key (for hardcoded public key) calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False) ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::signatures::eddsa_calldata_builder; let message = b"Hello, World!".to_vec(); // Generate calldata with public key included let calldata = eddsa_calldata_builder( ry_twisted, // Compressed R point y-coordinate s, // Signature scalar py_twisted, // Compressed public key y-coordinate message.clone(), true, // prepend_public_key )?; // Generate calldata without public key let calldata_no_pk = eddsa_calldata_builder(ry_twisted, s, py_twisted, message, false)?; ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import { eddsaCalldataBuilder } from 'garaga'; const message = new TextEncoder().encode("Hello, World!"); // Generate calldata with public key included const calldata = eddsaCalldataBuilder( ry_twisted_le, // Compressed R point (bigint, little-endian) s, // Signature scalar (bigint) py_twisted_le, // Compressed public key (bigint, little-endian) message, // Uint8Array true // prependPublickey ); // Generate calldata without public key const calldataNoKey = eddsaCalldataBuilder(ry_twisted_le, s, py_twisted_le, message, false); ``` {% endtab %} {% endtabs %} --- ## Curve Identifiers | Curve ID | Value | Notes | |----------|-------|-------| | BN254 | 0 | - | | BLS12_381 | 1 | - | | SECP256K1 | 2 | Bitcoin/Ethereum | | SECP256R1 | 3 | P-256/NIST | | ED25519 | 4 | Only for EdDSA | | GRUMPKIN | 5 | - | ================================================ FILE: docs/gitbook/using-garaga-libraries-in-your-cairo-project/hashing-functions.md ================================================ --- icon: binary-circle-check --- # Hashing functions Garaga provides implementations of common hash functions optimized for Cairo. *** ## SHA-512 A pure Cairo implementation of SHA-512 following [RFC-6234](https://datatracker.ietf.org/doc/html/rfc6234). This is used internally for EdDSA signature verification but is also available for general use. ### Usage ```rust use garaga::hashes::sha_512::sha512; fn hash_message() { // Hash a single byte let input: Array = array![49]; // ASCII '1' let hash: Array = sha512(input); // hash is a 64-byte (512-bit) array assert!(hash.len() == 64); } fn hash_empty() { // Hash empty input let empty: Array = array![]; let hash = sha512(empty); // SHA-512 of empty string assert!( hash.span() == array![ 0xcf, 0x83, 0xe1, 0x35, 0x7e, 0xef, 0xb8, 0xbd, 0xf1, 0x54, 0x28, 0x50, 0xd6, 0x6d, 0x80, 0x07, 0xd6, 0x20, 0xe4, 0x05, 0x0b, 0x57, 0x15, 0xdc, 0x83, 0xf4, 0xa9, 0x21, 0xd3, 0x6c, 0xe9, 0xce, 0x47, 0xd0, 0xd1, 0x3c, 0x5d, 0x85, 0xf2, 0xb0, 0xff, 0x83, 0x18, 0xd2, 0x87, 0x7e, 0xec, 0x2f, 0x63, 0xb9, 0x31, 0xbd, 0x47, 0x41, 0x7a, 0x81, 0xa5, 0x38, 0x32, 0x7a, 0xf9, 0x27, 0xda, 0x3e, ].span() ); } fn hash_text() { // Hash arbitrary text let msg: Array = array![ 0x4C, 0x6F, 0x72, 0x65, 0x6D, 0x20, 0x69, 0x70, 0x73, 0x75, 0x6D // "Lorem ipsum" ]; let hash = sha512(msg); // Returns 64-byte hash } ``` ### Function Signature ```rust pub fn sha512(data: Array) -> Array ``` * **Input**: `Array` - The message bytes to hash * **Output**: `Array` - 64-byte (512-bit) hash result *** ## Poseidon (BN254 Scalar Field) A ZK-friendly hash function operating on the BN254 scalar field. This implementation is compatible with: * [Circom Poseidon](https://github.com/iden3/circomlib/blob/252f8130105a66c8ae8b4a23c7f5662e17458f3f/circuits/poseidon.circom#L198-L208) (`nInputs=2`) * [Noir Poseidon](https://noir-lang.org/docs/noir/standard_library/cryptographic_primitives/hashes#poseidon) (`std::hash::poseidon::hash::hash_2`) ### Cross-Language Example The same hash computed in Noir and Cairo: {% tabs %} {% tab title="Noir" %} ```rust // For nargo < 1.0.0-beta.4: use std::hash::poseidon::bn254::hash_2; // For nargo >= 1.0.0-beta.4: (poseidon has been moved to a separate package) // Add to Nargo.toml: // [dependencies] // poseidon = { tag = "v0.1.1", git = "https://github.com/noir-lang/poseidon" } use poseidon::poseidon::bn254::hash_2; fn main(x: Field, y: pub Field) { let x1 = [x, y]; let z = hash_2(x1); assert(z == 7853200120776062878684798364095072458815029376092732009249414926327459813530); } #[test] fn test_main() { main(1, 2); } ``` {% endtab %} {% tab title="Cairo" %} ```rust use garaga::hashes::poseidon_hash_2_bn254; use garaga::definitions::u384; fn test_poseidon_bn254() { let x: u384 = u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }; let y: u384 = u384 { limb0: 2, limb1: 0, limb2: 0, limb3: 0 }; let expected: u384 = 7853200120776062878684798364095072458815029376092732009249414926327459813530_u256 .into(); assert_eq!(poseidon_hash_2_bn254(x, y), expected); } ``` {% endtab %} {% endtabs %} ### Function Signature ```rust pub fn poseidon_hash_2_bn254(x: u384, y: u384) -> u384 ``` * **Input**: Two `u384` field elements * **Output**: `u384` - The Poseidon hash result {% hint style="info" %} This hash function is particularly useful when building circuits in Noir that need to verify hashes computed on Starknet, or vice versa. {% endhint %} ================================================ FILE: docs/gitbook/using-garaga-libraries-in-your-cairo-project/rsa-signatures.md ================================================ --- icon: key --- # RSA-2048 Signature Verification Garaga provides on-chain RSA-2048 signature verification using multi-channel Residue Number System (RNS) arithmetic. The verifier checks that `s^{65537} ≡ m (mod n)` without native 2048-bit arithmetic by decomposing the exponentiation into 17 certified modular reductions verified through 11 independent RNS channels. {% hint style="warning" %} **Important:** The verification function `is_valid_rsa2048_signature_assuming_encoded_message` assumes the expected message `m` is already in its final encoded form (e.g., PKCS#1 v1.5 padded). The caller is responsible for constructing `m` from the message hash. A helper `pkcs1_v1_5_encode_sha256` is provided in the Python SDK. {% endhint %} ## How It Works 1. **RNS representation**: 2048-bit integers are decomposed into 6 chunks of 384 bits (top chunk: 128 bits), then evaluated modulo 11 pairwise coprime ~384-bit primes. 2. **Square-and-multiply**: For `e = 65537 = 2^16 + 1`, the chain consists of 16 squarings + 1 final multiplication = 17 reductions. 3. **CRT exactness**: Each reduction `a·b = q·n + r` is checked in all 11 RNS channels. Since the product of the channel primes exceeds the maximum deviation, channel congruences imply integer equality. ## Cairo Structs ```rust use garaga::signatures::rsa::{ RSA2048PublicKey, RSA2048SignatureWithHint, is_valid_rsa2048_signature_assuming_encoded_message, }; use garaga::definitions::{RSA2048Chunks, RSA2048ReductionWitness}; /// RSA-2048 public key (the modulus n) struct RSA2048PublicKey { modulus: RSA2048Chunks, // 6 chunks × 4 × u96 = 24 felt252 } /// Core signature data struct RSA2048Signature { signature: RSA2048Chunks, // s: the RSA signature expected_message: RSA2048Chunks, // m: the expected encoded message } /// Signature bundled with 17 reduction witnesses struct RSA2048SignatureWithHint { signature: RSA2048Signature, reductions_hint: Span, // 17 × (quotient + remainder) = 17 × 48 = 816 felt252 } ``` ## Usage Example ```rust use garaga::signatures::rsa::{ RSA2048PublicKey, RSA2048SignatureWithHint, is_valid_rsa2048_signature_assuming_encoded_message, }; fn verify_rsa_signature( serialized: Span, public_key: RSA2048PublicKey, ) -> bool { let mut data = serialized; let sig = Serde::::deserialize(ref data).unwrap(); is_valid_rsa2048_signature_assuming_encoded_message(@sig, @public_key) } ``` ## Calldata Generation {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.signatures import RSA2048Signature from garaga.rsa_rns import generate_rsa2048_witness, generate_rsa2048_sha256_witness # From pre-computed witness (raw expected_message) bundle = generate_rsa2048_witness(seed=0) sig = RSA2048Signature.from_bundle(bundle) # From SHA-256 message digest (PKCS#1 v1.5 encoded) bundle = generate_rsa2048_sha256_witness(b"hello", seed=0) sig = RSA2048Signature.from_bundle(bundle) # Generate calldata (Python path) calldata = sig.serialize_with_hints(prepend_public_key=True) # Generate calldata (Rust path, byte-for-byte identical) calldata = sig.serialize_with_hints(use_rust=True, prepend_public_key=True) # Without public key (when modulus is hardcoded in contract) calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False) ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::signatures::rsa_2048_calldata_builder; // signature, expected_message, modulus are BigUint values let calldata = rsa_2048_calldata_builder( signature, // s value expected_message, // m = s^65537 mod n (PKCS#1 v1.5 encoded) modulus, // RSA-2048 modulus n true, // prepend_public_key )?; ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import { rsa2048CalldataBuilder } from 'garaga'; const calldata = rsa2048CalldataBuilder( signature, // RSA signature (bigint) expectedMessage, // PKCS#1 v1.5 encoded message (bigint) modulus, // RSA-2048 modulus (bigint) true // prependPublicKey ); ``` {% endtab %} {% endtabs %} ## Calldata Layout | Section | Elements | Description | |---------|----------|-------------| | Public key (optional) | 24 | Modulus `n` as 6 chunks × 4 words | | Signature | 24 | `s` as 6 chunks × 4 words | | Expected message | 24 | `m` as 6 chunks × 4 words | | Reduction witnesses | 816 | 17 × (quotient 24 + remainder 24) | | **Total** | **888** (with key) / **864** (without) | | ## Full SHA-256 Verification For end-to-end verification where the raw message is provided and SHA-256 + PKCS#1 v1.5 encoding is computed on-chain, use `is_valid_rsa2048_sha256_signature`: ```rust use garaga::signatures::rsa::{ RSA2048PublicKey, RSA2048SignatureWithHint, is_valid_rsa2048_sha256_signature, }; fn verify_rsa_sha256( serialized: Span, public_key: RSA2048PublicKey, ) -> bool { let mut data = serialized; let sig = Serde::::deserialize(ref data).unwrap(); let message = Serde::::deserialize(ref data).unwrap(); is_valid_rsa2048_sha256_signature(@sig, @public_key, @message) } ``` This function: 1. Computes `SHA-256(message)` on-chain 2. Constructs the PKCS#1 v1.5 encoded message 3. Asserts it matches the `expected_message` hint 4. Verifies `s^{65537} ≡ m (mod n)` via RNS arithmetic ### SHA-256 Calldata Generation {% tabs %} {% tab title="Python" %} ```python from garaga.starknet.tests_and_calldata_generators.signatures import RSA2048Signature # Create signature from raw message sig = RSA2048Signature.from_sha256_message(b"hello garaga", seed=0) # Generate calldata (Python path) calldata = sig.serialize_sha256_with_hints( message=b"hello garaga", prepend_public_key=True ) # Generate calldata (Rust path, byte-for-byte identical) calldata = sig.serialize_sha256_with_hints( message=b"hello garaga", use_rust=True, prepend_public_key=True ) ``` {% endtab %} {% tab title="Rust" %} ```rust use garaga_rs::calldata::signatures::rsa_2048_sha256_calldata_builder; let calldata = rsa_2048_sha256_calldata_builder( signature, // RSA signature s b"hello", // raw message bytes modulus, // RSA-2048 modulus n true, // prepend_public_key )?; ``` {% endtab %} {% tab title="TypeScript" %} ```typescript import { rsa2048Sha256CalldataBuilder } from 'garaga'; const message = new TextEncoder().encode("hello garaga"); const calldata = rsa2048Sha256CalldataBuilder( signature, // RSA signature (bigint) message, // raw message (Uint8Array) modulus, // RSA-2048 modulus (bigint) true // prependPublicKey ); ``` {% endtab %} {% endtabs %} ### SHA-256 Calldata Layout | Section | Elements | Description | |---------|----------|-------------| | Public key (optional) | 24 | Modulus `n` as 6 chunks × 4 words | | Signature | 24 | `s` as 6 chunks × 4 words | | Expected message | 24 | `m` (PKCS#1 v1.5 encoded) as 6 chunks × 4 words | | Reduction witnesses | 816 | 17 × (quotient 24 + remainder 24) | | ByteArray message | variable | Cairo ByteArray serde format | | **Total** | **888 + ByteArray** (with key) | | ## PKCS#1 v1.5 Encoding For standard RSA signature verification with SHA-256, the expected message must be PKCS#1 v1.5 encoded (RFC 8017, Section 9.2): ``` 0x00 || 0x01 || PS(0xFF × 202) || 0x00 || DigestInfo(19 bytes) || SHA-256(msg)(32 bytes) ``` The Python SDK provides `pkcs1_v1_5_encode_sha256`: ```python from garaga.rsa_rns import pkcs1_v1_5_encode_sha256 import hashlib message_hash = hashlib.sha256(b"hello").digest() encoded_message = pkcs1_v1_5_encode_sha256(message_hash) # encoded_message is a 2048-bit integer ready for RSA verification ``` ## Performance RSA-2048 verification costs approximately **~11.8M Sierra gas** (L2 gas) on Starknet. For comparison: | Scheme | Sierra Gas | |--------|-----------| | ECDSA (SECP256R1) | ~4.5M | | Schnorr (SECP256K1) | ~4.2M | | EdDSA (Ed25519, short msg) | ~9.8M | | **RSA-2048** | **~11.8M** | ================================================ FILE: hydra/garaga/algebra.py ================================================ from __future__ import annotations import random from dataclasses import dataclass from typing import Generic, TypeVar from sympy import legendre_symbol, sqrt_mod T = TypeVar("T", "PyFelt", "Fp2") @dataclass(slots=True) class PyFelt: """ Represents an element of a finite field. The dataclass decorator automatically provides implementations for __init__, __repr__, __eq__, and __hash__ methods. Supports the following operations through magic methods: - Addition ((PyFelt | int) + (PyFelt | int)) - Subtraction ((PyFelt | int) - (PyFelt | int)) - Multiplication ((PyFelt | int) * (PyFelt | int)) - Division (PyFelt / PyFelt) - Negation (-PyFelt) - Inversion (inv(PyFelt)) - Exponentiation (PyFelt ** int) - Equality (PyFelt == PyFelt) - Inequality (PyFelt != PyFelt) """ value: int p: int @property def felt(self) -> PyFelt: return self def __repr__(self) -> str: p_str = f"0x{self.p:0x}" if len(p_str) > 10: p_str = f"{p_str[:6]}...{p_str[-4:]}" return f"PyFelt({self.value}, {p_str})" def __add__(self, right: PyFelt | int) -> PyFelt: p = self.p if isinstance(right, PyFelt): return PyFelt((self.value + right.value) % p, p) if isinstance(right, int): return PyFelt((self.value + right) % p, p) raise TypeError(f"Cannot add PyFelt and {type(right)}") def __neg__(self) -> PyFelt: p = self.p return PyFelt((-self.value) % p, p) def __sub__(self, right: PyFelt | int) -> PyFelt: p = self.p if isinstance(right, PyFelt): return PyFelt((self.value - right.value) % p, p) if isinstance(right, int): return PyFelt((self.value - right) % p, p) raise TypeError(f"Cannot subtract PyFelt and {type(right)}") def __mul__(self, right: PyFelt | int) -> PyFelt: p = self.p if isinstance(right, PyFelt): return PyFelt((self.value * right.value) % p, p) if isinstance(right, int): return PyFelt((self.value * right) % p, p) raise TypeError(f"Cannot multiply PyFelt and {type(right)}") def __rmul__(self, left: PyFelt | int) -> PyFelt: return self.__mul__(left) def __inv__(self) -> PyFelt: try: inv = pow(self.value, -1, self.p) except ValueError: raise ValueError(f"Cannot invert {self.value} modulo {self.p}") return PyFelt(inv, self.p) def __truediv__(self, right: PyFelt) -> PyFelt: assert isinstance(self, PyFelt) and isinstance( right, PyFelt ), f"Cannot divide {type(self)} by {type(right)}" return self * right.__inv__() def __pow__(self, exponent: int) -> PyFelt: return PyFelt(pow(self.value, exponent, self.p), self.p) def __eq__(self, other: object) -> bool: if isinstance(other, PyFelt): return self.value == other.value if isinstance(other, int): return self.value == other raise TypeError(f"Cannot compare PyFelt and {type(other)}") def __lt__(self, other: PyFelt | int) -> bool: if isinstance(other, PyFelt): return self.value < other.value if isinstance(other, int): return self.value < other raise TypeError(f"Cannot compare PyFelt and {type(other)}") def __le__(self, other: PyFelt | int) -> bool: if isinstance(other, PyFelt): return self.value <= other.value if isinstance(other, int): return self.value <= other raise TypeError(f"Cannot compare PyFelt and {type(other)}") def __gt__(self, other: PyFelt | int) -> bool: if isinstance(other, PyFelt): return self.value > other.value if isinstance(other, int): return self.value > other raise TypeError(f"Cannot compare PyFelt and {type(other)}") def __ge__(self, other: PyFelt | int) -> bool: if isinstance(other, PyFelt): return self.value >= other.value if isinstance(other, int): return self.value >= other raise TypeError(f"Cannot compare PyFelt and {type(other)}") def __rlt__(self, left: int) -> bool: return left < self.value def __rle__(self, left: int) -> bool: return left <= self.value def __rgt__(self, left: int) -> bool: return left > self.value def __rge__(self, left: int) -> bool: return left >= self.value def __ne__(self, other: object) -> bool: return not self.__eq__(other) def __radd__(self, left: PyFelt | int) -> PyFelt: return self.__add__(left) def __rsub__(self, left: PyFelt | int) -> PyFelt: return -self.__sub__(left) def __rtruediv__(self, left: PyFelt | int) -> PyFelt: return self.__inv__().__mul__(left) def is_quad_residue(self) -> bool: if self.value == 0: return True return legendre_symbol(self.value, self.p) == 1 def sqrt(self, min_root: bool = True) -> PyFelt: if not self.is_quad_residue(): raise ValueError("Cannot square root a non-quadratic residue") roots = sqrt_mod(self.value, self.p, all_roots=True) if min_root: return PyFelt(min(roots), self.p) else: return PyFelt(max(roots), self.p) @dataclass(slots=True) class Fp2: a0: PyFelt a1: PyFelt def __post_init__(self): assert self.a0.p == self.a1.p, "Fields must be the same" @property def p(self) -> int: return self.a0.p @property def value(self) -> tuple[int, int]: return self.a0.value, self.a1.value @staticmethod def random(p: int, max_value: int = None) -> Fp2: if max_value is None: max_value = p - 1 rnd1 = random.randint(0, max_value) rnd2 = random.randint(0, max_value) return Fp2( PyFelt(rnd1, p), PyFelt(rnd2, p), ) @staticmethod def one(p: int) -> Fp2: return Fp2(PyFelt(1, p), PyFelt(0, p)) @staticmethod def zero(p: int) -> Fp2: return Fp2(PyFelt(0, p), PyFelt(0, p)) def __repr__(self) -> str: return f"Fp2({self.a0}, {self.a1})" def __add__(self, other: Fp2) -> Fp2: if isinstance(other, Fp2): return Fp2(self.a0 + other.a0, self.a1 + other.a1) else: raise TypeError(f"Cannot add Fp2 and {type(other)}") def __eq__(self, other: object) -> bool: if isinstance(other, Fp2): return self.a0 == other.a0 and self.a1 == other.a1 and self.p == other.p else: raise TypeError(f"Cannot compare Fp2 and {type(other)}") def __neg__(self) -> Fp2: return Fp2(-self.a0, -self.a1) def __sub__(self, other: Fp2) -> Fp2: return self.__add__(-other) def __mul__(self, other: Fp2 | PyFelt | int) -> Fp2: if isinstance(other, PyFelt): assert other.p == self.a0.p, "Fields must be the same" return Fp2(self.a0 * other, self.a1 * other) elif isinstance(other, int): return Fp2(self.a0 * other, self.a1 * other) elif isinstance(other, Fp2): # (a0 + a1 * i) * (b0 + b1 * i) = a0 * b0 - a1 * b1 + (a0 * b1 + a1 * b0) * i return Fp2( self.a0 * other.a0 - self.a1 * other.a1, self.a0 * other.a1 + self.a1 * other.a0, ) else: raise TypeError(f"Cannot multiply Fp2 and {type(other)}") def __rmul__(self, other): return self.__mul__(other) def __truediv__(self, other): if isinstance(other, Fp2): return self * other.__inv__() elif isinstance(other, int): return self * pow(other, -1, self.p) return NotImplemented def __rtruediv__(self, other) -> Fp2: if isinstance(other, Fp2): return other * self.__inv__() elif isinstance(other, int): return other * self.__inv__() return NotImplemented def __inv__(self) -> Fp2: t0, t1 = (self.a0 * self.a0, self.a1 * self.a1) t0 = t0 + t1 t1 = pow(t0.value, -1, self.p) return Fp2(self.a0 * t1, -(self.a1 * t1)) def __pow__(self, p: int) -> Fp2: """ Compute x**p in F_p^2 using square-and-multiply algorithm. Args: p: The exponent, a non-negative integer. Returns: x**p in F_p^2, represented similarly as x. """ assert isinstance(p, int) and p >= 0 # Handle the easy cases. if p == 0: # x**0 = 1, where 1 is the multiplicative identity in F_p^2. return Fp2(PyFelt(1, self.p), PyFelt(0, self.p)) elif p == 1: # x**1 = x. return self # Start the computation. result = self.one( self.p ) # Initialize result as the multiplicative identity in F_p^2. temp = self # Initialize temp as self. # Loop through each bit of the exponent p. for bit in reversed(bin(p)[2:]): # [2:] to strip the "0b" prefix. if bit == "1": result = result * temp temp = temp * temp return result def norm(self) -> PyFelt: return self.a0 * self.a0 + self.a1 * self.a1 def legendre(self) -> int: norm = self.norm() return legendre_symbol(norm.value, self.p) def is_quad_residue(self) -> bool: return self.legendre() == 1 def sqrt(self) -> Fp2: if not self.is_quad_residue(): raise ValueError("Cannot square root a non-quadratic residue") assert self.p % 4 == 3, "p must be 3 mod 4 to use this sqrt" min_one = Fp2(PyFelt(-1 % self.p, self.p), PyFelt(0, self.p)) a = self a1 = a ** ((self.p - 3) // 4) alpha = a1 * a1 * a a0 = alpha**self.p * alpha if a0 == min_one: return ValueError("Cannot square root a non-quadratic residue") x0 = a1 * a if alpha == min_one: i = Fp2(PyFelt(0, self.p), PyFelt(1, self.p)) x = i * x0 else: b = (Fp2.one(self.p) + alpha) ** ((self.p - 1) // 2) x = b * x0 # Return the root as is, without forcing a specific sign return x def lexicographically_largest(self) -> bool: """Check if this Fp2 element is lexicographically largest.""" if self.a1.value > (self.p - 1) // 2: return True if self.a1.value < (self.p - 1) // 2: return False return self.a0.value > (self.p - 1) // 2 @dataclass(slots=True) class BaseField: p: int def __call__(self, integer: int) -> PyFelt: return PyFelt(integer % self.p, self.p) def zero(self) -> PyFelt: return PyFelt(0, self.p) def one(self) -> PyFelt: return PyFelt(1, self.p) def random(self, max_value: int = None) -> PyFelt: if max_value is None: max_value = self.p - 1 return PyFelt(random.randint(0, max_value), self.p) @property def type(self) -> type[PyFelt]: return PyFelt @dataclass(slots=True) class BaseFp2Field: p: int def __call__(self, a: tuple[int, int] | int) -> Fp2: if isinstance(a, tuple): a0, a1 = a else: a0, a1 = a, 0 return Fp2(PyFelt(a0 % self.p, self.p), PyFelt(a1 % self.p, self.p)) def zero(self) -> Fp2: return Fp2(PyFelt(0, self.p), PyFelt(0, self.p)) def one(self) -> Fp2: return Fp2(PyFelt(1, self.p), PyFelt(0, self.p)) def random(self) -> Fp2: return Fp2.random(self.p) @property def type(self) -> type[Fp2]: return Fp2 @dataclass(slots=True) class ModuloCircuitElement: """ Represents an element within a modulo circuit with its associated offset. Attributes: emulated_felt (PyFelt): The emulated field element in the modulo circuit offset (int): The offset in the values segment within the modulo circuit where the element is stored. """ emulated_felt: PyFelt offset: int __repr__ = lambda self: f"ModuloCircuitElement({hex(self.value)}, {self.offset})" @property def value(self) -> int: return self.emulated_felt.value @property def p(self) -> int: return self.emulated_felt.p @property def felt(self) -> PyFelt: return self.emulated_felt class Polynomial(Generic[T]): """ Represents a polynomial with coefficients in a finite field. Parameters : coefficients (list[PyFelt | ModuloCircuitElement]): A list of coefficients for the polynomial. Magic Methods Summary: - __init__: Initializes a polynomial with a list of coefficients. - __add__: (Polynomial + Polynomial) Adds two polynomials. - __neg__: (-Polynomial) Negates the polynomial. - __sub__: (Polynomial - Polynomial) Subtracts one polynomial from another. - __mul__: (Polynomial * PyFelt|Polynomial) Multiplies the polynomial by either a field element or another polynomial. - __truediv__: (Polynomial / Polynomial) Divides one polynomial by another, asserting no remainder. - __floordiv__: (Polynomial // Polynomial) Performs floor division on two polynomials. - __mod__: (Polynomial % Polynomial) Finds the remainder of polynomial division. - __divmod__: Divides one polynomial by another, returning both quotient and remainder. - __eq__: (Polynomial == Polynomial) Checks if two polynomials are equal. - __neq__: (Polynomial != Polynomial) Checks if two polynomials are not equal. - __str__: Returns a string representation of the polynomial. - __pow__: (Polynomial ** int) Raises the polynomial to a power. """ __slots__ = [ "coefficients", "coeff_type", "p", "field", "zero_field", "zero_field_value", ] def __init__(self, coefficients: list[T], raw_init: tuple = None): if raw_init is not None: self._raw_init(coefficients, *raw_init) else: coeffs_types = {type(c) for c in coefficients} if coeffs_types == {PyFelt}: self._initialize(coefficients, PyFelt, BaseField) elif coeffs_types == {ModuloCircuitElement}: self._initialize([c.felt for c in coefficients], PyFelt, BaseField) elif coeffs_types == {Fp2}: self._initialize(coefficients, Fp2, BaseFp2Field) else: raise TypeError( f"All elements in the list must be of the same type, either ModuloCircuitElement, PyFelt or Fp2., got {coeffs_types}" ) def _raw_init( self, coefficients: list[T], coeff_type: type[T], p: int, field, zero_field, zero_field_value, ) -> None: self.coefficients = coefficients self.coeff_type = coeff_type self.p = p self.field = field self.zero_field = zero_field self.zero_field_value = zero_field_value def _initialize( self, coefficients: list[T], coeff_type: type[T], field_class: type ): self.coefficients: list[T] = coefficients self.coeff_type = coeff_type self.p = coefficients[0].p self.field = field_class(self.p) self.zero_field = self.field.zero() self.zero_field_value = self.zero_field.value def __repr__(self) -> str: if self.coeff_type == PyFelt: return f"Polynomial({[x.value for x in self.get_coeffs()]})" elif self.coeff_type == Fp2: return f"Polynomial({[x for x in self.get_coeffs()]})" def print_as_sage_poly(self, var_name: str = "z", as_hex: bool = False) -> str: """ Prints the polynomial ready to be used in SageMath. """ if self.is_zero(): return "" coeffs = self.get_coeffs() string = "" zero = self.zero_field for i, coeff in enumerate(coeffs[::-1]): if coeff == zero: continue else: if self.coeff_type == PyFelt: coeff_str = hex(coeff.value) if as_hex else str(coeff.value) elif self.coeff_type == Fp2: coeff_str = f"({coeff.a1.value} * i + {coeff.a0.value})" if i == len(coeffs) - 1: string += f"{coeff_str}" elif i == len(coeffs) - 2: string += f"{coeff_str}*{var_name} + " else: string += f"{coeff_str}*{var_name}^{len(coeffs) - 1 - i} + " return string def __getitem__(self, i: int) -> PyFelt: try: return self.coefficients[i] except IndexError: return self.zero_field def __len__(self) -> int: return len(self.coefficients) def degree(self) -> int: for i, coeff in enumerate(self.coefficients[::-1]): if coeff.value != self.zero_field_value: return len(self.coefficients) - 1 - i return -1 def get_coeffs(self) -> list[T]: coeffs = self.coefficients[:] while len(coeffs) > 0 and coeffs[-1].value == self.zero_field_value: coeffs.pop() if coeffs == []: return [self.zero_field] return coeffs def get_value_coeffs(self) -> list[int]: if self.coeff_type == PyFelt: return [c.value for c in self.get_coeffs()] elif self.coeff_type == Fp2: raise NotImplementedError("Fp2 not implemented") def differentiate(self) -> "Polynomial": """ Differentiates the polynomial with respect to x. Returns: Polynomial: The derivative of the polynomial. """ if len(self.coefficients) <= 1: return Polynomial([self.zero_field]) derivative_coeffs = [ self.coefficients[i] * i for i in range(1, len(self.coefficients)) ] return Polynomial( derivative_coeffs, raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) def __add__(self, other: Polynomial) -> Polynomial: if self.coeff_type != other.coeff_type: raise TypeError( f"Cannot add Polynomial of type {self.coeff_type} and {other.coeff_type} \n self: {self} \n other: {other}" ) ns, no = len(self.coefficients), len(other.coefficients) if ns >= no: coeffs = self.coefficients[:] for i in range(no): coeffs[i] += other.coefficients[i] else: coeffs = other.coefficients[:] for i in range(ns): coeffs[i] += self.coefficients[i] return Polynomial( coeffs, raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) def __neg__(self) -> "Polynomial": return Polynomial( [-c for c in self.coefficients], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) def __sub__(self, other: Polynomial) -> Polynomial: if self.coeff_type != other.coeff_type: raise TypeError( f"Cannot add Polynomial of type {self.coeff_type} and {other.coeff_type} \n self: {self} \n other: {other}" ) ns, no = len(self.coefficients), len(other.coefficients) coeffs = self.coefficients[:] if ns >= no: for i in range(no): coeffs[i] -= other.coefficients[i] else: for i in range(ns): coeffs[i] -= other.coefficients[i] for i in range(ns, no): coeffs.append(-other.coefficients[i]) return Polynomial( coeffs, raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) def __mul__( self, other: "Polynomial" | PyFelt | ModuloCircuitElement ) -> "Polynomial": if isinstance(other, (PyFelt, ModuloCircuitElement)): return Polynomial( [c * other.felt for c in self.coefficients], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) elif isinstance(other, Fp2): return Polynomial( [c * other for c in self.coefficients], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) if self.coeff_type != other.coeff_type: raise TypeError( f"Cannot multiply polynomial of type {self.coeff_type} by polynomial of type {other.type}" ) len_self = len(self.coefficients) len_other = len(other.coefficients) buf = [self.zero_field] * (len_self + len_other - 1) for i in range(len_self): if self.coefficients[i].value == self.zero_field_value: continue # optimization for sparse polynomials for j in range(len_other): buf[i + j] += self.coefficients[i] * other.coefficients[j] while len(buf) > 0 and buf[-1].value == self.zero_field_value: buf.pop() if buf == []: return Polynomial( [self.zero_field], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) return Polynomial( buf, raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) def __rmul__( self, other: "Polynomial" | PyFelt | ModuloCircuitElement ) -> "Polynomial": return self.__mul__(other) def __truediv__(self, other): quo, rem = Polynomial.__divmod__(self, other) assert ( rem.is_zero() ), "cannot perform polynomial division because remainder is not zero" return quo def __floordiv__(self, other: "Polynomial") -> "Polynomial": quo, _ = Polynomial.__divmod__(self, other) return quo def __mod__(self, other: "Polynomial") -> "Polynomial": _, rem = Polynomial.__divmod__(self, other) return rem def __divmod__(self, denominator: "Polynomial") -> tuple[Polynomial, Polynomial]: den_deg = denominator.degree() if den_deg == -1: raise ValueError("Cannot divide by zero polynomial") num_deg = self.degree() if num_deg < den_deg: return (Polynomial.zero(self.p, self.coeff_type), self) remainder = Polynomial( self.coefficients[:], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) quotient_coefficients = [self.zero_field] * (num_deg - den_deg + 1) denom_lead_inv = denominator[den_deg].__inv__() rem_deg = num_deg while rem_deg >= den_deg: shift = rem_deg - den_deg coefficient = remainder[rem_deg] * denom_lead_inv quotient_coefficients[shift] = coefficient subtractee = ( Polynomial( [self.zero_field] * shift + [coefficient], raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) * denominator ) remainder = remainder - subtractee rem_deg = remainder.degree() quotient = Polynomial( quotient_coefficients, raw_init=( self.coeff_type, self.p, self.field, self.zero_field, self.zero_field_value, ), ) return quotient, remainder def __eq__(self, other: object) -> bool: if not isinstance(other, Polynomial): raise TypeError(f"Cannot compare Polynomial with {type(other)}") if self.degree() != other.degree(): return False if self.degree() == -1: return True return self.get_coeffs() == other.get_coeffs() def __neq__(self, other: object) -> bool: return not self.__eq__(other) def leading_coefficient(self) -> PyFelt: return self.coefficients[self.degree()] def is_zero(self) -> bool: if not self.coefficients: return True for c in self.coefficients: if c != self.zero_field: return False return True @staticmethod def zero(p: int, type: type[T] = PyFelt) -> "Polynomial[T]": if type == PyFelt: return Polynomial([PyFelt(0, p)]) elif type == Fp2: return Polynomial([Fp2.zero(p)]) else: raise ValueError(f"Unknown type {type}") @staticmethod def one(p: int, type: type[T] = PyFelt) -> "Polynomial[T]": if type == PyFelt: return Polynomial([PyFelt(1, p)]) elif type == Fp2: return Polynomial([Fp2.one(p)]) else: raise ValueError(f"Unknown type {type}") def evaluate(self, point: PyFelt | Fp2) -> PyFelt | Fp2: assert isinstance( point, self.coeff_type ), f"point type must match polynomial type {self.coeff_type}" xi = self.field.one() value = self.zero_field for c in self.coefficients: value = value + c * xi xi = xi * point return value def __pow__(self, exponent: int) -> "Polynomial": if exponent == 0: return Polynomial([self.field.one()]) acc = Polynomial([self.field.one()]) for i in reversed(range(len(bin(exponent)[2:]))): acc = acc * acc if (1 << i) & exponent != 0: acc = acc * self return acc def pow(self, exponent: int, modulo_poly: "Polynomial") -> "Polynomial": if self.coeff_type != modulo_poly.coeff_type: raise TypeError( f"Cannot pow polynomial of type {self.coeff_type} modulo a polynomial of type {modulo_poly.coeff_type}" ) one = Polynomial.one(self.p, self.coeff_type) if exponent == 0: return one acc = one for i in reversed(range(len(bin(exponent)[2:]))): acc = acc * acc % modulo_poly if (1 << i) & exponent != 0: acc = (acc * self) % modulo_poly return acc % modulo_poly def inv(self, modulo_poly: "Polynomial") -> "Polynomial": """ Inverts a polynomial modulo another polynomial over a finite field. Parameters: modulo_poly Polynomial: The polynomial to invert modulo. Returns: Polynomial: The inverted polynomial. """ if self.is_zero(): raise ValueError("Cannot invert zero polynomial") inv, _, gcd = Polynomial.xgcd(self, modulo_poly) assert ( gcd.degree() == 0 and gcd.coefficients[0] == 1 ), f"Polynomial {self} is not invertible modulo {modulo_poly}" return inv @staticmethod def xgcd(x: Polynomial, y: Polynomial) -> tuple[Polynomial, Polynomial, Polynomial]: """ Extended Euclidean Algorithm for polynomials. This method computes the extended greatest common divisor (GCD) of two polynomials x and y. It returns a tuple of three elements: (a, b, g) such that a * x + b * y = g, where g is the greatest common divisor of x and y. This is particularly useful in contexts like computational algebra or number theory where the coefficients of the polynomials are in a field. Parameters: x (Polynomial): The first polynomial. y (Polynomial): The second polynomial. Returns: tuple: A tuple (a, b, g) where: a (Polynomial): A polynomial such that a * x + b * y = g. b (Polynomial): A polynomial such that a * x + b * y = g. g (Polynomial): The greatest common divisor of x and y. """ one = Polynomial.one(x.p, x.coeff_type) zero = Polynomial.zero(x.p, x.coeff_type) old_r, r = (x, y) old_s, s = (one, zero) old_t, t = (zero, one) while not r.is_zero(): quotient = old_r // r old_r, r = (r, old_r - quotient * r) old_s, s = (s, old_s - quotient * s) old_t, t = (t, old_t - quotient * t) lcinv = old_r.leading_coefficient().__inv__() # a, b, g raw_init = (x.coeff_type, x.p, x.field, x.zero_field, x.zero_field_value) return ( Polynomial([c * lcinv for c in old_s.coefficients], raw_init=raw_init), Polynomial([c * lcinv for c in old_t.coefficients], raw_init=raw_init), Polynomial([c * lcinv for c in old_r.coefficients], raw_init=raw_init), ) @staticmethod def lagrange_interpolation( p: int, domain: list[PyFelt], values: list[PyFelt] ) -> Polynomial: """ Performs Lagrange interpolation on a set of points. Parameters: p (int): The prime modulus for the field. domain (list[PyFelt]): The domain of the interpolation. values (list[PyFelt]): The values corresponding to the domain. Returns: Polynomial: The interpolated polynomial. """ assert len(domain) == len( values ), "number of elements in domain does not match number of values -- cannot interpolate" assert len(domain) > 0, "cannot interpolate between zero points" field = BaseField(p) X = Polynomial([field.zero(), field.one()]) acc = Polynomial([field.zero()]) for i in range(len(domain)): prod = Polynomial([values[i]]) for j in range(len(domain)): if j == i: continue prod = ( prod * (X - Polynomial([domain[j]])) * Polynomial([(domain[i] - domain[j]).__inv__()]) ) acc = acc + prod return acc def sparsity(self) -> list[int]: return get_sparsity(self.coefficients) def get_sparsity(X: list[PyFelt | ModuloCircuitElement]) -> list[int]: """ Determines the sparsity of polynomial coefficients. This function evaluates a list of polynomial coefficients (`X`) and categorizes each based on its value: - 2: The coefficient is 1, indicating a direct representation of a polynomial power. - 1: The coefficient is non-zero but not 1, indicating a contributing non-zero coefficient. - 0: The coefficient is 0, indicating no contribution to the polynomial. Parameters: - X (list[PyFelt | ModuloCircuitElement]): Coefficients to evaluate. Returns: - list[int]: Sparsity categories for each coefficient in `X`. """ return [2 if x.value == 1 else 1 if x.value != 0 else 0 for x in X] @dataclass(slots=True) class RationalFunction(Generic[T]): numerator: Polynomial[T] denominator: Polynomial[T] @property def field(self) -> BaseField | BaseFp2Field: return self.numerator.field @classmethod def zero(cls, p: int, type: type[T] = PyFelt) -> "RationalFunction[T]": return cls(Polynomial.zero(p, type), Polynomial.one(p, type)) @classmethod def one(cls, p: int, type: type[T] = PyFelt) -> "RationalFunction[T]": return cls(Polynomial.one(p, type), Polynomial.one(p, type)) def simplify(self) -> "RationalFunction": _, _, gcd = Polynomial.xgcd(self.numerator, self.denominator) num_simplified = self.numerator // gcd den_simplified = self.denominator // gcd return RationalFunction( num_simplified * self.denominator.leading_coefficient().__inv__(), den_simplified * den_simplified.leading_coefficient().__inv__(), ) def __add__(self, other: "RationalFunction") -> "RationalFunction": return RationalFunction( self.numerator * other.denominator + other.numerator * self.denominator, self.denominator * other.denominator, ).simplify() def __mul__(self, other: int | PyFelt) -> "RationalFunction": if isinstance(other, int): other = self.field(other) elif isinstance(other, PyFelt): other = self.field(other.value) else: raise TypeError(f"Cannot multiply RationalFunction with {type(other)}") return RationalFunction(self.numerator * other, self.denominator) def evaluate(self, x: PyFelt | Fp2) -> PyFelt | Fp2: return self.numerator.evaluate(x) / self.denominator.evaluate(x) def degrees_infos(self) -> dict[str, int]: return { "numerator": self.numerator.degree(), "denominator": self.denominator.degree(), } @dataclass(slots=True) class FunctionFelt(Generic[T]): # f = a(x) + yb(x) a: RationalFunction[T] b: RationalFunction[T] @property def field(self) -> BaseField | BaseFp2Field: return self.a.numerator.field @classmethod def zero(cls, p: int, type: type[T] = PyFelt) -> "FunctionFelt[T]": return cls(RationalFunction.zero(p, type), RationalFunction.zero(p, type)) @classmethod def one(cls, p: int, type: type[T] = PyFelt) -> "FunctionFelt[T]": return cls(RationalFunction.one(p, type), RationalFunction.zero(p, type)) def simplify(self) -> "FunctionFelt": return FunctionFelt(self.a.simplify(), self.b.simplify()) def __add__(self, other: "FunctionFelt") -> "FunctionFelt": return FunctionFelt(self.a + other.a, self.b + other.b) def __mul__(self, other: PyFelt | int) -> "FunctionFelt": return FunctionFelt(self.a * other, self.b * other) def __rmul__(self, other: PyFelt | int) -> "FunctionFelt": return self.__mul__(other) def evaluate(self, x: PyFelt | Fp2, y: PyFelt | Fp2) -> PyFelt | Fp2: assert ( isinstance(x, self.field.type) and x.p == self.field.p ), f"x type must match field {self.field.type}, got {type(x)} over {hex(x.p)}" assert ( isinstance(y, self.field.type) and y.p == self.field.p ), f"y type must match field {self.field.type}, got {type(y)} over {hex(y.p)}" return self.a.evaluate(x) + y * self.b.evaluate(x) def degrees_infos(self) -> dict[str, dict[str, int]]: return { "a": self.a.degrees_infos(), "b": self.b.degrees_infos(), } def validate_degrees(self, msm_size: int, batched: bool = True) -> bool: degrees = self.degrees_infos() if batched: extra = 2 else: extra = 0 assert degrees["a"]["numerator"] <= msm_size + 1 + extra assert degrees["a"]["denominator"] <= msm_size + 2 + extra assert degrees["b"]["numerator"] <= msm_size + 2 + extra assert degrees["b"]["denominator"] <= msm_size + 5 + extra return True def print_as_sage_poly(self, var: str = "x", as_hex: bool = False) -> str: return f"(({self.b.numerator.print_as_sage_poly(var, as_hex)}) / ({self.b.denominator.print_as_sage_poly(var, as_hex)}) * y + ({self.a.numerator.print_as_sage_poly(var, as_hex)} / ({self.a.denominator.print_as_sage_poly(var, as_hex)})" ================================================ FILE: hydra/garaga/curves.py ================================================ from dataclasses import dataclass from enum import Enum from typing import TypeAlias from garaga.algebra import BaseField, BaseFp2Field, Fp2, Polynomial, PyFelt from garaga.hints.io import bigint_split, int_to_u256, int_to_u384 N_LIMBS = 4 BASE = 2**96 STARK = 0x800000000000011000000000000000000000000000000000000000000000001 BN254_ID = 0 BLS12_381_ID = 1 SECP256K1_ID = 2 SECP256R1_ID = 3 ED25519_ID = 4 GRUMPKIN_ID = 5 class ProofSystem(Enum): Groth16 = "groth16" # Works for Generic Groth16 (BN254/BLS12-381), Risc0 Groth16 (BN254), and SP1 Groth16 (BN254) UltraKeccakZKHonk = "ultra_keccak_zk_honk" # UltraStarknetZKHonk = "ultra_starknet_zk_honk" # Disabled. @property def supported_curves(self) -> set[int]: if self == ProofSystem.Groth16: return {BN254_ID, BLS12_381_ID} if self == ProofSystem.UltraKeccakHonk: return {BN254_ID} if self == ProofSystem.UltraStarknetHonk: return {BN254_ID} if self == ProofSystem.UltraKeccakZKHonk: return {BN254_ID} if self == ProofSystem.UltraStarknetZKHonk: return {BN254_ID} return set() class CurveID(Enum): BN254 = 0 BLS12_381 = 1 SECP256K1 = 2 SECP256R1 = 3 ED25519 = 4 GRUMPKIN = 5 @staticmethod def from_str(s: str) -> "CurveID": return CurveID(CurveID.find_value_in_string(s)) @property def p(self) -> int: return CURVES[self.value].p @staticmethod def find_value_in_string(s: str) -> int | None: """ Find the value of the curve ID in the string. """ if s.lower() == "bn128": return CurveID.BN254.value if s.lower() == "bls12381": return CurveID.BLS12_381.value for member in CurveID: if s.lower() in member.name.lower() or member.name.lower() in s.lower(): return member.value return None @staticmethod def get_proving_system_curve( curve_id: int, proving_system: ProofSystem ) -> "CurveID": """ Get the curve ID for proving systems. Only curves supported by the given proving system are valid. """ if curve_id not in CurveID._value2member_map_: raise ValueError( f"Invalid curve ID: {curve_id}. Supported curves are: {', '.join([f'{c.name} (ID: {c.value})' for c in CurveID])}" ) if curve_id not in proving_system.supported_curves: supported_curves = ", ".join( f"{CurveID(c).name} (ID: {c})" for c in proving_system.supported_curves ) raise ValueError( f"Invalid curve ID for {proving_system.name}. Supported curves are: {supported_curves}" ) return CurveID(curve_id) @dataclass class SWUParams: A: int B: int Z: int @dataclass(slots=True, frozen=True) class WeierstrassCurve: cairo_zero_namespace_name: str id: int p: int n: int # order h: int # cofactor a: int # y^2 = x^3 + ax + b b: int fp_generator: int # A generator of the field of the curve. To verify it, use is_generator function. Gx: int # x-coordinate of the generator point Gy: int # y-coordinate of the generator point swu_params: SWUParams eigen_value: int | None # Endomorphism eigenvalue third_root_of_unity: int | None # Endomorphism image def is_endomorphism_available(self) -> bool: return self.eigen_value is not None and self.third_root_of_unity is not None def to_cairo_zero(self) -> str: code = f"namespace {self.cairo_zero_namespace_name} {{\n" code += f"const CURVE_ID = {self.id};\n" p = bigint_split(self.p, N_LIMBS, BASE) n = bigint_split(self.n, N_LIMBS, BASE) a = bigint_split(self.a, N_LIMBS, BASE) b = bigint_split(self.b, N_LIMBS, BASE) g = bigint_split(self.fp_generator, N_LIMBS, BASE) min_one = bigint_split(-1 % self.p, N_LIMBS, BASE) for i, limb in enumerate(p): code += f"const P{i} = {hex(limb)};\n" for i, limb in enumerate(n): code += f"const N{i} = {hex(limb)};\n" for i, limb in enumerate(a): code += f"const A{i} = {hex(limb)};\n" for i, limb in enumerate(b): code += f"const B{i} = {hex(limb)};\n" for i, limb in enumerate(g): code += f"const G{i} = {hex(limb)};\n" for i, limb in enumerate(min_one): code += f"const MIN_ONE_D{i} = {hex(limb)};\n" code += "}\n" return code def to_cairo_one(self) -> str: code = f"const {self.cairo_zero_namespace_name.upper()}:Curve = \n" code += "Curve {\n" code += f"p:{int_to_u384(self.p)},\n" code += f"n:{int_to_u256(self.n)},\n" code += f"a:{int_to_u384(self.a)},\n" code += f"b:{int_to_u384(self.b)},\n" code += f"g:{int_to_u384(self.fp_generator)},\n" code += f"min_one:{int_to_u384(-1%self.p)},\n" code += f"G: {G1Point(self.Gx, self.Gy, CurveID(self.id)).to_cairo_1()},\n" code += "};\n" return code @dataclass(slots=True, frozen=True) class TwistedEdwardsCurve(WeierstrassCurve): """ Twisted Edwards curve is a curve of the form ax^2 + y^2 = 1 + dx^2y^2. Equivalent to a Weierstrass curve of the form y^2 = x^3 + ax + b. Automatic conversion of parameters is done in the constructor. """ a_twisted: int # Twisted Edwards curve parameter d_twisted: int # Twisted Edwards curve parameter def __init__( self, cairo_zero_namespace_name: str, id: int, p: int, n: int, h: int, d_twisted: int, a_twisted: int, fp_generator: int, Gx: int, Gy: int, swu_params: SWUParams, eigen_value: int | None = None, third_root_of_unity: int | None = None, ): assert a_twisted != 0 and d_twisted != 0 and a_twisted != d_twisted # Set attributes object.__setattr__(self, "d_twisted", d_twisted) object.__setattr__(self, "a_twisted", a_twisted) object.__setattr__(self, "p", p) object.__setattr__(self, "swu_params", swu_params) object.__setattr__(self, "eigen_value", eigen_value) object.__setattr__(self, "third_root_of_unity", third_root_of_unity) # Calculate Weierstrass parameters a = ( -1 * pow(48, -1, p) * (a_twisted**2 + 14 * a_twisted * d_twisted + d_twisted**2) % p ) b = ( pow(864, -1, p) * (a_twisted + d_twisted) * (-(a_twisted**2) + 34 * a_twisted * d_twisted - d_twisted**2) % p ) WeierstrassCurve.__init__( self, cairo_zero_namespace_name, id, p, n, h, a, b, fp_generator, *(self.to_weierstrass(Gx, Gy)), swu_params, eigen_value, third_root_of_unity, ) def to_weierstrass(self, x_twisted, y_twisted): a = self.a_twisted d = self.d_twisted return ( (5 * a + a * y_twisted - 5 * d * y_twisted - d) * pow(12 - 12 * y_twisted, -1, self.p) % self.p, (a + a * y_twisted - d * y_twisted - d) * pow(4 * x_twisted - 4 * x_twisted * y_twisted, -1, self.p) % self.p, ) def to_twistededwards(self, x_weirstrass: int, y_weirstrass: int): a = self.a_twisted d = self.d_twisted y = ( (5 * a - 12 * x_weirstrass - d) * pow(-12 * x_weirstrass - a + 5 * d, -1, self.p) % self.p ) x = ( (a + a * y - d * y - d) * pow(4 * y_weirstrass - 4 * y_weirstrass * y, -1, self.p) % self.p ) return (x, y) @dataclass(slots=True, frozen=True) class PairingCurve(WeierstrassCurve): x: int # curve x parameter irreducible_polys: dict[int, list[int]] nr_a0: int # E2 non residue nr_a1: int b20: int b21: int # E2: b is (b20, b21) loop_counter: list[int] line_function_sparsity: list[ int ] # 0: ==0, 1: !=0, 2: ==1.. L(x) = Σ(sparsity[i] * coeff[i] * x^i ) final_exp_cofactor: int G2x: tuple[int, int] G2y: tuple[int, int] def NAF(x): if x == 0: return [] z = 0 if x % 2 == 0 else 2 - (x % 4) return NAF((x - z) // 2) + [z] def jy00(value: int) -> list[int]: """ This is a minimum-Hamming-Weight left-to-right recoding. It outputs signed {-1, 0, 1} bits from MSB to LSB with minimal Hamming Weight to minimize operations in Miller Loops and vartime scalar multiplications - Optimal Left-to-Right Binary Signed-Digit Recoding Joye, Yen, 2000 https://marcjoye.github.io/papers/JY00sd2r.pdf """ def bit(value, index): return (value >> index) & 1 bi, bi1, ri, ri1, ri2 = 0, 0, 0, 0, 0 bits = value.bit_length() recoded = [] for i in range(bits, -1, -1): if i == bits: ri1, ri2 = bit(value, bits - 1), bit(value, bits - 2) else: bi, ri = bi1, ri1 ri1, ri2 = ri2, bit(value, i - 2) if i >= 2 else 0 bi1 = (bi + ri1 + ri2) >> 1 recoded.append(-2 * bi + ri + bi1) return recoded GARAGA_RS_SUPPORTED_CURVES = {BN254_ID, BLS12_381_ID} Curve: TypeAlias = WeierstrassCurve CURVES: dict[int, WeierstrassCurve] = { BN254_ID: PairingCurve( cairo_zero_namespace_name="bn", id=BN254_ID, p=0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD47, n=0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001, x=0x44E992B44A6909F1, h=1, irreducible_polys={ 6: [82, 0, 0, -18, 0, 0, 1], 12: [82, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1], }, nr_a0=9, nr_a1=1, a=0, b=3, b20=0x2B149D40CEB8AAAE81BE18991BE06AC3B5B4C5E559DBEFA33267E6DC24A138E5, b21=0x9713B03AF0FED4CD2CAFADEED8FDF4A74FA084E52D1852E4A2BD0685C315D2, loop_counter=jy00(6 * 0x44E992B44A6909F1 + 2)[::-1], line_function_sparsity=[ 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, ], final_exp_cofactor=1469306990098747947464455738335385361638823152381947992820, # cofactor = 2 * x0 * (6 * x0**2 + 3 * x0 + 1) fp_generator=3, Gx=0x1, Gy=0x2, G2x=( 0x1800DEEF121F1E76426A00665E5C4479674322D4F75EDADD46DEBD5CD992F6ED, 0x198E9393920D483A7260BFB731FB5D25F1AA493335A9E71297E485B7AEF312C2, ), G2y=( 0x12C85EA5DB8C6DEB4AAB71808DCB408FE3D1E7690C43D37B4CE6CC0166FA7DAA, 0x90689D0585FF075EC9E99AD690C3395BC4B313370B38EF355ACDADCD122975B, ), swu_params=None, eigen_value=0xB3C4D79D41A917585BFC41088D8DAAA78B17EA66B99C90DD, third_root_of_unity=0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFE, ), BLS12_381_ID: PairingCurve( cairo_zero_namespace_name="bls", id=BLS12_381_ID, p=0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAB, n=0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001, x=-0xD201000000010000, h=0x396C8C005555E1568C00AAAB0000AAAB, irreducible_polys={ 6: [2, 0, 0, -2, 0, 0, 1], 12: [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1], }, nr_a0=1, nr_a1=1, a=0, b=4, b20=4, b21=4, loop_counter=[int(x) for x in bin(0xD201000000010000)[2:][::-1]], line_function_sparsity=[ 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, ], final_exp_cofactor=3, fp_generator=3, Gx=0x17F1D3A73197D7942695638C4FA9AC0FC3688C4F9774B905A14E3A3F171BAC586C55E83FF97A1AEFFB3AF00ADB22C6BB, Gy=0x08B3F481E3AAA0F1A09E30ED741D8AE4FCF5E095D5D00AF600DB18CB2C04B3EDD03CC744A2888AE40CAA232946C5E7E1, G2x=( 0x24AA2B2F08F0A91260805272DC51051C6E47AD4FA403B02B4510B647AE3D1770BAC0326A805BBEFD48056C8C121BDB8, 0x13E02B6052719F607DACD3A088274F65596BD0D09920B61AB5DA61BBDC7F5049334CF11213945D57E5AC7D055D042B7E, ), G2y=( 0xCE5D527727D6E118CC9CDC6DA2E351AADFD9BAA8CBDD3A76D429A695160D12C923AC9CC3BACA289E193548608B82801, 0x606C4A02EA734CC32ACD2B02BC28B99CB3E287E85A763AF267492AB572E99AB3F370D275CEC1DA1AAA9075FF05F79BE, ), swu_params=SWUParams( A=0x144698A3B8E9433D693A02C96D4982B0EA985383EE66A8D8E8981AEFD881AC98936F8DA0E0F97F5CF428082D584C1D, B=0x12E2908D11688030018B12E8753EEE3B2016C1F0F24F4070A0B9C14FCEF35EF55A23215A316CEAA5D1CC48E98E172BE0, Z=11, ), eigen_value=0xAC45A4010001A40200000000FFFFFFFF, third_root_of_unity=0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAC, ), SECP256K1_ID: WeierstrassCurve( cairo_zero_namespace_name="secp256k1", id=SECP256K1_ID, p=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F, n=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141, h=1, a=0, b=7, fp_generator=3, Gx=0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, Gy=0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8, swu_params=None, eigen_value=0x5363AD4CC05C30E0A5261C028812645A122E22EA20816678DF02967C1B23BD72, third_root_of_unity=0x7AE96A2B657C07106E64479EAC3434E99CF0497512F58995C1396C28719501EE, ), SECP256R1_ID: WeierstrassCurve( cairo_zero_namespace_name="secp256r1", id=SECP256R1_ID, p=0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF, n=0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551, h=1, a=0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC, b=0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B, fp_generator=6, Gx=0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296, Gy=0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5, swu_params=None, eigen_value=None, third_root_of_unity=None, ), ED25519_ID: TwistedEdwardsCurve( cairo_zero_namespace_name="ED25519", # See https://neuromancer.sk/std/other/Ed25519 id=ED25519_ID, p=0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED, n=0x1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED, h=8, d_twisted=0x52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3, a_twisted=0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC, fp_generator=6, Gx=0x216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A, Gy=0x6666666666666666666666666666666666666666666666666666666666666658, swu_params=None, eigen_value=None, third_root_of_unity=None, ), GRUMPKIN_ID: WeierstrassCurve( cairo_zero_namespace_name="grumpkin", id=GRUMPKIN_ID, p=0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001, n=0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD47, h=1, a=0, b=-17 % 0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001, fp_generator=5, Gx=0x1, Gy=0x2CF135E7506A45D632D270D45F1181294833FC48D823F272C, swu_params=None, eigen_value=None, third_root_of_unity=None, ), } def is_generator(g: int, p: int) -> bool: """ Checks if a given integer g is a generator of the multiplicative group of integers modulo p. Parameters: g (int): The integer to check. p (int): The prime number defining the finite field Fp. Returns: bool: True if g is a generator, False otherwise. Raises: ValueError: If p is not a prime number. Detailed Explanation: 1. The order of an element g in the multiplicative group Fp* must divide p-1. - The multiplicative group Fp* consists of all non-zero elements of the finite field Fp. - The group has p-1 elements because there are p-1 non-zero elements in Fp. - By Lagrange's theorem, the order of any element in a finite group must divide the order of the group. - Therefore, the order of any element g in Fp* must divide p-1. 2. If g is a generator, its order must be exactly p-1. 3. To verify that g has order p-1, we need to ensure that g does not have any smaller order that divides p-1. 4. The prime factorization of p-1 gives us all the possible divisors of p-1. 5. By checking g^((p-1)/q) for each prime factor q of p-1, we ensure that g does not have an order that is a proper divisor of p-1. 6. If g passes all these checks, it must have the full order p-1, making it a generator. 7. This method is efficient because it reduces the problem to checking a few exponentiations rather than testing all possible orders. Example: - Let p = 7, then p-1 = 6. - The prime factors of 6 are 2 and 3. - To check if g is a generator, we test: - g^(6/2) = g^3 - g^(6/3) = g^2 - If neither g^3 ≡ 1 (mod 7) nor g^2 ≡ 1 (mod 7), then g is a generator. - This ensures that g has the full order 6, covering all elements of F7*. """ import sympy # Ensure that p is a prime number if not sympy.isprime(p): raise ValueError("p must be a prime number.") # Calculate p - 1, which is the order of the multiplicative group of integers modulo p p_minus_1 = p - 1 # Factorize p - 1 to get its prime factors and their exponents # This is necessary because we will use these factors to test if g is a generator factors = sympy.factorint(p_minus_1) # Check if g is a generator for q in factors.keys(): # For each prime factor q of p - 1, check if g^((p-1)/q) ≡ 1 (mod p) # If g^((p-1)/q) ≡ 1 (mod p), then g is not a generator because it does not have the full order p-1 # This is based on the fact that if g is a generator, its order must be exactly p-1 # If g^((p-1)/q) ≡ 1 (mod p), it means the order of g divides (p-1)/q, which is less than p-1 if pow(g, p_minus_1 // q, p) == 1: return False # If g^((p-1)/q) ≠ 1 (mod p) for all prime factors q, then g is a generator # This means g has the full order p-1 and can generate all elements of the multiplicative group return True def get_base_field( curve_id: int | CurveID, field_type: type[PyFelt] | type[Fp2] = PyFelt ) -> BaseField | BaseFp2Field: """ Returns the base field for a given elliptic curve. Parameters: curve_id (int | CurveID): The ID of the elliptic curve. field_type (PyFelt | Fp2): The type of the field (default is PyFelt). Returns: BaseField | BaseFp2Field: The base field corresponding to the curve and field type. Raises: ValueError: If the field_type is invalid. """ if isinstance(curve_id, CurveID): curve_id = curve_id.value curve = CURVES[curve_id] if field_type == PyFelt: return BaseField(curve.p) elif field_type == Fp2: assert isinstance(curve, PairingCurve) return BaseFp2Field(curve.p) else: raise ValueError(f"Invalid field type: {field_type}. Expected PyFelt or Fp2.") def get_irreducible_poly(curve_id: int | CurveID, extension_degree: int) -> Polynomial: if isinstance(curve_id, CurveID): curve_id = curve_id.value curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) field = get_base_field(curve_id) return Polynomial( coefficients=[field(x) for x in curve.irreducible_polys[extension_degree]] ) def replace_consecutive_zeros(lst): result = [] i = 0 while i < len(lst): if i < len(lst) - 1 and lst[i] == 0 and lst[i + 1] == 0: result.append(3) # Replace consecutive zeros with 3 i += 2 elif lst[i] == -1: result.append(2) # Replace -1 with 2 i += 1 else: result.append(lst[i]) i += 1 return result def recode_naf_bits(lst): result = [] i = 0 while i < len(lst): if i < len(lst) - 1 and lst[i] == 0 and (lst[i + 1] == 1 or lst[i + 1] == -1): # "01" or "0-1" if lst[i + 1] == 1: result.append(3) # Replace "01" with 3 else: result.append(4) # Replace "0-1" with 4 i += 2 elif i < len(lst) - 1 and (lst[i] == 1 or lst[i] == -1) and lst[i + 1] == 0: # "10" or "-10" if lst[i] == 1: result.append(1) # Replace 10 with 6 else: result.append(2) # Replace -10 with 7 i += 2 elif i < len(lst) - 1 and lst[i] == 0 and lst[i + 1] == 0: result.append(0) # Replace consecutive zeros with 0 i += 2 else: raise ValueError(f"Unexpected bit sequence at index {i}") return result if __name__ == "__main__": from garaga.points import G1Point r = recode_naf_bits(jy00(6 * 0x44E992B44A6909F1 + 2)[2:]) print(r, len(r)) from garaga.hints.io import int_to_u384 # bls = [int(x) for x in bin(0xD201000000010000)[2:]][2:] # recode_naf_bits(bls) def print_nbits_and_nG_glv_fake_glv(): for curve_id in CURVES: curve: WeierstrassCurve = CURVES[curve_id] if curve.is_endomorphism_available(): nbits = curve.n.bit_length() // 4 + 9 print( f"Curve {curve_id}: {nbits}, {G1Point.get_nG(CurveID(curve_id), 2 ** (nbits - 1)).to_cairo_1()}" ) print_nbits_and_nG_glv_fake_glv() def print_min_one_order(): for curve_id in CURVES: curve: WeierstrassCurve = CURVES[curve_id] print(f"Curve {curve_id}: min_one_order: {int_to_u384(-1 % curve.n)}") print_min_one_order() print() def print_third_root_of_unity(): for curve_id in CURVES: curve: WeierstrassCurve = CURVES[curve_id] if curve.is_endomorphism_available(): print( f"Curve {curve_id}: third_root_of_unity: {int_to_u384(curve.third_root_of_unity)}" ) print_third_root_of_unity() ================================================ FILE: hydra/garaga/drand/client.py ================================================ import binascii import functools import hashlib import random from dataclasses import dataclass from enum import Enum from typing import List, Optional, Union import requests from requests.exceptions import RequestException from garaga.curves import CurveID, Fp2, get_base_field from garaga.hints import io from garaga.points import G1Point, G2Point class DrandNetwork(Enum): default = "8990e7a9aaed2ffed73dbd7092123d6f289930540d7651336225dc172e51b2ce" quicknet = "52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971" def digest_func(round_number: int) -> bytes: assert isinstance(round_number, int) assert 0 <= round_number < 2**64 h = hashlib.sha256() h.update(round_number.to_bytes(8, byteorder="big")) return h.digest() @dataclass class NetworkInfo: public_key: Union[G1Point, G2Point] period: int genesis_time: int hash: str group_hash: str scheme_id: str beacon_id: Optional[str] = None @dataclass class RandomnessBeacon: round_number: int randomness: int signature: str previous_signature: Optional[str] = None @property def signature_point(self) -> G1Point | G2Point: return deserialize_bls_point(bytes.fromhex(self.signature)) BASE_URLS = [ "https://drand.cloudflare.com", "https://api.drand.sh", "https://api2.drand.sh", "https://api3.drand.sh", ] def make_request(endpoint: str) -> requests.Response: # Create a copy and shuffle instead of random.choice for better distribution base_urls = BASE_URLS.copy() random.shuffle(base_urls) last_error = None for url in base_urls: try: response = requests.get(f"{url}{endpoint}", timeout=5) # Add timeout response.raise_for_status() return response except Exception as e: print(f"Request to {url} failed: {str(e)}") last_error = e continue raise RequestException(f"All URLs failed. Last error: {last_error}") def deserialize_bls_point(s_string: bytes) -> Union[G1Point, G2Point]: m_byte = s_string[0] & 0xE0 if m_byte in (0x20, 0x60, 0xE0): raise ValueError("Invalid encoding") C_bit = (m_byte & 0x80) >> 7 # Compression bit I_bit = (m_byte & 0x40) >> 6 # Infinity bit S_bit = (m_byte & 0x20) >> 5 # Sign bit s_string = bytes([s_string[0] & 0x1F]) + s_string[1:] if I_bit == 1: if any(b != 0 for b in s_string): raise ValueError("Invalid encoding for point at infinity") return ( G1Point.infinity(CurveID.BLS12_381) if len(s_string) in (48, 96) else G2Point.infinity(CurveID.BLS12_381) ) if C_bit == 0: if len(s_string) == 96: # G1 point (uncompressed) x = int.from_bytes(s_string[:48], "big") y = int.from_bytes(s_string[48:], "big") return G1Point(x, y, CurveID.BLS12_381) elif len(s_string) == 192: # G2 point (uncompressed) x0 = int.from_bytes(s_string[:48], "big") x1 = int.from_bytes(s_string[48:96], "big") y0 = int.from_bytes(s_string[96:144], "big") y1 = int.from_bytes(s_string[144:], "big") return G2Point((x0, x1), (y0, y1), CurveID.BLS12_381) else: raise ValueError(f"Invalid length for uncompressed point: {len(s_string)}") else: # C_bit == 1 x = int.from_bytes(s_string, "big") if len(s_string) == 48: # G1 point (compressed) field = get_base_field(CurveID.BLS12_381) y2 = field(x**3 + 4) if S_bit == 1: y = y2.sqrt(min_root=False) else: y = y2.sqrt(min_root=True) return G1Point(x, y.value, CurveID.BLS12_381) elif len(s_string) == 96: # G2 point (compressed) field = get_base_field(CurveID.BLS12_381, Fp2) x = field((x & ((1 << 384) - 1), x >> 384)) y2 = x**3 + field((4, 4)) y = y2.sqrt() if S_bit == 1: # Choose largest root # print("choose largest") if not y.lexicographically_largest(): # print("root was not largest, negating") y = -y else: # Choose smallest root # print("choose smallest") if y.lexicographically_largest(): # print("root was largest, negating") y = -y return G2Point( (x.a0.value, x.a1.value), (y.a0.value, y.a1.value), CurveID.BLS12_381, ) else: raise ValueError(f"Invalid length for compressed point: {len(s_string)}") def get_chains() -> List[str]: response = make_request("/chains") all_chains = response.json() # only keep chains present in DrandNetwork enum chains = [ chain for chain in all_chains if chain in [network.value for network in DrandNetwork] ] return chains def get_chain_info(chain_hash: str) -> NetworkInfo: response = make_request(f"/{chain_hash}/info") data = response.json() # Parse the public key public_key_hex = data["public_key"] public_key_bytes = binascii.unhexlify(public_key_hex) try: public_key = deserialize_bls_point(public_key_bytes) except Exception as e: public_key = G2Point.infinity(CurveID.BLS12_381) return NetworkInfo( public_key=public_key, period=data["period"], genesis_time=data["genesis_time"], hash=data["hash"], group_hash=data["groupHash"], scheme_id=data["schemeID"], beacon_id=data.get("metadata", {}).get("beaconID"), ) def get_latest_randomness(chain_hash: str) -> RandomnessBeacon: response = make_request(f"/{chain_hash}/public/latest") return _parse_randomness_beacon(response.json()) def get_randomness(chain_hash: str, round_number: int) -> RandomnessBeacon: response = make_request(f"/{chain_hash}/public/{round_number}") return _parse_randomness_beacon(response.json()) def _parse_randomness_beacon(data: dict) -> RandomnessBeacon: return RandomnessBeacon( round_number=io.to_int(data["round"]), randomness=int(data["randomness"], 16), signature=data["signature"], previous_signature=data.get("previous_signature"), ) @functools.lru_cache(maxsize=None) def print_all_chain_info() -> dict[DrandNetwork, NetworkInfo]: # Try multiple times to get chains max_retries = 3 for attempt in range(max_retries): try: chains = get_chains() if not chains: raise ValueError("No chains returned") print(f"Found {len(chains)} chains: {chains}") print("-" * 40) chain_infos = {} expected_networks = set(DrandNetwork) for chain_hash in chains: try: info = get_chain_info(chain_hash) try: network = DrandNetwork(chain_hash) chain_infos[network] = info expected_networks.remove(network) print(f"Chain: {chain_hash}") print(f" Public Key: {info.public_key}") print(f" Period: {info.period} seconds") print(f" Genesis Time: {info.genesis_time}") print(f" Hash: {info.hash}") print(f" Group Hash: {info.group_hash}") print(f" Scheme ID: {info.scheme_id}") if info.beacon_id: print(f" Beacon ID: {info.beacon_id}") print("-" * 40) except ValueError: print(f"Unknown chain hash: {chain_hash}") continue except Exception as e: print(f"Error fetching info for chain {chain_hash}: {str(e)}") continue # If we found all expected networks, return the results if not expected_networks: return chain_infos print(f"Missing networks: {[n.name for n in expected_networks]}") except Exception as e: print(f"Attempt {attempt + 1}/{max_retries} failed: {str(e)}") if attempt < max_retries - 1: print("Retrying...") continue raise RuntimeError( f"Failed to get complete chain info after {max_retries} attempts" ) # Example usage if __name__ == "__main__": chain_infos = print_all_chain_info() from garaga.modulo_circuit_structs import StructArray from garaga.signature import hash_to_curve # latest_randomness = get_latest_randomness(chain_infos[DrandNetwork.default].hash) # print("Latest randomness:", latest_randomness) network = DrandNetwork.quicknet chain = chain_infos[network] print(chain.public_key) print(-chain.public_key) round = get_randomness(chain.hash, 1000) print("Randomness for round 1000:", round) sha256 = hashlib.sha256() sha256.update(bytes.fromhex(round.signature)) print("randomness", sha256.hexdigest()) print("random beacon", hex(round.randomness)) msg_point = hash_to_curve( digest_func(round.round_number), CurveID.BLS12_381, "sha256" ) print("message", msg_point) from garaga.modulo_circuit_structs import G2Line, StructArray from garaga.points import G1G2Pair from garaga.precompiled_circuits.multi_miller_loop import precompute_lines print( "pairing", G1G2Pair.pair( [ G1G2Pair( p=round.signature_point, q=G2Point.get_nG(CurveID.BLS12_381, 1) ), G1G2Pair(p=msg_point, q=-chain.public_key), ], curve_id=CurveID.BLS12_381, ).value_coeffs, ) lines = precompute_lines([G2Point.get_nG(CurveID.BLS12_381, 1), -chain.public_key]) precomputed_lines = StructArray( name="lines", elmts=[ G2Line(name=f"line{i}", elmts=lines[i : i + 4]) for i in range(0, len(lines), 4) ], ) def generate_precomputed_lines_code(precomputed_lines: StructArray) -> str: return f"pub const precomputed_lines: [G2Line; {len(precomputed_lines)//4}] = {precomputed_lines.serialize(raw=True, const=True)};" # print(generate_precomputed_lines_code(precomputed_lines)) ================================================ FILE: hydra/garaga/drand/tlock.py ================================================ import hashlib import secrets from dataclasses import dataclass from typing import Optional from garaga.curves import CURVES, CurveID from garaga.drand.client import DrandNetwork, digest_func from garaga.hints import io from garaga.hints.tower_backup import E12 from garaga.points import G1G2Pair, G1Point, G2Point from garaga.signature import hash_to_curve @dataclass class CipherText: U: G2Point V: bytes W: bytes def __post_init__(self): assert len(self.V) == len(self.W) == 16 def serialize_to_cairo(self): code = f"""CipherText {{ U: {self.U.serialize_to_cairo(name="U", raw=True)}, V: [{', '.join(f'0x{b:02x}' for b in self.V)}], W: [{', '.join(f'0x{b:02x}' for b in self.W)}], }} """ return code def serialize_to_calldata(self) -> list[int]: cd = [] cd.extend(io.bigint_split(self.U.x[0])) cd.extend(io.bigint_split(self.U.x[1])) cd.extend(io.bigint_split(self.U.y[0])) cd.extend(io.bigint_split(self.U.y[1])) for b in self.V: cd.append(b) for b in self.W: cd.append(b) return cd def encrypt_for_round( drand_public_key: G2Point, round: int, message: bytes, debug: bool = False, fixed_sigma: Optional[bytes] = None, ) -> CipherText: assert len(message) == 16, f"Message should be 16 bytes: {len(message)}" assert ( fixed_sigma is None or len(fixed_sigma) == 16 ), f"Fixed sigma should be 16 bytes: {len(fixed_sigma)}" msg_at_round = digest_func(round) # print(f"msg_at_round list of ints: {list(msg_at_round)}") pt_at_round = hash_to_curve(msg_at_round, CurveID.BLS12_381) gid: E12 = G1G2Pair.pair([G1G2Pair(p=pt_at_round, q=drand_public_key)]) if debug: # Use a fixed sigma for debugging: sigma = b"0000000000000000" if fixed_sigma is None else fixed_sigma else: sigma: bytes = secrets.token_bytes(16) assert len(sigma) == 16 hasher = hashlib.sha256() hasher.update(b"IBE-H3") hasher.update(sigma) hasher.update(message) r = int.from_bytes(expand_message_drand(hasher.digest(), 32), "little") # print(f"r list of ints: {r}") r = r % CURVES[CurveID.BLS12_381.value].n # U = r * G2 U = G2Point.get_nG(CurveID.BLS12_381, r) # print(f"U: {U}") # V = sigma XOR H (rGid) rGid: E12 = gid**r # print(f"rGid: {rGid.value_coeffs}") rgid_serialized = rGid.serialize() # Print bytes as hex strings: # print(f"rGid hex : {rgid_serialized.hex()}") # print(f"rGid serialized: {list(rgid_serialized)} len: {len(rgid_serialized)}") rgid_hash = hashlib.sha256() rgid_hash.update(b"IBE-H2") rgid_hash.update(rgid_serialized) rgid_hash = rgid_hash.digest() # Take first 16 bytes only : rgid_hash = rgid_hash[:16] # print(f"rgid_hash hex: {rgid_hash.hex()}") V = bytes([a ^ b for a, b in zip(sigma, rgid_hash)]) # print(f"V hex: {V.hex()}") # 6. Compute W = M XOR H(sigma) W = bytes([a ^ b for a, b in zip(message, rgid_hash)]) sigma_hash = hashlib.sha256() sigma_hash.update(b"IBE-H4") sigma_hash.update(sigma) sigma_hash = sigma_hash.digest()[:16] # First 16 bytes only # print(f"sigma_hash hex: {sigma_hash.hex()}") W = bytes([a ^ b for a, b in zip(message, sigma_hash)]) # print(f"W hex: {W.hex()}") return CipherText(U, V, W) def decrypt_at_round(signature_at_round: G1Point, c: CipherText): # 1. Compute sigma = V XOR H2(e(rP,Sig)) r_gid: E12 = G1G2Pair.pair([G1G2Pair(p=signature_at_round, q=c.U)]) # for i, v in enumerate(r_gid.value_coeffs): # print(f"rgid_{i}: {io.int_to_u384(v, as_hex=False)}") r_gid_serialized = r_gid.serialize() rgid_hash = hashlib.sha256() pre_image = bytearray(b"IBE-H2") pre_image.extend(r_gid_serialized) rgid_hash.update(pre_image) # for i in range(0, len(pre_image), 4): # print(f"pre_image[{i}:{i+4}]: {pre_image[i:i+4].hex()}") rgid_hash = rgid_hash.digest() rgid_hash = rgid_hash[:16] # First 16 bytes only sigma = bytes([a ^ b for a, b in zip(c.V, rgid_hash)]) # print(f"sigma hex: {sigma.hex()}") # 2. Compute Msg = W XOR H4(sigma) sigma_hash = hashlib.sha256() sigma_hash.update(b"IBE-H4") sigma_hash.update(sigma) sigma_hash = sigma_hash.digest()[:16] # First 16 bytes only message = bytes([a ^ b for a, b in zip(c.W, sigma_hash)]) # print(f"message utf-8: {message.decode('utf-8')}") # 3. Check U = G^r rh = hashlib.sha256() rh.update(b"IBE-H3") rh.update(sigma) rh.update(message) rh = rh.digest() rh = expand_message_drand(rh, 32) r = int.from_bytes(rh, "little") r = r % CURVES[CurveID.BLS12_381.value].n U = G2Point.get_nG(CurveID.BLS12_381, r) assert U == c.U return message def expand_message_drand(msg: bytes, buf_size: int) -> bytes: BITS_TO_MASK_FOR_BLS12381 = 1 order = CURVES[CurveID.BLS12_381.value].n for i in range(1, 65536): # u16::MAX is 65535 # Hash iteratively: H(i || msg) h = hashlib.sha256() pre_image = bytearray(i.to_bytes(2, byteorder="little")) pre_image.extend(msg) h.update(pre_image) hash_result = bytearray(h.digest()) # Mask the first byte hash_result[0] >>= BITS_TO_MASK_FOR_BLS12381 reversed_hash = hash_result[::-1] scalar = int.from_bytes(reversed_hash, "little") % order if scalar != 0: return reversed_hash[:buf_size] raise ValueError( "You are insanely unlucky and should have been hit by a meteor before now" ) def write_cairo1_test(msg: bytes, round: int, network: DrandNetwork): chain_infos = print_all_chain_info() chain = chain_infos[network] master = chain.public_key ciphertext: CipherText = encrypt_for_round(master, round, msg, debug=True) signature_at_round = get_randomness(chain.hash, round).signature_point _ = decrypt_at_round(signature_at_round, ciphertext) comment_with_params_used = f""" // msg: {msg} // round: {round} // network: {network} """ code = f""" #[test] fn test_decrypt_at_round() {{ {comment_with_params_used} {signature_at_round.serialize_to_cairo(name="signature_at_round")} let ciph = {ciphertext.serialize_to_cairo()}; let msg_decrypted = decrypt_at_round(signature_at_round, ciph); assert(msg_decrypted.span() == [{', '.join(f'0x{b:02x}' for b in msg)}].span(), 'wrong msg'); }} """ return code if __name__ == "__main__": from garaga.drand.client import DrandNetwork, get_randomness, print_all_chain_info # chain_infos = print_all_chain_info() network = DrandNetwork.quicknet # chain = chain_infos[network] # master = chain.public_key round = 128 msg = b"hello\x00\x00\x00\x00\x00\x00\x00\x00abc" # ciph = encrypt_for_round(master, round, msg) # # print(f"CipherText: {ciph}") # # print(f"V : {list(ciph.V)}") # # print(f"W : {list(ciph.W)}") # chain = chain_infos[network] # beacon = get_randomness(chain.hash, round) # signature_at_round = beacon.signature_point # print(f"signature_at_round: {signature_at_round}") # msg_decrypted = decrypt_at_round(signature_at_round, ciph) # assert msg_decrypted == msg # print(f"msg utf-8: {msg.decode('utf-8')}") # print(f"msg_decrypted utf-8: {msg_decrypted.decode('utf-8')}") code = write_cairo1_test(msg, round, network) print(code) ================================================ FILE: hydra/garaga/extension_field_modulo_circuit.py ================================================ from dataclasses import dataclass, field from enum import Enum from garaga.algebra import Polynomial, PyFelt from garaga.curves import N_LIMBS, get_irreducible_poly from garaga.hints.extf_mul import ( nondeterministic_extension_field_div, nondeterministic_extension_field_mul_divmod, ) from garaga.modulo_circuit import BATCH_SIZE, ModuloCircuitElement, WriteOps from garaga.poseidon_transcript import CairoPoseidonTranscript from garaga.precompiled_circuits.fp2 import Fp2Circuits POSEIDON_BUILTIN_SIZE = 6 POSEIDON_OUTPUT_S1_INDEX = 4 # Represents the state of the accumulation of the equation # c_i * Π(Pi(z)) = c_i*Q_i*P + c_i*R_i inside the circuit. # Only store ci*Π(Pi(z)) (as Emulated Field Element) and ci*R_i (as Polynomial) @dataclass(slots=True) class EuclideanPolyAccumulator: lhs: ModuloCircuitElement R: list[ModuloCircuitElement] R_evaluated: ModuloCircuitElement class AccPolyInstructionType(Enum): MUL = "MUL" DIV = "DIV" SQUARE_TORUS = "SQUARE_TORUS" @dataclass(slots=True) class AccumulatePolyInstructions: Pis: list[list[list[ModuloCircuitElement]]] = field(default_factory=list) Qis: list[Polynomial] = field(default_factory=list) Ris: list[list[ModuloCircuitElement]] = field(default_factory=list) Ps_sparsities: list[None | list[list[int]]] = field(default_factory=list) r_sparsities: list[None | list[int]] = field(default_factory=list) types: list[AccPolyInstructionType] = field(default_factory=list) n: int = field(default=0) rlc_coeffs: list[ModuloCircuitElement] = field(default_factory=list) Pis_of_Z: list[ModuloCircuitElement] = field(default_factory=list) def append( self, type: AccPolyInstructionType, Pis: list[list[ModuloCircuitElement]], Q: Polynomial, R: list[ModuloCircuitElement], Ps_sparsities: None | list[list[int] | None] = None, r_sparsity: None | list[int] = None, ): if type != AccPolyInstructionType.MUL: assert len(Pis) == 2 self.types.append(type) self.Pis.append(Pis) self.Qis.append(Q) self.Ris.append(R) self.Ps_sparsities.append(Ps_sparsities) self.r_sparsities.append(r_sparsity) self.n += 1 class ExtensionFieldModuloCircuit(Fp2Circuits): def __init__( self, name: str, curve_id: int, extension_degree: int, init_hash: int = None, hash_input: bool = True, compilation_mode: int = 0, generic_circuit: bool = False, ) -> None: super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=generic_circuit, ) self.class_name = "ExtensionFieldModuloCircuit" self.extension_degree = extension_degree self.z_powers: list[ModuloCircuitElement] = [] self.acc: list[EuclideanPolyAccumulator] = [ self._init_accumulator(self.extension_degree), self._init_accumulator(self.extension_degree * 2), ] self.hash_input = hash_input self.transcript: CairoPoseidonTranscript = CairoPoseidonTranscript( init_hash=( int.from_bytes(self.name.encode(), "big") if init_hash is None else init_hash ) ) self.z_powers: list[ModuloCircuitElement] = [] self.ops_counter = { "Circuit": self.name, "EXTF_SQUARE": 0, "EXTF_MUL_DENSE": 0, # "EXTF_DIV": 0, } self.accumulate_poly_instructions: list[AccumulatePolyInstructions] = [ AccumulatePolyInstructions(), AccumulatePolyInstructions(), ] def _init_accumulator(self, extension_degree: int = None): extension_degree = extension_degree or self.extension_degree # Todo : Add compilation mode 1 support if self.compilation_mode == 1: return EuclideanPolyAccumulator( lhs=None, R=[None] * extension_degree, R_evaluated=None, ) else: return EuclideanPolyAccumulator( lhs=self.set_or_get_constant(0), R=[None] * extension_degree, R_evaluated=self.set_or_get_constant(0), ) @property def commitments(self): return [ self.values_segment.segment_stacks[WriteOps.COMMIT][offset].felt for offset in sorted(self.values_segment.segment_stacks[WriteOps.COMMIT]) ] @property def circuit_input(self): return [ self.values_segment.segment_stacks[WriteOps.INPUT][offset].felt for offset in sorted(self.values_segment.segment_stacks[WriteOps.INPUT]) ] def create_lines_z_powers(self, z: PyFelt, add_extf_power: bool = False): """ Create powers of z for the evaluation of lines functions and the irreducible polynomial if add_extf_power is True. """ powers = [z] # z^1 at index 0 if self.curve_id == 0: powers.append(self.square(z, "compute z^2")) # z^2 at index 1 powers.append(self.mul(powers[-1], z, "compute z^3")) # z^3 at index 2 powers.append(None) # No z^4 at index 3 powers.append(None) # No z^5 at index 4 powers.append(self.square(powers[2], "compute z^6")) # z^6 at index 5 powers.append(self.mul(powers[5], z, "compute z^7")) # z^7 at index 6 powers.append(None) # No z^8 at index 7 powers.append( self.mul(powers[6], powers[1], "compute z^9") ) # z^9 at index 8 if add_extf_power: # Need to add z^12 : # z^12 = z^9 * z^3 powers.append(None) # No z^10 at index 9 powers.append(None) # No z^11 at index 10 powers.append(self.mul(powers[8], powers[2], "compute z^12")) self.z_powers = powers elif self.curve_id == 1: # Need z^2, z^3, z^6, Z^8: powers.append(self.square(z, "compute z^2")) # z^2 at index 1 powers.append(self.mul(powers[-1], z, "compute z^3")) # z^3 at index 2 powers.append(None) # No z^4 at index 3 powers.append(None) # No z^5 at index 4 powers.append(self.square(powers[2], "compute z^6")) # z^6 at index 5 powers.append(None) # No z^7 at index 6 powers.append( self.mul(powers[5], powers[1], "compute z^8") ) # z^8 at index 7 self.z_powers = powers if add_extf_power: # Need to add z^12 : # z^12 = z^7 * z^5 powers.append(None) # No z^9 at index 8 powers.append(None) # No z^10 at index 9 powers.append(None) # No z^11 at index 10 powers.append(self.mul(powers[7], powers[4], "compute z^12")) else: raise ValueError(f"Invalid curve id: {self.curve_id}") def create_powers_of_Z( self, Z: PyFelt | ModuloCircuitElement, max_degree: int = None, ) -> list[ModuloCircuitElement]: if max_degree is None: max_degree = self.extension_degree if isinstance(Z, PyFelt): Z = self.write_cairo_native_felt(Z) elif isinstance(Z, int): Z = self.write_cairo_native_felt(self.field(Z)) elif isinstance(Z, ModuloCircuitElement): pass else: raise ValueError(f"Invalid type for Z: {type(Z)}") powers = [Z] for i in range(2, max_degree + 1): powers.append(self.mul(powers[-1], powers[0], comment=f"Compute z^{i}")) self.z_powers = powers return powers def eval_poly_in_precomputed_Z( self, X: list[ModuloCircuitElement], sparsity: list[int] = None, poly_name: str = None, ) -> ModuloCircuitElement: """ Evaluates a polynomial with coefficients `X` at precomputed powers of z. X(z) = X_0 + X_1 * z + X_2 * z^2 + ... + X_n * z^n If a `sparsity` list is provided, it is used to optimize the evaluation by skipping zero coefficients and applying special handling based on sparsity values: - A sparsity value of 0 indicates that the corresponding coefficient X_i is zero and should be skipped. - A sparsity value of 1 indicates that the corresponding coefficient X_i is non-zero and should be included in the evaluation. - A sparsity value of 2 indicates a special case where the term is directly a power of z, implying the coefficient X_i is 1 in this case. Parameters: - X: list[ModuloCircuitElement] - The coefficients of the polynomial to be evaluated. - sparsity: list[int] (optional) - A list indicating the sparsity of the polynomial. If None, the polynomial is treated as fully dense. Returns: - ModuloCircuitElement: The result of evaluating the polynomial at the precomputed powers of z. """ if poly_name is None: poly_name = "UnnamedPoly" if sparsity: first_non_zero_idx = next( (i for i, x in enumerate(sparsity) if x != 0), None ) if first_non_zero_idx == 0: match sparsity[0]: case 0: X_of_z = self.set_or_get_constant(0) case 1: X_of_z = X[0] case 2: X_of_z = self.set_or_get_constant(1) case _: raise ValueError(f"Invalid sparsity value: {sparsity[0]}") else: match sparsity[first_non_zero_idx]: case 0: X_of_z = self.set_or_get_constant(0) case 1: X_of_z = self.mul( X[first_non_zero_idx], self.z_powers[first_non_zero_idx - 1], comment=f"Eval sparse poly {poly_name} step coeff_{first_non_zero_idx} * z^{first_non_zero_idx}", ) case 2: X_of_z = self.z_powers[first_non_zero_idx - 1] case _: raise ValueError(f"Invalid sparsity value: {sparsity[0]}") for i in range(first_non_zero_idx + 1, len(X)): match sparsity[i]: case 1: term = self.mul( X[i], self.z_powers[i - 1], comment=f"Eval sparse poly {poly_name} step coeff_{i} * z^{i}", ) add_comment = ( f"Eval sparse poly {poly_name} step + coeff_{i} * z^{i}" ) case 2: term = self.z_powers[ i - 1 ] # In this case, sparsity[i] == 2 => X[i] = 1 add_comment = f"Eval sparse poly {poly_name} step + 1*z^{i}" case 0: continue case _: raise ValueError(f"Invalid sparsity value: {sparsity[i]}") X_of_z = self.add( X_of_z, term, comment=add_comment, ) else: X_of_z = self.eval_poly(X, self.z_powers, poly_name, "z") return X_of_z def extf_mul( self, Ps: list[list[ModuloCircuitElement]], extension_degree: int, Ps_sparsities: list[list[int] | None] = None, r_sparsity: list[int] = None, acc_index: int = 0, ) -> list[ModuloCircuitElement]: """ Multiply in the extension field X * Y mod irreducible_poly Commit to R and add an EvalPolyInstruction to the accumulator. """ assert ( extension_degree > 2 ), f"extension_degree={extension_degree} <= 2. Use self.mul or self.fp2_square instead." if Ps_sparsities is None: Ps_sparsities = [None] * len(Ps) assert len(Ps_sparsities) == len( Ps ), f"len(Ps_sparsities)={len(Ps_sparsities)} != len(Ps)={len(Ps)}" Q, R = nondeterministic_extension_field_mul_divmod( Ps, self.curve_id, extension_degree ) R = self.write_elements(R, WriteOps.COMMIT, r_sparsity) if not any(sparsity for sparsity in Ps_sparsities) or not r_sparsity: self.ops_counter["EXTF_MUL_DENSE"] += 1 self.accumulate_poly_instructions[acc_index].append( AccPolyInstructionType.MUL, Ps, Polynomial(Q), R, Ps_sparsities, r_sparsity, ) return R def extf_div( self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement], extension_degree: int, acc_index: int = 0, ) -> list[ModuloCircuitElement]: x_over_y = nondeterministic_extension_field_div( X, Y, self.curve_id, extension_degree ) x_over_y = self.write_elements(x_over_y, WriteOps.COMMIT) Q, _ = nondeterministic_extension_field_mul_divmod( [x_over_y, Y], self.curve_id, extension_degree ) # R should be X Q = Polynomial(Q) self.accumulate_poly_instructions[acc_index].append( AccPolyInstructionType.DIV, Pis=[x_over_y, Y], Q=Q, R=X ) return x_over_y def extf_inv( self, Y: list[ModuloCircuitElement], extension_degree: int, acc_index: int = 0, ) -> list[ModuloCircuitElement]: one = [ModuloCircuitElement(self.field(1), -1)] + [ ModuloCircuitElement(self.field(0), -1) ] * (extension_degree - 1) y_inv = nondeterministic_extension_field_div( one, Y, self.curve_id, extension_degree, ) y_inv = self.write_elements(y_inv, WriteOps.COMMIT) Q, _ = nondeterministic_extension_field_mul_divmod( [y_inv, Y], self.curve_id, extension_degree ) # R should be One. Passed at mocked modulo circuits element since fully determined by its sparsity. Q = Polynomial(Q) self.accumulate_poly_instructions[acc_index].append( AccPolyInstructionType.DIV, Pis=[y_inv, Y], Q=Q, R=one, r_sparsity=[2] + [0] * (extension_degree - 1), ) return y_inv def conjugate_e12d( self, e12d: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: assert len(e12d) == 12 return [ e12d[0], self.neg(e12d[1]), e12d[2], self.neg(e12d[3]), e12d[4], self.neg(e12d[5]), e12d[6], self.neg(e12d[7]), e12d[8], self.neg(e12d[9]), e12d[10], self.neg(e12d[11]), ] def update_LHS_state( self, s1: PyFelt, Ps: list[list[ModuloCircuitElement]], Ps_sparsities: list[list[int] | None] = None, acc_index: int = 0, ): # Sanity checks for sparsities Ps_sparsities = Ps_sparsities or [None] * len(Ps) assert len(Ps_sparsities) == len( Ps ), f"len(Ps_sparsities)={len(Ps_sparsities)} != len(Ps)={len(Ps)}" for i, sparsity in enumerate(Ps_sparsities): if sparsity: assert all( Ps[i][j].value == 0 for j in range(len(Ps[i])) if sparsity[j] == 0 ) assert all( Ps[i][j].value == 1 for j in range(len(Ps[i])) if sparsity[j] == 2 ) # Evaluate LHS = Π(Pi(z)) inside circuit. # i=0 LHS = self.eval_poly_in_precomputed_Z(Ps[0], Ps_sparsities[0]) LHS_current_eval = LHS # Keep P0(z) self.accumulate_poly_instructions[acc_index].Pis_of_Z.append([]) self.accumulate_poly_instructions[acc_index].Pis_of_Z[-1].append(LHS) for i in range(1, len(Ps)): if Ps[i - 1] == Ps[i]: # Consecutives elements are the same : retrieve previous evaluation. LHS_current_eval = self.accumulate_poly_instructions[ acc_index ].Pis_of_Z[-1][-1] # Todo : support smarter analysis to save a few muls else: LHS_current_eval = self.eval_poly_in_precomputed_Z( Ps[i], Ps_sparsities[i] ) # Keep Pi(z) self.accumulate_poly_instructions[acc_index].Pis_of_Z[-1].append( LHS_current_eval ) # Update LHS LHS = self.mul(LHS, LHS_current_eval) ci_XY_of_z = self.mul(s1, LHS, "ci_XY_of_z") LHS_acc = self.add(self.acc[acc_index].lhs, ci_XY_of_z, "LHS_acc") # Update LHS only. self.acc[acc_index] = EuclideanPolyAccumulator( lhs=LHS_acc, R=self.acc[acc_index].R, R_evaluated=self.acc[acc_index].R_evaluated, ) return def update_RHS_state( self, type: AccPolyInstructionType, s1: ModuloCircuitElement, R: list[ModuloCircuitElement], r_sparsity: list[int] = None, acc_index: int = 0, instruction_index: int = 0, ): # Find if R_of_z is already computed in the first Pi of the next instruction. # In this case we avoid accumulating R as polynomial and can use directly R_of_z with the correct s1. if type != AccPolyInstructionType.SQUARE_TORUS: if instruction_index + 1 < self.accumulate_poly_instructions[acc_index].n: if ( self.accumulate_poly_instructions[acc_index].Pis[ instruction_index + 1 ][0] == R ): already_computed_R_of_z = self.accumulate_poly_instructions[ acc_index ].Pis_of_Z[instruction_index + 1][0] # Update direclty Rhs_evaluted self.acc[acc_index] = EuclideanPolyAccumulator( lhs=self.acc[acc_index].lhs, R=self.acc[acc_index].R, R_evaluated=self.add( self.acc[acc_index].R_evaluated, self.mul(s1, already_computed_R_of_z), ), ) return # If not found, computes R_acc = R_acc + s1 * R as a Polynomial inside circuit if r_sparsity: if type != AccPolyInstructionType.SQUARE_TORUS: # Sanity check is already done in square_torus function. # If the instruction is SQUARE_TORUS, then R is fully determined by its sparsity, R(x) = x. # Actual R value here is the SQ TORUS result. # See square torus function for this edge case. assert all(R[i].value == 0 for i in range(len(R)) if r_sparsity[i] == 0) R_acc = [] for i, (r_acc, r) in enumerate(zip(self.acc[acc_index].R, R)): match r_sparsity[i]: case 1: R_acc.append(self.add(r_acc, self.mul(s1, r))) case 2: R_acc.append(self.add(r_acc, s1)) case _: R_acc.append(r_acc) else: # Computes R_acc = R_acc + s1 * R without sparsity info. R_acc = [ self.add(r_acc, self.mul(s1, r)) for r_acc, r in zip(self.acc[acc_index].R, R) ] # Update accumulator state self.acc[acc_index] = EuclideanPolyAccumulator( lhs=self.acc[acc_index].lhs, R=R_acc, R_evaluated=self.acc[acc_index].R_evaluated, ) return def finalize_circuit( self, extension_degree: int = None, ): ######### Flags ######### extension_degree = extension_degree or self.extension_degree double_extension = self.accumulate_poly_instructions[1].n > 0 acc_indexes = [0, 1] if double_extension else [0] ######################### ################ Get base rlc coefficient c0 ################ if self.hash_input: self.transcript.hash_limbs_multi(self.circuit_input) self.transcript.hash_limbs_multi(self.commitments) c0 = self.write_cairo_native_felt(self.field(self.transcript.s1)) ################################################################## ################ Compute Qs ################ Qs = [Polynomial([self.field.zero()]) for _ in range(2)] for acc_index in acc_indexes: self.accumulate_poly_instructions[acc_index].rlc_coeffs.append(c0) # Computes Q = Σ(ci * Qi) Qs[acc_index] = self.accumulate_poly_instructions[acc_index].Qis[0] * c0 for i in range(1, self.accumulate_poly_instructions[acc_index].n): self.accumulate_poly_instructions[acc_index].rlc_coeffs.append( self.mul( self.accumulate_poly_instructions[acc_index].rlc_coeffs[i - 1], c0, ) ) Qs[acc_index] += ( self.accumulate_poly_instructions[acc_index].Qis[i] * self.accumulate_poly_instructions[acc_index].rlc_coeffs[i] ) Qs[acc_index] = Qs[acc_index].get_coeffs() # Extend Q with zeros if needed to match the minimal expected degree. Qs[acc_index] = Qs[acc_index] + [self.field.zero()] * ( (acc_index + 1) * extension_degree - 1 - len(Qs[acc_index]) ) ################################################################## Q = [self.write_elements(Qs[0], WriteOps.COMMIT)] compute_z_up_to = max(max(len(Qs[0]), len(Qs[1])) - 1, extension_degree) self.big_q_len = len(Q[0]) self.transcript.hash_limbs_multi(Q[0]) if double_extension: Q.append(self.write_elements(Qs[1], WriteOps.COMMIT)) self.transcript.hash_limbs_multi(Q[1]) compute_z_up_to = max(compute_z_up_to, extension_degree * 2) self.big_q_len = self.big_q_len + len(Q[1]) z = self.transcript.continuable_hash self.create_powers_of_Z(z, max_degree=compute_z_up_to) for acc_index in acc_indexes: for i in range(self.accumulate_poly_instructions[acc_index].n): self.update_LHS_state( s1=self.accumulate_poly_instructions[acc_index].rlc_coeffs[i], Ps=self.accumulate_poly_instructions[acc_index].Pis[i], Ps_sparsities=self.accumulate_poly_instructions[ acc_index ].Ps_sparsities[i], acc_index=acc_index, ) for i in range(self.accumulate_poly_instructions[acc_index].n): self.update_RHS_state( type=self.accumulate_poly_instructions[acc_index].types[i], s1=self.accumulate_poly_instructions[acc_index].rlc_coeffs[i], R=self.accumulate_poly_instructions[acc_index].Ris[i], r_sparsity=self.accumulate_poly_instructions[ acc_index ].r_sparsities[i], acc_index=acc_index, instruction_index=i, ) Q_of_Z = self.eval_poly_in_precomputed_Z(Q[acc_index]) P, P_sparsity = self.write_sparse_constant_elements( get_irreducible_poly( self.curve_id, (acc_index + 1) * extension_degree ).get_coeffs(), ) P_of_z = self.eval_poly_in_precomputed_Z(P, P_sparsity) R = self.acc[acc_index].R R_of_Z = self.eval_poly_in_precomputed_Z(R) lhs = self.acc[acc_index].lhs rhs = self.add( self.mul(Q_of_Z, P_of_z), self.add(R_of_Z, self.acc[acc_index].R_evaluated), ) assert lhs.value == rhs.value, f"{lhs.value} != {rhs.value}, {acc_index}" if self.compilation_mode == 0: self.sub_and_assert( lhs, rhs, self.set_or_get_constant(self.field.zero()) ) else: eq_check = self.sub(rhs, lhs) self.extend_output([eq_check]) return True def summarize(self): add_count, mul_count, assert_eq_count = self.values_segment.summarize() summary = { "circuit": self.name, "MULMOD": mul_count, "ADDMOD": add_count, "ASSERT_EQ": assert_eq_count, "POSEIDON": ( self.transcript.permutations_count if self.transcript.permutations_count > 1 else 0 ), "RLC": self.accumulate_poly_instructions[0].n + self.accumulate_poly_instructions[1].n, } return summary def compile_circuit_cairo_zero( self, function_name: str = None, returns: dict[str] = { "felt*": [ "constants_ptr", "add_offsets_ptr", "mul_offsets_ptr", "output_offsets_ptr", ], "felt": [ "constants_ptr_len", "input_len", "commitments_len", "big_Q_len", "witnesses_len", "output_len", "continuous_output", "add_mod_n", "mul_mod_n", "n_assert_eq", "N_Euclidean_equations", "name", "curve_id", ], }, ) -> str: dw_arrays = self.values_segment.get_dw_lookups() name = function_name or self.values_segment.name function_name = f"get_{name}_circuit" code = f"func {function_name}()->(circuit:{self.class_name}*)" + "{" + "\n" code += "alloc_locals;\n" code += "let (__fp__, _) = get_fp_and_pc();\n" for dw_array_name in returns["felt*"]: code += f"let ({dw_array_name}:felt*) = get_label_location({dw_array_name}_loc);\n" code += f"let constants_ptr_len = {len(dw_arrays['constants_ptr'])};\n" code += f"let input_len = {len(self.values_segment.segment_stacks[WriteOps.INPUT])*N_LIMBS};\n" code += f"let commitments_len = {len(self.commitments)*N_LIMBS};\n" code += f"let witnesses_len = {len(self.values_segment.segment_stacks[WriteOps.WITNESS])*N_LIMBS};\n" code += f"let big_Q_len = {self.big_q_len*N_LIMBS};\n" code += f"let output_len = {len(self.output)*N_LIMBS};\n" continuous_output = self.continuous_output code += f"let continuous_output = {1 if continuous_output else 0};\n" code += f"let add_mod_n = {len(dw_arrays['add_offsets_ptr'])};\n" code += f"let mul_mod_n = {len(dw_arrays['mul_offsets_ptr'])};\n" code += ( f"let n_assert_eq = {len(self.values_segment.assert_eq_instructions)};\n" ) code += ( f"let N_Euclidean_equations = {len(dw_arrays['poseidon_indexes_ptr'])};\n" ) code += f"let name = '{self.name}';\n" code += f"let curve_id = {self.curve_id};\n" code += f"local circuit:ExtensionFieldModuloCircuit = ExtensionFieldModuloCircuit({', '.join(returns['felt*'])}, {', '.join(returns['felt'])});\n" code += "return (&circuit,);\n" for dw_array_name in returns["felt*"]: dw_values = dw_arrays[dw_array_name] code += f"\t {dw_array_name}_loc:\n" if dw_array_name == "constants_ptr": for bigint in dw_values: for limb in bigint: code += f"\t dw {limb};\n" code += "\n" elif dw_array_name in ["add_offsets_ptr", "mul_offsets_ptr"]: num_instructions = len(dw_values) instructions_needed = ( BATCH_SIZE - (num_instructions % BATCH_SIZE) ) % BATCH_SIZE for left, right, result, comment in dw_values: code += ( f"\t dw {left}; // {comment}\n" + f"\t dw {right};\n" + f"\t dw {result};\n" ) if instructions_needed > 0: first_triplet = dw_values[0] for _ in range(instructions_needed): code += ( f"\t dw {first_triplet[0]};\n" + f"\t dw {first_triplet[1]};\n" + f"\t dw {first_triplet[2]};\n" ) code += "\n" elif dw_array_name in ["output_offsets_ptr"]: if continuous_output: code += f"\t dw {dw_values[0]};\n" else: for val in dw_values: code += f"\t dw {val};\n" code += "\n" code += "}\n" return code if __name__ == "__main__": pass ================================================ FILE: hydra/garaga/hints/bls.py ================================================ from math import gcd from garaga.curves import CURVES, CurveID from garaga.hints.tower_backup import E12 """ The goal of this script is to provide aux witness for efficient proving that Miller loop outputs of BLS12-381 curve are λ residues. Co-factor h = 27 * p * h3 and λ = r * 3 * p^2. We know that when pairings are equal multi Miller loop output is always r-th residue, but it is λ residue only when it is a cube and p-th residue too. This happens with a very small probability (1/3*p), but both 27th and p-th roots of unity are in the subfields of Fp12, Fp3 and Fp respectively. Thus we can simply clear their contribution and not affect he soundness of the method. Note that gcd(27*p, h3) = 1, therefore we do the following: i := inverse_mod(h3, 27*p) s := -i % 27*p Then given the Miller loop output x, computing w = (x^h3)^s gives exactly the inverse of 27*p-th root of unity contribution in x. By computing x_sh = w * x we are left with an element that is of order exactly h3. Since gcd(h1, λ) = 1 computing λ root of x_sh can be simply done by just raising x_sh^e where e = inverse_mod(h3, λ) """ # Bls x = CURVES[CurveID.BLS12_381.value].x k = 12 r = x**4 - x**2 + 1 q = ((x - 1) ** 2) // 3 * r + x h = (q**k - 1) // r lam = -x + q m = lam // r p = 5044125407647214251 h3 = h // (27 * p) e = pow(lam, -1, h3) s = (-1 * pow(h3, -1, p * 27)) % (p * 27) assert h % (27 * p) == 0 assert m == 3 * p**2 assert gcd(3, h3) == 1 assert gcd(p**2, h3) == 1 assert gcd(3, h3) == 1 assert gcd(p, h3) == 1 assert gcd(p, 27 * h3) == 1 assert gcd(27, p * h3) == 1 ONE = E12.one(curve_id=1) assert (q**3 - 1) % 27 == 0 def get_root_and_scaling_factor_bls(mlo: E12) -> tuple[E12, E12]: """ Takes a miller loop output and returns root, shift such that root**lam = shift * mlo, if and only if mlo**h == 1. """ x = mlo**h3 shift = x**s root = (shift * mlo) ** e return root, shift ================================================ FILE: hydra/garaga/hints/ecip.py ================================================ from __future__ import annotations import functools from dataclasses import dataclass from garaga import garaga_rs from garaga.algebra import Fp2, FunctionFelt, Polynomial, PyFelt, RationalFunction, T from garaga.curves import CURVES, CurveID, get_base_field from garaga.hints.neg_3 import ( construct_digit_vectors, neg_3_base_le, positive_negative_multiplicities, ) from garaga.points import G1Point, G2Point from garaga.poseidon_transcript import hades_permutation def get_field_type_from_ec_point(P: G1Point | G2Point) -> type[T]: """ Maps an elliptic curve point to the type of the field it belongs to. G1Point -> PyFelt G2Point -> Fp2 """ if isinstance(P, G1Point): return PyFelt elif isinstance(P, G2Point): return Fp2 else: raise ValueError(f"Invalid point type {type(P)}") def get_ec_group_class_from_ec_point(P: G1Point | G2Point) -> type[G1Point | G2Point]: """ Maps an elliptic curve point to the class of the elliptic curve group it belongs to. G1Point -> G1Point G2Point -> G2Point """ if isinstance(P, G1Point): return G1Point elif isinstance(P, G2Point): return G2Point else: raise ValueError(f"Invalid point type {type(P)}") def derive_ec_point_from_X( x: PyFelt | int | Fp2, curve_id: CurveID ) -> tuple[PyFelt, PyFelt, list[PyFelt]] | tuple[Fp2, Fp2, list[Fp2]]: """ From a "random" x coordinate (in practice obtained via the Cairo Poseidon252 hash), finds via a "try-and-increment" algorithm a point on the curve for a given curveID. Works for curves over base field ("PyFelt") or degree 2 extension field ("Fp2") Returns : - x (PyFelt or Fp2) - x coordinate of the obtained point after the try-and-increment - y (PyFelt or Fp2) - y coordinate of the obtained point after the try-and-increment - g_rhs_roots (list of PyFelt of Fp2). A list of square roots over the given field. At each attempt, if rhs(x) = x^3 + ax + b is not a quad residue (ie: the point is not on the curve), x is updated by hashing it with the attempt : new_x = poseidon(x, attempt) Since in a finite field, if z is not a quad residue, g*z is a quad residue (alternatively), at each attempt, the square root of g*x is stored in the g*rhs_roots array. This is used to verify the existence of the square roots in Cairo. See the derive_ec_point_from_X cairo function in ec_ops.cairo. """ field = get_base_field(curve_id.value) if isinstance(x, int): x = field(x) def rhs_compute(x: PyFelt | Fp2) -> PyFelt | Fp2: """ Compute the right hand side of the Weirstrass equation. rhs(x) = x^3 + ax + b """ if isinstance(x, Fp2): return ( x**3 + x * field(CURVES[curve_id.value].a) + Fp2( field(CURVES[curve_id.value].b20), field(CURVES[curve_id.value].b21) ) ) else: return ( x**3 + field(CURVES[curve_id.value].a) * x + field(CURVES[curve_id.value].b) ) if isinstance(x, Fp2): g = Fp2( field(CURVES[curve_id.value].nr_a0), field(CURVES[curve_id.value].nr_a1), ) else: g = field(CURVES[curve_id.value].fp_generator) rhs = rhs_compute(x) g_rhs_roots = [] attempt = 0 while not rhs.is_quad_residue(): g_rhs = rhs * g g_rhs_roots.append(g_rhs.sqrt()) if isinstance(x, Fp2): _s0, _, _ = hades_permutation(x.a0.value, x.a1.value, 2) _x0, _x1, _ = hades_permutation(_s0, attempt, 2) x = Fp2(field(_x0), field(_x1)) else: _x, _, _ = hades_permutation(x.value, attempt, 2) x = field(_x) rhs = rhs_compute(x) attempt += 1 y = rhs.sqrt() assert y**2 == rhs return x, y, g_rhs_roots def zk_ecip_hint( Bs: list[G1Point] | list[G2Point], scalars: list[int], use_rust: bool = True ) -> tuple[G1Point | G2Point, FunctionFelt[T]]: """ Inputs: - Bs: list of points on the curve - scalars: list of scalars Returns: - Q: MSM of Bs by scalars contained in dss matrix - sum_dlog: sum of the logarithmic derivatives of the functions in Ds Use this to verify equation 3 in https://eprint.iacr.org/2022/596.pdf Partial Ref : https://gist.github.com/Liam-Eagen/666d0771f4968adccd6087465b8c5bd4 Full algo verifying it in the function verify_ecip below. """ assert len(Bs) == len(scalars) ec_group_class = get_ec_group_class_from_ec_point(Bs[0]) if ec_group_class == G1Point and use_rust: pts = [] c_id = Bs[0].curve_id for pt in Bs: pts.extend([pt.x, pt.y]) field_type = get_field_type_from_ec_point(Bs[0]) field = get_base_field(c_id.value, field_type) q, a_num, a_den, b_num, b_den = garaga_rs.zk_ecip_hint( pts, list(scalars), c_id.value ) a_num = [field(f) for f in a_num] if len(a_num) > 0 else [field.zero()] a_den = [field(f) for f in a_den] if len(a_den) > 0 else [field.one()] b_num = [field(f) for f in b_num] if len(b_num) > 0 else [field.zero()] b_den = [field(f) for f in b_den] if len(b_den) > 0 else [field.one()] Q = G1Point(q[0], q[1], c_id) sum_dlog = FunctionFelt( RationalFunction(Polynomial(a_num), Polynomial(a_den)), RationalFunction(Polynomial(b_num), Polynomial(b_den)), ) else: dss = construct_digit_vectors(scalars) Q, Ds = ecip_functions(Bs, dss) dlogs = [dlog(D) for D in Ds] sum_dlog = dlogs[0] field = get_base_field(Q.curve_id.value, PyFelt) for i in range(1, len(dlogs)): sum_dlog = sum_dlog + (-3) ** i * dlogs[i] return Q, sum_dlog def verify_ecip( Bs: list[G1Point] | list[G2Point], scalars: list[int], Q: G1Point | G2Point = None, sum_dlog: FunctionFelt[T] = None, A0: G1Point | G2Point = None, use_rust: bool = True, ) -> bool: """ Verifies the zk-ecip hint. If Q, sum_dlog are not provided from a previous computation of the zk_ecip_hint, it will compute them. If the random point A0 is not provided for verifying the hint, a random one will be sampled. """ # Prover : if Q is None or sum_dlog is None: Q, sum_dlog = zk_ecip_hint(Bs, scalars, use_rust) else: Q = Q sum_dlog = sum_dlog # Verifier : assert sum_dlog.validate_degrees(len(Bs)) epns = [ positive_negative_multiplicities(neg_3_base_le(scalar)) for scalar in scalars ] c_id = Q.curve_id.value ec_group_class = get_ec_group_class_from_ec_point(Q) field_type = get_field_type_from_ec_point(Q) field = get_base_field(Q.curve_id.value, field_type) # Verifier must derive a random point A0. # In non-interactive context, hash public inputs (Bs, scalars) and prover info (Q, sum_dlog) then map the resulting field element to a point. if A0 is None: A0 = ec_group_class.gen_random_point(Q.curve_id) else: A0 = A0 A2 = A0.scalar_mul(-2) xA0 = field(A0.x) yA0 = field(A0.y) xA2 = field(A2.x) yA2 = field(A2.y) mA0, bA0 = slope_intercept(A0, A0) mA0A2, _ = slope_intercept(A2, A0) coeff2 = (2 * yA2 * (xA0 - xA2)) / ( 3 * xA2**2 + field(CURVES[c_id].a) - 2 * mA0A2 * yA2 ) coeff0 = coeff2 + 2 * mA0A2 basis_sum = field.zero() for i, (P, (ep, en)) in enumerate(zip(Bs, epns)): if P.is_infinity(): # print("skipping infinity") continue if ep - en == 0: # print("skipping 0") continue basis_sum += eval_point_challenge_signed(P, xA0, mA0, bA0, ep, en) # print(f"rhs_acc {i}: {basis_sum.value}") if Q.is_infinity(): RHS = basis_sum else: RHS = eval_point_challenge(-Q, xA0, mA0, bA0, 1) + basis_sum LHS = coeff0 * sum_dlog.evaluate(xA0, yA0) - coeff2 * sum_dlog.evaluate(xA2, yA2) # Verifier must check that LHS = RHS. assert LHS == RHS, f"LHS: {LHS}, RHS: {RHS}" ######### assert Q == ec_group_class.msm( Bs, scalars ) # Sanity check. Not part of the verification. ########## return True def slope_intercept( P: G1Point | G2Point, Q: G1Point | G2Point ) -> tuple[PyFelt, PyFelt] | tuple[Fp2, Fp2]: """ Returns the slope and intercept of the line passing through points P and Q. y = mx + b """ field = get_base_field(P.curve_id.value, get_field_type_from_ec_point(P)) if P == Q: px, py = field(P.x), field(P.y) m = (3 * px**2 + field(CURVES[P.curve_id.value].a)) / (2 * py) b = py - m * px return (m, b) else: px, py = field(P.x), field(P.y) qx, qy = field(Q.x), field(Q.y) m = (py - qy) / (px - qx) b = qy - m * qx return (m, b) def eval_point_challenge( P: G1Point | G2Point, xA0, mA0, bA0, multiplicity: int ) -> PyFelt | Fp2: field_type = get_field_type_from_ec_point(P) field = get_base_field(P.curve_id.value, field_type) xP, yP = field(P.x), field(P.y) num = xA0 - xP den = yP - mA0 * xP - bA0 res = multiplicity * num / den assert isinstance(res, field_type), f"Expected {field_type}, got {type(res)}" return res def eval_point_challenge_signed( P: G1Point | G2Point, xA0, mA0, bA0, ep: int, en: int ) -> PyFelt | Fp2: return eval_point_challenge(P, xA0, mA0, bA0, ep) + eval_point_challenge( -P, xA0, mA0, bA0, en ) def line(P: G1Point | G2Point, Q: G1Point | G2Point) -> FF[T]: """ Returns line function passing through points, works for all points and returns 1 for O + O = O """ assert ( P.curve_id == Q.curve_id ), f"Points must be on the same curve, got {P.curve_id} and {Q.curve_id}" assert isinstance( P, type(Q) ), f"Points must be in the same group, got {type(P)} and {type(Q)}" if isinstance(P, G1Point): field_type = PyFelt elif isinstance(P, G2Point): field_type = Fp2 else: raise ValueError(f"Invalid point type {type(P)}") field = get_base_field(P.curve_id.value, field_type) if P.is_infinity(): if Q.is_infinity(): return FF([Polynomial([field.one()])], P.curve_id) else: Qx = field(Q.x) return FF([Polynomial([-Qx, field.one()])], P.curve_id) if Q.is_infinity(): Px = field(P.x) return FF([Polynomial([-Px, field.one()])], P.curve_id) Px, Py = field(P.x), field(P.y) if P == Q: m = (3 * Px**2 + field(CURVES[P.curve_id.value].a)) / (2 * Py) b = Py - m * Px # -m*x + y -b return FF([Polynomial([-b, -m]), Polynomial([field.one()])], P.curve_id) if P == -Q: return FF([Polynomial([-Px, field.one()])], P.curve_id) Qx, Qy = field(Q.x), field(Q.y) m = (Py - Qy) / (Px - Qx) b = Qy - m * Qx return FF([Polynomial([-b, -m]), Polynomial([field.one()])], P.curve_id) @dataclass class FF: """ Represents a polynomial over F_p[x] or F_p^2[x] Example : F(x, y) = c0(x) + c1(x) * y + c2(x) * y^2 + ... where c0, c1, c2, ... are polynomials over F_p[x] or F_p^2[x] Used to represent a subset of the Function Field where coefficients are polynomials instead of rational functions. """ coeffs: list[Polynomial[T]] y2: Polynomial[T] # = x^3 + ax + b, where a, b are the curve parameters p: int curve_id: CurveID type: type[T] # PyFelt or Fp2 def __init__(self, coeffs: list[Polynomial[T]], curve_id: CurveID): self.coeffs = coeffs self.p = coeffs[0][0].p self.field = get_base_field(curve_id.value, type(coeffs[0][0])) self.curve_id = curve_id self.type = type(coeffs[0][0]) a = self.field(CURVES[curve_id.value].a) if self.type == PyFelt: b = self.field(CURVES[curve_id.value].b) else: b = self.field((CURVES[curve_id.value].b20, CURVES[curve_id.value].b21)) # y² = x³ + ax + b self.y2 = Polynomial([b, a, self.field.zero(), self.field.one()]) def degree(self) -> int: return len(self.coeffs) - 1 def __getitem__(self, i: int) -> Polynomial: try: return self.coeffs[i] except IndexError: return Polynomial.zero(self.p, self.type) def __add__(self, other: FF) -> FF: if not isinstance(other, FF): raise TypeError(f"Cannot add FF and {type(other)}") ns, no = len(self.coeffs), len(other.coeffs) if ns >= no: coeffs = self.coeffs[:] for i in range(no): coeffs[i] = coeffs[i] + other.coeffs[i] else: coeffs = other.coeffs[:] for i in range(ns): coeffs[i] = coeffs[i] + self.coeffs[i] return FF(coeffs, self.curve_id) def __mul__(self, other: "FF" | Polynomial | PyFelt) -> "FF": if isinstance(other, (PyFelt, Polynomial)): return FF([c * other for c in self.coeffs], self.curve_id) elif not isinstance(other, FF): raise TypeError( f"Cannot multiply polynomial by type {type(other)}, must be PyFelt, Polynomial, or FF" ) if self.coeffs == [] or other.coeffs == []: return FF([Polynomial([self.field.zero()])], self.curve_id) zero = Polynomial.zero(self.p, self.type) buf = [zero] * (len(self.coeffs) + len(other.coeffs) - 1) for i in range(len(self.coeffs)): if self.coeffs[i].is_zero(): continue # optimization for sparse polynomials for j in range(len(other.coeffs)): buf[i + j] = buf[i + j] + self.coeffs[i] * other.coeffs[j] res = FF(buf, self.curve_id) return res def neg_y(self) -> "FF": """Keeps all the coefficients the same but negate the degree 1 coeff""" if len(self.coeffs) < 2: return self coeffs = self.coeffs[:] coeffs[1] = -coeffs[1] return FF(coeffs, self.curve_id) def reduce(self) -> "FF": """ Reduces the polynomial modulo y² = x³ + ax + b Replaces y² with x³ + ax + b and reduces the degree of the polynomial Always returns a polynomial of at most degree 1. Enforce it has 2 coefficients (padding with zero polynomials if needed) """ if len(self.coeffs) <= 2: while len(self.coeffs) < 2: self.coeffs.append(Polynomial.zero(self.p, self.type)) return self y2 = self.y2 deg_0_coeff = self.coeffs[0] deg_1_coeff = self.coeffs[1] for i, poly in enumerate(self.coeffs): if i == 0 or i == 1: continue if i % 2 == 0: deg_0_coeff = deg_0_coeff + poly * y2 else: deg_1_coeff = deg_1_coeff + poly * y2 y2 = y2 * y2 return FF([deg_0_coeff, deg_1_coeff], self.curve_id) def to_poly(self) -> Polynomial[T]: """ "Downcasts" the FF to a Polynomial iff the FF is of degree 1. """ assert len(self.coeffs) == 1 return self.coeffs[0] def div_by_poly(self, poly: Polynomial[T]) -> "FF": return FF([c // poly for c in self.coeffs], self.curve_id) def normalize(self) -> "FF": """ Normalize the polynomial by dividing all coefficients by the first one """ coeff = self.coeffs[0][0] return FF([c * coeff.__inv__() for c in self.coeffs], self.curve_id) class EmptyListOfPoints(Exception): pass def construct_function(Ps: list[G1Point] | list[G2Point]) -> FF: """ Returns a function field element (class FF) exactly interpolating the points Ps. """ if len(Ps) == 0: raise EmptyListOfPoints( "Cannot construct a function from an empty list of points" ) xs = [(P, line(P, -P)) for P in Ps] while len(xs) != 1: xs2 = [] if len(xs) & 1: x0 = xs[0] xs = xs[1:] else: x0 = None for n in range(0, len(xs) // 2): A, aNum = xs[2 * n] B, bNum = xs[2 * n + 1] aNum_bNum = aNum * bNum line_AB = line(A, B) product = aNum_bNum * line_AB num = product.reduce() den = (line(A, -A) * line(B, -B)).to_poly() D = num.div_by_poly(den) xs2.append((A.add(B), D)) if x0 is not None: xs2.append(x0) xs = xs2 assert xs[0][0].is_infinity() return xs[-1][1].normalize() def row_function( ds: list[int], Ps: list[G1Point] | list[G2Point], Q: G1Point | G2Point ) -> tuple[FF, G1Point | G2Point]: ec_group_class = G1Point if isinstance(Q, G1Point) else G2Point infinity = ec_group_class.infinity(Q.curve_id) digits_points = [ P if d == 1 else -P if d == -1 else infinity for d, P in zip(ds, Ps) ] sum_digits_points = functools.reduce(lambda x, y: x.add(y), digits_points) Q2 = Q.scalar_mul(-3).add(sum_digits_points) Q_neg = -Q div_ = [Q_neg, Q_neg, Q_neg, -Q2] + digits_points div = [P for P in div_ if not P.is_infinity()] try: D = construct_function(div) except EmptyListOfPoints: field_type = get_field_type_from_ec_point(div_[0]) # Returning 1 so that dLog(D) = 0 and doesn't contribute to the sum. D = FF( [Polynomial.one(get_base_field(Q.curve_id, field_type).p, field_type)], Q.curve_id, ) return (D, Q2) def ecip_functions( Bs: list[G1Point] | list[G2Point], dss: list[list[int]] ) -> tuple[G1Point | G2Point, list[FF]]: dss.reverse() ec_group_class = G1Point if isinstance(Bs[0], G1Point) else G2Point Q = ec_group_class.infinity(Bs[0].curve_id) Ds = [] for i, ds in enumerate(dss): D, Q = row_function(ds, Bs, Q) Ds.append(D) Ds.reverse() return (Q, Ds) def dlog(d: FF) -> FunctionFelt: """ Compute the logarithmic derivative of a FunctionFieldElement (class FF), Returns a FunctionFelt such that F = a(x) + b(x) * y with a, b RationalFunctions Ref https://gist.github.com/Liam-Eagen/666d0771f4968adccd6087465b8c5bd4 (cell #12) Example values: D: (3*x + 11)*y + x^2 + x + 1 Dx: 3*y + 2*x + 1 Dy: 3*x + 11 Dz_tmp: (9*x^3 + 33*x^2)/(2*y) Dz: (6*y^2 + (4*x + 2)*y + 9*x^3 + 33*x^2)/(2*y) U=2*y*Dz: 6*y^2 + (4*x + 2)*y + 9*x^3 + 33*x^2 V=2*y*D: (6*x + 22)*y^2 + (2*x^2 + 2*x + 2)*y """ field = d.field d: FF = d.reduce() assert len(d.coeffs) == 2, f"D has {len(d.coeffs)} coeffs: {d.coeffs}" Dx = FF([d[0].differentiate(), d[1].differentiate()], d.curve_id) Dy: Polynomial = d[1] # B(x) TWO_Y: FF = FF( [Polynomial.zero(field.p, d.type), Polynomial([field(2)])], d.curve_id ) U: FF = Dx * TWO_Y + FF( [ Dy * Polynomial( [ field(CURVES[d.curve_id.value].a), field.zero(), field(3), ] # 3x^2 + A ), Polynomial.zero(field.p, d.type), ], d.curve_id, ) V: FF = TWO_Y * d # print(f"U: {print_ff(U)}") # print(f"V: {print_ff(V)}") Num: FF = (U * V.neg_y()).reduce() Den_FF: FF = (V * V.neg_y()).reduce() # print(f"Num: {print_ff(Num)}") # print(f"Den: {print_ff(Den_FF)}") assert Den_FF[ 1 ].is_zero(), f"Den[1] is not zero: {Den_FF[1].print_as_sage_poly('x')}" Den: Polynomial = Den_FF[0] _, _, gcd_0 = Polynomial.xgcd(Num[0], Den) # print(f"GCD_0: {gcd_0.print_as_sage_poly('x')}") _, _, gcd_1 = Polynomial.xgcd(Num[1], Den) # print(f"GCD_1: {gcd_1.print_as_sage_poly('x')}") # Simplify the numerator and denominator by dividing by the gcd a_num = Num[0] // gcd_0 a_den = Den // gcd_0 b_num = Num[1] // gcd_1 b_den = Den // gcd_1 # Normalize to obtain exactly Sage's coeffs. res = FunctionFelt( a=RationalFunction( a_num * Den.leading_coefficient().__inv__(), a_den * a_den.leading_coefficient().__inv__(), ), b=RationalFunction( b_num * Den.leading_coefficient().__inv__(), b_den * b_den.leading_coefficient().__inv__(), ), ) # print(f"res: {res.print_as_sage_poly()}\n") return res def print_ff(ff: FF): string = "" coeffs = ff.coeffs for i, p in enumerate(coeffs[::-1]): coeff_str = p.print_as_sage_poly(var_name="x", as_hex=True) if i == len(coeffs) - 1: if coeff_str == "": string = string[:-2] else: string += f"{coeff_str}" elif i == len(coeffs) - 2: string += f"({coeff_str})*y + " else: string += f"({coeff_str})*y^{len(coeffs) - i - 1} + " # print(string) return string def n_points_from_n_coeffs(n_coeffs: int, batched: bool) -> int: if batched: extra = 4 * 2 else: extra = 0 # n_coeffs = 10 + 4n_points => 4n_points = n_coeffs - 10 assert n_coeffs >= 10 + extra assert (n_coeffs - 10 - extra) % 4 == 0 return (n_coeffs - 10 - extra) // 4 def n_coeffs_from_n_points(n_points: int, batched: bool) -> tuple[int, int, int, int]: if batched: extra = 2 else: extra = 0 return ( 1 + n_points + extra, 1 + n_points + 1 + extra, 1 + n_points + 1 + extra, 1 + n_points + 4 + extra, ) if __name__ == "__main__": import random from garaga.curves import STARK from garaga.hints.io import int_array_to_u384_array, int_to_u384 random.seed(0) def build_cairo1_tests_derive_ec_point_from_X(x: int, curve_id: CurveID, idx: int): x_f, y, roots = derive_ec_point_from_X(x, curve_id) code = f""" #[test] fn derive_ec_point_from_X_{CurveID(curve_id).name}_{idx}() {{ let x: felt252 = {x%STARK}; let y: u384 = {int_to_u384(y)}; let grhs_roots:Array = {int_array_to_u384_array(roots)}; let result = derive_ec_point_from_X(x, y, grhs_roots, {curve_id.value}); assert!(result.x == {int_to_u384(x_f)}); assert!(result.y == y); }} """ return code # codes = "\n".join( # [ # build_cairo1_tests_derive_ec_point_from_X(x, curve_id, idx) # for idx, x in enumerate([random.randint(0, STARK - 1) for _ in range(2)]) # for curve_id in CurveID # ] # ) # print(codes) # average_n_roots = 0 # max_n_roots = 0 # n = 10000 # for i in range(n): # x, y, roots = derive_ec_point_from_X( # Fp2.random(CURVES[0].p, max_value=STARK), CurveID(0) # ) # # print(f"x: {x}, y: {y}, roots: {roots}") # max_n_roots = max(max_n_roots, len(roots)) # average_n_roots += len(roots) # print(f"Average number of roots: {average_n_roots / n}") # print(f"Max number of roots: {max_n_roots}") # verify_ecip([G1Point.gen_random_point(CurveID.SECP256K1)], scalars=[-1]) import time order = CURVES[CurveID.BN254.value].n n = 50 Bs = [G1Point.gen_random_point(CurveID.BN254) for _ in range(n)] ss = [random.randint(1, order) for _ in range(n)] t0 = time.time() ZZ = zk_ecip_hint(Bs, ss, use_rust=False) time_taken_py = time.time() - t0 print(f"Time taken py : {time_taken_py}") t0 = time.time() ZZ_rs = zk_ecip_hint(Bs, ss, use_rust=True) time_taken_rs = time.time() - t0 print(f"Time taken rs : {time_taken_rs}") print(f"Ratio: {time_taken_py / time_taken_rs}") assert ZZ == ZZ_rs ================================================ FILE: hydra/garaga/hints/eisenstein.py ================================================ """ ----------------------------------------------------------------------------- ε – Eisenstein integers in pure Python (fully commented) ----------------------------------------------------------------------------- A **beginner‑friendly walk‑through** ----------------------------------------------------------------------------- This file implements three things: • an *Eisenstein integer* class z = a0 + a1·ω with ω = e^{2πi/3} • an *exact* Euclidean division quo_rem() in the ring ℤ[ω] • the *Half‑GCD* algorithm, one of the fastest ways to compute a greatest common divisor when the inputs are very large """ from __future__ import annotations # ► allow the class to refer to itself in type hints import math from typing import Tuple # --------------------------------------------------------------------------- # 1. Tiny helper for the Euclidean division in ℤ[ω] # --------------------------------------------------------------------------- # The six **unit directions** of the hexagonal lattice. Graphically: # ↑ (0,1) # ↖ ↗ # (-1,1) (1,0) # ↙ ↘ # (-1,0) (1,-1) # ↓ (0,-1) _NEIGHBOURS = ((1, 0), (0, 1), (-1, 1), (-1, 0), (0, -1), (1, -1)) def _round_nearest(z: int, d: int) -> int: """Symmetric integer rounding —— ⌊ (z + d/2) / d ⌋ for *any* sign of *z*. • *d* is strictly positive (we only call this with norms, which are > 0). • For z ≥ 0 the formula above already works. • For z < 0 we cannot add +d/2 (would move us the wrong way), so we flip the sign, apply the positive rule, then flip back. """ half = d >> 1 # bit‑shift right by 1 ⇒ divide by 2 (fast, exact) return (z + half) // d if z >= 0 else -((-z + half) // d) # --------------------------------------------------------------------------- # 2. The EisensteinInteger class # --------------------------------------------------------------------------- class EisensteinInteger: """Eisenstein integers: *hexagonal* analogue of Gaussian integers. Definition ---------- ω (pronounced "omega") is the complex cube‑root of 1 with positive imaginary part: ω = e^{2πi/3} = −½ + i·√3/2. It satisfies ω² + ω + 1 = 0 and |ω| = 1. Every element of ℤ[ω] can be written uniquely as z = a₀ + a₁·ω, with a₀, a₁ ∈ ℤ. The pair (a₀, a₁) are the *hex‑coordinates* in the triangular lattice. In code we store just those two integers. """ # Class‑level constants (created *after* the class body below) ZERO: "EisensteinInteger" # 0 + 0·ω ONE: "EisensteinInteger" # 1 + 0·ω # ──────────────────────────────────────────────────────────────────── # Construction & basic utilities # ──────────────────────────────────────────────────────────────────── def __init__(self, a0: int = 0, a1: int = 0): if not isinstance(a0, int) or not isinstance(a1, int): raise TypeError("Coefficients a0 and a1 must be integers") self.a0 = a0 self.a1 = a1 def copy(self) -> "EisensteinInteger": """Clone *self* (handy for algorithms that mutate a temporary copy).""" return EisensteinInteger(self.a0, self.a1) def is_zero(self) -> bool: return self.a0 == 0 and self.a1 == 0 def __str__(self) -> str: """Pretty print 3 + 2·ω, −ω, 0, …""" if self.a1 == 0: return str(self.a0) a0_part = f"{self.a0}" if self.a0 != 0 else "" # coefficient of ω if self.a1 == 1: a1_part = "ω" elif self.a1 == -1: a1_part = "-ω" else: a1_part = f"{self.a1}*ω" if a0_part == "": return a1_part sign = " + " if self.a1 > 0 else " - " abs_a1_part = "ω" if abs(self.a1) == 1 else f"{abs(self.a1)}*ω" return f"{a0_part}{sign}{abs_a1_part}" def __repr__(self) -> str: """Unambiguous form so that eval(repr(z)) == z (useful in a REPL).""" return f"EisensteinInteger({self.a0}, {self.a1})" # ──────────────────────────────────────────────────────────────────── # Equality & negation # ──────────────────────────────────────────────────────────────────── def __eq__(self, other: object) -> bool: # called by z1 == z2 return ( isinstance(other, EisensteinInteger) and self.a0 == other.a0 and self.a1 == other.a1 ) def __neg__(self) -> "EisensteinInteger": # −z return EisensteinInteger(-self.a0, -self.a1) # ──────────────────────────────────────────────────────────────────── # Conjugation # ──────────────────────────────────────────────────────────────────── def conjugate(self) -> "EisensteinInteger": """Field automorphism ω ↦ ω² (complex conjugation). Algebraically: conj(a₀ + a₁·ω) = (a₀ − a₁) − a₁·ω. """ return EisensteinInteger(self.a0 - self.a1, -self.a1) # ──────────────────────────────────────────────────────────────────── # Addition, subtraction, multiplication # ──────────────────────────────────────────────────────────────────── def __add__(self, other: "EisensteinInteger") -> "EisensteinInteger": return EisensteinInteger(self.a0 + other.a0, self.a1 + other.a1) def __sub__(self, other: "EisensteinInteger") -> "EisensteinInteger": return EisensteinInteger(self.a0 - other.a0, self.a1 - other.a1) def __mul__(self, other: object) -> "EisensteinInteger": """Product formula derived from (x₀ + x₁ω)(y₀ + y₁ω). Expand and use ω² = −1 − ω. """ if isinstance(other, EisensteinInteger): x0, x1, y0, y1 = self.a0, self.a1, other.a0, other.a1 return EisensteinInteger( x0 * y0 - x1 * y1, # coefficient of 1 x0 * y1 + x1 * y0 - x1 * y1, # coefficient of ω ) elif isinstance(other, int): return EisensteinInteger(self.a0 * other, self.a1 * other) return NotImplemented # Support int * EisensteinInteger (commutative) __rmul__ = __mul__ # ──────────────────────────────────────────────────────────────────── # Norm (always a *plain* integer) # ──────────────────────────────────────────────────────────────────── def norm(self) -> int: """N(a₀ + a₁·ω) = a₀² + a₁² − a₀·a₁ ≥ 0 Proof: treat ω as −½ + i·√3/2 and compute |z|². """ return self.a0 * self.a0 + self.a1 * self.a1 - self.a0 * self.a1 # ------------------------------------------------------------------- # Euclidean division —— the heart of arithmetic in ℤ[ω] # ------------------------------------------------------------------- def quo_rem( self, y: "EisensteinInteger" ) -> Tuple["EisensteinInteger", "EisensteinInteger"]: """Return (q, r) such that self = q·y + r with N(r) < N(y). Strategy (all integer‑only): 1. Multiply by the *conjugate* of y to get an element of the lattice that is colinear with y – this is the usual trick to mimic complex division without leaving the ring. 2. Divide the two coordinates by the *positive* norm N(y) and apply symmetric rounding to obtain a *first guess* q. 3. If this guess does not yet satisfy the Euclidean inequality N(r) < N(y), walk at most two unit steps in the hex lattice until it does. Because ℤ[ω] is a Euclidean domain, this procedure is guaranteed to terminate and the while‑loop never needs more than two laps. """ if y.is_zero(): raise ZeroDivisionError("division by zero EisensteinInteger") nrm = y.norm() # denominator of the coordinates ( > 0 ) num = self * y.conjugate() # numerator in the same lattice line # --- 1st approximation by independent rounding ----------------- q0 = _round_nearest(num.a0, nrm) q1 = _round_nearest(num.a1, nrm) q = EisensteinInteger(q0, q1) r = self - q * y # --- Improve the quotient until Euclidean property holds -------- while r.norm() >= nrm: # very rarely true (≈ 1 in 12 cases) best_q, best_r, best_norm = None, None, r.norm() # test the 6 neighbours for dp, dq in _NEIGHBOURS: cand_q = EisensteinInteger(q0 + dp, q1 + dq) cand_r = self - cand_q * y cand_norm = cand_r.norm() if cand_norm < best_norm: best_q, best_r, best_norm = cand_q, cand_r, cand_norm # move to the better neighbour (Euclidean property assures one exists) q, r = best_q, best_r q0, q1 = q.a0, q.a1 # update centre for the *next* neighbour pass return q, r # Allow the syntactic sugar z // y and z % y ------------------------- def __floordiv__(self, other: "EisensteinInteger") -> "EisensteinInteger": return self.quo_rem(other)[0] def __mod__(self, other: "EisensteinInteger") -> "EisensteinInteger": return self.quo_rem(other)[1] # -------- class constants (must be assigned *after* the class is complete) --- EisensteinInteger.ZERO = EisensteinInteger(0, 0) EisensteinInteger.ONE = EisensteinInteger(1, 0) # --------------------------------------------------------------------------- # 3. Half‑GCD —— sub‑quadratic gcd via size halving # --------------------------------------------------------------------------- def half_gcd( a: EisensteinInteger, b: EisensteinInteger, ) -> Tuple[EisensteinInteger, EisensteinInteger, EisensteinInteger]: """Return (w, v, u) with w = a·u + b·v and N(w) < √N(a). Why is that useful? The classical Euclidean gcd repeatedly replaces the *larger* input by its remainder modulo the smaller one – this shrinks one argument at every step, but only by a *constant* factor, so it needs O(log N) iterations. **Half‑GCD** knocks out *half* the size (in bits) at every major step and therefore runs in roughly O(log N / log log N) time. The idea is to run the Euclidean algorithm *just long enough* for the remainder’s norm to dip below √N(a). The output coefficients u, v let us continue assembling the gcd later (the full gcd algorithm calls half_gcd recursively on smaller and smaller inputs). """ if not isinstance(a, EisensteinInteger) or not isinstance(b, EisensteinInteger): raise TypeError("Inputs must be EisensteinInteger instances") # Extended Euclidean bookkeeping matrices a_run, b_run = a.copy(), b.copy() u, v = EisensteinInteger.ONE.copy(), EisensteinInteger.ZERO.copy() u_, v_ = EisensteinInteger.ZERO.copy(), EisensteinInteger.ONE.copy() # Invariants throughout the loop: # a_run = a·u + b·v # b_run = a·u_ + b·v_ limit = math.isqrt(a.norm()) # √N(a) (integer square root) # Safety valve: more than ~2e5 iterations would imply a bug for _ in range(200_000): if b_run.norm() < limit or b_run.is_zero(): break q, r = a_run.quo_rem(b_run) # update (a_run, b_run) and the coefficient matrix simultaneously a_run, b_run = b_run, r u, u_ = u_, u - q * u_ v, v_ = v_, v - q * v_ else: raise RuntimeError("Half‑GCD failed to converge – too many steps") # *Return order* follows the classic Half‑GCD papers: (w, v, u) return b_run, v_, u_ if __name__ == "__main__": z1 = EisensteinInteger(3, 2) # 3 + 2ω z2 = EisensteinInteger(1, -1) # 1 - ω print(f"z1 = {z1}") print(f"z2 = {z2}") print(f"z1 + z2 = {z1 + z2}") print(f"z1 - z2 = {z1 - z2}") print(f"z1 * z2 = {z1 * z2}") print(f"Norm(z1) = {z1.norm()}") print(f"Conj(z1) = {z1.conjugate()}") print(f"-z1 = {-z1}") q, r = z1.quo_rem(z2) print(f"z1 // z2 = {q}") print(f"z1 % z2 = {r}") print(f"Check: z2 * q + r = {z2 * q + r}, Expected: {z1}") # Half GCD example a = EisensteinInteger(10, 3) b = EisensteinInteger(3, 1) print(f"\nHalf GCD for a = {a}, b = {b}") w, v_res, u_res = half_gcd(a, b) print(f" w = {w}") print(f" v = {v_res}") print(f" u = {u_res}") check = a * u_res + b * v_res print(f" Check: a*u + b*v = {check}, Expected w: {w}") print(f" Norm(w) = {w.norm()}, Limit = {math.isqrt(a.norm())}") # a = EisensteinInteger(8+7j * (math.sqrt(3)/2 + 0.5j)) # Approximate large number a_int = EisensteinInteger(13, 14) # Example large int coeffs b_int = EisensteinInteger(5, 3) print(f"\nHalf GCD for a = {a_int}, b = {b_int}") w, v_res, u_res = half_gcd(a_int, b_int) print(f" w = {w}") print(f" v = {v_res}") print(f" u = {u_res}") check = a_int * u_res + b_int * v_res print(f" Check: a*u + b*v = {check}, Expected w: {w}") print(f" Norm(w) = {w.norm()}, Limit = {math.isqrt(a_int.norm())}") ================================================ FILE: hydra/garaga/hints/extf_mul.py ================================================ from garaga import garaga_rs from garaga.algebra import ModuloCircuitElement, Polynomial, PyFelt from garaga.hints.tower_backup import E6, get_tower_object from garaga.points import ( direct_to_tower, get_base_field, get_irreducible_poly, tower_to_direct, ) def nondeterministic_extension_field_mul_divmod( Ps: list[list[PyFelt | ModuloCircuitElement]], curve_id: int, extension_degree: int, ) -> tuple[list[PyFelt], list[PyFelt]]: """ From a list of Polynomials Ps = [P1, ..., Pn] Returns (Q(X), R(X)) such that Π(Pi)(X) = Q(X) * P_irr(X) + R(X), for a given curve and extension degree. R(X) is the result of the multiplication in the extension field. Q(X) is used for verification. """ field = get_base_field(curve_id) ps = [[c.value for c in P] for P in Ps] q, r = garaga_rs.nondeterministic_extension_field_mul_divmod( curve_id, extension_degree, ps ) z_polyq_coeffs = [field(c) for c in q] if len(q) > 0 else [field.zero()] z_polyr_coeffs = [field(c) for c in r] if len(r) > 0 else [field.zero()] return (z_polyq_coeffs, z_polyr_coeffs) def nondeterministic_square_torus( A: list[PyFelt | ModuloCircuitElement], curve_id: int, biject_from_direct: bool = True, ) -> list[PyFelt]: """ Computes 1/2 * (A(x) + x/A(x)) Deprecated usage as Torus based arithmetic is not used anymore with the final exp witness. """ A = direct_to_tower(A, curve_id, 6) if biject_from_direct else A A = E6(A, curve_id) SQ: list[PyFelt] = A.square_torus().felt_coeffs return tower_to_direct(SQ, curve_id, 6) if biject_from_direct else SQ def nondeterministic_extension_field_div( A: list[PyFelt | ModuloCircuitElement], B: list[PyFelt | ModuloCircuitElement], curve_id: int, extension_degree: int = 6, ) -> tuple[list[PyFelt], list[PyFelt]]: """ From two Polynomials A and B Returns (A/B)(X) mod P_irr(X) Converts back and forth to tower representaion for faster inversion. """ A = direct_to_tower(A, curve_id, extension_degree) B = direct_to_tower(B, curve_id, extension_degree) A = get_tower_object(A, curve_id, extension_degree) B = get_tower_object(B, curve_id, extension_degree) DIV = A.div(B).felt_coeffs return tower_to_direct(DIV, curve_id, extension_degree) if __name__ == "__main__": from random import randint as rint from garaga.curves import ( BLS12_381_ID, BN254_ID, get_base_field, get_irreducible_poly, ) field = get_base_field(BN254_ID) p = field.p # ins = [rint(0, p - 1) for _ in range(6)] # sq = nondeterministic_square_torus( # [field_bn254(x) for x in ins], # BN254_ID, # ) # two_e6 = E6([2, 0, 0, 0, 0, 0], BN254_ID) # sq = E6(sq, BN254_ID) # x = E6(ins, BN254_ID) # print(f"Should be V : ", x * (two_e6 * sq - x)) A = [field(rint(0, p - 1)) for _ in range(12)] Q, R = nondeterministic_extension_field_mul_divmod([A, A, A], BN254_ID, 12) Q, R = Polynomial(Q), Polynomial(R) z = field(rint(0, p - 1)) P_irr = get_irreducible_poly(BN254_ID, 12) lhs = Polynomial(A).evaluate(z) lhs = lhs * lhs * lhs rhs = Q.evaluate(z) * P_irr.evaluate(z) + R.evaluate(z) assert lhs == rhs # Test BLS12-381 field = get_base_field(BLS12_381_ID) p = field.p A = [field(rint(0, p - 1)) for _ in range(12)] Q, R = nondeterministic_extension_field_mul_divmod([A, A], BLS12_381_ID, 12) Q, R = Polynomial(Q), Polynomial(R) def print_as_sage_poly(X: Polynomial, var_name="z"): coeffs = X.get_value_coeffs() string = "" for coeff in coeffs[::-1]: string += f"{hex(coeff)}*{var_name}^{coeffs.index(coeff)} + " print(string[:-3]) print_as_sage_poly(Polynomial(A)) print_as_sage_poly(R) ================================================ FILE: hydra/garaga/hints/fake_glv.py ================================================ #!/usr/bin/env python3 import math from dataclasses import dataclass from typing import List, Tuple import garaga.hints.eisenstein as eisenstein from garaga.curves import CURVES, CurveID from garaga.points import G1Point @dataclass class Lattice: """Represents a 2D lattice basis (V1, V2) derived from GLV decomposition. Attributes: V1: First basis vector [v11, v12]. V2: Second basis vector [v21, v22], chosen to be short. Det: Determinant of the lattice basis (v11*v22 - v12*v21). b1: Rounding coefficient derived from V2, used in scalar decomposition. b2: Rounding coefficient derived from V1, used in scalar decomposition. """ V1: Tuple[int, int] V2: Tuple[int, int] Det: int b1: int b2: int def half_gcd(mod: int, input_val: int) -> Tuple[int, int]: """ Computes the first vector of a GLV lattice basis for a given modulus and input. This is a Python adaptation of a Go function likely used for cryptographic scalar multiplication optimizations (GLV method). Args: mod (int): The modulus (often the group order `r`). input_val (int): The input value (often the eigenvalue `lambda`). Returns: Tuple[int, int]: The components (v11, |v12|) of the first basis vector V1. """ lattice = precompute_lattice(mod, input_val) output0 = lattice.V1[0] output1 = lattice.V1[1] # The GLV decomposition often requires the absolute value of the second component. return output0, abs(output1) def precompute_lattice(r: int, lam: int) -> Lattice: """ Computes a short 2D lattice basis related to parameters (r, lambda). Uses a variant of the Extended Euclidean Algorithm to find short vectors (v1, v2) such that v1 = [a, b] and v2 = [c, d] satisfy a + b*lambda = 0 (mod r) and c + d*lambda = 0 (mod r). See https://www.iacr.org/archive/crypto2001/21390189.pdf (Algorithm 3.7) Args: r (int): The modulus. lam (int): The lambda value (e.g., eigenvalue in GLV). Returns: Lattice: An object containing the lattice basis vectors (V1, V2), determinant (Det), and rounding coefficients (b1, b2). Raises: ValueError: If intermediate steps lead to division by zero (e.g., lam=0 mod r) or if the final determinant is zero. """ # Extended Euclidean Algorithm State: [[value, s_coeff, t_coeff], ...] # We maintain two states [ri, si, ti] such that ri = si*r + ti*lambda euclidean_state: List[List[int]] = [ [r, 1, 0], # Corresponds to r = 1*r + 0*lambda [lam, 0, 1], # Corresponds to lam = 0*r + 1*lambda ] # Compute the integer square root of r as the termination threshold sqrt_r: int = int(math.isqrt(r)) # Run Euclidean algorithm until the remainder (state[1][0]) is smaller than sqrt(r) while abs(euclidean_state[1][0]) >= sqrt_r: current_rem, s_curr, t_curr = euclidean_state[1] prev_rem, s_prev, t_prev = euclidean_state[0] if current_rem == 0: # This occurs if lambda is a multiple of r or lambda is 0. raise ValueError( "Division by zero in Euclidean algorithm. Check inputs r and lam." ) quotient: int = prev_rem // current_rem next_rem: int = prev_rem % current_rem # Update coefficients using the identity: R_next = R_prev - q * R_curr # where R represents [rem, s, t] s_next = s_prev - s_curr * quotient t_next = t_prev - t_curr * quotient # Shift states: current becomes previous, new becomes current euclidean_state[0] = [current_rem, s_curr, t_curr] euclidean_state[1] = [next_rem, s_next, t_next] # One final step to potentially find a shorter vector combination current_rem, s_curr, t_curr = euclidean_state[1] prev_rem, s_prev, t_prev = euclidean_state[0] if current_rem == 0: raise ValueError( "Division by zero in Euclidean algorithm final step. Check inputs r and lam." ) quotient = prev_rem // current_rem # Calculate the next potential remainder and t-coefficient final_rem = prev_rem % current_rem final_t = t_prev - t_curr * quotient # First basis vector: V1 = [current_rem, -t_curr] # Satisfies current_rem + (-t_curr)*lambda = 0 mod r (since current_rem = s_curr*r + t_curr*lambda) V1_list: List[int] = [current_rem, -t_curr] # Candidate vectors for the second basis vector V2 # Candidate 1: [prev_rem, -t_prev] cand1 = (prev_rem, -t_prev) # Candidate 2: [final_rem, -final_t] cand2 = (final_rem, -final_t) # Choose the shorter candidate vector based on squared Euclidean norm (||v||^2 = x^2 + y^2) norm1_sq: int = cand1[0] ** 2 + cand1[1] ** 2 norm2_sq: int = cand2[0] ** 2 + cand2[1] ** 2 if norm1_sq > norm2_sq: V2_list: List[int] = list(cand2) else: V2_list = list(cand1) # Calculate the determinant of the chosen basis {V1, V2} det: int = V1_list[0] * V2_list[1] - V1_list[1] * V2_list[0] if det == 0: # Basis vectors are linearly dependent, which shouldn't happen for typical inputs. raise ValueError( "Lattice determinant is zero. Input parameters might be unsuitable." ) def round_half_away_from_zero(a: int, b: int) -> int: """Computes round(a / b), rounding ties away from zero. Equivalent to standard mathematical rounding, differs from Python's default round() which rounds ties to the nearest even number. Needed to potentially match specific Go implementation behavior. """ if b == 0: raise ValueError("Division by zero in rounding.") # Perform division using absolute values quotient, remainder = divmod(abs(a), abs(b)) # Check if the remainder is large enough to round up (away from zero) if remainder * 2 >= abs(b): quotient += 1 # Restore the sign based on the original signs of a and b if (a < 0) != (b < 0): return -quotient # Result is negative else: return quotient # Result is positive # Compute rounding coefficients b1, b2 used in scalar decomposition # n is calculated to ensure 2^n is sufficiently larger than |det|, # potentially matching Go's fixed-size integer/word alignment logic. # The `+ 32 >> 6 << 6` part aligns the bit length to a multiple of 64. n_bit_length = max( 1, det ).bit_length() # Use max(1,...) for robustness if det=0 (though checked above) n: int = 2 * (((n_bit_length + 32) >> 6) << 6) # Calculate b1 = round(2^n * V2[1] / det) b1: int = round_half_away_from_zero(V2_list[1] << n, det) # Calculate b2 = round(2^n * V1[1] / det) b2: int = round_half_away_from_zero(V1_list[1] << n, det) # Return the results structured in the Lattice dataclass return Lattice(V1=tuple(V1_list), V2=tuple(V2_list), Det=det, b1=b1, b2=b2) def split_scalar(s: int, l: Lattice) -> Tuple[int, int]: """Splits a scalar s into components (u, v) using a precomputed GLV lattice. Based on the approach described in https://www.iacr.org/archive/crypto2001/21390189.pdf, this function finds a vector (u, v) such that s = u + v*lambda (mod r), where lambda and r are the parameters used to generate the lattice l. The vector (u, v) is typically chosen such that u and v have smaller magnitudes than s. Args: s: The scalar to split. l: The precomputed Lattice object containing basis V1, V2, determinant Det, and rounding coefficients b1, b2. Returns: A tuple (u, v) representing the scalar decomposition. """ # Calculate intermediate values k1, k2 using the scalar and rounding coefficients k1 = s * l.b1 k2 = -(s * l.b2) # Determine the shift amount 'n' used during lattice precomputation # This should match the logic in precompute_lattice n_bit_length = max(1, l.Det).bit_length() n = 2 * (((n_bit_length + 32) >> 6) << 6) # Right-shift k1 and k2 to effectively divide by 2^n, # approximating division by the determinant Det. # This gives the integer coefficients for the closest lattice vector approximation. k1 >>= n k2 >>= n # Calculate the lattice vector w = k1*V1 + k2*V2 w_vec0 = k1 * l.V1[0] + k2 * l.V2[0] w_vec1 = k1 * l.V1[1] + k2 * l.V2[1] # Calculate the final decomposition (u, v) # u = s - w[0] # v = -w[1] u = s - w_vec0 v = -w_vec1 return u, v def half_gcd_eisenstein_hint( modulus: int, scalar: int, eigen_value: int ) -> Tuple[int, int, int, int]: glv_basis = precompute_lattice(modulus, eigen_value) r = eisenstein.EisensteinInteger(glv_basis.V1[0], glv_basis.V1[1]) if scalar % modulus == modulus - 1: scalar = 1 # print(f"SPLIT SCALAR INPUT: {scalar}") sp = split_scalar(scalar, glv_basis) s = eisenstein.EisensteinInteger(sp[0], sp[1]) # in-circuit we check that Q - [s]P = 0 or equivalently Q + [-s]P = 0 # so here we return -s instead of s. s = -s # print(f"r: {r}, \ns: {s}") w, v_res, _ = eisenstein.half_gcd(r, s) # Note : outputs can be negative. return w.a0, w.a1, v_res.a0, v_res.a1 from garaga.hints.io import bigint_split def split(x): return bigint_split(x, 4, 2**64) def get_glv_fake_glv_hint( point: G1Point, scalar: int ) -> tuple[G1Point, int, int, int, int]: curve = CURVES[point.curve_id.value] assert ( curve.is_endomorphism_available() ), f"Curve {point.curve_id} does not have an endomorphism, use get_fake_glv_hint instead" eigen_value = curve.eigen_value u1, u2, v1, v2 = encode_glv_fake_glv_hint( *half_gcd_eisenstein_hint(curve.n, scalar, eigen_value) ) Q = point.scalar_mul(scalar) return Q, u1, u2, v1, v2 def encode(value: int) -> int: return abs(value) + 2**128 if value < 0 else value def encode_glv_fake_glv_hint( u1: int, u2: int, v1: int, v2: int ) -> tuple[int, int, int, int]: return encode(u1), encode(u2), encode(v1), encode(v2) def get_fake_glv_hint(point: G1Point, scalar: int) -> tuple[G1Point, int, int]: curve = CURVES[point.curve_id.value] if scalar == 0: scalar = 1 assert ( not curve.is_endomorphism_available() ), f"Curve {point.curve_id} has an endomorphism, use get_glv_fake_glv_hint instead" glv_basis = precompute_lattice(curve.n, scalar) s1, s2 = glv_basis.V1[0], glv_basis.V1[1] assert (s1 + scalar * s2) % curve.n == 0 assert 0 < s1 and s2 != 0 Q = point.scalar_mul(scalar) return Q, s1, encode(s2) def scalar_mul_glv_and_fake_glv(point: G1Point, scalar: int) -> G1Point: curve = CURVES[point.curve_id.value] assert scalar % curve.n != 0, f"Scalar is 0 for point {point}" assert point.is_infinity() == False, f"Point is infinity for scalar {scalar}" curve_id = point.curve_id if not curve.is_endomorphism_available(): raise ValueError( "Endomorphism not available for this curve. Use fake GLV instead." ) eigen_value = curve.eigen_value third_root_of_unity = curve.third_root_of_unity # %{ Hint : u1, u2, v1, v2 = half_gcd_eisenstein_hint(curve.n, scalar, eigen_value) Q = point.scalar_mul(scalar) # print(f"Q: {Q}") # %} # if scalar % curve.n == curve.n - 1: _scalar = 1 Q = G1Point.get_nG(curve_id, 2) else: _scalar = scalar # print(f"Q: {split(Q.x)}, {split(Q.y)}") # print(f"u1: {u1}, u2: {u2}, v1: {v1}, v2: {v2}") # print(f"encoded hint: {encode_glv_fake_glv_hint(u1, u2, v1, v2)}") # Verifier : # We need to check that: # s*(v1 + λ*v2) + u1 + λ*u2 = 0 assert ( _scalar * (v1 + eigen_value * v2) + u1 + eigen_value * u2 ) % curve.n == 0, f"Wrong decomposition for scalar {scalar}" # Precompute -P, -Φ(P), Φ(P): table_P = [None, None] if u1 < 0: table_P[1] = -point table_P[0] = point else: table_P[1] = point table_P[0] = -point table_Phi_P = [None, None] if u2 < 0: table_Phi_P[1] = G1Point(point.x * third_root_of_unity, -point.y, curve_id) table_Phi_P[0] = G1Point(point.x * third_root_of_unity, point.y, curve_id) else: table_Phi_P[1] = G1Point(point.x * third_root_of_unity, point.y, curve_id) table_Phi_P[0] = G1Point(point.x * third_root_of_unity, -point.y, curve_id) # precompute -Q, -Φ(Q), Φ(Q) table_Q = [None, None] if v1 < 0: table_Q[1] = -Q table_Q[0] = Q else: table_Q[1] = Q table_Q[0] = -Q table_Phi_Q = [None, None] if v2 < 0: table_Phi_Q[1] = G1Point(Q.x * third_root_of_unity, -Q.y, curve_id) table_Phi_Q[0] = G1Point(Q.x * third_root_of_unity, Q.y, curve_id) else: table_Phi_Q[1] = G1Point(Q.x * third_root_of_unity, Q.y, curve_id) table_Phi_Q[0] = G1Point(Q.x * third_root_of_unity, -Q.y, curve_id) # precompute -P-Q, P+Q, P-Q, -P+Q, -Φ(P)-Φ(Q), Φ(P)+Φ(Q), Φ(P)-Φ(Q), -Φ(P)+Φ(Q) table_S = [None, None, None, None] table_Phi_S = [None, None, None, None] table_S[0] = table_P[0].add(table_Q[0]) # -P-Q table_S[1] = -table_S[0] # P+Q table_S[2] = table_P[1].add(table_Q[0]) # P-Q table_S[3] = -table_S[2] # -P+Q # for i in range(4): # print(f"\nS{i}: {table_S[i].to_cairo_1(as_hex=False)}\n") # print(f"table_Phi_P[0]: {split(table_Phi_P[0].x)}, {split(table_Phi_P[0].y)}") # print(f"table_Phi_Q[0]: {split(table_Phi_Q[0].x)}, {split(table_Phi_Q[0].y)}") table_Phi_S[0] = table_Phi_P[0].add(table_Phi_Q[0]) # -Φ(P)-Φ(Q) table_Phi_S[1] = -table_Phi_S[0] # Φ(P)+Φ(Q) table_Phi_S[2] = table_Phi_P[1].add(table_Phi_Q[0]) # Φ(P)-Φ(Q) table_Phi_S[3] = -table_Phi_S[2] # -Φ(P)+Φ(Q) # we suppose that the first bits of the sub-scalars are 1 and set: # Acc = P + Q + Φ(P) + Φ(Q) Acc = table_S[1].add(table_Phi_S[1]) B1 = Acc # print(f"B1: {B1.to_cairo_1(as_hex=False)}") # print(f"B1: {split(B1.x)}, {split(B1.y)}") # then we add G (the base point) to Acc to avoid incomplete additions in # the loop, because when doing doubleAndAdd(Acc, Bi) as (Acc+Bi)+Acc it # might happen that Acc==Bi or Acc==-Bi. But now we force Acc to be # different than the stored Bi. However, at the end, Acc will not be the # point at infinity but [2^nbits]G. # # N.B.: Acc cannot be equal to G, otherwise this means G = -Φ²([s+1]P) Acc = Acc.add(G1Point.get_nG(point.curve_id, 1)) # // u1, u2, v1, v2 < r^{1/4} (up to a constant factor). # // We prove that the factor is log_(3/sqrt(3)))(r). # // so we need to add 9 bits to r^{1/4}.nbits(). # nbits := st.Modulus().BitLen()>>2 + 9 n_bits = curve.n.bit_length() // 4 + 9 # n_bits = 73 def to_bits_le(x: int) -> List[int]: """ ToBits returns the bit representation of the Element in little-endian (LSB first) order. """ # Convert to binary string, remove '0b' prefix, pad with zeros, and reverse bits_be = bin(x)[2:].zfill(n_bits) # print(bits_be) return [int(b) for b in bits_be[::-1]] u1_bits = to_bits_le(abs(u1)) u2_bits = to_bits_le(abs(u2)) v1_bits = to_bits_le(abs(v1)) v2_bits = to_bits_le(abs(v2)) # print(f"length of u1_bits: {len(u1_bits)}") # // At each iteration we look up the point Bi from: # // B1 = +P + Q + Φ(P) + Φ(Q) # // B2 = +P + Q + Φ(P) - Φ(Q) # At each iteration we look up the point Bi from: # B1 = +P + Q + Φ(P) + Φ(Q) # B2 = +P + Q + Φ(P) - Φ(Q) B2 = table_S[1].add(table_Phi_S[2]) # B3 = +P + Q - Φ(P) + Φ(Q) B3 = table_S[1].add(table_Phi_S[3]) # B4 = +P + Q - Φ(P) - Φ(Q) B4 = table_S[1].add(table_Phi_S[0]) # B5 = +P - Q + Φ(P) + Φ(Q) B5 = table_S[2].add(table_Phi_S[1]) # B6 = +P - Q + Φ(P) - Φ(Q) B6 = table_S[2].add(table_Phi_S[2]) # B7 = +P - Q - Φ(P) + Φ(Q) B7 = table_S[2].add(table_Phi_S[3]) # B8 = +P - Q - Φ(P) - Φ(Q) B8 = table_S[2].add(table_Phi_S[0]) # B9 = -P + Q + Φ(P) + Φ(Q) B9 = -B8 # B10 = -P + Q + Φ(P) - Φ(Q) B10 = -B7 # B11 = -P + Q - Φ(P) + Φ(Q) B11 = -B6 # B12 = -P + Q - Φ(P) - Φ(Q) B12 = -B5 # B13 = -P - Q + Φ(P) + Φ(Q) B13 = -B4 # B14 = -P - Q + Φ(P) - Φ(Q) B14 = -B3 # B15 = -P - Q - Φ(P) + Φ(Q) B15 = -B2 # B16 = -P - Q - Φ(P) - Φ(Q) B16 = -B1 # print(f"B1: {split(B1.x)}, {split(B1.y)}") # print(f"B2: {split(B2.x)}, {split(B2.y)}") # print(f"B3: {split(B3.x)}, {split(B3.y)}") # print(f"B4: {split(B4.x)}, {split(B4.y)}") # print(f"B5: {split(B5.x)}, {split(B5.y)}") # print(f"B6: {split(B6.x)}, {split(B6.y)}") # print(f"B7: {split(B7.x)}, {split(B7.y)}") # print(f"B8: {split(B8.x)}, {split(B8.y)}") # print(f"B9: {split(B9.x)}, {split(B9.y)}") # print(f"B10: {split(B10.x)}, {split(B10.y)}") # print(f"B11: {split(B11.x)}, {split(B11.y)}") # print(f"B12: {split(B12.x)}, {split(B12.y)}") # print(f"B13: {split(B13.x)}, {split(B13.y)}") # print(f"B14: {split(B14.x)}, {split(B14.y)}") # print(f"B15: {split(B15.x)}, {split(B15.y)}") # print(f"B16: {split(B16.x)}, {split(B16.y)}") # note that half the points are negatives of the other half, # hence have the same X coordinates. Bs = [B16, B8, B14, B6, B12, B4, B10, B2, B15, B7, B13, B5, B11, B3, B9, B1] # for i := nbits - 1; i > 0; i-- { # print(f"Acc; {Acc.to_cairo_1(as_hex=False)}") for i in range(n_bits - 1, 0, -1): # // selectorY takes values in [0,15] selector_y = u1_bits[i] + 2 * u2_bits[i] + 4 * v1_bits[i] + 8 * v2_bits[i] # print(f"selector_y_{i}: {selector_y}") # // selectorX takes values in [0,7] s.t.: # - when selectorY < 8: selectorX = selectorY # - when selectorY >= 8: selectorX = 15 - selectorY if selector_y < 8: selector_x = selector_y else: selector_x = 15 - selector_y # print(f"selector_x_{i}: {selector_x}") Bi = G1Point(Bs[selector_x].x, Bs[selector_y].y, point.curve_id) # // Acc = [2]Acc + Bi Acc = Acc.add(Acc) Acc = Acc.add(Bi) # print("Acc final: ", Acc.to_cairo_1(as_hex=False)) # i = 0 # # // i = 0 # // subtract the P, Q, Φ(P), Φ(Q) if the first bits are 0 # tableP[0] = c.Add(tableP[0], Acc) # Acc = c.Select(u1bits[0], Acc, tableP[0]) # tablePhiP[0] = c.Add(tablePhiP[0], Acc) # Acc = c.Select(u2bits[0], Acc, tablePhiP[0]) # tableQ[0] = c.Add(tableQ[0], Acc) # Acc = c.Select(v1bits[0], Acc, tableQ[0]) # tablePhiQ[0] = c.Add(tablePhiQ[0], Acc) # Acc = c.Select(v2bits[0], Acc, tablePhiQ[0]) if u1_bits[0] == 0: Acc = Acc.add(table_P[0]) if u2_bits[0] == 0: Acc = Acc.add(table_Phi_P[0]) if v1_bits[0] == 0: Acc = Acc.add(table_Q[0]) if v2_bits[0] == 0: Acc = Acc.add(table_Phi_Q[0]) # Acc should be now equal to [2^nbits]G gm = G1Point.get_nG(point.curve_id, 2 ** (n_bits - 1)) # print(f"gm: {split(gm.x)}, {split(gm.y)}") if scalar % curve.n == curve.n - 1: gm = Acc assert Acc == gm, f"Acc is not equal to [2^nbits]G, {Acc} != {gm}" return Q def _to_bits_le(value: int, length: int) -> List[int]: if value < 0: raise ValueError("Input value for _to_bits_le must be non-negative.") if length < 0: # zfill requires non-negative width length = 0 return [int(b) for b in bin(value)[2:].zfill(length)][::-1] def scalar_mul_fake_glv(point: G1Point, scalar: int) -> G1Point: curve = CURVES[point.curve_id.value] assert ( not curve.is_endomorphism_available() ), f"Curve {point.curve_id} has an endomorphism; this function is for curves without it." # Handle scalar multiple of curve order n: result is infinity. if scalar % curve.n == 0: return G1Point.infinity(point.curve_id) if point.is_infinity(): return G1Point.infinity(point.curve_id) # === Step 2: Handle Edge Cases & Initial Q_hinted === # Q_hinted is the actual result [scalar]P. We compute it first. # Verification steps below will ensure this computation was correct. # Handles point=infinity correctly via G1Point.scalar_mul. Q_hinted = point.scalar_mul(scalar) # Use scalar for decomposition. scalar=0 is handled above. scalar_for_decomposition = scalar # === Step 3: Scalar Decomposition === # Decompose scalar into s1, s2 such that s1 + scalar*s2 = 0 mod n glv_basis = precompute_lattice(curve.n, scalar_for_decomposition) s1 = glv_basis.V1[0] s2 = glv_basis.V1[1] # Note: s2 can be negative assert ( s1 + scalar_for_decomposition * s2 ) % curve.n == 0, f"Decomposition failed: {(s1 + scalar_for_decomposition * s2)=} % {curve.n=} != 0" assert ( s2 != 0 ), "s2 from decomposition should not be zero (required for verification logic)." # === Step 5: Prepare for Verification Loop === # Target bit length for decomposition components nbits = 128 assert ( nbits >= (curve.n.bit_length() + 1) // 2 ), f"nbits must be at least {(curve.n.bit_length() + 1) // 2}" s1_bits = _to_bits_le(abs(s1), nbits) s2_bits = _to_bits_le(abs(s2), nbits) s2_is_negative = s2 < 0 # === Step 6: Precomputation Tables for Verification === P_verify = point # Use the original input point for verification # Helper for tripling a point P -> P.add(P.add(P)) def _triple(p: G1Point) -> G1Point: if p.is_infinity(): return p p_doubled = p.add(p) return p_doubled.add(p) # Table for P_verify: [-P, P, 3P] table_P_verify = [-P_verify, P_verify, _triple(P_verify)] # Base point for R verification table is Q_hinted, potentially negated if s2 is negative. R_verify_base = Q_hinted R_signed_verify = -R_verify_base if s2_is_negative else R_verify_base # Table for R_signed_verify: [-R_signed, R_signed, 3R_signed] table_R_verify = [-R_signed_verify, R_signed_verify, _triple(R_signed_verify)] # === Step 7: Accumulator Initialization === # Initialize accumulator for the verification loop. # Acc = P_verify + R_signed_verify Acc = table_P_verify[1].add(table_R_verify[1]) # === Step 8: Precompute T_i Points for Merged Window === # These points are combinations of table_P_verify and table_R_verify elements # used in the optimized main loop (4*Acc + T computation). T1 = table_P_verify[2].add(table_R_verify[2]) T2 = Acc # T2 is the initial Accumulator value P + R_signed T3 = table_P_verify[2].add(table_R_verify[1]) T4 = table_P_verify[1].add(table_R_verify[2]) T5 = -T2 T6 = -T1 T7 = -T4 T8 = -T3 T9 = table_P_verify[2].add(table_R_verify[0]) _neg_table_R_verify_2 = -table_R_verify[2] T10 = table_P_verify[1].add(_neg_table_R_verify_2) T11 = table_P_verify[2].add(_neg_table_R_verify_2) T12 = table_R_verify[0].add(table_P_verify[1]) T13 = -T10 T14 = -T9 T15 = -T12 T16 = -T11 # selector_y maps directly to this 16-element list. T_mux_candidates_original = [ "T6", "T10", "T14", "T2", "T7", "T11", "T15", "T3", "T8", "T12", "T16", "T4", "T5", "T9", "T13", "T1", ] T_mux_candidates_new = [ "T6", "T7", "T10", "T11", "T8", "T5", "T12", "T9", "T14", "T15", "T2", "T3", "T16", "T13", "T4", "T1", ] # ['T6', 'T7', 'T10', 'T11', 'T8', 'T5', 'T12', 'T9', 'T14', 'T15', 'T2', 'T3', 'T16', 'T13', 'T4', 'T1'] T_mux_candidates = [ T6, # 0 T7, # 1 T10, # 2 T11, # 3 T8, # 4 T5, # 5 T12, # 6 T9, # 7 T14, # 8 T15, # 9 T2, # 10 T3, # 11 T16, # 12 T13, # 13 T4, # 14 T1, # 15 ] # for i, pt in enumerate(T_mux_candidates): # print(f"{i} {T_mux_candidates_new[i]}: {pt.to_cairo_1(as_hex=False)}") # === Step 9: Main Verification Loop === # Handle first iteration separately if nbits is even. assert nbits % 2 == 0 and nbits >= 2 # Inline the logic of _lookup2_point based on top two bits (MSB) b0 = s1_bits[nbits - 1] b1 = s2_bits[nbits - 1] # print(f"b0: {b0}, b1: {b1}") if not b0 and not b1: # 00 _T_current = T5 elif b0 and not b1: # 10 _T_current = T12 elif not b0 and b1: # 01 _T_current = T15 else: # b0 and b1: # 11 _T_current = T2 # assert _T_current == T12, f"_T_current: {_T_current.to_cairo_1(as_hex=False)} != T2: {T2.to_cairo_1(as_hex=False)}" # Acc = 2*Acc + _T_current # print(f"Acc before first iteration: {Acc.to_cairo_1(as_hex=False)}") # print(f"_T_current: {_T_current.to_cairo_1(as_hex=False)}") Acc = Acc.add(Acc) # Double Acc Acc = Acc.add(_T_current) # print(f"Acc before loop: {Acc.to_cairo_1(as_hex=False)}") _loop_start_idx = nbits - 2 # Start main loop from next lower index pair # Main loop: process bits in pairs using merged additions (4*Acc + T) iteration = 1 for i in range(_loop_start_idx, 2, -2): # Process indices i and i-1 # selector_y (0-15) encodes the 4 bits: (s1[i], s2[i], s1[i-1], s2[i-1]) selector_y = ( s1_bits[i] + (s2_bits[i] << 1) + (s1_bits[i - 1] << 2) + (s2_bits[i - 1] << 3) ) selector_old = T_mux_candidates_original[selector_y] selector_y = ( s1_bits[i - 1] + 2 * s1_bits[i] + 4 * (s2_bits[i - 1] + 2 * s2_bits[i]) ) # print(f"selector_{iteration-1}: {selector_y}") selector_new = T_mux_candidates_new[selector_y] assert ( selector_old == selector_new ), f"selector_old: {selector_old} != selector_new: {selector_new}" # Select the appropriate T point based on the 4 bits using the selectors _T_current = T_mux_candidates[selector_y] # Acc = 4*Acc + _T_current Acc = Acc.add(Acc) # Double Acc Acc = Acc.add(Acc) # Double Acc again Acc = Acc.add(_T_current) # print(f"i: {i}") # if iteration % 9 == 0: # print(f"Acc after iteration {iteration//9}: {Acc.to_cairo_1(as_hex=False)}") iteration += 1 # === Step 10: Last Merged Iteration === # Handles bits 2 and 1, with a final adjustment. if nbits >= 3: selector_y = ( s1_bits[2] + (s2_bits[2] << 1) + (s1_bits[1] << 2) + (s2_bits[1] << 3) ) selector_y = s1_bits[1] + 2 * s1_bits[2] + 4 * (s2_bits[1] + 2 * s2_bits[2]) _T_current = T_mux_candidates[selector_y] # Add the final adjustment term from table_R _T_current = _T_current.add(table_R_verify[2]) # print(f"last_selector_pt_corrected: {_T_current.to_cairo_1(as_hex=False)}") # Acc = 4*Acc + _T_current_adjusted Acc = Acc.add(Acc) # Double Acc Acc = Acc.add(Acc) # Double Acc again Acc = Acc.add(_T_current) # print(f"Acc after loop: {Acc.to_cairo_1(as_hex=False)}") # === Step 11: Final Additions Based on Bit 0 === # Adjust Acc based on the least significant bits s1[0] and s2[0]. if nbits >= 1: if s1_bits[0] == 0: Acc = table_P_verify[0].add(Acc) # Add -P_verify if s2_bits[0] == 0: Acc = table_R_verify[0].add(Acc) # Add -R_signed_verify # === Step 12: Final Assertion === # The final accumulator value should equal table_R_verify[2] (which is [3]R_signed_verify). AccToAssert = Acc # print(f"AccToAssert: {AccToAssert.to_cairo_1(as_hex=False)}") # print(f"R[2]: {table_R_verify[2].to_cairo_1(as_hex=False)}") assert ( AccToAssert == table_R_verify[2] ), f"Verification failed: {AccToAssert} != {table_R_verify[2]}. Scalar: {scalar}, Point Inf: {point.is_infinity()}" # === Step 13: Return Value === # Return the originally computed Q_hinted = [scalar]P return Q_hinted if __name__ == "__main__": pass pt = G1Point( x=41688611208562472964299242833 + 2**96 * 17729154263670546193656586433 + 2 ** (96 * 2) * 573097972700812243, y=17058526127824350916476358273 + 2**96 * 14653894641525928814918228506 + 2 ** (96 * 2) * 711563577730354681, curve_id=CurveID.GRUMPKIN, ) scalar = ( 77864287393115290533831713130 + 2**96 * 47687594959966383440346360609 + 2 ** (96 * 2) * 677739838819293451 ) _res = scalar_mul_fake_glv(pt, scalar) # random.seed(0) # s = 111793196543967404139194827996419963236210979610743141064269745943111491389390 # print(f"scalar: {s}") # g = G1Point.get_nG(CurveID.SECP256K1, 1) # res = scalar_mul_glv_and_fake_glv(g, s) # # print(g.to_cairo_1()) # # print(res.to_cairo_1()) # from garaga.curves import * # for curve_id in CURVES: # curve: WeierstrassCurve = CURVES[curve_id] # if curve.is_endomorphism_available(): # nbits = curve.n.bit_length() // 4 + 9 # used_nbits = 73 # assert ( # used_nbits >= nbits # ), f"Curve {curve_id} has {nbits} bits, but used {used_nbits} bits" # print( # f"Curve {curve_id}: {nbits}, {G1Point.get_nG(CurveID(curve_id), 2 ** (used_nbits -1)).to_cairo_1()}" # ) # T_mux_candidates = [ # "T6", # "T10", # "T14", # "T2", # "T7", # "T11", # "T15", # "T3", # "T8", # "T12", # "T16", # "T4", # "T5", # "T9", # "T13", # "T1", # ] # set_original = [] # set_new = [] # map_original = { # (u, u_min_1, v, v_min_1): "" # for u in [0, 1] # for u_min_1 in [0, 1] # for v in [0, 1] # for v_min_1 in [0, 1] # } # new_T_mux_candidates = [None] * 16 # for bit_u in [0, 1]: # for bit_u_min_1 in [0, 1]: # for bit_v in [0, 1]: # for bit_v_min_1 in [0, 1]: # selector_y = bit_u + 2 * bit_v + 4 * bit_u_min_1 + 8 * bit_v_min_1 # set_original.append(selector_y) # wanted = T_mux_candidates[selector_y] # map_original[(bit_u, bit_u_min_1, bit_v, bit_v_min_1)] = wanted # needed_bit = bit_u_min_1 + 2*bit_u + 4 * (bit_v_min_1 + 2 * bit_v) # new_T_mux_candidates[needed_bit] = wanted # set_new.append(needed_bit) # print( # f"{bit_u}, {bit_u_min_1}, {bit_v}, {bit_v_min_1} -> {selector_y} || {needed_bit} -> {wanted}" # ) # print(f"set_original: {sorted(set_original)}") # print(f"set_new: {sorted(set_new)}") # assert sorted(set_original) == sorted( # set_new # ), "set_original and set_new are not equal" # print(T_mux_candidates) # print(new_T_mux_candidates) ================================================ FILE: hydra/garaga/hints/frobenius.py ================================================ from functools import lru_cache from garaga.algebra import BaseField, Polynomial, PyFelt from garaga.curves import CURVES, CurveID, get_irreducible_poly from garaga.hints.tower_backup import E6, E12 # Cache directory path CACHE_DIR = "build/frobenius_cache" @lru_cache(maxsize=32) def get_p_powers_of_V(curve_id: int, extension_degree: int, k: int) -> list[Polynomial]: """ Computes V^(i*p^k) for i in range(extension_degree), where V is the polynomial V(X) = X. Args: curve_id (int): Identifier for the curve. extension_degree (int): Degree of the field extension. k (int): Exponent in p^k, must be 1, 2, or 3. Returns: list[Polynomial]: List of polynomials representing V^(i*p^k) for i in range(extension_degree). """ assert k in [1, 2, 3], f"Supported k values are 1, 2, 3. Received: {k}" field = BaseField(CURVES[curve_id].p) V = Polynomial( [field.zero() if i != 1 else field.one() for i in range(extension_degree)] ) if extension_degree == 12: V_tower = E12.from_poly(V, curve_id) elif extension_degree == 6: V_tower = E6.from_poly(V, curve_id) else: raise ValueError(f"Unsupported extension degree: {extension_degree}") V_pow_E12 = [V_tower ** (i * field.p**k) for i in range(extension_degree)] V_pow = [v.to_poly() for v in V_pow_E12] return V_pow @lru_cache(maxsize=32) def get_V_torus_powers(curve_id: int, extension_degree: int, k: int) -> Polynomial: """ Computes 1/V^((p^k - 1) // 2) where V is the polynomial V(X) = X. This is used to compute the Frobenius automorphism in the Torus. Usage is deprecated since torus arithmetic is not used anymore with the final exp witness. Args: curve_id (int): Identifier for the curve. extension_degree (int): Degree of the field extension. k (int): Exponent in p^k, must be 1, 2, or 3. Returns: list[Polynomial]: List of polynomials representing V^(i*p^k) for i in range(extension_degree). """ assert k in [1, 2, 3], f"Supported k values are 1, 2, 3. Received: {k}" field = BaseField(CURVES[curve_id].p) irr = get_irreducible_poly(curve_id, extension_degree) V = Polynomial( [field.zero() if i != 1 else field.one() for i in range(extension_degree)] ) V_pow = V.pow((field.p**k - 1) // 2, irr) inverse, _, _ = Polynomial.xgcd(V_pow, irr) return inverse def frobenius( F: list[PyFelt], V_pow: list[Polynomial], p: int, frob_power: int, irr: Polynomial ) -> Polynomial: """ Applies the Frobenius automorphism to a polynomial in a direct extension field. Args: F (list[PyFelt]): Coefficients of the polynomial. V_pow (list[Polynomial]): Precomputed powers of V (using get_p_powers_of_V). p (int): Prime number of the base field. frob_power (int): Power of the Frobenius automorphism. irr (Polynomial): Irreducible polynomial for the field extension. Returns: Polynomial: Result of applying Frobenius automorphism. """ assert len(F) == len(V_pow), "Mismatch in lengths of F and V_pow." acc = Polynomial([PyFelt(0, p)]) for i, f in enumerate(F): acc += V_pow[i] * f assert acc == ( Polynomial(F).pow(p**frob_power, irr) ), "Mismatch in expected result." return acc @lru_cache(maxsize=32) def generate_frobenius_maps( curve_id, extension_degree: int, frob_power: int ) -> tuple[list[str], list[list[tuple[int, int]]]]: """ Generates symbolic expressions for Frobenius map coefficients and a list of tuples with constants. Args: curve_id (CurveID): Identifier for the curve. extension_degree (int): Degree of the field extension. frob_power (int): Power of the Frobenius automorphism. Returns: tuple[list[str], list[list[tuple[int, int]]]]: Symbolic expressions for each coefficient and a list of tuples with constants. """ curve_id = curve_id if isinstance(curve_id, int) else curve_id.value V_pow = get_p_powers_of_V(curve_id, extension_degree, frob_power) k_expressions = ["" for _ in range(extension_degree)] constants_list = [[] for _ in range(extension_degree)] for i in range(extension_degree): for f_index, poly in enumerate(V_pow): if poly[i] != 0: hex_value = f"0x{poly[i].value:x}" compact_hex = ( f"{hex_value[:6]}...{hex_value[-4:]}" if len(hex_value) > 10 else hex_value ) k_expressions[i] += f" + {compact_hex} * f_{f_index}" constants_list[i].append([f_index, poly[i].value]) return k_expressions, constants_list def get_frobenius_maps(curve_id, extension_degree, frob_power): res = FROBENIUS_MAPS[curve_id][extension_degree][frob_power] return res["k_expressions"], res["constants_list"] FROBENIUS_MAPS = { CurveID.BN254.value: { 6: { 1: { "k_expressions": [ " + 0x1 * f_0 + 0x12 * f_3", " + 0x242b...21a7 * f_1 + 0x3598...2536 * f_4", " + 0x2c84...048b * f_2 + 0xc33b...a7b5 * f_5", " + 0x3064...fd46 * f_3", " + 0x16c9...cba2 * f_1 + 0xc38d...dba0 * f_4", " + 0x2c14...8126 * f_2 + 0x3df9...f8bc * f_5", ], "constants_list": [ [[0, 0x1], [3, 0x12]], [ [ 1, 0x242B719062F6737B8481D22C6934CE844D72F250FD28D102C0D147B2F4D521A7, ], [ 4, 0x359809094BD5C8E1B9C22D81246FFC2E794E17643AC198484B8D9094AA82536, ], ], [ [ 2, 0x2C84BBAD27C3671562B7ADEFD44038AB3C0BBAD96FC008E7D6998C82F7FC048B, ], [ 5, 0xC33B1C70E4FD11B6D1EAB6FCD18B99AD4AFD096A8697E0C9C36D8CA3339A7B5, ], ], [ [ 3, 0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD46, ] ], [ [ 1, 0x16C9E55061EBAE204BA4CC8BD75A079432AE2A1D0B7C9DCE1665D51C640FCBA2, ], [ 4, 0xC38DCE27E3B2CAE33CE738A184C89D94A0E78406B48F98A7B4F4463E3A7DBA0, ], ], [ [ 2, 0x2C145EDBE7FD8AEE9F3A80B03B0B1C923685D2EA1BDEC763C13B4711CD2B8126, ], [ 5, 0x3DF92C5B96E3914559897C6AD411FB25B75AFB7F8B1C1A56586FF93E080F8BC, ], ], ], }, 2: { "k_expressions": [ " + 0x1 * f_0", " + 0x3064...fd48 * f_1", " + 0x59e2...fffe * f_2", " + 0x1 * f_3", " + 0x3064...fd48 * f_4", " + 0x59e2...fffe * f_5", ], "constants_list": [ [[0, 0x1]], [ [ 1, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD48, ] ], [[2, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFE]], [[3, 0x1]], [ [ 4, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD48, ] ], [[5, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFE]], ], }, 3: { "k_expressions": [ " + 0x1 * f_0 + 0x12 * f_3", " + 0xc3a5...3ae6 * f_1 + 0x2ce0...77f4 * f_4", " + 0x1bfe...9cc0 * f_2 + 0x697b...2fbd * f_5", " + 0x3064...fd46 * f_3", " + 0x4f1d...86de * f_1 + 0x2429...c261 * f_4", " + 0x23d5...239f * f_2 + 0x1465...6087 * f_5", ], "constants_list": [ [[0, 0x1], [3, 0x12]], [ [ 1, 0xC3A5E9C462A654779C3E050C9CA2A428908A81264E2B5A5BF22F67654883AE6, ], [ 4, 0x2CE02AA5F9BF8CD65BDD2055C255CF9D9E08C1D9345582CC92FD973C74BD77F4, ], ], [ [ 2, 0x1BFE7B214C0294242FB81A8DCCD8A9B4441D64F34150A79753FB0CD31CC99CC0, ], [ 5, 0x697B9C523E0390ED15DA0EC97A9B8346513297B9EFAF0F0F1A228F0D5662FBD, ], ], [ [ 3, 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[6, 0x12]], [ [ 1, 0x1D8C8DAEF3EEE1E81B2522EC5EB28DED6895E1CDFDE6A43F5DAA971F3FA65955, ], [ 7, 0x217E400DC9351E774E34E2AC06EAD4000D14D1E242B29C567E9C385CE480A71A, ], ], [ [ 2, 0x242B719062F6737B8481D22C6934CE844D72F250FD28D102C0D147B2F4D521A7, ], [ 8, 0x359809094BD5C8E1B9C22D81246FFC2E794E17643AC198484B8D9094AA82536, ], ], [ [ 3, 0x21436D48FCB50CC60DD4EF1E69A0C1F0DD2949FA6DF7B44CBB259EF7CB58D5ED, ], [ 9, 0x18857A58F3B5BB3038A4311A86919D9C7C6C15F88A4F4F0831364CF35F78F771, ], ], [ [ 4, 0x2C84BBAD27C3671562B7ADEFD44038AB3C0BBAD96FC008E7D6998C82F7FC048B, ], [ 10, 0xC33B1C70E4FD11B6D1EAB6FCD18B99AD4AFD096A8697E0C9C36D8CA3339A7B5, ], ], [ [ 5, 0x1B007294A55ACCCE13FE08BEA73305FF6BDAC77C5371C546D428780A6E3DCFA8, ], [ 11, 0x215D42E7AC7BD17CEFE88DD8E6965B3ADAE92C974F501FE811493D72543A3977, ], ], [ [ 6, 0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD46, ] ], [ [ 1, 0x246996F3B4FAE7E6A6327CFE12150B8E747992778EEEC7E5CA5CF05F80F362AC, ], [ 7, 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0x59e2...ffff * f_11", ], "constants_list": [ [[0, 0x1]], [ [ 1, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD49, ] ], [ [ 2, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD48, ] ], [ [ 3, 0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD46, ] ], [[4, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFE]], [[5, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFF]], [[6, 0x1]], [ [ 7, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD49, ] ], [ [ 8, 0x30644E72E131A0295E6DD9E7E0ACCCB0C28F069FBB966E3DE4BD44E5607CFD48, ] ], [ [ 9, 0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD46, ] ], [[10, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFE]], [[11, 0x59E26BCEA0D48BACD4F263F1ACDB5C4F5763473177FFFFFF]], ], }, 3: { "k_expressions": [ " + 0x1 * f_0 + 0x12 * f_6", " + 0x13d0...dd76 * f_1 + 0x18a0...7a66 * f_7", " + 0xc3a5...3ae6 * f_2 + 0x2ce0...77f4 * f_8", " + 0xf20e...275a * f_3 + 0x17de...05d6 * f_9", " + 0x1bfe...9cc0 * f_4 + 0x697b...2fbd * f_10", " + 0x7a0e...c6fe * f_5 + 0x1b76...267f * f_11", " + 0x3064...fd46 * f_6", " + 0xabf8...c101 * f_1 + 0x1c93...1fd1 * f_7", " + 0x4f1d...86de * f_2 + 0x2429...c261 * f_8", " + 0x28a4...4c64 * f_3 + 0x2143...d5ed * f_9", " + 0x23d5...239f * f_4 + 0x1465...6087 * f_10", " + 0x16db...2499 * f_5 + 0x28c3...3649 * f_11", ], "constants_list": [ [[0, 0x1], [6, 0x12]], [ [ 1, 0x13D0C369615F7BB0B2BDFA8FEF85FA07122BDE8D67DFC8FABD3581AD840DDD76, ], [ 7, 0x18A0F4219F4FDFF6FC2BF531EB331A053A35744CAC285AF5685D3F90EACF7A66, ], ], [ [ 2, 0xC3A5E9C462A654779C3E050C9CA2A428908A81264E2B5A5BF22F67654883AE6, ], [ 8, 0x2CE02AA5F9BF8CD65BDD2055C255CF9D9E08C1D9345582CC92FD973C74BD77F4, ], ], [ [ 3, 0xF20E129E47C9363AA7B569817E0966CBA582096FA7A164080FAED1F0D24275A, ], [ 9, 0x17DED419ED7BE4F97FAC149BFAEFBAC11B155498DE227B850AEA3F23790405D6, ], ], [ [ 4, 0x1BFE7B214C0294242FB81A8DCCD8A9B4441D64F34150A79753FB0CD31CC99CC0, ], [ 10, 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0x2 * f_3", " + 0x1a01...aaaa * f_1", " + 0x1a01...aaaa * f_2 + 0x1a01...aaa9 * f_5", " + 0x1a01...aaaa * f_3", " + 0x1 * f_1 + 0x1 * f_4", " + 0x1 * f_5", ], "constants_list": [ [[0, 0x1], [3, 0x2]], [ [ 1, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [ [ 2, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ], [ 5, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAA9, ], ], [ [ 3, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [[1, 0x1], [4, 0x1]], [[5, 0x1]], ], }, }, 12: { 1: { "k_expressions": [ " + 0x1 * f_0 + 0x2 * f_6", " + 0x1808...14c5 * f_1 + 0x1808...14c5 * f_7", " + 0x5f19...ffff * f_2", " + 0xd5e1...9812 * f_9", " + 0x1a01...aaad * f_4 + 0x1a01...aaaf * f_10", " + 0xb659...022c * f_5 + 0xb659...022c * f_11", " + 0x1a01...aaaa * f_6", " + 0xfc3e...4af3 * f_1 + 0x1f87...95e6 * f_7", " + 0x1a01...aaac * f_2 + 0x1a01...aaac * f_8", " + 0x6af0...cc09 * f_3", " + 0x5f19...fffe * f_10", " + 0x144e...2995 * f_5 + 0xe9b7...a87f * f_11", ], "constants_list": [ [[0, 0x1], [6, 0x2]], [ [ 1, 0x18089593CBF626353947D5B1FD0C6D66BB34BC7585F5ABDF8F17B50E12C47D65CE514A7C167B027B600FEBDB244714C5, ], [ 7, 0x18089593CBF626353947D5B1FD0C6D66BB34BC7585F5ABDF8F17B50E12C47D65CE514A7C167B027B600FEBDB244714C5, ], ], [ [ 2, 0x5F19672FDF76CE51BA69C6076A0F77EADDB3A93BE6F89688DE17D813620A00022E01FFFFFFFEFFFF, ] ], [ [ 9, 0xD5E1C086FFE8016D063C6DAD7A2FFFC9072BB5785A686BCEFEEDC2E0124838BDCCF325EE5D80BE9902109F7DBC79812, ] ], [ [ 4, 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD, ], [ 10, 0x1A0111EA397FE6998CE8D956845E1033EFA3BF761F6622E9ABC9802928BFC912627C4FD7ED3FFFFB5DFB00000001AAAF, ], ], [ [ 5, 0xB659FB20274BFB1BE8FF4D69163C08BE7302C4818171FDD17D5BE9B1D380ACD8C747CDC4AFF0E653631F5D3000F022C, ], [ 11, 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0xE9B7238370B26E88C8BB2DFB1E7EC4B7D471F3CDB6DF2E24F5B1405D978EB56923783226654F19A83CD0A2CFFF0A87F, ], ], ], }, 2: { "k_expressions": [ " + 0x1 * f_0", " + 0x5f19...ffff * f_1", " + 0x5f19...fffe * f_2", " + 0x1a01...aaaa * f_3", " + 0x1a01...aaac * f_4", " + 0x1a01...aaad * f_5", " + 0x1 * f_6", " + 0x5f19...ffff * f_7", " + 0x5f19...fffe * f_8", " + 0x1a01...aaaa * f_9", " + 0x1a01...aaac * f_10", " + 0x1a01...aaad * f_11", ], "constants_list": [ [[0, 0x1]], [ [ 1, 0x5F19672FDF76CE51BA69C6076A0F77EADDB3A93BE6F89688DE17D813620A00022E01FFFFFFFEFFFF, ] ], [ [ 2, 0x5F19672FDF76CE51BA69C6076A0F77EADDB3A93BE6F89688DE17D813620A00022E01FFFFFFFEFFFE, ] ], [ [ 3, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [ [ 4, 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAC, ] ], [ [ 5, 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD, ] ], [[6, 0x1]], [ [ 7, 0x5F19672FDF76CE51BA69C6076A0F77EADDB3A93BE6F89688DE17D813620A00022E01FFFFFFFEFFFF, ] ], [ [ 8, 0x5F19672FDF76CE51BA69C6076A0F77EADDB3A93BE6F89688DE17D813620A00022E01FFFFFFFEFFFE, ] ], [ [ 9, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [ [ 10, 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAC, ] ], [ [ 11, 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD, ] ], ], }, 3: { "k_expressions": [ " + 0x1 * f_0 + 0x2 * f_6", " + 0xca2f...1299 * f_1 + 0xca2f...1299 * f_7", " + 0x1a01...aaaa * f_2", " + 0xca2f...1299 * f_9", " + 0x1a01...aaaa * f_4 + 0x1a01...aaa9 * f_10", " + 0xd5e1...9812 * f_5 + 0xd5e1...9812 * f_11", " + 0x1a01...aaaa * f_6", " + 0x6af0...cc09 * f_1 + 0xd5e1...9812 * f_7", " + 0x1 * f_2 + 0x1 * f_8", " + 0x1352...dea2 * f_3", " + 0x1 * f_10", " + 0x1352...dea2 * f_5 + 0xca2f...1299 * f_11", ], "constants_list": [ [[0, 0x1], [6, 0x2]], [ [ 1, 0xCA2F5E1C98166837AB7E0DB6BA8ACDAD404902D6DDE8C027741F672F58C729841DCCD9FCB7BF41629DDF60824381299, ], [ 7, 0xCA2F5E1C98166837AB7E0DB6BA8ACDAD404902D6DDE8C027741F672F58C729841DCCD9FCB7BF41629DDF60824381299, ], ], [ [ 2, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [ [ 9, 0xCA2F5E1C98166837AB7E0DB6BA8ACDAD404902D6DDE8C027741F672F58C729841DCCD9FCB7BF41629DDF60824381299, ] ], [ [ 4, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ], [ 10, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAA9, ], ], [ [ 5, 0xD5E1C086FFE8016D063C6DAD7A2FFFC9072BB5785A686BCEFEEDC2E0124838BDCCF325EE5D80BE9902109F7DBC79812, ], [ 11, 0xD5E1C086FFE8016D063C6DAD7A2FFFC9072BB5785A686BCEFEEDC2E0124838BDCCF325EE5D80BE9902109F7DBC79812, ], ], [ [ 6, 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAA, ] ], [ [ 1, 0x6AF0E0437FF400B6831E36D6BD17FFE48395DABC2D3435E77F76E17009241C5EE67992F72EC05F4C81084FBEDE3CC09, ], [ 7, 0xD5E1C086FFE8016D063C6DAD7A2FFFC9072BB5785A686BCEFEEDC2E0124838BDCCF325EE5D80BE9902109F7DBC79812, ], ], [[2, 0x1], [8, 0x1]], [ [ 3, 0x135203E60180A68EE2E9C448D77A2CD91C3DEDD930B1CF60EF396489F61EB45E304466CF3E67FA0AF1EE7B04121BDEA2, ] ], [[10, 0x1]], [ [ 5, 0x135203E60180A68EE2E9C448D77A2CD91C3DEDD930B1CF60EF396489F61EB45E304466CF3E67FA0AF1EE7B04121BDEA2, ], [ 11, 0xCA2F5E1C98166837AB7E0DB6BA8ACDAD404902D6DDE8C027741F672F58C729841DCCD9FCB7BF41629DDF60824381299, ], ], ], }, }, }, } if __name__ == "__main__": from random import randint # Frobenius maps def test_frobenius_maps(): constants_lists = {} for extension_degree in [6, 12]: for curve_id in [CurveID.BN254, CurveID.BLS12_381]: if curve_id.name not in constants_lists: constants_lists[curve_id.name] = {} if extension_degree not in constants_lists[curve_id.name]: constants_lists[curve_id.name][extension_degree] = {} p = CURVES[curve_id.value].p for frob_power in [1, 2, 3]: print( f"\nFrobenius^{frob_power} for {curve_id.name} Fp{extension_degree}" ) irr = get_irreducible_poly(curve_id.value, extension_degree) V_pow = get_p_powers_of_V( curve_id.value, extension_degree, frob_power ) # print( # f"Torus Inv: {get_V_torus_powers(curve_id.value, extension_degree, frob_power).get_value_coeffs()}" # ) F = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] _ = frobenius(F, V_pow, p, frob_power, irr) k_expressions, constants_list = generate_frobenius_maps( curve_id, extension_degree, frob_power ) print( f"f = f0 + f1v + ... + f{extension_degree-1}v^{extension_degree-1}" ) print( f"Frob(f) = f^p = f0 + f1v^(p^{frob_power}) + f2v^(2p^{frob_power}) + ... + f{extension_degree-1}*v^(({extension_degree-1})p^{frob_power})" ) print( f"Frob(f) = k0 + k1v + ... + k{extension_degree-1}v^{extension_degree-1}" ) for i, expr in enumerate(k_expressions): print(f"k_{i} = {expr}") print(f"Constants: {constants_list[i]}") constants_lists[curve_id.name][extension_degree][ frob_power ] = constants_list return constants_lists frobs = test_frobenius_maps() from garaga.hints.tower_backup import E12 x = E12.random(1) frobenius( x.to_poly().get_coeffs(), get_p_powers_of_V(1, 12, 1), CURVES[1].p, 1, get_irreducible_poly(1, 12), ) ================================================ FILE: hydra/garaga/hints/io.py ================================================ import functools from garaga.algebra import FunctionFelt, ModuloCircuitElement, PyFelt PRIME = 2**251 + 17 * 2**192 + 1 # STARK prime def assert_integer(val): """ Asserts that the input is an integer (and not relocatable value). """ assert isinstance(val, int), f"Expected integer, found: {val}." def as_int(val, prime): """ Returns the lift of the given field element, val, as an integer in the range (-prime/2, prime/2). """ assert_integer(val) return val if val < prime // 2 else val - prime def to_hex_str(value: str | int): if isinstance(value, str): value = value.strip() # Trim whitespaces if value.lower().startswith("0x"): try: # Validate hexadecimal and return in lowercase return "0x" + hex(int(value, 16))[2:].lower() except ValueError: raise ValueError(f"Invalid hexadecimal value: {value}") else: try: # Convert decimal string to int then to hex return hex(int(value)).lower() except ValueError: raise ValueError(f"Invalid decimal value: {value}") elif isinstance(value, int): return hex(value).lower() else: raise TypeError(f"Expected str or int, got {type(value).__name__}") # Split a bigint into its limbs. # Accepts int, ModuloCircuitElement, PyFelt, or bytes. # Returns the limbs in little-endian order. # Ie : x = d0 + d1 * base + d2 * base^2 + ... + dn * base^n # Returns the coefficients [d0, d1, d2, ..., dn] def bigint_split( x: int | ModuloCircuitElement | PyFelt | bytes, n_limbs: int = 4, base: int = 2**96 ) -> list[int]: if isinstance(x, int): pass elif isinstance(x, (ModuloCircuitElement, PyFelt)): x = x.value elif isinstance(x, bytes): x = int.from_bytes(x, byteorder="big") else: raise ValueError(f"Invalid type for bigint_split: {type(x)}") coeffs = [] degree = n_limbs - 1 for n in range(degree, 0, -1): q, r = divmod(x, base**n) coeffs.append(q) x = r coeffs.append(x) return coeffs[::-1] def bytes_to_u32_array(bytes_array: bytes, name: str) -> str: code = f"const {name}: [u32; {((len(bytes_array) + 3) // 4)}] = [" for i in range(0, len(bytes_array), 4): chunk = bytes_array[i : i + 4] u32_value = int.from_bytes(chunk, "big") code += f"{hex(u32_value)}, " code += "];" return code def to_int(value: str | int | bytes) -> int: """ Convert a string or integer to an integer. Supports hexadecimal and decimal strings. """ if isinstance(value, str): value = value.strip() # Trim whitespaces if value.lower().startswith("0x"): try: return int(value, 16) except ValueError: raise ValueError(f"Invalid hexadecimal value: {value}") else: try: return int(value) except ValueError: raise ValueError(f"Invalid decimal value: {value}") elif isinstance(value, int): return value elif isinstance(value, bytes): return int.from_bytes(value, byteorder="big") else: raise TypeError(f"Expected str, int, or bytes, got {type(value).__name__}") def int_to_u2XX(x: int | PyFelt, curve_id: int = 0, as_hex=True) -> str: if curve_id == 1: return int_to_u384(x, as_hex) else: return int_to_u288(x, as_hex) def int_to_u288(x: int | PyFelt, as_hex=True) -> str: limbs = bigint_split(x, 3, 2**96) if as_hex: return f"u288{{limb0:{hex(limbs[0])}, limb1:{hex(limbs[1])}, limb2:{hex(limbs[2])}}}" else: return f"u288{{limb0:{limbs[0]}, limb1:{limbs[1]}, limb2:{limbs[2]}}}" def int_to_u384(x: int | PyFelt, as_hex=True) -> str: limbs = bigint_split(x, 4, 2**96) if as_hex: return f"u384{{limb0:{hex(limbs[0])}, limb1:{hex(limbs[1])}, limb2:{hex(limbs[2])}, limb3:{hex(limbs[3])}}}" else: return f"u384{{limb0:{limbs[0]}, limb1:{limbs[1]}, limb2:{limbs[2]}, limb3:{limbs[3]}}}" def int_to_u256(x: int | PyFelt) -> str: assert 0 <= x < 2**256, f"Value {x} is too large to fit in a u256" limbs = bigint_split(x, 2, 2**128) return f"u256{{low:{hex(limbs[0])}, high:{hex(limbs[1])}}}" def int_to_u128(x: int | PyFelt) -> str: assert 0 <= x < 2**128, f"Value {x} is too large to fit in a u128" return hex(x) def int_array_to_u256_array(x: list[int] | list[PyFelt]) -> str: return f"array![{', '.join([int_to_u256(i) for i in x])}]" def int_array_to_u128_array(x: list[int] | list[PyFelt]) -> str: return f"array![{', '.join([int_to_u128(i) for i in x])}]" def int_array_to_u384_array(x: list[int] | list[PyFelt], const=False) -> str: if const: return f"[{', '.join([int_to_u384(i) for i in x])}]" else: return f"array![{', '.join([int_to_u384(i) for i in x])}]" def int_array_to_u288_array(x: list[int] | list[PyFelt], const=False) -> str: if const: return f"[{', '.join([int_to_u288(i) for i in x])}]" else: return f"array![{', '.join([int_to_u288(i) for i in x])}]" def int_array_to_u2XX_array( x: list[int] | list[PyFelt], curve_id: int, const=False ) -> str: if curve_id == 1: return int_array_to_u384_array(x, const) else: return int_array_to_u288_array(x, const) def bigint_pack(x: object, n_limbs: int, base: int) -> int: val = 0 for i in range(n_limbs): val += as_int(getattr(x, f"d{i}"), PRIME) * base**i return val def bigint_pack_ptr(memory: object, ptr: object, n_limbs: int, base: int) -> int: val = 0 for i in range(n_limbs): val += as_int(memory[ptr + i], PRIME) * base**i return val def pack_e12d(x: object, n_limbs: int, base: int): val = [] for i in range(12): val.append(bigint_pack(getattr(x, f"w{i}"), n_limbs, base)) return val def pack_e6d(x: object, n_limbs, base): val = [] for i in range(6): val.append(bigint_pack(getattr(x, f"v{i}"), n_limbs, base)) return val # ptr : Uint384* def pack_bigint_array( ptr: object, n_limbs: int, base: int, n_elements: int, offset: int = 0 ): val = [] for i in range(n_elements): val.append(bigint_pack(ptr[offset + i], n_limbs, base)) return val def pack_felt_ptr(memory: object, ptr: object, n_elements: int): val = [] for i in range(n_elements): val.append(memory[ptr + i]) return val def pack_bigint_ptr( memory: object, ptr: object, n_limbs: int, base: int, n_elements: int, ): val = [] for i in range(n_elements): val.append(bigint_pack_ptr(memory, ptr + i * n_limbs, n_limbs, base)) return val #### WRITE HINTS def bigint_fill(x: int, ids: object, n_limbs: int, base: int): xs = bigint_split(x, n_limbs, base) for i in range(n_limbs): setattr(ids, f"d{i}", xs[i]) return def fill_felt_ptr(x: list, memory: object, address: int): for i in range(len(x)): memory[address + i] = x[i] def fill_limbs(limbs: list, ids: object): """ limbs: list of integers ids: reference to Cairo object """ for i, limb in enumerate(limbs): setattr(ids, f"d{i}", limb) return def bigint_split_array( x: list[int | PyFelt | ModuloCircuitElement], n_limbs: int = 4, base: int = 2**96, prepend_length=False, ) -> list[int]: xs = [] if prepend_length: xs.append(len(x)) for e in x: xs.extend(bigint_split(e, n_limbs, base)) return xs def fill_bigint_array_into_felt_ptr( x: list, memory: object, address: int, base: int, n_limbs: int ): felts = [] for val in x: felts.extend(bigint_split(val, n_limbs, base)) fill_felt_ptr(felts, memory, address) def fill_e6d(x: list, ids: object, n_limbs: int, base: int): for i in range(6): bigint_fill(x[i], getattr(ids, f"v{i}"), n_limbs, base) return def fill_e12d(x: list, ids: object, n_limbs: int, base: int): for i in range(12): bigint_fill(x[i], getattr(ids, f"w{i}"), n_limbs, base) return def fill_uint256(x: int, ids: object): x0, x1 = split_128(x) setattr(ids, "low", x0) setattr(ids, "high", x1) return def padd_function_felt( f: FunctionFelt, n: int, py_felt: bool = False, batched: bool = False ) -> tuple[list[int], list[int], list[int], list[int]]: a_num = f.a.numerator.get_coeffs() if py_felt else f.a.numerator.get_value_coeffs() a_den = ( f.a.denominator.get_coeffs() if py_felt else f.a.denominator.get_value_coeffs() ) b_num = f.b.numerator.get_coeffs() if py_felt else f.b.numerator.get_value_coeffs() b_den = ( f.b.denominator.get_coeffs() if py_felt else f.b.denominator.get_value_coeffs() ) assert len(a_num) <= n + 1 + ( 2 if batched else 0 ), f"a_num has {len(a_num)} limbs, expected at most {n + 1 + (2 if batched else 0)}" assert len(a_den) <= n + 2 + ( 2 if batched else 0 ), f"a_den has {len(a_den)} limbs, expected at most {n + 2 + (2 if batched else 0)}" assert len(b_num) <= n + 2 + ( 2 if batched else 0 ), f"b_num has {len(b_num)} limbs, expected at most {n + 2 + (2 if batched else 0)}" assert len(b_den) <= n + 5 + ( 2 if batched else 0 ), f"b_den has {len(b_den)} limbs, expected at most {n + 5 + (2 if batched else 0)}" zero = [f.a.numerator.field.zero()] if py_felt else [0] a_num = a_num + zero * (n + 1 + (2 if batched else 0) - len(a_num)) a_den = a_den + zero * (n + 2 + (2 if batched else 0) - len(a_den)) b_num = b_num + zero * (n + 2 + (2 if batched else 0) - len(b_num)) b_den = b_den + zero * (n + 5 + (2 if batched else 0) - len(b_den)) return (a_num, a_den, b_num, b_den) def fill_sum_dlog_div(f: FunctionFelt, n: int, ref: object, segments: object): a_num, a_den, b_num, b_den = padd_function_felt(f, n) ref.a_num = segments.gen_arg(bigint_split_array(a_num, 4, 2**96)) ref.a_den = segments.gen_arg(bigint_split_array(a_den, 4, 2**96)) ref.b_num = segments.gen_arg(bigint_split_array(b_num, 4, 2**96)) ref.b_den = segments.gen_arg(bigint_split_array(b_den, 4, 2**96)) def fill_g1_point(p: tuple[int, int], ref: object): bigint_fill(p[0], ref.x, 4, 2**96) bigint_fill(p[1], ref.y, 4, 2**96) return ### OTHERS def flatten(t): result = [] for item in t: if isinstance(item, (tuple, list)): result.extend(flatten(item)) else: result.append(item) return result def split_128(a: int) -> tuple[int, int]: assert ( 0 <= a < 2**256 ), f"Value {hex(a)} {a.bit_length()}bits is too large to fit in a u256" """Takes in value, returns uint256-ish tuple (low, high).""" return (a & ((1 << 128) - 1), a >> 128) def rgetattr(obj, attr, *args): def _getattr(obj, attr): return getattr(obj, attr, *args) return functools.reduce(_getattr, [obj] + attr.split(".")) def rsetattr(obj, attr, val): pre, _, post = attr.rpartition(".") return setattr(rgetattr(obj, pre) if pre else obj, post, val) ================================================ FILE: hydra/garaga/hints/keccak256.py ================================================ from copy import deepcopy from functools import reduce from math import log from operator import xor # The Keccak-f round constants. RoundConstants = [ 0x0000000000000001, 0x0000000000008082, 0x800000000000808A, 0x8000000080008000, 0x000000000000808B, 0x0000000080000001, 0x8000000080008081, 0x8000000000008009, 0x000000000000008A, 0x0000000000000088, 0x0000000080008009, 0x000000008000000A, 0x000000008000808B, 0x800000000000008B, 0x8000000000008089, 0x8000000000008003, 0x8000000000008002, 0x8000000000000080, 0x000000000000800A, 0x800000008000000A, 0x8000000080008081, 0x8000000000008080, 0x0000000080000001, 0x8000000080008008, ] RotationConstants = [ [0, 1, 62, 28, 27], [36, 44, 6, 55, 20], [3, 10, 43, 25, 39], [41, 45, 15, 21, 8], [18, 2, 61, 56, 14], ] Masks = [(1 << i) - 1 for i in range(65)] def bits2bytes(x): return (int(x) + 7) // 8 def rol(value, left, bits): """ Circularly rotate 'value' to the left, treating it as a quantity of the given size in bits. """ top = value >> (bits - left) bot = (value & Masks[bits - left]) << left return bot | top def multirate_padding(used_bytes, align_bytes): """ The Keccak padding function. """ padlen = align_bytes - used_bytes if padlen == 0: padlen = align_bytes # note: padding done in 'internal bit ordering', wherein LSB is leftmost if padlen == 1: return [0x81] else: return [0x01] + ([0x00] * (padlen - 2)) + [0x80] def keccak_f(state): """ This is Keccak-f permutation. It operates on and mutates the passed-in KeccakState. It returns nothing. """ def keccak_round(a, rc): w, h = state.W, state.H rangew, rangeh = state.rangeW, state.rangeH lanew = state.lanew zero = state.zero # theta c = [reduce(xor, a[x]) for x in rangew] d = [0] * w for x in rangew: d[x] = c[(x - 1) % w] ^ rol(c[(x + 1) % w], 1, lanew) for y in rangeh: a[x][y] ^= d[x] # rho and pi b = zero() for x in rangew: for y in rangeh: b[y % w][(2 * x + 3 * y) % h] = rol( a[x][y], RotationConstants[y][x], lanew ) # chi for x in rangew: for y in rangeh: a[x][y] = b[x][y] ^ ((~b[(x + 1) % w][y]) & b[(x + 2) % w][y]) # iota a[0][0] ^= rc nr = 12 + 2 * int(log(state.lanew, 2)) for ir in range(nr): keccak_round(state.s, RoundConstants[ir]) class KeccakState: """ A keccak state container. The state is stored as a 5x5 table of integers. """ W = 5 H = 5 rangeW = range(W) rangeH = range(H) @staticmethod def zero(): """ Returns an zero state table. """ return [[0] * KeccakState.W for _ in KeccakState.rangeH] @staticmethod def format(st): """ Formats the given state as hex, in natural byte order. """ rows = [] def fmt(stx): return "%016x" % stx for y in KeccakState.rangeH: row = [] for x in KeccakState.rangeW: row.append(fmt(st[x][y])) rows.append(" ".join(row)) return "\n".join(rows) @staticmethod def lane2bytes(s, w): """ Converts the lane s to a sequence of byte values, assuming a lane is w bits. """ o = [] for b in range(0, w, 8): o.append((s >> b) & 0xFF) return o @staticmethod def bytes2lane(bb): """ Converts a sequence of byte values to a lane. """ r = 0 for b in reversed(bb): r = r << 8 | b return r @staticmethod def ilist2bytes(bb): """ Converts a sequence of byte values to a bytestring. """ return bytes(bb) @staticmethod def bytes2ilist(ss): """ Converts a string or bytestring to a sequence of byte values. """ return map(ord, ss) if isinstance(ss, str) else list(ss) def __init__(self, bitrate, b): self.bitrate = bitrate self.b = b # only byte-aligned assert self.bitrate % 8 == 0 self.bitrate_bytes = bits2bytes(self.bitrate) assert self.b % 25 == 0 self.lanew = self.b // 25 self.s = KeccakState.zero() def __str__(self): return KeccakState.format(self.s) def absorb(self, bb): """ Mixes in the given bitrate-length string to the state. """ assert len(bb) == self.bitrate_bytes bb += [0] * bits2bytes(self.b - self.bitrate) i = 0 for y in self.rangeH: for x in self.rangeW: self.s[x][y] ^= KeccakState.bytes2lane(bb[i : i + 8]) i += 8 def squeeze(self): """ Returns the bitrate-length prefix of the state to be output. """ return self.get_bytes()[: self.bitrate_bytes] def get_bytes(self): """ Convert whole state to a byte string. """ out = [0] * bits2bytes(self.b) i = 0 for y in self.rangeH: for x in self.rangeW: v = KeccakState.lane2bytes(self.s[x][y], self.lanew) out[i : i + 8] = v i += 8 return out def set_bytes(self, bb): """ Set whole state from byte string, which is assumed to be the correct length. """ i = 0 for y in self.rangeH: for x in self.rangeW: self.s[x][y] = KeccakState.bytes2lane(bb[i : i + 8]) i += 8 class KeccakSponge: def __init__(self, bitrate, width, padfn, permfn): self.state = KeccakState(bitrate, width) self.padfn = padfn self.permfn = permfn self.buffer = [] def copy(self): return deepcopy(self) def absorb_block(self, bb): assert len(bb) == self.state.bitrate_bytes self.state.absorb(bb) self.permfn(self.state) def absorb(self, s): self.buffer += s while len(self.buffer) >= self.state.bitrate_bytes: self.absorb_block(self.buffer[: self.state.bitrate_bytes]) self.buffer = self.buffer[self.state.bitrate_bytes :] def absorb_final(self): padded = self.buffer + self.padfn(len(self.buffer), self.state.bitrate_bytes) self.absorb_block(padded) self.buffer = [] def squeeze_once(self): rc = self.state.squeeze() self.permfn(self.state) return rc def squeeze(self, l): z = self.squeeze_once() while len(z) < l: z += self.squeeze_once() return z[:l] class KeccakHash: """ The Keccak hash function, with a hashlib-compatible interface. """ def __init__(self, bitrate_bits, capacity_bits, output_bits): # our in-absorption sponge. this is never given padding assert bitrate_bits + capacity_bits in (25, 50, 100, 200, 400, 800, 1600) self.sponge = KeccakSponge( bitrate_bits, bitrate_bits + capacity_bits, multirate_padding, keccak_f ) # hashlib interface members assert output_bits % 8 == 0 self.digest_size = bits2bytes(output_bits) self.block_size = bits2bytes(bitrate_bits) def __repr__(self): inf = ( self.sponge.state.bitrate, self.sponge.state.b - self.sponge.state.bitrate, self.digest_size * 8, ) return "" % inf def copy(self): return deepcopy(self) def update(self, s): self.sponge.absorb(s) def digest(self): finalised = self.sponge.copy() finalised.absorb_final() digest = finalised.squeeze(self.digest_size) return KeccakState.ilist2bytes(digest) def hexdigest(self): return self.digest().hex() @staticmethod def preset(bitrate_bits, capacity_bits, output_bits): """ Returns a factory function for the given bitrate, sponge capacity and output length. The function accepts an optional initial input, ala hashlib. """ def create(initial_input=None): h = KeccakHash(bitrate_bits, capacity_bits, output_bits) if initial_input is not None: h.update(initial_input) return h return create # Keccak parameter presets keccak_256 = KeccakHash.preset(1088, 512, 256) ================================================ FILE: hydra/garaga/hints/multi_miller_witness.py ================================================ import math from garaga import garaga_rs from garaga.algebra import PyFelt from garaga.curves import CURVES, CurveID from garaga.hints.bls import get_root_and_scaling_factor_bls from garaga.hints.tower_backup import E12 from garaga.points import G1G2Pair, G1Point, G2Point def get_final_exp_witness( curve_id: int, f: E12, use_rust: bool = True ) -> tuple[E12, E12]: """ From a miller loop output f of a given curve ID such that f^h == 1, Returns the witnesses c, w for the final exponentiation step, such that - f*w = c^lambda - w lies in a subfield of Fq12. """ if curve_id != CurveID.BN254.value and curve_id != CurveID.BLS12_381.value: raise ValueError(f"Curve ID {curve_id} not supported") curve = CURVES[curve_id] f_values = f.value_coeffs if use_rust: c_values, wi_values = garaga_rs.get_final_exp_witness(curve_id, f_values) c = E12([PyFelt(v, curve.p) for v in c_values], curve_id) wi = E12([PyFelt(v, curve.p) for v in wi_values], curve_id) else: if curve_id == CurveID.BN254.value: c, wi = find_c_e12(f, get_27th_bn254_root()) elif curve_id == CurveID.BLS12_381.value: c, wi = get_root_and_scaling_factor_bls(f) else: raise ValueError(f"Curve ID {curve_id} not supported") return c, wi def get_lambda(curve_id: CurveID) -> int: x = CURVES[curve_id.value].x q = CURVES[curve_id.value].p if curve_id == CurveID.BN254: λ = ( 6 * x + 2 + q - q**2 + q**3 ) # https://eprint.iacr.org/2008/096.pdf See section 4 for BN curves. return λ elif curve_id == CurveID.BLS12_381: λ = -x + q return λ else: raise ValueError(f"Curve ID {curve_id} not supported") def get_m_dash_root(f: E12) -> E12: assert f.curve_id == CurveID.BN254.value q = CURVES[f.curve_id].p x = CURVES[f.curve_id].x r = CURVES[f.curve_id].n h = (q**12 - 1) // r # = 3^3 · l # where gcd(l, 3) = 1 assert math.gcd(r, h) == 1 base = 3 k, l = decompose_scalar_into_b_powers_and_remainder(h, base) assert base**k * l == h, f"{base}^k * l should be h" assert h % (base**k) == 0, f"h should be a multiple of {base}^k" assert math.gcd(l, base) == 1, f"l should be coprime with {base}" λ = ( 6 * x + 2 + q - q**2 + q**3 ) # https://eprint.iacr.org/2008/096.pdf See section 4 for BN curves. assert λ % r == 0, "λ should be a multiple of r. See section 4.2.2" m = λ // r d = math.gcd(m, h) assert m % d == 0, "m should be a multiple of d" m_dash = m // d # m' = m/d assert m_dash % h != 0 "m/d should not divide h. See section 4.2.2 Theorem 2." assert d * r * m_dash == λ, "incorrect parameters" # sanity check assert math.gcd(λ, q**12 - 1) == d * r assert ( math.gcd(m_dash, q**12 - 1) == 1 ), "m_dash should be coprime with q**12 - 1 'by construction'. See 4.3.2 computing m-th root" m_d_inv = pow(m_dash, -1, h) return f**m_d_inv def decompose_scalar_into_b_powers_and_remainder(scalar: int, b: int): """ Decompose scalar into b^k * l, where l is not divisible by b. """ k = 0 l = scalar while l % b == 0: l //= b k += 1 assert l % b != 0, "l should not be divisible by b" assert scalar == b**k * l, "scalar should be the product of b^k * l" return k, l def pow_3_ord(a: E12): t = 0 FP12_ONE = E12.one(a.curve_id) while a != FP12_ONE: t += 1 a = a**3 return t def find_cube_root(a: E12, w: E12, q: int) -> E12: # Algorithm 4: Modified Tonelli-Shanks for cube roots # Input: Cube residue a, cube non residue w and write p − 1 = 3^r · s such that 3 ∤ s # Output: x such that x^3 = a # 1 exp = (s + 1)/3 _, s = decompose_scalar_into_b_powers_and_remainder(q**12 - 1, 3) exp: int = (s + 1) // 3 a_inv = a.__inv__() # 2 x ← a^exp x = a**exp # 3 3^t ← ord((x^3)/a) t = pow_3_ord(x**3 * a_inv) # 4 while t != 0 do while t != 0: # 5 exp = (s + 1)/3 # 6 x ← x · w^exp x = x * w**exp # 7 3^t ← ord(x^3/a) t = pow_3_ord(x**3 * a_inv) # 8 end # 9 return x return x def find_c_e12(f: E12, w: E12) -> tuple[E12, E12]: # Algorithm 5: Algorithm for computing λ residues over BN curve # Input: Output of a Miller loop f and fixed 27-th root of unity w # Output: (c, wi) such that c**λ = f · wi # 1 s = 0 s = 0 q = CURVES[f.curve_id].p exp = (q**12 - 1) // 3 FP12_ONE = E12.one(f.curve_id) # 2 if f**(q**k-1)/3 = 1 then if f**exp == FP12_ONE: # 3 continue # 4 end # 5 else if (f · w)**(q**k-1)/3 = 1 then c = f elif (f * w) ** exp == FP12_ONE: # 6 s = 1 s = 1 # 7 f ← f · w c = f * w # 8 end # 9 else else: # 10 s = 2 s = 2 # 11 f ← f · w**2 c = f * w * w # 12 end # 13 c ← f**r′ c = get_rth_root(c) # 14 c ← c**m′′ c = get_m_dash_root(c) # 15 c ← c**1/3 (by using modified Tonelli-Shanks 4) c = find_cube_root(c, w, q) # 16 return (c, ws) return c, w**s def get_rth_root(f: E12) -> E12: """ Computes x such that x^r = f """ r = CURVES[f.curve_id].n h = (CURVES[f.curve_id].p ** 12 - 1) // r r_inv = pow(r, -1, h) res = f**r_inv # assert res**r == f, "res**r should be f" return res def get_27th_bn254_root(): """ Retrieve a 27th root of unity over BN254 Fp^12 that isn't a 9th root of unity. """ root_27th = E12( [ 0, 0, 0, 0, 8204864362109909869166472767738877274689483185363591877943943203703805152849, 17912368812864921115467448876996876278487602260484145953989158612875588124088, 0, 0, 0, 0, 0, 0, ], CurveID.BN254.value, ) FP12_ONE = E12.one(CurveID.BN254.value) assert root_27th**27 == FP12_ONE, "root_27th**27 should be one" assert root_27th**9 != FP12_ONE, "root_27th**9 should not be one" return root_27th def get_miller_loop_output(curve_id: CurveID, will_be_one: bool = True) -> E12: """ Returns a random miller loop output f such that f**h = 1 """ g1, g2 = G1Point.gen_random_point(curve_id), G2Point.gen_random_point(curve_id) if will_be_one: # Miller (-g1, g2) * Miller (g1, g2) f = G1G2Pair.miller([G1G2Pair(-g1, g2), G1G2Pair(g1, g2)]) h = (CURVES[curve_id.value].p ** 12 - 1) // CURVES[curve_id.value].n assert f**h == E12.one(curve_id.value), "f**h should be one" else: f = G1G2Pair.miller([G1G2Pair(g1, g2)]) return f if __name__ == "__main__": def test_bn254(): f = get_miller_loop_output(CurveID.BN254) x = CURVES[CurveID.BN254.value].x q = CURVES[CurveID.BN254.value].p λ = ( 6 * x + 2 + q - q**2 + q**3 ) # https://eprint.iacr.org/2008/096.pdf See section 4 for BN curves. c, wi = find_c_e12(f, get_27th_bn254_root()) print(f"wi: {wi.value_coeffs}") c_inv = c.__inv__() result = c_inv**λ * f * wi assert result == E12.one(CurveID.BN254.value), "pairing not 1" for i in range(10): test_bn254() print(f"Test {i} passed") ================================================ FILE: hydra/garaga/hints/neg_3.py ================================================ def neg_3_base_le(scalar: int) -> list[int]: """ Decomposes a scalar into base -3 representation. :param scalar: The integer to be decomposed. :return: A list of coefficients in base -3 representation. (Least significant bit first), with digits [-1, 0, 1] such that scalar = sum((-3) ** i * d for (i, d) in enumerate(digits)) """ if scalar == 0: return [0] digits = [] while scalar != 0: remainder = scalar % 3 if ( remainder == 2 ): # if the remainder is 2, we set it to -1 and add 1 to the next digit remainder = -1 scalar += 1 # For remainder 1 and 0, no change is required digits.append(remainder) scalar = -(scalar // 3) # divide by -3 for the next digit return digits def construct_digit_vectors(es: list[int]) -> list[list[int]]: dss_ = [neg_3_base_le(e) for e in es] # Base -3 digits max_len = max(len(ds) for ds in dss_) dss_ = [ds + [0] * (max_len - len(ds)) for ds in dss_] # Transposing the matrix dss = [[dss_[row][col] for row in range(len(dss_))] for col in range(max_len)] return dss def positive_negative_multiplicities(digits: list[int]) -> tuple[int, int]: sum_p = sum((-3) ** i for (i, d) in enumerate(digits) if d == 1) sum_n = sum((-3) ** i for (i, d) in enumerate(digits) if d == -1) return (sum_p, sum_n) def scalar_to_base_neg3_le(u128: int) -> tuple[int, int, int, int]: def sign(felt252: int) -> int: # In cairo, the felt252 : # - is considered positive if it is in [0, STARK//2[ # - is considered negative if it is in ]STARK//2, STARK[ # Where STARK = 2**251+ 17* 2**192 + 1 # Note : value being exactly STARK//2 will not happen in the construction here. if felt252 > 0: return 1 elif felt252 < 0: return -1 else: # Note : the case where the input is 0, the sign does not matter. # Any value could be returned, so choose whatever is more performant in implementation. return 0 digits = neg_3_base_le(u128) # Even if input is u128, both sum_p and sum_n might be larger and negative. Output of positive_negative_multiplicities should be felt252. sum_p, sum_n = positive_negative_multiplicities(digits) # return type : felt252, felt252, felt252, felt252 return (abs(sum_p), abs(sum_n), sign(sum_p), sign(sum_n)) if __name__ == "__main__": print(positive_negative_multiplicities(neg_3_base_le(2**128))) ================================================ FILE: hydra/garaga/hints/tower_backup.py ================================================ """ Tower based arithmetic for BN254 and BLS12-381 on Fq2, Fq6, Fq12. """ import random from dataclasses import dataclass from garaga import garaga_rs from garaga.algebra import ModuloCircuitElement, Polynomial, PyFelt from garaga.curves import CURVES, get_base_field from garaga.points import direct_to_tower, tower_to_direct @dataclass(slots=True) class E2: a0: int a1: int p: int def __str__(self) -> str: return f"({(self.a0)} + {self.a1}*u)" def __eq__(self, other): return self.a0 == other.a0 and self.a1 == other.a1 @staticmethod def zero(p: int): return E2(0, 0, p) @staticmethod def one(p: int): return E2(1, 0, p) @staticmethod def random(p: int): return E2(random.randint(0, p - 1), random.randint(0, p - 1), p) @property def felt_coeffs(self) -> list[PyFelt]: return [PyFelt(self.a0, self.p), PyFelt(self.a1, self.p)] def __add__(self, other): a0 = (self.a0 + other.a0) % self.p a1 = (self.a1 + other.a1) % self.p return E2(a0, a1, self.p) def __radd__(self, other): return self.__add__(other) def __sub__(self, other): if isinstance(other, E2): a0 = (self.a0 - other.a0) % self.p a1 = (self.a1 - other.a1) % self.p return E2(a0, a1, self.p) elif isinstance(other, int): return E2((self.a0 - other) % self.p, (self.a1 - other) % self.p, self.p) return NotImplemented def __rsub__(self, other): return self.__neg__().__add__(other) def __mul__(self, other): if isinstance(other, E2): a = (self.a0 + self.a1) * (other.a0 + other.a1) % self.p b, c = self.a0 * other.a0 % self.p, self.a1 * other.a1 % self.p return E2((b - c) % self.p, (a - b - c) % self.p, self.p) elif isinstance(other, int): return E2(self.a0 * other % self.p, self.a1 * other % self.p, self.p) return NotImplemented def __rmul__(self, other): return self.__mul__(other) def __inv__(self): t0, t1 = (self.a0 * self.a0 % self.p, self.a1 * self.a1 % self.p) t0 = (t0 + t1) % self.p t1 = pow(t0, -1, self.p) return E2(self.a0 * t1 % self.p, -(self.a1 * t1) % self.p, self.p) def div(self, other): if isinstance(other, E2): return self * other.__inv__() return NotImplemented def __pow__(self, p: int): """ Compute x**p in F_p^2 using square-and-multiply algorithm. Args: p: The exponent, a non-negative integer. Returns: x**p in F_p^2, represented similarly as x. """ assert isinstance(p, int) and p >= 0 # Handle the easy cases. if p == 0: # x**0 = 1, where 1 is the multiplicative identity in F_p^2. return E2(1, 0, self.p) elif p == 1: # x**1 = x. return self # Start the computation. result = self.one( self.p ) # Initialize result as the multiplicative identity in F_p^2. temp = self # Initialize temp as self. # Loop through each bit of the exponent p. for bit in reversed(bin(p)[2:]): # [2:] to strip the "0b" prefix. if bit == "1": result = result * temp temp = temp * temp return result def __truediv__(self, other): if isinstance(other, E2): return self * other.__inv__() elif isinstance(other, int): return self * pow(other, -1, self.p) return NotImplemented def __rtruediv__(self, other): if isinstance(other, E2): return other * self.__inv__() elif isinstance(other, int): return other * self.__inv__() return NotImplemented def __neg__(self): return E2(-self.a0 % self.p, -self.a1 % self.p, self.p) def conjugate(self): return E2(self.a0, -self.a1 % self.p, self.p) @dataclass(slots=True, init=False) class E6: b0: E2 b1: E2 b2: E2 curve_id: int non_residue: E2 def __init__(self, x: list[int | PyFelt | E2], curve_id: int): curve = CURVES[curve_id] self.curve_id = curve_id self.non_residue = E2(curve.nr_a0, curve.nr_a1, curve.p) if isinstance(x[0], int): self.b0 = E2(x[0], x[1], curve.p) self.b1 = E2(x[2], x[3], curve.p) self.b2 = E2(x[4], x[5], curve.p) elif isinstance(x[0], E2): self.b0 = x[0] self.b1 = x[1] self.b2 = x[2] elif isinstance(x[0], PyFelt): self.b0 = E2(x[0].value, x[1].value, curve.p) self.b1 = E2(x[2].value, x[3].value, curve.p) self.b2 = E2(x[4].value, x[5].value, curve.p) else: raise ValueError(f"Invalid type {type(x[0])}") @property def coeffs(self) -> list[int]: return [self.b0.a0, self.b0.a1, self.b1.a0, self.b1.a1, self.b2.a0, self.b2.a1] @property def felt_coeffs(self) -> list[PyFelt]: return [PyFelt(c, self.b0.p) for c in self.coeffs] @property def value_coeffs(self) -> list[int]: return [ self.b0.a0, self.b0.a1, self.b1.a0, self.b1.a1, self.b2.a0, self.b2.a1, ] @staticmethod def from_poly(poly: Polynomial, curve_id: int): field = get_base_field(curve_id) coeffs = poly.get_coeffs() coeffs = coeffs + [field(0)] * (6 - len(coeffs)) coeffs = direct_to_tower(coeffs, curve_id, 6) return E6(coeffs, curve_id) def to_poly(self) -> Polynomial: field = get_base_field(self.curve_id) coeffs = [field(c) for c in self.value_coeffs] coeffs = tower_to_direct(coeffs, self.curve_id, 6) return Polynomial(coeffs) @staticmethod def zero(curve_id: int): p = CURVES[curve_id].p return E6([E2.zero(p), E2.zero(p), E2.zero(p)], curve_id) @staticmethod def one(curve_id: int): p = CURVES[curve_id].p return E6([E2.one(p), E2.zero(p), E2.zero(p)], curve_id) @staticmethod def random(curve_id: int): p = CURVES[curve_id].p return E6([E2.random(p), E2.random(p), E2.random(p)], curve_id) def __str__(self) -> str: return f"{self.b0} + {self.b1}*v + {self.b2}*v^2" def __add__(self, other): if isinstance(other, E6): return E6( [self.b0 + other.b0, self.b1 + other.b1, self.b2 + other.b2], self.curve_id, ) raise NotImplementedError def __sub__(self, other): if isinstance(other, E6): return E6( [self.b0 - other.b0, self.b1 - other.b1, self.b2 - other.b2], self.curve_id, ) raise NotImplementedError def __neg__(self): return E6([-self.b0, -self.b1, -self.b2], self.curve_id) def __mul__(self, other): x0, x1, x2 = self.b0, self.b1, self.b2 y0, y1, y2 = other.b0, other.b1, other.b2 t0 = x0 * y0 t1 = x1 * y1 t2 = x2 * y2 c0 = t0 + self.non_residue * ((x1 + x2) * (y1 + y2) - t1 - t2) c1 = (x0 + x1) * (y0 + y1) - t0 - t1 + self.non_residue * t2 c2 = (x0 + x2) * (y0 + y2) - t0 - t2 + t1 return E6([c0, c1, c2], self.curve_id) def __rmul__(self, other): return self.__mul__(other) def __inv__(self): t0, t1, t2 = self.b0 * self.b0, self.b1 * self.b1, self.b2 * self.b2 t3, t4, t5 = self.b0 * self.b1, self.b0 * self.b2, self.b1 * self.b2 c0 = t0 - self.non_residue * t5 c1 = self.non_residue * t2 - t3 c2 = t1 - t4 t6 = self.b0 * c0 d1 = self.b2 * c1 d2 = self.b1 * c2 d1 = self.non_residue * (d1 + d2) t6 = t6 + d1 t6 = t6.__inv__() return E6([c0 * t6, c1 * t6, c2 * t6], self.curve_id) def mul_by_non_residue(self): return E6([self.non_residue * self.b2, self.b0, self.b1], self.curve_id) def square_torus(self): # SQ = 1/2(x+ v/x) <=> v = x (2SQ - x) one_over_2 = E6([pow(2, -1, self.b0.p), 0, 0, 0, 0, 0], self.curve_id) v = E6([0, 0, 1, 0, 0, 0], self.curve_id) x_inv = self.__inv__() v_x_inv = v * x_inv sq = one_over_2 * (self + v_x_inv) return sq def div(self, other): if isinstance(other, E6): return self * other.__inv__() return NotImplementedError def __pow__(self, p: int): """ Compute x**p in F_p^6 using square-and-multiply algorithm. Args: p: The exponent, a non-negative integer. Returns: x**p in F_p^6, represented similarly as x. """ assert isinstance(p, int), f"Invalid exponent {p=}" # Handle the easy cases. if p == 0: # x**0 = 1, where 1 is the multiplicative identity in F_p^2. return self.one(self.curve_id) elif p == 1: # x**1 = x. return self elif p < 0: return self.__inv__() ** (-p) # Start the computation. result = self.one( self.curve_id ) # Initialize result as the multiplicative identity in F_p^2. temp = self # Initialize temp as self. # Loop through each bit of the exponent p. for bit in reversed(bin(p)[2:]): # [2:] to strip the "0b" prefix. if bit == "1": result = result * temp temp = temp * temp return result @dataclass(slots=True, init=False) class E12: c0: E6 c1: E6 curve_id: int def __init__(self, x: list[PyFelt | int | E6], curve_id: int): self.curve_id = curve_id if isinstance(x[0], (PyFelt, int)) and len(x) == 12: self.c0 = E6(x=x[0:6], curve_id=curve_id) self.c1 = E6(x=x[6:12], curve_id=curve_id) elif type(x[0] == E6 and len(x) == 2): self.c0 = x[0] self.c1 = x[1] else: raise ValueError def __hash__(self): return hash((tuple(self.value_coeffs), self.curve_id)) @property def value_coeffs(self) -> list[int]: return [ self.c0.b0.a0, self.c0.b0.a1, self.c0.b1.a0, self.c0.b1.a1, self.c0.b2.a0, self.c0.b2.a1, self.c1.b0.a0, self.c1.b0.a1, self.c1.b1.a0, self.c1.b1.a1, self.c1.b2.a0, self.c1.b2.a1, ] def print_as_sage_poly(self, var_name: str = "x"): field = get_base_field(self.curve_id) coeffs = [field(c) for c in self.value_coeffs] coeffs = tower_to_direct(coeffs, self.curve_id, 12) return Polynomial(coeffs).print_as_sage_poly(var_name) @staticmethod def from_poly(poly: Polynomial, curve_id: int): field = get_base_field(curve_id) coeffs = poly.get_coeffs() coeffs = coeffs + [field(0)] * (12 - len(coeffs)) coeffs = direct_to_tower(coeffs, curve_id, 12) return E12(coeffs, curve_id) @staticmethod def from_direct(coeffs: list[PyFelt | ModuloCircuitElement], curve_id: int): coeffs = direct_to_tower([c.felt for c in coeffs], curve_id, 12) return E12(coeffs, curve_id) def to_poly(self) -> Polynomial: field = get_base_field(self.curve_id) coeffs = [field(c) for c in self.value_coeffs] coeffs = tower_to_direct(coeffs, self.curve_id, 12) return Polynomial(coeffs) def to_direct(self) -> list[PyFelt]: field = get_base_field(self.curve_id) coeffs = [field(c) for c in self.value_coeffs] coeffs = tower_to_direct(coeffs, self.curve_id, 12) return coeffs @property def order(self): return self.c0.b0.p**12 @property def felt_coeffs(self) -> list[PyFelt]: return [PyFelt(c, self.c0.b0.p) for c in self.value_coeffs] @staticmethod def one(curve_id: int): return E12([E6.one(curve_id), E6.zero(curve_id)], curve_id) @staticmethod def zero(curve_id: int): return E12([E6.zero(curve_id), E6.zero(curve_id)], curve_id) @staticmethod def random(curve_id: int): field = get_base_field(curve_id) return E12([field(random.randint(0, field.p - 1)) for _ in range(12)], curve_id) def __mul__(self, other): a = self.c0 + self.c1 b = other.c0 + other.c1 a = a * b b = self.c0 * other.c0 c = self.c1 * other.c1 z1 = a - b - c c = c.mul_by_non_residue() z0 = c + b return E12([z0, z1], self.curve_id) def conjugate(self): return E12([self.c0, -self.c1], self.curve_id) def square(self): c0 = self.c0 - self.c1 c3 = -(self.c1.mul_by_non_residue()) + self.c0 c2 = self.c0 * self.c1 c0 = (c0 * c3) + c2 c1 = c2 + c2 c2 = c2.mul_by_non_residue() c0 = c0 + c2 return E12([c0, c1], self.curve_id) def __inv__(self): t0, t1 = self.c0 * self.c0, self.c1 * self.c1 tmp = t1.mul_by_non_residue() t0 = t0 - tmp t1 = t0.__inv__() c0 = self.c0 * t1 c1 = -self.c1 * t1 return E12([c0, c1], curve_id=self.curve_id) def div(self, other): if isinstance(other, E12): return self * other.__inv__() raise NotImplementedError def __pow__(self, p: int): """ Compute x**p in F_p^12 using square-and-multiply algorithm. Args: p: The exponent, a non-negative integer. Returns: x**p in F_p^12, represented similarly as x. """ assert isinstance(p, int), f"Invalid exponent {p=}" # Handle the easy cases. if p == 0: # x**0 = 1, where 1 is the multiplicative identity in F_p^2. return self.one(self.curve_id) elif p == 1: # x**1 = x. return self elif p < 0: return self.__inv__() ** (-p) # Start the computation. result = self.one( self.curve_id ) # Initialize result as the multiplicative identity in F_p^2. temp = self # Initialize temp as self. # Loop through each bit of the exponent p. for bit in reversed(bin(p)[2:]): # [2:] to strip the "0b" prefix. if bit == "1": result = result * temp temp = temp.square() return result def final_exp(self, use_rust: bool = True): if use_rust: coeffs = garaga_rs.final_exp(self.curve_id, self.value_coeffs) return E12(coeffs, self.curve_id) else: cofactor = CURVES[self.curve_id].final_exp_cofactor h = ( cofactor * (CURVES[self.curve_id].p ** 12 - 1) // CURVES[self.curve_id].n ) return self**h def serialize(self) -> bytes: # Implement serialization like ark-ff: serialized = bytearray() bit_size = CURVES[self.curve_id].p.bit_length() byte_size = (bit_size + 7) // 8 for c in self.value_coeffs[::-1]: serialized.extend(c.to_bytes(byte_size, byteorder="big")) return bytes(serialized) def get_tower_object(x: list[PyFelt], curve_id: int, extension_degree: int): if extension_degree == 2: return E2(x[0].value, x[1].value, x[0].p) if extension_degree == 6: return E6(x, curve_id) elif extension_degree == 12: return E12(x, curve_id) else: raise ValueError ================================================ FILE: hydra/garaga/modulo_circuit.py ================================================ from dataclasses import dataclass, field from enum import Enum, auto from typing import List, Union from garaga.algebra import BaseField, ModuloCircuitElement, PyFelt, get_sparsity from garaga.curves import BASE, CURVES, N_LIMBS, STARK, CurveID from garaga.hints.io import bigint_split from garaga.modulo_circuit_structs import ( Cairo1SerializableStruct, GenericT, u128, u256, u384, ) BATCH_SIZE = 1 # Batch Size, only used in cairo 0 mode. class WriteOps(Enum): """ Enum for the source of a write operation in the value segment. -CONSTANT | INPUT: The value was written by coping N_LIMBS from the allocation pointer to the value segment. -COMMIT: The value was written as a result of a hint value from the prover, and needs to be hashed. -WITNESS: Same as COMMIT, but do not need to be hashed. -FELT: The value was written by coping N_LIMBS from the allocation pointer, as a result of a non-deterministic felt252 to UInt384 decomposition. In CairoZero, the value segment is increased by 1 due to an extra range check needed. -BUILTIN: The value was written by the modulo builtin as result of a ADD or MUL instruction. """ CONSTANT = auto() INPUT = auto() COMMIT = auto() WITNESS = auto() FELT = auto() BUILTIN = auto() class ModBuiltinOps(Enum): """ Enum for the modulo builtin operations. """ ADD = "+" MUL = "*" class CairoVMOps(Enum): ASSERT_EQ = "==" @dataclass(slots=True, frozen=True) class ModuloCircuitInstruction: operation: ModBuiltinOps left_offset: int right_offset: int result_offset: int comment: str | None @dataclass(slots=True, frozen=True) class ValueSegmentItem: emulated_felt: PyFelt write_source: WriteOps instruction: None | ModuloCircuitInstruction @property def value(self) -> int: return self.emulated_felt.value @property def p(self): return self.emulated_felt.p @property def felt(self): return self.emulated_felt @dataclass(slots=True, init=False) class ValueSegment: segment: dict[int, ValueSegmentItem] assert_eq_instructions: list[ModuloCircuitInstruction] offset: int n_limbs: int debug: bool name: str output: list[ModuloCircuitElement] segment_stacks: dict[WriteOps, dict[int, ValueSegmentItem]] output_structs: list[Cairo1SerializableStruct] | None def __init__(self, name: str, debug: bool = False, compilation_mode: int = 0): self.segment: dict[int, ValueSegmentItem] = dict() self.assert_eq_instructions: list[ModuloCircuitInstruction] = [] self.output: list[ModuloCircuitElement] = [] self.offset = 0 self.n_limbs = N_LIMBS self.debug = debug self.name = name self.segment_stacks = {key: dict() for key in WriteOps} self.output_structs = None if compilation_mode == 0 else [] def __len__(self) -> int: return len(self.segment) def __getitem__(self, key: int) -> ValueSegmentItem: return self.segment[key] @property def input(self) -> list[ModuloCircuitElement]: combined_items = [ (offset, item) for stack in [ WriteOps.INPUT, WriteOps.COMMIT, WriteOps.WITNESS, WriteOps.FELT, ] for offset, item in self.segment_stacks[stack].items() ] combined_items.sort(key=lambda x: x[0]) # Sort by offset return [ ModuloCircuitElement(item.emulated_felt, offset) for offset, item in combined_items ] def write_to_segment(self, item: ValueSegmentItem) -> int: offset = self.offset self.segment[offset] = item self.segment_stacks[item.write_source][offset] = item self.offset += N_LIMBS if item.write_source == WriteOps.FELT: self.offset += 1 return offset def non_interactive_transform(self) -> "ValueSegment": """ Rebuild a new ValueSegment by re-ordering the current one in this order: CONSTANT INPUT COMMIT WITNESS FELT BUILTIN Order matters! """ res = ValueSegment(self.name) offset_map = {} for stacks_key in [ WriteOps.CONSTANT, WriteOps.INPUT, WriteOps.COMMIT, WriteOps.WITNESS, WriteOps.FELT, WriteOps.BUILTIN, ]: if self.debug: print(stacks_key, len(self.segment_stacks[stacks_key])) for old_offset, item in self.segment_stacks[stacks_key].items(): # print(offset_map) if item.instruction is None: new_offset = res.write_to_segment(item) else: # print(item.instruction) new_offset = res.write_to_segment( ValueSegmentItem( item.emulated_felt, item.write_source, ModuloCircuitInstruction( operation=item.instruction.operation, left_offset=offset_map.get( item.instruction.left_offset, res.offset ), right_offset=offset_map.get( item.instruction.right_offset, res.offset ), result_offset=offset_map.get( item.instruction.result_offset, res.offset ), comment=item.instruction.comment, ), ) ) offset_map[old_offset] = new_offset # Those are builtins instructions that did not create any new value. for assert_eq_instruction in self.assert_eq_instructions: res.assert_eq_instructions.append( ModuloCircuitInstruction( operation=assert_eq_instruction.operation, left_offset=offset_map[assert_eq_instruction.left_offset], right_offset=offset_map[assert_eq_instruction.right_offset], result_offset=offset_map[assert_eq_instruction.result_offset], comment=assert_eq_instruction.comment, ) ) new_output = [] new_output_structs = None if self.output_structs is None else [] for elmt in self.output: new_output.append(ModuloCircuitElement(elmt.felt, offset_map[elmt.offset])) if self.output_structs is not None: for struct in self.output_structs: new_output_structs.append( struct.__class__( struct.name, [ ModuloCircuitElement(elt.felt, offset_map[elt.offset]) for elt in struct.elmts ], ) ) res.output = new_output res.output_structs = new_output_structs return res def get_dw_lookups(self) -> dict: """ Returns the DW arrays for the compiled circuit. Only relevant in Cairo 0 mode. """ dw_arrays = { "constants_ptr": [], "add_offsets_ptr": [], "mul_offsets_ptr": [], "output_offsets_ptr": [], "poseidon_indexes_ptr": [], } for _, item in self.segment_stacks[WriteOps.CONSTANT].items(): dw_arrays["constants_ptr"].append( bigint_split(item.value, self.n_limbs, BASE) ) for write_op in [WriteOps.BUILTIN, WriteOps.WITNESS]: for result_offset, item in self.segment_stacks[write_op].items(): if not item.instruction: continue # print(item.instruction) dw_arrays[ item.instruction.operation.name.lower() + "_offsets_ptr" ].append( ( item.instruction.left_offset, item.instruction.right_offset, item.instruction.result_offset, item.instruction.comment, ) ) for assert_eq_instruction in self.assert_eq_instructions: dw_arrays[ assert_eq_instruction.operation.name.lower() + "_offsets_ptr" ].append( ( assert_eq_instruction.left_offset, assert_eq_instruction.right_offset, assert_eq_instruction.result_offset, assert_eq_instruction.comment, ) ) for output_elmt in self.output: dw_arrays["output_offsets_ptr"].append(output_elmt.offset) # print("dw_arrays[add_offsets_ptr]", dw_arrays["add_offsets_ptr"]) return dw_arrays def print(self): # ANSI escape codes for some colors RED = "\033[31m" # Red text GREEN = "\033[32m" # Green text BLUE = "\033[34m" # Blue text ORANGE = "\033[33m" # Orange text RESET = "\033[0m" # Reset to default color # print(f"{RED}This will be red!{RESET}") # print(f"{GREEN}This will be green!{RESET}") for i, (offset, val) in enumerate(self.segment.items()): row = "" row += f"{BLUE}{'['+str(i)+']':^7}{RESET}|{ORANGE}{'['+str(offset)+']':^7}{RESET}|" if val.instruction: row += f"{str(val.instruction.left_offset)+str(val.instruction.operation.value)+str(val.instruction.right_offset)+'='+str(val.instruction.result_offset):^9}|" else: row += f"{'_':^9}|" row += f"{val.write_source.name:^8}|" import numpy as np row += f"\t{RED}{np.base_repr(val.emulated_felt.value, base=36)}{RESET} {val.instruction.comment if val.instruction else ''}" print(row) def summarize(self): all_instructions = { item.instruction for item in self.segment.values() if item.instruction } all_assert_eq_instructions = set(self.assert_eq_instructions) all_instructions_except_assert_eq = ( all_instructions - all_assert_eq_instructions ) add_count: int = 0 mul_count: int = 0 for instruction in all_instructions_except_assert_eq: if instruction.operation.name == "ADD": add_count += 1 elif instruction.operation.name == "MUL": mul_count += 1 return add_count, mul_count, len(all_assert_eq_instructions) class ModuloCircuit: """ Represents a modulo circuit capable of performing arithmetic operations on base field elements, storing constants, and caching powers of base field elements. Attributes: circuit_name (str): The name of the circuit. last_offset (int): The last used offset in the circuit's memory. N_LIMBS (int): The number of limbs used in the circuit. values_segment (dict[int, BaseFieldElement]): A dictionary mapping offsets to base field elements. add_offsets (list[tuple]): A list of tuples representing the offsets involved in addition operations. mul_offsets (list[tuple]): A list of tuples representing the offsets involved in multiplication operations. constants (dict[str, ModuloElement]): A dictionary mapping constant names to their ModuloElement representations. """ def __init__( self, name: str, curve_id: int, generic_circuit: bool = False, generic_modulus: bool = False, compilation_mode: int = 0, ) -> None: assert ( len(name) <= 31 ), f"Name '{name}' is too long to fit in a felt252, size is: {len(name)}" self.name = name self.class_name = "ModuloCircuit" self.curve_id = curve_id self.field = BaseField(CURVES[curve_id].p) self.N_LIMBS = 4 self.values_segment: ValueSegment = ValueSegment( name=name, compilation_mode=compilation_mode ) self.constants: dict[int, ModuloCircuitElement] = dict() self.generic_circuit = generic_circuit self.generic_modulus = ( generic_modulus # Generic modulus has precedence over generic_circuit ) self.compilation_mode = compilation_mode self.exact_output_refs_needed = None self.input_structs: list[Cairo1SerializableStruct] = [] self.do_not_inline = False @property def values_offset(self) -> int: return self.values_segment.offset @property def output(self) -> list[ModuloCircuitElement]: return self.values_segment.output @property def input(self) -> list[ModuloCircuitElement]: return self.values_segment.input @property def output_structs(self) -> list[Cairo1SerializableStruct]: return self.values_segment.output_structs @property def continuous_output(self) -> bool: # Only useful in cairo 0 mode. return all( self.output[i + 1].offset - self.output[i].offset == N_LIMBS for i in range(len(self.output) - 1) ) @property def witnesses(self) -> list[PyFelt]: # Only useful in cairo 0 mode. return [ self.values_segment.segment_stacks[WriteOps.WITNESS][offset].felt for offset in sorted(self.values_segment.segment_stacks[WriteOps.WITNESS]) ] def is_empty_circuit(self) -> bool: return len(self.values_segment.segment_stacks[WriteOps.BUILTIN]) == 0 def write_element( self, elmt: PyFelt | int, write_source: WriteOps = WriteOps.INPUT, instruction: ModuloCircuitInstruction | None = None, ) -> ModuloCircuitElement: """ Register an emulated field element to the circuit given its value and the write source. Returns a ModuloCircuitElement representing the written element with its offset as identifier. """ assert isinstance(elmt, PyFelt) or isinstance( elmt, int ), f"Expected PyFelt or int, got {type(elmt)}" if isinstance(elmt, int): elmt = self.field(elmt) value_offset = self.values_segment.write_to_segment( ValueSegmentItem( elmt, write_source, instruction, ) ) res = ModuloCircuitElement(elmt, value_offset) return res def write_struct( self, struct: Cairo1SerializableStruct, write_source: WriteOps = WriteOps.INPUT, ) -> Union[ ModuloCircuitElement, List[ModuloCircuitElement], List[List[Union[ModuloCircuitElement, List[ModuloCircuitElement]]]], ]: all_pyfelt = all(type(elmt) == PyFelt for elmt in struct.elmts) all_cairo1serializablestruct = all( isinstance(elmt, Cairo1SerializableStruct) for elmt in struct.elmts ) assert ( all_pyfelt or all_cairo1serializablestruct ), f"Expected list of PyFelt or Cairo1SerializableStruct, got {[type(elmt) for elmt in struct.elmts]}" if all_pyfelt: self.input_structs.append(struct) if len(struct) == 1 and isinstance(struct, (u384, u256, u128, GenericT)): return self.write_element(struct.elmts[0], write_source) else: return self.write_elements(struct.elmts, write_source) elif all_cairo1serializablestruct: result = [self.write_struct(elmt, write_source) for elmt in struct.elmts] # Ensure only the larger struct is appended self.input_structs = [ s for s in self.input_structs if s not in struct.elmts ] self.input_structs.append(struct) return result def write_elements( self, elmts: list[PyFelt], operation: WriteOps = WriteOps.INPUT, sparsity: list[int] = None, ) -> list[ModuloCircuitElement]: if sparsity is not None: assert len(sparsity) == len( elmts ), f"Expected sparsity of length {len(elmts)}, got {len(sparsity)}" vals = [ ( self.write_element(elmt, operation) if sparsity[i] != 0 else self.set_or_get_constant(0) ) for i, elmt in enumerate(elmts) ] else: vals = [self.write_element(elmt, operation, None) for elmt in elmts] return vals def write_cairo_native_felt(self, native_felt: PyFelt): assert ( self.compilation_mode == 0 ), "write_cairo_native_felt is not supported in cairo 1 mode" assert isinstance( native_felt, PyFelt ), f"Expected PyFelt, got {type(native_felt)}" assert 0 <= native_felt.value < STARK res = self.write_element(elmt=native_felt, write_source=WriteOps.FELT) return res def write_sparse_constant_elements( self, elmts: list[PyFelt] ) -> tuple[list[ModuloCircuitElement], list[int]]: sparsity = get_sparsity(elmts) elements = [] for elmt, s in zip(elmts, sparsity): match s: case 0: # Mocked 0 element not written to the circuit. Be careful to pass sparsity when evaluating. elements.append(ModuloCircuitElement(self.field.zero(), -1)) case 2: # Mocked 1 element not written to the circuit. Be careful to pass sparsity when evaluating. elements.append(ModuloCircuitElement(self.field.one(), -1)) case _: elements.append(self.set_or_get_constant(elmt.value)) return elements, sparsity def set_or_get_constant(self, val: PyFelt | int) -> ModuloCircuitElement: if isinstance(val, int): val = self.field(val) if val.value in self.constants: # print((f"/!\ Constant '{hex(val.value)}' already exists.")) return self.constants[val.value] self.constants[val.value] = self.write_element(val, WriteOps.CONSTANT) return self.constants[val.value] def add( self, a: ModuloCircuitElement, b: ModuloCircuitElement, comment: str | None = None, ) -> ModuloCircuitElement: if a is None and isinstance(b, ModuloCircuitElement): return b elif b is None and isinstance(a, ModuloCircuitElement): return a else: assert isinstance(a, ModuloCircuitElement) and isinstance( b, ModuloCircuitElement ), f"Expected ModuloElement, got {type(a)}, {a} and {type(b)}, {b}" instruction = ModuloCircuitInstruction( ModBuiltinOps.ADD, a.offset, b.offset, self.values_offset, comment ) return self.write_element( a.emulated_felt + b.emulated_felt, WriteOps.BUILTIN, instruction ) def sum(self, args: list[ModuloCircuitElement], comment: str | None = None): if not args: raise ValueError("The 'args' list cannot be empty.") assert all(isinstance(elmt, ModuloCircuitElement) for elmt in args) result = args[0] for elmt in args[1:]: result = self.add(result, elmt, comment) return result def product(self, args: list[ModuloCircuitElement], comment: str | None = None): if not args: raise ValueError("The 'args' list cannot be empty.") assert all(isinstance(elmt, ModuloCircuitElement) for elmt in args) result = args[0] for elmt in args[1:]: result = self.mul(result, elmt, comment) return result def double(self, a: ModuloCircuitElement) -> ModuloCircuitElement: return self.add(a, a) def mul( self, a: ModuloCircuitElement, b: ModuloCircuitElement, comment: str | None = None, ) -> ModuloCircuitElement: if a is None and isinstance(b, ModuloCircuitElement): return self.set_or_get_constant(0) elif b is None and isinstance(a, ModuloCircuitElement): return self.set_or_get_constant(0) assert isinstance(a, ModuloCircuitElement) and isinstance( b, ModuloCircuitElement ), f"Expected ModuloElement, got lhs {type(a)}, {a} and rhs {type(b)}, {b}" instruction = ModuloCircuitInstruction( ModBuiltinOps.MUL, a.offset, b.offset, self.values_offset, comment ) return self.write_element( a.emulated_felt * b.emulated_felt, WriteOps.BUILTIN, instruction ) def square( self, a: ModuloCircuitElement, comment: str | None = None ) -> ModuloCircuitElement: return self.mul(a, a, comment) def neg( self, a: ModuloCircuitElement, comment: str | None = None ) -> ModuloCircuitElement: assert ( type(a) == ModuloCircuitElement ), f"Expected ModuloElement, got {type(a)}, {a}" res = self.sub(self.set_or_get_constant(self.field.zero()), a, comment) return res def sub( self, a: ModuloCircuitElement, b: ModuloCircuitElement, comment: str | None = None, ): assert isinstance(a, ModuloCircuitElement) and isinstance( b, ModuloCircuitElement ), f"Expected ModuloElement, got {type(a)}, {a} and {type(b)}, {b}" instruction = ModuloCircuitInstruction( ModBuiltinOps.ADD, b.offset, self.values_offset, a.offset, comment ) return self.write_element(a.felt - b.felt, WriteOps.BUILTIN, instruction) def inv( self, a: ModuloCircuitElement, comment: str | None = None, ): assert isinstance( a, ModuloCircuitElement ), f"Expected ModuloElement, got {type(a)}, {a}" if self.compilation_mode == 0: one = self.set_or_get_constant( 1 ) # Write one before accessing its offset so self.values_offset is correctly updated. instruction = ModuloCircuitInstruction( ModBuiltinOps.MUL, a.offset, self.values_offset, one.offset, comment, ) elif self.compilation_mode == 1: instruction = ModuloCircuitInstruction( ModBuiltinOps.MUL, a.offset, None, None, comment, ) return self.write_element(a.felt.__inv__(), WriteOps.BUILTIN, instruction) def div( self, a: ModuloCircuitElement, b: ModuloCircuitElement, comment: str | None = None, ): assert isinstance(a, ModuloCircuitElement) and isinstance( b, ModuloCircuitElement ), f"Expected ModuloElement, got {type(a)}, {a} and {type(b)}, {b}" if self.compilation_mode == 0: instruction = ModuloCircuitInstruction( ModBuiltinOps.MUL, b.offset, self.values_offset, a.offset, comment ) return self.write_element( a.felt * b.felt.__inv__(), WriteOps.BUILTIN, instruction ) else: return self.mul(a, self.inv(b)) def fp_sqrt(self, element: ModuloCircuitElement) -> ModuloCircuitElement: """ Computes "a" square root of a field element. /!\ Warning : This circuit is non deterministic /!\ /!\ Two square roots exist for any non-zero element, and no constraint is enforced to select any of them /!\ Raises ValueError if the element is not a quadratic residue. """ assert self.compilation_mode == 0, "fp_sqrt is not supported in cairo 1 mode" root = element.felt.sqrt(min_root=False) # Write the root as a witness and verify it root = self.write_element(root, WriteOps.WITNESS) self.mul_and_assert(root, root, element, comment="Fp sqrt") return root def fp_is_non_zero(self, a: ModuloCircuitElement) -> ModuloCircuitElement: """ Returns 1 if a != 0, 0 if a == 0. Enforces soundness by forcing `flag` to be a true indicator of whether 'a' is non-zero. Main Constraints: 1) flag * (1 - flag) = 0 - Ensures that `flag` ∈ {0,1}, i.e., it's a binary indicator. 2) Prover supplies a_inv as a “would-be” inverse of `a`. - If a != 0, a_inv should be the genuine inverse, i.e. a * a_inv = 1. - If a == 0, a_inv is irrelevant and effectively ignored. 3) flag*(a * a_inv) + (1 - flag)*(a + 1) == 1 - If a == 0 → the only way is flag=0, so: 0 * (0 * a_inv) + 1 * (0 + 1) = 1 which is satisfied. - If a != 0 → the only way is flag=1, so: 1 * (a * a_inv) + 0 * (a + 1) = 1 forcing a_inv to be a true inverse of a. Consequently: • When a == 0, the circuit forces flag=0 and ignores a_inv. • When a != 0, the circuit forces flag=1 and requires a_inv to be the correct inverse. Overall, this design prevents cheating (e.g. claiming a != 0 when it's actually 0, or supplying a bogus inverse) because the single equation in step (3) couples a, a_inv, and flag in a way that only the correct assignments can satisfy all constraints. """ assert ( self.compilation_mode == 0 ), "`fp_is_non_zero_flag` is only supported in cairo 0 mode." # Step 1: Prover declares a boolean-labeled witness: 1 if a != 0, else 0 is_non_zero_python_bool = int(a.value != 0) flag = self.write_element(is_non_zero_python_bool, WriteOps.WITNESS) # Step 2: Force the flag to be a single bit: flag * (1 - flag) == 0 one_minus_flag = self.sub(self.set_or_get_constant(1), flag) self.mul_and_assert( flag, one_minus_flag, self.set_or_get_constant(0), comment="flag ∈ {0,1}", ) # Step 3: The prover supplies a_inv as a witness. # If flag=1 (a != 0), a_inv must be the real inverse: a*a_inv = 1. # If flag=0 (a == 0), a_inv is irrelevant. a_inv_val = 0 if is_non_zero_python_bool: a_inv_val = a.felt.__inv__().value a_inv = self.write_element(a_inv_val, WriteOps.WITNESS) # Step 4: Combine them with the core check: # flag*(a*a_inv) + (1 - flag)*(a+1) == 1 # => forces correct assignments for (flag, a_inv) flag_eq_0_branch = self.add(a, self.set_or_get_constant(1)) flag_eq_1_branch = self.mul(a, a_inv) self.add_and_assert( self.mul(flag, flag_eq_1_branch), self.mul(one_minus_flag, flag_eq_0_branch), self.set_or_get_constant(1), ) # Return the final flag: 1 if a != 0, 0 if a == 0 return flag def vector_sub( self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: return [ self.sub(x, y, comment=f"Fp{len(X)} sub coeff {i}/{len(X)-1}") for i, (x, y) in enumerate(zip(X, Y)) ] def vector_scale( self, X: list[ModuloCircuitElement], c: ModuloCircuitElement ) -> list[ModuloCircuitElement]: """ Multiplies a polynomial with coefficients `X` by a scalar `c`. Input : I(x) = i0 + i1*x + i2*x^2 + ... + in-1*x^n-1 Output : O(x) = ci0 + ci1*x + ci2*x^2 + ... + cin-1*x^n-1. This is done in the circuit. """ assert isinstance(c, ModuloCircuitElement), "c must be a ModuloCircuitElement" return [ self.mul(x_i, c, comment=f"Fp{len(X)} scalar mul coeff {i}/{len(X)-1}") for i, x_i in enumerate(X) ] def vector_add( self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Adds two polynomials with coefficients `X` and `Y`. Returns R = [x0 + y0, x1 + y1, x2 + y2, ... + xn-1 + yn-1] mod p """ assert len(X) == len(Y), f"len(X)={len(X)} != len(Y)={len(Y)}" return [ self.add(x_i, y_i, comment=f"Fp{len(X)} add coeff {i}/{len(X)-1}") for i, (x_i, y_i) in enumerate(zip(X, Y)) ] def vector_neg(self, X: list[ModuloCircuitElement]) -> list[ModuloCircuitElement]: """ Negates a polynomial with coefficients `X`. Returns R = [-x0, -x1, -x2, ... -xn-1] mod p """ return [ self.neg(x_i, comment=f"Fp{len(X)} neg coeff {i}/{len(X)-1}") for i, x_i in enumerate(X) ] def sub_and_assert( self, a: ModuloCircuitElement, b: ModuloCircuitElement, c: ModuloCircuitElement, comment: str | None = None, ): """ Subtracts b from a and asserts that the result is equal to c. In practice, it checks that c + b = a [mod p]. All three values are expected to be already in the value segment, no new value is created. Costs 2 Steps. """ assert ( self.compilation_mode == 0 ), "sub_and_assert is not supported in cairo 1 mode" instruction = ModuloCircuitInstruction( ModBuiltinOps.ADD, c.offset, b.offset, a.offset, comment ) self.values_segment.assert_eq_instructions.append(instruction) return c def add_and_assert( self, a: ModuloCircuitElement, b: ModuloCircuitElement, c: ModuloCircuitElement, comment: str | None = None, ): """ Adds a and b and asserts that the result is equal to c. In practice, it only checks that a + b = c [mod p]. All three values are expected to be already in the value segment, no new value is created. Costs 2 Steps. """ assert ( self.compilation_mode == 0 ), "add_and_assert is not supported in cairo 1 mode" instruction = ModuloCircuitInstruction( ModBuiltinOps.ADD, a.offset, b.offset, c.offset, comment ) self.values_segment.assert_eq_instructions.append(instruction) return c def mul_and_assert( self, a: ModuloCircuitElement, b: ModuloCircuitElement, c: ModuloCircuitElement, comment: str | None = None, ): assert ( self.compilation_mode == 0 ), "mul_and_assert is not supported in cairo 1 mode" instruction = ModuloCircuitInstruction( ModBuiltinOps.MUL, a.offset, b.offset, c.offset, comment ) self.values_segment.assert_eq_instructions.append(instruction) return c def eval_horner( self, poly: list[ModuloCircuitElement], z: ModuloCircuitElement, poly_name: str = None, var_name: str = "z", ): """ Evaluates a polynomial at point z using Horner's method. Assumes that the polynomial is in the form a0 + a1*z + a2*z^2 + ... + an*z^n, indexed with the constant coefficient first. """ if poly_name is None: poly_name = "UnnamedPoly" # Regular Horner evaluation acc = poly[-1] # Start with the highest degree coefficient for i in range(len(poly) - 2, -1, -1): acc = self.add( poly[i], self.mul( acc, z, comment=f"Eval {poly_name} Horner step: multiply by {var_name}", ), comment=f"Eval {poly_name} Horner step: add coefficient_{i}", ) return acc def eval_poly( self, poly: list[ModuloCircuitElement], X_powers: list[ModuloCircuitElement], poly_name: str = None, var_name: str = "x", ): """ Evaluates a polynomial at precomputed powers of X. Assumes that the polynomial is in the form a0 + a1*x + a2*x^2 + ... + an*x^n, indexed with the constant coefficient first. Assumes that X_powers is a list of powers of X, such that X_powers[i] = X^(i+1). """ if poly_name is None: poly_name = "UnnamedPoly" assert len(poly) - 1 <= len( X_powers ), f"Expected at least {len(poly) - 1} powers of X to evaluate P, got {len(X_powers)}" acc = poly[0] for i in range(1, len(poly)): acc = self.add( acc, self.mul( poly[i], X_powers[i - 1], comment=f"Eval {poly_name} step coeff_{i} * {var_name}^{i}", ), comment=f"Eval {poly_name} step + (coeff_{i} * {var_name}^{i})", ) return acc def extend_output(self, elmts: list[ModuloCircuitElement]): """ Adds elements to the output of the circuit. """ assert isinstance(elmts, (list, tuple)) assert all(isinstance(x, ModuloCircuitElement) for x in elmts) self.output.extend(elmts) return def extend_struct_output(self, struct: Cairo1SerializableStruct): """ Adds elements to the output of the circuit in struct form. """ assert isinstance(struct, Cairo1SerializableStruct) if self.compilation_mode == 0: self.extend_output(struct.elmts) else: self.values_segment.output_structs.append(struct) self.extend_output(struct.elmts) return def print_value_segment(self): self.values_segment.print() def compile_circuit( self, function_name: str = None, pub: bool = True, inline: bool = True, generic_modulus: bool = False, ): if self.is_empty_circuit(): return "", "" self.values_segment = self.values_segment.non_interactive_transform() inline = inline and not self.do_not_inline if self.compilation_mode == 0: return self.compile_circuit_cairo_zero(function_name), None elif self.compilation_mode == 1: return self.compile_circuit_cairo_1( function_name, pub, inline, generic_modulus ) def compile_circuit_cairo_zero( self, function_name: str = None, returns: dict[str] = { "felt*": [ "constants_ptr", "add_offsets_ptr", "mul_offsets_ptr", "output_offsets_ptr", ], "felt": [ "constants_ptr_len", "input_len", "witnesses_len", "output_len", "continuous_output", "add_mod_n", "mul_mod_n", "n_assert_eq", "name", "curve_id", ], }, ) -> str: dw_arrays = self.values_segment.get_dw_lookups() name = function_name or self.values_segment.name function_name = f"get_{name}_circuit" if self.generic_circuit: code = ( f"func {function_name}(curve_id:felt)->(circuit:{self.class_name}*)" + "{" + "\n" ) else: code = f"func {function_name}()->(circuit:{self.class_name}*)" + "{" + "\n" code += "alloc_locals;\n" code += "let (__fp__, _) = get_fp_and_pc();\n" for dw_array_name in returns["felt*"]: code += f"let ({dw_array_name}:felt*) = get_label_location({dw_array_name}_loc);\n" code += f"let constants_ptr_len = {len(dw_arrays['constants_ptr'])};\n" code += f"let input_len = {len(self.values_segment.segment_stacks[WriteOps.INPUT])*N_LIMBS};\n" code += f"let witnesses_len = {len(self.values_segment.segment_stacks[WriteOps.WITNESS])*N_LIMBS};\n" code += f"let output_len = {len(self.output)*N_LIMBS};\n" continuous_output = self.continuous_output code += f"let continuous_output = {1 if continuous_output else 0};\n" code += f"let add_mod_n = {len(dw_arrays['add_offsets_ptr'])};\n" code += f"let mul_mod_n = {len(dw_arrays['mul_offsets_ptr'])};\n" code += ( f"let n_assert_eq = {len(self.values_segment.assert_eq_instructions)};\n" ) code += f"let name = '{self.name}';\n" code += ( f"let curve_id = {'curve_id' if self.generic_circuit else self.curve_id};\n" ) code += f"local circuit:{self.class_name} = {self.class_name}({', '.join(returns['felt*'])}, {', '.join(returns['felt'])});\n" code += "return (&circuit,);\n" for dw_array_name in returns["felt*"]: dw_values = dw_arrays[dw_array_name] code += f"\t {dw_array_name}_loc:\n" if dw_array_name == "constants_ptr": for bigint in dw_values: for limb in bigint: code += f"\t dw {limb};\n" code += "\n" elif dw_array_name in ["add_offsets_ptr", "mul_offsets_ptr"]: num_instructions = len(dw_values) instructions_needed = ( BATCH_SIZE - (num_instructions % BATCH_SIZE) ) % BATCH_SIZE # Must be a multiple of 8 (currently) for left, right, result, comment in dw_values: code += ( f"\t dw {left}; // {comment}\n" + f"\t dw {right};\n" + f"\t dw {result};\n" ) if instructions_needed > 0: first_triplet = dw_values[0] for _ in range(instructions_needed): code += ( f"\t dw {first_triplet[0]};\n" + f"\t dw {first_triplet[1]};\n" + f"\t dw {first_triplet[2]};\n" ) code += "\n" elif dw_array_name in ["output_offsets_ptr"]: if continuous_output: code += f"\t dw {dw_values[0]};\n" else: for val in dw_values: code += f"\t dw {val};\n" code += "\n" code += "}\n" return code def write_cairo1_input_stack( self, write_ops: WriteOps, code: str, offset_to_reference_map: dict[int, str], start_index: int, ) -> tuple: """ Defines the inputs for the compiled Cairo 1 circuit. """ len_stack = len(self.values_segment.segment_stacks[write_ops]) if len_stack > 0: code += f"\n // {write_ops.name} stack\n" offsets = list(self.values_segment.segment_stacks[write_ops].keys()) i = 0 while i < len_stack: if write_ops == WriteOps.CONSTANT: val = self.values_segment.segment[offsets[i]].value if 0 < -val % self.field.p <= 100: comment = f"// -{hex(-val%self.field.p)} % p" else: comment = f"// {hex(val)}" code += f"\t let in{start_index+i} = CE::> {{}}; {comment}\n" offset_to_reference_map[offsets[i]] = f"in{start_index+i}" i += 1 else: if i + 2 < len_stack: code += f"\t let (in{start_index+i}, in{start_index+i+1}, in{start_index+i+2}) = (CE::> {{}}, CE::> {{}}, CE::> {{}});\n" offset_to_reference_map[offsets[i]] = f"in{start_index+i}" offset_to_reference_map[offsets[i + 1]] = f"in{start_index+i+1}" offset_to_reference_map[offsets[i + 2]] = f"in{start_index+i+2}" i += 3 elif i + 1 < len_stack: code += f"\t let (in{start_index+i}, in{start_index+i+1}) = (CE::> {{}}, CE::> {{}});\n" offset_to_reference_map[offsets[i]] = f"in{start_index+i}" offset_to_reference_map[offsets[i + 1]] = f"in{start_index+i+1}" i += 2 else: code += f"\t let in{start_index+i} = CE::> {{}};\n" offset_to_reference_map[offsets[i]] = f"in{start_index+i}" i += 1 return ( code, offset_to_reference_map, start_index + len_stack, ) else: return code, offset_to_reference_map, start_index def fill_cairo_1_constants(self) -> tuple[str, str]: """ Return the part of the code that fills the constants to the circuit, and the constants array if there are more than 8 constants. In that case, .next_span() is used to save bytecode and the constants are stored in a const array. """ constants_ints = [ self.values_segment.segment[offset].value for offset in self.values_segment.segment_stacks[WriteOps.CONSTANT].keys() ] if len(constants_ints) < 8: constants_split = [bigint_split(x, N_LIMBS, BASE) for x in constants_ints] constants_filled = "\n".join( f"circuit_inputs = circuit_inputs.next_2([{','.join(hex(x) for x in constants_split[i])}]); // in{i}" for i in range(len(constants_ints)) ) return constants_filled, None else: import garaga.hints.io as io const_name = ( self.name.upper() + "_" + CurveID(self.curve_id).name.upper() + "_CONSTANTS" ) constants_filled = f""" circuit_inputs = circuit_inputs.next_span({const_name}.span()); // in{0} - in{len(constants_ints)-1} """ const_array = f"const {const_name}: [u384; {len(constants_ints)}] = {io.int_array_to_u384_array(constants_ints, const=True)};" return constants_filled, const_array def write_cairo1_circuit(self, offset_to_reference_map: dict[int, str]) -> str: """ Defines the arithmetic instructions for the compiled Cairo 1 circuit. """ code = "" for i, (offset, vs_item) in enumerate( self.values_segment.segment_stacks[WriteOps.BUILTIN].items() ): op = vs_item.instruction.operation left_offset = vs_item.instruction.left_offset right_offset = vs_item.instruction.right_offset result_offset = vs_item.instruction.result_offset comment = vs_item.instruction.comment or "" # print(i, op, left_offset, right_offset, result_offset) match op: case ModBuiltinOps.ADD: if right_offset > result_offset: # Case sub code += f"let t{i} = circuit_sub({offset_to_reference_map[result_offset]}, {offset_to_reference_map[left_offset]}); {'// '+comment if comment else ''}\n" offset_to_reference_map[offset] = f"t{i}" assert offset == right_offset else: code += f"let t{i} = circuit_add({offset_to_reference_map[left_offset]}, {offset_to_reference_map[right_offset]}); {'// '+comment if comment else ''}\n" offset_to_reference_map[offset] = f"t{i}" assert offset == result_offset case ModBuiltinOps.MUL: if right_offset == result_offset == offset: # Case inv # print(f"\t INV {left_offset} {right_offset} {result_offset}") code += f"let t{i} = circuit_inverse({offset_to_reference_map[left_offset]}); {'// '+comment if comment else ''}\n" offset_to_reference_map[offset] = f"t{i}" else: # print(f"MUL {left_offset} {right_offset} {result_offset}") code += f"let t{i} = circuit_mul({offset_to_reference_map[left_offset]}, {offset_to_reference_map[right_offset]}); {'// '+comment if comment else ''}\n" offset_to_reference_map[offset] = f"t{i}" assert offset == result_offset return code def compile_circuit_cairo_1( self, function_name: str = None, pub: bool = False, inline: bool = True, generic_modulus: bool = False, ) -> tuple[str, str]: """ Defines the Cairo 1 function code for the compiled circuit. """ name = function_name or self.values_segment.name function_name = f"run_{name}_circuit" curve_index = CurveID.find_value_in_string(name) return_is_struct = False input_is_struct = False if self.output_structs: if sum([len(x.elmts) for x in self.output_structs]) == len(self.output): return_is_struct = True signature_output = ( f"({','.join([x.struct_name for x in self.output_structs])}" ) signature_output += ",)" if len(self.output_structs) == 1 else ")" else: raise ValueError( f"Output structs must have the same number of elements as the output: {len(self.output_structs)=} != {len(self.output)=}" ) else: signature_output = "Array" if self.input_structs: if sum([len(x) for x in self.input_structs]) == len(self.input): input_is_struct = True signature_input = f"{','.join([x.serialize_input_signature() for x in self.input_structs])}" else: raise ValueError( f"Input structs must have the same number of elements as the input: {sum([len(x) for x in self.input_structs])=} != {len(self.input)=}" ) else: signature_input = "mut input: Array" if "" in signature_input or ":T," in signature_input: generic_input = ", +Drop, +Copy>" else: generic_input = "" if pub: prefix = "pub " else: prefix = "" if inline: if generic_input == "": attribute = "#[inline(always)]" else: attribute = "#[inline]" else: attribute = "" generic_modulus = generic_modulus or self.generic_modulus if generic_modulus: code = f"{attribute}\n{prefix}fn {function_name}{generic_input}({signature_input}, modulus:core::circuit::CircuitModulus)->{signature_output} {{\n" elif self.generic_circuit: code = f"{attribute}\n{prefix}fn {function_name}{generic_input}({signature_input}, curve_index:usize)->{signature_output} {{\n" else: code = f"{attribute}\n{prefix}fn {function_name}{generic_input}({signature_input})->{signature_output} {{\n" # Define the input for the circuit. code, offset_to_reference_map, start_index = self.write_cairo1_input_stack( WriteOps.CONSTANT, code, {}, 0 ) ( code, offset_to_reference_map, commit_start_index, ) = self.write_cairo1_input_stack( WriteOps.INPUT, code, offset_to_reference_map, start_index ) code, offset_to_reference_map, commit_end_index = self.write_cairo1_input_stack( WriteOps.COMMIT, code, offset_to_reference_map, commit_start_index ) code, offset_to_reference_map, start_index = self.write_cairo1_input_stack( WriteOps.WITNESS, code, offset_to_reference_map, commit_end_index ) code, offset_to_reference_map, start_index = self.write_cairo1_input_stack( WriteOps.FELT, code, offset_to_reference_map, start_index ) code += self.write_cairo1_circuit(offset_to_reference_map) outputs_refs = [] for out in self.output: if self.values_segment[out.offset].write_source == WriteOps.BUILTIN: outputs_refs.append(offset_to_reference_map[out.offset]) else: continue if self.exact_output_refs_needed: outputs_refs_needed = [ offset_to_reference_map[out.offset] for out in self.exact_output_refs_needed ] else: outputs_refs_needed = outputs_refs if generic_modulus: code += "\nlet modulus = modulus;\n" elif curve_index is not None: code += f""" let modulus = crate::definitions::get_{CurveID(self.curve_id).name}_modulus(); // {CurveID(self.curve_id).name} prime field modulus """ else: code += """ let modulus = crate::definitions::get_modulus(curve_index); """ code += f""" let mut circuit_inputs = ({','.join(outputs_refs_needed)},).new_inputs(); // Prefill constants: """ tmp, const_array = self.fill_cairo_1_constants() code += tmp code += """ // Fill inputs: """ acc_len = len(self.values_segment.segment_stacks[WriteOps.CONSTANT]) if input_is_struct: for struct in self.input_structs: struct_code = struct.dump_to_circuit_input() struct_code_lines = [ line for line in struct_code.split("\n") if line.strip() ] if "while let" not in struct_code and "for val in" not in struct_code: struct_code_with_counter = "\n".join( f"{line} // in{i+acc_len}" for i, line in enumerate(struct_code_lines) ) else: struct_code_with_counter = ( struct_code + f" // in{acc_len} - in{acc_len+len(struct)-1}\n" ) acc_len += len(struct) code += struct_code_with_counter + "\n" else: code += """ let mut input = input; while let Option::Some(val) = input.pop_front() { circuit_inputs = circuit_inputs.next_2(val); }; """ code += """ let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); """ if return_is_struct: code += "\n".join( [ struct.extract_from_circuit_output(offset_to_reference_map) for struct in self.output_structs ] ) code += ( f"return ({','.join([struct.name for struct in self.output_structs])}" ) code += ",);\n}" if len(self.output_structs) == 1 else ");\n}" else: code += f"let res=array![{','.join([f'outputs.get_output({ref})' for ref in outputs_refs])}];\n" code += "return res;\n" code += "}\n" if const_array: # Add the constants outside of the function if they are more than 8. code += "\n" code += const_array return code, function_name def summarize(self): add_count, mul_count, assert_eq_count = self.values_segment.summarize() summary = { "circuit": self.name, "MULMOD": mul_count, "ADDMOD": add_count, "ASSERT_EQ": assert_eq_count, "POSEIDON": 0, "RLC": 0, } return summary if __name__ == "__main__": from garaga.algebra import BaseField field = BaseField(256) circuit = ModuloCircuit("test_circuit", 0) a = circuit.write_element(field(1)) b = circuit.write_element(field(2)) c = circuit.add(a, b) d = circuit.mul(c, b) print(c) print(d) circuit = ModuloCircuit("test_empty_circuit", curve_id=0, compilation_mode=1) print(circuit.compile_circuit()) ================================================ FILE: hydra/garaga/modulo_circuit_structs.py ================================================ from __future__ import annotations from abc import ABC, abstractmethod from dataclasses import dataclass from typing import Generic, TypeVar from garaga.algebra import FunctionFelt, ModuloCircuitElement, PyFelt from garaga.curves import STARK, get_base_field from garaga.hints import io from garaga.hints.io import ( int_array_to_u384_array, int_to_u2XX, int_to_u256, int_to_u384, ) from garaga.points import G1Point, G2Point T = TypeVar("T", bound="Cairo1SerializableStruct") from enum import Enum class CairoOption(Enum): SOME = 0 NONE = 1 VOID = 2 # Special case to serialize nothing at all. @dataclass(slots=True) class Cairo1SerializableStruct(ABC): name: str elmts: list[ModuloCircuitElement | PyFelt | "Cairo1SerializableStruct"] def __post_init__(self): assert type(self.name) == str if isinstance(self.elmts, (list, tuple)): if len(self.elmts) > 0: if isinstance(self.elmts[0], Cairo1SerializableStruct): assert all( isinstance(elmt, self.elmts[0].__class__) for elmt in self.elmts ), f"All elements of {self.name} must be of the same type" else: assert all( isinstance(elmt, (ModuloCircuitElement, PyFelt)) for elmt in self.elmts ), f"All elements of {self.name} must be of type ModuloCircuitElement or PyFelt, got {type(self.elmts[0])}" else: assert self.elmts is None, f"Elmts must be a list or None, got {self.elmts}" @property def struct_name(self) -> str: return self.__class__.__name__ @property def bits(self) -> int: return self.elmts[0].p.bit_length() def serialize_input_signature(self) -> str: return f"{self.name}:{self.struct_name}" @abstractmethod def serialize(self, raw: bool = False) -> str: pass @abstractmethod def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: pass @abstractmethod def dump_to_circuit_input(self) -> str: pass @abstractmethod def __len__(self) -> int: pass def _serialize_to_calldata(self) -> list[int]: pass def serialize_to_calldata(self, *args, **kwargs) -> list[int]: data = self._serialize_to_calldata(*args, **kwargs) # print( # f"\nSerializing {self.name} {self.struct_name} to calldata: {data} {len(data)}" # ) return data class StructArray(Cairo1SerializableStruct, Generic[T]): elmts: list[T] @property def struct_name(self) -> str: return "Array<" + self.elmts[0].struct_name + ">" def dump_to_circuit_input(self) -> str: code = "" for struct in self.elmts: code += struct.dump_to_circuit_input() return code def __len__(self) -> int: return sum(len(struct) for struct in self.elmts) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def serialize(self, raw: bool = False, const: bool = False) -> str: if const: raw_struct = "[" else: raw_struct = "array![" for struct in self.elmts: raw_struct += struct.serialize(raw=True) + "," raw_struct += "]\n" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def serialize_to_calldata(self) -> list[int]: cd = [len(self)] for elmt in self.elmts: cd.extend(elmt.serialize_to_calldata()) return cd class Struct(Cairo1SerializableStruct): elmts: list[Cairo1SerializableStruct] def __init__( self, struct_name: str, name: str, elmts: list[Cairo1SerializableStruct] ): super().__init__(name, elmts) self._struct_name = struct_name @property def struct_name(self) -> str: return self._struct_name def __post_init__(self): assert all(isinstance(elmt, Cairo1SerializableStruct) for elmt in self.elmts) def dump_to_circuit_input(self) -> str: return NotImplementedError def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def serialize(self, raw: bool = False) -> str: if raw: code = f"{self.struct_name} {{" else: code = f"let {self.name} = {self.struct_name} {{" for struct in self.elmts: code += f"{struct.name}: {struct.serialize(raw=True)}," if raw: code += "}" else: code += "};" return code def __len__(self) -> int: return sum(len(elmt) for elmt in self.elmts) def _serialize_to_calldata(self) -> list[int]: cd = [] for elmt in self.elmts: cd.extend(elmt.serialize_to_calldata()) return cd class StructSpan(Cairo1SerializableStruct, Generic[T]): elmts: list[T] @property def struct_name(self) -> str: return "Span<" + self.elmts[0].struct_name + ">" def dump_to_circuit_input(self) -> str: code = f"let mut {self.name} = {self.name};\n" code += f"for val in {self.name} {{\n" self.elmts[0].name = "*val" code += self.elmts[0].dump_to_circuit_input() code += "};\n" return code def __len__(self) -> int: return sum(len(struct) for struct in self.elmts) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def serialize(self, raw: bool = False, is_option: bool = False) -> str: if self.elmts is None: raw_struct = "Option::None" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" else: raw_struct = "array![" for struct in self.elmts: raw_struct += struct.serialize(raw=True) + "," raw_struct += "].span()" if is_option: raw_struct = f"Option::Some({raw_struct})" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" def _serialize_to_calldata( self, option: CairoOption = None, as_pure_felt252_array: bool = False ) -> list[int]: cd = [] if option: if option == CairoOption.SOME: cd.append(0) elif option == CairoOption.NONE: cd.append(1) return cd elif option == CairoOption.VOID: return cd else: raise ValueError(f"Invalid option: {option}") cd.append(len(self.elmts)) for elmt in self.elmts: cd.extend(elmt._serialize_to_calldata()) if as_pure_felt252_array: cd[0] = len(cd) - 1 return cd # class u288(Cairo1SerializableStruct): # def serialize(self, raw: bool = False) -> str: # assert len(self.elmts) == 1 # raw_struct = f"{int_to_u288(self.elmts[0].value)}" # if raw: # return raw_struct # else: # return f"let {self.name}:{self.struct_name} = {raw_struct};\n" # def _serialize_to_calldata(self) -> list[int]: # assert len(self.elmts) == 1 # return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False) # def extract_from_circuit_output( # self, offset_to_reference_map: dict[int, str] # ) -> str: # assert len(self.elmts) == 1 # return f"let {self.name}:{self.struct_name} = outputs.get_output({offset_to_reference_map[self.elmts[0].offset]});" # def dump_to_circuit_input(self) -> str: # return f"circuit_inputs = circuit_inputs.next_u288({self.name});\n" # def __len__(self) -> int: # if self.elmts is not None: # assert len(self.elmts) == 1 # return 1 # else: # return 1 class u384(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 1 raw_struct = f"{int_to_u384(self.elmts[0].value)}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 1 return io.bigint_split_array(self.elmts, prepend_length=False) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 1 return f"let {self.name}:{self.struct_name} = outputs.get_output({offset_to_reference_map[self.elmts[0].offset]});" def dump_to_circuit_input(self) -> str: return f"circuit_inputs = circuit_inputs.next_2({self.name});\n" def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 1 return 1 else: return 1 class RSA2048Chunks(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("w0", "w1", "w2", "w3", "w4", "w5") @property def struct_name(self) -> str: return "RSA2048Chunks" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 6 raw_struct = ( f"{self.struct_name} {{" + ",".join( f"{self.members_names[i]}: {int_to_u384(self.elmts[i].value)}" for i in range(6) ) + "}" ) if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 6 return io.bigint_split_array(self.elmts, prepend_length=False) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 6 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(6)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 6 return 6 else: return 6 class RSA2048ReductionWitness(Cairo1SerializableStruct): """Composite struct: quotient (6 u384) + remainder (6 u384) = 12 elements.""" def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.chunk_names = ("w0", "w1", "w2", "w3", "w4", "w5") @property def struct_name(self) -> str: return "RSA2048ReductionWitness" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 12 quot = ", ".join( f"{self.chunk_names[i]}: {int_to_u384(self.elmts[i].value)}" for i in range(6) ) rem = ", ".join( f"{self.chunk_names[i]}: {int_to_u384(self.elmts[6 + i].value)}" for i in range(6) ) raw_struct = f"{self.struct_name} {{ quotient: RSA2048Chunks {{ {quot} }}, remainder: RSA2048Chunks {{ {rem} }} }}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 12 return io.bigint_split_array(self.elmts, prepend_length=False) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError("RSA2048ReductionWitness is input-only") def dump_to_circuit_input(self) -> str: code = "" for member in ("quotient", "remainder"): for chunk in self.chunk_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{member}.{chunk});\n" return code def __len__(self) -> int: return 12 class GenericT(Cairo1SerializableStruct): # => u384 or u288 @property def struct_name(self) -> str: return "T" def serialize(self, raw: bool = False) -> str: if self.bits <= 288: curve_id = 0 else: curve_id = 1 assert len(self.elmts) == 1 raw_struct = f"{int_to_u2XX(self.elmts[0].value, curve_id)}" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 1 if self.bits <= 288: return io.bigint_split_array(self.elmts, prepend_length=False) else: return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def dump_to_circuit_input(self) -> str: return f"circuit_inputs = circuit_inputs.next_2({self.name});\n" def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 1 return 1 else: return 1 class u256(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 1 raw_struct = f"{int_to_u256(self.elmts[0].value)}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 1 return list(io.split_128(self.elmts[0].value)) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def dump_to_circuit_input(self) -> str: raise NotImplementedError def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 1 return 1 else: return 1 class u256Span(Cairo1SerializableStruct): @property def struct_name(self) -> str: return "Span" def serialize(self, raw: bool = False) -> str: raw_struct = f"{io.int_array_to_u256_array(self.elmts)}.span()" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: return io.bigint_split_array( self.elmts, n_limbs=2, base=2**128, prepend_length=True ) def dump_to_circuit_input(self) -> str: code = f""" for val in {self.name} {{ circuit_inputs = circuit_inputs.next_u256(*val); }};""" return code def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def __len__(self) -> int: if self.elmts is not None: return len(self.elmts) else: return None class u128(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 1 assert 0 <= self.elmts[0].value < 2**128 raw_struct = f"{hex(self.elmts[0].value)}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 1 assert 0 <= self.elmts[0].value < 2**128 return [self.elmts[0].value] def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def dump_to_circuit_input(self) -> str: return f"circuit_inputs = circuit_inputs.next_u128({self.name});\n" def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 1 return 1 else: return 1 class u128Span(Cairo1SerializableStruct): @property def struct_name(self) -> str: return "Span" def serialize(self, raw: bool = False) -> str: raw_struct = f"{io.int_array_to_u128_array(self.elmts)}.span()" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: return io.bigint_split_array( self.elmts, n_limbs=1, base=2**128, prepend_length=True ) def dump_to_circuit_input(self) -> str: code = f""" for val in {self.name} {{ circuit_inputs = circuit_inputs.next_u128(*val); }};""" return code def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def __len__(self) -> int: if self.elmts is not None: return len(self.elmts) else: return None class Tuple(Cairo1SerializableStruct): elmts: list[Cairo1SerializableStruct] def __init__(self, name: str, elmts: list[Cairo1SerializableStruct]): super().__init__(name, elmts) self.members_names = [member.name for member in elmts] @property def struct_name(self) -> str: return f"({','.join([elmt.struct_name for elmt in self.elmts])})" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) > 0 raw_struct = f"({','.join([elmt.serialize(raw=True) for elmt in self.elmts])})" if raw: return raw_struct else: return f"let ({','.join([elmt.name for elmt in self.elmts])}):{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: cd = [] for elmt in self.elmts: cd.extend(elmt._serialize_to_calldata()) return cd def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def dump_to_circuit_input(self) -> str: code = "" # Need to unpack the tuple : code = f"let ({','.join([self.members_names[i] for i in range(len(self.elmts))])}) = {self.name};\n" # Now call dump_to_circuit_input for each member # Names must correspond to the members names for i, elmt in enumerate(self.elmts): assert ( elmt.name == self.members_names[i] ), f"Tuple member {i} has name {elmt.name} instead of {self.members_names[i]}" code += elmt.dump_to_circuit_input() return code def __len__(self) -> int: return sum(len(elmt) for elmt in self.elmts) class felt252(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 1 raw_struct = f"{hex(self.elmts[0].value)}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: assert len(self.elmts) == 1 return [self.elmts[0].value % STARK] def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError def dump_to_circuit_input(self) -> str: code = f"let {self.name}_384:u384 = {self.name}.into();\n" code += f"circuit_inputs = circuit_inputs.next_2({self.name}_384);\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 1 return 1 else: return 1 class u384Array(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: if len(self.elmts) == 0: raw_struct = "array![]" else: bits = self.bits if self.name == "g_rhs_sqrt": # Temp fix before we change the MSMHint and G1Points to depend on the curve id # Todo : remove this curve_id = 1 else: curve_id = 0 if bits <= 288 else 1 raw_struct = f"{io.int_array_to_u2XX_array(self.elmts, curve_id=curve_id)}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: if len(self.elmts) == 0: return [0] bits = self.bits if bits <= 288 and self.name != "g_rhs_sqrt": return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=True) else: return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=True) @property def struct_name(self) -> str: bits = self.bits if bits <= 288: return "Array" elif bits <= 384: return "Array" else: raise ValueError(f"Unsupported bit length for u384Array: {bits}") def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: return f"let {self.name} = array![{','.join([f'outputs.get_output({offset_to_reference_map[elmt.offset]})' for elmt in self.elmts])}];" def dump_to_circuit_input(self) -> str: next_fn = "next_2" code = f""" for val in {self.name}.span() {{ circuit_inputs = circuit_inputs.{next_fn}(*val); }};""" return code def __len__(self) -> int: if self.elmts is not None: return len(self.elmts) else: return None class FunctionFeltCircuit(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[u384Span]): super().__init__(name, elmts) self.members_names = ("a_num", "a_den", "b_num", "b_den") @property def a_num(self) -> list[ModuloCircuitElement | PyFelt]: return self.elmts[0].elmts @property def a_den(self) -> list[ModuloCircuitElement | PyFelt]: return self.elmts[1].elmts @property def b_num(self) -> list[ModuloCircuitElement | PyFelt]: return self.elmts[2].elmts @property def b_den(self) -> list[ModuloCircuitElement | PyFelt]: return self.elmts[3].elmts @property def struct_name(self) -> str: return "FunctionFelt" @staticmethod def from_FunctionFelt( name: str, f: FunctionFelt, msm_size: int, batched: bool = False ) -> "FunctionFeltCircuit": _a_num, _a_den, _b_num, _b_den = io.padd_function_felt( f, msm_size, py_felt=True, batched=batched ) return FunctionFeltCircuit( name=name, elmts=[ u384Span("a_num", _a_num), u384Span("a_den", _a_den), u384Span("b_num", _b_num), u384Span("b_den", _b_den), ], ) def _serialize_to_calldata(self) -> list[int]: cd = [] assert len(self.elmts) == 4 bits = self.elmts[0].bits if bits <= 288: for elmt in self.elmts: cd.extend( io.bigint_split_array(elmt.elmts, n_limbs=3, prepend_length=True) ) else: for elmt in self.elmts: cd.extend( io.bigint_split_array(elmt.elmts, n_limbs=4, prepend_length=True) ) return cd def serialize_input_signature(self) -> str: return f"{self.name}:FunctionFelt" def serialize(self, raw: bool = False) -> str: raw_struct = f"FunctionFelt {{ {','.join([f'{self.members_names[i]}: {self.elmts[i].serialize(raw=True)}' for i in range(4)])} }}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f""" for val in {self.name}.{mem_name} {{ circuit_inputs = circuit_inputs.next_2(*val); }}; """ return code def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: {self.elmts[i].extract_from_circuit_output(offset_to_reference_map)}' for i in range(4)])} }};" def __len__(self) -> int: return sum(len(elmt) for elmt in self.elmts) class u384Span(Cairo1SerializableStruct): def serialize(self, raw: bool = False) -> str: raw_struct = f"{int_array_to_u384_array(self.elmts)}.span()" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: return io.bigint_split_array(self.elmts, prepend_length=True) @property def struct_name(self) -> str: return "Span" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: return f"let {self.name}:{self.struct_name} = array![{','.join([f'outputs.get_output({offset_to_reference_map[elmt.offset]})' for elmt in self.elmts])}].span();" def dump_to_circuit_input(self) -> str: code = f"""let mut {self.name} = {self.name}; for val in {self.name} {{ circuit_inputs = circuit_inputs.next_2(*val); }}; """ return code def __len__(self) -> int: if self.elmts is not None: return len(self.elmts) else: return None class BLSProcessedPair(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("yInv", "xNegOverY") @property def struct_name(self) -> str: return "BLSProcessedPair" def serialize(self) -> str: assert len(self.elmts) == 2 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{yInv: {int_to_u384(self.elmts[0].value)}, xNegOverY: {int_to_u384(self.elmts[1].value)}}};" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 2 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(2)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 2 return 2 else: return 2 class BNProcessedPair(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("yInv", "xNegOverY", "QyNeg0", "QyNeg1") @property def struct_name(self) -> str: return "BNProcessedPair" def serialize(self) -> str: assert len(self.elmts) == 4 members = ", ".join( [ f"{name}: {int_to_u384(self.elmts[i].value)}" for i, name in enumerate(self.members_names) ] ) return ( f"let {self.name}:{self.struct_name} = {self.struct_name} {{{members}}};\n" ) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 4 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(4)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 4 return 4 else: return 4 class G1PointCircuit(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("x", "y") @staticmethod def from_G1Point(name: str, point: G1Point) -> "G1PointCircuit": field = get_base_field(point.curve_id) return G1PointCircuit(name=name, elmts=[field(point.x), field(point.y)]) @property def struct_name(self) -> str: return "G1Point" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 2 raw_struct = f"{self.struct_name} {{x: {int_to_u384(self.elmts[0].value)}, y: {int_to_u384(self.elmts[1].value)}}}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: return io.bigint_split_array(self.elmts, prepend_length=False) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 2 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(2)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 2 return 2 else: return 2 class G2PointCircuit(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("x0", "x1", "y0", "y1") @staticmethod def from_G2Point(name: str, point: G2Point) -> "G2PointCircuit": field = get_base_field(point.curve_id) return G2PointCircuit( name=name, elmts=[ field(point.x[0]), field(point.x[1]), field(point.y[0]), field(point.y[1]), ], ) @property def struct_name(self) -> str: return "G2Point" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 4 raw_struct = f"{self.struct_name} {{x0: {int_to_u384(self.elmts[0].value)}, x1: {int_to_u384(self.elmts[1].value)}, y0: {int_to_u384(self.elmts[2].value)}, y1: {int_to_u384(self.elmts[3].value)}}}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 4 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(4)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 4 return 4 else: return 4 class G2Line(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("r0a0", "r0a1", "r1a0", "r1a1") def serialize_input_signature(self) -> str: bits = self.bits if bits <= 288: return f"{self.name}:G2Line" else: return f"{self.name}:G2Line" def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 4 bits = self.bits if bits <= 288: curve_id = 0 else: curve_id = 1 raw_struct = f"{self.struct_name} {{r0a0: {int_to_u2XX(self.elmts[0].value, curve_id=curve_id)}, r0a1: {int_to_u2XX(self.elmts[1].value, curve_id=curve_id)}, r1a0: {int_to_u2XX(self.elmts[2].value, curve_id=curve_id)}, r1a1: {int_to_u2XX(self.elmts[3].value, curve_id=curve_id)}}}" if raw: return raw_struct else: return f"let {self.name}:{self.struct_name} = {raw_struct};\n" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 4 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(4)])} }};" def dump_to_circuit_input(self) -> str: code = "" next_fn = "next_2" for mem_name in self.members_names: code += ( f"circuit_inputs = circuit_inputs.{next_fn}({self.name}.{mem_name});\n" ) return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 4 return 4 else: return 4 class FunctionFeltEvaluations(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("a_num", "a_den", "b_num", "b_den") def serialize(self) -> str: assert len(self.elmts) == 4 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{a_num: {int_to_u384(self.elmts[0].value)}, a_den: {int_to_u384(self.elmts[1].value)}, b_num: {int_to_u384(self.elmts[2].value)}, b_den: {int_to_u384(self.elmts[3].value)}}};\n" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 4 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(4)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 4 return 4 else: return 4 class G1G2PairCircuit(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("p.x", "p.y", "q.x0", "q.x1", "q.y0", "q.y1") @property def struct_name(self) -> str: return "G1G2Pair" def serialize(self) -> str: return ( f"let {self.name}:{self.struct_name} = {self.struct_name} {{" f"p: G1Point{{ x:{int_to_u384(self.elmts[0].value)}, y: {int_to_u384(self.elmts[1].value)}}}, " f"q: G2Point{{ x0:{int_to_u384(self.elmts[2].value)}, x1: {int_to_u384(self.elmts[3].value)}, y0: {int_to_u384(self.elmts[4].value)}, y1: {int_to_u384(self.elmts[5].value)}}}}};\n" ) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 6 return f"let {self.name}:{self.struct_name} = {self.struct_name} {{ {','.join([f'{self.members_names[i]}: outputs.get_output({offset_to_reference_map[self.elmts[i].offset]})' for i in range(6)])} }};" def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 6 return 6 else: return 6 class E12D(Cairo1SerializableStruct): def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 12 code = ( f"let {self.name}:{self.__class__.__name__} = {self.__class__.__name__}{{\n" ) for i, elmt in enumerate(self.elmts): code += ( f"w{i}:outputs.get_output({offset_to_reference_map[elmt.offset]}),\n" ) code += "};" return code @property def struct_name(self) -> str: p = self.elmts[0].p if p.bit_length() <= 288: return "E12D" else: return "E12D" def serialize(self, raw: bool = False, is_option: bool = False) -> str: if self.elmts is None: raw_struct = "Option::None" if raw: return raw_struct else: return f"let {self.name}:Option<{self.__class__.__name__}> = {raw_struct};\n" else: assert len(self.elmts) == 12 bits: int = self.elmts[0].p.bit_length() if bits <= 288: curve_id = 0 else: curve_id = 1 raw_struct = ( f"{self.__class__.__name__}{{" + f"{','.join([f'w{i}: {int_to_u2XX(self.elmts[i].value, curve_id=curve_id)}' for i in range(len(self))])}}}" ) if is_option: raw_struct = f"Option::Some({raw_struct})" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: bits: int = self.bits if bits <= 288: return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False) elif bits <= 384: return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=False) else: raise ValueError(f"Unsupported bit length for E12D: {bits}") def dump_to_circuit_input(self) -> str: bits: int = self.elmts[0].p.bit_length() code = "" next_fn = "next_2" for i in range(len(self)): code += f"circuit_inputs = circuit_inputs.{next_fn}({self.name}.w{i});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 12 return 12 else: return 12 class E12T(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ( "c0b0a0", "c0b0a1", "c0b1a0", "c0b1a1", "c0b2a0", "c0b2a1", "c1b0a0", "c1b0a1", "c1b1a0", "c1b1a1", "c1b2a0", "c1b2a1", ) def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 12 code = ( f"let {self.name}:{self.__class__.__name__} = {self.__class__.__name__}{{\n" ) for i, elmt in enumerate(self.elmts): code += f"{self.members_names[i]}:outputs.get_output({offset_to_reference_map[elmt.offset]}),\n" code += "};" return code def serialize(self, raw: bool = False, is_option: bool = False) -> str: if self.elmts is None: raw_struct = "Option::None" if raw: return raw_struct else: return f"let {self.name}:Option<{self.__class__.__name__}> = {raw_struct};\n" else: assert len(self.elmts) == 12 raw_struct = ( f"{self.__class__.__name__}{{" + f"{','.join([f'{self.members_names[i]}: {int_to_u384(self.elmts[i].value)}' for i in range(len(self))])}}}" ) if is_option: raw_struct = f"Option::Some({raw_struct})" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=False) def dump_to_circuit_input(self) -> str: code = "" for i in range(len(self)): code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{self.members_names[i]});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 12 return 12 else: return 12 class E12DMulQuotient(Cairo1SerializableStruct): def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 11 code = ( f"let {self.name}:{self.__class__.__name__} = {self.__class__.__name__}{{\n" ) for i, elmt in enumerate(self.elmts): code += ( f"w{i}:outputs.get_output({offset_to_reference_map[elmt.offset]}),\n" ) code += "};" return code @property def struct_name(self) -> str: p = self.elmts[0].p if p.bit_length() <= 288: return "E12DMulQuotient" else: return "E12DMulQuotient" def serialize(self, raw: bool = False, is_option: bool = False) -> str: if self.elmts is None: raw_struct = "Option::None" if raw: return raw_struct else: return f"let {self.name}:Option<{self.__class__.__name__}> = {raw_struct};\n" else: assert len(self.elmts) == 11 bits: int = self.elmts[0].p.bit_length() if bits <= 288: curve_id = 0 else: curve_id = 1 raw_struct = ( f"{self.__class__.__name__}{{" + f"{','.join([f'w{i}: {int_to_u2XX(self.elmts[i].value, curve_id=curve_id)}' for i in range(len(self))])}}}" ) if is_option: raw_struct = f"Option::Some({raw_struct})" if raw: return raw_struct else: return f"let {self.name} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: bits: int = self.bits if bits <= 288: return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False) elif bits <= 384: return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=False) else: raise ValueError(f"Unsupported bit length for E12D: {bits}") def dump_to_circuit_input(self) -> str: code = "" next_fn = "next_2" for i in range(len(self)): code += f"circuit_inputs = circuit_inputs.{next_fn}({self.name}.w{i});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 11 return 11 else: return 11 class MillerLoopResultScalingFactor(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("w0", "w2", "w4", "w6", "w8", "w10") def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: raise NotImplementedError("Never used in practice") def serialize_input_signature(self) -> str: bits = self.bits if bits <= 288: return f"{self.name}:MillerLoopResultScalingFactor" else: return f"{self.name}:MillerLoopResultScalingFactor" def dump_to_circuit_input(self) -> str: code = "" next_fn = "next_2" for mem_name in self.members_names: code += ( f"circuit_inputs = circuit_inputs.{next_fn}({self.name}.{mem_name});\n" ) return code def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 6 bits = self.bits if bits <= 288: curve_id = 0 else: curve_id = 1 raw_struct = f"{self.__class__.__name__}{{{','.join([f'{self.members_names[i]}: {int_to_u2XX(self.elmts[i].value, curve_id=curve_id)}' for i in range(len(self))])}}}" if raw: return raw_struct else: return f"let {self.name}:{self.__class__.__name__} = {raw_struct};\n" def _serialize_to_calldata(self) -> list[int]: bits = self.bits if bits <= 288: return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False) else: return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=False) def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 6 return 6 else: return 6 class SlopeInterceptOutput(Cairo1SerializableStruct): def __init__(self, name: str, elmts: list[ModuloCircuitElement]): super().__init__(name, elmts) self.members_names = ("m_A0", "b_A0", "x_A2", "y_A2", "coeff0", "coeff2") def serialize(self, raw: bool = False) -> str: assert len(self.elmts) == 6 raw_struct = f"{self.__class__.__name__}{{{','.join([f'{self.members_names[i]}: {int_to_u384(self.elmts[i].value)}' for i in range(len(self))])}}}" if raw: return raw_struct else: return f"let {self.name}:{self.__class__.__name__} = {raw_struct};\n" def extract_from_circuit_output( self, offset_to_reference_map: dict[int, str] ) -> str: assert len(self.elmts) == 6 code = ( f"let {self.name}:{self.__class__.__name__} = {self.__class__.__name__}{{\n" ) for mem_name, elmt in zip(self.members_names, self.elmts): code += f"{mem_name}: outputs.get_output({offset_to_reference_map[elmt.offset]}),\n" code += "};" return code def dump_to_circuit_input(self) -> str: code = "" for mem_name in self.members_names: code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n" return code def __len__(self) -> int: if self.elmts is not None: assert len(self.elmts) == 6 return 6 else: return 6 ================================================ FILE: hydra/garaga/points.py ================================================ import functools import random from dataclasses import dataclass from fastecdsa import curvemath from garaga.algebra import Fp2, ModuloCircuitElement, Polynomial, PyFelt, get_sparsity from garaga.curves import ( CURVES, GARAGA_RS_SUPPORTED_CURVES, CurveID, PairingCurve, get_base_field, get_irreducible_poly, ) from garaga.hints.io import int_to_u384 @dataclass(slots=True) class G1Point: """ Represents a point on G1, the group of rational points on an elliptic curve over the base field. Attributes: x (int): The x-coordinate of the point. y (int): The y-coordinate of the point. curve_id (CurveID): The identifier of the elliptic curve. """ x: int y: int curve_id: CurveID iso_point: bool = False def __repr__(self) -> str: return f"G1Point({hex(self.x)}, {hex(self.y)}) on {self.curve_id.value}" def __str__(self) -> str: return f"G1Point({self.x}, {self.y}) on curve {self.curve_id}" def __hash__(self): return hash((self.x, self.y, self.curve_id, self.iso_point)) def __eq__(self, other: object) -> bool: """ Checks if two G1Point instances are equal. Args: other (G1Point): The other point to compare. Returns: bool: True if the points are equal, False otherwise. """ if not isinstance(other, G1Point): raise ValueError(f"Cannot compare G1Point with {type(other)}") return ( self.x == other.x and self.y == other.y and self.curve_id.value == other.curve_id.value and self.iso_point == other.iso_point ) def __post_init__(self): """ Post-initialization checks to ensure the point is valid. """ if self.is_infinity(): return if not self.is_on_curve(): raise ValueError(f"Point {self} is not on the curve {self.curve_id}") @staticmethod def infinity(curve_id: CurveID) -> "G1Point": """ Returns the point at infinity for the given curve. Args: curve_id (CurveID): The identifier of the elliptic curve. Returns: G1Point: The point at infinity. """ return G1Point(0, 0, curve_id) def is_infinity(self) -> bool: """ Checks if the point is the point at infinity. Returns: bool: True if the point is at infinity, False otherwise. """ return self.x == 0 and self.y == 0 def to_cairo_1(self, as_hex: bool = True) -> str: """ Converts the point to a Cairo 1 representation. Returns: str: The Cairo 1 representation of the point. """ return f"G1Point{{x: {int_to_u384(self.x, as_hex)}, y: {int_to_u384(self.y, as_hex)}}}" @staticmethod def gen_random_point_not_in_subgroup( curve_id: CurveID, force_gen: bool = False ) -> "G1Point": """ Generates a random point not in the prime order subgroup. Args: curve_id (CurveID): The identifier of the elliptic curve. force_gen (bool): Force generation even if the cofactor is 1. Returns: G1Point: A random point not in the prime order subgroup. Raises: ValueError: If the cofactor is 1 and force_gen is False. """ curve_idx = curve_id.value if CURVES[curve_idx].h == 1: if force_gen: return G1Point.gen_random_point(curve_id) else: raise ValueError( "Cofactor is 1, cannot generate a point not in the subgroup" ) else: field = get_base_field(curve_idx) while True: x = field.random() y2 = x**3 + CURVES[curve_idx].a * x + CURVES[curve_idx].b try: tentative_point = G1Point(x.value, y2.sqrt().value, curve_id) except ValueError: continue if not tentative_point.is_in_prime_order_subgroup_generic(): return tentative_point def is_in_prime_order_subgroup_generic(self) -> bool: """ Checks if the point is in the prime order subgroup. Returns: bool: True if the point is in the prime order subgroup, False otherwise. """ return self.scalar_mul(CURVES[self.curve_id.value].n).is_infinity() def is_in_prime_order_subgroup(self) -> bool: if CURVES[self.curve_id.value].h == 1: # Cofactor is 1 : points on the curve <=> points in the prime order subgroup return self.is_on_curve() or self.is_infinity() else: if self.curve_id == CurveID.BLS12_381: # we check that p+x²ϕ(p) # is the infinity. third_root_of_unity = 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAC phi_p = G1Point( self.x * third_root_of_unity % CURVES[self.curve_id.value].p, self.y, self.curve_id, ) x_seed_sq = (CURVES[self.curve_id.value].x) ** 2 return phi_p.scalar_mul(x_seed_sq).add(self).is_infinity() else: return self.is_in_prime_order_subgroup_generic() def is_on_curve(self) -> bool: """ Checks if the point is on the curve using the curve equation y^2 = x^3 + ax + b. Returns: bool: True if the point is on the curve, False otherwise. """ if self.iso_point: a = CURVES[self.curve_id.value].swu_params.A b = CURVES[self.curve_id.value].swu_params.B else: a = CURVES[self.curve_id.value].a b = CURVES[self.curve_id.value].b p = CURVES[self.curve_id.value].p lhs = self.y**2 % p rhs = (self.x**3 + a * self.x + b) % p return lhs == rhs @staticmethod def gen_random_point(curve_id: CurveID) -> "G1Point": """ Generates a random point on a given curve. Args: curve_id (CurveID): The identifier of the elliptic curve. Returns: G1Point: A random point on the curve. """ scalar = random.randint(1, CURVES[curve_id.value].n - 1) return G1Point.get_nG(curve_id, scalar) @staticmethod def get_nG(curve_id: CurveID, n: int) -> "G1Point": """ Returns the scalar multiplication of the generator point on a given curve by the scalar n. Args: curve_id (CurveID): The identifier of the elliptic curve. n (int): The scalar to multiply by. Returns: G1Point: The resulting point after scalar multiplication. Raises: AssertionError: If n is not less than the order of the curve. """ assert ( n < CURVES[curve_id.value].n ), "n must be less than the order of the curve" gen = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) return gen.scalar_mul(n) @staticmethod def msm(points: list["G1Point"], scalars: list[int]) -> "G1Point": """ Performs multi-scalar multiplication (MSM) on a list of points and scalars. Args: points (list[G1Point]): The list of points. scalars (list[int]): The list of scalars. Returns: G1Point: The resulting point after MSM. """ assert len(points) == len( scalars ), f"Points and scalar length mismatch: {len(points)} points and {len(scalars)} scalars" muls = [P.scalar_mul(s) for P, s in zip(points, scalars)] scalar_mul = functools.reduce(lambda acc, p: acc.add(p), muls) return scalar_mul def scalar_mul(self, scalar: int) -> "G1Point": """ Performs scalar multiplication on the point. Args: scalar (int): The scalar to multiply by. abs(scalar) should be less than the order of the curve. Returns: G1Point: The resulting point after scalar multiplication. """ if self.is_infinity(): return self if scalar == 0: return G1Point(0, 0, self.curve_id, self.iso_point) if self.iso_point: a = CURVES[self.curve_id.value].swu_params.A b = CURVES[self.curve_id.value].swu_params.B else: a = CURVES[self.curve_id.value].a b = CURVES[self.curve_id.value].b # Fastecdsa C binding. x, y = curvemath.mul( str(self.x), str(self.y), str(abs(scalar)), str(CURVES[self.curve_id.value].p), str(a), str(b), str(CURVES[self.curve_id.value].n), str(CURVES[self.curve_id.value].Gx), str(CURVES[self.curve_id.value].Gy), ) # Fastecdsa already returns (0, 0) for the identity element. if scalar < 0: return -G1Point(int(x), int(y), self.curve_id, self.iso_point) else: return G1Point(int(x), int(y), self.curve_id, self.iso_point) def add(self, other: "G1Point") -> "G1Point": """ Adds two points on the elliptic curve. Args: other (G1Point): The other point to add. Returns: G1Point: The resulting point after addition. Raises: ValueError: If the points are not on the same curve. """ if self.is_infinity(): return other if other.is_infinity(): return self if self.curve_id != other.curve_id: raise ValueError("Points are not on the same curve") if self.iso_point != other.iso_point: raise ValueError("Points are not on the same curve") if self.iso_point: a = CURVES[self.curve_id.value].swu_params.A b = CURVES[self.curve_id.value].swu_params.B else: a = CURVES[self.curve_id.value].a b = CURVES[self.curve_id.value].b x, y = curvemath.add( str(self.x), str(self.y), str(other.x), str(other.y), str(CURVES[self.curve_id.value].p), str(a), str(b), str(CURVES[self.curve_id.value].n), str(CURVES[self.curve_id.value].Gx), str(CURVES[self.curve_id.value].Gy), ) # NB : Fastecdsa returns (0, 0) for the identity element. return G1Point(int(x), int(y), self.curve_id, self.iso_point) def __neg__(self) -> "G1Point": """ Negates the point on the elliptic curve. Returns: G1Point: The negated point. """ return G1Point( self.x, -self.y % CURVES[self.curve_id.value].p, self.curve_id, self.iso_point, ) def to_pyfelt_list(self) -> list[PyFelt]: field = get_base_field(self.curve_id.value) return [field(self.x), field(self.y)] def serialize_to_cairo(self, name: str, raw: bool = False) -> str: import garaga.modulo_circuit_structs as structs return structs.G1PointCircuit(name=name, elmts=self.to_pyfelt_list()).serialize( raw ) @dataclass(frozen=True) class G2Point: """ Represents a point on G2, the group of rational points on an elliptic curve over an extension field. """ x: tuple[int, int] y: tuple[int, int] curve_id: CurveID def __repr__(self): return f"G2Point({hex(self.x[0])}, {hex(self.x[1])}, {hex(self.y[0])}, {hex(self.y[1])}, {self.curve_id})" def __post_init__(self): assert isinstance(CURVES[self.curve_id.value], PairingCurve) if self.is_infinity(): return if not self.is_on_curve(): raise ValueError(f"G2 Point is not on the curve {self.curve_id}") @staticmethod def infinity(curve_id: CurveID) -> "G2Point": return G2Point((0, 0), (0, 0), curve_id) def __eq__(self, other: "G2Point") -> bool: return ( self.x[0] == other.x[0] and self.x[1] == other.x[1] and self.y[0] == other.y[0] and self.y[1] == other.y[1] and self.curve_id == other.curve_id ) def is_infinity(self) -> bool: return self.x == (0, 0) and self.y == (0, 0) def is_on_curve(self) -> bool: """ Check if the point is on the curve using the curve equation y^2 = x^3 + ax + b in the extension field. """ from garaga.hints.tower_backup import E2 curve = CURVES[self.curve_id.value] assert isinstance(curve, PairingCurve) a = curve.a p = curve.p b = E2(curve.b20, curve.b21, p) y = E2(*self.y, p) x = E2(*self.x, p) return y**2 == x**3 + a * x + b @staticmethod def gen_random_point(curve_id: CurveID) -> "G2Point": """ Generates a random point on a given curve. """ from garaga import garaga_rs curve = CURVES[curve_id.value] assert isinstance(curve, PairingCurve) scalar = random.randint(1, curve.n - 1) a = (curve.G2x[0], curve.G2x[1], curve.G2y[0], curve.G2y[1]) b = garaga_rs.g2_scalar_mul(curve_id.value, a, scalar) return G2Point((b[0], b[1]), (b[2], b[3]), curve_id) def is_in_prime_order_subgroup_generic(self) -> bool: return self.scalar_mul(CURVES[self.curve_id.value].n).is_infinity() def is_in_prime_order_subgroup(self) -> bool: if CURVES[self.curve_id.value].h == 1: # Cofactor is 1 : points on the curve <=> points in the prime order subgroup return self.is_on_curve() or self.is_infinity() else: if self.curve_id == CurveID.BLS12_381: # https://github.com/Consensys/gnark/blob/9ed0eab21e8935cb180d1f75713cd2c29c91a3c9/std/algebra/emulated/sw_bls12381/g2.go field = get_base_field(self.curve_id.value) seed_Q = self.scalar_mul( -CURVES[self.curve_id.value].x ) # Note the negative sign. u1 = 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD v = Fp2( field( 0x135203E60180A68EE2E9C448D77A2CD91C3DEDD930B1CF60EF396489F61EB45E304466CF3E67FA0AF1EE7B04121BDEA2 ), field( 0x6AF0E0437FF400B6831E36D6BD17FFE48395DABC2D3435E77F76E17009241C5EE67992F72EC05F4C81084FBEDE3CC09 ), ) psi_Qx = ( (field(self.x[1]) * u1).value, (field(self.x[0]) * u1).value, ) # Note the reversal of x and y psi_Qy = Fp2(field(self.y[0]), -field(self.y[1])) * v psi_Qy = (psi_Qy.a0.value, psi_Qy.a1.value) psi_Q = G2Point(psi_Qx, psi_Qy, self.curve_id) # [r]Q == 0 <==> ψ(Q) == [x₀]Q <=> ψ(Q) + [-x₀]Q = 0 return psi_Q.add(seed_Q).is_infinity() else: return self.is_in_prime_order_subgroup_generic() @staticmethod def gen_random_point_not_in_subgroup( curve_id: CurveID, force_gen: bool = False ) -> "G2Point": """ Generates a random point not in the prime order subgroup. Args: curve_id (CurveID): The identifier of the elliptic curve. force_gen (bool): Force generation even if the cofactor is 1. Returns: G2Point: A random point not in the prime order subgroup. Raises: ValueError: If the cofactor is 1 and force_gen is False. """ curve_idx = curve_id.value if CURVES[curve_idx].h == 1: if force_gen: return G2Point.gen_random_point(curve_id) else: raise ValueError( "Cofactor is 1, cannot generate a point not in the subgroup" ) else: field = get_base_field(curve_idx) while True: x = field.random() y2 = x**3 + CURVES[curve_idx].a * x + CURVES[curve_idx].b try: tentative_point = G1Point(x.value, y2.sqrt().value, curve_id) except ValueError: continue if not tentative_point.is_in_prime_order_subgroup_generic(): return tentative_point @staticmethod def get_nG(curve_id: CurveID, n: int) -> "G2Point": """ Returns the scalar multiplication of the generator point on a given curve by the scalar n. """ from garaga import garaga_rs assert ( n < CURVES[curve_id.value].n ), "n must be less than the order of the curve" if curve_id.value in GARAGA_RS_SUPPORTED_CURVES: curve = CURVES[curve_id.value] a = (curve.G2x[0], curve.G2x[1], curve.G2y[0], curve.G2y[1]) b = garaga_rs.g2_scalar_mul(curve_id.value, a, n) return G2Point((b[0], b[1]), (b[2], b[3]), curve_id) else: raise NotImplementedError( "G2Point.get_nG is not implemented for this curve" ) def scalar_mul(self, scalar: int) -> "G2Point": if self.is_infinity(): return self if scalar == 0: return G2Point((0, 0), (0, 0), self.curve_id) if scalar < 0: return -self.scalar_mul(-scalar) if self.curve_id.value in GARAGA_RS_SUPPORTED_CURVES: from garaga import garaga_rs a = (self.x[0], self.x[1], self.y[0], self.y[1]) b = garaga_rs.g2_scalar_mul(self.curve_id.value, a, scalar) return G2Point((b[0], b[1]), (b[2], b[3]), self.curve_id) else: raise NotImplementedError( "G2Point.scalar_mul is not implemented for this curve" ) def add(self, other: "G2Point") -> "G2Point": if self.is_infinity(): return other if other.is_infinity(): return self if self.curve_id != other.curve_id: raise ValueError("Points are not on the same curve") if self.curve_id.value in GARAGA_RS_SUPPORTED_CURVES: from garaga import garaga_rs a = (self.x[0], self.x[1], self.y[0], self.y[1]) b = (other.x[0], other.x[1], other.y[0], other.y[1]) c = garaga_rs.g2_add(self.curve_id.value, a, b) return G2Point((c[0], c[1]), (c[2], c[3]), self.curve_id) else: raise NotImplementedError("G2Point.add is not implemented for this curve") def __neg__(self) -> "G2Point": p = CURVES[self.curve_id.value].p return G2Point( (self.x[0], self.x[1]), (-self.y[0] % p, -self.y[1] % p), self.curve_id ) @staticmethod def msm(points: list["G2Point"], scalars: list[int]) -> "G2Point": assert all(isinstance(p, G2Point) for p in points) assert len(points) == len(scalars) muls = [P.scalar_mul(s) for P, s in zip(points, scalars)] scalar_mul = functools.reduce(lambda acc, p: acc.add(p), muls) return scalar_mul def to_pyfelt_list(self) -> list[PyFelt]: field = get_base_field(self.curve_id.value) return [field(x) for x in self.x + self.y] def serialize_to_cairo(self, name: str, raw: bool = False) -> str: import garaga.modulo_circuit_structs as structs return structs.G2PointCircuit(name=name, elmts=self.to_pyfelt_list()).serialize( raw ) @dataclass(slots=True) class G1G2Pair: p: G1Point q: G2Point curve_id: CurveID = None def __hash__(self): return hash((self.p, self.q, self.curve_id)) def __post_init__(self): if self.p.curve_id != self.q.curve_id: raise ValueError("Points are not on the same curve") self.curve_id = self.p.curve_id def to_pyfelt_list(self) -> list[PyFelt]: field = get_base_field(self.curve_id.value) return [ field(x) for x in [ self.p.x, self.p.y, self.q.x[0], self.q.x[1], self.q.y[0], self.q.y[1], ] ] @staticmethod def pair(pairs: list["G1G2Pair"], curve_id: CurveID = None): from garaga.hints.tower_backup import E12 # avoids cycle if curve_id is None: if len(pairs) == 0: raise ValueError("Unspecified curve") curve_id = pairs[0].curve_id if curve_id.value in GARAGA_RS_SUPPORTED_CURVES: from garaga import garaga_rs args = [] for pair in pairs: if pair.curve_id != curve_id: raise ValueError("Pairs are not on the same curve") args.append(pair.p.x) args.append(pair.p.y) args.append(pair.q.x[0]) args.append(pair.q.x[1]) args.append(pair.q.y[0]) args.append(pair.q.y[1]) res = garaga_rs.multi_pairing(curve_id.value, args) return E12(res, curve_id.value) else: raise NotImplementedError("G1G2Pair.pair is not implemented for this curve") @staticmethod def miller(pairs: list["G1G2Pair"], curve_id: CurveID = None): from garaga.hints.tower_backup import E12 # avoids cycle if curve_id is None: if len(pairs) == 0: raise ValueError("Unspecified curve") curve_id = pairs[0].curve_id if curve_id.value in GARAGA_RS_SUPPORTED_CURVES: from garaga import garaga_rs args = [] for pair in pairs: if pair.curve_id != curve_id: raise ValueError("Pairs are not on the same curve") args.append(pair.p.x) args.append(pair.p.y) args.append(pair.q.x[0]) args.append(pair.q.x[1]) args.append(pair.q.y[0]) args.append(pair.q.y[1]) res = garaga_rs.multi_miller_loop(curve_id.value, args) return E12(res, curve_id.value) else: raise NotImplementedError( "G1G2Pair.miller is not implemented for this curve" ) # v^6 - 18v^3 + 82 # w^12 - 18w^6 + 82 # v^6 - 2v^3 + 2 # w^12 - 2w^6 + 2 def tower_to_direct( X: list[PyFelt], curve_id: int, extension_degree: int ) -> list[PyFelt]: """ Convert Tower to Direct extension field representation: T(u,v) = t0+t1u + (t2+t3u)v + (t4+t5u)v^2 D(v) = d0+d1v+d2v^2+d3v^3+d4v^4+d5v^5 Only tested with BN254 and BLS12_381 6th and 12th towers defined in this file. They were computed by hand then abstracted away with no guarantee of genericity under different tower constructions. """ assert len(X) == extension_degree and isinstance( X[0], PyFelt ), f"len(X)={len(X)}, type(X[0])={type(X[0])}" if extension_degree == 2: return X if extension_degree == 6: return TD6(X, curve_id) elif extension_degree == 12: return TD12(X, curve_id) else: raise ValueError(f"Unsupported extension degree {extension_degree}") def direct_to_tower( X: list[PyFelt | ModuloCircuitElement], curve_id: int, extension_degree: int ) -> list[PyFelt]: """ Convert Direct to Tower extension field representation: Input : D(v) = d0+d1v+d2v^2+d3v^3+d4v^4+d5v^5 Output: T(u,v) = t0+t1u + (t2+t3u)v + (t4+t5u)v^2 Only tested with BN254 and BLS12_381 6th and 12th towers defined in this file. They were computed by hand then abstracted away with no guarantee of genericity under different tower constructions. """ assert len(X) == extension_degree and isinstance( X[0], (PyFelt, ModuloCircuitElement) ), f"{type(X[0])}, len(X)={len(X)}" X = [x.felt for x in X] if extension_degree == 2: return X if extension_degree == 6: return DT6(X, curve_id) elif extension_degree == 12: return DT12(X, curve_id) else: raise ValueError(f"Unsupported extension degree {extension_degree}") def TD6(X: list[PyFelt], curve_id: int) -> list[PyFelt]: curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) nr_a0 = curve.nr_a0 return [ X[0] - nr_a0 * X[1], X[2] - nr_a0 * X[3], X[4] - nr_a0 * X[5], X[1], X[3], X[5], ] def DT6(X: list[PyFelt], curve_id: int) -> list[PyFelt]: curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) nr_a0 = curve.nr_a0 return [ X[0] + nr_a0 * X[3], X[3], X[1] + nr_a0 * X[4], X[4], X[2] + nr_a0 * X[5], X[5], ] def TD12(X: list[PyFelt], curve_id: int) -> list[PyFelt]: curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) nr_a0 = curve.nr_a0 return [ X[0] - nr_a0 * X[1], X[6] - nr_a0 * X[7], X[2] - nr_a0 * X[3], X[8] - nr_a0 * X[9], X[4] - nr_a0 * X[5], X[10] - nr_a0 * X[11], X[1], X[7], X[3], X[9], X[5], X[11], ] def DT12(X: list[PyFelt], curve_id: int) -> list[PyFelt]: X += (12 - len(X)) * [0] curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) nr_a0 = curve.nr_a0 return [ X[0] + nr_a0 * X[6], X[6], X[2] + nr_a0 * X[8], X[8], X[4] + nr_a0 * X[10], X[10], X[1] + nr_a0 * X[7], X[7], X[3] + nr_a0 * X[9], X[9], X[5] + nr_a0 * X[11], X[11], ] def precompute_lineline_sparsity(curve_id: int): curve = CURVES[curve_id] assert isinstance(curve, PairingCurve) field = get_base_field(curve_id) line_sparsity = curve.line_function_sparsity line = Polynomial([field(x) for x in line_sparsity]) ll = line * line % get_irreducible_poly(curve_id, 12) ll_sparsity = get_sparsity(ll.coefficients) return ll_sparsity[0:12] ================================================ FILE: hydra/garaga/poseidon_transcript.py ================================================ from typing import Iterable from garaga import garaga_rs from garaga.algebra import ModuloCircuitElement, PyFelt from garaga.curves import BASE, N_LIMBS, STARK from garaga.hints.io import bigint_split def hades_permutation(s0: int, s1: int, s2: int) -> tuple[int, int, int]: r0, r1, r2 = garaga_rs.hades_permutation( (s0 % STARK).to_bytes(32, "big"), (s1 % STARK).to_bytes(32, "big"), (s2 % STARK).to_bytes(32, "big"), ) return ( int.from_bytes(r0, "big"), int.from_bytes(r1, "big"), int.from_bytes(r2, "big"), ) class CairoPoseidonTranscript: """ The CairoPoseidonTranscript class mimics the behaviour of the Cairo functions hashing an array of u384 elements. """ def __init__(self, init_hash: int, three_limbs_only: bool = False) -> None: self.init_hash = init_hash self.s0, self.s1, self.s2 = hades_permutation( 0, 0, init_hash, ) self.permutations_count = 1 self.poseidon_ptr_indexes = [] self.z = None self.three_limbs_only = three_limbs_only @property def continuable_hash(self) -> int: return self.s0 @property def RLC_coeff(self): """ A function to retrieve the random linear combination coefficient after a permutation. Stores the index of the last permutation in the poseidon_ptr_indexes list, to be used to retrieve RLC coefficients later. """ self.poseidon_ptr_indexes.append(self.permutations_count - 1) return self.s1 def update_sponge_state(self, x, y): self.s0, self.s1, self.s2 = hades_permutation(self.s0 + x, self.s1 + y, self.s2) def hash_element(self, x: PyFelt | ModuloCircuitElement, debug: bool = False): # print(f"Will Hash PYTHON {hex(x.value)}") limbs = bigint_split(x, N_LIMBS, BASE) if debug: print(f"limbs : {limbs}") self.s0, self.s1, self.s2 = hades_permutation( self.s0 + limbs[0] + (BASE) * limbs[1], self.s1 + limbs[2] + (BASE) * limbs[3], self.s2, ) self.permutations_count += 1 return self.s0, self.s1 def hash_quadruple_u288( self, x: Iterable[PyFelt | ModuloCircuitElement], debug: bool = False ): assert len(x) == 4 x = [bigint_split(xi, 3, BASE) for xi in x] self.s0, self.s1, self.s2 = hades_permutation( self.s0 + x[0][0] + (BASE) * x[0][1], self.s1 + x[0][2] + (BASE) * x[1][0], self.s2, ) self.s0, self.s1, self.s2 = hades_permutation( self.s0 + x[1][1] + (BASE) * x[1][2], self.s1 + x[2][0] + (BASE) * x[2][1], self.s2, ) self.s0, self.s1, self.s2 = hades_permutation( self.s0 + x[2][2] + (BASE) * x[3][0], self.s1 + x[3][1] + (BASE) * x[3][2], self.s2, ) self.permutations_count += 3 return self.s0, self.s1 def hash_u256(self, x: PyFelt | int): assert isinstance(x, (PyFelt, int)) if isinstance(x, PyFelt): x = x.value assert 0 <= x < 2**256 low, high = bigint_split(x, 2, 2**128) self.s0, self.s1, self.s2 = hades_permutation( self.s0 + low, self.s1 + high, self.s2 ) self.permutations_count += 1 return self.s0 def hash_u128(self, x: PyFelt | int): assert isinstance(x, (PyFelt, int)) if isinstance(x, PyFelt): x = x.value assert 0 <= x < 2**128 self.s0, self.s1, self.s2 = hades_permutation(self.s0 + x, self.s1, self.s2) self.permutations_count += 1 return self.s0 def hash_u256_multi(self, X: list[PyFelt | int]): for x in X: self.hash_u256(x) return self.s0 def hash_limbs_multi( self, X: list[PyFelt | ModuloCircuitElement], sparsity: list[int] | None = None, debug: bool = False, three_limbs_only: bool = None, ): if three_limbs_only in [True, False]: three_limbs_only = three_limbs_only else: three_limbs_only = self.three_limbs_only if sparsity: X = [x for i, x in enumerate(X) if sparsity[i] != 0] if not three_limbs_only: for X_elem in X: if debug: print(f"\t s0 : {self.s0}") self.hash_element(X_elem, debug=debug) else: n_quadruples, rest = divmod(len(X), 4) for i in range(n_quadruples): self.hash_quadruple_u288(X[i * 4 : (i + 1) * 4], debug=debug) for i in range(rest): self.hash_element(X[n_quadruples * 4 + i], debug=debug) return None if __name__ == "__main__": import random random.seed(0) def gen_cairo_test_vectors(n_elmts: int): elmts = [PyFelt(random.randint(0, 2**384 - 1), 2**384) for _ in range(n_elmts)] transcript = CairoPoseidonTranscript(init_hash=0) for elmt in elmts: transcript.hash_element(elmt) expected_res = transcript.continuable_hash code = f""" #[test] fn test_hash_u384_{n_elmts}() {{ """ code += "// Auto-generated from garaga/poseidon_transcript.py\n" code += "let transcript: Array = array![" for elmt in elmts: limbs = bigint_split(elmt.value, N_LIMBS, BASE) code += f"u384 {{ limb0: {limbs[0]}, limb1: {limbs[1]}, limb2: {limbs[2]}, limb3: {limbs[3]} }}," code += "];\n" code += f"let expected_res: felt252 = {expected_res};\n" code += "let res = hash_u384_transcript(transcript.span(), 0);\n" code += "assert_eq!(res, expected_res);\n" code += "}\n\n" return code print(gen_cairo_test_vectors(1)) print(gen_cairo_test_vectors(2)) print(gen_cairo_test_vectors(3)) ================================================ FILE: hydra/garaga/precompiled_circuits/all_circuits.py ================================================ from enum import Enum from pathlib import Path from garaga.curves import CurveID from garaga.precompiled_circuits.compilable_circuits.apply_isogeny import ( ApplyIsogenyCircuit, ) from garaga.precompiled_circuits.compilable_circuits.base import ( cairo1_tests_header, collect_struct_dependencies, compilation_mode_to_file_header, compile_circuit, create_cairo1_test, format_cairo_files_in_parallel, ) from garaga.precompiled_circuits.compilable_circuits.cairo1_mpcheck_circuits import ( EvalE12D, FixedG2MPCheckBit0, FixedG2MPCheckBit00, FixedG2MPCheckBit1, FixedG2MPCheckBit01, FixedG2MPCheckBit10, FixedG2MPCheckInitBit, InitializeMPCheck, MPCheckFinalizeBLS, MPCheckFinalizeBN, MPCheckPreparePairs, ) from garaga.precompiled_circuits.compilable_circuits.cairo1_tower_pairing import ( E12TCyclotomicSquareCircuit, E12TCyclotomicSquareCompressedCircuit, E12TDecompressKarabinaPtIICircuit, E12TDecompressKarabinaPtINZCircuit, E12TDecompressKarabinaPtIZCircuit, E12TFrobeniusCircuit, E12TFrobeniusCubeCircuit, E12TFrobeniusSquareCircuit, E12TInverseCircuit, E12TMulCircuit, FP6NegCircuit, TowerMillerBit0, TowerMillerBit1, TowerMillerFinalizeBN, TowerMillerInitBit, ) from garaga.precompiled_circuits.compilable_circuits.common_cairo_fustat_circuits import ( AddECPointCircuit, AddECPointsG2Circuit, ClearCofactorBLS12_381Circuit, DoubleAndAddECPointsG2Circuit, DoubleECPointCircuit, DoubleECPointG2AEq0Circuit, DummyCircuit, IsOnCurveG1Circuit, IsOnCurveG1G2Circuit, IsOnCurveG2Circuit, PrepareFakeGLVPtsCircuit, PrepareGLVFakeGLVPtsCircuit, PsiG2BLS12_381Circuit, QuadrupleAndAdd9Circuit, ) from garaga.precompiled_circuits.compilable_circuits.rsa import ( RSAFullVerificationCircuit, ) from garaga.starknet.cli.utils import create_directory STARKNET_DIR = Path(__file__).parent.parent / "starknet" class CircuitID(Enum): DUMMY = int.from_bytes(b"dummy", "big") FP12_MUL = int.from_bytes(b"fp12_mul", "big") FP12_SUB = int.from_bytes(b"fp12_sub", "big") FINAL_EXP_PART_1 = int.from_bytes(b"final_exp_part_1", "big") FINAL_EXP_PART_2 = int.from_bytes(b"final_exp_part_2", "big") MULTI_MILLER_LOOP = int.from_bytes(b"multi_miller_loop", "big") MULTI_PAIRING_CHECK = int.from_bytes(b"multi_pairing_check", "big") IS_ON_CURVE_G1_G2 = int.from_bytes(b"is_on_curve_g1_g2", "big") IS_ON_CURVE_G1 = int.from_bytes(b"is_on_curve_g1", "big") IS_ON_CURVE_G2 = int.from_bytes(b"is_on_curve_g2", "big") CLEAR_COFACTOR_BLS12_381 = int.from_bytes(b"clear_cofactor_bls12_381", "big") ADD_EC_POINT = int.from_bytes(b"add_ec_point", "big") DOUBLE_EC_POINT = int.from_bytes(b"double_ec_point", "big") PREPARE_GLV_FAKE_GLV_PTS = int.from_bytes(b"prepare_glv_fake_glv_pts", "big") PREPARE_FAKE_GLV_PTS = int.from_bytes(b"prepare_fake_glv_pts", "big") QUADRUPLE_AND_ADD_9 = int.from_bytes(b"quadruple_and_add_9", "big") MP_CHECK_BIT0_LOOP = int.from_bytes(b"mp_check_bit0_loop", "big") MP_CHECK_BIT00_LOOP = int.from_bytes(b"mp_check_bit00_loop", "big") MP_CHECK_BIT1_LOOP = int.from_bytes(b"mp_check_bit1_loop", "big") MP_CHECK_BIT01_LOOP = int.from_bytes(b"mp_check_bit01_loop", "big") MP_CHECK_BIT10_LOOP = int.from_bytes(b"mp_check_bit10_loop", "big") MP_CHECK_PREPARE_PAIRS = int.from_bytes(b"mp_check_prepare_pairs", "big") MP_CHECK_INITIALIZE = int.from_bytes(b"mp_check_initialize", "big") MP_CHECK_INIT_BIT = int.from_bytes(b"mp_check_init_bit", "big") MP_CHECK_FINALIZE_BN = int.from_bytes(b"mp_check_finalize_bn", "big") MP_CHECK_FINALIZE_BLS = int.from_bytes(b"mp_check_finalize_bls", "big") FP12_MUL_ASSERT_ONE = int.from_bytes(b"fp12_mul_assert_one", "big") EVAL_E12D = int.from_bytes(b"eval_e12d", "big") APPLY_ISOGENY = int.from_bytes(b"apply_isogeny", "big") HONK_SUMCHECK_CIRCUIT = int.from_bytes(b"honk_sumcheck_circuit", "big") HONK_PREPARE_SCALARS_CIRCUIT = int.from_bytes( b"honk_prepare_scalars_circuit", "big" ) TOWER_MILLER_BIT0 = int.from_bytes(b"tower_miller_bit0", "big") TOWER_MILLER_BIT1 = int.from_bytes(b"tower_miller_bit1", "big") TOWER_MILLER_INIT_BIT = int.from_bytes(b"tower_miller_init_bit", "big") TOWER_MILLER_FINALIZE_BN = int.from_bytes(b"tower_miller_finalize_bn", "big") E12T_MUL = int.from_bytes(b"e12t_mul", "big") E12T_CYCLOTOMIC_SQUARE = int.from_bytes(b"e12t_cyclotomic_square", "big") E12T_FROBENIUS_SQUARE = int.from_bytes(b"e12t_frobenius_square", "big") FP6_NEG = int.from_bytes(b"fp6_neg", "big") E12T_INVERSE = int.from_bytes(b"e12t_inverse", "big") E12T_FROBENIUS = int.from_bytes(b"e12t_frobenius", "big") E12T_FROBENIUS_CUBE = int.from_bytes(b"e12t_frobenius_cube", "big") E12T_CYCLOTOMIC_SQUARE_COMPRESSED = int.from_bytes( b"e12t_cyclotomic_square_compressed", "big" ) E12T_DECOMPRESS_KARABINA_PT_INZ = int.from_bytes( b"e12t_decompress_karabina_pt_inz", "big" ) E12T_DECOMPRESS_KARABINA_PT_IZ = int.from_bytes( b"e12t_decompress_karabina_pt_iz", "big" ) E12T_DECOMPRESS_KARABINA_PT_II = int.from_bytes( b"e12t_decompress_karabina_pt_ii", "big" ) ADD_EC_POINT_G2 = int.from_bytes(b"add_ec_point_g2", "big") DOUBLE_EC_POINT_G2 = int.from_bytes(b"double_ec_point_g2", "big") DOUBLE_AND_ADD_EC_POINT_G2 = int.from_bytes(b"double_and_add_ec_point_g2", "big") PSI_G2_BLS12_381 = int.from_bytes(b"psi_g2_bls12_381", "big") FULL_ECIP_BATCHED = int.from_bytes(b"full_ecip__batched", "big") RSA_FULL_VERIFICATION = int.from_bytes(b"rsa_full_verif", "big") ALL_CAIRO_CIRCUITS = { CircuitID.DUMMY: {"class": DummyCircuit, "params": None, "filename": "dummy"}, CircuitID.IS_ON_CURVE_G1_G2: { "class": IsOnCurveG1G2Circuit, "params": None, "filename": "ec", }, CircuitID.IS_ON_CURVE_G1: { "class": IsOnCurveG1Circuit, "params": None, "filename": "ec", }, CircuitID.IS_ON_CURVE_G2: { "class": IsOnCurveG2Circuit, "params": None, "filename": "ec", }, CircuitID.CLEAR_COFACTOR_BLS12_381: { "class": ClearCofactorBLS12_381Circuit, "params": None, "filename": "ec", "curve_ids": [CurveID.BLS12_381], }, CircuitID.ADD_EC_POINT: { "class": AddECPointCircuit, "params": None, "filename": "ec", }, CircuitID.DOUBLE_EC_POINT: { "class": DoubleECPointCircuit, "params": None, "filename": "ec", }, CircuitID.PREPARE_GLV_FAKE_GLV_PTS: { "class": PrepareGLVFakeGLVPtsCircuit, "params": None, "filename": "ec", }, CircuitID.PREPARE_FAKE_GLV_PTS: { "class": PrepareFakeGLVPtsCircuit, "params": None, "filename": "ec", }, CircuitID.QUADRUPLE_AND_ADD_9: { "class": QuadrupleAndAdd9Circuit, "params": None, "filename": "ec", }, CircuitID.ADD_EC_POINT_G2: { "class": AddECPointsG2Circuit, "params": None, "filename": "ec", }, CircuitID.DOUBLE_EC_POINT_G2: { "class": DoubleECPointG2AEq0Circuit, "params": None, "filename": "ec", }, CircuitID.DOUBLE_AND_ADD_EC_POINT_G2: { "class": DoubleAndAddECPointsG2Circuit, "params": None, "filename": "ec", }, CircuitID.PSI_G2_BLS12_381: { "class": PsiG2BLS12_381Circuit, "params": None, "filename": "ec", "curve_ids": [CurveID.BLS12_381], }, CircuitID.RSA_FULL_VERIFICATION: { "class": RSAFullVerificationCircuit, "params": None, "filename": "rsa", "curve_ids": [CurveID.BLS12_381], }, CircuitID.MP_CHECK_BIT0_LOOP: { "class": FixedG2MPCheckBit0, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BLS12_381], }, CircuitID.MP_CHECK_BIT00_LOOP: { "class": FixedG2MPCheckBit00, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.MP_CHECK_BIT1_LOOP: { "class": FixedG2MPCheckBit1, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BLS12_381], }, CircuitID.MP_CHECK_BIT01_LOOP: { "class": FixedG2MPCheckBit01, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254], }, CircuitID.MP_CHECK_BIT10_LOOP: { "class": FixedG2MPCheckBit10, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254], }, CircuitID.MP_CHECK_PREPARE_PAIRS: { "class": MPCheckPreparePairs, "params": [{"n_pairs": k} for k in [1, 2, 3]], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.MP_CHECK_INITIALIZE: { "class": InitializeMPCheck, "params": [ {"extra_miller_loop_result": False}, {"extra_miller_loop_result": True}, ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.MP_CHECK_INIT_BIT: { "class": FixedG2MPCheckInitBit, "params": [ {"n_pairs": 2, "n_fixed_g2": 2}, # BLS SIG / KZG Verif {"n_pairs": 3, "n_fixed_g2": 2}, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.MP_CHECK_FINALIZE_BN: { "class": MPCheckFinalizeBN, "params": [ { "n_pairs": 2, "n_fixed_g2": 2, "extra_miller_loop_result": False, }, # BLS SIG / KZG Verif { "n_pairs": 3, "n_fixed_g2": 2, "extra_miller_loop_result": True, }, # Groth16 ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BN254], }, CircuitID.MP_CHECK_FINALIZE_BLS: { "class": MPCheckFinalizeBLS, "params": [ {"n_pairs": 2, "extra_miller_loop_result": False}, {"n_pairs": 3, "extra_miller_loop_result": True}, ], "filename": "multi_pairing_check", "curve_ids": [CurveID.BLS12_381], }, CircuitID.EVAL_E12D: { "class": EvalE12D, "params": None, "filename": "extf_mul", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.APPLY_ISOGENY: { "class": ApplyIsogenyCircuit, "params": None, "filename": "isogeny", "curve_ids": [CurveID.BLS12_381], }, CircuitID.TOWER_MILLER_BIT0: { "class": TowerMillerBit0, "params": [{"n_pairs": k} for k in [1]], "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.TOWER_MILLER_BIT1: { "class": TowerMillerBit1, "params": [{"n_pairs": k} for k in [1]], "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.TOWER_MILLER_INIT_BIT: { "class": TowerMillerInitBit, "params": [{"n_pairs": k} for k in [1]], "filename": "tower_circuits", "curve_ids": [CurveID.BLS12_381], }, CircuitID.TOWER_MILLER_FINALIZE_BN: { "class": TowerMillerFinalizeBN, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254], }, CircuitID.E12T_MUL: { "class": E12TMulCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_CYCLOTOMIC_SQUARE: { "class": E12TCyclotomicSquareCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_FROBENIUS_SQUARE: { "class": E12TFrobeniusSquareCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.FP6_NEG: { "class": FP6NegCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_INVERSE: { "class": E12TInverseCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_FROBENIUS: { "class": E12TFrobeniusCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_FROBENIUS_CUBE: { "class": E12TFrobeniusCubeCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BN254, CurveID.BLS12_381], }, CircuitID.E12T_CYCLOTOMIC_SQUARE_COMPRESSED: { "class": E12TCyclotomicSquareCompressedCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BLS12_381], }, CircuitID.E12T_DECOMPRESS_KARABINA_PT_INZ: { "class": E12TDecompressKarabinaPtINZCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BLS12_381], }, CircuitID.E12T_DECOMPRESS_KARABINA_PT_IZ: { "class": E12TDecompressKarabinaPtIZCircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BLS12_381], }, CircuitID.E12T_DECOMPRESS_KARABINA_PT_II: { "class": E12TDecompressKarabinaPtIICircuit, "params": None, "filename": "tower_circuits", "curve_ids": [CurveID.BLS12_381], }, # CircuitID.HONK_SUMCHECK_CIRCUIT: { # "class": SumCheckCircuit, # "params": [ # { # "vk": HonkVk.from_bytes( # open( # f"{STARKNET_DIR}/honk_contract_generator/examples/vk_ultra_keccak.bin", # "rb", # ).read() # ) # } # ], # "filename": "honk_circuits", # "curve_ids": [CurveID.GRUMPKIN], # }, # CircuitID.HONK_PREPARE_SCALARS_CIRCUIT: { # "class": PrepareScalarsCircuit, # "params": [ # { # "vk": HonkVk.from_bytes( # open( # f"{STARKNET_DIR}/honk_contract_generator/examples/vk_ultra_keccak.bin", # "rb", # ).read() # ) # } # ], # "filename": "honk_circuits", # "curve_ids": [CurveID.GRUMPKIN], # }, # CircuitID.FULL_ECIP_BATCHED: { # "class": FullECIPCircuitBatched, # "params": [{"n_points": k} for k in [1]], # "filename": "ec_batched", # "curve_ids": [CurveID.BN254], # }, } def initialize_compilation( PRECOMPILED_CIRCUITS_DIR: str, CIRCUITS_TO_COMPILE: dict ) -> tuple[ set[str], dict[str, set[str]], dict[str, set[str]], dict[str, set[str]], dict[str, open], ]: """ Initialize the compilation process by creating the necessary directories and files. Returns : - filenames_used: set of all filenames that will be used - codes: dict of sets of strings, where each set contains the compiled circuits for a given filename - cairo1_tests_functions: dict of sets of strings, where each set contains the cairo1 tests for a given filename - cairo1_full_function_names: dict of sets of strings, where each set contains the full function names for a given filename - files: dict of open files, where each file is for a given filename """ create_directory(PRECOMPILED_CIRCUITS_DIR) filenames_used = set([v["filename"] for v in CIRCUITS_TO_COMPILE.values()]) codes = {filename: set() for filename in filenames_used} cairo1_tests_functions = {filename: set() for filename in filenames_used} cairo1_full_function_names = {filename: set() for filename in filenames_used} files = { f: open(f"{PRECOMPILED_CIRCUITS_DIR}{f}.cairo", "w") for f in filenames_used } return ( filenames_used, codes, cairo1_tests_functions, cairo1_full_function_names, files, ) def write_headers( files: dict[str, open], compilation_mode: int, output_sizes_exceeding_limit: dict[str, set[int]], file_curve_ids: dict[str, set[CurveID]], file_struct_dependencies: dict[str, set[str]], ) -> None: """ Write the header to the files. Add a specific header if max output length exceeds the limit. """ for filename, curve_ids in file_curve_ids.items(): required_structs = file_struct_dependencies.get(filename, set()) HEADER = compilation_mode_to_file_header( compilation_mode, curve_ids, required_structs ) files[filename].write(HEADER) TEMPLATE = """ impl CircuitDefinition{num_outputs}< {elements} > of core::circuit::CircuitDefinition< ( {ce_elements} ) > {{ type CircuitType = core::circuit::Circuit< ({elements_tuple},) >; }} impl MyDrp_{num_outputs}< {elements} > of Drop< ( {ce_elements} ) >; """ for filename, file in files.items(): # Then write the template for each unique output size exceeding the limit for num_outputs in sorted(output_sizes_exceeding_limit[filename]): elements = ", ".join(f"E{i}" for i in range(num_outputs)) ce_elements = ", ".join(f"CE" for i in range(num_outputs)) elements_tuple = ", ".join(f"E{i}" for i in range(num_outputs)) file.write( TEMPLATE.format( num_outputs=num_outputs, elements=elements, ce_elements=ce_elements, elements_tuple=elements_tuple, ) ) def compile_circuits( CIRCUITS_TO_COMPILE: dict, compilation_mode: int, codes: dict[str, set[str]], cairo1_full_function_names: dict[str, set[str]], cairo1_tests_functions: dict[str, set[str]], output_sizes_exceeding_limit: dict[str, set[int]], file_struct_dependencies: dict[str, set[str]], limit: int, ) -> None: """ Compile the circuits and write them to the files. """ for circuit_id, circuit_info in CIRCUITS_TO_COMPILE.items(): for curve_id in circuit_info.get( "curve_ids", [CurveID.BN254, CurveID.BLS12_381] ): filename_key = circuit_info["filename"] compiled_circuits, full_function_names, circuit_instances = compile_circuit( curve_id, circuit_info["class"], circuit_info["params"], compilation_mode, ) codes[filename_key].update(compiled_circuits) # Collect struct dependencies for this file if compilation_mode == 1 if compilation_mode == 1: struct_deps = collect_struct_dependencies(circuit_instances) if filename_key not in file_struct_dependencies: file_struct_dependencies[filename_key] = set() file_struct_dependencies[filename_key].update(struct_deps) for circuit_instance in circuit_instances: output_length = len(circuit_instance.circuit.output) if ( output_length > limit and circuit_instance.circuit.exact_output_refs_needed is None ): output_sizes_exceeding_limit[filename_key].add(output_length) if compilation_mode == 1: cairo1_full_function_names[filename_key].update(full_function_names) generate_cairo1_tests( circuit_instances, full_function_names, curve_id, cairo1_tests_functions, filename_key, ) def generate_cairo1_tests( circuit_instances, full_function_names, curve_id, cairo1_tests_functions, filename_key, ): for circuit_instance, full_function_name in zip( circuit_instances, full_function_names ): circuit_input = circuit_instance.full_input_cairo1 circuit_output = ( circuit_instance.circuit.output_structs if sum([len(x.elmts) for x in circuit_instance.circuit.output_structs]) == len(circuit_instance.circuit.output) else circuit_instance.circuit.output ) cairo1_tests_functions[filename_key].add( create_cairo1_test( full_function_name, circuit_input, circuit_output, curve_id.value, ) ) def write_compiled_circuits( files: dict[str, open], codes: dict[str, set[str]], cairo1_full_function_names: dict[str, set[str]], cairo1_tests_functions: dict[str, set[str]], compilation_mode: int, ) -> None: """ Write the compiled circuits and the cairo1 tests to the files. """ print("Writing circuits and selectors to .cairo files...") for filename, file in files.items(): for compiled_circuit in sorted(codes[filename]): file.write(compiled_circuit + "\n") # if compilation_mode == 1: # write_cairo1_tests( # file, filename, cairo1_full_function_names, cairo1_tests_functions # ) def write_cairo1_tests( file: open, filename: str, cairo1_full_function_names: dict[str, set[str]], cairo1_tests_functions: dict[str, set[str]], ) -> None: file.write(cairo1_tests_header() + "\n") fns_to_import = sorted(cairo1_full_function_names[filename]) if "" in fns_to_import: fns_to_import.remove("") file.write(f"use super::{{{','.join(fns_to_import)}}};\n") for cairo1_test in sorted(cairo1_tests_functions[filename]): file.write(cairo1_test + "\n") file.write("}\n") def main( PRECOMPILED_CIRCUITS_DIR: str, CIRCUITS_TO_COMPILE: dict[CircuitID, dict], compilation_mode: int = 1, ): """Compiles and writes all circuits to .cairo files""" filenames_used, codes, cairo1_tests_functions, cairo1_full_function_names, files = ( initialize_compilation(PRECOMPILED_CIRCUITS_DIR, CIRCUITS_TO_COMPILE) ) file_curve_ids = {filename: set() for filename in filenames_used} file_struct_dependencies = {filename: set() for filename in filenames_used} # Populate file_curve_ids with curve IDs for circuit_info in CIRCUITS_TO_COMPILE.values(): filename = circuit_info["filename"] curve_ids = circuit_info.get("curve_ids", [CurveID.BN254, CurveID.BLS12_381]) file_curve_ids[filename].update(curve_ids) output_sizes_exceeding_limit = {filename: set() for filename in filenames_used} limit = 16 compile_circuits( CIRCUITS_TO_COMPILE, compilation_mode, codes, cairo1_full_function_names, cairo1_tests_functions, output_sizes_exceeding_limit, file_struct_dependencies, limit, ) write_headers( files, compilation_mode, output_sizes_exceeding_limit, file_curve_ids, file_struct_dependencies, ) write_compiled_circuits( files, codes, cairo1_full_function_names, cairo1_tests_functions, compilation_mode, ) for file in files.values(): file.close() format_cairo_files_in_parallel( filenames_used, compilation_mode, PRECOMPILED_CIRCUITS_DIR ) return None if __name__ == "__main__": import random random.seed(0) print("Compiling Cairo 1 circuits...") main( PRECOMPILED_CIRCUITS_DIR="src/src/circuits/", CIRCUITS_TO_COMPILE=ALL_CAIRO_CIRCUITS, compilation_mode=1, ) ================================================ FILE: hydra/garaga/precompiled_circuits/cofactor_clearing.py ================================================ from garaga.algebra import ModuloCircuitElement from garaga.curves import CurveID from garaga.precompiled_circuits.ec import BasicEC, BasicECG2 class SlowG2CofactorClearing(BasicECG2): """ Implements cofactor clearing for G2 points on BLS12-381 curve. Based on Teku's implementation of BLS signatures. """ def h2_chain( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ): """ Addition chain for multiplication by the E2 cofactor. Reference implementation: https://github.com/Consensys/teku/blob/55d04f87b422112312f79c1b4d662b3d58e3ca74/bls/src/main/java/tech/pegasys/teku/bls/impl/mikuli/hash2g2/Chains.java#L569 """ assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" # Initial point is t0 = P t0 = P t1 = self.double_point_a_eq_0(t0) t4 = self.add_points(t1, t0) t2 = self.add_points(t4, t1) t3 = self.add_points(t2, t1) t11 = self.add_points(t3, t1) t9 = self.add_points(t11, t1) t10 = self.add_points(t9, t1) t5 = self.add_points(t10, t1) t7 = self.add_points(t5, t1) t15 = self.add_points(t7, t1) t13 = self.add_points(t15, t1) t6 = self.add_points(t13, t1) t14 = self.add_points(t6, t1) t12 = self.add_points(t14, t1) t8 = self.add_points(t12, t1) # Start the main computation chain t1 = self.double_point_a_eq_0(t6) # t6.dbl() t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 2) # .dbls(2) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 9) # .dbls(9) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t11) # .add(t11) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t11) # .add(t11) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 9) # .dbls(9) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t11) # .add(t11) t1 = self.double_n_times(t1, 2) # .dbls(2) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 9) # .dbls(9) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 11) # .dbls(11) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t12) # .add(t12) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t7) # .add(t7) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t12) # .add(t12) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t14) # .add(t14) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t10) # .add(t10) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t10) # .add(t10) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 10) # .dbls(10) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t14) # .add(t14) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t15) # .add(t15) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t12) # .add(t12) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t15) # .add(t15) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t15) # .add(t15) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t14) # .add(t14) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 10) # .dbls(10) t1 = self.add_points(t1, t6) # .add(t6) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 3) # .dbls(3) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 9) # .dbls(9) t1 = self.add_points(t1, t13) # .add(t13) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t12) # .add(t12) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t11) # .add(t11) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t10) # .add(t10) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t4) # .add(t4) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t10) # .add(t10) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t7) # .add(t7) t1 = self.double_n_times(t1, 3) # .dbls(3) t1 = self.add_points(t1, t2) # .add(t2) t1 = self.double_n_times(t1, 4) # .dbls(4) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 8) # .dbls(8) t1 = self.add_points(t1, t9) # .add(t9) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t8) # .add(t8) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t7) # .add(t7) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t6) # .add(t6) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t4) # .add(t4) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t4) # .add(t4) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t4) # .add(t4) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t5) # .add(t5) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 7) # .dbls(7) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t4) # .add(t4) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 3) # .dbls(3) t1 = self.add_points(t1, t0) # .add(t0) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 6) # .dbls(6) t1 = self.add_points(t1, t3) # .add(t3) t1 = self.double_n_times(t1, 5) # .dbls(5) t1 = self.add_points(t1, t2) # .add(t2) return t1 def mx_chain(self, P): """ Addition chain for multiplication by 0xd201000000010000 == -x, where x is the BLS parameter. """ q = self.double_point_a_eq_0(P) # Sequence of doubles and adds as per Java implementation ndoubles = [2, 3, 9, 32, 16] for n in ndoubles: q = self.add_points(q, P) for _ in range(n): q = self.double_point_a_eq_0(q) return q def clear_cofactor(self, P): """ Complete cofactor clearing implementation following Teku's approach. This implements an optimized cofactor clearing method for BLS12-381 G2 that avoids patent-encumbered endomorphism techniques. Instead of directly multiplying by the G2 cofactor, it uses an efficient addition chain to compute an equivalent operation. The method follows the approach specified in draft-irtf-cfrg-hash-to-curve-05 section 8.9.2, which breaks down the operation into: 1. Apply h2 chain 2. Multiply by 3 3. Apply mx chain twice (z^2) 4. Subtract 3 * h2 result This gives the same result as multiplying by the effective cofactor, but is more computationally efficient due to the optimized addition chain implementation. Args: P: The point to clear the cofactor from Returns: A point in the correct subgroup after cofactor clearing """ assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" # Step 1: Apply h2 chain work = self.h2_chain(P) # Step 2: Multiply by 3 (add + double) work3 = self.add_points(work, self.double_point_a_eq_0(work)) # Step 3: Apply mx chain twice (z^2) work = self.mx_chain(work3) # First z work = self.mx_chain(work) # Second z # Step 4: Subtract 3 * h2 neg_work3 = self.negate_point(work3) final = self.add_points(work, neg_work3) return final class FastG2CofactorClearing(BasicECG2): """ Implements an efficient cofactor clearing method for G2 points on BLS12-381 curve using endomorphisms. This implementation avoids expensive scalar multiplications by utilizing the Frobenius endomorphism (ψ) and efficient addition chains. The cofactor clearing ensures that points are in the correct order-r subgroup of G2, which is essential for cryptographic operations like BLS signatures. Key operations: - ψ (psi): Frobenius endomorphism - ψ² (psi²): Double application of Frobenius - mul_by_x: Multiplication by BLS parameter x """ def psi( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: """ Implements the ψ (Frobenius endomorphism) map for BLS12-381 G₂ points. The Frobenius endomorphism ψ is defined as: ψ(P) = π(P) · [1/(u+1)^((p-1)/3), 1/(u+1)^((p-1)/2)] where π is the p-power Frobenius map that conjugates coordinates in Fp2. Args: P: A G2 point represented as ((x0, x1), (y0, y1)) where each coordinate is in Fp and (x0, x1) and (y0, y1) represent elements in Fp2 Returns: A new G2 point after applying the Frobenius endomorphism """ assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" x, y = P # x and y are lists [x0, x1] representing elements in Fp² # Apply the Frobenius map (conjugation in Fp2) x_frob = self.fp2_frobenius_map(x) y_frob = self.fp2_frobenius_map(y) # Constants for scaling after Frobenius map # PSI_X = 1/(u+1)^((p-1)/3) psi_coeff_x = [ self.set_or_get_constant(self.field(0)), self.set_or_get_constant( self.field( 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD ) ), ] # PSI_Y = 1/(u+1)^((p-1)/2) psi_coeff_y = [ self.set_or_get_constant( self.field( 0x135203E60180A68EE2E9C448D77A2CD91C3DEDD930B1CF60EF396489F61EB45E304466CF3E67FA0AF1EE7B04121BDEA2 ) ), self.set_or_get_constant( self.field( 0x6AF0E0437FF400B6831E36D6BD17FFE48395DABC2D3435E77F76E17009241C5EE67992F72EC05F4C81084FBEDE3CC09 ) ), ] # Scale the coordinates with the appropriate constants psi_x = self.fp2_mul(x_frob, psi_coeff_x) psi_y = self.fp2_mul(y_frob, psi_coeff_y) return (psi_x, psi_y) def mul_by_x( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: """ Multiplies a point by x = -0xd201000000010001 (BLS parameter) using double-and-add. The binary representation of x is: 1101 0010 0000 0001 0000 0000 0000 0000 0000 0000 0000 0001 0000 0000 0000 0000 Args: P: A G2 point to be multiplied by x Returns: [-x]P: The point multiplied by the negation of x """ assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" result = P # 1: Start with P. As a result we skip the first bit. result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) # 2: Double and add result = self.double_point_a_eq_0(result) # 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 2) # 2x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 8) # 8x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 31) # 31x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 16) # 16x 0: Double return self.negate_point(result) def double_psi( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: """ Implements ψ² (double Frobenius endomorphism) by applying psi twice. For BLS12-381, ψ² is a much cheaper operation than scalar multiplication and is used to optimize the cofactor clearing operation. Args: P: A G2 point Returns: ψ²(P): The point after applying the Frobenius endomorphism twice """ return self.psi(self.psi(P)) def clear_cofactor( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: """ Clears the cofactor of a G2 point using an optimized endomorphism-based method. This implementation follows the efficient approach described in: https://eprint.iacr.org/2017/419.pdf The formula implemented is: [h(ψ)]P = [x²-x-1]P + [x-1]ψ(P) + ψ²(2P) where x is the BLS parameter = -0xd201000000010000 This method is more efficient than the traditional scalar multiplication by the cofactor h, as it uses the efficiently computable endomorphism ψ and optimized multiplication by x. Args: P: A G2 point to clear the cofactor from Returns: A point in the correct order-r subgroup of G2 """ # Calculate [-x]P t1 = self.mul_by_x(P) # Calculate ψ(P) t2 = self.psi(P) # Calculate 2P and ψ²(2P) t3 = self.double_point_a_eq_0(P) # 2P t3 = self.double_psi(t3) # ψ²(2P) # Following steps compute: [x²-x-1]P + [x-1]ψ(P) + ψ²(2P) t3 = self.add_points(t3, self.negate_point(t2)) # ψ²(2P) - ψ(P) t2 = self.add_points(t1, t2) # [-x]P + ψ(P) t2 = self.mul_by_x(t2) # [x²]P - [x]ψ(P) t3 = self.add_points(t3, t2) # ψ²(2P) - ψ(P) + [x²]P - [x]ψ(P) t3 = self.add_points(t3, self.negate_point(t1)) # Add [x]P final = self.add_points(t3, self.negate_point(P)) # Subtract P return final class G1CofactorClearing(BasicEC): def mul_by_x( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement] ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """ Multiplies a point by x = 0xd201000000010000 (BLS parameter) using double-and-add. The binary representation of x is: 1101 0010 0000 0001 0000 0000 0000 0000 0000 0000 0000 0001 0000 0000 0000 0000 Args: P: A G1 point to be multiplied by x Returns: [x]P: The point multiplied by x """ # Todo : Incude automatic addition chain for any number computed at runtime ? assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" result = P # 1: Start with P. As a result we skip the first bit. result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) # 2: Double and add result = self.double_point_a_eq_0(result) # 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 2) # 2x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 8) # 8x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) result = self.double_n_times(result, 31) # 31x 0: Double result = self.double_point_a_eq_0(result) # 1: Double and add result = self.add_points(result, P) return self.double_n_times(result, 16) # 16x 0: Double def clear_cofactor( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement] ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """ Clears the cofactor of a G1 point using an efficient scalar multiplication method. Implementation follows the approach from: https://eprint.iacr.org/2019/403 The formula is: h_eff(P) = P - [-x]P = P + [x]P where x is the BLS parameter = -0xd201000000010000 This method is more efficient than multiplying by the full cofactor h, as it uses an optimized addition chain for multiplication by x. Args: P: A G1 point to clear the cofactor from Returns: A point in the correct order-r subgroup of G1 """ assert ( self.curve_id == CurveID.BLS12_381.value ), "This circuit is only supported for BLS12-381" # Calculate [x]P using the existing mul_by_x method # As shown below, we can save negation xP = self.mul_by_x(P) # Return P - [-x]P = P + [x]P return self.add_points(P, xP) if __name__ == "__main__": circuit = G1CofactorClearing(name="cofactor_clearing", curve_id=1) val_x = circuit.write_element( circuit.field( 3789617024712504402204306620295003375951143917889162928515122476381982967144814366712031831841518399614182231387665 ) ) val_y = circuit.write_element( circuit.field( 1292375129422168617658520396283100687686347104559592203462491249161639006037671760603453326853098986903549775136448 ) ) print(circuit.clear_cofactor((val_x, val_y))) ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/apply_isogeny.py ================================================ import garaga.modulo_circuit_structs as structs from garaga.curves import CurveID from garaga.precompiled_circuits.compilable_circuits.base import ( BaseModuloCircuit, ModuloCircuit, PyFelt, ) from garaga.precompiled_circuits.isogeny import IsogenyG1 class ApplyIsogenyCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1 ) -> None: super().__init__( name=f"apply_isogeny_{CurveID(curve_id).name.lower()}", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: return [self.field(44), self.field(4)] def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = IsogenyG1(self.name, self.curve_id, self.compilation_mode) px, py = circuit.write_struct(structs.G1PointCircuit(name="pt", elmts=input)) x_affine, y_affine = circuit.run_isogeny(px, py) circuit.extend_struct_output( structs.G1PointCircuit(name="res", elmts=[x_affine, y_affine]) ) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/base.py ================================================ import re import subprocess from abc import ABC, abstractmethod from concurrent.futures import ProcessPoolExecutor from typing import Type from garaga.curves import CurveID, get_base_field from garaga.hints.io import int_array_to_u384_array from garaga.modulo_circuit import ModuloCircuit, ModuloCircuitElement, PyFelt from garaga.modulo_circuit_structs import Cairo1SerializableStruct def get_circuit_definition_impl_template(num_outputs: int): TEMPLATE = """\n impl CircuitDefinition{num_outputs}< {elements} > of core::circuit::CircuitDefinition< ( {ce_elements} ) > {{ type CircuitType = core::circuit::Circuit< ({elements_tuple},) >; }} impl MyDrp_{num_outputs}< {elements} > of Drop< ( {ce_elements} ) >; """ elements = ", ".join(f"E{i}" for i in range(num_outputs)) ce_elements = ", ".join(f"CE" for i in range(num_outputs)) elements_tuple = ", ".join(f"E{i}" for i in range(num_outputs)) return TEMPLATE.format( num_outputs=num_outputs, elements=elements, ce_elements=ce_elements, elements_tuple=elements_tuple, ) class BaseModuloCircuit(ABC): """ Base class for all modulo circuits that will be compiled to Cairo code. Parameters: - name: str, the name of the circuit - curve_id: int, the id of the curve - auto_run: bool, whether to run the circuit automatically at initialization. When compiling, this flag is set to true so the ModuloCircuit class inside the ".circuit" member of this class holds the necessary metadata about the operations that will be compiled. For CairoZero, this flag will be set to False in the Python hint, so that BaseModuloCircuit.run_circuit() can be called on a segment parsed from the CairoZero VM. - compilation mode: 0 (CairoZero) or 1 (Cairo) """ def __init__( self, name: str, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ) -> None: self.name = name self.curve_id = curve_id self.field = get_base_field(curve_id) self.init_hash = None self.generic_over_curve = False self.compilation_mode = compilation_mode if auto_run: self.input = self.build_input() self.circuit: ModuloCircuit = self._run_circuit_inner(self.input.copy()) @abstractmethod def build_input(self) -> list[PyFelt]: """ This method is used to create the necessary inputs that will be written to the ModuloCircuit. It works in pair with the _run_circuit_inner function, where the _run_circuit_inner will use the output of the build_input function to "deserialize" the list of elements and write them to the ModuloCircuit class. """ @property def full_input_cairo1(self) -> list[PyFelt] | list[Cairo1SerializableStruct]: if self.circuit is None: raise ValueError("Circuit not run yet") if self.circuit.input_structs: return self.circuit.input_structs else: res = self.input + self.circuit.witnesses return res @abstractmethod def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: """ This method is responsible for - deserializing the input list of elements, - creating a ModuloCircuit class (or class that derives from ModuloCircuit) - "writing" the inputs to the ModuloCircuit class to obtain ModuloCircuitElements - using the methods add, sub, mul, inv (or higher level methods) of the ModuloCircuit class to define the list of operations on the given inputs - Returning the ModuloCircuit class in a state where the circuit has been run, and therefore holding the metadata so that its instructions can be compiled to Cairo code. """ def run_circuit(self, input: list[int]) -> ModuloCircuit: """ A simple wrapper around _run_circuit_inner that converts the input as a list of ints to a list of PyFelt. Used in CairoZero hint. """ # print( # f"Running circuit for {self.name} with CurveID {CurveID(self.curve_id).name}..." # ) circuit_input = [self.field(x) for x in input] return self._run_circuit_inner(circuit_input) class BaseEXTFCircuit(BaseModuloCircuit): """ A extension of the BaseModuloCircuit class that holds an init_hash, used for CairoZero. Not relevant for Cairo1 circuits. """ def __init__( self, name: str, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__(name, curve_id, auto_run, compilation_mode) self.init_hash = init_hash def compilation_mode_to_file_header( mode: int, curve_ids: set[CurveID], required_structs: set[str] = None ) -> str: if mode == 0: return """ from starkware.cairo.common.registers import get_fp_and_pc, get_label_location from modulo_circuit import ExtensionFieldModuloCircuit, ModuloCircuit, get_void_modulo_circuit, get_void_extension_field_modulo_circuit from definitions import bn, bls """ elif mode == 1: # Default structs (always included for backward compatibility if no required_structs specified) default_structs = [ "G1Point", "G2Point", "E12D", "u288", "G1G2Pair", "BNProcessedPair", "BLSProcessedPair", "MillerLoopResultScalingFactor", "G2Line", "E12T", ] # Use required_structs if provided, otherwise use default structs # If required_structs is an empty set, that means no structs are needed if required_structs is not None: structs_to_import = list(sorted(required_structs)) else: structs_to_import = default_structs.copy() # remove u384 from structs_to_import list if it exists if "u384" in structs_to_import: structs_to_import.remove("u384") # Combine all definitions all_definitions = structs_to_import definitions_import = "" if all_definitions: definitions_import = ( f"use garaga::definitions::{{{', '.join(all_definitions)}}};" ) return f""" use core::circuit::{{ u384, circuit_add, circuit_sub, circuit_mul, circuit_inverse, EvalCircuitTrait, CircuitOutputsTrait, CircuitInputs, }}; use garaga::core::circuit::{{AddInputResultTrait2, u288IntoCircuitInputValue}}; use core::circuit::CircuitElement as CE; use core::circuit::CircuitInput as CI; {definitions_import} """ def cairo1_tests_header() -> str: return """ #[cfg(test)] mod tests { use core::traits::TryInto; use core::circuit::{ RangeCheck96, AddMod, MulMod, CircuitElement, CircuitInput, circuit_add, circuit_sub, circuit_mul, circuit_inverse, EvalCircuitResult, EvalCircuitTrait, u384, CircuitOutputsTrait, CircuitModulus, AddInputResultTrait, CircuitInputs }; use garaga::definitions::{G1Point, G2Point, E12D, G1G2Pair, BNProcessedPair, BLSProcessedPair, MillerLoopResultScalingFactor, G2Line}; """ def parse_struct_name(struct_name: str) -> list[str]: """ Parse struct names and extract the types that need to be imported. Rules: - Span or Array -> only add T - Struct -> add Struct and T separately - Other structs -> add as is Returns: list[str]: List of struct names to import """ import re # Handle Span and Array - only add T span_array_match = re.match(r"^(Span|Array)<(.+)>$", struct_name) if span_array_match: inner_type = span_array_match.group(2) return [inner_type] # Handle other generic types like Struct - add both Struct and T generic_match = re.match(r"^([^<]+)<(.+)>$", struct_name) if generic_match: base_struct = generic_match.group(1) inner_type = generic_match.group(2) return [base_struct, inner_type] # Non-generic struct - add as is return [struct_name] def collect_struct_dependencies(circuit_instances: list[BaseModuloCircuit]) -> set[str]: """ Collect all Cairo1SerializableStruct types used in the input_structs and output_structs of the given circuit instances. Returns: set[str]: Set of struct class names that need to be imported """ struct_types = set() def add_struct_types(struct): """Helper function to add struct types recursively""" struct_name = struct.struct_name parsed_types = parse_struct_name(struct_name) struct_types.update(parsed_types) # Also add nested struct types if they exist if hasattr(struct, "elmts") and struct.elmts: for elmt in struct.elmts: if isinstance(elmt, Cairo1SerializableStruct): add_struct_types(elmt) for circuit_instance in circuit_instances: # Collect from input_structs if ( hasattr(circuit_instance.circuit, "input_structs") and circuit_instance.circuit.input_structs ): for struct in circuit_instance.circuit.input_structs: add_struct_types(struct) # Collect from output_structs if ( hasattr(circuit_instance.circuit, "output_structs") and circuit_instance.circuit.output_structs ): for struct in circuit_instance.circuit.output_structs: add_struct_types(struct) return struct_types def to_snake_case(s: str) -> str: return re.sub(r"(?<=[a-z])(?=[A-Z])|[^a-zA-Z0-9]", "_", s).lower() def create_circuit_instances( circuit_class: Type[BaseModuloCircuit], curve_id: CurveID, params: list[dict], compilation_mode: int, ) -> list[BaseModuloCircuit]: """ Create a list of circuit instances from a given circuit class, curve id, params and compilation mode. """ circuits = [] if params is None: circuit_instance = circuit_class( curve_id=curve_id.value, compilation_mode=compilation_mode, auto_run=True ) circuits.append(circuit_instance) else: for param in params: circuit_instance = circuit_class( curve_id=curve_id.value, compilation_mode=compilation_mode, auto_run=True, **param, ) circuits.append(circuit_instance) return circuits def compile_single_circuit( circuit_instance: BaseModuloCircuit, ) -> tuple[ModuloCircuit, str]: """ Compile a single circuit instance to Cairo code. Returns the compiled circuit and the full function name. """ curve_id = CurveID(circuit_instance.curve_id) function_name = ( f"{circuit_instance.name.upper()}" if circuit_instance.circuit.generic_circuit else f"{curve_id.name}_{circuit_instance.name.upper()}" ) compiled_circuit, full_function_name = circuit_instance.circuit.compile_circuit( function_name=function_name ) return compiled_circuit, full_function_name def compile_circuit( curve_id: CurveID, circuit_class: BaseModuloCircuit, params: list[dict], compilation_mode: int, ) -> tuple[list[str], list[str], list[BaseModuloCircuit]]: """ Compile a list of circuit instances to Cairo code. Returns : - compiled_circuits: list of compiled circuits as strings - full_function_names: list of full function names as strings - circuit_instances: list of circuit instances that have been compiled """ circuits = create_circuit_instances( circuit_class, curve_id, params, compilation_mode ) compiled_circuits = [] full_function_names = [] for circuit_instance in circuits: compiled_circuit, full_function_name = compile_single_circuit(circuit_instance) compiled_circuits.append(compiled_circuit) full_function_names.append(full_function_name) return compiled_circuits, full_function_names, circuits def create_cairo1_test(function_name: str, input: list, output: list, curve_id: int): return "" if function_name == "": # print(f"passing test") return "" include_curve_id = CurveID.find_value_in_string(function_name) == None if all(isinstance(i, Cairo1SerializableStruct) for i in input): input_code = "\n".join([i.serialize() for i in input]) input_params = ",".join([f"{i.name}" for i in input]) elif all(isinstance(i, PyFelt) for i in input): input_code = f"let input = {int_array_to_u384_array(input)};" input_params = "input" else: raise ValueError( f"Invalid input type for Cairo1 test : {[type(i) for i in input]}" ) if all(isinstance(i, Cairo1SerializableStruct) for i in output): output_code = f"let ({', '.join([i.name+'_result' for i in output])}) = {function_name}({input_params}{', ' + str(curve_id) if include_curve_id else ''});" output_code += "\n".join([i.serialize() for i in output]) for struct in output: output_code += f"assert_eq!({struct.name}_result, {struct.name});" elif all(isinstance(i, ModuloCircuitElement) for i in output): output_code = f"let got = {function_name}({input_params}{', ' + str(curve_id) if include_curve_id else ''});" output_code += f"let exp = {int_array_to_u384_array(output)};" output_code += "assert_eq!(got.len(), exp.len());" output_code += "assert_eq!(got, exp);" else: raise ValueError( f"Invalid output type for Cairo1 test : {[type(i) for i in output]}" ) code = f""" #[test] fn test_{function_name}_{CurveID(curve_id).name}() {{ {input_code} {output_code} }} """ return code def format_cairo_files_in_parallel( filenames, compilation_mode, precompiled_circuits_dir ): if compilation_mode == 0: print("Formatting .cairo zero files in parallel...") cairo_files = [f"{precompiled_circuits_dir}{f}.cairo" for f in filenames] with ProcessPoolExecutor() as executor: futures = [ executor.submit( subprocess.run, ["cairo-format", file, "-i"], check=True ) for file in cairo_files ] for future in futures: future.result() # Wait for all formatting tasks to complete print("Done!") elif compilation_mode == 1: subprocess.run(["scarb", "fmt", f"{precompiled_circuits_dir}"], check=True) ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/cairo1_mpcheck_circuits.py ================================================ from abc import ABC, abstractmethod from typing import Dict, List, Optional, Tuple, Type, Union import garaga.modulo_circuit_structs as structs from garaga.curves import BLS12_381_ID, BN254_ID, get_irreducible_poly from garaga.extension_field_modulo_circuit import ExtensionFieldModuloCircuit, PyFelt from garaga.modulo_circuit import ModuloCircuit from garaga.modulo_circuit_structs import ( E12D, BLSProcessedPair, BNProcessedPair, Cairo1SerializableStruct, G1PointCircuit, G2Line, G2PointCircuit, MillerLoopResultScalingFactor, u384, u384Array, ) from garaga.precompiled_circuits import multi_pairing_check from garaga.precompiled_circuits.compilable_circuits.base import BaseEXTFCircuit def split_4_sized_object_into_tuple_of_2_size( input: Union[List[PyFelt], Tuple[PyFelt, PyFelt, PyFelt, PyFelt]], ) -> Optional[Tuple[List[PyFelt], List[PyFelt]]]: if input is None: return None assert len(input) == 4, f"Expected input of length 4, got {len(input)}" return (list(input[0:2]), list(input[2:4])) def parse_precomputed_g1_consts_and_g2_points( circuit: multi_pairing_check.MultiPairingCheckCircuit, vars: dict, n_pairs: int, bit_1: bool = False, ) -> list[tuple[list[PyFelt], list[PyFelt]]]: current_points = [] q_or_q_neg_points = [] if bit_1 else None for i in range(n_pairs): circuit.yInv.append(vars[f"yInv_{i}"]) circuit.xNegOverY.append(vars[f"xNegOverY_{i}"]) current_points.append( split_4_sized_object_into_tuple_of_2_size(vars.get(f"Q_{i}", None)) ) # Return empty list if not present if bit_1: q_or_q_neg_points.append( split_4_sized_object_into_tuple_of_2_size( vars.get(f"Q_or_Q_neg_{i}", None) ) # Return empty list if not present ) return current_points, q_or_q_neg_points class BaseFixedG2PointsMPCheck(BaseEXTFCircuit, ABC): def __init__( self, name, curve_id, n_pairs: int, n_fixed_g2: int, auto_run=True, compilation_mode=1, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" if n_pairs and "mp_check_prepare_pairs" not in name: assert ( 2 <= n_pairs ), f"Multi-pairing check requires at least 2 pairs, got {n_pairs}" if n_fixed_g2: assert ( 0 <= n_fixed_g2 <= n_pairs ), f"Number of fixed G2 points must be between 0 and {n_pairs}, got {n_fixed_g2}" self.n_pairs = n_pairs self.n_fixed_g2 = n_fixed_g2 super().__init__( name=name, curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) self.generic_over_curve = True def _initialize_circuit(self): return multi_pairing_check.MultiPairingCheckCircuit( self.name, self.curve_id, n_pairs=self.n_pairs, hash_input=False, compilation_mode=self.compilation_mode, precompute_lines=True, n_points_precomputed_lines=self.n_fixed_g2, ) @property @abstractmethod def input_map( self, ) -> Dict[ str, Union[ Type[Cairo1SerializableStruct], Tuple[Type[Cairo1SerializableStruct], int] ], ]: """ Define the input map for the circuit in a dict. The key will be the name of the input variable, also used in the signature of the compiled Cairo code. The value will be either a Cairo1SerializableStruct type (which defines the struct in the Cairo code), or a tuple of the type and its size (for Array-like types). The reason behind this is that each Cairo1SerializableStruct defines the __len__ method, but for the array-like structs we need to specify the size in advance. """ def _base_input_map(self, bit_type: str) -> dict: """ Base input map for the bit 0, 1, 00, 01, and 10 cases. """ input_map = {} # Add pair inputs for k in range(self.n_fixed_g2): input_map[f"yInv_{k}"] = u384 input_map[f"xNegOverY_{k}"] = u384 input_map[f"G2_line_dbl_{k}"] = G2Line if bit_type in ("1"): input_map[f"G2_line_add_{k}"] = G2Line if bit_type == "10": input_map[f"G2_line_add_1_{k}"] = G2Line input_map[f"G2_line_dbl_0_{k}"] = G2Line if bit_type == "01": input_map[f"G2_line_dbl_1{k}"] = G2Line input_map[f"G2_line_add_1{k}"] = G2Line if bit_type == "00": input_map[f"G2_line_2nd_0_{k}"] = G2Line for k in range(self.n_fixed_g2, self.n_pairs): input_map[f"yInv_{k}"] = u384 input_map[f"xNegOverY_{k}"] = u384 input_map[f"Q_{k}"] = G2PointCircuit if bit_type in ("1", "01", "10"): input_map[f"Q_or_Q_neg_{k}"] = G2PointCircuit # Add common inputs input_map["lhs_i"] = u384 input_map["f_i_of_z"] = u384 input_map["f_i_plus_one_of_z"] = u384 # Add bit-specific inputs if bit_type in ("1", "01", "10"): input_map["c_or_cinv_of_z"] = u384 input_map["z"] = u384 input_map["c1"] = u384 return input_map def _process_input( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, input: list[PyFelt] ) -> dict: """ Method responsible for deserializing the input list of elements into the variables in the input map, and writing them to the circuit. The input list is expected to be in the same order as the input map. Since we use Python 3.10, the input map dict is ordered. Returns a vars dict with the same keys as the input map, but with the values being the instances of the structs, each struct holding ModuloCircuitElement(s). """ vars = {} for name, struct_info in self.input_map.items(): if isinstance(struct_info, tuple) and struct_info[0] == u384Array: # Handle u384Array with specified size struct_type, size = struct_info vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) elif struct_info == G2Line: # Internally appended to the precomputed_lines flattened list circuit.precomputed_lines.extend( circuit.write_struct( G2Line(name, elmts=[input.pop(0) for _ in range(4)]) ) ) else: struct_type = struct_info # For other types, create a temporary instance to get its length temp_instance = struct_type( name, None ) # Temporary instance with a dummy element size = len(temp_instance) if size == 1: vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0)]) ) else: # Convert to tuple so that it is Hashable vars[name] = tuple( circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) ) assert len(input) == 0, f"Expected input of length 0, got {len(input)}" # Create the precomputed lines generator circuit._precomputed_lines_generator = ( circuit._create_precomputed_lines_generator() ) return vars def build_input(self) -> list[PyFelt]: """ Extends the base method of BaseModuloCircuit, by reading the input map and returning a list of random elements of the total expected size. """ total_elements = 0 for name, struct_info in self.input_map.items(): if isinstance(struct_info, tuple): # Array-like case _, size = struct_info total_elements += size else: # For other structs, create a temporary instance to get its length temp_instance = struct_info(name, None) total_elements += len(temp_instance) return [self.field.random() for _ in range(total_elements)] def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = self._initialize_circuit() vars = self._process_input(circuit, input) return self._execute_circuit_logic(circuit, vars) @abstractmethod def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: """ Implement the circuit logic using the processed input variables. """ def _execute_circuit_bit_logic_base(self, circuit: ModuloCircuit, vars, bit_type): n_pairs = self.n_pairs assert n_pairs >= 2, f"n_pairs must be >= 2, got {n_pairs}" current_points, q_or_q_neg_points = parse_precomputed_g1_consts_and_g2_points( circuit, vars, n_pairs, bit_1=(bit_type == "1" or bit_type == "01" or bit_type == "10"), ) circuit.create_lines_z_powers(vars["z"]) sum_i_prod_k_P = circuit.mul( vars["f_i_of_z"], vars["f_i_of_z"], "Square f evaluation in Z, the result of previous bit.", ) new_points, sum_i_prod_k_P = self._process_points( circuit, current_points, q_or_q_neg_points, sum_i_prod_k_P, bit_type ) if bit_type in ("1", "01"): sum_i_prod_k_P = circuit.mul(sum_i_prod_k_P, vars["c_or_cinv_of_z"]) elif bit_type == "10": sum_i_prod_k_P = circuit.mul( sum_i_prod_k_P, circuit.square(vars["c_or_cinv_of_z"]) ) f_i_plus_one_of_z = vars["f_i_plus_one_of_z"] new_lhs = circuit.sub( sum_i_prod_k_P, f_i_plus_one_of_z, "(Π(i,k) (Pk(z))) - Ri(z)" ) lhs_i_plus_one = circuit.add( circuit.mul(vars["c1"], vars["lhs_i"]), new_lhs, "LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z))", ) self._extend_output(circuit, new_points, lhs_i_plus_one) return circuit def _process_points( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, current_points, q_or_q_neg_points, sum_i_prod_k_P, bit_type, ): new_points = [] if bit_type == "00": for k in range(self.n_pairs): T1, line_poly_1 = circuit.double_step(current_points[k], k) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1], k ) new_points.append(T1) sum_i_prod_k_P = circuit.mul( sum_i_prod_k_P, sum_i_prod_k_P, "Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2", ) new_new_points = [] for k in range(self.n_pairs): T, line_poly_2 = circuit.double_step(new_points[k], k) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_2], k ) new_new_points.append(T) return new_new_points, sum_i_prod_k_P elif bit_type == "01": for k in range(self.n_pairs): T, line_poly_1 = circuit.double_step(current_points[k], k) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1], k ) new_points.append(T) sum_i_prod_k_P = circuit.mul( sum_i_prod_k_P, sum_i_prod_k_P, "Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2", ) new_new_points = [] for k in range(self.n_pairs): T, line_poly_1, line_poly_2 = circuit.double_and_add_step( new_points[k], q_or_q_neg_points[k], k ) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1, line_poly_2], k ) new_new_points.append(T) return new_new_points, sum_i_prod_k_P elif bit_type == "10": for k in range(self.n_pairs): T, line_poly_1, line_poly_2 = circuit.double_and_add_step( current_points[k], q_or_q_neg_points[k], k ) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1, line_poly_2], k ) new_points.append(T) sum_i_prod_k_P = circuit.mul( sum_i_prod_k_P, sum_i_prod_k_P, "Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2", ) new_new_points = [] for k in range(self.n_pairs): T, line_poly_1 = circuit.double_step(new_points[k], k) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1], k ) new_new_points.append(T) return new_new_points, sum_i_prod_k_P elif bit_type == "0": for k in range(self.n_pairs): T, line_poly_1 = circuit.double_step(current_points[k], k) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1], k ) new_points.append(T) elif bit_type == "1": for k in range(self.n_pairs): T, line_poly_1, line_poly_2 = circuit.double_and_add_step( current_points[k], q_or_q_neg_points[k], k ) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line_poly_1, line_poly_2], k ) new_points.append(T) else: raise ValueError(f"Invalid bit type: {bit_type}") return new_points, sum_i_prod_k_P def _multiply_line_evaluations( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, sum_i_prod_k_P, line_polynomials, k, ): for i, line_poly in enumerate(line_polynomials): sum_i_prod_k_P = circuit.mul( sum_i_prod_k_P, circuit.eval_poly_in_precomputed_Z( line_poly, circuit.line_sparsity, f"line_{k}p_{i+1}" ), f"Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_{k}(z)", ) return sum_i_prod_k_P def _extend_output(self, circuit, new_points, lhs_i_plus_one): last_points = ( new_points[-(self.n_pairs - self.n_fixed_g2) :] if self.n_pairs != self.n_fixed_g2 else [] ) for i, point in enumerate(last_points): circuit.extend_struct_output( G2PointCircuit( name=f"Q{i}", elmts=[ point[0][0], point[0][1], point[1][0], point[1][1], ], ) ) circuit.extend_struct_output( u384(name="lhs_i_plus_one", elmts=[lhs_i_plus_one]) ) class FixedG2MPCheckBitBase(BaseFixedG2PointsMPCheck): """Base class for bit checking circuits with default parameters.""" BIT_TYPE = None # Override in subclasses DEFAULT_PAIRS = 3 DEFAULT_FIXED_G2 = 2 def __init__( self, curve_id: int, n_pairs: int = None, n_fixed_g2: int = None, auto_run: bool = True, compilation_mode: int = 1, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" n_pairs = n_pairs if n_pairs is not None else self.DEFAULT_PAIRS n_fixed_g2 = n_fixed_g2 if n_fixed_g2 is not None else self.DEFAULT_FIXED_G2 super().__init__( name=f"mp_check_bit{self.BIT_TYPE}_{n_pairs}P_{n_fixed_g2}F", curve_id=curve_id, n_pairs=n_pairs, n_fixed_g2=n_fixed_g2, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): return self._base_input_map(self.BIT_TYPE) def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: return self._execute_circuit_bit_logic_base(circuit, vars, self.BIT_TYPE) class FixedG2MPCheckBit0(FixedG2MPCheckBitBase): BIT_TYPE = "0" class FixedG2MPCheckBit00(FixedG2MPCheckBitBase): BIT_TYPE = "00" class FixedG2MPCheckBit1(FixedG2MPCheckBitBase): BIT_TYPE = "1" class FixedG2MPCheckBit01(FixedG2MPCheckBitBase): BIT_TYPE = "01" class FixedG2MPCheckBit10(FixedG2MPCheckBitBase): BIT_TYPE = "10" class FixedG2MPCheckInitBit(BaseFixedG2PointsMPCheck): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, n_pairs: int = 3, n_fixed_g2: int = 2, ): super().__init__( name=f"mp_check_init_bit_{n_pairs}P_{n_fixed_g2}F", curve_id=curve_id, n_pairs=n_pairs, n_fixed_g2=n_fixed_g2, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): input_map = {} for i in range(self.n_fixed_g2): input_map[f"yInv_{i}"] = u384 input_map[f"xNegOverY_{i}"] = u384 input_map[f"G2_line_{i}"] = G2Line if self.curve_id == BLS12_381_ID: input_map[f"G2_line_{i}_2"] = G2Line for i in range(self.n_fixed_g2, self.n_pairs): input_map[f"yInv_{i}"] = u384 input_map[f"xNegOverY_{i}"] = u384 input_map[f"Q_{i}"] = G2PointCircuit input_map.update( { "R_i_of_z": u384, "z": u384, "c_inv_of_z": u384, } ) if self.curve_id == BN254_ID: input_map["c1"] = u384 input_map["previous_lhs"] = u384 return input_map def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: n_pairs = self.n_pairs current_points, _ = parse_precomputed_g1_consts_and_g2_points( circuit, vars, n_pairs ) z = vars["z"] c_inv_of_z = vars["c_inv_of_z"] circuit.create_lines_z_powers(z) f_i_plus_one_of_z = vars["R_i_of_z"] sum_i_prod_k_P_of_z = circuit.mul( c_inv_of_z, c_inv_of_z ) # At initialisation, f=1/c so f^2 = 1/c^2 new_points = [] if self.curve_id == BN254_ID: # c_i = circuit.mul( # c0, c0 # ) # Second relation for BN at init bit, need to update c_i. for k in range(n_pairs): T, line_poly_1 = circuit.double_step(current_points[k], k) sum_i_prod_k_P_of_z = circuit.mul( sum_i_prod_k_P_of_z, circuit.eval_poly_in_precomputed_Z( line_poly_1, circuit.line_sparsity, f"line_{k}p_1" ), ) new_points.append(T) elif self.curve_id == BLS12_381_ID: # bit +1: multiply f^2 by 1/c sum_i_prod_k_P_of_z = circuit.mul(c_inv_of_z, sum_i_prod_k_P_of_z) for k in range(n_pairs): T, line_poly_1, line_poly_2 = circuit.triple_step(current_points[k], k) sum_i_prod_k_P_of_z = circuit.mul( sum_i_prod_k_P_of_z, circuit.eval_poly_in_precomputed_Z( line_poly_1, circuit.line_sparsity, f"line_{k}p_1" ), ) sum_i_prod_k_P_of_z = circuit.mul( sum_i_prod_k_P_of_z, circuit.eval_poly_in_precomputed_Z( line_poly_2, circuit.line_sparsity, f"line_{k}p_2" ), ) new_points.append(T) new_lhs = circuit.sub( sum_i_prod_k_P_of_z, f_i_plus_one_of_z, comment="((Π(i,k) (Pk(z)) - Ri(z))" ) if self.curve_id == BLS12_381_ID: pass elif self.curve_id == BN254_ID: c1 = vars["c1"] previous_lhs = vars["previous_lhs"] new_lhs = circuit.add(new_lhs, circuit.mul(c1, previous_lhs)) # OUTPUT last_points = ( new_points[-(self.n_pairs - self.n_fixed_g2) :] if self.n_fixed_g2 != self.n_pairs else [] ) for i, point in enumerate(last_points): circuit.extend_struct_output( G2PointCircuit( name=f"Q{i}", elmts=[ point[0][0], point[0][1], point[1][0], point[1][1], ], ) ) circuit.extend_struct_output(u384("new_lhs", elmts=[new_lhs])) return circuit class MPCheckFinalizeBN(BaseFixedG2PointsMPCheck): def __init__( self, curve_id: int, auto_run: bool = True, n_pairs: int = 3, n_fixed_g2: int = 2, compilation_mode: int = 1, extra_miller_loop_result: bool = False, ): self.max_q_degree = multi_pairing_check.get_max_Q_degree(curve_id, n_pairs) self.extra_miller_loop_result: bool = extra_miller_loop_result if extra_miller_loop_result: name = f"mp_check_finalize_{n_pairs}P_{n_fixed_g2}F_EXT_MLR" else: name = f"mp_check_finalize_{n_pairs}P_{n_fixed_g2}F" super().__init__( name=name, curve_id=curve_id, n_pairs=n_pairs, n_fixed_g2=n_fixed_g2, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): if self.curve_id == BLS12_381_ID: return {} input_map = {} for i in range(self.n_fixed_g2): input_map[f"yInv_{i}"] = u384 input_map[f"xNegOverY_{i}"] = u384 input_map[f"line_1_{i}"] = G2Line input_map[f"line_2_{i}"] = G2Line for i in range(self.n_fixed_g2, self.n_pairs): input_map[f"original_Q{i}"] = G2PointCircuit input_map[f"yInv_{i}"] = u384 input_map[f"xNegOverY_{i}"] = u384 input_map[f"Q_{i}"] = G2PointCircuit input_map.update( { "R_n_minus_2_of_z": u384, "R_n_minus_1_of_z": u384, "c_0": u384, "w_of_z": u384, "z": u384, "c_inv_frob_1_of_z": u384, "c_frob_2_of_z": u384, "c_inv_frob_3_of_z": u384, "previous_lhs": u384, "R_n_minus_3_of_z": u384, "Q": (structs.u384Array, self.max_q_degree + 1), } ) if self.extra_miller_loop_result: input_map["precomputed_miller_loop_result_of_z"] = u384 return input_map def _execute_circuit_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): if self.curve_id == BLS12_381_ID: return circuit n_pairs = self.n_pairs current_points = [] for k in range(n_pairs): circuit.Q.append( split_4_sized_object_into_tuple_of_2_size( vars.get(f"original_Q{k}", None) ) ) circuit.yInv.append(vars[f"yInv_{k}"]) circuit.xNegOverY.append(vars[f"xNegOverY_{k}"]) current_points.append( split_4_sized_object_into_tuple_of_2_size(vars.get(f"Q_{k}", None)) ) circuit.create_lines_z_powers(vars["z"], add_extf_power=True) c_0 = vars["c_0"] R_n_minus_2_of_z = vars["R_n_minus_2_of_z"] R_n_minus_1_of_z = vars["R_n_minus_1_of_z"] # Relation n-2 : f * line polynomials prod_k_P_of_z_n_minus_2 = vars["R_n_minus_3_of_z"] # Init line_polynomials = circuit.bn254_finalize_step(current_points) for idx, line_poly in enumerate(line_polynomials): prod_k_P_of_z_n_minus_2 = circuit.mul( prod_k_P_of_z_n_minus_2, circuit.eval_poly_in_precomputed_Z( line_poly, circuit.line_sparsity, f"line_{idx}" ), ) lhs_n_minus_2 = circuit.sub( prod_k_P_of_z_n_minus_2, R_n_minus_2_of_z, comment="((Π(n-2,k) (Pk(z)) - R_n_minus_2(z))", ) # Relation n-1 (last one) : f * w * c_inv_frob_1 * c_frob_2 * c_inv_frob_3 # If groth16 mode : * precomputed_miller_loop_result prod_k_P_of_z_n_minus_1 = circuit.product( [ R_n_minus_2_of_z, vars["c_inv_frob_1_of_z"], vars["c_frob_2_of_z"], vars["c_inv_frob_3_of_z"], vars["w_of_z"], ], ) if self.extra_miller_loop_result: prod_k_P_of_z_n_minus_1 = circuit.mul( prod_k_P_of_z_n_minus_1, vars["precomputed_miller_loop_result_of_z"] ) lhs_n_minus_1 = circuit.sub( prod_k_P_of_z_n_minus_1, R_n_minus_1_of_z, comment="((Π(n-1,k) (Pk(z)) - R_n_minus_1(z))", ) _final_lhs = circuit.add(circuit.mul(c_0, vars["previous_lhs"]), lhs_n_minus_2) final_lhs = circuit.add(circuit.mul(c_0, _final_lhs), lhs_n_minus_1) Q_of_z = circuit.eval_horner(vars["Q"], z=vars["z"], poly_name="big_Q") P_irr, P_irr_sparsity = circuit.write_sparse_constant_elements( get_irreducible_poly(self.curve_id, 12).get_coeffs(), ) P_of_z = circuit.eval_poly_in_precomputed_Z( P_irr, P_irr_sparsity, poly_name="P_irr" ) check = circuit.sub(final_lhs, circuit.mul(Q_of_z, P_of_z)) circuit.extend_struct_output(u384("final_check", elmts=[check])) return circuit class MPCheckFinalizeBLS(BaseFixedG2PointsMPCheck): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, n_pairs: int = 3, extra_miller_loop_result: bool = False, ): self.max_q_degree = multi_pairing_check.get_max_Q_degree(curve_id, n_pairs) self.extra_miller_loop_result: bool = extra_miller_loop_result if extra_miller_loop_result: name = f"mp_check_finalize_{n_pairs}P_EXT_MLR" else: name = f"mp_check_finalize_{n_pairs}P" super().__init__( name=name, curve_id=curve_id, n_pairs=n_pairs, n_fixed_g2=None, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): input_map = { "R_n_minus_1_of_z": u384, "c_1": u384, "w_of_z": u384, "z": u384, "c_inv_frob_1_of_z": u384, "previous_lhs": u384, "R_n_minus_2": E12D, "Q": (u384Array, self.max_q_degree + 1), } if self.extra_miller_loop_result: input_map["precomputed_miller_loop_result_of_z"] = u384 return input_map def _execute_circuit_logic(self, circuit: ModuloCircuit, vars) -> ModuloCircuit: if self.curve_id == BN254_ID: return circuit circuit.create_powers_of_Z(vars["z"], max_degree=12) c_1 = vars["c_1"] R_n_minus_1_of_z = vars["R_n_minus_1_of_z"] # Relation n-1 (last one) : f * w * c_inv_frob_1 R_n_minus_2 = vars["R_n_minus_2"] R_n_minus_2_conjugate = circuit.conjugate_e12d(R_n_minus_2) R_n_minus_2_conjugate_of_z = circuit.eval_poly_in_precomputed_Z( R_n_minus_2_conjugate, poly_name="R_n_minus_2_conjugate" ) prod_k_P_of_z_n_minus_1 = circuit.product( [R_n_minus_2_conjugate_of_z, vars["c_inv_frob_1_of_z"], vars["w_of_z"]] ) if self.extra_miller_loop_result: prod_k_P_of_z_n_minus_1 = circuit.mul( prod_k_P_of_z_n_minus_1, vars["precomputed_miller_loop_result_of_z"] ) lhs_n_minus_1 = circuit.sub( prod_k_P_of_z_n_minus_1, R_n_minus_1_of_z, comment="(Π(n-1,k) (Pk(z)) - R_n_minus_1(z))", ) final_lhs = circuit.add( circuit.mul(c_1, vars["previous_lhs"]), lhs_n_minus_1, comment="c_1 * previous_lhs + lhs_n_minus_1", ) P_irr, P_irr_sparsity = circuit.write_sparse_constant_elements( get_irreducible_poly(self.curve_id, 12).get_coeffs() ) P_of_z = circuit.eval_poly_in_precomputed_Z( P_irr, P_irr_sparsity, poly_name="P_irr" ) Q_of_z = circuit.eval_horner(vars["Q"], vars["z"], poly_name="big_Q") check = circuit.sub( final_lhs, circuit.mul(Q_of_z, P_of_z, comment="Q(z) * P(z)"), comment="final_lhs - Q(z) * P(z)", ) circuit.extend_struct_output(u384("final_check", elmts=[check])) return circuit class MPCheckPreparePairs(BaseFixedG2PointsMPCheck): """ This circuit is used to prepare points for the multi-pairing check. For BN curve, it will compute yInv and xNegOverY for each point + negate the y of the G2 point. For BLS curve, it will only compute yInv and xNegOverY for each point. """ def __init__( self, curve_id: int, n_pairs: int = 0, auto_run: bool = True, compilation_mode: int = 1, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" self.n_pairs = n_pairs super().__init__( name=f"mp_check_prepare_pairs_{n_pairs}P", curve_id=curve_id, n_pairs=n_pairs, n_fixed_g2=None, auto_run=auto_run, compilation_mode=compilation_mode, ) self.generic_over_curve = True @property def input_map(self): input_map = {} for i in range(self.n_pairs): input_map[f"p_{i}"] = G1PointCircuit if self.curve_id == BN254_ID: input_map[f"Qy0_{i}"] = u384 input_map[f"Qy1_{i}"] = u384 return input_map def _initialize_circuit(self): return multi_pairing_check.MultiMillerLoopCircuit( self.name, self.curve_id, n_pairs=self.n_pairs, compilation_mode=self.compilation_mode, ) def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: n_pairs = self.n_pairs for i in range(n_pairs): p = vars[f"p_{i}"] x, y = p yInv = circuit.inv(y) xNegOverY = circuit.neg(circuit.mul(x, yInv)) if self.curve_id == BN254_ID: Qy0 = vars[f"Qy0_{i}"] Qy1 = vars[f"Qy1_{i}"] Qyneg0 = circuit.neg(Qy0) Qyneg1 = circuit.neg(Qy1) circuit.extend_struct_output( BNProcessedPair( name=f"p_{i}", elmts=[yInv, xNegOverY, Qyneg0, Qyneg1] ) ) else: circuit.extend_struct_output( BLSProcessedPair(name=f"p_{i}", elmts=[yInv, xNegOverY]) ) return circuit class InitializeMPCheck(BaseFixedG2PointsMPCheck): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, extra_miller_loop_result: bool = False, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" self.extra_miller_loop_result: bool = extra_miller_loop_result if extra_miller_loop_result: name = "initialize_mpcheck_ext_mlr" else: name = "initialize_mpcheck" super().__init__( name=name, curve_id=curve_id, n_pairs=2, # Mocked value, not used in practice. n_fixed_g2=None, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): input_map = { "lambda_root" if self.curve_id == BN254_ID else "lambda_root_inverse": E12D, "z": u384, "scaling_factor": MillerLoopResultScalingFactor, } if self.curve_id == BN254_ID: input_map.update( { "c_inv": E12D, } ) if self.extra_miller_loop_result: input_map["precomputed_miller_loop_result"] = E12D return input_map def _execute_circuit_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): circuit.create_powers_of_Z(Z=vars["z"], max_degree=11) if self.curve_id == BLS12_381_ID: self._execute_bls12_381_logic(circuit, vars) elif self.curve_id == BN254_ID: self._execute_bn254_logic(circuit, vars) # Handle shared scaling factor computation (always executed after curve-specific c/c_inv logic) self._execute_shared_logic(circuit, vars) # Continue with curve-specific frobenius operations if self.curve_id == BLS12_381_ID: self._execute_bls12_381_frobenius_logic(circuit, vars) elif self.curve_id == BN254_ID: self._execute_bn254_frobenius_logic(circuit, vars) if self.extra_miller_loop_result: precomputed_miller_loop_result = vars["precomputed_miller_loop_result"] precomputed_miller_loop_result_of_z = circuit.eval_poly_in_precomputed_Z( precomputed_miller_loop_result, poly_name="precomputed_miller_loop_result", ) circuit.extend_struct_output( u384( "precomputed_miller_loop_result_of_z", elmts=[precomputed_miller_loop_result_of_z], ) ) return circuit def _execute_bls12_381_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): """Handle BLS12-381 specific logic with c_inverse - first part.""" # Get lambda_root_inverse (c_inverse for BLS12-381) lambda_root_inverse = vars["lambda_root_inverse"] # Conjugate c_inverse for BLS12-381 self.c_inv = circuit.conjugate_e12d(lambda_root_inverse) # Evaluate c_inverse polynomial at z c_inv_of_z = circuit.eval_poly_in_precomputed_Z(self.c_inv, poly_name="C_inv") circuit.extend_struct_output(u384(name="c_inv_of_z", elmts=[c_inv_of_z])) def _execute_bn254_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): """Handle BN254 specific logic with c (lambda_root) - first part.""" # Get lambda_root (c for BN254) lambda_root = vars["lambda_root"] self.c = lambda_root # Evaluate c polynomial at z self.c_of_z = circuit.eval_poly_in_precomputed_Z(self.c, poly_name="C") circuit.extend_struct_output(u384(name="c_of_z", elmts=[self.c_of_z])) def _execute_shared_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): """Handle shared scaling factor computation for both curves.""" scaling_factor_sparsity = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0] scaling_factor_compressed = vars["scaling_factor"] scaling_factor = [ scaling_factor_compressed[0], None, scaling_factor_compressed[1], None, scaling_factor_compressed[2], None, scaling_factor_compressed[3], None, scaling_factor_compressed[4], None, scaling_factor_compressed[5], None, ] scaling_factor_of_z = circuit.eval_poly_in_precomputed_Z( scaling_factor, sparsity=scaling_factor_sparsity, poly_name="W" ) circuit.extend_struct_output( u384("scaling_factor_of_z", elmts=[scaling_factor_of_z]) ) def _execute_bls12_381_frobenius_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): """Handle BLS12-381 specific frobenius logic - second part.""" # Compute frobenius of c_inverse c_inv_frob_1 = circuit.frobenius(self.c_inv, 1) c_inv_frob_1_conjugate = circuit.conjugate_e12d(c_inv_frob_1) c_inv_frob_1_conjugate_of_z = circuit.eval_poly_in_precomputed_Z( c_inv_frob_1_conjugate, poly_name="C_inv_frob_1" ) circuit.extend_struct_output( u384("c_inv_frob_1_conjugate_of_z", elmts=[c_inv_frob_1_conjugate_of_z]) ) def _execute_bn254_frobenius_logic( self, circuit: multi_pairing_check.MultiPairingCheckCircuit, vars ): """Handle BN254 specific frobenius logic - second part.""" # Additional BN254-specific variables c_inv = vars["c_inv"] # Evaluate c_inverse polynomial at z c_inv_of_z = circuit.eval_poly_in_precomputed_Z(c_inv, poly_name="C_inv") circuit.extend_struct_output(u384(name="c_inv_of_z", elmts=[c_inv_of_z])) # Compute lhs = c^0 * (c_of_z * c_inv_of_z - 1) (c^0=1) lhs = circuit.sub( circuit.mul(self.c_of_z, c_inv_of_z), circuit.set_or_get_constant(1), comment="c_of_z * c_inv_of_z - 1", ) circuit.extend_struct_output(u384("lhs", elmts=[lhs])) # Compute frobenius operations for BN254 c_inv_frob_1 = circuit.frobenius(c_inv, 1) c_frob_2 = circuit.frobenius(self.c, 2) c_inv_frob_3 = circuit.frobenius(c_inv, 3) c_inv_frob_1_of_z = circuit.eval_poly_in_precomputed_Z( c_inv_frob_1, poly_name="C_inv_frob_1" ) c_frob_2_of_z = circuit.eval_poly_in_precomputed_Z( c_frob_2, poly_name="C_frob_2" ) c_inv_frob_3_of_z = circuit.eval_poly_in_precomputed_Z( c_inv_frob_3, poly_name="C_inv_frob_3" ) circuit.extend_struct_output( u384("c_inv_frob_1_of_z", elmts=[c_inv_frob_1_of_z]) ) circuit.extend_struct_output(u384("c_frob_2_of_z", elmts=[c_frob_2_of_z])) circuit.extend_struct_output( u384("c_inv_frob_3_of_z", elmts=[c_inv_frob_3_of_z]) ) class FP12MulAssertOne(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "fp12_mul_assert_one", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # X input.extend([self.field.random() for _ in range(12)]) # Y input.extend([self.field.random() for _ in range(11)]) # Q # R is known to be 1. input.append(self.field.random()) # z return input def _run_circuit_inner(self, input: list[PyFelt]) -> ExtensionFieldModuloCircuit: circuit = ExtensionFieldModuloCircuit( self.name, self.curve_id, extension_degree=12, init_hash=self.init_hash, compilation_mode=self.compilation_mode, ) X = circuit.write_struct(E12D("X", elmts=[input.pop(0) for _ in range(12)])) Y = circuit.write_struct(E12D("Y", elmts=[input.pop(0) for _ in range(12)])) Q = circuit.write_struct( structs.E12DMulQuotient("Q", elmts=[input.pop(0) for _ in range(11)]) ) assert len(input) == 1 z = circuit.write_struct(u384("z", elmts=[input.pop(0)])) assert len(input) == 0 circuit.create_powers_of_Z(z, max_degree=12) P_irr, P_irr_sparsity = circuit.write_sparse_constant_elements( get_irreducible_poly(self.curve_id, 12).get_coeffs(), ) P_of_z = circuit.eval_poly_in_precomputed_Z( P_irr, P_irr_sparsity, poly_name="P_irr" ) Q_of_z = circuit.eval_poly_in_precomputed_Z(Q, poly_name="Q") R_of_z = circuit.set_or_get_constant(1) X_of_z = circuit.eval_poly_in_precomputed_Z(X, poly_name="X") Y_of_z = circuit.eval_poly_in_precomputed_Z(Y, poly_name="Y") check = circuit.sub( circuit.mul(X_of_z, Y_of_z, comment="X(z) * Y(z)"), circuit.mul(Q_of_z, P_of_z, comment="Q(z) * P(z)"), comment="(X(z) * Y(z)) - (Q(z) * P(z))", ) check = circuit.sub(check, R_of_z, comment="(X(z) * Y(z) - Q(z) * P(z)) - 1") circuit.extend_struct_output(u384("check", elmts=[check])) return circuit class EvalE12D(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__("eval_e12d", curve_id, auto_run, init_hash, compilation_mode) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # X input.append(self.field.random()) # z return input def _run_circuit_inner(self, input: list[PyFelt]) -> ExtensionFieldModuloCircuit: circuit = ExtensionFieldModuloCircuit( self.name, self.curve_id, extension_degree=12, init_hash=self.init_hash, compilation_mode=self.compilation_mode, ) X = circuit.write_struct(E12D("f", elmts=[input.pop(0) for _ in range(12)])) z = circuit.write_struct(u384("z", elmts=[input.pop(0)])) X_of_z = circuit.eval_horner(X, z, poly_name="X") circuit.extend_struct_output(u384("f_of_z", elmts=[X_of_z])) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/cairo1_tower_pairing.py ================================================ from abc import ABC, abstractmethod from typing import Dict, List, Optional, Tuple, Type, Union import garaga.modulo_circuit_structs as structs from garaga.curves import BLS12_381_ID from garaga.modulo_circuit import ModuloCircuit, PyFelt from garaga.modulo_circuit_structs import ( Cairo1SerializableStruct, G2Line, G2PointCircuit, u384, u384Array, ) from garaga.precompiled_circuits.compilable_circuits.base import ( BaseEXTFCircuit, BaseModuloCircuit, ) from garaga.precompiled_circuits.miller_tower import MillerTowerCircuit def split_4_sized_object_into_tuple_of_2_size( input: Union[List[PyFelt], Tuple[PyFelt, PyFelt, PyFelt, PyFelt]], ) -> Optional[Tuple[List[PyFelt], List[PyFelt]]]: if input is None: return None assert len(input) == 4, f"Expected input of length 4, got {len(input)}" return (list(input[0:2]), list(input[2:4])) def parse_precomputed_g1_consts_and_g2_points( circuit: MillerTowerCircuit, vars: dict, n_pairs: int, bit_1: bool = False, ) -> list[tuple[list[PyFelt], list[PyFelt]]]: current_points = [] q_or_q_neg_points = [] if bit_1 else None for i in range(n_pairs): circuit.yInv.append(vars[f"yInv_{i}"]) circuit.xNegOverY.append(vars[f"xNegOverY_{i}"]) current_points.append( split_4_sized_object_into_tuple_of_2_size(vars.get(f"Q_{i}", None)) ) # Return empty list if not present if bit_1: q_or_q_neg_points.append( split_4_sized_object_into_tuple_of_2_size( vars.get(f"Q_or_Q_neg_{i}", None) ) # Return empty list if not present ) return current_points, q_or_q_neg_points class BaseTowerMillerLoop(BaseEXTFCircuit, ABC): def __init__( self, name, curve_id, auto_run=True, compilation_mode=1, n_pairs: int = 1, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" self.n_pairs = n_pairs super().__init__( name=name, curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) self.generic_over_curve = True def _initialize_circuit(self): return MillerTowerCircuit( self.name, self.curve_id, n_pairs=self.n_pairs, compilation_mode=self.compilation_mode, ) @property @abstractmethod def input_map( self, ) -> Dict[ str, Union[ Type[Cairo1SerializableStruct], Tuple[Type[Cairo1SerializableStruct], int] ], ]: """ Define the input map for the circuit in a dict. The key will be the name of the input variable, also used in the signature of the compiled Cairo code. The value will be either a Cairo1SerializableStruct type (which defines the struct in the Cairo code), or a tuple of the type and its size (for Array-like types). The reason behind this is that each Cairo1SerializableStruct defines the __len__ method, but for the array-like structs we need to specify the size in advance. """ def _base_input_map(self, bit_type: str) -> dict: """ Base input map for the bit 0 and 1 """ input_map = {} for k in range(self.n_pairs): input_map[f"yInv_{k}"] = u384 input_map[f"xNegOverY_{k}"] = u384 input_map[f"Q_{k}"] = G2PointCircuit if bit_type == "1": input_map[f"Q_or_Q_neg_{k}"] = G2PointCircuit # Add common inputs input_map["M_i"] = structs.E12T return input_map def _process_input(self, circuit: MillerTowerCircuit, input: list[PyFelt]) -> dict: """ Method responsible for deserializing the input list of elements into the variables in the input map, and writing them to the circuit. The input list is expected to be in the same order as the input map. Since we use Python 3.10, the input map dict is ordered. Returns a vars dict with the same keys as the input map, but with the values being the instances of the structs, each struct holding ModuloCircuitElement(s). """ vars = {} for name, struct_info in self.input_map.items(): if isinstance(struct_info, tuple) and struct_info[0] == u384Array: # Handle u384Array with specified size struct_type, size = struct_info vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) elif struct_info == G2Line: # Internally appended to the precomputed_lines flattened list circuit.precomputed_lines.extend( circuit.write_struct( G2Line(name, elmts=[input.pop(0) for _ in range(4)]) ) ) else: struct_type = struct_info # For other types, create a temporary instance to get its length temp_instance = struct_type( name, None ) # Temporary instance with a dummy element size = len(temp_instance) if size == 1: vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0)]) ) else: # Convert to tuple so that it is Hashable vars[name] = tuple( circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) ) assert len(input) == 0, f"Expected input of length 0, got {len(input)}" # Create the precomputed lines generator circuit._precomputed_lines_generator = ( circuit._create_precomputed_lines_generator() ) return vars def build_input(self) -> list[PyFelt]: """ Extends the base method of BaseModuloCircuit, by reading the input map and returning a list of random elements of the total expected size. """ total_elements = 0 for name, struct_info in self.input_map.items(): if isinstance(struct_info, tuple): # Array-like case _, size = struct_info total_elements += size else: # For other structs, create a temporary instance to get its length temp_instance = struct_info(name, None) total_elements += len(temp_instance) return [self.field.random() for _ in range(total_elements)] def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = self._initialize_circuit() vars = self._process_input(circuit, input) return self._execute_circuit_logic(circuit, vars) @abstractmethod def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: """ Implement the circuit logic using the processed input variables. """ def _execute_circuit_bit_logic_base( self, circuit: MillerTowerCircuit, vars, bit_type ): n_pairs = self.n_pairs assert n_pairs >= 1, f"n_pairs must be >= 1, got {n_pairs}" current_points, q_or_q_neg_points = parse_precomputed_g1_consts_and_g2_points( circuit, vars, n_pairs, bit_1=(bit_type == "1") ) Mi_sq = circuit.fp12_square(vars["M_i"]) new_points, Mi_plus_one = self._process_points( circuit, current_points, q_or_q_neg_points, Mi_sq, bit_type ) self._extend_output(circuit, new_points, Mi_plus_one) return circuit def _process_points( self, circuit: MillerTowerCircuit, current_points, q_or_q_neg_points, sum_i_prod_k_P, bit_type, ): new_points = [] if bit_type == "0": for k in range(self.n_pairs): T, (lineR0, lineR1) = circuit._double(current_points[k], k) line = circuit.eval_tower_line( lineR0 + lineR1, circuit.yInv[k], circuit.xNegOverY[k] ) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line], k ) new_points.append(T) elif bit_type == "1": for k in range(self.n_pairs): # T, l1, l2 = circuit.double_and_add_step( # current_points[k], q_or_q_neg_points[k], k # ) T, (line1R0, line1R1), (line2R0, line2R1) = circuit._double_and_add( current_points[k], q_or_q_neg_points[k], k ) line1 = circuit.eval_tower_line( line1R0 + line1R1, circuit.yInv[k], circuit.xNegOverY[k] ) line2 = circuit.eval_tower_line( line2R0 + line2R1, circuit.yInv[k], circuit.xNegOverY[k] ) sum_i_prod_k_P = self._multiply_line_evaluations( circuit, sum_i_prod_k_P, [line1, line2], k ) new_points.append(T) return new_points, sum_i_prod_k_P def _multiply_line_evaluations( self, circuit: MillerTowerCircuit, sum_i_prod_k_P, lines, k, ): for i, l in enumerate(lines): sum_i_prod_k_P = circuit.mul_by_line_tower(sum_i_prod_k_P, l) return sum_i_prod_k_P def _extend_output(self, circuit: ModuloCircuit, new_points, Mi_plus_one): circuit.exact_output_refs_needed = [] for i, point in enumerate(new_points): sum_coords = circuit.sum( [point[0][0], point[0][1], point[1][0], point[1][1]] ) circuit.exact_output_refs_needed.append(sum_coords) circuit.extend_struct_output( G2PointCircuit( name=f"Q{i}", elmts=[ point[0][0], point[0][1], point[1][0], point[1][1], ], ) ) circuit.extend_struct_output( structs.E12T(name="Mi_plus_one", elmts=Mi_plus_one) ) circuit.exact_output_refs_needed.extend(Mi_plus_one) class TowerMillerBit0(BaseTowerMillerLoop): def __init__( self, curve_id: int, n_pairs: int, auto_run: bool = True, compilation_mode: int = 1, ): super().__init__( name=f"tower_miller_bit0_{n_pairs}P", curve_id=curve_id, n_pairs=n_pairs, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): return self._base_input_map("0") def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: return self._execute_circuit_bit_logic_base(circuit, vars, "0") class TowerMillerBit1(BaseTowerMillerLoop): def __init__( self, curve_id: int, auto_run: bool = True, n_pairs: int = 1, compilation_mode: int = 1, ): assert compilation_mode == 1, "Compilation mode 1 is required for this circuit" super().__init__( name=f"tower_miller_bit1_{n_pairs}P", curve_id=curve_id, n_pairs=n_pairs, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): return self._base_input_map("1") def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: return self._execute_circuit_bit_logic_base(circuit, vars, "1") class TowerMillerInitBit(BaseTowerMillerLoop): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, n_pairs: int = 3, ): super().__init__( name=f"tower_miller_init_bit_{n_pairs}P", curve_id=curve_id, n_pairs=n_pairs, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): if self.curve_id == BLS12_381_ID: input_map = {} for k in range(self.n_pairs): input_map[f"yInv_{k}"] = u384 input_map[f"xNegOverY_{k}"] = u384 input_map[f"Q_{k}"] = G2PointCircuit return input_map else: raise NotImplementedError(f"Curve {self.curve_id} not implemented") def _execute_circuit_logic( self, circuit: MillerTowerCircuit, vars ) -> ModuloCircuit: n_pairs = self.n_pairs assert n_pairs == 1, f"Only implemented for 1 pair for now, got {n_pairs}" current_points, q_or_q_neg_points = parse_precomputed_g1_consts_and_g2_points( circuit, vars, n_pairs, bit_1=False ) new_points = [] for k in range(self.n_pairs): T, (line1R0, line1R1), (line2R0, line2R1) = circuit._triple( current_points[k], k ) line1 = circuit.eval_tower_line( line1R0 + line1R1, circuit.yInv[k], circuit.xNegOverY[k] ) line2 = circuit.eval_tower_line( line2R0 + line2R1, circuit.yInv[k], circuit.xNegOverY[k] ) # result.C0.B0 = prodLines[0] # result.C0.B1 = prodLines[1] # result.C0.B2 = prodLines[2] # result.C1.B1 = prodLines[3] # result.C1.B2 = prodLines[4] ll = circuit.mul_line_by_line_tower(line1, line2) new_points.append(T) for i, point in enumerate(new_points): circuit.extend_struct_output( G2PointCircuit( name=f"Q{i}", elmts=[ point[0][0], point[0][1], point[1][0], point[1][1], ], ) ) circuit.extend_struct_output(structs.u384(name="c0b0a0", elmts=[ll[0]])) circuit.extend_struct_output(structs.u384(name="c0b0a1", elmts=[ll[1]])) circuit.extend_struct_output(structs.u384(name="c0b1a0", elmts=[ll[2]])) circuit.extend_struct_output(structs.u384(name="c0b1a1", elmts=[ll[3]])) circuit.extend_struct_output(structs.u384(name="c0b2a0", elmts=[ll[4]])) circuit.extend_struct_output(structs.u384(name="c0b2a1", elmts=[ll[5]])) circuit.extend_struct_output(structs.u384(name="c1b1a0", elmts=[ll[6]])) circuit.extend_struct_output(structs.u384(name="c1b1a1", elmts=[ll[7]])) circuit.extend_struct_output(structs.u384(name="c1b2a0", elmts=[ll[8]])) circuit.extend_struct_output(structs.u384(name="c1b2a1", elmts=[ll[9]])) return circuit class TowerMillerFinalizeBN(BaseTowerMillerLoop): def __init__( self, curve_id: int, auto_run: bool = True, n_pairs: int = 1, compilation_mode: int = 1, ): super().__init__( name=f"tower_miller_finalize_bn_{n_pairs}P", curve_id=curve_id, n_pairs=n_pairs, auto_run=auto_run, compilation_mode=compilation_mode, ) @property def input_map(self): if self.curve_id == BLS12_381_ID: return {} input_map = {} for i in range(self.n_pairs): input_map[f"original_Q{i}"] = G2PointCircuit input_map[f"yInv_{i}"] = u384 input_map[f"xNegOverY_{i}"] = u384 input_map[f"Q_{i}"] = G2PointCircuit input_map["Mi"] = structs.E12T return input_map def _execute_circuit_logic(self, circuit: MillerTowerCircuit, vars): if self.curve_id == BLS12_381_ID: return circuit n_pairs = self.n_pairs current_points = [] for k in range(n_pairs): circuit.Q.append( split_4_sized_object_into_tuple_of_2_size( vars.get(f"original_Q{k}", None) ) ) circuit.yInv.append(vars[f"yInv_{k}"]) circuit.xNegOverY.append(vars[f"xNegOverY_{k}"]) current_points.append( split_4_sized_object_into_tuple_of_2_size(vars.get(f"Q_{k}", None)) ) Mi = vars["Mi"] lines = circuit._bn254_finalize_step(current_points) for l in lines: (l1r0, l1r1), (l2r0, l2r1) = l l1_eval = circuit.eval_tower_line( l1r0 + l1r1, circuit.yInv[k], circuit.xNegOverY[k] ) l2_eval = circuit.eval_tower_line( l2r0 + l2r1, circuit.yInv[k], circuit.xNegOverY[k] ) ll = circuit.mul_line_by_line_tower(l1_eval, l2_eval) ll_full = ll + [ circuit.set_or_get_constant(0), circuit.set_or_get_constant(0), ] Mi = circuit.fp12_mul(Mi, ll_full) circuit.extend_struct_output(structs.E12T("Mi", elmts=Mi)) return circuit class E12TMulCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__("e12t_mul", curve_id, auto_run, init_hash, compilation_mode) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # X input.extend([self.field.random() for _ in range(12)]) # Y return input def _run_circuit_inner(self, input: list[PyFelt]) -> MillerTowerCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) X = circuit.write_struct( structs.E12T("X", elmts=[input.pop(0) for _ in range(12)]) ) Y = circuit.write_struct( structs.E12T("Y", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_mul(X, Y) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class FP6NegCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 1, ): super().__init__("fp6_neg", curve_id, auto_run, compilation_mode) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(6)]) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ModuloCircuit( self.name, self.curve_id, generic_circuit=True, compilation_mode=self.compilation_mode, ) fp6 = [ circuit.write_struct(structs.u384(name="b0a0", elmts=[input.pop(0)])), circuit.write_struct(structs.u384(name="b0a1", elmts=[input.pop(0)])), circuit.write_struct(structs.u384(name="b1a0", elmts=[input.pop(0)])), circuit.write_struct(structs.u384(name="b1a1", elmts=[input.pop(0)])), circuit.write_struct(structs.u384(name="b2a0", elmts=[input.pop(0)])), circuit.write_struct(structs.u384(name="b2a1", elmts=[input.pop(0)])), ] res = [circuit.neg(fp6[i]) for i in range(6)] circuit.extend_struct_output(structs.u384(name="r0", elmts=[res[0]])) circuit.extend_struct_output(structs.u384(name="r1", elmts=[res[1]])) circuit.extend_struct_output(structs.u384(name="r2", elmts=[res[2]])) circuit.extend_struct_output(structs.u384(name="r3", elmts=[res[3]])) circuit.extend_struct_output(structs.u384(name="r4", elmts=[res[4]])) circuit.extend_struct_output(structs.u384(name="r5", elmts=[res[5]])) return circuit class E12TInverseCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_inverse", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # M return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) M = circuit.write_struct( structs.E12T("M", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_inverse(M) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class E12TFrobeniusCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 1, ): super().__init__( "e12t_frobenius", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # M return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) M = circuit.write_struct( structs.E12T("M", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_frob(M) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class E12TFrobeniusSquareCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_frobenius_square", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # M return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) M = circuit.write_struct( structs.E12T("M", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_frob_square(M) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class E12TFrobeniusCubeCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_frobenius_cube", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # M return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) M = circuit.write_struct( structs.E12T("M", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_frob_cube(M) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class E12TCyclotomicSquareCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_cyclotomic_square", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) # M return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) M = circuit.write_struct( structs.E12T("M", elmts=[input.pop(0) for _ in range(12)]) ) res = circuit.fp12_cyclotomic_square(M) circuit.extend_struct_output(structs.E12T("res", elmts=res)) return circuit class E12TCyclotomicSquareCompressedCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_cyclo_square_compressed", curve_id, auto_run, init_hash, compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(8)]) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) xc0b1a0 = circuit.write_struct( structs.u384(name="xc0b1a0", elmts=[input.pop(0)]) ) xc0b1a1 = circuit.write_struct( structs.u384(name="xc0b1a1", elmts=[input.pop(0)]) ) xc0b2a0 = circuit.write_struct( structs.u384(name="xc0b2a0", elmts=[input.pop(0)]) ) xc0b2a1 = circuit.write_struct( structs.u384(name="xc0b2a1", elmts=[input.pop(0)]) ) xc1b0a0 = circuit.write_struct( structs.u384(name="xc1b0a0", elmts=[input.pop(0)]) ) xc1b0a1 = circuit.write_struct( structs.u384(name="xc1b0a1", elmts=[input.pop(0)]) ) xc1b2a0 = circuit.write_struct( structs.u384(name="xc1b2a0", elmts=[input.pop(0)]) ) xc1b2a1 = circuit.write_struct( structs.u384(name="xc1b2a1", elmts=[input.pop(0)]) ) res = circuit.fp12_cyclotomic_square_compressed( [xc0b1a0, xc0b1a1], [xc0b2a0, xc0b2a1], [xc1b0a0, xc1b0a1], [xc1b2a0, xc1b2a1], ) assert len(res) == 8 circuit.extend_struct_output(structs.u384(name="xc0b1a0", elmts=[res[0]])) circuit.extend_struct_output(structs.u384(name="xc0b1a1", elmts=[res[1]])) circuit.extend_struct_output(structs.u384(name="xc0b2a0", elmts=[res[2]])) circuit.extend_struct_output(structs.u384(name="xc0b2a1", elmts=[res[3]])) circuit.extend_struct_output(structs.u384(name="xc1b0a0", elmts=[res[4]])) circuit.extend_struct_output(structs.u384(name="xc1b0a1", elmts=[res[5]])) circuit.extend_struct_output(structs.u384(name="xc1b2a0", elmts=[res[6]])) circuit.extend_struct_output(structs.u384(name="xc1b2a1", elmts=[res[7]])) return circuit class E12TDecompressKarabinaPtIZCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_decomp_karabina_I_Z", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(4)]) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) xc0b1a0 = circuit.write_struct( structs.u384(name="xc0b1a0", elmts=[input.pop(0)]) ) xc0b1a1 = circuit.write_struct( structs.u384(name="xc0b1a1", elmts=[input.pop(0)]) ) xc1b2a0 = circuit.write_struct( structs.u384(name="xc1b2a0", elmts=[input.pop(0)]) ) xc1b2a1 = circuit.write_struct( structs.u384(name="xc1b2a1", elmts=[input.pop(0)]) ) res = circuit.fp12_decompress_karabina_pt_I_c1b2_Z( [xc0b1a0, xc0b1a1], [xc1b2a0, xc1b2a1] ) circuit.extend_struct_output(structs.u384(name="res0", elmts=[res[0]])) circuit.extend_struct_output(structs.u384(name="res1", elmts=[res[1]])) return circuit class E12TDecompressKarabinaPtINZCircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_decomp_karabina_I_NZ", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(8)]) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) xc0b1a0 = circuit.write_struct( structs.u384(name="xc0b1a0", elmts=[input.pop(0)]) ) xc0b1a1 = circuit.write_struct( structs.u384(name="xc0b1a1", elmts=[input.pop(0)]) ) xc0b2a0 = circuit.write_struct( structs.u384(name="xc0b2a0", elmts=[input.pop(0)]) ) xc0b2a1 = circuit.write_struct( structs.u384(name="xc0b2a1", elmts=[input.pop(0)]) ) xc1b0a0 = circuit.write_struct( structs.u384(name="xc1b0a0", elmts=[input.pop(0)]) ) xc1b0a1 = circuit.write_struct( structs.u384(name="xc1b0a1", elmts=[input.pop(0)]) ) xc1b2a0 = circuit.write_struct( structs.u384(name="xc1b2a0", elmts=[input.pop(0)]) ) xc1b2a1 = circuit.write_struct( structs.u384(name="xc1b2a1", elmts=[input.pop(0)]) ) t0, t1 = circuit.fp12_decompress_karabina_pt_I_c1b2_NZ( [xc0b1a0, xc0b1a1], [xc0b2a0, xc0b2a1], [xc1b0a0, xc1b0a1], [xc1b2a0, xc1b2a1], ) circuit.extend_struct_output(structs.u384(name="t0a0", elmts=[t0[0]])) circuit.extend_struct_output(structs.u384(name="t0a1", elmts=[t0[1]])) circuit.extend_struct_output(structs.u384(name="t1a0", elmts=[t1[0]])) circuit.extend_struct_output(structs.u384(name="t1a1", elmts=[t1[1]])) return circuit class E12TDecompressKarabinaPtIICircuit(BaseEXTFCircuit): def __init__( self, curve_id: int, auto_run: bool = True, init_hash: int = None, compilation_mode: int = 0, ): super().__init__( "e12t_decomp_karabina_II", curve_id, auto_run, init_hash, compilation_mode ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(12)]) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = MillerTowerCircuit(self.name, self.curve_id, n_pairs=None) t0a0 = circuit.write_struct(structs.u384(name="t0a0", elmts=[input.pop(0)])) t0a1 = circuit.write_struct(structs.u384(name="t0a1", elmts=[input.pop(0)])) t1a0 = circuit.write_struct(structs.u384(name="t1a0", elmts=[input.pop(0)])) t1a1 = circuit.write_struct(structs.u384(name="t1a1", elmts=[input.pop(0)])) xc0b1a0 = circuit.write_struct( structs.u384(name="xc0b1a0", elmts=[input.pop(0)]) ) xc0b1a1 = circuit.write_struct( structs.u384(name="xc0b1a1", elmts=[input.pop(0)]) ) xc0b2a0 = circuit.write_struct( structs.u384(name="xc0b2a0", elmts=[input.pop(0)]) ) xc0b2a1 = circuit.write_struct( structs.u384(name="xc0b2a1", elmts=[input.pop(0)]) ) xc1b0a0 = circuit.write_struct( structs.u384(name="xc1b0a0", elmts=[input.pop(0)]) ) xc1b0a1 = circuit.write_struct( structs.u384(name="xc1b0a1", elmts=[input.pop(0)]) ) xc1b2a0 = circuit.write_struct( structs.u384(name="xc1b2a0", elmts=[input.pop(0)]) ) xc1b2a1 = circuit.write_struct( structs.u384(name="xc1b2a1", elmts=[input.pop(0)]) ) zc0b0, zc1b1 = circuit.fp12_decompress_karabina_pt_II( [t0a0, t0a1], [t1a0, t1a1], [xc0b1a0, xc0b1a1], [xc0b2a0, xc0b2a1], [xc1b0a0, xc1b0a1], [xc1b2a0, xc1b2a1], ) circuit.extend_struct_output(structs.u384(name="zc0b0a0", elmts=[zc0b0[0]])) circuit.extend_struct_output(structs.u384(name="zc0b0a1", elmts=[zc0b0[1]])) circuit.extend_struct_output(structs.u384(name="zc1b1a0", elmts=[zc1b1[0]])) circuit.extend_struct_output(structs.u384(name="zc1b1a1", elmts=[zc1b1[1]])) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/common_cairo_fustat_circuits.py ================================================ from random import randint import garaga.modulo_circuit_structs as structs from garaga.curves import CURVES, CurveID from garaga.hints import neg_3 from garaga.hints.ecip import ( n_coeffs_from_n_points, n_points_from_n_coeffs, slope_intercept, ) from garaga.modulo_circuit import WriteOps from garaga.modulo_circuit_structs import G1PointCircuit, G2PointCircuit, u384 from garaga.points import G1Point, G2Point from garaga.precompiled_circuits.cofactor_clearing import G1CofactorClearing from garaga.precompiled_circuits.compilable_circuits.base import ( BaseModuloCircuit, ModuloCircuit, PyFelt, ) from garaga.precompiled_circuits.ec import ( BasicEC, BasicECG2, ECIPCircuits, FakeGLVCircuits, IsOnCurveCircuit, ) class DummyCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0 ) -> None: super().__init__( name="dummy", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: return [self.field(44), self.field(4)] def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ModuloCircuit( self.name, self.curve_id, generic_circuit=True, compilation_mode=self.compilation_mode, ) x, y = circuit.write_elements(input, WriteOps.INPUT) r = circuit.sub(x, y) # 40 z = circuit.div(x, y) # 4 c = circuit.add(r, z) # 44 d = circuit.sub(r, z) # 36 e = circuit.mul(r, z) # 120 f = circuit.div(r, z) # 8 circuit.extend_output([r, z, c, d, e, f]) return circuit class IsOnCurveG1G2Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="is_on_curve_g1_g2", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: curve_id = CurveID(self.curve_id) order = CURVES[self.curve_id].n input = [] n1, n2 = randint(1, order), randint(1, order) p1, p2 = G1Point.get_nG(curve_id, n1), G2Point.get_nG(curve_id, n2) pair = [p1.x, p1.y, p2.x[0], p2.x[1], p2.y[0], p2.y[1]] input.extend([self.field(x) for x in pair]) input.append(self.field(CURVES[self.curve_id].a)) input.append(self.field(CURVES[self.curve_id].b)) input.append(self.field(CURVES[self.curve_id].b20)) input.append(self.field(CURVES[self.curve_id].b21)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit: IsOnCurveCircuit = IsOnCurveCircuit( self.name, self.curve_id, compilation_mode=self.compilation_mode ) assert len(input) == 6 + 4, f"got {input} of len {len(input)}" p = circuit.write_struct(G1PointCircuit("p", input[0:2]), WriteOps.INPUT) q = circuit.write_struct(G2PointCircuit("q", input[2:6]), WriteOps.INPUT) a = circuit.write_struct(u384("a", [input[6]]), WriteOps.INPUT) b = circuit.write_struct(u384("b", [input[7]]), WriteOps.INPUT) b20 = circuit.write_struct(u384("b20", [input[8]]), WriteOps.INPUT) b21 = circuit.write_struct(u384("b21", [input[9]]), WriteOps.INPUT) circuit.set_consts(a, b, b20, b21) lhs, rhs = circuit._is_on_curve_G1(*p) lhs2, rhs2 = circuit._is_on_curve_G2(*q) zero_check = circuit.sub(lhs, rhs) zero_check_2 = [circuit.sub(lhs2[0], rhs2[0]), circuit.sub(lhs2[1], rhs2[1])] circuit.extend_struct_output(u384("zero_check_0", [zero_check])) circuit.extend_struct_output(u384("zero_check_1", [zero_check_2[0]])) circuit.extend_struct_output(u384("zero_check_2", [zero_check_2[1]])) return circuit class IsOnCurveG1Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="is_on_curve_g1", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] random_point = G1Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(random_point.x)) input.append(self.field(random_point.y)) input.append(self.field(CURVES[self.curve_id].a)) input.append(self.field(CURVES[self.curve_id].b)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicEC( self.name, self.curve_id, compilation_mode=self.compilation_mode ) px, py = circuit.write_struct(G1PointCircuit("p", input[0:2]), WriteOps.INPUT) a = circuit.write_struct(u384("a", [input[2]]), WriteOps.INPUT) b = circuit.write_struct(u384("b", [input[3]]), WriteOps.INPUT) lhs, rhs = circuit._is_on_curve_G1_weirstrass(px, py, a, b) zero_check = circuit.sub(lhs, rhs) circuit.extend_struct_output(u384("zero_check", [zero_check])) return circuit class IsOnCurveG2Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="is_on_curve_g2", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] random_point = G2Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(random_point.x[0])) input.append(self.field(random_point.x[1])) input.append(self.field(random_point.y[0])) input.append(self.field(random_point.y[1])) input.append(self.field(CURVES[self.curve_id].a)) input.append(self.field(CURVES[self.curve_id].b20)) input.append(self.field(CURVES[self.curve_id].b21)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicECG2( self.name, self.curve_id, compilation_mode=self.compilation_mode ) x0, x1, y0, y1 = circuit.write_struct( G2PointCircuit("p", input[0:4]), WriteOps.INPUT ) a = circuit.write_struct(u384("a", [input[4]]), WriteOps.INPUT) b20 = circuit.write_struct(u384("b20", [input[5]]), WriteOps.INPUT) b21 = circuit.write_struct(u384("b21", [input[6]]), WriteOps.INPUT) lhs, rhs = circuit._is_on_curve_G2_weirstrass(x0, x1, y0, y1, a, b20, b21) zero_check = [circuit.sub(lhs[0], rhs[0]), circuit.sub(lhs[1], rhs[1])] circuit.extend_struct_output(u384("zero_check_0", [zero_check[0]])) circuit.extend_struct_output(u384("zero_check_1", [zero_check[1]])) return circuit class AddECPointsG2Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="add_ec_points_g2", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G2Point.gen_random_point(CurveID(self.curve_id)) Q = G2Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x[0])) input.append(self.field(P.x[1])) input.append(self.field(P.y[0])) input.append(self.field(P.y[1])) input.append(self.field(Q.x[0])) input.append(self.field(Q.x[1])) input.append(self.field(Q.y[0])) input.append(self.field(Q.y[1])) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicECG2( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True px0, px1, py0, py1 = circuit.write_struct( G2PointCircuit("p", input[0:4]), WriteOps.INPUT ) qx0, qx1, qy0, qy1 = circuit.write_struct( G2PointCircuit("q", input[4:8]), WriteOps.INPUT ) (nx0, nx1), (ny0, ny1) = circuit.add_points( ((px0, px1), (py0, py1)), ((qx0, qx1), (qy0, qy1)) ) circuit.extend_struct_output(G2PointCircuit("result", [nx0, nx1, ny0, ny1])) return circuit class DoubleECPointG2AEq0Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="double_ec_point_g2_a_eq_0", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G2Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x[0])) input.append(self.field(P.x[1])) input.append(self.field(P.y[0])) input.append(self.field(P.y[1])) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicECG2( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True px0, px1, py0, py1 = circuit.write_struct( G2PointCircuit("p", input[0:4]), WriteOps.INPUT ) (nx0, nx1), (ny0, ny1) = circuit.double_point_a_eq_0(((px0, px1), (py0, py1))) circuit.extend_struct_output(G2PointCircuit("result", [nx0, nx1, ny0, ny1])) return circuit class DoubleAndAddECPointsG2Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="double_and_add_ec_points_g2", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G2Point.gen_random_point(CurveID(self.curve_id)) Q = G2Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x[0])) input.append(self.field(P.x[1])) input.append(self.field(P.y[0])) input.append(self.field(P.y[1])) input.append(self.field(Q.x[0])) input.append(self.field(Q.x[1])) input.append(self.field(Q.y[0])) input.append(self.field(Q.y[1])) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicECG2( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True px0, px1, py0, py1 = circuit.write_struct( G2PointCircuit("p", input[0:4]), WriteOps.INPUT ) qx0, qx1, qy0, qy1 = circuit.write_struct( G2PointCircuit("q", input[4:8]), WriteOps.INPUT ) (nx0, nx1), (ny0, ny1) = circuit.double_and_add( ((px0, px1), (py0, py1)), ((qx0, qx1), (qy0, qy1)) ) circuit.extend_struct_output(G2PointCircuit("result", [nx0, nx1, ny0, ny1])) return circuit class PsiG2BLS12_381Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="psi_g2_bls12_381", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G2Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x[0])) input.append(self.field(P.x[1])) input.append(self.field(P.y[0])) input.append(self.field(P.y[1])) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicECG2( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True px0, px1, py0, py1 = circuit.write_struct( G2PointCircuit("p", input[0:4]), WriteOps.INPUT ) # https://github.com/Consensys/gnark/blob/9ed0eab21e8935cb180d1f75713cd2c29c91a3c9/std/algebra/emulated/sw_bls12381/g2.go u1 = circuit.set_or_get_constant( 0x1A0111EA397FE699EC02408663D4DE85AA0D857D89759AD4897D29650FB85F9B409427EB4F49FFFD8BFD00000000AAAD ) v0 = circuit.set_or_get_constant( 0x135203E60180A68EE2E9C448D77A2CD91C3DEDD930B1CF60EF396489F61EB45E304466CF3E67FA0AF1EE7B04121BDEA2 ) v1 = circuit.set_or_get_constant( 0x6AF0E0437FF400B6831E36D6BD17FFE48395DABC2D3435E77F76E17009241C5EE67992F72EC05F4C81084FBEDE3CC09 ) psi_Qx = (circuit.mul(px1, u1), circuit.mul(px0, u1)) psi_Qy = circuit.fp2_mul([py0, circuit.neg(py1)], [v0, v1]) circuit.extend_struct_output( G2PointCircuit("result", [psi_Qx[0], psi_Qx[1], psi_Qy[0], psi_Qy[1]]) ) return circuit class SlopeInterceptSamePointCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0 ) -> None: super().__init__( name="slope_intercept_same_point", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] random_point = G1Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(random_point.x)) input.append(self.field(random_point.y)) input.append(self.field(CURVES[self.curve_id].a)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) px, py = circuit.write_struct(G1PointCircuit("p", input[0:2]), WriteOps.INPUT) a = circuit.write_struct(u384("a", [input[2]]), WriteOps.INPUT) m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2 = ( circuit._slope_intercept_same_point((px, py), a) ) if self.compilation_mode == 0: # In Cairo0, xA0 and yA0 are copied from the input circuit.extend_output([m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2]) else: # In Cairo1, xA0 and yA0 are not copied from the input circuit.extend_struct_output( structs.SlopeInterceptOutput( "mb", [m_A0, b_A0, xA2, yA2, coeff0, coeff2] ) ) return circuit class AccumulateEvalPointChallengeSignedCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0 ) -> None: super().__init__( name="acc_eval_point_challenge_signed", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: A0 = G1Point.gen_random_point(CurveID(self.curve_id)) m_A0, b_A0 = slope_intercept(A0, A0) input = [] random_point = G1Point.gen_random_point(CurveID(self.curve_id)) scalar = randint(0, 2**127) ep, en = neg_3.positive_negative_multiplicities(neg_3.neg_3_base_le(scalar)) input.append(self.field(randint(0, CURVES[self.curve_id].p - 1))) input.append(self.field(m_A0.value)) input.append(self.field(b_A0.value)) input.append(self.field(A0.x)) input.append(self.field(random_point.x)) input.append(self.field(random_point.y)) input.append(self.field(abs(ep))) input.append(self.field(abs(en))) input.append(self.field(1 if ep >= 0 else -1)) input.append(self.field(1 if en >= 0 else -1)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) # acc, m, b, xA, px, py, ep, en, sp, sn = circuit.write_elements( # input[0:10], WriteOps.INPUT # ) acc, m, b, xA = ( circuit.write_struct(u384("acc", [input[0]]), WriteOps.INPUT), circuit.write_struct(u384("m", [input[1]]), WriteOps.INPUT), circuit.write_struct(u384("b", [input[2]]), WriteOps.INPUT), circuit.write_struct(u384("xA", [input[3]]), WriteOps.INPUT), ) px, py = circuit.write_struct(G1PointCircuit("p", input[4:6]), WriteOps.INPUT) ep = circuit.write_struct(u384("ep", [input[6]]), WriteOps.INPUT) en = circuit.write_struct(u384("en", [input[7]]), WriteOps.INPUT) sp = circuit.write_struct(u384("sp", [input[8]]), WriteOps.INPUT) sn = circuit.write_struct(u384("sn", [input[9]]), WriteOps.INPUT) res_acc = circuit._accumulate_eval_point_challenge_signed_same_point( acc, (m, b), xA, (px, py), ep, en, sp, sn ) circuit.extend_struct_output(u384("res_acc", [res_acc])) return circuit class RHSFinalizeAccCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0 ) -> None: super().__init__( name="rhs_finalize_acc", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: A0 = G1Point.gen_random_point(CurveID(self.curve_id)) m_A0, b_A0 = slope_intercept(A0, A0) input = [] Q = G1Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(randint(0, CURVES[self.curve_id].p - 1))) input.append(self.field(m_A0.value)) input.append(self.field(b_A0.value)) input.append(self.field(A0.x)) input.append(self.field(Q.x)) input.append(self.field(Q.y)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) # acc, m, b, xA, Qx, Qy = circuit.write_elements(input[0:6], WriteOps.INPUT) acc, m, b, xA = ( circuit.write_struct(u384("acc", [input[0]]), WriteOps.INPUT), circuit.write_struct(u384("m", [input[1]]), WriteOps.INPUT), circuit.write_struct(u384("b", [input[2]]), WriteOps.INPUT), circuit.write_struct(u384("xA", [input[3]]), WriteOps.INPUT), ) Qx, Qy = circuit.write_struct( G1PointCircuit("Q_result", input[4:6]), WriteOps.INPUT ) res_acc = circuit._RHS_finalize_acc(acc, (m, b), xA, (Qx, Qy)) circuit.extend_struct_output(u384("rhs", [res_acc])) return circuit class EvalFunctionChallengeSingleCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, n_points: int = 1, auto_run: bool = True, compilation_mode: int = 0, batched: bool = False, generic_circuit: bool = True, ) -> None: self.n_points = n_points self.batched = batched self.generic_circuit = generic_circuit super().__init__( name=f"eval_fn_challenge_sing_{n_points}P" + ("_rlc" if batched else ""), curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] circuit = SlopeInterceptSamePointCircuit(self.curve_id, auto_run=False) xA, _yA, _A = circuit.build_input() m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2 = circuit._run_circuit_inner( [xA, _yA, _A] ).output input.extend([xA0.felt, _yA.felt, coeff0.felt]) n_coeffs = n_coeffs_from_n_points(self.n_points, self.batched) for _ in range(sum(n_coeffs)): input.append(self.field(randint(0, CURVES[self.curve_id].p - 1))) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode, generic_circuit=self.generic_circuit, ) xA0, yA0 = circuit.write_struct( G1PointCircuit("A", [input[0], input[1]]), WriteOps.INPUT ) coeff0 = circuit.write_struct(u384("coeff", [input[2]]), WriteOps.INPUT) all_coeffs = input[3:] def split_list(input_list, lengths): start_idx, result = 0, [] for length in lengths: result.append(input_list[start_idx : start_idx + length]) start_idx += length return result n_points = n_points_from_n_coeffs(len(all_coeffs), self.batched) _log_div_a_num, _log_div_a_den, _log_div_b_num, _log_div_b_den = split_list( all_coeffs, n_coeffs_from_n_points(n_points, self.batched) ) log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den = ( circuit.write_struct( structs.FunctionFeltCircuit( name="SumDlogDiv" + ("Batched" if self.batched else ""), elmts=[ structs.u384Span("log_div_a_num", _log_div_a_num), structs.u384Span("log_div_a_den", _log_div_a_den), structs.u384Span("log_div_b_num", _log_div_b_num), structs.u384Span("log_div_b_den", _log_div_b_den), ], ), WriteOps.INPUT, ) ) res = circuit._eval_function_challenge_single( (xA0, yA0), coeff0, log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den, ) circuit.extend_struct_output(u384("res", [res])) return circuit class EvalFunctionChallengeDuplCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, n_points: int = 1, auto_run: bool = True, compilation_mode: int = 0, batched: bool = False, generic_circuit: bool = True, ) -> None: self.n_points = n_points self.batched = batched self.generic_circuit = generic_circuit super().__init__( name=f"eval_fn_challenge_dupl_{n_points}P" + ("_rlc" if batched else ""), curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] circuit = SlopeInterceptSamePointCircuit(self.curve_id, auto_run=False) xA, _yA, _A = circuit.build_input() m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2 = circuit._run_circuit_inner( [xA, _yA, _A] ).output input.extend([xA0.felt, _yA.felt, xA2.felt, yA2.felt, coeff0.felt, coeff2.felt]) n_coeffs = n_coeffs_from_n_points(self.n_points, self.batched) for _ in range(sum(n_coeffs)): input.append(self.field(randint(0, CURVES[self.curve_id].p - 1))) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode, generic_circuit=self.generic_circuit, ) xA0, yA0 = circuit.write_struct( G1PointCircuit("A0", [input[0], input[1]]), WriteOps.INPUT ) xA2, yA2 = circuit.write_struct( G1PointCircuit("A2", [input[2], input[3]]), WriteOps.INPUT ) coeff0 = circuit.write_struct(u384("coeff0", [input[4]]), WriteOps.INPUT) coeff2 = circuit.write_struct(u384("coeff2", [input[5]]), WriteOps.INPUT) all_coeffs = input[6:] def split_list(input_list, lengths): start_idx, result = 0, [] for length in lengths: result.append(input_list[start_idx : start_idx + length]) start_idx += length return result n_points = n_points_from_n_coeffs(len(all_coeffs), self.batched) _log_div_a_num, _log_div_a_den, _log_div_b_num, _log_div_b_den = split_list( all_coeffs, n_coeffs_from_n_points(n_points, self.batched) ) log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den = ( circuit.write_struct( structs.FunctionFeltCircuit( name="SumDlogDiv" + ("Batched" if self.batched else ""), elmts=[ structs.u384Span("log_div_a_num", _log_div_a_num), structs.u384Span("log_div_a_den", _log_div_a_den), structs.u384Span("log_div_b_num", _log_div_b_num), structs.u384Span("log_div_b_den", _log_div_b_den), ], ), WriteOps.INPUT, ) ) res = circuit._eval_function_challenge_dupl( (xA0, yA0), (xA2, yA2), coeff0, coeff2, log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den, ) circuit.extend_struct_output(u384("res", [res])) return circuit class InitFunctionChallengeDuplCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, n_points: int = 1, auto_run: bool = True, batched: bool = False, compilation_mode: int = 0, ) -> None: self.n_points = n_points self.batched = batched super().__init__( name=f"init_fn_challenge_dupl_{n_points}P" + ("_rlc" if batched else ""), curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random(), self.field.random()]) # xA0, xA2 n_coeffs = n_coeffs_from_n_points(self.n_points, self.batched) for _ in range(sum(n_coeffs)): input.append(self.field(randint(0, CURVES[self.curve_id].p - 1))) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) xA0 = circuit.write_struct(u384("xA0", [input[0]]), WriteOps.INPUT) xA2 = circuit.write_struct(u384("xA2", [input[1]]), WriteOps.INPUT) all_coeffs = input[2:] def split_list(input_list, lengths): start_idx, result = 0, [] for length in lengths: result.append(input_list[start_idx : start_idx + length]) start_idx += length return result n_points = n_points_from_n_coeffs(len(all_coeffs), self.batched) _log_div_a_num, _log_div_a_den, _log_div_b_num, _log_div_b_den = split_list( all_coeffs, n_coeffs_from_n_points(n_points, self.batched) ) log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den = ( circuit.write_struct( structs.FunctionFeltCircuit( name="SumDlogDiv", elmts=[ structs.u384Span("log_div_a_num", _log_div_a_num), structs.u384Span("log_div_a_den", _log_div_a_den), structs.u384Span("log_div_b_num", _log_div_b_num), structs.u384Span("log_div_b_den", _log_div_b_den), ], ), WriteOps.INPUT, ) ) res = circuit._init_function_challenge_dupl( xA0, xA2, log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den ) circuit.extend_struct_output( structs.FunctionFeltEvaluations("A0_evals", res[0:4]) ) circuit.extend_struct_output( structs.FunctionFeltEvaluations("A2_evals", res[4:8]) ) circuit.extend_struct_output(u384("xA0_power", [res[8]])) circuit.extend_struct_output(u384("xA2_power", [res[9]])) return circuit class AccumulateFunctionChallengeDuplCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ): super().__init__( name="acc_function_challenge_dupl", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.extend( [self.field.random() for _ in range(8)] ) # a_num, a_den, b_num, b_den accumulation evals * 2 input.extend([self.field.random(), self.field.random()]) # xA0, xA2 input.extend( [self.field.random(), self.field.random()] ) # xA0_power, xA2_power, corresponding the max degree of a_den or b_num of the previous accumulator input.extend( [self.field.random() for _ in range(4)] ) # next coefficients of a_num, a_den, b_num, b_den return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) f_a0_accs = circuit.write_struct( structs.FunctionFeltEvaluations("f_a0_accs", input[0:4]), WriteOps.INPUT ) f_a1_accs = circuit.write_struct( structs.FunctionFeltEvaluations("f_a1_accs", input[4:8]), WriteOps.INPUT ) xA0 = circuit.write_struct(u384("xA0", [input[8]]), WriteOps.INPUT) xA2 = circuit.write_struct(u384("xA2", [input[9]]), WriteOps.INPUT) xA0_power = circuit.write_struct(u384("xA0_power", [input[10]]), WriteOps.INPUT) xA2_power = circuit.write_struct(u384("xA2_power", [input[11]]), WriteOps.INPUT) next_a_num_coeff = circuit.write_struct( structs.GenericT("next_a_num_coeff", [input[12]]), WriteOps.INPUT ) next_a_den_coeff = circuit.write_struct( structs.GenericT("next_a_den_coeff", [input[13]]), WriteOps.INPUT ) next_b_num_coeff = circuit.write_struct( structs.GenericT("next_b_num_coeff", [input[14]]), WriteOps.INPUT ) next_b_den_coeff = circuit.write_struct( structs.GenericT("next_b_den_coeff", [input[15]]), WriteOps.INPUT ) res = circuit._accumulate_function_challenge_dupl( *f_a0_accs, *f_a1_accs, xA0, xA2, xA0_power, xA2_power, next_a_num_coeff, next_a_den_coeff, next_b_num_coeff, next_b_den_coeff, ) circuit.extend_struct_output( structs.FunctionFeltEvaluations("next_f_a0_accs", res[0:4]) ) circuit.extend_struct_output( structs.FunctionFeltEvaluations("next_f_a1_accs", res[4:8]) ) circuit.extend_struct_output(u384("next_xA0_power", [res[8]])) circuit.extend_struct_output(u384("next_xA2_power", [res[9]])) return circuit class FinalizeFunctionChallengeDuplCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ): super().__init__( name="finalize_fn_challenge_dupl", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.extend([self.field.random() for _ in range(8)]) # f_a0_accs, f_a1_accs input.extend([self.field.random() for _ in range(2)]) # yA0, yA2 input.extend([self.field.random() for _ in range(2)]) # coeff_A0, coeff_A2 return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ECIPCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) f_a0_accs = circuit.write_struct( structs.FunctionFeltEvaluations("f_a0_accs", input[0:4]), WriteOps.INPUT ) f_a1_accs = circuit.write_struct( structs.FunctionFeltEvaluations("f_a1_accs", input[4:8]), WriteOps.INPUT ) yA0 = circuit.write_struct(u384("yA0", [input[8]]), WriteOps.INPUT) yA2 = circuit.write_struct(u384("yA2", [input[9]]), WriteOps.INPUT) coeff_A0 = circuit.write_struct(u384("coeff_A0", [input[10]]), WriteOps.INPUT) coeff_A2 = circuit.write_struct(u384("coeff_A2", [input[11]]), WriteOps.INPUT) res = circuit._finalize_function_challenge_dupl( *f_a0_accs, *f_a1_accs, yA0, yA2, coeff_A0, coeff_A2 ) circuit.extend_struct_output(u384("res", [res])) return circuit class AddECPointCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ): super().__init__( name="add_ec_point", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G1Point.gen_random_point(CurveID(self.curve_id)) Q = G1Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x)) input.append(self.field(P.y)) input.append(self.field(Q.x)) input.append(self.field(Q.y)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicEC( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True xP, yP = circuit.write_struct(G1PointCircuit("p", input[0:2]), WriteOps.INPUT) xQ, yQ = circuit.write_struct(G1PointCircuit("q", input[2:4]), WriteOps.INPUT) xR, yR = circuit.add_points((xP, yP), (xQ, yQ)) circuit.extend_struct_output(G1PointCircuit("r", [xR, yR])) return circuit class DoubleECPointCircuit(BaseModuloCircuit): def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ): super().__init__( name="double_ec_point", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] P = G1Point.gen_random_point(CurveID(self.curve_id)) input.append(self.field(P.x)) input.append(self.field(P.y)) input.append(self.field(CURVES[self.curve_id].a)) return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicEC( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True xP, yP = circuit.write_struct(G1PointCircuit("p", input[0:2]), WriteOps.INPUT) A = circuit.write_struct(u384("A_weirstrass", [input[2]])) xR, yR = circuit.double_point((xP, yP), A) circuit.extend_struct_output(G1PointCircuit("r", [xR, yR])) return circuit class PrepareGLVFakeGLVPtsCircuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="prepare_glv_fake_glv_pts", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.append(self.field.random()) # Px input.append(self.field.random()) # P0y input.append(self.field.random()) # P1y input.append(self.field.random()) # Qx input.append(self.field.random()) # Q0y input.append(self.field.random()) # Phi_P0y input.append(self.field.random()) # Phi_P1y input.append(self.field.random()) # Phi_Q0y input.append(self.field.random()) # Gen_x input.append(self.field.random()) # Gen_y input.append(self.field.random()) # third_root return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = FakeGLVCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True Px = circuit.write_struct(u384("Px", [input[0]]), WriteOps.INPUT) P0y = circuit.write_struct(u384("P0y", [input[1]]), WriteOps.INPUT) P1y = circuit.write_struct(u384("P1y", [input[2]]), WriteOps.INPUT) Qx = circuit.write_struct(u384("Qx", [input[3]]), WriteOps.INPUT) Q0y = circuit.write_struct(u384("Q0y", [input[4]]), WriteOps.INPUT) Phi_P0y = circuit.write_struct(u384("Phi_P0y", [input[5]]), WriteOps.INPUT) Phi_P1y = circuit.write_struct(u384("Phi_P1y", [input[6]]), WriteOps.INPUT) Phi_Q0y = circuit.write_struct(u384("Phi_Q0y", [input[7]]), WriteOps.INPUT) Gen = circuit.write_struct( G1PointCircuit("Gen", [input[8], input[9]]), WriteOps.INPUT ) third_root = circuit.write_struct( u384("third_root", [input[10]]), WriteOps.INPUT ) ( B1, B2, B3, B4, B5, B6, B7, B8, B9y, B10y, B11y, B12y, B13y, B14y, B15y, B16y, Phi_P0x, Phi_Q0x, Acc, ) = circuit.prepare_points_glv_fake_glv( Px, P0y, P1y, Qx, Q0y, Phi_P0y, Phi_P1y, Phi_Q0y, Gen, third_root ) # circuit.exact_output_refs_needed = [B2[0], B3[0], B4[0], B5[0], B6[0], B7[0], B8[0], B10y, B11y, B12y, B13y, B14y, B15y, B16y, Acc[0], Acc[1]] circuit.extend_struct_output(G1PointCircuit("B1", [B1[0], B1[1]])) circuit.extend_struct_output(G1PointCircuit("B2", [B2[0], B2[1]])) circuit.extend_struct_output(G1PointCircuit("B3", [B3[0], B3[1]])) circuit.extend_struct_output(G1PointCircuit("B4", [B4[0], B4[1]])) circuit.extend_struct_output(G1PointCircuit("B5", [B5[0], B5[1]])) circuit.extend_struct_output(G1PointCircuit("B6", [B6[0], B6[1]])) circuit.extend_struct_output(G1PointCircuit("B7", [B7[0], B7[1]])) circuit.extend_struct_output(G1PointCircuit("B8", [B8[0], B8[1]])) circuit.extend_struct_output(u384("B9y", [B9y])) circuit.extend_struct_output(u384("B10y", [B10y])) circuit.extend_struct_output(u384("B11y", [B11y])) circuit.extend_struct_output(u384("B12y", [B12y])) circuit.extend_struct_output(u384("B13y", [B13y])) circuit.extend_struct_output(u384("B14y", [B14y])) circuit.extend_struct_output(u384("B15y", [B15y])) circuit.extend_struct_output(u384("B16y", [B16y])) circuit.extend_struct_output(u384("Phi_P0x", [Phi_P0x])) circuit.extend_struct_output(u384("Phi_Q0x", [Phi_Q0x])) circuit.extend_struct_output(G1PointCircuit("Acc", [Acc[0], Acc[1]])) return circuit class PrepareFakeGLVPtsCircuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="prepare_fake_glv_pts", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.append(self.field.random()) # Px input.append(self.field.random()) # Py input.append(self.field.random()) # Qx input.append(self.field.random()) # Qy input.append(self.field.random()) # s2_sign input.append(self.field.random()) # A_weirstrass return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = FakeGLVCircuits( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True P = circuit.write_struct( G1PointCircuit("P", [input[0], input[1]]), WriteOps.INPUT ) Q = circuit.write_struct( G1PointCircuit("Q", [input[2], input[3]]), WriteOps.INPUT ) s2_sign = circuit.write_struct(u384("s2_sign", [input[4]]), WriteOps.INPUT) A_weirstrass = circuit.write_struct( u384("A_weirstrass", [input[5]]), WriteOps.INPUT ) ( T1, T2, T3, T4, T5y, T6y, T7y, T8y, T9, T10, T11, T12, T13y, T14y, T15y, T16y, R2, R0y, ) = circuit.prepare_points_fake_glv(P, Q, s2_sign, A_weirstrass) # circuit.exact_output_refs_needed = [B2[0], B3[0], B4[0], B5[0], B6[0], B7[0], B8[0], B10y, B11y, B12y, B13y, B14y, B15y, B16y, Acc[0], Acc[1]] circuit.extend_struct_output(G1PointCircuit("T1", [T1[0], T1[1]])) circuit.extend_struct_output(G1PointCircuit("T2", [T2[0], T2[1]])) circuit.extend_struct_output(G1PointCircuit("T3", [T3[0], T3[1]])) circuit.extend_struct_output(G1PointCircuit("T4", [T4[0], T4[1]])) circuit.extend_struct_output(u384("T5y", [T5y])) circuit.extend_struct_output(u384("T6y", [T6y])) circuit.extend_struct_output(u384("T7y", [T7y])) circuit.extend_struct_output(u384("T8y", [T8y])) circuit.extend_struct_output(G1PointCircuit("T9", [T9[0], T9[1]])) circuit.extend_struct_output(G1PointCircuit("T10", [T10[0], T10[1]])) circuit.extend_struct_output(G1PointCircuit("T11", [T11[0], T11[1]])) circuit.extend_struct_output(G1PointCircuit("T12", [T12[0], T12[1]])) circuit.extend_struct_output(u384("T13y", [T13y])) circuit.extend_struct_output(u384("T14y", [T14y])) circuit.extend_struct_output(u384("T15y", [T15y])) circuit.extend_struct_output(u384("T16y", [T16y])) circuit.extend_struct_output(G1PointCircuit("R2", [R2[0], R2[1]])) circuit.extend_struct_output(u384("R0y", [R0y])) return circuit class QuadrupleAndAdd9Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="quadruple_and_add_9", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.append(self.field.random()) # Px input.append(self.field.random()) # Py for _ in range(9): input.append(self.field.random()) # Qx input.append(self.field.random()) # Qy input.append(self.field.random()) # A_weirstrass return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = BasicEC( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True P = circuit.write_struct( G1PointCircuit("P", [input[0], input[1]]), WriteOps.INPUT ) Qs = [] for i in range(2, len(input) - 1, 2): Qs.append( circuit.write_struct( G1PointCircuit(f"Q_{i//2}", [input[i], input[i + 1]]), WriteOps.INPUT, ) ) A_weirstrass = circuit.write_struct( u384("A_weirstrass", [input[len(input) - 1]]), WriteOps.INPUT ) Rx, Ry = circuit.n_quadruple_and_add(P, Qs, A_weirstrass) circuit.extend_struct_output(G1PointCircuit("R", [Rx, Ry])) return circuit class ClearCofactorBLS12_381Circuit(BaseModuloCircuit): def __init__(self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0): super().__init__( name="clear_cofactor_bls12_381", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: input = [] input.append(self.field.random()) # Px input.append(self.field.random()) # Py return input def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = G1CofactorClearing( self.name, self.curve_id, compilation_mode=self.compilation_mode ) circuit.generic_modulus = True P = circuit.write_struct( G1PointCircuit("P", [input[0], input[1]]), WriteOps.INPUT ) res = circuit.clear_cofactor(P) circuit.extend_struct_output(G1PointCircuit("res", [res[0], res[1]])) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/rsa.py ================================================ from random import randrange from garaga.modulo_circuit import ModuloCircuit, WriteOps from garaga.modulo_circuit_structs import RSA2048Chunks, RSA2048ReductionWitness, u384 from garaga.precompiled_circuits.compilable_circuits.base import ( BaseModuloCircuit, PyFelt, ) RSA2048_N_CHUNKS = 6 RSA2048_TOP_CHUNK_BITS = 128 RSA2048_N_STEPS = 17 class RSAFullVerificationCircuit(BaseModuloCircuit): """RNS channel circuit for RSA-2048 modular exponentiation verification. Verifies all 17 reduction steps (16 squarings + 1 final multiply) of the square-and-multiply chain s^{65537} mod n within a single RNS channel. Each step a*b = q*n + r is checked by Horner evaluation of chunk polynomials at the channel's evaluation point alpha, asserting a(alpha)*b(alpha) - q(alpha)*n(alpha) - r(alpha) = 0. Inputs (217): n(6) + s(6) + 17 x (q_i(6) + r_i(6)) + alpha(1) Outputs (17): differences delta_i (zero iff all reductions are valid) """ def __init__( self, curve_id: int, auto_run: bool = True, compilation_mode: int = 0, ) -> None: super().__init__( name="rsa_full_verification", curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def build_input(self) -> list[PyFelt]: # mod_chunks (6) + sig_chunks (6) + 17*(quot(6)+rem(6)) + step(1) = 217 mod_chunks = [self.field.random() for _ in range(RSA2048_N_CHUNKS - 1)] mod_chunks.append(self.field(randrange(1 << RSA2048_TOP_CHUNK_BITS))) sig_chunks = [self.field.random() for _ in range(RSA2048_N_CHUNKS - 1)] sig_chunks.append(self.field(randrange(1 << RSA2048_TOP_CHUNK_BITS))) witness_chunks = [] for _ in range(RSA2048_N_STEPS): quot = [self.field.random() for _ in range(RSA2048_N_CHUNKS - 1)] quot.append(self.field(randrange(1 << RSA2048_TOP_CHUNK_BITS))) rem = [self.field.random() for _ in range(RSA2048_N_CHUNKS - 1)] rem.append(self.field(randrange(1 << RSA2048_TOP_CHUNK_BITS))) witness_chunks.extend(quot + rem) step = [self.field.random()] return mod_chunks + sig_chunks + witness_chunks + step def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = ModuloCircuit( self.name, self.curve_id, generic_circuit=True, generic_modulus=True, compilation_mode=self.compilation_mode, ) mod_chunks = circuit.write_struct( RSA2048Chunks( "mod_chunks", [input.pop(0) for _ in range(RSA2048_N_CHUNKS)], ), WriteOps.INPUT, ) sig_chunks = circuit.write_struct( RSA2048Chunks( "sig_chunks", [input.pop(0) for _ in range(RSA2048_N_CHUNKS)], ), WriteOps.INPUT, ) all_quot_chunks = [] all_rem_chunks = [] for i in range(RSA2048_N_STEPS): witness_elmts = [input.pop(0) for _ in range(2 * RSA2048_N_CHUNKS)] witness = circuit.write_struct( RSA2048ReductionWitness(f"w_{i}", witness_elmts), WriteOps.INPUT, ) all_quot_chunks.append(witness[:RSA2048_N_CHUNKS]) all_rem_chunks.append(witness[RSA2048_N_CHUNKS:]) step = circuit.write_struct(u384("step", [input.pop(0)]), WriteOps.INPUT) assert len(input) == 0, f"Expected empty input, got {len(input)} elements left" mod_res = circuit.eval_horner( mod_chunks, step, poly_name="mod_chunks", var_name="STEP" ) sig_res = circuit.eval_horner( sig_chunks, step, poly_name="sig_chunks", var_name="STEP" ) current = sig_res # first step squares sig_res diffs = [] for i in range(RSA2048_N_STEPS): q_res = circuit.eval_horner( all_quot_chunks[i], step, poly_name=f"quot_{i}", var_name="STEP" ) r_res = circuit.eval_horner( all_rem_chunks[i], step, poly_name=f"rem_{i}", var_name="STEP" ) if i < RSA2048_N_STEPS - 1: ab = circuit.mul(current, current, comment=f"square_{i}") else: ab = circuit.mul(current, sig_res, comment="final_multiply") qn = circuit.mul(q_res, mod_res, comment=f"quot*mod_{i}") diff = circuit.sub(ab, qn, comment=f"ab-qn_{i}") diff = circuit.sub(diff, r_res, comment=f"ab-qn-rem_{i}") diffs.append(diff) current = r_res for i, diff in enumerate(diffs): circuit.extend_struct_output(u384(f"diff_{i}", [diff])) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/compilable_circuits/ultra_honk.py ================================================ from abc import abstractmethod from typing import Dict, Tuple, Type, Union import garaga.modulo_circuit_structs as structs import garaga.precompiled_circuits.zk_honk as hk from garaga.curves import CurveID from garaga.modulo_circuit import ModuloCircuitElement from garaga.modulo_circuit_structs import u384 from garaga.precompiled_circuits.compilable_circuits.base import ( BaseModuloCircuit, ModuloCircuit, PyFelt, ) from garaga.precompiled_circuits.zk_honk import ( PAIRING_POINT_OBJECT_LENGTH, ZK_BATCHED_RELATION_PARTIAL_LENGTH, HonkVk, Wire, ZKHonkVerifierCircuits, ) from garaga.starknet.honk_contract_generator.calldata import filter_msm_scalars class BaseUltraHonkCircuit(BaseModuloCircuit): def __init__( self, name: str, log_n: int, curve_id: CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: self.log_n = log_n super().__init__( name=name, curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def _initialize_circuit(self) -> ZKHonkVerifierCircuits: return ZKHonkVerifierCircuits( name=self.name, log_n=self.log_n, curve_id=self.curve_id, ) def _process_input( self, circuit: ZKHonkVerifierCircuits, input: list[PyFelt] ) -> dict: """ Method responsible for deserializing the input list of elements into the variables in the input map, and writing them to the circuit. The input list is expected to be in the same order as the input map. Since we use Python 3.10, the input map dict is ordered. Returns a vars dict with the same keys as the input map, but with the values being the instances of the structs, each struct holding ModuloCircuitElement(s). """ vars = {} for name, struct_info in self.input_map.items(): if name == "sumcheck_evaluations": # Edge case, TABLE_SHIFTS are not used. Replace with mocked non part of circuit values. struct_type, size = struct_info assert size == len(Wire) - len(Wire.unused_indexes()) elements = circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) elements = Wire.insert_unused_indexes_with_nones(elements) assert len(elements) == len(Wire) vars[name] = elements elif isinstance(struct_info, tuple) and struct_info[0] in [ structs.u256Span, structs.u384Array, structs.u128Span, ]: # Handle u384Array with specified size struct_type, size = struct_info vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) else: struct_type = struct_info # For other types, create a temporary instance to get its length temp_instance = struct_type( name, None ) # Temporary instance with a dummy element size = len(temp_instance) if size == 1: vars[name] = circuit.write_struct( struct_type(name, elmts=[input.pop(0)]) ) else: # Convert to tuple so that it is Hashable vars[name] = tuple( circuit.write_struct( struct_type(name, elmts=[input.pop(0) for _ in range(size)]) ) ) assert len(input) == 0, f"Expected input of length 0, got {len(input)}" return vars @property @abstractmethod def input_map( self, ) -> Dict[ str, Union[ Type[structs.Cairo1SerializableStruct], Tuple[Type[structs.Cairo1SerializableStruct], int], ], ]: """ Define the input map for the circuit in a dict. The key will be the name of the input variable, also used in the signature of the compiled Cairo code. The value will be either a Cairo1SerializableStruct type (which defines the struct in the Cairo code), or a tuple of the type and its size (for Array-like types). The reason behind this is that each Cairo1SerializableStruct defines the __len__ method, but for the array-like structs we need to specify the size in advance. """ def build_input(self) -> list[PyFelt]: """ Extends the base method of BaseModuloCircuit, by reading the input map and returning a list of random elements of the total expected size. """ total_elements = 0 for name, struct_info in self.input_map.items(): if isinstance(struct_info, tuple): # Array-like case _, size = struct_info total_elements += size else: # For other structs, create a temporary instance to get its length temp_instance = struct_info(name, None) total_elements += len(temp_instance) # print(f"Total elements: {total_elements}") return [self.field.random() for _ in range(total_elements)] def _run_circuit_inner(self, input: list[PyFelt]) -> ModuloCircuit: circuit = self._initialize_circuit() vars = self._process_input(circuit, input) return self._execute_circuit_logic(circuit, vars) @abstractmethod def _execute_circuit_logic(self, circuit, vars) -> ModuloCircuit: """ Implement the circuit logic using the processed input variables. """ class ZKBaseUltraHonkCircuit(BaseUltraHonkCircuit): def __init__( self, name: str, log_n: int, curve_id: CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: super().__init__( name=name, log_n=log_n, curve_id=curve_id, auto_run=auto_run, compilation_mode=compilation_mode, ) def _initialize_circuit(self) -> ZKHonkVerifierCircuits: return ZKHonkVerifierCircuits( name=self.name, log_n=self.log_n, curve_id=self.curve_id, ) class ZKSumCheckCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: assert ( vk.public_inputs_size >= PAIRING_POINT_OBJECT_LENGTH ), f"vk.public_inputs_size: {vk.public_inputs_size}, PAIRING_POINT_OBJECT_LENGTH: {PAIRING_POINT_OBJECT_LENGTH}" name = ( f"zk_honk_sumcheck_size_{vk.log_circuit_size}_pub_{vk.public_inputs_size}" ) self.vk = vk super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["p_public_inputs"] = ( structs.u256Span, self.vk.public_inputs_size - PAIRING_POINT_OBJECT_LENGTH, ) imap["p_pairing_point_object"] = (structs.u256Span, PAIRING_POINT_OBJECT_LENGTH) imap["libra_sum"] = structs.u384 imap["sumcheck_univariates_flat"] = ( structs.u256Span, self.vk.log_circuit_size * ZK_BATCHED_RELATION_PARTIAL_LENGTH, ) imap["sumcheck_evaluations"] = ( structs.u256Span, hk.NUMBER_OF_ENTITIES - len(Wire.unused_indexes()), ) imap["libra_evaluation"] = structs.u384 imap["tp_sum_check_u_challenges"] = ( structs.u128Span, self.vk.log_circuit_size, ) imap["tp_gate_challenge"] = structs.u128 imap["tp_eta_1"] = structs.u384 imap["tp_eta_2"] = structs.u384 imap["tp_eta_3"] = structs.u384 imap["tp_beta"] = structs.u384 imap["tp_gamma"] = structs.u384 imap["tp_base_rlc"] = structs.u384 imap["tp_alpha"] = structs.u128 imap["tp_libra_challenge"] = structs.u384 return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: tp_delta = circuit.compute_public_input_delta( vars["p_public_inputs"], vars["p_pairing_point_object"], vars["tp_beta"], vars["tp_gamma"], ) sumcheck_univariates_flat = vars["sumcheck_univariates_flat"] sumcheck_univariates = [] for i in range(self.vk.log_circuit_size): sumcheck_univariates.append( sumcheck_univariates_flat[ i * ZK_BATCHED_RELATION_PARTIAL_LENGTH : (i + 1) * ZK_BATCHED_RELATION_PARTIAL_LENGTH ] ) assert len(sumcheck_univariates) == self.vk.log_circuit_size assert len(sumcheck_univariates[0]) == ZK_BATCHED_RELATION_PARTIAL_LENGTH assert len(vars["sumcheck_evaluations"]) == len(Wire) check_rlc, check = circuit.verify_sum_check( vars["libra_sum"], sumcheck_univariates, vars["sumcheck_evaluations"], vars["libra_evaluation"], vars["tp_beta"], vars["tp_gamma"], tp_delta, vars["tp_eta_1"], vars["tp_eta_2"], vars["tp_eta_3"], vars["tp_libra_challenge"], vars["tp_sum_check_u_challenges"], vars["tp_gate_challenge"], vars["tp_alpha"], self.vk.log_circuit_size, vars["tp_base_rlc"], ) assert type(check_rlc) == ModuloCircuitElement assert type(check) == ModuloCircuitElement circuit.extend_struct_output(u384("check_rlc", elmts=[check_rlc])) circuit.extend_struct_output(u384("check", elmts=[check])) return circuit class ZKPrepareScalarsCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: name = f"zkhonk_prep_msm_scalars_size_{vk.log_circuit_size}" self.vk = vk self.scalar_indexes = [] super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["p_sumcheck_evaluations"] = (structs.u256Span, hk.NUMBER_OF_ENTITIES) imap["p_gemini_masking_eval"] = structs.u384 imap["p_gemini_a_evaluations"] = (structs.u256Span, self.vk.log_circuit_size) imap["p_libra_poly_evals"] = (structs.u256Span, 4) imap["tp_gemini_r"] = structs.u384 imap["tp_rho"] = structs.u384 imap["tp_shplonk_z"] = structs.u384 imap["tp_shplonk_nu"] = structs.u384 imap["tp_sum_check_u_challenges"] = ( structs.u128Span, self.vk.log_circuit_size, ) return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: assert len(vars["p_sumcheck_evaluations"]) == len(Wire) scalars = circuit.compute_shplemini_msm_scalars( vars["p_sumcheck_evaluations"], vars["p_gemini_masking_eval"], vars["p_gemini_a_evaluations"], vars["p_libra_poly_evals"], vars["tp_gemini_r"], vars["tp_rho"], vars["tp_shplonk_z"], vars["tp_shplonk_nu"], vars["tp_sum_check_u_challenges"], ) scalars_filtered_no_nones = filter_msm_scalars( scalars, self.vk.log_circuit_size ) # Remove shplonk_z (last scalar) (included in transcript) scalars_filtered_no_nones = scalars_filtered_no_nones[:-1] self.msm_len = len(scalars_filtered_no_nones) + 1 # For each filtered scalar, find its original index by matching offset self.scalar_indexes = [] for scalar in scalars_filtered_no_nones: original_index = next( i for i, orig_scalar in enumerate(scalars) if orig_scalar is not None and orig_scalar.offset == scalar.offset ) self.scalar_indexes.append(original_index) circuit.extend_struct_output( u384(f"scalar_{original_index}", elmts=[scalar]) ) self.msm_len = len(scalars_filtered_no_nones) + 1 return circuit class ZKEvalsConsistencyCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: name = f"zk_honk_evals_consist_size_{vk.log_circuit_size}" self.vk = vk super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["p_libra_evaluation"] = structs.u384 imap["p_libra_poly_evals"] = (structs.u256Span, 4) imap["tp_gemini_r"] = structs.u384 imap["tp_sum_check_u_challenges"] = ( structs.u128Span, hk.CONST_PROOF_SIZE_LOG_N, ) return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: vanishing_check, diff_check = circuit.check_evals_consistency( vars["p_libra_evaluation"], vars["p_libra_poly_evals"], vars["tp_gemini_r"], vars["tp_sum_check_u_challenges"], ) assert type(vanishing_check) == ModuloCircuitElement assert type(diff_check) == ModuloCircuitElement circuit.extend_struct_output(u384("vanishing_check", elmts=[vanishing_check])) circuit.extend_struct_output(u384("diff_check", elmts=[diff_check])) return circuit class ZKEvalsConsistencyInitCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: name = f"zk_honk_evals_cons_init_size_{vk.log_circuit_size}" self.vk = vk super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["tp_gemini_r"] = structs.u384 return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: challenge_poly_eval, root_power_times_tp_gemini_r = ( circuit._check_evals_consistency_init( vars["tp_gemini_r"], ) ) assert type(challenge_poly_eval) == ModuloCircuitElement assert type(root_power_times_tp_gemini_r) == ModuloCircuitElement circuit.extend_struct_output( u384("challenge_poly_eval", elmts=[challenge_poly_eval]) ) circuit.extend_struct_output( u384("root_power_times_tp_gemini_r", elmts=[root_power_times_tp_gemini_r]) ) return circuit class ZKEvalsConsistencyLoopCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: name = f"zk_honk_evals_cons_loop_size_{vk.log_circuit_size}" self.vk = vk super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["challenge_poly_eval"] = structs.u384 imap["root_power_times_tp_gemini_r"] = structs.u384 imap["tp_sumcheck_u_challenge"] = structs.u384 return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: challenge_poly_eval, root_power_times_tp_gemini_r = ( circuit._check_evals_consistency_loop( vars["challenge_poly_eval"], vars["root_power_times_tp_gemini_r"], vars["tp_sumcheck_u_challenge"], ) ) assert type(challenge_poly_eval) == ModuloCircuitElement assert type(root_power_times_tp_gemini_r) == ModuloCircuitElement circuit.extend_struct_output( u384("challenge_poly_eval", elmts=[challenge_poly_eval]) ) circuit.extend_struct_output( u384("root_power_times_tp_gemini_r", elmts=[root_power_times_tp_gemini_r]) ) return circuit class ZKEvalsConsistencyDoneCircuit(ZKBaseUltraHonkCircuit): def __init__( self, vk: HonkVk, curve_id: int = CurveID.GRUMPKIN.value, auto_run: bool = True, compilation_mode: int = 1, ) -> None: name = f"zk_honk_evals_cons_done_size_{vk.log_circuit_size}" self.vk = vk super().__init__( name, vk.log_circuit_size, curve_id, auto_run, compilation_mode ) @property def input_map(self) -> dict: imap = {} imap["p_libra_evaluation"] = structs.u384 imap["p_libra_poly_evals"] = (structs.u256Span, 4) imap["tp_gemini_r"] = structs.u384 imap["challenge_poly_eval"] = structs.u384 imap["root_power_times_tp_gemini_r"] = structs.u384 return imap def _execute_circuit_logic( self, circuit: ZKHonkVerifierCircuits, vars: dict ) -> ModuloCircuit: vanishing_check, diff_check = circuit._check_evals_consistency_done( vars["p_libra_evaluation"], vars["p_libra_poly_evals"], vars["tp_gemini_r"], vars["challenge_poly_eval"], vars["root_power_times_tp_gemini_r"], ) assert type(vanishing_check) == ModuloCircuitElement assert type(diff_check) == ModuloCircuitElement circuit.extend_struct_output(u384("vanishing_check", elmts=[vanishing_check])) circuit.extend_struct_output(u384("diff_check", elmts=[diff_check])) return circuit ================================================ FILE: hydra/garaga/precompiled_circuits/ec.py ================================================ import sympy from garaga.curves import CURVES from garaga.modulo_circuit import ModuloCircuit, ModuloCircuitElement, PyFelt, WriteOps from garaga.precompiled_circuits.fp2 import Fp2Circuits def is_quad_residue(n, p): """ Returns True if n is a quadratic residue mod p. """ return sympy.ntheory.residue_ntheory.is_quad_residue(n, p) def sqrt_mod_p(n, p): """ Finds the minimum non-negative integer m such that (m*m) % p == n. """ return min(sympy.ntheory.residue_ntheory.sqrt_mod(n, p, all_roots=True)) class IsOnCurveCircuit(Fp2Circuits): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=True, ) self.curve = CURVES[curve_id] def set_consts( self, a: PyFelt | ModuloCircuitElement, b: PyFelt | ModuloCircuitElement, b20: PyFelt | ModuloCircuitElement, b21: PyFelt | ModuloCircuitElement, ): self.a = self.write_element(a) if isinstance(a, PyFelt) else a self.b = self.write_element(b) if isinstance(b, PyFelt) else b self.b20 = self.write_element(b20) if isinstance(b20, PyFelt) else b20 self.b21 = self.write_element(b21) if isinstance(b21, PyFelt) else b21 def _is_on_curve_G1( self, x: ModuloCircuitElement, y: ModuloCircuitElement ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: # y^2 = x^3 + ax + b a = self.a b = self.b y2 = self.mul(y, y) x3 = self.mul(x, self.mul(x, x)) if a.value != 0: ax = self.mul(a, x) x3_ax_b = self.add(x3, self.add(ax, b)) else: x3_ax_b = self.add(x3, b) return y2, x3_ax_b def _is_on_curve_G2( self, x0: ModuloCircuitElement, x1: ModuloCircuitElement, y0: ModuloCircuitElement, y1: ModuloCircuitElement, ): # y^2 = x^3 + ax + b [Fp2] a = self.a b0 = self.b20 b1 = self.b21 y2 = self.fp2_square([y0, y1]) x2 = self.fp2_square([x0, x1]) x3 = self.fp2_mul([x0, x1], x2) ax = [self.mul(a, x0), self.mul(a, x1)] ax_b = [self.add(ax[0], b0), self.add(ax[1], b1)] x3_ax_b = [self.add(x3[0], ax_b[0]), self.add(x3[1], ax_b[1])] return y2, x3_ax_b class DerivePointFromX(ModuloCircuit): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, generic_circuit=True, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] def _derive_point_from_x( self, x: ModuloCircuitElement, a: ModuloCircuitElement, b: ModuloCircuitElement, g: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: # y^2 = x^3 + ax + b # Assumes a == 0. x3 = self.mul(x, self.mul(x, x)) rhs = self.add(x3, self.add(self.mul(a, x), b)) grhs = self.mul(g, rhs) # WRITE g*rhs and rhs "square roots" to circuit. # If rhs is a square, write zero to gx and the square root of rhs to x3_ax_b_sqrt. # Otherwise, write the square root of gx to gx_sqrt and zero to x3_ax_b_sqrt. ## %{ if is_quad_residue(rhs.value, self.field.p): rhs_sqrt = self.write_element( self.field(sqrt_mod_p(rhs.value, self.field.p)), WriteOps.WITNESS, ) grhs_sqrt = self.write_element(self.field.zero(), WriteOps.WITNESS) else: assert is_quad_residue(grhs.value, self.field.p) # Sanity check. rhs_sqrt = self.write_element(self.field.zero(), WriteOps.WITNESS) grhs_sqrt = self.write_element( self.field(sqrt_mod_p(grhs.value, self.field.p)), WriteOps.WITNESS, ) ## %} should_be_rhs = self.mul(rhs_sqrt, rhs_sqrt) should_be_grhs = self.mul(grhs_sqrt, grhs_sqrt) return (rhs, grhs, should_be_rhs, should_be_grhs, rhs_sqrt) class DecompressG1Point(ModuloCircuit): """ A class to decompress a G1 point on an elliptic curve given the x-coordinate. This class is a specialized ModuloCircuit that uses the curve parameters to compute the y-coordinate from a given x-coordinate, ensuring that the point lies on the curve. The y-coordinate is determined using the s_bit, which is extracted from the compressed G1 point. The s_bit indicates which of the two possible y-coordinates (positive or negative) should be selected. """ def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, generic_circuit=True, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] def derive_y_from_x( self, b: ModuloCircuitElement, x: ModuloCircuitElement, ) -> ModuloCircuitElement: """ Derive the two possible y-coordinates from the given x-coordinate on the elliptic curve. Ensures that the point lies on the curve. Assumes that the curve equation is y^2 = x^3 + b. :param x: The x-coordinate as a ModuloCircuitElement. :param b: The curve parameter b as a ModuloCircuitElement. :return: The two possible y-coordinates as a ModuloCircuitElement. No assumption on the order of the two y-coordinates. :raises AssertionError: If the x-coordinate does not lie on the curve. """ assert ( CURVES[self.curve_id].a == 0 ), "This circuit is only supported for curves with a = 0" assert ( self.compilation_mode == 0 ), "This circuit is only supported for CairoZero" # y^2 = x^3 + b x3 = self.mul(x, self.mul(x, x)) rhs = self.add(x3, b) y = self.fp_sqrt(rhs) neg_y = self.neg(y) return (y, neg_y) class ECIPCircuits(ModuloCircuit): def __init__( self, name: str, curve_id: int, compilation_mode: int = 0, generic_circuit: bool = True, ): super().__init__( name=name, curve_id=curve_id, generic_circuit=generic_circuit, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] def _slope_intercept_same_point( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], A_weirstrass: ModuloCircuitElement, ): # Compute doubling slope m = (3x^2 + A) / 2y xA0, yA0 = P three = self.set_or_get_constant(self.field(3)) mA0_num = self.add( self.mul(three, self.mul(xA0, xA0)), A_weirstrass, ) mA0_den = self.add(yA0, yA0) m_A0 = self.div(mA0_num, mA0_den) # Compute intercept b = y - x*m b_A0 = self.sub(yA0, self.mul(xA0, m_A0)) # Compute A2 = -(2*P) xA2 = self.sub(self.mul(m_A0, m_A0), self.add(xA0, xA0)) yA2 = self.sub(self.mul(m_A0, self.sub(xA0, xA2)), yA0) yA2 = self.neg(yA2) # Compute slope between A0 and A2 mA0A2_num = self.sub(yA2, yA0) mA0A2_den = self.sub(xA2, xA0) m_A0A2 = self.div(mA0A2_num, mA0A2_den) # coeff2 = (2 * yA2) * (xA0 - xA2) / (3 * xA2^2 + A - 2 * m * yA2) m_yA2 = self.mul(m_A0A2, yA2) coeff2 = self.div( self.mul(self.add(yA2, yA2), self.sub(xA0, xA2)), self.add( self.mul(three, self.mul(xA2, xA2)), self.sub(A_weirstrass, self.add(m_yA2, m_yA2)), ), ) coeff0 = self.add(coeff2, self.add(m_A0A2, m_A0A2)) # Return slope intercept of A0 (for RHS) and coeff0/2 for LHS return ( m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2, ) def _accumulate_eval_point_challenge_signed_same_point( self, eval_accumulator: ModuloCircuitElement, slope_intercept: tuple[ModuloCircuitElement, ModuloCircuitElement], xA: ModuloCircuitElement, P: tuple[ModuloCircuitElement, ModuloCircuitElement], ep: ModuloCircuitElement, en: ModuloCircuitElement, sign_ep: ModuloCircuitElement, sign_en: ModuloCircuitElement, ) -> ModuloCircuitElement: assert isinstance(ep, ModuloCircuitElement) and isinstance( en, ModuloCircuitElement ) assert isinstance(sign_ep, ModuloCircuitElement) and isinstance( sign_en, ModuloCircuitElement ) m, b = slope_intercept xP, yP = P num = self.sub(xA, xP) # den_tmp = m*xP + b den_tmp = self.add(self.mul(m, xP), b) # den_pos = yP - (m*xP + b) = yP - m*xP - b den_pos = self.sub(yP, den_tmp) # den_neg = -yP - m*xP -b den_neg = self.sub(self.neg(yP), den_tmp) eval_pos = self.mul(self.mul(sign_ep, ep), self.div(num, den_pos)) eval_neg = self.mul(self.mul(sign_en, en), self.div(num, den_neg)) eval_signed = self.add(eval_pos, eval_neg) res = self.add(eval_accumulator, eval_signed) return res def _RHS_finalize_acc( self, eval_accumulator: ModuloCircuitElement, slope_intercept: tuple[ModuloCircuitElement, ModuloCircuitElement], xA: ModuloCircuitElement, Q: tuple[ModuloCircuitElement, ModuloCircuitElement], ): m, b = slope_intercept xQ, yQ = Q num = self.sub(xA, xQ) # den_tmp = m*xQ + b den_tmp = self.add(self.mul(m, xQ), b) # den_neg = -yQ - m*xQ -b den_neg = self.sub(self.neg(yQ), den_tmp) eval_neg = self.div(num, den_neg) res = self.add(eval_accumulator, eval_neg) return res def _eval_function_challenge_single( self, A: tuple[ModuloCircuitElement, ModuloCircuitElement], coeff: ModuloCircuitElement, log_div_a_num: list[ModuloCircuitElement], log_div_a_den: list[ModuloCircuitElement], log_div_b_num: list[ModuloCircuitElement], log_div_b_den: list[ModuloCircuitElement], var_name: str = "xA", ) -> ModuloCircuitElement: xA, yA = A F_A = self.add( self.div( self.eval_horner( log_div_a_num, xA, poly_name="sumdlogdiv_a_num", var_name=var_name ), self.eval_horner( log_div_a_den, xA, poly_name="sumdlogdiv_a_den", var_name=var_name ), ), self.mul( yA, self.div( self.eval_horner( log_div_b_num, xA, poly_name="sumdlogdiv_b_num", var_name=var_name, ), self.eval_horner( log_div_b_den, xA, poly_name="sumdlogdiv_b_den", var_name=var_name, ), ), ), ) return self.mul(coeff, F_A) def _eval_function_challenge_dupl( self, A0: tuple[ModuloCircuitElement, ModuloCircuitElement], A2: tuple[ModuloCircuitElement, ModuloCircuitElement], coeff0: ModuloCircuitElement, coeff2: ModuloCircuitElement, log_div_a_num: list[ModuloCircuitElement], log_div_a_den: list[ModuloCircuitElement], log_div_b_num: list[ModuloCircuitElement], log_div_b_den: list[ModuloCircuitElement], ) -> ModuloCircuitElement: # F = a(x) + y*b(x), a and b being rational functions. # computes coeff0*F(A0) - coeff2*F(A2) xA0, yA0 = A0 xA2, yA2 = A2 F_A0 = self._eval_function_challenge_single( A0, coeff0, log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den, var_name="xA0", ) F_A2 = self._eval_function_challenge_single( A2, coeff2, log_div_a_num, log_div_a_den, log_div_b_num, log_div_b_den, var_name="xA2", ) # return coeff0*F(A0) - coeff2*F(A2) res = self.sub(F_A0, F_A2) return res def _init_function_challenge_dupl( self, xA0: ModuloCircuitElement, xA2: ModuloCircuitElement, log_div_a_num: list[ModuloCircuitElement], log_div_a_den: list[ModuloCircuitElement], log_div_b_num: list[ModuloCircuitElement], log_div_b_den: list[ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: # F = a(x) + y*b(x), a and b being rational functions. # computes F(A0) and F(A2) # Precompute powers of xA0 and xA2 for evaluating the polynomials. xA0_powers = [xA0] xA2_powers = [xA2] for i in range(len(log_div_b_den) - 2): xA0_powers.append(self.mul(xA0_powers[-1], xA0, comment=f"xA0^{i+2}")) xA2_powers.append(self.mul(xA2_powers[-1], xA2, comment=f"xA2^{i+2}")) A_NUM_A0 = self.eval_poly( log_div_a_num, xA0_powers, poly_name="sumdlogdiv_a_num", var_name="xA0" ) A_DEN_A0 = self.eval_poly( log_div_a_den, xA0_powers, poly_name="sumdlogdiv_a_den", var_name="xA0" ) B_NUM_A0 = self.eval_poly( log_div_b_num, xA0_powers, poly_name="sumdlogdiv_b_num", var_name="xA0" ) B_DEN_A0 = self.eval_poly( log_div_b_den, xA0_powers, poly_name="sumdlogdiv_b_den", var_name="xA0" ) A_NUM_A2 = self.eval_poly( log_div_a_num, xA2_powers, poly_name="sumdlogdiv_a_num", var_name="xA2" ) A_DEN_A2 = self.eval_poly( log_div_a_den, xA2_powers, poly_name="sumdlogdiv_a_den", var_name="xA2" ) B_NUM_A2 = self.eval_poly( log_div_b_num, xA2_powers, poly_name="sumdlogdiv_b_num", var_name="xA2" ) B_DEN_A2 = self.eval_poly( log_div_b_den, xA2_powers, poly_name="sumdlogdiv_b_den", var_name="xA2" ) # return F(A0) and F(A2), and the last power of xA0 and xA2 used in a_den (also equal to b_num) a_den_degree = len(log_div_a_den) - 1 assert a_den_degree == len(log_div_b_num) - 1 return ( A_NUM_A0, A_DEN_A0, B_NUM_A0, B_DEN_A0, A_NUM_A2, A_DEN_A2, B_NUM_A2, B_DEN_A2, xA0_powers[a_den_degree - 1], xA2_powers[a_den_degree - 1], ) def _accumulate_function_challenge_dupl( self, a_num_acc_A0: ModuloCircuitElement, a_den_acc_A0: ModuloCircuitElement, b_num_acc_A0: ModuloCircuitElement, b_den_acc_A0: ModuloCircuitElement, a_num_acc_A2: ModuloCircuitElement, a_den_acc_A2: ModuloCircuitElement, b_num_acc_A2: ModuloCircuitElement, b_den_acc_A2: ModuloCircuitElement, xA0: ModuloCircuitElement, xA2: ModuloCircuitElement, xA0_power: ModuloCircuitElement, xA2_power: ModuloCircuitElement, next_a_num_coeff: ModuloCircuitElement, next_a_den_coeff: ModuloCircuitElement, next_b_num_coeff: ModuloCircuitElement, next_b_den_coeff: ModuloCircuitElement, ): # Update accumulators for A0 new_a_num_acc_A0 = self.add(a_num_acc_A0, self.mul(next_a_num_coeff, xA0_power)) next_xA0_power = self.mul(xA0_power, xA0) new_a_den_acc_A0 = self.add( a_den_acc_A0, self.mul(next_a_den_coeff, next_xA0_power) ) new_b_num_acc_A0 = self.add( b_num_acc_A0, self.mul(next_b_num_coeff, next_xA0_power) ) next_b_den_A0_power = self.mul(next_xA0_power, xA0) for _ in range(2): next_b_den_A0_power = self.mul(next_b_den_A0_power, xA0) new_b_den_acc_A0 = self.add( b_den_acc_A0, self.mul(next_b_den_coeff, next_b_den_A0_power) ) # Update accumulators for A2 new_a_num_acc_A2 = self.add(a_num_acc_A2, self.mul(next_a_num_coeff, xA2_power)) next_xA2_power = self.mul(xA2_power, xA2) new_a_den_acc_A2 = self.add( a_den_acc_A2, self.mul(next_a_den_coeff, next_xA2_power) ) new_b_num_acc_A2 = self.add( b_num_acc_A2, self.mul(next_b_num_coeff, next_xA2_power) ) next_b_den_A2_power = next_xA2_power for _ in range(3): next_b_den_A2_power = self.mul(next_b_den_A2_power, xA2) new_b_den_acc_A2 = self.add( b_den_acc_A2, self.mul(next_b_den_coeff, next_b_den_A2_power) ) return ( new_a_num_acc_A0, new_a_den_acc_A0, new_b_num_acc_A0, new_b_den_acc_A0, new_a_num_acc_A2, new_a_den_acc_A2, new_b_num_acc_A2, new_b_den_acc_A2, next_xA0_power, next_xA2_power, ) def _finalize_function_challenge_dupl( self, a_num_acc_A0: ModuloCircuitElement, a_den_acc_A0: ModuloCircuitElement, b_num_acc_A0: ModuloCircuitElement, b_den_acc_A0: ModuloCircuitElement, a_num_acc_A2: ModuloCircuitElement, a_den_acc_A2: ModuloCircuitElement, b_num_acc_A2: ModuloCircuitElement, b_den_acc_A2: ModuloCircuitElement, yA0: ModuloCircuitElement, yA2: ModuloCircuitElement, coeff_A0: ModuloCircuitElement, coeff_A2: ModuloCircuitElement, ): F_A0 = self.add( self.div(a_num_acc_A0, a_den_acc_A0), self.mul(yA0, self.div(b_num_acc_A0, b_den_acc_A0)), comment="a(x0) + y0 b(x0)", ) F_A2 = self.add( self.div(a_num_acc_A2, a_den_acc_A2), self.mul(yA2, self.div(b_num_acc_A2, b_den_acc_A2)), comment="a(x2) + y2 b(x2)", ) # return coeff0*F(A0) - coeff2*F(A2) res = self.sub(self.mul(coeff_A0, F_A0), self.mul(coeff_A2, F_A2)) return res class BasicEC(ModuloCircuit): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, generic_circuit=True, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] def _compute_adding_slope( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], Q: tuple[ModuloCircuitElement, ModuloCircuitElement], ): xP, yP = P xQ, yQ = Q slope = self.div(self.sub(yP, yQ), self.sub(xP, xQ)) return slope def _compute_doubling_slope( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], A: ModuloCircuitElement, ): xP, yP = P # Compute doubling slope m = (3x^2 + A) / 2y three = self.set_or_get_constant(self.field(3)) m_num = self.add( self.mul(three, self.mul(xP, xP)), A, ) m_den = self.add(yP, yP) m = self.div(m_num, m_den) return m def add_points( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], Q: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: xP, yP = P xQ, yQ = Q slope = self._compute_adding_slope(P, Q) slope_sqr = self.mul(slope, slope) nx = self.sub(self.sub(slope_sqr, xP), xQ) ny = self.sub(self.mul(slope, self.sub(xP, nx)), yP) return (nx, ny) def double_point( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], A: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: xP, yP = P slope = self._compute_doubling_slope(P, A) slope_sqr = self.mul(slope, slope) nx = self.sub(self.sub(slope_sqr, xP), xP) ny = self.sub(self.mul(slope, self.sub(xP, nx)), yP) return (nx, ny) def scalar_mul_2_pow_k( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], A: ModuloCircuitElement, k: int, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: for _ in range(k): P = self.double_point(P, A) return P def _is_on_curve_G1_weirstrass( self, x: ModuloCircuitElement, y: ModuloCircuitElement, A: ModuloCircuitElement, b: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: # y^2 = x^3 + ax + b y2 = self.mul(y, y) x3 = self.mul(x, self.mul(x, x)) ax = self.mul(A, x) x3_ax_b = self.add(x3, self.add(ax, b)) return y2, x3_ax_b def negate_point( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement] ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Negate a point in G1.""" x, y = P return (x, self.neg(y)) def add_points( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], Q: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Add two points in G1.""" xP, yP = P xQ, yQ = Q slope = self._compute_adding_slope(P, Q) slope_sqr = self.mul(slope, slope) nx = self.sub(self.sub(slope_sqr, xP), xQ) ny = self.sub(self.mul(slope, self.sub(xP, nx)), yP) return (nx, ny) def double_point_a_eq_0( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Double a point in G1 when curve parameter a=0.""" xP, yP = P three = self.set_or_get_constant(self.field(3)) slope = self.div( self.mul(three, self.mul(xP, xP)), self.add(yP, yP) # 3x^2 # 2y ) slope_sqr = self.mul(slope, slope) nx = self.sub(self.sub(slope_sqr, xP), xP) ny = self.sub(self.mul(slope, self.sub(xP, nx)), yP) return (nx, ny) def triple_point( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], A: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Triple a point in G1.""" xP, yP = P # compute λ1 = (3p.x²+a)/2p.y, xx = self.square(xP) three_xx = self.sum([xx, xx, xx]) m_num = self.add(three_xx, A) λ1 = self.div(m_num, self.double(yP)) # xr = λ1²-2p.x x2 = self.sub(self.square(λ1), self.add(xP, xP)) # omit y2 computation, and # compute λ2 = 2p.y/(x2 − p.x) − λ1. x1x2 = self.sub(xP, x2) λ2 = self.div(self.double(yP), x1x2) λ2 = self.sub(λ2, λ1) # xr = λ²-p.x-x2 xr = self.sub(self.square(λ2), self.add(xP, x2)) # yr = λ(p.x-xr) - p.y yr = self.sub(self.mul(λ2, self.sub(xP, xr)), yP) return (xr, yr) def double_n_times( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], n: int ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Double a point n times in G1.""" Q = P for _ in range(n): Q = self.double_point_a_eq_0(Q) return Q def n_quadruple_and_add( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], adds: list[tuple[ModuloCircuitElement, ModuloCircuitElement]], A_weirstrass: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Quadruple a point n times and add it to the point.""" Q = P for add in adds: Q = self.double_point(Q, A_weirstrass) Q = self.double_and_add(Q, add) return Q def double_and_add( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], add: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Double a point and add it to the point.""" Px, Py = P Qx, Qy = add # compute λ1 = (q.y-p.y)/(q.x-p.x) yqyp = self.sub(Qy, Py) xqxp = self.sub(Qx, Px) λ1 = self.div(yqyp, xqxp) # compute x2 = λ1²-p.x-q.x x2 = self.sub(self.square(λ1), self.add(Px, Qx)) # omit y2 computation # compute -λ2 = λ1+2*p.y/(x2-p.x) ypyp = self.double(Py) x2xp = self.sub(x2, Px) λ2 = self.div(ypyp, x2xp) λ2 = self.add(λ1, λ2) # compute x3 = (-λ2)²-p.x-x2 x3 = self.sub(self.square(λ2), self.add(Px, x2)) # compute y3 = -λ2*(x3 - p.x)-p.y y3 = self.sub(self.mul(λ2, self.sub(x3, Px)), Py) return (x3, y3) class BasicECG2(Fp2Circuits): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, generic_circuit=True, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] def _is_on_curve_G2_weirstrass( self, x0: ModuloCircuitElement, x1: ModuloCircuitElement, y0: ModuloCircuitElement, y1: ModuloCircuitElement, a: ModuloCircuitElement, b0: ModuloCircuitElement, b1: ModuloCircuitElement, ): # y^2 = x^3 + ax + b [Fp2] y2 = self.fp2_square([y0, y1]) x2 = self.fp2_square([x0, x1]) x3 = self.fp2_mul([x0, x1], x2) ax = [self.mul(a, x0), self.mul(a, x1)] ax_b = [self.add(ax[0], b0), self.add(ax[1], b1)] x3_ax_b = [self.add(x3[0], ax_b[0]), self.add(x3[1], ax_b[1])] return y2, x3_ax_b def _compute_adding_slope( self, P: tuple[ tuple[ModuloCircuitElement, ModuloCircuitElement], tuple[ModuloCircuitElement, ModuloCircuitElement], ], Q: tuple[ tuple[ModuloCircuitElement, ModuloCircuitElement], tuple[ModuloCircuitElement, ModuloCircuitElement], ], ): xP, yP = P xQ, yQ = Q slope = self.fp2_div(self.vector_sub(yP, yQ), self.vector_sub(xP, xQ)) return slope def _compute_doubling_slope_a_eq_0( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], ): xP, yP = P # Compute doubling slope m = (3x^2 + A) / 2y three = self.set_or_get_constant(self.field(3)) m_num = self.vector_scale(self.fp2_square(xP), three) m_den = self.vector_add(yP, yP) m = self.fp2_div(m_num, m_den) return m def add_points( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], Q: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: xP, yP = P xQ, yQ = Q slope = self._compute_adding_slope(P, Q) slope_sqr = self.fp2_square(slope) nx = self.vector_sub(self.vector_sub(slope_sqr, xP), xQ) ny = self.vector_sub(self.fp2_mul(slope, self.vector_sub(xP, nx)), yP) return (nx, ny) def double_point_a_eq_0( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: xP, yP = P slope = self._compute_doubling_slope_a_eq_0(P) slope_sqr = self.fp2_square(slope) nx = self.vector_sub(self.vector_sub(slope_sqr, xP), xP) ny = self.vector_sub(self.fp2_mul(slope, self.vector_sub(xP, nx)), yP) return (nx, ny) def double_n_times(self, P, n): Q = P for _ in range(n): Q = self.double_point_a_eq_0(Q) return Q def negate_point( self, P: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: x, y = P return (x, self.vector_neg(y)) def double_and_add( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], add: tuple[ModuloCircuitElement, ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """Double a point and add it to the point.""" Px, Py = P Qx, Qy = add # compute λ1 = (q.y-p.y)/(q.x-p.x) yqyp = self.vector_sub(Qy, Py) xqxp = self.vector_sub(Qx, Px) λ1 = self.fp2_div(yqyp, xqxp) # compute x2 = λ1²-p.x-q.x x2 = self.vector_sub(self.fp2_square(λ1), self.vector_add(Px, Qx)) # omit y2 computation # compute -λ2 = λ1+2*p.y/(x2-p.x) ypyp = self.vector_add(Py, Py) x2xp = self.vector_sub(x2, Px) λ2 = self.fp2_div(ypyp, x2xp) λ2 = self.vector_add(λ1, λ2) # compute x3 = (-λ2)²-p.x-x2 x3 = self.vector_sub(self.fp2_square(λ2), self.vector_add(Px, x2)) # compute y3 = -λ2*(x3 - p.x)-p.y y3 = self.vector_sub(self.fp2_mul(λ2, self.vector_sub(x3, Px)), Py) return (x3, y3) class FakeGLVCircuits(BasicEC): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__(name, curve_id, compilation_mode) def prepare_points_glv_fake_glv( self, Px, P0y, P1y, Qx, Q0y, Phi_P0y, Phi_P1y, Phi_Q0y, Gen, third_root ): P0 = (Px, P0y) P1 = (Px, P1y) Q0 = (Qx, Q0y) S0 = self.add_points(P0, Q0) S1 = (S0[0], self.neg(S0[1])) S2 = self.add_points(P1, Q0) Phi_P0x = self.mul(Px, third_root) Phi_P0 = (Phi_P0x, Phi_P0y) Phi_P1 = (Phi_P0x, Phi_P1y) Phi_Q0x = self.mul(Q0[0], third_root) Phi_Q0 = (Phi_Q0x, Phi_Q0y) Phi_S0 = self.add_points(Phi_P0, Phi_Q0) Phi_S1 = (Phi_S0[0], self.neg(Phi_S0[1])) Phi_S2 = self.add_points(Phi_P1, Phi_Q0) Phi_S3 = (Phi_S2[0], self.neg(Phi_S2[1])) B1 = self.add_points(S1, Phi_S1) # P + Q + Φ(P) + Φ(Q) B2 = self.add_points(S1, Phi_S2) # P + Q + Φ(P) - Φ(Q) B3 = self.add_points(S1, Phi_S3) # P + Q - Φ(P) + Φ(Q) B4 = self.add_points(S1, Phi_S0) # P + Q - Φ(P) - Φ(Q) B5 = self.add_points(S2, Phi_S1) # P - Q + Φ(P) + Φ(Q) B6 = self.add_points(S2, Phi_S2) # P - Q + Φ(P) - Φ(Q) B7 = self.add_points(S2, Phi_S3) # P - Q - Φ(P) + Φ(Q) B8 = self.add_points(S2, Phi_S0) # P - Q - Φ(P) - Φ(Q) B9y = self.neg(B8[1]) # -P + Q + Φ(P) + Φ(Q) B10y = self.neg(B7[1]) # -P + Q + Φ(P) - Φ(Q) B11y = self.neg(B6[1]) # -P + Q - Φ(P) + Φ(Q) B12y = self.neg(B5[1]) # -P + Q - Φ(P) - Φ(Q) B13y = self.neg(B4[1]) # -P - Q + Φ(P) + Φ(Q) B14y = self.neg(B3[1]) # -P - Q + Φ(P) - Φ(Q) B15y = self.neg(B2[1]) # -P - Q - Φ(P) + Φ(Q) B16y = self.neg(B1[1]) # -P - Q - Φ(P) - Φ(Q) Acc = self.add_points(B1, Gen) return ( B1, B2, B3, B4, B5, B6, B7, B8, B9y, B10y, B11y, B12y, B13y, B14y, B15y, B16y, Phi_P0x, Phi_Q0x, Acc, ) def prepare_points_fake_glv( self, P: tuple[ModuloCircuitElement, ModuloCircuitElement], Q: tuple[ModuloCircuitElement, ModuloCircuitElement], s2_sign: ModuloCircuitElement, A_weirstrass: ModuloCircuitElement, ): P = (P[0], P[1]) Q = (Q[0], Q[1]) table_P = [None, None, None] # table_P[0] = (P[0], self.neg(P[0])) # Unused table_P[1] = P table_P[2] = self.triple_point(P, A_weirstrass) table_R = [None, None, None] R_signed = [Q[0], self.mul(s2_sign, Q[1])] table_R[0] = self.negate_point(R_signed) table_R[1] = R_signed table_R[2] = self.triple_point(R_signed, A_weirstrass) T1 = self.add_points(table_P[2], table_R[2]) T2 = Acc = self.add_points(table_P[1], table_R[1]) T3 = self.add_points(table_P[2], table_R[1]) T4 = self.add_points(table_P[1], table_R[2]) T5y = self.neg(T2[1]) T6y = self.neg(T1[1]) T7y = self.neg(T4[1]) T8y = self.neg(T3[1]) T9 = self.add_points(table_P[2], table_R[0]) _neg_table_R_verify_2 = self.negate_point(table_R[2]) T10 = self.add_points(table_P[1], _neg_table_R_verify_2) T11 = self.add_points(table_P[2], _neg_table_R_verify_2) T12 = self.add_points(table_R[0], table_P[1]) T13y = self.neg(T10[1]) T14y = self.neg(T9[1]) T15y = self.neg(T12[1]) T16y = self.neg(T11[1]) # P0y = table_P[0][1] return ( T1, T2, T3, T4, T5y, T6y, T7y, T8y, T9, T10, T11, T12, T13y, T14y, T15y, T16y, table_R[2], table_R[0][1], # R0y ) ================================================ FILE: hydra/garaga/precompiled_circuits/final_exp.py ================================================ """ Deprecated Final Exp Circuits since we now use the final exp witness. Kept for reference/in case we need it in the future. """ import copy from random import randint from garaga.algebra import get_sparsity from garaga.curves import BLS12_381_ID, BN254_ID, CURVES, CurveID from garaga.extension_field_modulo_circuit import ( AccPolyInstructionType, ExtensionFieldModuloCircuit, ModuloCircuitElement, Polynomial, PyFelt, ) from garaga.hints.extf_mul import ( nondeterministic_extension_field_mul_divmod, nondeterministic_square_torus, ) from garaga.hints.frobenius import get_frobenius_maps, get_V_torus_powers from garaga.modulo_circuit import WriteOps from garaga.poseidon_transcript import CairoPoseidonTranscript class FinalExpTorusCircuit(ExtensionFieldModuloCircuit): def __init__( self, name: str, curve_id: int, extension_degree: int, hash_input: bool = True ): super().__init__( name=name, curve_id=curve_id, extension_degree=extension_degree, hash_input=hash_input, ) self.frobenius_maps = {} self.v_torus_powers_inv = {} for i in [1, 2, 3]: _, self.frobenius_maps[i] = get_frobenius_maps( curve_id=curve_id, extension_degree=extension_degree, frob_power=i ) self.v_torus_powers_inv[i] = get_V_torus_powers( curve_id, extension_degree, i ).get_coeffs() # Write to circuit. Note : add_constant will return existing circuit constant if it already exists. self.v_torus_powers_inv[i] = [ self.set_or_get_constant(v) for v in self.v_torus_powers_inv[i] ] self.ops_counter.update({"MUL_TORUS": 0, "SQUARE_TORUS": 0}) self.set_or_get_constant(self.field(-1)) def final_exp_part1(self, X: list[PyFelt]) -> list[ModuloCircuitElement]: return NotImplementedError def square_torus( self: ExtensionFieldModuloCircuit, X: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Computes the square of an element X in Torus Based Arithmetic SQ = 1/2(X+ v/X) <=> v = X (2SQ - X) Use hint to avoid v/X inversion. From SQ and X, compute v = X (2SQ - X). """ self.ops_counter["SQUARE_TORUS"] += 1 SQ: list[PyFelt] = nondeterministic_square_torus( X, self.curve_id, biject_from_direct=True ) SQ = self.write_elements(SQ, WriteOps.COMMIT) two_SQ = self.vector_add(SQ, SQ) two_SQ_min_X = self.vector_sub(two_SQ, X) # %{ Q, V = nondeterministic_extension_field_mul_divmod( [X, two_SQ_min_X], self.curve_id, self.extension_degree ) Q = Polynomial(Q) # Sanity check : ensure V is indeed V(x) = 1*x. assert all([v.value == 0 for i, v in enumerate(V) if i != 1]) assert V[1].value == 1, f"V(x) = {V[1].value}" # %} # Hacky way to pass SQ as R so that it is hashed. # Result is known in advance to be V, and not SQ. # R_sparsity encoded as this bypasses the usage of R coefficients. # Essentially, r_sparsity encodes R=V direcly by its static sparsity. self.accumulate_poly_instructions[0].append( AccPolyInstructionType.SQUARE_TORUS, Pis=[X, two_SQ_min_X], Q=Q, R=SQ, r_sparsity=[0, 2] + [0] * (self.extension_degree - 2), ) return SQ def n_square_torus(self, X: list[PyFelt], n: int) -> list[PyFelt]: result = self.square_torus(X) for _ in range(n - 1): result = self.square_torus(result) return result def mul_torus( self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Computes Mul(X,Y) = (X*Y + v)/(X+Y) """ self.ops_counter["MUL_TORUS"] += 1 xy = self.extf_mul([X, Y], self.extension_degree) num = copy.deepcopy(xy) num[1] = self.add(xy[1], self.set_or_get_constant(1)) den = self.vector_add(X, Y) return self.extf_div(num, den, self.extension_degree) def inverse_torus(self, X: list[ModuloCircuitElement]): return [self.neg(x) for x in X] def decompress_torus( self, X: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Returns (X + w) / (X - w). Size is doubled. """ zero = self.set_or_get_constant(0) num = [ X[0], self.set_or_get_constant(1), X[1], zero, X[2], zero, X[3], zero, X[4], zero, X[5], zero, ] den = num.copy() den[1] = self.set_or_get_constant(-1) return self.extf_div(num, den, 2 * self.extension_degree, acc_index=1) def frobenius_torus( self, X: list[ModuloCircuitElement], frob_power: int ) -> list[ModuloCircuitElement]: frob = [None] * self.extension_degree for i, list_op in enumerate(self.frobenius_maps[frob_power]): list_op_result = [] for index, constant in list_op: if constant == 1: list_op_result.append(X[index]) else: list_op_result.append( self.mul( X[index], self.set_or_get_constant(self.field(constant)) ) ) frob[i] = list_op_result[0] for op_res in list_op_result[1:]: frob[i] = self.add(frob[i], op_res) if len(self.v_torus_powers_inv[frob_power]) == 1: return self.vector_scale(frob, self.v_torus_powers_inv[frob_power][0]) else: Y = [ self.set_or_get_constant(v) for v in self.v_torus_powers_inv[frob_power] ] return self.extf_mul( Ps=[frob, Y], extension_degree=self.extension_degree, Ps_sparsities=[None, get_sparsity(Y)], ) def easy_part( self, num: list[PyFelt], den: list[PyFelt] ) -> list[ModuloCircuitElement]: """ Computes the easy part of the final exponentiation. """ assert len(num) == 6, f"Expected 6 elements in num, got {len(num)}" assert len(den) == 6, f"Expected 6 elements in den, got {len(den)}" num = self.write_elements(num, operation=WriteOps.INPUT) num = self.vector_neg(num) den = self.write_elements(den, WriteOps.INPUT) c = self.extf_div(num, den, self.extension_degree) t0 = self.frobenius_torus(c, 2) c = self.mul_torus(t0, c) return c def final_exp_finalize(self, t0: list[PyFelt], t2: list[PyFelt]): # Computes Decompress Torus(MulTorus(t0, t2)). # Only valid if (t0 + t2) != 0. t0 = self.write_elements(t0, WriteOps.INPUT) t2 = self.write_elements(t2, WriteOps.INPUT) # for x in t0: # print(f"T0 input {hex(x.value)}") # for x in t2: # print(f"T2 input {hex(x.value)}") mul = self.mul_torus(t0, t2) res = self.decompress_torus(mul) self.finalize_circuit() return res class GaragaBLS12_381FinalExp(FinalExpTorusCircuit): def __init__( self, name: str = None, hash_input: bool = True, init_hash: int = None ): super().__init__( name=name or "Final Exp BLS12_381", curve_id=BLS12_381_ID, extension_degree=6, hash_input=hash_input, ) if init_hash is not None: self.transcript = CairoPoseidonTranscript(init_hash) def expt_half_torus(self, X: list[ModuloCircuitElement]): z = self.square_torus(X) z = self.mul_torus(X, z) z = self.square_torus(z) z = self.square_torus(z) z = self.mul_torus(X, z) z = self.n_square_torus(z, 3) z = self.mul_torus(X, z) z = self.n_square_torus(z, 9) z = self.mul_torus(X, z) z = self.n_square_torus(z, 32) z = self.mul_torus(X, z) z = self.n_square_torus(z, 15) z = self.inverse_torus(z) return z def expt_torus(self, X): z = self.expt_half_torus(X) return self.square_torus(z) def final_exp_part1(self, num: list[PyFelt], den: list[PyFelt]) -> list[PyFelt]: """ X is a list of 12 elements in the tower of extension fields. """ c = self.easy_part(num, den) # 2. Hard part (up to permutation) # 3(p⁴-p²+1)/r # Daiki Hayashida, Kenichiro Hayasaka and Tadanori Teruya # https://eprint.iacr.org/2020/875.pdf # performed in torus compressed form t0_0 = self.square_torus(c) t1 = self.expt_half_torus(t0_0) t2 = self.inverse_torus(c) t1 = self.mul_torus(t1, t2) t2 = self.expt_torus(t1) t1 = self.inverse_torus(t1) t1 = self.mul_torus(t1, t2) t2 = self.expt_torus(t1) t1 = self.frobenius_torus(t1, 1) t1 = self.mul_torus(t1, t2) t0 = self.expt_torus(t1) t2 = self.expt_torus(t0) t0 = self.frobenius_torus(t1, 2) t1 = self.inverse_torus(t1) t1 = self.mul_torus(t1, t2) # Output in fixed order (t0, c, _sum): t1 = self.mul_torus(t1, t0) self.extend_output(t1) c = self.mul_torus(c, t0_0) self.extend_output(c) # The final exp result is DecompressTorus(MulTorus(c, t1) # MulTorus(t1, c) = (t1*c + v)/(t1 + c). # (t1+c = 0) ==> MulTorus(t1, c) is E12.One() in the Torus. _sum = self.vector_add(t1, c) self.extend_output(_sum) # From this case we can conclude the result is 1 or !=1 without decompression. # In case we want to decompress to get the result in GT, # we might need to decompress with another circuit, if the result is not 1 (_sum!=0). return t1, c, _sum class GaragaBN254FinalExp(FinalExpTorusCircuit): def __init__( self, name: str = None, hash_input: bool = True, init_hash: int = None ): super().__init__( name=name or "Final Exp BN254", curve_id=BN254_ID, extension_degree=6, hash_input=hash_input, ) if init_hash is not None: self.transcript = CairoPoseidonTranscript(init_hash) def expt_torus(self, X: list[PyFelt]): t3 = self.square_torus(X) t5 = self.square_torus(t3) result = self.square_torus(t5) t0 = self.square_torus(result) t2 = self.mul_torus(X, t0) t0 = self.mul_torus(t3, t2) t1 = self.mul_torus(X, t0) t4 = self.mul_torus(result, t2) t6 = self.square_torus(t2) t1 = self.mul_torus(t0, t1) t0 = self.mul_torus(t3, t1) t6 = self.n_square_torus(t6, 6) t5 = self.mul_torus(t5, t6) t5 = self.mul_torus(t4, t5) t5 = self.n_square_torus(t5, 7) t4 = self.mul_torus(t4, t5) t4 = self.n_square_torus(t4, 8) t4 = self.mul_torus(t0, t4) t3 = self.mul_torus(t3, t4) t3 = self.n_square_torus(t3, 6) t2 = self.mul_torus(t2, t3) t2 = self.n_square_torus(t2, 8) t2 = self.mul_torus(t0, t2) t2 = self.n_square_torus(t2, 6) t2 = self.mul_torus(t0, t2) t2 = self.n_square_torus(t2, 10) t1 = self.mul_torus(t1, t2) t1 = self.n_square_torus(t1, 6) t0 = self.mul_torus(t0, t1) z = self.mul_torus(result, t0) return z def final_exp_part1( self, num: list[PyFelt], den: list[PyFelt] ) -> list[ModuloCircuitElement]: """ single pairing -> unsafe = True = 1 double pairing -> unsafe = False = 0 """ c = self.easy_part(num, den) # 2. Hard part (up to permutation) # 2x₀(6x₀²+3x₀+1)(p⁴-p²+1)/r # Duquesne and Ghammam # https://eprint.iacr.org/2015/192.pdf # Fuentes et al. (alg. 6) # performed in torus compressed form t0 = self.expt_torus(c) t0 = self.inverse_torus(t0) t0 = self.square_torus(t0) t1 = self.square_torus(t0) t1 = self.mul_torus(t0, t1) t2 = self.expt_torus(t1) t2 = self.inverse_torus(t2) t3 = self.inverse_torus(t1) t1 = self.mul_torus(t2, t3) t3 = self.square_torus(t2) t4 = self.expt_torus(t3) t4 = self.mul_torus(t1, t4) t3 = self.mul_torus(t0, t4) t0 = self.mul_torus(t2, t4) t0 = self.mul_torus(c, t0) t2 = self.frobenius_torus(t3, 1) t0 = self.mul_torus(t2, t0) t2_tmp = self.frobenius_torus(t4, 2) t2 = self.inverse_torus(c) t2 = self.mul_torus(t2, t3) # Output in fixed order (t0, t2, _sum): t0 = self.mul_torus(t0, t2_tmp) self.extend_output(t0) t2 = self.frobenius_torus(t2, 3) self.extend_output(t2) # The final exp result is DecompressTorus(MulTorus(t0, t2)). # MulTorus(t0, t2) = (t0*t2 + v)/(t0 + t2). # (T0+T2 = 0) ==> MulTorus(t0, t2) is one in the Torus. _sum = self.vector_add(t0, t2) self.extend_output(_sum) # From this case we can conclude the result is 1 or !=1 without decompression. # In case we want to decompress to get the result in GT, # we might need to decompress with another circuit, if the result is not 1 (_sum!=0). return t0, t2, _sum GaragaFinalExp = { CurveID.BN254: GaragaBN254FinalExp, CurveID.BLS12_381: GaragaBLS12_381FinalExp, } def test_final_exp(curve_id: CurveID): from garaga.points import G1G2Pair, G1Point, G2Point, tower_to_direct order = CURVES[curve_id.value].n pairs = [] n_pairs = 1 unsafe = True if n_pairs == 1 else False for _ in range(n_pairs): n1, n2 = randint(1, order), randint(1, order) p1, p2 = G1Point.get_nG(curve_id, n1), G2Point.get_nG(curve_id, n2) pairs.append(G1G2Pair(p1, p2)) base_class = GaragaFinalExp[curve_id] part1 = base_class(hash_input=False) field = part1.field XT: list[int] = G1G2Pair.miller(pairs).value_coeffs ET: list[int] = G1G2Pair.pair(pairs).value_coeffs XT = [part1.field(x) for x in XT] ET = [part1.field(x) for x in ET] XD = tower_to_direct(XT, curve_id.value, 12) ED = tower_to_direct(ET, curve_id.value, 12) num_indexes = [0, 2, 4, 6, 8, 10] den_indexes = [1, 3, 5, 7, 9, 11] num = [XD[i] for i in num_indexes] if unsafe: den = [XD[i] for i in den_indexes] else: if [x.value for x in [XD[i] for i in den_indexes]] == [0, 0, 0, 0, 0, 0]: den = [ field.one(), field.zero(), field.zero(), field.zero(), field.zero(), field.zero(), ] else: den = [XD[i] for i in den_indexes] t0, t2, _sum = part1.final_exp_part1(num, den) part1.finalize_circuit() _sum = [x.value for x in _sum] part2 = base_class(hash_input=False) if _sum == [0, 0, 0, 0, 0, 0]: f = [field.one()] + [field.zero] * 11 else: t0 = [x.felt for x in t0] t2 = [x.felt for x in t2] f = part2.final_exp_finalize(t0, t2) assert [f.value for f in f] == [ e.value for e in ED ], f"Final exp in circuit and internal do not match f={[f.value for f in f]}\ne={[e.value for e in ED]}" # print(f"{curve_id} Final Exp random test pass") return part1, part2 if __name__ == "__main__": pass from garaga.curves import CurveID, Polynomial # def test_frobenius_torus(): # from archive_tmp.bn254.pairing_final_exp import frobenius_torus # field = get_base_field(CurveID.BN254.value) # X = [field(random.randint(0, field.p - 1)) for _ in range(6)] # t = FinalExpTorusCircuit("test", CurveID.BN254.value, 6) # t.create_powers_of_Z(field(2)) # X = t.write_elements(X) # XF = t.frobenius_torus(X, 1) # # Xpoly = Polynomial([x.felt for x in X]) # # XFpoly = Xpoly.pow(field.p, get_irreducible_poly(CurveID.BN254.value, )) # # assert t.finalize_circuit() # # t.values_segment = t.values_segment.non_interactive_transform() # TT = frobenius_torus([x.value for x in X]) # assert all(x.value == y for x, y in zip(XF, TT)) # t.print_value_segment() # test_final_exp(CurveID.BN254) # test_final_exp(CurveID.BLS12_381) ================================================ FILE: hydra/garaga/precompiled_circuits/fp2.py ================================================ from garaga.algebra import Fp2, ModuloCircuitElement from garaga.hints.extf_mul import nondeterministic_extension_field_div from garaga.modulo_circuit import ModuloCircuit, WriteOps class Fp2Circuits(ModuloCircuit): """ Implements circuits for Fp2 field operations. """ def __init__( self, name: str, curve_id: int, generic_circuit: bool = False, compilation_mode: int = 0, ): super().__init__( name=name, curve_id=curve_id, generic_circuit=generic_circuit, compilation_mode=compilation_mode, ) def fp2_is_non_zero( self, a: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Returns [1,0] if a ≠ 0, [0,0] if a == 0, working in Fp2. An Fp2 element is non-zero if either its real or imaginary part is non-zero. """ # Check if real part is non-zero real_is_non_zero = self.fp_is_non_zero(a[0]) # Check if imaginary part is non-zero imag_is_non_zero = self.fp_is_non_zero(a[1]) # Either part must be non-zero for the Fp2 element to be non-zero # Using 1-(1-a)(1-b) = a + b - ab to compute OR result = self.sub( self.add(real_is_non_zero, imag_is_non_zero), self.mul(real_is_non_zero, imag_is_non_zero), ) # Return as Fp2 element [result, 0] return [result, self.set_or_get_constant(0)] def fp2_mul(self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement]): # Assumes the irreducible poly is X^2 + 1. assert len(X) == len(Y) == 2 and all( isinstance(x, ModuloCircuitElement) and isinstance(y, ModuloCircuitElement) for x, y in zip(X, Y) ) # xy = (x0 + i*x1) * (y0 + i*y1) = (x0*y0 - x1*y1) + i * (x0*y1 + x1*y0) return [ self.sub( self.mul(X[0], Y[0], comment="Fp2 mul start"), self.mul(X[1], Y[1]), comment="Fp2 mul real part end", ), self.add( self.mul(X[0], Y[1]), self.mul(X[1], Y[0]), comment="Fp2 mul imag part end", ), ] def fp2_mul_by_non_residue(self, X: list[ModuloCircuitElement]): assert len(X) == 2 and all(isinstance(x, ModuloCircuitElement) for x in X) if self.curve_id == 1: # Non residue (1,1) # (a0 + i*a1) * (1 + i) a_tmp = self.add(X[0], X[1]) a = self.add(a_tmp, a_tmp) b = X[0] z_a0 = self.sub(b, X[1]) z_a1 = self.sub(self.sub(a, b), X[1]) return [z_a0, z_a1] elif self.curve_id == 0: # Non residue (9, 1) # (a0 + i*a1) * (9 + i) a_tmp = self.add(X[0], X[1]) a = self.mul(a_tmp, self.set_or_get_constant(10)) b = self.mul(X[0], self.set_or_get_constant(9)) z_a0 = self.sub(b, X[1]) z_a1 = self.sub(self.sub(a, b), X[1]) return [z_a0, z_a1] else: raise ValueError( f"Unsupported curve id for fp2 mul by non residue: {self.curve_id}" ) def fp2_square(self, X: list[ModuloCircuitElement]): # Assumes the irreducible poly is X^2 + 1. # x² = (x0 + i x1)² = (x0² - x1²) + 2 * i * x0 * x1 = (x0+x1)(x0-x1) + i * 2 * x0 * x1. # (x0+x1)*(x0-x1) is cheaper than x0² - x1². (2 ADD + 1 MUL) vs (1 ADD + 2 MUL) (16 vs 20 steps) assert len(X) == 2 and all(isinstance(x, ModuloCircuitElement) for x in X) return [ self.mul(self.add(X[0], X[1]), self.sub(X[0], X[1])), self.double(self.mul(X[0], X[1])), ] def fp2_sqrt( self, element: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Computes "a" square root of a field element. /!\ Warning : This circuit is non deterministic /!\ /!\ Two square roots exist for any non-zero element, and no constraint is enforced to select any of them /!\ Raises ValueError if the element is not a quadratic residue. """ assert self.compilation_mode == 0, "fp2_sqrt is not supported in cairo 1 mode" root = Fp2(element[0].felt, element[1].felt).sqrt() if root is None: raise ValueError("No square root found for the given element") if not root.lexicographically_largest: root = Fp2.zero(element[0].p).__sub__(root) root = self.write_elements([root.a0, root.a1], WriteOps.WITNESS) self.fp2_mul_and_assert(root, root, element, comment="Fp2 sqrt") return root def fp2_inv(self, X: list[ModuloCircuitElement]): assert len(X) == 2 and all(isinstance(x, ModuloCircuitElement) for x in X) t0 = self.mul(X[0], X[0], comment="Fp2 Inv start") t1 = self.mul(X[1], X[1]) t0 = self.add(t0, t1) t1 = self.inv(t0) inv0 = self.mul(X[0], t1, comment="Fp2 Inv real part end") inv1 = self.neg(self.mul(X[1], t1), comment="Fp2 Inv imag part end") return [inv0, inv1] def fp2_div(self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement]): assert len(X) == len(Y) == 2 and all( isinstance(x, ModuloCircuitElement) and isinstance(y, ModuloCircuitElement) for x, y in zip(X, Y) ) if self.compilation_mode == 0: x_over_y = nondeterministic_extension_field_div(X, Y, self.curve_id, 2) x_over_y = self.write_elements(x_over_y, WriteOps.WITNESS) # x_over_y = d0 + i * d1 # y = y0 + i * y1 # x = x_over_y*y = d0*y0 - d1*y1 + i * (d0*y1 + d1*y0) self.sub_and_assert( a=self.mul(x_over_y[0], Y[0]), b=self.mul(x_over_y[1], Y[1]), c=X[0] ) self.add_and_assert( a=self.mul(x_over_y[0], Y[1]), b=self.mul(x_over_y[1], Y[0]), c=X[1] ) return x_over_y elif self.compilation_mode == 1: # Todo : consider passing as calldata if possible. inv = self.fp2_inv(Y) return self.fp2_mul(X, inv) def fp2_frobenius_map( self, element: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Applies the Frobenius map to an element in F_{p^2}. For an element a + bi, returns a - bi. This is because: (a + bi)^p = a^p + (bi)^p = a^p + b^p * i^p In Fp: a^p = a, b^p = b In Fp2: i^p = -i (p is odd > 2) Therefore: (a + bi)^p = a - bi """ a, b = element # element = a + bi return [a, self.neg(b)] # return a - bi def fp2_add( self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: # Assumes elements are represented as pairs (a + bi) return self.vector_add(X, Y) def fp2_sub(self, X: list[ModuloCircuitElement], Y: list[ModuloCircuitElement]): # Assumes elements are represented as pairs (a + bi) return self.vector_sub(X, Y) def fp2_mul_and_assert( self, a: list[ModuloCircuitElement], b: list[ModuloCircuitElement], c: list[ModuloCircuitElement], comment: str | None = None, ): """ Multiplies two Fp2 elements a and b and asserts the result equals c. For a = (a0 + i*a1) and b = (b0 + i*b1), asserts: c0 = a0*b0 - a1*b1 c1 = a0*b1 + a1*b0 """ assert ( self.compilation_mode == 0 ), "fp2_mul_and_assert is not supported in cairo 1 mode" assert len(a) == len(b) == len(c) == 2, "Fp2 elements must be length 2" # Calculate intermediate products a0b0 = self.mul(a[0], b[0], comment=f"{comment}: a0*b0" if comment else None) a1b1 = self.mul(a[1], b[1], comment=f"{comment}: a1*b1" if comment else None) a0b1 = self.mul(a[0], b[1], comment=f"{comment}: a0*b1" if comment else None) a1b0 = self.mul(a[1], b[0], comment=f"{comment}: a1*b0" if comment else None) # Assert real part: c0 = a0*b0 - a1*b1 self.add_and_assert( a=a0b0, b=self.neg(a1b1), c=c[0], comment=f"{comment}: assert real part" if comment else None, ) # Assert imaginary part: c1 = a0*b1 + a1*b0 self.add_and_assert( a=a0b1, b=a1b0, c=c[1], comment=f"{comment}: assert imaginary part" if comment else None, ) return c def fp2_eval_horner( self, poly: list[ModuloCircuitElement], # [a0_real, a0_imag, a1_real, a1_imag, ...] z: list[ModuloCircuitElement], # z = [real, imag] poly_name: str = None, var_name: str = "z", ) -> list[ModuloCircuitElement]: """ Evaluates a polynomial with Fp2 coefficients at point z using Horner's method. Assumes that the polynomial is in the form a0 + a1*z + a2*z^2 + ... + an*z^n, indexed with the constant coefficient first. Coefficients are stored in a flat array where each consecutive pair represents the real and imaginary parts of an Fp2 element. Args: poly: Flat list of coefficients [a0_real, a0_imag, a1_real, a1_imag, ...] z: The Fp2 point to evaluate at, represented as [real, imag] poly_name: Optional name for debugging var_name: Optional variable name for debugging Returns: [real, imag] representing the result in Fp2 """ if poly_name is None: poly_name = "UnnamedPoly" assert len(poly) % 2 == 0, "Polynomial coefficients array must have even length" n_coeffs = len(poly) // 2 # Start with the highest degree coefficient acc = [poly[-2], poly[-1]] # Get last pair [real, imag] # Iterate through remaining coefficients in reverse order for i in range(n_coeffs - 2, -1, -1): acc = self.fp2_add( self.fp2_mul( acc, z, ), [poly[2 * i], poly[2 * i + 1]], # Get i-th coefficient pair ) return acc ================================================ FILE: hydra/garaga/precompiled_circuits/isogeny.py ================================================ from garaga.curves import CURVES, CurveID from garaga.extension_field_modulo_circuit import ModuloCircuitElement from garaga.modulo_circuit import ModuloCircuit from garaga.precompiled_circuits.fp2 import Fp2Circuits from garaga.signature import get_isogeny_to_g1_map, get_isogeny_to_g2_map class IsogenyG2(Fp2Circuits): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=False, ) self.curve = CURVES[curve_id] def set_consts(self): x_rational, y_rational = get_isogeny_to_g2_map(CurveID(self.curve_id)) self.x_num = [ self.set_or_get_constant(c) for c in x_rational.numerator.coefficients ] self.x_den = [ self.set_or_get_constant(c) for c in x_rational.denominator.coefficients ] self.y_num = [ self.set_or_get_constant(c) for c in y_rational.numerator.coefficients ] self.y_den = [ self.set_or_get_constant(c) for c in y_rational.denominator.coefficients ] def run_isogeny( self, x: list[ModuloCircuitElement], y: list[ModuloCircuitElement] ) -> tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]: """ Runs the isogeny to G2 map. """ self.set_consts() x_affine_num = self.fp2_eval_horner(self.x_num, x, "x_num") x_affine_den = self.fp2_eval_horner(self.x_den, x, "x_den") x_affine = self.fp2_div(x_affine_num, x_affine_den) y_affine_num = self.fp2_eval_horner(self.y_num, x, "y_num") y_affine_den = self.fp2_eval_horner(self.y_den, x, "y_den") y_affine_eval = self.fp2_div(y_affine_num, y_affine_den) y_affine = self.fp2_mul(y_affine_eval, y) return x_affine, y_affine class IsogenyG1(ModuloCircuit): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=False, ) self.curve = CURVES[curve_id] def set_consts(self): """ Sets the constants for the isogeny to G1 map. """ x_rational, y_rational = get_isogeny_to_g1_map(CurveID(self.curve_id)) self.x_num = [ self.set_or_get_constant(c) for c in x_rational.numerator.coefficients ] self.x_den = [ self.set_or_get_constant(c) for c in x_rational.denominator.coefficients ] self.y_num = [ self.set_or_get_constant(c) for c in y_rational.numerator.coefficients ] self.y_den = [ self.set_or_get_constant(c) for c in y_rational.denominator.coefficients ] def run_isogeny( self, x: ModuloCircuitElement, y: ModuloCircuitElement ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: """ Runs the isogeny to G1 map. """ self.set_consts() x_affine_num = self.eval_horner(self.x_num, x, "x_num") x_affine_den = self.eval_horner(self.x_den, x, "x_den") x_affine = self.div(x_affine_num, x_affine_den) y_affine_num = self.eval_horner(self.y_num, x, "y_num") y_affine_den = self.eval_horner(self.y_den, x, "y_den") y_affine_eval = self.div(y_affine_num, y_affine_den) y_affine = self.mul(y_affine_eval, y) return x_affine, y_affine if __name__ == "__main__": circuit = IsogenyG1("isogeny", 1) # BLS12-381 field_x = circuit.write_element( circuit.field( 1412853964218444964438936699552956047210482383152224645596624291427056376487356261681298103080878386132407858666637 ) ) field_y = circuit.write_element( circuit.field( 752734926215712395741522221355891264404138695398702662135908094550118515106801651502315795564392519475687558113863 ) ) x_affine, y_affine = circuit.run_isogeny(field_x, field_y) ================================================ FILE: hydra/garaga/precompiled_circuits/map_to_curve.py ================================================ from garaga.algebra import PyFelt from garaga.curves import CURVES from garaga.extension_field_modulo_circuit import ModuloCircuitElement from garaga.modulo_circuit import ModuloCircuit, WriteOps from garaga.precompiled_circuits.fp2 import Fp2Circuits class MapToCurveG2(Fp2Circuits): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=True, ) self.curve = CURVES[curve_id] def set_consts(self): # Standard G2 curve parameters for BLS12-381 # ToDo: Derive from definitions.py self.swu_a = [ self.set_or_get_constant(0), # real part self.set_or_get_constant(240), # imaginary part ] self.swu_b = [ self.set_or_get_constant(1012), # real part self.set_or_get_constant(1012), # imaginary part ] self.swu_z = [ self.set_or_get_constant(-2), # real part self.set_or_get_constant(-1), # imaginary part ] self.one = [ self.set_or_get_constant(1), # real part self.set_or_get_constant(0), # imaginary part ] self.zero = [ self.set_or_get_constant(0), # real part self.set_or_get_constant(0), # imaginary part ] def map_to_curve_part_1(self, input_value: list[ModuloCircuitElement]): """ Implements the first part of the Simplified SWU map-to-curve algorithm in G2. This maps a field element to a point on the curve E': y² = x³ + a*x + b. The algorithm follows these steps: 1. Let u be the input field element 2. Calculate intermediate values: - t = z²u⁴ + zu² (where z is the SWU constant) - x₁ = (-b/a) * (1 + 1/(z²u⁴ + zu²)) Args: input_value: Field element u in Fp2 to be mapped to the curve Returns: tuple: (g1x, div) where: - g1x is x³ + ax + b evaluated at the calculated x₁ - div is an intermediate value needed for the full calculation """ # Calculate u² and related terms u2 = self.fp2_square(input_value) # u² zeta_u2 = self.fp2_mul(self.swu_z, u2) # z·u² zeta_u2_square = self.fp2_square(zeta_u2) # z²u⁴ ta = self.fp2_add(zeta_u2_square, zeta_u2) # t = z²u⁴ + zu² neg_ta = self.fp2_sub(self.zero, ta) # -t num_x1 = self.fp2_mul(self.swu_b, self.fp2_add(ta, self.one)) # b(t + 1) # Handle special case when t = 0 is_non_zero = self.fp2_is_non_zero(neg_ta) # 1 if t ≠ 0, 0 if t = 0 neg_ta_or_z = self.fp2_add( self.fp2_mul(self.fp2_sub(self.one, is_non_zero), self.swu_z), # z if t = 0 self.fp2_mul(is_non_zero, neg_ta), # -t if t ≠ 0 ) # Calculate x₁ numerator and denominator div = self.fp2_mul(self.swu_a, neg_ta_or_z) # a·(-t) or a·z num2_x1 = self.fp2_square(num_x1) # (b(t + 1))² div2 = self.fp2_square(div) # (a·(-t))² div3 = self.fp2_mul(div, div2) # (a·(-t))³ # Calculate g(x₁) = x₁³ + ax₁ + b num_gx1 = self.fp2_add( self.fp2_mul( self.fp2_add(num2_x1, self.fp2_mul(self.swu_a, div2)), # x₁² # ax₁ num_x1, # ·x₁ (completing the x₁³ term) ), self.fp2_mul(self.swu_b, div3), # + b ) g1x = self.fp2_mul(num_gx1, self.fp2_inv(div3)) # Final result normalized return [g1x, div, num_x1, zeta_u2] def compute_initial_coordinates_quadratic( self, field: list[ModuloCircuitElement], g1x: list[ModuloCircuitElement], div: list[ModuloCircuitElement], num_x1: list[ModuloCircuitElement], ): """ Computes the initial coordinates for the map-to-curve operation when g1x is a quadratic residue. This function computes the initial y-coordinate before sign adjustment. IMPORTANT: This function should only be called when g1x is a quadratic residue, meaning there exists a y such that y² = g1x in the field Fp2. If g1x is not a quadratic residue, the fp2_sqrt operation will fail. The algorithm follows these steps: 1. Compute y = √(g1x) where g1x = x³ + ax + b (requires g1x to be a quadratic residue) 2. Compute x = num_x1/div to get the x-coordinate in affine form Args: field: The original input field element g1x: The value x³ + ax + b from the first part (must be a quadratic residue) div: The denominator from the first part num_x1: The numerator for x from the first part Returns: list: [x_affine, y_initial, field] where: - x_affine: The final x-coordinate - y_initial: The initial y-coordinate (needs sign adjustment) - field: The original field element (needed for sign adjustment) Note: The returned y_initial needs to be adjusted using adjust_y_sign() to ensure it has the correct sign relative to the input field element. """ # Compute y-coordinate as the square root of g1x # This will only work if g1x is a quadratic residue y = self.fp2_sqrt(g1x) # Convert x to affine coordinates x_affine = self.fp2_div(num_x1, div) return [x_affine, y, field] def compute_initial_coordinates_non_quadratic( self, field: list[ModuloCircuitElement], g1x: list[ModuloCircuitElement], div: list[ModuloCircuitElement], num_x1: list[ModuloCircuitElement], zeta_u2: list[ModuloCircuitElement], ): """ Computes the initial coordinates for the map-to-curve operation when g1x is NOT a quadratic residue. This function uses a clever mathematical property to compute a valid initial y-coordinate when direct square root is impossible. Key Mathematical Insight: When g1x is not a quadratic residue, we use the SWU constant z (which is also not a quadratic residue) to compute the y-coordinate. This works because: 1. If g1x is not a quadratic residue, then z·g1x IS a quadratic residue (product of two non-quadratic residues is a quadratic residue) 2. We can then compute y₁ = √(z·g1x) 3. The initial y is computed as y = zu·field·y₁ The algorithm: 1. Compute y₁ = √(z·g1x) [This is possible because z·g1x is a quadratic residue] 2. Compute initial y = zu·field·y₁ 3. Compute x = (zu·num_x1)/div Args: field: The original input field element g1x: The value x³ + ax + b (known to be a non-quadratic residue) zeta_u2: The value z·u² from the first part num_x1: The x numerator from the first part div: The denominator from the first part Returns: list: [x_affine, y_initial, field] where: - x_affine: The final x-coordinate - y_initial: The initial y-coordinate (needs sign adjustment) - field: The original field element (needed for sign adjustment) Note: The returned y_initial needs to be adjusted using adjust_y_sign() to ensure it has the correct sign relative to the input field element. """ # Since z·g1x is a quadratic residue (product of two non-quadratic residues), # this square root is guaranteed to exist y1 = self.fp2_sqrt(self.fp2_mul(self.swu_z, g1x)) # Compute initial y-coordinate y = self.fp2_mul(zeta_u2, self.fp2_mul(field, y1)) # Compute x-coordinate in affine form num_x = self.fp2_mul(zeta_u2, num_x1) x_affine = self.fp2_div(num_x, div) return [x_affine, y, field] def adjust_y_sign( self, y: list[ModuloCircuitElement], field: list[ModuloCircuitElement], ): # Handle sign adjustment as before qy, y_parity = self.fp2_parity(y) qfield, element_parity = self.fp2_parity(field) # Compute if parities are the same using XNOR (opposite of XOR) # XNOR(a,b) = 1 - (a + b - 2ab) = 2ab - a - b + 1 same_parity = [ self.add( self.sub( self.mul( self.set_or_get_constant(2), self.mul(y_parity[0], element_parity[0]), ), self.add(y_parity[0], element_parity[0]), ), self.set_or_get_constant(1), ), self.zero[0], # imaginary part is 0 ] # Adjust y sign if parities don't match: # y_affine = same_parity ? y : -y y_affine = self.fp2_add( self.fp2_mul([same_parity[0], same_parity[1]], y), # Keep y if same parity self.fp2_mul( [ self.sub(self.one[0], same_parity[0]), self.zero[0], ], # [1 - same_parity, 0] self.fp2_sub(self.zero, y), # -y ), ) return [y_affine, qfield, qy] # ATTENTION: this function is not sound by itself! # Two solutions are possible: # 1. (q, r) # 2. (q+ (p-1)/2, 1-r) # To constraint this properly, we still need assert: q <= (p-1)/2 # This needs to happen in the function wrapping the garaga circuit def fp2_parity( self, element: list[ModuloCircuitElement] ) -> list[ModuloCircuitElement]: """ Computes the parity of the first non-zero coefficient of the Fp2 element (element[0], element[1]) Returns [parity, 0] For an Fp2 element a + bi: 1. If a ≠ 0, returns parity of a 2. If a = 0 and b ≠ 0, returns parity of b 3. If both are 0, returns [0, 0] (even) Implements sgn0_m_eq_2 from RFC9380 using witness variables for validation. """ assert len(element) == 2 and all( isinstance(x, ModuloCircuitElement) for x in element ) two = self.set_or_get_constant(2) one = self.set_or_get_constant(1) zero = self.set_or_get_constant(0) # For element[0] (real part) # Witnesses: q0 (quotient), r0 (remainder) q0 = self.write_element( PyFelt(element[0].value // 2, element[0].p), WriteOps.WITNESS ) # Witness for q0 r0 = self.write_element( PyFelt(element[0].value % 2, element[0].p), WriteOps.WITNESS ) # Witness for r0 (parity of x0) # Enforce that r0 ∈ {0, 1} r0_sub_1 = self.sub(r0, one) r0_times_r0_sub_1 = self.mul(r0, r0_sub_1) self.sub_and_assert(r0_times_r0_sub_1, zero, zero, comment="Ensure r0 ∈ {0,1}") # Enforce x0 = 2 * q0 + r0 two_q0 = self.mul(q0, two) self.add_and_assert(two_q0, r0, element[0], comment="Validate x0 decomposition") # Similarly for element[1] (imaginary part) q1 = self.write_element( PyFelt(element[1].value // 2, element[1].p), WriteOps.WITNESS ) # Witness for q1 r1 = self.write_element( PyFelt((element[1].value % 2), element[1].p), WriteOps.WITNESS ) # Witness for r1 (parity of x1) # Enforce that r1 ∈ {0, 1} r1_sub_1 = self.sub(r1, one) r1_times_r1_sub_1 = self.mul(r1, r1_sub_1) self.sub_and_assert(r1_times_r1_sub_1, zero, zero, comment="Ensure r1 ∈ {0,1}") # Enforce x1 = 2 * q1 + r1 two_q1 = self.mul(q1, two) self.add_and_assert(two_q1, r1, element[1], comment="Validate x1 decomposition") # Compute zero_0 = 1 - fp_is_non_zero(x0) real_is_non_zero = self.fp_is_non_zero( element[0] ) # Returns 1 if x0 ≠ 0, else 0 zero_0 = self.sub(one, real_is_non_zero) # Compute s = r0 OR (zero_0 AND r1) # Implementing logical operations using arithmetic operations # zero_0 AND r1 zero_0_and_r1 = self.mul(zero_0, r1) # r0 OR (zero_0 AND r1) # OR(a, b) = a + b - a * b or_input = self.sub(self.add(r0, zero_0_and_r1), self.mul(r0, zero_0_and_r1)) s = or_input # Since values are in {0,1}, this computes the logical OR # select q based on s q = self.add( self.mul(q0, self.sub(one, zero_0_and_r1)), # q0 when not using r1 self.mul(q1, zero_0_and_r1), # q1 when using r1 ) # Return parity as [s, 0] return q, [s, zero] class MapToCurveG1(ModuloCircuit): def __init__(self, name: str, curve_id: int, compilation_mode: int = 0): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, generic_circuit=True, ) self.curve = CURVES[curve_id] def set_consts(self): params = self.curve.swu_params self.swu_a = self.set_or_get_constant(params.A) self.swu_b = self.set_or_get_constant(params.B) self.swu_z = self.set_or_get_constant(params.Z) self.zero = self.set_or_get_constant(0) self.one = self.set_or_get_constant(1) def map_to_curve_part_1(self, input_value: ModuloCircuitElement): """ Implements the first part of the Simplified SWU map-to-curve algorithm for G1. This maps a field element to a point on the curve E': y² = x³ + ax + b. The algorithm follows these steps: 1. Let u be the input field element 2. Calculate t = z²u⁴ + zu² (where z is the SWU constant) 3. Calculate x₁ = (-b/a) * (1 + 1/t) if t ≠ 0, or x₁ = (-b/(az)) if t = 0 4. Calculate g(x₁) = x₁³ + ax₁ + b Args: input_value (ModuloCircuitElement): Field element u to be mapped to the curve Returns: list: [g1x, div, num_x1, zeta_u2] where: - g1x: The value g(x₁) = x₁³ + ax₁ + b - div: The denominator used in x₁ calculation (needed for finalization) - num_x1: The numerator of x₁ (needed for finalization) - zeta_u2: The value z·u² (needed for non-quadratic case) Note: This is part 1 of the map-to-curve operation. The result needs to be finalized using either finalize_map_to_curve_quadratic or finalize_map_to_curve_non_quadratic, depending on whether g1x is a quadratic residue. """ # Calculate u² and related terms u2 = self.square(input_value) # u² zeta_u2 = self.mul(self.swu_z, u2) # z·u² zeta_u2_square = self.square(zeta_u2) # z²u⁴ ta = self.add(zeta_u2_square, zeta_u2) # t = z²u⁴ + zu² neg_ta = self.sub(self.zero, ta) # -t num_x1 = self.mul(self.swu_b, self.add(ta, self.one)) # b(t + 1) # Handle special case when t = 0 is_non_zero = self.fp_is_non_zero(neg_ta) # 1 if t ≠ 0, 0 if t = 0 neg_ta_or_z = self.add( self.mul(self.sub(self.one, is_non_zero), self.swu_z), # z if t = 0 self.mul(is_non_zero, neg_ta), # -t if t ≠ 0 ) # Calculate x₁ numerator and denominator div = self.mul(self.swu_a, neg_ta_or_z) # a·(-t) or a·z num2_x1 = self.square(num_x1) # (b(t + 1))² div2 = self.square(div) # (a·(-t))² div3 = self.mul(div, div2) # (a·(-t))³ # Calculate g(x₁) = x₁³ + ax₁ + b num_gx1 = self.add( self.mul( self.add(num2_x1, self.mul(self.swu_a, div2)), # x₁² # ax₁ num_x1, # ·x₁ (completing the x₁³ term) ), self.mul(self.swu_b, div3), # + b ) g1x = self.mul(num_gx1, self.inv(div3)) # Final result normalized return [g1x, div, num_x1, zeta_u2] def compute_initial_coordinates_quadratic( self, field: ModuloCircuitElement, g1x: ModuloCircuitElement, div: ModuloCircuitElement, num_x1: ModuloCircuitElement, ): """ Computes the x and y coordinates for the map-to-curve operation when g1x is a quadratic residue. This function computes the y-coordinate and ensures the point has the correct sign. IMPORTANT: This function should only be called when g1x is a quadratic residue, meaning there exists a y such that y² = g1x in the field. The algorithm follows these steps: 1. Compute y = √(g1x) where g1x = x³ + ax + b (requires g1x to be a quadratic residue) 2. Compute x = num_x1/div to get the x-coordinate in affine form 3. Adjust the sign of y to match the parity of the input field element The sign adjustment uses: - If sign(y) ≠ sign(field_element): y = -y - For field elements, parity is determined by the real part Args: field: The original input field element g1x: The value x³ + ax + b from the first part (must be a quadratic residue) div: The denominator from the first part num_x1: The numerator for x from the first part Returns: list: [x_affine, y_initial, field] where: - x_affine: The final x-coordinate - y_initial: The initial y-coordinate (needs sign adjustment) - field: The original field element (needed for sign adjustment) Note: When g1x is not a quadratic residue, the alternative function compute_initial_coordinates_non_quadratic should be used instead. """ # Compute y-coordinate as the square root of g1x y_initial = self.fp_sqrt(g1x) # Convert x to affine coordinates x_affine = self.div(num_x1, div) return [x_affine, y_initial, field] def compute_initial_coordinates_non_quadratic( self, field: ModuloCircuitElement, g1x: ModuloCircuitElement, div: ModuloCircuitElement, num_x1: ModuloCircuitElement, zeta_u2: ModuloCircuitElement, ): """ Computes the initial x and y coordinates for the map-to-curve operation when g1x is NOT a quadratic residue. The y-coordinate will need further sign adjustment using adjust_y_sign(). Key Mathematical Insight: When g1x is not a quadratic residue, we use the SWU constant z (which is also not a quadratic residue) to compute the y-coordinate. This works because: 1. If g1x is not a quadratic residue, then z·g1x IS a quadratic residue (product of two non-quadratic residues is a quadratic residue) 2. We can then compute y₁ = √(z·g1x) 3. The initial y is computed as y = zu·field·y₁ The algorithm: 1. Compute y₁ = √(z·g1x) [This is possible because z·g1x is a quadratic residue] 2. Compute initial y = zu·field·y₁ 3. Compute x = (zu·num_x1)/div Args: field: The original input field element g1x: The value x³ + ax + b (known to be a non-quadratic residue) zeta_u2: The value z·u² from the first part num_x1: The x numerator from the first part div: The denominator from the first part Returns: list: [x_affine, y_initial, field] where: - x_affine: The final x-coordinate - y_initial: The initial y-coordinate (needs sign adjustment) - field: The original field element (needed for sign adjustment) Note: The returned y_initial needs to be adjusted using adjust_y_sign() to ensure it has the correct sign relative to the input field element. """ # Since z·g1x is a quadratic residue (product of two non-quadratic residues), # this square root is guaranteed to exist y1 = self.fp_sqrt(self.mul(self.swu_z, g1x)) # Compute initial y-coordinate y_initial = self.mul(zeta_u2, self.mul(field, y1)) # Compute x-coordinate in affine form num_x = self.mul(zeta_u2, num_x1) x_affine = self.div(num_x, div) return [x_affine, y_initial, field] def adjust_y_sign( self, y: ModuloCircuitElement, field: ModuloCircuitElement, ): # Handle sign adjustment as before qy, y_parity = self.fp_parity(y) qfield, element_parity = self.fp_parity(field) # Compute if parities are the same using XNOR (opposite of XOR) # XNOR(a,b) = 1 - (a + b - 2ab) = 2ab - a - b + 1 same_parity = self.add( self.sub( self.mul( self.set_or_get_constant(2), self.mul(y_parity, element_parity), ), self.add(y_parity, element_parity), ), self.set_or_get_constant(1), ) # Adjust y sign if parities don't match: # y_affine = same_parity ? y : -y y_affine = self.add( self.mul(same_parity, y), # Keep y if same parity self.mul( self.sub(self.one, same_parity), self.sub(self.zero, y), # -y ), ) return [y_affine, qy, qfield] # ATTENTION: this function is not sound by itself! # Two solutions are possible: # 1. (q, r) # 2. (q+ (p-1)/2, 1-r) # To constraint this properly, we still need assert: q <= (p-1)/2 # This needs to happen in the function wrapping the garaga circuit def fp_parity(self, element: ModuloCircuitElement) -> ModuloCircuitElement: """ Computes the parity of a field element. Returns 0 if element is even, 1 if odd. Implements sgn0_m_eq_1 from RFC9380 using witness variables for validation. """ assert isinstance(element, ModuloCircuitElement) two = self.set_or_get_constant(2) one = self.set_or_get_constant(1) zero = self.set_or_get_constant(0) # Witnesses: q (quotient), r (remainder) q = self.write_element( PyFelt(element.value // 2, element.p), WriteOps.WITNESS ) # Witness for quotient r = self.write_element( PyFelt(element.value % 2, element.p), WriteOps.WITNESS ) # Witness for remainder (parity) # Enforce that r ∈ {0, 1} r_sub_1 = self.sub(r, one) r_times_r_sub_1 = self.mul(r, r_sub_1) self.sub_and_assert(r_times_r_sub_1, zero, zero, comment="Ensure r ∈ {0,1}") # Enforce element = 2 * q + r two_q = self.mul(q, two) self.add_and_assert(two_q, r, element, comment="Validate element decomposition") return q, r if __name__ == "__main__": circuit = MapToCurveG1("map_to_curve", 1) # BLS12-381 circuit.set_consts() field = circuit.write_element( circuit.field( 2231413721970278425038638834062370180699174210864795385441649994565282274875534254514118105433862522641883533654145 ) ) g1x, div, num_x1, zeta_u2 = circuit.map_to_curve_part_1(field) print("g1x", g1x) print("div", div) print("num_x1", num_x1) print("zeta_u2", zeta_u2) if g1x.felt.is_quad_residue(): print("Quadratic residue") x_affine, y_initial, field = circuit.compute_initial_coordinates_quadratic( field, g1x, div, num_x1 ) else: print("Non quadratic residue") x_affine, y_initial, field = circuit.compute_initial_coordinates_non_quadratic( field, g1x, div, num_x1, zeta_u2 ) # Adjust y sign y_affine, qy, qfield = circuit.adjust_y_sign(field, y_initial) print("x_affine", x_affine) print("y_affine", y_affine) ================================================ FILE: hydra/garaga/precompiled_circuits/miller_tower.py ================================================ from typing import Iterator from garaga.curves import BLS12_381_ID, BN254_ID, CURVES from garaga.extension_field_modulo_circuit import ModuloCircuitElement from garaga.precompiled_circuits.multi_miller_loop import MultiMillerLoopCircuit def tower_line_function_sparsity(curve_id: int) -> list[int]: match curve_id: case 0: return [2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0] case 1: return [1, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0] case _: raise ValueError(f"Invalid curve ID: {curve_id}") class MillerTowerCircuit(MultiMillerLoopCircuit): def __init__( self, name: str, curve_id: int, n_pairs: int, compilation_mode: int = 1, ): super().__init__( name=name, curve_id=curve_id, n_pairs=n_pairs, compilation_mode=compilation_mode, ) def eval_tower_line(self, line: Iterator[ModuloCircuitElement], yInv, xNegOverY): assert len(line) == 4 # Input is R0 = slope, R1 = intercept r0 = [line[0], line[1]] r1 = [line[2], line[3]] if self.curve_id == BN254_ID: return [ self.mul(r0[0], xNegOverY), self.mul(r0[1], xNegOverY), self.mul(r1[0], yInv), self.mul(r1[1], yInv), ] elif self.curve_id == BLS12_381_ID: return [ self.mul(r1[0], yInv), self.mul(r1[1], yInv), self.mul(r0[0], xNegOverY), self.mul(r0[1], xNegOverY), ] else: raise NotImplementedError def mul_by_line_tower( self, tower_fp12: list[ModuloCircuitElement], line_evaluated: list[ModuloCircuitElement], ): assert len(tower_fp12) == 12 assert ( len(line_evaluated) == 4 ), f"Expected 4 elements, got {len(line_evaluated)}" c0_fp6, c1_fp6 = tower_fp12[0:6], tower_fp12[6:12] # c0_b0, c0_b1, c0_b2 = c0[0:2], c0[2:4], c0[4:6] # c1_b0, c1_b1, c1_b2 = c1[0:2], c1[2:4], c1[4:6] # MulBy34. multiplication by sparse element (1,0,0,c3,c4,0) if self.curve_id == 0: a = c0_fp6 b = c1_fp6 c3, c4 = line_evaluated[0:2], line_evaluated[2:4] b = self._fp6_by_01(b, c3, c4) d0 = self.vector_add( [self.set_or_get_constant(1), self.set_or_get_constant(0)], c3 ) d = self.vector_add(c0_fp6, c1_fp6) d = self._fp6_by_01(d, d0, c4) z_c1 = self.vector_add(self.vector_neg(self.vector_add(a, b)), d) z_c0 = self.vector_add(self.fp6_mul_by_non_residue(b), a) return z_c0 + z_c1 elif self.curve_id == 1: # Mul By 01 # // MulBy01 multiplication by sparse element (c0, c1, 0, 0, 1) # func (z *E12) MulBy01(c0, c1 *E2) *E12 { # var a, b E6 # var d E2 # a.Set(&z.C0) # a.MulBy01(c0, c1) # b.MulByNonResidue(&z.C1) # d.SetOne().Add(c1, &d) # z.C1.Add(&z.C1, &z.C0) # z.C1.MulBy01(c0, &d) # z.C1.Sub(&z.C1, &a) # z.C1.Sub(&z.C1, &b) # z.C0.MulByNonResidue(&b) # z.C0.Add(&z.C0, &a) # return z # } c0, c1 = line_evaluated[0:2], line_evaluated[2:4] a = c0_fp6 a = self._fp6_by_01(a, c0, c1) b = self.fp6_mul_by_non_residue(c1_fp6) d = [self.add(self.set_or_get_constant(1), c1[0]), c1[1]] z_c1 = self.vector_add(c1_fp6, c0_fp6) z_c1 = self._fp6_by_01(z_c1, c0, d) z_c1 = self.vector_sub(z_c1, a) z_c1 = self.vector_sub(z_c1, b) z_c0 = self.fp6_mul_by_non_residue(b) z_c0 = self.vector_add(z_c0, a) return z_c0 + z_c1 def mul_by_line_line_tower(self, tower_fp12, line_line): assert len(tower_fp12) == 12 assert len(line_line) == 10 c0_fp6, c1_fp6 = tower_fp12[0:6], tower_fp12[6:12] def mul_line_by_line_tower(self, l1, l2): assert len(l1) == 4 assert len(l2) == 4 if self.curve_id == 0: d3, d4 = l1[0:2], l1[2:4] c3, c4 = l2[0:2], l2[2:4] x3 = self.fp2_mul(c3, d3) x4 = self.fp2_mul(c4, d4) x04 = self.vector_add(c4, d4) x03 = self.vector_add(c3, d3) tmp = self.vector_add(c3, c4) x34 = self.vector_sub( self.vector_sub(self.fp2_mul(self.vector_add(d3, d4), tmp), x3), x4 ) z00 = self.fp2_mul_by_non_residue(x4) z00 = [self.add(z00[0], self.set_or_get_constant(1)), z00[1]] return z00 + x3 + x34 + x03 + x04 if self.curve_id == 1: c0, c1 = l2[0:2], l2[2:4] d0, d1 = l1[0:2], l1[2:4] x0 = self.fp2_mul(c0, d0) x1 = self.fp2_mul(c1, d1) x04 = self.vector_add(d0, c0) tmp = self.vector_add(c0, c1) x01 = self.vector_sub( self.vector_sub(self.fp2_mul(self.vector_add(d0, d1), tmp), x0), x1 ) x14 = self.vector_add(d1, c1) z00 = self.fp2_mul_by_non_residue( [self.set_or_get_constant(1), self.set_or_get_constant(0)] ) z00 = self.vector_add(z00, x0) # C0B0 + C0B1 + C0B2 + C1B1 + C1B2 return z00 + x01 + x1 + x04 + x14 def _fp6_by_01(self, e6: list[ModuloCircuitElement], c0, c1): assert len(e6) == 6 assert len(c0) == 2 assert len(c1) == 2 b0, b1, b2 = e6[0:2], e6[2:4], e6[4:6] a = self.fp2_mul(b0, c0) b = self.fp2_mul(b1, c1) tmp = self.vector_add(b1, b2) t0 = self.fp2_mul(c1, tmp) t0 = self.vector_sub(t0, b) t0 = self.fp2_mul_by_non_residue(t0) t0 = self.vector_add(t0, a) tmp = self.vector_add(b0, b2) t2 = self.fp2_mul(c0, tmp) t2 = self.vector_sub(t2, a) t2 = self.vector_add(t2, b) t1 = self.vector_add(c0, c1) tmp = self.vector_add(b0, b1) t1 = self.fp2_mul(t1, tmp) t1 = self.vector_sub(t1, a) t1 = self.vector_sub(t1, b) b0 = t0 b1 = t1 b2 = t2 # flatten lists: return b0 + b1 + b2 def fp6_mul_by_non_residue(self, a: list[ModuloCircuitElement]): assert len(a) == 6 a = list(a) b0, b1, b2 = a[0:2], a[2:4], a[4:6] return self.fp2_mul_by_non_residue(b2) + b0 + b1 def fp12_square(self, a: list[ModuloCircuitElement]): assert len(a) == 12 xc0, xc1 = a[0:6], a[6:12] c0 = self.vector_sub(xc0, xc1) c3 = self.vector_add(xc0, self.vector_neg(self.fp6_mul_by_non_residue(xc1))) c2 = self.fp6_mul(xc0, xc1) c0 = self.vector_add(self.fp6_mul(c0, c3), c2) z_c1 = self.vector_add(c2, c2) z_c0 = self.vector_add(c0, self.fp6_mul_by_non_residue(c2)) return z_c0 + z_c1 def fp12_mul(self, x: list[ModuloCircuitElement], y: list[ModuloCircuitElement]): assert len(x) == 12 assert len(y) == 12 x_c0, x_c1 = x[0:6], x[6:12] y_c0, y_c1 = y[0:6], y[6:12] a = self.vector_add(x_c0, x_c1) b = self.vector_add(y_c0, y_c1) a = self.fp6_mul(a, b) b = self.fp6_mul(x_c0, y_c0) c = self.fp6_mul(x_c1, y_c1) z_c1 = self.vector_sub(a, b) z_c1 = self.vector_sub(z_c1, c) z_c0 = self.fp6_mul_by_non_residue(c) z_c0 = self.vector_add(z_c0, b) return z_c0 + z_c1 def fp6_mul(self, a: list[ModuloCircuitElement], b: list[ModuloCircuitElement]): assert len(a) == 6 assert len(b) == 6 xb0, xb1, xb2 = a[0:2], a[2:4], a[4:6] yb0, yb1, yb2 = b[0:2], b[2:4], b[4:6] t0 = self.fp2_mul(xb0, yb0) t1 = self.fp2_mul(xb1, yb1) t2 = self.fp2_mul(xb2, yb2) c0 = self.vector_add(xb1, xb2) tmp = self.vector_add(yb1, yb2) c0 = self.vector_add( self.fp2_mul_by_non_residue( self.vector_sub(self.vector_sub(self.fp2_mul(c0, tmp), t1), t2) ), t0, ) c1 = self.vector_add(xb0, xb1) tmp = self.vector_add(yb0, yb1) c1 = self.vector_sub(self.vector_sub(self.fp2_mul(c1, tmp), t0), t1) tmp = self.fp2_mul_by_non_residue(t2) c1 = self.vector_add(c1, tmp) tmp = self.vector_add(xb0, xb2) c2 = self.vector_add( self.vector_sub( self.vector_sub(self.fp2_mul(self.vector_add(yb0, yb2), tmp), t0), t2 ), t1, ) return c0 + c1 + c2 def fp12_inverse(self, a: list[ModuloCircuitElement]): assert len(a) == 12 xc0, xc1 = a[0:6], a[6:12] t0 = self.fp6_square(xc0) t1 = self.fp6_square(xc1) tmp = self.fp6_mul_by_non_residue(t1) t0 = self.vector_sub(t0, tmp) t1 = self.fp6_inverse(t0) z_c0 = self.fp6_mul(xc0, t1) z_c1 = self.fp6_mul(xc1, t1) z_c1 = self.vector_neg(z_c1) return z_c0 + z_c1 def fp6_inverse(self, a: list[ModuloCircuitElement]): assert len(a) == 6 # func (z *E6) Inverse(x *E6) *E6 { # // Algorithm 17 from https://eprint.iacr.org/2010/354.pdf # // step 9 is wrong in the paper it's t1-t4 # var t0, t1, t2, t3, t4, t5, t6, c0, c1, c2, d1, d2 E2 # t0.Square(&x.B0) # t1.Square(&x.B1) # t2.Square(&x.B2) # t3.Mul(&x.B0, &x.B1) # t4.Mul(&x.B0, &x.B2) # t5.Mul(&x.B1, &x.B2) # c0.MulByNonResidue(&t5).Neg(&c0).Add(&c0, &t0) # c1.MulByNonResidue(&t2).Sub(&c1, &t3) # c2.Sub(&t1, &t4) # t6.Mul(&x.B0, &c0) # d1.Mul(&x.B2, &c1) # d2.Mul(&x.B1, &c2) # d1.Add(&d1, &d2).MulByNonResidue(&d1) # t6.Add(&t6, &d1) # t6.Inverse(&t6) # z.B0.Mul(&c0, &t6) # z.B1.Mul(&c1, &t6) # z.B2.Mul(&c2, &t6) xb0, xb1, xb2 = a[0:2], a[2:4], a[4:6] t0 = self.fp2_square(xb0) t1 = self.fp2_square(xb1) t2 = self.fp2_square(xb2) t3 = self.fp2_mul(xb0, xb1) t4 = self.fp2_mul(xb0, xb2) t5 = self.fp2_mul(xb1, xb2) c0 = self.vector_add(self.vector_neg(self.fp2_mul_by_non_residue(t5)), t0) c1 = self.vector_sub(self.fp2_mul_by_non_residue(t2), t3) c2 = self.vector_sub(t1, t4) t6 = self.fp2_mul(xb0, c0) d1 = self.fp2_mul(xb2, c1) d2 = self.fp2_mul(xb1, c2) d1 = self.fp2_mul_by_non_residue(self.vector_add(d1, d2)) t6 = self.vector_add(t6, d1) t6 = self.fp2_inv(t6) zb0 = self.fp2_mul(c0, t6) zb1 = self.fp2_mul(c1, t6) zb2 = self.fp2_mul(c2, t6) return zb0 + zb1 + zb2 def fp6_square(self, a: list[ModuloCircuitElement]): assert len(a) == 6 xb0, xb1, xb2 = a[0:2], a[2:4], a[4:6] c4 = self.fp2_mul(xb0, xb1) c4 = self.vector_add(c4, c4) c5 = self.fp2_square(xb2) c1 = self.vector_add(self.fp2_mul_by_non_residue(c5), c4) c2 = self.vector_sub(c4, c5) c3 = self.fp2_square(xb0) c4 = self.vector_add(self.vector_sub(xb0, xb1), xb2) c5 = self.fp2_mul(xb1, xb2) c5 = self.vector_add(c5, c5) c4 = self.fp2_square(c4) c0 = self.vector_add(self.fp2_mul_by_non_residue(c5), c3) zb2 = self.vector_sub(self.vector_add(self.vector_add(c2, c4), c5), c3) zb0 = c0 zb1 = c1 return zb0 + zb1 + zb2 def fp12_conjugate(self, a: list[ModuloCircuitElement]): assert len(a) == 12 raise NotImplementedError("Not implemented") def fp12_cyclotomic_square(self, a: list[ModuloCircuitElement]): assert len(a) == 12 xc0, xc1 = a[0:6], a[6:12] xc0b0 = xc0[0:2] xc0b1 = xc0[2:4] xc0b2 = xc0[4:6] xc1b0 = xc1[0:2] xc1b1 = xc1[2:4] xc1b2 = xc1[4:6] t0 = self.fp2_square(xc1b1) t1 = self.fp2_square(xc0b0) t6 = self.vector_add(xc1b1, xc0b0) t6 = self.fp2_square(t6) t6 = self.vector_sub(t6, t0) t6 = self.vector_sub(t6, t1) t2 = self.fp2_square(xc0b2) t3 = self.fp2_square(xc1b0) t7 = self.vector_add(xc0b2, xc1b0) t7 = self.fp2_square(t7) t7 = self.vector_sub(t7, t2) t7 = self.vector_sub(t7, t3) t4 = self.fp2_square(xc1b2) t5 = self.fp2_square(xc0b1) t8 = self.vector_add(xc1b2, xc0b1) t8 = self.fp2_square(t8) t8 = self.vector_sub(t8, t4) t8 = self.vector_sub(t8, t5) t8 = self.fp2_mul_by_non_residue(t8) t0 = self.fp2_mul_by_non_residue(t0) t0 = self.vector_add(t0, t1) t2 = self.fp2_mul_by_non_residue(t2) t2 = self.vector_add(t2, t3) t4 = self.fp2_mul_by_non_residue(t4) t4 = self.vector_add(t4, t5) zc0b0 = self.vector_sub(t0, xc0b0) zc0b0 = self.vector_add(zc0b0, zc0b0) zc0b0 = self.vector_add(zc0b0, t0) zc0b1 = self.vector_sub(t2, xc0b1) zc0b1 = self.vector_add(zc0b1, zc0b1) zc0b1 = self.vector_add(zc0b1, t2) zc0b2 = self.vector_sub(t4, xc0b2) zc0b2 = self.vector_add(zc0b2, zc0b2) zc0b2 = self.vector_add(zc0b2, t4) zc1b0 = self.vector_add(t8, xc1b0) zc1b0 = self.vector_add(zc1b0, zc1b0) zc1b0 = self.vector_add(zc1b0, t8) zc1b1 = self.vector_add(t6, xc1b1) zc1b1 = self.vector_add(zc1b1, zc1b1) zc1b1 = self.vector_add(zc1b1, t6) zc1b2 = self.vector_add(t7, xc1b2) zc1b2 = self.vector_add(zc1b2, zc1b2) zc1b2 = self.vector_add(zc1b2, t7) return zc0b0 + zc0b1 + zc0b2 + zc1b0 + zc1b1 + zc1b2 def fp2_conjugate(self, a: list[ModuloCircuitElement]): assert len(a) == 2 return [a[0], self.neg(a[1])] def mul_by_non_residue_k_power_n( self, x: list[ModuloCircuitElement], k: int, n: int ): from garaga.hints.tower_backup import E2 assert len(x) == 2 curve = CURVES[self.curve_id] non_residue = E2(curve.nr_a0, curve.nr_a1, curve.p) # nr^(n*(p^k-1)/6) res: E2 = non_residue ** ((n * (curve.p**k - 1) // 6)) if res.a1 != 0: factor = [ self.set_or_get_constant(res.a0), self.set_or_get_constant(res.a1), ] return self.fp2_mul(factor, x) else: factor = self.set_or_get_constant(res.a0) return [self.mul(factor, x[0]), self.mul(factor, x[1])] def fp12_frob(self, a: list[ModuloCircuitElement]): assert len(a) == 12 c0b0 = self.fp2_conjugate(a[0:2]) c0b0[0] = self.add( c0b0[0], self.set_or_get_constant(0) ) # Input cannot be output. # TODO: Make a manual circuit or something better. c0b1 = self.fp2_conjugate(a[2:4]) c0b2 = self.fp2_conjugate(a[4:6]) c1b0 = self.fp2_conjugate(a[6:8]) c1b1 = self.fp2_conjugate(a[8:10]) c1b2 = self.fp2_conjugate(a[10:12]) c0b1 = self.mul_by_non_residue_k_power_n(c0b1, 1, 2) c0b2 = self.mul_by_non_residue_k_power_n(c0b2, 1, 4) c1b0 = self.mul_by_non_residue_k_power_n(c1b0, 1, 1) c1b1 = self.mul_by_non_residue_k_power_n(c1b1, 1, 3) c1b2 = self.mul_by_non_residue_k_power_n(c1b2, 1, 5) return c0b0 + c0b1 + c0b2 + c1b0 + c1b1 + c1b2 def fp12_frob_square(self, a: list[ModuloCircuitElement]): assert len(a) == 12 c0b0 = [ self.add(a[0], self.set_or_get_constant(0)), self.add(a[1], self.set_or_get_constant(0)), ] # Input cannot be output. # TODO: Make a manual circuit or something better. c0b1 = self.mul_by_non_residue_k_power_n(a[2:4], 2, 2) c0b2 = self.mul_by_non_residue_k_power_n(a[4:6], 2, 4) c1b0 = self.mul_by_non_residue_k_power_n(a[6:8], 2, 1) c1b1 = self.mul_by_non_residue_k_power_n(a[8:10], 2, 3) c1b2 = self.mul_by_non_residue_k_power_n(a[10:12], 2, 5) return c0b0 + c0b1 + c0b2 + c1b0 + c1b1 + c1b2 def fp12_frob_cube(self, a: list[ModuloCircuitElement]): assert len(a) == 12 c0b0 = self.fp2_conjugate(a[0:2]) c0b0[0] = self.add( c0b0[0], self.set_or_get_constant(0) ) # Input cannot be output. # TODO: Make a manual circuit or something better. c0b1 = self.fp2_conjugate(a[2:4]) c0b2 = self.fp2_conjugate(a[4:6]) c1b0 = self.fp2_conjugate(a[6:8]) c1b1 = self.fp2_conjugate(a[8:10]) c1b2 = self.fp2_conjugate(a[10:12]) c0b1 = self.mul_by_non_residue_k_power_n(c0b1, 3, 2) c0b2 = self.mul_by_non_residue_k_power_n(c0b2, 3, 4) c1b0 = self.mul_by_non_residue_k_power_n(c1b0, 3, 1) c1b1 = self.mul_by_non_residue_k_power_n(c1b1, 3, 3) c1b2 = self.mul_by_non_residue_k_power_n(c1b2, 3, 5) return c0b0 + c0b1 + c0b2 + c1b0 + c1b1 + c1b2 def fp12_cyclotomic_square_compressed( self, xc0b1: list[ModuloCircuitElement], xc0b2: list[ModuloCircuitElement], xc1b0: list[ModuloCircuitElement], xc1b2: list[ModuloCircuitElement], ): assert len(xc0b1) == len(xc0b2) == len(xc1b0) == len(xc1b2) == 2 t0 = self.fp2_square(xc0b1) t1 = self.fp2_square(xc1b2) t5 = self.vector_add(xc0b1, xc1b2) t2 = self.fp2_square(t5) t3 = self.vector_add(t0, t1) t5 = self.vector_sub(t2, t3) t6 = self.vector_add(xc1b0, xc0b2) t3 = self.fp2_square(t6) t2 = self.fp2_square(xc1b0) t6 = self.fp2_mul_by_non_residue(t5) t5 = self.vector_add(t6, xc1b0) t5 = self.vector_add(t5, t5) zc1b0 = self.vector_add(t5, t6) t4 = self.fp2_mul_by_non_residue(t1) t5 = self.vector_add(t0, t4) t6 = self.vector_sub(t5, xc0b2) t1 = self.fp2_square(xc0b2) t6 = self.vector_add(t6, t6) zc0b2 = self.vector_add(t6, t5) t4 = self.fp2_mul_by_non_residue(t1) t5 = self.vector_add(t2, t4) t6 = self.vector_sub(t5, xc0b1) t6 = self.vector_add(t6, t6) zc0b1 = self.vector_add(t6, t5) t0 = self.vector_add(t2, t1) t5 = self.vector_sub(t3, t0) t6 = self.vector_add(t5, xc1b2) t6 = self.vector_add(t6, t6) zc1b2 = self.vector_add(t5, t6) return zc0b1 + zc0b2 + zc1b0 + zc1b2 def fp12_decompress_karabina_pt_I_c1b2_Z(self, xc0b1, xc1b2): assert len(xc0b1) == len(xc1b2) == 2 t0 = self.fp2_mul(xc0b1, xc1b2) t0 = self.vector_add(t0, t0) # t1 = xc0b2 return t0 def fp12_decompress_karabina_pt_I_c1b2_NZ( self, xc0b1: list[ModuloCircuitElement], xc0b2: list[ModuloCircuitElement], xc1b0: list[ModuloCircuitElement], xc1b2: list[ModuloCircuitElement], ): assert len(xc0b1) == len(xc0b2) == len(xc1b0) == len(xc1b2) == 2 t0 = self.fp2_square(xc0b1) t1 = self.vector_sub(t0, xc0b2) t1 = self.vector_add(t1, t1) t1 = self.vector_add(t1, t0) t2 = self.fp2_square(xc1b2) t0 = self.vector_add(self.fp2_mul_by_non_residue(t2), t1) t1 = self.vector_add(xc1b0, xc1b0) t1 = self.vector_add(t1, t1) return t0, t1 def fp12_decompress_karabina_pt_II( self, t0: list[ModuloCircuitElement], t1: list[ModuloCircuitElement], xc0b1: list[ModuloCircuitElement], xc0b2: list[ModuloCircuitElement], xc1b0: list[ModuloCircuitElement], xc1b2: list[ModuloCircuitElement], ): assert len(t0) == len(t1) == 2 assert len(xc0b1) == len(xc0b2) == len(xc1b0) == len(xc1b2) == 2 zc1b1 = self.fp2_div(t0, t1) t1 = self.fp2_mul(xc0b2, xc0b1) t2 = self.vector_sub(self.fp2_square(zc1b1), t1) t2 = self.vector_add(t2, t2) t2 = self.vector_sub(t2, t1) t1 = self.fp2_mul(xc1b0, xc1b2) t2 = self.vector_add(t2, t1) zc0b0 = self.fp2_mul_by_non_residue(t2) zc0b0 = [ self.add(zc0b0[0], self.set_or_get_constant(1)), zc0b0[1], ] return zc0b0, zc1b1 ================================================ FILE: hydra/garaga/precompiled_circuits/multi_miller_loop.py ================================================ from typing import Iterator, Tuple from garaga.curves import BLS12_381_ID, BN254_ID, CURVES, CurveID from garaga.extension_field_modulo_circuit import ( ExtensionFieldModuloCircuit, ModuloCircuitElement, PyFelt, ) from garaga.hints.io import flatten from garaga.points import G1Point, G2Point, precompute_lineline_sparsity class MultiMillerLoopCircuit(ExtensionFieldModuloCircuit): def __init__( self, name: str, curve_id: int, n_pairs: int, hash_input: bool = True, init_hash: int = None, compilation_mode: int = 0, precompute_lines: bool = False, n_points_precomputed_lines: int = None, tower_mode: bool = False, ): super().__init__( name=name, curve_id=curve_id, extension_degree=12, hash_input=hash_input, init_hash=init_hash, compilation_mode=compilation_mode, ) self.curve = CURVES[curve_id] self.line_sparsity: list[int] = self.curve.line_function_sparsity self.line_line_sparsity: list[int] = precompute_lineline_sparsity(curve_id) self.n_pairs = n_pairs self.P = [] self.Q = [] self.yInv = [] self.xNegOverY = [] self.loop_counter = CURVES[self.curve_id].loop_counter self.ops_counter.update( { "Double Step": 0, "Double-and-Add Step": 0, "Triple Step": 0, "MUL_L_BY_L": 0, "MUL_LL_BY_LL": 0, "MUL_LL_BY_L": 0, "MUL_BY_L": 0, "MUL_BY_LL": 0, } ) self.n_points_precomputed_lines = n_points_precomputed_lines self.precompute_lines: bool = precompute_lines self.precomputed_lines: list[ModuloCircuitElement] = [] self._precomputed_lines_generator = None def _create_precomputed_lines_generator( self, ) -> Iterator[ Tuple[ Tuple[ModuloCircuitElement, ModuloCircuitElement], Tuple[ModuloCircuitElement, ModuloCircuitElement], ] ]: if self.precompute_lines: if len(self.precomputed_lines) % 4 != 0: raise ValueError( "Number of precomputed line elements must be a multiple of 4." ) for i in range(0, len(self.precomputed_lines), 4): yield ( (self.precomputed_lines[i], self.precomputed_lines[i + 1]), (self.precomputed_lines[i + 2], self.precomputed_lines[i + 3]), ) else: while True: yield ((None, None), (None, None)) def get_next_precomputed_line( self, ) -> Tuple[Tuple[PyFelt, PyFelt], Tuple[PyFelt, PyFelt]]: return next(self._precomputed_lines_generator) def write_p_and_q(self, P: list[G1Point], Q: list[G2Point]): assert len(P) == len(Q) == self.n_pairs assert set([P[i].curve_id for i in range(len(P))]) == set( [Q[i].curve_id for i in range(len(Q))] ) raw = [] for P, Q in zip(P, Q): raw.extend([self.field(P.x), self.field(P.y)]) raw.extend([self.field(Q.x[0]), self.field(Q.x[1])]) raw.extend([self.field(Q.y[0]), self.field(Q.y[1])]) self.write_p_and_q_raw(raw) return None def write_p_and_q_raw(self, input: list[PyFelt], precompute_consts: bool = True): assert ( len(input) == 6 * self.n_pairs ), f"Expected {6 * self.n_pairs} inputs, got {len(input)}" for i in range(self.n_pairs): self.P.append( ( self.write_element(input[6 * i]), self.write_element(input[6 * i + 1]), ) ) self.Q.append( ( [ self.write_element(input[6 * i + 2]), self.write_element(input[6 * i + 3]), ], [ self.write_element(input[6 * i + 4]), self.write_element(input[6 * i + 5]), ], ) ) if precompute_consts: self.precompute_consts() return None def precompute_consts(self, n_pairs: int = None, skip_P_precompute: bool = False): n_pairs = n_pairs or self.n_pairs if not skip_P_precompute: self.yInv = [self.inv(self.P[i][1]) for i in range(n_pairs)] self.xNegOverY = [ self.neg(self.div(self.P[i][0], self.P[i][1])) for i in range(n_pairs) ] if -1 in self.loop_counter: self.Qneg = [ (self.Q[i][0], self.vector_neg(self.Q[i][1])) for i in range(n_pairs) ] else: self.Qneg = None return None def compute_doubling_slope( self, Q: tuple[ list[ModuloCircuitElement], list[ModuloCircuitElement], ], ) -> list[ModuloCircuitElement, ModuloCircuitElement]: # num = 3 * x^2 # den = 2 * y x0, x1 = Q[0][0], Q[0][1] # x² = (x0 + i x1)² = (x0² - x1²) + 2 * i * x0 * x1 = (x0+x1)(x0-x1) + i * 2 * x0 * x1. # (x0+x1)*(x0-x1) is cheaper than x0² - x1². (2 ADD + 1 MUL) vs (1 ADD + 2 MUL) (16 vs 20 steps) # Omits mul by 2x for imaginary part to multiply once by 6 instead of doubling and multiplying by 3. num_tmp = [ self.mul( self.add(x0, x1, comment="Doubling slope numerator start"), self.sub(x0, x1), ), self.mul(x0, x1), ] num = [ self.mul(num_tmp[0], self.set_or_get_constant(3)), self.mul( num_tmp[1], self.set_or_get_constant(6), comment="Doubling slope numerator end", ), ] den = self.vector_add(Q[1], Q[1]) return self.fp2_div(num, den) def compute_adding_slope( self, Qa: tuple[ list[ModuloCircuitElement], list[ModuloCircuitElement], ], Qb: tuple[ list[ModuloCircuitElement], list[ModuloCircuitElement], ], ) -> list[ModuloCircuitElement]: # num = ya - yb # den = xa - xb num = self.vector_sub(Qa[1], Qb[1]) den = self.vector_sub(Qa[0], Qb[0]) return self.fp2_div(num, den) def build_sparse_line_eval( self, R0: tuple[ModuloCircuitElement, ModuloCircuitElement], R1: tuple[ModuloCircuitElement, ModuloCircuitElement], yInv: ModuloCircuitElement, xNegOverY: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: # Mocked ModuloCircuitElement for ZERO and ONE. # They are not part of the circuit because only the non-zero or non-ones will be used due do the # known-in-advance sparsity ZERO, ONE = ModuloCircuitElement(self.field(0), -1), ModuloCircuitElement( self.field(1), -1 ) if self.curve_id == BN254_ID: return [ ONE, self.mul( self.add(R0[0], self.mul(self.set_or_get_constant(-9), R0[1])), xNegOverY, comment="eval bn line by xNegOverY", ), ZERO, self.mul( self.add(R1[0], self.mul(self.set_or_get_constant(-9), R1[1])), yInv, comment="eval bn line by yInv", ), ZERO, ZERO, ZERO, self.mul(R0[1], xNegOverY, comment="eval bn line by xNegOverY"), ZERO, self.mul(R1[1], yInv, comment="eval bn line by yInv"), ZERO, ZERO, ] elif self.curve_id == BLS12_381_ID: return [ self.mul( self.sub(R1[0], R1[1]), yInv, comment="eval bls line by yInv" ), # nr=1 ZERO, self.mul( self.sub(R0[0], R0[1]), xNegOverY, comment="eval blsline by xNegOverY", ), # nr=1 ONE, ZERO, ZERO, self.mul(R1[1], yInv, comment="eval bls line by yInv"), ZERO, self.mul(R0[1], xNegOverY, comment="eval bls line by xNegOverY"), ZERO, ZERO, ZERO, ] else: raise NotImplementedError def _add( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: return (None, None), self.get_next_precomputed_line() λ = self.compute_adding_slope(Qa, Qb) xr = self.vector_sub(X=self.fp2_square(X=λ), Y=self.vector_add(Qa[0], Qb[0])) yr = self.vector_sub( X=self.fp2_mul(X=λ, Y=self.vector_sub(Qa[0], xr)), Y=Qa[1], ) p = (xr, yr) lineR0 = λ lineR1 = self.vector_sub(self.fp2_mul(λ, Qa[0]), Qa[1]) return p, (lineR0, lineR1) def add_step( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): p, (lineR0, lineR1) = self._add(Qa, Qb, k) line = self.build_sparse_line_eval( R0=lineR0, R1=lineR1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) return p, line def _line_compute( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: return self.get_next_precomputed_line() λ = self.compute_adding_slope(Qa, Qb) lineR0 = λ lineR1 = self.vector_sub(self.fp2_mul(λ, Qa[0]), Qa[1]) return lineR0, lineR1 def line_compute( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): lineR0, lineR1 = self._line_compute(Qa, Qb, k) line = self.build_sparse_line_eval( R0=lineR0, R1=lineR1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) return line def _double( self, Q: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int ): """ Perform a single doubling of a point on an elliptic curve and store the line evaluation, including computations that involve the y coordinate. :param p1: A tuple representing the point on the curve (x, y) in the extension field. :return: A tuple containing the doubled point and the line evaluation. """ if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: return ((None, None), self.get_next_precomputed_line()) self.ops_counter["Double Step"] += 1 λ = self.compute_doubling_slope(Q) # Compute λ = 3x² / 2y # Compute xr = λ² - 2x xr = self.vector_sub(X=self.fp2_square(X=λ), Y=self.vector_add(Q[0], Q[0])) # Compute yr = λ(x - xr) - y yr = self.vector_sub(X=self.fp2_mul(λ, self.vector_sub(Q[0], xr)), Y=Q[1]) p = (xr, yr) lineR0 = λ lineR1 = self.vector_sub(self.fp2_mul(λ, Q[0]), Q[1]) return p, (lineR0, lineR1) def double_step( self, Q: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): p, (lineR0, lineR1) = self._double(Q, k) line = self.build_sparse_line_eval( R0=lineR0, R1=lineR1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) return p, line def _double_and_add( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ) -> list[ModuloCircuitElement]: if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: return ( (None, None), self.get_next_precomputed_line(), self.get_next_precomputed_line(), ) self.ops_counter["Double-and-Add Step"] += 1 # Computes 2Qa+Qb as (Qa+Qb)+Qa # https://arxiv.org/pdf/math/0208038.pdf 3.1 λ1 = self.compute_adding_slope(Qa, Qb) # compute x3 = λ1²-x1-x2 x3 = self.vector_sub(X=self.fp2_square(X=λ1), Y=self.vector_add(Qa[0], Qb[0])) # omit y3 computation line1R0 = λ1 line1R1 = self.vector_sub(self.fp2_mul(λ1, Qa[0]), Qa[1]) # compute λ2 = -λ1-2y1/(x3-x1) num = self.vector_add(Qa[1], Qa[1]) den = self.vector_sub(x3, Qa[0]) λ2 = self.vector_neg(self.vector_add(λ1, self.fp2_div(num, den))) # compute xr = λ2²-x1-x3 x4 = self.vector_sub(self.vector_sub(self.fp2_square(λ2), Qa[0]), x3) # compute y4 = λ2(x1 - x4)-y1 y4 = self.vector_sub(self.fp2_mul(λ2, self.vector_sub(Qa[0], x4)), Qa[1]) line2R0 = λ2 line2R1 = self.vector_sub(self.fp2_mul(λ2, Qa[0]), Qa[1]) return (x4, y4), (line1R0, line1R1), (line2R0, line2R1) def double_and_add_step( self, Qa: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], Qb: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int, ): (new_x, new_y), (line1R0, line1R1), (line2R0, line2R1) = self._double_and_add( Qa, Qb, k ) line1 = self.build_sparse_line_eval( R0=line1R0, R1=line1R1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) line2 = self.build_sparse_line_eval( R0=line2R0, R1=line2R1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) return (new_x, new_y), line1, line2 def _triple( self, Q: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int ): if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: return ( (None, None), self.get_next_precomputed_line(), self.get_next_precomputed_line(), ) self.ops_counter["Triple Step"] += 1 # Compute λ = 3x² / 2y. Manually to keep den = 2y to be re-used for λ2. x0, x1 = Q[0][0], Q[0][1] num_tmp = [ self.mul(self.add(x0, x1), self.sub(x0, x1)), self.mul(x0, x1), ] num = [ self.mul(num_tmp[0], self.set_or_get_constant(3)), self.mul(num_tmp[1], self.set_or_get_constant(6)), ] den = self.vector_add(Q[1], Q[1]) λ1 = self.fp2_div(num, den) line1R0 = λ1 line1R1 = self.vector_sub(self.fp2_mul(λ1, Q[0]), Q[1]) # x2 = λ1^2 - 2x x2 = self.vector_sub(self.fp2_square(λ1), self.vector_add(Q[0], Q[0])) # ommit yr computation, and # compute λ2 = 2y/(x2 − x) − λ1. # However in https://github.com/Consensys/gnark/blob/7cfcd5a723b0726dcfe75a5fc7249a23d690b00b/std/algebra/emulated/sw_bls12381/pairing.go#L548 # It's coded as x - x2. λ2 = self.vector_sub(self.fp2_div(den, self.vector_sub(Q[0], x2)), λ1) line2R0 = λ2 line2R1 = self.vector_sub(self.fp2_mul(λ2, Q[0]), Q[1]) # // xr = λ²-p.x-x2 xr = self.vector_sub(self.fp2_square(λ2), self.vector_add(Q[0], x2)) # // yr = λ(p.x-xr) - p.y yr = self.vector_sub(self.fp2_mul(λ2, self.vector_sub(Q[0], xr)), Q[1]) return (xr, yr), (line1R0, line1R1), (line2R0, line2R1) def triple_step( self, Q: tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]], k: int ): (new_x, new_y), (line1R0, line1R1), (line2R0, line2R1) = self._triple(Q, k) line1 = self.build_sparse_line_eval( R0=line1R0, # Directly store λ as R0 R1=line1R1, # Compute R1 as λ*x - y yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) line2 = self.build_sparse_line_eval( R0=line2R0, R1=line2R1, yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) return (new_x, new_y), line1, line2 def bit_0_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, ): """ Compute the bit 0 case of the Miller loop. params : f : the current miller loop FP12 element points : the list of points to double n_pairs : the number of pairs to double returns : the new miller loop FP12 element and the new points """ assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1 = self.double_step(points[k], k) new_lines.append(l1) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, *new_lines], 12, Ps_sparsities=[None, None] + [self.line_sparsity] * n_pairs, ) return new_f, new_points def bit_1_init_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, ): """ Compute the bit 1 case of the Miller loop when it is the first bit. Uses triple step instead of double and add. """ assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1, l2 = self.triple_step(points[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, *new_lines], 12, Ps_sparsities=[None, None] + [self.line_sparsity] * n_pairs * 2, ) return new_f, new_points def bit_1_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], Q_select: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, ): """ Compute the bit 1 case of the Miller loop. params : f : the current miller loop FP12 element points : the list of points to double Q_select : the list of points to add. Q_select[k] is the point to add if the k-th bit is 1, and the negation of the point if the k-th bit is -1. n_pairs : the number of pairs to double returns : the new miller loop FP12 element and the new points """ assert len(points) == n_pairs == len(Q_select) new_lines = [] new_points = [] for k in range(n_pairs): T, l1, l2 = self.double_and_add_step(points[k], Q_select[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, *new_lines], 12, Ps_sparsities=[None, None] + [self.line_sparsity] * n_pairs * 2, ) return new_f, new_points def _bn254_finalize_step( self, Qs: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], ): def set_or_get_constants(): nr1p2 = [ self.set_or_get_constant( self.field( 21575463638280843010398324269430826099269044274347216827212613867836435027261 ) ), self.set_or_get_constant( self.field( 10307601595873709700152284273816112264069230130616436755625194854815875713954 ) ), ] # Non residue 1 power 2 nr1p3 = [ self.set_or_get_constant( self.field( 2821565182194536844548159561693502659359617185244120367078079554186484126554 ), ), self.set_or_get_constant( self.field( 3505843767911556378687030309984248845540243509899259641013678093033130930403 ), ), ] # Non residue 1 power 3 nr2p2 = self.set_or_get_constant( self.field( 21888242871839275220042445260109153167277707414472061641714758635765020556616 ) # non_residue_2_power_2 ) nr2p3 = self.set_or_get_constant( self.field( -21888242871839275222246405745257275088696311157297823662689037894645226208582 ) ) # (-1) * non_residue_2_power_3 return nr1p2, nr1p3, nr2p2, nr2p3 new_lines = [] for k in range(self.n_pairs): if self.precompute_lines and (k + 1) <= self.n_points_precomputed_lines: new_lines.append( (self.get_next_precomputed_line(), self.get_next_precomputed_line()) ) else: nr1p2, nr1p3, nr2p2, nr2p3 = set_or_get_constants() q1x = [self.Q[k][0][0], self.neg(self.Q[k][0][1])] q1y = [self.Q[k][1][0], self.neg(self.Q[k][1][1])] q1x = self.fp2_mul( q1x, nr1p2, ) q1y = self.fp2_mul( q1y, nr1p3, ) q2x = self.vector_scale( self.Q[k][0], nr2p2, ) q2y = self.vector_scale( self.Q[k][1], nr2p3, ) T, (l1R0, l1R1) = self._add(Qs[k], (q1x, q1y), k) l2R0, l2R1 = self._line_compute(T, (q2x, q2y), k) new_lines.append(((l1R0, l1R1), (l2R0, l2R1))) return new_lines def bn254_finalize_step( self, Qs: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], ): lines = self._bn254_finalize_step(Qs) lines_evaluated = [] for k, (l1, l2) in enumerate(lines): line_eval = self.build_sparse_line_eval( R0=l1[0], R1=l1[1], yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) line_eval2 = self.build_sparse_line_eval( R0=l2[0], R1=l2[1], yInv=self.yInv[k], xNegOverY=self.xNegOverY[k], ) lines_evaluated.append(line_eval) lines_evaluated.append(line_eval2) return lines_evaluated def miller_loop(self, n_pairs: int) -> list[ModuloCircuitElement]: f = [self.set_or_get_constant(1)] + [self.set_or_get_constant(0)] * 11 start_index = len(self.loop_counter) - 2 if self.loop_counter[start_index] == 1: # Handle case when first bit is +1, need to triple point instead of double and add. f, Qs = self.bit_1_init_case(f, self.Q, n_pairs) elif self.loop_counter[start_index] == 0: f, Qs = self.bit_0_case(f, self.Q, n_pairs) else: raise NotImplementedError( f"Init bit {self.loop_counter[start_index]} not implemented" ) # Rest of miller loop. for i in range(start_index - 1, -1, -1): if self.loop_counter[i] == 0: f, Qs = self.bit_0_case(f, Qs, n_pairs) elif self.loop_counter[i] == 1 or self.loop_counter[i] == -1: # Choose Q or -Q depending on the bit for the addition. Q_selects = [ self.Q[k] if self.loop_counter[i] == 1 else self.Qneg[k] for k in range(n_pairs) ] f, Qs = self.bit_1_case(f, Qs, Q_selects, n_pairs) else: raise NotImplementedError(f"Bit {self.loop_counter[i]} not implemented") if self.curve_id == CurveID.BN254.value: lines = self.bn254_finalize_step(Qs) f = self.extf_mul( [f, *lines], 12, Ps_sparsities=[None] + [self.line_sparsity] * self.n_pairs * 2, ) elif self.curve_id == CurveID.BLS12_381.value: f = [ f[0], self.neg(f[1]), f[2], self.neg(f[3]), f[4], self.neg(f[5]), f[6], self.neg(f[7]), f[8], self.neg(f[9]), f[10], self.neg(f[11]), ] else: raise NotImplementedError(f"Curve {self.curve_id} not implemented") return f def precompute_lines(Qs: list[G2Point]) -> list[PyFelt]: if len(Qs) == 0: return [] curve_id = Qs[0].curve_id.value loop_counter = CURVES[curve_id].loop_counter start_index = len(loop_counter) - 2 n_pairs = len(Qs) circuit = MultiMillerLoopCircuit( name="precompute_helper", curve_id=curve_id, n_pairs=n_pairs, hash_input=False, precompute_lines=False, ) field = circuit.field for Q in Qs: circuit.Q.append( ( [ circuit.write_element(field(Q.x[0])), circuit.write_element(field(Q.x[1])), ], [ circuit.write_element(field(Q.y[0])), circuit.write_element(field(Q.y[1])), ], ) ) circuit.precompute_consts(skip_P_precompute=True) lines = [] if loop_counter[start_index] == 1: # Handle case when first bit is +1, need to triple point instead of double and add. new_points = [] new_lines = [] for k in range(n_pairs): T, l1, l2 = circuit._triple(circuit.Q[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) elif loop_counter[start_index] == 0: new_lines = [] new_points = [] for k in range(n_pairs): T, l1 = circuit._double(circuit.Q[k], k) new_lines.append(l1) new_points.append(T) else: raise NotImplementedError( f"Init bit {loop_counter[start_index]} not implemented" ) points = new_points lines.append(new_lines) # Rest of miller loop.= for i in range(start_index - 1, -1, -1): new_lines = [] new_points = [] if loop_counter[i] == 0: for k in range(n_pairs): T, l1 = circuit._double(points[k], k) new_lines.append(l1) new_points.append(T) elif loop_counter[i] == 1 or loop_counter[i] == -1: # Choose Q or -Q depending on the bit for the addition. Q_selects = [ circuit.Q[k] if loop_counter[i] == 1 else circuit.Qneg[k] for k in range(n_pairs) ] for k in range(n_pairs): T, l1, l2 = circuit._double_and_add(points[k], Q_selects[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) else: raise NotImplementedError(f"Bit {loop_counter[i]} not implemented") points = new_points lines.append(new_lines) if curve_id == CurveID.BN254.value: final_lines = circuit._bn254_finalize_step(points) for l1, l2 in final_lines: lines.append(l1) lines.append(l2) elif curve_id == CurveID.BLS12_381.value: pass else: raise NotImplementedError(f"Curve {curve_id} not implemented") return [x.felt for x in flatten(lines)] ================================================ FILE: hydra/garaga/precompiled_circuits/multi_pairing_check.py ================================================ from garaga.algebra import get_sparsity from garaga.curves import CURVES, CurveID, get_base_field from garaga.hints.frobenius import get_frobenius_maps from garaga.hints.multi_miller_witness import get_final_exp_witness from garaga.hints.tower_backup import E6, E12 from garaga.modulo_circuit import ModuloCircuitElement, PyFelt, WriteOps from garaga.points import G1G2Pair, G1Point, G2Point from garaga.precompiled_circuits.multi_miller_loop import MultiMillerLoopCircuit def get_root_and_scaling_factor( curve_id: int, P: list[G1Point | tuple[ModuloCircuitElement, ModuloCircuitElement]], Q: list[ G2Point | tuple[ tuple[ModuloCircuitElement, ModuloCircuitElement], tuple[ModuloCircuitElement, ModuloCircuitElement], ] ], m: list[ModuloCircuitElement] = None, ) -> tuple[list[PyFelt], list[PyFelt], list[int]]: assert ( len(P) == len(Q) >= 2 ), f"P and Q must have the same length and >= 2, got {len(P)} and {len(Q)}" field = get_base_field(curve_id) c_input: list[PyFelt] = [] c: MultiMillerLoopCircuit = MultiMillerLoopCircuit( name="mock", curve_id=curve_id, n_pairs=len(P) ) if isinstance(P[0], G1Point): c.write_p_and_q(P, Q) elif isinstance(P[0], tuple) and isinstance(P[0][0], ModuloCircuitElement): for p, q in zip(P, Q): c_input.append(p[0].felt) c_input.append(p[1].felt) c_input.append(q[0][0].felt) c_input.append(q[0][1].felt) c_input.append(q[1][0].felt) c_input.append(q[1][1].felt) c.write_p_and_q_raw(c_input) f = E12.from_direct(c.miller_loop(len(P)), curve_id) if m is not None: M = E12.from_direct(m, curve_id) f = f * M # h = (CURVES[curve_id].p ** 12 - 1) // CURVES[curve_id].n # assert f**h == E12.one(curve_id) lambda_root_e12, scaling_factor_e12 = get_final_exp_witness(curve_id, f) lambda_root: list[PyFelt] scaling_factor: list[PyFelt] lambda_root, scaling_factor = ( ( lambda_root_e12.__inv__().to_direct() if curve_id == CurveID.BLS12_381.value else lambda_root_e12.to_direct() ), # Pass lambda_root inverse directly for BLS. scaling_factor_e12.to_direct(), ) e6_subfield = E12([E6.random(curve_id), E6.zero(curve_id)], curve_id) scaling_factor_sparsity = get_sparsity(e6_subfield.to_direct()) # Assert sparsity is correct: for every index where the sparsity is 0, the coefficient must 0 in scaling factor for i in range(len(scaling_factor_sparsity)): if scaling_factor_sparsity[i] == 0: assert scaling_factor[i].value == 0 # Therefore scaling factor lies in Fp6 return lambda_root, scaling_factor, scaling_factor_sparsity def get_max_Q_degree(curve_id: int, n_pairs: int) -> int: if curve_id == CurveID.BN254.value: line_degree = 9 elif curve_id == CurveID.BLS12_381.value: line_degree = 8 else: raise NotImplementedError(f"Curve {curve_id} not implemented") f_degree = 11 lambda_root_degree = 11 if curve_id == CurveID.BN254.value: # Largest degree happen in bit_10 case where we do (f*f*C * Π_n_pairs(line)^2 * Π_n_pairs(line)) max_q_degree = ( 4 * f_degree + 2 * lambda_root_degree + 4 * line_degree * n_pairs + line_degree * n_pairs - 12 ) else: # Largest Q happens in bit_00 case where we do (f*f* Π_n_pairs(line)^2 * Π_n_pairs(line) max_q_degree = ( 4 * f_degree + 2 * line_degree * n_pairs + line_degree * n_pairs - 12 ) return max_q_degree class MultiPairingCheckCircuit(MultiMillerLoopCircuit): def __init__( self, name: str, curve_id: int, n_pairs: int, hash_input: bool = True, init_hash: int = None, compilation_mode: int = 0, precompute_lines: bool = False, n_points_precomputed_lines: int = None, ): assert n_pairs >= 2, "n_pairs must be >= 2 for pairing checks" super().__init__( name=name, curve_id=curve_id, n_pairs=n_pairs, hash_input=hash_input, init_hash=init_hash, compilation_mode=compilation_mode, precompute_lines=precompute_lines, n_points_precomputed_lines=n_points_precomputed_lines, ) self.frobenius_maps = {} for i in [1, 2, 3]: _, self.frobenius_maps[i] = get_frobenius_maps( curve_id=curve_id, extension_degree=self.extension_degree, frob_power=i ) def frobenius( self, X: list[ModuloCircuitElement], frob_power: int ) -> list[ModuloCircuitElement]: frob = [None] * self.extension_degree for i, list_op in enumerate(self.frobenius_maps[frob_power]): list_op_result = [] for index, constant in list_op: if constant == 1: list_op_result.append(X[index]) else: list_op_result.append( self.mul( X[index], self.set_or_get_constant(self.field(constant)) ) ) frob[i] = list_op_result[0] for op_res in list_op_result[1:]: frob[i] = self.add(frob[i], op_res) return frob def bit_0_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, ): """ Compute the bit 0 case of the Miller loop. params : f : the current miller loop FP12 element points : the list of points to double n_pairs : the number of pairs to double returns : the new miller loop FP12 element and the new points """ assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1 = self.double_step(points[k], k) new_lines.append(l1) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, *new_lines], 12, Ps_sparsities=[None, None] + [self.line_sparsity] * n_pairs, ) return new_f, new_points def bit_00_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, ): """ Compute the bit 00 case of the Miller loop. params : f : the current miller loop FP12 element points : the list of points to double n_pairs : the number of pairs to double returns : the new miller loop FP12 element and the new points """ assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1 = self.double_step(points[k], k) new_lines.append(l1) new_lines.append(l1) # Double since it's going to be squared new_points.append(T) new_new_points = [] new_new_lines = [] for k in range(n_pairs): T, l1 = self.double_step(new_points[k], k) new_new_lines.append(l1) new_new_points.append(T) # (f^2 * Π_(new_lines))^2 * Π_new_new_lines = f^4 * Π_new_lines^2 * Π_new_new_lines new_f = self.extf_mul( [f, f, f, f, *new_lines, *new_new_lines], 12, Ps_sparsities=[None, None, None, None] + [self.line_sparsity] * n_pairs * 2 + [self.line_sparsity] * n_pairs, ) return new_f, new_new_points def bit_01_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], Q_selects: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], c_or_c_inv: list[ModuloCircuitElement], n_pairs: int, ): assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1 = self.double_step(points[k], k) new_lines.append(l1) new_lines.append(l1) # Double since it's going to be squared new_points.append(T) new_new_points = [] new_new_lines = [] for k in range(n_pairs): T, l1, l2 = self.double_and_add_step(new_points[k], Q_selects[k], k) new_new_lines.append(l1) new_new_lines.append(l2) new_new_points.append(T) # (f^2 * Π_(new_lines))^2 * Π_new_new_lines = f^4 * Π_new_lines^2 * Π_new_new_lines new_f = self.extf_mul( [f, f, f, f, *new_lines, *new_new_lines, c_or_c_inv], 12, Ps_sparsities=[None] * 4 + [self.line_sparsity] * n_pairs * 2 + [self.line_sparsity] * n_pairs * 2 + [None], ) return new_f, new_new_points def bit_10_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], Q_selects: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], c_or_c_inv: list[ModuloCircuitElement], n_pairs: int, ): assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1, l2 = self.double_and_add_step(points[k], Q_selects[k], k) new_lines.append(l1) new_lines.append(l1) # Double since it's going to be squared new_lines.append(l2) new_lines.append(l2) # Double since it's going to be squared new_points.append(T) new_new_points = [] new_new_lines = [] for k in range(n_pairs): T, l1 = self.double_step(new_points[k], k) new_new_lines.append(l1) new_new_points.append(T) new_f = self.extf_mul( [f, f, f, f, c_or_c_inv, c_or_c_inv, *new_lines, *new_new_lines], 12, Ps_sparsities=[None] * 4 + [None, None] + [self.line_sparsity] * n_pairs * 4 + [self.line_sparsity] * n_pairs, ) return new_f, new_new_points def bit_1_init_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, c: list[ModuloCircuitElement], ): """ Compute the bit 1 case of the Miller loop when it is the first bit (positive). Uses triple step instead of double and add. """ assert len(points) == n_pairs new_lines = [] new_points = [] for k in range(n_pairs): T, l1, l2 = self.triple_step(points[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, c, *new_lines], 12, Ps_sparsities=[None, None, None] + [self.line_sparsity] * n_pairs * 2, ) return new_f, new_points def bit_1_case( self, f: list[ModuloCircuitElement], points: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], Q_select: list[tuple[list[ModuloCircuitElement], list[ModuloCircuitElement]]], n_pairs: int, c_or_c_inv: list[ModuloCircuitElement], ): """ Compute the bit 1 case of the Miller loop. params : f : the current miller loop FP12 element points : the list of points to double Q_select : the list of points to add. Q_select[k] is the point to add if the k-th bit is 1, and the negation of the point if the k-th bit is -1. n_pairs : the number of pairs to double c_or_c_inv : the lambda-th root c or its inverse depending on the bit (c_inv if 1, c if -1) returns : the new miller loop FP12 element and the new points """ assert len(points) == n_pairs == len(Q_select) new_lines = [] new_points = [] for k in range(n_pairs): T, l1, l2 = self.double_and_add_step(points[k], Q_select[k], k) new_lines.append(l1) new_lines.append(l2) new_points.append(T) # Square f and multiply by lines for all pairs new_f = self.extf_mul( [f, f, c_or_c_inv, *new_lines], 12, Ps_sparsities=[None, None, None] + [self.line_sparsity] * n_pairs * 2, ) return new_f, new_points def multi_pairing_check( self, n_pairs: int, m: list[ModuloCircuitElement] | None = None ) -> tuple[ list[ModuloCircuitElement], list[ModuloCircuitElement], list[ModuloCircuitElement], ]: lambda_root, scaling_factor, scaling_factor_sparsity = ( get_root_and_scaling_factor(self.curve_id, self.P, self.Q, m) ) c_or_c_inv = self.write_elements(lambda_root, WriteOps.COMMIT) w = self.write_elements( scaling_factor, WriteOps.COMMIT, scaling_factor_sparsity ) if self.curve_id == CurveID.BLS12_381.value: # Conjugate c so that the final conjugate in BLS loop gives indeed f/c^(-x), as conjugate(f/conjugate(c^(-x))) = conjugate(f)/c^(-x) lambda_root = None lambda_root_inverse = c_or_c_inv c_inv = self.conjugate_e12d(lambda_root_inverse) elif self.curve_id == CurveID.BN254.value: lambda_root = c = c_or_c_inv lambda_root_inverse = c_inv = self.extf_inv(c_or_c_inv, 12) # Init f as 1/c = 1 / (λ-th √(f_output*scaling_factor)), where: # λ = 6 * x + 2 + q - q**2 + q**3 for BN # λ = -x + q for BLS # Miller loop will compute f_output/c^(6*x2) if BN, or f_output/c^(-x) if BLS f = c_inv start_index = len(self.loop_counter) - 2 if self.loop_counter[start_index] == 1: # Handle case when first bit is +1, need to triple point instead of double and add. f, Qs = self.bit_1_init_case(f, self.Q, n_pairs, c_inv) elif self.loop_counter[start_index] == 0: f, Qs = self.bit_0_case(f, self.Q, n_pairs) else: raise NotImplementedError( f"Init bit {self.loop_counter[start_index]} not implemented" ) i = start_index - 1 while i >= 0: if self.loop_counter[i] == 0: # First bit is 0 if i > 0: # Check next bit if it exists next_bit = self.loop_counter[i - 1] if next_bit == 0: # 00 case f, Qs = self.bit_00_case(f, Qs, n_pairs) i -= 1 # Skip next bit elif next_bit in (1, -1) and self.curve_id == CurveID.BN254.value: # 01 or 0(-1) case Q_selects = [ self.Q[k] if next_bit == 1 else self.Qneg[k] for k in range(n_pairs) ] c_or_c_inv = c_inv if next_bit == 1 else c f, Qs = self.bit_01_case(f, Qs, Q_selects, c_or_c_inv, n_pairs) i -= 1 # Skip next bit else: # Single 0 (BLS only) f, Qs = self.bit_0_case(f, Qs, n_pairs) else: # Single 0 at the end f, Qs = self.bit_0_case(f, Qs, n_pairs) elif self.loop_counter[i] in (1, -1): # First bit is ±1 # Calculate Q_selects and c_or_c_inv based on the si Q_selects = [ self.Q[k] if self.loop_counter[i] == 1 else self.Qneg[k] for k in range(n_pairs) ] c_or_c_inv = c_inv if self.loop_counter[i] == 1 else c if ( i > 0 and self.loop_counter[i - 1] == 0 and self.curve_id == CurveID.BN254.value ): # 10 or (-1)0 case f, Qs = self.bit_10_case(f, Qs, Q_selects, c_or_c_inv, n_pairs) i -= 1 # Skip next bit elif i == 0 or self.curve_id == CurveID.BLS12_381.value: # Single ±1 at the end f, Qs = self.bit_1_case(f, Qs, Q_selects, n_pairs, c_or_c_inv) else: raise NotImplementedError( f"Bit {self.loop_counter[i]} not implemented" ) else: raise NotImplementedError(f"Bit {self.loop_counter[i]} not implemented") i -= 1 final_r_sparsity = [1] + [0] * 11 if self.curve_id == CurveID.BN254.value: lines = self.bn254_finalize_step(Qs) f = self.extf_mul( [f, *lines], 12, Ps_sparsities=[None] + [self.line_sparsity] * self.n_pairs * 2, ) # λ = 6 * x + 2 + q - q**2 + q**3 c_inv_frob_1 = self.frobenius(c_inv, 1) c_frob_2 = self.frobenius(c, 2) c_inv_frob_3 = self.frobenius(c_inv, 3) f = self.extf_mul( ( [f, w, c_inv_frob_1, c_frob_2, c_inv_frob_3] + ([m] if m is not None else []) ), 12, Ps_sparsities=( [None, scaling_factor_sparsity, None, None, None] + ([None] if m is not None else []) ), r_sparsity=final_r_sparsity, ) elif self.curve_id == CurveID.BLS12_381.value: # λ = -x + q for BLS c_inv_frob_1 = self.frobenius(c_inv, 1) f = self.conjugate_e12d(f) w = self.conjugate_e12d(w) c_inv_frob_1 = self.conjugate_e12d(c_inv_frob_1) f = self.extf_mul( Ps=[f, w, c_inv_frob_1] + ([m] if m is not None else []), extension_degree=12, Ps_sparsities=[None, scaling_factor_sparsity, None] + ([None] if m is not None else []), r_sparsity=final_r_sparsity, ) else: raise NotImplementedError(f"Curve {self.curve_id} not implemented") assert [fi.value for fi in f] == [1] + [ 0 ] * 11, f"Pairing check failed: {[fi.value for fi in f]}" return ( f, lambda_root, lambda_root_inverse, scaling_factor, scaling_factor_sparsity, ) def get_pairing_check_input( curve_id: CurveID, n_pairs: int, include_m: bool = False, return_pairs: bool = False ) -> tuple[list[PyFelt | G1G2Pair], list[PyFelt] | G1G2Pair | None]: """ Generates test input data for pairing check circuits that satisfy e(P1,Q1) * ... * e(Pn,Qn) = 1. For n_pairs=2: Creates BLS signature verification scenario with (signature, message_hash) and (generator, -public_key). For n_pairs>2: Generates random points where the last pair is adjusted to make the product equal 1. Args: curve_id: The elliptic curve to generate points on n_pairs: Number of pairing pairs (minimum 2) include_m: If True, treats last pair separately and computes its Miller loop result return_pairs: If True, returns G1G2Pair objects; if False, returns flattened field elements Returns: - If return_pairs=True: (list of G1G2Pair objects, optional extra pair) - If return_pairs=False: (flattened field elements, optional Miller loop result) """ n_pairs = n_pairs + include_m assert n_pairs >= 2, "n_pairs must be >= 2 for pairing checks" field = get_base_field(curve_id.value) if n_pairs == 2: # Generate inputs resembling BLS signature verification curve = CURVES[curve_id.value] secret_key = field.random(curve.n).value public_key = G2Point.get_nG(curve_id, secret_key) message_hash = G1Point.gen_random_point(curve_id) signature = message_hash.scalar_mul(secret_key) P = [signature, message_hash] Q = [G2Point.get_nG(curve_id, 1), -public_key] else: p = G1Point.gen_random_point(curve_id) q = G2Point.gen_random_point(curve_id) P = [p] * n_pairs Q = [q] * n_pairs P[-1] = p.scalar_mul(-(n_pairs - 1)) c_input = [] for p, q in zip(P, Q): c_input.append(field(p.x)) c_input.append(field(p.y)) c_input.append(field(q.x[0])) c_input.append(field(q.x[1])) c_input.append(field(q.y[0])) c_input.append(field(q.y[1])) if return_pairs: if include_m: return [G1G2Pair(p, q) for p, q in zip(P[:-1], Q[:-1])], G1G2Pair( P[-1], Q[-1] ) else: return [G1G2Pair(p, q) for p, q in zip(P, Q)], None else: if include_m: mloop_circuit = MultiMillerLoopCircuit( name="mock", curve_id=curve_id.value, n_pairs=1 ) mloop_circuit.write_p_and_q_raw(c_input[-6:]) M = mloop_circuit.miller_loop(n_pairs=1) M = [mi.felt for mi in M] return c_input[:-6], M else: return c_input, None ================================================ FILE: hydra/garaga/precompiled_circuits/poseidon_bn254.py ================================================ from garaga.curves import CurveID, get_base_field from garaga.modulo_circuit import ModuloCircuit, ModuloCircuitElement from garaga.modulo_circuit_structs import u384 # Global circuit definition curve_id = CurveID.GRUMPKIN # BN254 field = get_base_field(curve_id) COMPILATION_MODE = 1 # 1 for Cairo, 0 for CairoZero. circuit = ModuloCircuit( name=f"poseidon_{curve_id.name.lower()}", curve_id=curve_id.value, generic_circuit=False, compilation_mode=COMPILATION_MODE, ) # Define inputs to the circuit x = circuit.write_struct(u384("x", [field(1)])) # Input x = 1 y = circuit.write_struct(u384("y", [field(2)])) # Input y = 2 # Utility functions for Poseidon hash def sigma(value): """Applies the Poseidon sigma function.""" x2 = circuit.mul(value, value) # (value * value) x4 = circuit.mul(x2, x2) # (x2 * x2) return circuit.mul(x4, value) # (x4 * value) def ark(t, C, r, state): """Applies the Ark step of the Poseidon hash.""" return [circuit.add(state[i], C[i + r]) for i in range(t)] def iterated_add(terms): """Performs iterative addition since circuit.add can only take two parameters.""" result = terms[0] for term in terms[1:]: result = circuit.add(result, term) return result def iterated_mul(terms): """Performs iterative multiplication since circuit.mul can only take two parameters.""" result = terms[0] for term in terms[1:]: result = circuit.mul(result, term) return result def mix(t, M, state): """Applies the Mix step of the Poseidon hash.""" return [ iterated_add([circuit.mul(M[j][i], state[j]) for j in range(t)]) for i in range(t) ] def mix_last(t, M, s, state): """Applies the MixLast step of the Poseidon hash.""" return iterated_add([circuit.mul(M[j][s], state[j]) for j in range(t)]) def mix_s(t, S, r, state): """Applies the MixS step of the Poseidon hash.""" result = [ iterated_add([circuit.mul(S[(t * 2 - 1) * r + i], state[i]) for i in range(t)]) ] result.extend( circuit.add(state[i], circuit.mul(state[0], S[(t * 2 - 1) * r + t + i - 1])) for i in range(1, t) ) return result def poseidon_hash( x: ModuloCircuitElement, y: ModuloCircuitElement ) -> ModuloCircuitElement: """Computes the Poseidon hash for two inputs x and y.""" if isinstance(x, int): x = circuit.write_element(x) if isinstance(y, int): y = circuit.write_element(y) if not isinstance(x, ModuloCircuitElement) or not isinstance( y, ModuloCircuitElement ): raise ValueError("x and y must be ModuloCircuitElement instances") t = 3 # 2 inputs + 1 state n_rounds_f = 8 # Full rounds n_rounds_p = 57 # Partial rounds state = [circuit.set_or_get_constant(0), x, y] # Example constants (these should match the specific Poseidon implementation) POSEIDON_C = [ 0xEE9A592BA9A9518D05986D656F40C2114C4993C11BB29938D21D47304CD8E6E, 0xF1445235F2148C5986587169FC1BCD887B08D4D00868DF5696FFF40956E864, 0x8DFF3487E8AC99E1F29A058D0FA80B930C728730B7AB36CE879F3890ECF73F5, 0x84D520E4E5BB469E1F9075CB7C490EFA59565EEDAE2D00CA8EF88CEEA2B0197, 0x2D15D982D99577FA33DA56722416FD734B3E667A2F9F15D8EB3E767AE0FD811E, 0xED2538844ABA161CF1578A43CF0364E91601F6536A5996D0EFBE65632C41B6D, 0x2600C27D879FBCA186E739E6363C71CF804C877D829B735DCC3E3AF02955E60A, 0x28F8BD44A583CBAA475BD15396430E7CCB99A5517440DFD970058558282BF2C5, 0x9CD7D4C380DC5488781AAD012E7EAEF1ED314D7F697A5572D030C55DF153221, 0x11BB6EE1291AABB206120ECAACE460D24B6713FEBE82234951E2BEE7D0F855F5, 0x2D74E8FA0637D9853310F3C0E3FAE1D06F171580F5B8FD05349CADEECFCEB230, 0x2735E4EC9D39BDFFAC9BEF31BACBA338B1A09559A511A18BE4B4D316ED889033, 0xF03C1E9E0895DB1A5DA6312FAA78E971106C33F826E08DCF617E24213132DFD, 0x17094CD297BF827CAF92920205B719C18741090B8F777811848A7E9EAD6778C4, 0xDB8F419C21F92461FC2B3219465798348DF90D4178042C81BA7D4B4D559E2B8, 0x243443613F64FFA417427ED5933FCFBC66809DB60B9CA1724A22709CECEEECE2, 0x22AF49FBFD5D7E9FCD256C25C07D3DD8ECBBAE6DEECD03AA04BB191FADA75411, 0x14FBD37FA8AD6E4E0C78A20D93C7230C4677F797B4327323F7F7C097C19420E0, 0x15A9298BBB882534D4B2C9FBC6E4EF4189420C4EB3F3E1EA22FAA7E18B5AE625, 0x2F7DE75F23DDAAA5221323EBCEB2F2AC83EEF92E854E75434C2F1D90562232BC, 0x36A4432A868283B78A315E84C4AE5AECA216F2FF9E9B2E623584F7479CD5C27, 0x2180D7786A8CF810E277218AB14A11E5E39F3C962F11E860AE1C5682C797DE5C, 0xA268EF870736EEBD0CB55BE640D73EE3778990484CC03CE53572377EEFFF8E4, 0x1EEFEFE11C0BE4664F2999031F15994829E982E8C90E09069DF9BAE16809A5B2, 0x27E87F033BD1E0A89CA596E8CB77FE3A4B8FB93D9A1129946571A3C3CF244C52, 0x1498A3E6599FE243321F57D6C5435889979C4F9D2A3E184D21451809178EE39, 0x27C0A41F4CB9FE67E9DD4D7CE33707F74D5D6BCC235BEF108DEA1BBEBDE507AA, 0x1F75230908B141B46637238B120FC770F4F4AE825D5004C16A7C91FE1DAE280F, 0x25F99A9198E923167BBA831B15FFFD2D7B97B3A089808D4EB1F0A085BEE21656, 0x101BC318E9EA5920D0F6ACDC2BB526593D3D56EC8ED14C67622974228BA900C6, 0x1A175607067D517397C1334ECB019754EBC0C852A3CF091EC1CCC43207A83C76, 0xF02F0E6D25F9EA3DEB245F3E8C381EE6B2EB380BA4AF5C1C4D89770155DF37B, 0x151D757ACC8237AF08D8A6677203EC9692565DE456AE789FF358B3163B393BC9, 0x256CD9577CEA143049E0A1FE0068DD20084980EE5B757890A79D13A3A624FAD4, 0x513ABAFF6195EA48833B13DA50E0884476682C3FBDD195497B8AE86E1937C61, 0x1D9570DC70A205F36F610251EE6E2E8039246E84E4AC448386D19DBAC4E4A655, 0x18F1A5194755B8C5D5D7F1BF8AAA6F56EFFB012DD784CF5E044EEC50B29FC9D4, 0x266B53B615EF73AC866512C091E4A4F2FA4BB0AF966EF420D88163238EEBBCA8, 0x2D63234C9207438AA42B8DE27644C02268304DFEB8C89A1A3F4FD6E8344AE0F7, 0x2AB30FBE51EE49BC7B3ADDE219A6F0B5FBB976205EF8DF7E0021DAEE6F55C693, 0x1AEE6D4B3EBE9366DCB9CCE48969D4DF1DC42ABCD528B270068D9207FA6A45C9, 0x1891AEAB71E34B895A79452E5864AE1D11F57646C60BB34AA211D123F6095219, 0x24492B5F95C0B0876437E94B4101C69118E16B2657771BD3A7CAAB01C818AA4B, 0x1752161B3350F7E1B3B2C8663A0D642964628213D66C10AB2FDDF71BCFDE68F, 0xAB676935722E2F67CFB84938E614C6C2F445B8D148DE54368CFB8F90A00F3A7, 0xB0F72472B9A2F5F45BC730117ED9AE5683FC2E6E227E3D4FE0DA1F7AA348189, 0x16AA6F9273ACD5631C201D1A52FC4F8ACAF2B2152C3AE6DF13A78A513EDCD369, 0x2F60B987E63614EB13C324C1D8716EB0BF62D9B155D23281A45C08D52435CD60, 0x18D24AE01DDE92FD7606BB7884554E9DF1CB89B042F508FD9DB76B7CC1B21212, 0x4FC3BF76FE31E2F8D776373130DF79D18C3185FDF1593960715D4724CFFA586, 0xD18F6B53FC69546CFDD670B41732BDF6DEE9E06B21260C6B5D26270468DBF82, 0xBA4231A918F13ACEC11FBAFA17C5223F1F70B4CDB045036FA5D7045BD10E24, 0x7B458B2E00CD7C6100985301663E7EC33C826DA0635FF1EBEDD0DD86120B4C8, 0x1C35C2D96DB90F4F6058E76F15A0C8286BBA24E2ED40B16CEC39E9FD7BAA5799, 0x1D12BEA3D8C32A5D766568F03DD1ECDB0A4F589ABBEF96945E0DDE688E292050, 0xD953E20022003270525F9A73526E9889C995BB62FDEA94313DB405A61300286, 0x29F053EC388795D786A40BEC4C875047F06FF0B610B4040A760E33506D2671E1, 0x4188E33735F46B14A4952A98463BC12E264D5F446E0C3F64B9679CAAAE44FC2, 0x149EC28846D4F438A84F1D0529431BB9E996A408B7E97EB3BF1735CDBE96F68F, 0xDE20FAE0AF5188BCA24B5F63630BAD47AEAFD98E651922D148CCE1C5FDDDEE8, 0x12D650E8F790B1253EA94350E722AD2F7D836C234B8660EDF449FBA6984C6709, 0x22AB53AA39F34AD30EA96717BA7446AAFDADBC1A8ABE28D78340DFC4BABB8F6C, 0x26503E8D4849BDF5450DABEA7907BC3DE0DE109871DD776904A129DB9149166C, 0x1D5E7A0E2965DFFA00F5454F5003C5C8EC34B23D897E7FC4C8064035B0D33850, 0xEE3D8DAA098BEE012D96B7EC48448C6BC9A6AEFA544615B9CB3C7BBD07104CB, 0x1BF282082A04979955D30754CD4D9056FA9EF7A7175703D91DC232B5F98EAD00, 0x7AE1344ABFC6C2CE3E951BC316BEE49971645F16B693733A0272173EE9AD461, 0x217E3A247827C376EC21B131D511D7DBDC98A36B7A47D97A5C8E89762EE80488, 0x215FFE584B0EB067A003D438E2FBE28BABE1E50EFC2894117509B616ADDC30EE, 0x1E770FC8ECBFDC8692DCEDC597C4CA0FBEC19B84E33DA57412A92D1D3CE3EC20, 0x2F6243CDA919BF4C9F1E3A8A6D66A05742914FC19338B3C0E50E828F69FF6D1F, 0x246EFDDC3117ECD39595D0046F44AB303A195D0E9CC89345D3C03FF87A11B693, 0x53E8D9B3EA5B8ED4FE006F139CBC4E0168B1C89A918DFBE602BC62CEC6ADF1, 0x1B894A2F45CB96647D910F6A710D38B7EB4F261BEEFFF135AEC04C1ABE59427B, 0xAEB1554E266693D8212652479107D5FDC077ABF88651F5A42553D54EC242CC0, 0x16A735F6F7209D24E6888680D1781C7F04BA7D71BD4B7D0E11FAF9DA8D9CA28E, 0x487B8B7FAB5FC8FD7C13B4DF0543CD260E4BCBB615B19374FF549DCF073D41B, 0x1E75B9D2C2006307124BEA26B0772493CFB5D512068C3AD677FDF51C92388793, 0x5120E3D0E28003C253B46D5FF77D272AE46FA1E239D1C6C961DCB02DA3B388F, 0xDA5FEB534576492B822E8763240119AC0900A053B171823F890F5FD55D78372, 0x2E211B39A023031A22ACC1A1F5F3BB6D8C2666A6379D9D2C40CC8F78B7BD9ABE, ] POSEIDON_M = [ [ 0x109B7F411BA0E4C9B2B70CAF5C36A7B194BE7C11AD24378BFEDB68592BA8118B, 0x2969F27EED31A480B9C36C764379DBCA2CC8FDD1415C3DDED62940BCDE0BD771, 0x143021EC686A3F330D5F9E654638065CE6CD79E28C5B3753326244EE65A1B1A7, ], [ 0x16ED41E13BB9C0C66AE119424FDDBCBC9314DC9FDBDEEA55D6C64543DC4903E0, 0x2E2419F9EC02EC394C9871C832963DC1B89D743C8C7B964029B2311687B1FE23, 0x176CC029695AD02582A70EFF08A6FD99D057E12E58E7D7B6B16CDFABC8EE2911, ], [ 0x2B90BBA00FCA0589F617E7DCBFE82E0DF706AB640CEB247B791A93B74E36736D, 0x101071F0032379B697315876690F053D148D4E109F5FB065C8AACC55A0F89BFA, 0x19A3FC0A56702BF417BA7FEE3802593FA644470307043F7773279CD71D25D5E0, ], ] POSEIDON_P = [ [ 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POSEIDON_C] POSEIDON_M = [[circuit.set_or_get_constant(y) for y in x] for x in POSEIDON_M] POSEIDON_P = [[circuit.set_or_get_constant(y) for y in x] for x in POSEIDON_P] POSEIDON_S = [circuit.set_or_get_constant(x) for x in POSEIDON_S] # Initial Ark state = ark(t, POSEIDON_C, 0, state) # # First half of full rounds for r in range(n_rounds_f // 2 - 1): state = [sigma(val) for val in state] state = ark(t, POSEIDON_C, (r + 1) * t, state) state = mix(t, POSEIDON_M, state) # # Middle round state = [sigma(val) for val in state] state = ark(t, POSEIDON_C, (n_rounds_f // 2) * t, state) state = mix(t, POSEIDON_P, state) # # Partial rounds for r in range(n_rounds_p): state[0] = sigma(state[0]) state = mix_s( t, POSEIDON_S, r, [circuit.add(state[0], POSEIDON_C[(n_rounds_f // 2 + 1) * t + r])] + state[1:], ) # # Second half of full rounds for r in range(n_rounds_f // 2 - 1): state = [sigma(val) for val in state] state = ark( t, POSEIDON_C, (n_rounds_f // 2 + 1) * t + n_rounds_p + r * t, state ) state = mix(t, POSEIDON_M, state) # # Final round state = [sigma(val) for val in state] # Final MixLast return mix_last(t, POSEIDON_M, 0, state) if __name__ == "__main__": # Compute the Poseidon hash z = poseidon_hash(x, y) # Define the output of the circuit circuit.extend_struct_output(u384("z", [z])) # Compile and print the compiled circuit compiled_code, function_name = circuit.compile_circuit() print(compiled_code) ================================================ FILE: hydra/garaga/precompiled_circuits/zk_honk.py ================================================ from abc import ABC, abstractmethod from dataclasses import dataclass, fields from enum import Enum, auto import garaga.hints.io as io import garaga.modulo_circuit_structs as structs from garaga.algebra import ModuloCircuitElement from garaga.curves import CURVES, CurveID, ProofSystem from garaga.hints.keccak256 import keccak_256 from garaga.modulo_circuit import ModuloCircuit from garaga.points import G1Point, G2Point from garaga.poseidon_transcript import hades_permutation NUMBER_OF_SUBRELATIONS = 28 NUMBER_OF_ALPHAS = NUMBER_OF_SUBRELATIONS - 1 NUMBER_OF_ENTITIES = 41 BATCHED_RELATION_PARTIAL_LENGTH = 8 CONST_PROOF_SIZE_LOG_N = 28 NUMBER_UNSHIFTED = 36 NUMBER_TO_BE_SHIFTED = 5 SHIFTED_COMMITMENTS_START = 30 PAIRING_POINT_OBJECT_LENGTH = 16 MAX_LOG_N = 23 # 2^23 = 8388608 MAX_CIRCUIT_SIZE = 1 << MAX_LOG_N G1_PROOF_POINT_SHIFT = 2**136 G1_PROOF_POINT_SIZE = NUM_ELEMENTS_COMM = 2 NUM_ELEMENTS_FR = 1 G2_POINT_KZG_1 = G2Point.get_nG(CurveID.BN254, 1) G2_POINT_KZG_2 = G2Point( x=( 0x0118C4D5B837BCC2BC89B5B398B5974E9F5944073B32078B7E231FEC938883B0, 0x260E01B251F6F1C7E7FF4E580791DEE8EA51D87A358E038B4EFE30FAC09383C1, ), y=( 0x22FEBDA3C0C0632A56475B4214E5615E11E6DD3F96E6CEA2854A87D4DACC5E55, 0x04FC6369F7110FE3D25156C1BB9A72859CF2A04641F99BA4EE413C80DA6A5FE4, ), curve_id=CurveID.BN254, ) NUM_WITNESS_ENTITIES = 8 NUM_LIBRA_EVALUATIONS = 4 ZK_BATCHED_RELATION_PARTIAL_LENGTH = 9 SUBGROUP_SIZE = 256 SUBGROUP_GENERATOR = 0x07B0C561A6148404F086204A9F36FFB0617942546750F230C893619174A57A76 SUBGROUP_GENERATOR_INVERSE = ( 0x204BD3277422FAD364751AD938E2B5E6A54CF8C68712848A692C553D0329F5D6 ) LIBRA_COMMITMENTS = 3 LIBRA_EVALUATIONS = 4 LIBRA_UNIVARIATES_LENGTH = 9 @dataclass class HonkVk: name: str log_circuit_size: int public_inputs_size: int qm: G1Point qc: G1Point ql: G1Point qr: G1Point qo: G1Point q4: G1Point qLookup: G1Point qArith: G1Point qDeltaRange: G1Point qElliptic: G1Point qMemory: G1Point qNnf: G1Point qPoseidon2External: G1Point qPoseidon2Internal: G1Point s1: G1Point s2: G1Point s3: G1Point s4: G1Point id1: G1Point id2: G1Point id3: G1Point id4: G1Point t1: G1Point t2: G1Point t3: G1Point t4: G1Point lagrange_first: G1Point lagrange_last: G1Point vk_hash: int vk_bytes: bytes def __repr__(self) -> str: # Print all fields line by line : return "\n".join( f"{field.name}: {getattr(self, field.name).__repr__()}" for field in fields(self) ) @classmethod def from_bytes(cls, vk_bytes: bytes) -> "HonkVk": vk_hash = ( int.from_bytes(keccak_256(vk_bytes).digest(), "big") % CURVES[CurveID.BN254.value].n ) log_circuit_size = int.from_bytes(vk_bytes[0:32], "big") public_inputs_size = int.from_bytes(vk_bytes[32:64], "big") public_inputs_offset = int.from_bytes(vk_bytes[64:96], "big") assert ( public_inputs_offset == 1 ), f"invalid public inputs offset: {public_inputs_offset}" cursor = 96 rest = vk_bytes[cursor:] assert ( len(rest) % 32 == 0 ), f"invalid vk_bytes length: {len(vk_bytes)}. Make sure you are using the correct version of bb or that the vk is not corrupted." # print(f"circuit_size: {circuit_size}") # print(f"log_circuit_size: {log_circuit_size}") # print(f"public_inputs_size: {public_inputs_size}") # Get all fields that are G1Points from the dataclass g1_fields = [ field.name for field in fields(cls) if field.type == G1Point and field.name != "name" ] # print(f"g1_fields: {g1_fields}") # Parse all G1Points into a dictionary points = {} for field_name in g1_fields: x = int.from_bytes(vk_bytes[cursor : cursor + 32], "big") y = int.from_bytes(vk_bytes[cursor + 32 : cursor + 64], "big") points[field_name] = G1Point(x=x, y=y, curve_id=CurveID.BN254) cursor += 64 # print(f"points: {points}") # Create instance with all parsed values return cls( name="", log_circuit_size=log_circuit_size, public_inputs_size=public_inputs_size, **points, vk_hash=vk_hash, vk_bytes=vk_bytes, ) def to_cairo(self, name: str = "vk") -> str: code = f"pub const {name}: HonkVk = HonkVk {{\n" code += f"vk_hash: {self.vk_hash},\n" code += f"log_circuit_size: {self.log_circuit_size},\n" code += f"public_inputs_size: {self.public_inputs_size},\n" g1_points = [ field.name for field in fields(self) if field.type == G1Point and field.name != "name" ] for field_name in g1_points: code += f"{field_name}: {getattr(self, field_name).serialize_to_cairo(name=field_name, raw=True)},\n" code += "};" return code def to_circuit_elements(self, circuit: ModuloCircuit) -> "HonkVk": return HonkVk( name=self.name, log_circuit_size=self.log_circuit_size, public_inputs_size=self.public_inputs_size, **{ field.name: circuit.write_struct( structs.G1PointCircuit.from_G1Point( field.name, getattr(self, field.name) ) ) for field in fields(self) if field.type == G1Point and field.name != "name" }, vk_hash=self.vk_hash, vk_bytes=self.vk_bytes, ) def flatten(self) -> list[int]: lst = [] lst.append(self.circuit_size) lst.append(self.log_circuit_size) lst.append(self.public_inputs_size) lst.append(self.public_inputs_offset) for field in fields(self): if field.type == G1Point and field.name != "name": point = getattr(self, field.name) lst.extend([point.x, point.y]) return lst class Transcript(ABC): def __init__(self): self.reset() @abstractmethod def reset(self): pass @abstractmethod def update(self, data: bytes): pass @abstractmethod def digest(self) -> bytes: pass def digest_reset(self) -> bytes: res_bytes = self.digest() self.reset() return res_bytes class Sha3Transcript(Transcript): def reset(self): self.hasher = keccak_256() def digest(self) -> bytes: res = self.hasher.digest() res_int = int.from_bytes(res, "big") res_mod = res_int % CURVES[CurveID.GRUMPKIN.value].p res_bytes = res_mod.to_bytes(32, "big") return res_bytes def update(self, data: bytes): self.hasher.update(data) class StarknetPoseidonTranscript(Transcript): def reset(self): self.s0, self.s1, self.s2 = hades_permutation( int.from_bytes(b"StarknetHonk", "big"), 0, 1 ) def digest(self) -> bytes: res_bytes = self.s0.to_bytes(32, "big") return res_bytes def update(self, data: bytes): val = int.from_bytes(data, "big") assert val < 2**256 high, low = divmod(val, 2**128) self.s0, self.s1, self.s2 = hades_permutation( self.s0 + low, self.s1 + high, self.s2 ) @dataclass class ZKHonkProof: log_circuit_size: int # from vk public_inputs: list[int] pairing_point_object: list[int] w1: G1Point w2: G1Point w3: G1Point w4: G1Point z_perm: G1Point lookup_read_counts: G1Point lookup_read_tags: G1Point lookup_inverses: G1Point libra_commitments: list[G1Point] libra_sum: int sumcheck_univariates: list[list[int]] sumcheck_evaluations: list[int] libra_evaluation: int gemini_masking_poly: G1Point gemini_masking_eval: int gemini_fold_comms: list[G1Point] gemini_a_evaluations: list[int] libra_poly_evals: list[int] shplonk_q: G1Point kzg_quotient: G1Point proof_bytes: bytes public_inputs_bytes: bytes def __post_init__(self): assert len(self.pairing_point_object) == PAIRING_POINT_OBJECT_LENGTH assert len(self.libra_commitments) == 3 assert all( len(univariate) == ZK_BATCHED_RELATION_PARTIAL_LENGTH for univariate in self.sumcheck_univariates ) assert len(self.sumcheck_evaluations) == NUMBER_OF_ENTITIES assert len(self.libra_poly_evals) == 4 assert len(self.gemini_fold_comms) == self.log_circuit_size - 1 assert len(self.gemini_a_evaluations) == self.log_circuit_size assert len(self.libra_poly_evals) == 4 @classmethod def from_bytes( cls, proof_bytes: bytes, public_inputs_bytes: bytes, vk: HonkVk ) -> "ZKHonkProof": FIELD_ELEMENT_SIZE = 32 n_elements = len(proof_bytes) // FIELD_ELEMENT_SIZE assert len(proof_bytes) % FIELD_ELEMENT_SIZE == 0 elements = [ int.from_bytes(proof_bytes[i : i + FIELD_ELEMENT_SIZE], "big") for i in range(0, len(proof_bytes), FIELD_ELEMENT_SIZE) ] assert ( len(elements) == n_elements == ZKHonkProof.calculate_proof_size(vk.log_circuit_size) ), f"{len(elements)} == {n_elements} == {ZKHonkProof.calculate_proof_size(vk.log_circuit_size)}" n_public_inputs = len(public_inputs_bytes) // FIELD_ELEMENT_SIZE assert len(public_inputs_bytes) % FIELD_ELEMENT_SIZE == 0 public_inputs = [ int.from_bytes(public_inputs_bytes[i : i + FIELD_ELEMENT_SIZE], "big") for i in range(0, len(public_inputs_bytes), FIELD_ELEMENT_SIZE) ] assert ( len(public_inputs) == n_public_inputs == vk.public_inputs_size - PAIRING_POINT_OBJECT_LENGTH ) pairing_point_object = [] cursor = 0 for i in range(PAIRING_POINT_OBJECT_LENGTH): pairing_point_object.append(elements[cursor + i]) cursor += PAIRING_POINT_OBJECT_LENGTH def parse_g1_proof_point(i: int) -> G1Point: p = CURVES[CurveID.BN254.value].p return G1Point( x=elements[i] % p, y=elements[i + 1] % p, curve_id=CurveID.BN254, ) w1 = parse_g1_proof_point(cursor) w2 = parse_g1_proof_point(cursor + G1_PROOF_POINT_SIZE) w3 = parse_g1_proof_point(cursor + 2 * G1_PROOF_POINT_SIZE) lookup_read_counts = parse_g1_proof_point(cursor + 3 * G1_PROOF_POINT_SIZE) lookup_read_tags = parse_g1_proof_point(cursor + 4 * G1_PROOF_POINT_SIZE) w4 = parse_g1_proof_point(cursor + 5 * G1_PROOF_POINT_SIZE) lookup_inverses = parse_g1_proof_point(cursor + 6 * G1_PROOF_POINT_SIZE) z_perm = parse_g1_proof_point(cursor + 7 * G1_PROOF_POINT_SIZE) libra_commitments = [None] * 3 libra_commitments[0] = parse_g1_proof_point(cursor + 8 * G1_PROOF_POINT_SIZE) cursor += 9 * G1_PROOF_POINT_SIZE libra_sum = elements[cursor] cursor += 1 # Parse sumcheck univariates. sumcheck_univariates = [] for i in range(vk.log_circuit_size): sumcheck_univariates.append( [ elements[cursor + i * ZK_BATCHED_RELATION_PARTIAL_LENGTH + j] for j in range(ZK_BATCHED_RELATION_PARTIAL_LENGTH) ] ) cursor += ZK_BATCHED_RELATION_PARTIAL_LENGTH * vk.log_circuit_size # Parse sumcheck_evaluations sumcheck_evaluations = elements[cursor : cursor + NUMBER_OF_ENTITIES] cursor += NUMBER_OF_ENTITIES libra_evaluation = elements[cursor] cursor += 1 libra_commitments[1] = parse_g1_proof_point(cursor) libra_commitments[2] = parse_g1_proof_point(cursor + G1_PROOF_POINT_SIZE) gemini_masking_poly = parse_g1_proof_point(cursor + 2 * G1_PROOF_POINT_SIZE) cursor += 3 * G1_PROOF_POINT_SIZE gemini_masking_eval = elements[cursor] cursor += 1 # Parse gemini fold comms gemini_fold_comms = [ parse_g1_proof_point(cursor + i * G1_PROOF_POINT_SIZE) for i in range(vk.log_circuit_size - 1) ] cursor += (vk.log_circuit_size - 1) * G1_PROOF_POINT_SIZE # Parse gemini a evaluations gemini_a_evaluations = elements[cursor : cursor + vk.log_circuit_size] cursor += vk.log_circuit_size libra_poly_evals = elements[cursor : cursor + 4] cursor += 4 shplonk_q = parse_g1_proof_point(cursor) kzg_quotient = parse_g1_proof_point(cursor + G1_PROOF_POINT_SIZE) cursor += 2 * G1_PROOF_POINT_SIZE assert cursor == len(elements) return ZKHonkProof( log_circuit_size=vk.log_circuit_size, public_inputs=public_inputs, pairing_point_object=pairing_point_object, w1=w1, w2=w2, w3=w3, w4=w4, z_perm=z_perm, lookup_read_counts=lookup_read_counts, lookup_read_tags=lookup_read_tags, lookup_inverses=lookup_inverses, libra_commitments=libra_commitments, libra_sum=libra_sum, sumcheck_univariates=sumcheck_univariates, sumcheck_evaluations=sumcheck_evaluations, libra_evaluation=libra_evaluation, gemini_masking_poly=gemini_masking_poly, gemini_masking_eval=gemini_masking_eval, gemini_fold_comms=gemini_fold_comms, gemini_a_evaluations=gemini_a_evaluations, libra_poly_evals=libra_poly_evals, shplonk_q=shplonk_q, kzg_quotient=kzg_quotient, proof_bytes=proof_bytes, public_inputs_bytes=public_inputs_bytes, ) def to_circuit_elements(self, circuit: ModuloCircuit) -> "ZKHonkProof": """Convert everything to ModuloCircuitElements given a circuit.""" return ZKHonkProof( log_circuit_size=self.log_circuit_size, public_inputs=circuit.write_elements(self.public_inputs), pairing_point_object=circuit.write_elements(self.pairing_point_object), w1=circuit.write_struct(structs.G1PointCircuit.from_G1Point("w1", self.w1)), w2=circuit.write_struct(structs.G1PointCircuit.from_G1Point("w2", self.w2)), w3=circuit.write_struct(structs.G1PointCircuit.from_G1Point("w3", self.w3)), w4=circuit.write_struct(structs.G1PointCircuit.from_G1Point("w4", self.w4)), z_perm=circuit.write_struct( structs.G1PointCircuit.from_G1Point("z_perm", self.z_perm) ), lookup_read_counts=circuit.write_struct( structs.G1PointCircuit.from_G1Point( "lookup_read_counts", self.lookup_read_counts ) ), lookup_read_tags=circuit.write_struct( structs.G1PointCircuit.from_G1Point( "lookup_read_tags", self.lookup_read_tags ) ), lookup_inverses=circuit.write_struct( structs.G1PointCircuit.from_G1Point( "lookup_inverses", self.lookup_inverses ) ), libra_commitments=[ circuit.write_struct( structs.G1PointCircuit.from_G1Point(f"libra_commitments_{i}", comm) ) for i, comm in enumerate(self.libra_commitments) ], libra_sum=circuit.write_element(self.libra_sum), sumcheck_univariates=[ circuit.write_elements(univariate) for univariate in self.sumcheck_univariates ], sumcheck_evaluations=circuit.write_elements(self.sumcheck_evaluations), libra_evaluation=circuit.write_element(self.libra_evaluation), gemini_masking_poly=circuit.write_struct( structs.G1PointCircuit.from_G1Point( "gemini_masking_poly", self.gemini_masking_poly ) ), gemini_masking_eval=circuit.write_element(self.gemini_masking_eval), gemini_fold_comms=[ circuit.write_struct( structs.G1PointCircuit.from_G1Point(f"gemini_fold_comm_{i}", comm) ) for i, comm in enumerate(self.gemini_fold_comms) ], gemini_a_evaluations=circuit.write_elements(self.gemini_a_evaluations), libra_poly_evals=circuit.write_elements(self.libra_poly_evals), shplonk_q=circuit.write_struct( structs.G1PointCircuit.from_G1Point("shplonk_q", self.shplonk_q) ), kzg_quotient=circuit.write_struct( structs.G1PointCircuit.from_G1Point("kzg_quotient", self.kzg_quotient) ), proof_bytes=self.proof_bytes, public_inputs_bytes=self.public_inputs_bytes, ) def to_cairo(self) -> str: def g1_to_g1point256(g1_point: G1Point) -> str: return f"G1Point256{{x: {hex(g1_point.x)}, y: {hex(g1_point.y)}}}" def format_array(elements: list, span: bool = False) -> str: """Helper function to format arrays with custom element formatting""" formatted_elements = [hex(el) for el in elements] arr = f"array![{', '.join(formatted_elements)}]" if span: return f"{arr}.span()" return arr code = f"ZKHonkProof {{\n" code += f"public_inputs: {format_array(self.public_inputs, span=True)},\n" code += f"pairing_point_object: {format_array(self.pairing_point_object, span=True)},\n" code += f"w1: {g1_to_g1point256(self.w1)},\n" code += f"w2: {g1_to_g1point256(self.w2)},\n" code += f"w3: {g1_to_g1point256(self.w3)},\n" code += f"w4: {g1_to_g1point256(self.w4)},\n" code += f"z_perm: {g1_to_g1point256(self.z_perm)},\n" code += f"lookup_read_counts: {g1_to_g1point256(self.lookup_read_counts)},\n" code += f"lookup_read_tags: {g1_to_g1point256(self.lookup_read_tags)},\n" code += f"lookup_inverses: {g1_to_g1point256(self.lookup_inverses)},\n" code += f"libra_commitments: array![{', '.join(g1_to_g1point256(comm) for comm in self.libra_commitments)}].span(),\n" code += f"libra_sum: {hex(self.libra_sum)},\n" # Flatten sumcheck_univariates array code += f"sumcheck_univariates: {format_array(io.flatten(self.sumcheck_univariates)[:self.log_circuit_size * ZK_BATCHED_RELATION_PARTIAL_LENGTH], span=True)},\n" code += f"sumcheck_evaluations: {format_array(self.sumcheck_evaluations, span=True)},\n" code += f"libra_evaluation: {hex(self.libra_evaluation)},\n" code += f"gemini_masking_poly: {g1_to_g1point256(self.gemini_masking_poly)},\n" code += f"gemini_masking_eval: {hex(self.gemini_masking_eval)},\n" code += f"gemini_fold_comms: array![{', '.join(g1_to_g1point256(comm) for comm in self.gemini_fold_comms[:self.log_circuit_size - 1])}].span(),\n" code += f"gemini_a_evaluations: {format_array(self.gemini_a_evaluations[:self.log_circuit_size], span=True)},\n" code += f"libra_poly_evals: {format_array(self.libra_poly_evals, span=True)},\n" code += f"shplonk_q: {g1_to_g1point256(self.shplonk_q)},\n" code += f"kzg_quotient: {g1_to_g1point256(self.kzg_quotient)},\n" code += "};" return code def serialize_to_calldata(self) -> list[int]: def serialize_G1Point256(g1_point: G1Point) -> list[int]: xl, xh = io.split_128(g1_point.x) yl, yh = io.split_128(g1_point.y) return [xl, xh, yl, yh] cd = [] cd.extend( io.bigint_split_array( x=self.public_inputs, n_limbs=2, base=2**128, prepend_length=True ) ) cd.extend( io.bigint_split_array( x=self.pairing_point_object, n_limbs=2, base=2**128, prepend_length=True, ) ) cd.extend(serialize_G1Point256(self.w1)) cd.extend(serialize_G1Point256(self.w2)) cd.extend(serialize_G1Point256(self.w3)) cd.extend(serialize_G1Point256(self.w4)) cd.extend(serialize_G1Point256(self.z_perm)) cd.extend(serialize_G1Point256(self.lookup_read_counts)) cd.extend(serialize_G1Point256(self.lookup_read_tags)) cd.extend(serialize_G1Point256(self.lookup_inverses)) cd.append(len(self.libra_commitments)) for pt in self.libra_commitments: cd.extend(serialize_G1Point256(pt)) cd.extend(io.bigint_split(self.libra_sum, n_limbs=2, base=2**128)) cd.extend( io.bigint_split_array( x=io.flatten(self.sumcheck_univariates)[ : ZK_BATCHED_RELATION_PARTIAL_LENGTH * self.log_circuit_size ], # The rest is 0. n_limbs=2, base=2**128, prepend_length=True, ) ) cd.extend( io.bigint_split_array( x=self.sumcheck_evaluations, n_limbs=2, base=2**128, prepend_length=True ) ) cd.extend(io.bigint_split(self.libra_evaluation, n_limbs=2, base=2**128)) cd.extend(serialize_G1Point256(self.gemini_masking_poly)) cd.extend(io.bigint_split(self.gemini_masking_eval, n_limbs=2, base=2**128)) cd.append(self.log_circuit_size - 1) for pt in self.gemini_fold_comms[ : self.log_circuit_size - 1 ]: # The rest is G(1, 2) cd.extend(serialize_G1Point256(pt)) cd.extend( io.bigint_split_array( x=self.gemini_a_evaluations[: self.log_circuit_size], n_limbs=2, base=2**128, prepend_length=True, ) ) cd.extend( io.bigint_split_array( x=self.libra_poly_evals, n_limbs=2, base=2**128, prepend_length=True, ) ) cd.extend(serialize_G1Point256(self.shplonk_q)) cd.extend(serialize_G1Point256(self.kzg_quotient)) return cd def flatten(self) -> list[int]: """Used to pass data to Rust""" lst = [] lst.extend(self.public_inputs) lst.extend(self.pairing_point_object) lst.extend(g1_to_g1_proof_point(self.w1)) lst.extend(g1_to_g1_proof_point(self.w2)) lst.extend(g1_to_g1_proof_point(self.w3)) lst.extend(g1_to_g1_proof_point(self.lookup_read_counts)) lst.extend(g1_to_g1_proof_point(self.lookup_read_tags)) lst.extend(g1_to_g1_proof_point(self.w4)) lst.extend(g1_to_g1_proof_point(self.lookup_inverses)) lst.extend(g1_to_g1_proof_point(self.z_perm)) lst.extend(g1_to_g1_proof_point(self.libra_commitments[0])) lst.append(self.libra_sum) for line in self.sumcheck_univariates: lst.extend(line) lst.extend(self.sumcheck_evaluations) lst.append(self.libra_evaluation) lst.extend(g1_to_g1_proof_point(self.libra_commitments[1])) lst.extend(g1_to_g1_proof_point(self.libra_commitments[2])) lst.extend(g1_to_g1_proof_point(self.gemini_masking_poly)) lst.append(self.gemini_masking_eval) for point in self.gemini_fold_comms: lst.extend(g1_to_g1_proof_point(point)) lst.extend(self.gemini_a_evaluations) lst.extend(self.libra_poly_evals) lst.extend(g1_to_g1_proof_point(self.shplonk_q)) lst.extend(g1_to_g1_proof_point(self.kzg_quotient)) return lst @staticmethod def calculate_proof_size(log_circuit_size: int): # Witness and Libra commitments proof_size = NUM_WITNESS_ENTITIES * NUM_ELEMENTS_COMM proof_size += ( NUM_ELEMENTS_COMM * 4 ) # Libra concat, grand sum, quotient comms + Gemini masking # Sumcheck proof_size += ( log_circuit_size * ZK_BATCHED_RELATION_PARTIAL_LENGTH * NUM_ELEMENTS_FR ) # sumcheck univariates proof_size += NUMBER_OF_ENTITIES * NUM_ELEMENTS_FR # sumcheck evaluations # Libra and Gemini proof_size += NUM_ELEMENTS_FR * 3 # Libra sum, claimed eval, Gemini masking eval proof_size += log_circuit_size * NUM_ELEMENTS_FR # Gemini a evaluations proof_size += NUM_LIBRA_EVALUATIONS * NUM_ELEMENTS_FR # libra evaluations # PCS commitments proof_size += (log_circuit_size - 1) * NUM_ELEMENTS_COMM # Gemini Fold commitments proof_size += NUM_ELEMENTS_COMM * 2 # Shplonk Q and KZG W commitments # Pairing points proof_size += PAIRING_POINT_OBJECT_LENGTH # pairing inputs carried on public inputs return proof_size @dataclass class ZKHonkTranscript: eta: int | ModuloCircuitElement etaTwo: int | ModuloCircuitElement etaThree: int | ModuloCircuitElement beta: int | ModuloCircuitElement gamma: int | ModuloCircuitElement alpha: int | ModuloCircuitElement gate_challenge: int | ModuloCircuitElement libra_challenge: int | ModuloCircuitElement sum_check_u_challenges: list[ModuloCircuitElement] rho: int | ModuloCircuitElement gemini_r: int | ModuloCircuitElement shplonk_nu: int | ModuloCircuitElement shplonk_z: int | ModuloCircuitElement last_state: tuple[int, int, int] public_inputs_delta: int | None = None # Derived. @classmethod def from_proof( cls, vk: HonkVk, proof: ZKHonkProof, system: ProofSystem = ProofSystem.UltraKeccakZKHonk, ) -> "ZKHonkTranscript": assert ( len(proof.public_inputs) == vk.public_inputs_size - PAIRING_POINT_OBJECT_LENGTH ) def split_challenge(ch: bytes) -> tuple[int, int]: ch_int = int.from_bytes(ch, "big") high_128, low_128 = divmod(ch_int, 2**128) return (low_128, high_128) FR = CURVES[CurveID.GRUMPKIN.value].p match system: case ProofSystem.UltraKeccakZKHonk: hasher = Sha3Transcript() case ProofSystem.UltraStarknetZKHonk: hasher = StarknetPoseidonTranscript() case _: raise ValueError(f"Proof system {system} not compatible") ## 1. Relation Parameters Challenges ## 1.1 eta_challenges ## 1.2 beta_and_gamma_challenges ## ## struct RelationParameters { # // challenges # Fr eta; # Fr etaTwo; # Fr etaThree; # Fr beta; # Fr gamma; # // derived # Fr publicInputsDelta; # } # Round 0 : circuit_size, public_inputs_size, public_input_offset, [public_inputs], w1, w2, w3 hasher.update(int.to_bytes(vk.vk_hash, 32, "big")) for pub_input in proof.public_inputs: hasher.update(int.to_bytes(pub_input, 32, "big")) for pub_input in proof.pairing_point_object: hasher.update(int.to_bytes(pub_input, 32, "big")) for g1_proof_point in [proof.w1, proof.w2, proof.w3]: # print(f"g1_proof_point: {g1_proof_point.__repr__()}") hasher.update(int.to_bytes(g1_proof_point.x, 32, "big")) hasher.update(int.to_bytes(g1_proof_point.y, 32, "big")) ch0 = hasher.digest_reset() eta, eta_two = split_challenge(ch0) hasher.update(ch0) ch0 = hasher.digest_reset() eta_three, _ = split_challenge(ch0) # print(f"eta: {hex(eta)}") # print(f"eta_two: {hex(eta_two)}") # print(f"eta_three: {hex(eta_three)}") # Round 1 : ch0, lookup_read_counts, lookup_read_tags, w4 hasher.update(ch0) for g1_proof_point in [ proof.lookup_read_counts, proof.lookup_read_tags, proof.w4, ]: hasher.update(int.to_bytes(g1_proof_point.x, 32, "big")) hasher.update(int.to_bytes(g1_proof_point.y, 32, "big")) ch1 = hasher.digest_reset() beta, gamma = split_challenge(ch1) ## 2. Alpha Challenges # Round 2: ch1, lookup_inverses, z_perm hasher.update(ch1) for g1_proof_point in [proof.lookup_inverses, proof.z_perm]: hasher.update(int.to_bytes(g1_proof_point.x, 32, "big")) hasher.update(int.to_bytes(g1_proof_point.y, 32, "big")) ch2 = hasher.digest_reset() alpha, _ = split_challenge(ch2) ## 3. Gate Challenges hasher.update(ch2) ch3 = hasher.digest_reset() gate_challenge, _ = split_challenge(ch3) ## 4. Libra Challenge # print(f"gate_challenges: {[hex(x) for x in gate_challenges]}") # print(f"len(gate_challenges): {len(gate_challenges)}") # Round 3 and 1/2: Libra challenge hasher.update(ch3) hasher.update(int.to_bytes(proof.libra_commitments[0].x, 32, "big")) hasher.update(int.to_bytes(proof.libra_commitments[0].y, 32, "big")) hasher.update(int.to_bytes(proof.libra_sum, 32, "big")) ch3 = hasher.digest_reset() libra_challenge, _ = split_challenge(ch3) ## 5. Sumcheck U Challenges # Round 4: Sumcheck u challenges ch4 = ch3 sum_check_u_challenges = [None] * vk.log_circuit_size # print(f"len(sumcheck_univariates): {len(proof.sumcheck_univariates)}") # print( # f"len(proof.sumcheck_univariates[0]): {len(proof.sumcheck_univariates[0])}" # ) for i in range(vk.log_circuit_size): # Create array of univariate challenges starting with previous challenge univariate_chal = [ch4] # Add the sumcheck univariates for this round for j in range(ZK_BATCHED_RELATION_PARTIAL_LENGTH): univariate_chal.append( int.to_bytes(proof.sumcheck_univariates[i][j], 32, "big") ) # Update hasher with all univariate challenges for chal in univariate_chal: hasher.update(chal) # Get next challenge ch4 = hasher.digest_reset() # Split challenge to get sumcheck challenge sum_check_u_challenges[i], _ = split_challenge(ch4) # print(f"sum_check_u_challenges: {[hex(x) for x in sum_check_u_challenges]}") # print(f"len(sum_check_u_challenges): {len(sum_check_u_challenges)}") ## 6. Rho Challenge # Rho challenge : hasher.update(ch4) for i in range(NUMBER_OF_ENTITIES): hasher.update(int.to_bytes(proof.sumcheck_evaluations[i], 32, "big")) hasher.update(int.to_bytes(proof.libra_evaluation, 32, "big")) for g1_proof_point in [ proof.libra_commitments[1], proof.libra_commitments[2], proof.gemini_masking_poly, ]: hasher.update(int.to_bytes(g1_proof_point.x, 32, "big")) hasher.update(int.to_bytes(g1_proof_point.y, 32, "big")) hasher.update(int.to_bytes(proof.gemini_masking_eval, 32, "big")) c5 = hasher.digest_reset() rho, _ = split_challenge(c5) # print(f"rho: {hex(rho)}") ## 7. Gemini R Challenge # Gemini R : hasher.update(c5) for i in range(vk.log_circuit_size - 1): hasher.update(int.to_bytes(proof.gemini_fold_comms[i].x, 32, "big")) hasher.update(int.to_bytes(proof.gemini_fold_comms[i].y, 32, "big")) c6 = hasher.digest_reset() gemini_r, _ = split_challenge(c6) # print(f"gemini_r: {hex(gemini_r)}") ## 8. Shplonk Nu Challenge # Shplonk Nu : hasher.update(c6) for i in range(vk.log_circuit_size): hasher.update(int.to_bytes(proof.gemini_a_evaluations[i], 32, "big")) for i in range(4): hasher.update(int.to_bytes(proof.libra_poly_evals[i], 32, "big")) c7 = hasher.digest_reset() shplonk_nu, _ = split_challenge(c7) # print(f"shplonk_nu: {hex(shplonk_nu)}") ## 9. Shplonk Z Challenge # Shplonk Z : hasher.update(c7) hasher.update(int.to_bytes(proof.shplonk_q.x, 32, "big")) hasher.update(int.to_bytes(proof.shplonk_q.y, 32, "big")) c8 = hasher.digest_reset() shplonk_z_low, shplonk_z_high = split_challenge(c8) # print(f"shplonk_z: {hex(shplonk_z)}") s0, s1, s2 = hades_permutation(shplonk_z_low, shplonk_z_high, 2) return cls( eta=eta, etaTwo=eta_two, etaThree=eta_three, beta=beta, gamma=gamma, alpha=alpha, gate_challenge=gate_challenge, libra_challenge=libra_challenge, sum_check_u_challenges=sum_check_u_challenges, rho=rho, gemini_r=gemini_r, shplonk_nu=shplonk_nu, shplonk_z=shplonk_z_low, last_state=(s0, s1, s2), public_inputs_delta=None, ) def to_circuit_elements(self, circuit: ModuloCircuit) -> "ZKHonkTranscript": return ZKHonkTranscript( eta=circuit.write_element(self.eta), etaTwo=circuit.write_element(self.etaTwo), etaThree=circuit.write_element(self.etaThree), beta=circuit.write_element(self.beta), gamma=circuit.write_element(self.gamma), alpha=circuit.write_element(self.alpha), gate_challenge=circuit.write_element(self.gate_challenge), libra_challenge=circuit.write_element(self.libra_challenge), sum_check_u_challenges=circuit.write_elements(self.sum_check_u_challenges), rho=circuit.write_element(self.rho), gemini_r=circuit.write_element(self.gemini_r), shplonk_nu=circuit.write_element(self.shplonk_nu), shplonk_z=circuit.write_element(self.shplonk_z), last_state=self.last_state, public_inputs_delta=None, ) def to_cairo(self) -> str: code = "ZKHonkTranscript{\n" code += f" eta: {hex(self.eta)},\n" code += f" eta_two: {hex(self.etaTwo)},\n" code += f" eta_three: {hex(self.etaThree)},\n" code += f" beta: {hex(self.beta)},\n" code += f" gamma: {hex(self.gamma)},\n" code += f" alpha: {hex(self.alpha)},\n" code += f" gate_challenge: {hex(self.gate_challenge)},\n" code += f" libra_challenge: {hex(self.libra_challenge)},\n" code += f" sum_check_u_challenges:array![{', '.join([hex(sum_check_u_challenge) for sum_check_u_challenge in self.sum_check_u_challenges])}],\n" code += f" rho: {hex(self.rho)},\n" code += f" gemini_r: {hex(self.gemini_r)},\n" code += f" shplonk_nu: {hex(self.shplonk_nu)},\n" code += f" shplonk_z: {hex(self.shplonk_z)},\n" code += "}" return code class ZKHonkVerifierCircuits(ModuloCircuit): def __init__( self, name: str, log_n: int, curve_id: int = CurveID.GRUMPKIN.value, compilation_mode: int = 1, ): super().__init__( name=name, curve_id=curve_id, compilation_mode=compilation_mode, ) self.log_n = log_n def compute_public_input_delta( self, public_inputs: list[ModuloCircuitElement], pairing_point_object: list[ModuloCircuitElement], beta: ModuloCircuitElement, gamma: ModuloCircuitElement, ) -> ModuloCircuitElement: assert len(public_inputs) > 0 assert len(pairing_point_object) == PAIRING_POINT_OBJECT_LENGTH offset: ModuloCircuitElement = self.set_or_get_constant(1) num = self.set_or_get_constant(1) den = self.set_or_get_constant(1) PERMUTATION_ARGUMENT_VALUE_SEPARATOR = 1 << 28 num_acc = self.add( gamma, self.mul( beta, self.add( self.set_or_get_constant(PERMUTATION_ARGUMENT_VALUE_SEPARATOR), offset, ), ), ) den_acc = self.sub( gamma, self.mul(beta, self.add(offset, self.set_or_get_constant(1))), ) for i, pub_input in enumerate(public_inputs): num = self.mul(num, self.add(num_acc, pub_input)) den = self.mul(den, self.add(den_acc, pub_input)) num_acc = self.add(num_acc, beta) den_acc = self.sub(den_acc, beta) for i, pub_input in enumerate(pairing_point_object): num = self.mul(num, self.add(num_acc, pub_input)) den = self.mul(den, self.add(den_acc, pub_input)) # skip last round (unused otherwise) if i != len(pairing_point_object) - 1: num_acc = self.add(num_acc, beta) den_acc = self.sub(den_acc, beta) return self.div(num, den) def verify_sum_check( self, libra_sum: ModuloCircuitElement, sumcheck_univariates: list[list[ModuloCircuitElement]], sumcheck_evaluations: list[ModuloCircuitElement], libra_evaluation: ModuloCircuitElement, beta: ModuloCircuitElement, gamma: ModuloCircuitElement, public_inputs_delta: ModuloCircuitElement, eta: ModuloCircuitElement, eta_two: ModuloCircuitElement, eta_three: ModuloCircuitElement, libra_challenge: ModuloCircuitElement, sum_check_u_challenges: list[ModuloCircuitElement], gate_challenge: ModuloCircuitElement, alpha: ModuloCircuitElement, log_n: int, base_rlc: ModuloCircuitElement, ) -> ModuloCircuitElement: """ We will add an extra challenge base_rlc to do a Sumcheck RLC since Cairo1 doesn't support assert_eq inside circuits (unlike Cairo0). """ pow_partial_evaluation = self.set_or_get_constant(1) round_target = self.mul(libra_challenge, libra_sum) check_rlc = None rlc_coeff = base_rlc current_gate_challenge = gate_challenge for i, round in enumerate(range(log_n)): round_univariate: list[ModuloCircuitElement] = sumcheck_univariates[round] total_sum = self.add(round_univariate[0], round_univariate[1]) check_rlc = self.add( check_rlc, self.mul(self.sub(total_sum, round_target), rlc_coeff) ) round_challenge = sum_check_u_challenges[round] round_target = self.compute_next_target_sum( round_univariate, round_challenge ) pow_partial_evaluation = self.partially_evaluate_pow( current_gate_challenge, pow_partial_evaluation, round_challenge, round, ) # Skip at the last round if i != log_n - 1: rlc_coeff = self.mul(rlc_coeff, base_rlc) current_gate_challenge = self.square(current_gate_challenge) # Last Round evaluations = self.accumulate_relation_evaluations( sumcheck_evaluations, beta, gamma, public_inputs_delta, eta, eta_two, eta_three, pow_partial_evaluation, ) assert ( len(evaluations) == NUMBER_OF_SUBRELATIONS ), f"Expected {NUMBER_OF_SUBRELATIONS}, got {len(evaluations)}" grand_honk_relation_sum = evaluations[0] alpha_i = alpha len_evaluations = len(evaluations) - 1 for i, evaluation in enumerate(evaluations[1:]): grand_honk_relation_sum = self.add( grand_honk_relation_sum, self.mul(evaluation, alpha_i), ) # Skip last update of alpha_i if i != len_evaluations - 1: alpha_i = self.mul(alpha_i, alpha) evaluation = sum_check_u_challenges[2] for i in range(3, log_n): evaluation = self.mul(evaluation, sum_check_u_challenges[i]) grand_honk_relation_sum = self.add( self.mul( grand_honk_relation_sum, self.sub(self.set_or_get_constant(1), evaluation), ), self.mul(libra_evaluation, libra_challenge), ) check = self.sub(grand_honk_relation_sum, round_target) return check_rlc, check def compute_next_target_sum( self, round_univariate: list[ModuloCircuitElement], challenge: ModuloCircuitElement, ) -> ModuloCircuitElement: BARYCENTRIC_LAGRANGE_DENOMINATORS = [ self.set_or_get_constant( 0x0000000000000000000000000000000000000000000000000000000000009D80 ), self.set_or_get_constant( 0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593EFFFEC51 ), self.set_or_get_constant( 0x00000000000000000000000000000000000000000000000000000000000005A0 ), self.set_or_get_constant( 0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593EFFFFD31 ), self.set_or_get_constant( 0x0000000000000000000000000000000000000000000000000000000000000240 ), self.set_or_get_constant( 0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593EFFFFD31 ), self.set_or_get_constant( 0x00000000000000000000000000000000000000000000000000000000000005A0 ), self.set_or_get_constant( 0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593EFFFEC51 ), self.set_or_get_constant( 0x0000000000000000000000000000000000000000000000000000000000009D80 ), ] assert ( len(BARYCENTRIC_LAGRANGE_DENOMINATORS) == ZK_BATCHED_RELATION_PARTIAL_LENGTH ) BARYCENTRIC_DOMAIN = [ self.set_or_get_constant(i) for i in range(ZK_BATCHED_RELATION_PARTIAL_LENGTH) ] numerator = self.set_or_get_constant(1) target_sum = self.set_or_get_constant(0) for i in range(ZK_BATCHED_RELATION_PARTIAL_LENGTH): # Update numerator numerator = self.mul( numerator, self.sub(challenge, self.set_or_get_constant(i)) ) # Calculate inverse of the denominator inv = self.inv( self.mul( BARYCENTRIC_LAGRANGE_DENOMINATORS[i], self.sub(challenge, BARYCENTRIC_DOMAIN[i]), ) ) # Calculate term and update target_sum term = round_univariate[i] term = self.mul(term, inv) target_sum = self.add(target_sum, term) # Scale the sum by the value of B(x) target_sum = self.mul(target_sum, numerator) return target_sum def partially_evaluate_pow( self, gate_challenge: ModuloCircuitElement, current_evaluation: ModuloCircuitElement, challenge: ModuloCircuitElement, round: int, ) -> ModuloCircuitElement: """ Univariate evaluation of the monomial ((1-X_l) + X_l.B_l) at the challenge point X_l=u_l """ univariate_eval = self.add( self.set_or_get_constant(1), self.mul(challenge, self.sub(gate_challenge, self.set_or_get_constant(1))), ) new_evaluation = self.mul(current_evaluation, univariate_eval) return new_evaluation def accumulate_relation_evaluations( self, sumcheck_evaluations: list[list[ModuloCircuitElement]], beta: ModuloCircuitElement, gamma: ModuloCircuitElement, public_inputs_delta: ModuloCircuitElement, eta: ModuloCircuitElement, eta_two: ModuloCircuitElement, eta_three: ModuloCircuitElement, pow_partial_evaluation: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: domain_separator = pow_partial_evaluation assert len(sumcheck_evaluations) == len( Wire ), f"Expected {len(Wire)}, got {len(sumcheck_evaluations)}" evaluations = [self.set_or_get_constant(0)] * NUMBER_OF_SUBRELATIONS evaluations = self.accumulate_arithmetic_relation( sumcheck_evaluations, evaluations, pow_partial_evaluation ) evaluations = self.accumulate_permutation_relation( sumcheck_evaluations, evaluations, beta, gamma, public_inputs_delta, domain_separator, ) evaluations = self.accumulate_log_derivative_lookup_relation( sumcheck_evaluations, evaluations, gamma, eta, eta_two, eta_three, domain_separator, ) evaluations = self.accumulate_delta_range_relation( sumcheck_evaluations, evaluations, domain_separator ) evaluations = self.accumulate_elliptic_relation( sumcheck_evaluations, evaluations, domain_separator ) evaluations = self.accumulate_memory_relation( sumcheck_evaluations, eta, eta_two, eta_three, evaluations, domain_separator, ) evaluations = self.accumulate_nnf_relation( sumcheck_evaluations, evaluations, domain_separator ) evaluations = self.accumulate_poseidon_external_relation( sumcheck_evaluations, evaluations, domain_separator ) evaluations = self.accumulate_poseidon_internal_relation( sumcheck_evaluations, evaluations, domain_separator ) return evaluations def accumulate_arithmetic_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> ModuloCircuitElement: p = purported_evaluations q_arith = p[Wire.Q_ARITH] # Relation 0 neg_half = self.set_or_get_constant(self.field(-2).__inv__()) accum = self.product( [ self.sub(q_arith, self.set_or_get_constant(3)), p[Wire.Q_M], p[Wire.W_R], p[Wire.W_L], neg_half, ] ) accum = self.sum( [ accum, self.mul(p[Wire.Q_L], p[Wire.W_L]), self.mul(p[Wire.Q_R], p[Wire.W_R]), self.mul(p[Wire.Q_O], p[Wire.W_O]), self.mul(p[Wire.Q_4], p[Wire.W_4]), p[Wire.Q_C], ] ) accum = self.add( accum, self.mul(self.sub(q_arith, self.set_or_get_constant(1)), p[Wire.W_4_SHIFT]), ) accum = self.product([accum, q_arith, domain_separator]) evaluations[0] = accum # Relation 1 accum = self.sum([p[Wire.W_L], p[Wire.W_4], p[Wire.Q_M]]) accum = self.sub(accum, p[Wire.W_L_SHIFT]) accum = self.mul(accum, self.sub(q_arith, self.set_or_get_constant(2))) accum = self.mul(accum, self.sub(q_arith, self.set_or_get_constant(1))) accum = self.mul(accum, q_arith) accum = self.mul(accum, domain_separator) evaluations[1] = accum return evaluations def accumulate_permutation_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], beta: ModuloCircuitElement, gamma: ModuloCircuitElement, public_inputs_delta: ModuloCircuitElement, domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations # Grand Product Numerator n = self.sum([p[Wire.W_L], self.mul(p[Wire.ID_1], beta), gamma]) n = self.mul(n, self.sum([p[Wire.W_R], self.mul(p[Wire.ID_2], beta), gamma])) n = self.mul(n, self.sum([p[Wire.W_O], self.mul(p[Wire.ID_3], beta), gamma])) n = self.mul(n, self.sum([p[Wire.W_4], self.mul(p[Wire.ID_4], beta), gamma])) # Grand Product Denominator d = self.sum([p[Wire.W_L], self.mul(p[Wire.SIGMA_1], beta), gamma]) d = self.mul(d, self.sum([p[Wire.W_R], self.mul(p[Wire.SIGMA_2], beta), gamma])) d = self.mul(d, self.sum([p[Wire.W_O], self.mul(p[Wire.SIGMA_3], beta), gamma])) d = self.mul(d, self.sum([p[Wire.W_4], self.mul(p[Wire.SIGMA_4], beta), gamma])) acc = self.mul(n, self.add(p[Wire.Z_PERM], p[Wire.LAGRANGE_FIRST])) acc = self.sub( acc, self.mul( d, self.add( p[Wire.Z_PERM_SHIFT], self.mul(p[Wire.LAGRANGE_LAST], public_inputs_delta), ), ), ) evaluations[2] = self.mul(acc, domain_separator) evaluations[3] = self.product( [p[Wire.LAGRANGE_LAST], p[Wire.Z_PERM_SHIFT], domain_separator] ) return evaluations def accumulate_log_derivative_lookup_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], gamma: ModuloCircuitElement, eta: ModuloCircuitElement, eta_two: ModuloCircuitElement, eta_three: ModuloCircuitElement, domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations write_term = self.sum( [ p[Wire.TABLE_1], gamma, self.mul(p[Wire.TABLE_2], eta), self.mul(p[Wire.TABLE_3], eta_two), self.mul(p[Wire.TABLE_4], eta_three), ] ) derived_entry_1 = self.sum( [p[Wire.W_L], gamma, self.mul(p[Wire.Q_R], p[Wire.W_L_SHIFT])] ) derived_entry_2 = self.add( p[Wire.W_R], self.mul(p[Wire.Q_M], p[Wire.W_R_SHIFT]) ) derived_entry_3 = self.add( p[Wire.W_O], self.mul(p[Wire.Q_C], p[Wire.W_O_SHIFT]) ) read_term = self.sum( [ derived_entry_1, self.mul(derived_entry_2, eta), self.mul(derived_entry_3, eta_two), self.mul(p[Wire.Q_O], eta_three), ] ) read_inverse = self.mul(p[Wire.LOOKUP_INVERSES], write_term) write_inverse = self.mul(p[Wire.LOOKUP_INVERSES], read_term) inverse_exists_xor = self.sub( self.add(p[Wire.LOOKUP_READ_TAGS], p[Wire.Q_LOOKUP]), self.mul(p[Wire.LOOKUP_READ_TAGS], p[Wire.Q_LOOKUP]), ) accumulator_none = self.product( [read_term, write_term, p[Wire.LOOKUP_INVERSES]] ) accumulator_none = self.sub(accumulator_none, inverse_exists_xor) accumulator_none = self.mul(accumulator_none, domain_separator) accumulator_one = self.mul(p[Wire.Q_LOOKUP], read_inverse) accumulator_one = self.sub( accumulator_one, self.mul(p[Wire.LOOKUP_READ_COUNTS], write_inverse) ) read_tag = p[Wire.LOOKUP_READ_TAGS] read_tag_boolean_relation = self.sub(self.square(read_tag), read_tag) evaluations[4] = accumulator_none evaluations[5] = accumulator_one evaluations[6] = self.mul(read_tag_boolean_relation, domain_separator) return evaluations def accumulate_delta_range_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations # Precompute constants minus_one = self.set_or_get_constant(-1) # Precompute common terms q_range = p[Wire.Q_RANGE] q_range_times_domain = self.mul(q_range, domain_separator) # Compute deltas delta_1 = self.sub(p[Wire.W_R], p[Wire.W_L]) delta_2 = self.sub(p[Wire.W_O], p[Wire.W_R]) delta_3 = self.sub(p[Wire.W_4], p[Wire.W_O]) delta_4 = self.sub(p[Wire.W_L_SHIFT], p[Wire.W_4]) # Process each delta for i, delta in enumerate([delta_1, delta_2, delta_3, delta_4]): # Compute delta + (-1), delta + (-2), delta + (-3) efficiently delta_minus_1 = self.add(delta, minus_one) delta_minus_2 = self.add(delta_minus_1, minus_one) # Reuse delta_minus_1 delta_minus_3 = self.add(delta_minus_2, minus_one) # Reuse delta_minus_2 # Compute product efficiently temp = self.mul(delta, delta_minus_1) temp = self.mul(temp, delta_minus_2) temp = self.mul(temp, delta_minus_3) evaluations[7 + i] = self.mul(temp, q_range_times_domain) return evaluations def accumulate_elliptic_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ): p = purported_evaluations # TODO : Do not use arithmetic circuit # Split in two and use Q_is_double as if-else condition in Cairo. x1 = p[Wire.W_R] y1 = p[Wire.W_O] x2 = p[Wire.W_L_SHIFT] y2 = p[Wire.W_4_SHIFT] y3 = p[Wire.W_O_SHIFT] x3 = p[Wire.W_R_SHIFT] q_sign = p[Wire.Q_L] q_is_double = p[Wire.Q_M] x_diff = self.sub(x2, x1) y1_sqr = self.mul(y1, y1) y2_sqr = self.mul(y2, y2) y1y2 = self.product([y1, y2, q_sign]) x_add_identity = self.sum([x3, x2, x1]) x_add_identity = self.product([x_add_identity, x_diff, x_diff]) x_add_identity = self.sub(x_add_identity, y2_sqr) x_add_identity = self.sub(x_add_identity, y1_sqr) x_add_identity = self.add(x_add_identity, y1y2) x_add_identity = self.add(x_add_identity, y1y2) q_is_add = self.sub(self.set_or_get_constant(1), q_is_double) # Point addition, x-coordinate check evaluations[11] = self.product( [ x_add_identity, domain_separator, p[Wire.Q_ELLIPTIC], q_is_add, ] ) # Point addition, y-coordinate check y1_plus_y3 = self.add(y1, y3) y_diff = self.sub(self.mul(y2, q_sign), y1) y_add_identity = self.add( self.mul(y1_plus_y3, x_diff), self.mul(self.sub(x3, x1), y_diff), ) evaluations[12] = self.product( [ y_add_identity, domain_separator, p[Wire.Q_ELLIPTIC], q_is_add, ] ) # Point doubling, x-coordinate check GRUMPKIN_CURVE_B_PARAMETER_NEGATED = self.set_or_get_constant(17) # - (- 17) x_pow_4 = self.mul(self.add(y1_sqr, GRUMPKIN_CURVE_B_PARAMETER_NEGATED), x1) y1_sqr_mul_4 = self.add(y1_sqr, y1_sqr) y1_sqr_mul_4 = self.add(y1_sqr_mul_4, y1_sqr_mul_4) x1_pow_4_mul_9 = self.mul(x_pow_4, self.set_or_get_constant(9)) x_double_identity = self.sub( self.mul(self.sum([x3, x1, x1]), y1_sqr_mul_4), x1_pow_4_mul_9 ) evaluations[11] = self.add( evaluations[11], self.product( [x_double_identity, domain_separator, p[Wire.Q_ELLIPTIC], q_is_double] ), ) # Point doubling, y-coordinate check x1_sqr_mul_3 = self.mul(self.sum([x1, x1, x1]), x1) y_double_identity = self.sub( self.mul(x1_sqr_mul_3, self.sub(x1, x3)), self.mul(self.add(y1, y1), self.add(y1, y3)), ) evaluations[12] = self.add( evaluations[12], self.product( [y_double_identity, domain_separator, p[Wire.Q_ELLIPTIC], q_is_double] ), ) return evaluations def accumulate_memory_relation( self, purported_evaluations: list[ModuloCircuitElement], eta: ModuloCircuitElement, eta_two: ModuloCircuitElement, eta_three: ModuloCircuitElement, evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations memory_record_check = self.mul(p[Wire.W_O], eta_three) memory_record_check = self.add( memory_record_check, self.mul(p[Wire.W_R], eta_two) ) memory_record_check = self.add(memory_record_check, self.mul(p[Wire.W_L], eta)) memory_record_check = self.add(memory_record_check, p[Wire.Q_C]) partial_record_check = memory_record_check memory_record_check = self.sub(memory_record_check, p[Wire.W_4]) index_delta = self.sub(p[Wire.W_L_SHIFT], p[Wire.W_L]) record_delta = self.sub(p[Wire.W_4_SHIFT], p[Wire.W_4]) index_is_monotonically_increasing = self.mul( index_delta, self.sub(index_delta, self.set_or_get_constant(1)) ) adjacent_values_match_if_adjacent_indices_match = self.mul( self.add( self.mul(index_delta, self.set_or_get_constant(-1)), self.set_or_get_constant(1), ), record_delta, ) wire_ql_times_qr = self.mul(p[Wire.Q_L], p[Wire.Q_R]) q_memory_times_domain = self.mul(p[Wire.Q_MEMORY], domain_separator) wire_ql_times_qr_times_qmemory_times_domain = self.product( [wire_ql_times_qr, q_memory_times_domain] ) evaluations[14] = self.mul( adjacent_values_match_if_adjacent_indices_match, wire_ql_times_qr_times_qmemory_times_domain, ) evaluations[15] = self.mul( index_is_monotonically_increasing, wire_ql_times_qr_times_qmemory_times_domain, ) ROM_consistency_check_identity = self.mul(memory_record_check, wire_ql_times_qr) access_type = self.sub(p[Wire.W_4], partial_record_check) access_check = self.mul( access_type, self.sub(access_type, self.set_or_get_constant(1)) ) next_gate_access_type = self.sum( [ self.mul(p[Wire.W_O_SHIFT], eta_three), self.mul(p[Wire.W_R_SHIFT], eta_two), self.mul(p[Wire.W_L_SHIFT], eta), ] ) next_gate_access_type = self.sub(p[Wire.W_4_SHIFT], next_gate_access_type) value_delta = self.sub(p[Wire.W_O_SHIFT], p[Wire.W_O]) adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation = self.product( [ self.add( self.mul(index_delta, self.set_or_get_constant(-1)), self.set_or_get_constant(1), ), value_delta, self.add( self.mul(next_gate_access_type, self.set_or_get_constant(-1)), self.set_or_get_constant(1), ), ] ) next_gate_access_type_is_boolean = self.sub( self.mul(next_gate_access_type, next_gate_access_type), next_gate_access_type, ) q_o_times_q_memory_times_domain = self.mul(p[Wire.Q_O], q_memory_times_domain) evaluations[16] = self.product( [ adjacent_values_match_if_adjacent_indices_match_and_next_access_is_a_read_operation, q_o_times_q_memory_times_domain, ] ) evaluations[17] = self.product( [ index_is_monotonically_increasing, q_o_times_q_memory_times_domain, ] ) evaluations[18] = self.product( [ next_gate_access_type_is_boolean, q_o_times_q_memory_times_domain, ] ) RAM_consistency_check_identity = self.mul(access_check, p[Wire.Q_O]) timestamp_delta = self.sub(p[Wire.W_R_SHIFT], p[Wire.W_R]) RAM_timestamp_check_identity = self.mul( self.add( self.mul(index_delta, self.set_or_get_constant(-1)), self.set_or_get_constant(1), ), timestamp_delta, ) RAM_timestamp_check_identity = self.sub( RAM_timestamp_check_identity, p[Wire.W_O] # Fixed: was p[Wire.Q_O] ) memory_identity = self.sum( [ ROM_consistency_check_identity, self.product( [RAM_timestamp_check_identity, self.mul(p[Wire.Q_4], p[Wire.Q_L])] ), self.product([memory_record_check, self.mul(p[Wire.Q_M], p[Wire.Q_L])]), RAM_consistency_check_identity, ] ) memory_identity = self.mul(memory_identity, q_memory_times_domain) evaluations[13] = memory_identity return evaluations def accumulate_nnf_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations limb_size = self.set_or_get_constant(2**68) sub_limb_shift = self.set_or_get_constant(2**14) limb_subproduct = self.add( self.mul(p[Wire.W_L], p[Wire.W_R_SHIFT]), self.mul(p[Wire.W_L_SHIFT], p[Wire.W_R]), ) non_native_field_gate_2 = self.sub( self.add( self.mul(p[Wire.W_L], p[Wire.W_4]), self.mul(p[Wire.W_R], p[Wire.W_O]), ), p[Wire.W_O_SHIFT], ) non_native_field_gate_2 = self.mul(non_native_field_gate_2, limb_size) non_native_field_gate_2 = self.sub(non_native_field_gate_2, p[Wire.W_4_SHIFT]) non_native_field_gate_2 = self.add(non_native_field_gate_2, limb_subproduct) non_native_field_gate_2 = self.mul(non_native_field_gate_2, p[Wire.Q_4]) limb_subproduct = self.mul(limb_subproduct, limb_size) limb_subproduct = self.add( limb_subproduct, self.mul(p[Wire.W_L_SHIFT], p[Wire.W_R_SHIFT]), ) non_native_field_gate_1 = limb_subproduct non_native_field_gate_1 = self.sub( non_native_field_gate_1, self.add(p[Wire.W_O], p[Wire.W_4]), ) non_native_field_gate_1 = self.mul(non_native_field_gate_1, p[Wire.Q_O]) non_native_field_gate_3 = limb_subproduct non_native_field_gate_3 = self.add(non_native_field_gate_3, p[Wire.W_4]) non_native_field_gate_3 = self.sub( non_native_field_gate_3, self.add(p[Wire.W_O_SHIFT], p[Wire.W_4_SHIFT]), ) non_native_field_gate_3 = self.mul(non_native_field_gate_3, p[Wire.Q_M]) non_native_field_identity = self.sum( [non_native_field_gate_1, non_native_field_gate_2, non_native_field_gate_3] ) non_native_field_identity = self.mul(non_native_field_identity, p[Wire.Q_R]) limb_accumulator_1 = self.mul(p[Wire.W_R_SHIFT], sub_limb_shift) limb_accumulator_1 = self.add(limb_accumulator_1, p[Wire.W_L_SHIFT]) limb_accumulator_1 = self.mul(limb_accumulator_1, sub_limb_shift) limb_accumulator_1 = self.add(limb_accumulator_1, p[Wire.W_O]) limb_accumulator_1 = self.mul(limb_accumulator_1, sub_limb_shift) limb_accumulator_1 = self.add(limb_accumulator_1, p[Wire.W_R]) limb_accumulator_1 = self.mul(limb_accumulator_1, sub_limb_shift) limb_accumulator_1 = self.add(limb_accumulator_1, p[Wire.W_L]) limb_accumulator_1 = self.sub(limb_accumulator_1, p[Wire.W_4]) limb_accumulator_1 = self.mul(limb_accumulator_1, p[Wire.Q_4]) limb_accumulator_2 = self.mul(p[Wire.W_O_SHIFT], sub_limb_shift) limb_accumulator_2 = self.add(limb_accumulator_2, p[Wire.W_R_SHIFT]) limb_accumulator_2 = self.mul(limb_accumulator_2, sub_limb_shift) limb_accumulator_2 = self.add(limb_accumulator_2, p[Wire.W_L_SHIFT]) limb_accumulator_2 = self.mul(limb_accumulator_2, sub_limb_shift) limb_accumulator_2 = self.add(limb_accumulator_2, p[Wire.W_4]) limb_accumulator_2 = self.mul(limb_accumulator_2, sub_limb_shift) limb_accumulator_2 = self.add(limb_accumulator_2, p[Wire.W_O]) limb_accumulator_2 = self.sub(limb_accumulator_2, p[Wire.W_4_SHIFT]) limb_accumulator_2 = self.mul(limb_accumulator_2, p[Wire.Q_M]) # Fr limb_accumulator_identity = ap.limb_accumulator_1 + ap.limb_accumulator_2; # limb_accumulator_identity = limb_accumulator_identity * wire(p, WIRE.Q_O); // deg 3 limb_accumulator_identity = self.add(limb_accumulator_1, limb_accumulator_2) limb_accumulator_identity = self.mul(limb_accumulator_identity, p[Wire.Q_O]) nnf_identiy = self.add(non_native_field_identity, limb_accumulator_identity) nnf_identiy = self.product([nnf_identiy, p[Wire.Q_NNF], domain_separator]) evaluations[19] = nnf_identiy return evaluations def accumulate_poseidon_external_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations s1 = self.add(p[Wire.W_L], p[Wire.Q_L]) s2 = self.add(p[Wire.W_R], p[Wire.Q_R]) s3 = self.add(p[Wire.W_O], p[Wire.Q_O]) s4 = self.add(p[Wire.W_4], p[Wire.Q_4]) u1 = self.pow5(s1) u2 = self.pow5(s2) u3 = self.pow5(s3) u4 = self.pow5(s4) t0 = self.add(u1, u2) t1 = self.add(u3, u4) t2 = self.add(self.add(u2, u2), t1) t3 = self.add(self.add(u4, u4), t0) v4 = self.add(t1, t1) v4 = self.add(self.add(v4, v4), t3) v2 = self.add(t0, t0) v2 = self.add(self.add(v2, v2), t2) v1 = self.add(t3, v2) v3 = self.add(t2, v4) q_pos_by_scaling = self.mul(p[Wire.Q_POSEIDON2_EXTERNAL], domain_separator) evaluations[20] = self.mul(q_pos_by_scaling, self.sub(v1, p[Wire.W_L_SHIFT])) evaluations[21] = self.mul(q_pos_by_scaling, self.sub(v2, p[Wire.W_R_SHIFT])) evaluations[22] = self.mul(q_pos_by_scaling, self.sub(v3, p[Wire.W_O_SHIFT])) evaluations[23] = self.mul(q_pos_by_scaling, self.sub(v4, p[Wire.W_4_SHIFT])) return evaluations def pow5(self, x: ModuloCircuitElement) -> ModuloCircuitElement: x2 = self.mul(x, x) x4 = self.mul(x2, x2) return self.mul(x4, x) def accumulate_poseidon_internal_relation( self, purported_evaluations: list[ModuloCircuitElement], evaluations: list[ModuloCircuitElement], domain_separator: ModuloCircuitElement, ) -> list[ModuloCircuitElement]: p = purported_evaluations INTERNAL_MATRIX_DIAGONAL = [ self.set_or_get_constant( 0x10DC6E9C006EA38B04B1E03B4BD9490C0D03F98929CA1D7FB56821FD19D3B6E7 ), self.set_or_get_constant( 0x0C28145B6A44DF3E0149B3D0A30B3BB599DF9756D4DD9B84A86B38CFB45A740B ), self.set_or_get_constant( 0x00544B8338791518B2C7645A50392798B21F75BB60E3596170067D00141CAC15 ), self.set_or_get_constant( 0x222C01175718386F2E2E82EB122789E352E105A3B8FA852613BC534433EE428B ), ] s1 = self.add(p[Wire.W_L], p[Wire.Q_L]) u1 = self.pow5(s1) u2 = p[Wire.W_R] u3 = p[Wire.W_O] u4 = p[Wire.W_4] u_sum = self.sum([u1, u2, u3, u4]) q_pos_by_scaling = self.mul(p[Wire.Q_POSEIDON2_INTERNAL], domain_separator) v1 = self.add(self.mul(u1, INTERNAL_MATRIX_DIAGONAL[0]), u_sum) evaluations[24] = self.mul(q_pos_by_scaling, self.sub(v1, p[Wire.W_L_SHIFT])) v2 = self.add(self.mul(u2, INTERNAL_MATRIX_DIAGONAL[1]), u_sum) evaluations[25] = self.mul(q_pos_by_scaling, self.sub(v2, p[Wire.W_R_SHIFT])) v3 = self.add(self.mul(u3, INTERNAL_MATRIX_DIAGONAL[2]), u_sum) evaluations[26] = self.mul(q_pos_by_scaling, self.sub(v3, p[Wire.W_O_SHIFT])) v4 = self.add(self.mul(u4, INTERNAL_MATRIX_DIAGONAL[3]), u_sum) evaluations[27] = self.mul(q_pos_by_scaling, self.sub(v4, p[Wire.W_4_SHIFT])) return evaluations def compute_shplemini_msm_scalars( self, p_sumcheck_evaluations: list[ ModuloCircuitElement ], # Full evaluations, not replaced. p_gemini_masking_eval: ModuloCircuitElement, p_gemini_a_evaluations: list[ModuloCircuitElement], p_libra_poly_evals: list[ModuloCircuitElement], tp_gemini_r: ModuloCircuitElement, tp_rho: ModuloCircuitElement, tp_shplonk_z: ModuloCircuitElement, tp_shplonk_nu: ModuloCircuitElement, tp_sumcheck_u_challenges: list[ModuloCircuitElement], ) -> list[ModuloCircuitElement]: assert all(isinstance(i, ModuloCircuitElement) for i in p_sumcheck_evaluations) powers_of_evaluations_challenge = [tp_gemini_r] for i in range(1, self.log_n): powers_of_evaluations_challenge.append( self.square( powers_of_evaluations_challenge[i - 1], ) ) scalars = [self.set_or_get_constant(0)] * ( NUMBER_UNSHIFTED + self.log_n + LIBRA_COMMITMENTS + 3 ) pos_inverted_denominator = self.inv( self.sub(tp_shplonk_z, powers_of_evaluations_challenge[0]) ) neg_inverted_denominator = self.inv( self.add(tp_shplonk_z, powers_of_evaluations_challenge[0]) ) unshifted_scalar = self.add( pos_inverted_denominator, self.mul(tp_shplonk_nu, neg_inverted_denominator), ) shifted_scalar_neg = self.neg( self.mul( self.inv(tp_gemini_r), self.sub( pos_inverted_denominator, self.mul(tp_shplonk_nu, neg_inverted_denominator), ), ) ) scalars[0] = self.set_or_get_constant(1) batching_challenge = tp_rho batched_evaluation = p_gemini_masking_eval unshifted_scalar_neg = self.neg(unshifted_scalar) scalars[1] = unshifted_scalar_neg for i in range(0, NUMBER_UNSHIFTED): scalars[i + 2] = self.mul(unshifted_scalar_neg, batching_challenge) batched_evaluation = self.add( batched_evaluation, self.mul(p_sumcheck_evaluations[i], batching_challenge), ) batching_challenge = self.mul(batching_challenge, tp_rho) for i in range(0, NUMBER_TO_BE_SHIFTED): scalar_offset = i + SHIFTED_COMMITMENTS_START evaluation_offset = i + NUMBER_UNSHIFTED scalars[scalar_offset] = self.add( scalars[scalar_offset], self.mul(shifted_scalar_neg, batching_challenge) ) batched_evaluation = self.add( batched_evaluation, self.mul(p_sumcheck_evaluations[evaluation_offset], batching_challenge), ) # skip last round: if i < NUMBER_TO_BE_SHIFTED - 1: batching_challenge = self.mul(batching_challenge, tp_rho) # computeFoldPosEvaluations def compute_fold_pos_evaluations( tp_sumcheck_u_challenges, batched_eval_accumulator, gemini_evaluations, gemini_eval_challenge_powers, ): fold_pos_evaluations = [self.set_or_get_constant(0)] * self.log_n for i in range(self.log_n, 0, -1): challenge_power = gemini_eval_challenge_powers[i - 1] u = tp_sumcheck_u_challenges[i - 1] eval_neg = gemini_evaluations[i - 1] # (challengePower * batchedEvalAccumulator * Fr.wrap(2)) - evalNeg * (challengePower * (Fr.wrap(1) - u) - u)) # (challengePower * (Fr.wrap(1) - u) term = self.mul( challenge_power, self.sub(self.set_or_get_constant(1), u) ) batched_eval_round_acc = self.sub( self.double(self.mul(challenge_power, batched_eval_accumulator)), self.mul(eval_neg, self.sub(term, u)), ) # (challengePower * (Fr.wrap(1) - u) + u).invert() den = self.add(term, u) batched_eval_round_acc = self.mul(batched_eval_round_acc, self.inv(den)) batched_eval_accumulator = batched_eval_round_acc fold_pos_evaluations[i - 1] = batched_eval_accumulator return fold_pos_evaluations fold_pos_evaluations = compute_fold_pos_evaluations( tp_sumcheck_u_challenges, batched_evaluation, p_gemini_a_evaluations, powers_of_evaluations_challenge, ) constant_term_accumulator = self.mul( fold_pos_evaluations[0], pos_inverted_denominator ) constant_term_accumulator = self.add( constant_term_accumulator, self.product( [ p_gemini_a_evaluations[0], tp_shplonk_nu, neg_inverted_denominator, ] ), ) batching_challenge = self.square(tp_shplonk_nu) boundary = NUMBER_UNSHIFTED + 2 for i in range(self.log_n - 1): dummy_round = i >= (self.log_n - 1) scaling_factor = self.set_or_get_constant(0) if not dummy_round: pos_inverted_denominator = self.inv( self.sub(tp_shplonk_z, powers_of_evaluations_challenge[i + 1]) ) neg_inverted_denominator = self.inv( self.add(tp_shplonk_z, powers_of_evaluations_challenge[i + 1]) ) scaling_factor_pos = self.mul( batching_challenge, pos_inverted_denominator ) scaling_factor_neg = self.mul( batching_challenge, self.mul(tp_shplonk_nu, neg_inverted_denominator), ) scalars[boundary + i] = self.neg( self.add(scaling_factor_neg, scaling_factor_pos) ) accum_contribution = self.mul( scaling_factor_neg, p_gemini_a_evaluations[i + 1] ) accum_contribution = self.add( accum_contribution, self.mul(scaling_factor_pos, fold_pos_evaluations[i + 1]), ) constant_term_accumulator = self.add( constant_term_accumulator, accum_contribution ) else: # print( # f"dummy round {i}, index {NUMBER_OF_ENTITIES + i + 1} is set to 0" # ) pass batching_challenge = self.mul( batching_challenge, self.square(tp_shplonk_nu) ) boundary += self.log_n - 1 denominators = [self.set_or_get_constant(0)] * 4 denominators[0] = self.inv(self.sub(tp_shplonk_z, tp_gemini_r)) denominators[1] = self.inv( self.sub( tp_shplonk_z, self.mul(self.set_or_get_constant(SUBGROUP_GENERATOR), tp_gemini_r), ), ) denominators[2] = denominators[0] denominators[3] = denominators[0] batching_scalars = [self.set_or_get_constant(0)] * 4 batching_challenge = self.mul(batching_challenge, self.square(tp_shplonk_nu)) for i in range(LIBRA_EVALUATIONS): scaling_factor = self.mul(denominators[i], batching_challenge) batching_scalars[i] = self.neg(scaling_factor) # skip last step: if i < LIBRA_EVALUATIONS - 1: batching_challenge = self.mul(batching_challenge, tp_shplonk_nu) constant_term_accumulator = self.add( constant_term_accumulator, self.mul(scaling_factor, p_libra_poly_evals[i]), ) scalars[boundary] = batching_scalars[0] scalars[boundary + 1] = self.add(batching_scalars[1], batching_scalars[2]) scalars[boundary + 2] = batching_scalars[3] scalars[boundary + 3] = constant_term_accumulator scalars[boundary + 4] = tp_shplonk_z return scalars def check_evals_consistency( self, p_libra_evaluation: ModuloCircuitElement, p_libra_poly_evals: list[ModuloCircuitElement], tp_gemini_r: ModuloCircuitElement, tp_sumcheck_u_challenges: list[ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: vanishing_poly_eval = self.sub( self.pow(tp_gemini_r, SUBGROUP_SIZE), self.set_or_get_constant(1) ) challenge_poly_lagrange = [self.set_or_get_constant(0)] * SUBGROUP_SIZE challenge_poly_lagrange[0] = self.set_or_get_constant(1) for r in range(self.log_n): curr_idx = 1 + LIBRA_UNIVARIATES_LENGTH * r challenge_poly_lagrange[curr_idx] = self.set_or_get_constant(1) for idx in range(curr_idx + 1, curr_idx + LIBRA_UNIVARIATES_LENGTH): challenge_poly_lagrange[idx] = self.mul( challenge_poly_lagrange[idx - 1], tp_sumcheck_u_challenges[r] ) root_power = self.set_or_get_constant(1) challenge_poly_eval = self.set_or_get_constant(0) denominators = [self.set_or_get_constant(0)] * SUBGROUP_SIZE for idx in range(SUBGROUP_SIZE): denominators[idx] = self.sub( self.mul(root_power, tp_gemini_r), self.set_or_get_constant(1) ) denominators[idx] = self.inv(denominators[idx]) challenge_poly_eval = self.add( challenge_poly_eval, self.mul(challenge_poly_lagrange[idx], denominators[idx]), ) # skip last step: if idx < SUBGROUP_SIZE - 1: root_power = self.mul( root_power, self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE) ) numerator = self.mul( vanishing_poly_eval, self.set_or_get_constant(pow(SUBGROUP_SIZE, -1, self.field.p)), ) challenge_poly_eval = self.mul(challenge_poly_eval, numerator) lagrange_first = self.mul(denominators[0], numerator) lagrange_last = self.mul(denominators[SUBGROUP_SIZE - 1], numerator) diff = self.mul(lagrange_first, p_libra_poly_evals[2]) diff = self.add( diff, self.mul( self.sub( tp_gemini_r, self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE) ), self.sub( self.sub(p_libra_poly_evals[1], p_libra_poly_evals[2]), self.mul(p_libra_poly_evals[0], challenge_poly_eval), ), ), ) diff = self.sub( self.add( diff, self.mul( lagrange_last, self.sub(p_libra_poly_evals[2], p_libra_evaluation) ), ), self.mul(vanishing_poly_eval, p_libra_poly_evals[3]), ) return vanishing_poly_eval, diff def check_evals_consistency_split( self, p_libra_evaluation: ModuloCircuitElement, p_libra_poly_evals: list[ModuloCircuitElement], tp_gemini_r: ModuloCircuitElement, tp_sumcheck_u_challenges: list[ModuloCircuitElement], ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: challenge_poly_eval, root_power_times_tp_gemini_r = ( self._check_evals_consistency_init(tp_gemini_r) ) for r in range(self.log_n): challenge_poly_eval, root_power_times_tp_gemini_r = ( self._check_evals_consistency_loop( challenge_poly_eval, root_power_times_tp_gemini_r, tp_sumcheck_u_challenges[r], ) ) vanishing_poly_eval, diff = self._check_evals_consistency_done( p_libra_evaluation, p_libra_poly_evals, tp_gemini_r, challenge_poly_eval, root_power_times_tp_gemini_r, ) return vanishing_poly_eval, diff def _check_evals_consistency_init( self, tp_gemini_r: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: challenge_poly_eval = self.inv( self.sub(tp_gemini_r, self.set_or_get_constant(1)) ) root_power_times_tp_gemini_r = self.mul( self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE), tp_gemini_r ) return challenge_poly_eval, root_power_times_tp_gemini_r def _check_evals_consistency_loop( self, challenge_poly_eval: ModuloCircuitElement, root_power_times_tp_gemini_r: ModuloCircuitElement, tp_sumcheck_u_challenge: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: challenge_poly_lagrange = self.set_or_get_constant(1) for i in range(LIBRA_UNIVARIATES_LENGTH): denominator = self.inv( self.sub(root_power_times_tp_gemini_r, self.set_or_get_constant(1)) ) challenge_poly_eval = self.add( challenge_poly_eval, self.mul(challenge_poly_lagrange, denominator) ) root_power_times_tp_gemini_r = self.mul( root_power_times_tp_gemini_r, self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE), ) # skip last step: if i < LIBRA_UNIVARIATES_LENGTH - 1: challenge_poly_lagrange = self.mul( challenge_poly_lagrange, tp_sumcheck_u_challenge ) return challenge_poly_eval, root_power_times_tp_gemini_r def _check_evals_consistency_done( self, p_libra_evaluation: ModuloCircuitElement, p_libra_poly_evals: list[ModuloCircuitElement], tp_gemini_r: ModuloCircuitElement, challenge_poly_eval: ModuloCircuitElement, root_power_times_tp_gemini_r: ModuloCircuitElement, ) -> tuple[ModuloCircuitElement, ModuloCircuitElement]: # We've processed indices 0 to (1 + log_n * 9 - 1) = log_n * 9 # Need to advance root_power for remaining indices up to SUBGROUP_SIZE - 2 # (SUBGROUP_SIZE - 1 is the last index, handled separately for lagrange_last) for _ in range(1 + self.log_n * LIBRA_UNIVARIATES_LENGTH, SUBGROUP_SIZE - 1): root_power_times_tp_gemini_r = self.mul( root_power_times_tp_gemini_r, self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE), ) denominator_first = self.inv(self.sub(tp_gemini_r, self.set_or_get_constant(1))) denominator_last = self.inv( self.sub(root_power_times_tp_gemini_r, self.set_or_get_constant(1)) ) vanishing_poly_eval = self.sub( self.pow(tp_gemini_r, SUBGROUP_SIZE), self.set_or_get_constant(1) ) numerator = self.mul( vanishing_poly_eval, self.set_or_get_constant(pow(SUBGROUP_SIZE, -1, self.field.p)), ) challenge_poly_eval = self.mul(challenge_poly_eval, numerator) lagrange_first = self.mul(denominator_first, numerator) lagrange_last = self.mul(denominator_last, numerator) diff = self.mul(lagrange_first, p_libra_poly_evals[2]) diff = self.add( diff, self.mul( self.sub( tp_gemini_r, self.set_or_get_constant(SUBGROUP_GENERATOR_INVERSE) ), self.sub( self.sub(p_libra_poly_evals[1], p_libra_poly_evals[2]), self.mul(p_libra_poly_evals[0], challenge_poly_eval), ), ), ) diff = self.sub( self.add( diff, self.mul( lagrange_last, self.sub(p_libra_poly_evals[2], p_libra_evaluation) ), ), self.mul(vanishing_poly_eval, p_libra_poly_evals[3]), ) return vanishing_poly_eval, diff def pow(self, x: ModuloCircuitElement, e: int) -> ModuloCircuitElement: assert e > 0 and ((e - 1) & e) == 0 # supports only powers of 2 shift = e.bit_length() - 1 y = x for i in range(shift): y = self.mul(y, y) return y def get_msm_points_from_vk_and_proof( vk: HonkVk, proof: ZKHonkProof, ) -> list[G1Point]: points = [ proof.shplonk_q, # 0 proof.gemini_masking_poly, # 1 vk.qm, # 2 vk.qc, # 3 vk.ql, # 4 vk.qr, # 5 vk.qo, # 6 vk.q4, # 7 vk.qLookup, # 8 vk.qArith, # 9 vk.qDeltaRange, # 10 vk.qElliptic, # 11 vk.qMemory, # 12 vk.qNnf, # 13 vk.qPoseidon2External, # 14 vk.qPoseidon2Internal, # 15 vk.s1, # 16 vk.s2, # 17 vk.s3, # 18 vk.s4, # 19 vk.id1, # 20 vk.id2, # 21 vk.id3, # 22 vk.id4, # 23 vk.t1, # 24 vk.t2, # 25 vk.t3, # 26 vk.t4, # 27 vk.lagrange_first, # 28 vk.lagrange_last, # 29 proof.w1, # 30 proof.w2, # 31 proof.w3, # 32 proof.w4, # 33 proof.z_perm, # 34 proof.lookup_inverses, # 35 proof.lookup_read_counts, # 36 proof.lookup_read_tags, # 37 ] points.extend(proof.gemini_fold_comms) points.extend(proof.libra_commitments) points.append(G1Point.get_nG(CurveID.BN254, 1)) points.append(proof.kzg_quotient) assert len(points) == NUMBER_UNSHIFTED + vk.log_circuit_size + LIBRA_COMMITMENTS + 3 return points def honk_proof_from_bytes( proof_bytes: bytes, public_inputs_bytes: bytes, vk: HonkVk, system: ProofSystem, ) -> ZKHonkProof: if system == ProofSystem.UltraKeccakZKHonk: return ZKHonkProof.from_bytes(proof_bytes, public_inputs_bytes, vk) else: raise ValueError(f"Invalid system: {system}") def honk_transcript_from_proof( vk: HonkVk, proof: ZKHonkProof, ) -> ZKHonkTranscript: return ZKHonkTranscript.from_proof(vk, proof) class AutoValueEnum(Enum): def __new__(cls, value): obj = object.__new__(cls) obj._value_ = value return obj def __int__(self): return self._value_ def __index__(self): return self._value_ class Wire(AutoValueEnum): Q_M = 0 # Start at 0 for array indexing Q_C = auto() Q_L = auto() Q_R = auto() Q_O = auto() Q_4 = auto() Q_LOOKUP = auto() Q_ARITH = auto() Q_RANGE = auto() Q_ELLIPTIC = auto() Q_MEMORY = auto() Q_NNF = auto() Q_POSEIDON2_EXTERNAL = auto() Q_POSEIDON2_INTERNAL = auto() SIGMA_1 = auto() SIGMA_2 = auto() SIGMA_3 = auto() SIGMA_4 = auto() ID_1 = auto() ID_2 = auto() ID_3 = auto() ID_4 = auto() TABLE_1 = auto() TABLE_2 = auto() TABLE_3 = auto() TABLE_4 = auto() LAGRANGE_FIRST = auto() LAGRANGE_LAST = auto() W_L = auto() W_R = auto() W_O = auto() W_4 = auto() Z_PERM = auto() LOOKUP_INVERSES = auto() LOOKUP_READ_COUNTS = auto() LOOKUP_READ_TAGS = auto() W_L_SHIFT = auto() W_R_SHIFT = auto() W_O_SHIFT = auto() W_4_SHIFT = auto() Z_PERM_SHIFT = auto() @staticmethod def unused_indexes(): return [] @staticmethod def insert_unused_indexes_with_nones(array: list) -> list: assert len(array) == len(Wire) - len(Wire.unused_indexes()) for i in Wire.unused_indexes(): array.insert(i, None) for i in Wire.unused_indexes(): assert array[i] is None assert len(array) == len(Wire) return array @staticmethod def replace_unused_indexes_with_nones(array: list) -> list: for i in Wire.unused_indexes(): array[i] = None return array @staticmethod def remove_unused_indexes(array: list) -> list: for i in Wire.unused_indexes(): array.pop(i) return array if __name__ == "__main__": vk = HonkVk.from_bytes( open( "hydra/garaga/starknet/honk_contract_generator/examples/vk_ultra_keccak.bin", "rb", ).read(), ) proof = honk_proof_from_bytes( open( "hydra/garaga/starknet/honk_contract_generator/examples/proof_ultra_keccak_zk.bin", "rb", ).read(), open( "hydra/garaga/starknet/honk_contract_generator/examples/public_inputs_ultra_keccak.bin", "rb", ).read(), vk, ProofSystem.UltraKeccakZKHonk, ) print(vk.to_cairo()) print(proof.to_cairo()) print(f"\n\n") tp = honk_transcript_from_proof(vk, proof) print(f"\n\n") print(tp.to_cairo()) print(f"\n\n") print(Wire.unused_indexes()) print(tp) ================================================ FILE: hydra/garaga/rsa_rns.py ================================================ """RSA-2048 signature verification via RNS arithmetic and CRT exactness. Implements RSA-2048 modular exponentiation verification suitable for provable computation (Cairo/STARK). Integers in [0, 2^2048) are represented in a Residue Number System (RNS) defined by 11 pairwise coprime ~384-bit primes. A modular product a·b ≡ r (mod n) is witnessed by the Euclidean quotient q satisfying a·b = q·n + r. Correctness is verified through: 1. Channel congruences: for each prime p_i, a·b ≡ q·n + r (mod p_i). 2. CRT exactness: since |a·b - q·n - r| < M = ∏ p_i and the congruences force a·b - q·n - r ≡ 0 (mod M), the relation holds exactly over ℤ. RSA-2048 verification computes s^{65537} mod n via square-and-multiply, yielding 16 squarings + 1 final multiplication = 17 certified reductions. """ from __future__ import annotations import hashlib import math import random from dataclasses import dataclass from typing import Sequence LIMB_BITS = 96 BASE = 1 << LIMB_BITS N_LIMBS = 22 RSA_BITS = 2048 TOP_LIMB_BITS = RSA_BITS - LIMB_BITS * (N_LIMBS - 1) TOP_LIMB_MAX = 1 << TOP_LIMB_BITS MAX_2048 = 1 << RSA_BITS N_CHUNKS = 6 CHUNK_LIMBS = 4 TOP_CHUNK_BITS = 128 RSA_REDUCTION_COUNT = 17 RSA_PUBLIC_EXPONENT = 65537 # Upper bound on |a·b - q·n - r| for a, b, q, n, r < 2^2048. # The CRT modulus M = ∏ p_i must exceed this to guarantee exactness. CRT_EXACTNESS_BOUND = (1 << (2 * RSA_BITS + 1)) + (1 << RSA_BITS) CHANNEL_MODULI = [ 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498787617, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498787149, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498785261, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498784349, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498783539, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498782649, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498782327, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498781403, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498781199, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498780291, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498779421, ] def modinv(a: int, m: int) -> int: return pow(a, -1, m) def split_words_96(x: int, n_words: int) -> list[int]: return [(x >> (LIMB_BITS * i)) & (BASE - 1) for i in range(n_words)] def join_words_96(words: Sequence[int]) -> int: out = 0 for i, word in enumerate(words): if not (0 <= word < BASE): raise ValueError(f"96-bit word {i} out of range") out |= word << (LIMB_BITS * i) return out def split_limbs_2048(x: int) -> list[int]: if not (0 <= x < MAX_2048): raise ValueError("value is not a non-negative 2048-bit integer") limbs = split_words_96(x, N_LIMBS) if limbs[-1] >= TOP_LIMB_MAX: raise ValueError("top limb exceeds the 32-bit RSA-2048 bound") return limbs def join_limbs_2048(limbs: Sequence[int]) -> int: if len(limbs) != N_LIMBS: raise ValueError(f"expected {N_LIMBS} limbs, got {len(limbs)}") x = join_words_96(limbs) if x >= MAX_2048: raise ValueError("reconstructed integer exceeds 2048 bits") if limbs[-1] >= TOP_LIMB_MAX: raise ValueError("top limb exceeds the 32-bit RSA-2048 bound") return x def limbs_to_chunks(limbs: Sequence[int]) -> tuple[int, ...]: """Group 22 limbs of 96 bits into 6 chunks of 384 bits (top chunk: 128 bits).""" if len(limbs) != N_LIMBS: raise ValueError(f"expected {N_LIMBS} limbs, got {len(limbs)}") padded_limbs = list(limbs) + [0, 0] chunks = [] for chunk_index in range(N_CHUNKS): start = chunk_index * CHUNK_LIMBS end = start + CHUNK_LIMBS chunks.append(join_words_96(padded_limbs[start:end])) if chunks[-1] >= (1 << TOP_CHUNK_BITS): raise ValueError("top chunk exceeds the 128-bit RSA-2048 bound") return tuple(chunks) def is_probable_prime(n: int, rounds: int = 24) -> bool: if n < 2: return False small_primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37) for p in small_primes: if n % p == 0: return n == p d = n - 1 s = 0 while d % 2 == 0: s += 1 d //= 2 rng = random.Random((n ^ 0x9E3779B97F4A7C15) & ((1 << 64) - 1)) for _ in range(rounds): a = rng.randrange(2, n - 1) x = pow(a, d, n) if x in (1, n - 1): continue for __ in range(s - 1): x = pow(x, 2, n) if x == n - 1: break else: return False return True def random_probable_prime(bits: int, rng: random.Random) -> int: while True: candidate = rng.getrandbits(bits) | (1 << (bits - 1)) | 1 while candidate.bit_length() == bits: if is_probable_prime(candidate): return candidate candidate += 2 @dataclass(frozen=True, slots=True) class RNSInteger: """An integer x in [0, 2^2048) together with its RNS representation. Attributes: value: The integer x. limbs: 96-bit limb decomposition, x = sum(limbs[i] * 2^{96i}). residues: Channel residues, residues[i] = x mod p_i. """ value: int limbs: tuple[int, ...] residues: tuple[int, ...] @staticmethod def from_int(x: int, channel_moduli: Sequence[int]) -> "RNSInteger": limbs = tuple(split_limbs_2048(x)) residues = tuple(x % p for p in channel_moduli) return RNSInteger(value=x, limbs=limbs, residues=residues) @property def chunks(self) -> tuple[int, ...]: return limbs_to_chunks(self.limbs) def serialize_to_calldata(self) -> list[int]: calldata = [] for chunk in self.chunks: calldata.extend(split_words_96(chunk, CHUNK_LIMBS)) return calldata @dataclass(frozen=True, slots=True) class ReductionWitness: """Witness for a modular reduction a * b = q * n + r over Z. Attributes: quotient: q = floor(a*b / n) as an RNS integer. remainder: r = (a*b) mod n as an RNS integer. """ quotient: RNSInteger remainder: RNSInteger def serialize_to_calldata(self) -> list[int]: return ( self.quotient.serialize_to_calldata() + self.remainder.serialize_to_calldata() ) @dataclass(frozen=True, slots=True) class RSA2048ExponentiationWitness: """Complete witness for RSA-2048 verification: s^e = m (mod n). Contains the modulus n, signature s, expected message m, and 17 reduction witnesses certifying the square-and-multiply chain for s^{65537} mod n. """ modulus: RNSInteger signature: RNSInteger expected_message: RNSInteger reductions: tuple[ReductionWitness, ...] def __post_init__(self) -> None: if len(self.reductions) != RSA_REDUCTION_COUNT: raise ValueError( f"expected {RSA_REDUCTION_COUNT} reductions, got {len(self.reductions)}" ) def serialize_public_key(self) -> list[int]: return self.modulus.serialize_to_calldata() def serialize_signature_with_hint(self) -> list[int]: calldata = ( self.signature.serialize_to_calldata() + self.expected_message.serialize_to_calldata() ) for witness in self.reductions: calldata.extend(witness.serialize_to_calldata()) return calldata def serialize(self, prepend_public_key: bool = True) -> list[int]: calldata = [] if prepend_public_key: calldata.extend(self.serialize_public_key()) calldata.extend(self.serialize_signature_with_hint()) return calldata class RNSContext: """RNS arithmetic context for CRT-based exact modular verification. Defines the RNS basis {p_1, ..., p_k} and precomputes CRT reconstruction coefficients. The product M = prod(p_i) must exceed CRT_EXACTNESS_BOUND to guarantee that channel congruences imply integer equality. Attributes: primes: Channel primes p_1, ..., p_k. M: CRT modulus, M = prod(p_i). cofactors: CRT cofactors, M_i = M / p_i. cofactor_inverses: CRT lifting coefficients, M_i^{-1} mod p_i. """ def __init__(self, channel_moduli: Sequence[int]) -> None: self.primes = list(channel_moduli) if not self.primes: raise ValueError("at least one channel modulus is required") if len(set(self.primes)) != len(self.primes): raise ValueError("channel moduli must be distinct") if not all(p < BASE**4 for p in self.primes): raise ValueError("channel moduli must fit in 4 x 96-bit words") if not all(is_probable_prime(p) for p in self.primes): raise ValueError("channel moduli must be prime") if math.prod(self.primes) <= CRT_EXACTNESS_BOUND: raise ValueError("CRT modulus is too small for exactness") self.M = math.prod(self.primes) self.cofactors = [self.M // p for p in self.primes] self.cofactor_inverses = [ pow(M_i, -1, p) for M_i, p in zip(self.cofactors, self.primes) ] def encode(self, x: int) -> RNSInteger: return RNSInteger.from_int(x, self.primes) def residues_from_limbs(self, limbs: Sequence[int]) -> tuple[int, ...]: """Compute channel residues directly from the limb decomposition.""" _ = join_limbs_2048(limbs) out = [] for p in self.primes: acc = 0 for limb in reversed(limbs): acc = (acc * BASE + limb) % p out.append(acc) return tuple(out) def crt_reconstruct(self, residues: Sequence[int]) -> int: """Reconstruct x in [0, M) from its channel residues via the CRT.""" if len(residues) != len(self.primes): raise ValueError("wrong number of residues") x = 0 for r_i, p_i, M_i, M_i_inv in zip( residues, self.primes, self.cofactors, self.cofactor_inverses ): if not (0 <= r_i < p_i): raise ValueError("residue out of range") x = (x + r_i * M_i * M_i_inv) % self.M return x def is_consistent_encoding(self, ev: RNSInteger) -> bool: """Check that limbs and residues are consistent with the integer value.""" try: value_from_limbs = join_limbs_2048(ev.limbs) except ValueError: return False if value_from_limbs != ev.value: return False return ev.residues == self.residues_from_limbs(ev.limbs) def rns_congruences_hold( self, a: RNSInteger, b: RNSInteger, modulus: RNSInteger, quotient: RNSInteger, remainder: RNSInteger, ) -> bool: """Check a*b = q*n + r (mod p_i) in every RNS channel.""" for ev in (a, b, modulus, quotient, remainder): if not self.is_consistent_encoding(ev): return False if not (0 <= remainder.value < modulus.value): return False for idx, p in enumerate(self.primes): lhs = (a.residues[idx] * b.residues[idx]) % p rhs = ( quotient.residues[idx] * modulus.residues[idx] + remainder.residues[idx] ) % p if lhs != rhs: return False return True def crt_exactness_holds( self, a: RNSInteger, b: RNSInteger, modulus: RNSInteger, quotient: RNSInteger, remainder: RNSInteger, ) -> bool: """Check |delta| < M and delta = 0 (mod M) where delta = a*b - q*n - r.""" delta = a.value * b.value - quotient.value * modulus.value - remainder.value return (delta % self.M == 0) and (abs(delta) < self.M) def verify_exact_modular_product( self, a: RNSInteger, b: RNSInteger, modulus: RNSInteger, quotient: RNSInteger, remainder: RNSInteger, ) -> bool: """Verify a*b = q*n + r exactly via RNS congruences and CRT exactness.""" if not self.rns_congruences_hold(a, b, modulus, quotient, remainder): return False if not self.crt_exactness_holds(a, b, modulus, quotient, remainder): return False return a.value * b.value == quotient.value * modulus.value + remainder.value def witness_modular_product( ctx: RNSContext, a: int, b: int, modulus: int ) -> tuple[RNSInteger, RNSInteger, RNSInteger, RNSInteger, RNSInteger]: """Compute the RNS encoding of (a, b, n, q, r) where a*b = q*n + r.""" if not (0 <= a < modulus and 0 <= b < modulus and 1 < modulus < MAX_2048): raise ValueError("require 0 <= a,b < modulus < 2^2048 and modulus > 1") quotient, remainder = divmod(a * b, modulus) return ( ctx.encode(a), ctx.encode(b), ctx.encode(modulus), ctx.encode(quotient), ctx.encode(remainder), ) def build_reduction_witness( ctx: RNSContext, a: int, b: int, modulus: int ) -> ReductionWitness: """Build and verify a reduction witness for a*b mod n.""" a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev = witness_modular_product( ctx, a, b, modulus ) if not ctx.verify_exact_modular_product( a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev ): raise AssertionError("exact RNS/CRT modular multiplication check failed") return ReductionWitness(quotient=quotient_ev, remainder=remainder_ev) def verified_mul_mod(ctx: RNSContext, x: int, y: int, modulus: int) -> int: """Compute x*y mod n with a verified RNS reduction.""" return build_reduction_witness(ctx, x, y, modulus).remainder.value def generate_demo_rsa_key( bits: int = RSA_BITS, e: int = RSA_PUBLIC_EXPONENT, seed: int = 20260305, ) -> tuple[int, int, int]: if bits != RSA_BITS: raise ValueError("this helper is written around RSA-2048") rng = random.Random(seed) half = bits // 2 while True: p = random_probable_prime(half, rng) if math.gcd(p - 1, e) == 1: break while True: q = random_probable_prime(half, rng) if q != p and math.gcd(q - 1, e) == 1: break modulus = p * q if modulus.bit_length() != bits: return generate_demo_rsa_key(bits=bits, e=e, seed=seed + 1) phi = (p - 1) * (q - 1) private_exponent = modinv(e, phi) return modulus, e, private_exponent def build_rsa2048_reductions( ctx: RNSContext, signature: int, expected_message: int, modulus: int, e: int = RSA_PUBLIC_EXPONENT, ) -> tuple[ReductionWitness, ...]: """Compute all reduction witnesses for the square-and-multiply chain s^e mod n. For e = 65537 = 2^16 + 1, the binary representation has 17 bits, yielding 16 squarings and 1 final multiplication = 17 reductions. """ bits = bin(e)[2:] if bits[0] != "1": raise ValueError("public exponent must be positive") acc = signature reductions = [] for bit in bits[1:]: squaring = build_reduction_witness(ctx, acc, acc, modulus) reductions.append(squaring) acc = squaring.remainder.value if bit == "1": multiply = build_reduction_witness(ctx, acc, signature, modulus) reductions.append(multiply) acc = multiply.remainder.value if acc != expected_message: raise AssertionError("witness path does not yield the expected message") if len(reductions) != RSA_REDUCTION_COUNT: raise AssertionError( f"expected {RSA_REDUCTION_COUNT} reductions, got {len(reductions)}" ) return tuple(reductions) def generate_rsa2048_witness(seed: int = 0) -> RSA2048ExponentiationWitness: """Generate a complete RSA-2048 verification witness from a deterministic seed.""" ctx = RNSContext(CHANNEL_MODULI) modulus, e, private_exponent = generate_demo_rsa_key(seed=20260305 + seed) rng = random.Random(0x5253412048 + seed) expected_message = rng.randrange(2, modulus - 1) signature = pow(expected_message, private_exponent, modulus) reductions = build_rsa2048_reductions( ctx, signature, expected_message, modulus, e=e ) return RSA2048ExponentiationWitness( modulus=ctx.encode(modulus), signature=ctx.encode(signature), expected_message=ctx.encode(expected_message), reductions=reductions, ) # PKCS#1 v1.5 SHA-256 DigestInfo prefix (DER-encoded AlgorithmIdentifier + NULL param). # RFC 8017, Section 9.2, Note 1. PKCS1_SHA256_DIGEST_INFO_PREFIX = bytes.fromhex( "3031300d060960864801650304020105000420" ) def pkcs1_v1_5_encode_sha256( message_hash: bytes, modulus_byte_length: int = 256 ) -> int: """Encode a SHA-256 hash as a PKCS#1 v1.5 padded integer. Constructs: 0x00 || 0x01 || PS || 0x00 || DigestInfo || H where PS is (modulus_byte_length - 3 - len(DigestInfo) - 32) bytes of 0xFF. For RSA-2048 (modulus_byte_length=256), PS is 202 bytes of 0xFF. """ if len(message_hash) != 32: raise ValueError("message_hash must be exactly 32 bytes (SHA-256)") digest_info = PKCS1_SHA256_DIGEST_INFO_PREFIX + message_hash ps_len = modulus_byte_length - 3 - len(digest_info) if ps_len < 8: raise ValueError("modulus too short for PKCS#1 v1.5 SHA-256 encoding") encoded = b"\x00\x01" + b"\xff" * ps_len + b"\x00" + digest_info return int.from_bytes(encoded, byteorder="big") def generate_rsa2048_sha256_witness( message: bytes, seed: int = 0 ) -> RSA2048ExponentiationWitness: """Generate an RSA-2048 verification witness for a SHA-256 message digest. Signs the PKCS#1 v1.5 encoding of SHA-256(message) under a deterministic demo key, then builds the full exponentiation witness. """ ctx = RNSContext(CHANNEL_MODULI) modulus, e, private_exponent = generate_demo_rsa_key(seed=20260305 + seed) message_hash = hashlib.sha256(message).digest() expected_message = pkcs1_v1_5_encode_sha256(message_hash) signature = pow(expected_message, private_exponent, modulus) reductions = build_rsa2048_reductions( ctx, signature, expected_message, modulus, e=e ) return RSA2048ExponentiationWitness( modulus=ctx.encode(modulus), signature=ctx.encode(signature), expected_message=ctx.encode(expected_message), reductions=reductions, ) def is_valid_rsa2048_witness( bundle: RSA2048ExponentiationWitness, ctx: RNSContext | None = None, ) -> bool: """Validate an RSA-2048 exponentiation witness. Checks encoding consistency, range constraints, and all 17 modular reduction steps of the square-and-multiply chain. """ ctx = ctx or RNSContext(CHANNEL_MODULI) if not ctx.is_consistent_encoding(bundle.modulus): return False if not ctx.is_consistent_encoding(bundle.signature): return False if not ctx.is_consistent_encoding(bundle.expected_message): return False if bundle.modulus.value <= 1 or bundle.modulus.value % 2 == 0: return False if bundle.signature.value >= bundle.modulus.value: return False if bundle.expected_message.value >= bundle.modulus.value: return False if len(bundle.reductions) != RSA_REDUCTION_COUNT: return False acc = bundle.signature for witness in bundle.reductions[:-1]: if not ctx.verify_exact_modular_product( acc, acc, bundle.modulus, witness.quotient, witness.remainder ): return False acc = witness.remainder last = bundle.reductions[-1] if not ctx.verify_exact_modular_product( acc, bundle.signature, bundle.modulus, last.quotient, last.remainder ): return False return last.remainder.value == bundle.expected_message.value def modular_exponentiation_with_proof( ctx: RNSContext, signature: int, e: int, modulus: int ) -> tuple[int, int]: """Compute s^e mod n via square-and-multiply with verified reductions. Returns (result, reduction_count). """ bits = bin(e)[2:] if bits[0] != "1": raise ValueError("public exponent must be positive") acc = signature reduction_count = 0 for bit in bits[1:]: acc = verified_mul_mod(ctx, acc, acc, modulus) reduction_count += 1 if bit == "1": acc = verified_mul_mod(ctx, acc, signature, modulus) reduction_count += 1 return acc, reduction_count def demo_context_summary(ctx: RNSContext) -> None: print("== RNS context for exact modular arithmetic ==") print(f"Base B = 2^{LIMB_BITS}") print( f"Big-int format = {N_LIMBS} limbs of 96 bits (top limb constrained to {TOP_LIMB_BITS} bits)" ) print(f"Number of CRT channels = {len(ctx.primes)}") print( f"Each channel prime fits in 4 x 96-bit words: {all(p < BASE**4 for p in ctx.primes)}" ) print(f"Channel prime bit lengths = {[p.bit_length() for p in ctx.primes]}") print(f"CRT modulus M bit length = {ctx.M.bit_length()}") print(f"CRT modulus M > exactness bound: {ctx.M > CRT_EXACTNESS_BOUND}") print("First channel prime split into four 96-bit words:") print(f" {split_words_96(ctx.primes[0], 4)}") print() def demo_crt_roundtrip(ctx: RNSContext, rng: random.Random) -> None: print("== CRT roundtrip from limb-consistent residues ==") for idx in range(1, 4): x = rng.getrandbits(RSA_BITS - 1) ev = ctx.encode(x) x_recovered = ctx.crt_reconstruct(ev.residues) assert x_recovered == x print( f" sample {idx}: recovered exact {x.bit_length()}-bit value from residues" ) print() def demo_single_exact_relation( ctx: RNSContext, modulus: int, rng: random.Random ) -> None: print("== One exact modular product witness check ==") a = rng.randrange(0, modulus) b = rng.randrange(0, modulus) a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev = witness_modular_product( ctx, a, b, modulus ) assert ctx.rns_congruences_hold(a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev) assert ctx.crt_exactness_holds(a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev) assert ctx.verify_exact_modular_product( a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev ) print(f" modulus bits = {modulus.bit_length()}") print(f" a bits = {a.bit_length()}") print(f" b bits = {b.bit_length()}") print(f" q bits = {quotient_ev.value.bit_length()}") print(f" r bits = {remainder_ev.value.bit_length()}") print(" All channel congruences passed, 0 <= r < n verified,") print(" and CRT exactness implies a*b = q*n + r over Z.") print() def demo_negative_tests(ctx: RNSContext, modulus: int, rng: random.Random) -> None: print("== Negative tests (tampering is detected) ==") a = rng.randrange(0, modulus) b = rng.randrange(0, modulus) a_ev, b_ev, modulus_ev, quotient_ev, remainder_ev = witness_modular_product( ctx, a, b, modulus ) bad_residues = list(remainder_ev.residues) bad_residues[0] = (bad_residues[0] + 1) % ctx.primes[0] bad_remainder = RNSInteger( remainder_ev.value, remainder_ev.limbs, tuple(bad_residues) ) assert not ctx.rns_congruences_hold( a_ev, b_ev, modulus_ev, quotient_ev, bad_remainder ) bad_limbs = list(quotient_ev.limbs) bad_limbs[1] ^= 1 bad_quotient = RNSInteger(quotient_ev.value, tuple(bad_limbs), quotient_ev.residues) assert not ctx.is_consistent_encoding(bad_quotient) print(" Tampered residue detected: PASS") print(" Tampered limb detected: PASS") print() def demo_full_rsa_verification(ctx: RNSContext) -> None: print("== Full RSA-2048 verification via square-and-multiply ==") modulus, e, private_exponent = generate_demo_rsa_key() rng = random.Random(999) message = rng.randrange(2, modulus - 1) signature = pow(message, private_exponent, modulus) verified_message, reduction_count = modular_exponentiation_with_proof( ctx, signature, e, modulus ) assert verified_message == message assert verified_message == pow(signature, e, modulus) print(f" RSA modulus bits = {modulus.bit_length()}") print(f" public exponent e = {e}") print(f" signature verification succeeded = {verified_message == message}") print(f" verified modular reductions = {reduction_count}") print( " For e = 65537 = 2^16 + 1, the chain uses 16 squarings + 1 multiply = 17 reductions." ) print() def run_self_tests() -> None: ctx = RNSContext(CHANNEL_MODULI) rng = random.Random(123456789) demo_context_summary(ctx) demo_crt_roundtrip(ctx, rng) modulus, _, _ = generate_demo_rsa_key() demo_single_exact_relation(ctx, modulus, rng) demo_negative_tests(ctx, modulus, rng) demo_full_rsa_verification(ctx) bundle = generate_rsa2048_witness() assert is_valid_rsa2048_witness(bundle, ctx) print("All demonstrations and assertions passed.") if __name__ == "__main__": run_self_tests() ================================================ FILE: hydra/garaga/signature.py ================================================ """ Various tools for bls signatures or other signature schemes. """ from __future__ import annotations import hashlib from typing import Protocol, TypeVar from garaga.algebra import Polynomial, PyFelt, RationalFunction from garaga.curves import CURVES, CurveID, get_base_field from garaga.points import G1Point T = TypeVar("T", bound="HashProtocol") class HashProtocol(Protocol): # Attributes block_size: int # digest_size: int # in bytes name: str # Methods def update(self, data: bytes) -> None: ... def digest(self) -> bytes: ... def hexdigest(self) -> str: ... def copy(self: T) -> T: ... import math G1_DOMAIN = DST = b"BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_" MAX_DST_LENGTH = 255 LONG_DST_PREFIX = b"H2C-OVERSIZE-DST-" class ExpanderXmd: def __init__( self, hash_name: str, dst: bytes = DST, curve_id: CurveID = CurveID.BLS12_381, ): self.hash_name = hash_name self.hasher = hashlib.new(hash_name) self.dst = dst self.curve_id = curve_id self.block_size = get_len_per_elem(get_base_field(curve_id).p) def construct_dst_prime(self) -> bytes: if len(self.dst) > MAX_DST_LENGTH: hasher_copy = self.hasher.copy() hasher_copy.update(LONG_DST_PREFIX) hasher_copy.update(self.dst) dst_prime = hasher_copy.digest() else: # print(f"dst len is < {MAX_DST_LENGTH}") dst_prime = self.dst dst_prime += bytes([len(dst_prime)]) return dst_prime def expand_message_xmd(self, msg: bytes, n: int) -> bytes: b_len = self.hasher.digest_size ell = (n + (b_len - 1)) // b_len assert ( ell <= 255 ), "The ratio of desired output to the output size of hash function is too large!" dst_prime = self.construct_dst_prime() # print(f"dst prime {dst_prime}") # print(f"block size {self.block_size}") z_pad = bytes([0] * self.block_size) # print(f"z pad {z_pad.hex()}") # print(f"len(z_pad) (bytes) {len(z_pad)}") assert n < (1 << 16), "Length should be smaller than 2^16" lib_str = n.to_bytes(2, "big") self.hasher.update(z_pad) self.hasher.update(msg) # Print separately lib_str+bytes([0])+dst_prime, in one bytes object lib_str_dst_prime = lib_str + bytes([0]) + dst_prime # print( # f"lib_str_dst_prime {lib_str_dst_prime}, len : {len(lib_str_dst_prime)}\n {bytes_to_u32_array(lib_str_dst_prime, 'lib_str_dst_prime')}" # ) self.hasher.update(lib_str_dst_prime) # self.hasher.update(bytes([0])) # self.hasher.update(dst_prime) b0 = self.hasher.digest() # print(f"b0 {b0.hex()}") hasher = hashlib.new(self.hash_name) hasher.update(b0) one_dst_prime = bytes([1]) + dst_prime hasher.update(one_dst_prime) bi = hasher.digest() uniform_bytes = bi for i in range(2, ell + 1): # print(f"loop: step {i}/{ell}") # print(f"zip {list(zip(b0, bi))}") b0_xor_bi = bytes(x ^ y for x, y in zip(b0, bi)) # print(f"b0_xor_bi {b0_xor_bi.hex()}") # print( # f"direct xor : {hex(int.from_bytes(b0, 'big') ^ int.from_bytes(bi, 'big'))}" # ) hasher = hashlib.new(self.hash_name) hasher.update(b0_xor_bi) bytes_i_dst_prime = bytes([i]) + dst_prime # print( # f"bytes_i_dst_prime {bytes_to_u32_array(bytes_i_dst_prime, f'bytes_{i}_dst_prime')}" # ) hasher.update(bytes_i_dst_prime) bi = hasher.digest() uniform_bytes += bi # print(f"len(uniform_bytes) {len(uniform_bytes)}") # print(f"len(uniform_bytes[:n]) {len(uniform_bytes[:n])}") return uniform_bytes[:n] def get_len_per_elem(p: int, sec_param: int = 128) -> int: """ This function computes the length in bytes that a hash function should output for hashing an element of type `Field`. :param p: The prime modulus of the base field. :param sec_param: The security parameter. :return: The length in bytes. """ # ceil(log2(p)) base_field_size_in_bits = p.bit_length() # ceil(log2(p)) + security_parameter base_field_size_with_security_padding_in_bits = base_field_size_in_bits + sec_param # ceil((ceil(log2(p)) + security_parameter) / 8) bytes_per_base_field_elem = math.ceil( base_field_size_with_security_padding_in_bits / 8 ) return bytes_per_base_field_elem def hash_to_field( message: bytes, count: int, curve_id: int, hash_name: str ) -> list[int]: field = get_base_field(curve_id) expander = ExpanderXmd(hash_name, dst=DST, curve_id=curve_id) len_per_elem = get_len_per_elem(field.p) len_in_bytes = count * len_per_elem # print(f"len per elem {len_per_elem}") # print(f"len in bytes: {len_in_bytes}") # print(f"message {message.hex()}") uniform_bytes = expander.expand_message_xmd(message, len_in_bytes) # print(f"uniform bytes {uniform_bytes.hex()}") output = [] for i in range(0, len_in_bytes, len_per_elem): element = int.from_bytes(uniform_bytes[i : i + len_per_elem], "big") # print(f"element {element.bit_length()}") output.append(element) return [field(x) for x in output] def hash_to_curve( message: bytes, curve_id: CurveID, hash_name: str = "sha256" ) -> G1Point: felt0, felt1 = hash_to_field(message, 2, curve_id, hash_name) pt0 = map_to_curve(felt0, curve_id) # print(f"pt0 {pt0}\n\n") pt1 = map_to_curve(felt1, curve_id) # print(f"pt1 {pt1}") assert pt0.iso_point == True, f"Point {pt0} is not an iso point" assert pt1.iso_point == True, f"Point {pt1} is not an iso point" if curve_id == CurveID.BLS12_381: x = CURVES[curve_id.value].x n = CURVES[curve_id.value].n cofactor = (1 - (x % n)) % n else: cofactor = CURVES[curve_id.value].h # print(f"cofactor {cofactor}") sum = pt0.add(pt1) assert sum.iso_point == True, f"Point {sum} is not an iso point" return apply_isogeny(sum).scalar_mul(cofactor) def map_to_curve(field_element: PyFelt, curve_id: CurveID) -> G1Point: field = get_base_field(curve_id) a = field(CURVES[curve_id.value].swu_params.A) b = field(CURVES[curve_id.value].swu_params.B) z = field(CURVES[curve_id.value].swu_params.Z) u = field_element zeta_u2 = z * u**2 ta = zeta_u2**2 + zeta_u2 num_x1 = b * (ta + field.one()) if ta.value == 0: div = a * z else: div = a * -ta num2_x1 = num_x1**2 div2 = div**2 div3 = div2 * div assert div3.value != 0 num_gx1 = (num2_x1 + a * div2) * num_x1 + b * div3 num_x2 = zeta_u2 * num_x1 gx1 = num_gx1 / div3 gx1_square = gx1.is_quad_residue() if gx1_square: y1 = gx1.sqrt(min_root=False) assert y1 * y1 == gx1 else: y1 = (z * gx1).sqrt(min_root=False) assert y1 * y1 == z * gx1 y2 = zeta_u2 * u * y1 num_x = num_x1 if gx1_square else num_x2 y = y1 if gx1_square else y2 x_affine = num_x / div y_affine = -y if y.value % 2 != u.value % 2 else y point_on_curve = G1Point(x_affine.value, y_affine.value, curve_id, iso_point=True) return point_on_curve # https://github.com/arkworks-rs/algebra/blob/master/curves/bls12_381/src/curves/g1_swu_iso.rs def get_isogeny_to_g1_map( curve_id: CurveID, ) -> tuple[RationalFunction, RationalFunction]: field = get_base_field(curve_id) match curve_id.value: case CurveID.BLS12_381.value: return RationalFunction( numerator=Polynomial( [ field(x) for x in [ 0x11A05F2B1E833340B809101DD99815856B303E88A2D7005FF2627B56CDB4E2C85610C2D5F2E62D6EAEAC1662734649B7, 0x17294ED3E943AB2F0588BAB22147A81C7C17E75B2F6A8417F565E33C70D1E86B4838F2A6F318C356E834EEF1B3CB83BB, 0xD54005DB97678EC1D1048C5D10A9A1BCE032473295983E56878E501EC68E25C958C3E3D2A09729FE0179F9DAC9EDCB0, 0x1778E7166FCC6DB74E0609D307E55412D7F5E4656A8DBF25F1B33289F1B330835336E25CE3107193C5B388641D9B6861, 0xE99726A3199F4436642B4B3E4118E5499DB995A1257FB3F086EEB65982FAC18985A286F301E77C451154CE9AC8895D9, 0x1630C3250D7313FF01D1201BF7A74AB5DB3CB17DD952799B9ED3AB9097E68F90A0870D2DCAE73D19CD13C1C66F652983, 0xD6ED6553FE44D296A3726C38AE652BFB11586264F0F8CE19008E218F9C86B2A8DA25128C1052ECADDD7F225A139ED84, 0x17B81E7701ABDBE2E8743884D1117E53356DE5AB275B4DB1A682C62EF0F2753339B7C8F8C8F475AF9CCB5618E3F0C88E, 0x80D3CF1F9A78FC47B90B33563BE990DC43B756CE79F5574A2C596C928C5D1DE4FA295F296B74E956D71986A8497E317, 0x169B1F8E1BCFA7C42E0C37515D138F22DD2ECB803A0C5C99676314BAF4BB1B7FA3190B2EDC0327797F241067BE390C9E, 0x10321DA079CE07E272D8EC09D2565B0DFA7DCCDDE6787F96D50AF36003B14866F69B771F8C285DECCA67DF3F1605FB7B, 0x6E08C248E260E70BD1E962381EDEE3D31D79D7E22C837BC23C0BF1BC24C6B68C24B1B80B64D391FA9C8BA2E8BA2D229, ] ] ), denominator=Polynomial( [ field(x) for x in [ 0x8CA8D548CFF19AE18B2E62F4BD3FA6F01D5EF4BA35B48BA9C9588617FC8AC62B558D681BE343DF8993CF9FA40D21B1C, 0x12561A5DEB559C4348B4711298E536367041E8CA0CF0800C0126C2588C48BF5713DAA8846CB026E9E5C8276EC82B3BFF, 0xB2962FE57A3225E8137E629BFF2991F6F89416F5A718CD1FCA64E00B11ACEACD6A3D0967C94FEDCFCC239BA5CB83E19, 0x3425581A58AE2FEC83AAFEF7C40EB545B08243F16B1655154CCA8ABC28D6FD04976D5243EECF5C4130DE8938DC62CD8, 0x13A8E162022914A80A6F1D5F43E7A07DFFDFC759A12062BB8D6B44E833B306DA9BD29BA81F35781D539D395B3532A21E, 0xE7355F8E4E667B955390F7F0506C6E9395735E9CE9CAD4D0A43BCEF24B8982F7400D24BC4228F11C02DF9A29F6304A5, 0x772CAACF16936190F3E0C63E0596721570F5799AF53A1894E2E073062AEDE9CEA73B3538F0DE06CEC2574496EE84A3A, 0x14A7AC2A9D64A8B230B3F5B074CF01996E7F63C21BCA68A81996E1CDF9822C580FA5B9489D11E2D311F7D99BBDCC5A5E, 0xA10ECF6ADA54F825E920B3DAFC7A3CCE07F8D1D7161366B74100DA67F39883503826692ABBA43704776EC3A79A1D641, 0x95FC13AB9E92AD4476D6E3EB3A56680F682B4EE96F7D03776DF533978F31C1593174E4B4B7865002D6384D168ECDD0A, 0x1, ] ] ), ), RationalFunction( numerator=Polynomial( [ field(x) for x in [ 1393399195776646641963150658816615410692049723305861307490980409834842911816308830479576739332720113414154429643571, 2968610969752762946134106091152102846225411740689724909058016729455736597929366401532929068084731548131227395540630, 122933100683284845219599644396874530871261396084070222155796123161881094323788483360414289333111221370374027338230, 303251954782077855462083823228569901064301365507057490567314302006681283228886645653148231378803311079384246777035, 1353972356724735644398279028378555627591260676383150667237975415318226973994509601413730187583692624416197017403099, 3443977503653895028417260979421240655844034880950251104724609885224259484262346958661845148165419691583810082940400, 718493410301850496156792713845282235942975872282052335612908458061560958159410402177452633054233549648465863759602, 1466864076415884313141727877156167508644960317046160398342634861648153052436926062434809922037623519108138661903145, 1536886493137106337339531461344158973554574987550750910027365237255347020572858445054025958480906372033954157667719, 2171468288973248519912068884667133903101171670397991979582205855298465414047741472281361964966463442016062407908400, 3915937073730221072189646057898966011292434045388986394373682715266664498392389619761133407846638689998746172899634, 3802409194827407598156407709510350851173404795262202653149767739163117554648574333789388883640862266596657730112910, 1707589313757812493102695021134258021969283151093981498394095062397393499601961942449581422761005023512037430861560, 349697005987545415860583335313370109325490073856352967581197273584891698473628451945217286148025358795756956811571, 885704436476567581377743161796735879083481447641210566405057346859953524538988296201011389016649354976986251207243, 3370924952219000111210625390420697640496067348723987858345031683392215988129398381698161406651860675722373763741188, ] ] ), denominator=Polynomial( [ field(x) for x in [ 3396434800020507717552209507749485772788165484415495716688989613875369612529138640646200921379825018840894888371137, 3907278185868397906991868466757978732688957419873771881240086730384895060595583602347317992689443299391009456758845, 854914566454823955479427412036002165304466268547334760894270240966182605542146252771872707010378658178126128834546, 3496628876382137961119423566187258795236027183112131017519536056628828830323846696121917502443333849318934945158166, 1828256966233331991927609917644344011503610008134915752990581590799656305331275863706710232159635159092657073225757, 1362317127649143894542621413133849052553333099883364300946623208643344298804722863920546222860227051989127113848748, 3443845896188810583748698342858554856823966611538932245284665132724280883115455093457486044009395063504744802318172, 3484671274283470572728732863557945897902920439975203610275006103818288159899345245633896492713412187296754791689945, 3755735109429418587065437067067640634211015783636675372165599470771975919172394156249639331555277748466603540045130, 3459661102222301807083870307127272890283709299202626530836335779816726101522661683404130556379097384249447658110805, 742483168411032072323733249644347333168432665415341249073150659015707795549260947228694495111018381111866512337576, 1662231279858095762833829698537304807741442669992646287950513237989158777254081548205552083108208170765474149568658, 1668238650112823419388205992952852912407572045257706138925379268508860023191233729074751042562151098884528280913356, 369162719928976119195087327055926326601627748362769544198813069133429557026740823593067700396825489145575282378487, 2164195715141237148945939585099633032390257748382945597506236650132835917087090097395995817229686247227784224263055, 1, ] ] ), ) case _: raise NotImplementedError( f"Isogeny for curve {curve_id} is not implemented" ) # https://github.com/arkworks-rs/algebra/blob/master/curves/bls12_381/src/curves/g2_swu_iso.rs def get_isogeny_to_g2_map( curve_id: CurveID, ) -> tuple[RationalFunction, RationalFunction]: field = get_base_field(curve_id) match curve_id.value: case CurveID.BLS12_381.value: return RationalFunction( numerator=Polynomial( [ field(x) for x in [ 889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235542, 889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235542, 0, 2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706522, 2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706526, 1334136518407222464472596608578634718852294273313002628444019378708010550163612621480895876376338554679298090853261, 3557697382419259905260257622876359250272784728834673675850718343221361467102966990615722337003569479144794908942033, 0, ] ] ), denominator=Polynomial( [ field(x) for x in [ 0, 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559715, 12, 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559775, 1, 0, ] ] ), ), RationalFunction( numerator=Polynomial( [ field(x) for x in [ 3261222600550988246488569487636662646083386001431784202863158481286248011511053074731078808919938689216061999863558, 3261222600550988246488569487636662646083386001431784202863158481286248011511053074731078808919938689216061999863558, 0, 889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235518, 2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706524, 1334136518407222464472596608578634718852294273313002628444019378708010550163612621480895876376338554679298090853263, 2816510427748580758331037284777117739799287910327449993381818688383577828123182200904113516794492504322962636245776, 0, ] ] ), denominator=Polynomial( [ field(x) for x in [ 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559355, 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559355, 0, 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559571, 18, 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559769, 1, 0, ] ] ), ) case _: raise NotImplementedError( f"Isogeny for curve {curve_id} is not implemented" ) def apply_isogeny(pt: G1Point) -> G1Point: assert pt.iso_point == True, f"Point {pt} is not an iso point" field = get_base_field(pt.curve_id) x_rational, y_rational = get_isogeny_to_g1_map(pt.curve_id) x_affine = x_rational.evaluate(field(pt.x)) y_affine = y_rational.evaluate(field(pt.x)) * field(pt.y) return G1Point(x_affine.value, y_affine.value, pt.curve_id, iso_point=False) if __name__ == "__main__": from garaga.hints.io import int_to_u384 field = get_base_field(CurveID.BLS12_381) message = b"Hello, World!" sha_message = hashlib.sha256(message).digest() # print(f"sha_message {sha_message.hex()}") message = sha_message def test_hash_to_field(message: bytes): res = hash_to_field( message=message, count=2, curve_id=CurveID.BLS12_381, hash_name="sha256", ) print(f"res {[int_to_u384(x) for x in res]}") expected = [ 2162792105491427725912070356725320455528056118179305300106498860235975843802512462082887053454085287130500476441750, 40368511435268498384669958495624628965655407346873103876018487738713032717501957266398124814691972213333393099218, ] # assert res == expected, f"Expected {expected}, got {res}" def test_map_to_curve(): u = field(42) res = map_to_curve(field_element=u, curve_id=CurveID.BLS12_381) print(f"res {int_to_u384(res.x)} {int_to_u384(res.y)}") def test_isogeny(): pt = G1Point( x=215777581081472667122506794895079133292851844364726904952688478479828790890150439604857229658591641382171852677524, y=1379746801043875097750009912574703067223644203712602673826050484796337984730238282465201134827010880864260517139932, curve_id=CurveID.BLS12_381, iso_point=True, ) expected = G1Point( x=2417697449117523569926871462160078790628278460141221111171958173864939056722835940739506331591809461977867457921129, y=2054645981348311902541581243120273427071170397909163934255295587636136055038499048700096920528935972380584458489355, curve_id=CurveID.BLS12_381, iso_point=False, ) res = apply_isogeny(pt=pt) assert res == expected, f"Expected {expected}, got {res}" # test_isogeny() def test_hash_to_curve(message: bytes): expected = G1Point( x=1427986885250946460144481685485785737438296207533779678983559530346613679756132883977754715392336662418069603153756, y=2665645453955482249178808933038784408956625041285885055194161860684118145927032784752731507519078519455031562783679, curve_id=CurveID.BLS12_381, ) res = hash_to_curve( message=message, curve_id=CurveID.BLS12_381, hash_name="sha256" ) # assert res == expected, f"Expected {expected}, got {res}" print(f"res {int_to_u384(res.x)} {int_to_u384(res.y)}") # test_hash_to_field(message=message) test_map_to_curve() test_hash_to_curve(message=message) ================================================ FILE: hydra/garaga/starknet/cli/declare.py ================================================ import asyncio import os from pathlib import Path from typing import Annotated import rich import typer from dotenv import load_dotenv from starknet_py.net.account.account import Account from starknet_py.net.full_node_client import FullNodeClient from starknet_py.net.models import StarknetChainId from starknet_py.net.signer.stark_curve_signer import KeyPair from garaga.hints.io import to_int from garaga.starknet.cli.smart_contract_project import SmartContractProject from garaga.starknet.cli.utils import Network, voyager_link_class app = typer.Typer() def declare( project_path: Annotated[ Path, typer.Option( help="Path to the Cairo project holding the Scarb.toml file to declare", file_okay=False, dir_okay=True, exists=True, autocompletion=lambda: [], ), ] = Path.cwd(), env_file: Annotated[ Path, typer.Option( help="Path to the environment file", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = str(Path.cwd() / ".secrets"), network: Annotated[ Network, typer.Option( help="Starknet network", case_sensitive=False, ), ] = Network.SEPOLIA.value, ): """Declare your smart contract to Starknet. Obtain its class hash and a explorer link.""" if Path(env_file).exists(): load_dotenv(env_file) else: raise FileNotFoundError(f"Environment file {env_file} does not exist") rpc_url = os.getenv(f"{network.name.upper()}_RPC_URL") account_address = os.getenv(f"{network.name.upper()}_ACCOUNT_ADDRESS") account_private_key = os.getenv(f"{network.name.upper()}_ACCOUNT_PRIVATE_KEY") if network == Network.MAINNET: chain = StarknetChainId.MAINNET else: chain = StarknetChainId.SEPOLIA client = FullNodeClient(node_url=rpc_url) account = Account( address=account_address, client=client, key_pair=KeyPair.from_private_key(to_int(account_private_key)), chain=chain, ) rich.print( f"Declaring project [bold cyan] {project_path}[/bold cyan] on [bold]{network.name}[/bold]" ) project = SmartContractProject(project_path) try: class_hash, _ = asyncio.run(project.declare_class_hash(account=account)) rich.print( f"[bold green]Class hash: {hex(class_hash)} [/bold green] is available on [bold]{network.name}[/bold]" ) rich.print( f"[bold green]Check it out on[/bold green] {voyager_link_class(network, class_hash)}" ) except Exception as e: rich.print(f"[bold red]Error during declaration: {e}[/bold red]") ================================================ FILE: hydra/garaga/starknet/cli/deploy.py ================================================ import asyncio from pathlib import Path from typing import Annotated, Optional import rich import typer from dotenv import load_dotenv from starknet_py.contract import Contract from starknet_py.hash.address import compute_address from starknet_py.hash.utils import pedersen_hash from garaga.hints.io import to_hex_str, to_int from garaga.starknet.cli.utils import ( Network, get_contract_if_exists, get_contract_if_exists_async, load_account, ) # Mainnet/Sepolia deployer address DEPLOYER_ADDRESS = 0x41A78E741E5AF2FEC34B695679BC6891742439F7AFB8484ECD7766661AD02BF app = typer.Typer() async def perform_contract_deployment( account, class_hash: str, salt: int, precomputed_address: int ) -> Optional[Contract]: """Attempt to deploy a contract with the given parameters.""" try: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=class_hash, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=salt, cairo_version=1, ) deploy_result = await deploy_result.wait_for_acceptance() return deploy_result.deployed_contract except Exception as e: print("Waiting for transaction to be accepted...") await asyncio.sleep(5.5) contract = await get_contract_if_exists_async(account, precomputed_address) if contract: return contract else: rich.print(f"[bold red]Deployment error: {e}[/bold red]") return None def print_contract_info(contract: Contract, network: Network): """Print information about the deployed contract.""" sepolia_prefix = "" if network == Network.MAINNET else "sepolia." rich.print(f"Contract address on {network.name}: {hex(contract.address)}") rich.print( f"Voyager link: https://{sepolia_prefix}voyager.online/contract/{hex(contract.address)}" ) rich.print(f"Available endpoints: {list(contract.functions.keys())}") def deploy( class_hash: Annotated[ str, typer.Option( help="Contract class hash to deploy. Can be decimal or hex string" ), ], env_file: Annotated[ Path, typer.Option( help="Path to the environment file containing rpc, address, private_key", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = str(Path.cwd() / ".secrets"), network: Annotated[ Network, typer.Option( help="Starknet network", case_sensitive=False, ), ] = Network.SEPOLIA.value, salt: Annotated[ int, typer.Option( help="Salt value for contract address calculation (default: 1)", ), ] = 1, ): """Deploy an instance of a smart contract class hash to Starknet. Obtain its address, the available endpoints and a explorer link.""" # Validate and load environment if not Path(env_file).exists(): raise FileNotFoundError(f"Environment file {env_file} does not exist") load_dotenv(env_file) # Prepare account and compute address account = load_account(network) class_hash = to_hex_str(class_hash) precomputed_address = compute_address( class_hash=to_int(class_hash), constructor_calldata=[], salt=pedersen_hash(to_int(account.address), salt), deployer_address=DEPLOYER_ADDRESS, ) # Check if contract already exists contract = get_contract_if_exists(account, precomputed_address) if contract: rich.print( f"[bold green]Contract already deployed at {hex(contract.address)}[/bold green]" ) print_contract_info(contract, network) return # Perform deployment rich.print(f"Deploying contract with class hash {class_hash}...") contract = asyncio.run( perform_contract_deployment(account, class_hash, salt, precomputed_address) ) # Handle deployment result if not contract: # Check if the contract exists despite the error (transaction might have completed) contract = get_contract_if_exists(account, precomputed_address) if contract: rich.print( f"[bold green]Contract found at {hex(contract.address)} despite deployment errors.[/bold green]" ) else: rich.print( f"[bold yellow]Contract not deployed. Try running the command again - it might be a temporary network issue.[/bold yellow]" ) return else: rich.print( f"[bold green]Contract successfully deployed at {hex(contract.address)}[/bold green]" ) # Print contract information print_contract_info(contract, network) ================================================ FILE: hydra/garaga/starknet/cli/gen.py ================================================ import subprocess from pathlib import Path from typing import Annotated import typer from rich import print from rich.console import Console from rich.panel import Panel from rich.progress import Progress, SpinnerColumn, TextColumn from rich.tree import Tree from garaga.curves import ProofSystem from garaga.starknet.cli.utils import complete_proof_system, get_package_version from garaga.starknet.constants import BB_VERSION, BBUP_VERSION, NARGO_VERSION from garaga.starknet.groth16_contract_generator.generator import ( ECIP_OPS_CLASS_HASH, gen_groth16_verifier, ) from garaga.starknet.honk_contract_generator.generator_honk import gen_honk_verifier def check_nargo_version(version: str) -> tuple[bool, str]: return check_version("nargo", version) def check_bb_version(version: str) -> tuple[bool, str]: return check_version("bb", version) def check_version(cmd: str, version: str) -> tuple[bool, str]: try: result = subprocess.run([cmd, "--version"], capture_output=True, text=True) result_version = result.stdout.strip() if result.returncode != 0: stderr_msg = result.stderr.strip() error_detail = stderr_msg or result_version or "unknown error" return ( False, f"'{cmd} --version' failed (exit code {result.returncode}): {error_detail}", ) if not result_version: return (False, f"'{cmd} --version' returned empty output") return (version in result_version, result_version) except (FileNotFoundError, OSError): # Command not found or other OS error return (False, f"Command '{cmd}' not found or not executable") def _get_bb_oracle_hash_options() -> list[str]: """Get the available oracle hash options from bb command""" try: result_hash = subprocess.run( ["bb", "prove", "-h"], capture_output=True, text=True ) if result_hash.returncode != 0: return [] # Extract oracle hash options oracle_hash_options = [] lines = result_hash.stdout.splitlines() for i, line in enumerate(lines): if "--oracle_hash" in line: # Look in the next few lines for the options for j in range(i + 1, min(i + 100, len(lines))): if "Options: {" in lines[j]: options_str = lines[j].split("{")[1].split("}")[0] oracle_hash_options = [ opt.strip() for opt in options_str.split(",") ] break break return oracle_hash_options except (FileNotFoundError, OSError): # Command not found or other OS error return [] def check_bb_starknet_support( version: str, with_starknet: bool = False ) -> tuple[bool, str, bool]: """Check if bb supports starknet and meets the version requirement""" version_ok, version_str = check_bb_version(version) oracle_options = _get_bb_oracle_hash_options() has_starknet = "starknet" in oracle_options if with_starknet: return (version_ok and has_starknet, version_str, has_starknet) else: return (version_ok, version_str, has_starknet) def print_bb_warning(soft: bool = False, with_starknet: bool = False): bb_version_ok, bb_version, _ = check_bb_starknet_support(BB_VERSION, with_starknet) nargo_version_ok, nargo_version = check_version("nargo", NARGO_VERSION) if not bb_version_ok or not nargo_version_ok: console = Console() console.print( Panel( f"[bold]Detected versions of bb and nargo are not compatible with the required versions by garaga {get_package_version()}.[/bold]\n" + (f"This is the most likely cause of the error." if not soft else f""), title="[bold red]Warning[/bold red]", border_style="red", ) ) console.print( f"Detected bb version: [bold red]{bb_version}[/bold red]\n" f"Detected nargo version: [bold red]{nargo_version}[/bold red]" ) console.print( Panel( "[bold]Please ensure you have the expected versions of bb and nargo installed for garaga to work correctly.[/bold]\n" + "You can install the required versions using the following commands:\n" + f"[bold yellow]bbup --version {BBUP_VERSION}[/bold yellow]\n" + f"[bold yellow]noirup --version {NARGO_VERSION}[/bold yellow]\n" + ( f"Check [blue]https://noir-lang.org/docs/getting_started/quick_start[/blue] for more information.\n" if not soft else "" ) + f"Please ensure the verifying key was generated with the correct versions of bb and nargo before generating the verifier.", border_style="yellow", title="[bold yellow]Fixing the issue[/bold yellow]", ) ) else: print( f"The detected versions of bb and nargo are correctly aligned with garaga {get_package_version()}. " ) def gen( system: Annotated[ ProofSystem, typer.Option(help="Proof system", autocompletion=complete_proof_system), ], project_name: Annotated[ str, typer.Option( help="The verifer name (used for the folder name, scarb project name, and contract name)", prompt="\033[1;35mPlease enter the name of your project. Press enter for default name.\033[0m", default_factory=lambda: "my_project", ), ], vk: Annotated[ Path, typer.Option( help="Path to the verification key file. Expects a JSON for groth16, binary format for Honk. Must be provided, except when the system supports an universal key (ex: Risc0)", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], # See https://github.com/fastapi/typer/discussions/731 ), ] = None, include_test_sample: Annotated[ bool, typer.Option( help="Include a sample test file in the generated project", ), ] = True, ): """ Generate a Cairo verifier for a given proof system. Automatically detects the curve from the verification key. """ cwd = Path.cwd() with Progress( SpinnerColumn(), TextColumn("[progress.description]{task.description}"), transient=False, console=Console(color_system="truecolor"), ) as progress: progress.add_task( f"[bold cyan]Generating Smart Contract project for [bold yellow]{system}[/bold yellow] using [bold yellow]{Path(vk).name}[/bold yellow]...[/bold cyan]", total=None, ) match system: case ProofSystem.Groth16: gen_groth16_verifier( vk=vk, output_folder_path=cwd, output_folder_name=project_name, ecip_class_hash=ECIP_OPS_CLASS_HASH, cli_mode=True, include_test_sample=include_test_sample, ) case ProofSystem.UltraKeccakZKHonk: try: gen_honk_verifier( vk=vk, output_folder_path=cwd, output_folder_name=project_name, cli_mode=True, include_test_sample=include_test_sample, ) except Exception as e: import traceback print( f"\n[bold red]Error:[/bold red] An error occurred while generating the verifier: \n{traceback.format_exc()}" ) # print_bb_warning( # with_starknet=system == ProofSystem.UltraStarknetHonk # or system == ProofSystem.UltraStarknetZKHonk # ) raise typer.Exit(code=1) case _: raise ValueError(f"Unsupported proof system: {system}") print("[bold green]Done![/bold green]") print("[bold cyan]Smart Contract project created:[/bold cyan]") def generate_tree(path: Path, tree: Tree) -> None: for entry in sorted(path.iterdir(), key=lambda e: e.name): if entry.is_dir(): branch = tree.add(f"[bold blue]{entry.name}/[/bold blue]") generate_tree(entry, branch) else: tree.add(f"[green]{entry.name}[/green]") root = Tree(f"[bold yellow]{cwd}/{project_name}/[/bold yellow]") generate_tree(cwd / project_name, root) print(root) print( f"[bold]You can now test the main endpoint of the verifier using a proof and `garaga calldata` command.[/bold]" ) if system in [ ProofSystem.UltraKeccakZKHonk, ]: print_bb_warning(soft=True, with_starknet=False) ================================================ FILE: hydra/garaga/starknet/cli/smart_contract_project.py ================================================ import functools from dataclasses import dataclass from pathlib import Path import filelock import starknet_py from starknet_py.common import create_casm_class, create_sierra_compiled_contract from starknet_py.contract import Contract, DeclareResult from starknet_py.hash.casm_class_hash import compute_casm_class_hash from starknet_py.hash.sierra_class_hash import compute_sierra_class_hash from starknet_py.net.account.account import Account from garaga.starknet.cli.utils import get_sierra_casm_artifacts from garaga.starknet.groth16_contract_generator.calldata import ( groth16_calldata_from_vk_and_proof, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, ) class EmptyContract(Exception): pass from functools import lru_cache import rich # Add at module level @lru_cache(maxsize=32) def _get_cached_artifacts(folder: Path) -> tuple[str, str]: """Module level cache for scarb build artifacts""" # Create lock file in the target directory of the contract lock_file = folder / "target" / ".build.lock" lock_file.parent.mkdir(parents=True, exist_ok=True) # Use a timeout to prevent deadlocks lock = filelock.FileLock(str(lock_file), timeout=300) # 5 minute timeout with lock: return get_sierra_casm_artifacts(folder) @dataclass class SmartContractProject: smart_contract_folder: Path # The folder which holds Scarb.toml. def __hash__(self) -> int: return hash(self.smart_contract_folder) def get_contract_artifacts(self) -> tuple[str, str]: """ Returns the sierra and casm artifacts for the contract (uses scarb to build the contract folder) """ return _get_cached_artifacts(self.smart_contract_folder) @lru_cache(maxsize=1) def get_casm_class_hash(self) -> int: """ Returns the class hash for the contract (uses scarb to build the contract folder) """ _, casm_artifact = self.get_contract_artifacts() casm_class = create_casm_class(casm_artifact) return compute_casm_class_hash(casm_class) @lru_cache(maxsize=1) def get_sierra_class_hash(self) -> int: """ Returns the class hash for the contract (uses scarb to build the contract folder) """ sierra_artifact, _ = self.get_contract_artifacts() return compute_sierra_class_hash( create_sierra_compiled_contract(sierra_artifact) ) @lru_cache(maxsize=1) def get_abi(self) -> str: """ Returns the abi for the contract (uses scarb to build the contract folder) """ sierra_artifact, _ = self.get_contract_artifacts() return create_sierra_compiled_contract(sierra_artifact).parsed_abi async def _check_class_exists(self, account: Account, class_hash: int) -> bool: """Helper method to check if class exists""" try: await account.client.get_class_by_hash(class_hash) return True except starknet_py.net.client_errors.ClientError as e: if e.code == 28: # Class hash not found return False raise e async def declare_class_hash(self, account: Account) -> tuple[int, str]: """Returns class hash and abi""" rich.print( f"[bold cyan]Contract project: {self.smart_contract_folder}[/bold cyan]" ) # Get artifacts once sierra, casm = self.get_contract_artifacts() if sierra is None or casm is None: raise EmptyContract # Use cached properties that don't trigger new builds class_hash = self.get_sierra_class_hash() abi = self.get_abi() if await self._check_class_exists(account, class_hash): rich.print( f"[bold cyan]Contract class for {self.smart_contract_folder} already exists: {hex(class_hash)}[/bold cyan]" ) return class_hash, abi rich.print( f"[bold cyan]class hash for {self.smart_contract_folder} not found - deploying[/bold cyan]" ) try: declare_result: DeclareResult = await Contract.declare_v3( account=account, compiled_contract=sierra, compiled_contract_casm=casm, auto_estimate=True, ) await declare_result.wait_for_acceptance() rich.print( f"[bold green]Contract class hash declared: {hex(declare_result.class_hash)}[/bold green]" ) except starknet_py.net.client_errors.ClientError as e: raise e except Exception as e: rich.print( f"[bold red]Unexpected error during contract class declaration: {type(e).__name__}: {e}[/bold red]" ) raise e return declare_result.class_hash, abi @dataclass class Groth16SmartContract(SmartContractProject): vk_path: Path # The json file which holds the verification key. def __hash__(self) -> int: return hash((self.smart_contract_folder, self.vk_path)) @functools.lru_cache(maxsize=128) def generate_calldata( self, proof_path: Path, public_inputs_path: Path | None = None ) -> list[int]: """ Generates the raw calldata for the contract. """ return groth16_calldata_from_vk_and_proof( vk=Groth16VerifyingKey.from_json(self.vk_path), proof=Groth16Proof.from_json(proof_path, public_inputs_path), ) ================================================ FILE: hydra/garaga/starknet/cli/starknet_cli.py ================================================ from typing import Optional import typer from garaga.starknet.cli.declare import declare from garaga.starknet.cli.deploy import deploy from garaga.starknet.cli.gen import gen from garaga.starknet.cli.utils import get_package_version from garaga.starknet.cli.verify import calldata, verify_onchain def version_callback(value: bool): if value: print(f"garaga version: {get_package_version()}") raise typer.Exit() app = typer.Typer( no_args_is_help=True, # Show help when no arguments are provided context_settings={"help_option_names": ["-h", "--help"]}, ) # Add version option that will be processed first @app.callback(invoke_without_command=True) def main( version: Optional[bool] = typer.Option( None, "--version", callback=version_callback, is_eager=True, help="Show the version and exit.", ), ): pass app.command(no_args_is_help=True)(gen) app.command(no_args_is_help=True)(declare) app.command(no_args_is_help=True)(deploy) app.command(no_args_is_help=True)(verify_onchain) app.command(no_args_is_help=True)(calldata) if __name__ == "__main__": app() ================================================ FILE: hydra/garaga/starknet/cli/utils.py ================================================ import asyncio import glob import json import os import shutil import subprocess import tempfile import time from enum import Enum from importlib.metadata import PackageNotFoundError, version from pathlib import Path import rich from starknet_py.contract import Contract from starknet_py.net.account.account import Account from starknet_py.net.client_errors import ClientError, ContractNotFoundError from starknet_py.net.full_node_client import FullNodeClient from starknet_py.net.models import StarknetChainId from starknet_py.net.signer.stark_curve_signer import KeyPair from garaga.curves import ProofSystem from garaga.hints.io import to_int def get_package_version(): try: __version__ = version("garaga") except PackageNotFoundError: # package is not installed __version__ = "dev" return __version__ class Network(Enum): SEPOLIA = "sepolia" MAINNET = "mainnet" def load_account(network: Network): rpc_url = os.getenv(f"{network.name.upper()}_RPC_URL") account_address = os.getenv(f"{network.name.upper()}_ACCOUNT_ADDRESS") account_private_key = os.getenv(f"{network.name.upper()}_ACCOUNT_PRIVATE_KEY") if network == Network.MAINNET: chain = StarknetChainId.MAINNET else: chain = StarknetChainId.SEPOLIA client = FullNodeClient(node_url=rpc_url) account = Account( address=account_address, client=client, key_pair=KeyPair.from_private_key(to_int(account_private_key)), chain=chain, ) account.ESTIMATED_AMOUNT_MULTIPLIER = 1.02 account.ESTIMATED_FEE_MULTIPLIER = 1.02 account.ESTIMATED_UNIT_PRICE_MULTIPLIER = 1.02 return account def get_contract_if_exists(account: Account, contract_address: int) -> Contract | None: try: res = asyncio.run(Contract.from_address(contract_address, account)) return res except ContractNotFoundError: return None except ClientError as e: if "no contract with address" in e.message.lower(): return None raise e async def get_contract_if_exists_async( account: Account, contract_address: int ) -> Contract | None: try: res = await Contract.from_address(contract_address, account) return res except ContractNotFoundError: return None except ClientError as e: if "no contract with address" in e.message.lower(): return None raise e def get_contract_iff_exists(account: Account, contract_address: int) -> Contract: contract = get_contract_if_exists(account, contract_address) if contract is None: rich.print( f"[red]Contract {contract_address} does not exists on {account._chain_id.name}[/red]" ) raise ValueError(f"Contract {contract_address} not found") return contract def create_directory(path: str): if not os.path.exists(path): os.makedirs(path) # print(f"Directory created: {path}") def complete_pairing_curve_id(incomplete: str): curve_ids = ["0", "1"] # Corresponding to BN254 and BLS12_381 return [cid for cid in curve_ids if cid.startswith(incomplete)] def complete_proof_system(incomplete: str): systems = [ps.value for ps in ProofSystem] return [system for system in systems if system.startswith(incomplete)] def complete_network(incomplete: str): networks = [network.name for network in StarknetChainId] return [network for network in networks if network.startswith(incomplete)] def get_voyager_network_prefix(network: Network) -> str: return "" if network == Network.MAINNET else "sepolia." def voyager_link_tx(network: Network, tx_hash: int) -> str: voyager_prefix = get_voyager_network_prefix(network) return f"https://{voyager_prefix}voyager.online/tx/{hex(tx_hash)}" def voyager_link_class(network: Network, class_hash: int) -> str: voyager_prefix = get_voyager_network_prefix(network) return f"https://{voyager_prefix}voyager.online/class/{hex(class_hash)}" def scarb_build_contract_folder(contract_folder_path: str): cmd = "scarb build" print(f"Running command: {cmd} in directory: {contract_folder_path}") try: subprocess.run( cmd, cwd=contract_folder_path, check=True, shell=True, capture_output=True, text=True, ) except subprocess.CalledProcessError as e: print(f"Error building contract: {e}") print(f"Command output:\n{e.output}") raise except FileNotFoundError as e: print(f"Error: {e}") raise except Exception as e: print(f"An unexpected error occurred: {e}") raise def _acquire_scarb_lock(): """ Acquire a file-based lock for scarb operations to prevent parallel execution issues. Returns the lock file path that should be released later. """ lock_dir = tempfile.gettempdir() lock_file = os.path.join(lock_dir, "garaga_scarb_metadata.lock") # Try to acquire lock with timeout timeout = 60 # 60 seconds timeout start_time = time.time() while time.time() - start_time < timeout: try: # Try to create lock file exclusively fd = os.open(lock_file, os.O_CREAT | os.O_EXCL | os.O_WRONLY) os.write(fd, str(os.getpid()).encode()) os.close(fd) return lock_file except OSError: # Lock file exists, wait a bit and retry time.sleep(0.1) raise TimeoutError("Could not acquire scarb lock within timeout") def _release_scarb_lock(lock_file: str): """Release the scarb lock by removing the lock file.""" try: os.remove(lock_file) except OSError: # Lock file might have been removed already pass def get_sierra_casm_artifacts( contract_folder_path: str, ) -> tuple[None, None] | tuple[str, str]: """ Get the Sierra and CASM artifacts for a contract. """ lock_file = _acquire_scarb_lock() try: process = subprocess.run( "scarb metadata --format-version 1", shell=True, capture_output=True, text=True, check=True, cwd=contract_folder_path, ) # Clean up any potential scarb warning messages from stdout stdout_lines = process.stdout.strip().split("\n") # Find the first line that starts with '{' (the JSON) json_start_idx = 0 for i, line in enumerate(stdout_lines): if line.strip().startswith("{"): json_start_idx = i break json_content = "\n".join(stdout_lines[json_start_idx:]) metadata = json.loads(json_content) finally: _release_scarb_lock(lock_file) target_dir = os.path.join(contract_folder_path, metadata["target_dir"], "dev") # Clean the target/dev/ folder if it already exists if os.path.exists(target_dir): shutil.rmtree(target_dir) os.makedirs(target_dir) scarb_build_contract_folder(contract_folder_path) artifacts_file = glob.glob(os.path.join(target_dir, "*.starknet_artifacts.json")) assert ( len(artifacts_file) == 1 ), f"Artifacts JSON file not found or multiple files found: {artifacts_file}" with open(artifacts_file[0], "r") as f: artifacts = json.load(f) contracts = artifacts["contracts"] if len(contracts) == 0: return None, None sierra_file = contracts[0]["artifacts"]["sierra"] casm_file = contracts[0]["artifacts"]["casm"] sierra_path = os.path.join(target_dir, sierra_file) casm_path = os.path.join(target_dir, casm_file) assert os.path.exists(sierra_path), f"Sierra file not found: {sierra_path}" assert os.path.exists(casm_path), f"CASM file not found: {casm_path}" with open(sierra_path, "r") as f: sierra = f.read() with open(casm_path, "r") as f: casm = f.read() return sierra, casm def get_default_vk_path(vk_type: str) -> Path: script_path = Path(__file__).resolve() script_folder_path = script_path.parent match vk_type: case "risc0": return ( script_folder_path.parent / "groth16_contract_generator" / "examples" / "vk_risc0.json" ) case "sp1": return ( script_folder_path.parent / "groth16_contract_generator" / "examples" / "vk_sp1.json" ) case _: raise ValueError( f"Unsupported default VK for proof type: {vk_type}. Please specify a vk." ) ================================================ FILE: hydra/garaga/starknet/cli/verify.py ================================================ import asyncio from enum import Enum from pathlib import Path from typing import Annotated import rich import typer from dotenv import load_dotenv from starknet_py.contract import ( ContractFunction, InvokeResult, PreparedFunctionInvokeV3, ) from garaga.curves import ProofSystem from garaga.hints.io import to_int from garaga.precompiled_circuits.zk_honk import honk_proof_from_bytes from garaga.starknet.cli.utils import ( Network, complete_proof_system, get_contract_iff_exists, get_default_vk_path, load_account, voyager_link_tx, ) from garaga.starknet.groth16_contract_generator.calldata import ( groth16_calldata_from_vk_and_proof, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, find_item_from_key_patterns, ) from garaga.starknet.honk_contract_generator.calldata import ( HonkVk, get_ultra_flavor_honk_calldata_from_vk_and_proof, ) app = typer.Typer() def verify_onchain( system: Annotated[ ProofSystem, typer.Option(help="Proof system", autocompletion=complete_proof_system), ], contract_address: Annotated[ str, typer.Option( help="Starknet contract address", ), ], proof: Annotated[ Path, typer.Option( help="Path to the proof JSON file", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ], vk: Annotated[ Path, typer.Option( help="Path to the verification key file. Expects a JSON for groth16, binary format for Honk. Must be provided, except when the system supports an universal key (ex: Risc0)", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = None, public_inputs: Annotated[ Path, typer.Option( help="Path to the public inputs file. Expects a JSON for groth16, binary format for Honk.", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = None, endpoint: Annotated[ str, typer.Option( help="Smart contract function name. If not provided, the default 'verify_[proof_system]_proof_[curve_name]' will be used.", ), ] = "", env_file: Annotated[ Path, typer.Option( help="Path to the environment file containing rpc, address, private_key", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = str(Path.cwd() / ".secrets"), network: Annotated[ Network, typer.Option( help="Starknet network", case_sensitive=False, ), ] = Network.SEPOLIA.value, ): """Invoke a SNARK verifier on Starknet given a contract address, a proof and a verification key.""" load_dotenv(env_file) account = load_account(network) contract = get_contract_iff_exists(account, to_int(contract_address)) try: function_call: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) except ValueError: rich.print( f"[red]Function {endpoint} not found on contract {contract_address}[/red]" ) raise ValueError( f"Function {endpoint} not found on contract {contract_address}" ) if public_inputs == "": public_inputs = None calldata = get_calldata_generic(system, vk, proof, public_inputs) prepare_invoke = PreparedFunctionInvokeV3( to_addr=function_call.contract_data.address, calldata=calldata, selector=function_call.get_selector(function_call.name), _contract_data=function_call.contract_data, _client=function_call.client, _account=function_call.account, _payload_transformer=function_call._payload_transformer, resource_bounds=None, ) invoke_result: InvokeResult = asyncio.run(prepare_invoke.invoke(auto_estimate=True)) asyncio.run(invoke_result.wait_for_acceptance()) rich.print(f"[bold]Transaction hash : {hex(invoke_result.hash)}[/bold]") rich.print( f"[bold green]Check it out on[/bold green] {voyager_link_tx(network, invoke_result.hash)}" ) class CalldataFormat(str, Enum): starkli = "starkli" array = "array" snforge = "snforge" def get_calldata_generic( system: ProofSystem, vk: Path | None, proof: Path, public_inputs: Path | None ) -> list[int]: match system: case ProofSystem.Groth16: proof_obj = Groth16Proof.from_json(proof, public_inputs) if vk is None: vk_obj = Groth16VerifyingKey.from_json( get_default_vk_path(proof_obj.vk_type) ) else: vk_obj = Groth16VerifyingKey.from_json(vk) return groth16_calldata_from_vk_and_proof(vk_obj, proof_obj) case ProofSystem.UltraKeccakZKHonk: vk_obj = HonkVk.from_bytes(open(vk, "rb").read()) proof_obj = honk_proof_from_bytes( open(proof, "rb").read(), open(public_inputs, "rb").read(), vk_obj, system, ) return get_ultra_flavor_honk_calldata_from_vk_and_proof( vk_obj, proof_obj, system ) case _: raise ValueError(f"Proof system {system} not supported") def calldata( system: Annotated[ ProofSystem, typer.Option(help="Proof system", autocompletion=complete_proof_system), ], proof: Annotated[ Path, typer.Option( help="Path to the proof file", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ], vk: Annotated[ Path, typer.Option( help="Path to the verification key file. Expects a JSON for groth16, binary format for Honk. Must be provided, except when the system supports an universal key (ex: Risc0)", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = None, public_inputs: Annotated[ Path, typer.Option( help="Path to the public inputs file. Optional, only used for Groth16 when pub inputs are not in the json proof (ex: SnarkJS)", file_okay=True, dir_okay=False, exists=True, autocompletion=lambda: [], ), ] = None, format: Annotated[ CalldataFormat, typer.Option( help="Format", case_sensitive=False, show_choices=True, ), ] = CalldataFormat.snforge, output_path: Annotated[ Path, typer.Option( help="Output directory path for snforge format (defaults to current directory)", file_okay=False, dir_okay=True, exists=True, autocompletion=lambda: [], ), ] = Path("."), ): """Generate Starknet verifier calldata given a proof and a verification key.""" if vk == None: vk = get_default_vk_path(system) calldata = get_calldata_generic(system, vk, proof, public_inputs) if format == CalldataFormat.starkli: print(" ".join([str(x) for x in calldata])) elif format == CalldataFormat.array: print(calldata[1:]) elif format == CalldataFormat.snforge: # Write the calldata to a file in the specified output path output_file = output_path / "proof_calldata.txt" with open(output_file, "w") as f: for x in calldata[1:]: f.write(f"{hex(x)}\n") print(f"Calldata written to: {output_file}") ================================================ FILE: hydra/garaga/starknet/constants.py ================================================ """ Auto-generated constants file from constants.json. Do not edit manually. """ # RISC0 Constants # https://github.com/risc0/risc0-ethereum/blob/v2.2.2/contracts/src/groth16/ControlID.sol # release v2.2.2 RISC0_CONTROL_ROOT = 0xCE52BF56033842021AF3CF6DB8A50D1B7535C125A34F1A22C6FDCF002C5A1529 RISC0_BN254_CONTROL_ID = ( 0x04446E66D300EB7FB45C9726BB53C793DDA407A62E9601618BB43C5C14657AC0 ) # SP1 Constants # https://github.com/succinctlabs/sp1-contracts/blob/main/contracts/src/v5.0.0/SP1VerifierGroth16.sol SP1_VERIFIER_VERSION = "v5.0.0" SP1_VERIFIER_HASH = bytes.fromhex( "a4594c59bbc142f3b81c3ecb7f50a7c34bc9af7c4c444b5d48b795427e285913" ) # Additional RISC0 constants for internal use RISC0_SYSTEM_STATE_ZERO_DIGEST = ( "0xA3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2" ) RISC0_TAG_DIGEST = "0xcb1fefcd1f2d9a64975cbbbf6e161e2914434b0cbb9960b84df5d717e86b48af" RISC0_OUTPUT_TAG = "0x77eafeb366a78b47747de0d7bb176284085ff5564887009a5be63da32d3559d4" RISC0_RELEASE_VERSION = "v2.2.2" # Version info CAIRO_VERSION = "2.16.1" STARKNET_FOUNDRY_VERSION = "0.57.0" BB_VERSION = "3.0.0-nightly.20251104" BBUP_VERSION = "3.0.0-nightly.20251104" NARGO_VERSION = "1.0.0-beta.16" ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/calldata.py ================================================ from garaga import garaga_rs from garaga.points import G1G2Pair, G1Point from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, ) from garaga.starknet.tests_and_calldata_generators.mpcheck import MPCheckCalldataBuilder from garaga.starknet.tests_and_calldata_generators.msm import MSMCalldataBuilder def groth16_calldata_from_vk_and_proof( vk: Groth16VerifyingKey, proof: Groth16Proof, use_rust: bool = False ) -> list[int]: if use_rust: return _groth16_calldata_from_vk_and_proof_rust(vk, proof) assert ( vk.curve_id == proof.curve_id ), f"Curve ID mismatch: {vk.curve_id} != {proof.curve_id}" vk_x = vk.ic[0].add(G1Point.msm(vk.ic[1:], proof.public_inputs)) calldata = [] mpc = MPCheckCalldataBuilder( vk.curve_id, pairs=[ G1G2Pair(p=vk_x, q=vk.gamma, curve_id=vk.curve_id), G1G2Pair(p=proof.c, q=vk.delta, curve_id=vk.curve_id), G1G2Pair(p=-proof.a, q=proof.b, curve_id=vk.curve_id), ], n_fixed_g2=2, public_pair=G1G2Pair(vk.alpha, vk.beta, vk.curve_id), ) calldata.extend(proof.serialize_to_calldata()) calldata.extend(mpc.serialize_to_calldata()) if proof.image_id and proof.journal: # Risc0 mode. print("Risc0 mode") msm = MSMCalldataBuilder( curve_id=vk.curve_id, points=[vk.ic[3], vk.ic[4]], scalars=[proof.public_inputs[2], proof.public_inputs[3]], ) calldata.extend( msm.serialize_to_calldata( include_points_and_scalars=False, serialize_as_pure_felt252_array=True, ) ) else: msm = MSMCalldataBuilder( curve_id=vk.curve_id, points=vk.ic[1:], scalars=proof.public_inputs, ) calldata.extend( msm.serialize_to_calldata( include_points_and_scalars=False, serialize_as_pure_felt252_array=True, ) ) # return calldata return [len(calldata)] + calldata def _groth16_calldata_from_vk_and_proof_rust( vk: Groth16VerifyingKey, proof: Groth16Proof ) -> list[int]: assert ( vk.curve_id == proof.curve_id ), f"Curve ID mismatch: {vk.curve_id} != {proof.curve_id}" # Determine vkey for SP1 proofs - it's embedded in public_inputs[0] vkey = None if proof.public_inputs_sp1 is not None: # For SP1 proofs, the vkey is stored as public_inputs[0] as a big integer # We need to convert it back to bytes (32 bytes, big endian) vkey_int = proof.public_inputs[0] vkey = vkey_int.to_bytes(32, byteorder="big") return garaga_rs.get_groth16_calldata( proof.flatten(), vk.flatten(), proof.curve_id.value, proof.image_id, proof.journal, proof.public_inputs_sp1, vkey, ) if __name__ == "__main__": VK_PATH = "hydra/garaga/starknet/groth16_contract_generator/examples/snarkjs_vk_bn254.json" PROOF_PATH = "hydra/garaga/starknet/groth16_contract_generator/examples/snarkjs_proof_bn254.json" PUBLIC_INPUTS_PATH = "hydra/garaga/starknet/groth16_contract_generator/examples/snarkjs_public_bn254.json" vk = Groth16VerifyingKey.from_json(file_path=VK_PATH) proof = Groth16Proof.from_json( proof_path=PROOF_PATH, public_inputs_path=PUBLIC_INPUTS_PATH ) calldata = groth16_calldata_from_vk_and_proof(vk, proof) print(calldata) print(len(calldata)) ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/examples/gnark_proof_bn254.json ================================================ { "Ar": { "X": "73845398786533896737633575350679623829088256804727703196883312716046720173", "Y": "3929126461430331964775340412981986240468451439560808746926369245425818473094" }, "Krs": { "X": "5190364967715151722457989459269945351663215722120167333837995313677944703903", "Y": "14199563643497455180373217971778460129125995041037663528128314360912908737780" }, "Bs": { "X": { "A0": "16632859667924688464448957536047018456099730057010042618872684676699665576215", "A1": 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"2223923876691923064813371578678400285087400227347901303400514986210692294428", "y": "3228708299174762375496115493137156328822199374794870011715145604387710550517" } ] } } ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/generator.py ================================================ import os import subprocess from pathlib import Path from garaga.curves import CurveID, ProofSystem from garaga.modulo_circuit_structs import G2Line, StructArray from garaga.precompiled_circuits.multi_miller_loop import precompute_lines from garaga.starknet.cli.utils import create_directory, get_package_version from garaga.starknet.constants import CAIRO_VERSION, STARKNET_FOUNDRY_VERSION from garaga.starknet.groth16_contract_generator.calldata import ( groth16_calldata_from_vk_and_proof, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, ) ECIP_OPS_CLASS_HASH = 0x396D5915ECF475AAB117BB25A0272B261E9E25FFE1C0CE05A51A3F77489C89E def precompute_lines_from_vk(vk: Groth16VerifyingKey) -> StructArray: # Precompute lines for fixed G2 points lines = precompute_lines([vk.gamma, vk.delta]) precomputed_lines = StructArray( name="lines", elmts=[ G2Line(name=f"line{i}", elmts=lines[i : i + 4]) for i in range(0, len(lines), 4) ], ) return precomputed_lines def gen_test_file( contract_name: str, verifier_name: str, system: ProofSystem, verification_function_name: str, package_name: str, rpc_url: str = "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", ): code = f""" //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use snforge_std::fs::{{FileTrait, read_txt}}; use snforge_std::{{DeclareResultTrait, declare}}; use {package_name}::{verifier_name}::{{ I{contract_name}LibraryDispatcher, I{contract_name}DispatcherTrait, }}; use starknet::ClassHash; /// Declare the {contract_name} contract for testing. /// /// This function declares a new instance of the {contract_name} contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("{contract_name}"); /// let dispatcher = I{contract_name}LibraryDispatcher {{ class_hash }}; /// ``` fn declare_contract(name: ByteArray) -> ClassHash {{ let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash }} /// Test the verification function {verification_function_name} with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by the garaga team /// - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system {system.value} /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "{rpc_url}", block_tag: latest)] fn test_{verification_function_name}() {{ // Step 1: Declare the verification contract let class_hash = declare_contract("{contract_name}"); let dispatcher = I{contract_name}LibraryDispatcher {{ class_hash }}; // Step 2: Load the proof fixture generated by the script // This file contains the {system.value} proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's {verification_function_name} function with the loaded proof data let result = dispatcher.{verification_function_name}(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here }} """ return code def get_scarb_toml_file(package_name: str, cli_mode: bool, inlining_level: int = 2): version = get_package_version() header = f"# Generated by Garaga version {version}\n" if version == "dev": suffix = "" else: suffix = ', tag = "v' + version + '"' if cli_mode: dep = 'git = "https://github.com/keep-starknet-strange/garaga.git"' + suffix else: dep = 'path = "../../../"' return header + f"""[package] name = "{package_name}" version = "0.1.0" edition = "2024_07" [dependencies] garaga = {{ {dep} }} starknet = "{CAIRO_VERSION}" [cairo] sierra-replace-ids = false inlining-strategy = {inlining_level} [dev-dependencies] snforge_std = "{STARKNET_FOUNDRY_VERSION}" assert_macros = "{CAIRO_VERSION}" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true """ def write_test_calldata_file( output_folder_path: str, vk: Groth16VerifyingKey, proof: Groth16Proof, ) -> None: """Write the test calldata file for a given verifying key and proof.""" tests_dir = os.path.join(output_folder_path, "tests") cd = groth16_calldata_from_vk_and_proof(vk, proof) with open(os.path.join(tests_dir, "proof_calldata.txt"), "w") as f: for x in cd[1:]: f.write(f"{hex(x)}\n") def create_verifier_directory_structure( output_folder_path: str, include_test_sample: bool = True ) -> tuple[str, str]: """Create the standard directory structure for a verifier contract. Returns: tuple: (src_dir, tests_dir) paths """ create_directory(output_folder_path) src_dir = os.path.join(output_folder_path, "src") tests_dir = ( os.path.join(output_folder_path, "tests") if include_test_sample else None ) create_directory(src_dir) if include_test_sample: create_directory(tests_dir) return src_dir, tests_dir def write_tool_versions_file(output_folder_path: str) -> None: """Write the .tool-versions file.""" with open(os.path.join(output_folder_path, ".tool-versions"), "w") as f: f.write(f"scarb {CAIRO_VERSION}\n") f.write(f"starknet-foundry {STARKNET_FOUNDRY_VERSION}\n") def write_lib_cairo_file(src_dir: str, modules: list[str] = None) -> None: """Write the lib.cairo file with specified modules.""" if modules is None: modules = ["groth16_verifier", "groth16_verifier_constants"] module_imports = "\n".join(f"pub mod {module};" for module in modules) with open(os.path.join(src_dir, "lib.cairo"), "w") as f: version = get_package_version() header = f"// Generated by Garaga version {version}\n" f.write(header + f"\n{module_imports}\n") def write_verifier_files( output_folder_path: str, package_name: str, constants_code: str | None, contract_code: str, contract_cairo_name: str, verification_function_name: str, system: ProofSystem, cli_mode: bool = False, circuits_code: str | None = None, modules: list[str] = None, constants_filename: str = "groth16_verifier_constants.cairo", contract_filename: str = "groth16_verifier.cairo", circuits_filename: str | None = None, include_test_sample: bool = True, constants_output_path: str | None = None, ) -> None: """Write all the standard verifier files (directories, constants, contract, scarb.toml, lib.cairo, test files).""" # Create directory structure src_dir, tests_dir = create_verifier_directory_structure( output_folder_path, include_test_sample ) # Write tool versions write_tool_versions_file(output_folder_path) # Build header once for Cairo files version = get_package_version() header_cairo = f"// Generated by Garaga version {version}\n" # Write Scarb.toml with open(os.path.join(output_folder_path, "Scarb.toml"), "w") as f: f.write(get_scarb_toml_file(package_name, cli_mode)) # Write lib.cairo write_lib_cairo_file(src_dir, modules) # Write constants file (if requested) if constants_code is not None: target_constants_path = constants_output_path or os.path.join( src_dir, constants_filename ) target_constants_dir = os.path.dirname(target_constants_path) os.makedirs(target_constants_dir, exist_ok=True) with open(target_constants_path, "w") as f: f.write(header_cairo + constants_code) subprocess.run(["scarb", "fmt", "."], cwd=target_constants_dir, check=True) # Write contract file with open(os.path.join(src_dir, contract_filename), "w") as f: f.write(header_cairo + contract_code) # Write circuits file if provided if circuits_code and circuits_filename: with open(os.path.join(src_dir, circuits_filename), "w") as f: f.write(header_cairo + circuits_code) # Write test file. if include_test_sample: with open(os.path.join(tests_dir, "test_contract.cairo"), "w") as f: f.write( header_cairo + gen_test_file( contract_cairo_name, contract_filename.removesuffix(".cairo"), system, verification_function_name, package_name, ) ) subprocess.run(["scarb", "fmt", "."], cwd=output_folder_path, check=True) def write_test_calldata_file_generic( output_folder_path: str, system: ProofSystem, vk_path: str, proof_path: str, public_inputs_path: str = None, ) -> None: """Write the test calldata file for any proof system using get_calldata_generic.""" from pathlib import Path as PathType from garaga.starknet.cli.verify import get_calldata_generic tests_dir = os.path.join(output_folder_path, "tests") cd = get_calldata_generic( system, PathType(vk_path), PathType(proof_path), PathType(public_inputs_path) if public_inputs_path else None, ) with open(os.path.join(tests_dir, "proof_calldata.txt"), "w") as f: for x in cd[1:]: f.write(f"{hex(x)}\n") def gen_groth16_verifier( vk: str | Path | Groth16VerifyingKey, output_folder_path: str, output_folder_name: str, ecip_class_hash: int = ECIP_OPS_CLASS_HASH, cli_mode: bool = False, include_test_sample: bool = True, ) -> str: if isinstance(vk, (Path, str)): vk = Groth16VerifyingKey.from_json(vk) else: vk = vk curve_id = vk.curve_id if cli_mode: output_folder_name = output_folder_name else: output_folder_name = output_folder_name + f"_{curve_id.name.lower()}" output_folder_path = os.path.join(output_folder_path, output_folder_name) precomputed_lines = precompute_lines_from_vk(vk) verification_function_name = f"verify_groth16_proof_{curve_id.name.lower()}" contract_cairo_name = f"Groth16Verifier{curve_id.name}" constants_code = f""" use garaga::definitions::{{G1Point, G2Point, E12D, G2Line, u384}}; {f"use garaga::definitions::u288;" if curve_id!=CurveID.BLS12_381 else ""} use garaga::groth16::Groth16VerifyingKey; pub const N_PUBLIC_INPUTS:usize = {len(vk.ic)-1}; {vk.serialize_to_cairo()} pub const precomputed_lines: [G2Line<{"u384" if curve_id==CurveID.BLS12_381 else "u288"}>; {len(precomputed_lines)//4}] = {precomputed_lines.serialize(raw=True, const=True)}; """ contract_code = f""" use super::groth16_verifier_constants::{{N_PUBLIC_INPUTS, vk, ic, precomputed_lines}}; #[starknet::interface] pub trait I{contract_cairo_name} {{ fn {verification_function_name}( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; }} #[starknet::contract] mod {contract_cairo_name} {{ use starknet::SyscallResultTrait; use garaga::definitions::{{G1Point, G1G2Pair}}; use garaga::groth16::{{multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result, Groth16ProofRawTrait}}; use garaga::ec_ops::{{G1PointTrait, ec_safe_add}}; use garaga::utils::calldata::{{deserialize_full_proof_with_hints_{curve_id.name.lower()}}}; use super::{{N_PUBLIC_INPUTS, vk, ic, precomputed_lines}}; const ECIP_OPS_CLASS_HASH: felt252 = {hex(ecip_class_hash)}; #[storage] struct Storage {{}} #[abi(embed_v0)] impl IGroth16Verifier{curve_id.name} of super::IGroth16Verifier{curve_id.name} {{ fn {verification_function_name}( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> {{ // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given a proof and a verifying key. let fph = deserialize_full_proof_with_hints_{curve_id.name.lower()}(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.raw.check_proof_points({curve_id.value}); let ic = ic.span(); let vk_x: G1Point = match ic.len() {{ 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => {{ // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); Serde::serialize(@groth16_proof.public_inputs, ref msm_calldata); // Complete with the curve indentifier ({curve_id.value} for {curve_id.name}): msm_calldata.append({curve_id.value}); // Add the hint array. for x in msm_hint {{ msm_calldata.append(*x); }} // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span() ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), {curve_id.value} ) }} }}; // Perform the pairing check. let check = multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result( G1G2Pair {{ p: vk_x, q: vk.gamma_g2 }}, G1G2Pair {{ p: groth16_proof.raw.c, q: vk.delta_g2 }}, G1G2Pair {{ p: groth16_proof.raw.a.negate({curve_id.value}), q: groth16_proof.raw.b }}, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check {{ Result::Ok(_) => Result::Ok(groth16_proof.public_inputs), Result::Err(error) => Result::Err(error), }} }} }} }} """ # Use the new reusable function to write all files write_verifier_files( output_folder_path, output_folder_name, constants_code, contract_code, contract_cairo_name, verification_function_name, ProofSystem.Groth16, cli_mode, include_test_sample=include_test_sample, ) return constants_code if __name__ == "__main__": EXAMPLES_FOLDER = "hydra/garaga/starknet/groth16_contract_generator/examples" vk_paths = [ os.path.join(EXAMPLES_FOLDER, "vk_bn254.json"), os.path.join(EXAMPLES_FOLDER, "vk_bls.json"), ] proof_paths = [ os.path.join(EXAMPLES_FOLDER, "proof_bn254.json"), os.path.join(EXAMPLES_FOLDER, "proof_bls.json"), ] CONTRACTS_FOLDER = "src/contracts/autogenerated/" # Do not change this FOLDER_NAME = "groth16_example" # '_curve_id' is appended in the end. def _generate_verifier(vk_path): try: gen_groth16_verifier( vk_path, CONTRACTS_FOLDER, FOLDER_NAME, ECIP_OPS_CLASS_HASH ) except Exception as e: print(f"An error occurred: {e}") raise e for vk_path in vk_paths: _generate_verifier(vk_path) FOLDER_NAMES = [f"groth16_example_bn254", "groth16_example_bls12_381"] for contract_name, vk_path, proof_path in zip(FOLDER_NAMES, vk_paths, proof_paths): vk = Groth16VerifyingKey.from_json(vk_path) proof = Groth16Proof.from_json(proof_path=proof_path) output_folder_path = os.path.join(CONTRACTS_FOLDER, contract_name) write_test_calldata_file_generic( output_folder_path, system=ProofSystem.Groth16, vk_path=vk_path, proof_path=proof_path, ) ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/generator_risc0.py ================================================ import os from garaga.curves import ProofSystem from garaga.modulo_circuit_structs import G1PointCircuit from garaga.starknet.constants import RISC0_RELEASE_VERSION from garaga.starknet.groth16_contract_generator.generator import ( ECIP_OPS_CLASS_HASH, precompute_lines_from_vk, write_test_calldata_file_generic, write_verifier_files, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( RISC0_BN254_CONTROL_ID, RISC0_CONTROL_ROOT, Groth16Proof, Groth16VerifyingKey, split_digest, ) PACKAGE_NAME = "risc0_verifier" def gen_risc0_groth16_verifier( vk_path: str, output_folder_path: str, output_folder_name: str, ecip_class_hash: int = ECIP_OPS_CLASS_HASH, control_root: int = RISC0_CONTROL_ROOT, control_id: int = RISC0_BN254_CONTROL_ID, cli_mode: bool = False, ) -> str: vk = Groth16VerifyingKey.from_json(vk_path) curve_id = vk.curve_id output_folder_name = output_folder_name + f"_{curve_id.name.lower()}" output_folder_path = os.path.join(output_folder_path, output_folder_name) precomputed_lines = precompute_lines_from_vk(vk) CONTROL_ROOT_0, CONTROL_ROOT_1 = split_digest(control_root) T = G1PointCircuit.from_G1Point( name="T", point=(vk.ic[1].scalar_mul(CONTROL_ROOT_0)) .add(vk.ic[2].scalar_mul(CONTROL_ROOT_1)) .add(vk.ic[5].scalar_mul(control_id).add(vk.ic[0])), ) contract_cairo_name = f"Risc0Groth16Verifier{curve_id.name}" constants_code = f""" use garaga::definitions::{{G1Point, G2Point, E12D, G2Line, u384, u288}}; use garaga::groth16::Groth16VerifyingKey; pub const N_FREE_PUBLIC_INPUTS:usize = 2; // RISC0 version tag : {RISC0_RELEASE_VERSION} // CONTROL ROOT USED : {hex(control_root)} // \t CONTROL_ROOT_0 : {hex(CONTROL_ROOT_0)} // \t CONTROL_ROOT_1 : {hex(CONTROL_ROOT_1)} // BN254 CONTROL ID USED : {hex(control_id)} pub const T: G1Point = {T.serialize(raw=True)}; // IC[0] + IC[1] * CONTROL_ROOT_0 + IC[2] * CONTROL_ROOT_1 + IC[5] * BN254_CONTROL_ID {vk.serialize_to_cairo()} pub const precomputed_lines: [G2Line; {len(precomputed_lines)//4}] = {precomputed_lines.serialize(raw=True, const=True)}; """ verification_function_name = f"verify_r0_groth16_proof_{curve_id.name.lower()}" contract_code = f""" use super::groth16_verifier_constants::{{N_FREE_PUBLIC_INPUTS, vk, ic, precomputed_lines, T}}; #[starknet::interface] pub trait IRisc0Groth16Verifier{curve_id.name} {{ fn {verification_function_name}( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; }} #[starknet::contract] mod Risc0Groth16Verifier{curve_id.name} {{ use starknet::SyscallResultTrait; use garaga::definitions::{{G1Point, G1G2Pair}}; use garaga::groth16::{{multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result, Groth16ProofRawTrait}}; use garaga::ec_ops::{{G1PointTrait, ec_safe_add}}; use garaga::apps::risc0::{{compute_receipt_claim, journal_sha256, deserialize_full_proof_with_hints_risc0}}; use super::{{N_FREE_PUBLIC_INPUTS, vk, ic, precomputed_lines, T}}; const ECIP_OPS_CLASS_HASH: felt252 = {hex(ecip_class_hash)}; #[storage] struct Storage {{}} #[abi(embed_v0)] impl IRisc0Groth16Verifier{curve_id.name} of super::IRisc0Groth16Verifier{curve_id.name} {{ fn {verification_function_name}( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> {{ // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given a proof and a verifying key. let fph = deserialize_full_proof_with_hints_risc0(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let image_id = fph.image_id; let journal = fph.journal; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.check_proof_points({curve_id.value}); let ic = ic.span(); let journal_digest = journal_sha256(journal); let claim_digest = compute_receipt_claim(image_id, journal_digest); // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK relative to the non-constant public inputs. Serde::serialize(@ic.slice(3, N_FREE_PUBLIC_INPUTS), ref msm_calldata); // Add the claim digest as u256 scalars for the msm. msm_calldata.append(2); msm_calldata.append(claim_digest.low.into()); msm_calldata.append(0); msm_calldata.append(claim_digest.high.into()); msm_calldata.append(0); // Complete with the curve indentifier ({curve_id.value} for {curve_id.name}): msm_calldata.append({curve_id.value}); // Add the hint array. for x in msm_hint {{ msm_calldata.append(*x); }} // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain claim0 * IC[3] + claim1 * IC[4]. let mut _msm_result_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span() ) .unwrap_syscall(); // Finalize vk_x computation by adding the precomputed T point. let vk_x = ec_safe_add( T, Serde::::deserialize(ref _msm_result_serialized).unwrap(), {curve_id.value} ); // Perform the pairing check. let check = multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result( G1G2Pair {{ p: vk_x, q: vk.gamma_g2 }}, G1G2Pair {{ p: groth16_proof.c, q: vk.delta_g2 }}, G1G2Pair {{ p: groth16_proof.a.negate({curve_id.value}), q: groth16_proof.b }}, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check {{ Result::Ok(_) => Result::Ok(journal), Result::Err(error) => Result::Err(error), }} }} }} }} """ # Use the reusable function to write all files write_verifier_files( output_folder_path, output_folder_name, constants_code, contract_code, contract_cairo_name, verification_function_name, ProofSystem.Groth16, cli_mode, ) return constants_code if __name__ == "__main__": pass RISCO_VK_PATH = ( "hydra/garaga/starknet/groth16_contract_generator/examples/vk_risc0.json" ) PROOF_PATH = ( "hydra/garaga/starknet/groth16_contract_generator/examples/proof_risc0.json" ) CONTRACTS_FOLDER = "src/contracts/autogenerated/" # Do not change this FOLDER_NAME = "risc0_verifier" # '_curve_id' is appended in the end. gen_risc0_groth16_verifier( RISCO_VK_PATH, CONTRACTS_FOLDER, FOLDER_NAME, ECIP_OPS_CLASS_HASH ) vk = Groth16VerifyingKey.from_json(file_path=RISCO_VK_PATH) proof = Groth16Proof.from_json(proof_path=PROOF_PATH) # Generate the calldata and write test calldata file: output_folder_path = os.path.join( CONTRACTS_FOLDER, f"{FOLDER_NAME}_{vk.curve_id.name.lower()}" ) write_test_calldata_file_generic( output_folder_path, system=ProofSystem.Groth16, # RISC0 uses Groth16 vk_path=RISCO_VK_PATH, proof_path=PROOF_PATH, ) ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/generator_sp1.py ================================================ import os from textwrap import dedent from garaga.curves import ProofSystem from garaga.starknet.groth16_contract_generator.generator import ( ECIP_OPS_CLASS_HASH, precompute_lines_from_vk, write_test_calldata_file_generic, write_verifier_files, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, ) def gen_sp1_groth16_verifier( vk_path: str, output_folder_path: str, output_folder_name: str, ecip_class_hash: int = ECIP_OPS_CLASS_HASH, cli_mode: bool = False, ) -> str: vk = Groth16VerifyingKey.from_json(vk_path) curve_id = vk.curve_id output_folder_name = output_folder_name + f"_{curve_id.name.lower()}" output_folder_path = os.path.join(output_folder_path, output_folder_name) precomputed_lines = precompute_lines_from_vk(vk) contract_cairo_name = f"SP1Groth16Verifier{curve_id.name}" constants_code = dedent(f""" use garaga::definitions::{{G1Point, G2Point, E12D, G2Line, u384, u288}}; use garaga::groth16::Groth16VerifyingKey; pub const N_PUBLIC_INPUTS: usize = {len(vk.ic) - 1}; {vk.serialize_to_cairo()} pub const precomputed_lines: [G2Line; {len(precomputed_lines) // 4}] = {precomputed_lines.serialize(raw=True, const=True)}; """).strip() + "\n" verification_function_name = f"verify_sp1_groth16_proof_{curve_id.name.lower()}" verification_function_name_u32 = ( f"verify_sp1_groth16_proof_{curve_id.name.lower()}_u32" ) contract_code = dedent(f""" #[starknet::interface] pub trait ISP1Groth16Verifier{curve_id.name} {{ fn {verification_function_name}( self: @TContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252>; fn {verification_function_name_u32}( self: @TContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252>; }} #[starknet::contract] mod SP1Groth16Verifier{curve_id.name} {{ use starknet::SyscallResultTrait; use garaga::definitions::{{G1Point, G1G2Pair}}; use garaga::groth16::{{multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result, Groth16ProofRawTrait}}; use garaga::ec_ops::{{G1PointTrait, ec_safe_add}}; use garaga::apps::sp1::{{deserialize_full_proof_with_hints_sp1, process_public_inputs_sp1}}; use garaga::apps::sp1_constants::{{vk, ic, precomputed_lines, N_PUBLIC_INPUTS}}; const ECIP_OPS_CLASS_HASH: felt252 = {hex(ecip_class_hash)}; #[storage] struct Storage {{}} /// Internal helper function that performs the core SP1 Groth16 verification. /// Returns (vkey, public_inputs_u256, public_inputs_u32) on success. fn verify_sp1_groth16_proof_inner( full_proof_with_hints: Span, ) -> Result<(u256, Span, Span), felt252> {{ // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok((vkey, public_inputs_u256, public_inputs_u32)) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given a proof and a verifying key. let fph = deserialize_full_proof_with_hints_sp1(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let vkey = fph.vkey; let public_inputs_sp1 = fph.public_inputs_sp1; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.check_proof_points({curve_id.value}); let ic = ic.span(); let public_inputs_u32 = public_inputs_sp1.span(); let (pub_inputs_256, pub_input_hash): (Span, u256) = process_public_inputs_sp1(public_inputs_sp1); let vk_x: G1Point = match ic.len() {{ 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => {{ let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); // Serialize public inputs as u256 array. Serde::serialize(@N_PUBLIC_INPUTS, ref msm_calldata); Serde::serialize(@vkey, ref msm_calldata); Serde::serialize(@pub_input_hash, ref msm_calldata); // Complete with the curve indentifier ({curve_id.value} for {curve_id.name}): msm_calldata.append({curve_id.value}); // Add the hint array. for x in msm_hint {{ msm_calldata.append(*x); }} // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span() ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), {curve_id.value} ) }} }}; // Perform the pairing check. let check = multi_pairing_check_{curve_id.name.lower()}_3P_2F_with_extra_miller_loop_result( G1G2Pair {{ p: vk_x, q: vk.gamma_g2 }}, G1G2Pair {{ p: groth16_proof.c, q: vk.delta_g2 }}, G1G2Pair {{ p: groth16_proof.a.negate({curve_id.value}), q: groth16_proof.b }}, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check {{ Result::Ok(_) => Result::Ok((vkey, pub_inputs_256, public_inputs_u32)), Result::Err(error) => Result::Err(error), }} }} #[abi(embed_v0)] impl ISP1Groth16Verifier{curve_id.name} of super::ISP1Groth16Verifier{curve_id.name} {{ fn {verification_function_name}( self: @ContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252> {{ match verify_sp1_groth16_proof_inner(full_proof_with_hints) {{ Result::Ok((vkey, pub_inputs_256, _)) => Result::Ok((vkey, pub_inputs_256)), Result::Err(error) => Result::Err(error), }} }} fn {verification_function_name_u32}( self: @ContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252> {{ match verify_sp1_groth16_proof_inner(full_proof_with_hints) {{ Result::Ok((vkey, _, pub_inputs_u32)) => Result::Ok((vkey, pub_inputs_u32)), Result::Err(error) => Result::Err(error), }} }} }} }} """).strip() + "\n" # Use the reusable function to write all files write_verifier_files( output_folder_path, output_folder_name, constants_code, contract_code, contract_cairo_name, verification_function_name, ProofSystem.Groth16, cli_mode, modules=["groth16_verifier"], constants_output_path=os.path.join("src", "src", "apps", "sp1_constants.cairo"), ) return constants_code if __name__ == "__main__": pass SP1_VK_PATH = ( "hydra/garaga/starknet/groth16_contract_generator/examples/vk_sp1.json" ) PROOF_PATH = ( "hydra/garaga/starknet/groth16_contract_generator/examples/proof_sp1.json" ) CONTRACTS_FOLDER = "src/contracts/autogenerated/" # Do not change this FOLDER_NAME = "sp1_verifier" # '_curve_id' is appended in the end. gen_sp1_groth16_verifier( SP1_VK_PATH, CONTRACTS_FOLDER, FOLDER_NAME, ECIP_OPS_CLASS_HASH ) # Check if proof file exists and generate calldata if it does if os.path.exists(PROOF_PATH): vk = Groth16VerifyingKey.from_json(file_path=SP1_VK_PATH) proof = Groth16Proof.from_json(proof_path=PROOF_PATH) # Generate the calldata and write test calldata file: output_folder_path = os.path.join( CONTRACTS_FOLDER, f"{FOLDER_NAME}_{vk.curve_id.name.lower()}" ) write_test_calldata_file_generic( output_folder_path, system=ProofSystem.Groth16, # SP1 uses Groth16 vk_path=SP1_VK_PATH, proof_path=PROOF_PATH, ) else: print( f"Warning: Proof file {PROOF_PATH} not found. Skipping calldata generation." ) ================================================ FILE: hydra/garaga/starknet/groth16_contract_generator/parsing_utils.py ================================================ import codecs import dataclasses import hashlib import json import os from pathlib import Path from typing import Any, List from garaga.curves import CURVES, CurveID from garaga.hints import io from garaga.hints.io import split_128 from garaga.modulo_circuit_structs import ( E12D, G1PointCircuit, G2PointCircuit, StructArray, ) from garaga.points import G1Point, G2Point from garaga.precompiled_circuits.multi_miller_loop import MultiMillerLoopCircuit # Import constants from generated file from garaga.starknet.constants import ( RISC0_BN254_CONTROL_ID, RISC0_CONTROL_ROOT, SP1_VERIFIER_HASH, SP1_VERIFIER_VERSION, ) class KeyPatternNotFound(Exception): def __init__(self, key_patterns): super().__init__(f"No key found with patterns {key_patterns}") self.key_patterns = key_patterns def iterate_nested_dict(d): for key, value in d.items(): if isinstance(value, dict): yield from iterate_nested_dict(value) else: yield value def find_item_from_key_patterns(data: dict, key_patterns: List[str]) -> Any: best_match = None best_score = -1 for key, value in data.items(): for pattern in key_patterns: if key.lower() == pattern.lower(): # Exact match return value elif pattern.lower() in key.lower(): # Partial match score = key.lower().count(pattern.lower()) if score > best_score: best_match = value best_score = score if best_match is not None: return best_match else: raise KeyPatternNotFound(key_patterns) def try_parse_g1_point_from_key( data: dict, key_patterns: List[str], curve_id: CurveID = None ) -> G1Point: point = find_item_from_key_patterns(data, key_patterns) return try_parse_g1_point(point, curve_id) def proj_to_affine(x, y, z, curve_id: CurveID) -> G1Point: x, y, z = io.to_int(x), io.to_int(y), io.to_int(z) p = curve_id.p z = pow(z, -1, p) x = x * z % p y = y * z % p return G1Point(x=x, y=y, curve_id=curve_id) def try_parse_g1_point(point: Any, curve_id: CurveID = None) -> G1Point: if isinstance(point, dict): return G1Point( x=io.to_int(find_item_from_key_patterns(point, ["x"])), y=io.to_int(find_item_from_key_patterns(point, ["y"])), curve_id=curve_id, ) elif isinstance(point, (tuple, list)): if len(point) == 2: return G1Point( x=io.to_int(point[0]), y=io.to_int(point[1]), curve_id=curve_id, ) elif len(point) == 3: return proj_to_affine(point[0], point[1], point[2], curve_id) else: raise ValueError(f"Invalid point: {point}") else: raise ValueError(f"Invalid point: {point}") def try_parse_g2_point_from_key( data: dict, key_patterns: List[str], curve_id: CurveID = None ) -> G2Point: point = find_item_from_key_patterns(data, key_patterns) return try_parse_g2_point(point, curve_id) def try_parse_g2_point(point: Any, curve_id: CurveID = None) -> G2Point: if isinstance(point, dict): x_g2 = find_item_from_key_patterns(point, ["x"]) y_g2 = find_item_from_key_patterns(point, ["y"]) if isinstance(x_g2, dict) and isinstance(y_g2, dict): return G2Point( x=( io.to_int(find_item_from_key_patterns(x_g2, ["a0"])), io.to_int(find_item_from_key_patterns(x_g2, ["a1"])), ), y=( io.to_int(find_item_from_key_patterns(y_g2, ["a0"])), io.to_int(find_item_from_key_patterns(y_g2, ["a1"])), ), curve_id=curve_id, ) elif isinstance(x_g2, (tuple, list)) and isinstance(y_g2, (tuple, list)): return G2Point( x=( io.to_int(x_g2[0]), io.to_int(x_g2[1]), ), y=( io.to_int(y_g2[0]), io.to_int(y_g2[1]), ), curve_id=curve_id, ) elif isinstance(point, (tuple, list)): if len(point) == 2: supposed_x = point[0] supposed_y = point[1] elif len(point) == 3: assert (io.to_int(point[2][0]), io.to_int(point[2][1])) == ( 1, 0, ), "Non standard projective coordinates" supposed_x = point[0] supposed_y = point[1] if isinstance(supposed_x, (tuple, list)): assert len(supposed_x) == 2, f"Invalid fp2 coordinates: {supposed_x}" supposed_x = (io.to_int(supposed_x[0]), io.to_int(supposed_x[1])) if isinstance(supposed_y, (tuple, list)): assert len(supposed_y) == 2, f"Invalid fp2 coordinates: {supposed_y}" supposed_y = (io.to_int(supposed_y[0]), io.to_int(supposed_y[1])) return G2Point(x=supposed_x, y=supposed_y, curve_id=curve_id) else: raise ValueError(f"Invalid point: {point}") def try_guessing_curve_id_from_json(data: dict) -> CurveID: try: curve_id = CurveID.from_str(find_item_from_key_patterns(data, ["curve"])) except (ValueError, KeyError, KeyPatternNotFound): # Try guessing the curve id from the bit size of the first found integer in the json. x = None for value in iterate_nested_dict(data): try: x = io.to_int(value) break except TypeError: continue if x is None: raise ValueError("No integer found in the JSON data.") if x.bit_length() > 256: curve_id = CurveID.BLS12_381 else: curve_id = CurveID.BN254 return curve_id @dataclasses.dataclass(slots=True) class Groth16VerifyingKey: alpha: G1Point beta: G2Point gamma: G2Point delta: G2Point ic: List[G1Point] def __post_init__(self): assert ( len(self.ic) > 1 ), "The verifying key must have at least two points in the ic array (one public input and one private input)" assert len(self.ic) == len( set(self.ic) ), "The ic array must not contain duplicate points." assert ( self.alpha.curve_id == self.beta.curve_id == self.gamma.curve_id == self.delta.curve_id ), "All points must be on the same curve." assert all(point.curve_id == self.alpha.curve_id for point in self.ic) @property def curve_id(self) -> CurveID: return self.alpha.curve_id def from_dict(data: dict) -> "Groth16VerifyingKey": try: curve_id = try_guessing_curve_id_from_json(data) try: verifying_key = find_item_from_key_patterns(data, ["verifying_key"]) except KeyPatternNotFound: verifying_key = data try: return Groth16VerifyingKey( alpha=try_parse_g1_point_from_key( verifying_key, ["alpha"], curve_id ), beta=try_parse_g2_point_from_key(verifying_key, ["beta"], curve_id), gamma=try_parse_g2_point_from_key( verifying_key, ["gamma"], curve_id ), delta=try_parse_g2_point_from_key( verifying_key, ["delta"], curve_id ), ic=[ try_parse_g1_point(point, curve_id) for point in find_item_from_key_patterns(verifying_key, ["ic"]) ], ) except (ValueError, KeyPatternNotFound): # Gnark case. g1_points = find_item_from_key_patterns(verifying_key, ["g1"]) g2_points = find_item_from_key_patterns(verifying_key, ["g2"]) return Groth16VerifyingKey( alpha=try_parse_g1_point_from_key(g1_points, ["alpha"], curve_id), beta=try_parse_g2_point_from_key(g2_points, ["beta"], curve_id), gamma=try_parse_g2_point_from_key(g2_points, ["gamma"], curve_id), delta=try_parse_g2_point_from_key(g2_points, ["delta"], curve_id), ic=[ try_parse_g1_point(point, curve_id) for point in find_item_from_key_patterns(g1_points, ["K"]) ], ) except KeyError as e: raise KeyError(f"The key {e} is missing from the JSON data.") def from_json(file_path: str | Path) -> "Groth16VerifyingKey": path = Path(file_path) try: with path.open("r") as f: data = json.load(f) except FileNotFoundError: cwd = os.getcwd() print(f"Current working directory: {cwd}") print(f"Attempted to access file: {os.path.abspath(file_path)}") raise FileNotFoundError(f"The file {file_path} was not found.") except json.JSONDecodeError: raise ValueError(f"The file {file_path} does not contain valid JSON.") return Groth16VerifyingKey.from_dict(data) def serialize_to_cairo(self) -> str: # Precompute M = miller_loop(public_pair) circuit = MultiMillerLoopCircuit( name="precompute M", curve_id=self.curve_id.value, n_pairs=1 ) circuit.write_p_and_q(P=[self.alpha], Q=[self.beta]) M = E12D("alpha_beta_miller_loop_result", circuit.miller_loop(n_pairs=1)) gamma_g2 = G2PointCircuit.from_G2Point("gamma_g2", self.gamma) delta_g2 = G2PointCircuit.from_G2Point("delta_g2", self.delta) ic = StructArray( name="ic", elmts=[ G1PointCircuit.from_G1Point(f"ic_{i}", point) for i, point in enumerate(self.ic) ], ) field_type = "u384" if self.curve_id == CurveID.BLS12_381 else "u288" code = f""" pub const vk:Groth16VerifyingKey<{field_type}> = Groth16VerifyingKey{{ alpha_beta_miller_loop_result: {M.serialize(raw=True)}, gamma_g2: {gamma_g2.serialize(raw=True)}, delta_g2: {delta_g2.serialize(raw=True)} }}; pub const ic: [G1Point; {len(self.ic)}] = {ic.serialize(raw=True, const=True)}; """ return code def flatten(self) -> list[int]: lst = [] lst.extend([self.alpha.x, self.alpha.y]) lst.extend([self.beta.x[0], self.beta.x[1], self.beta.y[0], self.beta.y[1]]) lst.extend([self.gamma.x[0], self.gamma.x[1], self.gamma.y[0], self.gamma.y[1]]) lst.extend([self.delta.x[0], self.delta.x[1], self.delta.y[0], self.delta.y[1]]) for point in self.ic: lst.extend([point.x, point.y]) return lst def reverse_byte_order_uint256(value: int | bytes) -> int: if isinstance(value, int): value_bytes = value.to_bytes(32, byteorder="big") else: value_bytes = value.ljust( 32, b"\x00" ) # Ensure 32 bytes, pad with zeros if needed return int.from_bytes(value_bytes[::-1], byteorder="big") def split_digest(digest: int | bytes): reversed_digest = reverse_byte_order_uint256(digest) return split_128(reversed_digest) @dataclasses.dataclass(slots=True) class Groth16Proof: a: G1Point b: G2Point c: G1Point public_inputs: List[int] = dataclasses.field(default_factory=list) curve_id: CurveID = None image_id: bytes = None # Only used for risc0 proofs journal: bytes = None # Only used for risc0 proofs public_inputs_sp1: bytes = None # Only used for sp1 proofs def __post_init__(self): assert ( self.a.curve_id == self.b.curve_id == self.c.curve_id ), f"All points must be on the same curve, got {self.a.curve_id}, {self.b.curve_id}, {self.c.curve_id}" self.curve_id = self.a.curve_id for pub in self.public_inputs: assert ( 0 <= pub < CURVES[self.curve_id.value].n ), f"Public input {pub} is out of bounds for curve {self.curve_id}" if self.public_inputs_sp1 is not None: assert isinstance( self.public_inputs_sp1, bytes ), "SP1 public inputs must be a bytes object" assert ( len(self.public_inputs_sp1) % 32 == 0 ), "SP1 public inputs must be a multiple of 32 bytes" @property def is_risc0(self) -> bool: return self.image_id is not None and self.journal is not None @property def is_sp1(self) -> bool: return self.public_inputs_sp1 is not None @property def vk_type(self) -> str: if self.is_risc0: return "risc0" elif self.is_sp1: return "sp1" else: return "groth16_generic" def from_dict( data: dict, public_inputs: None | list | dict = None ) -> "Groth16Proof": curve_id = try_guessing_curve_id_from_json(data) try: proof = find_item_from_key_patterns(data, ["proof"]) except KeyPatternNotFound: proof = data try: seal = find_item_from_key_patterns(data, ["seal"]) image_id = find_item_from_key_patterns(data, ["image_id"]) journal = find_item_from_key_patterns(data, ["journal"]) print("Seal: {}\nImage_id: {}\nJournal: {}".format(seal, image_id, journal)) return Groth16Proof._from_risc0( seal=codecs.decode(seal[2:].replace("\\x", ""), "hex"), image_id=codecs.decode(image_id[2:].replace("\\x", ""), "hex"), journal=codecs.decode(journal[2:].replace("\\x", ""), "hex"), ) except (ValueError, KeyError, KeyPatternNotFound): pass except Exception as e: print(f"Error when attempmting to parse as Risc0 proof: {e}") raise e try: sp1_vkey = find_item_from_key_patterns(data, ["vkey"]) public_inputs = find_item_from_key_patterns(data, ["publicValues"]) sp1_proof = find_item_from_key_patterns(data, ["proof"]) return Groth16Proof._from_sp1( vkey=codecs.decode(sp1_vkey[2:].replace("\\x", ""), "hex"), proof=codecs.decode(sp1_proof[2:].replace("\\x", ""), "hex"), public_inputs=codecs.decode( public_inputs[2:].replace("\\x", ""), "hex" ), ) except KeyPatternNotFound: pass except Exception as e: print(f"Error when attempmting to parse as SP1 proof: {e}") raise e if public_inputs is not None: if isinstance(public_inputs, dict): public_inputs = list(public_inputs.values()) elif isinstance(public_inputs, list): pass else: raise ValueError(f"Invalid public inputs format: {public_inputs}") else: try: public_inputs = find_item_from_key_patterns(data, ["public"]) except KeyPatternNotFound as e: print(f"Error: {e}") raise e return Groth16Proof( a=try_parse_g1_point_from_key(proof, ["a"], curve_id), b=try_parse_g2_point_from_key(proof, ["b"], curve_id), c=try_parse_g1_point_from_key(proof, ["c", "Krs"], curve_id), public_inputs=[io.to_int(pub) for pub in public_inputs], ) def from_json( proof_path: str | Path, public_inputs_path: str | Path = None ) -> "Groth16Proof": path = Path(proof_path) try: with path.open("r") as f: data = json.load(f) except FileNotFoundError: raise FileNotFoundError(f"The file {proof_path} was not found.") except json.JSONDecodeError: raise ValueError(f"The file {proof_path} does not contain valid JSON.") try: if public_inputs_path is not None: with Path(public_inputs_path).open("r") as f: public_inputs = json.load(f) else: public_inputs = None except FileNotFoundError: raise FileNotFoundError(f"The file {public_inputs_path} was not found.") except json.JSONDecodeError: raise ValueError( f"The file {public_inputs_path} does not contain valid JSON." ) return Groth16Proof.from_dict(data, public_inputs) def _from_risc0( seal: bytes, image_id: bytes, journal: bytes, CONTROL_ROOT: int = RISC0_CONTROL_ROOT, BN254_CONTROL_ID: int = RISC0_BN254_CONTROL_ID, ) -> "Groth16Proof": assert len(image_id) <= 32, "image_id must be 32 bytes" CONTROL_ROOT_0, CONTROL_ROOT_1 = split_digest(CONTROL_ROOT) proof = seal[4:] journal_digest = hashlib.sha256(journal).digest() claim_digest = ok(image_id, journal_digest).digest() claim0, claim1 = split_digest(claim_digest) return Groth16Proof( a=G1Point( x=int.from_bytes(proof[0:32], "big"), y=int.from_bytes(proof[32:64], "big"), curve_id=CurveID.BN254, ), b=G2Point( x=( int.from_bytes(proof[96:128], "big"), int.from_bytes(proof[64:96], "big"), ), y=( int.from_bytes(proof[160:192], "big"), int.from_bytes(proof[128:160], "big"), ), curve_id=CurveID.BN254, ), c=G1Point( x=int.from_bytes(proof[192:224], "big"), y=int.from_bytes(proof[224:256], "big"), curve_id=CurveID.BN254, ), public_inputs=[ CONTROL_ROOT_0, CONTROL_ROOT_1, claim0, claim1, BN254_CONTROL_ID, ], image_id=image_id, journal=journal, ) def _from_sp1( vkey: bytes, public_inputs: bytes, proof: bytes, ) -> "Groth16Proof": _selector, proof = proof[:4], proof[4:] assert ( _selector == SP1_VERIFIER_HASH[:4] ), f"Invalid SP1 proof version. Expected {SP1_VERIFIER_HASH[:4]} for version {SP1_VERIFIER_VERSION}, got {_selector}\n Please use SP1 verifier version {SP1_VERIFIER_VERSION} or contact garaga developers to update the SP1 verifier version." pub_input_hash: bytes = hashlib.sha256(public_inputs).digest() pub_input_hash: int = int.from_bytes(pub_input_hash, "big") % ( 2**253 ) # <=> & ((1 << 253) - 1) # print(f"pub_input_hash: {hex(pub_input_hash)}") return Groth16Proof( a=G1Point( x=int.from_bytes(proof[0:32], "big"), y=int.from_bytes(proof[32:64], "big"), curve_id=CurveID.BN254, ), b=G2Point( x=( int.from_bytes(proof[96:128], "big"), int.from_bytes(proof[64:96], "big"), ), y=( int.from_bytes(proof[160:192], "big"), int.from_bytes(proof[128:160], "big"), ), curve_id=CurveID.BN254, ), c=G1Point( x=int.from_bytes(proof[192:224], "big"), y=int.from_bytes(proof[224:256], "big"), curve_id=CurveID.BN254, ), public_inputs=[int.from_bytes(vkey, "big"), pub_input_hash], public_inputs_sp1=public_inputs, ) def serialize_to_calldata(self) -> list[int]: cd = [] cd.extend(io.bigint_split(self.a.x)) cd.extend(io.bigint_split(self.a.y)) cd.extend(io.bigint_split(self.b.x[0])) cd.extend(io.bigint_split(self.b.x[1])) cd.extend(io.bigint_split(self.b.y[0])) cd.extend(io.bigint_split(self.b.y[1])) cd.extend(io.bigint_split(self.c.x)) cd.extend(io.bigint_split(self.c.y)) if self.image_id and self.journal and self.public_inputs_sp1 is None: # Risc0 mode. # Public inputs will be reconstructed from image id and journal. image_id_u256 = io.bigint_split( int.from_bytes(self.image_id, "big"), 8, 2**32 )[::-1] journal = list(self.journal) # Span of u32, length 8. cd.append(8) cd.extend(image_id_u256) # Span of u8, length depends on input cd.append(len(self.journal)) cd.extend(journal) elif self.public_inputs_sp1 is not None: # SP1 mode. # Public inputs 0 is vkey cd.extend(io.bigint_split(self.public_inputs[0], 2, 2**128)) # Public inputs 1 is sha256(public_inputs_sp1) % 2**253 # We serialize pub_inputs_sp1 as u32 array for Cairo sha256. n_bytes = len(self.public_inputs_sp1) assert n_bytes % 32 == 0, "SP1 public inputs must be a multiple of 32 bytes" n_words = n_bytes // 32 cd.append(n_words) # Deserialization 8 by 8 for i in range(0, n_bytes, 4): cd.append(int.from_bytes(self.public_inputs_sp1[i : i + 4], "big")) else: # Normal mode. cd.append(len(self.public_inputs)) for pub in self.public_inputs: cd.extend(io.bigint_split(pub, 2, 2**128)) return cd def flatten(self, include_public_inputs: bool = True) -> list[int]: lst = [] lst.extend([self.a.x, self.a.y]) lst.extend([self.b.x[0], self.b.x[1]]) lst.extend([self.b.y[0], self.b.y[1]]) lst.extend([self.c.x, self.c.y]) if include_public_inputs: lst.extend(self.public_inputs) return lst class ExitCode: def __init__(self, system, user): self.system = system self.user = user class Output: def __init__(self, journal_digest, assumptions_digest): self.journal_digest = journal_digest self.assumptions_digest = assumptions_digest def digest(self): return hashlib.sha256( hashlib.sha256(b"risc0.Output").digest() + self.journal_digest + self.assumptions_digest + (2 << 8).to_bytes(2, byteorder="big") ).digest() class ReceiptClaim: def __init__( self, pre_state_digest, post_state_digest, exit_code, input, output, tag_digest: bytes = hashlib.sha256(b"risc0.ReceiptClaim").digest(), ): self.pre_state_digest = pre_state_digest self.post_state_digest = post_state_digest self.exit_code = exit_code self.input = input self.output = output.digest() self.TAG_DIGEST = tag_digest def digest(self): # print(f"TAG_DIGEST: {self.TAG_DIGEST.hex()}") # print(f"self.input: {self.input.hex()}") # print(f"self.pre_state_digest: {self.pre_state_digest.hex()}") # print(f"self.post_state_digest: {self.post_state_digest.hex()}") # print(f"self.output: {self.output.hex()}") # print(f"self.exit_code.system: {self.exit_code.system}") # print(f"self.exit_code.user: {self.exit_code.user}") return hashlib.sha256( self.TAG_DIGEST + self.input + self.pre_state_digest + self.post_state_digest + self.output + (self.exit_code.system << 24).to_bytes(4, byteorder="big") + (self.exit_code.user << 24).to_bytes(4, byteorder="big") + (4 << 8).to_bytes(2, byteorder="big") ).digest() def ok(image_id, journal_digest): SYSTEM_STATE_ZERO_DIGEST = bytes.fromhex( "A3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2" ) # https://github.com/risc0/risc0-ethereum/blob/34d2fee4ca6b5fb354a8a1a00c43f8945097bfe5/contracts/src/IRiscZeroVerifier.sol#L60 return ReceiptClaim( pre_state_digest=image_id, post_state_digest=SYSTEM_STATE_ZERO_DIGEST, exit_code=ExitCode(0, 0), # (Halted, 0) input=bytes(32), # bytes32(0) output=Output(journal_digest, bytes(32)), # Output(journalDigest, bytes32(0)) ) if __name__ == "__main__": # PATH = Path(__file__).parent # print(f"PATH: {PATH}") # proof = Groth16Proof.from_json( # f"{PATH}/examples/gnark_proof_bn254.json", # f"{PATH}/examples/gnark_public_bn254.json", # ) # # print(proof) # vk = Groth16VerifyingKey.from_json(f"{PATH}/examples/gnark_vk_bn254.json") # print(vk) # vk_risc0 = Groth16VerifyingKey.from_json(f"{PATH}/examples/vk_risc0.json") # # print(vk_risc0) # Risc0 proof extracted from https://sepolia.etherscan.io/tx/0x2308aeefef309097aeaf0e3660915d5b80813e693ac72147b651e0196155235d bproof = bytes.fromhex( "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" ) def parse_proof_and_signals(proof: bytes) -> Groth16Proof: proof = proof[4:] def bytes_32_iterator(data: bytes): for i in range(0, len(data), 32): yield io.to_int(data[i : i + 32]) it = bytes_32_iterator(proof) print(len(proof) / 32) _a = G1Point(x=next(it), y=next(it), curve_id=CurveID.BN254) _b = G2Point( x=[next(it), next(it)][::-1], y=[next(it), next(it)][::-1], curve_id=CurveID.BN254, ) _c = G1Point(x=next(it), y=next(it), curve_id=CurveID.BN254) public_inputs = list(it) print(len(public_inputs)) return Groth16Proof( a=_a, b=_b, c=_c, public_inputs=list(it), ) proof = parse_proof_and_signals(bproof) print(proof) ================================================ FILE: hydra/garaga/starknet/honk_contract_generator/calldata.py ================================================ from garaga import garaga_rs from garaga.curves import ProofSystem from garaga.points import G1G2Pair from garaga.precompiled_circuits.zk_honk import ( G2_POINT_KZG_1, G2_POINT_KZG_2, LIBRA_COMMITMENTS, NUMBER_UNSHIFTED, CurveID, G1Point, HonkVk, ModuloCircuitElement, ZKHonkProof, ZKHonkTranscript, ZKHonkVerifierCircuits, ) from garaga.starknet.tests_and_calldata_generators.mpcheck import MPCheckCalldataBuilder from garaga.starknet.tests_and_calldata_generators.msm import MSMCalldataBuilder def filter_msm_scalars( scalars: list[ModuloCircuitElement], log_n: int ) -> list[ModuloCircuitElement]: assert len(scalars) == NUMBER_UNSHIFTED + log_n + LIBRA_COMMITMENTS + 3 # Remove the first element (== 1) scalars_filtered = scalars[1:] return scalars_filtered def extract_msm_scalars( scalars: list[ModuloCircuitElement], log_n: int ) -> list[ModuloCircuitElement]: scalars_msm = filter_msm_scalars(scalars, log_n) return [s.value for s in scalars_msm] def get_ultra_flavor_honk_calldata_from_vk_and_proof( vk: HonkVk, proof: ZKHonkProof, system: ProofSystem = ProofSystem.UltraKeccakZKHonk, use_rust: bool = False, ) -> list[int]: if use_rust: return _honk_calldata_from_vk_and_proof_rust(vk, proof) assert isinstance(proof, ZKHonkProof) tp = ZKHonkTranscript.from_proof(vk, proof, system) circuit = ZKHonkVerifierCircuits(name="test", log_n=vk.log_circuit_size) vk_circuit = vk.to_circuit_elements(circuit) proof_circuit = proof.to_circuit_elements(circuit) tp = tp.to_circuit_elements(circuit) public_input_delta = circuit.compute_public_input_delta( public_inputs=proof_circuit.public_inputs, pairing_point_object=proof_circuit.pairing_point_object, beta=tp.beta, gamma=tp.gamma, ) rlc_check, check = circuit.verify_sum_check( libra_sum=proof_circuit.libra_sum, sumcheck_univariates=proof_circuit.sumcheck_univariates, sumcheck_evaluations=(proof_circuit.sumcheck_evaluations), libra_evaluation=proof_circuit.libra_evaluation, beta=tp.beta, gamma=tp.gamma, public_inputs_delta=public_input_delta, eta=tp.eta, eta_two=tp.etaTwo, eta_three=tp.etaThree, libra_challenge=tp.libra_challenge, sum_check_u_challenges=tp.sum_check_u_challenges, gate_challenge=tp.gate_challenge, alpha=tp.alpha, log_n=vk.log_circuit_size, base_rlc=circuit.write_element(1234), ) assert rlc_check.value == 0 assert check.value == 0 vanishing_check, diff_check = circuit.check_evals_consistency( proof_circuit.libra_evaluation, proof_circuit.libra_poly_evals, tp.gemini_r, tp.sum_check_u_challenges, ) assert vanishing_check.value != 0 assert diff_check.value == 0 scalars = circuit.compute_shplemini_msm_scalars( proof_circuit.sumcheck_evaluations, proof_circuit.gemini_masking_eval, proof_circuit.gemini_a_evaluations, proof_circuit.libra_poly_evals, tp.gemini_r, tp.rho, tp.shplonk_z, tp.shplonk_nu, tp.sum_check_u_challenges, ) scalars_msm = extract_msm_scalars(scalars, vk.log_circuit_size) # Swap last two scalars : scalars_msm = scalars_msm[:-2] + scalars_msm[-2:][::-1] # Place first scalar just after the vk_lagrange_last point (index 27) first_scalar = scalars_msm.pop(0) scalars_msm.insert(28, first_scalar) points = [ vk.qm, # 0 vk.qc, # 1 vk.ql, # 2 vk.qr, # 3 vk.qo, # 4 vk.q4, # 5 vk.qLookup, # 6 vk.qArith, # 7 vk.qDeltaRange, # 8 vk.qElliptic, # 9 vk.qMemory, # 10 vk.qNnf, # 11 vk.qPoseidon2External, # 12 vk.qPoseidon2Internal, # 13 vk.s1, # 14 vk.s2, # 15 vk.s3, # 16 vk.s4, # 17 vk.id1, # 18 vk.id2, # 19 vk.id3, # 20 vk.id4, # 21 vk.t1, # 22 vk.t2, # 23 vk.t3, # 24 vk.t4, # 25 vk.lagrange_first, # 26 vk.lagrange_last, # 27 proof.gemini_masking_poly, # 28 proof.w1, # 29 proof.w2, # 30 proof.w3, # 31 proof.w4, # 32 proof.z_perm, # 33 proof.lookup_inverses, # 34 proof.lookup_read_counts, # 35 proof.lookup_read_tags, # 36 ] points.extend(proof.gemini_fold_comms[: vk.log_circuit_size - 1]) points.extend(proof.libra_commitments) points.append(proof.kzg_quotient) points.append(G1Point.get_nG(CurveID.BN254, 1)) msm_builder = MSMCalldataBuilder( CurveID.BN254, points=points, scalars=scalars_msm, ) P_0 = G1Point.msm(points=points, scalars=scalars_msm).add(proof.shplonk_q) P_1 = -proof.kzg_quotient pairs = [G1G2Pair(P_0, G2_POINT_KZG_1), G1G2Pair(P_1, G2_POINT_KZG_2)] mpc_builder = MPCheckCalldataBuilder( curve_id=CurveID.BN254, pairs=pairs, n_fixed_g2=2, public_pair=None ) cd = [] cd.extend(proof.serialize_to_calldata()) cd.extend( msm_builder.serialize_to_calldata( include_points_and_scalars=False, serialize_as_pure_felt252_array=True, ) ) cd.extend(mpc_builder.serialize_to_calldata()) res = [len(cd)] + cd # print(f"HONK CALLDATA: {res}") # print(f"HONK CALLDATA LENGTH: {len(res)}") return res def _honk_calldata_from_vk_and_proof_rust( vk: HonkVk, proof: ZKHonkProof, ) -> list[int]: return garaga_rs.get_zk_honk_calldata( proof.proof_bytes, proof.public_inputs_bytes, vk.vk_bytes ) ================================================ FILE: hydra/garaga/starknet/honk_contract_generator/generator_honk.py ================================================ import argparse import os from pathlib import Path from garaga.curves import CurveID, ProofSystem from garaga.modulo_circuit_structs import G2Line, StructArray from garaga.precompiled_circuits.compilable_circuits.base import ( get_circuit_definition_impl_template, ) from garaga.precompiled_circuits.compilable_circuits.ultra_honk import ( ZKEvalsConsistencyDoneCircuit, ZKEvalsConsistencyInitCircuit, ZKEvalsConsistencyLoopCircuit, ZKPrepareScalarsCircuit, ZKSumCheckCircuit, ) from garaga.precompiled_circuits.multi_miller_loop import precompute_lines from garaga.precompiled_circuits.zk_honk import ( G2_POINT_KZG_1, G2_POINT_KZG_2, MAX_LOG_N, PAIRING_POINT_OBJECT_LENGTH, HonkVk, ) from garaga.starknet.groth16_contract_generator.generator import ( write_test_calldata_file_generic, write_verifier_files, ) def gen_honk_verifier( vk: str | Path | HonkVk | bytes, output_folder_path: str, output_folder_name: str, cli_mode: bool = False, include_test_sample: bool = True, ) -> bool: """ Generate the honk verifier files and write them to the output folder. """ output_folder_path_full = os.path.join(output_folder_path, output_folder_name) ( constants_code, circuits_code, contract_code, contract_name, verification_function_name, ) = gen_honk_verifier_files(vk) _write_and_format_project_files( output_folder_path_full, output_folder_name, cli_mode, constants_code, circuits_code, contract_code, contract_name, verification_function_name, include_test_sample, ) return True def gen_honk_verifier_files( vk: str | Path | HonkVk | bytes, ) -> tuple[str, str, str, str, str]: """ Returns in this order: - constants_code - circuits_code - contract_code - contract_name - verification_function_name """ # Parse vk if isinstance(vk, (Path, str)): vk = HonkVk.from_bytes(open(vk, "rb").read()) elif isinstance(vk, bytes): vk = HonkVk.from_bytes(vk) else: assert isinstance( vk, HonkVk ), f"Invalid type for vk: {type(vk)}. Should be str, Path, HonkVk or bytes." constants_code = _gen_constants_code(vk) ( circuits_code, sumcheck_function_name, prepare_scalars_function_name, consistency_function_names, scalar_indexes, msm_len, is_on_curve_function_name, ) = _gen_circuits_code(vk) points_code, (n_vk_points, n_proof_points) = _get_msm_points_array_code( log_n=vk.log_circuit_size ) scalars_tuple = ",\n ".join(f"scalar_{idx}" for idx in scalar_indexes) scalars_tuple_into = [f"scalar_{idx}" for idx in scalar_indexes] scalars_tuple_into.append("transcript.shplonk_z.into()") # Swap position of last two elements of scalars_tuple_into (KZG quotient & BN254 G1 generator) : scalars_tuple_into = scalars_tuple_into[:-2] + scalars_tuple_into[-2:][::-1] # Move first scalar after the first vk points [a, b, c, d, e] -> [b,c,d,a,e] if [b,c,d] are vk points: scalars_tuple_into = ( scalars_tuple_into[1 : n_vk_points + 1] + scalars_tuple_into[:1] + scalars_tuple_into[n_vk_points + 1 :] ) scalars_tuple_into = ",\n ".join(scalars_tuple_into) # Generate contract header contract_name = "UltraKeccakZKHonkVerifier" verification_function_name = "verify_ultra_keccak_zk_honk_proof" contract_header = _gen_contract_header( function_names=[ sumcheck_function_name, prepare_scalars_function_name, consistency_function_names[0], consistency_function_names[1], consistency_function_names[2], is_on_curve_function_name, ], ) contract_code = f"""{contract_header} let (transcript, _, base_rlc) = ZKHonkTranscriptTrait::from_proof::(full_proof.proof, vk.vk_hash, vk.log_circuit_size); let log_n = vk.log_circuit_size; let (sum_check_rlc, honk_check) = {sumcheck_function_name}( p_public_inputs: full_proof.proof.public_inputs, p_pairing_point_object: full_proof.proof.pairing_point_object, libra_sum: u256_to_u384(full_proof.proof.libra_sum), sumcheck_univariates_flat: full_proof.proof.sumcheck_univariates.slice(0, log_n * ZK_BATCHED_RELATION_PARTIAL_LENGTH), sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span(), tp_gate_challenge: transcript.gate_challenge, tp_eta_1: transcript.eta.into(), tp_eta_2: transcript.eta_two.into(), tp_eta_3: transcript.eta_three.into(), tp_beta: transcript.beta.into(), tp_gamma: transcript.gamma.into(), tp_base_rlc: base_rlc.into(), tp_alpha: transcript.alpha, tp_libra_challenge: transcript.libra_challenge.into(), modulus: mod_grumpkin, ); let (mut challenge_poly_eval, mut root_power_times_tp_gemini_r) = {consistency_function_names[0]}( tp_gemini_r: transcript.gemini_r.into(), modulus: mod_grumpkin, ); for i in 0..vk.log_circuit_size {{ let (new_challenge_poly_eval, new_root_power_times_tp_gemini_r) = {consistency_function_names[1]}( challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, tp_sumcheck_u_challenge: (*transcript.sum_check_u_challenges.at(i)).into(), modulus: mod_grumpkin, ); challenge_poly_eval = new_challenge_poly_eval; root_power_times_tp_gemini_r = new_root_power_times_tp_gemini_r; }}; let (vanishing_check, diff_check) = {consistency_function_names[2]}( p_libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, modulus: mod_grumpkin, ); let ( {scalars_tuple}, ) = {prepare_scalars_function_name}( p_sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, p_gemini_masking_eval: u256_to_u384(full_proof.proof.gemini_masking_eval), p_gemini_a_evaluations: full_proof.proof.gemini_a_evaluations, p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), tp_rho: transcript.rho.into(), tp_shplonk_z: transcript.shplonk_z.into(), tp_shplonk_nu: transcript.shplonk_nu.into(), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span().slice(0, log_n), modulus: mod_grumpkin, ); {points_code} let mut scalars: Span = array![{scalars_tuple_into}].span(); {_get_msm_kzg_template(msm_len, n_vk_points, n_proof_points, is_on_curve_function_name)} if sum_check_rlc.is_zero() && honk_check.is_zero() && !vanishing_check.is_zero() && diff_check.is_zero() && kzg_check.is_ok() {{ return Result::Ok(full_proof.proof.public_inputs); }} else {{ return Result::Err('Proof verification failed'); }} }} }} }} """ return ( constants_code, circuits_code, contract_code, contract_name, verification_function_name, ) def _get_msm_kzg_template( msm_size: int, n_vk_points: int, n_proof_points: int, is_on_curve_function_name: str, ): TEMPLATE = """\n // Check input points are on curve. // Skip the first {n_vk_points} points as they are from VK and keep the last {n_proof_points} proof points for point in points.slice({n_vk_points}, {n_proof_points}) {{ assert({is_on_curve_function_name}(*point, mod_bn), 'proof point not on curve'); }}; // Assert shplonk_q is on curve let shplonk_q_pt:G1Point = full_proof.proof.shplonk_q.into(); assert({is_on_curve_function_name}(shplonk_q_pt, mod_bn), 'shplonk_q not on curve'); let mut msm_hint = full_proof.msm_hint; assert(msm_hint.len() == {msm_len} * 12, 'wrong glv&fakeglv hint size'); let eigen = get_eigenvalue(0); let third_root_of_unity = get_third_root_of_unity(0); let min_one = get_min_one_order(0); let nG = get_nG_glv_fake_glv(0); let mut P_1 = shplonk_q_pt; while msm_hint.len() != 0 {{ let pt = *points.pop_front().unwrap(); let scalar = *scalars.pop_front().unwrap(); // Note : Scalars are below curve order by construction (circuit outputs mod n and transcript output (u128)) let glv_fake_glv_hint: GlvFakeGlvHint = Serde::deserialize(ref msm_hint).unwrap(); let temp = _scalar_mul_glv_and_fake_glv( pt, scalar, mod_grumpkin, mod_bn, glv_fake_glv_hint, eigen, third_root_of_unity, min_one, nG, 0, ); P_1 = _ec_safe_add(P_1, temp, mod_bn, 0); }} let P_2:G1Point = full_proof.proof.kzg_quotient.into(); // Perform the KZG pairing check. let kzg_check = multi_pairing_check_bn254_2P_2F( G1G2Pair {{ p: P_1, q: G2_POINT_KZG_1 }}, G1G2Pair {{ p: P_2.negate(0), q: G2_POINT_KZG_2 }}, precomputed_lines.span(), full_proof.kzg_hint, ); """.format( debug="{:?}", msm_len=msm_size, n_vk_points=n_vk_points, n_proof_points=n_proof_points, is_on_curve_function_name=is_on_curve_function_name, ) return TEMPLATE def _get_circuit_code_header(): header = """ use core::circuit::{ u384, circuit_add, circuit_sub, circuit_mul, circuit_inverse, EvalCircuitTrait, CircuitOutputsTrait, CircuitInputs, CircuitModulus, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use core::circuit::CircuitElement as CE; use core::circuit::CircuitInput as CI; use garaga::definitions::{G1Point};\n """ return header def _gen_circuits_code(vk: HonkVk) -> tuple[str, str, str, list[str], str, int, str]: """ Generate the code for the sumcheck circuit and related circuits. Args: vk: The verifying key Returns: Tuple containing: - The generated code - Sumcheck function name - Prepare scalars function name - List of consistency function names - Scalar indexes - MSM length - Is on curve function name """ code = _get_circuit_code_header() curve_id = CurveID.GRUMPKIN # Generate sumcheck circuit sumcheck_circuit = ZKSumCheckCircuit(vk) sumcheck_function_name = f"{curve_id.name}_{sumcheck_circuit.name.upper()}" sumcheck_code, sumcheck_function_name = sumcheck_circuit.circuit.compile_circuit( function_name=sumcheck_function_name, pub=True, generic_modulus=True ) # Generate prepare scalars circuit prepare_scalars_circuit = ZKPrepareScalarsCircuit(vk) scalar_indexes = prepare_scalars_circuit.scalar_indexes msm_len = prepare_scalars_circuit.msm_len prepare_scalars_function_name = ( f"{curve_id.name}_{prepare_scalars_circuit.name.upper()}" ) prepare_scalars_code, prepare_scalars_function_name = ( prepare_scalars_circuit.circuit.compile_circuit( function_name=prepare_scalars_function_name, pub=True, generic_modulus=True ) ) # Generate consistency circuits consistency_circuits = [] for circuit_class in [ ZKEvalsConsistencyInitCircuit, ZKEvalsConsistencyLoopCircuit, ZKEvalsConsistencyDoneCircuit, ]: circuit = circuit_class(vk) function_name = f"{curve_id.name}_{circuit.name.upper()}" circuit_code, function_name = circuit.circuit.compile_circuit( function_name=function_name, pub=True, generic_modulus=True ) consistency_circuits.append((circuit_code, function_name)) # Combine all circuit code code += sumcheck_code + prepare_scalars_code code += "".join(circuit_code for circuit_code, _ in consistency_circuits) code += get_circuit_definition_impl_template(len(scalar_indexes)) is_on_curve_code = """ #[inline(never)] pub fn is_on_curve_excluding_infinity_bn254(p: G1Point, modulus: CircuitModulus) -> bool { // INPUT stack // y^2 = x^3 + 3 let (in0, in1) = (CE::> {}, CE::> {}); let y2 = circuit_mul(in1, in1); let x2 = circuit_mul(in0, in0); let x3 = circuit_mul(in0, x2); let y2_minus_x3 = circuit_sub(y2, x3); let mut circuit_inputs = (y2_minus_x3,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check: u384 = outputs.get_output(y2_minus_x3); return zero_check == u384{limb0: 3, limb1: 0, limb2: 0, limb3: 0}; } """ code += is_on_curve_code is_on_curve_function_name = "is_on_curve_excluding_infinity_bn254" return ( code, sumcheck_function_name, prepare_scalars_function_name, [func_name for _, func_name in consistency_circuits], scalar_indexes, msm_len, is_on_curve_function_name, ) def _gen_contract_header(function_names: list[str]) -> str: """Generate the contract header and imports.""" imports_str = ", ".join(function_names) header = f""" use super::honk_verifier_constants::{{vk, precomputed_lines}}; use super::honk_verifier_circuits::{{{imports_str}}}; #[starknet::interface] pub trait IUltraKeccakZKHonkVerifier {{ fn verify_ultra_keccak_zk_honk_proof( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; }} #[starknet::contract] mod UltraKeccakZKHonkVerifier {{ use garaga::definitions::{{G1Point, G1G2Pair, BN254, get_BN254_modulus, get_GRUMPKIN_modulus, u384, get_eigenvalue, get_third_root_of_unity, get_min_one_order, get_nG_glv_fake_glv}}; use garaga::pairing_check::{{multi_pairing_check_bn254_2P_2F, MPCheckHintBN254}}; use garaga::ec_ops::{{G1PointTrait, _ec_safe_add, _scalar_mul_glv_and_fake_glv, GlvFakeGlvHint}}; use super::{{vk, precomputed_lines, {imports_str}}}; use garaga::apps::noir::{{ZKHonkProof, G2_POINT_KZG_1, G2_POINT_KZG_2}}; use garaga::apps::noir::zk_honk_transcript::{{Point256IntoCircuitPoint, KeccakHasherState, ZKHonkTranscriptTrait, ZK_BATCHED_RELATION_PARTIAL_LENGTH}}; use garaga::core::circuit::{{U32IntoU384, u288IntoCircuitInputValue, U64IntoU384, u256_to_u384}}; use core::num::traits::Zero; #[storage] struct Storage {{}} #[derive(Drop, Serde)] struct FullProof {{ proof: ZKHonkProof, msm_hint: Span, kzg_hint:MPCheckHintBN254, }} #[abi(embed_v0)] impl IUltraKeccakZKHonkVerifier of super::IUltraKeccakZKHonkVerifier {{ fn verify_ultra_keccak_zk_honk_proof( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> {{ // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given a proof and a verifying key. let mut full_proof_with_hints = full_proof_with_hints; let full_proof = Serde::::deserialize(ref full_proof_with_hints).expect('deserialization failed'); let mod_bn = get_BN254_modulus(); let mod_grumpkin = get_GRUMPKIN_modulus(); """ return header def _gen_constants_code(vk: HonkVk) -> str: """Generate the constants code for the contract.""" lines = precompute_lines([G2_POINT_KZG_1, G2_POINT_KZG_2]) precomputed_lines = StructArray( name="lines", elmts=[ G2Line(name=f"line{i}", elmts=lines[i : i + 4]) for i in range(0, len(lines), 4) ], ) return f""" use garaga::definitions::{{G1Point, G2Line, u384, u288}}; use garaga::apps::noir::HonkVk; {vk.to_cairo()}\n pub const precomputed_lines: [G2Line; {len(precomputed_lines)//4}] = {precomputed_lines.serialize(raw=True, const=True)}; """ def _get_msm_points_array_code(log_n: int) -> tuple[str, tuple[int, int]]: vk_points = [ "vk.qm", "vk.qc", "vk.ql", "vk.qr", "vk.qo", "vk.q4", "vk.qLookup", "vk.qArith", "vk.qDeltaRange", "vk.qElliptic", "vk.qMemory", "vk.qNnf", "vk.qPoseidon2External", "vk.qPoseidon2Internal", "vk.s1", "vk.s2", "vk.s3", "vk.s4", "vk.id1", "vk.id2", "vk.id3", "vk.id4", "vk.t1", "vk.t2", "vk.t3", "vk.t4", "vk.lagrange_first", "vk.lagrange_last", ] next_proof_point_counter = 1 proof_points = [ f"full_proof.proof.gemini_masking_poly.into(), // Proof point {next_proof_point_counter}" ] next_proof_point_counter += 1 proof_points += [ f"full_proof.proof.w1.into(), // Proof point {next_proof_point_counter}", f"full_proof.proof.w2.into(), // Proof point {next_proof_point_counter+1}", f"full_proof.proof.w3.into(), // Proof point {next_proof_point_counter+2}", f"full_proof.proof.w4.into(), // Proof point {next_proof_point_counter+3}", f"full_proof.proof.z_perm.into(), // Proof point {next_proof_point_counter+4}", f"full_proof.proof.lookup_inverses.into(), // Proof point {next_proof_point_counter+5}", f"full_proof.proof.lookup_read_counts.into(), // Proof point {next_proof_point_counter+6}", f"full_proof.proof.lookup_read_tags.into(), // Proof point {next_proof_point_counter+7}", ] next_proof_point_counter += 8 # Combine all points all_points = vk_points + proof_points points_str = ",\n".join(all_points) code = "// Starts with 1 * shplonk_q, not included in msm\n" code += f""" let mut _points: Array = array![{points_str}\n]; for gem_comm in full_proof.proof.gemini_fold_comms {{ _points.append((*gem_comm).into()); }}; // log_n -1 = {log_n-1} points || Proof points {next_proof_point_counter}-{next_proof_point_counter+(log_n-1) - 1}""" next_proof_point_counter += log_n - 1 # Add ZK-specific commitments code += f""" for lib_comm in full_proof.proof.libra_commitments {{ _points.append((*lib_comm).into()); }};// 3 points || Proof points {next_proof_point_counter}-{next_proof_point_counter+3-1}""" next_proof_point_counter += 3 # Add common final points code += f""" _points.append(full_proof.proof.kzg_quotient.into()); // Proof point {next_proof_point_counter} _points.append(BN254.G); let mut points = _points.span();""" proof_point_counter = next_proof_point_counter n_vk_points = len(vk_points) return code, (n_vk_points, proof_point_counter) def _write_and_format_project_files( output_folder_path: str, output_folder_name: str, cli_mode: bool, constants_code: str, circuits_code: str, contract_code: str, contract_name: str, verification_function_name: str, include_test_sample: bool = True, ): # Use the reusable function to write all files write_verifier_files( output_folder_path, output_folder_name, constants_code, contract_code, contract_name, verification_function_name, ProofSystem.UltraKeccakZKHonk, cli_mode, circuits_code=circuits_code, modules=["honk_verifier", "honk_verifier_constants", "honk_verifier_circuits"], constants_filename="honk_verifier_constants.cairo", contract_filename="honk_verifier.cairo", circuits_filename="honk_verifier_circuits.cairo", include_test_sample=include_test_sample, ) if __name__ == "__main__": parser = argparse.ArgumentParser(description="Generate HONK verifier contracts") parser.add_argument( "--max-log-n", action="store_true", help="Generate contracts with maximum log N size", ) args = parser.parse_args() VK_PATH = ( "hydra/garaga/starknet/honk_contract_generator/examples/vk_ultra_keccak.bin" ) CONTRACTS_FOLDER = "src/contracts/autogenerated/" # Do not change this EXAMPLES_FOLDER = "hydra/garaga/starknet/honk_contract_generator/examples" if not args.max_log_n: FOLDER_NAME = "noir_ultra_keccak_zk_honk_example" gen_honk_verifier( VK_PATH, CONTRACTS_FOLDER, FOLDER_NAME, ) # Generate calldata output_folder_path = os.path.join(CONTRACTS_FOLDER, FOLDER_NAME) proof_file = os.path.join(EXAMPLES_FOLDER, "proof_ultra_keccak_zk.bin") public_inputs_file = os.path.join( EXAMPLES_FOLDER, "public_inputs_ultra_keccak.bin" ) if os.path.exists(proof_file) and os.path.exists(public_inputs_file): try: write_test_calldata_file_generic( output_folder_path, ProofSystem.UltraKeccakZKHonk, VK_PATH, proof_file, public_inputs_file, ) print(f"Generated calldata for {FOLDER_NAME}") except Exception as e: print(f"Error generating calldata for {FOLDER_NAME}: {e}") raise e else: print(f"Warning: Proof or public inputs file not found for {FOLDER_NAME}") if args.max_log_n: # NOTE : each additional public input increase bytecode by ~ 21 felts. # each additional circuit size increase bytecode by ~ 372 felts. vk = HonkVk.from_bytes(open(VK_PATH, "rb").read()) vk.log_circuit_size = MAX_LOG_N vk.public_inputs_size = 4 + PAIRING_POINT_OBJECT_LENGTH gen_honk_verifier( vk, CONTRACTS_FOLDER, "ultra_keccak_zk_honk_max_log_n", ) ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/drand_calldata.py ================================================ import secrets from pathlib import Path from typing import Optional import garaga.hints.io as io from garaga import garaga_rs from garaga.drand.client import ( DrandNetwork, G2Point, digest_func, get_chain_info, get_randomness, ) from garaga.drand.tlock import encrypt_for_round from garaga.signature import hash_to_curve from garaga.starknet.tests_and_calldata_generators.map_to_curve import * from garaga.starknet.tests_and_calldata_generators.mpcheck import ( G1G2Pair, MPCheckCalldataBuilder, ) def drand_round_to_calldata(round_number: int, use_rust=False) -> list[int]: if use_rust: return _drand_round_to_calldata_rust(round_number) message = digest_func(round_number) # print(f"round {round_number} message {message}") msg_point = hash_to_curve(message, CurveID.BLS12_381, "sha256") chain = get_chain_info(DrandNetwork.quicknet.value) round = get_randomness(chain.hash, round_number) sig_pt = round.signature_point ################### mpc_builder = MPCheckCalldataBuilder( curve_id=CurveID.BLS12_381, pairs=[ G1G2Pair(p=sig_pt, q=G2Point.get_nG(CurveID.BLS12_381, 1)), G1G2Pair(p=msg_point, q=-chain.public_key), ], n_fixed_g2=2, public_pair=None, ) cd = [] sig_pt: G1Point cd.append(round_number) cd.extend(io.bigint_split(sig_pt.x)) cd.extend(io.bigint_split(sig_pt.y)) cd.extend(build_hash_to_curve_hint(message).to_calldata()) cd.extend(mpc_builder.serialize_to_calldata()) return [len(cd)] + cd def _drand_round_to_calldata_rust( round_number: int, ) -> list[int]: chain = get_chain_info(DrandNetwork.quicknet.value) round = get_randomness(chain.hash, round_number) randomness = round.randomness signature = int(round.signature, 16) data = [ round_number, randomness, signature, ] return garaga_rs.drand_calldata_builder(data) def drand_encrypt_to_calldata( round_number: int, message: bytes, randomness: Optional[bytes] = None, use_rust=False, ) -> list[int]: if use_rust: return _drand_encrypt_to_calldata(round_number, message, randomness) chain = get_chain_info(DrandNetwork.quicknet.value) cipher_text = encrypt_for_round( chain.public_key, round_number, message, randomness is not None, randomness ) cd = [] cd.append(round_number) cd.extend(cipher_text.serialize_to_calldata()) return [len(cd)] + cd def _drand_encrypt_to_calldata( round_number: int, message: bytes, randomness: Optional[bytes] = None, ) -> list[int]: if randomness is None: randomness = secrets.token_bytes(16) data = [ round_number, int.from_bytes(message, "big"), int.from_bytes(randomness, "big"), ] return garaga_rs.drand_tlock_encrypt_calldata_builder(data) def generate_drand_decrypt_constants( verifier_class_hash: int, decrypt_contract_path: Path ): """Write the verifier class hash to the decrypt contract's constants file.""" constants_file = decrypt_contract_path / "src" / "drand_decrypt_constants.cairo" constants_file.write_text( f"// Generated — do not edit manually.\n" f"pub const VERIFIER_CLASS_HASH: felt252 = {hex(verifier_class_hash)};\n" ) if __name__ == "__main__": drand_round_to_calldata(1) drand_round_to_calldata(2) # drand_round_to_calldata(3) ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/map_to_curve.py ================================================ from dataclasses import dataclass from garaga.algebra import PyFelt from garaga.curves import CURVES, CurveID, get_base_field from garaga.hints.io import bigint_split, int_to_u384 from garaga.points import G1Point from garaga.signature import apply_isogeny, hash_to_field @dataclass(slots=True) class MapToCurveHint: gx1_is_square: bool y1: PyFelt y_flag: bool def to_cairo(self) -> str: return f"MapToCurveHint {{ gx1_is_square: {str(self.gx1_is_square).lower()}, y1: {int_to_u384(self.y1.value, as_hex=True)}, y_flag: {str(self.y_flag).lower()} }}" def to_calldata(self) -> list[int]: cd = [] cd.append(int(self.gx1_is_square)) cd.extend(bigint_split(self.y1.value)) cd.append(int(self.y_flag)) return cd @dataclass(slots=True) class HashToCurveHint: f0_hint: MapToCurveHint f1_hint: MapToCurveHint def to_cairo(self) -> str: return f"""HashToCurveHint {{ f0_hint: {self.f0_hint.to_cairo()}, f1_hint: {self.f1_hint.to_cairo()} }}""" def to_calldata(self) -> list[int]: cd = [] cd.extend(self.f0_hint.to_calldata()) cd.extend(self.f1_hint.to_calldata()) return cd def build_map_to_curve_hint(u: PyFelt) -> tuple[G1Point, MapToCurveHint]: field = get_base_field(CurveID.BLS12_381) a = field(CURVES[CurveID.BLS12_381.value].swu_params.A) b = field(CURVES[CurveID.BLS12_381.value].swu_params.B) z = field(CURVES[CurveID.BLS12_381.value].swu_params.Z) zeta_u2 = z * u**2 ta = zeta_u2**2 + zeta_u2 num_x1 = b * (ta + field.one()) if ta.value == 0: div = a * z else: div = a * -ta num2_x1 = num_x1**2 div2 = div**2 div3 = div2 * div assert div3.value != 0 num_gx1 = (num2_x1 + a * div2) * num_x1 + b * div3 num_x2 = zeta_u2 * num_x1 gx1 = num_gx1 / div3 gx1_square = gx1.is_quad_residue() if gx1_square: y1 = gx1.sqrt(min_root=False) assert y1 * y1 == gx1 else: y1 = (z * gx1).sqrt(min_root=False) assert y1 * y1 == z * gx1 y2 = zeta_u2 * u * y1 y = y1 if gx1_square else y2 y_flag = y.value % 2 == u.value % 2 num_x = num_x1 if gx1_square else num_x2 x_affine = num_x / div y_affine = -y if y.value % 2 != u.value % 2 else y point_on_curve = G1Point( x_affine.value, y_affine.value, CurveID.BLS12_381, iso_point=True ) return point_on_curve, MapToCurveHint( gx1_is_square=gx1_square, y1=y1, y_flag=y_flag ) def build_hash_to_curve_hint(message: bytes) -> HashToCurveHint: felt0, felt1 = hash_to_field(message, 2, CurveID.BLS12_381.value, "sha256") pt0, f0_hint = build_map_to_curve_hint(felt0) pt1, f1_hint = build_map_to_curve_hint(felt1) sum_pt = pt0.add(pt1) # print( # f"sum_pt: {int_to_u384(sum_pt.x, as_hex=False)} {int_to_u384(sum_pt.y, as_hex=False)}" # ) sum_pt = apply_isogeny(sum_pt) # print( # f"sum_pt: {int_to_u384(sum_pt.x, as_hex=False)} {int_to_u384(sum_pt.y, as_hex=False)}" # ) x = CURVES[CurveID.BLS12_381.value].x n = CURVES[CurveID.BLS12_381.value].n cofactor = (1 - (x % n)) % n # 15132376222941642753 # print(f"cofactor: {cofactor}, hex :{hex(cofactor)}") return HashToCurveHint( f0_hint=f0_hint, f1_hint=f1_hint, ) if __name__ == "__main__": field = get_base_field(CurveID.BLS12_381) import hashlib hint = build_hash_to_curve_hint(hashlib.sha256(b"Hello, World!").digest()) print(hint.to_cairo()) # print(hint.to_calldata()) ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/mpcheck.py ================================================ import functools from dataclasses import dataclass from functools import lru_cache from garaga import garaga_rs from garaga import modulo_circuit_structs as structs from garaga.algebra import Polynomial, PyFelt from garaga.curves import CurveID, get_base_field, get_irreducible_poly from garaga.points import G1G2Pair from garaga.poseidon_transcript import CairoPoseidonTranscript from garaga.precompiled_circuits.multi_miller_loop import precompute_lines from garaga.precompiled_circuits.multi_pairing_check import ( MultiMillerLoopCircuit, MultiPairingCheckCircuit, WriteOps, get_max_Q_degree, ) @dataclass(slots=True) class MPCheckCalldataBuilder: curve_id: CurveID pairs: list[G1G2Pair] n_fixed_g2: int public_pair: G1G2Pair | None def __hash__(self): return hash( (self.curve_id, tuple(self.pairs), self.n_fixed_g2, self.public_pair) ) def __post_init__(self): # Validate input assert isinstance(self.pairs, (list, tuple)) assert all( isinstance(pair, G1G2Pair) for pair in self.pairs ), f"All pairs must be G1G2Pair, got {[type(pair) for pair in self.pairs]}" assert all( self.curve_id == pair.curve_id == self.pairs[0].curve_id for pair in self.pairs ), f"All pairs must be on the same curve, got {[pair.curve_id for pair in self.pairs]}" assert ( isinstance(self.public_pair, G1G2Pair) or self.public_pair is None ), f"Extra pair must be G1G2Pair or None, got {self.public_pair}" assert len(self.pairs) >= 2 assert 0 <= self.n_fixed_g2 <= len(self.pairs) @property def include_miller_loop_result(self): return self.public_pair is not None @property def field(self): return get_base_field(self.curve_id) @property def big_Q_expected_len(self): return get_max_Q_degree(self.curve_id.value, len(self.pairs)) + 1 @property def three_limbs_only(self): return self.curve_id != CurveID.BLS12_381 @lru_cache(maxsize=1) def extra_miller_loop_result(self) -> list[PyFelt] | None: if self.include_miller_loop_result: circuit = MultiMillerLoopCircuit( name="precompute M", curve_id=self.curve_id.value, n_pairs=1 ) circuit.write_p_and_q_raw(self.public_pair.to_pyfelt_list()) M = circuit.miller_loop(n_pairs=1) return [mi.felt for mi in M] else: return None @lru_cache(maxsize=1) def lines(self) -> list[PyFelt]: lines = precompute_lines([pair.q for pair in self.pairs[0 : self.n_fixed_g2]]) assert len(lines) % 4 == 0, f"Lines must be a multiple of 4, got {len(lines)}" return lines def _init_circuit(self) -> MultiPairingCheckCircuit: mpcheck_circuit = MultiPairingCheckCircuit( name="mpcheck", curve_id=self.curve_id.value, n_pairs=len(self.pairs), precompute_lines=bool(self.n_fixed_g2), n_points_precomputed_lines=self.n_fixed_g2, ) mpcheck_circuit.precomputed_lines = mpcheck_circuit.write_elements( self.lines(), WriteOps.INPUT ) mpcheck_circuit._precomputed_lines_generator = ( mpcheck_circuit._create_precomputed_lines_generator() ) p_q_input = [] for pair in self.pairs: p_q_input.extend(pair.to_pyfelt_list()) mpcheck_circuit.write_p_and_q_raw(p_q_input) return mpcheck_circuit def _retrieve_Pis_Qis_and_Ris_from_circuit( self, mpcheck_circuit: MultiPairingCheckCircuit ) -> tuple[list[list[PyFelt]], list[list[PyFelt]], list[list[PyFelt]]]: relations = mpcheck_circuit.accumulate_poly_instructions[0] Qis = relations.Qis Pis = relations.Pis Ris = relations.Ris return Pis, Qis, Ris def _get_passed_Ris_from_Ris(self, Ris: list[list[PyFelt]]) -> list[list[PyFelt]]: passed_Ris = ( Ris if self.curve_id == CurveID.BLS12_381 else Ris[1:] ) # Skip first Ri for BN254 as it known to be one (lambda_root*lambda_root_inverse) result return passed_Ris def _init_transcript(self) -> CairoPoseidonTranscript: transcript = self._new_transcript() # Hash inputs. for pair in self.pairs: transcript.hash_limbs_multi( pair.to_pyfelt_list(), three_limbs_only=False ) # False because G1Point is holding u384 only. return transcript def _hash_hints_and_get_base_random_rlc_coeff( self, transcript: CairoPoseidonTranscript, lambda_root: list[PyFelt], lambda_root_inverse: list[PyFelt], scaling_factor: list[PyFelt], scaling_factor_sparsity: list[PyFelt], Ris: list[list[PyFelt]], ) -> PyFelt: if self.curve_id == CurveID.BN254: transcript.hash_limbs_multi(lambda_root) transcript.hash_limbs_multi(lambda_root_inverse) transcript.hash_limbs_multi(scaling_factor, sparsity=scaling_factor_sparsity) for Ri in Ris: assert len(Ri) == 12 transcript.hash_limbs_multi(Ri) if self.include_miller_loop_result: transcript.hash_limbs_multi(self.extra_miller_loop_result()) return self.field(transcript.s1) def _hash_big_Q_and_get_z( self, transcript: CairoPoseidonTranscript, big_Q: list[PyFelt] ): # Start a fresh transcript for the second stage and seed it with the base RLC coefficient seeded_transcript = self._seed_transcript_with_base_rlc( self._new_transcript("_II"), transcript.s1 ) seeded_transcript.hash_limbs_multi(big_Q) return self.field(seeded_transcript.s0) def _new_transcript(self, stage_suffix: str = "") -> CairoPoseidonTranscript: init_hash = f"MPCHECK_{self.curve_id.name}_{len(self.pairs)}P_{self.n_fixed_g2}F{stage_suffix}" return CairoPoseidonTranscript( init_hash=int.from_bytes(init_hash.encode(), byteorder="big"), three_limbs_only=self.three_limbs_only, ) def _seed_transcript_with_base_rlc( self, transcript: CairoPoseidonTranscript, base_rlc: PyFelt ) -> CairoPoseidonTranscript: # Hash the base RLC coefficient from _hash_hints_and_get_base_random_rlc_coeff transcript.hash_element(base_rlc) return transcript def _sanity_check_verify_rlc_equation( self, z: PyFelt, c1: PyFelt, n_relations_with_ci: int, Pis: list[list[PyFelt]], big_Q: Polynomial, Ris: list[list[PyFelt]], ): lhs = self.field.zero() ci = self.field.one() k = 0 for i in range(n_relations_with_ci - 1, -1, -1): # if self.public_pair is None: # print(f"{self.curve_id.name} = LHS_{k} : {io.int_to_u384(lhs, False)}") k += 1 Prod_Pis_of_z = functools.reduce( lambda x, y: x * y, [Polynomial(pi).evaluate(z) for pi in Pis[i]] ) Ri_of_z = Polynomial(Ris[i]).evaluate(z) lhs += ci * (Prod_Pis_of_z - Ri_of_z) ci *= c1 # print(f"lhs_{i} : {io.int_to_u384(lhs)}") lhs_print = self.field.zero() k = 0 for i in range(n_relations_with_ci): # if self.public_pair is None: # print( # f"{self.curve_id.name} = LHS_{k} : {io.int_to_u384(lhs_print, False)}" # ) k += 1 Prod_Pis_of_z = functools.reduce( lambda x, y: x * y, [Polynomial(pi).evaluate(z) for pi in Pis[i]] ) Ri_of_z = Polynomial(Ris[i]).evaluate(z) __lhs = Prod_Pis_of_z - Ri_of_z lhs_print = lhs_print * c1 + __lhs P_irr = get_irreducible_poly(curve_id=self.curve_id, extension_degree=12) big_Q_of_z = big_Q.evaluate(z) P_of_z = P_irr.evaluate(z) # print(f"big_Q_of_z : {io.int_to_u384(big_Q_of_z)}") # print(f"P_of_z : {io.int_to_u384(P_of_z)}") assert lhs == big_Q_of_z * P_of_z, "Check failed." @lru_cache(maxsize=1) def build_mpcheck_hint( self, ) -> tuple[ structs.Cairo1SerializableStruct, structs.Cairo1SerializableStruct | None ]: """ Return MPCheckHint struct """ mpcheck_circuit = self._init_circuit() transcript = self._init_transcript() _, lambda_root, lambda_root_inverse, scaling_factor, scaling_factor_sparsity = ( mpcheck_circuit.multi_pairing_check( len(self.pairs), self.extra_miller_loop_result() ) ) Pis, Qis, Ris = self._retrieve_Pis_Qis_and_Ris_from_circuit(mpcheck_circuit) passed_Ris = self._get_passed_Ris_from_Ris(Ris) c1 = self._hash_hints_and_get_base_random_rlc_coeff( transcript, lambda_root, lambda_root_inverse, scaling_factor, scaling_factor_sparsity, passed_Ris, ) n_relations_with_ci = len(passed_Ris) + ( 1 if self.curve_id == CurveID.BN254 else 0 ) ci, big_Q = self.field.one(), Polynomial.zero(self.field.p) for i in range(n_relations_with_ci - 1, -1, -1): # print(f"c_{i} : {io.int_to_u384(ci)}") big_Q += Qis[i] * ci ci *= c1 # print(f"{i=}, {n_relations_with_ci=}") assert ci == c1 ** (n_relations_with_ci - i) big_Q_coeffs = big_Q.get_coeffs() big_Q_coeffs.extend( [self.field.zero()] * (self.big_Q_expected_len - len(big_Q_coeffs)) ) z = self._hash_big_Q_and_get_z(transcript, big_Q_coeffs) self._sanity_check_verify_rlc_equation( z, c1, n_relations_with_ci, Pis, big_Q, Ris ) # Skip last Ri as it is known to be 1 for pairing checks assert [x.value for x in passed_Ris[-1]] == [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ], f"Last Ri must be 1_Fp12, got {[x.value for x in passed_Ris[-1]]}" passed_Ris = passed_Ris[:-1] if self.curve_id == CurveID.BN254: hint_struct_list_init = [ structs.E12D(name="lambda_root", elmts=lambda_root) ] else: hint_struct_list_init = [] return structs.Struct( struct_name=f"MPCheckHint{self.curve_id.name}", name="hint", elmts=hint_struct_list_init + [ structs.E12D(name="lambda_root_inverse", elmts=lambda_root_inverse), structs.MillerLoopResultScalingFactor( name="w", elmts=[ wi for wi, si in zip(scaling_factor, scaling_factor_sparsity) if si != 0 ], ), structs.StructSpan( name="Ris", elmts=[ structs.E12D(name=f"R{i}", elmts=[ri.felt for ri in Ri]) for i, Ri in enumerate(passed_Ris) ], ), structs.u384Array(name="big_Q", elmts=big_Q_coeffs), ] + [structs.felt252(name="z", elmts=[z])], ) def _get_input_structs(self) -> list[structs.Cairo1SerializableStruct]: inputs = [] for i, pair in enumerate(self.pairs): inputs.append( structs.G1G2PairCircuit(name=f"pair{i}", elmts=pair.to_pyfelt_list()) ) if self.include_miller_loop_result: inputs.append( structs.E12D( name="precomputed_miller_loop_result", elmts=self.extra_miller_loop_result(), ) ) if self.n_fixed_g2 > 0: lines = self.lines() inputs.append( structs.StructSpan( name="lines", elmts=[ structs.G2Line(name=f"line{i}", elmts=lines[i : i + 4]) for i in range(0, len(lines), 4) ], ) ) mpcheck_hint = self.build_mpcheck_hint() inputs.append(mpcheck_hint) return inputs def to_cairo_1_test(self): # print( # f"Generating MPCheck test for {self.curve_id.name} with {len(self.pairs)} pairs and {self.n_fixed_g2} fixed G2 points, using extra Miller loop result: {self.include_miller_loop_result}" # ) with_extra = ( "_with_extra_miller_loop_result" if self.include_miller_loop_result else "" ) fn_name = f"multi_pairing_check_{self.curve_id.name.lower()}_{len(self.pairs)}P_{self.n_fixed_g2}F{with_extra}" inputs = self._get_input_structs() test_name = f"test_{self.curve_id.name}_mpcheck_{len(self.pairs)}P_{self.n_fixed_g2}F{with_extra}" input_code = "" for struct in inputs: input_code += struct.serialize() code = f""" #[test] fn {test_name}() {{ {input_code} let res = {fn_name}({', '.join([struct.name for struct in inputs])}); assert!(res.is_ok()); }} """ return code def _serialize_to_calldata_rust(self) -> list[int]: return garaga_rs.mpc_calldata_builder( self.curve_id.value, [element.value for pair in self.pairs for element in pair.to_pyfelt_list()], self.n_fixed_g2, ( [element.value for element in self.public_pair.to_pyfelt_list()] if self.public_pair is not None else [] ), ) def serialize_to_calldata( self, use_rust=False, ) -> list[int]: if use_rust: return self._serialize_to_calldata_rust() mpcheck_hint = self.build_mpcheck_hint() call_data: list[int] = [] call_data.extend(mpcheck_hint.serialize_to_calldata()) return call_data if __name__ == "__main__": from garaga.precompiled_circuits.multi_pairing_check import get_pairing_check_input pairs, public_pair = get_pairing_check_input( curve_id=CurveID.BLS12_381, n_pairs=3, include_m=True, return_pairs=True, ) mpc = MPCheckCalldataBuilder( curve_id=CurveID.BLS12_381, pairs=pairs, n_fixed_g2=2, public_pair=public_pair, ) print(mpc.serialize_to_calldata(use_rust=True)) ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/msm.py ================================================ from dataclasses import dataclass from functools import lru_cache from garaga import garaga_rs from garaga import modulo_circuit_structs as structs from garaga.algebra import PyFelt from garaga.curves import CURVES, STARK, CurveID, WeierstrassCurve, get_base_field from garaga.hints import fake_glv from garaga.points import G1Point @dataclass(slots=True) class MSMCalldataBuilder: curve_id: CurveID points: list[G1Point] scalars: list[int] def __post_init__(self): assert all( point.curve_id == self.curve_id for point in self.points ), "All points must be on the same curve." assert len(self.points) == len( self.scalars ), f"Number of points and scalars must be equal, got {len(self.points)} points and {len(self.scalars)} scalars" assert all( 0 <= s <= CURVES[self.curve_id.value].n for s in self.scalars ), f"Scalars must be in [0, {self.curve_id.name}'s order] == [0, {CURVES[self.curve_id.value].n}]." def __hash__(self) -> int: return hash((self.curve_id, tuple(self.points), tuple(self.scalars))) @property def field(self): return get_base_field(self.curve_id) @property def msm_size(self): return len(self.scalars) @property def curve(self) -> WeierstrassCurve: return CURVES[self.curve_id.value] @lru_cache(maxsize=2) def build_msm_hint(self) -> structs.StructArray: """ Returns the MSMHint """ hints_structs = [] for i, (point, scalar) in enumerate(zip(self.points, self.scalars)): if self.curve.is_endomorphism_available(): Q, u1, u2, v1, v2 = fake_glv.get_glv_fake_glv_hint(point, scalar) hints_structs.append( structs.Struct( struct_name=f"GlvFakeGlvHint", name=f"glv_fake_glv_hint_{i}", elmts=[ structs.G1PointCircuit.from_G1Point("Q", Q), structs.felt252(name=f"u1_{i}", elmts=[PyFelt(u1, STARK)]), structs.felt252(name=f"u2_{i}", elmts=[PyFelt(u2, STARK)]), structs.felt252(name=f"v1_{i}", elmts=[PyFelt(v1, STARK)]), structs.felt252(name=f"v2_{i}", elmts=[PyFelt(v2, STARK)]), ], ) ) else: Q, s1, s2 = fake_glv.get_fake_glv_hint(point, scalar) hints_structs.append( structs.Struct( struct_name=f"FakeGlvHint", name=f"fake_glv_hint_{i}", elmts=[ structs.G1PointCircuit.from_G1Point("Q", Q), structs.felt252(name=f"s1_{i}", elmts=[PyFelt(s1, STARK)]), structs.felt252(name=f"s2_{i}", elmts=[PyFelt(s2, STARK)]), ], ) ) return structs.StructSpan(name="msm_hint", elmts=hints_structs) def _get_input_structs( self, ) -> list[structs.Cairo1SerializableStruct]: """ """ inputs = [] inputs.append(self.build_msm_hint()) # msm_hint inputs.append( structs.StructSpan( name="points", elmts=[ structs.G1PointCircuit.from_G1Point(f"point{i}", point) for i, point in enumerate(self.points) ], ) ) inputs.append( structs.StructSpan( name="scalars", elmts=[ structs.u256(name=f"scalar{i}", elmts=[PyFelt(s, 2**256)]) for i, s in enumerate(self.scalars) ], ) ) return inputs def to_cairo_1_test(self, test_name: str = None, ignored=False): # print( # f"Generating MSM test for {self.curve_id.name} with {len(self.scalars)} points" # ) test_name = test_name or f"test_msm_{self.curve_id.name}_{len(self.scalars)}P" inputs = garaga_rs.msm_calldata_builder( [value for point in self.points for value in [point.x, point.y]], self.scalars, self.curve_id.value, True, False, ) Q = structs.G1PointCircuit.from_G1Point( "Q", G1Point.msm(self.points, self.scalars) ) T = "u384" if self.curve_id == CurveID.BLS12_381 else "u288" ignore_str = "\n#[ignore]" if ignored else "" code = f""" #[test]{ignore_str} fn {test_name}() {{ let mut data = array![{','.join([hex(value) for value in inputs])}].span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!(res == {Q.serialize(raw=True)}); }} """ return code def _serialize_to_calldata_rust( self, include_points_and_scalars=True, serialize_as_pure_felt252_array=False, ) -> list[int]: return garaga_rs.msm_calldata_builder( [value for point in self.points for value in [point.x, point.y]], self.scalars, self.curve_id.value, include_points_and_scalars, serialize_as_pure_felt252_array, ) def serialize_to_calldata( self, include_points_and_scalars=True, serialize_as_pure_felt252_array=False, use_rust=False, ) -> list[int]: if use_rust: return self._serialize_to_calldata_rust( include_points_and_scalars, serialize_as_pure_felt252_array, ) msm_hint, points, scalars = self._get_input_structs() call_data: list[int] = [] if include_points_and_scalars: call_data.extend(points.serialize_to_calldata()) call_data.extend(scalars.serialize_to_calldata()) call_data.append(self.curve_id.value) call_data.extend(msm_hint.serialize_to_calldata()[1:]) if serialize_as_pure_felt252_array: return [len(call_data)] + call_data else: return call_data if __name__ == "__main__": import random c = CurveID.SECP256K1 order = CURVES[c.value].n msm = MSMCalldataBuilder( curve_id=c, points=[G1Point.gen_random_point(c) for _ in range(1)], scalars=[random.randint(0, order) for _ in range(1)], ) cd = msm.serialize_to_calldata( include_points_and_scalars=True, serialize_as_pure_felt252_array=False, ) print(cd) print(len(cd)) ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/signatures.py ================================================ import random from dataclasses import dataclass from functools import lru_cache from hashlib import sha512 from garaga import garaga_rs from garaga.curves import BASE, CURVES, N_LIMBS, CurveID, TwistedEdwardsCurve from garaga.hints.io import bigint_split, split_128 from garaga.points import G1Point from garaga.rsa_rns import ( CHANNEL_MODULI, ReductionWitness, RNSContext, RNSInteger, RSA2048ExponentiationWitness, generate_rsa2048_sha256_witness, generate_rsa2048_witness, is_valid_rsa2048_witness, ) @dataclass(slots=True) class SchnorrSignature: """ A Schnorr signature with associated public key and challenge. Fields : rx : int - The x-coordinate of the R point from the signature. s : int - The s-coordinate of the signature. e : int - The challenge hash. px : int - The x-coordinate of the public key. py : int - The y-coordinate of the public key. curve_id : CurveID - The curve id. """ rx: int s: int e: int px: int py: int curve_id: CurveID def __post_init__(self): assert self.py % 2 == 0, "y-coordinate of public key must be even" n = CURVES[self.curve_id.value].n p = CURVES[self.curve_id.value].p assert ( 0 <= self.rx < p ), f"rx must be in range 0 < rx < {hex(p)}, got {hex(self.rx)}" assert 0 < self.s < n, f"s must be in range 0 < s < {hex(n)}, got {hex(self.s)}" assert 0 < self.e < n, f"e must be in range 0 < e < {hex(n)}, got {hex(self.e)}" @classmethod def sample(cls, curve_id: CurveID) -> "SchnorrSignature": """ Generate a valid Schnorr signature for the given curve. The algorithm: 1. Generate private key x 2. Compute public key P = xG 3. Generate random k (nonce) 4. Compute R = kG 5. Compute e (challenge) 6. Compute s = k + ex (mod n) """ curve = CURVES[curve_id.value] n = curve.n G = G1Point.get_nG(curve_id, 1) # Generate private key and compute public key x = random.randint(1, n - 1) Pk = G.scalar_mul(x) # Ensure public key has even y (BIP340 requirement) if Pk.y % 2 == 1: x = (-x) % n # Update the private key accordingly Pk = -Pk # Generate nonce and compute R point k = random.randint(1, n - 1) R = G.scalar_mul(k) # Ensure R has even y (BIP340 requirement) if R.y % 2 == 1: k = (-k) % n # Update the nonce accordingly R = -R # Generate challenge (in real usage this would be H(R.x || P.x || message)) e = random.randint(1, n - 1) # Compute s = k + ex mod n s = (k + e * x) % n res = SchnorrSignature(rx=R.x, s=s, e=e, px=Pk.x, py=Pk.y, curve_id=curve_id) assert res.is_valid(), "generated signature is invalid" return res def is_valid(self) -> bool: Pk = G1Point(self.px, self.py, self.curve_id) n = CURVES[self.curve_id.value].n G = G1Point.get_nG(self.curve_id, 1) res = G.scalar_mul(self.s).add(Pk.scalar_mul(-self.e % n)) return res.x == self.rx def serialize(self, prepend_public_key: bool = True) -> list[int]: cd = [] if prepend_public_key: cd.extend(bigint_split(self.px, N_LIMBS, BASE)) cd.extend(bigint_split(self.py, N_LIMBS, BASE)) cd.extend(bigint_split(self.rx, N_LIMBS, BASE)) cd.extend(split_128(self.s)) cd.extend(split_128(self.e)) return cd def serialize_with_hints( self, use_rust=False, as_str=False, prepend_public_key: bool = True ) -> list[int] | str: """Serialize the signature with hints for verification""" if use_rust: cd = garaga_rs.schnorr_calldata_builder( self.rx, self.s, self.e, self.px, self.py, prepend_public_key, self.curve_id.value, ) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd cd = self.serialize(prepend_public_key) e_neg = -self.e % CURVES[self.curve_id.value].n msm_calldata = garaga_rs.msm_calldata_builder( [ CURVES[self.curve_id.value].Gx, CURVES[self.curve_id.value].Gy, self.px, self.py, ], [self.s, e_neg], self.curve_id.value, False, # include_points_and_scalars True, # serialize_as_pure_felt252_array ) cd.extend(msm_calldata) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd @dataclass(slots=True) class ECDSASignature: """ An ECDSA signature with recovery parameter and associated public key and message hash. Fields: r : int - r component of the signature (derived from the ephemeral point R.x mod n). s : int - s component of the signature. v : int - Recovery parameter; 0 if R.y is even, otherwise 1. px : int - The x-coordinate of the public key. py : int - The y-coordinate of the public key. z : int - The message hash used in signing (in practice, z = H(message)). curve_id : CurveID - The identifier for the curve being used. """ r: int s: int v: int px: int py: int z: int curve_id: CurveID def __post_init__(self): curve = CURVES[self.curve_id.value] n = curve.n p = curve.p # For ECDSA, r and s must be nonzero and less than n. assert 0 < self.r < n, f"r must be in range 1..n-1, got {hex(self.r)}" assert 0 < self.s < n, f"s must be in range 1..n-1, got {hex(self.s)}" # v should be either 0 or 1. assert self.v in (0, 1), f"v must be 0 or 1, got {self.v}" # Ensure public key coordinates are in the field. assert 0 <= self.px < p, f"px must be in range 0..p-1, got {hex(self.px)}" assert 0 <= self.py < p, f"py must be in range 0..p-1, got {hex(self.py)}" @classmethod def sample(cls, curve_id: CurveID) -> "ECDSASignature": """ Generate a valid ECDSA signature for the given curve. The algorithm: 1. Generate a private key d. 2. Compute the public key Q = d * G. 3. Generate a random message hash z (in practice, z = H(message)). 4. Choose a random nonce k and compute R = k * G. 5. Let r = R.x mod n (with r != 0). 6. Compute s = k^{-1} * (z + r * d) mod n (with s != 0). 7. Set the recovery parameter v = 0 if R.y is even, else 1. """ curve = CURVES[curve_id.value] n = curve.n p = curve.p G = G1Point.get_nG(curve_id, 1) # Generate the private key d and public key Q. d = random.randint(1, n - 1) Q = G.scalar_mul(d) # Generate a random message hash (normally, this is H(message)). z = random.randint(1, n - 1) # Choose a nonce k until we get valid r and s. while True: k = random.randint(1, n - 1) R = G.scalar_mul(k) r = R.x % n # r is computed from the x-coordinate of R. if r == 0: continue try: k_inv = pow(k, -1, n) except ValueError: continue s = (k_inv * (z + r * d)) % n if s == 0: continue v = 0 if R.y % 2 == 0 else 1 break sig = cls(r=r, s=s, v=v, px=Q.x, py=Q.y, z=z, curve_id=curve_id) assert ( sig.is_valid() ), f"generated ECDSA signature on curve {curve_id.name} is invalid" return sig def is_valid(self) -> bool: """ Verify the ECDSA signature using the stored message hash and public key. Standard verification: 1. Compute w = s^{-1} mod n. 2. Compute u1 = z * w mod n and u2 = r * w mod n. 3. Compute R' = u1 * G + u2 * Q. 4. The signature is valid if (R'.x mod n) equals r. """ curve = CURVES[self.curve_id.value] n = curve.n G = G1Point.get_nG(self.curve_id, 1) Q = G1Point(self.px, self.py, self.curve_id) try: s_inv = pow(self.s, -1, n) except ValueError: return False u1 = (self.z * s_inv) % n u2 = (self.r * s_inv) % n R_prime = G.scalar_mul(u1).add(Q.scalar_mul(u2)) return (R_prime.x % n) == self.r def serialize(self, prepend_public_key: bool = True) -> list[int]: cd = [] if prepend_public_key: cd.extend(bigint_split(self.px, N_LIMBS, BASE)) cd.extend(bigint_split(self.py, N_LIMBS, BASE)) cd.extend(bigint_split(self.r, N_LIMBS, BASE)) cd.extend(split_128(self.s)) cd.append(self.v) cd.extend(split_128(self.z)) return cd def serialize_with_hints( self, use_rust=False, as_str=False, prepend_public_key: bool = True ) -> list[int] | str: """Serialize the signature with hints for verification""" if use_rust: cd = garaga_rs.ecdsa_calldata_builder( self.r, self.s, self.v, self.px, self.py, self.z, prepend_public_key, self.curve_id.value, ) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd cd = self.serialize(prepend_public_key) n = CURVES[self.curve_id.value].n s_inv = pow(self.s, -1, n) u1 = (self.z * s_inv) % n u2 = (self.r * s_inv) % n msm_calldata = garaga_rs.msm_calldata_builder( [ CURVES[self.curve_id.value].Gx, CURVES[self.curve_id.value].Gy, self.px, self.py, ], [u1, u2], self.curve_id.value, False, # include_points_and_scalars True, # serialize_as_pure_felt252_array ) cd.extend(msm_calldata) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd @dataclass(slots=True) class RSA2048Signature: """RSA-2048 signature with reduction witnesses for on-chain verification.""" modulus: RNSInteger signature: RNSInteger expected_message: RNSInteger reductions: tuple[ReductionWitness, ...] @classmethod def from_bundle(cls, bundle: RSA2048ExponentiationWitness) -> "RSA2048Signature": return cls( modulus=bundle.modulus, signature=bundle.signature, expected_message=bundle.expected_message, reductions=bundle.reductions, ) @classmethod def sample(cls, seed: int = 0) -> "RSA2048Signature": return cls.from_bundle(generate_rsa2048_witness(seed=seed)) @classmethod def tampered_residue_sample(cls, seed: int = 0) -> "RSA2048Signature": sample = cls.sample(seed=seed) first = sample.reductions[0] bad_residues = list(first.remainder.residues) bad_residues[0] = (bad_residues[0] + 1) % CHANNEL_MODULI[0] tampered_remainder = RNSInteger( value=first.remainder.value, limbs=first.remainder.limbs, residues=tuple(bad_residues), ) return cls( modulus=sample.modulus, signature=sample.signature, expected_message=sample.expected_message, reductions=( ReductionWitness( quotient=first.quotient, remainder=tampered_remainder, ), *sample.reductions[1:], ), ) @classmethod def tampered_limb_sample(cls, seed: int = 0) -> "RSA2048Signature": sample = cls.sample(seed=seed) first = sample.reductions[0] bad_limbs = list(first.quotient.limbs) bad_limbs[1] ^= 1 tampered_quotient = RNSInteger( value=first.quotient.value, limbs=tuple(bad_limbs), residues=first.quotient.residues, ) return cls( modulus=sample.modulus, signature=sample.signature, expected_message=sample.expected_message, reductions=( ReductionWitness( quotient=tampered_quotient, remainder=first.remainder, ), *sample.reductions[1:], ), ) @classmethod def tampered_expected_message_sample(cls, seed: int = 0) -> "RSA2048Signature": sample = cls.sample(seed=seed) bad_limbs = list(sample.expected_message.limbs) bad_limbs[0] ^= 1 tampered_expected_message = RNSInteger( value=sample.expected_message.value, limbs=tuple(bad_limbs), residues=sample.expected_message.residues, ) return cls( modulus=sample.modulus, signature=sample.signature, expected_message=tampered_expected_message, reductions=sample.reductions, ) def _to_bundle(self) -> RSA2048ExponentiationWitness: return RSA2048ExponentiationWitness( modulus=self.modulus, signature=self.signature, expected_message=self.expected_message, reductions=self.reductions, ) def is_valid(self) -> bool: return is_valid_rsa2048_witness( self._to_bundle(), ctx=RNSContext(CHANNEL_MODULI) ) def serialize_public_key(self) -> list[int]: return self.modulus.serialize_to_calldata() def serialize_signature_with_hints(self) -> list[int]: return self._to_bundle().serialize_signature_with_hint() def serialize(self, prepend_public_key: bool = True) -> list[int]: return self._to_bundle().serialize(prepend_public_key=prepend_public_key) def serialize_with_hints( self, use_rust: bool = False, as_str: bool = False, prepend_public_key: bool = True, ) -> list[int] | str: if use_rust: cd = garaga_rs.rsa_2048_calldata_builder( self.signature.value, self.expected_message.value, self.modulus.value, prepend_public_key, ) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd calldata = self.serialize(prepend_public_key=prepend_public_key) if as_str: return "[{}]".format(", ".join(map(hex, calldata))) return calldata @classmethod def from_sha256_message(cls, message: bytes, seed: int = 0) -> "RSA2048Signature": """Create an RSA2048Signature from a raw message using SHA-256.""" return cls.from_bundle(generate_rsa2048_sha256_witness(message, seed=seed)) def serialize_sha256_with_hints( self, message: bytes, use_rust: bool = False, as_str: bool = False, prepend_public_key: bool = True, ) -> list[int] | str: """Serialize the signature with hints for SHA-256 on-chain verification. Appends the ByteArray-serialized message after the RSA calldata. """ if use_rust: cd = garaga_rs.rsa_2048_sha256_calldata_builder( self.signature.value, message, self.modulus.value, prepend_public_key, ) if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd # Python path: RSA calldata + ByteArray serialization calldata = self.serialize(prepend_public_key=prepend_public_key) calldata.extend(_serialize_byte_array(message)) if as_str: return "[{}]".format(", ".join(map(hex, calldata))) return calldata def _serialize_byte_array(data: bytes) -> list[int]: """Serialize bytes as a Cairo ByteArray in felt252 calldata format. Layout: [num_full_words, word_0, ..., word_{n-1}, pending_word, pending_word_len] Each full word is 31 bytes. The pending word is 0-30 bytes. """ full_word_count = len(data) // 31 pending_len = len(data) % 31 cd = [full_word_count] for i in range(full_word_count): start = i * 31 word = int.from_bytes(data[start : start + 31], byteorder="big") cd.append(word) if pending_len > 0: pending = int.from_bytes(data[full_word_count * 31 :], byteorder="big") cd.append(pending) else: cd.append(0) cd.append(pending_len) return cd @dataclass(slots=True) class EdDSA25519Signature: """ An EdDSA25519 signature with associated public key and message. """ Ry_twisted: int s: int Py_twisted: int msg: bytes def __eq__(self, other) -> bool: if not isinstance(other, EdDSA25519Signature): return NotImplemented return ( self.Ry_twisted == other.Ry_twisted and self.s == other.s and self.Py_twisted == other.Py_twisted and self.msg == other.msg ) def __hash__(self) -> int: return hash((self.Ry_twisted, self.s, self.Py_twisted, self.msg)) def __post_init__(self): assert 0 <= self.Ry_twisted < 2**256 assert 0 <= self.Py_twisted < 2**256 assert 0 <= self.s < 2**256 @property def curve_id(self) -> CurveID: return CurveID.ED25519 @property def curve(self) -> TwistedEdwardsCurve: return CURVES[CurveID.ED25519.value] @classmethod def from_json(cls, json): public_key_bytes = bytes.fromhex(json["public_key"]) message_bytes = bytes.fromhex(json["message"]) signature_bytes = bytes.fromhex(json["signature"]) assert len(public_key_bytes) == 32 assert len(signature_bytes) == 64 return cls( Ry_twisted=int.from_bytes(signature_bytes[:32], "little"), s=int.from_bytes(signature_bytes[32:64], "little"), Py_twisted=int.from_bytes(public_key_bytes, "little"), msg=message_bytes, ) def serialize(self, prepend_public_key: bool = True) -> list[int]: cd = [] if prepend_public_key: cd.extend(split_128(self.Py_twisted)) cd.extend(split_128(self.Ry_twisted)) cd.extend(split_128(self.s)) cd.append(len(self.msg)) cd.extend(list(self.msg)) return cd def xrecover(self, y: int) -> int: p = self.curve.p D = self.curve.d_twisted I = pow(2, (p - 1) // 4, p) xx = (y * y - 1) * pow(D * y * y + 1, -1, p) x = pow(xx, (p + 3) // 8, p) if (x * x - xx) % p != 0: x = (x * I) % p assert (x * x - xx) % p == 0 if x % 2 != 0: x = p - x return x def decode_point(self, compressed_point_le: int) -> G1Point: sign_bit, y_twisted = divmod(compressed_point_le, 2 ** (255)) x_twisted = self.xrecover(y_twisted) if x_twisted % 2 != sign_bit: x_twisted = self.curve.p - x_twisted x_weierstrass, y_weierstrass = self.curve.to_weierstrass(x_twisted, y_twisted) return G1Point(x_weierstrass, y_weierstrass, self.curve_id) @lru_cache(maxsize=None) def deserialize_R_A_h(self) -> tuple[G1Point, G1Point, int]: R = self.decode_point(self.Ry_twisted) A = self.decode_point(self.Py_twisted) preimage = ( self.Ry_twisted.to_bytes(32, "little") + self.Py_twisted.to_bytes(32, "little") + self.msg ) H_bytes = sha512(preimage).digest() H = int.from_bytes(H_bytes, "little") h = H % self.curve.n return R, A, h def is_valid(self) -> bool: s = self.s R, A, h = self.deserialize_R_A_h() G_neg = G1Point.get_nG(self.curve_id, -1) msm_result = G1Point.msm(points=[G_neg, A], scalars=[s, h]) should_be_inf = msm_result.add(R) if R.is_infinity() or A.is_infinity(): return False return should_be_inf.is_infinity() def serialize_with_hints( self, use_rust=False, as_str=False, prepend_public_key: bool = True ) -> list[int] | str: """Serialize the signature with hints for verification""" if use_rust: return garaga_rs.eddsa_calldata_builder( self.Ry_twisted, self.s, self.Py_twisted, self.msg, prepend_public_key, ) cd = self.serialize(prepend_public_key) R, A, h = self.deserialize_R_A_h() msm_calldata = garaga_rs.msm_calldata_builder( [ CURVES[self.curve_id.value].Gx, -CURVES[self.curve_id.value].Gy % self.curve.p, A.x, A.y, ], [self.s, h], self.curve_id.value, False, # include_points_and_scalars True, # serialize_as_pure_felt252_array ) cd.extend(msm_calldata) Rx_twisted, _ = self.curve.to_twistededwards(R.x, R.y) cd.extend(split_128(Rx_twisted)) # sqrt_Rx_hint Px_twisted, _ = self.curve.to_twistededwards(A.x, A.y) cd.extend(split_128(Px_twisted)) # sqrt_Px_hint if as_str: return "[{}]".format(", ".join(map(hex, cd))) return cd def __eq__(self, other) -> bool: if not isinstance(other, EdDSA25519Signature): return NotImplemented return ( self.Ry_twisted == other.Ry_twisted and self.s == other.s and self.Py_twisted == other.Py_twisted and self.msg == other.msg ) def __hash__(self) -> int: return hash((self.Ry_twisted, self.s, self.Py_twisted, self.msg)) if __name__ == "__main__": import json with open("tests/ed25519_test_vectors.json", "r") as f: test_vectors = json.load(f) for i, test_vector in enumerate(test_vectors): signature = EdDSA25519Signature.from_json(test_vector) assert signature.is_valid(), f"Signature {i} is invalid" ================================================ FILE: hydra/garaga/starknet/tests_and_calldata_generators/test_writer.py ================================================ import concurrent.futures import json import random import subprocess import time import garaga.modulo_circuit_structs as structs from garaga.curves import CURVES, CurveID, get_base_field from garaga.points import G1G2Pair, G1Point, G2Point from garaga.precompiled_circuits.multi_pairing_check import get_pairing_check_input from garaga.starknet.cli.utils import create_directory from garaga.starknet.tests_and_calldata_generators.mpcheck import MPCheckCalldataBuilder from garaga.starknet.tests_and_calldata_generators.msm import MSMCalldataBuilder from garaga.starknet.tests_and_calldata_generators.signatures import ( ECDSASignature, EdDSA25519Signature, RSA2048Signature, SchnorrSignature, ) TESTS_DIR = "src/src/tests/autogenerated" IGNORE_STR = "\n#[ignore] // Ignored for auto-benchmarks" def generate_pairing_test(curve_id, n_pairs, n_fixed_g2, include_m, seed): random.seed(seed) pairs, public_pair = get_pairing_check_input( curve_id=curve_id, n_pairs=n_pairs, include_m=include_m, return_pairs=True, ) builder = MPCheckCalldataBuilder( curve_id=curve_id, pairs=pairs, n_fixed_g2=n_fixed_g2, public_pair=public_pair, ) return builder.to_cairo_1_test() def generate_msm_test(curve_id, n_points, seed): random.seed(seed) builder = MSMCalldataBuilder( curve_id=curve_id, points=[G1Point.gen_random_point(curve_id) for _ in range(n_points)], scalars=[random.randint(0, CURVES[curve_id.value].n) for _ in range(n_points)], ) ignored = False if curve_id in [CurveID.SECP256K1, CurveID.SECP256R1] else True ignored = ignored or (False if n_points in [1, 2, 3] else True) return builder.to_cairo_1_test(ignored=ignored) def generate_msm_test_edge_cases(curve_id, n_points, seed): random.seed(seed) points = ( [G1Point.gen_random_point(curve_id) for _ in range(n_points - 1)] + [G1Point.infinity(curve_id)] + [G1Point.get_nG(curve_id, 1)] ) scalars = ( [0] + [random.randint(0, CURVES[curve_id.value].n) for _ in range(n_points - 1)] + [CURVES[curve_id.value].n - 1] ) builder = MSMCalldataBuilder(curve_id=curve_id, points=points, scalars=scalars) return builder.to_cairo_1_test( test_name=f"test_msm_{curve_id.name}_{n_points}P_edge_case", ignored=True ) def generate_tower_pairing_test(curve_id, n_pairs, seed): random.seed(seed) pairs: list[G1G2Pair] if n_pairs == 1: pairs = [ G1G2Pair( p=G1Point.get_nG(curve_id, 1), q=G2Point.get_nG(curve_id, 1), ) ] else: pairs, _ = get_pairing_check_input( curve_id=curve_id, n_pairs=n_pairs, return_pairs=True ) res = G1G2Pair.pair(pairs, curve_id) res = res.felt_coeffs e12t = structs.E12T(name="expected_result", elmts=res) i_s = list(range(n_pairs)) code = f""" #[test] fn test_tower_pairing_{curve_id.name}_{n_pairs}P() {{ let mut res:E12T = One::one(); """ for i, pair in enumerate(pairs): code += f""" {structs.G1PointCircuit.from_G1Point(f"p{i}", pair.p).serialize()} p{i}.assert_on_curve_excluding_infinity({curve_id.value}); {structs.G2PointCircuit.from_G2Point(f"q{i}", pair.q).serialize()} q{i}.assert_on_curve_excluding_infinity({curve_id.value}); let (tmp{i}) = miller_loop_{pair.p.curve_id.name.lower()}_tower(p{i}, q{i}); let (res) = run_{pair.p.curve_id.name.upper()}_E12T_MUL_circuit(tmp{i}, res);""" code += f""" let final = final_exp_{curve_id.name.lower()}_tower(res); assert_eq!(final, {e12t.serialize(raw=True)}); }} """ return code def generate_tower_final_exp_test(curve_id, seed): from garaga.hints.tower_backup import E12 random.seed(seed) field = get_base_field(curve_id) elmts = [field.random() for _ in range(12)] e12 = E12(elmts, curve_id.value) e12t = structs.E12T(name="input", elmts=elmts) expected = structs.E12T(name="expected", elmts=(e12.final_exp()).felt_coeffs) code = f""" #[test] fn test_tower_final_exp_{curve_id.name}() {{ {e12t.serialize()} let res = final_exp_{curve_id.name.lower()}_tower(input); assert_eq!(res, {expected.serialize(raw=True)}); }} """ return code def generate_schnorr_test(curve_id, seed): random.seed(seed) schnorr_sig: SchnorrSignature = SchnorrSignature.sample(curve_id) ignored = False if curve_id in [CurveID.SECP256K1] else True ignored_str = IGNORE_STR if ignored else "" code = f""" #[test]{ignored_str} fn test_schnorr_{curve_id.name}() {{ let mut sch_sig_with_hints_serialized = array!{schnorr_sig.serialize_with_hints(as_str=True)}.span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized).expect('FailToDeserializePk'); let sch_with_hints = Serde::::deserialize(ref sch_sig_with_hints_serialized).expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, {curve_id.value}); assert!(is_valid); }} """ return code def generate_ecdsa_test(curve_id, seed): random.seed(seed) ecdsa_sig: ECDSASignature = ECDSASignature.sample(curve_id) ignored = False if curve_id in [CurveID.SECP256K1, CurveID.SECP256R1] else True ignored_str = IGNORE_STR if ignored else "" code = f""" #[test]{ignored_str} fn test_ecdsa_{curve_id.name}() {{ let mut ecdsa_sig_with_hints_serialized = array!{ecdsa_sig.serialize_with_hints(as_str=True)}.span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized).expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized).expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, {curve_id.value}); assert!(is_valid); }} """ return code def write_test_file( file_path: str, header: str, test_generators: list, curve_ids: list, **kwargs ): """Write a test file with the given header and test generators. Args: file_path: Path to write the test file header: Module header with imports test_generators: List of (generator_fn, params) tuples curve_ids: List of curve IDs to generate tests for **kwargs: Additional arguments passed to generators """ create_directory(TESTS_DIR) with open(f"{TESTS_DIR}/{file_path}", "w") as f: f.write(header) with concurrent.futures.ProcessPoolExecutor() as executor: futures = [] for gen_fn, params in test_generators: for curve_id in curve_ids: for param in params: futures.append( executor.submit( gen_fn, curve_id, *param, kwargs.get("seed", 0) ) ) results = [future.result() for future in futures] for result in results: f.write(result) f.write("\n") def get_tower_pairing_config(): """Configuration for tower pairing tests""" header = """ use garaga::single_pairing_tower::{ miller_loop_bls12_381_tower, miller_loop_bn254_tower, final_exp_bls12_381_tower, final_exp_bn254_tower, }; use core::num::traits::One; use garaga::definitions::{u384, G1Point, G2Point, E12T}; use garaga::ec_ops::{G1PointImpl}; use garaga::ec_ops_g2::{G2PointImpl}; use garaga::circuits::tower_circuits::{ run_BN254_E12T_MUL_circuit, run_BLS12_381_E12T_MUL_circuit }; """ test_generators = [ (generate_tower_pairing_test, [(n,) for n in [1, 2, 3]]), (generate_tower_final_exp_test, [()]), ] curve_ids = [CurveID.BN254, CurveID.BLS12_381] return "tower_pairing_tests.cairo", header, test_generators, curve_ids def get_pairing_config(): """Configuration for pairing tests""" header = """ use garaga::pairing_check::{ multi_pairing_check_bn254_2P_2F, multi_pairing_check_bls12_381_2P_2F, MPCheckHintBN254, MPCheckHintBLS12_381, }; use garaga::definitions::{u288, u384, G1Point, G2Point, G2Line, E12D,G1G2Pair, MillerLoopResultScalingFactor}; use garaga::groth16::{ multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result, multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result, }; """ params = [(2, 2, False), (3, 2, True)] test_generators = [(generate_pairing_test, params)] curve_ids = [CurveID.BN254, CurveID.BLS12_381] return "pairing_tests.cairo", header, test_generators, curve_ids def get_msm_config(): """Configuration for MSM tests""" header = """ use garaga::ec_ops::msm_g1; use garaga::definitions::{G1Point, u384}; use garaga::core::circuit::u288IntoCircuitInputValue; """ msm_sizes = [1, 2, 3, 4, 10, 11, 12] edge_cases = [1, 2, 3] test_generators = [ (generate_msm_test, [(n,) for n in msm_sizes]), (generate_msm_test_edge_cases, [(n,) for n in edge_cases]), ] curve_ids = [ CurveID.BN254, CurveID.BLS12_381, CurveID.SECP256R1, CurveID.SECP256K1, CurveID.ED25519, CurveID.GRUMPKIN, ] return "msm_tests.cairo", header, test_generators, curve_ids def get_schnorr_config(): """Configuration for Schnorr signature tests""" header = """ use garaga::definitions::G1Point; use garaga::signatures::schnorr::{ SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash, }; use garaga::core::circuit::u288IntoCircuitInputValue; """ test_generators = [(generate_schnorr_test, [()])] curve_ids = [ CurveID.BN254, CurveID.BLS12_381, CurveID.SECP256R1, CurveID.SECP256K1, CurveID.ED25519, CurveID.GRUMPKIN, ] return "schnorr_tests.cairo", header, test_generators, curve_ids def get_ecdsa_config(): """Configuration for ECDSA signature tests""" header = """ use garaga::definitions::G1Point; use garaga::signatures::ecdsa::{ ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash, }; use garaga::core::circuit::u288IntoCircuitInputValue; """ test_generators = [(generate_ecdsa_test, [()])] curve_ids = [ CurveID.BN254, CurveID.BLS12_381, CurveID.SECP256R1, CurveID.SECP256K1, CurveID.ED25519, CurveID.GRUMPKIN, ] return "ecdsa_tests.cairo", header, test_generators, curve_ids def generate_eddsa_test(sig: EdDSA25519Signature, test_index: int) -> str: assert sig.is_valid() msg_bytes_len = len(sig.msg) ignored = False if msg_bytes_len in [0, 32, 64] else True ignored_str = IGNORE_STR if ignored else "" code = f""" #[test]{ignored_str} fn test_eddsa_{test_index}_{msg_bytes_len}B() {{ let mut eddsa_sig_with_hints_serialized = array!{sig.serialize_with_hints(as_str=True)}.span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized).expect('FailToDeserializePk'); let eddsa_with_hints = Serde::::deserialize(ref eddsa_sig_with_hints_serialized).expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); }} """ return code def generate_test(index, vector): signature = EdDSA25519Signature.from_json(vector) return generate_eddsa_test(signature, index) def generate_eddsa_test_file() -> str: """Configuration for EDDSA signature tests""" code = """ use garaga::signatures::eddsa_25519::{ EdDSASignatureWithHint, is_valid_eddsa_signature, }; """ with open("tests/ed25519_test_vectors.json", "r") as f: test_vectors = json.load(f) test_vectors = test_vectors[0:66:2] with concurrent.futures.ProcessPoolExecutor() as executor: futures = { executor.submit(generate_test, i, vec): i for i, vec in enumerate(test_vectors) } results = [None] * len(test_vectors) for future in concurrent.futures.as_completed(futures): index = futures[future] results[index] = future.result() for result in results: code += result return code def generate_rsa_test( signature: RSA2048Signature, seed: int, suffix: str, should_be_valid: bool ) -> str: assertion = "assert!(is_valid);" if should_be_valid else "assert!(!is_valid);" return f""" #[test] fn test_rsa2048_{suffix}_seed_{seed}() {{ let mut rsa_sig_with_hints_serialized = array!{signature.serialize_with_hints(as_str=True)}.span(); let public_key = Serde::::deserialize(ref rsa_sig_with_hints_serialized).expect('FailToDeserializePk'); let rsa_with_hints = Serde::::deserialize(ref rsa_sig_with_hints_serialized).expect('FailToDeserializeSig'); let is_valid = is_valid_rsa2048_signature_assuming_encoded_message(@rsa_with_hints, @public_key); {assertion} }} """ def generate_rsa_tests(seed: int) -> str: fixtures = [ (RSA2048Signature.sample(seed=seed), "positive", True), ( RSA2048Signature.tampered_expected_message_sample(seed=seed), "tampered_message", False, ), ( RSA2048Signature.tampered_limb_sample(seed=seed), "tampered_limb", False, ), ] code = "" for signature, suffix, should_be_valid in fixtures: code += generate_rsa_test( signature=signature, seed=seed, suffix=suffix, should_be_valid=should_be_valid, ) return code def generate_rsa_sha256_test( signature: "RSA2048Signature", message: bytes, seed: int, suffix: str, ) -> str: calldata_str = signature.serialize_sha256_with_hints( message=message, as_str=True, prepend_public_key=True ) return f""" #[test] fn test_rsa2048_sha256_{suffix}_seed_{seed}() {{ let mut rsa_sha256_serialized = array!{calldata_str}.span(); let public_key = Serde::::deserialize(ref rsa_sha256_serialized).expect('FailToDeserializePk'); let rsa_with_hints = Serde::::deserialize(ref rsa_sha256_serialized).expect('FailToDeserializeSig'); let message = Serde::::deserialize(ref rsa_sha256_serialized).expect('FailToDeserializeMsg'); let is_valid = is_valid_rsa2048_sha256_signature(@rsa_with_hints, @public_key, @message); assert!(is_valid); }} """ def generate_rsa_sha256_tests(seed: int) -> str: message = b"hello garaga" sig = RSA2048Signature.from_sha256_message(message, seed=seed) return generate_rsa_sha256_test(sig, message, seed, "positive") def generate_rsa_test_file() -> str: code = """ use core::serde::Serde; use garaga::signatures::rsa::{ RSA2048PublicKey, RSA2048SignatureWithHint, is_valid_rsa2048_signature_assuming_encoded_message, is_valid_rsa2048_sha256_signature, }; """ code += generate_rsa_tests(seed=0) code += generate_rsa_sha256_tests(seed=0) return code def write_all_tests(): """Generate all test files""" random.seed(0) # Generate each test file for config_fn in [ get_tower_pairing_config, get_pairing_config, get_msm_config, get_schnorr_config, get_ecdsa_config, ]: file_path, header, test_generators, curve_ids = config_fn() write_test_file(file_path, header, test_generators, curve_ids, seed=0) with open("src/src/tests/autogenerated/eddsa_tests.cairo", "w") as f: f.write(generate_eddsa_test_file()) with open("src/src/tests/autogenerated/rsa_tests.cairo", "w") as f: f.write(generate_rsa_test_file()) subprocess.run(["scarb", "fmt", f"{TESTS_DIR}"], check=True) if __name__ == "__main__": import time start = time.time() write_all_tests() end = time.time() print(f"Time taken to write all tests: {end - start} seconds") ================================================ FILE: pyproject.toml ================================================ [build-system] requires = ["maturin>=1.7,<2.0"] build-backend = "maturin" [project] name = "garaga" version = "1.1.0" requires-python = ">=3.10,<3.15" dependencies = [ "fastecdsa>=3.0.0", "sympy", "typer", "python-dotenv", "starknet-py-unbroken==0.29.0rc3", "requests", "filelock", ] description = "State-of-the-art Elliptic Curve operations and SNARKS verification for Cairo & Starknet 🐺." readme = "docs/PYPI_README.md" license = { text = "MIT" } authors = [ { name = "feltroidprime" }, { name = "Keep Starknet Strange Contributors" }, ] keywords = [ "elliptic-curves", "pairing", "zero-knowledge", "zk-snarks", "zero-knowledge-proofs", "zkp", "elliptic-curve-cryptography", "starks", "snarks", "cairo-lang", "starknet", "cryptography", "blockchain", ] classifiers = [ "Development Status :: 4 - Beta", "Intended Audience :: Developers", "Intended Audience :: Science/Research", "License :: OSI Approved :: MIT License", "Programming Language :: Python :: 3", "Programming Language :: Python :: 3.10", "Programming Language :: Python :: 3.11", "Programming Language :: Python :: 3.12", "Programming Language :: Python :: 3.13", "Programming Language :: Python :: 3.14", "Topic :: Security :: Cryptography", "Topic :: Scientific/Engineering :: Mathematics", "Topic :: Software Development :: Libraries :: Python Modules", "Operating System :: OS Independent", ] [project.urls] Homepage = "https://github.com/keep-starknet-strange/garaga" Repository = "https://github.com/keep-starknet-strange/garaga" Documentation = "https://garaga.gitbook.io/" "Bug Reports" = "https://github.com/keep-starknet-strange/garaga/issues" "Source Code" = "https://github.com/keep-starknet-strange/garaga" [project.optional-dependencies] dev = [ "maturin", "pytest", "pytest-asyncio", "pytest-xdist", "black>=26.3.1", "pre-commit", "inquirer", "pandas", "tabulate", "hypothesis", "rich", ] [project.scripts] garaga = "garaga.starknet.cli.starknet_cli:app" [tool.maturin] features = ["pyo3/extension-module"] manifest-path = "tools/garaga_rs/Cargo.toml" # configures rust package as a module under garaga module-name = "garaga.garaga_rs" # python source root must be under / python-source = "hydra" [tool.uv] # Override ecdsa pinned by crypto-cpp-py to fix high-severity security vulnerability override-dependencies = ["ecdsa>=0.19.0"] [tool.isort] profile = "black" [tool.pytest.ini_options] cache_dir = ".cargo/.pytest_cache" testpaths = ["tests/hydra"] # addopts = "--tb=short --showlocals" asyncio_default_fixture_loop_scope = "function" # Explicitly set the loop scope [tool.black] line-length = 88 target-version = ['py310', 'py311', 'py312', 'py313'] include = '\.pyi?$' extend-exclude = ''' /( # directories \.eggs | \.git | \.hg | \.mypy_cache | \.tox | \.venv | \venv | build | dist )/ ''' ================================================ FILE: src/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/Scarb.toml ================================================ [package] name = "garaga" version = "1.1.0" edition = "2024_07" licence = "MIT" keywords = [ "zk", "snarks", "curve", "pairing", "groth16", "plonk", "bls", "elliptic", "signature", ] description = "State-of-the-art Elliptic Curve operations and SNARKS verification for Cairo & Starknet" readme = "../README.md" repository = "https://github.com/keep-starknet-strange/garaga" authors = ["feltroidprime", "Keep Starknet Strange Contributors"] documentation = "https://garaga.gitbook.io/garaga/" # See more keys and their definitions at https://docs.swmansion.com/scarb/docs/reference/manifest.html [features] full = [] [dependencies] corelib_imports = { path = "corelib_imports", version = "0.1.3" } starknet = "2.16.1" [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" #cairo_test = "2.16.1" cairo_execute = "2.16.1" [scripts] test = "snforge test -p garaga --include-ignored" ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/Scarb.toml ================================================ # Generated by Garaga version 1.1.0 [package] name = "groth16_example_bls12_381" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../../../" } starknet = "2.16.1" [cairo] sierra-replace-ids = false inlining-strategy = 2 [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/src/groth16_verifier.cairo ================================================ // Generated by Garaga version 1.1.0 use super::groth16_verifier_constants::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; #[starknet::interface] pub trait IGroth16VerifierBLS12_381 { fn verify_groth16_proof_bls12_381( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod Groth16VerifierBLS12_381 { use garaga::definitions::{G1G2Pair, G1Point}; use garaga::ec_ops::{G1PointTrait, ec_safe_add}; use garaga::groth16::{ Groth16ProofRawTrait, multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result, }; use garaga::utils::calldata::deserialize_full_proof_with_hints_bls12_381; use starknet::SyscallResultTrait; use super::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; const ECIP_OPS_CLASS_HASH: felt252 = 0x396d5915ecf475aab117bb25a0272b261e9e25ffe1c0ce05a51a3f77489c89e; #[storage] struct Storage {} #[abi(embed_v0)] impl IGroth16VerifierBLS12_381 of super::IGroth16VerifierBLS12_381 { fn verify_groth16_proof_bls12_381( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let fph = deserialize_full_proof_with_hints_bls12_381(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.raw.check_proof_points(1); let ic = ic.span(); let vk_x: G1Point = match ic.len() { 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => { // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); Serde::serialize(@groth16_proof.public_inputs, ref msm_calldata); // Complete with the curve indentifier (1 for BLS12_381): msm_calldata.append(1); // Add the hint array. for x in msm_hint { msm_calldata.append(*x); } // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span(), ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), 1, ) }, }; // Perform the pairing check. let check = multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: vk.gamma_g2 }, G1G2Pair { p: groth16_proof.raw.c, q: vk.delta_g2 }, G1G2Pair { p: groth16_proof.raw.a.negate(1), q: groth16_proof.raw.b }, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(groth16_proof.public_inputs), Result::Err(error) => Result::Err(error), } } } } ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/src/groth16_verifier_constants.cairo ================================================ // Generated by Garaga version 1.1.0 use garaga::definitions::{E12D, G1Point, G2Line, G2Point, u384}; use garaga::groth16::Groth16VerifyingKey; pub const N_PUBLIC_INPUTS: usize = 1; pub const vk: Groth16VerifyingKey = Groth16VerifyingKey { alpha_beta_miller_loop_result: E12D { w0: u384 { limb0: 0x90d1a47263d9c179e9d6bab3, limb1: 0xc8f52b7ac4908e42515e61a6, limb2: 0x85c60896512fc21fc50ce238, limb3: 0x15bb2157a1b9aab29d66c644, }, w1: u384 { limb0: 0xb3e77acb0d776ee38973b578, limb1: 0x7290c49d0303a7a719325387, limb2: 0x3104f09f1439bbd9b6e47310, limb3: 0x1794c7df23dbcfd21f7c96f5, }, w2: u384 { limb0: 0xd0ccdf6e1de037c5f25dbd53, limb1: 0x254a0c8d3849192e33a21665, limb2: 0xcc0375e474dc85925319c5ad, limb3: 0x59163bc09c3bb5cd5864b34, }, w3: u384 { limb0: 0x42951c5be1c30dd1f90a8da3, limb1: 0xffa3bb5d4cc66b3c5c927fe8, limb2: 0xb2bef79be9fc2df478672961, limb3: 0x13b08e1d6ece19818bc96ea9, }, w4: u384 { limb0: 0x93fd3339f961a2b9c29235bc, limb1: 0xf9bbad7b2c116dfe3ed68c7a, limb2: 0xbd2f1d7614ffe6107af3312d, limb3: 0x565882562afe825ad18d630, }, w5: u384 { limb0: 0xf8e9d91fd573068e500fe8cb, limb1: 0xc02aff1aead5aafc095b5d00, limb2: 0xd46507dd50d8e1e3519eab6d, limb3: 0x13644a50e3d92f7cb2062999, }, w6: u384 { limb0: 0x79f2b3fe166cf2dd0d2edd42, limb1: 0xee1d6de706ac7841d7ad70d1, limb2: 0x8eab5234da247c344e074188, limb3: 0x11a6213d5e5c30e24cbf89bc, }, w7: u384 { limb0: 0x2ce3e653f58dd851f1b19549, limb1: 0x4718d317cb6aa672d98ec0d0, limb2: 0x9ba7f0c53686e01b4ad95d5, limb3: 0x675ea9600256572394eb514, }, w8: u384 { limb0: 0x23db0a4c6695a271a863a4d0, limb1: 0xd6db4129528086db9190b64e, limb2: 0xd130bf6380241b158fecfd71, limb3: 0xa849cb6abd26359866b2ec8, }, w9: u384 { limb0: 0x60b534cf939afce26ebdf812, limb1: 0x8c24d81eb0180ec2a6cf0f34, limb2: 0x82a57803b293e76911f92c72, limb3: 0xc18dabb70953283ac0831cb, }, w10: u384 { limb0: 0xf4e4997640a0e73c8ced7b36, limb1: 0x81b60a120c6ac55184b13431, limb2: 0x12a9b15b12fddd8e7a1c3fa3, limb3: 0x6b3db04d04875ece12b9ff5, }, w11: u384 { limb0: 0x12e51658ef6c7052999e66af, limb1: 0x9549543304b8f59e1248a434, limb2: 0x52afd8a6dd047073d383da00, limb3: 0x4ded7b056b1316dac6713a6, }, }, gamma_g2: G2Point { x0: u384 { limb0: 0xaa65cdf007aef54c6f623dde, limb1: 0x221d9fa6582f8ab41f299a1d, limb2: 0xc274f8bcf99c710a010e41a0, limb3: 0xdd0d7c6d60ac00708ff7db2, }, x1: u384 { limb0: 0x734de87c275c5ff8648ec130, limb1: 0xee8326798aab2bfea23775cc, limb2: 0x451384c060e8865aff71dbef, limb3: 0x604b708bc781ae38a361b93, }, y0: u384 { limb0: 0xa6a2e609a74c6461dbb15b12, limb1: 0x1b15cfdecac55c2f6881eaa3, limb2: 0x1c77b46d0593da85473e42c4, limb3: 0x1541ecff208d5a5cd2d55296, }, y1: u384 { limb0: 0x699092f65f774234b7f31840, limb1: 0x4c6c5689af7c6b120e3ab986, limb2: 0x6b8b64d4ead6109ba5c739e4, limb3: 0x108c95049535bcd1117cdbdf, }, }, delta_g2: G2Point { x0: u384 { limb0: 0x6295df8b9ffbb9f638117fb4, limb1: 0xd83ce7d5ca555ae1cc54e530, limb2: 0xd0b71d6edfa740f665e34c84, limb3: 0x18b219a74108de96a9519a60, }, x1: u384 { limb0: 0x7e3c781dba158e67256dc98e, limb1: 0xa144ffba7defff7d45169d6f, limb2: 0x5f5d374324ad0e72809aeed, limb3: 0xe3e7a8c90ba5b5e266fea71, }, y0: u384 { limb0: 0x4573d43941a95edd7fc0b3c, limb1: 0xa5afe44806a147a2c04a80ae, limb2: 0x446f45ca171a1edf9abe76b8, limb3: 0x11b12761f310cbe4ba3e1ded, }, y1: u384 { limb0: 0x1af32f6be0d4fbaaa3a16480, limb1: 0x8a1e0e97cea1801e094fdc7, limb2: 0x12fe3d86972bfca288dc7d9b, limb3: 0x11ece09d0b6f1a1ea16238a5, }, }, }; pub const ic: [G1Point; 2] = [ G1Point { x: u384 { limb0: 0xaea925952b1d5dcc848e1107, limb1: 0x1d3926283f7823c830469f8d, limb2: 0x855a100cf099f5733048337, limb3: 0x126fbe91d07c71cd11847edc, }, y: u384 { limb0: 0xdffe1c953fd7a62db3ea0f7d, limb1: 0xe81081ed3027415c05028dc0, limb2: 0x8382ca23441bb4a34775829b, limb3: 0x11d4302c0095dfb2bcb31a44, }, }, G1Point { x: u384 { limb0: 0x46c87cd685c7c1d6fdcd1e9b, limb1: 0x2f62c85bb229d8c136b83c08, limb2: 0x5447e4279f17852eabd158fa, limb3: 0x17eb504b7c7c4fcec2570d70, }, y: u384 { limb0: 0x1af88a58b9173f40990d461d, limb1: 0xed8dc9e752c0f5ec50f0bf39, limb2: 0x620cad3e73faf12d0844d15f, limb3: 0x682ec2d49889aa39ae6f079, }, }, ]; pub const precomputed_lines: [G2Line; 136] = [ G2Line { r0a0: u384 { limb0: 0x306be1de1b04d2624e640455, limb1: 0xf2a2185fd41fca781bc97f37, limb2: 0x61bc1a3296c8468ccbfd0f00, limb3: 0xe34ab79b1474233817e576e, }, r0a1: u384 { limb0: 0xb2d501153392bd8774a608d8, limb1: 0x8bf8261f30c2770732ec1803, limb2: 0x54badbe21461d0daf83afabe, limb3: 0xf07ba4034e02ff1891990ed, }, r1a0: u384 { limb0: 0x32ea0796aef63117c6e0e6a1, limb1: 0xa45dad1f58021d08480cc168, limb2: 0xccdc578cc13456d86cd47734, limb3: 0xfd13ef0a99a6b73d52ca7b9, }, r1a1: u384 { limb0: 0xb3a2e4a310abfbef796714, limb1: 0xa555ba99515a0a5e2d59908c, limb2: 0x165b6bdd81d359126278cb48, limb3: 0xb4aa52b7c5b272cbf4fc038, }, }, G2Line { r0a0: u384 { limb0: 0x1b91ee6736aeabe4b5e40ccb, limb1: 0xd1e0bdffe69e623fa4977b7e, limb2: 0x3a38a366dca6ed3ac394edae, limb3: 0x17d86f3a6eadac41e32f85b, }, r0a1: u384 { limb0: 0x85526a142f1b602083c8d0e9, limb1: 0x9de43cde6d77997ea6be8502, limb2: 0x26f9e86d04c4567b4ce35680, limb3: 0x1426d177654bf0d7517048d4, }, r1a0: u384 { limb0: 0x47561557466bbd16edc89e91, limb1: 0xa569496f4dc6bd96e4917912, limb2: 0x8b21592e524eb1bc65bda550, limb3: 0x167eed299c6bd0497e52cbb8, }, r1a1: u384 { limb0: 0xa40e65e562f01cc7e697d44e, limb1: 0xf7e3075bffcb46efc4c7de85, limb2: 0x4837f7e7cd36e2ed7747ed42, limb3: 0x1401c25696479939c853129, }, }, G2Line { r0a0: u384 { limb0: 0xcf09df55ea243c0b5d27ea95, limb1: 0xa5c3c859310e651108ba35f9, limb2: 0xe22d5367257f2b7b07101881, limb3: 0x146fecb4aca9ed26211e6a1c, }, r0a1: u384 { limb0: 0xfb9b1aa00ba2314b499e9ad2, limb1: 0x25885d4aae86a2ee87249374, limb2: 0xebecd6bf5c617aba6840aa01, limb3: 0x463f1553e899e2adf4279f9, }, r1a0: u384 { limb0: 0x1aa0f311fb5027f4834da079, limb1: 0x7b26ff99d902997df1825c8c, limb2: 0xebc6228c9418dc5eebbf53b1, limb3: 0xe10e27eb7e14d9257ef5dc5, }, r1a1: u384 { limb0: 0xc89a8f1c1c6ae8707f8fa8fc, limb1: 0xb45e86fe1c988a090beb870d, limb2: 0x9b645529fd4c880478be7051, limb3: 0x173c6c7f6fa56c3d1f1961b3, }, }, G2Line { r0a0: u384 { limb0: 0xb58b9ab9d1892dd4c5543b36, limb1: 0xe3c36bb4c20608a534fd590b, limb2: 0xed0ee74781e598434a0b96ab, limb3: 0x6b2aa02643ac8ef76d9b262, }, r0a1: u384 { limb0: 0x3a1fbee97340bbd138b8ebb4, limb1: 0xfc724611032db25419c64333, limb2: 0x7b496eddcf55a6c83d880e5b, limb3: 0xdd344cd4cc6c1be8929497a, }, r1a0: u384 { limb0: 0xef38cfa96ccac703a2060cc1, limb1: 0x2f8106247ed8427f6104427, limb2: 0xa2e886264a53734039a28245, limb3: 0xfd9424926115c1f549c9fe6, }, r1a1: u384 { limb0: 0xef853c4c4bccb3964c46149c, limb1: 0x739746bb23813b366d6900e, limb2: 0xd46eb42d09315fa477d9661, limb3: 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0x77b5e69dffa452e710da671, }, r0a1: u384 { limb0: 0xfd475bb5cabda2ca66b8a9a2, limb1: 0xa2f483666599b3f38616a265, limb2: 0x2f50c3e13b47f9f013b110ae, limb3: 0xb90546cd4c81153ae816b28, }, r1a0: u384 { limb0: 0x5bb0532b9b631f6226209db4, limb1: 0x8af30847f24064aaea92f634, limb2: 0x63fc234f0211d3a48fd3794a, limb3: 0x186be21ff49b8619293b08a0, }, r1a1: u384 { limb0: 0x7257ceb68e224443379d4f3d, limb1: 0x832ff2fc38659e439e40d450, limb2: 0x2bc2eeb8acd74c13b35c613b, limb3: 0xc40014d71cb257fadad0453, }, }, ]; ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/src/lib.cairo ================================================ // Generated by Garaga version 1.1.0 pub mod groth16_verifier; pub mod groth16_verifier_constants; ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/tests/proof_calldata.txt ================================================ 0xfbf04de06661c03aa78411a8 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0x1533be839a58149180a81c12 0x160a7d8d9832c16f08b8ea60 0x5fdfbba9f25307249e94beb7 0x4e52f95f59a83567e2e94c4d 0x98c9e626e75dfbe9619b9ba8 0x1669b19cbacfd3d568389242 0x5ffc0d14a5f140e71dd32dde840adccbaa7b219338835c93b6f07ca32e2d8f2 0xc 0xa32ee30c3d029d864507394d 0xc3fd32fb148ef096d056a4cf 0xd6057025fd62f50ff367018b 0x14f5f43eaf8f65a0744c89ef 0x9fd18c27cba0985972317e8f 0xda8029593c35f82b1babf4a5 0x19d691e8ebf33b62a07dcc5e 0xc550a2b8af74ec248ef6142 0x10000000000000000c1ade26beca39798 0x94d2c61646aaca1 0x100000000000000002a7388403897adaf 0x100000000000000005c8fa4951f2ad290 ================================================ FILE: src/contracts/autogenerated/groth16_example_bls12_381/tests/test_contract.cairo ================================================ // Generated by Garaga version 1.1.0 //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use groth16_example_bls12_381::groth16_verifier::{ IGroth16VerifierBLS12_381DispatcherTrait, IGroth16VerifierBLS12_381LibraryDispatcher, }; use snforge_std::fs::{FileTrait, read_txt}; use snforge_std::{DeclareResultTrait, declare}; use starknet::ClassHash; /// Declare the Groth16VerifierBLS12_381 contract for testing. /// /// This function declares a new instance of the Groth16VerifierBLS12_381 contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("Groth16VerifierBLS12_381"); /// let dispatcher = IGroth16VerifierBLS12_381LibraryDispatcher { class_hash }; /// ``` fn declare_contract(name: ByteArray) -> ClassHash { let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash } /// Test the verification function verify_groth16_proof_bls12_381 with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by /// the garaga team - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system groth16 /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", block_tag: latest)] fn test_verify_groth16_proof_bls12_381() { // Step 1: Declare the verification contract let class_hash = declare_contract("Groth16VerifierBLS12_381"); let dispatcher = IGroth16VerifierBLS12_381LibraryDispatcher { class_hash }; // Step 2: Load the proof fixture generated by the script // This file contains the groth16 proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's verify_groth16_proof_bls12_381 function with the loaded proof data let result = dispatcher.verify_groth16_proof_bls12_381(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here } ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/Scarb.toml ================================================ # Generated by Garaga version 1.1.0 [package] name = "groth16_example_bn254" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../../../" } starknet = "2.16.1" [cairo] sierra-replace-ids = false inlining-strategy = 2 [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/src/groth16_verifier.cairo ================================================ // Generated by Garaga version 1.1.0 use super::groth16_verifier_constants::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; #[starknet::interface] pub trait IGroth16VerifierBN254 { fn verify_groth16_proof_bn254( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod Groth16VerifierBN254 { use garaga::definitions::{G1G2Pair, G1Point}; use garaga::ec_ops::{G1PointTrait, ec_safe_add}; use garaga::groth16::{ Groth16ProofRawTrait, multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result, }; use garaga::utils::calldata::deserialize_full_proof_with_hints_bn254; use starknet::SyscallResultTrait; use super::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; const ECIP_OPS_CLASS_HASH: felt252 = 0x396d5915ecf475aab117bb25a0272b261e9e25ffe1c0ce05a51a3f77489c89e; #[storage] struct Storage {} #[abi(embed_v0)] impl IGroth16VerifierBN254 of super::IGroth16VerifierBN254 { fn verify_groth16_proof_bn254( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let fph = deserialize_full_proof_with_hints_bn254(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.raw.check_proof_points(0); let ic = ic.span(); let vk_x: G1Point = match ic.len() { 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => { // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); Serde::serialize(@groth16_proof.public_inputs, ref msm_calldata); // Complete with the curve indentifier (0 for BN254): msm_calldata.append(0); // Add the hint array. for x in msm_hint { msm_calldata.append(*x); } // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span(), ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), 0, ) }, }; // Perform the pairing check. let check = multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: vk.gamma_g2 }, G1G2Pair { p: groth16_proof.raw.c, q: vk.delta_g2 }, G1G2Pair { p: groth16_proof.raw.a.negate(0), q: groth16_proof.raw.b }, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(groth16_proof.public_inputs), Result::Err(error) => Result::Err(error), } } } } ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/src/groth16_verifier_constants.cairo ================================================ // Generated by Garaga version 1.1.0 use garaga::definitions::{E12D, G1Point, G2Line, G2Point, u288, u384}; use garaga::groth16::Groth16VerifyingKey; pub const N_PUBLIC_INPUTS: usize = 1; pub const vk: Groth16VerifyingKey = Groth16VerifyingKey { alpha_beta_miller_loop_result: E12D { w0: u288 { limb0: 0x11a6ad63c049a0774b1f8d69, limb1: 0xf7fca2c91020c7f53e2beb4c, limb2: 0x2e0acf1407b6b19c, }, w1: u288 { limb0: 0xd4938178efd479c0f958db9a, limb1: 0x84c3c18b6204eec59b85778f, limb2: 0x73ca31ecae7d32e, }, w2: u288 { limb0: 0x72743eb58616c0e417c4aba3, limb1: 0xb4ac27c376d51ed710fba137, limb2: 0x1acbdf1cb7d3466, }, w3: u288 { limb0: 0x93acd00474adbe5d51facd39, limb1: 0xa9189ccc1f5ce888cac4749a, limb2: 0x1ae9e30c3e513da0, }, w4: u288 { limb0: 0x84916f4f6a4f628bdf86d2b1, limb1: 0x77860ba9a989de43f309fc67, limb2: 0x269bcad1c0ce254e, }, w5: u288 { limb0: 0x7138ef04bab92f97355093e0, limb1: 0x66da4e6149cb9e2d53894518, limb2: 0x39d844bb6b441d8, }, w6: u288 { limb0: 0x9e481d49fcbb14d72c8f3700, limb1: 0x582640a337edb441a9237eb0, limb2: 0x6ac2149bd480805, }, w7: u288 { limb0: 0xd952d96fdf1298e24de9a8ec, limb1: 0x6bde8fce1837818c1bb4c7d1, limb2: 0x173e64f406ad3079, }, w8: u288 { limb0: 0x7e3e90ad41525ee5ab604479, limb1: 0xc5868b5aaa79f89f3b0d38c6, limb2: 0xb2c95b493361fb1, }, w9: u288 { limb0: 0xf35cf1f086baf1880d2a6e2b, limb1: 0x500d80de07da8e3ee9d854b7, limb2: 0x59e0bc51eb3a8b1, }, w10: u288 { limb0: 0x84fbc02aadbc9e8ee74e83f7, limb1: 0x57960adc97b6def2fdd0c8a2, limb2: 0x17ef7d97b124dce5, }, w11: u288 { limb0: 0xdd2d75826bf4ec82eba0dcb5, limb1: 0x286e75e7626aa2c71f7ffc8e, limb2: 0xf330011992a685a, }, }, gamma_g2: G2Point { x0: u384 { limb0: 0x89e732f5f87195d15a4ce637, limb1: 0x884359c76cc9c6b81d289d33, limb2: 0x3541dacedd860ef, limb3: 0x0, }, x1: u384 { limb0: 0xe313e222b376d9a9da02f080, limb1: 0x272d9cc4aa2e71146c83c13b, limb2: 0x2eb7d1fa8416da97, limb3: 0x0, }, y0: u384 { limb0: 0xa7d48b949e86c8b00eef73f9, limb1: 0xefcb8bbb160b0f2ecb7cd98, limb2: 0x8dce093ad7f7fe2, limb3: 0x0, }, y1: u384 { limb0: 0xd917839a146ea15cd7493f1d, limb1: 0x6eb4af5910b954a713c49174, limb2: 0x29a4b793edc63974, limb3: 0x0, }, }, delta_g2: G2Point { x0: u384 { limb0: 0x63d786683ef471af4434acdc, limb1: 0x185580c9ee198f6cac8bc784, limb2: 0x34fc9ba8eba1e49, limb3: 0x0, }, x1: u384 { limb0: 0x161153d19ebc7f594246b9b0, limb1: 0x61912be284ecae3a3f0899bb, limb2: 0x17f115a16975c6f2, limb3: 0x0, }, y0: u384 { limb0: 0xb4dbc7294e1eacf59b3e2054, limb1: 0x31c92abab72ef0ed83a3c195, limb2: 0x17fd1ad43bbc8ef9, limb3: 0x0, }, y1: u384 { limb0: 0x55b6e98c187b34ca3e7cd1b, limb1: 0x6ff9481052ddb780a4cc43da, limb2: 0x1bd7d75bf918b676, limb3: 0x0, }, }, }; pub const ic: [G1Point; 2] = [ G1Point { x: u384 { limb0: 0x62587fa0f6c879156e7390bc, limb1: 0xc9da665a8bebfd01ce6489a4, limb2: 0x124e30bf4dff3ae9, limb3: 0x0, }, y: u384 { limb0: 0x50c0471724e1b022791c7532, limb1: 0x5e101dd2383fdc600dcb4a34, limb2: 0x1fdc3a96cea49b08, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0xedaa0ed100691cceb974c6a1, limb1: 0x26a8465790ba44ddb5716750, limb2: 0x164668f89d9d6c61, limb3: 0x0, }, y: u384 { limb0: 0xf3d9d0426a702f368be936da, limb1: 0x153290e7b5c8497412386c61, limb2: 0x1d9c7309625ec7cf, limb3: 0x0, }, }, ]; pub const precomputed_lines: [G2Line; 176] = [ G2Line { r0a0: u288 { limb0: 0x6262802b3d1fc57f02eb7de7, limb1: 0x90ccab72e89abbdc16280011, limb2: 0x178e51f74b0542e7, }, r0a1: u288 { limb0: 0x12a071ce64f150102f094209, limb1: 0xaaad51a68888c9f4d366eb85, limb2: 0xb854c3062c6dca4, }, r1a0: u288 { limb0: 0x88c793e1f884996295be7f4b, limb1: 0x9801cbb1add70980a565d93, limb2: 0x7f1a23af3e93b10, }, r1a1: u288 { limb0: 0x16b6ccc140737723f6fbf23c, limb1: 0xfaa6476d81d4fb40a38fa84e, limb2: 0x1d370360026ceef, }, }, G2Line { r0a0: u288 { limb0: 0x6768b1b65ac701242d58a4d5, limb1: 0x9a21b14a1117318e6e93346c, limb2: 0x28206643cf01adb6, }, r0a1: u288 { limb0: 0xc733c609365fab81f5bebf8c, limb1: 0xe7dba9325253668b9de809ab, limb2: 0x1e2aed8a72758ae3, }, r1a0: u288 { limb0: 0x95ec7d05aa1f4c5b117cc3df, limb1: 0xc9473775e0fd4d6797d4fe54, limb2: 0x28418cb32e9a4478, }, r1a1: u288 { limb0: 0x2a17416676088b3ed523bc76, limb1: 0xa7a7189cf0cb6f593da6398d, limb2: 0x1646a797175de826, }, }, G2Line { r0a0: u288 { limb0: 0x60f4a61ff00c697d5917f60, limb1: 0x27839a4398e69c8181596a80, limb2: 0x18d5fc7b962c5d42, }, r0a1: u288 { limb0: 0x55d158bed72f3c06a973bb3e, limb1: 0xda2f40ff8f88e68c41a7f0c, limb2: 0x24df02427e6ac385, }, r1a0: u288 { limb0: 0xdfaa36ab439bf2b442be7dfc, limb1: 0xaed028fb66a3e7c58d2b0cfd, limb2: 0x2872ac37ed486519, }, r1a1: u288 { limb0: 0x51bafdcbfbad14f2e1810b0b, limb1: 0xbda9fe48ffac5d1cf3f1c243, limb2: 0x2e90de3ce10ad139, }, }, G2Line { r0a0: u288 { limb0: 0x22f06d243ec31a24265558f6, limb1: 0x144f71a68e6e295284eaa624, limb2: 0xb114d08d4730af8, }, r0a1: u288 { limb0: 0xd3a0ee47077b6225045c67ee, limb1: 0xeec7cbf282c77e03df828f62, limb2: 0xbe64d352adee5f0, }, r1a0: u288 { limb0: 0xc7ec19dad21e785ffc755ad, limb1: 0xd24141743526f183d2654043, limb2: 0x1988f55b31c4faf3, }, r1a1: u288 { limb0: 0x994cab0255bb4272f95c3e23, limb1: 0xd922c9add52c749a87cf7c07, limb2: 0xaa4d57bef928d58, }, }, G2Line { r0a0: u288 { limb0: 0x10918d6e1598af2ab245872, limb1: 0x1e2e946c706a26cf28ee3625, limb2: 0x843e82f122ff273, }, r0a1: u288 { limb0: 0xa13e048405c0e094e2be3dbb, limb1: 0xd0749c842f2df1d1f99960e5, limb2: 0x123960e86ebc1545, }, r1a0: u288 { limb0: 0xd2854d8792013fbbc7003968, limb1: 0xef090e40a0840af5ffac6c3c, limb2: 0x822c1bfb2975bb0, }, r1a1: u288 { limb0: 0x3e5a8926c61800d8035940d1, limb1: 0x10a92d1990b5e90459db3104, limb2: 0x1a1da6dbc9d3b803, }, }, G2Line { r0a0: u288 { limb0: 0xf3c1aff57ebd4252b1ee0a92, limb1: 0x4dbf6eac239e2fd65d64b8f7, limb2: 0x26d1f994835b7b47, }, r0a1: u288 { limb0: 0x345e6aaef5a543714baced, limb1: 0xb490ac8096315947ee617410, limb2: 0x1a09bb8870da1b8a, }, r1a0: u288 { limb0: 0x5ebf58b2e5dd76b36593db9f, limb1: 0x8fa5c6ffbd16bb8a189499b2, limb2: 0xaf4be2ac3e90ead, }, r1a1: u288 { limb0: 0xd4b8cde758e0d235326f7919, limb1: 0xcd650faf49b3ee058023c216, limb2: 0x1c00cc9bd40f552b, }, }, G2Line { r0a0: u288 { limb0: 0xfc81a9267fe02a0e01e5690e, limb1: 0x935b7be9ed04f236f8ccb6d3, limb2: 0xd21be991cebbac7, }, r0a1: u288 { limb0: 0x823e612788adf8af694cadf8, limb1: 0x28ffb411c649c749b8b2ab3f, limb2: 0x29f85195d5ae6cb3, }, r1a0: u288 { limb0: 0xa4e79c63454447ad586868ed, limb1: 0x1d25998e1dee245a7a740dfd, limb2: 0x312f28354b440eb, }, r1a1: u288 { limb0: 0x230c5675e4713e459ecf6ee7, limb1: 0xf23579a5477f2fded9e59a95, limb2: 0x23effe3fb162cfa9, }, }, G2Line { r0a0: u288 { limb0: 0x6938a36b06b59bb433023aa9, limb1: 0x9f733207d38e4c21c5f938d4, limb2: 0xb694e7fb696f425, }, r0a1: u288 { limb0: 0x1fb7151f69662f3282addefa, limb1: 0x73b463adbed2a2c44be9521d, limb2: 0x1ce3d8bc49dd6f3f, }, r1a0: u288 { limb0: 0xcdefacedca9cea69a67218ef, limb1: 0x2a61c39d6c9e8df657e11fa2, limb2: 0x287b08ea40db8edf, }, r1a1: u288 { limb0: 0xf3493b34c974473567e0bfd, limb1: 0x62ec80dec81fe20e56185f3d, limb2: 0x2a9d8912a369f0fc, }, }, G2Line { r0a0: u288 { limb0: 0xb7482cd3a64ad7c6972ce18, limb1: 0xc612ec6a27ef894c2448e7e, limb2: 0xb0a181c0bc5bb35, }, r0a1: u288 { limb0: 0x77fd6133c7186e2a51fdfe8b, limb1: 0xb6d8557c94e885365cd1284f, limb2: 0x2807238c4095ab2e, }, r1a0: u288 { limb0: 0xac2bf429c889f4e4fca7ad87, limb1: 0x4e2138d3a53fab48b9372da0, limb2: 0x661b199c593f990, }, r1a1: u288 { limb0: 0x17ad71412ec95d2e450e4a9a, limb1: 0x5a390094f598fbc1c73ffc6f, limb2: 0x1745ca0ad68deb3c, }, }, G2Line { r0a0: u288 { limb0: 0x792e91102d6015db651264a5, limb1: 0xef1739e0f3140e7dae1b9f26, limb2: 0x2c68c775b43aa438, }, r0a1: u288 { limb0: 0x2d480c09009f63ff03bacd7e, limb1: 0xe49d79a774b60104278749bb, limb2: 0x28dd05053808f291, }, r1a0: u288 { limb0: 0xa4f235af16d6b1aa9cb935e0, limb1: 0x3356bbf421edd3b119a977a, limb2: 0x2c3a3e6fb5bf407a, }, r1a1: u288 { limb0: 0x475304a1c01b032aae98253d, limb1: 0xc07800c8acc177d31257f8a7, limb2: 0x2c17966ecef6d358, }, }, G2Line { r0a0: u288 { limb0: 0xe9cd661691f7215396894f0f, limb1: 0x9e3c0f429f703e40f5baa9bc, limb2: 0x1b94de4f8b072262, }, r0a1: u288 { limb0: 0xb2328b5f060b47983ead044a, limb1: 0x5d6772c45ac19b49a05cbb0b, limb2: 0xf6f282c18f98d7c, }, r1a0: u288 { limb0: 0x10f6b52bee174dc609820448, limb1: 0xa4d84cb409d798e1dc4d0880, limb2: 0x1e5bc83da6436d50, }, r1a1: u288 { limb0: 0xce182a96f56ced121091e41b, limb1: 0x8800263a87f78d7ab82d3e71, limb2: 0x2640778c4c20679b, }, }, G2Line { r0a0: u288 { limb0: 0xb78d8e331f9fde95d8762cbe, limb1: 0xe50fc6532130dcab69ccd2f3, limb2: 0x1c5ad86495e84014, }, r0a1: u288 { limb0: 0xfe7268e3ed4b6b97899984c4, limb1: 0xf2e63f6c60064bc7fb5fd561, limb2: 0x9717b3891610a6b, }, r1a0: u288 { limb0: 0xb6a3d0ad2be4cf8a6d7a4932, limb1: 0xf368ce713db6a7c85ce253e7, limb2: 0x11fb9d13419437db, }, r1a1: u288 { limb0: 0x6c0e91e32102a27c6bc0f117, limb1: 0x1580942374bdb287e34d50e8, limb2: 0x25451806c34da2eb, }, }, G2Line { r0a0: u288 { limb0: 0xecf4b439dcb55cb7cd17c938, limb1: 0xaa30677da06e04007bc10783, limb2: 0x5acf050d824c550, }, r0a1: u288 { limb0: 0xfdadd2fba222755a97b93bd8, limb1: 0xc5f72c5874f13b63850c7e3, limb2: 0x8d6e33876937270, }, r1a0: u288 { limb0: 0x48b70ead9b67d481e7fbac7c, limb1: 0xeea576a4020c901099fb5796, limb2: 0xe89161f969f758d, }, r1a1: u288 { limb0: 0x8081483546fdaca3e803ae13, limb1: 0x7b29b6041c0844fb7bd3c828, limb2: 0x840a11945bdaf61, }, }, G2Line { r0a0: u288 { limb0: 0x5257173c58d9ac477f4e7362, limb1: 0x4ac0a4b0a604dc11701ec7be, limb2: 0x2ced1a344a191870, }, r0a1: u288 { limb0: 0xced9cba631d33b433f4c02b7, limb1: 0xc83a4a272ab8c01b6631fd59, limb2: 0x201561c61f1309c6, }, r1a0: u288 { limb0: 0x6c107fe09b4144f1c2e218b4, limb1: 0x6bedd36ccbfb5eb21e3052b5, limb2: 0x1710d637ed85f3f4, }, r1a1: u288 { limb0: 0x2dbf59bd81c858f20f9a2c22, limb1: 0x538891d36da9558f005eaa18, limb2: 0x2e047a78332f57a7, }, }, G2Line { r0a0: u288 { limb0: 0x87ebd70984bc04919fc9986, limb1: 0x49e5baa3bf84014bbfa4b343, limb2: 0x13c681e8a87b09d5, }, r0a1: u288 { limb0: 0xc7ba9d524130fff410f86354, limb1: 0xe56c32754857a3eadf92430e, limb2: 0x12b61a869a91562d, }, r1a0: u288 { limb0: 0xcf43a1c9be7903f6823856c3, limb1: 0x17aa81a20cb8b6533b7e05ad, limb2: 0x8edd93c88eac470, }, r1a1: u288 { limb0: 0x61527058e2d37f7267e2d55b, limb1: 0x4133bd157d450dc27f32d457, limb2: 0x582ee28eaa58570, }, }, G2Line { r0a0: u288 { limb0: 0x8e35c54e5a8fc51ffe565808, limb1: 0x54a5c4c2ce68417d89a41927, limb2: 0x1bb192a0da69b4bc, }, r0a1: u288 { limb0: 0xb15a23caab89361c695304d, limb1: 0xa21ac5490dcc6ec31e532a00, limb2: 0x2c5d334f664f1db0, }, r1a0: u288 { limb0: 0x1513569aab675cc8a80d83b, limb1: 0x8823f86ca10c614200a888cd, limb2: 0x27e75cf5e6c5decb, }, r1a1: u288 { limb0: 0x7dfe801eafb39580b2591c53, limb1: 0x7ad779d2bc8b8960e97e8369, limb2: 0x2a2e897e4fcb8d03, }, }, G2Line { r0a0: u288 { limb0: 0xba5ea5187f76b5704defef65, limb1: 0x8a7319f0591a44264e9857c7, limb2: 0x2d9dd5412302fd6b, }, r0a1: u288 { limb0: 0xaa7e8dec15610116b7d0b0cf, limb1: 0xe5e0a55405629a2fe14bf3d5, limb2: 0x2dae2582a7c55627, }, r1a0: u288 { limb0: 0x303fd13168b5089e4e0e3fa2, limb1: 0xd1d646954006479380c9f8ab, limb2: 0x1b643b47405a9dd, }, r1a1: u288 { limb0: 0x893d761d04a60dae26f4e064, limb1: 0xf185cfd787972d2bed98ddf7, limb2: 0x27e2db3d67b8caa3, }, }, G2Line { r0a0: u288 { limb0: 0xb1fd301f8de9a4fdaa4a5688, limb1: 0x656432730487dbc9e9e29270, limb2: 0x17df9b19f2918abd, }, r0a1: u288 { limb0: 0x2d5832aab61dab3a5549a92, limb1: 0xe47839d4ca00888bb56afc4a, limb2: 0x3fe4c9d799a3bd1, }, r1a0: u288 { limb0: 0x2810fcc73bea01896cd75a0f, limb1: 0x2c92809424a97db06448759f, limb2: 0x123eff8f7259581a, }, r1a1: u288 { limb0: 0x601fdec3567703d1c3d34df0, limb1: 0x7f03a904345610b15ff1205a, limb2: 0x289705e3e298309a, }, }, G2Line { r0a0: u288 { limb0: 0xc16237e16f04d4855851266c, limb1: 0x216a15737a6b54352caee4fb, limb2: 0x2cb963083fceacfc, }, r0a1: u288 { limb0: 0x1d5728a99fc8a6b1501def7d, limb1: 0xc82efa12901500963bbfdfc1, limb2: 0x29472ad7813d3e51, }, r1a0: u288 { limb0: 0x4bc73fff7a02804f65a8b807, limb1: 0x55d252b720478bafee38f7e0, limb2: 0xb89e5290fecd5c4, }, r1a1: u288 { limb0: 0xcecce3e7e700ddfe8b57d681, limb1: 0x6ffd2dd49f2ff2ecf872f76b, limb2: 0x1834d8633ed7aa5e, }, }, G2Line { r0a0: u288 { limb0: 0x921d0a486c2af8e00aca15cf, limb1: 0xce5e704e01a8381a38da803c, limb2: 0x2a3b10f49d66db73, }, r0a1: u288 { limb0: 0x4d5fe5d5c9f584cffdde9b20, limb1: 0x694bbbada9b90b560fe95a28, limb2: 0x1f9131f7b839f971, }, r1a0: u288 { limb0: 0xb2a323906650185cccdc623c, limb1: 0x8643738b8d13209ced4a8401, limb2: 0x1afc7bd309bd2e6f, }, r1a1: u288 { limb0: 0x66a405a6925c6daf1121bfa8, limb1: 0xae0d46e02b0c767a8311def7, limb2: 0x1eac8613f1b73d0, }, }, G2Line { r0a0: u288 { limb0: 0xc0dc2ee8c1634b43c7c67a36, limb1: 0x44b5cda8cf434ecc7f4c6c75, limb2: 0x17ff23c44b249965, }, r0a1: u288 { 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0xb9ec4ca4d7d49a9822008dbe, limb2: 0x615661361045cf2, }, r0a1: u288 { limb0: 0xb42d676b3032557533fb7d13, limb1: 0xf3b06bc53cf3ef01a864ee38, limb2: 0x73c33be229ad89, }, r1a0: u288 { limb0: 0x942092185dc6ed03bdf0ab37, limb1: 0x43e304cbc5e653a44f0890b2, limb2: 0xb11bbd65dcfe3bc, }, r1a1: u288 { limb0: 0x9157802e363daff49f64ac5, limb1: 0x75e52d50100499365604decd, limb2: 0x2eb339b99d930ac0, }, }, ]; ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/src/lib.cairo ================================================ // Generated by Garaga version 1.1.0 pub mod groth16_verifier; pub mod groth16_verifier_constants; ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/tests/proof_calldata.txt ================================================ 0x1d02c87bce2e8363285990a 0xf5e071bca525a26d21e2400d 0x2abaae3dd6e4c662 0x0 0xde2cff83a6162de7c15674c2 0x6dd1651aadce6f72757beb89 0x24211ff0aa742a 0x0 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0x7fab709f10cfaf1 0x72a989405ea3494ed54b2564 0xcdc0041b4722845a98eb4157 0x12b1012f185a1925 0x89bbf3a40752d50534b51dd6 0xfe4518b527738171857802db 0x283cbf53bd30c1d7 0xe6e823b4ccec2b1c5cb6691 0xedc84a97c0612a88f1a22253 0xbee7aab3a1fbc76 0x1c087394d1a8efa53168abb874142e7c41239f8c3f4bbf49c89401054a5c15 0xc 0xee91d9c9a198518c670304d5 0xc1507dc82df312cf0b6825a4 0x1992d4e9d7792801 0x0 0x6675ab5a7ce9519d7f1790ca 0x617194577bc67dbe2efb7734 0x241115e9ee74e976 0x0 0x10000000000000000357f6ed9cfc20b18 0x269ff2576b528ed8 0x10000000000000000aa363b63e08441ab 0x100000000000000002b84e0957fd23880 ================================================ FILE: src/contracts/autogenerated/groth16_example_bn254/tests/test_contract.cairo ================================================ // Generated by Garaga version 1.1.0 //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use groth16_example_bn254::groth16_verifier::{ IGroth16VerifierBN254DispatcherTrait, IGroth16VerifierBN254LibraryDispatcher, }; use snforge_std::fs::{FileTrait, read_txt}; use snforge_std::{DeclareResultTrait, declare}; use starknet::ClassHash; /// Declare the Groth16VerifierBN254 contract for testing. /// /// This function declares a new instance of the Groth16VerifierBN254 contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("Groth16VerifierBN254"); /// let dispatcher = IGroth16VerifierBN254LibraryDispatcher { class_hash }; /// ``` fn declare_contract(name: ByteArray) -> ClassHash { let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash } /// Test the verification function verify_groth16_proof_bn254 with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by /// the garaga team - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system groth16 /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", block_tag: latest)] fn test_verify_groth16_proof_bn254() { // Step 1: Declare the verification contract let class_hash = declare_contract("Groth16VerifierBN254"); let dispatcher = IGroth16VerifierBN254LibraryDispatcher { class_hash }; // Step 2: Load the proof fixture generated by the script // This file contains the groth16 proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's verify_groth16_proof_bn254 function with the loaded proof data let result = dispatcher.verify_groth16_proof_bn254(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here } ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/Scarb.toml ================================================ # Generated by Garaga version 1.1.0 [package] name = "noir_ultra_keccak_zk_honk_example" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../../../" } starknet = "2.16.1" [cairo] sierra-replace-ids = false inlining-strategy = 2 [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/src/honk_verifier.cairo ================================================ // Generated by Garaga version 1.1.0 use super::honk_verifier_circuits::{ is_on_curve_excluding_infinity_bn254, run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_12_PUB_17_circuit, }; use super::honk_verifier_constants::{precomputed_lines, vk}; #[starknet::interface] pub trait IUltraKeccakZKHonkVerifier { fn verify_ultra_keccak_zk_honk_proof( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod UltraKeccakZKHonkVerifier { use core::num::traits::Zero; use garaga::apps::noir::zk_honk_transcript::{ KeccakHasherState, Point256IntoCircuitPoint, ZKHonkTranscriptTrait, ZK_BATCHED_RELATION_PARTIAL_LENGTH, }; use garaga::apps::noir::{G2_POINT_KZG_1, G2_POINT_KZG_2, ZKHonkProof}; use garaga::core::circuit::{U32IntoU384, U64IntoU384, u256_to_u384, u288IntoCircuitInputValue}; use garaga::definitions::{ BN254, G1G2Pair, G1Point, get_BN254_modulus, get_GRUMPKIN_modulus, get_eigenvalue, get_min_one_order, get_nG_glv_fake_glv, get_third_root_of_unity, u384, }; use garaga::ec_ops::{G1PointTrait, GlvFakeGlvHint, _ec_safe_add, _scalar_mul_glv_and_fake_glv}; use garaga::pairing_check::{MPCheckHintBN254, multi_pairing_check_bn254_2P_2F}; use super::{ is_on_curve_excluding_infinity_bn254, precomputed_lines, run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_12_circuit, run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_12_PUB_17_circuit, vk, }; #[storage] struct Storage {} #[derive(Drop, Serde)] struct FullProof { proof: ZKHonkProof, msm_hint: Span, kzg_hint: MPCheckHintBN254, } #[abi(embed_v0)] impl IUltraKeccakZKHonkVerifier of super::IUltraKeccakZKHonkVerifier { fn verify_ultra_keccak_zk_honk_proof( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let mut full_proof_with_hints = full_proof_with_hints; let full_proof = Serde::::deserialize(ref full_proof_with_hints) .expect('deserialization failed'); let mod_bn = get_BN254_modulus(); let mod_grumpkin = get_GRUMPKIN_modulus(); let (transcript, _, base_rlc) = ZKHonkTranscriptTrait::from_proof::< KeccakHasherState, >(full_proof.proof, vk.vk_hash, vk.log_circuit_size); let log_n = vk.log_circuit_size; let (sum_check_rlc, honk_check) = run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_12_PUB_17_circuit( p_public_inputs: full_proof.proof.public_inputs, p_pairing_point_object: full_proof.proof.pairing_point_object, libra_sum: u256_to_u384(full_proof.proof.libra_sum), sumcheck_univariates_flat: full_proof .proof .sumcheck_univariates .slice(0, log_n * ZK_BATCHED_RELATION_PARTIAL_LENGTH), sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span(), tp_gate_challenge: transcript.gate_challenge, tp_eta_1: transcript.eta.into(), tp_eta_2: transcript.eta_two.into(), tp_eta_3: transcript.eta_three.into(), tp_beta: transcript.beta.into(), tp_gamma: transcript.gamma.into(), tp_base_rlc: base_rlc.into(), tp_alpha: transcript.alpha, tp_libra_challenge: transcript.libra_challenge.into(), modulus: mod_grumpkin, ); let (mut challenge_poly_eval, mut root_power_times_tp_gemini_r) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_12_circuit( tp_gemini_r: transcript.gemini_r.into(), modulus: mod_grumpkin, ); for i in 0..vk.log_circuit_size { let (new_challenge_poly_eval, new_root_power_times_tp_gemini_r) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_12_circuit( challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, tp_sumcheck_u_challenge: (*transcript.sum_check_u_challenges.at(i)).into(), modulus: mod_grumpkin, ); challenge_poly_eval = new_challenge_poly_eval; root_power_times_tp_gemini_r = new_root_power_times_tp_gemini_r; } let (vanishing_check, diff_check) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_12_circuit( p_libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, modulus: mod_grumpkin, ); let ( scalar_1, scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, scalar_52, ) = run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_12_circuit( p_sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, p_gemini_masking_eval: u256_to_u384(full_proof.proof.gemini_masking_eval), p_gemini_a_evaluations: full_proof.proof.gemini_a_evaluations, p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), tp_rho: transcript.rho.into(), tp_shplonk_z: transcript.shplonk_z.into(), tp_shplonk_nu: transcript.shplonk_nu.into(), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span().slice(0, log_n), modulus: mod_grumpkin, ); // Starts with 1 * shplonk_q, not included in msm let mut _points: Array = array![ vk.qm, vk.qc, vk.ql, vk.qr, vk.qo, vk.q4, vk.qLookup, vk.qArith, vk.qDeltaRange, vk.qElliptic, vk.qMemory, vk.qNnf, vk.qPoseidon2External, vk.qPoseidon2Internal, vk.s1, vk.s2, vk.s3, vk.s4, vk.id1, vk.id2, vk.id3, vk.id4, vk.t1, vk.t2, vk.t3, vk.t4, vk.lagrange_first, vk.lagrange_last, full_proof.proof.gemini_masking_poly.into(), // Proof point 1, full_proof.proof.w1.into(), // Proof point 2, full_proof.proof.w2.into(), // Proof point 3, full_proof.proof.w3.into(), // Proof point 4, full_proof.proof.w4.into(), // Proof point 5, full_proof.proof.z_perm.into(), // Proof point 6, full_proof.proof.lookup_inverses.into(), // Proof point 7, full_proof.proof.lookup_read_counts.into(), // Proof point 8, full_proof.proof.lookup_read_tags.into() // Proof point 9 ]; for gem_comm in full_proof.proof.gemini_fold_comms { _points.append((*gem_comm).into()); } // log_n -1 = 11 points || Proof points 10-20 for lib_comm in full_proof.proof.libra_commitments { _points.append((*lib_comm).into()); } // 3 points || Proof points 21-23 _points.append(full_proof.proof.kzg_quotient.into()); // Proof point 24 _points.append(BN254.G); let mut points = _points.span(); let mut scalars: Span = array![ scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_1, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, transcript.shplonk_z.into(), scalar_52, ] .span(); // Check input points are on curve. // Skip the first 28 points as they are from VK and keep the last 24 proof points for point in points.slice(28, 24) { assert( is_on_curve_excluding_infinity_bn254(*point, mod_bn), 'proof point not on curve', ); } // Assert shplonk_q is on curve let shplonk_q_pt: G1Point = full_proof.proof.shplonk_q.into(); assert( is_on_curve_excluding_infinity_bn254(shplonk_q_pt, mod_bn), 'shplonk_q not on curve', ); let mut msm_hint = full_proof.msm_hint; assert(msm_hint.len() == 53 * 12, 'wrong glv&fakeglv hint size'); let eigen = get_eigenvalue(0); let third_root_of_unity = get_third_root_of_unity(0); let min_one = get_min_one_order(0); let nG = get_nG_glv_fake_glv(0); let mut P_1 = shplonk_q_pt; while msm_hint.len() != 0 { let pt = *points.pop_front().unwrap(); let scalar = *scalars.pop_front().unwrap(); // Note : Scalars are below curve order by construction (circuit outputs mod n and // transcript output (u128)) let glv_fake_glv_hint: GlvFakeGlvHint = Serde::deserialize(ref msm_hint).unwrap(); let temp = _scalar_mul_glv_and_fake_glv( pt, scalar, mod_grumpkin, mod_bn, glv_fake_glv_hint, eigen, third_root_of_unity, min_one, nG, 0, ); P_1 = _ec_safe_add(P_1, temp, mod_bn, 0); } let P_2: G1Point = full_proof.proof.kzg_quotient.into(); // Perform the KZG pairing check. let kzg_check = multi_pairing_check_bn254_2P_2F( G1G2Pair { p: P_1, q: G2_POINT_KZG_1 }, G1G2Pair { p: P_2.negate(0), q: G2_POINT_KZG_2 }, precomputed_lines.span(), full_proof.kzg_hint, ); if sum_check_rlc.is_zero() && honk_check.is_zero() && !vanishing_check.is_zero() && diff_check.is_zero() && kzg_check.is_ok() { return Result::Ok(full_proof.proof.public_inputs); } else { return Result::Err('Proof verification failed'); } } } } ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/src/honk_verifier_circuits.cairo ================================================ // Generated by Garaga version 1.1.0 use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::G1Point; #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_12_PUB_17_circuit( p_public_inputs: Span, p_pairing_point_object: Span, libra_sum: u384, sumcheck_univariates_flat: Span, sumcheck_evaluations: Span, libra_evaluation: u384, tp_sum_check_u_challenges: Span, tp_gate_challenge: u128, tp_eta_1: u384, tp_eta_2: u384, tp_eta_3: u384, tp_beta: u384, tp_gamma: u384, tp_base_rlc: u384, tp_alpha: u128, tp_libra_challenge: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x10000000 let in2 = CE::> {}; // 0x9d80 let in3 = CE::> {}; // 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593efffec51 let in4 = CE::> {}; // 0x5a0 let in5 = CE::> {}; // 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffd31 let in6 = CE::> {}; // 0x240 let in7 = CE::> {}; // 0x0 let in8 = CE::> {}; // 0x2 let in9 = CE::> {}; // 0x3 let in10 = CE::> {}; // 0x4 let in11 = CE::> {}; // 0x5 let in12 = CE::> {}; // 0x6 let in13 = CE::> {}; // 0x7 let in14 = CE::> {}; // 0x8 let in15 = CE::< CI<15>, > {}; // 0x183227397098d014dc2822db40c0ac2e9419f4243cdcb848a1f0fac9f8000000 let in16 = CE::> {}; // -0x1 % p let in17 = CE::> {}; // 0x11 let in18 = CE::> {}; // 0x9 let in19 = CE::> {}; // 0x100000000000000000 let in20 = CE::> {}; // 0x4000 let in21 = CE::< CI<21>, > {}; // 0x10dc6e9c006ea38b04b1e03b4bd9490c0d03f98929ca1d7fb56821fd19d3b6e7 let in22 = CE::> {}; // 0xc28145b6a44df3e0149b3d0a30b3bb599df9756d4dd9b84a86b38cfb45a740b let in23 = CE::> {}; // 0x544b8338791518b2c7645a50392798b21f75bb60e3596170067d00141cac15 let in24 = CE::< CI<24>, > {}; // 0x222c01175718386f2e2e82eb122789e352e105a3b8fa852613bc534433ee428b // INPUT stack let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let (in37, in38, in39) = (CE::> {}, CE::> {}, CE::> {}); let (in40, in41, in42) = (CE::> {}, CE::> {}, CE::> {}); let (in43, in44, in45) = (CE::> {}, CE::> {}, CE::> {}); let (in46, in47, in48) = (CE::> {}, CE::> {}, CE::> {}); let (in49, in50, in51) = (CE::> {}, CE::> {}, CE::> {}); let (in52, in53, in54) = (CE::> {}, CE::> {}, CE::> {}); let (in55, in56, in57) = (CE::> {}, CE::> {}, CE::> {}); let (in58, in59, in60) = (CE::> {}, CE::> {}, CE::> {}); let (in61, in62, in63) = (CE::> {}, CE::> {}, CE::> {}); let (in64, in65, in66) = (CE::> {}, CE::> {}, CE::> {}); let (in67, in68, in69) = (CE::> {}, CE::> {}, CE::> {}); let (in70, in71, in72) = (CE::> {}, CE::> {}, CE::> {}); let (in73, in74, in75) = (CE::> {}, CE::> {}, CE::> {}); let (in76, in77, in78) = (CE::> {}, CE::> {}, CE::> {}); let (in79, in80, in81) = (CE::> {}, CE::> {}, CE::> {}); let (in82, in83, in84) = (CE::> {}, CE::> {}, CE::> {}); let (in85, in86, in87) = (CE::> {}, CE::> {}, CE::> {}); let (in88, in89, in90) = (CE::> {}, CE::> {}, CE::> {}); let (in91, in92, in93) = (CE::> {}, CE::> {}, CE::> {}); let (in94, in95, in96) = (CE::> {}, CE::> {}, CE::> {}); let (in97, in98, in99) = (CE::> {}, CE::> {}, CE::> {}); let (in100, in101, in102) = (CE::> {}, CE::> {}, CE::> {}); let (in103, in104, in105) = (CE::> {}, CE::> {}, CE::> {}); let (in106, in107, in108) = (CE::> {}, CE::> {}, CE::> {}); let (in109, in110, in111) = (CE::> {}, CE::> {}, CE::> {}); let (in112, in113, in114) = (CE::> {}, CE::> {}, CE::> {}); let (in115, in116, in117) = (CE::> {}, CE::> {}, CE::> {}); let (in118, in119, in120) = (CE::> {}, CE::> {}, CE::> {}); let (in121, in122, in123) = (CE::> {}, CE::> {}, CE::> {}); let (in124, in125, in126) = (CE::> {}, CE::> {}, CE::> {}); let (in127, in128, in129) = (CE::> {}, CE::> {}, CE::> {}); let (in130, in131, in132) = (CE::> {}, CE::> {}, CE::> {}); let (in133, in134, in135) = (CE::> {}, CE::> {}, CE::> {}); let (in136, in137, in138) = (CE::> {}, CE::> {}, CE::> {}); let (in139, in140, in141) = (CE::> {}, CE::> {}, CE::> {}); let (in142, in143, in144) = (CE::> {}, CE::> {}, CE::> {}); let (in145, in146, in147) = (CE::> {}, CE::> {}, CE::> {}); let (in148, in149, in150) = (CE::> {}, CE::> {}, CE::> {}); let (in151, in152, in153) = (CE::> {}, CE::> {}, CE::> {}); let (in154, in155, in156) = (CE::> {}, CE::> {}, CE::> {}); let (in157, in158, in159) = (CE::> {}, CE::> {}, CE::> {}); let (in160, in161, in162) = (CE::> {}, CE::> {}, CE::> {}); let (in163, in164, in165) = (CE::> {}, CE::> {}, CE::> {}); let (in166, in167, in168) = (CE::> {}, CE::> {}, CE::> {}); let (in169, in170, in171) = (CE::> {}, CE::> {}, CE::> {}); let (in172, in173, in174) = (CE::> {}, CE::> {}, CE::> {}); let (in175, in176, in177) = (CE::> {}, CE::> {}, CE::> {}); let (in178, in179, in180) = (CE::> {}, CE::> {}, CE::> {}); let (in181, in182, in183) = (CE::> {}, CE::> {}, CE::> {}); let (in184, in185, in186) = (CE::> {}, CE::> {}, CE::> {}); let (in187, in188, in189) = (CE::> {}, CE::> {}, CE::> {}); let (in190, in191, in192) = (CE::> {}, CE::> {}, CE::> {}); let (in193, in194, in195) = (CE::> {}, CE::> {}, CE::> {}); let (in196, in197, in198) = (CE::> {}, CE::> {}, CE::> {}); let (in199, in200, in201) = (CE::> {}, CE::> {}, CE::> {}); let (in202, in203, in204) = (CE::> {}, CE::> {}, CE::> {}); let (in205, in206, in207) = (CE::> {}, CE::> {}, CE::> {}); let (in208, in209, in210) = (CE::> {}, CE::> {}, CE::> {}); let (in211, in212, in213) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in1, in0); let t1 = circuit_mul(in209, t0); let t2 = circuit_add(in210, t1); let t3 = circuit_add(in0, in0); let t4 = circuit_mul(in209, t3); let t5 = circuit_sub(in210, t4); let t6 = circuit_add(t2, in25); let t7 = circuit_mul(in0, t6); let t8 = circuit_add(t5, in25); let t9 = circuit_mul(in0, t8); let t10 = circuit_add(t2, in209); let t11 = circuit_sub(t5, in209); let t12 = circuit_add(t10, in26); let t13 = circuit_mul(t7, t12); let t14 = circuit_add(t11, in26); let t15 = circuit_mul(t9, t14); let t16 = circuit_add(t10, in209); let t17 = circuit_sub(t11, in209); let t18 = circuit_add(t16, in27); let t19 = circuit_mul(t13, t18); let t20 = circuit_add(t17, in27); let t21 = circuit_mul(t15, t20); let t22 = circuit_add(t16, in209); let t23 = circuit_sub(t17, in209); let t24 = circuit_add(t22, in28); let t25 = circuit_mul(t19, t24); let t26 = circuit_add(t23, in28); let t27 = circuit_mul(t21, t26); let t28 = circuit_add(t22, in209); let t29 = circuit_sub(t23, in209); let t30 = circuit_add(t28, in29); let t31 = circuit_mul(t25, t30); let t32 = circuit_add(t29, in29); let t33 = circuit_mul(t27, t32); let t34 = circuit_add(t28, in209); let t35 = circuit_sub(t29, in209); let t36 = circuit_add(t34, in30); let t37 = circuit_mul(t31, t36); let t38 = circuit_add(t35, in30); let t39 = circuit_mul(t33, t38); let t40 = circuit_add(t34, in209); let t41 = circuit_sub(t35, in209); let t42 = circuit_add(t40, in31); let t43 = circuit_mul(t37, t42); let t44 = circuit_add(t41, in31); let t45 = circuit_mul(t39, t44); let t46 = circuit_add(t40, in209); let t47 = circuit_sub(t41, in209); let t48 = circuit_add(t46, in32); let t49 = circuit_mul(t43, t48); let t50 = circuit_add(t47, in32); let t51 = circuit_mul(t45, t50); let t52 = circuit_add(t46, in209); let t53 = circuit_sub(t47, in209); let t54 = circuit_add(t52, in33); let t55 = circuit_mul(t49, t54); let t56 = circuit_add(t53, in33); let t57 = circuit_mul(t51, t56); let t58 = circuit_add(t52, in209); let t59 = circuit_sub(t53, in209); let t60 = circuit_add(t58, in34); let t61 = circuit_mul(t55, t60); let t62 = circuit_add(t59, in34); let t63 = circuit_mul(t57, t62); let t64 = circuit_add(t58, in209); let t65 = circuit_sub(t59, in209); let t66 = circuit_add(t64, in35); let t67 = circuit_mul(t61, t66); let t68 = circuit_add(t65, in35); let t69 = circuit_mul(t63, t68); let t70 = circuit_add(t64, in209); let t71 = circuit_sub(t65, in209); let t72 = circuit_add(t70, in36); let t73 = circuit_mul(t67, t72); let t74 = circuit_add(t71, in36); let t75 = circuit_mul(t69, t74); let t76 = circuit_add(t70, in209); let t77 = circuit_sub(t71, in209); let t78 = circuit_add(t76, in37); let t79 = circuit_mul(t73, t78); let t80 = circuit_add(t77, in37); let t81 = circuit_mul(t75, t80); let t82 = circuit_add(t76, in209); let t83 = circuit_sub(t77, in209); let t84 = circuit_add(t82, in38); let t85 = circuit_mul(t79, t84); let t86 = circuit_add(t83, in38); let t87 = circuit_mul(t81, t86); let t88 = circuit_add(t82, in209); let t89 = circuit_sub(t83, in209); let t90 = circuit_add(t88, in39); let t91 = circuit_mul(t85, t90); let t92 = circuit_add(t89, in39); let t93 = circuit_mul(t87, t92); let t94 = circuit_add(t88, in209); let t95 = circuit_sub(t89, in209); let t96 = circuit_add(t94, in40); let t97 = circuit_mul(t91, t96); let t98 = circuit_add(t95, in40); let t99 = circuit_mul(t93, t98); let t100 = circuit_add(t94, in209); let t101 = circuit_sub(t95, in209); let t102 = circuit_add(t100, in41); let t103 = circuit_mul(t97, t102); let t104 = circuit_add(t101, in41); let t105 = circuit_mul(t99, t104); let t106 = circuit_inverse(t105); let t107 = circuit_mul(t103, t106); let t108 = circuit_mul(in213, in42); let t109 = circuit_add(in43, in44); let t110 = circuit_sub(t109, t108); let t111 = circuit_mul(t110, in211); let t112 = circuit_sub(in193, in7); let t113 = circuit_mul(in0, t112); let t114 = circuit_sub(in193, in7); let t115 = circuit_mul(in2, t114); let t116 = circuit_inverse(t115); let t117 = circuit_mul(in43, t116); let t118 = circuit_add(in7, t117); let t119 = circuit_sub(in193, in0); let t120 = circuit_mul(t113, t119); let t121 = circuit_sub(in193, in0); let t122 = circuit_mul(in3, t121); let t123 = circuit_inverse(t122); let t124 = circuit_mul(in44, t123); let t125 = circuit_add(t118, t124); let t126 = circuit_sub(in193, in8); let t127 = circuit_mul(t120, t126); let t128 = circuit_sub(in193, in8); let t129 = circuit_mul(in4, t128); let t130 = circuit_inverse(t129); let t131 = circuit_mul(in45, t130); let t132 = circuit_add(t125, t131); let t133 = circuit_sub(in193, in9); let t134 = circuit_mul(t127, t133); let t135 = circuit_sub(in193, in9); let t136 = circuit_mul(in5, t135); let t137 = circuit_inverse(t136); let t138 = circuit_mul(in46, t137); let t139 = circuit_add(t132, t138); let t140 = circuit_sub(in193, in10); let t141 = circuit_mul(t134, t140); let t142 = circuit_sub(in193, in10); let t143 = circuit_mul(in6, t142); let t144 = circuit_inverse(t143); let t145 = circuit_mul(in47, t144); let t146 = circuit_add(t139, t145); let t147 = circuit_sub(in193, in11); let t148 = circuit_mul(t141, t147); let t149 = circuit_sub(in193, in11); let t150 = circuit_mul(in5, t149); let t151 = circuit_inverse(t150); let t152 = circuit_mul(in48, t151); let t153 = circuit_add(t146, t152); let t154 = circuit_sub(in193, in12); let t155 = circuit_mul(t148, t154); let t156 = circuit_sub(in193, in12); let t157 = circuit_mul(in4, t156); let t158 = circuit_inverse(t157); let t159 = circuit_mul(in49, t158); let t160 = circuit_add(t153, t159); let t161 = circuit_sub(in193, in13); let t162 = circuit_mul(t155, t161); let t163 = circuit_sub(in193, in13); let t164 = circuit_mul(in3, t163); let t165 = circuit_inverse(t164); let t166 = circuit_mul(in50, t165); let t167 = circuit_add(t160, t166); let t168 = circuit_sub(in193, in14); let t169 = circuit_mul(t162, t168); let t170 = circuit_sub(in193, in14); let t171 = circuit_mul(in2, t170); let t172 = circuit_inverse(t171); let t173 = circuit_mul(in51, t172); let t174 = circuit_add(t167, t173); let t175 = circuit_mul(t174, t169); let t176 = circuit_sub(in205, in0); let t177 = circuit_mul(in193, t176); let t178 = circuit_add(in0, t177); let t179 = circuit_mul(in0, t178); let t180 = circuit_mul(in211, in211); let t181 = circuit_mul(in205, in205); let t182 = circuit_add(in52, in53); let t183 = circuit_sub(t182, t175); let t184 = circuit_mul(t183, t180); let t185 = circuit_add(t111, t184); let t186 = circuit_sub(in194, in7); let t187 = circuit_mul(in0, t186); let t188 = circuit_sub(in194, in7); let t189 = circuit_mul(in2, t188); let t190 = circuit_inverse(t189); let t191 = circuit_mul(in52, t190); let t192 = circuit_add(in7, t191); let t193 = circuit_sub(in194, in0); let t194 = circuit_mul(t187, t193); let t195 = circuit_sub(in194, in0); let t196 = circuit_mul(in3, t195); let t197 = circuit_inverse(t196); let t198 = circuit_mul(in53, t197); let t199 = circuit_add(t192, t198); let t200 = circuit_sub(in194, in8); let t201 = circuit_mul(t194, t200); let t202 = circuit_sub(in194, in8); let t203 = circuit_mul(in4, t202); let t204 = circuit_inverse(t203); let t205 = circuit_mul(in54, t204); let t206 = circuit_add(t199, t205); let t207 = circuit_sub(in194, in9); let t208 = circuit_mul(t201, t207); let t209 = circuit_sub(in194, in9); let t210 = circuit_mul(in5, t209); let t211 = circuit_inverse(t210); let t212 = circuit_mul(in55, t211); let t213 = circuit_add(t206, t212); let t214 = circuit_sub(in194, in10); let t215 = circuit_mul(t208, t214); let t216 = circuit_sub(in194, in10); let t217 = circuit_mul(in6, t216); let t218 = circuit_inverse(t217); let t219 = circuit_mul(in56, t218); let t220 = circuit_add(t213, t219); let t221 = circuit_sub(in194, in11); let t222 = circuit_mul(t215, t221); let t223 = circuit_sub(in194, in11); let t224 = circuit_mul(in5, t223); let t225 = circuit_inverse(t224); let t226 = circuit_mul(in57, t225); let t227 = circuit_add(t220, t226); let t228 = circuit_sub(in194, in12); let t229 = circuit_mul(t222, t228); let t230 = circuit_sub(in194, in12); let t231 = circuit_mul(in4, t230); let t232 = circuit_inverse(t231); let t233 = circuit_mul(in58, t232); let t234 = circuit_add(t227, t233); let t235 = circuit_sub(in194, in13); let t236 = circuit_mul(t229, t235); let t237 = circuit_sub(in194, in13); let t238 = circuit_mul(in3, t237); let t239 = circuit_inverse(t238); let t240 = circuit_mul(in59, t239); let t241 = circuit_add(t234, t240); let t242 = circuit_sub(in194, in14); let t243 = circuit_mul(t236, t242); let t244 = circuit_sub(in194, in14); let t245 = circuit_mul(in2, t244); let t246 = circuit_inverse(t245); let t247 = circuit_mul(in60, t246); let t248 = circuit_add(t241, t247); let t249 = circuit_mul(t248, t243); let t250 = circuit_sub(t181, in0); let t251 = circuit_mul(in194, t250); let t252 = circuit_add(in0, t251); let t253 = circuit_mul(t179, t252); let t254 = circuit_mul(t180, in211); let t255 = circuit_mul(t181, t181); let t256 = circuit_add(in61, in62); let t257 = circuit_sub(t256, t249); let t258 = circuit_mul(t257, t254); let t259 = circuit_add(t185, t258); let t260 = circuit_sub(in195, in7); let t261 = circuit_mul(in0, t260); let t262 = circuit_sub(in195, in7); let t263 = circuit_mul(in2, t262); let t264 = circuit_inverse(t263); let t265 = circuit_mul(in61, t264); let t266 = circuit_add(in7, t265); let t267 = circuit_sub(in195, in0); let t268 = circuit_mul(t261, t267); let t269 = circuit_sub(in195, in0); let t270 = circuit_mul(in3, t269); let t271 = circuit_inverse(t270); let t272 = circuit_mul(in62, t271); let t273 = circuit_add(t266, t272); let t274 = circuit_sub(in195, in8); let t275 = circuit_mul(t268, t274); let t276 = circuit_sub(in195, in8); let t277 = circuit_mul(in4, t276); let t278 = circuit_inverse(t277); let t279 = circuit_mul(in63, t278); let t280 = circuit_add(t273, t279); let t281 = circuit_sub(in195, in9); let t282 = circuit_mul(t275, t281); let t283 = circuit_sub(in195, in9); let t284 = circuit_mul(in5, t283); let t285 = circuit_inverse(t284); let t286 = circuit_mul(in64, t285); let t287 = circuit_add(t280, t286); let t288 = circuit_sub(in195, in10); let t289 = circuit_mul(t282, t288); let t290 = circuit_sub(in195, in10); let t291 = circuit_mul(in6, t290); let t292 = circuit_inverse(t291); let t293 = circuit_mul(in65, t292); let t294 = circuit_add(t287, t293); let t295 = circuit_sub(in195, in11); let t296 = circuit_mul(t289, t295); let t297 = circuit_sub(in195, in11); let t298 = circuit_mul(in5, t297); let t299 = circuit_inverse(t298); let t300 = circuit_mul(in66, t299); let t301 = circuit_add(t294, t300); let t302 = circuit_sub(in195, in12); let t303 = circuit_mul(t296, t302); let t304 = circuit_sub(in195, in12); let t305 = circuit_mul(in4, t304); let t306 = circuit_inverse(t305); let t307 = circuit_mul(in67, t306); let t308 = circuit_add(t301, t307); let t309 = circuit_sub(in195, in13); let t310 = circuit_mul(t303, t309); let t311 = circuit_sub(in195, in13); let t312 = circuit_mul(in3, t311); let t313 = circuit_inverse(t312); let t314 = circuit_mul(in68, t313); let t315 = circuit_add(t308, t314); let t316 = circuit_sub(in195, in14); let t317 = circuit_mul(t310, t316); let t318 = circuit_sub(in195, in14); let t319 = circuit_mul(in2, t318); let t320 = circuit_inverse(t319); let t321 = circuit_mul(in69, t320); let t322 = circuit_add(t315, t321); let t323 = circuit_mul(t322, t317); let t324 = circuit_sub(t255, in0); let t325 = circuit_mul(in195, t324); let t326 = circuit_add(in0, t325); let t327 = circuit_mul(t253, t326); let t328 = circuit_mul(t254, in211); let t329 = circuit_mul(t255, t255); let t330 = circuit_add(in70, in71); let t331 = circuit_sub(t330, t323); let t332 = circuit_mul(t331, t328); let t333 = circuit_add(t259, t332); let t334 = circuit_sub(in196, in7); let t335 = circuit_mul(in0, t334); let t336 = circuit_sub(in196, in7); let t337 = circuit_mul(in2, t336); let t338 = circuit_inverse(t337); let t339 = circuit_mul(in70, t338); let t340 = circuit_add(in7, t339); let t341 = circuit_sub(in196, in0); let t342 = circuit_mul(t335, t341); let t343 = circuit_sub(in196, in0); let t344 = circuit_mul(in3, t343); let t345 = circuit_inverse(t344); let t346 = circuit_mul(in71, t345); let t347 = circuit_add(t340, t346); let t348 = circuit_sub(in196, in8); let t349 = circuit_mul(t342, t348); let t350 = circuit_sub(in196, in8); let t351 = circuit_mul(in4, t350); let t352 = circuit_inverse(t351); let t353 = circuit_mul(in72, t352); let t354 = circuit_add(t347, t353); let t355 = circuit_sub(in196, in9); let t356 = circuit_mul(t349, t355); let t357 = circuit_sub(in196, in9); let t358 = circuit_mul(in5, t357); let t359 = circuit_inverse(t358); let t360 = circuit_mul(in73, t359); let t361 = circuit_add(t354, t360); let t362 = circuit_sub(in196, in10); let t363 = circuit_mul(t356, t362); let t364 = circuit_sub(in196, in10); let t365 = circuit_mul(in6, t364); let t366 = circuit_inverse(t365); let t367 = circuit_mul(in74, t366); let t368 = circuit_add(t361, t367); let t369 = circuit_sub(in196, in11); let t370 = circuit_mul(t363, t369); let t371 = circuit_sub(in196, in11); let t372 = circuit_mul(in5, t371); let t373 = circuit_inverse(t372); let t374 = circuit_mul(in75, t373); let t375 = circuit_add(t368, t374); let t376 = circuit_sub(in196, in12); let t377 = circuit_mul(t370, t376); let t378 = circuit_sub(in196, in12); let t379 = circuit_mul(in4, t378); let t380 = circuit_inverse(t379); let t381 = circuit_mul(in76, t380); let t382 = circuit_add(t375, t381); let t383 = circuit_sub(in196, in13); let t384 = circuit_mul(t377, t383); let t385 = circuit_sub(in196, in13); let t386 = circuit_mul(in3, t385); let t387 = circuit_inverse(t386); let t388 = circuit_mul(in77, t387); let t389 = circuit_add(t382, t388); let t390 = circuit_sub(in196, in14); let t391 = circuit_mul(t384, t390); let t392 = circuit_sub(in196, in14); let t393 = circuit_mul(in2, t392); let t394 = circuit_inverse(t393); let t395 = circuit_mul(in78, t394); let t396 = circuit_add(t389, t395); let t397 = circuit_mul(t396, t391); let t398 = circuit_sub(t329, in0); let t399 = circuit_mul(in196, t398); let t400 = circuit_add(in0, t399); let t401 = circuit_mul(t327, t400); let t402 = circuit_mul(t328, in211); let t403 = circuit_mul(t329, t329); let t404 = circuit_add(in79, in80); let t405 = circuit_sub(t404, t397); let t406 = circuit_mul(t405, t402); let t407 = circuit_add(t333, t406); let t408 = circuit_sub(in197, in7); let t409 = circuit_mul(in0, t408); let t410 = circuit_sub(in197, in7); let t411 = circuit_mul(in2, t410); let t412 = circuit_inverse(t411); let t413 = circuit_mul(in79, t412); let t414 = circuit_add(in7, t413); let t415 = circuit_sub(in197, in0); let t416 = circuit_mul(t409, t415); let t417 = circuit_sub(in197, in0); let t418 = circuit_mul(in3, t417); let t419 = circuit_inverse(t418); let t420 = circuit_mul(in80, t419); let t421 = circuit_add(t414, t420); let t422 = circuit_sub(in197, in8); let t423 = circuit_mul(t416, t422); let t424 = circuit_sub(in197, in8); let t425 = circuit_mul(in4, t424); let t426 = circuit_inverse(t425); let t427 = circuit_mul(in81, t426); let t428 = circuit_add(t421, t427); let t429 = circuit_sub(in197, in9); let t430 = circuit_mul(t423, t429); let t431 = circuit_sub(in197, in9); let t432 = circuit_mul(in5, t431); let t433 = circuit_inverse(t432); let t434 = circuit_mul(in82, t433); let t435 = circuit_add(t428, t434); let t436 = circuit_sub(in197, in10); let t437 = circuit_mul(t430, t436); let t438 = circuit_sub(in197, in10); let t439 = circuit_mul(in6, t438); let t440 = circuit_inverse(t439); let t441 = circuit_mul(in83, t440); let t442 = circuit_add(t435, t441); let t443 = circuit_sub(in197, in11); let t444 = circuit_mul(t437, t443); let t445 = circuit_sub(in197, in11); let t446 = circuit_mul(in5, t445); let t447 = circuit_inverse(t446); let t448 = circuit_mul(in84, t447); let t449 = circuit_add(t442, t448); let t450 = circuit_sub(in197, in12); let t451 = circuit_mul(t444, t450); let t452 = circuit_sub(in197, in12); let t453 = circuit_mul(in4, t452); let t454 = circuit_inverse(t453); let t455 = circuit_mul(in85, t454); let t456 = circuit_add(t449, t455); let t457 = circuit_sub(in197, in13); let t458 = circuit_mul(t451, t457); let t459 = circuit_sub(in197, in13); let t460 = circuit_mul(in3, t459); let t461 = circuit_inverse(t460); let t462 = circuit_mul(in86, t461); let t463 = circuit_add(t456, t462); let t464 = circuit_sub(in197, in14); let t465 = circuit_mul(t458, t464); let t466 = circuit_sub(in197, in14); let t467 = circuit_mul(in2, t466); let t468 = circuit_inverse(t467); let t469 = circuit_mul(in87, t468); let t470 = circuit_add(t463, t469); let t471 = circuit_mul(t470, t465); let t472 = circuit_sub(t403, in0); let t473 = circuit_mul(in197, t472); let t474 = circuit_add(in0, t473); let t475 = circuit_mul(t401, t474); let t476 = circuit_mul(t402, in211); let t477 = circuit_mul(t403, t403); let t478 = circuit_add(in88, in89); let t479 = circuit_sub(t478, t471); let t480 = circuit_mul(t479, t476); let t481 = circuit_add(t407, t480); let t482 = circuit_sub(in198, in7); let t483 = circuit_mul(in0, t482); let t484 = circuit_sub(in198, in7); let t485 = circuit_mul(in2, t484); let t486 = circuit_inverse(t485); let t487 = circuit_mul(in88, t486); let t488 = circuit_add(in7, t487); let t489 = circuit_sub(in198, in0); let t490 = circuit_mul(t483, t489); let t491 = circuit_sub(in198, in0); let t492 = circuit_mul(in3, t491); let t493 = circuit_inverse(t492); let t494 = circuit_mul(in89, t493); let t495 = circuit_add(t488, t494); let t496 = circuit_sub(in198, in8); let t497 = circuit_mul(t490, t496); let t498 = circuit_sub(in198, in8); let t499 = circuit_mul(in4, t498); let t500 = circuit_inverse(t499); let t501 = circuit_mul(in90, t500); let t502 = circuit_add(t495, t501); let t503 = circuit_sub(in198, in9); let t504 = circuit_mul(t497, t503); let t505 = circuit_sub(in198, in9); let t506 = circuit_mul(in5, t505); let t507 = circuit_inverse(t506); let t508 = circuit_mul(in91, t507); let t509 = circuit_add(t502, t508); let t510 = circuit_sub(in198, in10); let t511 = circuit_mul(t504, t510); let t512 = circuit_sub(in198, in10); let t513 = circuit_mul(in6, t512); let t514 = circuit_inverse(t513); let t515 = circuit_mul(in92, t514); let t516 = circuit_add(t509, t515); let t517 = circuit_sub(in198, in11); let t518 = circuit_mul(t511, t517); let t519 = circuit_sub(in198, in11); let t520 = circuit_mul(in5, t519); let t521 = circuit_inverse(t520); let t522 = circuit_mul(in93, t521); let t523 = circuit_add(t516, t522); let t524 = circuit_sub(in198, in12); let t525 = circuit_mul(t518, t524); let t526 = circuit_sub(in198, in12); let t527 = circuit_mul(in4, t526); let t528 = circuit_inverse(t527); let t529 = circuit_mul(in94, t528); let t530 = circuit_add(t523, t529); let t531 = circuit_sub(in198, in13); let t532 = circuit_mul(t525, t531); let t533 = circuit_sub(in198, in13); let t534 = circuit_mul(in3, t533); let t535 = circuit_inverse(t534); let t536 = circuit_mul(in95, t535); let t537 = circuit_add(t530, t536); let t538 = circuit_sub(in198, in14); let t539 = circuit_mul(t532, t538); let t540 = circuit_sub(in198, in14); let t541 = circuit_mul(in2, t540); let t542 = circuit_inverse(t541); let t543 = circuit_mul(in96, t542); let t544 = circuit_add(t537, t543); let t545 = circuit_mul(t544, t539); let t546 = circuit_sub(t477, in0); let t547 = circuit_mul(in198, t546); let t548 = circuit_add(in0, t547); let t549 = circuit_mul(t475, t548); let t550 = circuit_mul(t476, in211); let t551 = circuit_mul(t477, t477); let t552 = circuit_add(in97, in98); let t553 = circuit_sub(t552, t545); let t554 = circuit_mul(t553, t550); let t555 = circuit_add(t481, t554); let t556 = circuit_sub(in199, in7); let t557 = circuit_mul(in0, t556); let t558 = circuit_sub(in199, in7); let t559 = circuit_mul(in2, t558); let t560 = circuit_inverse(t559); let t561 = circuit_mul(in97, t560); let t562 = circuit_add(in7, t561); let t563 = circuit_sub(in199, in0); let t564 = circuit_mul(t557, t563); let t565 = circuit_sub(in199, in0); let t566 = circuit_mul(in3, t565); let t567 = circuit_inverse(t566); let t568 = circuit_mul(in98, t567); let t569 = circuit_add(t562, t568); let t570 = circuit_sub(in199, in8); let t571 = circuit_mul(t564, t570); let t572 = circuit_sub(in199, in8); let t573 = circuit_mul(in4, t572); let t574 = circuit_inverse(t573); let t575 = circuit_mul(in99, t574); let t576 = circuit_add(t569, t575); let t577 = circuit_sub(in199, in9); let t578 = circuit_mul(t571, t577); let t579 = circuit_sub(in199, in9); let t580 = circuit_mul(in5, t579); let t581 = circuit_inverse(t580); let t582 = circuit_mul(in100, t581); let t583 = circuit_add(t576, t582); let t584 = circuit_sub(in199, in10); let t585 = circuit_mul(t578, t584); let t586 = circuit_sub(in199, in10); let t587 = circuit_mul(in6, t586); let t588 = circuit_inverse(t587); let t589 = circuit_mul(in101, t588); let t590 = circuit_add(t583, t589); let t591 = circuit_sub(in199, in11); let t592 = circuit_mul(t585, t591); let t593 = circuit_sub(in199, in11); let t594 = circuit_mul(in5, t593); let t595 = circuit_inverse(t594); let t596 = circuit_mul(in102, t595); let t597 = circuit_add(t590, t596); let t598 = circuit_sub(in199, in12); let t599 = circuit_mul(t592, t598); let t600 = circuit_sub(in199, in12); let t601 = circuit_mul(in4, t600); let t602 = circuit_inverse(t601); let t603 = circuit_mul(in103, t602); let t604 = circuit_add(t597, t603); let t605 = circuit_sub(in199, in13); let t606 = circuit_mul(t599, t605); let t607 = circuit_sub(in199, in13); let t608 = circuit_mul(in3, t607); let t609 = circuit_inverse(t608); let t610 = circuit_mul(in104, t609); let t611 = circuit_add(t604, t610); let t612 = circuit_sub(in199, in14); let t613 = circuit_mul(t606, t612); let t614 = circuit_sub(in199, in14); let t615 = circuit_mul(in2, t614); let t616 = circuit_inverse(t615); let t617 = circuit_mul(in105, t616); let t618 = circuit_add(t611, t617); let t619 = circuit_mul(t618, t613); let t620 = circuit_sub(t551, in0); let t621 = circuit_mul(in199, t620); let t622 = circuit_add(in0, t621); let t623 = circuit_mul(t549, t622); let t624 = circuit_mul(t550, in211); let t625 = circuit_mul(t551, t551); let t626 = circuit_add(in106, in107); let t627 = circuit_sub(t626, t619); let t628 = circuit_mul(t627, t624); let t629 = circuit_add(t555, t628); let t630 = circuit_sub(in200, in7); let t631 = circuit_mul(in0, t630); let t632 = circuit_sub(in200, in7); let t633 = circuit_mul(in2, t632); let t634 = circuit_inverse(t633); let t635 = circuit_mul(in106, t634); let t636 = circuit_add(in7, t635); let t637 = circuit_sub(in200, in0); let t638 = circuit_mul(t631, t637); let t639 = circuit_sub(in200, in0); let t640 = circuit_mul(in3, t639); let t641 = circuit_inverse(t640); let t642 = circuit_mul(in107, t641); let t643 = circuit_add(t636, t642); let t644 = circuit_sub(in200, in8); let t645 = circuit_mul(t638, t644); let t646 = circuit_sub(in200, in8); let t647 = circuit_mul(in4, t646); let t648 = circuit_inverse(t647); let t649 = circuit_mul(in108, t648); let t650 = circuit_add(t643, t649); let t651 = circuit_sub(in200, in9); let t652 = circuit_mul(t645, t651); let t653 = circuit_sub(in200, in9); let t654 = circuit_mul(in5, t653); let t655 = circuit_inverse(t654); let t656 = circuit_mul(in109, t655); let t657 = circuit_add(t650, t656); let t658 = circuit_sub(in200, in10); let t659 = circuit_mul(t652, t658); let t660 = circuit_sub(in200, in10); let t661 = circuit_mul(in6, t660); let t662 = circuit_inverse(t661); let t663 = circuit_mul(in110, t662); let t664 = circuit_add(t657, t663); let t665 = circuit_sub(in200, in11); let t666 = circuit_mul(t659, t665); let t667 = circuit_sub(in200, in11); let t668 = circuit_mul(in5, t667); let t669 = circuit_inverse(t668); let t670 = circuit_mul(in111, t669); let t671 = circuit_add(t664, t670); let t672 = circuit_sub(in200, in12); let t673 = circuit_mul(t666, t672); let t674 = circuit_sub(in200, in12); let t675 = circuit_mul(in4, t674); let t676 = circuit_inverse(t675); let t677 = circuit_mul(in112, t676); let t678 = circuit_add(t671, t677); let t679 = circuit_sub(in200, in13); let t680 = circuit_mul(t673, t679); let t681 = circuit_sub(in200, in13); let t682 = circuit_mul(in3, t681); let t683 = circuit_inverse(t682); let t684 = circuit_mul(in113, t683); let t685 = circuit_add(t678, t684); let t686 = circuit_sub(in200, in14); let t687 = circuit_mul(t680, t686); let t688 = circuit_sub(in200, in14); let t689 = circuit_mul(in2, t688); let t690 = circuit_inverse(t689); let t691 = circuit_mul(in114, t690); let t692 = circuit_add(t685, t691); let t693 = circuit_mul(t692, t687); let t694 = circuit_sub(t625, in0); let t695 = circuit_mul(in200, t694); let t696 = circuit_add(in0, t695); let t697 = circuit_mul(t623, t696); let t698 = circuit_mul(t624, in211); let t699 = circuit_mul(t625, t625); let t700 = circuit_add(in115, in116); let t701 = circuit_sub(t700, t693); let t702 = circuit_mul(t701, t698); let t703 = circuit_add(t629, t702); let t704 = circuit_sub(in201, in7); let t705 = circuit_mul(in0, t704); let t706 = circuit_sub(in201, in7); let t707 = circuit_mul(in2, t706); let t708 = circuit_inverse(t707); let t709 = circuit_mul(in115, t708); let t710 = circuit_add(in7, t709); let t711 = circuit_sub(in201, in0); let t712 = circuit_mul(t705, t711); let t713 = circuit_sub(in201, in0); let t714 = circuit_mul(in3, t713); let t715 = circuit_inverse(t714); let t716 = circuit_mul(in116, t715); let t717 = circuit_add(t710, t716); let t718 = circuit_sub(in201, in8); let t719 = circuit_mul(t712, t718); let t720 = circuit_sub(in201, in8); let t721 = circuit_mul(in4, t720); let t722 = circuit_inverse(t721); let t723 = circuit_mul(in117, t722); let t724 = circuit_add(t717, t723); let t725 = circuit_sub(in201, in9); let t726 = circuit_mul(t719, t725); let t727 = circuit_sub(in201, in9); let t728 = circuit_mul(in5, t727); let t729 = circuit_inverse(t728); let t730 = circuit_mul(in118, t729); let t731 = circuit_add(t724, t730); let t732 = circuit_sub(in201, in10); let t733 = circuit_mul(t726, t732); let t734 = circuit_sub(in201, in10); let t735 = circuit_mul(in6, t734); let t736 = circuit_inverse(t735); let t737 = circuit_mul(in119, t736); let t738 = circuit_add(t731, t737); let t739 = circuit_sub(in201, in11); let t740 = circuit_mul(t733, t739); let t741 = circuit_sub(in201, in11); let t742 = circuit_mul(in5, t741); let t743 = circuit_inverse(t742); let t744 = circuit_mul(in120, t743); let t745 = circuit_add(t738, t744); let t746 = circuit_sub(in201, in12); let t747 = circuit_mul(t740, t746); let t748 = circuit_sub(in201, in12); let t749 = circuit_mul(in4, t748); let t750 = circuit_inverse(t749); let t751 = circuit_mul(in121, t750); let t752 = circuit_add(t745, t751); let t753 = circuit_sub(in201, in13); let t754 = circuit_mul(t747, t753); let t755 = circuit_sub(in201, in13); let t756 = circuit_mul(in3, t755); let t757 = circuit_inverse(t756); let t758 = circuit_mul(in122, t757); let t759 = circuit_add(t752, t758); let t760 = circuit_sub(in201, in14); let t761 = circuit_mul(t754, t760); let t762 = circuit_sub(in201, in14); let t763 = circuit_mul(in2, t762); let t764 = circuit_inverse(t763); let t765 = circuit_mul(in123, t764); let t766 = circuit_add(t759, t765); let t767 = circuit_mul(t766, t761); let t768 = circuit_sub(t699, in0); let t769 = circuit_mul(in201, t768); let t770 = circuit_add(in0, t769); let t771 = circuit_mul(t697, t770); let t772 = circuit_mul(t698, in211); let t773 = circuit_mul(t699, t699); let t774 = circuit_add(in124, in125); let t775 = circuit_sub(t774, t767); let t776 = circuit_mul(t775, t772); let t777 = circuit_add(t703, t776); let t778 = circuit_sub(in202, in7); let t779 = circuit_mul(in0, t778); let t780 = circuit_sub(in202, in7); let t781 = circuit_mul(in2, t780); let t782 = circuit_inverse(t781); let t783 = circuit_mul(in124, t782); let t784 = circuit_add(in7, t783); let t785 = circuit_sub(in202, in0); let t786 = circuit_mul(t779, t785); let t787 = circuit_sub(in202, in0); let t788 = circuit_mul(in3, t787); let t789 = circuit_inverse(t788); let t790 = circuit_mul(in125, t789); let t791 = circuit_add(t784, t790); let t792 = circuit_sub(in202, in8); let t793 = circuit_mul(t786, t792); let t794 = circuit_sub(in202, in8); let t795 = circuit_mul(in4, t794); let t796 = circuit_inverse(t795); let t797 = circuit_mul(in126, t796); let t798 = circuit_add(t791, t797); let t799 = circuit_sub(in202, in9); let t800 = circuit_mul(t793, t799); let t801 = circuit_sub(in202, in9); let t802 = circuit_mul(in5, t801); let t803 = circuit_inverse(t802); let t804 = circuit_mul(in127, t803); let t805 = circuit_add(t798, t804); let t806 = circuit_sub(in202, in10); let t807 = circuit_mul(t800, t806); let t808 = circuit_sub(in202, in10); let t809 = circuit_mul(in6, t808); let t810 = circuit_inverse(t809); let t811 = circuit_mul(in128, t810); let t812 = circuit_add(t805, t811); let t813 = circuit_sub(in202, in11); let t814 = circuit_mul(t807, t813); let t815 = circuit_sub(in202, in11); let t816 = circuit_mul(in5, t815); let t817 = circuit_inverse(t816); let t818 = circuit_mul(in129, t817); let t819 = circuit_add(t812, t818); let t820 = circuit_sub(in202, in12); let t821 = circuit_mul(t814, t820); let t822 = circuit_sub(in202, in12); let t823 = circuit_mul(in4, t822); let t824 = circuit_inverse(t823); let t825 = circuit_mul(in130, t824); let t826 = circuit_add(t819, t825); let t827 = circuit_sub(in202, in13); let t828 = circuit_mul(t821, t827); let t829 = circuit_sub(in202, in13); let t830 = circuit_mul(in3, t829); let t831 = circuit_inverse(t830); let t832 = circuit_mul(in131, t831); let t833 = circuit_add(t826, t832); let t834 = circuit_sub(in202, in14); let t835 = circuit_mul(t828, t834); let t836 = circuit_sub(in202, in14); let t837 = circuit_mul(in2, t836); let t838 = circuit_inverse(t837); let t839 = circuit_mul(in132, t838); let t840 = circuit_add(t833, t839); let t841 = circuit_mul(t840, t835); let t842 = circuit_sub(t773, in0); let t843 = circuit_mul(in202, t842); let t844 = circuit_add(in0, t843); let t845 = circuit_mul(t771, t844); let t846 = circuit_mul(t772, in211); let t847 = circuit_mul(t773, t773); let t848 = circuit_add(in133, in134); let t849 = circuit_sub(t848, t841); let t850 = circuit_mul(t849, t846); let t851 = circuit_add(t777, t850); let t852 = circuit_sub(in203, in7); let t853 = circuit_mul(in0, t852); let t854 = circuit_sub(in203, in7); let t855 = circuit_mul(in2, t854); let t856 = circuit_inverse(t855); let t857 = circuit_mul(in133, t856); let t858 = circuit_add(in7, t857); let t859 = circuit_sub(in203, in0); let t860 = circuit_mul(t853, t859); let t861 = circuit_sub(in203, in0); let t862 = circuit_mul(in3, t861); let t863 = circuit_inverse(t862); let t864 = circuit_mul(in134, t863); let t865 = circuit_add(t858, t864); let t866 = circuit_sub(in203, in8); let t867 = circuit_mul(t860, t866); let t868 = circuit_sub(in203, in8); let t869 = circuit_mul(in4, t868); let t870 = circuit_inverse(t869); let t871 = circuit_mul(in135, t870); let t872 = circuit_add(t865, t871); let t873 = circuit_sub(in203, in9); let t874 = circuit_mul(t867, t873); let t875 = circuit_sub(in203, in9); let t876 = circuit_mul(in5, t875); let t877 = circuit_inverse(t876); let t878 = circuit_mul(in136, t877); let t879 = circuit_add(t872, t878); let t880 = circuit_sub(in203, in10); let t881 = circuit_mul(t874, t880); let t882 = circuit_sub(in203, in10); let t883 = circuit_mul(in6, t882); let t884 = circuit_inverse(t883); let t885 = circuit_mul(in137, t884); let t886 = circuit_add(t879, t885); let t887 = circuit_sub(in203, in11); let t888 = circuit_mul(t881, t887); let t889 = circuit_sub(in203, in11); let t890 = circuit_mul(in5, t889); let t891 = circuit_inverse(t890); let t892 = circuit_mul(in138, t891); let t893 = circuit_add(t886, t892); let t894 = circuit_sub(in203, in12); let t895 = circuit_mul(t888, t894); let t896 = circuit_sub(in203, in12); let t897 = circuit_mul(in4, t896); let t898 = circuit_inverse(t897); let t899 = circuit_mul(in139, t898); let t900 = circuit_add(t893, t899); let t901 = circuit_sub(in203, in13); let t902 = circuit_mul(t895, t901); let t903 = circuit_sub(in203, in13); let t904 = circuit_mul(in3, t903); let t905 = circuit_inverse(t904); let t906 = circuit_mul(in140, t905); let t907 = circuit_add(t900, t906); let t908 = circuit_sub(in203, in14); let t909 = circuit_mul(t902, t908); let t910 = circuit_sub(in203, in14); let t911 = circuit_mul(in2, t910); let t912 = circuit_inverse(t911); let t913 = circuit_mul(in141, t912); let t914 = circuit_add(t907, t913); let t915 = circuit_mul(t914, t909); let t916 = circuit_sub(t847, in0); let t917 = circuit_mul(in203, t916); let t918 = circuit_add(in0, t917); let t919 = circuit_mul(t845, t918); let t920 = circuit_mul(t846, in211); let t921 = circuit_mul(t847, t847); let t922 = circuit_add(in142, in143); let t923 = circuit_sub(t922, t915); let t924 = circuit_mul(t923, t920); let t925 = circuit_add(t851, t924); let t926 = circuit_sub(in204, in7); let t927 = circuit_mul(in0, t926); let t928 = circuit_sub(in204, in7); let t929 = circuit_mul(in2, t928); let t930 = circuit_inverse(t929); let t931 = circuit_mul(in142, t930); let t932 = circuit_add(in7, t931); let t933 = circuit_sub(in204, in0); let t934 = circuit_mul(t927, t933); let t935 = circuit_sub(in204, in0); let t936 = circuit_mul(in3, t935); let t937 = circuit_inverse(t936); let t938 = circuit_mul(in143, t937); let t939 = circuit_add(t932, t938); let t940 = circuit_sub(in204, in8); let t941 = circuit_mul(t934, t940); let t942 = circuit_sub(in204, in8); let t943 = circuit_mul(in4, t942); let t944 = circuit_inverse(t943); let t945 = circuit_mul(in144, t944); let t946 = circuit_add(t939, t945); let t947 = circuit_sub(in204, in9); let t948 = circuit_mul(t941, t947); let t949 = circuit_sub(in204, in9); let t950 = circuit_mul(in5, t949); let t951 = circuit_inverse(t950); let t952 = circuit_mul(in145, t951); let t953 = circuit_add(t946, t952); let t954 = circuit_sub(in204, in10); let t955 = circuit_mul(t948, t954); let t956 = circuit_sub(in204, in10); let t957 = circuit_mul(in6, t956); let t958 = circuit_inverse(t957); let t959 = circuit_mul(in146, t958); let t960 = circuit_add(t953, t959); let t961 = circuit_sub(in204, in11); let t962 = circuit_mul(t955, t961); let t963 = circuit_sub(in204, in11); let t964 = circuit_mul(in5, t963); let t965 = circuit_inverse(t964); let t966 = circuit_mul(in147, t965); let t967 = circuit_add(t960, t966); let t968 = circuit_sub(in204, in12); let t969 = circuit_mul(t962, t968); let t970 = circuit_sub(in204, in12); let t971 = circuit_mul(in4, t970); let t972 = circuit_inverse(t971); let t973 = circuit_mul(in148, t972); let t974 = circuit_add(t967, t973); let t975 = circuit_sub(in204, in13); let t976 = circuit_mul(t969, t975); let t977 = circuit_sub(in204, in13); let t978 = circuit_mul(in3, t977); let t979 = circuit_inverse(t978); let t980 = circuit_mul(in149, t979); let t981 = circuit_add(t974, t980); let t982 = circuit_sub(in204, in14); let t983 = circuit_mul(t976, t982); let t984 = circuit_sub(in204, in14); let t985 = circuit_mul(in2, t984); let t986 = circuit_inverse(t985); let t987 = circuit_mul(in150, t986); let t988 = circuit_add(t981, t987); let t989 = circuit_mul(t988, t983); let t990 = circuit_sub(t921, in0); let t991 = circuit_mul(in204, t990); let t992 = circuit_add(in0, t991); let t993 = circuit_mul(t919, t992); let t994 = circuit_sub(in158, in9); let t995 = circuit_mul(t994, in151); let t996 = circuit_mul(t995, in180); let t997 = circuit_mul(t996, in179); let t998 = circuit_mul(t997, in15); let t999 = circuit_mul(in153, in179); let t1000 = circuit_mul(in154, in180); let t1001 = circuit_mul(in155, in181); let t1002 = circuit_mul(in156, in182); let t1003 = circuit_add(t998, t999); let t1004 = circuit_add(t1003, t1000); let t1005 = circuit_add(t1004, t1001); let t1006 = circuit_add(t1005, t1002); let t1007 = circuit_add(t1006, in152); let t1008 = circuit_sub(in158, in0); let t1009 = circuit_mul(t1008, in190); let t1010 = circuit_add(t1007, t1009); let t1011 = circuit_mul(t1010, in158); let t1012 = circuit_mul(t1011, t993); let t1013 = circuit_add(in179, in182); let t1014 = circuit_add(t1013, in151); let t1015 = circuit_sub(t1014, in187); let t1016 = circuit_sub(in158, in8); let t1017 = circuit_mul(t1015, t1016); let t1018 = circuit_sub(in158, in0); let t1019 = circuit_mul(t1017, t1018); let t1020 = circuit_mul(t1019, in158); let t1021 = circuit_mul(t1020, t993); let t1022 = circuit_mul(in169, in209); let t1023 = circuit_add(in179, t1022); let t1024 = circuit_add(t1023, in210); let t1025 = circuit_mul(in170, in209); let t1026 = circuit_add(in180, t1025); let t1027 = circuit_add(t1026, in210); let t1028 = circuit_mul(t1024, t1027); let t1029 = circuit_mul(in171, in209); let t1030 = circuit_add(in181, t1029); let t1031 = circuit_add(t1030, in210); let t1032 = circuit_mul(t1028, t1031); let t1033 = circuit_mul(in172, in209); let t1034 = circuit_add(in182, t1033); let t1035 = circuit_add(t1034, in210); let t1036 = circuit_mul(t1032, t1035); let t1037 = circuit_mul(in165, in209); let t1038 = circuit_add(in179, t1037); let t1039 = circuit_add(t1038, in210); let t1040 = circuit_mul(in166, in209); let t1041 = circuit_add(in180, t1040); let t1042 = circuit_add(t1041, in210); let t1043 = circuit_mul(t1039, t1042); let t1044 = circuit_mul(in167, in209); let t1045 = circuit_add(in181, t1044); let t1046 = circuit_add(t1045, in210); let t1047 = circuit_mul(t1043, t1046); let t1048 = circuit_mul(in168, in209); let t1049 = circuit_add(in182, t1048); let t1050 = circuit_add(t1049, in210); let t1051 = circuit_mul(t1047, t1050); let t1052 = circuit_add(in183, in177); let t1053 = circuit_mul(t1036, t1052); let t1054 = circuit_mul(in178, t107); let t1055 = circuit_add(in191, t1054); let t1056 = circuit_mul(t1051, t1055); let t1057 = circuit_sub(t1053, t1056); let t1058 = circuit_mul(t1057, t993); let t1059 = circuit_mul(in178, in191); let t1060 = circuit_mul(t1059, t993); let t1061 = circuit_mul(in174, in206); let t1062 = circuit_mul(in175, in207); let t1063 = circuit_mul(in176, in208); let t1064 = circuit_add(in173, in210); let t1065 = circuit_add(t1064, t1061); let t1066 = circuit_add(t1065, t1062); let t1067 = circuit_add(t1066, t1063); let t1068 = circuit_mul(in154, in187); let t1069 = circuit_add(in179, in210); let t1070 = circuit_add(t1069, t1068); let t1071 = circuit_mul(in151, in188); let t1072 = circuit_add(in180, t1071); let t1073 = circuit_mul(in152, in189); let t1074 = circuit_add(in181, t1073); let t1075 = circuit_mul(t1072, in206); let t1076 = circuit_mul(t1074, in207); let t1077 = circuit_mul(in155, in208); let t1078 = circuit_add(t1070, t1075); let t1079 = circuit_add(t1078, t1076); let t1080 = circuit_add(t1079, t1077); let t1081 = circuit_mul(in184, t1067); let t1082 = circuit_mul(in184, t1080); let t1083 = circuit_add(in186, in157); let t1084 = circuit_mul(in186, in157); let t1085 = circuit_sub(t1083, t1084); let t1086 = circuit_mul(t1080, t1067); let t1087 = circuit_mul(t1086, in184); let t1088 = circuit_sub(t1087, t1085); let t1089 = circuit_mul(t1088, t993); let t1090 = circuit_mul(in157, t1081); let t1091 = circuit_mul(in185, t1082); let t1092 = circuit_sub(t1090, t1091); let t1093 = circuit_mul(in186, in186); let t1094 = circuit_sub(t1093, in186); let t1095 = circuit_mul(t1094, t993); let t1096 = circuit_mul(in159, t993); let t1097 = circuit_sub(in180, in179); let t1098 = circuit_sub(in181, in180); let t1099 = circuit_sub(in182, in181); let t1100 = circuit_sub(in187, in182); let t1101 = circuit_add(t1097, in16); let t1102 = circuit_add(t1101, in16); let t1103 = circuit_add(t1102, in16); let t1104 = circuit_mul(t1097, t1101); let t1105 = circuit_mul(t1104, t1102); let t1106 = circuit_mul(t1105, t1103); let t1107 = circuit_mul(t1106, t1096); let t1108 = circuit_add(t1098, in16); let t1109 = circuit_add(t1108, in16); let t1110 = circuit_add(t1109, in16); let t1111 = circuit_mul(t1098, t1108); let t1112 = circuit_mul(t1111, t1109); let t1113 = circuit_mul(t1112, t1110); let t1114 = circuit_mul(t1113, t1096); let t1115 = circuit_add(t1099, in16); let t1116 = circuit_add(t1115, in16); let t1117 = circuit_add(t1116, in16); let t1118 = circuit_mul(t1099, t1115); let t1119 = circuit_mul(t1118, t1116); let t1120 = circuit_mul(t1119, t1117); let t1121 = circuit_mul(t1120, t1096); let t1122 = circuit_add(t1100, in16); let t1123 = circuit_add(t1122, in16); let t1124 = circuit_add(t1123, in16); let t1125 = circuit_mul(t1100, t1122); let t1126 = circuit_mul(t1125, t1123); let t1127 = circuit_mul(t1126, t1124); let t1128 = circuit_mul(t1127, t1096); let t1129 = circuit_sub(in187, in180); let t1130 = circuit_mul(in181, in181); let t1131 = circuit_mul(in190, in190); let t1132 = circuit_mul(in181, in190); let t1133 = circuit_mul(t1132, in153); let t1134 = circuit_add(in188, in187); let t1135 = circuit_add(t1134, in180); let t1136 = circuit_mul(t1135, t1129); let t1137 = circuit_mul(t1136, t1129); let t1138 = circuit_sub(t1137, t1131); let t1139 = circuit_sub(t1138, t1130); let t1140 = circuit_add(t1139, t1133); let t1141 = circuit_add(t1140, t1133); let t1142 = circuit_sub(in0, in151); let t1143 = circuit_mul(t1141, t993); let t1144 = circuit_mul(t1143, in160); let t1145 = circuit_mul(t1144, t1142); let t1146 = circuit_add(in181, in189); let t1147 = circuit_mul(in190, in153); let t1148 = circuit_sub(t1147, in181); let t1149 = circuit_mul(t1146, t1129); let t1150 = circuit_sub(in188, in180); let t1151 = circuit_mul(t1150, t1148); let t1152 = circuit_add(t1149, t1151); let t1153 = circuit_mul(t1152, t993); let t1154 = circuit_mul(t1153, in160); let t1155 = circuit_mul(t1154, t1142); let t1156 = circuit_add(t1130, in17); let t1157 = circuit_mul(t1156, in180); let t1158 = circuit_add(t1130, t1130); let t1159 = circuit_add(t1158, t1158); let t1160 = circuit_mul(t1157, in18); let t1161 = circuit_add(in188, in180); let t1162 = circuit_add(t1161, in180); let t1163 = circuit_mul(t1162, t1159); let t1164 = circuit_sub(t1163, t1160); let t1165 = circuit_mul(t1164, t993); let t1166 = circuit_mul(t1165, in160); let t1167 = circuit_mul(t1166, in151); let t1168 = circuit_add(t1145, t1167); let t1169 = circuit_add(in180, in180); let t1170 = circuit_add(t1169, in180); let t1171 = circuit_mul(t1170, in180); let t1172 = circuit_sub(in180, in188); let t1173 = circuit_mul(t1171, t1172); let t1174 = circuit_add(in181, in181); let t1175 = circuit_add(in181, in189); let t1176 = circuit_mul(t1174, t1175); let t1177 = circuit_sub(t1173, t1176); let t1178 = circuit_mul(t1177, t993); let t1179 = circuit_mul(t1178, in160); let t1180 = circuit_mul(t1179, in151); let t1181 = circuit_add(t1155, t1180); let t1182 = circuit_mul(in181, in208); let t1183 = circuit_mul(in180, in207); let t1184 = circuit_add(t1182, t1183); let t1185 = circuit_mul(in179, in206); let t1186 = circuit_add(t1184, t1185); let t1187 = circuit_add(t1186, in152); let t1188 = circuit_sub(t1187, in182); let t1189 = circuit_sub(in187, in179); let t1190 = circuit_sub(in190, in182); let t1191 = circuit_sub(t1189, in0); let t1192 = circuit_mul(t1189, t1191); let t1193 = circuit_mul(t1189, in16); let t1194 = circuit_add(t1193, in0); let t1195 = circuit_mul(t1194, t1190); let t1196 = circuit_mul(in153, in154); let t1197 = circuit_mul(in161, t993); let t1198 = circuit_mul(t1196, t1197); let t1199 = circuit_mul(t1195, t1198); let t1200 = circuit_mul(t1192, t1198); let t1201 = circuit_mul(t1188, t1196); let t1202 = circuit_sub(in182, t1187); let t1203 = circuit_sub(t1202, in0); let t1204 = circuit_mul(t1202, t1203); let t1205 = circuit_mul(in189, in208); let t1206 = circuit_mul(in188, in207); let t1207 = circuit_mul(in187, in206); let t1208 = circuit_add(t1205, t1206); let t1209 = circuit_add(t1208, t1207); let t1210 = circuit_sub(in190, t1209); let t1211 = circuit_sub(in189, in181); let t1212 = circuit_mul(t1189, in16); let t1213 = circuit_add(t1212, in0); let t1214 = circuit_mul(t1210, in16); let t1215 = circuit_add(t1214, in0); let t1216 = circuit_mul(t1213, t1211); let t1217 = circuit_mul(t1216, t1215); let t1218 = circuit_mul(t1210, t1210); let t1219 = circuit_sub(t1218, t1210); let t1220 = circuit_mul(in155, t1197); let t1221 = circuit_mul(t1217, t1220); let t1222 = circuit_mul(t1192, t1220); let t1223 = circuit_mul(t1219, t1220); let t1224 = circuit_mul(t1204, in155); let t1225 = circuit_sub(in188, in180); let t1226 = circuit_mul(t1189, in16); let t1227 = circuit_add(t1226, in0); let t1228 = circuit_mul(t1227, t1225); let t1229 = circuit_sub(t1228, in181); let t1230 = circuit_mul(in156, in153); let t1231 = circuit_mul(t1229, t1230); let t1232 = circuit_mul(in151, in153); let t1233 = circuit_mul(t1188, t1232); let t1234 = circuit_add(t1201, t1231); let t1235 = circuit_add(t1234, t1233); let t1236 = circuit_add(t1235, t1224); let t1237 = circuit_mul(t1236, t1197); let t1238 = circuit_mul(in179, in188); let t1239 = circuit_mul(in187, in180); let t1240 = circuit_add(t1238, t1239); let t1241 = circuit_mul(in179, in182); let t1242 = circuit_mul(in180, in181); let t1243 = circuit_add(t1241, t1242); let t1244 = circuit_sub(t1243, in189); let t1245 = circuit_mul(t1244, in19); let t1246 = circuit_sub(t1245, in190); let t1247 = circuit_add(t1246, t1240); let t1248 = circuit_mul(t1247, in156); let t1249 = circuit_mul(t1240, in19); let t1250 = circuit_mul(in187, in188); let t1251 = circuit_add(t1249, t1250); let t1252 = circuit_add(in181, in182); let t1253 = circuit_sub(t1251, t1252); let t1254 = circuit_mul(t1253, in155); let t1255 = circuit_add(t1251, in182); let t1256 = circuit_add(in189, in190); let t1257 = circuit_sub(t1255, t1256); let t1258 = circuit_mul(t1257, in151); let t1259 = circuit_add(t1254, t1248); let t1260 = circuit_add(t1259, t1258); let t1261 = circuit_mul(t1260, in154); let t1262 = circuit_mul(in188, in20); let t1263 = circuit_add(t1262, in187); let t1264 = circuit_mul(t1263, in20); let t1265 = circuit_add(t1264, in181); let t1266 = circuit_mul(t1265, in20); let t1267 = circuit_add(t1266, in180); let t1268 = circuit_mul(t1267, in20); let t1269 = circuit_add(t1268, in179); let t1270 = circuit_sub(t1269, in182); let t1271 = circuit_mul(t1270, in156); let t1272 = circuit_mul(in189, in20); let t1273 = circuit_add(t1272, in188); let t1274 = circuit_mul(t1273, in20); let t1275 = circuit_add(t1274, in187); let t1276 = circuit_mul(t1275, in20); let t1277 = circuit_add(t1276, in182); let t1278 = circuit_mul(t1277, in20); let t1279 = circuit_add(t1278, in181); let t1280 = circuit_sub(t1279, in190); let t1281 = circuit_mul(t1280, in151); let t1282 = circuit_add(t1271, t1281); let t1283 = circuit_mul(t1282, in155); let t1284 = circuit_add(t1261, t1283); let t1285 = circuit_mul(t1284, in162); let t1286 = circuit_mul(t1285, t993); let t1287 = circuit_add(in179, in153); let t1288 = circuit_add(in180, in154); let t1289 = circuit_add(in181, in155); let t1290 = circuit_add(in182, in156); let t1291 = circuit_mul(t1287, t1287); let t1292 = circuit_mul(t1291, t1291); let t1293 = circuit_mul(t1292, t1287); let t1294 = circuit_mul(t1288, t1288); let t1295 = circuit_mul(t1294, t1294); let t1296 = circuit_mul(t1295, t1288); let t1297 = circuit_mul(t1289, t1289); let t1298 = circuit_mul(t1297, t1297); let t1299 = circuit_mul(t1298, t1289); let t1300 = circuit_mul(t1290, t1290); let t1301 = circuit_mul(t1300, t1300); let t1302 = circuit_mul(t1301, t1290); let t1303 = circuit_add(t1293, t1296); let t1304 = circuit_add(t1299, t1302); let t1305 = circuit_add(t1296, t1296); let t1306 = circuit_add(t1305, t1304); let t1307 = circuit_add(t1302, t1302); let t1308 = circuit_add(t1307, t1303); let t1309 = circuit_add(t1304, t1304); let t1310 = circuit_add(t1309, t1309); let t1311 = circuit_add(t1310, t1308); let t1312 = circuit_add(t1303, t1303); let t1313 = circuit_add(t1312, t1312); let t1314 = circuit_add(t1313, t1306); let t1315 = circuit_add(t1308, t1314); let t1316 = circuit_add(t1306, t1311); let t1317 = circuit_mul(in163, t993); let t1318 = circuit_sub(t1315, in187); let t1319 = circuit_mul(t1317, t1318); let t1320 = circuit_sub(t1314, in188); let t1321 = circuit_mul(t1317, t1320); let t1322 = circuit_sub(t1316, in189); let t1323 = circuit_mul(t1317, t1322); let t1324 = circuit_sub(t1311, in190); let t1325 = circuit_mul(t1317, t1324); let t1326 = circuit_add(in179, in153); let t1327 = circuit_mul(t1326, t1326); let t1328 = circuit_mul(t1327, t1327); let t1329 = circuit_mul(t1328, t1326); let t1330 = circuit_add(t1329, in180); let t1331 = circuit_add(t1330, in181); let t1332 = circuit_add(t1331, in182); let t1333 = circuit_mul(in164, t993); let t1334 = circuit_mul(t1329, in21); let t1335 = circuit_add(t1334, t1332); let t1336 = circuit_sub(t1335, in187); let t1337 = circuit_mul(t1333, t1336); let t1338 = circuit_mul(in180, in22); let t1339 = circuit_add(t1338, t1332); let t1340 = circuit_sub(t1339, in188); let t1341 = circuit_mul(t1333, t1340); let t1342 = circuit_mul(in181, in23); let t1343 = circuit_add(t1342, t1332); let t1344 = circuit_sub(t1343, in189); let t1345 = circuit_mul(t1333, t1344); let t1346 = circuit_mul(in182, in24); let t1347 = circuit_add(t1346, t1332); let t1348 = circuit_sub(t1347, in190); let t1349 = circuit_mul(t1333, t1348); let t1350 = circuit_mul(t1021, in212); let t1351 = circuit_add(t1012, t1350); let t1352 = circuit_mul(in212, in212); let t1353 = circuit_mul(t1058, t1352); let t1354 = circuit_add(t1351, t1353); let t1355 = circuit_mul(t1352, in212); let t1356 = circuit_mul(t1060, t1355); let t1357 = circuit_add(t1354, t1356); let t1358 = circuit_mul(t1355, in212); let t1359 = circuit_mul(t1089, t1358); let t1360 = circuit_add(t1357, t1359); let t1361 = circuit_mul(t1358, in212); let t1362 = circuit_mul(t1092, t1361); let t1363 = circuit_add(t1360, t1362); let t1364 = circuit_mul(t1361, in212); let t1365 = circuit_mul(t1095, t1364); let t1366 = circuit_add(t1363, t1365); let t1367 = circuit_mul(t1364, in212); let t1368 = circuit_mul(t1107, t1367); let t1369 = circuit_add(t1366, t1368); let t1370 = circuit_mul(t1367, in212); let t1371 = circuit_mul(t1114, t1370); let t1372 = circuit_add(t1369, t1371); let t1373 = circuit_mul(t1370, in212); let t1374 = circuit_mul(t1121, t1373); let t1375 = circuit_add(t1372, t1374); let t1376 = circuit_mul(t1373, in212); let t1377 = circuit_mul(t1128, t1376); let t1378 = circuit_add(t1375, t1377); let t1379 = circuit_mul(t1376, in212); let t1380 = circuit_mul(t1168, t1379); let t1381 = circuit_add(t1378, t1380); let t1382 = circuit_mul(t1379, in212); let t1383 = circuit_mul(t1181, t1382); let t1384 = circuit_add(t1381, t1383); let t1385 = circuit_mul(t1382, in212); let t1386 = circuit_mul(t1237, t1385); let t1387 = circuit_add(t1384, t1386); let t1388 = circuit_mul(t1385, in212); let t1389 = circuit_mul(t1199, t1388); let t1390 = circuit_add(t1387, t1389); let t1391 = circuit_mul(t1388, in212); let t1392 = circuit_mul(t1200, t1391); let t1393 = circuit_add(t1390, t1392); let t1394 = circuit_mul(t1391, in212); let t1395 = circuit_mul(t1221, t1394); let t1396 = circuit_add(t1393, t1395); let t1397 = circuit_mul(t1394, in212); let t1398 = circuit_mul(t1222, t1397); let t1399 = circuit_add(t1396, t1398); let t1400 = circuit_mul(t1397, in212); let t1401 = circuit_mul(t1223, t1400); let t1402 = circuit_add(t1399, t1401); let t1403 = circuit_mul(t1400, in212); let t1404 = circuit_mul(t1286, t1403); let t1405 = circuit_add(t1402, t1404); let t1406 = circuit_mul(t1403, in212); let t1407 = circuit_mul(t1319, t1406); let t1408 = circuit_add(t1405, t1407); let t1409 = circuit_mul(t1406, in212); let t1410 = circuit_mul(t1321, t1409); let t1411 = circuit_add(t1408, t1410); let t1412 = circuit_mul(t1409, in212); let t1413 = circuit_mul(t1323, t1412); let t1414 = circuit_add(t1411, t1413); let t1415 = circuit_mul(t1412, in212); let t1416 = circuit_mul(t1325, t1415); let t1417 = circuit_add(t1414, t1416); let t1418 = circuit_mul(t1415, in212); let t1419 = circuit_mul(t1337, t1418); let t1420 = circuit_add(t1417, t1419); let t1421 = circuit_mul(t1418, in212); let t1422 = circuit_mul(t1341, t1421); let t1423 = circuit_add(t1420, t1422); let t1424 = circuit_mul(t1421, in212); let t1425 = circuit_mul(t1345, t1424); let t1426 = circuit_add(t1423, t1425); let t1427 = circuit_mul(t1424, in212); let t1428 = circuit_mul(t1349, t1427); let t1429 = circuit_add(t1426, t1428); let t1430 = circuit_mul(in195, in196); let t1431 = circuit_mul(t1430, in197); let t1432 = circuit_mul(t1431, in198); let t1433 = circuit_mul(t1432, in199); let t1434 = circuit_mul(t1433, in200); let t1435 = circuit_mul(t1434, in201); let t1436 = circuit_mul(t1435, in202); let t1437 = circuit_mul(t1436, in203); let t1438 = circuit_mul(t1437, in204); let t1439 = circuit_sub(in0, t1438); let t1440 = circuit_mul(t1429, t1439); let t1441 = circuit_mul(in192, in213); let t1442 = circuit_add(t1440, t1441); let t1443 = circuit_sub(t1442, t989); let modulus = modulus; let mut circuit_inputs = (t925, t1443).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(ZK_HONK_SUMCHECK_SIZE_12_PUB_17_GRUMPKIN_CONSTANTS.span()); // in0 - in24 // Fill inputs: for val in p_public_inputs { circuit_inputs = circuit_inputs.next_u256(*val); } // in25 - in25 for val in p_pairing_point_object { circuit_inputs = circuit_inputs.next_u256(*val); } // in26 - in41 circuit_inputs = circuit_inputs.next_2(libra_sum); // in42 for val in sumcheck_univariates_flat { circuit_inputs = circuit_inputs.next_u256(*val); } // in43 - in150 for val in sumcheck_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in151 - in191 circuit_inputs = circuit_inputs.next_2(libra_evaluation); // in192 for val in tp_sum_check_u_challenges { circuit_inputs = circuit_inputs.next_u128(*val); } // in193 - in204 circuit_inputs = circuit_inputs.next_u128(tp_gate_challenge); // in205 circuit_inputs = circuit_inputs.next_2(tp_eta_1); // in206 circuit_inputs = circuit_inputs.next_2(tp_eta_2); // in207 circuit_inputs = circuit_inputs.next_2(tp_eta_3); // in208 circuit_inputs = circuit_inputs.next_2(tp_beta); // in209 circuit_inputs = circuit_inputs.next_2(tp_gamma); // in210 circuit_inputs = circuit_inputs.next_2(tp_base_rlc); // in211 circuit_inputs = circuit_inputs.next_u128(tp_alpha); // in212 circuit_inputs = circuit_inputs.next_2(tp_libra_challenge); // in213 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let check_rlc: u384 = outputs.get_output(t925); let check: u384 = outputs.get_output(t1443); return (check_rlc, check); } const ZK_HONK_SUMCHECK_SIZE_12_PUB_17_GRUMPKIN_CONSTANTS: [u384; 25] = [ u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x10000000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9d80, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x79b9709143e1f593efffec51, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x5a0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x79b9709143e1f593effffd31, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x240, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x4, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x5, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x6, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x7, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x8, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x3cdcb848a1f0fac9f8000000, limb1: 0xdc2822db40c0ac2e9419f424, limb2: 0x183227397098d014, limb3: 0x0, }, u384 { limb0: 0x79b9709143e1f593f0000000, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x11, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x100000000000000000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x4000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x29ca1d7fb56821fd19d3b6e7, limb1: 0x4b1e03b4bd9490c0d03f989, limb2: 0x10dc6e9c006ea38b, limb3: 0x0, }, u384 { limb0: 0xd4dd9b84a86b38cfb45a740b, limb1: 0x149b3d0a30b3bb599df9756, limb2: 0xc28145b6a44df3e, limb3: 0x0, }, u384 { limb0: 0x60e3596170067d00141cac15, limb1: 0xb2c7645a50392798b21f75bb, limb2: 0x544b8338791518, limb3: 0x0, }, u384 { limb0: 0xb8fa852613bc534433ee428b, limb1: 0x2e2e82eb122789e352e105a3, limb2: 0x222c01175718386f, limb3: 0x0, }, ]; #[inline(always)] pub fn run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_12_circuit( p_sumcheck_evaluations: Span, p_gemini_masking_eval: u384, p_gemini_a_evaluations: Span, p_libra_poly_evals: Span, tp_gemini_r: u384, tp_rho: u384, tp_shplonk_z: u384, tp_shplonk_nu: u384, tp_sum_check_u_challenges: Span, modulus: core::circuit::CircuitModulus, ) -> ( u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, ) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x7b0c561a6148404f086204a9f36ffb0617942546750f230c893619174a57a76 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let (in33, in34, in35) = (CE::> {}, CE::> {}, CE::> {}); let (in36, in37, in38) = (CE::> {}, CE::> {}, CE::> {}); let (in39, in40, in41) = (CE::> {}, CE::> {}, CE::> {}); let (in42, in43, in44) = (CE::> {}, CE::> {}, CE::> {}); let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in61, in61); let t1 = circuit_mul(t0, t0); let t2 = circuit_mul(t1, t1); let t3 = circuit_mul(t2, t2); let t4 = circuit_mul(t3, t3); let t5 = circuit_mul(t4, t4); let t6 = circuit_mul(t5, t5); let t7 = circuit_mul(t6, t6); let t8 = circuit_mul(t7, t7); let t9 = circuit_mul(t8, t8); let t10 = circuit_mul(t9, t9); let t11 = circuit_sub(in63, in61); let t12 = circuit_inverse(t11); let t13 = circuit_add(in63, in61); let t14 = circuit_inverse(t13); let t15 = circuit_mul(in64, t14); let t16 = circuit_add(t12, t15); let t17 = circuit_inverse(in61); let t18 = circuit_mul(in64, t14); let t19 = circuit_sub(t12, t18); let t20 = circuit_mul(t17, t19); let t21 = circuit_sub(in0, t20); let t22 = circuit_sub(in0, t16); let t23 = circuit_mul(t22, in62); let t24 = circuit_mul(in3, in62); let t25 = circuit_add(in44, t24); let t26 = circuit_mul(in62, in62); let t27 = circuit_mul(t22, t26); let t28 = circuit_mul(in4, t26); let t29 = circuit_add(t25, t28); let t30 = circuit_mul(t26, in62); let t31 = circuit_mul(t22, t30); let t32 = circuit_mul(in5, t30); let t33 = circuit_add(t29, t32); let t34 = circuit_mul(t30, in62); let t35 = circuit_mul(t22, t34); let t36 = circuit_mul(in6, t34); let t37 = circuit_add(t33, t36); let t38 = circuit_mul(t34, in62); let t39 = circuit_mul(t22, t38); let t40 = circuit_mul(in7, t38); let t41 = circuit_add(t37, t40); let t42 = circuit_mul(t38, in62); let t43 = circuit_mul(t22, t42); let t44 = circuit_mul(in8, t42); let t45 = circuit_add(t41, t44); let t46 = circuit_mul(t42, in62); let t47 = circuit_mul(t22, t46); let t48 = circuit_mul(in9, t46); let t49 = circuit_add(t45, t48); let t50 = circuit_mul(t46, in62); let t51 = circuit_mul(t22, t50); let t52 = circuit_mul(in10, t50); let t53 = circuit_add(t49, t52); let t54 = circuit_mul(t50, in62); let t55 = circuit_mul(t22, t54); let t56 = circuit_mul(in11, t54); let t57 = circuit_add(t53, t56); let t58 = circuit_mul(t54, in62); let t59 = circuit_mul(t22, t58); let t60 = circuit_mul(in12, t58); let t61 = circuit_add(t57, t60); let t62 = circuit_mul(t58, in62); let t63 = circuit_mul(t22, t62); let t64 = circuit_mul(in13, t62); let t65 = circuit_add(t61, t64); let t66 = circuit_mul(t62, in62); let t67 = circuit_mul(t22, t66); let t68 = circuit_mul(in14, t66); let t69 = circuit_add(t65, t68); let t70 = circuit_mul(t66, in62); let t71 = circuit_mul(t22, t70); let t72 = circuit_mul(in15, t70); let t73 = circuit_add(t69, t72); let t74 = circuit_mul(t70, in62); let t75 = circuit_mul(t22, t74); let t76 = circuit_mul(in16, t74); let t77 = circuit_add(t73, t76); let t78 = circuit_mul(t74, in62); let t79 = circuit_mul(t22, t78); let t80 = circuit_mul(in17, t78); let t81 = circuit_add(t77, t80); let t82 = circuit_mul(t78, in62); let t83 = circuit_mul(t22, t82); let t84 = circuit_mul(in18, t82); let t85 = circuit_add(t81, t84); let t86 = circuit_mul(t82, in62); let t87 = circuit_mul(t22, t86); let t88 = circuit_mul(in19, t86); let t89 = circuit_add(t85, t88); let t90 = circuit_mul(t86, in62); let t91 = circuit_mul(t22, t90); let t92 = circuit_mul(in20, t90); let t93 = circuit_add(t89, t92); let t94 = circuit_mul(t90, in62); let t95 = circuit_mul(t22, t94); let t96 = circuit_mul(in21, t94); let t97 = circuit_add(t93, t96); let t98 = circuit_mul(t94, in62); let t99 = circuit_mul(t22, t98); let t100 = circuit_mul(in22, t98); let t101 = circuit_add(t97, t100); let t102 = circuit_mul(t98, in62); let t103 = circuit_mul(t22, t102); let t104 = circuit_mul(in23, t102); let t105 = circuit_add(t101, t104); let t106 = circuit_mul(t102, in62); let t107 = circuit_mul(t22, t106); let t108 = circuit_mul(in24, t106); let t109 = circuit_add(t105, t108); let t110 = circuit_mul(t106, in62); let t111 = circuit_mul(t22, t110); let t112 = circuit_mul(in25, t110); let t113 = circuit_add(t109, t112); let t114 = circuit_mul(t110, in62); let t115 = circuit_mul(t22, t114); let t116 = circuit_mul(in26, t114); let t117 = circuit_add(t113, t116); let t118 = circuit_mul(t114, in62); let t119 = circuit_mul(t22, t118); let t120 = circuit_mul(in27, t118); let t121 = circuit_add(t117, t120); let t122 = circuit_mul(t118, in62); let t123 = circuit_mul(t22, t122); let t124 = circuit_mul(in28, t122); let t125 = circuit_add(t121, t124); let t126 = circuit_mul(t122, in62); let t127 = circuit_mul(t22, t126); let t128 = circuit_mul(in29, t126); let t129 = circuit_add(t125, t128); let t130 = circuit_mul(t126, in62); let t131 = circuit_mul(t22, t130); let t132 = circuit_mul(in30, t130); let t133 = circuit_add(t129, t132); let t134 = circuit_mul(t130, in62); let t135 = circuit_mul(t22, t134); let t136 = circuit_mul(in31, t134); let t137 = circuit_add(t133, t136); let t138 = circuit_mul(t134, in62); let t139 = circuit_mul(t22, t138); let t140 = circuit_mul(in32, t138); let t141 = circuit_add(t137, t140); let t142 = circuit_mul(t138, in62); let t143 = circuit_mul(t22, t142); let t144 = circuit_mul(in33, t142); let t145 = circuit_add(t141, t144); let t146 = circuit_mul(t142, in62); let t147 = circuit_mul(t22, t146); let t148 = circuit_mul(in34, t146); let t149 = circuit_add(t145, t148); let t150 = circuit_mul(t146, in62); let t151 = circuit_mul(t22, t150); let t152 = circuit_mul(in35, t150); let t153 = circuit_add(t149, t152); let t154 = circuit_mul(t150, in62); let t155 = circuit_mul(t22, t154); let t156 = circuit_mul(in36, t154); let t157 = circuit_add(t153, t156); let t158 = circuit_mul(t154, in62); let t159 = circuit_mul(t22, t158); let t160 = circuit_mul(in37, t158); let t161 = circuit_add(t157, t160); let t162 = circuit_mul(t158, in62); let t163 = circuit_mul(t22, t162); let t164 = circuit_mul(in38, t162); let t165 = circuit_add(t161, t164); let t166 = circuit_mul(t162, in62); let t167 = circuit_mul(t21, t166); let t168 = circuit_add(t135, t167); let t169 = circuit_mul(in39, t166); let t170 = circuit_add(t165, t169); let t171 = circuit_mul(t166, in62); let t172 = circuit_mul(t21, t171); let t173 = circuit_add(t139, t172); let t174 = circuit_mul(in40, t171); let t175 = circuit_add(t170, t174); let t176 = circuit_mul(t171, in62); let t177 = circuit_mul(t21, t176); let t178 = circuit_add(t143, t177); let t179 = circuit_mul(in41, t176); let t180 = circuit_add(t175, t179); let t181 = circuit_mul(t176, in62); let t182 = circuit_mul(t21, t181); let t183 = circuit_add(t147, t182); let t184 = circuit_mul(in42, t181); let t185 = circuit_add(t180, t184); let t186 = circuit_mul(t181, in62); let t187 = circuit_mul(t21, t186); let t188 = circuit_add(t151, t187); let t189 = circuit_mul(in43, t186); let t190 = circuit_add(t185, t189); let t191 = circuit_sub(in1, in76); let t192 = circuit_mul(t10, t191); let t193 = circuit_mul(t10, t190); let t194 = circuit_add(t193, t193); let t195 = circuit_sub(t192, in76); let t196 = circuit_mul(in56, t195); let t197 = circuit_sub(t194, t196); let t198 = circuit_add(t192, in76); let t199 = circuit_inverse(t198); let t200 = circuit_mul(t197, t199); let t201 = circuit_sub(in1, in75); let t202 = circuit_mul(t9, t201); let t203 = circuit_mul(t9, t200); let t204 = circuit_add(t203, t203); let t205 = circuit_sub(t202, in75); let t206 = circuit_mul(in55, t205); let t207 = circuit_sub(t204, t206); let t208 = circuit_add(t202, in75); let t209 = circuit_inverse(t208); let t210 = circuit_mul(t207, t209); let t211 = circuit_sub(in1, in74); let t212 = circuit_mul(t8, t211); let t213 = circuit_mul(t8, t210); let t214 = circuit_add(t213, t213); let t215 = circuit_sub(t212, in74); let t216 = circuit_mul(in54, t215); let t217 = circuit_sub(t214, t216); let t218 = circuit_add(t212, in74); let t219 = circuit_inverse(t218); let t220 = circuit_mul(t217, t219); let t221 = circuit_sub(in1, in73); let t222 = circuit_mul(t7, t221); let t223 = circuit_mul(t7, t220); let t224 = circuit_add(t223, t223); let t225 = circuit_sub(t222, in73); let t226 = circuit_mul(in53, t225); let t227 = circuit_sub(t224, t226); let t228 = circuit_add(t222, in73); let t229 = circuit_inverse(t228); let t230 = circuit_mul(t227, t229); let t231 = circuit_sub(in1, in72); let t232 = circuit_mul(t6, t231); let t233 = circuit_mul(t6, t230); let t234 = circuit_add(t233, t233); let t235 = circuit_sub(t232, in72); let t236 = circuit_mul(in52, t235); let t237 = circuit_sub(t234, t236); let t238 = circuit_add(t232, in72); let t239 = circuit_inverse(t238); let t240 = circuit_mul(t237, t239); let t241 = circuit_sub(in1, in71); let t242 = circuit_mul(t5, t241); let t243 = circuit_mul(t5, t240); let t244 = circuit_add(t243, t243); let t245 = circuit_sub(t242, in71); let t246 = circuit_mul(in51, t245); let t247 = circuit_sub(t244, t246); let t248 = circuit_add(t242, in71); let t249 = circuit_inverse(t248); let t250 = circuit_mul(t247, t249); let t251 = circuit_sub(in1, in70); let t252 = circuit_mul(t4, t251); let t253 = circuit_mul(t4, t250); let t254 = circuit_add(t253, t253); let t255 = circuit_sub(t252, in70); let t256 = circuit_mul(in50, t255); let t257 = circuit_sub(t254, t256); let t258 = circuit_add(t252, in70); let t259 = circuit_inverse(t258); let t260 = circuit_mul(t257, t259); let t261 = circuit_sub(in1, in69); let t262 = circuit_mul(t3, t261); let t263 = circuit_mul(t3, t260); let t264 = circuit_add(t263, t263); let t265 = circuit_sub(t262, in69); let t266 = circuit_mul(in49, t265); let t267 = circuit_sub(t264, t266); let t268 = circuit_add(t262, in69); let t269 = circuit_inverse(t268); let t270 = circuit_mul(t267, t269); let t271 = circuit_sub(in1, in68); let t272 = circuit_mul(t2, t271); let t273 = circuit_mul(t2, t270); let t274 = circuit_add(t273, t273); let t275 = circuit_sub(t272, in68); let t276 = circuit_mul(in48, t275); let t277 = circuit_sub(t274, t276); let t278 = circuit_add(t272, in68); let t279 = circuit_inverse(t278); let t280 = circuit_mul(t277, t279); let t281 = circuit_sub(in1, in67); let t282 = circuit_mul(t1, t281); let t283 = circuit_mul(t1, t280); let t284 = circuit_add(t283, t283); let t285 = circuit_sub(t282, in67); let t286 = circuit_mul(in47, t285); let t287 = circuit_sub(t284, t286); let t288 = circuit_add(t282, in67); let t289 = circuit_inverse(t288); let t290 = circuit_mul(t287, t289); let t291 = circuit_sub(in1, in66); let t292 = circuit_mul(t0, t291); let t293 = circuit_mul(t0, t290); let t294 = circuit_add(t293, t293); let t295 = circuit_sub(t292, in66); let t296 = circuit_mul(in46, t295); let t297 = circuit_sub(t294, t296); let t298 = circuit_add(t292, in66); let t299 = circuit_inverse(t298); let t300 = circuit_mul(t297, t299); let t301 = circuit_sub(in1, in65); let t302 = circuit_mul(in61, t301); let t303 = circuit_mul(in61, t300); let t304 = circuit_add(t303, t303); let t305 = circuit_sub(t302, in65); let t306 = circuit_mul(in45, t305); let t307 = circuit_sub(t304, t306); let t308 = circuit_add(t302, in65); let t309 = circuit_inverse(t308); let t310 = circuit_mul(t307, t309); let t311 = circuit_mul(t310, t12); let t312 = circuit_mul(in45, in64); let t313 = circuit_mul(t312, t14); let t314 = circuit_add(t311, t313); let t315 = circuit_mul(in64, in64); let t316 = circuit_sub(in63, t0); let t317 = circuit_inverse(t316); let t318 = circuit_add(in63, t0); let t319 = circuit_inverse(t318); let t320 = circuit_mul(t315, t317); let t321 = circuit_mul(in64, t319); let t322 = circuit_mul(t315, t321); let t323 = circuit_add(t322, t320); let t324 = circuit_sub(in0, t323); let t325 = circuit_mul(t322, in46); let t326 = circuit_mul(t320, t300); let t327 = circuit_add(t325, t326); let t328 = circuit_add(t314, t327); let t329 = circuit_mul(in64, in64); let t330 = circuit_mul(t315, t329); let t331 = circuit_sub(in63, t1); let t332 = circuit_inverse(t331); let t333 = circuit_add(in63, t1); let t334 = circuit_inverse(t333); let t335 = circuit_mul(t330, t332); let t336 = circuit_mul(in64, t334); let t337 = circuit_mul(t330, t336); let t338 = circuit_add(t337, t335); let t339 = circuit_sub(in0, t338); let t340 = circuit_mul(t337, in47); let t341 = circuit_mul(t335, t290); let t342 = circuit_add(t340, t341); let t343 = circuit_add(t328, t342); let t344 = circuit_mul(in64, in64); let t345 = circuit_mul(t330, t344); let t346 = circuit_sub(in63, t2); let t347 = circuit_inverse(t346); let t348 = circuit_add(in63, t2); let t349 = circuit_inverse(t348); let t350 = circuit_mul(t345, t347); let t351 = circuit_mul(in64, t349); let t352 = circuit_mul(t345, t351); let t353 = circuit_add(t352, t350); let t354 = circuit_sub(in0, t353); let t355 = circuit_mul(t352, in48); let t356 = circuit_mul(t350, t280); let t357 = circuit_add(t355, t356); let t358 = circuit_add(t343, t357); let t359 = circuit_mul(in64, in64); let t360 = circuit_mul(t345, t359); let t361 = circuit_sub(in63, t3); let t362 = circuit_inverse(t361); let t363 = circuit_add(in63, t3); let t364 = circuit_inverse(t363); let t365 = circuit_mul(t360, t362); let t366 = circuit_mul(in64, t364); let t367 = circuit_mul(t360, t366); let t368 = circuit_add(t367, t365); let t369 = circuit_sub(in0, t368); let t370 = circuit_mul(t367, in49); let t371 = circuit_mul(t365, t270); let t372 = circuit_add(t370, t371); let t373 = circuit_add(t358, t372); let t374 = circuit_mul(in64, in64); let t375 = circuit_mul(t360, t374); let t376 = circuit_sub(in63, t4); let t377 = circuit_inverse(t376); let t378 = circuit_add(in63, t4); let t379 = circuit_inverse(t378); let t380 = circuit_mul(t375, t377); let t381 = circuit_mul(in64, t379); let t382 = circuit_mul(t375, t381); let t383 = circuit_add(t382, t380); let t384 = circuit_sub(in0, t383); let t385 = circuit_mul(t382, in50); let t386 = circuit_mul(t380, t260); let t387 = circuit_add(t385, t386); let t388 = circuit_add(t373, t387); let t389 = circuit_mul(in64, in64); let t390 = circuit_mul(t375, t389); let t391 = circuit_sub(in63, t5); let t392 = circuit_inverse(t391); let t393 = circuit_add(in63, t5); let t394 = circuit_inverse(t393); let t395 = circuit_mul(t390, t392); let t396 = circuit_mul(in64, t394); let t397 = circuit_mul(t390, t396); let t398 = circuit_add(t397, t395); let t399 = circuit_sub(in0, t398); let t400 = circuit_mul(t397, in51); let t401 = circuit_mul(t395, t250); let t402 = circuit_add(t400, t401); let t403 = circuit_add(t388, t402); let t404 = circuit_mul(in64, in64); let t405 = circuit_mul(t390, t404); let t406 = circuit_sub(in63, t6); let t407 = circuit_inverse(t406); let t408 = circuit_add(in63, t6); let t409 = circuit_inverse(t408); let t410 = circuit_mul(t405, t407); let t411 = circuit_mul(in64, t409); let t412 = circuit_mul(t405, t411); let t413 = circuit_add(t412, t410); let t414 = circuit_sub(in0, t413); let t415 = circuit_mul(t412, in52); let t416 = circuit_mul(t410, t240); let t417 = circuit_add(t415, t416); let t418 = circuit_add(t403, t417); let t419 = circuit_mul(in64, in64); let t420 = circuit_mul(t405, t419); let t421 = circuit_sub(in63, t7); let t422 = circuit_inverse(t421); let t423 = circuit_add(in63, t7); let t424 = circuit_inverse(t423); let t425 = circuit_mul(t420, t422); let t426 = circuit_mul(in64, t424); let t427 = circuit_mul(t420, t426); let t428 = circuit_add(t427, t425); let t429 = circuit_sub(in0, t428); let t430 = circuit_mul(t427, in53); let t431 = circuit_mul(t425, t230); let t432 = circuit_add(t430, t431); let t433 = circuit_add(t418, t432); let t434 = circuit_mul(in64, in64); let t435 = circuit_mul(t420, t434); let t436 = circuit_sub(in63, t8); let t437 = circuit_inverse(t436); let t438 = circuit_add(in63, t8); let t439 = circuit_inverse(t438); let t440 = circuit_mul(t435, t437); let t441 = circuit_mul(in64, t439); let t442 = circuit_mul(t435, t441); let t443 = circuit_add(t442, t440); let t444 = circuit_sub(in0, t443); let t445 = circuit_mul(t442, in54); let t446 = circuit_mul(t440, t220); let t447 = circuit_add(t445, t446); let t448 = circuit_add(t433, t447); let t449 = circuit_mul(in64, in64); let t450 = circuit_mul(t435, t449); let t451 = circuit_sub(in63, t9); let t452 = circuit_inverse(t451); let t453 = circuit_add(in63, t9); let t454 = circuit_inverse(t453); let t455 = circuit_mul(t450, t452); let t456 = circuit_mul(in64, t454); let t457 = circuit_mul(t450, t456); let t458 = circuit_add(t457, t455); let t459 = circuit_sub(in0, t458); let t460 = circuit_mul(t457, in55); let t461 = circuit_mul(t455, t210); let t462 = circuit_add(t460, t461); let t463 = circuit_add(t448, t462); let t464 = circuit_mul(in64, in64); let t465 = circuit_mul(t450, t464); let t466 = circuit_sub(in63, t10); let t467 = circuit_inverse(t466); let t468 = circuit_add(in63, t10); let t469 = circuit_inverse(t468); let t470 = circuit_mul(t465, t467); let t471 = circuit_mul(in64, t469); let t472 = circuit_mul(t465, t471); let t473 = circuit_add(t472, t470); let t474 = circuit_sub(in0, t473); let t475 = circuit_mul(t472, in56); let t476 = circuit_mul(t470, t200); let t477 = circuit_add(t475, t476); let t478 = circuit_add(t463, t477); let t479 = circuit_mul(in64, in64); let t480 = circuit_mul(t465, t479); let t481 = circuit_sub(in63, in61); let t482 = circuit_inverse(t481); let t483 = circuit_mul(in2, in61); let t484 = circuit_sub(in63, t483); let t485 = circuit_inverse(t484); let t486 = circuit_mul(in64, in64); let t487 = circuit_mul(t480, t486); let t488 = circuit_mul(t482, t487); let t489 = circuit_sub(in0, t488); let t490 = circuit_mul(t487, in64); let t491 = circuit_mul(t488, in57); let t492 = circuit_add(t478, t491); let t493 = circuit_mul(t485, t490); let t494 = circuit_sub(in0, t493); let t495 = circuit_mul(t490, in64); let t496 = circuit_mul(t493, in58); let t497 = circuit_add(t492, t496); let t498 = circuit_mul(t482, t495); let t499 = circuit_sub(in0, t498); let t500 = circuit_mul(t495, in64); let t501 = circuit_mul(t498, in59); let t502 = circuit_add(t497, t501); let t503 = circuit_mul(t482, t500); let t504 = circuit_sub(in0, t503); let t505 = circuit_mul(t503, in60); let t506 = circuit_add(t502, t505); let t507 = circuit_add(t494, t499); let modulus = modulus; let mut circuit_inputs = ( t22, t23, t27, t31, t35, t39, t43, t47, t51, t55, t59, t63, t67, t71, t75, t79, t83, t87, t91, t95, t99, t103, t107, t111, t115, t119, t123, t127, t131, t168, t173, t178, t183, t188, t155, t159, t163, t324, t339, t354, t369, t384, t399, t414, t429, t444, t459, t474, t489, t507, t504, t506, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [0x6750f230c893619174a57a76, 0xf086204a9f36ffb061794254, 0x7b0c561a6148404, 0x0], ); // in2 // Fill inputs: for val in p_sumcheck_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in3 - in43 circuit_inputs = circuit_inputs.next_2(p_gemini_masking_eval); // in44 for val in p_gemini_a_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in45 - in56 for val in p_libra_poly_evals { circuit_inputs = circuit_inputs.next_u256(*val); } // in57 - in60 circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in61 circuit_inputs = circuit_inputs.next_2(tp_rho); // in62 circuit_inputs = circuit_inputs.next_2(tp_shplonk_z); // in63 circuit_inputs = circuit_inputs.next_2(tp_shplonk_nu); // in64 for val in tp_sum_check_u_challenges { circuit_inputs = circuit_inputs.next_u128(*val); } // in65 - in76 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let scalar_1: u384 = outputs.get_output(t22); let scalar_2: u384 = outputs.get_output(t23); let scalar_3: u384 = outputs.get_output(t27); let scalar_4: u384 = outputs.get_output(t31); let scalar_5: u384 = outputs.get_output(t35); let scalar_6: u384 = outputs.get_output(t39); let scalar_7: u384 = outputs.get_output(t43); let scalar_8: u384 = outputs.get_output(t47); let scalar_9: u384 = outputs.get_output(t51); let scalar_10: u384 = outputs.get_output(t55); let scalar_11: u384 = outputs.get_output(t59); let scalar_12: u384 = outputs.get_output(t63); let scalar_13: u384 = outputs.get_output(t67); let scalar_14: u384 = outputs.get_output(t71); let scalar_15: u384 = outputs.get_output(t75); let scalar_16: u384 = outputs.get_output(t79); let scalar_17: u384 = outputs.get_output(t83); let scalar_18: u384 = outputs.get_output(t87); let scalar_19: u384 = outputs.get_output(t91); let scalar_20: u384 = outputs.get_output(t95); let scalar_21: u384 = outputs.get_output(t99); let scalar_22: u384 = outputs.get_output(t103); let scalar_23: u384 = outputs.get_output(t107); let scalar_24: u384 = outputs.get_output(t111); let scalar_25: u384 = outputs.get_output(t115); let scalar_26: u384 = outputs.get_output(t119); let scalar_27: u384 = outputs.get_output(t123); let scalar_28: u384 = outputs.get_output(t127); let scalar_29: u384 = outputs.get_output(t131); let scalar_30: u384 = outputs.get_output(t168); let scalar_31: u384 = outputs.get_output(t173); let scalar_32: u384 = outputs.get_output(t178); let scalar_33: u384 = outputs.get_output(t183); let scalar_34: u384 = outputs.get_output(t188); let scalar_35: u384 = outputs.get_output(t155); let scalar_36: u384 = outputs.get_output(t159); let scalar_37: u384 = outputs.get_output(t163); let scalar_38: u384 = outputs.get_output(t324); let scalar_39: u384 = outputs.get_output(t339); let scalar_40: u384 = outputs.get_output(t354); let scalar_41: u384 = outputs.get_output(t369); let scalar_42: u384 = outputs.get_output(t384); let scalar_43: u384 = outputs.get_output(t399); let scalar_44: u384 = outputs.get_output(t414); let scalar_45: u384 = outputs.get_output(t429); let scalar_46: u384 = outputs.get_output(t444); let scalar_47: u384 = outputs.get_output(t459); let scalar_48: u384 = outputs.get_output(t474); let scalar_49: u384 = outputs.get_output(t489); let scalar_50: u384 = outputs.get_output(t507); let scalar_51: u384 = outputs.get_output(t504); let scalar_52: u384 = outputs.get_output(t506); return ( scalar_1, scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, scalar_52, ); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_12_circuit( tp_gemini_r: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 // INPUT stack let in2 = CE::> {}; let t0 = circuit_sub(in2, in0); let t1 = circuit_inverse(t0); let t2 = circuit_mul(in1, in2); let modulus = modulus; let mut circuit_inputs = (t1, t2).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in2 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let challenge_poly_eval: u384 = outputs.get_output(t1); let root_power_times_tp_gemini_r: u384 = outputs.get_output(t2); return (challenge_poly_eval, root_power_times_tp_gemini_r); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_12_circuit( challenge_poly_eval: u384, root_power_times_tp_gemini_r: u384, tp_sumcheck_u_challenge: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in3, in0); let t1 = circuit_inverse(t0); let t2 = circuit_mul(in0, t1); let t3 = circuit_add(in2, t2); let t4 = circuit_mul(in3, in1); let t5 = circuit_mul(in0, in4); let t6 = circuit_sub(t4, in0); let t7 = circuit_inverse(t6); let t8 = circuit_mul(t5, t7); let t9 = circuit_add(t3, t8); let t10 = circuit_mul(t4, in1); let t11 = circuit_mul(t5, in4); let t12 = circuit_sub(t10, in0); let t13 = circuit_inverse(t12); let t14 = circuit_mul(t11, t13); let t15 = circuit_add(t9, t14); let t16 = circuit_mul(t10, in1); let t17 = circuit_mul(t11, in4); let t18 = circuit_sub(t16, in0); let t19 = circuit_inverse(t18); let t20 = circuit_mul(t17, t19); let t21 = circuit_add(t15, t20); let t22 = circuit_mul(t16, in1); let t23 = circuit_mul(t17, in4); let t24 = circuit_sub(t22, in0); let t25 = circuit_inverse(t24); let t26 = circuit_mul(t23, t25); let t27 = circuit_add(t21, t26); let t28 = circuit_mul(t22, in1); let t29 = circuit_mul(t23, in4); let t30 = circuit_sub(t28, in0); let t31 = circuit_inverse(t30); let t32 = circuit_mul(t29, t31); let t33 = circuit_add(t27, t32); let t34 = circuit_mul(t28, in1); let t35 = circuit_mul(t29, in4); let t36 = circuit_sub(t34, in0); let t37 = circuit_inverse(t36); let t38 = circuit_mul(t35, t37); let t39 = circuit_add(t33, t38); let t40 = circuit_mul(t34, in1); let t41 = circuit_mul(t35, in4); let t42 = circuit_sub(t40, in0); let t43 = circuit_inverse(t42); let t44 = circuit_mul(t41, t43); let t45 = circuit_add(t39, t44); let t46 = circuit_mul(t40, in1); let t47 = circuit_mul(t41, in4); let t48 = circuit_sub(t46, in0); let t49 = circuit_inverse(t48); let t50 = circuit_mul(t47, t49); let t51 = circuit_add(t45, t50); let t52 = circuit_mul(t46, in1); let modulus = modulus; let mut circuit_inputs = (t51, t52).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(challenge_poly_eval); // in2 circuit_inputs = circuit_inputs.next_2(root_power_times_tp_gemini_r); // in3 circuit_inputs = circuit_inputs.next_2(tp_sumcheck_u_challenge); // in4 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let challenge_poly_eval: u384 = outputs.get_output(t51); let root_power_times_tp_gemini_r: u384 = outputs.get_output(t52); return (challenge_poly_eval, root_power_times_tp_gemini_r); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_12_circuit( p_libra_evaluation: u384, p_libra_poly_evals: Span, tp_gemini_r: u384, challenge_poly_eval: u384, root_power_times_tp_gemini_r: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x3033ea246e506e898e97f570caffd704cb0bb460313fb720b29e139e5c100001 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in10, in0); let t1 = circuit_mul(t0, in0); let t2 = circuit_mul(t1, in0); let t3 = circuit_mul(t2, in0); let t4 = circuit_mul(t3, in0); let t5 = circuit_mul(t4, in0); let t6 = circuit_mul(t5, in0); let t7 = circuit_mul(t6, in0); let t8 = circuit_mul(t7, in0); let t9 = circuit_mul(t8, in0); let t10 = circuit_mul(t9, in0); let t11 = circuit_mul(t10, in0); let t12 = circuit_mul(t11, in0); let t13 = circuit_mul(t12, in0); let t14 = circuit_mul(t13, in0); let t15 = circuit_mul(t14, in0); let t16 = circuit_mul(t15, in0); let t17 = circuit_mul(t16, in0); let t18 = circuit_mul(t17, in0); let t19 = circuit_mul(t18, in0); let t20 = circuit_mul(t19, in0); let t21 = circuit_mul(t20, in0); let t22 = circuit_mul(t21, in0); let t23 = circuit_mul(t22, in0); let t24 = circuit_mul(t23, in0); let t25 = circuit_mul(t24, in0); let t26 = circuit_mul(t25, in0); let t27 = circuit_mul(t26, in0); let t28 = circuit_mul(t27, in0); let t29 = circuit_mul(t28, in0); let t30 = circuit_mul(t29, in0); let t31 = circuit_mul(t30, in0); let t32 = circuit_mul(t31, in0); let t33 = circuit_mul(t32, in0); let t34 = circuit_mul(t33, in0); let t35 = circuit_mul(t34, in0); let t36 = circuit_mul(t35, in0); let t37 = circuit_mul(t36, in0); let t38 = circuit_mul(t37, in0); let t39 = circuit_mul(t38, in0); let t40 = circuit_mul(t39, in0); let t41 = circuit_mul(t40, in0); let t42 = circuit_mul(t41, in0); let t43 = circuit_mul(t42, in0); let t44 = circuit_mul(t43, in0); let t45 = circuit_mul(t44, in0); let t46 = circuit_mul(t45, in0); let t47 = circuit_mul(t46, in0); let t48 = circuit_mul(t47, in0); let t49 = circuit_mul(t48, in0); let t50 = circuit_mul(t49, in0); let t51 = circuit_mul(t50, in0); let t52 = circuit_mul(t51, in0); let t53 = circuit_mul(t52, in0); let t54 = circuit_mul(t53, in0); let t55 = circuit_mul(t54, in0); let t56 = circuit_mul(t55, in0); let t57 = circuit_mul(t56, in0); let t58 = circuit_mul(t57, in0); let t59 = circuit_mul(t58, in0); let t60 = circuit_mul(t59, in0); let t61 = circuit_mul(t60, in0); let t62 = circuit_mul(t61, in0); let t63 = circuit_mul(t62, in0); let t64 = circuit_mul(t63, in0); let t65 = circuit_mul(t64, in0); let t66 = circuit_mul(t65, in0); let t67 = circuit_mul(t66, in0); let t68 = circuit_mul(t67, in0); let t69 = circuit_mul(t68, in0); let t70 = circuit_mul(t69, in0); let t71 = circuit_mul(t70, in0); let t72 = circuit_mul(t71, in0); let t73 = circuit_mul(t72, in0); let t74 = circuit_mul(t73, in0); let t75 = circuit_mul(t74, in0); let t76 = circuit_mul(t75, in0); let t77 = circuit_mul(t76, in0); let t78 = circuit_mul(t77, in0); let t79 = circuit_mul(t78, in0); let t80 = circuit_mul(t79, in0); let t81 = circuit_mul(t80, in0); let t82 = circuit_mul(t81, in0); let t83 = circuit_mul(t82, in0); let t84 = circuit_mul(t83, in0); let t85 = circuit_mul(t84, in0); let t86 = circuit_mul(t85, in0); let t87 = circuit_mul(t86, in0); let t88 = circuit_mul(t87, in0); let t89 = circuit_mul(t88, in0); let t90 = circuit_mul(t89, in0); let t91 = circuit_mul(t90, in0); let t92 = circuit_mul(t91, in0); let t93 = circuit_mul(t92, in0); let t94 = circuit_mul(t93, in0); let t95 = circuit_mul(t94, in0); let t96 = circuit_mul(t95, in0); let t97 = circuit_mul(t96, in0); let t98 = circuit_mul(t97, in0); let t99 = circuit_mul(t98, in0); let t100 = circuit_mul(t99, in0); let t101 = circuit_mul(t100, in0); let t102 = circuit_mul(t101, in0); let t103 = circuit_mul(t102, in0); let t104 = circuit_mul(t103, in0); let t105 = circuit_mul(t104, in0); let t106 = circuit_mul(t105, in0); let t107 = circuit_mul(t106, in0); let t108 = circuit_mul(t107, in0); let t109 = circuit_mul(t108, in0); let t110 = circuit_mul(t109, in0); let t111 = circuit_mul(t110, in0); let t112 = circuit_mul(t111, in0); let t113 = circuit_mul(t112, in0); let t114 = circuit_mul(t113, in0); let t115 = circuit_mul(t114, in0); let t116 = circuit_mul(t115, in0); let t117 = circuit_mul(t116, in0); let t118 = circuit_mul(t117, in0); let t119 = circuit_mul(t118, in0); let t120 = circuit_mul(t119, in0); let t121 = circuit_mul(t120, in0); let t122 = circuit_mul(t121, in0); let t123 = circuit_mul(t122, in0); let t124 = circuit_mul(t123, in0); let t125 = circuit_mul(t124, in0); let t126 = circuit_mul(t125, in0); let t127 = circuit_mul(t126, in0); let t128 = circuit_mul(t127, in0); let t129 = circuit_mul(t128, in0); let t130 = circuit_mul(t129, in0); let t131 = circuit_mul(t130, in0); let t132 = circuit_mul(t131, in0); let t133 = circuit_mul(t132, in0); let t134 = circuit_mul(t133, in0); let t135 = circuit_mul(t134, in0); let t136 = circuit_mul(t135, in0); let t137 = circuit_mul(t136, in0); let t138 = circuit_mul(t137, in0); let t139 = circuit_mul(t138, in0); let t140 = circuit_mul(t139, in0); let t141 = circuit_mul(t140, in0); let t142 = circuit_mul(t141, in0); let t143 = circuit_mul(t142, in0); let t144 = circuit_mul(t143, in0); let t145 = circuit_mul(t144, in0); let t146 = circuit_sub(in8, in1); let t147 = circuit_inverse(t146); let t148 = circuit_sub(t145, in1); let t149 = circuit_inverse(t148); let t150 = circuit_mul(in8, in8); let t151 = circuit_mul(t150, t150); let t152 = circuit_mul(t151, t151); let t153 = circuit_mul(t152, t152); let t154 = circuit_mul(t153, t153); let t155 = circuit_mul(t154, t154); let t156 = circuit_mul(t155, t155); let t157 = circuit_mul(t156, t156); let t158 = circuit_sub(t157, in1); let t159 = circuit_mul(t158, in2); let t160 = circuit_mul(in9, t159); let t161 = circuit_mul(t147, t159); let t162 = circuit_mul(t149, t159); let t163 = circuit_mul(t161, in6); let t164 = circuit_sub(in8, in0); let t165 = circuit_sub(in5, in6); let t166 = circuit_mul(in4, t160); let t167 = circuit_sub(t165, t166); let t168 = circuit_mul(t164, t167); let t169 = circuit_add(t163, t168); let t170 = circuit_sub(in6, in3); let t171 = circuit_mul(t162, t170); let t172 = circuit_add(t169, t171); let t173 = circuit_mul(t158, in7); let t174 = circuit_sub(t172, t173); let modulus = modulus; let mut circuit_inputs = (t158, t174).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [0x313fb720b29e139e5c100001, 0x8e97f570caffd704cb0bb460, 0x3033ea246e506e89, 0x0], ); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_libra_evaluation); // in3 for val in p_libra_poly_evals { circuit_inputs = circuit_inputs.next_u256(*val); } // in4 - in7 circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in8 circuit_inputs = circuit_inputs.next_2(challenge_poly_eval); // in9 circuit_inputs = circuit_inputs.next_2(root_power_times_tp_gemini_r); // in10 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let vanishing_check: u384 = outputs.get_output(t158); let diff_check: u384 = outputs.get_output(t174); return (vanishing_check, diff_check); } impl CircuitDefinition52< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, > of core::circuit::CircuitDefinition< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), > { type CircuitType = core::circuit::Circuit< ( E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, ), >; } impl MyDrp_52< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, > of Drop< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), >; #[inline(never)] pub fn is_on_curve_excluding_infinity_bn254(p: G1Point, modulus: CircuitModulus) -> bool { // INPUT stack // y^2 = x^3 + 3 let (in0, in1) = (CE::> {}, CE::> {}); let y2 = circuit_mul(in1, in1); let x2 = circuit_mul(in0, in0); let x3 = circuit_mul(in0, x2); let y2_minus_x3 = circuit_sub(y2, x3); let mut circuit_inputs = (y2_minus_x3,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check: u384 = outputs.get_output(y2_minus_x3); return zero_check == u384 { limb0: 3, limb1: 0, limb2: 0, limb3: 0 }; } ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/src/honk_verifier_constants.cairo ================================================ // Generated by Garaga version 1.1.0 use garaga::apps::noir::HonkVk; use garaga::definitions::{G1Point, G2Line, u288, u384}; pub const vk: HonkVk = HonkVk { vk_hash: 1655602901159187576028713697867454584902070339986579942408953720408510516376, log_circuit_size: 12, public_inputs_size: 17, qm: G1Point { x: u384 { limb0: 0x1a11b55dce82f38413640a64, limb1: 0x25c78e040da5a5cbe6f296ee, limb2: 0x142bd66bdb7a2bc1, limb3: 0x0, }, y: u384 { limb0: 0x3dc8a5d19d0bf85b0fa95ad4, limb1: 0xaa34836fe60428f70dee9285, limb2: 0xd1415082e63c88e, limb3: 0x0, }, }, qc: G1Point { x: u384 { limb0: 0xcd51216bd8c56683467cd704, limb1: 0x7c77ce4f20f0fd5a3a264861, limb2: 0x2deae537974aa569, limb3: 0x0, }, y: u384 { limb0: 0xa1179c7a8ed5c59a1015e784, limb1: 0x714496966bf5f4374fb6087b, limb2: 0x68627460599c3db, limb3: 0x0, }, }, ql: G1Point { x: u384 { limb0: 0x36d34df5c2aab80f85a218f2, limb1: 0x864a67847d46222c9aee090f, limb2: 0x6681df238df2a0f, limb3: 0x0, }, y: u384 { limb0: 0xbc5d11d2d55e4ac8adccae27, limb1: 0xb9c1b8da3c671ec025fe40ee, limb2: 0x18e37167fd19d013, limb3: 0x0, }, }, qr: G1Point { x: u384 { limb0: 0xfe3f9cf39c6f73896b06e821, limb1: 0x3dc4669f3d97f847e96e4bce, limb2: 0x177c7a07701c29d1, limb3: 0x0, }, y: u384 { limb0: 0x7c23cf6fe4a49a8e4f4c5aba, limb1: 0x38f1a638b192ffc9b995fd68, limb2: 0x2d31ea12ba12ee23, limb3: 0x0, }, }, qo: G1Point { x: u384 { limb0: 0xd8b0a3fb6597416a145754e3, limb1: 0xac68b01fa7f3faaa5a881854, limb2: 0x2d623ef9f6f62903, limb3: 0x0, }, y: u384 { limb0: 0x6059e6db24a7e1bfc51be2ac, limb1: 0x52b442fa3ce1643a24c7ac8e, limb2: 0x20b75671e0dd20da, limb3: 0x0, }, }, q4: G1Point { x: u384 { limb0: 0x528aeba6bdb01913c3236ff8, limb1: 0xe2edafe7a56dfd287d677b48, limb2: 0x7ea8dd8b4d3fd18, limb3: 0x0, }, y: u384 { limb0: 0x853ad38b76968342e932d84b, limb1: 0xe23f777f35827a35ea2716bc, limb2: 0x2826602478d64dc4, limb3: 0x0, }, }, qLookup: G1Point { x: u384 { limb0: 0x53f9b24d923d8f404cb0bbc9, limb1: 0x75a8449d3d5ce8bc3661650d, limb2: 0xc4032c3079594eb, limb3: 0x0, }, y: u384 { limb0: 0xa0ca89441369b7c24301f851, limb1: 0xf0158fd6da81f54eb5fe796, limb2: 0x1084d709650356d4, limb3: 0x0, }, }, qArith: G1Point { x: u384 { limb0: 0x1c518c7ea0b38257198a9523, limb1: 0xc2c72a3c00da41d4c7c7b6d0, limb2: 0x3057f9cfd5edb0e7, limb3: 0x0, }, y: u384 { limb0: 0xf647b842154c13fa145167b7, limb1: 0x6a98575cedc65ee5700a7148, limb2: 0x27eb0839ef4980d, limb3: 0x0, }, }, qDeltaRange: G1Point { x: u384 { limb0: 0xbefcd8cd631818993e143702, limb1: 0x3b9a8bc08ae2fdbd8e9dc005, limb2: 0x1775fbd3ba5e4316, limb3: 0x0, }, y: u384 { limb0: 0xbdde06678d3bce4455d2086f, limb1: 0x9e409fcb2e19a72238c07631, limb2: 0x1d8011ee756abfa1, limb3: 0x0, }, }, qElliptic: G1Point { x: u384 { limb0: 0x990b1eaa86226b3574e5c43f, limb1: 0x50fb0eae1d72783faba96bc3, limb2: 0x9c706e73a00d844, limb3: 0x0, }, y: u384 { limb0: 0x9b1f547ec36638d7b5a1ecd9, limb1: 0x68fcae74683a84de1084739f, limb2: 0x276d401f1c0f9a26, limb3: 0x0, }, }, qMemory: G1Point { x: u384 { limb0: 0xc20dedd7ff81c5677d3286ce, limb1: 0x276f3537c64334419e05b13f, limb2: 0x12b12523f7d04a83, limb3: 0x0, }, y: u384 { limb0: 0x4e602d1c13a77a2472f082da, limb1: 0x55a526829445f3fda95e243c, limb2: 0x2e741be4fe42cc11, limb3: 0x0, }, }, qNnf: G1Point { x: u384 { limb0: 0x5526834f93c6db848d56dcb0, limb1: 0xe4e8e364439d0abba02dc62a, limb2: 0x16a1350662e14b4c, limb3: 0x0, }, y: u384 { limb0: 0xb2e746ed0b6e85782c26040e, limb1: 0x9296d71489889503dda143f0, limb2: 0x563b1f480cad906, limb3: 0x0, }, }, qPoseidon2External: G1Point { x: u384 { limb0: 0xe4d88b5517e40b2a0133f401, limb1: 0x42f6c756379f231d5f472088, limb2: 0x20e1bb3056279dc3, limb3: 0x0, }, y: u384 { limb0: 0x2c8d1a5a6b3bd0ec93b42e77, limb1: 0x9eb4da763de77062d23ce01e, limb2: 0x23ee36ecb11b6278, limb3: 0x0, }, }, qPoseidon2Internal: G1Point { x: u384 { limb0: 0x19d18424d0e92f60a31671d9, limb1: 0xfdda50b3205d5aa4486b6325, limb2: 0xd1611c856951969, limb3: 0x0, }, y: u384 { limb0: 0x94aa3cadd7cd42e719521e0f, limb1: 0x30c0b534ea958de4c47e2f4c, limb2: 0xce97ee59d45d762, limb3: 0x0, }, }, s1: G1Point { x: u384 { limb0: 0x1b074244b7337b923c097eaf, limb1: 0xd2ae3eafb3800ee0eaf997cb, limb2: 0x154bdee4123a9946, limb3: 0x0, }, y: u384 { limb0: 0xf34e2352250dd3fb63d6d8c6, limb1: 0x3c0953803a3a34d916eefb5b, limb2: 0xd5f22b8ade2c19f, limb3: 0x0, }, }, s2: G1Point { x: u384 { limb0: 0x111168b4d7ab689558c334db, limb1: 0x7c62cc30718076db1836d9e1, limb2: 0x22d2dd0a34c3a1da, limb3: 0x0, }, y: u384 { limb0: 0x98a26842094b80c6e88321bf, limb1: 0x243059518c261a4137e7f6a6, limb2: 0x262c701396f0e3ae, limb3: 0x0, }, }, s3: G1Point { x: u384 { limb0: 0xe1213cb7ef934c944e4e8374, limb1: 0x84b08b441d010fc2976235c0, limb2: 0x172f8c6455a2bfe2, limb3: 0x0, }, y: u384 { limb0: 0x960773bd1e8b46a6a182239d, limb1: 0x640beab3f563e0a2402c116a, limb2: 0x178afa12bf161e7e, limb3: 0x0, }, }, s4: G1Point { x: u384 { limb0: 0xd14c60e677f8e1897f658057, limb1: 0x33204ad4109fa0fbb54c4fea, limb2: 0x21f45516c16fcb30, limb3: 0x0, }, y: u384 { limb0: 0x52efc7a0ee6a29e06296bb4d, limb1: 0xb82792c925627d7348f0bf11, limb2: 0xa7a5c9f897fd8da, limb3: 0x0, }, }, id1: G1Point { x: u384 { limb0: 0xaa69e812f125d20848fd1c50, limb1: 0x621962d025f0fbb42467ce5c, limb2: 0x1d1934c19b595461, limb3: 0x0, }, y: u384 { limb0: 0x8971dba72882ee742a0b57f4, limb1: 0xdf91438bfa5b19a7bad0f91d, limb2: 0x10e15c437db6ae7e, limb3: 0x0, }, }, id2: G1Point { x: u384 { limb0: 0x3a6957e0c9aa54ec21894a61, limb1: 0x320938baa053cd1f3dccb71, limb2: 0x146dc127b5450502, limb3: 0x0, }, y: u384 { limb0: 0xfd19216bf0829882cdabebe6, limb1: 0x828ba063530a81a329131fb4, limb2: 0x2d5cbdbf9edeff0d, limb3: 0x0, }, }, id3: G1Point { x: u384 { limb0: 0xbe73592b0b543997ac9ec27b, limb1: 0x600ed91fa96cd915db4ed7fd, limb2: 0x1e214a8b0ce35f8e, limb3: 0x0, }, y: u384 { limb0: 0x5eb2130b9c574c4e04e6e477, limb1: 0x7203e26ecee99e2307846f5a, limb2: 0x214375d66b2db2ba, limb3: 0x0, }, }, id4: G1Point { x: u384 { limb0: 0xc0ed29b2c26f8c8cbcbd82cf, limb1: 0x9b46a4cf0acba266c2a9b02, limb2: 0x2825f908ee9357e4, limb3: 0x0, }, y: u384 { limb0: 0xf0bd3cf808a6d1bcd0d63ba, limb1: 0x8100429b213b9140ed25274a, limb2: 0x264ef648e6714012, limb3: 0x0, }, }, t1: G1Point { x: u384 { limb0: 0xa63b05df652b0d10ef146d26, limb1: 0xfe18040105b9b395b5d8b7b4, limb2: 0x99e3bd5a0a00ab7, limb3: 0x0, }, y: u384 { limb0: 0x7f5a622a32440f860d1e2a7f, limb1: 0xccec99dcd194592129af3a63, limb2: 0x15b8d2515d76e2, limb3: 0x0, }, }, t2: G1Point { x: u384 { limb0: 0xdc25d1aa450e0b4bc212c37e, limb1: 0x8bc01c9595092a222b888108, limb2: 0x1b917517920bad3d, limb3: 0x0, }, y: u384 { limb0: 0xe42000a1d58ccb74381f6d19, limb1: 0x22e6e992077a84482141c7eb, limb2: 0x305e8992b148eedb, limb3: 0x0, }, }, t3: G1Point { x: u384 { limb0: 0x400b2bca37e2b1085e924a77, limb1: 0x3ada15236ba5cfa60111b440, limb2: 0x13567e3b915c8101, limb3: 0x0, }, y: u384 { limb0: 0x904b434e748f9713de8cc3d7, limb1: 0x8f4674af5744dedafd63caea, limb2: 0x148d22589b91f0d, limb3: 0x0, }, }, t4: G1Point { x: u384 { limb0: 0x6c840d9c943fdf45521c64ce, limb1: 0x7342af45d0155a28edd1a7e4, limb2: 0x43d063b130adfb3, limb3: 0x0, }, y: u384 { limb0: 0x4c573d1686d9cb4a00733854, limb1: 0x6aff96736194949330952ae7, limb2: 0x261522c408933064, limb3: 0x0, }, }, lagrange_first: G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, lagrange_last: G1Point { x: u384 { limb0: 0xc894b742744cf102a554d06f, limb1: 0x9ed4d186a2debd4bfe72be9b, limb2: 0x6a032e44c27b0ce, limb3: 0x0, }, y: u384 { limb0: 0x26660c8385d13a63d2078399, limb1: 0xad76960162ff0d8c34d25b61, limb2: 0x53396ef4f905183, limb3: 0x0, }, }, }; pub const precomputed_lines: [G2Line; 176] = [ G2Line { r0a0: u288 { limb0: 0x4d347301094edcbfa224d3d5, limb1: 0x98005e68cacde68a193b54e6, limb2: 0x237db2935c4432bc, }, r0a1: u288 { limb0: 0x6b4ba735fba44e801d415637, limb1: 0x707c3ec1809ae9bafafa05dd, limb2: 0x124077e14a7d826a, }, r1a0: u288 { limb0: 0x49a8dc1dd6e067932b6a7e0d, limb1: 0x7676d0000961488f8fbce033, limb2: 0x3b7178c857630da, }, r1a1: u288 { limb0: 0x98c81278efe1e96b86397652, limb1: 0xe3520b9dfa601ead6f0bf9cd, limb2: 0x2b17c2b12c26fdd0, }, }, G2Line { r0a0: u288 { limb0: 0x19f2be813f1a2cc51a251901, limb1: 0xa120afb4bcd07fdae4c4c91b, limb2: 0xcd8c8d94eedaaa5, }, r0a1: u288 { limb0: 0xa3808ba2f25b910b50769d68, limb1: 0xda666e5fa50719fcd79ea2c7, limb2: 0x104262c7ecae13e5, }, r1a0: u288 { limb0: 0xd00c9d5338bfc75cd1fe4002, limb1: 0x25f7441c17b6428fffe6266b, limb2: 0x25d0502e1109204d, }, r1a1: u288 { limb0: 0x4ce60bf635ff0fe14cf89d2, limb1: 0x9ca0af889fc43d4423a03197, limb2: 0x1b323f9be536f345, }, }, G2Line { r0a0: u288 { limb0: 0x1b3d578c32d1af5736582972, limb1: 0x204fe74db6b371d37e4615ab, limb2: 0xce69bdf84ed6d6d, }, r0a1: u288 { limb0: 0xfd262357407c3d96bb3ba710, limb1: 0x47d406f500e66ea29c8764b3, limb2: 0x1e23d69196b41dbf, }, r1a0: u288 { limb0: 0x1ec8ee6f65402483ad127f3a, limb1: 0x41d975b678200fce07c48a5e, limb2: 0x2cad36e65bbb6f4f, }, r1a1: u288 { limb0: 0xcfa9b8144c3ea2ab524386f5, limb1: 0xd4fe3a18872139b0287570c3, limb2: 0x54c8bc1b50aa258, }, }, G2Line { r0a0: u288 { limb0: 0xb5ee22ba52a7ed0c533b7173, limb1: 0xbfa13123614ecf9c4853249b, limb2: 0x6567a7f6972b7bb, }, r0a1: u288 { limb0: 0xcf422f26ac76a450359f819e, limb1: 0xc42d7517ae6f59453eaf32c7, limb2: 0x899cb1e339f7582, }, r1a0: u288 { limb0: 0x9f287f4842d688d7afd9cd67, limb1: 0x30af75417670de33dfa95eda, limb2: 0x1121d4ca1c2cab36, }, r1a1: u288 { limb0: 0x7c4c55c27110f2c9a228f7d8, limb1: 0x8f14f6c3a2e2c9d74b347bfe, limb2: 0x83ef274ba7913a5, }, }, G2Line { r0a0: u288 { limb0: 0x4e7f0c0bfd065f51be57e446, limb1: 0x172f9601c4b0d882b2bca176, limb2: 0x238b85999243f584, }, r0a1: u288 { limb0: 0xc4f13eea49c4fb0b88065fdf, limb1: 0xdde9d756dc7a3e60bfe2c7c9, limb2: 0x2021ebaaf4838c43, }, r1a0: u288 { limb0: 0x98652d3a0360c4ba067ebd45, limb1: 0x9259019a69cb15cd979b4425, limb2: 0xa93fe44d0287fdc, }, r1a1: u288 { limb0: 0x63a369cdd8c09b18c3ad7375, limb1: 0x1baf962de1bd1b1973e138fa, limb2: 0x15320ed6fbfaace4, }, }, G2Line { r0a0: u288 { limb0: 0x1a9ecb5a41abb65787e46934, limb1: 0x28fec59f9911882bd4d50306, limb2: 0x25996b3cd58cce92, }, r0a1: u288 { limb0: 0x56f5cca0fddcae1bfbee4b4d, limb1: 0x4237b58cc71911abcefd1d92, limb2: 0x2d985c4da93484d4, }, r1a0: u288 { limb0: 0x406454881e1f6cab8a9ab13c, limb1: 0x2cdf1a77980edf520cc8f23f, limb2: 0x20ce11ddb649cf18, }, r1a1: u288 { limb0: 0xfe104a8fa2c57b6b94bf56d2, limb1: 0xe2debabd9212070fd38f818, limb2: 0x1c1a2364541a15be, }, }, G2Line { r0a0: u288 { limb0: 0xfc23a674d089e9cfdefb1db8, limb1: 0x9ddfd61d289b65a9b4254476, limb2: 0x1e2f561324ef4447, }, r0a1: u288 { limb0: 0xf67a6a9e31f6975b220642ea, limb1: 0xccd852893796296e4d1ed330, limb2: 0x94ff1987d19b62, }, r1a0: u288 { limb0: 0x360c2a5aca59996d24cc1947, limb1: 0x66c2d7d0d176a3bc53f386e8, limb2: 0x2cfcc62a17fbeecb, }, r1a1: u288 { limb0: 0x2ddc73389dd9a9e34168d8a9, limb1: 0xae9afc57944748b835cbda0f, limb2: 0x12f0a1f8cf564067, }, }, G2Line { r0a0: u288 { limb0: 0xef09c2458cc3abc041e9fa2d, limb1: 0x787c6d7a93e94be14277d18d, limb2: 0xbb1d328b2d75a8a, }, r0a1: u288 { limb0: 0x1911705c689a06b1dfab80c, limb1: 0x72781338c8dfb4eb593e44c, limb2: 0x1405249e47100437, }, r1a0: u288 { limb0: 0x4dca335dcaeaf9d99ab7ad63, limb1: 0xd36f68812432efaedffce9a7, limb2: 0x1131840a72c4fa9, }, r1a1: u288 { limb0: 0x5676dc996dc5b1ce91fd01c1, limb1: 0xbbf4fcfae2062f0031601f40, limb2: 0x2f8f5c5bff703235, }, }, G2Line { r0a0: u288 { limb0: 0x9c963c4bdade6ce3d460b077, limb1: 0x1738311feefc76f565e34e8a, limb2: 0x1aae0d6c9e9888ad, }, r0a1: u288 { limb0: 0x9272581fdf80b045c9c3f0a, limb1: 0x3946807b0756e87666798edb, limb2: 0x2bf6eeda2d8be192, }, r1a0: u288 { limb0: 0x3e957661b35995552fb475de, limb1: 0xd8076fa48f93f09d8128a2a8, limb2: 0xb6f87c3f00a6fcf, }, r1a1: u288 { limb0: 0xcf17d6cd2101301246a8f264, limb1: 0x514d04ad989b91e697aa5a0e, limb2: 0x175f17bbd0ad1219, }, }, G2Line { r0a0: u288 { limb0: 0x894bc18cc70ca1987e3b8f9f, limb1: 0xd4bfa535181f0f8659b063e3, limb2: 0x19168d524164f463, }, r0a1: u288 { limb0: 0x850ee8d0e9b58b82719a6e92, limb1: 0x9fc4eb75cbb027c137d48341, limb2: 0x2b2f8a383d944fa0, }, r1a0: u288 { limb0: 0x5451c8974a709483c2b07fbd, limb1: 0xd7e09837b8a2a3b78e7fe525, limb2: 0x347d96be5e7fa31, }, r1a1: u288 { limb0: 0x823f2ba2743ee254e4c18a1e, limb1: 0x6a61af5db035c443ed0f8172, limb2: 0x1e840eee275d1063, }, }, G2Line { r0a0: u288 { limb0: 0xdd132544fc661724c31c8a08, limb1: 0x287b549c39c0ea0a391cbe18, limb2: 0x29c2742c0ca03d7b, }, r0a1: u288 { limb0: 0xb3076d9218b75e044db009b0, limb1: 0xf0e2da346da73ed6e537273, limb2: 0x16cd48b0b23a5a69, }, r1a0: u288 { limb0: 0x5eeab759aec37540ef3b3200, limb1: 0x90c30b490593b4f0a2750f65, limb2: 0x263476e7a8250501, }, r1a1: u288 { limb0: 0x437a75606a5486770a5c4450, limb1: 0xbb6a0a3aa70be067ddcfdbfc, limb2: 0xc03b2e169fa0cd0, }, }, G2Line { r0a0: u288 { limb0: 0x185a998303998a727a80004d, limb1: 0xb23554df68e88aa4bcb90b09, limb2: 0x293e05c0080aedc, }, r0a1: u288 { limb0: 0xfcd79ce56915d6462fb8a51a, limb1: 0x8c7691de25e8c4b96117b24, limb2: 0xa849fd468442c55, }, r1a0: u288 { limb0: 0xc8661606e6d6b1e5a00268eb, limb1: 0xbe2235d18dd52b903e1858e2, limb2: 0x222c8e6db445fbf7, }, r1a1: u288 { limb0: 0x803355a17297b5f77e52231c, limb1: 0x7927c03bd5d3798208bf7a23, limb2: 0x111b3dbe82eb4f62, }, }, G2Line { r0a0: u288 { limb0: 0x18d630598e58bb5d0102b30e, limb1: 0x9767e27b02a8da37411a2787, limb2: 0x100a541662b9cd7c, }, r0a1: u288 { limb0: 0x4ca7313df2e168e7e5ea70, limb1: 0xd49cce6abd50b574f31c2d72, limb2: 0x78a2afbf72317e7, }, r1a0: u288 { limb0: 0x6d99388b0a1a67d6b48d87e0, limb1: 0x1d8711d321a193be3333bc68, limb2: 0x27e76de53a010ce1, }, r1a1: u288 { limb0: 0x77341bf4e1605e982fa50abd, limb1: 0xc5cf10db170b4feaaf5f8f1b, limb2: 0x762adef02274807, }, }, G2Line { r0a0: u288 { limb0: 0x401adda3a335074256e01cf5, limb1: 0x247f8405ee3a5143b8fc7947, limb2: 0x2c37793269c12835, }, r0a1: u288 { limb0: 0x9ecc215e40764ce6a6db3ce0, limb1: 0x14e8a7b5a57b166edcdfb52, limb2: 0x29e744551489dc3f, }, r1a0: u288 { limb0: 0xee025e7cc0634b8b2fcd88dd, limb1: 0x94b3602ee4867d04d1e549ae, limb2: 0xcce5739cfedc699, }, r1a1: u288 { limb0: 0x2c7318ae1f6db5d41f684334, limb1: 0xd1ba91922e100971bd11dbb5, limb2: 0x1d6c654d5c0913a4, }, }, G2Line { r0a0: u288 { limb0: 0xa137b991ba9048aee9fa0bc7, limb1: 0xf5433785c186cd1100ab6b80, limb2: 0xab519fd7cf8e7f9, }, r0a1: u288 { limb0: 0x90832f45d3398c60aa1a74e2, limb1: 0x17f7ac209532723f22a344b, limb2: 0x23db979f8481c5f, }, r1a0: u288 { limb0: 0x723b0e23c2808a5d1ea6b11d, limb1: 0x3030030d26411f84235c3af5, limb2: 0x122e78da5509eddb, }, r1a1: u288 { limb0: 0xf1718c1e21a9bc3ec822f319, limb1: 0xf5ee6dfa3bd3272b2f09f0c7, limb2: 0x5a29c1e27616b34, }, }, G2Line { r0a0: u288 { limb0: 0x6cf0dc0a1a42af130a792bff, limb1: 0x6eeb4dd41cb8967cd7416c41, limb2: 0x832ca9524375cb4, }, r0a1: u288 { limb0: 0x7e263bdeb1fedd385682b4fc, limb1: 0x3eee92fe8cdb332aeb31d573, limb2: 0x125dc8ce07406159, }, r1a0: u288 { limb0: 0x5fce3aa533d50f8eff589829, limb1: 0x15cefc9330a131dfb10a5ae6, limb2: 0x2fa0a33e98e84220, }, r1a1: u288 { limb0: 0xed6540b1d66bbf1f7bf86da8, limb1: 0x3a5266544635cad0d58d64d6, limb2: 0x149069d5ba2e34da, }, }, G2Line { r0a0: u288 { limb0: 0xbc1ede480873fceb8739511e, limb1: 0xd5a60533bd0ce7869efbc15, limb2: 0x182c17d793eba74d, }, r0a1: u288 { limb0: 0x83bf38d91876ad8999516bc2, limb1: 0x7756322ea3dc079289d51f2d, limb2: 0x1d0f6156a89a4244, }, r1a0: u288 { limb0: 0x6aba652f197be8f99707b88c, limb1: 0xbf94286c245794ea0f562f32, limb2: 0x25a358967a2ca81d, }, r1a1: u288 { limb0: 0xc028cbff48c01433e8b23568, limb1: 0xd2e791f5772ed43b056beba1, limb2: 0x83eb38dff4960e, }, }, G2Line { r0a0: u288 { limb0: 0xf0ea4a2e24640eb0043fa781, limb1: 0x8a5ca14e0ac3b7d4409fcb40, limb2: 0x67b373e8abc5602, }, r0a1: u288 { limb0: 0x7c391162763fc85bf5c94818, limb1: 0xb389e19eb97568e7e7e4617d, limb2: 0x1d3f1c590945ef5c, }, r1a0: u288 { limb0: 0xce60f9534da6a36cda2ebe99, limb1: 0x4a48ecfd6beb4596b2736458, limb2: 0x2a3e1d1f2d7f13e0, }, r1a1: u288 { limb0: 0x8546f7e328bc13d11bb19a65, limb1: 0xb68deedd4c4b131fa83bb2a5, limb2: 0x15f7b8d2c8e7626e, }, }, G2Line { r0a0: u288 { limb0: 0xc2a2b787d8e718e81970db80, limb1: 0x5372abeaf56844dee60d6198, 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0x118cc5a7ff22893002d401 0x2c9edcd67aba0031 0xda5db968b2e246c5a6a3ba78 0x3061578aa3da51ed5eb6b4dc 0x2f8a70016e099752 0x632166ac43572e640846724f 0x5dd9ce1441478f2d3cf15834 0x26f82bf35706f05d 0x84a11661b702bdfebd635ac4 0xaf699222f674c91580d09a1e 0xe74476d1cad37ea 0x2ec3b555114b77c19970202e 0x189944678eb335b13e0ae638 0x2dec55cd2f7b34fe 0xd812cf51757e64a9d8abb1a0 0x22d75169141019f56a9bc595 0xffb2d6eecc53c83 0x310a155bfac3ac0b0eeba0b2393d0415934710824640a529afb2da0901e680 ================================================ FILE: src/contracts/autogenerated/noir_ultra_keccak_zk_honk_example/tests/test_contract.cairo ================================================ // Generated by Garaga version 1.1.0 //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use noir_ultra_keccak_zk_honk_example::honk_verifier::{ IUltraKeccakZKHonkVerifierDispatcherTrait, IUltraKeccakZKHonkVerifierLibraryDispatcher, }; use snforge_std::fs::{FileTrait, read_txt}; use snforge_std::{DeclareResultTrait, declare}; use starknet::ClassHash; /// Declare the UltraKeccakZKHonkVerifier contract for testing. /// /// This function declares a new instance of the UltraKeccakZKHonkVerifier contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("UltraKeccakZKHonkVerifier"); /// let dispatcher = IUltraKeccakZKHonkVerifierLibraryDispatcher { class_hash }; /// ``` fn declare_contract(name: ByteArray) -> ClassHash { let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash } /// Test the verification function verify_ultra_keccak_zk_honk_proof with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by /// the garaga team - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system ultra_keccak_zk_honk /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", block_tag: latest)] fn test_verify_ultra_keccak_zk_honk_proof() { // Step 1: Declare the verification contract let class_hash = declare_contract("UltraKeccakZKHonkVerifier"); let dispatcher = IUltraKeccakZKHonkVerifierLibraryDispatcher { class_hash }; // Step 2: Load the proof fixture generated by the script // This file contains the ultra_keccak_zk_honk proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's verify_ultra_keccak_zk_honk_proof function with the loaded proof // data let result = dispatcher.verify_ultra_keccak_zk_honk_proof(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here } ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/Scarb.toml ================================================ # Generated by Garaga version 1.1.0 [package] name = "risc0_verifier_bn254" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../../../" } starknet = "2.16.1" [cairo] sierra-replace-ids = false inlining-strategy = 2 [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/src/groth16_verifier.cairo ================================================ // Generated by Garaga version 1.1.0 use super::groth16_verifier_constants::{N_FREE_PUBLIC_INPUTS, T, ic, precomputed_lines, vk}; #[starknet::interface] pub trait IRisc0Groth16VerifierBN254 { fn verify_r0_groth16_proof_bn254( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod Risc0Groth16VerifierBN254 { use garaga::apps::risc0::{ compute_receipt_claim, deserialize_full_proof_with_hints_risc0, journal_sha256, }; use garaga::definitions::{G1G2Pair, G1Point}; use garaga::ec_ops::{G1PointTrait, ec_safe_add}; use garaga::groth16::{ Groth16ProofRawTrait, multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result, }; use starknet::SyscallResultTrait; use super::{N_FREE_PUBLIC_INPUTS, T, ic, precomputed_lines, vk}; const ECIP_OPS_CLASS_HASH: felt252 = 0x396d5915ecf475aab117bb25a0272b261e9e25ffe1c0ce05a51a3f77489c89e; #[storage] struct Storage {} #[abi(embed_v0)] impl IRisc0Groth16VerifierBN254 of super::IRisc0Groth16VerifierBN254 { fn verify_r0_groth16_proof_bn254( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let fph = deserialize_full_proof_with_hints_risc0(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let image_id = fph.image_id; let journal = fph.journal; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.check_proof_points(0); let ic = ic.span(); let journal_digest = journal_sha256(journal); let claim_digest = compute_receipt_claim(image_id, journal_digest); // Start serialization with the hint array directly to avoid copying it. let mut msm_calldata: Array = array![]; // Add the points from VK relative to the non-constant public inputs. Serde::serialize(@ic.slice(3, N_FREE_PUBLIC_INPUTS), ref msm_calldata); // Add the claim digest as u256 scalars for the msm. msm_calldata.append(2); msm_calldata.append(claim_digest.low.into()); msm_calldata.append(0); msm_calldata.append(claim_digest.high.into()); msm_calldata.append(0); // Complete with the curve indentifier (0 for BN254): msm_calldata.append(0); // Add the hint array. for x in msm_hint { msm_calldata.append(*x); } // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain claim0 * IC[3] + claim1 * IC[4]. let mut _msm_result_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span(), ) .unwrap_syscall(); // Finalize vk_x computation by adding the precomputed T point. let vk_x = ec_safe_add( T, Serde::::deserialize(ref _msm_result_serialized).unwrap(), 0, ); // Perform the pairing check. let check = multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: vk.gamma_g2 }, G1G2Pair { p: groth16_proof.c, q: vk.delta_g2 }, G1G2Pair { p: groth16_proof.a.negate(0), q: groth16_proof.b }, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(journal), Result::Err(error) => Result::Err(error), } } } } ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/src/groth16_verifier_constants.cairo ================================================ // Generated by Garaga version 1.1.0 use garaga::definitions::{E12D, G1Point, G2Line, G2Point, u288, u384}; use garaga::groth16::Groth16VerifyingKey; pub const N_FREE_PUBLIC_INPUTS: usize = 2; // RISC0 version tag : v2.2.2 // CONTROL ROOT USED : 0xce52bf56033842021af3cf6db8a50d1b7535c125a34f1a22c6fdcf002c5a1529 // CONTROL_ROOT_0 : 0x1b0da5b86dcff31a0242380356bf52ce // CONTROL_ROOT_1 : 0x29155a2c00cffdc6221a4fa325c13575 // BN254 CONTROL ID USED : 0x4446e66d300eb7fb45c9726bb53c793dda407a62e9601618bb43c5c14657ac0 pub const T: G1Point = G1Point { x: u384 { limb0: 0x2612e4e2e1c0b9d602b7aa52, limb1: 0x4d5d3394a95b09366b3abb5e, limb2: 0x1f550d0d6161a44a, limb3: 0x0, }, y: u384 { limb0: 0x34475b4928c630e3330db9cb, limb1: 0x1d6305d30e66d5a8ce067302, limb2: 0x12a023f9110563f6, limb3: 0x0, }, }; // IC[0] + IC[1] * CONTROL_ROOT_0 + IC[2] * CONTROL_ROOT_1 + IC[5] * BN254_CONTROL_ID pub const vk: Groth16VerifyingKey = Groth16VerifyingKey { alpha_beta_miller_loop_result: E12D { w0: u288 { limb0: 0x38febe9f87f730fa3e5bd174, limb1: 0xf763950637a776ef9e248435, limb2: 0x29dc2d37c63acbda, }, w1: u288 { limb0: 0xa31610a97aa4e4539be919ff, limb1: 0xfa4d4bfb72b6a3c002018e97, limb2: 0x1968ab971e610fce, }, w2: u288 { limb0: 0xee6c1ce3a15313c6f9d57f7e, limb1: 0xd37e28396640fcfe5f122aae, limb2: 0x210d3763f7a27517, }, w3: u288 { limb0: 0x7746ddac185562e756b1b92f, limb1: 0x44f8b75638ef5a373f319cd8, limb2: 0x51e9605db4edac6, }, w4: u288 { limb0: 0xc29e0c2ac434301d671ffa56, limb1: 0xa06f1db2d4ca4dd88f979102, limb2: 0x1d0126fb7d721e02, }, w5: u288 { limb0: 0xed2e022e10acbeb35084dc1, limb1: 0xf9de514baee870f114669060, limb2: 0x10889a0f300ce96c, }, w6: u288 { limb0: 0xeec23aadde92d2dd00e4568e, limb1: 0x6d5b4b63667db8f10bd851ab, limb2: 0x18f1dd15d2e64c69, }, w7: u288 { limb0: 0x2131bad24ea07a033d0bf397, limb1: 0xb6312a7f2622146be93b5950, limb2: 0x227e61ca055f0ac3, }, w8: u288 { limb0: 0xb896f30b06350f012274ebcd, limb1: 0xd14298f13a76183170aafe08, limb2: 0x302bfd90358d23a0, }, w9: u288 { limb0: 0x679d91263798da428fa5ea62, limb1: 0x806797d163f4df8b55ec774c, limb2: 0x29b72d4ec063face, }, w10: u288 { limb0: 0x4dbef45fe0c5a14bef7c4a90, limb1: 0xd4ae215c443d0f0768198bc6, limb2: 0x2fcc02633e427272, }, w11: u288 { limb0: 0x7308cad65773475443cfbd80, limb1: 0x972f90a77f1a8aeece6571ff, limb2: 0x2d3a570362a9fd7f, }, }, gamma_g2: G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }, delta_g2: G2Point { x0: u384 { limb0: 0x69cfaa4e60401fea7f3e0333, limb1: 0xd922dba0547057ccaae94b9d, limb2: 0x1aa085ff28179a12, limb3: 0x0, }, x1: u384 { limb0: 0x2ccf0b4c91f42bb629f83a1c, limb1: 0x9bee94f1f5ef907157bda481, limb2: 0x3b03cd5effa95ac, limb3: 0x0, }, y0: u384 { limb0: 0x9e2fea1c7142df187d3fc6d3, limb1: 0x37e867178318832d0b2d74d5, limb2: 0x1e60f31fcbf757e8, limb3: 0x0, }, y1: u384 { limb0: 0xfb7228ca5c91d2940d030762, limb1: 0xf6490846d518c9aea868366e, limb2: 0x110c10134f200b19, limb3: 0x0, }, }, }; pub const ic: [G1Point; 6] = [ G1Point { x: u384 { limb0: 0x4d553505739d0f5d65dc3be4, limb1: 0x32a9061a082c15dd1d61aa9c, limb2: 0x12ac9a25dcd5e1a8, limb3: 0x0, }, y: u384 { limb0: 0xd30f3eee2b23c60ee980acd4, limb1: 0xd91731911c898569106ff5a2, limb2: 0x25aa744581ebe7a, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0x4ccc3c8769d883f688a1423f, limb1: 0xf292fae2036e057be5429411, limb2: 0x707b920bc978c02, limb3: 0x0, }, y: u384 { limb0: 0xc203383782a4650787ff6642, limb1: 0xf7bc357bf63481acd2d55555, limb2: 0x2e32a094b7589554, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0x48e336f4fd974644850fc347, limb1: 0x3e249751853f961511011c71, limb2: 0xbca36e2cbe6394b, limb3: 0x0, }, y: u384 { limb0: 0x6db8f7f409c153b1fcdf9b8b, limb1: 0x3729fa3d68714e2a8435d4fa, limb2: 0x2ede7c9acf48cf3a, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0xe2c6b6fb5a25f9112e04f2a7, limb1: 0x7c091cc2aaf201e488cbacc3, limb2: 0x1b8af999dbfbb392, limb3: 0x0, }, y: u384 { limb0: 0x1a60157f3e9cf04f679cccd6, limb1: 0x5722949f192a81c850d586d8, limb2: 0x2b91a26aa92e1b6f, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0x1dcefeddd06eda5a076ccd0d, limb1: 0x8ac1750bdfd5a7615f002d4a, limb2: 0x2b5f494ed674235b, limb3: 0x0, }, y: u384 { limb0: 0x8f14f912c5e71665b2ad5e82, limb1: 0xcbba817fcbb9a863b8a76ff8, limb2: 0x2fe520ad2020aab9, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0x2fce3c25d5940320b1c4d493, limb1: 0x3666843cde4e82e869ba525, limb2: 0xf1c3c0d5d9da0fa, limb3: 0x0, }, y: u384 { limb0: 0x3608f68287aa01bd0b69e809, limb1: 0xfe8c0d07b307482d8bc8bb2f, limb2: 0x214bfcff74f425f6, limb3: 0x0, }, }, ]; pub const precomputed_lines: [G2Line; 176] = [ G2Line { r0a0: u288 { limb0: 0x4d347301094edcbfa224d3d5, limb1: 0x98005e68cacde68a193b54e6, limb2: 0x237db2935c4432bc, }, r0a1: u288 { limb0: 0x6b4ba735fba44e801d415637, limb1: 0x707c3ec1809ae9bafafa05dd, limb2: 0x124077e14a7d826a, }, r1a0: u288 { limb0: 0x49a8dc1dd6e067932b6a7e0d, limb1: 0x7676d0000961488f8fbce033, limb2: 0x3b7178c857630da, }, r1a1: u288 { limb0: 0x98c81278efe1e96b86397652, limb1: 0xe3520b9dfa601ead6f0bf9cd, limb2: 0x2b17c2b12c26fdd0, }, }, G2Line { r0a0: u288 { limb0: 0xc1a48e9e12ff1dbf61883912, limb1: 0xaee1724a5332ee74b8ed9451, limb2: 0xfbb1e993e3695f0, }, r0a1: u288 { limb0: 0x7acaee831d920baf2a1bfde0, limb1: 0x4cf9ef8c77ec7a0195bee19d, limb2: 0x25757a99d16aa21c, }, r1a0: u288 { limb0: 0xe5847602f3a9790bf049b947, limb1: 0x934e2813cdc5d033f879cf93, limb2: 0x21249e515f664d4c, }, r1a1: u288 { limb0: 0xf19496daaae3309c391d0383, limb1: 0x408eeae0c5d549305a377fd8, limb2: 0x21282298fede4ac4, }, }, G2Line { r0a0: u288 { limb0: 0x1b3d578c32d1af5736582972, limb1: 0x204fe74db6b371d37e4615ab, limb2: 0xce69bdf84ed6d6d, }, r0a1: u288 { limb0: 0xfd262357407c3d96bb3ba710, limb1: 0x47d406f500e66ea29c8764b3, limb2: 0x1e23d69196b41dbf, }, r1a0: u288 { limb0: 0x1ec8ee6f65402483ad127f3a, limb1: 0x41d975b678200fce07c48a5e, limb2: 0x2cad36e65bbb6f4f, }, r1a1: u288 { limb0: 0xcfa9b8144c3ea2ab524386f5, limb1: 0xd4fe3a18872139b0287570c3, limb2: 0x54c8bc1b50aa258, }, }, G2Line { r0a0: u288 { limb0: 0xb5ee22ba52a7ed0c533b7173, limb1: 0xbfa13123614ecf9c4853249b, limb2: 0x6567a7f6972b7bb, }, r0a1: u288 { limb0: 0xcf422f26ac76a450359f819e, limb1: 0xc42d7517ae6f59453eaf32c7, limb2: 0x899cb1e339f7582, }, r1a0: u288 { limb0: 0x9f287f4842d688d7afd9cd67, limb1: 0x30af75417670de33dfa95eda, limb2: 0x1121d4ca1c2cab36, }, r1a1: u288 { limb0: 0x7c4c55c27110f2c9a228f7d8, limb1: 0x8f14f6c3a2e2c9d74b347bfe, limb2: 0x83ef274ba7913a5, }, }, G2Line { r0a0: u288 { limb0: 0xa6cd3bef29216e5776f4c435, limb1: 0x96ed36c2e4e69e8de93d63f, limb2: 0x20a92fd9a2fb0a39, }, r0a1: u288 { limb0: 0xeda6dc0a1e8e8067ae60ff67, limb1: 0x6b56562a0994de5c01c288f3, limb2: 0xaeed3d90fc6fe0d, }, r1a0: u288 { limb0: 0x82ed548a4877130ae8334400, limb1: 0x25021da2b3bb88299f079afd, limb2: 0xf3fb02181cb52dd, }, r1a1: u288 { limb0: 0x76dd33b2913d5b7a9f5ff9c4, limb1: 0x77c15ad5bbac0f2d3d49eab8, limb2: 0xf3c2bd9e2535565, }, }, G2Line { r0a0: u288 { limb0: 0xf9c98b4467592a57fca1c44f, limb1: 0x22c8464befc62af74bd7e13e, limb2: 0xf6fe51a099cedd, }, r0a1: u288 { limb0: 0x424a207247f0e4c27f38a1ae, limb1: 0xc0d1158c6df8f6ffa8d6a76e, limb2: 0xe16f63bee6733e5, }, r1a0: u288 { limb0: 0x747d2a41af96d81fb2585f8f, limb1: 0x1bedd2f049ce086610aca319, limb2: 0x18e887f968ab29d1, }, r1a1: u288 { limb0: 0x6f6eae477c15633e163e3366, limb1: 0x3d0cca9a15ddc9f899d906bf, limb2: 0x1a5066113f22d767, }, }, G2Line { r0a0: u288 { limb0: 0xfc23a674d089e9cfdefb1db8, limb1: 0x9ddfd61d289b65a9b4254476, limb2: 0x1e2f561324ef4447, }, r0a1: u288 { limb0: 0xf67a6a9e31f6975b220642ea, limb1: 0xccd852893796296e4d1ed330, limb2: 0x94ff1987d19b62, }, r1a0: u288 { limb0: 0x360c2a5aca59996d24cc1947, limb1: 0x66c2d7d0d176a3bc53f386e8, limb2: 0x2cfcc62a17fbeecb, }, r1a1: u288 { limb0: 0x2ddc73389dd9a9e34168d8a9, limb1: 0xae9afc57944748b835cbda0f, limb2: 0x12f0a1f8cf564067, }, }, G2Line { r0a0: u288 { limb0: 0x963c90609635263045a730, limb1: 0x25987316828b8c528c8dc05b, limb2: 0x1a52af70953e2d93, }, r0a1: u288 { limb0: 0x5cb801def7d800e0a2dcdc65, limb1: 0x7f06086a5846b035d7144e65, limb2: 0x264229f1b248db7a, }, r1a0: u288 { limb0: 0x1c8fe795c6a55dfe7abf119e, limb1: 0x98b10fc53fdbfce11d7827a0, limb2: 0x13551fa74e7af913, }, r1a1: u288 { limb0: 0xdde6f69885b07fe44d932a52, limb1: 0x9819b585503c5540fa115b13, limb2: 0x1f4507e84f016add, }, }, G2Line { r0a0: u288 { limb0: 0x9c963c4bdade6ce3d460b077, limb1: 0x1738311feefc76f565e34e8a, limb2: 0x1aae0d6c9e9888ad, }, r0a1: u288 { limb0: 0x9272581fdf80b045c9c3f0a, limb1: 0x3946807b0756e87666798edb, limb2: 0x2bf6eeda2d8be192, }, r1a0: u288 { limb0: 0x3e957661b35995552fb475de, limb1: 0xd8076fa48f93f09d8128a2a8, limb2: 0xb6f87c3f00a6fcf, }, r1a1: u288 { limb0: 0xcf17d6cd2101301246a8f264, limb1: 0x514d04ad989b91e697aa5a0e, limb2: 0x175f17bbd0ad1219, }, }, G2Line { r0a0: u288 { limb0: 0x894bc18cc70ca1987e3b8f9f, limb1: 0xd4bfa535181f0f8659b063e3, limb2: 0x19168d524164f463, }, r0a1: u288 { limb0: 0x850ee8d0e9b58b82719a6e92, limb1: 0x9fc4eb75cbb027c137d48341, limb2: 0x2b2f8a383d944fa0, }, r1a0: u288 { limb0: 0x5451c8974a709483c2b07fbd, limb1: 0xd7e09837b8a2a3b78e7fe525, limb2: 0x347d96be5e7fa31, }, r1a1: u288 { limb0: 0x823f2ba2743ee254e4c18a1e, limb1: 0x6a61af5db035c443ed0f8172, limb2: 0x1e840eee275d1063, }, }, G2Line { r0a0: u288 { limb0: 0x9cdb3f1da9cc795a6dd71925, limb1: 0xa6b72d99ea73e7ec479df7de, limb2: 0x2a0d16e5af0f972a, }, r0a1: u288 { limb0: 0x185981f7439b3abe06b2f010, limb1: 0x4afb801363c27041866471a0, limb2: 0x21a33b58bc0ebc30, }, r1a0: u288 { limb0: 0xd9c7c736ca2b67b6189ccfb9, limb1: 0x8dd913714e0c8c9468564883, limb2: 0x25e9300604680744, }, r1a1: u288 { limb0: 0xd2f83c58abf29fed21f8ac20, limb1: 0xf99df3b0aafc57db31256a85, limb2: 0x2ecdc1f4735da2e6, }, }, G2Line { r0a0: u288 { limb0: 0x3890eaf1d657d63d18eac82d, limb1: 0x962ede9002cf9e7fead8ac71, limb2: 0xa41c746d7a471e2, }, r0a1: u288 { limb0: 0xdd8017fb853f2df76c7dad20, limb1: 0x8ee50f79d3a8abfd3ccd4c1a, limb2: 0x7f77df5036f64d2, }, r1a0: u288 { limb0: 0x251f40aedb747d8748c907aa, limb1: 0xaff11c216293b73b2d2a53aa, limb2: 0x2f94413282c71d76, }, r1a1: u288 { limb0: 0x255cffb680c8482747fe7934, limb1: 0xc9b47382882ce9a2171f615c, limb2: 0x1e12dbcbfacba1a9, }, }, G2Line { r0a0: u288 { limb0: 0x18d630598e58bb5d0102b30e, limb1: 0x9767e27b02a8da37411a2787, limb2: 0x100a541662b9cd7c, }, r0a1: u288 { limb0: 0x4ca7313df2e168e7e5ea70, limb1: 0xd49cce6abd50b574f31c2d72, limb2: 0x78a2afbf72317e7, }, r1a0: u288 { limb0: 0x6d99388b0a1a67d6b48d87e0, limb1: 0x1d8711d321a193be3333bc68, limb2: 0x27e76de53a010ce1, }, r1a1: u288 { limb0: 0x77341bf4e1605e982fa50abd, limb1: 0xc5cf10db170b4feaaf5f8f1b, limb2: 0x762adef02274807, }, }, G2Line { r0a0: u288 { limb0: 0x7645fffb343e10e1e8748cb8, limb1: 0xb7ee813d501408d841ec8e65, limb2: 0xe90c74a2dd6516e, }, r0a1: u288 { limb0: 0x1491337b6e2af58a979eff05, limb1: 0x41a56da5e78ec6d2aedcfb3c, limb2: 0x234444f637b1fd1a, }, r1a0: u288 { limb0: 0x7f6df98a0ef48fea6a90a86d, limb1: 0x67fe1fde059c8fcc5f4d2e06, limb2: 0x2ba05dbf310dbde7, }, r1a1: u288 { limb0: 0xa0c862d762e402c3454d02b2, limb1: 0x1b96d5c6695fe143c37a671e, limb2: 0x24af700c84c87b54, }, }, G2Line { r0a0: u288 { limb0: 0xa137b991ba9048aee9fa0bc7, limb1: 0xf5433785c186cd1100ab6b80, limb2: 0xab519fd7cf8e7f9, }, r0a1: u288 { limb0: 0x90832f45d3398c60aa1a74e2, limb1: 0x17f7ac209532723f22a344b, limb2: 0x23db979f8481c5f, }, r1a0: u288 { limb0: 0x723b0e23c2808a5d1ea6b11d, limb1: 0x3030030d26411f84235c3af5, limb2: 0x122e78da5509eddb, }, r1a1: u288 { limb0: 0xf1718c1e21a9bc3ec822f319, limb1: 0xf5ee6dfa3bd3272b2f09f0c7, limb2: 0x5a29c1e27616b34, }, }, G2Line { r0a0: u288 { limb0: 0x1af83b0d07aaec86d9134a28, limb1: 0x77bdb3e9aa87662797059a9c, limb2: 0x273c84364e3713d2, }, r0a1: u288 { limb0: 0xcaf5ba9785faf45cfc296a4a, limb1: 0x3163afd1009dbadd9c5a70bd, limb2: 0x1aaea45eb51c82ce, }, r1a0: u288 { limb0: 0x5aba52ae705ce1af25e673aa, limb1: 0x2dc8896c9ff279f6655024ef, limb2: 0x300f0500b7b0b0d3, }, r1a1: u288 { limb0: 0x67f1e1afa662ba8900d60c26, limb1: 0xf93114d70a2a3321729a7d2c, limb2: 0x1cc57b64b47a626d, }, }, G2Line { r0a0: u288 { limb0: 0xbc1ede480873fceb8739511e, limb1: 0xd5a60533bd0ce7869efbc15, limb2: 0x182c17d793eba74d, }, r0a1: u288 { limb0: 0x83bf38d91876ad8999516bc2, limb1: 0x7756322ea3dc079289d51f2d, limb2: 0x1d0f6156a89a4244, }, r1a0: u288 { limb0: 0x6aba652f197be8f99707b88c, limb1: 0xbf94286c245794ea0f562f32, limb2: 0x25a358967a2ca81d, }, r1a1: u288 { limb0: 0xc028cbff48c01433e8b23568, limb1: 0xd2e791f5772ed43b056beba1, limb2: 0x83eb38dff4960e, }, }, G2Line { r0a0: u288 { limb0: 0x5fa7b4cb5791e57c2cf9780e, limb1: 0xf5062eb2c532788091de2118, limb2: 0xc38262afe4f4eac, }, r0a1: u288 { limb0: 0x6560785dd69d5a9a4917aa3b, limb1: 0x6240334397d0134760854bb1, limb2: 0x2d7c0dd3e38d8926, }, r1a0: u288 { limb0: 0xf3c91f209577810e63cbdf2f, limb1: 0xa8acef680c1be04d12d702c8, limb2: 0xa312088d3b32c07, }, r1a1: u288 { limb0: 0x96aa4853754a05becdc1bf51, limb1: 0xa6cc53c2c1b1d383517e44b4, limb2: 0x1f03c17658e08a24, }, }, G2Line { r0a0: u288 { limb0: 0xc2a2b787d8e718e81970db80, limb1: 0x5372abeaf56844dee60d6198, limb2: 0x131210153a2217d6, }, r0a1: u288 { limb0: 0x70421980313e09a8a0e5a82d, limb1: 0xf75ca1f68f4b8deafb1d3b48, limb2: 0x102113c9b6feb035, }, r1a0: u288 { limb0: 0x4654c11d73bda84873de9b86, limb1: 0xa67601bca2e595339833191a, limb2: 0x1c2b76e439adc8cc, }, r1a1: u288 { limb0: 0x9c53a48cc66c1f4d644105f2, limb1: 0xa17a18867557d96fb7c2f849, limb2: 0x1deb99799bd8b63a, }, }, G2Line { r0a0: u288 { limb0: 0xc32026c56341297fa080790c, limb1: 0xe23ad2ff283399133533b31f, limb2: 0xa6860f5c968f7ad, }, r0a1: u288 { limb0: 0x2966cf259dc612c6a4d8957d, limb1: 0xfba87ea86054f3db5774a08f, limb2: 0xc73408b6a646780, }, r1a0: u288 { limb0: 0x6272ce5976d8eeba08f66b48, limb1: 0x7dfbd78fa06509604c0cec8d, limb2: 0x181ec0eaa6660e45, }, r1a1: u288 { limb0: 0x48af37c1a2343555fbf8a357, limb1: 0xa7b5e1e20e64d6a9a9ce8e61, limb2: 0x1147dcea39a47abd, }, }, G2Line { r0a0: u288 { limb0: 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limb2: 0x10dfe73e58fcb4bd, }, }, G2Line { r0a0: u288 { limb0: 0x652eaf09821887db0de1f147, limb1: 0x75229b9972e31ba2e226bbcf, limb2: 0x161e5e72bf925c6d, }, r0a1: u288 { limb0: 0x856aa774394ef561669d1eab, limb1: 0xdd46a5dd8e6c4d775d36356d, limb2: 0x2d287f12b2a6700d, }, r1a0: u288 { limb0: 0x67ffd864a18bb2d4488c5d6a, limb1: 0x8d0ea9ad86d841741fe1d284, limb2: 0x43189ddb2f1e1cd, }, r1a1: u288 { limb0: 0xf42602a91d620c7003644ce4, limb1: 0x7d9f27e32a63153af2c65415, limb2: 0x1ee85832249a6300, }, }, ]; ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/src/lib.cairo ================================================ // Generated by Garaga version 1.1.0 pub mod groth16_verifier; pub mod groth16_verifier_constants; ================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/tests/proof_calldata.txt ================================================ 0x9ba602b4ce8728dc9e2eafbe 0xab7dd4d4e0cd8c4809abe8e1 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================================================ FILE: src/contracts/autogenerated/risc0_verifier_bn254/tests/test_contract.cairo ================================================ // Generated by Garaga version 1.1.0 //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use risc0_verifier_bn254::groth16_verifier::{ IRisc0Groth16VerifierBN254DispatcherTrait, IRisc0Groth16VerifierBN254LibraryDispatcher, }; use snforge_std::fs::{FileTrait, read_txt}; use snforge_std::{DeclareResultTrait, declare}; use starknet::ClassHash; /// Declare the Risc0Groth16VerifierBN254 contract for testing. /// /// This function declares a new instance of the Risc0Groth16VerifierBN254 contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("Risc0Groth16VerifierBN254"); /// let dispatcher = IRisc0Groth16VerifierBN254LibraryDispatcher { class_hash }; /// ``` fn declare_contract(name: ByteArray) -> ClassHash { let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash } /// Test the verification function verify_r0_groth16_proof_bn254 with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by /// the garaga team - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system groth16 /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", block_tag: latest)] fn test_verify_r0_groth16_proof_bn254() { // Step 1: Declare the verification contract let class_hash = declare_contract("Risc0Groth16VerifierBN254"); let dispatcher = IRisc0Groth16VerifierBN254LibraryDispatcher { class_hash }; // Step 2: Load the proof fixture generated by the script // This file contains the groth16 proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's verify_r0_groth16_proof_bn254 function with the loaded proof data let result = dispatcher.verify_r0_groth16_proof_bn254(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here } ================================================ FILE: src/contracts/autogenerated/sp1_verifier_bn254/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/autogenerated/sp1_verifier_bn254/Scarb.toml ================================================ # Generated by Garaga version 1.1.0 [package] name = "sp1_verifier_bn254" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../../../" } starknet = "2.16.1" [cairo] sierra-replace-ids = false inlining-strategy = 2 [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/autogenerated/sp1_verifier_bn254/src/groth16_verifier.cairo ================================================ // Generated by Garaga version 1.1.0 #[starknet::interface] pub trait ISP1Groth16VerifierBN254 { fn verify_sp1_groth16_proof_bn254( self: @TContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252>; fn verify_sp1_groth16_proof_bn254_u32( self: @TContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252>; } #[starknet::contract] mod SP1Groth16VerifierBN254 { use garaga::apps::sp1::{deserialize_full_proof_with_hints_sp1, process_public_inputs_sp1}; use garaga::apps::sp1_constants::{N_PUBLIC_INPUTS, ic, precomputed_lines, vk}; use garaga::definitions::{G1G2Pair, G1Point}; use garaga::ec_ops::{G1PointTrait, ec_safe_add}; use garaga::groth16::{ Groth16ProofRawTrait, multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result, }; use starknet::SyscallResultTrait; const ECIP_OPS_CLASS_HASH: felt252 = 0x396d5915ecf475aab117bb25a0272b261e9e25ffe1c0ce05a51a3f77489c89e; #[storage] struct Storage {} /// Internal helper function that performs the core SP1 Groth16 verification. /// Returns (vkey, public_inputs_u256, public_inputs_u32) on success. fn verify_sp1_groth16_proof_inner( full_proof_with_hints: Span, ) -> Result<(u256, Span, Span), felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok((vkey, public_inputs_u256, public_inputs_u32)) if the // proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given a // proof and a verifying key. let fph = deserialize_full_proof_with_hints_sp1(full_proof_with_hints); let groth16_proof = fph.groth16_proof; let vkey = fph.vkey; let public_inputs_sp1 = fph.public_inputs_sp1; let mpcheck_hint = fph.mpcheck_hint; let msm_hint = fph.msm_hint; groth16_proof.check_proof_points(0); let ic = ic.span(); let public_inputs_u32 = public_inputs_sp1.span(); let (pub_inputs_256, pub_input_hash): (Span, u256) = process_public_inputs_sp1( public_inputs_sp1, ); let vk_x: G1Point = match ic.len() { 0 => panic!("Malformed VK"), 1 => *ic.at(0), _ => { let mut msm_calldata: Array = array![]; // Add the points from VK and public inputs to the proof. Serde::serialize(@ic.slice(1, N_PUBLIC_INPUTS), ref msm_calldata); // Serialize public inputs as u256 array. Serde::serialize(@N_PUBLIC_INPUTS, ref msm_calldata); Serde::serialize(@vkey, ref msm_calldata); Serde::serialize(@pub_input_hash, ref msm_calldata); // Complete with the curve indentifier (0 for BN254): msm_calldata.append(0); // Add the hint array. for x in msm_hint { msm_calldata.append(*x); } // Call the multi scalar multiplication endpoint on the Garaga ECIP ops contract // to obtain vk_x. let mut _vx_x_serialized = starknet::syscalls::library_call_syscall( ECIP_OPS_CLASS_HASH.try_into().unwrap(), selector!("msm_g1"), msm_calldata.span(), ) .unwrap_syscall(); ec_safe_add( Serde::::deserialize(ref _vx_x_serialized).unwrap(), *ic.at(0), 0, ) }, }; // Perform the pairing check. let check = multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: vk.gamma_g2 }, G1G2Pair { p: groth16_proof.c, q: vk.delta_g2 }, G1G2Pair { p: groth16_proof.a.negate(0), q: groth16_proof.b }, vk.alpha_beta_miller_loop_result, precomputed_lines.span(), mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok((vkey, pub_inputs_256, public_inputs_u32)), Result::Err(error) => Result::Err(error), } } #[abi(embed_v0)] impl ISP1Groth16VerifierBN254 of super::ISP1Groth16VerifierBN254 { fn verify_sp1_groth16_proof_bn254( self: @ContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252> { match verify_sp1_groth16_proof_inner(full_proof_with_hints) { Result::Ok((vkey, pub_inputs_256, _)) => Result::Ok((vkey, pub_inputs_256)), Result::Err(error) => Result::Err(error), } } fn verify_sp1_groth16_proof_bn254_u32( self: @ContractState, full_proof_with_hints: Span, ) -> Result<(u256, Span), felt252> { match verify_sp1_groth16_proof_inner(full_proof_with_hints) { Result::Ok((vkey, _, pub_inputs_u32)) => Result::Ok((vkey, pub_inputs_u32)), Result::Err(error) => Result::Err(error), } } } } ================================================ FILE: src/contracts/autogenerated/sp1_verifier_bn254/src/lib.cairo ================================================ 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0x3a237bdbf87287c 0x0 0xd13f9298545a1d77942e20d7 0xa85510aa9d5e7b357755b5d6 0x15c764c1c5380102 0x0 0x100000000000000003aa0eb9486eaea7c 0x100000000000000003ed064b9068afd7b 0x100000000000000004e76be5e17f551d8 0x100000000000000008d717becec440328 ================================================ FILE: src/contracts/autogenerated/sp1_verifier_bn254/tests/test_contract.cairo ================================================ // Generated by Garaga version 1.1.0 //! # Starknet Verification Contract Tests //! //! This module contains comprehensive tests for the proof verification contract. //! The tests use Starknet Foundry's testing features to verify proofs. //! //! ## Test Strategy //! - Use real proof fixtures generated by the garaga CLI //! - Test both positive (valid proof) and negative (invalid proof) cases use snforge_std::fs::{FileTrait, read_txt}; use snforge_std::{DeclareResultTrait, declare}; use sp1_verifier_bn254::groth16_verifier::{ ISP1Groth16VerifierBN254DispatcherTrait, ISP1Groth16VerifierBN254LibraryDispatcher, }; use starknet::ClassHash; /// Declare the SP1Groth16VerifierBN254 contract for testing. /// /// This function declares a new instance of the SP1Groth16VerifierBN254 contract /// /// # Arguments /// * `name` - The contract name to declare /// /// # Returns /// * `ClassHash` - The class hash of the declared contract /// /// # Example /// ```cairo /// let class_hash = declare_contract("SP1Groth16VerifierBN254"); /// let dispatcher = ISP1Groth16VerifierBN254LibraryDispatcher { class_hash }; /// ``` fn declare_contract(name: ByteArray) -> ClassHash { let class_hash = *declare(name).unwrap().contract_class().class_hash; class_hash } /// Test the verification function verify_sp1_groth16_proof_bn254 with a valid proof. /// /// This test demonstrates the complete verification flow: /// 1. Declare the verification contract /// 2. Load a pre-generated proof fixture /// 3. Verify the proof on-chain /// 4. Assert that verification succeeds /// /// ## Test Setup /// - Uses fork testing against Sepolia testnet to access required declared contracts maintained by /// the garaga team - Loads proof calldata from `tests/proof_calldata.txt` /// - To generate the calldata, you can use the garaga CLI: /// ```bash /// garaga calldata /// --system groth16 /// --vk path/to/vk /// --proof path/to/proof /// --public-inputs path/to/public_inputs /// --format snforge /// --output-path path/to/tests /// ``` /// This will generate a file `proof_calldata.txt` in the specified output path. /// You can then use this file in the test. /// /// ## Expected Behavior /// - The proof should verify successfully /// - The function should return Ok(public_inputs) containing the expected public inputs /// - No panics or assertion failures should occur #[test] #[fork(url: "https://api.zan.top/public/starknet-sepolia/rpc/v0_10", block_tag: latest)] fn test_verify_sp1_groth16_proof_bn254() { // Step 1: Declare the verification contract let class_hash = declare_contract("SP1Groth16VerifierBN254"); let dispatcher = ISP1Groth16VerifierBN254LibraryDispatcher { class_hash }; // Step 2: Load the proof fixture generated by the script // This file contains the groth16 proof calldata formatted for Starknet let file = FileTrait::new("tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); // Step 3: Verify the proof on-chain // This calls the contract's verify_sp1_groth16_proof_bn254 function with the loaded proof data let result = dispatcher.verify_sp1_groth16_proof_bn254(calldata); // Step 4: Assert that verification succeeded // A valid proof should return Ok(public_inputs), not Err assert(result.is_ok(), 'Proof verification failed'); // Optional: You can also verify the public inputs contain expected values // let public_inputs = result.unwrap(); // assert(public_inputs.len() > 0, 'No public inputs'); // Additional assertions on the public input values can be added here } ================================================ FILE: src/contracts/drand_decrypt_quicknet/Scarb.toml ================================================ [package] name = "drand_decrypt_quicknet" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../.." } drand_quicknet = { path = "../drand_quicknet" } starknet = "2.16.1" [cairo] sierra-replace-ids = false [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/drand_decrypt_quicknet/src/drand_decrypt.cairo ================================================ use garaga::definitions::G1Point; #[starknet::interface] trait IDrandDecryptQuicknet { /// Verify a drand round BLS signature via library_call to the verifier class, /// which stores the signature in this contract's storage. fn verify_round( ref self: TContractState, full_proof_with_hints: Span, ) -> Result; /// Read the stored signature for a previously verified round. fn get_signature_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Get poseidon_hash(signature) for a previously verified round. fn get_randomness_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Decrypt a tlock ciphertext for a given round. /// If the round is not yet verified, a DrandHint must follow in the calldata. fn decrypt_cipher_text( ref self: TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod DrandDecryptQuicknet { use drand_quicknet::drand_verifier::{ IDrandQuicknetDispatcherTrait, IDrandQuicknetLibraryDispatcher, }; use garaga::apps::drand::{CipherText, decrypt_at_round}; use garaga::definitions::{G1Point, G1PointStorePacking, G1PointZero}; use starknet::storage::{Map, StoragePathEntry, StoragePointerReadAccess}; use super::super::drand_decrypt_constants::VERIFIER_CLASS_HASH; #[storage] struct Storage { signatures: Map, } #[derive(Drop, Serde)] struct DrandDecryptHint { round_number: u64, cipher_text: CipherText, } fn verifier() -> IDrandQuicknetLibraryDispatcher { IDrandQuicknetLibraryDispatcher { class_hash: VERIFIER_CLASS_HASH.try_into().unwrap() } } #[abi(embed_v0)] impl IDrandDecryptQuicknetImpl of super::IDrandDecryptQuicknet { fn verify_round( ref self: ContractState, full_proof_with_hints: Span, ) -> Result { let mut v = verifier(); v.verify_round(full_proof_with_hints) } fn get_signature_for_round( self: @ContractState, round_number: u64, ) -> Result { verifier().get_signature_for_round(round_number) } fn get_randomness_for_round( self: @ContractState, round_number: u64, ) -> Result { verifier().get_randomness_for_round(round_number) } fn decrypt_cipher_text( ref self: ContractState, mut full_proof_with_hints: Span, ) -> Result, felt252> { let hint = Serde::::deserialize(ref full_proof_with_hints) .ok_or('Bad calldata: DecryptHint')?; let signature = self.signatures.entry(hint.round_number).read(); let signature = if signature.is_zero() { let mut v = verifier(); v.verify_round(full_proof_with_hints)?; let sig = self.signatures.entry(hint.round_number).read(); if sig.is_zero() { return Result::Err('Verification did not store sig'); } sig } else { signature }; Result::Ok(decrypt_at_round(signature, hint.cipher_text).span()) } } } ================================================ FILE: src/contracts/drand_decrypt_quicknet/src/drand_decrypt_constants.cairo ================================================ // Generated — do not edit manually. pub const VERIFIER_CLASS_HASH: felt252 = 0x86bf4360e082cd786bd785d3345df32777db89cd26b761f3e85b1993addfd0; ================================================ FILE: src/contracts/drand_decrypt_quicknet/src/lib.cairo ================================================ mod drand_decrypt; mod drand_decrypt_constants; ================================================ FILE: src/contracts/drand_quicknet/.tool-versions ================================================ scarb 2.16.1 starknet-foundry 0.57.0 ================================================ FILE: src/contracts/drand_quicknet/Scarb.toml ================================================ [package] name = "drand_quicknet" version = "0.1.0" edition = "2024_07" [dependencies] garaga = { path = "../.." } starknet = "2.16.1" [lib] [cairo] sierra-replace-ids = false [[target.starknet-contract]] casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/drand_quicknet/src/drand_verifier.cairo ================================================ use super::drand_verifier_constants::{G2_GEN, precomputed_lines}; #[starknet::interface] pub trait IDrandQuicknet { /// Verify a drand round BLS signature and store it on-chain. /// Returns the round number on success. fn verify_round( ref self: TContractState, full_proof_with_hints: Span, ) -> Result; /// Look up the stored signature for a previously verified round. fn get_signature_for_round( self: @TContractState, round_number: u64, ) -> Result; /// Look up the randomness for a previously verified round. /// Randomness = poseidon_hash(signature). fn get_randomness_for_round( self: @TContractState, round_number: u64, ) -> Result; } use garaga::definitions::G1Point; #[starknet::contract] mod DrandQuicknet { use garaga::apps::drand::{DRAND_QUICKNET_PUBLIC_KEY, HashToCurveHint, round_to_curve_bls12_381}; use garaga::definitions::{G1G2Pair, G1Point, G1PointStorePacking, G1PointZero}; use garaga::pairing_check::{MPCheckHintBLS12_381, multi_pairing_check_bls12_381_2P_2F}; use garaga::utils::calldata::deserialize_mpcheck_hint_bls12_381; use garaga::utils::hashing::hash_G1Point; use starknet::storage::{ Map, StoragePathEntry, StoragePointerReadAccess, StoragePointerWriteAccess, }; use super::{G2_GEN, precomputed_lines}; #[storage] struct Storage { signatures: Map, } #[derive(Drop)] struct DrandHint { round_number: u64, signature: G1Point, hash_to_curve_hint: HashToCurveHint, mpcheck_hint: MPCheckHintBLS12_381, } impl DrandHintSerde of Serde { fn serialize(self: @DrandHint, ref output: Array) {} fn deserialize(ref serialized: Span) -> Option { let round_number = Serde::::deserialize(ref serialized)?; let signature = Serde::::deserialize(ref serialized)?; let hash_to_curve_hint = Serde::::deserialize(ref serialized)?; let mpcheck_hint = deserialize_mpcheck_hint_bls12_381(ref serialized); Option::Some(DrandHint { round_number, signature, hash_to_curve_hint, mpcheck_hint }) } } #[abi(embed_v0)] impl IDrandQuicknet of super::IDrandQuicknet { fn verify_round( ref self: ContractState, mut full_proof_with_hints: Span, ) -> Result { let hint = Serde::::deserialize(ref full_proof_with_hints) .ok_or('Bad calldata: DrandHint')?; let round_number = hint.round_number; let message = round_to_curve_bls12_381(hint.round_number, hint.hash_to_curve_hint); multi_pairing_check_bls12_381_2P_2F( pair0: G1G2Pair { p: hint.signature, q: G2_GEN }, pair1: G1G2Pair { p: message, q: DRAND_QUICKNET_PUBLIC_KEY }, lines: precomputed_lines.span(), hint: hint.mpcheck_hint, ) .map_err(|_e| 'BLS signature invalid')?; self.signatures.entry(round_number).write(hint.signature); Result::Ok(round_number) } fn get_signature_for_round( self: @ContractState, round_number: u64, ) -> Result { let signature = self.signatures.entry(round_number).read(); if signature.is_zero() { Result::Err('Round not verified yet') } else { Result::Ok(signature) } } fn get_randomness_for_round( self: @ContractState, round_number: u64, ) -> Result { let signature = self.signatures.entry(round_number).read(); if signature.is_zero() { Result::Err('Round not verified yet') } else { Result::Ok(hash_G1Point(signature)) } } } } ================================================ FILE: src/contracts/drand_quicknet/src/drand_verifier_constants.cairo ================================================ use garaga::definitions::{G2Line, G2Point, u384}; pub const G2_GEN: G2Point = G2Point { x0: u384 { limb0: 0xa805bbefd48056c8c121bdb8, limb1: 0xb4510b647ae3d1770bac0326, limb2: 0x2dc51051c6e47ad4fa403b02, limb3: 0x24aa2b2f08f0a9126080527, }, x1: u384 { limb0: 0x13945d57e5ac7d055d042b7e, limb1: 0xb5da61bbdc7f5049334cf112, limb2: 0x88274f65596bd0d09920b61a, limb3: 0x13e02b6052719f607dacd3a0, }, y0: u384 { limb0: 0x3baca289e193548608b82801, limb1: 0x6d429a695160d12c923ac9cc, limb2: 0xda2e351aadfd9baa8cbdd3a7, limb3: 0xce5d527727d6e118cc9cdc6, }, y1: u384 { limb0: 0x5cec1da1aaa9075ff05f79be, limb1: 0x267492ab572e99ab3f370d27, limb2: 0x2bc28b99cb3e287e85a763af, limb3: 0x606c4a02ea734cc32acd2b0, }, }; pub const precomputed_lines: [G2Line; 136] = [ G2Line { r0a0: u384 { limb0: 0x36701a5831c9fb39250e2ea9, limb1: 0x26ad0ec05ad6440f1df034cf, limb2: 0x67cd27cf7598a85f81c23cd9, limb3: 0x15a76ee3d8d1c3451005d560, }, r0a1: u384 { limb0: 0x9009367bbf6e6aa19488df66, limb1: 0xce5cd2ccda4704dc0e4b92b6, limb2: 0xd7656829a6a71c42deb7dd, limb3: 0x16d96e785c797fb5d6afcb14, }, r1a0: u384 { limb0: 0x9d68b0bdf431a2f53189c109, limb1: 0x70e39167384e44fdaf716fa4, limb2: 0x3768099390a3f9d581d88280, limb3: 0x4c208bdb300097927393e96, }, r1a1: u384 { limb0: 0x68ab4b88cf058f147ba2cda9, limb1: 0xce3b4d4da03cbdac75933b54, limb2: 0x1be2f7e6eaa0f1474cb64c53, limb3: 0x546ca700477f9c2f9def969, }, }, G2Line { r0a0: u384 { limb0: 0x96e0f84058018a4538d64e8b, limb1: 0xdb7b84172cb1e68ddd09eb12, limb2: 0xcf3aaa45c2b370e810ea9361, limb3: 0x14b92565b748c30f253912c6, }, r0a1: u384 { limb0: 0x9cdcddf4728a38086aebcd7, limb1: 0x7b8d9115b96656327dd79780, limb2: 0xbf914addbdcbe307142bf7cc, limb3: 0x3c50d0829bdc305ff694cc9, }, r1a0: u384 { limb0: 0xcc0dbe864e35231bdec2ef76, limb1: 0x4efa339ef551d8f751da95ba, limb2: 0xfde5910a13d5c428549ed3f5, limb3: 0x105e4803f5b8472a138e00b, }, r1a1: u384 { limb0: 0x584879d210eb30bfd6518cf2, limb1: 0xa7c4af01b40d0e68243b050c, limb2: 0xade596dd94a41e4aedec2196, limb3: 0x162a46f819eba8e3b9d215f9, }, }, G2Line { r0a0: u384 { limb0: 0xaa37b5f455262931a4a4b667, limb1: 0xd63d75f6f171228540731ca7, limb2: 0x1855073ef14fe67beee9ec53, limb3: 0x703f29e5b69ff1dd1441781, }, r0a1: u384 { limb0: 0x310c4b87c8dca9036f6be0c0, limb1: 0x4b940b400d665d605ca8924b, limb2: 0x6d53ff2907765e3888b9709e, limb3: 0x166de077ba25fe21aafb8d8, }, r1a0: u384 { limb0: 0xa28a55b43c534d6caa724f82, limb1: 0x5f55bbeb19616aec79892386, limb2: 0x3aacfc3b6bd889cf57af9e40, limb3: 0x72ff7d1d3328dbb7c821e1, }, r1a1: u384 { limb0: 0xd5e91f70851719038228e756, limb1: 0xb4f970b567fc2d6738d65700, limb2: 0x8c886fe7294c08b41dc5dcbe, limb3: 0x782b1bf6e81fef26d367768, }, }, G2Line { r0a0: u384 { limb0: 0x8d8ec958debf40520de5d867, limb1: 0x57bad55eb06d937414e80cc9, limb2: 0xcb178ebae0f48eb14ad4fba0, limb3: 0x13aa75258cc1d54eb767a47e, }, r0a1: u384 { limb0: 0x7aec4216b9f9e33aa4f5af6, limb1: 0x607eabc6cb65b9f4b850a042, limb2: 0x1d93b61b06f4e64902410902, limb3: 0x1860921bbe145ede9350b867, }, r1a0: u384 { limb0: 0xe104b73f6d12d90e3c339c6c, limb1: 0x27bab1ac67f3132355d4c1a0, limb2: 0x63ecc80d6bd96b3d592f63d9, limb3: 0xdcb608c9ce643f854507b05, }, r1a1: u384 { limb0: 0xe3895865374c9b06b8d02a7f, limb1: 0x8c09a76a05340ce642b99a1a, limb2: 0x4a4afdbe107c0182cfe2e6e7, limb3: 0x1056de76a10fe55b2659ea44, }, }, G2Line { r0a0: u384 { limb0: 0x6a72f085ee4e78bd4c2aef8e, limb1: 0xdec05cffe4a869aed2a64ee8, limb2: 0xd41aa908b1a833b94e768d2, limb3: 0x56ceab5d5d994dee0ca07fc, }, r0a1: u384 { limb0: 0xd23aad6cd3e84e398a4e7bc8, limb1: 0xb343a6878db6ec20bcac1275, limb2: 0x3111e14b674a67295a242cf3, limb3: 0x39b596a976f556e5ea4016a, }, r1a0: u384 { limb0: 0x19fcdcac7feb1f0edbefdbf8, limb1: 0x71bc60f1a68459eb52df6a92, limb2: 0x2827dbba9d5d8516fb557dfb, limb3: 0x4786cc02b147d13e701c1f5, }, r1a1: u384 { limb0: 0xcb7555c0db86510eb99cfadd, limb1: 0x43387d10f8329296e43e6610, limb2: 0xbf6789475132950c583823a, limb3: 0x145f508c63c10d270e027b2b, }, }, G2Line { r0a0: u384 { limb0: 0x411944418a1e44d0fbd8a4bd, limb1: 0xfa3933a100d5d920bb158196, limb2: 0xaf6096a850d10c6ee57b7d3f, limb3: 0x7bc245f0c719ec216f4f7e7, }, r0a1: u384 { limb0: 0xd5f88a09ab7912a54504534a, limb1: 0x6c7b84068e05767f3ac72003, limb2: 0x2e783a6cd8933e5ce254ff56, limb3: 0x648a93088ef22f73be5e1d5, }, r1a0: u384 { limb0: 0x72f4d88bd20cecc4c1d57b8f, limb1: 0x2164d957d0e784aca77a27b6, limb2: 0xe45f0a865306a8c7ccf8e465, limb3: 0x182e7e79c81e19c5e6dba3b8, }, r1a1: u384 { limb0: 0xf2b21292475b313a8591d232, limb1: 0x31975a79dd261ef9304ae69f, limb2: 0x3fca7e570497ea425d166e3f, limb3: 0xb1e493cae679afa3aeeb48e, }, }, G2Line { r0a0: u384 { limb0: 0x7bd212f8f60967471e995a8e, limb1: 0xec76fa31d0fd358f36ee756e, limb2: 0xa63e06c40964532a724817c3, limb3: 0xd860767952ed2b694b64eea, }, r0a1: u384 { limb0: 0xd18f8b1de21e64c50d3c6fc2, limb1: 0x456cec057d45521c48d0b547, limb2: 0x23fb8276293fac77c9a38c1b, limb3: 0x1469d7cf50d58855fa523aa8, }, r1a0: u384 { limb0: 0x52f1d22ea6bfc23435bf7e3b, limb1: 0x3e2d5122467bf39f2573a57b, limb2: 0x378db9e77f53b5b1e38981da, limb3: 0x1015deb442db265529d8948, }, r1a1: u384 { limb0: 0x73c44618fb7917b2596bd460, limb1: 0x598ee13313073cf3232e1b37, limb2: 0xbd63e58ae4aa477bcd459ef2, limb3: 0x272bfde06aa8302ab8c70d6, }, }, G2Line { r0a0: u384 { limb0: 0x84d7880d9c5ad98d07f1b961, limb1: 0xd5be4b6e58ad745353113073, limb2: 0x592ecc7534e44983a06d755c, limb3: 0x15d60a0d6d8a2e4543194737, }, r0a1: u384 { limb0: 0x9ba63990e4f1ea4875173006, limb1: 0xf84fa98d5f3742b3c571f427, limb2: 0xdd28189a4a2e3a70f78a170e, limb3: 0x1ad5bc82425c66f655a75db, }, r1a0: u384 { limb0: 0x49306522c22ca321950bf155, limb1: 0x369a747f27aa6472ebc5d290, limb2: 0x20d8977cbe5acf112574c70a, limb3: 0xcdc103da1aac9ec5f855b64, }, r1a1: u384 { limb0: 0x74517cbd651af3940075c057, limb1: 0x94d3802d81c93d69eb13518b, limb2: 0x76411c393dd03e5381661629, limb3: 0x16e57b05faef24ef64868a07, }, }, G2Line { r0a0: u384 { limb0: 0x1a30592d98290c72cccd458b, limb1: 0x140a621ff20376f808a589fd, limb2: 0x49ba32b20969590620d93359, limb3: 0x8505a11bd1aa7d53fffa788, }, r0a1: u384 { limb0: 0xbedeeea8460644391170d35f, limb1: 0xcfc8f5f9f7606a79990e9242, limb2: 0x2747fe157739059a9b528ae0, limb3: 0x13386caa378815cd519166ec, }, r1a0: u384 { limb0: 0x2adf79c700fc3a5a36c5ec26, limb1: 0x4f168c2853c5ec65b71b40ca, limb2: 0x7e0c13754f775e73a9419653, limb3: 0x10616cc67745c7887ca4898e, }, r1a1: u384 { limb0: 0xde84fc636c0a8697ac4d8960, limb1: 0xdd66e4fac060783909cc83c4, limb2: 0x86edc8b2faa981346da2237c, limb3: 0x11c912ed6ea0e8f7768ac884, }, }, G2Line { r0a0: u384 { limb0: 0x6b6c23b2b461087f63e2fd50, limb1: 0x8454a8c69f81cfea8edb19ba, limb2: 0x2133ca31f8dd40f674513fd8, limb3: 0x171663bdebf2ef26dc306e13, }, r0a1: u384 { limb0: 0x6b95f25b75fe9a8aa69ae917, limb1: 0x2f15c87206b024c108e4f4d4, limb2: 0xc4e3e65f02f2e19326083300, limb3: 0x16172a9e775f111d4bf432bf, }, r1a0: u384 { limb0: 0xc4289527cdf4e1662f27e1f9, limb1: 0x7f6c52aaea1458a5388d10eb, limb2: 0x4f6130d75d26097d0a4fa02a, limb3: 0x16f8a911b684b408bbd72650, }, r1a1: u384 { limb0: 0x648a1498ebbbd0e225db1ffc, limb1: 0xa36cfb4b46195b619bb220bf, limb2: 0xe327926a1726c7e5bb70bc97, limb3: 0xfcef666ce7ecc2915258730, }, }, G2Line { r0a0: u384 { limb0: 0xb5abe92a46d0ff04a4205803, limb1: 0xdb760c98b7aad959e5dfc28d, limb2: 0xbea9b6e4adf41fa1060713ee, limb3: 0x75707a467e7543c28370330, }, r0a1: u384 { limb0: 0x8b0715d2f6a16be8d5828197, limb1: 0x598a8a6da7ed2bcc091f594d, limb2: 0x18cfc9c1ee8960c06ff2c240, limb3: 0x14061839f139644bb20e8647, }, r1a0: u384 { limb0: 0xd529f0561fff46258f565dec, limb1: 0x80402f61ae7ce96272aff23b, limb2: 0x883367465c3a4bde2507377a, limb3: 0x14fc234296369891318c6245, }, r1a1: u384 { limb0: 0x9fdc0242b4d20c44b72c8d49, limb1: 0x37e047238dd417acab9ea0c2, limb2: 0xc424c8845919fe27ac23e9, limb3: 0x151e87d65d95c3b1cc9b1de6, }, }, G2Line { r0a0: u384 { limb0: 0xf5a9a8a9d8ecd9df033bb53b, limb1: 0x6f13c1f15ca3c43bd8dc862c, limb2: 0xaf9fffe39ed8b6f589e47e4f, limb3: 0x1355d3f3bda0ba53c342406b, }, r0a1: u384 { limb0: 0x13c7baebedc25cd07fa0b8ea, limb1: 0x4e29e5e7fd865c69feb81131, limb2: 0xdcf94191f24d657ae6fc8c5c, limb3: 0x162398b0a01eff8f7149ab6c, }, r1a0: u384 { limb0: 0x8cf50d2f7aa3da376e8317d5, limb1: 0x490a7502e8f6bc788f715c7a, limb2: 0xe6db018fa6b084ae40896c2b, limb3: 0x184f93ce89fff4893629db4d, }, r1a1: u384 { limb0: 0x53e941ac4d20f05b66f3b0ec, limb1: 0x82b8a8efafffe40798a1d5da, limb2: 0xd08e35da426abf3dd1ce8bb, limb3: 0xd49095a9c436bd86f9d4736, }, }, G2Line { r0a0: u384 { limb0: 0x9bd8fa7a943e0e3a924e7492, limb1: 0xad948685eedfe9d3ac7315ff, limb2: 0x8148910d6004895792caa88d, limb3: 0x1deabfaeb3374b50119ecb9, }, r0a1: u384 { limb0: 0xfedf28954ae85d6e9f58c709, limb1: 0x7c01f5d8a4b9368fc9cbb8eb, limb2: 0xbe98bf07cbd25fe6f4ac154f, limb3: 0x7c9b05e8adef4de506459f7, }, r1a0: u384 { limb0: 0x71812aeba8c33457117bfb0, limb1: 0xaf1a11b5a7571775ec17c1, limb2: 0x721e08542ff85e7037b2c02f, limb3: 0x991d1db86230da71efb4475, }, r1a1: u384 { limb0: 0x4122fa433f37c5e6888de07c, limb1: 0x144d977681671d8cd0854c34, limb2: 0x93981673fae1df08d18161aa, limb3: 0x145eae6a49c250f2435d1ec8, }, }, G2Line { r0a0: u384 { limb0: 0x3ab208ad049d8dbf41ab2d8c, limb1: 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0x1163f7e15fbd10f4086aad86, }, }, G2Line { r0a0: u384 { limb0: 0x95151ea18c775b54deb3d8d2, limb1: 0x12d5d14c1a1e5e441f80f7f0, limb2: 0x441e9ed1c76ca5b0a9a2c673, limb3: 0x5ed345d22ce7a2820a566a6, }, r0a1: u384 { limb0: 0x85f7fcc07f1acb58e2b2b71d, limb1: 0xf54880edf6b069d9be9739e7, limb2: 0xb25f1683eedccd9cddb2592e, limb3: 0x1287330ba9caab2bef8676e5, }, r1a0: u384 { limb0: 0x418096781d6bdd8438f7d0fa, limb1: 0xde2b0883a520a29780fe7f9, limb2: 0x858acb343f8b338095664988, limb3: 0x1213109d451b7b62be0e7837, }, r1a1: u384 { limb0: 0x13c30921c6ad44eef236dc4e, limb1: 0x97d1525a1c3fa2dfe5f32aa7, limb2: 0x7071a595e981dc71b225c544, limb3: 0x6f31cf2562cca8a820178ab, }, }, ]; ================================================ FILE: src/contracts/drand_quicknet/src/lib.cairo ================================================ pub mod drand_verifier; mod drand_verifier_constants; ================================================ FILE: src/contracts/mutator_set/.tool-versions ================================================ starknet-foundry 0.57.0 scarb 2.16.1 ================================================ FILE: src/contracts/mutator_set/Makefile ================================================ regen: python3 ./scripts/regenerate_verifier.py NOIR_FOLDER = "zk_program" build: cd ${NOIR_FOLDER} && nargo build && nargo execute witness prove: cd ${NOIR_FOLDER} && bb prove -s ultra_honk --oracle_hash keccak -b ./target/zk_program.json -w ./target/witness.gz -o ./target/ verify: cd ${NOIR_FOLDER} && bb verify -s ultra_honk -p ./target/proof -k ./target/vk --oracle_hash keccak ================================================ FILE: src/contracts/mutator_set/Scarb.toml ================================================ [package] name = "mutator_set" version = "0.1.0" edition = "2024_07" # See more keys and their definitions at https://docs.swmansion.com/scarb/docs/reference/manifest.html [dependencies] starknet = "2.16.1" garaga = { path = "../../" } [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [cairo] sierra-replace-ids = false [[target.starknet-contract]] sierra = true [scripts] test = "snforge test" [tool.scarb] allow-prebuilt-plugins = ["snforge_std"] # Visit https://foundry-rs.github.io/starknet-foundry/appendix/scarb-toml.html for more information # [tool.snforge] # Define `snforge` tool section # exit_first = true # Stop tests execution immediately upon the first failure # fuzzer_runs = 1234 # Number of runs of the random fuzzer # fuzzer_seed = 1111 # Seed for the random fuzzer # [[tool.snforge.fork]] # Used for fork testing # name = "SOME_NAME" # Fork name # url = "http://your.rpc.url" # Url of the RPC provider # block_id.tag = "latest" # Block to fork from (block tag) # [[tool.snforge.fork]] # name = "SOME_SECOND_NAME" # url = "http://your.second.rpc.url" # block_id.number = "123" # Block to fork from (block number) # [[tool.snforge.fork]] # name = "SOME_THIRD_NAME" # url = "http://your.third.rpc.url" # block_id.hash = "0x123" # Block to fork from (block hash) # [profile.dev.cairo] # Configure Cairo compiler # unstable-add-statements-code-locations-debug-info = true # Should be used if you want to use coverage # unstable-add-statements-functions-debug-info = true # Should be used if you want to use coverage/profiler # inlining-strategy = "avoid" # Should be used if you want to use coverage # [features] # Used for conditional compilation # enable_for_tests = [] # Feature name and list of other features that should be enabled with it ================================================ FILE: src/contracts/mutator_set/scripts/prover.py ================================================ import os from dataclasses import dataclass from typing import List import toml MAX_PEAKS = 32 MAX_PROOF_DEPTH = 32 @dataclass class StorageElement: hash: str @dataclass class Proof: len: str storage: List[StorageElement] @dataclass class ProverConfig: leaf_index: str leaf_premiage: str num_leafs: str peaks: List[str] root_hash: str proof: Proof def to_dict(self) -> dict: """Convert the dataclass to a dictionary format suitable for TOML serialization.""" return { "leaf_index": self.leaf_index, "leaf_premiage": self.leaf_premiage, "num_leafs": self.num_leafs, "peaks": self.peaks, "root_hash": self.root_hash, "proof": { "len": self.proof.len, "storage": [{"hash": s.hash} for s in self.proof.storage], }, } def save_to_toml(self, filepath: str) -> None: """Save the configuration to a TOML file.""" config_dict = self.to_dict() with open(filepath, "w") as f: toml.dump(config_dict, f) @classmethod def load_from_toml(cls, filepath: str) -> "ProverConfig": """Load configuration from a TOML file.""" with open(filepath, "r") as f: config_dict = toml.load(f) # Convert the dictionary back to ProverConfig proof_dict = config_dict["proof"] storage = [StorageElement(hash=s["hash"]) for s in proof_dict["storage"]] proof = Proof(len=proof_dict["len"], storage=storage) return cls( leaf_index=config_dict["leaf_index"], leaf_premiage=config_dict["leaf_premiage"], num_leafs=config_dict["num_leafs"], peaks=config_dict["peaks"], root_hash=config_dict["root_hash"], proof=proof, ) def create_default_config() -> ProverConfig: """Create a default configuration matching the example Prover.toml.""" storage_elements = [StorageElement(hash="0") for _ in range(MAX_PROOF_DEPTH)] storage_elements[1] = StorageElement( hash="0x2098f5fb9e239eab3ceac3f27b81e481dc3124d55ffed523a839ee8446b64864" ) peaks = ( ["0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1"] + ["0x0"] + ["0x0"] * (MAX_PEAKS - 2) ) return ProverConfig( leaf_index=hex(2), leaf_premiage=hex(0), num_leafs=hex(5), peaks=peaks, root_hash="0x1ba30aaf15c7694786a1f118ca39fcc6c997b48da9dfa62e9ec3e83ac7d6304d", proof=Proof(len=hex(2), storage=storage_elements), ) if __name__ == "__main__": # Example usage config = create_default_config() # Save to TOML output_path = os.path.join( os.path.dirname(os.path.dirname(__file__)), "zk_program", "Prover.toml" ) config.save_to_toml(output_path) print(f"Saved configuration to {output_path}") # Load from TOML loaded_config = ProverConfig.load_from_toml(output_path) print("Successfully loaded configuration from TOML") ================================================ FILE: src/contracts/mutator_set/scripts/regenerate_verifier.py ================================================ import logging import os import subprocess from dataclasses import dataclass from pathlib import Path from typing import Optional from garaga.starknet.cli.utils import create_directory from garaga.starknet.honk_contract_generator.generator_honk import ( HonkVk, ProofSystem, gen_honk_verifier_files, ) # Configure logging logging.basicConfig( level=logging.INFO, format="%(asctime)s - %(levelname)s - %(message)s" ) logger = logging.getLogger(__name__) @dataclass class VerifierConfig: """Configuration for verifier generation.""" program_name: str = "zk_program" bb_path: str = "bb" scheme: str = "ultra_honk" oracle_hash: str = "keccak" proof_system: ProofSystem = ProofSystem.UltraKeccakZKHonk @property def paths(self) -> dict: """Get all relevant paths based on the script location.""" script_dir = Path(__file__).parent project_root = script_dir.parent return { "noir_program_dir": project_root / self.program_name, "target_dir": project_root / self.program_name / "target", "verifier_dir": project_root / "src" / f"zk_verifier", "lib_cairo": project_root / "src" / "lib.cairo", "contract_class": project_root / "target" / "dev" / "mutator_set_UltraKeccakZKHonkVerifier.contract_class.json", } class VerifierGenerator: """Handles the generation of verifier files for the ZK program.""" def __init__(self, config: VerifierConfig): self.config = config self.paths = config.paths def run_command(self, cmd: list, cwd: Optional[Path] = None) -> str: logger.info(f"Running: {' '.join(cmd)}") try: result = subprocess.run( cmd, cwd=cwd, check=True, text=True, capture_output=True ) return result.stdout.strip() except subprocess.CalledProcessError as e: error_msg = f"Command failed with output:\nstdout: {e.stdout.strip()}\nstderr: {e.stderr.strip()}" logger.error(error_msg) raise def update_class_hash(self, class_hash: str): """Update the class hash in lib.cairo.""" try: content = f"""pub mod mutator_set_contract; pub mod zk_verifier {{ pub mod honk_verifier_circuits; pub mod honk_verifier_constants; pub mod honk_verifier_contract; }} const VERIFIER_CLASS_HASH: felt252 = {class_hash}; """ with open(self.paths["lib_cairo"], "w") as f: f.write(content) logger.info(f"Updated class hash in {self.paths['lib_cairo']}") except Exception as e: logger.error(f"Failed to update class hash: {str(e)}") raise def generate(self) -> bool: """Generate verifier files for the ZK program.""" try: original_dir = os.getcwd() os.chdir(self.paths["noir_program_dir"]) # Build project and generate verification key os.makedirs(self.paths["target_dir"], exist_ok=True) self.run_command(["nargo", "build"]) self.run_command( [ self.config.bb_path, "write_vk", "--scheme", self.config.scheme, "--oracle_hash", self.config.oracle_hash, "-b", str(self.paths["target_dir"] / f"{self.config.program_name}.json"), "-o", str(self.paths["target_dir"]), ] ) # Generate and write verifier files with open(self.paths["target_dir"] / "vk", "rb") as f: vk = HonkVk.from_bytes(f.read()) ( constants_code, circuits_code, contract_code, contract_name, verification_function_name, ) = gen_honk_verifier_files(vk) # Write files create_directory(self.paths["verifier_dir"]) # Remove existing files for filename in os.listdir(self.paths["verifier_dir"]): os.remove(self.paths["verifier_dir"] / filename) for filename, content in { "honk_verifier_constants.cairo": constants_code, "honk_verifier_circuits.cairo": circuits_code, "honk_verifier_contract.cairo": contract_code, }.items(): with open(self.paths["verifier_dir"] / filename, "w") as f: f.write(content) self.run_command(["scarb", "fmt", str(self.paths["verifier_dir"])]) # Change to project root and run scarb build os.chdir(self.paths["noir_program_dir"].parent) self.run_command(["scarb", "build"]) # Get class hash class_hash = self.run_command( ["starkli", "class-hash", str(self.paths["contract_class"])] ) logger.info(f"Generated class hash: {class_hash}") # Update class hash in lib.cairo self.update_class_hash(class_hash) # Format lib.cairo self.run_command(["scarb", "fmt", str(self.paths["lib_cairo"])]) os.chdir(original_dir) return True except Exception as e: logger.error(f"Verifier generation failed: {str(e)}") raise def main(): """Main function to build project and generate verifiers.""" try: generator = VerifierGenerator(VerifierConfig()) generator.generate() logger.info("Verifier generation completed successfully") except Exception as e: logger.error(f"Failed to generate verifier: {str(e)}") raise if __name__ == "__main__": main() ================================================ FILE: src/contracts/mutator_set/snfoundry.toml ================================================ # Visit https://foundry-rs.github.io/starknet-foundry/appendix/snfoundry-toml.html # and https://foundry-rs.github.io/starknet-foundry/projects/configuration.html for more information # [sncast.default] # Define a profile name # url = "https://free-rpc.nethermind.io/sepolia-juno/v0_7" # Url of the RPC provider # accounts-file = "../account-file" # Path to the file with the account data # account = "mainuser" # Account from `accounts_file` or default account file that will be used for the transactions # keystore = "~/keystore" # Path to the keystore file # wait-params = { timeout = 300, retry-interval = 10 } # Wait for submitted transaction parameters # block-explorer = "StarkScan" # Block explorer service used to display links to transaction details # show-explorer-links = true # Print links pointing to pages with transaction details in the chosen block explorer ================================================ FILE: src/contracts/mutator_set/src/lib.cairo ================================================ pub mod mutator_set_contract; pub mod zk_verifier { pub mod honk_verifier_circuits; pub mod honk_verifier_constants; pub mod honk_verifier_contract; } const VERIFIER_CLASS_HASH: felt252 = 0x05afe47f53c8833bae809202f397c3beeae83b912928c10f2c6db517fc3b8463; ================================================ FILE: src/contracts/mutator_set/src/mutator_set_contract.cairo ================================================ use mutator_set::zk_verifier::honk_verifier_contract::IUltraKeccakZKHonkVerifier; #[starknet::interface] pub trait IMutatorSetContract { fn get_n_leaves_aocl(self: @TContractState) -> u64; fn get_n_peaks_aocl(self: @TContractState) -> u64; fn append_leaf_aocl(ref self: TContractState, leaf: u256); fn get_peaks_aocl(self: @TContractState) -> Array; fn verify_inclusion_proof_aocl( ref self: TContractState, full_proof_with_hints: Span, ) -> bool; } #[starknet::contract] mod MutatorSetContract { use garaga::crypto::mmr::trailing_ones; use garaga::hashes::poseidon_bn254::poseidon_hash_2 as hash_2; use mutator_set::VERIFIER_CLASS_HASH; use starknet::SyscallResultTrait; use starknet::storage::{ MutableVecTrait, StoragePointerReadAccess, StoragePointerWriteAccess, Vec, VecTrait, }; const BN254_CURVE_ORDER: u256 = u256 { low: 0x2833e84879b9709143e1f593f0000001, high: 0x30644e72e131a029b85045b68181585d, }; const AOCL_INIT_VALUE: u256 = 0; // Append-only commitment list #[starknet::storage_node] struct AOCL { n_leaves: u64, peaks: Vec, last_peak_index: u64, } #[starknet::storage_node] struct AOCLState { n_leaves: u64, root: u256, } #[storage] struct Storage { aocl: AOCL, aocl_state: AOCL, } #[constructor] fn constructor(ref self: ContractState) { // Init both AOCLs self.aocl.peaks.push(AOCL_INIT_VALUE); self.aocl.n_leaves.write(1); self.aocl.last_peak_index.write(0); self.aocl_state.peaks.push(AOCL_INIT_VALUE); self.aocl_state.n_leaves.write(1); self.aocl_state.last_peak_index.write(0); } #[event] #[derive(Drop, starknet::Event)] pub enum Event { LeafAppended: LeafAppended, } #[derive(Drop, starknet::Event)] struct LeafAppended { leaf: u256, n_leaves: u64, } #[abi(embed_v0)] impl MutatorSetContractImpl of super::IMutatorSetContract { fn get_n_leaves_aocl(self: @ContractState) -> u64 { self.aocl.n_leaves.read() } fn get_peaks_aocl(self: @ContractState) -> Array { let n_peaks = self.aocl.last_peak_index.read() + 1; let mut peaks = array![]; for i in 0..n_peaks { peaks.append(self.aocl.peaks.get(i).expect('Invalid peak index').read()); } peaks } fn get_n_peaks_aocl(self: @ContractState) -> u64 { self.aocl.last_peak_index.read() + 1 } fn append_leaf_aocl(ref self: ContractState, leaf: u256) { assert(leaf < BN254_CURVE_ORDER, 'Invalid leaf value'); let n_leaves = self.aocl.n_leaves.read(); let n_parents = trailing_ones(n_leaves); let mut last_peak_idx = self.aocl.last_peak_index.read(); match n_parents { 0 => { let peaks_vec_last_idx = self.aocl.peaks.len() - 1; let new_peak_idx = last_peak_idx + 1; match new_peak_idx <= peaks_vec_last_idx { true => { self.aocl.peaks.get(new_peak_idx).unwrap().write(leaf); self.aocl.last_peak_index.write(new_peak_idx); }, false => { self.aocl.peaks.push(leaf); self.aocl.last_peak_index.write(new_peak_idx); }, } }, 1 => { let mut last_peak_ptr = self .aocl .peaks .get(last_peak_idx) .expect('Invalid last peak index'); let last_peak = last_peak_ptr.read(); let parent: u256 = hash_2(last_peak, leaf); last_peak_ptr.write(parent); // No change on last_peak_idx. (It was a single leaf that got merged into a // peak) }, _ => { let mut last_peak_ptr = self .aocl .peaks .get(last_peak_idx) .expect('Invalid last peak index'); let last_peak: u256 = last_peak_ptr.read(); let parent: u256 = hash_2(last_peak, leaf); last_peak_ptr.write(parent); for _ in 0..n_parents - 1 { let in_progress_peak = self.aocl.peaks.get(last_peak_idx).unwrap().read(); let previous_peak = self.aocl.peaks.get(last_peak_idx - 1).unwrap().read(); let parent: u256 = hash_2(previous_peak, in_progress_peak); last_peak_idx -= 1; let mut last_peak_ptr = self.aocl.peaks.get(last_peak_idx).unwrap(); last_peak_ptr.write(parent); } self.aocl.last_peak_index.write(last_peak_idx); }, } let new_n_leaves = n_leaves + 1; self.aocl.n_leaves.write(new_n_leaves); self.emit(LeafAppended { leaf: leaf, n_leaves: new_n_leaves }); } fn verify_inclusion_proof_aocl( ref self: ContractState, full_proof_with_hints: Span, ) -> bool { let mut res = starknet::syscalls::library_call_syscall( VERIFIER_CLASS_HASH.try_into().unwrap(), selector!("verify_ultra_keccak_zk_honk_proof"), full_proof_with_hints, ) .unwrap_syscall(); Serde::::deserialize(ref res).unwrap() } } // Private function fn _update_aocl_state( ref self: ContractState, peaks: Array, n_leaves: u64, last_peak_index: u64, ) { // Copy the AOCL into the AOCL state for i in 0..peaks.len() { self.aocl_state.peaks.get(i.into()).unwrap().write(*peaks[i]); } self.aocl_state.n_leaves.write(n_leaves); self.aocl_state.last_peak_index.write(last_peak_index); } } ================================================ FILE: src/contracts/mutator_set/src/zk_verifier/honk_verifier_circuits.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::G1Point; #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_17_PUB_19_circuit( p_public_inputs: Span, p_pairing_point_object: Span, libra_sum: u384, sumcheck_univariates_flat: Span, sumcheck_evaluations: Span, libra_evaluation: u384, tp_sum_check_u_challenges: Span, tp_gate_challenge: u128, tp_eta_1: u384, tp_eta_2: u384, tp_eta_3: u384, tp_beta: u384, tp_gamma: u384, tp_base_rlc: u384, tp_alpha: u128, tp_libra_challenge: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x10000000 let in2 = CE::> {}; // 0x9d80 let in3 = CE::> {}; // 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593efffec51 let in4 = CE::> {}; // 0x5a0 let in5 = CE::> {}; // 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffd31 let in6 = CE::> {}; // 0x240 let in7 = CE::> {}; // 0x0 let in8 = CE::> {}; // 0x2 let in9 = CE::> {}; // 0x3 let in10 = CE::> {}; // 0x4 let in11 = CE::> {}; // 0x5 let in12 = CE::> {}; // 0x6 let in13 = CE::> {}; // 0x7 let in14 = CE::> {}; // 0x8 let in15 = CE::< CI<15>, > {}; // 0x183227397098d014dc2822db40c0ac2e9419f4243cdcb848a1f0fac9f8000000 let in16 = CE::> {}; // -0x1 % p let in17 = CE::> {}; // 0x11 let in18 = CE::> {}; // 0x9 let in19 = CE::> {}; // 0x100000000000000000 let in20 = CE::> {}; // 0x4000 let in21 = CE::< CI<21>, > {}; // 0x10dc6e9c006ea38b04b1e03b4bd9490c0d03f98929ca1d7fb56821fd19d3b6e7 let in22 = CE::> {}; // 0xc28145b6a44df3e0149b3d0a30b3bb599df9756d4dd9b84a86b38cfb45a740b let in23 = CE::> {}; // 0x544b8338791518b2c7645a50392798b21f75bb60e3596170067d00141cac15 let in24 = CE::< CI<24>, > {}; // 0x222c01175718386f2e2e82eb122789e352e105a3b8fa852613bc534433ee428b // INPUT stack let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let (in37, in38, in39) = (CE::> {}, CE::> {}, CE::> {}); let (in40, in41, in42) = (CE::> {}, CE::> {}, CE::> {}); let (in43, in44, in45) = (CE::> {}, CE::> {}, CE::> {}); let (in46, in47, in48) = (CE::> {}, CE::> {}, CE::> {}); let (in49, in50, in51) = (CE::> {}, CE::> {}, CE::> {}); let (in52, in53, in54) = (CE::> {}, CE::> {}, CE::> {}); let (in55, in56, in57) = (CE::> {}, CE::> {}, CE::> {}); let (in58, in59, in60) = (CE::> {}, CE::> {}, CE::> {}); let (in61, in62, in63) = (CE::> {}, CE::> {}, CE::> {}); let (in64, in65, in66) = (CE::> {}, CE::> {}, CE::> {}); let (in67, in68, in69) = (CE::> {}, CE::> {}, CE::> {}); let (in70, in71, in72) = (CE::> {}, CE::> {}, CE::> {}); let (in73, in74, in75) = (CE::> {}, CE::> {}, CE::> {}); let (in76, in77, in78) = (CE::> {}, CE::> {}, CE::> {}); let (in79, in80, in81) = (CE::> {}, CE::> {}, CE::> {}); let (in82, in83, in84) = (CE::> {}, CE::> {}, CE::> {}); let (in85, in86, in87) = (CE::> {}, CE::> {}, CE::> {}); let (in88, in89, in90) = (CE::> {}, CE::> {}, CE::> {}); let (in91, in92, in93) = (CE::> {}, CE::> {}, CE::> {}); let (in94, in95, in96) = (CE::> {}, CE::> {}, CE::> {}); let (in97, in98, in99) = (CE::> {}, CE::> {}, CE::> {}); let (in100, in101, in102) = (CE::> {}, CE::> {}, CE::> {}); let (in103, in104, in105) = (CE::> {}, CE::> {}, CE::> {}); let (in106, in107, in108) = (CE::> {}, CE::> {}, CE::> {}); let (in109, in110, in111) = (CE::> {}, CE::> {}, CE::> {}); let (in112, in113, in114) = (CE::> {}, CE::> {}, CE::> {}); let (in115, in116, in117) = (CE::> {}, CE::> {}, CE::> {}); let (in118, in119, in120) = (CE::> {}, CE::> {}, CE::> {}); let (in121, in122, in123) = (CE::> {}, CE::> {}, CE::> {}); let (in124, in125, in126) = (CE::> {}, CE::> {}, CE::> {}); let (in127, in128, in129) = (CE::> {}, CE::> {}, CE::> {}); let (in130, in131, in132) = (CE::> {}, CE::> {}, CE::> {}); let (in133, in134, in135) = (CE::> {}, CE::> {}, CE::> {}); let (in136, in137, in138) = (CE::> {}, CE::> {}, CE::> {}); let (in139, in140, in141) = (CE::> {}, CE::> {}, CE::> {}); let (in142, in143, in144) = (CE::> {}, CE::> {}, CE::> {}); let (in145, in146, in147) = (CE::> {}, CE::> {}, CE::> {}); let (in148, in149, in150) = (CE::> {}, CE::> {}, CE::> {}); let (in151, in152, in153) = (CE::> {}, CE::> {}, CE::> {}); let (in154, in155, in156) = (CE::> {}, CE::> {}, CE::> {}); let (in157, in158, in159) = (CE::> {}, CE::> {}, CE::> {}); let (in160, in161, in162) = (CE::> {}, CE::> {}, CE::> {}); let (in163, in164, in165) = (CE::> {}, CE::> {}, CE::> {}); let (in166, in167, in168) = (CE::> {}, CE::> {}, CE::> {}); let (in169, in170, in171) = (CE::> {}, CE::> {}, CE::> {}); let (in172, in173, in174) = (CE::> {}, CE::> {}, CE::> {}); let (in175, in176, in177) = (CE::> {}, CE::> {}, CE::> {}); let (in178, in179, in180) = (CE::> {}, CE::> {}, CE::> {}); let (in181, in182, in183) = (CE::> {}, CE::> {}, CE::> {}); let (in184, in185, in186) = (CE::> {}, CE::> {}, CE::> {}); let (in187, in188, in189) = (CE::> {}, CE::> {}, CE::> {}); let (in190, in191, in192) = (CE::> {}, CE::> {}, CE::> {}); let (in193, in194, in195) = (CE::> {}, CE::> {}, CE::> {}); let (in196, in197, in198) = (CE::> {}, CE::> {}, CE::> {}); let (in199, in200, in201) = (CE::> {}, CE::> {}, CE::> {}); let (in202, in203, in204) = (CE::> {}, CE::> {}, CE::> {}); let (in205, in206, in207) = (CE::> {}, CE::> {}, CE::> {}); let (in208, in209, in210) = (CE::> {}, CE::> {}, CE::> {}); let (in211, in212, in213) = (CE::> {}, CE::> {}, CE::> {}); let (in214, in215, in216) = (CE::> {}, CE::> {}, CE::> {}); let (in217, in218, in219) = (CE::> {}, CE::> {}, CE::> {}); let (in220, in221, in222) = (CE::> {}, CE::> {}, CE::> {}); let (in223, in224, in225) = (CE::> {}, CE::> {}, CE::> {}); let (in226, in227, in228) = (CE::> {}, CE::> {}, CE::> {}); let (in229, in230, in231) = (CE::> {}, CE::> {}, CE::> {}); let (in232, in233, in234) = (CE::> {}, CE::> {}, CE::> {}); let (in235, in236, in237) = (CE::> {}, CE::> {}, CE::> {}); let (in238, in239, in240) = (CE::> {}, CE::> {}, CE::> {}); let (in241, in242, in243) = (CE::> {}, CE::> {}, CE::> {}); let (in244, in245, in246) = (CE::> {}, CE::> {}, CE::> {}); let (in247, in248, in249) = (CE::> {}, CE::> {}, CE::> {}); let (in250, in251, in252) = (CE::> {}, CE::> {}, CE::> {}); let (in253, in254, in255) = (CE::> {}, CE::> {}, CE::> {}); let (in256, in257, in258) = (CE::> {}, CE::> {}, CE::> {}); let (in259, in260, in261) = (CE::> {}, CE::> {}, CE::> {}); let (in262, in263, in264) = (CE::> {}, CE::> {}, CE::> {}); let in265 = CE::> {}; let t0 = circuit_add(in1, in0); let t1 = circuit_mul(in261, t0); let t2 = circuit_add(in262, t1); let t3 = circuit_add(in0, in0); let t4 = circuit_mul(in261, t3); let t5 = circuit_sub(in262, t4); let t6 = circuit_add(t2, in25); let t7 = circuit_mul(in0, t6); let t8 = circuit_add(t5, in25); let t9 = circuit_mul(in0, t8); let t10 = circuit_add(t2, in261); let t11 = circuit_sub(t5, in261); let t12 = circuit_add(t10, in26); let t13 = circuit_mul(t7, t12); let t14 = circuit_add(t11, in26); let t15 = circuit_mul(t9, t14); let t16 = circuit_add(t10, in261); let t17 = circuit_sub(t11, in261); let t18 = circuit_add(t16, in27); let t19 = circuit_mul(t13, t18); let t20 = circuit_add(t17, in27); let t21 = circuit_mul(t15, t20); let t22 = circuit_add(t16, in261); let t23 = circuit_sub(t17, in261); let t24 = circuit_add(t22, in28); let t25 = circuit_mul(t19, t24); let t26 = circuit_add(t23, in28); let t27 = circuit_mul(t21, t26); let t28 = circuit_add(t22, in261); let t29 = circuit_sub(t23, in261); let t30 = circuit_add(t28, in29); let t31 = circuit_mul(t25, t30); let t32 = circuit_add(t29, in29); let t33 = circuit_mul(t27, t32); let t34 = circuit_add(t28, in261); let t35 = circuit_sub(t29, in261); let t36 = circuit_add(t34, in30); let t37 = circuit_mul(t31, t36); let t38 = circuit_add(t35, in30); let t39 = circuit_mul(t33, t38); let t40 = circuit_add(t34, in261); let t41 = circuit_sub(t35, in261); let t42 = circuit_add(t40, in31); let t43 = circuit_mul(t37, t42); let t44 = circuit_add(t41, in31); let t45 = circuit_mul(t39, t44); let t46 = circuit_add(t40, in261); let t47 = circuit_sub(t41, in261); let t48 = circuit_add(t46, in32); let t49 = circuit_mul(t43, t48); let t50 = circuit_add(t47, in32); let t51 = circuit_mul(t45, t50); let t52 = circuit_add(t46, in261); let t53 = circuit_sub(t47, in261); let t54 = circuit_add(t52, in33); let t55 = circuit_mul(t49, t54); let t56 = circuit_add(t53, in33); let t57 = circuit_mul(t51, t56); let t58 = circuit_add(t52, in261); let t59 = circuit_sub(t53, in261); let t60 = circuit_add(t58, in34); let t61 = circuit_mul(t55, t60); let t62 = circuit_add(t59, in34); let t63 = circuit_mul(t57, t62); let t64 = circuit_add(t58, in261); let t65 = circuit_sub(t59, in261); let t66 = circuit_add(t64, in35); let t67 = circuit_mul(t61, t66); let t68 = circuit_add(t65, in35); let t69 = circuit_mul(t63, t68); let t70 = circuit_add(t64, in261); let t71 = circuit_sub(t65, in261); let t72 = circuit_add(t70, in36); let t73 = circuit_mul(t67, t72); let t74 = circuit_add(t71, in36); let t75 = circuit_mul(t69, t74); let t76 = circuit_add(t70, in261); let t77 = circuit_sub(t71, in261); let t78 = circuit_add(t76, in37); let t79 = circuit_mul(t73, t78); let t80 = circuit_add(t77, in37); let t81 = circuit_mul(t75, t80); let t82 = circuit_add(t76, in261); let t83 = circuit_sub(t77, in261); let t84 = circuit_add(t82, in38); let t85 = circuit_mul(t79, t84); let t86 = circuit_add(t83, in38); let t87 = circuit_mul(t81, t86); let t88 = circuit_add(t82, in261); let t89 = circuit_sub(t83, in261); let t90 = circuit_add(t88, in39); let t91 = circuit_mul(t85, t90); let t92 = circuit_add(t89, in39); let t93 = circuit_mul(t87, t92); let t94 = circuit_add(t88, in261); let t95 = circuit_sub(t89, in261); let t96 = circuit_add(t94, in40); let t97 = circuit_mul(t91, t96); let t98 = circuit_add(t95, in40); let t99 = circuit_mul(t93, t98); let t100 = circuit_add(t94, in261); let t101 = circuit_sub(t95, in261); let t102 = circuit_add(t100, in41); let t103 = circuit_mul(t97, t102); let t104 = circuit_add(t101, in41); let t105 = circuit_mul(t99, t104); let t106 = circuit_add(t100, in261); let t107 = circuit_sub(t101, in261); let t108 = circuit_add(t106, in42); let t109 = circuit_mul(t103, t108); let t110 = circuit_add(t107, in42); let t111 = circuit_mul(t105, t110); let t112 = circuit_add(t106, in261); let t113 = circuit_sub(t107, in261); let t114 = circuit_add(t112, in43); let t115 = circuit_mul(t109, t114); let t116 = circuit_add(t113, in43); let t117 = circuit_mul(t111, t116); let t118 = circuit_inverse(t117); let t119 = circuit_mul(t115, t118); let t120 = circuit_mul(in265, in44); let t121 = circuit_add(in45, in46); let t122 = circuit_sub(t121, t120); let t123 = circuit_mul(t122, in263); let t124 = circuit_sub(in240, in7); let t125 = circuit_mul(in0, t124); let t126 = circuit_sub(in240, in7); let t127 = circuit_mul(in2, t126); let t128 = circuit_inverse(t127); let t129 = circuit_mul(in45, t128); let t130 = circuit_add(in7, t129); let t131 = circuit_sub(in240, in0); let t132 = circuit_mul(t125, t131); let t133 = circuit_sub(in240, in0); let t134 = circuit_mul(in3, t133); let t135 = circuit_inverse(t134); let t136 = circuit_mul(in46, t135); let t137 = circuit_add(t130, t136); let t138 = circuit_sub(in240, in8); let t139 = circuit_mul(t132, t138); let t140 = circuit_sub(in240, in8); let t141 = circuit_mul(in4, t140); let t142 = circuit_inverse(t141); let t143 = circuit_mul(in47, t142); let t144 = circuit_add(t137, t143); let t145 = circuit_sub(in240, in9); let t146 = circuit_mul(t139, t145); let t147 = circuit_sub(in240, in9); let t148 = circuit_mul(in5, t147); let t149 = circuit_inverse(t148); let t150 = circuit_mul(in48, t149); let t151 = circuit_add(t144, t150); let t152 = circuit_sub(in240, in10); let t153 = circuit_mul(t146, t152); let t154 = circuit_sub(in240, in10); let t155 = circuit_mul(in6, t154); let t156 = circuit_inverse(t155); let t157 = circuit_mul(in49, t156); let t158 = circuit_add(t151, t157); let t159 = circuit_sub(in240, in11); let t160 = circuit_mul(t153, t159); let t161 = circuit_sub(in240, in11); let t162 = circuit_mul(in5, t161); let t163 = circuit_inverse(t162); let t164 = circuit_mul(in50, t163); let t165 = circuit_add(t158, t164); let t166 = circuit_sub(in240, in12); let t167 = circuit_mul(t160, t166); let t168 = circuit_sub(in240, in12); let t169 = circuit_mul(in4, t168); let t170 = circuit_inverse(t169); let t171 = circuit_mul(in51, t170); let t172 = circuit_add(t165, t171); let t173 = circuit_sub(in240, in13); let t174 = circuit_mul(t167, t173); let t175 = circuit_sub(in240, in13); let t176 = circuit_mul(in3, t175); let t177 = circuit_inverse(t176); let t178 = circuit_mul(in52, t177); let t179 = circuit_add(t172, t178); let t180 = circuit_sub(in240, in14); let t181 = circuit_mul(t174, t180); let t182 = circuit_sub(in240, in14); let t183 = circuit_mul(in2, t182); let t184 = circuit_inverse(t183); let t185 = circuit_mul(in53, t184); let t186 = circuit_add(t179, t185); let t187 = circuit_mul(t186, t181); let t188 = circuit_sub(in257, in0); let t189 = circuit_mul(in240, t188); let t190 = circuit_add(in0, t189); let t191 = circuit_mul(in0, t190); let t192 = circuit_mul(in263, in263); let t193 = circuit_mul(in257, in257); let t194 = circuit_add(in54, in55); let t195 = circuit_sub(t194, t187); let t196 = circuit_mul(t195, t192); let t197 = circuit_add(t123, t196); let t198 = circuit_sub(in241, in7); let t199 = circuit_mul(in0, t198); let t200 = circuit_sub(in241, in7); let t201 = circuit_mul(in2, t200); let t202 = circuit_inverse(t201); let t203 = circuit_mul(in54, t202); let t204 = circuit_add(in7, t203); let t205 = circuit_sub(in241, in0); let t206 = circuit_mul(t199, t205); let t207 = circuit_sub(in241, in0); let t208 = circuit_mul(in3, t207); let t209 = circuit_inverse(t208); let t210 = circuit_mul(in55, t209); let t211 = circuit_add(t204, t210); let t212 = circuit_sub(in241, in8); let t213 = circuit_mul(t206, t212); let t214 = circuit_sub(in241, in8); let t215 = circuit_mul(in4, t214); let t216 = circuit_inverse(t215); let t217 = circuit_mul(in56, t216); let t218 = circuit_add(t211, t217); let t219 = circuit_sub(in241, in9); let t220 = circuit_mul(t213, t219); let t221 = circuit_sub(in241, in9); let t222 = circuit_mul(in5, t221); let t223 = circuit_inverse(t222); let t224 = circuit_mul(in57, t223); let t225 = circuit_add(t218, t224); let t226 = circuit_sub(in241, in10); let t227 = circuit_mul(t220, t226); let t228 = circuit_sub(in241, in10); let t229 = circuit_mul(in6, t228); let t230 = circuit_inverse(t229); let t231 = circuit_mul(in58, t230); let t232 = circuit_add(t225, t231); let t233 = circuit_sub(in241, in11); let t234 = circuit_mul(t227, t233); let t235 = circuit_sub(in241, in11); let t236 = circuit_mul(in5, t235); let t237 = circuit_inverse(t236); let t238 = circuit_mul(in59, t237); let t239 = circuit_add(t232, t238); let t240 = circuit_sub(in241, in12); let t241 = circuit_mul(t234, t240); let t242 = circuit_sub(in241, in12); let t243 = circuit_mul(in4, t242); let t244 = circuit_inverse(t243); let t245 = circuit_mul(in60, t244); let t246 = circuit_add(t239, t245); let t247 = circuit_sub(in241, in13); let t248 = circuit_mul(t241, t247); let t249 = circuit_sub(in241, in13); let t250 = circuit_mul(in3, t249); let t251 = circuit_inverse(t250); let t252 = circuit_mul(in61, t251); let t253 = circuit_add(t246, t252); let t254 = circuit_sub(in241, in14); let t255 = circuit_mul(t248, t254); let t256 = circuit_sub(in241, in14); let t257 = circuit_mul(in2, t256); let t258 = circuit_inverse(t257); let t259 = circuit_mul(in62, t258); let t260 = circuit_add(t253, t259); let t261 = circuit_mul(t260, t255); let t262 = circuit_sub(t193, in0); let t263 = circuit_mul(in241, t262); let t264 = circuit_add(in0, t263); let t265 = circuit_mul(t191, t264); let t266 = circuit_mul(t192, in263); let t267 = circuit_mul(t193, t193); let t268 = circuit_add(in63, in64); let t269 = circuit_sub(t268, t261); let t270 = circuit_mul(t269, t266); let t271 = circuit_add(t197, t270); let t272 = circuit_sub(in242, in7); let t273 = circuit_mul(in0, t272); let t274 = circuit_sub(in242, in7); let t275 = circuit_mul(in2, t274); let t276 = circuit_inverse(t275); let t277 = circuit_mul(in63, t276); let t278 = circuit_add(in7, t277); let t279 = circuit_sub(in242, in0); let t280 = circuit_mul(t273, t279); let t281 = circuit_sub(in242, in0); let t282 = circuit_mul(in3, t281); let t283 = circuit_inverse(t282); let t284 = circuit_mul(in64, t283); let t285 = circuit_add(t278, t284); let t286 = circuit_sub(in242, in8); let t287 = circuit_mul(t280, t286); let t288 = circuit_sub(in242, in8); let t289 = circuit_mul(in4, t288); let t290 = circuit_inverse(t289); let t291 = circuit_mul(in65, t290); let t292 = circuit_add(t285, t291); let t293 = circuit_sub(in242, in9); let t294 = circuit_mul(t287, t293); let t295 = circuit_sub(in242, in9); let t296 = circuit_mul(in5, t295); let t297 = circuit_inverse(t296); let t298 = circuit_mul(in66, t297); let t299 = circuit_add(t292, t298); let t300 = circuit_sub(in242, in10); let t301 = circuit_mul(t294, t300); let t302 = circuit_sub(in242, in10); let t303 = circuit_mul(in6, t302); let t304 = circuit_inverse(t303); let t305 = circuit_mul(in67, t304); let t306 = circuit_add(t299, t305); let t307 = circuit_sub(in242, in11); let t308 = circuit_mul(t301, t307); let t309 = circuit_sub(in242, in11); let t310 = circuit_mul(in5, t309); let t311 = circuit_inverse(t310); let t312 = circuit_mul(in68, t311); let t313 = circuit_add(t306, t312); let t314 = circuit_sub(in242, in12); let t315 = circuit_mul(t308, t314); let t316 = circuit_sub(in242, in12); let t317 = circuit_mul(in4, t316); let t318 = circuit_inverse(t317); let t319 = circuit_mul(in69, t318); let t320 = circuit_add(t313, t319); let t321 = circuit_sub(in242, in13); let t322 = circuit_mul(t315, t321); let t323 = circuit_sub(in242, in13); let t324 = circuit_mul(in3, t323); let t325 = circuit_inverse(t324); let t326 = circuit_mul(in70, t325); let t327 = circuit_add(t320, t326); let t328 = circuit_sub(in242, in14); let t329 = circuit_mul(t322, t328); let t330 = circuit_sub(in242, in14); let t331 = circuit_mul(in2, t330); let t332 = circuit_inverse(t331); let t333 = circuit_mul(in71, t332); let t334 = circuit_add(t327, t333); let t335 = circuit_mul(t334, t329); let t336 = circuit_sub(t267, in0); let t337 = circuit_mul(in242, t336); let t338 = circuit_add(in0, t337); let t339 = circuit_mul(t265, t338); let t340 = circuit_mul(t266, in263); let t341 = circuit_mul(t267, t267); let t342 = circuit_add(in72, in73); let t343 = circuit_sub(t342, t335); let t344 = circuit_mul(t343, t340); let t345 = circuit_add(t271, t344); let t346 = circuit_sub(in243, in7); let t347 = circuit_mul(in0, t346); let t348 = circuit_sub(in243, in7); let t349 = circuit_mul(in2, t348); let t350 = circuit_inverse(t349); let t351 = circuit_mul(in72, t350); let t352 = circuit_add(in7, t351); let t353 = circuit_sub(in243, in0); let t354 = circuit_mul(t347, t353); let t355 = circuit_sub(in243, in0); let t356 = circuit_mul(in3, t355); let t357 = circuit_inverse(t356); let t358 = circuit_mul(in73, t357); let t359 = circuit_add(t352, t358); let t360 = circuit_sub(in243, in8); let t361 = circuit_mul(t354, t360); let t362 = circuit_sub(in243, in8); let t363 = circuit_mul(in4, t362); let t364 = circuit_inverse(t363); let t365 = circuit_mul(in74, t364); let t366 = circuit_add(t359, t365); let t367 = circuit_sub(in243, in9); let t368 = circuit_mul(t361, t367); let t369 = circuit_sub(in243, in9); let t370 = circuit_mul(in5, t369); let t371 = circuit_inverse(t370); let t372 = circuit_mul(in75, t371); let t373 = circuit_add(t366, t372); let t374 = circuit_sub(in243, in10); let t375 = circuit_mul(t368, t374); let t376 = circuit_sub(in243, in10); let t377 = circuit_mul(in6, t376); let t378 = circuit_inverse(t377); let t379 = circuit_mul(in76, t378); let t380 = circuit_add(t373, t379); let t381 = circuit_sub(in243, in11); let t382 = circuit_mul(t375, t381); let t383 = circuit_sub(in243, in11); let t384 = circuit_mul(in5, t383); let t385 = circuit_inverse(t384); let t386 = circuit_mul(in77, t385); let t387 = circuit_add(t380, t386); let t388 = circuit_sub(in243, in12); let t389 = circuit_mul(t382, t388); let t390 = circuit_sub(in243, in12); let t391 = circuit_mul(in4, t390); let t392 = circuit_inverse(t391); let t393 = circuit_mul(in78, t392); let t394 = circuit_add(t387, t393); let t395 = circuit_sub(in243, in13); let t396 = circuit_mul(t389, t395); let t397 = circuit_sub(in243, in13); let t398 = circuit_mul(in3, t397); let t399 = circuit_inverse(t398); let t400 = circuit_mul(in79, t399); let t401 = circuit_add(t394, t400); let t402 = circuit_sub(in243, in14); let t403 = circuit_mul(t396, t402); let t404 = circuit_sub(in243, in14); let t405 = circuit_mul(in2, t404); let t406 = circuit_inverse(t405); let t407 = circuit_mul(in80, t406); let t408 = circuit_add(t401, t407); let t409 = circuit_mul(t408, t403); let t410 = circuit_sub(t341, in0); let t411 = circuit_mul(in243, t410); let t412 = circuit_add(in0, t411); let t413 = circuit_mul(t339, t412); let t414 = circuit_mul(t340, in263); let t415 = circuit_mul(t341, t341); let t416 = circuit_add(in81, in82); let t417 = circuit_sub(t416, t409); let t418 = circuit_mul(t417, t414); let t419 = circuit_add(t345, t418); let t420 = circuit_sub(in244, in7); let t421 = circuit_mul(in0, t420); let t422 = circuit_sub(in244, in7); let t423 = circuit_mul(in2, t422); let t424 = circuit_inverse(t423); let t425 = circuit_mul(in81, t424); let t426 = circuit_add(in7, t425); let t427 = circuit_sub(in244, in0); let t428 = circuit_mul(t421, t427); let t429 = circuit_sub(in244, in0); let t430 = circuit_mul(in3, t429); let t431 = circuit_inverse(t430); let t432 = circuit_mul(in82, t431); let t433 = circuit_add(t426, t432); let t434 = circuit_sub(in244, in8); let t435 = circuit_mul(t428, t434); let t436 = circuit_sub(in244, in8); let t437 = circuit_mul(in4, t436); let t438 = circuit_inverse(t437); let t439 = circuit_mul(in83, t438); let t440 = circuit_add(t433, t439); let t441 = circuit_sub(in244, in9); let t442 = circuit_mul(t435, t441); let t443 = circuit_sub(in244, in9); let t444 = circuit_mul(in5, t443); let t445 = circuit_inverse(t444); let t446 = circuit_mul(in84, t445); let t447 = circuit_add(t440, t446); let t448 = circuit_sub(in244, in10); let t449 = circuit_mul(t442, t448); let t450 = circuit_sub(in244, in10); let t451 = circuit_mul(in6, t450); let t452 = circuit_inverse(t451); let t453 = circuit_mul(in85, t452); let t454 = circuit_add(t447, t453); let t455 = circuit_sub(in244, in11); let t456 = circuit_mul(t449, t455); let t457 = circuit_sub(in244, in11); let t458 = circuit_mul(in5, t457); let t459 = circuit_inverse(t458); let t460 = circuit_mul(in86, t459); let t461 = circuit_add(t454, t460); let t462 = circuit_sub(in244, in12); let t463 = circuit_mul(t456, t462); let t464 = circuit_sub(in244, in12); let t465 = circuit_mul(in4, t464); let t466 = circuit_inverse(t465); let t467 = circuit_mul(in87, t466); let t468 = circuit_add(t461, t467); let t469 = circuit_sub(in244, in13); let t470 = circuit_mul(t463, t469); let t471 = circuit_sub(in244, in13); let t472 = circuit_mul(in3, t471); let t473 = circuit_inverse(t472); let t474 = circuit_mul(in88, t473); let t475 = circuit_add(t468, t474); let t476 = circuit_sub(in244, in14); let t477 = circuit_mul(t470, t476); let t478 = circuit_sub(in244, in14); let t479 = circuit_mul(in2, t478); let t480 = circuit_inverse(t479); let t481 = circuit_mul(in89, t480); let t482 = circuit_add(t475, t481); let t483 = circuit_mul(t482, t477); let t484 = circuit_sub(t415, in0); let t485 = circuit_mul(in244, t484); let t486 = circuit_add(in0, t485); let t487 = circuit_mul(t413, t486); let t488 = circuit_mul(t414, in263); let t489 = circuit_mul(t415, t415); let t490 = circuit_add(in90, in91); let t491 = circuit_sub(t490, t483); let t492 = circuit_mul(t491, t488); let t493 = circuit_add(t419, t492); let t494 = circuit_sub(in245, in7); let t495 = circuit_mul(in0, t494); let t496 = circuit_sub(in245, in7); let t497 = circuit_mul(in2, t496); let t498 = circuit_inverse(t497); let t499 = circuit_mul(in90, t498); let t500 = circuit_add(in7, t499); let t501 = circuit_sub(in245, in0); let t502 = circuit_mul(t495, t501); let t503 = circuit_sub(in245, in0); let t504 = circuit_mul(in3, t503); let t505 = circuit_inverse(t504); let t506 = circuit_mul(in91, t505); let t507 = circuit_add(t500, t506); let t508 = circuit_sub(in245, in8); let t509 = circuit_mul(t502, t508); let t510 = circuit_sub(in245, in8); let t511 = circuit_mul(in4, t510); let t512 = circuit_inverse(t511); let t513 = circuit_mul(in92, t512); let t514 = circuit_add(t507, t513); let t515 = circuit_sub(in245, in9); let t516 = circuit_mul(t509, t515); let t517 = circuit_sub(in245, in9); let t518 = circuit_mul(in5, t517); let t519 = circuit_inverse(t518); let t520 = circuit_mul(in93, t519); let t521 = circuit_add(t514, t520); let t522 = circuit_sub(in245, in10); let t523 = circuit_mul(t516, t522); let t524 = circuit_sub(in245, in10); let t525 = circuit_mul(in6, t524); let t526 = circuit_inverse(t525); let t527 = circuit_mul(in94, t526); let t528 = circuit_add(t521, t527); let t529 = circuit_sub(in245, in11); let t530 = circuit_mul(t523, t529); let t531 = circuit_sub(in245, in11); let t532 = circuit_mul(in5, t531); let t533 = circuit_inverse(t532); let t534 = circuit_mul(in95, t533); let t535 = circuit_add(t528, t534); let t536 = circuit_sub(in245, in12); let t537 = circuit_mul(t530, t536); let t538 = circuit_sub(in245, in12); let t539 = circuit_mul(in4, t538); let t540 = circuit_inverse(t539); let t541 = circuit_mul(in96, t540); let t542 = circuit_add(t535, t541); let t543 = circuit_sub(in245, in13); let t544 = circuit_mul(t537, t543); let t545 = circuit_sub(in245, in13); let t546 = circuit_mul(in3, t545); let t547 = circuit_inverse(t546); let t548 = circuit_mul(in97, t547); let t549 = circuit_add(t542, t548); let t550 = circuit_sub(in245, in14); let t551 = circuit_mul(t544, t550); let t552 = circuit_sub(in245, in14); let t553 = circuit_mul(in2, t552); let t554 = circuit_inverse(t553); let t555 = circuit_mul(in98, t554); let t556 = circuit_add(t549, t555); let t557 = circuit_mul(t556, t551); let t558 = circuit_sub(t489, in0); let t559 = circuit_mul(in245, t558); let t560 = circuit_add(in0, t559); let t561 = circuit_mul(t487, t560); let t562 = circuit_mul(t488, in263); let t563 = circuit_mul(t489, t489); let t564 = circuit_add(in99, in100); let t565 = circuit_sub(t564, t557); let t566 = circuit_mul(t565, t562); let t567 = circuit_add(t493, t566); let t568 = circuit_sub(in246, in7); let t569 = circuit_mul(in0, t568); let t570 = circuit_sub(in246, in7); let t571 = circuit_mul(in2, t570); let t572 = circuit_inverse(t571); let t573 = circuit_mul(in99, t572); let t574 = circuit_add(in7, t573); let t575 = circuit_sub(in246, in0); let t576 = circuit_mul(t569, t575); let t577 = circuit_sub(in246, in0); let t578 = circuit_mul(in3, t577); let t579 = circuit_inverse(t578); let t580 = circuit_mul(in100, t579); let t581 = circuit_add(t574, t580); let t582 = circuit_sub(in246, in8); let t583 = circuit_mul(t576, t582); let t584 = circuit_sub(in246, in8); let t585 = circuit_mul(in4, t584); let t586 = circuit_inverse(t585); let t587 = circuit_mul(in101, t586); let t588 = circuit_add(t581, t587); let t589 = circuit_sub(in246, in9); let t590 = circuit_mul(t583, t589); let t591 = circuit_sub(in246, in9); let t592 = circuit_mul(in5, t591); let t593 = circuit_inverse(t592); let t594 = circuit_mul(in102, t593); let t595 = circuit_add(t588, t594); let t596 = circuit_sub(in246, in10); let t597 = circuit_mul(t590, t596); let t598 = circuit_sub(in246, in10); let t599 = circuit_mul(in6, t598); let t600 = circuit_inverse(t599); let t601 = circuit_mul(in103, t600); let t602 = circuit_add(t595, t601); let t603 = circuit_sub(in246, in11); let t604 = circuit_mul(t597, t603); let t605 = circuit_sub(in246, in11); let t606 = circuit_mul(in5, t605); let t607 = circuit_inverse(t606); let t608 = circuit_mul(in104, t607); let t609 = circuit_add(t602, t608); let t610 = circuit_sub(in246, in12); let t611 = circuit_mul(t604, t610); let t612 = circuit_sub(in246, in12); let t613 = circuit_mul(in4, t612); let t614 = circuit_inverse(t613); let t615 = circuit_mul(in105, t614); let t616 = circuit_add(t609, t615); let t617 = circuit_sub(in246, in13); let t618 = circuit_mul(t611, t617); let t619 = circuit_sub(in246, in13); let t620 = circuit_mul(in3, t619); let t621 = circuit_inverse(t620); let t622 = circuit_mul(in106, t621); let t623 = circuit_add(t616, t622); let t624 = circuit_sub(in246, in14); let t625 = circuit_mul(t618, t624); let t626 = circuit_sub(in246, in14); let t627 = circuit_mul(in2, t626); let t628 = circuit_inverse(t627); let t629 = circuit_mul(in107, t628); let t630 = circuit_add(t623, t629); let t631 = circuit_mul(t630, t625); let t632 = circuit_sub(t563, in0); let t633 = circuit_mul(in246, t632); let t634 = circuit_add(in0, t633); let t635 = circuit_mul(t561, t634); let t636 = circuit_mul(t562, in263); let t637 = circuit_mul(t563, t563); let t638 = circuit_add(in108, in109); let t639 = circuit_sub(t638, t631); let t640 = circuit_mul(t639, t636); let t641 = circuit_add(t567, t640); let t642 = circuit_sub(in247, in7); let t643 = circuit_mul(in0, t642); let t644 = circuit_sub(in247, in7); let t645 = circuit_mul(in2, t644); let t646 = circuit_inverse(t645); let t647 = circuit_mul(in108, t646); let t648 = circuit_add(in7, t647); let t649 = circuit_sub(in247, in0); let t650 = circuit_mul(t643, t649); let t651 = circuit_sub(in247, in0); let t652 = circuit_mul(in3, t651); let t653 = circuit_inverse(t652); let t654 = circuit_mul(in109, t653); let t655 = circuit_add(t648, t654); let t656 = circuit_sub(in247, in8); let t657 = circuit_mul(t650, t656); let t658 = circuit_sub(in247, in8); let t659 = circuit_mul(in4, t658); let t660 = circuit_inverse(t659); let t661 = circuit_mul(in110, t660); let t662 = circuit_add(t655, t661); let t663 = circuit_sub(in247, in9); let t664 = circuit_mul(t657, t663); let t665 = circuit_sub(in247, in9); let t666 = circuit_mul(in5, t665); let t667 = circuit_inverse(t666); let t668 = circuit_mul(in111, t667); let t669 = circuit_add(t662, t668); let t670 = circuit_sub(in247, in10); let t671 = circuit_mul(t664, t670); let t672 = circuit_sub(in247, in10); let t673 = circuit_mul(in6, t672); let t674 = circuit_inverse(t673); let t675 = circuit_mul(in112, t674); let t676 = circuit_add(t669, t675); let t677 = circuit_sub(in247, in11); let t678 = circuit_mul(t671, t677); let t679 = circuit_sub(in247, in11); let t680 = circuit_mul(in5, t679); let t681 = circuit_inverse(t680); let t682 = circuit_mul(in113, t681); let t683 = circuit_add(t676, t682); let t684 = circuit_sub(in247, in12); let t685 = circuit_mul(t678, t684); let t686 = circuit_sub(in247, in12); let t687 = circuit_mul(in4, t686); let t688 = circuit_inverse(t687); let t689 = circuit_mul(in114, t688); let t690 = circuit_add(t683, t689); let t691 = circuit_sub(in247, in13); let t692 = circuit_mul(t685, t691); let t693 = circuit_sub(in247, in13); let t694 = circuit_mul(in3, t693); let t695 = circuit_inverse(t694); let t696 = circuit_mul(in115, t695); let t697 = circuit_add(t690, t696); let t698 = circuit_sub(in247, in14); let t699 = circuit_mul(t692, t698); let t700 = circuit_sub(in247, in14); let t701 = circuit_mul(in2, t700); let t702 = circuit_inverse(t701); let t703 = circuit_mul(in116, t702); let t704 = circuit_add(t697, t703); let t705 = circuit_mul(t704, t699); let t706 = circuit_sub(t637, in0); let t707 = circuit_mul(in247, t706); let t708 = circuit_add(in0, t707); let t709 = circuit_mul(t635, t708); let t710 = circuit_mul(t636, in263); let t711 = circuit_mul(t637, t637); let t712 = circuit_add(in117, in118); let t713 = circuit_sub(t712, t705); let t714 = circuit_mul(t713, t710); let t715 = circuit_add(t641, t714); let t716 = circuit_sub(in248, in7); let t717 = circuit_mul(in0, t716); let t718 = circuit_sub(in248, in7); let t719 = circuit_mul(in2, t718); let t720 = circuit_inverse(t719); let t721 = circuit_mul(in117, t720); let t722 = circuit_add(in7, t721); let t723 = circuit_sub(in248, in0); let t724 = circuit_mul(t717, t723); let t725 = circuit_sub(in248, in0); let t726 = circuit_mul(in3, t725); let t727 = circuit_inverse(t726); let t728 = circuit_mul(in118, t727); let t729 = circuit_add(t722, t728); let t730 = circuit_sub(in248, in8); let t731 = circuit_mul(t724, t730); let t732 = circuit_sub(in248, in8); let t733 = circuit_mul(in4, t732); let t734 = circuit_inverse(t733); let t735 = circuit_mul(in119, t734); let t736 = circuit_add(t729, t735); let t737 = circuit_sub(in248, in9); let t738 = circuit_mul(t731, t737); let t739 = circuit_sub(in248, in9); let t740 = circuit_mul(in5, t739); let t741 = circuit_inverse(t740); let t742 = circuit_mul(in120, t741); let t743 = circuit_add(t736, t742); let t744 = circuit_sub(in248, in10); let t745 = circuit_mul(t738, t744); let t746 = circuit_sub(in248, in10); let t747 = circuit_mul(in6, t746); let t748 = circuit_inverse(t747); let t749 = circuit_mul(in121, t748); let t750 = circuit_add(t743, t749); let t751 = circuit_sub(in248, in11); let t752 = circuit_mul(t745, t751); let t753 = circuit_sub(in248, in11); let t754 = circuit_mul(in5, t753); let t755 = circuit_inverse(t754); let t756 = circuit_mul(in122, t755); let t757 = circuit_add(t750, t756); let t758 = circuit_sub(in248, in12); let t759 = circuit_mul(t752, t758); let t760 = circuit_sub(in248, in12); let t761 = circuit_mul(in4, t760); let t762 = circuit_inverse(t761); let t763 = circuit_mul(in123, t762); let t764 = circuit_add(t757, t763); let t765 = circuit_sub(in248, in13); let t766 = circuit_mul(t759, t765); let t767 = circuit_sub(in248, in13); let t768 = circuit_mul(in3, t767); let t769 = circuit_inverse(t768); let t770 = circuit_mul(in124, t769); let t771 = circuit_add(t764, t770); let t772 = circuit_sub(in248, in14); let t773 = circuit_mul(t766, t772); let t774 = circuit_sub(in248, in14); let t775 = circuit_mul(in2, t774); let t776 = circuit_inverse(t775); let t777 = circuit_mul(in125, t776); let t778 = circuit_add(t771, t777); let t779 = circuit_mul(t778, t773); let t780 = circuit_sub(t711, in0); let t781 = circuit_mul(in248, t780); let t782 = circuit_add(in0, t781); let t783 = circuit_mul(t709, t782); let t784 = circuit_mul(t710, in263); let t785 = circuit_mul(t711, t711); let t786 = circuit_add(in126, in127); let t787 = circuit_sub(t786, t779); let t788 = circuit_mul(t787, t784); let t789 = circuit_add(t715, t788); let t790 = circuit_sub(in249, in7); let t791 = circuit_mul(in0, t790); let t792 = circuit_sub(in249, in7); let t793 = circuit_mul(in2, t792); let t794 = circuit_inverse(t793); let t795 = circuit_mul(in126, t794); let t796 = circuit_add(in7, t795); let t797 = circuit_sub(in249, in0); let t798 = circuit_mul(t791, t797); let t799 = circuit_sub(in249, in0); let t800 = circuit_mul(in3, t799); let t801 = circuit_inverse(t800); let t802 = circuit_mul(in127, t801); let t803 = circuit_add(t796, t802); let t804 = circuit_sub(in249, in8); let t805 = circuit_mul(t798, t804); let t806 = circuit_sub(in249, in8); let t807 = circuit_mul(in4, t806); let t808 = circuit_inverse(t807); let t809 = circuit_mul(in128, t808); let t810 = circuit_add(t803, t809); let t811 = circuit_sub(in249, in9); let t812 = circuit_mul(t805, t811); let t813 = circuit_sub(in249, in9); let t814 = circuit_mul(in5, t813); let t815 = circuit_inverse(t814); let t816 = circuit_mul(in129, t815); let t817 = circuit_add(t810, t816); let t818 = circuit_sub(in249, in10); let t819 = circuit_mul(t812, t818); let t820 = circuit_sub(in249, in10); let t821 = circuit_mul(in6, t820); let t822 = circuit_inverse(t821); let t823 = circuit_mul(in130, t822); let t824 = circuit_add(t817, t823); let t825 = circuit_sub(in249, in11); let t826 = circuit_mul(t819, t825); let t827 = circuit_sub(in249, in11); let t828 = circuit_mul(in5, t827); let t829 = circuit_inverse(t828); let t830 = circuit_mul(in131, t829); let t831 = circuit_add(t824, t830); let t832 = circuit_sub(in249, in12); let t833 = circuit_mul(t826, t832); let t834 = circuit_sub(in249, in12); let t835 = circuit_mul(in4, t834); let t836 = circuit_inverse(t835); let t837 = circuit_mul(in132, t836); let t838 = circuit_add(t831, t837); let t839 = circuit_sub(in249, in13); let t840 = circuit_mul(t833, t839); let t841 = circuit_sub(in249, in13); let t842 = circuit_mul(in3, t841); let t843 = circuit_inverse(t842); let t844 = circuit_mul(in133, t843); let t845 = circuit_add(t838, t844); let t846 = circuit_sub(in249, in14); let t847 = circuit_mul(t840, t846); let t848 = circuit_sub(in249, in14); let t849 = circuit_mul(in2, t848); let t850 = circuit_inverse(t849); let t851 = circuit_mul(in134, t850); let t852 = circuit_add(t845, t851); let t853 = circuit_mul(t852, t847); let t854 = circuit_sub(t785, in0); let t855 = circuit_mul(in249, t854); let t856 = circuit_add(in0, t855); let t857 = circuit_mul(t783, t856); let t858 = circuit_mul(t784, in263); let t859 = circuit_mul(t785, t785); let t860 = circuit_add(in135, in136); let t861 = circuit_sub(t860, t853); let t862 = circuit_mul(t861, t858); let t863 = circuit_add(t789, t862); let t864 = circuit_sub(in250, in7); let t865 = circuit_mul(in0, t864); let t866 = circuit_sub(in250, in7); let t867 = circuit_mul(in2, t866); let t868 = circuit_inverse(t867); let t869 = circuit_mul(in135, t868); let t870 = circuit_add(in7, t869); let t871 = circuit_sub(in250, in0); let t872 = circuit_mul(t865, t871); let t873 = circuit_sub(in250, in0); let t874 = circuit_mul(in3, t873); let t875 = circuit_inverse(t874); let t876 = circuit_mul(in136, t875); let t877 = circuit_add(t870, t876); let t878 = circuit_sub(in250, in8); let t879 = circuit_mul(t872, t878); let t880 = circuit_sub(in250, in8); let t881 = circuit_mul(in4, t880); let t882 = circuit_inverse(t881); let t883 = circuit_mul(in137, t882); let t884 = circuit_add(t877, t883); let t885 = circuit_sub(in250, in9); let t886 = circuit_mul(t879, t885); let t887 = circuit_sub(in250, in9); let t888 = circuit_mul(in5, t887); let t889 = circuit_inverse(t888); let t890 = circuit_mul(in138, t889); let t891 = circuit_add(t884, t890); let t892 = circuit_sub(in250, in10); let t893 = circuit_mul(t886, t892); let t894 = circuit_sub(in250, in10); let t895 = circuit_mul(in6, t894); let t896 = circuit_inverse(t895); let t897 = circuit_mul(in139, t896); let t898 = circuit_add(t891, t897); let t899 = circuit_sub(in250, in11); let t900 = circuit_mul(t893, t899); let t901 = circuit_sub(in250, in11); let t902 = circuit_mul(in5, t901); let t903 = circuit_inverse(t902); let t904 = circuit_mul(in140, t903); let t905 = circuit_add(t898, t904); let t906 = circuit_sub(in250, in12); let t907 = circuit_mul(t900, t906); let t908 = circuit_sub(in250, in12); let t909 = circuit_mul(in4, t908); let t910 = circuit_inverse(t909); let t911 = circuit_mul(in141, t910); let t912 = circuit_add(t905, t911); let t913 = circuit_sub(in250, in13); let t914 = circuit_mul(t907, t913); let t915 = circuit_sub(in250, in13); let t916 = circuit_mul(in3, t915); let t917 = circuit_inverse(t916); let t918 = circuit_mul(in142, t917); let t919 = circuit_add(t912, t918); let t920 = circuit_sub(in250, in14); let t921 = circuit_mul(t914, t920); let t922 = circuit_sub(in250, in14); let t923 = circuit_mul(in2, t922); let t924 = circuit_inverse(t923); let t925 = circuit_mul(in143, t924); let t926 = circuit_add(t919, t925); let t927 = circuit_mul(t926, t921); let t928 = circuit_sub(t859, in0); let t929 = circuit_mul(in250, t928); let t930 = circuit_add(in0, t929); let t931 = circuit_mul(t857, t930); let t932 = circuit_mul(t858, in263); let t933 = circuit_mul(t859, t859); let t934 = circuit_add(in144, in145); let t935 = circuit_sub(t934, t927); let t936 = circuit_mul(t935, t932); let t937 = circuit_add(t863, t936); let t938 = circuit_sub(in251, in7); let t939 = circuit_mul(in0, t938); let t940 = circuit_sub(in251, in7); let t941 = circuit_mul(in2, t940); let t942 = circuit_inverse(t941); let t943 = circuit_mul(in144, t942); let t944 = circuit_add(in7, t943); let t945 = circuit_sub(in251, in0); let t946 = circuit_mul(t939, t945); let t947 = circuit_sub(in251, in0); let t948 = circuit_mul(in3, t947); let t949 = circuit_inverse(t948); let t950 = circuit_mul(in145, t949); let t951 = circuit_add(t944, t950); let t952 = circuit_sub(in251, in8); let t953 = circuit_mul(t946, t952); let t954 = circuit_sub(in251, in8); let t955 = circuit_mul(in4, t954); let t956 = circuit_inverse(t955); let t957 = circuit_mul(in146, t956); let t958 = circuit_add(t951, t957); let t959 = circuit_sub(in251, in9); let t960 = circuit_mul(t953, t959); let t961 = circuit_sub(in251, in9); let t962 = circuit_mul(in5, t961); let t963 = circuit_inverse(t962); let t964 = circuit_mul(in147, t963); let t965 = circuit_add(t958, t964); let t966 = circuit_sub(in251, in10); let t967 = circuit_mul(t960, t966); let t968 = circuit_sub(in251, in10); let t969 = circuit_mul(in6, t968); let t970 = circuit_inverse(t969); let t971 = circuit_mul(in148, t970); let t972 = circuit_add(t965, t971); let t973 = circuit_sub(in251, in11); let t974 = circuit_mul(t967, t973); let t975 = circuit_sub(in251, in11); let t976 = circuit_mul(in5, t975); let t977 = circuit_inverse(t976); let t978 = circuit_mul(in149, t977); let t979 = circuit_add(t972, t978); let t980 = circuit_sub(in251, in12); let t981 = circuit_mul(t974, t980); let t982 = circuit_sub(in251, in12); let t983 = circuit_mul(in4, t982); let t984 = circuit_inverse(t983); let t985 = circuit_mul(in150, t984); let t986 = circuit_add(t979, t985); let t987 = circuit_sub(in251, in13); let t988 = circuit_mul(t981, t987); let t989 = circuit_sub(in251, in13); let t990 = circuit_mul(in3, t989); let t991 = circuit_inverse(t990); let t992 = circuit_mul(in151, t991); let t993 = circuit_add(t986, t992); let t994 = circuit_sub(in251, in14); let t995 = circuit_mul(t988, t994); let t996 = circuit_sub(in251, in14); let t997 = circuit_mul(in2, t996); let t998 = circuit_inverse(t997); let t999 = circuit_mul(in152, t998); let t1000 = circuit_add(t993, t999); let t1001 = circuit_mul(t1000, t995); let t1002 = circuit_sub(t933, in0); let t1003 = circuit_mul(in251, t1002); let t1004 = circuit_add(in0, t1003); let t1005 = circuit_mul(t931, t1004); let t1006 = circuit_mul(t932, in263); let t1007 = circuit_mul(t933, t933); let t1008 = circuit_add(in153, in154); let t1009 = circuit_sub(t1008, t1001); let t1010 = circuit_mul(t1009, t1006); let t1011 = circuit_add(t937, t1010); let t1012 = circuit_sub(in252, in7); let t1013 = circuit_mul(in0, t1012); let t1014 = circuit_sub(in252, in7); let t1015 = circuit_mul(in2, t1014); let t1016 = circuit_inverse(t1015); let t1017 = circuit_mul(in153, t1016); let t1018 = circuit_add(in7, t1017); let t1019 = circuit_sub(in252, in0); let t1020 = circuit_mul(t1013, t1019); let t1021 = circuit_sub(in252, in0); let t1022 = circuit_mul(in3, t1021); let t1023 = circuit_inverse(t1022); let t1024 = circuit_mul(in154, t1023); let t1025 = circuit_add(t1018, t1024); let t1026 = circuit_sub(in252, in8); let t1027 = circuit_mul(t1020, t1026); let t1028 = circuit_sub(in252, in8); let t1029 = circuit_mul(in4, t1028); let t1030 = circuit_inverse(t1029); let t1031 = circuit_mul(in155, t1030); let t1032 = circuit_add(t1025, t1031); let t1033 = circuit_sub(in252, in9); let t1034 = circuit_mul(t1027, t1033); let t1035 = circuit_sub(in252, in9); let t1036 = circuit_mul(in5, t1035); let t1037 = circuit_inverse(t1036); let t1038 = circuit_mul(in156, t1037); let t1039 = circuit_add(t1032, t1038); let t1040 = circuit_sub(in252, in10); let t1041 = circuit_mul(t1034, t1040); let t1042 = circuit_sub(in252, in10); let t1043 = circuit_mul(in6, t1042); let t1044 = circuit_inverse(t1043); let t1045 = circuit_mul(in157, t1044); let t1046 = circuit_add(t1039, t1045); let t1047 = circuit_sub(in252, in11); let t1048 = circuit_mul(t1041, t1047); let t1049 = circuit_sub(in252, in11); let t1050 = circuit_mul(in5, t1049); let t1051 = circuit_inverse(t1050); let t1052 = circuit_mul(in158, t1051); let t1053 = circuit_add(t1046, t1052); let t1054 = circuit_sub(in252, in12); let t1055 = circuit_mul(t1048, t1054); let t1056 = circuit_sub(in252, in12); let t1057 = circuit_mul(in4, t1056); let t1058 = circuit_inverse(t1057); let t1059 = circuit_mul(in159, t1058); let t1060 = circuit_add(t1053, t1059); let t1061 = circuit_sub(in252, in13); let t1062 = circuit_mul(t1055, t1061); let t1063 = circuit_sub(in252, in13); let t1064 = circuit_mul(in3, t1063); let t1065 = circuit_inverse(t1064); let t1066 = circuit_mul(in160, t1065); let t1067 = circuit_add(t1060, t1066); let t1068 = circuit_sub(in252, in14); let t1069 = circuit_mul(t1062, t1068); let t1070 = circuit_sub(in252, in14); let t1071 = circuit_mul(in2, t1070); let t1072 = circuit_inverse(t1071); let t1073 = circuit_mul(in161, t1072); let t1074 = circuit_add(t1067, t1073); let t1075 = circuit_mul(t1074, t1069); let t1076 = circuit_sub(t1007, in0); let t1077 = circuit_mul(in252, t1076); let t1078 = circuit_add(in0, t1077); let t1079 = circuit_mul(t1005, t1078); let t1080 = circuit_mul(t1006, in263); let t1081 = circuit_mul(t1007, t1007); let t1082 = circuit_add(in162, in163); let t1083 = circuit_sub(t1082, t1075); let t1084 = circuit_mul(t1083, t1080); let t1085 = circuit_add(t1011, t1084); let t1086 = circuit_sub(in253, in7); let t1087 = circuit_mul(in0, t1086); let t1088 = circuit_sub(in253, in7); let t1089 = circuit_mul(in2, t1088); let t1090 = circuit_inverse(t1089); let t1091 = circuit_mul(in162, t1090); let t1092 = circuit_add(in7, t1091); let t1093 = circuit_sub(in253, in0); let t1094 = circuit_mul(t1087, t1093); let t1095 = circuit_sub(in253, in0); let t1096 = circuit_mul(in3, t1095); let t1097 = circuit_inverse(t1096); let t1098 = circuit_mul(in163, t1097); let t1099 = circuit_add(t1092, t1098); let t1100 = circuit_sub(in253, in8); let t1101 = circuit_mul(t1094, t1100); let t1102 = circuit_sub(in253, in8); let t1103 = circuit_mul(in4, t1102); let t1104 = circuit_inverse(t1103); let t1105 = circuit_mul(in164, t1104); let t1106 = circuit_add(t1099, t1105); let t1107 = circuit_sub(in253, in9); let t1108 = circuit_mul(t1101, t1107); let t1109 = circuit_sub(in253, in9); let t1110 = circuit_mul(in5, t1109); let t1111 = circuit_inverse(t1110); let t1112 = circuit_mul(in165, t1111); let t1113 = circuit_add(t1106, t1112); let t1114 = circuit_sub(in253, in10); let t1115 = circuit_mul(t1108, t1114); let t1116 = circuit_sub(in253, in10); let t1117 = circuit_mul(in6, t1116); let t1118 = circuit_inverse(t1117); let t1119 = circuit_mul(in166, t1118); let t1120 = circuit_add(t1113, t1119); let t1121 = circuit_sub(in253, in11); let t1122 = circuit_mul(t1115, t1121); let t1123 = circuit_sub(in253, in11); let t1124 = circuit_mul(in5, t1123); let t1125 = circuit_inverse(t1124); let t1126 = circuit_mul(in167, t1125); let t1127 = circuit_add(t1120, t1126); let t1128 = circuit_sub(in253, in12); let t1129 = circuit_mul(t1122, t1128); let t1130 = circuit_sub(in253, in12); let t1131 = circuit_mul(in4, t1130); let t1132 = circuit_inverse(t1131); let t1133 = circuit_mul(in168, t1132); let t1134 = circuit_add(t1127, t1133); let t1135 = circuit_sub(in253, in13); let t1136 = circuit_mul(t1129, t1135); let t1137 = circuit_sub(in253, in13); let t1138 = circuit_mul(in3, t1137); let t1139 = circuit_inverse(t1138); let t1140 = circuit_mul(in169, t1139); let t1141 = circuit_add(t1134, t1140); let t1142 = circuit_sub(in253, in14); let t1143 = circuit_mul(t1136, t1142); let t1144 = circuit_sub(in253, in14); let t1145 = circuit_mul(in2, t1144); let t1146 = circuit_inverse(t1145); let t1147 = circuit_mul(in170, t1146); let t1148 = circuit_add(t1141, t1147); let t1149 = circuit_mul(t1148, t1143); let t1150 = circuit_sub(t1081, in0); let t1151 = circuit_mul(in253, t1150); let t1152 = circuit_add(in0, t1151); let t1153 = circuit_mul(t1079, t1152); let t1154 = circuit_mul(t1080, in263); let t1155 = circuit_mul(t1081, t1081); let t1156 = circuit_add(in171, in172); let t1157 = circuit_sub(t1156, t1149); let t1158 = circuit_mul(t1157, t1154); let t1159 = circuit_add(t1085, t1158); let t1160 = circuit_sub(in254, in7); let t1161 = circuit_mul(in0, t1160); let t1162 = circuit_sub(in254, in7); let t1163 = circuit_mul(in2, t1162); let t1164 = circuit_inverse(t1163); let t1165 = circuit_mul(in171, t1164); let t1166 = circuit_add(in7, t1165); let t1167 = circuit_sub(in254, in0); let t1168 = circuit_mul(t1161, t1167); let t1169 = circuit_sub(in254, in0); let t1170 = circuit_mul(in3, t1169); let t1171 = circuit_inverse(t1170); let t1172 = circuit_mul(in172, t1171); let t1173 = circuit_add(t1166, t1172); let t1174 = circuit_sub(in254, in8); let t1175 = circuit_mul(t1168, t1174); let t1176 = circuit_sub(in254, in8); let t1177 = circuit_mul(in4, t1176); let t1178 = circuit_inverse(t1177); let t1179 = circuit_mul(in173, t1178); let t1180 = circuit_add(t1173, t1179); let t1181 = circuit_sub(in254, in9); let t1182 = circuit_mul(t1175, t1181); let t1183 = circuit_sub(in254, in9); let t1184 = circuit_mul(in5, t1183); let t1185 = circuit_inverse(t1184); let t1186 = circuit_mul(in174, t1185); let t1187 = circuit_add(t1180, t1186); let t1188 = circuit_sub(in254, in10); let t1189 = circuit_mul(t1182, t1188); let t1190 = circuit_sub(in254, in10); let t1191 = circuit_mul(in6, t1190); let t1192 = circuit_inverse(t1191); let t1193 = circuit_mul(in175, t1192); let t1194 = circuit_add(t1187, t1193); let t1195 = circuit_sub(in254, in11); let t1196 = circuit_mul(t1189, t1195); let t1197 = circuit_sub(in254, in11); let t1198 = circuit_mul(in5, t1197); let t1199 = circuit_inverse(t1198); let t1200 = circuit_mul(in176, t1199); let t1201 = circuit_add(t1194, t1200); let t1202 = circuit_sub(in254, in12); let t1203 = circuit_mul(t1196, t1202); let t1204 = circuit_sub(in254, in12); let t1205 = circuit_mul(in4, t1204); let t1206 = circuit_inverse(t1205); let t1207 = circuit_mul(in177, t1206); let t1208 = circuit_add(t1201, t1207); let t1209 = circuit_sub(in254, in13); let t1210 = circuit_mul(t1203, t1209); let t1211 = circuit_sub(in254, in13); let t1212 = circuit_mul(in3, t1211); let t1213 = circuit_inverse(t1212); let t1214 = circuit_mul(in178, t1213); let t1215 = circuit_add(t1208, t1214); let t1216 = circuit_sub(in254, in14); let t1217 = circuit_mul(t1210, t1216); let t1218 = circuit_sub(in254, in14); let t1219 = circuit_mul(in2, t1218); let t1220 = circuit_inverse(t1219); let t1221 = circuit_mul(in179, t1220); let t1222 = circuit_add(t1215, t1221); let t1223 = circuit_mul(t1222, t1217); let t1224 = circuit_sub(t1155, in0); let t1225 = circuit_mul(in254, t1224); let t1226 = circuit_add(in0, t1225); let t1227 = circuit_mul(t1153, t1226); let t1228 = circuit_mul(t1154, in263); let t1229 = circuit_mul(t1155, t1155); let t1230 = circuit_add(in180, in181); let t1231 = circuit_sub(t1230, t1223); let t1232 = circuit_mul(t1231, t1228); let t1233 = circuit_add(t1159, t1232); let t1234 = circuit_sub(in255, in7); let t1235 = circuit_mul(in0, t1234); let t1236 = circuit_sub(in255, in7); let t1237 = circuit_mul(in2, t1236); let t1238 = circuit_inverse(t1237); let t1239 = circuit_mul(in180, t1238); let t1240 = circuit_add(in7, t1239); let t1241 = circuit_sub(in255, in0); let t1242 = circuit_mul(t1235, t1241); let t1243 = circuit_sub(in255, in0); let t1244 = circuit_mul(in3, t1243); let t1245 = circuit_inverse(t1244); let t1246 = circuit_mul(in181, t1245); let t1247 = circuit_add(t1240, t1246); let t1248 = circuit_sub(in255, in8); let t1249 = circuit_mul(t1242, t1248); let t1250 = circuit_sub(in255, in8); let t1251 = circuit_mul(in4, t1250); let t1252 = circuit_inverse(t1251); let t1253 = circuit_mul(in182, t1252); let t1254 = circuit_add(t1247, t1253); let t1255 = circuit_sub(in255, in9); let t1256 = circuit_mul(t1249, t1255); let t1257 = circuit_sub(in255, in9); let t1258 = circuit_mul(in5, t1257); let t1259 = circuit_inverse(t1258); let t1260 = circuit_mul(in183, t1259); let t1261 = circuit_add(t1254, t1260); let t1262 = circuit_sub(in255, in10); let t1263 = circuit_mul(t1256, t1262); let t1264 = circuit_sub(in255, in10); let t1265 = circuit_mul(in6, t1264); let t1266 = circuit_inverse(t1265); let t1267 = circuit_mul(in184, t1266); let t1268 = circuit_add(t1261, t1267); let t1269 = circuit_sub(in255, in11); let t1270 = circuit_mul(t1263, t1269); let t1271 = circuit_sub(in255, in11); let t1272 = circuit_mul(in5, t1271); let t1273 = circuit_inverse(t1272); let t1274 = circuit_mul(in185, t1273); let t1275 = circuit_add(t1268, t1274); let t1276 = circuit_sub(in255, in12); let t1277 = circuit_mul(t1270, t1276); let t1278 = circuit_sub(in255, in12); let t1279 = circuit_mul(in4, t1278); let t1280 = circuit_inverse(t1279); let t1281 = circuit_mul(in186, t1280); let t1282 = circuit_add(t1275, t1281); let t1283 = circuit_sub(in255, in13); let t1284 = circuit_mul(t1277, t1283); let t1285 = circuit_sub(in255, in13); let t1286 = circuit_mul(in3, t1285); let t1287 = circuit_inverse(t1286); let t1288 = circuit_mul(in187, t1287); let t1289 = circuit_add(t1282, t1288); let t1290 = circuit_sub(in255, in14); let t1291 = circuit_mul(t1284, t1290); let t1292 = circuit_sub(in255, in14); let t1293 = circuit_mul(in2, t1292); let t1294 = circuit_inverse(t1293); let t1295 = circuit_mul(in188, t1294); let t1296 = circuit_add(t1289, t1295); let t1297 = circuit_mul(t1296, t1291); let t1298 = circuit_sub(t1229, in0); let t1299 = circuit_mul(in255, t1298); let t1300 = circuit_add(in0, t1299); let t1301 = circuit_mul(t1227, t1300); let t1302 = circuit_mul(t1228, in263); let t1303 = circuit_mul(t1229, t1229); let t1304 = circuit_add(in189, in190); let t1305 = circuit_sub(t1304, t1297); let t1306 = circuit_mul(t1305, t1302); let t1307 = circuit_add(t1233, t1306); let t1308 = circuit_sub(in256, in7); let t1309 = circuit_mul(in0, t1308); let t1310 = circuit_sub(in256, in7); let t1311 = circuit_mul(in2, t1310); let t1312 = circuit_inverse(t1311); let t1313 = circuit_mul(in189, t1312); let t1314 = circuit_add(in7, t1313); let t1315 = circuit_sub(in256, in0); let t1316 = circuit_mul(t1309, t1315); let t1317 = circuit_sub(in256, in0); let t1318 = circuit_mul(in3, t1317); let t1319 = circuit_inverse(t1318); let t1320 = circuit_mul(in190, t1319); let t1321 = circuit_add(t1314, t1320); let t1322 = circuit_sub(in256, in8); let t1323 = circuit_mul(t1316, t1322); let t1324 = circuit_sub(in256, in8); let t1325 = circuit_mul(in4, t1324); let t1326 = circuit_inverse(t1325); let t1327 = circuit_mul(in191, t1326); let t1328 = circuit_add(t1321, t1327); let t1329 = circuit_sub(in256, in9); let t1330 = circuit_mul(t1323, t1329); let t1331 = circuit_sub(in256, in9); let t1332 = circuit_mul(in5, t1331); let t1333 = circuit_inverse(t1332); let t1334 = circuit_mul(in192, t1333); let t1335 = circuit_add(t1328, t1334); let t1336 = circuit_sub(in256, in10); let t1337 = circuit_mul(t1330, t1336); let t1338 = circuit_sub(in256, in10); let t1339 = circuit_mul(in6, t1338); let t1340 = circuit_inverse(t1339); let t1341 = circuit_mul(in193, t1340); let t1342 = circuit_add(t1335, t1341); let t1343 = circuit_sub(in256, in11); let t1344 = circuit_mul(t1337, t1343); let t1345 = circuit_sub(in256, in11); let t1346 = circuit_mul(in5, t1345); let t1347 = circuit_inverse(t1346); let t1348 = circuit_mul(in194, t1347); let t1349 = circuit_add(t1342, t1348); let t1350 = circuit_sub(in256, in12); let t1351 = circuit_mul(t1344, t1350); let t1352 = circuit_sub(in256, in12); let t1353 = circuit_mul(in4, t1352); let t1354 = circuit_inverse(t1353); let t1355 = circuit_mul(in195, t1354); let t1356 = circuit_add(t1349, t1355); let t1357 = circuit_sub(in256, in13); let t1358 = circuit_mul(t1351, t1357); let t1359 = circuit_sub(in256, in13); let t1360 = circuit_mul(in3, t1359); let t1361 = circuit_inverse(t1360); let t1362 = circuit_mul(in196, t1361); let t1363 = circuit_add(t1356, t1362); let t1364 = circuit_sub(in256, in14); let t1365 = circuit_mul(t1358, t1364); let t1366 = circuit_sub(in256, in14); let t1367 = circuit_mul(in2, t1366); let t1368 = circuit_inverse(t1367); let t1369 = circuit_mul(in197, t1368); let t1370 = circuit_add(t1363, t1369); let t1371 = circuit_mul(t1370, t1365); let t1372 = circuit_sub(t1303, in0); let t1373 = circuit_mul(in256, t1372); let t1374 = circuit_add(in0, t1373); let t1375 = circuit_mul(t1301, t1374); let t1376 = circuit_sub(in205, in9); let t1377 = circuit_mul(t1376, in198); let t1378 = circuit_mul(t1377, in227); let t1379 = circuit_mul(t1378, in226); let t1380 = circuit_mul(t1379, in15); let t1381 = circuit_mul(in200, in226); let t1382 = circuit_mul(in201, in227); let t1383 = circuit_mul(in202, in228); let t1384 = circuit_mul(in203, in229); let t1385 = circuit_add(t1380, t1381); let t1386 = circuit_add(t1385, t1382); let t1387 = circuit_add(t1386, t1383); let t1388 = circuit_add(t1387, t1384); let t1389 = circuit_add(t1388, in199); let t1390 = circuit_sub(in205, in0); let t1391 = circuit_mul(t1390, in237); let t1392 = circuit_add(t1389, t1391); let t1393 = circuit_mul(t1392, in205); let t1394 = circuit_mul(t1393, t1375); let t1395 = circuit_add(in226, in229); let t1396 = circuit_add(t1395, in198); let t1397 = circuit_sub(t1396, in234); let t1398 = circuit_sub(in205, in8); let t1399 = circuit_mul(t1397, t1398); let t1400 = circuit_sub(in205, in0); let t1401 = circuit_mul(t1399, t1400); let t1402 = circuit_mul(t1401, in205); let t1403 = circuit_mul(t1402, t1375); let t1404 = circuit_mul(in216, in261); let t1405 = circuit_add(in226, t1404); let t1406 = circuit_add(t1405, in262); let t1407 = circuit_mul(in217, in261); let t1408 = circuit_add(in227, t1407); let t1409 = circuit_add(t1408, in262); let t1410 = circuit_mul(t1406, t1409); let t1411 = circuit_mul(in218, in261); let t1412 = circuit_add(in228, t1411); let t1413 = circuit_add(t1412, in262); let t1414 = circuit_mul(t1410, t1413); let t1415 = circuit_mul(in219, in261); let t1416 = circuit_add(in229, t1415); let t1417 = circuit_add(t1416, in262); let t1418 = circuit_mul(t1414, t1417); let t1419 = circuit_mul(in212, in261); let t1420 = circuit_add(in226, t1419); let t1421 = circuit_add(t1420, in262); let t1422 = circuit_mul(in213, in261); let t1423 = circuit_add(in227, t1422); let t1424 = circuit_add(t1423, in262); let t1425 = circuit_mul(t1421, t1424); let t1426 = circuit_mul(in214, in261); let t1427 = circuit_add(in228, t1426); let t1428 = circuit_add(t1427, in262); let t1429 = circuit_mul(t1425, t1428); let t1430 = circuit_mul(in215, in261); let t1431 = circuit_add(in229, t1430); let t1432 = circuit_add(t1431, in262); let t1433 = circuit_mul(t1429, t1432); let t1434 = circuit_add(in230, in224); let t1435 = circuit_mul(t1418, t1434); let t1436 = circuit_mul(in225, t119); let t1437 = circuit_add(in238, t1436); let t1438 = circuit_mul(t1433, t1437); let t1439 = circuit_sub(t1435, t1438); let t1440 = circuit_mul(t1439, t1375); let t1441 = circuit_mul(in225, in238); let t1442 = circuit_mul(t1441, t1375); let t1443 = circuit_mul(in221, in258); let t1444 = circuit_mul(in222, in259); let t1445 = circuit_mul(in223, in260); let t1446 = circuit_add(in220, in262); let t1447 = circuit_add(t1446, t1443); let t1448 = circuit_add(t1447, t1444); let t1449 = circuit_add(t1448, t1445); let t1450 = circuit_mul(in201, in234); let t1451 = circuit_add(in226, in262); let t1452 = circuit_add(t1451, t1450); let t1453 = circuit_mul(in198, in235); let t1454 = circuit_add(in227, t1453); let t1455 = circuit_mul(in199, in236); let t1456 = circuit_add(in228, t1455); let t1457 = circuit_mul(t1454, in258); let t1458 = circuit_mul(t1456, in259); let t1459 = circuit_mul(in202, in260); let t1460 = circuit_add(t1452, t1457); let t1461 = circuit_add(t1460, t1458); let t1462 = circuit_add(t1461, t1459); let t1463 = circuit_mul(in231, t1449); let t1464 = circuit_mul(in231, t1462); let t1465 = circuit_add(in233, in204); let t1466 = circuit_mul(in233, in204); let t1467 = circuit_sub(t1465, t1466); let t1468 = circuit_mul(t1462, t1449); let t1469 = circuit_mul(t1468, in231); let t1470 = circuit_sub(t1469, t1467); let t1471 = circuit_mul(t1470, t1375); let t1472 = circuit_mul(in204, t1463); let t1473 = circuit_mul(in232, t1464); let t1474 = circuit_sub(t1472, t1473); let t1475 = circuit_mul(in233, in233); let t1476 = circuit_sub(t1475, in233); let t1477 = circuit_mul(t1476, t1375); let t1478 = circuit_mul(in206, t1375); let t1479 = circuit_sub(in227, in226); let t1480 = circuit_sub(in228, in227); let t1481 = circuit_sub(in229, in228); let t1482 = circuit_sub(in234, in229); let t1483 = circuit_add(t1479, in16); let t1484 = circuit_add(t1483, in16); let t1485 = circuit_add(t1484, in16); let t1486 = circuit_mul(t1479, t1483); let t1487 = circuit_mul(t1486, t1484); let t1488 = circuit_mul(t1487, t1485); let t1489 = circuit_mul(t1488, t1478); let t1490 = circuit_add(t1480, in16); let t1491 = circuit_add(t1490, in16); let t1492 = circuit_add(t1491, in16); let t1493 = circuit_mul(t1480, t1490); let t1494 = circuit_mul(t1493, t1491); let t1495 = circuit_mul(t1494, t1492); let t1496 = circuit_mul(t1495, t1478); let t1497 = circuit_add(t1481, in16); let t1498 = circuit_add(t1497, in16); let t1499 = circuit_add(t1498, in16); let t1500 = circuit_mul(t1481, t1497); let t1501 = circuit_mul(t1500, t1498); let t1502 = circuit_mul(t1501, t1499); let t1503 = circuit_mul(t1502, t1478); let t1504 = circuit_add(t1482, in16); let t1505 = circuit_add(t1504, in16); let t1506 = circuit_add(t1505, in16); let t1507 = circuit_mul(t1482, t1504); let t1508 = circuit_mul(t1507, t1505); let t1509 = circuit_mul(t1508, t1506); let t1510 = circuit_mul(t1509, t1478); let t1511 = circuit_sub(in234, in227); let t1512 = circuit_mul(in228, in228); let t1513 = circuit_mul(in237, in237); let t1514 = circuit_mul(in228, in237); let t1515 = circuit_mul(t1514, in200); let t1516 = circuit_add(in235, in234); let t1517 = circuit_add(t1516, in227); let t1518 = circuit_mul(t1517, t1511); let t1519 = circuit_mul(t1518, t1511); let t1520 = circuit_sub(t1519, t1513); let t1521 = circuit_sub(t1520, t1512); let t1522 = circuit_add(t1521, t1515); let t1523 = circuit_add(t1522, t1515); let t1524 = circuit_sub(in0, in198); let t1525 = circuit_mul(t1523, t1375); let t1526 = circuit_mul(t1525, in207); let t1527 = circuit_mul(t1526, t1524); let t1528 = circuit_add(in228, in236); let t1529 = circuit_mul(in237, in200); let t1530 = circuit_sub(t1529, in228); let t1531 = circuit_mul(t1528, t1511); let t1532 = circuit_sub(in235, in227); let t1533 = circuit_mul(t1532, t1530); let t1534 = circuit_add(t1531, t1533); let t1535 = circuit_mul(t1534, t1375); let t1536 = circuit_mul(t1535, in207); let t1537 = circuit_mul(t1536, t1524); let t1538 = circuit_add(t1512, in17); let t1539 = circuit_mul(t1538, in227); let t1540 = circuit_add(t1512, t1512); let t1541 = circuit_add(t1540, t1540); let t1542 = circuit_mul(t1539, in18); let t1543 = circuit_add(in235, in227); let t1544 = circuit_add(t1543, in227); let t1545 = circuit_mul(t1544, t1541); let t1546 = circuit_sub(t1545, t1542); let t1547 = circuit_mul(t1546, t1375); let t1548 = circuit_mul(t1547, in207); let t1549 = circuit_mul(t1548, in198); let t1550 = circuit_add(t1527, t1549); let t1551 = circuit_add(in227, in227); let t1552 = circuit_add(t1551, in227); let t1553 = circuit_mul(t1552, in227); let t1554 = circuit_sub(in227, in235); let t1555 = circuit_mul(t1553, t1554); let t1556 = circuit_add(in228, in228); let t1557 = circuit_add(in228, in236); let t1558 = circuit_mul(t1556, t1557); let t1559 = circuit_sub(t1555, t1558); let t1560 = circuit_mul(t1559, t1375); let t1561 = circuit_mul(t1560, in207); let t1562 = circuit_mul(t1561, in198); let t1563 = circuit_add(t1537, t1562); let t1564 = circuit_mul(in228, in260); let t1565 = circuit_mul(in227, in259); let t1566 = circuit_add(t1564, t1565); let t1567 = circuit_mul(in226, in258); let t1568 = circuit_add(t1566, t1567); let t1569 = circuit_add(t1568, in199); let t1570 = circuit_sub(t1569, in229); let t1571 = circuit_sub(in234, in226); let t1572 = circuit_sub(in237, in229); let t1573 = circuit_sub(t1571, in0); let t1574 = circuit_mul(t1571, t1573); let t1575 = circuit_mul(t1571, in16); let t1576 = circuit_add(t1575, in0); let t1577 = circuit_mul(t1576, t1572); let t1578 = circuit_mul(in200, in201); let t1579 = circuit_mul(in208, t1375); let t1580 = circuit_mul(t1578, t1579); let t1581 = circuit_mul(t1577, t1580); let t1582 = circuit_mul(t1574, t1580); let t1583 = circuit_mul(t1570, t1578); let t1584 = circuit_sub(in229, t1569); let t1585 = circuit_sub(t1584, in0); let t1586 = circuit_mul(t1584, t1585); let t1587 = circuit_mul(in236, in260); let t1588 = circuit_mul(in235, in259); let t1589 = circuit_mul(in234, in258); let t1590 = circuit_add(t1587, t1588); let t1591 = circuit_add(t1590, t1589); let t1592 = circuit_sub(in237, t1591); let t1593 = circuit_sub(in236, in228); let t1594 = circuit_mul(t1571, in16); let t1595 = circuit_add(t1594, in0); let t1596 = circuit_mul(t1592, in16); let t1597 = circuit_add(t1596, in0); let t1598 = circuit_mul(t1595, t1593); let t1599 = circuit_mul(t1598, t1597); let t1600 = circuit_mul(t1592, t1592); let t1601 = circuit_sub(t1600, t1592); let t1602 = circuit_mul(in202, t1579); let t1603 = circuit_mul(t1599, t1602); let t1604 = circuit_mul(t1574, t1602); let t1605 = circuit_mul(t1601, t1602); let t1606 = circuit_mul(t1586, in202); let t1607 = circuit_sub(in235, in227); let t1608 = circuit_mul(t1571, in16); let t1609 = circuit_add(t1608, in0); let t1610 = circuit_mul(t1609, t1607); let t1611 = circuit_sub(t1610, in228); let t1612 = circuit_mul(in203, in200); let t1613 = circuit_mul(t1611, t1612); let t1614 = circuit_mul(in198, in200); let t1615 = circuit_mul(t1570, t1614); let t1616 = circuit_add(t1583, t1613); let t1617 = circuit_add(t1616, t1615); let t1618 = circuit_add(t1617, t1606); let t1619 = circuit_mul(t1618, t1579); let t1620 = circuit_mul(in226, in235); let t1621 = circuit_mul(in234, in227); let t1622 = circuit_add(t1620, t1621); let t1623 = circuit_mul(in226, in229); let t1624 = circuit_mul(in227, in228); let t1625 = circuit_add(t1623, t1624); let t1626 = circuit_sub(t1625, in236); let t1627 = circuit_mul(t1626, in19); let t1628 = circuit_sub(t1627, in237); let t1629 = circuit_add(t1628, t1622); let t1630 = circuit_mul(t1629, in203); let t1631 = circuit_mul(t1622, in19); let t1632 = circuit_mul(in234, in235); let t1633 = circuit_add(t1631, t1632); let t1634 = circuit_add(in228, in229); let t1635 = circuit_sub(t1633, t1634); let t1636 = circuit_mul(t1635, in202); let t1637 = circuit_add(t1633, in229); let t1638 = circuit_add(in236, in237); let t1639 = circuit_sub(t1637, t1638); let t1640 = circuit_mul(t1639, in198); let t1641 = circuit_add(t1636, t1630); let t1642 = circuit_add(t1641, t1640); let t1643 = circuit_mul(t1642, in201); let t1644 = circuit_mul(in235, in20); let t1645 = circuit_add(t1644, in234); let t1646 = circuit_mul(t1645, in20); let t1647 = circuit_add(t1646, in228); let t1648 = circuit_mul(t1647, in20); let t1649 = circuit_add(t1648, in227); let t1650 = circuit_mul(t1649, in20); let t1651 = circuit_add(t1650, in226); let t1652 = circuit_sub(t1651, in229); let t1653 = circuit_mul(t1652, in203); let t1654 = circuit_mul(in236, in20); let t1655 = circuit_add(t1654, in235); let t1656 = circuit_mul(t1655, in20); let t1657 = circuit_add(t1656, in234); let t1658 = circuit_mul(t1657, in20); let t1659 = circuit_add(t1658, in229); let t1660 = circuit_mul(t1659, in20); let t1661 = circuit_add(t1660, in228); let t1662 = circuit_sub(t1661, in237); let t1663 = circuit_mul(t1662, in198); let t1664 = circuit_add(t1653, t1663); let t1665 = circuit_mul(t1664, in202); let t1666 = circuit_add(t1643, t1665); let t1667 = circuit_mul(t1666, in209); let t1668 = circuit_mul(t1667, t1375); let t1669 = circuit_add(in226, in200); let t1670 = circuit_add(in227, in201); let t1671 = circuit_add(in228, in202); let t1672 = circuit_add(in229, in203); let t1673 = circuit_mul(t1669, t1669); let t1674 = circuit_mul(t1673, t1673); let t1675 = circuit_mul(t1674, t1669); let t1676 = circuit_mul(t1670, t1670); let t1677 = circuit_mul(t1676, t1676); let t1678 = circuit_mul(t1677, t1670); let t1679 = circuit_mul(t1671, t1671); let t1680 = circuit_mul(t1679, t1679); let t1681 = circuit_mul(t1680, t1671); let t1682 = circuit_mul(t1672, t1672); let t1683 = circuit_mul(t1682, t1682); let t1684 = circuit_mul(t1683, t1672); let t1685 = circuit_add(t1675, t1678); let t1686 = circuit_add(t1681, t1684); let t1687 = circuit_add(t1678, t1678); let t1688 = circuit_add(t1687, t1686); let t1689 = circuit_add(t1684, t1684); let t1690 = circuit_add(t1689, t1685); let t1691 = circuit_add(t1686, t1686); let t1692 = circuit_add(t1691, t1691); let t1693 = circuit_add(t1692, t1690); let t1694 = circuit_add(t1685, t1685); let t1695 = circuit_add(t1694, t1694); let t1696 = circuit_add(t1695, t1688); let t1697 = circuit_add(t1690, t1696); let t1698 = circuit_add(t1688, t1693); let t1699 = circuit_mul(in210, t1375); let t1700 = circuit_sub(t1697, in234); let t1701 = circuit_mul(t1699, t1700); let t1702 = circuit_sub(t1696, in235); let t1703 = circuit_mul(t1699, t1702); let t1704 = circuit_sub(t1698, in236); let t1705 = circuit_mul(t1699, t1704); let t1706 = circuit_sub(t1693, in237); let t1707 = circuit_mul(t1699, t1706); let t1708 = circuit_add(in226, in200); let t1709 = circuit_mul(t1708, t1708); let t1710 = circuit_mul(t1709, t1709); let t1711 = circuit_mul(t1710, t1708); let t1712 = circuit_add(t1711, in227); let t1713 = circuit_add(t1712, in228); let t1714 = circuit_add(t1713, in229); let t1715 = circuit_mul(in211, t1375); let t1716 = circuit_mul(t1711, in21); let t1717 = circuit_add(t1716, t1714); let t1718 = circuit_sub(t1717, in234); let t1719 = circuit_mul(t1715, t1718); let t1720 = circuit_mul(in227, in22); let t1721 = circuit_add(t1720, t1714); let t1722 = circuit_sub(t1721, in235); let t1723 = circuit_mul(t1715, t1722); let t1724 = circuit_mul(in228, in23); let t1725 = circuit_add(t1724, t1714); let t1726 = circuit_sub(t1725, in236); let t1727 = circuit_mul(t1715, t1726); let t1728 = circuit_mul(in229, in24); let t1729 = circuit_add(t1728, t1714); let t1730 = circuit_sub(t1729, in237); let t1731 = circuit_mul(t1715, t1730); let t1732 = circuit_mul(t1403, in264); let t1733 = circuit_add(t1394, t1732); let t1734 = circuit_mul(in264, in264); let t1735 = circuit_mul(t1440, t1734); let t1736 = circuit_add(t1733, t1735); let t1737 = circuit_mul(t1734, in264); let t1738 = circuit_mul(t1442, t1737); let t1739 = circuit_add(t1736, t1738); let t1740 = circuit_mul(t1737, in264); let t1741 = circuit_mul(t1471, t1740); let t1742 = circuit_add(t1739, t1741); let t1743 = circuit_mul(t1740, in264); let t1744 = circuit_mul(t1474, t1743); let t1745 = circuit_add(t1742, t1744); let t1746 = circuit_mul(t1743, in264); let t1747 = circuit_mul(t1477, t1746); let t1748 = circuit_add(t1745, t1747); let t1749 = circuit_mul(t1746, in264); let t1750 = circuit_mul(t1489, t1749); let t1751 = circuit_add(t1748, t1750); let t1752 = circuit_mul(t1749, in264); let t1753 = circuit_mul(t1496, t1752); let t1754 = circuit_add(t1751, t1753); let t1755 = circuit_mul(t1752, in264); let t1756 = circuit_mul(t1503, t1755); let t1757 = circuit_add(t1754, t1756); let t1758 = circuit_mul(t1755, in264); let t1759 = circuit_mul(t1510, t1758); let t1760 = circuit_add(t1757, t1759); let t1761 = circuit_mul(t1758, in264); let t1762 = circuit_mul(t1550, t1761); let t1763 = circuit_add(t1760, t1762); let t1764 = circuit_mul(t1761, in264); let t1765 = circuit_mul(t1563, t1764); let t1766 = circuit_add(t1763, t1765); let t1767 = circuit_mul(t1764, in264); let t1768 = circuit_mul(t1619, t1767); let t1769 = circuit_add(t1766, t1768); let t1770 = circuit_mul(t1767, in264); let t1771 = circuit_mul(t1581, t1770); let t1772 = circuit_add(t1769, t1771); let t1773 = circuit_mul(t1770, in264); let t1774 = circuit_mul(t1582, t1773); let t1775 = circuit_add(t1772, t1774); let t1776 = circuit_mul(t1773, in264); let t1777 = circuit_mul(t1603, t1776); let t1778 = circuit_add(t1775, t1777); let t1779 = circuit_mul(t1776, in264); let t1780 = circuit_mul(t1604, t1779); let t1781 = circuit_add(t1778, t1780); let t1782 = circuit_mul(t1779, in264); let t1783 = circuit_mul(t1605, t1782); let t1784 = circuit_add(t1781, t1783); let t1785 = circuit_mul(t1782, in264); let t1786 = circuit_mul(t1668, t1785); let t1787 = circuit_add(t1784, t1786); let t1788 = circuit_mul(t1785, in264); let t1789 = circuit_mul(t1701, t1788); let t1790 = circuit_add(t1787, t1789); let t1791 = circuit_mul(t1788, in264); let t1792 = circuit_mul(t1703, t1791); let t1793 = circuit_add(t1790, t1792); let t1794 = circuit_mul(t1791, in264); let t1795 = circuit_mul(t1705, t1794); let t1796 = circuit_add(t1793, t1795); let t1797 = circuit_mul(t1794, in264); let t1798 = circuit_mul(t1707, t1797); let t1799 = circuit_add(t1796, t1798); let t1800 = circuit_mul(t1797, in264); let t1801 = circuit_mul(t1719, t1800); let t1802 = circuit_add(t1799, t1801); let t1803 = circuit_mul(t1800, in264); let t1804 = circuit_mul(t1723, t1803); let t1805 = circuit_add(t1802, t1804); let t1806 = circuit_mul(t1803, in264); let t1807 = circuit_mul(t1727, t1806); let t1808 = circuit_add(t1805, t1807); let t1809 = circuit_mul(t1806, in264); let t1810 = circuit_mul(t1731, t1809); let t1811 = circuit_add(t1808, t1810); let t1812 = circuit_mul(in242, in243); let t1813 = circuit_mul(t1812, in244); let t1814 = circuit_mul(t1813, in245); let t1815 = circuit_mul(t1814, in246); let t1816 = circuit_mul(t1815, in247); let t1817 = circuit_mul(t1816, in248); let t1818 = circuit_mul(t1817, in249); let t1819 = circuit_mul(t1818, in250); let t1820 = circuit_mul(t1819, in251); let t1821 = circuit_mul(t1820, in252); let t1822 = circuit_mul(t1821, in253); let t1823 = circuit_mul(t1822, in254); let t1824 = circuit_mul(t1823, in255); let t1825 = circuit_mul(t1824, in256); let t1826 = circuit_sub(in0, t1825); let t1827 = circuit_mul(t1811, t1826); let t1828 = circuit_mul(in239, in265); let t1829 = circuit_add(t1827, t1828); let t1830 = circuit_sub(t1829, t1371); let modulus = modulus; let mut circuit_inputs = (t1307, t1830).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(ZK_HONK_SUMCHECK_SIZE_17_PUB_19_GRUMPKIN_CONSTANTS.span()); // in0 - in24 // Fill inputs: for val in p_public_inputs { circuit_inputs = circuit_inputs.next_u256(*val); } // in25 - in27 for val in p_pairing_point_object { circuit_inputs = circuit_inputs.next_u256(*val); } // in28 - in43 circuit_inputs = circuit_inputs.next_2(libra_sum); // in44 for val in sumcheck_univariates_flat { circuit_inputs = circuit_inputs.next_u256(*val); } // in45 - in197 for val in sumcheck_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in198 - in238 circuit_inputs = circuit_inputs.next_2(libra_evaluation); // in239 for val in tp_sum_check_u_challenges { circuit_inputs = circuit_inputs.next_u128(*val); } // in240 - in256 circuit_inputs = circuit_inputs.next_u128(tp_gate_challenge); // in257 circuit_inputs = circuit_inputs.next_2(tp_eta_1); // in258 circuit_inputs = circuit_inputs.next_2(tp_eta_2); // in259 circuit_inputs = circuit_inputs.next_2(tp_eta_3); // in260 circuit_inputs = circuit_inputs.next_2(tp_beta); // in261 circuit_inputs = circuit_inputs.next_2(tp_gamma); // in262 circuit_inputs = circuit_inputs.next_2(tp_base_rlc); // in263 circuit_inputs = circuit_inputs.next_u128(tp_alpha); // in264 circuit_inputs = circuit_inputs.next_2(tp_libra_challenge); // in265 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let check_rlc: u384 = outputs.get_output(t1307); let check: u384 = outputs.get_output(t1830); return (check_rlc, check); } const ZK_HONK_SUMCHECK_SIZE_17_PUB_19_GRUMPKIN_CONSTANTS: [u384; 25] = [ u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x10000000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9d80, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x79b9709143e1f593efffec51, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x5a0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x79b9709143e1f593effffd31, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x240, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x4, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x5, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x6, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x7, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x8, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x3cdcb848a1f0fac9f8000000, limb1: 0xdc2822db40c0ac2e9419f424, limb2: 0x183227397098d014, limb3: 0x0, }, u384 { limb0: 0x79b9709143e1f593f0000000, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x11, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x100000000000000000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x4000, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x29ca1d7fb56821fd19d3b6e7, limb1: 0x4b1e03b4bd9490c0d03f989, limb2: 0x10dc6e9c006ea38b, limb3: 0x0, }, u384 { limb0: 0xd4dd9b84a86b38cfb45a740b, limb1: 0x149b3d0a30b3bb599df9756, limb2: 0xc28145b6a44df3e, limb3: 0x0, }, u384 { limb0: 0x60e3596170067d00141cac15, limb1: 0xb2c7645a50392798b21f75bb, limb2: 0x544b8338791518, limb3: 0x0, }, u384 { limb0: 0xb8fa852613bc534433ee428b, limb1: 0x2e2e82eb122789e352e105a3, limb2: 0x222c01175718386f, limb3: 0x0, }, ]; #[inline(always)] pub fn run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_17_circuit( p_sumcheck_evaluations: Span, p_gemini_masking_eval: u384, p_gemini_a_evaluations: Span, p_libra_poly_evals: Span, tp_gemini_r: u384, tp_rho: u384, tp_shplonk_z: u384, tp_shplonk_nu: u384, tp_sum_check_u_challenges: Span, modulus: core::circuit::CircuitModulus, ) -> ( u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, ) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x7b0c561a6148404f086204a9f36ffb0617942546750f230c893619174a57a76 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let (in33, in34, in35) = (CE::> {}, CE::> {}, CE::> {}); let (in36, in37, in38) = (CE::> {}, CE::> {}, CE::> {}); let (in39, in40, in41) = (CE::> {}, CE::> {}, CE::> {}); let (in42, in43, in44) = (CE::> {}, CE::> {}, CE::> {}); let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76, in77) = (CE::> {}, CE::> {}, CE::> {}); let (in78, in79, in80) = (CE::> {}, CE::> {}, CE::> {}); let (in81, in82, in83) = (CE::> {}, CE::> {}, CE::> {}); let (in84, in85, in86) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in66, in66); let t1 = circuit_mul(t0, t0); let t2 = circuit_mul(t1, t1); let t3 = circuit_mul(t2, t2); let t4 = circuit_mul(t3, t3); let t5 = circuit_mul(t4, t4); let t6 = circuit_mul(t5, t5); let t7 = circuit_mul(t6, t6); let t8 = circuit_mul(t7, t7); let t9 = circuit_mul(t8, t8); let t10 = circuit_mul(t9, t9); let t11 = circuit_mul(t10, t10); let t12 = circuit_mul(t11, t11); let t13 = circuit_mul(t12, t12); let t14 = circuit_mul(t13, t13); let t15 = circuit_mul(t14, t14); let t16 = circuit_sub(in68, in66); let t17 = circuit_inverse(t16); let t18 = circuit_add(in68, in66); let t19 = circuit_inverse(t18); let t20 = circuit_mul(in69, t19); let t21 = circuit_add(t17, t20); let t22 = circuit_inverse(in66); let t23 = circuit_mul(in69, t19); let t24 = circuit_sub(t17, t23); let t25 = circuit_mul(t22, t24); let t26 = circuit_sub(in0, t25); let t27 = circuit_sub(in0, t21); let t28 = circuit_mul(t27, in67); let t29 = circuit_mul(in3, in67); let t30 = circuit_add(in44, t29); let t31 = circuit_mul(in67, in67); let t32 = circuit_mul(t27, t31); let t33 = circuit_mul(in4, t31); let t34 = circuit_add(t30, t33); let t35 = circuit_mul(t31, in67); let t36 = circuit_mul(t27, t35); let t37 = circuit_mul(in5, t35); let t38 = circuit_add(t34, t37); let t39 = circuit_mul(t35, in67); let t40 = circuit_mul(t27, t39); let t41 = circuit_mul(in6, t39); let t42 = circuit_add(t38, t41); let t43 = circuit_mul(t39, in67); let t44 = circuit_mul(t27, t43); let t45 = circuit_mul(in7, t43); let t46 = circuit_add(t42, t45); let t47 = circuit_mul(t43, in67); let t48 = circuit_mul(t27, t47); let t49 = circuit_mul(in8, t47); let t50 = circuit_add(t46, t49); let t51 = circuit_mul(t47, in67); let t52 = circuit_mul(t27, t51); let t53 = circuit_mul(in9, t51); let t54 = circuit_add(t50, t53); let t55 = circuit_mul(t51, in67); let t56 = circuit_mul(t27, t55); let t57 = circuit_mul(in10, t55); let t58 = circuit_add(t54, t57); let t59 = circuit_mul(t55, in67); let t60 = circuit_mul(t27, t59); let t61 = circuit_mul(in11, t59); let t62 = circuit_add(t58, t61); let t63 = circuit_mul(t59, in67); let t64 = circuit_mul(t27, t63); let t65 = circuit_mul(in12, t63); let t66 = circuit_add(t62, t65); let t67 = circuit_mul(t63, in67); let t68 = circuit_mul(t27, t67); let t69 = circuit_mul(in13, t67); let t70 = circuit_add(t66, t69); let t71 = circuit_mul(t67, in67); let t72 = circuit_mul(t27, t71); let t73 = circuit_mul(in14, t71); let t74 = circuit_add(t70, t73); let t75 = circuit_mul(t71, in67); let t76 = circuit_mul(t27, t75); let t77 = circuit_mul(in15, t75); let t78 = circuit_add(t74, t77); let t79 = circuit_mul(t75, in67); let t80 = circuit_mul(t27, t79); let t81 = circuit_mul(in16, t79); let t82 = circuit_add(t78, t81); let t83 = circuit_mul(t79, in67); let t84 = circuit_mul(t27, t83); let t85 = circuit_mul(in17, t83); let t86 = circuit_add(t82, t85); let t87 = circuit_mul(t83, in67); let t88 = circuit_mul(t27, t87); let t89 = circuit_mul(in18, t87); let t90 = circuit_add(t86, t89); let t91 = circuit_mul(t87, in67); let t92 = circuit_mul(t27, t91); let t93 = circuit_mul(in19, t91); let t94 = circuit_add(t90, t93); let t95 = circuit_mul(t91, in67); let t96 = circuit_mul(t27, t95); let t97 = circuit_mul(in20, t95); let t98 = circuit_add(t94, t97); let t99 = circuit_mul(t95, in67); let t100 = circuit_mul(t27, t99); let t101 = circuit_mul(in21, t99); let t102 = circuit_add(t98, t101); let t103 = circuit_mul(t99, in67); let t104 = circuit_mul(t27, t103); let t105 = circuit_mul(in22, t103); let t106 = circuit_add(t102, t105); let t107 = circuit_mul(t103, in67); let t108 = circuit_mul(t27, t107); let t109 = circuit_mul(in23, t107); let t110 = circuit_add(t106, t109); let t111 = circuit_mul(t107, in67); let t112 = circuit_mul(t27, t111); let t113 = circuit_mul(in24, t111); let t114 = circuit_add(t110, t113); let t115 = circuit_mul(t111, in67); let t116 = circuit_mul(t27, t115); let t117 = circuit_mul(in25, t115); let t118 = circuit_add(t114, t117); let t119 = circuit_mul(t115, in67); let t120 = circuit_mul(t27, t119); let t121 = circuit_mul(in26, t119); let t122 = circuit_add(t118, t121); let t123 = circuit_mul(t119, in67); let t124 = circuit_mul(t27, t123); let t125 = circuit_mul(in27, t123); let t126 = circuit_add(t122, t125); let t127 = circuit_mul(t123, in67); let t128 = circuit_mul(t27, t127); let t129 = circuit_mul(in28, t127); let t130 = circuit_add(t126, t129); let t131 = circuit_mul(t127, in67); let t132 = circuit_mul(t27, t131); let t133 = circuit_mul(in29, t131); let t134 = circuit_add(t130, t133); let t135 = circuit_mul(t131, in67); let t136 = circuit_mul(t27, t135); let t137 = circuit_mul(in30, t135); let t138 = circuit_add(t134, t137); let t139 = circuit_mul(t135, in67); let t140 = circuit_mul(t27, t139); let t141 = circuit_mul(in31, t139); let t142 = circuit_add(t138, t141); let t143 = circuit_mul(t139, in67); let t144 = circuit_mul(t27, t143); let t145 = circuit_mul(in32, t143); let t146 = circuit_add(t142, t145); let t147 = circuit_mul(t143, in67); let t148 = circuit_mul(t27, t147); let t149 = circuit_mul(in33, t147); let t150 = circuit_add(t146, t149); let t151 = circuit_mul(t147, in67); let t152 = circuit_mul(t27, t151); let t153 = circuit_mul(in34, t151); let t154 = circuit_add(t150, t153); let t155 = circuit_mul(t151, in67); let t156 = circuit_mul(t27, t155); let t157 = circuit_mul(in35, t155); let t158 = circuit_add(t154, t157); let t159 = circuit_mul(t155, in67); let t160 = circuit_mul(t27, t159); let t161 = circuit_mul(in36, t159); let t162 = circuit_add(t158, t161); let t163 = circuit_mul(t159, in67); let t164 = circuit_mul(t27, t163); let t165 = circuit_mul(in37, t163); let t166 = circuit_add(t162, t165); let t167 = circuit_mul(t163, in67); let t168 = circuit_mul(t27, t167); let t169 = circuit_mul(in38, t167); let t170 = circuit_add(t166, t169); let t171 = circuit_mul(t167, in67); let t172 = circuit_mul(t26, t171); let t173 = circuit_add(t140, t172); let t174 = circuit_mul(in39, t171); let t175 = circuit_add(t170, t174); let t176 = circuit_mul(t171, in67); let t177 = circuit_mul(t26, t176); let t178 = circuit_add(t144, t177); let t179 = circuit_mul(in40, t176); let t180 = circuit_add(t175, t179); let t181 = circuit_mul(t176, in67); let t182 = circuit_mul(t26, t181); let t183 = circuit_add(t148, t182); let t184 = circuit_mul(in41, t181); let t185 = circuit_add(t180, t184); let t186 = circuit_mul(t181, in67); let t187 = circuit_mul(t26, t186); let t188 = circuit_add(t152, t187); let t189 = circuit_mul(in42, t186); let t190 = circuit_add(t185, t189); let t191 = circuit_mul(t186, in67); let t192 = circuit_mul(t26, t191); let t193 = circuit_add(t156, t192); let t194 = circuit_mul(in43, t191); let t195 = circuit_add(t190, t194); let t196 = circuit_sub(in1, in86); let t197 = circuit_mul(t15, t196); let t198 = circuit_mul(t15, t195); let t199 = circuit_add(t198, t198); let t200 = circuit_sub(t197, in86); let t201 = circuit_mul(in61, t200); let t202 = circuit_sub(t199, t201); let t203 = circuit_add(t197, in86); let t204 = circuit_inverse(t203); let t205 = circuit_mul(t202, t204); let t206 = circuit_sub(in1, in85); let t207 = circuit_mul(t14, t206); let t208 = circuit_mul(t14, t205); let t209 = circuit_add(t208, t208); let t210 = circuit_sub(t207, in85); let t211 = circuit_mul(in60, t210); let t212 = circuit_sub(t209, t211); let t213 = circuit_add(t207, in85); let t214 = circuit_inverse(t213); let t215 = circuit_mul(t212, t214); let t216 = circuit_sub(in1, in84); let t217 = circuit_mul(t13, t216); let t218 = circuit_mul(t13, t215); let t219 = circuit_add(t218, t218); let t220 = circuit_sub(t217, in84); let t221 = circuit_mul(in59, t220); let t222 = circuit_sub(t219, t221); let t223 = circuit_add(t217, in84); let t224 = circuit_inverse(t223); let t225 = circuit_mul(t222, t224); let t226 = circuit_sub(in1, in83); let t227 = circuit_mul(t12, t226); let t228 = circuit_mul(t12, t225); let t229 = circuit_add(t228, t228); let t230 = circuit_sub(t227, in83); let t231 = circuit_mul(in58, t230); let t232 = circuit_sub(t229, t231); let t233 = circuit_add(t227, in83); let t234 = circuit_inverse(t233); let t235 = circuit_mul(t232, t234); let t236 = circuit_sub(in1, in82); let t237 = circuit_mul(t11, t236); let t238 = circuit_mul(t11, t235); let t239 = circuit_add(t238, t238); let t240 = circuit_sub(t237, in82); let t241 = circuit_mul(in57, t240); let t242 = circuit_sub(t239, t241); let t243 = circuit_add(t237, in82); let t244 = circuit_inverse(t243); let t245 = circuit_mul(t242, t244); let t246 = circuit_sub(in1, in81); let t247 = circuit_mul(t10, t246); let t248 = circuit_mul(t10, t245); let t249 = circuit_add(t248, t248); let t250 = circuit_sub(t247, in81); let t251 = circuit_mul(in56, t250); let t252 = circuit_sub(t249, t251); let t253 = circuit_add(t247, in81); let t254 = circuit_inverse(t253); let t255 = circuit_mul(t252, t254); let t256 = circuit_sub(in1, in80); let t257 = circuit_mul(t9, t256); let t258 = circuit_mul(t9, t255); let t259 = circuit_add(t258, t258); let t260 = circuit_sub(t257, in80); let t261 = circuit_mul(in55, t260); let t262 = circuit_sub(t259, t261); let t263 = circuit_add(t257, in80); let t264 = circuit_inverse(t263); let t265 = circuit_mul(t262, t264); let t266 = circuit_sub(in1, in79); let t267 = circuit_mul(t8, t266); let t268 = circuit_mul(t8, t265); let t269 = circuit_add(t268, t268); let t270 = circuit_sub(t267, in79); let t271 = circuit_mul(in54, t270); let t272 = circuit_sub(t269, t271); let t273 = circuit_add(t267, in79); let t274 = circuit_inverse(t273); let t275 = circuit_mul(t272, t274); let t276 = circuit_sub(in1, in78); let t277 = circuit_mul(t7, t276); let t278 = circuit_mul(t7, t275); let t279 = circuit_add(t278, t278); let t280 = circuit_sub(t277, in78); let t281 = circuit_mul(in53, t280); let t282 = circuit_sub(t279, t281); let t283 = circuit_add(t277, in78); let t284 = circuit_inverse(t283); let t285 = circuit_mul(t282, t284); let t286 = circuit_sub(in1, in77); let t287 = circuit_mul(t6, t286); let t288 = circuit_mul(t6, t285); let t289 = circuit_add(t288, t288); let t290 = circuit_sub(t287, in77); let t291 = circuit_mul(in52, t290); let t292 = circuit_sub(t289, t291); let t293 = circuit_add(t287, in77); let t294 = circuit_inverse(t293); let t295 = circuit_mul(t292, t294); let t296 = circuit_sub(in1, in76); let t297 = circuit_mul(t5, t296); let t298 = circuit_mul(t5, t295); let t299 = circuit_add(t298, t298); let t300 = circuit_sub(t297, in76); let t301 = circuit_mul(in51, t300); let t302 = circuit_sub(t299, t301); let t303 = circuit_add(t297, in76); let t304 = circuit_inverse(t303); let t305 = circuit_mul(t302, t304); let t306 = circuit_sub(in1, in75); let t307 = circuit_mul(t4, t306); let t308 = circuit_mul(t4, t305); let t309 = circuit_add(t308, t308); let t310 = circuit_sub(t307, in75); let t311 = circuit_mul(in50, t310); let t312 = circuit_sub(t309, t311); let t313 = circuit_add(t307, in75); let t314 = circuit_inverse(t313); let t315 = circuit_mul(t312, t314); let t316 = circuit_sub(in1, in74); let t317 = circuit_mul(t3, t316); let t318 = circuit_mul(t3, t315); let t319 = circuit_add(t318, t318); let t320 = circuit_sub(t317, in74); let t321 = circuit_mul(in49, t320); let t322 = circuit_sub(t319, t321); let t323 = circuit_add(t317, in74); let t324 = circuit_inverse(t323); let t325 = circuit_mul(t322, t324); let t326 = circuit_sub(in1, in73); let t327 = circuit_mul(t2, t326); let t328 = circuit_mul(t2, t325); let t329 = circuit_add(t328, t328); let t330 = circuit_sub(t327, in73); let t331 = circuit_mul(in48, t330); let t332 = circuit_sub(t329, t331); let t333 = circuit_add(t327, in73); let t334 = circuit_inverse(t333); let t335 = circuit_mul(t332, t334); let t336 = circuit_sub(in1, in72); let t337 = circuit_mul(t1, t336); let t338 = circuit_mul(t1, t335); let t339 = circuit_add(t338, t338); let t340 = circuit_sub(t337, in72); let t341 = circuit_mul(in47, t340); let t342 = circuit_sub(t339, t341); let t343 = circuit_add(t337, in72); let t344 = circuit_inverse(t343); let t345 = circuit_mul(t342, t344); let t346 = circuit_sub(in1, in71); let t347 = circuit_mul(t0, t346); let t348 = circuit_mul(t0, t345); let t349 = circuit_add(t348, t348); let t350 = circuit_sub(t347, in71); let t351 = circuit_mul(in46, t350); let t352 = circuit_sub(t349, t351); let t353 = circuit_add(t347, in71); let t354 = circuit_inverse(t353); let t355 = circuit_mul(t352, t354); let t356 = circuit_sub(in1, in70); let t357 = circuit_mul(in66, t356); let t358 = circuit_mul(in66, t355); let t359 = circuit_add(t358, t358); let t360 = circuit_sub(t357, in70); let t361 = circuit_mul(in45, t360); let t362 = circuit_sub(t359, t361); let t363 = circuit_add(t357, in70); let t364 = circuit_inverse(t363); let t365 = circuit_mul(t362, t364); let t366 = circuit_mul(t365, t17); let t367 = circuit_mul(in45, in69); let t368 = circuit_mul(t367, t19); let t369 = circuit_add(t366, t368); let t370 = circuit_mul(in69, in69); let t371 = circuit_sub(in68, t0); let t372 = circuit_inverse(t371); let t373 = circuit_add(in68, t0); let t374 = circuit_inverse(t373); let t375 = circuit_mul(t370, t372); let t376 = circuit_mul(in69, t374); let t377 = circuit_mul(t370, t376); let t378 = circuit_add(t377, t375); let t379 = circuit_sub(in0, t378); let t380 = circuit_mul(t377, in46); let t381 = circuit_mul(t375, t355); let t382 = circuit_add(t380, t381); let t383 = circuit_add(t369, t382); let t384 = circuit_mul(in69, in69); let t385 = circuit_mul(t370, t384); let t386 = circuit_sub(in68, t1); let t387 = circuit_inverse(t386); let t388 = circuit_add(in68, t1); let t389 = circuit_inverse(t388); let t390 = circuit_mul(t385, t387); let t391 = circuit_mul(in69, t389); let t392 = circuit_mul(t385, t391); let t393 = circuit_add(t392, t390); let t394 = circuit_sub(in0, t393); let t395 = circuit_mul(t392, in47); let t396 = circuit_mul(t390, t345); let t397 = circuit_add(t395, t396); let t398 = circuit_add(t383, t397); let t399 = circuit_mul(in69, in69); let t400 = circuit_mul(t385, t399); let t401 = circuit_sub(in68, t2); let t402 = circuit_inverse(t401); let t403 = circuit_add(in68, t2); let t404 = circuit_inverse(t403); let t405 = circuit_mul(t400, t402); let t406 = circuit_mul(in69, t404); let t407 = circuit_mul(t400, t406); let t408 = circuit_add(t407, t405); let t409 = circuit_sub(in0, t408); let t410 = circuit_mul(t407, in48); let t411 = circuit_mul(t405, t335); let t412 = circuit_add(t410, t411); let t413 = circuit_add(t398, t412); let t414 = circuit_mul(in69, in69); let t415 = circuit_mul(t400, t414); let t416 = circuit_sub(in68, t3); let t417 = circuit_inverse(t416); let t418 = circuit_add(in68, t3); let t419 = circuit_inverse(t418); let t420 = circuit_mul(t415, t417); let t421 = circuit_mul(in69, t419); let t422 = circuit_mul(t415, t421); let t423 = circuit_add(t422, t420); let t424 = circuit_sub(in0, t423); let t425 = circuit_mul(t422, in49); let t426 = circuit_mul(t420, t325); let t427 = circuit_add(t425, t426); let t428 = circuit_add(t413, t427); let t429 = circuit_mul(in69, in69); let t430 = circuit_mul(t415, t429); let t431 = circuit_sub(in68, t4); let t432 = circuit_inverse(t431); let t433 = circuit_add(in68, t4); let t434 = circuit_inverse(t433); let t435 = circuit_mul(t430, t432); let t436 = circuit_mul(in69, t434); let t437 = circuit_mul(t430, t436); let t438 = circuit_add(t437, t435); let t439 = circuit_sub(in0, t438); let t440 = circuit_mul(t437, in50); let t441 = circuit_mul(t435, t315); let t442 = circuit_add(t440, t441); let t443 = circuit_add(t428, t442); let t444 = circuit_mul(in69, in69); let t445 = circuit_mul(t430, t444); let t446 = circuit_sub(in68, t5); let t447 = circuit_inverse(t446); let t448 = circuit_add(in68, t5); let t449 = circuit_inverse(t448); let t450 = circuit_mul(t445, t447); let t451 = circuit_mul(in69, t449); let t452 = circuit_mul(t445, t451); let t453 = circuit_add(t452, t450); let t454 = circuit_sub(in0, t453); let t455 = circuit_mul(t452, in51); let t456 = circuit_mul(t450, t305); let t457 = circuit_add(t455, t456); let t458 = circuit_add(t443, t457); let t459 = circuit_mul(in69, in69); let t460 = circuit_mul(t445, t459); let t461 = circuit_sub(in68, t6); let t462 = circuit_inverse(t461); let t463 = circuit_add(in68, t6); let t464 = circuit_inverse(t463); let t465 = circuit_mul(t460, t462); let t466 = circuit_mul(in69, t464); let t467 = circuit_mul(t460, t466); let t468 = circuit_add(t467, t465); let t469 = circuit_sub(in0, t468); let t470 = circuit_mul(t467, in52); let t471 = circuit_mul(t465, t295); let t472 = circuit_add(t470, t471); let t473 = circuit_add(t458, t472); let t474 = circuit_mul(in69, in69); let t475 = circuit_mul(t460, t474); let t476 = circuit_sub(in68, t7); let t477 = circuit_inverse(t476); let t478 = circuit_add(in68, t7); let t479 = circuit_inverse(t478); let t480 = circuit_mul(t475, t477); let t481 = circuit_mul(in69, t479); let t482 = circuit_mul(t475, t481); let t483 = circuit_add(t482, t480); let t484 = circuit_sub(in0, t483); let t485 = circuit_mul(t482, in53); let t486 = circuit_mul(t480, t285); let t487 = circuit_add(t485, t486); let t488 = circuit_add(t473, t487); let t489 = circuit_mul(in69, in69); let t490 = circuit_mul(t475, t489); let t491 = circuit_sub(in68, t8); let t492 = circuit_inverse(t491); let t493 = circuit_add(in68, t8); let t494 = circuit_inverse(t493); let t495 = circuit_mul(t490, t492); let t496 = circuit_mul(in69, t494); let t497 = circuit_mul(t490, t496); let t498 = circuit_add(t497, t495); let t499 = circuit_sub(in0, t498); let t500 = circuit_mul(t497, in54); let t501 = circuit_mul(t495, t275); let t502 = circuit_add(t500, t501); let t503 = circuit_add(t488, t502); let t504 = circuit_mul(in69, in69); let t505 = circuit_mul(t490, t504); let t506 = circuit_sub(in68, t9); let t507 = circuit_inverse(t506); let t508 = circuit_add(in68, t9); let t509 = circuit_inverse(t508); let t510 = circuit_mul(t505, t507); let t511 = circuit_mul(in69, t509); let t512 = circuit_mul(t505, t511); let t513 = circuit_add(t512, t510); let t514 = circuit_sub(in0, t513); let t515 = circuit_mul(t512, in55); let t516 = circuit_mul(t510, t265); let t517 = circuit_add(t515, t516); let t518 = circuit_add(t503, t517); let t519 = circuit_mul(in69, in69); let t520 = circuit_mul(t505, t519); let t521 = circuit_sub(in68, t10); let t522 = circuit_inverse(t521); let t523 = circuit_add(in68, t10); let t524 = circuit_inverse(t523); let t525 = circuit_mul(t520, t522); let t526 = circuit_mul(in69, t524); let t527 = circuit_mul(t520, t526); let t528 = circuit_add(t527, t525); let t529 = circuit_sub(in0, t528); let t530 = circuit_mul(t527, in56); let t531 = circuit_mul(t525, t255); let t532 = circuit_add(t530, t531); let t533 = circuit_add(t518, t532); let t534 = circuit_mul(in69, in69); let t535 = circuit_mul(t520, t534); let t536 = circuit_sub(in68, t11); let t537 = circuit_inverse(t536); let t538 = circuit_add(in68, t11); let t539 = circuit_inverse(t538); let t540 = circuit_mul(t535, t537); let t541 = circuit_mul(in69, t539); let t542 = circuit_mul(t535, t541); let t543 = circuit_add(t542, t540); let t544 = circuit_sub(in0, t543); let t545 = circuit_mul(t542, in57); let t546 = circuit_mul(t540, t245); let t547 = circuit_add(t545, t546); let t548 = circuit_add(t533, t547); let t549 = circuit_mul(in69, in69); let t550 = circuit_mul(t535, t549); let t551 = circuit_sub(in68, t12); let t552 = circuit_inverse(t551); let t553 = circuit_add(in68, t12); let t554 = circuit_inverse(t553); let t555 = circuit_mul(t550, t552); let t556 = circuit_mul(in69, t554); let t557 = circuit_mul(t550, t556); let t558 = circuit_add(t557, t555); let t559 = circuit_sub(in0, t558); let t560 = circuit_mul(t557, in58); let t561 = circuit_mul(t555, t235); let t562 = circuit_add(t560, t561); let t563 = circuit_add(t548, t562); let t564 = circuit_mul(in69, in69); let t565 = circuit_mul(t550, t564); let t566 = circuit_sub(in68, t13); let t567 = circuit_inverse(t566); let t568 = circuit_add(in68, t13); let t569 = circuit_inverse(t568); let t570 = circuit_mul(t565, t567); let t571 = circuit_mul(in69, t569); let t572 = circuit_mul(t565, t571); let t573 = circuit_add(t572, t570); let t574 = circuit_sub(in0, t573); let t575 = circuit_mul(t572, in59); let t576 = circuit_mul(t570, t225); let t577 = circuit_add(t575, t576); let t578 = circuit_add(t563, t577); let t579 = circuit_mul(in69, in69); let t580 = circuit_mul(t565, t579); let t581 = circuit_sub(in68, t14); let t582 = circuit_inverse(t581); let t583 = circuit_add(in68, t14); let t584 = circuit_inverse(t583); let t585 = circuit_mul(t580, t582); let t586 = circuit_mul(in69, t584); let t587 = circuit_mul(t580, t586); let t588 = circuit_add(t587, t585); let t589 = circuit_sub(in0, t588); let t590 = circuit_mul(t587, in60); let t591 = circuit_mul(t585, t215); let t592 = circuit_add(t590, t591); let t593 = circuit_add(t578, t592); let t594 = circuit_mul(in69, in69); let t595 = circuit_mul(t580, t594); let t596 = circuit_sub(in68, t15); let t597 = circuit_inverse(t596); let t598 = circuit_add(in68, t15); let t599 = circuit_inverse(t598); let t600 = circuit_mul(t595, t597); let t601 = circuit_mul(in69, t599); let t602 = circuit_mul(t595, t601); let t603 = circuit_add(t602, t600); let t604 = circuit_sub(in0, t603); let t605 = circuit_mul(t602, in61); let t606 = circuit_mul(t600, t205); let t607 = circuit_add(t605, t606); let t608 = circuit_add(t593, t607); let t609 = circuit_mul(in69, in69); let t610 = circuit_mul(t595, t609); let t611 = circuit_sub(in68, in66); let t612 = circuit_inverse(t611); let t613 = circuit_mul(in2, in66); let t614 = circuit_sub(in68, t613); let t615 = circuit_inverse(t614); let t616 = circuit_mul(in69, in69); let t617 = circuit_mul(t610, t616); let t618 = circuit_mul(t612, t617); let t619 = circuit_sub(in0, t618); let t620 = circuit_mul(t617, in69); let t621 = circuit_mul(t618, in62); let t622 = circuit_add(t608, t621); let t623 = circuit_mul(t615, t620); let t624 = circuit_sub(in0, t623); let t625 = circuit_mul(t620, in69); let t626 = circuit_mul(t623, in63); let t627 = circuit_add(t622, t626); let t628 = circuit_mul(t612, t625); let t629 = circuit_sub(in0, t628); let t630 = circuit_mul(t625, in69); let t631 = circuit_mul(t628, in64); let t632 = circuit_add(t627, t631); let t633 = circuit_mul(t612, t630); let t634 = circuit_sub(in0, t633); let t635 = circuit_mul(t633, in65); let t636 = circuit_add(t632, t635); let t637 = circuit_add(t624, t629); let modulus = modulus; let mut circuit_inputs = ( t27, t28, t32, t36, t40, t44, t48, t52, t56, t60, t64, t68, t72, t76, t80, t84, t88, t92, t96, t100, t104, t108, t112, t116, t120, t124, t128, t132, t136, t173, t178, t183, t188, t193, t160, t164, t168, t379, t394, t409, t424, t439, t454, t469, t484, t499, t514, t529, t544, t559, t574, t589, t604, t619, t637, t634, t636, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [0x6750f230c893619174a57a76, 0xf086204a9f36ffb061794254, 0x7b0c561a6148404, 0x0], ); // in2 // Fill inputs: for val in p_sumcheck_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in3 - in43 circuit_inputs = circuit_inputs.next_2(p_gemini_masking_eval); // in44 for val in p_gemini_a_evaluations { circuit_inputs = circuit_inputs.next_u256(*val); } // in45 - in61 for val in p_libra_poly_evals { circuit_inputs = circuit_inputs.next_u256(*val); } // in62 - in65 circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in66 circuit_inputs = circuit_inputs.next_2(tp_rho); // in67 circuit_inputs = circuit_inputs.next_2(tp_shplonk_z); // in68 circuit_inputs = circuit_inputs.next_2(tp_shplonk_nu); // in69 for val in tp_sum_check_u_challenges { circuit_inputs = circuit_inputs.next_u128(*val); } // in70 - in86 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let scalar_1: u384 = outputs.get_output(t27); let scalar_2: u384 = outputs.get_output(t28); let scalar_3: u384 = outputs.get_output(t32); let scalar_4: u384 = outputs.get_output(t36); let scalar_5: u384 = outputs.get_output(t40); let scalar_6: u384 = outputs.get_output(t44); let scalar_7: u384 = outputs.get_output(t48); let scalar_8: u384 = outputs.get_output(t52); let scalar_9: u384 = outputs.get_output(t56); let scalar_10: u384 = outputs.get_output(t60); let scalar_11: u384 = outputs.get_output(t64); let scalar_12: u384 = outputs.get_output(t68); let scalar_13: u384 = outputs.get_output(t72); let scalar_14: u384 = outputs.get_output(t76); let scalar_15: u384 = outputs.get_output(t80); let scalar_16: u384 = outputs.get_output(t84); let scalar_17: u384 = outputs.get_output(t88); let scalar_18: u384 = outputs.get_output(t92); let scalar_19: u384 = outputs.get_output(t96); let scalar_20: u384 = outputs.get_output(t100); let scalar_21: u384 = outputs.get_output(t104); let scalar_22: u384 = outputs.get_output(t108); let scalar_23: u384 = outputs.get_output(t112); let scalar_24: u384 = outputs.get_output(t116); let scalar_25: u384 = outputs.get_output(t120); let scalar_26: u384 = outputs.get_output(t124); let scalar_27: u384 = outputs.get_output(t128); let scalar_28: u384 = outputs.get_output(t132); let scalar_29: u384 = outputs.get_output(t136); let scalar_30: u384 = outputs.get_output(t173); let scalar_31: u384 = outputs.get_output(t178); let scalar_32: u384 = outputs.get_output(t183); let scalar_33: u384 = outputs.get_output(t188); let scalar_34: u384 = outputs.get_output(t193); let scalar_35: u384 = outputs.get_output(t160); let scalar_36: u384 = outputs.get_output(t164); let scalar_37: u384 = outputs.get_output(t168); let scalar_38: u384 = outputs.get_output(t379); let scalar_39: u384 = outputs.get_output(t394); let scalar_40: u384 = outputs.get_output(t409); let scalar_41: u384 = outputs.get_output(t424); let scalar_42: u384 = outputs.get_output(t439); let scalar_43: u384 = outputs.get_output(t454); let scalar_44: u384 = outputs.get_output(t469); let scalar_45: u384 = outputs.get_output(t484); let scalar_46: u384 = outputs.get_output(t499); let scalar_47: u384 = outputs.get_output(t514); let scalar_48: u384 = outputs.get_output(t529); let scalar_49: u384 = outputs.get_output(t544); let scalar_50: u384 = outputs.get_output(t559); let scalar_51: u384 = outputs.get_output(t574); let scalar_52: u384 = outputs.get_output(t589); let scalar_53: u384 = outputs.get_output(t604); let scalar_54: u384 = outputs.get_output(t619); let scalar_55: u384 = outputs.get_output(t637); let scalar_56: u384 = outputs.get_output(t634); let scalar_57: u384 = outputs.get_output(t636); return ( scalar_1, scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, scalar_52, scalar_53, scalar_54, scalar_55, scalar_56, scalar_57, ); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_17_circuit( tp_gemini_r: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 // INPUT stack let in2 = CE::> {}; let t0 = circuit_sub(in2, in0); let t1 = circuit_inverse(t0); let t2 = circuit_mul(in1, in2); let modulus = modulus; let mut circuit_inputs = (t1, t2).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in2 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let challenge_poly_eval: u384 = outputs.get_output(t1); let root_power_times_tp_gemini_r: u384 = outputs.get_output(t2); return (challenge_poly_eval, root_power_times_tp_gemini_r); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_17_circuit( challenge_poly_eval: u384, root_power_times_tp_gemini_r: u384, tp_sumcheck_u_challenge: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in3, in0); let t1 = circuit_inverse(t0); let t2 = circuit_mul(in0, t1); let t3 = circuit_add(in2, t2); let t4 = circuit_mul(in3, in1); let t5 = circuit_mul(in0, in4); let t6 = circuit_sub(t4, in0); let t7 = circuit_inverse(t6); let t8 = circuit_mul(t5, t7); let t9 = circuit_add(t3, t8); let t10 = circuit_mul(t4, in1); let t11 = circuit_mul(t5, in4); let t12 = circuit_sub(t10, in0); let t13 = circuit_inverse(t12); let t14 = circuit_mul(t11, t13); let t15 = circuit_add(t9, t14); let t16 = circuit_mul(t10, in1); let t17 = circuit_mul(t11, in4); let t18 = circuit_sub(t16, in0); let t19 = circuit_inverse(t18); let t20 = circuit_mul(t17, t19); let t21 = circuit_add(t15, t20); let t22 = circuit_mul(t16, in1); let t23 = circuit_mul(t17, in4); let t24 = circuit_sub(t22, in0); let t25 = circuit_inverse(t24); let t26 = circuit_mul(t23, t25); let t27 = circuit_add(t21, t26); let t28 = circuit_mul(t22, in1); let t29 = circuit_mul(t23, in4); let t30 = circuit_sub(t28, in0); let t31 = circuit_inverse(t30); let t32 = circuit_mul(t29, t31); let t33 = circuit_add(t27, t32); let t34 = circuit_mul(t28, in1); let t35 = circuit_mul(t29, in4); let t36 = circuit_sub(t34, in0); let t37 = circuit_inverse(t36); let t38 = circuit_mul(t35, t37); let t39 = circuit_add(t33, t38); let t40 = circuit_mul(t34, in1); let t41 = circuit_mul(t35, in4); let t42 = circuit_sub(t40, in0); let t43 = circuit_inverse(t42); let t44 = circuit_mul(t41, t43); let t45 = circuit_add(t39, t44); let t46 = circuit_mul(t40, in1); let t47 = circuit_mul(t41, in4); let t48 = circuit_sub(t46, in0); let t49 = circuit_inverse(t48); let t50 = circuit_mul(t47, t49); let t51 = circuit_add(t45, t50); let t52 = circuit_mul(t46, in1); let modulus = modulus; let mut circuit_inputs = (t51, t52).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(challenge_poly_eval); // in2 circuit_inputs = circuit_inputs.next_2(root_power_times_tp_gemini_r); // in3 circuit_inputs = circuit_inputs.next_2(tp_sumcheck_u_challenge); // in4 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let challenge_poly_eval: u384 = outputs.get_output(t51); let root_power_times_tp_gemini_r: u384 = outputs.get_output(t52); return (challenge_poly_eval, root_power_times_tp_gemini_r); } #[inline(always)] pub fn run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_17_circuit( p_libra_evaluation: u384, p_libra_poly_evals: Span, tp_gemini_r: u384, challenge_poly_eval: u384, root_power_times_tp_gemini_r: u384, modulus: core::circuit::CircuitModulus, ) -> (u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6 let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x3033ea246e506e898e97f570caffd704cb0bb460313fb720b29e139e5c100001 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in10, in0); let t1 = circuit_mul(t0, in0); let t2 = circuit_mul(t1, in0); let t3 = circuit_mul(t2, in0); let t4 = circuit_mul(t3, in0); let t5 = circuit_mul(t4, in0); let t6 = circuit_mul(t5, in0); let t7 = circuit_mul(t6, in0); let t8 = circuit_mul(t7, in0); let t9 = circuit_mul(t8, in0); let t10 = circuit_mul(t9, in0); let t11 = circuit_mul(t10, in0); let t12 = circuit_mul(t11, in0); let t13 = circuit_mul(t12, in0); let t14 = circuit_mul(t13, in0); let t15 = circuit_mul(t14, in0); let t16 = circuit_mul(t15, in0); let t17 = circuit_mul(t16, in0); let t18 = circuit_mul(t17, in0); let t19 = circuit_mul(t18, in0); let t20 = circuit_mul(t19, in0); let t21 = circuit_mul(t20, in0); let t22 = circuit_mul(t21, in0); let t23 = circuit_mul(t22, in0); let t24 = circuit_mul(t23, in0); let t25 = circuit_mul(t24, in0); let t26 = circuit_mul(t25, in0); let t27 = circuit_mul(t26, in0); let t28 = circuit_mul(t27, in0); let t29 = circuit_mul(t28, in0); let t30 = circuit_mul(t29, in0); let t31 = circuit_mul(t30, in0); let t32 = circuit_mul(t31, in0); let t33 = circuit_mul(t32, in0); let t34 = circuit_mul(t33, in0); let t35 = circuit_mul(t34, in0); let t36 = circuit_mul(t35, in0); let t37 = circuit_mul(t36, in0); let t38 = circuit_mul(t37, in0); let t39 = circuit_mul(t38, in0); let t40 = circuit_mul(t39, in0); let t41 = circuit_mul(t40, in0); let t42 = circuit_mul(t41, in0); let t43 = circuit_mul(t42, in0); let t44 = circuit_mul(t43, in0); let t45 = circuit_mul(t44, in0); let t46 = circuit_mul(t45, in0); let t47 = circuit_mul(t46, in0); let t48 = circuit_mul(t47, in0); let t49 = circuit_mul(t48, in0); let t50 = circuit_mul(t49, in0); let t51 = circuit_mul(t50, in0); let t52 = circuit_mul(t51, in0); let t53 = circuit_mul(t52, in0); let t54 = circuit_mul(t53, in0); let t55 = circuit_mul(t54, in0); let t56 = circuit_mul(t55, in0); let t57 = circuit_mul(t56, in0); let t58 = circuit_mul(t57, in0); let t59 = circuit_mul(t58, in0); let t60 = circuit_mul(t59, in0); let t61 = circuit_mul(t60, in0); let t62 = circuit_mul(t61, in0); let t63 = circuit_mul(t62, in0); let t64 = circuit_mul(t63, in0); let t65 = circuit_mul(t64, in0); let t66 = circuit_mul(t65, in0); let t67 = circuit_mul(t66, in0); let t68 = circuit_mul(t67, in0); let t69 = circuit_mul(t68, in0); let t70 = circuit_mul(t69, in0); let t71 = circuit_mul(t70, in0); let t72 = circuit_mul(t71, in0); let t73 = circuit_mul(t72, in0); let t74 = circuit_mul(t73, in0); let t75 = circuit_mul(t74, in0); let t76 = circuit_mul(t75, in0); let t77 = circuit_mul(t76, in0); let t78 = circuit_mul(t77, in0); let t79 = circuit_mul(t78, in0); let t80 = circuit_mul(t79, in0); let t81 = circuit_mul(t80, in0); let t82 = circuit_mul(t81, in0); let t83 = circuit_mul(t82, in0); let t84 = circuit_mul(t83, in0); let t85 = circuit_mul(t84, in0); let t86 = circuit_mul(t85, in0); let t87 = circuit_mul(t86, in0); let t88 = circuit_mul(t87, in0); let t89 = circuit_mul(t88, in0); let t90 = circuit_mul(t89, in0); let t91 = circuit_mul(t90, in0); let t92 = circuit_mul(t91, in0); let t93 = circuit_mul(t92, in0); let t94 = circuit_mul(t93, in0); let t95 = circuit_mul(t94, in0); let t96 = circuit_mul(t95, in0); let t97 = circuit_mul(t96, in0); let t98 = circuit_mul(t97, in0); let t99 = circuit_mul(t98, in0); let t100 = circuit_mul(t99, in0); let t101 = circuit_sub(in8, in1); let t102 = circuit_inverse(t101); let t103 = circuit_sub(t100, in1); let t104 = circuit_inverse(t103); let t105 = circuit_mul(in8, in8); let t106 = circuit_mul(t105, t105); let t107 = circuit_mul(t106, t106); let t108 = circuit_mul(t107, t107); let t109 = circuit_mul(t108, t108); let t110 = circuit_mul(t109, t109); let t111 = circuit_mul(t110, t110); let t112 = circuit_mul(t111, t111); let t113 = circuit_sub(t112, in1); let t114 = circuit_mul(t113, in2); let t115 = circuit_mul(in9, t114); let t116 = circuit_mul(t102, t114); let t117 = circuit_mul(t104, t114); let t118 = circuit_mul(t116, in6); let t119 = circuit_sub(in8, in0); let t120 = circuit_sub(in5, in6); let t121 = circuit_mul(in4, t115); let t122 = circuit_sub(t120, t121); let t123 = circuit_mul(t119, t122); let t124 = circuit_add(t118, t123); let t125 = circuit_sub(in6, in3); let t126 = circuit_mul(t117, t125); let t127 = circuit_add(t124, t126); let t128 = circuit_mul(t113, in7); let t129 = circuit_sub(t127, t128); let modulus = modulus; let mut circuit_inputs = (t113, t129).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x8712848a692c553d0329f5d6, 0x64751ad938e2b5e6a54cf8c6, 0x204bd3277422fad3, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [0x313fb720b29e139e5c100001, 0x8e97f570caffd704cb0bb460, 0x3033ea246e506e89, 0x0], ); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_libra_evaluation); // in3 for val in p_libra_poly_evals { circuit_inputs = circuit_inputs.next_u256(*val); } // in4 - in7 circuit_inputs = circuit_inputs.next_2(tp_gemini_r); // in8 circuit_inputs = circuit_inputs.next_2(challenge_poly_eval); // in9 circuit_inputs = circuit_inputs.next_2(root_power_times_tp_gemini_r); // in10 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let vanishing_check: u384 = outputs.get_output(t113); let diff_check: u384 = outputs.get_output(t129); return (vanishing_check, diff_check); } impl CircuitDefinition57< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, E52, E53, E54, E55, E56, > of core::circuit::CircuitDefinition< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), > { type CircuitType = core::circuit::Circuit< ( E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, E52, E53, E54, E55, E56, ), >; } impl MyDrp_57< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, E28, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, E51, E52, E53, E54, E55, E56, > of Drop< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), >; #[inline(never)] pub fn is_on_curve_excluding_infinity_bn254(p: G1Point, modulus: CircuitModulus) -> bool { // INPUT stack // y^2 = x^3 + 3 let (in0, in1) = (CE::> {}, CE::> {}); let y2 = circuit_mul(in1, in1); let x2 = circuit_mul(in0, in0); let x3 = circuit_mul(in0, x2); let y2_minus_x3 = circuit_sub(y2, x3); let mut circuit_inputs = (y2_minus_x3,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check: u384 = outputs.get_output(y2_minus_x3); return zero_check == u384 { limb0: 3, limb1: 0, limb2: 0, limb3: 0 }; } ================================================ FILE: src/contracts/mutator_set/src/zk_verifier/honk_verifier_constants.cairo ================================================ use garaga::apps::noir::HonkVk; use garaga::definitions::{G1Point, G2Line, u288, u384}; pub const vk: HonkVk = HonkVk { vk_hash: 8648913451078603841425108107713111136913298359786830997742829131199771092709, log_circuit_size: 17, public_inputs_size: 19, qm: G1Point { x: u384 { limb0: 0xc9879d00a38708b38625ac44, limb1: 0x9ef7e0ada113660b7c7c1bfa, limb2: 0x1aad08a358acb08f, limb3: 0x0, }, y: u384 { limb0: 0xf724d70bdd99cca8b136516c, limb1: 0x4c788cf832602e3b7d33776e, limb2: 0x1cb6cf3305414863, limb3: 0x0, }, }, qc: G1Point { x: u384 { limb0: 0x9d9bcd021c055bb75dbd4512, limb1: 0x780d1d84481443889feb0344, limb2: 0x2f48f208bf2113ca, limb3: 0x0, }, y: u384 { limb0: 0xa7b307a6772179f94fa5ea6, limb1: 0x2bdd28321b8d24a9a4d68b3, limb2: 0x12131ffca858a35f, limb3: 0x0, }, }, ql: G1Point { x: u384 { limb0: 0xf28a408137475eb81810aa81, limb1: 0x1d00fedbbea4d1bf591decfc, limb2: 0x7dd8d544fca06cf, limb3: 0x0, }, y: u384 { limb0: 0x87f6900c2c82a1370469ae4e, limb1: 0xb26862eaa22ad4f564f16dc3, limb2: 0x19fa88ac971a9dce, limb3: 0x0, }, }, qr: G1Point { x: u384 { limb0: 0x73f3ba3bbf8ca96e672cbce2, limb1: 0xa3e373bcc21f45c528485515, limb2: 0x563be38b959ef47, limb3: 0x0, }, y: u384 { limb0: 0xd8efd2f9a41938ceb32b5a39, limb1: 0xf5e89041fec12a15a7e5555e, limb2: 0x205321350b7fb55, limb3: 0x0, }, }, qo: G1Point { x: u384 { limb0: 0xaebeeca06b6691fa3251b8c3, limb1: 0xc58f419fb4d44301670d2c95, limb2: 0x17aec007ff309cae, limb3: 0x0, }, y: u384 { limb0: 0xcb6122bfb69b5d6f0f10c45a, limb1: 0xce5407747e1e0b4831fa6971, limb2: 0x2ca94e49d53e2bfb, limb3: 0x0, }, }, q4: G1Point { x: u384 { limb0: 0x16a58f20d203d6998bedca0e, limb1: 0xf4749c68dc18379ed2cfd90f, limb2: 0x11e16a6d0f456496, limb3: 0x0, }, y: u384 { limb0: 0x7109c3364d8d5386f7834314, limb1: 0xa19192358f604f5e132e1134, limb2: 0x1dfb10789425f1c1, limb3: 0x0, }, }, qLookup: G1Point { x: u384 { limb0: 0xbf2ed757ab4abba92c67c48b, limb1: 0x3f63d5ad361a9fbf5fb92f0a, limb2: 0x140da9d775b7988a, limb3: 0x0, }, y: u384 { limb0: 0x72bc367b61bd04386c012fd8, limb1: 0x7aa1ab7396853dec5c74fb1e, limb2: 0x13ce9d2c1b64cd99, limb3: 0x0, }, }, qArith: G1Point { x: u384 { limb0: 0x3aa740bd1a5e8a47b3d2de10, limb1: 0xcc88c141090121fd92f68a6c, limb2: 0x8a2516f74638847, limb3: 0x0, }, y: u384 { limb0: 0xc710b72ff8cc890a46f57a90, limb1: 0x5a58c14222b39cfb1feb5292, limb2: 0xe38ae4e93ca3eae, limb3: 0x0, }, }, qDeltaRange: G1Point { x: u384 { limb0: 0x70ae35f1b8a0695b260e2feb, limb1: 0x105e723f90f620c9a957fc8d, limb2: 0x2c5de9a00448559, limb3: 0x0, }, y: u384 { limb0: 0xdaa421b8aa8ae3979076f0c3, limb1: 0x1358e1c210c87f84f65bba4b, limb2: 0x2d1012a20c0ca795, limb3: 0x0, }, }, qElliptic: G1Point { x: u384 { limb0: 0x4d27199ae4f48a5583fee4f3, limb1: 0x3e0bc0150e688f6c46f25745, limb2: 0x1c24be1be708f683, limb3: 0x0, }, y: u384 { limb0: 0x2187718a0f48380b39fac203, limb1: 0x418bf428f1c8e4cc01de2fa0, limb2: 0x215490b46e1ff77d, limb3: 0x0, }, }, qMemory: G1Point { x: u384 { limb0: 0x46fd0721214ab6dc7d78a012, limb1: 0xb3b50980deb6ce9bc88da500, limb2: 0x245ea5b6146dcc90, limb3: 0x0, }, y: u384 { limb0: 0xd5a93e279c05327d08d7e9e8, limb1: 0xf5adc6210b0399467c54c042, limb2: 0x1e727f815c7221f2, limb3: 0x0, }, }, qNnf: G1Point { x: u384 { limb0: 0xc8169df9b9fe24d1db0c6c37, limb1: 0x394f6d05c4a634eebc93546e, limb2: 0x2787a029626f7fef, limb3: 0x0, }, y: u384 { limb0: 0x125331ed5965e81567c35fef, limb1: 0x28f728f64243bc3eda44264f, limb2: 0x1c65ceb8bd2d3ba1, limb3: 0x0, }, }, qPoseidon2External: G1Point { x: u384 { limb0: 0x80c77770decd9af8eb397e9f, limb1: 0xa7f054ed839373c32380a122, limb2: 0x3bb5f8c665e6222, limb3: 0x0, }, y: u384 { limb0: 0x6cf73a911a7669454e742240, limb1: 0x22ce0664fd72c62b3fef3c52, limb2: 0x5ffe72ea68db37e, limb3: 0x0, }, }, qPoseidon2Internal: G1Point { x: u384 { limb0: 0x599f75e13d5fc1ddd625af3d, limb1: 0x35e95eb75dbcfb94576425e3, limb2: 0x21cf4a0b4ded78c8, limb3: 0x0, }, y: u384 { limb0: 0xf4e804d55eef280e63845a98, limb1: 0xa4391af391b562982739f5fd, limb2: 0x2d80057bb2d0ac54, limb3: 0x0, }, }, s1: G1Point { x: u384 { limb0: 0x2735a6945bfcc575b47b551b, limb1: 0x90e9781e87dc298bdef34482, limb2: 0x2ecd5089375735ff, limb3: 0x0, }, y: u384 { limb0: 0xd6c5b651258d085fb2c08479, limb1: 0xf55b1a28766f224e0198d9bc, limb2: 0xfcf4a0af691f887, limb3: 0x0, }, }, s2: G1Point { x: u384 { limb0: 0xc4ed539d45106213d9773e23, limb1: 0x8eaee56ac89019dfe6c61608, limb2: 0x6bb671b009b334, limb3: 0x0, }, y: u384 { limb0: 0xee3d4e41cd48e1f504ec8725, limb1: 0xbedb6b6c7414fb432ea7fbb1, limb2: 0x18ef92eff8a8214b, limb3: 0x0, }, }, s3: G1Point { x: u384 { limb0: 0xfd4c9cbb70bd5ed33e7f6230, limb1: 0x98500ef521527b9fd37b98aa, limb2: 0x9d18733c6d2ec15, limb3: 0x0, }, y: u384 { limb0: 0x82098b38d2b8548f15b51bc5, limb1: 0x8c9b3875390b26c889aec49b, limb2: 0x237aeb3aad51315e, limb3: 0x0, }, }, s4: G1Point { x: u384 { limb0: 0xc2e3448b290ed14332d835ff, limb1: 0x4261b7b47a679659e0db8b2, limb2: 0x68805c74a3e3341, limb3: 0x0, }, y: u384 { limb0: 0x638d679a090054c17b55a21e, limb1: 0x913b0e7f906efd58e885e853, limb2: 0x2e6fd1d72edcd21c, limb3: 0x0, }, }, id1: G1Point { x: u384 { limb0: 0xb5aecd13170ddb4422f04935, limb1: 0x9a078c7623842ce27367584a, limb2: 0x8dda9400ce64482, limb3: 0x0, }, y: u384 { limb0: 0xfb78f4f8f69ff971bfc5f06f, limb1: 0x26a42b2a150848b6a4e0dbc5, limb2: 0x1beb83b38357031c, limb3: 0x0, }, }, id2: G1Point { x: u384 { limb0: 0xf043d40b7003a5d6c3e897b6, limb1: 0x7473a63e06067d5ae07bda16, limb2: 0x1587ae4d0e40d580, limb3: 0x0, }, y: u384 { limb0: 0x7bd7d4e411e65490f5a7cc07, limb1: 0xaa52483c8b51cdeaada6c3ad, limb2: 0x23c966fe09c0b750, limb3: 0x0, }, }, id3: G1Point { x: u384 { limb0: 0x6a5f8b839f79f6632b3d3846, limb1: 0x7dceb6e16ac96a826af16b8e, limb2: 0x8e59de8c7ec9d1e, limb3: 0x0, }, y: u384 { limb0: 0x39070ff6fc023aa36aa560d6, limb1: 0x65d334abfd3a999331625437, limb2: 0x1540433e1d162232, limb3: 0x0, }, }, id4: G1Point { x: u384 { limb0: 0x8dcb81e2267c6ce0ec1d3808, limb1: 0xf0e2b4fce3bb28d444920fed, limb2: 0x1e00fc5b0e46caaf, limb3: 0x0, }, y: u384 { limb0: 0x189add7063bc6235eb050d20, limb1: 0x974d5b407537f937ff12471a, limb2: 0x2a65e90c138645af, limb3: 0x0, }, }, t1: G1Point { x: u384 { limb0: 0x338b2ec7a36993e51f217041, limb1: 0xc5578d44a19745a2e9b4fa73, limb2: 0x19bbebad91acf7e2, limb3: 0x0, }, y: u384 { limb0: 0xe8cc18957e5ca1c759a71e0, limb1: 0x485b4fc1723a3cf89dbb3d3, limb2: 0xb703659ad78da28, limb3: 0x0, }, }, t2: G1Point { x: u384 { limb0: 0xbc74c15287eb0b5691d6aedc, limb1: 0x80ee61926466bd391e8401c4, limb2: 0x229b0caf7eefd786, limb3: 0x0, }, y: u384 { limb0: 0x1d439725611f90819c503377, limb1: 0x4f97d5cc218ce5cad2724ee, limb2: 0x1e12a50561bcdc89, limb3: 0x0, }, }, t3: G1Point { x: u384 { limb0: 0x301aa9412c245623efa87a56, limb1: 0x26de6abc9119742c54b6ee25, limb2: 0x2d54532863a43d99, limb3: 0x0, }, y: u384 { limb0: 0xc90c9b882e9a231ae7f1a121, limb1: 0xac98d5fd202605b1d25cb91b, limb2: 0x103edb2d7d28f820, limb3: 0x0, }, }, t4: G1Point { x: u384 { limb0: 0x7f4e1e5d9273e820fac64728, limb1: 0xb6838f56e2b805cc06a79522, limb2: 0x155bba2e9214537c, limb3: 0x0, }, y: u384 { limb0: 0x69eeff16b7218dc48ef412b4, limb1: 0x48bff8d843d20fe5ec0702db, limb2: 0x26ba44b80af446f0, limb3: 0x0, }, }, lagrange_first: G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, lagrange_last: G1Point { x: u384 { limb0: 0x5fa2f3b50f0d5494f99668f8, limb1: 0x2b3d28853349f2b74055496e, limb2: 0x14c89754aed58171, limb3: 0x0, }, y: u384 { limb0: 0x24ce342a89643205b5c346fe, limb1: 0x6336e9f9001bd4a7f22da775, limb2: 0x13c5b1bd3f802852, limb3: 0x0, }, }, }; pub const precomputed_lines: [G2Line; 176] = [ G2Line { r0a0: u288 { limb0: 0x4d347301094edcbfa224d3d5, limb1: 0x98005e68cacde68a193b54e6, limb2: 0x237db2935c4432bc, }, r0a1: u288 { limb0: 0x6b4ba735fba44e801d415637, limb1: 0x707c3ec1809ae9bafafa05dd, limb2: 0x124077e14a7d826a, }, r1a0: u288 { limb0: 0x49a8dc1dd6e067932b6a7e0d, limb1: 0x7676d0000961488f8fbce033, limb2: 0x3b7178c857630da, }, r1a1: u288 { limb0: 0x98c81278efe1e96b86397652, limb1: 0xe3520b9dfa601ead6f0bf9cd, limb2: 0x2b17c2b12c26fdd0, }, }, G2Line { r0a0: u288 { limb0: 0x19f2be813f1a2cc51a251901, limb1: 0xa120afb4bcd07fdae4c4c91b, limb2: 0xcd8c8d94eedaaa5, }, r0a1: u288 { limb0: 0xa3808ba2f25b910b50769d68, limb1: 0xda666e5fa50719fcd79ea2c7, limb2: 0x104262c7ecae13e5, }, r1a0: u288 { limb0: 0xd00c9d5338bfc75cd1fe4002, limb1: 0x25f7441c17b6428fffe6266b, limb2: 0x25d0502e1109204d, }, r1a1: u288 { limb0: 0x4ce60bf635ff0fe14cf89d2, limb1: 0x9ca0af889fc43d4423a03197, limb2: 0x1b323f9be536f345, }, }, G2Line { r0a0: u288 { limb0: 0x1b3d578c32d1af5736582972, limb1: 0x204fe74db6b371d37e4615ab, limb2: 0xce69bdf84ed6d6d, }, r0a1: u288 { limb0: 0xfd262357407c3d96bb3ba710, limb1: 0x47d406f500e66ea29c8764b3, limb2: 0x1e23d69196b41dbf, }, r1a0: u288 { limb0: 0x1ec8ee6f65402483ad127f3a, limb1: 0x41d975b678200fce07c48a5e, limb2: 0x2cad36e65bbb6f4f, }, r1a1: u288 { limb0: 0xcfa9b8144c3ea2ab524386f5, limb1: 0xd4fe3a18872139b0287570c3, limb2: 0x54c8bc1b50aa258, }, }, G2Line { r0a0: u288 { limb0: 0xb5ee22ba52a7ed0c533b7173, limb1: 0xbfa13123614ecf9c4853249b, limb2: 0x6567a7f6972b7bb, }, r0a1: u288 { limb0: 0xcf422f26ac76a450359f819e, limb1: 0xc42d7517ae6f59453eaf32c7, limb2: 0x899cb1e339f7582, }, r1a0: u288 { limb0: 0x9f287f4842d688d7afd9cd67, limb1: 0x30af75417670de33dfa95eda, limb2: 0x1121d4ca1c2cab36, }, r1a1: u288 { limb0: 0x7c4c55c27110f2c9a228f7d8, limb1: 0x8f14f6c3a2e2c9d74b347bfe, limb2: 0x83ef274ba7913a5, }, }, G2Line { r0a0: u288 { limb0: 0x4e7f0c0bfd065f51be57e446, limb1: 0x172f9601c4b0d882b2bca176, limb2: 0x238b85999243f584, }, r0a1: u288 { limb0: 0xc4f13eea49c4fb0b88065fdf, limb1: 0xdde9d756dc7a3e60bfe2c7c9, limb2: 0x2021ebaaf4838c43, }, r1a0: u288 { limb0: 0x98652d3a0360c4ba067ebd45, limb1: 0x9259019a69cb15cd979b4425, limb2: 0xa93fe44d0287fdc, }, r1a1: u288 { limb0: 0x63a369cdd8c09b18c3ad7375, limb1: 0x1baf962de1bd1b1973e138fa, limb2: 0x15320ed6fbfaace4, }, }, G2Line { r0a0: u288 { limb0: 0x1a9ecb5a41abb65787e46934, limb1: 0x28fec59f9911882bd4d50306, limb2: 0x25996b3cd58cce92, }, r0a1: u288 { limb0: 0x56f5cca0fddcae1bfbee4b4d, limb1: 0x4237b58cc71911abcefd1d92, limb2: 0x2d985c4da93484d4, }, r1a0: u288 { limb0: 0x406454881e1f6cab8a9ab13c, limb1: 0x2cdf1a77980edf520cc8f23f, limb2: 0x20ce11ddb649cf18, }, r1a1: u288 { limb0: 0xfe104a8fa2c57b6b94bf56d2, limb1: 0xe2debabd9212070fd38f818, limb2: 0x1c1a2364541a15be, }, }, G2Line { r0a0: u288 { limb0: 0xfc23a674d089e9cfdefb1db8, limb1: 0x9ddfd61d289b65a9b4254476, limb2: 0x1e2f561324ef4447, }, r0a1: u288 { limb0: 0xf67a6a9e31f6975b220642ea, limb1: 0xccd852893796296e4d1ed330, 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limb1: 0x12b76b14785c6e62da580b73, limb2: 0x15b1b31fd06f755f, }, r1a0: u288 { limb0: 0x92dd2c2444d613dfaa53a1e3, limb1: 0xec043691d9b8376ef4c32dbb, limb2: 0x1804f2db8a7b3a55, }, r1a1: u288 { limb0: 0xe8ad6e24b323fdb6cc8189a9, limb1: 0x501fc22cd9d6c75bfcfe658e, limb2: 0x4669f457c82b8e1, }, }, G2Line { r0a0: u288 { limb0: 0x537ecf0916b38aeea21d4e47, limb1: 0x181a00de27ba4be1b380d6c8, limb2: 0x8c2fe2799316543, }, r0a1: u288 { limb0: 0xe68fff5ee73364fff3fe403b, limb1: 0x7b8685c8a725ae79cfac8f99, limb2: 0x7b4be349766aba4, }, r1a0: u288 { limb0: 0xdf7c93c0095545ad5e5361ea, limb1: 0xce316c76191f1e7cd7d03f3, limb2: 0x22ea21f18ddec947, }, r1a1: u288 { limb0: 0xa19620b4c32db68cc1c2ef0c, limb1: 0xffa1e4be3bed5faba2ccbbf4, limb2: 0x16fc78a64c45f518, }, }, G2Line { r0a0: u288 { limb0: 0x2b6af476f520b4bf804415bc, limb1: 0xd949ee7f9e8874698b090fca, limb2: 0x34db5e5ec2180cf, }, r0a1: u288 { limb0: 0x3e06a324f038ac8abcfb28d7, limb1: 0xc2e6375b7a83c0a0145f8942, limb2: 0x2247e79161483763, }, r1a0: u288 { limb0: 0x708773d8ae3a13918382fb9d, limb1: 0xaf83f409556e32aa85ae92bf, limb2: 0x9af0a924ae43ba, }, r1a1: u288 { limb0: 0xa6fded212ff5b2ce79755af7, limb1: 0x55a2adfb2699ef5de6581b21, limb2: 0x2476e83cfe8daa5c, }, }, G2Line { r0a0: u288 { limb0: 0x9ab1f3d5a481c50cff61b4ab, limb1: 0x11f4705a4954e6a036be2ad2, limb2: 0x308f243a8a83264, }, r0a1: u288 { limb0: 0x5f19b29c09416b2fd501f695, limb1: 0xd0a5c0a568ca5e38f82b2f7a, limb2: 0x8abaf41ba2b92f5, }, r1a0: u288 { limb0: 0x6cc5a6aa31c75bfb717c7828, limb1: 0x96fe9ee8789208c41d57d3b8, limb2: 0x1ff348bb7825845a, }, r1a1: u288 { limb0: 0x23e6063e1cca25fa4a6e992e, limb1: 0xe94e827315d1667557cbe7de, limb2: 0x2cc27fe4c068e1df, }, }, G2Line { r0a0: u288 { limb0: 0x5de7a643e301caa63b685021, limb1: 0x933a277a93f708227c90f768, limb2: 0x426809a902d5047, }, r0a1: u288 { limb0: 0xbb25fb66cb4bf4c7ec50bdbd, limb1: 0x52a75a0facd2b7bf0ea93bec, limb2: 0x1f265ce4dbe1a42b, }, r1a0: u288 { limb0: 0xc5717cea7518c3550b4d5f4, limb1: 0xc95394cb07fdfc22e63d990a, limb2: 0x2b4bcc47347e8eb5, }, r1a1: u288 { limb0: 0xc5a6f1284ee2bdd4922c2508, limb1: 0xcd55e1d8ff43e6dd59224505, limb2: 0x2c376da2c4c11de5, }, }, G2Line { r0a0: u288 { limb0: 0x1c4759bcf7c607fe3f839d4d, limb1: 0xea91f311da73327e2ed40785, limb2: 0x2017052c72360f42, }, r0a1: u288 { limb0: 0x38cf8a4368c0709980199fc3, limb1: 0xfc9047885996c19e84d7d4ea, limb2: 0x1795549eb0b97783, }, r1a0: u288 { limb0: 0xb70f7ecfbec0eaf46845e8cc, limb1: 0x9ddf274c2a9f89ea3bc4d66f, limb2: 0xcc6f106abfcf377, }, r1a1: u288 { limb0: 0xf6ff11ce29186237468c2698, limb1: 0x5c629ad27bb61e4826bb1313, limb2: 0x2014c6623f1fb55e, }, }, G2Line { r0a0: u288 { limb0: 0xc403ea5ad65aadd602c8c76f, limb1: 0x7a8d2727cd7fa40d97615b39, limb2: 0x14bd9b9bc6c2c1c1, }, r0a1: u288 { limb0: 0xcd28af7919b01761c69bd246, limb1: 0x8a1a211a81094740e2cc984e, limb2: 0x2766e09571dc194c, }, r1a0: u288 { limb0: 0xa24dbe5f1fb539a5d9d39db7, limb1: 0xd7eef78019e82d7e1f77d2f5, limb2: 0x6d7b6e70105c87d, }, r1a1: u288 { limb0: 0x30836b87e6e8553c665ffbe0, limb1: 0xb0474bb94febd802f9049ad0, limb2: 0x2774e72d0844eea4, }, }, G2Line { r0a0: u288 { limb0: 0xc648054e4b6134bbfd68487f, limb1: 0xdf0506dad3f3d098c13a6386, limb2: 0x26bebeb6f46c2e8c, }, r0a1: u288 { limb0: 0x9d0cdb28a94204776c6e6ba6, limb1: 0x303f02dfe619752b1607951d, limb2: 0x1127d8b17ef2c064, }, r1a0: u288 { limb0: 0xe34ca1188b8db4e4694a696c, limb1: 0x243553602481d9b88ca1211, limb2: 0x1f8ef034831d0132, }, r1a1: u288 { limb0: 0xe3a5dfb1785690dad89ad10c, limb1: 0xd690b583ace24ba033dd23e0, limb2: 0x405d0709e110c03, }, }, G2Line { r0a0: u288 { limb0: 0x3b5aa24fe300f5bef5aefca, limb1: 0x5d5566dc41ca40c4af2bf978, limb2: 0x39a42540cb68ab8, }, r0a1: u288 { limb0: 0xe21ea63fac2d99bf899d8353, limb1: 0xecdf87c89dafc1f9be69379b, limb2: 0x1c75e3d0966038ad, }, r1a0: u288 { limb0: 0x7c9f991de50f505a8dc707e7, limb1: 0x259d423172d9927ffb0e98d1, limb2: 0x15fb83693066d1ff, }, r1a1: u288 { limb0: 0x72c144b5e7d364d572576db6, limb1: 0x5d75c50c43614aea3e81a99b, limb2: 0x1ef4651860019554, }, }, G2Line { r0a0: u288 { limb0: 0x72cc2cef2785ce4ff4e9b7af, limb1: 0x60ed5b9c207d7f31fb6234ab, limb2: 0x1bb17a4bc7b643ed, }, r0a1: u288 { limb0: 0x9424eb15b502cde7927c7530, limb1: 0xa0e33edbbaa9de8e9c206059, limb2: 0x2b9a3a63bbf4af99, }, r1a0: u288 { limb0: 0x423811cb6386e606cf274a3c, limb1: 0x8adcc0e471ecfe526f56dc39, limb2: 0x9169a8660d14368, }, r1a1: u288 { limb0: 0xf616c863890c3c8e33127931, limb1: 0xcc9414078a6da6989dae6b91, limb2: 0x594d6a7e6b34ab2, }, }, G2Line { r0a0: u288 { limb0: 0x4617750de3208c0a42bf7c07, limb1: 0x7e2d94e31538522d38df8b23, limb2: 0x23954455da7aef56, }, r0a1: u288 { limb0: 0x6fef0ba4bbf6577133bdc9ae, limb1: 0xcab064e22aaf2ceec03f1b77, limb2: 0x274369683ff67155, }, r1a0: u288 { limb0: 0x5dce7b13d41ff1b90727094f, limb1: 0x426ef23f29c4df03dc8edf8, limb2: 0x313b4cdbf3d9c5e, }, r1a1: u288 { limb0: 0x62c5ac5fd0d7b3ef591e828, limb1: 0x650f8fc6b0fe55eb28d0fca8, limb2: 0xf5bb0abe931a208, }, }, G2Line { r0a0: u288 { limb0: 0xf2d619ae78049bf9141c35cf, limb1: 0x717f8b10d469a1ee2d91f191, limb2: 0x2c72c82fa8afe345, }, r0a1: u288 { limb0: 0xb89321223b82a2dc793c0185, limb1: 0x71506a0cf4adb8e51bb7b759, limb2: 0x2c13b92a98651492, }, r1a0: u288 { limb0: 0x4947ef2c89276f77f9d20942, limb1: 0xb454d68685ab6b6976e71ec5, limb2: 0x19a938d0e78a3593, }, r1a1: u288 { limb0: 0xbe883eb119609b489c01c905, limb1: 0xaa06779922047f52feac5ce6, limb2: 0x76977a3015dc164, }, }, G2Line { r0a0: u288 { limb0: 0x43a96a588005043a46aadf2c, limb1: 0xa37b89d8a1784582f0c52126, limb2: 0x22e9ef3f5d4b2297, }, r0a1: u288 { limb0: 0x8c6f6d8474cf6e5a58468a31, limb1: 0xeb1ce6ac75930ef1c79b07e5, limb2: 0xf49839a756c7230, }, r1a0: u288 { limb0: 0x82b84693a656c8e8c1f962fd, limb1: 0x2c1c8918ae80282208b6b23d, limb2: 0x14d3504b5c8d428f, }, r1a1: u288 { limb0: 0x60ef4f4324d5619b60a3bb84, limb1: 0x6d3090caefeedbc33638c77a, limb2: 0x159264c370c89fec, }, }, G2Line { r0a0: u288 { limb0: 0xa3343aa671fa957f64383174, limb1: 0x5d0fbca92791fb10ca8bfba7, limb2: 0x114f2c6ae3a67df6, }, r0a1: u288 { limb0: 0x50f6b86be16e52076b114eac, limb1: 0x780e63533112887af8e1b20a, limb2: 0x63e07909f8e5150, }, r1a0: u288 { limb0: 0xf4d68bdb295f81fb688b56c9, limb1: 0xabc9867b1aae2bca05251e19, limb2: 0x1a4d8e8bbc5dc905, }, r1a1: u288 { limb0: 0x1072bd332617ade1aa5f283e, limb1: 0x50dc088ed02b4ee5c8114042, limb2: 0x92f0fffce502d7c, }, }, G2Line { r0a0: u288 { limb0: 0xf21ea2700d86757c9edc60fc, limb1: 0x4ed3a4f31b13fbb9fdabfe54, limb2: 0xefdc83e2cd29ae1, }, r0a1: u288 { limb0: 0x36771d39b743a658ed812080, limb1: 0x506453f18d56ef30476706cd, limb2: 0x2658fa02d8abf7ce, }, r1a0: u288 { limb0: 0x4aad4f76dd2af32ff8a6f388, limb1: 0x6aebd448524150ae6bb57548, limb2: 0x2702b8c1fb9a5bfb, }, r1a1: u288 { limb0: 0xe1462da76f807e5e73062316, limb1: 0x244b002de9ef9e9d65b40718, limb2: 0x2672d0c637a3cc19, }, }, ]; ================================================ FILE: src/contracts/mutator_set/src/zk_verifier/honk_verifier_contract.cairo ================================================ use super::honk_verifier_circuits::{ is_on_curve_excluding_infinity_bn254, run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_17_PUB_19_circuit, }; use super::honk_verifier_constants::{precomputed_lines, vk}; #[starknet::interface] pub trait IUltraKeccakZKHonkVerifier { fn verify_ultra_keccak_zk_honk_proof( self: @TContractState, full_proof_with_hints: Span, ) -> Result, felt252>; } #[starknet::contract] mod UltraKeccakZKHonkVerifier { use core::num::traits::Zero; use garaga::apps::noir::zk_honk_transcript::{ KeccakHasherState, Point256IntoCircuitPoint, ZKHonkTranscriptTrait, ZK_BATCHED_RELATION_PARTIAL_LENGTH, }; use garaga::apps::noir::{G2_POINT_KZG_1, G2_POINT_KZG_2, ZKHonkProof}; use garaga::core::circuit::{U32IntoU384, U64IntoU384, u256_to_u384, u288IntoCircuitInputValue}; use garaga::definitions::{ BN254, G1G2Pair, G1Point, get_BN254_modulus, get_GRUMPKIN_modulus, get_eigenvalue, get_min_one_order, get_nG_glv_fake_glv, get_third_root_of_unity, u384, }; use garaga::ec_ops::{G1PointTrait, GlvFakeGlvHint, _ec_safe_add, _scalar_mul_glv_and_fake_glv}; use garaga::pairing_check::{MPCheckHintBN254, multi_pairing_check_bn254_2P_2F}; use super::{ is_on_curve_excluding_infinity_bn254, precomputed_lines, run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_17_circuit, run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_17_PUB_19_circuit, vk, }; #[storage] struct Storage {} #[derive(Drop, Serde)] struct FullProof { proof: ZKHonkProof, msm_hint: Span, kzg_hint: MPCheckHintBN254, } #[abi(embed_v0)] impl IUltraKeccakZKHonkVerifier of super::IUltraKeccakZKHonkVerifier { fn verify_ultra_keccak_zk_honk_proof( self: @ContractState, full_proof_with_hints: Span, ) -> Result, felt252> { // DO NOT EDIT THIS FUNCTION UNLESS YOU KNOW WHAT YOU ARE DOING. // This function returns Result::Ok(public_inputs) if the proof is valid. // If the proof is invalid, it returns Result::Err(error). // Read the documentation to learn how to generate the full_proof_with_hints array given // a proof and a verifying key. let mut full_proof_with_hints = full_proof_with_hints; let full_proof = Serde::::deserialize(ref full_proof_with_hints) .expect('deserialization failed'); let mod_bn = get_BN254_modulus(); let mod_grumpkin = get_GRUMPKIN_modulus(); let (transcript, _, base_rlc) = ZKHonkTranscriptTrait::from_proof::< KeccakHasherState, >(full_proof.proof, vk.vk_hash, vk.log_circuit_size); let log_n = vk.log_circuit_size; let (sum_check_rlc, honk_check) = run_GRUMPKIN_ZK_HONK_SUMCHECK_SIZE_17_PUB_19_circuit( p_public_inputs: full_proof.proof.public_inputs, p_pairing_point_object: full_proof.proof.pairing_point_object, libra_sum: u256_to_u384(full_proof.proof.libra_sum), sumcheck_univariates_flat: full_proof .proof .sumcheck_univariates .slice(0, log_n * ZK_BATCHED_RELATION_PARTIAL_LENGTH), sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span(), tp_gate_challenge: transcript.gate_challenge, tp_eta_1: transcript.eta.into(), tp_eta_2: transcript.eta_two.into(), tp_eta_3: transcript.eta_three.into(), tp_beta: transcript.beta.into(), tp_gamma: transcript.gamma.into(), tp_base_rlc: base_rlc.into(), tp_alpha: transcript.alpha, tp_libra_challenge: transcript.libra_challenge.into(), modulus: mod_grumpkin, ); let (mut challenge_poly_eval, mut root_power_times_tp_gemini_r) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_INIT_SIZE_17_circuit( tp_gemini_r: transcript.gemini_r.into(), modulus: mod_grumpkin, ); for i in 0..vk.log_circuit_size { let (new_challenge_poly_eval, new_root_power_times_tp_gemini_r) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_LOOP_SIZE_17_circuit( challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, tp_sumcheck_u_challenge: (*transcript.sum_check_u_challenges.at(i)).into(), modulus: mod_grumpkin, ); challenge_poly_eval = new_challenge_poly_eval; root_power_times_tp_gemini_r = new_root_power_times_tp_gemini_r; } let (vanishing_check, diff_check) = run_GRUMPKIN_ZK_HONK_EVALS_CONS_DONE_SIZE_17_circuit( p_libra_evaluation: u256_to_u384(full_proof.proof.libra_evaluation), p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), challenge_poly_eval: challenge_poly_eval, root_power_times_tp_gemini_r: root_power_times_tp_gemini_r, modulus: mod_grumpkin, ); let ( scalar_1, scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, scalar_52, scalar_53, scalar_54, scalar_55, scalar_56, scalar_57, ) = run_GRUMPKIN_ZKHONK_PREP_MSM_SCALARS_SIZE_17_circuit( p_sumcheck_evaluations: full_proof.proof.sumcheck_evaluations, p_gemini_masking_eval: u256_to_u384(full_proof.proof.gemini_masking_eval), p_gemini_a_evaluations: full_proof.proof.gemini_a_evaluations, p_libra_poly_evals: full_proof.proof.libra_poly_evals, tp_gemini_r: transcript.gemini_r.into(), tp_rho: transcript.rho.into(), tp_shplonk_z: transcript.shplonk_z.into(), tp_shplonk_nu: transcript.shplonk_nu.into(), tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span().slice(0, log_n), modulus: mod_grumpkin, ); // Starts with 1 * shplonk_q, not included in msm let mut _points: Array = array![ vk.qm, vk.qc, vk.ql, vk.qr, vk.qo, vk.q4, vk.qLookup, vk.qArith, vk.qDeltaRange, vk.qElliptic, vk.qMemory, vk.qNnf, vk.qPoseidon2External, vk.qPoseidon2Internal, vk.s1, vk.s2, vk.s3, vk.s4, vk.id1, vk.id2, vk.id3, vk.id4, vk.t1, vk.t2, vk.t3, vk.t4, vk.lagrange_first, vk.lagrange_last, full_proof.proof.gemini_masking_poly.into(), // Proof point 1, full_proof.proof.w1.into(), // Proof point 2, full_proof.proof.w2.into(), // Proof point 3, full_proof.proof.w3.into(), // Proof point 4, full_proof.proof.w4.into(), // Proof point 5, full_proof.proof.z_perm.into(), // Proof point 6, full_proof.proof.lookup_inverses.into(), // Proof point 7, full_proof.proof.lookup_read_counts.into(), // Proof point 8, full_proof.proof.lookup_read_tags.into() // Proof point 9 ]; for gem_comm in full_proof.proof.gemini_fold_comms { _points.append((*gem_comm).into()); } // log_n -1 = 16 points || Proof points 10-25 for lib_comm in full_proof.proof.libra_commitments { _points.append((*lib_comm).into()); } // 3 points || Proof points 26-28 _points.append(full_proof.proof.kzg_quotient.into()); // Proof point 29 _points.append(BN254.G); let mut points = _points.span(); let mut scalars: Span = array![ scalar_2, scalar_3, scalar_4, scalar_5, scalar_6, scalar_7, scalar_8, scalar_9, scalar_10, scalar_11, scalar_12, scalar_13, scalar_14, scalar_15, scalar_16, scalar_17, scalar_18, scalar_19, scalar_20, scalar_21, scalar_22, scalar_23, scalar_24, scalar_25, scalar_26, scalar_27, scalar_28, scalar_29, scalar_1, scalar_30, scalar_31, scalar_32, scalar_33, scalar_34, scalar_35, scalar_36, scalar_37, scalar_38, scalar_39, scalar_40, scalar_41, scalar_42, scalar_43, scalar_44, scalar_45, scalar_46, scalar_47, scalar_48, scalar_49, scalar_50, scalar_51, scalar_52, scalar_53, scalar_54, scalar_55, scalar_56, transcript.shplonk_z.into(), scalar_57, ] .span(); // Check input points are on curve. // Skip the first 28 points as they are from VK and keep the last 29 proof points for point in points.slice(28, 29) { assert( is_on_curve_excluding_infinity_bn254(*point, mod_bn), 'proof point not on curve', ); } // Assert shplonk_q is on curve let shplonk_q_pt: G1Point = full_proof.proof.shplonk_q.into(); assert( is_on_curve_excluding_infinity_bn254(shplonk_q_pt, mod_bn), 'shplonk_q not on curve', ); let mut msm_hint = full_proof.msm_hint; assert(msm_hint.len() == 58 * 12, 'wrong glv&fakeglv hint size'); let eigen = get_eigenvalue(0); let third_root_of_unity = get_third_root_of_unity(0); let min_one = get_min_one_order(0); let nG = get_nG_glv_fake_glv(0); let mut P_1 = shplonk_q_pt; while msm_hint.len() != 0 { let pt = *points.pop_front().unwrap(); let scalar = *scalars.pop_front().unwrap(); // Note : Scalars are below curve order by construction (circuit outputs mod n and // transcript output (u128)) let glv_fake_glv_hint: GlvFakeGlvHint = Serde::deserialize(ref msm_hint).unwrap(); let temp = _scalar_mul_glv_and_fake_glv( pt, scalar, mod_grumpkin, mod_bn, glv_fake_glv_hint, eigen, third_root_of_unity, min_one, nG, 0, ); P_1 = _ec_safe_add(P_1, temp, mod_bn, 0); } let P_2: G1Point = full_proof.proof.kzg_quotient.into(); // Perform the KZG pairing check. let kzg_check = multi_pairing_check_bn254_2P_2F( G1G2Pair { p: P_1, q: G2_POINT_KZG_1 }, G1G2Pair { p: P_2.negate(0), q: G2_POINT_KZG_2 }, precomputed_lines.span(), full_proof.kzg_hint, ); if sum_check_rlc.is_zero() && honk_check.is_zero() && !vanishing_check.is_zero() && diff_check.is_zero() && kzg_check.is_ok() { return Result::Ok(full_proof.proof.public_inputs); } else { return Result::Err('Proof verification failed'); } } } } ================================================ FILE: src/contracts/mutator_set/tests/test_contract.cairo ================================================ use garaga::definitions::u384; use garaga::hashes::poseidon_hash_2_bn254; use mutator_set::mutator_set_contract::{ IMutatorSetContractDispatcher, IMutatorSetContractDispatcherTrait, }; // use mutator_set::IMutatorSetContractSafeDispatcher; use snforge_std::{ContractClassTrait, DeclareResultTrait, declare}; use starknet::ContractAddress; fn deploy_contract(name: ByteArray) -> ContractAddress { let contract = declare(name).unwrap().contract_class(); let (contract_address, _) = contract.deploy(@ArrayTrait::new()).unwrap(); contract_address } #[test] fn test_poseidon_hash_2_bn254() { let first_leaf: u256 = 'hello_world'; let first_leaf_u384: u384 = first_leaf.into(); let _ = poseidon_hash_2_bn254( first_leaf_u384, u384 { limb0: 42, limb1: 0, limb2: 0, limb3: 0 }, ); } #[test] fn test_append_leaf_aocl() { let contract_address = deploy_contract("MutatorSetContract"); let dispatcher = IMutatorSetContractDispatcher { contract_address }; // Initial state (1 leaf) let n_leaves_aocl_before = dispatcher.get_n_leaves_aocl(); let peaks_before = dispatcher.get_peaks_aocl(); let n_peaks_before = dispatcher.get_n_peaks_aocl(); assert(n_leaves_aocl_before == 1, 'Invalid n_leaves_aocl'); assert(n_peaks_before == 1, 'Invalid n_peaks'); assert(peaks_before == array![0], 'Invalid peaks_before'); // Append second leaf dispatcher.append_leaf_aocl(0); // println!("Appended second leaf"); let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); let n_peaks_after = dispatcher.get_n_peaks_aocl(); assert(n_leaves_aocl_after == 2, 'Invalid n_leaves_aocl'); assert(n_peaks_after == 1, 'Invalid n_peaks'); let peaks_after = dispatcher.get_peaks_aocl(); assert( peaks_after == array![0x2098f5fb9e239eab3ceac3f27b81e481dc3124d55ffed523a839ee8446b64864], 'Invalid peaks_after', ); // Append third leaf dispatcher.append_leaf_aocl(0); // println!("Appended third leaf"); let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); let n_peaks_after = dispatcher.get_n_peaks_aocl(); assert(n_leaves_aocl_after == 3, 'Invalid n_leaves_aocl'); assert(n_peaks_after == 2, 'Invalid n_peaks'); let peaks_after = dispatcher.get_peaks_aocl(); assert( peaks_after == array![ 0x2098f5fb9e239eab3ceac3f27b81e481dc3124d55ffed523a839ee8446b64864, 0, ], 'Invalid peaks_after', ); // Append 4th leaf : // println!("---Appending leaf {}----", 4); dispatcher.append_leaf_aocl(0); let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); assert(n_leaves_aocl_after == 4, 'Invalid n_leaves_aocl'); let n_peaks_after = dispatcher.get_n_peaks_aocl(); assert(n_peaks_after == 1, 'Invalid n_peaks_4'); let peaks_after = dispatcher.get_peaks_aocl(); assert( peaks_after == array![0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1], 'Invalid peaks_after_4', ); // println!("---Appending leaf 5----"); dispatcher.append_leaf_aocl(0); let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); assert(n_leaves_aocl_after == 5, 'Invalid n_leaves_aocl'); let n_peaks_after = dispatcher.get_n_peaks_aocl(); assert(n_peaks_after == 2, 'Invalid n_peaks_5'); let peaks_after = dispatcher.get_peaks_aocl(); assert_eq!( peaks_after, array![0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1, 0], ); for _ in 6..14_usize { // println!("Appending leaf {}", i); dispatcher.append_leaf_aocl(0); // let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); // println!(" LOOP: n_leaves_aocl: {}", n_leaves_aocl_after); } let n_leaves_aocl_after = dispatcher.get_n_leaves_aocl(); let n_peaks_after = dispatcher.get_n_peaks_aocl(); assert(n_leaves_aocl_after == 13, 'Invalid n_leaves_aocl'); assert(n_peaks_after == 3, 'Invalid n_peaks'); let peaks_after = dispatcher.get_peaks_aocl(); assert( peaks_after == array![ 0x18f43331537ee2af2e3d758d50f72106467c6eea50371dd528d57eb2b856d238, 0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1, 0, ], 'Invalid peaks_after', ); } // #[test] // #[feature("safe_dispatcher")] // fn test_cannot_increase_balance_with_zero_value() { // let contract_address = deploy_contract("HelloStarknet"); // let safe_dispatcher = IHelloStarknetSafeDispatcher { contract_address }; // let balance_before = safe_dispatcher.get_balance().unwrap(); // assert(balance_before == 0, 'Invalid balance'); // match safe_dispatcher.increase_balance(0) { // Result::Ok(_) => core::panic_with_felt252('Should have panicked'), // Result::Err(panic_data) => { // assert(*panic_data.at(0) == 'Amount cannot be 0', *panic_data.at(0)); // }, // }; // } ================================================ FILE: src/contracts/mutator_set/zk_program/Nargo.toml ================================================ [package] name = "zk_program" type = "bin" authors = [""] [dependencies] poseidon = { tag = "v0.1.1", git = "https://github.com/noir-lang/poseidon" } ================================================ FILE: src/contracts/mutator_set/zk_program/Prover.toml ================================================ leaf_index = "0x2" leaf_premiage = "0x0" num_leafs = "0x5" peaks = [ "0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0",] root_hash = "0x1ba30aaf15c7694786a1f118ca39fcc6c997b48da9dfa62e9ec3e83ac7d6304d" [proof] len = "0x2" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0x2098f5fb9e239eab3ceac3f27b81e481dc3124d55ffed523a839ee8446b64864" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" [[proof.storage]] hash = "0" ================================================ FILE: src/contracts/mutator_set/zk_program/src/main.nr ================================================ pub mod mmr; pub mod mmr_tests; // use dep::std::hash::poseidon::bn254::hash_2; use mmr::{MMRProofElement, verify_mmr_inclusion}; fn main( // MMR verification inputs leaf_premiage: Field, root_hash: pub Field, num_leafs: pub u64, leaf_index: pub u64, proof: BoundedVec, peaks: [Field; 32], ) { // Prove knowledge of pre-image // let leaf_hash = hash_2([leaf_premiage, 0]); let leaf_hash = leaf_premiage; // Verify MMR inclusion verify_mmr_inclusion(leaf_hash, root_hash, leaf_index, num_leafs, proof, peaks); // Todo derive bloom filter bits from pre-image. } #[test] fn test_main() { // Test data for MMR verification let leaf1 = 0; // Create proof for leaf1 (padding with empty elements to match size 32) let mut proof = BoundedVec::new(); proof.push(MMRProofElement { hash: 0 }); // Sibling of leaf1 proof.push( MMRProofElement { hash: 0x2098f5fb9e239eab3ceac3f27b81e481dc3124d55ffed523a839ee8446b64864, }, ); // Sibling of hash12 let mut peaks = [0; 32]; peaks[0] = 0x1069673dcdb12263df301a6ff584a7ec261a44cb9dc68df067a4774460b1f1e1; peaks[1] = 0; let root = 0x1ba30aaf15c7694786a1f118ca39fcc6c997b48da9dfa62e9ec3e83ac7d6304d; // Test the main function main(leaf1, root, 5, 2, proof, peaks); } ================================================ FILE: src/contracts/mutator_set/zk_program/src/mmr.nr ================================================ use poseidon::poseidon::bn254::hash_2; // Represents a Merkle Mountain Range proof element pub struct MMRProofElement { // The sibling hash at this level pub hash: Field, } // Helper function to calculate the number of ones in a Field value fn count_ones(value: u64) -> u32 { let mut count = 0; let mut v = value; for _ in 0..64 { let bit = (v & 1) as u32; count = count + bit; v = v / 2; } count } // Helper function to calculate log2 of a Field value fn log2(value: u64) -> u32 { let mut result = 0; let mut v = value; for _ in 0..64 { let should_continue = v > 1; result = if should_continue { result + 1 } else { result }; v = if should_continue { v / 2 } else { v }; } result } // Helper function to calculate leaf_index_to_mt_index_and_peak_index pub fn leaf_index_to_mt_index_and_peak_index(leaf_index: u64, num_leafs: u64) -> (u64, u32) { // Check if leaf_index is out of bounds let is_valid = leaf_index < num_leafs; assert(is_valid, "Leaf index must be strictly smaller than the number of leafs"); // Calculate discrepancies to find local Merkle tree height let discrepancies = leaf_index ^ num_leafs; let local_mt_height = log2(discrepancies); let local_mt_num_leafs = 1 << (local_mt_height as u8); let remainder_bitmask = (local_mt_num_leafs - 1) as u64; let local_leaf_index = leaf_index & (remainder_bitmask as u64); let mt_node_index = local_leaf_index + (local_mt_num_leafs as u64); // Calculate peak index let num_peaks = count_ones(num_leafs); let num_peaks_smaller_or_equal_own_peak = count_ones(((num_leafs as u64) & remainder_bitmask) as u64); let peak_index = num_peaks - num_peaks_smaller_or_equal_own_peak - 1; (mt_node_index, peak_index) } // Verifies that a leaf exists in an MMR using an inclusion proof pub fn verify_mmr_inclusion( // The leaf hash to verify leaf_hash: Field, // The MMR root hash root_hash: Field, // The position of the leaf in the MMR (0-based) leaf_index: u64, // The number of leafs in the MMR num_leafs: u64, // The array of proof elements authentication_path: BoundedVec, // peaks of the MMR peaks: [Field; 32], ) { // Check if leaf index is out of bounds assert(leaf_index < num_leafs, "Leaf index must be strictly smaller than the number of leafs"); // Get Merkle tree index and peak index let (mut mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(leaf_index, num_leafs); // Verify peak count matches let expected_peak_count = count_ones(num_leafs); // assert(peaks.len() == expected_peak_count, "Invalid peaks length"); // Verify authentication path length matches Merkle tree height let merkle_tree_height = log2(mt_index); assert(authentication_path.len() == merkle_tree_height, "Invalid authentication path length"); // Process the authentication path let mut current_node = leaf_hash; for i in 0..32 { // print(i); // Compute the hash of the current node with its sibling if i < merkle_tree_height { let proof_element = authentication_path.get(i); let current_node_is_left_sibling = ((mt_index as u64) % 2) == 0; if current_node_is_left_sibling { // println("current_node_is_left_sibling"); current_node = hash_2([current_node, proof_element.hash]); } else { // println("current_node_is_right_sibling"); current_node = hash_2([proof_element.hash, current_node]); } // Move up one level in the tree mt_index = mt_index / 2; } } assert(mt_index == 1, "Invalid mt_index"); // Verify against the root hash assert(peaks[peak_index] == current_node, "Invalid inclusion proof"); let bag = bag_peaks(peaks, expected_peak_count); assert(bag == root_hash, "Invalid root hash"); } pub fn bag_peaks(mut peaks: [Field; 32], n_peaks: u32) -> Field { let mut bag = peaks[n_peaks - 1]; for i in 1..31 { if i < n_peaks { bag = hash_2([peaks[n_peaks - i - 1], bag]); } } bag } ================================================ FILE: src/contracts/mutator_set/zk_program/src/mmr_tests.nr ================================================ use super::mmr::leaf_index_to_mt_index_and_peak_index; #[test] fn test_leaf_index_to_mt_index_and_peak_index() { // 1 leaf let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(0, 1); assert(mt_index == 1, "1 leaf mt_index should be 1"); assert(peak_index == 0, "1 leaf peak_index should be 0"); // 2 leafs let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(0, 2); assert(mt_index == 2, "2 leafs - first leaf mt_index should be 2"); assert(peak_index == 0, "2 leafs - first leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(1, 2); assert(mt_index == 3, "2 leafs - second leaf mt_index should be 3"); assert(peak_index == 0, "2 leafs - second leaf peak_index should be 0"); // 3 leafs let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(0, 3); assert(mt_index == 2, "3 leafs - first leaf mt_index should be 2"); assert(peak_index == 0, "3 leafs - first leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(1, 3); assert(mt_index == 3, "3 leafs - second leaf mt_index should be 3"); assert(peak_index == 0, "3 leafs - second leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(2, 3); assert(mt_index == 1, "3 leafs - third leaf mt_index should be 1"); assert(peak_index == 1, "3 leafs - third leaf peak_index should be 1"); // 4 leafs let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(0, 4); assert(mt_index == 4, "4 leafs - first leaf mt_index should be 4"); assert(peak_index == 0, "4 leafs - first leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(1, 4); assert(mt_index == 5, "4 leafs - second leaf mt_index should be 5"); assert(peak_index == 0, "4 leafs - second leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(2, 4); assert(mt_index == 6, "4 leafs - third leaf mt_index should be 6"); assert(peak_index == 0, "4 leafs - third leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(3, 4); assert(mt_index == 7, "4 leafs - fourth leaf mt_index should be 7"); assert(peak_index == 0, "4 leafs - fourth leaf peak_index should be 0"); // 14 leafs let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(0, 14); assert(mt_index == 8, "14 leafs - first leaf mt_index should be 8"); assert(peak_index == 0, "14 leafs - first leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(7, 14); assert(mt_index == 15, "14 leafs - eighth leaf mt_index should be 15"); assert(peak_index == 0, "14 leafs - eighth leaf peak_index should be 0"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(8, 14); assert(mt_index == 4, "14 leafs - ninth leaf mt_index should be 4"); assert(peak_index == 1, "14 leafs - ninth leaf peak_index should be 1"); // 32 leafs for i in 0..32 { let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(i, 32); assert(mt_index == 32 + i, "32 leafs - mt_index should be 32 + i"); assert(peak_index == 0, "32 leafs - peak_index should be 0"); } // 33 leafs for i in 0..32 { let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(i, 33); assert(mt_index == 32 + i, "33 leafs - first 32 leaves mt_index should be 32 + i"); assert(peak_index == 0, "33 leafs - first 32 leaves peak_index should be 0"); } let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(32, 33); assert(mt_index == 1, "33 leafs - last leaf mt_index should be 1"); assert(peak_index == 1, "33 leafs - last leaf peak_index should be 1"); // 34 leafs for i in 0..32 { let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(i, 34); assert(mt_index == 32 + i, "34 leafs - first 32 leaves mt_index should be 32 + i"); assert(peak_index == 0, "34 leafs - first 32 leaves peak_index should be 0"); } let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(32, 34); assert(mt_index == 2, "34 leafs - 33rd leaf mt_index should be 2"); assert(peak_index == 1, "34 leafs - 33rd leaf peak_index should be 1"); let (mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(33, 34); assert(mt_index == 3, "34 leafs - 34th leaf mt_index should be 3"); assert(peak_index == 1, "34 leafs - 34th leaf peak_index should be 1"); } ================================================ FILE: src/contracts/risc0_sample_app/README.md ================================================ # RiscZero Sample App For details on how to use Garaga to run this **RiscZero** sample application, please refer to the [GitBook documentation](https://garaga.gitbook.io/garaga/maintained-smart-contracts/risczero). ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/.gitignore ================================================ Cargo.lock methods/guest/Cargo.lock target/ ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/Cargo.toml ================================================ [workspace] resolver = "2" members = ["host", "methods"] # Always optimize; building and running the guest takes much longer without optimization. [profile.dev] opt-level = 3 [profile.release] debug = 1 lto = true ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/README.md ================================================ # RISC Zero Rust Starter Template Welcome to the RISC Zero Rust Starter Template! This template is intended to give you a starting point for building a project using the RISC Zero zkVM. Throughout the template (including in this README), you'll find comments labelled `TODO` in places where you'll need to make changes. To better understand the concepts behind this template, check out the [zkVM Overview][zkvm-overview]. ## Quick Start First, make sure [rustup] is installed. The [`rust-toolchain.toml`][rust-toolchain] file will be used by `cargo` to automatically install the correct version. To build all methods and execute the method within the zkVM, run the following command: ```bash cargo run ``` This is an empty template, and so there is no expected output (until you modify the code). ### Executing the Project Locally in Development Mode During development, faster iteration upon code changes can be achieved by leveraging [dev-mode], we strongly suggest activating it during your early development phase. Furthermore, you might want to get insights into the execution statistics of your project, and this can be achieved by specifying the environment variable `RUST_LOG="[executor]=info"` before running your project. Put together, the command to run your project in development mode while getting execution statistics is: ```bash RUST_LOG="[executor]=info" RISC0_DEV_MODE=1 cargo run ``` ### Running Proofs Remotely on Bonsai _Note: The Bonsai proving service is still in early Alpha; an API key is required for access. [Click here to request access][bonsai access]._ If you have access to the URL and API key to Bonsai you can run your proofs remotely. To prove in Bonsai mode, invoke `cargo run` with two additional environment variables: ```bash BONSAI_API_KEY="YOUR_API_KEY" BONSAI_API_URL="BONSAI_URL" cargo run ``` ## How to Create a Project Based on This Template Search this template for the string `TODO`, and make the necessary changes to implement the required feature described by the `TODO` comment. Some of these changes will be complex, and so we have a number of instructional resources to assist you in learning how to write your own code for the RISC Zero zkVM: - The [RISC Zero Developer Docs][dev-docs] is a great place to get started. - Example projects are available in the [examples folder][examples] of [`risc0`][risc0-repo] repository. - Reference documentation is available at [https://docs.rs][docs.rs], including [`risc0-zkvm`][risc0-zkvm], [`cargo-risczero`][cargo-risczero], [`risc0-build`][risc0-build], and [others][crates]. ## Directory Structure It is possible to organize the files for these components in various ways. However, in this starter template we use a standard directory structure for zkVM applications, which we think is a good starting point for your applications. ```text project_name ├── Cargo.toml ├── host │ ├── Cargo.toml │ └── src │ └── main.rs <-- [Host code goes here] └── methods ├── Cargo.toml ├── build.rs ├── guest │ ├── Cargo.toml │ └── src │ └── method_name.rs <-- [Guest code goes here] └── src └── lib.rs ``` ## Video Tutorial For a walk-through of how to build with this template, check out this [excerpt from our workshop at ZK HACK III][zkhack-iii]. ## Questions, Feedback, and Collaborations We'd love to hear from you on [Discord][discord] or [Twitter][twitter]. [bonsai access]: https://bonsai.xyz/apply [cargo-risczero]: https://docs.rs/cargo-risczero [crates]: https://github.com/risc0/risc0/blob/main/README.md#rust-binaries [dev-docs]: https://dev.risczero.com [dev-mode]: https://dev.risczero.com/api/generating-proofs/dev-mode [discord]: https://discord.gg/risczero [docs.rs]: https://docs.rs/releases/search?query=risc0 [examples]: https://github.com/risc0/risc0/tree/main/examples [risc0-build]: https://docs.rs/risc0-build [risc0-repo]: https://www.github.com/risc0/risc0 [risc0-zkvm]: https://docs.rs/risc0-zkvm [rust-toolchain]: rust-toolchain.toml [rustup]: https://rustup.rs [twitter]: https://twitter.com/risczero [zkhack-iii]: https://www.youtube.com/watch?v=Yg_BGqj_6lg&list=PLcPzhUaCxlCgig7ofeARMPwQ8vbuD6hC5&index=5 [zkvm-overview]: https://dev.risczero.com/zkvm ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/host/Cargo.toml ================================================ [package] name = "host" version = "0.1.0" edition = "2021" [dependencies] methods = { path = "../methods" } risc0-zkvm = { version = "2.3.1" } risc0-ethereum-contracts = { version = "2.2.2" } garaga_rs = { path = "../../../../../tools/garaga_rs" } hex = "0.4" tracing-subscriber = { version = "0.3", features = ["env-filter"] } serde = "1.0" ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/host/src/main.rs ================================================ // These constants represent the RISC-V ELF and the image ID generated by risc0-build. // The ELF is used for proving and the ID is used for verification. use garaga_rs::calldata::full_proof_with_hints::groth16::risc0_utils::get_risc0_vk; use garaga_rs::calldata::full_proof_with_hints::groth16::{get_groth16_calldata, Groth16Proof}; use garaga_rs::definitions::CurveID; use methods::FIBONACCI_GUEST_ELF; use risc0_ethereum_contracts::encode_seal; use risc0_zkvm::{compute_image_id, default_prover, ExecutorEnv, ProverOpts, VerifierContext}; fn main() { // Initialize tracing. In order to view logs, run `RUST_LOG=info cargo run` tracing_subscriber::fmt() .with_env_filter(tracing_subscriber::filter::EnvFilter::from_default_env()) .init(); // An executor environment describes the configurations for the zkVM // including program inputs. // A default ExecutorEnv can be created like so: // `let env = ExecutorEnv::builder().build().unwrap();` // However, this `env` does not have any inputs. // // To add guest input to the executor environment, use // ExecutorEnvBuilder::write(). // To access this method, you'll need to use ExecutorEnv::builder(), which // creates an ExecutorEnvBuilder. When you're done adding input, call // ExecutorEnvBuilder::build(). // For example: let l: u32 = 3; // public lower bound for n let u: u32 = 8; // public upper bound for n let n: u32 = 6; // private n for which we will compute fibonacci(n) let env = ExecutorEnv::builder() .write(&l) .unwrap() .write(&u) .unwrap() .write(&n) .unwrap() .build() .unwrap(); // Obtain the default prover. let prover = default_prover(); // Proof information by proving the specified ELF binary. // This struct contains the receipt along with statistics about execution of the guest let prove_info = prover .prove_with_ctx( env, &VerifierContext::default(), FIBONACCI_GUEST_ELF, &ProverOpts::groth16(), ) .unwrap(); // extract the receipt. let receipt = prove_info.receipt; let seal = to_bytes(encode_seal(&receipt).unwrap()); let image_id = to_bytes(compute_image_id(&FIBONACCI_GUEST_ELF).unwrap()); let journal = to_bytes(receipt.journal); // prints the proof artifact as JSON println!( "{{\"seal\": \"0x{}\", \"image_id\": \"0x{}\", \"journal\": \"0x{}\"}}", hex::encode(&seal), hex::encode(&image_id), hex::encode(&journal) ); // helper function to convert objects to array of bytes fn to_bytes>(obj: T) -> Vec { obj.as_ref().to_vec() } // prints the calldata as JSON let proof = Groth16Proof::from_risc0(seal, image_id, journal); let calldata = get_groth16_calldata(&proof, &get_risc0_vk(), CurveID::BN254).unwrap(); println!( "[{}]", calldata .iter() .skip(1) .map(|v| format!("\"{}\"", v)) .collect::>() .join(", ") ); } ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/methods/Cargo.toml ================================================ [package] name = "methods" version = "0.1.0" edition = "2021" [build-dependencies] risc0-build = { version = "2.3.1" } [package.metadata.risc0] methods = ["guest"] ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/methods/build.rs ================================================ fn main() { risc0_build::embed_methods(); } ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/methods/guest/Cargo.toml ================================================ [package] name = "fibonacci_guest" version = "0.1.0" edition = "2021" [workspace] [dependencies] risc0-zkvm = { version = "2.3.1", default-features = false, features = ['std'] } ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/methods/guest/src/main.rs ================================================ use risc0_zkvm::guest::env; fn main() { // reads the public bounds and private n provided by the Host let l: u32 = env::read(); let u: u32 = env::read(); let n: u32 = env::read(); // sanity check for the bounds assert!(l <= n && n < u); // performs the computation let fib_n: u32 = fibonacci(n); fn fibonacci(n: u32) -> u32 { let mut a = 0; let mut b = 1; for _ in 0..n { (a, b) = (b, a + b); } a } // writes the public inputs and output to the journal env::commit(&l); env::commit(&u); env::commit(&fib_n); } ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/methods/src/lib.rs ================================================ include!(concat!(env!("OUT_DIR"), "/methods.rs")); ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_prover/rust-toolchain.toml ================================================ [toolchain] channel = "stable" components = ["rustfmt", "rust-src"] profile = "minimal" ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_sequencer/.gitignore ================================================ target .snfoundry_cache/ ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_sequencer/Scarb.toml ================================================ [package] name = "fibonacci_sequencer" version = "0.1.0" edition = "2024_07" # See more keys and their definitions at https://docs.swmansion.com/scarb/docs/reference/manifest.html [dependencies] starknet = "2.16.1" [dev-dependencies] snforge_std = "0.57.0" assert_macros = "2.16.1" [[target.starknet-contract]] sierra = true casm = true casm-add-pythonic-hints = true [scripts] test = "snforge test" # Visit https://foundry-rs.github.io/starknet-foundry/appendix/scarb-toml.html for more information # [tool.snforge] # Define `snforge` tool section # exit_first = true # Stop tests execution immediately upon the first failure # fuzzer_runs = 1234 # Number of runs of the random fuzzer # fuzzer_seed = 1111 # Seed for the random fuzzer # [[tool.snforge.fork]] # Used for fork testing # name = "SOME_NAME" # Fork name # url = "http://your.rpc.url" # Url of the RPC provider # block_id.tag = "latest" # Block to fork from (block tag) # [[tool.snforge.fork]] # name = "SOME_SECOND_NAME" # url = "http://your.second.rpc.url" # block_id.number = "123" # Block to fork from (block number) # [[tool.snforge.fork]] # name = "SOME_THIRD_NAME" # url = "http://your.third.rpc.url" # block_id.hash = "0x123" # Block to fork from (block hash) # [profile.dev.cairo] # Configure Cairo compiler # unstable-add-statements-code-locations-debug-info = true # Should be used if you want to use coverage # unstable-add-statements-functions-debug-info = true # Should be used if you want to use coverage/profiler # inlining-strategy = "avoid" # Should be used if you want to use coverage # [features] # Used for conditional compilation # enable_for_tests = [] # Feature name and list of other features that should be enabled with it ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_sequencer/snfoundry.toml ================================================ # Visit https://foundry-rs.github.io/starknet-foundry/appendix/snfoundry-toml.html # and https://foundry-rs.github.io/starknet-foundry/projects/configuration.html for more information # [sncast.default] # Define a profile name # url = "https://free-rpc.nethermind.io/sepolia-juno/v0_7" # Url of the RPC provider # accounts-file = "../account-file" # Path to the file with the account data # account = "mainuser" # Account from `accounts_file` or default account file that will be used for the transactions # keystore = "~/keystore" # Path to the keystore file # wait-params = { timeout = 300, retry-interval = 10 } # Wait for submitted transaction parameters # block-explorer = "StarkScan" # Block explorer service used to display links to transaction details # show-explorer-links = true # Print links pointing to pages with transaction details in the chosen block explorer [sncast.sepolia] account = "deployer" accounts-file = "./accounts.json" url = "https://starknet-sepolia.public.blastapi.io/rpc/v0_7" ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_sequencer/src/lib.cairo ================================================ #[starknet::interface] pub trait IFibonacciSequencer { fn verify_and_submit_fibonacci_number( ref self: TContractState, full_proof_with_hints: Span, ); } #[starknet::contract] mod FibonacciSequencer { use starknet::ClassHash; use starknet::storage::{StoragePointerReadAccess, StoragePointerWriteAccess}; pub const RISC_ZERO_VERIFIER_CLASS_HASH: felt252 = 0x41d5e111b93acbf1afb531253e0bc64d43f90a8a99290361e851ec0c4968ab1; #[storage] struct Storage { lower_bound: u32, } #[abi(embed_v0)] impl FibonacciSequencerImpl of super::IFibonacciSequencer { fn verify_and_submit_fibonacci_number( ref self: ContractState, full_proof_with_hints: Span, ) { // sets the class hash for the RiscZero verifier already declared on-chain // by the Garaga team let class_hash: ClassHash = RISC_ZERO_VERIFIER_CLASS_HASH.try_into().unwrap(); // instantiate a library dispatcher to perform the library call // to the RiscZero verifier class, given that verifying a proof is // a read-only operation let dispatcher = IRisc0Groth16VerifierBN254LibraryDispatcher { class_hash }; // calls the RiscZero verifier passing along the proof artifact and // checks whether the proof is valid or not, aborting the transaction if not let optional_journal = dispatcher.verify_r0_groth16_proof_bn254(full_proof_with_hints); assert(optional_journal != Option::None, 'Invalid proof'); // parses the public inputs and output from the journal let mut journal = optional_journal.unwrap(); let l = pop_front_u32_le(ref journal); let u = pop_front_u32_le(ref journal); let fib_n = pop_front_u32_le(ref journal); // performs the necessary state update check, updates the state, // and emits an event with the new fibnoacci number submitted // the smart contract invariant guarantees that every fiboacci number // accepted comes later in the fibonacci sequence without revealing // its index, which is trivial for monotonic sequences like fibnacci, // but would also work as expected also for non-monotonic ones let b = self.lower_bound.read(); assert(l >= b, 'Invalid lower bound'); self.lower_bound.write(u); self.emit(FibonnacciNumberSubmitted { n: fib_n }); self.emit(LowerBoundUpdated { n: u }); } } fn pop_front_u32_le(ref bytes: Span) -> u32 { let [b0, b1, b2, b3] = (*bytes.multi_pop_front::<4>().unwrap()).unbox(); let b0: u32 = b0.into(); let b1: u32 = b1.into(); let b2: u32 = b2.into(); let b3: u32 = b3.into(); b0 + 256 * (b1 + 256 * (b2 + 256 * b3)) } #[event] #[derive(Drop, starknet::Event)] enum Event { FibonnacciNumberSubmitted: FibonnacciNumberSubmitted, LowerBoundUpdated: LowerBoundUpdated, } #[derive(Drop, starknet::Event)] struct FibonnacciNumberSubmitted { #[key] n: u32, } #[derive(Drop, starknet::Event)] struct LowerBoundUpdated { #[key] n: u32, } #[starknet::interface] trait IRisc0Groth16VerifierBN254 { fn verify_r0_groth16_proof_bn254( self: @TContractState, full_proof_with_hints: Span, ) -> Option>; } } ================================================ FILE: src/contracts/risc0_sample_app/fibonacci_sequencer/tests/test_contract.cairo ================================================ use fibonacci_sequencer::{IFibonacciSequencerDispatcher, IFibonacciSequencerDispatcherTrait}; use snforge_std::{ContractClassTrait, DeclareResultTrait, declare}; use starknet::ContractAddress; fn deploy_contract(name: ByteArray) -> ContractAddress { let contract = declare(name).unwrap().contract_class(); let (contract_address, _) = contract.deploy(@ArrayTrait::new()).unwrap(); contract_address } #[test] #[fork(url: "https://starknet-sepolia.public.blastapi.io/rpc/v0_8", block_tag: latest)] fn test_using_forked_state() { let contract_address = deploy_contract("FibonacciSequencer"); let dispatcher = IFibonacciSequencerDispatcher { contract_address }; // Generated with // garaga calldata // --system groth16 // --proof src/contracts/risc0_sample_app/fibonacci_prover/proof.json // --vk hydra/garaga/starknet/groth16_contract_generator/examples/vk_risc0.json // --format array let calldata: Array = array![ 10313708969354158917967222113, 50267649714470381823581225990, 68921961243555163, 0, 46290583222980871151183921591, 4301093058224347754247855122, 1162760382227106560, 0, 24819230280640842784327799227, 29215605766976866277419122168, 1808142039149740796, 0, 39970134346975989818674078489, 3936215012720214372783898310, 2755310503244839950, 0, 10008210460600043468605009819, 5134088462908765651216846940, 548621717748290851, 0, 52073651593444857523464173785, 76173007636674752150960882367, 1989852830911987504, 0, 37843478955940902971626538675, 51487780532431296010323197290, 224964057096925175, 0, 52769853187791807058501612138, 18499899756995874154999451581, 2652790000201915092, 0, 8, 2053329358, 2206211296, 38805000, 4116461829, 1020971636, 3479402811, 2149017453, 1885829375, 12, 3, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 67110097341386670036774239297, 13427688709271065544749007076, 61998020686717975, 24950728289913553492905070844, 41338110835098902024801133866, 1926599594904525212, 49180962753194629969032522397, 18683289622619758709651796328, 2322548236816591081, 13777997333488195788972438786, 38195864551149721700102291303, 2096871835550112999, 57461822935248779146096669748, 63868881672888503510396685863, 2927643925868048643, 57882494364401687532204184645, 77064301337750944900057687182, 267580645098775586, 63832900139379554772626768003, 29079614675932695500868920547, 1697338607874777837, 13820245196087287279705420328, 45300240058713116745673941050, 2294499228727579498, 21764563697118840926227639154, 25188648591388018983369960932, 2953390198513702930, 7498684187777915752213167858, 55228804274201371180030455309, 2847354578579959092, 15435568331327776497941779773, 28893295361569522918496417700, 863647595501061687, 35302451000412228734699052367, 22457850952863143233325656339, 1401767062286425255, 51476042181496768465160915178, 10138610283257573438879144688, 1935188165376748165, 2607974614136254198207269069, 65923379203933185953178362077, 1736442677132969807, 28998805280904070766222869461, 71739253543289788494168851923, 1666168593466061290, 11598394446893917972904765463, 38368876867378744049854307764, 357609731026298670, 18381959417766430591221349706, 56568223146963862145607563003, 1653316243217612846, 1532011105146822016900691973, 49853661497349396119734430336, 128223370870951394, 74269898268093533317708905191, 6064542112071456493775622576, 897376613914460874, 65999414010440756273816590021, 31351058327199593499861985845, 2647438822048910788, 48205353039842416879228228410, 39166874119798698748815259789, 1963948305806486212, 78171073915930823358190752912, 42432726154597990157661008330, 502888311305518184, 71268398440539498978585013972, 13496144499382435728441052893, 1228680712056379000, 6744502773106524459562211501, 26234470583206688250660206108, 1869453274075343125, 0, 0, 0, 60184622296806572439997666907, 75008714795759192705677030670, 3262785094589981400, 0, 0, 0, 0, 0, 0, 50185732680358774463548804626, 10607397758555418006709821705, 1206124784999809577, 0, 0, 0, 35, 12360594968262131338834950053, 29157813032367243817624618064, 1249176918977039501, 4295852892538527433181634157, 32408611964222354943894990211, 3081069739022633520, 48008414502801231336586977304, 10695353845533787710119952480, 2461284468148709923, 41424670137457659138316034002, 22704208483523527472760209687, 366988915687364039, 17390414117185975115314456765, 19899765771554787204557749565, 2426644609974225253, 39168384437801305002828652709, 63995845102202908056262969347, 1231262696770817384, 79001875949392935046839734146, 67858923451040823945953945772, 1475081209791838033, 10449387844431475556675852647, 23115748550791645591068351732, 1715421325480013368, 44721182901846674225538961665, 64638199388846426866197918856, 898421411213295026, 55621973480014006124115532829, 13012389169361599871153984529, 3160472654674284962, 55508613442680258763935969213, 34746301440097605805226636186, 734918348439328496, 55736029307188839838515311861, 13731812987259286528859095281, 2282641966194969923, 20791395889687384125688119756, 6989397587960164917946580933, 1765451686580892148, 52406674109961525801961192114, 35821500349487483240557623463, 32470852909215135, 3953835811560950536563745592, 65737295267830154570147278118, 3230583914443581448, 55596875411839172693842327129, 94443789363036885006823824, 3336417763008413204, 52907783319647596216035183513, 54114917331759988367183704291, 1078863918351929539, 9743733652522201172278700788, 52747862860772113517684171279, 2106505140994262297, 54138378922280519909387645902, 59006165532860325511159562688, 2733912037122560096, 24830989612348935007812695331, 23111235460663267971948348557, 480020646269586667, 65561583184371514519437135483, 10855304295069896300987376868, 637290028443393757, 53593402770083338856380373435, 68128000340724951096820458371, 2302249138431258780, 16155562814866536950816994055, 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casm = true casm-add-pythonic-hints = true ================================================ FILE: src/contracts/universal_ecip/src/lib.cairo ================================================ use garaga::definitions::G1Point; #[starknet::interface] trait IUniversalECIP { fn msm_g1( self: @TContractState, points: Span, scalars: Span, curve_index: usize, msm_hint: Span, ) -> G1Point; } #[starknet::contract] mod UniversalECIP { use garaga::definitions::G1Point; use garaga::ec_ops::msm_g1; #[storage] struct Storage {} #[abi(embed_v0)] impl IUniversalECIP of super::IUniversalECIP { fn msm_g1( self: @ContractState, points: Span, scalars: Span, curve_index: usize, msm_hint: Span, ) -> G1Point { msm_g1(points, scalars, curve_index, msm_hint) } } } ================================================ FILE: src/corelib_imports/README.md ================================================ # Corelib Imports This package provides controlled access to non-public functions, structs, and traits from the Cairo Corelib library through selective re-exports. ## Overview The package leverages Cairo edition 2023_10 to access internal Cairo Corelib components that are not part of the standard public API. These utilities expose performance-critical operations for cryptographic computations, particularly optimized bounded integer arithmetic and circuit operations used throughout the Garaga ecosystem. ## Visibility Rules and Architecture Cairo's visibility system restricts access to internal modules by default. This package uses feature flags (e.g., `#[feature("bounded-int-utils")]`) to expose specific internal APIs that would otherwise be inaccessible. The approach follows established patterns in the Cairo ecosystem, similar to the [Stwo Cairo verifier's bounded integer utilities](https://github.com/starkware-libs/stwo-cairo/blob/a9cc98cc78f39e30a5aea71af7421a09f764df0a/stwo_cairo_verifier/crates/bounded_int/src/lib.cairo). ## Exported Modules ### `bounded_int` Re-exports core bounded integer utilities with compile-time guarantees: - `BoundedInt`: Type-safe integer arithmetic with compile-time bounds - `AddHelper`, `MulHelper`, `DivRemHelper`: Optimized arithmetic operations - `upcast`, `downcast`: Safe type conversions between integer bounds - `bounded_int_div_rem`: Efficient division with remainder operations ### `circuit` Circuit construction and optimization utilities: - `CircuitData`, `CircuitDefinition`: Circuit representation types - `u384`, `u96`: Extended precision integer types for cryptographic operations - `AddInputResult`: Circuit input accumulation - `conversions`: Specialized arithmetic helpers for multi-precision operations ### `integer` Extended integer operations: - `u128s_from_felt252`: Efficient felt252 to u128 conversion utilities - `U128sFromFelt252Result`: Result type for safe conversions ### `array` & `keccak` Utility functions: - `array_slice`: Efficient array slicing operations - `cairo_keccak`, `keccak_add_u256_be`: Keccak hash operations ## Usage Examples ### Bounded Integer Arithmetic ```cairo use corelib_imports::bounded_int::{BoundedInt, DivRemHelper, bounded_int_div_rem}; // Efficient division with compile-time bounds checking let result = bounded_int_div_rem(dividend, divisor); ``` ### Circuit Operations ```cairo use corelib_imports::circuit::conversions::{ DivRemU96By32, NZ_POW64_TYPED, POW32, UnitInt }; // High-precision arithmetic for cryptographic circuits let quotient = DivRemU96By32::div_rem(value, NZ_POW32_TYPED); ``` ### Type Conversions ```cairo use corelib_imports::bounded_int::{downcast, upcast}; use corelib_imports::integer::{u128s_from_felt252}; // Safe conversions between integer types let converted = upcast(bounded_value); let (low, high) = u128s_from_felt252(felt_value); ``` These utilities are extensively used across Garaga's elliptic curve operations, finite field arithmetic, and cryptographic circuit implementations for optimal performance. ================================================ FILE: src/corelib_imports/Scarb.toml ================================================ [package] name = "corelib_imports" version = "0.1.3" edition = "2023_10" description = "Useful Corelib non-public functions, structs, and traits made public and re-exported through 2023_10 edition" readme = "README.md" repository = "https://github.com/keep-starknet-strange/garaga/tree/main/src/corelib_imports" authors = ["feltroidprime"] [lib] [dependencies] [dev-dependencies] cairo_test = "2.16.1" ================================================ FILE: src/corelib_imports/src/lib.cairo ================================================ pub mod array { pub use core::array::array_slice; } pub mod integer { pub use core::integer::{U128sFromFelt252Result, u128s_from_felt252}; } pub mod keccak { pub use core::keccak::{cairo_keccak, keccak_add_u256_be}; } pub mod bounded_int { #[feature("bounded-int-utils")] pub use core::internal::bounded_int; #[feature("bounded-int-utils")] pub use core::internal::bounded_int::{ AddHelper, BoundedInt, DivRemHelper, MulHelper, UnitInt, bounded_int_div_rem, downcast, upcast, }; } pub mod circuit { pub use core::circuit::{ AddInputResult, CircuitData, CircuitDefinition, CircuitInputAccumulator, IntoCircuitInputValue, U96Guarantee, add_circuit_input, init_circuit_data, into_u96_guarantee, u384, u96, }; pub mod conversions { pub use core::circuit::conversions::{ AddHelperTo128By64Impl, AddHelperTo128By96Impl, AddHelperTo96By32Impl, DivRemU128By64, DivRemU128By96, DivRemU96By32, DivRemU96By64, MulHelper32By96Impl, MulHelper64By32Impl, MulHelper64By64Impl, NZ_POW32_TYPED, NZ_POW64_TYPED, NZ_POW96_TYPED, POW32, POW32_TYPED, POW64, POW64_TYPED, POW96_TYPED, UnitInt, felt252_try_into_two_u96, two_u96_into_felt252, upcast, }; } } ================================================ FILE: src/src/apps/drand.cairo ================================================ use core::circuit::{ CircuitElement, CircuitInput, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, u96, }; use core::num::traits::Zero; use core::sha256::compute_sha256_u32_array; use garaga::basic_field_ops::{is_even_u384, u32_8_to_u384, u512_mod_p}; use garaga::circuits::ec::{run_ADD_EC_POINT_circuit, run_CLEAR_COFACTOR_BLS12_381_circuit}; use garaga::circuits::isogeny::run_BLS12_381_APPLY_ISOGENY_BLS12_381_circuit; use garaga::core::circuit::AddInputResultTrait2; use garaga::definitions::{ BLS_G2_GENERATOR, G1Point, G2Point, deserialize_u384, get_BLS12_381_modulus, serialize_u384, }; use garaga::ec_ops_g2; use garaga::single_pairing_tower::{final_exp_bls12_381_tower, miller_loop_bls12_381_tower}; // Chain: 52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971 // Public Key: // G2Point(x=(2020076495541918814736776030432697997716141464538799718886374996015782362070437455929656164150586936230283253179482, // 586231829158603972936263795113906716025771067144631327612230935308837823978471744132589153452744931590357767971921), // y=(1791278522428100783277199431487181031376873968689022069271761201187685493801088467849610331824611383166297460070456, // 3748041376541174045371877684805027382480271890984968787916314231755985669195299696440090936404461850913289003455520), // curve_id=) // Period: 3 seconds // Genesis Time: 1692803367 // Hash: 52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971 // Group Hash: f477d5c89f21a17c863a7f937c6a6d15859414d2be09cd448d4279af331c5d3e // Scheme ID: bls-unchained-g1-rfc9380 // Beacon ID: quicknet // ---------------------------------------- // Note : Negated to use in pairing check. pub const DRAND_QUICKNET_PUBLIC_KEY: G2Point = G2Point { x0: u384 { limb0: 0x4bc09e76eae8991ef5ece45a, limb1: 0xbd274ca73bab4af5a6e9c76a, limb2: 0x3aaf4bcb5ed66304de9cf809, limb3: 0xd1fec758c921cc22b0e17e6, }, x1: u384 { limb0: 0x6a0a6c3ac6a5776a2d106451, limb1: 0xb90022d3e760183c8c4b450b, limb2: 0xcad3912212c437e0073e911f, limb3: 0x3cf0f2896adee7eb8b5f01f, }, y0: u384 { limb0: 0xdfd038b83dbad4e0fbae5838, limb1: 0x942ea644bed4152aa6d85248, limb2: 0x43812423f8525883c7e472fa, limb3: 0xba35f3379c4e4d1e3a70b08, }, y1: u384 { limb0: 0xd9aa8e74b5823224c149d420, limb1: 0x1851f5129301fe6603fc716a, limb2: 0x9b84512e61a5e814e923569d, limb3: 0x1859fcf74bc8a580a828f6e0, }, }; pub const DRAND_QUICKNET_GENESIS_TIME: u64 = 1692803367; pub const DRAND_QUICKNET_PERIOD: u64 = 3; const a_iso_swu: u384 = u384 { limb0: 0xa0e0f97f5cf428082d584c1d, limb1: 0xd8e8981aefd881ac98936f8d, limb2: 0xc96d4982b0ea985383ee66a8, limb3: 0x144698a3b8e9433d693a02, }; const b_iso_swu: u384 = u384 { limb0: 0x316ceaa5d1cc48e98e172be0, limb1: 0xa0b9c14fcef35ef55a23215a, limb2: 0x753eee3b2016c1f0f24f4070, limb3: 0x12e2908d11688030018b12e8, }; const z_iso_swu: u384 = u384 { limb0: 11, limb1: 0, limb2: 0, limb3: 0 }; const NZ_POW2_32_64: NonZero = 0x100000000; // lib_str + bytes([0]) + dst_prime // LIB_DST = b'\x00\x80\x00BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_+' // bytes len : 47. const LIB_DST: [u32; 11] = [ 0x800042, 0x4c535f53, 0x49475f42, 0x4c533132, 0x33383147, 0x315f584d, 0x443a5348, 0x412d3235, 0x365f5353, 0x57555f52, 0x4f5f4e55, ]; const LIB_DST_LAST_WORD: u32 = 0x4c5f2b; const I_DST_PRIME: [u32; 10] = [ 0x5f534947, 0x5f424c53, 0x31323338, 0x3147315f, 0x584d443a, 0x5348412d, 0x3235365f, 0x53535755, 0x5f524f5f, 0x4e554c5f, ]; const I_DST_PRIME_LAST_WORD: u32 = 0x2b; fn get_i_dst_prime_first_word(i: usize) -> u32 { return i.into() * 0x1000000 + 0x424c53; } // Used in drand verifier contract. #[derive(Drop, Serde)] pub struct DrandResult { pub round_number: u64, pub randomness: felt252, } #[derive(Drop)] pub struct MapToCurveHint { pub gx1_is_square: bool, pub y1: u384, pub y_flag: bool // true if y and u have same parity, false otherwise } pub impl MapToCurveHintSerde of Serde { fn serialize(self: @MapToCurveHint, ref output: Array) { Serde::::serialize(self.gx1_is_square, ref output); serialize_u384(self.y1, ref output); Serde::::serialize(self.y_flag, ref output); } fn deserialize(ref serialized: Span) -> Option { let gx1_is_square = Serde::::deserialize(ref serialized); let y1 = deserialize_u384(ref serialized); let y_flag = Serde::::deserialize(ref serialized); return Option::Some( MapToCurveHint { gx1_is_square: gx1_is_square.unwrap(), y1: y1, y_flag: y_flag.unwrap(), }, ); } } #[derive(Drop, Serde)] pub struct HashToCurveHint { pub f0_hint: MapToCurveHint, pub f1_hint: MapToCurveHint, } // Like hash to curve but we start with the drand round number for simplicity. pub fn round_to_curve_bls12_381(round: u64, hash_to_curve_hint: HashToCurveHint) -> G1Point { let message = round_to_message(round); return hash_to_curve_bls12_381(message, hash_to_curve_hint); } #[inline] pub fn hash_to_curve_bls12_381(message: [u32; 8], hash_to_curve_hint: HashToCurveHint) -> G1Point { let (felt0, felt1) = hash_to_two_bls_felts(message); let pt0 = map_to_curve(felt0, hash_to_curve_hint.f0_hint); let pt1 = map_to_curve(felt1, hash_to_curve_hint.f1_hint); let modulus = get_BLS12_381_modulus(); let (sum) = run_ADD_EC_POINT_circuit(pt0, pt1, modulus); let (sum) = run_BLS12_381_APPLY_ISOGENY_BLS12_381_circuit(sum); // clear cofactor : let (res) = run_CLEAR_COFACTOR_BLS12_381_circuit(sum, modulus); return res; } // x = BLS seed // n = BLS12_381 EC prime order subgroup // cofactor = (1 - (x % n)) % n // const bls_cofactor: u128 = 0xd201000000010001; pub const BLS_COFACTOR_EPNS: (felt252, felt252, felt252, felt252) = ( 12124305939094075449, 3008070283847567304, 1, -1, ); pub const BLS_COFACTOR: u128 = 0xd201000000010001; // "digest function" pub fn round_to_message(round: u64) -> [u32; 8] { let (high, low) = DivRem::div_rem(round, NZ_POW2_32_64); let mut array: Array = array![]; array.append(high.try_into().unwrap()); array.append(low.try_into().unwrap()); return compute_sha256_u32_array(input: array, last_input_word: 0, last_input_num_bytes: 0); } #[inline] fn xor_u32_array_8(a: [u32; 8], b: [u32; 8]) -> [u32; 8] { let [a0, a1, a2, a3, a4, a5, a6, a7] = a; let [b0, b1, b2, b3, b4, b5, b6, b7] = b; return [a0 ^ b0, a1 ^ b1, a2 ^ b2, a3 ^ b3, a4 ^ b4, a5 ^ b5, a6 ^ b6, a7 ^ b7]; } #[inline] fn xor_u32_array_4(a: [u32; 4], b: [u32; 4]) -> [u32; 4] { let [a0, a1, a2, a3] = a; let [b0, b1, b2, b3] = b; return [a0 ^ b0, a1 ^ b1, a2 ^ b2, a3 ^ b3]; } const POW_2_32: u128 = 0x100000000; const POW_2_64: u128 = 0x10000000000000000; const POW_2_96: u128 = 0x1000000000000000000000000; fn u32_array_to_u256(d: [u32; 8]) -> u256 { let [d0, d1, d2, d3, d4, d5, d6, d7] = d; let high: felt252 = d0.into() * POW_2_96.into() + d1.into() * POW_2_64.into() + d2.into() * POW_2_32.into() + d3.into(); let low: felt252 = d4.into() * POW_2_96.into() + d5.into() * POW_2_64.into() + d6.into() * POW_2_32.into() + d7.into(); return u256 { low: low.try_into().unwrap(), high: high.try_into().unwrap() }; } fn hash_to_two_bls_felts(message: [u32; 8]) -> (u384, u384) { let mut array: Array = array![]; // Pad with 64 0-bytes. In u32, this is 64 / 4 = 16 elements. // "Z_padd" array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); array.append(0); // msg. 8*4 = 32 bytes for v in message.span() { array.append(*v); } // LIB_DST 47 bytes for v in LIB_DST.span() { array.append(*v); } // Total : 64 + 32 + 47 = 143 bytes = 1144 bits. let b0 = compute_sha256_u32_array( input: array, last_input_word: LIB_DST_LAST_WORD, last_input_num_bytes: 3, ); let mut array: Array = array![]; for v in b0.span() { array.append(*v); } array.append(get_i_dst_prime_first_word(1)); for v in I_DST_PRIME.span() { array.append(*v); } let bi = compute_sha256_u32_array( input: array, last_input_word: I_DST_PRIME_LAST_WORD, last_input_num_bytes: 1, ); let bi_xor_b0 = xor_u32_array_8(bi, b0); let mut array: Array = array![]; for v in bi_xor_b0.span() { array.append(*v); } array.append(get_i_dst_prime_first_word(2)); for v in I_DST_PRIME.span() { array.append(*v); } let bi_1 = compute_sha256_u32_array(array, I_DST_PRIME_LAST_WORD, 1); let bi1_xor_b0 = xor_u32_array_8(bi_1, b0); let mut array: Array = array![]; for v in bi1_xor_b0.span() { array.append(*v); } array.append(get_i_dst_prime_first_word(3)); for v in I_DST_PRIME.span() { array.append(*v); } let bi_2 = compute_sha256_u32_array(array, I_DST_PRIME_LAST_WORD, 1); let bi2_xor_b0 = xor_u32_array_8(bi_2, b0); let mut array: Array = array![]; for v in bi2_xor_b0.span() { array.append(*v); } array.append(get_i_dst_prime_first_word(4)); for v in I_DST_PRIME.span() { array.append(*v); } let bi_3 = compute_sha256_u32_array(array, I_DST_PRIME_LAST_WORD, 1); let modulus = get_BLS12_381_modulus(); return ( u512_mod_p(u32_8_to_u384(bi), u32_8_to_u384(bi_1), modulus), u512_mod_p(u32_8_to_u384(bi_2), u32_8_to_u384(bi_3), modulus), ); } fn map_to_curve(_u: u384, hint: MapToCurveHint) -> G1Point { let (neg_ta, num_x1) = map_to_curve_inner_1(_u); let (gx1, div) = map_to_curve_inner_2(neg_ta, num_x1); match hint.gx1_is_square { true => map_to_curve_inner_final_quad_res(num_x1, gx1, hint.y1, hint.y_flag, div, _u), false => map_to_curve_inner_final_not_quad_res(num_x1, hint.y1, hint.y_flag, div, _u, gx1), } } fn map_to_curve_inner_1(_u: u384) -> (u384, u384) { let z = CircuitElement::> {}; let u = CircuitElement::> {}; let zero = CircuitElement::> {}; let one = CircuitElement::> {}; let b = CircuitElement::> {}; let u2 = circuit_mul(u, u); let zeta_u2 = circuit_mul(z, u2); let zeta_u2_square = circuit_mul(zeta_u2, zeta_u2); let ta = circuit_add(zeta_u2_square, zeta_u2); let neg_ta = circuit_sub(zero, ta); let num_x1 = circuit_mul(b, circuit_add(ta, one)); let modulus = TryInto::< _, CircuitModulus, >::try_into( [ 0xb153ffffb9feffffffffaaab, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ) .unwrap(); // BLS12_381 prime field modulus let outputs = (neg_ta, num_x1) .new_inputs() .next_2(z_iso_swu) .next_2(_u) .next_2([0, 0, 0, 0]) .next_2([1, 0, 0, 0]) .next_2(b_iso_swu) .done_2() .eval(modulus) .unwrap(); return (outputs.get_output(neg_ta), outputs.get_output(num_x1)); } fn map_to_curve_inner_2(_neg_ta: u384, _num_x1: u384) -> (u384, u384) { let neg_ta_or_z = CircuitElement::> {}; let a = CircuitElement::> {}; let b = CircuitElement::> {}; // let quad_res_correction = CircuitElement::> {}; // let y1_hint = CircuitElement::> {}; let num_x1 = CircuitElement::> {}; // let zeta_u2 = CircuitElement::> {}; // let u = CircuitElement::> {}; let div = circuit_mul(a, neg_ta_or_z); let num2_x1 = circuit_mul(num_x1, num_x1); let div2 = circuit_mul(div, div); let div3 = circuit_mul(div2, div); // num_gx1 = (num2_x1 + a * div2) * num_x1 + b * div3 let num_gx1 = circuit_add( circuit_mul(circuit_add(num2_x1, circuit_mul(a, div2)), num_x1), circuit_mul(b, div3), ); // let num_x2 = circuit_mul(zeta_u2, num_x1); let gx1 = circuit_mul(num_gx1, circuit_inverse(div3)); // let gx1_quad_res = circuit_mul(gx1, quad_res_correction); // let check = circuit_sub(gx1_quad_res, circuit_mul(y1_hint, y1_hint)); // let y2 = circuit_mul(zeta_u2, circuit_mul(u, y1_hint)); let _neg_ta_or_z = match _neg_ta.is_zero() { true => z_iso_swu, false => _neg_ta, }; // let _quad_res_correction = match hint.gx1_is_square { // true => u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0, }, // false => z_iso_swu, // }; let modulus = TryInto::< _, CircuitModulus, >::try_into( [ 0xb153ffffb9feffffffffaaab, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ) .unwrap(); // BLS12_381 prime field modulus let outputs = (gx1, div) .new_inputs() .next_2(_neg_ta_or_z) .next_2(a_iso_swu) .next_2(b_iso_swu) .next_2(_num_x1) .done_2() .eval(modulus) .unwrap(); return (outputs.get_output(gx1), outputs.get_output(div)); } fn map_to_curve_inner_final_quad_res( _num_x1: u384, _gx1: u384, _y1_hint: u384, __parity_flag: bool, _div: u384, u: u384, ) -> G1Point { let num_x1 = CircuitElement::> {}; let gx1 = CircuitElement::> {}; let y1_hint = CircuitElement::> {}; let parity_flag = CircuitElement::> {}; let div = CircuitElement::> {}; let check = circuit_sub(gx1, circuit_mul(y1_hint, y1_hint)); let x_affine = circuit_mul(num_x1, circuit_inverse(div)); let y_affine = circuit_mul(parity_flag, y1_hint); let modulus = TryInto::< _, CircuitModulus, >::try_into( [ 0xb153ffffb9feffffffffaaab, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ) .unwrap(); // BLS12_381 prime field modulus // Flag = -1 if y%2 !=u%1 ; 1 if y%2 == u%2. let _parity_flag: u384 = match __parity_flag { true => u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, false => crate::definitions::get_min_one(curve_index: 1), }; let outputs = (x_affine, y_affine, check) .new_inputs() .next_2(_num_x1) .next_2(_gx1) .next_2(_y1_hint) .next_2(_parity_flag) .next_2(_div) .done_2() .eval(modulus) .unwrap(); let chk = outputs.get_output(check); assert(chk == Zero::zero(), 'm2cI wrong square root'); // Verify parity. base is even so high parts doesn't affect parity. // (l0 + l1*2^b + l2*2^2b + l3*2^3b % 2 // l0 % 2 + (l1 % 2)*2^b % 2 + (l2 % 2)*2^2b % 2 + (l3 % 2)*2^3b % 2 // 2^b = 0 for all b>=1 // so u384 % 2 = limb0 % 2. match __parity_flag { true => assert(is_even_u384(_y1_hint) == is_even_u384(u), 'm2cI wrong parity'), false => assert(is_even_u384(_y1_hint) != is_even_u384(u), 'm2cI wrong parity'), } return G1Point { x: outputs.get_output(x_affine), y: outputs.get_output(y_affine) }; } fn map_to_curve_inner_final_not_quad_res( _num_x1: u384, _y1_hint: u384, __parity_flag: bool, _div: u384, _u: u384, _gx1: u384, ) -> G1Point { let num_x1 = CircuitElement::> {}; let y1_hint = CircuitElement::> {}; let parity_flag = CircuitElement::> {}; let div = CircuitElement::> {}; let u = CircuitElement::> {}; let gx1 = CircuitElement::> {}; let z = CircuitElement::> {}; let u2 = circuit_mul(u, u); let zeta_u2 = circuit_mul(z, u2); let gx1_quad_res = circuit_mul(gx1, z); let check = circuit_sub(gx1_quad_res, circuit_mul(y1_hint, y1_hint)); let y2 = circuit_mul(zeta_u2, circuit_mul(u, y1_hint)); let num_x = circuit_mul(zeta_u2, num_x1); let x_affine = circuit_mul(num_x, circuit_inverse(div)); let y_affine = circuit_mul(parity_flag, y2); // Flag = -1 if y%2 !=u%1 ; 1 if y%2 == u%2. let _parity_flag: u384 = match __parity_flag { true => u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, false => crate::definitions::get_min_one(curve_index: 1), }; let modulus = TryInto::< _, CircuitModulus, >::try_into( [ 0xb153ffffb9feffffffffaaab, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ) .unwrap(); // BLS12_381 prime field modulus let outputs = (x_affine, y_affine, check) .new_inputs() .next_2(_num_x1) .next_2(_y1_hint) .next_2(_parity_flag) .next_2(_div) .next_2(_u) .next_2(_gx1) .next_2(z_iso_swu) .done_2() .eval(modulus) .unwrap(); let chk = outputs.get_output(check); assert(chk == Zero::zero(), 'm2cII wrong square root'); // Verify parity. base is even so high parts doesn't affect parity. match __parity_flag { true => assert( is_even_u384(outputs.get_output(y2)) == is_even_u384(_u), 'm2cI wrong parity', ), false => assert( is_even_u384(outputs.get_output(y2)) != is_even_u384(_u), 'm2cI wrong parity', ), } return G1Point { x: outputs.get_output(x_affine), y: outputs.get_output(y_affine) }; } // The result of a timelock encryption over drand quicknet. #[derive(Drop, Serde)] pub struct CipherText { pub U: G2Point, pub V: [u8; 16], pub W: [u8; 16], } // bytes("IBE-H2") (4 + 2 bytes) const IBE_H2: [u32; 2] = [0x4942452d, 0x4832]; // bytes("IBE-H4") (4 + 2 bytes) const IBE_H4: [u32; 2] = [0x4942452d, 0x4834]; const IBE_H3: [u32; 2] = [0x4942452d, 0x4833]; use corelib_imports::bounded_int::{BoundedInt, DivRemHelper, bounded_int_div_rem}; use corelib_imports::circuit::conversions::{ DivRemU96By32, DivRemU96By64, NZ_POW32_TYPED, NZ_POW64_TYPED, POW32, POW64, UnitInt, }; const POW80: felt252 = 0x100000000000000000000; const NZ_POW80_TYPED: NonZero> = 0x100000000000000000000; const POW16: felt252 = 0x10000; const NZ_POW16_TYPED: NonZero> = 0x10000; const POW48: felt252 = 0x1000000000000; const NZ_POW48_TYPED: NonZero> = 0x1000000000000; const POW24: felt252 = 0x1000000; const POW8: felt252 = 0x100; type u64_bi = BoundedInt<0, { POW64 - 1 }>; type u80_bi = BoundedInt<0, { POW80 - 1 }>; type u48_bi = BoundedInt<0, { POW48 - 1 }>; type u32_bi = BoundedInt<0, { POW32 - 1 }>; impl DivRemU64By32 of DivRemHelper> { type DivT = BoundedInt<0, { POW32 - 1 }>; type RemT = BoundedInt<0, { POW32 - 1 }>; } impl DivRemU96By80 of DivRemHelper> { type DivT = BoundedInt<0, { POW16 - 1 }>; type RemT = BoundedInt<0, { POW80 - 1 }>; } impl DivRemU80By48 of DivRemHelper> { type DivT = BoundedInt<0, { POW32 - 1 }>; type RemT = BoundedInt<0, { POW48 - 1 }>; } impl DivRemU48By16 of DivRemHelper> { type DivT = BoundedInt<0, { POW32 - 1 }>; type RemT = BoundedInt<0, { POW16 - 1 }>; } impl DivRemU32By16 of DivRemHelper> { type DivT = BoundedInt<0, { POW16 - 1 }>; type RemT = BoundedInt<0, { POW16 - 1 }>; } #[inline(always)] pub fn append_u96_to_u32_array(ref array: Array, u: u96) { let (u32_h, u64_l): (DivRemU96By64::DivT, DivRemU96By64::RemT) = bounded_int_div_rem( u, NZ_POW64_TYPED, ); let (u32_mid, u32_low): (DivRemU64By32::DivT, DivRemU64By32::RemT) = bounded_int_div_rem( u64_l, NZ_POW32_TYPED, ); let u32_hf: felt252 = u32_h.into(); let u32_mf: felt252 = u32_mid.into(); let u32_lf: felt252 = u32_low.into(); array.append(u32_hf.try_into().unwrap()); array.append(u32_mf.try_into().unwrap()); array.append(u32_lf.try_into().unwrap()); } #[inline] pub fn append_u384_be_to_u32_array(ref array: Array, u: u384) { append_u96_to_u32_array(ref array, u.limb3); append_u96_to_u32_array(ref array, u.limb2); append_u96_to_u32_array(ref array, u.limb1); append_u96_to_u32_array(ref array, u.limb0); } const NZ_POW24_32: NonZero = 0x1000000; const NZ_POW16_32: NonZero = 0x10000; const NZ_POW8_32: NonZero = 0x100; #[inline(always)] pub fn u32_to_u8_4(a: u32) -> [u8; 4] { let (b3, r) = DivRem::div_rem(a, NZ_POW24_32); let (b2, r) = DivRem::div_rem(r, NZ_POW16_32); let (b1, b0) = DivRem::div_rem(r, NZ_POW8_32); return [ b3.try_into().unwrap(), b2.try_into().unwrap(), b1.try_into().unwrap(), b0.try_into().unwrap(), ]; } #[inline(always)] pub fn u32_4_to_u8_16(a: [u32; 4]) -> [u8; 16] { let [a3, a2, a1, a0] = a; let [b15, b14, b13, b12] = u32_to_u8_4(a3); let [b11, b10, b9, b8] = u32_to_u8_4(a2); let [b7, b6, b5, b4] = u32_to_u8_4(a1); let [b3, b2, b1, b0] = u32_to_u8_4(a0); return [b15, b14, b13, b12, b11, b10, b9, b8, b7, b6, b5, b4, b3, b2, b1, b0]; } #[inline(always)] pub fn append_u96_with_pending_u16(ref array: Array, pending_u16: u32, u: u96) -> u32 { let (u16_h, u80_l): (DivRemU96By80::DivT, DivRemU96By80::RemT) = bounded_int_div_rem( u, NZ_POW80_TYPED, ); let (u32_mid, u48_low): (DivRemU80By48::DivT, DivRemU80By48::RemT) = bounded_int_div_rem( u80_l, NZ_POW48_TYPED, ); let (u32_low, u16_low): (DivRemU48By16::DivT, DivRemU48By16::RemT) = bounded_int_div_rem( u48_low, NZ_POW16_TYPED, ); let u16_hf: felt252 = u16_h.into(); let u32_mf: felt252 = u32_mid.into(); let u32_lf: felt252 = u32_low.into(); let next_u16_pending: felt252 = u16_low.into(); array.append((pending_u16.into() * POW16 + u16_hf).try_into().unwrap()); array.append(u32_mf.try_into().unwrap()); array.append(u32_lf.try_into().unwrap()); return next_u16_pending.try_into().unwrap(); } #[inline(always)] pub fn append_u32_with_pending_u16(ref array: Array, pending_u16: u32, u: u32) -> u32 { let (u16_h, next_pending) = DivRem::div_rem(u, NZ_POW16_32); let u16_hf: felt252 = u16_h.into(); array.append((pending_u16.into() * POW16 + u16_hf).try_into().unwrap()); return next_pending; } pub fn append_u384_with_pending_u16(ref array: Array, pending_u16: u32, u: u384) -> u32 { let pending_u16 = append_u96_with_pending_u16(ref array, pending_u16, u.limb3); let pending_u16 = append_u96_with_pending_u16(ref array, pending_u16, u.limb2); let pending_u16 = append_u96_with_pending_u16(ref array, pending_u16, u.limb1); let pending_u16 = append_u96_with_pending_u16(ref array, pending_u16, u.limb0); return pending_u16; } pub fn u8_16_to_u32_4(a: [u8; 16]) -> [u32; 4] { let [a15, a14, a13, a12, a11, a10, a9, a8, a7, a6, a5, a4, a3, a2, a1, a0] = a; let w3: felt252 = a15.into() * POW24 + a14.into() * POW16 + a13.into() * POW8 + a12.into(); let w2: felt252 = a11.into() * POW24 + a10.into() * POW16 + a9.into() * POW8 + a8.into(); let w1: felt252 = a7.into() * POW24 + a6.into() * POW16 + a5.into() * POW8 + a4.into(); let w0: felt252 = a3.into() * POW24 + a2.into() * POW16 + a1.into() * POW8 + a0.into(); return [ w3.try_into().unwrap(), w2.try_into().unwrap(), w1.try_into().unwrap(), w0.try_into().unwrap(), ]; } pub fn decrypt_at_round(signature_at_round: G1Point, ciphertext: CipherText) -> [u8; 16] { let (M) = miller_loop_bls12_381_tower(signature_at_round, ciphertext.U); let rgid = final_exp_bls12_381_tower(M); let mut array: Array = array![]; let [ibe_h2_0, ibe_h2_1] = IBE_H2; array.append(ibe_h2_0); let pending = append_u384_with_pending_u16(ref array, ibe_h2_1, rgid.c1b2a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c1b2a0); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c1b1a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c1b1a0); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c1b0a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c1b0a0); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b2a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b2a0); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b1a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b1a0); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b0a1); let pending = append_u384_with_pending_u16(ref array, pending, rgid.c0b0a0); let [r7, r6, r5, r4, _, _, _, _] = compute_sha256_u32_array( input: array, last_input_word: pending, last_input_num_bytes: 2, ); let v: [u32; 4] = u8_16_to_u32_4(ciphertext.V); let sigma: [u32; 4] = xor_u32_array_4([r7, r6, r5, r4], v); let mut array: Array = array![]; let [ibe_h4_0, ibe_h4_1] = IBE_H4; array.append(ibe_h4_0); let [s3, s2, s1, s0] = sigma; let pending = append_u32_with_pending_u16(ref array, ibe_h4_1, s3); let pending = append_u32_with_pending_u16(ref array, pending, s2); let pending = append_u32_with_pending_u16(ref array, pending, s1); let pending = append_u32_with_pending_u16(ref array, pending, s0); let [sh7, sh6, sh5, sh4, _, _, _, _] = compute_sha256_u32_array( input: array, last_input_word: pending, last_input_num_bytes: 2, ); let w = u8_16_to_u32_4(ciphertext.W); let message: [u32; 4] = xor_u32_array_4([sh7, sh6, sh5, sh4], w); let [m3, m2, m1, m0] = message; // Convert to bytes : let message_bytes = u32_4_to_u8_16(message); // Verify U = G^R let mut array: Array = array![]; let [ibe_h3_0, ibe_h3_1] = IBE_H3; array.append(ibe_h3_0); // Append sigma let pending = append_u32_with_pending_u16(ref array, ibe_h3_1, s3); let pending = append_u32_with_pending_u16(ref array, pending, s2); let pending = append_u32_with_pending_u16(ref array, pending, s1); let pending = append_u32_with_pending_u16(ref array, pending, s0); // Append message : let pending = append_u32_with_pending_u16(ref array, pending, m3); let pending = append_u32_with_pending_u16(ref array, pending, m2); let pending = append_u32_with_pending_u16(ref array, pending, m1); let pending = append_u32_with_pending_u16(ref array, pending, m0); // Little endian let rh = compute_sha256_u32_array( input: array, last_input_word: pending, last_input_num_bytes: 2, ); let mut i = 1; let mut r = expand_message_drand(rh, i); // r must be non-zero: while r == 0 { i += 1; let _r = expand_message_drand(rh, i); r = _r; } let U = ec_ops_g2::ec_mul(BLS_G2_GENERATOR, r, 1).unwrap(); assert(U == ciphertext.U, 'Incorrect ciphertext proof.'); return message_bytes; } pub fn expand_message_drand(msg: [u32; 8], i: u8) -> u256 { let mut array: Array = array![]; let [m7, m6, m5, m4, m3, m2, m1, m0] = msg; // i.to_bytes(2, byteorder="little") let pending = append_u32_with_pending_u16(ref array, i.into() * 0x100, m7); let pending = append_u32_with_pending_u16(ref array, pending, m6); let pending = append_u32_with_pending_u16(ref array, pending, m5); let pending = append_u32_with_pending_u16(ref array, pending, m4); let pending = append_u32_with_pending_u16(ref array, pending, m3); let pending = append_u32_with_pending_u16(ref array, pending, m2); let pending = append_u32_with_pending_u16(ref array, pending, m1); let pending = append_u32_with_pending_u16(ref array, pending, m0); let hash_result = compute_sha256_u32_array( input: array, last_input_word: pending, last_input_num_bytes: 2, ); let [r0, r1, r2, r3, r4, r5, r6, r7] = hash_result; // Mask the first byte of r0 // Extract the leftmost byte let first_byte = r0 & 0xFF000000; // Right shift the first byte by 1 bit let shifted_byte = first_byte / 2; // Combine the shifted byte back with the rest of r0 let r0 = shifted_byte | (r0 & 0x00FFFFFF); return hash_to_u256([r0, r1, r2, r3, r4, r5, r6, r7]); } pub fn hash_to_u256(msg: [u32; 8]) -> u256 { let [a, b, c, d, e, f, g, h] = msg; let low: u128 = h.into() + g.into() * POW_2_32 + f.into() * POW_2_64 + e.into() * POW_2_96; let high: u128 = d.into() + c.into() * POW_2_32 + b.into() * POW_2_64 + a.into() * POW_2_96; u256 { low: low, high: high } } pub fn timestamp_to_round(timestamp: u64) -> u64 { // If timestamp is before genesis, return 0 (no round has started yet) if timestamp < DRAND_QUICKNET_GENESIS_TIME { return 0; } let elapsed_time: u64 = timestamp - DRAND_QUICKNET_GENESIS_TIME; return (elapsed_time / DRAND_QUICKNET_PERIOD) + 1; } pub fn round_to_timestamp(round: u64) -> u64 { // Round 0 is invalid if round == 0 { return 0; } // Calculate timestamp: genesis + (round-1) * period // We subtract 1 from the round because round 1 starts at genesis return DRAND_QUICKNET_GENESIS_TIME + ((round - 1) * DRAND_QUICKNET_PERIOD); } #[cfg(test)] mod tests { use garaga::ec_ops_g2::G2PointTrait; use super::{ CipherText, DRAND_QUICKNET_PUBLIC_KEY, G1Point, G2Point, HashToCurveHint, MapToCurveHint, decrypt_at_round, hash_to_curve_bls12_381, hash_to_two_bls_felts, map_to_curve, run_BLS12_381_APPLY_ISOGENY_BLS12_381_circuit, u384, }; #[test] fn test_drand_quicknet_public_key() { DRAND_QUICKNET_PUBLIC_KEY.assert_in_subgroup_excluding_infinity(1); } #[test] fn test_hash_to_two_bls_felts() { // sha256("Hello, World!") let message: [u32; 8] = [ 0xdffd6021, 0xbb2bd5b0, 0xaf676290, 0x809ec3a5, 0x3191dd81, 0xc7f70a4b, 0x28688a36, 0x2182986f, ]; let (a, b) = hash_to_two_bls_felts(message); assert_eq!( a, u384 { limb0: 0x3424dff585d947fedf210456, limb1: 0xd67576428da87a9356340b2e, limb2: 0x135e368f3927494b3933a985, limb3: 0x85a31dc6b81af709df9ba4e, }, ); assert_eq!( b, u384 { limb0: 0xdb509060a0293b7d9e20ae9, limb1: 0x189ad7a1508b89604e165848, limb2: 0x74a42a64a63d7c9dd6bfec2c, limb3: 0x1049922d5dcd716806ccfa3e, }, ); } #[test] fn test_map_to_curve() { let u = u384 { limb0: 42, limb1: 0x0, limb2: 0x0, limb3: 0x0 }; let expected = G1Point { x: u384 { limb0: 0x1c94f3121ca3e1454e60bded, limb1: 0xe09a5f66977f922ae74baf50, limb2: 0xa471b958de9a5099a84aca44, limb3: 0x923f1e3115dc78a457fffa1, }, y: u384 { limb0: 0xaa8806e6b469554a91758ec, limb1: 0xdbfb03df4a53a534ac80def7, limb2: 0xb81c6297bbac342050bff567, limb3: 0xfb9022e050807db4b155d87, }, }; let hint = MapToCurveHint { gx1_is_square: false, y1: u384 { limb0: 0x8c74c126c6351052ebf1965, limb1: 0x979aba6acb3e5dfca5581a51, limb2: 0x49e43c123f4e034706485bde, limb3: 0x152ffaf0e2cd3fbbb102b5e1, }, y_flag: false, }; let res = map_to_curve(u, hint); assert_eq!(res, expected); } #[test] fn test_isogeny() { let pt = G1Point { x: u384 { limb0: 0xfe95b6d6dc4c28b03aa82194, limb1: 0xc06a9cdc69f9d39a1cb3c132, limb2: 0xc0637d447baf4f55d4658b59, limb3: 0x166e53a3af1733961f92e08, }, y: u384 { limb0: 0x5dc860b68c76e432263e15dc, limb1: 0x8c9990a0f89eadd580f71395, limb2: 0xaf300dff12d93cfe32b45c5d, limb3: 0x8f6e2a59628049aecb84109, }, }; let expected = G1Point { x: u384 { limb0: 0x5fad5b4abf0d9b5a5500069, limb1: 0x88e3293255d2172755b29514, limb2: 0x2562887a0b9a729cf8f6f807, limb3: 0xfb545dd46e90e6f6bd679a1, }, y: u384 { limb0: 0xbea8d03c186753a97b5e8e0b, limb1: 0xbe3e7a1eb25cf6d7fa6f686d, limb2: 0x72026b41a862ff1fa8508191, limb3: 0xd596c01e510faf25030e9a5, }, }; let (res) = run_BLS12_381_APPLY_ISOGENY_BLS12_381_circuit(pt); assert_eq!(res, expected); } #[test] fn test_hash_to_curve() { let message: [u32; 8] = [ 0xdffd6021, 0xbb2bd5b0, 0xaf676290, 0x809ec3a5, 0x3191dd81, 0xc7f70a4b, 0x28688a36, 0x2182986f, ]; let hint = HashToCurveHint { f0_hint: MapToCurveHint { gx1_is_square: true, y1: u384 { limb0: 0xf26e7fd3c2733a0413db4463, limb1: 0xa1562d011f360461be8e36dd, limb2: 0x84a83147a7e7a1311a712501, limb3: 0x1290f63f6daa85ad6bf7088a, }, y_flag: false, }, f1_hint: MapToCurveHint { gx1_is_square: false, y1: u384 { limb0: 0xb88f6c46cebe267f9e2afa6c, limb1: 0xa845982734193f6f44e49212, limb2: 0x63e1f53f7553752da88fb12c, limb3: 0xd613d3f488be39870f05a5c, }, y_flag: false, }, }; let expected = G1Point { x: u384 { limb0: 0x931f614913b4e856c2a5dd1b, limb1: 0xce68eade0d43210615956b1d, limb2: 0x4f2c8c74301387552679068d, limb3: 0xcc12bfa116dae0017adb178, }, y: u384 { limb0: 0x6b02cc408fda040be6918d1e, limb1: 0x325a198e22c4131c6fed473b, limb2: 0xf0bbbddfea59e5a96a11bd20, limb3: 0xeb05659d43180b59cee2ea0, }, }; let res = hash_to_curve_bls12_381(message, hint); assert_eq!(res, expected); } #[test] fn test_decrypt_at_round() { // msg: b'hello\x00\x00\x00\x00\x00\x00\x00\x00abc' // round: 128 // network: DrandNetwork.quicknet let signature_at_round: G1Point = G1Point { x: u384 { limb0: 0xc0bcbd3576ff11f14722cf6c, limb1: 0xd452247305c00e921bd480d6, limb2: 0x8b9980255afbf088406ce2e9, limb3: 0x3783c94f8000028fa31f457, }, y: u384 { limb0: 0x2b4d36d607cf825974c364b4, limb1: 0x44cd6938390204bd3a17bf08, limb2: 0x92d3ea3afc64bf69e6c4cf27, limb3: 0x9ee7907fd3b11fa8ec81ccc, }, }; let ciph = CipherText { U: G2Point { x0: u384 { limb0: 0x340fdd978d12a78af62a4938, limb1: 0xf70620e8446a28e3d2071039, limb2: 0xe08fd6ca0d6e9bdcb5dbf048, limb3: 0x14fb6e4f383578999fe9250, }, x1: u384 { limb0: 0x25a2b053807bd5aa950143b1, limb1: 0x845c1664a97d715be868b2d2, limb2: 0x5c1891819cbeaf9241827325, limb3: 0x1db774cee6dd8860aad23b7, }, y0: u384 { limb0: 0x941e76c3d4243c3a29eb37b6, limb1: 0xeb7d54ef8c76445a546aa67e, limb2: 0x945908b037be402a146d92cc, limb3: 0x51401dcca71a5b8e961858, }, y1: u384 { limb0: 0x83136ccccc82c994f1c19abe, limb1: 0x638557d8f6ba3dbceffb0d86, limb2: 0xd81843d33e29bd92ca715eca, limb3: 0x12d802c5957e9cab6e1e8c82, }, }, V: [ 0xa7, 0x35, 0xd6, 0x12, 0x47, 0x88, 0xc9, 0x3f, 0x2c, 0xc4, 0xdd, 0xe5, 0x5d, 0x54, 0x31, 0x15, ], W: [ 0x7f, 0x10, 0x1c, 0x52, 0x8b, 0xf7, 0x63, 0x15, 0x57, 0x8d, 0x77, 0x2e, 0x79, 0x3f, 0x01, 0x29, ], }; let msg_decrypted = decrypt_at_round(signature_at_round, ciph); assert( msg_decrypted .span() == [ 0x68, 0x65, 0x6c, 0x6c, 0x6f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x61, 0x62, 0x63, ] .span(), 'wrong msg', ); } } ================================================ FILE: src/src/apps/noir/zk_honk_transcript.cairo ================================================ use core::poseidon::hades_permutation; use core::traits::Into; use corelib_imports::keccak; use garaga::apps::noir::{G1Point256, ZKHonkProof}; use garaga::definitions::G1Point; pub const POW2_136: u256 = 0x10000000000000000000000000000000000; pub const POW2_136_NZ: NonZero = 0x10000000000000000000000000000000000; pub const POW2_8: NonZero = 0x100; pub const Fr: u256 = 21888242871839275222246405745257275088548364400416034343698204186575808495617; pub const ZK_BATCHED_RELATION_PARTIAL_LENGTH: usize = 9; pub const NUMBER_OF_SUBRELATIONS: usize = 26; pub const NUMBER_OF_ALPHAS: usize = NUMBER_OF_SUBRELATIONS - 1; pub const CONST_PROOF_SIZE_LOG_N: usize = 28; pub const NUMBER_OF_ENTITIES: usize = 41; pub impl Point256IntoCircuitPoint of Into { fn into(self: G1Point256) -> G1Point { G1Point { x: self.x.into(), y: self.y.into() } } } pub trait IHasher { fn new() -> T; fn update_u64_as_u256(ref self: T, v: u64); fn update_0_256(ref self: T); fn update(ref self: T, v: u256); fn digest(ref self: T) -> u256; } #[derive(Drop, Debug)] pub struct KeccakHasherState { pub arr: Array, } pub impl KeccakHasher of IHasher { #[inline] fn new() -> KeccakHasherState { KeccakHasherState { arr: array![] } } #[inline(never)] fn update_u64_as_u256(ref self: KeccakHasherState, v: u64) { self.arr.append(0); self.arr.append(0); self.arr.append(0); self.arr.append(u64_byte_reverse(v)); } #[inline] fn update(ref self: KeccakHasherState, v: u256) { keccak::keccak_add_u256_be(ref self.arr, v); } #[inline] fn update_0_256(ref self: KeccakHasherState) { self.arr.append(0); self.arr.append(0); self.arr.append(0); self.arr.append(0); } #[inline] fn digest(ref self: KeccakHasherState) -> u256 { ke_le_out_to_ch_be( keccak::cairo_keccak(ref self.arr, last_input_word: 0, last_input_num_bytes: 0), ) } } #[inline] fn u64_byte_reverse(word: u64) -> u64 { (core::integer::u128_byte_reverse(word.into()) / 0x10000000000000000).try_into().unwrap() } #[inline] fn u256_byte_reverse(word: u256) -> u256 { u256 { low: core::integer::u128_byte_reverse(word.high), high: core::integer::u128_byte_reverse(word.low), } } #[inline(never)] pub fn append_proof_point>(ref hasher: T, point: G1Point256) { hasher.update(point.x); hasher.update(point.y); } // Hasher little endian output to big endian challenge. // Converts to big endian, then takes modulo Fr. fn ke_le_out_to_ch_be(ke_le_out: u256) -> u256 { let ke_be: u256 = u256_byte_reverse(ke_le_out); let ch_be: u256 = ke_be % Fr; ch_be } #[derive(Drop, Debug, PartialEq)] pub struct ZKHonkTranscript { pub eta: u128, pub eta_two: u128, pub eta_three: u128, pub beta: u128, pub gamma: u128, pub alpha: u128, pub gate_challenge: u128, pub libra_challenge: u128, pub sum_check_u_challenges: Array, pub rho: u128, pub gemini_r: u128, pub shplonk_nu: u128, pub shplonk_z: u128, } #[derive(Drop)] pub struct Etas { pub eta: u128, pub eta2: u128, pub eta3: u128, } #[generate_trait] pub impl ZKHonkTranscriptImpl of ZKHonkTranscriptTrait { fn from_proof, impl Drop: Drop>( honk_proof: ZKHonkProof, vk_hash: u256, log_circuit_size: usize, ) -> (ZKHonkTranscript, felt252, felt252) { let (etas, challenge) = get_eta_challenges::< T, >( honk_proof.public_inputs, honk_proof.pairing_point_object, honk_proof.w1, honk_proof.w2, honk_proof.w3, vk_hash, ); let beta_gamma = get_beta_gamma_challenges::< T, >(challenge, honk_proof.lookup_read_counts, honk_proof.lookup_read_tags, honk_proof.w4); let alpha_challenge = generate_alpha_challenge::< T, >(beta_gamma, honk_proof.lookup_inverses, honk_proof.z_perm); let gate_challenge = generate_gate_challenge::(alpha_challenge); let libra_challenge = generate_libra_challenge::< T, >(gate_challenge, honk_proof.libra_commitments, honk_proof.libra_sum); let (sum_check_u_challenges, challenge) = generate_sumcheck_u_challenges::< T, >(libra_challenge, honk_proof.sumcheck_univariates, log_circuit_size); let rho_challenge = generate_rho_challenge::< T, >( challenge, honk_proof.sumcheck_evaluations, honk_proof.libra_evaluation, honk_proof.libra_commitments, honk_proof.gemini_masking_poly, honk_proof.gemini_masking_eval, ); let gemini_r_challenge = generate_gemini_r_challenge::< T, >(rho_challenge, honk_proof.gemini_fold_comms, log_circuit_size); let shplonk_nu_challenge = generate_shplonk_nu_challenge::< T, >( gemini_r_challenge, honk_proof.gemini_a_evaluations, honk_proof.libra_poly_evals, log_circuit_size, ); let shplonk_z_challenge = generate_shplonk_z_challenge::< T, >(shplonk_nu_challenge, honk_proof.shplonk_q); let (transcript_state, base_rlc, _) = hades_permutation( shplonk_z_challenge.low.into(), shplonk_z_challenge.high.into(), 2, ); return ( ZKHonkTranscript { eta: etas.eta, eta_two: etas.eta2, eta_three: etas.eta3, beta: beta_gamma.low, gamma: beta_gamma.high, alpha: alpha_challenge.low, gate_challenge: gate_challenge.low, libra_challenge: libra_challenge.low, sum_check_u_challenges: sum_check_u_challenges, rho: rho_challenge.low, gemini_r: gemini_r_challenge.low, shplonk_nu: shplonk_nu_challenge.low, shplonk_z: shplonk_z_challenge.low, }, transcript_state, base_rlc, ); } } // Return eta and last hasher output #[inline] pub fn get_eta_challenges, impl Drop: Drop>( pub_inputs: Span, pairing_point_object: Span, w1: G1Point256, w2: G1Point256, w3: G1Point256, vk_hash: u256, ) -> (Etas, u256) { let mut hasher = Hasher::new(); hasher.update(vk_hash); for pub_i in pub_inputs { hasher.update(*pub_i); } for pub_i in pairing_point_object { hasher.update(*pub_i); } append_proof_point(ref hasher, w1); append_proof_point(ref hasher, w2); append_proof_point(ref hasher, w3); let ch_be: u256 = hasher.digest(); let mut hasher_2 = Hasher::new(); hasher_2.update(ch_be); let ch_2_be: u256 = hasher_2.digest(); (Etas { eta: ch_be.low, eta2: ch_be.high, eta3: ch_2_be.low }, ch_2_be) } // Return beta, gamma, and last hasher output. // Outut : // ch_be. // beta = ch_be.low, gamma = ch_be.high, last_hasher_output = ch_be. #[inline] pub fn get_beta_gamma_challenges, impl Drop: Drop>( prev_hasher_output: u256, lookup_read_counts: G1Point256, lookup_read_tags: G1Point256, w4: G1Point256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); append_proof_point(ref hasher, lookup_read_counts); append_proof_point(ref hasher, lookup_read_tags); append_proof_point(ref hasher, w4); let ch_be: u256 = hasher.digest(); ch_be } #[inline] pub fn generate_alpha_challenge, impl Drop: Drop>( prev_hasher_output: u256, lookup_inverse: G1Point256, z_perm: G1Point256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); append_proof_point(ref hasher, lookup_inverse); append_proof_point(ref hasher, z_perm); let challenge: u256 = hasher.digest(); challenge } #[inline] pub fn generate_gate_challenge, impl Drop: Drop>( prev_hasher_output: u256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); let gate_challenge: u256 = hasher.digest(); gate_challenge } #[inline] pub fn generate_libra_challenge, impl Drop: Drop>( prev_hasher_output: u256, libra_commitments: Span, libra_sum: u256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); append_proof_point(ref hasher, (*libra_commitments.at(0)).into()); hasher.update(libra_sum); hasher.digest() } #[inline] pub fn generate_sumcheck_u_challenges, impl Drop: Drop>( prev_hasher_output: u256, sumcheck_univariates: Span, log_circuit_size: usize, ) -> (Array, u256) { let mut sum_check_u_challenges: Array = array![]; let mut challenge: u256 = prev_hasher_output; for i in 0..log_circuit_size { let mut hasher = Hasher::new(); hasher.update(challenge); for univariate in sumcheck_univariates .slice(i * ZK_BATCHED_RELATION_PARTIAL_LENGTH, ZK_BATCHED_RELATION_PARTIAL_LENGTH) { hasher.update(*univariate); } challenge = hasher.digest(); sum_check_u_challenges.append(challenge.low); } (sum_check_u_challenges, challenge) } #[inline] pub fn generate_rho_challenge, impl Drop: Drop>( prev_hasher_output: u256, sumcheck_evaluations: Span, libra_evaluation: u256, libra_commitments: Span, gemini_masking_poly: G1Point256, gemini_masking_eval: u256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); assert(sumcheck_evaluations.len() == NUMBER_OF_ENTITIES, 'Wrong # of sumcheck evaluations'); for eval in sumcheck_evaluations { hasher.update(*eval); } hasher.update(libra_evaluation); append_proof_point(ref hasher, (*libra_commitments.at(1))); append_proof_point(ref hasher, (*libra_commitments.at(2))); append_proof_point(ref hasher, gemini_masking_poly); hasher.update(gemini_masking_eval); hasher.digest() } #[inline] pub fn generate_gemini_r_challenge, impl Drop: Drop>( prev_hasher_output: u256, gemini_fold_comms: Span, log_circuit_size: usize, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); // Log_n - 1 points assert(gemini_fold_comms.len() == log_circuit_size - 1, 'Wrong # gemini fold commitments'); for pt in gemini_fold_comms { append_proof_point(ref hasher, (*pt)); } hasher.digest() } #[inline] pub fn generate_shplonk_nu_challenge, impl Drop: Drop>( prev_hasher_output: u256, gemini_a_evaluations: Span, libra_poly_evals: Span, log_circuit_size: usize, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); assert(gemini_a_evaluations.len() == log_circuit_size, 'Wrong # gemini a evaluations'); for eval in gemini_a_evaluations { hasher.update(*eval); } assert(libra_poly_evals.len() == 4, 'Wrong # libra poly evals'); for eval in libra_poly_evals { hasher.update(*eval); } hasher.digest() } #[inline] pub fn generate_shplonk_z_challenge, impl Drop: Drop>( prev_hasher_output: u256, shplonk_q: G1Point256, ) -> u256 { let mut hasher = Hasher::new(); hasher.update(prev_hasher_output); append_proof_point(ref hasher, shplonk_q); hasher.digest() } #[cfg(test)] mod tests { use garaga::apps::noir::{get_vk, get_zk_proof_keccak}; use super::{KeccakHasherState, ZKHonkTranscript, ZKHonkTranscriptTrait}; #[test] fn test_transcript_zk_keccak() { let vk = get_vk(); let proof = get_zk_proof_keccak(); let (transcript, _, _) = ZKHonkTranscriptTrait::from_proof::< KeccakHasherState, >(proof, vk.vk_hash, vk.log_circuit_size); let expected = ZKHonkTranscript { eta: 0xe06b1fc6aaa49ae9fd402ada2b9134b9, eta_two: 0xe542c4b5332d3d478ddb457634915e1, eta_three: 0x8e6609b790521615a5280fb48742cad8, beta: 0x72d843c38074ab30feda0c1fec6c1b3a, gamma: 0x2a2d65e61cca6188a3a8923aa8e5f0fd, alpha: 0x9a4e2bc96d7e1dd703244eef656760ad, gate_challenge: 0x93408fac46045cb577fef77c8ae160e5, libra_challenge: 0x3d7684814dfcb8a69e8ed0d6811500ce, sum_check_u_challenges: array![ 0xdd54b9aefc090c30ea2968d1f2f2875b, 0x5b2c6faddf41ec1b5b0d30441320df35, 0x31a05c60e4601a6e5dd0cbf00ba66d4d, 0x78fd67e59d93d13bd9f90fe775d88759, 0x64d775cbd626fc667f7ef431d7a8a026, 0x5a389eb79d036095de26968eff05a52f, 0xad7a51b6745cf979f995c463b7c84b33, 0x396d8c7eb553dc399585fcbb227d8819, 0x9fbb8219244d68f56af6042a9aed2a6f, 0x8abf1fe8e59622f23abaefbbf040b77a, 0x2d8091d0fa8dbe6da6e339538144f442, 0xfc2b3617ce73378503ccce368a9010d5, ], rho: 0x193ead6536b4ba765236aa95c50de7f6, gemini_r: 0x7defebd9a6f21decaac79819dc18596e, shplonk_nu: 0xf2a3267c336f0ee4ab6f5a2b60b47647, shplonk_z: 0x1369879dd6918cd679e6295a75569269, }; assert_eq!(transcript.eta, expected.eta); assert_eq!(transcript.eta_two, expected.eta_two); assert_eq!(transcript.eta_three, expected.eta_three); assert_eq!(transcript.beta, expected.beta); assert_eq!(transcript.gamma, expected.gamma); assert_eq!(transcript.alpha, expected.alpha); assert_eq!(transcript.gate_challenge, expected.gate_challenge); assert_eq!(transcript.libra_challenge, expected.libra_challenge); assert_eq!(transcript.sum_check_u_challenges, expected.sum_check_u_challenges); assert_eq!(transcript.rho, expected.rho); assert_eq!(transcript.gemini_r, expected.gemini_r); assert_eq!(transcript.shplonk_nu, expected.shplonk_nu); assert_eq!(transcript.shplonk_z, expected.shplonk_z); } } ================================================ FILE: src/src/apps/noir.cairo ================================================ pub mod zk_honk_transcript; // use garaga::core::circuit::U64IntoU384; use garaga::definitions::{G1Point, G2Point, u384}; #[derive(Drop, Copy, Serde)] pub struct G1Point256 { pub x: u256, pub y: u256, } #[derive(Drop, Serde, Copy)] pub struct ZKHonkProof { pub public_inputs: Span, pub pairing_point_object: Span, pub w1: G1Point256, pub w2: G1Point256, pub w3: G1Point256, pub w4: G1Point256, pub z_perm: G1Point256, pub lookup_read_counts: G1Point256, pub lookup_read_tags: G1Point256, pub lookup_inverses: G1Point256, pub libra_commitments: Span, pub libra_sum: u256, pub sumcheck_univariates: Span, pub sumcheck_evaluations: Span, pub libra_evaluation: u256, pub gemini_masking_poly: G1Point256, pub gemini_masking_eval: u256, pub gemini_fold_comms: Span, pub gemini_a_evaluations: Span, pub libra_poly_evals: Span, pub shplonk_q: G1Point256, pub kzg_quotient: G1Point256, } #[derive(Drop, Copy)] pub struct HonkVk { pub vk_hash: u256, // keccak256(vk_bytes) % BN254_Fr pub log_circuit_size: usize, pub public_inputs_size: usize, pub qm: G1Point, pub qc: G1Point, pub ql: G1Point, pub qr: G1Point, pub qo: G1Point, pub q4: G1Point, pub qLookup: G1Point, pub qArith: G1Point, pub qDeltaRange: G1Point, pub qElliptic: G1Point, pub qMemory: G1Point, pub qNnf: G1Point, pub qPoseidon2External: G1Point, pub qPoseidon2Internal: G1Point, pub s1: G1Point, pub s2: G1Point, pub s3: G1Point, pub s4: G1Point, pub id1: G1Point, pub id2: G1Point, pub id3: G1Point, pub id4: G1Point, pub t1: G1Point, pub t2: G1Point, pub t3: G1Point, pub t4: G1Point, pub lagrange_first: G1Point, pub lagrange_last: G1Point, } pub const G2_POINT_KZG_1: G2Point = G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }; pub const G2_POINT_KZG_2: G2Point = G2Point { x0: u384 { limb0: 0x3b32078b7e231fec938883b0, limb1: 0xbc89b5b398b5974e9f594407, limb2: 0x118c4d5b837bcc2, limb3: 0x0, }, x1: u384 { limb0: 0x358e038b4efe30fac09383c1, limb1: 0xe7ff4e580791dee8ea51d87a, limb2: 0x260e01b251f6f1c7, limb3: 0x0, }, y0: u384 { limb0: 0x96e6cea2854a87d4dacc5e55, limb1: 0x56475b4214e5615e11e6dd3f, limb2: 0x22febda3c0c0632a, limb3: 0x0, }, y1: u384 { limb0: 0x41f99ba4ee413c80da6a5fe4, limb1: 0xd25156c1bb9a72859cf2a046, limb2: 0x4fc6369f7110fe3, limb3: 0x0, }, }; pub fn get_vk() -> HonkVk { HonkVk { vk_hash: 1655602901159187576028713697867454584902070339986579942408953720408510516376, log_circuit_size: 12, public_inputs_size: 17, qm: G1Point { x: u384 { limb0: 0x1a11b55dce82f38413640a64, limb1: 0x25c78e040da5a5cbe6f296ee, limb2: 0x142bd66bdb7a2bc1, limb3: 0x0, }, y: u384 { limb0: 0x3dc8a5d19d0bf85b0fa95ad4, limb1: 0xaa34836fe60428f70dee9285, limb2: 0xd1415082e63c88e, limb3: 0x0, }, }, qc: G1Point { x: u384 { limb0: 0xcd51216bd8c56683467cd704, limb1: 0x7c77ce4f20f0fd5a3a264861, limb2: 0x2deae537974aa569, limb3: 0x0, }, y: u384 { limb0: 0xa1179c7a8ed5c59a1015e784, limb1: 0x714496966bf5f4374fb6087b, limb2: 0x68627460599c3db, limb3: 0x0, }, }, ql: G1Point { x: u384 { limb0: 0x36d34df5c2aab80f85a218f2, limb1: 0x864a67847d46222c9aee090f, limb2: 0x6681df238df2a0f, limb3: 0x0, }, y: u384 { limb0: 0xbc5d11d2d55e4ac8adccae27, limb1: 0xb9c1b8da3c671ec025fe40ee, limb2: 0x18e37167fd19d013, limb3: 0x0, }, }, qr: G1Point { x: u384 { limb0: 0xfe3f9cf39c6f73896b06e821, limb1: 0x3dc4669f3d97f847e96e4bce, limb2: 0x177c7a07701c29d1, limb3: 0x0, }, y: u384 { limb0: 0x7c23cf6fe4a49a8e4f4c5aba, limb1: 0x38f1a638b192ffc9b995fd68, limb2: 0x2d31ea12ba12ee23, limb3: 0x0, }, }, qo: G1Point { x: u384 { limb0: 0xd8b0a3fb6597416a145754e3, limb1: 0xac68b01fa7f3faaa5a881854, limb2: 0x2d623ef9f6f62903, limb3: 0x0, }, y: u384 { limb0: 0x6059e6db24a7e1bfc51be2ac, limb1: 0x52b442fa3ce1643a24c7ac8e, limb2: 0x20b75671e0dd20da, limb3: 0x0, }, }, q4: G1Point { x: u384 { limb0: 0x528aeba6bdb01913c3236ff8, limb1: 0xe2edafe7a56dfd287d677b48, limb2: 0x7ea8dd8b4d3fd18, limb3: 0x0, }, y: u384 { limb0: 0x853ad38b76968342e932d84b, limb1: 0xe23f777f35827a35ea2716bc, limb2: 0x2826602478d64dc4, limb3: 0x0, }, }, qLookup: G1Point { x: u384 { limb0: 0x53f9b24d923d8f404cb0bbc9, limb1: 0x75a8449d3d5ce8bc3661650d, limb2: 0xc4032c3079594eb, limb3: 0x0, }, y: u384 { limb0: 0xa0ca89441369b7c24301f851, limb1: 0xf0158fd6da81f54eb5fe796, limb2: 0x1084d709650356d4, limb3: 0x0, }, }, qArith: G1Point { x: u384 { limb0: 0x1c518c7ea0b38257198a9523, limb1: 0xc2c72a3c00da41d4c7c7b6d0, limb2: 0x3057f9cfd5edb0e7, limb3: 0x0, }, y: u384 { limb0: 0xf647b842154c13fa145167b7, limb1: 0x6a98575cedc65ee5700a7148, limb2: 0x27eb0839ef4980d, limb3: 0x0, }, }, qDeltaRange: G1Point { x: u384 { limb0: 0xbefcd8cd631818993e143702, limb1: 0x3b9a8bc08ae2fdbd8e9dc005, limb2: 0x1775fbd3ba5e4316, limb3: 0x0, }, y: u384 { limb0: 0xbdde06678d3bce4455d2086f, limb1: 0x9e409fcb2e19a72238c07631, limb2: 0x1d8011ee756abfa1, limb3: 0x0, }, }, qElliptic: G1Point { x: u384 { limb0: 0x990b1eaa86226b3574e5c43f, limb1: 0x50fb0eae1d72783faba96bc3, limb2: 0x9c706e73a00d844, limb3: 0x0, }, y: u384 { limb0: 0x9b1f547ec36638d7b5a1ecd9, limb1: 0x68fcae74683a84de1084739f, limb2: 0x276d401f1c0f9a26, limb3: 0x0, }, }, qMemory: G1Point { x: u384 { limb0: 0xc20dedd7ff81c5677d3286ce, limb1: 0x276f3537c64334419e05b13f, limb2: 0x12b12523f7d04a83, limb3: 0x0, }, y: u384 { limb0: 0x4e602d1c13a77a2472f082da, limb1: 0x55a526829445f3fda95e243c, limb2: 0x2e741be4fe42cc11, limb3: 0x0, }, }, qNnf: G1Point { x: u384 { limb0: 0x5526834f93c6db848d56dcb0, limb1: 0xe4e8e364439d0abba02dc62a, limb2: 0x16a1350662e14b4c, limb3: 0x0, }, y: u384 { limb0: 0xb2e746ed0b6e85782c26040e, limb1: 0x9296d71489889503dda143f0, limb2: 0x563b1f480cad906, limb3: 0x0, }, }, qPoseidon2External: G1Point { x: u384 { limb0: 0xe4d88b5517e40b2a0133f401, limb1: 0x42f6c756379f231d5f472088, limb2: 0x20e1bb3056279dc3, limb3: 0x0, }, y: u384 { limb0: 0x2c8d1a5a6b3bd0ec93b42e77, limb1: 0x9eb4da763de77062d23ce01e, limb2: 0x23ee36ecb11b6278, limb3: 0x0, }, }, qPoseidon2Internal: G1Point { x: u384 { limb0: 0x19d18424d0e92f60a31671d9, limb1: 0xfdda50b3205d5aa4486b6325, limb2: 0xd1611c856951969, limb3: 0x0, }, y: u384 { limb0: 0x94aa3cadd7cd42e719521e0f, limb1: 0x30c0b534ea958de4c47e2f4c, limb2: 0xce97ee59d45d762, limb3: 0x0, }, }, s1: G1Point { x: u384 { limb0: 0x1b074244b7337b923c097eaf, limb1: 0xd2ae3eafb3800ee0eaf997cb, limb2: 0x154bdee4123a9946, limb3: 0x0, }, y: u384 { limb0: 0xf34e2352250dd3fb63d6d8c6, limb1: 0x3c0953803a3a34d916eefb5b, limb2: 0xd5f22b8ade2c19f, limb3: 0x0, }, }, s2: G1Point { x: u384 { limb0: 0x111168b4d7ab689558c334db, limb1: 0x7c62cc30718076db1836d9e1, limb2: 0x22d2dd0a34c3a1da, limb3: 0x0, }, y: u384 { limb0: 0x98a26842094b80c6e88321bf, limb1: 0x243059518c261a4137e7f6a6, limb2: 0x262c701396f0e3ae, limb3: 0x0, }, }, s3: G1Point { x: u384 { limb0: 0xe1213cb7ef934c944e4e8374, limb1: 0x84b08b441d010fc2976235c0, limb2: 0x172f8c6455a2bfe2, limb3: 0x0, }, y: u384 { limb0: 0x960773bd1e8b46a6a182239d, limb1: 0x640beab3f563e0a2402c116a, limb2: 0x178afa12bf161e7e, limb3: 0x0, }, }, s4: G1Point { x: u384 { limb0: 0xd14c60e677f8e1897f658057, limb1: 0x33204ad4109fa0fbb54c4fea, limb2: 0x21f45516c16fcb30, limb3: 0x0, }, y: u384 { limb0: 0x52efc7a0ee6a29e06296bb4d, limb1: 0xb82792c925627d7348f0bf11, limb2: 0xa7a5c9f897fd8da, limb3: 0x0, }, }, id1: G1Point { x: u384 { limb0: 0xaa69e812f125d20848fd1c50, limb1: 0x621962d025f0fbb42467ce5c, limb2: 0x1d1934c19b595461, limb3: 0x0, }, y: u384 { limb0: 0x8971dba72882ee742a0b57f4, limb1: 0xdf91438bfa5b19a7bad0f91d, limb2: 0x10e15c437db6ae7e, limb3: 0x0, }, }, id2: G1Point { x: u384 { limb0: 0x3a6957e0c9aa54ec21894a61, limb1: 0x320938baa053cd1f3dccb71, limb2: 0x146dc127b5450502, limb3: 0x0, }, y: u384 { limb0: 0xfd19216bf0829882cdabebe6, limb1: 0x828ba063530a81a329131fb4, limb2: 0x2d5cbdbf9edeff0d, limb3: 0x0, }, }, id3: G1Point { x: u384 { limb0: 0xbe73592b0b543997ac9ec27b, limb1: 0x600ed91fa96cd915db4ed7fd, limb2: 0x1e214a8b0ce35f8e, limb3: 0x0, }, y: u384 { limb0: 0x5eb2130b9c574c4e04e6e477, limb1: 0x7203e26ecee99e2307846f5a, limb2: 0x214375d66b2db2ba, limb3: 0x0, }, }, id4: G1Point { x: u384 { limb0: 0xc0ed29b2c26f8c8cbcbd82cf, limb1: 0x9b46a4cf0acba266c2a9b02, limb2: 0x2825f908ee9357e4, limb3: 0x0, }, y: u384 { limb0: 0xf0bd3cf808a6d1bcd0d63ba, limb1: 0x8100429b213b9140ed25274a, limb2: 0x264ef648e6714012, limb3: 0x0, }, }, t1: G1Point { x: u384 { limb0: 0xa63b05df652b0d10ef146d26, limb1: 0xfe18040105b9b395b5d8b7b4, limb2: 0x99e3bd5a0a00ab7, limb3: 0x0, }, y: u384 { limb0: 0x7f5a622a32440f860d1e2a7f, limb1: 0xccec99dcd194592129af3a63, limb2: 0x15b8d2515d76e2, limb3: 0x0, }, }, t2: G1Point { x: u384 { limb0: 0xdc25d1aa450e0b4bc212c37e, limb1: 0x8bc01c9595092a222b888108, limb2: 0x1b917517920bad3d, limb3: 0x0, }, y: u384 { limb0: 0xe42000a1d58ccb74381f6d19, limb1: 0x22e6e992077a84482141c7eb, limb2: 0x305e8992b148eedb, limb3: 0x0, }, }, t3: G1Point { x: u384 { limb0: 0x400b2bca37e2b1085e924a77, limb1: 0x3ada15236ba5cfa60111b440, limb2: 0x13567e3b915c8101, limb3: 0x0, }, y: u384 { limb0: 0x904b434e748f9713de8cc3d7, limb1: 0x8f4674af5744dedafd63caea, limb2: 0x148d22589b91f0d, limb3: 0x0, }, }, t4: G1Point { x: u384 { limb0: 0x6c840d9c943fdf45521c64ce, limb1: 0x7342af45d0155a28edd1a7e4, limb2: 0x43d063b130adfb3, limb3: 0x0, }, y: u384 { limb0: 0x4c573d1686d9cb4a00733854, limb1: 0x6aff96736194949330952ae7, limb2: 0x261522c408933064, limb3: 0x0, }, }, lagrange_first: G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, lagrange_last: G1Point { x: u384 { limb0: 0xc894b742744cf102a554d06f, limb1: 0x9ed4d186a2debd4bfe72be9b, limb2: 0x6a032e44c27b0ce, limb3: 0x0, }, y: u384 { limb0: 0x26660c8385d13a63d2078399, limb1: 0xad76960162ff0d8c34d25b61, limb2: 0x53396ef4f905183, limb3: 0x0, }, }, } } pub fn get_zk_proof_keccak() -> ZKHonkProof { ZKHonkProof { public_inputs: array![0x2].span(), pairing_point_object: array![ 0x42ab5d6d1986846cf, 0xb75c020998797da78, 0x5a107acb64952eca, 0x31e97a575e9d, 0xb5666547acf8bd5a4, 0xc410db10a01750aeb, 0xd722669117f9758a4, 0x178cbf4206471, 0xe91b8a11e7842c38, 0x7fd51009034b3357f, 0x9889939f81e9c7402, 0xf94656a2ca48, 0x6fb128b46c1ddb67f, 0x93fe27776f50224bd, 0x4a0c80c0da527a081, 0x1b52c2020d746, ] .span(), w1: G1Point256 { x: 0x1e34c173234bc959a7180a6bcc4400e875f693f8ba7aa39f084be9ffe2a7030e, y: 0x2b746f5a836e791d389755abda9fb5c9d749337fb05852bff6277a689620de9f, }, w2: G1Point256 { x: 0xfbd3eedde3a077f81b3f6e19e88da20865e0d96ac30dcea46367405b98e7ee8, y: 0x2d9de94695b5f22e2e76d7bbf3c9f2574f674330802f0ead9b527154f08708c8, }, w3: G1Point256 { x: 0x14a120ab523b85cb55ffddc33d5004ad91474cde957a6fdbaf145d18d45ed987, y: 0x1343a5fd555b6456db3af84e21a912c297379b278609d25591063bd444ce1697, }, w4: G1Point256 { x: 0xeba60f911766695f96f1cc1087203076722a4275781461c1cb8512937e9ca09, y: 0x2531eee848f996051e53e155e72d4e2e36d6a192cef36c46d92a9d9573f5c802, }, z_perm: G1Point256 { x: 0x2f4d259d57533bb5b04a62e10b3312b1d57c31a72daf5114e65fa1bacf2db0b4, y: 0x122fe61c0c3e49d24cdc6dcfe202787fbf2c12d8de5ec018c5e82491f0a58d26, }, lookup_read_counts: G1Point256 { x: 0x1c205828426756e2d6fe1a24e7d2a3f572b75a0b9ca18b0bf2098d68efdb4fd6, y: 0x13d3a102f9b15308b0233b512847b2ed03fe0b9f1eadb624596edda65af3ffae, }, lookup_read_tags: G1Point256 { x: 0x1af83bd052017a1caef1cb49f7493688e4b1d2291a8c81ee828b6d8cd5a3929c, y: 0xeb612b6d43562a5a959a8b335e0e8e699ccedd4331ac12ad01091ebc990b296, }, lookup_inverses: G1Point256 { x: 0x8dfe2b0529d66494e26f702f13284b1ec31bccde949e11bb9dcf2f9204b0f72, y: 0x1a17d9e42eeca241deb7880a1987676cbe1043c4b4e39cb8393753d2cbb3b752, }, libra_commitments: array![ G1Point256 { x: 0x170915817e4884ee05a88ce77c8a34875a1821758557e2a15e451c9b44e2bf77, y: 0x2687de64a3db7ce4da18126d442d00cc5a4ed4220812c29b54bd3e0a13dcb1bb, }, G1Point256 { x: 0x2be452b393768e61cfdfeccade5cdf0d1766bbf5e528b5aa1a393e49fa3e5ca9, y: 0x2852b988ed0d271109741f930ea0924fcd94eb67b505d4c88d47ba12d6cfe4e5, }, G1Point256 { x: 0xd22d803fc19a867752924eb0a1cabb3d416b43cadeace3a3ebc42b49ff1ad06, y: 0x27b8cd7a0a74924ed8c7d07ee75907cfade7005eb42492f8519c62020183be00, }, ] .span(), libra_sum: 0x90144f9a53cfc333c47451b4adcfe1c23478b5fedc99ded280b54409de73c26, sumcheck_univariates: array![ 0x3149d68db6edb589893c337f6fa124a4e1e21c4d04fa5de31b29889da3634ec, 0x16d5d9a40812efff9f08eb10fbdee1c124d1d7195922927816ce778691e08152, 0xe8a05f197b383bbcd4cfa0972e429fc5e35c2d18079035e4979223b3fa5a7fa, 0x24f6a24319cafae3b708e9148a9b28d1f26ae5091c97c3a7fbe95c6571aa270, 0x151107311f5801d6792bc44aea560e400de6c372dfa64eec2962b1d179ba59b, 0xab68b23d47720b06bf7f3a4fad1958f0b036c0cea11533eea85b6831d85a1fa, 0x26f4315868b55f723f1c2d036316ea5125f90ecf027262126a7385f4e296e2c, 0x1eeb97671be33f66bca8fb643ab214d82cd46ae5afbb60f8a786d164f1f80934, 0x24faae84d5ee43de3815a5be73d77e2a8600526f7fc2a76fddc7238089f322e7, 0x18a9cb845a1fb2d9625b2251b0953b02f156c09696c3602b5286f06a4205c89, 0x7e42892aefeaa5209c01c9e098de4e7f0858dda32bc95da8ec08ab8220e48d8, 0x1d3592e48b62d8743793a25cca0e51e716fc09d7fd8f7d1d537ecc204d167d1, 0x2997d5b42e40cab8d9b0f7909a6b5c5fab84ba180a0c5a91a3e0b12ebfad76f5, 0xa419cbd276cc548aea0f9c168bbfece44382fae6fcebe2659e285655129428a, 0x632e4f72070d900a143fb798907979956955681b98feb27169b71caca0825e5, 0x2b423792b6cc5bbbb86c7889ee1a9caaa505797f3c0cf0d083c3c732dad38289, 0x104a3c02a4c581859887647e5ea591a4cc9ae3ca3f6ea459ca06624a74a6a0ee, 0x231fdb9a35dd4a8c5a6d0fd65195ccef5291f4944c627677c24ad42f0150941e, 0xb305bdc9fddd22f488eaac6187dae6a0e115b5209f0cbab2600d08767f73d7e, 0x22c974bf215ae21071ec73d7b7edc30d12b37737a248881d48ba8aba75110760, 0x9b0a436158fb0f2a4888e55b672aaf161884d29b1c92fc566a4769fad1f1662, 0x28b84b03b50c5ab8dfd459531675fddac1e9fef6747b724d4aafadd7701ad0b3, 0xe12eed7ece4b17ed9aefa90c4f858550d1227af01f5093ea2e1194d01dd5c1b, 0x236fd96ffb804945c9705b3eeb39af98329b94ff1e7e1120f1461369e2c1f7a0, 0x1945bc69ae6755998f65deff579a24fd45721ac071144d902329d2811c7c7fd9, 0x6c58d2ee567254ab86864b4652423a1a938270c740ac0aaa48bc458ee290f15, 0x9eab94ff32c8d5e6592803954e3cbfb66e7f2b429bbbbfaeb84480dc31ba603, 0x25c025181fb1cb6ac8b54d80d73dd505abebb610e12c4086ce37ef02781d09a7, 0x10f6a28fb969623c13a8d03de2d64a46305a1b57a4aeea72b7bb13cb20eecd36, 0xfccac954245c3c67536ebafb134c6beaf8068d692d82edef7071f1eec1876f2, 0x13bf9c5b2bb484a95f0a9805abb41a5690e353315635b39c21fbd7f580270fc4, 0x1933fed4de4ca7ea196d299d5bb300ecf9edbd3d6dfbdb64a17658d20021a4d9, 0x265815656b600b952d2e1f1c7819ca82fca81e49888abae58687e8a16440d5e8, 0x2ea8b4c68b9f4319d41fadb8687f840a30ad87aaa8066e57e593004f3532e134, 0x27f0e547478d3dc127439447953643959ae08665ccb625067efaff37414a7333, 0x16091d3d50a304b2711e8ab203f5c75058ccc96ae7805786f284a8ae4dba022c, 0x20b017ce49f243ab96013aca53b99ed0ef64836ed7b7111e75c051c042b70b1d, 0x16c3c2093db68946aa8daf3b183dacc7cdc72ebf291eb8eff7eb90d30eb04edb, 0x1ec3ca15c7f742c257cedc604dd201202ce3248cd37b4005f433688199d56196, 0x17952c04233c59b0394e7f6cb5c613807fdb4c99f77c2a496faeefac3b0670c8, 0x2cbc304b746d10106d5ca386ff1f4e3cfc7e569c04e46ecd9d69f791f8aab6eb, 0x1c77bd01f0bd518100a1454b33bbbdf5e4e93d6cb428894cd6fcb3b022d1e8b4, 0x132e106c58142b5679e7006fd3c9bf8ce55ae3e53312b62a1e7a3e3a983f8c24, 0x24a0381969a5bb634111aa3e613bf0f7f57a2b1a08cd10855a6cd50539008d17, 0x22cacd970c627c6cd704c36c516c89566870a0f05a105b877b0581088e69b35f, 0x2afaf6bf152ebd048ee022eb3897a2e7820c4cb8f8466df4c40755a513e33d1d, 0x264f26a5e116d1b8167c6d90eeefbb52e7b40ee168a81ef21d0c21a275f36043, 0x294253bdea2bf3dcd61bd93732f536a5bc49b57f9bd225766fecbdbab43db963, 0x12d8c95ede7c15ddb6ecf9fe0e42baa67e689c3200aad123b59d1cbebc0af2e0, 0x104510383e6234abd06c3aeec9fb08854a82620a35e45247b6cd8de461b0259a, 0x7d219662f75b601dc2d55fd7da3fcd5a9a18f3858b6ae8a6b043d06a4ea9b44, 0xaa4013906a98a1341f5a816f03e9e163eaa64baa846718e56b55255ab82bbe, 0x28f931b264c9a2b1e951bb4344c1136d53c6e49d5f44ae07a93b24f300077006, 0x27b12d853426db59cc2dbcbcc4f4f65d97f36c42ce8d1b35618cc2406f6bcc2f, 0x121d138ad4faf57b387a0c6ceabbcf40d267ba1a57274779d30e82eebf33f499, 0x1f4e057d79b4f5067e639ac93daac5c15930ed56fc4668633eec1e0171fc1e1e, 0x301e110c5f4bb410002752fadb973462699f99eff2c522bb29fcc3d268838969, 0x179b4a790c726b98fdb4e8f3538205caea13c58b21fa5e4744b5f2b32117c6bb, 0xfcb8cf6b078413f39e5d03c9a0764144cf69674cf3e8f947adac1867ef5dd25, 0x2405407e10a6d25bfc82bd8296581caf938d28ebcbd24b0203b5d24a56a046ac, 0x2b50b38db9a82cc14d258e8a3d7447e56ae8525ec296898c97ee2ff8d6c829d7, 0x27d6d4a65a494950fd8ee286c4de6d1918e30901f81185d0280a83c925546597, 0x66a2b7ccc890a7b28d360e935e3cc649b2ebd93c65e7971993e5d4f8419a88d, 0x577eb50c286a240c191897c73621c9a7a5a7eb061fa395d790e38bb3bf0ffa0, 0x843ed2873262d670315de6d882611c31934d04f25e7e275ec73cc0322da3204, 0x2a9064d23951b7392a196dfb9c89e66c824275ccba1ebdd070f95d1729b06293, 0x218eb8c4a137172fe1ced0281376d26148cc83b728964e04aec9d3c9bc2ca0e5, 0xb28012720a35d1fde5fc838f56b97e14e831b280dc9d3c5d2cd90f662acb50a, 0xa0c9e4e4ae3e002615dd5c69f2165acf31c64d5327df16d46d4f74eac718265, 0xce7ff6c1981b21a195472b06ce7d22335b13bf12e76e3070ac90adb7fd95616, 0x16a5335bdf6596ac1351dc015c1316098ce91c57d5b5ea50c949fd652bfc815f, 0xfe114dc57f1a2f4bae55b57b366d0b499f956da79b1b6736df7fb9dcc4547ca, 0x147892a2bba985b7a415c2c108bb60a413581331c4aa3df48abe41bec92bffb7, 0x13ecd1b079e18b2a84cc1f92af470baf348518ec044dc4fe416336bcca53b38a, 0x1569b0c81db8022270d0af9cafbe881173d952ddf37c07ec2a766b6c578f37d7, 0x10db7d41f627623b905f28baed9ae528272d131e9c899885037f7fcd8083b177, 0x24c3021fb55a11c5833d4141c529a2166afa1d94208dad69f9ac2a19516ed28f, 0x2e7d5fc72956e9825f0f14fb3c0fd27ffbf6de4b248773759f39a30956270c1a, 0x2c7a64b108fe865fb1ee22323c3cab2b2d949b80d24642d131b4ff4643a9b9c9, 0x2b3c851da00e8c3b44422c1522fe5cf884a786626c34c6e4426a35ec221ce0b7, 0x165853d1ecaad0c5aea08d3ddc6511d174697f594afeca57a1ce8f6fda021c14, 0x10931a4f5f8e17c9233ae0b7f675ace7d056c244f376958041579b9bf897652d, 0x684e5cd9e7d09d905e11e660b811d2afc1e8a248f822cceb80d085e15d37c1f, 0x1cfbc7620177d24eab2b2c3184e70d04eb289f87a0d9c141d4d820f7a2eb87c0, 0x2471650400ec3bb9ae965ea280132cdd6db6305b1e7503648a42badf4b831bda, 0x106f62d6823cae740320e3efa8928f916bf79cebccfd9f6e8c19213d1403df05, 0x8c796662cf9ee1ad01ff917be730cbfde624286c76c54a2edc6d202c2b407c8, 0x146c0f4c6464f9fb5b15300f2e69c9b08624734c2f68cea603580fd08715822, 0x1e519b10d4404fa71f34885ffe96929ba174696f1f683c21d1f97cb04bd4d22b, 0x1db5c6b7ffa992613926b14dc9e2d38ccaf540b28989b454b9ba6e827921619c, 0x221294410242d3af8f43fb85acaef03ef5f25f9d04334fd7e293355f85d512bd, 0x1943b5ae1d9f077ab778c538e49a62e7d4d28b597446b560d16e72da8072bb3d, 0x4a9f7d95827a54eee2c8242d174c95ddc3f9d8d69507de49ca41adea8261d19, 0xa1810218a2aa24b3aced9a70886da5bf931e5482a7eebc805330e435a0285ad, 0x21c33cbe7a21ba6b7abfe15937c1b295bc12afbf582512bdc8bbf5655164c494, 0x2ca72a8a3499bfe2d0eb23e7bfe3244f9125ef19f3353bdecb99957b351bdf23, 0x236c92d20e92a0670678bd93b9a8d2ce5cd777407337dba37afcde2c73b296e8, 0x112ae8a0c5764d4c0de96f7001857726904dab3b66324a96b9272a18185a7761, 0x294dc118f95f01a6a77d01341801a12ea3ca8135eea4c593d0e3ab020b17eb3f, 0x2d9a0c73e31475e0b545e497b562a3c51340e0a9578ce78019a07f2ea8780d71, 0x16538f95bff012672df3fa422dcebc32600ae0cf100b72bbf0e5f36ca55c079c, 0x2c141dc8ef9c6ee31c17a04af6ba16b3489956dfd601437312be4571f909a5b, 0x231ba01c0cea4e1634851d2195e5bdff65ca184b39812e03be83aa269ba4c094, 0x2891195c085604acfdf93ef63e535eced06d41bc8058c31c6e7ab680de727540, 0x2cb5ccf9dc7fba5b62f47e20f1dc78bbac5741016e67df2678dac62da61c9ce6, 0xd9c684b8b528dea680d100518355c92c9707aae4bbcdcc221c9b947864cfdba, 0x18957cdde94d31a2b9961d680b45158e0522d6eaa79daff030d123f0fe463b2e, 0x24df9e3fbd718e06157a9de498e0d97becc7ed30174041a90de1cec78cc74fe9, ] .span(), sumcheck_evaluations: array![ 0xda1f5a72d1ec76cda05874ef901ba28ce501879ad38eaf3f9b6361df206a973, 0x1ed85d53329e768dd416a57420e6d9cb5932c1882cf4a63394634de89452176a, 0x1d04ffeaff81057edef1460352e01891da17828af736f9f25d7e6c0f1ff07596, 0x2c9c0a7f812b743a24af92cb933ef6fe0e57872bafe7bcf09edb1ad91a80880b, 0x24d368974add765b0465b03cd25e8fa707aa07ac132275bd8f152648626eff34, 0x196bc2a2c56b57e59f6a5e9f8776e01d0576858ce4790b584e478242f29e2bff, 0x159fb5b8f9d76812eeab102d5881cedaeeb0b57e98e6b4b8466916e3b268aa9c, 0x17208caf6206925146bbaf5ba306efd47fa53dbc3d33696a9b33194db83e585e, 0x61d45cf35212d7214c22ff7ff9e6ef520b6773d493640fb2988550f972c8802, 0x7b91f492b587fade1b237adfeefe507fc76bcbf5a4faafc76ecf7b0346b88b5, 0x1dbe57d9bbe4f32165b4e6264ae69058d3143fbb6d01bfa839de3cd003a246a6, 0x1612ca4aa2cf172583d2cd1c3a67221abecb16d91d9c4fb067b784d4fdb4c112, 0x2266a0bca10cd57eba99438f820e8a0a91f7095831a474510110ce030d68bfbf, 0x28a2fb53bc4d65fbd7902353d352fc3ff9f10baf0f565221ba3ccf3a02596e40, 0x1a7eb155f45e7585bd3f000ff98c57a44f23df666585dbd04d3f881a8d5c841c, 0x1878c1e0ea64fa025d989d85081ddb3c0b3caf1b83f950bdb746cb052f7516a0, 0x276dd76fb0ca6fe37e4aa87d9107abd1d499af57e6bb587dfff5fd61969f7b6e, 0x1308a2d137e657fcacc9368b5c4dc672ee358f9878dece5aff25994b9797ae9a, 0x1f030b8b61847b35361104ae7ed473b72f57126323d35ca00189b532c7a2976, 0x2be3abfd1d75a1c0c1c121f602ee6c51c098474b2541c8758cb98bcc1350413c, 0x1bb5b1028805b0c1a875939537de220777403b1ef8787b361872cf715cd2c3e9, 0x1abafb4da41750fdfbea04d59ec64bb90fb4451b0b24e30035ec08fe832babb2, 0x1e9682feb5c4594b7acfe9fa6c8bad335e3c91d215c68034e3b46f11f9f2c61f, 0x2658a073798adbbce5691192977b2316626731acd49565ee30953275f96d0f8d, 0x25c0a364baa8f10aea8f4295f44e30817662f6c2e446dd71941fcfe377a2500b, 0x185ebc437928bcdbb426d9612d876c0b3aa89b5c8987014fdd040e0de6357039, 0x832fd6a95e9d33d53d1867f40fe6f5eb2c742c89ffe534ab5fa4b9f28e45192, 0x15bba137e6114ef194c6dd0c4a294047720a52ba05bfb3232113fb9c03a2740b, 0x20c8d9a09290bf43a0346153491f693ca3af127d9842fe196310bf5e3863a41b, 0x2996bbc4aac149f9e1176c8a10e731642acd43ee45b4f39eea30502e7c7b23cf, 0x1678d7bdb6529a27bd8bcd78df9237ce30bc8b161c9a03220b27d777694ea3c5, 0x26e6234272e92ff6eff8e8391567528de1e1c82f66628aa2679343319fedbdab, 0x56d249e93995c56591338bec2af3b770ed0ab09cf9b15c30245268c7c08316d, 0x5db0360469781fab0e6e0adc65adf68490b2b4d46bc43a584694e8eaf56f65c, 0x2d98fef4d951abf9a4724f5f960a6813fcd1b5bb0e5bcd390a8d5b457fc89c14, 0x291453c614c83070310f7eee9103d15858371cf28460788799ba673c94eeeae3, 0x9051b6d85fea1b22e85cc849c153074c399f81a241abea2121972ccac321fda, 0xc6a75a540dcb928e18bf7b90d1243a7ffe96db6cdf90cdb4698ff4ada76a6e3, 0x2ad59d311c014d11a8b906f3696fc86193cc6d228f568b45b06a7ffff25675ce, 0x158b238a3c1c894a9c7ab11bedfe7564af3d5fd8c15c8d208c1f347ff2a33ca0, 0x703886f358e78a25a832d65cc8fbe5367da5082435cd734f0e796576637d2a1, ] .span(), libra_evaluation: 0x1132ace165bbb656b51a3e2cc2afd3233ec2bec2784a63214acb8615929266e3, gemini_masking_poly: G1Point256 { x: 0x26014e34fea9af7f7811011ecbde8ebfd88e0756b5a07ddaf6282295fe8b5d2b, y: 0x1f82c2e2c6d56563ffcaf90b0164fed63750d10f0f62e0d436090346b51281da, }, gemini_masking_eval: 0x1c9d49995b00c7ac2b1bd1c5d3c4cc9e3f7e06e37b66a4ed37fcbc212c6b21a2, gemini_fold_comms: array![ G1Point256 { x: 0x2918d3bea258d9e87d3c1864cc4b51e2a660f22b6835bea39099e8d28b644d49, y: 0x1c04a1962be87e2cca7683eeeb89df859b71be6e49bb9addbf6020e1b80af882, }, G1Point256 { x: 0xad8457e1af0a0b9c009c589dc2aa7c6ca8184e5ab3b8547eb924c051969d87c, y: 0x1e8136880bc80710c9746ca9ab32e1355814e73bdf996fbb95161a43212c0476, }, G1Point256 { x: 0x8dcff84c035e66e9fea2edd57edc0299678373ccfb62264b3f9fb0fa5d85b3b, y: 0x299f4b10d489ce2001d7f05a1a98f120d2088abdb1f1cf6f668aae0519362cce, }, G1Point256 { x: 0x21a02af46e8a9449d16f1359f2c0e44484388d70e838c07b826182d4386bf875, y: 0x1489e07ff0ea2d7ed52a64476b9365ceac3268fa3cf4a008243d92c2fa1aa500, }, G1Point256 { x: 0x2fe2ca7bc51f9426d7ac008e8d18f0779f132c5f7b14f8a7070cff82951bfffe, y: 0x21ebd772c6ce32090a524a1fe16b88e1b5acb76a9f553133c15ca0a529eb71d9, }, G1Point256 { x: 0x483d5e7e02ffadc40e03af829fab2d1ec4c3ec2273865ced6f8c9bec0db89a9, y: 0x24cee8d6fd9d9cd11a136c01b160e8ebc63e78fdf2b6bafc0a11ceaf0c7a082a, }, G1Point256 { x: 0x1a3ec43fbb203ca00bf3d5206c7399ed48027170e5b4704ac969ce730e5d974b, y: 0x21f38a577ade9fd8bbcf3510a97c358b0c660216e4a83c368406cca6b2fd2799, }, G1Point256 { x: 0x1466ac7fe3cec7cfc27e88415660f632b6a5651f45818a033afc3dd4066f23f1, y: 0xecd64b04c089455277f46b3a946046f1445674cbcb2c537bba2498f34efd7f2, }, G1Point256 { x: 0x1dccac0dff547f871103577bd87509dfa0103188faadeddca36dea513dcccd6f, y: 0x8f41998df00acf151dcea7d61f38dcb0f12ba94eba520755684230e1dc43e79, }, G1Point256 { x: 0x2201ff1c5b0bc9d9304c8fcb5ceaab7389aaaa639fccc15c99757ae33d0a0bab, y: 0xe817c9e51dca78ff6d0d9390884deac07919706599688a3663e45761c185287, }, G1Point256 { x: 0x1b44c9747e5e2e9a8084ff374bedc82ee9c02079cd7017a7f3de5fe6735d9a87, y: 0x23a08eadc1723f6c47ae0da29880b3122be4d80c1c161955be55a7de1ef634b4, }, ] .span(), gemini_a_evaluations: array![ 0x26a6901a61216f8b4252c1d327711877a6078f277643443896f1f832c6da1f66, 0x1bbacd086d6b20ace675bf297a3fcfc6865e986c78ae9171d774d22d1242cbb1, 0x27a5d919bb1cecac67cc4bd6b260a04e33a91283e4b9cf071399e8249743876a, 0x2bce80ffb28871803bb5cf5dbfa65b9256e0dea0dd9449104ba26ab8db5c7bbb, 0x252d45f8db3a296d722dc7df3d9e640b1ee375d598bbf51cd5584ed52e67ae62, 0x12e77f2aaf87ba208a822b98f2e02a7928236fcbdc413b9bad32d2bc7bee9c52, 0x8c56bc9d6093c8a56d94d7987331aa6cb17008b9460f76785ed2d57ef600d70, 0x2cad2a1c5329e115d078e74b264e937adaf4e0eb1ed682424789b6ee340387c1, 0x522e03828a6195d3279fffb5b805666a69a582c5c90b17c2a719f790f443483, 0x247d32c70f1aadddd49ed465539f1e544b1c9dd7478b4077adf8cae1bae7dad7, 0x1e69b320445a0e22ccfbbdb54eee09bf9bd5b293b8d7d727fe8c8e7064b7768d, 0x2b592160911cb387fd83294230672bc528a6c25d9b3fb99417c74f7de7f197c2, ] .span(), libra_poly_evals: array![ 0x41fd901c2fda436051e8923e20fcc27afb24a65d70eb00473f172e9f7f9776, 0xd794e3a56c5c5fb5f5a48ef6f17f1956ef8197b7bfe838e685acae0efcb8d90, 0x2f4b4a38d4ecc05f39865b2b05731bde72a9c7b36e3f9cb6486f3653806a56ef, 0x131bcf56f4b07e163b777029ef66826bfcdad7f1fd2c881d8e06f2d9b98148fc, ] .span(), shplonk_q: G1Point256 { x: 0xc1728e9f86fb53fe3befee017177d6a30a27feb87dfa78846a7fd510618d3b5, y: 0x67583f1cd028a2b317f924ead8e3a00884dfc6966442521972479b22d7d82d5, }, kzg_quotient: G1Point256 { x: 0x145edb11f0b06a0cccd6233a0f9659439b7c0cf388f18aad29cbe3eb5ae61eb7, y: 0x1912b95a1b1811be10bd6149227d5c11d47c78b76ded7a17e4c77bd1f9b9a841, }, } } // #[cfg(test)] // mod tests { // use super::{ // HonkProof, HonkVk, G1Point256, G1PointProof, get_proof, // remove_unused_variables_sumcheck_evaluations, U64IntoU384 // }; // use core::num::traits::{Zero, One}; // use core::circuit::u384; // use garaga::apps::noir::keccak_transcript::{HonkTranscriptTrait}; // use garaga::circuits::honk_circuits::{ // run_GRUMPKIN_HONK_SUMCHECK_SIZE_5_PUB_1_circuit, // run_GRUMPKIN_HONK_PREPARE_MSM_SCALARS_SIZE_5_circuit, // }; // #[test] // fn test_sumcheck() { // let proof = get_proof(); // let (transcript, base_rlc) = HonkTranscriptTrait::from_proof(proof); // let log_n = 5; // let (check_rlc, check) = run_GRUMPKIN_HONK_SUMCHECK_SIZE_5_PUB_1_circuit( // p_public_inputs: proof.public_inputs, // p_public_inputs_offset: proof.public_inputs_offset.into(), // sumcheck_univariate_0: (*proof.sumcheck_univariates.at(0)), // sumcheck_univariate_1: (*proof.sumcheck_univariates.at(1)), // sumcheck_univariate_2: (*proof.sumcheck_univariates.at(2)), // sumcheck_univariate_3: (*proof.sumcheck_univariates.at(3)), // sumcheck_univariate_4: (*proof.sumcheck_univariates.at(4)), // sumcheck_evaluations: remove_unused_variables_sumcheck_evaluations( // proof.sumcheck_evaluations // ), // tp_sum_check_u_challenges: transcript.sum_check_u_challenges.span().slice(0, log_n), // tp_gate_challenges: transcript.gate_challenges.span().slice(0, log_n), // tp_eta_1: transcript.eta.into(), // tp_eta_2: transcript.eta_two.into(), // tp_eta_3: transcript.eta_three.into(), // tp_beta: transcript.beta.into(), // tp_gamma: transcript.gamma.into(), // tp_base_rlc: base_rlc.into(), // tp_alphas: transcript.alphas.span(), // ); // assert(check_rlc.is_zero(), 'check_rlc should be zero'); // assert(check.is_zero(), 'check should be zero'); // } // } ================================================ FILE: src/src/apps/risc0.cairo ================================================ use core::integer; use core::sha256::{compute_sha256_byte_array, compute_sha256_u32_array}; use garaga::pairing_check::MPCheckHintBN254; use garaga::utils::calldata::{ Groth16ProofRaw, _deserialize_groth16_proof_points, _deserialize_mpcheck_hint_bn254, }; use garaga::utils::usize_assert_eq; #[derive(Drop)] pub struct FullProofWithHintsRisc0 { pub groth16_proof: Groth16ProofRaw, pub image_id: Span, pub journal: Span, pub mpcheck_hint: MPCheckHintBN254, pub msm_hint: Span, } // sha256(b"risc0.ReceiptClaim") = // 0xcb1fefcd1f2d9a64975cbbbf6e161e2914434b0cbb9960b84df5d717e86b48af const TAG_DIGEST: [u32; 8] = [ 0xcb1fefcd, 0x1f2d9a64, 0x975cbbbf, 0x6e161e29, 0x14434b0c, 0xbb9960b8, 0x4df5d717, 0xe86b48af, ]; // 0xA3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2 // https://github.com/risc0/risc0-ethereum/blob/34d2fee4ca6b5fb354a8a1a00c43f8945097bfe5/contracts/src/IRiscZeroVerifier.sol#L60 const SYSTEM_STATE_ZERO_DIGEST: [u32; 8] = [ 0xa3acc271, 0x17418996, 0x340b84e5, 0xa90f3ef4, 0xc49d22c7, 0x9e44aad8, 0x22ec9c31, 0x3e1eb8e2, ]; const INPUT_ZERO: [u32; 8] = [0, 0, 0, 0, 0, 0, 0, 0]; // sha256(b"risc0.Output") = // 0x77eafeb366a78b47747de0d7bb176284085ff5564887009a5be63da32d3559d4 const RISC0_OUTPUT_TAG: [u32; 8] = [ 0x77eafeb3, 0x66a78b47, 0x747de0d7, 0xbb176284, 0x85ff556, 0x4887009a, 0x5be63da3, 0x2d3559d4, ]; fn uint256_byte_reverse(x: u256) -> u256 { let new_low = integer::u128_byte_reverse(x.high); let new_high = integer::u128_byte_reverse(x.low); return u256 { low: new_low, high: new_high }; } pub fn journal_sha256(journal: Span) -> Span { let journal_arr: Array = journal.into(); let mut journal_byte_arr = ""; for byte in journal_arr { journal_byte_arr.append_byte(byte); } let journal_digest = compute_sha256_byte_array(@journal_byte_arr); return journal_digest.span(); } // https://github.com/risc0/risc0-ethereum/blob/34d2fee4ca6b5fb354a8a1a00c43f8945097bfe5/contracts/src/IRiscZeroVerifier.sol#L71-L98 pub fn compute_receipt_claim(image_id: Span, journal_digest: Span) -> u256 { usize_assert_eq(image_id.len(), 8); let mut array = array![]; // Tag digest for v in TAG_DIGEST.span() { array.append(*v); } // Input for v in INPUT_ZERO.span() { array.append(*v); } // Pre state digest for v in image_id { array.append(*v); } // Post state digest for v in SYSTEM_STATE_ZERO_DIGEST.span() { array.append(*v); } // Output let output_digest = output_digest(journal_digest); for v in output_digest.span() { array.append(*v); } // Exit_code system (0) (4 bytes) + Exit Code User (0) (4 bytes) array.append(0); array.append(0); // Append 4 << 8 = 1024 to the end of the array (2 bytes) let res_u32 = compute_sha256_u32_array( input: array, last_input_word: 1024, last_input_num_bytes: 2, ) .span(); let res_low: felt252 = (*res_u32[7]).into() + (*res_u32[6]).into() * 0x100000000 + (*res_u32[5]).into() * 0x10000000000000000 + (*res_u32[4]).into() * 0x1000000000000000000000000; let res_high: felt252 = (*res_u32[3]).into() + (*res_u32[2]).into() * 0x100000000 + (*res_u32[1]).into() * 0x10000000000000000 + (*res_u32[0]).into() * 0x1000000000000000000000000; return uint256_byte_reverse( u256 { low: res_low.try_into().unwrap(), high: res_high.try_into().unwrap() }, ); } fn output_digest(journal_digest: Span) -> [u32; 8] { let mut array = array![]; usize_assert_eq(journal_digest.len(), 8); for v in RISC0_OUTPUT_TAG.span() { array.append(*v); } for v in journal_digest { array.append(*v); } // Assumptions digest for v in INPUT_ZERO.span() { array.append(*v); } // Add 2 << 8 = 512 to the end of the array (2 bytes) compute_sha256_u32_array(input: array, last_input_word: 512, last_input_num_bytes: 2) } pub fn deserialize_full_proof_with_hints_risc0( mut serialized: Span, ) -> FullProofWithHintsRisc0 { let groth16_proof_raw = _deserialize_groth16_proof_points(ref serialized); let n_image_id: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mut image_id: Array = array![]; for _ in 0..n_image_id { image_id.append((*serialized.pop_front().unwrap()).try_into().unwrap()); } let n_journal: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mut journal: Array = array![]; for _ in 0..n_journal { journal.append((*serialized.pop_front().unwrap()).try_into().unwrap()); } let mpcheck_hint = _deserialize_mpcheck_hint_bn254(ref serialized); let msm_hint = serialized; return FullProofWithHintsRisc0 { groth16_proof: groth16_proof_raw, image_id: image_id.span(), journal: journal.span(), mpcheck_hint: mpcheck_hint, msm_hint: msm_hint, }; } #[cfg(test)] mod risc0_utils_tests { use super::{compute_receipt_claim, output_digest, uint256_byte_reverse}; #[test] fn test_receipt_claim() { let image_id: [u32; 8] = [ 3491501487, 2808651867, 557489759, 3452720932, 2727640576, 160202435, 1288430228, 1807482899, ]; let journal_digest: [u32; 8] = [ 998783442, 2641348904, 1804572153, 3329687312, 3249394632, 3219372246, 356247808, 552440254, ]; let receipt_claim = compute_receipt_claim(image_id.span(), journal_digest.span()); assert_eq!( receipt_claim, uint256_byte_reverse( 0xe58e40abecebcfa4af85692fca5ed77d4ccb4b3f640f5e684e4faf3a36b0c4e0, ), ); } #[test] fn test_output_digest() { let journal_digest: [u32; 8] = [ 998783442, 2641348904, 1804572153, 3329687312, 3249394632, 3219372246, 356247808, 552440254, ]; let out = output_digest(journal_digest.span()); assert_eq!( out, [ 0x6293f84a, 0xf9e28fcc, 0x43eb4d3d, 0xf962d8d8, 0x1364db76, 0x22a407a1, 0xab5be010, 0x1a1f0a26, ], ); } } ================================================ FILE: src/src/apps/sp1.cairo ================================================ use core::sha256::compute_sha256_u32_array; use corelib_imports::bounded_int::{AddHelper, BoundedInt, MulHelper, UnitInt, bounded_int, upcast}; use garaga::ec::pairing::groth16::{Groth16Proof, verify_groth16_bn254}; use garaga::pairing_check::MPCheckHintBN254; use garaga::utils::calldata::{ Groth16ProofRaw, _deserialize_groth16_proof_points, _deserialize_mpcheck_hint_bn254, }; use super::sp1_constants::{ic, precomputed_lines, vk}; #[derive(Drop)] pub struct FullProofWithHintsSP1 { pub groth16_proof: Groth16ProofRaw, pub vkey: u256, pub public_inputs_sp1: Array, pub mpcheck_hint: MPCheckHintBN254, pub msm_hint: Span, } const POW_32: felt252 = 0x100000000; const POW_64: felt252 = 0x10000000000000000; const POW_96: felt252 = 0x1000000000000000000000000; const POW_32_UI: UnitInt = 0x100000000; const POW_64_UI: UnitInt = 0x10000000000000000; const POW_96_UI: UnitInt = 0x1000000000000000000000000; const POW_128: felt252 = 0x100000000000000000000000000000000; pub type u32_bi = BoundedInt<0, { POW_32 - 1 }>; pub type u64_bi = BoundedInt<0, { POW_64 - 1 }>; pub type u96_bi = BoundedInt<0, { POW_96 - 1 }>; pub type u128_bi = BoundedInt<0, { POW_128 - 1 }>; pub type w1_shift_32 = BoundedInt<0, { 0xffffffff00000000 }>; // (2**32)-1 * 2**32 pub type w2_shift_64 = BoundedInt<0, { 0xffffffff0000000000000000 }>; // (2**32)-1 * 2**64 pub type w3_shift_96 = BoundedInt<0, { 0xffffffff000000000000000000000000 }>; // (2**32)-1 * 2**96 impl MulHelperU32ByPow32Impl of MulHelper> { type Result = w1_shift_32; } impl MulHelperU32ByPow64Impl of MulHelper> { type Result = w2_shift_64; } impl MulHelperU32ByPow96Impl of MulHelper> { type Result = w3_shift_96; } impl AddHelperU32ByW1Impl of AddHelper { type Result = u64_bi; } impl AddHelperU64ByW2Impl of AddHelper { type Result = u96_bi; } impl AddHelperU96ByW3Impl of AddHelper { type Result = u128_bi; } pub fn convert_u32_to_u128(input: [u32; 4]) -> u128 { let [w3, w2, w1, w0] = input; let w3_bi: u32_bi = upcast(w3); let w2_bi: u32_bi = upcast(w2); let w1_bi: u32_bi = upcast(w1); let w0_bi: u32_bi = upcast(w0); let tmp: u64_bi = bounded_int::add(w0_bi, bounded_int::mul(w1_bi, POW_32_UI)); let tmp: u96_bi = bounded_int::add(tmp, bounded_int::mul(w2_bi, POW_64_UI)); let result: u128_bi = bounded_int::add(tmp, bounded_int::mul(w3_bi, POW_96_UI)); return upcast(result); } // 2**253 const POW_253: u256 = 0x2000000000000000000000000000000000000000000000000000000000000000; pub fn process_public_inputs_sp1(public_inputs: Array) -> (Span, u256) { let mut pi = public_inputs.span(); let mut pub_inputs_256: Array = array![]; assert(public_inputs.len() % 8 == 0, 'wrong sp1 pub inputs size'); while let Option::Some(word) = pi.multi_pop_front::<8>() { let [w7, w6, w5, w4, w3, w2, w1, w0] = (*word).unbox(); let high_128 = convert_u32_to_u128([w7, w6, w5, w4]); let low_128 = convert_u32_to_u128([w3, w2, w1, w0]); pub_inputs_256.append(u256 { low: low_128, high: high_128 }); } let [h7, h6, h5, h4, h3, h2, h1, h0] = compute_sha256_u32_array( input: public_inputs, last_input_word: 0, last_input_num_bytes: 0, ); let hash_raw = u256 { low: convert_u32_to_u128([h3, h2, h1, h0]), high: convert_u32_to_u128([h7, h6, h5, h4]), }; let hash_mod = hash_raw % POW_253; return (pub_inputs_256.span(), hash_mod); } pub fn deserialize_full_proof_with_hints_sp1( mut serialized: Span, ) -> FullProofWithHintsSP1 { let groth16_proof_raw = _deserialize_groth16_proof_points(ref serialized); let vkey = u256 { low: (*serialized.pop_front().unwrap()).try_into().unwrap(), high: (*serialized.pop_front().unwrap()).try_into().unwrap(), }; let n_words: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mut public_inputs_sp1: Array = array![]; for _ in 0..n_words { let [w7, w6, w5, w4, w3, w2, w1, w0] = (*serialized.multi_pop_front::<8>().unwrap()) .unbox(); public_inputs_sp1.append(w7.try_into().unwrap()); public_inputs_sp1.append(w6.try_into().unwrap()); public_inputs_sp1.append(w5.try_into().unwrap()); public_inputs_sp1.append(w4.try_into().unwrap()); public_inputs_sp1.append(w3.try_into().unwrap()); public_inputs_sp1.append(w2.try_into().unwrap()); public_inputs_sp1.append(w1.try_into().unwrap()); public_inputs_sp1.append(w0.try_into().unwrap()); } let mpcheck_hint = _deserialize_mpcheck_hint_bn254(ref serialized); let msm_hint = serialized; return FullProofWithHintsSP1 { groth16_proof: groth16_proof_raw, vkey: vkey, public_inputs_sp1: public_inputs_sp1, mpcheck_hint: mpcheck_hint, msm_hint: msm_hint, }; } pub fn verify_groth16_sp1(proof: FullProofWithHintsSP1) -> Result, felt252> { let groth16_proof_raw = proof.groth16_proof; let vkey = proof.vkey; let public_inputs_sp1 = proof.public_inputs_sp1; let mpcheck_hint = proof.mpcheck_hint; let mut msm_hint = proof.msm_hint; let _ = msm_hint.pop_front().unwrap(); let (_pub_inputs_256, pub_input_hash): (Span, u256) = process_public_inputs_sp1( public_inputs_sp1, ); let proof_pub_input = array![vkey, pub_input_hash]; let proof = Groth16Proof { raw: groth16_proof_raw, public_inputs: proof_pub_input.span() }; let result = verify_groth16_bn254( vk, precomputed_lines.span(), ic.span(), proof, msm_hint, mpcheck_hint, ); match result { Result::Ok(_) => Result::Ok(proof.public_inputs), Result::Err(error) => Result::Err(error), } } #[cfg(test)] mod tests { use super::convert_u32_to_u128; #[test] fn test_convert_u32_to_u128() { let input = [0, 0, 0, 1]; let result = convert_u32_to_u128(input); assert_eq!(result, 1); } } ================================================ FILE: src/src/apps/sp1_constants.cairo ================================================ // Generated by Garaga version 1.1.0 use garaga::definitions::{E12D, G1Point, G2Line, G2Point, u288, u384}; use garaga::groth16::Groth16VerifyingKey; pub const N_PUBLIC_INPUTS: usize = 2; pub const vk: Groth16VerifyingKey = Groth16VerifyingKey { alpha_beta_miller_loop_result: E12D { w0: u288 { limb0: 0x38febe9f87f730fa3e5bd174, limb1: 0xf763950637a776ef9e248435, limb2: 0x29dc2d37c63acbda, }, w1: u288 { limb0: 0xa31610a97aa4e4539be919ff, limb1: 0xfa4d4bfb72b6a3c002018e97, limb2: 0x1968ab971e610fce, }, w2: u288 { limb0: 0xee6c1ce3a15313c6f9d57f7e, limb1: 0xd37e28396640fcfe5f122aae, limb2: 0x210d3763f7a27517, }, w3: u288 { limb0: 0x7746ddac185562e756b1b92f, limb1: 0x44f8b75638ef5a373f319cd8, limb2: 0x51e9605db4edac6, }, w4: u288 { limb0: 0xc29e0c2ac434301d671ffa56, limb1: 0xa06f1db2d4ca4dd88f979102, limb2: 0x1d0126fb7d721e02, }, w5: u288 { limb0: 0xed2e022e10acbeb35084dc1, limb1: 0xf9de514baee870f114669060, limb2: 0x10889a0f300ce96c, }, w6: u288 { limb0: 0xeec23aadde92d2dd00e4568e, limb1: 0x6d5b4b63667db8f10bd851ab, limb2: 0x18f1dd15d2e64c69, }, w7: u288 { limb0: 0x2131bad24ea07a033d0bf397, limb1: 0xb6312a7f2622146be93b5950, limb2: 0x227e61ca055f0ac3, }, w8: u288 { limb0: 0xb896f30b06350f012274ebcd, limb1: 0xd14298f13a76183170aafe08, limb2: 0x302bfd90358d23a0, }, w9: u288 { limb0: 0x679d91263798da428fa5ea62, limb1: 0x806797d163f4df8b55ec774c, limb2: 0x29b72d4ec063face, }, w10: u288 { limb0: 0x4dbef45fe0c5a14bef7c4a90, limb1: 0xd4ae215c443d0f0768198bc6, limb2: 0x2fcc02633e427272, }, w11: u288 { limb0: 0x7308cad65773475443cfbd80, limb1: 0x972f90a77f1a8aeece6571ff, limb2: 0x2d3a570362a9fd7f, }, }, gamma_g2: G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }, delta_g2: G2Point { x0: u384 { limb0: 0x777a63b327d736bffb0122ed, limb1: 0x2caf27354d28e4b8f83d3b76, limb2: 0x3ff41f4ba0c37fe, limb3: 0x0, }, x1: u384 { limb0: 0xc020024521998269845f74e6, limb1: 0x21f01ecc9b46d236e0865e0c, limb2: 0x1cc7cb8de715675f, limb3: 0x0, }, y0: u384 { limb0: 0x264a04499f7e2f6df690dd85, limb1: 0x909b4f1c3d80fcd6865afc4a, limb2: 0x17387b4b9cf03927, limb3: 0x0, }, y1: u384 { limb0: 0xf614f4fd11b56b3c5e53c44c, limb1: 0xd19a3d72dcd590ac85a971de, limb2: 0x2ed3b19b5eb39db0, limb3: 0x0, }, }, }; pub const ic: [G1Point; 3] = [ G1Point { x: u384 { limb0: 0x33db734c451d28b58aa9758e, limb1: 0x4ea0a694cd3743ebf5247792, limb2: 0x26091e1cafb0ad8a, limb3: 0x0, }, y: u384 { limb0: 0xefa65a3e782e7ba70b66690e, limb1: 0xca6fdb2690a124f8ce25489f, limb2: 0x9ff50a6b8b11c3, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0xec878755e537c1c48951fb4c, limb1: 0x2607c227d090cca750ed36c6, limb2: 0x61c3fd0fd3da25d, limb3: 0x0, }, y: u384 { limb0: 0x3e6119a212dd09eb51707219, limb1: 0xdf7b5c65eff0e107055e9a27, limb2: 0xfa17ae9c2033379, limb3: 0x0, }, }, G1Point { x: u384 { limb0: 0xa16028dee020634fd129e71c, limb1: 0x7fe0e0e2ead0b2ec4ffdec51, limb2: 0x4eab241388a7981, limb3: 0x0, }, y: u384 { limb0: 0xca56b18d5544b0889a65c1f5, limb1: 0x2f0bdbf95cff83e03ea9e16f, limb2: 0x7236256d21c60d0, limb3: 0x0, }, }, ]; pub const precomputed_lines: [G2Line; 176] = [ G2Line { r0a0: u288 { limb0: 0x4d347301094edcbfa224d3d5, limb1: 0x98005e68cacde68a193b54e6, limb2: 0x237db2935c4432bc, }, r0a1: u288 { limb0: 0x6b4ba735fba44e801d415637, limb1: 0x707c3ec1809ae9bafafa05dd, limb2: 0x124077e14a7d826a, }, r1a0: u288 { limb0: 0x49a8dc1dd6e067932b6a7e0d, limb1: 0x7676d0000961488f8fbce033, limb2: 0x3b7178c857630da, }, r1a1: u288 { limb0: 0x98c81278efe1e96b86397652, limb1: 0xe3520b9dfa601ead6f0bf9cd, limb2: 0x2b17c2b12c26fdd0, }, }, G2Line { r0a0: u288 { limb0: 0x7cbf2d97579849ed7f37f916, limb1: 0x7c7c7cabc0338914ae612207, limb2: 0x7f04129bafedc9a, }, r0a1: u288 { limb0: 0x28db0f05530a21fac876cfe4, limb1: 0xb08060f001e32bf0f4beff7a, limb2: 0x1758a3c93ad8f055, }, r1a0: u288 { limb0: 0x53ad64ec102823f3f1d3fd30, limb1: 0xe512e2de1e37f60219c44720, limb2: 0xb05a57aa94413c8, }, r1a1: u288 { limb0: 0x3c6bb091ccdadd1f42045694, limb1: 0x5756eeec096f1de96f136d22, limb2: 0xe9421367ecf6d7f, }, }, G2Line { r0a0: u288 { limb0: 0x1b3d578c32d1af5736582972, limb1: 0x204fe74db6b371d37e4615ab, limb2: 0xce69bdf84ed6d6d, }, r0a1: u288 { limb0: 0xfd262357407c3d96bb3ba710, limb1: 0x47d406f500e66ea29c8764b3, limb2: 0x1e23d69196b41dbf, }, r1a0: u288 { limb0: 0x1ec8ee6f65402483ad127f3a, limb1: 0x41d975b678200fce07c48a5e, limb2: 0x2cad36e65bbb6f4f, }, r1a1: u288 { limb0: 0xcfa9b8144c3ea2ab524386f5, limb1: 0xd4fe3a18872139b0287570c3, limb2: 0x54c8bc1b50aa258, }, }, G2Line { r0a0: u288 { limb0: 0xb5ee22ba52a7ed0c533b7173, limb1: 0xbfa13123614ecf9c4853249b, limb2: 0x6567a7f6972b7bb, }, r0a1: u288 { limb0: 0xcf422f26ac76a450359f819e, limb1: 0xc42d7517ae6f59453eaf32c7, limb2: 0x899cb1e339f7582, }, r1a0: u288 { limb0: 0x9f287f4842d688d7afd9cd67, limb1: 0x30af75417670de33dfa95eda, limb2: 0x1121d4ca1c2cab36, }, r1a1: u288 { limb0: 0x7c4c55c27110f2c9a228f7d8, limb1: 0x8f14f6c3a2e2c9d74b347bfe, limb2: 0x83ef274ba7913a5, }, }, G2Line { r0a0: u288 { limb0: 0xebb29cf5e488422959450431, limb1: 0x3bd3c90ac14dcf48e9204889, limb2: 0x28740d492632c38f, }, r0a1: u288 { limb0: 0x3f96bb87e9166a1c10062d63, limb1: 0x7cfe4c67f9e2c6ca2c26b17, limb2: 0x190baaa9a658afd4, }, r1a0: u288 { limb0: 0x14c465a12bf86822e6a90017, limb1: 0xd33d62d86349625b7dbd2371, limb2: 0x255ea8f837ed8c60, }, r1a1: u288 { limb0: 0x2c0619fb6f45aef79678a6b3, limb1: 0x60f956ca78123a74286dfd6f, limb2: 0x21d02d3c626232aa, }, }, G2Line { r0a0: u288 { limb0: 0xc6a50211bb4e98f1dbcc18c6, limb1: 0x9847d0e53a837fae823cd4ea, 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0x41ac3502f8b693b2f9ed1a29, limb2: 0x12d36862936402d, }, r0a1: u288 { limb0: 0xaade7b42e239d7be07481e78, limb1: 0x3f8243ee7eb4a9c3b7cbb956, limb2: 0xaf29236a909acbb, }, r1a0: u288 { limb0: 0xbfa7efb7457cc99dd4b66e37, limb1: 0x1aff3d917e026429380e9dc6, limb2: 0x87399bf2ca178f4, }, r1a1: u288 { limb0: 0x351e9fa186b018907f3dfd58, limb1: 0x7027b103c6f3030eb6f019b0, limb2: 0x288a941ff1ef82c8, }, }, G2Line { r0a0: u288 { limb0: 0x280d19be00a1fbb9ccaafb46, limb1: 0x4d694832b9452e3da1f121cd, limb2: 0x2a866c481e54b43e, }, r0a1: u288 { limb0: 0x94acc4d34d73a6813c99def3, limb1: 0x2e9a78d89158c8144f4a163d, limb2: 0x6a7ba87130777b1, }, r1a0: u288 { limb0: 0xa171b01ed37b9874fc4b2fd1, limb1: 0x644415f2fadd9f5572937ff, limb2: 0x188c19a6dbd348f6, }, r1a1: u288 { limb0: 0xa8b807a7d82b4ca8813e6c16, limb1: 0xd36395399fea43c401b55926, limb2: 0x1ebe1e6668036172, }, }, G2Line { r0a0: u288 { limb0: 0x537ecf0916b38aeea21d4e47, limb1: 0x181a00de27ba4be1b380d6c8, limb2: 0x8c2fe2799316543, }, r0a1: u288 { limb0: 0xe68fff5ee73364fff3fe403b, limb1: 0x7b8685c8a725ae79cfac8f99, limb2: 0x7b4be349766aba4, }, r1a0: u288 { limb0: 0xdf7c93c0095545ad5e5361ea, limb1: 0xce316c76191f1e7cd7d03f3, limb2: 0x22ea21f18ddec947, }, r1a1: u288 { limb0: 0xa19620b4c32db68cc1c2ef0c, limb1: 0xffa1e4be3bed5faba2ccbbf4, limb2: 0x16fc78a64c45f518, }, }, G2Line { r0a0: u288 { limb0: 0x2b6af476f520b4bf804415bc, limb1: 0xd949ee7f9e8874698b090fca, limb2: 0x34db5e5ec2180cf, }, r0a1: u288 { limb0: 0x3e06a324f038ac8abcfb28d7, limb1: 0xc2e6375b7a83c0a0145f8942, limb2: 0x2247e79161483763, }, r1a0: u288 { limb0: 0x708773d8ae3a13918382fb9d, limb1: 0xaf83f409556e32aa85ae92bf, limb2: 0x9af0a924ae43ba, }, r1a1: u288 { limb0: 0xa6fded212ff5b2ce79755af7, limb1: 0x55a2adfb2699ef5de6581b21, limb2: 0x2476e83cfe8daa5c, }, }, G2Line { r0a0: u288 { limb0: 0x732b1d0e86389fae1b305692, limb1: 0x5e1ed01fae18aa2d2e501b89, limb2: 0x198dc823ba823f13, }, r0a1: u288 { limb0: 0x395ecb34fbf15f7b72c54317, limb1: 0x19fb1bd9a5cabbf5eb248610, limb2: 0xb73bf1e6f4b2b31, }, r1a0: u288 { limb0: 0x69471a9ea2a3b85c26c836d9, limb1: 0xe814a8008320f1fe43f51f0a, limb2: 0x2d0070077956b257, }, r1a1: u288 { limb0: 0xc2ed008982c3b3a2381a1d13, limb1: 0x3aa758745a68a1c386ea1919, limb2: 0x1f719f31da901ffd, }, }, G2Line { r0a0: u288 { limb0: 0xa773ff432f3fcb587a0ba2dd, limb1: 0xa72f6d2ad27b55412047c8a2, limb2: 0x196c95f5075736cc, }, r0a1: u288 { limb0: 0x8d46b81c8d7815fb84f68477, limb1: 0x759aa3f94e1cbaff6069a0e0, limb2: 0x25349de9eb818c1b, }, r1a0: u288 { limb0: 0x7e987a2cbb6794ba7ad8226b, limb1: 0x37b8b1d26e87ac1cc75bc768, limb2: 0x1b6594b5683fb78c, }, r1a1: u288 { limb0: 0x6db02d761232580559059396, limb1: 0x4608f90f5be37fcf1ca05d00, limb2: 0x8280f225a44efb3, }, }, G2Line { r0a0: u288 { limb0: 0x1c4759bcf7c607fe3f839d4d, limb1: 0xea91f311da73327e2ed40785, limb2: 0x2017052c72360f42, }, r0a1: u288 { limb0: 0x38cf8a4368c0709980199fc3, limb1: 0xfc9047885996c19e84d7d4ea, limb2: 0x1795549eb0b97783, }, r1a0: u288 { limb0: 0xb70f7ecfbec0eaf46845e8cc, limb1: 0x9ddf274c2a9f89ea3bc4d66f, limb2: 0xcc6f106abfcf377, }, r1a1: u288 { limb0: 0xf6ff11ce29186237468c2698, limb1: 0x5c629ad27bb61e4826bb1313, limb2: 0x2014c6623f1fb55e, }, }, G2Line { r0a0: u288 { limb0: 0xeba6e51ec8e06f1a878b476b, limb1: 0xc701590aac4f7059ebebecc7, limb2: 0x178ad12f64b4cce0, }, r0a1: u288 { limb0: 0xd26c1a0c4cd1c5e42e3b29b1, limb1: 0x344935f56b019eefc0ae9366, limb2: 0x2ac2051a8e04afa1, }, r1a0: u288 { limb0: 0x5d6f37a0a446777c90c36deb, limb1: 0x2fb002f2be492ec5d334587f, limb2: 0x2300ad73e7a9475e, }, r1a1: u288 { limb0: 0x579a05a596e27b546604bf72, limb1: 0x9062b97873327607c1e5fce4, limb2: 0x2d3543a9b5a8d09, }, }, G2Line { r0a0: u288 { limb0: 0xc648054e4b6134bbfd68487f, limb1: 0xdf0506dad3f3d098c13a6386, limb2: 0x26bebeb6f46c2e8c, }, r0a1: u288 { limb0: 0x9d0cdb28a94204776c6e6ba6, limb1: 0x303f02dfe619752b1607951d, limb2: 0x1127d8b17ef2c064, }, r1a0: u288 { limb0: 0xe34ca1188b8db4e4694a696c, limb1: 0x243553602481d9b88ca1211, limb2: 0x1f8ef034831d0132, }, r1a1: u288 { limb0: 0xe3a5dfb1785690dad89ad10c, limb1: 0xd690b583ace24ba033dd23e0, limb2: 0x405d0709e110c03, }, }, G2Line { r0a0: u288 { limb0: 0xe64904238461826f7b9b6bd1, limb1: 0x7eef335c29c10b073c3c8df, limb2: 0x11ab7f696cecd13b, }, r0a1: u288 { limb0: 0xa4ee9a0489ebf368f8d5b7df, limb1: 0xfc2fb710377d3a9b68d87438, limb2: 0xbb582e949e0b05c, }, r1a0: u288 { limb0: 0x4942e63133bef00be3e86722, limb1: 0x159a6773262b5a5ffe915583, limb2: 0x26cb6b36d9d079a0, }, r1a1: u288 { limb0: 0x923f51c6ac50ef980fc5c63e, limb1: 0x7431352b389608ee374cc6f7, limb2: 0x205d7212a2bb155f, }, }, G2Line { r0a0: u288 { limb0: 0x72cc2cef2785ce4ff4e9b7af, limb1: 0x60ed5b9c207d7f31fb6234ab, limb2: 0x1bb17a4bc7b643ed, }, r0a1: u288 { limb0: 0x9424eb15b502cde7927c7530, limb1: 0xa0e33edbbaa9de8e9c206059, limb2: 0x2b9a3a63bbf4af99, }, r1a0: u288 { limb0: 0x423811cb6386e606cf274a3c, limb1: 0x8adcc0e471ecfe526f56dc39, limb2: 0x9169a8660d14368, }, r1a1: u288 { limb0: 0xf616c863890c3c8e33127931, limb1: 0xcc9414078a6da6989dae6b91, limb2: 0x594d6a7e6b34ab2, }, }, G2Line { r0a0: u288 { limb0: 0xd1ef4e012e4ddec967871f0c, limb1: 0x73a1f0eaa41d3b58b2410cc5, limb2: 0x678a431a3208d78, }, r0a1: u288 { limb0: 0x1182bff7a17bbcb072bce5d2, limb1: 0xe8d0894231092859c53b6a86, limb2: 0x2a8df47f9e66fa63, }, r1a0: u288 { limb0: 0xef6ef9aa3976f4dd18917f5a, limb1: 0x544992409f5d8c72277c40a5, limb2: 0x269adf40fda899e9, }, r1a1: u288 { limb0: 0x1272a877af1721f324764564, limb1: 0x9cfb207d93eef259ff85dd53, limb2: 0x1738f274efa92229, }, }, G2Line { r0a0: u288 { limb0: 0xf2d619ae78049bf9141c35cf, limb1: 0x717f8b10d469a1ee2d91f191, limb2: 0x2c72c82fa8afe345, }, r0a1: u288 { limb0: 0xb89321223b82a2dc793c0185, limb1: 0x71506a0cf4adb8e51bb7b759, limb2: 0x2c13b92a98651492, }, r1a0: u288 { limb0: 0x4947ef2c89276f77f9d20942, limb1: 0xb454d68685ab6b6976e71ec5, limb2: 0x19a938d0e78a3593, }, r1a1: u288 { limb0: 0xbe883eb119609b489c01c905, limb1: 0xaa06779922047f52feac5ce6, limb2: 0x76977a3015dc164, }, }, G2Line { r0a0: u288 { limb0: 0x43a96a588005043a46aadf2c, limb1: 0xa37b89d8a1784582f0c52126, limb2: 0x22e9ef3f5d4b2297, }, r0a1: u288 { limb0: 0x8c6f6d8474cf6e5a58468a31, limb1: 0xeb1ce6ac75930ef1c79b07e5, limb2: 0xf49839a756c7230, }, r1a0: u288 { limb0: 0x82b84693a656c8e8c1f962fd, limb1: 0x2c1c8918ae80282208b6b23d, limb2: 0x14d3504b5c8d428f, }, r1a1: u288 { limb0: 0x60ef4f4324d5619b60a3bb84, limb1: 0x6d3090caefeedbc33638c77a, limb2: 0x159264c370c89fec, }, }, G2Line { r0a0: u288 { limb0: 0x3a0493f840a637df757ffbd, limb1: 0x78784ce2127de5ab9fd43f98, limb2: 0x404e6e7d65575af, }, r0a1: u288 { limb0: 0x40a91253ff86fe1a9f30b23, limb1: 0x9876650a81d21ccadf7b5a47, limb2: 0x23641d1989cf0d22, }, r1a0: u288 { limb0: 0xd686edf528c50fe4b5fc743d, limb1: 0xaff67da08ae2568924ba172c, limb2: 0x147e9121533c6431, }, r1a1: u288 { limb0: 0xad80f0aa65056d5483a4ab44, limb1: 0x6e8e1992f62ad66fac7881b4, limb2: 0x24a28d1d5d8e8f3b, }, }, G2Line { r0a0: u288 { limb0: 0xea1771c5a15aef9e3079786d, limb1: 0x77a90b139183352b680523a0, limb2: 0x232c100c95eae30e, }, r0a1: u288 { limb0: 0x6b283b2e00ceee9181913d03, limb1: 0x977d294255416755d5596a3d, limb2: 0x25678644f6a5053d, }, r1a0: u288 { limb0: 0xa543b526974a72bd42654bfb, limb1: 0xdf95c5b8a9328fc318d7b435, limb2: 0x161ef71b5e24d302, }, r1a1: u288 { limb0: 0x7412e2b94a4551851b42cd3, limb1: 0xac25f9bbd0d7eb7e7789a8af, limb2: 0x26d86a5064526fcb, }, }, ]; ================================================ FILE: src/src/basic_field_ops.cairo ================================================ use core::circuit::{ CircuitElement, CircuitElement as CE, CircuitInput, CircuitInput as CI, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use core::num::traits::Zero; use corelib_imports::bounded_int::upcast; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{E12D, get_BLS12_381_modulus, get_BN254_modulus, u288}; use garaga::utils::hashing::{PoseidonState, hades_permutation, hash_quadruple_u288}; const POW_2_32_252: felt252 = 0x100000000; const POW_2_64_252: felt252 = 0x10000000000000000; const POW_2_256_384: u384 = u384 { limb0: 0x0, limb1: 0x0, limb2: 0x10000000000000000, limb3: 0x0 }; // Reduces a u384 given a circuit modulus by computing (a + 0) mod p. // Circuits outputs are reduced mod p. pub fn reduce_mod_p(a: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let reduce = circuit_add(in1, in2); let outputs = (reduce,) .new_inputs() .next_2(a) .next_2([0, 0, 0, 0]) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(reduce); } pub fn neg_mod_p(a: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let neg = circuit_sub(in1, in2); let outputs = (neg,) .new_inputs() .next_2([0, 0, 0, 0]) .next_2(a) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(neg); } // Returns true if a == -b mod p (a + b = 0 mod p) pub fn is_opposite_mod_p(a: u384, b: u384, modulus: CircuitModulus) -> bool { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let sum = circuit_add(in1, in2); let outputs = (sum,).new_inputs().next_2(a).next_2(b).done_2().eval(modulus).unwrap(); return outputs.get_output(sum).is_zero(); } // Returns true if a == 0 mod p (p must be odd prime) pub fn is_zero_mod_p(a: u384, modulus: CircuitModulus) -> bool { let in1 = CircuitElement::> {}; let sum = circuit_add(in1, in1); let outputs = (sum,).new_inputs().next_2(a).done_2().eval(modulus).unwrap(); return outputs.get_output(sum).is_zero(); } pub fn is_even_u384(a: u384) -> bool { let limb0_u128: u128 = upcast(a.limb0); limb0_u128 % 2 == 0 } pub fn u32_8_to_u384(a: [u32; 8]) -> u384 { let [a_0, a_1, a_2, a_3, a_4, a_5, a_6, a_7] = a; let l0: felt252 = a_7.into() + a_6.into() * POW_2_32_252 + a_5.into() * POW_2_64_252; let l1: felt252 = a_4.into() + a_3.into() * POW_2_32_252 + a_2.into() * POW_2_64_252; let l2: felt252 = a_1.into() + a_0.into() * POW_2_32_252; u384 { limb0: l0.try_into().unwrap(), limb1: l1.try_into().unwrap(), limb2: l2.try_into().unwrap(), limb3: 0, } } // Takes big endian u512 and returns a u384 mod modulus // u512 = low_256 + high_256 * 2^256 // u512 % p = (low_256 + high_256 * 2^256) % p // = (low_256 % p + high_256 * 2^256 % p) % p // CAUTION : a_high and a_low are expected to be < 2^256. No check is performed. pub fn u512_mod_p(high_256: u384, low_256: u384, modulus: CircuitModulus) -> u384 { let low = CircuitElement::> {}; let high = CircuitElement::> {}; let shift = CircuitElement::> {}; let high_shifted = circuit_mul(high, shift); let res = circuit_add(low, high_shifted); let outputs = (res,) .new_inputs() .next_2(low_256) .next_2(high_256) .next_2(POW_2_256_384) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(res); } pub fn add_mod_p(a: u384, b: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let add = circuit_add(in1, in2); let outputs = (add,).new_inputs().next_2(a).next_2(b).done_2().eval(modulus).unwrap(); return outputs.get_output(add); } pub fn sub_mod_p(a: u384, b: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let sub = circuit_sub(in1, in2); let outputs = (sub,).new_inputs().next_2(a).next_2(b).done_2().eval(modulus).unwrap(); return outputs.get_output(sub); } pub fn mul_mod_p(a: u384, b: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let mul = circuit_mul(in1, in2); let outputs = (mul,).new_inputs().next_2(a).next_2(b).done_2().eval(modulus).unwrap(); return outputs.get_output(mul); } #[inline(always)] pub fn batch_3_mod_p(x: u384, y: u384, z: u384, c0: u384, modulus: CircuitModulus) -> u384 { let _x = CircuitElement::> {}; let _y = CircuitElement::> {}; let _z = CircuitElement::> {}; let _c0 = CircuitElement::> {}; let _c1 = circuit_mul(_c0, _c0); let _c2 = circuit_mul(_c1, _c0); let _mul1 = circuit_mul(_x, _c0); let _mul2 = circuit_mul(_y, _c1); let _mul3 = circuit_mul(_z, _c2); let res = circuit_add(circuit_add(_mul1, _mul2), _mul3); let outputs = (res,) .new_inputs() .next_2(x) .next_2(y) .next_2(z) .next_2(c0) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(res); } pub fn inv_mod_p(a: u384, modulus: CircuitModulus) -> u384 { let in1 = CircuitElement::> {}; let inv = circuit_inverse(in1); let outputs = (inv,).new_inputs().next_2(a).done_2().eval(modulus).unwrap(); return outputs.get_output(inv); } #[inline(always)] pub fn eval_and_hash_E12D_u288_transcript( transcript: Span>, mut s: PoseidonState, z: u384, ) -> (PoseidonState, Array) { let base: felt252 = 79228162514264337593543950336; // 2**96 let mut evals: Array = array![]; let modulus = get_BN254_modulus(); // BN254 prime field modulus for elmt in transcript { let elmt = *elmt; let _s = hash_quadruple_u288(elmt.w0, elmt.w1, elmt.w2, elmt.w3, base, s); let _s = hash_quadruple_u288(elmt.w4, elmt.w5, elmt.w6, elmt.w7, base, _s); let _s = hash_quadruple_u288(elmt.w8, elmt.w9, elmt.w10, elmt.w11, base, _s); s = _s; let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let in12 = CE::> {}; let t0 = circuit_mul(in11, in12); // Eval X Horner step: multiply by z let t1 = circuit_add(in10, t0); // Eval X Horner step: add coefficient_10 let t2 = circuit_mul(t1, in12); // Eval X Horner step: multiply by z let t3 = circuit_add(in9, t2); // Eval X Horner step: add coefficient_9 let t4 = circuit_mul(t3, in12); // Eval X Horner step: multiply by z let t5 = circuit_add(in8, t4); // Eval X Horner step: add coefficient_8 let t6 = circuit_mul(t5, in12); // Eval X Horner step: multiply by z let t7 = circuit_add(in7, t6); // Eval X Horner step: add coefficient_7 let t8 = circuit_mul(t7, in12); // Eval X Horner step: multiply by z let t9 = circuit_add(in6, t8); // Eval X Horner step: add coefficient_6 let t10 = circuit_mul(t9, in12); // Eval X Horner step: multiply by z let t11 = circuit_add(in5, t10); // Eval X Horner step: add coefficient_5 let t12 = circuit_mul(t11, in12); // Eval X Horner step: multiply by z let t13 = circuit_add(in4, t12); // Eval X Horner step: add coefficient_4 let t14 = circuit_mul(t13, in12); // Eval X Horner step: multiply by z let t15 = circuit_add(in3, t14); // Eval X Horner step: add coefficient_3 let t16 = circuit_mul(t15, in12); // Eval X Horner step: multiply by z let t17 = circuit_add(in2, t16); // Eval X Horner step: add coefficient_2 let t18 = circuit_mul(t17, in12); // Eval X Horner step: multiply by z let t19 = circuit_add(in1, t18); // Eval X Horner step: add coefficient_1 let t20 = circuit_mul(t19, in12); // Eval X Horner step: multiply by z let t21 = circuit_add(in0, t20); // Eval X Horner step: add coefficient_0 let mut circuit_inputs = (t21,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(elmt.w0); // in0 circuit_inputs = circuit_inputs.next_2(elmt.w1); // in1 circuit_inputs = circuit_inputs.next_2(elmt.w2); // in2 circuit_inputs = circuit_inputs.next_2(elmt.w3); // in3 circuit_inputs = circuit_inputs.next_2(elmt.w4); // in4 circuit_inputs = circuit_inputs.next_2(elmt.w5); // in5 circuit_inputs = circuit_inputs.next_2(elmt.w6); // in6 circuit_inputs = circuit_inputs.next_2(elmt.w7); // in7 circuit_inputs = circuit_inputs.next_2(elmt.w8); // in8 circuit_inputs = circuit_inputs.next_2(elmt.w9); // in9 circuit_inputs = circuit_inputs.next_2(elmt.w10); // in10 circuit_inputs = circuit_inputs.next_2(elmt.w11); // in11 circuit_inputs = circuit_inputs.next_2(z); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let f_of_z: u384 = outputs.get_output(t21); evals.append(f_of_z); } return (s, evals); } #[inline(always)] pub fn eval_and_hash_E12D_u384_transcript( transcript: Span>, mut s: PoseidonState, z: u384, ) -> (PoseidonState, Array) { let base: felt252 = 79228162514264337593543950336; // 2**96 let mut evals: Array = array![]; let modulus = get_BLS12_381_modulus(); // BLS12_381 prime field modulus for elmt in transcript { let elmt = *elmt; let in_1 = s.s0 + elmt.w0.limb0.into() + base * elmt.w0.limb1.into(); let in_2 = s.s1 + elmt.w0.limb2.into() + base * elmt.w0.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); let in_1 = _s0 + elmt.w1.limb0.into() + base * elmt.w1.limb1.into(); let in_2 = _s1 + elmt.w1.limb2.into() + base * elmt.w1.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w2.limb0.into() + base * elmt.w2.limb1.into(); let in_2 = _s1 + elmt.w2.limb2.into() + base * elmt.w2.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w3.limb0.into() + base * elmt.w3.limb1.into(); let in_2 = _s1 + elmt.w3.limb2.into() + base * elmt.w3.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w4.limb0.into() + base * elmt.w4.limb1.into(); let in_2 = _s1 + elmt.w4.limb2.into() + base * elmt.w4.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w5.limb0.into() + base * elmt.w5.limb1.into(); let in_2 = _s1 + elmt.w5.limb2.into() + base * elmt.w5.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w6.limb0.into() + base * elmt.w6.limb1.into(); let in_2 = _s1 + elmt.w6.limb2.into() + base * elmt.w6.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w7.limb0.into() + base * elmt.w7.limb1.into(); let in_2 = _s1 + elmt.w7.limb2.into() + base * elmt.w7.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w8.limb0.into() + base * elmt.w8.limb1.into(); let in_2 = _s1 + elmt.w8.limb2.into() + base * elmt.w8.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w9.limb0.into() + base * elmt.w9.limb1.into(); let in_2 = _s1 + elmt.w9.limb2.into() + base * elmt.w9.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w10.limb0.into() + base * elmt.w10.limb1.into(); let in_2 = _s1 + elmt.w10.limb2.into() + base * elmt.w10.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt.w11.limb0.into() + base * elmt.w11.limb1.into(); let in_2 = _s1 + elmt.w11.limb2.into() + base * elmt.w11.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); s = PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let in12 = CE::> {}; let t0 = circuit_mul(in11, in12); // Eval X Horner step: multiply by z let t1 = circuit_add(in10, t0); // Eval X Horner step: add coefficient_10 let t2 = circuit_mul(t1, in12); // Eval X Horner step: multiply by z let t3 = circuit_add(in9, t2); // Eval X Horner step: add coefficient_9 let t4 = circuit_mul(t3, in12); // Eval X Horner step: multiply by z let t5 = circuit_add(in8, t4); // Eval X Horner step: add coefficient_8 let t6 = circuit_mul(t5, in12); // Eval X Horner step: multiply by z let t7 = circuit_add(in7, t6); // Eval X Horner step: add coefficient_7 let t8 = circuit_mul(t7, in12); // Eval X Horner step: multiply by z let t9 = circuit_add(in6, t8); // Eval X Horner step: add coefficient_6 let t10 = circuit_mul(t9, in12); // Eval X Horner step: multiply by z let t11 = circuit_add(in5, t10); // Eval X Horner step: add coefficient_5 let t12 = circuit_mul(t11, in12); // Eval X Horner step: multiply by z let t13 = circuit_add(in4, t12); // Eval X Horner step: add coefficient_4 let t14 = circuit_mul(t13, in12); // Eval X Horner step: multiply by z let t15 = circuit_add(in3, t14); // Eval X Horner step: add coefficient_3 let t16 = circuit_mul(t15, in12); // Eval X Horner step: multiply by z let t17 = circuit_add(in2, t16); // Eval X Horner step: add coefficient_2 let t18 = circuit_mul(t17, in12); // Eval X Horner step: multiply by z let t19 = circuit_add(in1, t18); // Eval X Horner step: add coefficient_1 let t20 = circuit_mul(t19, in12); // Eval X Horner step: multiply by z let t21 = circuit_add(in0, t20); // Eval X Horner step: add coefficient_0 let mut circuit_inputs = (t21,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(elmt.w0); // in0 circuit_inputs = circuit_inputs.next_2(elmt.w1); // in1 circuit_inputs = circuit_inputs.next_2(elmt.w2); // in2 circuit_inputs = circuit_inputs.next_2(elmt.w3); // in3 circuit_inputs = circuit_inputs.next_2(elmt.w4); // in4 circuit_inputs = circuit_inputs.next_2(elmt.w5); // in5 circuit_inputs = circuit_inputs.next_2(elmt.w6); // in6 circuit_inputs = circuit_inputs.next_2(elmt.w7); // in7 circuit_inputs = circuit_inputs.next_2(elmt.w8); // in8 circuit_inputs = circuit_inputs.next_2(elmt.w9); // in9 circuit_inputs = circuit_inputs.next_2(elmt.w10); // in10 circuit_inputs = circuit_inputs.next_2(elmt.w11); // in11 circuit_inputs = circuit_inputs.next_2(z); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let f_of_z: u384 = outputs.get_output(t21); evals.append(f_of_z); } return (s, evals); } ================================================ FILE: src/src/circuits/README.md ================================================ This folder contains autogenerated circuits only. To regenerate the circuits, run the following command from the root of the repository: ```bash make rewrite ``` See the corresponding script in [tools/make/rewrite.sh](../../../tools/make/rewrite.sh) ================================================ FILE: src/src/circuits/dummy.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; #[inline(always)] pub fn run_DUMMY_circuit(mut input: Array, curve_index: usize) -> Array { // INPUT stack let (in0, in1) = (CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in1); let t1 = circuit_inverse(in1); let t2 = circuit_mul(in0, t1); let t3 = circuit_add(t0, t2); let t4 = circuit_sub(t0, t2); let t5 = circuit_mul(t0, t2); let t6 = circuit_inverse(t2); let t7 = circuit_mul(t0, t6); let modulus = crate::definitions::get_modulus(curve_index); let mut circuit_inputs = (t0, t2, t3, t4, t5, t7).new_inputs(); // Prefill constants: // Fill inputs: let mut input = input; while let Option::Some(val) = input.pop_front() { circuit_inputs = circuit_inputs.next_2(val); } let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res = array![ outputs.get_output(t0), outputs.get_output(t2), outputs.get_output(t3), outputs.get_output(t4), outputs.get_output(t5), outputs.get_output(t7), ]; return res; } ================================================ FILE: src/src/circuits/ec.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{G1Point, G2Point}; impl CircuitDefinition27< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, > of core::circuit::CircuitDefinition< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), > { type CircuitType = core::circuit::Circuit< ( E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, ), >; } impl MyDrp_27< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, > of Drop< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), >; impl CircuitDefinition28< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, > of core::circuit::CircuitDefinition< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), > { type CircuitType = core::circuit::Circuit< ( E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, ), >; } impl MyDrp_28< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, E25, E26, E27, > of Drop< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), >; #[inline(always)] pub fn run_ADD_EC_POINTS_G2_circuit( p: G2Point, q: G2Point, modulus: core::circuit::CircuitModulus, ) -> (G2Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8) = (CE::> {}, CE::> {}); let t0 = circuit_sub(in3, in7); // Fp2 sub coeff 0/1 let t1 = circuit_sub(in4, in8); // Fp2 sub coeff 1/1 let t2 = circuit_sub(in1, in5); // Fp2 sub coeff 0/1 let t3 = circuit_sub(in2, in6); // Fp2 sub coeff 1/1 let t4 = circuit_mul(t2, t2); // Fp2 Inv start let t5 = circuit_mul(t3, t3); let t6 = circuit_add(t4, t5); let t7 = circuit_inverse(t6); let t8 = circuit_mul(t2, t7); // Fp2 Inv real part end let t9 = circuit_mul(t3, t7); let t10 = circuit_sub(in0, t9); // Fp2 Inv imag part end let t11 = circuit_mul(t0, t8); // Fp2 mul start let t12 = circuit_mul(t1, t10); let t13 = circuit_sub(t11, t12); // Fp2 mul real part end let t14 = circuit_mul(t0, t10); let t15 = circuit_mul(t1, t8); let t16 = circuit_add(t14, t15); // Fp2 mul imag part end let t17 = circuit_add(t13, t16); let t18 = circuit_sub(t13, t16); let t19 = circuit_mul(t17, t18); let t20 = circuit_mul(t13, t16); let t21 = circuit_add(t20, t20); let t22 = circuit_sub(t19, in1); // Fp2 sub coeff 0/1 let t23 = circuit_sub(t21, in2); // Fp2 sub coeff 1/1 let t24 = circuit_sub(t22, in5); // Fp2 sub coeff 0/1 let t25 = circuit_sub(t23, in6); // Fp2 sub coeff 1/1 let t26 = circuit_sub(in1, t24); // Fp2 sub coeff 0/1 let t27 = circuit_sub(in2, t25); // Fp2 sub coeff 1/1 let t28 = circuit_mul(t13, t26); // Fp2 mul start let t29 = circuit_mul(t16, t27); let t30 = circuit_sub(t28, t29); // Fp2 mul real part end let t31 = circuit_mul(t13, t27); let t32 = circuit_mul(t16, t26); let t33 = circuit_add(t31, t32); // Fp2 mul imag part end let t34 = circuit_sub(t30, in3); // Fp2 sub coeff 0/1 let t35 = circuit_sub(t33, in4); // Fp2 sub coeff 1/1 let modulus = modulus; let mut circuit_inputs = (t24, t25, t34, t35).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x0); // in1 circuit_inputs = circuit_inputs.next_2(p.x1); // in2 circuit_inputs = circuit_inputs.next_2(p.y0); // in3 circuit_inputs = circuit_inputs.next_2(p.y1); // in4 circuit_inputs = circuit_inputs.next_2(q.x0); // in5 circuit_inputs = circuit_inputs.next_2(q.x1); // in6 circuit_inputs = circuit_inputs.next_2(q.y0); // in7 circuit_inputs = circuit_inputs.next_2(q.y1); // in8 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let result: G2Point = G2Point { x0: outputs.get_output(t24), x1: outputs.get_output(t25), y0: outputs.get_output(t34), y1: outputs.get_output(t35), }; return (result,); } #[inline(always)] pub fn run_ADD_EC_POINT_circuit( p: G1Point, q: G1Point, modulus: core::circuit::CircuitModulus, ) -> (G1Point,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let in3 = CE::> {}; let t0 = circuit_sub(in1, in3); let t1 = circuit_sub(in0, in2); let t2 = circuit_inverse(t1); let t3 = circuit_mul(t0, t2); let t4 = circuit_mul(t3, t3); let t5 = circuit_sub(t4, in0); let t6 = circuit_sub(t5, in2); let t7 = circuit_sub(in0, t6); let t8 = circuit_mul(t3, t7); let t9 = circuit_sub(t8, in1); let modulus = modulus; let mut circuit_inputs = (t6, t9).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 circuit_inputs = circuit_inputs.next_2(q.x); // in2 circuit_inputs = circuit_inputs.next_2(q.y); // in3 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let r: G1Point = G1Point { x: outputs.get_output(t6), y: outputs.get_output(t9) }; return (r,); } #[inline(always)] pub fn run_CLEAR_COFACTOR_BLS12_381_circuit( P: G1Point, modulus: core::circuit::CircuitModulus, ) -> (G1Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x3 // INPUT stack let (in1, in2) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in1, in1); let t1 = circuit_mul(in0, t0); let t2 = circuit_add(in2, in2); let t3 = circuit_inverse(t2); let t4 = circuit_mul(t1, t3); let t5 = circuit_mul(t4, t4); let t6 = circuit_sub(t5, in1); let t7 = circuit_sub(t6, in1); let t8 = circuit_sub(in1, t7); let t9 = circuit_mul(t4, t8); let t10 = circuit_sub(t9, in2); let t11 = circuit_sub(t10, in2); let t12 = circuit_sub(t7, in1); let t13 = circuit_inverse(t12); let t14 = circuit_mul(t11, t13); let t15 = circuit_mul(t14, t14); let t16 = circuit_sub(t15, t7); let t17 = circuit_sub(t16, in1); let t18 = circuit_sub(t7, t17); let t19 = circuit_mul(t14, t18); let t20 = circuit_sub(t19, t10); let t21 = circuit_mul(t17, t17); let t22 = circuit_mul(in0, t21); let t23 = circuit_add(t20, t20); let t24 = circuit_inverse(t23); let t25 = circuit_mul(t22, t24); let t26 = circuit_mul(t25, t25); let t27 = circuit_sub(t26, t17); let t28 = circuit_sub(t27, t17); let t29 = circuit_sub(t17, t28); let t30 = circuit_mul(t25, t29); let t31 = circuit_sub(t30, t20); let t32 = circuit_mul(t28, t28); let t33 = circuit_mul(in0, t32); let t34 = circuit_add(t31, t31); let t35 = circuit_inverse(t34); let t36 = circuit_mul(t33, t35); let t37 = circuit_mul(t36, t36); let t38 = circuit_sub(t37, t28); let t39 = circuit_sub(t38, t28); let t40 = circuit_sub(t28, t39); let t41 = circuit_mul(t36, t40); let t42 = circuit_sub(t41, t31); let t43 = circuit_sub(t42, in2); let t44 = circuit_sub(t39, in1); let t45 = circuit_inverse(t44); let t46 = circuit_mul(t43, t45); let t47 = circuit_mul(t46, t46); let t48 = circuit_sub(t47, t39); let t49 = circuit_sub(t48, in1); let t50 = circuit_sub(t39, t49); let t51 = circuit_mul(t46, t50); let t52 = circuit_sub(t51, t42); let t53 = circuit_mul(t49, t49); let t54 = circuit_mul(in0, t53); let t55 = circuit_add(t52, t52); let t56 = circuit_inverse(t55); let t57 = circuit_mul(t54, t56); let t58 = circuit_mul(t57, t57); let t59 = circuit_sub(t58, t49); let t60 = circuit_sub(t59, t49); let t61 = circuit_sub(t49, t60); let t62 = circuit_mul(t57, t61); let t63 = circuit_sub(t62, t52); let t64 = circuit_mul(t60, t60); let t65 = circuit_mul(in0, t64); let t66 = circuit_add(t63, t63); let t67 = circuit_inverse(t66); let t68 = circuit_mul(t65, t67); let t69 = circuit_mul(t68, t68); let t70 = circuit_sub(t69, t60); let t71 = circuit_sub(t70, t60); let t72 = circuit_sub(t60, t71); let t73 = circuit_mul(t68, t72); let t74 = circuit_sub(t73, t63); let t75 = circuit_mul(t71, t71); let t76 = circuit_mul(in0, t75); let t77 = circuit_add(t74, t74); let t78 = circuit_inverse(t77); let t79 = circuit_mul(t76, t78); let t80 = circuit_mul(t79, t79); let t81 = circuit_sub(t80, t71); let t82 = circuit_sub(t81, t71); let t83 = circuit_sub(t71, t82); let t84 = circuit_mul(t79, t83); let t85 = circuit_sub(t84, t74); let t86 = circuit_sub(t85, in2); let t87 = circuit_sub(t82, in1); let t88 = circuit_inverse(t87); let t89 = circuit_mul(t86, t88); let t90 = circuit_mul(t89, t89); let t91 = circuit_sub(t90, t82); let t92 = circuit_sub(t91, in1); let t93 = circuit_sub(t82, t92); let t94 = circuit_mul(t89, t93); let t95 = circuit_sub(t94, t85); let t96 = circuit_mul(t92, t92); let t97 = circuit_mul(in0, t96); let t98 = circuit_add(t95, t95); let t99 = circuit_inverse(t98); let t100 = circuit_mul(t97, t99); let t101 = circuit_mul(t100, t100); let t102 = circuit_sub(t101, t92); let t103 = circuit_sub(t102, t92); let t104 = circuit_sub(t92, t103); let t105 = circuit_mul(t100, t104); let t106 = circuit_sub(t105, t95); let t107 = circuit_mul(t103, t103); let t108 = circuit_mul(in0, t107); let t109 = circuit_add(t106, t106); let t110 = circuit_inverse(t109); let t111 = circuit_mul(t108, t110); let t112 = circuit_mul(t111, t111); let t113 = circuit_sub(t112, t103); let t114 = circuit_sub(t113, t103); let t115 = circuit_sub(t103, t114); let t116 = circuit_mul(t111, t115); let t117 = circuit_sub(t116, t106); let t118 = circuit_mul(t114, t114); let t119 = circuit_mul(in0, t118); let t120 = circuit_add(t117, t117); let t121 = circuit_inverse(t120); let t122 = circuit_mul(t119, t121); let t123 = circuit_mul(t122, t122); let t124 = circuit_sub(t123, t114); let t125 = circuit_sub(t124, t114); let t126 = circuit_sub(t114, t125); let t127 = circuit_mul(t122, t126); let t128 = circuit_sub(t127, t117); let t129 = circuit_mul(t125, t125); let t130 = circuit_mul(in0, t129); let t131 = circuit_add(t128, t128); let t132 = circuit_inverse(t131); let t133 = circuit_mul(t130, t132); let t134 = circuit_mul(t133, t133); let t135 = circuit_sub(t134, t125); let t136 = circuit_sub(t135, t125); let t137 = circuit_sub(t125, t136); let t138 = circuit_mul(t133, t137); let t139 = circuit_sub(t138, t128); let t140 = circuit_mul(t136, t136); let t141 = circuit_mul(in0, t140); let t142 = circuit_add(t139, t139); let t143 = circuit_inverse(t142); let t144 = circuit_mul(t141, t143); let t145 = circuit_mul(t144, t144); let t146 = circuit_sub(t145, t136); let t147 = circuit_sub(t146, t136); let t148 = circuit_sub(t136, t147); let t149 = circuit_mul(t144, t148); let t150 = circuit_sub(t149, t139); let t151 = circuit_mul(t147, t147); let t152 = circuit_mul(in0, t151); let t153 = circuit_add(t150, t150); let t154 = circuit_inverse(t153); let t155 = circuit_mul(t152, t154); let t156 = circuit_mul(t155, t155); let t157 = circuit_sub(t156, t147); let t158 = circuit_sub(t157, t147); let t159 = circuit_sub(t147, t158); let t160 = circuit_mul(t155, t159); let t161 = circuit_sub(t160, t150); let t162 = circuit_mul(t158, t158); let t163 = circuit_mul(in0, t162); let t164 = circuit_add(t161, t161); let t165 = circuit_inverse(t164); let t166 = circuit_mul(t163, t165); let t167 = circuit_mul(t166, t166); let t168 = circuit_sub(t167, t158); let t169 = circuit_sub(t168, t158); let t170 = circuit_sub(t158, t169); let t171 = circuit_mul(t166, t170); let t172 = circuit_sub(t171, t161); let t173 = circuit_mul(t169, t169); let t174 = circuit_mul(in0, t173); let t175 = circuit_add(t172, t172); let t176 = circuit_inverse(t175); let t177 = circuit_mul(t174, t176); let t178 = circuit_mul(t177, t177); let t179 = circuit_sub(t178, t169); let t180 = circuit_sub(t179, t169); let t181 = circuit_sub(t169, t180); let t182 = circuit_mul(t177, t181); let t183 = circuit_sub(t182, t172); let t184 = circuit_mul(t180, t180); let t185 = circuit_mul(in0, t184); let t186 = circuit_add(t183, t183); let t187 = circuit_inverse(t186); let t188 = circuit_mul(t185, t187); let t189 = circuit_mul(t188, t188); let t190 = circuit_sub(t189, t180); let t191 = circuit_sub(t190, t180); let t192 = circuit_sub(t180, t191); let t193 = circuit_mul(t188, t192); let t194 = circuit_sub(t193, t183); let t195 = circuit_sub(t194, in2); let t196 = circuit_sub(t191, in1); let t197 = circuit_inverse(t196); let t198 = circuit_mul(t195, t197); let t199 = circuit_mul(t198, t198); let t200 = circuit_sub(t199, t191); let t201 = circuit_sub(t200, in1); let t202 = circuit_sub(t191, t201); let t203 = circuit_mul(t198, t202); let t204 = circuit_sub(t203, t194); let t205 = circuit_mul(t201, t201); let t206 = circuit_mul(in0, t205); let t207 = circuit_add(t204, t204); let t208 = circuit_inverse(t207); let t209 = circuit_mul(t206, t208); let t210 = circuit_mul(t209, t209); let t211 = circuit_sub(t210, t201); let t212 = circuit_sub(t211, t201); let t213 = circuit_sub(t201, t212); let t214 = circuit_mul(t209, t213); let t215 = circuit_sub(t214, t204); let t216 = circuit_mul(t212, t212); let t217 = circuit_mul(in0, t216); let t218 = circuit_add(t215, t215); let t219 = circuit_inverse(t218); let t220 = circuit_mul(t217, t219); let t221 = circuit_mul(t220, t220); let t222 = circuit_sub(t221, t212); let t223 = circuit_sub(t222, t212); let t224 = circuit_sub(t212, t223); let t225 = circuit_mul(t220, t224); let t226 = circuit_sub(t225, t215); let t227 = circuit_mul(t223, t223); let t228 = circuit_mul(in0, t227); let t229 = circuit_add(t226, t226); let t230 = circuit_inverse(t229); let t231 = circuit_mul(t228, t230); let t232 = circuit_mul(t231, t231); let t233 = circuit_sub(t232, t223); let t234 = circuit_sub(t233, t223); let t235 = circuit_sub(t223, t234); let t236 = circuit_mul(t231, t235); let t237 = circuit_sub(t236, t226); let t238 = circuit_mul(t234, t234); let t239 = circuit_mul(in0, t238); let t240 = circuit_add(t237, t237); let t241 = circuit_inverse(t240); let t242 = circuit_mul(t239, t241); let t243 = circuit_mul(t242, t242); let t244 = circuit_sub(t243, t234); let t245 = circuit_sub(t244, t234); let t246 = circuit_sub(t234, t245); let t247 = circuit_mul(t242, t246); let t248 = circuit_sub(t247, t237); let t249 = circuit_mul(t245, t245); let t250 = circuit_mul(in0, t249); let t251 = circuit_add(t248, t248); let t252 = circuit_inverse(t251); let t253 = circuit_mul(t250, t252); let t254 = circuit_mul(t253, t253); let t255 = circuit_sub(t254, t245); let t256 = circuit_sub(t255, t245); let t257 = circuit_sub(t245, t256); let t258 = circuit_mul(t253, t257); let t259 = circuit_sub(t258, t248); let t260 = circuit_mul(t256, t256); let t261 = circuit_mul(in0, t260); let t262 = circuit_add(t259, t259); let t263 = circuit_inverse(t262); let t264 = circuit_mul(t261, t263); let t265 = circuit_mul(t264, t264); let t266 = circuit_sub(t265, t256); let t267 = circuit_sub(t266, t256); let t268 = circuit_sub(t256, t267); let t269 = circuit_mul(t264, t268); let t270 = circuit_sub(t269, t259); let t271 = circuit_mul(t267, t267); let t272 = circuit_mul(in0, t271); let t273 = circuit_add(t270, t270); let t274 = circuit_inverse(t273); let t275 = circuit_mul(t272, t274); let t276 = circuit_mul(t275, t275); let t277 = circuit_sub(t276, t267); let t278 = circuit_sub(t277, t267); let t279 = circuit_sub(t267, t278); let t280 = circuit_mul(t275, t279); let t281 = circuit_sub(t280, t270); let t282 = circuit_mul(t278, t278); let t283 = circuit_mul(in0, t282); let t284 = circuit_add(t281, t281); let t285 = circuit_inverse(t284); let t286 = circuit_mul(t283, t285); let t287 = circuit_mul(t286, t286); let t288 = circuit_sub(t287, t278); let t289 = circuit_sub(t288, t278); let t290 = circuit_sub(t278, t289); let t291 = circuit_mul(t286, t290); let t292 = circuit_sub(t291, t281); let t293 = circuit_mul(t289, t289); let t294 = circuit_mul(in0, t293); let t295 = circuit_add(t292, t292); let t296 = circuit_inverse(t295); let t297 = circuit_mul(t294, t296); let t298 = circuit_mul(t297, t297); let t299 = circuit_sub(t298, t289); let t300 = circuit_sub(t299, t289); let t301 = circuit_sub(t289, t300); let t302 = circuit_mul(t297, t301); let t303 = circuit_sub(t302, t292); let t304 = circuit_mul(t300, t300); let t305 = circuit_mul(in0, t304); let t306 = circuit_add(t303, t303); let t307 = circuit_inverse(t306); let t308 = circuit_mul(t305, t307); let t309 = circuit_mul(t308, t308); let t310 = circuit_sub(t309, t300); let t311 = circuit_sub(t310, t300); let t312 = circuit_sub(t300, t311); let t313 = circuit_mul(t308, t312); let t314 = circuit_sub(t313, t303); let t315 = circuit_mul(t311, t311); let t316 = circuit_mul(in0, t315); let t317 = circuit_add(t314, t314); let t318 = circuit_inverse(t317); let t319 = circuit_mul(t316, t318); let t320 = circuit_mul(t319, t319); let t321 = circuit_sub(t320, t311); let t322 = circuit_sub(t321, t311); let t323 = circuit_sub(t311, t322); let t324 = circuit_mul(t319, t323); let t325 = circuit_sub(t324, t314); let t326 = circuit_mul(t322, t322); let t327 = circuit_mul(in0, t326); let t328 = circuit_add(t325, t325); let t329 = circuit_inverse(t328); let t330 = circuit_mul(t327, t329); let t331 = circuit_mul(t330, t330); let t332 = circuit_sub(t331, t322); let t333 = circuit_sub(t332, t322); let t334 = circuit_sub(t322, t333); let t335 = circuit_mul(t330, t334); let t336 = circuit_sub(t335, t325); let t337 = circuit_mul(t333, t333); let t338 = circuit_mul(in0, t337); let t339 = circuit_add(t336, t336); let t340 = circuit_inverse(t339); let t341 = circuit_mul(t338, t340); let t342 = circuit_mul(t341, t341); let t343 = circuit_sub(t342, t333); let t344 = circuit_sub(t343, t333); let t345 = circuit_sub(t333, t344); let t346 = circuit_mul(t341, t345); let t347 = circuit_sub(t346, t336); let t348 = circuit_mul(t344, t344); let t349 = circuit_mul(in0, t348); let t350 = circuit_add(t347, t347); let t351 = circuit_inverse(t350); let t352 = circuit_mul(t349, t351); let t353 = circuit_mul(t352, t352); let t354 = circuit_sub(t353, t344); let t355 = circuit_sub(t354, t344); let t356 = circuit_sub(t344, t355); let t357 = circuit_mul(t352, t356); let t358 = circuit_sub(t357, t347); let t359 = circuit_mul(t355, t355); let t360 = circuit_mul(in0, t359); let t361 = circuit_add(t358, t358); let t362 = circuit_inverse(t361); let t363 = circuit_mul(t360, t362); let t364 = circuit_mul(t363, t363); let t365 = circuit_sub(t364, t355); let t366 = circuit_sub(t365, t355); let t367 = circuit_sub(t355, t366); let t368 = circuit_mul(t363, t367); let t369 = circuit_sub(t368, t358); let t370 = circuit_mul(t366, t366); let t371 = circuit_mul(in0, t370); let t372 = circuit_add(t369, t369); let t373 = circuit_inverse(t372); let t374 = circuit_mul(t371, t373); let t375 = circuit_mul(t374, t374); let t376 = circuit_sub(t375, t366); let t377 = circuit_sub(t376, t366); let t378 = circuit_sub(t366, t377); let t379 = circuit_mul(t374, t378); let t380 = circuit_sub(t379, t369); let t381 = circuit_mul(t377, t377); let t382 = circuit_mul(in0, t381); let t383 = circuit_add(t380, t380); let t384 = circuit_inverse(t383); let t385 = circuit_mul(t382, t384); let t386 = circuit_mul(t385, t385); let t387 = circuit_sub(t386, t377); let t388 = circuit_sub(t387, t377); let t389 = circuit_sub(t377, t388); let t390 = circuit_mul(t385, t389); let t391 = circuit_sub(t390, t380); let t392 = circuit_mul(t388, t388); let t393 = circuit_mul(in0, t392); let t394 = circuit_add(t391, t391); let t395 = circuit_inverse(t394); let t396 = circuit_mul(t393, t395); let t397 = circuit_mul(t396, t396); let t398 = circuit_sub(t397, t388); let t399 = circuit_sub(t398, t388); let t400 = circuit_sub(t388, t399); let t401 = circuit_mul(t396, t400); let t402 = circuit_sub(t401, t391); let t403 = circuit_mul(t399, t399); let t404 = circuit_mul(in0, t403); let t405 = circuit_add(t402, t402); let t406 = circuit_inverse(t405); let t407 = circuit_mul(t404, t406); let t408 = circuit_mul(t407, t407); let t409 = circuit_sub(t408, t399); let t410 = circuit_sub(t409, t399); let t411 = circuit_sub(t399, t410); let t412 = circuit_mul(t407, t411); let t413 = circuit_sub(t412, t402); let t414 = circuit_mul(t410, t410); let t415 = circuit_mul(in0, t414); let t416 = circuit_add(t413, t413); let t417 = circuit_inverse(t416); let t418 = circuit_mul(t415, t417); let t419 = circuit_mul(t418, t418); let t420 = circuit_sub(t419, t410); let t421 = circuit_sub(t420, t410); let t422 = circuit_sub(t410, t421); let t423 = circuit_mul(t418, t422); let t424 = circuit_sub(t423, t413); let t425 = circuit_mul(t421, t421); let t426 = circuit_mul(in0, t425); let t427 = circuit_add(t424, t424); let t428 = circuit_inverse(t427); let t429 = circuit_mul(t426, t428); let t430 = circuit_mul(t429, t429); let t431 = circuit_sub(t430, t421); let t432 = circuit_sub(t431, t421); let t433 = circuit_sub(t421, t432); let t434 = circuit_mul(t429, t433); let t435 = circuit_sub(t434, t424); let t436 = circuit_mul(t432, t432); let t437 = circuit_mul(in0, t436); let t438 = circuit_add(t435, t435); let t439 = circuit_inverse(t438); let t440 = circuit_mul(t437, t439); let t441 = circuit_mul(t440, t440); let t442 = circuit_sub(t441, t432); let t443 = circuit_sub(t442, t432); let t444 = circuit_sub(t432, t443); let t445 = circuit_mul(t440, t444); let t446 = circuit_sub(t445, t435); let t447 = circuit_mul(t443, t443); let t448 = circuit_mul(in0, t447); let t449 = circuit_add(t446, t446); let t450 = circuit_inverse(t449); let t451 = circuit_mul(t448, t450); let t452 = circuit_mul(t451, t451); let t453 = circuit_sub(t452, t443); let t454 = circuit_sub(t453, t443); let t455 = circuit_sub(t443, t454); let t456 = circuit_mul(t451, t455); let t457 = circuit_sub(t456, t446); let t458 = circuit_mul(t454, t454); let t459 = circuit_mul(in0, t458); let t460 = circuit_add(t457, t457); let t461 = circuit_inverse(t460); let t462 = circuit_mul(t459, t461); let t463 = circuit_mul(t462, t462); let t464 = circuit_sub(t463, t454); let t465 = circuit_sub(t464, t454); let t466 = circuit_sub(t454, t465); let t467 = circuit_mul(t462, t466); let t468 = circuit_sub(t467, t457); let t469 = circuit_mul(t465, t465); let t470 = circuit_mul(in0, t469); let t471 = circuit_add(t468, t468); let t472 = circuit_inverse(t471); let t473 = circuit_mul(t470, t472); let t474 = circuit_mul(t473, t473); let t475 = circuit_sub(t474, t465); let t476 = circuit_sub(t475, t465); let t477 = circuit_sub(t465, t476); let t478 = circuit_mul(t473, t477); let t479 = circuit_sub(t478, t468); let t480 = circuit_mul(t476, t476); let t481 = circuit_mul(in0, t480); let t482 = circuit_add(t479, t479); let t483 = circuit_inverse(t482); let t484 = circuit_mul(t481, t483); let t485 = circuit_mul(t484, t484); let t486 = circuit_sub(t485, t476); let t487 = circuit_sub(t486, t476); let t488 = circuit_sub(t476, t487); let t489 = circuit_mul(t484, t488); let t490 = circuit_sub(t489, t479); let t491 = circuit_mul(t487, t487); let t492 = circuit_mul(in0, t491); let t493 = circuit_add(t490, t490); let t494 = circuit_inverse(t493); let t495 = circuit_mul(t492, t494); let t496 = circuit_mul(t495, t495); let t497 = circuit_sub(t496, t487); let t498 = circuit_sub(t497, t487); let t499 = circuit_sub(t487, t498); let t500 = circuit_mul(t495, t499); let t501 = circuit_sub(t500, t490); let t502 = circuit_mul(t498, t498); let t503 = circuit_mul(in0, t502); let t504 = circuit_add(t501, t501); let t505 = circuit_inverse(t504); let t506 = circuit_mul(t503, t505); let t507 = circuit_mul(t506, t506); let t508 = circuit_sub(t507, t498); let t509 = circuit_sub(t508, t498); let t510 = circuit_sub(t498, t509); let t511 = circuit_mul(t506, t510); let t512 = circuit_sub(t511, t501); let t513 = circuit_mul(t509, t509); let t514 = circuit_mul(in0, t513); let t515 = circuit_add(t512, t512); let t516 = circuit_inverse(t515); let t517 = circuit_mul(t514, t516); let t518 = circuit_mul(t517, t517); let t519 = circuit_sub(t518, t509); let t520 = circuit_sub(t519, t509); let t521 = circuit_sub(t509, t520); let t522 = circuit_mul(t517, t521); let t523 = circuit_sub(t522, t512); let t524 = circuit_mul(t520, t520); let t525 = circuit_mul(in0, t524); let t526 = circuit_add(t523, t523); let t527 = circuit_inverse(t526); let t528 = circuit_mul(t525, t527); let t529 = circuit_mul(t528, t528); let t530 = circuit_sub(t529, t520); let t531 = circuit_sub(t530, t520); let t532 = circuit_sub(t520, t531); let t533 = circuit_mul(t528, t532); let t534 = circuit_sub(t533, t523); let t535 = circuit_mul(t531, t531); let t536 = circuit_mul(in0, t535); let t537 = circuit_add(t534, t534); let t538 = circuit_inverse(t537); let t539 = circuit_mul(t536, t538); let t540 = circuit_mul(t539, t539); let t541 = circuit_sub(t540, t531); let t542 = circuit_sub(t541, t531); let t543 = circuit_sub(t531, t542); let t544 = circuit_mul(t539, t543); let t545 = circuit_sub(t544, t534); let t546 = circuit_mul(t542, t542); let t547 = circuit_mul(in0, t546); let t548 = circuit_add(t545, t545); let t549 = circuit_inverse(t548); let t550 = circuit_mul(t547, t549); let t551 = circuit_mul(t550, t550); let t552 = circuit_sub(t551, t542); let t553 = circuit_sub(t552, t542); let t554 = circuit_sub(t542, t553); let t555 = circuit_mul(t550, t554); let t556 = circuit_sub(t555, t545); let t557 = circuit_sub(t556, in2); let t558 = circuit_sub(t553, in1); let t559 = circuit_inverse(t558); let t560 = circuit_mul(t557, t559); let t561 = circuit_mul(t560, t560); let t562 = circuit_sub(t561, t553); let t563 = circuit_sub(t562, in1); let t564 = circuit_sub(t553, t563); let t565 = circuit_mul(t560, t564); let t566 = circuit_sub(t565, t556); let t567 = circuit_mul(t563, t563); let t568 = circuit_mul(in0, t567); let t569 = circuit_add(t566, t566); let t570 = circuit_inverse(t569); let t571 = circuit_mul(t568, t570); let t572 = circuit_mul(t571, t571); let t573 = circuit_sub(t572, t563); let t574 = circuit_sub(t573, t563); let t575 = circuit_sub(t563, t574); let t576 = circuit_mul(t571, t575); let t577 = circuit_sub(t576, t566); let t578 = circuit_mul(t574, t574); let t579 = circuit_mul(in0, t578); let t580 = circuit_add(t577, t577); let t581 = circuit_inverse(t580); let t582 = circuit_mul(t579, t581); let t583 = circuit_mul(t582, t582); let t584 = circuit_sub(t583, t574); let t585 = circuit_sub(t584, t574); let t586 = circuit_sub(t574, t585); let t587 = circuit_mul(t582, t586); let t588 = circuit_sub(t587, t577); let t589 = circuit_mul(t585, t585); let t590 = circuit_mul(in0, t589); let t591 = circuit_add(t588, t588); let t592 = circuit_inverse(t591); let t593 = circuit_mul(t590, t592); let t594 = circuit_mul(t593, t593); let t595 = circuit_sub(t594, t585); let t596 = circuit_sub(t595, t585); let t597 = circuit_sub(t585, t596); let t598 = circuit_mul(t593, t597); let t599 = circuit_sub(t598, t588); let t600 = circuit_mul(t596, t596); let t601 = circuit_mul(in0, t600); let t602 = circuit_add(t599, t599); let t603 = circuit_inverse(t602); let t604 = circuit_mul(t601, t603); let t605 = circuit_mul(t604, t604); let t606 = circuit_sub(t605, t596); let t607 = circuit_sub(t606, t596); let t608 = circuit_sub(t596, t607); let t609 = circuit_mul(t604, t608); let t610 = circuit_sub(t609, t599); let t611 = circuit_mul(t607, t607); let t612 = circuit_mul(in0, t611); let t613 = circuit_add(t610, t610); let t614 = circuit_inverse(t613); let t615 = circuit_mul(t612, t614); let t616 = circuit_mul(t615, t615); let t617 = circuit_sub(t616, t607); let t618 = circuit_sub(t617, t607); let t619 = circuit_sub(t607, t618); let t620 = circuit_mul(t615, t619); let t621 = circuit_sub(t620, t610); let t622 = circuit_mul(t618, t618); let t623 = circuit_mul(in0, t622); let t624 = circuit_add(t621, t621); let t625 = circuit_inverse(t624); let t626 = circuit_mul(t623, t625); let t627 = circuit_mul(t626, t626); let t628 = circuit_sub(t627, t618); let t629 = circuit_sub(t628, t618); let t630 = circuit_sub(t618, t629); let t631 = circuit_mul(t626, t630); let t632 = circuit_sub(t631, t621); let t633 = circuit_mul(t629, t629); let t634 = circuit_mul(in0, t633); let t635 = circuit_add(t632, t632); let t636 = circuit_inverse(t635); let t637 = circuit_mul(t634, t636); let t638 = circuit_mul(t637, t637); let t639 = circuit_sub(t638, t629); let t640 = circuit_sub(t639, t629); let t641 = circuit_sub(t629, t640); let t642 = circuit_mul(t637, t641); let t643 = circuit_sub(t642, t632); let t644 = circuit_mul(t640, t640); let t645 = circuit_mul(in0, t644); let t646 = circuit_add(t643, t643); let t647 = circuit_inverse(t646); let t648 = circuit_mul(t645, t647); let t649 = circuit_mul(t648, t648); let t650 = circuit_sub(t649, t640); let t651 = circuit_sub(t650, t640); let t652 = circuit_sub(t640, t651); let t653 = circuit_mul(t648, t652); let t654 = circuit_sub(t653, t643); let t655 = circuit_mul(t651, t651); let t656 = circuit_mul(in0, t655); let t657 = circuit_add(t654, t654); let t658 = circuit_inverse(t657); let t659 = circuit_mul(t656, t658); let t660 = circuit_mul(t659, t659); let t661 = circuit_sub(t660, t651); let t662 = circuit_sub(t661, t651); let t663 = circuit_sub(t651, t662); let t664 = circuit_mul(t659, t663); let t665 = circuit_sub(t664, t654); let t666 = circuit_mul(t662, t662); let t667 = circuit_mul(in0, t666); let t668 = circuit_add(t665, t665); let t669 = circuit_inverse(t668); let t670 = circuit_mul(t667, t669); let t671 = circuit_mul(t670, t670); let t672 = circuit_sub(t671, t662); let t673 = circuit_sub(t672, t662); let t674 = circuit_sub(t662, t673); let t675 = circuit_mul(t670, t674); let t676 = circuit_sub(t675, t665); let t677 = circuit_mul(t673, t673); let t678 = circuit_mul(in0, t677); let t679 = circuit_add(t676, t676); let t680 = circuit_inverse(t679); let t681 = circuit_mul(t678, t680); let t682 = circuit_mul(t681, t681); let t683 = circuit_sub(t682, t673); let t684 = circuit_sub(t683, t673); let t685 = circuit_sub(t673, t684); let t686 = circuit_mul(t681, t685); let t687 = circuit_sub(t686, t676); let t688 = circuit_mul(t684, t684); let t689 = circuit_mul(in0, t688); let t690 = circuit_add(t687, t687); let t691 = circuit_inverse(t690); let t692 = circuit_mul(t689, t691); let t693 = circuit_mul(t692, t692); let t694 = circuit_sub(t693, t684); let t695 = circuit_sub(t694, t684); let t696 = circuit_sub(t684, t695); let t697 = circuit_mul(t692, t696); let t698 = circuit_sub(t697, t687); let t699 = circuit_mul(t695, t695); let t700 = circuit_mul(in0, t699); let t701 = circuit_add(t698, t698); let t702 = circuit_inverse(t701); let t703 = circuit_mul(t700, t702); let t704 = circuit_mul(t703, t703); let t705 = circuit_sub(t704, t695); let t706 = circuit_sub(t705, t695); let t707 = circuit_sub(t695, t706); let t708 = circuit_mul(t703, t707); let t709 = circuit_sub(t708, t698); let t710 = circuit_mul(t706, t706); let t711 = circuit_mul(in0, t710); let t712 = circuit_add(t709, t709); let t713 = circuit_inverse(t712); let t714 = circuit_mul(t711, t713); let t715 = circuit_mul(t714, t714); let t716 = circuit_sub(t715, t706); let t717 = circuit_sub(t716, t706); let t718 = circuit_sub(t706, t717); let t719 = circuit_mul(t714, t718); let t720 = circuit_sub(t719, t709); let t721 = circuit_mul(t717, t717); let t722 = circuit_mul(in0, t721); let t723 = circuit_add(t720, t720); let t724 = circuit_inverse(t723); let t725 = circuit_mul(t722, t724); let t726 = circuit_mul(t725, t725); let t727 = circuit_sub(t726, t717); let t728 = circuit_sub(t727, t717); let t729 = circuit_sub(t717, t728); let t730 = circuit_mul(t725, t729); let t731 = circuit_sub(t730, t720); let t732 = circuit_mul(t728, t728); let t733 = circuit_mul(in0, t732); let t734 = circuit_add(t731, t731); let t735 = circuit_inverse(t734); let t736 = circuit_mul(t733, t735); let t737 = circuit_mul(t736, t736); let t738 = circuit_sub(t737, t728); let t739 = circuit_sub(t738, t728); let t740 = circuit_sub(t728, t739); let t741 = circuit_mul(t736, t740); let t742 = circuit_sub(t741, t731); let t743 = circuit_sub(in2, t742); let t744 = circuit_sub(in1, t739); let t745 = circuit_inverse(t744); let t746 = circuit_mul(t743, t745); let t747 = circuit_mul(t746, t746); let t748 = circuit_sub(t747, in1); let t749 = circuit_sub(t748, t739); let t750 = circuit_sub(in1, t749); let t751 = circuit_mul(t746, t750); let t752 = circuit_sub(t751, in2); let modulus = modulus; let mut circuit_inputs = (t749, t752).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(P.x); // in1 circuit_inputs = circuit_inputs.next_2(P.y); // in2 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: G1Point = G1Point { x: outputs.get_output(t749), y: outputs.get_output(t752) }; return (res,); } #[inline(always)] pub fn run_DOUBLE_AND_ADD_EC_POINTS_G2_circuit( p: G2Point, q: G2Point, modulus: core::circuit::CircuitModulus, ) -> (G2Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8) = (CE::> {}, CE::> {}); let t0 = circuit_sub(in7, in3); // Fp2 sub coeff 0/1 let t1 = circuit_sub(in8, in4); // Fp2 sub coeff 1/1 let t2 = circuit_sub(in5, in1); // Fp2 sub coeff 0/1 let t3 = circuit_sub(in6, in2); // Fp2 sub coeff 1/1 let t4 = circuit_mul(t2, t2); // Fp2 Inv start let t5 = circuit_mul(t3, t3); let t6 = circuit_add(t4, t5); let t7 = circuit_inverse(t6); let t8 = circuit_mul(t2, t7); // Fp2 Inv real part end let t9 = circuit_mul(t3, t7); let t10 = circuit_sub(in0, t9); // Fp2 Inv imag part end let t11 = circuit_mul(t0, t8); // Fp2 mul start let t12 = circuit_mul(t1, t10); let t13 = circuit_sub(t11, t12); // Fp2 mul real part end let t14 = circuit_mul(t0, t10); let t15 = circuit_mul(t1, t8); let t16 = circuit_add(t14, t15); // Fp2 mul imag part end let t17 = circuit_add(t13, t16); let t18 = circuit_sub(t13, t16); let t19 = circuit_mul(t17, t18); let t20 = circuit_mul(t13, t16); let t21 = circuit_add(t20, t20); let t22 = circuit_add(in1, in5); // Fp2 add coeff 0/1 let t23 = circuit_add(in2, in6); // Fp2 add coeff 1/1 let t24 = circuit_sub(t19, t22); // Fp2 sub coeff 0/1 let t25 = circuit_sub(t21, t23); // Fp2 sub coeff 1/1 let t26 = circuit_add(in3, in3); // Fp2 add coeff 0/1 let t27 = circuit_add(in4, in4); // Fp2 add coeff 1/1 let t28 = circuit_sub(t24, in1); // Fp2 sub coeff 0/1 let t29 = circuit_sub(t25, in2); // Fp2 sub coeff 1/1 let t30 = circuit_mul(t28, t28); // Fp2 Inv start let t31 = circuit_mul(t29, t29); let t32 = circuit_add(t30, t31); let t33 = circuit_inverse(t32); let t34 = circuit_mul(t28, t33); // Fp2 Inv real part end let t35 = circuit_mul(t29, t33); let t36 = circuit_sub(in0, t35); // Fp2 Inv imag part end let t37 = circuit_mul(t26, t34); // Fp2 mul start let t38 = circuit_mul(t27, t36); let t39 = circuit_sub(t37, t38); // Fp2 mul real part end let t40 = circuit_mul(t26, t36); let t41 = circuit_mul(t27, t34); let t42 = circuit_add(t40, t41); // Fp2 mul imag part end let t43 = circuit_add(t13, t39); // Fp2 add coeff 0/1 let t44 = circuit_add(t16, t42); // Fp2 add coeff 1/1 let t45 = circuit_add(t43, t44); let t46 = circuit_sub(t43, t44); let t47 = circuit_mul(t45, t46); let t48 = circuit_mul(t43, t44); let t49 = circuit_add(t48, t48); let t50 = circuit_add(in1, t24); // Fp2 add coeff 0/1 let t51 = circuit_add(in2, t25); // Fp2 add coeff 1/1 let t52 = circuit_sub(t47, t50); // Fp2 sub coeff 0/1 let t53 = circuit_sub(t49, t51); // Fp2 sub coeff 1/1 let t54 = circuit_sub(t52, in1); // Fp2 sub coeff 0/1 let t55 = circuit_sub(t53, in2); // Fp2 sub coeff 1/1 let t56 = circuit_mul(t43, t54); // Fp2 mul start let t57 = circuit_mul(t44, t55); let t58 = circuit_sub(t56, t57); // Fp2 mul real part end let t59 = circuit_mul(t43, t55); let t60 = circuit_mul(t44, t54); let t61 = circuit_add(t59, t60); // Fp2 mul imag part end let t62 = circuit_sub(t58, in3); // Fp2 sub coeff 0/1 let t63 = circuit_sub(t61, in4); // Fp2 sub coeff 1/1 let modulus = modulus; let mut circuit_inputs = (t52, t53, t62, t63).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x0); // in1 circuit_inputs = circuit_inputs.next_2(p.x1); // in2 circuit_inputs = circuit_inputs.next_2(p.y0); // in3 circuit_inputs = circuit_inputs.next_2(p.y1); // in4 circuit_inputs = circuit_inputs.next_2(q.x0); // in5 circuit_inputs = circuit_inputs.next_2(q.x1); // in6 circuit_inputs = circuit_inputs.next_2(q.y0); // in7 circuit_inputs = circuit_inputs.next_2(q.y1); // in8 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let result: G2Point = G2Point { x0: outputs.get_output(t52), x1: outputs.get_output(t53), y0: outputs.get_output(t62), y1: outputs.get_output(t63), }; return (result,); } #[inline(always)] pub fn run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit( p: G2Point, modulus: core::circuit::CircuitModulus, ) -> (G2Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x3 let in1 = CE::> {}; // 0x0 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let in5 = CE::> {}; let t0 = circuit_add(in2, in3); let t1 = circuit_sub(in2, in3); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in2, in3); let t4 = circuit_add(t3, t3); let t5 = circuit_mul(t2, in0); // Fp2 scalar mul coeff 0/1 let t6 = circuit_mul(t4, in0); // Fp2 scalar mul coeff 1/1 let t7 = circuit_add(in4, in4); // Fp2 add coeff 0/1 let t8 = circuit_add(in5, in5); // Fp2 add coeff 1/1 let t9 = circuit_mul(t7, t7); // Fp2 Inv start let t10 = circuit_mul(t8, t8); let t11 = circuit_add(t9, t10); let t12 = circuit_inverse(t11); let t13 = circuit_mul(t7, t12); // Fp2 Inv real part end let t14 = circuit_mul(t8, t12); let t15 = circuit_sub(in1, t14); // Fp2 Inv imag part end let t16 = circuit_mul(t5, t13); // Fp2 mul start let t17 = circuit_mul(t6, t15); let t18 = circuit_sub(t16, t17); // Fp2 mul real part end let t19 = circuit_mul(t5, t15); let t20 = circuit_mul(t6, t13); let t21 = circuit_add(t19, t20); // Fp2 mul imag part end let t22 = circuit_add(t18, t21); let t23 = circuit_sub(t18, t21); let t24 = circuit_mul(t22, t23); let t25 = circuit_mul(t18, t21); let t26 = circuit_add(t25, t25); let t27 = circuit_sub(t24, in2); // Fp2 sub coeff 0/1 let t28 = circuit_sub(t26, in3); // Fp2 sub coeff 1/1 let t29 = circuit_sub(t27, in2); // Fp2 sub coeff 0/1 let t30 = circuit_sub(t28, in3); // Fp2 sub coeff 1/1 let t31 = circuit_sub(in2, t29); // Fp2 sub coeff 0/1 let t32 = circuit_sub(in3, t30); // Fp2 sub coeff 1/1 let t33 = circuit_mul(t18, t31); // Fp2 mul start let t34 = circuit_mul(t21, t32); let t35 = circuit_sub(t33, t34); // Fp2 mul real part end let t36 = circuit_mul(t18, t32); let t37 = circuit_mul(t21, t31); let t38 = circuit_add(t36, t37); // Fp2 mul imag part end let t39 = circuit_sub(t35, in4); // Fp2 sub coeff 0/1 let t40 = circuit_sub(t38, in5); // Fp2 sub coeff 1/1 let modulus = modulus; let mut circuit_inputs = (t29, t30, t39, t40).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x0); // in2 circuit_inputs = circuit_inputs.next_2(p.x1); // in3 circuit_inputs = circuit_inputs.next_2(p.y0); // in4 circuit_inputs = circuit_inputs.next_2(p.y1); // in5 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let result: G2Point = G2Point { x0: outputs.get_output(t29), x1: outputs.get_output(t30), y0: outputs.get_output(t39), y1: outputs.get_output(t40), }; return (result,); } #[inline(always)] pub fn run_DOUBLE_EC_POINT_circuit( p: G1Point, A_weirstrass: u384, modulus: core::circuit::CircuitModulus, ) -> (G1Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x3 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in1, in1); let t1 = circuit_mul(in0, t0); let t2 = circuit_add(t1, in3); let t3 = circuit_add(in2, in2); let t4 = circuit_inverse(t3); let t5 = circuit_mul(t2, t4); let t6 = circuit_mul(t5, t5); let t7 = circuit_sub(t6, in1); let t8 = circuit_sub(t7, in1); let t9 = circuit_sub(in1, t8); let t10 = circuit_mul(t5, t9); let t11 = circuit_sub(t10, in2); let modulus = modulus; let mut circuit_inputs = (t8, t11).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in1 circuit_inputs = circuit_inputs.next_2(p.y); // in2 circuit_inputs = circuit_inputs.next_2(A_weirstrass); // in3 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let r: G1Point = G1Point { x: outputs.get_output(t8), y: outputs.get_output(t11) }; return (r,); } #[inline(always)] pub fn run_IS_ON_CURVE_G1_G2_circuit( p: G1Point, q: G2Point, a: u384, b: u384, b20: u384, b21: u384, curve_index: usize, ) -> (u384, u384, u384) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let in9 = CE::> {}; let t0 = circuit_mul(in1, in1); let t1 = circuit_mul(in0, in0); let t2 = circuit_mul(in0, t1); let t3 = circuit_add(t2, in7); let t4 = circuit_add(in4, in5); let t5 = circuit_sub(in4, in5); let t6 = circuit_mul(t4, t5); let t7 = circuit_mul(in4, in5); let t8 = circuit_add(t7, t7); let t9 = circuit_add(in2, in3); let t10 = circuit_sub(in2, in3); let t11 = circuit_mul(t9, t10); let t12 = circuit_mul(in2, in3); let t13 = circuit_add(t12, t12); let t14 = circuit_mul(in2, t11); // Fp2 mul start let t15 = circuit_mul(in3, t13); let t16 = circuit_sub(t14, t15); // Fp2 mul real part end let t17 = circuit_mul(in2, t13); let t18 = circuit_mul(in3, t11); let t19 = circuit_add(t17, t18); // Fp2 mul imag part end let t20 = circuit_mul(in6, in2); let t21 = circuit_mul(in6, in3); let t22 = circuit_add(t20, in8); let t23 = circuit_add(t21, in9); let t24 = circuit_add(t16, t22); let t25 = circuit_add(t19, t23); let t26 = circuit_sub(t0, t3); let t27 = circuit_sub(t6, t24); let t28 = circuit_sub(t8, t25); let modulus = crate::definitions::get_modulus(curve_index); let mut circuit_inputs = (t26, t27, t28).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 circuit_inputs = circuit_inputs.next_2(q.x0); // in2 circuit_inputs = circuit_inputs.next_2(q.x1); // in3 circuit_inputs = circuit_inputs.next_2(q.y0); // in4 circuit_inputs = circuit_inputs.next_2(q.y1); // in5 circuit_inputs = circuit_inputs.next_2(a); // in6 circuit_inputs = circuit_inputs.next_2(b); // in7 circuit_inputs = circuit_inputs.next_2(b20); // in8 circuit_inputs = circuit_inputs.next_2(b21); // in9 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check_0: u384 = outputs.get_output(t26); let zero_check_1: u384 = outputs.get_output(t27); let zero_check_2: u384 = outputs.get_output(t28); return (zero_check_0, zero_check_1, zero_check_2); } #[inline(always)] pub fn run_IS_ON_CURVE_G1_circuit(p: G1Point, a: u384, b: u384, curve_index: usize) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let in3 = CE::> {}; let t0 = circuit_mul(in1, in1); let t1 = circuit_mul(in0, in0); let t2 = circuit_mul(in0, t1); let t3 = circuit_mul(in2, in0); let t4 = circuit_add(t3, in3); let t5 = circuit_add(t2, t4); let t6 = circuit_sub(t0, t5); let modulus = crate::definitions::get_modulus(curve_index); let mut circuit_inputs = (t6,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x); // in0 circuit_inputs = circuit_inputs.next_2(p.y); // in1 circuit_inputs = circuit_inputs.next_2(a); // in2 circuit_inputs = circuit_inputs.next_2(b); // in3 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check: u384 = outputs.get_output(t6); return (zero_check,); } #[inline(always)] pub fn run_IS_ON_CURVE_G2_circuit( p: G2Point, a: u384, b20: u384, b21: u384, curve_index: usize, ) -> (u384, u384) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let in6 = CE::> {}; let t0 = circuit_add(in2, in3); let t1 = circuit_sub(in2, in3); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in2, in3); let t4 = circuit_add(t3, t3); let t5 = circuit_add(in0, in1); let t6 = circuit_sub(in0, in1); let t7 = circuit_mul(t5, t6); let t8 = circuit_mul(in0, in1); let t9 = circuit_add(t8, t8); let t10 = circuit_mul(in0, t7); // Fp2 mul start let t11 = circuit_mul(in1, t9); let t12 = circuit_sub(t10, t11); // Fp2 mul real part end let t13 = circuit_mul(in0, t9); let t14 = circuit_mul(in1, t7); let t15 = circuit_add(t13, t14); // Fp2 mul imag part end let t16 = circuit_mul(in4, in0); let t17 = circuit_mul(in4, in1); let t18 = circuit_add(t16, in5); let t19 = circuit_add(t17, in6); let t20 = circuit_add(t12, t18); let t21 = circuit_add(t15, t19); let t22 = circuit_sub(t2, t20); let t23 = circuit_sub(t4, t21); let modulus = crate::definitions::get_modulus(curve_index); let mut circuit_inputs = (t22, t23).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x0); // in0 circuit_inputs = circuit_inputs.next_2(p.x1); // in1 circuit_inputs = circuit_inputs.next_2(p.y0); // in2 circuit_inputs = circuit_inputs.next_2(p.y1); // in3 circuit_inputs = circuit_inputs.next_2(a); // in4 circuit_inputs = circuit_inputs.next_2(b20); // in5 circuit_inputs = circuit_inputs.next_2(b21); // in6 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zero_check_0: u384 = outputs.get_output(t22); let zero_check_1: u384 = outputs.get_output(t23); return (zero_check_0, zero_check_1); } #[inline(always)] pub fn run_PREPARE_FAKE_GLV_PTS_circuit( P: G1Point, Q: G1Point, s2_sign: u384, A_weirstrass: u384, modulus: core::circuit::CircuitModulus, ) -> ( G1Point, G1Point, G1Point, G1Point, u384, u384, u384, u384, G1Point, G1Point, G1Point, G1Point, u384, u384, u384, u384, G1Point, u384, ) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in1, in1); let t1 = circuit_add(t0, t0); let t2 = circuit_add(t1, t0); let t3 = circuit_add(t2, in6); let t4 = circuit_add(in2, in2); let t5 = circuit_inverse(t4); let t6 = circuit_mul(t3, t5); let t7 = circuit_mul(t6, t6); let t8 = circuit_add(in1, in1); let t9 = circuit_sub(t7, t8); let t10 = circuit_sub(in1, t9); let t11 = circuit_add(in2, in2); let t12 = circuit_inverse(t10); let t13 = circuit_mul(t11, t12); let t14 = circuit_sub(t13, t6); let t15 = circuit_mul(t14, t14); let t16 = circuit_add(in1, t9); let t17 = circuit_sub(t15, t16); let t18 = circuit_sub(in1, t17); let t19 = circuit_mul(t14, t18); let t20 = circuit_sub(t19, in2); let t21 = circuit_mul(in5, in4); let t22 = circuit_sub(in0, t21); let t23 = circuit_mul(in3, in3); let t24 = circuit_add(t23, t23); let t25 = circuit_add(t24, t23); let t26 = circuit_add(t25, in6); let t27 = circuit_add(t21, t21); let t28 = circuit_inverse(t27); let t29 = circuit_mul(t26, t28); let t30 = circuit_mul(t29, t29); let t31 = circuit_add(in3, in3); let t32 = circuit_sub(t30, t31); let t33 = circuit_sub(in3, t32); let t34 = circuit_add(t21, t21); let t35 = circuit_inverse(t33); let t36 = circuit_mul(t34, t35); let t37 = circuit_sub(t36, t29); let t38 = circuit_mul(t37, t37); let t39 = circuit_add(in3, t32); let t40 = circuit_sub(t38, t39); let t41 = circuit_sub(in3, t40); let t42 = circuit_mul(t37, t41); let t43 = circuit_sub(t42, t21); let t44 = circuit_sub(t20, t43); let t45 = circuit_sub(t17, t40); let t46 = circuit_inverse(t45); let t47 = circuit_mul(t44, t46); let t48 = circuit_mul(t47, t47); let t49 = circuit_sub(t48, t17); let t50 = circuit_sub(t49, t40); let t51 = circuit_sub(t17, t50); let t52 = circuit_mul(t47, t51); let t53 = circuit_sub(t52, t20); let t54 = circuit_sub(in2, t21); let t55 = circuit_sub(in1, in3); let t56 = circuit_inverse(t55); let t57 = circuit_mul(t54, t56); let t58 = circuit_mul(t57, t57); let t59 = circuit_sub(t58, in1); let t60 = circuit_sub(t59, in3); let t61 = circuit_sub(in1, t60); let t62 = circuit_mul(t57, t61); let t63 = circuit_sub(t62, in2); let t64 = circuit_sub(t20, t21); let t65 = circuit_sub(t17, in3); let t66 = circuit_inverse(t65); let t67 = circuit_mul(t64, t66); let t68 = circuit_mul(t67, t67); let t69 = circuit_sub(t68, t17); let t70 = circuit_sub(t69, in3); let t71 = circuit_sub(t17, t70); let t72 = circuit_mul(t67, t71); let t73 = circuit_sub(t72, t20); let t74 = circuit_sub(in2, t43); let t75 = circuit_sub(in1, t40); let t76 = circuit_inverse(t75); let t77 = circuit_mul(t74, t76); let t78 = circuit_mul(t77, t77); let t79 = circuit_sub(t78, in1); let t80 = circuit_sub(t79, t40); let t81 = circuit_sub(in1, t80); let t82 = circuit_mul(t77, t81); let t83 = circuit_sub(t82, in2); let t84 = circuit_sub(in0, t63); let t85 = circuit_sub(in0, t53); let t86 = circuit_sub(in0, t83); let t87 = circuit_sub(in0, t73); let t88 = circuit_sub(t20, t22); let t89 = circuit_sub(t17, in3); let t90 = circuit_inverse(t89); let t91 = circuit_mul(t88, t90); let t92 = circuit_mul(t91, t91); let t93 = circuit_sub(t92, t17); let t94 = circuit_sub(t93, in3); let t95 = circuit_sub(t17, t94); let t96 = circuit_mul(t91, t95); let t97 = circuit_sub(t96, t20); let t98 = circuit_sub(in0, t43); let t99 = circuit_sub(in2, t98); let t100 = circuit_sub(in1, t40); let t101 = circuit_inverse(t100); let t102 = circuit_mul(t99, t101); let t103 = circuit_mul(t102, t102); let t104 = circuit_sub(t103, in1); let t105 = circuit_sub(t104, t40); let t106 = circuit_sub(in1, t105); let t107 = circuit_mul(t102, t106); let t108 = circuit_sub(t107, in2); let t109 = circuit_sub(t20, t98); let t110 = circuit_sub(t17, t40); let t111 = circuit_inverse(t110); let t112 = circuit_mul(t109, t111); let t113 = circuit_mul(t112, t112); let t114 = circuit_sub(t113, t17); let t115 = circuit_sub(t114, t40); let t116 = circuit_sub(t17, t115); let t117 = circuit_mul(t112, t116); let t118 = circuit_sub(t117, t20); let t119 = circuit_sub(t22, in2); let t120 = circuit_sub(in3, in1); let t121 = circuit_inverse(t120); let t122 = circuit_mul(t119, t121); let t123 = circuit_mul(t122, t122); let t124 = circuit_sub(t123, in3); let t125 = circuit_sub(t124, in1); let t126 = circuit_sub(in3, t125); let t127 = circuit_mul(t122, t126); let t128 = circuit_sub(t127, t22); let t129 = circuit_sub(in0, t108); let t130 = circuit_sub(in0, t97); let t131 = circuit_sub(in0, t128); let t132 = circuit_sub(in0, t118); let modulus = modulus; let mut circuit_inputs = ( t50, t53, t60, t63, t70, t73, t80, t83, t84, t85, t86, t87, t94, t97, t105, t108, t115, t118, t125, t128, t129, t130, t131, t132, t40, t43, t22, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(P.x); // in1 circuit_inputs = circuit_inputs.next_2(P.y); // in2 circuit_inputs = circuit_inputs.next_2(Q.x); // in3 circuit_inputs = circuit_inputs.next_2(Q.y); // in4 circuit_inputs = circuit_inputs.next_2(s2_sign); // in5 circuit_inputs = circuit_inputs.next_2(A_weirstrass); // in6 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let T1: G1Point = G1Point { x: outputs.get_output(t50), y: outputs.get_output(t53) }; let T2: G1Point = G1Point { x: outputs.get_output(t60), y: outputs.get_output(t63) }; let T3: G1Point = G1Point { x: outputs.get_output(t70), y: outputs.get_output(t73) }; let T4: G1Point = G1Point { x: outputs.get_output(t80), y: outputs.get_output(t83) }; let T5y: u384 = outputs.get_output(t84); let T6y: u384 = outputs.get_output(t85); let T7y: u384 = outputs.get_output(t86); let T8y: u384 = outputs.get_output(t87); let T9: G1Point = G1Point { x: outputs.get_output(t94), y: outputs.get_output(t97) }; let T10: G1Point = G1Point { x: outputs.get_output(t105), y: outputs.get_output(t108) }; let T11: G1Point = G1Point { x: outputs.get_output(t115), y: outputs.get_output(t118) }; let T12: G1Point = G1Point { x: outputs.get_output(t125), y: outputs.get_output(t128) }; let T13y: u384 = outputs.get_output(t129); let T14y: u384 = outputs.get_output(t130); let T15y: u384 = outputs.get_output(t131); let T16y: u384 = outputs.get_output(t132); let R2: G1Point = G1Point { x: outputs.get_output(t40), y: outputs.get_output(t43) }; let R0y: u384 = outputs.get_output(t22); return (T1, T2, T3, T4, T5y, T6y, T7y, T8y, T9, T10, T11, T12, T13y, T14y, T15y, T16y, R2, R0y); } #[inline(always)] pub fn run_PREPARE_GLV_FAKE_GLV_PTS_circuit( Px: u384, P0y: u384, P1y: u384, Qx: u384, Q0y: u384, Phi_P0y: u384, Phi_P1y: u384, Phi_Q0y: u384, Gen: G1Point, third_root: u384, modulus: core::circuit::CircuitModulus, ) -> ( G1Point, G1Point, G1Point, G1Point, G1Point, G1Point, G1Point, G1Point, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, G1Point, ) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11) = (CE::> {}, CE::> {}); let t0 = circuit_sub(in2, in5); let t1 = circuit_sub(in1, in4); let t2 = circuit_inverse(t1); let t3 = circuit_mul(t0, t2); let t4 = circuit_mul(t3, t3); let t5 = circuit_sub(t4, in1); let t6 = circuit_sub(t5, in4); let t7 = circuit_sub(in1, t6); let t8 = circuit_mul(t3, t7); let t9 = circuit_sub(t8, in2); let t10 = circuit_sub(in0, t9); let t11 = circuit_sub(in3, in5); let t12 = circuit_sub(in1, in4); let t13 = circuit_inverse(t12); let t14 = circuit_mul(t11, t13); let t15 = circuit_mul(t14, t14); let t16 = circuit_sub(t15, in1); let t17 = circuit_sub(t16, in4); let t18 = circuit_sub(in1, t17); let t19 = circuit_mul(t14, t18); let t20 = circuit_sub(t19, in3); let t21 = circuit_mul(in1, in11); let t22 = circuit_mul(in4, in11); let t23 = circuit_sub(in6, in8); let t24 = circuit_sub(t21, t22); let t25 = circuit_inverse(t24); let t26 = circuit_mul(t23, t25); let t27 = circuit_mul(t26, t26); let t28 = circuit_sub(t27, t21); let t29 = circuit_sub(t28, t22); let t30 = circuit_sub(t21, t29); let t31 = circuit_mul(t26, t30); let t32 = circuit_sub(t31, in6); let t33 = circuit_sub(in0, t32); let t34 = circuit_sub(in7, in8); let t35 = circuit_sub(t21, t22); let t36 = circuit_inverse(t35); let t37 = circuit_mul(t34, t36); let t38 = circuit_mul(t37, t37); let t39 = circuit_sub(t38, t21); let t40 = circuit_sub(t39, t22); let t41 = circuit_sub(t21, t40); let t42 = circuit_mul(t37, t41); let t43 = circuit_sub(t42, in7); let t44 = circuit_sub(in0, t43); let t45 = circuit_sub(t10, t33); let t46 = circuit_sub(t6, t29); let t47 = circuit_inverse(t46); let t48 = circuit_mul(t45, t47); let t49 = circuit_mul(t48, t48); let t50 = circuit_sub(t49, t6); let t51 = circuit_sub(t50, t29); let t52 = circuit_sub(t6, t51); let t53 = circuit_mul(t48, t52); let t54 = circuit_sub(t53, t10); let t55 = circuit_sub(t10, t43); let t56 = circuit_sub(t6, t40); let t57 = circuit_inverse(t56); let t58 = circuit_mul(t55, t57); let t59 = circuit_mul(t58, t58); let t60 = circuit_sub(t59, t6); let t61 = circuit_sub(t60, t40); let t62 = circuit_sub(t6, t61); let t63 = circuit_mul(t58, t62); let t64 = circuit_sub(t63, t10); let t65 = circuit_sub(t10, t44); let t66 = circuit_sub(t6, t40); let t67 = circuit_inverse(t66); let t68 = circuit_mul(t65, t67); let t69 = circuit_mul(t68, t68); let t70 = circuit_sub(t69, t6); let t71 = circuit_sub(t70, t40); let t72 = circuit_sub(t6, t71); let t73 = circuit_mul(t68, t72); let t74 = circuit_sub(t73, t10); let t75 = circuit_sub(t10, t32); let t76 = circuit_sub(t6, t29); let t77 = circuit_inverse(t76); let t78 = circuit_mul(t75, t77); let t79 = circuit_mul(t78, t78); let t80 = circuit_sub(t79, t6); let t81 = circuit_sub(t80, t29); let t82 = circuit_sub(t6, t81); let t83 = circuit_mul(t78, t82); let t84 = circuit_sub(t83, t10); let t85 = circuit_sub(t20, t33); let t86 = circuit_sub(t17, t29); let t87 = circuit_inverse(t86); let t88 = circuit_mul(t85, t87); let t89 = circuit_mul(t88, t88); let t90 = circuit_sub(t89, t17); let t91 = circuit_sub(t90, t29); let t92 = circuit_sub(t17, t91); let t93 = circuit_mul(t88, t92); let t94 = circuit_sub(t93, t20); let t95 = circuit_sub(t20, t43); let t96 = circuit_sub(t17, t40); let t97 = circuit_inverse(t96); let t98 = circuit_mul(t95, t97); let t99 = circuit_mul(t98, t98); let t100 = circuit_sub(t99, t17); let t101 = circuit_sub(t100, t40); let t102 = circuit_sub(t17, t101); let t103 = circuit_mul(t98, t102); let t104 = circuit_sub(t103, t20); let t105 = circuit_sub(t20, t44); let t106 = circuit_sub(t17, t40); let t107 = circuit_inverse(t106); let t108 = circuit_mul(t105, t107); let t109 = circuit_mul(t108, t108); let t110 = circuit_sub(t109, t17); let t111 = circuit_sub(t110, t40); let t112 = circuit_sub(t17, t111); let t113 = circuit_mul(t108, t112); let t114 = circuit_sub(t113, t20); let t115 = circuit_sub(t20, t32); let t116 = circuit_sub(t17, t29); let t117 = circuit_inverse(t116); let t118 = circuit_mul(t115, t117); let t119 = circuit_mul(t118, t118); let t120 = circuit_sub(t119, t17); let t121 = circuit_sub(t120, t29); let t122 = circuit_sub(t17, t121); let t123 = circuit_mul(t118, t122); let t124 = circuit_sub(t123, t20); let t125 = circuit_sub(in0, t124); let t126 = circuit_sub(in0, t114); let t127 = circuit_sub(in0, t104); let t128 = circuit_sub(in0, t94); let t129 = circuit_sub(in0, t84); let t130 = circuit_sub(in0, t74); let t131 = circuit_sub(in0, t64); let t132 = circuit_sub(in0, t54); let t133 = circuit_sub(t54, in10); let t134 = circuit_sub(t51, in9); let t135 = circuit_inverse(t134); let t136 = circuit_mul(t133, t135); let t137 = circuit_mul(t136, t136); let t138 = circuit_sub(t137, t51); let t139 = circuit_sub(t138, in9); let t140 = circuit_sub(t51, t139); let t141 = circuit_mul(t136, t140); let t142 = circuit_sub(t141, t54); let modulus = modulus; let mut circuit_inputs = ( t51, t54, t61, t64, t71, t74, t81, t84, t91, t94, t101, t104, t111, t114, t121, t124, t125, t126, t127, t128, t129, t130, t131, t132, t21, t22, t139, t142, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(Px); // in1 circuit_inputs = circuit_inputs.next_2(P0y); // in2 circuit_inputs = circuit_inputs.next_2(P1y); // in3 circuit_inputs = circuit_inputs.next_2(Qx); // in4 circuit_inputs = circuit_inputs.next_2(Q0y); // in5 circuit_inputs = circuit_inputs.next_2(Phi_P0y); // in6 circuit_inputs = circuit_inputs.next_2(Phi_P1y); // in7 circuit_inputs = circuit_inputs.next_2(Phi_Q0y); // in8 circuit_inputs = circuit_inputs.next_2(Gen.x); // in9 circuit_inputs = circuit_inputs.next_2(Gen.y); // in10 circuit_inputs = circuit_inputs.next_2(third_root); // in11 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let B1: G1Point = G1Point { x: outputs.get_output(t51), y: outputs.get_output(t54) }; let B2: G1Point = G1Point { x: outputs.get_output(t61), y: outputs.get_output(t64) }; let B3: G1Point = G1Point { x: outputs.get_output(t71), y: outputs.get_output(t74) }; let B4: G1Point = G1Point { x: outputs.get_output(t81), y: outputs.get_output(t84) }; let B5: G1Point = G1Point { x: outputs.get_output(t91), y: outputs.get_output(t94) }; let B6: G1Point = G1Point { x: outputs.get_output(t101), y: outputs.get_output(t104) }; let B7: G1Point = G1Point { x: outputs.get_output(t111), y: outputs.get_output(t114) }; let B8: G1Point = G1Point { x: outputs.get_output(t121), y: outputs.get_output(t124) }; let B9y: u384 = outputs.get_output(t125); let B10y: u384 = outputs.get_output(t126); let B11y: u384 = outputs.get_output(t127); let B12y: u384 = outputs.get_output(t128); let B13y: u384 = outputs.get_output(t129); let B14y: u384 = outputs.get_output(t130); let B15y: u384 = outputs.get_output(t131); let B16y: u384 = outputs.get_output(t132); let Phi_P0x: u384 = outputs.get_output(t21); let Phi_Q0x: u384 = outputs.get_output(t22); let Acc: G1Point = G1Point { x: outputs.get_output(t139), y: outputs.get_output(t142) }; return ( B1, B2, B3, B4, B5, B6, B7, B8, B9y, B10y, B11y, B12y, B13y, B14y, B15y, B16y, Phi_P0x, Phi_Q0x, Acc, ); } #[inline(always)] pub fn run_PSI_G2_BLS12_381_circuit( p: G2Point, modulus: core::circuit::CircuitModulus, ) -> (G2Point,) { // CONSTANT stack let in0 = CE::< CI<0>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad let in1 = CE::< CI<1>, > {}; // 0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2 let in2 = CE::< CI<2>, > {}; // 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09 let in3 = CE::> {}; // 0x0 // INPUT stack let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let in7 = CE::> {}; let t0 = circuit_mul(in5, in0); let t1 = circuit_mul(in4, in0); let t2 = circuit_sub(in3, in7); let t3 = circuit_mul(in6, in1); // Fp2 mul start let t4 = circuit_mul(t2, in2); let t5 = circuit_sub(t3, t4); // Fp2 mul real part end let t6 = circuit_mul(in6, in2); let t7 = circuit_mul(t2, in1); let t8 = circuit_add(t6, t7); // Fp2 mul imag part end let modulus = modulus; let mut circuit_inputs = (t0, t1, t5, t8).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [ 0x4f49fffd8bfd00000000aaad, 0x897d29650fb85f9b409427eb, 0x63d4de85aa0d857d89759ad4, 0x1a0111ea397fe699ec024086, ], ); // in0 circuit_inputs = circuit_inputs .next_2( [ 0x3e67fa0af1ee7b04121bdea2, 0xef396489f61eb45e304466cf, 0xd77a2cd91c3dedd930b1cf60, 0x135203e60180a68ee2e9c448, ], ); // in1 circuit_inputs = circuit_inputs .next_2( [ 0x72ec05f4c81084fbede3cc09, 0x77f76e17009241c5ee67992f, 0x6bd17ffe48395dabc2d3435e, 0x6af0e0437ff400b6831e36d, ], ); // in2 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in3 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p.x0); // in4 circuit_inputs = circuit_inputs.next_2(p.x1); // in5 circuit_inputs = circuit_inputs.next_2(p.y0); // in6 circuit_inputs = circuit_inputs.next_2(p.y1); // in7 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let result: G2Point = G2Point { x0: outputs.get_output(t0), x1: outputs.get_output(t1), y0: outputs.get_output(t5), y1: outputs.get_output(t8), }; return (result,); } #[inline(always)] pub fn run_QUADRUPLE_AND_ADD_9_circuit( P: G1Point, Q_1: G1Point, Q_2: G1Point, Q_3: G1Point, Q_4: G1Point, Q_5: G1Point, Q_6: G1Point, Q_7: G1Point, Q_8: G1Point, Q_9: G1Point, A_weirstrass: u384, modulus: core::circuit::CircuitModulus, ) -> (G1Point,) { // CONSTANT stack let in0 = CE::> {}; // 0x3 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in1, in1); let t1 = circuit_mul(in0, t0); let t2 = circuit_add(t1, in21); let t3 = circuit_add(in2, in2); let t4 = circuit_inverse(t3); let t5 = circuit_mul(t2, t4); let t6 = circuit_mul(t5, t5); let t7 = circuit_sub(t6, in1); let t8 = circuit_sub(t7, in1); let t9 = circuit_sub(in1, t8); let t10 = circuit_mul(t5, t9); let t11 = circuit_sub(t10, in2); let t12 = circuit_sub(in4, t11); let t13 = circuit_sub(in3, t8); let t14 = circuit_inverse(t13); let t15 = circuit_mul(t12, t14); let t16 = circuit_mul(t15, t15); let t17 = circuit_add(t8, in3); let t18 = circuit_sub(t16, t17); let t19 = circuit_add(t11, t11); let t20 = circuit_sub(t18, t8); let t21 = circuit_inverse(t20); let t22 = circuit_mul(t19, t21); let t23 = circuit_add(t15, t22); let t24 = circuit_mul(t23, t23); let t25 = circuit_add(t8, t18); let t26 = circuit_sub(t24, t25); let t27 = circuit_sub(t26, t8); let t28 = circuit_mul(t23, t27); let t29 = circuit_sub(t28, t11); let t30 = circuit_mul(t26, t26); let t31 = circuit_mul(in0, t30); let t32 = circuit_add(t31, in21); let t33 = circuit_add(t29, t29); let t34 = circuit_inverse(t33); let t35 = circuit_mul(t32, t34); let t36 = circuit_mul(t35, t35); let t37 = circuit_sub(t36, t26); let t38 = circuit_sub(t37, t26); let t39 = circuit_sub(t26, t38); let t40 = circuit_mul(t35, t39); let t41 = circuit_sub(t40, t29); let t42 = circuit_sub(in6, t41); let t43 = circuit_sub(in5, t38); let t44 = circuit_inverse(t43); let t45 = circuit_mul(t42, t44); let t46 = circuit_mul(t45, t45); let t47 = circuit_add(t38, in5); let t48 = circuit_sub(t46, t47); let t49 = circuit_add(t41, t41); let t50 = circuit_sub(t48, t38); let t51 = circuit_inverse(t50); let t52 = circuit_mul(t49, t51); let t53 = circuit_add(t45, t52); let t54 = circuit_mul(t53, t53); let t55 = circuit_add(t38, t48); let t56 = circuit_sub(t54, t55); let t57 = circuit_sub(t56, t38); let t58 = circuit_mul(t53, t57); let t59 = circuit_sub(t58, t41); let t60 = circuit_mul(t56, t56); let t61 = circuit_mul(in0, t60); let t62 = circuit_add(t61, in21); let t63 = circuit_add(t59, t59); let t64 = circuit_inverse(t63); let t65 = circuit_mul(t62, t64); let t66 = circuit_mul(t65, t65); let t67 = circuit_sub(t66, t56); let t68 = circuit_sub(t67, t56); let t69 = circuit_sub(t56, t68); let t70 = circuit_mul(t65, t69); let t71 = circuit_sub(t70, t59); let t72 = circuit_sub(in8, t71); let t73 = circuit_sub(in7, t68); let t74 = circuit_inverse(t73); let t75 = circuit_mul(t72, t74); let t76 = circuit_mul(t75, t75); let t77 = circuit_add(t68, in7); let t78 = circuit_sub(t76, t77); let t79 = circuit_add(t71, t71); let t80 = circuit_sub(t78, t68); let t81 = circuit_inverse(t80); let t82 = circuit_mul(t79, t81); let t83 = circuit_add(t75, t82); let t84 = circuit_mul(t83, t83); let t85 = circuit_add(t68, t78); let t86 = circuit_sub(t84, t85); let t87 = circuit_sub(t86, t68); let t88 = circuit_mul(t83, t87); let t89 = circuit_sub(t88, t71); let t90 = circuit_mul(t86, t86); let t91 = circuit_mul(in0, t90); let t92 = circuit_add(t91, in21); let t93 = circuit_add(t89, t89); let t94 = circuit_inverse(t93); let t95 = circuit_mul(t92, t94); let t96 = circuit_mul(t95, t95); let t97 = circuit_sub(t96, t86); let t98 = circuit_sub(t97, t86); let t99 = circuit_sub(t86, t98); let t100 = circuit_mul(t95, t99); let t101 = circuit_sub(t100, t89); let t102 = circuit_sub(in10, t101); let t103 = circuit_sub(in9, t98); let t104 = circuit_inverse(t103); let t105 = circuit_mul(t102, t104); let t106 = circuit_mul(t105, t105); let t107 = circuit_add(t98, in9); let t108 = circuit_sub(t106, t107); let t109 = circuit_add(t101, t101); let t110 = circuit_sub(t108, t98); let t111 = circuit_inverse(t110); let t112 = circuit_mul(t109, t111); let t113 = circuit_add(t105, t112); let t114 = circuit_mul(t113, t113); let t115 = circuit_add(t98, t108); let t116 = circuit_sub(t114, t115); let t117 = circuit_sub(t116, t98); let t118 = circuit_mul(t113, t117); let t119 = circuit_sub(t118, t101); let t120 = circuit_mul(t116, t116); let t121 = circuit_mul(in0, t120); let t122 = circuit_add(t121, in21); let t123 = circuit_add(t119, t119); let t124 = circuit_inverse(t123); let t125 = circuit_mul(t122, t124); let t126 = circuit_mul(t125, t125); let t127 = circuit_sub(t126, t116); let t128 = circuit_sub(t127, t116); let t129 = circuit_sub(t116, t128); let t130 = circuit_mul(t125, t129); let t131 = circuit_sub(t130, t119); let t132 = circuit_sub(in12, t131); let t133 = circuit_sub(in11, t128); let t134 = circuit_inverse(t133); let t135 = circuit_mul(t132, t134); let t136 = circuit_mul(t135, t135); let t137 = circuit_add(t128, in11); let t138 = circuit_sub(t136, t137); let t139 = circuit_add(t131, t131); let t140 = circuit_sub(t138, t128); let t141 = circuit_inverse(t140); let t142 = circuit_mul(t139, t141); let t143 = circuit_add(t135, t142); let t144 = circuit_mul(t143, t143); let t145 = circuit_add(t128, t138); let t146 = circuit_sub(t144, t145); let t147 = circuit_sub(t146, t128); let t148 = circuit_mul(t143, t147); let t149 = circuit_sub(t148, t131); let t150 = circuit_mul(t146, t146); let t151 = circuit_mul(in0, t150); let t152 = circuit_add(t151, in21); let t153 = circuit_add(t149, t149); let t154 = circuit_inverse(t153); let t155 = circuit_mul(t152, t154); let t156 = circuit_mul(t155, t155); let t157 = circuit_sub(t156, t146); let t158 = circuit_sub(t157, t146); let t159 = circuit_sub(t146, t158); let t160 = circuit_mul(t155, t159); let t161 = circuit_sub(t160, t149); let t162 = circuit_sub(in14, t161); let t163 = circuit_sub(in13, t158); let t164 = circuit_inverse(t163); let t165 = circuit_mul(t162, t164); let t166 = circuit_mul(t165, t165); let t167 = circuit_add(t158, in13); let t168 = circuit_sub(t166, t167); let t169 = circuit_add(t161, t161); let t170 = circuit_sub(t168, t158); let t171 = circuit_inverse(t170); let t172 = circuit_mul(t169, t171); let t173 = circuit_add(t165, t172); let t174 = circuit_mul(t173, t173); let t175 = circuit_add(t158, t168); let t176 = circuit_sub(t174, t175); let t177 = circuit_sub(t176, t158); let t178 = circuit_mul(t173, t177); let t179 = circuit_sub(t178, t161); let t180 = circuit_mul(t176, t176); let t181 = circuit_mul(in0, t180); let t182 = circuit_add(t181, in21); let t183 = circuit_add(t179, t179); let t184 = circuit_inverse(t183); let t185 = circuit_mul(t182, t184); let t186 = circuit_mul(t185, t185); let t187 = circuit_sub(t186, t176); let t188 = circuit_sub(t187, t176); let t189 = circuit_sub(t176, t188); let t190 = circuit_mul(t185, t189); let t191 = circuit_sub(t190, t179); let t192 = circuit_sub(in16, t191); let t193 = circuit_sub(in15, t188); let t194 = circuit_inverse(t193); let t195 = circuit_mul(t192, t194); let t196 = circuit_mul(t195, t195); let t197 = circuit_add(t188, in15); let t198 = circuit_sub(t196, t197); let t199 = circuit_add(t191, t191); let t200 = circuit_sub(t198, t188); let t201 = circuit_inverse(t200); let t202 = circuit_mul(t199, t201); let t203 = circuit_add(t195, t202); let t204 = circuit_mul(t203, t203); let t205 = circuit_add(t188, t198); let t206 = circuit_sub(t204, t205); let t207 = circuit_sub(t206, t188); let t208 = circuit_mul(t203, t207); let t209 = circuit_sub(t208, t191); let t210 = circuit_mul(t206, t206); let t211 = circuit_mul(in0, t210); let t212 = circuit_add(t211, in21); let t213 = circuit_add(t209, t209); let t214 = circuit_inverse(t213); let t215 = circuit_mul(t212, t214); let t216 = circuit_mul(t215, t215); let t217 = circuit_sub(t216, t206); let t218 = circuit_sub(t217, t206); let t219 = circuit_sub(t206, t218); let t220 = circuit_mul(t215, t219); let t221 = circuit_sub(t220, t209); let t222 = circuit_sub(in18, t221); let t223 = circuit_sub(in17, t218); let t224 = circuit_inverse(t223); let t225 = circuit_mul(t222, t224); let t226 = circuit_mul(t225, t225); let t227 = circuit_add(t218, in17); let t228 = circuit_sub(t226, t227); let t229 = circuit_add(t221, t221); let t230 = circuit_sub(t228, t218); let t231 = circuit_inverse(t230); let t232 = circuit_mul(t229, t231); let t233 = circuit_add(t225, t232); let t234 = circuit_mul(t233, t233); let t235 = circuit_add(t218, t228); let t236 = circuit_sub(t234, t235); let t237 = circuit_sub(t236, t218); let t238 = circuit_mul(t233, t237); let t239 = circuit_sub(t238, t221); let t240 = circuit_mul(t236, t236); let t241 = circuit_mul(in0, t240); let t242 = circuit_add(t241, in21); let t243 = circuit_add(t239, t239); let t244 = circuit_inverse(t243); let t245 = circuit_mul(t242, t244); let t246 = circuit_mul(t245, t245); let t247 = circuit_sub(t246, t236); let t248 = circuit_sub(t247, t236); let t249 = circuit_sub(t236, t248); let t250 = circuit_mul(t245, t249); let t251 = circuit_sub(t250, t239); let t252 = circuit_sub(in20, t251); let t253 = circuit_sub(in19, t248); let t254 = circuit_inverse(t253); let t255 = circuit_mul(t252, t254); let t256 = circuit_mul(t255, t255); let t257 = circuit_add(t248, in19); let t258 = circuit_sub(t256, t257); let t259 = circuit_add(t251, t251); let t260 = circuit_sub(t258, t248); let t261 = circuit_inverse(t260); let t262 = circuit_mul(t259, t261); let t263 = circuit_add(t255, t262); let t264 = circuit_mul(t263, t263); let t265 = circuit_add(t248, t258); let t266 = circuit_sub(t264, t265); let t267 = circuit_sub(t266, t248); let t268 = circuit_mul(t263, t267); let t269 = circuit_sub(t268, t251); let modulus = modulus; let mut circuit_inputs = (t266, t269).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(P.x); // in1 circuit_inputs = circuit_inputs.next_2(P.y); // in2 circuit_inputs = circuit_inputs.next_2(Q_1.x); // in3 circuit_inputs = circuit_inputs.next_2(Q_1.y); // in4 circuit_inputs = circuit_inputs.next_2(Q_2.x); // in5 circuit_inputs = circuit_inputs.next_2(Q_2.y); // in6 circuit_inputs = circuit_inputs.next_2(Q_3.x); // in7 circuit_inputs = circuit_inputs.next_2(Q_3.y); // in8 circuit_inputs = circuit_inputs.next_2(Q_4.x); // in9 circuit_inputs = circuit_inputs.next_2(Q_4.y); // in10 circuit_inputs = circuit_inputs.next_2(Q_5.x); // in11 circuit_inputs = circuit_inputs.next_2(Q_5.y); // in12 circuit_inputs = circuit_inputs.next_2(Q_6.x); // in13 circuit_inputs = circuit_inputs.next_2(Q_6.y); // in14 circuit_inputs = circuit_inputs.next_2(Q_7.x); // in15 circuit_inputs = circuit_inputs.next_2(Q_7.y); // in16 circuit_inputs = circuit_inputs.next_2(Q_8.x); // in17 circuit_inputs = circuit_inputs.next_2(Q_8.y); // in18 circuit_inputs = circuit_inputs.next_2(Q_9.x); // in19 circuit_inputs = circuit_inputs.next_2(Q_9.y); // in20 circuit_inputs = circuit_inputs.next_2(A_weirstrass); // in21 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let R: G1Point = G1Point { x: outputs.get_output(t266), y: outputs.get_output(t269) }; return (R,); } ================================================ FILE: src/src/circuits/extf_mul.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{E12D, u288}; #[inline(always)] pub fn run_BLS12_381_EVAL_E12D_circuit(f: E12D, z: u384) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let in12 = CE::> {}; let t0 = circuit_mul(in11, in12); // Eval X Horner step: multiply by z let t1 = circuit_add(in10, t0); // Eval X Horner step: add coefficient_10 let t2 = circuit_mul(t1, in12); // Eval X Horner step: multiply by z let t3 = circuit_add(in9, t2); // Eval X Horner step: add coefficient_9 let t4 = circuit_mul(t3, in12); // Eval X Horner step: multiply by z let t5 = circuit_add(in8, t4); // Eval X Horner step: add coefficient_8 let t6 = circuit_mul(t5, in12); // Eval X Horner step: multiply by z let t7 = circuit_add(in7, t6); // Eval X Horner step: add coefficient_7 let t8 = circuit_mul(t7, in12); // Eval X Horner step: multiply by z let t9 = circuit_add(in6, t8); // Eval X Horner step: add coefficient_6 let t10 = circuit_mul(t9, in12); // Eval X Horner step: multiply by z let t11 = circuit_add(in5, t10); // Eval X Horner step: add coefficient_5 let t12 = circuit_mul(t11, in12); // Eval X Horner step: multiply by z let t13 = circuit_add(in4, t12); // Eval X Horner step: add coefficient_4 let t14 = circuit_mul(t13, in12); // Eval X Horner step: multiply by z let t15 = circuit_add(in3, t14); // Eval X Horner step: add coefficient_3 let t16 = circuit_mul(t15, in12); // Eval X Horner step: multiply by z let t17 = circuit_add(in2, t16); // Eval X Horner step: add coefficient_2 let t18 = circuit_mul(t17, in12); // Eval X Horner step: multiply by z let t19 = circuit_add(in1, t18); // Eval X Horner step: add coefficient_1 let t20 = circuit_mul(t19, in12); // Eval X Horner step: multiply by z let t21 = circuit_add(in0, t20); // Eval X Horner step: add coefficient_0 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t21,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(f.w0); // in0 circuit_inputs = circuit_inputs.next_2(f.w1); // in1 circuit_inputs = circuit_inputs.next_2(f.w2); // in2 circuit_inputs = circuit_inputs.next_2(f.w3); // in3 circuit_inputs = circuit_inputs.next_2(f.w4); // in4 circuit_inputs = circuit_inputs.next_2(f.w5); // in5 circuit_inputs = circuit_inputs.next_2(f.w6); // in6 circuit_inputs = circuit_inputs.next_2(f.w7); // in7 circuit_inputs = circuit_inputs.next_2(f.w8); // in8 circuit_inputs = circuit_inputs.next_2(f.w9); // in9 circuit_inputs = circuit_inputs.next_2(f.w10); // in10 circuit_inputs = circuit_inputs.next_2(f.w11); // in11 circuit_inputs = circuit_inputs.next_2(z); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let f_of_z: u384 = outputs.get_output(t21); return (f_of_z,); } #[inline(always)] pub fn run_BN254_EVAL_E12D_circuit(f: E12D, z: u384) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let in12 = CE::> {}; let t0 = circuit_mul(in11, in12); // Eval X Horner step: multiply by z let t1 = circuit_add(in10, t0); // Eval X Horner step: add coefficient_10 let t2 = circuit_mul(t1, in12); // Eval X Horner step: multiply by z let t3 = circuit_add(in9, t2); // Eval X Horner step: add coefficient_9 let t4 = circuit_mul(t3, in12); // Eval X Horner step: multiply by z let t5 = circuit_add(in8, t4); // Eval X Horner step: add coefficient_8 let t6 = circuit_mul(t5, in12); // Eval X Horner step: multiply by z let t7 = circuit_add(in7, t6); // Eval X Horner step: add coefficient_7 let t8 = circuit_mul(t7, in12); // Eval X Horner step: multiply by z let t9 = circuit_add(in6, t8); // Eval X Horner step: add coefficient_6 let t10 = circuit_mul(t9, in12); // Eval X Horner step: multiply by z let t11 = circuit_add(in5, t10); // Eval X Horner step: add coefficient_5 let t12 = circuit_mul(t11, in12); // Eval X Horner step: multiply by z let t13 = circuit_add(in4, t12); // Eval X Horner step: add coefficient_4 let t14 = circuit_mul(t13, in12); // Eval X Horner step: multiply by z let t15 = circuit_add(in3, t14); // Eval X Horner step: add coefficient_3 let t16 = circuit_mul(t15, in12); // Eval X Horner step: multiply by z let t17 = circuit_add(in2, t16); // Eval X Horner step: add coefficient_2 let t18 = circuit_mul(t17, in12); // Eval X Horner step: multiply by z let t19 = circuit_add(in1, t18); // Eval X Horner step: add coefficient_1 let t20 = circuit_mul(t19, in12); // Eval X Horner step: multiply by z let t21 = circuit_add(in0, t20); // Eval X Horner step: add coefficient_0 let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t21,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(f.w0); // in0 circuit_inputs = circuit_inputs.next_2(f.w1); // in1 circuit_inputs = circuit_inputs.next_2(f.w2); // in2 circuit_inputs = circuit_inputs.next_2(f.w3); // in3 circuit_inputs = circuit_inputs.next_2(f.w4); // in4 circuit_inputs = circuit_inputs.next_2(f.w5); // in5 circuit_inputs = circuit_inputs.next_2(f.w6); // in6 circuit_inputs = circuit_inputs.next_2(f.w7); // in7 circuit_inputs = circuit_inputs.next_2(f.w8); // in8 circuit_inputs = circuit_inputs.next_2(f.w9); // in9 circuit_inputs = circuit_inputs.next_2(f.w10); // in10 circuit_inputs = circuit_inputs.next_2(f.w11); // in11 circuit_inputs = circuit_inputs.next_2(z); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let f_of_z: u384 = outputs.get_output(t21); return (f_of_z,); } ================================================ FILE: src/src/circuits/isogeny.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::G1Point; #[inline(always)] pub fn run_BLS12_381_APPLY_ISOGENY_BLS12_381_circuit(pt: G1Point) -> (G1Point,) { // CONSTANT stack let in0 = CE::< CI<0>, > {}; // 0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7 let in1 = CE::< CI<1>, > {}; // 0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb let in2 = CE::< CI<2>, > {}; // 0xd54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0 let in3 = CE::< CI<3>, > {}; // 0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861 let in4 = CE::< CI<4>, > {}; // 0xe99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9 let in5 = CE::< CI<5>, > {}; // 0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983 let in6 = CE::< CI<6>, > {}; // 0xd6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84 let in7 = CE::< CI<7>, > {}; // 0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e let in8 = CE::< CI<8>, > {}; // 0x80d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317 let in9 = CE::< CI<9>, > {}; // 0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e let in10 = CE::< CI<10>, > {}; // 0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b let in11 = CE::< CI<11>, > {}; // 0x6e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229 let in12 = CE::< CI<12>, > {}; // 0x8ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c let in13 = CE::< CI<13>, > {}; // 0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff let in14 = CE::< CI<14>, > {}; // 0xb2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19 let in15 = CE::< CI<15>, > {}; // 0x3425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8 let in16 = CE::< CI<16>, > {}; // 0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e let in17 = CE::< CI<17>, > {}; // 0xe7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5 let in18 = CE::< CI<18>, > {}; // 0x772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a let in19 = CE::< CI<19>, > {}; // 0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e let in20 = CE::< CI<20>, > {}; // 0xa10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641 let in21 = CE::< CI<21>, > {}; // 0x95fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a let in22 = CE::> {}; // 0x1 let in23 = CE::< CI<23>, > {}; // 0x90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33 let in24 = CE::< CI<24>, > {}; // 0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696 let in25 = CE::< CI<25>, > {}; // 0xcc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6 let in26 = CE::< CI<26>, > {}; // 0x1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb let in27 = CE::< CI<27>, > {}; // 0x8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb let in28 = CE::< CI<28>, > {}; // 0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0 let in29 = CE::< CI<29>, > {}; // 0x4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2 let in30 = CE::< CI<30>, > {}; // 0x987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29 let in31 = CE::< CI<31>, > {}; // 0x9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587 let in32 = CE::< CI<32>, > {}; // 0xe1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30 let in33 = CE::< CI<33>, > {}; // 0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132 let in34 = CE::< CI<34>, > {}; // 0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e let in35 = CE::< CI<35>, > {}; // 0xb182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8 let in36 = CE::< CI<36>, > {}; // 0x245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133 let in37 = CE::< CI<37>, > {}; // 0x5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b let in38 = CE::< CI<38>, > {}; // 0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604 let in39 = CE::< CI<39>, > {}; // 0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1 let in40 = CE::< CI<40>, > {}; // 0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d let in41 = CE::< CI<41>, > {}; // 0x58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2 let in42 = CE::< CI<42>, > {}; // 0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416 let in43 = CE::< CI<43>, > {}; // 0xbe0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d let in44 = CE::< CI<44>, > {}; // 0x8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac let in45 = CE::< CI<45>, > {}; // 0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c let in46 = CE::< CI<46>, > {}; // 0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9 let in47 = CE::< CI<47>, > {}; // 0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a let in48 = CE::< CI<48>, > {}; // 0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55 let in49 = CE::< CI<49>, > {}; // 0x4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8 let in50 = CE::< CI<50>, > {}; // 0xaccbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092 let in51 = CE::< CI<51>, > {}; // 0xad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc let in52 = CE::< CI<52>, > {}; // 0x2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7 let in53 = CE::< CI<53>, > {}; // 0xe0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f // INPUT stack let (in54, in55) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in11, in54); // Eval x_num Horner step: multiply by z let t1 = circuit_add(in10, t0); // Eval x_num Horner step: add coefficient_10 let t2 = circuit_mul(t1, in54); // Eval x_num Horner step: multiply by z let t3 = circuit_add(in9, t2); // Eval x_num Horner step: add coefficient_9 let t4 = circuit_mul(t3, in54); // Eval x_num Horner step: multiply by z let t5 = circuit_add(in8, t4); // Eval x_num Horner step: add coefficient_8 let t6 = circuit_mul(t5, in54); // Eval x_num Horner step: multiply by z let t7 = circuit_add(in7, t6); // Eval x_num Horner step: add coefficient_7 let t8 = circuit_mul(t7, in54); // Eval x_num Horner step: multiply by z let t9 = circuit_add(in6, t8); // Eval x_num Horner step: add coefficient_6 let t10 = circuit_mul(t9, in54); // Eval x_num Horner step: multiply by z let t11 = circuit_add(in5, t10); // Eval x_num Horner step: add coefficient_5 let t12 = circuit_mul(t11, in54); // Eval x_num Horner step: multiply by z let t13 = circuit_add(in4, t12); // Eval x_num Horner step: add coefficient_4 let t14 = circuit_mul(t13, in54); // Eval x_num Horner step: multiply by z let t15 = circuit_add(in3, t14); // Eval x_num Horner step: add coefficient_3 let t16 = circuit_mul(t15, in54); // Eval x_num Horner step: multiply by z let t17 = circuit_add(in2, t16); // Eval x_num Horner step: add coefficient_2 let t18 = circuit_mul(t17, in54); // Eval x_num Horner step: multiply by z let t19 = circuit_add(in1, t18); // Eval x_num Horner step: add coefficient_1 let t20 = circuit_mul(t19, in54); // Eval x_num Horner step: multiply by z let t21 = circuit_add(in0, t20); // Eval x_num Horner step: add coefficient_0 let t22 = circuit_mul(in22, in54); // Eval x_den Horner step: multiply by z let t23 = circuit_add(in21, t22); // Eval x_den Horner step: add coefficient_9 let t24 = circuit_mul(t23, in54); // Eval x_den Horner step: multiply by z let t25 = circuit_add(in20, t24); // Eval x_den Horner step: add coefficient_8 let t26 = circuit_mul(t25, in54); // Eval x_den Horner step: multiply by z let t27 = circuit_add(in19, t26); // Eval x_den Horner step: add coefficient_7 let t28 = circuit_mul(t27, in54); // Eval x_den Horner step: multiply by z let t29 = circuit_add(in18, t28); // Eval x_den Horner step: add coefficient_6 let t30 = circuit_mul(t29, in54); // Eval x_den Horner step: multiply by z let t31 = circuit_add(in17, t30); // Eval x_den Horner step: add coefficient_5 let t32 = circuit_mul(t31, in54); // Eval x_den Horner step: multiply by z let t33 = circuit_add(in16, t32); // Eval x_den Horner step: add coefficient_4 let t34 = circuit_mul(t33, in54); // Eval x_den Horner step: multiply by z let t35 = circuit_add(in15, t34); // Eval x_den Horner step: add coefficient_3 let t36 = circuit_mul(t35, in54); // Eval x_den Horner step: multiply by z let t37 = circuit_add(in14, t36); // Eval x_den Horner step: add coefficient_2 let t38 = circuit_mul(t37, in54); // Eval x_den Horner step: multiply by z let t39 = circuit_add(in13, t38); // Eval x_den Horner step: add coefficient_1 let t40 = circuit_mul(t39, in54); // Eval x_den Horner step: multiply by z let t41 = circuit_add(in12, t40); // Eval x_den Horner step: add coefficient_0 let t42 = circuit_inverse(t41); let t43 = circuit_mul(t21, t42); let t44 = circuit_mul(in38, in54); // Eval y_num Horner step: multiply by z let t45 = circuit_add(in37, t44); // Eval y_num Horner step: add coefficient_14 let t46 = circuit_mul(t45, in54); // Eval y_num Horner step: multiply by z let t47 = circuit_add(in36, t46); // Eval y_num Horner step: add coefficient_13 let t48 = circuit_mul(t47, in54); // Eval y_num Horner step: multiply by z let t49 = circuit_add(in35, t48); // Eval y_num Horner step: add coefficient_12 let t50 = circuit_mul(t49, in54); // Eval y_num Horner step: multiply by z let t51 = circuit_add(in34, t50); // Eval y_num Horner step: add coefficient_11 let t52 = circuit_mul(t51, in54); // Eval y_num Horner step: multiply by z let t53 = circuit_add(in33, t52); // Eval y_num Horner step: add coefficient_10 let t54 = circuit_mul(t53, in54); // Eval y_num Horner step: multiply by z let t55 = circuit_add(in32, t54); // Eval y_num Horner step: add coefficient_9 let t56 = circuit_mul(t55, in54); // Eval y_num Horner step: multiply by z let t57 = circuit_add(in31, t56); // Eval y_num Horner step: add coefficient_8 let t58 = circuit_mul(t57, in54); // Eval y_num Horner step: multiply by z let t59 = circuit_add(in30, t58); // Eval y_num Horner step: add coefficient_7 let t60 = circuit_mul(t59, in54); // Eval y_num Horner step: multiply by z let t61 = circuit_add(in29, t60); // Eval y_num Horner step: add coefficient_6 let t62 = circuit_mul(t61, in54); // Eval y_num Horner step: multiply by z let t63 = circuit_add(in28, t62); // Eval y_num Horner step: add coefficient_5 let t64 = circuit_mul(t63, in54); // Eval y_num Horner step: multiply by z let t65 = circuit_add(in27, t64); // Eval y_num Horner step: add coefficient_4 let t66 = circuit_mul(t65, in54); // Eval y_num Horner step: multiply by z let t67 = circuit_add(in26, t66); // Eval y_num Horner step: add coefficient_3 let t68 = circuit_mul(t67, in54); // Eval y_num Horner step: multiply by z let t69 = circuit_add(in25, t68); // Eval y_num Horner step: add coefficient_2 let t70 = circuit_mul(t69, in54); // Eval y_num Horner step: multiply by z let t71 = circuit_add(in24, t70); // Eval y_num Horner step: add coefficient_1 let t72 = circuit_mul(t71, in54); // Eval y_num Horner step: multiply by z let t73 = circuit_add(in23, t72); // Eval y_num Horner step: add coefficient_0 let t74 = circuit_mul(in22, in54); // Eval y_den Horner step: multiply by z let t75 = circuit_add(in53, t74); // Eval y_den Horner step: add coefficient_14 let t76 = circuit_mul(t75, in54); // Eval y_den Horner step: multiply by z let t77 = circuit_add(in52, t76); // Eval y_den Horner step: add coefficient_13 let t78 = circuit_mul(t77, in54); // Eval y_den Horner step: multiply by z let t79 = circuit_add(in51, t78); // Eval y_den Horner step: add coefficient_12 let t80 = circuit_mul(t79, in54); // Eval y_den Horner step: multiply by z let t81 = circuit_add(in50, t80); // Eval y_den Horner step: add coefficient_11 let t82 = circuit_mul(t81, in54); // Eval y_den Horner step: multiply by z let t83 = circuit_add(in49, t82); // Eval y_den Horner step: add coefficient_10 let t84 = circuit_mul(t83, in54); // Eval y_den Horner step: multiply by z let t85 = circuit_add(in48, t84); // Eval y_den Horner step: add coefficient_9 let t86 = circuit_mul(t85, in54); // Eval y_den Horner step: multiply by z let t87 = circuit_add(in47, t86); // Eval y_den Horner step: add coefficient_8 let t88 = circuit_mul(t87, in54); // Eval y_den Horner step: multiply by z let t89 = circuit_add(in46, t88); // Eval y_den Horner step: add coefficient_7 let t90 = circuit_mul(t89, in54); // Eval y_den Horner step: multiply by z let t91 = circuit_add(in45, t90); // Eval y_den Horner step: add coefficient_6 let t92 = circuit_mul(t91, in54); // Eval y_den Horner step: multiply by z let t93 = circuit_add(in44, t92); // Eval y_den Horner step: add coefficient_5 let t94 = circuit_mul(t93, in54); // Eval y_den Horner step: multiply by z let t95 = circuit_add(in43, t94); // Eval y_den Horner step: add coefficient_4 let t96 = circuit_mul(t95, in54); // Eval y_den Horner step: multiply by z let t97 = circuit_add(in42, t96); // Eval y_den Horner step: add coefficient_3 let t98 = circuit_mul(t97, in54); // Eval y_den Horner step: multiply by z let t99 = circuit_add(in41, t98); // Eval y_den Horner step: add coefficient_2 let t100 = circuit_mul(t99, in54); // Eval y_den Horner step: multiply by z let t101 = circuit_add(in40, t100); // Eval y_den Horner step: add coefficient_1 let t102 = circuit_mul(t101, in54); // Eval y_den Horner step: multiply by z let t103 = circuit_add(in39, t102); // Eval y_den Horner step: add coefficient_0 let t104 = circuit_inverse(t103); let t105 = circuit_mul(t73, t104); let t106 = circuit_mul(t105, in55); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t43, t106).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(APPLY_ISOGENY_BLS12_381_BLS12_381_CONSTANTS.span()); // in0 - in53 // Fill inputs: circuit_inputs = circuit_inputs.next_2(pt.x); // in54 circuit_inputs = circuit_inputs.next_2(pt.y); // in55 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: G1Point = G1Point { x: outputs.get_output(t43), y: outputs.get_output(t106) }; return (res,); } const APPLY_ISOGENY_BLS12_381_BLS12_381_CONSTANTS: [u384; 54] = [ u384 { limb0: 0xf2e62d6eaeac1662734649b7, limb1: 0xf2627b56cdb4e2c85610c2d5, limb2: 0xd99815856b303e88a2d7005f, limb3: 0x11a05f2b1e833340b809101d, }, u384 { limb0: 0xf318c356e834eef1b3cb83bb, limb1: 0xf565e33c70d1e86b4838f2a6, limb2: 0x2147a81c7c17e75b2f6a8417, limb3: 0x17294ed3e943ab2f0588bab2, }, u384 { limb0: 0x2a09729fe0179f9dac9edcb0, limb1: 0x6878e501ec68e25c958c3e3d, limb2: 0xd10a9a1bce032473295983e5, limb3: 0xd54005db97678ec1d1048c5, }, u384 { limb0: 0xe3107193c5b388641d9b6861, limb1: 0xf1b33289f1b330835336e25c, limb2: 0x7e55412d7f5e4656a8dbf25, limb3: 0x1778e7166fcc6db74e0609d3, }, u384 { limb0: 0x301e77c451154ce9ac8895d9, limb1: 0x86eeb65982fac18985a286f, limb2: 0xe4118e5499db995a1257fb3f, limb3: 0xe99726a3199f4436642b4b3, }, u384 { limb0: 0xcae73d19cd13c1c66f652983, limb1: 0x9ed3ab9097e68f90a0870d2d, limb2: 0xf7a74ab5db3cb17dd952799b, limb3: 0x1630c3250d7313ff01d1201b, }, u384 { limb0: 0xc1052ecaddd7f225a139ed84, limb1: 0x9008e218f9c86b2a8da25128, limb2: 0x8ae652bfb11586264f0f8ce1, limb3: 0xd6ed6553fe44d296a3726c3, }, u384 { limb0: 0xc8f475af9ccb5618e3f0c88e, limb1: 0xa682c62ef0f2753339b7c8f8, limb2: 0xd1117e53356de5ab275b4db1, limb3: 0x17b81e7701abdbe2e8743884, }, u384 { limb0: 0x96b74e956d71986a8497e317, limb1: 0xa2c596c928c5d1de4fa295f2, limb2: 0x63be990dc43b756ce79f5574, limb3: 0x80d3cf1f9a78fc47b90b335, }, u384 { limb0: 0xdc0327797f241067be390c9e, limb1: 0x676314baf4bb1b7fa3190b2e, limb2: 0x5d138f22dd2ecb803a0c5c99, limb3: 0x169b1f8e1bcfa7c42e0c3751, }, u384 { limb0: 0x8c285decca67df3f1605fb7b, limb1: 0xd50af36003b14866f69b771f, limb2: 0xd2565b0dfa7dccdde6787f96, limb3: 0x10321da079ce07e272d8ec09, }, u384 { limb0: 0xb64d391fa9c8ba2e8ba2d229, limb1: 0x23c0bf1bc24c6b68c24b1b80, limb2: 0x81edee3d31d79d7e22c837bc, limb3: 0x6e08c248e260e70bd1e9623, }, u384 { limb0: 0xbe343df8993cf9fa40d21b1c, limb1: 0x9c9588617fc8ac62b558d681, limb2: 0x4bd3fa6f01d5ef4ba35b48ba, limb3: 0x8ca8d548cff19ae18b2e62f, }, u384 { limb0: 0x6cb026e9e5c8276ec82b3bff, limb1: 0x126c2588c48bf5713daa884, limb2: 0x98e536367041e8ca0cf0800c, limb3: 0x12561a5deb559c4348b47112, }, u384 { limb0: 0x7c94fedcfcc239ba5cb83e19, limb1: 0xfca64e00b11aceacd6a3d096, limb2: 0xbff2991f6f89416f5a718cd1, limb3: 0xb2962fe57a3225e8137e629, }, u384 { limb0: 0x3eecf5c4130de8938dc62cd8, limb1: 0x54cca8abc28d6fd04976d524, limb2: 0x7c40eb545b08243f16b16551, limb3: 0x3425581a58ae2fec83aafef, }, u384 { limb0: 0x1f35781d539d395b3532a21e, limb1: 0x8d6b44e833b306da9bd29ba8, limb2: 0x43e7a07dffdfc759a12062bb, limb3: 0x13a8e162022914a80a6f1d5f, }, u384 { limb0: 0xc4228f11c02df9a29f6304a5, limb1: 0xa43bcef24b8982f7400d24b, limb2: 0x506c6e9395735e9ce9cad4d, limb3: 0xe7355f8e4e667b955390f7f, }, u384 { limb0: 0x8f0de06cec2574496ee84a3a, limb1: 0x4e2e073062aede9cea73b353, limb2: 0xe0596721570f5799af53a189, limb3: 0x772caacf16936190f3e0c63, }, u384 { limb0: 0x9d11e2d311f7d99bbdcc5a5e, limb1: 0x1996e1cdf9822c580fa5b948, limb2: 0x74cf01996e7f63c21bca68a8, limb3: 0x14a7ac2a9d64a8b230b3f5b0, }, u384 { limb0: 0xabba43704776ec3a79a1d641, limb1: 0x74100da67f39883503826692, limb2: 0xafc7a3cce07f8d1d7161366b, limb3: 0xa10ecf6ada54f825e920b3d, }, u384 { limb0: 0x4b7865002d6384d168ecdd0a, limb1: 0x76df533978f31c1593174e4b, limb2: 0xb3a56680f682b4ee96f7d037, limb3: 0x95fc13ab9e92ad4476d6e3e, }, u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9b3ba3c2be9845719707bb33, limb1: 0x2b52af6c956543d3cd0c7aee, limb2: 0x4980dcfa11ad138e48a86952, limb3: 0x90d97c81ba24ee0259d1f09, }, u384 { limb0: 0x962fa8bfe097e75a2e41c696, limb1: 0xf906343eb67ad34d6c56711, limb2: 0x76fb46831223e96c254f383d, limb3: 0x134996a104ee5811d51036d7, }, u384 { limb0: 0x28b00523b8dfe240c72de1f6, limb1: 0xc344be4b91400da7d26d5216, limb2: 0x6a3b49942552e2d658a31ce2, limb3: 0xcc786baa966e66f4a384c8, }, u384 { limb0: 0x9ec61deca6355c77b0e5f4cb, limb1: 0x9e4a3ec03251cf9de405aba, limb2: 0xd8746757d42aa7b90eeb791c, limb3: 0x1f86376e8981c217898751a, }, u384 { limb0: 0x99040a841b6daecf2e8fedb, limb1: 0x79833fd221351adc2ee7f8dc, limb2: 0xa21529c4195536fbe3ce50b8, limb3: 0x8cc03fdefe0ff135caf4fe2, }, u384 { limb0: 0xc95a807299b23ab13633a5f0, limb1: 0x76505c3d3ad5544e203f6326, limb2: 0xb8f0a6a074a7d0d4afadb7bd, limb3: 0x16603fca40634b6a2211e11d, }, u384 { limb0: 0x460f415ec961f8855fe9d6f2, limb1: 0x5231413c4d634f3747a87ac2, limb2: 0x27796b3ce75bb8ca2be184cb, limb3: 0x4ab0b9bcfac1bbcb2c977d0, }, u384 { limb0: 0xfedfe935a15e4ca31870fb29, limb1: 0xfd038da6c26c842642f64550, limb2: 0x2ca6c674170a05bfe3bdd81f, limb3: 0x987c8d5333ab86fde9926bd, }, u384 { limb0: 0xc78607a360370e577bdba587, limb1: 0x1e8b6e6a1f20cabe69d65201, limb2: 0x1e4da1bb8f3abd16679dc26c, limb3: 0x9fc4018bd96684be88c9e22, }, u384 { limb0: 0xdd4eba6f2bafaaebca731c30, limb1: 0x6985e7ed1e4d43b9b3f7055, limb2: 0xada14a23c42a0ca7915af6fe, limb3: 0xe1bba7a1186bdb5223abde7, }, u384 { limb0: 0xce3fbafce813711ad011c132, limb1: 0xd1183e416389e61031bf3a5c, limb2: 0x1d43fb93cd2fcbcb6caf493f, limb3: 0x19713e47937cd1be0dfd0b8f, }, u384 { limb0: 0x1b44d606ce07c8a4d0074d8e, limb1: 0x2e6bfe7f911f643249d9cdf4, limb2: 0xfed2edcc523559b8aaf0c246, limb3: 0x18b46a908f36f6deb918c143, }, u384 { limb0: 0x919211f20d4c04f00b971ef8, limb1: 0xc02710e807b4633f06c851c1, limb2: 0x4f53f447aa7b12a3426b08e, limb3: 0xb182cac101b9399d1550960, }, u384 { limb0: 0x1c232a6442d9d3f5db980133, limb1: 0x13e6632d3c40659cc6cf90ad, limb2: 0x7be315dc757b3b080d4c1580, limb3: 0x245a394ad1eca9b72fc00ae, }, u384 { limb0: 0x6579afb7866b1e715475224b, limb1: 0xd9ab0f5d396a7ce46ba1049b, limb2: 0x48c4a3fc5e673d81d7e86568, limb3: 0x5c129645e44cf1102a159f7, }, u384 { limb0: 0xfec01c7704b456be69c8b604, limb1: 0x57add4fa95af01b2b665027e, limb2: 0x42df2eb5cb181d8f84965a39, limb3: 0x15e6be4e990f03ce4ea50b3b, }, u384 { limb0: 0xf60c206d01479253b03663c1, limb1: 0xeec3232b5be72e7a07f3688e, limb2: 0xfad0eae9601a6de578980be6, limb3: 0x16112c4c3a9c98b252181140, }, u384 { limb0: 0x63529e3532f6102c2e49a03d, limb1: 0xa4a10356f453e01f78a42607, limb2: 0x43c348b885c84ff731c4d59c, limb3: 0x1962d75c2381201e1a0cbd6c, }, u384 { limb0: 0x36f96f891e2538b53dbf67f2, limb1: 0xc35a5dd279cd2eca6757cd6, limb2: 0x6e8eb15778c4855551ae7f31, limb3: 0x58df3306640da276faaae7d, }, u384 { limb0: 0xc28297ada8d26d98445f5416, limb1: 0x123da489e726af41727364f2, limb2: 0x89edb4d1d115c5dbddbcd30e, limb3: 0x16b7d288798e5395f20d23bf, }, u384 { limb0: 0xfd2ededda39142311a5001d, limb1: 0x542eda0fc9dec916a20b15dc, limb2: 0xf8228ddcc6d19c9f0f69bbb0, limb3: 0xbe0e079545f43e4b00cc912, }, u384 { limb0: 0xdfa9cce202c6477faaf9b7ac, limb1: 0xc5ecd87b6f0f5a6449f38db9, limb2: 0xac783182b70152c65550d881, limb3: 0x8d9e5297186db2d9fb266ea, }, u384 { limb0: 0xa58b1fb93d1a1399126a775c, limb1: 0x5dd365bc400a0051d5fa9c01, limb2: 0xace9824b5eecfdfa8d0cf8ef, limb3: 0x166007c08a99db2fc3ba8734, }, u384 { limb0: 0x801dee460ee415a15812ed9, limb1: 0xfeb34fd206357132b920f5b0, limb2: 0xbba6ff6ee5a4375efa1f4fd7, limb3: 0x16a3ef08be3ea7ea03bcddfa, }, u384 { limb0: 0xbb9248836b233d9d55535d4a, limb1: 0xabc5750c4bf39b4852cfe2f7, limb2: 0xd1d74cc4f9fb0ce4c6af5920, limb3: 0x1866c8ed336c61231a1be54f, }, u384 { limb0: 0xd529b35e346ef48bb8913f55, limb1: 0x5308592e7ea7d4fbc7385ea3, limb2: 0xd94a84903216f763e13d87bb, limb3: 0x167a55cda70a6e1cea820597, }, u384 { limb0: 0x4f83060400f8b49cba8f6aa8, limb1: 0xe591b36e636a5c871a5c29f, limb2: 0x1ad2911d9c6dd039bb61a629, limb3: 0x4d2f259eea405bd48f010a0, }, u384 { limb0: 0x6f7ebbea9684b529e2561092, limb1: 0x8c0f9a88cea7913516f96898, limb2: 0x48c50c477f94ff8aefce42d2, limb3: 0xaccbb67481d033ff5852c1e, }, u384 { limb0: 0xe3b90ac11e99b138573345cc, limb1: 0x7d5ceef9a00d9b8693000763, limb2: 0xb45f1496543346d98adf0226, limb3: 0xad6b9514c767fe3c3613144, }, u384 { limb0: 0x8714cc80d1fadc1326ed06f7, limb1: 0xcb748df27942480e420517bd, limb2: 0x53cd76f2bf565b94e72927c1, limb3: 0x2660400eb2e4f3b628bdd0d, }, u384 { limb0: 0xf13497804415473a1d634b8f, limb1: 0x324efcd6356caa205ca2f570, limb2: 0xd7819c171c40f65e273b853, limb3: 0xe0fa1d816ddc03e6b24255e, }, ]; ================================================ FILE: src/src/circuits/multi_pairing_check.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{ BLSProcessedPair, BNProcessedPair, E12D, G1Point, G2Line, G2Point, MillerLoopResultScalingFactor, u288, }; #[inline(always)] pub fn run_BLS12_381_INITIALIZE_MPCHECK_EXT_MLR_circuit( lambda_root_inverse: E12D, z: u384, scaling_factor: MillerLoopResultScalingFactor, precomputed_miller_loop_result: E12D, ) -> (u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x2 let in2 = CE::< CI<2>, > {}; // 0x18089593cbf626353947d5b1fd0c6d66bb34bc7585f5abdf8f17b50e12c47d65ce514a7c167b027b600febdb244714c5 let in3 = CE::< CI<3>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff let in4 = CE::< CI<4>, > {}; // 0xd5e1c086ffe8016d063c6dad7a2fffc9072bb5785a686bcefeedc2e0124838bdccf325ee5d80be9902109f7dbc79812 let in5 = CE::< CI<5>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad let in6 = CE::< CI<6>, > {}; // 0x1a0111ea397fe6998ce8d956845e1033efa3bf761f6622e9abc9802928bfc912627c4fd7ed3ffffb5dfb00000001aaaf let in7 = CE::< CI<7>, > {}; // 0xb659fb20274bfb1be8ff4d69163c08be7302c4818171fdd17d5be9b1d380acd8c747cdc4aff0e653631f5d3000f022c let in8 = CE::> {}; // -0x1 % p let in9 = CE::< CI<9>, > {}; // 0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3 let in10 = CE::< CI<10>, > {}; // 0x1f87c566d89c06511d3d204463f3f70a9428f0f6d8f66dfd8191d92e3ec78be505ab5829ad8fd8459ef1424dbb895e6 let in11 = CE::< CI<11>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac let in12 = CE::< CI<12>, > {}; // 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09 let in13 = CE::< CI<13>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe let in14 = CE::< CI<14>, > {}; // 0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995 let in15 = CE::< CI<15>, > {}; // 0xe9b7238370b26e88c8bb2dfb1e7ec4b7d471f3cdb6df2e24f5b1405d978eb56923783226654f19a83cd0a2cfff0a87f // INPUT stack let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let (in37, in38, in39) = (CE::> {}, CE::> {}, CE::> {}); let (in40, in41, in42) = (CE::> {}, CE::> {}, CE::> {}); let (in43, in44, in45) = (CE::> {}, CE::> {}, CE::> {}); let in46 = CE::> {}; let t0 = circuit_mul(in28, in28); // Compute z^2 let t1 = circuit_mul(t0, in28); // Compute z^3 let t2 = circuit_mul(t1, in28); // Compute z^4 let t3 = circuit_mul(t2, in28); // Compute z^5 let t4 = circuit_mul(t3, in28); // Compute z^6 let t5 = circuit_mul(t4, in28); // Compute z^7 let t6 = circuit_mul(t5, in28); // Compute z^8 let t7 = circuit_mul(t6, in28); // Compute z^9 let t8 = circuit_mul(t7, in28); // Compute z^10 let t9 = circuit_mul(t8, in28); // Compute z^11 let t10 = circuit_sub(in0, in17); let t11 = circuit_sub(in0, in19); let t12 = circuit_sub(in0, in21); let t13 = circuit_sub(in0, in23); let t14 = circuit_sub(in0, in25); let t15 = circuit_sub(in0, in27); let t16 = circuit_mul(t10, in28); // Eval C_inv step coeff_1 * z^1 let t17 = circuit_add(in16, t16); // Eval C_inv step + (coeff_1 * z^1) let t18 = circuit_mul(in18, t0); // Eval C_inv step coeff_2 * z^2 let t19 = circuit_add(t17, t18); // Eval C_inv step + (coeff_2 * z^2) let t20 = circuit_mul(t11, t1); // Eval C_inv step coeff_3 * z^3 let t21 = circuit_add(t19, t20); // Eval C_inv step + (coeff_3 * z^3) let t22 = circuit_mul(in20, t2); // Eval C_inv step coeff_4 * z^4 let t23 = circuit_add(t21, t22); // Eval C_inv step + (coeff_4 * z^4) let t24 = circuit_mul(t12, t3); // Eval C_inv step coeff_5 * z^5 let t25 = circuit_add(t23, t24); // Eval C_inv step + (coeff_5 * z^5) let t26 = circuit_mul(in22, t4); // Eval C_inv step coeff_6 * z^6 let t27 = circuit_add(t25, t26); // Eval C_inv step + (coeff_6 * z^6) let t28 = circuit_mul(t13, t5); // Eval C_inv step coeff_7 * z^7 let t29 = circuit_add(t27, t28); // Eval C_inv step + (coeff_7 * z^7) let t30 = circuit_mul(in24, t6); // Eval C_inv step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval C_inv step + (coeff_8 * z^8) let t32 = circuit_mul(t14, t7); // Eval C_inv step coeff_9 * z^9 let t33 = circuit_add(t31, t32); // Eval C_inv step + (coeff_9 * z^9) let t34 = circuit_mul(in26, t8); // Eval C_inv step coeff_10 * z^10 let t35 = circuit_add(t33, t34); // Eval C_inv step + (coeff_10 * z^10) let t36 = circuit_mul(t15, t9); // Eval C_inv step coeff_11 * z^11 let t37 = circuit_add(t35, t36); // Eval C_inv step + (coeff_11 * z^11) let t38 = circuit_mul(in30, t0); // Eval sparse poly W step coeff_2 * z^2 let t39 = circuit_add(in29, t38); // Eval sparse poly W step + coeff_2 * z^2 let t40 = circuit_mul(in31, t2); // Eval sparse poly W step coeff_4 * z^4 let t41 = circuit_add(t39, t40); // Eval sparse poly W step + coeff_4 * z^4 let t42 = circuit_mul(in32, t4); // Eval sparse poly W step coeff_6 * z^6 let t43 = circuit_add(t41, t42); // Eval sparse poly W step + coeff_6 * z^6 let t44 = circuit_mul(in33, t6); // Eval sparse poly W step coeff_8 * z^8 let t45 = circuit_add(t43, t44); // Eval sparse poly W step + coeff_8 * z^8 let t46 = circuit_mul(in34, t8); // Eval sparse poly W step coeff_10 * z^10 let t47 = circuit_add(t45, t46); // Eval sparse poly W step + coeff_10 * z^10 let t48 = circuit_mul(in22, in1); let t49 = circuit_add(in16, t48); let t50 = circuit_mul(t10, in2); let t51 = circuit_mul(t13, in2); let t52 = circuit_add(t50, t51); let t53 = circuit_mul(in18, in3); let t54 = circuit_mul(t14, in4); let t55 = circuit_mul(in20, in5); let t56 = circuit_mul(in26, in6); let t57 = circuit_add(t55, t56); let t58 = circuit_mul(t12, in7); let t59 = circuit_mul(t15, in7); let t60 = circuit_add(t58, t59); let t61 = circuit_mul(in22, in8); let t62 = circuit_mul(t10, in9); let t63 = circuit_mul(t13, in10); let t64 = circuit_add(t62, t63); let t65 = circuit_mul(in18, in11); let t66 = circuit_mul(in24, in11); let t67 = circuit_add(t65, t66); let t68 = circuit_mul(t11, in12); let t69 = circuit_mul(in26, in13); let t70 = circuit_mul(t12, in14); let t71 = circuit_mul(t15, in15); let t72 = circuit_add(t70, t71); let t73 = circuit_sub(in0, t52); let t74 = circuit_sub(in0, t54); let t75 = circuit_sub(in0, t60); let t76 = circuit_sub(in0, t64); let t77 = circuit_sub(in0, t68); let t78 = circuit_sub(in0, t72); let t79 = circuit_mul(t73, in28); // Eval C_inv_frob_1 step coeff_1 * z^1 let t80 = circuit_add(t49, t79); // Eval C_inv_frob_1 step + (coeff_1 * z^1) let t81 = circuit_mul(t53, t0); // Eval C_inv_frob_1 step coeff_2 * z^2 let t82 = circuit_add(t80, t81); // Eval C_inv_frob_1 step + (coeff_2 * z^2) let t83 = circuit_mul(t74, t1); // Eval C_inv_frob_1 step coeff_3 * z^3 let t84 = circuit_add(t82, t83); // Eval C_inv_frob_1 step + (coeff_3 * z^3) let t85 = circuit_mul(t57, t2); // Eval C_inv_frob_1 step coeff_4 * z^4 let t86 = circuit_add(t84, t85); // Eval C_inv_frob_1 step + (coeff_4 * z^4) let t87 = circuit_mul(t75, t3); // Eval C_inv_frob_1 step coeff_5 * z^5 let t88 = circuit_add(t86, t87); // Eval C_inv_frob_1 step + (coeff_5 * z^5) let t89 = circuit_mul(t61, t4); // Eval C_inv_frob_1 step coeff_6 * z^6 let t90 = circuit_add(t88, t89); // Eval C_inv_frob_1 step + (coeff_6 * z^6) let t91 = circuit_mul(t76, t5); // Eval C_inv_frob_1 step coeff_7 * z^7 let t92 = circuit_add(t90, t91); // Eval C_inv_frob_1 step + (coeff_7 * z^7) let t93 = circuit_mul(t67, t6); // Eval C_inv_frob_1 step coeff_8 * z^8 let t94 = circuit_add(t92, t93); // Eval C_inv_frob_1 step + (coeff_8 * z^8) let t95 = circuit_mul(t77, t7); // Eval C_inv_frob_1 step coeff_9 * z^9 let t96 = circuit_add(t94, t95); // Eval C_inv_frob_1 step + (coeff_9 * z^9) let t97 = circuit_mul(t69, t8); // Eval C_inv_frob_1 step coeff_10 * z^10 let t98 = circuit_add(t96, t97); // Eval C_inv_frob_1 step + (coeff_10 * z^10) let t99 = circuit_mul(t78, t9); // Eval C_inv_frob_1 step coeff_11 * z^11 let t100 = circuit_add(t98, t99); // Eval C_inv_frob_1 step + (coeff_11 * z^11) let t101 = circuit_mul(in36, in28); // Eval precomputed_miller_loop_result step coeff_1 * z^1 let t102 = circuit_add( in35, t101, ); // Eval precomputed_miller_loop_result step + (coeff_1 * z^1) let t103 = circuit_mul(in37, t0); // Eval precomputed_miller_loop_result step coeff_2 * z^2 let t104 = circuit_add( t102, t103, ); // Eval precomputed_miller_loop_result step + (coeff_2 * z^2) let t105 = circuit_mul(in38, t1); // Eval precomputed_miller_loop_result step coeff_3 * z^3 let t106 = circuit_add( t104, t105, ); // Eval precomputed_miller_loop_result step + (coeff_3 * z^3) let t107 = circuit_mul(in39, t2); // Eval precomputed_miller_loop_result step coeff_4 * z^4 let t108 = circuit_add( t106, t107, ); // Eval precomputed_miller_loop_result step + (coeff_4 * z^4) let t109 = circuit_mul(in40, t3); // Eval precomputed_miller_loop_result step coeff_5 * z^5 let t110 = circuit_add( t108, t109, ); // Eval precomputed_miller_loop_result step + (coeff_5 * z^5) let t111 = circuit_mul(in41, t4); // Eval precomputed_miller_loop_result step coeff_6 * z^6 let t112 = circuit_add( t110, t111, ); // Eval precomputed_miller_loop_result step + (coeff_6 * z^6) let t113 = circuit_mul(in42, t5); // Eval precomputed_miller_loop_result step coeff_7 * z^7 let t114 = circuit_add( t112, t113, ); // Eval precomputed_miller_loop_result step + (coeff_7 * z^7) let t115 = circuit_mul(in43, t6); // Eval precomputed_miller_loop_result step coeff_8 * z^8 let t116 = circuit_add( t114, t115, ); // Eval precomputed_miller_loop_result step + (coeff_8 * z^8) let t117 = circuit_mul(in44, t7); // Eval precomputed_miller_loop_result step coeff_9 * z^9 let t118 = circuit_add( t116, t117, ); // Eval precomputed_miller_loop_result step + (coeff_9 * z^9) let t119 = circuit_mul(in45, t8); // Eval precomputed_miller_loop_result step coeff_10 * z^10 let t120 = circuit_add( t118, t119, ); // Eval precomputed_miller_loop_result step + (coeff_10 * z^10) let t121 = circuit_mul(in46, t9); // Eval precomputed_miller_loop_result step coeff_11 * z^11 let t122 = circuit_add( t120, t121, ); // Eval precomputed_miller_loop_result step + (coeff_11 * z^11) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t37, t47, t100, t122).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(INITIALIZE_MPCHECK_EXT_MLR_BLS12_381_CONSTANTS.span()); // in0 - in15 // Fill inputs: circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w0); // in16 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w1); // in17 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w2); // in18 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w3); // in19 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w4); // in20 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w5); // in21 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w6); // in22 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w7); // in23 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w8); // in24 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w9); // in25 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w10); // in26 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w11); // in27 circuit_inputs = circuit_inputs.next_2(z); // in28 circuit_inputs = circuit_inputs.next_2(scaling_factor.w0); // in29 circuit_inputs = circuit_inputs.next_2(scaling_factor.w2); // in30 circuit_inputs = circuit_inputs.next_2(scaling_factor.w4); // in31 circuit_inputs = circuit_inputs.next_2(scaling_factor.w6); // in32 circuit_inputs = circuit_inputs.next_2(scaling_factor.w8); // in33 circuit_inputs = circuit_inputs.next_2(scaling_factor.w10); // in34 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w0); // in35 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w1); // in36 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w2); // in37 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w3); // in38 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w4); // in39 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w5); // in40 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w6); // in41 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w7); // in42 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w8); // in43 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w9); // in44 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w10); // in45 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w11); // in46 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let c_inv_of_z: u384 = outputs.get_output(t37); let scaling_factor_of_z: u384 = outputs.get_output(t47); let c_inv_frob_1_conjugate_of_z: u384 = outputs.get_output(t100); let precomputed_miller_loop_result_of_z: u384 = outputs.get_output(t122); return ( c_inv_of_z, scaling_factor_of_z, c_inv_frob_1_conjugate_of_z, precomputed_miller_loop_result_of_z, ); } const INITIALIZE_MPCHECK_EXT_MLR_BLS12_381_CONSTANTS: [u384; 16] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x167b027b600febdb244714c5, limb1: 0x8f17b50e12c47d65ce514a7c, limb2: 0xfd0c6d66bb34bc7585f5abdf, limb3: 0x18089593cbf626353947d5b1, }, u384 { limb0: 0x620a00022e01fffffffeffff, limb1: 0xddb3a93be6f89688de17d813, limb2: 0xdf76ce51ba69c6076a0f77ea, limb3: 0x5f19672f, }, u384 { limb0: 0xe5d80be9902109f7dbc79812, limb1: 0xefeedc2e0124838bdccf325e, limb2: 0xd7a2fffc9072bb5785a686bc, limb3: 0xd5e1c086ffe8016d063c6da, }, u384 { limb0: 0x4f49fffd8bfd00000000aaad, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0xed3ffffb5dfb00000001aaaf, limb1: 0xabc9802928bfc912627c4fd7, limb2: 0x845e1033efa3bf761f6622e9, limb3: 0x1a0111ea397fe6998ce8d956, }, u384 { limb0: 0x4aff0e653631f5d3000f022c, limb1: 0x17d5be9b1d380acd8c747cdc, limb2: 0x9163c08be7302c4818171fdd, limb3: 0xb659fb20274bfb1be8ff4d6, }, u384 { limb0: 0xb153ffffb9feffffffffaaaa, limb1: 0x6730d2a0f6b0f6241eabfffe, limb2: 0x434bacd764774b84f38512bf, limb3: 0x1a0111ea397fe69a4b1ba7b6, }, u384 { limb0: 0x4d6c7ec22cf78a126ddc4af3, limb1: 0xec0c8ec971f63c5f282d5ac1, limb2: 0x231f9fb854a14787b6c7b36f, limb3: 0xfc3e2b36c4e03288e9e902, }, u384 { limb0: 0x9ad8fd8459ef1424dbb895e6, limb1: 0xd8191d92e3ec78be505ab582, limb2: 0x463f3f70a9428f0f6d8f66df, limb3: 0x1f87c566d89c06511d3d204, }, u384 { limb0: 0x4f49fffd8bfd00000000aaac, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0x72ec05f4c81084fbede3cc09, limb1: 0x77f76e17009241c5ee67992f, limb2: 0x6bd17ffe48395dabc2d3435e, limb3: 0x6af0e0437ff400b6831e36d, }, u384 { limb0: 0x620a00022e01fffffffefffe, limb1: 0xddb3a93be6f89688de17d813, limb2: 0xdf76ce51ba69c6076a0f77ea, limb3: 0x5f19672f, }, u384 { limb0: 0x8bd478cd1ee605167ff82995, limb1: 0xdb45f3536814f0bd5871c190, limb2: 0xfa99cc9170df3560e77982d0, limb3: 0x144e4211384586c16bd3ad4a, }, u384 { limb0: 0x6654f19a83cd0a2cfff0a87f, limb1: 0x4f5b1405d978eb5692378322, limb2: 0xb1e7ec4b7d471f3cdb6df2e2, limb3: 0xe9b7238370b26e88c8bb2df, }, ]; #[inline(always)] pub fn run_BLS12_381_INITIALIZE_MPCHECK_circuit( lambda_root_inverse: E12D, z: u384, scaling_factor: MillerLoopResultScalingFactor, ) -> (u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x2 let in2 = CE::< CI<2>, > {}; // 0x18089593cbf626353947d5b1fd0c6d66bb34bc7585f5abdf8f17b50e12c47d65ce514a7c167b027b600febdb244714c5 let in3 = CE::< CI<3>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff let in4 = CE::< CI<4>, > {}; // 0xd5e1c086ffe8016d063c6dad7a2fffc9072bb5785a686bcefeedc2e0124838bdccf325ee5d80be9902109f7dbc79812 let in5 = CE::< CI<5>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad let in6 = CE::< CI<6>, > {}; // 0x1a0111ea397fe6998ce8d956845e1033efa3bf761f6622e9abc9802928bfc912627c4fd7ed3ffffb5dfb00000001aaaf let in7 = CE::< CI<7>, > {}; // 0xb659fb20274bfb1be8ff4d69163c08be7302c4818171fdd17d5be9b1d380acd8c747cdc4aff0e653631f5d3000f022c let in8 = CE::> {}; // -0x1 % p let in9 = CE::< CI<9>, > {}; // 0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3 let in10 = CE::< CI<10>, > {}; // 0x1f87c566d89c06511d3d204463f3f70a9428f0f6d8f66dfd8191d92e3ec78be505ab5829ad8fd8459ef1424dbb895e6 let in11 = CE::< CI<11>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac let in12 = CE::< CI<12>, > {}; // 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09 let in13 = CE::< CI<13>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe let in14 = CE::< CI<14>, > {}; // 0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995 let in15 = CE::< CI<15>, > {}; // 0xe9b7238370b26e88c8bb2dfb1e7ec4b7d471f3cdb6df2e24f5b1405d978eb56923783226654f19a83cd0a2cfff0a87f // INPUT stack let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let in34 = CE::> {}; let t0 = circuit_mul(in28, in28); // Compute z^2 let t1 = circuit_mul(t0, in28); // Compute z^3 let t2 = circuit_mul(t1, in28); // Compute z^4 let t3 = circuit_mul(t2, in28); // Compute z^5 let t4 = circuit_mul(t3, in28); // Compute z^6 let t5 = circuit_mul(t4, in28); // Compute z^7 let t6 = circuit_mul(t5, in28); // Compute z^8 let t7 = circuit_mul(t6, in28); // Compute z^9 let t8 = circuit_mul(t7, in28); // Compute z^10 let t9 = circuit_mul(t8, in28); // Compute z^11 let t10 = circuit_sub(in0, in17); let t11 = circuit_sub(in0, in19); let t12 = circuit_sub(in0, in21); let t13 = circuit_sub(in0, in23); let t14 = circuit_sub(in0, in25); let t15 = circuit_sub(in0, in27); let t16 = circuit_mul(t10, in28); // Eval C_inv step coeff_1 * z^1 let t17 = circuit_add(in16, t16); // Eval C_inv step + (coeff_1 * z^1) let t18 = circuit_mul(in18, t0); // Eval C_inv step coeff_2 * z^2 let t19 = circuit_add(t17, t18); // Eval C_inv step + (coeff_2 * z^2) let t20 = circuit_mul(t11, t1); // Eval C_inv step coeff_3 * z^3 let t21 = circuit_add(t19, t20); // Eval C_inv step + (coeff_3 * z^3) let t22 = circuit_mul(in20, t2); // Eval C_inv step coeff_4 * z^4 let t23 = circuit_add(t21, t22); // Eval C_inv step + (coeff_4 * z^4) let t24 = circuit_mul(t12, t3); // Eval C_inv step coeff_5 * z^5 let t25 = circuit_add(t23, t24); // Eval C_inv step + (coeff_5 * z^5) let t26 = circuit_mul(in22, t4); // Eval C_inv step coeff_6 * z^6 let t27 = circuit_add(t25, t26); // Eval C_inv step + (coeff_6 * z^6) let t28 = circuit_mul(t13, t5); // Eval C_inv step coeff_7 * z^7 let t29 = circuit_add(t27, t28); // Eval C_inv step + (coeff_7 * z^7) let t30 = circuit_mul(in24, t6); // Eval C_inv step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval C_inv step + (coeff_8 * z^8) let t32 = circuit_mul(t14, t7); // Eval C_inv step coeff_9 * z^9 let t33 = circuit_add(t31, t32); // Eval C_inv step + (coeff_9 * z^9) let t34 = circuit_mul(in26, t8); // Eval C_inv step coeff_10 * z^10 let t35 = circuit_add(t33, t34); // Eval C_inv step + (coeff_10 * z^10) let t36 = circuit_mul(t15, t9); // Eval C_inv step coeff_11 * z^11 let t37 = circuit_add(t35, t36); // Eval C_inv step + (coeff_11 * z^11) let t38 = circuit_mul(in30, t0); // Eval sparse poly W step coeff_2 * z^2 let t39 = circuit_add(in29, t38); // Eval sparse poly W step + coeff_2 * z^2 let t40 = circuit_mul(in31, t2); // Eval sparse poly W step coeff_4 * z^4 let t41 = circuit_add(t39, t40); // Eval sparse poly W step + coeff_4 * z^4 let t42 = circuit_mul(in32, t4); // Eval sparse poly W step coeff_6 * z^6 let t43 = circuit_add(t41, t42); // Eval sparse poly W step + coeff_6 * z^6 let t44 = circuit_mul(in33, t6); // Eval sparse poly W step coeff_8 * z^8 let t45 = circuit_add(t43, t44); // Eval sparse poly W step + coeff_8 * z^8 let t46 = circuit_mul(in34, t8); // Eval sparse poly W step coeff_10 * z^10 let t47 = circuit_add(t45, t46); // Eval sparse poly W step + coeff_10 * z^10 let t48 = circuit_mul(in22, in1); let t49 = circuit_add(in16, t48); let t50 = circuit_mul(t10, in2); let t51 = circuit_mul(t13, in2); let t52 = circuit_add(t50, t51); let t53 = circuit_mul(in18, in3); let t54 = circuit_mul(t14, in4); let t55 = circuit_mul(in20, in5); let t56 = circuit_mul(in26, in6); let t57 = circuit_add(t55, t56); let t58 = circuit_mul(t12, in7); let t59 = circuit_mul(t15, in7); let t60 = circuit_add(t58, t59); let t61 = circuit_mul(in22, in8); let t62 = circuit_mul(t10, in9); let t63 = circuit_mul(t13, in10); let t64 = circuit_add(t62, t63); let t65 = circuit_mul(in18, in11); let t66 = circuit_mul(in24, in11); let t67 = circuit_add(t65, t66); let t68 = circuit_mul(t11, in12); let t69 = circuit_mul(in26, in13); let t70 = circuit_mul(t12, in14); let t71 = circuit_mul(t15, in15); let t72 = circuit_add(t70, t71); let t73 = circuit_sub(in0, t52); let t74 = circuit_sub(in0, t54); let t75 = circuit_sub(in0, t60); let t76 = circuit_sub(in0, t64); let t77 = circuit_sub(in0, t68); let t78 = circuit_sub(in0, t72); let t79 = circuit_mul(t73, in28); // Eval C_inv_frob_1 step coeff_1 * z^1 let t80 = circuit_add(t49, t79); // Eval C_inv_frob_1 step + (coeff_1 * z^1) let t81 = circuit_mul(t53, t0); // Eval C_inv_frob_1 step coeff_2 * z^2 let t82 = circuit_add(t80, t81); // Eval C_inv_frob_1 step + (coeff_2 * z^2) let t83 = circuit_mul(t74, t1); // Eval C_inv_frob_1 step coeff_3 * z^3 let t84 = circuit_add(t82, t83); // Eval C_inv_frob_1 step + (coeff_3 * z^3) let t85 = circuit_mul(t57, t2); // Eval C_inv_frob_1 step coeff_4 * z^4 let t86 = circuit_add(t84, t85); // Eval C_inv_frob_1 step + (coeff_4 * z^4) let t87 = circuit_mul(t75, t3); // Eval C_inv_frob_1 step coeff_5 * z^5 let t88 = circuit_add(t86, t87); // Eval C_inv_frob_1 step + (coeff_5 * z^5) let t89 = circuit_mul(t61, t4); // Eval C_inv_frob_1 step coeff_6 * z^6 let t90 = circuit_add(t88, t89); // Eval C_inv_frob_1 step + (coeff_6 * z^6) let t91 = circuit_mul(t76, t5); // Eval C_inv_frob_1 step coeff_7 * z^7 let t92 = circuit_add(t90, t91); // Eval C_inv_frob_1 step + (coeff_7 * z^7) let t93 = circuit_mul(t67, t6); // Eval C_inv_frob_1 step coeff_8 * z^8 let t94 = circuit_add(t92, t93); // Eval C_inv_frob_1 step + (coeff_8 * z^8) let t95 = circuit_mul(t77, t7); // Eval C_inv_frob_1 step coeff_9 * z^9 let t96 = circuit_add(t94, t95); // Eval C_inv_frob_1 step + (coeff_9 * z^9) let t97 = circuit_mul(t69, t8); // Eval C_inv_frob_1 step coeff_10 * z^10 let t98 = circuit_add(t96, t97); // Eval C_inv_frob_1 step + (coeff_10 * z^10) let t99 = circuit_mul(t78, t9); // Eval C_inv_frob_1 step coeff_11 * z^11 let t100 = circuit_add(t98, t99); // Eval C_inv_frob_1 step + (coeff_11 * z^11) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t37, t47, t100).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(INITIALIZE_MPCHECK_BLS12_381_CONSTANTS.span()); // in0 - in15 // Fill inputs: circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w0); // in16 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w1); // in17 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w2); // in18 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w3); // in19 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w4); // in20 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w5); // in21 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w6); // in22 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w7); // in23 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w8); // in24 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w9); // in25 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w10); // in26 circuit_inputs = circuit_inputs.next_2(lambda_root_inverse.w11); // in27 circuit_inputs = circuit_inputs.next_2(z); // in28 circuit_inputs = circuit_inputs.next_2(scaling_factor.w0); // in29 circuit_inputs = circuit_inputs.next_2(scaling_factor.w2); // in30 circuit_inputs = circuit_inputs.next_2(scaling_factor.w4); // in31 circuit_inputs = circuit_inputs.next_2(scaling_factor.w6); // in32 circuit_inputs = circuit_inputs.next_2(scaling_factor.w8); // in33 circuit_inputs = circuit_inputs.next_2(scaling_factor.w10); // in34 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let c_inv_of_z: u384 = outputs.get_output(t37); let scaling_factor_of_z: u384 = outputs.get_output(t47); let c_inv_frob_1_conjugate_of_z: u384 = outputs.get_output(t100); return (c_inv_of_z, scaling_factor_of_z, c_inv_frob_1_conjugate_of_z); } const INITIALIZE_MPCHECK_BLS12_381_CONSTANTS: [u384; 16] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x167b027b600febdb244714c5, limb1: 0x8f17b50e12c47d65ce514a7c, limb2: 0xfd0c6d66bb34bc7585f5abdf, limb3: 0x18089593cbf626353947d5b1, }, u384 { limb0: 0x620a00022e01fffffffeffff, limb1: 0xddb3a93be6f89688de17d813, limb2: 0xdf76ce51ba69c6076a0f77ea, limb3: 0x5f19672f, }, u384 { limb0: 0xe5d80be9902109f7dbc79812, limb1: 0xefeedc2e0124838bdccf325e, limb2: 0xd7a2fffc9072bb5785a686bc, limb3: 0xd5e1c086ffe8016d063c6da, }, u384 { limb0: 0x4f49fffd8bfd00000000aaad, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0xed3ffffb5dfb00000001aaaf, limb1: 0xabc9802928bfc912627c4fd7, limb2: 0x845e1033efa3bf761f6622e9, limb3: 0x1a0111ea397fe6998ce8d956, }, u384 { limb0: 0x4aff0e653631f5d3000f022c, limb1: 0x17d5be9b1d380acd8c747cdc, limb2: 0x9163c08be7302c4818171fdd, limb3: 0xb659fb20274bfb1be8ff4d6, }, u384 { limb0: 0xb153ffffb9feffffffffaaaa, limb1: 0x6730d2a0f6b0f6241eabfffe, limb2: 0x434bacd764774b84f38512bf, limb3: 0x1a0111ea397fe69a4b1ba7b6, }, u384 { limb0: 0x4d6c7ec22cf78a126ddc4af3, limb1: 0xec0c8ec971f63c5f282d5ac1, limb2: 0x231f9fb854a14787b6c7b36f, limb3: 0xfc3e2b36c4e03288e9e902, }, u384 { limb0: 0x9ad8fd8459ef1424dbb895e6, limb1: 0xd8191d92e3ec78be505ab582, limb2: 0x463f3f70a9428f0f6d8f66df, limb3: 0x1f87c566d89c06511d3d204, }, u384 { limb0: 0x4f49fffd8bfd00000000aaac, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0x72ec05f4c81084fbede3cc09, limb1: 0x77f76e17009241c5ee67992f, limb2: 0x6bd17ffe48395dabc2d3435e, limb3: 0x6af0e0437ff400b6831e36d, }, u384 { limb0: 0x620a00022e01fffffffefffe, limb1: 0xddb3a93be6f89688de17d813, limb2: 0xdf76ce51ba69c6076a0f77ea, limb3: 0x5f19672f, }, u384 { limb0: 0x8bd478cd1ee605167ff82995, limb1: 0xdb45f3536814f0bd5871c190, limb2: 0xfa99cc9170df3560e77982d0, limb3: 0x144e4211384586c16bd3ad4a, }, u384 { limb0: 0x6654f19a83cd0a2cfff0a87f, limb1: 0x4f5b1405d978eb5692378322, limb2: 0xb1e7ec4b7d471f3cdb6df2e2, limb3: 0xe9b7238370b26e88c8bb2df, }, ]; #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT00_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_2nd_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_2nd_0_1: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let in24 = CE::> {}; let t0 = circuit_mul(in23, in23); // compute z^2 let t1 = circuit_mul(t0, in23); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in21, in21); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in4, in5); let t6 = circuit_mul(t5, in0); // eval bls line by yInv let t7 = circuit_sub(in2, in3); let t8 = circuit_mul(t7, in1); // eval blsline by xNegOverY let t9 = circuit_mul(in5, in0); // eval bls line by yInv let t10 = circuit_mul(in3, in1); // eval bls line by xNegOverY let t11 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t12 = circuit_add(t6, t11); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t13 = circuit_add(t12, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t14 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t15 = circuit_add(t13, t14); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t16 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t18 = circuit_mul(t4, t17); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t19 = circuit_sub(in8, in9); let t20 = circuit_mul(t19, in10); // eval bls line by yInv let t21 = circuit_sub(in6, in7); let t22 = circuit_mul(t21, in11); // eval blsline by xNegOverY let t23 = circuit_mul(in9, in10); // eval bls line by yInv let t24 = circuit_mul(in7, in11); // eval bls line by xNegOverY let t25 = circuit_mul(t22, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t26 = circuit_add(t20, t25); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t28 = circuit_mul(t23, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t30 = circuit_mul(t24, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t32 = circuit_mul(t18, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t33 = circuit_mul( t32, t32, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t34 = circuit_sub(in14, in15); let t35 = circuit_mul(t34, in0); // eval bls line by yInv let t36 = circuit_sub(in12, in13); let t37 = circuit_mul(t36, in1); // eval blsline by xNegOverY let t38 = circuit_mul(in15, in0); // eval bls line by yInv let t39 = circuit_mul(in13, in1); // eval bls line by xNegOverY let t40 = circuit_mul(t37, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t41 = circuit_add(t35, t40); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t42 = circuit_add(t41, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t43 = circuit_mul(t38, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t44 = circuit_add(t42, t43); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t45 = circuit_mul(t39, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t46 = circuit_add(t44, t45); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t47 = circuit_mul(t33, t46); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t48 = circuit_sub(in18, in19); let t49 = circuit_mul(t48, in10); // eval bls line by yInv let t50 = circuit_sub(in16, in17); let t51 = circuit_mul(t50, in11); // eval blsline by xNegOverY let t52 = circuit_mul(in19, in10); // eval bls line by yInv let t53 = circuit_mul(in17, in11); // eval bls line by xNegOverY let t54 = circuit_mul(t51, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t55 = circuit_add(t49, t54); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t56 = circuit_add(t55, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t57 = circuit_mul(t52, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t58 = circuit_add(t56, t57); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t59 = circuit_mul(t53, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t60 = circuit_add(t58, t59); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t61 = circuit_mul(t47, t60); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t62 = circuit_sub(t61, in22); // (Π(i,k) (Pk(z))) - Ri(z) let t63 = circuit_mul(in24, in20); let t64 = circuit_add(t63, t62); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t64,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in0 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in1 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in2 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a1); // in9 circuit_inputs = circuit_inputs.next_2(yInv_1); // in10 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a0); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a1); // in19 circuit_inputs = circuit_inputs.next_2(lhs_i); // in20 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in21 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in22 circuit_inputs = circuit_inputs.next_2(z); // in23 circuit_inputs = circuit_inputs.next_2(c1); // in24 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t64); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT00_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_2nd_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_2nd_0_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x3 let in1 = CE::> {}; // 0x6 let in2 = CE::> {}; // 0x0 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let in33 = CE::> {}; let t0 = circuit_mul(in32, in32); // compute z^2 let t1 = circuit_mul(t0, in32); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in30, in30); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in7, in8); let t6 = circuit_mul(t5, in3); // eval bls line by yInv let t7 = circuit_sub(in5, in6); let t8 = circuit_mul(t7, in4); // eval blsline by xNegOverY let t9 = circuit_mul(in8, in3); // eval bls line by yInv let t10 = circuit_mul(in6, in4); // eval bls line by xNegOverY let t11 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t12 = circuit_add(t6, t11); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t13 = circuit_add(t12, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t14 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t15 = circuit_add(t13, t14); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t16 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t18 = circuit_mul(t4, t17); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t19 = circuit_sub(in11, in12); let t20 = circuit_mul(t19, in13); // eval bls line by yInv let t21 = circuit_sub(in9, in10); let t22 = circuit_mul(t21, in14); // eval blsline by xNegOverY let t23 = circuit_mul(in12, in13); // eval bls line by yInv let t24 = circuit_mul(in10, in14); // eval bls line by xNegOverY let t25 = circuit_mul(t22, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t26 = circuit_add(t20, t25); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t28 = circuit_mul(t23, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t30 = circuit_mul(t24, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t32 = circuit_mul(t18, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t33 = circuit_add(in25, in26); // Doubling slope numerator start let t34 = circuit_sub(in25, in26); let t35 = circuit_mul(t33, t34); let t36 = circuit_mul(in25, in26); let t37 = circuit_mul(t35, in0); let t38 = circuit_mul(t36, in1); // Doubling slope numerator end let t39 = circuit_add(in27, in27); // Fp2 add coeff 0/1 let t40 = circuit_add(in28, in28); // Fp2 add coeff 1/1 let t41 = circuit_mul(t39, t39); // Fp2 Inv start let t42 = circuit_mul(t40, t40); let t43 = circuit_add(t41, t42); let t44 = circuit_inverse(t43); let t45 = circuit_mul(t39, t44); // Fp2 Inv real part end let t46 = circuit_mul(t40, t44); let t47 = circuit_sub(in2, t46); // Fp2 Inv imag part end let t48 = circuit_mul(t37, t45); // Fp2 mul start let t49 = circuit_mul(t38, t47); let t50 = circuit_sub(t48, t49); // Fp2 mul real part end let t51 = circuit_mul(t37, t47); let t52 = circuit_mul(t38, t45); let t53 = circuit_add(t51, t52); // Fp2 mul imag part end let t54 = circuit_add(t50, t53); let t55 = circuit_sub(t50, t53); let t56 = circuit_mul(t54, t55); let t57 = circuit_mul(t50, t53); let t58 = circuit_add(t57, t57); let t59 = circuit_add(in25, in25); // Fp2 add coeff 0/1 let t60 = circuit_add(in26, in26); // Fp2 add coeff 1/1 let t61 = circuit_sub(t56, t59); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t58, t60); // Fp2 sub coeff 1/1 let t63 = circuit_sub(in25, t61); // Fp2 sub coeff 0/1 let t64 = circuit_sub(in26, t62); // Fp2 sub coeff 1/1 let t65 = circuit_mul(t50, t63); // Fp2 mul start let t66 = circuit_mul(t53, t64); let t67 = circuit_sub(t65, t66); // Fp2 mul real part end let t68 = circuit_mul(t50, t64); let t69 = circuit_mul(t53, t63); let t70 = circuit_add(t68, t69); // Fp2 mul imag part end let t71 = circuit_sub(t67, in27); // Fp2 sub coeff 0/1 let t72 = circuit_sub(t70, in28); // Fp2 sub coeff 1/1 let t73 = circuit_mul(t50, in25); // Fp2 mul start let t74 = circuit_mul(t53, in26); let t75 = circuit_sub(t73, t74); // Fp2 mul real part end let t76 = circuit_mul(t50, in26); let t77 = circuit_mul(t53, in25); let t78 = circuit_add(t76, t77); // Fp2 mul imag part end let t79 = circuit_sub(t75, in27); // Fp2 sub coeff 0/1 let t80 = circuit_sub(t78, in28); // Fp2 sub coeff 1/1 let t81 = circuit_sub(t79, t80); let t82 = circuit_mul(t81, in23); // eval bls line by yInv let t83 = circuit_sub(t50, t53); let t84 = circuit_mul(t83, in24); // eval blsline by xNegOverY let t85 = circuit_mul(t80, in23); // eval bls line by yInv let t86 = circuit_mul(t53, in24); // eval bls line by xNegOverY let t87 = circuit_mul(t84, t0); // Eval sparse poly line_2p_1 step coeff_2 * z^2 let t88 = circuit_add(t82, t87); // Eval sparse poly line_2p_1 step + coeff_2 * z^2 let t89 = circuit_add(t88, t1); // Eval sparse poly line_2p_1 step + 1*z^3 let t90 = circuit_mul(t85, t2); // Eval sparse poly line_2p_1 step coeff_6 * z^6 let t91 = circuit_add(t89, t90); // Eval sparse poly line_2p_1 step + coeff_6 * z^6 let t92 = circuit_mul(t86, t3); // Eval sparse poly line_2p_1 step coeff_8 * z^8 let t93 = circuit_add(t91, t92); // Eval sparse poly line_2p_1 step + coeff_8 * z^8 let t94 = circuit_mul(t32, t93); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t95 = circuit_mul( t94, t94, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t96 = circuit_sub(in17, in18); let t97 = circuit_mul(t96, in3); // eval bls line by yInv let t98 = circuit_sub(in15, in16); let t99 = circuit_mul(t98, in4); // eval blsline by xNegOverY let t100 = circuit_mul(in18, in3); // eval bls line by yInv let t101 = circuit_mul(in16, in4); // eval bls line by xNegOverY let t102 = circuit_mul(t99, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t103 = circuit_add(t97, t102); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t104 = circuit_add(t103, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t105 = circuit_mul(t100, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t106 = circuit_add(t104, t105); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t107 = circuit_mul(t101, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t108 = circuit_add(t106, t107); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t109 = circuit_mul(t95, t108); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t110 = circuit_sub(in21, in22); let t111 = circuit_mul(t110, in13); // eval bls line by yInv let t112 = circuit_sub(in19, in20); let t113 = circuit_mul(t112, in14); // eval blsline by xNegOverY let t114 = circuit_mul(in22, in13); // eval bls line by yInv let t115 = circuit_mul(in20, in14); // eval bls line by xNegOverY let t116 = circuit_mul(t113, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t117 = circuit_add(t111, t116); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t118 = circuit_add(t117, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t119 = circuit_mul(t114, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t120 = circuit_add(t118, t119); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t121 = circuit_mul(t115, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t122 = circuit_add(t120, t121); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t123 = circuit_mul(t109, t122); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t124 = circuit_add(t61, t62); // Doubling slope numerator start let t125 = circuit_sub(t61, t62); let t126 = circuit_mul(t124, t125); let t127 = circuit_mul(t61, t62); let t128 = circuit_mul(t126, in0); let t129 = circuit_mul(t127, in1); // Doubling slope numerator end let t130 = circuit_add(t71, t71); // Fp2 add coeff 0/1 let t131 = circuit_add(t72, t72); // Fp2 add coeff 1/1 let t132 = circuit_mul(t130, t130); // Fp2 Inv start let t133 = circuit_mul(t131, t131); let t134 = circuit_add(t132, t133); let t135 = circuit_inverse(t134); let t136 = circuit_mul(t130, t135); // Fp2 Inv real part end let t137 = circuit_mul(t131, t135); let t138 = circuit_sub(in2, t137); // Fp2 Inv imag part end let t139 = circuit_mul(t128, t136); // Fp2 mul start let t140 = circuit_mul(t129, t138); let t141 = circuit_sub(t139, t140); // Fp2 mul real part end let t142 = circuit_mul(t128, t138); let t143 = circuit_mul(t129, t136); let t144 = circuit_add(t142, t143); // Fp2 mul imag part end let t145 = circuit_add(t141, t144); let t146 = circuit_sub(t141, t144); let t147 = circuit_mul(t145, t146); let t148 = circuit_mul(t141, t144); let t149 = circuit_add(t148, t148); let t150 = circuit_add(t61, t61); // Fp2 add coeff 0/1 let t151 = circuit_add(t62, t62); // Fp2 add coeff 1/1 let t152 = circuit_sub(t147, t150); // Fp2 sub coeff 0/1 let t153 = circuit_sub(t149, t151); // Fp2 sub coeff 1/1 let t154 = circuit_sub(t61, t152); // Fp2 sub coeff 0/1 let t155 = circuit_sub(t62, t153); // Fp2 sub coeff 1/1 let t156 = circuit_mul(t141, t154); // Fp2 mul start let t157 = circuit_mul(t144, t155); let t158 = circuit_sub(t156, t157); // Fp2 mul real part end let t159 = circuit_mul(t141, t155); let t160 = circuit_mul(t144, t154); let t161 = circuit_add(t159, t160); // Fp2 mul imag part end let t162 = circuit_sub(t158, t71); // Fp2 sub coeff 0/1 let t163 = circuit_sub(t161, t72); // Fp2 sub coeff 1/1 let t164 = circuit_mul(t141, t61); // Fp2 mul start let t165 = circuit_mul(t144, t62); let t166 = circuit_sub(t164, t165); // Fp2 mul real part end let t167 = circuit_mul(t141, t62); let t168 = circuit_mul(t144, t61); let t169 = circuit_add(t167, t168); // Fp2 mul imag part end let t170 = circuit_sub(t166, t71); // Fp2 sub coeff 0/1 let t171 = circuit_sub(t169, t72); // Fp2 sub coeff 1/1 let t172 = circuit_sub(t170, t171); let t173 = circuit_mul(t172, in23); // eval bls line by yInv let t174 = circuit_sub(t141, t144); let t175 = circuit_mul(t174, in24); // eval blsline by xNegOverY let t176 = circuit_mul(t171, in23); // eval bls line by yInv let t177 = circuit_mul(t144, in24); // eval bls line by xNegOverY let t178 = circuit_mul(t175, t0); // Eval sparse poly line_2p_1 step coeff_2 * z^2 let t179 = circuit_add(t173, t178); // Eval sparse poly line_2p_1 step + coeff_2 * z^2 let t180 = circuit_add(t179, t1); // Eval sparse poly line_2p_1 step + 1*z^3 let t181 = circuit_mul(t176, t2); // Eval sparse poly line_2p_1 step coeff_6 * z^6 let t182 = circuit_add(t180, t181); // Eval sparse poly line_2p_1 step + coeff_6 * z^6 let t183 = circuit_mul(t177, t3); // Eval sparse poly line_2p_1 step coeff_8 * z^8 let t184 = circuit_add(t182, t183); // Eval sparse poly line_2p_1 step + coeff_8 * z^8 let t185 = circuit_mul(t123, t184); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t186 = circuit_sub(t185, in31); // (Π(i,k) (Pk(z))) - Ri(z) let t187 = circuit_mul(in33, in29); let t188 = circuit_add(t187, t186); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t152, t153, t162, t163, t188).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in3 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a1); // in12 circuit_inputs = circuit_inputs.next_2(yInv_1); // in13 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a0); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a1); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a0); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a1); // in22 circuit_inputs = circuit_inputs.next_2(yInv_2); // in23 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in24 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in25 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in26 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in27 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in28 circuit_inputs = circuit_inputs.next_2(lhs_i); // in29 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in30 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in31 circuit_inputs = circuit_inputs.next_2(z); // in32 circuit_inputs = circuit_inputs.next_2(c1); // in33 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t152), x1: outputs.get_output(t153), y0: outputs.get_output(t162), y1: outputs.get_output(t163), }; let lhs_i_plus_one: u384 = outputs.get_output(t188); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT0_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in15, in15); // compute z^2 let t1 = circuit_mul(t0, in15); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in13, in13); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in4, in5); let t6 = circuit_mul(t5, in0); // eval bls line by yInv let t7 = circuit_sub(in2, in3); let t8 = circuit_mul(t7, in1); // eval blsline by xNegOverY let t9 = circuit_mul(in5, in0); // eval bls line by yInv let t10 = circuit_mul(in3, in1); // eval bls line by xNegOverY let t11 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t12 = circuit_add(t6, t11); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t13 = circuit_add(t12, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t14 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t15 = circuit_add(t13, t14); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t16 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t18 = circuit_mul(t4, t17); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t19 = circuit_sub(in10, in11); let t20 = circuit_mul(t19, in6); // eval bls line by yInv let t21 = circuit_sub(in8, in9); let t22 = circuit_mul(t21, in7); // eval blsline by xNegOverY let t23 = circuit_mul(in11, in6); // eval bls line by yInv let t24 = circuit_mul(in9, in7); // eval bls line by xNegOverY let t25 = circuit_mul(t22, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t26 = circuit_add(t20, t25); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t28 = circuit_mul(t23, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t30 = circuit_mul(t24, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t32 = circuit_mul(t18, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t33 = circuit_sub(t32, in14); // (Π(i,k) (Pk(z))) - Ri(z) let t34 = circuit_mul(in16, in12); let t35 = circuit_add(t34, t33); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t35,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in0 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in1 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in2 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in5 circuit_inputs = circuit_inputs.next_2(yInv_1); // in6 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in11 circuit_inputs = circuit_inputs.next_2(lhs_i); // in12 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in13 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in14 circuit_inputs = circuit_inputs.next_2(z); // in15 circuit_inputs = circuit_inputs.next_2(c1); // in16 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t35); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT0_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x3 let in1 = CE::> {}; // 0x6 let in2 = CE::> {}; // 0x0 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in24, in24); // compute z^2 let t1 = circuit_mul(t0, in24); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in22, in22); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in7, in8); let t6 = circuit_mul(t5, in3); // eval bls line by yInv let t7 = circuit_sub(in5, in6); let t8 = circuit_mul(t7, in4); // eval blsline by xNegOverY let t9 = circuit_mul(in8, in3); // eval bls line by yInv let t10 = circuit_mul(in6, in4); // eval bls line by xNegOverY let t11 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t12 = circuit_add(t6, t11); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t13 = circuit_add(t12, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t14 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t15 = circuit_add(t13, t14); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t16 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t18 = circuit_mul(t4, t17); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t19 = circuit_sub(in13, in14); let t20 = circuit_mul(t19, in9); // eval bls line by yInv let t21 = circuit_sub(in11, in12); let t22 = circuit_mul(t21, in10); // eval blsline by xNegOverY let t23 = circuit_mul(in14, in9); // eval bls line by yInv let t24 = circuit_mul(in12, in10); // eval bls line by xNegOverY let t25 = circuit_mul(t22, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t26 = circuit_add(t20, t25); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t28 = circuit_mul(t23, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t30 = circuit_mul(t24, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t32 = circuit_mul(t18, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t33 = circuit_add(in17, in18); // Doubling slope numerator start let t34 = circuit_sub(in17, in18); let t35 = circuit_mul(t33, t34); let t36 = circuit_mul(in17, in18); let t37 = circuit_mul(t35, in0); let t38 = circuit_mul(t36, in1); // Doubling slope numerator end let t39 = circuit_add(in19, in19); // Fp2 add coeff 0/1 let t40 = circuit_add(in20, in20); // Fp2 add coeff 1/1 let t41 = circuit_mul(t39, t39); // Fp2 Inv start let t42 = circuit_mul(t40, t40); let t43 = circuit_add(t41, t42); let t44 = circuit_inverse(t43); let t45 = circuit_mul(t39, t44); // Fp2 Inv real part end let t46 = circuit_mul(t40, t44); let t47 = circuit_sub(in2, t46); // Fp2 Inv imag part end let t48 = circuit_mul(t37, t45); // Fp2 mul start let t49 = circuit_mul(t38, t47); let t50 = circuit_sub(t48, t49); // Fp2 mul real part end let t51 = circuit_mul(t37, t47); let t52 = circuit_mul(t38, t45); let t53 = circuit_add(t51, t52); // Fp2 mul imag part end let t54 = circuit_add(t50, t53); let t55 = circuit_sub(t50, t53); let t56 = circuit_mul(t54, t55); let t57 = circuit_mul(t50, t53); let t58 = circuit_add(t57, t57); let t59 = circuit_add(in17, in17); // Fp2 add coeff 0/1 let t60 = circuit_add(in18, in18); // Fp2 add coeff 1/1 let t61 = circuit_sub(t56, t59); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t58, t60); // Fp2 sub coeff 1/1 let t63 = circuit_sub(in17, t61); // Fp2 sub coeff 0/1 let t64 = circuit_sub(in18, t62); // Fp2 sub coeff 1/1 let t65 = circuit_mul(t50, t63); // Fp2 mul start let t66 = circuit_mul(t53, t64); let t67 = circuit_sub(t65, t66); // Fp2 mul real part end let t68 = circuit_mul(t50, t64); let t69 = circuit_mul(t53, t63); let t70 = circuit_add(t68, t69); // Fp2 mul imag part end let t71 = circuit_sub(t67, in19); // Fp2 sub coeff 0/1 let t72 = circuit_sub(t70, in20); // Fp2 sub coeff 1/1 let t73 = circuit_mul(t50, in17); // Fp2 mul start let t74 = circuit_mul(t53, in18); let t75 = circuit_sub(t73, t74); // Fp2 mul real part end let t76 = circuit_mul(t50, in18); let t77 = circuit_mul(t53, in17); let t78 = circuit_add(t76, t77); // Fp2 mul imag part end let t79 = circuit_sub(t75, in19); // Fp2 sub coeff 0/1 let t80 = circuit_sub(t78, in20); // Fp2 sub coeff 1/1 let t81 = circuit_sub(t79, t80); let t82 = circuit_mul(t81, in15); // eval bls line by yInv let t83 = circuit_sub(t50, t53); let t84 = circuit_mul(t83, in16); // eval blsline by xNegOverY let t85 = circuit_mul(t80, in15); // eval bls line by yInv let t86 = circuit_mul(t53, in16); // eval bls line by xNegOverY let t87 = circuit_mul(t84, t0); // Eval sparse poly line_2p_1 step coeff_2 * z^2 let t88 = circuit_add(t82, t87); // Eval sparse poly line_2p_1 step + coeff_2 * z^2 let t89 = circuit_add(t88, t1); // Eval sparse poly line_2p_1 step + 1*z^3 let t90 = circuit_mul(t85, t2); // Eval sparse poly line_2p_1 step coeff_6 * z^6 let t91 = circuit_add(t89, t90); // Eval sparse poly line_2p_1 step + coeff_6 * z^6 let t92 = circuit_mul(t86, t3); // Eval sparse poly line_2p_1 step coeff_8 * z^8 let t93 = circuit_add(t91, t92); // Eval sparse poly line_2p_1 step + coeff_8 * z^8 let t94 = circuit_mul(t32, t93); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t95 = circuit_sub(t94, in23); // (Π(i,k) (Pk(z))) - Ri(z) let t96 = circuit_mul(in25, in21); let t97 = circuit_add(t96, t95); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t61, t62, t71, t72, t97).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in3 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in8 circuit_inputs = circuit_inputs.next_2(yInv_1); // in9 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in14 circuit_inputs = circuit_inputs.next_2(yInv_2); // in15 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in16 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in17 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in18 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in19 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in20 circuit_inputs = circuit_inputs.next_2(lhs_i); // in21 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in22 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in23 circuit_inputs = circuit_inputs.next_2(z); // in24 circuit_inputs = circuit_inputs.next_2(c1); // in25 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t61), x1: outputs.get_output(t62), y0: outputs.get_output(t71), y1: outputs.get_output(t72), }; let lhs_i_plus_one: u384 = outputs.get_output(t97); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT1_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_add_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_add_1: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in24, in24); // compute z^2 let t1 = circuit_mul(t0, in24); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in21, in21); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in4, in5); let t6 = circuit_mul(t5, in0); // eval bls line by yInv let t7 = circuit_sub(in2, in3); let t8 = circuit_mul(t7, in1); // eval blsline by xNegOverY let t9 = circuit_mul(in5, in0); // eval bls line by yInv let t10 = circuit_mul(in3, in1); // eval bls line by xNegOverY let t11 = circuit_sub(in8, in9); let t12 = circuit_mul(t11, in0); // eval bls line by yInv let t13 = circuit_sub(in6, in7); let t14 = circuit_mul(t13, in1); // eval blsline by xNegOverY let t15 = circuit_mul(in9, in0); // eval bls line by yInv let t16 = circuit_mul(in7, in1); // eval bls line by xNegOverY let t17 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t18 = circuit_add(t6, t17); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t19 = circuit_add(t18, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t20 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t22 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t23 = circuit_add(t21, t22); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t24 = circuit_mul(t4, t23); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t25 = circuit_mul(t14, t0); // Eval sparse poly line_0p_2 step coeff_2 * z^2 let t26 = circuit_add(t12, t25); // Eval sparse poly line_0p_2 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_0p_2 step + 1*z^3 let t28 = circuit_mul(t15, t2); // Eval sparse poly line_0p_2 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_0p_2 step + coeff_6 * z^6 let t30 = circuit_mul(t16, t3); // Eval sparse poly line_0p_2 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_0p_2 step + coeff_8 * z^8 let t32 = circuit_mul(t24, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t33 = circuit_sub(in14, in15); let t34 = circuit_mul(t33, in10); // eval bls line by yInv let t35 = circuit_sub(in12, in13); let t36 = circuit_mul(t35, in11); // eval blsline by xNegOverY let t37 = circuit_mul(in15, in10); // eval bls line by yInv let t38 = circuit_mul(in13, in11); // eval bls line by xNegOverY let t39 = circuit_sub(in18, in19); let t40 = circuit_mul(t39, in10); // eval bls line by yInv let t41 = circuit_sub(in16, in17); let t42 = circuit_mul(t41, in11); // eval blsline by xNegOverY let t43 = circuit_mul(in19, in10); // eval bls line by yInv let t44 = circuit_mul(in17, in11); // eval bls line by xNegOverY let t45 = circuit_mul(t36, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t46 = circuit_add(t34, t45); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t47 = circuit_add(t46, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t48 = circuit_mul(t37, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t49 = circuit_add(t47, t48); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t50 = circuit_mul(t38, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t51 = circuit_add(t49, t50); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t52 = circuit_mul(t32, t51); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t53 = circuit_mul(t42, t0); // Eval sparse poly line_1p_2 step coeff_2 * z^2 let t54 = circuit_add(t40, t53); // Eval sparse poly line_1p_2 step + coeff_2 * z^2 let t55 = circuit_add(t54, t1); // Eval sparse poly line_1p_2 step + 1*z^3 let t56 = circuit_mul(t43, t2); // Eval sparse poly line_1p_2 step coeff_6 * z^6 let t57 = circuit_add(t55, t56); // Eval sparse poly line_1p_2 step + coeff_6 * z^6 let t58 = circuit_mul(t44, t3); // Eval sparse poly line_1p_2 step coeff_8 * z^8 let t59 = circuit_add(t57, t58); // Eval sparse poly line_1p_2 step + coeff_8 * z^8 let t60 = circuit_mul(t52, t59); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t61 = circuit_mul(t60, in23); let t62 = circuit_sub(t61, in22); // (Π(i,k) (Pk(z))) - Ri(z) let t63 = circuit_mul(in25, in20); let t64 = circuit_add(t63, t62); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t64,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in0 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in1 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in2 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r0a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r0a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r1a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r1a1); // in9 circuit_inputs = circuit_inputs.next_2(yInv_1); // in10 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r0a0); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r0a1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r1a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r1a1); // in19 circuit_inputs = circuit_inputs.next_2(lhs_i); // in20 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in21 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in22 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in23 circuit_inputs = circuit_inputs.next_2(z); // in24 circuit_inputs = circuit_inputs.next_2(c1); // in25 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t64); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_BIT1_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_add_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_add_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, Q_or_Q_neg_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in35, in35); // compute z^2 let t1 = circuit_mul(t0, in35); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in32, in32); // Square f evaluation in Z, the result of previous bit. let t5 = circuit_sub(in5, in6); let t6 = circuit_mul(t5, in1); // eval bls line by yInv let t7 = circuit_sub(in3, in4); let t8 = circuit_mul(t7, in2); // eval blsline by xNegOverY let t9 = circuit_mul(in6, in1); // eval bls line by yInv let t10 = circuit_mul(in4, in2); // eval bls line by xNegOverY let t11 = circuit_sub(in9, in10); let t12 = circuit_mul(t11, in1); // eval bls line by yInv let t13 = circuit_sub(in7, in8); let t14 = circuit_mul(t13, in2); // eval blsline by xNegOverY let t15 = circuit_mul(in10, in1); // eval bls line by yInv let t16 = circuit_mul(in8, in2); // eval bls line by xNegOverY let t17 = circuit_mul(t8, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t18 = circuit_add(t6, t17); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t19 = circuit_add(t18, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t20 = circuit_mul(t9, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t22 = circuit_mul(t10, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t23 = circuit_add(t21, t22); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t24 = circuit_mul(t4, t23); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t25 = circuit_mul(t14, t0); // Eval sparse poly line_0p_2 step coeff_2 * z^2 let t26 = circuit_add(t12, t25); // Eval sparse poly line_0p_2 step + coeff_2 * z^2 let t27 = circuit_add(t26, t1); // Eval sparse poly line_0p_2 step + 1*z^3 let t28 = circuit_mul(t15, t2); // Eval sparse poly line_0p_2 step coeff_6 * z^6 let t29 = circuit_add(t27, t28); // Eval sparse poly line_0p_2 step + coeff_6 * z^6 let t30 = circuit_mul(t16, t3); // Eval sparse poly line_0p_2 step coeff_8 * z^8 let t31 = circuit_add(t29, t30); // Eval sparse poly line_0p_2 step + coeff_8 * z^8 let t32 = circuit_mul(t24, t31); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t33 = circuit_sub(in15, in16); let t34 = circuit_mul(t33, in11); // eval bls line by yInv let t35 = circuit_sub(in13, in14); let t36 = circuit_mul(t35, in12); // eval blsline by xNegOverY let t37 = circuit_mul(in16, in11); // eval bls line by yInv let t38 = circuit_mul(in14, in12); // eval bls line by xNegOverY let t39 = circuit_sub(in19, in20); let t40 = circuit_mul(t39, in11); // eval bls line by yInv let t41 = circuit_sub(in17, in18); let t42 = circuit_mul(t41, in12); // eval blsline by xNegOverY let t43 = circuit_mul(in20, in11); // eval bls line by yInv let t44 = circuit_mul(in18, in12); // eval bls line by xNegOverY let t45 = circuit_mul(t36, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t46 = circuit_add(t34, t45); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t47 = circuit_add(t46, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t48 = circuit_mul(t37, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t49 = circuit_add(t47, t48); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t50 = circuit_mul(t38, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t51 = circuit_add(t49, t50); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t52 = circuit_mul(t32, t51); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t53 = circuit_mul(t42, t0); // Eval sparse poly line_1p_2 step coeff_2 * z^2 let t54 = circuit_add(t40, t53); // Eval sparse poly line_1p_2 step + coeff_2 * z^2 let t55 = circuit_add(t54, t1); // Eval sparse poly line_1p_2 step + 1*z^3 let t56 = circuit_mul(t43, t2); // Eval sparse poly line_1p_2 step coeff_6 * z^6 let t57 = circuit_add(t55, t56); // Eval sparse poly line_1p_2 step + coeff_6 * z^6 let t58 = circuit_mul(t44, t3); // Eval sparse poly line_1p_2 step coeff_8 * z^8 let t59 = circuit_add(t57, t58); // Eval sparse poly line_1p_2 step + coeff_8 * z^8 let t60 = circuit_mul(t52, t59); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t61 = circuit_sub(in25, in29); // Fp2 sub coeff 0/1 let t62 = circuit_sub(in26, in30); // Fp2 sub coeff 1/1 let t63 = circuit_sub(in23, in27); // Fp2 sub coeff 0/1 let t64 = circuit_sub(in24, in28); // Fp2 sub coeff 1/1 let t65 = circuit_mul(t63, t63); // Fp2 Inv start let t66 = circuit_mul(t64, t64); let t67 = circuit_add(t65, t66); let t68 = circuit_inverse(t67); let t69 = circuit_mul(t63, t68); // Fp2 Inv real part end let t70 = circuit_mul(t64, t68); let t71 = circuit_sub(in0, t70); // Fp2 Inv imag part end let t72 = circuit_mul(t61, t69); // Fp2 mul start let t73 = circuit_mul(t62, t71); let t74 = circuit_sub(t72, t73); // Fp2 mul real part end let t75 = circuit_mul(t61, t71); let t76 = circuit_mul(t62, t69); let t77 = circuit_add(t75, t76); // Fp2 mul imag part end let t78 = circuit_add(t74, t77); let t79 = circuit_sub(t74, t77); let t80 = circuit_mul(t78, t79); let t81 = circuit_mul(t74, t77); let t82 = circuit_add(t81, t81); let t83 = circuit_add(in23, in27); // Fp2 add coeff 0/1 let t84 = circuit_add(in24, in28); // Fp2 add coeff 1/1 let t85 = circuit_sub(t80, t83); // Fp2 sub coeff 0/1 let t86 = circuit_sub(t82, t84); // Fp2 sub coeff 1/1 let t87 = circuit_mul(t74, in23); // Fp2 mul start let t88 = circuit_mul(t77, in24); let t89 = circuit_sub(t87, t88); // Fp2 mul real part end let t90 = circuit_mul(t74, in24); let t91 = circuit_mul(t77, in23); let t92 = circuit_add(t90, t91); // Fp2 mul imag part end let t93 = circuit_sub(t89, in25); // Fp2 sub coeff 0/1 let t94 = circuit_sub(t92, in26); // Fp2 sub coeff 1/1 let t95 = circuit_add(in25, in25); // Fp2 add coeff 0/1 let t96 = circuit_add(in26, in26); // Fp2 add coeff 1/1 let t97 = circuit_sub(t85, in23); // Fp2 sub coeff 0/1 let t98 = circuit_sub(t86, in24); // Fp2 sub coeff 1/1 let t99 = circuit_mul(t97, t97); // Fp2 Inv start let t100 = circuit_mul(t98, t98); let t101 = circuit_add(t99, t100); let t102 = circuit_inverse(t101); let t103 = circuit_mul(t97, t102); // Fp2 Inv real part end let t104 = circuit_mul(t98, t102); let t105 = circuit_sub(in0, t104); // Fp2 Inv imag part end let t106 = circuit_mul(t95, t103); // Fp2 mul start let t107 = circuit_mul(t96, t105); let t108 = circuit_sub(t106, t107); // Fp2 mul real part end let t109 = circuit_mul(t95, t105); let t110 = circuit_mul(t96, t103); let t111 = circuit_add(t109, t110); // Fp2 mul imag part end let t112 = circuit_add(t74, t108); // Fp2 add coeff 0/1 let t113 = circuit_add(t77, t111); // Fp2 add coeff 1/1 let t114 = circuit_sub(in0, t112); // Fp2 neg coeff 0/1 let t115 = circuit_sub(in0, t113); // Fp2 neg coeff 1/1 let t116 = circuit_add(t114, t115); let t117 = circuit_sub(t114, t115); let t118 = circuit_mul(t116, t117); let t119 = circuit_mul(t114, t115); let t120 = circuit_add(t119, t119); let t121 = circuit_sub(t118, in23); // Fp2 sub coeff 0/1 let t122 = circuit_sub(t120, in24); // Fp2 sub coeff 1/1 let t123 = circuit_sub(t121, t85); // Fp2 sub coeff 0/1 let t124 = circuit_sub(t122, t86); // Fp2 sub coeff 1/1 let t125 = circuit_sub(in23, t123); // Fp2 sub coeff 0/1 let t126 = circuit_sub(in24, t124); // Fp2 sub coeff 1/1 let t127 = circuit_mul(t114, t125); // Fp2 mul start let t128 = circuit_mul(t115, t126); let t129 = circuit_sub(t127, t128); // Fp2 mul real part end let t130 = circuit_mul(t114, t126); let t131 = circuit_mul(t115, t125); let t132 = circuit_add(t130, t131); // Fp2 mul imag part end let t133 = circuit_sub(t129, in25); // Fp2 sub coeff 0/1 let t134 = circuit_sub(t132, in26); // Fp2 sub coeff 1/1 let t135 = circuit_mul(t114, in23); // Fp2 mul start let t136 = circuit_mul(t115, in24); let t137 = circuit_sub(t135, t136); // Fp2 mul real part end let t138 = circuit_mul(t114, in24); let t139 = circuit_mul(t115, in23); let t140 = circuit_add(t138, t139); // Fp2 mul imag part end let t141 = circuit_sub(t137, in25); // Fp2 sub coeff 0/1 let t142 = circuit_sub(t140, in26); // Fp2 sub coeff 1/1 let t143 = circuit_sub(t93, t94); let t144 = circuit_mul(t143, in21); // eval bls line by yInv let t145 = circuit_sub(t74, t77); let t146 = circuit_mul(t145, in22); // eval blsline by xNegOverY let t147 = circuit_mul(t94, in21); // eval bls line by yInv let t148 = circuit_mul(t77, in22); // eval bls line by xNegOverY let t149 = circuit_sub(t141, t142); let t150 = circuit_mul(t149, in21); // eval bls line by yInv let t151 = circuit_sub(t114, t115); let t152 = circuit_mul(t151, in22); // eval blsline by xNegOverY let t153 = circuit_mul(t142, in21); // eval bls line by yInv let t154 = circuit_mul(t115, in22); // eval bls line by xNegOverY let t155 = circuit_mul(t146, t0); // Eval sparse poly line_2p_1 step coeff_2 * z^2 let t156 = circuit_add(t144, t155); // Eval sparse poly line_2p_1 step + coeff_2 * z^2 let t157 = circuit_add(t156, t1); // Eval sparse poly line_2p_1 step + 1*z^3 let t158 = circuit_mul(t147, t2); // Eval sparse poly line_2p_1 step coeff_6 * z^6 let t159 = circuit_add(t157, t158); // Eval sparse poly line_2p_1 step + coeff_6 * z^6 let t160 = circuit_mul(t148, t3); // Eval sparse poly line_2p_1 step coeff_8 * z^8 let t161 = circuit_add(t159, t160); // Eval sparse poly line_2p_1 step + coeff_8 * z^8 let t162 = circuit_mul(t60, t161); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t163 = circuit_mul(t152, t0); // Eval sparse poly line_2p_2 step coeff_2 * z^2 let t164 = circuit_add(t150, t163); // Eval sparse poly line_2p_2 step + coeff_2 * z^2 let t165 = circuit_add(t164, t1); // Eval sparse poly line_2p_2 step + 1*z^3 let t166 = circuit_mul(t153, t2); // Eval sparse poly line_2p_2 step coeff_6 * z^6 let t167 = circuit_add(t165, t166); // Eval sparse poly line_2p_2 step + coeff_6 * z^6 let t168 = circuit_mul(t154, t3); // Eval sparse poly line_2p_2 step coeff_8 * z^8 let t169 = circuit_add(t167, t168); // Eval sparse poly line_2p_2 step + coeff_8 * z^8 let t170 = circuit_mul(t162, t169); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t171 = circuit_mul(t170, in34); let t172 = circuit_sub(t171, in33); // (Π(i,k) (Pk(z))) - Ri(z) let t173 = circuit_mul(in36, in31); let t174 = circuit_add(t173, t172); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t123, t124, t133, t134, t174).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in1 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in2 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r0a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r0a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r1a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_add_0.r1a1); // in10 circuit_inputs = circuit_inputs.next_2(yInv_1); // in11 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r0a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r0a1); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r1a0); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_add_1.r1a1); // in20 circuit_inputs = circuit_inputs.next_2(yInv_2); // in21 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in22 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in23 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in24 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in25 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in26 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x0); // in27 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x1); // in28 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y0); // in29 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y1); // in30 circuit_inputs = circuit_inputs.next_2(lhs_i); // in31 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in32 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in33 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in34 circuit_inputs = circuit_inputs.next_2(z); // in35 circuit_inputs = circuit_inputs.next_2(c1); // in36 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t123), x1: outputs.get_output(t124), y0: outputs.get_output(t133), y1: outputs.get_output(t134), }; let lhs_i_plus_one: u384 = outputs.get_output(t174); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_FINALIZE_2P_circuit( R_n_minus_1_of_z: u384, c_1: u384, w_of_z: u384, z: u384, c_inv_frob_1_of_z: u384, previous_lhs: u384, R_n_minus_2: E12D, Q: Array, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x2 let in2 = CE::> {}; // -0x2 % p // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let (in33, in34, in35) = (CE::> {}, CE::> {}, CE::> {}); let (in36, in37, in38) = (CE::> {}, CE::> {}, CE::> {}); let (in39, in40, in41) = (CE::> {}, CE::> {}, CE::> {}); let (in42, in43, in44) = (CE::> {}, CE::> {}, CE::> {}); let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76, in77) = (CE::> {}, CE::> {}, CE::> {}); let (in78, in79, in80) = (CE::> {}, CE::> {}, CE::> {}); let (in81, in82, in83) = (CE::> {}, CE::> {}, CE::> {}); let (in84, in85, in86) = (CE::> {}, CE::> {}, CE::> {}); let (in87, in88, in89) = (CE::> {}, CE::> {}, CE::> {}); let (in90, in91, in92) = (CE::> {}, CE::> {}, CE::> {}); let (in93, in94, in95) = (CE::> {}, CE::> {}, CE::> {}); let (in96, in97, in98) = (CE::> {}, CE::> {}, CE::> {}); let (in99, in100, in101) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in6, in6); // Compute z^2 let t1 = circuit_mul(t0, in6); // Compute z^3 let t2 = circuit_mul(t1, in6); // Compute z^4 let t3 = circuit_mul(t2, in6); // Compute z^5 let t4 = circuit_mul(t3, in6); // Compute z^6 let t5 = circuit_mul(t4, in6); // Compute z^7 let t6 = circuit_mul(t5, in6); // Compute z^8 let t7 = circuit_mul(t6, in6); // Compute z^9 let t8 = circuit_mul(t7, in6); // Compute z^10 let t9 = circuit_mul(t8, in6); // Compute z^11 let t10 = circuit_mul(t9, in6); // Compute z^12 let t11 = circuit_sub(in0, in10); let t12 = circuit_sub(in0, in12); let t13 = circuit_sub(in0, in14); let t14 = circuit_sub(in0, in16); let t15 = circuit_sub(in0, in18); let t16 = circuit_sub(in0, in20); let t17 = circuit_mul(t11, in6); // Eval R_n_minus_2_conjugate step coeff_1 * z^1 let t18 = circuit_add(in9, t17); // Eval R_n_minus_2_conjugate step + (coeff_1 * z^1) let t19 = circuit_mul(in11, t0); // Eval R_n_minus_2_conjugate step coeff_2 * z^2 let t20 = circuit_add(t18, t19); // Eval R_n_minus_2_conjugate step + (coeff_2 * z^2) let t21 = circuit_mul(t12, t1); // Eval R_n_minus_2_conjugate step coeff_3 * z^3 let t22 = circuit_add(t20, t21); // Eval R_n_minus_2_conjugate step + (coeff_3 * z^3) let t23 = circuit_mul(in13, t2); // Eval R_n_minus_2_conjugate step coeff_4 * z^4 let t24 = circuit_add(t22, t23); // Eval R_n_minus_2_conjugate step + (coeff_4 * z^4) let t25 = circuit_mul(t13, t3); // Eval R_n_minus_2_conjugate step coeff_5 * z^5 let t26 = circuit_add(t24, t25); // Eval R_n_minus_2_conjugate step + (coeff_5 * z^5) let t27 = circuit_mul(in15, t4); // Eval R_n_minus_2_conjugate step coeff_6 * z^6 let t28 = circuit_add(t26, t27); // Eval R_n_minus_2_conjugate step + (coeff_6 * z^6) let t29 = circuit_mul(t14, t5); // Eval R_n_minus_2_conjugate step coeff_7 * z^7 let t30 = circuit_add(t28, t29); // Eval R_n_minus_2_conjugate step + (coeff_7 * z^7) let t31 = circuit_mul(in17, t6); // Eval R_n_minus_2_conjugate step coeff_8 * z^8 let t32 = circuit_add(t30, t31); // Eval R_n_minus_2_conjugate step + (coeff_8 * z^8) let t33 = circuit_mul(t15, t7); // Eval R_n_minus_2_conjugate step coeff_9 * z^9 let t34 = circuit_add(t32, t33); // Eval R_n_minus_2_conjugate step + (coeff_9 * z^9) let t35 = circuit_mul(in19, t8); // Eval R_n_minus_2_conjugate step coeff_10 * z^10 let t36 = circuit_add(t34, t35); // Eval R_n_minus_2_conjugate step + (coeff_10 * z^10) let t37 = circuit_mul(t16, t9); // Eval R_n_minus_2_conjugate step coeff_11 * z^11 let t38 = circuit_add(t36, t37); // Eval R_n_minus_2_conjugate step + (coeff_11 * z^11) let t39 = circuit_mul(t38, in7); let t40 = circuit_mul(t39, in5); let t41 = circuit_sub(t40, in3); // (Π(n-1,k) (Pk(z)) - R_n_minus_1(z)) let t42 = circuit_mul(in4, in8); let t43 = circuit_add(t42, t41); // c_1 * previous_lhs + lhs_n_minus_1 let t44 = circuit_mul(in2, t4); // Eval sparse poly P_irr step coeff_6 * z^6 let t45 = circuit_add(in1, t44); // Eval sparse poly P_irr step + coeff_6 * z^6 let t46 = circuit_add(t45, t10); // Eval sparse poly P_irr step + 1*z^12 let t47 = circuit_mul(in101, in6); // Eval big_Q Horner step: multiply by z let t48 = circuit_add(in100, t47); // Eval big_Q Horner step: add coefficient_79 let t49 = circuit_mul(t48, in6); // Eval big_Q Horner step: multiply by z let t50 = circuit_add(in99, t49); // Eval big_Q Horner step: add coefficient_78 let t51 = circuit_mul(t50, in6); // Eval big_Q Horner step: multiply by z let t52 = circuit_add(in98, t51); // Eval big_Q Horner step: add coefficient_77 let t53 = circuit_mul(t52, in6); // Eval big_Q Horner step: multiply by z let t54 = circuit_add(in97, t53); // Eval big_Q Horner step: add coefficient_76 let t55 = circuit_mul(t54, in6); // Eval big_Q Horner step: multiply by z let t56 = circuit_add(in96, t55); // Eval big_Q Horner step: add coefficient_75 let t57 = circuit_mul(t56, in6); // Eval big_Q Horner step: multiply by z let t58 = circuit_add(in95, t57); // Eval big_Q Horner step: add coefficient_74 let t59 = circuit_mul(t58, in6); // Eval big_Q Horner step: multiply by z let t60 = circuit_add(in94, t59); // Eval big_Q Horner step: add coefficient_73 let t61 = circuit_mul(t60, in6); // Eval big_Q Horner step: multiply by z let t62 = circuit_add(in93, t61); // Eval big_Q Horner step: add coefficient_72 let t63 = circuit_mul(t62, in6); // Eval big_Q Horner step: multiply by z let t64 = circuit_add(in92, t63); // Eval big_Q Horner step: add coefficient_71 let t65 = circuit_mul(t64, in6); // Eval big_Q Horner step: multiply by z let t66 = circuit_add(in91, t65); // Eval big_Q Horner step: add coefficient_70 let t67 = circuit_mul(t66, in6); // Eval big_Q Horner step: multiply by z let t68 = circuit_add(in90, t67); // Eval big_Q Horner step: add coefficient_69 let t69 = circuit_mul(t68, in6); // Eval big_Q Horner step: multiply by z let t70 = circuit_add(in89, t69); // Eval big_Q Horner step: add coefficient_68 let t71 = circuit_mul(t70, in6); // Eval big_Q Horner step: multiply by z let t72 = circuit_add(in88, t71); // Eval big_Q Horner step: add coefficient_67 let t73 = circuit_mul(t72, in6); // Eval big_Q Horner step: multiply by z let t74 = circuit_add(in87, t73); // Eval big_Q Horner step: add coefficient_66 let t75 = circuit_mul(t74, in6); // Eval big_Q Horner step: multiply by z let t76 = circuit_add(in86, t75); // Eval big_Q Horner step: add coefficient_65 let t77 = circuit_mul(t76, in6); // Eval big_Q Horner step: multiply by z let t78 = circuit_add(in85, t77); // Eval big_Q Horner step: add coefficient_64 let t79 = circuit_mul(t78, in6); // Eval big_Q Horner step: multiply by z let t80 = circuit_add(in84, t79); // Eval big_Q Horner step: add coefficient_63 let t81 = circuit_mul(t80, in6); // Eval big_Q Horner step: multiply by z let t82 = circuit_add(in83, t81); // Eval big_Q Horner step: add coefficient_62 let t83 = circuit_mul(t82, in6); // Eval big_Q Horner step: multiply by z let t84 = circuit_add(in82, t83); // Eval big_Q Horner step: add coefficient_61 let t85 = circuit_mul(t84, in6); // Eval big_Q Horner step: multiply by z let t86 = circuit_add(in81, t85); // Eval big_Q Horner step: add coefficient_60 let t87 = circuit_mul(t86, in6); // Eval big_Q Horner step: multiply by z let t88 = circuit_add(in80, t87); // Eval big_Q Horner step: add coefficient_59 let t89 = circuit_mul(t88, in6); // Eval big_Q Horner step: multiply by z let t90 = circuit_add(in79, t89); // Eval big_Q Horner step: add coefficient_58 let t91 = circuit_mul(t90, in6); // Eval big_Q Horner step: multiply by z let t92 = circuit_add(in78, t91); // Eval big_Q Horner step: add coefficient_57 let t93 = circuit_mul(t92, in6); // Eval big_Q Horner step: multiply by z let t94 = circuit_add(in77, t93); // Eval big_Q Horner step: add coefficient_56 let t95 = circuit_mul(t94, in6); // Eval big_Q Horner step: multiply by z let t96 = circuit_add(in76, t95); // Eval big_Q Horner step: add coefficient_55 let t97 = circuit_mul(t96, in6); // Eval big_Q Horner step: multiply by z let t98 = circuit_add(in75, t97); // Eval big_Q Horner step: add coefficient_54 let t99 = circuit_mul(t98, in6); // Eval big_Q Horner step: multiply by z let t100 = circuit_add(in74, t99); // Eval big_Q Horner step: add coefficient_53 let t101 = circuit_mul(t100, in6); // Eval big_Q Horner step: multiply by z let t102 = circuit_add(in73, t101); // Eval big_Q Horner step: add coefficient_52 let t103 = circuit_mul(t102, in6); // Eval big_Q Horner step: multiply by z let t104 = circuit_add(in72, t103); // Eval big_Q Horner step: add coefficient_51 let t105 = circuit_mul(t104, in6); // Eval big_Q Horner step: multiply by z let t106 = circuit_add(in71, t105); // Eval big_Q Horner step: add coefficient_50 let t107 = circuit_mul(t106, in6); // Eval big_Q Horner step: multiply by z let t108 = circuit_add(in70, t107); // Eval big_Q Horner step: add coefficient_49 let t109 = circuit_mul(t108, in6); // Eval big_Q Horner step: multiply by z let t110 = circuit_add(in69, t109); // Eval big_Q Horner step: add coefficient_48 let t111 = circuit_mul(t110, in6); // Eval big_Q Horner step: multiply by z let t112 = circuit_add(in68, t111); // Eval big_Q Horner step: add coefficient_47 let t113 = circuit_mul(t112, in6); // Eval big_Q Horner step: multiply by z let t114 = circuit_add(in67, t113); // Eval big_Q Horner step: add coefficient_46 let t115 = circuit_mul(t114, in6); // Eval big_Q Horner step: multiply by z let t116 = circuit_add(in66, t115); // Eval big_Q Horner step: add coefficient_45 let t117 = circuit_mul(t116, in6); // Eval big_Q Horner step: multiply by z let t118 = circuit_add(in65, t117); // Eval big_Q Horner step: add coefficient_44 let t119 = circuit_mul(t118, in6); // Eval big_Q Horner step: multiply by z let t120 = circuit_add(in64, t119); // Eval big_Q Horner step: add coefficient_43 let t121 = circuit_mul(t120, in6); // Eval big_Q Horner step: multiply by z let t122 = circuit_add(in63, t121); // Eval big_Q Horner step: add coefficient_42 let t123 = circuit_mul(t122, in6); // Eval big_Q Horner step: multiply by z let t124 = circuit_add(in62, t123); // Eval big_Q Horner step: add coefficient_41 let t125 = circuit_mul(t124, in6); // Eval big_Q Horner step: multiply by z let t126 = circuit_add(in61, t125); // Eval big_Q Horner step: add coefficient_40 let t127 = circuit_mul(t126, in6); // Eval big_Q Horner step: multiply by z let t128 = circuit_add(in60, t127); // Eval big_Q Horner step: add coefficient_39 let t129 = circuit_mul(t128, in6); // Eval big_Q Horner step: multiply by z let t130 = circuit_add(in59, t129); // Eval big_Q Horner step: add coefficient_38 let t131 = circuit_mul(t130, in6); // Eval big_Q Horner step: multiply by z let t132 = circuit_add(in58, t131); // Eval big_Q Horner step: add coefficient_37 let t133 = circuit_mul(t132, in6); // Eval big_Q Horner step: multiply by z let t134 = circuit_add(in57, t133); // Eval big_Q Horner step: add coefficient_36 let t135 = circuit_mul(t134, in6); // Eval big_Q Horner step: multiply by z let t136 = circuit_add(in56, t135); // Eval big_Q Horner step: add coefficient_35 let t137 = circuit_mul(t136, in6); // Eval big_Q Horner step: multiply by z let t138 = circuit_add(in55, t137); // Eval big_Q Horner step: add coefficient_34 let t139 = circuit_mul(t138, in6); // Eval big_Q Horner step: multiply by z let t140 = circuit_add(in54, t139); // Eval big_Q Horner step: add coefficient_33 let t141 = circuit_mul(t140, in6); // Eval big_Q Horner step: multiply by z let t142 = circuit_add(in53, t141); // Eval big_Q Horner step: add coefficient_32 let t143 = circuit_mul(t142, in6); // Eval big_Q Horner step: multiply by z let t144 = circuit_add(in52, t143); // Eval big_Q Horner step: add coefficient_31 let t145 = circuit_mul(t144, in6); // Eval big_Q Horner step: multiply by z let t146 = circuit_add(in51, t145); // Eval big_Q Horner step: add coefficient_30 let t147 = circuit_mul(t146, in6); // Eval big_Q Horner step: multiply by z let t148 = circuit_add(in50, t147); // Eval big_Q Horner step: add coefficient_29 let t149 = circuit_mul(t148, in6); // Eval big_Q Horner step: multiply by z let t150 = circuit_add(in49, t149); // Eval big_Q Horner step: add coefficient_28 let t151 = circuit_mul(t150, in6); // Eval big_Q Horner step: multiply by z let t152 = circuit_add(in48, t151); // Eval big_Q Horner step: add coefficient_27 let t153 = circuit_mul(t152, in6); // Eval big_Q Horner step: multiply by z let t154 = circuit_add(in47, t153); // Eval big_Q Horner step: add coefficient_26 let t155 = circuit_mul(t154, in6); // Eval big_Q Horner step: multiply by z let t156 = circuit_add(in46, t155); // Eval big_Q Horner step: add coefficient_25 let t157 = circuit_mul(t156, in6); // Eval big_Q Horner step: multiply by z let t158 = circuit_add(in45, t157); // Eval big_Q Horner step: add coefficient_24 let t159 = circuit_mul(t158, in6); // Eval big_Q Horner step: multiply by z let t160 = circuit_add(in44, t159); // Eval big_Q Horner step: add coefficient_23 let t161 = circuit_mul(t160, in6); // Eval big_Q Horner step: multiply by z let t162 = circuit_add(in43, t161); // Eval big_Q Horner step: add coefficient_22 let t163 = circuit_mul(t162, in6); // Eval big_Q Horner step: multiply by z let t164 = circuit_add(in42, t163); // Eval big_Q Horner step: add coefficient_21 let t165 = circuit_mul(t164, in6); // Eval big_Q Horner step: multiply by z let t166 = circuit_add(in41, t165); // Eval big_Q Horner step: add coefficient_20 let t167 = circuit_mul(t166, in6); // Eval big_Q Horner step: multiply by z let t168 = circuit_add(in40, t167); // Eval big_Q Horner step: add coefficient_19 let t169 = circuit_mul(t168, in6); // Eval big_Q Horner step: multiply by z let t170 = circuit_add(in39, t169); // Eval big_Q Horner step: add coefficient_18 let t171 = circuit_mul(t170, in6); // Eval big_Q Horner step: multiply by z let t172 = circuit_add(in38, t171); // Eval big_Q Horner step: add coefficient_17 let t173 = circuit_mul(t172, in6); // Eval big_Q Horner step: multiply by z let t174 = circuit_add(in37, t173); // Eval big_Q Horner step: add coefficient_16 let t175 = circuit_mul(t174, in6); // Eval big_Q Horner step: multiply by z let t176 = circuit_add(in36, t175); // Eval big_Q Horner step: add coefficient_15 let t177 = circuit_mul(t176, in6); // Eval big_Q Horner step: multiply by z let t178 = circuit_add(in35, t177); // Eval big_Q Horner step: add coefficient_14 let t179 = circuit_mul(t178, in6); // Eval big_Q Horner step: multiply by z let t180 = circuit_add(in34, t179); // Eval big_Q Horner step: add coefficient_13 let t181 = circuit_mul(t180, in6); // Eval big_Q Horner step: multiply by z let t182 = circuit_add(in33, t181); // Eval big_Q Horner step: add coefficient_12 let t183 = circuit_mul(t182, in6); // Eval big_Q Horner step: multiply by z let t184 = circuit_add(in32, t183); // Eval big_Q Horner step: add coefficient_11 let t185 = circuit_mul(t184, in6); // Eval big_Q Horner step: multiply by z let t186 = circuit_add(in31, t185); // Eval big_Q Horner step: add coefficient_10 let t187 = circuit_mul(t186, in6); // Eval big_Q Horner step: multiply by z let t188 = circuit_add(in30, t187); // Eval big_Q Horner step: add coefficient_9 let t189 = circuit_mul(t188, in6); // Eval big_Q Horner step: multiply by z let t190 = circuit_add(in29, t189); // Eval big_Q Horner step: add coefficient_8 let t191 = circuit_mul(t190, in6); // Eval big_Q Horner step: multiply by z let t192 = circuit_add(in28, t191); // Eval big_Q Horner step: add coefficient_7 let t193 = circuit_mul(t192, in6); // Eval big_Q Horner step: multiply by z let t194 = circuit_add(in27, t193); // Eval big_Q Horner step: add coefficient_6 let t195 = circuit_mul(t194, in6); // Eval big_Q Horner step: multiply by z let t196 = circuit_add(in26, t195); // Eval big_Q Horner step: add coefficient_5 let t197 = circuit_mul(t196, in6); // Eval big_Q Horner step: multiply by z let t198 = circuit_add(in25, t197); // Eval big_Q Horner step: add coefficient_4 let t199 = circuit_mul(t198, in6); // Eval big_Q Horner step: multiply by z let t200 = circuit_add(in24, t199); // Eval big_Q Horner step: add coefficient_3 let t201 = circuit_mul(t200, in6); // Eval big_Q Horner step: multiply by z let t202 = circuit_add(in23, t201); // Eval big_Q Horner step: add coefficient_2 let t203 = circuit_mul(t202, in6); // Eval big_Q Horner step: multiply by z let t204 = circuit_add(in22, t203); // Eval big_Q Horner step: add coefficient_1 let t205 = circuit_mul(t204, in6); // Eval big_Q Horner step: multiply by z let t206 = circuit_add(in21, t205); // Eval big_Q Horner step: add coefficient_0 let t207 = circuit_mul(t206, t46); // Q(z) * P(z) let t208 = circuit_sub(t43, t207); // final_lhs - Q(z) * P(z) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t208,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x2, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [ 0xb153ffffb9feffffffffaaa9, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(R_n_minus_1_of_z); // in3 circuit_inputs = circuit_inputs.next_2(c_1); // in4 circuit_inputs = circuit_inputs.next_2(w_of_z); // in5 circuit_inputs = circuit_inputs.next_2(z); // in6 circuit_inputs = circuit_inputs.next_2(c_inv_frob_1_of_z); // in7 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in8 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w0); // in9 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w1); // in10 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w2); // in11 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w3); // in12 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w4); // in13 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w5); // in14 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w6); // in15 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w7); // in16 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w8); // in17 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w9); // in18 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w10); // in19 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w11); // in20 for val in Q.span() { circuit_inputs = circuit_inputs.next_2(*val); } // in21 - in101 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let final_check: u384 = outputs.get_output(t208); return (final_check,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_FINALIZE_3P_EXT_MLR_circuit( R_n_minus_1_of_z: u384, c_1: u384, w_of_z: u384, z: u384, c_inv_frob_1_of_z: u384, previous_lhs: u384, R_n_minus_2: E12D, Q: Array, precomputed_miller_loop_result_of_z: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x2 let in2 = CE::> {}; // -0x2 % p // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let (in33, in34, in35) = (CE::> {}, CE::> {}, CE::> {}); let (in36, in37, in38) = (CE::> {}, CE::> {}, CE::> {}); let (in39, in40, in41) = (CE::> {}, CE::> {}, CE::> {}); let (in42, in43, in44) = (CE::> {}, CE::> {}, CE::> {}); let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76, in77) = (CE::> {}, CE::> {}, CE::> {}); let (in78, in79, in80) = (CE::> {}, CE::> {}, CE::> {}); let (in81, in82, in83) = (CE::> {}, CE::> {}, CE::> {}); let (in84, in85, in86) = (CE::> {}, CE::> {}, CE::> {}); let (in87, in88, in89) = (CE::> {}, CE::> {}, CE::> {}); let (in90, in91, in92) = (CE::> {}, CE::> {}, CE::> {}); let (in93, in94, in95) = (CE::> {}, CE::> {}, CE::> {}); let (in96, in97, in98) = (CE::> {}, CE::> {}, CE::> {}); let (in99, in100, in101) = (CE::> {}, CE::> {}, CE::> {}); let (in102, in103, in104) = (CE::> {}, CE::> {}, CE::> {}); let (in105, in106, in107) = (CE::> {}, CE::> {}, CE::> {}); let (in108, in109, in110) = (CE::> {}, CE::> {}, CE::> {}); let (in111, in112, in113) = (CE::> {}, CE::> {}, CE::> {}); let (in114, in115, in116) = (CE::> {}, CE::> {}, CE::> {}); let (in117, in118, in119) = (CE::> {}, CE::> {}, CE::> {}); let (in120, in121, in122) = (CE::> {}, CE::> {}, CE::> {}); let (in123, in124, in125) = (CE::> {}, CE::> {}, CE::> {}); let in126 = CE::> {}; let t0 = circuit_mul(in6, in6); // Compute z^2 let t1 = circuit_mul(t0, in6); // Compute z^3 let t2 = circuit_mul(t1, in6); // Compute z^4 let t3 = circuit_mul(t2, in6); // Compute z^5 let t4 = circuit_mul(t3, in6); // Compute z^6 let t5 = circuit_mul(t4, in6); // Compute z^7 let t6 = circuit_mul(t5, in6); // Compute z^8 let t7 = circuit_mul(t6, in6); // Compute z^9 let t8 = circuit_mul(t7, in6); // Compute z^10 let t9 = circuit_mul(t8, in6); // Compute z^11 let t10 = circuit_mul(t9, in6); // Compute z^12 let t11 = circuit_sub(in0, in10); let t12 = circuit_sub(in0, in12); let t13 = circuit_sub(in0, in14); let t14 = circuit_sub(in0, in16); let t15 = circuit_sub(in0, in18); let t16 = circuit_sub(in0, in20); let t17 = circuit_mul(t11, in6); // Eval R_n_minus_2_conjugate step coeff_1 * z^1 let t18 = circuit_add(in9, t17); // Eval R_n_minus_2_conjugate step + (coeff_1 * z^1) let t19 = circuit_mul(in11, t0); // Eval R_n_minus_2_conjugate step coeff_2 * z^2 let t20 = circuit_add(t18, t19); // Eval R_n_minus_2_conjugate step + (coeff_2 * z^2) let t21 = circuit_mul(t12, t1); // Eval R_n_minus_2_conjugate step coeff_3 * z^3 let t22 = circuit_add(t20, t21); // Eval R_n_minus_2_conjugate step + (coeff_3 * z^3) let t23 = circuit_mul(in13, t2); // Eval R_n_minus_2_conjugate step coeff_4 * z^4 let t24 = circuit_add(t22, t23); // Eval R_n_minus_2_conjugate step + (coeff_4 * z^4) let t25 = circuit_mul(t13, t3); // Eval R_n_minus_2_conjugate step coeff_5 * z^5 let t26 = circuit_add(t24, t25); // Eval R_n_minus_2_conjugate step + (coeff_5 * z^5) let t27 = circuit_mul(in15, t4); // Eval R_n_minus_2_conjugate step coeff_6 * z^6 let t28 = circuit_add(t26, t27); // Eval R_n_minus_2_conjugate step + (coeff_6 * z^6) let t29 = circuit_mul(t14, t5); // Eval R_n_minus_2_conjugate step coeff_7 * z^7 let t30 = circuit_add(t28, t29); // Eval R_n_minus_2_conjugate step + (coeff_7 * z^7) let t31 = circuit_mul(in17, t6); // Eval R_n_minus_2_conjugate step coeff_8 * z^8 let t32 = circuit_add(t30, t31); // Eval R_n_minus_2_conjugate step + (coeff_8 * z^8) let t33 = circuit_mul(t15, t7); // Eval R_n_minus_2_conjugate step coeff_9 * z^9 let t34 = circuit_add(t32, t33); // Eval R_n_minus_2_conjugate step + (coeff_9 * z^9) let t35 = circuit_mul(in19, t8); // Eval R_n_minus_2_conjugate step coeff_10 * z^10 let t36 = circuit_add(t34, t35); // Eval R_n_minus_2_conjugate step + (coeff_10 * z^10) let t37 = circuit_mul(t16, t9); // Eval R_n_minus_2_conjugate step coeff_11 * z^11 let t38 = circuit_add(t36, t37); // Eval R_n_minus_2_conjugate step + (coeff_11 * z^11) let t39 = circuit_mul(t38, in7); let t40 = circuit_mul(t39, in5); let t41 = circuit_mul(t40, in126); let t42 = circuit_sub(t41, in3); // (Π(n-1,k) (Pk(z)) - R_n_minus_1(z)) let t43 = circuit_mul(in4, in8); let t44 = circuit_add(t43, t42); // c_1 * previous_lhs + lhs_n_minus_1 let t45 = circuit_mul(in2, t4); // Eval sparse poly P_irr step coeff_6 * z^6 let t46 = circuit_add(in1, t45); // Eval sparse poly P_irr step + coeff_6 * z^6 let t47 = circuit_add(t46, t10); // Eval sparse poly P_irr step + 1*z^12 let t48 = circuit_mul(in125, in6); // Eval big_Q Horner step: multiply by z let t49 = circuit_add(in124, t48); // Eval big_Q Horner step: add coefficient_103 let t50 = circuit_mul(t49, in6); // Eval big_Q Horner step: multiply by z let t51 = circuit_add(in123, t50); // Eval big_Q Horner step: add coefficient_102 let t52 = circuit_mul(t51, in6); // Eval big_Q Horner step: multiply by z let t53 = circuit_add(in122, t52); // Eval big_Q Horner step: add coefficient_101 let t54 = circuit_mul(t53, in6); // Eval big_Q Horner step: multiply by z let t55 = circuit_add(in121, t54); // Eval big_Q Horner step: add coefficient_100 let t56 = circuit_mul(t55, in6); // Eval big_Q Horner step: multiply by z let t57 = circuit_add(in120, t56); // Eval big_Q Horner step: add coefficient_99 let t58 = circuit_mul(t57, in6); // Eval big_Q Horner step: multiply by z let t59 = circuit_add(in119, t58); // Eval big_Q Horner step: add coefficient_98 let t60 = circuit_mul(t59, in6); // Eval big_Q Horner step: multiply by z let t61 = circuit_add(in118, t60); // Eval big_Q Horner step: add coefficient_97 let t62 = circuit_mul(t61, in6); // Eval big_Q Horner step: multiply by z let t63 = circuit_add(in117, t62); // Eval big_Q Horner step: add coefficient_96 let t64 = circuit_mul(t63, in6); // Eval big_Q Horner step: multiply by z let t65 = circuit_add(in116, t64); // Eval big_Q Horner step: add coefficient_95 let t66 = circuit_mul(t65, in6); // Eval big_Q Horner step: multiply by z let t67 = circuit_add(in115, t66); // Eval big_Q Horner step: add coefficient_94 let t68 = circuit_mul(t67, in6); // Eval big_Q Horner step: multiply by z let t69 = circuit_add(in114, t68); // Eval big_Q Horner step: add coefficient_93 let t70 = circuit_mul(t69, in6); // Eval big_Q Horner step: multiply by z let t71 = circuit_add(in113, t70); // Eval big_Q Horner step: add coefficient_92 let t72 = circuit_mul(t71, in6); // Eval big_Q Horner step: multiply by z let t73 = circuit_add(in112, t72); // Eval big_Q Horner step: add coefficient_91 let t74 = circuit_mul(t73, in6); // Eval big_Q Horner step: multiply by z let t75 = circuit_add(in111, t74); // Eval big_Q Horner step: add coefficient_90 let t76 = circuit_mul(t75, in6); // Eval big_Q Horner step: multiply by z let t77 = circuit_add(in110, t76); // Eval big_Q Horner step: add coefficient_89 let t78 = circuit_mul(t77, in6); // Eval big_Q Horner step: multiply by z let t79 = circuit_add(in109, t78); // Eval big_Q Horner step: add coefficient_88 let t80 = circuit_mul(t79, in6); // Eval big_Q Horner step: multiply by z let t81 = circuit_add(in108, t80); // Eval big_Q Horner step: add coefficient_87 let t82 = circuit_mul(t81, in6); // Eval big_Q Horner step: multiply by z let t83 = circuit_add(in107, t82); // Eval big_Q Horner step: add coefficient_86 let t84 = circuit_mul(t83, in6); // Eval big_Q Horner step: multiply by z let t85 = circuit_add(in106, t84); // Eval big_Q Horner step: add coefficient_85 let t86 = circuit_mul(t85, in6); // Eval big_Q Horner step: multiply by z let t87 = circuit_add(in105, t86); // Eval big_Q Horner step: add coefficient_84 let t88 = circuit_mul(t87, in6); // Eval big_Q Horner step: multiply by z let t89 = circuit_add(in104, t88); // Eval big_Q Horner step: add coefficient_83 let t90 = circuit_mul(t89, in6); // Eval big_Q Horner step: multiply by z let t91 = circuit_add(in103, t90); // Eval big_Q Horner step: add coefficient_82 let t92 = circuit_mul(t91, in6); // Eval big_Q Horner step: multiply by z let t93 = circuit_add(in102, t92); // Eval big_Q Horner step: add coefficient_81 let t94 = circuit_mul(t93, in6); // Eval big_Q Horner step: multiply by z let t95 = circuit_add(in101, t94); // Eval big_Q Horner step: add coefficient_80 let t96 = circuit_mul(t95, in6); // Eval big_Q Horner step: multiply by z let t97 = circuit_add(in100, t96); // Eval big_Q Horner step: add coefficient_79 let t98 = circuit_mul(t97, in6); // Eval big_Q Horner step: multiply by z let t99 = circuit_add(in99, t98); // Eval big_Q Horner step: add coefficient_78 let t100 = circuit_mul(t99, in6); // Eval big_Q Horner step: multiply by z let t101 = circuit_add(in98, t100); // Eval big_Q Horner step: add coefficient_77 let t102 = circuit_mul(t101, in6); // Eval big_Q Horner step: multiply by z let t103 = circuit_add(in97, t102); // Eval big_Q Horner step: add coefficient_76 let t104 = circuit_mul(t103, in6); // Eval big_Q Horner step: multiply by z let t105 = circuit_add(in96, t104); // Eval big_Q Horner step: add coefficient_75 let t106 = circuit_mul(t105, in6); // Eval big_Q Horner step: multiply by z let t107 = circuit_add(in95, t106); // Eval big_Q Horner step: add coefficient_74 let t108 = circuit_mul(t107, in6); // Eval big_Q Horner step: multiply by z let t109 = circuit_add(in94, t108); // Eval big_Q Horner step: add coefficient_73 let t110 = circuit_mul(t109, in6); // Eval big_Q Horner step: multiply by z let t111 = circuit_add(in93, t110); // Eval big_Q Horner step: add coefficient_72 let t112 = circuit_mul(t111, in6); // Eval big_Q Horner step: multiply by z let t113 = circuit_add(in92, t112); // Eval big_Q Horner step: add coefficient_71 let t114 = circuit_mul(t113, in6); // Eval big_Q Horner step: multiply by z let t115 = circuit_add(in91, t114); // Eval big_Q Horner step: add coefficient_70 let t116 = circuit_mul(t115, in6); // Eval big_Q Horner step: multiply by z let t117 = circuit_add(in90, t116); // Eval big_Q Horner step: add coefficient_69 let t118 = circuit_mul(t117, in6); // Eval big_Q Horner step: multiply by z let t119 = circuit_add(in89, t118); // Eval big_Q Horner step: add coefficient_68 let t120 = circuit_mul(t119, in6); // Eval big_Q Horner step: multiply by z let t121 = circuit_add(in88, t120); // Eval big_Q Horner step: add coefficient_67 let t122 = circuit_mul(t121, in6); // Eval big_Q Horner step: multiply by z let t123 = circuit_add(in87, t122); // Eval big_Q Horner step: add coefficient_66 let t124 = circuit_mul(t123, in6); // Eval big_Q Horner step: multiply by z let t125 = circuit_add(in86, t124); // Eval big_Q Horner step: add coefficient_65 let t126 = circuit_mul(t125, in6); // Eval big_Q Horner step: multiply by z let t127 = circuit_add(in85, t126); // Eval big_Q Horner step: add coefficient_64 let t128 = circuit_mul(t127, in6); // Eval big_Q Horner step: multiply by z let t129 = circuit_add(in84, t128); // Eval big_Q Horner step: add coefficient_63 let t130 = circuit_mul(t129, in6); // Eval big_Q Horner step: multiply by z let t131 = circuit_add(in83, t130); // Eval big_Q Horner step: add coefficient_62 let t132 = circuit_mul(t131, in6); // Eval big_Q Horner step: multiply by z let t133 = circuit_add(in82, t132); // Eval big_Q Horner step: add coefficient_61 let t134 = circuit_mul(t133, in6); // Eval big_Q Horner step: multiply by z let t135 = circuit_add(in81, t134); // Eval big_Q Horner step: add coefficient_60 let t136 = circuit_mul(t135, in6); // Eval big_Q Horner step: multiply by z let t137 = circuit_add(in80, t136); // Eval big_Q Horner step: add coefficient_59 let t138 = circuit_mul(t137, in6); // Eval big_Q Horner step: multiply by z let t139 = circuit_add(in79, t138); // Eval big_Q Horner step: add coefficient_58 let t140 = circuit_mul(t139, in6); // Eval big_Q Horner step: multiply by z let t141 = circuit_add(in78, t140); // Eval big_Q Horner step: add coefficient_57 let t142 = circuit_mul(t141, in6); // Eval big_Q Horner step: multiply by z let t143 = circuit_add(in77, t142); // Eval big_Q Horner step: add coefficient_56 let t144 = circuit_mul(t143, in6); // Eval big_Q Horner step: multiply by z let t145 = circuit_add(in76, t144); // Eval big_Q Horner step: add coefficient_55 let t146 = circuit_mul(t145, in6); // Eval big_Q Horner step: multiply by z let t147 = circuit_add(in75, t146); // Eval big_Q Horner step: add coefficient_54 let t148 = circuit_mul(t147, in6); // Eval big_Q Horner step: multiply by z let t149 = circuit_add(in74, t148); // Eval big_Q Horner step: add coefficient_53 let t150 = circuit_mul(t149, in6); // Eval big_Q Horner step: multiply by z let t151 = circuit_add(in73, t150); // Eval big_Q Horner step: add coefficient_52 let t152 = circuit_mul(t151, in6); // Eval big_Q Horner step: multiply by z let t153 = circuit_add(in72, t152); // Eval big_Q Horner step: add coefficient_51 let t154 = circuit_mul(t153, in6); // Eval big_Q Horner step: multiply by z let t155 = circuit_add(in71, t154); // Eval big_Q Horner step: add coefficient_50 let t156 = circuit_mul(t155, in6); // Eval big_Q Horner step: multiply by z let t157 = circuit_add(in70, t156); // Eval big_Q Horner step: add coefficient_49 let t158 = circuit_mul(t157, in6); // Eval big_Q Horner step: multiply by z let t159 = circuit_add(in69, t158); // Eval big_Q Horner step: add coefficient_48 let t160 = circuit_mul(t159, in6); // Eval big_Q Horner step: multiply by z let t161 = circuit_add(in68, t160); // Eval big_Q Horner step: add coefficient_47 let t162 = circuit_mul(t161, in6); // Eval big_Q Horner step: multiply by z let t163 = circuit_add(in67, t162); // Eval big_Q Horner step: add coefficient_46 let t164 = circuit_mul(t163, in6); // Eval big_Q Horner step: multiply by z let t165 = circuit_add(in66, t164); // Eval big_Q Horner step: add coefficient_45 let t166 = circuit_mul(t165, in6); // Eval big_Q Horner step: multiply by z let t167 = circuit_add(in65, t166); // Eval big_Q Horner step: add coefficient_44 let t168 = circuit_mul(t167, in6); // Eval big_Q Horner step: multiply by z let t169 = circuit_add(in64, t168); // Eval big_Q Horner step: add coefficient_43 let t170 = circuit_mul(t169, in6); // Eval big_Q Horner step: multiply by z let t171 = circuit_add(in63, t170); // Eval big_Q Horner step: add coefficient_42 let t172 = circuit_mul(t171, in6); // Eval big_Q Horner step: multiply by z let t173 = circuit_add(in62, t172); // Eval big_Q Horner step: add coefficient_41 let t174 = circuit_mul(t173, in6); // Eval big_Q Horner step: multiply by z let t175 = circuit_add(in61, t174); // Eval big_Q Horner step: add coefficient_40 let t176 = circuit_mul(t175, in6); // Eval big_Q Horner step: multiply by z let t177 = circuit_add(in60, t176); // Eval big_Q Horner step: add coefficient_39 let t178 = circuit_mul(t177, in6); // Eval big_Q Horner step: multiply by z let t179 = circuit_add(in59, t178); // Eval big_Q Horner step: add coefficient_38 let t180 = circuit_mul(t179, in6); // Eval big_Q Horner step: multiply by z let t181 = circuit_add(in58, t180); // Eval big_Q Horner step: add coefficient_37 let t182 = circuit_mul(t181, in6); // Eval big_Q Horner step: multiply by z let t183 = circuit_add(in57, t182); // Eval big_Q Horner step: add coefficient_36 let t184 = circuit_mul(t183, in6); // Eval big_Q Horner step: multiply by z let t185 = circuit_add(in56, t184); // Eval big_Q Horner step: add coefficient_35 let t186 = circuit_mul(t185, in6); // Eval big_Q Horner step: multiply by z let t187 = circuit_add(in55, t186); // Eval big_Q Horner step: add coefficient_34 let t188 = circuit_mul(t187, in6); // Eval big_Q Horner step: multiply by z let t189 = circuit_add(in54, t188); // Eval big_Q Horner step: add coefficient_33 let t190 = circuit_mul(t189, in6); // Eval big_Q Horner step: multiply by z let t191 = circuit_add(in53, t190); // Eval big_Q Horner step: add coefficient_32 let t192 = circuit_mul(t191, in6); // Eval big_Q Horner step: multiply by z let t193 = circuit_add(in52, t192); // Eval big_Q Horner step: add coefficient_31 let t194 = circuit_mul(t193, in6); // Eval big_Q Horner step: multiply by z let t195 = circuit_add(in51, t194); // Eval big_Q Horner step: add coefficient_30 let t196 = circuit_mul(t195, in6); // Eval big_Q Horner step: multiply by z let t197 = circuit_add(in50, t196); // Eval big_Q Horner step: add coefficient_29 let t198 = circuit_mul(t197, in6); // Eval big_Q Horner step: multiply by z let t199 = circuit_add(in49, t198); // Eval big_Q Horner step: add coefficient_28 let t200 = circuit_mul(t199, in6); // Eval big_Q Horner step: multiply by z let t201 = circuit_add(in48, t200); // Eval big_Q Horner step: add coefficient_27 let t202 = circuit_mul(t201, in6); // Eval big_Q Horner step: multiply by z let t203 = circuit_add(in47, t202); // Eval big_Q Horner step: add coefficient_26 let t204 = circuit_mul(t203, in6); // Eval big_Q Horner step: multiply by z let t205 = circuit_add(in46, t204); // Eval big_Q Horner step: add coefficient_25 let t206 = circuit_mul(t205, in6); // Eval big_Q Horner step: multiply by z let t207 = circuit_add(in45, t206); // Eval big_Q Horner step: add coefficient_24 let t208 = circuit_mul(t207, in6); // Eval big_Q Horner step: multiply by z let t209 = circuit_add(in44, t208); // Eval big_Q Horner step: add coefficient_23 let t210 = circuit_mul(t209, in6); // Eval big_Q Horner step: multiply by z let t211 = circuit_add(in43, t210); // Eval big_Q Horner step: add coefficient_22 let t212 = circuit_mul(t211, in6); // Eval big_Q Horner step: multiply by z let t213 = circuit_add(in42, t212); // Eval big_Q Horner step: add coefficient_21 let t214 = circuit_mul(t213, in6); // Eval big_Q Horner step: multiply by z let t215 = circuit_add(in41, t214); // Eval big_Q Horner step: add coefficient_20 let t216 = circuit_mul(t215, in6); // Eval big_Q Horner step: multiply by z let t217 = circuit_add(in40, t216); // Eval big_Q Horner step: add coefficient_19 let t218 = circuit_mul(t217, in6); // Eval big_Q Horner step: multiply by z let t219 = circuit_add(in39, t218); // Eval big_Q Horner step: add coefficient_18 let t220 = circuit_mul(t219, in6); // Eval big_Q Horner step: multiply by z let t221 = circuit_add(in38, t220); // Eval big_Q Horner step: add coefficient_17 let t222 = circuit_mul(t221, in6); // Eval big_Q Horner step: multiply by z let t223 = circuit_add(in37, t222); // Eval big_Q Horner step: add coefficient_16 let t224 = circuit_mul(t223, in6); // Eval big_Q Horner step: multiply by z let t225 = circuit_add(in36, t224); // Eval big_Q Horner step: add coefficient_15 let t226 = circuit_mul(t225, in6); // Eval big_Q Horner step: multiply by z let t227 = circuit_add(in35, t226); // Eval big_Q Horner step: add coefficient_14 let t228 = circuit_mul(t227, in6); // Eval big_Q Horner step: multiply by z let t229 = circuit_add(in34, t228); // Eval big_Q Horner step: add coefficient_13 let t230 = circuit_mul(t229, in6); // Eval big_Q Horner step: multiply by z let t231 = circuit_add(in33, t230); // Eval big_Q Horner step: add coefficient_12 let t232 = circuit_mul(t231, in6); // Eval big_Q Horner step: multiply by z let t233 = circuit_add(in32, t232); // Eval big_Q Horner step: add coefficient_11 let t234 = circuit_mul(t233, in6); // Eval big_Q Horner step: multiply by z let t235 = circuit_add(in31, t234); // Eval big_Q Horner step: add coefficient_10 let t236 = circuit_mul(t235, in6); // Eval big_Q Horner step: multiply by z let t237 = circuit_add(in30, t236); // Eval big_Q Horner step: add coefficient_9 let t238 = circuit_mul(t237, in6); // Eval big_Q Horner step: multiply by z let t239 = circuit_add(in29, t238); // Eval big_Q Horner step: add coefficient_8 let t240 = circuit_mul(t239, in6); // Eval big_Q Horner step: multiply by z let t241 = circuit_add(in28, t240); // Eval big_Q Horner step: add coefficient_7 let t242 = circuit_mul(t241, in6); // Eval big_Q Horner step: multiply by z let t243 = circuit_add(in27, t242); // Eval big_Q Horner step: add coefficient_6 let t244 = circuit_mul(t243, in6); // Eval big_Q Horner step: multiply by z let t245 = circuit_add(in26, t244); // Eval big_Q Horner step: add coefficient_5 let t246 = circuit_mul(t245, in6); // Eval big_Q Horner step: multiply by z let t247 = circuit_add(in25, t246); // Eval big_Q Horner step: add coefficient_4 let t248 = circuit_mul(t247, in6); // Eval big_Q Horner step: multiply by z let t249 = circuit_add(in24, t248); // Eval big_Q Horner step: add coefficient_3 let t250 = circuit_mul(t249, in6); // Eval big_Q Horner step: multiply by z let t251 = circuit_add(in23, t250); // Eval big_Q Horner step: add coefficient_2 let t252 = circuit_mul(t251, in6); // Eval big_Q Horner step: multiply by z let t253 = circuit_add(in22, t252); // Eval big_Q Horner step: add coefficient_1 let t254 = circuit_mul(t253, in6); // Eval big_Q Horner step: multiply by z let t255 = circuit_add(in21, t254); // Eval big_Q Horner step: add coefficient_0 let t256 = circuit_mul(t255, t47); // Q(z) * P(z) let t257 = circuit_sub(t44, t256); // final_lhs - Q(z) * P(z) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t257,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x2, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [ 0xb153ffffb9feffffffffaaa9, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(R_n_minus_1_of_z); // in3 circuit_inputs = circuit_inputs.next_2(c_1); // in4 circuit_inputs = circuit_inputs.next_2(w_of_z); // in5 circuit_inputs = circuit_inputs.next_2(z); // in6 circuit_inputs = circuit_inputs.next_2(c_inv_frob_1_of_z); // in7 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in8 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w0); // in9 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w1); // in10 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w2); // in11 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w3); // in12 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w4); // in13 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w5); // in14 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w6); // in15 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w7); // in16 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w8); // in17 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w9); // in18 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w10); // in19 circuit_inputs = circuit_inputs.next_2(R_n_minus_2.w11); // in20 for val in Q.span() { circuit_inputs = circuit_inputs.next_2(*val); } // in21 - in125 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result_of_z); // in126 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let final_check: u384 = outputs.get_output(t257); return (final_check,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_INIT_BIT_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_0: G2Line, G2_line_0_2: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_1: G2Line, G2_line_1_2: G2Line, R_i_of_z: u384, z: u384, c_inv_of_z: u384, ) -> (u384,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in21, in21); // compute z^2 let t1 = circuit_mul(t0, in21); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in22, in22); let t5 = circuit_mul(in22, t4); let t6 = circuit_sub(in4, in5); let t7 = circuit_mul(t6, in0); // eval bls line by yInv let t8 = circuit_sub(in2, in3); let t9 = circuit_mul(t8, in1); // eval blsline by xNegOverY let t10 = circuit_mul(in5, in0); // eval bls line by yInv let t11 = circuit_mul(in3, in1); // eval bls line by xNegOverY let t12 = circuit_sub(in8, in9); let t13 = circuit_mul(t12, in0); // eval bls line by yInv let t14 = circuit_sub(in6, in7); let t15 = circuit_mul(t14, in1); // eval blsline by xNegOverY let t16 = circuit_mul(in9, in0); // eval bls line by yInv let t17 = circuit_mul(in7, in1); // eval bls line by xNegOverY let t18 = circuit_mul(t9, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t19 = circuit_add(t7, t18); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t20 = circuit_add(t19, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t21 = circuit_mul(t10, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t22 = circuit_add(t20, t21); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t23 = circuit_mul(t11, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t24 = circuit_add(t22, t23); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t25 = circuit_mul(t5, t24); let t26 = circuit_mul(t15, t0); // Eval sparse poly line_0p_2 step coeff_2 * z^2 let t27 = circuit_add(t13, t26); // Eval sparse poly line_0p_2 step + coeff_2 * z^2 let t28 = circuit_add(t27, t1); // Eval sparse poly line_0p_2 step + 1*z^3 let t29 = circuit_mul(t16, t2); // Eval sparse poly line_0p_2 step coeff_6 * z^6 let t30 = circuit_add(t28, t29); // Eval sparse poly line_0p_2 step + coeff_6 * z^6 let t31 = circuit_mul(t17, t3); // Eval sparse poly line_0p_2 step coeff_8 * z^8 let t32 = circuit_add(t30, t31); // Eval sparse poly line_0p_2 step + coeff_8 * z^8 let t33 = circuit_mul(t25, t32); let t34 = circuit_sub(in14, in15); let t35 = circuit_mul(t34, in10); // eval bls line by yInv let t36 = circuit_sub(in12, in13); let t37 = circuit_mul(t36, in11); // eval blsline by xNegOverY let t38 = circuit_mul(in15, in10); // eval bls line by yInv let t39 = circuit_mul(in13, in11); // eval bls line by xNegOverY let t40 = circuit_sub(in18, in19); let t41 = circuit_mul(t40, in10); // eval bls line by yInv let t42 = circuit_sub(in16, in17); let t43 = circuit_mul(t42, in11); // eval blsline by xNegOverY let t44 = circuit_mul(in19, in10); // eval bls line by yInv let t45 = circuit_mul(in17, in11); // eval bls line by xNegOverY let t46 = circuit_mul(t37, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t47 = circuit_add(t35, t46); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t48 = circuit_add(t47, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t49 = circuit_mul(t38, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t50 = circuit_add(t48, t49); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t51 = circuit_mul(t39, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t52 = circuit_add(t50, t51); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t53 = circuit_mul(t33, t52); let t54 = circuit_mul(t43, t0); // Eval sparse poly line_1p_2 step coeff_2 * z^2 let t55 = circuit_add(t41, t54); // Eval sparse poly line_1p_2 step + coeff_2 * z^2 let t56 = circuit_add(t55, t1); // Eval sparse poly line_1p_2 step + 1*z^3 let t57 = circuit_mul(t44, t2); // Eval sparse poly line_1p_2 step coeff_6 * z^6 let t58 = circuit_add(t56, t57); // Eval sparse poly line_1p_2 step + coeff_6 * z^6 let t59 = circuit_mul(t45, t3); // Eval sparse poly line_1p_2 step coeff_8 * z^8 let t60 = circuit_add(t58, t59); // Eval sparse poly line_1p_2 step + coeff_8 * z^8 let t61 = circuit_mul(t53, t60); let t62 = circuit_sub(t61, in20); // ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t62,).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in0 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in1 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a0); // in2 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a1); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r0a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r0a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r1a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r1a1); // in9 circuit_inputs = circuit_inputs.next_2(yInv_1); // in10 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r0a0); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r0a1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r1a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r1a1); // in19 circuit_inputs = circuit_inputs.next_2(R_i_of_z); // in20 circuit_inputs = circuit_inputs.next_2(z); // in21 circuit_inputs = circuit_inputs.next_2(c_inv_of_z); // in22 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let new_lhs: u384 = outputs.get_output(t62); return (new_lhs,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_INIT_BIT_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_0: G2Line, G2_line_0_2: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_1: G2Line, G2_line_1_2: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, R_i_of_z: u384, z: u384, c_inv_of_z: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x3 let in1 = CE::> {}; // 0x6 let in2 = CE::> {}; // 0x0 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in30, in30); // compute z^2 let t1 = circuit_mul(t0, in30); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, t0); // compute z^8 let t4 = circuit_mul(in31, in31); let t5 = circuit_mul(in31, t4); let t6 = circuit_sub(in7, in8); let t7 = circuit_mul(t6, in3); // eval bls line by yInv let t8 = circuit_sub(in5, in6); let t9 = circuit_mul(t8, in4); // eval blsline by xNegOverY let t10 = circuit_mul(in8, in3); // eval bls line by yInv let t11 = circuit_mul(in6, in4); // eval bls line by xNegOverY let t12 = circuit_sub(in11, in12); let t13 = circuit_mul(t12, in3); // eval bls line by yInv let t14 = circuit_sub(in9, in10); let t15 = circuit_mul(t14, in4); // eval blsline by xNegOverY let t16 = circuit_mul(in12, in3); // eval bls line by yInv let t17 = circuit_mul(in10, in4); // eval bls line by xNegOverY let t18 = circuit_mul(t9, t0); // Eval sparse poly line_0p_1 step coeff_2 * z^2 let t19 = circuit_add(t7, t18); // Eval sparse poly line_0p_1 step + coeff_2 * z^2 let t20 = circuit_add(t19, t1); // Eval sparse poly line_0p_1 step + 1*z^3 let t21 = circuit_mul(t10, t2); // Eval sparse poly line_0p_1 step coeff_6 * z^6 let t22 = circuit_add(t20, t21); // Eval sparse poly line_0p_1 step + coeff_6 * z^6 let t23 = circuit_mul(t11, t3); // Eval sparse poly line_0p_1 step coeff_8 * z^8 let t24 = circuit_add(t22, t23); // Eval sparse poly line_0p_1 step + coeff_8 * z^8 let t25 = circuit_mul(t5, t24); let t26 = circuit_mul(t15, t0); // Eval sparse poly line_0p_2 step coeff_2 * z^2 let t27 = circuit_add(t13, t26); // Eval sparse poly line_0p_2 step + coeff_2 * z^2 let t28 = circuit_add(t27, t1); // Eval sparse poly line_0p_2 step + 1*z^3 let t29 = circuit_mul(t16, t2); // Eval sparse poly line_0p_2 step coeff_6 * z^6 let t30 = circuit_add(t28, t29); // Eval sparse poly line_0p_2 step + coeff_6 * z^6 let t31 = circuit_mul(t17, t3); // Eval sparse poly line_0p_2 step coeff_8 * z^8 let t32 = circuit_add(t30, t31); // Eval sparse poly line_0p_2 step + coeff_8 * z^8 let t33 = circuit_mul(t25, t32); let t34 = circuit_sub(in17, in18); let t35 = circuit_mul(t34, in13); // eval bls line by yInv let t36 = circuit_sub(in15, in16); let t37 = circuit_mul(t36, in14); // eval blsline by xNegOverY let t38 = circuit_mul(in18, in13); // eval bls line by yInv let t39 = circuit_mul(in16, in14); // eval bls line by xNegOverY let t40 = circuit_sub(in21, in22); let t41 = circuit_mul(t40, in13); // eval bls line by yInv let t42 = circuit_sub(in19, in20); let t43 = circuit_mul(t42, in14); // eval blsline by xNegOverY let t44 = circuit_mul(in22, in13); // eval bls line by yInv let t45 = circuit_mul(in20, in14); // eval bls line by xNegOverY let t46 = circuit_mul(t37, t0); // Eval sparse poly line_1p_1 step coeff_2 * z^2 let t47 = circuit_add(t35, t46); // Eval sparse poly line_1p_1 step + coeff_2 * z^2 let t48 = circuit_add(t47, t1); // Eval sparse poly line_1p_1 step + 1*z^3 let t49 = circuit_mul(t38, t2); // Eval sparse poly line_1p_1 step coeff_6 * z^6 let t50 = circuit_add(t48, t49); // Eval sparse poly line_1p_1 step + coeff_6 * z^6 let t51 = circuit_mul(t39, t3); // Eval sparse poly line_1p_1 step coeff_8 * z^8 let t52 = circuit_add(t50, t51); // Eval sparse poly line_1p_1 step + coeff_8 * z^8 let t53 = circuit_mul(t33, t52); let t54 = circuit_mul(t43, t0); // Eval sparse poly line_1p_2 step coeff_2 * z^2 let t55 = circuit_add(t41, t54); // Eval sparse poly line_1p_2 step + coeff_2 * z^2 let t56 = circuit_add(t55, t1); // Eval sparse poly line_1p_2 step + 1*z^3 let t57 = circuit_mul(t44, t2); // Eval sparse poly line_1p_2 step coeff_6 * z^6 let t58 = circuit_add(t56, t57); // Eval sparse poly line_1p_2 step + coeff_6 * z^6 let t59 = circuit_mul(t45, t3); // Eval sparse poly line_1p_2 step coeff_8 * z^8 let t60 = circuit_add(t58, t59); // Eval sparse poly line_1p_2 step + coeff_8 * z^8 let t61 = circuit_mul(t53, t60); let t62 = circuit_add(in25, in26); let t63 = circuit_sub(in25, in26); let t64 = circuit_mul(t62, t63); let t65 = circuit_mul(in25, in26); let t66 = circuit_mul(t64, in0); let t67 = circuit_mul(t65, in1); let t68 = circuit_add(in27, in27); // Fp2 add coeff 0/1 let t69 = circuit_add(in28, in28); // Fp2 add coeff 1/1 let t70 = circuit_mul(t68, t68); // Fp2 Inv start let t71 = circuit_mul(t69, t69); let t72 = circuit_add(t70, t71); let t73 = circuit_inverse(t72); let t74 = circuit_mul(t68, t73); // Fp2 Inv real part end let t75 = circuit_mul(t69, t73); let t76 = circuit_sub(in2, t75); // Fp2 Inv imag part end let t77 = circuit_mul(t66, t74); // Fp2 mul start let t78 = circuit_mul(t67, t76); let t79 = circuit_sub(t77, t78); // Fp2 mul real part end let t80 = circuit_mul(t66, t76); let t81 = circuit_mul(t67, t74); let t82 = circuit_add(t80, t81); // Fp2 mul imag part end let t83 = circuit_mul(t79, in25); // Fp2 mul start let t84 = circuit_mul(t82, in26); let t85 = circuit_sub(t83, t84); // Fp2 mul real part end let t86 = circuit_mul(t79, in26); let t87 = circuit_mul(t82, in25); let t88 = circuit_add(t86, t87); // Fp2 mul imag part end let t89 = circuit_sub(t85, in27); // Fp2 sub coeff 0/1 let t90 = circuit_sub(t88, in28); // Fp2 sub coeff 1/1 let t91 = circuit_add(t79, t82); let t92 = circuit_sub(t79, t82); let t93 = circuit_mul(t91, t92); let t94 = circuit_mul(t79, t82); let t95 = circuit_add(t94, t94); let t96 = circuit_add(in25, in25); // Fp2 add coeff 0/1 let t97 = circuit_add(in26, in26); // Fp2 add coeff 1/1 let t98 = circuit_sub(t93, t96); // Fp2 sub coeff 0/1 let t99 = circuit_sub(t95, t97); // Fp2 sub coeff 1/1 let t100 = circuit_sub(in25, t98); // Fp2 sub coeff 0/1 let t101 = circuit_sub(in26, t99); // Fp2 sub coeff 1/1 let t102 = circuit_mul(t100, t100); // Fp2 Inv start let t103 = circuit_mul(t101, t101); let t104 = circuit_add(t102, t103); let t105 = circuit_inverse(t104); let t106 = circuit_mul(t100, t105); // Fp2 Inv real part end let t107 = circuit_mul(t101, t105); let t108 = circuit_sub(in2, t107); // Fp2 Inv imag part end let t109 = circuit_mul(t68, t106); // Fp2 mul start let t110 = circuit_mul(t69, t108); let t111 = circuit_sub(t109, t110); // Fp2 mul real part end let t112 = circuit_mul(t68, t108); let t113 = circuit_mul(t69, t106); let t114 = circuit_add(t112, t113); // Fp2 mul imag part end let t115 = circuit_sub(t111, t79); // Fp2 sub coeff 0/1 let t116 = circuit_sub(t114, t82); // Fp2 sub coeff 1/1 let t117 = circuit_mul(t115, in25); // Fp2 mul start let t118 = circuit_mul(t116, in26); let t119 = circuit_sub(t117, t118); // Fp2 mul real part end let t120 = circuit_mul(t115, in26); let t121 = circuit_mul(t116, in25); let t122 = circuit_add(t120, t121); // Fp2 mul imag part end let t123 = circuit_sub(t119, in27); // Fp2 sub coeff 0/1 let t124 = circuit_sub(t122, in28); // Fp2 sub coeff 1/1 let t125 = circuit_add(t115, t116); let t126 = circuit_sub(t115, t116); let t127 = circuit_mul(t125, t126); let t128 = circuit_mul(t115, t116); let t129 = circuit_add(t128, t128); let t130 = circuit_add(in25, t98); // Fp2 add coeff 0/1 let t131 = circuit_add(in26, t99); // Fp2 add coeff 1/1 let t132 = circuit_sub(t127, t130); // Fp2 sub coeff 0/1 let t133 = circuit_sub(t129, t131); // Fp2 sub coeff 1/1 let t134 = circuit_sub(in25, t132); // Fp2 sub coeff 0/1 let t135 = circuit_sub(in26, t133); // Fp2 sub coeff 1/1 let t136 = circuit_mul(t115, t134); // Fp2 mul start let t137 = circuit_mul(t116, t135); let t138 = circuit_sub(t136, t137); // Fp2 mul real part end let t139 = circuit_mul(t115, t135); let t140 = circuit_mul(t116, t134); let t141 = circuit_add(t139, t140); // Fp2 mul imag part end let t142 = circuit_sub(t138, in27); // Fp2 sub coeff 0/1 let t143 = circuit_sub(t141, in28); // Fp2 sub coeff 1/1 let t144 = circuit_sub(t89, t90); let t145 = circuit_mul(t144, in23); // eval bls line by yInv let t146 = circuit_sub(t79, t82); let t147 = circuit_mul(t146, in24); // eval blsline by xNegOverY let t148 = circuit_mul(t90, in23); // eval bls line by yInv let t149 = circuit_mul(t82, in24); // eval bls line by xNegOverY let t150 = circuit_sub(t123, t124); let t151 = circuit_mul(t150, in23); // eval bls line by yInv let t152 = circuit_sub(t115, t116); let t153 = circuit_mul(t152, in24); // eval blsline by xNegOverY let t154 = circuit_mul(t124, in23); // eval bls line by yInv let t155 = circuit_mul(t116, in24); // eval bls line by xNegOverY let t156 = circuit_mul(t147, t0); // Eval sparse poly line_2p_1 step coeff_2 * z^2 let t157 = circuit_add(t145, t156); // Eval sparse poly line_2p_1 step + coeff_2 * z^2 let t158 = circuit_add(t157, t1); // Eval sparse poly line_2p_1 step + 1*z^3 let t159 = circuit_mul(t148, t2); // Eval sparse poly line_2p_1 step coeff_6 * z^6 let t160 = circuit_add(t158, t159); // Eval sparse poly line_2p_1 step + coeff_6 * z^6 let t161 = circuit_mul(t149, t3); // Eval sparse poly line_2p_1 step coeff_8 * z^8 let t162 = circuit_add(t160, t161); // Eval sparse poly line_2p_1 step + coeff_8 * z^8 let t163 = circuit_mul(t61, t162); let t164 = circuit_mul(t153, t0); // Eval sparse poly line_2p_2 step coeff_2 * z^2 let t165 = circuit_add(t151, t164); // Eval sparse poly line_2p_2 step + coeff_2 * z^2 let t166 = circuit_add(t165, t1); // Eval sparse poly line_2p_2 step + 1*z^3 let t167 = circuit_mul(t154, t2); // Eval sparse poly line_2p_2 step coeff_6 * z^6 let t168 = circuit_add(t166, t167); // Eval sparse poly line_2p_2 step + coeff_6 * z^6 let t169 = circuit_mul(t155, t3); // Eval sparse poly line_2p_2 step coeff_8 * z^8 let t170 = circuit_add(t168, t169); // Eval sparse poly line_2p_2 step + coeff_8 * z^8 let t171 = circuit_mul(t163, t170); let t172 = circuit_sub(t171, in29); // ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t132, t133, t142, t143, t172).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in3 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a0); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a1); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r0a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r0a1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r1a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_0_2.r1a1); // in12 circuit_inputs = circuit_inputs.next_2(yInv_1); // in13 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a1); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r0a0); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r0a1); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r1a0); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_1_2.r1a1); // in22 circuit_inputs = circuit_inputs.next_2(yInv_2); // in23 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in24 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in25 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in26 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in27 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in28 circuit_inputs = circuit_inputs.next_2(R_i_of_z); // in29 circuit_inputs = circuit_inputs.next_2(z); // in30 circuit_inputs = circuit_inputs.next_2(c_inv_of_z); // in31 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t132), x1: outputs.get_output(t133), y0: outputs.get_output(t142), y1: outputs.get_output(t143), }; let new_lhs: u384 = outputs.get_output(t172); return (Q0, new_lhs); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_PREPARE_PAIRS_1P_circuit(p_0: G1Point) -> (BLSProcessedPair,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2) = (CE::> {}, CE::> {}); let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t0, t2).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), }; return (p_0,); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_PREPARE_PAIRS_2P_circuit( p_0: G1Point, p_1: G1Point, ) -> (BLSProcessedPair, BLSProcessedPair) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let in4 = CE::> {}; let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let t3 = circuit_inverse(in4); let t4 = circuit_mul(in3, t3); let t5 = circuit_sub(in0, t4); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t0, t2, t3, t5).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 circuit_inputs = circuit_inputs.next_2(p_1.x); // in3 circuit_inputs = circuit_inputs.next_2(p_1.y); // in4 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), }; let p_1: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t3), xNegOverY: outputs.get_output(t5), }; return (p_0, p_1); } #[inline(always)] pub fn run_BLS12_381_MP_CHECK_PREPARE_PAIRS_3P_circuit( p_0: G1Point, p_1: G1Point, p_2: G1Point, ) -> (BLSProcessedPair, BLSProcessedPair, BLSProcessedPair) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let t3 = circuit_inverse(in4); let t4 = circuit_mul(in3, t3); let t5 = circuit_sub(in0, t4); let t6 = circuit_inverse(in6); let t7 = circuit_mul(in5, t6); let t8 = circuit_sub(in0, t7); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t0, t2, t3, t5, t6, t8).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 circuit_inputs = circuit_inputs.next_2(p_1.x); // in3 circuit_inputs = circuit_inputs.next_2(p_1.y); // in4 circuit_inputs = circuit_inputs.next_2(p_2.x); // in5 circuit_inputs = circuit_inputs.next_2(p_2.y); // in6 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), }; let p_1: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t3), xNegOverY: outputs.get_output(t5), }; let p_2: BLSProcessedPair = BLSProcessedPair { yInv: outputs.get_output(t6), xNegOverY: outputs.get_output(t8), }; return (p_0, p_1, p_2); } #[inline(always)] pub fn run_BN254_INITIALIZE_MPCHECK_EXT_MLR_circuit( lambda_root: E12D, z: u384, scaling_factor: MillerLoopResultScalingFactor, c_inv: E12D, precomputed_miller_loop_result: E12D, ) -> (u384, u384, u384, u384, u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x12 let in2 = CE::> {}; // 0x1d8c8daef3eee1e81b2522ec5eb28ded6895e1cdfde6a43f5daa971f3fa65955 let in3 = CE::> {}; // 0x217e400dc9351e774e34e2ac06ead4000d14d1e242b29c567e9c385ce480a71a let in4 = CE::> {}; // 0x242b719062f6737b8481d22c6934ce844d72f250fd28d102c0d147b2f4d521a7 let in5 = CE::> {}; // 0x359809094bd5c8e1b9c22d81246ffc2e794e17643ac198484b8d9094aa82536 let in6 = CE::> {}; // 0x21436d48fcb50cc60dd4ef1e69a0c1f0dd2949fa6df7b44cbb259ef7cb58d5ed let in7 = CE::> {}; // 0x18857a58f3b5bb3038a4311a86919d9c7c6c15f88a4f4f0831364cf35f78f771 let in8 = CE::> {}; // 0x2c84bbad27c3671562b7adefd44038ab3c0bbad96fc008e7d6998c82f7fc048b let in9 = CE::> {}; // 0xc33b1c70e4fd11b6d1eab6fcd18b99ad4afd096a8697e0c9c36d8ca3339a7b5 let in10 = CE::< CI<10>, > {}; // 0x1b007294a55accce13fe08bea73305ff6bdac77c5371c546d428780a6e3dcfa8 let in11 = CE::< CI<11>, > {}; // 0x215d42e7ac7bd17cefe88dd8e6965b3adae92c974f501fe811493d72543a3977 let in12 = CE::> {}; // -0x1 % p let in13 = CE::< CI<13>, > {}; // 0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac let in14 = CE::< CI<14>, > {}; // 0x12d7c0c3ed42be419d2b22ca22ceca702eeb88c36a8b264dde75f4f798d6a3f2 let in15 = CE::< CI<15>, > {}; // 0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2 let in16 = CE::> {}; // 0xc38dce27e3b2cae33ce738a184c89d94a0e78406b48f98a7b4f4463e3a7dba0 let in17 = CE::> {}; // 0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3 let in18 = CE::> {}; // 0xf20e129e47c9363aa7b569817e0966cba582096fa7a164080faed1f0d24275a let in19 = CE::< CI<19>, > {}; // 0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126 let in20 = CE::> {}; // 0x3df92c5b96e3914559897c6ad411fb25b75afb7f8b1c1a56586ff93e080f8bc let in21 = CE::< CI<21>, > {}; // 0x12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b let in22 = CE::< CI<22>, > {}; // 0x1563dbde3bd6d35ba4523cf7da4e525e2ba6a3151500054667f8140c6a3f2d9f let in23 = CE::< CI<23>, > {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49 let in24 = CE::< CI<24>, > {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48 let in25 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe let in26 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff let in27 = CE::< CI<27>, > {}; // 0x13d0c369615f7bb0b2bdfa8fef85fa07122bde8d67dfc8fabd3581ad840ddd76 let in28 = CE::< CI<28>, > {}; // 0x18a0f4219f4fdff6fc2bf531eb331a053a35744cac285af5685d3f90eacf7a66 let in29 = CE::> {}; // 0xc3a5e9c462a654779c3e050c9ca2a428908a81264e2b5a5bf22f67654883ae6 let in30 = CE::< CI<30>, > {}; // 0x2ce02aa5f9bf8cd65bdd2055c255cf9d9e08c1d9345582cc92fd973c74bd77f4 let in31 = CE::< CI<31>, > {}; // 0x17ded419ed7be4f97fac149bfaefbac11b155498de227b850aea3f23790405d6 let in32 = CE::< CI<32>, > {}; // 0x1bfe7b214c0294242fb81a8dccd8a9b4441d64f34150a79753fb0cd31cc99cc0 let in33 = CE::> {}; // 0x697b9c523e0390ed15da0ec97a9b8346513297b9efaf0f0f1a228f0d5662fbd let in34 = CE::> {}; // 0x7a0e052f2b1c443b5186d6ac4c723b85d3f78a3182d2db0c413901c32b0c6fe let in35 = CE::< CI<35>, > {}; // 0x1b76a37fba85f3cd5dc79824a3792597356c892c39c0d06b220500933945267f let in36 = CE::> {}; // 0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101 let in37 = CE::< CI<37>, > {}; // 0x1c938b097fd2247905924b2691fb5e5685558c04009201927eeb0a69546f1fd1 let in38 = CE::> {}; // 0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de let in39 = CE::< CI<39>, > {}; // 0x2429efd69b073ae23e8c6565b7b72e1b0e78c27f038f14e77cfd95a083f4c261 let in40 = CE::< CI<40>, > {}; // 0x28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64 let in41 = CE::< CI<41>, > {}; // 0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f let in42 = CE::< CI<42>, > {}; // 0x1465d351952f0c0588982b28b4a8aea95364059e272122f5e8257f43bbb36087 let in43 = CE::< CI<43>, > {}; // 0x16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499 let in44 = CE::< CI<44>, > {}; // 0x28c36e1fee7fdbe60337d84bbcba34a53a41f1ee50449cdc780cfbfaa5cc3649 // INPUT stack let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76, in77) = (CE::> {}, CE::> {}, CE::> {}); let (in78, in79, in80) = (CE::> {}, CE::> {}, CE::> {}); let (in81, in82, in83) = (CE::> {}, CE::> {}, CE::> {}); let (in84, in85, in86) = (CE::> {}, CE::> {}, CE::> {}); let in87 = CE::> {}; let t0 = circuit_mul(in57, in57); // Compute z^2 let t1 = circuit_mul(t0, in57); // Compute z^3 let t2 = circuit_mul(t1, in57); // Compute z^4 let t3 = circuit_mul(t2, in57); // Compute z^5 let t4 = circuit_mul(t3, in57); // Compute z^6 let t5 = circuit_mul(t4, in57); // Compute z^7 let t6 = circuit_mul(t5, in57); // Compute z^8 let t7 = circuit_mul(t6, in57); // Compute z^9 let t8 = circuit_mul(t7, in57); // Compute z^10 let t9 = circuit_mul(t8, in57); // Compute z^11 let t10 = circuit_mul(in46, in57); // Eval C step coeff_1 * z^1 let t11 = circuit_add(in45, t10); // Eval C step + (coeff_1 * z^1) let t12 = circuit_mul(in47, t0); // Eval C step coeff_2 * z^2 let t13 = circuit_add(t11, t12); // Eval C step + (coeff_2 * z^2) let t14 = circuit_mul(in48, t1); // Eval C step coeff_3 * z^3 let t15 = circuit_add(t13, t14); // Eval C step + (coeff_3 * z^3) let t16 = circuit_mul(in49, t2); // Eval C step coeff_4 * z^4 let t17 = circuit_add(t15, t16); // Eval C step + (coeff_4 * z^4) let t18 = circuit_mul(in50, t3); // Eval C step coeff_5 * z^5 let t19 = circuit_add(t17, t18); // Eval C step + (coeff_5 * z^5) let t20 = circuit_mul(in51, t4); // Eval C step coeff_6 * z^6 let t21 = circuit_add(t19, t20); // Eval C step + (coeff_6 * z^6) let t22 = circuit_mul(in52, t5); // Eval C step coeff_7 * z^7 let t23 = circuit_add(t21, t22); // Eval C step + (coeff_7 * z^7) let t24 = circuit_mul(in53, t6); // Eval C step coeff_8 * z^8 let t25 = circuit_add(t23, t24); // Eval C step + (coeff_8 * z^8) let t26 = circuit_mul(in54, t7); // Eval C step coeff_9 * z^9 let t27 = circuit_add(t25, t26); // Eval C step + (coeff_9 * z^9) let t28 = circuit_mul(in55, t8); // Eval C step coeff_10 * z^10 let t29 = circuit_add(t27, t28); // Eval C step + (coeff_10 * z^10) let t30 = circuit_mul(in56, t9); // Eval C step coeff_11 * z^11 let t31 = circuit_add(t29, t30); // Eval C step + (coeff_11 * z^11) let t32 = circuit_mul(in59, t0); // Eval sparse poly W step coeff_2 * z^2 let t33 = circuit_add(in58, t32); // Eval sparse poly W step + coeff_2 * z^2 let t34 = circuit_mul(in60, t2); // Eval sparse poly W step coeff_4 * z^4 let t35 = circuit_add(t33, t34); // Eval sparse poly W step + coeff_4 * z^4 let t36 = circuit_mul(in61, t4); // Eval sparse poly W step coeff_6 * z^6 let t37 = circuit_add(t35, t36); // Eval sparse poly W step + coeff_6 * z^6 let t38 = circuit_mul(in62, t6); // Eval sparse poly W step coeff_8 * z^8 let t39 = circuit_add(t37, t38); // Eval sparse poly W step + coeff_8 * z^8 let t40 = circuit_mul(in63, t8); // Eval sparse poly W step coeff_10 * z^10 let t41 = circuit_add(t39, t40); // Eval sparse poly W step + coeff_10 * z^10 let t42 = circuit_mul(in65, in57); // Eval C_inv step coeff_1 * z^1 let t43 = circuit_add(in64, t42); // Eval C_inv step + (coeff_1 * z^1) let t44 = circuit_mul(in66, t0); // Eval C_inv step coeff_2 * z^2 let t45 = circuit_add(t43, t44); // Eval C_inv step + (coeff_2 * z^2) let t46 = circuit_mul(in67, t1); // Eval C_inv step coeff_3 * z^3 let t47 = circuit_add(t45, t46); // Eval C_inv step + (coeff_3 * z^3) let t48 = circuit_mul(in68, t2); // Eval C_inv step coeff_4 * z^4 let t49 = circuit_add(t47, t48); // Eval C_inv step + (coeff_4 * z^4) let t50 = circuit_mul(in69, t3); // Eval C_inv step coeff_5 * z^5 let t51 = circuit_add(t49, t50); // Eval C_inv step + (coeff_5 * z^5) let t52 = circuit_mul(in70, t4); // Eval C_inv step coeff_6 * z^6 let t53 = circuit_add(t51, t52); // Eval C_inv step + (coeff_6 * z^6) let t54 = circuit_mul(in71, t5); // Eval C_inv step coeff_7 * z^7 let t55 = circuit_add(t53, t54); // Eval C_inv step + (coeff_7 * z^7) let t56 = circuit_mul(in72, t6); // Eval C_inv step coeff_8 * z^8 let t57 = circuit_add(t55, t56); // Eval C_inv step + (coeff_8 * z^8) let t58 = circuit_mul(in73, t7); // Eval C_inv step coeff_9 * z^9 let t59 = circuit_add(t57, t58); // Eval C_inv step + (coeff_9 * z^9) let t60 = circuit_mul(in74, t8); // Eval C_inv step coeff_10 * z^10 let t61 = circuit_add(t59, t60); // Eval C_inv step + (coeff_10 * z^10) let t62 = circuit_mul(in75, t9); // Eval C_inv step coeff_11 * z^11 let t63 = circuit_add(t61, t62); // Eval C_inv step + (coeff_11 * z^11) let t64 = circuit_mul(t31, t63); let t65 = circuit_sub(t64, in0); // c_of_z * c_inv_of_z - 1 let t66 = circuit_mul(in70, in1); let t67 = circuit_add(in64, t66); let t68 = circuit_mul(in65, in2); let t69 = circuit_mul(in71, in3); let t70 = circuit_add(t68, t69); let t71 = circuit_mul(in66, in4); let t72 = circuit_mul(in72, in5); let t73 = circuit_add(t71, t72); let t74 = circuit_mul(in67, in6); let t75 = circuit_mul(in73, in7); let t76 = circuit_add(t74, t75); let t77 = circuit_mul(in68, in8); let t78 = circuit_mul(in74, in9); let t79 = circuit_add(t77, t78); let t80 = circuit_mul(in69, in10); let t81 = circuit_mul(in75, in11); let t82 = circuit_add(t80, t81); let t83 = circuit_mul(in70, in12); let t84 = circuit_mul(in65, in13); let t85 = circuit_mul(in71, in14); let t86 = circuit_add(t84, t85); let t87 = circuit_mul(in66, in15); let t88 = circuit_mul(in72, in16); let t89 = circuit_add(t87, t88); let t90 = circuit_mul(in67, in17); let t91 = circuit_mul(in73, in18); let t92 = circuit_add(t90, t91); let t93 = circuit_mul(in68, in19); let t94 = circuit_mul(in74, in20); let t95 = circuit_add(t93, t94); let t96 = circuit_mul(in69, in21); let t97 = circuit_mul(in75, in22); let t98 = circuit_add(t96, t97); let t99 = circuit_mul(in46, in23); let t100 = circuit_mul(in47, in24); let t101 = circuit_mul(in48, in12); let t102 = circuit_mul(in49, in25); let t103 = circuit_mul(in50, in26); let t104 = circuit_mul(in52, in23); let t105 = circuit_mul(in53, in24); let t106 = circuit_mul(in54, in12); let t107 = circuit_mul(in55, in25); let t108 = circuit_mul(in56, in26); let t109 = circuit_mul(in70, in1); let t110 = circuit_add(in64, t109); let t111 = circuit_mul(in65, in27); let t112 = circuit_mul(in71, in28); let t113 = circuit_add(t111, t112); let t114 = circuit_mul(in66, in29); let t115 = circuit_mul(in72, in30); let t116 = circuit_add(t114, t115); let t117 = circuit_mul(in67, in18); let t118 = circuit_mul(in73, in31); let t119 = circuit_add(t117, t118); let t120 = circuit_mul(in68, in32); let t121 = circuit_mul(in74, in33); let t122 = circuit_add(t120, t121); let t123 = circuit_mul(in69, in34); let t124 = circuit_mul(in75, in35); let t125 = circuit_add(t123, t124); let t126 = circuit_mul(in70, in12); let t127 = circuit_mul(in65, in36); let t128 = circuit_mul(in71, in37); let t129 = circuit_add(t127, t128); let t130 = circuit_mul(in66, in38); let t131 = circuit_mul(in72, in39); let t132 = circuit_add(t130, t131); let t133 = circuit_mul(in67, in40); let t134 = circuit_mul(in73, in6); let t135 = circuit_add(t133, t134); let t136 = circuit_mul(in68, in41); let t137 = circuit_mul(in74, in42); let t138 = circuit_add(t136, t137); let t139 = circuit_mul(in69, in43); let t140 = circuit_mul(in75, in44); let t141 = circuit_add(t139, t140); let t142 = circuit_mul(t70, in57); // Eval C_inv_frob_1 step coeff_1 * z^1 let t143 = circuit_add(t67, t142); // Eval C_inv_frob_1 step + (coeff_1 * z^1) let t144 = circuit_mul(t73, t0); // Eval C_inv_frob_1 step coeff_2 * z^2 let t145 = circuit_add(t143, t144); // Eval C_inv_frob_1 step + (coeff_2 * z^2) let t146 = circuit_mul(t76, t1); // Eval C_inv_frob_1 step coeff_3 * z^3 let t147 = circuit_add(t145, t146); // Eval C_inv_frob_1 step + (coeff_3 * z^3) let t148 = circuit_mul(t79, t2); // Eval C_inv_frob_1 step coeff_4 * z^4 let t149 = circuit_add(t147, t148); // Eval C_inv_frob_1 step + (coeff_4 * z^4) let t150 = circuit_mul(t82, t3); // Eval C_inv_frob_1 step coeff_5 * z^5 let t151 = circuit_add(t149, t150); // Eval C_inv_frob_1 step + (coeff_5 * z^5) let t152 = circuit_mul(t83, t4); // Eval C_inv_frob_1 step coeff_6 * z^6 let t153 = circuit_add(t151, t152); // Eval C_inv_frob_1 step + (coeff_6 * z^6) let t154 = circuit_mul(t86, t5); // Eval C_inv_frob_1 step coeff_7 * z^7 let t155 = circuit_add(t153, t154); // Eval C_inv_frob_1 step + (coeff_7 * z^7) let t156 = circuit_mul(t89, t6); // Eval C_inv_frob_1 step coeff_8 * z^8 let t157 = circuit_add(t155, t156); // Eval C_inv_frob_1 step + (coeff_8 * z^8) let t158 = circuit_mul(t92, t7); // Eval C_inv_frob_1 step coeff_9 * z^9 let t159 = circuit_add(t157, t158); // Eval C_inv_frob_1 step + (coeff_9 * z^9) let t160 = circuit_mul(t95, t8); // Eval C_inv_frob_1 step coeff_10 * z^10 let t161 = circuit_add(t159, t160); // Eval C_inv_frob_1 step + (coeff_10 * z^10) let t162 = circuit_mul(t98, t9); // Eval C_inv_frob_1 step coeff_11 * z^11 let t163 = circuit_add(t161, t162); // Eval C_inv_frob_1 step + (coeff_11 * z^11) let t164 = circuit_mul(t99, in57); // Eval C_frob_2 step coeff_1 * z^1 let t165 = circuit_add(in45, t164); // Eval C_frob_2 step + (coeff_1 * z^1) let t166 = circuit_mul(t100, t0); // Eval C_frob_2 step coeff_2 * z^2 let t167 = circuit_add(t165, t166); // Eval C_frob_2 step + (coeff_2 * z^2) let t168 = circuit_mul(t101, t1); // Eval C_frob_2 step coeff_3 * z^3 let t169 = circuit_add(t167, t168); // Eval C_frob_2 step + (coeff_3 * z^3) let t170 = circuit_mul(t102, t2); // Eval C_frob_2 step coeff_4 * z^4 let t171 = circuit_add(t169, t170); // Eval C_frob_2 step + (coeff_4 * z^4) let t172 = circuit_mul(t103, t3); // Eval C_frob_2 step coeff_5 * z^5 let t173 = circuit_add(t171, t172); // Eval C_frob_2 step + (coeff_5 * z^5) let t174 = circuit_mul(in51, t4); // Eval C_frob_2 step coeff_6 * z^6 let t175 = circuit_add(t173, t174); // Eval C_frob_2 step + (coeff_6 * z^6) let t176 = circuit_mul(t104, t5); // Eval C_frob_2 step coeff_7 * z^7 let t177 = circuit_add(t175, t176); // Eval C_frob_2 step + (coeff_7 * z^7) let t178 = circuit_mul(t105, t6); // Eval C_frob_2 step coeff_8 * z^8 let t179 = circuit_add(t177, t178); // Eval C_frob_2 step + (coeff_8 * z^8) let t180 = circuit_mul(t106, t7); // Eval C_frob_2 step coeff_9 * z^9 let t181 = circuit_add(t179, t180); // Eval C_frob_2 step + (coeff_9 * z^9) let t182 = circuit_mul(t107, t8); // Eval C_frob_2 step coeff_10 * z^10 let t183 = circuit_add(t181, t182); // Eval C_frob_2 step + (coeff_10 * z^10) let t184 = circuit_mul(t108, t9); // Eval C_frob_2 step coeff_11 * z^11 let t185 = circuit_add(t183, t184); // Eval C_frob_2 step + (coeff_11 * z^11) let t186 = circuit_mul(t113, in57); // Eval C_inv_frob_3 step coeff_1 * z^1 let t187 = circuit_add(t110, t186); // Eval C_inv_frob_3 step + (coeff_1 * z^1) let t188 = circuit_mul(t116, t0); // Eval C_inv_frob_3 step coeff_2 * z^2 let t189 = circuit_add(t187, t188); // Eval C_inv_frob_3 step + (coeff_2 * z^2) let t190 = circuit_mul(t119, t1); // Eval C_inv_frob_3 step coeff_3 * z^3 let t191 = circuit_add(t189, t190); // Eval C_inv_frob_3 step + (coeff_3 * z^3) let t192 = circuit_mul(t122, t2); // Eval C_inv_frob_3 step coeff_4 * z^4 let t193 = circuit_add(t191, t192); // Eval C_inv_frob_3 step + (coeff_4 * z^4) let t194 = circuit_mul(t125, t3); // Eval C_inv_frob_3 step coeff_5 * z^5 let t195 = circuit_add(t193, t194); // Eval C_inv_frob_3 step + (coeff_5 * z^5) let t196 = circuit_mul(t126, t4); // Eval C_inv_frob_3 step coeff_6 * z^6 let t197 = circuit_add(t195, t196); // Eval C_inv_frob_3 step + (coeff_6 * z^6) let t198 = circuit_mul(t129, t5); // Eval C_inv_frob_3 step coeff_7 * z^7 let t199 = circuit_add(t197, t198); // Eval C_inv_frob_3 step + (coeff_7 * z^7) let t200 = circuit_mul(t132, t6); // Eval C_inv_frob_3 step coeff_8 * z^8 let t201 = circuit_add(t199, t200); // Eval C_inv_frob_3 step + (coeff_8 * z^8) let t202 = circuit_mul(t135, t7); // Eval C_inv_frob_3 step coeff_9 * z^9 let t203 = circuit_add(t201, t202); // Eval C_inv_frob_3 step + (coeff_9 * z^9) let t204 = circuit_mul(t138, t8); // Eval C_inv_frob_3 step coeff_10 * z^10 let t205 = circuit_add(t203, t204); // Eval C_inv_frob_3 step + (coeff_10 * z^10) let t206 = circuit_mul(t141, t9); // Eval C_inv_frob_3 step coeff_11 * z^11 let t207 = circuit_add(t205, t206); // Eval C_inv_frob_3 step + (coeff_11 * z^11) let t208 = circuit_mul(in77, in57); // Eval precomputed_miller_loop_result step coeff_1 * z^1 let t209 = circuit_add( in76, t208, ); // Eval precomputed_miller_loop_result step + (coeff_1 * z^1) let t210 = circuit_mul(in78, t0); // Eval precomputed_miller_loop_result step coeff_2 * z^2 let t211 = circuit_add( t209, t210, ); // Eval precomputed_miller_loop_result step + (coeff_2 * z^2) let t212 = circuit_mul(in79, t1); // Eval precomputed_miller_loop_result step coeff_3 * z^3 let t213 = circuit_add( t211, t212, ); // Eval precomputed_miller_loop_result step + (coeff_3 * z^3) let t214 = circuit_mul(in80, t2); // Eval precomputed_miller_loop_result step coeff_4 * z^4 let t215 = circuit_add( t213, t214, ); // Eval precomputed_miller_loop_result step + (coeff_4 * z^4) let t216 = circuit_mul(in81, t3); // Eval precomputed_miller_loop_result step coeff_5 * z^5 let t217 = circuit_add( t215, t216, ); // Eval precomputed_miller_loop_result step + (coeff_5 * z^5) let t218 = circuit_mul(in82, t4); // Eval precomputed_miller_loop_result step coeff_6 * z^6 let t219 = circuit_add( t217, t218, ); // Eval precomputed_miller_loop_result step + (coeff_6 * z^6) let t220 = circuit_mul(in83, t5); // Eval precomputed_miller_loop_result step coeff_7 * z^7 let t221 = circuit_add( t219, t220, ); // Eval precomputed_miller_loop_result step + (coeff_7 * z^7) let t222 = circuit_mul(in84, t6); // Eval precomputed_miller_loop_result step coeff_8 * z^8 let t223 = circuit_add( t221, t222, ); // Eval precomputed_miller_loop_result step + (coeff_8 * z^8) let t224 = circuit_mul(in85, t7); // Eval precomputed_miller_loop_result step coeff_9 * z^9 let t225 = circuit_add( t223, t224, ); // Eval precomputed_miller_loop_result step + (coeff_9 * z^9) let t226 = circuit_mul(in86, t8); // Eval precomputed_miller_loop_result step coeff_10 * z^10 let t227 = circuit_add( t225, t226, ); // Eval precomputed_miller_loop_result step + (coeff_10 * z^10) let t228 = circuit_mul(in87, t9); // Eval precomputed_miller_loop_result step coeff_11 * z^11 let t229 = circuit_add( t227, t228, ); // Eval precomputed_miller_loop_result step + (coeff_11 * z^11) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t31, t41, t63, t65, t163, t185, t207, t229).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(INITIALIZE_MPCHECK_EXT_MLR_BN254_CONSTANTS.span()); // in0 - in44 // Fill inputs: circuit_inputs = circuit_inputs.next_2(lambda_root.w0); // in45 circuit_inputs = circuit_inputs.next_2(lambda_root.w1); // in46 circuit_inputs = circuit_inputs.next_2(lambda_root.w2); // in47 circuit_inputs = circuit_inputs.next_2(lambda_root.w3); // in48 circuit_inputs = circuit_inputs.next_2(lambda_root.w4); // in49 circuit_inputs = circuit_inputs.next_2(lambda_root.w5); // in50 circuit_inputs = circuit_inputs.next_2(lambda_root.w6); // in51 circuit_inputs = circuit_inputs.next_2(lambda_root.w7); // in52 circuit_inputs = circuit_inputs.next_2(lambda_root.w8); // in53 circuit_inputs = circuit_inputs.next_2(lambda_root.w9); // in54 circuit_inputs = circuit_inputs.next_2(lambda_root.w10); // in55 circuit_inputs = circuit_inputs.next_2(lambda_root.w11); // in56 circuit_inputs = circuit_inputs.next_2(z); // in57 circuit_inputs = circuit_inputs.next_2(scaling_factor.w0); // in58 circuit_inputs = circuit_inputs.next_2(scaling_factor.w2); // in59 circuit_inputs = circuit_inputs.next_2(scaling_factor.w4); // in60 circuit_inputs = circuit_inputs.next_2(scaling_factor.w6); // in61 circuit_inputs = circuit_inputs.next_2(scaling_factor.w8); // in62 circuit_inputs = circuit_inputs.next_2(scaling_factor.w10); // in63 circuit_inputs = circuit_inputs.next_2(c_inv.w0); // in64 circuit_inputs = circuit_inputs.next_2(c_inv.w1); // in65 circuit_inputs = circuit_inputs.next_2(c_inv.w2); // in66 circuit_inputs = circuit_inputs.next_2(c_inv.w3); // in67 circuit_inputs = circuit_inputs.next_2(c_inv.w4); // in68 circuit_inputs = circuit_inputs.next_2(c_inv.w5); // in69 circuit_inputs = circuit_inputs.next_2(c_inv.w6); // in70 circuit_inputs = circuit_inputs.next_2(c_inv.w7); // in71 circuit_inputs = circuit_inputs.next_2(c_inv.w8); // in72 circuit_inputs = circuit_inputs.next_2(c_inv.w9); // in73 circuit_inputs = circuit_inputs.next_2(c_inv.w10); // in74 circuit_inputs = circuit_inputs.next_2(c_inv.w11); // in75 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w0); // in76 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w1); // in77 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w2); // in78 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w3); // in79 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w4); // in80 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w5); // in81 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w6); // in82 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w7); // in83 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w8); // in84 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w9); // in85 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w10); // in86 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result.w11); // in87 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let c_of_z: u384 = outputs.get_output(t31); let scaling_factor_of_z: u384 = outputs.get_output(t41); let c_inv_of_z: u384 = outputs.get_output(t63); let lhs: u384 = outputs.get_output(t65); let c_inv_frob_1_of_z: u384 = outputs.get_output(t163); let c_frob_2_of_z: u384 = outputs.get_output(t185); let c_inv_frob_3_of_z: u384 = outputs.get_output(t207); let precomputed_miller_loop_result_of_z: u384 = outputs.get_output(t229); return ( c_of_z, scaling_factor_of_z, c_inv_of_z, lhs, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, precomputed_miller_loop_result_of_z, ); } const INITIALIZE_MPCHECK_EXT_MLR_BN254_CONSTANTS: [u384; 45] = [ u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x12, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xfde6a43f5daa971f3fa65955, limb1: 0x1b2522ec5eb28ded6895e1cd, limb2: 0x1d8c8daef3eee1e8, limb3: 0x0, }, u384 { limb0: 0x42b29c567e9c385ce480a71a, limb1: 0x4e34e2ac06ead4000d14d1e2, limb2: 0x217e400dc9351e77, limb3: 0x0, }, u384 { limb0: 0xfd28d102c0d147b2f4d521a7, limb1: 0x8481d22c6934ce844d72f250, limb2: 0x242b719062f6737b, limb3: 0x0, }, u384 { limb0: 0x43ac198484b8d9094aa82536, limb1: 0x1b9c22d81246ffc2e794e176, limb2: 0x359809094bd5c8e, limb3: 0x0, }, u384 { limb0: 0x6df7b44cbb259ef7cb58d5ed, limb1: 0xdd4ef1e69a0c1f0dd2949fa, limb2: 0x21436d48fcb50cc6, limb3: 0x0, }, u384 { limb0: 0x8a4f4f0831364cf35f78f771, limb1: 0x38a4311a86919d9c7c6c15f8, limb2: 0x18857a58f3b5bb30, limb3: 0x0, }, u384 { limb0: 0x6fc008e7d6998c82f7fc048b, limb1: 0x62b7adefd44038ab3c0bbad9, limb2: 0x2c84bbad27c36715, limb3: 0x0, }, u384 { limb0: 0xa8697e0c9c36d8ca3339a7b5, limb1: 0x6d1eab6fcd18b99ad4afd096, limb2: 0xc33b1c70e4fd11b, limb3: 0x0, }, u384 { limb0: 0x5371c546d428780a6e3dcfa8, limb1: 0x13fe08bea73305ff6bdac77c, limb2: 0x1b007294a55accce, limb3: 0x0, }, u384 { limb0: 0x4f501fe811493d72543a3977, limb1: 0xefe88dd8e6965b3adae92c97, limb2: 0x215d42e7ac7bd17c, limb3: 0x0, }, u384 { limb0: 0x6871ca8d3c208c16d87cfd46, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x8eeec7e5ca5cf05f80f362ac, limb1: 0xa6327cfe12150b8e74799277, limb2: 0x246996f3b4fae7e6, limb3: 0x0, }, u384 { limb0: 0x6a8b264dde75f4f798d6a3f2, limb1: 0x9d2b22ca22ceca702eeb88c3, limb2: 0x12d7c0c3ed42be41, limb3: 0x0, }, u384 { limb0: 0xb7c9dce1665d51c640fcba2, limb1: 0x4ba4cc8bd75a079432ae2a1d, limb2: 0x16c9e55061ebae20, limb3: 0x0, }, u384 { limb0: 0x6b48f98a7b4f4463e3a7dba0, limb1: 0x33ce738a184c89d94a0e7840, limb2: 0xc38dce27e3b2cae, limb3: 0x0, }, u384 { limb0: 0x8fa25bd282d37f632623b0e3, limb1: 0x704b5a7ec796f2b21807dc9, limb2: 0x7c03cbcac41049a, limb3: 0x0, }, u384 { limb0: 0xfa7a164080faed1f0d24275a, limb1: 0xaa7b569817e0966cba582096, limb2: 0xf20e129e47c9363, limb3: 0x0, }, u384 { limb0: 0x1bdec763c13b4711cd2b8126, limb1: 0x9f3a80b03b0b1c923685d2ea, limb2: 0x2c145edbe7fd8aee, limb3: 0x0, }, u384 { limb0: 0xf8b1c1a56586ff93e080f8bc, limb1: 0x559897c6ad411fb25b75afb7, limb2: 0x3df92c5b96e3914, limb3: 0x0, }, u384 { limb0: 0x678e2ac024c6b8ee6e0c2c4b, limb1: 0xa27fb246c7729f7db080cb99, limb2: 0x12acf2ca76fd0675, limb3: 0x0, }, u384 { limb0: 0x1500054667f8140c6a3f2d9f, limb1: 0xa4523cf7da4e525e2ba6a315, limb2: 0x1563dbde3bd6d35b, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd49, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd48, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0xacdb5c4f5763473177fffffe, limb1: 0x59e26bcea0d48bacd4f263f1, limb2: 0x0, limb3: 0x0, }, u384 { limb0: 0xacdb5c4f5763473177ffffff, limb1: 0x59e26bcea0d48bacd4f263f1, limb2: 0x0, limb3: 0x0, }, u384 { limb0: 0x67dfc8fabd3581ad840ddd76, limb1: 0xb2bdfa8fef85fa07122bde8d, limb2: 0x13d0c369615f7bb0, limb3: 0x0, }, u384 { limb0: 0xac285af5685d3f90eacf7a66, limb1: 0xfc2bf531eb331a053a35744c, limb2: 0x18a0f4219f4fdff6, limb3: 0x0, }, u384 { limb0: 0x64e2b5a5bf22f67654883ae6, limb1: 0x79c3e050c9ca2a428908a812, limb2: 0xc3a5e9c462a6547, limb3: 0x0, }, u384 { limb0: 0x345582cc92fd973c74bd77f4, limb1: 0x5bdd2055c255cf9d9e08c1d9, limb2: 0x2ce02aa5f9bf8cd6, limb3: 0x0, }, u384 { limb0: 0xde227b850aea3f23790405d6, limb1: 0x7fac149bfaefbac11b155498, limb2: 0x17ded419ed7be4f9, limb3: 0x0, }, u384 { limb0: 0x4150a79753fb0cd31cc99cc0, limb1: 0x2fb81a8dccd8a9b4441d64f3, limb2: 0x1bfe7b214c029424, limb3: 0x0, }, u384 { limb0: 0x9efaf0f0f1a228f0d5662fbd, limb1: 0xd15da0ec97a9b8346513297b, limb2: 0x697b9c523e0390e, limb3: 0x0, }, u384 { limb0: 0x182d2db0c413901c32b0c6fe, limb1: 0xb5186d6ac4c723b85d3f78a3, limb2: 0x7a0e052f2b1c443, limb3: 0x0, }, u384 { limb0: 0x39c0d06b220500933945267f, limb1: 0x5dc79824a3792597356c892c, limb2: 0x1b76a37fba85f3cd, limb3: 0x0, }, u384 { limb0: 0x97d439ec7694aa2bf4c0c101, limb1: 0x6cbeee33576139d7f03a5e3, limb2: 0xabf8b60be77d73, limb3: 0x0, }, u384 { limb0: 0x9201927eeb0a69546f1fd1, limb1: 0x5924b2691fb5e5685558c04, limb2: 0x1c938b097fd22479, limb3: 0x0, }, u384 { limb0: 0x98ff2631380cab2baaa586de, limb1: 0xa9f30e6dec26094f0fdf31bf, limb2: 0x4f1de41b3d1766f, limb3: 0x0, }, u384 { limb0: 0x38f14e77cfd95a083f4c261, limb1: 0x3e8c6565b7b72e1b0e78c27f, limb2: 0x2429efd69b073ae2, limb3: 0x0, }, u384 { limb0: 0xd8cf6ebab94d0cb3b2594c64, limb1: 0xb14b900e9507e9327600ecc7, limb2: 0x28a411b634f09b8f, limb3: 0x0, }, u384 { limb0: 0x737f96e55fe3ed9d730c239f, limb1: 0xfeb0f6ef0cd21d04a44a9e08, limb2: 0x23d5e999e1910a12, limb3: 0x0, }, u384 { limb0: 0x272122f5e8257f43bbb36087, limb1: 0x88982b28b4a8aea95364059e, limb2: 0x1465d351952f0c05, limb3: 0x0, }, u384 { limb0: 0x200280211f25041384282499, limb1: 0x9fb1b2282a48633d3e2ddaea, limb2: 0x16db366a59b1dd0b, limb3: 0x0, }, u384 { limb0: 0x50449cdc780cfbfaa5cc3649, limb1: 0x337d84bbcba34a53a41f1ee, limb2: 0x28c36e1fee7fdbe6, limb3: 0x0, }, ]; #[inline(always)] pub fn run_BN254_INITIALIZE_MPCHECK_circuit( lambda_root: E12D, z: u384, scaling_factor: MillerLoopResultScalingFactor, c_inv: E12D, ) -> (u384, u384, u384, u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x1 let in1 = CE::> {}; // 0x12 let in2 = CE::> {}; // 0x1d8c8daef3eee1e81b2522ec5eb28ded6895e1cdfde6a43f5daa971f3fa65955 let in3 = CE::> {}; // 0x217e400dc9351e774e34e2ac06ead4000d14d1e242b29c567e9c385ce480a71a let in4 = CE::> {}; // 0x242b719062f6737b8481d22c6934ce844d72f250fd28d102c0d147b2f4d521a7 let in5 = CE::> {}; // 0x359809094bd5c8e1b9c22d81246ffc2e794e17643ac198484b8d9094aa82536 let in6 = CE::> {}; // 0x21436d48fcb50cc60dd4ef1e69a0c1f0dd2949fa6df7b44cbb259ef7cb58d5ed let in7 = CE::> {}; // 0x18857a58f3b5bb3038a4311a86919d9c7c6c15f88a4f4f0831364cf35f78f771 let in8 = CE::> {}; // 0x2c84bbad27c3671562b7adefd44038ab3c0bbad96fc008e7d6998c82f7fc048b let in9 = CE::> {}; // 0xc33b1c70e4fd11b6d1eab6fcd18b99ad4afd096a8697e0c9c36d8ca3339a7b5 let in10 = CE::< CI<10>, > {}; // 0x1b007294a55accce13fe08bea73305ff6bdac77c5371c546d428780a6e3dcfa8 let in11 = CE::< CI<11>, > {}; // 0x215d42e7ac7bd17cefe88dd8e6965b3adae92c974f501fe811493d72543a3977 let in12 = CE::> {}; // -0x1 % p let in13 = CE::< CI<13>, > {}; // 0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac let in14 = CE::< CI<14>, > {}; // 0x12d7c0c3ed42be419d2b22ca22ceca702eeb88c36a8b264dde75f4f798d6a3f2 let in15 = CE::< CI<15>, > {}; // 0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2 let in16 = CE::> {}; // 0xc38dce27e3b2cae33ce738a184c89d94a0e78406b48f98a7b4f4463e3a7dba0 let in17 = CE::> {}; // 0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3 let in18 = CE::> {}; // 0xf20e129e47c9363aa7b569817e0966cba582096fa7a164080faed1f0d24275a let in19 = CE::< CI<19>, > {}; // 0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126 let in20 = CE::> {}; // 0x3df92c5b96e3914559897c6ad411fb25b75afb7f8b1c1a56586ff93e080f8bc let in21 = CE::< CI<21>, > {}; // 0x12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b let in22 = CE::< CI<22>, > {}; // 0x1563dbde3bd6d35ba4523cf7da4e525e2ba6a3151500054667f8140c6a3f2d9f let in23 = CE::< CI<23>, > {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49 let in24 = CE::< CI<24>, > {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48 let in25 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe let in26 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff let in27 = CE::< CI<27>, > {}; // 0x13d0c369615f7bb0b2bdfa8fef85fa07122bde8d67dfc8fabd3581ad840ddd76 let in28 = CE::< CI<28>, > {}; // 0x18a0f4219f4fdff6fc2bf531eb331a053a35744cac285af5685d3f90eacf7a66 let in29 = CE::> {}; // 0xc3a5e9c462a654779c3e050c9ca2a428908a81264e2b5a5bf22f67654883ae6 let in30 = CE::< CI<30>, > {}; // 0x2ce02aa5f9bf8cd65bdd2055c255cf9d9e08c1d9345582cc92fd973c74bd77f4 let in31 = CE::< CI<31>, > {}; // 0x17ded419ed7be4f97fac149bfaefbac11b155498de227b850aea3f23790405d6 let in32 = CE::< CI<32>, > {}; // 0x1bfe7b214c0294242fb81a8dccd8a9b4441d64f34150a79753fb0cd31cc99cc0 let in33 = CE::> {}; // 0x697b9c523e0390ed15da0ec97a9b8346513297b9efaf0f0f1a228f0d5662fbd let in34 = CE::> {}; // 0x7a0e052f2b1c443b5186d6ac4c723b85d3f78a3182d2db0c413901c32b0c6fe let in35 = CE::< CI<35>, > {}; // 0x1b76a37fba85f3cd5dc79824a3792597356c892c39c0d06b220500933945267f let in36 = CE::> {}; // 0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101 let in37 = CE::< CI<37>, > {}; // 0x1c938b097fd2247905924b2691fb5e5685558c04009201927eeb0a69546f1fd1 let in38 = CE::> {}; // 0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de let in39 = CE::< CI<39>, > {}; // 0x2429efd69b073ae23e8c6565b7b72e1b0e78c27f038f14e77cfd95a083f4c261 let in40 = CE::< CI<40>, > {}; // 0x28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64 let in41 = CE::< CI<41>, > {}; // 0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f let in42 = CE::< CI<42>, > {}; // 0x1465d351952f0c0588982b28b4a8aea95364059e272122f5e8257f43bbb36087 let in43 = CE::< CI<43>, > {}; // 0x16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499 let in44 = CE::< CI<44>, > {}; // 0x28c36e1fee7fdbe60337d84bbcba34a53a41f1ee50449cdc780cfbfaa5cc3649 // INPUT stack let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let in75 = CE::> {}; let t0 = circuit_mul(in57, in57); // Compute z^2 let t1 = circuit_mul(t0, in57); // Compute z^3 let t2 = circuit_mul(t1, in57); // Compute z^4 let t3 = circuit_mul(t2, in57); // Compute z^5 let t4 = circuit_mul(t3, in57); // Compute z^6 let t5 = circuit_mul(t4, in57); // Compute z^7 let t6 = circuit_mul(t5, in57); // Compute z^8 let t7 = circuit_mul(t6, in57); // Compute z^9 let t8 = circuit_mul(t7, in57); // Compute z^10 let t9 = circuit_mul(t8, in57); // Compute z^11 let t10 = circuit_mul(in46, in57); // Eval C step coeff_1 * z^1 let t11 = circuit_add(in45, t10); // Eval C step + (coeff_1 * z^1) let t12 = circuit_mul(in47, t0); // Eval C step coeff_2 * z^2 let t13 = circuit_add(t11, t12); // Eval C step + (coeff_2 * z^2) let t14 = circuit_mul(in48, t1); // Eval C step coeff_3 * z^3 let t15 = circuit_add(t13, t14); // Eval C step + (coeff_3 * z^3) let t16 = circuit_mul(in49, t2); // Eval C step coeff_4 * z^4 let t17 = circuit_add(t15, t16); // Eval C step + (coeff_4 * z^4) let t18 = circuit_mul(in50, t3); // Eval C step coeff_5 * z^5 let t19 = circuit_add(t17, t18); // Eval C step + (coeff_5 * z^5) let t20 = circuit_mul(in51, t4); // Eval C step coeff_6 * z^6 let t21 = circuit_add(t19, t20); // Eval C step + (coeff_6 * z^6) let t22 = circuit_mul(in52, t5); // Eval C step coeff_7 * z^7 let t23 = circuit_add(t21, t22); // Eval C step + (coeff_7 * z^7) let t24 = circuit_mul(in53, t6); // Eval C step coeff_8 * z^8 let t25 = circuit_add(t23, t24); // Eval C step + (coeff_8 * z^8) let t26 = circuit_mul(in54, t7); // Eval C step coeff_9 * z^9 let t27 = circuit_add(t25, t26); // Eval C step + (coeff_9 * z^9) let t28 = circuit_mul(in55, t8); // Eval C step coeff_10 * z^10 let t29 = circuit_add(t27, t28); // Eval C step + (coeff_10 * z^10) let t30 = circuit_mul(in56, t9); // Eval C step coeff_11 * z^11 let t31 = circuit_add(t29, t30); // Eval C step + (coeff_11 * z^11) let t32 = circuit_mul(in59, t0); // Eval sparse poly W step coeff_2 * z^2 let t33 = circuit_add(in58, t32); // Eval sparse poly W step + coeff_2 * z^2 let t34 = circuit_mul(in60, t2); // Eval sparse poly W step coeff_4 * z^4 let t35 = circuit_add(t33, t34); // Eval sparse poly W step + coeff_4 * z^4 let t36 = circuit_mul(in61, t4); // Eval sparse poly W step coeff_6 * z^6 let t37 = circuit_add(t35, t36); // Eval sparse poly W step + coeff_6 * z^6 let t38 = circuit_mul(in62, t6); // Eval sparse poly W step coeff_8 * z^8 let t39 = circuit_add(t37, t38); // Eval sparse poly W step + coeff_8 * z^8 let t40 = circuit_mul(in63, t8); // Eval sparse poly W step coeff_10 * z^10 let t41 = circuit_add(t39, t40); // Eval sparse poly W step + coeff_10 * z^10 let t42 = circuit_mul(in65, in57); // Eval C_inv step coeff_1 * z^1 let t43 = circuit_add(in64, t42); // Eval C_inv step + (coeff_1 * z^1) let t44 = circuit_mul(in66, t0); // Eval C_inv step coeff_2 * z^2 let t45 = circuit_add(t43, t44); // Eval C_inv step + (coeff_2 * z^2) let t46 = circuit_mul(in67, t1); // Eval C_inv step coeff_3 * z^3 let t47 = circuit_add(t45, t46); // Eval C_inv step + (coeff_3 * z^3) let t48 = circuit_mul(in68, t2); // Eval C_inv step coeff_4 * z^4 let t49 = circuit_add(t47, t48); // Eval C_inv step + (coeff_4 * z^4) let t50 = circuit_mul(in69, t3); // Eval C_inv step coeff_5 * z^5 let t51 = circuit_add(t49, t50); // Eval C_inv step + (coeff_5 * z^5) let t52 = circuit_mul(in70, t4); // Eval C_inv step coeff_6 * z^6 let t53 = circuit_add(t51, t52); // Eval C_inv step + (coeff_6 * z^6) let t54 = circuit_mul(in71, t5); // Eval C_inv step coeff_7 * z^7 let t55 = circuit_add(t53, t54); // Eval C_inv step + (coeff_7 * z^7) let t56 = circuit_mul(in72, t6); // Eval C_inv step coeff_8 * z^8 let t57 = circuit_add(t55, t56); // Eval C_inv step + (coeff_8 * z^8) let t58 = circuit_mul(in73, t7); // Eval C_inv step coeff_9 * z^9 let t59 = circuit_add(t57, t58); // Eval C_inv step + (coeff_9 * z^9) let t60 = circuit_mul(in74, t8); // Eval C_inv step coeff_10 * z^10 let t61 = circuit_add(t59, t60); // Eval C_inv step + (coeff_10 * z^10) let t62 = circuit_mul(in75, t9); // Eval C_inv step coeff_11 * z^11 let t63 = circuit_add(t61, t62); // Eval C_inv step + (coeff_11 * z^11) let t64 = circuit_mul(t31, t63); let t65 = circuit_sub(t64, in0); // c_of_z * c_inv_of_z - 1 let t66 = circuit_mul(in70, in1); let t67 = circuit_add(in64, t66); let t68 = circuit_mul(in65, in2); let t69 = circuit_mul(in71, in3); let t70 = circuit_add(t68, t69); let t71 = circuit_mul(in66, in4); let t72 = circuit_mul(in72, in5); let t73 = circuit_add(t71, t72); let t74 = circuit_mul(in67, in6); let t75 = circuit_mul(in73, in7); let t76 = circuit_add(t74, t75); let t77 = circuit_mul(in68, in8); let t78 = circuit_mul(in74, in9); let t79 = circuit_add(t77, t78); let t80 = circuit_mul(in69, in10); let t81 = circuit_mul(in75, in11); let t82 = circuit_add(t80, t81); let t83 = circuit_mul(in70, in12); let t84 = circuit_mul(in65, in13); let t85 = circuit_mul(in71, in14); let t86 = circuit_add(t84, t85); let t87 = circuit_mul(in66, in15); let t88 = circuit_mul(in72, in16); let t89 = circuit_add(t87, t88); let t90 = circuit_mul(in67, in17); let t91 = circuit_mul(in73, in18); let t92 = circuit_add(t90, t91); let t93 = circuit_mul(in68, in19); let t94 = circuit_mul(in74, in20); let t95 = circuit_add(t93, t94); let t96 = circuit_mul(in69, in21); let t97 = circuit_mul(in75, in22); let t98 = circuit_add(t96, t97); let t99 = circuit_mul(in46, in23); let t100 = circuit_mul(in47, in24); let t101 = circuit_mul(in48, in12); let t102 = circuit_mul(in49, in25); let t103 = circuit_mul(in50, in26); let t104 = circuit_mul(in52, in23); let t105 = circuit_mul(in53, in24); let t106 = circuit_mul(in54, in12); let t107 = circuit_mul(in55, in25); let t108 = circuit_mul(in56, in26); let t109 = circuit_mul(in70, in1); let t110 = circuit_add(in64, t109); let t111 = circuit_mul(in65, in27); let t112 = circuit_mul(in71, in28); let t113 = circuit_add(t111, t112); let t114 = circuit_mul(in66, in29); let t115 = circuit_mul(in72, in30); let t116 = circuit_add(t114, t115); let t117 = circuit_mul(in67, in18); let t118 = circuit_mul(in73, in31); let t119 = circuit_add(t117, t118); let t120 = circuit_mul(in68, in32); let t121 = circuit_mul(in74, in33); let t122 = circuit_add(t120, t121); let t123 = circuit_mul(in69, in34); let t124 = circuit_mul(in75, in35); let t125 = circuit_add(t123, t124); let t126 = circuit_mul(in70, in12); let t127 = circuit_mul(in65, in36); let t128 = circuit_mul(in71, in37); let t129 = circuit_add(t127, t128); let t130 = circuit_mul(in66, in38); let t131 = circuit_mul(in72, in39); let t132 = circuit_add(t130, t131); let t133 = circuit_mul(in67, in40); let t134 = circuit_mul(in73, in6); let t135 = circuit_add(t133, t134); let t136 = circuit_mul(in68, in41); let t137 = circuit_mul(in74, in42); let t138 = circuit_add(t136, t137); let t139 = circuit_mul(in69, in43); let t140 = circuit_mul(in75, in44); let t141 = circuit_add(t139, t140); let t142 = circuit_mul(t70, in57); // Eval C_inv_frob_1 step coeff_1 * z^1 let t143 = circuit_add(t67, t142); // Eval C_inv_frob_1 step + (coeff_1 * z^1) let t144 = circuit_mul(t73, t0); // Eval C_inv_frob_1 step coeff_2 * z^2 let t145 = circuit_add(t143, t144); // Eval C_inv_frob_1 step + (coeff_2 * z^2) let t146 = circuit_mul(t76, t1); // Eval C_inv_frob_1 step coeff_3 * z^3 let t147 = circuit_add(t145, t146); // Eval C_inv_frob_1 step + (coeff_3 * z^3) let t148 = circuit_mul(t79, t2); // Eval C_inv_frob_1 step coeff_4 * z^4 let t149 = circuit_add(t147, t148); // Eval C_inv_frob_1 step + (coeff_4 * z^4) let t150 = circuit_mul(t82, t3); // Eval C_inv_frob_1 step coeff_5 * z^5 let t151 = circuit_add(t149, t150); // Eval C_inv_frob_1 step + (coeff_5 * z^5) let t152 = circuit_mul(t83, t4); // Eval C_inv_frob_1 step coeff_6 * z^6 let t153 = circuit_add(t151, t152); // Eval C_inv_frob_1 step + (coeff_6 * z^6) let t154 = circuit_mul(t86, t5); // Eval C_inv_frob_1 step coeff_7 * z^7 let t155 = circuit_add(t153, t154); // Eval C_inv_frob_1 step + (coeff_7 * z^7) let t156 = circuit_mul(t89, t6); // Eval C_inv_frob_1 step coeff_8 * z^8 let t157 = circuit_add(t155, t156); // Eval C_inv_frob_1 step + (coeff_8 * z^8) let t158 = circuit_mul(t92, t7); // Eval C_inv_frob_1 step coeff_9 * z^9 let t159 = circuit_add(t157, t158); // Eval C_inv_frob_1 step + (coeff_9 * z^9) let t160 = circuit_mul(t95, t8); // Eval C_inv_frob_1 step coeff_10 * z^10 let t161 = circuit_add(t159, t160); // Eval C_inv_frob_1 step + (coeff_10 * z^10) let t162 = circuit_mul(t98, t9); // Eval C_inv_frob_1 step coeff_11 * z^11 let t163 = circuit_add(t161, t162); // Eval C_inv_frob_1 step + (coeff_11 * z^11) let t164 = circuit_mul(t99, in57); // Eval C_frob_2 step coeff_1 * z^1 let t165 = circuit_add(in45, t164); // Eval C_frob_2 step + (coeff_1 * z^1) let t166 = circuit_mul(t100, t0); // Eval C_frob_2 step coeff_2 * z^2 let t167 = circuit_add(t165, t166); // Eval C_frob_2 step + (coeff_2 * z^2) let t168 = circuit_mul(t101, t1); // Eval C_frob_2 step coeff_3 * z^3 let t169 = circuit_add(t167, t168); // Eval C_frob_2 step + (coeff_3 * z^3) let t170 = circuit_mul(t102, t2); // Eval C_frob_2 step coeff_4 * z^4 let t171 = circuit_add(t169, t170); // Eval C_frob_2 step + (coeff_4 * z^4) let t172 = circuit_mul(t103, t3); // Eval C_frob_2 step coeff_5 * z^5 let t173 = circuit_add(t171, t172); // Eval C_frob_2 step + (coeff_5 * z^5) let t174 = circuit_mul(in51, t4); // Eval C_frob_2 step coeff_6 * z^6 let t175 = circuit_add(t173, t174); // Eval C_frob_2 step + (coeff_6 * z^6) let t176 = circuit_mul(t104, t5); // Eval C_frob_2 step coeff_7 * z^7 let t177 = circuit_add(t175, t176); // Eval C_frob_2 step + (coeff_7 * z^7) let t178 = circuit_mul(t105, t6); // Eval C_frob_2 step coeff_8 * z^8 let t179 = circuit_add(t177, t178); // Eval C_frob_2 step + (coeff_8 * z^8) let t180 = circuit_mul(t106, t7); // Eval C_frob_2 step coeff_9 * z^9 let t181 = circuit_add(t179, t180); // Eval C_frob_2 step + (coeff_9 * z^9) let t182 = circuit_mul(t107, t8); // Eval C_frob_2 step coeff_10 * z^10 let t183 = circuit_add(t181, t182); // Eval C_frob_2 step + (coeff_10 * z^10) let t184 = circuit_mul(t108, t9); // Eval C_frob_2 step coeff_11 * z^11 let t185 = circuit_add(t183, t184); // Eval C_frob_2 step + (coeff_11 * z^11) let t186 = circuit_mul(t113, in57); // Eval C_inv_frob_3 step coeff_1 * z^1 let t187 = circuit_add(t110, t186); // Eval C_inv_frob_3 step + (coeff_1 * z^1) let t188 = circuit_mul(t116, t0); // Eval C_inv_frob_3 step coeff_2 * z^2 let t189 = circuit_add(t187, t188); // Eval C_inv_frob_3 step + (coeff_2 * z^2) let t190 = circuit_mul(t119, t1); // Eval C_inv_frob_3 step coeff_3 * z^3 let t191 = circuit_add(t189, t190); // Eval C_inv_frob_3 step + (coeff_3 * z^3) let t192 = circuit_mul(t122, t2); // Eval C_inv_frob_3 step coeff_4 * z^4 let t193 = circuit_add(t191, t192); // Eval C_inv_frob_3 step + (coeff_4 * z^4) let t194 = circuit_mul(t125, t3); // Eval C_inv_frob_3 step coeff_5 * z^5 let t195 = circuit_add(t193, t194); // Eval C_inv_frob_3 step + (coeff_5 * z^5) let t196 = circuit_mul(t126, t4); // Eval C_inv_frob_3 step coeff_6 * z^6 let t197 = circuit_add(t195, t196); // Eval C_inv_frob_3 step + (coeff_6 * z^6) let t198 = circuit_mul(t129, t5); // Eval C_inv_frob_3 step coeff_7 * z^7 let t199 = circuit_add(t197, t198); // Eval C_inv_frob_3 step + (coeff_7 * z^7) let t200 = circuit_mul(t132, t6); // Eval C_inv_frob_3 step coeff_8 * z^8 let t201 = circuit_add(t199, t200); // Eval C_inv_frob_3 step + (coeff_8 * z^8) let t202 = circuit_mul(t135, t7); // Eval C_inv_frob_3 step coeff_9 * z^9 let t203 = circuit_add(t201, t202); // Eval C_inv_frob_3 step + (coeff_9 * z^9) let t204 = circuit_mul(t138, t8); // Eval C_inv_frob_3 step coeff_10 * z^10 let t205 = circuit_add(t203, t204); // Eval C_inv_frob_3 step + (coeff_10 * z^10) let t206 = circuit_mul(t141, t9); // Eval C_inv_frob_3 step coeff_11 * z^11 let t207 = circuit_add(t205, t206); // Eval C_inv_frob_3 step + (coeff_11 * z^11) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t31, t41, t63, t65, t163, t185, t207).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(INITIALIZE_MPCHECK_BN254_CONSTANTS.span()); // in0 - in44 // Fill inputs: circuit_inputs = circuit_inputs.next_2(lambda_root.w0); // in45 circuit_inputs = circuit_inputs.next_2(lambda_root.w1); // in46 circuit_inputs = circuit_inputs.next_2(lambda_root.w2); // in47 circuit_inputs = circuit_inputs.next_2(lambda_root.w3); // in48 circuit_inputs = circuit_inputs.next_2(lambda_root.w4); // in49 circuit_inputs = circuit_inputs.next_2(lambda_root.w5); // in50 circuit_inputs = circuit_inputs.next_2(lambda_root.w6); // in51 circuit_inputs = circuit_inputs.next_2(lambda_root.w7); // in52 circuit_inputs = circuit_inputs.next_2(lambda_root.w8); // in53 circuit_inputs = circuit_inputs.next_2(lambda_root.w9); // in54 circuit_inputs = circuit_inputs.next_2(lambda_root.w10); // in55 circuit_inputs = circuit_inputs.next_2(lambda_root.w11); // in56 circuit_inputs = circuit_inputs.next_2(z); // in57 circuit_inputs = circuit_inputs.next_2(scaling_factor.w0); // in58 circuit_inputs = circuit_inputs.next_2(scaling_factor.w2); // in59 circuit_inputs = circuit_inputs.next_2(scaling_factor.w4); // in60 circuit_inputs = circuit_inputs.next_2(scaling_factor.w6); // in61 circuit_inputs = circuit_inputs.next_2(scaling_factor.w8); // in62 circuit_inputs = circuit_inputs.next_2(scaling_factor.w10); // in63 circuit_inputs = circuit_inputs.next_2(c_inv.w0); // in64 circuit_inputs = circuit_inputs.next_2(c_inv.w1); // in65 circuit_inputs = circuit_inputs.next_2(c_inv.w2); // in66 circuit_inputs = circuit_inputs.next_2(c_inv.w3); // in67 circuit_inputs = circuit_inputs.next_2(c_inv.w4); // in68 circuit_inputs = circuit_inputs.next_2(c_inv.w5); // in69 circuit_inputs = circuit_inputs.next_2(c_inv.w6); // in70 circuit_inputs = circuit_inputs.next_2(c_inv.w7); // in71 circuit_inputs = circuit_inputs.next_2(c_inv.w8); // in72 circuit_inputs = circuit_inputs.next_2(c_inv.w9); // in73 circuit_inputs = circuit_inputs.next_2(c_inv.w10); // in74 circuit_inputs = circuit_inputs.next_2(c_inv.w11); // in75 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let c_of_z: u384 = outputs.get_output(t31); let scaling_factor_of_z: u384 = outputs.get_output(t41); let c_inv_of_z: u384 = outputs.get_output(t63); let lhs: u384 = outputs.get_output(t65); let c_inv_frob_1_of_z: u384 = outputs.get_output(t163); let c_frob_2_of_z: u384 = outputs.get_output(t185); let c_inv_frob_3_of_z: u384 = outputs.get_output(t207); return ( c_of_z, scaling_factor_of_z, c_inv_of_z, lhs, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, ); } const INITIALIZE_MPCHECK_BN254_CONSTANTS: [u384; 45] = [ u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x12, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xfde6a43f5daa971f3fa65955, limb1: 0x1b2522ec5eb28ded6895e1cd, limb2: 0x1d8c8daef3eee1e8, limb3: 0x0, }, u384 { limb0: 0x42b29c567e9c385ce480a71a, limb1: 0x4e34e2ac06ead4000d14d1e2, limb2: 0x217e400dc9351e77, limb3: 0x0, }, u384 { limb0: 0xfd28d102c0d147b2f4d521a7, limb1: 0x8481d22c6934ce844d72f250, limb2: 0x242b719062f6737b, limb3: 0x0, }, u384 { limb0: 0x43ac198484b8d9094aa82536, limb1: 0x1b9c22d81246ffc2e794e176, limb2: 0x359809094bd5c8e, limb3: 0x0, }, u384 { limb0: 0x6df7b44cbb259ef7cb58d5ed, limb1: 0xdd4ef1e69a0c1f0dd2949fa, limb2: 0x21436d48fcb50cc6, limb3: 0x0, }, u384 { limb0: 0x8a4f4f0831364cf35f78f771, limb1: 0x38a4311a86919d9c7c6c15f8, limb2: 0x18857a58f3b5bb30, limb3: 0x0, }, u384 { limb0: 0x6fc008e7d6998c82f7fc048b, limb1: 0x62b7adefd44038ab3c0bbad9, limb2: 0x2c84bbad27c36715, limb3: 0x0, }, u384 { limb0: 0xa8697e0c9c36d8ca3339a7b5, limb1: 0x6d1eab6fcd18b99ad4afd096, limb2: 0xc33b1c70e4fd11b, limb3: 0x0, }, u384 { limb0: 0x5371c546d428780a6e3dcfa8, limb1: 0x13fe08bea73305ff6bdac77c, limb2: 0x1b007294a55accce, limb3: 0x0, }, u384 { limb0: 0x4f501fe811493d72543a3977, limb1: 0xefe88dd8e6965b3adae92c97, limb2: 0x215d42e7ac7bd17c, limb3: 0x0, }, u384 { limb0: 0x6871ca8d3c208c16d87cfd46, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x8eeec7e5ca5cf05f80f362ac, limb1: 0xa6327cfe12150b8e74799277, limb2: 0x246996f3b4fae7e6, limb3: 0x0, }, u384 { limb0: 0x6a8b264dde75f4f798d6a3f2, limb1: 0x9d2b22ca22ceca702eeb88c3, limb2: 0x12d7c0c3ed42be41, limb3: 0x0, }, u384 { limb0: 0xb7c9dce1665d51c640fcba2, limb1: 0x4ba4cc8bd75a079432ae2a1d, limb2: 0x16c9e55061ebae20, limb3: 0x0, }, u384 { limb0: 0x6b48f98a7b4f4463e3a7dba0, limb1: 0x33ce738a184c89d94a0e7840, limb2: 0xc38dce27e3b2cae, limb3: 0x0, }, u384 { limb0: 0x8fa25bd282d37f632623b0e3, limb1: 0x704b5a7ec796f2b21807dc9, limb2: 0x7c03cbcac41049a, limb3: 0x0, }, u384 { limb0: 0xfa7a164080faed1f0d24275a, limb1: 0xaa7b569817e0966cba582096, limb2: 0xf20e129e47c9363, limb3: 0x0, }, u384 { limb0: 0x1bdec763c13b4711cd2b8126, limb1: 0x9f3a80b03b0b1c923685d2ea, limb2: 0x2c145edbe7fd8aee, limb3: 0x0, }, u384 { limb0: 0xf8b1c1a56586ff93e080f8bc, limb1: 0x559897c6ad411fb25b75afb7, limb2: 0x3df92c5b96e3914, limb3: 0x0, }, u384 { limb0: 0x678e2ac024c6b8ee6e0c2c4b, limb1: 0xa27fb246c7729f7db080cb99, limb2: 0x12acf2ca76fd0675, limb3: 0x0, }, u384 { limb0: 0x1500054667f8140c6a3f2d9f, limb1: 0xa4523cf7da4e525e2ba6a315, limb2: 0x1563dbde3bd6d35b, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd49, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd48, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0xacdb5c4f5763473177fffffe, limb1: 0x59e26bcea0d48bacd4f263f1, limb2: 0x0, limb3: 0x0, }, u384 { limb0: 0xacdb5c4f5763473177ffffff, limb1: 0x59e26bcea0d48bacd4f263f1, limb2: 0x0, limb3: 0x0, }, u384 { limb0: 0x67dfc8fabd3581ad840ddd76, limb1: 0xb2bdfa8fef85fa07122bde8d, limb2: 0x13d0c369615f7bb0, limb3: 0x0, }, u384 { limb0: 0xac285af5685d3f90eacf7a66, limb1: 0xfc2bf531eb331a053a35744c, limb2: 0x18a0f4219f4fdff6, limb3: 0x0, }, u384 { limb0: 0x64e2b5a5bf22f67654883ae6, limb1: 0x79c3e050c9ca2a428908a812, limb2: 0xc3a5e9c462a6547, limb3: 0x0, }, u384 { limb0: 0x345582cc92fd973c74bd77f4, limb1: 0x5bdd2055c255cf9d9e08c1d9, limb2: 0x2ce02aa5f9bf8cd6, limb3: 0x0, }, u384 { limb0: 0xde227b850aea3f23790405d6, limb1: 0x7fac149bfaefbac11b155498, limb2: 0x17ded419ed7be4f9, limb3: 0x0, }, u384 { limb0: 0x4150a79753fb0cd31cc99cc0, limb1: 0x2fb81a8dccd8a9b4441d64f3, limb2: 0x1bfe7b214c029424, limb3: 0x0, }, u384 { limb0: 0x9efaf0f0f1a228f0d5662fbd, limb1: 0xd15da0ec97a9b8346513297b, limb2: 0x697b9c523e0390e, limb3: 0x0, }, u384 { limb0: 0x182d2db0c413901c32b0c6fe, limb1: 0xb5186d6ac4c723b85d3f78a3, limb2: 0x7a0e052f2b1c443, limb3: 0x0, }, u384 { limb0: 0x39c0d06b220500933945267f, limb1: 0x5dc79824a3792597356c892c, limb2: 0x1b76a37fba85f3cd, limb3: 0x0, }, u384 { limb0: 0x97d439ec7694aa2bf4c0c101, limb1: 0x6cbeee33576139d7f03a5e3, limb2: 0xabf8b60be77d73, limb3: 0x0, }, u384 { limb0: 0x9201927eeb0a69546f1fd1, limb1: 0x5924b2691fb5e5685558c04, limb2: 0x1c938b097fd22479, limb3: 0x0, }, u384 { limb0: 0x98ff2631380cab2baaa586de, limb1: 0xa9f30e6dec26094f0fdf31bf, limb2: 0x4f1de41b3d1766f, limb3: 0x0, }, u384 { limb0: 0x38f14e77cfd95a083f4c261, limb1: 0x3e8c6565b7b72e1b0e78c27f, limb2: 0x2429efd69b073ae2, limb3: 0x0, }, u384 { limb0: 0xd8cf6ebab94d0cb3b2594c64, limb1: 0xb14b900e9507e9327600ecc7, limb2: 0x28a411b634f09b8f, limb3: 0x0, }, u384 { limb0: 0x737f96e55fe3ed9d730c239f, limb1: 0xfeb0f6ef0cd21d04a44a9e08, limb2: 0x23d5e999e1910a12, limb3: 0x0, }, u384 { limb0: 0x272122f5e8257f43bbb36087, limb1: 0x88982b28b4a8aea95364059e, limb2: 0x1465d351952f0c05, limb3: 0x0, }, u384 { limb0: 0x200280211f25041384282499, limb1: 0x9fb1b2282a48633d3e2ddaea, limb2: 0x16db366a59b1dd0b, limb3: 0x0, }, u384 { limb0: 0x50449cdc780cfbfaa5cc3649, limb1: 0x337d84bbcba34a53a41f1ee, limb2: 0x28c36e1fee7fdbe6, limb3: 0x0, }, ]; #[inline(always)] pub fn run_BN254_MP_CHECK_BIT00_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_2nd_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_2nd_0_1: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let in26 = CE::> {}; let t0 = circuit_mul(in25, in25); // compute z^2 let t1 = circuit_mul(t0, in25); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in25); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in23, in23); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in5); let t7 = circuit_add(in4, t6); let t8 = circuit_mul(t7, in3); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in7); let t10 = circuit_add(in6, t9); let t11 = circuit_mul(t10, in2); // eval bn line by yInv let t12 = circuit_mul(in5, in3); // eval bn line by xNegOverY let t13 = circuit_mul(in7, in2); // eval bn line by yInv let t14 = circuit_mul(t8, in25); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t23 = circuit_mul(in0, in9); let t24 = circuit_add(in8, t23); let t25 = circuit_mul(t24, in13); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in11); let t27 = circuit_add(in10, t26); let t28 = circuit_mul(t27, in12); // eval bn line by yInv let t29 = circuit_mul(in9, in13); // eval bn line by xNegOverY let t30 = circuit_mul(in11, in12); // eval bn line by yInv let t31 = circuit_mul(t25, in25); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t40 = circuit_mul( t39, t39, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t41 = circuit_mul(in0, in15); let t42 = circuit_add(in14, t41); let t43 = circuit_mul(t42, in3); // eval bn line by xNegOverY let t44 = circuit_mul(in0, in17); let t45 = circuit_add(in16, t44); let t46 = circuit_mul(t45, in2); // eval bn line by yInv let t47 = circuit_mul(in15, in3); // eval bn line by xNegOverY let t48 = circuit_mul(in17, in2); // eval bn line by yInv let t49 = circuit_mul(t43, in25); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t50 = circuit_add(in1, t49); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t51 = circuit_mul(t46, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t52 = circuit_add(t50, t51); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t53 = circuit_mul(t47, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t54 = circuit_add(t52, t53); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t55 = circuit_mul(t48, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t56 = circuit_add(t54, t55); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t57 = circuit_mul(t40, t56); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t58 = circuit_mul(in0, in19); let t59 = circuit_add(in18, t58); let t60 = circuit_mul(t59, in13); // eval bn line by xNegOverY let t61 = circuit_mul(in0, in21); let t62 = circuit_add(in20, t61); let t63 = circuit_mul(t62, in12); // eval bn line by yInv let t64 = circuit_mul(in19, in13); // eval bn line by xNegOverY let t65 = circuit_mul(in21, in12); // eval bn line by yInv let t66 = circuit_mul(t60, in25); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t67 = circuit_add(in1, t66); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t68 = circuit_mul(t63, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t69 = circuit_add(t67, t68); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t70 = circuit_mul(t64, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t71 = circuit_add(t69, t70); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t72 = circuit_mul(t65, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t73 = circuit_add(t71, t72); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t74 = circuit_mul(t57, t73); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t75 = circuit_sub(t74, in24); // (Π(i,k) (Pk(z))) - Ri(z) let t76 = circuit_mul(in26, in22); let t77 = circuit_add(t76, t75); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t77,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in2 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a1); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a0); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a1); // in11 circuit_inputs = circuit_inputs.next_2(yInv_1); // in12 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a1); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a0); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a1); // in21 circuit_inputs = circuit_inputs.next_2(lhs_i); // in22 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in23 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in24 circuit_inputs = circuit_inputs.next_2(z); // in25 circuit_inputs = circuit_inputs.next_2(c1); // in26 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t77); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BN254_MP_CHECK_BIT00_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_2nd_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_2nd_0_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x3 let in3 = CE::> {}; // 0x6 let in4 = CE::> {}; // 0x0 // INPUT stack let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27, in28) = (CE::> {}, CE::> {}, CE::> {}); let (in29, in30, in31) = (CE::> {}, CE::> {}, CE::> {}); let (in32, in33, in34) = (CE::> {}, CE::> {}, CE::> {}); let in35 = CE::> {}; let t0 = circuit_mul(in34, in34); // compute z^2 let t1 = circuit_mul(t0, in34); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in34); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in32, in32); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in8); let t7 = circuit_add(in7, t6); let t8 = circuit_mul(t7, in6); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in10); let t10 = circuit_add(in9, t9); let t11 = circuit_mul(t10, in5); // eval bn line by yInv let t12 = circuit_mul(in8, in6); // eval bn line by xNegOverY let t13 = circuit_mul(in10, in5); // eval bn line by yInv let t14 = circuit_mul(t8, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t23 = circuit_mul(in0, in12); let t24 = circuit_add(in11, t23); let t25 = circuit_mul(t24, in16); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in14); let t27 = circuit_add(in13, t26); let t28 = circuit_mul(t27, in15); // eval bn line by yInv let t29 = circuit_mul(in12, in16); // eval bn line by xNegOverY let t30 = circuit_mul(in14, in15); // eval bn line by yInv let t31 = circuit_mul(t25, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t40 = circuit_add(in27, in28); // Doubling slope numerator start let t41 = circuit_sub(in27, in28); let t42 = circuit_mul(t40, t41); let t43 = circuit_mul(in27, in28); let t44 = circuit_mul(t42, in2); let t45 = circuit_mul(t43, in3); // Doubling slope numerator end let t46 = circuit_add(in29, in29); // Fp2 add coeff 0/1 let t47 = circuit_add(in30, in30); // Fp2 add coeff 1/1 let t48 = circuit_mul(t46, t46); // Fp2 Inv start let t49 = circuit_mul(t47, t47); let t50 = circuit_add(t48, t49); let t51 = circuit_inverse(t50); let t52 = circuit_mul(t46, t51); // Fp2 Inv real part end let t53 = circuit_mul(t47, t51); let t54 = circuit_sub(in4, t53); // Fp2 Inv imag part end let t55 = circuit_mul(t44, t52); // Fp2 mul start let t56 = circuit_mul(t45, t54); let t57 = circuit_sub(t55, t56); // Fp2 mul real part end let t58 = circuit_mul(t44, t54); let t59 = circuit_mul(t45, t52); let t60 = circuit_add(t58, t59); // Fp2 mul imag part end let t61 = circuit_add(t57, t60); let t62 = circuit_sub(t57, t60); let t63 = circuit_mul(t61, t62); let t64 = circuit_mul(t57, t60); let t65 = circuit_add(t64, t64); let t66 = circuit_add(in27, in27); // Fp2 add coeff 0/1 let t67 = circuit_add(in28, in28); // Fp2 add coeff 1/1 let t68 = circuit_sub(t63, t66); // Fp2 sub coeff 0/1 let t69 = circuit_sub(t65, t67); // Fp2 sub coeff 1/1 let t70 = circuit_sub(in27, t68); // Fp2 sub coeff 0/1 let t71 = circuit_sub(in28, t69); // Fp2 sub coeff 1/1 let t72 = circuit_mul(t57, t70); // Fp2 mul start let t73 = circuit_mul(t60, t71); let t74 = circuit_sub(t72, t73); // Fp2 mul real part end let t75 = circuit_mul(t57, t71); let t76 = circuit_mul(t60, t70); let t77 = circuit_add(t75, t76); // Fp2 mul imag part end let t78 = circuit_sub(t74, in29); // Fp2 sub coeff 0/1 let t79 = circuit_sub(t77, in30); // Fp2 sub coeff 1/1 let t80 = circuit_mul(t57, in27); // Fp2 mul start let t81 = circuit_mul(t60, in28); let t82 = circuit_sub(t80, t81); // Fp2 mul real part end let t83 = circuit_mul(t57, in28); let t84 = circuit_mul(t60, in27); let t85 = circuit_add(t83, t84); // Fp2 mul imag part end let t86 = circuit_sub(t82, in29); // Fp2 sub coeff 0/1 let t87 = circuit_sub(t85, in30); // Fp2 sub coeff 1/1 let t88 = circuit_mul(in0, t60); let t89 = circuit_add(t57, t88); let t90 = circuit_mul(t89, in26); // eval bn line by xNegOverY let t91 = circuit_mul(in0, t87); let t92 = circuit_add(t86, t91); let t93 = circuit_mul(t92, in25); // eval bn line by yInv let t94 = circuit_mul(t60, in26); // eval bn line by xNegOverY let t95 = circuit_mul(t87, in25); // eval bn line by yInv let t96 = circuit_mul(t90, in34); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t97 = circuit_add(in1, t96); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t98 = circuit_mul(t93, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t99 = circuit_add(t97, t98); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t100 = circuit_mul(t94, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t101 = circuit_add(t99, t100); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t102 = circuit_mul(t95, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t103 = circuit_add(t101, t102); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t104 = circuit_mul(t39, t103); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t105 = circuit_mul( t104, t104, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t106 = circuit_mul(in0, in18); let t107 = circuit_add(in17, t106); let t108 = circuit_mul(t107, in6); // eval bn line by xNegOverY let t109 = circuit_mul(in0, in20); let t110 = circuit_add(in19, t109); let t111 = circuit_mul(t110, in5); // eval bn line by yInv let t112 = circuit_mul(in18, in6); // eval bn line by xNegOverY let t113 = circuit_mul(in20, in5); // eval bn line by yInv let t114 = circuit_mul(t108, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t115 = circuit_add(in1, t114); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t116 = circuit_mul(t111, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t117 = circuit_add(t115, t116); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t118 = circuit_mul(t112, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t119 = circuit_add(t117, t118); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t120 = circuit_mul(t113, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t121 = circuit_add(t119, t120); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t122 = circuit_mul(t105, t121); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t123 = circuit_mul(in0, in22); let t124 = circuit_add(in21, t123); let t125 = circuit_mul(t124, in16); // eval bn line by xNegOverY let t126 = circuit_mul(in0, in24); let t127 = circuit_add(in23, t126); let t128 = circuit_mul(t127, in15); // eval bn line by yInv let t129 = circuit_mul(in22, in16); // eval bn line by xNegOverY let t130 = circuit_mul(in24, in15); // eval bn line by yInv let t131 = circuit_mul(t125, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t132 = circuit_add(in1, t131); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t133 = circuit_mul(t128, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t134 = circuit_add(t132, t133); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t135 = circuit_mul(t129, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t136 = circuit_add(t134, t135); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t137 = circuit_mul(t130, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t138 = circuit_add(t136, t137); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t139 = circuit_mul(t122, t138); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t140 = circuit_add(t68, t69); // Doubling slope numerator start let t141 = circuit_sub(t68, t69); let t142 = circuit_mul(t140, t141); let t143 = circuit_mul(t68, t69); let t144 = circuit_mul(t142, in2); let t145 = circuit_mul(t143, in3); // Doubling slope numerator end let t146 = circuit_add(t78, t78); // Fp2 add coeff 0/1 let t147 = circuit_add(t79, t79); // Fp2 add coeff 1/1 let t148 = circuit_mul(t146, t146); // Fp2 Inv start let t149 = circuit_mul(t147, t147); let t150 = circuit_add(t148, t149); let t151 = circuit_inverse(t150); let t152 = circuit_mul(t146, t151); // Fp2 Inv real part end let t153 = circuit_mul(t147, t151); let t154 = circuit_sub(in4, t153); // Fp2 Inv imag part end let t155 = circuit_mul(t144, t152); // Fp2 mul start let t156 = circuit_mul(t145, t154); let t157 = circuit_sub(t155, t156); // Fp2 mul real part end let t158 = circuit_mul(t144, t154); let t159 = circuit_mul(t145, t152); let t160 = circuit_add(t158, t159); // Fp2 mul imag part end let t161 = circuit_add(t157, t160); let t162 = circuit_sub(t157, t160); let t163 = circuit_mul(t161, t162); let t164 = circuit_mul(t157, t160); let t165 = circuit_add(t164, t164); let t166 = circuit_add(t68, t68); // Fp2 add coeff 0/1 let t167 = circuit_add(t69, t69); // Fp2 add coeff 1/1 let t168 = circuit_sub(t163, t166); // Fp2 sub coeff 0/1 let t169 = circuit_sub(t165, t167); // Fp2 sub coeff 1/1 let t170 = circuit_sub(t68, t168); // Fp2 sub coeff 0/1 let t171 = circuit_sub(t69, t169); // Fp2 sub coeff 1/1 let t172 = circuit_mul(t157, t170); // Fp2 mul start let t173 = circuit_mul(t160, t171); let t174 = circuit_sub(t172, t173); // Fp2 mul real part end let t175 = circuit_mul(t157, t171); let t176 = circuit_mul(t160, t170); let t177 = circuit_add(t175, t176); // Fp2 mul imag part end let t178 = circuit_sub(t174, t78); // Fp2 sub coeff 0/1 let t179 = circuit_sub(t177, t79); // Fp2 sub coeff 1/1 let t180 = circuit_mul(t157, t68); // Fp2 mul start let t181 = circuit_mul(t160, t69); let t182 = circuit_sub(t180, t181); // Fp2 mul real part end let t183 = circuit_mul(t157, t69); let t184 = circuit_mul(t160, t68); let t185 = circuit_add(t183, t184); // Fp2 mul imag part end let t186 = circuit_sub(t182, t78); // Fp2 sub coeff 0/1 let t187 = circuit_sub(t185, t79); // Fp2 sub coeff 1/1 let t188 = circuit_mul(in0, t160); let t189 = circuit_add(t157, t188); let t190 = circuit_mul(t189, in26); // eval bn line by xNegOverY let t191 = circuit_mul(in0, t187); let t192 = circuit_add(t186, t191); let t193 = circuit_mul(t192, in25); // eval bn line by yInv let t194 = circuit_mul(t160, in26); // eval bn line by xNegOverY let t195 = circuit_mul(t187, in25); // eval bn line by yInv let t196 = circuit_mul(t190, in34); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t197 = circuit_add(in1, t196); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t198 = circuit_mul(t193, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t199 = circuit_add(t197, t198); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t200 = circuit_mul(t194, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t201 = circuit_add(t199, t200); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t202 = circuit_mul(t195, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t203 = circuit_add(t201, t202); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t204 = circuit_mul(t139, t203); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t205 = circuit_sub(t204, in33); // (Π(i,k) (Pk(z))) - Ri(z) let t206 = circuit_mul(in35, in31); let t207 = circuit_add(t206, t205); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t168, t169, t178, t179, t207).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in3 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in4 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in5 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r0a1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_0.r1a1); // in14 circuit_inputs = circuit_inputs.next_2(yInv_1); // in15 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a0); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r0a1); // in22 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a0); // in23 circuit_inputs = circuit_inputs.next_2(G2_line_2nd_0_1.r1a1); // in24 circuit_inputs = circuit_inputs.next_2(yInv_2); // in25 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in26 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in27 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in28 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in29 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in30 circuit_inputs = circuit_inputs.next_2(lhs_i); // in31 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in32 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in33 circuit_inputs = circuit_inputs.next_2(z); // in34 circuit_inputs = circuit_inputs.next_2(c1); // in35 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t168), x1: outputs.get_output(t169), y0: outputs.get_output(t178), y1: outputs.get_output(t179), }; let lhs_i_plus_one: u384 = outputs.get_output(t207); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BN254_MP_CHECK_BIT01_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_dbl_10: G2Line, G2_line_add_10: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_dbl_11: G2Line, G2_line_add_11: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27, in28) = (CE::> {}, CE::> {}, CE::> {}); let (in29, in30, in31) = (CE::> {}, CE::> {}, CE::> {}); let (in32, in33, in34) = (CE::> {}, CE::> {}, CE::> {}); let in35 = CE::> {}; let t0 = circuit_mul(in34, in34); // compute z^2 let t1 = circuit_mul(t0, in34); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in34); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in31, in31); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in5); let t7 = circuit_add(in4, t6); let t8 = circuit_mul(t7, in3); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in7); let t10 = circuit_add(in6, t9); let t11 = circuit_mul(t10, in2); // eval bn line by yInv let t12 = circuit_mul(in5, in3); // eval bn line by xNegOverY let t13 = circuit_mul(in7, in2); // eval bn line by yInv let t14 = circuit_mul(t8, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t23 = circuit_mul(in0, in9); let t24 = circuit_add(in8, t23); let t25 = circuit_mul(t24, in17); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in11); let t27 = circuit_add(in10, t26); let t28 = circuit_mul(t27, in16); // eval bn line by yInv let t29 = circuit_mul(in9, in17); // eval bn line by xNegOverY let t30 = circuit_mul(in11, in16); // eval bn line by yInv let t31 = circuit_mul(t25, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t40 = circuit_mul( t39, t39, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t41 = circuit_mul(in0, in13); let t42 = circuit_add(in12, t41); let t43 = circuit_mul(t42, in3); // eval bn line by xNegOverY let t44 = circuit_mul(in0, in15); let t45 = circuit_add(in14, t44); let t46 = circuit_mul(t45, in2); // eval bn line by yInv let t47 = circuit_mul(in13, in3); // eval bn line by xNegOverY let t48 = circuit_mul(in15, in2); // eval bn line by yInv let t49 = circuit_mul(in0, in19); let t50 = circuit_add(in18, t49); let t51 = circuit_mul(t50, in3); // eval bn line by xNegOverY let t52 = circuit_mul(in0, in21); let t53 = circuit_add(in20, t52); let t54 = circuit_mul(t53, in2); // eval bn line by yInv let t55 = circuit_mul(in19, in3); // eval bn line by xNegOverY let t56 = circuit_mul(in21, in2); // eval bn line by yInv let t57 = circuit_mul(t43, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t58 = circuit_add(in1, t57); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t59 = circuit_mul(t46, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t60 = circuit_add(t58, t59); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t61 = circuit_mul(t47, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t62 = circuit_add(t60, t61); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t63 = circuit_mul(t48, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t64 = circuit_add(t62, t63); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t65 = circuit_mul(t40, t64); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t66 = circuit_mul(t51, in34); // Eval sparse poly line_0p_2 step coeff_1 * z^1 let t67 = circuit_add(in1, t66); // Eval sparse poly line_0p_2 step + coeff_1 * z^1 let t68 = circuit_mul(t54, t1); // Eval sparse poly line_0p_2 step coeff_3 * z^3 let t69 = circuit_add(t67, t68); // Eval sparse poly line_0p_2 step + coeff_3 * z^3 let t70 = circuit_mul(t55, t3); // Eval sparse poly line_0p_2 step coeff_7 * z^7 let t71 = circuit_add(t69, t70); // Eval sparse poly line_0p_2 step + coeff_7 * z^7 let t72 = circuit_mul(t56, t4); // Eval sparse poly line_0p_2 step coeff_9 * z^9 let t73 = circuit_add(t71, t72); // Eval sparse poly line_0p_2 step + coeff_9 * z^9 let t74 = circuit_mul(t65, t73); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t75 = circuit_mul(in0, in23); let t76 = circuit_add(in22, t75); let t77 = circuit_mul(t76, in17); // eval bn line by xNegOverY let t78 = circuit_mul(in0, in25); let t79 = circuit_add(in24, t78); let t80 = circuit_mul(t79, in16); // eval bn line by yInv let t81 = circuit_mul(in23, in17); // eval bn line by xNegOverY let t82 = circuit_mul(in25, in16); // eval bn line by yInv let t83 = circuit_mul(in0, in27); let t84 = circuit_add(in26, t83); let t85 = circuit_mul(t84, in17); // eval bn line by xNegOverY let t86 = circuit_mul(in0, in29); let t87 = circuit_add(in28, t86); let t88 = circuit_mul(t87, in16); // eval bn line by yInv let t89 = circuit_mul(in27, in17); // eval bn line by xNegOverY let t90 = circuit_mul(in29, in16); // eval bn line by yInv let t91 = circuit_mul(t77, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t92 = circuit_add(in1, t91); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t93 = circuit_mul(t80, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t94 = circuit_add(t92, t93); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t95 = circuit_mul(t81, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t96 = circuit_add(t94, t95); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t97 = circuit_mul(t82, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t98 = circuit_add(t96, t97); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t99 = circuit_mul(t74, t98); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t100 = circuit_mul(t85, in34); // Eval sparse poly line_1p_2 step coeff_1 * z^1 let t101 = circuit_add(in1, t100); // Eval sparse poly line_1p_2 step + coeff_1 * z^1 let t102 = circuit_mul(t88, t1); // Eval sparse poly line_1p_2 step coeff_3 * z^3 let t103 = circuit_add(t101, t102); // Eval sparse poly line_1p_2 step + coeff_3 * z^3 let t104 = circuit_mul(t89, t3); // Eval sparse poly line_1p_2 step coeff_7 * z^7 let t105 = circuit_add(t103, t104); // Eval sparse poly line_1p_2 step + coeff_7 * z^7 let t106 = circuit_mul(t90, t4); // Eval sparse poly line_1p_2 step coeff_9 * z^9 let t107 = circuit_add(t105, t106); // Eval sparse poly line_1p_2 step + coeff_9 * z^9 let t108 = circuit_mul(t99, t107); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t109 = circuit_mul(t108, in33); let t110 = circuit_sub(t109, in32); // (Π(i,k) (Pk(z))) - Ri(z) let t111 = circuit_mul(in35, in30); let t112 = circuit_add(t111, t110); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t112,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in2 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r0a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r0a1); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r1a0); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r1a1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(yInv_1); // in16 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r0a0); // in22 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r0a1); // in23 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r1a0); // in24 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r1a1); // in25 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r0a0); // in26 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r0a1); // in27 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r1a0); // in28 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r1a1); // in29 circuit_inputs = circuit_inputs.next_2(lhs_i); // in30 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in31 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in32 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in33 circuit_inputs = circuit_inputs.next_2(z); // in34 circuit_inputs = circuit_inputs.next_2(c1); // in35 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t112); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BN254_MP_CHECK_BIT01_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_dbl_10: G2Line, G2_line_add_10: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_dbl_11: G2Line, G2_line_add_11: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, Q_or_Q_neg_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x3 let in3 = CE::> {}; // 0x6 let in4 = CE::> {}; // 0x0 // INPUT stack let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27, in28) = (CE::> {}, CE::> {}, CE::> {}); let (in29, in30, in31) = (CE::> {}, CE::> {}, CE::> {}); let (in32, in33, in34) = (CE::> {}, CE::> {}, CE::> {}); let (in35, in36, in37) = (CE::> {}, CE::> {}, CE::> {}); let (in38, in39, in40) = (CE::> {}, CE::> {}, CE::> {}); let (in41, in42, in43) = (CE::> {}, CE::> {}, CE::> {}); let (in44, in45, in46) = (CE::> {}, CE::> {}, CE::> {}); let (in47, in48) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in47, in47); // compute z^2 let t1 = circuit_mul(t0, in47); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in47); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in44, in44); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in8); let t7 = circuit_add(in7, t6); let t8 = circuit_mul(t7, in6); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in10); let t10 = circuit_add(in9, t9); let t11 = circuit_mul(t10, in5); // eval bn line by yInv let t12 = circuit_mul(in8, in6); // eval bn line by xNegOverY let t13 = circuit_mul(in10, in5); // eval bn line by yInv let t14 = circuit_mul(t8, in47); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t23 = circuit_mul(in0, in12); let t24 = circuit_add(in11, t23); let t25 = circuit_mul(t24, in20); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in14); let t27 = circuit_add(in13, t26); let t28 = circuit_mul(t27, in19); // eval bn line by yInv let t29 = circuit_mul(in12, in20); // eval bn line by xNegOverY let t30 = circuit_mul(in14, in19); // eval bn line by yInv let t31 = circuit_mul(t25, in47); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t40 = circuit_add(in35, in36); // Doubling slope numerator start let t41 = circuit_sub(in35, in36); let t42 = circuit_mul(t40, t41); let t43 = circuit_mul(in35, in36); let t44 = circuit_mul(t42, in2); let t45 = circuit_mul(t43, in3); // Doubling slope numerator end let t46 = circuit_add(in37, in37); // Fp2 add coeff 0/1 let t47 = circuit_add(in38, in38); // Fp2 add coeff 1/1 let t48 = circuit_mul(t46, t46); // Fp2 Inv start let t49 = circuit_mul(t47, t47); let t50 = circuit_add(t48, t49); let t51 = circuit_inverse(t50); let t52 = circuit_mul(t46, t51); // Fp2 Inv real part end let t53 = circuit_mul(t47, t51); let t54 = circuit_sub(in4, t53); // Fp2 Inv imag part end let t55 = circuit_mul(t44, t52); // Fp2 mul start let t56 = circuit_mul(t45, t54); let t57 = circuit_sub(t55, t56); // Fp2 mul real part end let t58 = circuit_mul(t44, t54); let t59 = circuit_mul(t45, t52); let t60 = circuit_add(t58, t59); // Fp2 mul imag part end let t61 = circuit_add(t57, t60); let t62 = circuit_sub(t57, t60); let t63 = circuit_mul(t61, t62); let t64 = circuit_mul(t57, t60); let t65 = circuit_add(t64, t64); let t66 = circuit_add(in35, in35); // Fp2 add coeff 0/1 let t67 = circuit_add(in36, in36); // Fp2 add coeff 1/1 let t68 = circuit_sub(t63, t66); // Fp2 sub coeff 0/1 let t69 = circuit_sub(t65, t67); // Fp2 sub coeff 1/1 let t70 = circuit_sub(in35, t68); // Fp2 sub coeff 0/1 let t71 = circuit_sub(in36, t69); // Fp2 sub coeff 1/1 let t72 = circuit_mul(t57, t70); // Fp2 mul start let t73 = circuit_mul(t60, t71); let t74 = circuit_sub(t72, t73); // Fp2 mul real part end let t75 = circuit_mul(t57, t71); let t76 = circuit_mul(t60, t70); let t77 = circuit_add(t75, t76); // Fp2 mul imag part end let t78 = circuit_sub(t74, in37); // Fp2 sub coeff 0/1 let t79 = circuit_sub(t77, in38); // Fp2 sub coeff 1/1 let t80 = circuit_mul(t57, in35); // Fp2 mul start let t81 = circuit_mul(t60, in36); let t82 = circuit_sub(t80, t81); // Fp2 mul real part end let t83 = circuit_mul(t57, in36); let t84 = circuit_mul(t60, in35); let t85 = circuit_add(t83, t84); // Fp2 mul imag part end let t86 = circuit_sub(t82, in37); // Fp2 sub coeff 0/1 let t87 = circuit_sub(t85, in38); // Fp2 sub coeff 1/1 let t88 = circuit_mul(in0, t60); let t89 = circuit_add(t57, t88); let t90 = circuit_mul(t89, in34); // eval bn line by xNegOverY let t91 = circuit_mul(in0, t87); let t92 = circuit_add(t86, t91); let t93 = circuit_mul(t92, in33); // eval bn line by yInv let t94 = circuit_mul(t60, in34); // eval bn line by xNegOverY let t95 = circuit_mul(t87, in33); // eval bn line by yInv let t96 = circuit_mul(t90, in47); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t97 = circuit_add(in1, t96); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t98 = circuit_mul(t93, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t99 = circuit_add(t97, t98); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t100 = circuit_mul(t94, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t101 = circuit_add(t99, t100); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t102 = circuit_mul(t95, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t103 = circuit_add(t101, t102); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t104 = circuit_mul(t39, t103); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t105 = circuit_mul( t104, t104, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t106 = circuit_mul(in0, in16); let t107 = circuit_add(in15, t106); let t108 = circuit_mul(t107, in6); // eval bn line by xNegOverY let t109 = circuit_mul(in0, in18); let t110 = circuit_add(in17, t109); let t111 = circuit_mul(t110, in5); // eval bn line by yInv let t112 = circuit_mul(in16, in6); // eval bn line by xNegOverY let t113 = circuit_mul(in18, in5); // eval bn line by yInv let t114 = circuit_mul(in0, in22); let t115 = circuit_add(in21, t114); let t116 = circuit_mul(t115, in6); // eval bn line by xNegOverY let t117 = circuit_mul(in0, in24); let t118 = circuit_add(in23, t117); let t119 = circuit_mul(t118, in5); // eval bn line by yInv let t120 = circuit_mul(in22, in6); // eval bn line by xNegOverY let t121 = circuit_mul(in24, in5); // eval bn line by yInv let t122 = circuit_mul(t108, in47); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t123 = circuit_add(in1, t122); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t124 = circuit_mul(t111, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t125 = circuit_add(t123, t124); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t126 = circuit_mul(t112, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t127 = circuit_add(t125, t126); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t128 = circuit_mul(t113, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t129 = circuit_add(t127, t128); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t130 = circuit_mul(t105, t129); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t131 = circuit_mul(t116, in47); // Eval sparse poly line_0p_2 step coeff_1 * z^1 let t132 = circuit_add(in1, t131); // Eval sparse poly line_0p_2 step + coeff_1 * z^1 let t133 = circuit_mul(t119, t1); // Eval sparse poly line_0p_2 step coeff_3 * z^3 let t134 = circuit_add(t132, t133); // Eval sparse poly line_0p_2 step + coeff_3 * z^3 let t135 = circuit_mul(t120, t3); // Eval sparse poly line_0p_2 step coeff_7 * z^7 let t136 = circuit_add(t134, t135); // Eval sparse poly line_0p_2 step + coeff_7 * z^7 let t137 = circuit_mul(t121, t4); // Eval sparse poly line_0p_2 step coeff_9 * z^9 let t138 = circuit_add(t136, t137); // Eval sparse poly line_0p_2 step + coeff_9 * z^9 let t139 = circuit_mul(t130, t138); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t140 = circuit_mul(in0, in26); let t141 = circuit_add(in25, t140); let t142 = circuit_mul(t141, in20); // eval bn line by xNegOverY let t143 = circuit_mul(in0, in28); let t144 = circuit_add(in27, t143); let t145 = circuit_mul(t144, in19); // eval bn line by yInv let t146 = circuit_mul(in26, in20); // eval bn line by xNegOverY let t147 = circuit_mul(in28, in19); // eval bn line by yInv let t148 = circuit_mul(in0, in30); let t149 = circuit_add(in29, t148); let t150 = circuit_mul(t149, in20); // eval bn line by xNegOverY let t151 = circuit_mul(in0, in32); let t152 = circuit_add(in31, t151); let t153 = circuit_mul(t152, in19); // eval bn line by yInv let t154 = circuit_mul(in30, in20); // eval bn line by xNegOverY let t155 = circuit_mul(in32, in19); // eval bn line by yInv let t156 = circuit_mul(t142, in47); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t157 = circuit_add(in1, t156); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t158 = circuit_mul(t145, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t159 = circuit_add(t157, t158); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t160 = circuit_mul(t146, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t161 = circuit_add(t159, t160); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t162 = circuit_mul(t147, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t163 = circuit_add(t161, t162); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t164 = circuit_mul(t139, t163); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t165 = circuit_mul(t150, in47); // Eval sparse poly line_1p_2 step coeff_1 * z^1 let t166 = circuit_add(in1, t165); // Eval sparse poly line_1p_2 step + coeff_1 * z^1 let t167 = circuit_mul(t153, t1); // Eval sparse poly line_1p_2 step coeff_3 * z^3 let t168 = circuit_add(t166, t167); // Eval sparse poly line_1p_2 step + coeff_3 * z^3 let t169 = circuit_mul(t154, t3); // Eval sparse poly line_1p_2 step coeff_7 * z^7 let t170 = circuit_add(t168, t169); // Eval sparse poly line_1p_2 step + coeff_7 * z^7 let t171 = circuit_mul(t155, t4); // Eval sparse poly line_1p_2 step coeff_9 * z^9 let t172 = circuit_add(t170, t171); // Eval sparse poly line_1p_2 step + coeff_9 * z^9 let t173 = circuit_mul(t164, t172); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t174 = circuit_sub(t78, in41); // Fp2 sub coeff 0/1 let t175 = circuit_sub(t79, in42); // Fp2 sub coeff 1/1 let t176 = circuit_sub(t68, in39); // Fp2 sub coeff 0/1 let t177 = circuit_sub(t69, in40); // Fp2 sub coeff 1/1 let t178 = circuit_mul(t176, t176); // Fp2 Inv start let t179 = circuit_mul(t177, t177); let t180 = circuit_add(t178, t179); let t181 = circuit_inverse(t180); let t182 = circuit_mul(t176, t181); // Fp2 Inv real part end let t183 = circuit_mul(t177, t181); let t184 = circuit_sub(in4, t183); // Fp2 Inv imag part end let t185 = circuit_mul(t174, t182); // Fp2 mul start let t186 = circuit_mul(t175, t184); let t187 = circuit_sub(t185, t186); // Fp2 mul real part end let t188 = circuit_mul(t174, t184); let t189 = circuit_mul(t175, t182); let t190 = circuit_add(t188, t189); // Fp2 mul imag part end let t191 = circuit_add(t187, t190); let t192 = circuit_sub(t187, t190); let t193 = circuit_mul(t191, t192); let t194 = circuit_mul(t187, t190); let t195 = circuit_add(t194, t194); let t196 = circuit_add(t68, in39); // Fp2 add coeff 0/1 let t197 = circuit_add(t69, in40); // Fp2 add coeff 1/1 let t198 = circuit_sub(t193, t196); // Fp2 sub coeff 0/1 let t199 = circuit_sub(t195, t197); // Fp2 sub coeff 1/1 let t200 = circuit_mul(t187, t68); // Fp2 mul start let t201 = circuit_mul(t190, t69); let t202 = circuit_sub(t200, t201); // Fp2 mul real part end let t203 = circuit_mul(t187, t69); let t204 = circuit_mul(t190, t68); let t205 = circuit_add(t203, t204); // Fp2 mul imag part end let t206 = circuit_sub(t202, t78); // Fp2 sub coeff 0/1 let t207 = circuit_sub(t205, t79); // Fp2 sub coeff 1/1 let t208 = circuit_add(t78, t78); // Fp2 add coeff 0/1 let t209 = circuit_add(t79, t79); // Fp2 add coeff 1/1 let t210 = circuit_sub(t198, t68); // Fp2 sub coeff 0/1 let t211 = circuit_sub(t199, t69); // Fp2 sub coeff 1/1 let t212 = circuit_mul(t210, t210); // Fp2 Inv start let t213 = circuit_mul(t211, t211); let t214 = circuit_add(t212, t213); let t215 = circuit_inverse(t214); let t216 = circuit_mul(t210, t215); // Fp2 Inv real part end let t217 = circuit_mul(t211, t215); let t218 = circuit_sub(in4, t217); // Fp2 Inv imag part end let t219 = circuit_mul(t208, t216); // Fp2 mul start let t220 = circuit_mul(t209, t218); let t221 = circuit_sub(t219, t220); // Fp2 mul real part end let t222 = circuit_mul(t208, t218); let t223 = circuit_mul(t209, t216); let t224 = circuit_add(t222, t223); // Fp2 mul imag part end let t225 = circuit_add(t187, t221); // Fp2 add coeff 0/1 let t226 = circuit_add(t190, t224); // Fp2 add coeff 1/1 let t227 = circuit_sub(in4, t225); // Fp2 neg coeff 0/1 let t228 = circuit_sub(in4, t226); // Fp2 neg coeff 1/1 let t229 = circuit_add(t227, t228); let t230 = circuit_sub(t227, t228); let t231 = circuit_mul(t229, t230); let t232 = circuit_mul(t227, t228); let t233 = circuit_add(t232, t232); let t234 = circuit_sub(t231, t68); // Fp2 sub coeff 0/1 let t235 = circuit_sub(t233, t69); // Fp2 sub coeff 1/1 let t236 = circuit_sub(t234, t198); // Fp2 sub coeff 0/1 let t237 = circuit_sub(t235, t199); // Fp2 sub coeff 1/1 let t238 = circuit_sub(t68, t236); // Fp2 sub coeff 0/1 let t239 = circuit_sub(t69, t237); // Fp2 sub coeff 1/1 let t240 = circuit_mul(t227, t238); // Fp2 mul start let t241 = circuit_mul(t228, t239); let t242 = circuit_sub(t240, t241); // Fp2 mul real part end let t243 = circuit_mul(t227, t239); let t244 = circuit_mul(t228, t238); let t245 = circuit_add(t243, t244); // Fp2 mul imag part end let t246 = circuit_sub(t242, t78); // Fp2 sub coeff 0/1 let t247 = circuit_sub(t245, t79); // Fp2 sub coeff 1/1 let t248 = circuit_mul(t227, t68); // Fp2 mul start let t249 = circuit_mul(t228, t69); let t250 = circuit_sub(t248, t249); // Fp2 mul real part end let t251 = circuit_mul(t227, t69); let t252 = circuit_mul(t228, t68); let t253 = circuit_add(t251, t252); // Fp2 mul imag part end let t254 = circuit_sub(t250, t78); // Fp2 sub coeff 0/1 let t255 = circuit_sub(t253, t79); // Fp2 sub coeff 1/1 let t256 = circuit_mul(in0, t190); let t257 = circuit_add(t187, t256); let t258 = circuit_mul(t257, in34); // eval bn line by xNegOverY let t259 = circuit_mul(in0, t207); let t260 = circuit_add(t206, t259); let t261 = circuit_mul(t260, in33); // eval bn line by yInv let t262 = circuit_mul(t190, in34); // eval bn line by xNegOverY let t263 = circuit_mul(t207, in33); // eval bn line by yInv let t264 = circuit_mul(in0, t228); let t265 = circuit_add(t227, t264); let t266 = circuit_mul(t265, in34); // eval bn line by xNegOverY let t267 = circuit_mul(in0, t255); let t268 = circuit_add(t254, t267); let t269 = circuit_mul(t268, in33); // eval bn line by yInv let t270 = circuit_mul(t228, in34); // eval bn line by xNegOverY let t271 = circuit_mul(t255, in33); // eval bn line by yInv let t272 = circuit_mul(t258, in47); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t273 = circuit_add(in1, t272); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t274 = circuit_mul(t261, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t275 = circuit_add(t273, t274); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t276 = circuit_mul(t262, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t277 = circuit_add(t275, t276); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t278 = circuit_mul(t263, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t279 = circuit_add(t277, t278); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t280 = circuit_mul(t173, t279); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t281 = circuit_mul(t266, in47); // Eval sparse poly line_2p_2 step coeff_1 * z^1 let t282 = circuit_add(in1, t281); // Eval sparse poly line_2p_2 step + coeff_1 * z^1 let t283 = circuit_mul(t269, t1); // Eval sparse poly line_2p_2 step coeff_3 * z^3 let t284 = circuit_add(t282, t283); // Eval sparse poly line_2p_2 step + coeff_3 * z^3 let t285 = circuit_mul(t270, t3); // Eval sparse poly line_2p_2 step coeff_7 * z^7 let t286 = circuit_add(t284, t285); // Eval sparse poly line_2p_2 step + coeff_7 * z^7 let t287 = circuit_mul(t271, t4); // Eval sparse poly line_2p_2 step coeff_9 * z^9 let t288 = circuit_add(t286, t287); // Eval sparse poly line_2p_2 step + coeff_9 * z^9 let t289 = circuit_mul(t280, t288); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t290 = circuit_mul(t289, in46); let t291 = circuit_sub(t290, in45); // (Π(i,k) (Pk(z))) - Ri(z) let t292 = circuit_mul(in48, in43); let t293 = circuit_add(t292, t291); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t236, t237, t246, t247, t293).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in3 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in4 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in5 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r0a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r0a1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r1a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_10.r1a1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r0a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r0a1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r1a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_add_10.r1a1); // in18 circuit_inputs = circuit_inputs.next_2(yInv_1); // in19 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in22 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in23 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in24 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r0a0); // in25 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r0a1); // in26 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r1a0); // in27 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_11.r1a1); // in28 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r0a0); // in29 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r0a1); // in30 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r1a0); // in31 circuit_inputs = circuit_inputs.next_2(G2_line_add_11.r1a1); // in32 circuit_inputs = circuit_inputs.next_2(yInv_2); // in33 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in34 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in35 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in36 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in37 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in38 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x0); // in39 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x1); // in40 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y0); // in41 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y1); // in42 circuit_inputs = circuit_inputs.next_2(lhs_i); // in43 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in44 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in45 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in46 circuit_inputs = circuit_inputs.next_2(z); // in47 circuit_inputs = circuit_inputs.next_2(c1); // in48 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t236), x1: outputs.get_output(t237), y0: outputs.get_output(t246), y1: outputs.get_output(t247), }; let lhs_i_plus_one: u384 = outputs.get_output(t293); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BN254_MP_CHECK_BIT10_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_add_1_0: G2Line, G2_line_dbl_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_add_1_1: G2Line, G2_line_dbl_0_1: G2Line, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27, in28) = (CE::> {}, CE::> {}, CE::> {}); let (in29, in30, in31) = (CE::> {}, CE::> {}, CE::> {}); let (in32, in33, in34) = (CE::> {}, CE::> {}, CE::> {}); let in35 = CE::> {}; let t0 = circuit_mul(in34, in34); // compute z^2 let t1 = circuit_mul(t0, in34); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in34); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in31, in31); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in5); let t7 = circuit_add(in4, t6); let t8 = circuit_mul(t7, in3); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in7); let t10 = circuit_add(in6, t9); let t11 = circuit_mul(t10, in2); // eval bn line by yInv let t12 = circuit_mul(in5, in3); // eval bn line by xNegOverY let t13 = circuit_mul(in7, in2); // eval bn line by yInv let t14 = circuit_mul(in0, in9); let t15 = circuit_add(in8, t14); let t16 = circuit_mul(t15, in3); // eval bn line by xNegOverY let t17 = circuit_mul(in0, in11); let t18 = circuit_add(in10, t17); let t19 = circuit_mul(t18, in2); // eval bn line by yInv let t20 = circuit_mul(in9, in3); // eval bn line by xNegOverY let t21 = circuit_mul(in11, in2); // eval bn line by yInv let t22 = circuit_mul(t8, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t23 = circuit_add(in1, t22); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t24 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t25 = circuit_add(t23, t24); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t26 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t27 = circuit_add(t25, t26); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t28 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t29 = circuit_add(t27, t28); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t30 = circuit_mul(t5, t29); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t31 = circuit_mul(t16, in34); // Eval sparse poly line_0p_2 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_0p_2 step + coeff_1 * z^1 let t33 = circuit_mul(t19, t1); // Eval sparse poly line_0p_2 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_0p_2 step + coeff_3 * z^3 let t35 = circuit_mul(t20, t3); // Eval sparse poly line_0p_2 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_0p_2 step + coeff_7 * z^7 let t37 = circuit_mul(t21, t4); // Eval sparse poly line_0p_2 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_0p_2 step + coeff_9 * z^9 let t39 = circuit_mul(t30, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t40 = circuit_mul(in0, in13); let t41 = circuit_add(in12, t40); let t42 = circuit_mul(t41, in17); // eval bn line by xNegOverY let t43 = circuit_mul(in0, in15); let t44 = circuit_add(in14, t43); let t45 = circuit_mul(t44, in16); // eval bn line by yInv let t46 = circuit_mul(in13, in17); // eval bn line by xNegOverY let t47 = circuit_mul(in15, in16); // eval bn line by yInv let t48 = circuit_mul(in0, in19); let t49 = circuit_add(in18, t48); let t50 = circuit_mul(t49, in17); // eval bn line by xNegOverY let t51 = circuit_mul(in0, in21); let t52 = circuit_add(in20, t51); let t53 = circuit_mul(t52, in16); // eval bn line by yInv let t54 = circuit_mul(in19, in17); // eval bn line by xNegOverY let t55 = circuit_mul(in21, in16); // eval bn line by yInv let t56 = circuit_mul(t42, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t57 = circuit_add(in1, t56); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t58 = circuit_mul(t45, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t59 = circuit_add(t57, t58); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t60 = circuit_mul(t46, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t61 = circuit_add(t59, t60); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t62 = circuit_mul(t47, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t63 = circuit_add(t61, t62); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t64 = circuit_mul(t39, t63); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t65 = circuit_mul(t50, in34); // Eval sparse poly line_1p_2 step coeff_1 * z^1 let t66 = circuit_add(in1, t65); // Eval sparse poly line_1p_2 step + coeff_1 * z^1 let t67 = circuit_mul(t53, t1); // Eval sparse poly line_1p_2 step coeff_3 * z^3 let t68 = circuit_add(t66, t67); // Eval sparse poly line_1p_2 step + coeff_3 * z^3 let t69 = circuit_mul(t54, t3); // Eval sparse poly line_1p_2 step coeff_7 * z^7 let t70 = circuit_add(t68, t69); // Eval sparse poly line_1p_2 step + coeff_7 * z^7 let t71 = circuit_mul(t55, t4); // Eval sparse poly line_1p_2 step coeff_9 * z^9 let t72 = circuit_add(t70, t71); // Eval sparse poly line_1p_2 step + coeff_9 * z^9 let t73 = circuit_mul(t64, t72); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t74 = circuit_mul( t73, t73, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t75 = circuit_mul(in0, in23); let t76 = circuit_add(in22, t75); let t77 = circuit_mul(t76, in3); // eval bn line by xNegOverY let t78 = circuit_mul(in0, in25); let t79 = circuit_add(in24, t78); let t80 = circuit_mul(t79, in2); // eval bn line by yInv let t81 = circuit_mul(in23, in3); // eval bn line by xNegOverY let t82 = circuit_mul(in25, in2); // eval bn line by yInv let t83 = circuit_mul(t77, in34); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t84 = circuit_add(in1, t83); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t85 = circuit_mul(t80, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t86 = circuit_add(t84, t85); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t87 = circuit_mul(t81, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t88 = circuit_add(t86, t87); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t89 = circuit_mul(t82, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t90 = circuit_add(t88, t89); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t91 = circuit_mul(t74, t90); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t92 = circuit_mul(in0, in27); let t93 = circuit_add(in26, t92); let t94 = circuit_mul(t93, in17); // eval bn line by xNegOverY let t95 = circuit_mul(in0, in29); let t96 = circuit_add(in28, t95); let t97 = circuit_mul(t96, in16); // eval bn line by yInv let t98 = circuit_mul(in27, in17); // eval bn line by xNegOverY let t99 = circuit_mul(in29, in16); // eval bn line by yInv let t100 = circuit_mul(t94, in34); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t101 = circuit_add(in1, t100); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t102 = circuit_mul(t97, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t103 = circuit_add(t101, t102); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t104 = circuit_mul(t98, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t105 = circuit_add(t103, t104); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t106 = circuit_mul(t99, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t107 = circuit_add(t105, t106); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t108 = circuit_mul(t91, t107); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t109 = circuit_mul(in33, in33); let t110 = circuit_mul(t108, t109); let t111 = circuit_sub(t110, in32); // (Π(i,k) (Pk(z))) - Ri(z) let t112 = circuit_mul(in35, in30); let t113 = circuit_add(t112, t111); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t113,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in2 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r0a0); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r0a1); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r1a0); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r1a1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(yInv_1); // in16 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in18 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in19 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r0a0); // in22 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r0a1); // in23 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r1a0); // in24 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r1a1); // in25 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r0a0); // in26 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r0a1); // in27 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r1a0); // in28 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r1a1); // in29 circuit_inputs = circuit_inputs.next_2(lhs_i); // in30 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in31 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in32 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in33 circuit_inputs = circuit_inputs.next_2(z); // in34 circuit_inputs = circuit_inputs.next_2(c1); // in35 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let lhs_i_plus_one: u384 = outputs.get_output(t113); return (lhs_i_plus_one,); } #[inline(always)] pub fn run_BN254_MP_CHECK_BIT10_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_dbl_0: G2Line, G2_line_add_1_0: G2Line, G2_line_dbl_0_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_dbl_1: G2Line, G2_line_add_1_1: G2Line, G2_line_dbl_0_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, Q_or_Q_neg_2: G2Point, lhs_i: u384, f_i_of_z: u384, f_i_plus_one_of_z: u384, c_or_cinv_of_z: u384, z: u384, c1: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x0 let in3 = CE::> {}; // 0x3 let in4 = CE::> {}; // 0x6 // INPUT stack let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27, in28) = (CE::> {}, CE::> {}, CE::> {}); let (in29, in30, in31) = (CE::> {}, CE::> {}, CE::> {}); let (in32, in33, in34) = (CE::> {}, CE::> {}, CE::> {}); let (in35, in36, in37) = (CE::> {}, CE::> {}, CE::> {}); let (in38, in39, in40) = (CE::> {}, CE::> {}, CE::> {}); let (in41, in42, in43) = (CE::> {}, CE::> {}, CE::> {}); let (in44, in45, in46) = (CE::> {}, CE::> {}, CE::> {}); let (in47, in48) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in47, in47); // compute z^2 let t1 = circuit_mul(t0, in47); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in47); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in44, in44); // Square f evaluation in Z, the result of previous bit. let t6 = circuit_mul(in0, in8); let t7 = circuit_add(in7, t6); let t8 = circuit_mul(t7, in6); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in10); let t10 = circuit_add(in9, t9); let t11 = circuit_mul(t10, in5); // eval bn line by yInv let t12 = circuit_mul(in8, in6); // eval bn line by xNegOverY let t13 = circuit_mul(in10, in5); // eval bn line by yInv let t14 = circuit_mul(in0, in12); let t15 = circuit_add(in11, t14); let t16 = circuit_mul(t15, in6); // eval bn line by xNegOverY let t17 = circuit_mul(in0, in14); let t18 = circuit_add(in13, t17); let t19 = circuit_mul(t18, in5); // eval bn line by yInv let t20 = circuit_mul(in12, in6); // eval bn line by xNegOverY let t21 = circuit_mul(in14, in5); // eval bn line by yInv let t22 = circuit_mul(t8, in47); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t23 = circuit_add(in1, t22); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t24 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t25 = circuit_add(t23, t24); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t26 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t27 = circuit_add(t25, t26); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t28 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t29 = circuit_add(t27, t28); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t30 = circuit_mul(t5, t29); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t31 = circuit_mul(t16, in47); // Eval sparse poly line_0p_2 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_0p_2 step + coeff_1 * z^1 let t33 = circuit_mul(t19, t1); // Eval sparse poly line_0p_2 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_0p_2 step + coeff_3 * z^3 let t35 = circuit_mul(t20, t3); // Eval sparse poly line_0p_2 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_0p_2 step + coeff_7 * z^7 let t37 = circuit_mul(t21, t4); // Eval sparse poly line_0p_2 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_0p_2 step + coeff_9 * z^9 let t39 = circuit_mul(t30, t38); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t40 = circuit_mul(in0, in16); let t41 = circuit_add(in15, t40); let t42 = circuit_mul(t41, in20); // eval bn line by xNegOverY let t43 = circuit_mul(in0, in18); let t44 = circuit_add(in17, t43); let t45 = circuit_mul(t44, in19); // eval bn line by yInv let t46 = circuit_mul(in16, in20); // eval bn line by xNegOverY let t47 = circuit_mul(in18, in19); // eval bn line by yInv let t48 = circuit_mul(in0, in22); let t49 = circuit_add(in21, t48); let t50 = circuit_mul(t49, in20); // eval bn line by xNegOverY let t51 = circuit_mul(in0, in24); let t52 = circuit_add(in23, t51); let t53 = circuit_mul(t52, in19); // eval bn line by yInv let t54 = circuit_mul(in22, in20); // eval bn line by xNegOverY let t55 = circuit_mul(in24, in19); // eval bn line by yInv let t56 = circuit_mul(t42, in47); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t57 = circuit_add(in1, t56); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t58 = circuit_mul(t45, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t59 = circuit_add(t57, t58); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t60 = circuit_mul(t46, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t61 = circuit_add(t59, t60); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t62 = circuit_mul(t47, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t63 = circuit_add(t61, t62); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t64 = circuit_mul(t39, t63); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t65 = circuit_mul(t50, in47); // Eval sparse poly line_1p_2 step coeff_1 * z^1 let t66 = circuit_add(in1, t65); // Eval sparse poly line_1p_2 step + coeff_1 * z^1 let t67 = circuit_mul(t53, t1); // Eval sparse poly line_1p_2 step coeff_3 * z^3 let t68 = circuit_add(t66, t67); // Eval sparse poly line_1p_2 step + coeff_3 * z^3 let t69 = circuit_mul(t54, t3); // Eval sparse poly line_1p_2 step coeff_7 * z^7 let t70 = circuit_add(t68, t69); // Eval sparse poly line_1p_2 step + coeff_7 * z^7 let t71 = circuit_mul(t55, t4); // Eval sparse poly line_1p_2 step coeff_9 * z^9 let t72 = circuit_add(t70, t71); // Eval sparse poly line_1p_2 step + coeff_9 * z^9 let t73 = circuit_mul(t64, t72); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t74 = circuit_sub(in37, in41); // Fp2 sub coeff 0/1 let t75 = circuit_sub(in38, in42); // Fp2 sub coeff 1/1 let t76 = circuit_sub(in35, in39); // Fp2 sub coeff 0/1 let t77 = circuit_sub(in36, in40); // Fp2 sub coeff 1/1 let t78 = circuit_mul(t76, t76); // Fp2 Inv start let t79 = circuit_mul(t77, t77); let t80 = circuit_add(t78, t79); let t81 = circuit_inverse(t80); let t82 = circuit_mul(t76, t81); // Fp2 Inv real part end let t83 = circuit_mul(t77, t81); let t84 = circuit_sub(in2, t83); // Fp2 Inv imag part end let t85 = circuit_mul(t74, t82); // Fp2 mul start let t86 = circuit_mul(t75, t84); let t87 = circuit_sub(t85, t86); // Fp2 mul real part end let t88 = circuit_mul(t74, t84); let t89 = circuit_mul(t75, t82); let t90 = circuit_add(t88, t89); // Fp2 mul imag part end let t91 = circuit_add(t87, t90); let t92 = circuit_sub(t87, t90); let t93 = circuit_mul(t91, t92); let t94 = circuit_mul(t87, t90); let t95 = circuit_add(t94, t94); let t96 = circuit_add(in35, in39); // Fp2 add coeff 0/1 let t97 = circuit_add(in36, in40); // Fp2 add coeff 1/1 let t98 = circuit_sub(t93, t96); // Fp2 sub coeff 0/1 let t99 = circuit_sub(t95, t97); // Fp2 sub coeff 1/1 let t100 = circuit_mul(t87, in35); // Fp2 mul start let t101 = circuit_mul(t90, in36); let t102 = circuit_sub(t100, t101); // Fp2 mul real part end let t103 = circuit_mul(t87, in36); let t104 = circuit_mul(t90, in35); let t105 = circuit_add(t103, t104); // Fp2 mul imag part end let t106 = circuit_sub(t102, in37); // Fp2 sub coeff 0/1 let t107 = circuit_sub(t105, in38); // Fp2 sub coeff 1/1 let t108 = circuit_add(in37, in37); // Fp2 add coeff 0/1 let t109 = circuit_add(in38, in38); // Fp2 add coeff 1/1 let t110 = circuit_sub(t98, in35); // Fp2 sub coeff 0/1 let t111 = circuit_sub(t99, in36); // Fp2 sub coeff 1/1 let t112 = circuit_mul(t110, t110); // Fp2 Inv start let t113 = circuit_mul(t111, t111); let t114 = circuit_add(t112, t113); let t115 = circuit_inverse(t114); let t116 = circuit_mul(t110, t115); // Fp2 Inv real part end let t117 = circuit_mul(t111, t115); let t118 = circuit_sub(in2, t117); // Fp2 Inv imag part end let t119 = circuit_mul(t108, t116); // Fp2 mul start let t120 = circuit_mul(t109, t118); let t121 = circuit_sub(t119, t120); // Fp2 mul real part end let t122 = circuit_mul(t108, t118); let t123 = circuit_mul(t109, t116); let t124 = circuit_add(t122, t123); // Fp2 mul imag part end let t125 = circuit_add(t87, t121); // Fp2 add coeff 0/1 let t126 = circuit_add(t90, t124); // Fp2 add coeff 1/1 let t127 = circuit_sub(in2, t125); // Fp2 neg coeff 0/1 let t128 = circuit_sub(in2, t126); // Fp2 neg coeff 1/1 let t129 = circuit_add(t127, t128); let t130 = circuit_sub(t127, t128); let t131 = circuit_mul(t129, t130); let t132 = circuit_mul(t127, t128); let t133 = circuit_add(t132, t132); let t134 = circuit_sub(t131, in35); // Fp2 sub coeff 0/1 let t135 = circuit_sub(t133, in36); // Fp2 sub coeff 1/1 let t136 = circuit_sub(t134, t98); // Fp2 sub coeff 0/1 let t137 = circuit_sub(t135, t99); // Fp2 sub coeff 1/1 let t138 = circuit_sub(in35, t136); // Fp2 sub coeff 0/1 let t139 = circuit_sub(in36, t137); // Fp2 sub coeff 1/1 let t140 = circuit_mul(t127, t138); // Fp2 mul start let t141 = circuit_mul(t128, t139); let t142 = circuit_sub(t140, t141); // Fp2 mul real part end let t143 = circuit_mul(t127, t139); let t144 = circuit_mul(t128, t138); let t145 = circuit_add(t143, t144); // Fp2 mul imag part end let t146 = circuit_sub(t142, in37); // Fp2 sub coeff 0/1 let t147 = circuit_sub(t145, in38); // Fp2 sub coeff 1/1 let t148 = circuit_mul(t127, in35); // Fp2 mul start let t149 = circuit_mul(t128, in36); let t150 = circuit_sub(t148, t149); // Fp2 mul real part end let t151 = circuit_mul(t127, in36); let t152 = circuit_mul(t128, in35); let t153 = circuit_add(t151, t152); // Fp2 mul imag part end let t154 = circuit_sub(t150, in37); // Fp2 sub coeff 0/1 let t155 = circuit_sub(t153, in38); // Fp2 sub coeff 1/1 let t156 = circuit_mul(in0, t90); let t157 = circuit_add(t87, t156); let t158 = circuit_mul(t157, in34); // eval bn line by xNegOverY let t159 = circuit_mul(in0, t107); let t160 = circuit_add(t106, t159); let t161 = circuit_mul(t160, in33); // eval bn line by yInv let t162 = circuit_mul(t90, in34); // eval bn line by xNegOverY let t163 = circuit_mul(t107, in33); // eval bn line by yInv let t164 = circuit_mul(in0, t128); let t165 = circuit_add(t127, t164); let t166 = circuit_mul(t165, in34); // eval bn line by xNegOverY let t167 = circuit_mul(in0, t155); let t168 = circuit_add(t154, t167); let t169 = circuit_mul(t168, in33); // eval bn line by yInv let t170 = circuit_mul(t128, in34); // eval bn line by xNegOverY let t171 = circuit_mul(t155, in33); // eval bn line by yInv let t172 = circuit_mul(t158, in47); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t173 = circuit_add(in1, t172); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t174 = circuit_mul(t161, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t175 = circuit_add(t173, t174); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t176 = circuit_mul(t162, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t177 = circuit_add(t175, t176); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t178 = circuit_mul(t163, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t179 = circuit_add(t177, t178); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t180 = circuit_mul(t73, t179); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t181 = circuit_mul(t166, in47); // Eval sparse poly line_2p_2 step coeff_1 * z^1 let t182 = circuit_add(in1, t181); // Eval sparse poly line_2p_2 step + coeff_1 * z^1 let t183 = circuit_mul(t169, t1); // Eval sparse poly line_2p_2 step coeff_3 * z^3 let t184 = circuit_add(t182, t183); // Eval sparse poly line_2p_2 step + coeff_3 * z^3 let t185 = circuit_mul(t170, t3); // Eval sparse poly line_2p_2 step coeff_7 * z^7 let t186 = circuit_add(t184, t185); // Eval sparse poly line_2p_2 step + coeff_7 * z^7 let t187 = circuit_mul(t171, t4); // Eval sparse poly line_2p_2 step coeff_9 * z^9 let t188 = circuit_add(t186, t187); // Eval sparse poly line_2p_2 step + coeff_9 * z^9 let t189 = circuit_mul(t180, t188); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t190 = circuit_mul( t189, t189, ); // Compute (f^2 * Π(i,k) (line_i,k(z))) ^ 2 = f^4 * (Π(i,k) (line_i,k(z)))^2 let t191 = circuit_mul(in0, in26); let t192 = circuit_add(in25, t191); let t193 = circuit_mul(t192, in6); // eval bn line by xNegOverY let t194 = circuit_mul(in0, in28); let t195 = circuit_add(in27, t194); let t196 = circuit_mul(t195, in5); // eval bn line by yInv let t197 = circuit_mul(in26, in6); // eval bn line by xNegOverY let t198 = circuit_mul(in28, in5); // eval bn line by yInv let t199 = circuit_mul(t193, in47); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t200 = circuit_add(in1, t199); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t201 = circuit_mul(t196, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t202 = circuit_add(t200, t201); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t203 = circuit_mul(t197, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t204 = circuit_add(t202, t203); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t205 = circuit_mul(t198, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t206 = circuit_add(t204, t205); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t207 = circuit_mul(t190, t206); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_0(z) let t208 = circuit_mul(in0, in30); let t209 = circuit_add(in29, t208); let t210 = circuit_mul(t209, in20); // eval bn line by xNegOverY let t211 = circuit_mul(in0, in32); let t212 = circuit_add(in31, t211); let t213 = circuit_mul(t212, in19); // eval bn line by yInv let t214 = circuit_mul(in30, in20); // eval bn line by xNegOverY let t215 = circuit_mul(in32, in19); // eval bn line by yInv let t216 = circuit_mul(t210, in47); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t217 = circuit_add(in1, t216); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t218 = circuit_mul(t213, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t219 = circuit_add(t217, t218); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t220 = circuit_mul(t214, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t221 = circuit_add(t219, t220); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t222 = circuit_mul(t215, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t223 = circuit_add(t221, t222); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t224 = circuit_mul(t207, t223); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_1(z) let t225 = circuit_add(t136, t137); // Doubling slope numerator start let t226 = circuit_sub(t136, t137); let t227 = circuit_mul(t225, t226); let t228 = circuit_mul(t136, t137); let t229 = circuit_mul(t227, in3); let t230 = circuit_mul(t228, in4); // Doubling slope numerator end let t231 = circuit_add(t146, t146); // Fp2 add coeff 0/1 let t232 = circuit_add(t147, t147); // Fp2 add coeff 1/1 let t233 = circuit_mul(t231, t231); // Fp2 Inv start let t234 = circuit_mul(t232, t232); let t235 = circuit_add(t233, t234); let t236 = circuit_inverse(t235); let t237 = circuit_mul(t231, t236); // Fp2 Inv real part end let t238 = circuit_mul(t232, t236); let t239 = circuit_sub(in2, t238); // Fp2 Inv imag part end let t240 = circuit_mul(t229, t237); // Fp2 mul start let t241 = circuit_mul(t230, t239); let t242 = circuit_sub(t240, t241); // Fp2 mul real part end let t243 = circuit_mul(t229, t239); let t244 = circuit_mul(t230, t237); let t245 = circuit_add(t243, t244); // Fp2 mul imag part end let t246 = circuit_add(t242, t245); let t247 = circuit_sub(t242, t245); let t248 = circuit_mul(t246, t247); let t249 = circuit_mul(t242, t245); let t250 = circuit_add(t249, t249); let t251 = circuit_add(t136, t136); // Fp2 add coeff 0/1 let t252 = circuit_add(t137, t137); // Fp2 add coeff 1/1 let t253 = circuit_sub(t248, t251); // Fp2 sub coeff 0/1 let t254 = circuit_sub(t250, t252); // Fp2 sub coeff 1/1 let t255 = circuit_sub(t136, t253); // Fp2 sub coeff 0/1 let t256 = circuit_sub(t137, t254); // Fp2 sub coeff 1/1 let t257 = circuit_mul(t242, t255); // Fp2 mul start let t258 = circuit_mul(t245, t256); let t259 = circuit_sub(t257, t258); // Fp2 mul real part end let t260 = circuit_mul(t242, t256); let t261 = circuit_mul(t245, t255); let t262 = circuit_add(t260, t261); // Fp2 mul imag part end let t263 = circuit_sub(t259, t146); // Fp2 sub coeff 0/1 let t264 = circuit_sub(t262, t147); // Fp2 sub coeff 1/1 let t265 = circuit_mul(t242, t136); // Fp2 mul start let t266 = circuit_mul(t245, t137); let t267 = circuit_sub(t265, t266); // Fp2 mul real part end let t268 = circuit_mul(t242, t137); let t269 = circuit_mul(t245, t136); let t270 = circuit_add(t268, t269); // Fp2 mul imag part end let t271 = circuit_sub(t267, t146); // Fp2 sub coeff 0/1 let t272 = circuit_sub(t270, t147); // Fp2 sub coeff 1/1 let t273 = circuit_mul(in0, t245); let t274 = circuit_add(t242, t273); let t275 = circuit_mul(t274, in34); // eval bn line by xNegOverY let t276 = circuit_mul(in0, t272); let t277 = circuit_add(t271, t276); let t278 = circuit_mul(t277, in33); // eval bn line by yInv let t279 = circuit_mul(t245, in34); // eval bn line by xNegOverY let t280 = circuit_mul(t272, in33); // eval bn line by yInv let t281 = circuit_mul(t275, in47); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t282 = circuit_add(in1, t281); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t283 = circuit_mul(t278, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t284 = circuit_add(t282, t283); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t285 = circuit_mul(t279, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t286 = circuit_add(t284, t285); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t287 = circuit_mul(t280, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t288 = circuit_add(t286, t287); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t289 = circuit_mul(t224, t288); // Mul (f(z)^2 * Π_0_k-1(line_k(z))) * line_i_2(z) let t290 = circuit_mul(in46, in46); let t291 = circuit_mul(t289, t290); let t292 = circuit_sub(t291, in45); // (Π(i,k) (Pk(z))) - Ri(z) let t293 = circuit_mul(in48, in43); let t294 = circuit_add(t293, t292); // LHS = c1 * LHS + ((Π(i,k) (Pk(z)) - Ri(z)) let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t253, t254, t263, t264, t294).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in3 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in4 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in5 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r0a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0.r1a1); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r0a0); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r0a1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r1a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_0.r1a1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r0a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r0a1); // in16 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r1a0); // in17 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_0.r1a1); // in18 circuit_inputs = circuit_inputs.next_2(yInv_1); // in19 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in20 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a0); // in21 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r0a1); // in22 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a0); // in23 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_1.r1a1); // in24 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r0a0); // in25 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r0a1); // in26 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r1a0); // in27 circuit_inputs = circuit_inputs.next_2(G2_line_add_1_1.r1a1); // in28 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r0a0); // in29 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r0a1); // in30 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r1a0); // in31 circuit_inputs = circuit_inputs.next_2(G2_line_dbl_0_1.r1a1); // in32 circuit_inputs = circuit_inputs.next_2(yInv_2); // in33 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in34 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in35 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in36 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in37 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in38 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x0); // in39 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.x1); // in40 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y0); // in41 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_2.y1); // in42 circuit_inputs = circuit_inputs.next_2(lhs_i); // in43 circuit_inputs = circuit_inputs.next_2(f_i_of_z); // in44 circuit_inputs = circuit_inputs.next_2(f_i_plus_one_of_z); // in45 circuit_inputs = circuit_inputs.next_2(c_or_cinv_of_z); // in46 circuit_inputs = circuit_inputs.next_2(z); // in47 circuit_inputs = circuit_inputs.next_2(c1); // in48 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t253), x1: outputs.get_output(t254), y0: outputs.get_output(t263), y1: outputs.get_output(t264), }; let lhs_i_plus_one: u384 = outputs.get_output(t294); return (Q0, lhs_i_plus_one); } #[inline(always)] pub fn run_BN254_MP_CHECK_FINALIZE_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, line_1_0: G2Line, line_2_0: G2Line, yInv_1: u384, xNegOverY_1: u384, line_1_1: G2Line, line_2_1: G2Line, R_n_minus_2_of_z: u384, R_n_minus_1_of_z: u384, c_0: u384, w_of_z: u384, z: u384, c_inv_frob_1_of_z: u384, c_frob_2_of_z: u384, c_inv_frob_3_of_z: u384, previous_lhs: u384, R_n_minus_3_of_z: u384, Q: Array, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x52 let in3 = CE::> {}; // -0x12 % p // INPUT stack let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let (in37, in38, in39) = (CE::> {}, CE::> {}, CE::> {}); let (in40, in41, in42) = (CE::> {}, CE::> {}, CE::> {}); let (in43, in44, in45) = (CE::> {}, CE::> {}, CE::> {}); let (in46, in47, in48) = (CE::> {}, CE::> {}, CE::> {}); let (in49, in50, in51) = (CE::> {}, CE::> {}, CE::> {}); let (in52, in53, in54) = (CE::> {}, CE::> {}, CE::> {}); let (in55, in56, in57) = (CE::> {}, CE::> {}, CE::> {}); let (in58, in59, in60) = (CE::> {}, CE::> {}, CE::> {}); let (in61, in62, in63) = (CE::> {}, CE::> {}, CE::> {}); let (in64, in65, in66) = (CE::> {}, CE::> {}, CE::> {}); let (in67, in68, in69) = (CE::> {}, CE::> {}, CE::> {}); let (in70, in71, in72) = (CE::> {}, CE::> {}, CE::> {}); let (in73, in74, in75) = (CE::> {}, CE::> {}, CE::> {}); let (in76, in77, in78) = (CE::> {}, CE::> {}, CE::> {}); let (in79, in80, in81) = (CE::> {}, CE::> {}, CE::> {}); let (in82, in83, in84) = (CE::> {}, CE::> {}, CE::> {}); let (in85, in86, in87) = (CE::> {}, CE::> {}, CE::> {}); let (in88, in89, in90) = (CE::> {}, CE::> {}, CE::> {}); let (in91, in92, in93) = (CE::> {}, CE::> {}, CE::> {}); let (in94, in95, in96) = (CE::> {}, CE::> {}, CE::> {}); let (in97, in98, in99) = (CE::> {}, CE::> {}, CE::> {}); let (in100, in101, in102) = (CE::> {}, CE::> {}, CE::> {}); let (in103, in104, in105) = (CE::> {}, CE::> {}, CE::> {}); let (in106, in107, in108) = (CE::> {}, CE::> {}, CE::> {}); let (in109, in110, in111) = (CE::> {}, CE::> {}, CE::> {}); let (in112, in113, in114) = (CE::> {}, CE::> {}, CE::> {}); let (in115, in116, in117) = (CE::> {}, CE::> {}, CE::> {}); let (in118, in119, in120) = (CE::> {}, CE::> {}, CE::> {}); let (in121, in122, in123) = (CE::> {}, CE::> {}, CE::> {}); let (in124, in125, in126) = (CE::> {}, CE::> {}, CE::> {}); let (in127, in128, in129) = (CE::> {}, CE::> {}, CE::> {}); let (in130, in131, in132) = (CE::> {}, CE::> {}, CE::> {}); let (in133, in134, in135) = (CE::> {}, CE::> {}, CE::> {}); let (in136, in137, in138) = (CE::> {}, CE::> {}, CE::> {}); let (in139, in140, in141) = (CE::> {}, CE::> {}, CE::> {}); let (in142, in143, in144) = (CE::> {}, CE::> {}, CE::> {}); let (in145, in146, in147) = (CE::> {}, CE::> {}, CE::> {}); let (in148, in149, in150) = (CE::> {}, CE::> {}, CE::> {}); let (in151, in152, in153) = (CE::> {}, CE::> {}, CE::> {}); let (in154, in155, in156) = (CE::> {}, CE::> {}, CE::> {}); let (in157, in158, in159) = (CE::> {}, CE::> {}, CE::> {}); let (in160, in161, in162) = (CE::> {}, CE::> {}, CE::> {}); let (in163, in164, in165) = (CE::> {}, CE::> {}, CE::> {}); let (in166, in167, in168) = (CE::> {}, CE::> {}, CE::> {}); let (in169, in170, in171) = (CE::> {}, CE::> {}, CE::> {}); let (in172, in173, in174) = (CE::> {}, CE::> {}, CE::> {}); let (in175, in176, in177) = (CE::> {}, CE::> {}, CE::> {}); let in178 = CE::> {}; let t0 = circuit_mul(in28, in28); // compute z^2 let t1 = circuit_mul(t0, in28); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in28); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(t4, t1); // compute z^12 let t6 = circuit_mul(in0, in7); let t7 = circuit_add(in6, t6); let t8 = circuit_mul(t7, in5); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in9); let t10 = circuit_add(in8, t9); let t11 = circuit_mul(t10, in4); // eval bn line by yInv let t12 = circuit_mul(in7, in5); // eval bn line by xNegOverY let t13 = circuit_mul(in9, in4); // eval bn line by yInv let t14 = circuit_mul(in0, in11); let t15 = circuit_add(in10, t14); let t16 = circuit_mul(t15, in5); // eval bn line by xNegOverY let t17 = circuit_mul(in0, in13); let t18 = circuit_add(in12, t17); let t19 = circuit_mul(t18, in4); // eval bn line by yInv let t20 = circuit_mul(in11, in5); // eval bn line by xNegOverY let t21 = circuit_mul(in13, in4); // eval bn line by yInv let t22 = circuit_mul(in0, in17); let t23 = circuit_add(in16, t22); let t24 = circuit_mul(t23, in15); // eval bn line by xNegOverY let t25 = circuit_mul(in0, in19); let t26 = circuit_add(in18, t25); let t27 = circuit_mul(t26, in14); // eval bn line by yInv let t28 = circuit_mul(in17, in15); // eval bn line by xNegOverY let t29 = circuit_mul(in19, in14); // eval bn line by yInv let t30 = circuit_mul(in0, in21); let t31 = circuit_add(in20, t30); let t32 = circuit_mul(t31, in15); // eval bn line by xNegOverY let t33 = circuit_mul(in0, in23); let t34 = circuit_add(in22, t33); let t35 = circuit_mul(t34, in14); // eval bn line by yInv let t36 = circuit_mul(in21, in15); // eval bn line by xNegOverY let t37 = circuit_mul(in23, in14); // eval bn line by yInv let t38 = circuit_mul(t8, in28); // Eval sparse poly line_0 step coeff_1 * z^1 let t39 = circuit_add(in1, t38); // Eval sparse poly line_0 step + coeff_1 * z^1 let t40 = circuit_mul(t11, t1); // Eval sparse poly line_0 step coeff_3 * z^3 let t41 = circuit_add(t39, t40); // Eval sparse poly line_0 step + coeff_3 * z^3 let t42 = circuit_mul(t12, t3); // Eval sparse poly line_0 step coeff_7 * z^7 let t43 = circuit_add(t41, t42); // Eval sparse poly line_0 step + coeff_7 * z^7 let t44 = circuit_mul(t13, t4); // Eval sparse poly line_0 step coeff_9 * z^9 let t45 = circuit_add(t43, t44); // Eval sparse poly line_0 step + coeff_9 * z^9 let t46 = circuit_mul(in33, t45); let t47 = circuit_mul(t16, in28); // Eval sparse poly line_1 step coeff_1 * z^1 let t48 = circuit_add(in1, t47); // Eval sparse poly line_1 step + coeff_1 * z^1 let t49 = circuit_mul(t19, t1); // Eval sparse poly line_1 step coeff_3 * z^3 let t50 = circuit_add(t48, t49); // Eval sparse poly line_1 step + coeff_3 * z^3 let t51 = circuit_mul(t20, t3); // Eval sparse poly line_1 step coeff_7 * z^7 let t52 = circuit_add(t50, t51); // Eval sparse poly line_1 step + coeff_7 * z^7 let t53 = circuit_mul(t21, t4); // Eval sparse poly line_1 step coeff_9 * z^9 let t54 = circuit_add(t52, t53); // Eval sparse poly line_1 step + coeff_9 * z^9 let t55 = circuit_mul(t46, t54); let t56 = circuit_mul(t24, in28); // Eval sparse poly line_2 step coeff_1 * z^1 let t57 = circuit_add(in1, t56); // Eval sparse poly line_2 step + coeff_1 * z^1 let t58 = circuit_mul(t27, t1); // Eval sparse poly line_2 step coeff_3 * z^3 let t59 = circuit_add(t57, t58); // Eval sparse poly line_2 step + coeff_3 * z^3 let t60 = circuit_mul(t28, t3); // Eval sparse poly line_2 step coeff_7 * z^7 let t61 = circuit_add(t59, t60); // Eval sparse poly line_2 step + coeff_7 * z^7 let t62 = circuit_mul(t29, t4); // Eval sparse poly line_2 step coeff_9 * z^9 let t63 = circuit_add(t61, t62); // Eval sparse poly line_2 step + coeff_9 * z^9 let t64 = circuit_mul(t55, t63); let t65 = circuit_mul(t32, in28); // Eval sparse poly line_3 step coeff_1 * z^1 let t66 = circuit_add(in1, t65); // Eval sparse poly line_3 step + coeff_1 * z^1 let t67 = circuit_mul(t35, t1); // Eval sparse poly line_3 step coeff_3 * z^3 let t68 = circuit_add(t66, t67); // Eval sparse poly line_3 step + coeff_3 * z^3 let t69 = circuit_mul(t36, t3); // Eval sparse poly line_3 step coeff_7 * z^7 let t70 = circuit_add(t68, t69); // Eval sparse poly line_3 step + coeff_7 * z^7 let t71 = circuit_mul(t37, t4); // Eval sparse poly line_3 step coeff_9 * z^9 let t72 = circuit_add(t70, t71); // Eval sparse poly line_3 step + coeff_9 * z^9 let t73 = circuit_mul(t64, t72); let t74 = circuit_sub(t73, in24); // ((Π(n-2,k) (Pk(z)) - R_n_minus_2(z)) let t75 = circuit_mul(in24, in29); let t76 = circuit_mul(t75, in30); let t77 = circuit_mul(t76, in31); let t78 = circuit_mul(t77, in27); let t79 = circuit_sub(t78, in25); // ((Π(n-1,k) (Pk(z)) - R_n_minus_1(z)) let t80 = circuit_mul(in26, in32); let t81 = circuit_add(t80, t74); let t82 = circuit_mul(in26, t81); let t83 = circuit_add(t82, t79); let t84 = circuit_mul(in178, in28); // Eval big_Q Horner step: multiply by z let t85 = circuit_add(in177, t84); // Eval big_Q Horner step: add coefficient_143 let t86 = circuit_mul(t85, in28); // Eval big_Q Horner step: multiply by z let t87 = circuit_add(in176, t86); // Eval big_Q Horner step: add coefficient_142 let t88 = circuit_mul(t87, in28); // Eval big_Q Horner step: multiply by z let t89 = circuit_add(in175, t88); // Eval big_Q Horner step: add coefficient_141 let t90 = circuit_mul(t89, in28); // Eval big_Q Horner step: multiply by z let t91 = circuit_add(in174, t90); // Eval big_Q Horner step: add coefficient_140 let t92 = circuit_mul(t91, in28); // Eval big_Q Horner step: multiply by z let t93 = circuit_add(in173, t92); // Eval big_Q Horner step: add coefficient_139 let t94 = circuit_mul(t93, in28); // Eval big_Q Horner step: multiply by z let t95 = circuit_add(in172, t94); // Eval big_Q Horner step: add coefficient_138 let t96 = circuit_mul(t95, in28); // Eval big_Q Horner step: multiply by z let t97 = circuit_add(in171, t96); // Eval big_Q Horner step: add coefficient_137 let t98 = circuit_mul(t97, in28); // Eval big_Q Horner step: multiply by z let t99 = circuit_add(in170, t98); // Eval big_Q Horner step: add coefficient_136 let t100 = circuit_mul(t99, in28); // Eval big_Q Horner step: multiply by z let t101 = circuit_add(in169, t100); // Eval big_Q Horner step: add coefficient_135 let t102 = circuit_mul(t101, in28); // Eval big_Q Horner step: multiply by z let t103 = circuit_add(in168, t102); // Eval big_Q Horner step: add coefficient_134 let t104 = circuit_mul(t103, in28); // Eval big_Q Horner step: multiply by z let t105 = circuit_add(in167, t104); // Eval big_Q Horner step: add coefficient_133 let t106 = circuit_mul(t105, in28); // Eval big_Q Horner step: multiply by z let t107 = circuit_add(in166, t106); // Eval big_Q Horner step: add coefficient_132 let t108 = circuit_mul(t107, in28); // Eval big_Q Horner step: multiply by z let t109 = circuit_add(in165, t108); // Eval big_Q Horner step: add coefficient_131 let t110 = circuit_mul(t109, in28); // Eval big_Q Horner step: multiply by z let t111 = circuit_add(in164, t110); // Eval big_Q Horner step: add coefficient_130 let t112 = circuit_mul(t111, in28); // Eval big_Q Horner step: multiply by z let t113 = circuit_add(in163, t112); // Eval big_Q Horner step: add coefficient_129 let t114 = circuit_mul(t113, in28); // Eval big_Q Horner step: multiply by z let t115 = circuit_add(in162, t114); // Eval big_Q Horner step: add coefficient_128 let t116 = circuit_mul(t115, in28); // Eval big_Q Horner step: multiply by z let t117 = circuit_add(in161, t116); // Eval big_Q Horner step: add coefficient_127 let t118 = circuit_mul(t117, in28); // Eval big_Q Horner step: multiply by z let t119 = circuit_add(in160, t118); // Eval big_Q Horner step: add coefficient_126 let t120 = circuit_mul(t119, in28); // Eval big_Q Horner step: multiply by z let t121 = circuit_add(in159, t120); // Eval big_Q Horner step: add coefficient_125 let t122 = circuit_mul(t121, in28); // Eval big_Q Horner step: multiply by z let t123 = circuit_add(in158, t122); // Eval big_Q Horner step: add coefficient_124 let t124 = circuit_mul(t123, in28); // Eval big_Q Horner step: multiply by z let t125 = circuit_add(in157, t124); // Eval big_Q Horner step: add coefficient_123 let t126 = circuit_mul(t125, in28); // Eval big_Q Horner step: multiply by z let t127 = circuit_add(in156, t126); // Eval big_Q Horner step: add coefficient_122 let t128 = circuit_mul(t127, in28); // Eval big_Q Horner step: multiply by z let t129 = circuit_add(in155, t128); // Eval big_Q Horner step: add coefficient_121 let t130 = circuit_mul(t129, in28); // Eval big_Q Horner step: multiply by z let t131 = circuit_add(in154, t130); // Eval big_Q Horner step: add coefficient_120 let t132 = circuit_mul(t131, in28); // Eval big_Q Horner step: multiply by z let t133 = circuit_add(in153, t132); // Eval big_Q Horner step: add coefficient_119 let t134 = circuit_mul(t133, in28); // Eval big_Q Horner step: multiply by z let t135 = circuit_add(in152, t134); // Eval big_Q Horner step: add coefficient_118 let t136 = circuit_mul(t135, in28); // Eval big_Q Horner step: multiply by z let t137 = circuit_add(in151, t136); // Eval big_Q Horner step: add coefficient_117 let t138 = circuit_mul(t137, in28); // Eval big_Q Horner step: multiply by z let t139 = circuit_add(in150, t138); // Eval big_Q Horner step: add coefficient_116 let t140 = circuit_mul(t139, in28); // Eval big_Q Horner step: multiply by z let t141 = circuit_add(in149, t140); // Eval big_Q Horner step: add coefficient_115 let t142 = circuit_mul(t141, in28); // Eval big_Q Horner step: multiply by z let t143 = circuit_add(in148, t142); // Eval big_Q Horner step: add coefficient_114 let t144 = circuit_mul(t143, in28); // Eval big_Q Horner step: multiply by z let t145 = circuit_add(in147, t144); // Eval big_Q Horner step: add coefficient_113 let t146 = circuit_mul(t145, in28); // Eval big_Q Horner step: multiply by z let t147 = circuit_add(in146, t146); // Eval big_Q Horner step: add coefficient_112 let t148 = circuit_mul(t147, in28); // Eval big_Q Horner step: multiply by z let t149 = circuit_add(in145, t148); // Eval big_Q Horner step: add coefficient_111 let t150 = circuit_mul(t149, in28); // Eval big_Q Horner step: multiply by z let t151 = circuit_add(in144, t150); // Eval big_Q Horner step: add coefficient_110 let t152 = circuit_mul(t151, in28); // Eval big_Q Horner step: multiply by z let t153 = circuit_add(in143, t152); // Eval big_Q Horner step: add coefficient_109 let t154 = circuit_mul(t153, in28); // Eval big_Q Horner step: multiply by z let t155 = circuit_add(in142, t154); // Eval big_Q Horner step: add coefficient_108 let t156 = circuit_mul(t155, in28); // Eval big_Q Horner step: multiply by z let t157 = circuit_add(in141, t156); // Eval big_Q Horner step: add coefficient_107 let t158 = circuit_mul(t157, in28); // Eval big_Q Horner step: multiply by z let t159 = circuit_add(in140, t158); // Eval big_Q Horner step: add coefficient_106 let t160 = circuit_mul(t159, in28); // Eval big_Q Horner step: multiply by z let t161 = circuit_add(in139, t160); // Eval big_Q Horner step: add coefficient_105 let t162 = circuit_mul(t161, in28); // Eval big_Q Horner step: multiply by z let t163 = circuit_add(in138, t162); // Eval big_Q Horner step: add coefficient_104 let t164 = circuit_mul(t163, in28); // Eval big_Q Horner step: multiply by z let t165 = circuit_add(in137, t164); // Eval big_Q Horner step: add coefficient_103 let t166 = circuit_mul(t165, in28); // Eval big_Q Horner step: multiply by z let t167 = circuit_add(in136, t166); // Eval big_Q Horner step: add coefficient_102 let t168 = circuit_mul(t167, in28); // Eval big_Q Horner step: multiply by z let t169 = circuit_add(in135, t168); // Eval big_Q Horner step: add coefficient_101 let t170 = circuit_mul(t169, in28); // Eval big_Q Horner step: multiply by z let t171 = circuit_add(in134, t170); // Eval big_Q Horner step: add coefficient_100 let t172 = circuit_mul(t171, in28); // Eval big_Q Horner step: multiply by z let t173 = circuit_add(in133, t172); // Eval big_Q Horner step: add coefficient_99 let t174 = circuit_mul(t173, in28); // Eval big_Q Horner step: multiply by z let t175 = circuit_add(in132, t174); // Eval big_Q Horner step: add coefficient_98 let t176 = circuit_mul(t175, in28); // Eval big_Q Horner step: multiply by z let t177 = circuit_add(in131, t176); // Eval big_Q Horner step: add coefficient_97 let t178 = circuit_mul(t177, in28); // Eval big_Q Horner step: multiply by z let t179 = circuit_add(in130, t178); // Eval big_Q Horner step: add coefficient_96 let t180 = circuit_mul(t179, in28); // Eval big_Q Horner step: multiply by z let t181 = circuit_add(in129, t180); // Eval big_Q Horner step: add coefficient_95 let t182 = circuit_mul(t181, in28); // Eval big_Q Horner step: multiply by z let t183 = circuit_add(in128, t182); // Eval big_Q Horner step: add coefficient_94 let t184 = circuit_mul(t183, in28); // Eval big_Q Horner step: multiply by z let t185 = circuit_add(in127, t184); // Eval big_Q Horner step: add coefficient_93 let t186 = circuit_mul(t185, in28); // Eval big_Q Horner step: multiply by z let t187 = circuit_add(in126, t186); // Eval big_Q Horner step: add coefficient_92 let t188 = circuit_mul(t187, in28); // Eval big_Q Horner step: multiply by z let t189 = circuit_add(in125, t188); // Eval big_Q Horner step: add coefficient_91 let t190 = circuit_mul(t189, in28); // Eval big_Q Horner step: multiply by z let t191 = circuit_add(in124, t190); // Eval big_Q Horner step: add coefficient_90 let t192 = circuit_mul(t191, in28); // Eval big_Q Horner step: multiply by z let t193 = circuit_add(in123, t192); // Eval big_Q Horner step: add coefficient_89 let t194 = circuit_mul(t193, in28); // Eval big_Q Horner step: multiply by z let t195 = circuit_add(in122, t194); // Eval big_Q Horner step: add coefficient_88 let t196 = circuit_mul(t195, in28); // Eval big_Q Horner step: multiply by z let t197 = circuit_add(in121, t196); // Eval big_Q Horner step: add coefficient_87 let t198 = circuit_mul(t197, in28); // Eval big_Q Horner step: multiply by z let t199 = circuit_add(in120, t198); // Eval big_Q Horner step: add coefficient_86 let t200 = circuit_mul(t199, in28); // Eval big_Q Horner step: multiply by z let t201 = circuit_add(in119, t200); // Eval big_Q Horner step: add coefficient_85 let t202 = circuit_mul(t201, in28); // Eval big_Q Horner step: multiply by z let t203 = circuit_add(in118, t202); // Eval big_Q Horner step: add coefficient_84 let t204 = circuit_mul(t203, in28); // Eval big_Q Horner step: multiply by z let t205 = circuit_add(in117, t204); // Eval big_Q Horner step: add coefficient_83 let t206 = circuit_mul(t205, in28); // Eval big_Q Horner step: multiply by z let t207 = circuit_add(in116, t206); // Eval big_Q Horner step: add coefficient_82 let t208 = circuit_mul(t207, in28); // Eval big_Q Horner step: multiply by z let t209 = circuit_add(in115, t208); // Eval big_Q Horner step: add coefficient_81 let t210 = circuit_mul(t209, in28); // Eval big_Q Horner step: multiply by z let t211 = circuit_add(in114, t210); // Eval big_Q Horner step: add coefficient_80 let t212 = circuit_mul(t211, in28); // Eval big_Q Horner step: multiply by z let t213 = circuit_add(in113, t212); // Eval big_Q Horner step: add coefficient_79 let t214 = circuit_mul(t213, in28); // Eval big_Q Horner step: multiply by z let t215 = circuit_add(in112, t214); // Eval big_Q Horner step: add coefficient_78 let t216 = circuit_mul(t215, in28); // Eval big_Q Horner step: multiply by z let t217 = circuit_add(in111, t216); // Eval big_Q Horner step: add coefficient_77 let t218 = circuit_mul(t217, in28); // Eval big_Q Horner step: multiply by z let t219 = circuit_add(in110, t218); // Eval big_Q Horner step: add coefficient_76 let t220 = circuit_mul(t219, in28); // Eval big_Q Horner step: multiply by z let t221 = circuit_add(in109, t220); // Eval big_Q Horner step: add coefficient_75 let t222 = circuit_mul(t221, in28); // Eval big_Q Horner step: multiply by z let t223 = circuit_add(in108, t222); // Eval big_Q Horner step: add coefficient_74 let t224 = circuit_mul(t223, in28); // Eval big_Q Horner step: multiply by z let t225 = circuit_add(in107, t224); // Eval big_Q Horner step: add coefficient_73 let t226 = circuit_mul(t225, in28); // Eval big_Q Horner step: multiply by z let t227 = circuit_add(in106, t226); // Eval big_Q Horner step: add coefficient_72 let t228 = circuit_mul(t227, in28); // Eval big_Q Horner step: multiply by z let t229 = circuit_add(in105, t228); // Eval big_Q Horner step: add coefficient_71 let t230 = circuit_mul(t229, in28); // Eval big_Q Horner step: multiply by z let t231 = circuit_add(in104, t230); // Eval big_Q Horner step: add coefficient_70 let t232 = circuit_mul(t231, in28); // Eval big_Q Horner step: multiply by z let t233 = circuit_add(in103, t232); // Eval big_Q Horner step: add coefficient_69 let t234 = circuit_mul(t233, in28); // Eval big_Q Horner step: multiply by z let t235 = circuit_add(in102, t234); // Eval big_Q Horner step: add coefficient_68 let t236 = circuit_mul(t235, in28); // Eval big_Q Horner step: multiply by z let t237 = circuit_add(in101, t236); // Eval big_Q Horner step: add coefficient_67 let t238 = circuit_mul(t237, in28); // Eval big_Q Horner step: multiply by z let t239 = circuit_add(in100, t238); // Eval big_Q Horner step: add coefficient_66 let t240 = circuit_mul(t239, in28); // Eval big_Q Horner step: multiply by z let t241 = circuit_add(in99, t240); // Eval big_Q Horner step: add coefficient_65 let t242 = circuit_mul(t241, in28); // Eval big_Q Horner step: multiply by z let t243 = circuit_add(in98, t242); // Eval big_Q Horner step: add coefficient_64 let t244 = circuit_mul(t243, in28); // Eval big_Q Horner step: multiply by z let t245 = circuit_add(in97, t244); // Eval big_Q Horner step: add coefficient_63 let t246 = circuit_mul(t245, in28); // Eval big_Q Horner step: multiply by z let t247 = circuit_add(in96, t246); // Eval big_Q Horner step: add coefficient_62 let t248 = circuit_mul(t247, in28); // Eval big_Q Horner step: multiply by z let t249 = circuit_add(in95, t248); // Eval big_Q Horner step: add coefficient_61 let t250 = circuit_mul(t249, in28); // Eval big_Q Horner step: multiply by z let t251 = circuit_add(in94, t250); // Eval big_Q Horner step: add coefficient_60 let t252 = circuit_mul(t251, in28); // Eval big_Q Horner step: multiply by z let t253 = circuit_add(in93, t252); // Eval big_Q Horner step: add coefficient_59 let t254 = circuit_mul(t253, in28); // Eval big_Q Horner step: multiply by z let t255 = circuit_add(in92, t254); // Eval big_Q Horner step: add coefficient_58 let t256 = circuit_mul(t255, in28); // Eval big_Q Horner step: multiply by z let t257 = circuit_add(in91, t256); // Eval big_Q Horner step: add coefficient_57 let t258 = circuit_mul(t257, in28); // Eval big_Q Horner step: multiply by z let t259 = circuit_add(in90, t258); // Eval big_Q Horner step: add coefficient_56 let t260 = circuit_mul(t259, in28); // Eval big_Q Horner step: multiply by z let t261 = circuit_add(in89, t260); // Eval big_Q Horner step: add coefficient_55 let t262 = circuit_mul(t261, in28); // Eval big_Q Horner step: multiply by z let t263 = circuit_add(in88, t262); // Eval big_Q Horner step: add coefficient_54 let t264 = circuit_mul(t263, in28); // Eval big_Q Horner step: multiply by z let t265 = circuit_add(in87, t264); // Eval big_Q Horner step: add coefficient_53 let t266 = circuit_mul(t265, in28); // Eval big_Q Horner step: multiply by z let t267 = circuit_add(in86, t266); // Eval big_Q Horner step: add coefficient_52 let t268 = circuit_mul(t267, in28); // Eval big_Q Horner step: multiply by z let t269 = circuit_add(in85, t268); // Eval big_Q Horner step: add coefficient_51 let t270 = circuit_mul(t269, in28); // Eval big_Q Horner step: multiply by z let t271 = circuit_add(in84, t270); // Eval big_Q Horner step: add coefficient_50 let t272 = circuit_mul(t271, in28); // Eval big_Q Horner step: multiply by z let t273 = circuit_add(in83, t272); // Eval big_Q Horner step: add coefficient_49 let t274 = circuit_mul(t273, in28); // Eval big_Q Horner step: multiply by z let t275 = circuit_add(in82, t274); // Eval big_Q Horner step: add coefficient_48 let t276 = circuit_mul(t275, in28); // Eval big_Q Horner step: multiply by z let t277 = circuit_add(in81, t276); // Eval big_Q Horner step: add coefficient_47 let t278 = circuit_mul(t277, in28); // Eval big_Q Horner step: multiply by z let t279 = circuit_add(in80, t278); // Eval big_Q Horner step: add coefficient_46 let t280 = circuit_mul(t279, in28); // Eval big_Q Horner step: multiply by z let t281 = circuit_add(in79, t280); // Eval big_Q Horner step: add coefficient_45 let t282 = circuit_mul(t281, in28); // Eval big_Q Horner step: multiply by z let t283 = circuit_add(in78, t282); // Eval big_Q Horner step: add coefficient_44 let t284 = circuit_mul(t283, in28); // Eval big_Q Horner step: multiply by z let t285 = circuit_add(in77, t284); // Eval big_Q Horner step: add coefficient_43 let t286 = circuit_mul(t285, in28); // Eval big_Q Horner step: multiply by z let t287 = circuit_add(in76, t286); // Eval big_Q Horner step: add coefficient_42 let t288 = circuit_mul(t287, in28); // Eval big_Q Horner step: multiply by z let t289 = circuit_add(in75, t288); // Eval big_Q Horner step: add coefficient_41 let t290 = circuit_mul(t289, in28); // Eval big_Q Horner step: multiply by z let t291 = circuit_add(in74, t290); // Eval big_Q Horner step: add coefficient_40 let t292 = circuit_mul(t291, in28); // Eval big_Q Horner step: multiply by z let t293 = circuit_add(in73, t292); // Eval big_Q Horner step: add coefficient_39 let t294 = circuit_mul(t293, in28); // Eval big_Q Horner step: multiply by z let t295 = circuit_add(in72, t294); // Eval big_Q Horner step: add coefficient_38 let t296 = circuit_mul(t295, in28); // Eval big_Q Horner step: multiply by z let t297 = circuit_add(in71, t296); // Eval big_Q Horner step: add coefficient_37 let t298 = circuit_mul(t297, in28); // Eval big_Q Horner step: multiply by z let t299 = circuit_add(in70, t298); // Eval big_Q Horner step: add coefficient_36 let t300 = circuit_mul(t299, in28); // Eval big_Q Horner step: multiply by z let t301 = circuit_add(in69, t300); // Eval big_Q Horner step: add coefficient_35 let t302 = circuit_mul(t301, in28); // Eval big_Q Horner step: multiply by z let t303 = circuit_add(in68, t302); // Eval big_Q Horner step: add coefficient_34 let t304 = circuit_mul(t303, in28); // Eval big_Q Horner step: multiply by z let t305 = circuit_add(in67, t304); // Eval big_Q Horner step: add coefficient_33 let t306 = circuit_mul(t305, in28); // Eval big_Q Horner step: multiply by z let t307 = circuit_add(in66, t306); // Eval big_Q Horner step: add coefficient_32 let t308 = circuit_mul(t307, in28); // Eval big_Q Horner step: multiply by z let t309 = circuit_add(in65, t308); // Eval big_Q Horner step: add coefficient_31 let t310 = circuit_mul(t309, in28); // Eval big_Q Horner step: multiply by z let t311 = circuit_add(in64, t310); // Eval big_Q Horner step: add coefficient_30 let t312 = circuit_mul(t311, in28); // Eval big_Q Horner step: multiply by z let t313 = circuit_add(in63, t312); // Eval big_Q Horner step: add coefficient_29 let t314 = circuit_mul(t313, in28); // Eval big_Q Horner step: multiply by z let t315 = circuit_add(in62, t314); // Eval big_Q Horner step: add coefficient_28 let t316 = circuit_mul(t315, in28); // Eval big_Q Horner step: multiply by z let t317 = circuit_add(in61, t316); // Eval big_Q Horner step: add coefficient_27 let t318 = circuit_mul(t317, in28); // Eval big_Q Horner step: multiply by z let t319 = circuit_add(in60, t318); // Eval big_Q Horner step: add coefficient_26 let t320 = circuit_mul(t319, in28); // Eval big_Q Horner step: multiply by z let t321 = circuit_add(in59, t320); // Eval big_Q Horner step: add coefficient_25 let t322 = circuit_mul(t321, in28); // Eval big_Q Horner step: multiply by z let t323 = circuit_add(in58, t322); // Eval big_Q Horner step: add coefficient_24 let t324 = circuit_mul(t323, in28); // Eval big_Q Horner step: multiply by z let t325 = circuit_add(in57, t324); // Eval big_Q Horner step: add coefficient_23 let t326 = circuit_mul(t325, in28); // Eval big_Q Horner step: multiply by z let t327 = circuit_add(in56, t326); // Eval big_Q Horner step: add coefficient_22 let t328 = circuit_mul(t327, in28); // Eval big_Q Horner step: multiply by z let t329 = circuit_add(in55, t328); // Eval big_Q Horner step: add coefficient_21 let t330 = circuit_mul(t329, in28); // Eval big_Q Horner step: multiply by z let t331 = circuit_add(in54, t330); // Eval big_Q Horner step: add coefficient_20 let t332 = circuit_mul(t331, in28); // Eval big_Q Horner step: multiply by z let t333 = circuit_add(in53, t332); // Eval big_Q Horner step: add coefficient_19 let t334 = circuit_mul(t333, in28); // Eval big_Q Horner step: multiply by z let t335 = circuit_add(in52, t334); // Eval big_Q Horner step: add coefficient_18 let t336 = circuit_mul(t335, in28); // Eval big_Q Horner step: multiply by z let t337 = circuit_add(in51, t336); // Eval big_Q Horner step: add coefficient_17 let t338 = circuit_mul(t337, in28); // Eval big_Q Horner step: multiply by z let t339 = circuit_add(in50, t338); // Eval big_Q Horner step: add coefficient_16 let t340 = circuit_mul(t339, in28); // Eval big_Q Horner step: multiply by z let t341 = circuit_add(in49, t340); // Eval big_Q Horner step: add coefficient_15 let t342 = circuit_mul(t341, in28); // Eval big_Q Horner step: multiply by z let t343 = circuit_add(in48, t342); // Eval big_Q Horner step: add coefficient_14 let t344 = circuit_mul(t343, in28); // Eval big_Q Horner step: multiply by z let t345 = circuit_add(in47, t344); // Eval big_Q Horner step: add coefficient_13 let t346 = circuit_mul(t345, in28); // Eval big_Q Horner step: multiply by z let t347 = circuit_add(in46, t346); // Eval big_Q Horner step: add coefficient_12 let t348 = circuit_mul(t347, in28); // Eval big_Q Horner step: multiply by z let t349 = circuit_add(in45, t348); // Eval big_Q Horner step: add coefficient_11 let t350 = circuit_mul(t349, in28); // Eval big_Q Horner step: multiply by z let t351 = circuit_add(in44, t350); // Eval big_Q Horner step: add coefficient_10 let t352 = circuit_mul(t351, in28); // Eval big_Q Horner step: multiply by z let t353 = circuit_add(in43, t352); // Eval big_Q Horner step: add coefficient_9 let t354 = circuit_mul(t353, in28); // Eval big_Q Horner step: multiply by z let t355 = circuit_add(in42, t354); // Eval big_Q Horner step: add coefficient_8 let t356 = circuit_mul(t355, in28); // Eval big_Q Horner step: multiply by z let t357 = circuit_add(in41, t356); // Eval big_Q Horner step: add coefficient_7 let t358 = circuit_mul(t357, in28); // Eval big_Q Horner step: multiply by z let t359 = circuit_add(in40, t358); // Eval big_Q Horner step: add coefficient_6 let t360 = circuit_mul(t359, in28); // Eval big_Q Horner step: multiply by z let t361 = circuit_add(in39, t360); // Eval big_Q Horner step: add coefficient_5 let t362 = circuit_mul(t361, in28); // Eval big_Q Horner step: multiply by z let t363 = circuit_add(in38, t362); // Eval big_Q Horner step: add coefficient_4 let t364 = circuit_mul(t363, in28); // Eval big_Q Horner step: multiply by z let t365 = circuit_add(in37, t364); // Eval big_Q Horner step: add coefficient_3 let t366 = circuit_mul(t365, in28); // Eval big_Q Horner step: multiply by z let t367 = circuit_add(in36, t366); // Eval big_Q Horner step: add coefficient_2 let t368 = circuit_mul(t367, in28); // Eval big_Q Horner step: multiply by z let t369 = circuit_add(in35, t368); // Eval big_Q Horner step: add coefficient_1 let t370 = circuit_mul(t369, in28); // Eval big_Q Horner step: multiply by z let t371 = circuit_add(in34, t370); // Eval big_Q Horner step: add coefficient_0 let t372 = circuit_mul(in3, t2); // Eval sparse poly P_irr step coeff_6 * z^6 let t373 = circuit_add(in2, t372); // Eval sparse poly P_irr step + coeff_6 * z^6 let t374 = circuit_add(t373, t5); // Eval sparse poly P_irr step + 1*z^12 let t375 = circuit_mul(t371, t374); let t376 = circuit_sub(t83, t375); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t376,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x52, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd35, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in3 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in4 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in5 circuit_inputs = circuit_inputs.next_2(line_1_0.r0a0); // in6 circuit_inputs = circuit_inputs.next_2(line_1_0.r0a1); // in7 circuit_inputs = circuit_inputs.next_2(line_1_0.r1a0); // in8 circuit_inputs = circuit_inputs.next_2(line_1_0.r1a1); // in9 circuit_inputs = circuit_inputs.next_2(line_2_0.r0a0); // in10 circuit_inputs = circuit_inputs.next_2(line_2_0.r0a1); // in11 circuit_inputs = circuit_inputs.next_2(line_2_0.r1a0); // in12 circuit_inputs = circuit_inputs.next_2(line_2_0.r1a1); // in13 circuit_inputs = circuit_inputs.next_2(yInv_1); // in14 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in15 circuit_inputs = circuit_inputs.next_2(line_1_1.r0a0); // in16 circuit_inputs = circuit_inputs.next_2(line_1_1.r0a1); // in17 circuit_inputs = circuit_inputs.next_2(line_1_1.r1a0); // in18 circuit_inputs = circuit_inputs.next_2(line_1_1.r1a1); // in19 circuit_inputs = circuit_inputs.next_2(line_2_1.r0a0); // in20 circuit_inputs = circuit_inputs.next_2(line_2_1.r0a1); // in21 circuit_inputs = circuit_inputs.next_2(line_2_1.r1a0); // in22 circuit_inputs = circuit_inputs.next_2(line_2_1.r1a1); // in23 circuit_inputs = circuit_inputs.next_2(R_n_minus_2_of_z); // in24 circuit_inputs = circuit_inputs.next_2(R_n_minus_1_of_z); // in25 circuit_inputs = circuit_inputs.next_2(c_0); // in26 circuit_inputs = circuit_inputs.next_2(w_of_z); // in27 circuit_inputs = circuit_inputs.next_2(z); // in28 circuit_inputs = circuit_inputs.next_2(c_inv_frob_1_of_z); // in29 circuit_inputs = circuit_inputs.next_2(c_frob_2_of_z); // in30 circuit_inputs = circuit_inputs.next_2(c_inv_frob_3_of_z); // in31 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in32 circuit_inputs = circuit_inputs.next_2(R_n_minus_3_of_z); // in33 for val in Q.span() { circuit_inputs = circuit_inputs.next_2(*val); } // in34 - in178 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let final_check: u384 = outputs.get_output(t376); return (final_check,); } #[inline(always)] pub fn run_BN254_MP_CHECK_FINALIZE_3P_2F_EXT_MLR_circuit( yInv_0: u384, xNegOverY_0: u384, line_1_0: G2Line, line_2_0: G2Line, yInv_1: u384, xNegOverY_1: u384, line_1_1: G2Line, line_2_1: G2Line, original_Q2: G2Point, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, R_n_minus_2_of_z: u384, R_n_minus_1_of_z: u384, c_0: u384, w_of_z: u384, z: u384, c_inv_frob_1_of_z: u384, c_frob_2_of_z: u384, c_inv_frob_3_of_z: u384, previous_lhs: u384, R_n_minus_3_of_z: u384, Q: Array, precomputed_miller_loop_result_of_z: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // 0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d let in1 = CE::> {}; // 0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2 let in2 = CE::> {}; // 0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a let in3 = CE::> {}; // 0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3 let in4 = CE::> {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48 let in5 = CE::> {}; // 0x1 let in6 = CE::> {}; // 0x0 let in7 = CE::> {}; // -0x9 % p let in8 = CE::> {}; // 0x52 let in9 = CE::> {}; // -0x12 % p // INPUT stack let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let (in25, in26, in27) = (CE::> {}, CE::> {}, CE::> {}); let (in28, in29, in30) = (CE::> {}, CE::> {}, CE::> {}); let (in31, in32, in33) = (CE::> {}, CE::> {}, CE::> {}); let (in34, in35, in36) = (CE::> {}, CE::> {}, CE::> {}); let (in37, in38, in39) = (CE::> {}, CE::> {}, CE::> {}); let (in40, in41, in42) = (CE::> {}, CE::> {}, CE::> {}); let (in43, in44, in45) = (CE::> {}, CE::> {}, CE::> {}); let (in46, in47, in48) = (CE::> {}, CE::> {}, CE::> {}); let (in49, in50, in51) = (CE::> {}, CE::> {}, CE::> {}); let (in52, in53, in54) = (CE::> {}, CE::> {}, CE::> {}); let (in55, in56, in57) = (CE::> {}, CE::> {}, CE::> {}); let (in58, in59, in60) = (CE::> {}, CE::> {}, CE::> {}); let (in61, in62, in63) = (CE::> {}, CE::> {}, CE::> {}); let (in64, in65, in66) = (CE::> {}, CE::> {}, CE::> {}); let (in67, in68, in69) = (CE::> {}, CE::> {}, CE::> {}); let (in70, in71, in72) = (CE::> {}, CE::> {}, CE::> {}); let (in73, in74, in75) = (CE::> {}, CE::> {}, CE::> {}); let (in76, in77, in78) = (CE::> {}, CE::> {}, CE::> {}); let (in79, in80, in81) = (CE::> {}, CE::> {}, CE::> {}); let (in82, in83, in84) = (CE::> {}, CE::> {}, CE::> {}); let (in85, in86, in87) = (CE::> {}, CE::> {}, CE::> {}); let (in88, in89, in90) = (CE::> {}, CE::> {}, CE::> {}); let (in91, in92, in93) = (CE::> {}, CE::> {}, CE::> {}); let (in94, in95, in96) = (CE::> {}, CE::> {}, CE::> {}); let (in97, in98, in99) = (CE::> {}, CE::> {}, CE::> {}); let (in100, in101, in102) = (CE::> {}, CE::> {}, CE::> {}); let (in103, in104, in105) = (CE::> {}, CE::> {}, CE::> {}); let (in106, in107, in108) = (CE::> {}, CE::> {}, CE::> {}); let (in109, in110, in111) = (CE::> {}, CE::> {}, CE::> {}); let (in112, in113, in114) = (CE::> {}, CE::> {}, CE::> {}); let (in115, in116, in117) = (CE::> {}, CE::> {}, CE::> {}); let (in118, in119, in120) = (CE::> {}, CE::> {}, CE::> {}); let (in121, in122, in123) = (CE::> {}, CE::> {}, CE::> {}); let (in124, in125, in126) = (CE::> {}, CE::> {}, CE::> {}); let (in127, in128, in129) = (CE::> {}, CE::> {}, CE::> {}); let (in130, in131, in132) = (CE::> {}, CE::> {}, CE::> {}); let (in133, in134, in135) = (CE::> {}, CE::> {}, CE::> {}); let (in136, in137, in138) = (CE::> {}, CE::> {}, CE::> {}); let (in139, in140, in141) = (CE::> {}, CE::> {}, CE::> {}); let (in142, in143, in144) = (CE::> {}, CE::> {}, CE::> {}); let (in145, in146, in147) = (CE::> {}, CE::> {}, CE::> {}); let (in148, in149, in150) = (CE::> {}, CE::> {}, CE::> {}); let (in151, in152, in153) = (CE::> {}, CE::> {}, CE::> {}); let (in154, in155, in156) = (CE::> {}, CE::> {}, CE::> {}); let (in157, in158, in159) = (CE::> {}, CE::> {}, CE::> {}); let (in160, in161, in162) = (CE::> {}, CE::> {}, CE::> {}); let (in163, in164, in165) = (CE::> {}, CE::> {}, CE::> {}); let (in166, in167, in168) = (CE::> {}, CE::> {}, CE::> {}); let (in169, in170, in171) = (CE::> {}, CE::> {}, CE::> {}); let (in172, in173, in174) = (CE::> {}, CE::> {}, CE::> {}); let (in175, in176, in177) = (CE::> {}, CE::> {}, CE::> {}); let (in178, in179, in180) = (CE::> {}, CE::> {}, CE::> {}); let (in181, in182, in183) = (CE::> {}, CE::> {}, CE::> {}); let (in184, in185, in186) = (CE::> {}, CE::> {}, CE::> {}); let (in187, in188, in189) = (CE::> {}, CE::> {}, CE::> {}); let (in190, in191, in192) = (CE::> {}, CE::> {}, CE::> {}); let (in193, in194, in195) = (CE::> {}, CE::> {}, CE::> {}); let (in196, in197, in198) = (CE::> {}, CE::> {}, CE::> {}); let (in199, in200, in201) = (CE::> {}, CE::> {}, CE::> {}); let (in202, in203, in204) = (CE::> {}, CE::> {}, CE::> {}); let (in205, in206, in207) = (CE::> {}, CE::> {}, CE::> {}); let (in208, in209, in210) = (CE::> {}, CE::> {}, CE::> {}); let (in211, in212, in213) = (CE::> {}, CE::> {}, CE::> {}); let (in214, in215, in216) = (CE::> {}, CE::> {}, CE::> {}); let (in217, in218, in219) = (CE::> {}, CE::> {}, CE::> {}); let (in220, in221, in222) = (CE::> {}, CE::> {}, CE::> {}); let (in223, in224, in225) = (CE::> {}, CE::> {}, CE::> {}); let (in226, in227, in228) = (CE::> {}, CE::> {}, CE::> {}); let (in229, in230, in231) = (CE::> {}, CE::> {}, CE::> {}); let (in232, in233, in234) = (CE::> {}, CE::> {}, CE::> {}); let (in235, in236, in237) = (CE::> {}, CE::> {}, CE::> {}); let (in238, in239, in240) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in44, in44); // compute z^2 let t1 = circuit_mul(t0, in44); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in44); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(t4, t1); // compute z^12 let t6 = circuit_sub(in6, in31); let t7 = circuit_sub(in6, in33); let t8 = circuit_mul(in30, in0); // Fp2 mul start let t9 = circuit_mul(t6, in1); let t10 = circuit_sub(t8, t9); // Fp2 mul real part end let t11 = circuit_mul(in30, in1); let t12 = circuit_mul(t6, in0); let t13 = circuit_add(t11, t12); // Fp2 mul imag part end let t14 = circuit_mul(in32, in2); // Fp2 mul start let t15 = circuit_mul(t7, in3); let t16 = circuit_sub(t14, t15); // Fp2 mul real part end let t17 = circuit_mul(in32, in3); let t18 = circuit_mul(t7, in2); let t19 = circuit_add(t17, t18); // Fp2 mul imag part end let t20 = circuit_mul(in30, in4); // Fp2 scalar mul coeff 0/1 let t21 = circuit_mul(in31, in4); // Fp2 scalar mul coeff 1/1 let t22 = circuit_mul(in32, in5); // Fp2 scalar mul coeff 0/1 let t23 = circuit_mul(in33, in5); // Fp2 scalar mul coeff 1/1 let t24 = circuit_sub(in38, t16); // Fp2 sub coeff 0/1 let t25 = circuit_sub(in39, t19); // Fp2 sub coeff 1/1 let t26 = circuit_sub(in36, t10); // Fp2 sub coeff 0/1 let t27 = circuit_sub(in37, t13); // Fp2 sub coeff 1/1 let t28 = circuit_mul(t26, t26); // Fp2 Inv start let t29 = circuit_mul(t27, t27); let t30 = circuit_add(t28, t29); let t31 = circuit_inverse(t30); let t32 = circuit_mul(t26, t31); // Fp2 Inv real part end let t33 = circuit_mul(t27, t31); let t34 = circuit_sub(in6, t33); // Fp2 Inv imag part end let t35 = circuit_mul(t24, t32); // Fp2 mul start let t36 = circuit_mul(t25, t34); let t37 = circuit_sub(t35, t36); // Fp2 mul real part end let t38 = circuit_mul(t24, t34); let t39 = circuit_mul(t25, t32); let t40 = circuit_add(t38, t39); // Fp2 mul imag part end let t41 = circuit_add(t37, t40); let t42 = circuit_sub(t37, t40); let t43 = circuit_mul(t41, t42); let t44 = circuit_mul(t37, t40); let t45 = circuit_add(t44, t44); let t46 = circuit_add(in36, t10); // Fp2 add coeff 0/1 let t47 = circuit_add(in37, t13); // Fp2 add coeff 1/1 let t48 = circuit_sub(t43, t46); // Fp2 sub coeff 0/1 let t49 = circuit_sub(t45, t47); // Fp2 sub coeff 1/1 let t50 = circuit_sub(in36, t48); // Fp2 sub coeff 0/1 let t51 = circuit_sub(in37, t49); // Fp2 sub coeff 1/1 let t52 = circuit_mul(t37, t50); // Fp2 mul start let t53 = circuit_mul(t40, t51); let t54 = circuit_sub(t52, t53); // Fp2 mul real part end let t55 = circuit_mul(t37, t51); let t56 = circuit_mul(t40, t50); let t57 = circuit_add(t55, t56); // Fp2 mul imag part end let t58 = circuit_sub(t54, in38); // Fp2 sub coeff 0/1 let t59 = circuit_sub(t57, in39); // Fp2 sub coeff 1/1 let t60 = circuit_mul(t37, in36); // Fp2 mul start let t61 = circuit_mul(t40, in37); let t62 = circuit_sub(t60, t61); // Fp2 mul real part end let t63 = circuit_mul(t37, in37); let t64 = circuit_mul(t40, in36); let t65 = circuit_add(t63, t64); // Fp2 mul imag part end let t66 = circuit_sub(t62, in38); // Fp2 sub coeff 0/1 let t67 = circuit_sub(t65, in39); // Fp2 sub coeff 1/1 let t68 = circuit_sub(t58, t22); // Fp2 sub coeff 0/1 let t69 = circuit_sub(t59, t23); // Fp2 sub coeff 1/1 let t70 = circuit_sub(t48, t20); // Fp2 sub coeff 0/1 let t71 = circuit_sub(t49, t21); // Fp2 sub coeff 1/1 let t72 = circuit_mul(t70, t70); // Fp2 Inv start let t73 = circuit_mul(t71, t71); let t74 = circuit_add(t72, t73); let t75 = circuit_inverse(t74); let t76 = circuit_mul(t70, t75); // Fp2 Inv real part end let t77 = circuit_mul(t71, t75); let t78 = circuit_sub(in6, t77); // Fp2 Inv imag part end let t79 = circuit_mul(t68, t76); // Fp2 mul start let t80 = circuit_mul(t69, t78); let t81 = circuit_sub(t79, t80); // Fp2 mul real part end let t82 = circuit_mul(t68, t78); let t83 = circuit_mul(t69, t76); let t84 = circuit_add(t82, t83); // Fp2 mul imag part end let t85 = circuit_mul(t81, t48); // Fp2 mul start let t86 = circuit_mul(t84, t49); let t87 = circuit_sub(t85, t86); // Fp2 mul real part end let t88 = circuit_mul(t81, t49); let t89 = circuit_mul(t84, t48); let t90 = circuit_add(t88, t89); // Fp2 mul imag part end let t91 = circuit_sub(t87, t58); // Fp2 sub coeff 0/1 let t92 = circuit_sub(t90, t59); // Fp2 sub coeff 1/1 let t93 = circuit_mul(in7, in13); let t94 = circuit_add(in12, t93); let t95 = circuit_mul(t94, in11); // eval bn line by xNegOverY let t96 = circuit_mul(in7, in15); let t97 = circuit_add(in14, t96); let t98 = circuit_mul(t97, in10); // eval bn line by yInv let t99 = circuit_mul(in13, in11); // eval bn line by xNegOverY let t100 = circuit_mul(in15, in10); // eval bn line by yInv let t101 = circuit_mul(in7, in17); let t102 = circuit_add(in16, t101); let t103 = circuit_mul(t102, in11); // eval bn line by xNegOverY let t104 = circuit_mul(in7, in19); let t105 = circuit_add(in18, t104); let t106 = circuit_mul(t105, in10); // eval bn line by yInv let t107 = circuit_mul(in17, in11); // eval bn line by xNegOverY let t108 = circuit_mul(in19, in10); // eval bn line by yInv let t109 = circuit_mul(in7, in23); let t110 = circuit_add(in22, t109); let t111 = circuit_mul(t110, in21); // eval bn line by xNegOverY let t112 = circuit_mul(in7, in25); let t113 = circuit_add(in24, t112); let t114 = circuit_mul(t113, in20); // eval bn line by yInv let t115 = circuit_mul(in23, in21); // eval bn line by xNegOverY let t116 = circuit_mul(in25, in20); // eval bn line by yInv let t117 = circuit_mul(in7, in27); let t118 = circuit_add(in26, t117); let t119 = circuit_mul(t118, in21); // eval bn line by xNegOverY let t120 = circuit_mul(in7, in29); let t121 = circuit_add(in28, t120); let t122 = circuit_mul(t121, in20); // eval bn line by yInv let t123 = circuit_mul(in27, in21); // eval bn line by xNegOverY let t124 = circuit_mul(in29, in20); // eval bn line by yInv let t125 = circuit_mul(in7, t40); let t126 = circuit_add(t37, t125); let t127 = circuit_mul(t126, in35); // eval bn line by xNegOverY let t128 = circuit_mul(in7, t67); let t129 = circuit_add(t66, t128); let t130 = circuit_mul(t129, in34); // eval bn line by yInv let t131 = circuit_mul(t40, in35); // eval bn line by xNegOverY let t132 = circuit_mul(t67, in34); // eval bn line by yInv let t133 = circuit_mul(in7, t84); let t134 = circuit_add(t81, t133); let t135 = circuit_mul(t134, in35); // eval bn line by xNegOverY let t136 = circuit_mul(in7, t92); let t137 = circuit_add(t91, t136); let t138 = circuit_mul(t137, in34); // eval bn line by yInv let t139 = circuit_mul(t84, in35); // eval bn line by xNegOverY let t140 = circuit_mul(t92, in34); // eval bn line by yInv let t141 = circuit_mul(t95, in44); // Eval sparse poly line_0 step coeff_1 * z^1 let t142 = circuit_add(in5, t141); // Eval sparse poly line_0 step + coeff_1 * z^1 let t143 = circuit_mul(t98, t1); // Eval sparse poly line_0 step coeff_3 * z^3 let t144 = circuit_add(t142, t143); // Eval sparse poly line_0 step + coeff_3 * z^3 let t145 = circuit_mul(t99, t3); // Eval sparse poly line_0 step coeff_7 * z^7 let t146 = circuit_add(t144, t145); // Eval sparse poly line_0 step + coeff_7 * z^7 let t147 = circuit_mul(t100, t4); // Eval sparse poly line_0 step coeff_9 * z^9 let t148 = circuit_add(t146, t147); // Eval sparse poly line_0 step + coeff_9 * z^9 let t149 = circuit_mul(in49, t148); let t150 = circuit_mul(t103, in44); // Eval sparse poly line_1 step coeff_1 * z^1 let t151 = circuit_add(in5, t150); // Eval sparse poly line_1 step + coeff_1 * z^1 let t152 = circuit_mul(t106, t1); // Eval sparse poly line_1 step coeff_3 * z^3 let t153 = circuit_add(t151, t152); // Eval sparse poly line_1 step + coeff_3 * z^3 let t154 = circuit_mul(t107, t3); // Eval sparse poly line_1 step coeff_7 * z^7 let t155 = circuit_add(t153, t154); // Eval sparse poly line_1 step + coeff_7 * z^7 let t156 = circuit_mul(t108, t4); // Eval sparse poly line_1 step coeff_9 * z^9 let t157 = circuit_add(t155, t156); // Eval sparse poly line_1 step + coeff_9 * z^9 let t158 = circuit_mul(t149, t157); let t159 = circuit_mul(t111, in44); // Eval sparse poly line_2 step coeff_1 * z^1 let t160 = circuit_add(in5, t159); // Eval sparse poly line_2 step + coeff_1 * z^1 let t161 = circuit_mul(t114, t1); // Eval sparse poly line_2 step coeff_3 * z^3 let t162 = circuit_add(t160, t161); // Eval sparse poly line_2 step + coeff_3 * z^3 let t163 = circuit_mul(t115, t3); // Eval sparse poly line_2 step coeff_7 * z^7 let t164 = circuit_add(t162, t163); // Eval sparse poly line_2 step + coeff_7 * z^7 let t165 = circuit_mul(t116, t4); // Eval sparse poly line_2 step coeff_9 * z^9 let t166 = circuit_add(t164, t165); // Eval sparse poly line_2 step + coeff_9 * z^9 let t167 = circuit_mul(t158, t166); let t168 = circuit_mul(t119, in44); // Eval sparse poly line_3 step coeff_1 * z^1 let t169 = circuit_add(in5, t168); // Eval sparse poly line_3 step + coeff_1 * z^1 let t170 = circuit_mul(t122, t1); // Eval sparse poly line_3 step coeff_3 * z^3 let t171 = circuit_add(t169, t170); // Eval sparse poly line_3 step + coeff_3 * z^3 let t172 = circuit_mul(t123, t3); // Eval sparse poly line_3 step coeff_7 * z^7 let t173 = circuit_add(t171, t172); // Eval sparse poly line_3 step + coeff_7 * z^7 let t174 = circuit_mul(t124, t4); // Eval sparse poly line_3 step coeff_9 * z^9 let t175 = circuit_add(t173, t174); // Eval sparse poly line_3 step + coeff_9 * z^9 let t176 = circuit_mul(t167, t175); let t177 = circuit_mul(t127, in44); // Eval sparse poly line_4 step coeff_1 * z^1 let t178 = circuit_add(in5, t177); // Eval sparse poly line_4 step + coeff_1 * z^1 let t179 = circuit_mul(t130, t1); // Eval sparse poly line_4 step coeff_3 * z^3 let t180 = circuit_add(t178, t179); // Eval sparse poly line_4 step + coeff_3 * z^3 let t181 = circuit_mul(t131, t3); // Eval sparse poly line_4 step coeff_7 * z^7 let t182 = circuit_add(t180, t181); // Eval sparse poly line_4 step + coeff_7 * z^7 let t183 = circuit_mul(t132, t4); // Eval sparse poly line_4 step coeff_9 * z^9 let t184 = circuit_add(t182, t183); // Eval sparse poly line_4 step + coeff_9 * z^9 let t185 = circuit_mul(t176, t184); let t186 = circuit_mul(t135, in44); // Eval sparse poly line_5 step coeff_1 * z^1 let t187 = circuit_add(in5, t186); // Eval sparse poly line_5 step + coeff_1 * z^1 let t188 = circuit_mul(t138, t1); // Eval sparse poly line_5 step coeff_3 * z^3 let t189 = circuit_add(t187, t188); // Eval sparse poly line_5 step + coeff_3 * z^3 let t190 = circuit_mul(t139, t3); // Eval sparse poly line_5 step coeff_7 * z^7 let t191 = circuit_add(t189, t190); // Eval sparse poly line_5 step + coeff_7 * z^7 let t192 = circuit_mul(t140, t4); // Eval sparse poly line_5 step coeff_9 * z^9 let t193 = circuit_add(t191, t192); // Eval sparse poly line_5 step + coeff_9 * z^9 let t194 = circuit_mul(t185, t193); let t195 = circuit_sub(t194, in40); // ((Π(n-2,k) (Pk(z)) - R_n_minus_2(z)) let t196 = circuit_mul(in40, in45); let t197 = circuit_mul(t196, in46); let t198 = circuit_mul(t197, in47); let t199 = circuit_mul(t198, in43); let t200 = circuit_mul(t199, in240); let t201 = circuit_sub(t200, in41); // ((Π(n-1,k) (Pk(z)) - R_n_minus_1(z)) let t202 = circuit_mul(in42, in48); let t203 = circuit_add(t202, t195); let t204 = circuit_mul(in42, t203); let t205 = circuit_add(t204, t201); let t206 = circuit_mul(in239, in44); // Eval big_Q Horner step: multiply by z let t207 = circuit_add(in238, t206); // Eval big_Q Horner step: add coefficient_188 let t208 = circuit_mul(t207, in44); // Eval big_Q Horner step: multiply by z let t209 = circuit_add(in237, t208); // Eval big_Q Horner step: add coefficient_187 let t210 = circuit_mul(t209, in44); // Eval big_Q Horner step: multiply by z let t211 = circuit_add(in236, t210); // Eval big_Q Horner step: add coefficient_186 let t212 = circuit_mul(t211, in44); // Eval big_Q Horner step: multiply by z let t213 = circuit_add(in235, t212); // Eval big_Q Horner step: add coefficient_185 let t214 = circuit_mul(t213, in44); // Eval big_Q Horner step: multiply by z let t215 = circuit_add(in234, t214); // Eval big_Q Horner step: add coefficient_184 let t216 = circuit_mul(t215, in44); // Eval big_Q Horner step: multiply by z let t217 = circuit_add(in233, t216); // Eval big_Q Horner step: add coefficient_183 let t218 = circuit_mul(t217, in44); // Eval big_Q Horner step: multiply by z let t219 = circuit_add(in232, t218); // Eval big_Q Horner step: add coefficient_182 let t220 = circuit_mul(t219, in44); // Eval big_Q Horner step: multiply by z let t221 = circuit_add(in231, t220); // Eval big_Q Horner step: add coefficient_181 let t222 = circuit_mul(t221, in44); // Eval big_Q Horner step: multiply by z let t223 = circuit_add(in230, t222); // Eval big_Q Horner step: add coefficient_180 let t224 = circuit_mul(t223, in44); // Eval big_Q Horner step: multiply by z let t225 = circuit_add(in229, t224); // Eval big_Q Horner step: add coefficient_179 let t226 = circuit_mul(t225, in44); // Eval big_Q Horner step: multiply by z let t227 = circuit_add(in228, t226); // Eval big_Q Horner step: add coefficient_178 let t228 = circuit_mul(t227, in44); // Eval big_Q Horner step: multiply by z let t229 = circuit_add(in227, t228); // Eval big_Q Horner step: add coefficient_177 let t230 = circuit_mul(t229, in44); // Eval big_Q Horner step: multiply by z let t231 = circuit_add(in226, t230); // Eval big_Q Horner step: add coefficient_176 let t232 = circuit_mul(t231, in44); // Eval big_Q Horner step: multiply by z let t233 = circuit_add(in225, t232); // Eval big_Q Horner step: add coefficient_175 let t234 = circuit_mul(t233, in44); // Eval big_Q Horner step: multiply by z let t235 = circuit_add(in224, t234); // Eval big_Q Horner step: add coefficient_174 let t236 = circuit_mul(t235, in44); // Eval big_Q Horner step: multiply by z let t237 = circuit_add(in223, t236); // Eval big_Q Horner step: add coefficient_173 let t238 = circuit_mul(t237, in44); // Eval big_Q Horner step: multiply by z let t239 = circuit_add(in222, t238); // Eval big_Q Horner step: add coefficient_172 let t240 = circuit_mul(t239, in44); // Eval big_Q Horner step: multiply by z let t241 = circuit_add(in221, t240); // Eval big_Q Horner step: add coefficient_171 let t242 = circuit_mul(t241, in44); // Eval big_Q Horner step: multiply by z let t243 = circuit_add(in220, t242); // Eval big_Q Horner step: add coefficient_170 let t244 = circuit_mul(t243, in44); // Eval big_Q Horner step: multiply by z let t245 = circuit_add(in219, t244); // Eval big_Q Horner step: add coefficient_169 let t246 = circuit_mul(t245, in44); // Eval big_Q Horner step: multiply by z let t247 = circuit_add(in218, t246); // Eval big_Q Horner step: add coefficient_168 let t248 = circuit_mul(t247, in44); // Eval big_Q Horner step: multiply by z let t249 = circuit_add(in217, t248); // Eval big_Q Horner step: add coefficient_167 let t250 = circuit_mul(t249, in44); // Eval big_Q Horner step: multiply by z let t251 = circuit_add(in216, t250); // Eval big_Q Horner step: add coefficient_166 let t252 = circuit_mul(t251, in44); // Eval big_Q Horner step: multiply by z let t253 = circuit_add(in215, t252); // Eval big_Q Horner step: add coefficient_165 let t254 = circuit_mul(t253, in44); // Eval big_Q Horner step: multiply by z let t255 = circuit_add(in214, t254); // Eval big_Q Horner step: add coefficient_164 let t256 = circuit_mul(t255, in44); // Eval big_Q Horner step: multiply by z let t257 = circuit_add(in213, t256); // Eval big_Q Horner step: add coefficient_163 let t258 = circuit_mul(t257, in44); // Eval big_Q Horner step: multiply by z let t259 = circuit_add(in212, t258); // Eval big_Q Horner step: add coefficient_162 let t260 = circuit_mul(t259, in44); // Eval big_Q Horner step: multiply by z let t261 = circuit_add(in211, t260); // Eval big_Q Horner step: add coefficient_161 let t262 = circuit_mul(t261, in44); // Eval big_Q Horner step: multiply by z let t263 = circuit_add(in210, t262); // Eval big_Q Horner step: add coefficient_160 let t264 = circuit_mul(t263, in44); // Eval big_Q Horner step: multiply by z let t265 = circuit_add(in209, t264); // Eval big_Q Horner step: add coefficient_159 let t266 = circuit_mul(t265, in44); // Eval big_Q Horner step: multiply by z let t267 = circuit_add(in208, t266); // Eval big_Q Horner step: add coefficient_158 let t268 = circuit_mul(t267, in44); // Eval big_Q Horner step: multiply by z let t269 = circuit_add(in207, t268); // Eval big_Q Horner step: add coefficient_157 let t270 = circuit_mul(t269, in44); // Eval big_Q Horner step: multiply by z let t271 = circuit_add(in206, t270); // Eval big_Q Horner step: add coefficient_156 let t272 = circuit_mul(t271, in44); // Eval big_Q Horner step: multiply by z let t273 = circuit_add(in205, t272); // Eval big_Q Horner step: add coefficient_155 let t274 = circuit_mul(t273, in44); // Eval big_Q Horner step: multiply by z let t275 = circuit_add(in204, t274); // Eval big_Q Horner step: add coefficient_154 let t276 = circuit_mul(t275, in44); // Eval big_Q Horner step: multiply by z let t277 = circuit_add(in203, t276); // Eval big_Q Horner step: add coefficient_153 let t278 = circuit_mul(t277, in44); // Eval big_Q Horner step: multiply by z let t279 = circuit_add(in202, t278); // Eval big_Q Horner step: add coefficient_152 let t280 = circuit_mul(t279, in44); // Eval big_Q Horner step: multiply by z let t281 = circuit_add(in201, t280); // Eval big_Q Horner step: add coefficient_151 let t282 = circuit_mul(t281, in44); // Eval big_Q Horner step: multiply by z let t283 = circuit_add(in200, t282); // Eval big_Q Horner step: add coefficient_150 let t284 = circuit_mul(t283, in44); // Eval big_Q Horner step: multiply by z let t285 = circuit_add(in199, t284); // Eval big_Q Horner step: add coefficient_149 let t286 = circuit_mul(t285, in44); // Eval big_Q Horner step: multiply by z let t287 = circuit_add(in198, t286); // Eval big_Q Horner step: add coefficient_148 let t288 = circuit_mul(t287, in44); // Eval big_Q Horner step: multiply by z let t289 = circuit_add(in197, t288); // Eval big_Q Horner step: add coefficient_147 let t290 = circuit_mul(t289, in44); // Eval big_Q Horner step: multiply by z let t291 = circuit_add(in196, t290); // Eval big_Q Horner step: add coefficient_146 let t292 = circuit_mul(t291, in44); // Eval big_Q Horner step: multiply by z let t293 = circuit_add(in195, t292); // Eval big_Q Horner step: add coefficient_145 let t294 = circuit_mul(t293, in44); // Eval big_Q Horner step: multiply by z let t295 = circuit_add(in194, t294); // Eval big_Q Horner step: add coefficient_144 let t296 = circuit_mul(t295, in44); // Eval big_Q Horner step: multiply by z let t297 = circuit_add(in193, t296); // Eval big_Q Horner step: add coefficient_143 let t298 = circuit_mul(t297, in44); // Eval big_Q Horner step: multiply by z let t299 = circuit_add(in192, t298); // Eval big_Q Horner step: add coefficient_142 let t300 = circuit_mul(t299, in44); // Eval big_Q Horner step: multiply by z let t301 = circuit_add(in191, t300); // Eval big_Q Horner step: add coefficient_141 let t302 = circuit_mul(t301, in44); // Eval big_Q Horner step: multiply by z let t303 = circuit_add(in190, t302); // Eval big_Q Horner step: add coefficient_140 let t304 = circuit_mul(t303, in44); // Eval big_Q Horner step: multiply by z let t305 = circuit_add(in189, t304); // Eval big_Q Horner step: add coefficient_139 let t306 = circuit_mul(t305, in44); // Eval big_Q Horner step: multiply by z let t307 = circuit_add(in188, t306); // Eval big_Q Horner step: add coefficient_138 let t308 = circuit_mul(t307, in44); // Eval big_Q Horner step: multiply by z let t309 = circuit_add(in187, t308); // Eval big_Q Horner step: add coefficient_137 let t310 = circuit_mul(t309, in44); // Eval big_Q Horner step: multiply by z let t311 = circuit_add(in186, t310); // Eval big_Q Horner step: add coefficient_136 let t312 = circuit_mul(t311, in44); // Eval big_Q Horner step: multiply by z let t313 = circuit_add(in185, t312); // Eval big_Q Horner step: add coefficient_135 let t314 = circuit_mul(t313, in44); // Eval big_Q Horner step: multiply by z let t315 = circuit_add(in184, t314); // Eval big_Q Horner step: add coefficient_134 let t316 = circuit_mul(t315, in44); // Eval big_Q Horner step: multiply by z let t317 = circuit_add(in183, t316); // Eval big_Q Horner step: add coefficient_133 let t318 = circuit_mul(t317, in44); // Eval big_Q Horner step: multiply by z let t319 = circuit_add(in182, t318); // Eval big_Q Horner step: add coefficient_132 let t320 = circuit_mul(t319, in44); // Eval big_Q Horner step: multiply by z let t321 = circuit_add(in181, t320); // Eval big_Q Horner step: add coefficient_131 let t322 = circuit_mul(t321, in44); // Eval big_Q Horner step: multiply by z let t323 = circuit_add(in180, t322); // Eval big_Q Horner step: add coefficient_130 let t324 = circuit_mul(t323, in44); // Eval big_Q Horner step: multiply by z let t325 = circuit_add(in179, t324); // Eval big_Q Horner step: add coefficient_129 let t326 = circuit_mul(t325, in44); // Eval big_Q Horner step: multiply by z let t327 = circuit_add(in178, t326); // Eval big_Q Horner step: add coefficient_128 let t328 = circuit_mul(t327, in44); // Eval big_Q Horner step: multiply by z let t329 = circuit_add(in177, t328); // Eval big_Q Horner step: add coefficient_127 let t330 = circuit_mul(t329, in44); // Eval big_Q Horner step: multiply by z let t331 = circuit_add(in176, t330); // Eval big_Q Horner step: add coefficient_126 let t332 = circuit_mul(t331, in44); // Eval big_Q Horner step: multiply by z let t333 = circuit_add(in175, t332); // Eval big_Q Horner step: add coefficient_125 let t334 = circuit_mul(t333, in44); // Eval big_Q Horner step: multiply by z let t335 = circuit_add(in174, t334); // Eval big_Q Horner step: add coefficient_124 let t336 = circuit_mul(t335, in44); // Eval big_Q Horner step: multiply by z let t337 = circuit_add(in173, t336); // Eval big_Q Horner step: add coefficient_123 let t338 = circuit_mul(t337, in44); // Eval big_Q Horner step: multiply by z let t339 = circuit_add(in172, t338); // Eval big_Q Horner step: add coefficient_122 let t340 = circuit_mul(t339, in44); // Eval big_Q Horner step: multiply by z let t341 = circuit_add(in171, t340); // Eval big_Q Horner step: add coefficient_121 let t342 = circuit_mul(t341, in44); // Eval big_Q Horner step: multiply by z let t343 = circuit_add(in170, t342); // Eval big_Q Horner step: add coefficient_120 let t344 = circuit_mul(t343, in44); // Eval big_Q Horner step: multiply by z let t345 = circuit_add(in169, t344); // Eval big_Q Horner step: add coefficient_119 let t346 = circuit_mul(t345, in44); // Eval big_Q Horner step: multiply by z let t347 = circuit_add(in168, t346); // Eval big_Q Horner step: add coefficient_118 let t348 = circuit_mul(t347, in44); // Eval big_Q Horner step: multiply by z let t349 = circuit_add(in167, t348); // Eval big_Q Horner step: add coefficient_117 let t350 = circuit_mul(t349, in44); // Eval big_Q Horner step: multiply by z let t351 = circuit_add(in166, t350); // Eval big_Q Horner step: add coefficient_116 let t352 = circuit_mul(t351, in44); // Eval big_Q Horner step: multiply by z let t353 = circuit_add(in165, t352); // Eval big_Q Horner step: add coefficient_115 let t354 = circuit_mul(t353, in44); // Eval big_Q Horner step: multiply by z let t355 = circuit_add(in164, t354); // Eval big_Q Horner step: add coefficient_114 let t356 = circuit_mul(t355, in44); // Eval big_Q Horner step: multiply by z let t357 = circuit_add(in163, t356); // Eval big_Q Horner step: add coefficient_113 let t358 = circuit_mul(t357, in44); // Eval big_Q Horner step: multiply by z let t359 = circuit_add(in162, t358); // Eval big_Q Horner step: add coefficient_112 let t360 = circuit_mul(t359, in44); // Eval big_Q Horner step: multiply by z let t361 = circuit_add(in161, t360); // Eval big_Q Horner step: add coefficient_111 let t362 = circuit_mul(t361, in44); // Eval big_Q Horner step: multiply by z let t363 = circuit_add(in160, t362); // Eval big_Q Horner step: add coefficient_110 let t364 = circuit_mul(t363, in44); // Eval big_Q Horner step: multiply by z let t365 = circuit_add(in159, t364); // Eval big_Q Horner step: add coefficient_109 let t366 = circuit_mul(t365, in44); // Eval big_Q Horner step: multiply by z let t367 = circuit_add(in158, t366); // Eval big_Q Horner step: add coefficient_108 let t368 = circuit_mul(t367, in44); // Eval big_Q Horner step: multiply by z let t369 = circuit_add(in157, t368); // Eval big_Q Horner step: add coefficient_107 let t370 = circuit_mul(t369, in44); // Eval big_Q Horner step: multiply by z let t371 = circuit_add(in156, t370); // Eval big_Q Horner step: add coefficient_106 let t372 = circuit_mul(t371, in44); // Eval big_Q Horner step: multiply by z let t373 = circuit_add(in155, t372); // Eval big_Q Horner step: add coefficient_105 let t374 = circuit_mul(t373, in44); // Eval big_Q Horner step: multiply by z let t375 = circuit_add(in154, t374); // Eval big_Q Horner step: add coefficient_104 let t376 = circuit_mul(t375, in44); // Eval big_Q Horner step: multiply by z let t377 = circuit_add(in153, t376); // Eval big_Q Horner step: add coefficient_103 let t378 = circuit_mul(t377, in44); // Eval big_Q Horner step: multiply by z let t379 = circuit_add(in152, t378); // Eval big_Q Horner step: add coefficient_102 let t380 = circuit_mul(t379, in44); // Eval big_Q Horner step: multiply by z let t381 = circuit_add(in151, t380); // Eval big_Q Horner step: add coefficient_101 let t382 = circuit_mul(t381, in44); // Eval big_Q Horner step: multiply by z let t383 = circuit_add(in150, t382); // Eval big_Q Horner step: add coefficient_100 let t384 = circuit_mul(t383, in44); // Eval big_Q Horner step: multiply by z let t385 = circuit_add(in149, t384); // Eval big_Q Horner step: add coefficient_99 let t386 = circuit_mul(t385, in44); // Eval big_Q Horner step: multiply by z let t387 = circuit_add(in148, t386); // Eval big_Q Horner step: add coefficient_98 let t388 = circuit_mul(t387, in44); // Eval big_Q Horner step: multiply by z let t389 = circuit_add(in147, t388); // Eval big_Q Horner step: add coefficient_97 let t390 = circuit_mul(t389, in44); // Eval big_Q Horner step: multiply by z let t391 = circuit_add(in146, t390); // Eval big_Q Horner step: add coefficient_96 let t392 = circuit_mul(t391, in44); // Eval big_Q Horner step: multiply by z let t393 = circuit_add(in145, t392); // Eval big_Q Horner step: add coefficient_95 let t394 = circuit_mul(t393, in44); // Eval big_Q Horner step: multiply by z let t395 = circuit_add(in144, t394); // Eval big_Q Horner step: add coefficient_94 let t396 = circuit_mul(t395, in44); // Eval big_Q Horner step: multiply by z let t397 = circuit_add(in143, t396); // Eval big_Q Horner step: add coefficient_93 let t398 = circuit_mul(t397, in44); // Eval big_Q Horner step: multiply by z let t399 = circuit_add(in142, t398); // Eval big_Q Horner step: add coefficient_92 let t400 = circuit_mul(t399, in44); // Eval big_Q Horner step: multiply by z let t401 = circuit_add(in141, t400); // Eval big_Q Horner step: add coefficient_91 let t402 = circuit_mul(t401, in44); // Eval big_Q Horner step: multiply by z let t403 = circuit_add(in140, t402); // Eval big_Q Horner step: add coefficient_90 let t404 = circuit_mul(t403, in44); // Eval big_Q Horner step: multiply by z let t405 = circuit_add(in139, t404); // Eval big_Q Horner step: add coefficient_89 let t406 = circuit_mul(t405, in44); // Eval big_Q Horner step: multiply by z let t407 = circuit_add(in138, t406); // Eval big_Q Horner step: add coefficient_88 let t408 = circuit_mul(t407, in44); // Eval big_Q Horner step: multiply by z let t409 = circuit_add(in137, t408); // Eval big_Q Horner step: add coefficient_87 let t410 = circuit_mul(t409, in44); // Eval big_Q Horner step: multiply by z let t411 = circuit_add(in136, t410); // Eval big_Q Horner step: add coefficient_86 let t412 = circuit_mul(t411, in44); // Eval big_Q Horner step: multiply by z let t413 = circuit_add(in135, t412); // Eval big_Q Horner step: add coefficient_85 let t414 = circuit_mul(t413, in44); // Eval big_Q Horner step: multiply by z let t415 = circuit_add(in134, t414); // Eval big_Q Horner step: add coefficient_84 let t416 = circuit_mul(t415, in44); // Eval big_Q Horner step: multiply by z let t417 = circuit_add(in133, t416); // Eval big_Q Horner step: add coefficient_83 let t418 = circuit_mul(t417, in44); // Eval big_Q Horner step: multiply by z let t419 = circuit_add(in132, t418); // Eval big_Q Horner step: add coefficient_82 let t420 = circuit_mul(t419, in44); // Eval big_Q Horner step: multiply by z let t421 = circuit_add(in131, t420); // Eval big_Q Horner step: add coefficient_81 let t422 = circuit_mul(t421, in44); // Eval big_Q Horner step: multiply by z let t423 = circuit_add(in130, t422); // Eval big_Q Horner step: add coefficient_80 let t424 = circuit_mul(t423, in44); // Eval big_Q Horner step: multiply by z let t425 = circuit_add(in129, t424); // Eval big_Q Horner step: add coefficient_79 let t426 = circuit_mul(t425, in44); // Eval big_Q Horner step: multiply by z let t427 = circuit_add(in128, t426); // Eval big_Q Horner step: add coefficient_78 let t428 = circuit_mul(t427, in44); // Eval big_Q Horner step: multiply by z let t429 = circuit_add(in127, t428); // Eval big_Q Horner step: add coefficient_77 let t430 = circuit_mul(t429, in44); // Eval big_Q Horner step: multiply by z let t431 = circuit_add(in126, t430); // Eval big_Q Horner step: add coefficient_76 let t432 = circuit_mul(t431, in44); // Eval big_Q Horner step: multiply by z let t433 = circuit_add(in125, t432); // Eval big_Q Horner step: add coefficient_75 let t434 = circuit_mul(t433, in44); // Eval big_Q Horner step: multiply by z let t435 = circuit_add(in124, t434); // Eval big_Q Horner step: add coefficient_74 let t436 = circuit_mul(t435, in44); // Eval big_Q Horner step: multiply by z let t437 = circuit_add(in123, t436); // Eval big_Q Horner step: add coefficient_73 let t438 = circuit_mul(t437, in44); // Eval big_Q Horner step: multiply by z let t439 = circuit_add(in122, t438); // Eval big_Q Horner step: add coefficient_72 let t440 = circuit_mul(t439, in44); // Eval big_Q Horner step: multiply by z let t441 = circuit_add(in121, t440); // Eval big_Q Horner step: add coefficient_71 let t442 = circuit_mul(t441, in44); // Eval big_Q Horner step: multiply by z let t443 = circuit_add(in120, t442); // Eval big_Q Horner step: add coefficient_70 let t444 = circuit_mul(t443, in44); // Eval big_Q Horner step: multiply by z let t445 = circuit_add(in119, t444); // Eval big_Q Horner step: add coefficient_69 let t446 = circuit_mul(t445, in44); // Eval big_Q Horner step: multiply by z let t447 = circuit_add(in118, t446); // Eval big_Q Horner step: add coefficient_68 let t448 = circuit_mul(t447, in44); // Eval big_Q Horner step: multiply by z let t449 = circuit_add(in117, t448); // Eval big_Q Horner step: add coefficient_67 let t450 = circuit_mul(t449, in44); // Eval big_Q Horner step: multiply by z let t451 = circuit_add(in116, t450); // Eval big_Q Horner step: add coefficient_66 let t452 = circuit_mul(t451, in44); // Eval big_Q Horner step: multiply by z let t453 = circuit_add(in115, t452); // Eval big_Q Horner step: add coefficient_65 let t454 = circuit_mul(t453, in44); // Eval big_Q Horner step: multiply by z let t455 = circuit_add(in114, t454); // Eval big_Q Horner step: add coefficient_64 let t456 = circuit_mul(t455, in44); // Eval big_Q Horner step: multiply by z let t457 = circuit_add(in113, t456); // Eval big_Q Horner step: add coefficient_63 let t458 = circuit_mul(t457, in44); // Eval big_Q Horner step: multiply by z let t459 = circuit_add(in112, t458); // Eval big_Q Horner step: add coefficient_62 let t460 = circuit_mul(t459, in44); // Eval big_Q Horner step: multiply by z let t461 = circuit_add(in111, t460); // Eval big_Q Horner step: add coefficient_61 let t462 = circuit_mul(t461, in44); // Eval big_Q Horner step: multiply by z let t463 = circuit_add(in110, t462); // Eval big_Q Horner step: add coefficient_60 let t464 = circuit_mul(t463, in44); // Eval big_Q Horner step: multiply by z let t465 = circuit_add(in109, t464); // Eval big_Q Horner step: add coefficient_59 let t466 = circuit_mul(t465, in44); // Eval big_Q Horner step: multiply by z let t467 = circuit_add(in108, t466); // Eval big_Q Horner step: add coefficient_58 let t468 = circuit_mul(t467, in44); // Eval big_Q Horner step: multiply by z let t469 = circuit_add(in107, t468); // Eval big_Q Horner step: add coefficient_57 let t470 = circuit_mul(t469, in44); // Eval big_Q Horner step: multiply by z let t471 = circuit_add(in106, t470); // Eval big_Q Horner step: add coefficient_56 let t472 = circuit_mul(t471, in44); // Eval big_Q Horner step: multiply by z let t473 = circuit_add(in105, t472); // Eval big_Q Horner step: add coefficient_55 let t474 = circuit_mul(t473, in44); // Eval big_Q Horner step: multiply by z let t475 = circuit_add(in104, t474); // Eval big_Q Horner step: add coefficient_54 let t476 = circuit_mul(t475, in44); // Eval big_Q Horner step: multiply by z let t477 = circuit_add(in103, t476); // Eval big_Q Horner step: add coefficient_53 let t478 = circuit_mul(t477, in44); // Eval big_Q Horner step: multiply by z let t479 = circuit_add(in102, t478); // Eval big_Q Horner step: add coefficient_52 let t480 = circuit_mul(t479, in44); // Eval big_Q Horner step: multiply by z let t481 = circuit_add(in101, t480); // Eval big_Q Horner step: add coefficient_51 let t482 = circuit_mul(t481, in44); // Eval big_Q Horner step: multiply by z let t483 = circuit_add(in100, t482); // Eval big_Q Horner step: add coefficient_50 let t484 = circuit_mul(t483, in44); // Eval big_Q Horner step: multiply by z let t485 = circuit_add(in99, t484); // Eval big_Q Horner step: add coefficient_49 let t486 = circuit_mul(t485, in44); // Eval big_Q Horner step: multiply by z let t487 = circuit_add(in98, t486); // Eval big_Q Horner step: add coefficient_48 let t488 = circuit_mul(t487, in44); // Eval big_Q Horner step: multiply by z let t489 = circuit_add(in97, t488); // Eval big_Q Horner step: add coefficient_47 let t490 = circuit_mul(t489, in44); // Eval big_Q Horner step: multiply by z let t491 = circuit_add(in96, t490); // Eval big_Q Horner step: add coefficient_46 let t492 = circuit_mul(t491, in44); // Eval big_Q Horner step: multiply by z let t493 = circuit_add(in95, t492); // Eval big_Q Horner step: add coefficient_45 let t494 = circuit_mul(t493, in44); // Eval big_Q Horner step: multiply by z let t495 = circuit_add(in94, t494); // Eval big_Q Horner step: add coefficient_44 let t496 = circuit_mul(t495, in44); // Eval big_Q Horner step: multiply by z let t497 = circuit_add(in93, t496); // Eval big_Q Horner step: add coefficient_43 let t498 = circuit_mul(t497, in44); // Eval big_Q Horner step: multiply by z let t499 = circuit_add(in92, t498); // Eval big_Q Horner step: add coefficient_42 let t500 = circuit_mul(t499, in44); // Eval big_Q Horner step: multiply by z let t501 = circuit_add(in91, t500); // Eval big_Q Horner step: add coefficient_41 let t502 = circuit_mul(t501, in44); // Eval big_Q Horner step: multiply by z let t503 = circuit_add(in90, t502); // Eval big_Q Horner step: add coefficient_40 let t504 = circuit_mul(t503, in44); // Eval big_Q Horner step: multiply by z let t505 = circuit_add(in89, t504); // Eval big_Q Horner step: add coefficient_39 let t506 = circuit_mul(t505, in44); // Eval big_Q Horner step: multiply by z let t507 = circuit_add(in88, t506); // Eval big_Q Horner step: add coefficient_38 let t508 = circuit_mul(t507, in44); // Eval big_Q Horner step: multiply by z let t509 = circuit_add(in87, t508); // Eval big_Q Horner step: add coefficient_37 let t510 = circuit_mul(t509, in44); // Eval big_Q Horner step: multiply by z let t511 = circuit_add(in86, t510); // Eval big_Q Horner step: add coefficient_36 let t512 = circuit_mul(t511, in44); // Eval big_Q Horner step: multiply by z let t513 = circuit_add(in85, t512); // Eval big_Q Horner step: add coefficient_35 let t514 = circuit_mul(t513, in44); // Eval big_Q Horner step: multiply by z let t515 = circuit_add(in84, t514); // Eval big_Q Horner step: add coefficient_34 let t516 = circuit_mul(t515, in44); // Eval big_Q Horner step: multiply by z let t517 = circuit_add(in83, t516); // Eval big_Q Horner step: add coefficient_33 let t518 = circuit_mul(t517, in44); // Eval big_Q Horner step: multiply by z let t519 = circuit_add(in82, t518); // Eval big_Q Horner step: add coefficient_32 let t520 = circuit_mul(t519, in44); // Eval big_Q Horner step: multiply by z let t521 = circuit_add(in81, t520); // Eval big_Q Horner step: add coefficient_31 let t522 = circuit_mul(t521, in44); // Eval big_Q Horner step: multiply by z let t523 = circuit_add(in80, t522); // Eval big_Q Horner step: add coefficient_30 let t524 = circuit_mul(t523, in44); // Eval big_Q Horner step: multiply by z let t525 = circuit_add(in79, t524); // Eval big_Q Horner step: add coefficient_29 let t526 = circuit_mul(t525, in44); // Eval big_Q Horner step: multiply by z let t527 = circuit_add(in78, t526); // Eval big_Q Horner step: add coefficient_28 let t528 = circuit_mul(t527, in44); // Eval big_Q Horner step: multiply by z let t529 = circuit_add(in77, t528); // Eval big_Q Horner step: add coefficient_27 let t530 = circuit_mul(t529, in44); // Eval big_Q Horner step: multiply by z let t531 = circuit_add(in76, t530); // Eval big_Q Horner step: add coefficient_26 let t532 = circuit_mul(t531, in44); // Eval big_Q Horner step: multiply by z let t533 = circuit_add(in75, t532); // Eval big_Q Horner step: add coefficient_25 let t534 = circuit_mul(t533, in44); // Eval big_Q Horner step: multiply by z let t535 = circuit_add(in74, t534); // Eval big_Q Horner step: add coefficient_24 let t536 = circuit_mul(t535, in44); // Eval big_Q Horner step: multiply by z let t537 = circuit_add(in73, t536); // Eval big_Q Horner step: add coefficient_23 let t538 = circuit_mul(t537, in44); // Eval big_Q Horner step: multiply by z let t539 = circuit_add(in72, t538); // Eval big_Q Horner step: add coefficient_22 let t540 = circuit_mul(t539, in44); // Eval big_Q Horner step: multiply by z let t541 = circuit_add(in71, t540); // Eval big_Q Horner step: add coefficient_21 let t542 = circuit_mul(t541, in44); // Eval big_Q Horner step: multiply by z let t543 = circuit_add(in70, t542); // Eval big_Q Horner step: add coefficient_20 let t544 = circuit_mul(t543, in44); // Eval big_Q Horner step: multiply by z let t545 = circuit_add(in69, t544); // Eval big_Q Horner step: add coefficient_19 let t546 = circuit_mul(t545, in44); // Eval big_Q Horner step: multiply by z let t547 = circuit_add(in68, t546); // Eval big_Q Horner step: add coefficient_18 let t548 = circuit_mul(t547, in44); // Eval big_Q Horner step: multiply by z let t549 = circuit_add(in67, t548); // Eval big_Q Horner step: add coefficient_17 let t550 = circuit_mul(t549, in44); // Eval big_Q Horner step: multiply by z let t551 = circuit_add(in66, t550); // Eval big_Q Horner step: add coefficient_16 let t552 = circuit_mul(t551, in44); // Eval big_Q Horner step: multiply by z let t553 = circuit_add(in65, t552); // Eval big_Q Horner step: add coefficient_15 let t554 = circuit_mul(t553, in44); // Eval big_Q Horner step: multiply by z let t555 = circuit_add(in64, t554); // Eval big_Q Horner step: add coefficient_14 let t556 = circuit_mul(t555, in44); // Eval big_Q Horner step: multiply by z let t557 = circuit_add(in63, t556); // Eval big_Q Horner step: add coefficient_13 let t558 = circuit_mul(t557, in44); // Eval big_Q Horner step: multiply by z let t559 = circuit_add(in62, t558); // Eval big_Q Horner step: add coefficient_12 let t560 = circuit_mul(t559, in44); // Eval big_Q Horner step: multiply by z let t561 = circuit_add(in61, t560); // Eval big_Q Horner step: add coefficient_11 let t562 = circuit_mul(t561, in44); // Eval big_Q Horner step: multiply by z let t563 = circuit_add(in60, t562); // Eval big_Q Horner step: add coefficient_10 let t564 = circuit_mul(t563, in44); // Eval big_Q Horner step: multiply by z let t565 = circuit_add(in59, t564); // Eval big_Q Horner step: add coefficient_9 let t566 = circuit_mul(t565, in44); // Eval big_Q Horner step: multiply by z let t567 = circuit_add(in58, t566); // Eval big_Q Horner step: add coefficient_8 let t568 = circuit_mul(t567, in44); // Eval big_Q Horner step: multiply by z let t569 = circuit_add(in57, t568); // Eval big_Q Horner step: add coefficient_7 let t570 = circuit_mul(t569, in44); // Eval big_Q Horner step: multiply by z let t571 = circuit_add(in56, t570); // Eval big_Q Horner step: add coefficient_6 let t572 = circuit_mul(t571, in44); // Eval big_Q Horner step: multiply by z let t573 = circuit_add(in55, t572); // Eval big_Q Horner step: add coefficient_5 let t574 = circuit_mul(t573, in44); // Eval big_Q Horner step: multiply by z let t575 = circuit_add(in54, t574); // Eval big_Q Horner step: add coefficient_4 let t576 = circuit_mul(t575, in44); // Eval big_Q Horner step: multiply by z let t577 = circuit_add(in53, t576); // Eval big_Q Horner step: add coefficient_3 let t578 = circuit_mul(t577, in44); // Eval big_Q Horner step: multiply by z let t579 = circuit_add(in52, t578); // Eval big_Q Horner step: add coefficient_2 let t580 = circuit_mul(t579, in44); // Eval big_Q Horner step: multiply by z let t581 = circuit_add(in51, t580); // Eval big_Q Horner step: add coefficient_1 let t582 = circuit_mul(t581, in44); // Eval big_Q Horner step: multiply by z let t583 = circuit_add(in50, t582); // Eval big_Q Horner step: add coefficient_0 let t584 = circuit_mul(in9, t2); // Eval sparse poly P_irr step coeff_6 * z^6 let t585 = circuit_add(in8, t584); // Eval sparse poly P_irr step + coeff_6 * z^6 let t586 = circuit_add(t585, t5); // Eval sparse poly P_irr step + 1*z^12 let t587 = circuit_mul(t583, t586); let t588 = circuit_sub(t205, t587); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t588,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(MP_CHECK_FINALIZE_3P_2F_EXT_MLR_BN254_CONSTANTS.span()); // in0 - in9 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in10 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in11 circuit_inputs = circuit_inputs.next_2(line_1_0.r0a0); // in12 circuit_inputs = circuit_inputs.next_2(line_1_0.r0a1); // in13 circuit_inputs = circuit_inputs.next_2(line_1_0.r1a0); // in14 circuit_inputs = circuit_inputs.next_2(line_1_0.r1a1); // in15 circuit_inputs = circuit_inputs.next_2(line_2_0.r0a0); // in16 circuit_inputs = circuit_inputs.next_2(line_2_0.r0a1); // in17 circuit_inputs = circuit_inputs.next_2(line_2_0.r1a0); // in18 circuit_inputs = circuit_inputs.next_2(line_2_0.r1a1); // in19 circuit_inputs = circuit_inputs.next_2(yInv_1); // in20 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in21 circuit_inputs = circuit_inputs.next_2(line_1_1.r0a0); // in22 circuit_inputs = circuit_inputs.next_2(line_1_1.r0a1); // in23 circuit_inputs = circuit_inputs.next_2(line_1_1.r1a0); // in24 circuit_inputs = circuit_inputs.next_2(line_1_1.r1a1); // in25 circuit_inputs = circuit_inputs.next_2(line_2_1.r0a0); // in26 circuit_inputs = circuit_inputs.next_2(line_2_1.r0a1); // in27 circuit_inputs = circuit_inputs.next_2(line_2_1.r1a0); // in28 circuit_inputs = circuit_inputs.next_2(line_2_1.r1a1); // in29 circuit_inputs = circuit_inputs.next_2(original_Q2.x0); // in30 circuit_inputs = circuit_inputs.next_2(original_Q2.x1); // in31 circuit_inputs = circuit_inputs.next_2(original_Q2.y0); // in32 circuit_inputs = circuit_inputs.next_2(original_Q2.y1); // in33 circuit_inputs = circuit_inputs.next_2(yInv_2); // in34 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in35 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in36 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in37 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in38 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in39 circuit_inputs = circuit_inputs.next_2(R_n_minus_2_of_z); // in40 circuit_inputs = circuit_inputs.next_2(R_n_minus_1_of_z); // in41 circuit_inputs = circuit_inputs.next_2(c_0); // in42 circuit_inputs = circuit_inputs.next_2(w_of_z); // in43 circuit_inputs = circuit_inputs.next_2(z); // in44 circuit_inputs = circuit_inputs.next_2(c_inv_frob_1_of_z); // in45 circuit_inputs = circuit_inputs.next_2(c_frob_2_of_z); // in46 circuit_inputs = circuit_inputs.next_2(c_inv_frob_3_of_z); // in47 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in48 circuit_inputs = circuit_inputs.next_2(R_n_minus_3_of_z); // in49 for val in Q.span() { circuit_inputs = circuit_inputs.next_2(*val); } // in50 - in239 circuit_inputs = circuit_inputs.next_2(precomputed_miller_loop_result_of_z); // in240 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let final_check: u384 = outputs.get_output(t588); return (final_check,); } const MP_CHECK_FINALIZE_3P_2F_EXT_MLR_BN254_CONSTANTS: [u384; 10] = [ u384 { limb0: 0xc2c3330c99e39557176f553d, limb1: 0x4c0bec3cf559b143b78cc310, limb2: 0x2fb347984f7911f7, limb3: 0x0, }, u384 { limb0: 0xb7c9dce1665d51c640fcba2, limb1: 0x4ba4cc8bd75a079432ae2a1d, limb2: 0x16c9e55061ebae20, limb3: 0x0, }, u384 { limb0: 0xa9c95998dc54014671a0135a, limb1: 0xdc5ec698b6e2f9b9dbaae0ed, limb2: 0x63cf305489af5dc, limb3: 0x0, }, u384 { limb0: 0x8fa25bd282d37f632623b0e3, limb1: 0x704b5a7ec796f2b21807dc9, limb2: 0x7c03cbcac41049a, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd48, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x6871ca8d3c208c16d87cfd3e, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x52, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x6871ca8d3c208c16d87cfd35, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, ]; #[inline(always)] pub fn run_BN254_MP_CHECK_INIT_BIT_2P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_1: G2Line, R_i_of_z: u384, z: u384, c_inv_of_z: u384, c1: u384, previous_lhs: u384, ) -> (u384,) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in15, in15); // compute z^2 let t1 = circuit_mul(t0, in15); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in15); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in16, in16); let t6 = circuit_mul(in0, in5); let t7 = circuit_add(in4, t6); let t8 = circuit_mul(t7, in3); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in7); let t10 = circuit_add(in6, t9); let t11 = circuit_mul(t10, in2); // eval bn line by yInv let t12 = circuit_mul(in5, in3); // eval bn line by xNegOverY let t13 = circuit_mul(in7, in2); // eval bn line by yInv let t14 = circuit_mul(t8, in15); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); let t23 = circuit_mul(in0, in11); let t24 = circuit_add(in10, t23); let t25 = circuit_mul(t24, in9); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in13); let t27 = circuit_add(in12, t26); let t28 = circuit_mul(t27, in8); // eval bn line by yInv let t29 = circuit_mul(in11, in9); // eval bn line by xNegOverY let t30 = circuit_mul(in13, in8); // eval bn line by yInv let t31 = circuit_mul(t25, in15); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); let t40 = circuit_sub(t39, in14); // ((Π(i,k) (Pk(z)) - Ri(z)) let t41 = circuit_mul(in17, in18); let t42 = circuit_add(t40, t41); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t42,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in2 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in3 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a0); // in4 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a1); // in5 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a1); // in7 circuit_inputs = circuit_inputs.next_2(yInv_1); // in8 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a0); // in10 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a1); // in11 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a0); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a1); // in13 circuit_inputs = circuit_inputs.next_2(R_i_of_z); // in14 circuit_inputs = circuit_inputs.next_2(z); // in15 circuit_inputs = circuit_inputs.next_2(c_inv_of_z); // in16 circuit_inputs = circuit_inputs.next_2(c1); // in17 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in18 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let new_lhs: u384 = outputs.get_output(t42); return (new_lhs,); } #[inline(always)] pub fn run_BN254_MP_CHECK_INIT_BIT_3P_2F_circuit( yInv_0: u384, xNegOverY_0: u384, G2_line_0: G2Line, yInv_1: u384, xNegOverY_1: u384, G2_line_1: G2Line, yInv_2: u384, xNegOverY_2: u384, Q_2: G2Point, R_i_of_z: u384, z: u384, c_inv_of_z: u384, c1: u384, previous_lhs: u384, ) -> (G2Point, u384) { // CONSTANT stack let in0 = CE::> {}; // -0x9 % p let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // 0x3 let in3 = CE::> {}; // 0x6 let in4 = CE::> {}; // 0x0 // INPUT stack let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let (in26, in27) = (CE::> {}, CE::> {}); let t0 = circuit_mul(in24, in24); // compute z^2 let t1 = circuit_mul(t0, in24); // compute z^3 let t2 = circuit_mul(t1, t1); // compute z^6 let t3 = circuit_mul(t2, in24); // compute z^7 let t4 = circuit_mul(t3, t0); // compute z^9 let t5 = circuit_mul(in25, in25); let t6 = circuit_mul(in0, in8); let t7 = circuit_add(in7, t6); let t8 = circuit_mul(t7, in6); // eval bn line by xNegOverY let t9 = circuit_mul(in0, in10); let t10 = circuit_add(in9, t9); let t11 = circuit_mul(t10, in5); // eval bn line by yInv let t12 = circuit_mul(in8, in6); // eval bn line by xNegOverY let t13 = circuit_mul(in10, in5); // eval bn line by yInv let t14 = circuit_mul(t8, in24); // Eval sparse poly line_0p_1 step coeff_1 * z^1 let t15 = circuit_add(in1, t14); // Eval sparse poly line_0p_1 step + coeff_1 * z^1 let t16 = circuit_mul(t11, t1); // Eval sparse poly line_0p_1 step coeff_3 * z^3 let t17 = circuit_add(t15, t16); // Eval sparse poly line_0p_1 step + coeff_3 * z^3 let t18 = circuit_mul(t12, t3); // Eval sparse poly line_0p_1 step coeff_7 * z^7 let t19 = circuit_add(t17, t18); // Eval sparse poly line_0p_1 step + coeff_7 * z^7 let t20 = circuit_mul(t13, t4); // Eval sparse poly line_0p_1 step coeff_9 * z^9 let t21 = circuit_add(t19, t20); // Eval sparse poly line_0p_1 step + coeff_9 * z^9 let t22 = circuit_mul(t5, t21); let t23 = circuit_mul(in0, in14); let t24 = circuit_add(in13, t23); let t25 = circuit_mul(t24, in12); // eval bn line by xNegOverY let t26 = circuit_mul(in0, in16); let t27 = circuit_add(in15, t26); let t28 = circuit_mul(t27, in11); // eval bn line by yInv let t29 = circuit_mul(in14, in12); // eval bn line by xNegOverY let t30 = circuit_mul(in16, in11); // eval bn line by yInv let t31 = circuit_mul(t25, in24); // Eval sparse poly line_1p_1 step coeff_1 * z^1 let t32 = circuit_add(in1, t31); // Eval sparse poly line_1p_1 step + coeff_1 * z^1 let t33 = circuit_mul(t28, t1); // Eval sparse poly line_1p_1 step coeff_3 * z^3 let t34 = circuit_add(t32, t33); // Eval sparse poly line_1p_1 step + coeff_3 * z^3 let t35 = circuit_mul(t29, t3); // Eval sparse poly line_1p_1 step coeff_7 * z^7 let t36 = circuit_add(t34, t35); // Eval sparse poly line_1p_1 step + coeff_7 * z^7 let t37 = circuit_mul(t30, t4); // Eval sparse poly line_1p_1 step coeff_9 * z^9 let t38 = circuit_add(t36, t37); // Eval sparse poly line_1p_1 step + coeff_9 * z^9 let t39 = circuit_mul(t22, t38); let t40 = circuit_add(in19, in20); // Doubling slope numerator start let t41 = circuit_sub(in19, in20); let t42 = circuit_mul(t40, t41); let t43 = circuit_mul(in19, in20); let t44 = circuit_mul(t42, in2); let t45 = circuit_mul(t43, in3); // Doubling slope numerator end let t46 = circuit_add(in21, in21); // Fp2 add coeff 0/1 let t47 = circuit_add(in22, in22); // Fp2 add coeff 1/1 let t48 = circuit_mul(t46, t46); // Fp2 Inv start let t49 = circuit_mul(t47, t47); let t50 = circuit_add(t48, t49); let t51 = circuit_inverse(t50); let t52 = circuit_mul(t46, t51); // Fp2 Inv real part end let t53 = circuit_mul(t47, t51); let t54 = circuit_sub(in4, t53); // Fp2 Inv imag part end let t55 = circuit_mul(t44, t52); // Fp2 mul start let t56 = circuit_mul(t45, t54); let t57 = circuit_sub(t55, t56); // Fp2 mul real part end let t58 = circuit_mul(t44, t54); let t59 = circuit_mul(t45, t52); let t60 = circuit_add(t58, t59); // Fp2 mul imag part end let t61 = circuit_add(t57, t60); let t62 = circuit_sub(t57, t60); let t63 = circuit_mul(t61, t62); let t64 = circuit_mul(t57, t60); let t65 = circuit_add(t64, t64); let t66 = circuit_add(in19, in19); // Fp2 add coeff 0/1 let t67 = circuit_add(in20, in20); // Fp2 add coeff 1/1 let t68 = circuit_sub(t63, t66); // Fp2 sub coeff 0/1 let t69 = circuit_sub(t65, t67); // Fp2 sub coeff 1/1 let t70 = circuit_sub(in19, t68); // Fp2 sub coeff 0/1 let t71 = circuit_sub(in20, t69); // Fp2 sub coeff 1/1 let t72 = circuit_mul(t57, t70); // Fp2 mul start let t73 = circuit_mul(t60, t71); let t74 = circuit_sub(t72, t73); // Fp2 mul real part end let t75 = circuit_mul(t57, t71); let t76 = circuit_mul(t60, t70); let t77 = circuit_add(t75, t76); // Fp2 mul imag part end let t78 = circuit_sub(t74, in21); // Fp2 sub coeff 0/1 let t79 = circuit_sub(t77, in22); // Fp2 sub coeff 1/1 let t80 = circuit_mul(t57, in19); // Fp2 mul start let t81 = circuit_mul(t60, in20); let t82 = circuit_sub(t80, t81); // Fp2 mul real part end let t83 = circuit_mul(t57, in20); let t84 = circuit_mul(t60, in19); let t85 = circuit_add(t83, t84); // Fp2 mul imag part end let t86 = circuit_sub(t82, in21); // Fp2 sub coeff 0/1 let t87 = circuit_sub(t85, in22); // Fp2 sub coeff 1/1 let t88 = circuit_mul(in0, t60); let t89 = circuit_add(t57, t88); let t90 = circuit_mul(t89, in18); // eval bn line by xNegOverY let t91 = circuit_mul(in0, t87); let t92 = circuit_add(t86, t91); let t93 = circuit_mul(t92, in17); // eval bn line by yInv let t94 = circuit_mul(t60, in18); // eval bn line by xNegOverY let t95 = circuit_mul(t87, in17); // eval bn line by yInv let t96 = circuit_mul(t90, in24); // Eval sparse poly line_2p_1 step coeff_1 * z^1 let t97 = circuit_add(in1, t96); // Eval sparse poly line_2p_1 step + coeff_1 * z^1 let t98 = circuit_mul(t93, t1); // Eval sparse poly line_2p_1 step coeff_3 * z^3 let t99 = circuit_add(t97, t98); // Eval sparse poly line_2p_1 step + coeff_3 * z^3 let t100 = circuit_mul(t94, t3); // Eval sparse poly line_2p_1 step coeff_7 * z^7 let t101 = circuit_add(t99, t100); // Eval sparse poly line_2p_1 step + coeff_7 * z^7 let t102 = circuit_mul(t95, t4); // Eval sparse poly line_2p_1 step coeff_9 * z^9 let t103 = circuit_add(t101, t102); // Eval sparse poly line_2p_1 step + coeff_9 * z^9 let t104 = circuit_mul(t39, t103); let t105 = circuit_sub(t104, in23); // ((Π(i,k) (Pk(z)) - Ri(z)) let t106 = circuit_mul(in26, in27); let t107 = circuit_add(t105, t106); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t68, t69, t78, t79, t107).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd3e, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in3 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in4 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in5 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in6 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a0); // in7 circuit_inputs = circuit_inputs.next_2(G2_line_0.r0a1); // in8 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a0); // in9 circuit_inputs = circuit_inputs.next_2(G2_line_0.r1a1); // in10 circuit_inputs = circuit_inputs.next_2(yInv_1); // in11 circuit_inputs = circuit_inputs.next_2(xNegOverY_1); // in12 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a0); // in13 circuit_inputs = circuit_inputs.next_2(G2_line_1.r0a1); // in14 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a0); // in15 circuit_inputs = circuit_inputs.next_2(G2_line_1.r1a1); // in16 circuit_inputs = circuit_inputs.next_2(yInv_2); // in17 circuit_inputs = circuit_inputs.next_2(xNegOverY_2); // in18 circuit_inputs = circuit_inputs.next_2(Q_2.x0); // in19 circuit_inputs = circuit_inputs.next_2(Q_2.x1); // in20 circuit_inputs = circuit_inputs.next_2(Q_2.y0); // in21 circuit_inputs = circuit_inputs.next_2(Q_2.y1); // in22 circuit_inputs = circuit_inputs.next_2(R_i_of_z); // in23 circuit_inputs = circuit_inputs.next_2(z); // in24 circuit_inputs = circuit_inputs.next_2(c_inv_of_z); // in25 circuit_inputs = circuit_inputs.next_2(c1); // in26 circuit_inputs = circuit_inputs.next_2(previous_lhs); // in27 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t68), x1: outputs.get_output(t69), y0: outputs.get_output(t78), y1: outputs.get_output(t79), }; let new_lhs: u384 = outputs.get_output(t107); return (Q0, new_lhs); } #[inline(always)] pub fn run_BN254_MP_CHECK_PREPARE_PAIRS_1P_circuit( p_0: G1Point, Qy0_0: u384, Qy1_0: u384, ) -> (BNProcessedPair,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let in4 = CE::> {}; let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let t3 = circuit_sub(in0, in3); let t4 = circuit_sub(in0, in4); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t0, t2, t3, t4).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 circuit_inputs = circuit_inputs.next_2(Qy0_0); // in3 circuit_inputs = circuit_inputs.next_2(Qy1_0); // in4 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), QyNeg0: outputs.get_output(t3), QyNeg1: outputs.get_output(t4), }; return (p_0,); } #[inline(always)] pub fn run_BN254_MP_CHECK_PREPARE_PAIRS_2P_circuit( p_0: G1Point, Qy0_0: u384, Qy1_0: u384, p_1: G1Point, Qy0_1: u384, Qy1_1: u384, ) -> (BNProcessedPair, BNProcessedPair) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8) = (CE::> {}, CE::> {}); let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let t3 = circuit_sub(in0, in3); let t4 = circuit_sub(in0, in4); let t5 = circuit_inverse(in6); let t6 = circuit_mul(in5, t5); let t7 = circuit_sub(in0, t6); let t8 = circuit_sub(in0, in7); let t9 = circuit_sub(in0, in8); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t0, t2, t3, t4, t5, t7, t8, t9).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 circuit_inputs = circuit_inputs.next_2(Qy0_0); // in3 circuit_inputs = circuit_inputs.next_2(Qy1_0); // in4 circuit_inputs = circuit_inputs.next_2(p_1.x); // in5 circuit_inputs = circuit_inputs.next_2(p_1.y); // in6 circuit_inputs = circuit_inputs.next_2(Qy0_1); // in7 circuit_inputs = circuit_inputs.next_2(Qy1_1); // in8 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), QyNeg0: outputs.get_output(t3), QyNeg1: outputs.get_output(t4), }; let p_1: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t5), xNegOverY: outputs.get_output(t7), QyNeg0: outputs.get_output(t8), QyNeg1: outputs.get_output(t9), }; return (p_0, p_1); } #[inline(always)] pub fn run_BN254_MP_CHECK_PREPARE_PAIRS_3P_circuit( p_0: G1Point, Qy0_0: u384, Qy1_0: u384, p_1: G1Point, Qy0_1: u384, Qy1_1: u384, p_2: G1Point, Qy0_2: u384, Qy1_2: u384, ) -> (BNProcessedPair, BNProcessedPair, BNProcessedPair) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_inverse(in2); let t1 = circuit_mul(in1, t0); let t2 = circuit_sub(in0, t1); let t3 = circuit_sub(in0, in3); let t4 = circuit_sub(in0, in4); let t5 = circuit_inverse(in6); let t6 = circuit_mul(in5, t5); let t7 = circuit_sub(in0, t6); let t8 = circuit_sub(in0, in7); let t9 = circuit_sub(in0, in8); let t10 = circuit_inverse(in10); let t11 = circuit_mul(in9, t10); let t12 = circuit_sub(in0, t11); let t13 = circuit_sub(in0, in11); let t14 = circuit_sub(in0, in12); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t0, t2, t3, t4, t5, t7, t8, t9, t10, t12, t13, t14).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(p_0.x); // in1 circuit_inputs = circuit_inputs.next_2(p_0.y); // in2 circuit_inputs = circuit_inputs.next_2(Qy0_0); // in3 circuit_inputs = circuit_inputs.next_2(Qy1_0); // in4 circuit_inputs = circuit_inputs.next_2(p_1.x); // in5 circuit_inputs = circuit_inputs.next_2(p_1.y); // in6 circuit_inputs = circuit_inputs.next_2(Qy0_1); // in7 circuit_inputs = circuit_inputs.next_2(Qy1_1); // in8 circuit_inputs = circuit_inputs.next_2(p_2.x); // in9 circuit_inputs = circuit_inputs.next_2(p_2.y); // in10 circuit_inputs = circuit_inputs.next_2(Qy0_2); // in11 circuit_inputs = circuit_inputs.next_2(Qy1_2); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let p_0: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t0), xNegOverY: outputs.get_output(t2), QyNeg0: outputs.get_output(t3), QyNeg1: outputs.get_output(t4), }; let p_1: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t5), xNegOverY: outputs.get_output(t7), QyNeg0: outputs.get_output(t8), QyNeg1: outputs.get_output(t9), }; let p_2: BNProcessedPair = BNProcessedPair { yInv: outputs.get_output(t10), xNegOverY: outputs.get_output(t12), QyNeg0: outputs.get_output(t13), QyNeg1: outputs.get_output(t14), }; return (p_0, p_1, p_2); } ================================================ FILE: src/src/circuits/rsa.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{RSA2048Chunks, RSA2048ReductionWitness}; impl CircuitDefinition17< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, > of core::circuit::CircuitDefinition< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), > { type CircuitType = core::circuit::Circuit< (E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16), >; } impl MyDrp_17< E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, > of Drop< ( CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, CE, ), >; #[inline(always)] pub fn run_RSA_FULL_VERIFICATION_circuit( mod_chunks: RSA2048Chunks, sig_chunks: RSA2048Chunks, w_0: RSA2048ReductionWitness, w_1: RSA2048ReductionWitness, w_2: RSA2048ReductionWitness, w_3: RSA2048ReductionWitness, w_4: RSA2048ReductionWitness, w_5: RSA2048ReductionWitness, w_6: RSA2048ReductionWitness, w_7: RSA2048ReductionWitness, w_8: RSA2048ReductionWitness, w_9: RSA2048ReductionWitness, w_10: RSA2048ReductionWitness, w_11: RSA2048ReductionWitness, w_12: RSA2048ReductionWitness, w_13: RSA2048ReductionWitness, w_14: RSA2048ReductionWitness, w_15: RSA2048ReductionWitness, w_16: RSA2048ReductionWitness, step: u384, modulus: core::circuit::CircuitModulus, ) -> ( u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384, ) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let (in30, in31, in32) = (CE::> {}, CE::> {}, CE::> {}); let (in33, in34, in35) = (CE::> {}, CE::> {}, CE::> {}); let (in36, in37, in38) = (CE::> {}, CE::> {}, CE::> {}); let (in39, in40, in41) = (CE::> {}, CE::> {}, CE::> {}); let (in42, in43, in44) = (CE::> {}, CE::> {}, CE::> {}); let (in45, in46, in47) = (CE::> {}, CE::> {}, CE::> {}); let (in48, in49, in50) = (CE::> {}, CE::> {}, CE::> {}); let (in51, in52, in53) = (CE::> {}, CE::> {}, CE::> {}); let (in54, in55, in56) = (CE::> {}, CE::> {}, CE::> {}); let (in57, in58, in59) = (CE::> {}, CE::> {}, CE::> {}); let (in60, in61, in62) = (CE::> {}, CE::> {}, CE::> {}); let (in63, in64, in65) = (CE::> {}, CE::> {}, CE::> {}); let (in66, in67, in68) = (CE::> {}, CE::> {}, CE::> {}); let (in69, in70, in71) = (CE::> {}, CE::> {}, CE::> {}); let (in72, in73, in74) = (CE::> {}, CE::> {}, CE::> {}); let (in75, in76, in77) = (CE::> {}, CE::> {}, CE::> {}); let (in78, in79, in80) = (CE::> {}, CE::> {}, CE::> {}); let (in81, in82, in83) = (CE::> {}, CE::> {}, CE::> {}); let (in84, in85, in86) = (CE::> {}, CE::> {}, CE::> {}); let (in87, in88, in89) = (CE::> {}, CE::> {}, CE::> {}); let (in90, in91, in92) = (CE::> {}, CE::> {}, CE::> {}); let (in93, in94, in95) = (CE::> {}, CE::> {}, CE::> {}); let (in96, in97, in98) = (CE::> {}, CE::> {}, CE::> {}); let (in99, in100, in101) = (CE::> {}, CE::> {}, CE::> {}); let (in102, in103, in104) = (CE::> {}, CE::> {}, CE::> {}); let (in105, in106, in107) = (CE::> {}, CE::> {}, CE::> {}); let (in108, in109, in110) = (CE::> {}, CE::> {}, CE::> {}); let (in111, in112, in113) = (CE::> {}, CE::> {}, CE::> {}); let (in114, in115, in116) = (CE::> {}, CE::> {}, CE::> {}); let (in117, in118, in119) = (CE::> {}, CE::> {}, CE::> {}); let (in120, in121, in122) = (CE::> {}, CE::> {}, CE::> {}); let (in123, in124, in125) = (CE::> {}, CE::> {}, CE::> {}); let (in126, in127, in128) = (CE::> {}, CE::> {}, CE::> {}); let (in129, in130, in131) = (CE::> {}, CE::> {}, CE::> {}); let (in132, in133, in134) = (CE::> {}, CE::> {}, CE::> {}); let (in135, in136, in137) = (CE::> {}, CE::> {}, CE::> {}); let (in138, in139, in140) = (CE::> {}, CE::> {}, CE::> {}); let (in141, in142, in143) = (CE::> {}, CE::> {}, CE::> {}); let (in144, in145, in146) = (CE::> {}, CE::> {}, CE::> {}); let (in147, in148, in149) = (CE::> {}, CE::> {}, CE::> {}); let (in150, in151, in152) = (CE::> {}, CE::> {}, CE::> {}); let (in153, in154, in155) = (CE::> {}, CE::> {}, CE::> {}); let (in156, in157, in158) = (CE::> {}, CE::> {}, CE::> {}); let (in159, in160, in161) = (CE::> {}, CE::> {}, CE::> {}); let (in162, in163, in164) = (CE::> {}, CE::> {}, CE::> {}); let (in165, in166, in167) = (CE::> {}, CE::> {}, CE::> {}); let (in168, in169, in170) = (CE::> {}, CE::> {}, CE::> {}); let (in171, in172, in173) = (CE::> {}, CE::> {}, CE::> {}); let (in174, in175, in176) = (CE::> {}, CE::> {}, CE::> {}); let (in177, in178, in179) = (CE::> {}, CE::> {}, CE::> {}); let (in180, in181, in182) = (CE::> {}, CE::> {}, CE::> {}); let (in183, in184, in185) = (CE::> {}, CE::> {}, CE::> {}); let (in186, in187, in188) = (CE::> {}, CE::> {}, CE::> {}); let (in189, in190, in191) = (CE::> {}, CE::> {}, CE::> {}); let (in192, in193, in194) = (CE::> {}, CE::> {}, CE::> {}); let (in195, in196, in197) = (CE::> {}, CE::> {}, CE::> {}); let (in198, in199, in200) = (CE::> {}, CE::> {}, CE::> {}); let (in201, in202, in203) = (CE::> {}, CE::> {}, CE::> {}); let (in204, in205, in206) = (CE::> {}, CE::> {}, CE::> {}); let (in207, in208, in209) = (CE::> {}, CE::> {}, CE::> {}); let (in210, in211, in212) = (CE::> {}, CE::> {}, CE::> {}); let (in213, in214, in215) = (CE::> {}, CE::> {}, CE::> {}); let in216 = CE::> {}; let t0 = circuit_mul(in5, in216); // Eval mod_chunks Horner step: multiply by STEP let t1 = circuit_add(in4, t0); // Eval mod_chunks Horner step: add coefficient_4 let t2 = circuit_mul(t1, in216); // Eval mod_chunks Horner step: multiply by STEP let t3 = circuit_add(in3, t2); // Eval mod_chunks Horner step: add coefficient_3 let t4 = circuit_mul(t3, in216); // Eval mod_chunks Horner step: multiply by STEP let t5 = circuit_add(in2, t4); // Eval mod_chunks Horner step: add coefficient_2 let t6 = circuit_mul(t5, in216); // Eval mod_chunks Horner step: multiply by STEP let t7 = circuit_add(in1, t6); // Eval mod_chunks Horner step: add coefficient_1 let t8 = circuit_mul(t7, in216); // Eval mod_chunks Horner step: multiply by STEP let t9 = circuit_add(in0, t8); // Eval mod_chunks Horner step: add coefficient_0 let t10 = circuit_mul(in11, in216); // Eval sig_chunks Horner step: multiply by STEP let t11 = circuit_add(in10, t10); // Eval sig_chunks Horner step: add coefficient_4 let t12 = circuit_mul(t11, in216); // Eval sig_chunks Horner step: multiply by STEP let t13 = circuit_add(in9, t12); // Eval sig_chunks Horner step: add coefficient_3 let t14 = circuit_mul(t13, in216); // Eval sig_chunks Horner step: multiply by STEP let t15 = circuit_add(in8, t14); // Eval sig_chunks Horner step: add coefficient_2 let t16 = circuit_mul(t15, in216); // Eval sig_chunks Horner step: multiply by STEP let t17 = circuit_add(in7, t16); // Eval sig_chunks Horner step: add coefficient_1 let t18 = circuit_mul(t17, in216); // Eval sig_chunks Horner step: multiply by STEP let t19 = circuit_add(in6, t18); // Eval sig_chunks Horner step: add coefficient_0 let t20 = circuit_mul(in17, in216); // Eval quot_0 Horner step: multiply by STEP let t21 = circuit_add(in16, t20); // Eval quot_0 Horner step: add coefficient_4 let t22 = circuit_mul(t21, in216); // Eval quot_0 Horner step: multiply by STEP let t23 = circuit_add(in15, t22); // Eval quot_0 Horner step: add coefficient_3 let t24 = circuit_mul(t23, in216); // Eval quot_0 Horner step: multiply by STEP let t25 = circuit_add(in14, t24); // Eval quot_0 Horner step: add coefficient_2 let t26 = circuit_mul(t25, in216); // Eval quot_0 Horner step: multiply by STEP let t27 = circuit_add(in13, t26); // Eval quot_0 Horner step: add coefficient_1 let t28 = circuit_mul(t27, in216); // Eval quot_0 Horner step: multiply by STEP let t29 = circuit_add(in12, t28); // Eval quot_0 Horner step: add coefficient_0 let t30 = circuit_mul(in23, in216); // Eval rem_0 Horner step: multiply by STEP let t31 = circuit_add(in22, t30); // Eval rem_0 Horner step: add coefficient_4 let t32 = circuit_mul(t31, in216); // Eval rem_0 Horner step: multiply by STEP let t33 = circuit_add(in21, t32); // Eval rem_0 Horner step: add coefficient_3 let t34 = circuit_mul(t33, in216); // Eval rem_0 Horner step: multiply by STEP let t35 = circuit_add(in20, t34); // Eval rem_0 Horner step: add coefficient_2 let t36 = circuit_mul(t35, in216); // Eval rem_0 Horner step: multiply by STEP let t37 = circuit_add(in19, t36); // Eval rem_0 Horner step: add coefficient_1 let t38 = circuit_mul(t37, in216); // Eval rem_0 Horner step: multiply by STEP let t39 = circuit_add(in18, t38); // Eval rem_0 Horner step: add coefficient_0 let t40 = circuit_mul(t19, t19); // square_0 let t41 = circuit_mul(t29, t9); // quot*mod_0 let t42 = circuit_sub(t40, t41); // ab-qn_0 let t43 = circuit_sub(t42, t39); // ab-qn-rem_0 let t44 = circuit_mul(in29, in216); // Eval quot_1 Horner step: multiply by STEP let t45 = circuit_add(in28, t44); // Eval quot_1 Horner step: add coefficient_4 let t46 = circuit_mul(t45, in216); // Eval quot_1 Horner step: multiply by STEP let t47 = circuit_add(in27, t46); // Eval quot_1 Horner step: add coefficient_3 let t48 = circuit_mul(t47, in216); // Eval quot_1 Horner step: multiply by STEP let t49 = circuit_add(in26, t48); // Eval quot_1 Horner step: add coefficient_2 let t50 = circuit_mul(t49, in216); // Eval quot_1 Horner step: multiply by STEP let t51 = circuit_add(in25, t50); // Eval quot_1 Horner step: add coefficient_1 let t52 = circuit_mul(t51, in216); // Eval quot_1 Horner step: multiply by STEP let t53 = circuit_add(in24, t52); // Eval quot_1 Horner step: add coefficient_0 let t54 = circuit_mul(in35, in216); // Eval rem_1 Horner step: multiply by STEP let t55 = circuit_add(in34, t54); // Eval rem_1 Horner step: add coefficient_4 let t56 = circuit_mul(t55, in216); // Eval rem_1 Horner step: multiply by STEP let t57 = circuit_add(in33, t56); // Eval rem_1 Horner step: add coefficient_3 let t58 = circuit_mul(t57, in216); // Eval rem_1 Horner step: multiply by STEP let t59 = circuit_add(in32, t58); // Eval rem_1 Horner step: add coefficient_2 let t60 = circuit_mul(t59, in216); // Eval rem_1 Horner step: multiply by STEP let t61 = circuit_add(in31, t60); // Eval rem_1 Horner step: add coefficient_1 let t62 = circuit_mul(t61, in216); // Eval rem_1 Horner step: multiply by STEP let t63 = circuit_add(in30, t62); // Eval rem_1 Horner step: add coefficient_0 let t64 = circuit_mul(t39, t39); // square_1 let t65 = circuit_mul(t53, t9); // quot*mod_1 let t66 = circuit_sub(t64, t65); // ab-qn_1 let t67 = circuit_sub(t66, t63); // ab-qn-rem_1 let t68 = circuit_mul(in41, in216); // Eval quot_2 Horner step: multiply by STEP let t69 = circuit_add(in40, t68); // Eval quot_2 Horner step: add coefficient_4 let t70 = circuit_mul(t69, in216); // Eval quot_2 Horner step: multiply by STEP let t71 = circuit_add(in39, t70); // Eval quot_2 Horner step: add coefficient_3 let t72 = circuit_mul(t71, in216); // Eval quot_2 Horner step: multiply by STEP let t73 = circuit_add(in38, t72); // Eval quot_2 Horner step: add coefficient_2 let t74 = circuit_mul(t73, in216); // Eval quot_2 Horner step: multiply by STEP let t75 = circuit_add(in37, t74); // Eval quot_2 Horner step: add coefficient_1 let t76 = circuit_mul(t75, in216); // Eval quot_2 Horner step: multiply by STEP let t77 = circuit_add(in36, t76); // Eval quot_2 Horner step: add coefficient_0 let t78 = circuit_mul(in47, in216); // Eval rem_2 Horner step: multiply by STEP let t79 = circuit_add(in46, t78); // Eval rem_2 Horner step: add coefficient_4 let t80 = circuit_mul(t79, in216); // Eval rem_2 Horner step: multiply by STEP let t81 = circuit_add(in45, t80); // Eval rem_2 Horner step: add coefficient_3 let t82 = circuit_mul(t81, in216); // Eval rem_2 Horner step: multiply by STEP let t83 = circuit_add(in44, t82); // Eval rem_2 Horner step: add coefficient_2 let t84 = circuit_mul(t83, in216); // Eval rem_2 Horner step: multiply by STEP let t85 = circuit_add(in43, t84); // Eval rem_2 Horner step: add coefficient_1 let t86 = circuit_mul(t85, in216); // Eval rem_2 Horner step: multiply by STEP let t87 = circuit_add(in42, t86); // Eval rem_2 Horner step: add coefficient_0 let t88 = circuit_mul(t63, t63); // square_2 let t89 = circuit_mul(t77, t9); // quot*mod_2 let t90 = circuit_sub(t88, t89); // ab-qn_2 let t91 = circuit_sub(t90, t87); // ab-qn-rem_2 let t92 = circuit_mul(in53, in216); // Eval quot_3 Horner step: multiply by STEP let t93 = circuit_add(in52, t92); // Eval quot_3 Horner step: add coefficient_4 let t94 = circuit_mul(t93, in216); // Eval quot_3 Horner step: multiply by STEP let t95 = circuit_add(in51, t94); // Eval quot_3 Horner step: add coefficient_3 let t96 = circuit_mul(t95, in216); // Eval quot_3 Horner step: multiply by STEP let t97 = circuit_add(in50, t96); // Eval quot_3 Horner step: add coefficient_2 let t98 = circuit_mul(t97, in216); // Eval quot_3 Horner step: multiply by STEP let t99 = circuit_add(in49, t98); // Eval quot_3 Horner step: add coefficient_1 let t100 = circuit_mul(t99, in216); // Eval quot_3 Horner step: multiply by STEP let t101 = circuit_add(in48, t100); // Eval quot_3 Horner step: add coefficient_0 let t102 = circuit_mul(in59, in216); // Eval rem_3 Horner step: multiply by STEP let t103 = circuit_add(in58, t102); // Eval rem_3 Horner step: add coefficient_4 let t104 = circuit_mul(t103, in216); // Eval rem_3 Horner step: multiply by STEP let t105 = circuit_add(in57, t104); // Eval rem_3 Horner step: add coefficient_3 let t106 = circuit_mul(t105, in216); // Eval rem_3 Horner step: multiply by STEP let t107 = circuit_add(in56, t106); // Eval rem_3 Horner step: add coefficient_2 let t108 = circuit_mul(t107, in216); // Eval rem_3 Horner step: multiply by STEP let t109 = circuit_add(in55, t108); // Eval rem_3 Horner step: add coefficient_1 let t110 = circuit_mul(t109, in216); // Eval rem_3 Horner step: multiply by STEP let t111 = circuit_add(in54, t110); // Eval rem_3 Horner step: add coefficient_0 let t112 = circuit_mul(t87, t87); // square_3 let t113 = circuit_mul(t101, t9); // quot*mod_3 let t114 = circuit_sub(t112, t113); // ab-qn_3 let t115 = circuit_sub(t114, t111); // ab-qn-rem_3 let t116 = circuit_mul(in65, in216); // Eval quot_4 Horner step: multiply by STEP let t117 = circuit_add(in64, t116); // Eval quot_4 Horner step: add coefficient_4 let t118 = circuit_mul(t117, in216); // Eval quot_4 Horner step: multiply by STEP let t119 = circuit_add(in63, t118); // Eval quot_4 Horner step: add coefficient_3 let t120 = circuit_mul(t119, in216); // Eval quot_4 Horner step: multiply by STEP let t121 = circuit_add(in62, t120); // Eval quot_4 Horner step: add coefficient_2 let t122 = circuit_mul(t121, in216); // Eval quot_4 Horner step: multiply by STEP let t123 = circuit_add(in61, t122); // Eval quot_4 Horner step: add coefficient_1 let t124 = circuit_mul(t123, in216); // Eval quot_4 Horner step: multiply by STEP let t125 = circuit_add(in60, t124); // Eval quot_4 Horner step: add coefficient_0 let t126 = circuit_mul(in71, in216); // Eval rem_4 Horner step: multiply by STEP let t127 = circuit_add(in70, t126); // Eval rem_4 Horner step: add coefficient_4 let t128 = circuit_mul(t127, in216); // Eval rem_4 Horner step: multiply by STEP let t129 = circuit_add(in69, t128); // Eval rem_4 Horner step: add coefficient_3 let t130 = circuit_mul(t129, in216); // Eval rem_4 Horner step: multiply by STEP let t131 = circuit_add(in68, t130); // Eval rem_4 Horner step: add coefficient_2 let t132 = circuit_mul(t131, in216); // Eval rem_4 Horner step: multiply by STEP let t133 = circuit_add(in67, t132); // Eval rem_4 Horner step: add coefficient_1 let t134 = circuit_mul(t133, in216); // Eval rem_4 Horner step: multiply by STEP let t135 = circuit_add(in66, t134); // Eval rem_4 Horner step: add coefficient_0 let t136 = circuit_mul(t111, t111); // square_4 let t137 = circuit_mul(t125, t9); // quot*mod_4 let t138 = circuit_sub(t136, t137); // ab-qn_4 let t139 = circuit_sub(t138, t135); // ab-qn-rem_4 let t140 = circuit_mul(in77, in216); // Eval quot_5 Horner step: multiply by STEP let t141 = circuit_add(in76, t140); // Eval quot_5 Horner step: add coefficient_4 let t142 = circuit_mul(t141, in216); // Eval quot_5 Horner step: multiply by STEP let t143 = circuit_add(in75, t142); // Eval quot_5 Horner step: add coefficient_3 let t144 = circuit_mul(t143, in216); // Eval quot_5 Horner step: multiply by STEP let t145 = circuit_add(in74, t144); // Eval quot_5 Horner step: add coefficient_2 let t146 = circuit_mul(t145, in216); // Eval quot_5 Horner step: multiply by STEP let t147 = circuit_add(in73, t146); // Eval quot_5 Horner step: add coefficient_1 let t148 = circuit_mul(t147, in216); // Eval quot_5 Horner step: multiply by STEP let t149 = circuit_add(in72, t148); // Eval quot_5 Horner step: add coefficient_0 let t150 = circuit_mul(in83, in216); // Eval rem_5 Horner step: multiply by STEP let t151 = circuit_add(in82, t150); // Eval rem_5 Horner step: add coefficient_4 let t152 = circuit_mul(t151, in216); // Eval rem_5 Horner step: multiply by STEP let t153 = circuit_add(in81, t152); // Eval rem_5 Horner step: add coefficient_3 let t154 = circuit_mul(t153, in216); // Eval rem_5 Horner step: multiply by STEP let t155 = circuit_add(in80, t154); // Eval rem_5 Horner step: add coefficient_2 let t156 = circuit_mul(t155, in216); // Eval rem_5 Horner step: multiply by STEP let t157 = circuit_add(in79, t156); // Eval rem_5 Horner step: add coefficient_1 let t158 = circuit_mul(t157, in216); // Eval rem_5 Horner step: multiply by STEP let t159 = circuit_add(in78, t158); // Eval rem_5 Horner step: add coefficient_0 let t160 = circuit_mul(t135, t135); // square_5 let t161 = circuit_mul(t149, t9); // quot*mod_5 let t162 = circuit_sub(t160, t161); // ab-qn_5 let t163 = circuit_sub(t162, t159); // ab-qn-rem_5 let t164 = circuit_mul(in89, in216); // Eval quot_6 Horner step: multiply by STEP let t165 = circuit_add(in88, t164); // Eval quot_6 Horner step: add coefficient_4 let t166 = circuit_mul(t165, in216); // Eval quot_6 Horner step: multiply by STEP let t167 = circuit_add(in87, t166); // Eval quot_6 Horner step: add coefficient_3 let t168 = circuit_mul(t167, in216); // Eval quot_6 Horner step: multiply by STEP let t169 = circuit_add(in86, t168); // Eval quot_6 Horner step: add coefficient_2 let t170 = circuit_mul(t169, in216); // Eval quot_6 Horner step: multiply by STEP let t171 = circuit_add(in85, t170); // Eval quot_6 Horner step: add coefficient_1 let t172 = circuit_mul(t171, in216); // Eval quot_6 Horner step: multiply by STEP let t173 = circuit_add(in84, t172); // Eval quot_6 Horner step: add coefficient_0 let t174 = circuit_mul(in95, in216); // Eval rem_6 Horner step: multiply by STEP let t175 = circuit_add(in94, t174); // Eval rem_6 Horner step: add coefficient_4 let t176 = circuit_mul(t175, in216); // Eval rem_6 Horner step: multiply by STEP let t177 = circuit_add(in93, t176); // Eval rem_6 Horner step: add coefficient_3 let t178 = circuit_mul(t177, in216); // Eval rem_6 Horner step: multiply by STEP let t179 = circuit_add(in92, t178); // Eval rem_6 Horner step: add coefficient_2 let t180 = circuit_mul(t179, in216); // Eval rem_6 Horner step: multiply by STEP let t181 = circuit_add(in91, t180); // Eval rem_6 Horner step: add coefficient_1 let t182 = circuit_mul(t181, in216); // Eval rem_6 Horner step: multiply by STEP let t183 = circuit_add(in90, t182); // Eval rem_6 Horner step: add coefficient_0 let t184 = circuit_mul(t159, t159); // square_6 let t185 = circuit_mul(t173, t9); // quot*mod_6 let t186 = circuit_sub(t184, t185); // ab-qn_6 let t187 = circuit_sub(t186, t183); // ab-qn-rem_6 let t188 = circuit_mul(in101, in216); // Eval quot_7 Horner step: multiply by STEP let t189 = circuit_add(in100, t188); // Eval quot_7 Horner step: add coefficient_4 let t190 = circuit_mul(t189, in216); // Eval quot_7 Horner step: multiply by STEP let t191 = circuit_add(in99, t190); // Eval quot_7 Horner step: add coefficient_3 let t192 = circuit_mul(t191, in216); // Eval quot_7 Horner step: multiply by STEP let t193 = circuit_add(in98, t192); // Eval quot_7 Horner step: add coefficient_2 let t194 = circuit_mul(t193, in216); // Eval quot_7 Horner step: multiply by STEP let t195 = circuit_add(in97, t194); // Eval quot_7 Horner step: add coefficient_1 let t196 = circuit_mul(t195, in216); // Eval quot_7 Horner step: multiply by STEP let t197 = circuit_add(in96, t196); // Eval quot_7 Horner step: add coefficient_0 let t198 = circuit_mul(in107, in216); // Eval rem_7 Horner step: multiply by STEP let t199 = circuit_add(in106, t198); // Eval rem_7 Horner step: add coefficient_4 let t200 = circuit_mul(t199, in216); // Eval rem_7 Horner step: multiply by STEP let t201 = circuit_add(in105, t200); // Eval rem_7 Horner step: add coefficient_3 let t202 = circuit_mul(t201, in216); // Eval rem_7 Horner step: multiply by STEP let t203 = circuit_add(in104, t202); // Eval rem_7 Horner step: add coefficient_2 let t204 = circuit_mul(t203, in216); // Eval rem_7 Horner step: multiply by STEP let t205 = circuit_add(in103, t204); // Eval rem_7 Horner step: add coefficient_1 let t206 = circuit_mul(t205, in216); // Eval rem_7 Horner step: multiply by STEP let t207 = circuit_add(in102, t206); // Eval rem_7 Horner step: add coefficient_0 let t208 = circuit_mul(t183, t183); // square_7 let t209 = circuit_mul(t197, t9); // quot*mod_7 let t210 = circuit_sub(t208, t209); // ab-qn_7 let t211 = circuit_sub(t210, t207); // ab-qn-rem_7 let t212 = circuit_mul(in113, in216); // Eval quot_8 Horner step: multiply by STEP let t213 = circuit_add(in112, t212); // Eval quot_8 Horner step: add coefficient_4 let t214 = circuit_mul(t213, in216); // Eval quot_8 Horner step: multiply by STEP let t215 = circuit_add(in111, t214); // Eval quot_8 Horner step: add coefficient_3 let t216 = circuit_mul(t215, in216); // Eval quot_8 Horner step: multiply by STEP let t217 = circuit_add(in110, t216); // Eval quot_8 Horner step: add coefficient_2 let t218 = circuit_mul(t217, in216); // Eval quot_8 Horner step: multiply by STEP let t219 = circuit_add(in109, t218); // Eval quot_8 Horner step: add coefficient_1 let t220 = circuit_mul(t219, in216); // Eval quot_8 Horner step: multiply by STEP let t221 = circuit_add(in108, t220); // Eval quot_8 Horner step: add coefficient_0 let t222 = circuit_mul(in119, in216); // Eval rem_8 Horner step: multiply by STEP let t223 = circuit_add(in118, t222); // Eval rem_8 Horner step: add coefficient_4 let t224 = circuit_mul(t223, in216); // Eval rem_8 Horner step: multiply by STEP let t225 = circuit_add(in117, t224); // Eval rem_8 Horner step: add coefficient_3 let t226 = circuit_mul(t225, in216); // Eval rem_8 Horner step: multiply by STEP let t227 = circuit_add(in116, t226); // Eval rem_8 Horner step: add coefficient_2 let t228 = circuit_mul(t227, in216); // Eval rem_8 Horner step: multiply by STEP let t229 = circuit_add(in115, t228); // Eval rem_8 Horner step: add coefficient_1 let t230 = circuit_mul(t229, in216); // Eval rem_8 Horner step: multiply by STEP let t231 = circuit_add(in114, t230); // Eval rem_8 Horner step: add coefficient_0 let t232 = circuit_mul(t207, t207); // square_8 let t233 = circuit_mul(t221, t9); // quot*mod_8 let t234 = circuit_sub(t232, t233); // ab-qn_8 let t235 = circuit_sub(t234, t231); // ab-qn-rem_8 let t236 = circuit_mul(in125, in216); // Eval quot_9 Horner step: multiply by STEP let t237 = circuit_add(in124, t236); // Eval quot_9 Horner step: add coefficient_4 let t238 = circuit_mul(t237, in216); // Eval quot_9 Horner step: multiply by STEP let t239 = circuit_add(in123, t238); // Eval quot_9 Horner step: add coefficient_3 let t240 = circuit_mul(t239, in216); // Eval quot_9 Horner step: multiply by STEP let t241 = circuit_add(in122, t240); // Eval quot_9 Horner step: add coefficient_2 let t242 = circuit_mul(t241, in216); // Eval quot_9 Horner step: multiply by STEP let t243 = circuit_add(in121, t242); // Eval quot_9 Horner step: add coefficient_1 let t244 = circuit_mul(t243, in216); // Eval quot_9 Horner step: multiply by STEP let t245 = circuit_add(in120, t244); // Eval quot_9 Horner step: add coefficient_0 let t246 = circuit_mul(in131, in216); // Eval rem_9 Horner step: multiply by STEP let t247 = circuit_add(in130, t246); // Eval rem_9 Horner step: add coefficient_4 let t248 = circuit_mul(t247, in216); // Eval rem_9 Horner step: multiply by STEP let t249 = circuit_add(in129, t248); // Eval rem_9 Horner step: add coefficient_3 let t250 = circuit_mul(t249, in216); // Eval rem_9 Horner step: multiply by STEP let t251 = circuit_add(in128, t250); // Eval rem_9 Horner step: add coefficient_2 let t252 = circuit_mul(t251, in216); // Eval rem_9 Horner step: multiply by STEP let t253 = circuit_add(in127, t252); // Eval rem_9 Horner step: add coefficient_1 let t254 = circuit_mul(t253, in216); // Eval rem_9 Horner step: multiply by STEP let t255 = circuit_add(in126, t254); // Eval rem_9 Horner step: add coefficient_0 let t256 = circuit_mul(t231, t231); // square_9 let t257 = circuit_mul(t245, t9); // quot*mod_9 let t258 = circuit_sub(t256, t257); // ab-qn_9 let t259 = circuit_sub(t258, t255); // ab-qn-rem_9 let t260 = circuit_mul(in137, in216); // Eval quot_10 Horner step: multiply by STEP let t261 = circuit_add(in136, t260); // Eval quot_10 Horner step: add coefficient_4 let t262 = circuit_mul(t261, in216); // Eval quot_10 Horner step: multiply by STEP let t263 = circuit_add(in135, t262); // Eval quot_10 Horner step: add coefficient_3 let t264 = circuit_mul(t263, in216); // Eval quot_10 Horner step: multiply by STEP let t265 = circuit_add(in134, t264); // Eval quot_10 Horner step: add coefficient_2 let t266 = circuit_mul(t265, in216); // Eval quot_10 Horner step: multiply by STEP let t267 = circuit_add(in133, t266); // Eval quot_10 Horner step: add coefficient_1 let t268 = circuit_mul(t267, in216); // Eval quot_10 Horner step: multiply by STEP let t269 = circuit_add(in132, t268); // Eval quot_10 Horner step: add coefficient_0 let t270 = circuit_mul(in143, in216); // Eval rem_10 Horner step: multiply by STEP let t271 = circuit_add(in142, t270); // Eval rem_10 Horner step: add coefficient_4 let t272 = circuit_mul(t271, in216); // Eval rem_10 Horner step: multiply by STEP let t273 = circuit_add(in141, t272); // Eval rem_10 Horner step: add coefficient_3 let t274 = circuit_mul(t273, in216); // Eval rem_10 Horner step: multiply by STEP let t275 = circuit_add(in140, t274); // Eval rem_10 Horner step: add coefficient_2 let t276 = circuit_mul(t275, in216); // Eval rem_10 Horner step: multiply by STEP let t277 = circuit_add(in139, t276); // Eval rem_10 Horner step: add coefficient_1 let t278 = circuit_mul(t277, in216); // Eval rem_10 Horner step: multiply by STEP let t279 = circuit_add(in138, t278); // Eval rem_10 Horner step: add coefficient_0 let t280 = circuit_mul(t255, t255); // square_10 let t281 = circuit_mul(t269, t9); // quot*mod_10 let t282 = circuit_sub(t280, t281); // ab-qn_10 let t283 = circuit_sub(t282, t279); // ab-qn-rem_10 let t284 = circuit_mul(in149, in216); // Eval quot_11 Horner step: multiply by STEP let t285 = circuit_add(in148, t284); // Eval quot_11 Horner step: add coefficient_4 let t286 = circuit_mul(t285, in216); // Eval quot_11 Horner step: multiply by STEP let t287 = circuit_add(in147, t286); // Eval quot_11 Horner step: add coefficient_3 let t288 = circuit_mul(t287, in216); // Eval quot_11 Horner step: multiply by STEP let t289 = circuit_add(in146, t288); // Eval quot_11 Horner step: add coefficient_2 let t290 = circuit_mul(t289, in216); // Eval quot_11 Horner step: multiply by STEP let t291 = circuit_add(in145, t290); // Eval quot_11 Horner step: add coefficient_1 let t292 = circuit_mul(t291, in216); // Eval quot_11 Horner step: multiply by STEP let t293 = circuit_add(in144, t292); // Eval quot_11 Horner step: add coefficient_0 let t294 = circuit_mul(in155, in216); // Eval rem_11 Horner step: multiply by STEP let t295 = circuit_add(in154, t294); // Eval rem_11 Horner step: add coefficient_4 let t296 = circuit_mul(t295, in216); // Eval rem_11 Horner step: multiply by STEP let t297 = circuit_add(in153, t296); // Eval rem_11 Horner step: add coefficient_3 let t298 = circuit_mul(t297, in216); // Eval rem_11 Horner step: multiply by STEP let t299 = circuit_add(in152, t298); // Eval rem_11 Horner step: add coefficient_2 let t300 = circuit_mul(t299, in216); // Eval rem_11 Horner step: multiply by STEP let t301 = circuit_add(in151, t300); // Eval rem_11 Horner step: add coefficient_1 let t302 = circuit_mul(t301, in216); // Eval rem_11 Horner step: multiply by STEP let t303 = circuit_add(in150, t302); // Eval rem_11 Horner step: add coefficient_0 let t304 = circuit_mul(t279, t279); // square_11 let t305 = circuit_mul(t293, t9); // quot*mod_11 let t306 = circuit_sub(t304, t305); // ab-qn_11 let t307 = circuit_sub(t306, t303); // ab-qn-rem_11 let t308 = circuit_mul(in161, in216); // Eval quot_12 Horner step: multiply by STEP let t309 = circuit_add(in160, t308); // Eval quot_12 Horner step: add coefficient_4 let t310 = circuit_mul(t309, in216); // Eval quot_12 Horner step: multiply by STEP let t311 = circuit_add(in159, t310); // Eval quot_12 Horner step: add coefficient_3 let t312 = circuit_mul(t311, in216); // Eval quot_12 Horner step: multiply by STEP let t313 = circuit_add(in158, t312); // Eval quot_12 Horner step: add coefficient_2 let t314 = circuit_mul(t313, in216); // Eval quot_12 Horner step: multiply by STEP let t315 = circuit_add(in157, t314); // Eval quot_12 Horner step: add coefficient_1 let t316 = circuit_mul(t315, in216); // Eval quot_12 Horner step: multiply by STEP let t317 = circuit_add(in156, t316); // Eval quot_12 Horner step: add coefficient_0 let t318 = circuit_mul(in167, in216); // Eval rem_12 Horner step: multiply by STEP let t319 = circuit_add(in166, t318); // Eval rem_12 Horner step: add coefficient_4 let t320 = circuit_mul(t319, in216); // Eval rem_12 Horner step: multiply by STEP let t321 = circuit_add(in165, t320); // Eval rem_12 Horner step: add coefficient_3 let t322 = circuit_mul(t321, in216); // Eval rem_12 Horner step: multiply by STEP let t323 = circuit_add(in164, t322); // Eval rem_12 Horner step: add coefficient_2 let t324 = circuit_mul(t323, in216); // Eval rem_12 Horner step: multiply by STEP let t325 = circuit_add(in163, t324); // Eval rem_12 Horner step: add coefficient_1 let t326 = circuit_mul(t325, in216); // Eval rem_12 Horner step: multiply by STEP let t327 = circuit_add(in162, t326); // Eval rem_12 Horner step: add coefficient_0 let t328 = circuit_mul(t303, t303); // square_12 let t329 = circuit_mul(t317, t9); // quot*mod_12 let t330 = circuit_sub(t328, t329); // ab-qn_12 let t331 = circuit_sub(t330, t327); // ab-qn-rem_12 let t332 = circuit_mul(in173, in216); // Eval quot_13 Horner step: multiply by STEP let t333 = circuit_add(in172, t332); // Eval quot_13 Horner step: add coefficient_4 let t334 = circuit_mul(t333, in216); // Eval quot_13 Horner step: multiply by STEP let t335 = circuit_add(in171, t334); // Eval quot_13 Horner step: add coefficient_3 let t336 = circuit_mul(t335, in216); // Eval quot_13 Horner step: multiply by STEP let t337 = circuit_add(in170, t336); // Eval quot_13 Horner step: add coefficient_2 let t338 = circuit_mul(t337, in216); // Eval quot_13 Horner step: multiply by STEP let t339 = circuit_add(in169, t338); // Eval quot_13 Horner step: add coefficient_1 let t340 = circuit_mul(t339, in216); // Eval quot_13 Horner step: multiply by STEP let t341 = circuit_add(in168, t340); // Eval quot_13 Horner step: add coefficient_0 let t342 = circuit_mul(in179, in216); // Eval rem_13 Horner step: multiply by STEP let t343 = circuit_add(in178, t342); // Eval rem_13 Horner step: add coefficient_4 let t344 = circuit_mul(t343, in216); // Eval rem_13 Horner step: multiply by STEP let t345 = circuit_add(in177, t344); // Eval rem_13 Horner step: add coefficient_3 let t346 = circuit_mul(t345, in216); // Eval rem_13 Horner step: multiply by STEP let t347 = circuit_add(in176, t346); // Eval rem_13 Horner step: add coefficient_2 let t348 = circuit_mul(t347, in216); // Eval rem_13 Horner step: multiply by STEP let t349 = circuit_add(in175, t348); // Eval rem_13 Horner step: add coefficient_1 let t350 = circuit_mul(t349, in216); // Eval rem_13 Horner step: multiply by STEP let t351 = circuit_add(in174, t350); // Eval rem_13 Horner step: add coefficient_0 let t352 = circuit_mul(t327, t327); // square_13 let t353 = circuit_mul(t341, t9); // quot*mod_13 let t354 = circuit_sub(t352, t353); // ab-qn_13 let t355 = circuit_sub(t354, t351); // ab-qn-rem_13 let t356 = circuit_mul(in185, in216); // Eval quot_14 Horner step: multiply by STEP let t357 = circuit_add(in184, t356); // Eval quot_14 Horner step: add coefficient_4 let t358 = circuit_mul(t357, in216); // Eval quot_14 Horner step: multiply by STEP let t359 = circuit_add(in183, t358); // Eval quot_14 Horner step: add coefficient_3 let t360 = circuit_mul(t359, in216); // Eval quot_14 Horner step: multiply by STEP let t361 = circuit_add(in182, t360); // Eval quot_14 Horner step: add coefficient_2 let t362 = circuit_mul(t361, in216); // Eval quot_14 Horner step: multiply by STEP let t363 = circuit_add(in181, t362); // Eval quot_14 Horner step: add coefficient_1 let t364 = circuit_mul(t363, in216); // Eval quot_14 Horner step: multiply by STEP let t365 = circuit_add(in180, t364); // Eval quot_14 Horner step: add coefficient_0 let t366 = circuit_mul(in191, in216); // Eval rem_14 Horner step: multiply by STEP let t367 = circuit_add(in190, t366); // Eval rem_14 Horner step: add coefficient_4 let t368 = circuit_mul(t367, in216); // Eval rem_14 Horner step: multiply by STEP let t369 = circuit_add(in189, t368); // Eval rem_14 Horner step: add coefficient_3 let t370 = circuit_mul(t369, in216); // Eval rem_14 Horner step: multiply by STEP let t371 = circuit_add(in188, t370); // Eval rem_14 Horner step: add coefficient_2 let t372 = circuit_mul(t371, in216); // Eval rem_14 Horner step: multiply by STEP let t373 = circuit_add(in187, t372); // Eval rem_14 Horner step: add coefficient_1 let t374 = circuit_mul(t373, in216); // Eval rem_14 Horner step: multiply by STEP let t375 = circuit_add(in186, t374); // Eval rem_14 Horner step: add coefficient_0 let t376 = circuit_mul(t351, t351); // square_14 let t377 = circuit_mul(t365, t9); // quot*mod_14 let t378 = circuit_sub(t376, t377); // ab-qn_14 let t379 = circuit_sub(t378, t375); // ab-qn-rem_14 let t380 = circuit_mul(in197, in216); // Eval quot_15 Horner step: multiply by STEP let t381 = circuit_add(in196, t380); // Eval quot_15 Horner step: add coefficient_4 let t382 = circuit_mul(t381, in216); // Eval quot_15 Horner step: multiply by STEP let t383 = circuit_add(in195, t382); // Eval quot_15 Horner step: add coefficient_3 let t384 = circuit_mul(t383, in216); // Eval quot_15 Horner step: multiply by STEP let t385 = circuit_add(in194, t384); // Eval quot_15 Horner step: add coefficient_2 let t386 = circuit_mul(t385, in216); // Eval quot_15 Horner step: multiply by STEP let t387 = circuit_add(in193, t386); // Eval quot_15 Horner step: add coefficient_1 let t388 = circuit_mul(t387, in216); // Eval quot_15 Horner step: multiply by STEP let t389 = circuit_add(in192, t388); // Eval quot_15 Horner step: add coefficient_0 let t390 = circuit_mul(in203, in216); // Eval rem_15 Horner step: multiply by STEP let t391 = circuit_add(in202, t390); // Eval rem_15 Horner step: add coefficient_4 let t392 = circuit_mul(t391, in216); // Eval rem_15 Horner step: multiply by STEP let t393 = circuit_add(in201, t392); // Eval rem_15 Horner step: add coefficient_3 let t394 = circuit_mul(t393, in216); // Eval rem_15 Horner step: multiply by STEP let t395 = circuit_add(in200, t394); // Eval rem_15 Horner step: add coefficient_2 let t396 = circuit_mul(t395, in216); // Eval rem_15 Horner step: multiply by STEP let t397 = circuit_add(in199, t396); // Eval rem_15 Horner step: add coefficient_1 let t398 = circuit_mul(t397, in216); // Eval rem_15 Horner step: multiply by STEP let t399 = circuit_add(in198, t398); // Eval rem_15 Horner step: add coefficient_0 let t400 = circuit_mul(t375, t375); // square_15 let t401 = circuit_mul(t389, t9); // quot*mod_15 let t402 = circuit_sub(t400, t401); // ab-qn_15 let t403 = circuit_sub(t402, t399); // ab-qn-rem_15 let t404 = circuit_mul(in209, in216); // Eval quot_16 Horner step: multiply by STEP let t405 = circuit_add(in208, t404); // Eval quot_16 Horner step: add coefficient_4 let t406 = circuit_mul(t405, in216); // Eval quot_16 Horner step: multiply by STEP let t407 = circuit_add(in207, t406); // Eval quot_16 Horner step: add coefficient_3 let t408 = circuit_mul(t407, in216); // Eval quot_16 Horner step: multiply by STEP let t409 = circuit_add(in206, t408); // Eval quot_16 Horner step: add coefficient_2 let t410 = circuit_mul(t409, in216); // Eval quot_16 Horner step: multiply by STEP let t411 = circuit_add(in205, t410); // Eval quot_16 Horner step: add coefficient_1 let t412 = circuit_mul(t411, in216); // Eval quot_16 Horner step: multiply by STEP let t413 = circuit_add(in204, t412); // Eval quot_16 Horner step: add coefficient_0 let t414 = circuit_mul(in215, in216); // Eval rem_16 Horner step: multiply by STEP let t415 = circuit_add(in214, t414); // Eval rem_16 Horner step: add coefficient_4 let t416 = circuit_mul(t415, in216); // Eval rem_16 Horner step: multiply by STEP let t417 = circuit_add(in213, t416); // Eval rem_16 Horner step: add coefficient_3 let t418 = circuit_mul(t417, in216); // Eval rem_16 Horner step: multiply by STEP let t419 = circuit_add(in212, t418); // Eval rem_16 Horner step: add coefficient_2 let t420 = circuit_mul(t419, in216); // Eval rem_16 Horner step: multiply by STEP let t421 = circuit_add(in211, t420); // Eval rem_16 Horner step: add coefficient_1 let t422 = circuit_mul(t421, in216); // Eval rem_16 Horner step: multiply by STEP let t423 = circuit_add(in210, t422); // Eval rem_16 Horner step: add coefficient_0 let t424 = circuit_mul(t399, t19); // final_multiply let t425 = circuit_mul(t413, t9); // quot*mod_16 let t426 = circuit_sub(t424, t425); // ab-qn_16 let t427 = circuit_sub(t426, t423); // ab-qn-rem_16 let modulus = modulus; let mut circuit_inputs = ( t43, t67, t91, t115, t139, t163, t187, t211, t235, t259, t283, t307, t331, t355, t379, t403, t427, ) .new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(mod_chunks.w0); // in0 circuit_inputs = circuit_inputs.next_2(mod_chunks.w1); // in1 circuit_inputs = circuit_inputs.next_2(mod_chunks.w2); // in2 circuit_inputs = circuit_inputs.next_2(mod_chunks.w3); // in3 circuit_inputs = circuit_inputs.next_2(mod_chunks.w4); // in4 circuit_inputs = circuit_inputs.next_2(mod_chunks.w5); // in5 circuit_inputs = circuit_inputs.next_2(sig_chunks.w0); // in6 circuit_inputs = circuit_inputs.next_2(sig_chunks.w1); // in7 circuit_inputs = circuit_inputs.next_2(sig_chunks.w2); // in8 circuit_inputs = circuit_inputs.next_2(sig_chunks.w3); // in9 circuit_inputs = circuit_inputs.next_2(sig_chunks.w4); // in10 circuit_inputs = circuit_inputs.next_2(sig_chunks.w5); // in11 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w0); // in12 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w1); // in13 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w2); // in14 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w3); // in15 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w4); // in16 circuit_inputs = circuit_inputs.next_2(w_0.quotient.w5); // in17 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w0); // in18 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w1); // in19 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w2); // in20 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w3); // in21 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w4); // in22 circuit_inputs = circuit_inputs.next_2(w_0.remainder.w5); // in23 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w0); // in24 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w1); // in25 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w2); // in26 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w3); // in27 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w4); // in28 circuit_inputs = circuit_inputs.next_2(w_1.quotient.w5); // in29 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w0); // in30 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w1); // in31 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w2); // in32 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w3); // in33 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w4); // in34 circuit_inputs = circuit_inputs.next_2(w_1.remainder.w5); // in35 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w0); // in36 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w1); // in37 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w2); // in38 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w3); // in39 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w4); // in40 circuit_inputs = circuit_inputs.next_2(w_2.quotient.w5); // in41 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w0); // in42 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w1); // in43 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w2); // in44 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w3); // in45 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w4); // in46 circuit_inputs = circuit_inputs.next_2(w_2.remainder.w5); // in47 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w0); // in48 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w1); // in49 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w2); // in50 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w3); // in51 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w4); // in52 circuit_inputs = circuit_inputs.next_2(w_3.quotient.w5); // in53 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w0); // in54 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w1); // in55 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w2); // in56 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w3); // in57 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w4); // in58 circuit_inputs = circuit_inputs.next_2(w_3.remainder.w5); // in59 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w0); // in60 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w1); // in61 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w2); // in62 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w3); // in63 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w4); // in64 circuit_inputs = circuit_inputs.next_2(w_4.quotient.w5); // in65 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w0); // in66 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w1); // in67 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w2); // in68 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w3); // in69 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w4); // in70 circuit_inputs = circuit_inputs.next_2(w_4.remainder.w5); // in71 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w0); // in72 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w1); // in73 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w2); // in74 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w3); // in75 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w4); // in76 circuit_inputs = circuit_inputs.next_2(w_5.quotient.w5); // in77 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w0); // in78 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w1); // in79 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w2); // in80 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w3); // in81 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w4); // in82 circuit_inputs = circuit_inputs.next_2(w_5.remainder.w5); // in83 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w0); // in84 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w1); // in85 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w2); // in86 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w3); // in87 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w4); // in88 circuit_inputs = circuit_inputs.next_2(w_6.quotient.w5); // in89 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w0); // in90 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w1); // in91 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w2); // in92 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w3); // in93 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w4); // in94 circuit_inputs = circuit_inputs.next_2(w_6.remainder.w5); // in95 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w0); // in96 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w1); // in97 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w2); // in98 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w3); // in99 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w4); // in100 circuit_inputs = circuit_inputs.next_2(w_7.quotient.w5); // in101 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w0); // in102 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w1); // in103 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w2); // in104 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w3); // in105 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w4); // in106 circuit_inputs = circuit_inputs.next_2(w_7.remainder.w5); // in107 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w0); // in108 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w1); // in109 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w2); // in110 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w3); // in111 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w4); // in112 circuit_inputs = circuit_inputs.next_2(w_8.quotient.w5); // in113 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w0); // in114 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w1); // in115 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w2); // in116 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w3); // in117 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w4); // in118 circuit_inputs = circuit_inputs.next_2(w_8.remainder.w5); // in119 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w0); // in120 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w1); // in121 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w2); // in122 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w3); // in123 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w4); // in124 circuit_inputs = circuit_inputs.next_2(w_9.quotient.w5); // in125 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w0); // in126 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w1); // in127 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w2); // in128 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w3); // in129 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w4); // in130 circuit_inputs = circuit_inputs.next_2(w_9.remainder.w5); // in131 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w0); // in132 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w1); // in133 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w2); // in134 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w3); // in135 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w4); // in136 circuit_inputs = circuit_inputs.next_2(w_10.quotient.w5); // in137 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w0); // in138 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w1); // in139 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w2); // in140 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w3); // in141 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w4); // in142 circuit_inputs = circuit_inputs.next_2(w_10.remainder.w5); // in143 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w0); // in144 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w1); // in145 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w2); // in146 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w3); // in147 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w4); // in148 circuit_inputs = circuit_inputs.next_2(w_11.quotient.w5); // in149 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w0); // in150 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w1); // in151 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w2); // in152 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w3); // in153 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w4); // in154 circuit_inputs = circuit_inputs.next_2(w_11.remainder.w5); // in155 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w0); // in156 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w1); // in157 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w2); // in158 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w3); // in159 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w4); // in160 circuit_inputs = circuit_inputs.next_2(w_12.quotient.w5); // in161 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w0); // in162 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w1); // in163 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w2); // in164 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w3); // in165 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w4); // in166 circuit_inputs = circuit_inputs.next_2(w_12.remainder.w5); // in167 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w0); // in168 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w1); // in169 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w2); // in170 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w3); // in171 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w4); // in172 circuit_inputs = circuit_inputs.next_2(w_13.quotient.w5); // in173 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w0); // in174 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w1); // in175 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w2); // in176 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w3); // in177 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w4); // in178 circuit_inputs = circuit_inputs.next_2(w_13.remainder.w5); // in179 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w0); // in180 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w1); // in181 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w2); // in182 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w3); // in183 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w4); // in184 circuit_inputs = circuit_inputs.next_2(w_14.quotient.w5); // in185 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w0); // in186 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w1); // in187 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w2); // in188 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w3); // in189 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w4); // in190 circuit_inputs = circuit_inputs.next_2(w_14.remainder.w5); // in191 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w0); // in192 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w1); // in193 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w2); // in194 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w3); // in195 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w4); // in196 circuit_inputs = circuit_inputs.next_2(w_15.quotient.w5); // in197 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w0); // in198 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w1); // in199 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w2); // in200 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w3); // in201 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w4); // in202 circuit_inputs = circuit_inputs.next_2(w_15.remainder.w5); // in203 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w0); // in204 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w1); // in205 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w2); // in206 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w3); // in207 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w4); // in208 circuit_inputs = circuit_inputs.next_2(w_16.quotient.w5); // in209 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w0); // in210 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w1); // in211 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w2); // in212 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w3); // in213 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w4); // in214 circuit_inputs = circuit_inputs.next_2(w_16.remainder.w5); // in215 circuit_inputs = circuit_inputs.next_2(step); // in216 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let diff_0: u384 = outputs.get_output(t43); let diff_1: u384 = outputs.get_output(t67); let diff_2: u384 = outputs.get_output(t91); let diff_3: u384 = outputs.get_output(t115); let diff_4: u384 = outputs.get_output(t139); let diff_5: u384 = outputs.get_output(t163); let diff_6: u384 = outputs.get_output(t187); let diff_7: u384 = outputs.get_output(t211); let diff_8: u384 = outputs.get_output(t235); let diff_9: u384 = outputs.get_output(t259); let diff_10: u384 = outputs.get_output(t283); let diff_11: u384 = outputs.get_output(t307); let diff_12: u384 = outputs.get_output(t331); let diff_13: u384 = outputs.get_output(t355); let diff_14: u384 = outputs.get_output(t379); let diff_15: u384 = outputs.get_output(t403); let diff_16: u384 = outputs.get_output(t427); return ( diff_0, diff_1, diff_2, diff_3, diff_4, diff_5, diff_6, diff_7, diff_8, diff_9, diff_10, diff_11, diff_12, diff_13, diff_14, diff_15, diff_16, ); } ================================================ FILE: src/src/circuits/tower_circuits.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{E12T, G2Point}; #[inline(always)] pub fn run_BLS12_381_E12T_CYCLOTOMIC_SQUARE_circuit(M: E12T) -> (E12T,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in8, in9); let t1 = circuit_sub(in8, in9); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in8, in9); let t4 = circuit_add(t3, t3); let t5 = circuit_add(in0, in1); let t6 = circuit_sub(in0, in1); let t7 = circuit_mul(t5, t6); let t8 = circuit_mul(in0, in1); let t9 = circuit_add(t8, t8); let t10 = circuit_add(in8, in0); // Fp2 add coeff 0/1 let t11 = circuit_add(in9, in1); // Fp2 add coeff 1/1 let t12 = circuit_add(t10, t11); let t13 = circuit_sub(t10, t11); let t14 = circuit_mul(t12, t13); let t15 = circuit_mul(t10, t11); let t16 = circuit_add(t15, t15); let t17 = circuit_sub(t14, t2); // Fp2 sub coeff 0/1 let t18 = circuit_sub(t16, t4); // Fp2 sub coeff 1/1 let t19 = circuit_sub(t17, t7); // Fp2 sub coeff 0/1 let t20 = circuit_sub(t18, t9); // Fp2 sub coeff 1/1 let t21 = circuit_add(in4, in5); let t22 = circuit_sub(in4, in5); let t23 = circuit_mul(t21, t22); let t24 = circuit_mul(in4, in5); let t25 = circuit_add(t24, t24); let t26 = circuit_add(in6, in7); let t27 = circuit_sub(in6, in7); let t28 = circuit_mul(t26, t27); let t29 = circuit_mul(in6, in7); let t30 = circuit_add(t29, t29); let t31 = circuit_add(in4, in6); // Fp2 add coeff 0/1 let t32 = circuit_add(in5, in7); // Fp2 add coeff 1/1 let t33 = circuit_add(t31, t32); let t34 = circuit_sub(t31, t32); let t35 = circuit_mul(t33, t34); let t36 = circuit_mul(t31, t32); let t37 = circuit_add(t36, t36); let t38 = circuit_sub(t35, t23); // Fp2 sub coeff 0/1 let t39 = circuit_sub(t37, t25); // Fp2 sub coeff 1/1 let t40 = circuit_sub(t38, t28); // Fp2 sub coeff 0/1 let t41 = circuit_sub(t39, t30); // Fp2 sub coeff 1/1 let t42 = circuit_add(in10, in11); let t43 = circuit_sub(in10, in11); let t44 = circuit_mul(t42, t43); let t45 = circuit_mul(in10, in11); let t46 = circuit_add(t45, t45); let t47 = circuit_add(in2, in3); let t48 = circuit_sub(in2, in3); let t49 = circuit_mul(t47, t48); let t50 = circuit_mul(in2, in3); let t51 = circuit_add(t50, t50); let t52 = circuit_add(in10, in2); // Fp2 add coeff 0/1 let t53 = circuit_add(in11, in3); // Fp2 add coeff 1/1 let t54 = circuit_add(t52, t53); let t55 = circuit_sub(t52, t53); let t56 = circuit_mul(t54, t55); let t57 = circuit_mul(t52, t53); let t58 = circuit_add(t57, t57); let t59 = circuit_sub(t56, t44); // Fp2 sub coeff 0/1 let t60 = circuit_sub(t58, t46); // Fp2 sub coeff 1/1 let t61 = circuit_sub(t59, t49); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t60, t51); // Fp2 sub coeff 1/1 let t63 = circuit_add(t61, t62); let t64 = circuit_add(t63, t63); let t65 = circuit_sub(t61, t62); let t66 = circuit_sub(t64, t61); let t67 = circuit_sub(t66, t62); let t68 = circuit_add(t2, t4); let t69 = circuit_add(t68, t68); let t70 = circuit_sub(t2, t4); let t71 = circuit_sub(t69, t2); let t72 = circuit_sub(t71, t4); let t73 = circuit_add(t70, t7); // Fp2 add coeff 0/1 let t74 = circuit_add(t72, t9); // Fp2 add coeff 1/1 let t75 = circuit_add(t23, t25); let t76 = circuit_add(t75, t75); let t77 = circuit_sub(t23, t25); let t78 = circuit_sub(t76, t23); let t79 = circuit_sub(t78, t25); let t80 = circuit_add(t77, t28); // Fp2 add coeff 0/1 let t81 = circuit_add(t79, t30); // Fp2 add coeff 1/1 let t82 = circuit_add(t44, t46); let t83 = circuit_add(t82, t82); let t84 = circuit_sub(t44, t46); let t85 = circuit_sub(t83, t44); let t86 = circuit_sub(t85, t46); let t87 = circuit_add(t84, t49); // Fp2 add coeff 0/1 let t88 = circuit_add(t86, t51); // Fp2 add coeff 1/1 let t89 = circuit_sub(t73, in0); // Fp2 sub coeff 0/1 let t90 = circuit_sub(t74, in1); // Fp2 sub coeff 1/1 let t91 = circuit_add(t89, t89); // Fp2 add coeff 0/1 let t92 = circuit_add(t90, t90); // Fp2 add coeff 1/1 let t93 = circuit_add(t91, t73); // Fp2 add coeff 0/1 let t94 = circuit_add(t92, t74); // Fp2 add coeff 1/1 let t95 = circuit_sub(t80, in2); // Fp2 sub coeff 0/1 let t96 = circuit_sub(t81, in3); // Fp2 sub coeff 1/1 let t97 = circuit_add(t95, t95); // Fp2 add coeff 0/1 let t98 = circuit_add(t96, t96); // Fp2 add coeff 1/1 let t99 = circuit_add(t97, t80); // Fp2 add coeff 0/1 let t100 = circuit_add(t98, t81); // Fp2 add coeff 1/1 let t101 = circuit_sub(t87, in4); // Fp2 sub coeff 0/1 let t102 = circuit_sub(t88, in5); // Fp2 sub coeff 1/1 let t103 = circuit_add(t101, t101); // Fp2 add coeff 0/1 let t104 = circuit_add(t102, t102); // Fp2 add coeff 1/1 let t105 = circuit_add(t103, t87); // Fp2 add coeff 0/1 let t106 = circuit_add(t104, t88); // Fp2 add coeff 1/1 let t107 = circuit_add(t65, in6); // Fp2 add coeff 0/1 let t108 = circuit_add(t67, in7); // Fp2 add coeff 1/1 let t109 = circuit_add(t107, t107); // Fp2 add coeff 0/1 let t110 = circuit_add(t108, t108); // Fp2 add coeff 1/1 let t111 = circuit_add(t109, t65); // Fp2 add coeff 0/1 let t112 = circuit_add(t110, t67); // Fp2 add coeff 1/1 let t113 = circuit_add(t19, in8); // Fp2 add coeff 0/1 let t114 = circuit_add(t20, in9); // Fp2 add coeff 1/1 let t115 = circuit_add(t113, t113); // Fp2 add coeff 0/1 let t116 = circuit_add(t114, t114); // Fp2 add coeff 1/1 let t117 = circuit_add(t115, t19); // Fp2 add coeff 0/1 let t118 = circuit_add(t116, t20); // Fp2 add coeff 1/1 let t119 = circuit_add(t40, in10); // Fp2 add coeff 0/1 let t120 = circuit_add(t41, in11); // Fp2 add coeff 1/1 let t121 = circuit_add(t119, t119); // Fp2 add coeff 0/1 let t122 = circuit_add(t120, t120); // Fp2 add coeff 1/1 let t123 = circuit_add(t121, t40); // Fp2 add coeff 0/1 let t124 = circuit_add(t122, t41); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t93, t94, t99, t100, t105, t106, t111, t112, t117, t118, t123, t124) .new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in0 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in1 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in2 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in3 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in4 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in5 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in6 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in7 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in8 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in9 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in10 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in11 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t93), c0b0a1: outputs.get_output(t94), c0b1a0: outputs.get_output(t99), c0b1a1: outputs.get_output(t100), c0b2a0: outputs.get_output(t105), c0b2a1: outputs.get_output(t106), c1b0a0: outputs.get_output(t111), c1b0a1: outputs.get_output(t112), c1b1a0: outputs.get_output(t117), c1b1a1: outputs.get_output(t118), c1b2a0: outputs.get_output(t123), c1b2a1: outputs.get_output(t124), }; return (res,); } #[inline(always)] pub fn run_BLS12_381_E12T_CYCLO_SQUARE_COMPRESSED_circuit( xc0b1a0: u384, xc0b1a1: u384, xc0b2a0: u384, xc0b2a1: u384, xc1b0a0: u384, xc1b0a1: u384, xc1b2a0: u384, xc1b2a1: u384, ) -> (u384, u384, u384, u384, u384, u384, u384, u384) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7) = (CE::> {}, CE::> {}); let t0 = circuit_add(in0, in1); let t1 = circuit_sub(in0, in1); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in0, in1); let t4 = circuit_add(t3, t3); let t5 = circuit_add(in6, in7); let t6 = circuit_sub(in6, in7); let t7 = circuit_mul(t5, t6); let t8 = circuit_mul(in6, in7); let t9 = circuit_add(t8, t8); let t10 = circuit_add(in0, in6); // Fp2 add coeff 0/1 let t11 = circuit_add(in1, in7); // Fp2 add coeff 1/1 let t12 = circuit_add(t10, t11); let t13 = circuit_sub(t10, t11); let t14 = circuit_mul(t12, t13); let t15 = circuit_mul(t10, t11); let t16 = circuit_add(t15, t15); let t17 = circuit_add(t2, t7); // Fp2 add coeff 0/1 let t18 = circuit_add(t4, t9); // Fp2 add coeff 1/1 let t19 = circuit_sub(t14, t17); // Fp2 sub coeff 0/1 let t20 = circuit_sub(t16, t18); // Fp2 sub coeff 1/1 let t21 = circuit_add(in4, in2); // Fp2 add coeff 0/1 let t22 = circuit_add(in5, in3); // Fp2 add coeff 1/1 let t23 = circuit_add(t21, t22); let t24 = circuit_sub(t21, t22); let t25 = circuit_mul(t23, t24); let t26 = circuit_mul(t21, t22); let t27 = circuit_add(t26, t26); let t28 = circuit_add(in4, in5); let t29 = circuit_sub(in4, in5); let t30 = circuit_mul(t28, t29); let t31 = circuit_mul(in4, in5); let t32 = circuit_add(t31, t31); let t33 = circuit_add(t19, t20); let t34 = circuit_add(t33, t33); let t35 = circuit_sub(t19, t20); let t36 = circuit_sub(t34, t19); let t37 = circuit_sub(t36, t20); let t38 = circuit_add(t35, in4); // Fp2 add coeff 0/1 let t39 = circuit_add(t37, in5); // Fp2 add coeff 1/1 let t40 = circuit_add(t38, t38); // Fp2 add coeff 0/1 let t41 = circuit_add(t39, t39); // Fp2 add coeff 1/1 let t42 = circuit_add(t40, t35); // Fp2 add coeff 0/1 let t43 = circuit_add(t41, t37); // Fp2 add coeff 1/1 let t44 = circuit_add(t7, t9); let t45 = circuit_add(t44, t44); let t46 = circuit_sub(t7, t9); let t47 = circuit_sub(t45, t7); let t48 = circuit_sub(t47, t9); let t49 = circuit_add(t2, t46); // Fp2 add coeff 0/1 let t50 = circuit_add(t4, t48); // Fp2 add coeff 1/1 let t51 = circuit_sub(t49, in2); // Fp2 sub coeff 0/1 let t52 = circuit_sub(t50, in3); // Fp2 sub coeff 1/1 let t53 = circuit_add(in2, in3); let t54 = circuit_sub(in2, in3); let t55 = circuit_mul(t53, t54); let t56 = circuit_mul(in2, in3); let t57 = circuit_add(t56, t56); let t58 = circuit_add(t51, t51); // Fp2 add coeff 0/1 let t59 = circuit_add(t52, t52); // Fp2 add coeff 1/1 let t60 = circuit_add(t58, t49); // Fp2 add coeff 0/1 let t61 = circuit_add(t59, t50); // Fp2 add coeff 1/1 let t62 = circuit_add(t55, t57); let t63 = circuit_add(t62, t62); let t64 = circuit_sub(t55, t57); let t65 = circuit_sub(t63, t55); let t66 = circuit_sub(t65, t57); let t67 = circuit_add(t30, t64); // Fp2 add coeff 0/1 let t68 = circuit_add(t32, t66); // Fp2 add coeff 1/1 let t69 = circuit_sub(t67, in0); // Fp2 sub coeff 0/1 let t70 = circuit_sub(t68, in1); // Fp2 sub coeff 1/1 let t71 = circuit_add(t69, t69); // Fp2 add coeff 0/1 let t72 = circuit_add(t70, t70); // Fp2 add coeff 1/1 let t73 = circuit_add(t71, t67); // Fp2 add coeff 0/1 let t74 = circuit_add(t72, t68); // Fp2 add coeff 1/1 let t75 = circuit_add(t30, t55); // Fp2 add coeff 0/1 let t76 = circuit_add(t32, t57); // Fp2 add coeff 1/1 let t77 = circuit_sub(t25, t75); // Fp2 sub coeff 0/1 let t78 = circuit_sub(t27, t76); // Fp2 sub coeff 1/1 let t79 = circuit_add(t77, in6); // Fp2 add coeff 0/1 let t80 = circuit_add(t78, in7); // Fp2 add coeff 1/1 let t81 = circuit_add(t79, t79); // Fp2 add coeff 0/1 let t82 = circuit_add(t80, t80); // Fp2 add coeff 1/1 let t83 = circuit_add(t77, t81); // Fp2 add coeff 0/1 let t84 = circuit_add(t78, t82); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t73, t74, t60, t61, t42, t43, t83, t84).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(xc0b1a0); // in0 circuit_inputs = circuit_inputs.next_2(xc0b1a1); // in1 circuit_inputs = circuit_inputs.next_2(xc0b2a0); // in2 circuit_inputs = circuit_inputs.next_2(xc0b2a1); // in3 circuit_inputs = circuit_inputs.next_2(xc1b0a0); // in4 circuit_inputs = circuit_inputs.next_2(xc1b0a1); // in5 circuit_inputs = circuit_inputs.next_2(xc1b2a0); // in6 circuit_inputs = circuit_inputs.next_2(xc1b2a1); // in7 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let xc0b1a0: u384 = outputs.get_output(t73); let xc0b1a1: u384 = outputs.get_output(t74); let xc0b2a0: u384 = outputs.get_output(t60); let xc0b2a1: u384 = outputs.get_output(t61); let xc1b0a0: u384 = outputs.get_output(t42); let xc1b0a1: u384 = outputs.get_output(t43); let xc1b2a0: u384 = outputs.get_output(t83); let xc1b2a1: u384 = outputs.get_output(t84); return (xc0b1a0, xc0b1a1, xc0b2a0, xc0b2a1, xc1b0a0, xc1b0a1, xc1b2a0, xc1b2a1); } #[inline(always)] pub fn run_BLS12_381_E12T_DECOMP_KARABINA_II_circuit( t0a0: u384, t0a1: u384, t1a0: u384, t1a1: u384, xc0b1a0: u384, xc0b1a1: u384, xc0b2a0: u384, xc0b2a1: u384, xc1b0a0: u384, xc1b0a1: u384, xc1b2a0: u384, xc1b2a1: u384, ) -> (u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in4, in4); // Fp2 Inv start let t1 = circuit_mul(in5, in5); let t2 = circuit_add(t0, t1); let t3 = circuit_inverse(t2); let t4 = circuit_mul(in4, t3); // Fp2 Inv real part end let t5 = circuit_mul(in5, t3); let t6 = circuit_sub(in0, t5); // Fp2 Inv imag part end let t7 = circuit_mul(in2, t4); // Fp2 mul start let t8 = circuit_mul(in3, t6); let t9 = circuit_sub(t7, t8); // Fp2 mul real part end let t10 = circuit_mul(in2, t6); let t11 = circuit_mul(in3, t4); let t12 = circuit_add(t10, t11); // Fp2 mul imag part end let t13 = circuit_mul(in8, in6); // Fp2 mul start let t14 = circuit_mul(in9, in7); let t15 = circuit_sub(t13, t14); // Fp2 mul real part end let t16 = circuit_mul(in8, in7); let t17 = circuit_mul(in9, in6); let t18 = circuit_add(t16, t17); // Fp2 mul imag part end let t19 = circuit_add(t9, t12); let t20 = circuit_sub(t9, t12); let t21 = circuit_mul(t19, t20); let t22 = circuit_mul(t9, t12); let t23 = circuit_add(t22, t22); let t24 = circuit_sub(t21, t15); // Fp2 sub coeff 0/1 let t25 = circuit_sub(t23, t18); // Fp2 sub coeff 1/1 let t26 = circuit_add(t24, t24); // Fp2 add coeff 0/1 let t27 = circuit_add(t25, t25); // Fp2 add coeff 1/1 let t28 = circuit_sub(t26, t15); // Fp2 sub coeff 0/1 let t29 = circuit_sub(t27, t18); // Fp2 sub coeff 1/1 let t30 = circuit_mul(in10, in12); // Fp2 mul start let t31 = circuit_mul(in11, in13); let t32 = circuit_sub(t30, t31); // Fp2 mul real part end let t33 = circuit_mul(in10, in13); let t34 = circuit_mul(in11, in12); let t35 = circuit_add(t33, t34); // Fp2 mul imag part end let t36 = circuit_add(t28, t32); // Fp2 add coeff 0/1 let t37 = circuit_add(t29, t35); // Fp2 add coeff 1/1 let t38 = circuit_add(t36, t37); let t39 = circuit_add(t38, t38); let t40 = circuit_sub(t36, t37); let t41 = circuit_sub(t39, t36); let t42 = circuit_sub(t41, t37); let t43 = circuit_add(t40, in1); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t43, t42, t9, t12).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(t0a0); // in2 circuit_inputs = circuit_inputs.next_2(t0a1); // in3 circuit_inputs = circuit_inputs.next_2(t1a0); // in4 circuit_inputs = circuit_inputs.next_2(t1a1); // in5 circuit_inputs = circuit_inputs.next_2(xc0b1a0); // in6 circuit_inputs = circuit_inputs.next_2(xc0b1a1); // in7 circuit_inputs = circuit_inputs.next_2(xc0b2a0); // in8 circuit_inputs = circuit_inputs.next_2(xc0b2a1); // in9 circuit_inputs = circuit_inputs.next_2(xc1b0a0); // in10 circuit_inputs = circuit_inputs.next_2(xc1b0a1); // in11 circuit_inputs = circuit_inputs.next_2(xc1b2a0); // in12 circuit_inputs = circuit_inputs.next_2(xc1b2a1); // in13 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let zc0b0a0: u384 = outputs.get_output(t43); let zc0b0a1: u384 = outputs.get_output(t42); let zc1b1a0: u384 = outputs.get_output(t9); let zc1b1a1: u384 = outputs.get_output(t12); return (zc0b0a0, zc0b0a1, zc1b1a0, zc1b1a1); } #[inline(always)] pub fn run_BLS12_381_E12T_DECOMP_KARABINA_I_NZ_circuit( xc0b1a0: u384, xc0b1a1: u384, xc0b2a0: u384, xc0b2a1: u384, xc1b0a0: u384, xc1b0a1: u384, xc1b2a0: u384, xc1b2a1: u384, ) -> (u384, u384, u384, u384) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7) = (CE::> {}, CE::> {}); let t0 = circuit_add(in0, in1); let t1 = circuit_sub(in0, in1); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in0, in1); let t4 = circuit_add(t3, t3); let t5 = circuit_sub(t2, in2); // Fp2 sub coeff 0/1 let t6 = circuit_sub(t4, in3); // Fp2 sub coeff 1/1 let t7 = circuit_add(t5, t5); // Fp2 add coeff 0/1 let t8 = circuit_add(t6, t6); // Fp2 add coeff 1/1 let t9 = circuit_add(t7, t2); // Fp2 add coeff 0/1 let t10 = circuit_add(t8, t4); // Fp2 add coeff 1/1 let t11 = circuit_add(in6, in7); let t12 = circuit_sub(in6, in7); let t13 = circuit_mul(t11, t12); let t14 = circuit_mul(in6, in7); let t15 = circuit_add(t14, t14); let t16 = circuit_add(t13, t15); let t17 = circuit_add(t16, t16); let t18 = circuit_sub(t13, t15); let t19 = circuit_sub(t17, t13); let t20 = circuit_sub(t19, t15); let t21 = circuit_add(t18, t9); // Fp2 add coeff 0/1 let t22 = circuit_add(t20, t10); // Fp2 add coeff 1/1 let t23 = circuit_add(in4, in4); // Fp2 add coeff 0/1 let t24 = circuit_add(in5, in5); // Fp2 add coeff 1/1 let t25 = circuit_add(t23, t23); // Fp2 add coeff 0/1 let t26 = circuit_add(t24, t24); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t21, t22, t25, t26).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(xc0b1a0); // in0 circuit_inputs = circuit_inputs.next_2(xc0b1a1); // in1 circuit_inputs = circuit_inputs.next_2(xc0b2a0); // in2 circuit_inputs = circuit_inputs.next_2(xc0b2a1); // in3 circuit_inputs = circuit_inputs.next_2(xc1b0a0); // in4 circuit_inputs = circuit_inputs.next_2(xc1b0a1); // in5 circuit_inputs = circuit_inputs.next_2(xc1b2a0); // in6 circuit_inputs = circuit_inputs.next_2(xc1b2a1); // in7 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let t0a0: u384 = outputs.get_output(t21); let t0a1: u384 = outputs.get_output(t22); let t1a0: u384 = outputs.get_output(t25); let t1a1: u384 = outputs.get_output(t26); return (t0a0, t0a1, t1a0, t1a1); } #[inline(always)] pub fn run_BLS12_381_E12T_DECOMP_KARABINA_I_Z_circuit( xc0b1a0: u384, xc0b1a1: u384, xc1b2a0: u384, xc1b2a1: u384, ) -> (u384, u384) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let in3 = CE::> {}; let t0 = circuit_mul(in0, in2); // Fp2 mul start let t1 = circuit_mul(in1, in3); let t2 = circuit_sub(t0, t1); // Fp2 mul real part end let t3 = circuit_mul(in0, in3); let t4 = circuit_mul(in1, in2); let t5 = circuit_add(t3, t4); // Fp2 mul imag part end let t6 = circuit_add(t2, t2); // Fp2 add coeff 0/1 let t7 = circuit_add(t5, t5); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t6, t7).new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(xc0b1a0); // in0 circuit_inputs = circuit_inputs.next_2(xc0b1a1); // in1 circuit_inputs = circuit_inputs.next_2(xc1b2a0); // in2 circuit_inputs = circuit_inputs.next_2(xc1b2a1); // in3 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res0: u384 = outputs.get_output(t6); let res1: u384 = outputs.get_output(t7); return (res0, res1); } #[inline(always)] pub fn run_BLS12_381_E12T_FROBENIUS_CUBE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x1 let in2 = CE::> {}; // -0x1 % p let in3 = CE::< CI<3>, > {}; // 0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2 let in4 = CE::< CI<4>, > {}; // 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09 // INPUT stack let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in6); let t1 = circuit_add(in5, in0); let t2 = circuit_sub(in0, in8); let t3 = circuit_sub(in0, in10); let t4 = circuit_sub(in0, in12); let t5 = circuit_sub(in0, in14); let t6 = circuit_sub(in0, in16); let t7 = circuit_mul(in0, in7); // Fp2 mul start let t8 = circuit_mul(in1, t2); let t9 = circuit_sub(t7, t8); // Fp2 mul real part end let t10 = circuit_mul(in0, t2); let t11 = circuit_mul(in1, in7); let t12 = circuit_add(t10, t11); // Fp2 mul imag part end let t13 = circuit_mul(in2, in9); let t14 = circuit_mul(in2, t3); let t15 = circuit_mul(in3, in11); // Fp2 mul start let t16 = circuit_mul(in4, t4); let t17 = circuit_sub(t15, t16); // Fp2 mul real part end let t18 = circuit_mul(in3, t4); let t19 = circuit_mul(in4, in11); let t20 = circuit_add(t18, t19); // Fp2 mul imag part end let t21 = circuit_mul(in3, in13); // Fp2 mul start let t22 = circuit_mul(in3, t5); let t23 = circuit_sub(t21, t22); // Fp2 mul real part end let t24 = circuit_mul(in3, t5); let t25 = circuit_mul(in3, in13); let t26 = circuit_add(t24, t25); // Fp2 mul imag part end let t27 = circuit_mul(in4, in15); // Fp2 mul start let t28 = circuit_mul(in3, t6); let t29 = circuit_sub(t27, t28); // Fp2 mul real part end let t30 = circuit_mul(in4, t6); let t31 = circuit_mul(in3, in15); let t32 = circuit_add(t30, t31); // Fp2 mul imag part end let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t1, t0, t9, t12, t13, t14, t17, t20, t23, t26, t29, t32).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs .next_2( [ 0xb153ffffb9feffffffffaaaa, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ); // in2 circuit_inputs = circuit_inputs .next_2( [ 0x3e67fa0af1ee7b04121bdea2, 0xef396489f61eb45e304466cf, 0xd77a2cd91c3dedd930b1cf60, 0x135203e60180a68ee2e9c448, ], ); // in3 circuit_inputs = circuit_inputs .next_2( [ 0x72ec05f4c81084fbede3cc09, 0x77f76e17009241c5ee67992f, 0x6bd17ffe48395dabc2d3435e, 0x6af0e0437ff400b6831e36d, ], ); // in4 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in5 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in6 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in7 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in8 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in9 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in10 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in12 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in13 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in14 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in15 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in16 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t1), c0b0a1: outputs.get_output(t0), c0b1a0: outputs.get_output(t9), c0b1a1: outputs.get_output(t12), c0b2a0: outputs.get_output(t13), c0b2a1: outputs.get_output(t14), c1b0a0: outputs.get_output(t17), c1b0a1: outputs.get_output(t20), c1b1a0: outputs.get_output(t23), c1b1a1: outputs.get_output(t26), c1b2a0: outputs.get_output(t29), c1b2a1: outputs.get_output(t32), }; return (res,); } #[inline(always)] pub fn run_BLS12_381_E12T_FROBENIUS_SQUARE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::< CI<1>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe let in2 = CE::< CI<2>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac let in3 = CE::< CI<3>, > {}; // 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff let in4 = CE::> {}; // -0x1 % p let in5 = CE::< CI<5>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad // INPUT stack let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in6, in0); let t1 = circuit_add(in7, in0); let t2 = circuit_mul(in1, in8); let t3 = circuit_mul(in1, in9); let t4 = circuit_mul(in2, in10); let t5 = circuit_mul(in2, in11); let t6 = circuit_mul(in3, in12); let t7 = circuit_mul(in3, in13); let t8 = circuit_mul(in4, in14); let t9 = circuit_mul(in4, in15); let t10 = circuit_mul(in5, in16); let t11 = circuit_mul(in5, in17); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [ 0x620a00022e01fffffffefffe, 0xddb3a93be6f89688de17d813, 0xdf76ce51ba69c6076a0f77ea, 0x5f19672f, ], ); // in1 circuit_inputs = circuit_inputs .next_2( [ 0x4f49fffd8bfd00000000aaac, 0x897d29650fb85f9b409427eb, 0x63d4de85aa0d857d89759ad4, 0x1a0111ea397fe699ec024086, ], ); // in2 circuit_inputs = circuit_inputs .next_2( [ 0x620a00022e01fffffffeffff, 0xddb3a93be6f89688de17d813, 0xdf76ce51ba69c6076a0f77ea, 0x5f19672f, ], ); // in3 circuit_inputs = circuit_inputs .next_2( [ 0xb153ffffb9feffffffffaaaa, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], ); // in4 circuit_inputs = circuit_inputs .next_2( [ 0x4f49fffd8bfd00000000aaad, 0x897d29650fb85f9b409427eb, 0x63d4de85aa0d857d89759ad4, 0x1a0111ea397fe699ec024086, ], ); // in5 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in6 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in7 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in8 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in9 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in10 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in12 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in13 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in14 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in15 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in16 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in17 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t0), c0b0a1: outputs.get_output(t1), c0b1a0: outputs.get_output(t2), c0b1a1: outputs.get_output(t3), c0b2a0: outputs.get_output(t4), c0b2a1: outputs.get_output(t5), c1b0a0: outputs.get_output(t6), c1b0a1: outputs.get_output(t7), c1b1a0: outputs.get_output(t8), c1b1a1: outputs.get_output(t9), c1b2a0: outputs.get_output(t10), c1b2a1: outputs.get_output(t11), }; return (res,); } #[inline(always)] pub fn run_BLS12_381_E12T_FROBENIUS_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::< CI<1>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac let in2 = CE::< CI<2>, > {}; // 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad let in3 = CE::< CI<3>, > {}; // 0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8 let in4 = CE::< CI<4>, > {}; // 0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3 let in5 = CE::< CI<5>, > {}; // 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09 let in6 = CE::< CI<6>, > {}; // 0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116 let in7 = CE::< CI<7>, > {}; // 0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995 // INPUT stack let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in9); let t1 = circuit_add(in8, in0); let t2 = circuit_sub(in0, in11); let t3 = circuit_sub(in0, in13); let t4 = circuit_sub(in0, in15); let t5 = circuit_sub(in0, in17); let t6 = circuit_sub(in0, in19); let t7 = circuit_mul(in0, in10); // Fp2 mul start let t8 = circuit_mul(in1, t2); let t9 = circuit_sub(t7, t8); // Fp2 mul real part end let t10 = circuit_mul(in0, t2); let t11 = circuit_mul(in1, in10); let t12 = circuit_add(t10, t11); // Fp2 mul imag part end let t13 = circuit_mul(in2, in12); let t14 = circuit_mul(in2, t3); let t15 = circuit_mul(in3, in14); // Fp2 mul start let t16 = circuit_mul(in4, t4); let t17 = circuit_sub(t15, t16); // Fp2 mul real part end let t18 = circuit_mul(in3, t4); let t19 = circuit_mul(in4, in14); let t20 = circuit_add(t18, t19); // Fp2 mul imag part end let t21 = circuit_mul(in5, in16); // Fp2 mul start let t22 = circuit_mul(in5, t5); let t23 = circuit_sub(t21, t22); // Fp2 mul real part end let t24 = circuit_mul(in5, t5); let t25 = circuit_mul(in5, in16); let t26 = circuit_add(t24, t25); // Fp2 mul imag part end let t27 = circuit_mul(in6, in18); // Fp2 mul start let t28 = circuit_mul(in7, t6); let t29 = circuit_sub(t27, t28); // Fp2 mul real part end let t30 = circuit_mul(in6, t6); let t31 = circuit_mul(in7, in18); let t32 = circuit_add(t30, t31); // Fp2 mul imag part end let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = (t1, t0, t9, t12, t13, t14, t17, t20, t23, t26, t29, t32).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(E12T_FROBENIUS_BLS12_381_CONSTANTS.span()); // in0 - in7 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in8 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in9 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in10 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in11 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in12 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in13 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in14 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in15 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in16 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in17 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in18 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in19 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t1), c0b0a1: outputs.get_output(t0), c0b1a0: outputs.get_output(t9), c0b1a1: outputs.get_output(t12), c0b2a0: outputs.get_output(t13), c0b2a1: outputs.get_output(t14), c1b0a0: outputs.get_output(t17), c1b0a1: outputs.get_output(t20), c1b1a0: outputs.get_output(t23), c1b1a1: outputs.get_output(t26), c1b2a0: outputs.get_output(t29), c1b2a1: outputs.get_output(t32), }; return (res,); } const E12T_FROBENIUS_BLS12_381_CONSTANTS: [u384; 8] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x4f49fffd8bfd00000000aaac, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0x4f49fffd8bfd00000000aaad, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, u384 { limb0: 0x63e7813d8d0775ed92235fb8, limb1: 0x7b2443d784bab9c4f67ea53d, limb2: 0x202c0d1f0fd603fd3cbd5f4f, limb3: 0x1904d3bf02bb0667c231beb4, }, u384 { limb0: 0x4d6c7ec22cf78a126ddc4af3, limb1: 0xec0c8ec971f63c5f282d5ac1, limb2: 0x231f9fb854a14787b6c7b36f, limb3: 0xfc3e2b36c4e03288e9e902, }, u384 { limb0: 0x72ec05f4c81084fbede3cc09, limb1: 0x77f76e17009241c5ee67992f, limb2: 0x6bd17ffe48395dabc2d3435e, limb3: 0x6af0e0437ff400b6831e36d, }, u384 { limb0: 0x257f87329b18fae980078116, limb1: 0x8beadf4d8e9c0566c63a3e6e, limb2: 0x48b1e045f39816240c0b8fee, limb3: 0x5b2cfd9013a5fd8df47fa6b, }, u384 { limb0: 0x8bd478cd1ee605167ff82995, limb1: 0xdb45f3536814f0bd5871c190, limb2: 0xfa99cc9170df3560e77982d0, limb3: 0x144e4211384586c16bd3ad4a, }, ]; #[inline(always)] pub fn run_BLS12_381_E12T_INVERSE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in1, in3); // Fp2 mul start let t1 = circuit_mul(in2, in4); let t2 = circuit_sub(t0, t1); // Fp2 mul real part end let t3 = circuit_mul(in1, in4); let t4 = circuit_mul(in2, in3); let t5 = circuit_add(t3, t4); // Fp2 mul imag part end let t6 = circuit_add(t2, t2); // Fp2 add coeff 0/1 let t7 = circuit_add(t5, t5); // Fp2 add coeff 1/1 let t8 = circuit_add(in5, in6); let t9 = circuit_sub(in5, in6); let t10 = circuit_mul(t8, t9); let t11 = circuit_mul(in5, in6); let t12 = circuit_add(t11, t11); let t13 = circuit_add(t10, t12); let t14 = circuit_add(t13, t13); let t15 = circuit_sub(t10, t12); let t16 = circuit_sub(t14, t10); let t17 = circuit_sub(t16, t12); let t18 = circuit_add(t15, t6); // Fp2 add coeff 0/1 let t19 = circuit_add(t17, t7); // Fp2 add coeff 1/1 let t20 = circuit_sub(t6, t10); // Fp2 sub coeff 0/1 let t21 = circuit_sub(t7, t12); // Fp2 sub coeff 1/1 let t22 = circuit_add(in1, in2); let t23 = circuit_sub(in1, in2); let t24 = circuit_mul(t22, t23); let t25 = circuit_mul(in1, in2); let t26 = circuit_add(t25, t25); let t27 = circuit_sub(in1, in3); // Fp2 sub coeff 0/1 let t28 = circuit_sub(in2, in4); // Fp2 sub coeff 1/1 let t29 = circuit_add(t27, in5); // Fp2 add coeff 0/1 let t30 = circuit_add(t28, in6); // Fp2 add coeff 1/1 let t31 = circuit_mul(in3, in5); // Fp2 mul start let t32 = circuit_mul(in4, in6); let t33 = circuit_sub(t31, t32); // Fp2 mul real part end let t34 = circuit_mul(in3, in6); let t35 = circuit_mul(in4, in5); let t36 = circuit_add(t34, t35); // Fp2 mul imag part end let t37 = circuit_add(t33, t33); // Fp2 add coeff 0/1 let t38 = circuit_add(t36, t36); // Fp2 add coeff 1/1 let t39 = circuit_add(t29, t30); let t40 = circuit_sub(t29, t30); let t41 = circuit_mul(t39, t40); let t42 = circuit_mul(t29, t30); let t43 = circuit_add(t42, t42); let t44 = circuit_add(t37, t38); let t45 = circuit_add(t44, t44); let t46 = circuit_sub(t37, t38); let t47 = circuit_sub(t45, t37); let t48 = circuit_sub(t47, t38); let t49 = circuit_add(t46, t24); // Fp2 add coeff 0/1 let t50 = circuit_add(t48, t26); // Fp2 add coeff 1/1 let t51 = circuit_add(t20, t41); // Fp2 add coeff 0/1 let t52 = circuit_add(t21, t43); // Fp2 add coeff 1/1 let t53 = circuit_add(t51, t37); // Fp2 add coeff 0/1 let t54 = circuit_add(t52, t38); // Fp2 add coeff 1/1 let t55 = circuit_sub(t53, t24); // Fp2 sub coeff 0/1 let t56 = circuit_sub(t54, t26); // Fp2 sub coeff 1/1 let t57 = circuit_mul(in7, in9); // Fp2 mul start let t58 = circuit_mul(in8, in10); let t59 = circuit_sub(t57, t58); // Fp2 mul real part end let t60 = circuit_mul(in7, in10); let t61 = circuit_mul(in8, in9); let t62 = circuit_add(t60, t61); // Fp2 mul imag part end let t63 = circuit_add(t59, t59); // Fp2 add coeff 0/1 let t64 = circuit_add(t62, t62); // Fp2 add coeff 1/1 let t65 = circuit_add(in11, in12); let t66 = circuit_sub(in11, in12); let t67 = circuit_mul(t65, t66); let t68 = circuit_mul(in11, in12); let t69 = circuit_add(t68, t68); let t70 = circuit_add(t67, t69); let t71 = circuit_add(t70, t70); let t72 = circuit_sub(t67, t69); let t73 = circuit_sub(t71, t67); let t74 = circuit_sub(t73, t69); let t75 = circuit_add(t72, t63); // Fp2 add coeff 0/1 let t76 = circuit_add(t74, t64); // Fp2 add coeff 1/1 let t77 = circuit_sub(t63, t67); // Fp2 sub coeff 0/1 let t78 = circuit_sub(t64, t69); // Fp2 sub coeff 1/1 let t79 = circuit_add(in7, in8); let t80 = circuit_sub(in7, in8); let t81 = circuit_mul(t79, t80); let t82 = circuit_mul(in7, in8); let t83 = circuit_add(t82, t82); let t84 = circuit_sub(in7, in9); // Fp2 sub coeff 0/1 let t85 = circuit_sub(in8, in10); // Fp2 sub coeff 1/1 let t86 = circuit_add(t84, in11); // Fp2 add coeff 0/1 let t87 = circuit_add(t85, in12); // Fp2 add coeff 1/1 let t88 = circuit_mul(in9, in11); // Fp2 mul start let t89 = circuit_mul(in10, in12); let t90 = circuit_sub(t88, t89); // Fp2 mul real part end let t91 = circuit_mul(in9, in12); let t92 = circuit_mul(in10, in11); let t93 = circuit_add(t91, t92); // Fp2 mul imag part end let t94 = circuit_add(t90, t90); // Fp2 add coeff 0/1 let t95 = circuit_add(t93, t93); // Fp2 add coeff 1/1 let t96 = circuit_add(t86, t87); let t97 = circuit_sub(t86, t87); let t98 = circuit_mul(t96, t97); let t99 = circuit_mul(t86, t87); let t100 = circuit_add(t99, t99); let t101 = circuit_add(t94, t95); let t102 = circuit_add(t101, t101); let t103 = circuit_sub(t94, t95); let t104 = circuit_sub(t102, t94); let t105 = circuit_sub(t104, t95); let t106 = circuit_add(t103, t81); // Fp2 add coeff 0/1 let t107 = circuit_add(t105, t83); // Fp2 add coeff 1/1 let t108 = circuit_add(t77, t98); // Fp2 add coeff 0/1 let t109 = circuit_add(t78, t100); // Fp2 add coeff 1/1 let t110 = circuit_add(t108, t94); // Fp2 add coeff 0/1 let t111 = circuit_add(t109, t95); // Fp2 add coeff 1/1 let t112 = circuit_sub(t110, t81); // Fp2 sub coeff 0/1 let t113 = circuit_sub(t111, t83); // Fp2 sub coeff 1/1 let t114 = circuit_add(t112, t113); let t115 = circuit_add(t114, t114); let t116 = circuit_sub(t112, t113); let t117 = circuit_sub(t115, t112); let t118 = circuit_sub(t117, t113); let t119 = circuit_sub(t49, t116); // Fp6 sub coeff 0/5 let t120 = circuit_sub(t50, t118); // Fp6 sub coeff 1/5 let t121 = circuit_sub(t18, t106); // Fp6 sub coeff 2/5 let t122 = circuit_sub(t19, t107); // Fp6 sub coeff 3/5 let t123 = circuit_sub(t55, t75); // Fp6 sub coeff 4/5 let t124 = circuit_sub(t56, t76); // Fp6 sub coeff 5/5 let t125 = circuit_add(t119, t120); let t126 = circuit_sub(t119, t120); let t127 = circuit_mul(t125, t126); let t128 = circuit_mul(t119, t120); let t129 = circuit_add(t128, t128); let t130 = circuit_add(t121, t122); let t131 = circuit_sub(t121, t122); let t132 = circuit_mul(t130, t131); let t133 = circuit_mul(t121, t122); let t134 = circuit_add(t133, t133); let t135 = circuit_add(t123, t124); let t136 = circuit_sub(t123, t124); let t137 = circuit_mul(t135, t136); let t138 = circuit_mul(t123, t124); let t139 = circuit_add(t138, t138); let t140 = circuit_mul(t119, t121); // Fp2 mul start let t141 = circuit_mul(t120, t122); let t142 = circuit_sub(t140, t141); // Fp2 mul real part end let t143 = circuit_mul(t119, t122); let t144 = circuit_mul(t120, t121); let t145 = circuit_add(t143, t144); // Fp2 mul imag part end let t146 = circuit_mul(t119, t123); // Fp2 mul start let t147 = circuit_mul(t120, t124); let t148 = circuit_sub(t146, t147); // Fp2 mul real part end let t149 = circuit_mul(t119, t124); let t150 = circuit_mul(t120, t123); let t151 = circuit_add(t149, t150); // Fp2 mul imag part end let t152 = circuit_mul(t121, t123); // Fp2 mul start let t153 = circuit_mul(t122, t124); let t154 = circuit_sub(t152, t153); // Fp2 mul real part end let t155 = circuit_mul(t121, t124); let t156 = circuit_mul(t122, t123); let t157 = circuit_add(t155, t156); // Fp2 mul imag part end let t158 = circuit_add(t154, t157); let t159 = circuit_add(t158, t158); let t160 = circuit_sub(t154, t157); let t161 = circuit_sub(t159, t154); let t162 = circuit_sub(t161, t157); let t163 = circuit_sub(in0, t160); // Fp2 neg coeff 0/1 let t164 = circuit_sub(in0, t162); // Fp2 neg coeff 1/1 let t165 = circuit_add(t163, t127); // Fp2 add coeff 0/1 let t166 = circuit_add(t164, t129); // Fp2 add coeff 1/1 let t167 = circuit_add(t137, t139); let t168 = circuit_add(t167, t167); let t169 = circuit_sub(t137, t139); let t170 = circuit_sub(t168, t137); let t171 = circuit_sub(t170, t139); let t172 = circuit_sub(t169, t142); // Fp2 sub coeff 0/1 let t173 = circuit_sub(t171, t145); // Fp2 sub coeff 1/1 let t174 = circuit_sub(t132, t148); // Fp2 sub coeff 0/1 let t175 = circuit_sub(t134, t151); // Fp2 sub coeff 1/1 let t176 = circuit_mul(t119, t165); // Fp2 mul start let t177 = circuit_mul(t120, t166); let t178 = circuit_sub(t176, t177); // Fp2 mul real part end let t179 = circuit_mul(t119, t166); let t180 = circuit_mul(t120, t165); let t181 = circuit_add(t179, t180); // Fp2 mul imag part end let t182 = circuit_mul(t123, t172); // Fp2 mul start let t183 = circuit_mul(t124, t173); let t184 = circuit_sub(t182, t183); // Fp2 mul real part end let t185 = circuit_mul(t123, t173); let t186 = circuit_mul(t124, t172); let t187 = circuit_add(t185, t186); // Fp2 mul imag part end let t188 = circuit_mul(t121, t174); // Fp2 mul start let t189 = circuit_mul(t122, t175); let t190 = circuit_sub(t188, t189); // Fp2 mul real part end let t191 = circuit_mul(t121, t175); let t192 = circuit_mul(t122, t174); let t193 = circuit_add(t191, t192); // Fp2 mul imag part end let t194 = circuit_add(t184, t190); // Fp2 add coeff 0/1 let t195 = circuit_add(t187, t193); // Fp2 add coeff 1/1 let t196 = circuit_add(t194, t195); let t197 = circuit_add(t196, t196); let t198 = circuit_sub(t194, t195); let t199 = circuit_sub(t197, t194); let t200 = circuit_sub(t199, t195); let t201 = circuit_add(t178, t198); // Fp2 add coeff 0/1 let t202 = circuit_add(t181, t200); // Fp2 add coeff 1/1 let t203 = circuit_mul(t201, t201); // Fp2 Inv start let t204 = circuit_mul(t202, t202); let t205 = circuit_add(t203, t204); let t206 = circuit_inverse(t205); let t207 = circuit_mul(t201, t206); // Fp2 Inv real part end let t208 = circuit_mul(t202, t206); let t209 = circuit_sub(in0, t208); // Fp2 Inv imag part end let t210 = circuit_mul(t165, t207); // Fp2 mul start let t211 = circuit_mul(t166, t209); let t212 = circuit_sub(t210, t211); // Fp2 mul real part end let t213 = circuit_mul(t165, t209); let t214 = circuit_mul(t166, t207); let t215 = circuit_add(t213, t214); // Fp2 mul imag part end let t216 = circuit_mul(t172, t207); // Fp2 mul start let t217 = circuit_mul(t173, t209); let t218 = circuit_sub(t216, t217); // Fp2 mul real part end let t219 = circuit_mul(t172, t209); let t220 = circuit_mul(t173, t207); let t221 = circuit_add(t219, t220); // Fp2 mul imag part end let t222 = circuit_mul(t174, t207); // Fp2 mul start let t223 = circuit_mul(t175, t209); let t224 = circuit_sub(t222, t223); // Fp2 mul real part end let t225 = circuit_mul(t174, t209); let t226 = circuit_mul(t175, t207); let t227 = circuit_add(t225, t226); // Fp2 mul imag part end let t228 = circuit_mul(in1, t212); // Fp2 mul start let t229 = circuit_mul(in2, t215); let t230 = circuit_sub(t228, t229); // Fp2 mul real part end let t231 = circuit_mul(in1, t215); let t232 = circuit_mul(in2, t212); let t233 = circuit_add(t231, t232); // Fp2 mul imag part end let t234 = circuit_mul(in3, t218); // Fp2 mul start let t235 = circuit_mul(in4, t221); let t236 = circuit_sub(t234, t235); // Fp2 mul real part end let t237 = circuit_mul(in3, t221); let t238 = circuit_mul(in4, t218); let t239 = circuit_add(t237, t238); // Fp2 mul imag part end let t240 = circuit_mul(in5, t224); // Fp2 mul start let t241 = circuit_mul(in6, t227); let t242 = circuit_sub(t240, t241); // Fp2 mul real part end let t243 = circuit_mul(in5, t227); let t244 = circuit_mul(in6, t224); let t245 = circuit_add(t243, t244); // Fp2 mul imag part end let t246 = circuit_add(in3, in5); // Fp2 add coeff 0/1 let t247 = circuit_add(in4, in6); // Fp2 add coeff 1/1 let t248 = circuit_add(t218, t224); // Fp2 add coeff 0/1 let t249 = circuit_add(t221, t227); // Fp2 add coeff 1/1 let t250 = circuit_mul(t246, t248); // Fp2 mul start let t251 = circuit_mul(t247, t249); let t252 = circuit_sub(t250, t251); // Fp2 mul real part end let t253 = circuit_mul(t246, t249); let t254 = circuit_mul(t247, t248); let t255 = circuit_add(t253, t254); // Fp2 mul imag part end let t256 = circuit_sub(t252, t236); // Fp2 sub coeff 0/1 let t257 = circuit_sub(t255, t239); // Fp2 sub coeff 1/1 let t258 = circuit_sub(t256, t242); // Fp2 sub coeff 0/1 let t259 = circuit_sub(t257, t245); // Fp2 sub coeff 1/1 let t260 = circuit_add(t258, t259); let t261 = circuit_add(t260, t260); let t262 = circuit_sub(t258, t259); let t263 = circuit_sub(t261, t258); let t264 = circuit_sub(t263, t259); let t265 = circuit_add(t262, t230); // Fp2 add coeff 0/1 let t266 = circuit_add(t264, t233); // Fp2 add coeff 1/1 let t267 = circuit_add(in1, in3); // Fp2 add coeff 0/1 let t268 = circuit_add(in2, in4); // Fp2 add coeff 1/1 let t269 = circuit_add(t212, t218); // Fp2 add coeff 0/1 let t270 = circuit_add(t215, t221); // Fp2 add coeff 1/1 let t271 = circuit_mul(t267, t269); // Fp2 mul start let t272 = circuit_mul(t268, t270); let t273 = circuit_sub(t271, t272); // Fp2 mul real part end let t274 = circuit_mul(t267, t270); let t275 = circuit_mul(t268, t269); let t276 = circuit_add(t274, t275); // Fp2 mul imag part end let t277 = circuit_sub(t273, t230); // Fp2 sub coeff 0/1 let t278 = circuit_sub(t276, t233); // Fp2 sub coeff 1/1 let t279 = circuit_sub(t277, t236); // Fp2 sub coeff 0/1 let t280 = circuit_sub(t278, t239); // Fp2 sub coeff 1/1 let t281 = circuit_add(t242, t245); let t282 = circuit_add(t281, t281); let t283 = circuit_sub(t242, t245); let t284 = circuit_sub(t282, t242); let t285 = circuit_sub(t284, t245); let t286 = circuit_add(t279, t283); // Fp2 add coeff 0/1 let t287 = circuit_add(t280, t285); // Fp2 add coeff 1/1 let t288 = circuit_add(in1, in5); // Fp2 add coeff 0/1 let t289 = circuit_add(in2, in6); // Fp2 add coeff 1/1 let t290 = circuit_add(t212, t224); // Fp2 add coeff 0/1 let t291 = circuit_add(t215, t227); // Fp2 add coeff 1/1 let t292 = circuit_mul(t290, t288); // Fp2 mul start let t293 = circuit_mul(t291, t289); let t294 = circuit_sub(t292, t293); // Fp2 mul real part end let t295 = circuit_mul(t290, t289); let t296 = circuit_mul(t291, t288); let t297 = circuit_add(t295, t296); // Fp2 mul imag part end let t298 = circuit_sub(t294, t230); // Fp2 sub coeff 0/1 let t299 = circuit_sub(t297, t233); // Fp2 sub coeff 1/1 let t300 = circuit_sub(t298, t242); // Fp2 sub coeff 0/1 let t301 = circuit_sub(t299, t245); // Fp2 sub coeff 1/1 let t302 = circuit_add(t300, t236); // Fp2 add coeff 0/1 let t303 = circuit_add(t301, t239); // Fp2 add coeff 1/1 let t304 = circuit_mul(in7, t212); // Fp2 mul start let t305 = circuit_mul(in8, t215); let t306 = circuit_sub(t304, t305); // Fp2 mul real part end let t307 = circuit_mul(in7, t215); let t308 = circuit_mul(in8, t212); let t309 = circuit_add(t307, t308); // Fp2 mul imag part end let t310 = circuit_mul(in9, t218); // Fp2 mul start let t311 = circuit_mul(in10, t221); let t312 = circuit_sub(t310, t311); // Fp2 mul real part end let t313 = circuit_mul(in9, t221); let t314 = circuit_mul(in10, t218); let t315 = circuit_add(t313, t314); // Fp2 mul imag part end let t316 = circuit_mul(in11, t224); // Fp2 mul start let t317 = circuit_mul(in12, t227); let t318 = circuit_sub(t316, t317); // Fp2 mul real part end let t319 = circuit_mul(in11, t227); let t320 = circuit_mul(in12, t224); let t321 = circuit_add(t319, t320); // Fp2 mul imag part end let t322 = circuit_add(in9, in11); // Fp2 add coeff 0/1 let t323 = circuit_add(in10, in12); // Fp2 add coeff 1/1 let t324 = circuit_add(t218, t224); // Fp2 add coeff 0/1 let t325 = circuit_add(t221, t227); // Fp2 add coeff 1/1 let t326 = circuit_mul(t322, t324); // Fp2 mul start let t327 = circuit_mul(t323, t325); let t328 = circuit_sub(t326, t327); // Fp2 mul real part end let t329 = circuit_mul(t322, t325); let t330 = circuit_mul(t323, t324); let t331 = circuit_add(t329, t330); // Fp2 mul imag part end let t332 = circuit_sub(t328, t312); // Fp2 sub coeff 0/1 let t333 = circuit_sub(t331, t315); // Fp2 sub coeff 1/1 let t334 = circuit_sub(t332, t318); // Fp2 sub coeff 0/1 let t335 = circuit_sub(t333, t321); // Fp2 sub coeff 1/1 let t336 = circuit_add(t334, t335); let t337 = circuit_add(t336, t336); let t338 = circuit_sub(t334, t335); let t339 = circuit_sub(t337, t334); let t340 = circuit_sub(t339, t335); let t341 = circuit_add(t338, t306); // Fp2 add coeff 0/1 let t342 = circuit_add(t340, t309); // Fp2 add coeff 1/1 let t343 = circuit_add(in7, in9); // Fp2 add coeff 0/1 let t344 = circuit_add(in8, in10); // Fp2 add coeff 1/1 let t345 = circuit_add(t212, t218); // Fp2 add coeff 0/1 let t346 = circuit_add(t215, t221); // Fp2 add coeff 1/1 let t347 = circuit_mul(t343, t345); // Fp2 mul start let t348 = circuit_mul(t344, t346); let t349 = circuit_sub(t347, t348); // Fp2 mul real part end let t350 = circuit_mul(t343, t346); let t351 = circuit_mul(t344, t345); let t352 = circuit_add(t350, t351); // Fp2 mul imag part end let t353 = circuit_sub(t349, t306); // Fp2 sub coeff 0/1 let t354 = circuit_sub(t352, t309); // Fp2 sub coeff 1/1 let t355 = circuit_sub(t353, t312); // Fp2 sub coeff 0/1 let t356 = circuit_sub(t354, t315); // Fp2 sub coeff 1/1 let t357 = circuit_add(t318, t321); let t358 = circuit_add(t357, t357); let t359 = circuit_sub(t318, t321); let t360 = circuit_sub(t358, t318); let t361 = circuit_sub(t360, t321); let t362 = circuit_add(t355, t359); // Fp2 add coeff 0/1 let t363 = circuit_add(t356, t361); // Fp2 add coeff 1/1 let t364 = circuit_add(in7, in11); // Fp2 add coeff 0/1 let t365 = circuit_add(in8, in12); // Fp2 add coeff 1/1 let t366 = circuit_add(t212, t224); // Fp2 add coeff 0/1 let t367 = circuit_add(t215, t227); // Fp2 add coeff 1/1 let t368 = circuit_mul(t366, t364); // Fp2 mul start let t369 = circuit_mul(t367, t365); let t370 = circuit_sub(t368, t369); // Fp2 mul real part end let t371 = circuit_mul(t366, t365); let t372 = circuit_mul(t367, t364); let t373 = circuit_add(t371, t372); // Fp2 mul imag part end let t374 = circuit_sub(t370, t306); // Fp2 sub coeff 0/1 let t375 = circuit_sub(t373, t309); // Fp2 sub coeff 1/1 let t376 = circuit_sub(t374, t318); // Fp2 sub coeff 0/1 let t377 = circuit_sub(t375, t321); // Fp2 sub coeff 1/1 let t378 = circuit_add(t376, t312); // Fp2 add coeff 0/1 let t379 = circuit_add(t377, t315); // Fp2 add coeff 1/1 let t380 = circuit_sub(in0, t341); // Fp6 neg coeff 0/5 let t381 = circuit_sub(in0, t342); // Fp6 neg coeff 1/5 let t382 = circuit_sub(in0, t362); // Fp6 neg coeff 2/5 let t383 = circuit_sub(in0, t363); // Fp6 neg coeff 3/5 let t384 = circuit_sub(in0, t378); // Fp6 neg coeff 4/5 let t385 = circuit_sub(in0, t379); // Fp6 neg coeff 5/5 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = ( t265, t266, t286, t287, t302, t303, t380, t381, t382, t383, t384, t385, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in1 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in2 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in3 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in4 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in5 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in6 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in7 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in8 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in9 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in10 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in12 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t265), c0b0a1: outputs.get_output(t266), c0b1a0: outputs.get_output(t286), c0b1a1: outputs.get_output(t287), c0b2a0: outputs.get_output(t302), c0b2a1: outputs.get_output(t303), c1b0a0: outputs.get_output(t380), c1b0a1: outputs.get_output(t381), c1b1a0: outputs.get_output(t382), c1b1a1: outputs.get_output(t383), c1b2a0: outputs.get_output(t384), c1b2a1: outputs.get_output(t385), }; return (res,); } #[inline(always)] pub fn run_BLS12_381_E12T_MUL_circuit(X: E12T, Y: E12T) -> (E12T,) { // INPUT stack let (in0, in1, in2) = (CE::> {}, CE::> {}, CE::> {}); let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in0, in6); // Fp6 add coeff 0/5 let t1 = circuit_add(in1, in7); // Fp6 add coeff 1/5 let t2 = circuit_add(in2, in8); // Fp6 add coeff 2/5 let t3 = circuit_add(in3, in9); // Fp6 add coeff 3/5 let t4 = circuit_add(in4, in10); // Fp6 add coeff 4/5 let t5 = circuit_add(in5, in11); // Fp6 add coeff 5/5 let t6 = circuit_add(in12, in18); // Fp6 add coeff 0/5 let t7 = circuit_add(in13, in19); // Fp6 add coeff 1/5 let t8 = circuit_add(in14, in20); // Fp6 add coeff 2/5 let t9 = circuit_add(in15, in21); // Fp6 add coeff 3/5 let t10 = circuit_add(in16, in22); // Fp6 add coeff 4/5 let t11 = circuit_add(in17, in23); // Fp6 add coeff 5/5 let t12 = circuit_mul(t0, t6); // Fp2 mul start let t13 = circuit_mul(t1, t7); let t14 = circuit_sub(t12, t13); // Fp2 mul real part end let t15 = circuit_mul(t0, t7); let t16 = circuit_mul(t1, t6); let t17 = circuit_add(t15, t16); // Fp2 mul imag part end let t18 = circuit_mul(t2, t8); // Fp2 mul start let t19 = circuit_mul(t3, t9); let t20 = circuit_sub(t18, t19); // Fp2 mul real part end let t21 = circuit_mul(t2, t9); let t22 = circuit_mul(t3, t8); let t23 = circuit_add(t21, t22); // Fp2 mul imag part end let t24 = circuit_mul(t4, t10); // Fp2 mul start let t25 = circuit_mul(t5, t11); let t26 = circuit_sub(t24, t25); // Fp2 mul real part end let t27 = circuit_mul(t4, t11); let t28 = circuit_mul(t5, t10); let t29 = circuit_add(t27, t28); // Fp2 mul imag part end let t30 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t31 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t32 = circuit_add(t8, t10); // Fp2 add coeff 0/1 let t33 = circuit_add(t9, t11); // Fp2 add coeff 1/1 let t34 = circuit_mul(t30, t32); // Fp2 mul start let t35 = circuit_mul(t31, t33); let t36 = circuit_sub(t34, t35); // Fp2 mul real part end let t37 = circuit_mul(t30, t33); let t38 = circuit_mul(t31, t32); let t39 = circuit_add(t37, t38); // Fp2 mul imag part end let t40 = circuit_sub(t36, t20); // Fp2 sub coeff 0/1 let t41 = circuit_sub(t39, t23); // Fp2 sub coeff 1/1 let t42 = circuit_sub(t40, t26); // Fp2 sub coeff 0/1 let t43 = circuit_sub(t41, t29); // Fp2 sub coeff 1/1 let t44 = circuit_add(t42, t43); let t45 = circuit_add(t44, t44); let t46 = circuit_sub(t42, t43); let t47 = circuit_sub(t45, t42); let t48 = circuit_sub(t47, t43); let t49 = circuit_add(t46, t14); // Fp2 add coeff 0/1 let t50 = circuit_add(t48, t17); // Fp2 add coeff 1/1 let t51 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t52 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t53 = circuit_add(t6, t8); // Fp2 add coeff 0/1 let t54 = circuit_add(t7, t9); // Fp2 add coeff 1/1 let t55 = circuit_mul(t51, t53); // Fp2 mul start let t56 = circuit_mul(t52, t54); let t57 = circuit_sub(t55, t56); // Fp2 mul real part end let t58 = circuit_mul(t51, t54); let t59 = circuit_mul(t52, t53); let t60 = circuit_add(t58, t59); // Fp2 mul imag part end let t61 = circuit_sub(t57, t14); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t60, t17); // Fp2 sub coeff 1/1 let t63 = circuit_sub(t61, t20); // Fp2 sub coeff 0/1 let t64 = circuit_sub(t62, t23); // Fp2 sub coeff 1/1 let t65 = circuit_add(t26, t29); let t66 = circuit_add(t65, t65); let t67 = circuit_sub(t26, t29); let t68 = circuit_sub(t66, t26); let t69 = circuit_sub(t68, t29); let t70 = circuit_add(t63, t67); // Fp2 add coeff 0/1 let t71 = circuit_add(t64, t69); // Fp2 add coeff 1/1 let t72 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t73 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t74 = circuit_add(t6, t10); // Fp2 add coeff 0/1 let t75 = circuit_add(t7, t11); // Fp2 add coeff 1/1 let t76 = circuit_mul(t74, t72); // Fp2 mul start let t77 = circuit_mul(t75, t73); let t78 = circuit_sub(t76, t77); // Fp2 mul real part end let t79 = circuit_mul(t74, t73); let t80 = circuit_mul(t75, t72); let t81 = circuit_add(t79, t80); // Fp2 mul imag part end let t82 = circuit_sub(t78, t14); // Fp2 sub coeff 0/1 let t83 = circuit_sub(t81, t17); // Fp2 sub coeff 1/1 let t84 = circuit_sub(t82, t26); // Fp2 sub coeff 0/1 let t85 = circuit_sub(t83, t29); // Fp2 sub coeff 1/1 let t86 = circuit_add(t84, t20); // Fp2 add coeff 0/1 let t87 = circuit_add(t85, t23); // Fp2 add coeff 1/1 let t88 = circuit_mul(in0, in12); // Fp2 mul start let t89 = circuit_mul(in1, in13); let t90 = circuit_sub(t88, t89); // Fp2 mul real part end let t91 = circuit_mul(in0, in13); let t92 = circuit_mul(in1, in12); let t93 = circuit_add(t91, t92); // Fp2 mul imag part end let t94 = circuit_mul(in2, in14); // Fp2 mul start let t95 = circuit_mul(in3, in15); let t96 = circuit_sub(t94, t95); // Fp2 mul real part end let t97 = circuit_mul(in2, in15); let t98 = circuit_mul(in3, in14); let t99 = circuit_add(t97, t98); // Fp2 mul imag part end let t100 = circuit_mul(in4, in16); // Fp2 mul start let t101 = circuit_mul(in5, in17); let t102 = circuit_sub(t100, t101); // Fp2 mul real part end let t103 = circuit_mul(in4, in17); let t104 = circuit_mul(in5, in16); let t105 = circuit_add(t103, t104); // Fp2 mul imag part end let t106 = circuit_add(in2, in4); // Fp2 add coeff 0/1 let t107 = circuit_add(in3, in5); // Fp2 add coeff 1/1 let t108 = circuit_add(in14, in16); // Fp2 add coeff 0/1 let t109 = circuit_add(in15, in17); // Fp2 add coeff 1/1 let t110 = circuit_mul(t106, t108); // Fp2 mul start let t111 = circuit_mul(t107, t109); let t112 = circuit_sub(t110, t111); // Fp2 mul real part end let t113 = circuit_mul(t106, t109); let t114 = circuit_mul(t107, t108); let t115 = circuit_add(t113, t114); // Fp2 mul imag part end let t116 = circuit_sub(t112, t96); // Fp2 sub coeff 0/1 let t117 = circuit_sub(t115, t99); // Fp2 sub coeff 1/1 let t118 = circuit_sub(t116, t102); // Fp2 sub coeff 0/1 let t119 = circuit_sub(t117, t105); // Fp2 sub coeff 1/1 let t120 = circuit_add(t118, t119); let t121 = circuit_add(t120, t120); let t122 = circuit_sub(t118, t119); let t123 = circuit_sub(t121, t118); let t124 = circuit_sub(t123, t119); let t125 = circuit_add(t122, t90); // Fp2 add coeff 0/1 let t126 = circuit_add(t124, t93); // Fp2 add coeff 1/1 let t127 = circuit_add(in0, in2); // Fp2 add coeff 0/1 let t128 = circuit_add(in1, in3); // Fp2 add coeff 1/1 let t129 = circuit_add(in12, in14); // Fp2 add coeff 0/1 let t130 = circuit_add(in13, in15); // Fp2 add coeff 1/1 let t131 = circuit_mul(t127, t129); // Fp2 mul start let t132 = circuit_mul(t128, t130); let t133 = circuit_sub(t131, t132); // Fp2 mul real part end let t134 = circuit_mul(t127, t130); let t135 = circuit_mul(t128, t129); let t136 = circuit_add(t134, t135); // Fp2 mul imag part end let t137 = circuit_sub(t133, t90); // Fp2 sub coeff 0/1 let t138 = circuit_sub(t136, t93); // Fp2 sub coeff 1/1 let t139 = circuit_sub(t137, t96); // Fp2 sub coeff 0/1 let t140 = circuit_sub(t138, t99); // Fp2 sub coeff 1/1 let t141 = circuit_add(t102, t105); let t142 = circuit_add(t141, t141); let t143 = circuit_sub(t102, t105); let t144 = circuit_sub(t142, t102); let t145 = circuit_sub(t144, t105); let t146 = circuit_add(t139, t143); // Fp2 add coeff 0/1 let t147 = circuit_add(t140, t145); // Fp2 add coeff 1/1 let t148 = circuit_add(in0, in4); // Fp2 add coeff 0/1 let t149 = circuit_add(in1, in5); // Fp2 add coeff 1/1 let t150 = circuit_add(in12, in16); // Fp2 add coeff 0/1 let t151 = circuit_add(in13, in17); // Fp2 add coeff 1/1 let t152 = circuit_mul(t150, t148); // Fp2 mul start let t153 = circuit_mul(t151, t149); let t154 = circuit_sub(t152, t153); // Fp2 mul real part end let t155 = circuit_mul(t150, t149); let t156 = circuit_mul(t151, t148); let t157 = circuit_add(t155, t156); // Fp2 mul imag part end let t158 = circuit_sub(t154, t90); // Fp2 sub coeff 0/1 let t159 = circuit_sub(t157, t93); // Fp2 sub coeff 1/1 let t160 = circuit_sub(t158, t102); // Fp2 sub coeff 0/1 let t161 = circuit_sub(t159, t105); // Fp2 sub coeff 1/1 let t162 = circuit_add(t160, t96); // Fp2 add coeff 0/1 let t163 = circuit_add(t161, t99); // Fp2 add coeff 1/1 let t164 = circuit_mul(in6, in18); // Fp2 mul start let t165 = circuit_mul(in7, in19); let t166 = circuit_sub(t164, t165); // Fp2 mul real part end let t167 = circuit_mul(in6, in19); let t168 = circuit_mul(in7, in18); let t169 = circuit_add(t167, t168); // Fp2 mul imag part end let t170 = circuit_mul(in8, in20); // Fp2 mul start let t171 = circuit_mul(in9, in21); let t172 = circuit_sub(t170, t171); // Fp2 mul real part end let t173 = circuit_mul(in8, in21); let t174 = circuit_mul(in9, in20); let t175 = circuit_add(t173, t174); // Fp2 mul imag part end let t176 = circuit_mul(in10, in22); // Fp2 mul start let t177 = circuit_mul(in11, in23); let t178 = circuit_sub(t176, t177); // Fp2 mul real part end let t179 = circuit_mul(in10, in23); let t180 = circuit_mul(in11, in22); let t181 = circuit_add(t179, t180); // Fp2 mul imag part end let t182 = circuit_add(in8, in10); // Fp2 add coeff 0/1 let t183 = circuit_add(in9, in11); // Fp2 add coeff 1/1 let t184 = circuit_add(in20, in22); // Fp2 add coeff 0/1 let t185 = circuit_add(in21, in23); // Fp2 add coeff 1/1 let t186 = circuit_mul(t182, t184); // Fp2 mul start let t187 = circuit_mul(t183, t185); let t188 = circuit_sub(t186, t187); // Fp2 mul real part end let t189 = circuit_mul(t182, t185); let t190 = circuit_mul(t183, t184); let t191 = circuit_add(t189, t190); // Fp2 mul imag part end let t192 = circuit_sub(t188, t172); // Fp2 sub coeff 0/1 let t193 = circuit_sub(t191, t175); // Fp2 sub coeff 1/1 let t194 = circuit_sub(t192, t178); // Fp2 sub coeff 0/1 let t195 = circuit_sub(t193, t181); // Fp2 sub coeff 1/1 let t196 = circuit_add(t194, t195); let t197 = circuit_add(t196, t196); let t198 = circuit_sub(t194, t195); let t199 = circuit_sub(t197, t194); let t200 = circuit_sub(t199, t195); let t201 = circuit_add(t198, t166); // Fp2 add coeff 0/1 let t202 = circuit_add(t200, t169); // Fp2 add coeff 1/1 let t203 = circuit_add(in6, in8); // Fp2 add coeff 0/1 let t204 = circuit_add(in7, in9); // Fp2 add coeff 1/1 let t205 = circuit_add(in18, in20); // Fp2 add coeff 0/1 let t206 = circuit_add(in19, in21); // Fp2 add coeff 1/1 let t207 = circuit_mul(t203, t205); // Fp2 mul start let t208 = circuit_mul(t204, t206); let t209 = circuit_sub(t207, t208); // Fp2 mul real part end let t210 = circuit_mul(t203, t206); let t211 = circuit_mul(t204, t205); let t212 = circuit_add(t210, t211); // Fp2 mul imag part end let t213 = circuit_sub(t209, t166); // Fp2 sub coeff 0/1 let t214 = circuit_sub(t212, t169); // Fp2 sub coeff 1/1 let t215 = circuit_sub(t213, t172); // Fp2 sub coeff 0/1 let t216 = circuit_sub(t214, t175); // Fp2 sub coeff 1/1 let t217 = circuit_add(t178, t181); let t218 = circuit_add(t217, t217); let t219 = circuit_sub(t178, t181); let t220 = circuit_sub(t218, t178); let t221 = circuit_sub(t220, t181); let t222 = circuit_add(t215, t219); // Fp2 add coeff 0/1 let t223 = circuit_add(t216, t221); // Fp2 add coeff 1/1 let t224 = circuit_add(in6, in10); // Fp2 add coeff 0/1 let t225 = circuit_add(in7, in11); // Fp2 add coeff 1/1 let t226 = circuit_add(in18, in22); // Fp2 add coeff 0/1 let t227 = circuit_add(in19, in23); // Fp2 add coeff 1/1 let t228 = circuit_mul(t226, t224); // Fp2 mul start let t229 = circuit_mul(t227, t225); let t230 = circuit_sub(t228, t229); // Fp2 mul real part end let t231 = circuit_mul(t226, t225); let t232 = circuit_mul(t227, t224); let t233 = circuit_add(t231, t232); // Fp2 mul imag part end let t234 = circuit_sub(t230, t166); // Fp2 sub coeff 0/1 let t235 = circuit_sub(t233, t169); // Fp2 sub coeff 1/1 let t236 = circuit_sub(t234, t178); // Fp2 sub coeff 0/1 let t237 = circuit_sub(t235, t181); // Fp2 sub coeff 1/1 let t238 = circuit_add(t236, t172); // Fp2 add coeff 0/1 let t239 = circuit_add(t237, t175); // Fp2 add coeff 1/1 let t240 = circuit_sub(t49, t125); // Fp6 sub coeff 0/5 let t241 = circuit_sub(t50, t126); // Fp6 sub coeff 1/5 let t242 = circuit_sub(t70, t146); // Fp6 sub coeff 2/5 let t243 = circuit_sub(t71, t147); // Fp6 sub coeff 3/5 let t244 = circuit_sub(t86, t162); // Fp6 sub coeff 4/5 let t245 = circuit_sub(t87, t163); // Fp6 sub coeff 5/5 let t246 = circuit_sub(t240, t201); // Fp6 sub coeff 0/5 let t247 = circuit_sub(t241, t202); // Fp6 sub coeff 1/5 let t248 = circuit_sub(t242, t222); // Fp6 sub coeff 2/5 let t249 = circuit_sub(t243, t223); // Fp6 sub coeff 3/5 let t250 = circuit_sub(t244, t238); // Fp6 sub coeff 4/5 let t251 = circuit_sub(t245, t239); // Fp6 sub coeff 5/5 let t252 = circuit_add(t238, t239); let t253 = circuit_add(t252, t252); let t254 = circuit_sub(t238, t239); let t255 = circuit_sub(t253, t238); let t256 = circuit_sub(t255, t239); let t257 = circuit_add(t254, t125); // Fp6 add coeff 0/5 let t258 = circuit_add(t256, t126); // Fp6 add coeff 1/5 let t259 = circuit_add(t201, t146); // Fp6 add coeff 2/5 let t260 = circuit_add(t202, t147); // Fp6 add coeff 3/5 let t261 = circuit_add(t222, t162); // Fp6 add coeff 4/5 let t262 = circuit_add(t223, t163); // Fp6 add coeff 5/5 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = ( t257, t258, t259, t260, t261, t262, t246, t247, t248, t249, t250, t251, ) .new_inputs(); // Prefill constants: // Fill inputs: circuit_inputs = circuit_inputs.next_2(X.c0b0a0); // in0 circuit_inputs = circuit_inputs.next_2(X.c0b0a1); // in1 circuit_inputs = circuit_inputs.next_2(X.c0b1a0); // in2 circuit_inputs = circuit_inputs.next_2(X.c0b1a1); // in3 circuit_inputs = circuit_inputs.next_2(X.c0b2a0); // in4 circuit_inputs = circuit_inputs.next_2(X.c0b2a1); // in5 circuit_inputs = circuit_inputs.next_2(X.c1b0a0); // in6 circuit_inputs = circuit_inputs.next_2(X.c1b0a1); // in7 circuit_inputs = circuit_inputs.next_2(X.c1b1a0); // in8 circuit_inputs = circuit_inputs.next_2(X.c1b1a1); // in9 circuit_inputs = circuit_inputs.next_2(X.c1b2a0); // in10 circuit_inputs = circuit_inputs.next_2(X.c1b2a1); // in11 circuit_inputs = circuit_inputs.next_2(Y.c0b0a0); // in12 circuit_inputs = circuit_inputs.next_2(Y.c0b0a1); // in13 circuit_inputs = circuit_inputs.next_2(Y.c0b1a0); // in14 circuit_inputs = circuit_inputs.next_2(Y.c0b1a1); // in15 circuit_inputs = circuit_inputs.next_2(Y.c0b2a0); // in16 circuit_inputs = circuit_inputs.next_2(Y.c0b2a1); // in17 circuit_inputs = circuit_inputs.next_2(Y.c1b0a0); // in18 circuit_inputs = circuit_inputs.next_2(Y.c1b0a1); // in19 circuit_inputs = circuit_inputs.next_2(Y.c1b1a0); // in20 circuit_inputs = circuit_inputs.next_2(Y.c1b1a1); // in21 circuit_inputs = circuit_inputs.next_2(Y.c1b2a0); // in22 circuit_inputs = circuit_inputs.next_2(Y.c1b2a1); // in23 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t257), c0b0a1: outputs.get_output(t258), c0b1a0: outputs.get_output(t259), c0b1a1: outputs.get_output(t260), c0b2a0: outputs.get_output(t261), c0b2a1: outputs.get_output(t262), c1b0a0: outputs.get_output(t246), c1b0a1: outputs.get_output(t247), c1b1a0: outputs.get_output(t248), c1b1a1: outputs.get_output(t249), c1b2a0: outputs.get_output(t250), c1b2a1: outputs.get_output(t251), }; return (res,); } #[inline(always)] pub fn run_BLS12_381_TOWER_MILLER_BIT0_1P_circuit( yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, M_i: E12T, ) -> (G2Point, E12T) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x3 let in2 = CE::> {}; // 0x6 let in3 = CE::> {}; // 0x1 // INPUT stack let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in10, in16); // Fp6 sub coeff 0/5 let t1 = circuit_sub(in11, in17); // Fp6 sub coeff 1/5 let t2 = circuit_sub(in12, in18); // Fp6 sub coeff 2/5 let t3 = circuit_sub(in13, in19); // Fp6 sub coeff 3/5 let t4 = circuit_sub(in14, in20); // Fp6 sub coeff 4/5 let t5 = circuit_sub(in15, in21); // Fp6 sub coeff 5/5 let t6 = circuit_add(in20, in21); let t7 = circuit_add(t6, t6); let t8 = circuit_sub(in20, in21); let t9 = circuit_sub(t7, in20); let t10 = circuit_sub(t9, in21); let t11 = circuit_sub(in0, t8); // Fp6 neg coeff 0/5 let t12 = circuit_sub(in0, t10); // Fp6 neg coeff 1/5 let t13 = circuit_sub(in0, in16); // Fp6 neg coeff 2/5 let t14 = circuit_sub(in0, in17); // Fp6 neg coeff 3/5 let t15 = circuit_sub(in0, in18); // Fp6 neg coeff 4/5 let t16 = circuit_sub(in0, in19); // Fp6 neg coeff 5/5 let t17 = circuit_add(in10, t11); // Fp6 add coeff 0/5 let t18 = circuit_add(in11, t12); // Fp6 add coeff 1/5 let t19 = circuit_add(in12, t13); // Fp6 add coeff 2/5 let t20 = circuit_add(in13, t14); // Fp6 add coeff 3/5 let t21 = circuit_add(in14, t15); // Fp6 add coeff 4/5 let t22 = circuit_add(in15, t16); // Fp6 add coeff 5/5 let t23 = circuit_mul(in10, in16); // Fp2 mul start let t24 = circuit_mul(in11, in17); let t25 = circuit_sub(t23, t24); // Fp2 mul real part end let t26 = circuit_mul(in10, in17); let t27 = circuit_mul(in11, in16); let t28 = circuit_add(t26, t27); // Fp2 mul imag part end let t29 = circuit_mul(in12, in18); // Fp2 mul start let t30 = circuit_mul(in13, in19); let t31 = circuit_sub(t29, t30); // Fp2 mul real part end let t32 = circuit_mul(in12, in19); let t33 = circuit_mul(in13, in18); let t34 = circuit_add(t32, t33); // Fp2 mul imag part end let t35 = circuit_mul(in14, in20); // Fp2 mul start let t36 = circuit_mul(in15, in21); let t37 = circuit_sub(t35, t36); // Fp2 mul real part end let t38 = circuit_mul(in14, in21); let t39 = circuit_mul(in15, in20); let t40 = circuit_add(t38, t39); // Fp2 mul imag part end let t41 = circuit_add(in12, in14); // Fp2 add coeff 0/1 let t42 = circuit_add(in13, in15); // Fp2 add coeff 1/1 let t43 = circuit_add(in18, in20); // Fp2 add coeff 0/1 let t44 = circuit_add(in19, in21); // Fp2 add coeff 1/1 let t45 = circuit_mul(t41, t43); // Fp2 mul start let t46 = circuit_mul(t42, t44); let t47 = circuit_sub(t45, t46); // Fp2 mul real part end let t48 = circuit_mul(t41, t44); let t49 = circuit_mul(t42, t43); let t50 = circuit_add(t48, t49); // Fp2 mul imag part end let t51 = circuit_sub(t47, t31); // Fp2 sub coeff 0/1 let t52 = circuit_sub(t50, t34); // Fp2 sub coeff 1/1 let t53 = circuit_sub(t51, t37); // Fp2 sub coeff 0/1 let t54 = circuit_sub(t52, t40); // Fp2 sub coeff 1/1 let t55 = circuit_add(t53, t54); let t56 = circuit_add(t55, t55); let t57 = circuit_sub(t53, t54); let t58 = circuit_sub(t56, t53); let t59 = circuit_sub(t58, t54); let t60 = circuit_add(t57, t25); // Fp2 add coeff 0/1 let t61 = circuit_add(t59, t28); // Fp2 add coeff 1/1 let t62 = circuit_add(in10, in12); // Fp2 add coeff 0/1 let t63 = circuit_add(in11, in13); // Fp2 add coeff 1/1 let t64 = circuit_add(in16, in18); // Fp2 add coeff 0/1 let t65 = circuit_add(in17, in19); // Fp2 add coeff 1/1 let t66 = circuit_mul(t62, t64); // Fp2 mul start let t67 = circuit_mul(t63, t65); let t68 = circuit_sub(t66, t67); // Fp2 mul real part end let t69 = circuit_mul(t62, t65); let t70 = circuit_mul(t63, t64); let t71 = circuit_add(t69, t70); // Fp2 mul imag part end let t72 = circuit_sub(t68, t25); // Fp2 sub coeff 0/1 let t73 = circuit_sub(t71, t28); // Fp2 sub coeff 1/1 let t74 = circuit_sub(t72, t31); // Fp2 sub coeff 0/1 let t75 = circuit_sub(t73, t34); // Fp2 sub coeff 1/1 let t76 = circuit_add(t37, t40); let t77 = circuit_add(t76, t76); let t78 = circuit_sub(t37, t40); let t79 = circuit_sub(t77, t37); let t80 = circuit_sub(t79, t40); let t81 = circuit_add(t74, t78); // Fp2 add coeff 0/1 let t82 = circuit_add(t75, t80); // Fp2 add coeff 1/1 let t83 = circuit_add(in10, in14); // Fp2 add coeff 0/1 let t84 = circuit_add(in11, in15); // Fp2 add coeff 1/1 let t85 = circuit_add(in16, in20); // Fp2 add coeff 0/1 let t86 = circuit_add(in17, in21); // Fp2 add coeff 1/1 let t87 = circuit_mul(t85, t83); // Fp2 mul start let t88 = circuit_mul(t86, t84); let t89 = circuit_sub(t87, t88); // Fp2 mul real part end let t90 = circuit_mul(t85, t84); let t91 = circuit_mul(t86, t83); let t92 = circuit_add(t90, t91); // Fp2 mul imag part end let t93 = circuit_sub(t89, t25); // Fp2 sub coeff 0/1 let t94 = circuit_sub(t92, t28); // Fp2 sub coeff 1/1 let t95 = circuit_sub(t93, t37); // Fp2 sub coeff 0/1 let t96 = circuit_sub(t94, t40); // Fp2 sub coeff 1/1 let t97 = circuit_add(t95, t31); // Fp2 add coeff 0/1 let t98 = circuit_add(t96, t34); // Fp2 add coeff 1/1 let t99 = circuit_mul(t0, t17); // Fp2 mul start let t100 = circuit_mul(t1, t18); let t101 = circuit_sub(t99, t100); // Fp2 mul real part end let t102 = circuit_mul(t0, t18); let t103 = circuit_mul(t1, t17); let t104 = circuit_add(t102, t103); // Fp2 mul imag part end let t105 = circuit_mul(t2, t19); // Fp2 mul start let t106 = circuit_mul(t3, t20); let t107 = circuit_sub(t105, t106); // Fp2 mul real part end let t108 = circuit_mul(t2, t20); let t109 = circuit_mul(t3, t19); let t110 = circuit_add(t108, t109); // Fp2 mul imag part end let t111 = circuit_mul(t4, t21); // Fp2 mul start let t112 = circuit_mul(t5, t22); let t113 = circuit_sub(t111, t112); // Fp2 mul real part end let t114 = circuit_mul(t4, t22); let t115 = circuit_mul(t5, t21); let t116 = circuit_add(t114, t115); // Fp2 mul imag part end let t117 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t118 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t119 = circuit_add(t19, t21); // Fp2 add coeff 0/1 let t120 = circuit_add(t20, t22); // Fp2 add coeff 1/1 let t121 = circuit_mul(t117, t119); // Fp2 mul start let t122 = circuit_mul(t118, t120); let t123 = circuit_sub(t121, t122); // Fp2 mul real part end let t124 = circuit_mul(t117, t120); let t125 = circuit_mul(t118, t119); let t126 = circuit_add(t124, t125); // Fp2 mul imag part end let t127 = circuit_sub(t123, t107); // Fp2 sub coeff 0/1 let t128 = circuit_sub(t126, t110); // Fp2 sub coeff 1/1 let t129 = circuit_sub(t127, t113); // Fp2 sub coeff 0/1 let t130 = circuit_sub(t128, t116); // Fp2 sub coeff 1/1 let t131 = circuit_add(t129, t130); let t132 = circuit_add(t131, t131); let t133 = circuit_sub(t129, t130); let t134 = circuit_sub(t132, t129); let t135 = circuit_sub(t134, t130); let t136 = circuit_add(t133, t101); // Fp2 add coeff 0/1 let t137 = circuit_add(t135, t104); // Fp2 add coeff 1/1 let t138 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t139 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t140 = circuit_add(t17, t19); // Fp2 add coeff 0/1 let t141 = circuit_add(t18, t20); // Fp2 add coeff 1/1 let t142 = circuit_mul(t138, t140); // Fp2 mul start let t143 = circuit_mul(t139, t141); let t144 = circuit_sub(t142, t143); // Fp2 mul real part end let t145 = circuit_mul(t138, t141); let t146 = circuit_mul(t139, t140); let t147 = circuit_add(t145, t146); // Fp2 mul imag part end let t148 = circuit_sub(t144, t101); // Fp2 sub coeff 0/1 let t149 = circuit_sub(t147, t104); // Fp2 sub coeff 1/1 let t150 = circuit_sub(t148, t107); // Fp2 sub coeff 0/1 let t151 = circuit_sub(t149, t110); // Fp2 sub coeff 1/1 let t152 = circuit_add(t113, t116); let t153 = circuit_add(t152, t152); let t154 = circuit_sub(t113, t116); let t155 = circuit_sub(t153, t113); let t156 = circuit_sub(t155, t116); let t157 = circuit_add(t150, t154); // Fp2 add coeff 0/1 let t158 = circuit_add(t151, t156); // Fp2 add coeff 1/1 let t159 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t160 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t161 = circuit_add(t17, t21); // Fp2 add coeff 0/1 let t162 = circuit_add(t18, t22); // Fp2 add coeff 1/1 let t163 = circuit_mul(t161, t159); // Fp2 mul start let t164 = circuit_mul(t162, t160); let t165 = circuit_sub(t163, t164); // Fp2 mul real part end let t166 = circuit_mul(t161, t160); let t167 = circuit_mul(t162, t159); let t168 = circuit_add(t166, t167); // Fp2 mul imag part end let t169 = circuit_sub(t165, t101); // Fp2 sub coeff 0/1 let t170 = circuit_sub(t168, t104); // Fp2 sub coeff 1/1 let t171 = circuit_sub(t169, t113); // Fp2 sub coeff 0/1 let t172 = circuit_sub(t170, t116); // Fp2 sub coeff 1/1 let t173 = circuit_add(t171, t107); // Fp2 add coeff 0/1 let t174 = circuit_add(t172, t110); // Fp2 add coeff 1/1 let t175 = circuit_add(t136, t60); // Fp6 add coeff 0/5 let t176 = circuit_add(t137, t61); // Fp6 add coeff 1/5 let t177 = circuit_add(t157, t81); // Fp6 add coeff 2/5 let t178 = circuit_add(t158, t82); // Fp6 add coeff 3/5 let t179 = circuit_add(t173, t97); // Fp6 add coeff 4/5 let t180 = circuit_add(t174, t98); // Fp6 add coeff 5/5 let t181 = circuit_add(t60, t60); // Fp6 add coeff 0/5 let t182 = circuit_add(t61, t61); // Fp6 add coeff 1/5 let t183 = circuit_add(t81, t81); // Fp6 add coeff 2/5 let t184 = circuit_add(t82, t82); // Fp6 add coeff 3/5 let t185 = circuit_add(t97, t97); // Fp6 add coeff 4/5 let t186 = circuit_add(t98, t98); // Fp6 add coeff 5/5 let t187 = circuit_add(t97, t98); let t188 = circuit_add(t187, t187); let t189 = circuit_sub(t97, t98); let t190 = circuit_sub(t188, t97); let t191 = circuit_sub(t190, t98); let t192 = circuit_add(t175, t189); // Fp6 add coeff 0/5 let t193 = circuit_add(t176, t191); // Fp6 add coeff 1/5 let t194 = circuit_add(t177, t60); // Fp6 add coeff 2/5 let t195 = circuit_add(t178, t61); // Fp6 add coeff 3/5 let t196 = circuit_add(t179, t81); // Fp6 add coeff 4/5 let t197 = circuit_add(t180, t82); // Fp6 add coeff 5/5 let t198 = circuit_add(in6, in7); // Doubling slope numerator start let t199 = circuit_sub(in6, in7); let t200 = circuit_mul(t198, t199); let t201 = circuit_mul(in6, in7); let t202 = circuit_mul(t200, in1); let t203 = circuit_mul(t201, in2); // Doubling slope numerator end let t204 = circuit_add(in8, in8); // Fp2 add coeff 0/1 let t205 = circuit_add(in9, in9); // Fp2 add coeff 1/1 let t206 = circuit_mul(t204, t204); // Fp2 Inv start let t207 = circuit_mul(t205, t205); let t208 = circuit_add(t206, t207); let t209 = circuit_inverse(t208); let t210 = circuit_mul(t204, t209); // Fp2 Inv real part end let t211 = circuit_mul(t205, t209); let t212 = circuit_sub(in0, t211); // Fp2 Inv imag part end let t213 = circuit_mul(t202, t210); // Fp2 mul start let t214 = circuit_mul(t203, t212); let t215 = circuit_sub(t213, t214); // Fp2 mul real part end let t216 = circuit_mul(t202, t212); let t217 = circuit_mul(t203, t210); let t218 = circuit_add(t216, t217); // Fp2 mul imag part end let t219 = circuit_add(t215, t218); let t220 = circuit_sub(t215, t218); let t221 = circuit_mul(t219, t220); let t222 = circuit_mul(t215, t218); let t223 = circuit_add(t222, t222); let t224 = circuit_add(in6, in6); // Fp2 add coeff 0/1 let t225 = circuit_add(in7, in7); // Fp2 add coeff 1/1 let t226 = circuit_sub(t221, t224); // Fp2 sub coeff 0/1 let t227 = circuit_sub(t223, t225); // Fp2 sub coeff 1/1 let t228 = circuit_sub(in6, t226); // Fp2 sub coeff 0/1 let t229 = circuit_sub(in7, t227); // Fp2 sub coeff 1/1 let t230 = circuit_mul(t215, t228); // Fp2 mul start let t231 = circuit_mul(t218, t229); let t232 = circuit_sub(t230, t231); // Fp2 mul real part end let t233 = circuit_mul(t215, t229); let t234 = circuit_mul(t218, t228); let t235 = circuit_add(t233, t234); // Fp2 mul imag part end let t236 = circuit_sub(t232, in8); // Fp2 sub coeff 0/1 let t237 = circuit_sub(t235, in9); // Fp2 sub coeff 1/1 let t238 = circuit_mul(t215, in6); // Fp2 mul start let t239 = circuit_mul(t218, in7); let t240 = circuit_sub(t238, t239); // Fp2 mul real part end let t241 = circuit_mul(t215, in7); let t242 = circuit_mul(t218, in6); let t243 = circuit_add(t241, t242); // Fp2 mul imag part end let t244 = circuit_sub(t240, in8); // Fp2 sub coeff 0/1 let t245 = circuit_sub(t243, in9); // Fp2 sub coeff 1/1 let t246 = circuit_mul(t244, in4); let t247 = circuit_mul(t245, in4); let t248 = circuit_mul(t215, in5); let t249 = circuit_mul(t218, in5); let t250 = circuit_mul(t192, t246); // Fp2 mul start let t251 = circuit_mul(t193, t247); let t252 = circuit_sub(t250, t251); // Fp2 mul real part end let t253 = circuit_mul(t192, t247); let t254 = circuit_mul(t193, t246); let t255 = circuit_add(t253, t254); // Fp2 mul imag part end let t256 = circuit_mul(t194, t248); // Fp2 mul start let t257 = circuit_mul(t195, t249); let t258 = circuit_sub(t256, t257); // Fp2 mul real part end let t259 = circuit_mul(t194, t249); let t260 = circuit_mul(t195, t248); let t261 = circuit_add(t259, t260); // Fp2 mul imag part end let t262 = circuit_add(t194, t196); // Fp2 add coeff 0/1 let t263 = circuit_add(t195, t197); // Fp2 add coeff 1/1 let t264 = circuit_mul(t248, t262); // Fp2 mul start let t265 = circuit_mul(t249, t263); let t266 = circuit_sub(t264, t265); // Fp2 mul real part end let t267 = circuit_mul(t248, t263); let t268 = circuit_mul(t249, t262); let t269 = circuit_add(t267, t268); // Fp2 mul imag part end let t270 = circuit_sub(t266, t258); // Fp2 sub coeff 0/1 let t271 = circuit_sub(t269, t261); // Fp2 sub coeff 1/1 let t272 = circuit_add(t270, t271); let t273 = circuit_add(t272, t272); let t274 = circuit_sub(t270, t271); let t275 = circuit_sub(t273, t270); let t276 = circuit_sub(t275, t271); let t277 = circuit_add(t274, t252); // Fp2 add coeff 0/1 let t278 = circuit_add(t276, t255); // Fp2 add coeff 1/1 let t279 = circuit_add(t192, t196); // Fp2 add coeff 0/1 let t280 = circuit_add(t193, t197); // Fp2 add coeff 1/1 let t281 = circuit_mul(t246, t279); // Fp2 mul start let t282 = circuit_mul(t247, t280); let t283 = circuit_sub(t281, t282); // Fp2 mul real part end let t284 = circuit_mul(t246, t280); let t285 = circuit_mul(t247, t279); let t286 = circuit_add(t284, t285); // Fp2 mul imag part end let t287 = circuit_sub(t283, t252); // Fp2 sub coeff 0/1 let t288 = circuit_sub(t286, t255); // Fp2 sub coeff 1/1 let t289 = circuit_add(t287, t258); // Fp2 add coeff 0/1 let t290 = circuit_add(t288, t261); // Fp2 add coeff 1/1 let t291 = circuit_add(t246, t248); // Fp2 add coeff 0/1 let t292 = circuit_add(t247, t249); // Fp2 add coeff 1/1 let t293 = circuit_add(t192, t194); // Fp2 add coeff 0/1 let t294 = circuit_add(t193, t195); // Fp2 add coeff 1/1 let t295 = circuit_mul(t291, t293); // Fp2 mul start let t296 = circuit_mul(t292, t294); let t297 = circuit_sub(t295, t296); // Fp2 mul real part end let t298 = circuit_mul(t291, t294); let t299 = circuit_mul(t292, t293); let t300 = circuit_add(t298, t299); // Fp2 mul imag part end let t301 = circuit_sub(t297, t252); // Fp2 sub coeff 0/1 let t302 = circuit_sub(t300, t255); // Fp2 sub coeff 1/1 let t303 = circuit_sub(t301, t258); // Fp2 sub coeff 0/1 let t304 = circuit_sub(t302, t261); // Fp2 sub coeff 1/1 let t305 = circuit_add(t185, t186); let t306 = circuit_add(t305, t305); let t307 = circuit_sub(t185, t186); let t308 = circuit_sub(t306, t185); let t309 = circuit_sub(t308, t186); let t310 = circuit_add(in3, t248); let t311 = circuit_add(t181, t192); // Fp6 add coeff 0/5 let t312 = circuit_add(t182, t193); // Fp6 add coeff 1/5 let t313 = circuit_add(t183, t194); // Fp6 add coeff 2/5 let t314 = circuit_add(t184, t195); // Fp6 add coeff 3/5 let t315 = circuit_add(t185, t196); // Fp6 add coeff 4/5 let t316 = circuit_add(t186, t197); // Fp6 add coeff 5/5 let t317 = circuit_mul(t311, t246); // Fp2 mul start let t318 = circuit_mul(t312, t247); let t319 = circuit_sub(t317, t318); // Fp2 mul real part end let t320 = circuit_mul(t311, t247); let t321 = circuit_mul(t312, t246); let t322 = circuit_add(t320, t321); // Fp2 mul imag part end let t323 = circuit_mul(t313, t310); // Fp2 mul start let t324 = circuit_mul(t314, t249); let t325 = circuit_sub(t323, t324); // Fp2 mul real part end let t326 = circuit_mul(t313, t249); let t327 = circuit_mul(t314, t310); let t328 = circuit_add(t326, t327); // Fp2 mul imag part end let t329 = circuit_add(t313, t315); // Fp2 add coeff 0/1 let t330 = circuit_add(t314, t316); // Fp2 add coeff 1/1 let t331 = circuit_mul(t310, t329); // Fp2 mul start let t332 = circuit_mul(t249, t330); let t333 = circuit_sub(t331, t332); // Fp2 mul real part end let t334 = circuit_mul(t310, t330); let t335 = circuit_mul(t249, t329); let t336 = circuit_add(t334, t335); // Fp2 mul imag part end let t337 = circuit_sub(t333, t325); // Fp2 sub coeff 0/1 let t338 = circuit_sub(t336, t328); // Fp2 sub coeff 1/1 let t339 = circuit_add(t337, t338); let t340 = circuit_add(t339, t339); let t341 = circuit_sub(t337, t338); let t342 = circuit_sub(t340, t337); let t343 = circuit_sub(t342, t338); let t344 = circuit_add(t341, t319); // Fp2 add coeff 0/1 let t345 = circuit_add(t343, t322); // Fp2 add coeff 1/1 let t346 = circuit_add(t311, t315); // Fp2 add coeff 0/1 let t347 = circuit_add(t312, t316); // Fp2 add coeff 1/1 let t348 = circuit_mul(t246, t346); // Fp2 mul start let t349 = circuit_mul(t247, t347); let t350 = circuit_sub(t348, t349); // Fp2 mul real part end let t351 = circuit_mul(t246, t347); let t352 = circuit_mul(t247, t346); let t353 = circuit_add(t351, t352); // Fp2 mul imag part end let t354 = circuit_sub(t350, t319); // Fp2 sub coeff 0/1 let t355 = circuit_sub(t353, t322); // Fp2 sub coeff 1/1 let t356 = circuit_add(t354, t325); // Fp2 add coeff 0/1 let t357 = circuit_add(t355, t328); // Fp2 add coeff 1/1 let t358 = circuit_add(t246, t310); // Fp2 add coeff 0/1 let t359 = circuit_add(t247, t249); // Fp2 add coeff 1/1 let t360 = circuit_add(t311, t313); // Fp2 add coeff 0/1 let t361 = circuit_add(t312, t314); // Fp2 add coeff 1/1 let t362 = circuit_mul(t358, t360); // Fp2 mul start let t363 = circuit_mul(t359, t361); let t364 = circuit_sub(t362, t363); // Fp2 mul real part end let t365 = circuit_mul(t358, t361); let t366 = circuit_mul(t359, t360); let t367 = circuit_add(t365, t366); // Fp2 mul imag part end let t368 = circuit_sub(t364, t319); // Fp2 sub coeff 0/1 let t369 = circuit_sub(t367, t322); // Fp2 sub coeff 1/1 let t370 = circuit_sub(t368, t325); // Fp2 sub coeff 0/1 let t371 = circuit_sub(t369, t328); // Fp2 sub coeff 1/1 let t372 = circuit_sub(t344, t277); // Fp6 sub coeff 0/5 let t373 = circuit_sub(t345, t278); // Fp6 sub coeff 1/5 let t374 = circuit_sub(t370, t303); // Fp6 sub coeff 2/5 let t375 = circuit_sub(t371, t304); // Fp6 sub coeff 3/5 let t376 = circuit_sub(t356, t289); // Fp6 sub coeff 4/5 let t377 = circuit_sub(t357, t290); // Fp6 sub coeff 5/5 let t378 = circuit_sub(t372, t307); // Fp6 sub coeff 0/5 let t379 = circuit_sub(t373, t309); // Fp6 sub coeff 1/5 let t380 = circuit_sub(t374, t181); // Fp6 sub coeff 2/5 let t381 = circuit_sub(t375, t182); // Fp6 sub coeff 3/5 let t382 = circuit_sub(t376, t183); // Fp6 sub coeff 4/5 let t383 = circuit_sub(t377, t184); // Fp6 sub coeff 5/5 let t384 = circuit_add(t183, t184); let t385 = circuit_add(t384, t384); let t386 = circuit_sub(t183, t184); let t387 = circuit_sub(t385, t183); let t388 = circuit_sub(t387, t184); let t389 = circuit_add(t386, t277); // Fp6 add coeff 0/5 let t390 = circuit_add(t388, t278); // Fp6 add coeff 1/5 let t391 = circuit_add(t307, t303); // Fp6 add coeff 2/5 let t392 = circuit_add(t309, t304); // Fp6 add coeff 3/5 let t393 = circuit_add(t181, t289); // Fp6 add coeff 4/5 let t394 = circuit_add(t182, t290); // Fp6 add coeff 5/5 let t395 = circuit_add(t226, t227); let t396 = circuit_add(t395, t236); let t397 = circuit_add(t396, t237); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = ( t397, t389, t390, t391, t392, t393, t394, t378, t379, t380, t381, t382, t383, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in3 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in4 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in5 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in6 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in7 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in8 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in9 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a0); // in10 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a1); // in11 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a0); // in12 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a1); // in13 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a0); // in14 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a1); // in15 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a0); // in16 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a1); // in17 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a0); // in18 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a1); // in19 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a0); // in20 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a1); // in21 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t226), x1: outputs.get_output(t227), y0: outputs.get_output(t236), y1: outputs.get_output(t237), }; let Mi_plus_one: E12T = E12T { c0b0a0: outputs.get_output(t389), c0b0a1: outputs.get_output(t390), c0b1a0: outputs.get_output(t391), c0b1a1: outputs.get_output(t392), c0b2a0: outputs.get_output(t393), c0b2a1: outputs.get_output(t394), c1b0a0: outputs.get_output(t378), c1b0a1: outputs.get_output(t379), c1b1a0: outputs.get_output(t380), c1b1a1: outputs.get_output(t381), c1b2a0: outputs.get_output(t382), c1b2a1: outputs.get_output(t383), }; return (Q0, Mi_plus_one); } #[inline(always)] pub fn run_BLS12_381_TOWER_MILLER_BIT1_1P_circuit( yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, Q_or_Q_neg_0: G2Point, M_i: E12T, ) -> (G2Point, E12T) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x1 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let in23 = CE::> {}; let t0 = circuit_sub(in12, in18); // Fp6 sub coeff 0/5 let t1 = circuit_sub(in13, in19); // Fp6 sub coeff 1/5 let t2 = circuit_sub(in14, in20); // Fp6 sub coeff 2/5 let t3 = circuit_sub(in15, in21); // Fp6 sub coeff 3/5 let t4 = circuit_sub(in16, in22); // Fp6 sub coeff 4/5 let t5 = circuit_sub(in17, in23); // Fp6 sub coeff 5/5 let t6 = circuit_add(in22, in23); let t7 = circuit_add(t6, t6); let t8 = circuit_sub(in22, in23); let t9 = circuit_sub(t7, in22); let t10 = circuit_sub(t9, in23); let t11 = circuit_sub(in0, t8); // Fp6 neg coeff 0/5 let t12 = circuit_sub(in0, t10); // Fp6 neg coeff 1/5 let t13 = circuit_sub(in0, in18); // Fp6 neg coeff 2/5 let t14 = circuit_sub(in0, in19); // Fp6 neg coeff 3/5 let t15 = circuit_sub(in0, in20); // Fp6 neg coeff 4/5 let t16 = circuit_sub(in0, in21); // Fp6 neg coeff 5/5 let t17 = circuit_add(in12, t11); // Fp6 add coeff 0/5 let t18 = circuit_add(in13, t12); // Fp6 add coeff 1/5 let t19 = circuit_add(in14, t13); // Fp6 add coeff 2/5 let t20 = circuit_add(in15, t14); // Fp6 add coeff 3/5 let t21 = circuit_add(in16, t15); // Fp6 add coeff 4/5 let t22 = circuit_add(in17, t16); // Fp6 add coeff 5/5 let t23 = circuit_mul(in12, in18); // Fp2 mul start let t24 = circuit_mul(in13, in19); let t25 = circuit_sub(t23, t24); // Fp2 mul real part end let t26 = circuit_mul(in12, in19); let t27 = circuit_mul(in13, in18); let t28 = circuit_add(t26, t27); // Fp2 mul imag part end let t29 = circuit_mul(in14, in20); // Fp2 mul start let t30 = circuit_mul(in15, in21); let t31 = circuit_sub(t29, t30); // Fp2 mul real part end let t32 = circuit_mul(in14, in21); let t33 = circuit_mul(in15, in20); let t34 = circuit_add(t32, t33); // Fp2 mul imag part end let t35 = circuit_mul(in16, in22); // Fp2 mul start let t36 = circuit_mul(in17, in23); let t37 = circuit_sub(t35, t36); // Fp2 mul real part end let t38 = circuit_mul(in16, in23); let t39 = circuit_mul(in17, in22); let t40 = circuit_add(t38, t39); // Fp2 mul imag part end let t41 = circuit_add(in14, in16); // Fp2 add coeff 0/1 let t42 = circuit_add(in15, in17); // Fp2 add coeff 1/1 let t43 = circuit_add(in20, in22); // Fp2 add coeff 0/1 let t44 = circuit_add(in21, in23); // Fp2 add coeff 1/1 let t45 = circuit_mul(t41, t43); // Fp2 mul start let t46 = circuit_mul(t42, t44); let t47 = circuit_sub(t45, t46); // Fp2 mul real part end let t48 = circuit_mul(t41, t44); let t49 = circuit_mul(t42, t43); let t50 = circuit_add(t48, t49); // Fp2 mul imag part end let t51 = circuit_sub(t47, t31); // Fp2 sub coeff 0/1 let t52 = circuit_sub(t50, t34); // Fp2 sub coeff 1/1 let t53 = circuit_sub(t51, t37); // Fp2 sub coeff 0/1 let t54 = circuit_sub(t52, t40); // Fp2 sub coeff 1/1 let t55 = circuit_add(t53, t54); let t56 = circuit_add(t55, t55); let t57 = circuit_sub(t53, t54); let t58 = circuit_sub(t56, t53); let t59 = circuit_sub(t58, t54); let t60 = circuit_add(t57, t25); // Fp2 add coeff 0/1 let t61 = circuit_add(t59, t28); // Fp2 add coeff 1/1 let t62 = circuit_add(in12, in14); // Fp2 add coeff 0/1 let t63 = circuit_add(in13, in15); // Fp2 add coeff 1/1 let t64 = circuit_add(in18, in20); // Fp2 add coeff 0/1 let t65 = circuit_add(in19, in21); // Fp2 add coeff 1/1 let t66 = circuit_mul(t62, t64); // Fp2 mul start let t67 = circuit_mul(t63, t65); let t68 = circuit_sub(t66, t67); // Fp2 mul real part end let t69 = circuit_mul(t62, t65); let t70 = circuit_mul(t63, t64); let t71 = circuit_add(t69, t70); // Fp2 mul imag part end let t72 = circuit_sub(t68, t25); // Fp2 sub coeff 0/1 let t73 = circuit_sub(t71, t28); // Fp2 sub coeff 1/1 let t74 = circuit_sub(t72, t31); // Fp2 sub coeff 0/1 let t75 = circuit_sub(t73, t34); // Fp2 sub coeff 1/1 let t76 = circuit_add(t37, t40); let t77 = circuit_add(t76, t76); let t78 = circuit_sub(t37, t40); let t79 = circuit_sub(t77, t37); let t80 = circuit_sub(t79, t40); let t81 = circuit_add(t74, t78); // Fp2 add coeff 0/1 let t82 = circuit_add(t75, t80); // Fp2 add coeff 1/1 let t83 = circuit_add(in12, in16); // Fp2 add coeff 0/1 let t84 = circuit_add(in13, in17); // Fp2 add coeff 1/1 let t85 = circuit_add(in18, in22); // Fp2 add coeff 0/1 let t86 = circuit_add(in19, in23); // Fp2 add coeff 1/1 let t87 = circuit_mul(t85, t83); // Fp2 mul start let t88 = circuit_mul(t86, t84); let t89 = circuit_sub(t87, t88); // Fp2 mul real part end let t90 = circuit_mul(t85, t84); let t91 = circuit_mul(t86, t83); let t92 = circuit_add(t90, t91); // Fp2 mul imag part end let t93 = circuit_sub(t89, t25); // Fp2 sub coeff 0/1 let t94 = circuit_sub(t92, t28); // Fp2 sub coeff 1/1 let t95 = circuit_sub(t93, t37); // Fp2 sub coeff 0/1 let t96 = circuit_sub(t94, t40); // Fp2 sub coeff 1/1 let t97 = circuit_add(t95, t31); // Fp2 add coeff 0/1 let t98 = circuit_add(t96, t34); // Fp2 add coeff 1/1 let t99 = circuit_mul(t0, t17); // Fp2 mul start let t100 = circuit_mul(t1, t18); let t101 = circuit_sub(t99, t100); // Fp2 mul real part end let t102 = circuit_mul(t0, t18); let t103 = circuit_mul(t1, t17); let t104 = circuit_add(t102, t103); // Fp2 mul imag part end let t105 = circuit_mul(t2, t19); // Fp2 mul start let t106 = circuit_mul(t3, t20); let t107 = circuit_sub(t105, t106); // Fp2 mul real part end let t108 = circuit_mul(t2, t20); let t109 = circuit_mul(t3, t19); let t110 = circuit_add(t108, t109); // Fp2 mul imag part end let t111 = circuit_mul(t4, t21); // Fp2 mul start let t112 = circuit_mul(t5, t22); let t113 = circuit_sub(t111, t112); // Fp2 mul real part end let t114 = circuit_mul(t4, t22); let t115 = circuit_mul(t5, t21); let t116 = circuit_add(t114, t115); // Fp2 mul imag part end let t117 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t118 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t119 = circuit_add(t19, t21); // Fp2 add coeff 0/1 let t120 = circuit_add(t20, t22); // Fp2 add coeff 1/1 let t121 = circuit_mul(t117, t119); // Fp2 mul start let t122 = circuit_mul(t118, t120); let t123 = circuit_sub(t121, t122); // Fp2 mul real part end let t124 = circuit_mul(t117, t120); let t125 = circuit_mul(t118, t119); let t126 = circuit_add(t124, t125); // Fp2 mul imag part end let t127 = circuit_sub(t123, t107); // Fp2 sub coeff 0/1 let t128 = circuit_sub(t126, t110); // Fp2 sub coeff 1/1 let t129 = circuit_sub(t127, t113); // Fp2 sub coeff 0/1 let t130 = circuit_sub(t128, t116); // Fp2 sub coeff 1/1 let t131 = circuit_add(t129, t130); let t132 = circuit_add(t131, t131); let t133 = circuit_sub(t129, t130); let t134 = circuit_sub(t132, t129); let t135 = circuit_sub(t134, t130); let t136 = circuit_add(t133, t101); // Fp2 add coeff 0/1 let t137 = circuit_add(t135, t104); // Fp2 add coeff 1/1 let t138 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t139 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t140 = circuit_add(t17, t19); // Fp2 add coeff 0/1 let t141 = circuit_add(t18, t20); // Fp2 add coeff 1/1 let t142 = circuit_mul(t138, t140); // Fp2 mul start let t143 = circuit_mul(t139, t141); let t144 = circuit_sub(t142, t143); // Fp2 mul real part end let t145 = circuit_mul(t138, t141); let t146 = circuit_mul(t139, t140); let t147 = circuit_add(t145, t146); // Fp2 mul imag part end let t148 = circuit_sub(t144, t101); // Fp2 sub coeff 0/1 let t149 = circuit_sub(t147, t104); // Fp2 sub coeff 1/1 let t150 = circuit_sub(t148, t107); // Fp2 sub coeff 0/1 let t151 = circuit_sub(t149, t110); // Fp2 sub coeff 1/1 let t152 = circuit_add(t113, t116); let t153 = circuit_add(t152, t152); let t154 = circuit_sub(t113, t116); let t155 = circuit_sub(t153, t113); let t156 = circuit_sub(t155, t116); let t157 = circuit_add(t150, t154); // Fp2 add coeff 0/1 let t158 = circuit_add(t151, t156); // Fp2 add coeff 1/1 let t159 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t160 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t161 = circuit_add(t17, t21); // Fp2 add coeff 0/1 let t162 = circuit_add(t18, t22); // Fp2 add coeff 1/1 let t163 = circuit_mul(t161, t159); // Fp2 mul start let t164 = circuit_mul(t162, t160); let t165 = circuit_sub(t163, t164); // Fp2 mul real part end let t166 = circuit_mul(t161, t160); let t167 = circuit_mul(t162, t159); let t168 = circuit_add(t166, t167); // Fp2 mul imag part end let t169 = circuit_sub(t165, t101); // Fp2 sub coeff 0/1 let t170 = circuit_sub(t168, t104); // Fp2 sub coeff 1/1 let t171 = circuit_sub(t169, t113); // Fp2 sub coeff 0/1 let t172 = circuit_sub(t170, t116); // Fp2 sub coeff 1/1 let t173 = circuit_add(t171, t107); // Fp2 add coeff 0/1 let t174 = circuit_add(t172, t110); // Fp2 add coeff 1/1 let t175 = circuit_add(t136, t60); // Fp6 add coeff 0/5 let t176 = circuit_add(t137, t61); // Fp6 add coeff 1/5 let t177 = circuit_add(t157, t81); // Fp6 add coeff 2/5 let t178 = circuit_add(t158, t82); // Fp6 add coeff 3/5 let t179 = circuit_add(t173, t97); // Fp6 add coeff 4/5 let t180 = circuit_add(t174, t98); // Fp6 add coeff 5/5 let t181 = circuit_add(t60, t60); // Fp6 add coeff 0/5 let t182 = circuit_add(t61, t61); // Fp6 add coeff 1/5 let t183 = circuit_add(t81, t81); // Fp6 add coeff 2/5 let t184 = circuit_add(t82, t82); // Fp6 add coeff 3/5 let t185 = circuit_add(t97, t97); // Fp6 add coeff 4/5 let t186 = circuit_add(t98, t98); // Fp6 add coeff 5/5 let t187 = circuit_add(t97, t98); let t188 = circuit_add(t187, t187); let t189 = circuit_sub(t97, t98); let t190 = circuit_sub(t188, t97); let t191 = circuit_sub(t190, t98); let t192 = circuit_add(t175, t189); // Fp6 add coeff 0/5 let t193 = circuit_add(t176, t191); // Fp6 add coeff 1/5 let t194 = circuit_add(t177, t60); // Fp6 add coeff 2/5 let t195 = circuit_add(t178, t61); // Fp6 add coeff 3/5 let t196 = circuit_add(t179, t81); // Fp6 add coeff 4/5 let t197 = circuit_add(t180, t82); // Fp6 add coeff 5/5 let t198 = circuit_sub(in6, in10); // Fp2 sub coeff 0/1 let t199 = circuit_sub(in7, in11); // Fp2 sub coeff 1/1 let t200 = circuit_sub(in4, in8); // Fp2 sub coeff 0/1 let t201 = circuit_sub(in5, in9); // Fp2 sub coeff 1/1 let t202 = circuit_mul(t200, t200); // Fp2 Inv start let t203 = circuit_mul(t201, t201); let t204 = circuit_add(t202, t203); let t205 = circuit_inverse(t204); let t206 = circuit_mul(t200, t205); // Fp2 Inv real part end let t207 = circuit_mul(t201, t205); let t208 = circuit_sub(in0, t207); // Fp2 Inv imag part end let t209 = circuit_mul(t198, t206); // Fp2 mul start let t210 = circuit_mul(t199, t208); let t211 = circuit_sub(t209, t210); // Fp2 mul real part end let t212 = circuit_mul(t198, t208); let t213 = circuit_mul(t199, t206); let t214 = circuit_add(t212, t213); // Fp2 mul imag part end let t215 = circuit_add(t211, t214); let t216 = circuit_sub(t211, t214); let t217 = circuit_mul(t215, t216); let t218 = circuit_mul(t211, t214); let t219 = circuit_add(t218, t218); let t220 = circuit_add(in4, in8); // Fp2 add coeff 0/1 let t221 = circuit_add(in5, in9); // Fp2 add coeff 1/1 let t222 = circuit_sub(t217, t220); // Fp2 sub coeff 0/1 let t223 = circuit_sub(t219, t221); // Fp2 sub coeff 1/1 let t224 = circuit_mul(t211, in4); // Fp2 mul start let t225 = circuit_mul(t214, in5); let t226 = circuit_sub(t224, t225); // Fp2 mul real part end let t227 = circuit_mul(t211, in5); let t228 = circuit_mul(t214, in4); let t229 = circuit_add(t227, t228); // Fp2 mul imag part end let t230 = circuit_sub(t226, in6); // Fp2 sub coeff 0/1 let t231 = circuit_sub(t229, in7); // Fp2 sub coeff 1/1 let t232 = circuit_add(in6, in6); // Fp2 add coeff 0/1 let t233 = circuit_add(in7, in7); // Fp2 add coeff 1/1 let t234 = circuit_sub(t222, in4); // Fp2 sub coeff 0/1 let t235 = circuit_sub(t223, in5); // Fp2 sub coeff 1/1 let t236 = circuit_mul(t234, t234); // Fp2 Inv start let t237 = circuit_mul(t235, t235); let t238 = circuit_add(t236, t237); let t239 = circuit_inverse(t238); let t240 = circuit_mul(t234, t239); // Fp2 Inv real part end let t241 = circuit_mul(t235, t239); let t242 = circuit_sub(in0, t241); // Fp2 Inv imag part end let t243 = circuit_mul(t232, t240); // Fp2 mul start let t244 = circuit_mul(t233, t242); let t245 = circuit_sub(t243, t244); // Fp2 mul real part end let t246 = circuit_mul(t232, t242); let t247 = circuit_mul(t233, t240); let t248 = circuit_add(t246, t247); // Fp2 mul imag part end let t249 = circuit_add(t211, t245); // Fp2 add coeff 0/1 let t250 = circuit_add(t214, t248); // Fp2 add coeff 1/1 let t251 = circuit_sub(in0, t249); // Fp2 neg coeff 0/1 let t252 = circuit_sub(in0, t250); // Fp2 neg coeff 1/1 let t253 = circuit_add(t251, t252); let t254 = circuit_sub(t251, t252); let t255 = circuit_mul(t253, t254); let t256 = circuit_mul(t251, t252); let t257 = circuit_add(t256, t256); let t258 = circuit_sub(t255, in4); // Fp2 sub coeff 0/1 let t259 = circuit_sub(t257, in5); // Fp2 sub coeff 1/1 let t260 = circuit_sub(t258, t222); // Fp2 sub coeff 0/1 let t261 = circuit_sub(t259, t223); // Fp2 sub coeff 1/1 let t262 = circuit_sub(in4, t260); // Fp2 sub coeff 0/1 let t263 = circuit_sub(in5, t261); // Fp2 sub coeff 1/1 let t264 = circuit_mul(t251, t262); // Fp2 mul start let t265 = circuit_mul(t252, t263); let t266 = circuit_sub(t264, t265); // Fp2 mul real part end let t267 = circuit_mul(t251, t263); let t268 = circuit_mul(t252, t262); let t269 = circuit_add(t267, t268); // Fp2 mul imag part end let t270 = circuit_sub(t266, in6); // Fp2 sub coeff 0/1 let t271 = circuit_sub(t269, in7); // Fp2 sub coeff 1/1 let t272 = circuit_mul(t251, in4); // Fp2 mul start let t273 = circuit_mul(t252, in5); let t274 = circuit_sub(t272, t273); // Fp2 mul real part end let t275 = circuit_mul(t251, in5); let t276 = circuit_mul(t252, in4); let t277 = circuit_add(t275, t276); // Fp2 mul imag part end let t278 = circuit_sub(t274, in6); // Fp2 sub coeff 0/1 let t279 = circuit_sub(t277, in7); // Fp2 sub coeff 1/1 let t280 = circuit_mul(t230, in2); let t281 = circuit_mul(t231, in2); let t282 = circuit_mul(t211, in3); let t283 = circuit_mul(t214, in3); let t284 = circuit_mul(t278, in2); let t285 = circuit_mul(t279, in2); let t286 = circuit_mul(t251, in3); let t287 = circuit_mul(t252, in3); let t288 = circuit_mul(t192, t280); // Fp2 mul start let t289 = circuit_mul(t193, t281); let t290 = circuit_sub(t288, t289); // Fp2 mul real part end let t291 = circuit_mul(t192, t281); let t292 = circuit_mul(t193, t280); let t293 = circuit_add(t291, t292); // Fp2 mul imag part end let t294 = circuit_mul(t194, t282); // Fp2 mul start let t295 = circuit_mul(t195, t283); let t296 = circuit_sub(t294, t295); // Fp2 mul real part end let t297 = circuit_mul(t194, t283); let t298 = circuit_mul(t195, t282); let t299 = circuit_add(t297, t298); // Fp2 mul imag part end let t300 = circuit_add(t194, t196); // Fp2 add coeff 0/1 let t301 = circuit_add(t195, t197); // Fp2 add coeff 1/1 let t302 = circuit_mul(t282, t300); // Fp2 mul start let t303 = circuit_mul(t283, t301); let t304 = circuit_sub(t302, t303); // Fp2 mul real part end let t305 = circuit_mul(t282, t301); let t306 = circuit_mul(t283, t300); let t307 = circuit_add(t305, t306); // Fp2 mul imag part end let t308 = circuit_sub(t304, t296); // Fp2 sub coeff 0/1 let t309 = circuit_sub(t307, t299); // Fp2 sub coeff 1/1 let t310 = circuit_add(t308, t309); let t311 = circuit_add(t310, t310); let t312 = circuit_sub(t308, t309); let t313 = circuit_sub(t311, t308); let t314 = circuit_sub(t313, t309); let t315 = circuit_add(t312, t290); // Fp2 add coeff 0/1 let t316 = circuit_add(t314, t293); // Fp2 add coeff 1/1 let t317 = circuit_add(t192, t196); // Fp2 add coeff 0/1 let t318 = circuit_add(t193, t197); // Fp2 add coeff 1/1 let t319 = circuit_mul(t280, t317); // Fp2 mul start let t320 = circuit_mul(t281, t318); let t321 = circuit_sub(t319, t320); // Fp2 mul real part end let t322 = circuit_mul(t280, t318); let t323 = circuit_mul(t281, t317); let t324 = circuit_add(t322, t323); // Fp2 mul imag part end let t325 = circuit_sub(t321, t290); // Fp2 sub coeff 0/1 let t326 = circuit_sub(t324, t293); // Fp2 sub coeff 1/1 let t327 = circuit_add(t325, t296); // Fp2 add coeff 0/1 let t328 = circuit_add(t326, t299); // Fp2 add coeff 1/1 let t329 = circuit_add(t280, t282); // Fp2 add coeff 0/1 let t330 = circuit_add(t281, t283); // Fp2 add coeff 1/1 let t331 = circuit_add(t192, t194); // Fp2 add coeff 0/1 let t332 = circuit_add(t193, t195); // Fp2 add coeff 1/1 let t333 = circuit_mul(t329, t331); // Fp2 mul start let t334 = circuit_mul(t330, t332); let t335 = circuit_sub(t333, t334); // Fp2 mul real part end let t336 = circuit_mul(t329, t332); let t337 = circuit_mul(t330, t331); let t338 = circuit_add(t336, t337); // Fp2 mul imag part end let t339 = circuit_sub(t335, t290); // Fp2 sub coeff 0/1 let t340 = circuit_sub(t338, t293); // Fp2 sub coeff 1/1 let t341 = circuit_sub(t339, t296); // Fp2 sub coeff 0/1 let t342 = circuit_sub(t340, t299); // Fp2 sub coeff 1/1 let t343 = circuit_add(t185, t186); let t344 = circuit_add(t343, t343); let t345 = circuit_sub(t185, t186); let t346 = circuit_sub(t344, t185); let t347 = circuit_sub(t346, t186); let t348 = circuit_add(in1, t282); let t349 = circuit_add(t181, t192); // Fp6 add coeff 0/5 let t350 = circuit_add(t182, t193); // Fp6 add coeff 1/5 let t351 = circuit_add(t183, t194); // Fp6 add coeff 2/5 let t352 = circuit_add(t184, t195); // Fp6 add coeff 3/5 let t353 = circuit_add(t185, t196); // Fp6 add coeff 4/5 let t354 = circuit_add(t186, t197); // Fp6 add coeff 5/5 let t355 = circuit_mul(t349, t280); // Fp2 mul start let t356 = circuit_mul(t350, t281); let t357 = circuit_sub(t355, t356); // Fp2 mul real part end let t358 = circuit_mul(t349, t281); let t359 = circuit_mul(t350, t280); let t360 = circuit_add(t358, t359); // Fp2 mul imag part end let t361 = circuit_mul(t351, t348); // Fp2 mul start let t362 = circuit_mul(t352, t283); let t363 = circuit_sub(t361, t362); // Fp2 mul real part end let t364 = circuit_mul(t351, t283); let t365 = circuit_mul(t352, t348); let t366 = circuit_add(t364, t365); // Fp2 mul imag part end let t367 = circuit_add(t351, t353); // Fp2 add coeff 0/1 let t368 = circuit_add(t352, t354); // Fp2 add coeff 1/1 let t369 = circuit_mul(t348, t367); // Fp2 mul start let t370 = circuit_mul(t283, t368); let t371 = circuit_sub(t369, t370); // Fp2 mul real part end let t372 = circuit_mul(t348, t368); let t373 = circuit_mul(t283, t367); let t374 = circuit_add(t372, t373); // Fp2 mul imag part end let t375 = circuit_sub(t371, t363); // Fp2 sub coeff 0/1 let t376 = circuit_sub(t374, t366); // Fp2 sub coeff 1/1 let t377 = circuit_add(t375, t376); let t378 = circuit_add(t377, t377); let t379 = circuit_sub(t375, t376); let t380 = circuit_sub(t378, t375); let t381 = circuit_sub(t380, t376); let t382 = circuit_add(t379, t357); // Fp2 add coeff 0/1 let t383 = circuit_add(t381, t360); // Fp2 add coeff 1/1 let t384 = circuit_add(t349, t353); // Fp2 add coeff 0/1 let t385 = circuit_add(t350, t354); // Fp2 add coeff 1/1 let t386 = circuit_mul(t280, t384); // Fp2 mul start let t387 = circuit_mul(t281, t385); let t388 = circuit_sub(t386, t387); // Fp2 mul real part end let t389 = circuit_mul(t280, t385); let t390 = circuit_mul(t281, t384); let t391 = circuit_add(t389, t390); // Fp2 mul imag part end let t392 = circuit_sub(t388, t357); // Fp2 sub coeff 0/1 let t393 = circuit_sub(t391, t360); // Fp2 sub coeff 1/1 let t394 = circuit_add(t392, t363); // Fp2 add coeff 0/1 let t395 = circuit_add(t393, t366); // Fp2 add coeff 1/1 let t396 = circuit_add(t280, t348); // Fp2 add coeff 0/1 let t397 = circuit_add(t281, t283); // Fp2 add coeff 1/1 let t398 = circuit_add(t349, t351); // Fp2 add coeff 0/1 let t399 = circuit_add(t350, t352); // Fp2 add coeff 1/1 let t400 = circuit_mul(t396, t398); // Fp2 mul start let t401 = circuit_mul(t397, t399); let t402 = circuit_sub(t400, t401); // Fp2 mul real part end let t403 = circuit_mul(t396, t399); let t404 = circuit_mul(t397, t398); let t405 = circuit_add(t403, t404); // Fp2 mul imag part end let t406 = circuit_sub(t402, t357); // Fp2 sub coeff 0/1 let t407 = circuit_sub(t405, t360); // Fp2 sub coeff 1/1 let t408 = circuit_sub(t406, t363); // Fp2 sub coeff 0/1 let t409 = circuit_sub(t407, t366); // Fp2 sub coeff 1/1 let t410 = circuit_sub(t382, t315); // Fp6 sub coeff 0/5 let t411 = circuit_sub(t383, t316); // Fp6 sub coeff 1/5 let t412 = circuit_sub(t408, t341); // Fp6 sub coeff 2/5 let t413 = circuit_sub(t409, t342); // Fp6 sub coeff 3/5 let t414 = circuit_sub(t394, t327); // Fp6 sub coeff 4/5 let t415 = circuit_sub(t395, t328); // Fp6 sub coeff 5/5 let t416 = circuit_sub(t410, t345); // Fp6 sub coeff 0/5 let t417 = circuit_sub(t411, t347); // Fp6 sub coeff 1/5 let t418 = circuit_sub(t412, t181); // Fp6 sub coeff 2/5 let t419 = circuit_sub(t413, t182); // Fp6 sub coeff 3/5 let t420 = circuit_sub(t414, t183); // Fp6 sub coeff 4/5 let t421 = circuit_sub(t415, t184); // Fp6 sub coeff 5/5 let t422 = circuit_add(t183, t184); let t423 = circuit_add(t422, t422); let t424 = circuit_sub(t183, t184); let t425 = circuit_sub(t423, t183); let t426 = circuit_sub(t425, t184); let t427 = circuit_add(t424, t315); // Fp6 add coeff 0/5 let t428 = circuit_add(t426, t316); // Fp6 add coeff 1/5 let t429 = circuit_add(t345, t341); // Fp6 add coeff 2/5 let t430 = circuit_add(t347, t342); // Fp6 add coeff 3/5 let t431 = circuit_add(t181, t327); // Fp6 add coeff 4/5 let t432 = circuit_add(t182, t328); // Fp6 add coeff 5/5 let t433 = circuit_mul(t427, t284); // Fp2 mul start let t434 = circuit_mul(t428, t285); let t435 = circuit_sub(t433, t434); // Fp2 mul real part end let t436 = circuit_mul(t427, t285); let t437 = circuit_mul(t428, t284); let t438 = circuit_add(t436, t437); // Fp2 mul imag part end let t439 = circuit_mul(t429, t286); // Fp2 mul start let t440 = circuit_mul(t430, t287); let t441 = circuit_sub(t439, t440); // Fp2 mul real part end let t442 = circuit_mul(t429, t287); let t443 = circuit_mul(t430, t286); let t444 = circuit_add(t442, t443); // Fp2 mul imag part end let t445 = circuit_add(t429, t431); // Fp2 add coeff 0/1 let t446 = circuit_add(t430, t432); // Fp2 add coeff 1/1 let t447 = circuit_mul(t286, t445); // Fp2 mul start let t448 = circuit_mul(t287, t446); let t449 = circuit_sub(t447, t448); // Fp2 mul real part end let t450 = circuit_mul(t286, t446); let t451 = circuit_mul(t287, t445); let t452 = circuit_add(t450, t451); // Fp2 mul imag part end let t453 = circuit_sub(t449, t441); // Fp2 sub coeff 0/1 let t454 = circuit_sub(t452, t444); // Fp2 sub coeff 1/1 let t455 = circuit_add(t453, t454); let t456 = circuit_add(t455, t455); let t457 = circuit_sub(t453, t454); let t458 = circuit_sub(t456, t453); let t459 = circuit_sub(t458, t454); let t460 = circuit_add(t457, t435); // Fp2 add coeff 0/1 let t461 = circuit_add(t459, t438); // Fp2 add coeff 1/1 let t462 = circuit_add(t427, t431); // Fp2 add coeff 0/1 let t463 = circuit_add(t428, t432); // Fp2 add coeff 1/1 let t464 = circuit_mul(t284, t462); // Fp2 mul start let t465 = circuit_mul(t285, t463); let t466 = circuit_sub(t464, t465); // Fp2 mul real part end let t467 = circuit_mul(t284, t463); let t468 = circuit_mul(t285, t462); let t469 = circuit_add(t467, t468); // Fp2 mul imag part end let t470 = circuit_sub(t466, t435); // Fp2 sub coeff 0/1 let t471 = circuit_sub(t469, t438); // Fp2 sub coeff 1/1 let t472 = circuit_add(t470, t441); // Fp2 add coeff 0/1 let t473 = circuit_add(t471, t444); // Fp2 add coeff 1/1 let t474 = circuit_add(t284, t286); // Fp2 add coeff 0/1 let t475 = circuit_add(t285, t287); // Fp2 add coeff 1/1 let t476 = circuit_add(t427, t429); // Fp2 add coeff 0/1 let t477 = circuit_add(t428, t430); // Fp2 add coeff 1/1 let t478 = circuit_mul(t474, t476); // Fp2 mul start let t479 = circuit_mul(t475, t477); let t480 = circuit_sub(t478, t479); // Fp2 mul real part end let t481 = circuit_mul(t474, t477); let t482 = circuit_mul(t475, t476); let t483 = circuit_add(t481, t482); // Fp2 mul imag part end let t484 = circuit_sub(t480, t435); // Fp2 sub coeff 0/1 let t485 = circuit_sub(t483, t438); // Fp2 sub coeff 1/1 let t486 = circuit_sub(t484, t441); // Fp2 sub coeff 0/1 let t487 = circuit_sub(t485, t444); // Fp2 sub coeff 1/1 let t488 = circuit_add(t420, t421); let t489 = circuit_add(t488, t488); let t490 = circuit_sub(t420, t421); let t491 = circuit_sub(t489, t420); let t492 = circuit_sub(t491, t421); let t493 = circuit_add(in1, t286); let t494 = circuit_add(t416, t427); // Fp6 add coeff 0/5 let t495 = circuit_add(t417, t428); // Fp6 add coeff 1/5 let t496 = circuit_add(t418, t429); // Fp6 add coeff 2/5 let t497 = circuit_add(t419, t430); // Fp6 add coeff 3/5 let t498 = circuit_add(t420, t431); // Fp6 add coeff 4/5 let t499 = circuit_add(t421, t432); // Fp6 add coeff 5/5 let t500 = circuit_mul(t494, t284); // Fp2 mul start let t501 = circuit_mul(t495, t285); let t502 = circuit_sub(t500, t501); // Fp2 mul real part end let t503 = circuit_mul(t494, t285); let t504 = circuit_mul(t495, t284); let t505 = circuit_add(t503, t504); // Fp2 mul imag part end let t506 = circuit_mul(t496, t493); // Fp2 mul start let t507 = circuit_mul(t497, t287); let t508 = circuit_sub(t506, t507); // Fp2 mul real part end let t509 = circuit_mul(t496, t287); let t510 = circuit_mul(t497, t493); let t511 = circuit_add(t509, t510); // Fp2 mul imag part end let t512 = circuit_add(t496, t498); // Fp2 add coeff 0/1 let t513 = circuit_add(t497, t499); // Fp2 add coeff 1/1 let t514 = circuit_mul(t493, t512); // Fp2 mul start let t515 = circuit_mul(t287, t513); let t516 = circuit_sub(t514, t515); // Fp2 mul real part end let t517 = circuit_mul(t493, t513); let t518 = circuit_mul(t287, t512); let t519 = circuit_add(t517, t518); // Fp2 mul imag part end let t520 = circuit_sub(t516, t508); // Fp2 sub coeff 0/1 let t521 = circuit_sub(t519, t511); // Fp2 sub coeff 1/1 let t522 = circuit_add(t520, t521); let t523 = circuit_add(t522, t522); let t524 = circuit_sub(t520, t521); let t525 = circuit_sub(t523, t520); let t526 = circuit_sub(t525, t521); let t527 = circuit_add(t524, t502); // Fp2 add coeff 0/1 let t528 = circuit_add(t526, t505); // Fp2 add coeff 1/1 let t529 = circuit_add(t494, t498); // Fp2 add coeff 0/1 let t530 = circuit_add(t495, t499); // Fp2 add coeff 1/1 let t531 = circuit_mul(t284, t529); // Fp2 mul start let t532 = circuit_mul(t285, t530); let t533 = circuit_sub(t531, t532); // Fp2 mul real part end let t534 = circuit_mul(t284, t530); let t535 = circuit_mul(t285, t529); let t536 = circuit_add(t534, t535); // Fp2 mul imag part end let t537 = circuit_sub(t533, t502); // Fp2 sub coeff 0/1 let t538 = circuit_sub(t536, t505); // Fp2 sub coeff 1/1 let t539 = circuit_add(t537, t508); // Fp2 add coeff 0/1 let t540 = circuit_add(t538, t511); // Fp2 add coeff 1/1 let t541 = circuit_add(t284, t493); // Fp2 add coeff 0/1 let t542 = circuit_add(t285, t287); // Fp2 add coeff 1/1 let t543 = circuit_add(t494, t496); // Fp2 add coeff 0/1 let t544 = circuit_add(t495, t497); // Fp2 add coeff 1/1 let t545 = circuit_mul(t541, t543); // Fp2 mul start let t546 = circuit_mul(t542, t544); let t547 = circuit_sub(t545, t546); // Fp2 mul real part end let t548 = circuit_mul(t541, t544); let t549 = circuit_mul(t542, t543); let t550 = circuit_add(t548, t549); // Fp2 mul imag part end let t551 = circuit_sub(t547, t502); // Fp2 sub coeff 0/1 let t552 = circuit_sub(t550, t505); // Fp2 sub coeff 1/1 let t553 = circuit_sub(t551, t508); // Fp2 sub coeff 0/1 let t554 = circuit_sub(t552, t511); // Fp2 sub coeff 1/1 let t555 = circuit_sub(t527, t460); // Fp6 sub coeff 0/5 let t556 = circuit_sub(t528, t461); // Fp6 sub coeff 1/5 let t557 = circuit_sub(t553, t486); // Fp6 sub coeff 2/5 let t558 = circuit_sub(t554, t487); // Fp6 sub coeff 3/5 let t559 = circuit_sub(t539, t472); // Fp6 sub coeff 4/5 let t560 = circuit_sub(t540, t473); // Fp6 sub coeff 5/5 let t561 = circuit_sub(t555, t490); // Fp6 sub coeff 0/5 let t562 = circuit_sub(t556, t492); // Fp6 sub coeff 1/5 let t563 = circuit_sub(t557, t416); // Fp6 sub coeff 2/5 let t564 = circuit_sub(t558, t417); // Fp6 sub coeff 3/5 let t565 = circuit_sub(t559, t418); // Fp6 sub coeff 4/5 let t566 = circuit_sub(t560, t419); // Fp6 sub coeff 5/5 let t567 = circuit_add(t418, t419); let t568 = circuit_add(t567, t567); let t569 = circuit_sub(t418, t419); let t570 = circuit_sub(t568, t418); let t571 = circuit_sub(t570, t419); let t572 = circuit_add(t569, t460); // Fp6 add coeff 0/5 let t573 = circuit_add(t571, t461); // Fp6 add coeff 1/5 let t574 = circuit_add(t490, t486); // Fp6 add coeff 2/5 let t575 = circuit_add(t492, t487); // Fp6 add coeff 3/5 let t576 = circuit_add(t416, t472); // Fp6 add coeff 4/5 let t577 = circuit_add(t417, t473); // Fp6 add coeff 5/5 let t578 = circuit_add(t260, t261); let t579 = circuit_add(t578, t270); let t580 = circuit_add(t579, t271); let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = ( t580, t572, t573, t574, t575, t576, t577, t561, t562, t563, t564, t565, t566, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in2 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in3 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in4 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in5 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in6 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in7 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.x0); // in8 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.x1); // in9 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.y0); // in10 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.y1); // in11 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a0); // in12 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a1); // in13 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a0); // in14 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a1); // in15 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a0); // in16 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a1); // in17 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a0); // in18 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a1); // in19 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a0); // in20 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a1); // in21 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a0); // in22 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a1); // in23 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t260), x1: outputs.get_output(t261), y0: outputs.get_output(t270), y1: outputs.get_output(t271), }; let Mi_plus_one: E12T = E12T { c0b0a0: outputs.get_output(t572), c0b0a1: outputs.get_output(t573), c0b1a0: outputs.get_output(t574), c0b1a1: outputs.get_output(t575), c0b2a0: outputs.get_output(t576), c0b2a1: outputs.get_output(t577), c1b0a0: outputs.get_output(t561), c1b0a1: outputs.get_output(t562), c1b1a0: outputs.get_output(t563), c1b1a1: outputs.get_output(t564), c1b2a0: outputs.get_output(t565), c1b2a1: outputs.get_output(t566), }; return (Q0, Mi_plus_one); } #[inline(always)] pub fn run_BLS12_381_TOWER_MILLER_INIT_BIT_1P_circuit( yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, ) -> (G2Point, u384, u384, u384, u384, u384, u384, u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x3 let in1 = CE::> {}; // 0x6 let in2 = CE::> {}; // 0x0 let in3 = CE::> {}; // 0x1 // INPUT stack let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in6, in7); let t1 = circuit_sub(in6, in7); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in6, in7); let t4 = circuit_mul(t2, in0); let t5 = circuit_mul(t3, in1); let t6 = circuit_add(in8, in8); // Fp2 add coeff 0/1 let t7 = circuit_add(in9, in9); // Fp2 add coeff 1/1 let t8 = circuit_mul(t6, t6); // Fp2 Inv start let t9 = circuit_mul(t7, t7); let t10 = circuit_add(t8, t9); let t11 = circuit_inverse(t10); let t12 = circuit_mul(t6, t11); // Fp2 Inv real part end let t13 = circuit_mul(t7, t11); let t14 = circuit_sub(in2, t13); // Fp2 Inv imag part end let t15 = circuit_mul(t4, t12); // Fp2 mul start let t16 = circuit_mul(t5, t14); let t17 = circuit_sub(t15, t16); // Fp2 mul real part end let t18 = circuit_mul(t4, t14); let t19 = circuit_mul(t5, t12); let t20 = circuit_add(t18, t19); // Fp2 mul imag part end let t21 = circuit_mul(t17, in6); // Fp2 mul start let t22 = circuit_mul(t20, in7); let t23 = circuit_sub(t21, t22); // Fp2 mul real part end let t24 = circuit_mul(t17, in7); let t25 = circuit_mul(t20, in6); let t26 = circuit_add(t24, t25); // Fp2 mul imag part end let t27 = circuit_sub(t23, in8); // Fp2 sub coeff 0/1 let t28 = circuit_sub(t26, in9); // Fp2 sub coeff 1/1 let t29 = circuit_add(t17, t20); let t30 = circuit_sub(t17, t20); let t31 = circuit_mul(t29, t30); let t32 = circuit_mul(t17, t20); let t33 = circuit_add(t32, t32); let t34 = circuit_add(in6, in6); // Fp2 add coeff 0/1 let t35 = circuit_add(in7, in7); // Fp2 add coeff 1/1 let t36 = circuit_sub(t31, t34); // Fp2 sub coeff 0/1 let t37 = circuit_sub(t33, t35); // Fp2 sub coeff 1/1 let t38 = circuit_sub(in6, t36); // Fp2 sub coeff 0/1 let t39 = circuit_sub(in7, t37); // Fp2 sub coeff 1/1 let t40 = circuit_mul(t38, t38); // Fp2 Inv start let t41 = circuit_mul(t39, t39); let t42 = circuit_add(t40, t41); let t43 = circuit_inverse(t42); let t44 = circuit_mul(t38, t43); // Fp2 Inv real part end let t45 = circuit_mul(t39, t43); let t46 = circuit_sub(in2, t45); // Fp2 Inv imag part end let t47 = circuit_mul(t6, t44); // Fp2 mul start let t48 = circuit_mul(t7, t46); let t49 = circuit_sub(t47, t48); // Fp2 mul real part end let t50 = circuit_mul(t6, t46); let t51 = circuit_mul(t7, t44); let t52 = circuit_add(t50, t51); // Fp2 mul imag part end let t53 = circuit_sub(t49, t17); // Fp2 sub coeff 0/1 let t54 = circuit_sub(t52, t20); // Fp2 sub coeff 1/1 let t55 = circuit_mul(t53, in6); // Fp2 mul start let t56 = circuit_mul(t54, in7); let t57 = circuit_sub(t55, t56); // Fp2 mul real part end let t58 = circuit_mul(t53, in7); let t59 = circuit_mul(t54, in6); let t60 = circuit_add(t58, t59); // Fp2 mul imag part end let t61 = circuit_sub(t57, in8); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t60, in9); // Fp2 sub coeff 1/1 let t63 = circuit_add(t53, t54); let t64 = circuit_sub(t53, t54); let t65 = circuit_mul(t63, t64); let t66 = circuit_mul(t53, t54); let t67 = circuit_add(t66, t66); let t68 = circuit_add(in6, t36); // Fp2 add coeff 0/1 let t69 = circuit_add(in7, t37); // Fp2 add coeff 1/1 let t70 = circuit_sub(t65, t68); // Fp2 sub coeff 0/1 let t71 = circuit_sub(t67, t69); // Fp2 sub coeff 1/1 let t72 = circuit_sub(in6, t70); // Fp2 sub coeff 0/1 let t73 = circuit_sub(in7, t71); // Fp2 sub coeff 1/1 let t74 = circuit_mul(t53, t72); // Fp2 mul start let t75 = circuit_mul(t54, t73); let t76 = circuit_sub(t74, t75); // Fp2 mul real part end let t77 = circuit_mul(t53, t73); let t78 = circuit_mul(t54, t72); let t79 = circuit_add(t77, t78); // Fp2 mul imag part end let t80 = circuit_sub(t76, in8); // Fp2 sub coeff 0/1 let t81 = circuit_sub(t79, in9); // Fp2 sub coeff 1/1 let t82 = circuit_mul(t27, in4); let t83 = circuit_mul(t28, in4); let t84 = circuit_mul(t17, in5); let t85 = circuit_mul(t20, in5); let t86 = circuit_mul(t61, in4); let t87 = circuit_mul(t62, in4); let t88 = circuit_mul(t53, in5); let t89 = circuit_mul(t54, in5); let t90 = circuit_mul(t86, t82); // Fp2 mul start let t91 = circuit_mul(t87, t83); let t92 = circuit_sub(t90, t91); // Fp2 mul real part end let t93 = circuit_mul(t86, t83); let t94 = circuit_mul(t87, t82); let t95 = circuit_add(t93, t94); // Fp2 mul imag part end let t96 = circuit_mul(t88, t84); // Fp2 mul start let t97 = circuit_mul(t89, t85); let t98 = circuit_sub(t96, t97); // Fp2 mul real part end let t99 = circuit_mul(t88, t85); let t100 = circuit_mul(t89, t84); let t101 = circuit_add(t99, t100); // Fp2 mul imag part end let t102 = circuit_add(t82, t86); // Fp2 add coeff 0/1 let t103 = circuit_add(t83, t87); // Fp2 add coeff 1/1 let t104 = circuit_add(t86, t88); // Fp2 add coeff 0/1 let t105 = circuit_add(t87, t89); // Fp2 add coeff 1/1 let t106 = circuit_add(t82, t84); // Fp2 add coeff 0/1 let t107 = circuit_add(t83, t85); // Fp2 add coeff 1/1 let t108 = circuit_mul(t106, t104); // Fp2 mul start let t109 = circuit_mul(t107, t105); let t110 = circuit_sub(t108, t109); // Fp2 mul real part end let t111 = circuit_mul(t106, t105); let t112 = circuit_mul(t107, t104); let t113 = circuit_add(t111, t112); // Fp2 mul imag part end let t114 = circuit_sub(t110, t92); // Fp2 sub coeff 0/1 let t115 = circuit_sub(t113, t95); // Fp2 sub coeff 1/1 let t116 = circuit_sub(t114, t98); // Fp2 sub coeff 0/1 let t117 = circuit_sub(t115, t101); // Fp2 sub coeff 1/1 let t118 = circuit_add(t84, t88); // Fp2 add coeff 0/1 let t119 = circuit_add(t85, t89); // Fp2 add coeff 1/1 let t120 = circuit_add(in3, in2); let t121 = circuit_add(t120, t120); let t122 = circuit_sub(in3, in2); let t123 = circuit_sub(t121, in3); let t124 = circuit_sub(t123, in2); let t125 = circuit_add(t122, t92); // Fp2 add coeff 0/1 let t126 = circuit_add(t124, t95); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BLS12_381_modulus(); // BLS12_381 prime field modulus let mut circuit_inputs = ( t70, t71, t80, t81, t125, t126, t116, t117, t98, t101, t102, t103, t118, t119, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in3 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in4 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in5 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in6 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in7 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in8 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in9 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t70), x1: outputs.get_output(t71), y0: outputs.get_output(t80), y1: outputs.get_output(t81), }; let c0b0a0: u384 = outputs.get_output(t125); let c0b0a1: u384 = outputs.get_output(t126); let c0b1a0: u384 = outputs.get_output(t116); let c0b1a1: u384 = outputs.get_output(t117); let c0b2a0: u384 = outputs.get_output(t98); let c0b2a1: u384 = outputs.get_output(t101); let c1b1a0: u384 = outputs.get_output(t102); let c1b1a1: u384 = outputs.get_output(t103); let c1b2a0: u384 = outputs.get_output(t118); let c1b2a1: u384 = outputs.get_output(t119); return (Q0, c0b0a0, c0b0a1, c0b1a0, c0b1a1, c0b2a0, c0b2a1, c1b1a0, c1b1a1, c1b2a0, c1b2a1); } #[inline(always)] pub fn run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0xa let in1 = CE::> {}; // 0x9 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in10, in11); let t1 = circuit_sub(in10, in11); let t2 = circuit_mul(t0, t1); let t3 = circuit_mul(in10, in11); let t4 = circuit_add(t3, t3); let t5 = circuit_add(in2, in3); let t6 = circuit_sub(in2, in3); let t7 = circuit_mul(t5, t6); let t8 = circuit_mul(in2, in3); let t9 = circuit_add(t8, t8); let t10 = circuit_add(in10, in2); // Fp2 add coeff 0/1 let t11 = circuit_add(in11, in3); // Fp2 add coeff 1/1 let t12 = circuit_add(t10, t11); let t13 = circuit_sub(t10, t11); let t14 = circuit_mul(t12, t13); let t15 = circuit_mul(t10, t11); let t16 = circuit_add(t15, t15); let t17 = circuit_sub(t14, t2); // Fp2 sub coeff 0/1 let t18 = circuit_sub(t16, t4); // Fp2 sub coeff 1/1 let t19 = circuit_sub(t17, t7); // Fp2 sub coeff 0/1 let t20 = circuit_sub(t18, t9); // Fp2 sub coeff 1/1 let t21 = circuit_add(in6, in7); let t22 = circuit_sub(in6, in7); let t23 = circuit_mul(t21, t22); let t24 = circuit_mul(in6, in7); let t25 = circuit_add(t24, t24); let t26 = circuit_add(in8, in9); let t27 = circuit_sub(in8, in9); let t28 = circuit_mul(t26, t27); let t29 = circuit_mul(in8, in9); let t30 = circuit_add(t29, t29); let t31 = circuit_add(in6, in8); // Fp2 add coeff 0/1 let t32 = circuit_add(in7, in9); // Fp2 add coeff 1/1 let t33 = circuit_add(t31, t32); let t34 = circuit_sub(t31, t32); let t35 = circuit_mul(t33, t34); let t36 = circuit_mul(t31, t32); let t37 = circuit_add(t36, t36); let t38 = circuit_sub(t35, t23); // Fp2 sub coeff 0/1 let t39 = circuit_sub(t37, t25); // Fp2 sub coeff 1/1 let t40 = circuit_sub(t38, t28); // Fp2 sub coeff 0/1 let t41 = circuit_sub(t39, t30); // Fp2 sub coeff 1/1 let t42 = circuit_add(in12, in13); let t43 = circuit_sub(in12, in13); let t44 = circuit_mul(t42, t43); let t45 = circuit_mul(in12, in13); let t46 = circuit_add(t45, t45); let t47 = circuit_add(in4, in5); let t48 = circuit_sub(in4, in5); let t49 = circuit_mul(t47, t48); let t50 = circuit_mul(in4, in5); let t51 = circuit_add(t50, t50); let t52 = circuit_add(in12, in4); // Fp2 add coeff 0/1 let t53 = circuit_add(in13, in5); // Fp2 add coeff 1/1 let t54 = circuit_add(t52, t53); let t55 = circuit_sub(t52, t53); let t56 = circuit_mul(t54, t55); let t57 = circuit_mul(t52, t53); let t58 = circuit_add(t57, t57); let t59 = circuit_sub(t56, t44); // Fp2 sub coeff 0/1 let t60 = circuit_sub(t58, t46); // Fp2 sub coeff 1/1 let t61 = circuit_sub(t59, t49); // Fp2 sub coeff 0/1 let t62 = circuit_sub(t60, t51); // Fp2 sub coeff 1/1 let t63 = circuit_add(t61, t62); let t64 = circuit_mul(t63, in0); let t65 = circuit_mul(t61, in1); let t66 = circuit_sub(t65, t62); let t67 = circuit_sub(t64, t65); let t68 = circuit_sub(t67, t62); let t69 = circuit_add(t2, t4); let t70 = circuit_mul(t69, in0); let t71 = circuit_mul(t2, in1); let t72 = circuit_sub(t71, t4); let t73 = circuit_sub(t70, t71); let t74 = circuit_sub(t73, t4); let t75 = circuit_add(t72, t7); // Fp2 add coeff 0/1 let t76 = circuit_add(t74, t9); // Fp2 add coeff 1/1 let t77 = circuit_add(t23, t25); let t78 = circuit_mul(t77, in0); let t79 = circuit_mul(t23, in1); let t80 = circuit_sub(t79, t25); let t81 = circuit_sub(t78, t79); let t82 = circuit_sub(t81, t25); let t83 = circuit_add(t80, t28); // Fp2 add coeff 0/1 let t84 = circuit_add(t82, t30); // Fp2 add coeff 1/1 let t85 = circuit_add(t44, t46); let t86 = circuit_mul(t85, in0); let t87 = circuit_mul(t44, in1); let t88 = circuit_sub(t87, t46); let t89 = circuit_sub(t86, t87); let t90 = circuit_sub(t89, t46); let t91 = circuit_add(t88, t49); // Fp2 add coeff 0/1 let t92 = circuit_add(t90, t51); // Fp2 add coeff 1/1 let t93 = circuit_sub(t75, in2); // Fp2 sub coeff 0/1 let t94 = circuit_sub(t76, in3); // Fp2 sub coeff 1/1 let t95 = circuit_add(t93, t93); // Fp2 add coeff 0/1 let t96 = circuit_add(t94, t94); // Fp2 add coeff 1/1 let t97 = circuit_add(t95, t75); // Fp2 add coeff 0/1 let t98 = circuit_add(t96, t76); // Fp2 add coeff 1/1 let t99 = circuit_sub(t83, in4); // Fp2 sub coeff 0/1 let t100 = circuit_sub(t84, in5); // Fp2 sub coeff 1/1 let t101 = circuit_add(t99, t99); // Fp2 add coeff 0/1 let t102 = circuit_add(t100, t100); // Fp2 add coeff 1/1 let t103 = circuit_add(t101, t83); // Fp2 add coeff 0/1 let t104 = circuit_add(t102, t84); // Fp2 add coeff 1/1 let t105 = circuit_sub(t91, in6); // Fp2 sub coeff 0/1 let t106 = circuit_sub(t92, in7); // Fp2 sub coeff 1/1 let t107 = circuit_add(t105, t105); // Fp2 add coeff 0/1 let t108 = circuit_add(t106, t106); // Fp2 add coeff 1/1 let t109 = circuit_add(t107, t91); // Fp2 add coeff 0/1 let t110 = circuit_add(t108, t92); // Fp2 add coeff 1/1 let t111 = circuit_add(t66, in8); // Fp2 add coeff 0/1 let t112 = circuit_add(t68, in9); // Fp2 add coeff 1/1 let t113 = circuit_add(t111, t111); // Fp2 add coeff 0/1 let t114 = circuit_add(t112, t112); // Fp2 add coeff 1/1 let t115 = circuit_add(t113, t66); // Fp2 add coeff 0/1 let t116 = circuit_add(t114, t68); // Fp2 add coeff 1/1 let t117 = circuit_add(t19, in10); // Fp2 add coeff 0/1 let t118 = circuit_add(t20, in11); // Fp2 add coeff 1/1 let t119 = circuit_add(t117, t117); // Fp2 add coeff 0/1 let t120 = circuit_add(t118, t118); // Fp2 add coeff 1/1 let t121 = circuit_add(t119, t19); // Fp2 add coeff 0/1 let t122 = circuit_add(t120, t20); // Fp2 add coeff 1/1 let t123 = circuit_add(t40, in12); // Fp2 add coeff 0/1 let t124 = circuit_add(t41, in13); // Fp2 add coeff 1/1 let t125 = circuit_add(t123, t123); // Fp2 add coeff 0/1 let t126 = circuit_add(t124, t124); // Fp2 add coeff 1/1 let t127 = circuit_add(t125, t40); // Fp2 add coeff 0/1 let t128 = circuit_add(t126, t41); // Fp2 add coeff 1/1 let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t97, t98, t103, t104, t109, t110, t115, t116, t121, t122, t127, t128) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0xa, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x9, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in2 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in3 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in4 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in5 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in6 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in7 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in8 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in9 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in10 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in12 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in13 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t97), c0b0a1: outputs.get_output(t98), c0b1a0: outputs.get_output(t103), c0b1a1: outputs.get_output(t104), c0b2a0: outputs.get_output(t109), c0b2a1: outputs.get_output(t110), c1b0a0: outputs.get_output(t115), c1b0a1: outputs.get_output(t116), c1b1a0: outputs.get_output(t121), c1b1a1: outputs.get_output(t122), c1b2a0: outputs.get_output(t127), c1b2a1: outputs.get_output(t128), }; return (res,); } #[inline(always)] pub fn run_BN254_E12T_FROBENIUS_CUBE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x856e078b755ef0abaff1c77959f25ac805ffd3d5d6942d37b746ee87bdcfb6d let in2 = CE::> {}; // 0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de let in3 = CE::> {}; // 0xbc58c6611c08dab19bee0f7b5b2444ee633094575b06bcb0e1a92bc3ccbf066 let in4 = CE::> {}; // 0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f let in5 = CE::> {}; // 0x19dc81cfcc82e4bbefe9608cd0acaa90894cb38dbe55d24ae86f7d391ed4a67f let in6 = CE::> {}; // 0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101 let in7 = CE::> {}; // 0x2a275b6d9896aa4cdbf17f1dca9e5ea3bbd689a3bea870f45fcc8ad066dce9ed let in8 = CE::> {}; // 0x28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64 let in9 = CE::> {}; // 0x13c49044952c0905711699fa3b4d3f692ed68098967c84a5ebde847076261b43 let in10 = CE::< CI<10>, > {}; // 0x16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499 // INPUT stack let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in12); let t1 = circuit_add(in11, in0); let t2 = circuit_sub(in0, in14); let t3 = circuit_sub(in0, in16); let t4 = circuit_sub(in0, in18); let t5 = circuit_sub(in0, in20); let t6 = circuit_sub(in0, in22); let t7 = circuit_mul(in1, in13); // Fp2 mul start let t8 = circuit_mul(in2, t2); let t9 = circuit_sub(t7, t8); // Fp2 mul real part end let t10 = circuit_mul(in1, t2); let t11 = circuit_mul(in2, in13); let t12 = circuit_add(t10, t11); // Fp2 mul imag part end let t13 = circuit_mul(in3, in15); // Fp2 mul start let t14 = circuit_mul(in4, t3); let t15 = circuit_sub(t13, t14); // Fp2 mul real part end let t16 = circuit_mul(in3, t3); let t17 = circuit_mul(in4, in15); let t18 = circuit_add(t16, t17); // Fp2 mul imag part end let t19 = circuit_mul(in5, in17); // Fp2 mul start let t20 = circuit_mul(in6, t4); let t21 = circuit_sub(t19, t20); // Fp2 mul real part end let t22 = circuit_mul(in5, t4); let t23 = circuit_mul(in6, in17); let t24 = circuit_add(t22, t23); // Fp2 mul imag part end let t25 = circuit_mul(in7, in19); // Fp2 mul start let t26 = circuit_mul(in8, t5); let t27 = circuit_sub(t25, t26); // Fp2 mul real part end let t28 = circuit_mul(in7, t5); let t29 = circuit_mul(in8, in19); let t30 = circuit_add(t28, t29); // Fp2 mul imag part end let t31 = circuit_mul(in9, in21); // Fp2 mul start let t32 = circuit_mul(in10, t6); let t33 = circuit_sub(t31, t32); // Fp2 mul real part end let t34 = circuit_mul(in9, t6); let t35 = circuit_mul(in10, in21); let t36 = circuit_add(t34, t35); // Fp2 mul imag part end let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t1, t0, t9, t12, t15, t18, t21, t24, t27, t30, t33, t36).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(E12T_FROBENIUS_CUBE_BN254_CONSTANTS.span()); // in0 - in10 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in11 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in12 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in13 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in14 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in15 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in16 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in17 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in18 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in19 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in20 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in21 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in22 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t1), c0b0a1: outputs.get_output(t0), c0b1a0: outputs.get_output(t9), c0b1a1: outputs.get_output(t12), c0b2a0: outputs.get_output(t15), c0b2a1: outputs.get_output(t18), c1b0a0: outputs.get_output(t21), c1b0a1: outputs.get_output(t24), c1b1a0: outputs.get_output(t27), c1b1a1: outputs.get_output(t30), c1b2a0: outputs.get_output(t33), c1b2a1: outputs.get_output(t36), }; return (res,); } const E12T_FROBENIUS_CUBE_BN254_CONSTANTS: [u384; 11] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x5d6942d37b746ee87bdcfb6d, limb1: 0xbaff1c77959f25ac805ffd3d, limb2: 0x856e078b755ef0a, limb3: 0x0, }, u384 { limb0: 0x98ff2631380cab2baaa586de, limb1: 0xa9f30e6dec26094f0fdf31bf, limb2: 0x4f1de41b3d1766f, limb3: 0x0, }, u384 { limb0: 0x75b06bcb0e1a92bc3ccbf066, limb1: 0x19bee0f7b5b2444ee6330945, limb2: 0xbc58c6611c08dab, limb3: 0x0, }, u384 { limb0: 0x737f96e55fe3ed9d730c239f, limb1: 0xfeb0f6ef0cd21d04a44a9e08, limb2: 0x23d5e999e1910a12, limb3: 0x0, }, u384 { limb0: 0xbe55d24ae86f7d391ed4a67f, limb1: 0xefe9608cd0acaa90894cb38d, limb2: 0x19dc81cfcc82e4bb, limb3: 0x0, }, u384 { limb0: 0x97d439ec7694aa2bf4c0c101, limb1: 0x6cbeee33576139d7f03a5e3, limb2: 0xabf8b60be77d73, limb3: 0x0, }, u384 { limb0: 0xbea870f45fcc8ad066dce9ed, limb1: 0xdbf17f1dca9e5ea3bbd689a3, limb2: 0x2a275b6d9896aa4c, limb3: 0x0, }, u384 { limb0: 0xd8cf6ebab94d0cb3b2594c64, limb1: 0xb14b900e9507e9327600ecc7, limb2: 0x28a411b634f09b8f, limb3: 0x0, }, u384 { limb0: 0x967c84a5ebde847076261b43, limb1: 0x711699fa3b4d3f692ed68098, limb2: 0x13c49044952c0905, limb3: 0x0, }, u384 { limb0: 0x200280211f25041384282499, limb1: 0x9fb1b2282a48633d3e2ddaea, limb2: 0x16db366a59b1dd0b, limb3: 0x0, }, ]; #[inline(always)] pub fn run_BN254_E12T_FROBENIUS_SQUARE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48 let in2 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe let in3 = CE::> {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49 let in4 = CE::> {}; // -0x1 % p let in5 = CE::> {}; // 0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff // INPUT stack let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in6, in0); let t1 = circuit_add(in7, in0); let t2 = circuit_mul(in1, in8); let t3 = circuit_mul(in1, in9); let t4 = circuit_mul(in2, in10); let t5 = circuit_mul(in2, in11); let t6 = circuit_mul(in3, in12); let t7 = circuit_mul(in3, in13); let t8 = circuit_mul(in4, in14); let t9 = circuit_mul(in4, in15); let t10 = circuit_mul(in5, in16); let t11 = circuit_mul(in5, in17); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs .next_2( [0xbb966e3de4bd44e5607cfd48, 0x5e6dd9e7e0acccb0c28f069f, 0x30644e72e131a029, 0x0], ); // in1 circuit_inputs = circuit_inputs .next_2([0xacdb5c4f5763473177fffffe, 0x59e26bcea0d48bacd4f263f1, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs .next_2( [0xbb966e3de4bd44e5607cfd49, 0x5e6dd9e7e0acccb0c28f069f, 0x30644e72e131a029, 0x0], ); // in3 circuit_inputs = circuit_inputs .next_2( [0x6871ca8d3c208c16d87cfd46, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], ); // in4 circuit_inputs = circuit_inputs .next_2([0xacdb5c4f5763473177ffffff, 0x59e26bcea0d48bacd4f263f1, 0x0, 0x0]); // in5 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in6 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in7 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in8 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in9 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in10 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in12 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in13 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in14 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in15 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in16 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in17 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t0), c0b0a1: outputs.get_output(t1), c0b1a0: outputs.get_output(t2), c0b1a1: outputs.get_output(t3), c0b2a0: outputs.get_output(t4), c0b2a1: outputs.get_output(t5), c1b0a0: outputs.get_output(t6), c1b0a1: outputs.get_output(t7), c1b1a0: outputs.get_output(t8), c1b1a1: outputs.get_output(t9), c1b2a0: outputs.get_output(t10), c1b2a1: outputs.get_output(t11), }; return (res,); } #[inline(always)] pub fn run_BN254_E12T_FROBENIUS_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d let in2 = CE::> {}; // 0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2 let in3 = CE::> {}; // 0x5b54f5e64eea80180f3c0b75a181e84d33365f7be94ec72848a1f55921ea762 let in4 = CE::> {}; // 0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126 let in5 = CE::> {}; // 0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470 let in6 = CE::> {}; // 0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac let in7 = CE::> {}; // 0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a let in8 = CE::> {}; // 0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3 let in9 = CE::> {}; // 0x183c1e74f798649e93a3661a4353ff4425c459b55aa1bd32ea2c810eab7692f let in10 = CE::< CI<10>, > {}; // 0x12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b // INPUT stack let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in12); let t1 = circuit_add(in11, in0); let t2 = circuit_sub(in0, in14); let t3 = circuit_sub(in0, in16); let t4 = circuit_sub(in0, in18); let t5 = circuit_sub(in0, in20); let t6 = circuit_sub(in0, in22); let t7 = circuit_mul(in1, in13); // Fp2 mul start let t8 = circuit_mul(in2, t2); let t9 = circuit_sub(t7, t8); // Fp2 mul real part end let t10 = circuit_mul(in1, t2); let t11 = circuit_mul(in2, in13); let t12 = circuit_add(t10, t11); // Fp2 mul imag part end let t13 = circuit_mul(in3, in15); // Fp2 mul start let t14 = circuit_mul(in4, t3); let t15 = circuit_sub(t13, t14); // Fp2 mul real part end let t16 = circuit_mul(in3, t3); let t17 = circuit_mul(in4, in15); let t18 = circuit_add(t16, t17); // Fp2 mul imag part end let t19 = circuit_mul(in5, in17); // Fp2 mul start let t20 = circuit_mul(in6, t4); let t21 = circuit_sub(t19, t20); // Fp2 mul real part end let t22 = circuit_mul(in5, t4); let t23 = circuit_mul(in6, in17); let t24 = circuit_add(t22, t23); // Fp2 mul imag part end let t25 = circuit_mul(in7, in19); // Fp2 mul start let t26 = circuit_mul(in8, t5); let t27 = circuit_sub(t25, t26); // Fp2 mul real part end let t28 = circuit_mul(in7, t5); let t29 = circuit_mul(in8, in19); let t30 = circuit_add(t28, t29); // Fp2 mul imag part end let t31 = circuit_mul(in9, in21); // Fp2 mul start let t32 = circuit_mul(in10, t6); let t33 = circuit_sub(t31, t32); // Fp2 mul real part end let t34 = circuit_mul(in9, t6); let t35 = circuit_mul(in10, in21); let t36 = circuit_add(t34, t35); // Fp2 mul imag part end let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = (t1, t0, t9, t12, t15, t18, t21, t24, t27, t30, t33, t36).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_span(E12T_FROBENIUS_BN254_CONSTANTS.span()); // in0 - in10 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in11 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in12 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in13 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in14 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in15 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in16 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in17 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in18 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in19 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in20 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in21 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in22 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t1), c0b0a1: outputs.get_output(t0), c0b1a0: outputs.get_output(t9), c0b1a1: outputs.get_output(t12), c0b2a0: outputs.get_output(t15), c0b2a1: outputs.get_output(t18), c1b0a0: outputs.get_output(t21), c1b0a1: outputs.get_output(t24), c1b1a0: outputs.get_output(t27), c1b1a1: outputs.get_output(t30), c1b2a0: outputs.get_output(t33), c1b2a1: outputs.get_output(t36), }; return (res,); } const E12T_FROBENIUS_BN254_CONSTANTS: [u384; 11] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xc2c3330c99e39557176f553d, limb1: 0x4c0bec3cf559b143b78cc310, limb2: 0x2fb347984f7911f7, limb3: 0x0, }, u384 { limb0: 0xb7c9dce1665d51c640fcba2, limb1: 0x4ba4cc8bd75a079432ae2a1d, limb2: 0x16c9e55061ebae20, limb3: 0x0, }, u384 { limb0: 0xbe94ec72848a1f55921ea762, limb1: 0x80f3c0b75a181e84d33365f7, limb2: 0x5b54f5e64eea801, limb3: 0x0, }, u384 { limb0: 0x1bdec763c13b4711cd2b8126, limb1: 0x9f3a80b03b0b1c923685d2ea, limb2: 0x2c145edbe7fd8aee, limb3: 0x0, }, u384 { limb0: 0x292f2176d60b35dadcc9e470, limb1: 0xe8b99fdd76e68b605c521e08, limb2: 0x1284b71c2865a7df, limb3: 0x0, }, u384 { limb0: 0x8eeec7e5ca5cf05f80f362ac, limb1: 0xa6327cfe12150b8e74799277, limb2: 0x246996f3b4fae7e6, limb3: 0x0, }, u384 { limb0: 0xa9c95998dc54014671a0135a, limb1: 0xdc5ec698b6e2f9b9dbaae0ed, limb2: 0x63cf305489af5dc, limb3: 0x0, }, u384 { limb0: 0x8fa25bd282d37f632623b0e3, limb1: 0x704b5a7ec796f2b21807dc9, limb2: 0x7c03cbcac41049a, limb3: 0x0, }, u384 { limb0: 0x55aa1bd32ea2c810eab7692f, limb1: 0xe93a3661a4353ff4425c459b, limb2: 0x183c1e74f798649, limb3: 0x0, }, u384 { limb0: 0x678e2ac024c6b8ee6e0c2c4b, limb1: 0xa27fb246c7729f7db080cb99, limb2: 0x12acf2ca76fd0675, limb3: 0x0, }, ]; #[inline(always)] pub fn run_BN254_E12T_INVERSE_circuit(M: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0xa let in1 = CE::> {}; // 0x9 let in2 = CE::> {}; // 0x0 // INPUT stack let (in3, in4, in5) = (CE::> {}, CE::> {}, CE::> {}); let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_mul(in3, in5); // Fp2 mul start let t1 = circuit_mul(in4, in6); let t2 = circuit_sub(t0, t1); // Fp2 mul real part end let t3 = circuit_mul(in3, in6); let t4 = circuit_mul(in4, in5); let t5 = circuit_add(t3, t4); // Fp2 mul imag part end let t6 = circuit_add(t2, t2); // Fp2 add coeff 0/1 let t7 = circuit_add(t5, t5); // Fp2 add coeff 1/1 let t8 = circuit_add(in7, in8); let t9 = circuit_sub(in7, in8); let t10 = circuit_mul(t8, t9); let t11 = circuit_mul(in7, in8); let t12 = circuit_add(t11, t11); let t13 = circuit_add(t10, t12); let t14 = circuit_mul(t13, in0); let t15 = circuit_mul(t10, in1); let t16 = circuit_sub(t15, t12); let t17 = circuit_sub(t14, t15); let t18 = circuit_sub(t17, t12); let t19 = circuit_add(t16, t6); // Fp2 add coeff 0/1 let t20 = circuit_add(t18, t7); // Fp2 add coeff 1/1 let t21 = circuit_sub(t6, t10); // Fp2 sub coeff 0/1 let t22 = circuit_sub(t7, t12); // Fp2 sub coeff 1/1 let t23 = circuit_add(in3, in4); let t24 = circuit_sub(in3, in4); let t25 = circuit_mul(t23, t24); let t26 = circuit_mul(in3, in4); let t27 = circuit_add(t26, t26); let t28 = circuit_sub(in3, in5); // Fp2 sub coeff 0/1 let t29 = circuit_sub(in4, in6); // Fp2 sub coeff 1/1 let t30 = circuit_add(t28, in7); // Fp2 add coeff 0/1 let t31 = circuit_add(t29, in8); // Fp2 add coeff 1/1 let t32 = circuit_mul(in5, in7); // Fp2 mul start let t33 = circuit_mul(in6, in8); let t34 = circuit_sub(t32, t33); // Fp2 mul real part end let t35 = circuit_mul(in5, in8); let t36 = circuit_mul(in6, in7); let t37 = circuit_add(t35, t36); // Fp2 mul imag part end let t38 = circuit_add(t34, t34); // Fp2 add coeff 0/1 let t39 = circuit_add(t37, t37); // Fp2 add coeff 1/1 let t40 = circuit_add(t30, t31); let t41 = circuit_sub(t30, t31); let t42 = circuit_mul(t40, t41); let t43 = circuit_mul(t30, t31); let t44 = circuit_add(t43, t43); let t45 = circuit_add(t38, t39); let t46 = circuit_mul(t45, in0); let t47 = circuit_mul(t38, in1); let t48 = circuit_sub(t47, t39); let t49 = circuit_sub(t46, t47); let t50 = circuit_sub(t49, t39); let t51 = circuit_add(t48, t25); // Fp2 add coeff 0/1 let t52 = circuit_add(t50, t27); // Fp2 add coeff 1/1 let t53 = circuit_add(t21, t42); // Fp2 add coeff 0/1 let t54 = circuit_add(t22, t44); // Fp2 add coeff 1/1 let t55 = circuit_add(t53, t38); // Fp2 add coeff 0/1 let t56 = circuit_add(t54, t39); // Fp2 add coeff 1/1 let t57 = circuit_sub(t55, t25); // Fp2 sub coeff 0/1 let t58 = circuit_sub(t56, t27); // Fp2 sub coeff 1/1 let t59 = circuit_mul(in9, in11); // Fp2 mul start let t60 = circuit_mul(in10, in12); let t61 = circuit_sub(t59, t60); // Fp2 mul real part end let t62 = circuit_mul(in9, in12); let t63 = circuit_mul(in10, in11); let t64 = circuit_add(t62, t63); // Fp2 mul imag part end let t65 = circuit_add(t61, t61); // Fp2 add coeff 0/1 let t66 = circuit_add(t64, t64); // Fp2 add coeff 1/1 let t67 = circuit_add(in13, in14); let t68 = circuit_sub(in13, in14); let t69 = circuit_mul(t67, t68); let t70 = circuit_mul(in13, in14); let t71 = circuit_add(t70, t70); let t72 = circuit_add(t69, t71); let t73 = circuit_mul(t72, in0); let t74 = circuit_mul(t69, in1); let t75 = circuit_sub(t74, t71); let t76 = circuit_sub(t73, t74); let t77 = circuit_sub(t76, t71); let t78 = circuit_add(t75, t65); // Fp2 add coeff 0/1 let t79 = circuit_add(t77, t66); // Fp2 add coeff 1/1 let t80 = circuit_sub(t65, t69); // Fp2 sub coeff 0/1 let t81 = circuit_sub(t66, t71); // Fp2 sub coeff 1/1 let t82 = circuit_add(in9, in10); let t83 = circuit_sub(in9, in10); let t84 = circuit_mul(t82, t83); let t85 = circuit_mul(in9, in10); let t86 = circuit_add(t85, t85); let t87 = circuit_sub(in9, in11); // Fp2 sub coeff 0/1 let t88 = circuit_sub(in10, in12); // Fp2 sub coeff 1/1 let t89 = circuit_add(t87, in13); // Fp2 add coeff 0/1 let t90 = circuit_add(t88, in14); // Fp2 add coeff 1/1 let t91 = circuit_mul(in11, in13); // Fp2 mul start let t92 = circuit_mul(in12, in14); let t93 = circuit_sub(t91, t92); // Fp2 mul real part end let t94 = circuit_mul(in11, in14); let t95 = circuit_mul(in12, in13); let t96 = circuit_add(t94, t95); // Fp2 mul imag part end let t97 = circuit_add(t93, t93); // Fp2 add coeff 0/1 let t98 = circuit_add(t96, t96); // Fp2 add coeff 1/1 let t99 = circuit_add(t89, t90); let t100 = circuit_sub(t89, t90); let t101 = circuit_mul(t99, t100); let t102 = circuit_mul(t89, t90); let t103 = circuit_add(t102, t102); let t104 = circuit_add(t97, t98); let t105 = circuit_mul(t104, in0); let t106 = circuit_mul(t97, in1); let t107 = circuit_sub(t106, t98); let t108 = circuit_sub(t105, t106); let t109 = circuit_sub(t108, t98); let t110 = circuit_add(t107, t84); // Fp2 add coeff 0/1 let t111 = circuit_add(t109, t86); // Fp2 add coeff 1/1 let t112 = circuit_add(t80, t101); // Fp2 add coeff 0/1 let t113 = circuit_add(t81, t103); // Fp2 add coeff 1/1 let t114 = circuit_add(t112, t97); // Fp2 add coeff 0/1 let t115 = circuit_add(t113, t98); // Fp2 add coeff 1/1 let t116 = circuit_sub(t114, t84); // Fp2 sub coeff 0/1 let t117 = circuit_sub(t115, t86); // Fp2 sub coeff 1/1 let t118 = circuit_add(t116, t117); let t119 = circuit_mul(t118, in0); let t120 = circuit_mul(t116, in1); let t121 = circuit_sub(t120, t117); let t122 = circuit_sub(t119, t120); let t123 = circuit_sub(t122, t117); let t124 = circuit_sub(t51, t121); // Fp6 sub coeff 0/5 let t125 = circuit_sub(t52, t123); // Fp6 sub coeff 1/5 let t126 = circuit_sub(t19, t110); // Fp6 sub coeff 2/5 let t127 = circuit_sub(t20, t111); // Fp6 sub coeff 3/5 let t128 = circuit_sub(t57, t78); // Fp6 sub coeff 4/5 let t129 = circuit_sub(t58, t79); // Fp6 sub coeff 5/5 let t130 = circuit_add(t124, t125); let t131 = circuit_sub(t124, t125); let t132 = circuit_mul(t130, t131); let t133 = circuit_mul(t124, t125); let t134 = circuit_add(t133, t133); let t135 = circuit_add(t126, t127); let t136 = circuit_sub(t126, t127); let t137 = circuit_mul(t135, t136); let t138 = circuit_mul(t126, t127); let t139 = circuit_add(t138, t138); let t140 = circuit_add(t128, t129); let t141 = circuit_sub(t128, t129); let t142 = circuit_mul(t140, t141); let t143 = circuit_mul(t128, t129); let t144 = circuit_add(t143, t143); let t145 = circuit_mul(t124, t126); // Fp2 mul start let t146 = circuit_mul(t125, t127); let t147 = circuit_sub(t145, t146); // Fp2 mul real part end let t148 = circuit_mul(t124, t127); let t149 = circuit_mul(t125, t126); let t150 = circuit_add(t148, t149); // Fp2 mul imag part end let t151 = circuit_mul(t124, t128); // Fp2 mul start let t152 = circuit_mul(t125, t129); let t153 = circuit_sub(t151, t152); // Fp2 mul real part end let t154 = circuit_mul(t124, t129); let t155 = circuit_mul(t125, t128); let t156 = circuit_add(t154, t155); // Fp2 mul imag part end let t157 = circuit_mul(t126, t128); // Fp2 mul start let t158 = circuit_mul(t127, t129); let t159 = circuit_sub(t157, t158); // Fp2 mul real part end let t160 = circuit_mul(t126, t129); let t161 = circuit_mul(t127, t128); let t162 = circuit_add(t160, t161); // Fp2 mul imag part end let t163 = circuit_add(t159, t162); let t164 = circuit_mul(t163, in0); let t165 = circuit_mul(t159, in1); let t166 = circuit_sub(t165, t162); let t167 = circuit_sub(t164, t165); let t168 = circuit_sub(t167, t162); let t169 = circuit_sub(in2, t166); // Fp2 neg coeff 0/1 let t170 = circuit_sub(in2, t168); // Fp2 neg coeff 1/1 let t171 = circuit_add(t169, t132); // Fp2 add coeff 0/1 let t172 = circuit_add(t170, t134); // Fp2 add coeff 1/1 let t173 = circuit_add(t142, t144); let t174 = circuit_mul(t173, in0); let t175 = circuit_mul(t142, in1); let t176 = circuit_sub(t175, t144); let t177 = circuit_sub(t174, t175); let t178 = circuit_sub(t177, t144); let t179 = circuit_sub(t176, t147); // Fp2 sub coeff 0/1 let t180 = circuit_sub(t178, t150); // Fp2 sub coeff 1/1 let t181 = circuit_sub(t137, t153); // Fp2 sub coeff 0/1 let t182 = circuit_sub(t139, t156); // Fp2 sub coeff 1/1 let t183 = circuit_mul(t124, t171); // Fp2 mul start let t184 = circuit_mul(t125, t172); let t185 = circuit_sub(t183, t184); // Fp2 mul real part end let t186 = circuit_mul(t124, t172); let t187 = circuit_mul(t125, t171); let t188 = circuit_add(t186, t187); // Fp2 mul imag part end let t189 = circuit_mul(t128, t179); // Fp2 mul start let t190 = circuit_mul(t129, t180); let t191 = circuit_sub(t189, t190); // Fp2 mul real part end let t192 = circuit_mul(t128, t180); let t193 = circuit_mul(t129, t179); let t194 = circuit_add(t192, t193); // Fp2 mul imag part end let t195 = circuit_mul(t126, t181); // Fp2 mul start let t196 = circuit_mul(t127, t182); let t197 = circuit_sub(t195, t196); // Fp2 mul real part end let t198 = circuit_mul(t126, t182); let t199 = circuit_mul(t127, t181); let t200 = circuit_add(t198, t199); // Fp2 mul imag part end let t201 = circuit_add(t191, t197); // Fp2 add coeff 0/1 let t202 = circuit_add(t194, t200); // Fp2 add coeff 1/1 let t203 = circuit_add(t201, t202); let t204 = circuit_mul(t203, in0); let t205 = circuit_mul(t201, in1); let t206 = circuit_sub(t205, t202); let t207 = circuit_sub(t204, t205); let t208 = circuit_sub(t207, t202); let t209 = circuit_add(t185, t206); // Fp2 add coeff 0/1 let t210 = circuit_add(t188, t208); // Fp2 add coeff 1/1 let t211 = circuit_mul(t209, t209); // Fp2 Inv start let t212 = circuit_mul(t210, t210); let t213 = circuit_add(t211, t212); let t214 = circuit_inverse(t213); let t215 = circuit_mul(t209, t214); // Fp2 Inv real part end let t216 = circuit_mul(t210, t214); let t217 = circuit_sub(in2, t216); // Fp2 Inv imag part end let t218 = circuit_mul(t171, t215); // Fp2 mul start let t219 = circuit_mul(t172, t217); let t220 = circuit_sub(t218, t219); // Fp2 mul real part end let t221 = circuit_mul(t171, t217); let t222 = circuit_mul(t172, t215); let t223 = circuit_add(t221, t222); // Fp2 mul imag part end let t224 = circuit_mul(t179, t215); // Fp2 mul start let t225 = circuit_mul(t180, t217); let t226 = circuit_sub(t224, t225); // Fp2 mul real part end let t227 = circuit_mul(t179, t217); let t228 = circuit_mul(t180, t215); let t229 = circuit_add(t227, t228); // Fp2 mul imag part end let t230 = circuit_mul(t181, t215); // Fp2 mul start let t231 = circuit_mul(t182, t217); let t232 = circuit_sub(t230, t231); // Fp2 mul real part end let t233 = circuit_mul(t181, t217); let t234 = circuit_mul(t182, t215); let t235 = circuit_add(t233, t234); // Fp2 mul imag part end let t236 = circuit_mul(in3, t220); // Fp2 mul start let t237 = circuit_mul(in4, t223); let t238 = circuit_sub(t236, t237); // Fp2 mul real part end let t239 = circuit_mul(in3, t223); let t240 = circuit_mul(in4, t220); let t241 = circuit_add(t239, t240); // Fp2 mul imag part end let t242 = circuit_mul(in5, t226); // Fp2 mul start let t243 = circuit_mul(in6, t229); let t244 = circuit_sub(t242, t243); // Fp2 mul real part end let t245 = circuit_mul(in5, t229); let t246 = circuit_mul(in6, t226); let t247 = circuit_add(t245, t246); // Fp2 mul imag part end let t248 = circuit_mul(in7, t232); // Fp2 mul start let t249 = circuit_mul(in8, t235); let t250 = circuit_sub(t248, t249); // Fp2 mul real part end let t251 = circuit_mul(in7, t235); let t252 = circuit_mul(in8, t232); let t253 = circuit_add(t251, t252); // Fp2 mul imag part end let t254 = circuit_add(in5, in7); // Fp2 add coeff 0/1 let t255 = circuit_add(in6, in8); // Fp2 add coeff 1/1 let t256 = circuit_add(t226, t232); // Fp2 add coeff 0/1 let t257 = circuit_add(t229, t235); // Fp2 add coeff 1/1 let t258 = circuit_mul(t254, t256); // Fp2 mul start let t259 = circuit_mul(t255, t257); let t260 = circuit_sub(t258, t259); // Fp2 mul real part end let t261 = circuit_mul(t254, t257); let t262 = circuit_mul(t255, t256); let t263 = circuit_add(t261, t262); // Fp2 mul imag part end let t264 = circuit_sub(t260, t244); // Fp2 sub coeff 0/1 let t265 = circuit_sub(t263, t247); // Fp2 sub coeff 1/1 let t266 = circuit_sub(t264, t250); // Fp2 sub coeff 0/1 let t267 = circuit_sub(t265, t253); // Fp2 sub coeff 1/1 let t268 = circuit_add(t266, t267); let t269 = circuit_mul(t268, in0); let t270 = circuit_mul(t266, in1); let t271 = circuit_sub(t270, t267); let t272 = circuit_sub(t269, t270); let t273 = circuit_sub(t272, t267); let t274 = circuit_add(t271, t238); // Fp2 add coeff 0/1 let t275 = circuit_add(t273, t241); // Fp2 add coeff 1/1 let t276 = circuit_add(in3, in5); // Fp2 add coeff 0/1 let t277 = circuit_add(in4, in6); // Fp2 add coeff 1/1 let t278 = circuit_add(t220, t226); // Fp2 add coeff 0/1 let t279 = circuit_add(t223, t229); // Fp2 add coeff 1/1 let t280 = circuit_mul(t276, t278); // Fp2 mul start let t281 = circuit_mul(t277, t279); let t282 = circuit_sub(t280, t281); // Fp2 mul real part end let t283 = circuit_mul(t276, t279); let t284 = circuit_mul(t277, t278); let t285 = circuit_add(t283, t284); // Fp2 mul imag part end let t286 = circuit_sub(t282, t238); // Fp2 sub coeff 0/1 let t287 = circuit_sub(t285, t241); // Fp2 sub coeff 1/1 let t288 = circuit_sub(t286, t244); // Fp2 sub coeff 0/1 let t289 = circuit_sub(t287, t247); // Fp2 sub coeff 1/1 let t290 = circuit_add(t250, t253); let t291 = circuit_mul(t290, in0); let t292 = circuit_mul(t250, in1); let t293 = circuit_sub(t292, t253); let t294 = circuit_sub(t291, t292); let t295 = circuit_sub(t294, t253); let t296 = circuit_add(t288, t293); // Fp2 add coeff 0/1 let t297 = circuit_add(t289, t295); // Fp2 add coeff 1/1 let t298 = circuit_add(in3, in7); // Fp2 add coeff 0/1 let t299 = circuit_add(in4, in8); // Fp2 add coeff 1/1 let t300 = circuit_add(t220, t232); // Fp2 add coeff 0/1 let t301 = circuit_add(t223, t235); // Fp2 add coeff 1/1 let t302 = circuit_mul(t300, t298); // Fp2 mul start let t303 = circuit_mul(t301, t299); let t304 = circuit_sub(t302, t303); // Fp2 mul real part end let t305 = circuit_mul(t300, t299); let t306 = circuit_mul(t301, t298); let t307 = circuit_add(t305, t306); // Fp2 mul imag part end let t308 = circuit_sub(t304, t238); // Fp2 sub coeff 0/1 let t309 = circuit_sub(t307, t241); // Fp2 sub coeff 1/1 let t310 = circuit_sub(t308, t250); // Fp2 sub coeff 0/1 let t311 = circuit_sub(t309, t253); // Fp2 sub coeff 1/1 let t312 = circuit_add(t310, t244); // Fp2 add coeff 0/1 let t313 = circuit_add(t311, t247); // Fp2 add coeff 1/1 let t314 = circuit_mul(in9, t220); // Fp2 mul start let t315 = circuit_mul(in10, t223); let t316 = circuit_sub(t314, t315); // Fp2 mul real part end let t317 = circuit_mul(in9, t223); let t318 = circuit_mul(in10, t220); let t319 = circuit_add(t317, t318); // Fp2 mul imag part end let t320 = circuit_mul(in11, t226); // Fp2 mul start let t321 = circuit_mul(in12, t229); let t322 = circuit_sub(t320, t321); // Fp2 mul real part end let t323 = circuit_mul(in11, t229); let t324 = circuit_mul(in12, t226); let t325 = circuit_add(t323, t324); // Fp2 mul imag part end let t326 = circuit_mul(in13, t232); // Fp2 mul start let t327 = circuit_mul(in14, t235); let t328 = circuit_sub(t326, t327); // Fp2 mul real part end let t329 = circuit_mul(in13, t235); let t330 = circuit_mul(in14, t232); let t331 = circuit_add(t329, t330); // Fp2 mul imag part end let t332 = circuit_add(in11, in13); // Fp2 add coeff 0/1 let t333 = circuit_add(in12, in14); // Fp2 add coeff 1/1 let t334 = circuit_add(t226, t232); // Fp2 add coeff 0/1 let t335 = circuit_add(t229, t235); // Fp2 add coeff 1/1 let t336 = circuit_mul(t332, t334); // Fp2 mul start let t337 = circuit_mul(t333, t335); let t338 = circuit_sub(t336, t337); // Fp2 mul real part end let t339 = circuit_mul(t332, t335); let t340 = circuit_mul(t333, t334); let t341 = circuit_add(t339, t340); // Fp2 mul imag part end let t342 = circuit_sub(t338, t322); // Fp2 sub coeff 0/1 let t343 = circuit_sub(t341, t325); // Fp2 sub coeff 1/1 let t344 = circuit_sub(t342, t328); // Fp2 sub coeff 0/1 let t345 = circuit_sub(t343, t331); // Fp2 sub coeff 1/1 let t346 = circuit_add(t344, t345); let t347 = circuit_mul(t346, in0); let t348 = circuit_mul(t344, in1); let t349 = circuit_sub(t348, t345); let t350 = circuit_sub(t347, t348); let t351 = circuit_sub(t350, t345); let t352 = circuit_add(t349, t316); // Fp2 add coeff 0/1 let t353 = circuit_add(t351, t319); // Fp2 add coeff 1/1 let t354 = circuit_add(in9, in11); // Fp2 add coeff 0/1 let t355 = circuit_add(in10, in12); // Fp2 add coeff 1/1 let t356 = circuit_add(t220, t226); // Fp2 add coeff 0/1 let t357 = circuit_add(t223, t229); // Fp2 add coeff 1/1 let t358 = circuit_mul(t354, t356); // Fp2 mul start let t359 = circuit_mul(t355, t357); let t360 = circuit_sub(t358, t359); // Fp2 mul real part end let t361 = circuit_mul(t354, t357); let t362 = circuit_mul(t355, t356); let t363 = circuit_add(t361, t362); // Fp2 mul imag part end let t364 = circuit_sub(t360, t316); // Fp2 sub coeff 0/1 let t365 = circuit_sub(t363, t319); // Fp2 sub coeff 1/1 let t366 = circuit_sub(t364, t322); // Fp2 sub coeff 0/1 let t367 = circuit_sub(t365, t325); // Fp2 sub coeff 1/1 let t368 = circuit_add(t328, t331); let t369 = circuit_mul(t368, in0); let t370 = circuit_mul(t328, in1); let t371 = circuit_sub(t370, t331); let t372 = circuit_sub(t369, t370); let t373 = circuit_sub(t372, t331); let t374 = circuit_add(t366, t371); // Fp2 add coeff 0/1 let t375 = circuit_add(t367, t373); // Fp2 add coeff 1/1 let t376 = circuit_add(in9, in13); // Fp2 add coeff 0/1 let t377 = circuit_add(in10, in14); // Fp2 add coeff 1/1 let t378 = circuit_add(t220, t232); // Fp2 add coeff 0/1 let t379 = circuit_add(t223, t235); // Fp2 add coeff 1/1 let t380 = circuit_mul(t378, t376); // Fp2 mul start let t381 = circuit_mul(t379, t377); let t382 = circuit_sub(t380, t381); // Fp2 mul real part end let t383 = circuit_mul(t378, t377); let t384 = circuit_mul(t379, t376); let t385 = circuit_add(t383, t384); // Fp2 mul imag part end let t386 = circuit_sub(t382, t316); // Fp2 sub coeff 0/1 let t387 = circuit_sub(t385, t319); // Fp2 sub coeff 1/1 let t388 = circuit_sub(t386, t328); // Fp2 sub coeff 0/1 let t389 = circuit_sub(t387, t331); // Fp2 sub coeff 1/1 let t390 = circuit_add(t388, t322); // Fp2 add coeff 0/1 let t391 = circuit_add(t389, t325); // Fp2 add coeff 1/1 let t392 = circuit_sub(in2, t352); // Fp6 neg coeff 0/5 let t393 = circuit_sub(in2, t353); // Fp6 neg coeff 1/5 let t394 = circuit_sub(in2, t374); // Fp6 neg coeff 2/5 let t395 = circuit_sub(in2, t375); // Fp6 neg coeff 3/5 let t396 = circuit_sub(in2, t390); // Fp6 neg coeff 4/5 let t397 = circuit_sub(in2, t391); // Fp6 neg coeff 5/5 let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = ( t274, t275, t296, t297, t312, t313, t392, t393, t394, t395, t396, t397, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0xa, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x9, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 // Fill inputs: circuit_inputs = circuit_inputs.next_2(M.c0b0a0); // in3 circuit_inputs = circuit_inputs.next_2(M.c0b0a1); // in4 circuit_inputs = circuit_inputs.next_2(M.c0b1a0); // in5 circuit_inputs = circuit_inputs.next_2(M.c0b1a1); // in6 circuit_inputs = circuit_inputs.next_2(M.c0b2a0); // in7 circuit_inputs = circuit_inputs.next_2(M.c0b2a1); // in8 circuit_inputs = circuit_inputs.next_2(M.c1b0a0); // in9 circuit_inputs = circuit_inputs.next_2(M.c1b0a1); // in10 circuit_inputs = circuit_inputs.next_2(M.c1b1a0); // in11 circuit_inputs = circuit_inputs.next_2(M.c1b1a1); // in12 circuit_inputs = circuit_inputs.next_2(M.c1b2a0); // in13 circuit_inputs = circuit_inputs.next_2(M.c1b2a1); // in14 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t274), c0b0a1: outputs.get_output(t275), c0b1a0: outputs.get_output(t296), c0b1a1: outputs.get_output(t297), c0b2a0: outputs.get_output(t312), c0b2a1: outputs.get_output(t313), c1b0a0: outputs.get_output(t392), c1b0a1: outputs.get_output(t393), c1b1a0: outputs.get_output(t394), c1b1a1: outputs.get_output(t395), c1b2a0: outputs.get_output(t396), c1b2a1: outputs.get_output(t397), }; return (res,); } #[inline(always)] pub fn run_BN254_E12T_MUL_circuit(X: E12T, Y: E12T) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0xa let in1 = CE::> {}; // 0x9 // INPUT stack let (in2, in3, in4) = (CE::> {}, CE::> {}, CE::> {}); let (in5, in6, in7) = (CE::> {}, CE::> {}, CE::> {}); let (in8, in9, in10) = (CE::> {}, CE::> {}, CE::> {}); let (in11, in12, in13) = (CE::> {}, CE::> {}, CE::> {}); let (in14, in15, in16) = (CE::> {}, CE::> {}, CE::> {}); let (in17, in18, in19) = (CE::> {}, CE::> {}, CE::> {}); let (in20, in21, in22) = (CE::> {}, CE::> {}, CE::> {}); let (in23, in24, in25) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_add(in2, in8); // Fp6 add coeff 0/5 let t1 = circuit_add(in3, in9); // Fp6 add coeff 1/5 let t2 = circuit_add(in4, in10); // Fp6 add coeff 2/5 let t3 = circuit_add(in5, in11); // Fp6 add coeff 3/5 let t4 = circuit_add(in6, in12); // Fp6 add coeff 4/5 let t5 = circuit_add(in7, in13); // Fp6 add coeff 5/5 let t6 = circuit_add(in14, in20); // Fp6 add coeff 0/5 let t7 = circuit_add(in15, in21); // Fp6 add coeff 1/5 let t8 = circuit_add(in16, in22); // Fp6 add coeff 2/5 let t9 = circuit_add(in17, in23); // Fp6 add coeff 3/5 let t10 = circuit_add(in18, in24); // Fp6 add coeff 4/5 let t11 = circuit_add(in19, in25); // Fp6 add coeff 5/5 let t12 = circuit_mul(t0, t6); // Fp2 mul start let t13 = circuit_mul(t1, t7); let t14 = circuit_sub(t12, t13); // Fp2 mul real part end let t15 = circuit_mul(t0, t7); let t16 = circuit_mul(t1, t6); let t17 = circuit_add(t15, t16); // Fp2 mul imag part end let t18 = circuit_mul(t2, t8); // Fp2 mul start let t19 = circuit_mul(t3, t9); let t20 = circuit_sub(t18, t19); // Fp2 mul real part end let t21 = circuit_mul(t2, t9); let t22 = circuit_mul(t3, t8); let t23 = circuit_add(t21, t22); // Fp2 mul imag part end let t24 = circuit_mul(t4, t10); // Fp2 mul start let t25 = circuit_mul(t5, t11); let t26 = circuit_sub(t24, t25); // Fp2 mul real part end let t27 = circuit_mul(t4, t11); let t28 = circuit_mul(t5, t10); let t29 = circuit_add(t27, t28); // Fp2 mul imag part end let t30 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t31 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t32 = circuit_add(t8, t10); // Fp2 add coeff 0/1 let t33 = circuit_add(t9, t11); // Fp2 add coeff 1/1 let t34 = circuit_mul(t30, t32); // Fp2 mul start let t35 = circuit_mul(t31, t33); let t36 = circuit_sub(t34, t35); // Fp2 mul real part end let t37 = circuit_mul(t30, t33); let t38 = circuit_mul(t31, t32); let t39 = circuit_add(t37, t38); // Fp2 mul imag part end let t40 = circuit_sub(t36, t20); // Fp2 sub coeff 0/1 let t41 = circuit_sub(t39, t23); // Fp2 sub coeff 1/1 let t42 = circuit_sub(t40, t26); // Fp2 sub coeff 0/1 let t43 = circuit_sub(t41, t29); // Fp2 sub coeff 1/1 let t44 = circuit_add(t42, t43); let t45 = circuit_mul(t44, in0); let t46 = circuit_mul(t42, in1); let t47 = circuit_sub(t46, t43); let t48 = circuit_sub(t45, t46); let t49 = circuit_sub(t48, t43); let t50 = circuit_add(t47, t14); // Fp2 add coeff 0/1 let t51 = circuit_add(t49, t17); // Fp2 add coeff 1/1 let t52 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t53 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t54 = circuit_add(t6, t8); // Fp2 add coeff 0/1 let t55 = circuit_add(t7, t9); // Fp2 add coeff 1/1 let t56 = circuit_mul(t52, t54); // Fp2 mul start let t57 = circuit_mul(t53, t55); let t58 = circuit_sub(t56, t57); // Fp2 mul real part end let t59 = circuit_mul(t52, t55); let t60 = circuit_mul(t53, t54); let t61 = circuit_add(t59, t60); // Fp2 mul imag part end let t62 = circuit_sub(t58, t14); // Fp2 sub coeff 0/1 let t63 = circuit_sub(t61, t17); // Fp2 sub coeff 1/1 let t64 = circuit_sub(t62, t20); // Fp2 sub coeff 0/1 let t65 = circuit_sub(t63, t23); // Fp2 sub coeff 1/1 let t66 = circuit_add(t26, t29); let t67 = circuit_mul(t66, in0); let t68 = circuit_mul(t26, in1); let t69 = circuit_sub(t68, t29); let t70 = circuit_sub(t67, t68); let t71 = circuit_sub(t70, t29); let t72 = circuit_add(t64, t69); // Fp2 add coeff 0/1 let t73 = circuit_add(t65, t71); // Fp2 add coeff 1/1 let t74 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t75 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t76 = circuit_add(t6, t10); // Fp2 add coeff 0/1 let t77 = circuit_add(t7, t11); // Fp2 add coeff 1/1 let t78 = circuit_mul(t76, t74); // Fp2 mul start let t79 = circuit_mul(t77, t75); let t80 = circuit_sub(t78, t79); // Fp2 mul real part end let t81 = circuit_mul(t76, t75); let t82 = circuit_mul(t77, t74); let t83 = circuit_add(t81, t82); // Fp2 mul imag part end let t84 = circuit_sub(t80, t14); // Fp2 sub coeff 0/1 let t85 = circuit_sub(t83, t17); // Fp2 sub coeff 1/1 let t86 = circuit_sub(t84, t26); // Fp2 sub coeff 0/1 let t87 = circuit_sub(t85, t29); // Fp2 sub coeff 1/1 let t88 = circuit_add(t86, t20); // Fp2 add coeff 0/1 let t89 = circuit_add(t87, t23); // Fp2 add coeff 1/1 let t90 = circuit_mul(in2, in14); // Fp2 mul start let t91 = circuit_mul(in3, in15); let t92 = circuit_sub(t90, t91); // Fp2 mul real part end let t93 = circuit_mul(in2, in15); let t94 = circuit_mul(in3, in14); let t95 = circuit_add(t93, t94); // Fp2 mul imag part end let t96 = circuit_mul(in4, in16); // Fp2 mul start let t97 = circuit_mul(in5, in17); let t98 = circuit_sub(t96, t97); // Fp2 mul real part end let t99 = circuit_mul(in4, in17); let t100 = circuit_mul(in5, in16); let t101 = circuit_add(t99, t100); // Fp2 mul imag part end let t102 = circuit_mul(in6, in18); // Fp2 mul start let t103 = circuit_mul(in7, in19); let t104 = circuit_sub(t102, t103); // Fp2 mul real part end let t105 = circuit_mul(in6, in19); let t106 = circuit_mul(in7, in18); let t107 = circuit_add(t105, t106); // Fp2 mul imag part end let t108 = circuit_add(in4, in6); // Fp2 add coeff 0/1 let t109 = circuit_add(in5, in7); // Fp2 add coeff 1/1 let t110 = circuit_add(in16, in18); // Fp2 add coeff 0/1 let t111 = circuit_add(in17, in19); // Fp2 add coeff 1/1 let t112 = circuit_mul(t108, t110); // Fp2 mul start let t113 = circuit_mul(t109, t111); let t114 = circuit_sub(t112, t113); // Fp2 mul real part end let t115 = circuit_mul(t108, t111); let t116 = circuit_mul(t109, t110); let t117 = circuit_add(t115, t116); // Fp2 mul imag part end let t118 = circuit_sub(t114, t98); // Fp2 sub coeff 0/1 let t119 = circuit_sub(t117, t101); // Fp2 sub coeff 1/1 let t120 = circuit_sub(t118, t104); // Fp2 sub coeff 0/1 let t121 = circuit_sub(t119, t107); // Fp2 sub coeff 1/1 let t122 = circuit_add(t120, t121); let t123 = circuit_mul(t122, in0); let t124 = circuit_mul(t120, in1); let t125 = circuit_sub(t124, t121); let t126 = circuit_sub(t123, t124); let t127 = circuit_sub(t126, t121); let t128 = circuit_add(t125, t92); // Fp2 add coeff 0/1 let t129 = circuit_add(t127, t95); // Fp2 add coeff 1/1 let t130 = circuit_add(in2, in4); // Fp2 add coeff 0/1 let t131 = circuit_add(in3, in5); // Fp2 add coeff 1/1 let t132 = circuit_add(in14, in16); // Fp2 add coeff 0/1 let t133 = circuit_add(in15, in17); // Fp2 add coeff 1/1 let t134 = circuit_mul(t130, t132); // Fp2 mul start let t135 = circuit_mul(t131, t133); let t136 = circuit_sub(t134, t135); // Fp2 mul real part end let t137 = circuit_mul(t130, t133); let t138 = circuit_mul(t131, t132); let t139 = circuit_add(t137, t138); // Fp2 mul imag part end let t140 = circuit_sub(t136, t92); // Fp2 sub coeff 0/1 let t141 = circuit_sub(t139, t95); // Fp2 sub coeff 1/1 let t142 = circuit_sub(t140, t98); // Fp2 sub coeff 0/1 let t143 = circuit_sub(t141, t101); // Fp2 sub coeff 1/1 let t144 = circuit_add(t104, t107); let t145 = circuit_mul(t144, in0); let t146 = circuit_mul(t104, in1); let t147 = circuit_sub(t146, t107); let t148 = circuit_sub(t145, t146); let t149 = circuit_sub(t148, t107); let t150 = circuit_add(t142, t147); // Fp2 add coeff 0/1 let t151 = circuit_add(t143, t149); // Fp2 add coeff 1/1 let t152 = circuit_add(in2, in6); // Fp2 add coeff 0/1 let t153 = circuit_add(in3, in7); // Fp2 add coeff 1/1 let t154 = circuit_add(in14, in18); // Fp2 add coeff 0/1 let t155 = circuit_add(in15, in19); // Fp2 add coeff 1/1 let t156 = circuit_mul(t154, t152); // Fp2 mul start let t157 = circuit_mul(t155, t153); let t158 = circuit_sub(t156, t157); // Fp2 mul real part end let t159 = circuit_mul(t154, t153); let t160 = circuit_mul(t155, t152); let t161 = circuit_add(t159, t160); // Fp2 mul imag part end let t162 = circuit_sub(t158, t92); // Fp2 sub coeff 0/1 let t163 = circuit_sub(t161, t95); // Fp2 sub coeff 1/1 let t164 = circuit_sub(t162, t104); // Fp2 sub coeff 0/1 let t165 = circuit_sub(t163, t107); // Fp2 sub coeff 1/1 let t166 = circuit_add(t164, t98); // Fp2 add coeff 0/1 let t167 = circuit_add(t165, t101); // Fp2 add coeff 1/1 let t168 = circuit_mul(in8, in20); // Fp2 mul start let t169 = circuit_mul(in9, in21); let t170 = circuit_sub(t168, t169); // Fp2 mul real part end let t171 = circuit_mul(in8, in21); let t172 = circuit_mul(in9, in20); let t173 = circuit_add(t171, t172); // Fp2 mul imag part end let t174 = circuit_mul(in10, in22); // Fp2 mul start let t175 = circuit_mul(in11, in23); let t176 = circuit_sub(t174, t175); // Fp2 mul real part end let t177 = circuit_mul(in10, in23); let t178 = circuit_mul(in11, in22); let t179 = circuit_add(t177, t178); // Fp2 mul imag part end let t180 = circuit_mul(in12, in24); // Fp2 mul start let t181 = circuit_mul(in13, in25); let t182 = circuit_sub(t180, t181); // Fp2 mul real part end let t183 = circuit_mul(in12, in25); let t184 = circuit_mul(in13, in24); let t185 = circuit_add(t183, t184); // Fp2 mul imag part end let t186 = circuit_add(in10, in12); // Fp2 add coeff 0/1 let t187 = circuit_add(in11, in13); // Fp2 add coeff 1/1 let t188 = circuit_add(in22, in24); // Fp2 add coeff 0/1 let t189 = circuit_add(in23, in25); // Fp2 add coeff 1/1 let t190 = circuit_mul(t186, t188); // Fp2 mul start let t191 = circuit_mul(t187, t189); let t192 = circuit_sub(t190, t191); // Fp2 mul real part end let t193 = circuit_mul(t186, t189); let t194 = circuit_mul(t187, t188); let t195 = circuit_add(t193, t194); // Fp2 mul imag part end let t196 = circuit_sub(t192, t176); // Fp2 sub coeff 0/1 let t197 = circuit_sub(t195, t179); // Fp2 sub coeff 1/1 let t198 = circuit_sub(t196, t182); // Fp2 sub coeff 0/1 let t199 = circuit_sub(t197, t185); // Fp2 sub coeff 1/1 let t200 = circuit_add(t198, t199); let t201 = circuit_mul(t200, in0); let t202 = circuit_mul(t198, in1); let t203 = circuit_sub(t202, t199); let t204 = circuit_sub(t201, t202); let t205 = circuit_sub(t204, t199); let t206 = circuit_add(t203, t170); // Fp2 add coeff 0/1 let t207 = circuit_add(t205, t173); // Fp2 add coeff 1/1 let t208 = circuit_add(in8, in10); // Fp2 add coeff 0/1 let t209 = circuit_add(in9, in11); // Fp2 add coeff 1/1 let t210 = circuit_add(in20, in22); // Fp2 add coeff 0/1 let t211 = circuit_add(in21, in23); // Fp2 add coeff 1/1 let t212 = circuit_mul(t208, t210); // Fp2 mul start let t213 = circuit_mul(t209, t211); let t214 = circuit_sub(t212, t213); // Fp2 mul real part end let t215 = circuit_mul(t208, t211); let t216 = circuit_mul(t209, t210); let t217 = circuit_add(t215, t216); // Fp2 mul imag part end let t218 = circuit_sub(t214, t170); // Fp2 sub coeff 0/1 let t219 = circuit_sub(t217, t173); // Fp2 sub coeff 1/1 let t220 = circuit_sub(t218, t176); // Fp2 sub coeff 0/1 let t221 = circuit_sub(t219, t179); // Fp2 sub coeff 1/1 let t222 = circuit_add(t182, t185); let t223 = circuit_mul(t222, in0); let t224 = circuit_mul(t182, in1); let t225 = circuit_sub(t224, t185); let t226 = circuit_sub(t223, t224); let t227 = circuit_sub(t226, t185); let t228 = circuit_add(t220, t225); // Fp2 add coeff 0/1 let t229 = circuit_add(t221, t227); // Fp2 add coeff 1/1 let t230 = circuit_add(in8, in12); // Fp2 add coeff 0/1 let t231 = circuit_add(in9, in13); // Fp2 add coeff 1/1 let t232 = circuit_add(in20, in24); // Fp2 add coeff 0/1 let t233 = circuit_add(in21, in25); // Fp2 add coeff 1/1 let t234 = circuit_mul(t232, t230); // Fp2 mul start let t235 = circuit_mul(t233, t231); let t236 = circuit_sub(t234, t235); // Fp2 mul real part end let t237 = circuit_mul(t232, t231); let t238 = circuit_mul(t233, t230); let t239 = circuit_add(t237, t238); // Fp2 mul imag part end let t240 = circuit_sub(t236, t170); // Fp2 sub coeff 0/1 let t241 = circuit_sub(t239, t173); // Fp2 sub coeff 1/1 let t242 = circuit_sub(t240, t182); // Fp2 sub coeff 0/1 let t243 = circuit_sub(t241, t185); // Fp2 sub coeff 1/1 let t244 = circuit_add(t242, t176); // Fp2 add coeff 0/1 let t245 = circuit_add(t243, t179); // Fp2 add coeff 1/1 let t246 = circuit_sub(t50, t128); // Fp6 sub coeff 0/5 let t247 = circuit_sub(t51, t129); // Fp6 sub coeff 1/5 let t248 = circuit_sub(t72, t150); // Fp6 sub coeff 2/5 let t249 = circuit_sub(t73, t151); // Fp6 sub coeff 3/5 let t250 = circuit_sub(t88, t166); // Fp6 sub coeff 4/5 let t251 = circuit_sub(t89, t167); // Fp6 sub coeff 5/5 let t252 = circuit_sub(t246, t206); // Fp6 sub coeff 0/5 let t253 = circuit_sub(t247, t207); // Fp6 sub coeff 1/5 let t254 = circuit_sub(t248, t228); // Fp6 sub coeff 2/5 let t255 = circuit_sub(t249, t229); // Fp6 sub coeff 3/5 let t256 = circuit_sub(t250, t244); // Fp6 sub coeff 4/5 let t257 = circuit_sub(t251, t245); // Fp6 sub coeff 5/5 let t258 = circuit_add(t244, t245); let t259 = circuit_mul(t258, in0); let t260 = circuit_mul(t244, in1); let t261 = circuit_sub(t260, t245); let t262 = circuit_sub(t259, t260); let t263 = circuit_sub(t262, t245); let t264 = circuit_add(t261, t128); // Fp6 add coeff 0/5 let t265 = circuit_add(t263, t129); // Fp6 add coeff 1/5 let t266 = circuit_add(t206, t150); // Fp6 add coeff 2/5 let t267 = circuit_add(t207, t151); // Fp6 add coeff 3/5 let t268 = circuit_add(t228, t166); // Fp6 add coeff 4/5 let t269 = circuit_add(t229, t167); // Fp6 add coeff 5/5 let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = ( t264, t265, t266, t267, t268, t269, t252, t253, t254, t255, t256, t257, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0xa, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x9, 0x0, 0x0, 0x0]); // in1 // Fill inputs: circuit_inputs = circuit_inputs.next_2(X.c0b0a0); // in2 circuit_inputs = circuit_inputs.next_2(X.c0b0a1); // in3 circuit_inputs = circuit_inputs.next_2(X.c0b1a0); // in4 circuit_inputs = circuit_inputs.next_2(X.c0b1a1); // in5 circuit_inputs = circuit_inputs.next_2(X.c0b2a0); // in6 circuit_inputs = circuit_inputs.next_2(X.c0b2a1); // in7 circuit_inputs = circuit_inputs.next_2(X.c1b0a0); // in8 circuit_inputs = circuit_inputs.next_2(X.c1b0a1); // in9 circuit_inputs = circuit_inputs.next_2(X.c1b1a0); // in10 circuit_inputs = circuit_inputs.next_2(X.c1b1a1); // in11 circuit_inputs = circuit_inputs.next_2(X.c1b2a0); // in12 circuit_inputs = circuit_inputs.next_2(X.c1b2a1); // in13 circuit_inputs = circuit_inputs.next_2(Y.c0b0a0); // in14 circuit_inputs = circuit_inputs.next_2(Y.c0b0a1); // in15 circuit_inputs = circuit_inputs.next_2(Y.c0b1a0); // in16 circuit_inputs = circuit_inputs.next_2(Y.c0b1a1); // in17 circuit_inputs = circuit_inputs.next_2(Y.c0b2a0); // in18 circuit_inputs = circuit_inputs.next_2(Y.c0b2a1); // in19 circuit_inputs = circuit_inputs.next_2(Y.c1b0a0); // in20 circuit_inputs = circuit_inputs.next_2(Y.c1b0a1); // in21 circuit_inputs = circuit_inputs.next_2(Y.c1b1a0); // in22 circuit_inputs = circuit_inputs.next_2(Y.c1b1a1); // in23 circuit_inputs = circuit_inputs.next_2(Y.c1b2a0); // in24 circuit_inputs = circuit_inputs.next_2(Y.c1b2a1); // in25 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let res: E12T = E12T { c0b0a0: outputs.get_output(t264), c0b0a1: outputs.get_output(t265), c0b1a0: outputs.get_output(t266), c0b1a1: outputs.get_output(t267), c0b2a0: outputs.get_output(t268), c0b2a1: outputs.get_output(t269), c1b0a0: outputs.get_output(t252), c1b0a1: outputs.get_output(t253), c1b1a0: outputs.get_output(t254), c1b1a1: outputs.get_output(t255), c1b2a0: outputs.get_output(t256), c1b2a1: outputs.get_output(t257), }; return (res,); } #[inline(always)] pub fn run_BN254_TOWER_MILLER_BIT0_1P_circuit( yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, M_i: E12T, ) -> (G2Point, E12T) { // CONSTANT stack let in0 = CE::> {}; // 0xa let in1 = CE::> {}; // 0x9 let in2 = CE::> {}; // 0x0 let in3 = CE::> {}; // 0x3 let in4 = CE::> {}; // 0x6 let in5 = CE::> {}; // 0x1 // INPUT stack let (in6, in7, in8) = (CE::> {}, CE::> {}, CE::> {}); let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in12, in18); // Fp6 sub coeff 0/5 let t1 = circuit_sub(in13, in19); // Fp6 sub coeff 1/5 let t2 = circuit_sub(in14, in20); // Fp6 sub coeff 2/5 let t3 = circuit_sub(in15, in21); // Fp6 sub coeff 3/5 let t4 = circuit_sub(in16, in22); // Fp6 sub coeff 4/5 let t5 = circuit_sub(in17, in23); // Fp6 sub coeff 5/5 let t6 = circuit_add(in22, in23); let t7 = circuit_mul(t6, in0); let t8 = circuit_mul(in22, in1); let t9 = circuit_sub(t8, in23); let t10 = circuit_sub(t7, t8); let t11 = circuit_sub(t10, in23); let t12 = circuit_sub(in2, t9); // Fp6 neg coeff 0/5 let t13 = circuit_sub(in2, t11); // Fp6 neg coeff 1/5 let t14 = circuit_sub(in2, in18); // Fp6 neg coeff 2/5 let t15 = circuit_sub(in2, in19); // Fp6 neg coeff 3/5 let t16 = circuit_sub(in2, in20); // Fp6 neg coeff 4/5 let t17 = circuit_sub(in2, in21); // Fp6 neg coeff 5/5 let t18 = circuit_add(in12, t12); // Fp6 add coeff 0/5 let t19 = circuit_add(in13, t13); // Fp6 add coeff 1/5 let t20 = circuit_add(in14, t14); // Fp6 add coeff 2/5 let t21 = circuit_add(in15, t15); // Fp6 add coeff 3/5 let t22 = circuit_add(in16, t16); // Fp6 add coeff 4/5 let t23 = circuit_add(in17, t17); // Fp6 add coeff 5/5 let t24 = circuit_mul(in12, in18); // Fp2 mul start let t25 = circuit_mul(in13, in19); let t26 = circuit_sub(t24, t25); // Fp2 mul real part end let t27 = circuit_mul(in12, in19); let t28 = circuit_mul(in13, in18); let t29 = circuit_add(t27, t28); // Fp2 mul imag part end let t30 = circuit_mul(in14, in20); // Fp2 mul start let t31 = circuit_mul(in15, in21); let t32 = circuit_sub(t30, t31); // Fp2 mul real part end let t33 = circuit_mul(in14, in21); let t34 = circuit_mul(in15, in20); let t35 = circuit_add(t33, t34); // Fp2 mul imag part end let t36 = circuit_mul(in16, in22); // Fp2 mul start let t37 = circuit_mul(in17, in23); let t38 = circuit_sub(t36, t37); // Fp2 mul real part end let t39 = circuit_mul(in16, in23); let t40 = circuit_mul(in17, in22); let t41 = circuit_add(t39, t40); // Fp2 mul imag part end let t42 = circuit_add(in14, in16); // Fp2 add coeff 0/1 let t43 = circuit_add(in15, in17); // Fp2 add coeff 1/1 let t44 = circuit_add(in20, in22); // Fp2 add coeff 0/1 let t45 = circuit_add(in21, in23); // Fp2 add coeff 1/1 let t46 = circuit_mul(t42, t44); // Fp2 mul start let t47 = circuit_mul(t43, t45); let t48 = circuit_sub(t46, t47); // Fp2 mul real part end let t49 = circuit_mul(t42, t45); let t50 = circuit_mul(t43, t44); let t51 = circuit_add(t49, t50); // Fp2 mul imag part end let t52 = circuit_sub(t48, t32); // Fp2 sub coeff 0/1 let t53 = circuit_sub(t51, t35); // Fp2 sub coeff 1/1 let t54 = circuit_sub(t52, t38); // Fp2 sub coeff 0/1 let t55 = circuit_sub(t53, t41); // Fp2 sub coeff 1/1 let t56 = circuit_add(t54, t55); let t57 = circuit_mul(t56, in0); let t58 = circuit_mul(t54, in1); let t59 = circuit_sub(t58, t55); let t60 = circuit_sub(t57, t58); let t61 = circuit_sub(t60, t55); let t62 = circuit_add(t59, t26); // Fp2 add coeff 0/1 let t63 = circuit_add(t61, t29); // Fp2 add coeff 1/1 let t64 = circuit_add(in12, in14); // Fp2 add coeff 0/1 let t65 = circuit_add(in13, in15); // Fp2 add coeff 1/1 let t66 = circuit_add(in18, in20); // Fp2 add coeff 0/1 let t67 = circuit_add(in19, in21); // Fp2 add coeff 1/1 let t68 = circuit_mul(t64, t66); // Fp2 mul start let t69 = circuit_mul(t65, t67); let t70 = circuit_sub(t68, t69); // Fp2 mul real part end let t71 = circuit_mul(t64, t67); let t72 = circuit_mul(t65, t66); let t73 = circuit_add(t71, t72); // Fp2 mul imag part end let t74 = circuit_sub(t70, t26); // Fp2 sub coeff 0/1 let t75 = circuit_sub(t73, t29); // Fp2 sub coeff 1/1 let t76 = circuit_sub(t74, t32); // Fp2 sub coeff 0/1 let t77 = circuit_sub(t75, t35); // Fp2 sub coeff 1/1 let t78 = circuit_add(t38, t41); let t79 = circuit_mul(t78, in0); let t80 = circuit_mul(t38, in1); let t81 = circuit_sub(t80, t41); let t82 = circuit_sub(t79, t80); let t83 = circuit_sub(t82, t41); let t84 = circuit_add(t76, t81); // Fp2 add coeff 0/1 let t85 = circuit_add(t77, t83); // Fp2 add coeff 1/1 let t86 = circuit_add(in12, in16); // Fp2 add coeff 0/1 let t87 = circuit_add(in13, in17); // Fp2 add coeff 1/1 let t88 = circuit_add(in18, in22); // Fp2 add coeff 0/1 let t89 = circuit_add(in19, in23); // Fp2 add coeff 1/1 let t90 = circuit_mul(t88, t86); // Fp2 mul start let t91 = circuit_mul(t89, t87); let t92 = circuit_sub(t90, t91); // Fp2 mul real part end let t93 = circuit_mul(t88, t87); let t94 = circuit_mul(t89, t86); let t95 = circuit_add(t93, t94); // Fp2 mul imag part end let t96 = circuit_sub(t92, t26); // Fp2 sub coeff 0/1 let t97 = circuit_sub(t95, t29); // Fp2 sub coeff 1/1 let t98 = circuit_sub(t96, t38); // Fp2 sub coeff 0/1 let t99 = circuit_sub(t97, t41); // Fp2 sub coeff 1/1 let t100 = circuit_add(t98, t32); // Fp2 add coeff 0/1 let t101 = circuit_add(t99, t35); // Fp2 add coeff 1/1 let t102 = circuit_mul(t0, t18); // Fp2 mul start let t103 = circuit_mul(t1, t19); let t104 = circuit_sub(t102, t103); // Fp2 mul real part end let t105 = circuit_mul(t0, t19); let t106 = circuit_mul(t1, t18); let t107 = circuit_add(t105, t106); // Fp2 mul imag part end let t108 = circuit_mul(t2, t20); // Fp2 mul start let t109 = circuit_mul(t3, t21); let t110 = circuit_sub(t108, t109); // Fp2 mul real part end let t111 = circuit_mul(t2, t21); let t112 = circuit_mul(t3, t20); let t113 = circuit_add(t111, t112); // Fp2 mul imag part end let t114 = circuit_mul(t4, t22); // Fp2 mul start let t115 = circuit_mul(t5, t23); let t116 = circuit_sub(t114, t115); // Fp2 mul real part end let t117 = circuit_mul(t4, t23); let t118 = circuit_mul(t5, t22); let t119 = circuit_add(t117, t118); // Fp2 mul imag part end let t120 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t121 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t122 = circuit_add(t20, t22); // Fp2 add coeff 0/1 let t123 = circuit_add(t21, t23); // Fp2 add coeff 1/1 let t124 = circuit_mul(t120, t122); // Fp2 mul start let t125 = circuit_mul(t121, t123); let t126 = circuit_sub(t124, t125); // Fp2 mul real part end let t127 = circuit_mul(t120, t123); let t128 = circuit_mul(t121, t122); let t129 = circuit_add(t127, t128); // Fp2 mul imag part end let t130 = circuit_sub(t126, t110); // Fp2 sub coeff 0/1 let t131 = circuit_sub(t129, t113); // Fp2 sub coeff 1/1 let t132 = circuit_sub(t130, t116); // Fp2 sub coeff 0/1 let t133 = circuit_sub(t131, t119); // Fp2 sub coeff 1/1 let t134 = circuit_add(t132, t133); let t135 = circuit_mul(t134, in0); let t136 = circuit_mul(t132, in1); let t137 = circuit_sub(t136, t133); let t138 = circuit_sub(t135, t136); let t139 = circuit_sub(t138, t133); let t140 = circuit_add(t137, t104); // Fp2 add coeff 0/1 let t141 = circuit_add(t139, t107); // Fp2 add coeff 1/1 let t142 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t143 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t144 = circuit_add(t18, t20); // Fp2 add coeff 0/1 let t145 = circuit_add(t19, t21); // Fp2 add coeff 1/1 let t146 = circuit_mul(t142, t144); // Fp2 mul start let t147 = circuit_mul(t143, t145); let t148 = circuit_sub(t146, t147); // Fp2 mul real part end let t149 = circuit_mul(t142, t145); let t150 = circuit_mul(t143, t144); let t151 = circuit_add(t149, t150); // Fp2 mul imag part end let t152 = circuit_sub(t148, t104); // Fp2 sub coeff 0/1 let t153 = circuit_sub(t151, t107); // Fp2 sub coeff 1/1 let t154 = circuit_sub(t152, t110); // Fp2 sub coeff 0/1 let t155 = circuit_sub(t153, t113); // Fp2 sub coeff 1/1 let t156 = circuit_add(t116, t119); let t157 = circuit_mul(t156, in0); let t158 = circuit_mul(t116, in1); let t159 = circuit_sub(t158, t119); let t160 = circuit_sub(t157, t158); let t161 = circuit_sub(t160, t119); let t162 = circuit_add(t154, t159); // Fp2 add coeff 0/1 let t163 = circuit_add(t155, t161); // Fp2 add coeff 1/1 let t164 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t165 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t166 = circuit_add(t18, t22); // Fp2 add coeff 0/1 let t167 = circuit_add(t19, t23); // Fp2 add coeff 1/1 let t168 = circuit_mul(t166, t164); // Fp2 mul start let t169 = circuit_mul(t167, t165); let t170 = circuit_sub(t168, t169); // Fp2 mul real part end let t171 = circuit_mul(t166, t165); let t172 = circuit_mul(t167, t164); let t173 = circuit_add(t171, t172); // Fp2 mul imag part end let t174 = circuit_sub(t170, t104); // Fp2 sub coeff 0/1 let t175 = circuit_sub(t173, t107); // Fp2 sub coeff 1/1 let t176 = circuit_sub(t174, t116); // Fp2 sub coeff 0/1 let t177 = circuit_sub(t175, t119); // Fp2 sub coeff 1/1 let t178 = circuit_add(t176, t110); // Fp2 add coeff 0/1 let t179 = circuit_add(t177, t113); // Fp2 add coeff 1/1 let t180 = circuit_add(t140, t62); // Fp6 add coeff 0/5 let t181 = circuit_add(t141, t63); // Fp6 add coeff 1/5 let t182 = circuit_add(t162, t84); // Fp6 add coeff 2/5 let t183 = circuit_add(t163, t85); // Fp6 add coeff 3/5 let t184 = circuit_add(t178, t100); // Fp6 add coeff 4/5 let t185 = circuit_add(t179, t101); // Fp6 add coeff 5/5 let t186 = circuit_add(t62, t62); // Fp6 add coeff 0/5 let t187 = circuit_add(t63, t63); // Fp6 add coeff 1/5 let t188 = circuit_add(t84, t84); // Fp6 add coeff 2/5 let t189 = circuit_add(t85, t85); // Fp6 add coeff 3/5 let t190 = circuit_add(t100, t100); // Fp6 add coeff 4/5 let t191 = circuit_add(t101, t101); // Fp6 add coeff 5/5 let t192 = circuit_add(t100, t101); let t193 = circuit_mul(t192, in0); let t194 = circuit_mul(t100, in1); let t195 = circuit_sub(t194, t101); let t196 = circuit_sub(t193, t194); let t197 = circuit_sub(t196, t101); let t198 = circuit_add(t180, t195); // Fp6 add coeff 0/5 let t199 = circuit_add(t181, t197); // Fp6 add coeff 1/5 let t200 = circuit_add(t182, t62); // Fp6 add coeff 2/5 let t201 = circuit_add(t183, t63); // Fp6 add coeff 3/5 let t202 = circuit_add(t184, t84); // Fp6 add coeff 4/5 let t203 = circuit_add(t185, t85); // Fp6 add coeff 5/5 let t204 = circuit_add(in8, in9); // Doubling slope numerator start let t205 = circuit_sub(in8, in9); let t206 = circuit_mul(t204, t205); let t207 = circuit_mul(in8, in9); let t208 = circuit_mul(t206, in3); let t209 = circuit_mul(t207, in4); // Doubling slope numerator end let t210 = circuit_add(in10, in10); // Fp2 add coeff 0/1 let t211 = circuit_add(in11, in11); // Fp2 add coeff 1/1 let t212 = circuit_mul(t210, t210); // Fp2 Inv start let t213 = circuit_mul(t211, t211); let t214 = circuit_add(t212, t213); let t215 = circuit_inverse(t214); let t216 = circuit_mul(t210, t215); // Fp2 Inv real part end let t217 = circuit_mul(t211, t215); let t218 = circuit_sub(in2, t217); // Fp2 Inv imag part end let t219 = circuit_mul(t208, t216); // Fp2 mul start let t220 = circuit_mul(t209, t218); let t221 = circuit_sub(t219, t220); // Fp2 mul real part end let t222 = circuit_mul(t208, t218); let t223 = circuit_mul(t209, t216); let t224 = circuit_add(t222, t223); // Fp2 mul imag part end let t225 = circuit_add(t221, t224); let t226 = circuit_sub(t221, t224); let t227 = circuit_mul(t225, t226); let t228 = circuit_mul(t221, t224); let t229 = circuit_add(t228, t228); let t230 = circuit_add(in8, in8); // Fp2 add coeff 0/1 let t231 = circuit_add(in9, in9); // Fp2 add coeff 1/1 let t232 = circuit_sub(t227, t230); // Fp2 sub coeff 0/1 let t233 = circuit_sub(t229, t231); // Fp2 sub coeff 1/1 let t234 = circuit_sub(in8, t232); // Fp2 sub coeff 0/1 let t235 = circuit_sub(in9, t233); // Fp2 sub coeff 1/1 let t236 = circuit_mul(t221, t234); // Fp2 mul start let t237 = circuit_mul(t224, t235); let t238 = circuit_sub(t236, t237); // Fp2 mul real part end let t239 = circuit_mul(t221, t235); let t240 = circuit_mul(t224, t234); let t241 = circuit_add(t239, t240); // Fp2 mul imag part end let t242 = circuit_sub(t238, in10); // Fp2 sub coeff 0/1 let t243 = circuit_sub(t241, in11); // Fp2 sub coeff 1/1 let t244 = circuit_mul(t221, in8); // Fp2 mul start let t245 = circuit_mul(t224, in9); let t246 = circuit_sub(t244, t245); // Fp2 mul real part end let t247 = circuit_mul(t221, in9); let t248 = circuit_mul(t224, in8); let t249 = circuit_add(t247, t248); // Fp2 mul imag part end let t250 = circuit_sub(t246, in10); // Fp2 sub coeff 0/1 let t251 = circuit_sub(t249, in11); // Fp2 sub coeff 1/1 let t252 = circuit_mul(t221, in7); let t253 = circuit_mul(t224, in7); let t254 = circuit_mul(t250, in6); let t255 = circuit_mul(t251, in6); let t256 = circuit_mul(t186, t252); // Fp2 mul start let t257 = circuit_mul(t187, t253); let t258 = circuit_sub(t256, t257); // Fp2 mul real part end let t259 = circuit_mul(t186, t253); let t260 = circuit_mul(t187, t252); let t261 = circuit_add(t259, t260); // Fp2 mul imag part end let t262 = circuit_mul(t188, t254); // Fp2 mul start let t263 = circuit_mul(t189, t255); let t264 = circuit_sub(t262, t263); // Fp2 mul real part end let t265 = circuit_mul(t188, t255); let t266 = circuit_mul(t189, t254); let t267 = circuit_add(t265, t266); // Fp2 mul imag part end let t268 = circuit_add(t188, t190); // Fp2 add coeff 0/1 let t269 = circuit_add(t189, t191); // Fp2 add coeff 1/1 let t270 = circuit_mul(t254, t268); // Fp2 mul start let t271 = circuit_mul(t255, t269); let t272 = circuit_sub(t270, t271); // Fp2 mul real part end let t273 = circuit_mul(t254, t269); let t274 = circuit_mul(t255, t268); let t275 = circuit_add(t273, t274); // Fp2 mul imag part end let t276 = circuit_sub(t272, t264); // Fp2 sub coeff 0/1 let t277 = circuit_sub(t275, t267); // Fp2 sub coeff 1/1 let t278 = circuit_add(t276, t277); let t279 = circuit_mul(t278, in0); let t280 = circuit_mul(t276, in1); let t281 = circuit_sub(t280, t277); let t282 = circuit_sub(t279, t280); let t283 = circuit_sub(t282, t277); let t284 = circuit_add(t281, t258); // Fp2 add coeff 0/1 let t285 = circuit_add(t283, t261); // Fp2 add coeff 1/1 let t286 = circuit_add(t186, t190); // Fp2 add coeff 0/1 let t287 = circuit_add(t187, t191); // Fp2 add coeff 1/1 let t288 = circuit_mul(t252, t286); // Fp2 mul start let t289 = circuit_mul(t253, t287); let t290 = circuit_sub(t288, t289); // Fp2 mul real part end let t291 = circuit_mul(t252, t287); let t292 = circuit_mul(t253, t286); let t293 = circuit_add(t291, t292); // Fp2 mul imag part end let t294 = circuit_sub(t290, t258); // Fp2 sub coeff 0/1 let t295 = circuit_sub(t293, t261); // Fp2 sub coeff 1/1 let t296 = circuit_add(t294, t264); // Fp2 add coeff 0/1 let t297 = circuit_add(t295, t267); // Fp2 add coeff 1/1 let t298 = circuit_add(t252, t254); // Fp2 add coeff 0/1 let t299 = circuit_add(t253, t255); // Fp2 add coeff 1/1 let t300 = circuit_add(t186, t188); // Fp2 add coeff 0/1 let t301 = circuit_add(t187, t189); // Fp2 add coeff 1/1 let t302 = circuit_mul(t298, t300); // Fp2 mul start let t303 = circuit_mul(t299, t301); let t304 = circuit_sub(t302, t303); // Fp2 mul real part end let t305 = circuit_mul(t298, t301); let t306 = circuit_mul(t299, t300); let t307 = circuit_add(t305, t306); // Fp2 mul imag part end let t308 = circuit_sub(t304, t258); // Fp2 sub coeff 0/1 let t309 = circuit_sub(t307, t261); // Fp2 sub coeff 1/1 let t310 = circuit_sub(t308, t264); // Fp2 sub coeff 0/1 let t311 = circuit_sub(t309, t267); // Fp2 sub coeff 1/1 let t312 = circuit_add(in5, t252); // Fp2 add coeff 0/1 let t313 = circuit_add(in2, t253); // Fp2 add coeff 1/1 let t314 = circuit_add(t198, t186); // Fp6 add coeff 0/5 let t315 = circuit_add(t199, t187); // Fp6 add coeff 1/5 let t316 = circuit_add(t200, t188); // Fp6 add coeff 2/5 let t317 = circuit_add(t201, t189); // Fp6 add coeff 3/5 let t318 = circuit_add(t202, t190); // Fp6 add coeff 4/5 let t319 = circuit_add(t203, t191); // Fp6 add coeff 5/5 let t320 = circuit_mul(t314, t312); // Fp2 mul start let t321 = circuit_mul(t315, t313); let t322 = circuit_sub(t320, t321); // Fp2 mul real part end let t323 = circuit_mul(t314, t313); let t324 = circuit_mul(t315, t312); let t325 = circuit_add(t323, t324); // Fp2 mul imag part end let t326 = circuit_mul(t316, t254); // Fp2 mul start let t327 = circuit_mul(t317, t255); let t328 = circuit_sub(t326, t327); // Fp2 mul real part end let t329 = circuit_mul(t316, t255); let t330 = circuit_mul(t317, t254); let t331 = circuit_add(t329, t330); // Fp2 mul imag part end let t332 = circuit_add(t316, t318); // Fp2 add coeff 0/1 let t333 = circuit_add(t317, t319); // Fp2 add coeff 1/1 let t334 = circuit_mul(t254, t332); // Fp2 mul start let t335 = circuit_mul(t255, t333); let t336 = circuit_sub(t334, t335); // Fp2 mul real part end let t337 = circuit_mul(t254, t333); let t338 = circuit_mul(t255, t332); let t339 = circuit_add(t337, t338); // Fp2 mul imag part end let t340 = circuit_sub(t336, t328); // Fp2 sub coeff 0/1 let t341 = circuit_sub(t339, t331); // Fp2 sub coeff 1/1 let t342 = circuit_add(t340, t341); let t343 = circuit_mul(t342, in0); let t344 = circuit_mul(t340, in1); let t345 = circuit_sub(t344, t341); let t346 = circuit_sub(t343, t344); let t347 = circuit_sub(t346, t341); let t348 = circuit_add(t345, t322); // Fp2 add coeff 0/1 let t349 = circuit_add(t347, t325); // Fp2 add coeff 1/1 let t350 = circuit_add(t314, t318); // Fp2 add coeff 0/1 let t351 = circuit_add(t315, t319); // Fp2 add coeff 1/1 let t352 = circuit_mul(t312, t350); // Fp2 mul start let t353 = circuit_mul(t313, t351); let t354 = circuit_sub(t352, t353); // Fp2 mul real part end let t355 = circuit_mul(t312, t351); let t356 = circuit_mul(t313, t350); let t357 = circuit_add(t355, t356); // Fp2 mul imag part end let t358 = circuit_sub(t354, t322); // Fp2 sub coeff 0/1 let t359 = circuit_sub(t357, t325); // Fp2 sub coeff 1/1 let t360 = circuit_add(t358, t328); // Fp2 add coeff 0/1 let t361 = circuit_add(t359, t331); // Fp2 add coeff 1/1 let t362 = circuit_add(t312, t254); // Fp2 add coeff 0/1 let t363 = circuit_add(t313, t255); // Fp2 add coeff 1/1 let t364 = circuit_add(t314, t316); // Fp2 add coeff 0/1 let t365 = circuit_add(t315, t317); // Fp2 add coeff 1/1 let t366 = circuit_mul(t362, t364); // Fp2 mul start let t367 = circuit_mul(t363, t365); let t368 = circuit_sub(t366, t367); // Fp2 mul real part end let t369 = circuit_mul(t362, t365); let t370 = circuit_mul(t363, t364); let t371 = circuit_add(t369, t370); // Fp2 mul imag part end let t372 = circuit_sub(t368, t322); // Fp2 sub coeff 0/1 let t373 = circuit_sub(t371, t325); // Fp2 sub coeff 1/1 let t374 = circuit_sub(t372, t328); // Fp2 sub coeff 0/1 let t375 = circuit_sub(t373, t331); // Fp2 sub coeff 1/1 let t376 = circuit_add(t198, t284); // Fp6 add coeff 0/5 let t377 = circuit_add(t199, t285); // Fp6 add coeff 1/5 let t378 = circuit_add(t200, t310); // Fp6 add coeff 2/5 let t379 = circuit_add(t201, t311); // Fp6 add coeff 3/5 let t380 = circuit_add(t202, t296); // Fp6 add coeff 4/5 let t381 = circuit_add(t203, t297); // Fp6 add coeff 5/5 let t382 = circuit_sub(in2, t376); // Fp6 neg coeff 0/5 let t383 = circuit_sub(in2, t377); // Fp6 neg coeff 1/5 let t384 = circuit_sub(in2, t378); // Fp6 neg coeff 2/5 let t385 = circuit_sub(in2, t379); // Fp6 neg coeff 3/5 let t386 = circuit_sub(in2, t380); // Fp6 neg coeff 4/5 let t387 = circuit_sub(in2, t381); // Fp6 neg coeff 5/5 let t388 = circuit_add(t382, t348); // Fp6 add coeff 0/5 let t389 = circuit_add(t383, t349); // Fp6 add coeff 1/5 let t390 = circuit_add(t384, t374); // Fp6 add coeff 2/5 let t391 = circuit_add(t385, t375); // Fp6 add coeff 3/5 let t392 = circuit_add(t386, t360); // Fp6 add coeff 4/5 let t393 = circuit_add(t387, t361); // Fp6 add coeff 5/5 let t394 = circuit_add(t296, t297); let t395 = circuit_mul(t394, in0); let t396 = circuit_mul(t296, in1); let t397 = circuit_sub(t396, t297); let t398 = circuit_sub(t395, t396); let t399 = circuit_sub(t398, t297); let t400 = circuit_add(t397, t198); // Fp6 add coeff 0/5 let t401 = circuit_add(t399, t199); // Fp6 add coeff 1/5 let t402 = circuit_add(t284, t200); // Fp6 add coeff 2/5 let t403 = circuit_add(t285, t201); // Fp6 add coeff 3/5 let t404 = circuit_add(t310, t202); // Fp6 add coeff 4/5 let t405 = circuit_add(t311, t203); // Fp6 add coeff 5/5 let t406 = circuit_add(t232, t233); let t407 = circuit_add(t406, t242); let t408 = circuit_add(t407, t243); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = ( t408, t400, t401, t402, t403, t404, t405, t388, t389, t390, t391, t392, t393, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0xa, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x9, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x3, 0x0, 0x0, 0x0]); // in3 circuit_inputs = circuit_inputs.next_2([0x6, 0x0, 0x0, 0x0]); // in4 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in5 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in6 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in7 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in8 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in9 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in10 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in11 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a0); // in12 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a1); // in13 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a0); // in14 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a1); // in15 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a0); // in16 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a1); // in17 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a0); // in18 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a1); // in19 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a0); // in20 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a1); // in21 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a0); // in22 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a1); // in23 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t232), x1: outputs.get_output(t233), y0: outputs.get_output(t242), y1: outputs.get_output(t243), }; let Mi_plus_one: E12T = E12T { c0b0a0: outputs.get_output(t400), c0b0a1: outputs.get_output(t401), c0b1a0: outputs.get_output(t402), c0b1a1: outputs.get_output(t403), c0b2a0: outputs.get_output(t404), c0b2a1: outputs.get_output(t405), c1b0a0: outputs.get_output(t388), c1b0a1: outputs.get_output(t389), c1b1a0: outputs.get_output(t390), c1b1a1: outputs.get_output(t391), c1b2a0: outputs.get_output(t392), c1b2a1: outputs.get_output(t393), }; return (Q0, Mi_plus_one); } #[inline(always)] pub fn run_BN254_TOWER_MILLER_BIT1_1P_circuit( yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, Q_or_Q_neg_0: G2Point, M_i: E12T, ) -> (G2Point, E12T) { // CONSTANT stack let in0 = CE::> {}; // 0xa let in1 = CE::> {}; // 0x9 let in2 = CE::> {}; // 0x0 let in3 = CE::> {}; // 0x1 // INPUT stack let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let (in7, in8, in9) = (CE::> {}, CE::> {}, CE::> {}); let (in10, in11, in12) = (CE::> {}, CE::> {}, CE::> {}); let (in13, in14, in15) = (CE::> {}, CE::> {}, CE::> {}); let (in16, in17, in18) = (CE::> {}, CE::> {}, CE::> {}); let (in19, in20, in21) = (CE::> {}, CE::> {}, CE::> {}); let (in22, in23, in24) = (CE::> {}, CE::> {}, CE::> {}); let in25 = CE::> {}; let t0 = circuit_sub(in14, in20); // Fp6 sub coeff 0/5 let t1 = circuit_sub(in15, in21); // Fp6 sub coeff 1/5 let t2 = circuit_sub(in16, in22); // Fp6 sub coeff 2/5 let t3 = circuit_sub(in17, in23); // Fp6 sub coeff 3/5 let t4 = circuit_sub(in18, in24); // Fp6 sub coeff 4/5 let t5 = circuit_sub(in19, in25); // Fp6 sub coeff 5/5 let t6 = circuit_add(in24, in25); let t7 = circuit_mul(t6, in0); let t8 = circuit_mul(in24, in1); let t9 = circuit_sub(t8, in25); let t10 = circuit_sub(t7, t8); let t11 = circuit_sub(t10, in25); let t12 = circuit_sub(in2, t9); // Fp6 neg coeff 0/5 let t13 = circuit_sub(in2, t11); // Fp6 neg coeff 1/5 let t14 = circuit_sub(in2, in20); // Fp6 neg coeff 2/5 let t15 = circuit_sub(in2, in21); // Fp6 neg coeff 3/5 let t16 = circuit_sub(in2, in22); // Fp6 neg coeff 4/5 let t17 = circuit_sub(in2, in23); // Fp6 neg coeff 5/5 let t18 = circuit_add(in14, t12); // Fp6 add coeff 0/5 let t19 = circuit_add(in15, t13); // Fp6 add coeff 1/5 let t20 = circuit_add(in16, t14); // Fp6 add coeff 2/5 let t21 = circuit_add(in17, t15); // Fp6 add coeff 3/5 let t22 = circuit_add(in18, t16); // Fp6 add coeff 4/5 let t23 = circuit_add(in19, t17); // Fp6 add coeff 5/5 let t24 = circuit_mul(in14, in20); // Fp2 mul start let t25 = circuit_mul(in15, in21); let t26 = circuit_sub(t24, t25); // Fp2 mul real part end let t27 = circuit_mul(in14, in21); let t28 = circuit_mul(in15, in20); let t29 = circuit_add(t27, t28); // Fp2 mul imag part end let t30 = circuit_mul(in16, in22); // Fp2 mul start let t31 = circuit_mul(in17, in23); let t32 = circuit_sub(t30, t31); // Fp2 mul real part end let t33 = circuit_mul(in16, in23); let t34 = circuit_mul(in17, in22); let t35 = circuit_add(t33, t34); // Fp2 mul imag part end let t36 = circuit_mul(in18, in24); // Fp2 mul start let t37 = circuit_mul(in19, in25); let t38 = circuit_sub(t36, t37); // Fp2 mul real part end let t39 = circuit_mul(in18, in25); let t40 = circuit_mul(in19, in24); let t41 = circuit_add(t39, t40); // Fp2 mul imag part end let t42 = circuit_add(in16, in18); // Fp2 add coeff 0/1 let t43 = circuit_add(in17, in19); // Fp2 add coeff 1/1 let t44 = circuit_add(in22, in24); // Fp2 add coeff 0/1 let t45 = circuit_add(in23, in25); // Fp2 add coeff 1/1 let t46 = circuit_mul(t42, t44); // Fp2 mul start let t47 = circuit_mul(t43, t45); let t48 = circuit_sub(t46, t47); // Fp2 mul real part end let t49 = circuit_mul(t42, t45); let t50 = circuit_mul(t43, t44); let t51 = circuit_add(t49, t50); // Fp2 mul imag part end let t52 = circuit_sub(t48, t32); // Fp2 sub coeff 0/1 let t53 = circuit_sub(t51, t35); // Fp2 sub coeff 1/1 let t54 = circuit_sub(t52, t38); // Fp2 sub coeff 0/1 let t55 = circuit_sub(t53, t41); // Fp2 sub coeff 1/1 let t56 = circuit_add(t54, t55); let t57 = circuit_mul(t56, in0); let t58 = circuit_mul(t54, in1); let t59 = circuit_sub(t58, t55); let t60 = circuit_sub(t57, t58); let t61 = circuit_sub(t60, t55); let t62 = circuit_add(t59, t26); // Fp2 add coeff 0/1 let t63 = circuit_add(t61, t29); // Fp2 add coeff 1/1 let t64 = circuit_add(in14, in16); // Fp2 add coeff 0/1 let t65 = circuit_add(in15, in17); // Fp2 add coeff 1/1 let t66 = circuit_add(in20, in22); // Fp2 add coeff 0/1 let t67 = circuit_add(in21, in23); // Fp2 add coeff 1/1 let t68 = circuit_mul(t64, t66); // Fp2 mul start let t69 = circuit_mul(t65, t67); let t70 = circuit_sub(t68, t69); // Fp2 mul real part end let t71 = circuit_mul(t64, t67); let t72 = circuit_mul(t65, t66); let t73 = circuit_add(t71, t72); // Fp2 mul imag part end let t74 = circuit_sub(t70, t26); // Fp2 sub coeff 0/1 let t75 = circuit_sub(t73, t29); // Fp2 sub coeff 1/1 let t76 = circuit_sub(t74, t32); // Fp2 sub coeff 0/1 let t77 = circuit_sub(t75, t35); // Fp2 sub coeff 1/1 let t78 = circuit_add(t38, t41); let t79 = circuit_mul(t78, in0); let t80 = circuit_mul(t38, in1); let t81 = circuit_sub(t80, t41); let t82 = circuit_sub(t79, t80); let t83 = circuit_sub(t82, t41); let t84 = circuit_add(t76, t81); // Fp2 add coeff 0/1 let t85 = circuit_add(t77, t83); // Fp2 add coeff 1/1 let t86 = circuit_add(in14, in18); // Fp2 add coeff 0/1 let t87 = circuit_add(in15, in19); // Fp2 add coeff 1/1 let t88 = circuit_add(in20, in24); // Fp2 add coeff 0/1 let t89 = circuit_add(in21, in25); // Fp2 add coeff 1/1 let t90 = circuit_mul(t88, t86); // Fp2 mul start let t91 = circuit_mul(t89, t87); let t92 = circuit_sub(t90, t91); // Fp2 mul real part end let t93 = circuit_mul(t88, t87); let t94 = circuit_mul(t89, t86); let t95 = circuit_add(t93, t94); // Fp2 mul imag part end let t96 = circuit_sub(t92, t26); // Fp2 sub coeff 0/1 let t97 = circuit_sub(t95, t29); // Fp2 sub coeff 1/1 let t98 = circuit_sub(t96, t38); // Fp2 sub coeff 0/1 let t99 = circuit_sub(t97, t41); // Fp2 sub coeff 1/1 let t100 = circuit_add(t98, t32); // Fp2 add coeff 0/1 let t101 = circuit_add(t99, t35); // Fp2 add coeff 1/1 let t102 = circuit_mul(t0, t18); // Fp2 mul start let t103 = circuit_mul(t1, t19); let t104 = circuit_sub(t102, t103); // Fp2 mul real part end let t105 = circuit_mul(t0, t19); let t106 = circuit_mul(t1, t18); let t107 = circuit_add(t105, t106); // Fp2 mul imag part end let t108 = circuit_mul(t2, t20); // Fp2 mul start let t109 = circuit_mul(t3, t21); let t110 = circuit_sub(t108, t109); // Fp2 mul real part end let t111 = circuit_mul(t2, t21); let t112 = circuit_mul(t3, t20); let t113 = circuit_add(t111, t112); // Fp2 mul imag part end let t114 = circuit_mul(t4, t22); // Fp2 mul start let t115 = circuit_mul(t5, t23); let t116 = circuit_sub(t114, t115); // Fp2 mul real part end let t117 = circuit_mul(t4, t23); let t118 = circuit_mul(t5, t22); let t119 = circuit_add(t117, t118); // Fp2 mul imag part end let t120 = circuit_add(t2, t4); // Fp2 add coeff 0/1 let t121 = circuit_add(t3, t5); // Fp2 add coeff 1/1 let t122 = circuit_add(t20, t22); // Fp2 add coeff 0/1 let t123 = circuit_add(t21, t23); // Fp2 add coeff 1/1 let t124 = circuit_mul(t120, t122); // Fp2 mul start let t125 = circuit_mul(t121, t123); let t126 = circuit_sub(t124, t125); // Fp2 mul real part end let t127 = circuit_mul(t120, t123); let t128 = circuit_mul(t121, t122); let t129 = circuit_add(t127, t128); // Fp2 mul imag part end let t130 = circuit_sub(t126, t110); // Fp2 sub coeff 0/1 let t131 = circuit_sub(t129, t113); // Fp2 sub coeff 1/1 let t132 = circuit_sub(t130, t116); // Fp2 sub coeff 0/1 let t133 = circuit_sub(t131, t119); // Fp2 sub coeff 1/1 let t134 = circuit_add(t132, t133); let t135 = circuit_mul(t134, in0); let t136 = circuit_mul(t132, in1); let t137 = circuit_sub(t136, t133); let t138 = circuit_sub(t135, t136); let t139 = circuit_sub(t138, t133); let t140 = circuit_add(t137, t104); // Fp2 add coeff 0/1 let t141 = circuit_add(t139, t107); // Fp2 add coeff 1/1 let t142 = circuit_add(t0, t2); // Fp2 add coeff 0/1 let t143 = circuit_add(t1, t3); // Fp2 add coeff 1/1 let t144 = circuit_add(t18, t20); // Fp2 add coeff 0/1 let t145 = circuit_add(t19, t21); // Fp2 add coeff 1/1 let t146 = circuit_mul(t142, t144); // Fp2 mul start let t147 = circuit_mul(t143, t145); let t148 = circuit_sub(t146, t147); // Fp2 mul real part end let t149 = circuit_mul(t142, t145); let t150 = circuit_mul(t143, t144); let t151 = circuit_add(t149, t150); // Fp2 mul imag part end let t152 = circuit_sub(t148, t104); // Fp2 sub coeff 0/1 let t153 = circuit_sub(t151, t107); // Fp2 sub coeff 1/1 let t154 = circuit_sub(t152, t110); // Fp2 sub coeff 0/1 let t155 = circuit_sub(t153, t113); // Fp2 sub coeff 1/1 let t156 = circuit_add(t116, t119); let t157 = circuit_mul(t156, in0); let t158 = circuit_mul(t116, in1); let t159 = circuit_sub(t158, t119); let t160 = circuit_sub(t157, t158); let t161 = circuit_sub(t160, t119); let t162 = circuit_add(t154, t159); // Fp2 add coeff 0/1 let t163 = circuit_add(t155, t161); // Fp2 add coeff 1/1 let t164 = circuit_add(t0, t4); // Fp2 add coeff 0/1 let t165 = circuit_add(t1, t5); // Fp2 add coeff 1/1 let t166 = circuit_add(t18, t22); // Fp2 add coeff 0/1 let t167 = circuit_add(t19, t23); // Fp2 add coeff 1/1 let t168 = circuit_mul(t166, t164); // Fp2 mul start let t169 = circuit_mul(t167, t165); let t170 = circuit_sub(t168, t169); // Fp2 mul real part end let t171 = circuit_mul(t166, t165); let t172 = circuit_mul(t167, t164); let t173 = circuit_add(t171, t172); // Fp2 mul imag part end let t174 = circuit_sub(t170, t104); // Fp2 sub coeff 0/1 let t175 = circuit_sub(t173, t107); // Fp2 sub coeff 1/1 let t176 = circuit_sub(t174, t116); // Fp2 sub coeff 0/1 let t177 = circuit_sub(t175, t119); // Fp2 sub coeff 1/1 let t178 = circuit_add(t176, t110); // Fp2 add coeff 0/1 let t179 = circuit_add(t177, t113); // Fp2 add coeff 1/1 let t180 = circuit_add(t140, t62); // Fp6 add coeff 0/5 let t181 = circuit_add(t141, t63); // Fp6 add coeff 1/5 let t182 = circuit_add(t162, t84); // Fp6 add coeff 2/5 let t183 = circuit_add(t163, t85); // Fp6 add coeff 3/5 let t184 = circuit_add(t178, t100); // Fp6 add coeff 4/5 let t185 = circuit_add(t179, t101); // Fp6 add coeff 5/5 let t186 = circuit_add(t62, t62); // Fp6 add coeff 0/5 let t187 = circuit_add(t63, t63); // Fp6 add coeff 1/5 let t188 = circuit_add(t84, t84); // Fp6 add coeff 2/5 let t189 = circuit_add(t85, t85); // Fp6 add coeff 3/5 let t190 = circuit_add(t100, t100); // Fp6 add coeff 4/5 let t191 = circuit_add(t101, t101); // Fp6 add coeff 5/5 let t192 = circuit_add(t100, t101); let t193 = circuit_mul(t192, in0); let t194 = circuit_mul(t100, in1); let t195 = circuit_sub(t194, t101); let t196 = circuit_sub(t193, t194); let t197 = circuit_sub(t196, t101); let t198 = circuit_add(t180, t195); // Fp6 add coeff 0/5 let t199 = circuit_add(t181, t197); // Fp6 add coeff 1/5 let t200 = circuit_add(t182, t62); // Fp6 add coeff 2/5 let t201 = circuit_add(t183, t63); // Fp6 add coeff 3/5 let t202 = circuit_add(t184, t84); // Fp6 add coeff 4/5 let t203 = circuit_add(t185, t85); // Fp6 add coeff 5/5 let t204 = circuit_sub(in8, in12); // Fp2 sub coeff 0/1 let t205 = circuit_sub(in9, in13); // Fp2 sub coeff 1/1 let t206 = circuit_sub(in6, in10); // Fp2 sub coeff 0/1 let t207 = circuit_sub(in7, in11); // Fp2 sub coeff 1/1 let t208 = circuit_mul(t206, t206); // Fp2 Inv start let t209 = circuit_mul(t207, t207); let t210 = circuit_add(t208, t209); let t211 = circuit_inverse(t210); let t212 = circuit_mul(t206, t211); // Fp2 Inv real part end let t213 = circuit_mul(t207, t211); let t214 = circuit_sub(in2, t213); // Fp2 Inv imag part end let t215 = circuit_mul(t204, t212); // Fp2 mul start let t216 = circuit_mul(t205, t214); let t217 = circuit_sub(t215, t216); // Fp2 mul real part end let t218 = circuit_mul(t204, t214); let t219 = circuit_mul(t205, t212); let t220 = circuit_add(t218, t219); // Fp2 mul imag part end let t221 = circuit_add(t217, t220); let t222 = circuit_sub(t217, t220); let t223 = circuit_mul(t221, t222); let t224 = circuit_mul(t217, t220); let t225 = circuit_add(t224, t224); let t226 = circuit_add(in6, in10); // Fp2 add coeff 0/1 let t227 = circuit_add(in7, in11); // Fp2 add coeff 1/1 let t228 = circuit_sub(t223, t226); // Fp2 sub coeff 0/1 let t229 = circuit_sub(t225, t227); // Fp2 sub coeff 1/1 let t230 = circuit_mul(t217, in6); // Fp2 mul start let t231 = circuit_mul(t220, in7); let t232 = circuit_sub(t230, t231); // Fp2 mul real part end let t233 = circuit_mul(t217, in7); let t234 = circuit_mul(t220, in6); let t235 = circuit_add(t233, t234); // Fp2 mul imag part end let t236 = circuit_sub(t232, in8); // Fp2 sub coeff 0/1 let t237 = circuit_sub(t235, in9); // Fp2 sub coeff 1/1 let t238 = circuit_add(in8, in8); // Fp2 add coeff 0/1 let t239 = circuit_add(in9, in9); // Fp2 add coeff 1/1 let t240 = circuit_sub(t228, in6); // Fp2 sub coeff 0/1 let t241 = circuit_sub(t229, in7); // Fp2 sub coeff 1/1 let t242 = circuit_mul(t240, t240); // Fp2 Inv start let t243 = circuit_mul(t241, t241); let t244 = circuit_add(t242, t243); let t245 = circuit_inverse(t244); let t246 = circuit_mul(t240, t245); // Fp2 Inv real part end let t247 = circuit_mul(t241, t245); let t248 = circuit_sub(in2, t247); // Fp2 Inv imag part end let t249 = circuit_mul(t238, t246); // Fp2 mul start let t250 = circuit_mul(t239, t248); let t251 = circuit_sub(t249, t250); // Fp2 mul real part end let t252 = circuit_mul(t238, t248); let t253 = circuit_mul(t239, t246); let t254 = circuit_add(t252, t253); // Fp2 mul imag part end let t255 = circuit_add(t217, t251); // Fp2 add coeff 0/1 let t256 = circuit_add(t220, t254); // Fp2 add coeff 1/1 let t257 = circuit_sub(in2, t255); // Fp2 neg coeff 0/1 let t258 = circuit_sub(in2, t256); // Fp2 neg coeff 1/1 let t259 = circuit_add(t257, t258); let t260 = circuit_sub(t257, t258); let t261 = circuit_mul(t259, t260); let t262 = circuit_mul(t257, t258); let t263 = circuit_add(t262, t262); let t264 = circuit_sub(t261, in6); // Fp2 sub coeff 0/1 let t265 = circuit_sub(t263, in7); // Fp2 sub coeff 1/1 let t266 = circuit_sub(t264, t228); // Fp2 sub coeff 0/1 let t267 = circuit_sub(t265, t229); // Fp2 sub coeff 1/1 let t268 = circuit_sub(in6, t266); // Fp2 sub coeff 0/1 let t269 = circuit_sub(in7, t267); // Fp2 sub coeff 1/1 let t270 = circuit_mul(t257, t268); // Fp2 mul start let t271 = circuit_mul(t258, t269); let t272 = circuit_sub(t270, t271); // Fp2 mul real part end let t273 = circuit_mul(t257, t269); let t274 = circuit_mul(t258, t268); let t275 = circuit_add(t273, t274); // Fp2 mul imag part end let t276 = circuit_sub(t272, in8); // Fp2 sub coeff 0/1 let t277 = circuit_sub(t275, in9); // Fp2 sub coeff 1/1 let t278 = circuit_mul(t257, in6); // Fp2 mul start let t279 = circuit_mul(t258, in7); let t280 = circuit_sub(t278, t279); // Fp2 mul real part end let t281 = circuit_mul(t257, in7); let t282 = circuit_mul(t258, in6); let t283 = circuit_add(t281, t282); // Fp2 mul imag part end let t284 = circuit_sub(t280, in8); // Fp2 sub coeff 0/1 let t285 = circuit_sub(t283, in9); // Fp2 sub coeff 1/1 let t286 = circuit_mul(t217, in5); let t287 = circuit_mul(t220, in5); let t288 = circuit_mul(t236, in4); let t289 = circuit_mul(t237, in4); let t290 = circuit_mul(t257, in5); let t291 = circuit_mul(t258, in5); let t292 = circuit_mul(t284, in4); let t293 = circuit_mul(t285, in4); let t294 = circuit_mul(t186, t286); // Fp2 mul start let t295 = circuit_mul(t187, t287); let t296 = circuit_sub(t294, t295); // Fp2 mul real part end let t297 = circuit_mul(t186, t287); let t298 = circuit_mul(t187, t286); let t299 = circuit_add(t297, t298); // Fp2 mul imag part end let t300 = circuit_mul(t188, t288); // Fp2 mul start let t301 = circuit_mul(t189, t289); let t302 = circuit_sub(t300, t301); // Fp2 mul real part end let t303 = circuit_mul(t188, t289); let t304 = circuit_mul(t189, t288); let t305 = circuit_add(t303, t304); // Fp2 mul imag part end let t306 = circuit_add(t188, t190); // Fp2 add coeff 0/1 let t307 = circuit_add(t189, t191); // Fp2 add coeff 1/1 let t308 = circuit_mul(t288, t306); // Fp2 mul start let t309 = circuit_mul(t289, t307); let t310 = circuit_sub(t308, t309); // Fp2 mul real part end let t311 = circuit_mul(t288, t307); let t312 = circuit_mul(t289, t306); let t313 = circuit_add(t311, t312); // Fp2 mul imag part end let t314 = circuit_sub(t310, t302); // Fp2 sub coeff 0/1 let t315 = circuit_sub(t313, t305); // Fp2 sub coeff 1/1 let t316 = circuit_add(t314, t315); let t317 = circuit_mul(t316, in0); let t318 = circuit_mul(t314, in1); let t319 = circuit_sub(t318, t315); let t320 = circuit_sub(t317, t318); let t321 = circuit_sub(t320, t315); let t322 = circuit_add(t319, t296); // Fp2 add coeff 0/1 let t323 = circuit_add(t321, t299); // Fp2 add coeff 1/1 let t324 = circuit_add(t186, t190); // Fp2 add coeff 0/1 let t325 = circuit_add(t187, t191); // Fp2 add coeff 1/1 let t326 = circuit_mul(t286, t324); // Fp2 mul start let t327 = circuit_mul(t287, t325); let t328 = circuit_sub(t326, t327); // Fp2 mul real part end let t329 = circuit_mul(t286, t325); let t330 = circuit_mul(t287, t324); let t331 = circuit_add(t329, t330); // Fp2 mul imag part end let t332 = circuit_sub(t328, t296); // Fp2 sub coeff 0/1 let t333 = circuit_sub(t331, t299); // Fp2 sub coeff 1/1 let t334 = circuit_add(t332, t302); // Fp2 add coeff 0/1 let t335 = circuit_add(t333, t305); // Fp2 add coeff 1/1 let t336 = circuit_add(t286, t288); // Fp2 add coeff 0/1 let t337 = circuit_add(t287, t289); // Fp2 add coeff 1/1 let t338 = circuit_add(t186, t188); // Fp2 add coeff 0/1 let t339 = circuit_add(t187, t189); // Fp2 add coeff 1/1 let t340 = circuit_mul(t336, t338); // Fp2 mul start let t341 = circuit_mul(t337, t339); let t342 = circuit_sub(t340, t341); // Fp2 mul real part end let t343 = circuit_mul(t336, t339); let t344 = circuit_mul(t337, t338); let t345 = circuit_add(t343, t344); // Fp2 mul imag part end let t346 = circuit_sub(t342, t296); // Fp2 sub coeff 0/1 let t347 = circuit_sub(t345, t299); // Fp2 sub coeff 1/1 let t348 = circuit_sub(t346, t302); // Fp2 sub coeff 0/1 let t349 = circuit_sub(t347, t305); // Fp2 sub coeff 1/1 let t350 = circuit_add(in3, t286); // Fp2 add coeff 0/1 let t351 = circuit_add(in2, t287); // Fp2 add coeff 1/1 let t352 = circuit_add(t198, t186); // Fp6 add coeff 0/5 let t353 = circuit_add(t199, t187); // Fp6 add coeff 1/5 let t354 = circuit_add(t200, t188); // Fp6 add coeff 2/5 let t355 = circuit_add(t201, t189); // Fp6 add coeff 3/5 let t356 = circuit_add(t202, t190); // Fp6 add coeff 4/5 let t357 = circuit_add(t203, t191); // Fp6 add coeff 5/5 let t358 = circuit_mul(t352, t350); // Fp2 mul start let t359 = circuit_mul(t353, t351); let t360 = circuit_sub(t358, t359); // Fp2 mul real part end let t361 = circuit_mul(t352, t351); let t362 = circuit_mul(t353, t350); let t363 = circuit_add(t361, t362); // Fp2 mul imag part end let t364 = circuit_mul(t354, t288); // Fp2 mul start let t365 = circuit_mul(t355, t289); let t366 = circuit_sub(t364, t365); // Fp2 mul real part end let t367 = circuit_mul(t354, t289); let t368 = circuit_mul(t355, t288); let t369 = circuit_add(t367, t368); // Fp2 mul imag part end let t370 = circuit_add(t354, t356); // Fp2 add coeff 0/1 let t371 = circuit_add(t355, t357); // Fp2 add coeff 1/1 let t372 = circuit_mul(t288, t370); // Fp2 mul start let t373 = circuit_mul(t289, t371); let t374 = circuit_sub(t372, t373); // Fp2 mul real part end let t375 = circuit_mul(t288, t371); let t376 = circuit_mul(t289, t370); let t377 = circuit_add(t375, t376); // Fp2 mul imag part end let t378 = circuit_sub(t374, t366); // Fp2 sub coeff 0/1 let t379 = circuit_sub(t377, t369); // Fp2 sub coeff 1/1 let t380 = circuit_add(t378, t379); let t381 = circuit_mul(t380, in0); let t382 = circuit_mul(t378, in1); let t383 = circuit_sub(t382, t379); let t384 = circuit_sub(t381, t382); let t385 = circuit_sub(t384, t379); let t386 = circuit_add(t383, t360); // Fp2 add coeff 0/1 let t387 = circuit_add(t385, t363); // Fp2 add coeff 1/1 let t388 = circuit_add(t352, t356); // Fp2 add coeff 0/1 let t389 = circuit_add(t353, t357); // Fp2 add coeff 1/1 let t390 = circuit_mul(t350, t388); // Fp2 mul start let t391 = circuit_mul(t351, t389); let t392 = circuit_sub(t390, t391); // Fp2 mul real part end let t393 = circuit_mul(t350, t389); let t394 = circuit_mul(t351, t388); let t395 = circuit_add(t393, t394); // Fp2 mul imag part end let t396 = circuit_sub(t392, t360); // Fp2 sub coeff 0/1 let t397 = circuit_sub(t395, t363); // Fp2 sub coeff 1/1 let t398 = circuit_add(t396, t366); // Fp2 add coeff 0/1 let t399 = circuit_add(t397, t369); // Fp2 add coeff 1/1 let t400 = circuit_add(t350, t288); // Fp2 add coeff 0/1 let t401 = circuit_add(t351, t289); // Fp2 add coeff 1/1 let t402 = circuit_add(t352, t354); // Fp2 add coeff 0/1 let t403 = circuit_add(t353, t355); // Fp2 add coeff 1/1 let t404 = circuit_mul(t400, t402); // Fp2 mul start let t405 = circuit_mul(t401, t403); let t406 = circuit_sub(t404, t405); // Fp2 mul real part end let t407 = circuit_mul(t400, t403); let t408 = circuit_mul(t401, t402); let t409 = circuit_add(t407, t408); // Fp2 mul imag part end let t410 = circuit_sub(t406, t360); // Fp2 sub coeff 0/1 let t411 = circuit_sub(t409, t363); // Fp2 sub coeff 1/1 let t412 = circuit_sub(t410, t366); // Fp2 sub coeff 0/1 let t413 = circuit_sub(t411, t369); // Fp2 sub coeff 1/1 let t414 = circuit_add(t198, t322); // Fp6 add coeff 0/5 let t415 = circuit_add(t199, t323); // Fp6 add coeff 1/5 let t416 = circuit_add(t200, t348); // Fp6 add coeff 2/5 let t417 = circuit_add(t201, t349); // Fp6 add coeff 3/5 let t418 = circuit_add(t202, t334); // Fp6 add coeff 4/5 let t419 = circuit_add(t203, t335); // Fp6 add coeff 5/5 let t420 = circuit_sub(in2, t414); // Fp6 neg coeff 0/5 let t421 = circuit_sub(in2, t415); // Fp6 neg coeff 1/5 let t422 = circuit_sub(in2, t416); // Fp6 neg coeff 2/5 let t423 = circuit_sub(in2, t417); // Fp6 neg coeff 3/5 let t424 = circuit_sub(in2, t418); // Fp6 neg coeff 4/5 let t425 = circuit_sub(in2, t419); // Fp6 neg coeff 5/5 let t426 = circuit_add(t420, t386); // Fp6 add coeff 0/5 let t427 = circuit_add(t421, t387); // Fp6 add coeff 1/5 let t428 = circuit_add(t422, t412); // Fp6 add coeff 2/5 let t429 = circuit_add(t423, t413); // Fp6 add coeff 3/5 let t430 = circuit_add(t424, t398); // Fp6 add coeff 4/5 let t431 = circuit_add(t425, t399); // Fp6 add coeff 5/5 let t432 = circuit_add(t334, t335); let t433 = circuit_mul(t432, in0); let t434 = circuit_mul(t334, in1); let t435 = circuit_sub(t434, t335); let t436 = circuit_sub(t433, t434); let t437 = circuit_sub(t436, t335); let t438 = circuit_add(t435, t198); // Fp6 add coeff 0/5 let t439 = circuit_add(t437, t199); // Fp6 add coeff 1/5 let t440 = circuit_add(t322, t200); // Fp6 add coeff 2/5 let t441 = circuit_add(t323, t201); // Fp6 add coeff 3/5 let t442 = circuit_add(t348, t202); // Fp6 add coeff 4/5 let t443 = circuit_add(t349, t203); // Fp6 add coeff 5/5 let t444 = circuit_mul(t426, t290); // Fp2 mul start let t445 = circuit_mul(t427, t291); let t446 = circuit_sub(t444, t445); // Fp2 mul real part end let t447 = circuit_mul(t426, t291); let t448 = circuit_mul(t427, t290); let t449 = circuit_add(t447, t448); // Fp2 mul imag part end let t450 = circuit_mul(t428, t292); // Fp2 mul start let t451 = circuit_mul(t429, t293); let t452 = circuit_sub(t450, t451); // Fp2 mul real part end let t453 = circuit_mul(t428, t293); let t454 = circuit_mul(t429, t292); let t455 = circuit_add(t453, t454); // Fp2 mul imag part end let t456 = circuit_add(t428, t430); // Fp2 add coeff 0/1 let t457 = circuit_add(t429, t431); // Fp2 add coeff 1/1 let t458 = circuit_mul(t292, t456); // Fp2 mul start let t459 = circuit_mul(t293, t457); let t460 = circuit_sub(t458, t459); // Fp2 mul real part end let t461 = circuit_mul(t292, t457); let t462 = circuit_mul(t293, t456); let t463 = circuit_add(t461, t462); // Fp2 mul imag part end let t464 = circuit_sub(t460, t452); // Fp2 sub coeff 0/1 let t465 = circuit_sub(t463, t455); // Fp2 sub coeff 1/1 let t466 = circuit_add(t464, t465); let t467 = circuit_mul(t466, in0); let t468 = circuit_mul(t464, in1); let t469 = circuit_sub(t468, t465); let t470 = circuit_sub(t467, t468); let t471 = circuit_sub(t470, t465); let t472 = circuit_add(t469, t446); // Fp2 add coeff 0/1 let t473 = circuit_add(t471, t449); // Fp2 add coeff 1/1 let t474 = circuit_add(t426, t430); // Fp2 add coeff 0/1 let t475 = circuit_add(t427, t431); // Fp2 add coeff 1/1 let t476 = circuit_mul(t290, t474); // Fp2 mul start let t477 = circuit_mul(t291, t475); let t478 = circuit_sub(t476, t477); // Fp2 mul real part end let t479 = circuit_mul(t290, t475); let t480 = circuit_mul(t291, t474); let t481 = circuit_add(t479, t480); // Fp2 mul imag part end let t482 = circuit_sub(t478, t446); // Fp2 sub coeff 0/1 let t483 = circuit_sub(t481, t449); // Fp2 sub coeff 1/1 let t484 = circuit_add(t482, t452); // Fp2 add coeff 0/1 let t485 = circuit_add(t483, t455); // Fp2 add coeff 1/1 let t486 = circuit_add(t290, t292); // Fp2 add coeff 0/1 let t487 = circuit_add(t291, t293); // Fp2 add coeff 1/1 let t488 = circuit_add(t426, t428); // Fp2 add coeff 0/1 let t489 = circuit_add(t427, t429); // Fp2 add coeff 1/1 let t490 = circuit_mul(t486, t488); // Fp2 mul start let t491 = circuit_mul(t487, t489); let t492 = circuit_sub(t490, t491); // Fp2 mul real part end let t493 = circuit_mul(t486, t489); let t494 = circuit_mul(t487, t488); let t495 = circuit_add(t493, t494); // Fp2 mul imag part end let t496 = circuit_sub(t492, t446); // Fp2 sub coeff 0/1 let t497 = circuit_sub(t495, t449); // Fp2 sub coeff 1/1 let t498 = circuit_sub(t496, t452); // Fp2 sub coeff 0/1 let t499 = circuit_sub(t497, t455); // Fp2 sub coeff 1/1 let t500 = circuit_add(in3, t290); // Fp2 add coeff 0/1 let t501 = circuit_add(in2, t291); // Fp2 add coeff 1/1 let t502 = circuit_add(t438, t426); // Fp6 add coeff 0/5 let t503 = circuit_add(t439, t427); // Fp6 add coeff 1/5 let t504 = circuit_add(t440, t428); // Fp6 add coeff 2/5 let t505 = circuit_add(t441, t429); // Fp6 add coeff 3/5 let t506 = circuit_add(t442, t430); // Fp6 add coeff 4/5 let t507 = circuit_add(t443, t431); // Fp6 add coeff 5/5 let t508 = circuit_mul(t502, t500); // Fp2 mul start let t509 = circuit_mul(t503, t501); let t510 = circuit_sub(t508, t509); // Fp2 mul real part end let t511 = circuit_mul(t502, t501); let t512 = circuit_mul(t503, t500); let t513 = circuit_add(t511, t512); // Fp2 mul imag part end let t514 = circuit_mul(t504, t292); // Fp2 mul start let t515 = circuit_mul(t505, t293); let t516 = circuit_sub(t514, t515); // Fp2 mul real part end let t517 = circuit_mul(t504, t293); let t518 = circuit_mul(t505, t292); let t519 = circuit_add(t517, t518); // Fp2 mul imag part end let t520 = circuit_add(t504, t506); // Fp2 add coeff 0/1 let t521 = circuit_add(t505, t507); // Fp2 add coeff 1/1 let t522 = circuit_mul(t292, t520); // Fp2 mul start let t523 = circuit_mul(t293, t521); let t524 = circuit_sub(t522, t523); // Fp2 mul real part end let t525 = circuit_mul(t292, t521); let t526 = circuit_mul(t293, t520); let t527 = circuit_add(t525, t526); // Fp2 mul imag part end let t528 = circuit_sub(t524, t516); // Fp2 sub coeff 0/1 let t529 = circuit_sub(t527, t519); // Fp2 sub coeff 1/1 let t530 = circuit_add(t528, t529); let t531 = circuit_mul(t530, in0); let t532 = circuit_mul(t528, in1); let t533 = circuit_sub(t532, t529); let t534 = circuit_sub(t531, t532); let t535 = circuit_sub(t534, t529); let t536 = circuit_add(t533, t510); // Fp2 add coeff 0/1 let t537 = circuit_add(t535, t513); // Fp2 add coeff 1/1 let t538 = circuit_add(t502, t506); // Fp2 add coeff 0/1 let t539 = circuit_add(t503, t507); // Fp2 add coeff 1/1 let t540 = circuit_mul(t500, t538); // Fp2 mul start let t541 = circuit_mul(t501, t539); let t542 = circuit_sub(t540, t541); // Fp2 mul real part end let t543 = circuit_mul(t500, t539); let t544 = circuit_mul(t501, t538); let t545 = circuit_add(t543, t544); // Fp2 mul imag part end let t546 = circuit_sub(t542, t510); // Fp2 sub coeff 0/1 let t547 = circuit_sub(t545, t513); // Fp2 sub coeff 1/1 let t548 = circuit_add(t546, t516); // Fp2 add coeff 0/1 let t549 = circuit_add(t547, t519); // Fp2 add coeff 1/1 let t550 = circuit_add(t500, t292); // Fp2 add coeff 0/1 let t551 = circuit_add(t501, t293); // Fp2 add coeff 1/1 let t552 = circuit_add(t502, t504); // Fp2 add coeff 0/1 let t553 = circuit_add(t503, t505); // Fp2 add coeff 1/1 let t554 = circuit_mul(t550, t552); // Fp2 mul start let t555 = circuit_mul(t551, t553); let t556 = circuit_sub(t554, t555); // Fp2 mul real part end let t557 = circuit_mul(t550, t553); let t558 = circuit_mul(t551, t552); let t559 = circuit_add(t557, t558); // Fp2 mul imag part end let t560 = circuit_sub(t556, t510); // Fp2 sub coeff 0/1 let t561 = circuit_sub(t559, t513); // Fp2 sub coeff 1/1 let t562 = circuit_sub(t560, t516); // Fp2 sub coeff 0/1 let t563 = circuit_sub(t561, t519); // Fp2 sub coeff 1/1 let t564 = circuit_add(t438, t472); // Fp6 add coeff 0/5 let t565 = circuit_add(t439, t473); // Fp6 add coeff 1/5 let t566 = circuit_add(t440, t498); // Fp6 add coeff 2/5 let t567 = circuit_add(t441, t499); // Fp6 add coeff 3/5 let t568 = circuit_add(t442, t484); // Fp6 add coeff 4/5 let t569 = circuit_add(t443, t485); // Fp6 add coeff 5/5 let t570 = circuit_sub(in2, t564); // Fp6 neg coeff 0/5 let t571 = circuit_sub(in2, t565); // Fp6 neg coeff 1/5 let t572 = circuit_sub(in2, t566); // Fp6 neg coeff 2/5 let t573 = circuit_sub(in2, t567); // Fp6 neg coeff 3/5 let t574 = circuit_sub(in2, t568); // Fp6 neg coeff 4/5 let t575 = circuit_sub(in2, t569); // Fp6 neg coeff 5/5 let t576 = circuit_add(t570, t536); // Fp6 add coeff 0/5 let t577 = circuit_add(t571, t537); // Fp6 add coeff 1/5 let t578 = circuit_add(t572, t562); // Fp6 add coeff 2/5 let t579 = circuit_add(t573, t563); // Fp6 add coeff 3/5 let t580 = circuit_add(t574, t548); // Fp6 add coeff 4/5 let t581 = circuit_add(t575, t549); // Fp6 add coeff 5/5 let t582 = circuit_add(t484, t485); let t583 = circuit_mul(t582, in0); let t584 = circuit_mul(t484, in1); let t585 = circuit_sub(t584, t485); let t586 = circuit_sub(t583, t584); let t587 = circuit_sub(t586, t485); let t588 = circuit_add(t585, t438); // Fp6 add coeff 0/5 let t589 = circuit_add(t587, t439); // Fp6 add coeff 1/5 let t590 = circuit_add(t472, t440); // Fp6 add coeff 2/5 let t591 = circuit_add(t473, t441); // Fp6 add coeff 3/5 let t592 = circuit_add(t498, t442); // Fp6 add coeff 4/5 let t593 = circuit_add(t499, t443); // Fp6 add coeff 5/5 let t594 = circuit_add(t266, t267); let t595 = circuit_add(t594, t276); let t596 = circuit_add(t595, t277); let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = ( t596, t588, t589, t590, t591, t592, t593, t576, t577, t578, t579, t580, t581, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0xa, 0x0, 0x0, 0x0]); // in0 circuit_inputs = circuit_inputs.next_2([0x9, 0x0, 0x0, 0x0]); // in1 circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in2 circuit_inputs = circuit_inputs.next_2([0x1, 0x0, 0x0, 0x0]); // in3 // Fill inputs: circuit_inputs = circuit_inputs.next_2(yInv_0); // in4 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in5 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in6 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in7 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in8 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in9 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.x0); // in10 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.x1); // in11 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.y0); // in12 circuit_inputs = circuit_inputs.next_2(Q_or_Q_neg_0.y1); // in13 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a0); // in14 circuit_inputs = circuit_inputs.next_2(M_i.c0b0a1); // in15 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a0); // in16 circuit_inputs = circuit_inputs.next_2(M_i.c0b1a1); // in17 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a0); // in18 circuit_inputs = circuit_inputs.next_2(M_i.c0b2a1); // in19 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a0); // in20 circuit_inputs = circuit_inputs.next_2(M_i.c1b0a1); // in21 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a0); // in22 circuit_inputs = circuit_inputs.next_2(M_i.c1b1a1); // in23 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a0); // in24 circuit_inputs = circuit_inputs.next_2(M_i.c1b2a1); // in25 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Q0: G2Point = G2Point { x0: outputs.get_output(t266), x1: outputs.get_output(t267), y0: outputs.get_output(t276), y1: outputs.get_output(t277), }; let Mi_plus_one: E12T = E12T { c0b0a0: outputs.get_output(t588), c0b0a1: outputs.get_output(t589), c0b1a0: outputs.get_output(t590), c0b1a1: outputs.get_output(t591), c0b2a0: outputs.get_output(t592), c0b2a1: outputs.get_output(t593), c1b0a0: outputs.get_output(t576), c1b0a1: outputs.get_output(t577), c1b1a0: outputs.get_output(t578), c1b1a1: outputs.get_output(t579), c1b2a0: outputs.get_output(t580), c1b2a1: outputs.get_output(t581), }; return (Q0, Mi_plus_one); } #[inline(always)] pub fn run_BN254_TOWER_MILLER_FINALIZE_BN_1P_circuit( original_Q0: G2Point, yInv_0: u384, xNegOverY_0: u384, Q_0: G2Point, Mi: E12T, ) -> (E12T,) { // CONSTANT stack let in0 = CE::> {}; // 0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d let in1 = CE::> {}; // 0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2 let in2 = CE::> {}; // 0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a let in3 = CE::> {}; // 0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3 let in4 = CE::> {}; // 0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48 let in5 = CE::> {}; // 0x1 let in6 = CE::> {}; // 0x0 let in7 = CE::> {}; // 0xa let in8 = CE::> {}; // 0x9 // INPUT stack let (in9, in10, in11) = (CE::> {}, CE::> {}, CE::> {}); let (in12, in13, in14) = (CE::> {}, CE::> {}, CE::> {}); let (in15, in16, in17) = (CE::> {}, CE::> {}, CE::> {}); let (in18, in19, in20) = (CE::> {}, CE::> {}, CE::> {}); let (in21, in22, in23) = (CE::> {}, CE::> {}, CE::> {}); let (in24, in25, in26) = (CE::> {}, CE::> {}, CE::> {}); let (in27, in28, in29) = (CE::> {}, CE::> {}, CE::> {}); let in30 = CE::> {}; let t0 = circuit_sub(in6, in10); let t1 = circuit_sub(in6, in12); let t2 = circuit_mul(in9, in0); // Fp2 mul start let t3 = circuit_mul(t0, in1); let t4 = circuit_sub(t2, t3); // Fp2 mul real part end let t5 = circuit_mul(in9, in1); let t6 = circuit_mul(t0, in0); let t7 = circuit_add(t5, t6); // Fp2 mul imag part end let t8 = circuit_mul(in11, in2); // Fp2 mul start let t9 = circuit_mul(t1, in3); let t10 = circuit_sub(t8, t9); // Fp2 mul real part end let t11 = circuit_mul(in11, in3); let t12 = circuit_mul(t1, in2); let t13 = circuit_add(t11, t12); // Fp2 mul imag part end let t14 = circuit_mul(in9, in4); // Fp2 scalar mul coeff 0/1 let t15 = circuit_mul(in10, in4); // Fp2 scalar mul coeff 1/1 let t16 = circuit_mul(in11, in5); // Fp2 scalar mul coeff 0/1 let t17 = circuit_mul(in12, in5); // Fp2 scalar mul coeff 1/1 let t18 = circuit_sub(in17, t10); // Fp2 sub coeff 0/1 let t19 = circuit_sub(in18, t13); // Fp2 sub coeff 1/1 let t20 = circuit_sub(in15, t4); // Fp2 sub coeff 0/1 let t21 = circuit_sub(in16, t7); // Fp2 sub coeff 1/1 let t22 = circuit_mul(t20, t20); // Fp2 Inv start let t23 = circuit_mul(t21, t21); let t24 = circuit_add(t22, t23); let t25 = circuit_inverse(t24); let t26 = circuit_mul(t20, t25); // Fp2 Inv real part end let t27 = circuit_mul(t21, t25); let t28 = circuit_sub(in6, t27); // Fp2 Inv imag part end let t29 = circuit_mul(t18, t26); // Fp2 mul start let t30 = circuit_mul(t19, t28); let t31 = circuit_sub(t29, t30); // Fp2 mul real part end let t32 = circuit_mul(t18, t28); let t33 = circuit_mul(t19, t26); let t34 = circuit_add(t32, t33); // Fp2 mul imag part end let t35 = circuit_add(t31, t34); let t36 = circuit_sub(t31, t34); let t37 = circuit_mul(t35, t36); let t38 = circuit_mul(t31, t34); let t39 = circuit_add(t38, t38); let t40 = circuit_add(in15, t4); // Fp2 add coeff 0/1 let t41 = circuit_add(in16, t7); // Fp2 add coeff 1/1 let t42 = circuit_sub(t37, t40); // Fp2 sub coeff 0/1 let t43 = circuit_sub(t39, t41); // Fp2 sub coeff 1/1 let t44 = circuit_sub(in15, t42); // Fp2 sub coeff 0/1 let t45 = circuit_sub(in16, t43); // Fp2 sub coeff 1/1 let t46 = circuit_mul(t31, t44); // Fp2 mul start let t47 = circuit_mul(t34, t45); let t48 = circuit_sub(t46, t47); // Fp2 mul real part end let t49 = circuit_mul(t31, t45); let t50 = circuit_mul(t34, t44); let t51 = circuit_add(t49, t50); // Fp2 mul imag part end let t52 = circuit_sub(t48, in17); // Fp2 sub coeff 0/1 let t53 = circuit_sub(t51, in18); // Fp2 sub coeff 1/1 let t54 = circuit_mul(t31, in15); // Fp2 mul start let t55 = circuit_mul(t34, in16); let t56 = circuit_sub(t54, t55); // Fp2 mul real part end let t57 = circuit_mul(t31, in16); let t58 = circuit_mul(t34, in15); let t59 = circuit_add(t57, t58); // Fp2 mul imag part end let t60 = circuit_sub(t56, in17); // Fp2 sub coeff 0/1 let t61 = circuit_sub(t59, in18); // Fp2 sub coeff 1/1 let t62 = circuit_sub(t52, t16); // Fp2 sub coeff 0/1 let t63 = circuit_sub(t53, t17); // Fp2 sub coeff 1/1 let t64 = circuit_sub(t42, t14); // Fp2 sub coeff 0/1 let t65 = circuit_sub(t43, t15); // Fp2 sub coeff 1/1 let t66 = circuit_mul(t64, t64); // Fp2 Inv start let t67 = circuit_mul(t65, t65); let t68 = circuit_add(t66, t67); let t69 = circuit_inverse(t68); let t70 = circuit_mul(t64, t69); // Fp2 Inv real part end let t71 = circuit_mul(t65, t69); let t72 = circuit_sub(in6, t71); // Fp2 Inv imag part end let t73 = circuit_mul(t62, t70); // Fp2 mul start let t74 = circuit_mul(t63, t72); let t75 = circuit_sub(t73, t74); // Fp2 mul real part end let t76 = circuit_mul(t62, t72); let t77 = circuit_mul(t63, t70); let t78 = circuit_add(t76, t77); // Fp2 mul imag part end let t79 = circuit_mul(t75, t42); // Fp2 mul start let t80 = circuit_mul(t78, t43); let t81 = circuit_sub(t79, t80); // Fp2 mul real part end let t82 = circuit_mul(t75, t43); let t83 = circuit_mul(t78, t42); let t84 = circuit_add(t82, t83); // Fp2 mul imag part end let t85 = circuit_sub(t81, t52); // Fp2 sub coeff 0/1 let t86 = circuit_sub(t84, t53); // Fp2 sub coeff 1/1 let t87 = circuit_mul(t31, in14); let t88 = circuit_mul(t34, in14); let t89 = circuit_mul(t60, in13); let t90 = circuit_mul(t61, in13); let t91 = circuit_mul(t75, in14); let t92 = circuit_mul(t78, in14); let t93 = circuit_mul(t85, in13); let t94 = circuit_mul(t86, in13); let t95 = circuit_mul(t91, t87); // Fp2 mul start let t96 = circuit_mul(t92, t88); let t97 = circuit_sub(t95, t96); // Fp2 mul real part end let t98 = circuit_mul(t91, t88); let t99 = circuit_mul(t92, t87); let t100 = circuit_add(t98, t99); // Fp2 mul imag part end let t101 = circuit_mul(t93, t89); // Fp2 mul start let t102 = circuit_mul(t94, t90); let t103 = circuit_sub(t101, t102); // Fp2 mul real part end let t104 = circuit_mul(t93, t90); let t105 = circuit_mul(t94, t89); let t106 = circuit_add(t104, t105); // Fp2 mul imag part end let t107 = circuit_add(t93, t89); // Fp2 add coeff 0/1 let t108 = circuit_add(t94, t90); // Fp2 add coeff 1/1 let t109 = circuit_add(t91, t87); // Fp2 add coeff 0/1 let t110 = circuit_add(t92, t88); // Fp2 add coeff 1/1 let t111 = circuit_add(t91, t93); // Fp2 add coeff 0/1 let t112 = circuit_add(t92, t94); // Fp2 add coeff 1/1 let t113 = circuit_add(t87, t89); // Fp2 add coeff 0/1 let t114 = circuit_add(t88, t90); // Fp2 add coeff 1/1 let t115 = circuit_mul(t113, t111); // Fp2 mul start let t116 = circuit_mul(t114, t112); let t117 = circuit_sub(t115, t116); // Fp2 mul real part end let t118 = circuit_mul(t113, t112); let t119 = circuit_mul(t114, t111); let t120 = circuit_add(t118, t119); // Fp2 mul imag part end let t121 = circuit_sub(t117, t97); // Fp2 sub coeff 0/1 let t122 = circuit_sub(t120, t100); // Fp2 sub coeff 1/1 let t123 = circuit_sub(t121, t103); // Fp2 sub coeff 0/1 let t124 = circuit_sub(t122, t106); // Fp2 sub coeff 1/1 let t125 = circuit_add(t103, t106); let t126 = circuit_mul(t125, in7); let t127 = circuit_mul(t103, in8); let t128 = circuit_sub(t127, t106); let t129 = circuit_sub(t126, t127); let t130 = circuit_sub(t129, t106); let t131 = circuit_add(t128, in5); let t132 = circuit_add(in19, in25); // Fp6 add coeff 0/5 let t133 = circuit_add(in20, in26); // Fp6 add coeff 1/5 let t134 = circuit_add(in21, in27); // Fp6 add coeff 2/5 let t135 = circuit_add(in22, in28); // Fp6 add coeff 3/5 let t136 = circuit_add(in23, in29); // Fp6 add coeff 4/5 let t137 = circuit_add(in24, in30); // Fp6 add coeff 5/5 let t138 = circuit_add(t131, t109); // Fp6 add coeff 0/5 let t139 = circuit_add(t130, t110); // Fp6 add coeff 1/5 let t140 = circuit_add(t97, t107); // Fp6 add coeff 2/5 let t141 = circuit_add(t100, t108); // Fp6 add coeff 3/5 let t142 = circuit_add(t123, in6); // Fp6 add coeff 4/5 let t143 = circuit_add(t124, in6); // Fp6 add coeff 5/5 let t144 = circuit_mul(t132, t138); // Fp2 mul start let t145 = circuit_mul(t133, t139); let t146 = circuit_sub(t144, t145); // Fp2 mul real part end let t147 = circuit_mul(t132, t139); let t148 = circuit_mul(t133, t138); let t149 = circuit_add(t147, t148); // Fp2 mul imag part end let t150 = circuit_mul(t134, t140); // Fp2 mul start let t151 = circuit_mul(t135, t141); let t152 = circuit_sub(t150, t151); // Fp2 mul real part end let t153 = circuit_mul(t134, t141); let t154 = circuit_mul(t135, t140); let t155 = circuit_add(t153, t154); // Fp2 mul imag part end let t156 = circuit_mul(t136, t142); // Fp2 mul start let t157 = circuit_mul(t137, t143); let t158 = circuit_sub(t156, t157); // Fp2 mul real part end let t159 = circuit_mul(t136, t143); let t160 = circuit_mul(t137, t142); let t161 = circuit_add(t159, t160); // Fp2 mul imag part end let t162 = circuit_add(t134, t136); // Fp2 add coeff 0/1 let t163 = circuit_add(t135, t137); // Fp2 add coeff 1/1 let t164 = circuit_add(t140, t142); // Fp2 add coeff 0/1 let t165 = circuit_add(t141, t143); // Fp2 add coeff 1/1 let t166 = circuit_mul(t162, t164); // Fp2 mul start let t167 = circuit_mul(t163, t165); let t168 = circuit_sub(t166, t167); // Fp2 mul real part end let t169 = circuit_mul(t162, t165); let t170 = circuit_mul(t163, t164); let t171 = circuit_add(t169, t170); // Fp2 mul imag part end let t172 = circuit_sub(t168, t152); // Fp2 sub coeff 0/1 let t173 = circuit_sub(t171, t155); // Fp2 sub coeff 1/1 let t174 = circuit_sub(t172, t158); // Fp2 sub coeff 0/1 let t175 = circuit_sub(t173, t161); // Fp2 sub coeff 1/1 let t176 = circuit_add(t174, t175); let t177 = circuit_mul(t176, in7); let t178 = circuit_mul(t174, in8); let t179 = circuit_sub(t178, t175); let t180 = circuit_sub(t177, t178); let t181 = circuit_sub(t180, t175); let t182 = circuit_add(t179, t146); // Fp2 add coeff 0/1 let t183 = circuit_add(t181, t149); // Fp2 add coeff 1/1 let t184 = circuit_add(t132, t134); // Fp2 add coeff 0/1 let t185 = circuit_add(t133, t135); // Fp2 add coeff 1/1 let t186 = circuit_add(t138, t140); // Fp2 add coeff 0/1 let t187 = circuit_add(t139, t141); // Fp2 add coeff 1/1 let t188 = circuit_mul(t184, t186); // Fp2 mul start let t189 = circuit_mul(t185, t187); let t190 = circuit_sub(t188, t189); // Fp2 mul real part end let t191 = circuit_mul(t184, t187); let t192 = circuit_mul(t185, t186); let t193 = circuit_add(t191, t192); // Fp2 mul imag part end let t194 = circuit_sub(t190, t146); // Fp2 sub coeff 0/1 let t195 = circuit_sub(t193, t149); // Fp2 sub coeff 1/1 let t196 = circuit_sub(t194, t152); // Fp2 sub coeff 0/1 let t197 = circuit_sub(t195, t155); // Fp2 sub coeff 1/1 let t198 = circuit_add(t158, t161); let t199 = circuit_mul(t198, in7); let t200 = circuit_mul(t158, in8); let t201 = circuit_sub(t200, t161); let t202 = circuit_sub(t199, t200); let t203 = circuit_sub(t202, t161); let t204 = circuit_add(t196, t201); // Fp2 add coeff 0/1 let t205 = circuit_add(t197, t203); // Fp2 add coeff 1/1 let t206 = circuit_add(t132, t136); // Fp2 add coeff 0/1 let t207 = circuit_add(t133, t137); // Fp2 add coeff 1/1 let t208 = circuit_add(t138, t142); // Fp2 add coeff 0/1 let t209 = circuit_add(t139, t143); // Fp2 add coeff 1/1 let t210 = circuit_mul(t208, t206); // Fp2 mul start let t211 = circuit_mul(t209, t207); let t212 = circuit_sub(t210, t211); // Fp2 mul real part end let t213 = circuit_mul(t208, t207); let t214 = circuit_mul(t209, t206); let t215 = circuit_add(t213, t214); // Fp2 mul imag part end let t216 = circuit_sub(t212, t146); // Fp2 sub coeff 0/1 let t217 = circuit_sub(t215, t149); // Fp2 sub coeff 1/1 let t218 = circuit_sub(t216, t158); // Fp2 sub coeff 0/1 let t219 = circuit_sub(t217, t161); // Fp2 sub coeff 1/1 let t220 = circuit_add(t218, t152); // Fp2 add coeff 0/1 let t221 = circuit_add(t219, t155); // Fp2 add coeff 1/1 let t222 = circuit_mul(in19, t131); // Fp2 mul start let t223 = circuit_mul(in20, t130); let t224 = circuit_sub(t222, t223); // Fp2 mul real part end let t225 = circuit_mul(in19, t130); let t226 = circuit_mul(in20, t131); let t227 = circuit_add(t225, t226); // Fp2 mul imag part end let t228 = circuit_mul(in21, t97); // Fp2 mul start let t229 = circuit_mul(in22, t100); let t230 = circuit_sub(t228, t229); // Fp2 mul real part end let t231 = circuit_mul(in21, t100); let t232 = circuit_mul(in22, t97); let t233 = circuit_add(t231, t232); // Fp2 mul imag part end let t234 = circuit_mul(in23, t123); // Fp2 mul start let t235 = circuit_mul(in24, t124); let t236 = circuit_sub(t234, t235); // Fp2 mul real part end let t237 = circuit_mul(in23, t124); let t238 = circuit_mul(in24, t123); let t239 = circuit_add(t237, t238); // Fp2 mul imag part end let t240 = circuit_add(in21, in23); // Fp2 add coeff 0/1 let t241 = circuit_add(in22, in24); // Fp2 add coeff 1/1 let t242 = circuit_add(t97, t123); // Fp2 add coeff 0/1 let t243 = circuit_add(t100, t124); // Fp2 add coeff 1/1 let t244 = circuit_mul(t240, t242); // Fp2 mul start let t245 = circuit_mul(t241, t243); let t246 = circuit_sub(t244, t245); // Fp2 mul real part end let t247 = circuit_mul(t240, t243); let t248 = circuit_mul(t241, t242); let t249 = circuit_add(t247, t248); // Fp2 mul imag part end let t250 = circuit_sub(t246, t230); // Fp2 sub coeff 0/1 let t251 = circuit_sub(t249, t233); // Fp2 sub coeff 1/1 let t252 = circuit_sub(t250, t236); // Fp2 sub coeff 0/1 let t253 = circuit_sub(t251, t239); // Fp2 sub coeff 1/1 let t254 = circuit_add(t252, t253); let t255 = circuit_mul(t254, in7); let t256 = circuit_mul(t252, in8); let t257 = circuit_sub(t256, t253); let t258 = circuit_sub(t255, t256); let t259 = circuit_sub(t258, t253); let t260 = circuit_add(t257, t224); // Fp2 add coeff 0/1 let t261 = circuit_add(t259, t227); // Fp2 add coeff 1/1 let t262 = circuit_add(in19, in21); // Fp2 add coeff 0/1 let t263 = circuit_add(in20, in22); // Fp2 add coeff 1/1 let t264 = circuit_add(t131, t97); // Fp2 add coeff 0/1 let t265 = circuit_add(t130, t100); // Fp2 add coeff 1/1 let t266 = circuit_mul(t262, t264); // Fp2 mul start let t267 = circuit_mul(t263, t265); let t268 = circuit_sub(t266, t267); // Fp2 mul real part end let t269 = circuit_mul(t262, t265); let t270 = circuit_mul(t263, t264); let t271 = circuit_add(t269, t270); // Fp2 mul imag part end let t272 = circuit_sub(t268, t224); // Fp2 sub coeff 0/1 let t273 = circuit_sub(t271, t227); // Fp2 sub coeff 1/1 let t274 = circuit_sub(t272, t230); // Fp2 sub coeff 0/1 let t275 = circuit_sub(t273, t233); // Fp2 sub coeff 1/1 let t276 = circuit_add(t236, t239); let t277 = circuit_mul(t276, in7); let t278 = circuit_mul(t236, in8); let t279 = circuit_sub(t278, t239); let t280 = circuit_sub(t277, t278); let t281 = circuit_sub(t280, t239); let t282 = circuit_add(t274, t279); // Fp2 add coeff 0/1 let t283 = circuit_add(t275, t281); // Fp2 add coeff 1/1 let t284 = circuit_add(in19, in23); // Fp2 add coeff 0/1 let t285 = circuit_add(in20, in24); // Fp2 add coeff 1/1 let t286 = circuit_add(t131, t123); // Fp2 add coeff 0/1 let t287 = circuit_add(t130, t124); // Fp2 add coeff 1/1 let t288 = circuit_mul(t286, t284); // Fp2 mul start let t289 = circuit_mul(t287, t285); let t290 = circuit_sub(t288, t289); // Fp2 mul real part end let t291 = circuit_mul(t286, t285); let t292 = circuit_mul(t287, t284); let t293 = circuit_add(t291, t292); // Fp2 mul imag part end let t294 = circuit_sub(t290, t224); // Fp2 sub coeff 0/1 let t295 = circuit_sub(t293, t227); // Fp2 sub coeff 1/1 let t296 = circuit_sub(t294, t236); // Fp2 sub coeff 0/1 let t297 = circuit_sub(t295, t239); // Fp2 sub coeff 1/1 let t298 = circuit_add(t296, t230); // Fp2 add coeff 0/1 let t299 = circuit_add(t297, t233); // Fp2 add coeff 1/1 let t300 = circuit_mul(in25, t109); // Fp2 mul start let t301 = circuit_mul(in26, t110); let t302 = circuit_sub(t300, t301); // Fp2 mul real part end let t303 = circuit_mul(in25, t110); let t304 = circuit_mul(in26, t109); let t305 = circuit_add(t303, t304); // Fp2 mul imag part end let t306 = circuit_mul(in27, t107); // Fp2 mul start let t307 = circuit_mul(in28, t108); let t308 = circuit_sub(t306, t307); // Fp2 mul real part end let t309 = circuit_mul(in27, t108); let t310 = circuit_mul(in28, t107); let t311 = circuit_add(t309, t310); // Fp2 mul imag part end let t312 = circuit_mul(in29, in6); // Fp2 mul start let t313 = circuit_mul(in30, in6); let t314 = circuit_sub(t312, t313); // Fp2 mul real part end let t315 = circuit_mul(in29, in6); let t316 = circuit_mul(in30, in6); let t317 = circuit_add(t315, t316); // Fp2 mul imag part end let t318 = circuit_add(in27, in29); // Fp2 add coeff 0/1 let t319 = circuit_add(in28, in30); // Fp2 add coeff 1/1 let t320 = circuit_add(t107, in6); // Fp2 add coeff 0/1 let t321 = circuit_add(t108, in6); // Fp2 add coeff 1/1 let t322 = circuit_mul(t318, t320); // Fp2 mul start let t323 = circuit_mul(t319, t321); let t324 = circuit_sub(t322, t323); // Fp2 mul real part end let t325 = circuit_mul(t318, t321); let t326 = circuit_mul(t319, t320); let t327 = circuit_add(t325, t326); // Fp2 mul imag part end let t328 = circuit_sub(t324, t308); // Fp2 sub coeff 0/1 let t329 = circuit_sub(t327, t311); // Fp2 sub coeff 1/1 let t330 = circuit_sub(t328, t314); // Fp2 sub coeff 0/1 let t331 = circuit_sub(t329, t317); // Fp2 sub coeff 1/1 let t332 = circuit_add(t330, t331); let t333 = circuit_mul(t332, in7); let t334 = circuit_mul(t330, in8); let t335 = circuit_sub(t334, t331); let t336 = circuit_sub(t333, t334); let t337 = circuit_sub(t336, t331); let t338 = circuit_add(t335, t302); // Fp2 add coeff 0/1 let t339 = circuit_add(t337, t305); // Fp2 add coeff 1/1 let t340 = circuit_add(in25, in27); // Fp2 add coeff 0/1 let t341 = circuit_add(in26, in28); // Fp2 add coeff 1/1 let t342 = circuit_add(t109, t107); // Fp2 add coeff 0/1 let t343 = circuit_add(t110, t108); // Fp2 add coeff 1/1 let t344 = circuit_mul(t340, t342); // Fp2 mul start let t345 = circuit_mul(t341, t343); let t346 = circuit_sub(t344, t345); // Fp2 mul real part end let t347 = circuit_mul(t340, t343); let t348 = circuit_mul(t341, t342); let t349 = circuit_add(t347, t348); // Fp2 mul imag part end let t350 = circuit_sub(t346, t302); // Fp2 sub coeff 0/1 let t351 = circuit_sub(t349, t305); // Fp2 sub coeff 1/1 let t352 = circuit_sub(t350, t308); // Fp2 sub coeff 0/1 let t353 = circuit_sub(t351, t311); // Fp2 sub coeff 1/1 let t354 = circuit_add(t314, t317); let t355 = circuit_mul(t354, in7); let t356 = circuit_mul(t314, in8); let t357 = circuit_sub(t356, t317); let t358 = circuit_sub(t355, t356); let t359 = circuit_sub(t358, t317); let t360 = circuit_add(t352, t357); // Fp2 add coeff 0/1 let t361 = circuit_add(t353, t359); // Fp2 add coeff 1/1 let t362 = circuit_add(in25, in29); // Fp2 add coeff 0/1 let t363 = circuit_add(in26, in30); // Fp2 add coeff 1/1 let t364 = circuit_add(t109, in6); // Fp2 add coeff 0/1 let t365 = circuit_add(t110, in6); // Fp2 add coeff 1/1 let t366 = circuit_mul(t364, t362); // Fp2 mul start let t367 = circuit_mul(t365, t363); let t368 = circuit_sub(t366, t367); // Fp2 mul real part end let t369 = circuit_mul(t364, t363); let t370 = circuit_mul(t365, t362); let t371 = circuit_add(t369, t370); // Fp2 mul imag part end let t372 = circuit_sub(t368, t302); // Fp2 sub coeff 0/1 let t373 = circuit_sub(t371, t305); // Fp2 sub coeff 1/1 let t374 = circuit_sub(t372, t314); // Fp2 sub coeff 0/1 let t375 = circuit_sub(t373, t317); // Fp2 sub coeff 1/1 let t376 = circuit_add(t374, t308); // Fp2 add coeff 0/1 let t377 = circuit_add(t375, t311); // Fp2 add coeff 1/1 let t378 = circuit_sub(t182, t260); // Fp6 sub coeff 0/5 let t379 = circuit_sub(t183, t261); // Fp6 sub coeff 1/5 let t380 = circuit_sub(t204, t282); // Fp6 sub coeff 2/5 let t381 = circuit_sub(t205, t283); // Fp6 sub coeff 3/5 let t382 = circuit_sub(t220, t298); // Fp6 sub coeff 4/5 let t383 = circuit_sub(t221, t299); // Fp6 sub coeff 5/5 let t384 = circuit_sub(t378, t338); // Fp6 sub coeff 0/5 let t385 = circuit_sub(t379, t339); // Fp6 sub coeff 1/5 let t386 = circuit_sub(t380, t360); // Fp6 sub coeff 2/5 let t387 = circuit_sub(t381, t361); // Fp6 sub coeff 3/5 let t388 = circuit_sub(t382, t376); // Fp6 sub coeff 4/5 let t389 = circuit_sub(t383, t377); // Fp6 sub coeff 5/5 let t390 = circuit_add(t376, t377); let t391 = circuit_mul(t390, in7); let t392 = circuit_mul(t376, in8); let t393 = circuit_sub(t392, t377); let t394 = circuit_sub(t391, t392); let t395 = circuit_sub(t394, t377); let t396 = circuit_add(t393, t260); // Fp6 add coeff 0/5 let t397 = circuit_add(t395, t261); // Fp6 add coeff 1/5 let t398 = circuit_add(t338, t282); // Fp6 add coeff 2/5 let t399 = circuit_add(t339, t283); // Fp6 add coeff 3/5 let t400 = circuit_add(t360, t298); // Fp6 add coeff 4/5 let t401 = circuit_add(t361, t299); // Fp6 add coeff 5/5 let modulus = crate::definitions::get_BN254_modulus(); // BN254 prime field modulus let mut circuit_inputs = ( t396, t397, t398, t399, t400, t401, t384, t385, t386, t387, t388, t389, ) .new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(TOWER_MILLER_FINALIZE_BN_1P_BN254_CONSTANTS.span()); // in0 - in8 // Fill inputs: circuit_inputs = circuit_inputs.next_2(original_Q0.x0); // in9 circuit_inputs = circuit_inputs.next_2(original_Q0.x1); // in10 circuit_inputs = circuit_inputs.next_2(original_Q0.y0); // in11 circuit_inputs = circuit_inputs.next_2(original_Q0.y1); // in12 circuit_inputs = circuit_inputs.next_2(yInv_0); // in13 circuit_inputs = circuit_inputs.next_2(xNegOverY_0); // in14 circuit_inputs = circuit_inputs.next_2(Q_0.x0); // in15 circuit_inputs = circuit_inputs.next_2(Q_0.x1); // in16 circuit_inputs = circuit_inputs.next_2(Q_0.y0); // in17 circuit_inputs = circuit_inputs.next_2(Q_0.y1); // in18 circuit_inputs = circuit_inputs.next_2(Mi.c0b0a0); // in19 circuit_inputs = circuit_inputs.next_2(Mi.c0b0a1); // in20 circuit_inputs = circuit_inputs.next_2(Mi.c0b1a0); // in21 circuit_inputs = circuit_inputs.next_2(Mi.c0b1a1); // in22 circuit_inputs = circuit_inputs.next_2(Mi.c0b2a0); // in23 circuit_inputs = circuit_inputs.next_2(Mi.c0b2a1); // in24 circuit_inputs = circuit_inputs.next_2(Mi.c1b0a0); // in25 circuit_inputs = circuit_inputs.next_2(Mi.c1b0a1); // in26 circuit_inputs = circuit_inputs.next_2(Mi.c1b1a0); // in27 circuit_inputs = circuit_inputs.next_2(Mi.c1b1a1); // in28 circuit_inputs = circuit_inputs.next_2(Mi.c1b2a0); // in29 circuit_inputs = circuit_inputs.next_2(Mi.c1b2a1); // in30 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let Mi: E12T = E12T { c0b0a0: outputs.get_output(t396), c0b0a1: outputs.get_output(t397), c0b1a0: outputs.get_output(t398), c0b1a1: outputs.get_output(t399), c0b2a0: outputs.get_output(t400), c0b2a1: outputs.get_output(t401), c1b0a0: outputs.get_output(t384), c1b0a1: outputs.get_output(t385), c1b1a0: outputs.get_output(t386), c1b1a1: outputs.get_output(t387), c1b2a0: outputs.get_output(t388), c1b2a1: outputs.get_output(t389), }; return (Mi,); } const TOWER_MILLER_FINALIZE_BN_1P_BN254_CONSTANTS: [u384; 9] = [ u384 { limb0: 0xc2c3330c99e39557176f553d, limb1: 0x4c0bec3cf559b143b78cc310, limb2: 0x2fb347984f7911f7, limb3: 0x0, }, u384 { limb0: 0xb7c9dce1665d51c640fcba2, limb1: 0x4ba4cc8bd75a079432ae2a1d, limb2: 0x16c9e55061ebae20, limb3: 0x0, }, u384 { limb0: 0xa9c95998dc54014671a0135a, limb1: 0xdc5ec698b6e2f9b9dbaae0ed, limb2: 0x63cf305489af5dc, limb3: 0x0, }, u384 { limb0: 0x8fa25bd282d37f632623b0e3, limb1: 0x704b5a7ec796f2b21807dc9, limb2: 0x7c03cbcac41049a, limb3: 0x0, }, u384 { limb0: 0xbb966e3de4bd44e5607cfd48, limb1: 0x5e6dd9e7e0acccb0c28f069f, limb2: 0x30644e72e131a029, limb3: 0x0, }, u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xa, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, ]; #[inline(always)] pub fn run_FP6_NEG_circuit( b0a0: u384, b0a1: u384, b1a0: u384, b1a1: u384, b2a0: u384, b2a1: u384, curve_index: usize, ) -> (u384, u384, u384, u384, u384, u384) { // CONSTANT stack let in0 = CE::> {}; // 0x0 // INPUT stack let (in1, in2, in3) = (CE::> {}, CE::> {}, CE::> {}); let (in4, in5, in6) = (CE::> {}, CE::> {}, CE::> {}); let t0 = circuit_sub(in0, in1); let t1 = circuit_sub(in0, in2); let t2 = circuit_sub(in0, in3); let t3 = circuit_sub(in0, in4); let t4 = circuit_sub(in0, in5); let t5 = circuit_sub(in0, in6); let modulus = crate::definitions::get_modulus(curve_index); let mut circuit_inputs = (t0, t1, t2, t3, t4, t5).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs.next_2([0x0, 0x0, 0x0, 0x0]); // in0 // Fill inputs: circuit_inputs = circuit_inputs.next_2(b0a0); // in1 circuit_inputs = circuit_inputs.next_2(b0a1); // in2 circuit_inputs = circuit_inputs.next_2(b1a0); // in3 circuit_inputs = circuit_inputs.next_2(b1a1); // in4 circuit_inputs = circuit_inputs.next_2(b2a0); // in5 circuit_inputs = circuit_inputs.next_2(b2a1); // in6 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let r0: u384 = outputs.get_output(t0); let r1: u384 = outputs.get_output(t1); let r2: u384 = outputs.get_output(t2); let r3: u384 = outputs.get_output(t3); let r4: u384 = outputs.get_output(t4); let r5: u384 = outputs.get_output(t5); return (r0, r1, r2, r3, r4, r5); } ================================================ FILE: src/src/core/circuit.cairo ================================================ use core::panic_with_felt252; use corelib_imports::bounded_int::bounded_int; use corelib_imports::circuit::conversions::{ AddHelperTo128By64Impl, AddHelperTo128By96Impl, AddHelperTo96By32Impl, DivRemU128By96, DivRemU96By32, DivRemU96By64, MulHelper32By96Impl, MulHelper64By32Impl, MulHelper64By64Impl, NZ_POW32_TYPED, NZ_POW64_TYPED, NZ_POW96_TYPED, POW64_TYPED, POW96_TYPED, upcast, }; use corelib_imports::circuit::{ AddInputResult, CircuitData, IntoCircuitInputValue, U96Guarantee, add_circuit_input, into_u96_guarantee, u384, u96, }; use garaga::definitions::u288; pub impl U32IntoU384 of Into { fn into(self: u32) -> u384 { u384 { limb0: upcast(self), limb1: 0, limb2: 0, limb3: 0 } } } pub impl U64IntoU384 of Into { fn into(self: u64) -> u384 { u384 { limb0: upcast(self), limb1: 0, limb2: 0, limb3: 0 } } } // Cuts a u384 into a u256. // This is unsafe because it assumes the value is less than 2^256. // Only use when computing circuit with a modulus less than 2^256. #[inline(never)] pub fn into_u256_unchecked(value: u384) -> u256 { let (_, limb2_low) = bounded_int::div_rem(value.limb2, NZ_POW64_TYPED); let (limb1_high, limb1_low) = bounded_int::div_rem(value.limb1, NZ_POW32_TYPED); u256 { high: upcast(bounded_int::add(bounded_int::mul(limb2_low, POW64_TYPED), limb1_high)), low: upcast(bounded_int::add(bounded_int::mul(limb1_low, POW96_TYPED), value.limb0)), } } pub fn u256_to_u384(value: u256) -> u384 { value.into() } pub impl u288IntoCircuitInputValue of IntoCircuitInputValue { fn into_circuit_input_value(self: u288) -> [U96Guarantee; 4] { [ into_u96_guarantee(self.limb0), into_u96_guarantee(self.limb1), into_u96_guarantee(self.limb2), into_u96_guarantee(0_u8), ] } } #[generate_trait] pub impl AddInputResultImpl2 of AddInputResultTrait2 { /// Adds an input to the accumulator. // Inlining to make sure possibly huge `C` won't be in a user function name. // #[inline(never)] fn next_2, +Drop>( self: AddInputResult, value: Value, ) -> AddInputResult { match self { AddInputResult::More(accumulator) => add_circuit_input( accumulator, value.into_circuit_input_value(), ), AddInputResult::Done(_) => panic_with_felt252('All inputs have been filled'), } } // #[inline(never)] fn next_u256(self: AddInputResult, value: u256) -> AddInputResult { let val_u384: u384 = value.into(); self.next_2(val_u384) } // #[inline(never)] fn next_u128(self: AddInputResult, value: u128) -> AddInputResult { let (limb1, limb0) = bounded_int::div_rem(value, NZ_POW96_TYPED); let limb1: u96 = upcast(limb1); let c = match self { AddInputResult::More(accumulator) => add_circuit_input( accumulator, [ into_u96_guarantee(limb0), into_u96_guarantee(limb1), into_u96_guarantee(0_u8), into_u96_guarantee(0_u8), ], ), AddInputResult::Done(_) => panic_with_felt252(0), }; c } // fn next_e12d(self: AddInputResult, value: E12D) -> AddInputResult { // let c = match self { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w0.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w1.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w2.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w3.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w4.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w5.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w6.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w7.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w8.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w9.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w10.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // let c = match c { // AddInputResult::More(accumulator) => add_circuit_input( // accumulator, value.w11.into_circuit_input_value() // ), // AddInputResult::Done(_) => panic_with_felt252(0), // }; // c // } // #[inline] // fn next_array, +Drop>( // self: AddInputResult, value: Array // ) -> AddInputResult { // let mut add_input_result = self; // for v in value { // add_input_result = // add_circuit_input( // match add_input_result { // AddInputResult::More(acc) => acc, // AddInputResult::Done(_) => panic_with_felt252(0), // }, // v.into_circuit_input_value() // ); // }; // add_input_result // } #[inline] fn next_span(self: AddInputResult, value: Span) -> AddInputResult { let mut add_input_result = self; for v in value { add_input_result = add_circuit_input( match add_input_result { AddInputResult::More(acc) => acc, AddInputResult::Done(_) => panic_with_felt252('all inputs filled'), }, (*v).into_circuit_input_value(), ); } add_input_result } // Inlining to make sure possibly huge `C` won't be in a user function name. #[inline(always)] fn done_2(self: AddInputResult) -> CircuitData { match self { AddInputResult::Done(data) => data, AddInputResult::More(_) => panic_with_felt252('not all inputs filled'), } } } ================================================ FILE: src/src/crypto/mmr.cairo ================================================ use crate::hashes::poseidon_bn254::poseidon_hash_2; // Return the number of trailing ones in a 64-bit unsigned integer. // Ex : trailing_ones(0b111) = 3 // The number of parents that need to be added when a new leaf is inserted (using the # of leaves // before insertion) // Ex if n=1 leaf, trailing_ones(1) = 1, when adding a new leave, 1 parent will be created. pub fn trailing_ones(n: u64) -> usize { if n == 0 { return 0; } let mut count = 0; let (mut n, mut mod_n) = DivRem::div_rem(n, 2); while mod_n != 0 { let (_n, _mod_n) = DivRem::div_rem(n, 2); n = _n; mod_n = _mod_n; count += 1; } return count; } // // // def bag_peaks(self, peaks: List[int]) -> int: // bags = peaks[-1] // for peak in reversed(peaks[:-1]): // self._hasher.update(peak) // self._hasher.update(bags) // bags = self._hasher.digest() // return bags pub fn root_from_peaks(n_leaves: u64, peaks: Span) -> u256 { let bagged_peaks = bag_peaks(peaks); return bagged_peaks; } pub fn bag_peaks(mut peaks: Span) -> u256 { let mut res = *peaks.pop_back().unwrap(); while let Some(peak) = peaks.pop_back() { res = poseidon_hash_2(*peak, res); } return res; } #[cfg(test)] mod tests { use super::trailing_ones; #[test] fn test_trailing_ones() { assert(trailing_ones(7) == 3, 'Invalid trailing_ones'); assert(trailing_ones(11) == 2, 'Invalid trailing_ones'); assert(trailing_ones(0) == 0, 'Invalid trailing_ones'); assert(trailing_ones(1) == 1, 'Invalid trailing_ones'); assert(trailing_ones(2) == 0, 'Invalid trailing_ones'); assert(trailing_ones(3) == 2, 'Invalid trailing_ones'); assert(trailing_ones(9) == 1, 'Invalid trailing_ones'); assert(trailing_ones(5) == 1, 'Invalid trailing_ones'); assert(trailing_ones(6) == 0, 'Invalid trailing_ones'); } } ================================================ FILE: src/src/definitions/curves.cairo ================================================ pub use core::circuit::{CircuitModulus, u384, u96}; use garaga::definitions::{G1Point, G1PointZero, G2Point}; /// Square of the BLS12-381 x seed parameter used in curve generation pub const BLS_X_SEED_SQ: u128 = 0xac45a4010001a4020000000100000000; // Curve indices used throughout Garaga: // curve_index 0: BN254 // curve_index 1: BLS12_381 // curve_index 2: SECP256K1 // curve_index 3: SECP256R1 // curve_index 4: ED25519 (stored in Weierstrass form) // curve_index 5: GRUMPKIN /// Complete curve parameters for elliptic curves in Weierstrass form: y² = x³ + ax + b /// /// # Fields /// * `p`: Prime modulus of the base field Fp /// * `n`: Order of the curve (number of points in the prime-order subgroup) /// * `a`: Weierstrass a parameter /// * `b`: Weierstrass b parameter /// * `g`: Generator of the multiplicative group Fp* (for field operations) /// * `min_one`: (-1) mod p, precomputed for efficiency /// * `min_one_order`: (-1) mod n, precomputed for efficiency /// * `G`: Generator point of the curve's prime-order subgroup /// * `b_twist`: Twist curve b parameter (b₀, b₁) where b = b₀ + i·b₁ in Fp2 (for pairing /// curves only) /// * `modulus`: Prime modulus p as 4 limbs of u96 for CircuitModulus operations /// * `order_modulus`: Curve order n as 4 limbs of u96 for CircuitModulus operations /// * `eigenvalue`: GLV endomorphism eigenvalue λ (for curves with efficient endomorphism) /// * `nG_glv_fake_glv`: Precomputed point 2^(nbits-1)·G for GLV decomposition /// * `third_root_of_unity`: Cubic root of unity in Fp (for curves supporting GLV/fake-GLV) pub struct Curve { pub p: u384, // Prime modulus pub n: u256, // Order of the curve pub a: u384, // Weierstrass a parameter in eqn: y^2 = x^3 + ax + b pub b: u384, // Weierstrass b parameter in eqn: y^2 = x^3 + ax + b pub g: u384, // Generator of Fp* (the multiplicative group of the field) pub min_one: u384, // (-1) % p pub min_one_order: u384, // (-1) % n pub G: G1Point, // Generator of the curve pub b_twist: Option< (u384, u384), >, // b parameter for twisted curve (b0, b1) such that b = b0 + i*b1 pub modulus: [u96; 4], // Prime modulus as 4 limbs for CircuitModulus pub order_modulus: [u96; 4], // Curve order as 4 limbs for CircuitModulus pub eigenvalue: Option, // Eigenvalue for endomorphism (if available) pub nG_glv_fake_glv: Option, // 2^(nbits-1)*G for GLV/fake GLV (if available) pub third_root_of_unity: Option // Third root of unity in the base field (if available) } pub const BN254: Curve = Curve { p: u384 { limb0: 0x6871ca8d3c208c16d87cfd47, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, n: u256 { low: 0x2833e84879b9709143e1f593f0000001, high: 0x30644e72e131a029b85045b68181585d }, a: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, b: u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, g: u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0x6871ca8d3c208c16d87cfd46, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, min_one_order: u384 { limb0: 0x79b9709143e1f593f0000000, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, b_twist: Some( ( u384 { limb0: 27810052284636130223308486885, limb1: 40153378333836448380344387045, limb2: 3104278944836790958, limb3: 0, }, u384 { limb0: 70926583776874220189091304914, limb1: 63498449372070794915149226116, limb2: 42524369107353300, limb3: 0, }, ), ), modulus: [0x6871ca8d3c208c16d87cfd47, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0], order_modulus: [ 0x79b9709143e1f593f0000001, 0xb85045b68181585d2833e848, 0x30644e72e131a029, 0x0, ], eigenvalue: Some( u384 { limb0: 0x8d8daaa78b17ea66b99c90dd, limb1: 0xb3c4d79d41a917585bfc4108, limb2: 0x0, limb3: 0x0, }, ), nG_glv_fake_glv: Some( G1Point { x: u384 { limb0: 0x804f4c2700adf08a0214e529, limb1: 0xa68b293da254e1b0049b5825, limb2: 0x2715e750e68b52fa, limb3: 0x0, }, y: u384 { limb0: 0x15c090b1de77447950003fc9, limb1: 0xfb5afe510e7c4e23f41e4bad, limb2: 0x3921d1862445f32, limb3: 0x0, }, }, ), third_root_of_unity: Some( u384 { limb0: 0xacdb5c4f5763473177fffffe, limb1: 0x59e26bcea0d48bacd4f263f1, limb2: 0x0, limb3: 0x0, }, ), }; pub const BLS12_381: Curve = Curve { p: u384 { limb0: 0xb153ffffb9feffffffffaaab, limb1: 0x6730d2a0f6b0f6241eabfffe, limb2: 0x434bacd764774b84f38512bf, limb3: 0x1a0111ea397fe69a4b1ba7b6, }, n: u256 { low: 0x53bda402fffe5bfeffffffff00000001, high: 0x73eda753299d7d483339d80809a1d805 }, a: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, b: u384 { limb0: 0x4, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, g: u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0xb153ffffb9feffffffffaaaa, limb1: 0x6730d2a0f6b0f6241eabfffe, limb2: 0x434bacd764774b84f38512bf, limb3: 0x1a0111ea397fe69a4b1ba7b6, }, min_one_order: u384 { limb0: 0xfffe5bfeffffffff00000000, limb1: 0x3339d80809a1d80553bda402, limb2: 0x73eda753299d7d48, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0xf97a1aeffb3af00adb22c6bb, limb1: 0xa14e3a3f171bac586c55e83f, limb2: 0x4fa9ac0fc3688c4f9774b905, limb3: 0x17f1d3a73197d7942695638c, }, y: u384 { limb0: 0xa2888ae40caa232946c5e7e1, limb1: 0xdb18cb2c04b3edd03cc744, limb2: 0x741d8ae4fcf5e095d5d00af6, limb3: 0x8b3f481e3aaa0f1a09e30ed, }, }, b_twist: Some( ( u384 { limb0: 4, limb1: 0, limb2: 0, limb3: 0 }, u384 { limb0: 4, limb1: 0, limb2: 0, limb3: 0 }, ), ), modulus: [ 0xb153ffffb9feffffffffaaab, 0x6730d2a0f6b0f6241eabfffe, 0x434bacd764774b84f38512bf, 0x1a0111ea397fe69a4b1ba7b6, ], order_modulus: [ 0xfffe5bfeffffffff00000001, 0x3339d80809a1d80553bda402, 0x73eda753299d7d48, 0x0, ], eigenvalue: Some( u384 { limb0: 0x1a40200000000ffffffff, limb1: 0xac45a401, limb2: 0x0, limb3: 0x0 }, ), nG_glv_fake_glv: Some( G1Point { x: u384 { limb0: 0xcf4357bd59d6560f96d34480, limb1: 0x1c2b3f4bb7a8579e7473612d, limb2: 0x44f04a3ee426074a0864fc6e, limb3: 0x60aa1307100d28a9c44cc51, }, y: u384 { limb0: 0x365913fecd5eb4667fe5e1ea, limb1: 0xa456de882c324863cdfcf5b5, limb2: 0xbaaa2be88ae9a807b36465b8, limb3: 0x31152c621ab7ca0e5a2ab1c, }, }, ), third_root_of_unity: Some( u384 { limb0: 0x4f49fffd8bfd00000000aaac, limb1: 0x897d29650fb85f9b409427eb, limb2: 0x63d4de85aa0d857d89759ad4, limb3: 0x1a0111ea397fe699ec024086, }, ), }; pub const SECP256K1: Curve = Curve { p: u384 { limb0: 0xfffffffffffffffefffffc2f, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffff, limb3: 0x0, }, n: u256 { low: 0xbaaedce6af48a03bbfd25e8cd0364141, high: 0xfffffffffffffffffffffffffffffffe }, a: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, b: u384 { limb0: 0x7, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, g: u384 { limb0: 0x3, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0xfffffffffffffffefffffc2e, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffff, limb3: 0x0, }, min_one_order: u384 { limb0: 0xaf48a03bbfd25e8cd0364140, limb1: 0xfffffffffffffffebaaedce6, limb2: 0xffffffffffffffff, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0x2dce28d959f2815b16f81798, limb1: 0x55a06295ce870b07029bfcdb, limb2: 0x79be667ef9dcbbac, limb3: 0x0, }, y: u384 { limb0: 0xa68554199c47d08ffb10d4b8, limb1: 0x5da4fbfc0e1108a8fd17b448, limb2: 0x483ada7726a3c465, limb3: 0x0, }, }, b_twist: Option::None, modulus: [0xfffffffffffffffefffffc2f, 0xffffffffffffffffffffffff, 0xffffffffffffffff, 0x0], order_modulus: [ 0xaf48a03bbfd25e8cd0364141, 0xfffffffffffffffebaaedce6, 0xffffffffffffffff, 0x0, ], eigenvalue: Some( u384 { limb0: 0x20816678df02967c1b23bd72, limb1: 0xa5261c028812645a122e22ea, limb2: 0x5363ad4cc05c30e0, limb3: 0x0, }, ), nG_glv_fake_glv: Some( G1Point { x: u384 { limb0: 0xf668832ffd959af60c82a0a, limb1: 0x6b06c9f1919413b10f9226c6, limb2: 0x948bf809b1988a4, limb3: 0x0, }, y: u384 { limb0: 0xc97cd2bed4cb7f88d8c8e589, limb1: 0xdc6b74c5d1c3418c6d4dff08, limb2: 0x53a562856dcb6646, limb3: 0x0, }, }, ), third_root_of_unity: Some( u384 { limb0: 0x12f58995c1396c28719501ee, limb1: 0x6e64479eac3434e99cf04975, limb2: 0x7ae96a2b657c0710, limb3: 0x0, }, ), }; pub const SECP256R1: Curve = Curve { p: u384 { limb0: 0xffffffffffffffffffffffff, limb1: 0x0, limb2: 0xffffffff00000001, limb3: 0x0, }, n: u256 { low: 0xbce6faada7179e84f3b9cac2fc632551, high: 0xffffffff00000000ffffffffffffffff }, a: u384 { limb0: 0xfffffffffffffffffffffffc, limb1: 0x0, limb2: 0xffffffff00000001, limb3: 0x0, }, b: u384 { limb0: 0xcc53b0f63bce3c3e27d2604b, limb1: 0xb3ebbd55769886bc651d06b0, limb2: 0x5ac635d8aa3a93e7, limb3: 0x0, }, g: u384 { limb0: 0x6, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0xfffffffffffffffffffffffe, limb1: 0x0, limb2: 0xffffffff00000001, limb3: 0x0, }, min_one_order: u384 { limb0: 0xa7179e84f3b9cac2fc632550, limb1: 0xffffffffffffffffbce6faad, limb2: 0xffffffff00000000, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0x2deb33a0f4a13945d898c296, limb1: 0xf8bce6e563a440f277037d81, limb2: 0x6b17d1f2e12c4247, limb3: 0x0, }, y: u384 { limb0: 0x6b315ececbb6406837bf51f5, limb1: 0x8ee7eb4a7c0f9e162bce3357, limb2: 0x4fe342e2fe1a7f9b, limb3: 0x0, }, }, b_twist: None, modulus: [0xffffffffffffffffffffffff, 0x0, 0xffffffff00000001, 0x0], order_modulus: [ 0xa7179e84f3b9cac2fc632551, 0xffffffffffffffffbce6faad, 0xffffffff00000000, 0x0, ], eigenvalue: None, nG_glv_fake_glv: None, third_root_of_unity: None, }; pub const ED25519: Curve = Curve { p: u384 { limb0: 0xffffffffffffffffffffffed, limb1: 0xffffffffffffffffffffffff, limb2: 0x7fffffffffffffff, limb3: 0x0, }, n: u256 { low: 0x14def9dea2f79cd65812631a5cf5d3ed, high: 0x10000000000000000000000000000000 }, a: u384 { limb0: 0xca52af7ac71e18ef8bc172d, limb1: 0x3197e10d617b3dd66bb8b65d, limb2: 0x5d4eacd3a5b9bee6, limb3: 0x0, }, b: u384 { limb0: 0x6b9fbc329004ebc1f364b2a4, limb1: 0x550ddb06105780d5f5483197, limb2: 0x1d11b29bcfd0b3e0, limb3: 0x0, }, g: u384 { limb0: 0x6, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0xffffffffffffffffffffffec, limb1: 0xffffffffffffffffffffffff, limb2: 0x7fffffffffffffff, limb3: 0x0, }, min_one_order: u384 { limb0: 0xa2f79cd65812631a5cf5d3ec, limb1: 0x14def9de, limb2: 0x1000000000000000, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0xd617c9aca55c89b025aef35, limb1: 0xf00b8f02f1c20618a9c13fdf, limb2: 0x2a78dd0fd02c0339, limb3: 0x0, }, y: u384 { limb0: 0x807131659b7830f3f62c1d14, limb1: 0xbe483ba563798323cf6fd061, limb2: 0x29c644a5c71da22e, limb3: 0x0, }, }, b_twist: None, modulus: [0xffffffffffffffffffffffed, 0xffffffffffffffffffffffff, 0x7fffffffffffffff, 0x0], order_modulus: [0xa2f79cd65812631a5cf5d3ed, 0x14def9de, 0x1000000000000000, 0x0], eigenvalue: None, nG_glv_fake_glv: None, third_root_of_unity: None, }; pub const GRUMPKIN: Curve = Curve { p: u384 { limb0: 0x79b9709143e1f593f0000001, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, n: u256 { low: 0x97816a916871ca8d3c208c16d87cfd47, high: 0x30644e72e131a029b85045b68181585d }, a: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, b: u384 { limb0: 0x79b9709143e1f593effffff0, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, g: u384 { limb0: 0x5, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, min_one: u384 { limb0: 0x79b9709143e1f593f0000000, limb1: 0xb85045b68181585d2833e848, limb2: 0x30644e72e131a029, limb3: 0x0, }, min_one_order: u384 { limb0: 0x6871ca8d3c208c16d87cfd46, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, G: G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0xf1181294833fc48d823f272c, limb1: 0xcf135e7506a45d632d270d45, limb2: 0x2, limb3: 0x0, }, }, b_twist: None, modulus: [0x79b9709143e1f593f0000001, 0xb85045b68181585d2833e848, 0x30644e72e131a029, 0x0], order_modulus: [ 0x6871ca8d3c208c16d87cfd47, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0, ], eigenvalue: None, nG_glv_fake_glv: None, third_root_of_unity: None, }; /// Generator point for the G2 subgroup of BLS12-381's twisted curve E'(Fp2) /// Coordinates are in Fp2 represented as (x₀ + i·x₁, y₀ + i·y₁) pub const BLS_G2_GENERATOR: G2Point = G2Point { x0: u384 { limb0: 0xa805bbefd48056c8c121bdb8, limb1: 0xb4510b647ae3d1770bac0326, limb2: 0x2dc51051c6e47ad4fa403b02, limb3: 0x24aa2b2f08f0a9126080527, }, x1: u384 { limb0: 0x13945d57e5ac7d055d042b7e, limb1: 0xb5da61bbdc7f5049334cf112, limb2: 0x88274f65596bd0d09920b61a, limb3: 0x13e02b6052719f607dacd3a0, }, y0: u384 { limb0: 0x3baca289e193548608b82801, limb1: 0x6d429a695160d12c923ac9cc, limb2: 0xda2e351aadfd9baa8cbdd3a7, limb3: 0xce5d527727d6e118cc9cdc6, }, y1: u384 { limb0: 0x5cec1da1aaa9075ff05f79be, limb1: 0x267492ab572e99ab3f370d27, limb2: 0x2bc28b99cb3e287e85a763af, limb3: 0x606c4a02ea734cc32acd2b0, }, }; /// Compressed NAF (Non-Adjacent Form) representation of BN254 seed parameter /// for efficient Miller loop computation in pairing operations. /// /// Computed as: recode_naf_bits(jy00(6·x + 2)[2:]) where x = 0x44E992B44A6909F1 /// Encoding: "00"→0, "10"→1, "-10"→2, "01"→3, "0-1"→4 /// See hydra/garaga/definitions.py for the encoding algorithm pub const BN254_SEED_BITS_JY00_COMPRESSED: [felt252; 32] = [ 2, 1, 0, 2, 2, 0, 2, 3, 1, 4, 0, 0, 3, 0, 2, 1, 4, 0, 0, 2, 1, 0, 2, 2, 3, 0, 4, 0, 4, 4, 2, 0, ]; /// Compressed binary representation of BLS12-381 seed parameter x = 0xD201000000010000 /// for efficient Miller loop computation. /// /// Binary digits with consecutive zeros replaced by 3 for compression /// Format: bin(x)[2:][2:] with "00" → 3 pub const BLS12_381_SEED_BITS_COMPRESSED: [felt252; 34] = [ 0, 1, 3, 1, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 1, 3, 3, 3, 3, 3, 3, 3, 3, ]; /// NAF (Non-Adjacent Form) representation of BN254 seed parameter /// for Miller loop computation in pairing operations. /// /// Computed as: NAF(6·x + 2)[1:] where x = 0x44E992B44A6909F1 /// Encoding: -1 is replaced by 2 (values are 0, 1, or 2) /// See hydra/garaga/definitions.py for the NAF algorithm pub const BN254_SEED_BITS_NAF: [usize; 65] = [ 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, ]; /// Standard binary representation of BLS12-381 seed parameter x = 0xD201000000010000 /// Used for basic Miller loop operations /// Format: bin(x)[2:][2:] (binary digits after "0b" prefix, skipping first two) pub const BLS12_381_SEED_BITS: [usize; 62] = [ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]; /// GETTER FUNCTIONS /// /// Returns the prime modulus p of the base field Fp for a given curve. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5, see curve index mapping above) /// /// # Returns /// * The prime modulus p as u384, or zero for invalid indices pub fn get_p(curve_index: usize) -> u384 { match curve_index { 0 => BN254.p, 1 => BLS12_381.p, 2 => SECP256K1.p, 3 => SECP256R1.p, 4 => ED25519.p, 5 => GRUMPKIN.p, _ => u384 { limb0: 0, limb1: 0, limb2: 0, limb3: 0 }, } } /// Checks if a curve has an efficient endomorphism available for GLV decomposition. /// /// GLV (Gallant-Lambert-Vanstone) decomposition accelerates scalar multiplication /// by utilizing the curve's endomorphism structure. /// /// # Arguments /// * `curve_index` - Index of the curve /// /// # Returns /// * `true` for BN254, BLS12_381, and SECP256K1 (curves 0, 1, 2) /// * `false` for all other curves pub fn has_endomorphism_available(curve_index: usize) -> bool { match curve_index { 0 | 1 | 2 => true, _ => false, } } /// Returns the Weierstrass 'a' parameter for a given curve. /// /// For Weierstrass curves: y² = x³ + ax + b /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The 'a' parameter as u384, or zero for invalid indices /// /// # Note /// For ED25519 (index 4), this returns the 'a' parameter of the birationally /// equivalent Weierstrass curve, not the Edwards curve parameter. pub fn get_a(curve_index: usize) -> u384 { match curve_index { 0 => BN254.a, 1 => BLS12_381.a, 2 => SECP256K1.a, 3 => SECP256R1.a, 4 => ED25519.a, 5 => GRUMPKIN.a, _ => u384 { limb0: 0, limb1: 0, limb2: 0, limb3: 0 }, } } /// Returns the Weierstrass 'b' parameter for a given curve. /// /// For Weierstrass curves: y² = x³ + ax + b /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The 'b' parameter as u384, or zero for invalid indices /// /// # Note /// For ED25519 (index 4), this returns the 'b' parameter of the birationally /// equivalent Weierstrass curve, not the Edwards curve parameter. pub fn get_b(curve_index: usize) -> u384 { match curve_index { 0 => BN254.b, 1 => BLS12_381.b, 2 => SECP256K1.b, 3 => SECP256R1.b, 4 => ED25519.b, 5 => GRUMPKIN.b, _ => u384 { limb0: 0, limb1: 0, limb2: 0, limb3: 0 }, } } /// Returns the b parameter for the twisted curve E'(Fp2) used in pairing operations. /// /// The twisted curve has equation: y² = x³ + b' where b' is in Fp2. /// /// # Arguments /// * `curve_index` - Index of the curve (must be 0 for BN254 or 1 for BLS12_381) /// /// # Returns /// * Tuple (b₀, b₁) where b' = b₀ + i·b₁ in Fp2 = Fp[i]/(i² + 1) /// /// # Panics /// * Panics for curves without pairing support (not BN254 or BLS12_381) pub fn get_b_twist(curve_index: usize) -> (u384, u384) { match curve_index { 0 => BN254.b_twist.unwrap(), 1 => BLS12_381.b_twist.unwrap(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns a generator g of the multiplicative group Fp* for a given curve. /// /// This generator is used for various field operations and exponentiations. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * A generator element g ∈ Fp* as u384 /// /// # Panics /// * Panics for invalid curve indices pub fn get_g(curve_index: usize) -> u384 { match curve_index { 0 => BN254.g, 1 => BLS12_381.g, 2 => SECP256K1.g, 3 => SECP256R1.g, 4 => ED25519.g, 5 => GRUMPKIN.g, _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the order n of the curve's prime-order subgroup. /// /// This is the number of points in the main cryptographic subgroup. /// For most curves, this equals #E(Fp)/cofactor. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The subgroup order n as u256 /// /// # Panics /// * Panics for invalid curve indices pub fn get_n(curve_index: usize) -> u256 { match curve_index { 0 => BN254.n, 1 => BLS12_381.n, 2 => SECP256K1.n, 3 => SECP256R1.n, 4 => ED25519.n, 5 => GRUMPKIN.n, _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns (-1) mod p precomputed for the base field Fp. /// /// This is equivalent to (p - 1) and is frequently used in field arithmetic. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The value (-1) mod p as u384 /// /// # Panics /// * Panics for invalid curve indices pub fn get_min_one(curve_index: usize) -> u384 { match curve_index { 0 => BN254.min_one, 1 => BLS12_381.min_one, 2 => SECP256K1.min_one, 3 => SECP256R1.min_one, 4 => ED25519.min_one, 5 => GRUMPKIN.min_one, _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns (-1) mod n precomputed for the scalar field (curve order). /// /// This is equivalent to (n - 1) and is used for scalar arithmetic operations. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The value (-1) mod n as u384 /// /// # Panics /// * Panics for invalid curve indices pub fn get_min_one_order(curve_index: usize) -> u384 { match curve_index { 0 => BN254.min_one_order, 1 => BLS12_381.min_one_order, 2 => SECP256K1.min_one_order, 3 => SECP256R1.min_one_order, 4 => ED25519.min_one_order, 5 => GRUMPKIN.min_one_order, _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the base field modulus p as a CircuitModulus for circuit operations. /// /// CircuitModulus is used by Cairo's circuit builtins for modular arithmetic. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The prime modulus p as CircuitModulus /// /// # Panics /// * Panics for invalid curve indices pub fn get_modulus(curve_index: usize) -> CircuitModulus { match curve_index { 0 => get_BN254_modulus(), 1 => get_BLS12_381_modulus(), 2 => get_SECP256K1_modulus(), 3 => get_SECP256R1_modulus(), 4 => get_ED25519_modulus(), 5 => get_GRUMPKIN_modulus(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the curve order n as a CircuitModulus for circuit operations. /// /// CircuitModulus is used by Cairo's circuit builtins for modular arithmetic /// in the scalar field. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The curve order n as CircuitModulus /// /// # Panics /// * Panics for invalid curve indices pub fn get_curve_order_modulus(curve_index: usize) -> CircuitModulus { match curve_index { 0 => get_BN254_order_modulus(), 1 => get_BLS12_381_order_modulus(), 2 => get_SECP256K1_order_modulus(), 3 => get_SECP256R1_order_modulus(), 4 => get_ED25519_order_modulus(), 5 => get_GRUMPKIN_order_modulus(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the standard generator point G of the curve's prime-order subgroup. /// /// This is the base point used for scalar multiplication and key generation. /// /// # Arguments /// * `curve_index` - Index of the curve (0-5) /// /// # Returns /// * The generator point G as G1Point /// /// # Panics /// * Panics for invalid curve indices /// /// # Note /// For ED25519 (index 4), returns the generator in Weierstrass form. pub fn get_G(curve_index: usize) -> G1Point { match curve_index { 0 => BN254.G, 1 => BLS12_381.G, 2 => SECP256K1.G, 3 => SECP256R1.G, 4 => ED25519.G, 5 => GRUMPKIN.G, _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the eigenvalue λ for the curve's efficiently computable endomorphism. /// /// The endomorphism φ satisfies φ(P) = λ·P for points P on the curve. /// This eigenvalue is used in GLV decomposition to accelerate scalar multiplication. /// /// # Arguments /// * `curve_index` - Index of the curve (must be 0, 1, or 2) /// /// # Returns /// * The eigenvalue λ as u384 /// /// # Panics /// * Panics for curves without efficient endomorphism (not BN254, BLS12_381, or SECP256K1) pub fn get_eigenvalue(curve_index: usize) -> u384 { match curve_index { 0 => BN254.eigenvalue.unwrap(), 1 => BLS12_381.eigenvalue.unwrap(), 2 => SECP256K1.eigenvalue.unwrap(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the precomputed point 2^(nbits-1)·G for GLV/fake-GLV decomposition. /// /// This precomputed value is used to accelerate scalar multiplication via /// GLV (Gallant-Lambert-Vanstone) or fake-GLV decomposition techniques. /// /// The nbits parameter is computed as: nbits = n.bit_length() // 4 + 9 /// where n is the curve order. /// /// # Arguments /// * `curve_index` - Index of the curve (must be 0, 1, or 2) /// /// # Returns /// * The point 2^(nbits-1)·G as G1Point /// - For BN254: 2^72·G (nbits=73) /// - For BLS12_381: 2^72·G (nbits=73) /// - For SECP256K1: 2^72·G (nbits=73) /// /// # Panics /// * Panics for curves without efficient endomorphism (not BN254, BLS12_381, or SECP256K1) pub fn get_nG_glv_fake_glv(curve_index: usize) -> G1Point { match curve_index { 0 => BN254.nG_glv_fake_glv.unwrap(), 1 => BLS12_381.nG_glv_fake_glv.unwrap(), 2 => SECP256K1.nG_glv_fake_glv.unwrap(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns a primitive cube root of unity ω in the base field Fp. /// /// This element satisfies ω³ = 1 and ω ≠ 1, and is used in GLV endomorphism /// computations for accelerating scalar multiplication. /// /// # Arguments /// * `curve_index` - Index of the curve (must be 0, 1, or 2) /// /// # Returns /// * A third root of unity ω ∈ Fp as u384 /// /// # Panics /// * Panics for curves without efficient endomorphism (not BN254, BLS12_381, or SECP256K1) pub fn get_third_root_of_unity(curve_index: usize) -> u384 { match curve_index { 0 => BN254.third_root_of_unity.unwrap(), 1 => BLS12_381.third_root_of_unity.unwrap(), 2 => SECP256K1.third_root_of_unity.unwrap(), _ => core::panic_with_felt252('Invalid curve index'), } } /// Returns the BLS12-381 base field modulus as CircuitModulus. #[inline(always)] pub fn get_BLS12_381_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(BLS12_381.modulus).unwrap() } /// Returns the BN254 base field modulus as CircuitModulus. #[inline(always)] pub fn get_BN254_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(BN254.modulus).unwrap() } /// Returns the SECP256K1 base field modulus as CircuitModulus. #[inline(always)] pub fn get_SECP256K1_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(SECP256K1.modulus).unwrap() } /// Returns the SECP256R1 (P-256) base field modulus as CircuitModulus. #[inline(always)] pub fn get_SECP256R1_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(SECP256R1.modulus).unwrap() } /// Returns the ED25519 base field modulus as CircuitModulus. /// (Modulus of the birationally equivalent Weierstrass curve) #[inline(always)] pub fn get_ED25519_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(ED25519.modulus).unwrap() } /// Returns the GRUMPKIN base field modulus as CircuitModulus. #[inline(always)] pub fn get_GRUMPKIN_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(GRUMPKIN.modulus).unwrap() } /// Returns the BN254 curve order as CircuitModulus. #[inline(always)] pub fn get_BN254_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(BN254.order_modulus).unwrap() } /// Returns the BLS12-381 curve order as CircuitModulus. #[inline(always)] pub fn get_BLS12_381_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(BLS12_381.order_modulus).unwrap() } /// Returns the SECP256K1 curve order as CircuitModulus. #[inline(always)] pub fn get_SECP256K1_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(SECP256K1.order_modulus).unwrap() } /// Returns the SECP256R1 (P-256) curve order as CircuitModulus. #[inline(always)] pub fn get_SECP256R1_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(SECP256R1.order_modulus).unwrap() } /// Returns the ED25519 curve order as CircuitModulus. #[inline(always)] pub fn get_ED25519_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(ED25519.order_modulus).unwrap() } /// Returns the GRUMPKIN curve order as CircuitModulus. #[inline(always)] pub fn get_GRUMPKIN_order_modulus() -> CircuitModulus { TryInto::<_, CircuitModulus>::try_into(GRUMPKIN.order_modulus).unwrap() } ================================================ FILE: src/src/definitions/structs/fields.cairo ================================================ //! Field structures for degree-12 extension fields used by the circuits. //! //! - [`E12D`] models a polynomial representation with 12 coefficients. //! - [`E12T`] models a 2-3-2 tower representation with named coefficients. //! //! Documentation follows Scarb's doc conventions (`///` and `//!` comments), so it can be //! rendered with `scarb doc`. use core::circuit::{u384, u96}; use core::num; use core::num::traits::{One, Zero}; use core::serde::Serde; use corelib_imports::bounded_int::downcast; #[derive(Copy, Drop, Debug, PartialEq)] pub struct u288 { pub limb0: u96, pub limb1: u96, pub limb2: u96, } /// A 2048-bit integer packed into 6 chunks of at most 384 bits each /// (the top chunk w5 is constrained to 128 bits). /// /// Given 22 limbs of 96 bits, groups of 4 consecutive limbs form one u384 /// chunk. The last group uses only 2 limbs, yielding a 128-bit top chunk. #[derive(Copy, Drop, Debug, PartialEq)] pub struct RSA2048Chunks { pub w0: u384, pub w1: u384, pub w2: u384, pub w3: u384, pub w4: u384, pub w5: u384, } /// Witness for one modular reduction a * b = q * n + r over Z, /// where q (quotient) and r (remainder) are 2048-bit integers /// in chunk representation. #[derive(Copy, Drop, Debug, PartialEq)] pub struct RSA2048ReductionWitness { pub quotient: RSA2048Chunks, pub remainder: RSA2048Chunks, } /// Degree-12 extension field element (generic coefficients). /// /// Represents an element of the extension field F_{q^12} modeled as the /// quotient ring F_q[w]/p(w), where p(w) is an irreducible polynomial of /// degree 12. Canonical polynomial form: /// /// ```text /// w0 + w1*w + w2*w^2 + w3*w^3 + w4*w^4 + w5*w^5 /// + w6*w^6 + w7*w^7 + w8*w^8 + w9*w^9 + w10*w^10 + w11*w^11 /// ``` /// /// Coefficients w0 ... w11 are of type `T`. /// /// When `T` is a limb-based integer type used in this codebase: /// - `T = [u384]` (4 x u96 limbs) or `T = [u288]` (3 x u96 limbs). Helpers /// below serialize/deserialize to a flat `Array` (12x4 for `u384`, /// 12x3 for `u288`). /// - [`num::traits::One`] is implemented for `E12D` and `E12D`; the /// multiplicative identity is `w0 = 1` and all other coefficients are zero. /// /// Example: create the multiplicative identity for `u288` coefficients. /// ```text /// let one: E12D = E12D { /// w0: U288One::one(), /// w1: U288Zero::zero(), /// w2: U288Zero::zero(), /// w3: U288Zero::zero(), /// w4: U288Zero::zero(), /// w5: U288Zero::zero(), /// w6: U288Zero::zero(), /// w7: U288Zero::zero(), /// w8: U288Zero::zero(), /// w9: U288Zero::zero(), /// w10: U288Zero::zero(), /// w11: U288Zero::zero(), /// }; /// ``` #[derive(Copy, Drop, Debug, PartialEq)] pub struct E12D { pub w0: T, pub w1: T, pub w2: T, pub w3: T, pub w4: T, pub w5: T, pub w6: T, pub w7: T, pub w8: T, pub w9: T, pub w10: T, pub w11: T, } /// Degree-12 extension field element using a 2-3-2 tower construction. /// /// The field F_{q^12} is built in three steps: /// - F_{q^2} ~= F_q[u]/p1(u) /// - F_{q^6} ~= F_{q^2}[v]/p2(v) /// - F_{q^12} ~= F_{q^6}[w]/p3(w) /// /// Any element has the form: /// /// ```text /// [ (c1b2a1*u + c1b2a0)*v^2 + (c1b1a1*u + c1b1a0)*v + (c1b0a1*u + c1b0a0) ]*w /// + [ (c0b2a1*u + c0b2a0)*v^2 + (c0b1a1*u + c0b1a0)*v + (c0b0a1*u + c0b0a0) ] /// ``` /// /// This yields 12 base-field coefficients. Field names follow `c{c}b{b}a{a}`: /// - `c` in {0,1} selects the coefficient of 1 (c=0) or of w (c=1) /// - `b` in {0,1,2} selects the power of v (0, 1, or 2) /// - `a` in {0,1} selects the component in the quadratic basis over u /// /// All twelve attributes are [`u384`] values (unsigned 384-bit integers) used by /// the surrounding circuits and serializers. /// /// Example: zero element (schematic — any `u384` zero can be reused across fields). /// ```cairo /// let z: u384 = Zero::zero(); /// let e = E12T { /// c0b0a0: z, c0b0a1: z, /// c0b1a0: z, c0b1a1: z, /// c0b2a0: z, c0b2a1: z, /// c1b0a0: z, c1b0a1: z, /// c1b1a0: z, c1b1a1: z, /// c1b2a0: z, c1b2a1: z, /// }; /// ``` #[derive(Drop, Copy, Debug, PartialEq)] pub struct E12T { pub c0b0a0: u384, pub c0b0a1: u384, pub c0b1a0: u384, pub c0b1a1: u384, pub c0b2a0: u384, pub c0b2a1: u384, pub c1b0a0: u384, pub c1b0a1: u384, pub c1b1a0: u384, pub c1b1a1: u384, pub c1b2a0: u384, pub c1b2a1: u384, } pub fn serialize_u384(self: @u384, ref output: Array) { output.append((*self.limb0).into()); output.append((*self.limb1).into()); output.append((*self.limb2).into()); output.append((*self.limb3).into()); } pub fn deserialize_u384(ref serialized: Span) -> u384 { let [l0, l1, l2, l3] = (*serialized.multi_pop_front::<4>().unwrap()).unbox(); let limb0: u96 = downcast(l0).unwrap(); let limb1: u96 = downcast(l1).unwrap(); let limb2: u96 = downcast(l2).unwrap(); let limb3: u96 = downcast(l3).unwrap(); return u384 { limb0: limb0, limb1: limb1, limb2: limb2, limb3: limb3 }; } pub fn serialize_u384_array(self: @Array, ref output: Array) { self.len().serialize(ref output); serialize_u384_array_helper(self.span(), ref output); } pub impl RSA2048ChunksSerde of Serde { fn serialize(self: @RSA2048Chunks, ref output: Array) { serialize_u384(self.w0, ref output); serialize_u384(self.w1, ref output); serialize_u384(self.w2, ref output); serialize_u384(self.w3, ref output); serialize_u384(self.w4, ref output); serialize_u384(self.w5, ref output); } fn deserialize(ref serialized: Span) -> Option { let w0 = deserialize_u384(ref serialized); let w1 = deserialize_u384(ref serialized); let w2 = deserialize_u384(ref serialized); let w3 = deserialize_u384(ref serialized); let w4 = deserialize_u384(ref serialized); let w5 = deserialize_u384(ref serialized); return Option::Some(RSA2048Chunks { w0, w1, w2, w3, w4, w5 }); } } pub fn serialize_u384_array_helper(mut input: Span, ref output: Array) { if let Option::Some(value) = input.pop_front() { serialize_u384(value, ref output); serialize_u384_array_helper(input, ref output); } } pub fn deserialize_u384_array(ref serialized: Span) -> Array { let length = *serialized.pop_front().unwrap(); let mut arr = array![]; deserialize_u384_array_helper(ref serialized, arr, length) } pub fn deserialize_u384_array_helper( ref serialized: Span, mut curr_output: Array, remaining: felt252, ) -> Array { if remaining == 0 { return curr_output; } curr_output.append(deserialize_u384(ref serialized)); deserialize_u384_array_helper(ref serialized, curr_output, remaining - 1) } pub impl u288Serde of Serde { fn serialize(self: @u288, ref output: Array) { output.append((*self.limb0).into()); output.append((*self.limb1).into()); output.append((*self.limb2).into()); } fn deserialize(ref serialized: Span) -> Option { let [l0, l1, l2] = (*serialized.multi_pop_front::<3>().unwrap()).unbox(); let limb0 = downcast(l0).unwrap(); let limb1 = downcast(l1).unwrap(); let limb2 = downcast(l2).unwrap(); return Option::Some(u288 { limb0: limb0, limb1: limb1, limb2: limb2 }); } } impl U288Zero of num::traits::Zero { fn zero() -> u288 { u288 { limb0: 0, limb1: 0, limb2: 0 } } fn is_zero(self: @u288) -> bool { *self == Self::zero() } fn is_non_zero(self: @u288) -> bool { !self.is_zero() } } impl U288One of num::traits::One { fn one() -> u288 { u288 { limb0: 1, limb1: 0, limb2: 0 } } fn is_one(self: @u288) -> bool { *self == Self::one() } fn is_non_one(self: @u288) -> bool { !self.is_one() } } impl E12DOneU384 of num::traits::One> { fn one() -> E12D { E12D { w0: One::one(), w1: Zero::zero(), w2: Zero::zero(), w3: Zero::zero(), w4: Zero::zero(), w5: Zero::zero(), w6: Zero::zero(), w7: Zero::zero(), w8: Zero::zero(), w9: Zero::zero(), w10: Zero::zero(), w11: Zero::zero(), } } fn is_one(self: @E12D) -> bool { *self == Self::one() } fn is_non_one(self: @E12D) -> bool { !self.is_one() } } impl E12DOneU288 of num::traits::One> { fn one() -> E12D { E12D { w0: U288One::one(), w1: U288Zero::zero(), w2: U288Zero::zero(), w3: U288Zero::zero(), w4: U288Zero::zero(), w5: U288Zero::zero(), w6: U288Zero::zero(), w7: U288Zero::zero(), w8: U288Zero::zero(), w9: U288Zero::zero(), w10: U288Zero::zero(), w11: U288Zero::zero(), } } fn is_one(self: @E12D) -> bool { *self == Self::one() } fn is_non_one(self: @E12D) -> bool { !self.is_one() } } pub impl E12TOne of One { fn one() -> E12T { E12T { c0b0a0: One::one(), c0b0a1: Zero::zero(), c0b1a0: Zero::zero(), c0b1a1: Zero::zero(), c0b2a0: Zero::zero(), c0b2a1: Zero::zero(), c1b0a0: Zero::zero(), c1b0a1: Zero::zero(), c1b1a0: Zero::zero(), c1b1a1: Zero::zero(), c1b2a0: Zero::zero(), c1b2a1: Zero::zero(), } } fn is_one(self: @E12T) -> bool { *self == Self::one() } fn is_non_one(self: @E12T) -> bool { !Self::is_one(self) } } impl E12DSerde384 of Serde> { fn serialize(self: @E12D, ref output: Array) { let val = *self; output.append(val.w0.limb0.into()); output.append(val.w0.limb1.into()); output.append(val.w0.limb2.into()); output.append(val.w0.limb3.into()); output.append(val.w1.limb0.into()); output.append(val.w1.limb1.into()); output.append(val.w1.limb2.into()); output.append(val.w1.limb3.into()); output.append(val.w2.limb0.into()); output.append(val.w2.limb1.into()); output.append(val.w2.limb2.into()); output.append(val.w2.limb3.into()); output.append(val.w3.limb0.into()); output.append(val.w3.limb1.into()); output.append(val.w3.limb2.into()); output.append(val.w3.limb3.into()); output.append(val.w4.limb0.into()); output.append(val.w4.limb1.into()); output.append(val.w4.limb2.into()); output.append(val.w4.limb3.into()); output.append(val.w5.limb0.into()); output.append(val.w5.limb1.into()); output.append(val.w5.limb2.into()); output.append(val.w5.limb3.into()); output.append(val.w6.limb0.into()); output.append(val.w6.limb1.into()); output.append(val.w6.limb2.into()); output.append(val.w6.limb3.into()); output.append(val.w7.limb0.into()); output.append(val.w7.limb1.into()); output.append(val.w7.limb2.into()); output.append(val.w7.limb3.into()); output.append(val.w8.limb0.into()); output.append(val.w8.limb1.into()); output.append(val.w8.limb2.into()); output.append(val.w8.limb3.into()); output.append(val.w9.limb0.into()); output.append(val.w9.limb1.into()); output.append(val.w9.limb2.into()); output.append(val.w9.limb3.into()); output.append(val.w10.limb0.into()); output.append(val.w10.limb1.into()); output.append(val.w10.limb2.into()); output.append(val.w10.limb3.into()); output.append(val.w11.limb0.into()); output.append(val.w11.limb1.into()); output.append(val.w11.limb2.into()); output.append(val.w11.limb3.into()); } fn deserialize(ref serialized: Span) -> Option> { let [ w0l0, w0l1, w0l2, w0l3, w1l0, w1l1, w1l2, w1l3, w2l0, w2l1, w2l2, w2l3, w3l0, w3l1, w3l2, w3l3, w4l0, w4l1, w4l2, w4l3, w5l0, w5l1, w5l2, w5l3, w6l0, w6l1, w6l2, w6l3, w7l0, w7l1, w7l2, w7l3, w8l0, w8l1, w8l2, w8l3, w9l0, w9l1, w9l2, w9l3, w10l0, w10l1, w10l2, w10l3, w11l0, w11l1, w11l2, w11l3, ] = (*serialized .multi_pop_front::<48>() .unwrap()) .unbox(); Option::Some( E12D { w0: u384 { limb0: downcast(w0l0).unwrap(), limb1: downcast(w0l1).unwrap(), limb2: downcast(w0l2).unwrap(), limb3: downcast(w0l3).unwrap(), }, w1: u384 { limb0: downcast(w1l0).unwrap(), limb1: downcast(w1l1).unwrap(), limb2: downcast(w1l2).unwrap(), limb3: downcast(w1l3).unwrap(), }, w2: u384 { limb0: downcast(w2l0).unwrap(), limb1: downcast(w2l1).unwrap(), limb2: downcast(w2l2).unwrap(), limb3: downcast(w2l3).unwrap(), }, w3: u384 { limb0: downcast(w3l0).unwrap(), limb1: downcast(w3l1).unwrap(), limb2: downcast(w3l2).unwrap(), limb3: downcast(w3l3).unwrap(), }, w4: u384 { limb0: downcast(w4l0).unwrap(), limb1: downcast(w4l1).unwrap(), limb2: downcast(w4l2).unwrap(), limb3: downcast(w4l3).unwrap(), }, w5: u384 { limb0: downcast(w5l0).unwrap(), limb1: downcast(w5l1).unwrap(), limb2: downcast(w5l2).unwrap(), limb3: downcast(w5l3).unwrap(), }, w6: u384 { limb0: downcast(w6l0).unwrap(), limb1: downcast(w6l1).unwrap(), limb2: downcast(w6l2).unwrap(), limb3: downcast(w6l3).unwrap(), }, w7: u384 { limb0: downcast(w7l0).unwrap(), limb1: downcast(w7l1).unwrap(), limb2: downcast(w7l2).unwrap(), limb3: downcast(w7l3).unwrap(), }, w8: u384 { limb0: downcast(w8l0).unwrap(), limb1: downcast(w8l1).unwrap(), limb2: downcast(w8l2).unwrap(), limb3: downcast(w8l3).unwrap(), }, w9: u384 { limb0: downcast(w9l0).unwrap(), limb1: downcast(w9l1).unwrap(), limb2: downcast(w9l2).unwrap(), limb3: downcast(w9l3).unwrap(), }, w10: u384 { limb0: downcast(w10l0).unwrap(), limb1: downcast(w10l1).unwrap(), limb2: downcast(w10l2).unwrap(), limb3: downcast(w10l3).unwrap(), }, w11: u384 { limb0: downcast(w11l0).unwrap(), limb1: downcast(w11l1).unwrap(), limb2: downcast(w11l2).unwrap(), limb3: downcast(w11l3).unwrap(), }, }, ) } } impl E12DSerde288 of Serde> { fn serialize(self: @E12D, ref output: Array) { let val = *self; output.append(val.w0.limb0.into()); output.append(val.w0.limb1.into()); output.append(val.w0.limb2.into()); output.append(val.w1.limb0.into()); output.append(val.w1.limb1.into()); output.append(val.w1.limb2.into()); output.append(val.w2.limb0.into()); output.append(val.w2.limb1.into()); output.append(val.w2.limb2.into()); output.append(val.w3.limb0.into()); output.append(val.w3.limb1.into()); output.append(val.w3.limb2.into()); output.append(val.w4.limb0.into()); output.append(val.w4.limb1.into()); output.append(val.w4.limb2.into()); output.append(val.w5.limb0.into()); output.append(val.w5.limb1.into()); output.append(val.w5.limb2.into()); output.append(val.w6.limb0.into()); output.append(val.w6.limb1.into()); output.append(val.w6.limb2.into()); output.append(val.w7.limb0.into()); output.append(val.w7.limb1.into()); output.append(val.w7.limb2.into()); output.append(val.w8.limb0.into()); output.append(val.w8.limb1.into()); output.append(val.w8.limb2.into()); output.append(val.w9.limb0.into()); output.append(val.w9.limb1.into()); output.append(val.w9.limb2.into()); output.append(val.w10.limb0.into()); output.append(val.w10.limb1.into()); output.append(val.w10.limb2.into()); output.append(val.w11.limb0.into()); output.append(val.w11.limb1.into()); output.append(val.w11.limb2.into()); } fn deserialize(ref serialized: Span) -> Option> { let [ w0l0, w0l1, w0l2, w1l0, w1l1, w1l2, w2l0, w2l1, w2l2, w3l0, w3l1, w3l2, w4l0, w4l1, w4l2, w5l0, w5l1, w5l2, w6l0, w6l1, w6l2, w7l0, w7l1, w7l2, w8l0, w8l1, w8l2, w9l0, w9l1, w9l2, w10l0, w10l1, w10l2, w11l0, w11l1, w11l2, ] = (*serialized .multi_pop_front::<36>() .unwrap()) .unbox(); Option::Some( E12D { w0: u288 { limb0: downcast(w0l0).unwrap(), limb1: downcast(w0l1).unwrap(), limb2: downcast(w0l2).unwrap(), }, w1: u288 { limb0: downcast(w1l0).unwrap(), limb1: downcast(w1l1).unwrap(), limb2: downcast(w1l2).unwrap(), }, w2: u288 { limb0: downcast(w2l0).unwrap(), limb1: downcast(w2l1).unwrap(), limb2: downcast(w2l2).unwrap(), }, w3: u288 { limb0: downcast(w3l0).unwrap(), limb1: downcast(w3l1).unwrap(), limb2: downcast(w3l2).unwrap(), }, w4: u288 { limb0: downcast(w4l0).unwrap(), limb1: downcast(w4l1).unwrap(), limb2: downcast(w4l2).unwrap(), }, w5: u288 { limb0: downcast(w5l0).unwrap(), limb1: downcast(w5l1).unwrap(), limb2: downcast(w5l2).unwrap(), }, w6: u288 { limb0: downcast(w6l0).unwrap(), limb1: downcast(w6l1).unwrap(), limb2: downcast(w6l2).unwrap(), }, w7: u288 { limb0: downcast(w7l0).unwrap(), limb1: downcast(w7l1).unwrap(), limb2: downcast(w7l2).unwrap(), }, w8: u288 { limb0: downcast(w8l0).unwrap(), limb1: downcast(w8l1).unwrap(), limb2: downcast(w8l2).unwrap(), }, w9: u288 { limb0: downcast(w9l0).unwrap(), limb1: downcast(w9l1).unwrap(), limb2: downcast(w9l2).unwrap(), }, w10: u288 { limb0: downcast(w10l0).unwrap(), limb1: downcast(w10l1).unwrap(), limb2: downcast(w10l2).unwrap(), }, w11: u288 { limb0: downcast(w11l0).unwrap(), limb1: downcast(w11l1).unwrap(), limb2: downcast(w11l2).unwrap(), }, }, ) } } ================================================ FILE: src/src/definitions/structs/points.cairo ================================================ use core::circuit::u384; use core::num::traits::Zero; use core::serde::Serde; use corelib_imports::circuit::conversions; use garaga::definitions::{deserialize_u384, serialize_u384}; use starknet::storage_access::StorePacking; #[derive(Copy, Drop, Debug, PartialEq)] pub struct G1Point { pub x: u384, pub y: u384, } pub impl G1PointSerde of Serde { fn serialize(self: @G1Point, ref output: Array) { serialize_u384(self.x, ref output); serialize_u384(self.y, ref output); } fn deserialize(ref serialized: Span) -> Option { let x = deserialize_u384(ref serialized); let y = deserialize_u384(ref serialized); return Option::Some(G1Point { x: x, y: y }); } } pub impl G1PointStorePacking of StorePacking { fn pack(value: G1Point) -> [felt252; 4] { let x0 = conversions::two_u96_into_felt252(value.x.limb0, value.x.limb1); let x1 = conversions::two_u96_into_felt252(value.x.limb2, value.x.limb3); let y0 = conversions::two_u96_into_felt252(value.y.limb0, value.y.limb1); let y1 = conversions::two_u96_into_felt252(value.y.limb2, value.y.limb3); [x0, x1, y0, y1] } fn unpack(value: [felt252; 4]) -> G1Point { let [x0, x1, y0, y1] = value; let x = { let (limb0, limb1) = conversions::felt252_try_into_two_u96(x0).unwrap(); let (limb2, limb3) = conversions::felt252_try_into_two_u96(x1).unwrap(); u384 { limb0, limb1, limb2, limb3 } }; let y = { let (limb0, limb1) = conversions::felt252_try_into_two_u96(y0).unwrap(); let (limb2, limb3) = conversions::felt252_try_into_two_u96(y1).unwrap(); u384 { limb0, limb1, limb2, limb3 } }; return G1Point { x: x, y: y }; } } #[derive(Copy, Drop, Debug, PartialEq)] pub struct G2Point { pub x0: u384, pub x1: u384, pub y0: u384, pub y1: u384, } pub impl G2PointSerde of Serde { fn serialize(self: @G2Point, ref output: Array) { serialize_u384(self.x0, ref output); serialize_u384(self.x1, ref output); serialize_u384(self.y0, ref output); serialize_u384(self.y1, ref output); } fn deserialize(ref serialized: Span) -> Option { let x0 = deserialize_u384(ref serialized); let x1 = deserialize_u384(ref serialized); let y0 = deserialize_u384(ref serialized); let y1 = deserialize_u384(ref serialized); return Option::Some(G2Point { x0: x0, x1: x1, y0: y0, y1: y1 }); } } #[derive(Copy, Drop, Debug, PartialEq)] pub struct G2Line { pub r0a0: T, pub r0a1: T, pub r1a0: T, pub r1a1: T, } #[derive(Copy, Drop, Debug, PartialEq, Serde)] pub struct G1G2Pair { pub p: G1Point, pub q: G2Point, } // Represents the point at infinity pub impl G1PointZero of Zero { fn zero() -> G1Point { G1Point { x: Zero::zero(), y: Zero::zero() } } fn is_zero(self: @G1Point) -> bool { *self == Self::zero() } fn is_non_zero(self: @G1Point) -> bool { !self.is_zero() } } // Represents the point at infinity pub impl G2PointZero of Zero { fn zero() -> G2Point { G2Point { x0: Zero::zero(), x1: Zero::zero(), y0: Zero::zero(), y1: Zero::zero() } } fn is_zero(self: @G2Point) -> bool { *self == Self::zero() } fn is_non_zero(self: @G2Point) -> bool { !self.is_zero() } } ================================================ FILE: src/src/definitions.cairo ================================================ pub mod curves; pub mod structs { pub mod fields; pub mod points; } pub use core::circuit::{u384, u96}; pub use core::num::traits::{One, Zero}; pub use curves::{ BLS12_381, BLS12_381_SEED_BITS, BLS12_381_SEED_BITS_COMPRESSED, BLS_G2_GENERATOR, BLS_X_SEED_SQ, BN254, BN254_SEED_BITS_JY00_COMPRESSED, BN254_SEED_BITS_NAF, Curve, ED25519, GRUMPKIN, SECP256K1, SECP256R1, get_BLS12_381_modulus, get_BLS12_381_order_modulus, get_BN254_modulus, get_BN254_order_modulus, get_ED25519_modulus, get_ED25519_order_modulus, get_G, get_GRUMPKIN_modulus, get_GRUMPKIN_order_modulus, get_SECP256K1_modulus, get_SECP256K1_order_modulus, get_SECP256R1_modulus, get_SECP256R1_order_modulus, get_a, get_b, get_b_twist, get_curve_order_modulus, get_eigenvalue, get_g, get_min_one, get_min_one_order, get_modulus, get_n, get_nG_glv_fake_glv, get_p, get_third_root_of_unity, has_endomorphism_available, }; pub use structs::fields::{ E12D, E12T, RSA2048Chunks, RSA2048ChunksSerde, RSA2048ReductionWitness, deserialize_u384, deserialize_u384_array, serialize_u384, serialize_u384_array, u288, u288Serde, }; pub use structs::points::{ G1G2Pair, G1Point, G1PointSerde, G1PointStorePacking, G1PointZero, G2Line, G2Point, G2PointSerde, G2PointZero, }; pub use crate::ec::pairing::pairing_check::{ BLSProcessedPair, BNProcessedPair, MillerLoopResultScalingFactor, }; ================================================ FILE: src/src/ec/ec_ops.cairo ================================================ use core::array::ArrayTrait; use core::circuit::{ CircuitElement, CircuitInput, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, u96, }; use core::num::traits::{One, Zero}; use core::panic_with_felt252; use core::poseidon::hades_permutation; use core::result::ResultTrait; use corelib_imports::bounded_int::{downcast, upcast}; use corelib_imports::integer::{U128sFromFelt252Result, u128s_from_felt252}; use garaga::basic_field_ops::{is_opposite_mod_p, mul_mod_p, neg_mod_p, sub_mod_p}; use garaga::circuits::ec; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{ G1Point, G1PointZero, get_G, get_a, get_b, get_curve_order_modulus, get_eigenvalue, get_min_one, get_min_one_order, get_modulus, get_n, get_nG_glv_fake_glv, get_third_root_of_unity, }; use garaga::ec::selectors; #[generate_trait] pub impl G1PointImpl of G1PointTrait { fn assert_on_curve_excluding_infinity(self: @G1Point, curve_index: usize) { if self.is_on_curve_excluding_infinity(curve_index) == false { panic_with_felt252('point not on curve'); } } fn is_on_curve_excluding_infinity(self: @G1Point, curve_index: usize) -> bool { let (check) = ec::run_IS_ON_CURVE_G1_circuit( *self, get_a(curve_index), get_b(curve_index), curve_index, ); check.is_zero() } fn negate(self: @G1Point, curve_index: usize) -> G1Point { let modulus = get_modulus(curve_index); G1Point { x: *self.x, y: neg_mod_p(*self.y, modulus) } } fn assert_in_subgroup_excluding_infinity(self: @G1Point, curve_index: usize) { self.assert_on_curve_excluding_infinity(curve_index); match curve_index { 0 => {}, // BN254 (cofactor 1) 1 => { // https://github.com/Consensys/gnark-crypto/blob/ff4c0ddbe1ef37d1c1c6bec8c36fc43a84c86be5/ecc/bls12-381/g1.go#L492 let modulus = get_modulus(curve_index); let phi_p = G1Point { x: mul_mod_p(get_third_root_of_unity(curve_index), *self.x, modulus), y: *self.y, }; let x_sq_phi_P = scalar_mul_by_bls12_381_seed_square(phi_p); if !ec_safe_add(*self, x_sq_phi_P, curve_index).is_infinity() { panic_with_felt252('bls12-381 pt not in subgroup'); } }, // BLS12-381 2 => {}, // SECP256K1 (cofactor 1) 3 => {}, // SECP256R1 (cofactor 1) 4 => { panic_with_felt252('ED25519 not implemented'); }, 5 => {}, // GRUMPKIN (cofactor 1) _ => { panic_with_felt252('invalid curve index') }, } } fn is_infinity(self: @G1Point) -> bool { return self.is_zero(); } fn update_hash_state( self: @G1Point, s0: felt252, s1: felt252, s2: felt252, ) -> (felt252, felt252, felt252) { let base: felt252 = 79228162514264337593543950336; // 2**96 let self = *self; let in_1 = s0 + self.x.limb0.into() + base * self.x.limb1.into(); let in_2 = s1 + self.x.limb2.into() + base * self.x.limb3.into(); let (s0, s1, s2) = hades_permutation(in_1, in_2, s2); let in_1 = s0 + self.y.limb0.into() + base * self.y.limb1.into(); let in_2 = s1 + self.y.limb2.into() + base * self.y.limb3.into(); let (s0, s1, s2) = hades_permutation(in_1, in_2, s2); return (s0, s1, s2); } } // Adds two elliptic curve points on a given curve. // Does not check the input points are on the curve. pub fn ec_safe_add(p: G1Point, q: G1Point, curve_index: usize) -> G1Point { if p.is_infinity() { return q; } if q.is_infinity() { return p; } let modulus = get_modulus(curve_index); let same_x = sub_mod_p(p.x, q.x, modulus).is_zero(); if same_x { let opposite_y = is_opposite_mod_p(p.y, q.y, modulus); if opposite_y { return G1PointZero::zero(); } else { let (res) = ec::run_DOUBLE_EC_POINT_circuit(p, get_a(curve_index), modulus); return res; } } else { let (res) = ec::run_ADD_EC_POINT_circuit(p, q, modulus); return res; } } pub fn _ec_safe_add( p: G1Point, q: G1Point, modulus: CircuitModulus, curve_index: usize, ) -> G1Point { if p.is_infinity() { return q; } if q.is_infinity() { return p; } let same_x = sub_mod_p(p.x, q.x, modulus).is_zero(); if same_x { let opposite_y = is_opposite_mod_p(p.y, q.y, modulus); if opposite_y { return G1PointZero::zero(); } else { let (res) = ec::run_DOUBLE_EC_POINT_circuit(p, get_a(curve_index), modulus); return res; } } else { let (res) = ec::run_ADD_EC_POINT_circuit(p, q, modulus); return res; } } #[derive(Drop, Serde)] pub struct GlvFakeGlvHint { pub Q: G1Point, pub u1: felt252, // Encoded as 2^128 * sign + abs(u1) pub u2: felt252, // Encoded as 2^128 * sign + abs(u2) pub v1: felt252, // Encoded as 2^128 * sign + abs(v1) pub v2: felt252 // Encoded as 2^128 * sign + abs(v2) } #[derive(Drop, Serde)] pub struct FakeGlvHint { pub Q: G1Point, pub s1: u128, // (s1)_u128 (always positive) pub s2: felt252 // Encoded as 2^128 * sign + abs(s2)_u128 } pub fn msm_g1( points: Span, scalars: Span, curve_index: usize, mut hint: Span, ) -> G1Point { match curve_index { 0 | 1 | 2 => { return msm_glv_fake_glv(points, scalars, curve_index, ref hint); }, _ => { return msm_fake_glv(points, scalars, curve_index, ref hint); }, } } pub fn msm_fake_glv( mut points: Span, mut scalars: Span, curve_index: usize, ref hint: Span, ) -> G1Point { let n = scalars.len(); assert(n == points.len(), 'n_pts!=n_scalars'); if n == 0 { panic_with_felt252('Msm size must be >= 1'); } assert(hint.len() == n * 10, 'wrong fakeglv hint size'); let order_modulus = get_curve_order_modulus(curve_index); let curve_order: u256 = get_n(curve_index); let modulus = get_modulus(curve_index); let A_weirstrass = get_a(curve_index); let order_minus_one = get_min_one_order(curve_index); let base_min_one = get_min_one(curve_index); let mut acc = G1PointZero::zero(); while hint.len() != 0 { let pt = *points.pop_front().unwrap(); let scalar = *scalars.pop_front().unwrap(); assert(scalar < curve_order, 'unreduced scalar'); let scalar_u384: u384 = scalar.into(); let fake_glv_hint: FakeGlvHint = Serde::deserialize(ref hint).unwrap(); let temp = _scalar_mul_fake_glv( pt, scalar_u384, order_modulus, modulus, A_weirstrass, order_minus_one, base_min_one, fake_glv_hint, curve_index, ); acc = _ec_safe_add(acc, temp, modulus, curve_index); } return acc; } pub fn _scalar_mul_fake_glv( point: G1Point, scalar: u384, order_modulus: CircuitModulus, modulus: CircuitModulus, A_weirstrass: u384, order_minus_one: u384, base_min_one: u384, hint: FakeGlvHint, curve_index: usize, ) -> G1Point { if scalar.is_zero() || point.is_infinity() { return G1PointZero::zero(); } point.assert_on_curve_excluding_infinity(curve_index); if scalar.is_one() { return point; } if scalar == order_minus_one { return G1Point { x: point.x, y: neg_mod_p(point.y, modulus) }; } hint.Q.assert_on_curve_excluding_infinity(curve_index); let (_s2_sign_order, _s2_sign_base, _s2_abs): (u384, u384, u128) = match u128s_from_felt252(hint.s2) { U128sFromFelt252Result::Narrow(low) => { ( u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }, u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }, low, ) }, U128sFromFelt252Result::Wide((_, low)) => { (order_minus_one, base_min_one, low) }, }; // Verify decomposition : s1 + scalar*s2 = 0 mod n && s2!=0. let s1 = CircuitElement::> {}; let S = CircuitElement::> {}; let s2 = CircuitElement::> {}; let s2_sign = CircuitElement::> {}; let check = circuit_add(s1, circuit_mul(S, circuit_mul(s2_sign, s2))); let s1_u384: u384 = hint.s1.into(); let s2_u384: u384 = _s2_abs.into(); let outputs = (check,) .new_inputs() .next_2(s1_u384) .next_2(scalar) .next_2(s2_u384) .next_2(_s2_sign_order) .done_2() .eval(order_modulus) .unwrap(); assert(_s2_abs != 0, 'FakeGLV: s2=0'); assert(outputs.get_output(check).is_zero(), 'Wrong FakeGLV decomposition'); let (T1, T2, T3, T4, T5y, T6y, T7y, T8y, T9, T10, T11, T12, T13y, T14y, T15y, T16y, R2, R0y) = ec::run_PREPARE_FAKE_GLV_PTS_circuit( point, hint.Q, _s2_sign_base, A_weirstrass, modulus, ); // ['T6', 'T7', 'T10', 'T11', 'T8', 'T5', 'T12', 'T9', 'T14', 'T15', 'T2', 'T3', 'T16', 'T13', // 'T4', 'T1'] let mut Ts: Array = array![ G1Point { x: T1.x, y: T6y }, G1Point { x: T4.x, y: T7y }, T10, T11, G1Point { x: T3.x, y: T8y }, G1Point { x: T2.x, y: T5y }, T12, T9, G1Point { x: T9.x, y: T14y }, G1Point { x: T12.x, y: T15y }, T2, T3, G1Point { x: T11.x, y: T16y }, G1Point { x: T10.x, y: T13y }, T4, T1, ]; let (mut selectors, s1lsb, s2lsb) = selectors::build_selectors_inlined_fake_glv( hint.s1, _s2_abs, ); // Add corrected point for the last bits 2-1 at position 16 in Ts array. let last_selector = *selectors.pop_front().unwrap(); let last_selector_pt = *Ts[last_selector]; let (last_selector_pt_corrected) = ec::run_ADD_EC_POINT_circuit(last_selector_pt, R2, modulus); Ts.append(last_selector_pt_corrected); let Ts = Ts.span(); // now the first selector should be 16 and will select the corrected point in the last // iteration. // First iteration (bit 128) let selector_y = *selectors.pop_back().unwrap(); let Bi = *Ts[selector_y]; let (Acc) = ec::run_DOUBLE_EC_POINT_circuit(T2, A_weirstrass, modulus); let (mut Acc) = ec::run_ADD_EC_POINT_circuit(Acc, Bi, modulus); // assert(selectors.len() == 63, 'wrong number of selectors'); // 7 iterations* 9 * 2 bits = 63 * 2 = 126 bits. while let Some(selector_y) = selectors.multi_pop_back::<9>() { let [ selector_y8, selector_y7, selector_y6, selector_y5, selector_y4, selector_y3, selector_y2, selector_y1, selector_y0, ] = selector_y .unbox(); let Bi = *Ts.at(selector_y0); let Bi1 = *Ts.at(selector_y1); let Bi2 = *Ts.at(selector_y2); let Bi3 = *Ts.at(selector_y3); let Bi4 = *Ts.at(selector_y4); let Bi5 = *Ts.at(selector_y5); let Bi6 = *Ts.at(selector_y6); let Bi7 = *Ts.at(selector_y7); let Bi8 = *Ts.at(selector_y8); let (_Acc) = ec::run_QUADRUPLE_AND_ADD_9_circuit( Acc, Bi, Bi1, Bi2, Bi3, Bi4, Bi5, Bi6, Bi7, Bi8, A_weirstrass, modulus, ); Acc = _Acc; } let (Acc) = if s1lsb == 0 { ec::run_ADD_EC_POINT_circuit( Acc, G1Point { x: point.x, y: neg_mod_p(point.y, modulus) }, modulus, ) } else { (Acc,) }; let (Acc) = if s2lsb == 0 { ec::run_ADD_EC_POINT_circuit(Acc, G1Point { x: hint.Q.x, y: R0y }, modulus) } else { (Acc,) }; // Assert. assert(Acc == R2, 'wrong FakeGLV result'); return hint.Q; } fn msm_glv_fake_glv( mut points: Span, mut scalars: Span, curve_index: usize, ref hint: Span, ) -> G1Point { let n = scalars.len(); assert!(n == points.len(), "scalars and points length mismatch"); if n == 0 { panic_with_felt252('Msm size must be >= 1'); } assert(hint.len() == n * 12, 'wrong glv&fakeglv hint size'); let eigen = get_eigenvalue(curve_index); let third_root_of_unity = get_third_root_of_unity(curve_index); let modulus = get_modulus(curve_index); let order_modulus = get_curve_order_modulus(curve_index); let curve_order: u256 = get_n(curve_index); let min_one = get_min_one_order(curve_index); let nG = get_nG_glv_fake_glv(curve_index); let mut acc = G1PointZero::zero(); while hint.len() != 0 { let pt = *points.pop_front().unwrap(); let scalar = *scalars.pop_front().unwrap(); assert(scalar < curve_order, 'unreduced scalar'); let scalar_u384: u384 = scalar.into(); let glv_fake_glv_hint: GlvFakeGlvHint = Serde::deserialize(ref hint).unwrap(); match pt.is_infinity() { true => { acc = acc; }, false => { pt.assert_on_curve_excluding_infinity(curve_index); let temp = _scalar_mul_glv_and_fake_glv( pt, scalar_u384, order_modulus, modulus, glv_fake_glv_hint, eigen, third_root_of_unity, min_one, nG, curve_index, ); acc = _ec_safe_add(acc, temp, modulus, curve_index); }, } } return acc; } #[inline(always)] // /!\ Assumes point is on curve (not infinity) and scalar is reduced mod n. /!\ pub fn _scalar_mul_glv_and_fake_glv( point: G1Point, scalar: u384, order_modulus: CircuitModulus, modulus: CircuitModulus, hint: GlvFakeGlvHint, _lambda: u384, third_root_of_unity: u384, minus_one: u384, n_bits_G: G1Point, curve_index: usize, ) -> G1Point { if scalar.is_zero() { return G1PointZero::zero(); } if scalar.is_one() { return point; } hint.Q.assert_on_curve_excluding_infinity(curve_index); if scalar == minus_one { return G1Point { x: point.x, y: neg_mod_p(point.y, modulus) }; } let one_u384: u384 = u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }; // Retrieve the u1, u2, v1, v2 values from the hint // They are encoded as 2^128 * sign + abs(value) // If high_128 limbs are != 0, we consider the value is negative, otherwise it is positive. // We also precompute the negated value of the y coordinate of the points based on the sign in // the same match condition for efficiency. let (_u1_sign, _u1_abs, P0y, P1y): (u384, u96, u384, u384) = match u128s_from_felt252(hint.u1) { U128sFromFelt252Result::Narrow(low) => { (one_u384, downcast(low).unwrap(), neg_mod_p(point.y, modulus), point.y) }, U128sFromFelt252Result::Wide(( _, low, )) => { (minus_one, downcast(low).unwrap(), point.y, neg_mod_p(point.y, modulus)) }, }; let (_u2_sign, _u2_abs, Phi_P0y, Phi_P1y): (u384, u96, u384, u384) = match u128s_from_felt252(hint.u2) { U128sFromFelt252Result::Narrow(low) => { (one_u384, downcast(low).unwrap(), neg_mod_p(point.y, modulus), point.y) }, U128sFromFelt252Result::Wide(( _, low, )) => { (minus_one, downcast(low).unwrap(), point.y, neg_mod_p(point.y, modulus)) }, }; let (_v1_sign, _v1_abs, Q0y): (u384, u96, u384) = match u128s_from_felt252(hint.v1) { U128sFromFelt252Result::Narrow(low) => { (one_u384, downcast(low).unwrap(), neg_mod_p(hint.Q.y, modulus)) }, U128sFromFelt252Result::Wide((_, low)) => { (minus_one, downcast(low).unwrap(), hint.Q.y) }, }; let (_v2_sign, _v2_abs, Phi_Q0y): (u384, u96, u384) = match u128s_from_felt252(hint.v2) { U128sFromFelt252Result::Narrow(low) => { (one_u384, downcast(low).unwrap(), neg_mod_p(hint.Q.y, modulus)) }, U128sFromFelt252Result::Wide((_, low)) => { (minus_one, downcast(low).unwrap(), hint.Q.y) }, }; // At this point ~ 631 steps. // Check that the GLV/FakeGLV decomposition is valid: // # s*(v1 + λ*v2) + u1 + λ*u2 = 0 let s = CircuitElement::> {}; let lambda = CircuitElement::> {}; let u1_abs = CircuitElement::> {}; let u1_sign = CircuitElement::> {}; let u2_abs = CircuitElement::> {}; let u2_sign = CircuitElement::> {}; let v1_abs = CircuitElement::> {}; let v1_sign = CircuitElement::> {}; let v2_abs = CircuitElement::> {}; let v2_sign = CircuitElement::> {}; let u1 = circuit_mul(u1_abs, u1_sign); let u2 = circuit_mul(u2_abs, u2_sign); let v1 = circuit_mul(v1_abs, v1_sign); let v2 = circuit_mul(v2_abs, v2_sign); // u1 + λ*u2 let lambda_u2 = circuit_mul(lambda, u2); let u1_lambda_u2 = circuit_add(u1, lambda_u2); // s*(v1 + λ*v2) let lambda_v2 = circuit_mul(lambda, v2); let v1_lambda_v2 = circuit_add(v1, lambda_v2); let s_v1_lambda_v2 = circuit_mul(s, v1_lambda_v2); // s*(v1 + λ*v2) + u1 + λ*u2 let res = circuit_add(s_v1_lambda_v2, u1_lambda_u2); let outputs = (res,) .new_inputs() .next_2(scalar) .next_2(_lambda) .next_2([_u1_abs, 0, 0, 0]) .next_2(_u1_sign) .next_2([_u2_abs, 0, 0, 0]) .next_2(_u2_sign) .next_2([_v1_abs, 0, 0, 0]) .next_2(_v1_sign) .next_2([_v2_abs, 0, 0, 0]) .next_2(_v2_sign) .done_2() .eval(order_modulus) .unwrap(); assert(outputs.get_output(res).is_zero(), 'Wrong GLV/FakeGLV decomposition'); // At this point, ~ 836 steps // Note : P != Q (scalar != 1) let P0 = G1Point { x: point.x, y: P0y }; let Q0 = G1Point { x: hint.Q.x, y: Q0y }; let ( B1, B2, B3, B4, B5, B6, B7, B8, B9y, B10y, B11y, B12y, B13y, B14y, B15y, B16y, Phi_P0x, Phi_Q0x, mut Acc, ) = ec::run_PREPARE_GLV_FAKE_GLV_PTS_circuit( point.x, P0y, P1y, hint.Q.x, Q0y, Phi_P0y, Phi_P1y, Phi_Q0y, get_G(curve_index), third_root_of_unity, modulus, ); let Bs: Span = array![ G1Point { x: B1.x, y: B16y }, B8, G1Point { x: B3.x, y: B14y }, B6, G1Point { x: B5.x, y: B12y }, B4, G1Point { x: B7.x, y: B10y }, B2, G1Point { x: B2.x, y: B15y }, B7, G1Point { x: B4.x, y: B13y }, B5, G1Point { x: B6.x, y: B11y }, B3, G1Point { x: B8.x, y: B9y }, B1, ] .span(); // At this point, ~ 1643 steps. // println!("Bs: {:?}", Bs); // println!("Acc: {:?}", Acc); let mut _u1: u128 = upcast(_u1_abs); let mut _u2: u128 = upcast(_u2_abs); let mut _v1: u128 = upcast(_v1_abs); let mut _v2: u128 = upcast(_v2_abs); let (mut selectors, u1lsb, u2lsb, v1lsb, v2lsb) = selectors::build_selectors_inlined( _u1, _u2, _v1, _v2, ); // Process 8 bits per iteration while let Some(selector_y) = selectors.multi_pop_back::<8>() { let [ selector_y7, selector_y6, selector_y5, selector_y4, selector_y3, selector_y2, selector_y1, selector_y0, ] = (*selector_y) .unbox(); let Bi = *Bs.at(selector_y0); let Bi1 = *Bs.at(selector_y1); let Bi2 = *Bs.at(selector_y2); let Bi3 = *Bs.at(selector_y3); let Bi4 = *Bs.at(selector_y4); let Bi5 = *Bs.at(selector_y5); let Bi6 = *Bs.at(selector_y6); let Bi7 = *Bs.at(selector_y7); Acc = double_and_add_8(Acc, Bi, Bi1, Bi2, Bi3, Bi4, Bi5, Bi6, Bi7, modulus); } // println!("Acc final: {:?}", Acc); let (Acc) = if u1lsb == 0 { ec::run_ADD_EC_POINT_circuit(Acc, P0, modulus) } else { (Acc,) }; let (Acc) = if u2lsb == 0 { ec::run_ADD_EC_POINT_circuit(Acc, G1Point { x: Phi_P0x, y: Phi_P0y }, modulus) } else { (Acc,) }; let (Acc) = if v1lsb == 0 { ec::run_ADD_EC_POINT_circuit(Acc, Q0, modulus) } else { (Acc,) }; let (Acc) = if v2lsb == 0 { ec::run_ADD_EC_POINT_circuit(Acc, G1Point { x: Phi_Q0x, y: Phi_Q0y }, modulus) } else { (Acc,) }; assert(Acc == n_bits_G, 'Wrong Glv&FakeGLV result'); return hint.Q; } fn scalar_mul_by_bls12_381_seed_square(q: G1Point) -> G1Point { let a = get_a(1); let modulus = get_modulus(1); let (z) = ec::run_DOUBLE_EC_POINT_circuit(q, a, modulus); // z := g1.double(q) let (z) = ec::run_ADD_EC_POINT_circuit(q, z, modulus); // z = g1.add(q, z) let (z) = ec::run_DOUBLE_EC_POINT_circuit(z, a, modulus); // z = g1.double(z) let z = double_and_add(z, q, modulus); // z = g1.doubleAndAdd(z, q) let z = double_n_times(z, 2, modulus, a); // z = g1.doubleN(z, 2) let z = double_and_add(z, q, modulus); // z = g1.doubleAndAdd(z, q) let z = double_n_times(z, 8, modulus, a); // z = g1.doubleN(z, 8) let z = double_and_add(z, q, modulus); // z = g1.doubleAndAdd(z, q) let (t0) = ec::run_DOUBLE_EC_POINT_circuit(z, a, modulus); // t0 := g1.double(z) let (t0) = ec::run_ADD_EC_POINT_circuit(z, t0, modulus); // t0 = g1.add(z, t0) let (t0) = ec::run_DOUBLE_EC_POINT_circuit(t0, a, modulus); // t0 = g1.double(t0) let t0 = double_and_add(t0, z, modulus); // t0 = g1.doubleAndAdd(t0, z) let t0 = double_n_times(t0, 2, modulus, a); // t0 = g1.doubleN(t0, 2) let t0 = double_and_add(t0, z, modulus); // t0 = g1.doubleAndAdd(t0, z) let t0 = double_n_times(t0, 8, modulus, a); // t0 = g1.doubleN(t0, 8) let t0 = double_and_add(t0, z, modulus); // t0 = g1.doubleAndAdd(t0, z) let t0 = double_n_times(t0, 31, modulus, a); // t0 = g1.doubleN(t0, 31) let (z) = ec::run_ADD_EC_POINT_circuit(t0, z, modulus); // z = g1.add(t0, z) let z = double_n_times(z, 32, modulus, a); // z = g1.doubleN(z, 32) let z = double_and_add(z, q, modulus); // z = g1.doubleAndAdd(z, q) let z = double_n_times(z, 32, modulus, a); // z = g1.doubleN(z, 32) return z; } pub fn double_n_times(p: G1Point, n: usize, modulus: CircuitModulus, a: u384) -> G1Point { let mut res = p; for _ in 0..n { let (tmp) = ec::run_DOUBLE_EC_POINT_circuit(res, a, modulus); res = tmp; } return res; } // Computes 2*P + Q pub fn double_and_add(p: G1Point, q: G1Point, modulus: CircuitModulus) -> G1Point { let px = CircuitElement::> {}; let py = CircuitElement::> {}; let qx = CircuitElement::> {}; let qy = CircuitElement::> {}; // Compute lambda1 for P + Q let num_lambda1 = circuit_sub(qy, py); let den_lambda1 = circuit_sub(qx, px); let lambda1 = circuit_mul(num_lambda1, circuit_inverse(den_lambda1)); // Compute x-coordinate of P + Q let lambda1_sq = circuit_mul(lambda1, lambda1); let x2 = circuit_sub(lambda1_sq, px); let x2 = circuit_sub(x2, qx); // Compute lambda2 for 2*P let den_lambda2 = circuit_sub(x2, px); let num_lambda2 = circuit_add(py, py); let term2_lambda2 = circuit_mul(num_lambda2, circuit_inverse(den_lambda2)); let lambda2 = circuit_add(lambda1, term2_lambda2); // Compute final coordinates of 2*P + Q let lambda2_sq = circuit_mul(lambda2, lambda2); let tx_temp = circuit_sub(lambda2_sq, px); let result_x = circuit_sub(tx_temp, x2); let tx_sub_px = circuit_sub(result_x, px); let term1_ty = circuit_mul(lambda2, tx_sub_px); let result_y = circuit_sub(term1_ty, py); let outputs = (result_x, result_y) .new_inputs() .next_2(p.x) .next_2(p.y) .next_2(q.x) .next_2(q.y) .done_2() .eval(modulus) .expect('double_and_add failed'); return G1Point { x: outputs.get_output(result_x), y: outputs.get_output(result_y) }; } // Computes 2*(2*(2*(2*(2*(2*(2*(2*P + Q0) + Q1) + Q2) + Q3) + Q4) + Q5) + Q6) + Q7 #[inline(always)] pub fn double_and_add_8( p: G1Point, q0: G1Point, q1: G1Point, q2: G1Point, q3: G1Point, q4: G1Point, q5: G1Point, q6: G1Point, q7: G1Point, modulus: CircuitModulus, ) -> G1Point { let px = CircuitElement::> {}; let py = CircuitElement::> {}; let q0x = CircuitElement::> {}; let q0y = CircuitElement::> {}; let q1x = CircuitElement::> {}; let q1y = CircuitElement::> {}; let q2x = CircuitElement::> {}; let q2y = CircuitElement::> {}; let q3x = CircuitElement::> {}; let q3y = CircuitElement::> {}; let q4x = CircuitElement::> {}; let q4y = CircuitElement::> {}; let q5x = CircuitElement::> {}; let q5y = CircuitElement::> {}; let q6x = CircuitElement::> {}; let q6y = CircuitElement::> {}; let q7x = CircuitElement::> {}; let q7y = CircuitElement::> {}; // --- Step 1: (2 * CurrentP) + Q0 --- let num_lambda1_0 = circuit_sub(q0y, py); let den_lambda1_0 = circuit_sub(q0x, px); let lambda1_0 = circuit_mul(num_lambda1_0, circuit_inverse(den_lambda1_0)); let lambda1_sq_0 = circuit_mul(lambda1_0, lambda1_0); let x2_0 = circuit_sub(lambda1_sq_0, px); let x2_0 = circuit_sub(x2_0, q0x); let den_lambda2_0 = circuit_sub(x2_0, px); let num_lambda2_0 = circuit_add(py, py); let term2_lambda2_0 = circuit_mul(num_lambda2_0, circuit_inverse(den_lambda2_0)); let lambda2_0 = circuit_add(lambda1_0, term2_lambda2_0); let lambda2_sq_0 = circuit_mul(lambda2_0, lambda2_0); let tx_temp_0 = circuit_sub(lambda2_sq_0, px); let T1x = circuit_sub(tx_temp_0, x2_0); let tx_sub_px_0 = circuit_sub(T1x, px); let term1_ty_0 = circuit_mul(lambda2_0, tx_sub_px_0); let T1y = circuit_sub(term1_ty_0, py); // --- Step 2: (2 * CurrentP) + Q1 --- let num_lambda1_1 = circuit_sub(q1y, T1y); let den_lambda1_1 = circuit_sub(q1x, T1x); let lambda1_1 = circuit_mul(num_lambda1_1, circuit_inverse(den_lambda1_1)); let lambda1_sq_1 = circuit_mul(lambda1_1, lambda1_1); let x2_1 = circuit_sub(lambda1_sq_1, T1x); let x2_1 = circuit_sub(x2_1, q1x); let den_lambda2_1 = circuit_sub(x2_1, T1x); let num_lambda2_1 = circuit_add(T1y, T1y); let term2_lambda2_1 = circuit_mul(num_lambda2_1, circuit_inverse(den_lambda2_1)); let lambda2_1 = circuit_add(lambda1_1, term2_lambda2_1); let lambda2_sq_1 = circuit_mul(lambda2_1, lambda2_1); let tx_temp_1 = circuit_sub(lambda2_sq_1, T1x); let T2x = circuit_sub(tx_temp_1, x2_1); let tx_sub_px_1 = circuit_sub(T2x, T1x); let term1_ty_1 = circuit_mul(lambda2_1, tx_sub_px_1); let T2y = circuit_sub(term1_ty_1, T1y); // --- Step 3: (2 * CurrentP) + Q2 --- let num_lambda1_2 = circuit_sub(q2y, T2y); let den_lambda1_2 = circuit_sub(q2x, T2x); let lambda1_2 = circuit_mul(num_lambda1_2, circuit_inverse(den_lambda1_2)); let lambda1_sq_2 = circuit_mul(lambda1_2, lambda1_2); let x2_2 = circuit_sub(lambda1_sq_2, T2x); let x2_2 = circuit_sub(x2_2, q2x); let den_lambda2_2 = circuit_sub(x2_2, T2x); let num_lambda2_2 = circuit_add(T2y, T2y); let term2_lambda2_2 = circuit_mul(num_lambda2_2, circuit_inverse(den_lambda2_2)); let lambda2_2 = circuit_add(lambda1_2, term2_lambda2_2); let lambda2_sq_2 = circuit_mul(lambda2_2, lambda2_2); let tx_temp_2 = circuit_sub(lambda2_sq_2, T2x); let T3x = circuit_sub(tx_temp_2, x2_2); let tx_sub_px_2 = circuit_sub(T3x, T2x); let term1_ty_2 = circuit_mul(lambda2_2, tx_sub_px_2); let T3y = circuit_sub(term1_ty_2, T2y); // --- Step 4: (2 * CurrentP) + Q3 --- let num_lambda1_3 = circuit_sub(q3y, T3y); let den_lambda1_3 = circuit_sub(q3x, T3x); let lambda1_3 = circuit_mul(num_lambda1_3, circuit_inverse(den_lambda1_3)); let lambda1_sq_3 = circuit_mul(lambda1_3, lambda1_3); let x2_3 = circuit_sub(lambda1_sq_3, T3x); let x2_3 = circuit_sub(x2_3, q3x); let den_lambda2_3 = circuit_sub(x2_3, T3x); let num_lambda2_3 = circuit_add(T3y, T3y); let term2_lambda2_3 = circuit_mul(num_lambda2_3, circuit_inverse(den_lambda2_3)); let lambda2_3 = circuit_add(lambda1_3, term2_lambda2_3); let lambda2_sq_3 = circuit_mul(lambda2_3, lambda2_3); let tx_temp_3 = circuit_sub(lambda2_sq_3, T3x); let T4x = circuit_sub(tx_temp_3, x2_3); let tx_sub_px_3 = circuit_sub(T4x, T3x); let term1_ty_3 = circuit_mul(lambda2_3, tx_sub_px_3); let T4y = circuit_sub(term1_ty_3, T3y); // --- Step 5: (2 * CurrentP) + Q4 --- let num_lambda1_4 = circuit_sub(q4y, T4y); let den_lambda1_4 = circuit_sub(q4x, T4x); let lambda1_4 = circuit_mul(num_lambda1_4, circuit_inverse(den_lambda1_4)); let lambda1_sq_4 = circuit_mul(lambda1_4, lambda1_4); let x2_4 = circuit_sub(lambda1_sq_4, T4x); let x2_4 = circuit_sub(x2_4, q4x); let den_lambda2_4 = circuit_sub(x2_4, T4x); let num_lambda2_4 = circuit_add(T4y, T4y); let term2_lambda2_4 = circuit_mul(num_lambda2_4, circuit_inverse(den_lambda2_4)); let lambda2_4 = circuit_add(lambda1_4, term2_lambda2_4); let lambda2_sq_4 = circuit_mul(lambda2_4, lambda2_4); let tx_temp_4 = circuit_sub(lambda2_sq_4, T4x); let T5x = circuit_sub(tx_temp_4, x2_4); let tx_sub_px_4 = circuit_sub(T5x, T4x); let term1_ty_4 = circuit_mul(lambda2_4, tx_sub_px_4); let T5y = circuit_sub(term1_ty_4, T4y); // --- Step 6: (2 * CurrentP) + Q5 --- let num_lambda1_5 = circuit_sub(q5y, T5y); let den_lambda1_5 = circuit_sub(q5x, T5x); let lambda1_5 = circuit_mul(num_lambda1_5, circuit_inverse(den_lambda1_5)); let lambda1_sq_5 = circuit_mul(lambda1_5, lambda1_5); let x2_5 = circuit_sub(lambda1_sq_5, T5x); let x2_5 = circuit_sub(x2_5, q5x); let den_lambda2_5 = circuit_sub(x2_5, T5x); let num_lambda2_5 = circuit_add(T5y, T5y); let term2_lambda2_5 = circuit_mul(num_lambda2_5, circuit_inverse(den_lambda2_5)); let lambda2_5 = circuit_add(lambda1_5, term2_lambda2_5); let lambda2_sq_5 = circuit_mul(lambda2_5, lambda2_5); let tx_temp_5 = circuit_sub(lambda2_sq_5, T5x); let T6x = circuit_sub(tx_temp_5, x2_5); let tx_sub_px_5 = circuit_sub(T6x, T5x); let term1_ty_5 = circuit_mul(lambda2_5, tx_sub_px_5); let T6y = circuit_sub(term1_ty_5, T5y); // --- Step 7: (2 * CurrentP) + Q6 --- let num_lambda1_6 = circuit_sub(q6y, T6y); let den_lambda1_6 = circuit_sub(q6x, T6x); let lambda1_6 = circuit_mul(num_lambda1_6, circuit_inverse(den_lambda1_6)); let lambda1_sq_6 = circuit_mul(lambda1_6, lambda1_6); let x2_6 = circuit_sub(lambda1_sq_6, T6x); let x2_6 = circuit_sub(x2_6, q6x); let den_lambda2_6 = circuit_sub(x2_6, T6x); let num_lambda2_6 = circuit_add(T6y, T6y); let term2_lambda2_6 = circuit_mul(num_lambda2_6, circuit_inverse(den_lambda2_6)); let lambda2_6 = circuit_add(lambda1_6, term2_lambda2_6); let lambda2_sq_6 = circuit_mul(lambda2_6, lambda2_6); let tx_temp_6 = circuit_sub(lambda2_sq_6, T6x); let T7x = circuit_sub(tx_temp_6, x2_6); let tx_sub_px_6 = circuit_sub(T7x, T6x); let term1_ty_6 = circuit_mul(lambda2_6, tx_sub_px_6); let T7y = circuit_sub(term1_ty_6, T6y); // --- Step 8: (2 * CurrentP) + Q7 --- let num_lambda1_7 = circuit_sub(q7y, T7y); let den_lambda1_7 = circuit_sub(q7x, T7x); let lambda1_7 = circuit_mul(num_lambda1_7, circuit_inverse(den_lambda1_7)); let lambda1_sq_7 = circuit_mul(lambda1_7, lambda1_7); let x2_7 = circuit_sub(lambda1_sq_7, T7x); let x2_7 = circuit_sub(x2_7, q7x); let den_lambda2_7 = circuit_sub(x2_7, T7x); let num_lambda2_7 = circuit_add(T7y, T7y); let term2_lambda2_7 = circuit_mul(num_lambda2_7, circuit_inverse(den_lambda2_7)); let lambda2_7 = circuit_add(lambda1_7, term2_lambda2_7); let lambda2_sq_7 = circuit_mul(lambda2_7, lambda2_7); let tx_temp_7 = circuit_sub(lambda2_sq_7, T7x); let T8x = circuit_sub(tx_temp_7, x2_7); let tx_sub_px_7 = circuit_sub(T8x, T7x); let term1_ty_7 = circuit_mul(lambda2_7, tx_sub_px_7); let T8y = circuit_sub(term1_ty_7, T7y); let outputs = (T8x, T8y) .new_inputs() .next_2(p.x) .next_2(p.y) .next_2(q0.x) .next_2(q0.y) .next_2(q1.x) .next_2(q1.y) .next_2(q2.x) .next_2(q2.y) .next_2(q3.x) .next_2(q3.y) .next_2(q4.x) .next_2(q4.y) .next_2(q5.x) .next_2(q5.y) .next_2(q6.x) .next_2(q6.y) .next_2(q7.x) .next_2(q7.y) .done_2() .eval(modulus) .expect('double_and_add_8 failed'); return G1Point { x: outputs.get_output(T8x), y: outputs.get_output(T8y) }; } ================================================ FILE: src/src/ec/ec_ops_g2.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_sub, u384, }; use core::num::traits::Zero; use core::option::Option; use garaga::basic_field_ops::{neg_mod_p, reduce_mod_p}; use garaga::circuits::ec; use garaga::core::circuit::AddInputResultTrait2; use garaga::definitions::{G2Point, G2PointZero, get_a, get_b_twist, get_modulus}; use garaga::utils::u384_assert_zero; #[generate_trait] pub impl G2PointImpl of G2PointTrait { fn assert_on_curve_excluding_infinity(self: @G2Point, curve_index: usize) { let (b20, b21) = get_b_twist(curve_index); let (check0, check1) = ec::run_IS_ON_CURVE_G2_circuit( *self, get_a(curve_index), b20, b21, curve_index, ); u384_assert_zero(check0); u384_assert_zero(check1); } fn is_on_curve_excluding_infinity(self: @G2Point, curve_index: usize) -> bool { let (b20, b21) = get_b_twist(curve_index); let (check0, check1) = ec::run_IS_ON_CURVE_G2_circuit( *self, get_a(curve_index), b20, b21, curve_index, ); return check0.is_zero() && check1.is_zero(); } fn is_infinity(self: @G2Point) -> bool { return self.is_zero(); } fn negate(self: @G2Point, curve_index: usize) -> G2Point { let modulus = get_modulus(curve_index); G2Point { x0: *self.x0, x1: *self.x1, y0: neg_mod_p(*self.y0, modulus), y1: neg_mod_p(*self.y1, modulus), } } fn assert_in_subgroup_excluding_infinity(self: @G2Point, curve_index: usize) { self.assert_on_curve_excluding_infinity(curve_index); match curve_index { 0 => {}, // BN254 (cofactor 1, nothing to do) 1 => { let modulus = get_modulus(curve_index); let (psi_Q) = ec::run_PSI_G2_BLS12_381_circuit(*self, modulus); let seed_Q = scalar_mul_by_bls12_381_seed(*self); if psi_Q != seed_Q { core::panic_with_felt252('bls12-381 pt not in subgroup'); } }, _ => { core::panic_with_felt252('invalid curve index') }, } } } /// G2 Ops for BLS12-381. /// Adds two elliptic curve points on a given curve twist. /// /// # Assumptions /// - The curve equation is of the form y^2 = x^3 + b [Fp2] (i.e. a = 0) for the given curve index. /// - The curve index should be either 0 (BN254) or 1 (BLS12_381). Behavior is undefined otherwise. /// - The points are on the curve (can be the point at infinity as well). /// /// # Returns /// - Point at infinity if the points have the same x coordinate and opposite y coordinates. /// - The result of the addition otherwise. pub fn ec_safe_add_g2(p: G2Point, q: G2Point, curve_index: usize) -> G2Point { if p.is_infinity() { return q; } if q.is_infinity() { return p; } let modulus = get_modulus(curve_index); let same_x = eq_mod_p(p.x0, p.x1, q.x0, q.x1, modulus); if same_x { let opposite_y = eq_neg_mod_p(p.y0, p.y1, q.y0, q.y1, modulus); if opposite_y { return G2PointZero::zero(); // Point at infinity } else { let (res) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(p, modulus); return res; } } else { let (res) = ec::run_ADD_EC_POINTS_G2_circuit(p, q, modulus); return res; } } /// Multiplies a G2 point by a u256 scalar. /// /// # Returns /// - `Option::None` if the point is not on the curve. /// /// # Notes /// - `curve_index` should be either 0 (BN254) or 1 (BLS12_381). Behavior is undefined otherwise. /// - Input points outside of the r-torsion subgroup are supported. pub fn ec_mul(pt: G2Point, s: u256, curve_index: usize) -> Option { if pt.is_zero() { // Input point is at infinity, return it return Option::Some(pt); } else if pt.is_on_curve_excluding_infinity(curve_index) { if s == 0 { return Option::Some(G2PointZero::zero()); } else if s == 1 { return Option::Some(pt); } else { // Point is on the curve. // s is >= 2. let bits = get_bits_little(s); let pt = ec_mul_inner(pt, bits, curve_index); return Option::Some(pt); } } else { // Point is not on the curve return Option::None; } } // Returns the bits of a 256 bit number in little endian format. pub fn get_bits_little(s: u256) -> Array { let mut bits = ArrayTrait::new(); let mut s_low = s.low; while s_low != 0 { let (q, r) = core::traits::DivRem::div_rem(s_low, 2); bits.append(r.into()); s_low = q; } let mut s_high = s.high; if s_high != 0 { while bits.len() != 128 { bits.append(0); } } while s_high != 0 { let (q, r) = core::traits::DivRem::div_rem(s_high, 2); bits.append(r.into()); s_high = q; } bits } // Should not be called outside of ec_mul. // The size of bits array must be at minimum 2 and the point must be strictly on the curve. fn ec_mul_inner(pt: G2Point, mut bits: Array, curve_index: usize) -> G2Point { let mut temp = pt; // 2^0 * pt let mut result: G2Point = G2PointZero::zero(); let modulus = get_modulus(curve_index); // Make sure input x coordinate is reduced mod p before the loop for check inside ec_add_inner. temp.x0 = reduce_mod_p(temp.x0, modulus); temp.x1 = reduce_mod_p(temp.x1, modulus); // Make sure input y coordinate is reduced mod p before the loop for the check before doubling. temp.y0 = reduce_mod_p(temp.y0, modulus); temp.y1 = reduce_mod_p(temp.y1, modulus); for bit in bits { if bit != 0 { result = _ec_add_inner(temp, result, modulus); } if temp.y0.is_zero() && temp.y1.is_zero() { // P = -P. Doubling will result in a point at infinity. temp = G2PointZero::zero(); } else { let (_temp) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(temp, modulus); temp = _temp; // 2^i * pt } } return result; } // Inner add function for ec_mul_inner. // Assumptions: // - The points are on the curve (can be the point at infinity as well) // - p and q have their coordinates in reduced form. #[inline] fn _ec_add_inner(p: G2Point, q: G2Point, modulus: CircuitModulus) -> G2Point { if p.is_infinity() { return q; } if q.is_infinity() { return p; } let same_x = (p.x0 == q.x0 && p.x1 == q.x1); if same_x { let opposite_y = eq_neg_mod_p(p.y0, p.y1, q.y0, q.y1, modulus); if opposite_y { return G2PointZero::zero(); // Point at infinity } else { let (res) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(p, modulus); return res; } } else { let (res) = ec::run_ADD_EC_POINTS_G2_circuit(p, q, modulus); return res; } } // returns true if a == b mod p bls12-381 #[inline] pub fn eq_mod_p(a0: u384, a1: u384, b0: u384, b1: u384, modulus: CircuitModulus) -> bool { let _a0 = CE::> {}; let _a1 = CE::> {}; let _b0 = CE::> {}; let _b1 = CE::> {}; let sub0 = circuit_sub(_a0, _b0); let sub1 = circuit_sub(_a1, _b1); let outputs = (sub0, sub1) .new_inputs() .next_2(a0) .next_2(a1) .next_2(b0) .next_2(b1) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(sub0).is_zero() && outputs.get_output(sub1).is_zero(); } // returns true if a == -b mod p bls12-381 #[inline] pub fn eq_neg_mod_p(a0: u384, a1: u384, b0: u384, b1: u384, modulus: CircuitModulus) -> bool { let _a0 = CE::> {}; let _a1 = CE::> {}; let _b0 = CE::> {}; let _b1 = CE::> {}; let check0 = circuit_add(_a0, _b0); let check1 = circuit_add(_a1, _b1); let outputs = (check0, check1) .new_inputs() .next_2(a0) .next_2(a1) .next_2(b0) .next_2(b1) .done_2() .eval(modulus) .unwrap(); return outputs.get_output(check0).is_zero() && outputs.get_output(check1).is_zero(); } // Computes [x]Q where x is the BLS12-381 seed parameter. // // # Assumptions // - Q lies on the BLS12-381 G2 twist curve // - Q is not the point at infinity // // # Completeness // During the fixed addition chain an intermediate point may become // P = (x, 0). Such a point is a 2-torsion element (order 2) and doubling it // yields the point at infinity, causing the doubling circuit to fail. // // The BLS12-381 G2 twist contains exactly three finite 2-torsion points // (all with y = (0,0)) plus the point at infinity. // // • If the input Q is already in the prime-order subgroup r, // no 2-torsion point can ever be reached; the probability is exactly 0. // • For a uniformly random point of E(Fₚ²) the probability of hitting such an // intermediate is 3 / |E(Fₚ²)| ≈ 2⁻⁷⁶¹, which is cryptographically // negligible. // // Hence the routine is complete for all subgroup inputs and may only fail on // an astronomically small fraction of out-of-subgroup points. // This is acceptable because the function is invoked precisely for subgroup testing. pub fn scalar_mul_by_bls12_381_seed(q: G2Point) -> G2Point { let modulus = get_modulus(1); // Triple. let (z) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(q, modulus); let (z) = ec::run_ADD_EC_POINTS_G2_circuit(z, q, modulus); // Double. let (z) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(z, modulus); // Double and add. let (z) = ec::run_DOUBLE_AND_ADD_EC_POINTS_G2_circuit(z, q, modulus); // Double 2 times. let (z) = double_n_times(z, 2, modulus); // Double and add. let (z) = ec::run_DOUBLE_AND_ADD_EC_POINTS_G2_circuit(z, q, modulus); // Double 8 times. let (z) = double_n_times(z, 8, modulus); // Double and add. let (z) = ec::run_DOUBLE_AND_ADD_EC_POINTS_G2_circuit(z, q, modulus); // Double 31 times. let (z) = double_n_times(z, 31, modulus); // Double and add. let (z) = ec::run_DOUBLE_AND_ADD_EC_POINTS_G2_circuit(z, q, modulus); // Double 16 times. let (z) = double_n_times(z, 16, modulus); return z.negate(1); // Negative seed parameter. } fn double_n_times(p: G2Point, n: usize, modulus: CircuitModulus) -> (G2Point,) { let mut res = p; for _ in 0..n { let (tmp) = ec::run_DOUBLE_EC_POINT_G2_A_EQ_0_circuit(res, modulus); res = tmp; } return (res,); } #[cfg(test)] mod tests { use garaga::definitions::BLS_G2_GENERATOR; use super::{G2Point, G2PointZero, ec_mul, u384}; #[test] fn test_ec_mul_g2() { let g = BLS_G2_GENERATOR; let s = 0; let curve_index = 1; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == G2PointZero::zero()); let s: u256 = 1; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == g); let s: u256 = 2; let g2: G2Point = G2Point { x0: u384 { limb0: 0xf3611b78c952aacab827a053, limb1: 0xe1ea1e1e4d00dbae81f14b0b, limb2: 0xcc7ed5863bc0b995b8825e0e, limb3: 0x1638533957d540a9d2370f17, }, x1: u384 { limb0: 0xb57ec72a6178288c47c33577, limb1: 0x728114d1031e1572c6c886f6, limb2: 0x730a124fd70662a904ba1074, limb3: 0xa4edef9c1ed7f729f520e47, }, y0: u384 { limb0: 0x764bf3bd999d95d71e4c9899, limb1: 0xbfe6bd221e47aa8ae88dece9, limb2: 0x2b5256789a66da69bf91009c, limb3: 0x468fb440d82b0630aeb8dca, }, y1: u384 { limb0: 0xa59c8967acdefd8b6e36ccf3, limb1: 0x97003f7a13c308f5422e1aa0, limb2: 0x3f887136a43253d9c66c4116, limb3: 0xf6d4552fa65dd2638b36154, }, }; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == g2); let s: u256 = 3; let g3: G2Point = G2Point { x0: u384 { limb0: 0x866f09d516020ef82324afae, limb1: 0xa0c75df1c04d6d7a50a030fc, limb2: 0xdccb23ae691ae54329781315, limb3: 0x122915c824a0857e2ee414a3, }, x1: u384 { limb0: 0x937cc6d9d6a44aaa56ca66dc, limb1: 0x5062650f8d251c96eb480673, limb2: 0x7e0550ff2ac480905396eda5, limb3: 0x9380275bbc8e5dcea7dc4dd, }, y0: u384 { limb0: 0x8b52fdf2455e44813ecfd892, limb1: 0x326ac738fef5c721479dfd94, limb2: 0xbc1a6f0136961d1e3b20b1a7, limb3: 0xb21da7955969e61010c7a1a, }, y1: u384 { limb0: 0xb975b9edea56d53f23a0e849, limb1: 0x714150a166bfbd6bcf6b3b58, limb2: 0xa36cfe5f62a7e42e0bf1c1ed, limb3: 0x8f239ba329b3967fe48d718, }, }; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == g3); let s = 0xffffffffffffffffffffffffffffffff; let g4: G2Point = G2Point { x0: u384 { limb0: 0xae40a8b5aee95e54aedee2e7, limb1: 0x6e0699501c5035eed8fc5162, limb2: 0xbee76829b76806d1b6617bf8, limb3: 0x5026c3305c1267922077393, }, x1: u384 { limb0: 0x10c08c4b0a70e02491c3c435, limb1: 0x591ef738050b3ce067e2016f, limb2: 0xdd6e0a179e2ce3c1399c5273, limb3: 0xd5c9af9b97e94f90cb4aba3, }, y0: u384 { limb0: 0x93be53660cebb92c90d4fa87, limb1: 0xfbf63ca94e1d0ffd65801863, limb2: 0xd24fd9a06d72f1dc57f15f0a, limb3: 0x100dbfd4f271378e85171313, }, y1: u384 { limb0: 0xb7296e587409163eecd3ef5d, limb1: 0x8a065d6871fa185d15703e78, limb2: 0x8a85fb95bb90eb5c7a0d81a9, limb3: 0x157cf362e91a3c96640bd973, }, }; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == g4); // let s = 0x100000000000000000000000000000001; let g5: G2Point = G2Point { x0: u384 { limb0: 0x2131be4b061714de5a11407d, limb1: 0xd41318f9bcade1fee985310b, limb2: 0xb2669e638a7b78b7ba5c6751, limb3: 0xa5284fb2911d4e2f445e714, }, x1: u384 { limb0: 0x712edcaf95ed642a8237e6fd, limb1: 0xed6fccd7b64896ebb6ffb3d9, limb2: 0xfcb88d23294a46657b8d2482, limb3: 0x143ef485b660d37036fc18e2, }, y0: u384 { limb0: 0xaa5b7ff57bdbf47e6ab49121, limb1: 0xc14cded56b4a44e022320616, limb2: 0xdd5105feb3fdc5b10edb5afa, limb3: 0x175d2c78538490ce02fcead8, }, y1: u384 { limb0: 0x23893f1bb0fdb0533584b05f, limb1: 0x420d425d79dcd48b26d87814, limb2: 0xc932fa90468e6b9dfd658cc9, limb3: 0xe5fac70e9096e97adc6dd89, }, }; let r = ec_mul(g, s, curve_index).unwrap(); assert!(r == g5); } } ================================================ FILE: src/src/ec/generate_selector_code.py ================================================ # generate_selector_code.py import os # Import os module for path manipulation import subprocess # Import subprocess to run scarb fmt import sys import textwrap # Header content including necessary imports, constants, and impls CAIRO_HEADER = """\ use core::internal::bounded_int; use core::internal::bounded_int::{AddHelper, BoundedInt, DivRemHelper, MulHelper, UnitInt, upcast}; const TWO: felt252 = 2; const TWO_UI: UnitInt = 2; const FOUR_UI: UnitInt = 4; const EIGHT_UI: UnitInt = 8; const TWO_NZ_TYPED: NonZero> = 2; const FOUR_NZ_TYPED: NonZero> = 4; const POW128_DIV_2: felt252 = 0x7fffffffffffffffffffffffffffffff; // ((2^128-1) // 2) const POW128_DIV_4: felt252 = 0x3fffffffffffffffffffffffffffffff; // ((2^128-1) // 4) const POW128: felt252 = 0x100000000000000000000000000000000; const FOUR: felt252 = 4; const EIGHT: felt252 = 8; pub type u15_bi = BoundedInt<0, { 15 }>; pub type u12_bi = BoundedInt<0, { 12 }>; pub type u1_bi = BoundedInt<0, { 1 }>; pub type u2_bi = BoundedInt<0, { 2 }>; pub type u3_bi = BoundedInt<0, { 3 }>; pub type u4_bi = BoundedInt<0, { 4 }>; pub type u5_bi = BoundedInt<0, { 5 }>; pub type u6_bi = BoundedInt<0, { 6 }>; pub type u7_bi = BoundedInt<0, { 7 }>; pub type u8_bi = BoundedInt<0, { 8 }>; impl DivRemU128By2 of DivRemHelper, UnitInt> { type DivT = BoundedInt<0, { POW128_DIV_2 }>; type RemT = u1_bi; } impl DivRemU128By4 of DivRemHelper, UnitInt> { type DivT = BoundedInt<0, { POW128_DIV_4 }>; type RemT = u3_bi; } impl MulHelperBitBy2Impl of MulHelper> { type Result = u2_bi; } impl MulHelperBitBy4Impl of MulHelper> { type Result = u4_bi; } impl MulHelperBit3By4Impl of MulHelper> { type Result = u12_bi; } impl MulHelperBitBy8Impl of MulHelper> { type Result = u8_bi; } impl AddHelperU1ByU2Impl of AddHelper { type Result = u3_bi; } impl AddHelperU3ByU4Impl of AddHelper { type Result = u7_bi; } impl AddHelperU7ByU8Impl of AddHelper { type Result = u15_bi; } impl AddHelperU3ByU12Impl of AddHelper { type Result = u15_bi; } """ # Removed extra newline for cleaner concatenation # Define the new helper function as a string first CAIRO_HELPER_FUNCTION = """\ #[inline(always)] fn _extract_and_calculate_selector_bit_inlined( mut u1: BoundedInt<0, { POW128 - 1 }>, mut u2: BoundedInt<0, { POW128 - 1 }>, mut v1: BoundedInt<0, { POW128 - 1 }>, mut v2: BoundedInt<0, { POW128 - 1 }>, ) -> (BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, u15_bi) { let (qu1, u1b) = bounded_int::div_rem(u1, TWO_NZ_TYPED); let (qu2, u2b) = bounded_int::div_rem(u2, TWO_NZ_TYPED); let (qv1, v1b) = bounded_int::div_rem(v1, TWO_NZ_TYPED); let (qv2, v2b) = bounded_int::div_rem(v2, TWO_NZ_TYPED); u1 = upcast(qu1); u2 = upcast(qu2); v1 = upcast(qv1); v2 = upcast(qv2); let selector: u15_bi = bounded_int::add(bounded_int::add(bounded_int::add(u1b, bounded_int::mul(u2b, TWO_UI)),bounded_int::mul(v1b, FOUR_UI)),bounded_int::mul(v2b, EIGHT_UI)); return (u1, u2, v1, v2, selector); } #[inline(always)] fn _extract_and_calculate_selector_bit_inlined_fake_glv( mut s1: BoundedInt<0, { POW128 - 1 }>, mut s2: BoundedInt<0, { POW128 - 1 }>, ) -> ( BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, u15_bi, ) { let (qs1, s1b) = bounded_int::div_rem(s1, FOUR_NZ_TYPED); let (qs2, s2b) = bounded_int::div_rem(s2, FOUR_NZ_TYPED); s1 = upcast(qs1); s2 = upcast(qs2); let selector: u15_bi = bounded_int::add( s1b, bounded_int::mul(s2b, FOUR_UI), ); return (s1, s2, selector); } """ def generate_build_selectors_inlined(n_bits: int) -> str: """ Generates a complete Cairo module string containing the build_selectors_inlined function, which calls an inlined helper for its main loop. Args: n_bits: The number of bits, determining the loop count. Returns: A string containing the complete generated Cairo module code. Raises: ValueError: If n_bits is not positive. """ if n_bits <= 0: raise ValueError("n_bits must be positive") code = [ "#[inline(always)]", "pub fn build_selectors_inlined(_u1: u128, _u2: u128, _v1: u128, _v2: u128) -> (Span, u128, u128, u128, u128) {", " // Generated code for n_bits = {}".format(n_bits), " let mut selectors: Array = array![];", "", " let mut u1: BoundedInt<0, { POW128 - 1 }> = upcast(_u1);", " let mut u2: BoundedInt<0, { POW128 - 1 }> = upcast(_u2);", " let mut v1: BoundedInt<0, { POW128 - 1 }> = upcast(_v1);", " let mut v2: BoundedInt<0, { POW128 - 1 }> = upcast(_v2);", "", " // Initial division and remainder to get LSBs", " let (qu1, u1lsb) = bounded_int::div_rem(u1, TWO_NZ_TYPED);", " let (qu2, u2lsb) = bounded_int::div_rem(u2, TWO_NZ_TYPED);", " let (qv1, v1lsb) = bounded_int::div_rem(v1, TWO_NZ_TYPED);", " let (qv2, v2lsb) = bounded_int::div_rem(v2, TWO_NZ_TYPED);", " u1 = upcast(qu1);", " u2 = upcast(qu2);", " v1 = upcast(qv1);", " v2 = upcast(qv2);", "", f" // Inlined loop ({n_bits - 1} iterations)", ] for i in range(n_bits - 2): code.extend( [ f" let (u1, u2, v1, v2, selector_{i}) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2);", f" selectors.append(upcast(selector_{i}));", ] ) code.extend( [ f" let (_, _, _, _, selector_{n_bits - 2}) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2);", f" selectors.append(upcast(selector_{n_bits - 2}));", ] ) code.append( " return (selectors.span(), upcast(u1lsb), upcast(u2lsb), upcast(v1lsb), upcast(v2lsb));" ) code.append("}") function_body_str = "\n".join(code[1:]) indented_body = textwrap.indent(function_body_str, " ") generated_function_code = code[0] + "\n" + indented_body # Combine header, helper function, and main generated function return CAIRO_HEADER + "\n" + CAIRO_HELPER_FUNCTION + "\n" + generated_function_code def generate_build_selectors_inlined_fake_glv(n_bits: int = 128) -> str: """ Generates a complete Cairo module string containing the build_selectors_inlined function, which calls an inlined helper for its main loop. Args: n_bits: The number of bits, determining the loop count. Returns: A string containing the complete generated Cairo module code. Raises: ValueError: If n_bits is not positive. """ if n_bits <= 0: raise ValueError("n_bits must be positive") code = [ "#[inline(always)]", "pub fn build_selectors_inlined_fake_glv(_s1: u128, _s2: u128) -> (Span, u128, u128) {", " // Generated code for n_bits = {}".format(n_bits), " let mut selectors: Array = array![];", "", " let mut s1: BoundedInt<0, { POW128 - 1 }> = upcast(_s1);", " let mut s2: BoundedInt<0, { POW128 - 1 }> = upcast(_s2);", "", " // Initial division and remainder to get LSBs", " let (qs1, s1lsb) = bounded_int::div_rem(s1, TWO_NZ_TYPED);", " let (qs2, s2lsb) = bounded_int::div_rem(s2, TWO_NZ_TYPED);", " s1 = upcast(qs1);", " s2 = upcast(qs2);", "", f" // Inlined loop (63 2-bit iterations for 128 bits)", ] for i in range(63): code.extend( [ f" let (s1, s2, selector_{i}) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2);", f" selectors.append(upcast(selector_{i}));", ] ) if i == 0: code.extend( [ " // Correction for the last bits 2-1.", " selectors.append(16);", ] ) code.extend( [ "// At this point s1, and s2 are the MSB (last bit).", " if s1 != 0 {", " if s2 != 0 {", " // 11 T2 index : 10", " selectors.append(10);", " } else {", " // 10 T12 index : 6", " selectors.append(6);", " }", " } else {", " if s2 != 0 {", " // 01 T15 index : 9", " selectors.append(9);", " } else {", " // 00 T5 index : 5", " selectors.append(5);", " }", " }", " return (selectors.span(), upcast(s1lsb), upcast(s2lsb));", ] ) code.append("}") function_body_str = "\n".join(code[1:]) indented_body = textwrap.indent(function_body_str, " ") generated_function_code = code[0] + "\n" + indented_body # Combine header, helper function, and main generated function return generated_function_code def generate_double_and_add_n(n_points: int) -> str: """ Generates Cairo code for a double_and_add function variant that processes n_points additions. Assumes necessary imports (G1Point, CircuitElement, CircuitInput, CircuitModulus, circuit_add, circuit_sub, circuit_mul, circuit_inverse, etc.) are in scope. Args: n_points: The number of Q points to add (e.g., 1, 2, 4, 8). Returns: A string containing the generated Cairo function code. """ if n_points not in [1, 2, 4, 8]: # Or check if it's a power of 2 raise ValueError( "n_points must be 1, 2, 4, or 8 for this specific generator pattern" ) func_name = f"double_and_add_{n_points}" if n_points == 1: func_name = "double_and_add" # Match original naming for n=1 # Function signature q_params = [f"q{i}: G1Point" for i in range(n_points)] signature = f"pub fn {func_name}(p: G1Point, {', '.join(q_params)}, modulus: CircuitModulus) -> G1Point {{" lines = ["#[inline(always)]", signature] # CircuitElement inputs lines.append(f" let px = CircuitElement::> {{}}; ") lines.append(f" let py = CircuitElement::> {{}}; ") for i in range(n_points): lines.append( f" let q{i}x = CircuitElement::> {{}}; " ) lines.append( f" let q{i}y = CircuitElement::> {{}}; " ) lines.append("") current_px = "px" current_py = "py" next_tx = "" next_ty = "" # Doubling and Adding loop for i in range(n_points): lines.append(f" // --- Step {i+1}: (2 * CurrentP) + Q{i} --- ") qix = f"q{i}x" qiy = f"q{i}y" # Compute λ1 = (qiy - current_py) / (qix - current_px) lines.append(f" let num_lambda1_{i} = circuit_sub({qiy}, {current_py});") lines.append(f" let den_lambda1_{i} = circuit_sub({qix}, {current_px});") lines.append( f" let lambda1_{i} = circuit_mul(num_lambda1_{i}, circuit_inverse(den_lambda1_{i}));" ) lines.append("") # Compute x2 = λ1² - current_px - qix lines.append(f" let lambda1_sq_{i} = circuit_mul(lambda1_{i}, lambda1_{i});") lines.append(f" let x2_{i} = circuit_sub(lambda1_sq_{i}, {current_px});") lines.append(f" let x2_{i} = circuit_sub(x2_{i}, {qix});") lines.append("") # Compute -λ2 = λ1 + 2 * current_py / (x2 - current_px) lines.append(f" let den_lambda2_{i} = circuit_sub(x2_{i}, {current_px});") lines.append( f" let num_lambda2_{i} = circuit_add({current_py}, {current_py});" ) lines.append( f" let term2_lambda2_{i} = circuit_mul(num_lambda2_{i}, circuit_inverse(den_lambda2_{i}));" ) lines.append( f" let lambda2_{i} = circuit_add(lambda1_{i}, term2_lambda2_{i});" ) lines.append("") # Compute intermediate Tx = (-λ2)² - current_px - x2 lines.append(f" let lambda2_sq_{i} = circuit_mul(lambda2_{i}, lambda2_{i});") lines.append( f" let tx_temp_{i} = circuit_sub(lambda2_sq_{i}, {current_px});" ) next_tx = f"T{i+1}x" lines.append(f" let {next_tx} = circuit_sub(tx_temp_{i}, x2_{i});") lines.append("") # Compute intermediate Ty = -λ2 * (Tx - current_px) - current_py lines.append(f" let tx_sub_px_{i} = circuit_sub({next_tx}, {current_px});") lines.append(f" let term1_ty_{i} = circuit_mul(lambda2_{i}, tx_sub_px_{i});") next_ty = f"T{i+1}y" lines.append( f" let {next_ty} = circuit_sub(term1_ty_{i}, {current_py});" ) # Note: lambda2 corresponds to -lambda2 in standard formulas lines.append("") # Update current P for the next iteration current_px = next_tx current_py = next_ty # Final outputs and evaluation final_x = current_px final_y = current_py lines.append(f" let outputs = ({final_x}, {final_y})") lines.append(f" .new_inputs()") lines.append(f" .next_2(p.x)") lines.append(f" .next_2(p.y)") for i in range(n_points): lines.append(f" .next_2(q{i}.x)") lines.append(f" .next_2(q{i}.y)") lines.append(f" .done_2()") lines.append(f" .eval(modulus)") lines.append(f" .expect('{func_name} failed');") lines.append("") lines.append( f" return G1Point {{ x: outputs.get_output({final_x}), y: outputs.get_output({final_y}) }};" ) lines.append("}") # Join lines with proper indentation # Indent lines starting from the third line (index 2) indented_body = textwrap.indent("\n".join(lines[2:]), " ") return "\n".join(lines[:2]) + "\n" + indented_body if __name__ == "__main__": # Example usage: Generate selectors.cairo with n_bits=71 (default/example) # To generate double_and_add_8, you might run this script differently # or integrate argument parsing. For now, demonstrating selector generation. # --- Selector Generation --- try: n_bits_arg = 73 # Default or example value if len(sys.argv) > 1: try: n_bits_arg = int(sys.argv[1]) except ValueError: print( "Warning: Invalid integer for n_bits, using default {}. Usage: python ... ".format( n_bits_arg ) ) if n_bits_arg < 1: raise ValueError("n_bits must be at least 1") # Generate the complete Cairo code for selectors generated_cairo_code_selectors = generate_build_selectors_inlined(n_bits_arg) generated_cairo_code_selectors_fake_glv = ( generate_build_selectors_inlined_fake_glv() ) # Define the output file path output_file_path_selectors = "src/src/ec/selectors.cairo" # Write the generated code to the file with open(output_file_path_selectors, "w") as f: f.write( generated_cairo_code_selectors + "\n\n" + generated_cairo_code_selectors_fake_glv ) print( f"Successfully generated Cairo code to {output_file_path_selectors} for n_bits = {n_bits_arg}" ) # Format the generated file using scarb fmt try: print( f"Attempting to format {output_file_path_selectors} using scarb fmt..." ) process = subprocess.run( ["scarb", "fmt", output_file_path_selectors], check=True, capture_output=True, text=True, ) print("Formatting successful.") except FileNotFoundError: print( "Error: 'scarb' command not found. Please ensure Scarb is installed and in your PATH." ) except subprocess.CalledProcessError as e: print(f"Error during formatting: {e}") print(f"scarb fmt stdout:\n{e.stdout}") print(f"scarb fmt stderr:\n{e.stderr}") except ValueError as e: print(f"Error generating selectors: {e}") # Decide if we should exit here or continue to double_and_add generation except Exception as e: print(f"An unexpected error occurred during selector generation: {e}") print("\n" + "-" * 20 + "\n") # --- Double and Add 8 Generation (Example) --- try: n_points_to_gen = 8 print(f"Generating Cairo code for double_and_add_{n_points_to_gen}...") generated_double_add_code = generate_double_and_add_n(n_points_to_gen) # Print the generated code to console (or write to a file) print(f"\n// --- Generated code for double_and_add_{n_points_to_gen} ---") print("// Add this function to your ec_ops.cairo or similar file.") print( "// Ensure necessary imports and structs (G1Point, CircuitElement, etc.) are available." ) print(generated_double_add_code) # Example: Write to a separate file # output_file_path_double_add = f"src/src/ec/double_and_add_{n_points_to_gen}_generated.cairo" # with open(output_file_path_double_add, 'w') as f: # f.write("// NOTE: This file needs imports like G1Point, circuit ops etc.\n") # f.write(generated_double_add_code) # print(f"\nCode also written to {output_file_path_double_add}") # # Optionally format this file too # try: # subprocess.run(["scarb", "fmt", output_file_path_double_add], check=True) # except Exception as fmt_e: # print(f"Could not format {output_file_path_double_add}: {fmt_e}") except ValueError as e: print(f"Error generating double_and_add: {e}") except Exception as e: print(f"An unexpected error occurred during double_and_add generation: {e}") sys.exit(1) ================================================ FILE: src/src/ec/pairing/groth16.cairo ================================================ /// This file contains utilities to verify a pairing check of the form : /// e(P1, Qf1) * e(P2, Qf2) * e(P3, Q3) * e(Pf4, Qf4) == 1, where /// - Qf1 and Qf2 are fixed known G2 points. /// - Pf4 and Qf4 is a fixed pair of G1 and G2 points. /// The result of e(Pf4, Qf4) is precomputed and provided to the circuit as a the miller loop result /// precomputed_miller_loop_result = MillerLoop(Pf4, Qf4) ∈ Gt/Fp12. /// /// MultiPairing chekcs circuit in the "3P_2F" mode is used for triple pairs and double fixed G2 /// points /// /// Qf1 and Qf2 are represented by their pre-computed line functions for the specifc miller loop /// implementation. /// /// Two functions are provided for BN254 and BLS12-381 respectively. /// To generate the lines functions and the precomputed miller loop result, refer to garaga's /// documentation. /// /// Moreover, the file contains the full groth16 verification function for BN254 and BLS12-381. use core::circuit::u384; use core::num::traits::{One, Zero}; use core::option::Option; use garaga::basic_field_ops; use garaga::basic_field_ops::neg_mod_p; use garaga::circuits::multi_pairing_check as mpc; use garaga::circuits::multi_pairing_check::{ run_BLS12_381_INITIALIZE_MPCHECK_EXT_MLR_circuit, run_BLS12_381_MP_CHECK_PREPARE_PAIRS_3P_circuit, run_BN254_INITIALIZE_MPCHECK_EXT_MLR_circuit, run_BN254_MP_CHECK_PREPARE_PAIRS_1P_circuit, }; use garaga::definitions::{ BLS12_381_SEED_BITS_COMPRESSED, BN254_SEED_BITS_JY00_COMPRESSED, E12D, G1G2Pair, G1Point, G2Line, G2Point, get_BN254_modulus, get_modulus, u288, }; use garaga::ec_ops::{G1PointTrait, ec_safe_add, msm_g1}; use garaga::ec_ops_g2::G2PointTrait; use garaga::pairing_check::{ BLSProcessedPair, BNProcessedPair, MPCheckHintBLS12_381, MPCheckHintBN254, compute_yInvXnegOverY, }; use garaga::utils::hashing; use garaga::utils::hashing::{PoseidonState, TWO_POW_96}; #[derive(Copy, Drop, Serde, Debug, PartialEq)] pub struct Groth16ProofRaw { pub a: G1Point, pub b: G2Point, pub c: G1Point, } // Groth16 proof structure, generic for both BN254 and BLS12-381. #[derive(Copy, Drop, Serde, Debug, PartialEq)] pub struct Groth16Proof { pub raw: Groth16ProofRaw, pub public_inputs: Span, } // Groth16 verifying key structure, consisting of the two fixed G2 points and the precomputed // miller loop result miller_loop(alpha, beta) // Does not include gamma and delta lines inside, although it should be part of the key. // Does not include IC either as its size is not fixed and we want to write it as constant in smart // contracts. #[derive(Drop)] pub struct Groth16VerifyingKey { pub alpha_beta_miller_loop_result: E12D, pub gamma_g2: G2Point, pub delta_g2: G2Point, } #[generate_trait] pub impl Groth16RawProofImpl of Groth16ProofRawTrait { fn check_proof_points(self: @Groth16ProofRaw, curve_id: u32) { self.a.assert_in_subgroup_excluding_infinity(curve_id); self.b.assert_in_subgroup_excluding_infinity(curve_id); self.c.assert_in_subgroup_excluding_infinity(curve_id); } } #[inline] fn _groth16_get_vk_x( proof: Groth16Proof, ic: Span, public_inputs_msm_hint: Span, curve_id: u32, ) -> G1Point { let vk_x_x: G1Point = msm_g1( ic.slice(1, ic.len() - 1), proof.public_inputs, curve_id, public_inputs_msm_hint, ); let vk_x = ec_safe_add(vk_x_x, *ic.at(0), curve_id); return vk_x; } // Verify a groth16 proof for BN254. // Parameters: // - proof: the proof to verify // - verification_key: the verifying key // - lines: the lines of the gamma and delta points. Must correspond to the ones of gamma and // delta. // - ic: the points in the VK corresponding to the public inputs. The length must correspond to the // number of public inputs in the proof. // - public_inputs_msm_hint: the MSM hint of the public inputs // - mpcheck_hint: the MPCheck hint of the proof pub fn verify_groth16_bn254( verification_key: Groth16VerifyingKey, mut lines: Span>, ic: Span, proof: Groth16Proof, public_inputs_msm_hint: Span, mpcheck_hint: MPCheckHintBN254, ) -> Result, felt252> { proof.raw.check_proof_points(0); let vk_x = _groth16_get_vk_x(proof, ic, public_inputs_msm_hint, 0); let check = multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: verification_key.gamma_g2 }, G1G2Pair { p: proof.raw.c, q: verification_key.delta_g2 }, G1G2Pair { p: proof.raw.a.negate(0), q: proof.raw.b }, verification_key.alpha_beta_miller_loop_result, lines, mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(proof.public_inputs), Result::Err(error) => Result::Err(error), } } // Verify a groth16 proof for BN254. // Parameters: // - proof: the proof to verify // - verification_key: the verifying key // - lines: the lines of the gamma and delta points. Must correspond to the ones of gamma and // delta. // - ic: the points in the VK corresponding to the public inputs. The length must correspond to the // number of public inputs in the proof. // - public_inputs_msm_hint: the MSM hint of the public inputs // - mpcheck_hint: the MPCheck hint of the proof pub fn verify_groth16_bls12_381( proof: Groth16Proof, verification_key: Groth16VerifyingKey, mut lines: Span>, ic: Span, public_inputs_msm_hint: Span, mpcheck_hint: MPCheckHintBLS12_381, ) -> Result, felt252> { proof.raw.check_proof_points(1); let vk_x = _groth16_get_vk_x(proof, ic, public_inputs_msm_hint, 1); let check = multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result( G1G2Pair { p: vk_x, q: verification_key.gamma_g2 }, G1G2Pair { p: proof.raw.c, q: verification_key.delta_g2 }, G1G2Pair { p: proof.raw.a.negate(1), q: proof.raw.b }, verification_key.alpha_beta_miller_loop_result, lines, mpcheck_hint, ); match check { Result::Ok(_) => Result::Ok(proof.public_inputs), Result::Err(error) => Result::Err(error), } } // This function verifies that // miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result * // hint.MillerLoopResultScalingFactor == hint.lambda_root ^ λ (1) // <=> e(P0, Q0) * e(P1, Q1) * e(P2, Q2) * final_exp(precomputed_miller_loop_result) == 1 (2) // It is based on the paper "On Proving Pairings" by Andrija Novakovic and Liam Eagen: // https://eprint.iacr.org/2024/640 to eliminate the cost of the final exponentiation. // Where : // - Q1 and Q2 are known G2 points, represented by their precomputed lines functions. // - λ = 6x + 2 + q - q^2 + q^3 with x the seed of the bn curve, and q the prime modulus of // the base field. // - MillerLoopResultScalingFactor is a factor lying in the Fq6 subfield such that it makes // miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result a lambda // residue. // To compute efficiently lambda_root^λ in (1) and take advantage of the squarings in the miller // function that is iterating over the bits of x, we initialize the miller loop result to // (1/hint.lambda_root), obtaining as an intermediate result in M = (f/hint.lambda_root^x), // where f = miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result. // // Finally, we verify that M * hint.MillerLoopResultScalingFactor * (1/hint.lambda_root)^q == 1, // using the Frobenius endomorphism for cheap exponentiation by q. // On top of this, all extension fields multiplications are verified and batched using // randomized extension field arithmetic. // For each bit of the miller loop (0, 1, -1, or 00), we compute the next miller loop intermediate, // depending on the bit case: // // - 0: f₍ᵢ₊₁₎ = fᵢ² * Πⱼ (Lᵢⱼ), // - (+1): f₍ᵢ₊₁₎ = fᵢ² * Πⱼ (Lᵢⱼ) * (1/lambda_root) // - (-1): f₍ᵢ₊₁₎ = fᵢ² * Πⱼ (Lᵢⱼ) * (lambda_root) // - 00: f₍ᵢ₊₂₎ = (fᵢ² * Πⱼ (Lᵢⱼ) )² * Πⱼ (L₍ᵢ₊₁₎ⱼ) // // where Lᵢⱼ is the j-th line of the i-th bit of the miller loop, evaluated at point Pⱼ. // Since we have 3 pairs, for bit "0", we have 3 lines, and for bit "1", we have 6 lines. // Instead of performing full extension field multiplications, we ask the caller to provide as hint // all the fᵢ as Fq12 elements inside hint.Ris. // We then hash (s₀, c₀, _) = Poseidon(Pair₀, Pair₁, Pair₂, // hint.MillerLoopResultScalingFactor, hint.Ris) // And we use the definition cᵢ₊₁ = cᵢ² to derive a random coefficient for all relations. // We also ask the prover to provide a quotient polynomial big_Q such that // Σᵢ cᵢ * (fᵢ₋₁)² * Πⱼ (Lᵢⱼ) = big_Q * P_irr + Σᵢ cᵢ * fᵢ , where P_irr // is the irreducible polynomial of the extension field. // From this, we derive a random point z = Poseidon(s0, hint.big_Q) // And finally verify that // Σᵢ cᵢ * (fᵢ₋₁(z))² * Πⱼ (Lᵢⱼ(z)) = big_Q(z) * P_irr(z) + Σᵢ cᵢ * fᵢ(z), // reusing fᵢ(z) evaluations in the next step. #[inline] pub fn multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( pair0: G1G2Pair, pair1: G1G2Pair, pair2: G1G2Pair, precomputed_miller_loop_result: E12D, mut lines: Span>, mpcheck_hint: MPCheckHintBN254, ) -> Result { if mpcheck_hint.big_Q.len() != 190 { return Result::Err('WRONG_BIG_Q_LEN'); } if mpcheck_hint.Ris.len() != 34 { return Result::Err('WRONG_RIS_LEN'); } let modulus = get_BN254_modulus(); // BN254 prime field modulus let (yInv_0, xNegOverY_0) = compute_yInvXnegOverY(pair0.p.x, pair0.p.y, modulus); let (yInv_1, xNegOverY_1) = compute_yInvXnegOverY(pair1.p.x, pair1.p.y, modulus); let (processed_pair2): (BNProcessedPair,) = run_BN254_MP_CHECK_PREPARE_PAIRS_1P_circuit( pair2.p, pair2.q.y0, pair2.q.y1, ); // Init sponge state == hades_permutation(0, 0, int.from_bytes(b"MPCHECK_BN254_3P_2F", "big")) let hash_state = PoseidonState { s0: 0x63dd5cf2946ee642aef494d22ee96f6e9168664a2f9c485a6084bd03289b83f, s1: 0x22380e74267f899ea972f4f0fc327a181ed44093d778c9ad778437c7a41e418, s2: 0x3c3e169429d0a04b80b97617d27b5b37b8e7734bf57faaffc841b8f2cfb6bc7, }; // Hash Inputs let hash_state = hashing::hash_G1G2Pair(pair0, hash_state); let hash_state = hashing::hash_G1G2Pair(pair1, hash_state); let hash_state = hashing::hash_G1G2Pair(pair2, hash_state); let hash_state = hashing::hash_E12D_u288(mpcheck_hint.lambda_root, hash_state); let hash_state = hashing::hash_E12D_u288(mpcheck_hint.lambda_root_inverse, hash_state); let hash_state = hashing::hash_MillerLoopResultScalingFactor_u288(mpcheck_hint.w, hash_state); // Hash Ris to obtain base random coefficient c1 let z: u384 = mpcheck_hint.z.into(); let (hash_state, mut evals) = basic_field_ops::eval_and_hash_E12D_u288_transcript( mpcheck_hint.Ris, hash_state, z, ); let hash_state = hashing::hash_E12D_one_u288(hash_state); let hash_state = hashing::hash_E12D_u288(precomputed_miller_loop_result, hash_state); let mut evals = evals.span(); let c_1: u384 = hash_state.s1.into(); // hades_permutation(0,0,int.from_bytes(b"MPCHECK_BN254_3P_2F_II", "big")) let part_II_state = PoseidonState { s0: 0xe973a7c87240c35289f5fdac2ea94f1848022f9499f37b4ab94172b6742649, s1: 0x30d584d4a24b6615090c37103916bac45ed17401b63596cd0c29167e5fe1267, s2: 0x2073c3846b613a00ccc615a8ac460c372105a979ddde4ef9d484c15aca2b874, }; let hash_state = hashing::hash_u384(c_1, TWO_POW_96, part_II_state); // Hash Q = (Σ_i c_i*Q_i) to obtain random evaluation point z let z_felt252 = hashing::hash_u288_transcript(mpcheck_hint.big_Q.span(), hash_state).s0; if z_felt252 != mpcheck_hint.z { return Result::Err('WRONG_Z'); } let ( c_of_z, w_of_z, c_inv_of_z, LHS, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, mlr_of_z, ): (u384, u384, u384, u384, u384, u384, u384, u384) = run_BN254_INITIALIZE_MPCHECK_EXT_MLR_circuit( mpcheck_hint.lambda_root, z, mpcheck_hint.w, mpcheck_hint.lambda_root_inverse, precomputed_miller_loop_result, ); // init bit for bn254 is 0: // let mut Ris = mpcheck_hint.Ris; let R_0_of_Z = *evals.pop_front().unwrap(); let [l0, l1] = (*lines.multi_pop_front::<2>().unwrap()).unbox(); let (_Q2, _lhs) = mpc::run_BN254_MP_CHECK_INIT_BIT_3P_2F_circuit( yInv_0, xNegOverY_0, l0, yInv_1, xNegOverY_1, l1, processed_pair2.yInv, processed_pair2.xNegOverY, pair2.q, R_0_of_Z, z, c_inv_of_z, c_1, LHS, ); let mut Q2 = _Q2; let mut LHS = _lhs; let mut f_i_of_z = R_0_of_Z; // rest of miller loop let mut bits = BN254_SEED_BITS_JY00_COMPRESSED.span(); while let Option::Some(bit) = bits.pop_front() { let R_i_of_z = *evals.pop_front().unwrap(); let (_Q2, _LHS): (G2Point, u384) = match *bit { 0 => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); mpc::run_BN254_MP_CHECK_BIT00_3P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, 1 | 2 => { // 1 -> 10 // 2 -> -10 let [l0, l1, l2, l3, l4, l5] = (*lines.multi_pop_front::<6>().unwrap()).unbox(); let (Q_or_Q_neg, c_or_c_inv_of_z) = match (*bit - 1) { 0 => (pair2.q, c_inv_of_z), _ => ( G2Point { x0: pair2.q.x0, x1: pair2.q.x1, y0: processed_pair2.QyNeg0, y1: processed_pair2.QyNeg1, }, c_of_z, ), }; mpc::run_BN254_MP_CHECK_BIT10_3P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, l2, yInv_1, xNegOverY_1, l3, l4, l5, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, Q_or_Q_neg, LHS, f_i_of_z, R_i_of_z, c_or_c_inv_of_z, z, c_1, ) }, _ => { // 3 -> 01, 4 -> 0-1 let [l0, l1, l2, l3, l4, l5] = (*lines.multi_pop_front::<6>().unwrap()).unbox(); let (Q_or_Q_neg, c_or_c_inv_of_z) = match (*bit - 3) { 0 => (pair2.q, c_inv_of_z), _ => ( G2Point { x0: pair2.q.x0, x1: pair2.q.x1, y0: processed_pair2.QyNeg0, y1: processed_pair2.QyNeg1, }, c_of_z, ), }; mpc::run_BN254_MP_CHECK_BIT01_3P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, l2, yInv_1, xNegOverY_1, l3, l4, l5, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, Q_or_Q_neg, LHS, f_i_of_z, R_i_of_z, c_or_c_inv_of_z, z, c_1, ) }, }; Q2 = _Q2; LHS = _LHS; f_i_of_z = R_i_of_z; } let R_n_minus_2_of_z = *evals.pop_front().unwrap(); let R_n_minus_1_of_z: u384 = One::one(); let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); let (check) = mpc::run_BN254_MP_CHECK_FINALIZE_3P_2F_EXT_MLR_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, pair2.q, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, R_n_minus_2_of_z, R_n_minus_1_of_z, c_1, w_of_z, z, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, LHS, f_i_of_z, mpcheck_hint.big_Q, mlr_of_z, ); // Checks that LHS = Q(z) * P_irr(z) match check.is_zero() { true => Result::Ok(true), false => Result::Err('FINAL_CHECK_FAILED'), } } // This function verifies that // miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result * // hint.MillerLoopResultScalingFactor == hint.lambda_root ^ λ (1) // <=> e(P0, Q0) * e(P1, Q1) * e(P2, Q2) * final_exp(precomputed_miller_loop_result) == 1 (2) // It is based on the paper "On Proving Pairings" by Andrija Novakovic and Liam Eagen: // https://eprint.iacr.org/2024/640 to eliminate the cost of the final exponentiation. // Where : // - Q1 and Q2 are known G2 points, represented by their precomputed lines functions. // - λ = -x + q, with x the seed of the bls curve, and q the prime modulus of the base field. // - MillerLoopResultScalingFactor is a factor lying in the Fq6 subfield such that it makes // miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result a lambda // residue. // To compute efficiently lambda_root^λ in (1) and take advantage of the squarings in the miller // function that is iterating over the bits of x, we initialize the miller loop result to // (1/hint.lambda_root), obtaining as an intermediate result in M = (f/hint.lambda_root^x), // where f = miller(P0, Q0) * miller(P1, Q1) * miller(P2, Q2) * precomputed_miller_loop_result. // // Finally, we verify that M * hint.MillerLoopResultScalingFactor * (1/hint.lambda_root)^q == 1, // using the Frobenius endomorphism for cheap exponentiation by q. // On top of this, all extension fields multiplications are verified and batched using // randomized extension field arithmetic. // For each bit of the miller loop (0, 1, or 00), we compute the next miller loop intermediate, // depending on the bit case: // // - 0: f₍ᵢ₊₁₎ = fᵢ² * Πⱼ (Lᵢⱼ), // - 1: f₍ᵢ₊₁₎ = fᵢ² * Πⱼ (Lᵢⱼ) * (1/lambda_root) // - 00: f₍ᵢ₊₂₎ = (fᵢ² * Πⱼ (Lᵢⱼ) )² * Πⱼ (L₍ᵢ₊₁₎ⱼ) // // where Lᵢⱼ is the j-th line of the i-th bit of the miller loop. // Since we have 3 pairs, for bit "0", we have 3 lines, and for bit "1", we have 6 lines. // Instead of performing full extension field multiplications, we ask the caller to provide as hint // all the fᵢ as Fq12 elements inside hint.Ris. // We then hash (s₀, c₀, _) = Poseidon(Pair₀, Pair₁, Pair₂, // hint.MillerLoopResultScalingFactor, hint.Ris) // And we use the definition cᵢ₊₁ = cᵢ² to derive a random coefficient for all relations. // We also ask the prover to provide a quotient polynomial big_Q such that // Σᵢ cᵢ * (fᵢ₋₁)² * Πⱼ (Lᵢⱼ) = big_Q * P_irr + Σᵢ cᵢ * fᵢ , where P_irr // is the irreducible polynomial of the extension field. // From this, we derive a random point z = Poseidon(s0, hint.big_Q) // And finally verify that // Σᵢ cᵢ * (fᵢ₋₁(z))² * Πⱼ (Lᵢⱼ(z)) = big_Q(z) * P_irr(z) + Σᵢ cᵢ * fᵢ(z), // reusing fᵢ(z) evaluations in the next step. #[inline] pub fn multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result( pair0: G1G2Pair, pair1: G1G2Pair, pair2: G1G2Pair, precomputed_miller_loop_result: E12D, mut lines: Span>, hint: MPCheckHintBLS12_381, ) -> Result { if hint.big_Q.len() != 105 { return Result::Err('WRONG_BIG_Q_LEN'); } if hint.Ris.len() != 35 { return Result::Err('WRONG_RIS_LEN'); } let ( processed_pair0, processed_pair1, processed_pair2, ): (BLSProcessedPair, BLSProcessedPair, BLSProcessedPair) = run_BLS12_381_MP_CHECK_PREPARE_PAIRS_3P_circuit( pair0.p, pair1.p, pair2.p, ); // Init sponge state : // >>> hades_permutation(0, 0, int.from_bytes(b"MPCHECK_BLS12_381_3P_2F", "big")) let hash_state = PoseidonState { s0: 0x2cdfabd228064e9e12d17c6b3c59bff3db6b737403a03e9b5f5e9f53409097b, s1: 0x37fe3519c1f442f6e45b0abd23d975f1937365ed27e08019d58d011269ecac2, s2: 0x2eec9f98b93d8f14927c5de60386404306a0e55acb61076c1ad847b456efe0e, }; // Hash Inputs. let hash_state = hashing::hash_G1G2Pair(pair0, hash_state); let hash_state = hashing::hash_G1G2Pair(pair1, hash_state); let hash_state = hashing::hash_G1G2Pair(pair2, hash_state); let hash_state = hashing::hash_E12D_u384(hint.lambda_root_inverse, hash_state); let hash_state = hashing::hash_MillerLoopResultScalingFactor_u384(hint.w, hash_state); // Hash Ris to obtain base random coefficient c0 let z: u384 = hint.z.into(); let (hash_state, mut evals) = basic_field_ops::eval_and_hash_E12D_u384_transcript( hint.Ris, hash_state, z, ); let hash_state = hashing::hash_E12D_one_u384(hash_state); let hash_state = hashing::hash_E12D_u384(precomputed_miller_loop_result, hash_state); let mut evals = evals.span(); let c_1: u384 = hash_state.s1.into(); // hades_permutation(0,0,int.from_bytes(b"MPCHECK_BLS12_381_3P_2F_II", "big")) let part_II_state = PoseidonState { s0: 0x145195a6df395d777bf1be74601510cbf888ca638394385ade2f0bd91396a34, s1: 0x1f144143bab9bbc63c8376ae067c0b15ae4611b1aa725dd654cd41c25e0c20f, s2: 0x25df9ac859e9e9db19383887d5c27d94b619b6c8d1de37b8e713cb653f7b55f, }; let hash_state = hashing::hash_u384(c_1, TWO_POW_96, part_II_state); // Hash Q = (Σ_i c_i*Q_i) to obtain random evaluation point z let z_felt252 = hashing::hash_u384_transcript(hint.big_Q.span(), hash_state).s0; if z_felt252 != hint.z { return Result::Err('WRONG_Z'); } // Precompute lambda root evaluated in Z: let (conjugate_c_inv_of_z, w_of_z, c_inv_of_z_frob_1, mlr_of_z): (u384, u384, u384, u384) = run_BLS12_381_INITIALIZE_MPCHECK_EXT_MLR_circuit( hint.lambda_root_inverse, z, hint.w, precomputed_miller_loop_result, ); // init bit for bls is 1: let R_0_of_Z = *evals.pop_front().unwrap(); let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); let (_Q2, _lhs) = mpc::run_BLS12_381_MP_CHECK_INIT_BIT_3P_2F_circuit( processed_pair0.yInv, processed_pair0.xNegOverY, l0, l1, processed_pair1.yInv, processed_pair1.xNegOverY, l2, l3, processed_pair2.yInv, processed_pair2.xNegOverY, pair2.q, R_0_of_Z, z, conjugate_c_inv_of_z, ); let mut Q2 = _Q2; let mut LHS = _lhs; let mut f_i_of_z = R_0_of_Z; // Σ_i (Π_k (c_i*P_k(z))) = (Σ_i c_i*Q_i(z)) * P(z) + Σ_i c_i * R_i(z) // <=> Σ_i (Π_k (c_i*P_k(z))) - Σ_i c_i * R_i(z) = (Σ_i c_i*Q_i(z)) * P(z) // => LHS = Σ_i (Π_k (c_i*P_k(z))) - Σ_i c_i * R_i(z) // rest of miller loop let mut bits = BLS12_381_SEED_BITS_COMPRESSED.span(); while let Option::Some(bit) = bits.pop_front() { let R_i_of_z = *evals.pop_front().unwrap(); let (_Q2, _LHS): (G2Point, u384) = match *bit { 0 => { let [l0, l1] = (*lines.multi_pop_front::<2>().unwrap()).unbox(); mpc::run_BLS12_381_MP_CHECK_BIT0_3P_2F_circuit( processed_pair0.yInv, processed_pair0.xNegOverY, l0, processed_pair1.yInv, processed_pair1.xNegOverY, l1, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, 1 => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); mpc::run_BLS12_381_MP_CHECK_BIT1_3P_2F_circuit( processed_pair0.yInv, processed_pair0.xNegOverY, l0, l1, processed_pair1.yInv, processed_pair1.xNegOverY, l2, l3, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, pair2.q, LHS, f_i_of_z, R_i_of_z, conjugate_c_inv_of_z, z, c_1, ) }, _ => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); mpc::run_BLS12_381_MP_CHECK_BIT00_3P_2F_circuit( processed_pair0.yInv, processed_pair0.xNegOverY, l0, l1, processed_pair1.yInv, processed_pair1.xNegOverY, l2, l3, processed_pair2.yInv, processed_pair2.xNegOverY, Q2, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, }; Q2 = _Q2; LHS = _LHS; f_i_of_z = R_i_of_z; } let R_last_of_z: u384 = One::one(); // Checks that LHS = Q(z) * P_irr(z) let (check) = mpc::run_BLS12_381_MP_CHECK_FINALIZE_3P_EXT_MLR_circuit( R_last_of_z, c_1, w_of_z, z, c_inv_of_z_frob_1, LHS, *hint.Ris.at(34), hint.big_Q, mlr_of_z, ); match check.is_zero() { true => Result::Ok(true), false => Result::Err('FINAL_CHECK_FAILED'), } } pub fn conjugate_e12D(self: E12D, curve_index: usize) -> E12D { let modulus = get_modulus(curve_index); E12D { w0: self.w0, w1: neg_mod_p(self.w1, modulus), w2: self.w2, w3: neg_mod_p(self.w3, modulus), w4: self.w4, w5: neg_mod_p(self.w5, modulus), w6: self.w6, w7: neg_mod_p(self.w7, modulus), w8: self.w8, w9: neg_mod_p(self.w9, modulus), w10: self.w10, w11: neg_mod_p(self.w11, modulus), } } ================================================ FILE: src/src/ec/pairing/pairing_check.cairo ================================================ use core::array::{ArrayTrait, SpanTrait}; use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, circuit_inverse, circuit_mul, circuit_sub, u384, }; use core::num::traits::{One, Zero}; use core::option::Option; /// This file contains utilities to verify a pairing check of the form : /// e(P1, Qf1) * e(P2, Qf2) == 1, where Qf1 and Qf2 are fixed known points. (2P_2F circuits are used /// for double pairs and double fixed G2 points) /// Qf1 and Qf2 are represented by their pre-computed line functions for the specifc miller loop /// implementation. /// Two functions are provided for BN254 and BLS12-381 respectively. /// To generate the lines functions, you can use garaga's python backend. use core::option::OptionTrait; use garaga::basic_field_ops; use garaga::circuits::multi_pairing_check::{ run_BLS12_381_INITIALIZE_MPCHECK_circuit, run_BLS12_381_MP_CHECK_BIT00_2P_2F_circuit, run_BLS12_381_MP_CHECK_BIT0_2P_2F_circuit, run_BLS12_381_MP_CHECK_BIT1_2P_2F_circuit, run_BLS12_381_MP_CHECK_FINALIZE_2P_circuit, run_BLS12_381_MP_CHECK_INIT_BIT_2P_2F_circuit, run_BN254_INITIALIZE_MPCHECK_circuit, run_BN254_MP_CHECK_BIT00_2P_2F_circuit, run_BN254_MP_CHECK_BIT01_2P_2F_circuit, run_BN254_MP_CHECK_BIT10_2P_2F_circuit, run_BN254_MP_CHECK_FINALIZE_2P_2F_circuit, run_BN254_MP_CHECK_INIT_BIT_2P_2F_circuit, }; use garaga::definitions::{ BLS12_381_SEED_BITS_COMPRESSED, BN254_SEED_BITS_JY00_COMPRESSED, E12D, G1G2Pair, G2Line, get_BLS12_381_modulus, get_BN254_modulus, u288, }; use garaga::utils::hashing; use garaga::utils::hashing::{PoseidonState, TWO_POW_96}; use crate::core::circuit::AddInputResultTrait2; #[derive(Copy, Drop, Debug, PartialEq, Serde)] pub struct MillerLoopResultScalingFactor { pub w0: T, pub w2: T, pub w4: T, pub w6: T, pub w8: T, pub w10: T, } #[derive(Drop, Serde, Debug)] pub struct MPCheckHintBN254 { pub lambda_root: E12D, pub lambda_root_inverse: E12D, pub w: MillerLoopResultScalingFactor, pub Ris: Span>, pub big_Q: Array, pub z: felt252, } #[derive(Drop, Debug, PartialEq)] pub struct MPCheckHintBLS12_381 { pub lambda_root_inverse: E12D, pub w: MillerLoopResultScalingFactor, pub Ris: Span>, pub big_Q: Array, pub z: felt252, } // From a G1G2Pair(Px, Py, Qx0, Qx1, Qy0, Qy1), returns (1/Py, -Px/Py) #[derive(Drop, Debug, PartialEq)] pub struct BLSProcessedPair { pub yInv: u384, pub xNegOverY: u384, } // From a G1G2Pair(Px, Py, Qx0, Qx1, Qy0, Qy1), returns (1/Py, -Px/Py,-Qy0, -Qy1) #[derive(Drop, Debug, PartialEq)] pub struct BNProcessedPair { pub yInv: u384, pub xNegOverY: u384, pub QyNeg0: u384, pub QyNeg1: u384, } // From a point (x, y), returns (1/y, -x/y) pub fn compute_yInvXnegOverY(x: u384, y: u384, modulus: CircuitModulus) -> (u384, u384) { let in1 = CE::> {}; let in2 = CE::> {}; let in3 = CE::> {}; let yInv = circuit_inverse(in3); let xNeg = circuit_sub(in1, in2); let xNegOverY = circuit_mul(xNeg, yInv); let outputs = (yInv, xNegOverY) .new_inputs() .next_2([0, 0, 0, 0]) .next_2(x) .next_2(y) .done_2() .eval(modulus) .unwrap(); return (outputs.get_output(yInv), outputs.get_output(xNegOverY)); } #[inline(always)] pub fn multi_pairing_check_bn254_2P_2F( pair0: G1G2Pair, pair1: G1G2Pair, mut lines: Span>, hint: MPCheckHintBN254, ) -> Result { if hint.big_Q.len() != 145 { return Result::Err('WRONG_BIG_Q_LEN'); } if hint.Ris.len() != 34 { return Result::Err('WRONG_RIS_LEN'); } let modulus = get_BN254_modulus(); // BN254 prime field modulus let (yInv_0, xNegOverY_0) = compute_yInvXnegOverY(pair0.p.x, pair0.p.y, modulus); let (yInv_1, xNegOverY_1) = compute_yInvXnegOverY(pair1.p.x, pair1.p.y, modulus); // Init sponge state // >>> hades_permutation(0, 0, int.from_bytes(b"MPCHECK_BN254_2P_2F", "big")) let hash_state = PoseidonState { s0: 0x1a0eeac356472db3074d1ca6bb7bbb60fa9f0d53b34ef38a4eddde21b332b28, s1: 0x2783a4227674921675bfa12e30fda0dad992bb9be9785908ac1338b14018182, s2: 0x5d4b7659197d4e54258057765dd5e6dbf106bb3bd5a559fe1951303901e2e81, }; // Hash Inputs let hash_state = hashing::hash_G1G2Pair(pair0, hash_state); let hash_state = hashing::hash_G1G2Pair(pair1, hash_state); let hash_state = hashing::hash_E12D_u288(hint.lambda_root, hash_state); let hash_state = hashing::hash_E12D_u288(hint.lambda_root_inverse, hash_state); let hash_state = hashing::hash_MillerLoopResultScalingFactor_u288(hint.w, hash_state); // Hash Ris to obtain base random coefficient c0 and evals let z: u384 = hint.z.into(); let (hash_state, mut evals) = basic_field_ops::eval_and_hash_E12D_u288_transcript( hint.Ris, hash_state, z, ); // Last Ri is known to be 1: let hash_state = hashing::hash_E12D_one_u288(hash_state); let mut evals = evals.span(); let c_1: u384 = hash_state.s1.into(); // hades_permutation(0,0,int.from_bytes(b"MPCHECK_BN254_2P_2F_II", "big")) let part_II_state = PoseidonState { s0: 0x61306dbf52f13cce66776e642d58f27a1dc58ae7172565dd1d1555ac3bfbede, s1: 0x5895a3e8e579ff7c9a9bda84916ace794bc48e009dc6c76104a127111aef035, s2: 0x5ff2c406897ea02acecbbc03b4718c8e4a42cc5bb60d738ad60a58918aaa868, }; let hash_state = hashing::hash_u384(c_1, TWO_POW_96, part_II_state); // Hash Q = (Σ_i c_i*Q_i) to obtain random evaluation point z let z_felt252 = hashing::hash_u288_transcript(hint.big_Q.span(), hash_state).s0; if z_felt252 != hint.z { return Result::Err('WRONG_Z'); } let ( c_of_z, w_of_z, c_inv_of_z, LHS, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, ): (u384, u384, u384, u384, u384, u384, u384) = run_BN254_INITIALIZE_MPCHECK_circuit( hint.lambda_root, z, hint.w, hint.lambda_root_inverse, ); let R_0_of_Z = *evals.pop_front().unwrap(); let [l0, l1] = (*lines.multi_pop_front::<2>().unwrap()).unbox(); let (_lhs) = run_BN254_MP_CHECK_INIT_BIT_2P_2F_circuit( yInv_0, xNegOverY_0, l0, yInv_1, xNegOverY_1, l1, R_0_of_Z, z, c_inv_of_z, c_1, LHS, ); let mut LHS = _lhs; let mut f_i_of_z = R_0_of_Z; // rest of miller loop let mut bits = BN254_SEED_BITS_JY00_COMPRESSED.span(); while let Option::Some(bit) = bits.pop_front() { // println!("bit {}", *bit); let R_i_of_z = *evals.pop_front().unwrap(); let (_LHS): (u384,) = match *bit { 0 => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); run_BN254_MP_CHECK_BIT00_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, 1 | 2 => { let [l0, l1, l2, l3, l4, l5] = (*lines.multi_pop_front::<6>().unwrap()).unbox(); let c_or_c_inv_of_z = match (*bit - 1) { 0 => c_inv_of_z, _ => c_of_z, }; run_BN254_MP_CHECK_BIT10_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, l2, yInv_1, xNegOverY_1, l3, l4, l5, LHS, f_i_of_z, R_i_of_z, c_or_c_inv_of_z, z, c_1, ) }, _ => { // 3 -> 01, 4 -> 10 let [l0, l1, l2, l3, l4, l5] = (*lines.multi_pop_front::<6>().unwrap()).unbox(); let c_or_c_inv_of_z = match (*bit - 3) { 0 => c_inv_of_z, _ => c_of_z, }; run_BN254_MP_CHECK_BIT01_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, l2, yInv_1, xNegOverY_1, l3, l4, l5, LHS, f_i_of_z, R_i_of_z, c_or_c_inv_of_z, z, c_1, ) }, }; LHS = _LHS; f_i_of_z = R_i_of_z; } let R_n_minus_2_of_z = *evals.pop_front().unwrap(); let R_n_minus_1_of_z: u384 = One::one(); let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); let (check) = run_BN254_MP_CHECK_FINALIZE_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, R_n_minus_2_of_z, R_n_minus_1_of_z, c_1, w_of_z, z, c_inv_frob_1_of_z, c_frob_2_of_z, c_inv_frob_3_of_z, LHS, f_i_of_z, hint.big_Q, ); match check.is_zero() { true => Result::Ok(true), false => Result::Err('FINAL_CHECK_FAILED'), } } #[inline(always)] pub fn multi_pairing_check_bls12_381_2P_2F( pair0: G1G2Pair, pair1: G1G2Pair, mut lines: Span>, hint: MPCheckHintBLS12_381, ) -> Result { if hint.big_Q.len() != 81 { return Result::Err('WRONG_BIG_Q_LEN'); } if hint.Ris.len() != 35 { return Result::Err('WRONG_RIS_LEN'); } let modulus = get_BLS12_381_modulus(); // BLS12_381 prime field modulus let (yInv_0, xNegOverY_0) = compute_yInvXnegOverY(pair0.p.x, pair0.p.y, modulus); let (yInv_1, xNegOverY_1) = compute_yInvXnegOverY(pair1.p.x, pair1.p.y, modulus); // Init sponge state // >>> hades_permutation(0, 0, int.from_bytes(b"MPCHECK_BLS12_381_2P_2F", "big")) let hash_state = PoseidonState { s0: 0x38fc487c6a5413cb099f102857912e93570c7a3628b34722ec1fff8cefa6f5f, s1: 0x3cec4f7f551bccf7cbfbfd86cde672f2104b89d5443707c7ca7aca8196f4d0f, s2: 0x5ff52024b20f5cd082b347b5455a15a265874a39983c38ed544090b750ee718, }; // Hash Inputs let hash_state = hashing::hash_G1G2Pair(pair0, hash_state); let hash_state = hashing::hash_G1G2Pair(pair1, hash_state); let hash_state = hashing::hash_E12D_u384(hint.lambda_root_inverse, hash_state); let hash_state = hashing::hash_MillerLoopResultScalingFactor_u384(hint.w, hash_state); // Hash Ris to obtain base random coefficient c0 & evaluate all Ris at z (given in advance). let z: u384 = hint.z.into(); let (hash_state, mut evals) = basic_field_ops::eval_and_hash_E12D_u384_transcript( hint.Ris, hash_state, z, ); // Last Ri is known to be 1: let hash_state = hashing::hash_E12D_one_u384(hash_state); let mut evals = evals.span(); let c_1: u384 = hash_state.s1.into(); // hades_permutation(0,0,int.from_bytes(b"MPCHECK_BLS12_381_2P_2F_II", "big")) let part_II_state = PoseidonState { s0: 0x68148a435d9f7b0d7bfa42c9fa6b8c0441fd8a741fc024c547445b689d294b9, s1: 0x3076763e35be672b2cc79293b3d9c3899d8b4f083b484ae6d591b8d582e3471, s2: 0x29153e786b3c7f75891c98d853cf2db3125f434b25f2b38fb8be850009713d0, }; let hash_state = hashing::hash_u384(c_1, TWO_POW_96, part_II_state); // Hash Q = (Σ_i c_i*Q_i) to obtain random evaluation point z let z_felt252 = hashing::hash_u384_transcript(hint.big_Q.span(), hash_state).s0; if z_felt252 != hint.z { return Result::Err('WRONG_Z'); } // Precompute lambda root evaluated in Z: let (conjugate_c_inv_of_z, w_of_z, c_inv_of_z_frob_1): (u384, u384, u384) = run_BLS12_381_INITIALIZE_MPCHECK_circuit( hint.lambda_root_inverse, z, hint.w, ); // init bit for bls is 1: let R_0_of_Z = *evals.pop_front().unwrap(); let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); let (_lhs) = run_BLS12_381_MP_CHECK_INIT_BIT_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, R_0_of_Z, z, conjugate_c_inv_of_z, ); let mut LHS = _lhs; let mut f_i_of_z = R_0_of_Z; // Σ_i (Π_k (c_i*P_k(z))) = (Σ_i c_i*Q_i(z)) * P(z) + Σ_i c_i * R_i(z) // <=> Σ_i (Π_k (c_i*P_k(z))) - Σ_i c_i * R_i(z) = (Σ_i c_i*Q_i(z)) * P(z) // => LHS = Σ_i (Π_k (c_i*P_k(z))) - Σ_i c_i * R_i(z) // rest of miller loop let mut bits = BLS12_381_SEED_BITS_COMPRESSED.span(); while let Option::Some(bit) = bits.pop_front() { let R_i_of_z = *evals.pop_front().unwrap(); let (_LHS): (u384,) = match *bit { 0 => { let [l0, l1] = (*lines.multi_pop_front::<2>().unwrap()).unbox(); run_BLS12_381_MP_CHECK_BIT0_2P_2F_circuit( yInv_0, xNegOverY_0, l0, yInv_1, xNegOverY_1, l1, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, 1 => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); run_BLS12_381_MP_CHECK_BIT1_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, LHS, f_i_of_z, R_i_of_z, conjugate_c_inv_of_z, z, c_1, ) }, _ => { let [l0, l1, l2, l3] = (*lines.multi_pop_front::<4>().unwrap()).unbox(); run_BLS12_381_MP_CHECK_BIT00_2P_2F_circuit( yInv_0, xNegOverY_0, l0, l1, yInv_1, xNegOverY_1, l2, l3, LHS, f_i_of_z, R_i_of_z, z, c_1, ) }, }; LHS = _LHS; f_i_of_z = R_i_of_z; } let R_last_of_z: u384 = One::one(); let (check,) = run_BLS12_381_MP_CHECK_FINALIZE_2P_circuit( R_last_of_z, c_1, w_of_z, z, c_inv_of_z_frob_1, LHS, *hint.Ris.at(34), hint.big_Q, ); match check.is_zero() { true => Result::Ok(true), false => Result::Err('FINAL_CHECK_FAILED'), } } ================================================ FILE: src/src/ec/pairing/single_pairing_tower.cairo ================================================ use core::circuit::u384; use core::num::traits::{One, Zero}; use garaga::circuits::multi_pairing_check::run_BN254_MP_CHECK_PREPARE_PAIRS_1P_circuit; use garaga::circuits::tower_circuits as tw; use garaga::definitions::curves::{BLS12_381_SEED_BITS, BN254_SEED_BITS_NAF, get_BLS12_381_modulus}; use garaga::definitions::{BNProcessedPair, E12T, G1Point, G2Point}; use garaga::ec::pairing::pairing_check::compute_yInvXnegOverY; pub fn miller_loop_bn254_tower(P: G1Point, Q: G2Point) -> (E12T,) { let bits = BN254_SEED_BITS_NAF.span(); let (processed_pair): (BNProcessedPair,) = run_BN254_MP_CHECK_PREPARE_PAIRS_1P_circuit( P, Q.y0, Q.y1, ); let mut Mi: E12T = One::one(); let mut Qi = Q; for bit in bits { let (_Qi, _Mi) = match *bit { 0 => { tw::run_BN254_TOWER_MILLER_BIT0_1P_circuit( processed_pair.yInv, processed_pair.xNegOverY, Qi, Mi, ) }, 1 => { tw::run_BN254_TOWER_MILLER_BIT1_1P_circuit( processed_pair.yInv, processed_pair.xNegOverY, Qi, Q, Mi, ) }, _ => { tw::run_BN254_TOWER_MILLER_BIT1_1P_circuit( processed_pair.yInv, processed_pair.xNegOverY, Qi, G2Point { x0: Q.x0, x1: Q.x1, y0: processed_pair.QyNeg0, y1: processed_pair.QyNeg1, }, Mi, ) }, }; Qi = _Qi; Mi = _Mi; } tw::run_BN254_TOWER_MILLER_FINALIZE_BN_1P_circuit( Q, processed_pair.yInv, processed_pair.xNegOverY, Qi, Mi, ) } pub fn expt_bn254_tower(X: E12T) -> (E12T,) { // Step 1 let (t3) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(X); // Step 2 let (t5) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t3); // Step 3 let (result) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t5); // Step 4 let (t0) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(result); // Step 5 let (t2) = tw::run_BN254_E12T_MUL_circuit(X, t0); // Step 6 let (t0) = tw::run_BN254_E12T_MUL_circuit(t3, t2); // Step 7 let (t1) = tw::run_BN254_E12T_MUL_circuit(X, t0); // Step 8 let (t4) = tw::run_BN254_E12T_MUL_circuit(result, t2); // Step 9 let (t6) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t2); // Step 10 let (t1) = tw::run_BN254_E12T_MUL_circuit(t0, t1); // Step 11 let (t0) = tw::run_BN254_E12T_MUL_circuit(t3, t1); // Step 17 let mut t6 = t6; for _ in 0..6_u8 { let (_t6) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t6); t6 = _t6; } // Step 18 let (t5) = tw::run_BN254_E12T_MUL_circuit(t5, t6); // Step 19 let (mut t5) = tw::run_BN254_E12T_MUL_circuit(t4, t5); // Step 26 for _ in 0..7_u8 { let (_t5) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t5); t5 = _t5; } // Step 27 let (mut t4) = tw::run_BN254_E12T_MUL_circuit(t4, t5); // Step 35 for _ in 0..8_u8 { let (_t4) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t4); t4 = _t4; } // Step 36 let (t4) = tw::run_BN254_E12T_MUL_circuit(t0, t4); // Step 37 let (mut t3) = tw::run_BN254_E12T_MUL_circuit(t3, t4); // Step 43 for _ in 0..6_u8 { let (_t3) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t3); t3 = _t3; } // Step 44 let (mut t2) = tw::run_BN254_E12T_MUL_circuit(t2, t3); // Step 52 for _ in 0..8_u8 { let (_t2) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t2); t2 = _t2; } // Step 53 let (mut t2) = tw::run_BN254_E12T_MUL_circuit(t0, t2); // Step 59 for _ in 0..6_u8 { let (_t2) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t2); t2 = _t2; } // Step 60 let (mut t2) = tw::run_BN254_E12T_MUL_circuit(t0, t2); // Step 70 for _ in 0..10_u8 { let (_t2) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t2); t2 = _t2; } // Step 71 let (mut t1) = tw::run_BN254_E12T_MUL_circuit(t1, t2); // Step 77 for _ in 0..6_u8 { let (_t1) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t1); t1 = _t1; } // Step 78 let (t0) = tw::run_BN254_E12T_MUL_circuit(t0, t1); // Step 79 let (result) = tw::run_BN254_E12T_MUL_circuit(result, t0); return (result,); } pub fn final_exp_bn254_tower(M: E12T) -> E12T { let curve_id = 0; let (t0) = fp12_conjugate(M, curve_id); let (result) = tw::run_BN254_E12T_INVERSE_circuit(M); let (t0) = tw::run_BN254_E12T_MUL_circuit(t0, result); let (result) = tw::run_BN254_E12T_FROBENIUS_SQUARE_circuit(t0); let (result) = tw::run_BN254_E12T_MUL_circuit(result, t0); // Hard part let (t0) = expt_bn254_tower(result); let (t0) = fp12_conjugate(t0, curve_id); let (t0) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t0); let (t1) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t0); let (t1) = tw::run_BN254_E12T_MUL_circuit(t0, t1); let (t2) = expt_bn254_tower(t1); let (t2) = fp12_conjugate(t2, curve_id); let (t3) = fp12_conjugate(t1, curve_id); let (t1) = tw::run_BN254_E12T_MUL_circuit(t2, t3); let (t3) = tw::run_BN254_E12T_CYCLOTOMIC_SQUARE_circuit(t2); let (t4) = expt_bn254_tower(t3); let (t4) = tw::run_BN254_E12T_MUL_circuit(t1, t4); let (t3) = tw::run_BN254_E12T_MUL_circuit(t0, t4); let (t0) = tw::run_BN254_E12T_MUL_circuit(t2, t4); let (t0) = tw::run_BN254_E12T_MUL_circuit(result, t0); let (t2) = tw::run_BN254_E12T_FROBENIUS_circuit(t3); let (t0) = tw::run_BN254_E12T_MUL_circuit(t2, t0); let (t2) = tw::run_BN254_E12T_FROBENIUS_SQUARE_circuit(t4); let (t0) = tw::run_BN254_E12T_MUL_circuit(t2, t0); let (t2) = fp12_conjugate(result, curve_id); let (t2) = tw::run_BN254_E12T_MUL_circuit(t2, t3); let (t2) = tw::run_BN254_E12T_FROBENIUS_CUBE_circuit(t2); let (result) = tw::run_BN254_E12T_MUL_circuit(t2, t0); result } #[inline] pub fn fp12_conjugate(X: E12T, curve_id: usize) -> (E12T,) { let (b0a0, b0a1, b1a0, b1a1, b2a0, b2a1) = tw::run_FP6_NEG_circuit( X.c1b0a0, X.c1b0a1, X.c1b1a0, X.c1b1a1, X.c1b2a0, X.c1b2a1, curve_id, ); ( E12T { c0b0a0: X.c0b0a0, c0b0a1: X.c0b0a1, c0b1a0: X.c0b1a0, c0b1a1: X.c0b1a1, c0b2a0: X.c0b2a0, c0b2a1: X.c0b2a1, c1b0a0: b0a0, c1b0a1: b0a1, c1b1a0: b1a0, c1b1a1: b1a1, c1b2a0: b2a0, c1b2a1: b2a1, }, ) } pub fn final_exp_bls12_381_tower(M: E12T) -> E12T { let result = M; let (t0) = fp12_conjugate(M, 1); let (result) = tw::run_BLS12_381_E12T_INVERSE_circuit(result); let (t0) = tw::run_BLS12_381_E12T_MUL_circuit(t0, result); let (result) = tw::run_BLS12_381_E12T_FROBENIUS_SQUARE_circuit(t0); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t0); let (t0) = tw::run_BLS12_381_E12T_CYCLOTOMIC_SQUARE_circuit(result); let (t1) = expt_half_bls12_381_tower(t0); let (t2) = fp12_conjugate(result, 1); let (t1) = tw::run_BLS12_381_E12T_MUL_circuit(t1, t2); let (t2) = expt_bls12_381_tower(t1); let (t1) = fp12_conjugate(t1, 1); let (t1) = tw::run_BLS12_381_E12T_MUL_circuit(t1, t2); let (t2) = expt_bls12_381_tower(t1); let (t1) = tw::run_BLS12_381_E12T_FROBENIUS_circuit(t1); let (t1) = tw::run_BLS12_381_E12T_MUL_circuit(t1, t2); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t0); let (t0) = expt_bls12_381_tower(t1); let (t2) = expt_bls12_381_tower(t0); let (t0) = tw::run_BLS12_381_E12T_FROBENIUS_SQUARE_circuit(t1); let (t1) = fp12_conjugate(t1, 1); let (t1) = tw::run_BLS12_381_E12T_MUL_circuit(t1, t2); let (t1) = tw::run_BLS12_381_E12T_MUL_circuit(t1, t0); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t1); result } /// Dedicated structure for compressed elements in the cyclotomic subgroup G_phi ⊂ Fq^12 /// /// Background and intent (Observation 47): /// - Elements in the cyclotomic subgroup admit the Karabina compression where two of the /// Fp6 components (c0.b0 and c1.b1 in our tower representation) can be recovered from the /// remaining ones. Squaring in this form is cheaper and is implemented by the circuit /// `run_BLS12_381_E12T_CYCLO_SQUARE_COMPRESSED_circuit` that takes eight Fp limbs. /// - We represent such compressed elements explicitly instead of overloading `E12T`. /// This avoids confusing unused fields and makes the intent of “compressed cyclotomic /// value” explicit at the type level. /// /// Representation details: /// - `E12T` is modeled as Fp12 via the tower (Fp2 → Fp6 → Fp12) with coordinates /// `c{i}.b{j}.a{k}`. The compressed form stores exactly the eight limbs required by the /// Karabina formulas: c0.b1, c0.b2, c1.b0 and c1.b2 (each over Fp2 → a0,a1). /// - The fields `c0.b0` and `c1.b1` are intentionally absent; they are reconstructed during /// decompression using `DECOMP_KARABINA_*` circuits. /// - Validity invariant: values of this type must come from the cyclotomic subgroup; using /// arbitrary Fp12 elements here is undefined. /// /// Usage: /// - Squaring: feed the eight limbs directly to /// `run_BLS12_381_E12T_CYCLO_SQUARE_COMPRESSED_circuit`. /// - Multiplication or any generic operation: first call /// `decompress_karabina_bls12_381_compressed` to recover a full `E12T`. /// - Zero-branch: when `c1b2 == 0`, decompression uses the cheaper "I_Z" path. /// /// Security/correctness notes: /// - Decompression returns `One` when the Karabina t1 component is zero, matching the /// standard algorithmic edge case. /// - The helper `to_compressed(E12T)` merely copies the eight required limbs; it does not /// check subgroup membership. #[derive(Copy, Drop, Debug, PartialEq)] pub struct CompressedE12T { pub c0b1a0: u384, pub c0b1a1: u384, pub c0b2a0: u384, pub c0b2a1: u384, pub c1b0a0: u384, pub c1b0a1: u384, pub c1b2a0: u384, pub c1b2a1: u384, } /// Convert a full `E12T` (assumed in G_phi) into its Karabina compressed form by /// extracting the eight required limbs (c0.b1, c0.b2, c1.b0, c1.b2). #[inline] fn to_compressed(X: E12T) -> (CompressedE12T,) { ( CompressedE12T { c0b1a0: X.c0b1a0, c0b1a1: X.c0b1a1, c0b2a0: X.c0b2a0, c0b2a1: X.c0b2a1, c1b0a0: X.c1b0a0, c1b0a1: X.c1b0a1, c1b2a0: X.c1b2a0, c1b2a1: X.c1b2a1, }, ) } /// Decompress a Karabina-compressed cyclotomic element back to `E12T`. /// /// The implementation mirrors the two-step Karabina decompression and branches between /// the “I_Z” and “I_NZ” circuits depending on whether `c1b2 == 0`. pub fn decompress_karabina_bls12_381_compressed(X: CompressedE12T) -> (E12T,) { let (t0a0, t0a1, t1a0, t1a1) = match (X.c1b2a0.is_zero() && X.c1b2a1.is_zero()) { true => { let (t0a0, t0a1) = tw::run_BLS12_381_E12T_DECOMP_KARABINA_I_Z_circuit( X.c0b1a0, X.c0b1a1, X.c1b2a0, X.c1b2a1, ); (t0a0, t0a1, X.c0b2a0, X.c0b2a1) }, false => { tw::run_BLS12_381_E12T_DECOMP_KARABINA_I_NZ_circuit( X.c0b1a0, X.c0b1a1, X.c0b2a0, X.c0b2a1, X.c1b0a0, X.c1b0a1, X.c1b2a0, X.c1b2a1, ) }, }; if t1a0.is_zero() && t1a1.is_zero() { return (One::one(),); } let (zc0b0a0, zc0b0a1, zc1b1a0, zc1b1a1) = tw::run_BLS12_381_E12T_DECOMP_KARABINA_II_circuit( t0a0, t0a1, t1a0, t1a1, X.c0b1a0, X.c0b1a1, X.c0b2a0, X.c0b2a1, X.c1b0a0, X.c1b0a1, X.c1b2a0, X.c1b2a1, ); ( E12T { c0b0a0: zc0b0a0, c0b0a1: zc0b0a1, c0b1a0: X.c0b1a0, c0b1a1: X.c0b1a1, c0b2a0: X.c0b2a0, c0b2a1: X.c0b2a1, c1b0a0: X.c1b0a0, c1b0a1: X.c1b0a1, c1b1a0: zc1b1a0, c1b1a1: zc1b1a1, c1b2a0: X.c1b2a0, c1b2a1: X.c1b2a1, }, ) } /// Apply `times` Karabina cyclotomic squarings on a value in the compressed domain and /// return the decompressed `E12T`. /// /// This keeps the element compressed between squarings (cheap), and only performs the /// final decompression once at the end when a full `E12T` is needed for multiplication or /// other generic operations. fn cyclo_square_compressed_then_decompress_k(X: E12T, times: u32) -> (E12T,) { let (mut C) = to_compressed(X); for _ in 0..times { let (_c0b1a0, _c0b1a1, _c0b2a0, _c0b2a1, _c1b0a0, _c1b0a1, _c1b2a0, _c1b2a1) = tw::run_BLS12_381_E12T_CYCLO_SQUARE_COMPRESSED_circuit( C.c0b1a0, C.c0b1a1, C.c0b2a0, C.c0b2a1, C.c1b0a0, C.c1b0a1, C.c1b2a0, C.c1b2a1, ); C = CompressedE12T { c0b1a0: _c0b1a0, c0b1a1: _c0b1a1, c0b2a0: _c0b2a0, c0b2a1: _c0b2a1, c1b0a0: _c1b0a0, c1b0a1: _c1b0a1, c1b2a0: _c1b2a0, c1b2a1: _c1b2a1, }; } decompress_karabina_bls12_381_compressed(C) } pub fn expt_half_bls12_381_tower(M: E12T) -> (E12T,) { let (t0) = cyclo_square_compressed_then_decompress_k(M, 15_u32); let (t1) = cyclo_square_compressed_then_decompress_k(t0, 32_u32); let (mut result) = tw::run_BLS12_381_E12T_MUL_circuit(t0, t1); let (t1) = cyclo_square_compressed_then_decompress_k(t1, 9_u32); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t1); let (t1) = cyclo_square_compressed_then_decompress_k(t1, 3_u32); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t1); let (t1) = cyclo_square_compressed_then_decompress_k(t1, 2_u32); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t1); let (t1) = tw::run_BLS12_381_E12T_CYCLOTOMIC_SQUARE_circuit(t1); let (result) = tw::run_BLS12_381_E12T_MUL_circuit(result, t1); let (result) = fp12_conjugate(result, 1); (result,) } pub fn expt_bls12_381_tower(M: E12T) -> (E12T,) { let (t0) = expt_half_bls12_381_tower(M); return tw::run_BLS12_381_E12T_CYCLOTOMIC_SQUARE_circuit(t0); } pub fn miller_loop_bls12_381_tower(P: G1Point, Q: G2Point) -> (E12T,) { let bits = BLS12_381_SEED_BITS.span(); let modulus = get_BLS12_381_modulus(); let (yInv, xNegOverY) = compute_yInvXnegOverY(P.x, P.y, modulus); let (TripleQ, c0b0a0, c0b0a1, c0b1a0, c0b1a1, c0b2a0, c0b2a1, c1b1a0, c1b1a1, c1b2a0, c1b2a1) = tw::run_BLS12_381_TOWER_MILLER_INIT_BIT_1P_circuit( yInv, xNegOverY, Q, ); let mut Mi: E12T = E12T { c0b0a0: c0b0a0, c0b0a1: c0b0a1, c0b1a0: c0b1a0, c0b1a1: c0b1a1, c0b2a0: c0b2a0, c0b2a1: c0b2a1, c1b0a0: Zero::zero(), c1b0a1: Zero::zero(), c1b1a0: c1b1a0, c1b1a1: c1b1a1, c1b2a0: c1b2a0, c1b2a1: c1b2a1, }; let mut Qi = TripleQ; for bit in bits { let (_Qi, _Mi) = match *bit { 0 => { tw::run_BLS12_381_TOWER_MILLER_BIT0_1P_circuit(yInv, xNegOverY, Qi, Mi) }, _ => { tw::run_BLS12_381_TOWER_MILLER_BIT1_1P_circuit(yInv, xNegOverY, Qi, Q, Mi) }, }; Qi = _Qi; Mi = _Mi; } return fp12_conjugate(Mi, 1); } ================================================ FILE: src/src/ec/selectors.cairo ================================================ use corelib_imports::bounded_int::{ AddHelper, BoundedInt, DivRemHelper, MulHelper, UnitInt, bounded_int, upcast, }; const TWO: felt252 = 2; const TWO_UI: UnitInt = 2; const FOUR_UI: UnitInt = 4; const EIGHT_UI: UnitInt = 8; const TWO_NZ_TYPED: NonZero> = 2; const FOUR_NZ_TYPED: NonZero> = 4; const POW128_DIV_2: felt252 = 0x7fffffffffffffffffffffffffffffff; // ((2^128-1) // 2) const POW128_DIV_4: felt252 = 0x3fffffffffffffffffffffffffffffff; // ((2^128-1) // 4) const POW128: felt252 = 0x100000000000000000000000000000000; const FOUR: felt252 = 4; const EIGHT: felt252 = 8; pub type u15_bi = BoundedInt<0, { 15 }>; pub type u12_bi = BoundedInt<0, { 12 }>; pub type u1_bi = BoundedInt<0, { 1 }>; pub type u2_bi = BoundedInt<0, { 2 }>; pub type u3_bi = BoundedInt<0, { 3 }>; pub type u4_bi = BoundedInt<0, { 4 }>; pub type u5_bi = BoundedInt<0, { 5 }>; pub type u6_bi = BoundedInt<0, { 6 }>; pub type u7_bi = BoundedInt<0, { 7 }>; pub type u8_bi = BoundedInt<0, { 8 }>; impl DivRemU128By2 of DivRemHelper, UnitInt> { type DivT = BoundedInt<0, { POW128_DIV_2 }>; type RemT = u1_bi; } impl DivRemU128By4 of DivRemHelper, UnitInt> { type DivT = BoundedInt<0, { POW128_DIV_4 }>; type RemT = u3_bi; } impl MulHelperBitBy2Impl of MulHelper> { type Result = u2_bi; } impl MulHelperBitBy4Impl of MulHelper> { type Result = u4_bi; } impl MulHelperBit3By4Impl of MulHelper> { type Result = u12_bi; } impl MulHelperBitBy8Impl of MulHelper> { type Result = u8_bi; } impl AddHelperU1ByU2Impl of AddHelper { type Result = u3_bi; } impl AddHelperU3ByU4Impl of AddHelper { type Result = u7_bi; } impl AddHelperU7ByU8Impl of AddHelper { type Result = u15_bi; } impl AddHelperU3ByU12Impl of AddHelper { type Result = u15_bi; } #[inline(always)] fn _extract_and_calculate_selector_bit_inlined( mut u1: BoundedInt<0, { POW128 - 1 }>, mut u2: BoundedInt<0, { POW128 - 1 }>, mut v1: BoundedInt<0, { POW128 - 1 }>, mut v2: BoundedInt<0, { POW128 - 1 }>, ) -> ( BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, u15_bi, ) { let (qu1, u1b) = bounded_int::div_rem(u1, TWO_NZ_TYPED); let (qu2, u2b) = bounded_int::div_rem(u2, TWO_NZ_TYPED); let (qv1, v1b) = bounded_int::div_rem(v1, TWO_NZ_TYPED); let (qv2, v2b) = bounded_int::div_rem(v2, TWO_NZ_TYPED); u1 = upcast(qu1); u2 = upcast(qu2); v1 = upcast(qv1); v2 = upcast(qv2); let selector: u15_bi = bounded_int::add( bounded_int::add( bounded_int::add(u1b, bounded_int::mul(u2b, TWO_UI)), bounded_int::mul(v1b, FOUR_UI), ), bounded_int::mul(v2b, EIGHT_UI), ); return (u1, u2, v1, v2, selector); } #[inline(always)] fn _extract_and_calculate_selector_bit_inlined_fake_glv( mut s1: BoundedInt<0, { POW128 - 1 }>, mut s2: BoundedInt<0, { POW128 - 1 }>, ) -> (BoundedInt<0, { POW128 - 1 }>, BoundedInt<0, { POW128 - 1 }>, u15_bi) { let (qs1, s1b) = bounded_int::div_rem(s1, FOUR_NZ_TYPED); let (qs2, s2b) = bounded_int::div_rem(s2, FOUR_NZ_TYPED); s1 = upcast(qs1); s2 = upcast(qs2); let selector: u15_bi = bounded_int::add(s1b, bounded_int::mul(s2b, FOUR_UI)); return (s1, s2, selector); } #[inline(always)] pub fn build_selectors_inlined( _u1: u128, _u2: u128, _v1: u128, _v2: u128, ) -> (Span, u128, u128, u128, u128) { // Generated code for n_bits = 73 let mut selectors: Array = array![]; let mut u1: BoundedInt<0, { POW128 - 1 }> = upcast(_u1); let mut u2: BoundedInt<0, { POW128 - 1 }> = upcast(_u2); let mut v1: BoundedInt<0, { POW128 - 1 }> = upcast(_v1); let mut v2: BoundedInt<0, { POW128 - 1 }> = upcast(_v2); // Initial division and remainder to get LSBs let (qu1, u1lsb) = bounded_int::div_rem(u1, TWO_NZ_TYPED); let (qu2, u2lsb) = bounded_int::div_rem(u2, TWO_NZ_TYPED); let (qv1, v1lsb) = bounded_int::div_rem(v1, TWO_NZ_TYPED); let (qv2, v2lsb) = bounded_int::div_rem(v2, TWO_NZ_TYPED); u1 = upcast(qu1); u2 = upcast(qu2); v1 = upcast(qv1); v2 = upcast(qv2); // Inlined loop (72 iterations) let (u1, u2, v1, v2, selector_0) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_0)); let (u1, u2, v1, v2, selector_1) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_1)); let (u1, u2, v1, v2, selector_2) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_2)); let (u1, u2, v1, v2, selector_3) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_3)); let (u1, u2, v1, v2, selector_4) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_4)); let (u1, u2, v1, v2, selector_5) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_5)); let (u1, u2, v1, v2, selector_6) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_6)); let (u1, u2, v1, v2, selector_7) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_7)); let (u1, u2, v1, v2, selector_8) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_8)); let (u1, u2, v1, v2, selector_9) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_9)); let (u1, u2, v1, v2, selector_10) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_10)); let (u1, u2, v1, v2, selector_11) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_11)); let (u1, u2, v1, v2, selector_12) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_12)); let (u1, u2, v1, v2, selector_13) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_13)); let (u1, u2, v1, v2, selector_14) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_14)); let (u1, u2, v1, v2, selector_15) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_15)); let (u1, u2, v1, v2, selector_16) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_16)); let (u1, u2, v1, v2, selector_17) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_17)); let (u1, u2, v1, v2, selector_18) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_18)); let (u1, u2, v1, v2, selector_19) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_19)); let (u1, u2, v1, v2, selector_20) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_20)); let (u1, u2, v1, v2, selector_21) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_21)); let (u1, u2, v1, v2, selector_22) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_22)); let (u1, u2, v1, v2, selector_23) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_23)); let (u1, u2, v1, v2, selector_24) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_24)); let (u1, u2, v1, v2, selector_25) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_25)); let (u1, u2, v1, v2, selector_26) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_26)); let (u1, u2, v1, v2, selector_27) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_27)); let (u1, u2, v1, v2, selector_28) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_28)); let (u1, u2, v1, v2, selector_29) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_29)); let (u1, u2, v1, v2, selector_30) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_30)); let (u1, u2, v1, v2, selector_31) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_31)); let (u1, u2, v1, v2, selector_32) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_32)); let (u1, u2, v1, v2, selector_33) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_33)); let (u1, u2, v1, v2, selector_34) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_34)); let (u1, u2, v1, v2, selector_35) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_35)); let (u1, u2, v1, v2, selector_36) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_36)); let (u1, u2, v1, v2, selector_37) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_37)); let (u1, u2, v1, v2, selector_38) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_38)); let (u1, u2, v1, v2, selector_39) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_39)); let (u1, u2, v1, v2, selector_40) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_40)); let (u1, u2, v1, v2, selector_41) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_41)); let (u1, u2, v1, v2, selector_42) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_42)); let (u1, u2, v1, v2, selector_43) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_43)); let (u1, u2, v1, v2, selector_44) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_44)); let (u1, u2, v1, v2, selector_45) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_45)); let (u1, u2, v1, v2, selector_46) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_46)); let (u1, u2, v1, v2, selector_47) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_47)); let (u1, u2, v1, v2, selector_48) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_48)); let (u1, u2, v1, v2, selector_49) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_49)); let (u1, u2, v1, v2, selector_50) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_50)); let (u1, u2, v1, v2, selector_51) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_51)); let (u1, u2, v1, v2, selector_52) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_52)); let (u1, u2, v1, v2, selector_53) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_53)); let (u1, u2, v1, v2, selector_54) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_54)); let (u1, u2, v1, v2, selector_55) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_55)); let (u1, u2, v1, v2, selector_56) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_56)); let (u1, u2, v1, v2, selector_57) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_57)); let (u1, u2, v1, v2, selector_58) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_58)); let (u1, u2, v1, v2, selector_59) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_59)); let (u1, u2, v1, v2, selector_60) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_60)); let (u1, u2, v1, v2, selector_61) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_61)); let (u1, u2, v1, v2, selector_62) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_62)); let (u1, u2, v1, v2, selector_63) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_63)); let (u1, u2, v1, v2, selector_64) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_64)); let (u1, u2, v1, v2, selector_65) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_65)); let (u1, u2, v1, v2, selector_66) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_66)); let (u1, u2, v1, v2, selector_67) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_67)); let (u1, u2, v1, v2, selector_68) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_68)); let (u1, u2, v1, v2, selector_69) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_69)); let (u1, u2, v1, v2, selector_70) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_70)); let (_, _, _, _, selector_71) = _extract_and_calculate_selector_bit_inlined(u1, u2, v1, v2); selectors.append(upcast(selector_71)); return (selectors.span(), upcast(u1lsb), upcast(u2lsb), upcast(v1lsb), upcast(v2lsb)); } #[inline(always)] pub fn build_selectors_inlined_fake_glv(_s1: u128, _s2: u128) -> (Span, u128, u128) { // Generated code for n_bits = 128 let mut selectors: Array = array![]; let mut s1: BoundedInt<0, { POW128 - 1 }> = upcast(_s1); let mut s2: BoundedInt<0, { POW128 - 1 }> = upcast(_s2); // Initial division and remainder to get LSBs let (qs1, s1lsb) = bounded_int::div_rem(s1, TWO_NZ_TYPED); let (qs2, s2lsb) = bounded_int::div_rem(s2, TWO_NZ_TYPED); s1 = upcast(qs1); s2 = upcast(qs2); // Inlined loop (63 2-bit iterations for 128 bits) let (s1, s2, selector_0) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_0)); // Correction for the last bits 2-1. selectors.append(16); let (s1, s2, selector_1) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_1)); let (s1, s2, selector_2) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_2)); let (s1, s2, selector_3) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_3)); let (s1, s2, selector_4) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_4)); let (s1, s2, selector_5) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_5)); let (s1, s2, selector_6) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_6)); let (s1, s2, selector_7) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_7)); let (s1, s2, selector_8) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_8)); let (s1, s2, selector_9) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_9)); let (s1, s2, selector_10) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_10)); let (s1, s2, selector_11) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_11)); let (s1, s2, selector_12) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_12)); let (s1, s2, selector_13) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_13)); let (s1, s2, selector_14) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_14)); let (s1, s2, selector_15) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_15)); let (s1, s2, selector_16) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_16)); let (s1, s2, selector_17) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_17)); let (s1, s2, selector_18) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_18)); let (s1, s2, selector_19) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_19)); let (s1, s2, selector_20) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_20)); let (s1, s2, selector_21) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_21)); let (s1, s2, selector_22) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_22)); let (s1, s2, selector_23) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_23)); let (s1, s2, selector_24) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_24)); let (s1, s2, selector_25) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_25)); let (s1, s2, selector_26) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_26)); let (s1, s2, selector_27) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_27)); let (s1, s2, selector_28) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_28)); let (s1, s2, selector_29) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_29)); let (s1, s2, selector_30) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_30)); let (s1, s2, selector_31) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_31)); let (s1, s2, selector_32) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_32)); let (s1, s2, selector_33) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_33)); let (s1, s2, selector_34) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_34)); let (s1, s2, selector_35) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_35)); let (s1, s2, selector_36) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_36)); let (s1, s2, selector_37) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_37)); let (s1, s2, selector_38) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_38)); let (s1, s2, selector_39) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_39)); let (s1, s2, selector_40) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_40)); let (s1, s2, selector_41) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_41)); let (s1, s2, selector_42) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_42)); let (s1, s2, selector_43) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_43)); let (s1, s2, selector_44) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_44)); let (s1, s2, selector_45) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_45)); let (s1, s2, selector_46) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_46)); let (s1, s2, selector_47) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_47)); let (s1, s2, selector_48) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_48)); let (s1, s2, selector_49) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_49)); let (s1, s2, selector_50) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_50)); let (s1, s2, selector_51) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_51)); let (s1, s2, selector_52) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_52)); let (s1, s2, selector_53) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_53)); let (s1, s2, selector_54) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_54)); let (s1, s2, selector_55) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_55)); let (s1, s2, selector_56) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_56)); let (s1, s2, selector_57) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_57)); let (s1, s2, selector_58) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_58)); let (s1, s2, selector_59) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_59)); let (s1, s2, selector_60) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_60)); let (s1, s2, selector_61) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_61)); let (s1, s2, selector_62) = _extract_and_calculate_selector_bit_inlined_fake_glv(s1, s2); selectors.append(upcast(selector_62)); // At this point s1, and s2 are the MSB (last bit). if s1 != 0 { if s2 != 0 { // 11 T2 index : 10 selectors.append(10); } else { // 10 T12 index : 6 selectors.append(6); } } else { if s2 != 0 { // 01 T15 index : 9 selectors.append(9); } else { // 00 T5 index : 5 selectors.append(5); } } return (selectors.span(), upcast(s1lsb), upcast(s2lsb)); } ================================================ FILE: src/src/hashes/poseidon_bn254.cairo ================================================ use core::circuit::{ CircuitElement as CE, CircuitInput as CI, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_mul, u384, }; use garaga::core::circuit::AddInputResultTrait2; use garaga::definitions::get_GRUMPKIN_modulus; pub fn poseidon_hash_2(x: u256, y: u256) -> u256 { let x_u384: u384 = x.into(); let y_u384: u384 = y.into(); poseidon_hash_2_bn254(x_u384, y_u384).try_into().unwrap() } // Compute the poseidon hash of two elements for the BN254 scalar field (Fr). // Comptaible with circomlib poseidon hash (2 inputs) and Noir's hash 2 poseidon::bn254::hash_2 pub fn poseidon_hash_2_bn254(x: u384, y: u384) -> u384 { // CONSTANT stack let in0 = CE::> {}; // 0x0 let in1 = CE::> {}; // 0xee9a592ba9a9518d05986d656f40c2114c4993c11bb29938d21d47304cd8e6e let in2 = CE::> {}; // 0xf1445235f2148c5986587169fc1bcd887b08d4d00868df5696fff40956e864 let in3 = CE::> {}; // 0x8dff3487e8ac99e1f29a058d0fa80b930c728730b7ab36ce879f3890ecf73f5 let in4 = CE::> {}; // 0x84d520e4e5bb469e1f9075cb7c490efa59565eedae2d00ca8ef88ceea2b0197 let in5 = CE::> {}; // 0x2d15d982d99577fa33da56722416fd734b3e667a2f9f15d8eb3e767ae0fd811e let in6 = CE::> {}; // 0xed2538844aba161cf1578a43cf0364e91601f6536a5996d0efbe65632c41b6d let in7 = CE::> {}; // 0x2600c27d879fbca186e739e6363c71cf804c877d829b735dcc3e3af02955e60a let in8 = CE::> {}; // 0x28f8bd44a583cbaa475bd15396430e7ccb99a5517440dfd970058558282bf2c5 let in9 = CE::> {}; // 0x9cd7d4c380dc5488781aad012e7eaef1ed314d7f697a5572d030c55df153221 let in10 = CE::< CI<10>, > {}; // 0x11bb6ee1291aabb206120ecaace460d24b6713febe82234951e2bee7d0f855f5 let in11 = CE::< CI<11>, > {}; // 0x2d74e8fa0637d9853310f3c0e3fae1d06f171580f5b8fd05349cadeecfceb230 let in12 = CE::< CI<12>, > {}; // 0x2735e4ec9d39bdffac9bef31bacba338b1a09559a511a18be4b4d316ed889033 let in13 = CE::> {}; // 0xf03c1e9e0895db1a5da6312faa78e971106c33f826e08dcf617e24213132dfd let in14 = CE::< CI<14>, > {}; // 0x17094cd297bf827caf92920205b719c18741090b8f777811848a7e9ead6778c4 let in15 = CE::> {}; // 0xdb8f419c21f92461fc2b3219465798348df90d4178042c81ba7d4b4d559e2b8 let in16 = CE::< CI<16>, > {}; // 0x243443613f64ffa417427ed5933fcfbc66809db60b9ca1724a22709ceceeece2 let in17 = CE::< CI<17>, > {}; // 0x22af49fbfd5d7e9fcd256c25c07d3dd8ecbbae6deecd03aa04bb191fada75411 let in18 = CE::< CI<18>, > {}; // 0x14fbd37fa8ad6e4e0c78a20d93c7230c4677f797b4327323f7f7c097c19420e0 let in19 = CE::< CI<19>, > {}; // 0x15a9298bbb882534d4b2c9fbc6e4ef4189420c4eb3f3e1ea22faa7e18b5ae625 let in20 = CE::< CI<20>, > {}; // 0x2f7de75f23ddaaa5221323ebceb2f2ac83eef92e854e75434c2f1d90562232bc let in21 = CE::> {}; // 0x36a4432a868283b78a315e84c4ae5aeca216f2ff9e9b2e623584f7479cd5c27 let in22 = CE::< CI<22>, > {}; // 0x2180d7786a8cf810e277218ab14a11e5e39f3c962f11e860ae1c5682c797de5c let in23 = CE::> {}; // 0xa268ef870736eebd0cb55be640d73ee3778990484cc03ce53572377eefff8e4 let in24 = CE::< CI<24>, > {}; // 0x1eefefe11c0be4664f2999031f15994829e982e8c90e09069df9bae16809a5b2 let in25 = CE::< CI<25>, > {}; // 0x27e87f033bd1e0a89ca596e8cb77fe3a4b8fb93d9a1129946571a3c3cf244c52 let in26 = CE::> {}; // 0x1498a3e6599fe243321f57d6c5435889979c4f9d2a3e184d21451809178ee39 let in27 = CE::< CI<27>, > {}; // 0x27c0a41f4cb9fe67e9dd4d7ce33707f74d5d6bcc235bef108dea1bbebde507aa let in28 = CE::< CI<28>, > {}; // 0x1f75230908b141b46637238b120fc770f4f4ae825d5004c16a7c91fe1dae280f let in29 = CE::< CI<29>, > {}; // 0x25f99a9198e923167bba831b15fffd2d7b97b3a089808d4eb1f0a085bee21656 let in30 = CE::< CI<30>, > {}; // 0x101bc318e9ea5920d0f6acdc2bb526593d3d56ec8ed14c67622974228ba900c6 let in31 = CE::< CI<31>, > {}; // 0x1a175607067d517397c1334ecb019754ebc0c852a3cf091ec1ccc43207a83c76 let in32 = CE::> {}; // 0xf02f0e6d25f9ea3deb245f3e8c381ee6b2eb380ba4af5c1c4d89770155df37b let in33 = CE::< CI<33>, > {}; // 0x151d757acc8237af08d8a6677203ec9692565de456ae789ff358b3163b393bc9 let in34 = CE::< CI<34>, > {}; // 0x256cd9577cea143049e0a1fe0068dd20084980ee5b757890a79d13a3a624fad4 let in35 = CE::> {}; // 0x513abaff6195ea48833b13da50e0884476682c3fbdd195497b8ae86e1937c61 let in36 = CE::< CI<36>, > {}; // 0x1d9570dc70a205f36f610251ee6e2e8039246e84e4ac448386d19dbac4e4a655 let in37 = CE::< CI<37>, > {}; // 0x18f1a5194755b8c5d5d7f1bf8aaa6f56effb012dd784cf5e044eec50b29fc9d4 let in38 = CE::< CI<38>, > {}; // 0x266b53b615ef73ac866512c091e4a4f2fa4bb0af966ef420d88163238eebbca8 let in39 = CE::< CI<39>, > {}; // 0x2d63234c9207438aa42b8de27644c02268304dfeb8c89a1a3f4fd6e8344ae0f7 let in40 = CE::< CI<40>, > {}; // 0x2ab30fbe51ee49bc7b3adde219a6f0b5fbb976205ef8df7e0021daee6f55c693 let in41 = CE::< CI<41>, > {}; // 0x1aee6d4b3ebe9366dcb9cce48969d4df1dc42abcd528b270068d9207fa6a45c9 let in42 = CE::< CI<42>, > {}; // 0x1891aeab71e34b895a79452e5864ae1d11f57646c60bb34aa211d123f6095219 let in43 = CE::< CI<43>, > {}; // 0x24492b5f95c0b0876437e94b4101c69118e16b2657771bd3a7caab01c818aa4b let in44 = CE::> {}; // 0x1752161b3350f7e1b3b2c8663a0d642964628213d66c10ab2fddf71bcfde68f let in45 = CE::> {}; // 0xab676935722e2f67cfb84938e614c6c2f445b8d148de54368cfb8f90a00f3a7 let in46 = CE::> {}; // 0xb0f72472b9a2f5f45bc730117ed9ae5683fc2e6e227e3d4fe0da1f7aa348189 let in47 = CE::< CI<47>, > {}; // 0x16aa6f9273acd5631c201d1a52fc4f8acaf2b2152c3ae6df13a78a513edcd369 let in48 = CE::< CI<48>, > {}; // 0x2f60b987e63614eb13c324c1d8716eb0bf62d9b155d23281a45c08d52435cd60 let in49 = CE::< CI<49>, > {}; // 0x18d24ae01dde92fd7606bb7884554e9df1cb89b042f508fd9db76b7cc1b21212 let in50 = CE::> {}; // 0x4fc3bf76fe31e2f8d776373130df79d18c3185fdf1593960715d4724cffa586 let in51 = CE::> {}; // 0xd18f6b53fc69546cfdd670b41732bdf6dee9e06b21260c6b5d26270468dbf82 let in52 = CE::> {}; // 0xba4231a918f13acec11fbafa17c5223f1f70b4cdb045036fa5d7045bd10e24 let in53 = CE::> {}; // 0x7b458b2e00cd7c6100985301663e7ec33c826da0635ff1ebedd0dd86120b4c8 let in54 = CE::< CI<54>, > {}; // 0x1c35c2d96db90f4f6058e76f15a0c8286bba24e2ed40b16cec39e9fd7baa5799 let in55 = CE::< CI<55>, > {}; // 0x1d12bea3d8c32a5d766568f03dd1ecdb0a4f589abbef96945e0dde688e292050 let in56 = CE::> {}; // 0xd953e20022003270525f9a73526e9889c995bb62fdea94313db405a61300286 let in57 = CE::< CI<57>, > {}; // 0x29f053ec388795d786a40bec4c875047f06ff0b610b4040a760e33506d2671e1 let in58 = CE::> {}; // 0x4188e33735f46b14a4952a98463bc12e264d5f446e0c3f64b9679caaae44fc2 let in59 = CE::< CI<59>, > {}; // 0x149ec28846d4f438a84f1d0529431bb9e996a408b7e97eb3bf1735cdbe96f68f let in60 = CE::> {}; // 0xde20fae0af5188bca24b5f63630bad47aeafd98e651922d148cce1c5fdddee8 let in61 = CE::< CI<61>, > {}; // 0x12d650e8f790b1253ea94350e722ad2f7d836c234b8660edf449fba6984c6709 let in62 = CE::< CI<62>, > {}; // 0x22ab53aa39f34ad30ea96717ba7446aafdadbc1a8abe28d78340dfc4babb8f6c let in63 = CE::< CI<63>, > {}; // 0x26503e8d4849bdf5450dabea7907bc3de0de109871dd776904a129db9149166c let in64 = CE::< CI<64>, > {}; // 0x1d5e7a0e2965dffa00f5454f5003c5c8ec34b23d897e7fc4c8064035b0d33850 let in65 = CE::> {}; // 0xee3d8daa098bee012d96b7ec48448c6bc9a6aefa544615b9cb3c7bbd07104cb let in66 = CE::< CI<66>, > {}; // 0x1bf282082a04979955d30754cd4d9056fa9ef7a7175703d91dc232b5f98ead00 let in67 = CE::> {}; // 0x7ae1344abfc6c2ce3e951bc316bee49971645f16b693733a0272173ee9ad461 let in68 = CE::< CI<68>, > {}; // 0x217e3a247827c376ec21b131d511d7dbdc98a36b7a47d97a5c8e89762ee80488 let in69 = CE::< CI<69>, > {}; // 0x215ffe584b0eb067a003d438e2fbe28babe1e50efc2894117509b616addc30ee let in70 = CE::< CI<70>, > {}; // 0x1e770fc8ecbfdc8692dcedc597c4ca0fbec19b84e33da57412a92d1d3ce3ec20 let in71 = CE::< CI<71>, > {}; // 0x2f6243cda919bf4c9f1e3a8a6d66a05742914fc19338b3c0e50e828f69ff6d1f let in72 = CE::< CI<72>, > {}; // 0x246efddc3117ecd39595d0046f44ab303a195d0e9cc89345d3c03ff87a11b693 let in73 = CE::> {}; // 0x53e8d9b3ea5b8ed4fe006f139cbc4e0168b1c89a918dfbe602bc62cec6adf1 let in74 = CE::< CI<74>, > {}; // 0x1b894a2f45cb96647d910f6a710d38b7eb4f261beefff135aec04c1abe59427b let in75 = CE::> {}; // 0xaeb1554e266693d8212652479107d5fdc077abf88651f5a42553d54ec242cc0 let in76 = CE::< CI<76>, > {}; // 0x16a735f6f7209d24e6888680d1781c7f04ba7d71bd4b7d0e11faf9da8d9ca28e let in77 = CE::> {}; // 0x487b8b7fab5fc8fd7c13b4df0543cd260e4bcbb615b19374ff549dcf073d41b let in78 = CE::< CI<78>, > {}; // 0x1e75b9d2c2006307124bea26b0772493cfb5d512068c3ad677fdf51c92388793 let in79 = CE::> {}; // 0x5120e3d0e28003c253b46d5ff77d272ae46fa1e239d1c6c961dcb02da3b388f let in80 = CE::> {}; // 0xda5feb534576492b822e8763240119ac0900a053b171823f890f5fd55d78372 let in81 = CE::< CI<81>, > {}; // 0x2e211b39a023031a22acc1a1f5f3bb6d8c2666a6379d9d2c40cc8f78b7bd9abe let in82 = CE::< CI<82>, > {}; // 0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b let in83 = CE::< CI<83>, > {}; // 0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771 let in84 = CE::< CI<84>, > {}; // 0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7 let in85 = CE::< CI<85>, > {}; // 0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0 let in86 = CE::< CI<86>, > {}; // 0x2e2419f9ec02ec394c9871c832963dc1b89d743c8c7b964029b2311687b1fe23 let in87 = CE::< CI<87>, > {}; // 0x176cc029695ad02582a70eff08a6fd99d057e12e58e7d7b6b16cdfabc8ee2911 let in88 = CE::< CI<88>, > {}; // 0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736d let in89 = CE::< CI<89>, > {}; // 0x101071f0032379b697315876690f053d148d4e109f5fb065c8aacc55a0f89bfa let in90 = CE::< CI<90>, > {}; // 0x19a3fc0a56702bf417ba7fee3802593fa644470307043f7773279cd71d25d5e0 let in91 = CE::< CI<91>, > {}; // 0x1e6f20a11d1e31e43f83dcedddb9a0236203f5f24ae72c925a8a79a66831f51d let in92 = CE::< CI<92>, > {}; // 0x1bd8c528472e57bdc722a141f8785694484f426725403ae24084e3027e782467 let in93 = CE::< CI<93>, > {}; // 0x2d51ba82c8073c6d6bacf1ad5e56655b7143625b0a9e9c3190527a1a5f05079a let in94 = CE::< CI<94>, > {}; // 0x1b07d6d51e6f7e97e0ab10fc2e51ea83ce0611f940ff0731b5f927fe8d6a77c9 let in95 = CE::< CI<95>, > {}; // 0x11e12a40d262ae88e8376f62d19edf43093cdef1ccf34d985a3e53f0bc5765a0 let in96 = CE::< CI<96>, > {}; // 0x221c170e4d02a2479c6f3e47b5ff55781574f980d89038308a3ef37cce8463bd let in97 = CE::> {}; // 0x3f0815ab463f1b76ee25a9b8768b3231a89752f427f4f063ab718e707576b31 let in98 = CE::< CI<98>, > {}; // 0x15648bf46f60d82954c7e33029b3617357012a3d3b1d34c8e008859f1dbfb317 let in99 = CE::< CI<99>, > {}; // 0x127e00c2253de07818ca7f2eafdd7564d05ea850cf61f1daa0cfefbf7fbfba85 let in100 = CE::< CI<100>, > {}; // 0x66365afd18a41ef9382fc0b1d265cb4d3ce470a8cbbb878f7d48051630747bd let in101 = CE::< CI<101>, > {}; // 0x219d14f823513140dc69a96f7fe7e086f4fa24c84e57dcf2b099715c4404aae7 let in102 = CE::< CI<102>, > {}; // 0x3a30bfbbf2cb86d4a6a63a8050d91f9f14f4d33696d37ebaefa9ac2302132d5 let in103 = CE::< CI<103>, > {}; // 0x2121bbcdeaa33a35b0270fb7d5c9f94edad5a84d74b06e3385104b0b41935bcc let in104 = CE::< CI<104>, > {}; // 0x196b544fbeb0a792cfbb82c289e579b7cd5580c2e338a389d053ef8b3d10e70e let in105 = CE::< CI<105>, > {}; // 0x2809c3a1547c0cee89c1db270ef479c26973ec73edb4bd4e7d907ea0202f560f let in106 = CE::< CI<106>, > {}; // 0x11c34446b083ef92ca157585a02b8b342a4c67175b31f4b5d40d4e96dfc5c8f1 let in107 = CE::< CI<107>, > {}; // 0x253ea0b33a8bf3b2367c030e3289cbe0f6242ad7709d90b86d9d8026e2e39925 let in108 = CE::< CI<108>, > {}; // 0x30467dc1930f6afe90c89d4007ad29fc4f5a19c006d1030438c16df85637bd5f let in109 = CE::< CI<109>, > {}; // 0x2f9d4b55495f7e377e20e6f5a3a88af7aa6a536458b38bbe13c8ebfbbba54f44 let in110 = CE::< CI<110>, > {}; // 0x1d9e9d5c736e3151f11d36d499e7e093d8ee2353be18aad54cfd03ff0feac4b8 let in111 = CE::< CI<111>, > {}; // 0x124b617b43e598f9ebf622f7823a3de7d1bfedb87e097c315f343de301e54841 let in112 = CE::< CI<112>, > {}; // 0x198e7cfc66ae45774055cf073bedc945a5f9c5b19cae08d789cc5748ffe199b2 let in113 = CE::< CI<113>, > {}; // 0x2eac25b3498dfadffd124ab3aad57789eb945ba57443099c5bb6c27ed977fe24 let in114 = CE::< CI<114>, > {}; // 0x1ee02c175cdfe1871b378305c1bb9c904e8af1d4454ed3550b3c6ab5f4f90126 let in115 = CE::< CI<115>, > {}; // 0x616f8c34c607266b29ea8f9d2dfa47ff6fbb1d9745c48609fa98301d0f679d5 let in116 = CE::< CI<116>, > {}; // 0x181d68b0a188504958b9f19cbbdb972a853e51ed385e4883a43a42832803370b let in117 = CE::< CI<117>, > {}; // 0x2d5397ce863464a25d6b7f5b015d579181d1ce2f24cbabf6059e9327f5ba7004 let in118 = CE::< CI<118>, > {}; // 0x15bf817491b94d71e8912940cc0b80277713e7d32da2b6591724d8dbd4bc2618 let in119 = CE::< CI<119>, > {}; // 0x2a7cbd11460b177ab76feab28b69485ac8cc687740bc910994a3827d29c08714 let in120 = CE::< CI<120>, > {}; // 0xf7cd5ffa4661730ab56e447fae5cc1763cb462da80a85614c237b290de9d502 let in121 = CE::< CI<121>, > {}; // 0xe0766004b4c4176eb13273508eb6575f768137d86d305be644ce04531008100 let in122 = CE::< CI<122>, > {}; // 0x625fa7145813481f6d148be6b9c8bb7b54ee3c1afac00104e1f763000b9924c let in123 = CE::< CI<123>, > {}; // 0x7c5472508b459916ee0f5461aad2e0b19cd9c7b184f515b65136318ce2c6a5 let in124 = CE::< CI<124>, > {}; // 0x567375470d189b693ac77ab3fb7557231d53073951d43c54685879cb7a89fcb let in125 = CE::< CI<125>, > {}; // 0x1d0406bcbec83f8d5165f56c063e42108ad21f51ea4bfc71601174ba5c7b8bcc let in126 = CE::< CI<126>, > {}; // 0xc02b18eef22332d280a8aa1f86405f3375f06342f8696ee7c73b46c63272cb7 let in127 = CE::< CI<127>, > {}; // 0x17c1fc174cd9a6ebeaa7add2f801a664823509ad4fd1b15aad053a55ad6da4cf let in128 = CE::< CI<128>, > {}; // 0x5f843c23024eb1dab7ebbc86709a021aaa6caf433f7ed258a08638e9584b32d let in129 = CE::< CI<129>, > {}; // 0x22df2420697ca28b5cc51c53165e002727b45ccd90a55c87589f792f0ad8cb37 let in130 = CE::< CI<130>, > {}; // 0x2f1438303a7b49d473400aaedf0f48009fd3af804b76be86417588efc4d7302a let in131 = CE::< CI<131>, > {}; // 0x2323d5fcf2da8965c6b2b7b4fbf9a24bbaa7f4dccd35d5ca6155c5463093b23b let in132 = CE::< CI<132>, > {}; // 0x26c85b9dfbbe48fe83b753a5e7336b9f40f7b961e9c54f94e37700073d4d26e let in133 = CE::< CI<133>, > {}; // 0x31511000251ec86feb38b5ab4e335f070b271df4c20979528e41d65384c318f let in134 = CE::< CI<134>, > {}; // 0x18e588324a9bbaacb42fa69e5d90a0c0e27cd16b941e34a60ff5df9a26c03af1 let in135 = CE::< CI<135>, > {}; // 0x2642b5d8e16b953b070635775c8d3c9498357d6ad9bef2e7d99f03c10ea1f95f let in136 = CE::< CI<136>, > {}; // 0x21fc313ba11c60e8e84ff60db906a0f031189b0b48335c4221f909aef836c133 let in137 = CE::< CI<137>, > {}; // 0x2d3562e3d4b42bc6890b698cc6ab89f7311298bcbac6e4e9f2f4d93d06dae151 let in138 = CE::< CI<138>, > {}; // 0xa74ef541d360e842e3e0b6ff7e5c7c77934a5f67616f01c189d886dfd2e0808 let in139 = CE::< CI<139>, > {}; // 0x140564b53e0a812ac3983d6e3b433afa43f434087d9e754967c2c9b1b02caf8a let in140 = CE::< CI<140>, > {}; // 0x14709e32d98ae4cd18b400181e71ab9759c436c8e83fa6993adb6f2db6bba9d0 let in141 = CE::< CI<141>, > {}; // 0x734b2366c59e394423f179e1266dd392372db4f2dba651f4a619a4b52bdc010 let in142 = CE::< CI<142>, > {}; // 0x11fb2d705c94b08d5ad3e3c5fb6629abe963ed92913642c7d02d7e71088fd2d4 let in143 = CE::< CI<143>, > {}; // 0x27d03abf5c1f290e5d715eba19371050ef6eb7f78fd84be834e4cc3618059484 let in144 = CE::< CI<144>, > {}; // 0x13ed9e9e6b452df27fb3353cfc2cd63ebe817f212a39c6a8bb9b441ac1395861 let in145 = CE::< CI<145>, > {}; // 0x1319c51cf37aaa10246cdaaa04a12e88795de4452604263a7c5b79ab99cbd23c let in146 = CE::> {}; // 0xbca25588d187b7f9dad839f2c8cb526a4cf444eebbd0e715b6cea019ac3f2 let in147 = CE::< CI<147>, > {}; // 0x1d837ea0341c5964181226874b923cd01a069b493f02f7a3c01be23cf51d593f let in148 = CE::< CI<148>, > {}; // 0x1b41ce9ed3634cbd42c427ce4c5c83774149e2a6dbd25f24012090db7de4e7f9 let in149 = CE::< CI<149>, > {}; // 0x671f0e3b674ae7cddc790ecc4e946f4bca74b98b78a127c7b56bd6673f1ce1f let in150 = CE::< CI<150>, > {}; // 0x19fc073797a39b272e40cd30615f55fefeb682c1ac14143071d0449a5426e4e let in151 = CE::< CI<151>, > {}; // 0x17bee47d262a497fd1f7c5c6d5a7c70fa4209480bf5d97311c5096619e9fd13 let in152 = CE::< CI<152>, > {}; // 0x2073cff92d3141b480763539cff2978a4c7944721cc937ba00cc8527274471e3 let in153 = CE::< CI<153>, > {}; // 0x3bd7b3e2c1885877f43182a55a91d48f9c58d152e730fe2c7aa46b1fa663baa let in154 = CE::< CI<154>, > {}; // 0x226ebc9a538b5bbaff128edfb9bbf5fa0ceb100719a14c8dfed9ffbbbad9b6b7 let in155 = CE::< CI<155>, > {}; // 0xd395f0b08b9fede0373a06e1552c0e634a49572af1d830dc6e394e8a5d3b21a let in156 = CE::< CI<156>, > {}; // 0x28242439b524540a30d49b68e19e31ba5284bd3bcf1e0f2f41f77d5331f99ffa let in157 = CE::< CI<157>, > {}; // 0x370d6fa19eaac142d2de034801ab85e0b457e129e91f929754b48c6154d4df6 let in158 = CE::< CI<158>, > {}; // 0x9a16f573b3280f390762abf269579eaa37939bc0c753feb0a2b2e0bcbde1659 let in159 = CE::< CI<159>, > {}; // 0x2228e360fb5b162b496ac443f98127ee3c0021a690b71b268d99981368231d97 let in160 = CE::< CI<160>, > {}; // 0x7e42c2ca633d2c49fabf83991476d209431e34d8032b6a1b97675f3c567f944 let in161 = CE::< CI<161>, > {}; // 0x2ce12d7269663770c3cab85a6215a32eed35fda1d8e9d753a50fe96097724a9f let in162 = CE::< CI<162>, > {}; // 0x3d7427704c61e2009eeb9b1b45a0125084bc4daf70973a7ba0b2231815b15de let in163 = CE::< CI<163>, > {}; // 0x10f8abf0764185861c1267fcf4b4b33ca096fb4ddc4626732d86921e553e69c6 let in164 = CE::< CI<164>, > {}; // 0x17ccaf6f26f7267a025d7cb456e3aeb251a1a620aaf6568a5c95644c7c5914cc let in165 = CE::< CI<165>, > {}; // 0x63bb306b96310051385c3ce00ca820ad0e3651a6e55754d59de6df28cea4d51 let in166 = CE::< CI<166>, > {}; // 0x1f761ee5553c5e86f2c304a18095ab7403242e0b65e608bc920cf993a4169974 let in167 = CE::< CI<167>, > {}; // 0xdc5f00bbfd7c1d9a23c0e666859ba6564bcde8761b45717cd6bdfc09de4e8f2 let in168 = CE::< CI<168>, > {}; // 0x6de511520e277b7df07c3536381c13eb44cf790a230abc391089760bfc40ef2 let in169 = CE::< CI<169>, > {}; // 0x2a134348c8660efcf9ef54863e70528a1fd4481b50a1fe21f24a8c06e10cca03 let in170 = CE::< CI<170>, > {}; // 0xaeb5023bbb9a64c4bd80089e99edf8ed5f6f1ffb63a7dbba1b33520bcfce37b let in171 = CE::< CI<171>, > {}; // 0x141a6d0810366ae225ecb5f0bfdc9995406c5960ab26155836fc51fb7cb933d1 let in172 = CE::< CI<172>, > {}; // 0x9d2ea05ef54dadbbe776f404dca6626cc0b2539990bc0b8bfe87497f1e2c5b7 let in173 = CE::< CI<173>, > {}; // 0x1e56d244a8e41be5d104d5f8ef70891d22d4a5432441bfe8ff1a16e91719cdde let in174 = CE::< CI<174>, > {}; // 0x1d4f020c57c4f14aec908b2f99b5c4fd5e09447fa85c2fd68ba4d5c5f50c7b49 let in175 = CE::< CI<175>, > {}; // 0x763911a3a92a4f0e09f4e14cd03398d8d82a1e09db80fb0ee1e833764c18fd3 let in176 = CE::< CI<176>, > {}; // 0x12857275be2fe6b9ba2ec68f9061643f1fc5d9a2c5e47e55684366e54b302946 let in177 = CE::< CI<177>, > {}; // 0x2ed11ccd2e2e2376655ffe9a96c4b81adc0a60353c5d83d4d0ebf50d1bbf87c0 let in178 = CE::< CI<178>, > {}; // 0x3e31de8958e82645b320d5e3e966ef4726d5b1c2cfbb4acd288a21543c6d594 let in179 = CE::< CI<179>, > {}; // 0x11e880dfefdbd08858ae890046533d58da28a608d7e905366ec2ca4a36e71963 let in180 = CE::< CI<180>, > {}; // 0x1835b275deaed2d00704a9c3cc21ab7a44a34662978d53c190dc25e969a507b2 let in181 = CE::< CI<181>, > {}; // 0x68b75315e25ed4ace5a4a9480e1d82ce5d44f76f1324240419f372ff8d3c3f5 let in182 = CE::< CI<182>, > {}; // 0x1b7ef7d04aec73d62b052d2ad12b92a4268fccd795c839d698ad3b22823274d1 let in183 = CE::< CI<183>, > {}; // 0x28c0c848022a90606f6193ff5501b57216b670727f4b8efcc240d30bbaa9f03f let in184 = CE::< CI<184>, > {}; // 0x13bda49296cbcc51686a7bfb1c39f3f254370985a16660efd6e5d82d4f068e1b let in185 = CE::< CI<185>, > {}; // 0x2e7987ea8204389d11eb10b34265e378a945729f86c3e0e2fd38490d3a594141 let in186 = CE::< CI<186>, > {}; // 0x826d4a2324ad3aa4b2b45c10a190fedef702aeffda3226ce5415fffd03935c8 let in187 = CE::< CI<187>, > {}; // 0x2dbeee85eaeaa9fa3675ef541c9df7bb964a85435c3b59685f93b434036ded let in188 = CE::< CI<188>, > {}; // 0x227ee7a945edaee6919418ecb3279b11e6fa44f5f5c5abfb966a4be599cb86c7 let in189 = CE::< CI<189>, > {}; // 0x1d0a6d1a9519877805ac90d696faf2a5ffadc23986de8c698d541471c7244220 let in190 = CE::< CI<190>, > {}; // 0x2208aaba508ae816da4f333b7854fbbcd10eea1db284ec3e9f4de02b25f6e9d4 let in191 = CE::< CI<191>, > {}; // 0x28a58901035b2c99e36a7d29b587a215c9e59268e2f8e01a175720971ccf04ec let in192 = CE::< CI<192>, > {}; // 0x112f6d8d42b0a0d123a07865ca1376df317a2a14ffc0191226f38a8adfd6238 let in193 = CE::< CI<193>, > {}; // 0x8c6eb19c016d1833174dda182d266d5c727f97fb4d01f1daf906b6d3c6e2308 let in194 = CE::< CI<194>, > {}; // 0x1359d2d6c8b5a116d0b38b95f9c642df75b1be9a48c8698ecfea9103f73f1879 let in195 = CE::< CI<195>, > {}; // 0x10c5052ec67ab9b6a467c1cc1878d91aaa07aacf7725f8a5ed42b699c4af3ca7 let in196 = CE::< CI<196>, > {}; // 0x583c4d292d54f3cdb708803e6338fc6afdb188d5d4e9f060193823684c96c75 let in197 = CE::< CI<197>, > {}; // 0x2d94a1c55be382151a4054c5b96322e7bcd1fe2b3e076e16ee2c18bfc06f57b4 let in198 = CE::< CI<198>, > {}; // 0x15e3402fdde8770fb997369579c1b1703ef77c671927ead80dbc64dd2211c3ec let in199 = CE::< CI<199>, > {}; // 0x185be98784817f22f7b21e6b867d5a71b5000bef8bb902eb302677e20a727be3 let in200 = CE::< CI<200>, > {}; // 0x18db4321c721c03666ed8927c89890aa8aad1b00c054547b5ca14cd94de467b6 let in201 = CE::< CI<201>, > {}; // 0x2a852b6247f5d61f0c390b3f3d799188528849bcd2cd0aff4eb2134a039b5126 let in202 = CE::< CI<202>, > {}; // 0x2510aeed51b7f506e65fb9a18ee0124aa5276f6de1cd771b165930204da58f22 let in203 = CE::< CI<203>, > {}; // 0xf2074a32eb8260fb5bd3a236f03a47b47b7fb54dcad1d7977d6486513bab5f2 let in204 = CE::< CI<204>, > {}; // 0x2f4c69297866bd45a8270e19941926cec3531c9e12c4c2c84971404bfa044090 let in205 = CE::< CI<205>, > {}; // 0x154668727d2dbadf05d083a65093c0d0e92df5fd5f3fd75e9b792c562a37473f let in206 = CE::< CI<206>, > {}; // 0x1e6ffc5d6a1ff5dc4fd77fc5ab5c8c4e8d3e2e375bcd1194a91e5b0f7b13cadf let in207 = CE::< CI<207>, > {}; // 0x2cf1a1d7c44309109d75acbc9395cb8398c8b2d428538571fafa389da29990c6 let in208 = CE::< CI<208>, > {}; // 0x140fb39a89f26f6d87cf76cd5ce8da47aa5d8a023e24cf016ecf64cf793c9880 let in209 = CE::< CI<209>, > {}; // 0x1289d13d58a17b5bf0712b201fb3cddfce2c16dac159990b8298a93a8589f9e8 let in210 = CE::< CI<210>, > {}; // 0xf45cf974d2c9edb5781e8d3d207adc8370cf56bc5218749610920fe98b2db2e let in211 = CE::< CI<211>, > {}; // 0x11909c81a16518046b79edfd24f5abcc585a81d1b333568b8687a1c9eceb44d4 let in212 = CE::< CI<212>, > {}; // 0x2990b23c81882f7709f3b891a0e3da4d6917672f2d5a1041fd7bbd6792330d16 let in213 = CE::< CI<213>, > {}; // 0x609551b14716ca3cd5560e0821e7285e0a083ea9a16dc102ecf461e4aef7277 let in214 = CE::< CI<214>, > {}; // 0xc8c1abdfab99d03fd93dced2467354b6175de1755f4f93dc0880eaa08d03f77 let in215 = CE::< CI<215>, > {}; // 0x138bd098c4923b9fbd02f33f8bec6c730db3fed298ec09f78a7a55d08f2e0b10 let in216 = CE::< CI<216>, > {}; // 0x2e61e4bc021630114673f0f77161ae55dcd0b45ce07d9ae3f21bb5a3190f14c0 let in217 = CE::< CI<217>, > {}; // 0x124860913e3df8f65a9c4060ce3297c626abd1c22401c905ddb408260d8e910 let in218 = CE::< CI<218>, > {}; // 0x13807f89c394a133ec104804d955cbe125f24c5701d98286c6ac8b7ed052ec8 let in219 = CE::< CI<219>, > {}; // 0x2e88d1a6938f0788132aa9eeaec08d2f59aa444050c8f4c4e85578abb0fc2fe5 let in220 = CE::< CI<220>, > {}; // 0x1f3d24f17cfc6050a0cbf64e1f1787e2257be3c3ba607c2e8fcc1f26abf3104 let in221 = CE::< CI<221>, > {}; // 0x1fe1cb0e2ae169f83b9d4f133d41fb5b3fe6c76a82a916bfd9b62f82f0f8d0bf let in222 = CE::< CI<222>, > {}; // 0xef79351229409cd353329221229827e19946f3d8d1c48bf5e3377f9177071f3 let in223 = CE::< CI<223>, > {}; // 0x18fb2e46fc1b90fe1c4893ef77a9d111507551883127860e89088608373beda9 let in224 = CE::< CI<224>, > {}; // 0x77afe2579f42ec14c32ef0761e23a3cc0ad6263a68c5cb61916bd57120d1868 let in225 = CE::< CI<225>, > {}; // 0x79769092daa5a752642c04ccf8a6ea54e2ac9836fdd65d248b186f1490b7b99 let in226 = CE::< CI<226>, > {}; // 0x1d8bf229c19968f0254eb6e09c5c8bfd67eb9734606b676b663c76cf76bab4a5 let in227 = CE::< CI<227>, > {}; // 0x2a33b7d855e7fe55f93556e49e4b37737664f14236f17256428f29f6ec1bddad let in228 = CE::< CI<228>, > {}; // 0x25b0331d7e2b15af4ec161c86e84ba6ab2056077e7aa7536340dc3187ccca8b2 let in229 = CE::< CI<229>, > {}; // 0x762098f5fe26598ccbf45e4810211b0ffcf8ccbb92c16e2f4f13f22342474e2 let in230 = CE::< CI<230>, > {}; // 0xe234d720d70b2886d0da4c007b1bda42362e144185c70716dece2b6172c2514 let in231 = CE::< CI<231>, > {}; // 0x1d82bedccd2bc8a06e3742e720b7fec2ea72182f11c0c60d135c811152aa4b60 let in232 = CE::< CI<232>, > {}; // 0x480064d4b3eb0ada5e9a3e7d05930b7c3397fd6b94d481314bd1c690a17c979 let in233 = CE::< CI<233>, > {}; // 0x10a892763b3cca9ef7593fbb1140edc8c8e4580568560cf41867f7464fb0c11a let in234 = CE::< CI<234>, > {}; // 0xb5ec64548ea841ac921f9b2553680785978b315667ae4714dde4cd7f4de8b91 let in235 = CE::< CI<235>, > {}; // 0x10554aca4e348e5949761bd7131dfaebd78010edd030e1a9ce3c65c9db931d46 let in236 = CE::< CI<236>, > {}; // 0x15be66f38d86b0998b93655462b1f475b9be9de306e150d4ac648fab3db0cff6 let in237 = CE::< CI<237>, > {}; // 0x176ad3600fd3491182d182957ffad01bf6c26e9d4ab0c23caaf308e427d3dbe8 let in238 = CE::< CI<238>, > {}; // 0x2b6f355b3dbf65f09335001d705ac125e3beb20f4fc11bd3ce82b5cf0af2e6f2 let in239 = CE::< CI<239>, > {}; // 0x1c85c06a6d5d40d81d7c89edefb32d1a8448c51288fa296b6de9ff788c77451 let in240 = CE::< CI<240>, > {}; // 0x20e1e876c4746a0cbd9a51d76b2e25f82361c389e43f7d1f51a70aaac2460d79 let in241 = CE::< CI<241>, > {}; // 0x20e46219f684186d2a024b637bc35a29ee3b08ce737701392d987dda9217fa08 let in242 = CE::< CI<242>, > {}; // 0x2ea7279db9f2aa0f654e987907277c24480766367a8bd90e28be0f2ed6091367 let in243 = CE::< CI<243>, > {}; // 0x136be2a7f18924c9362096d472bc75ca0969dc077c9171b1641be95091780f74 let in244 = CE::< CI<244>, > {}; // 0x1ca2033501baa3f73067c4300fb0f51119ed5736fbc8f1f6c924baf0df5a0e9e let in245 = CE::< CI<245>, > {}; // 0xa82f199c2505277ecaa75e495f34e3525824f7a4a9d9fa1da810832b48a50c7 let in246 = CE::< CI<246>, > {}; // 0xecf10485307b4bae92fefb0d7f7782a9f37a2722e7ed9eb7925a2dea580b7d5 let in247 = CE::< CI<247>, > {}; // 0x7b642138dfd6a6dd12aa22f08a8296d68615c8478f13af16aebbbb339a3936b let in248 = CE::< CI<248>, > {}; // 0x1d9dda43a25593ffd2256d34921fb86ed70e760ba76d61e9cbc3b6dd0f1a2150 let in249 = CE::< CI<249>, > {}; // 0x2f1af228520c8b751dc91136c91c6bccd5367eb08213d392958ce2fd3d7d2fce let in250 = CE::< CI<250>, > {}; // 0x1fecfe833ad540455c6d6c1ab3de4abae61ada625a1a2b6b18551a45a6cde123 let in251 = CE::< CI<251>, > {}; // 0x18fc8e608c735b2b3b0d7583460227575657ff8a77abe637bdd3ad28e4a23c88 let in252 = CE::< CI<252>, > {}; // 0x28f740bc1182e9706ebf03cb3f53aba8a43ce0b618783a5586388a7547faa815 let in253 = CE::< CI<253>, > {}; // 0x47998cc0af5a26b94ad301e4b998d29e960a4851cfd13822bed35b7146966a4 let in254 = CE::< CI<254>, > {}; // 0x1b5f1525b31db911dda43e415e1b9a3a9725c7b52e880ee130a14a692b777b70 let in255 = CE::< CI<255>, > {}; // 0x275a83fa5d19b4535f65e965a90eac9bf770ae9bd1d7b1af945fa57ed5c8de6e let in256 = CE::< CI<256>, > {}; // 0x2e8789257ed2cbcccb430568e49bc9dc2a563359808c9897ce3e40a6f6a27aa8 let in257 = CE::< CI<257>, > {}; // 0x927f46cfe80feefeb2721a4c09e9d17f60c34500dcd6e41e2925a39c8e2c7c1 let in258 = CE::< CI<258>, > {}; // 0x1f868ae04832a5dbc37619bfe6ab6a97fd8fb2cfbc1ecf9e0e484bbfe7698101 let in259 = CE::< CI<259>, > {}; // 0x9d7a11e27d2f53109b73f745b2defed65d94ba80f308fb19ce6d56c9b45eff4 let in260 = CE::< CI<260>, > {}; // 0x282d857cfe8da3b5104e1c2823fb7c5b9a7b25924fda5995b0c351aa2b879dff let in261 = CE::< CI<261>, > {}; // 0x20ba8a9fcec815b13f349ff830ae663b27576e135c0744f6987fb0f6ff49c217 let in262 = CE::< CI<262>, > {}; // 0x11b6afc91e32f1ca4589fba12e657d226d57b471ddd2ab1b66a8ae4dcbfb136e let in263 = CE::< CI<263>, > {}; // 0x2e666402ac9cc588316e335c7d93db344788eec2c72ddf3f908141736cebc3be let in264 = CE::< CI<264>, > {}; // 0x17522e0e9e64f795a202a110e283faad7057aec5c9ed9a1a74920f2794f18595 let in265 = CE::< CI<265>, > {}; // 0x2d2ed17f7a1f3ee9e20b470cad4cc7319e6adb40e2ff24b7878cb9878edbd3b9 let in266 = CE::< CI<266>, > {}; // 0x1a81efb19d7e1edaa96fa276e89e85d08f75e54a8136f4d73c937da16c7bf9f4 let in267 = CE::< CI<267>, > {}; // 0x27ff57c1ca847e57210a7b44e52e5630f299c5f451c7a0d515a16bb3bd33e237 let in268 = CE::< CI<268>, > {}; // 0x1c1a8e22230abcd13c5be96031bfa167840d117b3c6a5a0a11be26a7f5fb1a94 let in269 = CE::< CI<269>, > {}; // 0x2a1c3f15d4927c843627a9cd533e4250d81e7774d2c32b59d5836f9c19a5657 let in270 = CE::< CI<270>, > {}; // 0x2ddbb7239eb904d81c52499b37cb4be1af0373a10ac112e185acb219899357e4 let in271 = CE::< CI<271>, > {}; // 0xdff198393085a754e0d6faec54be81d8edf8bc25edadab48a86fad6da0afb60 let in272 = CE::< CI<272>, > {}; // 0x10d50c2473146bbc76275fcc589d038dec8db28728789f28b6d5f504bd1645ca let in273 = CE::< CI<273>, > {}; // 0x61e8328fb5593f92a53dfd40e1022e6231ba45948506282536b08b4476c1538 let in274 = CE::< CI<274>, > {}; // 0x1b589243847198ded90b644bee31ac58067debf3f07d3c51cfa5a0dd9f6d9784 let in275 = CE::< CI<275>, > {}; // 0x4b00c0da1f851e59863b053bd4c6087190f0bdcced99d5ce6f67a420a3bd1f7 let in276 = CE::< CI<276>, > {}; // 0x239941a46c2b93d9126a70163009a7ac27f8a8d42e35018b3bec8cdcb5ddfd67 let in277 = CE::< CI<277>, > {}; // 0x204f26ca7993b03ac2c35377cb0a3712bfc9bc3ec0bfecb4e87ef6814acf2ea2 let in278 = CE::< CI<278>, > {}; // 0x85aff9c7fdadba039d832d8be165a1e5747cf7308d515e348ef117e926d721c let in279 = CE::< CI<279>, > {}; // 0x249042a8dc111f27c4ae9db044c0b0b3f10e57d05e093158efd375df00ea2068 let in280 = CE::< CI<280>, > {}; // 0x6e799bcdf2b4a74542854f3029803e2f84550665203327b3e0825977413e96b let in281 = CE::< CI<281>, > {}; // 0x1cb3caed4bffb6aca9f4d2c002921bc3fffed333cae12085c612496183b87996 let in282 = CE::< CI<282>, > {}; // 0xb47e9755fae480128a128bfd4faa6a3dd6ea03cab566889dcd99e84d310d51c let in283 = CE::< CI<283>, > {}; // 0xc7e4cea365c2061920a0c9fd2c360a6506293bc024fd1ca3f0bb730da886a4f let in284 = CE::< CI<284>, > {}; // 0x21da1f701bac77bcbbaa30d964d6f6f63dbe1b20d9d6988c8dcd7ba4187215df let in285 = CE::< CI<285>, > {}; // 0x9ae612e8ba1ca1370905fb67899d10db86b47bd19965b6edd1a9486e3c6cc55 let in286 = CE::< CI<286>, > {}; // 0x262e1e0b56cac47fc150f284491190e6aab75445b0c99373fe1f7a0e3b95cf3d let in287 = CE::< CI<287>, > {}; // 0x234bf4a7dce7587c2c87c293e3bb7c9e2a7bfa5f29fd4ddeaa5d3f67491d34bd let in288 = CE::< CI<288>, > {}; // 0x2f6cbac694c886b02d0a527cac744fb658d2690e213d7432eee67f6cb69f70c2 let in289 = CE::< CI<289>, > {}; // 0x22accb18b7c49b4b7bb8c9fdf78b7aded52aa1842fff818d9a3300876dec3ad9 let in290 = CE::< CI<290>, > {}; // 0x81e2f0652f898c6d659f22d2c77be302eabd9182a0b3d3cbf623a1df7f8f2fc let in291 = CE::< CI<291>, > {}; // 0x12c0a25e70d006eccea3ada75d669b8c534b962890f3ffc016b3186ad675b935 let in292 = CE::< CI<292>, > {}; // 0x10ef9c23848128cc2fd6fc869df24d7ab56efd349edd56f49f8d4f2381df3259 let in293 = CE::< CI<293>, > {}; // 0x2161cd280772819dd4a81262b71df1bcc2c1d41b9491e0620bda347962b240f0 let in294 = CE::< CI<294>, > {}; // 0x2cebb0ae5108318eb406590041b5248292533364f799bc41b7f4fdd12cb8d38a let in295 = CE::< CI<295>, > {}; // 0x2b2092f86b5979a7fe4f7c22d9561f3bf2852283a656880fb759e08709a0a62f let in296 = CE::< CI<296>, > {}; // 0x1566b3402d774b8c08146188425a442450cfc900cf643e7382b2d8507a065fed let in297 = CE::< CI<297>, > {}; // 0x11a316aa31607f268fb4c56d6c57ba01627c3635fccf8d3d1a163e601d1a0173 let in298 = CE::< CI<298>, > {}; // 0xde7ee069c934256b782648b560e595408a5e8434644609152e353d9c2874e44 let in299 = CE::< CI<299>, > {}; // 0x2d36f4029245704cc84df0297708c5e5845c36ae706c72e67128b8949eab1af let in300 = CE::< CI<300>, > {}; // 0x1b8cc326b5ee160f53198c217fb34e899bde46cd82dabdc284d7951d546f858 let in301 = CE::< CI<301>, > {}; // 0x27625da0f73ea07110689fb2187b71694cbf9203fd4ddf8a96ece85407550ebb let in302 = CE::< CI<302>, > {}; // 0x1cd8338a3e5b1ad7cdc0da581a6950f6dea349c3edda06cb99ba025b94e4790d let in303 = CE::< CI<303>, > {}; // 0x5ea02d65b209f6da763856c94b6438c78a8aed8d3e67e877a10a84072741a56 let in304 = CE::< CI<304>, > {}; // 0x9f7cb68d4e388f85366cfcf284a895d8b6250ced627e810817743ce03330a55 let in305 = CE::< CI<305>, > {}; // 0x18c6230ddc0f896827b043f5e58dbd1aec13995a202e4ebcdfeb969e9d5c1212 let in306 = CE::< CI<306>, > {}; // 0x73a6114b997285e1a91c0a0fdccdaa8452e4f07bfd2e1a10578232096db6dcd let in307 = CE::< CI<307>, > {}; // 0x2e78746340b2a6d222c6a1fc0838adf5fe013f39b1660ce7a3e7742b2f37be7f let in308 = CE::< CI<308>, > {}; // 0x7aa27e7150baddd06303ad8e5e4bf4249b7ea846553def28e675259d3e5c851 let in309 = CE::< CI<309>, > {}; // 0xb66fdec210ea4eabf623d2712cf4d9fa90273ccb4643f680cbc98345715ead8 let in310 = CE::< CI<310>, > {}; // 0x2fb6a29d9f394a589b633b8a4d6be51c9c0601ce0b140be641acea41c49aa5e3 let in311 = CE::< CI<311>, > {}; // 0x29025cc66fd041c4fc845e9c1c2cd1288569fb243d049bd675a69dc889b2ce2a let in312 = CE::< CI<312>, > {}; // 0x150963f0aca9bcbe4126214ab9c627a6f7ed731cfa695168b85d534b17be3f48 let in313 = CE::< CI<313>, > {}; // 0xed59780302257663f72c1bfc6656eb7b5bca2e47bec0d5798a08a32a61a8a65 let in314 = CE::< CI<314>, > {}; // 0x7e19cb8a893369b3d30ae188c767f391c11888a3000debfc8d30c06143cc084 let in315 = CE::< CI<315>, > {}; // 0x600c7d2b6946345e5f1eeeafb5eb8ec2b6ecfe528d2c052cd860afb4a3aa272 let in316 = CE::< CI<316>, > {}; // 0x596083b6c972bc13022a1f33d6523b4773f2cd0a480e19ea0125119f0385705 let in317 = CE::< CI<317>, > {}; // 0x210b5c36f27a07d97f98b9d8663d85db2e64513099a8e1ef6db21043631e24c4 let in318 = CE::< CI<318>, > {}; // 0x13bb2764bf1475cfc7bb9f3d563c5cc201c2489874e9159326a8f4930b7883f9 let in319 = CE::< CI<319>, > {}; // 0x202cf557d625c26080eb082862a76757287872b181e89997219e4b7576e24d30 let in320 = CE::< CI<320>, > {}; // 0xe561c3f8bd4f76e76d49e97142d220601fbc5a03d905a4728ea1f95fd8824b2 let in321 = CE::< CI<321>, > {}; // 0xde20097480e7555471785de07bd9809d57dd859bbe827307c33ae9ed7890597 let in322 = CE::< CI<322>, > {}; // 0x72f2a6287fb984bb810df8c5788eebcfd2825613cb72bb80cde8edd76d2e97d // INPUT stack let (in323, in324) = (CE::> {}, CE::> {}); let t0 = circuit_add(in0, in1); let t1 = circuit_add(in323, in2); let t2 = circuit_add(in324, in3); let t3 = circuit_mul(t0, t0); let t4 = circuit_mul(t3, t3); let t5 = circuit_mul(t4, t0); let t6 = circuit_mul(t1, t1); let t7 = circuit_mul(t6, t6); let t8 = circuit_mul(t7, t1); let t9 = circuit_mul(t2, t2); let t10 = circuit_mul(t9, t9); let t11 = circuit_mul(t10, t2); let t12 = circuit_add(t5, in4); let t13 = circuit_add(t8, in5); let t14 = circuit_add(t11, in6); let t15 = circuit_mul(in82, t12); let t16 = circuit_mul(in85, t13); let t17 = circuit_mul(in88, t14); let t18 = circuit_add(t15, t16); let t19 = circuit_add(t18, t17); let t20 = circuit_mul(in83, t12); let t21 = circuit_mul(in86, t13); let t22 = circuit_mul(in89, t14); let t23 = circuit_add(t20, t21); let t24 = circuit_add(t23, t22); let t25 = circuit_mul(in84, t12); let t26 = circuit_mul(in87, t13); let t27 = circuit_mul(in90, t14); let t28 = circuit_add(t25, t26); let t29 = circuit_add(t28, t27); let t30 = circuit_mul(t19, t19); let t31 = circuit_mul(t30, t30); let t32 = circuit_mul(t31, t19); let t33 = circuit_mul(t24, t24); let t34 = circuit_mul(t33, t33); let t35 = circuit_mul(t34, t24); let t36 = circuit_mul(t29, t29); let t37 = circuit_mul(t36, t36); let t38 = circuit_mul(t37, t29); let t39 = circuit_add(t32, in7); let t40 = circuit_add(t35, in8); let t41 = circuit_add(t38, in9); let t42 = circuit_mul(in82, t39); let t43 = circuit_mul(in85, t40); let t44 = circuit_mul(in88, t41); let t45 = circuit_add(t42, t43); let t46 = circuit_add(t45, t44); let t47 = circuit_mul(in83, t39); let t48 = circuit_mul(in86, t40); let t49 = circuit_mul(in89, t41); let t50 = circuit_add(t47, t48); let t51 = circuit_add(t50, t49); let t52 = circuit_mul(in84, t39); let t53 = circuit_mul(in87, t40); let t54 = circuit_mul(in90, t41); let t55 = circuit_add(t52, t53); let t56 = circuit_add(t55, t54); let t57 = circuit_mul(t46, t46); let t58 = circuit_mul(t57, t57); let t59 = circuit_mul(t58, t46); let t60 = circuit_mul(t51, t51); let t61 = circuit_mul(t60, t60); let t62 = circuit_mul(t61, t51); let t63 = circuit_mul(t56, t56); let t64 = circuit_mul(t63, t63); let t65 = circuit_mul(t64, t56); let t66 = circuit_add(t59, in10); let t67 = circuit_add(t62, in11); let t68 = circuit_add(t65, in12); let t69 = circuit_mul(in82, t66); let t70 = circuit_mul(in85, t67); let t71 = circuit_mul(in88, t68); let t72 = circuit_add(t69, t70); let t73 = circuit_add(t72, t71); let t74 = circuit_mul(in83, t66); let t75 = circuit_mul(in86, t67); let t76 = circuit_mul(in89, t68); let t77 = circuit_add(t74, t75); let t78 = circuit_add(t77, t76); let t79 = circuit_mul(in84, t66); let t80 = circuit_mul(in87, t67); let t81 = circuit_mul(in90, t68); let t82 = circuit_add(t79, t80); let t83 = circuit_add(t82, t81); let t84 = circuit_mul(t73, t73); let t85 = circuit_mul(t84, t84); let t86 = circuit_mul(t85, t73); let t87 = circuit_mul(t78, t78); let t88 = circuit_mul(t87, t87); let t89 = circuit_mul(t88, t78); let t90 = circuit_mul(t83, t83); let t91 = circuit_mul(t90, t90); let t92 = circuit_mul(t91, t83); let t93 = circuit_add(t86, in13); let t94 = circuit_add(t89, in14); let t95 = circuit_add(t92, in15); let t96 = circuit_mul(in82, t93); let t97 = circuit_mul(in85, t94); let t98 = circuit_mul(in88, t95); let t99 = circuit_add(t96, t97); let t100 = circuit_add(t99, t98); let t101 = circuit_mul(in91, t93); let t102 = circuit_mul(in93, t94); let t103 = circuit_mul(in95, t95); let t104 = circuit_add(t101, t102); let t105 = circuit_add(t104, t103); let t106 = circuit_mul(in92, t93); let t107 = circuit_mul(in94, t94); let t108 = circuit_mul(in96, t95); let t109 = circuit_add(t106, t107); let t110 = circuit_add(t109, t108); let t111 = circuit_mul(t100, t100); let t112 = circuit_mul(t111, t111); let t113 = circuit_mul(t112, t100); let t114 = circuit_add(t113, in16); let t115 = circuit_mul(in82, t114); let t116 = circuit_mul(in97, t105); let t117 = circuit_mul(in98, t110); let t118 = circuit_add(t115, t116); let t119 = circuit_add(t118, t117); let t120 = circuit_mul(t114, in99); let t121 = circuit_add(t105, t120); let t122 = circuit_mul(t114, in100); let t123 = circuit_add(t110, t122); let t124 = circuit_mul(t119, t119); let t125 = circuit_mul(t124, t124); let t126 = circuit_mul(t125, t119); let t127 = circuit_add(t126, in17); let t128 = circuit_mul(in82, t127); let t129 = circuit_mul(in101, t121); let t130 = circuit_mul(in102, t123); let t131 = circuit_add(t128, t129); let t132 = circuit_add(t131, t130); let t133 = circuit_mul(t127, in103); let t134 = circuit_add(t121, t133); let t135 = circuit_mul(t127, in104); let t136 = circuit_add(t123, t135); let t137 = circuit_mul(t132, t132); let t138 = circuit_mul(t137, t137); let t139 = circuit_mul(t138, t132); let t140 = circuit_add(t139, in18); let t141 = circuit_mul(in82, t140); let t142 = circuit_mul(in105, t134); let t143 = circuit_mul(in106, t136); let t144 = circuit_add(t141, t142); let t145 = circuit_add(t144, t143); let t146 = circuit_mul(t140, in107); let t147 = circuit_add(t134, t146); let t148 = circuit_mul(t140, in108); let t149 = circuit_add(t136, t148); let t150 = circuit_mul(t145, t145); let t151 = circuit_mul(t150, t150); let t152 = circuit_mul(t151, t145); let t153 = circuit_add(t152, in19); let t154 = circuit_mul(in82, t153); let t155 = circuit_mul(in109, t147); let t156 = circuit_mul(in110, t149); let t157 = circuit_add(t154, t155); let t158 = circuit_add(t157, t156); let t159 = circuit_mul(t153, in111); let t160 = circuit_add(t147, t159); let t161 = circuit_mul(t153, in112); let t162 = circuit_add(t149, t161); let t163 = circuit_mul(t158, t158); let t164 = circuit_mul(t163, t163); let t165 = circuit_mul(t164, t158); let t166 = circuit_add(t165, in20); let t167 = circuit_mul(in82, t166); let t168 = circuit_mul(in113, t160); let t169 = circuit_mul(in114, t162); let t170 = circuit_add(t167, t168); let t171 = circuit_add(t170, t169); let t172 = circuit_mul(t166, in115); let t173 = circuit_add(t160, t172); let t174 = circuit_mul(t166, in116); let t175 = circuit_add(t162, t174); let t176 = circuit_mul(t171, t171); let t177 = circuit_mul(t176, t176); let t178 = circuit_mul(t177, t171); let t179 = circuit_add(t178, in21); let t180 = circuit_mul(in82, t179); let t181 = circuit_mul(in117, t173); let t182 = circuit_mul(in118, t175); let t183 = circuit_add(t180, t181); let t184 = circuit_add(t183, t182); let t185 = circuit_mul(t179, in119); let t186 = circuit_add(t173, t185); let t187 = circuit_mul(t179, in120); let t188 = circuit_add(t175, t187); let t189 = circuit_mul(t184, t184); let t190 = circuit_mul(t189, t189); let t191 = circuit_mul(t190, t184); let t192 = circuit_add(t191, in22); let t193 = circuit_mul(in82, t192); let t194 = circuit_mul(in121, t186); let t195 = circuit_mul(in122, t188); let t196 = circuit_add(t193, t194); let t197 = circuit_add(t196, t195); let t198 = circuit_mul(t192, in123); let t199 = circuit_add(t186, t198); let t200 = circuit_mul(t192, in124); let t201 = circuit_add(t188, t200); let t202 = circuit_mul(t197, t197); let t203 = circuit_mul(t202, t202); let t204 = circuit_mul(t203, t197); let t205 = circuit_add(t204, in23); let t206 = circuit_mul(in82, t205); let t207 = circuit_mul(in125, t199); let t208 = circuit_mul(in126, t201); let t209 = circuit_add(t206, t207); let t210 = circuit_add(t209, t208); let t211 = circuit_mul(t205, in127); let t212 = circuit_add(t199, t211); let t213 = circuit_mul(t205, in128); let t214 = circuit_add(t201, t213); let t215 = circuit_mul(t210, t210); let t216 = circuit_mul(t215, t215); let t217 = circuit_mul(t216, t210); let t218 = circuit_add(t217, in24); let t219 = circuit_mul(in82, t218); let t220 = circuit_mul(in129, t212); let t221 = circuit_mul(in130, t214); let t222 = circuit_add(t219, t220); let t223 = circuit_add(t222, t221); let t224 = circuit_mul(t218, in131); let t225 = circuit_add(t212, t224); let t226 = circuit_mul(t218, in132); let t227 = circuit_add(t214, t226); let t228 = circuit_mul(t223, t223); let t229 = circuit_mul(t228, t228); let t230 = circuit_mul(t229, t223); let t231 = circuit_add(t230, in25); let t232 = circuit_mul(in82, t231); let t233 = circuit_mul(in133, t225); let t234 = circuit_mul(in134, t227); let t235 = circuit_add(t232, t233); let t236 = circuit_add(t235, t234); let t237 = circuit_mul(t231, in135); let t238 = circuit_add(t225, t237); let t239 = circuit_mul(t231, in136); let t240 = circuit_add(t227, t239); let t241 = circuit_mul(t236, t236); let t242 = circuit_mul(t241, t241); let t243 = circuit_mul(t242, t236); let t244 = circuit_add(t243, in26); let t245 = circuit_mul(in82, t244); let t246 = circuit_mul(in137, t238); let t247 = circuit_mul(in138, t240); let t248 = circuit_add(t245, t246); let t249 = circuit_add(t248, t247); let t250 = circuit_mul(t244, in139); let t251 = circuit_add(t238, t250); let t252 = circuit_mul(t244, in140); let t253 = circuit_add(t240, t252); let t254 = circuit_mul(t249, t249); let t255 = circuit_mul(t254, t254); let t256 = circuit_mul(t255, t249); let t257 = circuit_add(t256, in27); let t258 = circuit_mul(in82, t257); let t259 = circuit_mul(in141, t251); let t260 = circuit_mul(in142, t253); let t261 = circuit_add(t258, t259); let t262 = circuit_add(t261, t260); let t263 = circuit_mul(t257, in143); let t264 = circuit_add(t251, t263); let t265 = circuit_mul(t257, in144); let t266 = circuit_add(t253, t265); let t267 = circuit_mul(t262, t262); let t268 = circuit_mul(t267, t267); let t269 = circuit_mul(t268, t262); let t270 = circuit_add(t269, in28); let t271 = circuit_mul(in82, t270); let t272 = circuit_mul(in145, t264); let t273 = circuit_mul(in146, t266); let t274 = circuit_add(t271, t272); let t275 = circuit_add(t274, t273); let t276 = circuit_mul(t270, in147); let t277 = circuit_add(t264, t276); let t278 = circuit_mul(t270, in148); let t279 = circuit_add(t266, t278); let t280 = circuit_mul(t275, t275); let t281 = circuit_mul(t280, t280); let t282 = circuit_mul(t281, t275); let t283 = circuit_add(t282, in29); let t284 = circuit_mul(in82, t283); let t285 = circuit_mul(in149, t277); let t286 = circuit_mul(in150, t279); let t287 = circuit_add(t284, t285); let t288 = circuit_add(t287, t286); let t289 = circuit_mul(t283, in151); let t290 = circuit_add(t277, t289); let t291 = circuit_mul(t283, in152); let t292 = circuit_add(t279, t291); let t293 = circuit_mul(t288, t288); let t294 = circuit_mul(t293, t293); let t295 = circuit_mul(t294, t288); let t296 = circuit_add(t295, in30); let t297 = circuit_mul(in82, t296); let t298 = circuit_mul(in153, t290); let t299 = circuit_mul(in154, t292); let t300 = circuit_add(t297, t298); let t301 = circuit_add(t300, t299); let t302 = circuit_mul(t296, in155); let t303 = circuit_add(t290, t302); let t304 = circuit_mul(t296, in156); let t305 = circuit_add(t292, t304); let t306 = circuit_mul(t301, t301); let t307 = circuit_mul(t306, t306); let t308 = circuit_mul(t307, t301); let t309 = circuit_add(t308, in31); let t310 = circuit_mul(in82, t309); let t311 = circuit_mul(in157, t303); let t312 = circuit_mul(in158, t305); let t313 = circuit_add(t310, t311); let t314 = circuit_add(t313, t312); let t315 = circuit_mul(t309, in159); let t316 = circuit_add(t303, t315); let t317 = circuit_mul(t309, in160); let t318 = circuit_add(t305, t317); let t319 = circuit_mul(t314, t314); let t320 = circuit_mul(t319, t319); let t321 = circuit_mul(t320, t314); let t322 = circuit_add(t321, in32); let t323 = circuit_mul(in82, t322); let t324 = circuit_mul(in161, t316); let t325 = circuit_mul(in162, t318); let t326 = circuit_add(t323, t324); let t327 = circuit_add(t326, t325); let t328 = circuit_mul(t322, in163); let t329 = circuit_add(t316, t328); let t330 = circuit_mul(t322, in164); let t331 = circuit_add(t318, t330); let t332 = circuit_mul(t327, t327); let t333 = circuit_mul(t332, t332); let t334 = circuit_mul(t333, t327); let t335 = circuit_add(t334, in33); let t336 = circuit_mul(in82, t335); let t337 = circuit_mul(in165, t329); let t338 = circuit_mul(in166, t331); let t339 = circuit_add(t336, t337); let t340 = circuit_add(t339, t338); let t341 = circuit_mul(t335, in167); let t342 = circuit_add(t329, t341); let t343 = circuit_mul(t335, in168); let t344 = circuit_add(t331, t343); let t345 = circuit_mul(t340, t340); let t346 = circuit_mul(t345, t345); let t347 = circuit_mul(t346, t340); let t348 = circuit_add(t347, in34); let t349 = circuit_mul(in82, t348); let t350 = circuit_mul(in169, t342); let t351 = circuit_mul(in170, t344); let t352 = circuit_add(t349, t350); let t353 = circuit_add(t352, t351); let t354 = circuit_mul(t348, in171); let t355 = circuit_add(t342, t354); let t356 = circuit_mul(t348, in172); let t357 = circuit_add(t344, t356); let t358 = circuit_mul(t353, t353); let t359 = circuit_mul(t358, t358); let t360 = circuit_mul(t359, t353); let t361 = circuit_add(t360, in35); let t362 = circuit_mul(in82, t361); let t363 = circuit_mul(in173, t355); let t364 = circuit_mul(in174, t357); let t365 = circuit_add(t362, t363); let t366 = circuit_add(t365, t364); let t367 = circuit_mul(t361, in175); let t368 = circuit_add(t355, t367); let t369 = circuit_mul(t361, in176); let t370 = circuit_add(t357, t369); let t371 = circuit_mul(t366, t366); let t372 = circuit_mul(t371, t371); let t373 = circuit_mul(t372, t366); let t374 = circuit_add(t373, in36); let t375 = circuit_mul(in82, t374); let t376 = circuit_mul(in177, t368); let t377 = circuit_mul(in178, t370); let t378 = circuit_add(t375, t376); let t379 = circuit_add(t378, t377); let t380 = circuit_mul(t374, in179); let t381 = circuit_add(t368, t380); let t382 = circuit_mul(t374, in180); let t383 = circuit_add(t370, t382); let t384 = circuit_mul(t379, t379); let t385 = circuit_mul(t384, t384); let t386 = circuit_mul(t385, t379); let t387 = circuit_add(t386, in37); let t388 = circuit_mul(in82, t387); let t389 = circuit_mul(in181, t381); let t390 = circuit_mul(in182, t383); let t391 = circuit_add(t388, t389); let t392 = circuit_add(t391, t390); let t393 = circuit_mul(t387, in183); let t394 = circuit_add(t381, t393); let t395 = circuit_mul(t387, in184); let t396 = circuit_add(t383, t395); let t397 = circuit_mul(t392, t392); let t398 = circuit_mul(t397, t397); let t399 = circuit_mul(t398, t392); let t400 = circuit_add(t399, in38); let t401 = circuit_mul(in82, t400); let t402 = circuit_mul(in185, t394); let t403 = circuit_mul(in186, t396); let t404 = circuit_add(t401, t402); let t405 = circuit_add(t404, t403); let t406 = circuit_mul(t400, in187); let t407 = circuit_add(t394, t406); let t408 = circuit_mul(t400, in188); let t409 = circuit_add(t396, t408); let t410 = circuit_mul(t405, t405); let t411 = circuit_mul(t410, t410); let t412 = circuit_mul(t411, t405); let t413 = circuit_add(t412, in39); let t414 = circuit_mul(in82, t413); let t415 = circuit_mul(in189, t407); let t416 = circuit_mul(in190, t409); let t417 = circuit_add(t414, t415); let t418 = circuit_add(t417, t416); let t419 = circuit_mul(t413, in191); let t420 = circuit_add(t407, t419); let t421 = circuit_mul(t413, in192); let t422 = circuit_add(t409, t421); let t423 = circuit_mul(t418, t418); let t424 = circuit_mul(t423, t423); let t425 = circuit_mul(t424, t418); let t426 = circuit_add(t425, in40); let t427 = circuit_mul(in82, t426); let t428 = circuit_mul(in193, t420); let t429 = circuit_mul(in194, t422); let t430 = circuit_add(t427, t428); let t431 = circuit_add(t430, t429); let t432 = circuit_mul(t426, in195); let t433 = circuit_add(t420, t432); let t434 = circuit_mul(t426, in196); let t435 = circuit_add(t422, t434); let t436 = circuit_mul(t431, t431); let t437 = circuit_mul(t436, t436); let t438 = circuit_mul(t437, t431); let t439 = circuit_add(t438, in41); let t440 = circuit_mul(in82, t439); let t441 = circuit_mul(in197, t433); let t442 = circuit_mul(in198, t435); let t443 = circuit_add(t440, t441); let t444 = circuit_add(t443, t442); let t445 = circuit_mul(t439, in199); let t446 = circuit_add(t433, t445); let t447 = circuit_mul(t439, in200); let t448 = circuit_add(t435, t447); let t449 = circuit_mul(t444, t444); let t450 = circuit_mul(t449, t449); let t451 = circuit_mul(t450, t444); let t452 = circuit_add(t451, in42); let t453 = circuit_mul(in82, t452); let t454 = circuit_mul(in201, t446); let t455 = circuit_mul(in202, t448); let t456 = circuit_add(t453, t454); let t457 = circuit_add(t456, t455); let t458 = circuit_mul(t452, in203); let t459 = circuit_add(t446, t458); let t460 = circuit_mul(t452, in204); let t461 = circuit_add(t448, t460); let t462 = circuit_mul(t457, t457); let t463 = circuit_mul(t462, t462); let t464 = circuit_mul(t463, t457); let t465 = circuit_add(t464, in43); let t466 = circuit_mul(in82, t465); let t467 = circuit_mul(in205, t459); let t468 = circuit_mul(in206, t461); let t469 = circuit_add(t466, t467); let t470 = circuit_add(t469, t468); let t471 = circuit_mul(t465, in207); let t472 = circuit_add(t459, t471); let t473 = circuit_mul(t465, in208); let t474 = circuit_add(t461, t473); let t475 = circuit_mul(t470, t470); let t476 = circuit_mul(t475, t475); let t477 = circuit_mul(t476, t470); let t478 = circuit_add(t477, in44); let t479 = circuit_mul(in82, t478); let t480 = circuit_mul(in209, t472); let t481 = circuit_mul(in210, t474); let t482 = circuit_add(t479, t480); let t483 = circuit_add(t482, t481); let t484 = circuit_mul(t478, in211); let t485 = circuit_add(t472, t484); let t486 = circuit_mul(t478, in212); let t487 = circuit_add(t474, t486); let t488 = circuit_mul(t483, t483); let t489 = circuit_mul(t488, t488); let t490 = circuit_mul(t489, t483); let t491 = circuit_add(t490, in45); let t492 = circuit_mul(in82, t491); let t493 = circuit_mul(in213, t485); let t494 = circuit_mul(in214, t487); let t495 = circuit_add(t492, t493); let t496 = circuit_add(t495, t494); let t497 = circuit_mul(t491, in215); let t498 = circuit_add(t485, t497); let t499 = circuit_mul(t491, in216); let t500 = circuit_add(t487, t499); let t501 = circuit_mul(t496, t496); let t502 = circuit_mul(t501, t501); let t503 = circuit_mul(t502, t496); let t504 = circuit_add(t503, in46); let t505 = circuit_mul(in82, t504); let t506 = circuit_mul(in217, t498); let t507 = circuit_mul(in218, t500); let t508 = circuit_add(t505, t506); let t509 = circuit_add(t508, t507); let t510 = circuit_mul(t504, in219); let t511 = circuit_add(t498, t510); let t512 = circuit_mul(t504, in220); let t513 = circuit_add(t500, t512); let t514 = circuit_mul(t509, t509); let t515 = circuit_mul(t514, t514); let t516 = circuit_mul(t515, t509); let t517 = circuit_add(t516, in47); let t518 = circuit_mul(in82, t517); let t519 = circuit_mul(in221, t511); let t520 = circuit_mul(in222, t513); let t521 = circuit_add(t518, t519); let t522 = circuit_add(t521, t520); let t523 = circuit_mul(t517, in223); let t524 = circuit_add(t511, t523); let t525 = circuit_mul(t517, in224); let t526 = circuit_add(t513, t525); let t527 = circuit_mul(t522, t522); let t528 = circuit_mul(t527, t527); let t529 = circuit_mul(t528, t522); let t530 = circuit_add(t529, in48); let t531 = circuit_mul(in82, t530); let t532 = circuit_mul(in225, t524); let t533 = circuit_mul(in226, t526); let t534 = circuit_add(t531, t532); let t535 = circuit_add(t534, t533); let t536 = circuit_mul(t530, in227); let t537 = circuit_add(t524, t536); let t538 = circuit_mul(t530, in228); let t539 = circuit_add(t526, t538); let t540 = circuit_mul(t535, t535); let t541 = circuit_mul(t540, t540); let t542 = circuit_mul(t541, t535); let t543 = circuit_add(t542, in49); let t544 = circuit_mul(in82, t543); let t545 = circuit_mul(in229, t537); let t546 = circuit_mul(in230, t539); let t547 = circuit_add(t544, t545); let t548 = circuit_add(t547, t546); let t549 = circuit_mul(t543, in231); let t550 = circuit_add(t537, t549); let t551 = circuit_mul(t543, in232); let t552 = circuit_add(t539, t551); let t553 = circuit_mul(t548, t548); let t554 = circuit_mul(t553, t553); let t555 = circuit_mul(t554, t548); let t556 = circuit_add(t555, in50); let t557 = circuit_mul(in82, t556); let t558 = circuit_mul(in233, t550); let t559 = circuit_mul(in234, t552); let t560 = circuit_add(t557, t558); let t561 = circuit_add(t560, t559); let t562 = circuit_mul(t556, in235); let t563 = circuit_add(t550, t562); let t564 = circuit_mul(t556, in236); let t565 = circuit_add(t552, t564); let t566 = circuit_mul(t561, t561); let t567 = circuit_mul(t566, t566); let t568 = circuit_mul(t567, t561); let t569 = circuit_add(t568, in51); let t570 = circuit_mul(in82, t569); let t571 = circuit_mul(in237, t563); let t572 = circuit_mul(in238, t565); let t573 = circuit_add(t570, t571); let t574 = circuit_add(t573, t572); let t575 = circuit_mul(t569, in239); let t576 = circuit_add(t563, t575); let t577 = circuit_mul(t569, in240); let t578 = circuit_add(t565, t577); let t579 = circuit_mul(t574, t574); let t580 = circuit_mul(t579, t579); let t581 = circuit_mul(t580, t574); let t582 = circuit_add(t581, in52); let t583 = circuit_mul(in82, t582); let t584 = circuit_mul(in241, t576); let t585 = circuit_mul(in242, t578); let t586 = circuit_add(t583, t584); let t587 = circuit_add(t586, t585); let t588 = circuit_mul(t582, in243); let t589 = circuit_add(t576, t588); let t590 = circuit_mul(t582, in244); let t591 = circuit_add(t578, t590); let t592 = circuit_mul(t587, t587); let t593 = circuit_mul(t592, t592); let t594 = circuit_mul(t593, t587); let t595 = circuit_add(t594, in53); let t596 = circuit_mul(in82, t595); let t597 = circuit_mul(in245, t589); let t598 = circuit_mul(in246, t591); let t599 = circuit_add(t596, t597); let t600 = circuit_add(t599, t598); let t601 = circuit_mul(t595, in247); let t602 = circuit_add(t589, t601); let t603 = circuit_mul(t595, in248); let t604 = circuit_add(t591, t603); let t605 = circuit_mul(t600, t600); let t606 = circuit_mul(t605, t605); let t607 = circuit_mul(t606, t600); let t608 = circuit_add(t607, in54); let t609 = circuit_mul(in82, t608); let t610 = circuit_mul(in249, t602); let t611 = circuit_mul(in250, t604); let t612 = circuit_add(t609, t610); let t613 = circuit_add(t612, t611); let t614 = circuit_mul(t608, in251); let t615 = circuit_add(t602, t614); let t616 = circuit_mul(t608, in252); let t617 = circuit_add(t604, t616); let t618 = circuit_mul(t613, t613); let t619 = circuit_mul(t618, t618); let t620 = circuit_mul(t619, t613); let t621 = circuit_add(t620, in55); let t622 = circuit_mul(in82, t621); let t623 = circuit_mul(in253, t615); let t624 = circuit_mul(in254, t617); let t625 = circuit_add(t622, t623); let t626 = circuit_add(t625, t624); let t627 = circuit_mul(t621, in255); let t628 = circuit_add(t615, t627); let t629 = circuit_mul(t621, in256); let t630 = circuit_add(t617, t629); let t631 = circuit_mul(t626, t626); let t632 = circuit_mul(t631, t631); let t633 = circuit_mul(t632, t626); let t634 = circuit_add(t633, in56); let t635 = circuit_mul(in82, t634); let t636 = circuit_mul(in257, t628); let t637 = circuit_mul(in258, t630); let t638 = circuit_add(t635, t636); let t639 = circuit_add(t638, t637); let t640 = circuit_mul(t634, in259); let t641 = circuit_add(t628, t640); let t642 = circuit_mul(t634, in260); let t643 = circuit_add(t630, t642); let t644 = circuit_mul(t639, t639); let t645 = circuit_mul(t644, t644); let t646 = circuit_mul(t645, t639); let t647 = circuit_add(t646, in57); let t648 = circuit_mul(in82, t647); let t649 = circuit_mul(in261, t641); let t650 = circuit_mul(in262, t643); let t651 = circuit_add(t648, t649); let t652 = circuit_add(t651, t650); let t653 = circuit_mul(t647, in263); let t654 = circuit_add(t641, t653); let t655 = circuit_mul(t647, in264); let t656 = circuit_add(t643, t655); let t657 = circuit_mul(t652, t652); let t658 = circuit_mul(t657, t657); let t659 = circuit_mul(t658, t652); let t660 = circuit_add(t659, in58); let t661 = circuit_mul(in82, t660); let t662 = circuit_mul(in265, t654); let t663 = circuit_mul(in266, t656); let t664 = circuit_add(t661, t662); let t665 = circuit_add(t664, t663); let t666 = circuit_mul(t660, in267); let t667 = circuit_add(t654, t666); let t668 = circuit_mul(t660, in268); let t669 = circuit_add(t656, t668); let t670 = circuit_mul(t665, t665); let t671 = circuit_mul(t670, t670); let t672 = circuit_mul(t671, t665); let t673 = circuit_add(t672, in59); let t674 = circuit_mul(in82, t673); let t675 = circuit_mul(in269, t667); let t676 = circuit_mul(in270, t669); let t677 = circuit_add(t674, t675); let t678 = circuit_add(t677, t676); let t679 = circuit_mul(t673, in271); let t680 = circuit_add(t667, t679); let t681 = circuit_mul(t673, in272); let t682 = circuit_add(t669, t681); let t683 = circuit_mul(t678, t678); let t684 = circuit_mul(t683, t683); let t685 = circuit_mul(t684, t678); let t686 = circuit_add(t685, in60); let t687 = circuit_mul(in82, t686); let t688 = circuit_mul(in273, t680); let t689 = circuit_mul(in274, t682); let t690 = circuit_add(t687, t688); let t691 = circuit_add(t690, t689); let t692 = circuit_mul(t686, in275); let t693 = circuit_add(t680, t692); let t694 = circuit_mul(t686, in276); let t695 = circuit_add(t682, t694); let t696 = circuit_mul(t691, t691); let t697 = circuit_mul(t696, t696); let t698 = circuit_mul(t697, t691); let t699 = circuit_add(t698, in61); let t700 = circuit_mul(in82, t699); let t701 = circuit_mul(in277, t693); let t702 = circuit_mul(in278, t695); let t703 = circuit_add(t700, t701); let t704 = circuit_add(t703, t702); let t705 = circuit_mul(t699, in279); let t706 = circuit_add(t693, t705); let t707 = circuit_mul(t699, in280); let t708 = circuit_add(t695, t707); let t709 = circuit_mul(t704, t704); let t710 = circuit_mul(t709, t709); let t711 = circuit_mul(t710, t704); let t712 = circuit_add(t711, in62); let t713 = circuit_mul(in82, t712); let t714 = circuit_mul(in281, t706); let t715 = circuit_mul(in282, t708); let t716 = circuit_add(t713, t714); let t717 = circuit_add(t716, t715); let t718 = circuit_mul(t712, in283); let t719 = circuit_add(t706, t718); let t720 = circuit_mul(t712, in284); let t721 = circuit_add(t708, t720); let t722 = circuit_mul(t717, t717); let t723 = circuit_mul(t722, t722); let t724 = circuit_mul(t723, t717); let t725 = circuit_add(t724, in63); let t726 = circuit_mul(in82, t725); let t727 = circuit_mul(in285, t719); let t728 = circuit_mul(in286, t721); let t729 = circuit_add(t726, t727); let t730 = circuit_add(t729, t728); let t731 = circuit_mul(t725, in287); let t732 = circuit_add(t719, t731); let t733 = circuit_mul(t725, in288); let t734 = circuit_add(t721, t733); let t735 = circuit_mul(t730, t730); let t736 = circuit_mul(t735, t735); let t737 = circuit_mul(t736, t730); let t738 = circuit_add(t737, in64); let t739 = circuit_mul(in82, t738); let t740 = circuit_mul(in289, t732); let t741 = circuit_mul(in290, t734); let t742 = circuit_add(t739, t740); let t743 = circuit_add(t742, t741); let t744 = circuit_mul(t738, in291); let t745 = circuit_add(t732, t744); let t746 = circuit_mul(t738, in292); let t747 = circuit_add(t734, t746); let t748 = circuit_mul(t743, t743); let t749 = circuit_mul(t748, t748); let t750 = circuit_mul(t749, t743); let t751 = circuit_add(t750, in65); let t752 = circuit_mul(in82, t751); let t753 = circuit_mul(in293, t745); let t754 = circuit_mul(in294, t747); let t755 = circuit_add(t752, t753); let t756 = circuit_add(t755, t754); let t757 = circuit_mul(t751, in295); let t758 = circuit_add(t745, t757); let t759 = circuit_mul(t751, in296); let t760 = circuit_add(t747, t759); let t761 = circuit_mul(t756, t756); let t762 = circuit_mul(t761, t761); let t763 = circuit_mul(t762, t756); let t764 = circuit_add(t763, in66); let t765 = circuit_mul(in82, t764); let t766 = circuit_mul(in297, t758); let t767 = circuit_mul(in298, t760); let t768 = circuit_add(t765, t766); let t769 = circuit_add(t768, t767); let t770 = circuit_mul(t764, in299); let t771 = circuit_add(t758, t770); let t772 = circuit_mul(t764, in300); let t773 = circuit_add(t760, t772); let t774 = circuit_mul(t769, t769); let t775 = circuit_mul(t774, t774); let t776 = circuit_mul(t775, t769); let t777 = circuit_add(t776, in67); let t778 = circuit_mul(in82, t777); let t779 = circuit_mul(in301, t771); let t780 = circuit_mul(in302, t773); let t781 = circuit_add(t778, t779); let t782 = circuit_add(t781, t780); let t783 = circuit_mul(t777, in303); let t784 = circuit_add(t771, t783); let t785 = circuit_mul(t777, in304); let t786 = circuit_add(t773, t785); let t787 = circuit_mul(t782, t782); let t788 = circuit_mul(t787, t787); let t789 = circuit_mul(t788, t782); let t790 = circuit_add(t789, in68); let t791 = circuit_mul(in82, t790); let t792 = circuit_mul(in305, t784); let t793 = circuit_mul(in306, t786); let t794 = circuit_add(t791, t792); let t795 = circuit_add(t794, t793); let t796 = circuit_mul(t790, in307); let t797 = circuit_add(t784, t796); let t798 = circuit_mul(t790, in308); let t799 = circuit_add(t786, t798); let t800 = circuit_mul(t795, t795); let t801 = circuit_mul(t800, t800); let t802 = circuit_mul(t801, t795); let t803 = circuit_add(t802, in69); let t804 = circuit_mul(in82, t803); let t805 = circuit_mul(in309, t797); let t806 = circuit_mul(in310, t799); let t807 = circuit_add(t804, t805); let t808 = circuit_add(t807, t806); let t809 = circuit_mul(t803, in311); let t810 = circuit_add(t797, t809); let t811 = circuit_mul(t803, in312); let t812 = circuit_add(t799, t811); let t813 = circuit_mul(t808, t808); let t814 = circuit_mul(t813, t813); let t815 = circuit_mul(t814, t808); let t816 = circuit_add(t815, in70); let t817 = circuit_mul(in82, t816); let t818 = circuit_mul(in313, t810); let t819 = circuit_mul(in314, t812); let t820 = circuit_add(t817, t818); let t821 = circuit_add(t820, t819); let t822 = circuit_mul(t816, in315); let t823 = circuit_add(t810, t822); let t824 = circuit_mul(t816, in316); let t825 = circuit_add(t812, t824); let t826 = circuit_mul(t821, t821); let t827 = circuit_mul(t826, t826); let t828 = circuit_mul(t827, t821); let t829 = circuit_add(t828, in71); let t830 = circuit_mul(in82, t829); let t831 = circuit_mul(in317, t823); let t832 = circuit_mul(in318, t825); let t833 = circuit_add(t830, t831); let t834 = circuit_add(t833, t832); let t835 = circuit_mul(t829, in319); let t836 = circuit_add(t823, t835); let t837 = circuit_mul(t829, in320); let t838 = circuit_add(t825, t837); let t839 = circuit_mul(t834, t834); let t840 = circuit_mul(t839, t839); let t841 = circuit_mul(t840, t834); let t842 = circuit_add(t841, in72); let t843 = circuit_mul(in82, t842); let t844 = circuit_mul(in321, t836); let t845 = circuit_mul(in322, t838); let t846 = circuit_add(t843, t844); let t847 = circuit_add(t846, t845); let t848 = circuit_mul(t842, in83); let t849 = circuit_add(t836, t848); let t850 = circuit_mul(t842, in84); let t851 = circuit_add(t838, t850); let t852 = circuit_mul(t847, t847); let t853 = circuit_mul(t852, t852); let t854 = circuit_mul(t853, t847); let t855 = circuit_mul(t849, t849); let t856 = circuit_mul(t855, t855); let t857 = circuit_mul(t856, t849); let t858 = circuit_mul(t851, t851); let t859 = circuit_mul(t858, t858); let t860 = circuit_mul(t859, t851); let t861 = circuit_add(t854, in73); let t862 = circuit_add(t857, in74); let t863 = circuit_add(t860, in75); let t864 = circuit_mul(in82, t861); let t865 = circuit_mul(in85, t862); let t866 = circuit_mul(in88, t863); let t867 = circuit_add(t864, t865); let t868 = circuit_add(t867, t866); let t869 = circuit_mul(in83, t861); let t870 = circuit_mul(in86, t862); let t871 = circuit_mul(in89, t863); let t872 = circuit_add(t869, t870); let t873 = circuit_add(t872, t871); let t874 = circuit_mul(in84, t861); let t875 = circuit_mul(in87, t862); let t876 = circuit_mul(in90, t863); let t877 = circuit_add(t874, t875); let t878 = circuit_add(t877, t876); let t879 = circuit_mul(t868, t868); let t880 = circuit_mul(t879, t879); let t881 = circuit_mul(t880, t868); let t882 = circuit_mul(t873, t873); let t883 = circuit_mul(t882, t882); let t884 = circuit_mul(t883, t873); let t885 = circuit_mul(t878, t878); let t886 = circuit_mul(t885, t885); let t887 = circuit_mul(t886, t878); let t888 = circuit_add(t881, in76); let t889 = circuit_add(t884, in77); let t890 = circuit_add(t887, in78); let t891 = circuit_mul(in82, t888); let t892 = circuit_mul(in85, t889); let t893 = circuit_mul(in88, t890); let t894 = circuit_add(t891, t892); let t895 = circuit_add(t894, t893); let t896 = circuit_mul(in83, t888); let t897 = circuit_mul(in86, t889); let t898 = circuit_mul(in89, t890); let t899 = circuit_add(t896, t897); let t900 = circuit_add(t899, t898); let t901 = circuit_mul(in84, t888); let t902 = circuit_mul(in87, t889); let t903 = circuit_mul(in90, t890); let t904 = circuit_add(t901, t902); let t905 = circuit_add(t904, t903); let t906 = circuit_mul(t895, t895); let t907 = circuit_mul(t906, t906); let t908 = circuit_mul(t907, t895); let t909 = circuit_mul(t900, t900); let t910 = circuit_mul(t909, t909); let t911 = circuit_mul(t910, t900); let t912 = circuit_mul(t905, t905); let t913 = circuit_mul(t912, t912); let t914 = circuit_mul(t913, t905); let t915 = circuit_add(t908, in79); let t916 = circuit_add(t911, in80); let t917 = circuit_add(t914, in81); let t918 = circuit_mul(in82, t915); let t919 = circuit_mul(in85, t916); let t920 = circuit_mul(in88, t917); let t921 = circuit_add(t918, t919); let t922 = circuit_add(t921, t920); let t923 = circuit_mul(in83, t915); let t924 = circuit_mul(in86, t916); let t925 = circuit_mul(in89, t917); let t926 = circuit_add(t923, t924); let t927 = circuit_add(t926, t925); let t928 = circuit_mul(in84, t915); let t929 = circuit_mul(in87, t916); let t930 = circuit_mul(in90, t917); let t931 = circuit_add(t928, t929); let t932 = circuit_add(t931, t930); let t933 = circuit_mul(t922, t922); let t934 = circuit_mul(t933, t933); let t935 = circuit_mul(t934, t922); let t936 = circuit_mul(t927, t927); let t937 = circuit_mul(t936, t936); let t938 = circuit_mul(t937, t927); let t939 = circuit_mul(t932, t932); let t940 = circuit_mul(t939, t939); let t941 = circuit_mul(t940, t932); let t942 = circuit_mul(in82, t935); let t943 = circuit_mul(in85, t938); let t944 = circuit_mul(in88, t941); let t945 = circuit_add(t942, t943); let t946 = circuit_add(t945, t944); let modulus = get_GRUMPKIN_modulus(); // GRUMPKIN prime field modulus let mut circuit_inputs = (t946,).new_inputs(); // Prefill constants: circuit_inputs = circuit_inputs .next_span(POSEIDON_GRUMPKIN_GRUMPKIN_CONSTANTS.span()); // in0 - in322 // Fill inputs: circuit_inputs = circuit_inputs.next_2(x); // in323 circuit_inputs = circuit_inputs.next_2(y); // in324 let outputs = circuit_inputs.done_2().eval(modulus).unwrap(); let z: u384 = outputs.get_output(t946); return z; } const POSEIDON_GRUMPKIN_GRUMPKIN_CONSTANTS: [u384; 323] = [ u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x11bb29938d21d47304cd8e6e, limb1: 0xd05986d656f40c2114c4993c, limb2: 0xee9a592ba9a9518, limb3: 0x0, }, u384 { limb0: 0xd00868df5696fff40956e864, limb1: 0x5986587169fc1bcd887b08d4, limb2: 0xf1445235f2148c, limb3: 0x0, }, u384 { limb0: 0xb7ab36ce879f3890ecf73f5, limb1: 0x1f29a058d0fa80b930c72873, limb2: 0x8dff3487e8ac99e, limb3: 0x0, }, u384 { limb0: 0xdae2d00ca8ef88ceea2b0197, limb1: 0xe1f9075cb7c490efa59565ee, limb2: 0x84d520e4e5bb469, limb3: 0x0, }, u384 { limb0: 0x2f9f15d8eb3e767ae0fd811e, limb1: 0x33da56722416fd734b3e667a, limb2: 0x2d15d982d99577fa, limb3: 0x0, }, u384 { limb0: 0x36a5996d0efbe65632c41b6d, limb1: 0xcf1578a43cf0364e91601f65, limb2: 0xed2538844aba161, limb3: 0x0, }, u384 { limb0: 0x829b735dcc3e3af02955e60a, limb1: 0x86e739e6363c71cf804c877d, limb2: 0x2600c27d879fbca1, limb3: 0x0, }, u384 { limb0: 0x7440dfd970058558282bf2c5, limb1: 0x475bd15396430e7ccb99a551, limb2: 0x28f8bd44a583cbaa, limb3: 0x0, }, u384 { limb0: 0xf697a5572d030c55df153221, limb1: 0x8781aad012e7eaef1ed314d7, limb2: 0x9cd7d4c380dc548, limb3: 0x0, }, u384 { limb0: 0xbe82234951e2bee7d0f855f5, limb1: 0x6120ecaace460d24b6713fe, limb2: 0x11bb6ee1291aabb2, limb3: 0x0, }, u384 { limb0: 0xf5b8fd05349cadeecfceb230, limb1: 0x3310f3c0e3fae1d06f171580, limb2: 0x2d74e8fa0637d985, limb3: 0x0, }, u384 { limb0: 0xa511a18be4b4d316ed889033, limb1: 0xac9bef31bacba338b1a09559, limb2: 0x2735e4ec9d39bdff, limb3: 0x0, }, u384 { limb0: 0x826e08dcf617e24213132dfd, limb1: 0xa5da6312faa78e971106c33f, limb2: 0xf03c1e9e0895db1, limb3: 0x0, }, u384 { limb0: 0x8f777811848a7e9ead6778c4, limb1: 0xaf92920205b719c18741090b, limb2: 0x17094cd297bf827c, limb3: 0x0, }, u384 { limb0: 0x178042c81ba7d4b4d559e2b8, limb1: 0x1fc2b3219465798348df90d4, limb2: 0xdb8f419c21f9246, limb3: 0x0, }, u384 { limb0: 0xb9ca1724a22709ceceeece2, limb1: 0x17427ed5933fcfbc66809db6, limb2: 0x243443613f64ffa4, limb3: 0x0, }, u384 { limb0: 0xeecd03aa04bb191fada75411, limb1: 0xcd256c25c07d3dd8ecbbae6d, limb2: 0x22af49fbfd5d7e9f, limb3: 0x0, }, u384 { limb0: 0xb4327323f7f7c097c19420e0, limb1: 0xc78a20d93c7230c4677f797, limb2: 0x14fbd37fa8ad6e4e, limb3: 0x0, }, u384 { limb0: 0xb3f3e1ea22faa7e18b5ae625, limb1: 0xd4b2c9fbc6e4ef4189420c4e, limb2: 0x15a9298bbb882534, limb3: 0x0, }, u384 { limb0: 0x854e75434c2f1d90562232bc, limb1: 0x221323ebceb2f2ac83eef92e, limb2: 0x2f7de75f23ddaaa5, limb3: 0x0, }, u384 { limb0: 0xf9e9b2e623584f7479cd5c27, limb1: 0x78a315e84c4ae5aeca216f2f, limb2: 0x36a4432a868283b, limb3: 0x0, }, u384 { limb0: 0x2f11e860ae1c5682c797de5c, limb1: 0xe277218ab14a11e5e39f3c96, limb2: 0x2180d7786a8cf810, limb3: 0x0, }, u384 { limb0: 0x84cc03ce53572377eefff8e4, limb1: 0xd0cb55be640d73ee37789904, limb2: 0xa268ef870736eeb, limb3: 0x0, }, u384 { limb0: 0xc90e09069df9bae16809a5b2, limb1: 0x4f2999031f15994829e982e8, limb2: 0x1eefefe11c0be466, limb3: 0x0, }, u384 { limb0: 0x9a1129946571a3c3cf244c52, limb1: 0x9ca596e8cb77fe3a4b8fb93d, limb2: 0x27e87f033bd1e0a8, limb3: 0x0, }, u384 { limb0: 0xd2a3e184d21451809178ee39, limb1: 0x3321f57d6c5435889979c4f9, limb2: 0x1498a3e6599fe24, limb3: 0x0, }, u384 { limb0: 0x235bef108dea1bbebde507aa, limb1: 0xe9dd4d7ce33707f74d5d6bcc, limb2: 0x27c0a41f4cb9fe67, limb3: 0x0, }, u384 { limb0: 0x5d5004c16a7c91fe1dae280f, limb1: 0x6637238b120fc770f4f4ae82, limb2: 0x1f75230908b141b4, limb3: 0x0, }, u384 { limb0: 0x89808d4eb1f0a085bee21656, limb1: 0x7bba831b15fffd2d7b97b3a0, limb2: 0x25f99a9198e92316, limb3: 0x0, }, u384 { limb0: 0x8ed14c67622974228ba900c6, limb1: 0xd0f6acdc2bb526593d3d56ec, limb2: 0x101bc318e9ea5920, limb3: 0x0, }, u384 { limb0: 0xa3cf091ec1ccc43207a83c76, limb1: 0x97c1334ecb019754ebc0c852, limb2: 0x1a175607067d5173, limb3: 0x0, }, u384 { limb0: 0xba4af5c1c4d89770155df37b, limb1: 0xdeb245f3e8c381ee6b2eb380, limb2: 0xf02f0e6d25f9ea3, limb3: 0x0, }, u384 { limb0: 0x56ae789ff358b3163b393bc9, limb1: 0x8d8a6677203ec9692565de4, limb2: 0x151d757acc8237af, limb3: 0x0, }, u384 { limb0: 0x5b757890a79d13a3a624fad4, limb1: 0x49e0a1fe0068dd20084980ee, limb2: 0x256cd9577cea1430, limb3: 0x0, }, u384 { limb0: 0xfbdd195497b8ae86e1937c61, limb1: 0x8833b13da50e0884476682c3, limb2: 0x513abaff6195ea4, limb3: 0x0, }, u384 { limb0: 0xe4ac448386d19dbac4e4a655, limb1: 0x6f610251ee6e2e8039246e84, limb2: 0x1d9570dc70a205f3, limb3: 0x0, }, u384 { limb0: 0xd784cf5e044eec50b29fc9d4, limb1: 0xd5d7f1bf8aaa6f56effb012d, limb2: 0x18f1a5194755b8c5, limb3: 0x0, }, u384 { limb0: 0x966ef420d88163238eebbca8, limb1: 0x866512c091e4a4f2fa4bb0af, limb2: 0x266b53b615ef73ac, limb3: 0x0, }, u384 { limb0: 0xb8c89a1a3f4fd6e8344ae0f7, limb1: 0xa42b8de27644c02268304dfe, limb2: 0x2d63234c9207438a, limb3: 0x0, }, u384 { limb0: 0x5ef8df7e0021daee6f55c693, limb1: 0x7b3adde219a6f0b5fbb97620, limb2: 0x2ab30fbe51ee49bc, limb3: 0x0, }, u384 { limb0: 0xd528b270068d9207fa6a45c9, limb1: 0xdcb9cce48969d4df1dc42abc, limb2: 0x1aee6d4b3ebe9366, limb3: 0x0, }, u384 { limb0: 0xc60bb34aa211d123f6095219, limb1: 0x5a79452e5864ae1d11f57646, limb2: 0x1891aeab71e34b89, limb3: 0x0, }, u384 { limb0: 0x57771bd3a7caab01c818aa4b, limb1: 0x6437e94b4101c69118e16b26, limb2: 0x24492b5f95c0b087, limb3: 0x0, }, u384 { limb0: 0x3d66c10ab2fddf71bcfde68f, limb1: 0x1b3b2c8663a0d64296462821, limb2: 0x1752161b3350f7e, limb3: 0x0, }, u384 { limb0: 0x148de54368cfb8f90a00f3a7, limb1: 0x7cfb84938e614c6c2f445b8d, limb2: 0xab676935722e2f6, limb3: 0x0, }, u384 { limb0: 0xe227e3d4fe0da1f7aa348189, limb1: 0x45bc730117ed9ae5683fc2e6, limb2: 0xb0f72472b9a2f5f, limb3: 0x0, }, u384 { limb0: 0x2c3ae6df13a78a513edcd369, limb1: 0x1c201d1a52fc4f8acaf2b215, limb2: 0x16aa6f9273acd563, limb3: 0x0, }, u384 { limb0: 0x55d23281a45c08d52435cd60, limb1: 0x13c324c1d8716eb0bf62d9b1, limb2: 0x2f60b987e63614eb, limb3: 0x0, }, u384 { limb0: 0x42f508fd9db76b7cc1b21212, limb1: 0x7606bb7884554e9df1cb89b0, limb2: 0x18d24ae01dde92fd, limb3: 0x0, }, u384 { limb0: 0xdf1593960715d4724cffa586, limb1: 0x8d776373130df79d18c3185f, limb2: 0x4fc3bf76fe31e2f, limb3: 0x0, }, u384 { limb0: 0xb21260c6b5d26270468dbf82, limb1: 0xcfdd670b41732bdf6dee9e06, limb2: 0xd18f6b53fc69546, limb3: 0x0, }, u384 { limb0: 0xcdb045036fa5d7045bd10e24, limb1: 0xcec11fbafa17c5223f1f70b4, limb2: 0xba4231a918f13a, limb3: 0x0, }, u384 { limb0: 0x635ff1ebedd0dd86120b4c8, limb1: 0x100985301663e7ec33c826da, limb2: 0x7b458b2e00cd7c6, limb3: 0x0, }, u384 { limb0: 0xed40b16cec39e9fd7baa5799, limb1: 0x6058e76f15a0c8286bba24e2, limb2: 0x1c35c2d96db90f4f, limb3: 0x0, }, u384 { limb0: 0xbbef96945e0dde688e292050, limb1: 0x766568f03dd1ecdb0a4f589a, limb2: 0x1d12bea3d8c32a5d, limb3: 0x0, }, u384 { limb0: 0x2fdea94313db405a61300286, limb1: 0x525f9a73526e9889c995bb6, limb2: 0xd953e2002200327, limb3: 0x0, }, u384 { limb0: 0x10b4040a760e33506d2671e1, limb1: 0x86a40bec4c875047f06ff0b6, limb2: 0x29f053ec388795d7, limb3: 0x0, }, u384 { limb0: 0x46e0c3f64b9679caaae44fc2, limb1: 0x4a4952a98463bc12e264d5f4, limb2: 0x4188e33735f46b1, limb3: 0x0, }, u384 { limb0: 0xb7e97eb3bf1735cdbe96f68f, limb1: 0xa84f1d0529431bb9e996a408, limb2: 0x149ec28846d4f438, limb3: 0x0, }, u384 { limb0: 0xe651922d148cce1c5fdddee8, limb1: 0xca24b5f63630bad47aeafd98, limb2: 0xde20fae0af5188b, limb3: 0x0, }, u384 { limb0: 0x4b8660edf449fba6984c6709, limb1: 0x3ea94350e722ad2f7d836c23, limb2: 0x12d650e8f790b125, limb3: 0x0, }, u384 { limb0: 0x8abe28d78340dfc4babb8f6c, limb1: 0xea96717ba7446aafdadbc1a, limb2: 0x22ab53aa39f34ad3, limb3: 0x0, }, u384 { limb0: 0x71dd776904a129db9149166c, limb1: 0x450dabea7907bc3de0de1098, limb2: 0x26503e8d4849bdf5, limb3: 0x0, }, u384 { limb0: 0x897e7fc4c8064035b0d33850, limb1: 0xf5454f5003c5c8ec34b23d, limb2: 0x1d5e7a0e2965dffa, limb3: 0x0, }, u384 { limb0: 0xa544615b9cb3c7bbd07104cb, limb1: 0x12d96b7ec48448c6bc9a6aef, limb2: 0xee3d8daa098bee0, limb3: 0x0, }, u384 { limb0: 0x175703d91dc232b5f98ead00, limb1: 0x55d30754cd4d9056fa9ef7a7, limb2: 0x1bf282082a049799, limb3: 0x0, }, u384 { limb0: 0x6b693733a0272173ee9ad461, limb1: 0xe3e951bc316bee49971645f1, limb2: 0x7ae1344abfc6c2c, limb3: 0x0, }, u384 { limb0: 0x7a47d97a5c8e89762ee80488, limb1: 0xec21b131d511d7dbdc98a36b, limb2: 0x217e3a247827c376, limb3: 0x0, }, u384 { limb0: 0xfc2894117509b616addc30ee, limb1: 0xa003d438e2fbe28babe1e50e, limb2: 0x215ffe584b0eb067, limb3: 0x0, }, u384 { limb0: 0xe33da57412a92d1d3ce3ec20, limb1: 0x92dcedc597c4ca0fbec19b84, limb2: 0x1e770fc8ecbfdc86, limb3: 0x0, }, u384 { limb0: 0x9338b3c0e50e828f69ff6d1f, limb1: 0x9f1e3a8a6d66a05742914fc1, limb2: 0x2f6243cda919bf4c, limb3: 0x0, }, u384 { limb0: 0x9cc89345d3c03ff87a11b693, limb1: 0x9595d0046f44ab303a195d0e, limb2: 0x246efddc3117ecd3, limb3: 0x0, }, u384 { limb0: 0x9a918dfbe602bc62cec6adf1, limb1: 0xd4fe006f139cbc4e0168b1c8, limb2: 0x53e8d9b3ea5b8e, limb3: 0x0, }, u384 { limb0: 0xeefff135aec04c1abe59427b, limb1: 0x7d910f6a710d38b7eb4f261b, limb2: 0x1b894a2f45cb9664, limb3: 0x0, }, u384 { limb0: 0x88651f5a42553d54ec242cc0, limb1: 0x8212652479107d5fdc077abf, limb2: 0xaeb1554e266693d, limb3: 0x0, }, u384 { limb0: 0xbd4b7d0e11faf9da8d9ca28e, limb1: 0xe6888680d1781c7f04ba7d71, limb2: 0x16a735f6f7209d24, limb3: 0x0, }, u384 { limb0: 0x615b19374ff549dcf073d41b, limb1: 0xd7c13b4df0543cd260e4bcbb, limb2: 0x487b8b7fab5fc8f, limb3: 0x0, }, u384 { limb0: 0x68c3ad677fdf51c92388793, limb1: 0x124bea26b0772493cfb5d512, limb2: 0x1e75b9d2c2006307, limb3: 0x0, }, u384 { limb0: 0x239d1c6c961dcb02da3b388f, limb1: 0x253b46d5ff77d272ae46fa1e, limb2: 0x5120e3d0e28003c, limb3: 0x0, }, u384 { limb0: 0x3b171823f890f5fd55d78372, limb1: 0xb822e8763240119ac0900a05, limb2: 0xda5feb534576492, limb3: 0x0, }, u384 { limb0: 0x379d9d2c40cc8f78b7bd9abe, limb1: 0x22acc1a1f5f3bb6d8c2666a6, limb2: 0x2e211b39a023031a, limb3: 0x0, }, u384 { limb0: 0xad24378bfedb68592ba8118b, limb1: 0xb2b70caf5c36a7b194be7c11, limb2: 0x109b7f411ba0e4c9, limb3: 0x0, }, u384 { limb0: 0x415c3dded62940bcde0bd771, limb1: 0xb9c36c764379dbca2cc8fdd1, limb2: 0x2969f27eed31a480, limb3: 0x0, }, u384 { limb0: 0x8c5b3753326244ee65a1b1a7, limb1: 0xd5f9e654638065ce6cd79e2, limb2: 0x143021ec686a3f33, limb3: 0x0, }, u384 { limb0: 0xdbdeea55d6c64543dc4903e0, limb1: 0x6ae119424fddbcbc9314dc9f, limb2: 0x16ed41e13bb9c0c6, limb3: 0x0, }, u384 { limb0: 0x8c7b964029b2311687b1fe23, limb1: 0x4c9871c832963dc1b89d743c, limb2: 0x2e2419f9ec02ec39, limb3: 0x0, }, u384 { limb0: 0x58e7d7b6b16cdfabc8ee2911, limb1: 0x82a70eff08a6fd99d057e12e, limb2: 0x176cc029695ad025, limb3: 0x0, }, u384 { limb0: 0xceb247b791a93b74e36736d, limb1: 0xf617e7dcbfe82e0df706ab64, limb2: 0x2b90bba00fca0589, limb3: 0x0, }, u384 { limb0: 0x9f5fb065c8aacc55a0f89bfa, limb1: 0x97315876690f053d148d4e10, limb2: 0x101071f0032379b6, limb3: 0x0, }, u384 { limb0: 0x7043f7773279cd71d25d5e0, limb1: 0x17ba7fee3802593fa6444703, limb2: 0x19a3fc0a56702bf4, limb3: 0x0, }, u384 { limb0: 0x4ae72c925a8a79a66831f51d, limb1: 0x3f83dcedddb9a0236203f5f2, limb2: 0x1e6f20a11d1e31e4, limb3: 0x0, }, u384 { limb0: 0x25403ae24084e3027e782467, limb1: 0xc722a141f8785694484f4267, limb2: 0x1bd8c528472e57bd, limb3: 0x0, }, u384 { limb0: 0xa9e9c3190527a1a5f05079a, limb1: 0x6bacf1ad5e56655b7143625b, limb2: 0x2d51ba82c8073c6d, limb3: 0x0, }, u384 { limb0: 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0xc2c35377cb0a3712bfc9bc3e, limb2: 0x204f26ca7993b03a, limb3: 0x0, }, u384 { limb0: 0x8d515e348ef117e926d721c, limb1: 0x39d832d8be165a1e5747cf73, limb2: 0x85aff9c7fdadba0, limb3: 0x0, }, u384 { limb0: 0x5e093158efd375df00ea2068, limb1: 0xc4ae9db044c0b0b3f10e57d0, limb2: 0x249042a8dc111f27, limb3: 0x0, }, u384 { limb0: 0x5203327b3e0825977413e96b, limb1: 0x542854f3029803e2f8455066, limb2: 0x6e799bcdf2b4a74, limb3: 0x0, }, u384 { limb0: 0xcae12085c612496183b87996, limb1: 0xa9f4d2c002921bc3fffed333, limb2: 0x1cb3caed4bffb6ac, limb3: 0x0, }, u384 { limb0: 0xab566889dcd99e84d310d51c, limb1: 0x28a128bfd4faa6a3dd6ea03c, limb2: 0xb47e9755fae4801, limb3: 0x0, }, u384 { limb0: 0x24fd1ca3f0bb730da886a4f, limb1: 0x920a0c9fd2c360a6506293bc, limb2: 0xc7e4cea365c2061, limb3: 0x0, }, u384 { limb0: 0xd9d6988c8dcd7ba4187215df, limb1: 0xbbaa30d964d6f6f63dbe1b20, limb2: 0x21da1f701bac77bc, limb3: 0x0, }, u384 { limb0: 0x19965b6edd1a9486e3c6cc55, limb1: 0x70905fb67899d10db86b47bd, limb2: 0x9ae612e8ba1ca13, limb3: 0x0, }, u384 { limb0: 0xb0c99373fe1f7a0e3b95cf3d, limb1: 0xc150f284491190e6aab75445, limb2: 0x262e1e0b56cac47f, limb3: 0x0, }, u384 { limb0: 0x29fd4ddeaa5d3f67491d34bd, limb1: 0x2c87c293e3bb7c9e2a7bfa5f, limb2: 0x234bf4a7dce7587c, limb3: 0x0, }, u384 { limb0: 0x213d7432eee67f6cb69f70c2, limb1: 0x2d0a527cac744fb658d2690e, limb2: 0x2f6cbac694c886b0, limb3: 0x0, }, u384 { limb0: 0x2fff818d9a3300876dec3ad9, limb1: 0x7bb8c9fdf78b7aded52aa184, limb2: 0x22accb18b7c49b4b, limb3: 0x0, }, u384 { limb0: 0x2a0b3d3cbf623a1df7f8f2fc, limb1: 0xd659f22d2c77be302eabd918, limb2: 0x81e2f0652f898c6, limb3: 0x0, }, u384 { limb0: 0x90f3ffc016b3186ad675b935, limb1: 0xcea3ada75d669b8c534b9628, limb2: 0x12c0a25e70d006ec, limb3: 0x0, }, u384 { limb0: 0x9edd56f49f8d4f2381df3259, limb1: 0x2fd6fc869df24d7ab56efd34, limb2: 0x10ef9c23848128cc, limb3: 0x0, }, u384 { limb0: 0x9491e0620bda347962b240f0, limb1: 0xd4a81262b71df1bcc2c1d41b, limb2: 0x2161cd280772819d, limb3: 0x0, }, u384 { limb0: 0xf799bc41b7f4fdd12cb8d38a, limb1: 0xb406590041b5248292533364, limb2: 0x2cebb0ae5108318e, limb3: 0x0, }, u384 { limb0: 0xa656880fb759e08709a0a62f, limb1: 0xfe4f7c22d9561f3bf2852283, limb2: 0x2b2092f86b5979a7, limb3: 0x0, }, u384 { limb0: 0xcf643e7382b2d8507a065fed, limb1: 0x8146188425a442450cfc900, limb2: 0x1566b3402d774b8c, limb3: 0x0, }, u384 { limb0: 0xfccf8d3d1a163e601d1a0173, limb1: 0x8fb4c56d6c57ba01627c3635, limb2: 0x11a316aa31607f26, limb3: 0x0, }, u384 { limb0: 0x4644609152e353d9c2874e44, limb1: 0xb782648b560e595408a5e843, limb2: 0xde7ee069c934256, limb3: 0x0, }, u384 { limb0: 0xe706c72e67128b8949eab1af, limb1: 0xcc84df0297708c5e5845c36a, limb2: 0x2d36f4029245704, limb3: 0x0, }, u384 { limb0: 0xd82dabdc284d7951d546f858, limb1: 0xf53198c217fb34e899bde46c, limb2: 0x1b8cc326b5ee160, limb3: 0x0, }, u384 { limb0: 0xfd4ddf8a96ece85407550ebb, limb1: 0x10689fb2187b71694cbf9203, limb2: 0x27625da0f73ea071, limb3: 0x0, }, u384 { limb0: 0xedda06cb99ba025b94e4790d, limb1: 0xcdc0da581a6950f6dea349c3, limb2: 0x1cd8338a3e5b1ad7, limb3: 0x0, }, u384 { limb0: 0xd3e67e877a10a84072741a56, limb1: 0xa763856c94b6438c78a8aed8, limb2: 0x5ea02d65b209f6d, limb3: 0x0, }, u384 { limb0: 0xd627e810817743ce03330a55, limb1: 0x5366cfcf284a895d8b6250ce, limb2: 0x9f7cb68d4e388f8, limb3: 0x0, }, u384 { limb0: 0x202e4ebcdfeb969e9d5c1212, limb1: 0x27b043f5e58dbd1aec13995a, limb2: 0x18c6230ddc0f8968, limb3: 0x0, }, u384 { limb0: 0xbfd2e1a10578232096db6dcd, limb1: 0x1a91c0a0fdccdaa8452e4f07, limb2: 0x73a6114b997285e, limb3: 0x0, }, u384 { limb0: 0xb1660ce7a3e7742b2f37be7f, limb1: 0x22c6a1fc0838adf5fe013f39, limb2: 0x2e78746340b2a6d2, limb3: 0x0, }, u384 { limb0: 0x6553def28e675259d3e5c851, limb1: 0x6303ad8e5e4bf4249b7ea84, limb2: 0x7aa27e7150baddd, limb3: 0x0, }, u384 { limb0: 0xb4643f680cbc98345715ead8, limb1: 0xbf623d2712cf4d9fa90273cc, limb2: 0xb66fdec210ea4ea, limb3: 0x0, }, u384 { limb0: 0xb140be641acea41c49aa5e3, limb1: 0x9b633b8a4d6be51c9c0601ce, limb2: 0x2fb6a29d9f394a58, limb3: 0x0, }, u384 { limb0: 0x3d049bd675a69dc889b2ce2a, limb1: 0xfc845e9c1c2cd1288569fb24, limb2: 0x29025cc66fd041c4, limb3: 0x0, }, u384 { limb0: 0xfa695168b85d534b17be3f48, limb1: 0x4126214ab9c627a6f7ed731c, limb2: 0x150963f0aca9bcbe, limb3: 0x0, }, u384 { limb0: 0x7bec0d5798a08a32a61a8a65, limb1: 0x3f72c1bfc6656eb7b5bca2e4, limb2: 0xed5978030225766, limb3: 0x0, }, u384 { limb0: 0x3000debfc8d30c06143cc084, limb1: 0x3d30ae188c767f391c11888a, limb2: 0x7e19cb8a893369b, limb3: 0x0, }, u384 { limb0: 0x28d2c052cd860afb4a3aa272, limb1: 0xe5f1eeeafb5eb8ec2b6ecfe5, limb2: 0x600c7d2b6946345, limb3: 0x0, }, u384 { limb0: 0xa480e19ea0125119f0385705, limb1: 0x3022a1f33d6523b4773f2cd0, limb2: 0x596083b6c972bc1, limb3: 0x0, }, u384 { limb0: 0x99a8e1ef6db21043631e24c4, limb1: 0x7f98b9d8663d85db2e645130, limb2: 0x210b5c36f27a07d9, limb3: 0x0, }, u384 { limb0: 0x74e9159326a8f4930b7883f9, limb1: 0xc7bb9f3d563c5cc201c24898, limb2: 0x13bb2764bf1475cf, limb3: 0x0, }, u384 { limb0: 0x81e89997219e4b7576e24d30, limb1: 0x80eb082862a76757287872b1, limb2: 0x202cf557d625c260, limb3: 0x0, }, u384 { limb0: 0x3d905a4728ea1f95fd8824b2, limb1: 0x76d49e97142d220601fbc5a0, limb2: 0xe561c3f8bd4f76e, limb3: 0x0, }, u384 { limb0: 0xbbe827307c33ae9ed7890597, limb1: 0x471785de07bd9809d57dd859, limb2: 0xde20097480e7555, limb3: 0x0, }, u384 { limb0: 0x3cb72bb80cde8edd76d2e97d, limb1: 0xb810df8c5788eebcfd282561, limb2: 0x72f2a6287fb984b, limb3: 0x0, }, ]; #[cfg(test)] mod tests { use core::circuit::u384; use super::poseidon_hash_2_bn254; #[test] fn test_run_poseidon_grumpkin_circuit_1() { let x: u384 = u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }; let y: u384 = u384 { limb0: 2, limb1: 0, limb2: 0, limb3: 0 }; let z: u384 = u384 { limb0: 35961034779122590217458358426, limb1: 19176342235218042678530152434, limb2: 1251086958891274305, limb3: 0, }; assert_eq!(poseidon_hash_2_bn254(x, y), z); } #[ignore] // Ignored for auto-benchmarks #[test] fn test_run_poseidon_grumpkin_circuit_2() { let x: u384 = u384 { limb0: 1234556789, limb1: 0, limb2: 0, limb3: 0 }; let y: u384 = u384 { limb0: 987654321, limb1: 0, limb2: 0, limb3: 0 }; let z: u384 = u384 { limb0: 8305167385555799669027062613, limb1: 57704763612671584465832054609, limb2: 430243426511221670, limb3: 0, }; assert_eq!(poseidon_hash_2_bn254(x, y), z); } } ================================================ FILE: src/src/hashes/sha_512.cairo ================================================ // Optimized version, originally from Alexandria library. // use core::integer::{bitwise, u64_bitwise}; use core::num::traits::WrappingAdd; use core::traits::{BitAnd, BitNot, BitOr, BitXor}; // Variable naming is compliant to RFC-6234 (https://datatracker.ietf.org/doc/html/rfc6234) pub const SHA512_LEN: usize = 64; pub const TWO_POW_56_NZ: NonZero = 0x100000000000000; pub const TWO_POW_48_NZ: NonZero = 0x1000000000000; pub const TWO_POW_40_NZ: NonZero = 0x10000000000; pub const TWO_POW_32_NZ: NonZero = 0x100000000; pub const TWO_POW_24_NZ: NonZero = 0x1000000; pub const TWO_POW_16_NZ: NonZero = 0x10000; pub const TWO_POW_8_NZ: NonZero = 0x100; pub const TWO_POW_56: u64 = 0x100000000000000; pub const TWO_POW_48: u64 = 0x1000000000000; pub const TWO_POW_40: u64 = 0x10000000000; pub const TWO_POW_32: u64 = 0x100000000; pub const TWO_POW_24: u64 = 0x1000000; pub const TWO_POW_16: u64 = 0x10000; pub const TWO_POW_8: u64 = 0x100; pub const TWO_POW_4: u64 = 0x10; pub const TWO_POW_2: u64 = 0x4; pub const TWO_POW_1: u64 = 0x2; pub const TWO_POW_0: u64 = 0x1; const TWO_POW_6: u64 = 0x40; const TWO_POW_7: u64 = 0x80; const TWO_POW_14: u64 = 0x4000; const TWO_POW_18: u64 = 0x40000; const TWO_POW_19: u64 = 0x80000; const TWO_POW_28: u64 = 0x10000000; const TWO_POW_34: u64 = 0x400000000; const TWO_POW_39: u64 = 0x8000000000; const TWO_POW_41: u64 = 0x20000000000; const TWO_POW_61: u64 = 0x2000000000000000; const TWO_POW_64: u128 = 0x10000000000000000; const TWO_POW_64_MINUS_1: u64 = 0x8000000000000000; const TWO_POW_64_MINUS_8: u64 = 0x100000000000000; const TWO_POW_64_MINUS_14: u64 = 0x4000000000000; const TWO_POW_64_MINUS_18: u64 = 0x400000000000; const TWO_POW_64_MINUS_19: u64 = 0x200000000000; const TWO_POW_64_MINUS_28: u64 = 0x1000000000; const TWO_POW_64_MINUS_34: u64 = 0x40000000; const TWO_POW_64_MINUS_39: u64 = 0x2000000; const TWO_POW_64_MINUS_41: u64 = 0x800000; const TWO_POW_64_MINUS_61: u64 = 0x8; // Max u8 and u64 for bitwise operations pub const MAX_U8: u64 = 0xff; pub const MAX_U64: u128 = 0xffffffffffffffff; #[derive(Drop, Copy)] pub struct Word64 { pub data: u64, } impl WordBitAnd of BitAnd { fn bitand(lhs: Word64, rhs: Word64) -> Word64 { Word64 { data: lhs.data & rhs.data } } } impl WordBitXor of BitXor { fn bitxor(lhs: Word64, rhs: Word64) -> Word64 { Word64 { data: lhs.data ^ rhs.data } } } impl WordBitOr of BitOr { fn bitor(lhs: Word64, rhs: Word64) -> Word64 { Word64 { data: lhs.data | rhs.data } } } impl WordBitNot of BitNot { fn bitnot(a: Word64) -> Word64 { Word64 { data: ~a.data } } } impl WordAdd of Add { fn add(lhs: Word64, rhs: Word64) -> Word64 { Word64 { data: lhs.data.wrapping_add(rhs.data) } } } impl U128IntoWord of Into { fn into(self: u128) -> Word64 { Word64 { data: self.try_into().unwrap() } } } impl U64IntoWord of Into { fn into(self: u64) -> Word64 { Word64 { data: self } } } impl WordIntoFelt252 of Into { fn into(self: Word64) -> felt252 { self.data.into() } } use corelib_imports::bounded_int::{bounded_int, upcast}; use corelib_imports::circuit::conversions::{DivRemU128By64, NZ_POW64_TYPED}; impl Felt252IntoWord of Into { fn into(self: felt252) -> Word64 { let f_128: u128 = self.try_into().unwrap(); let (_, rem) = bounded_int::div_rem(f_128, NZ_POW64_TYPED); Word64 { data: upcast(rem) } } } pub trait WordOperations { fn rotr_precomputed(self: T, two_pow_n: u64, two_pow_64_n: u64) -> u128; } pub impl Word64WordOperations of WordOperations { // does the work of rotr but with precomputed values 2**n and 2**(64-n) fn rotr_precomputed(self: Word64, two_pow_n: u64, two_pow_64_n: u64) -> u128 { let data = self.data.into(); let data: u128 = math_shr_precomputed::(data, two_pow_n.into()) | math_shl_precomputed_u128(data, two_pow_64_n.into()); data } } fn ch(e: Word64, f: Word64, g: Word64) -> felt252 { (e & f).into() + (~e & g).into() } fn maj(x: Word64, y: Word64, z: Word64) -> felt252 { // (x & y) ^ (x & z) ^ (y & z) let x_xor_y = x ^ y; let x_xor_y_xor_z = x_xor_y ^ z; let res: felt252 = core::felt252_div( (x.into() + y.into() + z.into() - x_xor_y_xor_z.into()), 2, ); res } /// Performs x.rotr(28) ^ x.rotr(34) ^ x.rotr(39), /// Using precomputed values to avoid recomputation fn bsig0(x: Word64) -> u128 { // x.rotr(28) ^ x.rotr(34) ^ x.rotr(39) x.rotr_precomputed(TWO_POW_28, TWO_POW_64_MINUS_28) ^ x.rotr_precomputed(TWO_POW_34, TWO_POW_64_MINUS_34) ^ x.rotr_precomputed(TWO_POW_39, TWO_POW_64_MINUS_39) } /// Performs x.rotr(14) ^ x.rotr(18) ^ x.rotr(41), /// Using precomputed values to avoid recomputation fn bsig1(x: Word64) -> u128 { // x.rotr(14) ^ x.rotr(18) ^ x.rotr(41) x.rotr_precomputed(TWO_POW_14, TWO_POW_64_MINUS_14) ^ x.rotr_precomputed(TWO_POW_18, TWO_POW_64_MINUS_18) ^ x.rotr_precomputed(TWO_POW_41, TWO_POW_64_MINUS_41) } /// Performs x.rotr(1) ^ x.rotr(8) ^ x.shr(7), /// Using precomputed values to avoid recomputation fn ssig0(x: Word64) -> u128 { // x.rotr(1) ^ x.rotr(8) ^ x.shr(7) x.rotr_precomputed(TWO_POW_1, TWO_POW_64_MINUS_1) ^ x.rotr_precomputed(TWO_POW_8, TWO_POW_64_MINUS_8) ^ math_shr_precomputed::(x.data.into(), TWO_POW_7).into() // 2 ** 7 } /// Performs x.rotr(19) ^ x.rotr(61) ^ x.shr(6), /// Using precomputed values to avoid recomputation fn ssig1(x: Word64) -> u128 { // x.rotr(19) ^ x.rotr(61) ^ x.shr(6) x.rotr_precomputed(TWO_POW_19, TWO_POW_64_MINUS_19) ^ x.rotr_precomputed(TWO_POW_61, TWO_POW_64_MINUS_61) ^ math_shr_precomputed::(x.data, TWO_POW_6).into() // 2 ** 6 } // Shift left with precomputed powers of 2 // Only use in this file. Unsafe otherwise. fn math_shl_precomputed_u128(x: u128, two_power_n: u128) -> u128 { let mul: felt252 = x.into() * two_power_n.into(); mul.try_into().unwrap() } // Shift right with precomputed powers of 2 fn math_shr_precomputed, +Rem, +Drop, +Copy, +Into>( x: T, two_power_n: T, ) -> T { x / two_power_n } fn add_trailing_zeroes(ref data: Array, msg_len: usize) { let mdi = msg_len % 128; let padding_len = if (mdi < 112) { 119 - mdi } else { 247 - mdi }; let mut i = 0; while (i != padding_len) { data.append(0); i += 1; }; } // Input must be a multiple of 8. fn from_u8Array_to_WordArray(mut data: Span) -> Array { let mut new_arr: Array = array![]; while let Some(b8) = data.multi_pop_front::<8>() { let [b7, b6, b5, b4, b3, b2, b1, b0] = b8.unbox(); let b0: felt252 = b0.into(); let b1: felt252 = b1.into(); let b2: felt252 = b2.into(); let b3: felt252 = b3.into(); let b4: felt252 = b4.into(); let b5: felt252 = b5.into(); let b6: felt252 = b6.into(); let b7: felt252 = b7.into(); let new_word: felt252 = b0 + 256 * (b1 + 256 * (b2 + 256 * (b3 + 256 * (b4 + 256 * (b5 + 256 * (b6 + 256 * b7)))))); new_arr.append(Word64 { data: new_word.try_into().unwrap() }); } new_arr } fn from_WordArray_to_u8array(data: Span) -> Array { let mut arr: Array = array![]; // Use precomputed powers of 2 for shift right to avoid recomputation for word in data { let data_i: u64 = *word.data; let (w7, w) = DivRem::div_rem(data_i, TWO_POW_56_NZ); let (w6, w) = DivRem::div_rem(w, TWO_POW_48_NZ); let (w5, w) = DivRem::div_rem(w, TWO_POW_40_NZ); let (w4, w) = DivRem::div_rem(w, TWO_POW_32_NZ); let (w3, w) = DivRem::div_rem(w, TWO_POW_24_NZ); let (w2, w) = DivRem::div_rem(w, TWO_POW_16_NZ); let (w1, w0) = DivRem::div_rem(w, TWO_POW_8_NZ); arr.append(w7.try_into().unwrap()); arr.append(w6.try_into().unwrap()); arr.append(w5.try_into().unwrap()); arr.append(w4.try_into().unwrap()); arr.append(w3.try_into().unwrap()); arr.append(w2.try_into().unwrap()); arr.append(w1.try_into().unwrap()); arr.append(w0.try_into().unwrap()); } arr } fn digest_hash(data: Span, msg_len: usize) -> [Word64; 8] { let k = K.span(); let block_nb = msg_len / 128; let [mut h_0, mut h_1, mut h_2, mut h_3, mut h_4, mut h_5, mut h_6, mut h_7] = H; let mut i = 0; while (i != block_nb) { // Prepare message schedule let mut t: usize = 0; let mut W: Array = array![]; while (t != 80) { if t < 16 { W.append(*data.at(i * 16 + t)); } else { let buf_felt252: felt252 = ssig1(*W.at(t - 2)).into() + (*W.at(t - 7)).into() + ssig0(*W.at(t - 15)).into() + (*W.at(t - 16)).into(); let buf: Word64 = buf_felt252.into(); W.append(buf); } t += 1; } let mut a = h_0; let mut b = h_1; let mut c = h_2; let mut d = h_3; let mut e = h_4; let mut f = h_5; let mut g = h_6; let mut h = h_7; let mut W = W.span(); for _k in k { let T1_felt252: felt252 = h.into() + bsig1(e).into() + ch(e, f, g) + (*_k).into() + (*W.pop_front().unwrap()).into(); let T1_T2_felt252: felt252 = bsig0(a).into() + maj(a, b, c) + T1_felt252; h = g; g = f; f = e; e = d + T1_felt252.into(); d = c; c = b; b = a; a = T1_T2_felt252.into(); } h_0 = a + h_0; h_1 = b + h_1; h_2 = c + h_2; h_3 = d + h_3; h_4 = e + h_4; h_5 = f + h_5; h_6 = g + h_6; h_7 = h + h_7; i += 1; } return [h_0, h_1, h_2, h_3, h_4, h_5, h_6, h_7]; } pub fn sha512(mut data: Array) -> Array { let hash = _sha512(data); from_WordArray_to_u8array(hash.span()) } pub fn _sha512(mut data: Array) -> [Word64; 8] { let bit_numbers: u128 = data.len().into() * 8; // any u32 * 8 fits in u64 // let bit_numbers = bit_numbers & Bounded::::MAX.into(); let max_u8: u128 = MAX_U8.into(); let mut msg_len = data.len(); // Appends 1 data.append(0x80); add_trailing_zeroes(ref data, msg_len); // add length to the end // Use precomputed powers of 2 for shift right to avoid recomputation let mut res: u128 = math_shr_precomputed(bit_numbers, TWO_POW_56.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_48.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_40.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_32.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_24.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_16.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_8.into()) & max_u8; data.append(res.try_into().unwrap()); res = math_shr_precomputed(bit_numbers, TWO_POW_0.into()) & max_u8; data.append(res.try_into().unwrap()); msg_len = data.len(); let mut data = from_u8Array_to_WordArray(data.span()); let hash = digest_hash(data.span(), msg_len); hash } const H: [Word64; 8] = [ Word64 { data: 0x6a09e667f3bcc908 }, Word64 { data: 0xbb67ae8584caa73b }, Word64 { data: 0x3c6ef372fe94f82b }, Word64 { data: 0xa54ff53a5f1d36f1 }, Word64 { data: 0x510e527fade682d1 }, Word64 { data: 0x9b05688c2b3e6c1f }, Word64 { data: 0x1f83d9abfb41bd6b }, Word64 { data: 0x5be0cd19137e2179 }, ]; const K: [Word64; 80] = [ Word64 { data: 0x428a2f98d728ae22 }, Word64 { data: 0x7137449123ef65cd }, Word64 { data: 0xb5c0fbcfec4d3b2f }, Word64 { data: 0xe9b5dba58189dbbc }, Word64 { data: 0x3956c25bf348b538 }, Word64 { data: 0x59f111f1b605d019 }, Word64 { data: 0x923f82a4af194f9b }, Word64 { data: 0xab1c5ed5da6d8118 }, Word64 { data: 0xd807aa98a3030242 }, Word64 { data: 0x12835b0145706fbe }, Word64 { data: 0x243185be4ee4b28c }, Word64 { data: 0x550c7dc3d5ffb4e2 }, Word64 { data: 0x72be5d74f27b896f }, Word64 { data: 0x80deb1fe3b1696b1 }, Word64 { data: 0x9bdc06a725c71235 }, Word64 { data: 0xc19bf174cf692694 }, Word64 { data: 0xe49b69c19ef14ad2 }, Word64 { data: 0xefbe4786384f25e3 }, Word64 { data: 0x0fc19dc68b8cd5b5 }, Word64 { data: 0x240ca1cc77ac9c65 }, Word64 { data: 0x2de92c6f592b0275 }, Word64 { data: 0x4a7484aa6ea6e483 }, Word64 { data: 0x5cb0a9dcbd41fbd4 }, Word64 { data: 0x76f988da831153b5 }, Word64 { data: 0x983e5152ee66dfab }, Word64 { data: 0xa831c66d2db43210 }, Word64 { data: 0xb00327c898fb213f }, Word64 { data: 0xbf597fc7beef0ee4 }, Word64 { data: 0xc6e00bf33da88fc2 }, Word64 { data: 0xd5a79147930aa725 }, Word64 { data: 0x06ca6351e003826f }, Word64 { data: 0x142929670a0e6e70 }, Word64 { data: 0x27b70a8546d22ffc }, Word64 { data: 0x2e1b21385c26c926 }, Word64 { data: 0x4d2c6dfc5ac42aed }, Word64 { data: 0x53380d139d95b3df }, Word64 { data: 0x650a73548baf63de }, Word64 { data: 0x766a0abb3c77b2a8 }, Word64 { data: 0x81c2c92e47edaee6 }, Word64 { data: 0x92722c851482353b }, Word64 { data: 0xa2bfe8a14cf10364 }, Word64 { data: 0xa81a664bbc423001 }, Word64 { data: 0xc24b8b70d0f89791 }, Word64 { data: 0xc76c51a30654be30 }, Word64 { data: 0xd192e819d6ef5218 }, Word64 { data: 0xd69906245565a910 }, Word64 { data: 0xf40e35855771202a }, Word64 { data: 0x106aa07032bbd1b8 }, Word64 { data: 0x19a4c116b8d2d0c8 }, Word64 { data: 0x1e376c085141ab53 }, Word64 { data: 0x2748774cdf8eeb99 }, Word64 { data: 0x34b0bcb5e19b48a8 }, Word64 { data: 0x391c0cb3c5c95a63 }, Word64 { data: 0x4ed8aa4ae3418acb }, Word64 { data: 0x5b9cca4f7763e373 }, Word64 { data: 0x682e6ff3d6b2b8a3 }, Word64 { data: 0x748f82ee5defb2fc }, Word64 { data: 0x78a5636f43172f60 }, Word64 { data: 0x84c87814a1f0ab72 }, Word64 { data: 0x8cc702081a6439ec }, Word64 { data: 0x90befffa23631e28 }, Word64 { data: 0xa4506cebde82bde9 }, Word64 { data: 0xbef9a3f7b2c67915 }, Word64 { data: 0xc67178f2e372532b }, Word64 { data: 0xca273eceea26619c }, Word64 { data: 0xd186b8c721c0c207 }, Word64 { data: 0xeada7dd6cde0eb1e }, Word64 { data: 0xf57d4f7fee6ed178 }, Word64 { data: 0x06f067aa72176fba }, Word64 { data: 0x0a637dc5a2c898a6 }, Word64 { data: 0x113f9804bef90dae }, Word64 { data: 0x1b710b35131c471b }, Word64 { data: 0x28db77f523047d84 }, Word64 { data: 0x32caab7b40c72493 }, Word64 { data: 0x3c9ebe0a15c9bebc }, Word64 { data: 0x431d67c49c100d4c }, Word64 { data: 0x4cc5d4becb3e42b6 }, Word64 { data: 0x597f299cfc657e2a }, Word64 { data: 0x5fcb6fab3ad6faec }, Word64 { data: 0x6c44198c4a475817 }, ]; ================================================ FILE: src/src/lib.cairo ================================================ pub mod apps { pub mod drand; pub mod noir; pub mod risc0; pub mod sp1; pub mod sp1_constants; } pub mod basic_field_ops; pub mod core { pub mod circuit; } pub mod circuits { pub(crate) mod dummy; pub(crate) mod ec; pub(crate) mod extf_mul; pub(crate) mod isogeny; pub(crate) mod multi_pairing_check; pub(crate) mod rsa; pub(crate) mod tower_circuits; } pub mod crypto { pub mod mmr; } pub mod definitions; pub mod ec { pub mod ec_ops; pub mod ec_ops_g2; pub mod selectors; pub mod pairing { pub mod groth16; pub mod pairing_check; pub mod single_pairing_tower; } } pub mod hashes { pub mod poseidon_bn254; pub mod sha_512; pub use poseidon_bn254::poseidon_hash_2_bn254; pub use sha_512::sha512; } pub mod signatures { pub mod ecdsa; pub mod eddsa_25519; pub mod rsa; pub mod schnorr; } mod tests { mod autogenerated { #[cfg(test)] mod ecdsa_tests; #[cfg(test)] mod eddsa_tests; #[cfg(test)] mod msm_tests; #[cfg(test)] mod pairing_tests; #[cfg(test)] mod rsa_tests; #[cfg(test)] mod schnorr_tests; #[cfg(test)] mod tower_pairing_tests; } #[cfg(test)] mod calldata_tests; #[cfg(test)] mod sha512_tests; #[cfg(test)] mod sp1_groth_16_tests; } pub mod utils { pub mod calldata; pub mod hashing; pub mod neg_3; use core::circuit::u384; use core::panic_with_felt252; pub fn u384_assert_zero(x: u384) { if x.limb0 != 0 { panic_with_felt252('not zero l0'); } if x.limb1 != 0 { panic_with_felt252('not zero l1'); } if x.limb2 != 0 { panic_with_felt252('not zero l2'); } if x.limb3 != 0 { panic_with_felt252('not zero l3'); } } pub fn u384_assert_eq(x: u384, y: u384) { if x.limb0 != y.limb0 { panic_with_felt252('not equal l0'); } if x.limb1 != y.limb1 { panic_with_felt252('not equal l1'); } if x.limb2 != y.limb2 { panic_with_felt252('not equal l2'); } if x.limb3 != y.limb3 { panic_with_felt252('not equal l3'); } } pub fn usize_assert_eq(x: usize, y: usize) { if x != y { panic_with_felt252('not equal usize'); } } // Returns true if all limbs of x are zero, false otherwise. pub fn u384_eq_zero(x: u384) -> bool { if x.limb0 != 0 { return false; } if x.limb1 != 0 { return false; } if x.limb2 != 0 { return false; } if x.limb3 != 0 { return false; } true } } pub use garaga::ec::ec_ops; pub use garaga::ec::ec_ops_g2; pub use garaga::ec::pairing::{groth16, pairing_check, single_pairing_tower}; #[cfg(test)] mod tests_lib { use core::circuit::{ AddInputResultTrait, AddMod, CircuitElement, CircuitInput, CircuitInputs, CircuitModulus, CircuitOutputsTrait, EvalCircuitTrait, MulMod, RangeCheck96, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, u96, }; use core::traits::TryInto; #[test] #[ignore] // Ignored for auto-benchmarks fn test_u96() { let a: u96 = 0x123; assert_eq!(a, 0x123); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_builtins() { core::internal::require_implicit::(); core::internal::require_implicit::(); core::internal::require_implicit::(); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_circuit_success() { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let add = circuit_add(in1, in2); let inv = circuit_inverse(add); let sub = circuit_sub(inv, in2); let mul = circuit_mul(inv, sub); let modulus = TryInto::<_, CircuitModulus>::try_into([7, 0, 0, 0]).unwrap(); let outputs = (mul, add, inv) .new_inputs() .next([3, 0, 0, 0]) .next([6, 0, 0, 0]) .done() .eval(modulus) .unwrap(); assert_eq!(outputs.get_output(add), u384 { limb0: 2, limb1: 0, limb2: 0, limb3: 0 }); assert_eq!(outputs.get_output(inv), u384 { limb0: 4, limb1: 0, limb2: 0, limb3: 0 }); assert_eq!(outputs.get_output(sub), u384 { limb0: 5, limb1: 0, limb2: 0, limb3: 0 }); assert_eq!(outputs.get_output(mul), u384 { limb0: 6, limb1: 0, limb2: 0, limb3: 0 }); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_circuit_failure() { let in0 = CircuitElement::> {}; let out0 = circuit_inverse(in0); let modulus = TryInto::<_, CircuitModulus>::try_into([55, 0, 0, 0]).unwrap(); (out0,).new_inputs().next([11, 0, 0, 0]).done().eval(modulus).unwrap_err(); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_fill_inputs_loop() { let in1 = CircuitElement::> {}; let in2 = CircuitElement::> {}; let add = circuit_add(in1, in2); let mut inputs: Array<[u96; 4]> = array![[1, 0, 0, 0], [2, 0, 0, 0]]; let mut circuit_inputs = (add,).new_inputs(); while let Option::Some(input) = inputs.pop_front() { circuit_inputs = circuit_inputs.next(input); } let modulus = TryInto::<_, CircuitModulus>::try_into([55, 0, 0, 0]).unwrap(); circuit_inputs.done().eval(modulus).unwrap(); } } ================================================ FILE: src/src/signatures/ecdsa.cairo ================================================ use garaga::basic_field_ops::{inv_mod_p, is_even_u384, mul_mod_p, reduce_mod_p}; use garaga::definitions::{ G1Point, Zero, deserialize_u384, get_G, get_curve_order_modulus, get_n, serialize_u384, u384, }; use garaga::ec_ops::{G1PointTrait, msm_g1}; use garaga::utils::u384_eq_zero; /// An ECDSA signature with message hash. /// /// # Fields /// * `rx`: `u384` - The r component (R.x mod n) of the signature. /// * `s`: `u256` - The s component of the signature. /// * `v`: `bool` - The parity of R.y (false if R.y is even, true if odd). /// * `z`: `u256` - The message hash. #[derive(Drop, Debug, PartialEq)] pub struct ECDSASignature { pub rx: u384, pub s: u256, pub v: bool, pub z: u256, } pub impl SerdeECDSASignature of Serde { fn serialize(self: @ECDSASignature, ref output: Array) { serialize_u384(self.rx, ref output); Serde::::serialize(self.s, ref output); Serde::::serialize(self.v, ref output); Serde::::serialize(self.z, ref output); } fn deserialize(ref serialized: Span) -> Option { let rx = deserialize_u384(ref serialized); let s = Serde::::deserialize(ref serialized).unwrap(); let v = Serde::::deserialize(ref serialized).unwrap(); let z = Serde::::deserialize(ref serialized).unwrap(); return Option::Some(ECDSASignature { rx, s, v, z }); } } /// An ECDSA signature bundled with computation hints required for Cairo verification. /// /// # Fields /// * `signature`: `ECDSASignature` - The core signature data. /// * `msm_hint`: `Span` - Hint for multi-scalar multiplication computation. #[derive(Drop, Debug, PartialEq, Serde)] pub struct ECDSASignatureWithHint { pub signature: ECDSASignature, pub msm_hint: Span, } /// Verifies an ECDSA signature with associated hints, assuming the message hash is correct. /// /// # Important Assumption /// **This function assumes that the message hash `z` has been correctly computed from the message /// by the caller.** It does not compute or verify the hash derivation itself. The caller is /// responsible for ensuring that `z = H(message)` (or the appropriate hash function for their /// protocol) before calling this function. /// /// # Arguments /// * `signature`: `ECDSASignatureWithHint` - The signature and verification data bundle containing: /// - rx: The r component (R.x mod n) of the signature /// - s: The s component of the signature /// - v: The parity of R.y /// - z: The message hash (assumed to be correctly computed by the caller) /// - msm_hint: Hint for multi-scalar multiplication /// * `public_key`: `G1Point` - The public key to verify against. /// * `curve_id`: `usize` - The curve identifier /// /// # Algorithm /// The ECDSA signature verification checks if the signature (r,s) is valid for a given message hash /// z: /// 1. Verify that r is non-zero and s ∈ {1, ..., n-1} /// 2. Verify that the public key P is on the curve /// 3. Compute w = s⁻¹ mod n /// 4. Compute u₁ = zw mod n and u₂ = rw mod n /// 5. Compute R' = u₁G + u₂P /// 6. Verify that R'.x mod n equals r (implicitly checks r < n) and R'.y's parity does NOT match v /// /!\ Note: Behaviour for cofactor > 1 only tested on curves with cofactor 1 /// (BN254, SECP256K1/R1, GRUMPKIN). pub fn is_valid_ecdsa_signature_assuming_hash( signature: ECDSASignatureWithHint, public_key: G1Point, curve_id: usize, ) -> bool { let ECDSASignatureWithHint { signature, msm_hint } = signature; let ECDSASignature { rx, s, v, z } = signature; let n: u256 = get_n(curve_id); let modulus = get_curve_order_modulus(curve_id); // Check that r is non-zero and s is in range {1, ..., n-1} // Note: r < n is implicitly checked later when comparing r_prime.x mod n == r if u384_eq_zero(rx) || s >= n || s == 0 { return false; } // Verify public key is on curve if !public_key.is_on_curve_excluding_infinity(curve_id) { return false; } // Compute s⁻¹ mod n using the inv_mod_p function let s_u384: u384 = s.into(); let s_inv = inv_mod_p(s_u384, modulus); // Compute u₁ = z·s⁻¹ mod n and u₂ = r·s⁻¹ mod n let u1: u256 = mul_mod_p(z.into(), s_inv, modulus).try_into().unwrap(); let u2: u256 = mul_mod_p(rx, s_inv, modulus).try_into().unwrap(); // Compute R' = u₁G + u₂P using MSM let points = array![get_G(curve_id), public_key].span(); let scalars = array![u1, u2].span(); let R_prime = msm_g1(points, scalars, curve_id, msm_hint); // Check R'.x mod n equals r and R'.y parity matches v // Note : if cofactor is 1, no need to reduce r_prime.x mod n let ry_prime_parity = is_even_u384(R_prime.y); let r_prime_x_mod_n = reduce_mod_p(R_prime.x, modulus); if R_prime.is_zero() || r_prime_x_mod_n != rx || ry_prime_parity == v { return false; } true } ================================================ FILE: src/src/signatures/eddsa_25519.cairo ================================================ use core::circuit::{ CircuitElement, CircuitInput, CircuitInputs, CircuitOutputsTrait, EvalCircuitTrait, circuit_add, circuit_inverse, circuit_mul, circuit_sub, u384, }; use core::integer::u128_byte_reverse; use garaga::basic_field_ops::{neg_mod_p, u512_mod_p}; use garaga::circuits::ec; use garaga::core::circuit::{AddInputResultTrait2, u288IntoCircuitInputValue}; use garaga::definitions::{ G1Point, Zero, get_ED25519_modulus, get_a, get_curve_order_modulus, get_modulus, u288Serde, }; use garaga::ec_ops::{G1PointTrait, ec_safe_add, msm_fake_glv}; use garaga::hashes::sha_512::_sha512; const POW_2_32_u64: NonZero = 0x100000000; const POW_2_127_u128: NonZero = 0x80000000000000000000000000000000; const POW_2_8_u128: NonZero = 0x100; const POW_2_64_u128: u128 = 0x10000000000000000; const X22519_u256: u256 = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed; const D_TWISTED: u384 = u384 { limb0: 0x4141d8ab75eb4dca135978a3, limb1: 0x8cc740797779e89800700a4d, limb2: 0x52036cee2b6ffe73, limb3: 0x0, }; const A_TWISTED: u384 = u384 { limb0: 0xffffffffffffffffffffffec, limb1: 0xffffffffffffffffffffffff, limb2: 0x7fffffffffffffff, limb3: 0x0, }; const G_neg: G1Point = G1Point { x: u384 { limb0: 0xd617c9aca55c89b025aef35, limb1: 0xf00b8f02f1c20618a9c13fdf, limb2: 0x2a78dd0fd02c0339, limb3: 0x0, }, y: u384 { limb0: 0x7f8ece9a6487cf0c09d3e2d9, limb1: 0x41b7c45a9c867cdc30902f9e, limb2: 0x5639bb5a38e25dd1, limb3: 0x0, }, }; #[derive(Copy, Drop, Debug, PartialEq, Serde)] pub struct EdDSASignature { pub Ry_twisted: u256, // Compressed form of Ry (converted to integer from little endian bytes) pub s: u256, pub msg: Span, } #[derive(Copy, Drop, Debug, PartialEq, Serde)] pub struct EdDSASignatureWithHint { pub signature: EdDSASignature, pub msm_hint: Span, pub sqrt_Rx_hint: u256, pub sqrt_Px_hint: u256, } /// Verifies an Ed25519 signature according to RFC 8032. /// /// # Security /// This implementation follows RFC 8032 Section 5.1.7 by explicitly rejecting /// small-order points. Both the signature point R and public key A are tested /// to ensure [8]P ≠ 𝒪, preventing key-compromise and signature-malleability /// attacks that could arise from small-order components. /// /// # Parameters /// - `signature`: The signature with hints for point decompression and MSM /// - `Py_twisted`: Compressed form of Public Key y-coordinate (converted to integer from little /// endian bytes) /// /// # Returns /// - `true` if the signature is valid /// - `false` if the signature is invalid or contains small-order points pub fn is_valid_eddsa_signature(signature: EdDSASignatureWithHint, Py_twisted: u256) -> bool { let EdDSASignatureWithHint { signature, mut msm_hint, sqrt_Rx_hint, sqrt_Px_hint } = signature; let EdDSASignature { Ry_twisted, s, msg } = signature; let R_opt: Option = decompress_edwards_pt_from_y_compressed_le_into_weirstrass_point( Ry_twisted, sqrt_Rx_hint, ); let P_opt: Option = decompress_edwards_pt_from_y_compressed_le_into_weirstrass_point( Py_twisted, sqrt_Px_hint, ); if P_opt.is_none() || R_opt.is_none() { return false; } let P: G1Point = P_opt.unwrap(); let R: G1Point = R_opt.unwrap(); // Verify points lie on the curve (but may be outside the prime-order subgroup) if !R.is_on_curve_excluding_infinity(4) || !P.is_on_curve_excluding_infinity(4) { return false; } // Reject small-order points explicitly to prevent key-compromise and // signature-malleability attacks. Check [8]P = 𝒪 for both R and the public key. if is_small_order_point(R, 4) || is_small_order_point(P, 4) { return false; } let mut data: Array = array![]; // Hash(Ry + Py + msg) append_u256_le_to_u8_be_array(Ry_twisted, ref data); append_u256_le_to_u8_be_array(Py_twisted, ref data); for byte in msg { data.append(*byte); } // println!("preimage: {:?}", data); let hash = _sha512(data); let [h0, h1, h2, h3, h4, h5, h6, h7] = hash; // println!("hash_bytes: {:?}", hash_bytes); let high_high_128: u128 = h1.data.into() + h0.data.into() * POW_2_64_u128; let high_low_128: u128 = h3.data.into() + h2.data.into() * POW_2_64_u128; let low_high_128: u128 = h5.data.into() + h4.data.into() * POW_2_64_u128; let low_low_128: u128 = h7.data.into() + h6.data.into() * POW_2_64_u128; let high_256 = u256 { low: high_low_128, high: high_high_128 }; let low_256 = u256 { low: low_low_128, high: low_high_128 }; // [hh0, ..., hh15] [hl0, ..., hl15] [lh0, ..., lh15] [ll0, ..., ll15] let hh_le = u128_byte_reverse(low_256.low); let hl_le = u128_byte_reverse(low_256.high); let lh_le = u128_byte_reverse(high_256.low); let ll_le = u128_byte_reverse(high_256.high); // u512 from hash bytes (little endian) // [ll15, ..., ll0] [lh15, ..., lh0] [hl15, ..., hl0] [hh15, ..., hh0] let h_le: u384 = u256 { low: hl_le, high: hh_le }.into(); let l_le: u384 = u256 { low: ll_le, high: lh_le }.into(); // println!("h_le: {:?}", h_le); // println!("l_le: {:?}", l_le); let order_modulus = get_curve_order_modulus(4); let h_mod_p = u512_mod_p(h_le, l_le, order_modulus); // Calculate h = hash(R + pubKey + msg) mod q // Calculate P1 = s * G // Calculate P2 = R + h * pubKey // Return s*G == R + h * pubKey // <=> s*(-G) + h * pubKey + R == 0 let points: Span = array![G_neg, P].span(); let scalars: Span = array![s, h_mod_p.try_into().unwrap()].span(); let msm_result = msm_fake_glv(points, scalars, 4, ref msm_hint); return ec_safe_add(msm_result, R, 4).is_infinity(); } /// Checks if a point has small order (order dividing the cofactor 8). /// /// For Ed25519 the full curve has order 8×ℓ where ℓ is the prime-order subgroup. /// Small-order points (orders 1, 2, 4, 8) can enable attacks, so they must be rejected. /// /// # Implementation /// Tests for small-order by checking if [2^k]P = 𝒪 for k = 1, 2, or 3 (i.e., orders 2, 4, or 8). /// Uses the fact that on Weierstrass curves, a point equals its negation (hence has order 2) /// iff its y-coordinate is zero. Returns true if P has order dividing 8. /// /// # Parameters /// - `p`: The point to test /// - `curve_index`: Must be 4 (Ed25519) /// /// # Returns /// - `true` if P has small order (should be rejected) /// - `false` if P is in the large subgroup (acceptable) fn is_small_order_point(p: G1Point, curve_index: usize) -> bool { // Compute [8]P = [2^3]P by three doublings if p.y.is_zero() { // => P=-P => 2P = 0 return true; } let modulus = get_modulus(curve_index); let a = get_a(curve_index); let (p2) = ec::run_DOUBLE_EC_POINT_circuit(p, a, modulus); if p2.y.is_zero() { // => 2P=-2P => 4P = 0 return true; } let (p4) = ec::run_DOUBLE_EC_POINT_circuit(p2, a, modulus); if p4.y.is_zero() { // => 4P=-4P => 8P = 0 return true; } // If [8]P = 𝒪 then P has order dividing 8 (small-order point) return false; } pub fn decompress_edwards_pt_from_y_compressed_le_into_weirstrass_point( y_twisted_compressed: u256, sqrt_hint: u256, ) -> Option { let (bit_sign, y_high): (u128, u128) = DivRem::div_rem( y_twisted_compressed.high, POW_2_127_u128, ); let modulus = get_ED25519_modulus(); // println!("sqrt_hint: 0x{:x}", sqrt_hint); let sqrt_hint_384: u384 = sqrt_hint.into(); let x_384: u384 = match sqrt_hint.low % 2 == bit_sign % 2 { true => sqrt_hint_384, false => neg_mod_p(sqrt_hint_384, modulus), }; let y = u256 { low: y_twisted_compressed.low, high: y_high }; let y_u384: u384 = y.into(); let y = CircuitElement::> {}; let f1 = CircuitElement::> {}; let d = CircuitElement::> {}; let sqrt_x = CircuitElement::> {}; let y_sq = circuit_mul(y, y); let num = circuit_sub(y_sq, f1); let d_mul_y_sq = circuit_mul(d, y_sq); let den = circuit_add(d_mul_y_sq, f1); let inv_den = circuit_inverse(den); let x_sq = circuit_mul(num, inv_den); let sqrt_x_sq = circuit_mul(sqrt_x, sqrt_x); let check = circuit_sub(sqrt_x_sq, x_sq); let outputs = (check,) .new_inputs() .next_2(y_u384) .next_2([1, 0, 0, 0]) .next_2([0x4141d8ab75eb4dca135978a3, 0x8cc740797779e89800700a4d, 0x52036cee2b6ffe73, 0x0]) .next_2(x_384) .done_2() .eval(modulus) .unwrap(); let sqrt_check = outputs.get_output(check); if sqrt_check.is_non_zero() { return None; } if sqrt_hint >= X22519_u256 { return None; } return Some(to_weierstrass(x_384, y_u384)); } // Convert twisted Edwards Ed25519 point to equivalent Weierstrass point pub fn to_weierstrass(x_twisted: u384, y_twisted: u384) -> G1Point { let x_t = CircuitElement::> {}; let y_t = CircuitElement::> {}; let a = CircuitElement::> {}; let d = CircuitElement::> {}; let four = CircuitElement::> {}; let five = CircuitElement::> {}; let twelve = CircuitElement::> {}; let modulus = get_ED25519_modulus(); let five_a = circuit_mul(five, a); let a_y_twisted = circuit_mul(a, y_t); let d_y_twisted = circuit_mul(d, y_t); let five_d_y_twisted = circuit_mul(five, d_y_twisted); let num_x = circuit_sub(circuit_add(five_a, a_y_twisted), circuit_add(five_d_y_twisted, d)); let den_x = circuit_sub(twelve, circuit_mul(twelve, y_t)); let _x = circuit_mul(num_x, circuit_inverse(den_x)); let num_y = circuit_sub(circuit_add(a, a_y_twisted), circuit_add(d_y_twisted, d)); let four_xt = circuit_mul(four, x_t); let den_y = circuit_sub(four_xt, circuit_mul(four_xt, y_t)); let _y = circuit_mul(num_y, circuit_inverse(den_y)); let outputs = (_x, _y) .new_inputs() .next_2(x_twisted) .next_2(y_twisted) .next_2(A_TWISTED) .next_2(D_TWISTED) .next_2([4, 0, 0, 0]) .next_2([5, 0, 0, 0]) .next_2([12, 0, 0, 0]) .done_2() .eval(modulus) .unwrap(); let x = outputs.get_output(_x); let y = outputs.get_output(_y); G1Point { x: x, y: y } } #[inline] pub fn u256_byte_reverse(word: u256) -> u256 { u256 { low: core::integer::u128_byte_reverse(word.high), high: core::integer::u128_byte_reverse(word.low), } } // Append u256 as little endian to u8 array fn append_u256_le_to_u8_be_array(x_le: u256, ref arr: Array) { let mut high = x_le.high; let mut low = x_le.low; let mut i: felt252 = 0; while (i != 16) { let (temp_remaining, byte) = DivRem::div_rem(low, POW_2_8_u128); arr.append(byte.try_into().unwrap()); low = temp_remaining; i += 1; } let mut j: felt252 = 0; while (j != 16) { let (temp_remaining, byte) = DivRem::div_rem(high, POW_2_8_u128); arr.append(byte.try_into().unwrap()); high = temp_remaining; j += 1; } } ================================================ FILE: src/src/signatures/rsa.cairo ================================================ //! RSA-2048 signature verification via multi-channel RNS arithmetic. //! //! Verifies s^{65537} ≡ m (mod n) for a 2048-bit RSA modulus n without //! native 2048-bit arithmetic. Integers are represented in a Residue Number //! System (RNS) defined by 11 pairwise coprime ~384-bit primes p_1, ..., p_{11}. //! //! Each modular reduction a·b = q·n + r in the exponentiation chain is verified //! by evaluating chunk polynomials at α_i = (2^{96})^4 mod p_i via Horner's method //! and checking a(α_i)·b(α_i) - q(α_i)·n(α_i) - r(α_i) = 0 for all i. //! //! The CRT exactness theorem guarantees that if all 11 channel checks pass and //! ∏ p_i exceeds the maximum deviation |a·b - q·n - r|, then the integer //! relation holds exactly. use core::circuit::{CircuitModulus, u384, u96}; use core::num::traits::Zero; use core::serde::Serde; use core::sha256::compute_sha256_byte_array; use core::traits::TryInto; use corelib_imports::bounded_int::{downcast, upcast}; use garaga::basic_field_ops::is_even_u384; use garaga::circuits::rsa::run_RSA_FULL_VERIFICATION_circuit; use garaga::definitions::{RSA2048Chunks, RSA2048ReductionWitness, deserialize_u384, serialize_u384}; const RSA_TOP_CHUNK_LIMB1_MAX: u128 = 0xFFFF_FFFF_u128; const RSA2048_CHUNKS_SERIALIZED_LEN: usize = 24; const RSA2048_REDUCTION_WITNESS_SERIALIZED_LEN: usize = 2 * RSA2048_CHUNKS_SERIALIZED_LEN; const RSA2048_REDUCTION_COUNT: usize = 17; const RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN: usize = RSA2048_REDUCTION_COUNT * RSA2048_REDUCTION_WITNESS_SERIALIZED_LEN; const RSA_CHANNEL_MODULI: [[u96; 4]; 11] = [ [ 0xfffffffffffffffffffffd21, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xfffffffffffffffffffffb4d, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xfffffffffffffffffffff3ed, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xfffffffffffffffffffff05d, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffed33, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffe9b9, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffe877, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffe4db, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffe40f, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffe083, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], [ 0xffffffffffffffffffffdd1d, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1fffffffffffffffffffffff, ], ]; const U384_ZERO: u384 = u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }; const U384_ONE: u384 = u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }; /// The multiplicative identity 1 in chunk representation. const RSA_ONE_CHUNKS: RSA2048Chunks = RSA2048Chunks { w0: U384_ONE, w1: U384_ZERO, w2: U384_ZERO, w3: U384_ZERO, w4: U384_ZERO, w5: U384_ZERO, }; /// Horner evaluation bases: α_i = (2^96)^4 mod p_i for each of the 11 channel primes. /// Used to evaluate the chunk polynomial representation of 2048-bit integers /// within each RNS channel circuit. const RSA_CHUNK_STEPS: [u384; 11] = [ u384 { limb0: 0x16f8, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x2598, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x6098, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x7d18, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x9668, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xb238, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xbc48, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xd928, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xdf88, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0xfbe8, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, u384 { limb0: 0x11718, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, ]; fn serialize_rsa2048_chunks(self: @RSA2048Chunks, ref output: Array) { serialize_u384(self.w0, ref output); serialize_u384(self.w1, ref output); serialize_u384(self.w2, ref output); serialize_u384(self.w3, ref output); serialize_u384(self.w4, ref output); serialize_u384(self.w5, ref output); } fn deserialize_rsa2048_chunks(ref serialized: Span) -> RSA2048Chunks { let w0 = deserialize_u384(ref serialized); let w1 = deserialize_u384(ref serialized); let w2 = deserialize_u384(ref serialized); let w3 = deserialize_u384(ref serialized); let w4 = deserialize_u384(ref serialized); let w5 = deserialize_u384(ref serialized); RSA2048Chunks { w0, w1, w2, w3, w4, w5 } } #[derive(Copy, Drop, Debug, PartialEq)] pub struct RSA2048PublicKey { pub modulus: RSA2048Chunks, } pub impl RSA2048PublicKeySerde of Serde { fn serialize(self: @RSA2048PublicKey, ref output: Array) { serialize_rsa2048_chunks(self.modulus, ref output); } fn deserialize(ref serialized: Span) -> Option { Option::Some(RSA2048PublicKey { modulus: deserialize_rsa2048_chunks(ref serialized) }) } } #[derive(Copy, Drop, Debug, PartialEq)] pub struct RSA2048Signature { pub signature: RSA2048Chunks, pub expected_message: RSA2048Chunks, } pub impl RSA2048SignatureSerde of Serde { fn serialize(self: @RSA2048Signature, ref output: Array) { serialize_rsa2048_chunks(self.signature, ref output); serialize_rsa2048_chunks(self.expected_message, ref output); } fn deserialize(ref serialized: Span) -> Option { let signature = deserialize_rsa2048_chunks(ref serialized); let expected_message = deserialize_rsa2048_chunks(ref serialized); Option::Some(RSA2048Signature { signature, expected_message }) } } pub impl RSA2048ReductionWitnessSerde of Serde { fn serialize(self: @RSA2048ReductionWitness, ref output: Array) { serialize_rsa2048_chunks(self.quotient, ref output); serialize_rsa2048_chunks(self.remainder, ref output); } fn deserialize(ref serialized: Span) -> Option { let quotient = deserialize_rsa2048_chunks(ref serialized); let remainder = deserialize_rsa2048_chunks(ref serialized); Option::Some(RSA2048ReductionWitness { quotient, remainder }) } } #[derive(Drop, Debug, PartialEq)] pub struct RSA2048SignatureWithHint { pub signature: RSA2048Signature, pub reductions_hint: Span, } pub impl SerdeRSA2048SignatureWithHint of Serde { fn serialize(self: @RSA2048SignatureWithHint, ref output: Array) { Serde::::serialize(self.signature, ref output); output.append_span(*self.reductions_hint); } fn deserialize(ref serialized: Span) -> Option { let signature = Serde::::deserialize(ref serialized)?; let serialized_len = serialized.len(); if serialized_len < RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN { return Option::None; } let reductions_hint = serialized.slice(0, RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN); serialized = serialized .slice( RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN, serialized_len - RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN, ); Option::Some(RSA2048SignatureWithHint { signature, reductions_hint }) } } fn limb_lt(lhs: u96, rhs: u96) -> bool { let lhs_u128: u128 = upcast(lhs); let rhs_u128: u128 = upcast(rhs); lhs_u128 < rhs_u128 } fn u384_lt(lhs: u384, rhs: u384) -> bool { if lhs.limb3 != rhs.limb3 { return limb_lt(lhs.limb3, rhs.limb3); } if lhs.limb2 != rhs.limb2 { return limb_lt(lhs.limb2, rhs.limb2); } if lhs.limb1 != rhs.limb1 { return limb_lt(lhs.limb1, rhs.limb1); } return limb_lt(lhs.limb0, rhs.limb0); } fn chunks_lt(lhs: RSA2048Chunks, rhs: RSA2048Chunks) -> bool { if lhs.w5 != rhs.w5 { return u384_lt(lhs.w5, rhs.w5); } if lhs.w4 != rhs.w4 { return u384_lt(lhs.w4, rhs.w4); } if lhs.w3 != rhs.w3 { return u384_lt(lhs.w3, rhs.w3); } if lhs.w2 != rhs.w2 { return u384_lt(lhs.w2, rhs.w2); } if lhs.w1 != rhs.w1 { return u384_lt(lhs.w1, rhs.w1); } return u384_lt(lhs.w0, rhs.w0); } fn chunks_le(lhs: RSA2048Chunks, rhs: RSA2048Chunks) -> bool { lhs == rhs || chunks_lt(lhs, rhs) } fn top_chunk_is_well_formed(top: u384) -> bool { if top.limb2 != 0 { return false; } if top.limb3 != 0 { return false; } let limb1: u128 = upcast(top.limb1); limb1 <= RSA_TOP_CHUNK_LIMB1_MAX } /// Deserialize and validate a modular reduction witness (q, r) from raw felt252 data. /// Checks that both quotient and remainder have well-formed top chunks, /// and that the remainder is strictly less than the modulus. fn deserialize_and_validate_witness( ref hint: Span, modulus_chunks: RSA2048Chunks, ) -> RSA2048ReductionWitness { let quotient = deserialize_rsa2048_chunks(ref hint); let remainder = deserialize_rsa2048_chunks(ref hint); assert(top_chunk_is_well_formed(quotient.w5), 'RSA:bad quotient top chunk'); assert(top_chunk_is_well_formed(remainder.w5), 'RSA:bad remainder top chunk'); assert(chunks_lt(remainder, modulus_chunks), 'RSA:remainder >= modulus'); RSA2048ReductionWitness { quotient, remainder } } /// Verify an RSA-2048 signature assuming the message is already encoded. /// /// Given public key n and signature data (s, m, 17 reduction witnesses), /// verifies s^{65537} ≡ m (mod n) by: /// 1. Well-formedness: n > 1 odd, 0 ≤ s < n, 0 ≤ m < n, valid chunk bounds. /// 2. For each of 11 RNS channels: run the mega-circuit to verify all 17 /// reduction steps of the square-and-multiply chain. /// 3. Final equality: the last reduction remainder equals the expected message m. #[inline(never)] pub fn is_valid_rsa2048_signature_assuming_encoded_message( signature: @RSA2048SignatureWithHint, public_key: @RSA2048PublicKey, ) -> bool { let modulus_chunks = *public_key.modulus; let sig_chunks = *signature.signature.signature; let expected_message_chunks = *signature.signature.expected_message; if !top_chunk_is_well_formed(modulus_chunks.w5) { return false; } if !top_chunk_is_well_formed(sig_chunks.w5) { return false; } if !top_chunk_is_well_formed(expected_message_chunks.w5) { return false; } if chunks_le(modulus_chunks, RSA_ONE_CHUNKS) { return false; } if is_even_u384(modulus_chunks.w0) { return false; } if !chunks_lt(sig_chunks, modulus_chunks) { return false; } if !chunks_lt(expected_message_chunks, modulus_chunks) { return false; } let mut reductions_hint = *signature.reductions_hint; // Deserialize and validate all 17 modular reduction witnesses (q_i, r_i) if reductions_hint.len() < RSA2048_REDUCTIONS_HINT_SERIALIZED_LEN { return false; } let w0 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w1 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w2 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w3 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w4 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w5 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w6 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w7 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w8 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w9 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w10 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w11 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w12 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w13 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w14 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w15 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); let w16 = deserialize_and_validate_witness(ref reductions_hint, modulus_chunks); if !reductions_hint.is_empty() { return false; } // For each RNS channel p_i, verify all 17 reductions via the fused circuit let mut steps = RSA_CHUNK_STEPS.span(); for channel_modulus_limbs in RSA_CHANNEL_MODULI.span() { let step = *steps.pop_front().unwrap(); let channel_modulus: CircuitModulus = (*channel_modulus_limbs).try_into().unwrap(); let (d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11, d12, d13, d14, d15, d16) = run_RSA_FULL_VERIFICATION_circuit( modulus_chunks, sig_chunks, w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, step, channel_modulus, ); if !d0.is_zero() || !d1.is_zero() || !d2.is_zero() || !d3.is_zero() || !d4.is_zero() || !d5.is_zero() || !d6.is_zero() || !d7.is_zero() || !d8.is_zero() || !d9.is_zero() || !d10.is_zero() || !d11.is_zero() || !d12.is_zero() || !d13.is_zero() || !d14.is_zero() || !d15.is_zero() || !d16.is_zero() { return false; } } // The final remainder r_{16} must equal the expected message m w16.remainder == expected_message_chunks } // PKCS#1 v1.5 SHA-256 constant chunks (W1..W5). // These encode: 0x00||0x01||0xFF×202||0x00||DigestInfo[12:19] // W0 depends on the hash and is built dynamically. const PKCS1_SHA256_W5: u384 = u384 { limb0: 0xffffffffffffffffffffffff, limb1: 0x0001ffff, limb2: 0x0, limb3: 0x0, }; const PKCS1_SHA256_W4: u384 = u384 { limb0: 0xffffffffffffffffffffffff, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffffffffffff, limb3: 0xffffffffffffffffffffffff, }; const PKCS1_SHA256_W3: u384 = u384 { limb0: 0xffffffffffffffffffffffff, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffffffffffff, limb3: 0xffffffffffffffffffffffff, }; const PKCS1_SHA256_W2: u384 = u384 { limb0: 0xffffffffffffffffffffffff, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffffffffffff, limb3: 0xffffffffffffffffffffffff, }; const PKCS1_SHA256_W1: u384 = u384 { limb0: 0xffffffffffffffff00303130, limb1: 0xffffffffffffffffffffffff, limb2: 0xffffffffffffffffffffffff, limb3: 0xffffffffffffffffffffffff, }; // W0.limb3 is the constant part: DigestInfo[3:15] encoded as 96 bits. const PKCS1_SHA256_W0_LIMB3: u96 = 0x0d0609608648016503040201; /// Build the PKCS#1 v1.5 SHA-256 encoded message from 8 hash words. /// /// Layout (256 bytes big-endian): /// 0x00||0x01||PS(0xFF×202)||0x00||DigestInfo(19)||SHA-256(32) /// /// W0 limb packing: /// limb0 = hw5 * 2^64 + hw6 * 2^32 + hw7 /// limb1 = hw2 * 2^64 + hw3 * 2^32 + hw4 /// limb2 = 0x05000420 * 2^64 + hw0 * 2^32 + hw1 /// limb3 = 0x0d0609608648016503040201 (constant) fn pkcs1_v1_5_sha256_encode(hash: [u32; 8]) -> RSA2048Chunks { let [hw0, hw1, hw2, hw3, hw4, hw5, hw6, hw7] = hash; let hw0: felt252 = hw0.into(); let hw1: felt252 = hw1.into(); let hw2: felt252 = hw2.into(); let hw3: felt252 = hw3.into(); let hw4: felt252 = hw4.into(); let hw5: felt252 = hw5.into(); let hw6: felt252 = hw6.into(); let hw7: felt252 = hw7.into(); let limb0: u96 = downcast(hw5 * 0x10000000000000000 + hw6 * 0x100000000 + hw7).unwrap(); let limb1: u96 = downcast(hw2 * 0x10000000000000000 + hw3 * 0x100000000 + hw4).unwrap(); let limb2: u96 = downcast(0x05000420 * 0x10000000000000000 + hw0 * 0x100000000 + hw1).unwrap(); let w0 = u384 { limb0, limb1, limb2, limb3: PKCS1_SHA256_W0_LIMB3 }; RSA2048Chunks { w0, w1: PKCS1_SHA256_W1, w2: PKCS1_SHA256_W2, w3: PKCS1_SHA256_W3, w4: PKCS1_SHA256_W4, w5: PKCS1_SHA256_W5, } } /// Verify an RSA-2048 signature against a raw message using SHA-256. /// /// Computes SHA-256(message) on-chain, constructs the PKCS#1 v1.5 encoding, /// asserts it matches the expected_message hint, then delegates to the /// existing RNS-based RSA verification. #[inline(never)] pub fn is_valid_rsa2048_sha256_signature( signature: @RSA2048SignatureWithHint, public_key: @RSA2048PublicKey, message: @ByteArray, ) -> bool { // Compute SHA-256 of the message on-chain let hash: [u32; 8] = compute_sha256_byte_array(message); // Build the PKCS#1 v1.5 encoded message from the hash let encoded = pkcs1_v1_5_sha256_encode(hash); // Assert the hint matches the on-chain computation if encoded != *signature.signature.expected_message { return false; } // Delegate to the existing RSA verifier is_valid_rsa2048_signature_assuming_encoded_message(signature, public_key) } ================================================ FILE: src/src/signatures/schnorr.cairo ================================================ use garaga::basic_field_ops::{is_even_u384, neg_mod_p}; use garaga::definitions::{ G1Point, Zero, deserialize_u384, get_G, get_curve_order_modulus, get_n, serialize_u384, u384, }; use garaga::ec_ops::{G1PointTrait, msm_g1}; use garaga::utils::u384_eq_zero; /// A Schnorr signature. /// /// # Fields /// * `rx`: `u384` - The x-coordinate of the R point from the signature. /// * `s`: `u256` - The s component of the signature. /// * `e`: `u256` - The challenge hash. #[derive(Drop, Debug, PartialEq)] pub struct SchnorrSignature { pub rx: u384, pub s: u256, pub e: u256, } pub impl SerdeSchnorrSignature of Serde { fn serialize(self: @SchnorrSignature, ref output: Array) { serialize_u384(self.rx, ref output); Serde::::serialize(self.s, ref output); Serde::::serialize(self.e, ref output); } fn deserialize(ref serialized: Span) -> Option { let rx = deserialize_u384(ref serialized); let s = Serde::::deserialize(ref serialized).unwrap(); let e = Serde::::deserialize(ref serialized).unwrap(); return Option::Some(SchnorrSignature { rx: rx, s: s, e: e }); } } /// A Schnorr signature bundled with computation hints required for Cairo verification. /// /// # Fields /// * `signature`: `SchnorrSignature` - The core signature data. /// * `msm_hint`: `Span` - Hint for multi-scalar multiplication computation. #[derive(Drop, Debug, PartialEq, Serde)] pub struct SchnorrSignatureWithHint { pub signature: SchnorrSignature, pub msm_hint: Span, } /// Verifies a Schnorr signature with associated hints, assuming the hash challenge is correct. /// /// # Important Assumption /// **This function assumes that the hash `e` has been correctly derived from `x_R` and the message /// by the caller.** It does not compute or verify the hash derivation itself. The caller is /// responsible for ensuring that `e = H(x_R || message)` (or the appropriate hash construction for /// their protocol) before calling this function. /// /// # Arguments /// * `signature`: `SchnorrSignatureWithHint` - The signature and verification data bundle /// containing: /// - rx: The x-coordinate of the R point /// - s: The s component of the signature /// - e: The challenge hash (assumed to be correctly computed by the caller) /// - msm_hint: Hint for multi-scalar multiplication /// * `public_key`: `G1Point` - The public key to verify against. /// * `curve_id`: `usize` - The id of the curve. (0 for BN254, 1 for BLS12_381, 2 for SECP256K1, 3 /// for SECP256R1, 4 for ED25519, 5 for GRUMPKIN) /// /// # Algorithm /// The Schnorr signature verification checks if the signature (R, s) is valid for a given challenge /// hash e and public key P: /// 1. Verify that all inputs (rx, s, e) are non-zero and less than the curve order n /// 2. Verify that the public key P is on the curve and has even y-coordinate (BIP340 requirement, /// see /// https://github.com/bitcoin/bips/blob/58ffd93812ff25e87d53d1f202fbb389fdfb85bb/bip-0340/reference.py#L71) /// 3. Compute sG - eP where G is the generator point (using MSM) /// 4. Verify that the result equals R (matching x-coordinate and even y-coordinate) /// 5. The signature is valid if all checks pass /// /// This implements the verification equation: sG - eP = R /// Which proves the signer knew the private key x where P = xG, given that e was correctly derived. /// Returns false if the signature is invalid. pub fn is_valid_schnorr_signature_assuming_hash( signature: SchnorrSignatureWithHint, public_key: G1Point, curve_id: usize, ) -> bool { let SchnorrSignatureWithHint { signature, msm_hint } = signature; let SchnorrSignature { rx, s, e } = signature; let n: u256 = get_n(curve_id); if u384_eq_zero(rx) || s >= n || s == 0 || e >= n || e == 0 || is_even_u384(public_key.y) == false { return false; } let pk_on_curve = public_key.is_on_curve_excluding_infinity(curve_id); if pk_on_curve == false { return false; } let n_modulus = get_curve_order_modulus(curve_id); let e_neg: u256 = neg_mod_p(e.into(), n_modulus).try_into().unwrap(); let points = array![get_G(curve_id), public_key].span(); let scalars = array![s, e_neg].span(); let res = msm_g1(points, scalars, curve_id, msm_hint); let ry_l0_f252: felt252 = res.y.limb0.into(); let ry_l0_u128: u128 = ry_l0_f252.try_into().unwrap(); if res.is_zero() || res.x != rx || (ry_l0_u128 % 2) != 0 { return false; } true } ================================================ FILE: src/src/tests/autogenerated/ecdsa_tests.cairo ================================================ use garaga::core::circuit::u288IntoCircuitInputValue; use garaga::definitions::G1Point; use garaga::signatures::ecdsa::{ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash}; #[test] #[ignore] // Ignored for auto-benchmarks fn test_ecdsa_BN254() { let mut ecdsa_sig_with_hints_serialized = array![ 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xbf6659a4013d8a0bc49c2bba0fe0b551, 0x2667e798582a362fb041cb7c36d149a8, 0x1, 0xb4862b21fb97d43588561712e8e5216b, 0x967d0cae6f4590b9a164106cf6a659e, 0x18, 0x1f553b3c905bf06693d39af3, 0x22a1bf1fdfb897a2e2368128, 0x56d66d1d4d06ac4, 0x0, 0xf6482bdbc7401ca9a5730403, 0x75053f99e9420c530d43ee42, 0x1fe46da1cc905e5d, 0x0, 0x1a59f6054bfb443f, 0x1000000000000000005d7679874156a92, 0xa19cd0d3b84ff34, 0x4aae535488bc0171, 0xb2b487addb0999f4b7e26ef8, 0xab2d694c6f3e51b16518f05b, 0x206ee9b43426de0b, 0x0, 0x43ad5aba55c006f840ef53f6, 0xd90cb92d61bdf082a563725f, 0x28e0a95f5fae45b5, 0x0, 0xa0b063933d8e3f54, 0x1000000000000000003fc2ccc129935ee, 0x1000000000000000030112506a6d6deff, 0x21d269100269048a, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 0); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_ecdsa_BLS12_381() { let mut ecdsa_sig_with_hints_serialized = array![ 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0x867620dc5a8fd7ecbe07be76, 0x11d338240a4de8ca41217d43, 0x2c7753c1707137bf, 0x0, 0x94796ffb457f39ac41d6612e5ce0a191, 0x356631f83b3d990d4f60bada0d2ecc95, 0x1, 0xb4862b21fb97d43588561712e8e5216b, 0x12cfa194e6f4590b9a164106cf6a659e, 0x18, 0x6c178cfd0b3cfa1cdc9611c2, 0x2e2e9b5b3dc7495056fcb216, 0xdc6b710b9b8d6af1b0d9662f, 0x144281277c62ad45fcc361df, 0xdd51112be4c794ba47bc61bb, 0xba737e0b6d17079da040afaf, 0x93d8c4b8589d2520cda8c68a, 0x1492245eaba8fad13666bf8, 0x2da17082600f7add, 0x1cbcf87b9857ba44, 0x989a085f93dfee0, 0x100000000000000002e5733515f6dc037, 0xcb7778677f6122a2ad987779, 0xf6d1d01660d142741ae0a2c9, 0x5d1be8a4ebf8d22589f99a46, 0xbcaa099b6ef5b8ac192db47, 0xe6dd3401412576d3a894bcf2, 0x2a839ac601bb4ed694e4724b, 0xa6ee37842198c02e8bc4074b, 0x107f65d9ec3f6a9587cfe814, 0x4c5ccbf186df2adb, 0x100000000000000009289460599d5e6be, 0x100000000000000003f0c985cb7645566, 0x396e116d375dd2dd, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 1); assert!(is_valid); } #[test] fn test_ecdsa_SECP256R1() { let mut ecdsa_sig_with_hints_serialized = array![ 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0x47e8f962616a171283a1176e90490f33, 0xde5c72ea3ea08688ab2876686671cca8, 0x1, 0xeb1167b367a9c3787c65c1e582e2e663, 0xf7c1bd874da5e709d4713d60c8a70639, 0x14, 0x286091616e02ba0069d28be8, 0x1d9745f8427b797bfae94bc9, 0xb3eb1f4823aa5b9f, 0x0, 0xd955b1c2d5dbf2b7ce1f8cc0, 0xd9d9fdc9f4834421e0583e30, 0x8bab0f5e16efdcd5, 0x0, 0xeae9da0724797b8c4deebd03881e0a93, 0x168a1a12c6aaa58209ea9db2a7f1a2b2f, 0x94038dc6b682d83583f52251, 0x2c3509157e0085975bedd577, 0x1e00bb14af9e8bf8, 0x0, 0x3017341aa1f59a0d17c013c5, 0x51583e6cc584e0a8145045aa, 0xb9220afd0e923820, 0x0, 0xd0446b1605d4f3bfb5a82b168ba1b43, 0x1ab0f41000c73e671352e746066899a70, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 3); assert!(is_valid); } #[test] fn test_ecdsa_SECP256K1() { let mut ecdsa_sig_with_hints_serialized = array![ 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x6bb797837f385ccf8ea3b9b6e7074b68, 0x123ea74e335845008c7f5f797313610f, 0x0, 0xeb1167b367a9c3787c65c1e582e2e663, 0xf7c1bd874da5e709d4713d60c8a70639, 0x18, 0xed540ba7da3f81bbaa728909, 0x893eeca8c449fc9407668128, 0x4c72a831e28b48, 0x0, 0xf7ae1bf4ac84c840ee8163eb, 0xfb80d24687ae79865523f56d, 0xebddaf8646d563b7, 0x0, 0x5763a6a1517232b0, 0x100000000000000003fa616b9d1aa135b, 0x2ee3ef80f868d011, 0x100000000000000003fe78eccc1da3303, 0x3baca0be7f388c0f13f91502, 0x279cead44672432f6083c7de, 0x7b7ead3b5811d2dd, 0x0, 0x5bbc00623473536e653b34f3, 0xe4d94e156ddc62c1d41c68f4, 0xe635b285558b642c, 0x0, 0x1000000000000000097e848fb19a47c06, 0x100000000000000003dc81ff2129521cf, 0xdfac131bb3bb11de, 0xafc939cc6fed0eee, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 2); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_ecdsa_ED25519() { let mut ecdsa_sig_with_hints_serialized = array![ 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0xd4b581f1ee29a4dfba0aa2d4, 0xf18a70dbf1dc5a76494bff12, 0xac1b7bfc409119f, 0x0, 0xd75af662c90a1cb06a531ce8992bfda2, 0x9c65af0ba668f70fb54682dc51dddb4, 0x1, 0xb4862b21fb97d43588561712e8e5216b, 0x4b3e865e6f4590b9a164106cf6a659e, 0x14, 0x8e4ebbfe9103ea220b651a02, 0x18ce985bbcad7e677405dafb, 0x69d6abb9648d50ad, 0x0, 0xc1ce73f105e57f3a39f4ed13, 0xcd2f4939fe1a2abf2a689253, 0x34f18a43f7786d73, 0x0, 0x28c38021207719b4c15ec8e3585a12b, 0x12f56bf5ab761b880d6d797751d76c911, 0x378b92a7d8456bc43b2417e1, 0xca39a3a66b3713d3f07aa06c, 0x2aa069ab39cf3c36, 0x0, 0x3d54f7790b6544e46aa424c4, 0x2fad442bf9ae38403e9616c2, 0xda201ff9acac7ac, 0x0, 0xa9c80a21b193cc891541d32627df585, 0x113108f379dac95a41e3221331fd0f214, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 4); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_ecdsa_GRUMPKIN() { let mut ecdsa_sig_with_hints_serialized = array![ 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0x4be0b43c26c6f414a5ea9ea34cff6d0c, 0x14d85887ecbe1e0c06e6a8310bf6d595, 0x0, 0xb4862b21fb97d43588561712e8e5216b, 0x967d0cae6f4590b9a164106cf6a659e, 0x14, 0xa92ff39dc786d18400f152fa, 0x20eafe86707668d52aa0d2, 0x6b08f8ea2e0d3ff, 0x0, 0x7e5a501bb54172443d6608ac, 0xe03026c1fc3a1c6ead58dafd, 0xa6f4d2409778496, 0x0, 0x5291f4cf1867b05ae7b1d1bbabfd2ac3, 0x26042d2cad5454bf11c7d3f813c42338, 0x3b840ebf6e6c7b9ad848e269, 0xc10e351a38f60bd193db9784, 0x16a66333126cff05, 0x0, 0x8f5f58884224366a4b4708a4, 0xee5fc2fc6e001cdb0584bd57, 0x1d311cc64e5601b2, 0x0, 0xab7959b0b8b002ec27721af3d0ccf03, 0x357d7828010d521de3fe6fc9427ab043, ] .span(); let public_key = Serde::::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let ecdsa_with_hints = Serde::< ECDSASignatureWithHint, >::deserialize(ref ecdsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_ecdsa_signature_assuming_hash(ecdsa_with_hints, public_key, 5); assert!(is_valid); } ================================================ FILE: src/src/tests/autogenerated/eddsa_tests.cairo ================================================ use garaga::signatures::eddsa_25519::{EdDSASignatureWithHint, is_valid_eddsa_signature}; #[test] fn test_eddsa_0_0B() { let mut eddsa_sig_with_hints_serialized = array![ 0x3a0764c9d3fe4bd5b70ab18201985ad7, 0x1a5107f7681a02af2523a6daf372e10e, 0x8a826e80cce2869072ac60c3004356e5, 0x5501492265e073d874d9e5b81e7f8784, 0x6bb4f91c70391ec6ac3ba3901582b85f, 0xb107a8e4341516524be5b59f0f55bd2, 0x0, 0x14, 0xea59f1a1b369842eaf693886, 0xf9224e07ed11424e3ec1fa70, 0x4a92acec2f8e1cbe, 0x0, 0xe590d7d2c7256a3e0ead52f, 0xd86b5e53124f1f969c189730, 0x537563cb5552be8d, 0x0, 0x138c5052d6a27a4e4c9560fdd264cfd3, 0x11a2728b581551e5fb75531f987dd1989, 0x21ed5fd748dd92098b05acad, 0x7994ad2b8159fd82cc56b3ef, 0x50b6933858654726, 0x0, 0xe2c7733e684c969b9e877cc9, 0x5b1f73e8e98e8c71a215ef2d, 0x697849ab9ad5648, 0x0, 0x336adfeb48576dcc2cbe3d6bcebf0290, 0xde93b33a51de734be6bf4494c1e417d, 0x82324bd01ce6f3cf81ab44e62959c82a, 0x6218e309d40065fcc338b3127f468371, 0xc513d47253187c24b12786bd777645ce, 0x55d0e09a2b9d34292297e08d60d0f620, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_1_2B() { let mut eddsa_sig_with_hints_serialized = array![ 0x58f03002d07ea48da3a118628ecd51fc, 0x258090481591eb5dac0333ba13ed1608, 0xa301be3a9ce627480224ecde57d69162, 0xacc35adbd780365e443a7484a248e50c, 0x59c64d9860f767ae90f2168d539bff18, 0xac41eeacebe27c08dd26e71e9157c4a, 0x2, 0xaf, 0x82, 0x14, 0x6dcaf738b22009c93c0bdb87, 0x3bf824e64854c39e4f4b4d71, 0x2ba562c0a5855870, 0x0, 0xd156c934e0630b6b1cade37c, 0xf9592c2a8d4525621a66ff9e, 0x6ea3c2799dcb0791, 0x0, 0x2b7d8065ce28f598d400cb3247955529, 0x11805a2d4008709e8bf8df99ecd21a9c8, 0xbea748bd8161e9392414c6af, 0xfb78a46df09a3550b0f40b90, 0x1736a99e1e6b6b2a, 0x0, 0xcd40357ed01033e3ff528c49, 0xc3d6cd32c65892252ebd9898, 0x11d058072223478a, 0x0, 0x941c53d6db9e9db6634c5d73d8a9cf3, 0x12d39e660f6e64df38adf8625e063b3cf, 0x98f8f7962a1ed013293448bba5b444f, 0x39a50ed09ff56e66f9db162c5fb6791a, 0x18236f1734e3e9b945a9ff5486cdbd02, 0x61213aa2dc9d68833f65d1b48dcf8598, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_2_4B() { let mut eddsa_sig_with_hints_serialized = array![ 0x5323472831c45de2863153c402c1dac0, 0xa73302d9921f008eeb2a158b87dbabea, 0x4d6630d51be769278400d1b0c66f4f12, 0x1634b9ae09b5fded6dc5f67d50f88d88, 0x2a8bc1975609f35d3006aa388d916be2, 0x70c155ea8e5ba9fe40adc2ea5ea32a8, 0x4, 0x5f, 0x4c, 0x89, 0x89, 0x14, 0xfc2e795891abcdefc79c39ab, 0xc39ec060c9acab62d783f744, 0x7edd959fdf5944aa, 0x0, 0xb9af3f53cf443ce8258ce9d8, 0x25a93844e779d9acf1a76582, 0x6044e088dd26d914, 0x0, 0x367ea01340ed3f4eb35fc0b5d6909880, 0x65becb59a33390e7a8eeb2961732995, 0x4d1173ab1a7126cd6f3553e5, 0x737d4ab842a32b29798c247e, 0x7175327fc8d35a1d, 0x0, 0xd940bd48ba9f49f998750045, 0x6a748e9b4454606da58d20fa, 0x1e0a3bd228532c1, 0x0, 0x683951430b64535637cbe187fb571f2, 0x1426013715579b3cf9108dacbc5d24c5, 0xafd7a14549a75297ba0c7c7b8bf58cc2, 0x6b0c3a1c5526758320ce254b6896d815, 0x44c071ef224e23c3376a6cfaf588f8b1, 0x15daf15d98e9a7cec9a0d949aa8a1010, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_3_6B() { let mut eddsa_sig_with_hints_serialized = array![ 0x54cc85d1334a44bef2d70505a4bfcffb, 0x3d64e33eb887502b0b64e16052616de1, 0x3f5a6d63ff558746e1e99c1dfc29d66e, 0x29fae5f73018249db793fd1ac9d9a540, 0x994ed1168dbd8d24bbec6ecc208f4b85, 0x239d831895634dc7094d90e4942175, 0x6, 0x89, 0x1, 0xd, 0x85, 0x59, 0x72, 0x14, 0x80741b4318d18819882bb551, 0xb2779f18fc7fb12feb65a53, 0x142ca3875044978f, 0x0, 0xa93609d4fc6719102719e96b, 0x6d8f72df2fdf0661b61a1139, 0x2a9bc38a67fdf1af, 0x0, 0xeba21cc2b39436195b0b53a4dd3d7e5, 0x126aa5d255d4eb38e1d8919974d3f183e, 0x72b49563bd0280d6978d8f59, 0xee4b484f08eead598602db92, 0x1d762afb1672ad6f, 0x0, 0x54194dff66204d8aa3eef75b, 0xc8e4dab18ef2e40c806b2245, 0x5b786f9856ffe227, 0x0, 0x3c7b94be6b7e6bfa95bee538eefe5fef, 0x94070cbd62a695ecf77e388896f23b0, 0x166b7bb41838af3515acc516812d7b0a, 0xc9430416260957f2798ebc1f4c0820, 0xfd1009be194ba52c4c3af995f41ea6de, 0x28ea2ab7b73169d1eb053770cc4c90cc, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_4_8B() { let mut eddsa_sig_with_hints_serialized = array![ 0x403164cdaf33b05ed9ce5f824ab51ff8, 0x63b8346f4303258970a920bd0afbab75, 0x88f2e7d378b17bc18a52b0afc5deadd6, 0x23def957bcf35e5410e116adb1db9a7f, 0x59620cc93a0fbe07893b728f38c8a514, 0x8fa05f888d4b73ddf4576c1ec85e8bb, 0x8, 0x42, 0x84, 0xab, 0xc5, 0x1b, 0xb6, 0x72, 0x35, 0x14, 0x62920ccda7a4a43580c16a97, 0xbc42ab1a6625ff1e10cf6704, 0xddd34ffe3defba, 0x0, 0x21bd69a53ef0e957f99488cf, 0x951d5e6a7d167e2c8b9c8ee8, 0x27d72985e7a6135f, 0x0, 0x3af1a7897e95058b0a1f9e6f8c89504a, 0x228f99300a1dbd3aa20393f9adaa37c9, 0x99acfb45641fa7e3e18424da, 0x44eec67bb79d7b7b0a740c2f, 0x102c2cdf25176fb7, 0x0, 0x1b86dd209edc5f7108c52dd0, 0x67ab6794197e33768c702848, 0x754e75fee6b042b, 0x0, 0x39e458b6a016bff5cc4ee182498edeaa, 0x3489b4d0d7178376a2f9c2366c0d415, 0xba02b3f75514da3d99a7c37c948ff75a, 0x758f833d060d0a8a117ec27148c907fd, 0x46eadcf85f952099fbb70cdb91f10610, 0x54c40a9283a8e6206a15e02b64b46288, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_5_10B() { let mut eddsa_sig_with_hints_serialized = array![ 0xe938c55c67fafa1dabf748834b52b231, 0xff4d6ea3c1bbd82ac1279e81e53f4ea8, 0x914eab3f9f3ff001dee95a418c59e428, 0x9949c55e6b9796edf0c2bdd37f58b9e, 0x258894367c6237391983f0404c1a15d9, 0x8ced65d6a69a67f49870a9f5ada999e, 0xa, 0x33, 0xd7, 0xa7, 0x86, 0xad, 0xed, 0x8c, 0x1b, 0xf6, 0x91, 0x14, 0x38c8023c9fb41d7b6939d204, 0x6c47c9dcf6dd08f0027d26cb, 0x7643328979691ed8, 0x0, 0xf539d2a0878555c6a28113ce, 0xd28009225c7af9f44698b284, 0x748c3d43195e54b8, 0x0, 0x37fb348b196c8215fbfea725d82bec57, 0x1070137c89b13bc46aaaa21e205c4982d, 0xb35abd3c324790d8a654aa98, 0xe5e89428ddbb53e8b5978536, 0x107329dcf2c18f83, 0x0, 0xc569bab4c0dd2d506349ad99, 0x40a1ce7bc71879d83ddb9493, 0x7d172c2321d811d4, 0x0, 0x238c19411579a152ed700c6fed5a148d, 0x1265553ee261600443f5b5980f90b6abe, 0x75f6f309f81f9e8aa1f24f9c28eab288, 0x256a25046b0c5c6e6e7a0eee192ff255, 0x26d6d2c886c8d8938da2c0c48aaa27ab, 0x4cd530baaf96cfce24c4baf37493d3cc, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_6_12B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa940aaba3f4f1c1311d111d09336e86f, 0x5782b17ac29ee3b03bf72f01306bd7d3, 0x1e38377d274b6106faa2333079d99a0f, 0x582292ced69ed05845a9a5c25af6946d, 0xddc8d0c0c3ae9742c93a862e9567a5c1, 0xec4ad559b4427bab60b8604e58410f7, 0xc, 0x5a, 0x8d, 0x9d, 0xa, 0x22, 0x35, 0x7e, 0x66, 0x55, 0xf9, 0xc7, 0x85, 0x14, 0x9b1776a1824355ed0f31d4b6, 0x9ba13aeac727ec1c4c3989d7, 0x1c20c27b1b41836f, 0x0, 0xad7ca35f9f1a595260a64136, 0x9b28c807d04f47f3e7ba89ae, 0x76a7aad88686c4cd, 0x0, 0x360399ddbc65be2e628e3fae9ee6d55c, 0x11c8a2911627601b102062e50546df703, 0xfbc5708cfe886fd0498219ad, 0xbd3fded76459b0468208d2b7, 0x66086effa4c818f0, 0x0, 0xbcdf5d18e7a01ecc5fcbc1aa, 0xb7733fa1f254458c678f0c4, 0x6ade3a37aaa14389, 0x0, 0x1b635746f2ada962d38fcba9f0aec343, 0x193ab04b7e052b85dcd94e7d6e265dfc, 0x7ec01a0af470fa5a48b1b20af07af00a, 0x5fca1ee5ddca2e7454275f8125d54949, 0x141afcb83c809f637a968f7a694d9a6a, 0xb2e763e5c5d8d490ad567a99d254c52, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_7_14B() { let mut eddsa_sig_with_hints_serialized = array![ 0x267e03bc533dd3527a5b7a4698f83acf, 0x91f2e233c0e9172225fc036999daa842, 0xe6253b6b00b21223eb603ce281fee36e, 0xb06ad6af8ddb4ec444f8236610028e83, 0x9042af526e1d8af5b8f55d19fd871067, 0x6cf94ef95877492000121735cd55380, 0xe, 0x55, 0xc7, 0xfa, 0x43, 0x4f, 0x5e, 0xd8, 0xcd, 0xec, 0x2b, 0x7a, 0xea, 0xc1, 0x73, 0x14, 0xc1e32736d15729299aaa09e7, 0x8e424562b0b2d4e10849f3f7, 0x4638985f6c4eecb8, 0x0, 0xf6f8582e11475ecce6e33473, 0x602deb6eefe4e4c17c82e744, 0x3abfa51751dcd4a0, 0x0, 0x249f7fab0b194de4a84fcbf4d04b48a2, 0x12e9de13153f96a14ecb14d5df17d9e2d, 0x63296c74f8e9485907858fda, 0xa300e4caed5ea8cfc94893a3, 0x4a781002e18f5dea, 0x0, 0xb6accf3462884fda4c7da786, 0x57c6fccffb3d8e0dd16d6d28, 0x184c57d464a36acc, 0x0, 0x227d1381630c922e8c77a0be24f969f7, 0x983ecf169859b172a652dab7630e8b, 0xf51214784e30f6963636248940f4bd31, 0x673970dc3e5bec3f2a44fc4e7518e66d, 0x1750714406fc2d2876ff75bc2cad8e11, 0x100e3069d5815a94db87c734f43b368b, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_8_16B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa2debae466c062697443478c50a8e534, 0x5b954321cd6c47944f5cde84b48a1b20, 0x68b308f9b7a3497912a8d040dc273d2a, 0x87ae2db0b9415d7ac1a654ff1b7638f, 0x53ce87ba90a44fe4e1b07af442c1aa09, 0xc5054ae7c364ceff1ca3915893af392, 0x10, 0xc9, 0x42, 0xfa, 0x7a, 0xc6, 0xb2, 0x3a, 0xb7, 0xff, 0x61, 0x2f, 0xdc, 0x8e, 0x68, 0xef, 0x39, 0x14, 0x2ccc5c7cac2eee8b2e47375, 0xbe3457718bcbd53b10b92cf9, 0x47d2b530179b9892, 0x0, 0xa0d5148d627eff7de3695066, 0xfbbf54cf338c905e6d373cd9, 0x51a1142c5de46d49, 0x0, 0x3540f747691b1589c7246b2a16cb78f, 0x127059d142c92015acd6f16fcc0f6aca0, 0xcf28c60e976b78e041947ee, 0xd1a14bd8d8623e6a8a8e9b0a, 0x21bcebc8f8c18ced, 0x0, 0x5e9d79fb649eeffc22a13d52, 0x6d83860361dd3223bf842efe, 0x4e148cceb02ebe6f, 0x0, 0x1175e121aacfeb9369560423064b5895, 0x101759331499142832f566dbd72c777cb, 0x1ea7db3fb12901a9622ff15d26e3634e, 0x5b4066ef8eb5ea44ae38dc24f9b8ce84, 0x6fe7a48b2b9e4c036d80526005e9e3aa, 0x64599205bcb26f328e09b76cea8e9f6, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_9_18B() { let mut eddsa_sig_with_hints_serialized = array![ 0xf2e34c3bc3ae76866ad899f12791d274, 0x6b3a2165ca8c1ecd1c192cf591b1cc25, 0xee92302f49750591173ca043d729e9fb, 0xf5134738ca574ecacfca3604af12b2a, 0x80db0a70f1418c6c2d32912758db62c2, 0xa3e62e73eae4434700b2714bcca7e02, 0x12, 0xbd, 0x8e, 0x5, 0x3, 0x3f, 0x3a, 0x8b, 0xcd, 0xcb, 0xf4, 0xbe, 0xce, 0xb7, 0x9, 0x1, 0xc8, 0x2e, 0x31, 0x14, 0xfa1252aa123e86ee87f8c8c7, 0xa2218cc84ca64ab31a5bdbf9, 0x760ea6e91bcff0fd, 0x0, 0xbc93a87ac4c455717816c9d1, 0x88c7777545d6c5afdfd4387a, 0x4dd7be231e07a6b8, 0x0, 0x3662cbc08efd2b73724c4b64e181fe3f, 0x220b0e53b6a13c6efb4727fc6922ae1c, 0x20ff2c17be4383c0c7b3461, 0xcee6248e4f8755edfae5b7e, 0x7584f114bf6892a4, 0x0, 0xeb29df4ea33769a5027a031, 0x677e70b90c46b0141bae3def, 0x5bee213f1981b3be, 0x0, 0x379f66621fb39f0dcb0c73e8ad7ba68f, 0x129078edcd97e548881a71998959917dc, 0x12f9c9f73a8645fb1ec4f7e542186624, 0x1faf3db7e89ef842c31398dc78b1d6a4, 0xbb608ba1755964b8a7e626f14eb5a33c, 0x46e151b817dfa0805ffc863f3ba6a850, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_10_20B() { let mut eddsa_sig_with_hints_serialized = array![ 0x5b0884354e71a735658929859381a21c, 0x7f81008c5dddc89f81423f72ec9fef86, 0x4d42f6df7f7e676206982d6abcc2ada1, 0x85326f256ee9f3fd90ca95570fa5dbe7, 0xc44c74eba94023d992e4860331dc7ca, 0x5f193db373926046e3ee85ff3fdaf61, 0x14, 0x8b, 0xa6, 0xa4, 0xc9, 0xa1, 0x5a, 0x24, 0x4a, 0x9c, 0x26, 0xbb, 0x2a, 0x59, 0xb1, 0x2, 0x6f, 0x21, 0x34, 0x8b, 0x49, 0x14, 0x937d82291b7f8dc2781d4e5f, 0xa937d9ca11ae15eff034e737, 0x34b1848dd33cc4bc, 0x0, 0x1aa605be8f31fb5fa2f72f6d, 0x2b625f928529ba42e9970fea, 0x52f1e366d79e7073, 0x0, 0x387306bd9bc7a9af9d7ca633a58771b9, 0x243411ab947bef8f30e95cdb895fa8c1, 0x37e3b62e93ef9a9e5987db54, 0x1ffee904ff81caa82c12aba7, 0x18f6049707602a63, 0x0, 0xe2045701aec1245297f05444, 0xf0506a3f16f97c20c745af91, 0x6341e55f4b7c38c7, 0x0, 0x29ddad2d13e8fcc5f380cdc5ad8dc7fb, 0x1df6c6969ff415bd6ab279f827575811, 0x6120e97100cf4aaebfcf1db80e51bdbb, 0x6ef0677f61dbc7d5f23697cafb1ff6af, 0xc0decbf4f20c787447d823b0dd40639c, 0x37a3fb1811a6325320bf08033e450a8f, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_11_22B() { let mut eddsa_sig_with_hints_serialized = array![ 0x147e5eb78bbb945d71f0230d859b3548, 0x85fc02a0bd3f4005a8286ff014af2e32, 0x1d6e8787cea32243c5badf8999d0dcb6, 0x6ad897a7a6d70bb5249dc798a94d1362, 0x9fecfb2c653c674ac1d691749ddc140e, 0x13928ab6d079082f3bda45c9382a96, 0x16, 0x1b, 0xa, 0xfb, 0xa, 0xc4, 0xba, 0x9a, 0xb7, 0xb7, 0x17, 0x2c, 0xdd, 0xc9, 0xeb, 0x42, 0xbb, 0xa1, 0xa6, 0x4b, 0xce, 0x47, 0xd4, 0x14, 0x95156f4654352c47d318d763, 0x60bbfcd2afac5410c4e71df8, 0x15b6c8789497160a, 0x0, 0x8b5ca313032ef0415a347710, 0x5804f93938239c9afbc99e9e, 0x7c65c4735c4ffbd8, 0x0, 0x28a74c9dce2b2e4a842e33e399863e1f, 0x11da7a8750a2ce61ed28c38c0d512155d, 0x189e561188bc49a918bafffe, 0xfc6b5aae2395e9e47a2ba2a2, 0xc37c6f902c1d20c, 0x0, 0x876528e8db7ca14d83a81e9c, 0xaacbaa6e2bb209db25f41261, 0x370d6bc6274f3efe, 0x0, 0x196f76c318589c37468b549f759bb8bb, 0x117d80ddf19758192660aa5d7d49050f3, 0xc0d2ff32c5a6af243630ec9259c6af2c, 0x61aea3a5983fd6cae64eb8e88b96850d, 0xafe00c80288a3f318befb32b139a5437, 0x5c7c637a089f1adb6ead8f3bf7b7eddf, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_12_24B() { let mut eddsa_sig_with_hints_serialized = array![ 0x5819635133648c8ad52720890198d3b1, 0x71137301f7e496032cabe1db6c1bf93, 0x974e658b38a47047aa489c4d76fa6a83, 0x24d9df7dc42f7fa2bcfe6729086fc1b3, 0x230bb64643700951cf8a6929c7cf034b, 0xae72d12d199239156dc9d083054250f, 0x18, 0xd3, 0xd6, 0x15, 0xa8, 0x47, 0x2d, 0x99, 0x62, 0xbb, 0x70, 0xc5, 0xb5, 0x46, 0x6a, 0x3d, 0x98, 0x3a, 0x48, 0x11, 0x4, 0x6e, 0x2a, 0xe, 0xf5, 0x14, 0x93365d4deeadd32cb6bef2eb, 0xb1e8c7218c86075e32aee0, 0x1d7d22ed34f1149, 0x0, 0xe0f56ac073d697677a6fe5e5, 0x96d8c7060abc38fe9aca1fa8, 0x49724abc771d47ee, 0x0, 0x160b0f9b0c4c14a731464bb6d1b233d7, 0xd2e63ee4fa297d82b689e05eb59b317, 0xb184e835deae44e701bcd4c3, 0x89e0109a1956c9ad42d7eb0e, 0x4c9b77572f7eba05, 0x0, 0x6d672251bdafa6854506ba2c, 0xed6dbbf342430dda8e232a5, 0x522281f8c2485961, 0x0, 0x12bc7ea1134aefe5e5b12d22ad5b534d, 0x1243a10433596b92d64a074d7e1776fca, 0x82b993a0531c7dd032b01d860a0439de, 0x7bd75a648b9b9f011eb35a457c8f0fa8, 0xfae6685f07ce72100cf3cb675d2dff5e, 0x71631f2614a7d8451b8e92b94431e353, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_13_26B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa0ee85cd9ee2f3d82246ba42a12bf32b, 0x238b21dd270b519b2c41649dbe479c7b, 0x27dd70b034665bf7f00d035a8c5b1f88, 0xf9bb6964eeb3389334ae3887c0e31ebd, 0x2831212de5e5382517d238a57130b76, 0xf9a04447ba0dc37653ad665f8b5907a, 0x1a, 0x82, 0xcb, 0x53, 0xc4, 0xd5, 0xa0, 0x13, 0xba, 0xe5, 0x7, 0x7, 0x59, 0xec, 0x6, 0xc3, 0xc6, 0x95, 0x5a, 0xb7, 0xa4, 0x5, 0x9, 0x58, 0xec, 0x32, 0x8c, 0x14, 0xdc02485645b64ce43298b09c, 0xc5b33942074cdd7280920b92, 0x6ab46e3a2ba409d6, 0x0, 0x41ba3f26848b6a909d587a94, 0xfdbf13ee5884324e413206d9, 0x3a09c07e27fd90b2, 0x0, 0x16e65808b9c27d57d7cd996821a0eff, 0x22b34ea38eebdbf4fbfde51a1faefa0e, 0xf772d2a88ec86f5ce6a7877e, 0x117c7f63e5c11f2b8d94f370, 0x692164d4228964e1, 0x0, 0x320d098d9fa46ac8495c66a0, 0xfd7ce2c6687abd6fb03ed1a0, 0x7b1010a7831bec78, 0x0, 0x3102b7637f8a45b26c33aaf26633fd91, 0x11c35669269462aabc3a7d66234b45bb3, 0xc9035a46924bf4932cd117694695e539, 0x6ce4dac054bc1a31f39854152016223e, 0x667226bfd4e63a2380c6eb6b8f164376, 0x7287797999af616511d3b1c69188181c, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_14_28B() { let mut eddsa_sig_with_hints_serialized = array![ 0x336ff7c6db96a4af9b6b7ab9a84a089d, 0x7e426943910f0a5281e617d9c916a106, 0xffd9e58d99e8b56c21661b78235487f5, 0x81efc3a9034537e3ac547010671d9dc2, 0xca78c41a6f70bd44672981de69f27715, 0x191cba6f957bd02f8b371f8cd549bf0, 0x1c, 0x5c, 0xb6, 0xf9, 0xaa, 0x59, 0xb8, 0xe, 0xca, 0x14, 0xf6, 0xa6, 0x8f, 0xb4, 0xc, 0xf0, 0x7b, 0x79, 0x4e, 0x75, 0x17, 0x1f, 0xba, 0x96, 0x26, 0x2c, 0x1c, 0x6a, 0xdc, 0x14, 0xc64d7b617fdd5e1dbfba3d1c, 0xdfc0e53f0dc3699f5e6cc2c6, 0x144281755c7dcb1f, 0x0, 0xd2a954957a5a6f44af21b472, 0x32241a2bbac5dcaa73d93ee7, 0x3f300f37829c6980, 0x0, 0x2db8a4f9c475029ff4a31fd1468b1d9d, 0x105400ba14430012a90e043fe206b7f80, 0x2916403d6d09a3606f2bb0e1, 0x9a8c140557d268d2555dc87d, 0x2750f18a91ffb29f, 0x0, 0xc0ea955da0b0dd810bdc057c, 0xaa16523f1baed52398fc986e, 0x76b7543e99975ea1, 0x0, 0xaea7956216a955368dbcfbf36879b7f, 0x1226e3a51516bc1bad4960660c8167217, 0xb4bd4eea06387163676c44a6cd8d3bd3, 0x7001ba4f029bd407b7f030ec050834e8, 0xac5166adc37dd52a5364e38f13cd26e0, 0x2eca1086c3bd55727b33c81bb9a08aa2, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_15_30B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa3746aa5bbf565ce71fd2d563c32be23, 0x5b5afdb4f9c735f6942f3d576bc3dfa6, 0x8b375cc7ea20544f1b77de6b1ead8f0f, 0x482b433b82c110c22bcd5066acb56dae, 0xce93b289897a2fb9fa8f459505b116e0, 0x26ff1aa2a6506fc38203a246ceddfb8, 0x1e, 0xbb, 0x31, 0x72, 0x79, 0x57, 0x10, 0xfe, 0x0, 0x5, 0x4d, 0x3b, 0x5d, 0xfe, 0xf8, 0xa1, 0x16, 0x23, 0x58, 0x2d, 0xa6, 0x8b, 0xf8, 0xe4, 0x6d, 0x72, 0xd2, 0x7c, 0xec, 0xe2, 0xaa, 0x14, 0x695dff34554d1a4dc482d768, 0xd80b6ba6d7fa574d4d3290e7, 0x2a7ec089be1f9cbc, 0x0, 0x9d67cc27cacb90f274d3b80e, 0xe5f1d418344e291b7d9b6672, 0x1a29179e69f6518b, 0x0, 0x2148218957c9696ee542bcbdba204bb4, 0x10c6379409ee699507ba2a0c374d2adf7, 0x4739284c7860670641e3c224, 0xda1134a29f016547e345c4f0, 0x59dd1b7111fe87a, 0x0, 0x410b16bb6b54b3fe38806104, 0xaee2032adbd06d2248f8bfd5, 0x57dc9745231a60b, 0x0, 0xe956cf464450cbc9d6b0fba01bc8249, 0x1227d4b51278afc080aecbff814bf4a0f, 0x51dbe64d8ca775957a1e4bc33415af30, 0x4f2937cc1546c324d01dbb640cb6b0e9, 0x9b9a4ef694420c49e77e74c2e8d4b572, 0x2a0ac0449362354f213d5b96a050528c, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] fn test_eddsa_16_32B() { let mut eddsa_sig_with_hints_serialized = array![ 0x920ebc336f46f3a8fca7c6b1783a9fb4, 0xd9169375c3465f46a7c20643a0fb019f, 0xcfff01c94634eb2c32c1913b036c2604, 0xb33a73b89a17c59c987e834400cc43c, 0xf96da651bac612c035ef4281b4d8bbec, 0xb79952410703eb0e4b1d68a26b68c30, 0x20, 0xa7, 0x50, 0xc2, 0x32, 0x93, 0x3d, 0xc1, 0x4b, 0x11, 0x84, 0xd8, 0x6d, 0x8b, 0x4c, 0xe7, 0x2e, 0x16, 0xd6, 0x97, 0x44, 0xba, 0x69, 0x81, 0x8b, 0x6a, 0xc3, 0x3b, 0x1d, 0x82, 0x3b, 0xb2, 0xc3, 0x14, 0x662dc9a0c76e92de64ec1a88, 0xd2d804748dd9b3bca82dd8bd, 0x457a1c7d45c2e9a7, 0x0, 0x11a47f8c54b597cc233eb3c6, 0x63336aece841abd85253fd9a, 0x6ea4440a5a4d3f30, 0x0, 0x25bf29e718cebe0ce36dd0d4940f9d9d, 0x14fba393e8cd1b8036af3f707a8d9bfc, 0xfe9858637aa58ff5156e78d4, 0x956a2b8e1e2e952d10372d02, 0x6e43afd2c1a07d87, 0x0, 0x427e477e25b26ddcf82d0b31, 0xcbbb0211b0fa3200f1155f46, 0x78d4ba282e9fa7d4, 0x0, 0x28a9d1a11a601216ef8957600ea23a3f, 0x256a50b455e31ea6fd318955d93f2727, 0x9256394c23e0a68b4782cb46ae015318, 0x3357ca9c3c92a0fbc7694fcf95f4a6, 0x454ef0b5785b42c24de91294328ace85, 0x7dc110abca7f279ee8797a0fbd3d1bc0, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_17_34B() { let mut eddsa_sig_with_hints_serialized = array![ 0x4434db9c3af99a4b95c94d4745716baf, 0xc059ce3300b930e2244d821c657c5b9d, 0x7e2eb16ba77c2fdee09a99f2b1edc16, 0x3cc381f6897a04c578de3c14915edab8, 0x522d00ec11a803590928c9d528344e4e, 0x43eabb9d06d0c202719feb3f8d79ea3, 0x22, 0x8b, 0xc4, 0x18, 0x5e, 0x50, 0xe5, 0x7d, 0x5f, 0x87, 0xf4, 0x75, 0x15, 0xfe, 0x2b, 0x18, 0x37, 0xd5, 0x85, 0xf0, 0xaa, 0xe9, 0xe1, 0xca, 0x38, 0x3b, 0x3e, 0xc9, 0x8, 0x88, 0x4b, 0xb9, 0x0, 0xff, 0x27, 0x14, 0x8574ce95d05ba104575918c8, 0x478f99955bb34eafda2c4ef3, 0x76569cefd127cdc3, 0x0, 0x431e7bf616e082984d43819b, 0xd3de171509f57d53c66792c1, 0x12e6b6b75421ba59, 0x0, 0x42d2ba3c9b2a04ea6efa1fb2c448b27, 0x13c1fbc940e682b14e2822fd823c59374, 0x5a14bca84136abbbf31fa2b5, 0xc6a3506b2be99c8ce20d3fdf, 0x48fb6aec47c72452, 0x0, 0x5da1125f4fa6cded1ed8e483, 0xc2b212667311e55132b3860c, 0x3ac68f0d30d25ab2, 0x0, 0xae2fc31954b7bc1d2b8aac8de538e91, 0x12f8f3fcfcd9732eb74c7f05846518331, 0x4b0a8d3f7b856f0ccd6b58fa2d44a71c, 0x83744d08483ecb443579ded32c9c548, 0x40d42f7668f5a94e643c14c7da1fdebd, 0x6d275cfcf946e02027096f961f1121f2, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_18_36B() { let mut eddsa_sig_with_hints_serialized = array![ 0xaae380fcc272f2c7810a0979c8707301, 0x265b74ab60116998fc9a37cb3f60bcc2, 0xeecce3639db5961e14a75a33827f95ac, 0xfdd53395dc42afc24065027dc4a2c395, 0xb1755e913478f3ea7a18ad79167d8281, 0xc5e1a05dd43ba167501c8066828a947, 0x24, 0xe0, 0x5f, 0x71, 0xe4, 0xe4, 0x9a, 0x72, 0xec, 0x55, 0xc, 0x44, 0xa3, 0xb8, 0x5a, 0xca, 0x8f, 0x20, 0xff, 0x26, 0xc3, 0xee, 0x94, 0xa8, 0xf, 0x1b, 0x43, 0x1c, 0x7d, 0x15, 0x4e, 0xc9, 0x60, 0x3e, 0xe0, 0x25, 0x31, 0x14, 0xae93b41734e620cdee334fa0, 0xd352ee5d019527eb8c98e8f1, 0x33ec5f8898a0b075, 0x0, 0xb7b28970512e699b3a38463f, 0x6ddca8144ee02b3057724405, 0x38d2dfd4057d68ba, 0x0, 0xbd218002a44c7b51960ce902651c697, 0x1111b38650a75851b477de2ab9df44637, 0x84021670d8df0bfb2b628b5d, 0x11e4264eb37f2d5374f3a81, 0x7411fca07291f143, 0x0, 0xeb56b6b0af302d8903d0f9b7, 0x1ecf1d9759518efbfbce8f53, 0x6fab7cf11da9bf96, 0x0, 0x99aea252a91ad794073425c9eb7ca69, 0x16838f2988f00e1efa919551d94ce0b8, 0x115b8c0b51e3124c0c202c162992a1ab, 0x78e0429e2308507c6259d6eeeb977dde, 0x8e42671bc55a1b56d9411c574a12fdb0, 0x3f318627b427cd4f04c4bcb332869caf, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_19_38B() { let mut eddsa_sig_with_hints_serialized = array![ 0x3df5a88a1f2b1ca8076556b2bd0fad34, 0x30e9ee070d903e901ba9ad87cc64aacc, 0x4973c8372e2332c7549c489c1655b22a, 0xfd08ef29d3fee7abdb0905a2ebb186d4, 0x43b3ca51ccb56ca22e7be645d11cba75, 0x5f979b9d9fc6a4cecb0d71ffe85b0ee, 0x26, 0x83, 0x83, 0x67, 0x47, 0x11, 0x83, 0xc7, 0x1f, 0x7e, 0x71, 0x77, 0x24, 0xf8, 0x9d, 0x40, 0x1c, 0x3a, 0xd9, 0x86, 0x3f, 0xd9, 0xcc, 0x7a, 0xa3, 0xcf, 0x33, 0xd3, 0xc5, 0x29, 0x86, 0xc, 0xb5, 0x81, 0xf3, 0x9, 0x3d, 0x87, 0xda, 0x14, 0xa6292f8e5d044b22c5c63f84, 0xb5185d5bf28c5010285e7757, 0x455da0f9cd7bf6b0, 0x0, 0x765e6b22af349115fad57451, 0x59540b16237f6a1b57b61ec9, 0x62f01856724d22d6, 0x0, 0x17e85b805b8f90696245d1b1b1649e49, 0x3d44174a16f4dfe2ba3435e92180d6c8, 0x4981e32164acf5f47ec1644b, 0xc9771971ecf4273b72688ecf, 0x6d903846fdffebc, 0x0, 0xf9f67f8a29cbbb2787d26da9, 0xe579cb390629c7b291f9b184, 0x59c8c0216b2de9e0, 0x0, 0x2248d914e046643681fcff8df64e4d19, 0x110cf02766d970c48e424aa5132ad8c4a, 0x26c5bcd8bb36d24db3e484b1d29db41d, 0x5a146fe46aad15a653ebf45fc80274c1, 0xc49b3df64adbc040338abbe815fd2b80, 0x5fd235e9d5bdd1630c10d1de12b63e15, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_20_40B() { let mut eddsa_sig_with_hints_serialized = array![ 0x3cbce77b25c3d1f9d23fd2c2abc57217, 0xb864f9d243773a9b744b8440ee9cd71c, 0x5b972a3c6db9cea4b893e72476cd2868, 0x5283581e6258406153f34566ffe573f7, 0x321e5144266f736dafe6df421ff3e789, 0x8cbe8d30e73188d77792a5898a60f0c, 0x28, 0xda, 0x9c, 0x55, 0x59, 0xd0, 0xea, 0x51, 0xd2, 0x55, 0xb6, 0xbd, 0x9d, 0x76, 0x38, 0xb8, 0x76, 0x47, 0x2f, 0x94, 0x2b, 0x33, 0xf, 0xc0, 0xe2, 0xb3, 0xa, 0xea, 0x68, 0xd7, 0x73, 0x68, 0xfc, 0xe4, 0x94, 0x82, 0x72, 0x99, 0x1d, 0x25, 0x7e, 0x14, 0x5fa522a4fef55e8e23ddadc9, 0x4162b9c3d065c6877fcae158, 0x2c69d38963d3bbb0, 0x0, 0xa32c421a1744326f2487aa9d, 0x5d3a2032e251af5714e7268, 0x6f0b4dcca7119894, 0x0, 0x1eb1fc609d94408338932e6571331544, 0x106e4b717d15ec8ce530c18b4be2f30bf, 0x948833f5f59ff99bb96d7d9a, 0x1972451c30b9681ac6cc4894, 0x71db24cb9a8e37e5, 0x0, 0x5b05737bf52d3fac0da1105c, 0xdb567e54ca42d6c5bcaee354, 0xd21c41d6e5278aa, 0x0, 0x4a10590868e679657c16429324bdd19, 0x363fc94159c3ad82e51877bd206d3da4, 0x649a1364d8d8f4e98bc74329570bfc96, 0x3a80f629c7d3bc576d89c9d496ee9f95, 0x57b85b2b20263ab1877dcbc3614d71ed, 0x39711965fa2e49141a67dce0499f9413, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_21_42B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa3ff77a0b64bf8a53add37c4208b76da, 0x8d39c2e67fcefdc35c2b35c50185b64a, 0x6e7ca9c4d5e470a6262477c6203a721c, 0x2203296e40441e6315a4b01bf74791be, 0x5fe90f5d23dc8e6a85e78f347d97cae4, 0xa2f558ffddbc7e2778af2ddef1ad97e, 0x2a, 0x56, 0xf1, 0x32, 0x9d, 0x9a, 0x6b, 0xe2, 0x5a, 0x61, 0x59, 0xc7, 0x2f, 0x12, 0x68, 0x8d, 0xc8, 0x31, 0x4e, 0x85, 0xdd, 0x9e, 0x7e, 0x4d, 0xc0, 0x5b, 0xbe, 0xcb, 0x77, 0x29, 0xe0, 0x23, 0xc8, 0x6f, 0x8e, 0x9, 0x37, 0x35, 0x3f, 0x27, 0xc7, 0xed, 0xe9, 0x14, 0x6b84c39c4ad9cb2e9fa5c149, 0x78c59746fc3088327d4bbd98, 0x68c11f92ae24ca72, 0x0, 0x1ced9f7228d7051e25a21ff2, 0x5ad874fcfa9ef5ba64690548, 0x51bb8c3d280a1573, 0x0, 0x13a34b7d33dc76aaae012b70bcf1acd0, 0x2e42e245d8c7acb1d38141d0f2db3a2d, 0x3e1169a11a78e93989c338ab, 0x899bef2f13548199aa4ef880, 0x4f1ae0fecc6a40e4, 0x0, 0x99a7d8e333508e404954f77b, 0x6a763523b369a5647f1c3231, 0x24569ad8c201845a, 0x0, 0x66ff6748d8f79e3c78e61150ca8a367, 0x222ba2090a2091dccb807d3796e4bcba, 0xe4a0af74125fe32ce5ba54d9150a8f70, 0x2f9b4728682aa4dc6c45b098f9fa09c7, 0xe1c91d844f3ac84d0a918cb52493a511, 0x3b5e09022b3317db3e3908788aa7e0f8, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_22_44B() { let mut eddsa_sig_with_hints_serialized = array![ 0x476be4e75dba5012b6312fd42b6afbec, 0x37be3a0a7bdfd17b1ab70d66bcdfaf19, 0xb801bc80df12f7989423c74c3485f89a, 0xf6e2727a014555aa8bd2a1d41e293806, 0xa46c3a54f5b9fa5beba63d60f9cc4956, 0xcb015f6de95bf66bf763c156638afa7, 0x2c, 0x63, 0xb8, 0xb, 0x79, 0x56, 0xac, 0xbe, 0xcf, 0xc, 0x35, 0xe9, 0xab, 0x6, 0xb9, 0x14, 0xb0, 0xc7, 0x1, 0x4f, 0xe1, 0xa4, 0xbb, 0xc0, 0x21, 0x72, 0x40, 0xc1, 0xa3, 0x30, 0x95, 0xd7, 0x7, 0x95, 0x3e, 0xd7, 0x7b, 0x15, 0xd2, 0x11, 0xad, 0xaf, 0x9b, 0x97, 0xdc, 0x14, 0x8e7a92dea46f5561cf42f4bf, 0x3c16c9f7e12c8031937b5841, 0x2fad501544bd25c3, 0x0, 0x9a42264efd722de5794de5a1, 0x8ad70bf5e54d7c1e3e4833a8, 0x52e0fbeffe0d8623, 0x0, 0x63dda375cf39add7aff7470ead0dda5, 0x128071e01fe406fbeba88b7ccaa65a4a4, 0x6527a45e52b613894241f38, 0x27f84d85b97550d9cff0469e, 0xeff192310afb7, 0x0, 0x57d8a273d2fa8a6a0a827f15, 0xca33afdf5da8a3e129924e5e, 0x17dbe1f0ad58ba4e, 0x0, 0x235bfdd3d4df5fbab9ebc276cf04fa73, 0x1024324259d46313353e5ba361cda0906, 0x20866b32fd08893480bdca692eb706b5, 0x44899a259832955b940237cc48fa0d8, 0x396285d427e7e9697dd65ae4a51141ba, 0x257ce91e91c41dabaf781533a67e1b9e, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_23_46B() { let mut eddsa_sig_with_hints_serialized = array![ 0xeedad93b7bddeacc2a01b2aa95e7a3ab, 0x32386e83a3c29936c9d7dc8b25f56fed, 0xe016915541fad2d520ce87d4a81f692c, 0xf76cd64135185625150e24f57c39f4bb, 0x4347384defdb3903398d38a401245853, 0xb6e8a1a13b9a78ba6ab8d5ff546a3ca, 0x2e, 0x4f, 0x18, 0x46, 0xdd, 0x7a, 0xd5, 0xe, 0x54, 0x5d, 0x4c, 0xfb, 0xff, 0xbb, 0x1d, 0xc2, 0xff, 0x14, 0x5d, 0xc1, 0x23, 0x75, 0x4d, 0x8, 0xaf, 0x4e, 0x44, 0xec, 0xc0, 0xbc, 0x8c, 0x91, 0x41, 0x13, 0x88, 0xbc, 0x76, 0x53, 0xe2, 0xd8, 0x93, 0xd1, 0xea, 0xc2, 0x10, 0x7d, 0x5, 0x14, 0xf6aa1c3bcc6e9700fc72b9ec, 0x681c04f4d32e18731212375d, 0x5e0dd71647da599c, 0x0, 0x8e0f72c3b68f7ebafcec36a9, 0xbfdb6659c14511f534e282e1, 0x560f035da03f446c, 0x0, 0x6754299b9230b4b748b81c8773dcc0b, 0x11e0735b5b5d8d1e8a026d71f4944f30f, 0x7b9ba4e30b721ef913b4b6af, 0x23173f3fe90e6b5dec2fab9b, 0x230513fc8fe0951c, 0x0, 0x561a02e5dfbd78c8fb30a94b, 0x9b595711a1baf14fbec9b24b, 0x4c2dfe6dc0026e8b, 0x0, 0xffb8cc0ac6f793bee4a03695b069793, 0x1028d22f7af6abfad53ca95e74b6d75dc, 0x5c419a73d0a5de49c039f6583bfa4681, 0x6706312f873431995171f83697a97122, 0xc3aee7a86e08b3325330143719401486, 0x6faf8d956cf70dd2ebc8a45c3391c21, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_24_48B() { let mut eddsa_sig_with_hints_serialized = array![ 0xcfdb8360a12c992b6b3ed4a4bbefd290, 0x7fc4d34558e9f375eeb007393822b3a2, 0xd2cb053d81746685d5f1ae2144992efa, 0x60fec2bdfdc60dcd6eaf24b45eef84cf, 0x9e14c9f1b2bf594ff3ec12338885e95f, 0xbaedd28edf3301173b205daecc99c5b, 0x30, 0x78, 0x3e, 0x33, 0xc3, 0xac, 0xbd, 0xbb, 0x36, 0xe8, 0x19, 0xf5, 0x44, 0xa7, 0x78, 0x1d, 0x83, 0xfc, 0x28, 0x3d, 0x33, 0x9, 0xf5, 0xd3, 0xd1, 0x2c, 0x8d, 0xcd, 0x6b, 0xb, 0x3d, 0xe, 0x89, 0xe3, 0x8c, 0xfd, 0x3b, 0x4d, 0x8, 0x85, 0x66, 0x1c, 0xa5, 0x47, 0xfb, 0x97, 0x64, 0xab, 0xff, 0x14, 0xc17a6d05aaa41f9149dcdb2b, 0x402616ffdb4be4a39136a15a, 0x5ba0b15e673922b, 0x0, 0xdf4a5ed66de118a654bb55b4, 0x49018cec5c513896e1d4a5e6, 0x6ae98c1c50103d05, 0x0, 0x723647dbe73565e7b296b665b6be597, 0x19ef237fc11b456bec481912e370bb95, 0x71388f6384ec1f413bb64710, 0x5df63eb4f74230be958e4991, 0x562fa915201de425, 0x0, 0xa445ce534badd02fdfd8f5cc, 0x73ac7e1c6a395204156ead87, 0x3824d1eac362f57c, 0x0, 0x334bb82d22d7cc13bf79805b67a26a85, 0x12582916a2d746811cf563824ac031712, 0xce5742cee59b900d9b3befe2ee496042, 0x5d32a7afdf3f080544d2ce6e7ca33834, 0x69b771d216a328ed57ed6b4ec1cad004, 0x75fe7470f00d84132c4a40f8d601283c, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_25_50B() { let mut eddsa_sig_with_hints_serialized = array![ 0x9fb36f3a5f8c20a6bb348ee70f8502c, 0xea3e15166e0a2078e025ccdb5030110b, 0xdcda74b5f6ae8167383631a49a4e669, 0x82d3d8fdbe897cc664a2d0f158cc1e73, 0x579680c715179313f50bcc333be18d9d, 0xe593607433d771c964c7e560b9bfe2, 0x32, 0xf3, 0x99, 0x2c, 0xde, 0x64, 0x93, 0xe6, 0x71, 0xf1, 0xe1, 0x29, 0xdd, 0xca, 0x80, 0x38, 0xb0, 0xab, 0xdb, 0x77, 0xbb, 0x90, 0x35, 0xf9, 0xf8, 0xbe, 0x54, 0xbd, 0x5d, 0x68, 0xc1, 0xae, 0xff, 0x72, 0x4f, 0xf4, 0x7d, 0x29, 0x34, 0x43, 0x91, 0xdc, 0x53, 0x61, 0x66, 0xb8, 0x67, 0x1c, 0xbb, 0xf1, 0x23, 0x14, 0xb3b35fd5c7c76a8ea5b2a6ba, 0x6c0a0a53693666bd25ee428c, 0x202f90c8ef321f6f, 0x0, 0x3c08c085af81e14f87c4bc03, 0x3afe55b3061dc180489354f, 0x837540e0ecd67a3, 0x0, 0x333eda5ec9a4997625f1b53f1102021d, 0x1079bddd98bb1a199c2d8b57dcb5dc00f, 0xa9db5a3566d6d7bf3cf98b58, 0xd867c7904c4254f037ab74f5, 0x19c96b03ef8562cd, 0x0, 0xaae27af9c2298bc97cd34493, 0xfc562747747b0394b3f02019, 0x1a01d22c3d2fa4a0, 0x0, 0x111acf0e8d550078a432773811d0e09, 0x21bb5e205ac4f9c793f53dabc51b401e, 0x83c9cb27881166dc58f55d24a3cc5629, 0x13943760e9fccf769ae50fa9cbe54f4, 0xac766d9b53daefcb66a02c6d840691a3, 0x49509ad5e9d477ad6c36d0b0d515bdb4, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_26_52B() { let mut eddsa_sig_with_hints_serialized = array![ 0xe1405cbd4e9a829f72cf5a41f2193c5e, 0x1ae53709ed876037a90357a9bc9fbca6, 0xcc2c3c13dd3b0b36d4f91e81a1c3d427, 0x139b7f17e47eb06c771582242f2cd030, 0x2e187f3c66c725f2d8fec2a670dd42fc, 0x1eab1c54e83d5e1b0c70df2cfece87e, 0x34, 0xf8, 0xb2, 0x19, 0x62, 0x44, 0x7b, 0xa, 0x8f, 0x2e, 0x42, 0x79, 0xde, 0x41, 0x1b, 0xea, 0x12, 0x8e, 0xb, 0xe4, 0x4b, 0x69, 0x15, 0xe6, 0xcd, 0xa8, 0x83, 0x41, 0xa6, 0x8a, 0xd, 0x81, 0x83, 0x57, 0xdb, 0x93, 0x8e, 0xac, 0x73, 0xe0, 0xaf, 0x6d, 0x31, 0x20, 0x6b, 0x39, 0x48, 0xf8, 0xc4, 0x8a, 0x44, 0x73, 0x8, 0x14, 0xe65e7fe469389002fc7e8a57, 0xf5b85bed46a00c3b565ebe3, 0xdfb32e26ef297ed, 0x0, 0xafa8530415d22760c6d2b82a, 0x3d4cf9af9e321a9d52458d29, 0x1017dee106d78e13, 0x0, 0x204988f6a59dff4ef4bfb55d11ab1ec5, 0x1c7564759fa0994497c7b23d5195c3af, 0x67cd465864680f744b4c139f, 0x1f6118c3db728c0b671289a0, 0x526a6d0a81c6de17, 0x0, 0x7e2abbcc7e46b7f2a07873eb, 0x6d925be11b749e01fbed5766, 0x42b07313b6687cad, 0x0, 0x753cc470c1cbef106b37c0820954b69, 0x107776920c1afb3097c6af04856fcc034, 0x2949b860890c89625374cd3a9b74b1b2, 0x3e8bf981fa03c01cc7dccd738a261f28, 0x8ab1c1445f2f250fc8c354c959da80, 0x238e9c2dd40f5ec92dd14281c6e86509, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_27_54B() { let mut eddsa_sig_with_hints_serialized = array![ 0xe205910db2c633ec94a8fe163e9ca965, 0x2e4aabfeac8b4dbd9b9d76a464274ea0, 0xa27b806af44a61d382b6b8831d90bb01, 0x75a50aff49f523345d3275b7fe581369, 0xf4d419b354f3d821970fc7e9741a4e7e, 0xd736446d6fe94fb0ffd70c84514d9a1, 0x36, 0xe0, 0x72, 0x41, 0xdb, 0xd3, 0xad, 0xbe, 0x61, 0xb, 0xbe, 0x4d, 0x0, 0x5d, 0xd4, 0x67, 0x32, 0xa4, 0xc2, 0x50, 0x86, 0xec, 0xb8, 0xec, 0x29, 0xcd, 0x7b, 0xca, 0x11, 0x6e, 0x1b, 0xf9, 0xf5, 0x3b, 0xfb, 0xf3, 0xe1, 0x1f, 0xa4, 0x90, 0x18, 0xd3, 0x9f, 0xf1, 0x15, 0x4a, 0x6, 0x66, 0x8e, 0xf7, 0xdf, 0x5c, 0x67, 0x8e, 0x6a, 0x14, 0x8fd48a5f0cbc7cd551b22b8f, 0xf70280b61c3739182e9707c5, 0x1bb4d9afe2b6388a, 0x0, 0xedd3e73dfef36cf88bd9c61d, 0xaec12bf9f55127130f8749cc, 0x4c9f640f4dd1e2af, 0x0, 0x188b5300042082233b95b31db38d6faf, 0x9223932d7b504223f930056888ac19c, 0x2e970b3220987939bb229eaa, 0x47a6fa0b58ad803d3daaf244, 0x5f1c153a8b5f9869, 0x0, 0xb3795852b41dd54acd555598, 0x8d67b51c5ff50eb415b43815, 0x326cc94912a4cc3e, 0x0, 0x165d26c1c61e237b08433ed3d7ee3ca7, 0x124bbe48efb6b7c2e2caf70c2e3cb5d1c, 0xe98560f4b05a42b6abfd7d4381e6ea5c, 0x791bc3d6e37de6c41a20af9aac189a7d, 0x4c6aaaebe23953c625e6c2ce955a818c, 0x6286fc75f531a5a68b22af0e38eb4903, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_28_56B() { let mut eddsa_sig_with_hints_serialized = array![ 0x6cd49146124c9ae4dfcd13517a4ca057, 0xda1fa7ec0a33a172cb9d3f348fdc9c1f, 0x90c02885701acf55147dc8f947c9cba6, 0xfa55dea45474f4adba1d5d85e4ce1ef1, 0x2d9921cf8c29598f5f5b3ad7364be84c, 0xb66c3f2329d7e3b75873d1634ef92f4, 0x38, 0x7f, 0x31, 0x8d, 0xbd, 0x12, 0x1c, 0x8, 0xbf, 0xdd, 0xfe, 0xff, 0x4f, 0x6a, 0xff, 0x4e, 0x45, 0x79, 0x32, 0x51, 0xf8, 0xab, 0xf6, 0x58, 0x40, 0x33, 0x58, 0x23, 0x89, 0x84, 0x36, 0x0, 0x54, 0xf2, 0xa8, 0x62, 0xc5, 0xbb, 0x83, 0xed, 0x89, 0x2, 0x5d, 0x20, 0x14, 0xa7, 0xa0, 0xce, 0xe5, 0xd, 0xa3, 0xcb, 0xe, 0x76, 0xbb, 0xb6, 0xbf, 0x14, 0x221f8ae08ba5a8b36e213773, 0x3b5c2e1a0eb0f0dbbf806105, 0x4193c37bae1895cf, 0x0, 0x93b2e4cb7b4cb75620dd80ad, 0x30c7fe492e2173818988c7b, 0x13c907b836ebd26d, 0x0, 0x1892c94646453a6599670cbf4d7329cb, 0x26c90b82594af5ef94487cfcd2106d53, 0xd9ddc94af516fb8449f061a8, 0xc0fb572fdbe70b1d59d80007, 0x2d8b0f14c92d1cdd, 0x0, 0xcddf1ba9914ce12c8cc36a68, 0x79e032c4c246b23cd4943fa7, 0x33443ad08a8b45d4, 0x0, 0x2e324828471c960e7c93d1f2920a0f3b, 0x10d9e8be6f56de45c5a85896623d83ef0, 0x7d5783030cd8e4017806134ff0ebf737, 0x3e70836352841b985940286dd86ee97e, 0xe730705124f314044c5f7421d9b16011, 0x90ad7fad39fa85be8e39c6bed340cbb, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_29_58B() { let mut eddsa_sig_with_hints_serialized = array![ 0xa5cd35ea3685ae2b5e62991409da7e0f, 0x123634832c6f1d346b417e9c6ad13b48, 0xe074ecb682f8165568625d6af241bdef, 0x78659c9ae9268f2431c203d23018a7d5, 0x9fbcecf9240dad1672fab8cd680d90ec, 0x4a71fa395536426f6826566515365fa, 0x3a, 0x8d, 0xdc, 0xd6, 0x30, 0x43, 0xf5, 0x5e, 0xc3, 0xbf, 0xc8, 0x3d, 0xce, 0xae, 0x69, 0xd8, 0xf8, 0xb3, 0x2f, 0x4c, 0xdb, 0x6e, 0x2a, 0xeb, 0xd9, 0x4b, 0x43, 0x14, 0xf8, 0xfe, 0x72, 0x87, 0xdc, 0xb6, 0x27, 0x32, 0xc9, 0x5, 0x2e, 0x75, 0x57, 0xfe, 0x63, 0x53, 0x43, 0x38, 0xef, 0xb5, 0xb6, 0x25, 0x4c, 0x5d, 0x41, 0xd2, 0x69, 0xc, 0xf5, 0x14, 0x4f, 0x14, 0x9b1c19208091298d52b36ff8, 0x86a37c43e6283f0de97ec43c, 0x4a72aab104cfe59c, 0x0, 0xdea3ba3657ed19626b8a6032, 0x41ae598bba09f743633bf037, 0x1dbd4c50f393a85f, 0x0, 0x1bc74f1028aeb6f6970483ae9cc95d63, 0x2025f40277c842f6a70792a848c26cb4, 0x50994f1284796db6fad98849, 0x30278b2241f9ac8d9d9adcfb, 0x6ae23674d14c9829, 0x0, 0x4ee6e2f223e8d6739f5f5880, 0x236022ff45332e17e050ef89, 0x4e62795b32055a40, 0x0, 0x3e5d60e5fc3b1f7d57a9c5f4a661cef3, 0x134cf865b10157749c76a5699e5a54c9f, 0xf044d65abce84b8879ae487d70dbcb0c, 0x18b94c37ce13d3ab114b84324e8fd5e7, 0xe2358f86e3017a6600ec864c9b562c80, 0x4252d8aff604e746087ad8b8c79e7bd5, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_30_60B() { let mut eddsa_sig_with_hints_serialized = array![ 0x9b7290b34092910ceb3f4d5440e58d78, 0x135f2ec69465bb63e97ad644be987e4, 0x409078c3a7fa07258520e79127e0fdd2, 0x42154902407f55ac13f321636486efd9, 0x88515dbc1f5095d4b0cd90695cd067dd, 0xf69c27fa40306ee8b09f61bdc84bbbf, 0x3c, 0x3a, 0x53, 0x59, 0x4f, 0x3f, 0xba, 0x3, 0x2, 0x93, 0x18, 0xf5, 0x12, 0xb0, 0x84, 0xa0, 0x71, 0xeb, 0xd6, 0xb, 0xae, 0xc7, 0xf5, 0x5b, 0x2, 0x8d, 0xc7, 0x3b, 0xfc, 0x9c, 0x74, 0xe0, 0xca, 0x49, 0x6b, 0xf8, 0x19, 0xdd, 0x92, 0xab, 0x61, 0xcd, 0x8b, 0x74, 0xbe, 0x3c, 0xd, 0x6d, 0xcd, 0x12, 0x8e, 0xfc, 0x5e, 0xd3, 0x34, 0x2c, 0xba, 0x12, 0x4f, 0x72, 0x6c, 0x14, 0x767582504fcdf5c532ae821f, 0x369283997ece24f13874c7f3, 0x2c98a25fbbac87a0, 0x0, 0xb605dd1a7fd4bc65bfa1cc37, 0xa8f7771da5567342f07d981f, 0x70c2347f0c6cad9d, 0x0, 0x2374543478d593b0338a55f4bfc170d1, 0x1091fb47f6277c497014342fd6302db4f, 0x75607a81fc9dfdbce0a61099, 0xaaf1cdc31dac2c136d9f0796, 0x320d0d002388dca2, 0x0, 0xd52681f4406522dfe89abd4b, 0x16c7f383c6733c5126d3ef23, 0x705ed4abf42a6a8b, 0x0, 0x28b688ea47e475fbe26e2054b2f25ec5, 0x12c0f45dc3f535dd3bda5ee32c863aa05, 0x3c11a7163b0a795314eedc7f9f209cf2, 0x38b48bcaf3ce9863ef2021828e2f49c3, 0x25b049f36336d365154fee2d92f7209a, 0x7afa60ee9713dfea9945e105904bb927, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_eddsa_31_62B() { let mut eddsa_sig_with_hints_serialized = array![ 0xe2c6f49b0327d5e1b001737df5ea1005, 0xb15103103c20f3345476b4613a0a3092, 0xec38dd1c63f1903a5b70c76a43d8e506, 0xad60d5e7a4be5efaf2b9a97897a43f1a, 0xca1a7642373220a48bfafa42ff26dda7, 0xb435db4aa2df73ff6be1bc20d940469, 0x3e, 0x54, 0xe0, 0xca, 0xa8, 0xe6, 0x39, 0x19, 0xca, 0x61, 0x4b, 0x2b, 0xfd, 0x30, 0x8c, 0xcf, 0xe5, 0xc, 0x9e, 0xa8, 0x88, 0xe1, 0xee, 0x44, 0x46, 0xd6, 0x82, 0xcb, 0x50, 0x34, 0x62, 0x7f, 0x97, 0xb0, 0x53, 0x92, 0xc0, 0x4e, 0x83, 0x55, 0x56, 0xc3, 0x1c, 0x52, 0x81, 0x6a, 0x48, 0xe4, 0xfb, 0x19, 0x66, 0x93, 0x20, 0x6b, 0x8a, 0xfb, 0x44, 0x8, 0x66, 0x2b, 0x3c, 0xb5, 0x75, 0x14, 0x962624a2b58a3398a4cb5f20, 0xa2f7b76e2e5211d70478e1c4, 0x34f1dbb6c3a2820f, 0x0, 0xb1959060b4fbc9fdbf1fbd3d, 0xb65e79dd2152fee4e722175b, 0x1e30caa19014bf94, 0x0, 0x566024cc1d8444077611d2dbc0124c0, 0x838993ad8b06741eb5a8c34b36a8ab9, 0xa8daf3da5d467d1f8f78fa2e, 0xda73157212cd2884342c6fe5, 0x2027ede735f65b7d, 0x0, 0x66c3c9bb08d3e040fcfc08b1, 0x2653aa90486e889f8d9527d9, 0x5fd1337521e862db, 0x0, 0x5dca01e9cbf9f2873a07d909c4bc1d9, 0x1703982ac551c4c9dbe2856f29d22033, 0xbed3d85b70b069b3447e8327aaf8695f, 0x408a942fe8f45cddd22487f5180e39a3, 0x8c9bf6a015c76f19883037c34ca77b45, 0x566af0d91aa86827627d0323bd33fdb9, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } #[test] fn test_eddsa_32_64B() { let mut eddsa_sig_with_hints_serialized = array![ 0x51e367ada5fda575b66d4bf876a03ff7, 0xccc6e9870301ca0968d1ad297f8e1ea4, 0xa1ea48dde7ba2174837f2011a7d2b957, 0x3a8f457be1fe065830f1a0709a1aab8e, 0x770b006f49e8c90a3e4d83d102b36409, 0x66aee0e84c7fb32e657a9f8413b08f0, 0x40, 0x4b, 0xaf, 0xda, 0xc9, 0x9, 0x9d, 0x40, 0x57, 0xed, 0x6d, 0xd0, 0x8b, 0xca, 0xee, 0x87, 0x56, 0xe9, 0xa4, 0xf, 0x2c, 0xb9, 0x59, 0x80, 0x20, 0xeb, 0x95, 0x1, 0x95, 0x28, 0x40, 0x9b, 0xbe, 0xa3, 0x8b, 0x38, 0x4a, 0x59, 0xf1, 0x19, 0xf5, 0x72, 0x97, 0xbf, 0xb2, 0xfa, 0x14, 0x2f, 0xc7, 0xbb, 0x1d, 0x90, 0xdb, 0xdd, 0xde, 0x77, 0x2b, 0xcd, 0xe4, 0x8c, 0x56, 0x70, 0xd5, 0xfa, 0x13, 0x14, 0xd161fc726de012c0e0743e7, 0x42acee4e16921c0867f97342, 0x3df8d27df4355025, 0x0, 0x417af9c7a0442b578a1bc6fd, 0x8b47ac563f259260e2b0f80, 0x6c6ff02c28f84b7c, 0x0, 0xa02b77f8fd8b7c1eb63155c5ea920a5, 0x106d7cd46cb0e0c81f3d995c3bc47503d, 0xb4630746992c8a357d6df9eb, 0x5fdba5230f13b83f1c2abc8e, 0x23b4e6d66fd0dd34, 0x0, 0x7670dc68e4c7436863f0f4e, 0xf570573dc0f1cc0cdc47bf49, 0x5e0b72bc8a7978af, 0x0, 0x211da8e595abb9413372df7309b63acf, 0x1085d544d1097dd536984587f626dac87, 0xf72722a04d4e780bc03c03781212ceac, 0x7d057bb78a4c6624f1754cb4366b1757, 0xdb32bb362e6f4e4ab652852ea150f205, 0x745397cfb61e599ed42508c8e6169142, ] .span(); let public_key_y = Serde::::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let eddsa_with_hints = Serde::< EdDSASignatureWithHint, >::deserialize(ref eddsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_eddsa_signature(eddsa_with_hints, public_key_y); assert!(is_valid); } ================================================ FILE: src/src/tests/autogenerated/msm_tests.cairo ================================================ use garaga::core::circuit::u288IntoCircuitInputValue; use garaga::definitions::{G1Point, u384}; use garaga::ec_ops::msm_g1; #[test] #[ignore] fn test_msm_BN254_1P() { let mut data = array![ 0x1, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x1, 0xb4862b21fb97d43588561712e8e5216a, 0x967d0cae6f4590b9a164106cf6a659e, 0x0, 0xa9f0001b3fc543c76e78dbe5, 0x59d3efe5fc893f110337f203, 0x2a3c4edaf4eb5933, 0x0, 0x47c7d40af526b19cd3c8e9d6, 0x77e086d9ab1747415c8a345, 0x2ecf62cd2d14d49c, 0x0, 0x10000000000000000358f1af3ace11fdc, 0x100000000000000004ac9542b22967d33, 0x100000000000000000cf05f964742cc6d, 0x1000000000000000081d342cffb91cba7, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xa9f0001b3fc543c76e78dbe5, limb1: 0x59d3efe5fc893f110337f203, limb2: 0x2a3c4edaf4eb5933, limb3: 0x0, }, y: u384 { limb0: 0x47c7d40af526b19cd3c8e9d6, limb1: 0x77e086d9ab1747415c8a345, limb2: 0x2ecf62cd2d14d49c, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_2P() { let mut data = array![ 0x2, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x2, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x1521f387af19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x0, 0x3e478e7543d16c51c9284bef, 0xc686c1c872c6e2c5037128b3, 0x199c5e1c0cdf53c8, 0x0, 0xf388e0c9512c46adb6327d02, 0xfeecfb56cfd9a1509392beb3, 0x2ccad398d3b28843, 0x0, 0x9be5263ddc8a3746, 0x3b9c1e56ffcfcc82, 0x1000000000000000041c754da808c6d02, 0x277449c3e218531f, 0x5211712cf983c9bb37a437a3, 0x3c9da9e18a4323d2ed3b9bcb, 0x135de21f5341b7ec, 0x0, 0x3c22df03e388c6cea0664c2b, 0xc1036691dedbab22e63b1e2a, 0x104e399500d777b8, 0x0, 0x100000000000000005fcd1b724f1296a6, 0x1000000000000000016e3236cbd22722f, 0x4dac40f4f32b51f2, 0x1000000000000000000417aa85f133ffd, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x9234d7617541ef6bd6a55e9e, limb1: 0x7a1353bb00de9de1d818c849, limb2: 0x21e43e4fdf41dbf4, limb3: 0x0, }, y: u384 { limb0: 0x30dd41ab3aae480eb7924f99, limb1: 0xa94c0b54f99635a912b59f0f, limb2: 0x187498a467804f5b, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_3P() { let mut data = array![ 0x3, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xc7ab5834609a54b8993ffd79, 0xe81cd490528b814ca632aace, 0x2d9ff53d3009e6f7, 0x0, 0x3, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x8d723104f77383c13458a748e9bb17bc, 0x215ddba6dd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x5f82a8f03983ca8ea7e9d498c778ea6, 0x0, 0xeb6c64e1541feb4cd5958beb, 0x69953b682ac9e3bef74198ea, 0xf357da3c551bd01, 0x0, 0x8cf96097b6703380dee48cfa, 0xaf4c872e1b6551bf875c946f, 0x30549c20b1c1e0ff, 0x0, 0x100000000000000005fcd1b724f1296a6, 0x1000000000000000016e3236cbd22722f, 0x4dac40f4f32b51f2, 0x1000000000000000000417aa85f133ffd, 0x71c5aa9b358faf4569aead5, 0x5b16db715ec2839da79801db, 0x33ab1528e0d2ba4, 0x0, 0x1d4cf315732c8bfaf74e675a, 0x81e4a39e6f6fca6f89cc94f0, 0x2939221afe7a9318, 0x0, 0x100000000000000001ab0231e3f1af32b, 0x1f1689eda0b7325, 0x8211c744ee497946, 0x100000000000000001401005296ba5335, 0x9f30216b591e9f34501cf268, 0x7aebbd8d9c7bedb729aab01f, 0x16413acc47520c69, 0x0, 0x596a902a02766a7777a12a86, 0xcd89979d5d539a6d7dfb9208, 0x12c9d036ab478f21, 0x0, 0x257275fdb7e6a5fd, 0x437a0a16546be43f, 0x100000000000000001e20dc33694e8500, 0x4c004b142b3cda1a, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xa505aa539534e1ed3825e1d3, limb1: 0xd3d6e50ccbd336be810ae134, limb2: 0x2b8806194c015dab, limb3: 0x0, }, y: u384 { limb0: 0xe3066db5d6cc9577162aa35c, limb1: 0x3ab20c13b3f5fdea9441aaa8, limb2: 0xc21ee843d06bdd4, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_4P() { let mut data = array![ 0x4, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xc7ab5834609a54b8993ffd79, 0xe81cd490528b814ca632aace, 0x2d9ff53d3009e6f7, 0x0, 0x163df40cafbf585ca5b2ab44, 0xb4752e4666c88dbbe23783a0, 0x1a801462ac9cb657, 0x0, 0xac9b557d7ca8625d957263c6, 0xdc6f75fa8339a78b998ae54a, 0x28683293b6494d9f, 0x0, 0x4, 0x8d723104f77383c13458a748e9bb17bc, 0x215ddba6dd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x5f82a8f03983ca8ea7e9d498c778ea6, 0xb5d32b1666194cb1d71037d1b83e90ec, 0x28045af9ab0c1681c8f8e3d0d3290a4c, 0xd3fbf47a7e5b1e7f9ca5499d004ae545, 0x2ebce25e3e70f16a55485822de1b372a, 0x0, 0x6cb501b0f2f9a414f1369408, 0x6ca7b1f397dfefc2369e7f77, 0x135eb18352681cd0, 0x0, 0xbddf987b8ac91c298eae5fb6, 0x9c1baec61cca6ff8093200df, 0x1db47142bcb9084e, 0x0, 0x100000000000000001ab0231e3f1af32b, 0x1f1689eda0b7325, 0x8211c744ee497946, 0x100000000000000001401005296ba5335, 0x975b5f57e34be656906b1316, 0x4365ddb9eb3fb542f4a81fa5, 0x1e4b71ab4bb74438, 0x0, 0x661840b85c4650ab80d6abfc, 0x6bedd43f4682513b3f26e3b9, 0x1bfbc09bedc6e6a1, 0x0, 0x257275fdb7e6a5fd, 0x437a0a16546be43f, 0x100000000000000001e20dc33694e8500, 0x4c004b142b3cda1a, 0x15e4e2a08ec22ffe7c9bb956, 0x50cedfd39b0f587f62445c96, 0xbfefc101da6032d, 0x0, 0x626cafb2e14919812dc11374, 0xd8702613e26c1c5acbb0502a, 0xac9c3b014f6663, 0x0, 0x1000000000000000001067d48d1582ff7, 0x35ded9055ac1fce, 0x100000000000000009f949519947d21c6, 0x1000000000000000008e3b423119eedaf, 0xfa187fa0605efdbcf49ce5e0, 0x9bba09b74197b6f6a0c7d548, 0x15f5043298d09f8f, 0x0, 0x69bb1bf803d830390621ff4b, 0xeab9213022b9471b2f5ffb27, 0x20e0ff3bce0d13ab, 0x0, 0x6d0d75af97fefa50, 0x1000000000000000021d60bf2c3658c74, 0x1000000000000000034f51fecbdff851a, 0x1000000000000000002c54143b4f61e7f, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xda530556c75d2e27b35e716b, limb1: 0xe263c10943a7c230d41bb940, limb2: 0x1d051a29c6a2eafe, limb3: 0x0, }, y: u384 { limb0: 0x679ed4b58350eefe8c88ae2a, limb1: 0x46b4e4ba8a6a9374a0120664, limb2: 0x121c2c711b7c7f40, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_10P() { let mut data = array![ 0xa, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xc7ab5834609a54b8993ffd79, 0xe81cd490528b814ca632aace, 0x2d9ff53d3009e6f7, 0x0, 0x163df40cafbf585ca5b2ab44, 0xb4752e4666c88dbbe23783a0, 0x1a801462ac9cb657, 0x0, 0xac9b557d7ca8625d957263c6, 0xdc6f75fa8339a78b998ae54a, 0x28683293b6494d9f, 0x0, 0x5c4f5dca0c973b7f70bfff9, 0x188c2afab11eef5d48ecda3c, 0xc2fed35d36c49f1, 0x0, 0x9d7244ea10697ca42e2e066b, 0xfe18a519c7d68770dc48dbf9, 0x149bb528db998529, 0x0, 0xffc057151b06c496e6fdd440, 0x5a01bae0c7441f08c7af1cf9, 0x274e0e02529e6d26, 0x0, 0x65ceb8977413bc9798681ecb, 0x19ffb287b45234f0c28fd1a7, 0x28dbbd2f9267be76, 0x0, 0xcfcdbfdb2056ff1a64bf1d47, 0xf26fe2dae9f693d9b4aab2e6, 0x12d66ad4802d841e, 0x0, 0xe6e34ebfa2e18dce86cadbdc, 0x7ce096238b3d4b1b8fba6a55, 0x2e0a660b1549800c, 0x0, 0xd2dd03b29d58d045656ecf33, 0xeddac3cf7a123aae2180739b, 0x215bec6e0a03c924, 0x0, 0xe5201e51828eb11589d8619f, 0xa6563c760aa3a2c9d15af235, 0x7ed0c9b2e7811fb, 0x0, 0xc33ac21c67b06a9994457b4c, 0xa9aa5573bf7a92aab85366eb, 0x1a407281e1d92e91, 0x0, 0x5a306649d971b115d71a78b1, 0xa70687a9b5132e26b2cfbb37, 0x2031920af5d6c9db, 0x0, 0x58a3cea1103f16402eb74c08, 0xdfefcd91df2f4295ec21e03a, 0x1150bcc09ac40007, 0x0, 0x57ed7d356f91abcef751889f, 0x5c668cded3599c9af5a7e5fa, 0x2ccf74197cb9bc13, 0x0, 0xa, 0xe005b86051ef1922fe43c49e149818d1, 0x1f507980eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x154bc8ce8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x0, 0x61e02fbc1bed21b7bcf46f4c, 0xa6effae60cef67c2b63c39bb, 0x2ab9fc18a6615fb, 0x0, 0x4b3724a1eaa0e523a8201b45, 0x62b04965c68922390462b7a3, 0x2198f058f64e1c43, 0x0, 0x100000000000000003ff332cfc13ea1b7, 0x1000000000000000017a384910097a0a6, 0x100000000000000008a1753b1b37a6668, 0xbf55a306145dc38, 0x698fa5385db63a1c306f31a6, 0xbf42f2af27151fb1080c4e1b, 0x1fb3b32ec12c4f, 0x0, 0xce605cbc0a47803533df71b7, 0x5e11c8521b0dd8cf8f000ffe, 0x7cb22177b9f6c9f, 0x0, 0x7661ed95c25cdb91, 0x10b644cef3d30c35, 0x100000000000000006f577c0b4a402ddc, 0x100000000000000001a7d3ea294939351, 0xa645e8eb1794e374ba58a593, 0x1efd47471ced39aacc2c4663, 0x2728f58a400a469f, 0x0, 0x9bd43dd33e0aab21c26f95c5, 0xd0e362800d54bbfbc6c4fe83, 0x2f76d907a29973cd, 0x0, 0x3d2887de3517544e, 0x7509da3e05adfa0a, 0x1000000000000000008604e989fdb09b5, 0x100000000000000002c850eaa7c78bdc0, 0x5fe0d34aad545b3c4ef06b35, 0x5bff1849e6dc24399ac732fd, 0x1e6185c8691064be, 0x0, 0xea77a9d5f1cd74b987667e33, 0xdc6d8e6d769c20731a299dbc, 0x1198dca5bf14851b, 0x0, 0x10000000000000000026898e43eca56c7, 0x30387575e4bac6c6, 0x20776c3ca242b7de, 0x100000000000000007d486e28cf4b0e10, 0x4d7402b67e248a1511a0841e, 0x9c7a8605f376bd75aeb721e4, 0x16a48728caed67a6, 0x0, 0x3269769473a96aba2d5b866a, 0x9fa613baafe4ff9c9827622, 0x83acb5fbc7fad50, 0x0, 0x1000000000000000025897c91d7b8d1f1, 0x3fd9c240adbcce3, 0x100000000000000009a89d61b8c513677, 0x100000000000000001d92935462ea59df, 0x8373942d7372f9b1f8b95c4c, 0x3d9f31bb677a013ba4cdd49f, 0x2a30441dde9012f4, 0x0, 0x7d526a9f384aa7db749876de, 0x9c9092ab98018ed02c205430, 0xcdd28eac120a42f, 0x0, 0x100000000000000002fc911da020d2f55, 0x11da5e7b097ee9cd, 0x10000000000000000ad5176da721b78b7, 0x100000000000000004102d2a01b7fbf5f, 0x7d8d69262635c81c7aef2d75, 0xa11a1dba95b5b955c00180c3, 0x76e4b2ad1aa3378, 0x0, 0xb71796d33a53c64cf156350c, 0x2a66cebb6ad6a9131e268eb8, 0xb500720ebb9a86d, 0x0, 0x35d8a8c78484d0c2, 0x37b379080cbcb6f7, 0x6b7a53f07ab793f1, 0x449bac4fffe801bc, 0x71c6ac67d5825359f2b87c45, 0xd7353e8c0a5d50546cf6c671, 0x2ae62bb2dabe475f, 0x0, 0xf0766ee822be9548105cadfb, 0x3a54b0466d91cbcacb90e0a, 0x5e9d7884973f330, 0x0, 0x10b1947ddf58a676, 0x103c836271b652be, 0x100000000000000007e3b371d8da612a2, 0x10000000000000000afdc716fd42dcebf, 0xb0bf2c61b4f4cbdead74273e, 0xb96526c6288d150336e0ee96, 0x12948db5514c09a7, 0x0, 0xf3d8437a14c19236c52edcfc, 0xffd55886b031537735e02f78, 0x2ce46f7b1c749b99, 0x0, 0x62e2e02294e2c662, 0xb7b29a6b2600fb8d, 0x12dfa3a68a5aa4b8, 0x15945e750a0443c5, 0x7f83b4b51d00fc80bb831daf, 0x25d239976a348f767993ced5, 0x2b84658d4f6cb5c8, 0x0, 0xfff31f69291319d397b31124, 0x156bf2f02ea3e4621278874b, 0x103cc7bade9316ae, 0x0, 0x1ac00f1b74998794, 0x1000000000000000024c1b4e8a2305293, 0x59d3cc6f01477796, 0xc9c2a2cd82f7e2d, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x7f5a9b9409f2cc39825a02c, limb1: 0xcae0e79fbccb0daf22e3d147, limb2: 0xe6a2d797f40f61, limb3: 0x0, }, y: u384 { limb0: 0x2a28940c5db0b16b11bcb83b, limb1: 0x909e67a632b9f3e09db0636b, limb2: 0x18643fa5fa438363, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_11P() { let mut data = array![ 0xb, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xc7ab5834609a54b8993ffd79, 0xe81cd490528b814ca632aace, 0x2d9ff53d3009e6f7, 0x0, 0x163df40cafbf585ca5b2ab44, 0xb4752e4666c88dbbe23783a0, 0x1a801462ac9cb657, 0x0, 0xac9b557d7ca8625d957263c6, 0xdc6f75fa8339a78b998ae54a, 0x28683293b6494d9f, 0x0, 0x5c4f5dca0c973b7f70bfff9, 0x188c2afab11eef5d48ecda3c, 0xc2fed35d36c49f1, 0x0, 0x9d7244ea10697ca42e2e066b, 0xfe18a519c7d68770dc48dbf9, 0x149bb528db998529, 0x0, 0xffc057151b06c496e6fdd440, 0x5a01bae0c7441f08c7af1cf9, 0x274e0e02529e6d26, 0x0, 0x65ceb8977413bc9798681ecb, 0x19ffb287b45234f0c28fd1a7, 0x28dbbd2f9267be76, 0x0, 0xcfcdbfdb2056ff1a64bf1d47, 0xf26fe2dae9f693d9b4aab2e6, 0x12d66ad4802d841e, 0x0, 0xe6e34ebfa2e18dce86cadbdc, 0x7ce096238b3d4b1b8fba6a55, 0x2e0a660b1549800c, 0x0, 0xd2dd03b29d58d045656ecf33, 0xeddac3cf7a123aae2180739b, 0x215bec6e0a03c924, 0x0, 0xe5201e51828eb11589d8619f, 0xa6563c760aa3a2c9d15af235, 0x7ed0c9b2e7811fb, 0x0, 0xc33ac21c67b06a9994457b4c, 0xa9aa5573bf7a92aab85366eb, 0x1a407281e1d92e91, 0x0, 0x5a306649d971b115d71a78b1, 0xa70687a9b5132e26b2cfbb37, 0x2031920af5d6c9db, 0x0, 0x58a3cea1103f16402eb74c08, 0xdfefcd91df2f4295ec21e03a, 0x1150bcc09ac40007, 0x0, 0x57ed7d356f91abcef751889f, 0x5c668cded3599c9af5a7e5fa, 0x2ccf74197cb9bc13, 0x0, 0x529118e291927516dfbcba2d, 0x440af959472c61e99aac7977, 0x218bbc79509b59ce, 0x0, 0x226044f7331ccf82af7afb39, 0xc1953da25a89d084dcfaea76, 0x1042fdc36b43dac3, 0x0, 0xb, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x154bc8ce8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x1158af9fbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0x1b45bb86552116dd2ba4b180cb69ca38, 0x0, 0xf59b76239fad9eb74730cd7, 0xa1143b2f09cd01fbb559c486, 0x2f8d04122e8fbde7, 0x0, 0xa4777776f13805422915c296, 0x1c2749af3d7f4b652217ddae, 0xd4e2c28702c3059, 0x0, 0x7661ed95c25cdb91, 0x10b644cef3d30c35, 0x100000000000000006f577c0b4a402ddc, 0x100000000000000001a7d3ea294939351, 0x38ffcd70be2dbbae82096a26, 0xcfeb56ca9f8a8a2384543b8e, 0x73059fa2677d1e5, 0x0, 0xa84366869190b93d9d917bf, 0xc455446eda9f79d73aa0cbad, 0x2641bc3008f8cc9e, 0x0, 0x3d2887de3517544e, 0x7509da3e05adfa0a, 0x1000000000000000008604e989fdb09b5, 0x100000000000000002c850eaa7c78bdc0, 0xb4ec8b46be22584530b7b3e, 0xb6fd065dbd73e3d763c2e67c, 0x2e111c1d191de144, 0x0, 0x81464c2ae0122148a3ddad93, 0x44c76e3df069bedffabb2d13, 0x1bf97d9ca1c2f369, 0x0, 0x10000000000000000026898e43eca56c7, 0x30387575e4bac6c6, 0x20776c3ca242b7de, 0x100000000000000007d486e28cf4b0e10, 0x64b2119b459e63324fbafc05, 0x66502154bd1382ce47b7681e, 0x2ddfe6039dcfde7, 0x0, 0x529aa77c8e7a1d4ca0e64359, 0x2e01879e99328b28e513ff1c, 0x44ef12a2f42ec77, 0x0, 0x1000000000000000025897c91d7b8d1f1, 0x3fd9c240adbcce3, 0x100000000000000009a89d61b8c513677, 0x100000000000000001d92935462ea59df, 0x8d414937f9c4a302b137537b, 0xa386777f18abfefe85c31058, 0x257b5a32a23f40a3, 0x0, 0x3e95a9ff945e0553c85cfe2c, 0x4c5e5834c653623c13fec9b6, 0x1664b40825e1a905, 0x0, 0x100000000000000002fc911da020d2f55, 0x11da5e7b097ee9cd, 0x10000000000000000ad5176da721b78b7, 0x100000000000000004102d2a01b7fbf5f, 0xa66fcc2f529276b780499985, 0xf69c7da32d819f1f4f193fc1, 0x1805e698d92c3ac0, 0x0, 0xb9abf7ad6d28c58e2cc31b94, 0xf074390b2247dfaf60121eda, 0x27b2e899ed29cf1a, 0x0, 0x35d8a8c78484d0c2, 0x37b379080cbcb6f7, 0x6b7a53f07ab793f1, 0x449bac4fffe801bc, 0x5a1cd56b595531e6a3d814bf, 0x525e7a8c84a1f276259877a8, 0x7d7c34039bc644d, 0x0, 0x97125887d88507b5fe4333b9, 0xdf81a585fe7f350ed9d80836, 0x197c0dbf47481ded, 0x0, 0x10b1947ddf58a676, 0x103c836271b652be, 0x100000000000000007e3b371d8da612a2, 0x10000000000000000afdc716fd42dcebf, 0xca590b79acc3248cf7071af2, 0xf8f64dd38ddb672cfe35764, 0xa4a93bb49cda78e, 0x0, 0x7fca5043edf56dfce89121b9, 0x5a1191ede225c26c4e2fdd0e, 0x1b28478576081b5e, 0x0, 0x62e2e02294e2c662, 0xb7b29a6b2600fb8d, 0x12dfa3a68a5aa4b8, 0x15945e750a0443c5, 0x29281279f0958f532340b1e, 0x9c3f90c5b44db2da51242b88, 0x18c51e06011b8dbf, 0x0, 0x1fce97d7fe0ad6091ef99256, 0x37115682a1c2995a8f46348, 0x1fe22395832d2e61, 0x0, 0x1ac00f1b74998794, 0x1000000000000000024c1b4e8a2305293, 0x59d3cc6f01477796, 0xc9c2a2cd82f7e2d, 0x3bb0f32e0eb9448943980b5c, 0xaf7fdc854146e31d92761fa8, 0x247b7d3680ef0e4b, 0x0, 0xb46343f09e9d87fd5b9796cd, 0xd0a6f8103729c2dc3c47dbe9, 0x2eaaab3d9d415e13, 0x0, 0x1000000000000000057e1f3bedd0842d4, 0x10000000000000000255df8d996acfae5, 0x100000000000000000318c2486aecb245, 0x1000000000000000023ae98fa95aa07b8, 0x4b9261005811ccafc4725902, 0x689c7c5528fbcab2ffdd0e45, 0xee7f574a2b0c0fe, 0x0, 0x98e15c5c68cffe74a22c43c7, 0x77bc1a28c4ad8e05bfa5a214, 0xb4a65415b0eba66, 0x0, 0x1000000000000000059cfa117d9318779, 0x100000000000000008ef4027bb5693ee0, 0x3ae8a87244a109a4, 0x558c79eb7e83bb58, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x8f1d04d9dacdeb4b06745aae, limb1: 0x5c68471b1c99a97baed7f423, limb2: 0x1e8ed25080c73efd, limb3: 0x0, }, y: u384 { limb0: 0xc479efb2cb1c33352e438dbe, limb1: 0x1f9fcbf3fb537094c9816470, limb2: 0x2e15234a5a95acac, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_12P() { let mut data = array![ 0xc, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x236ca9312dad3661a37f2d6f, 0x98424c01caad7592315715d1, 0x795b9fd941b23c4, 0x0, 0xc7ab5834609a54b8993ffd79, 0xe81cd490528b814ca632aace, 0x2d9ff53d3009e6f7, 0x0, 0x163df40cafbf585ca5b2ab44, 0xb4752e4666c88dbbe23783a0, 0x1a801462ac9cb657, 0x0, 0xac9b557d7ca8625d957263c6, 0xdc6f75fa8339a78b998ae54a, 0x28683293b6494d9f, 0x0, 0x5c4f5dca0c973b7f70bfff9, 0x188c2afab11eef5d48ecda3c, 0xc2fed35d36c49f1, 0x0, 0x9d7244ea10697ca42e2e066b, 0xfe18a519c7d68770dc48dbf9, 0x149bb528db998529, 0x0, 0xffc057151b06c496e6fdd440, 0x5a01bae0c7441f08c7af1cf9, 0x274e0e02529e6d26, 0x0, 0x65ceb8977413bc9798681ecb, 0x19ffb287b45234f0c28fd1a7, 0x28dbbd2f9267be76, 0x0, 0xcfcdbfdb2056ff1a64bf1d47, 0xf26fe2dae9f693d9b4aab2e6, 0x12d66ad4802d841e, 0x0, 0xe6e34ebfa2e18dce86cadbdc, 0x7ce096238b3d4b1b8fba6a55, 0x2e0a660b1549800c, 0x0, 0xd2dd03b29d58d045656ecf33, 0xeddac3cf7a123aae2180739b, 0x215bec6e0a03c924, 0x0, 0xe5201e51828eb11589d8619f, 0xa6563c760aa3a2c9d15af235, 0x7ed0c9b2e7811fb, 0x0, 0xc33ac21c67b06a9994457b4c, 0xa9aa5573bf7a92aab85366eb, 0x1a407281e1d92e91, 0x0, 0x5a306649d971b115d71a78b1, 0xa70687a9b5132e26b2cfbb37, 0x2031920af5d6c9db, 0x0, 0x58a3cea1103f16402eb74c08, 0xdfefcd91df2f4295ec21e03a, 0x1150bcc09ac40007, 0x0, 0x57ed7d356f91abcef751889f, 0x5c668cded3599c9af5a7e5fa, 0x2ccf74197cb9bc13, 0x0, 0x529118e291927516dfbcba2d, 0x440af959472c61e99aac7977, 0x218bbc79509b59ce, 0x0, 0x226044f7331ccf82af7afb39, 0xc1953da25a89d084dcfaea76, 0x1042fdc36b43dac3, 0x0, 0xf1581f4d2c98dddd1045823a, 0x4c70cf5d1fe8d72e2b0eda8, 0x2dd6cf0e5b99415d, 0x0, 0xc3ebcba51d8891914acc5129, 0xa68f2b05936baf6578514dbf, 0xc4404c6b9b7453d, 0x0, 0xc, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x1158af9fbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0x1b45bb86552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0xe0062d1b29a8b06daf66c5f2577bffa, 0xa25b59fd92e8e269d12ecbc40b9475b1, 0x2689f61688c132adefbfc19ee8f6cf32, 0x0, 0xa35f081ddc3964fef11b87ba, 0x7926593494405c5ed2a7c203, 0xb1fe4cb2b23209a, 0x0, 0x1c0a838ac08fb4060688ee71, 0xfce2bda26b33f861d57cd974, 0x1ac64db61ee9a873, 0x0, 0x3d2887de3517544e, 0x7509da3e05adfa0a, 0x1000000000000000008604e989fdb09b5, 0x100000000000000002c850eaa7c78bdc0, 0xa74372df079d8431e9b18880, 0x6cd132648c2b9586f34ba4e5, 0x17c5e79c26faf814, 0x0, 0x4e00fca0765a5dc39716592c, 0x62608fda1d9eb8ac692327ab, 0x2efd2837ff622761, 0x0, 0x10000000000000000026898e43eca56c7, 0x30387575e4bac6c6, 0x20776c3ca242b7de, 0x100000000000000007d486e28cf4b0e10, 0x7948eabf056257f90152cce1, 0xfbefb6402b0f561fc2895f89, 0x7f3f0f1b174e884, 0x0, 0x3c76805faa60392fe4b110d3, 0xba4b2232318a58138b8716b0, 0x31586d69a9e9d5f, 0x0, 0x1000000000000000025897c91d7b8d1f1, 0x3fd9c240adbcce3, 0x100000000000000009a89d61b8c513677, 0x100000000000000001d92935462ea59df, 0x68e1b7bda4cc53d96d5d21fc, 0x224cbbd937d29f5c8f33af33, 0x1eecbf09aea2ba62, 0x0, 0x9ba28499df4dc86dba4834c9, 0x593878cb3634fbf4ad666d2f, 0x8d61bffa7ed1cf4, 0x0, 0x100000000000000002fc911da020d2f55, 0x11da5e7b097ee9cd, 0x10000000000000000ad5176da721b78b7, 0x100000000000000004102d2a01b7fbf5f, 0x6404129b95705ec3758c3c32, 0xfee2f803c30b9c60ec9058c9, 0x1c4acdc80de3ff15, 0x0, 0xeef9c5c2c7dd04d9ef28627, 0x85f67ca8fb3693eb3d49e733, 0x23179b3241d8554e, 0x0, 0x35d8a8c78484d0c2, 0x37b379080cbcb6f7, 0x6b7a53f07ab793f1, 0x449bac4fffe801bc, 0x127b307b02001ee53147974e, 0x19d13f1496e714d0e81eb452, 0x2d6284b456ce4016, 0x0, 0xddba124fb48f7a6a17ffd3e9, 0xf09236f948f55c12f051316d, 0x1d89cad2e98d792b, 0x0, 0x10b1947ddf58a676, 0x103c836271b652be, 0x100000000000000007e3b371d8da612a2, 0x10000000000000000afdc716fd42dcebf, 0x9933f565ff29445c4095b6bc, 0x657f8c9411abc5bbcc136d8a, 0x73e7ef94ba9d52e, 0x0, 0x6c40ee001e861af8b54083f9, 0xcd5e9710c4a04d282ce7349a, 0x690a0b30371b326, 0x0, 0x62e2e02294e2c662, 0xb7b29a6b2600fb8d, 0x12dfa3a68a5aa4b8, 0x15945e750a0443c5, 0xe73c8b0ec70203c2e8989117, 0x7ddfadad5f08ce1aa07c411c, 0x13613f779a31d6ff, 0x0, 0x638429e6306a39c9e31a3603, 0x327c5d8bef475c0133cb5d8b, 0x27096fced1ae8ce9, 0x0, 0x1ac00f1b74998794, 0x1000000000000000024c1b4e8a2305293, 0x59d3cc6f01477796, 0xc9c2a2cd82f7e2d, 0xdcaf34a4eef803781d3022, 0xbc09ae870f85a6cf01c65e44, 0x385ae0f48077e7e, 0x0, 0x61a1baa7bab47c085609a548, 0x914206f8e0e04938aee16726, 0x389734c913660f7, 0x0, 0x1000000000000000057e1f3bedd0842d4, 0x10000000000000000255df8d996acfae5, 0x100000000000000000318c2486aecb245, 0x1000000000000000023ae98fa95aa07b8, 0x88adbf9219029597e553bb04, 0xeb6747eb6284e8b022461ec2, 0x14a572f4f58c464f, 0x0, 0xeb6bac7a6c66241c45996655, 0xbd605734ae6e9a1ddcf2eb6e, 0x7fbe6469eaad0bb, 0x0, 0x1000000000000000059cfa117d9318779, 0x100000000000000008ef4027bb5693ee0, 0x3ae8a87244a109a4, 0x558c79eb7e83bb58, 0xd37309fe22d9e35f307c3a6b, 0xe5de80a909551c749fca4879, 0x21fd1084d81d15e7, 0x0, 0x8a05d9d6713308396ada192b, 0x5126361876e6ce50233c747c, 0x21db15f93ac460fe, 0x0, 0x9af91b3e36abc612, 0x86643c813ecda430, 0x100000000000000000e467a16915fd7e5, 0x100000000000000004a115b9161854fec, 0xe936353409de55cec6156fe6, 0xcb2d34e3b109e4ab4f9bfac3, 0x8435d0668aada26, 0x0, 0x6d5907f5ae10fced2d3d609d, 0x4720c6ca15b721ac824fd1dc, 0x28fd8e028bbd4327, 0x0, 0x100000000000000000615f3f7b8d448b9, 0x100000000000000007f9651eee6b31ff4, 0x1000000000000000016a63b2f0da9904c, 0x1000000000000000047f4ef94b6a2cc82, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x744865055917ca125348c4f8, limb1: 0x5c545244519dd218c72f1665, limb2: 0xcc6f1868dc806a6, limb3: 0x0, }, y: u384 { limb0: 0xcbb128d3e724151be03bef12, limb1: 0x3d9dca95a86b6ea20b40f368, limb2: 0x1d2cfc3fd3c3ff7f, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_1P() { let mut data = array![ 0x1, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0x1, 0xb4862b21fb97d43588561712e8e5216a, 0x12cfa194e6f4590b9a164106cf6a659e, 0x1, 0xb603ffc901ec7f3e42216ae4, 0x269adaf11286bf338b9dacb1, 0xab33b097e05378c0867894f, 0xbfd8ef26d4610b8e77f5c28, 0x9afe78c2bb0f305eccbffb90, 0xc8b06f9aaf49eda1f9fd6cfd, 0xc422cd476b9611aef3a1ee3, 0x1201e1e9a2b0867eb9da1725, 0x1000000000000000062a39ac9655a0af5, 0x10000000000000000b59da527feb9e759, 0x885278dc00a1125a, 0x2fe0754b9fadfe7b, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xb603ffc901ec7f3e42216ae4, limb1: 0x269adaf11286bf338b9dacb1, limb2: 0xab33b097e05378c0867894f, limb3: 0xbfd8ef26d4610b8e77f5c28, }, y: u384 { limb0: 0x9afe78c2bb0f305eccbffb90, limb1: 0xc8b06f9aaf49eda1f9fd6cfd, limb2: 0xc422cd476b9611aef3a1ee3, limb3: 0x1201e1e9a2b0867eb9da1725, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_2P() { let mut data = array![ 0x2, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0x2, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x2a43e70faf19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x51f964df9c6316b950f244556f25e2a2, 0x1, 0x767bdb83da4925db077ac23d, 0x51fcd455bd59b97a1e4a2d02, 0xf9650cba7ed29c8f01577a4d, 0x13e6deb52a57b03867f2c663, 0x2170a02826a65df5fff9fc69, 0xcdef32f5872257c0f74a4983, 0x275718e62abbba48d224fc01, 0x16e4935008c1ecbfc238a44c, 0x97ac96128760678, 0x1b8269c5da3a7aa, 0x946f8bb609f9ba7d, 0x4e77077ba28bdfd6, 0xe6c4136fba2947157839fc3f, 0x58df45b89ea1d6fd003f377d, 0x428ff9cfd30586deea516488, 0xc0c17be01b5ec83544d88ff, 0xfdf2fbfb66f355ed990a534f, 0x98f6b2b220c2c0e179e4d145, 0xe2766e3b994a5f31518b1b4, 0xb1861e2a35c8eceb1eb84bf, 0x3827704126429022, 0x59c3b34a3b390fcf, 0x1000000000000000076a605fca076460a, 0x2f4183d416809c9a, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x32321a942ef961780ca91c06, limb1: 0x57e5605fbba104f908e63665, limb2: 0x843c0bbd70b5a837b690bd95, limb3: 0xbe7f58485672327a5c447c1, }, y: u384 { limb0: 0x2150b2afd97c7793d20d0ecc, limb1: 0x4f6a0ae7eaf68e727f2fcb5d, limb2: 0x96407ddecb1fe770faf07c8c, limb3: 0x4c4183b2e457821188d59e7, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_3P() { let mut data = array![ 0x3, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0xcf86158ab69213388e721bb7, 0x5f7812269d790797cad9aa15, 0xb1c3622a0177001d9ed8e25f, 0x115cf429f459884785c6ba46, 0x1e81341e2f3f988ff115dda3, 0xad22946489db6ee4954fa5e1, 0x83bed94412e19d92b73cc763, 0x2074c7bceff87d0d41edba1, 0x3, 0x5a92118719c78df48f4ff31e78de5857, 0x51f964df9c6316b950f244556f25e2a2, 0x8d723104f77383c13458a748e9bb17bc, 0x42bbb74ddd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0xbf0551e03983ca8ea7e9d498c778ea6, 0x1, 0xa212d9c99e9c04c4d5c9413e, 0x396a875482462ca6c1340431, 0xc2162538b674feeff3abfd69, 0x753e02471aea6c84aaa5ffc, 0x929a8f9dbb886a14600841b2, 0xd2549b8930caba7ed2b7f6f0, 0x35911c87fe8cfc373e803e14, 0x180e16c3ae7f7949857d4ca0, 0x3827704126429022, 0x59c3b34a3b390fcf, 0x1000000000000000076a605fca076460a, 0x2f4183d416809c9a, 0x201564ee2f51efc0dd066bf4, 0x631f5532a8b44cccd0c4ae3a, 0x56a5d8f1e24804c51d3baba8, 0x155dcc0adb758a4caede5e39, 0x4e0b78c88baeacb640f333c4, 0x2a16352f6da4000344ea35b3, 0xe58d1f7ed72ebc3a1aced4bb, 0x7b09c3c38b9665bb6dcd1a3, 0x89ec0bb47cfdf6b1, 0xb71533d7b1764557, 0x340a863c788b8bd1, 0x100000000000000001b03838bf180c6bb, 0x8070e05e9145d1c520b0bc9f, 0xd2505d00fcfa7f814e629e1f, 0x789f47493e01360b240d31be, 0xd4d252b4e71c49b728891b0, 0x32fd0164a7284bf6631f2131, 0xbf29e9b9d14edb8796f7c003, 0x73032a27b08ccde5970c792a, 0x14128a5b1473f5285668a863, 0x29d77abed65ff201, 0x4ea390aeeae13c8a, 0x426754eb9138bd09, 0x100000000000000007ebb92a3d2545c26, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x21b85c07d97d8ad7ed64cf5c, limb1: 0xc68ab576217c87f6afe7e8f6, limb2: 0x8aecb918175dcc693f68b02c, limb3: 0x16bdc982d01b9f8d1782060e, }, y: u384 { limb0: 0x11cf0b8dceb54a416ec13f47, limb1: 0x81a05b3acc5b76a765127289, limb2: 0xcdbd38ba08efd726fae10661, limb3: 0x9747640d51b315635b0059a, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_4P() { let mut data = array![ 0x4, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0xcf86158ab69213388e721bb7, 0x5f7812269d790797cad9aa15, 0xb1c3622a0177001d9ed8e25f, 0x115cf429f459884785c6ba46, 0x1e81341e2f3f988ff115dda3, 0xad22946489db6ee4954fa5e1, 0x83bed94412e19d92b73cc763, 0x2074c7bceff87d0d41edba1, 0xe2955c55da59eba4b7b57d3d, 0x1e6629b0431bce67cf28c22, 0x1c35b7efd5b67f87221b8bfc, 0x3e53df9e3488a9e42acd87e, 0x2e089afa726154d40dd12102, 0x5391613ecf49db2bcf1cad86, 0x84a2abb2de6b3a6e09026a50, 0x19557a3a3c1d62a205d5dc87, 0x4, 0x8d723104f77383c13458a748e9bb17bc, 0x42bbb74ddd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0xbf0551e03983ca8ea7e9d498c778ea6, 0xb5d32b1666194cb1d71037d1b83e90ec, 0x5008b5f2ab0c1681c8f8e3d0d3290a4c, 0xd3fbf47a7e5b1e7f9ca5499d004ae545, 0x5d79c4bd3e70f16a55485822de1b372a, 0x1, 0x44bb6f75a004bca814756b12, 0x1818b158d2190e6e0fc9e550, 0x2c30743bfb89fd6efbecc08b, 0x37837c70d528dd05cbf07e7, 0x492cb4f7c261d2d0b24d8b02, 0x230240dd9634dc222a23cb1a, 0xe3eec79d41d215665e8c84cb, 0xeff88e6c2c0702d1d489a73, 0x89ec0bb47cfdf6b1, 0xb71533d7b1764557, 0x340a863c788b8bd1, 0x100000000000000001b03838bf180c6bb, 0xf88a71d0107733babbd62a8a, 0x5c8822f79ed71c8bbfa7ff17, 0x7a8298e09fc3cb760af959c9, 0x71970cd5e563018d29192bc, 0x6d859bf8574d99e4aa0d6235, 0x743b1ed749ce3385e004fd1e, 0x40b348aadf32289fd4ba39a2, 0x117e2219a46e398da3a4bcfb, 0x29d77abed65ff201, 0x4ea390aeeae13c8a, 0x426754eb9138bd09, 0x100000000000000007ebb92a3d2545c26, 0x62a1dd00d0d70c14a6483357, 0xd3311030294d0ecbd126a83c, 0x9ab588fa5774077b42bfaf84, 0x2ca8d2c572fb8a41c46768, 0x9078c212d37a3119918e97e2, 0x7bfd90eaf25c921f82205790, 0x87a6d075aaafcb12c6615ced, 0x14c4cdf3aa2c27b1ab23e540, 0x3a52f2488abaf3cf, 0x100000000000000002db717c471a1fc21, 0x10000000000000000644c4a2d385dbb8f, 0x10000000000000000a04a3389734226f8, 0xae129d9a602a42cc514ab5bd, 0x6b8ff0a7bab2c6cf01ab2b0d, 0xe54a1c91c8cebd80422d7472, 0x18f20ed943760167480b399c, 0x3c855ffac29166b79418290c, 0x16673746c28add51dbb908b6, 0x6bba7b68853a2592c3ab118d, 0x56b1a0d430dbe3db167379b, 0x100000000000000004bed5581e0e7a253, 0x100000000000000009c34387abab6c0fe, 0xb72bffe782e92797, 0x3a8e5d970236b4f1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x7406fee5d57362d0bd20a5fe, limb1: 0x9c148946ef3f3c63933238ab, limb2: 0x29449d34c8a2d4f2985f3c36, limb3: 0xa598551ba8198a566f2d4be, }, y: u384 { limb0: 0x79e483b729f05957e7c73f33, limb1: 0x3a0046ded0b81194df4ad0d5, limb2: 0x6bb49380867caf051586303a, limb3: 0xc750343cc7a561d93f3d0c0, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_10P() { let mut data = array![ 0xa, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0xcf86158ab69213388e721bb7, 0x5f7812269d790797cad9aa15, 0xb1c3622a0177001d9ed8e25f, 0x115cf429f459884785c6ba46, 0x1e81341e2f3f988ff115dda3, 0xad22946489db6ee4954fa5e1, 0x83bed94412e19d92b73cc763, 0x2074c7bceff87d0d41edba1, 0xe2955c55da59eba4b7b57d3d, 0x1e6629b0431bce67cf28c22, 0x1c35b7efd5b67f87221b8bfc, 0x3e53df9e3488a9e42acd87e, 0x2e089afa726154d40dd12102, 0x5391613ecf49db2bcf1cad86, 0x84a2abb2de6b3a6e09026a50, 0x19557a3a3c1d62a205d5dc87, 0x490bf40774926e8b279947c, 0xeabab6aef9e9d2a4f64f4e7d, 0x3e309fe1b1c8247abab20d7e, 0x79c527862917f69ac58fcc4, 0xacb18f2da2b425c2ff50dafd, 0x7623850d87e279a8a30f31ff, 0x777564c7291d95fa80203ade, 0x1764ce0e7fb626109b63789b, 0x42f2f3f4f6b9d2c2b73a361f, 0xcd78c070c184c38b1e5716aa, 0x72cbc24cd90da89e0e3cefe4, 0x19485e1c46d0dce75f8b192b, 0xb56b3539074b3c47b3f504d9, 0x2c229530bddedd8851b03dcc, 0xc93eef8474c4e18d6378e7f0, 0x173d36f17a3c9ae77a2acc25, 0x5fbf29cf20556a11621a6639, 0xdfda5b7dbf0b226822094787, 0x4a3b059e521b4b0445df96d5, 0x333988c2c09f5af061cdfb, 0x13d3570be6d27d1d588b22fc, 0x20c763e58d4df3e4990cdae9, 0x2c3301367f400c31f4bded26, 0x16a6c25d133fba74b4c55972, 0xcb24d12438557639f52df5fd, 0x4a6a46feebe8a88a8062bd0e, 0x65f04211af4b168b1e25787d, 0x17935d6f4fa575744ca46f75, 0x644f324be8a5c152625a5b8a, 0x501e52e8c5707d7a3a77ee18, 0x9636c463c14c5b85c2e6d3b1, 0x1939b6f297f7b5b7fd0ac458, 0xde1d8e2670532ec5bba60ade, 0x1154f5064f7dd38656f7f82b, 0xc9bec68372b7d07dcf66270c, 0x315ced00b3153219bbd430, 0xc48b3bc110e208d827b13f4d, 0x87d82592699bca3dbf847c2b, 0xff04f0f2c8be12365aa73443, 0x1739c8c450ac994a5326c809, 0x8904b74d5d114b5416df0ed6, 0x479ee13e49cde067742c2655, 0x45b9359bfa338dd432ca9ff1, 0x12bf6460e7a42942be6c16a0, 0x3a8b37aacb2f620bc41c6109, 0x91f68edf90b5947273b0aadf, 0x265d48695a73800b7404124c, 0x141e3d99b3ab683bdb0ce70f, 0xa, 0xe005b86051ef1922fe43c49e149818d1, 0x3ea0f301eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x2a97919d8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x460ba2d39a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x2894fdbe6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x43870ae2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x56e06d3d16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0xa4593acd7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0x6b3f2afe642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x1b8bb742d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x233a1ba09466e4726b5f5241f323ca74, 0x1, 0x4fec1bc3c60e1e8698dead7e, 0x5d71a7fdab6311661050245a, 0xe05d09f0bc4a8f934ca0be3, 0x3e410c8ef8929e597fc5e16, 0x2cb369f5527d80a3f85dfe16, 0x23136c25c83e8f7bbec1cf73, 0xff512e4a07edaf5b49d3d728, 0x12d5dbede4328cb09da72b84, 0x100000000000000004292942fff5c5c73, 0x100000000000000006f8e81274b1b80e7, 0x3b3d1e96d895314d, 0x1000000000000000084bf5385aab534ac, 0x60a1a3ab0c7177eab76fff39, 0xc0be22d12b053ffe9ca14f59, 0x181af3ad4d7e2a3d70d0d390, 0xa7fcec07bd4cbf86517c4ab, 0x225dafa45afbf8fdc096ca46, 0x83fe86ca3674bc4f0fa1be03, 0x1419a6d50b39b38488129411, 0x673aa0dca89d43027ecf344, 0x10000000000000000cea55d261de27134, 0x4945ad0e7a3ff67, 0x2fc459c3edadc3a2, 0x10000000000000000061e3b8d4a2b7b49, 0x17f488f0ade4733d6ef16e5, 0x2345447ae416edecd39537f0, 0xb6b696b8639e7cf9895c5cc4, 0x9e0e0023c554f7dcea9988f, 0x9d39eb85ff093ed952b7b83e, 0xe97ebfec0868fb25fc01f0d2, 0x10ad24a237318d2b9652aa09, 0x13254cc65058dd9358b96239, 0xab1e43002be79daa, 0x4647693a000da8bb, 0x100000000000000007d866035ad43d2cd, 0x100000000000000008ac469986dc04381, 0x1c0101fbd27c0a2fce7dea00, 0xa1754f662e645363a3d7555e, 0xf500d7bbb858b228f7566d60, 0x123c9acdbe8c6cd24ca87a2d, 0x49abf7cca1720df09b8013e8, 0x58d4d7df624dc9492bdd5f14, 0xd885e40ee88b16151fc21f83, 0x18bc3ac505215228c26ed360, 0x100000000000000008f832425d3465a7d, 0x100000000000000007a1648de1b75e170, 0x10000000000000000782f24b2b6f99caa, 0x10000000000000000a46207414514e0b7, 0xb680e2ee3456fa57129b0045, 0xfc71104d4fa38e9455aa5cd8, 0x9d5f6b4a7451e6cd2c4f7c7e, 0xfefc054f2225661c3586c55, 0xbabd33086acd589bbb7df2d8, 0xea6d9ef8b309c10adde6756d, 0x717bd330e5157289ed69b9ba, 0xb919c30025518a30b26a33b, 0x10000000000000000ae0ed118d80201db, 0x100000000000000007dad72d6582f2e8a, 0x3e9b7c2f776f9ad1, 0x33c103bec8d8dd99, 0xa05e97f79f1da1a74d36f934, 0x82cf8025c3bdc887ecdaff73, 0x24a11bec2b7777732ea49307, 0x156f141bcbaef8188730e3d3, 0x5630c9208c0eb9c6338de7e, 0x1b5aaef757b58eb36a731689, 0x3fa1031d312ad2881206f852, 0x12b8899d4af7a8c34e2a9d46, 0x10000000000000000022bf071f1160083, 0x1000000000000000057d827f50ce811a1, 0x21e30fccd874a3e1, 0x1000000000000000081bff70857d935ca, 0x7053f48d9623a0772224604c, 0xb11da71ba9823dc5c04dd4dd, 0x184deafecb58abd1e56400b1, 0x157346717db5b34fd548cd32, 0xd9cadf87641980d152d6537d, 0xee861d7d0a13c67b7217634, 0x7826079f0eee56e4e5c062fc, 0x191da207fdd5403838e0728e, 0x10000000000000000ed6a42a626d0b5c2, 0x100000000000000008251f67200c0fd29, 0x3753a6d93f053e65, 0x39f069691aa27848, 0xc378beb21e5b84edd744923f, 0x9b228eaa8c0baec7dadb455a, 0x186026cdb53d6b03ac71faf9, 0x30663d24fb4b20705ac56ce, 0x8b26b689e5b52df6b3b59981, 0x49a372daaf7ae6845981a370, 0x191c1c0b1921fa467089cad9, 0x11bd657f852a9cc7b38ac45, 0xabf8f0133c1f072e, 0x161489d2a4ae8501, 0x10000000000000000a422466a58575055, 0x100000000000000010d01a10c0ddec2b7, 0xc17c00c80be4888b417fcab7, 0x237837a17d7f044145e07dd0, 0xdd4c4c3ee185dede22941eee, 0x10bcc285e222e3edf5a3bb26, 0x3e1c8591502f1fa558f9f37f, 0xd279a8b40c7d82a067c1a9e0, 0x8ebeb1d2a390ea6cc8282d68, 0x1859d1c72735f018ea45dea3, 0x1000000000000000005f68a6ba1476c4c, 0x1badaadb9ef013b5, 0x100000000000000009d7e4713e105078d, 0x10000000000000000704d4f90616d782f, 0xd7734cfb87bdee6ddbecba22, 0xb5be04f83be44ace5a664a82, 0xa924b5316afad687fc174c75, 0x136a13276f643b22873d7490, 0xfa56e794ab2e49db1a65d154, 0xa8c32e8861e673612ae9f3a2, 0xd12e4badeb492211212793, 0x5fe3e9844a34155419eb432, 0x100000000000000000d9e2865dd56177d, 0x1000000000000000027d8ecbd5198c228, 0x1000000000000000022c5f7e952ac9b2b, 0x10000000000000000a2e9b304305db746, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x85cd6b5af7b7cca272f94a3, limb1: 0x55be389217b4b81baee9530f, limb2: 0x1b5a70fff8b31b3cfc4b68de, limb3: 0x101c3dcc7f2a1be1afe50e39, }, y: u384 { limb0: 0xdc944be6d0d78b23304e3193, limb1: 0xe1cdd664f4036ec4bd90db8, limb2: 0xf9e55c43073f3a6163464638, limb3: 0x14396fc17f6c6bc8f76ea501, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_11P() { let mut data = array![ 0xb, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0xcf86158ab69213388e721bb7, 0x5f7812269d790797cad9aa15, 0xb1c3622a0177001d9ed8e25f, 0x115cf429f459884785c6ba46, 0x1e81341e2f3f988ff115dda3, 0xad22946489db6ee4954fa5e1, 0x83bed94412e19d92b73cc763, 0x2074c7bceff87d0d41edba1, 0xe2955c55da59eba4b7b57d3d, 0x1e6629b0431bce67cf28c22, 0x1c35b7efd5b67f87221b8bfc, 0x3e53df9e3488a9e42acd87e, 0x2e089afa726154d40dd12102, 0x5391613ecf49db2bcf1cad86, 0x84a2abb2de6b3a6e09026a50, 0x19557a3a3c1d62a205d5dc87, 0x490bf40774926e8b279947c, 0xeabab6aef9e9d2a4f64f4e7d, 0x3e309fe1b1c8247abab20d7e, 0x79c527862917f69ac58fcc4, 0xacb18f2da2b425c2ff50dafd, 0x7623850d87e279a8a30f31ff, 0x777564c7291d95fa80203ade, 0x1764ce0e7fb626109b63789b, 0x42f2f3f4f6b9d2c2b73a361f, 0xcd78c070c184c38b1e5716aa, 0x72cbc24cd90da89e0e3cefe4, 0x19485e1c46d0dce75f8b192b, 0xb56b3539074b3c47b3f504d9, 0x2c229530bddedd8851b03dcc, 0xc93eef8474c4e18d6378e7f0, 0x173d36f17a3c9ae77a2acc25, 0x5fbf29cf20556a11621a6639, 0xdfda5b7dbf0b226822094787, 0x4a3b059e521b4b0445df96d5, 0x333988c2c09f5af061cdfb, 0x13d3570be6d27d1d588b22fc, 0x20c763e58d4df3e4990cdae9, 0x2c3301367f400c31f4bded26, 0x16a6c25d133fba74b4c55972, 0xcb24d12438557639f52df5fd, 0x4a6a46feebe8a88a8062bd0e, 0x65f04211af4b168b1e25787d, 0x17935d6f4fa575744ca46f75, 0x644f324be8a5c152625a5b8a, 0x501e52e8c5707d7a3a77ee18, 0x9636c463c14c5b85c2e6d3b1, 0x1939b6f297f7b5b7fd0ac458, 0xde1d8e2670532ec5bba60ade, 0x1154f5064f7dd38656f7f82b, 0xc9bec68372b7d07dcf66270c, 0x315ced00b3153219bbd430, 0xc48b3bc110e208d827b13f4d, 0x87d82592699bca3dbf847c2b, 0xff04f0f2c8be12365aa73443, 0x1739c8c450ac994a5326c809, 0x8904b74d5d114b5416df0ed6, 0x479ee13e49cde067742c2655, 0x45b9359bfa338dd432ca9ff1, 0x12bf6460e7a42942be6c16a0, 0x3a8b37aacb2f620bc41c6109, 0x91f68edf90b5947273b0aadf, 0x265d48695a73800b7404124c, 0x141e3d99b3ab683bdb0ce70f, 0x6d6db022a8549ee86374b69a, 0x3e98f7258170733507d8709b, 0x10b4337a56d4cd17ab2fe1d5, 0x11366a6fecb124757076f4b6, 0x77b25b600d3baa1a2f54f826, 0x924c3c1a699e9b27b3612246, 0x6a253cae0097b1955d4f0cfd, 0xd2bd6591140d2faabafefac, 0xb, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x2a97919d8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x460ba2d39a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x2894fdbe6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x43870ae2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x56e06d3d16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0xa4593acd7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0x6b3f2afe642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x1b8bb742d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x233a1ba09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x4b2543867c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x22b15f3fbb42e0b20426465e3e37952d, 0x1, 0x19eea9b02b0269a828e87bbc, 0x67bd46455c26c6ca390ae0ba, 0xa9dc83672893066741fa95e1, 0x14a2ab6a3bc68452c5582829, 0x2a53345d1b34e4641cc38c3d, 0xc82502e6ee206ff835917eb7, 0xb6c87f3b28288a29296a7059, 0x1361292ebd69db3c0b2f9180, 0x10000000000000000cea55d261de27134, 0x4945ad0e7a3ff67, 0x2fc459c3edadc3a2, 0x10000000000000000061e3b8d4a2b7b49, 0xcca46ee7e7d728cf4687644, 0x3ade741f416cf509a8d72a4c, 0x8e7572df6c768d460cb201d1, 0x1298c2031c383f68f18d47, 0xa554139550742d2c1c2dbfcc, 0x179852f9e707ce5dfc6c509, 0x307f6d2c8b88fb29906b9668, 0xce27f25b13c90cd75581cd7, 0xab1e43002be79daa, 0x4647693a000da8bb, 0x100000000000000007d866035ad43d2cd, 0x100000000000000008ac469986dc04381, 0x77117911414f1a8ba740937f, 0xfa4b42c9e27b825abb6e1932, 0x1957cbae8168c2a9ea426a5a, 0x10cae1885e14624756a7eba6, 0xa3cd665fc42827532aaa2ea, 0x8af3e1bc51da81d7990f227e, 0x788c055adcefcc69a3a5d382, 0x1003592246083ca043286287, 0x100000000000000008f832425d3465a7d, 0x100000000000000007a1648de1b75e170, 0x10000000000000000782f24b2b6f99caa, 0x10000000000000000a46207414514e0b7, 0xbe9bca3bf5eec6cc9844c551, 0xe0d5a94e288ef5adcba43ed7, 0xe9e85c194dff7c219c6d8ca3, 0x1254bb7494352e470a3b0a40, 0x747bed6d938a5434bfd865e3, 0x3d5af5929e771b0b1a09959b, 0x78e81d642b9ecee32d559eb, 0x14cc935a8ea60d9c8231390c, 0x10000000000000000ae0ed118d80201db, 0x100000000000000007dad72d6582f2e8a, 0x3e9b7c2f776f9ad1, 0x33c103bec8d8dd99, 0xac99a8072958d59134f663b9, 0xb30bb7a088fd8458abe354a5, 0x1d1dacff16391acd20b4eaea, 0x7b73f92d3f09b43016e07b3, 0xf6ae86523c0174ca5b1b0fc8, 0x73380bbaaba7c2034a6c5c63, 0x74bb326851d9f4a7c3e2c22, 0xbadb8e20341bc68ee0d62fb, 0x10000000000000000022bf071f1160083, 0x1000000000000000057d827f50ce811a1, 0x21e30fccd874a3e1, 0x1000000000000000081bff70857d935ca, 0xd1db88e35a5fd4b22e8a7242, 0xcf4280e99dabae608abafd04, 0x46af27b56584cc2c598e71ed, 0x14e9eb8a645712d6102c0a9e, 0xd7eb2bc34e0a3094c44bacf3, 0xd0c67ab4ba8aaa1ddd0d6652, 0xb581c278d1737880614fa64d, 0x99a3a36cbc29026cdb989a3, 0x10000000000000000ed6a42a626d0b5c2, 0x100000000000000008251f67200c0fd29, 0x3753a6d93f053e65, 0x39f069691aa27848, 0xb96cfe43c16c753450704e86, 0x2a10f11f55f81a94dd748595, 0x974380349665cfafcdae9c95, 0x866a4b640813c8ed4602e74, 0xda29c08c0e39dbfd34e194b7, 0x76eda22634152a733d1bb476, 0x3ccf70b893cad74b3949dcab, 0x11ae5fe6d5c14a6d2752cef6, 0xabf8f0133c1f072e, 0x161489d2a4ae8501, 0x10000000000000000a422466a58575055, 0x100000000000000010d01a10c0ddec2b7, 0xdc59ecc95ada6a3cddec47f, 0xbd9358cf424cddcab08790fa, 0x50659409e42159c50d14ced0, 0x8306fb79b2c290cc5c1fd38, 0x4ca0ea4e89d982c06289a0c4, 0x37e68136c605119f244d8150, 0xab4fee3c3a973c68f7f97975, 0xf51d92010bec98bd50ac787, 0x1000000000000000005f68a6ba1476c4c, 0x1badaadb9ef013b5, 0x100000000000000009d7e4713e105078d, 0x10000000000000000704d4f90616d782f, 0x86c26fd1dd2a50ee0449c352, 0x1b4d11d7f532f65e13dcba4e, 0x9015975fbc0102c1ff188862, 0x7e1482bb4fc0ef8853ca0c, 0x94cc4d2e3c7efb6f9333e845, 0xb0e5f311c82f55c14cd25a55, 0x507353e7c8312a9919c42bd9, 0xd36d6a8ef21c5f12abba7b0, 0x100000000000000000d9e2865dd56177d, 0x1000000000000000027d8ecbd5198c228, 0x1000000000000000022c5f7e952ac9b2b, 0x10000000000000000a2e9b304305db746, 0x6c4a291f3b18b98c85df2dc3, 0xc22d37b8b13205d494623e06, 0x4d3d27bda9b62c0f25a91194, 0x11bc318214ab34ab5197de3d, 0xf96d5803e611f1ad039b8569, 0x8846b82a7c6d0744b0ce648d, 0x4a92230e8cec10baf31a9ca8, 0x61491babdbf49d8a7f52951, 0xbda83aa75e798d1, 0x100000000000000006286d6ba5e14f26e, 0x38e7f7d2ae5ed155, 0x568116e3630d2d3c, 0x6eda656d7e631870e3600441, 0x170f2b8ebab1a7c6884463a3, 0xd7bfea3459a831bff9178452, 0xf1e34eceee6376fc7ca9b25, 0x9245d44dca719c11569e91c5, 0x829977ffedfa58f78ae0959e, 0xcbb65cb0a53b9639d2fcd418, 0x7635fac8f26c4762db2fb7, 0x100000000000000003b4d8d413c8654e3, 0x480407e0ff6c1d6c, 0x1011af9ee2cc20e6, 0x2dde429d4509a6dc, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x20ed31b5bd1a6a99cbc5f536, limb1: 0x455cd2878abeba8b867a4290, limb2: 0x9dfb4341a83a69b41feb23e4, limb3: 0x16dfcd6d60e4be40819587ca, }, y: u384 { limb0: 0xe898728a87fdf94569d6fc7b, limb1: 0xebd6dcf86bcbaf6626552df1, limb2: 0x3892cf6167890a8cfbb63c03, limb3: 0xcc772bf8b9e03accf1bd62, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_12P() { let mut data = array![ 0xc, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0xcf86158ab69213388e721bb7, 0x5f7812269d790797cad9aa15, 0xb1c3622a0177001d9ed8e25f, 0x115cf429f459884785c6ba46, 0x1e81341e2f3f988ff115dda3, 0xad22946489db6ee4954fa5e1, 0x83bed94412e19d92b73cc763, 0x2074c7bceff87d0d41edba1, 0xe2955c55da59eba4b7b57d3d, 0x1e6629b0431bce67cf28c22, 0x1c35b7efd5b67f87221b8bfc, 0x3e53df9e3488a9e42acd87e, 0x2e089afa726154d40dd12102, 0x5391613ecf49db2bcf1cad86, 0x84a2abb2de6b3a6e09026a50, 0x19557a3a3c1d62a205d5dc87, 0x490bf40774926e8b279947c, 0xeabab6aef9e9d2a4f64f4e7d, 0x3e309fe1b1c8247abab20d7e, 0x79c527862917f69ac58fcc4, 0xacb18f2da2b425c2ff50dafd, 0x7623850d87e279a8a30f31ff, 0x777564c7291d95fa80203ade, 0x1764ce0e7fb626109b63789b, 0x42f2f3f4f6b9d2c2b73a361f, 0xcd78c070c184c38b1e5716aa, 0x72cbc24cd90da89e0e3cefe4, 0x19485e1c46d0dce75f8b192b, 0xb56b3539074b3c47b3f504d9, 0x2c229530bddedd8851b03dcc, 0xc93eef8474c4e18d6378e7f0, 0x173d36f17a3c9ae77a2acc25, 0x5fbf29cf20556a11621a6639, 0xdfda5b7dbf0b226822094787, 0x4a3b059e521b4b0445df96d5, 0x333988c2c09f5af061cdfb, 0x13d3570be6d27d1d588b22fc, 0x20c763e58d4df3e4990cdae9, 0x2c3301367f400c31f4bded26, 0x16a6c25d133fba74b4c55972, 0xcb24d12438557639f52df5fd, 0x4a6a46feebe8a88a8062bd0e, 0x65f04211af4b168b1e25787d, 0x17935d6f4fa575744ca46f75, 0x644f324be8a5c152625a5b8a, 0x501e52e8c5707d7a3a77ee18, 0x9636c463c14c5b85c2e6d3b1, 0x1939b6f297f7b5b7fd0ac458, 0xde1d8e2670532ec5bba60ade, 0x1154f5064f7dd38656f7f82b, 0xc9bec68372b7d07dcf66270c, 0x315ced00b3153219bbd430, 0xc48b3bc110e208d827b13f4d, 0x87d82592699bca3dbf847c2b, 0xff04f0f2c8be12365aa73443, 0x1739c8c450ac994a5326c809, 0x8904b74d5d114b5416df0ed6, 0x479ee13e49cde067742c2655, 0x45b9359bfa338dd432ca9ff1, 0x12bf6460e7a42942be6c16a0, 0x3a8b37aacb2f620bc41c6109, 0x91f68edf90b5947273b0aadf, 0x265d48695a73800b7404124c, 0x141e3d99b3ab683bdb0ce70f, 0x6d6db022a8549ee86374b69a, 0x3e98f7258170733507d8709b, 0x10b4337a56d4cd17ab2fe1d5, 0x11366a6fecb124757076f4b6, 0x77b25b600d3baa1a2f54f826, 0x924c3c1a699e9b27b3612246, 0x6a253cae0097b1955d4f0cfd, 0xd2bd6591140d2faabafefac, 0xe706f12d726b82e518e76de2, 0xcbc3fafc8178466a6bfb6b20, 0x27d77f8bd8c4a2d2333b94e2, 0x3fd4d3cb36a5470ac66276d, 0xaa24c8373ee67a1fdcfeddd6, 0xb14ff80cfb97cbe0062505e6, 0x1f3cff0169eb74ea25e4b514, 0x9c9767230b739e24df854f7, 0xc, 0x3405095c8a5006c1ec188efbd080e66e, 0x460ba2d39a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x2894fdbe6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x43870ae2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x56e06d3d16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0xa4593acd7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0x6b3f2afe642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x1b8bb742d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x233a1ba09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x4b2543867c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x22b15f3fbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0x368b770c552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0x1c00c5a3b29a8b06daf66c5f2577bffa, 0x1, 0x662eb982d85d057e3ecd3e80, 0xb4a9a06f1870cef04d259893, 0x13c63b08919789f6693ac767, 0x46b57475ebe2592c180602a, 0xa29ba889efae66ae28b5a21c, 0x90db50a5f6fd2bd2f903028a, 0x2ff1e2429fbd64dfa2d6ad63, 0x12dafd8eb8056d84ec28ec15, 0xab1e43002be79daa, 0x4647693a000da8bb, 0x100000000000000007d866035ad43d2cd, 0x100000000000000008ac469986dc04381, 0xae2f33a9d9cb4b15ee0ad6b1, 0xf3a69411c14fe8a373bca88b, 0x217b85cd445d90ff0e4660be, 0xcd5e4ff4b00690b55b4ccab, 0x6eed9ed30f4774665c816e0c, 0x41cd754068d68ea27a0b5a89, 0xa959aebee91fe56aa2e55599, 0x1979875ae2f9097a371a56f, 0x100000000000000008f832425d3465a7d, 0x100000000000000007a1648de1b75e170, 0x10000000000000000782f24b2b6f99caa, 0x10000000000000000a46207414514e0b7, 0xdfb5306dcb37c28c478de377, 0x82bf6e7247d010b3b88124e, 0x1350fed73699712cd10e4997, 0x264ec684e80ad573730987b, 0x7e9381355a8d8cf41277ab35, 0x1dd2f50a04724803c09295fb, 0xd59632cde5cb28cb87504b56, 0x150c5c0d0a3bcdb7fd2c4431, 0x10000000000000000ae0ed118d80201db, 0x100000000000000007dad72d6582f2e8a, 0x3e9b7c2f776f9ad1, 0x33c103bec8d8dd99, 0x6adb19e05054bbfb8a53d37b, 0x2c394966e7282d8a110f2653, 0x512faaf7af9cfceb077d30e7, 0x13427ec47a05bb56e340d4d7, 0xc5ee5e3724d194a0d2791d0f, 0x5d820084f43d9203e1e31a16, 0xa67dc8923161c3bc6ae1f4f5, 0x1dc8d7785737a204ad5d5e5, 0x10000000000000000022bf071f1160083, 0x1000000000000000057d827f50ce811a1, 0x21e30fccd874a3e1, 0x1000000000000000081bff70857d935ca, 0x382cac990c38c14a85724327, 0x98521dab0ab80ddee741516f, 0xafe85b60155438f1d4633925, 0x45c68724b994edb98efb200, 0xdbf686bb85160b27e6488220, 0x59414eea0e11ecf7c9d22ae3, 0x40d4f4747cb840ea3899a9b, 0x2861afe5dbb737326928b2b, 0x10000000000000000ed6a42a626d0b5c2, 0x100000000000000008251f67200c0fd29, 0x3753a6d93f053e65, 0x39f069691aa27848, 0x849645de9e01e7a980f44c83, 0x73c2ecb8cb203193684963db, 0x9945175490a2d564c0840500, 0x15307d5f56f347db9f7d7438, 0x376ccbcc1e7cff3de0291c4d, 0xaea02820b94f9707dd1845c, 0x352c307a3c4c5a6903a65295, 0x136ac345ecdf8cdb887a13e5, 0xabf8f0133c1f072e, 0x161489d2a4ae8501, 0x10000000000000000a422466a58575055, 0x100000000000000010d01a10c0ddec2b7, 0x71a63008c587621a4f6f2fa1, 0x82ce5f249132fd11542b71b2, 0x4069ad0155b3070b2b6f4203, 0x1126657c4bb0502d5248df50, 0x97eb128e69157b31c5de2a51, 0x627ccbf06c57855ca24f82a3, 0xba851322224041050c2c7b0b, 0x166b10a0c76fedee06db3e9a, 0x1000000000000000005f68a6ba1476c4c, 0x1badaadb9ef013b5, 0x100000000000000009d7e4713e105078d, 0x10000000000000000704d4f90616d782f, 0xda173dac5e6d0480ba667f76, 0x322fa6cc1fec8d7c415cf100, 0xfef7b6962ba4e32e16c004d7, 0xabbcb2d8ced3d51e8a78865, 0x2d862d3014969ce931cd1262, 0xcafd95d76195abeda17c7f45, 0x69277501e6ac90cabbfd905b, 0x2104682267f86645d8554d4, 0x100000000000000000d9e2865dd56177d, 0x1000000000000000027d8ecbd5198c228, 0x1000000000000000022c5f7e952ac9b2b, 0x10000000000000000a2e9b304305db746, 0xe86bdaffc7d80a66c773f278, 0xa3367d8c785f430e9f7ab55c, 0x347404e9a1d224b1a7e64804, 0x17887f8a85307d4c5ccc2bbc, 0xdcd40632f732048108cef9f5, 0x494a6fe05b3b9d1ebc125f36, 0x18a01df527ac65db6aa8e28b, 0x15157ba64035c63122bcc5cf, 0xbda83aa75e798d1, 0x100000000000000006286d6ba5e14f26e, 0x38e7f7d2ae5ed155, 0x568116e3630d2d3c, 0x65253fd616826b1dd8c6236a, 0x493a8f8b6538bb9a725be42c, 0x5a1a1e203464a4e5f03885d8, 0xf2c7a601a50541e04819723, 0x9fdb8a5060ab7533fe50a415, 0xf4dd7e344ccc7f09843b76af, 0xc660f2fffacb256a3e366c57, 0xcc76384b035432da44ba0c3, 0x100000000000000003b4d8d413c8654e3, 0x480407e0ff6c1d6c, 0x1011af9ee2cc20e6, 0x2dde429d4509a6dc, 0x9a04f7c7cf9cf95db3549484, 0x4a0c467c3a6e7c13b6bbb2e6, 0xdb99b99a930fe293db1b8e80, 0x10c8dfe8a58baf24cbb10f59, 0xc6d991cbebf3f9fa457915ba, 0xa520ddf24608d77a970d70ae, 0x1c1b315ab5926bca556680a7, 0x55733b5e405e88290930f38, 0x10000000000000000a857f257ed546ea8, 0x100000000000000001c358602b6f2cc63, 0x100000000000000000cfc85c4f3f5d8b2, 0x5dc2c695f99c34b6, 0x15fe07945fe2e77a80e4179c, 0x1ec2648a2cb50e385ba8a01a, 0x4ad0adea7d44208504ffa544, 0x122dbd49c1be9a7cede8f22d, 0xa7a998d5d885d32646167830, 0x5f83ce9f704555fd5177aa16, 0x95cdcf02e2e556a08a988e4, 0xdac0c3fac6c4b903f15e3af, 0x6249de39f2cc9280, 0x100000000000000008d2562f99f8222e7, 0x28c4e5bf72e345ad, 0x10000000000000000222b64363b6a2501, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x8bce5042829fff73a3bcf235, limb1: 0x24302605af7afd068c1bac35, limb2: 0x37e884c17dfeef6ccab457b5, limb3: 0xd33acb51b348e3a6fe9f58b, }, y: u384 { limb0: 0x26976f00ce9dc19a844a55bf, limb1: 0x305566a6af04e25742e40b78, limb2: 0xeb73722c02dbef5226438532, limb3: 0x1618caeaf7d7b6c6e1bf656, }, }, ); } #[test] fn test_msm_SECP256R1_1P() { let mut data = array![ 0x1, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0x1, 0xeb1167b367a9c3787c65c1e582e2e662, 0xf7c1bd874da5e709d4713d60c8a70639, 0x3, 0x5ecaccc77099015edd4567b8, 0xa82e8c31fd89230e9e054b35, 0x9b8f95662d8ac62b, 0x0, 0x197a10d65c49dfb9020a06d1, 0x385d645da0e58782b062bea8, 0xce16e956485f6821, 0x0, 0x35a5b9ab55bd33dd4dec8ec8c85b8754, 0x1256a1018e9a2606d3efc444e5bc9e97, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x5ecaccc77099015edd4567b8, limb1: 0xa82e8c31fd89230e9e054b35, limb2: 0x9b8f95662d8ac62b, limb3: 0x0, }, y: u384 { limb0: 0x197a10d65c49dfb9020a06d1, limb1: 0x385d645da0e58782b062bea8, limb2: 0xce16e956485f6821, limb3: 0x0, }, }, ); } #[test] fn test_msm_SECP256R1_2P() { let mut data = array![ 0x2, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x2, 0xe443df789558867f5ba91faf7a024204, 0x23a7711a8133287637ebdcd9e87a1613, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0x3, 0x69ad05b5d409fdd74ff3606a, 0xa4cd8f1dd82b0b833eb4f2e7, 0x24b24c3d5a6a9dfd, 0x0, 0xd836719652e6763c9000c8bf, 0xf5a12b525077946be38f884b, 0x648707519821f2b4, 0x0, 0x29fa93ff2e088f257810ffaf340cbe2f, 0x67db401fe06eea845a19e61367b76a34, 0xf89789bfc970e55d00b6c590, 0xf75a68e0b3fa2545ac20867c, 0x2960649db3055cd8, 0x0, 0x89f368de0f28fdf05075bde, 0x528cd10ce08cfe5ddb208066, 0xda975b1ed45230dd, 0x0, 0x44faf735503f8d6a4fd7c1f1541b0e83, 0x108efc1b039167d94064f65615a509dcb, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x7c99e6e15710cca6d05a228c, limb1: 0xb3b0695cd0bcf4e2fff2aa40, limb2: 0xf51b415c36a8d206, limb3: 0x0, }, y: u384 { limb0: 0x3ed9af037beeebe8a4e51272, limb1: 0x59c17339e41ffb8881d8ff31, limb2: 0x8659e768c3fbaf89, limb3: 0x0, }, }, ); } #[test] fn test_msm_SECP256R1_3P() { let mut data = array![ 0x3, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0xaec889b9d8ce51c4a2c3586f, 0xa2b07874c333bfee9f78e13e, 0xc445de21be8d8709, 0x0, 0x3, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0xb4862b21fb97d43588561712e8e5216a, 0x259f4329e6f4590b9a164106cf6a659e, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x5487ce1eaf19922ad9b8a714e61a441c, 0x3, 0x21932ec80e1487c9cfaca85, 0xc186376df1525312e49b706e, 0xc31cc2013df9b079, 0x0, 0xfc2a2329e088a2bf919713c2, 0x6f226891c087240877728fb4, 0x8c2581e103f28987, 0x0, 0x44faf735503f8d6a4fd7c1f1541b0e83, 0x108efc1b039167d94064f65615a509dcb, 0x771ae9413e9a50212f4cab04, 0xe237a7ac362eb52c39a5693d, 0xfed723892728a27d, 0x0, 0x22cef04d0e2d637e3ac6f9dc, 0xfe6992a829bc39d46025402c, 0xf9f46dc5ec2a3be2, 0x0, 0x97f029beb074caf4db383ce1b6f43018, 0x676a9d25b186deaeeb154f6f81c3cac5, 0xcb6fdbee18c8593a5411d8d4, 0xb5481fe44962e7d3e222115, 0x871c9156dc079065, 0x0, 0x8c26b99697ee8e8f646fc0eb, 0x73d06be2b40891cb15d4a6c8, 0x97c7a60ae52be2f, 0x0, 0xe1a61de4d41b08744b95b20a4e12fcb3, 0x153b6b6be0d5eaf38f83e1294ef38c98b, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x60a04d1cd61720fd649a635, limb1: 0x4de992ec1fe826266faf9542, limb2: 0x7fcc86284cb4d8d5, limb3: 0x0, }, y: u384 { limb0: 0xc5cc56bee25131b3aec25cee, limb1: 0x60f429ebbf34f181ee9e0f69, limb2: 0xeaba7780c9c9f8a8, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_4P() { let mut data = array![ 0x4, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0xaec889b9d8ce51c4a2c3586f, 0xa2b07874c333bfee9f78e13e, 0xc445de21be8d8709, 0x0, 0x7e47d1c2d19c21b2f6870259, 0xe701b40af42001c38bca00db, 0xd87ea1720d4dd3d6, 0x0, 0x5b1d6cc74985ce49a1f737fe, 0xb9127c572c3f091c031c249c, 0x1392711e1576aa6f, 0x0, 0x4, 0xb4862b21fb97d43588561712e8e5216a, 0x259f4329e6f4590b9a164106cf6a659e, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x5487ce1eaf19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0xa3f2c9bf9c6316b950f244556f25e2a2, 0x8d723104f77383c13458a748e9bb17bc, 0x85776e9add84f39e71545a137a1d5006, 0x3, 0x9921ded7d529ce361c8e3ff0, 0xdc220d0b5287d69a714d190b, 0x1b76478b4180189d, 0x0, 0xb1d2a54b21c1ad7f7d0f9027, 0x7e58d3d0b7e2a537a993411c, 0x7985849f9dd8119, 0x0, 0x97f029beb074caf4db383ce1b6f43018, 0x676a9d25b186deaeeb154f6f81c3cac5, 0xe25b3d09a0ca15758eec5c35, 0x4eb2ac787bfa862b05c37a19, 0x485dc9be973d40ad, 0x0, 0xc544faf31ae71d76185ae1c9, 0xe7c7a3e02b520e65be0e955f, 0x56d97c994d146f8a, 0x0, 0xe1a61de4d41b08744b95b20a4e12fcb3, 0x153b6b6be0d5eaf38f83e1294ef38c98b, 0x57748c8a004a6262d9e306a3, 0x96a084f871c636d34425a103, 0xb3c2b8700cd7d920, 0x0, 0x4ad02dbf9a1e3ee40e1e3d8d, 0xf797030462c8333af23d3f54, 0x1dc280acb99e5f4c, 0x0, 0x26994a6057531b28435aaa960f280193, 0x30924dc9b5e85e844f4ee14d4bfe0e12, 0xfeea2dd70b8a91873d10df4b, 0xb8e2d33a659ef7fa87e3fa0, 0x74fc51cbe8e5400d, 0x0, 0xe4d3e3cf55a86291a7c5da22, 0xd3b103edfa5860bd1f94cdf8, 0x3480d7e452a5d2b5, 0x0, 0x935644fe1e5f8844579a502568d12dc6, 0x177896bfd1e087a003ea64e9eaecd32d3, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x34c12d0510448edd8a4f435e, limb1: 0x1c1b70597d3d6f0ffda68cdc, limb2: 0x8f60be7a69fb2da6, limb3: 0x0, }, y: u384 { limb0: 0x67b330ca24613a628c5f1d44, limb1: 0xa12378b8d8a57f7ee45cf035, limb2: 0x7f7102c7548d7593, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_10P() { let mut data = array![ 0xa, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0xaec889b9d8ce51c4a2c3586f, 0xa2b07874c333bfee9f78e13e, 0xc445de21be8d8709, 0x0, 0x7e47d1c2d19c21b2f6870259, 0xe701b40af42001c38bca00db, 0xd87ea1720d4dd3d6, 0x0, 0x5b1d6cc74985ce49a1f737fe, 0xb9127c572c3f091c031c249c, 0x1392711e1576aa6f, 0x0, 0xb71f95ea692ed186e06e4c37, 0x807276cd9cc59718bb11dbe9, 0x10756a25836d67ca, 0x0, 0xd34211b3520c83c5f9be99af, 0x8f19a28ceef67bbda102ffe7, 0x7ac2b92030d351cc, 0x0, 0x411bb5d0fbe844f025c7178c, 0xcf603787227b7ac499d6d1c4, 0x5f6b2479862eb2f8, 0x0, 0xce60303cfcb98726ff64a1e5, 0xa64534c614754b3527588d25, 0x44f75e245622181, 0x0, 0x8a703177da18d4ede707c057, 0x7d6c11e754ab6fbe73deea43, 0xdf9787168190a047, 0x0, 0x2e6585ab5f125a34fef37875, 0xb70e9f02ce7744197172a117, 0x60e305f9fe6f2298, 0x0, 0x712f72f3929408ff68af059d, 0x4f72cea12cd115dc1c8639f5, 0xc6d5ae1b897ffe77, 0x0, 0xfcf91f56bad0659142668837, 0xa15458b49bcdad6c870e3889, 0x81a1342e70b1b765, 0x0, 0x461d7579f9613d3168fc6220, 0x7626024a6195fe0eafcea08b, 0x32e91b268a032443, 0x0, 0xcdc7ae298071a741aafd4035, 0x9a9bdfbdb824dc1278457a10, 0x17fbec3713dfd145, 0x0, 0x9b85054533e9d24310265ee0, 0x51cbb79b2625c435ba43bbef, 0x1fd81fcb136c629b, 0x0, 0x96378a2e47ab50246a9cf131, 0x4d0f08867537268cf39eae04, 0x4eeb60396f3e5f52, 0x0, 0xa, 0xd3fbf47a7e5b1e7f9ca5499d004ae545, 0xbaf3897a3e70f16a55485822de1b372a, 0x101fbcccded733e8b421eaeb534097ca, 0x38c1962e9148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0x3, 0x38561918155956c9814da8c1, 0x4ee05f58a1e16b839f0d9c00, 0xecde93203b4a7dfa, 0x0, 0xa685cbd24295124d7e743db7, 0x839d0ebc27e44d043d77eded, 0xe795a8a4341deaa3, 0x0, 0xed0428b23446f2526c2e4e7b07209994, 0x10210ae4a0d0485cb56c075354424cf5d, 0xa3dad4276a73d4c09d6159d4, 0x993f51a3b23380f272860899, 0x32c55c9bd7a08a15, 0x0, 0xc5e4a047ae1c8e94b7d2caf4, 0xb641a3a56bdde831271d3274, 0x33595945536b7789, 0x0, 0xc0845253484d89c1d1ccaf50b5524f81, 0x559558f8096b66022bac83a15eb9ff6f, 0x6b1cb9b2433fb61e81654c3b, 0x67617c9e3a607fac036ceecb, 0x97c35ee2d0c73db6, 0x0, 0xf0c3a4705c96d01f668e05ce, 0xeafdbf139502919889b40454, 0xc935a5c99c11cf36, 0x0, 0x44922bc02cadce44e7b7886df54150df, 0x1c077ddb46086b3c48c0151e702cff2f6, 0x65677810a039bc3e3c9be37c, 0x7d16040d79afaf58b3f80fa9, 0xfae349c7861f6f48, 0x0, 0xd89bebc35496c77341e51852, 0x2358a145b3d17fa89be6dbdc, 0xd3b85a68d5dc2676, 0x0, 0xc9ed151811182720cf9615e71e9fa060, 0x142125c7f17a0f71398604210c95e5ca5, 0x4b3c7e7ccefc0fae7b0f55bb, 0xef7afabc6323803d011d8d2, 0x60a2c23d746b1a06, 0x0, 0xb25819a91f97473e0339cd04, 0xaf305d5c7986ca879648d39e, 0xda3801752ba46faa, 0x0, 0xae8d22acf2919234f64b2558ab7b67df, 0x11041f8236fcac05059b625657966610f, 0x4c3728ed346a68dbf7e146f7, 0x678f6cd8ef42911e63db5bec, 0x77f7f11c0623961b, 0x0, 0x685ae2d8682fb6e5bddbf735, 0x1f03b99ca6329f7dc3a47dd, 0x711f6d38f7342bbc, 0x0, 0x1f14954c7b5ac5b971b602c56df47bc3, 0x12d076b9e2d6f7ff90377d25582942bfe, 0x3b04be6e199cf2f9e01b8e25, 0xfcf54a6935861246f40ccf8c, 0xfbadcace1d51d441, 0x0, 0xd70f738575d4a0269184b8ff, 0x3b4408df2be178958c3bf10c, 0x79e7079bd76a7b55, 0x0, 0x6436caaee772af5fc76e60b7db77afc1, 0x1c3e3905b638753f3071cef680336e7fe, 0xfe871f11377ae9427e3685f9, 0x7e050d6b4465549c28c47dc0, 0xc4902f8601ad20c0, 0x0, 0xe79c221af2b5a795ce938be6, 0x97c17d2cd373c628e73940b, 0xe94b501243f485aa, 0x0, 0x16f8de87b088d889a9fe62c941cfad9b, 0x181d97eccb30bde04756f33bbfe09ac77, 0x34be9f4109fde722b0ad2953, 0x61c76a815bc4e8e49f2f6f22, 0x45c8af482d122938, 0x0, 0x23cef567487cef807c8f37df, 0xb06e7986c8691afa2c56be48, 0x2f6997e366662173, 0x0, 0x10c6c0d26e3816ea1b2e066d32578f8e, 0xe883f51850260b2857cb5d63a26adb1d, 0x642b3b250974accb2a19bddd, 0xab3e89d8cf48dc55485119e6, 0xc5f80116c5e9c74, 0x0, 0xff9bfb138c144d05684a114c, 0x7e7e1ae6a3570325390ed38e, 0x92eb23ab15e45e63, 0x0, 0xa318a477495afb754a1e314186443137, 0x1a9d9d5e84e930f6526918aa8ca162b82, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xfba2105cfbf4fb86b8691c25, limb1: 0x737afa206da896812a1683ed, limb2: 0x3770a73db013e250, limb3: 0x0, }, y: u384 { limb0: 0x5590076303a44e451ab3856b, limb1: 0xd5fcd660db51d063c730f5c7, limb2: 0x506410f9c703c100, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_11P() { let mut data = array![ 0xb, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0xaec889b9d8ce51c4a2c3586f, 0xa2b07874c333bfee9f78e13e, 0xc445de21be8d8709, 0x0, 0x7e47d1c2d19c21b2f6870259, 0xe701b40af42001c38bca00db, 0xd87ea1720d4dd3d6, 0x0, 0x5b1d6cc74985ce49a1f737fe, 0xb9127c572c3f091c031c249c, 0x1392711e1576aa6f, 0x0, 0xb71f95ea692ed186e06e4c37, 0x807276cd9cc59718bb11dbe9, 0x10756a25836d67ca, 0x0, 0xd34211b3520c83c5f9be99af, 0x8f19a28ceef67bbda102ffe7, 0x7ac2b92030d351cc, 0x0, 0x411bb5d0fbe844f025c7178c, 0xcf603787227b7ac499d6d1c4, 0x5f6b2479862eb2f8, 0x0, 0xce60303cfcb98726ff64a1e5, 0xa64534c614754b3527588d25, 0x44f75e245622181, 0x0, 0x8a703177da18d4ede707c057, 0x7d6c11e754ab6fbe73deea43, 0xdf9787168190a047, 0x0, 0x2e6585ab5f125a34fef37875, 0xb70e9f02ce7744197172a117, 0x60e305f9fe6f2298, 0x0, 0x712f72f3929408ff68af059d, 0x4f72cea12cd115dc1c8639f5, 0xc6d5ae1b897ffe77, 0x0, 0xfcf91f56bad0659142668837, 0xa15458b49bcdad6c870e3889, 0x81a1342e70b1b765, 0x0, 0x461d7579f9613d3168fc6220, 0x7626024a6195fe0eafcea08b, 0x32e91b268a032443, 0x0, 0xcdc7ae298071a741aafd4035, 0x9a9bdfbdb824dc1278457a10, 0x17fbec3713dfd145, 0x0, 0x9b85054533e9d24310265ee0, 0x51cbb79b2625c435ba43bbef, 0x1fd81fcb136c629b, 0x0, 0x96378a2e47ab50246a9cf131, 0x4d0f08867537268cf39eae04, 0x4eeb60396f3e5f52, 0x0, 0x4e9960d402494fb117251955, 0xc0fb055de656d6ac2ba4da86, 0x800a21e8619f448f, 0x0, 0x21ba9af739425b664464e3d5, 0xd09194888c2ffcf16e93e0c9, 0x5d4d3cd0684b6cd1, 0x0, 0xb, 0x101fbcccded733e8b421eaeb534097ca, 0x38c1962e9148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0xd67e55fd642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x37176e84d977e9933c49d76fcfc6e625, 0x3, 0xb16bff1ced538bfd53bae25e, 0xbf1402b7e25844a265c1bdd5, 0x1be24841a28b989f, 0x0, 0xf986f402c5573e161419f24a, 0x7b675d2f5f2da582d6fe8f9e, 0x6aeca6fa85a397dc, 0x0, 0xc0845253484d89c1d1ccaf50b5524f81, 0x559558f8096b66022bac83a15eb9ff6f, 0x962f32f58256def96811a9d0, 0xa1b9c86a62821a4cfcd4a227, 0xef591311df6d01e4, 0x0, 0x742d94ecec04d08af134a72f, 0xad0028269dacda27bef683c4, 0x298a3de72a4ed3cf, 0x0, 0x44922bc02cadce44e7b7886df54150df, 0x1c077ddb46086b3c48c0151e702cff2f6, 0x45a06c488f5dcafb092b1d04, 0x1da9b0f063b8d103454f7cc4, 0xd913f452d9dd6f57, 0x0, 0x75d6dd631f23b758508fcb4, 0xf21f94eae9d1c6ed2aa4fb67, 0xdf5004b53571e9a9, 0x0, 0xc9ed151811182720cf9615e71e9fa060, 0x142125c7f17a0f71398604210c95e5ca5, 0x8d9a40cc54f2cc7d02b7e0b0, 0xe36d1ca0c233cf2ec25c402f, 0x94f2e92234345839, 0x0, 0x7939e94d8e6282dd8964091f, 0x98530c37ba4b3964a3a0fe4a, 0x982d6fbcc9b50a64, 0x0, 0xae8d22acf2919234f64b2558ab7b67df, 0x11041f8236fcac05059b625657966610f, 0x21c3e96235c9016bf0a84114, 0x247ff7af02d28a262889b947, 0x92f35a496b19286d, 0x0, 0x343cd3d8bf84c15a702e7657, 0x5e021f090c2b6c54bb8bcf1f, 0x5d1e6f00fb3793c5, 0x0, 0x1f14954c7b5ac5b971b602c56df47bc3, 0x12d076b9e2d6f7ff90377d25582942bfe, 0x2b574bbd9c8f851c273ff965, 0x6e259626c2a5c8caa331135b, 0x36ae66488788bb25, 0x0, 0xb143e40a36ef2d4c7875e024, 0x62bbca04aa3439b4100d24c9, 0x49c3be30dc73a5fe, 0x0, 0x6436caaee772af5fc76e60b7db77afc1, 0x1c3e3905b638753f3071cef680336e7fe, 0xb50c01b147f62f5ced402fc7, 0x916dc3141db597cb65f49535, 0xfa26dd483341953, 0x0, 0x83482d67557d46be990aeb2b, 0x879cc943ac21722d332e0387, 0x53e3c2b4d5a19544, 0x0, 0x16f8de87b088d889a9fe62c941cfad9b, 0x181d97eccb30bde04756f33bbfe09ac77, 0x39a4c7a121736d93c8c46aca, 0xd75c5f684d85cbf35b9f803d, 0xa71f416ba3e8524f, 0x0, 0x3fb43e42616b1d7de570fd52, 0xe64815507843d1afb0823f58, 0xb0ed6357a48b8b89, 0x0, 0x10c6c0d26e3816ea1b2e066d32578f8e, 0xe883f51850260b2857cb5d63a26adb1d, 0xd9b0171c1f079d16eb88b0b5, 0xc10f56ec85cc7f859a09f8de, 0x215108f002c87662, 0x0, 0x5e4c522f974963e8bf756e19, 0xe603a1ddbea2d112fc889233, 0x5fc356df32962109, 0x0, 0xa318a477495afb754a1e314186443137, 0x1a9d9d5e84e930f6526918aa8ca162b82, 0x145a727889f0bb4d53d6fbaa, 0x4155f220ac0460cd7ed04829, 0xb3ed8c7049dc43dc, 0x0, 0x8a4850ae0cc7d3a0fc4a4a8e, 0x47478a0e45160288b6680b05, 0x10bdda9cc7016108, 0x0, 0x2785e73e00b487bf30548408ffb58c02, 0x15f510a537d9b81be6f4a2335fa207095, 0xff532f80c81fe274ac646064, 0x8c46882da4fde0295beab9e1, 0xc2b5cd8a7a93240a, 0x0, 0xc949597e8e67ebee593df861, 0xa4849c0210fd9206fdaffcfd, 0x510cde5a5da7c46e, 0x0, 0xe293dda213f46bf461aba1d96a9d193b, 0x15cb16111d99d7ae505af716e48e6b599, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xe702738c3be4c98312c6fd8, limb1: 0xdf289702da4292e2baf6d123, limb2: 0xd2e3d9fa85ae9ec9, limb3: 0x0, }, y: u384 { limb0: 0xb24620fd1d6468e74e756e09, limb1: 0xa92f0cfbb6159a6b7d73d3c8, limb2: 0xfdfb28f19d569756, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_12P() { let mut data = array![ 0xc, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x46ae31f6fc294ad0814552b6, 0x2d54cc811efaf988efb3de23, 0x2a2cc02b8f0c419f, 0x0, 0xaec889b9d8ce51c4a2c3586f, 0xa2b07874c333bfee9f78e13e, 0xc445de21be8d8709, 0x0, 0x7e47d1c2d19c21b2f6870259, 0xe701b40af42001c38bca00db, 0xd87ea1720d4dd3d6, 0x0, 0x5b1d6cc74985ce49a1f737fe, 0xb9127c572c3f091c031c249c, 0x1392711e1576aa6f, 0x0, 0xb71f95ea692ed186e06e4c37, 0x807276cd9cc59718bb11dbe9, 0x10756a25836d67ca, 0x0, 0xd34211b3520c83c5f9be99af, 0x8f19a28ceef67bbda102ffe7, 0x7ac2b92030d351cc, 0x0, 0x411bb5d0fbe844f025c7178c, 0xcf603787227b7ac499d6d1c4, 0x5f6b2479862eb2f8, 0x0, 0xce60303cfcb98726ff64a1e5, 0xa64534c614754b3527588d25, 0x44f75e245622181, 0x0, 0x8a703177da18d4ede707c057, 0x7d6c11e754ab6fbe73deea43, 0xdf9787168190a047, 0x0, 0x2e6585ab5f125a34fef37875, 0xb70e9f02ce7744197172a117, 0x60e305f9fe6f2298, 0x0, 0x712f72f3929408ff68af059d, 0x4f72cea12cd115dc1c8639f5, 0xc6d5ae1b897ffe77, 0x0, 0xfcf91f56bad0659142668837, 0xa15458b49bcdad6c870e3889, 0x81a1342e70b1b765, 0x0, 0x461d7579f9613d3168fc6220, 0x7626024a6195fe0eafcea08b, 0x32e91b268a032443, 0x0, 0xcdc7ae298071a741aafd4035, 0x9a9bdfbdb824dc1278457a10, 0x17fbec3713dfd145, 0x0, 0x9b85054533e9d24310265ee0, 0x51cbb79b2625c435ba43bbef, 0x1fd81fcb136c629b, 0x0, 0x96378a2e47ab50246a9cf131, 0x4d0f08867537268cf39eae04, 0x4eeb60396f3e5f52, 0x0, 0x4e9960d402494fb117251955, 0xc0fb055de656d6ac2ba4da86, 0x800a21e8619f448f, 0x0, 0x21ba9af739425b664464e3d5, 0xd09194888c2ffcf16e93e0c9, 0x5d4d3cd0684b6cd1, 0x0, 0x4bec631b62d40e5b8aaff33e, 0xf7161e0a086fb1c95bc84eab, 0xfbff400a905bf4cf, 0x0, 0x482ffa9e045ec6f1e1e09d6e, 0x9a75ce6f11a020bef0b9b3f3, 0x253b9af963b9e192, 0x0, 0xc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0xd67e55fd642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x37176e84d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x467437419466e4726b5f5241f323ca74, 0xa425799aa905d7507e1ea9c573581a81, 0xfb82860deabca8d0b341facdff0ac0f1, 0x3, 0xf21b3e6af6d840760fa8411f, 0xd677b055694872a38d273ef1, 0x150932895e8f8c82, 0x0, 0x45195680cc81c556f391cc4b, 0xdde61f43811514fa59ed06e9, 0x220cfb9298b8cc55, 0x0, 0x44922bc02cadce44e7b7886df54150df, 0x1c077ddb46086b3c48c0151e702cff2f6, 0x2b346d6b79e589393cf0d61b, 0x4f58aa4dd49fc3dd5924c7f9, 0x386d7047f06ea697, 0x0, 0x3a470a888b07a992eebf9389, 0x8324abb26382c12bce482ab1, 0xb384c6bec834d324, 0x0, 0xc9ed151811182720cf9615e71e9fa060, 0x142125c7f17a0f71398604210c95e5ca5, 0x9c891702b89da5331cb7832e, 0x2731f6bc2f1aa2eb186b25c5, 0x2ad90d0df0c3682c, 0x0, 0xcd1df42426c63336a3458fe5, 0x7c918ae249bb546477383a55, 0x44e172d8e00fd452, 0x0, 0xae8d22acf2919234f64b2558ab7b67df, 0x11041f8236fcac05059b625657966610f, 0xd6cf6a25a18ed80eb0e6190e, 0x3c774b8768bc771fab9fdcc9, 0x47c91895e8b1d94e, 0x0, 0x272762d65915cc5033c101ea, 0x99426a49b9b07e18aded6f42, 0xca92ae7e999ccfaa, 0x0, 0x1f14954c7b5ac5b971b602c56df47bc3, 0x12d076b9e2d6f7ff90377d25582942bfe, 0x394cc425f5996a29056252d1, 0xd2b3ec664a7880e8d35f183f, 0xc828b02c43406f58, 0x0, 0x804960c086f17cae9d5ad279, 0x484702a1d46ed78aefb3e507, 0x1e99ac387923772, 0x0, 0x6436caaee772af5fc76e60b7db77afc1, 0x1c3e3905b638753f3071cef680336e7fe, 0x26ce92552827bb2fa63cca66, 0xc39a63811359b427370b0575, 0xae807a141eaa26dc, 0x0, 0xc0c2b78a71d509508baf0f2a, 0x2feadccb72de72e9f5fc6138, 0xc0382fd27bb08ce3, 0x0, 0x16f8de87b088d889a9fe62c941cfad9b, 0x181d97eccb30bde04756f33bbfe09ac77, 0x78113c1d4dfdf1520f3f1999, 0x2c5b0f78ece4dbf13818b6da, 0x91423833a8a23044, 0x0, 0x4f72d597c449ae91c028fe43, 0x6254a79f46e2eba930ff0922, 0x2fe944a98818b85, 0x0, 0x10c6c0d26e3816ea1b2e066d32578f8e, 0xe883f51850260b2857cb5d63a26adb1d, 0x6623d54c69187cc05a7d25f1, 0x4f1c622a1f647d93565c3832, 0x6a79e7e30dd11556, 0x0, 0x1fce6face866ebb2c02113a5, 0xdeff94345f28459d5573a31b, 0xae91e80a1d94d7e5, 0x0, 0xa318a477495afb754a1e314186443137, 0x1a9d9d5e84e930f6526918aa8ca162b82, 0x8cf51eb38bcb71c8f648bcff, 0x4c19c480af80b7e6a658baa2, 0xcf2c5e5a5d2ebee5, 0x0, 0x19103765b836ea25211d48d7, 0xfe67a940dcd330efe84be2dd, 0x8d56f6b8b35dbce5, 0x0, 0x2785e73e00b487bf30548408ffb58c02, 0x15f510a537d9b81be6f4a2335fa207095, 0x8bfd5afc63995feebc71e165, 0xe7d8abd837751c2eb24eef3e, 0xee5889cb9dcfbaf5, 0x0, 0x1f5083d084d6f44e5bfbbb5b, 0x2b94b883ed3e33932b61c480, 0xe267eab32408be05, 0x0, 0xe293dda213f46bf461aba1d96a9d193b, 0x15cb16111d99d7ae505af716e48e6b599, 0x5c19035d92c3b9e269ca9231, 0x305af2b3721b71e18b9f971, 0x174d9aaf6ed44af2, 0x0, 0x7b91bd8b08dd4844dd8b2f3e, 0xe8174f87ddde9f6c71c644ff, 0x8b0c88aa96b2ff53, 0x0, 0x5747d2a86b06c3af37767b79685e955a, 0x12d5f64271c5145c58fdf6149840ae47, 0x93b81d705fbc02e172727cfd, 0x4de473fa4428b4c924d7bd53, 0x1939f32498b8d75d, 0x0, 0x8ab3d19f0f073043eb950bf9, 0xee1962e119ef85b4c508ad6d, 0x6808f2627e81135c, 0x0, 0xf49af9f8629ea294f624aa92983015e9, 0x1046b42b340cdb380acd6a9b3aecef690, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xce6a9b69daea1558dcbe14f1, limb1: 0x3d82daa514f325d29522e5e7, limb2: 0xc9833209611997e9, limb3: 0x0, }, y: u384 { limb0: 0x84af480eeea70b1a6120dc57, limb1: 0xc6df620bb03464672b4e6d28, limb2: 0x53ae491c8e1b5177, limb3: 0x0, }, }, ); } #[test] fn test_msm_SECP256K1_1P() { let mut data = array![ 0x1, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0x1, 0xeb1167b367a9c3787c65c1e582e2e662, 0xf7c1bd874da5e709d4713d60c8a70639, 0x2, 0xc20f5aa13afc3a2097ce088b, 0x50220928f8ca04bf313c1d7, 0x70743ffac9bb07f9, 0x0, 0xfa42792834ae5445fcaca832, 0x6796f84b7340adf44ed49d33, 0x62fd8a76eedcb778, 0x0, 0x100000000000000006d17da9dde38d3aa, 0x100000000000000008e0801a3d001f325, 0x87ea3597eb650e8, 0xe42d003a1f0e89bd, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xc20f5aa13afc3a2097ce088b, limb1: 0x50220928f8ca04bf313c1d7, limb2: 0x70743ffac9bb07f9, limb3: 0x0, }, y: u384 { limb0: 0xfa42792834ae5445fcaca832, limb1: 0x6796f84b7340adf44ed49d33, limb2: 0x62fd8a76eedcb778, limb3: 0x0, }, }, ); } #[test] fn test_msm_SECP256K1_2P() { let mut data = array![ 0x2, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2, 0xe443df789558867f5ba91faf7a024204, 0x23a7711a8133287637ebdcd9e87a1613, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0x2, 0x889ef9db2dcca93176722661, 0x30f90e4e5ea1e991ccf9dd07, 0xe840f7e9e3d96c65, 0x0, 0x6b95984b663cf4ffcd07d9c7, 0x952dac88c6a40f73979028d6, 0xc5e5fd89e078d389, 0x0, 0x4bab076cac43472e, 0x896dcc1031d19f2d, 0x100000000000000006f45630d920758e7, 0x13bfcc5670fee7eb, 0xef8bfd5fa527215c20165899, 0x7e263c9c3df47bc32eb4890b, 0x9a3ee712d779bbf1, 0x0, 0x7d54e9e980c0873b3755c17e, 0x22a963dcae22fec5cacd5431, 0x817adf30a086d140, 0x0, 0x40c3f72fa123bad6, 0x461e3a87e8955f53, 0x53ec0e0286c9f6ad, 0x1000000000000000074832ec5bb09d4f6, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x97ad9ae598203a75c13a895, limb1: 0xed9fb4bee5b2f54ca5cffb42, limb2: 0x284782b62d08871c, limb3: 0x0, }, y: u384 { limb0: 0xfb082c65dab4069694f90f18, limb1: 0xb12d25f5fb5e746c12686571, limb2: 0x7d0eb16046d10c7e, limb3: 0x0, }, }, ); } #[test] fn test_msm_SECP256K1_3P() { let mut data = array![ 0x3, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x155b35991489db2fdf4de620, 0xf24ce461346a182d67eeccf0, 0xb4122bb4b37cc7d5, 0x0, 0x3, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0xb4862b21fb97d43588561712e8e5216a, 0x259f4329e6f4590b9a164106cf6a659e, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x5487ce1eaf19922ad9b8a714e61a441c, 0x2, 0xa9ca5eaf239f624e5f32d52c, 0xe8781b10ffc1e9d6b65fcf8e, 0xa99e25b10243bc1b, 0x0, 0x48c471108b3d056fc7043965, 0xa13fee6c99e702aaa40e511e, 0x3dabf3e8f614a3e, 0x0, 0x40c3f72fa123bad6, 0x461e3a87e8955f53, 0x53ec0e0286c9f6ad, 0x1000000000000000074832ec5bb09d4f6, 0x280f3fa841c7bf6d615bcb53, 0x276795ef2ecbbe7e2012f4cd, 0x81043aa56aa2d4a, 0x0, 0x6ed67d338a2a9b542f54ec66, 0x6b2b2546eb3b1938441381f5, 0x4dbf81ca0dfc9cdf, 0x0, 0x100000000000000008a16fd00888d3c49, 0x10000000000000000701b1de1a64611a5, 0x7bb19b6adc4d85f4, 0x2fd5ac7d0446c0d3, 0x8a41f2a7e7ad4089990a1bcd, 0xec1d1ff466f58331529b0acd, 0x5649d8d001330363, 0x0, 0xfc543db1835e8a78f0994291, 0x43c390ccae632a174f607c8a, 0x813ee8122c9dfa7b, 0x0, 0x7f7b9792bad13df8, 0xf56d08780b0b13f5, 0x535b7499f702bf5d, 0xce3ee818c4660dc, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x793f03cb81255db0817da454, limb1: 0x5ed27cf7207443f37bfeee3c, limb2: 0x42943c6416752a12, limb3: 0x0, }, y: u384 { limb0: 0xf2d25838b8b95a3caaef5ce4, limb1: 0xce58bfff9d25e997305603f3, limb2: 0x5d776495b03d0b6c, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_4P() { let mut data = array![ 0x4, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x155b35991489db2fdf4de620, 0xf24ce461346a182d67eeccf0, 0xb4122bb4b37cc7d5, 0x0, 0x12815740835b12f70b96c66f, 0xbfa76a8b80aec9f2e31c40cc, 0xcd8a26d17d33c7c1, 0x0, 0x9a8f496f09402b8fd6beb89b, 0x28e48918dad2123d7f202bef, 0xcdd11b6ffb3f8614, 0x0, 0x4, 0xb4862b21fb97d43588561712e8e5216a, 0x259f4329e6f4590b9a164106cf6a659e, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x5487ce1eaf19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0xa3f2c9bf9c6316b950f244556f25e2a2, 0x8d723104f77383c13458a748e9bb17bc, 0x85776e9add84f39e71545a137a1d5006, 0x2, 0x7c5bbcc9341cd7fab6ad4876, 0x3c6a25a05d905654bd812731, 0xf473dbb400e14df5, 0x0, 0x5f748642ae1443931d093af4, 0xddca2248291c024312127d87, 0xbbb00af8a51cc511, 0x0, 0x100000000000000008a16fd00888d3c49, 0x10000000000000000701b1de1a64611a5, 0x7bb19b6adc4d85f4, 0x2fd5ac7d0446c0d3, 0xd548dda6e1f541d784d4c228, 0x3bc7fbd282f26a90865b5b09, 0x3b648ed118007c3, 0x0, 0x5a28118c93a1de7664b1d6ba, 0x919d9a3d5dfce3b255589541, 0x883bab5b394b16cf, 0x0, 0x7f7b9792bad13df8, 0xf56d08780b0b13f5, 0x535b7499f702bf5d, 0xce3ee818c4660dc, 0xbc08950bb2cf7b7d9eeda922, 0xb2b86106457dfc8ec9cffb7e, 0xe835a6fda5354661, 0x0, 0xdca7ee443dbdfb5bab9335d5, 0x1e062663e3974b0f7b798cb4, 0x37d153aaefa189f2, 0x0, 0x5aba5c5df852e79b, 0x10000000000000000a37bff5d07f4f628, 0x399451b7748ce4b8, 0x1000000000000000006a4728421f58565, 0xa46be4f636be4779570df4e8, 0x7380a6e3dc3aa91b3650ca10, 0x3ef088ac9bc45c0e, 0x0, 0xce7710a9c0715f82fea0f76a, 0xf51283a23eaaaca518d43319, 0x5069f990b18886d0, 0x0, 0xa5ba5bf9830a178c, 0xf8d715433d751f7e, 0x1000000000000000001b585fab6a98780, 0x100000000000000001ee3ebda652c4c63, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xafc19dabd2b0bef1f47a78e4, limb1: 0x64c8cfa2f6ce21bd45380a70, limb2: 0xd6ec71e82872d984, limb3: 0x0, }, y: u384 { limb0: 0x1afed7037f7e7362dceb03ec, limb1: 0x149013c6ed7333d6e4ded96a, limb2: 0xaf1489c5a6180b55, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_10P() { let mut data = array![ 0xa, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x155b35991489db2fdf4de620, 0xf24ce461346a182d67eeccf0, 0xb4122bb4b37cc7d5, 0x0, 0x12815740835b12f70b96c66f, 0xbfa76a8b80aec9f2e31c40cc, 0xcd8a26d17d33c7c1, 0x0, 0x9a8f496f09402b8fd6beb89b, 0x28e48918dad2123d7f202bef, 0xcdd11b6ffb3f8614, 0x0, 0xb5076be8537cff2a42c6db68, 0x1066d40cbd01a3752e4e069c, 0x123ec2fd302cb0f9, 0x0, 0xc85f5e5efdf415f8081bf53f, 0xadc5010e9d9ac6c64000d33d, 0xf81314011d8852e4, 0x0, 0xd5915098d3d2001310b0b935, 0x88bb4507ebf1be82cfba2397, 0x8a463f1c00ce885f, 0x0, 0x414858f8a83f9d4498890137, 0xa09c4658c47ace74c42cdb60, 0x8aaf300ff3ab7d98, 0x0, 0x1772eb803ddc8a82e23b1c05, 0xc26baeb89b03fd69eb64b337, 0x4ea7131b2d873a45, 0x0, 0xc9d16330db15efd90235eed9, 0x1b586ef360673d36baa16189, 0xee652d2b848ad111, 0x0, 0x68f9e7942638253f3b596f1f, 0xb37e6153d9accd97a344f384, 0xda48eae9ff614551, 0x0, 0xc58be8ed857035b34f51c620, 0x3b14ed53116cb7c1db000006, 0x7dfa292fe99b77dd, 0x0, 0xf7f7bd2513c1b31de932bbd2, 0x627e2fa74b7ac891f7d555c7, 0x7f8a094f818e7192, 0x0, 0x9b47b9326b668e62071faf18, 0xe21058cb6937afa89be6931a, 0x21a4bfb4cce2ac8c, 0x0, 0xaf4ad4d7d582b10b14c97e6c, 0xadf808c85e766e997e470fd0, 0x2714571e587ce46d, 0x0, 0x86a7815dad7e8a53b19fee2, 0x1922fc1efcc51e68146ffa1b, 0x9e19b7c1f886488e, 0x0, 0xa, 0xd3fbf47a7e5b1e7f9ca5499d004ae545, 0xbaf3897a3e70f16a55485822de1b372a, 0x101fbcccded733e8b421eaeb534097ca, 0x38c1962e9148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0x2, 0x278357bca21047e53cebcc8a, 0x5e183af032bbb7d3addb0053, 0x69f0f0d699ad0da, 0x0, 0x4f4baec4857a9e113c4bc046, 0x59934dd81f724602c55be112, 0x8ce0ab262b3c3676, 0x0, 0x2ef5cbfbef5479e9, 0x6fffb6b3d9f3ca00, 0xf99949f846de0180, 0x19226f35ed7d16dd, 0xb153c64d6f19ccd0278c6b94, 0x398a04c551fc8f74aa610c1, 0x2d39d1e12f83b407, 0x0, 0x8feed9f3a486593099594eab, 0x2571bc5e1f54fbed340811bf, 0xbbd2a19c5275b47c, 0x0, 0x8950a7e57cb188c3, 0x915677115b4cd35f, 0x10000000000000000adff605ec8f8e9b5, 0x10000000000000000ebfc6d2272e97ea1, 0x4caef24e507f272f30b7c823, 0x5273dc9feb3629a58072cedb, 0x2854b0b223aa71f0, 0x0, 0xac66b42ece626c4bf206c037, 0xc8b1c6f40a2edf407ce41397, 0x7c13db0a671e8662, 0x0, 0xa5060dbc57d602fe, 0x6914b48dc0c5534, 0x1b984728b0823ac8, 0x10000000000000000040e1ff5866bad1f, 0xc0ea96b4755baeb8090366aa, 0xcbfcbba1c8e0c3aa488fe399, 0xb1f7eea21e3d2ebe, 0x0, 0x769b003ec5b35afb7a3a9dbb, 0x2a28c3b33652ef6083180502, 0xb8a171b80bdab536, 0x0, 0x100000000000000007cbe66bb133fe6dc, 0x10000000000000000f0156c908c9d979c, 0x6b7c419ad9ed10d3, 0x1007811bd8c66050, 0x196c84114c4e6fd84943ae10, 0xb2b1bfb6e4a2d665b61a30e8, 0x3f7696cdb3ac6c, 0x0, 0x532d5b9de002db8f9775590d, 0x113ca5d5d68dbb4ad52542cb, 0xd4ebd6d9511abbd8, 0x0, 0x100000000000000001ee58c7660c5446b, 0x6ec3e8f177762e53, 0x100000000000000004538bd9c129bed52, 0x10000000000000000680a1770588f346e, 0x7d64eea8c9bb0b269ceb0809, 0x35432fa6ed8233fa1a176ea9, 0x4bb75b24119f877, 0x0, 0x68c57d7b2100616b5d4f104e, 0x8f4d438beb46139b440e571a, 0x3e63373ef063d4df, 0x0, 0x31b70045caadb0df, 0x3c110d9c03771d4f, 0x10000000000000000d3c49e4016b7ecb4, 0x10000000000000000cc890a6969b1a6e8, 0x2b695a4e6347bbe52bec6d29, 0xdd7ea9c6e862c5502f09e620, 0x94eed93be116d060, 0x0, 0xdbc07e9625599f80c1d400b, 0x33ba3da84dfdc5a2156437fc, 0x5baa7e2b8dd19cf3, 0x0, 0x22c35f43afc49a04, 0x267ff348a27461d3, 0x4a5f5d7ebb83d89c, 0x100000000000000002481d409cb1131a6, 0x25d13d57845635a3e479c501, 0x4bf3cea4d7858ac08ea61048, 0xeb01baa639087890, 0x0, 0xbf474987bdb67ad514ce70d, 0x25fa6f5fd0491ecf3c292ad7, 0xc7fdc6797752a36f, 0x0, 0x7c6ad3604c315150, 0x100000000000000002bc61778337cab95, 0xa8c3d96ce6c35e35, 0x79d7ca1b47402407, 0xc67a7a0c9df3fdf85ec5e7bb, 0x5670672aadc54cf37a60ad0f, 0xa123dd3cd9abff2, 0x0, 0x7df5d7f0d76e984c5f7c7d1b, 0x28ea2c9960be29367b03d650, 0x217ad558610431f, 0x0, 0x4dcbb5eb0dd68cef, 0x85c36b384754ae7e, 0x100000000000000006cb2ed250bb203bb, 0x100000000000000004be1fd4931e473e2, 0x5d40472f64481ec66b6dfdcb, 0xd9d5a457d4f31dcc2466d69c, 0x449dc00f6eae442, 0x0, 0x6c92237c0eb59cbc2c25069c, 0x11d28a7835aabe323b14a8c6, 0x921e2140e6ae64cd, 0x0, 0x1000000000000000065147afbdc695a04, 0x10000000000000000018d0e419fe453c3, 0x1000000000000000032ded75d2eb0eb80, 0x10000000000000000ee7c926d371453c4, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1c835913f9cca4833f4dee66, limb1: 0x192924721b46c95f86539366, limb2: 0xb6324fc7eea725e5, limb3: 0x0, }, y: u384 { limb0: 0x1655ccd2f516c24c8b23cd23, limb1: 0x5a78708d282fbf676e9eafa4, limb2: 0x8f71e12b03a69c94, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_11P() { let mut data = array![ 0xb, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x155b35991489db2fdf4de620, 0xf24ce461346a182d67eeccf0, 0xb4122bb4b37cc7d5, 0x0, 0x12815740835b12f70b96c66f, 0xbfa76a8b80aec9f2e31c40cc, 0xcd8a26d17d33c7c1, 0x0, 0x9a8f496f09402b8fd6beb89b, 0x28e48918dad2123d7f202bef, 0xcdd11b6ffb3f8614, 0x0, 0xb5076be8537cff2a42c6db68, 0x1066d40cbd01a3752e4e069c, 0x123ec2fd302cb0f9, 0x0, 0xc85f5e5efdf415f8081bf53f, 0xadc5010e9d9ac6c64000d33d, 0xf81314011d8852e4, 0x0, 0xd5915098d3d2001310b0b935, 0x88bb4507ebf1be82cfba2397, 0x8a463f1c00ce885f, 0x0, 0x414858f8a83f9d4498890137, 0xa09c4658c47ace74c42cdb60, 0x8aaf300ff3ab7d98, 0x0, 0x1772eb803ddc8a82e23b1c05, 0xc26baeb89b03fd69eb64b337, 0x4ea7131b2d873a45, 0x0, 0xc9d16330db15efd90235eed9, 0x1b586ef360673d36baa16189, 0xee652d2b848ad111, 0x0, 0x68f9e7942638253f3b596f1f, 0xb37e6153d9accd97a344f384, 0xda48eae9ff614551, 0x0, 0xc58be8ed857035b34f51c620, 0x3b14ed53116cb7c1db000006, 0x7dfa292fe99b77dd, 0x0, 0xf7f7bd2513c1b31de932bbd2, 0x627e2fa74b7ac891f7d555c7, 0x7f8a094f818e7192, 0x0, 0x9b47b9326b668e62071faf18, 0xe21058cb6937afa89be6931a, 0x21a4bfb4cce2ac8c, 0x0, 0xaf4ad4d7d582b10b14c97e6c, 0xadf808c85e766e997e470fd0, 0x2714571e587ce46d, 0x0, 0x86a7815dad7e8a53b19fee2, 0x1922fc1efcc51e68146ffa1b, 0x9e19b7c1f886488e, 0x0, 0x17bc74c409191a2b2249d987, 0xf4fe5f79db38f3064f7d093e, 0x3536ce04295e2a42, 0x0, 0xb1d36a10f008c1c24de1ad7d, 0xa4f2190c71ee5e0ff07c48f8, 0x21c1a2d4cfff3233, 0x0, 0xb, 0x101fbcccded733e8b421eaeb534097ca, 0x38c1962e9148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0xd67e55fd642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x37176e84d977e9933c49d76fcfc6e625, 0x2, 0x7a385b48241ff9b7472584bc, 0xfb86d85d87b00caed733ad64, 0xa1b750a9ad42265e, 0x0, 0x3c91608638f07e6b127effa, 0xbeb39c70848314492f0b1e9c, 0xba02c3181f197560, 0x0, 0x8950a7e57cb188c3, 0x915677115b4cd35f, 0x10000000000000000adff605ec8f8e9b5, 0x10000000000000000ebfc6d2272e97ea1, 0x17404de3e819f065de7c1017, 0x536d661a4644833c20a0cb4, 0x1f70dd88b20f7871, 0x0, 0x1aaa9311df61995c80ac577e, 0xa164780ea8788997ea2c423f, 0x83592576e08cd1fc, 0x0, 0xa5060dbc57d602fe, 0x6914b48dc0c5534, 0x1b984728b0823ac8, 0x10000000000000000040e1ff5866bad1f, 0x20ff56624796b65fd048677d, 0xe383e9098b0d38b210aecacc, 0xc935268d99a6ed4f, 0x0, 0xa4c981a051c154841b31dd75, 0x13a468f6a24a22757a8a9380, 0x3d65cc664e17a287, 0x0, 0x100000000000000007cbe66bb133fe6dc, 0x10000000000000000f0156c908c9d979c, 0x6b7c419ad9ed10d3, 0x1007811bd8c66050, 0x72ce4e4dc43d1db4a97b15eb, 0x9ac63f1462d8befc6ff716f2, 0xdd1b010de89e6bc9, 0x0, 0xc040c8c28bb16bed1cb5c089, 0xdb44fcda4787ab558fea8dd4, 0xd22d7176551ddc90, 0x0, 0x100000000000000001ee58c7660c5446b, 0x6ec3e8f177762e53, 0x100000000000000004538bd9c129bed52, 0x10000000000000000680a1770588f346e, 0xd7ed39d04214f124fb9a5454, 0x86156f125d3f2fd0836c41f4, 0x5b9651563d384ca0, 0x0, 0x1b663c9b6d949019c972b35f, 0x57c5020ee6fa7595d7ff9733, 0x34a8daa071411071, 0x0, 0x31b70045caadb0df, 0x3c110d9c03771d4f, 0x10000000000000000d3c49e4016b7ecb4, 0x10000000000000000cc890a6969b1a6e8, 0xfd20e510eb06b6b6cd26caa1, 0x4ed7a07b13deb87f778930b1, 0xf32b6d3cca1243b3, 0x0, 0x3cc0c83359b0da6a89b90f6f, 0xcc2ad62f07d5162679f1aead, 0xfab1a759721ba470, 0x0, 0x22c35f43afc49a04, 0x267ff348a27461d3, 0x4a5f5d7ebb83d89c, 0x100000000000000002481d409cb1131a6, 0x7ab94096eb99e777f21f264a, 0x2833b6cb1e9b57aca3255927, 0xe9577cffafa96848, 0x0, 0x211e8205578e14223b57d0e, 0x7524d5e57dfb8062ee504b92, 0x699257546ab9c7fc, 0x0, 0x7c6ad3604c315150, 0x100000000000000002bc61778337cab95, 0xa8c3d96ce6c35e35, 0x79d7ca1b47402407, 0xaa1d36523b9bbf173e28862b, 0x5cef005c976b645423a14da0, 0x5457f1479f27d0c4, 0x0, 0x6e15d05091cef49e6e490159, 0xebc02df9a0a4608fe67588c1, 0x23eaba74cbb63d26, 0x0, 0x4dcbb5eb0dd68cef, 0x85c36b384754ae7e, 0x100000000000000006cb2ed250bb203bb, 0x100000000000000004be1fd4931e473e2, 0x910d0a96046e92b7cd582798, 0xbff23854f39adfd43e26c5d4, 0xb51e917d6c662c76, 0x0, 0x292829fd70bf0df94c146d72, 0xdca27ae811d3ebc462421967, 0x1b2a813516fdba2c, 0x0, 0x1000000000000000065147afbdc695a04, 0x10000000000000000018d0e419fe453c3, 0x1000000000000000032ded75d2eb0eb80, 0x10000000000000000ee7c926d371453c4, 0xe5fe5d19f302b11f287cc8be, 0x247647c30315ec0eb6056189, 0x9de7876737227ed5, 0x0, 0xf98723a6e18a798271d5b545, 0x58f73113c3451ed86535f3f2, 0x7c4449246418862d, 0x0, 0x100000000000000000139803cda63f3ba, 0x1000000000000000016b7cf2653dc74a8, 0x1089abd09e19fd5df, 0xc69eeeb967755694, 0xfdaa8c8434c1fdf1f6736acd, 0xbb1563781b62fc9b97ec831c, 0x4a33d42ad138f3ae, 0x0, 0x61cfb29de0788d394e459f95, 0x4c2cf12dc88f92c32a6186ae, 0xa44f474e566f0d73, 0x0, 0x4f62e61d803963a6, 0x6f08b65992670489, 0x67cea05dbb9a909d, 0x96fb2bd0b03403bc, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x64fc5a7a1dbb0ded5877d244, limb1: 0x690efd6ba8db4b9093e04859, limb2: 0x4a95e2ad2036bb89, limb3: 0x0, }, y: u384 { limb0: 0x787161946cccf45a982322c8, limb1: 0xfb559d2c2a26b632cf7c2894, limb2: 0x4ed9af33445b7a3f, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_12P() { let mut data = array![ 0xc, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x2965eeb3ec1fe786a6abe874, 0x33e2545f82bb6add02788b8e, 0xf586bc0db335d7b8, 0x0, 0x155b35991489db2fdf4de620, 0xf24ce461346a182d67eeccf0, 0xb4122bb4b37cc7d5, 0x0, 0x12815740835b12f70b96c66f, 0xbfa76a8b80aec9f2e31c40cc, 0xcd8a26d17d33c7c1, 0x0, 0x9a8f496f09402b8fd6beb89b, 0x28e48918dad2123d7f202bef, 0xcdd11b6ffb3f8614, 0x0, 0xb5076be8537cff2a42c6db68, 0x1066d40cbd01a3752e4e069c, 0x123ec2fd302cb0f9, 0x0, 0xc85f5e5efdf415f8081bf53f, 0xadc5010e9d9ac6c64000d33d, 0xf81314011d8852e4, 0x0, 0xd5915098d3d2001310b0b935, 0x88bb4507ebf1be82cfba2397, 0x8a463f1c00ce885f, 0x0, 0x414858f8a83f9d4498890137, 0xa09c4658c47ace74c42cdb60, 0x8aaf300ff3ab7d98, 0x0, 0x1772eb803ddc8a82e23b1c05, 0xc26baeb89b03fd69eb64b337, 0x4ea7131b2d873a45, 0x0, 0xc9d16330db15efd90235eed9, 0x1b586ef360673d36baa16189, 0xee652d2b848ad111, 0x0, 0x68f9e7942638253f3b596f1f, 0xb37e6153d9accd97a344f384, 0xda48eae9ff614551, 0x0, 0xc58be8ed857035b34f51c620, 0x3b14ed53116cb7c1db000006, 0x7dfa292fe99b77dd, 0x0, 0xf7f7bd2513c1b31de932bbd2, 0x627e2fa74b7ac891f7d555c7, 0x7f8a094f818e7192, 0x0, 0x9b47b9326b668e62071faf18, 0xe21058cb6937afa89be6931a, 0x21a4bfb4cce2ac8c, 0x0, 0xaf4ad4d7d582b10b14c97e6c, 0xadf808c85e766e997e470fd0, 0x2714571e587ce46d, 0x0, 0x86a7815dad7e8a53b19fee2, 0x1922fc1efcc51e68146ffa1b, 0x9e19b7c1f886488e, 0x0, 0x17bc74c409191a2b2249d987, 0xf4fe5f79db38f3064f7d093e, 0x3536ce04295e2a42, 0x0, 0xb1d36a10f008c1c24de1ad7d, 0xa4f2190c71ee5e0ff07c48f8, 0x21c1a2d4cfff3233, 0x0, 0xef493bf7016f192140ec0c20, 0x489bc5a24a83819834b3c08c, 0xcccdd6728670ed1e, 0x0, 0xb2d8f23e9b244453602fae5a, 0x76fafc92aa2ea44429a3050e, 0xc6c6fb7c62dc6c2f, 0x0, 0xc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x1759edc372ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0x7d41e602eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x552f233a8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x8c1745a79a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x5129fb7c6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x870e15c2fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0xadc0da7a16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x148b2758d7ab792809e469e6ec62b2c8, 0xd450fe4aec4f217bb306d1a8e5eeac76, 0xd67e55fd642bfa42aef9c00b8a64c1b9, 0x85940927468ff53d864a7a50b48d73f1, 0x37176e84d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x467437419466e4726b5f5241f323ca74, 0xa425799aa905d7507e1ea9c573581a81, 0xfb82860deabca8d0b341facdff0ac0f1, 0x2, 0xa87e6d457192ad65d259e791, 0x9228287912a17822cfae6f8f, 0x622e90ac5ea25d59, 0x0, 0xef651884d008a32a2d116a87, 0xbdc4cdc9a1445b7005e4b44c, 0xdf1337bf8228bb28, 0x0, 0xa5060dbc57d602fe, 0x6914b48dc0c5534, 0x1b984728b0823ac8, 0x10000000000000000040e1ff5866bad1f, 0x48ff078b363f5d94cc9f63eb, 0x115c8cf2a38d0da440ebcbae, 0x1b816a5e72b58557, 0x0, 0xfb6369ff14a7b85e6d35f7bf, 0x4e00e50aca1aa90a598bd7b3, 0x8e70e3f336057410, 0x0, 0x100000000000000007cbe66bb133fe6dc, 0x10000000000000000f0156c908c9d979c, 0x6b7c419ad9ed10d3, 0x1007811bd8c66050, 0x8780bf2048f368173bec0c07, 0x5be44a71954e17bc36eccfd5, 0x4236fb0e86bcdf32, 0x0, 0x8ec2eb1532b2b96c14bebef9, 0x7b980c967373d71a38ebf92, 0xb4336cf34bb238f5, 0x0, 0x100000000000000001ee58c7660c5446b, 0x6ec3e8f177762e53, 0x100000000000000004538bd9c129bed52, 0x10000000000000000680a1770588f346e, 0x2b4f07edf389acd027af1e2b, 0xab8850651076565399b13fb, 0x501f99d468b51a7e, 0x0, 0x8d3259be568e4af9d34e488a, 0x11366602fb75ddb2a230c632, 0x2eb403dd3d7fa0e8, 0x0, 0x31b70045caadb0df, 0x3c110d9c03771d4f, 0x10000000000000000d3c49e4016b7ecb4, 0x10000000000000000cc890a6969b1a6e8, 0xf1d15e674b76c9d0cb85672c, 0x2e8098be6d52b92e20c98bab, 0x8acdee9ae1736d12, 0x0, 0x24f1249583774bb75801caa3, 0xaead17e1dc834bd1a624ac48, 0x6a22bf5e98d9d9b7, 0x0, 0x22c35f43afc49a04, 0x267ff348a27461d3, 0x4a5f5d7ebb83d89c, 0x100000000000000002481d409cb1131a6, 0x3494a03c71f4399881fd8880, 0x6ac1b4b6ca039c3d1286e70e, 0xf2d9a056ea050a57, 0x0, 0xeaf37f80878445372361b216, 0xd41e8bc2aadf12bbc38751ef, 0xa79a8a4e997661e5, 0x0, 0x7c6ad3604c315150, 0x100000000000000002bc61778337cab95, 0xa8c3d96ce6c35e35, 0x79d7ca1b47402407, 0x6b284c5645d14cd1e45ce41d, 0xef7365195e7be14a08d63f9, 0x79ebfed96dcb4d8c, 0x0, 0xa32f8ed8fc4e2819dbf5d354, 0xbe62aa24eb445342493fb1c4, 0xdcc7ad508612f5f4, 0x0, 0x4dcbb5eb0dd68cef, 0x85c36b384754ae7e, 0x100000000000000006cb2ed250bb203bb, 0x100000000000000004be1fd4931e473e2, 0x13b1bbb13f7da105749db0c7, 0x65d1c3c7fbdeb2befeb39fec, 0x24e9141cf844f065, 0x0, 0xfbb506c8ebd4fc51735b3359, 0x6319c6fb9d75f3f8d0fb8575, 0xc49721294a562789, 0x0, 0x1000000000000000065147afbdc695a04, 0x10000000000000000018d0e419fe453c3, 0x1000000000000000032ded75d2eb0eb80, 0x10000000000000000ee7c926d371453c4, 0x93c576094dc85b72f72c8832, 0x654b95f3c73106a0d4381f75, 0xd731fce177c83fd9, 0x0, 0xabbb1b3a35e3d538325af014, 0x259217577cc285a6b83953ee, 0x6383caf5d18c3339, 0x0, 0x100000000000000000139803cda63f3ba, 0x1000000000000000016b7cf2653dc74a8, 0x1089abd09e19fd5df, 0xc69eeeb967755694, 0xfb261e5abbce9c6f9a27475e, 0x60775102ab55d73e343fc464, 0x92ed6dd8fd0f867a, 0x0, 0xf5668dbab0802c48eca685fb, 0xe0ee5cbcf3dda9b624126e28, 0xd133f8ecb79a5748, 0x0, 0x4f62e61d803963a6, 0x6f08b65992670489, 0x67cea05dbb9a909d, 0x96fb2bd0b03403bc, 0xdb5b96b385bbefcb8a8381ba, 0x356746189fa0ba9f09af67fb, 0xb0aa6be9137e6b04, 0x0, 0x504768e8026a92690411fdf1, 0x8f2862bfadfa61b926a651c7, 0xa2b129ae94ecfbc0, 0x0, 0x903c783ffbbcfae, 0x10000000000000000a9647c65c4885765, 0x100000000000000004b4be4ce034de996, 0x8fc19cd46a492745, 0x278a81bdcc0f4f0f1b17c004, 0xf44d7e6bc07af6f2ee512475, 0x999ae67b5d65554a, 0x0, 0x6f57b1bfa3ea31cc6d8812f7, 0x709574ee1724876336af416d, 0x6b54f96429ec82f6, 0x0, 0x984e110d1ee38dcc, 0x1000000000000000004d4f2a3b925c2b8, 0x1000000000000000008b29d4fa5dec6e5, 0x100000000000000004e45715b78d9bfec, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x37558e45b8041762de768836, limb1: 0x5d514037c232b89fb7a06905, limb2: 0x2515485638a3a199, limb3: 0x0, }, y: u384 { limb0: 0xb85967bc1c9cde890f6a236f, limb1: 0xeece653858fb74a34a817724, limb2: 0x71995703660dd489, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_1P() { let mut data = array![ 0x1, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x1, 0xb4862b21fb97d43588561712e8e5216a, 0x4b3e865e6f4590b9a164106cf6a659e, 0x4, 0x62c2b89a3152e22243cf864d, 0xaf83913cf31609fd7b4f9a32, 0x6da9a48b077c3954, 0x0, 0xa54703c64365ab4373eae904, 0x87e47f46101c003371e14338, 0x462e50d88b5b5c17, 0x0, 0x21ef407bea1953254c1bc318a0af2527, 0x1c147c0993c84eed5f426b94b3350045, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x62c2b89a3152e22243cf864d, limb1: 0xaf83913cf31609fd7b4f9a32, limb2: 0x6da9a48b077c3954, limb3: 0x0, }, y: u384 { limb0: 0xa54703c64365ab4373eae904, limb1: 0x87e47f46101c003371e14338, limb2: 0x462e50d88b5b5c17, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_2P() { let mut data = array![ 0x2, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0x2, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0xa90f9c3af19922ad9b8a714e61a441c, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x2fc154703983ca8ea7e9d498c778ea6, 0x4, 0xcd7471596402adb99c204f6a, 0x71072cc6a799ca5492c35787, 0xaaecc4b08ca80c, 0x0, 0x9df62dff1b19647a74925491, 0xcff3a8ebb8f88bfdab94c62, 0x7561a9c9a4e6450a, 0x0, 0x211c4f690d00cb3af0b34c381ddf6429, 0x10dbbf233e0f266b14c85329c2440c426, 0x20b84e815be93309f3490609, 0xcddf2646d9499c09fa01ac80, 0x47a3d45b5433479c, 0x0, 0x257b7612e4301ed9448341a6, 0x4f3236c077377add9253d652, 0x3b0d15e6632e50c, 0x0, 0x3242668a77ced3cb6ca4b87c1b759c91, 0x128e825972592d2a632df711368a1c105, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x78cd6990a813b6a2588ccb19, limb1: 0xcb57433fd1eaa5787491656f, limb2: 0x70e4c58e64e4a9f3, limb3: 0x0, }, y: u384 { limb0: 0x428873cad69986b7befbd0f0, limb1: 0x5dde16f78dd45ec0c5a51f9d, limb2: 0x67295fe953f1c748, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_3P() { let mut data = array![ 0x3, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0xa6832ef7fe97f77de7cd9a62, 0xf18a70dbf1dc5a76c685da4a, 0x6ac1b7bfc409119f, 0x0, 0x7751161b1a9ef600b865a5af, 0xed28aad4835a39a9e8318ceb, 0x572e95c429f0e07a, 0x0, 0x3, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x2fc154703983ca8ea7e9d498c778ea6, 0x101fbcccded733e8b421eaeb534097ca, 0x71832c59148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x2eb3db872ae22448b0163c1cd9d2b7d, 0x4, 0xac2b5804f3b5ea6a7c385142, 0x67878b88a9a9d518e06d811c, 0x4549187a243009c8, 0x0, 0x77b113304bc4ddbb1d09761d, 0xdeac72115bc7d3e18f4a0a72, 0x52c6b8f99ceb4be4, 0x0, 0x3242668a77ced3cb6ca4b87c1b759c91, 0x128e825972592d2a632df711368a1c105, 0xd4eecb0109a013892abd75e5, 0x167aa57abaa882be1301e3dd, 0x2457e48112697980, 0x0, 0xb26742ddc3687f7d8983bc6e, 0xc6eb0f3fd431dccb4cd39680, 0x31fb690012ae0317, 0x0, 0x25b58a4ace1755dfa44b5f1f5d91fdcb, 0x23fa824d04875112a551d6ef70fef39, 0x6444144efd61c928f158778, 0x90d9eaffbf7e696c0b22614, 0x6879c7c3d7314db0, 0x0, 0xd6ae7f02956e20ce1359317d, 0x3545b77c84a0952ba44fa34, 0x54c416a35489a439, 0x0, 0x46f42706c0113ff0ccf72fe8f742fd2, 0x1035b8cd8e980519d9ab6ef3f50ee8fa9, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x9292b7770106624b91a73738, limb1: 0x2c9a7c1a0496485effe3922e, limb2: 0x7cc025fefaaec43f, limb3: 0x0, }, y: u384 { limb0: 0x44e571d5378b2d6e5b1d7114, limb1: 0x5d34cb1a17260d862ef07e73, limb2: 0x3d6ee7ee0c8df451, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_4P() { let mut data = array![ 0x4, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0xa6832ef7fe97f77de7cd9a62, 0xf18a70dbf1dc5a76c685da4a, 0x6ac1b7bfc409119f, 0x0, 0x7751161b1a9ef600b865a5af, 0xed28aad4835a39a9e8318ceb, 0x572e95c429f0e07a, 0x0, 0x5e71d0fc5d1c016834779173, 0xadd002dfc0ebf1b25c23c252, 0x40a868d928ae5233, 0x0, 0x423fa293418d6e3f59c2e830, 0x7a4bcf26f93e71ffd903e68e, 0x7837b851ad8da6e3, 0x0, 0x4, 0x101fbcccded733e8b421eaeb534097ca, 0x71832c59148624feac1c14f30e9c5cc, 0x247a8333f7b0b7d2cda8056c3d15eef7, 0x2eb3db872ae22448b0163c1cd9d2b7d, 0xe005b86051ef1922fe43c49e149818d1, 0xfa83cc0eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0xaa5e4678c25166a1ff39849b4e1357d, 0x4, 0x338e295a7da6c8dc47afeb59, 0x93a4ff4ae149504868278a09, 0x418e9170913c0f5b, 0x0, 0x5b20ca7e0ef2c05cc66e6a84, 0xdc8feaa2fc336cdbce46f0fa, 0x5e556f7c5bd833ed, 0x0, 0x25b58a4ace1755dfa44b5f1f5d91fdcb, 0x23fa824d04875112a551d6ef70fef39, 0xdf877be8a80fdde7e3b855b0, 0x91e54f2f86bd9262717e6b75, 0x7062334bd4c7b885, 0x0, 0x9320d417f7513821af6e0284, 0x96ed52f40e0c8b60098260d8, 0xf8afa50615dfd75, 0x0, 0x46f42706c0113ff0ccf72fe8f742fd2, 0x1035b8cd8e980519d9ab6ef3f50ee8fa9, 0xfeec5e7debf32dad5e019ae9, 0x8bf005c9328632982aeaeed2, 0x1933fdb9e8d9ea7a, 0x0, 0x56826fcbe77185341a6d2b8f, 0x69cbccb406ae88585a522de9, 0x76fc50497be174d7, 0x0, 0x25f8e65eae4eb72e4febaca4a978a32e, 0x3138e75e7839c1e424a845740cd897e1, 0xa2afdf272784379c88d18a53, 0x15e4f535a988eb9702bc3741, 0x2317d852a07769d1, 0x0, 0x29cd9f41fe12ae23c14fe282, 0x85611a868445899f82b3529c, 0x676eb93f52742f3f, 0x0, 0x1efc8eeeff5d60d288b61287fc750073, 0x1205819efd721c8fa9d99528aa8086dd8, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x54e30b1dbc54acd91542088c, limb1: 0x702b532dab377f0636d9f465, limb2: 0x25ee2efd1d7ca3f6, limb3: 0x0, }, y: u384 { limb0: 0xd25f547d7c2f7258cbdb9c6b, limb1: 0xcae4d4cae9a1aba26935de1e, limb2: 0x277ff10c5815321e, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_10P() { let mut data = array![ 0xa, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0xa6832ef7fe97f77de7cd9a62, 0xf18a70dbf1dc5a76c685da4a, 0x6ac1b7bfc409119f, 0x0, 0x7751161b1a9ef600b865a5af, 0xed28aad4835a39a9e8318ceb, 0x572e95c429f0e07a, 0x0, 0x5e71d0fc5d1c016834779173, 0xadd002dfc0ebf1b25c23c252, 0x40a868d928ae5233, 0x0, 0x423fa293418d6e3f59c2e830, 0x7a4bcf26f93e71ffd903e68e, 0x7837b851ad8da6e3, 0x0, 0x5907087f8e8e4dacdd039371, 0xc390e2073b4e64b9ede0570d, 0x6b039a85962f1594, 0x0, 0xc45eefa03155b8f7eb780b42, 0x3db57eb22f9b0394a4d7b78e, 0x6cf45b6d90883f60, 0x0, 0x60dd8ed0a614b596fb37eb1f, 0xabb99f371be41e26ec2d8e4b, 0x187ecd72c40f159d, 0x0, 0x7b66c9263de5e1663622985d, 0x118b032cc27a1d6dd192eca6, 0x312fb405788616e8, 0x0, 0xf4ac3e1f1f068dd64c86fdda, 0x24594e591d82a7f964b5ec9f, 0x6ca311b5421c57fc, 0x0, 0x42745cd7b146012455434d0f, 0x6aa4f552b7bdc93a613bd9df, 0x5832a065d7199c7a, 0x0, 0x341786b7854e3e0104e2e416, 0xbb368441c295043bee7b1d2f, 0x35c88542e11463b4, 0x0, 0x3c36e7fcc4e2fde28308132, 0xf58043d0e3d1a36d1f8137fc, 0x58c1508fbe8868a8, 0x0, 0x560a37951d69a6c8d7138239, 0x462d454a509846714184ef71, 0x3aaf8fb4f60e3e9c, 0x0, 0xb70cea4e13db5322899753f9, 0x6c62656b6d7ffb5c2af44fd5, 0x4b5ae4567dc6a7c0, 0x0, 0xb06cccb4b425d5179f528270, 0xce017c281a3861570706cd86, 0x42d14846dc4860ab, 0x0, 0x646bf486f6e77663c597ece8, 0xd87c8c36a430a6fe42305b88, 0x7964c7742b6f13da, 0x0, 0xa, 0x2648ee38e07405eb215663abc1f254b8, 0x29164ebd7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0x6e2edd0d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x8ce86e89466e4726b5f5241f323ca74, 0x30bcab0ed857010255d44936a1515607, 0x8ac57cfbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0xda2ddc3552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0x7003168b29a8b06daf66c5f2577bffa, 0x176ea1b164264cd51ea45cd69371a71f, 0x3b6a666fb0323a1d576d4155ec17dbe, 0x9edfa3da6cf55b158b53031d05d51433, 0x23d79a9428a1c22d5fdb76a19fbeb1d, 0x4d125e7fa59cec98126cbc8f38884479, 0x1f40f472e2950656fa231e959acdd98, 0x98b33c6e0a14b90a7795e98680ee526e, 0xc8555a9fcfcfa81b306d70019d5f970, 0x4, 0xb51ed06dd615b64d198d6b40, 0xc6014a9ec6d192c15f73d83, 0x4236ece07ab7f046, 0x0, 0x8f62a668da7f4862606fc8ee, 0xc2af7ed7c76e0384d7f30cb1, 0x2ee4a538de1cb3e1, 0x0, 0x109e48ca918759429cee2d75a919bf, 0x254dce38863be7379de4e89912d39a24, 0xd64052a1c3dddd0acfc5f6de, 0x81b4284ddeec997a06f7adbb, 0x2a3e2e0b8b6db118, 0x0, 0xeb1fb40ed774d5a5a932cbcd, 0x69a12cf14a2add045b8a6b2a, 0x5b9b707cde7cba42, 0x0, 0x62af3a314ed8541630e74b78e9f03a0, 0x3e5106e138112347fd7dbb662f3fb959, 0x76a17d0e9a7acdde761cf17e, 0x9df10374167580666440f792, 0x71e338c631665afe, 0x0, 0xa37e8ec892cfd84673ff810f, 0x4ff99d688a4d76e5fae62c7c, 0x10ab842e4b509be8, 0x0, 0x100999da2383a787fc58bce955201c59, 0x2d492fcea91c7b9e8fa3931db543fa13, 0x9c40d5ca5c4f37890bb899f8, 0x39b20e332317d1cc680cac6b, 0x2c9116e237dcd2c2, 0x0, 0xee4f6acf3ccd375ceb6fda83, 0x82a46494eb678a382d67337b, 0xa451fa8fc325a99, 0x0, 0x2be10b93bdf768ae7778b99191b2cf05, 0x19d5b37430b75b04d20856a7ba530478, 0xde61d931ad4af1b6aa3b7420, 0xebfb852ab0963b3bd6b97d01, 0x62f2626356a4e691, 0x0, 0x311bab2cac0350b9be3e7c11, 0x213c4209753d44f212a6085f, 0x7ef9ef4df118cf30, 0x0, 0x306359e58443dc9fa7b677c05b67bc03, 0x22f5c652ce175682bece3c707b7f0c64, 0xc22428dd359a4d97677d1a2a, 0x6a403588ae0f11e6852c9003, 0x265ca2a9c81b7fcd, 0x0, 0x41e8bf26a5f61a80ed2a1a4f, 0x4816633adc2e1a1ecbdefd13, 0x78d97cf47703cd10, 0x0, 0x1af8531e7421e1b5fc3f282922950413, 0x12802c684a9d9ebd5f6c8d17c2c0dce9a, 0xf78d57c527f35f5b17341ad, 0x9b93fae1633f0f504ea60e41, 0x23373872d46eb70b, 0x0, 0x654177c81ab44be525fc8a10, 0xcf56847d39c0dc1808c5626c, 0x692fda489d9ad018, 0x0, 0x3e15cff10f1609922ab32f8f9278107, 0x10a16e8bfef9be00041b12d3df0ab90d2, 0x32ffdcb0ebe78606cfda3864, 0x810f43c0463b6222100c039d, 0x2676d3d3af79c942, 0x0, 0xe20135efdb9ce9d0b1f0b087, 0x16a1b8a19bb224519871ad10, 0x54b74ede0f974b53, 0x0, 0x2be5e02dea43047daaed4fbaf06fafca, 0x1de6096b4f0d2f729b2b56af6ca9e273, 0x1395db0ef36c4e2931f84d21, 0x27adbaec38ab1b5c362047ca, 0x39e135d80347ccff, 0x0, 0xddfc395884c79d27da8fb121, 0x3ed6197d9e6d701775f0b246, 0x4f49fa341a6be18, 0x0, 0x5e0ad7648a4f59729af8617b82d4b15, 0x1204a5942db3ff32572d539505799c162, 0xfed466728e21ebb6ec730686, 0x4c84b97d2b2b549c0205e93d, 0x6d18c143ec437b75, 0x0, 0x1375c64d45b624c9fcbbbfc7, 0xa154d66ebcc37fc1b61f1bd0, 0x35765a06dfd06c00, 0x0, 0x1bb625624ceab37b75f8eb6d9baaec37, 0x8869d6e2bfcd45999b706e500bdf6e9, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x9dd56ed7fdf1e5a3e9cbb3b5, limb1: 0xd0df8ca018c550bbd230f67, limb2: 0x75b3c38a01fed369, limb3: 0x0, }, y: u384 { limb0: 0xa1bb56d8c1b7c9598a692c1c, limb1: 0xc940b96f597931f22e3c4b07, limb2: 0x41ca6082f12494f3, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_11P() { let mut data = array![ 0xb, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0xa6832ef7fe97f77de7cd9a62, 0xf18a70dbf1dc5a76c685da4a, 0x6ac1b7bfc409119f, 0x0, 0x7751161b1a9ef600b865a5af, 0xed28aad4835a39a9e8318ceb, 0x572e95c429f0e07a, 0x0, 0x5e71d0fc5d1c016834779173, 0xadd002dfc0ebf1b25c23c252, 0x40a868d928ae5233, 0x0, 0x423fa293418d6e3f59c2e830, 0x7a4bcf26f93e71ffd903e68e, 0x7837b851ad8da6e3, 0x0, 0x5907087f8e8e4dacdd039371, 0xc390e2073b4e64b9ede0570d, 0x6b039a85962f1594, 0x0, 0xc45eefa03155b8f7eb780b42, 0x3db57eb22f9b0394a4d7b78e, 0x6cf45b6d90883f60, 0x0, 0x60dd8ed0a614b596fb37eb1f, 0xabb99f371be41e26ec2d8e4b, 0x187ecd72c40f159d, 0x0, 0x7b66c9263de5e1663622985d, 0x118b032cc27a1d6dd192eca6, 0x312fb405788616e8, 0x0, 0xf4ac3e1f1f068dd64c86fdda, 0x24594e591d82a7f964b5ec9f, 0x6ca311b5421c57fc, 0x0, 0x42745cd7b146012455434d0f, 0x6aa4f552b7bdc93a613bd9df, 0x5832a065d7199c7a, 0x0, 0x341786b7854e3e0104e2e416, 0xbb368441c295043bee7b1d2f, 0x35c88542e11463b4, 0x0, 0x3c36e7fcc4e2fde28308132, 0xf58043d0e3d1a36d1f8137fc, 0x58c1508fbe8868a8, 0x0, 0x560a37951d69a6c8d7138239, 0x462d454a509846714184ef71, 0x3aaf8fb4f60e3e9c, 0x0, 0xb70cea4e13db5322899753f9, 0x6c62656b6d7ffb5c2af44fd5, 0x4b5ae4567dc6a7c0, 0x0, 0xb06cccb4b425d5179f528270, 0xce017c281a3861570706cd86, 0x42d14846dc4860ab, 0x0, 0x646bf486f6e77663c597ece8, 0xd87c8c36a430a6fe42305b88, 0x7964c7742b6f13da, 0x0, 0x52c487a17925c92335926072, 0x13155d04b743220ba9c4dd31, 0x1106c832e8e52057, 0x0, 0xbc69df5aa9a21ba08f160d5f, 0xc207c95ac5d454f546b05fc3, 0x574515b32b35f440, 0x0, 0xb, 0x85940927468ff53d864a7a50b48d73f1, 0x6e2edd0d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x8ce86e89466e4726b5f5241f323ca74, 0x30bcab0ed857010255d44936a1515607, 0x8ac57cfbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0xda2ddc3552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0x7003168b29a8b06daf66c5f2577bffa, 0x176ea1b164264cd51ea45cd69371a71f, 0x3b6a666fb0323a1d576d4155ec17dbe, 0x9edfa3da6cf55b158b53031d05d51433, 0x23d79a9428a1c22d5fdb76a19fbeb1d, 0x4d125e7fa59cec98126cbc8f38884479, 0x1f40f472e2950656fa231e959acdd98, 0x98b33c6e0a14b90a7795e98680ee526e, 0xc8555a9fcfcfa81b306d70019d5f970, 0xebe2136898c752051e01a934402d0baf, 0x6c2a492cc0f859aa6524ab713b7e05, 0x637e0edc5b6e4ae7a62081434fbaecc0, 0x4e8c1e4403d1f83a859890cd670f668, 0x4, 0x8d9da7701d08684a79c3c9a, 0x7b0faee9af3327934d090e7b, 0x151533e6a0b794f9, 0x0, 0xac7e4649ec69e08fa2aa440b, 0xd82ea8c5365beebbfc40ecc, 0x38290dcf3704f737, 0x0, 0x62af3a314ed8541630e74b78e9f03a0, 0x3e5106e138112347fd7dbb662f3fb959, 0x78f18f4fb87ce5e32a5ac01, 0x84e0525afbc64b068cb6e83f, 0x679bfbb0e8f543d, 0x0, 0x6fc9c69b7f2a72ee149372db, 0x5365848854ebf2c4cc13846c, 0x159f12f1f03023c3, 0x0, 0x100999da2383a787fc58bce955201c59, 0x2d492fcea91c7b9e8fa3931db543fa13, 0x9c5453b82378379d24968334, 0xfd07ecb3fa7e01e989a2c80e, 0x2abb3011d1e59739, 0x0, 0x70aab3462dc41390fb5d5945, 0x370b9445bf570bbc08f08c5e, 0x5a10e78a2d5b49fe, 0x0, 0x2be10b93bdf768ae7778b99191b2cf05, 0x19d5b37430b75b04d20856a7ba530478, 0xe20e3a8f807f193989382239, 0x3ab3cda492b3306dc2b43c41, 0x6c0baedb36072eff, 0x0, 0xd3c4bb13b9e5e81a81545d4e, 0xd51c83211a5f2730fbba7376, 0x4a495b6570c26a1e, 0x0, 0x306359e58443dc9fa7b677c05b67bc03, 0x22f5c652ce175682bece3c707b7f0c64, 0x6e30168d06be82ea3d69d68a, 0xda5ae968ed031509a07db5ea, 0x5762b3c39c6fe86f, 0x0, 0x74419c84014bf3e0732f88a3, 0x838840e4c0101d2d3541fb62, 0x74c06cf05074141d, 0x0, 0x1af8531e7421e1b5fc3f282922950413, 0x12802c684a9d9ebd5f6c8d17c2c0dce9a, 0xbb52092c3e73614686ee83b5, 0xf204cfa0ed9c00d274e448af, 0x588759dedfb95ed, 0x0, 0x13596038783eaa2228a4350d, 0x8ae684504a218717c9e052a4, 0x5bd31f41a2d7a4e4, 0x0, 0x3e15cff10f1609922ab32f8f9278107, 0x10a16e8bfef9be00041b12d3df0ab90d2, 0x8df66128d3c7762f2e4ddc59, 0x183a5335a9b651a5d1e85f56, 0x1619dd97c40a41f0, 0x0, 0x552c3d261e98b36a60543610, 0x24f4791bbcdc4290045ca9c, 0x3c7f7ce3551d7fdd, 0x0, 0x2be5e02dea43047daaed4fbaf06fafca, 0x1de6096b4f0d2f729b2b56af6ca9e273, 0xbf23cd7c25b12a0d92c6b1c2, 0x821033c574b23f4fbc286f90, 0xfa21edaab8d6f72, 0x0, 0xc9ac857dc9f3d10bbb9e967c, 0x644a0414354d3a76d9c25fdd, 0x51b76f634c812ae6, 0x0, 0x5e0ad7648a4f59729af8617b82d4b15, 0x1204a5942db3ff32572d539505799c162, 0xcf1ad31679ec4c27e3830f3a, 0xa017f3868f913c86551ad885, 0x314bccf1c49a9154, 0x0, 0x3fbe277240930e0039b24d90, 0x44c3f435ed00859eaef40526, 0xaf4e10850bd6cb6, 0x0, 0x1bb625624ceab37b75f8eb6d9baaec37, 0x8869d6e2bfcd45999b706e500bdf6e9, 0x9008bb2465decd0de32e352b, 0xde20aad12ffa049c38c36b98, 0x7f70d611ad868171, 0x0, 0xe1e028e0788998638bf9bac7, 0xfa52b231caf7768fab52216a, 0x597888666ca85946, 0x0, 0x4f7c63b27ca63da0b0528098af0dab, 0xf35e51f8509ab42e70f2e964b3fd8c, 0x93dd0836e7e13591e646d775, 0x165ef3a2c6f0a3c905a9eb74, 0x41d60538e230bb0, 0x0, 0xa8dc2a660b9336e923e82fd8, 0xf329310a470287aef66cbfc9, 0x5d6441cffa1f00d2, 0x0, 0x122200117465217fb53ec8140b91481, 0x13d5f8e8fedb409022970ed842b78a9c4, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1518e158cd20a0734c8395d6, limb1: 0x9e542f72e122bba6f1c46e7, limb2: 0x74cb223a70d329c9, limb3: 0x0, }, y: u384 { limb0: 0x779bfa346b625483d1999346, limb1: 0xf6901ab1d5d3d000b7fb3634, limb2: 0x6898c5fa74d3665a, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_12P() { let mut data = array![ 0xc, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0xa6832ef7fe97f77de7cd9a62, 0xf18a70dbf1dc5a76c685da4a, 0x6ac1b7bfc409119f, 0x0, 0x7751161b1a9ef600b865a5af, 0xed28aad4835a39a9e8318ceb, 0x572e95c429f0e07a, 0x0, 0x5e71d0fc5d1c016834779173, 0xadd002dfc0ebf1b25c23c252, 0x40a868d928ae5233, 0x0, 0x423fa293418d6e3f59c2e830, 0x7a4bcf26f93e71ffd903e68e, 0x7837b851ad8da6e3, 0x0, 0x5907087f8e8e4dacdd039371, 0xc390e2073b4e64b9ede0570d, 0x6b039a85962f1594, 0x0, 0xc45eefa03155b8f7eb780b42, 0x3db57eb22f9b0394a4d7b78e, 0x6cf45b6d90883f60, 0x0, 0x60dd8ed0a614b596fb37eb1f, 0xabb99f371be41e26ec2d8e4b, 0x187ecd72c40f159d, 0x0, 0x7b66c9263de5e1663622985d, 0x118b032cc27a1d6dd192eca6, 0x312fb405788616e8, 0x0, 0xf4ac3e1f1f068dd64c86fdda, 0x24594e591d82a7f964b5ec9f, 0x6ca311b5421c57fc, 0x0, 0x42745cd7b146012455434d0f, 0x6aa4f552b7bdc93a613bd9df, 0x5832a065d7199c7a, 0x0, 0x341786b7854e3e0104e2e416, 0xbb368441c295043bee7b1d2f, 0x35c88542e11463b4, 0x0, 0x3c36e7fcc4e2fde28308132, 0xf58043d0e3d1a36d1f8137fc, 0x58c1508fbe8868a8, 0x0, 0x560a37951d69a6c8d7138239, 0x462d454a509846714184ef71, 0x3aaf8fb4f60e3e9c, 0x0, 0xb70cea4e13db5322899753f9, 0x6c62656b6d7ffb5c2af44fd5, 0x4b5ae4567dc6a7c0, 0x0, 0xb06cccb4b425d5179f528270, 0xce017c281a3861570706cd86, 0x42d14846dc4860ab, 0x0, 0x646bf486f6e77663c597ece8, 0xd87c8c36a430a6fe42305b88, 0x7964c7742b6f13da, 0x0, 0x52c487a17925c92335926072, 0x13155d04b743220ba9c4dd31, 0x1106c832e8e52057, 0x0, 0xbc69df5aa9a21ba08f160d5f, 0xc207c95ac5d454f546b05fc3, 0x574515b32b35f440, 0x0, 0x4f068c66f642eed6b2a9cf28, 0x5cde9d21988aa8eed49fbe13, 0x5847165150f2b16b, 0x0, 0xdf6b306bce93c8248de1b0ab, 0x5d126993fea5de605b6d6f73, 0xb2fd0f2d63c2503, 0x0, 0xc, 0xd344749096fd35d0adf20806e5214606, 0x8ce86e89466e4726b5f5241f323ca74, 0x30bcab0ed857010255d44936a1515607, 0x8ac57cfbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0xda2ddc3552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0x7003168b29a8b06daf66c5f2577bffa, 0x176ea1b164264cd51ea45cd69371a71f, 0x3b6a666fb0323a1d576d4155ec17dbe, 0x9edfa3da6cf55b158b53031d05d51433, 0x23d79a9428a1c22d5fdb76a19fbeb1d, 0x4d125e7fa59cec98126cbc8f38884479, 0x1f40f472e2950656fa231e959acdd98, 0x98b33c6e0a14b90a7795e98680ee526e, 0xc8555a9fcfcfa81b306d70019d5f970, 0xebe2136898c752051e01a934402d0baf, 0x6c2a492cc0f859aa6524ab713b7e05, 0x637e0edc5b6e4ae7a62081434fbaecc0, 0x4e8c1e4403d1f83a859890cd670f668, 0x2284b7a447e7f5938b5885ca0bb2c3f0, 0xf6b20a3f40048d7c31d5a973d792fa1, 0xc5adf6816b10e53a9145de05b3ab1b2c, 0x54d35980bf9c0efb5816b74a985ab61, 0x4, 0xfa06825a3970e5b2395be2b, 0x4e5a7ba3551df3652d46082d, 0xcfca9a525fe359, 0x0, 0x4b5b3f76f46f535ef91e563e, 0x7966c4c81669a7d88fb8ff47, 0x5319f116c45c71a8, 0x0, 0x100999da2383a787fc58bce955201c59, 0x2d492fcea91c7b9e8fa3931db543fa13, 0x7f99cd69e93181300ddb085a, 0x2a1d1771927bbfe32603da8b, 0x1b74f12f3379df06, 0x0, 0x9c6622f17ebe2c6e5ff51ed2, 0x204fecff8a5332121c431d6c, 0x5aef5ec5cb6f461e, 0x0, 0x2be10b93bdf768ae7778b99191b2cf05, 0x19d5b37430b75b04d20856a7ba530478, 0xfb04ee0dc3febe0615ddb0f8, 0xdb1a0ab954022ed49344333d, 0xc954e46c5b77f1, 0x0, 0x9ce91f8ebf3d15bd8a382b6e, 0xdfabad49441c0d28944c6b9c, 0x50386dc8735ea9aa, 0x0, 0x306359e58443dc9fa7b677c05b67bc03, 0x22f5c652ce175682bece3c707b7f0c64, 0x4a3eb763e06c59a43ee29389, 0x1bccf75e9f35eef7529a1ef5, 0x10fda802117cdfa6, 0x0, 0xa7ef2ec0616f2443afd7cfbb, 0xd9cea79fbf13150fc3cd14eb, 0x4716f7e70987aa10, 0x0, 0x1af8531e7421e1b5fc3f282922950413, 0x12802c684a9d9ebd5f6c8d17c2c0dce9a, 0x8d97858df9c229a8d620899, 0x7db5c765b658f7a25710c917, 0xcf309068ad0dba9, 0x0, 0x910500da56aeb50040a7dcc4, 0x3f3a644f90034e28ba18da95, 0x175ed58aa3954930, 0x0, 0x3e15cff10f1609922ab32f8f9278107, 0x10a16e8bfef9be00041b12d3df0ab90d2, 0x979bd1588dea18a8b58a36af, 0x3b2b0ed61e1178cba7126bb7, 0x785cdb331bd169df, 0x0, 0xfa4fe3f5b031c72c034663a2, 0xb0e20f66408902c55e655ba1, 0x75bd7b3b090eed75, 0x0, 0x2be5e02dea43047daaed4fbaf06fafca, 0x1de6096b4f0d2f729b2b56af6ca9e273, 0x3fce6566c5bcd92f4f85fa83, 0x623822e4a6f44b0bf23c8675, 0x6e423031e41718c0, 0x0, 0x16cc5bb608bc6da0bdb24659, 0x14a20f3a350b3c92c8985f2c, 0x62b6194db85582a7, 0x0, 0x5e0ad7648a4f59729af8617b82d4b15, 0x1204a5942db3ff32572d539505799c162, 0x695752f39d6ec14aacfbee31, 0xf8dd60148b6b6cd713f249de, 0x4ae3fa433428da67, 0x0, 0x2fc01927924d2423beeabc84, 0x8d3ab58869e8b96487a1c521, 0x47292b4a7182ce7f, 0x0, 0x1bb625624ceab37b75f8eb6d9baaec37, 0x8869d6e2bfcd45999b706e500bdf6e9, 0x6474fbdb6af73701de45f274, 0x6094e5f591a45f3bf08427c8, 0x103a5881e0aef8e4, 0x0, 0xa14105659db45179803bc1ee, 0xcd28f77e60c994a87a8e0d3d, 0x57e7812e2c87633c, 0x0, 0x4f7c63b27ca63da0b0528098af0dab, 0xf35e51f8509ab42e70f2e964b3fd8c, 0xa25e04756aa0d3cf7a58d681, 0xf525fde801d661e742afdf23, 0xb8057a3525f95e3, 0x0, 0x6423b1c187fb4699d91e7961, 0x97ed6053542a17b2ee5a276d, 0x24f4c3823852a469, 0x0, 0x122200117465217fb53ec8140b91481, 0x13d5f8e8fedb409022970ed842b78a9c4, 0xc4c0db3983aec6a159c5bc04, 0x5f92edcb20df32b1cfb385f, 0x300014ec8791a43a, 0x0, 0x17b89b207ec56f494c10480a, 0x610f69ebee5483ba4bd0d917, 0x2bec654de3ea3a80, 0x0, 0x37b10ae5354582f85190f7870b858c63, 0x1316ba5fddb42e06735d0f1fdcc24a38, 0x45a14721d6abe459bc5aea8, 0x1568bffaa9565041d7dbaf28, 0x3e6067b9f8935c8, 0x0, 0x26d59ad679daa7e759147eba, 0x9503c0a1029b0f7ce7406c4b, 0x3db5661841ebce66, 0x0, 0x121b5378cd43ffc919a2305e76423029, 0x18300af219c488c1a25884d5c7401c30, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x4ee4167708b29620b1a9e142, limb1: 0x6fd520385a98769aa6f2e833, limb2: 0x29e58ca78283490e, limb3: 0x0, }, y: u384 { limb0: 0xf78829d77fe7c51b0788aa60, limb1: 0x98af3b491451a91c0de5fdab, limb2: 0x4ba4b20ac788a99, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_1P() { let mut data = array![ 0x1, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x1, 0xb4862b21fb97d43588561712e8e5216a, 0x967d0cae6f4590b9a164106cf6a659e, 0x5, 0x41c610705003caeb41ebc2e1, 0x7e86ece0ef89d80aca46deac, 0x121b38a9ddb387ef, 0x0, 0x5d4d7ed98f7bc32e88ca220f, 0xc1b7d0a1662fc4fbf7fefffe, 0x24a447a3fd6b6dd0, 0x0, 0x5520c252aad219e02bf5055a4ed023b7, 0x197e50b8e7adb6dd93eeede129c12721, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x41c610705003caeb41ebc2e1, limb1: 0x7e86ece0ef89d80aca46deac, limb2: 0x121b38a9ddb387ef, limb3: 0x0, }, y: u384 { limb0: 0x5d4d7ed98f7bc32e88ca220f, limb1: 0xc1b7d0a1662fc4fbf7fefffe, limb2: 0x24a447a3fd6b6dd0, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_2P() { let mut data = array![ 0x2, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x2, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x1521f387af19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x5, 0x32536984a4baf6f115cbb0bd, 0xdae1afb06300dbd4fde0fe2a, 0x1f1896139ffba76b, 0x0, 0xdf40e1ffc936ca509fbb16a8, 0xca2a5643c84ea6749543ee4c, 0x29b131b03ad6f119, 0x0, 0x39dea48eef47b3e6bcae980c9112d477, 0x538cc4627274d8f320bf5df15c887356, 0xc0a469a5b7f47ad22e92fe7d, 0xd7d5b526e50c6900bdcfeb9d, 0x21df2654af8f907c, 0x0, 0x19ca14fef97aef829a022e99, 0x3436a3a9d29787ffa53573f3, 0x16d3f0d2e78b2950, 0x0, 0x10a2e45b33049f11b360c09b6389565b, 0x63f1d0c59d848c415389772b72561b3d, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x512920e074cbe690304d839e, limb1: 0xb077d5884dbdc5fcb9424a35, limb2: 0x16cd67edce8be7ac, limb3: 0x0, }, y: u384 { limb0: 0x70cd2c4a003d407aabc7cc, limb1: 0xe2748dd5f8c2a0e1dadd02d5, limb2: 0x1c1cfa79fda07581, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_3P() { let mut data = array![ 0x3, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0xa893636703904fcbe984618c, 0x73b210a224190b9b7b28784c, 0x20f05486689dff6c, 0x0, 0x3, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x8d723104f77383c13458a748e9bb17bc, 0x215ddba6dd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x5f82a8f03983ca8ea7e9d498c778ea6, 0x5, 0xe7bee0981732826e6716a8b9, 0x8001b0e38269465d6a3ba48f, 0x1a727a8f4b29ab8, 0x0, 0x8180b66bf02ff17b607d43de, 0xfaf5d89afaaafcba4c3a43ef, 0xb1992b294551079, 0x0, 0x10a2e45b33049f11b360c09b6389565b, 0x63f1d0c59d848c415389772b72561b3d, 0x74575ca46c143d22121ea904, 0x77200655d23500648b27cb30, 0xaa0637dd46a67ab, 0x0, 0xfe93e7c36bbe7d7cde12c6ac, 0x51cb8066bcd86f62f01ec58, 0x1f28f657f6b9dadd, 0x0, 0x4330e45cf056866449d6d2b7255a6d25, 0x102e9d68e73086da22f4b98d2103a3c22, 0x2e20c00e88de121d37fa2696, 0x86ac870558aabfae43dc69a0, 0x26095fa9606bf53, 0x0, 0x327031fef1203666f47f2099, 0xdb951627a7f45379f1e51f4f, 0x376fe09acf51529, 0x0, 0x32cbca2bbd2f37ecb19ba4403b940cc1, 0x12977bae8a28f111cf0a43807982d3bb7, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x213a074a0215934c65d47250, limb1: 0x57ceadf09cd8ebde50476db0, limb2: 0x1f82780f1a4c3d23, limb3: 0x0, }, y: u384 { limb0: 0x7282af42d1608d1f8c034960, limb1: 0x81214b248c88a391f72dd6e0, limb2: 0x5df1db744450be3, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_4P() { let mut data = array![ 0x4, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0xa893636703904fcbe984618c, 0x73b210a224190b9b7b28784c, 0x20f05486689dff6c, 0x0, 0x74f2a24c1853d803c1b9e310, 0x9e78bb9233603b686b9d27, 0x1d13a84fbcd96e81, 0x0, 0xe5bc08950f2f1accd92245f4, 0x3b653bbe7b6cfd9074b07f89, 0x1638a8a07b89463b, 0x0, 0x4, 0x8d723104f77383c13458a748e9bb17bc, 0x215ddba6dd84f39e71545a137a1d5006, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x5f82a8f03983ca8ea7e9d498c778ea6, 0xb5d32b1666194cb1d71037d1b83e90ec, 0x28045af9ab0c1681c8f8e3d0d3290a4c, 0xd3fbf47a7e5b1e7f9ca5499d004ae545, 0x2ebce25e3e70f16a55485822de1b372a, 0x5, 0x6463bd58916931d0ac4eb128, 0x36bcb9db9fbc494127d685b9, 0xbe0d59677fd6637, 0x0, 0xfdfd5ee62a80a8195a667cd1, 0x8eb9b531d1c1bed421f1d865, 0x2fbd2d2aa811c3e1, 0x0, 0x4330e45cf056866449d6d2b7255a6d25, 0x102e9d68e73086da22f4b98d2103a3c22, 0x8fd7943c409c6d0b97790c17, 0x6609bc50ae73b6db4a08db2e, 0x1a5a408e625e1019, 0x0, 0x56e67a10d45628f5fcf8d390, 0xe19469815ce43c544151b3ac, 0xeb5ad829227a07f, 0x0, 0x32cbca2bbd2f37ecb19ba4403b940cc1, 0x12977bae8a28f111cf0a43807982d3bb7, 0xd49218ddf86e81250924e4ed, 0xf193c73d0d41e7f71dd4d878, 0x21192796ca5e2dac, 0x0, 0xbb5b1bfe4b3be7d06581a624, 0x57281f4af424359f81b5526a, 0x2f72bb4496fb4ce4, 0x0, 0x453503237fe891d4168e4f9228c400b7, 0x72e13e861339a4b3dab61e0d640fc66, 0x7ec3a5c2c9499344ac050cdd, 0x791b53545bf433b7079614ac, 0x21453b32e9702074, 0x0, 0xdb015deb84bb2b7b687999ca, 0xf553ab53e8fed39de94cc1f5, 0x1c73bed188a1cf2f, 0x0, 0x3370dc3b2f6a7a7d6a4917e6cae4e0e1, 0x14488bb2a825221dfb2b87de071f1b27c, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x577ddc8cb42b7a3b83e4d525, limb1: 0x74e9415eb1dbca9529930fc, limb2: 0x26b61a5d6d67dd31, limb3: 0x0, }, y: u384 { limb0: 0x6cc0d22d0549fc5bbbb24080, limb1: 0x315ae072448564ca12dc062e, limb2: 0x2d218fcb973e8f23, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_10P() { let mut data = array![ 0xa, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0xa893636703904fcbe984618c, 0x73b210a224190b9b7b28784c, 0x20f05486689dff6c, 0x0, 0x74f2a24c1853d803c1b9e310, 0x9e78bb9233603b686b9d27, 0x1d13a84fbcd96e81, 0x0, 0xe5bc08950f2f1accd92245f4, 0x3b653bbe7b6cfd9074b07f89, 0x1638a8a07b89463b, 0x0, 0x549a4dee31909bd274709d7c, 0x2628a928b4ed90e98d5de1f, 0x1f2c2eeb200495b, 0x0, 0xbae71f4f781675cce1119290, 0x18995b20b8d0966bac7f5c23, 0x1f7a255155ab7785, 0x0, 0x616d2877cb47206e625b0076, 0xa7255531af3575b0a682d6df, 0xdd4a0db8187661d, 0x0, 0xea99c54030edacb739c9ad0f, 0x1e2e84792f7a12b330406ecd, 0x70f1e1a9673a240, 0x0, 0x4ca9473b8cae66da0baf8eca, 0x9ca627187edabffeb80da281, 0xda800cad866dc3c, 0x0, 0x6dcd62554ccd88a00f3e90b3, 0x141b8118cd6873dc9ac01a64, 0x19146bc96fa6a4bd, 0x0, 0xd21eca6170588371cf0fef12, 0x2aae89b6d1784d7fe5d6f233, 0x2fa67b7cd137898c, 0x0, 0xb20856046d39da92c0a6898a, 0xc9dba030db3ed937e781ae4d, 0x695a8c76fb0f771, 0x0, 0x919e8724022c5bd17875261b, 0x3a2b09cc9362be43a8573a0, 0x2cf4abb949016ad7, 0x0, 0x89062bf5adf784b526337420, 0xf710d8fb0beb9551fe0e08f3, 0x1577b6c8f024c52d, 0x0, 0x2cb6c8386e51647e028876a2, 0x3eeb71e38623705690872fa1, 0xbf610b0d76e1a8f, 0x0, 0x92f468ac225e9f9a2b52929d, 0x28e7d79e30f3f4d4abf38c05, 0x2e2ba523e6456871, 0x0, 0xa, 0xe005b86051ef1922fe43c49e149818d1, 0x1f507980eece328bff7b118e820865d6, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x154bc8ce8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x5, 0x32eb30f6f18b90fd2c54a7bc, 0x3c30d2c79fedd11320172c6b, 0x1c24ff684f9b5d37, 0x0, 0x30da50af17d999a6e4f507cc, 0x8b68b2e39f2184199c693db6, 0x29406ed67ec36daa, 0x0, 0x44a6ec700b7df57842dc495ff54035ab, 0x1a16322818541ea7ff83fb7401b38645, 0xf988d8bc102cc5827e4caa0f, 0x49d307fa622f159f155a1d5d, 0x279bbe5814108d5, 0x0, 0x8175447243fbd59a37850f7e, 0x97eab11e0760e9d18ebd0279, 0x207bde70fd6ed720, 0x0, 0x2f98f4efaa736ab4d7bfb789bfba3055, 0x13cd9b8573802529fd653bb6e0d2b9003, 0x52463a5e56dce95d52653f6c, 0xc486275eefc0a3085d30994f, 0x1911dc07106bf4ba, 0x0, 0x50eeee6f973b2226963afb66, 0x1afe5cccc2c986ed4ae0d870, 0x1164fff2e2c71e0a, 0x0, 0x4bf90ecc32be6be1a6c37a7a9d07c71d, 0xf44e3c518c0a9551bc4adf61e4848ba, 0x2704d0e441c6416e0fca2d7c, 0x2210d1dbdbe71c652f93ab45, 0x22a59daf5cbe974b, 0x0, 0xfa94c262d139c0ee254542eb, 0x2d6985158d5a69f37216750b, 0x196f95cbe169d63, 0x0, 0x5ef24d1d34d20af1accc99a7a47ced7, 0x15a3bf99ae0dc9de808f9f24fc67eb36b, 0x90e925805f4e493a98513928, 0x20747869ef32538aca7f3a98, 0x1d9ba510fc4dbce1, 0x0, 0x19866ab554bc8233e08b4443, 0xa95c235c28b853948e2ab1bf, 0x167644ace98da43f, 0x0, 0x2cb938e8d1c7a21ed6905354bb26d393, 0x5531d3f34afddbea08c69f58e5606d44, 0xe8975bf70ea1a1253b0d37d2, 0xc825272fb51f264751b2a16e, 0x82a1f118fcda22c, 0x0, 0x2f242762bb612f6c60c0126c, 0x919d79be09b46ad1f5cebf8e, 0x6b9c0cfd4951eec, 0x0, 0x60e45e17bea8d8126f02e5a29022aee5, 0x132504ebb936117e97628b682972007b8, 0x6fd67ead04596b5005a7175b, 0x9da6449170ac81a2f6cc28a, 0x1413b85981e32e9e, 0x0, 0x3ff0bf0cd595a2bd615527a3, 0x94482e2708c6ae32d5bd1b5f, 0xfcfed4eeb170294, 0x0, 0x516c64bbee2a8bf42f7414f288f1f846, 0x145799d59f914437c97585c53ceb86623, 0xc71e8a64b2f862ae51d2200a, 0x39cef19185293495361def27, 0x2e0a4cb3b5568f75, 0x0, 0x85d0d27771793625c874ebbf, 0xce9e91179dc4f4b408181c1f, 0x261a1cca4c19631a, 0x0, 0xcefe84e1bdce362a5bd286f90a8b1cb, 0x3717c82dc5b0858c3ba6f188e61330a, 0x67427da6ac310253c4305f51, 0x4b8a13108dbfa4be65e8debc, 0x17a3550c4017bb7a, 0x0, 0xc1b3b3c0adb4ea9812127500, 0xe8a20b9f8ad97a21e3450200, 0x1dcd89db1920a499, 0x0, 0x146dc11c44642a7552be554048969667, 0x1240b81ea23b0099fa77c5be92a2a8286, 0xead19fc6d1fe6777fc7fe69f, 0x75f5a9115bf9d3ee7a306806, 0x325b9bf2679afd4, 0x0, 0x69479ee6fe51ea5b53a60c39, 0xb467acaf148cd9cc4e51a679, 0x1aa47e4314e976ec, 0x0, 0x2024c45822518dadf0322fb9e8b505e1, 0x1581e6419c45af5a4b61bbe76efb6a640, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x664e7a2a841e9440a32b6d19, limb1: 0xafdb5f6d16a62de9213ee040, limb2: 0x13f95a9cdebbf34c, limb3: 0x0, }, y: u384 { limb0: 0x7ff039b0dc46b2d7c69d0faf, limb1: 0x2e4a2bd3a50e076ea1b3056, limb2: 0x2dbf12d12987fc34, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_11P() { let mut data = array![ 0xb, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0xa893636703904fcbe984618c, 0x73b210a224190b9b7b28784c, 0x20f05486689dff6c, 0x0, 0x74f2a24c1853d803c1b9e310, 0x9e78bb9233603b686b9d27, 0x1d13a84fbcd96e81, 0x0, 0xe5bc08950f2f1accd92245f4, 0x3b653bbe7b6cfd9074b07f89, 0x1638a8a07b89463b, 0x0, 0x549a4dee31909bd274709d7c, 0x2628a928b4ed90e98d5de1f, 0x1f2c2eeb200495b, 0x0, 0xbae71f4f781675cce1119290, 0x18995b20b8d0966bac7f5c23, 0x1f7a255155ab7785, 0x0, 0x616d2877cb47206e625b0076, 0xa7255531af3575b0a682d6df, 0xdd4a0db8187661d, 0x0, 0xea99c54030edacb739c9ad0f, 0x1e2e84792f7a12b330406ecd, 0x70f1e1a9673a240, 0x0, 0x4ca9473b8cae66da0baf8eca, 0x9ca627187edabffeb80da281, 0xda800cad866dc3c, 0x0, 0x6dcd62554ccd88a00f3e90b3, 0x141b8118cd6873dc9ac01a64, 0x19146bc96fa6a4bd, 0x0, 0xd21eca6170588371cf0fef12, 0x2aae89b6d1784d7fe5d6f233, 0x2fa67b7cd137898c, 0x0, 0xb20856046d39da92c0a6898a, 0xc9dba030db3ed937e781ae4d, 0x695a8c76fb0f771, 0x0, 0x919e8724022c5bd17875261b, 0x3a2b09cc9362be43a8573a0, 0x2cf4abb949016ad7, 0x0, 0x89062bf5adf784b526337420, 0xf710d8fb0beb9551fe0e08f3, 0x1577b6c8f024c52d, 0x0, 0x2cb6c8386e51647e028876a2, 0x3eeb71e38623705690872fa1, 0xbf610b0d76e1a8f, 0x0, 0x92f468ac225e9f9a2b52929d, 0x28e7d79e30f3f4d4abf38c05, 0x2e2ba523e6456871, 0x0, 0x7bfeb500d87c8d6a89e3b500, 0x114bfa8db0c1f0065e73cf9a, 0x129e9c5a3641b28e, 0x0, 0x755ef61cf917721bfef36992, 0x8f3d6b6348b89a2c0cfa9d3f, 0x272de7db2186fd11, 0x0, 0xb, 0x4a84eb038d1fd9b74d2b9deb1beb3711, 0x154bc8ce8c25166a1ff39849b4e1357d, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x1158af9fbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0x1b45bb86552116dd2ba4b180cb69ca38, 0x5, 0x82a38d8c5a5ed06e02f523ea, 0x82af79a6bf3ac89993eab3e8, 0x1be27c5dcf4d031, 0x0, 0x47cd0a6bf8f3e2719f3676c3, 0xb52e9a47fb56e1d543047f8b, 0x2d0102ccf985e7db, 0x0, 0x2f98f4efaa736ab4d7bfb789bfba3055, 0x13cd9b8573802529fd653bb6e0d2b9003, 0xfc1dd0e74df0a1a8d64f91ef, 0x7152ce13dd09af9d91af51a5, 0x1f20f94df2d7fe74, 0x0, 0x7e05f6cc422c4a84b77ae1c4, 0xce37231b21808d9920cd5380, 0x111ebb3c2386a02a, 0x0, 0x4bf90ecc32be6be1a6c37a7a9d07c71d, 0xf44e3c518c0a9551bc4adf61e4848ba, 0xa237e5e2279f34d3f8c9d69c, 0xff7f5d3ae502e52c40306b83, 0x1337f2421463490b, 0x0, 0x45b6a863b5abf54962d9b884, 0x30a306da962a35989645725e, 0x99a1ae365a1daf2, 0x0, 0x5ef24d1d34d20af1accc99a7a47ced7, 0x15a3bf99ae0dc9de808f9f24fc67eb36b, 0xb84b0e70b2875bab51e9d89a, 0x2091fcf632cf164d90c07d54, 0x1817470ef8567bdd, 0x0, 0x6cfa31ea1faa7f591e0c9898, 0x91ae224d73336f6aea463d10, 0x1a76f383b7ffeff9, 0x0, 0x2cb938e8d1c7a21ed6905354bb26d393, 0x5531d3f34afddbea08c69f58e5606d44, 0x70b4837532b9116ba15cb044, 0x8dc6e9f1aec52fcb46bbea60, 0x1de8b549ffcc3ab3, 0x0, 0x8ebe92f66b5744c974e0ae04, 0xf4f8ffe04323fde3bc621b11, 0x177ac0d85f238570, 0x0, 0x60e45e17bea8d8126f02e5a29022aee5, 0x132504ebb936117e97628b682972007b8, 0xf69fee0280761794b8af094d, 0x2cab3532c766373f21f01ea1, 0xb2a41c7c05cf495, 0x0, 0x47c5682cc4d62cd6a6b5c399, 0xff9caa6f33c1d17ec353d81e, 0x424b8d93bc33ee3, 0x0, 0x516c64bbee2a8bf42f7414f288f1f846, 0x145799d59f914437c97585c53ceb86623, 0x91abb630ebe86fa5ed36f08, 0x8792ec1248359362df03ea13, 0xa395ae138e67d28, 0x0, 0xea244ec29efaa151ea8df973, 0x1066b45d5cfb0ecf6b1c83d, 0x29bc678e1f1a863b, 0x0, 0xcefe84e1bdce362a5bd286f90a8b1cb, 0x3717c82dc5b0858c3ba6f188e61330a, 0x4e0af46df62ebdf83ef8427a, 0xe920eb4917f8088bed5a0ff1, 0x290d2f419d55f05, 0x0, 0xc99e48407b226ca08f8edcd0, 0xa26bf316d4aa7e7801849498, 0xe537c8f794284fb, 0x0, 0x146dc11c44642a7552be554048969667, 0x1240b81ea23b0099fa77c5be92a2a8286, 0x4e0ff52d69dc8189069ca894, 0xbb8275552c772e2c5ab6a827, 0x304d9f7b60971a3a, 0x0, 0x2c86e8197dada4886b64d972, 0x7c82e3ee4a0890e23f95a00e, 0x223e0af0a2ca1d7f, 0x0, 0x2024c45822518dadf0322fb9e8b505e1, 0x1581e6419c45af5a4b61bbe76efb6a640, 0xd2f1ac9e8e396d2773eb4815, 0xff66e9037c285a85f82cd552, 0x17f35aece5c7a033, 0x0, 0xa9f477c2284f410dcf3e9b, 0x4c5370e3920042051b704352, 0x16d56bd7c7796d7c, 0x0, 0x32d3a03325ee181cc9c2b39a4e2916d9, 0x219449b8074d447b4f3f2fb27633a5e1, 0x85028124eee08fb0e6ef7707, 0x91fb6fec286026bab476ba92, 0x2733c400e9b74caf, 0x0, 0x7660634344195f9b47cdb6ca, 0x4fdc765e611b89333602fe6d, 0x1152965b31d3e6b7, 0x0, 0xa131e2b48ec3bee1efa6016b50ac441, 0x10c7fd5e62bf48ea70c58c0cfa9a06e45, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xffdf31426d80fe0e0c50bc6c, limb1: 0x3f2ee5e0c6081e2b90431a5d, limb2: 0xee45d84f0c8d969, limb3: 0x0, }, y: u384 { limb0: 0xe2ce9a7cc98cfccbbfd0057, limb1: 0xcb704f80e53cbafb61a4cf65, limb2: 0x2249c2809c6b67ce, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_12P() { let mut data = array![ 0xc, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x3c26f4ff476ab777dc184776, 0xbccb2cba46cf421f11eb4d14, 0x27ec44064c727a3d, 0x0, 0xa893636703904fcbe984618c, 0x73b210a224190b9b7b28784c, 0x20f05486689dff6c, 0x0, 0x74f2a24c1853d803c1b9e310, 0x9e78bb9233603b686b9d27, 0x1d13a84fbcd96e81, 0x0, 0xe5bc08950f2f1accd92245f4, 0x3b653bbe7b6cfd9074b07f89, 0x1638a8a07b89463b, 0x0, 0x549a4dee31909bd274709d7c, 0x2628a928b4ed90e98d5de1f, 0x1f2c2eeb200495b, 0x0, 0xbae71f4f781675cce1119290, 0x18995b20b8d0966bac7f5c23, 0x1f7a255155ab7785, 0x0, 0x616d2877cb47206e625b0076, 0xa7255531af3575b0a682d6df, 0xdd4a0db8187661d, 0x0, 0xea99c54030edacb739c9ad0f, 0x1e2e84792f7a12b330406ecd, 0x70f1e1a9673a240, 0x0, 0x4ca9473b8cae66da0baf8eca, 0x9ca627187edabffeb80da281, 0xda800cad866dc3c, 0x0, 0x6dcd62554ccd88a00f3e90b3, 0x141b8118cd6873dc9ac01a64, 0x19146bc96fa6a4bd, 0x0, 0xd21eca6170588371cf0fef12, 0x2aae89b6d1784d7fe5d6f233, 0x2fa67b7cd137898c, 0x0, 0xb20856046d39da92c0a6898a, 0xc9dba030db3ed937e781ae4d, 0x695a8c76fb0f771, 0x0, 0x919e8724022c5bd17875261b, 0x3a2b09cc9362be43a8573a0, 0x2cf4abb949016ad7, 0x0, 0x89062bf5adf784b526337420, 0xf710d8fb0beb9551fe0e08f3, 0x1577b6c8f024c52d, 0x0, 0x2cb6c8386e51647e028876a2, 0x3eeb71e38623705690872fa1, 0xbf610b0d76e1a8f, 0x0, 0x92f468ac225e9f9a2b52929d, 0x28e7d79e30f3f4d4abf38c05, 0x2e2ba523e6456871, 0x0, 0x7bfeb500d87c8d6a89e3b500, 0x114bfa8db0c1f0065e73cf9a, 0x129e9c5a3641b28e, 0x0, 0x755ef61cf917721bfef36992, 0x8f3d6b6348b89a2c0cfa9d3f, 0x272de7db2186fd11, 0x0, 0x499828e9a86afe3b8c909275, 0xb8910cabe37f6e8f4bd4b4c1, 0x2634fe56d6751316, 0x0, 0x777228ef48ddade6caeb3c9, 0x6e0e16c7f54463307a858b78, 0x6e2e3e3a1dc83da, 0x0, 0xc, 0x3405095c8a5006c1ec188efbd080e66e, 0x2305d1699a6a5f92cca74147f6be1f72, 0x1775336d71eacd0549a3e80e966e1277, 0x144a7edf6288e1a5cc45782198a6416d, 0x2f1205544a5308cc3dfabc08935ddd72, 0x21c38572fcd81b5d24bace4307bf326, 0x42930b33a81ad477fb3675b89cdeb3e6, 0x2b70369e16febaa011af923d79fdef7c, 0x2648ee38e07405eb215663abc1f254b8, 0x522c9d6d7ab792809e469e6ec62b2c8, 0x85940927468ff53d864a7a50b48d73f1, 0xdc5dba1d977e9933c49d76fcfc6e625, 0xd344749096fd35d0adf20806e5214606, 0x119d0dd09466e4726b5f5241f323ca74, 0x5306f3f5151665705b7c709acb175a5a, 0x2592a1c37c879b741d878f9f9cdf5a86, 0x30bcab0ed857010255d44936a1515607, 0x1158af9fbb42e0b20426465e3e37952d, 0x5f3f563838701a14b490b6081dfc8352, 0x1b45bb86552116dd2ba4b180cb69ca38, 0xc87a746319c16a0d0febd845d0dfae43, 0xe0062d1b29a8b06daf66c5f2577bffa, 0xa25b59fd92e8e269d12ecbc40b9475b1, 0x2689f61688c132adefbfc19ee8f6cf32, 0x5, 0xf9033eff6f190d31c0c4211d, 0x5695a5c1624dd1742a3cdfe9, 0x179c263b9b4504b8, 0x0, 0x28d168c4ac03deddb2bfced2, 0x70704860340808682034ce25, 0x128005647d6a6d42, 0x0, 0x4bf90ecc32be6be1a6c37a7a9d07c71d, 0xf44e3c518c0a9551bc4adf61e4848ba, 0x8064a8fdea100eeea33de95e, 0x48241e9bcc914c3f4688d747, 0x36d11122251d0be, 0x0, 0xed92f97ad0666c54c0c7c322, 0xb8286940afc6cb2b56a8186f, 0x2998081bd2a6cc53, 0x0, 0x5ef24d1d34d20af1accc99a7a47ced7, 0x15a3bf99ae0dc9de808f9f24fc67eb36b, 0x9091115a73842d352e7260c2, 0x7c9c3b4234d11be97c3a47c2, 0x20f7f327ca913b6, 0x0, 0x554304ae2efdf0b481bef53a, 0x2ec24f5512a59f6d9389adb7, 0xf108022c4d70cb1, 0x0, 0x2cb938e8d1c7a21ed6905354bb26d393, 0x5531d3f34afddbea08c69f58e5606d44, 0xaf21babf96dd103773c072ef, 0x7ce5ce3522b6ea4c0e3ec87c, 0x949d7f5b6f58cf0, 0x0, 0x997fee3b8a7a55ed6c3ce35a, 0x85dc08d63c739254f7cd9e08, 0x1e8720754774e3be, 0x0, 0x60e45e17bea8d8126f02e5a29022aee5, 0x132504ebb936117e97628b682972007b8, 0x949ac2b0821b3f17297f3379, 0x68229918ea7af402a38533f4, 0x2218e85e6418087f, 0x0, 0x8240596af6fd6399672c6fc7, 0x7f7eb048cdb769efa3581400, 0x2300655984a19dfc, 0x0, 0x516c64bbee2a8bf42f7414f288f1f846, 0x145799d59f914437c97585c53ceb86623, 0xf2116223dcea1035d6598225, 0xec21b290a7a3b366b93dc6c5, 0x19ba2583fa478605, 0x0, 0xe2501715d7aa98cae184ce22, 0x23c9c5d67009ad497435a9cd, 0x17f114ad703e0cf1, 0x0, 0xcefe84e1bdce362a5bd286f90a8b1cb, 0x3717c82dc5b0858c3ba6f188e61330a, 0x6b7bafcd4192510084e8f673, 0x4fac1a2d0116dc53ad2667fa, 0x1ed9f98441a2478c, 0x0, 0xf1355b40d63ec40e1e343f5c, 0x4cada2fa0416e8c573e54188, 0x2c486d8ca96cef62, 0x0, 0x146dc11c44642a7552be554048969667, 0x1240b81ea23b0099fa77c5be92a2a8286, 0x5b9ecbfbecd3454955d82d52, 0xdb7b0c28a61b88ec3874eaf4, 0x1d92b948e287e544, 0x0, 0xbc95b0afca3a981ea9d42a63, 0xf6b2fcafda97e7d50eae45a2, 0x67531d1cc994e69, 0x0, 0x2024c45822518dadf0322fb9e8b505e1, 0x1581e6419c45af5a4b61bbe76efb6a640, 0xeccb4b446b26500e9b2af328, 0x438e22ee4ae8272a0464cc1a, 0x1187394d50486a03, 0x0, 0x28bb06c6fbae4aa8769a05e1, 0x3c6ae34464712ecdb77f360f, 0x141ed6d5a2aba61e, 0x0, 0x32d3a03325ee181cc9c2b39a4e2916d9, 0x219449b8074d447b4f3f2fb27633a5e1, 0x7d2d0722d87337ba712167c5, 0xc3cc9233aa74d73f553e65b6, 0x518142076033a0c, 0x0, 0x5669e2a9f99dec284bd9833e, 0x7ff81fdc9b9fe048166702e, 0x23306f377d466ff8, 0x0, 0xa131e2b48ec3bee1efa6016b50ac441, 0x10c7fd5e62bf48ea70c58c0cfa9a06e45, 0xac500059bd0254354a7eb10d, 0x57846864e2cc212729077c5f, 0x1779a3734e112297, 0x0, 0x95dab19850fefcce556c2e45, 0x8508e9c2e5ccb68087e137a9, 0x47ca47056355729, 0x0, 0x14a37dd97b695d69cf3442e2c033af3c, 0x21a0482fffb4108132fea168f764c63f, 0x6ea786336e5cc29f4f62bb0a, 0xfe31116e59152678d3e658f7, 0x1d659cd996e57821, 0x0, 0x7f9bfd31230be6f74a939865, 0xceae5af5704b817d79a4b61e, 0x11c5608e4816db0f, 0x0, 0x5396fa1ad3cb506768c58b91578ff06d, 0x542910fa71de1143e977087fee8f6313, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xcb36822ddaf2d31c783a48a, limb1: 0x8bdd749154654edb9553e2d, limb2: 0x27b9db3dc009b797, limb3: 0x0, }, y: u384 { limb0: 0x98d17fd0a10d23d8218f14dc, limb1: 0xe9084619146a3dc82331192, limb2: 0xd5e171223497006, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x2, 0x0, 0x0, 0x0, 0x2, 0x0, 0x0, 0x2833e84879b9709143e1f593f0000000, 0x30644e72e131a029b85045b68181585d, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x6871ca8d3c208c16d87cfd45, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x6871ca8d3c208c16d87cfd45, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_2P_edge_case() { let mut data = array![ 0x3, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x2, 0x0, 0x0, 0x0, 0x3, 0x0, 0x0, 0xb4862b21fb97d43588561712e8e5216a, 0x967d0cae6f4590b9a164106cf6a659e, 0x2833e84879b9709143e1f593f0000000, 0x30644e72e131a029b85045b68181585d, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10000000000000000358f1af3ace11fdc, 0x100000000000000004ac9542b22967d33, 0x100000000000000000cf05f964742cc6d, 0x1000000000000000081d342cffb91cba7, 0x1, 0x0, 0x0, 0x0, 0x6871ca8d3c208c16d87cfd45, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x6871ca8d3c208c16d87cfd45, limb1: 0xb85045b68181585d97816a91, limb2: 0x30644e72e131a029, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BN254_3P_edge_case() { let mut data = array![ 0x4, 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0x772ca79c580e121ca148fe75, 0xce2f55e418ca01b3d6d1014b, 0x2884b1dc4e84e30f, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x57fa42444057cf0c1d62ae3c, 0x4f48d341183118d68ea41313, 0x1d2d2799db056ed1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x2, 0x0, 0x0, 0x0, 0x4, 0x0, 0x0, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x1521f387af19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x2833e84879b9709143e1f593f0000000, 0x30644e72e131a029b85045b68181585d, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x21725fdb9f487676e547051, 0xc23930e4f96498a77a316418, 0x1244cb13309195ed, 0x0, 0x6251c487cf0f5a44ac24a45b, 0xf1db336c10ce7fae206dd8dd, 0x1da9c56792006d76, 0x0, 0x9be5263ddc8a3746, 0x3b9c1e56ffcfcc82, 0x1000000000000000041c754da808c6d02, 0x277449c3e218531f, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x100000000000000005fcd1b724f1296a6, 0x1000000000000000016e3236cbd22722f, 0x4dac40f4f32b51f2, 0x1000000000000000000417aa85f133ffd, 0x1, 0x0, 0x0, 0x0, 0x6871ca8d3c208c16d87cfd45, 0xb85045b68181585d97816a91, 0x30644e72e131a029, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x8cb92121f4f98343b28bd83d, limb1: 0xa60bedf2a6dc9ea3a4503a84, limb2: 0x242282a9381754f, limb3: 0x0, }, y: u384 { limb0: 0x41c01095a54c1bf16eec174b, limb1: 0x84b781a7f16d430823b44408, limb2: 0x26bc23f1f4abf016, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xa2888ae40caa232946c5e7e1, 0xdb18cb2c04b3edd03cc744, 0x741d8ae4fcf5e095d5d00af6, 0x8b3f481e3aaa0f1a09e30ed, 0x2, 0x0, 0x0, 0x53bda402fffe5bfeffffffff00000000, 0x73eda753299d7d483339d80809a1d805, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xecb751bad54dcd6b939c2ca, 0x6655b9d5caac42364e6f38ba, 0xcf2e21f267816aef1db507c9, 0x114d1d6855d545a8aa7d76c8, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xf97a1aeffb3af00adb22c6bb, limb1: 0xa14e3a3f171bac586c55e83f, limb2: 0x4fa9ac0fc3688c4f9774b905, limb3: 0x17f1d3a73197d7942695638c, }, y: u384 { limb0: 0xecb751bad54dcd6b939c2ca, limb1: 0x6655b9d5caac42364e6f38ba, limb2: 0xcf2e21f267816aef1db507c9, limb3: 0x114d1d6855d545a8aa7d76c8, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_2P_edge_case() { let mut data = array![ 0x3, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xa2888ae40caa232946c5e7e1, 0xdb18cb2c04b3edd03cc744, 0x741d8ae4fcf5e095d5d00af6, 0x8b3f481e3aaa0f1a09e30ed, 0x3, 0x0, 0x0, 0xb4862b21fb97d43588561712e8e5216a, 0x12cfa194e6f4590b9a164106cf6a659e, 0x53bda402fffe5bfeffffffff00000000, 0x73eda753299d7d483339d80809a1d805, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1000000000000000062a39ac9655a0af5, 0x10000000000000000b59da527feb9e759, 0x885278dc00a1125a, 0x2fe0754b9fadfe7b, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xecb751bad54dcd6b939c2ca, 0x6655b9d5caac42364e6f38ba, 0xcf2e21f267816aef1db507c9, 0x114d1d6855d545a8aa7d76c8, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xf97a1aeffb3af00adb22c6bb, limb1: 0xa14e3a3f171bac586c55e83f, limb2: 0x4fa9ac0fc3688c4f9774b905, limb3: 0x17f1d3a73197d7942695638c, }, y: u384 { limb0: 0xecb751bad54dcd6b939c2ca, limb1: 0x6655b9d5caac42364e6f38ba, limb2: 0xcf2e21f267816aef1db507c9, limb3: 0x114d1d6855d545a8aa7d76c8, }, }, ); } #[test] #[ignore] fn test_msm_BLS12_381_3P_edge_case() { let mut data = array![ 0x4, 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x3d77d61326ef5a9a5a681757, 0xd3070afd4f0e121de7fcee60, 0xdf9ef4088763fe611fb85858, 0x11a612bdd0bc09562856a70, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xaefd0d854043fd325dd3c34f, 0x9b63c98d9a7845c52e1e2b0f, 0x9db0be660d847ccc58358f3f, 0x17cb6c41f0c4e1a7394ab62a, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xa2888ae40caa232946c5e7e1, 0xdb18cb2c04b3edd03cc744, 0x741d8ae4fcf5e095d5d00af6, 0x8b3f481e3aaa0f1a09e30ed, 0x4, 0x0, 0x0, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x2a43e70faf19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x51f964df9c6316b950f244556f25e2a2, 0x53bda402fffe5bfeffffffff00000000, 0x73eda753299d7d483339d80809a1d805, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x2b828af1f5fe30bbe7a1074a, 0x5669beaa69827b52dc874c9f, 0x648af2c24d82a5a758c96b8e, 0x188bc245620ae6b6afec9dc3, 0xdc96192f803ef92f56d59758, 0xfc6139925c05a030065d564, 0xb24447300bec56efec94dcf4, 0x156f97e5d31055c0a5fe154d, 0x97ac96128760678, 0x1b8269c5da3a7aa, 0x946f8bb609f9ba7d, 0x4e77077ba28bdfd6, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x3827704126429022, 0x59c3b34a3b390fcf, 0x1000000000000000076a605fca076460a, 0x2f4183d416809c9a, 0xf97a1aeffb3af00adb22c6bb, 0xa14e3a3f171bac586c55e83f, 0x4fa9ac0fc3688c4f9774b905, 0x17f1d3a73197d7942695638c, 0xecb751bad54dcd6b939c2ca, 0x6655b9d5caac42364e6f38ba, 0xcf2e21f267816aef1db507c9, 0x114d1d6855d545a8aa7d76c8, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xba6f9a258a5c81eb5c00d6d3, limb1: 0xa5d26fbf164440da345149b7, limb2: 0xf226b85ccdee44779e368a95, limb3: 0x187795607228007e29c792fb, }, y: u384 { limb0: 0x7393cfd2196053529ef8ea01, limb1: 0xf856ee4c4e2adaa88c09b7d9, limb2: 0x499710d15a098f2ff8b26e13, limb3: 0x119aed04afd21b50d616ee0e, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x6b315ececbb6406837bf51f5, 0x8ee7eb4a7c0f9e162bce3357, 0x4fe342e2fe1a7f9b, 0x0, 0x2, 0x0, 0x0, 0xbce6faada7179e84f3b9cac2fc632550, 0xffffffff00000000ffffffffffffffff, 0x3, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x100000000000000000000000000000001, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x94cea1313449bf97c840ae0a, 0x711814b583f061e9d431cca9, 0xb01cbd1c01e58065, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x2deb33a0f4a13945d898c296, limb1: 0xf8bce6e563a440f277037d81, limb2: 0x6b17d1f2e12c4247, limb3: 0x0, }, y: u384 { limb0: 0x94cea1313449bf97c840ae0a, limb1: 0x711814b583f061e9d431cca9, limb2: 0xb01cbd1c01e58065, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_2P_edge_case() { let mut data = array![ 0x3, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x6b315ececbb6406837bf51f5, 0x8ee7eb4a7c0f9e162bce3357, 0x4fe342e2fe1a7f9b, 0x0, 0x3, 0x0, 0x0, 0xeb1167b367a9c3787c65c1e582e2e662, 0xf7c1bd874da5e709d4713d60c8a70639, 0xbce6faada7179e84f3b9cac2fc632550, 0xffffffff00000000ffffffffffffffff, 0x3, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0x1, 0x100000000000000000000000000000001, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x35a5b9ab55bd33dd4dec8ec8c85b8754, 0x1256a1018e9a2606d3efc444e5bc9e97, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x94cea1313449bf97c840ae0a, 0x711814b583f061e9d431cca9, 0xb01cbd1c01e58065, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x2deb33a0f4a13945d898c296, limb1: 0xf8bce6e563a440f277037d81, limb2: 0x6b17d1f2e12c4247, limb3: 0x0, }, y: u384 { limb0: 0x94cea1313449bf97c840ae0a, limb1: 0x711814b583f061e9d431cca9, limb2: 0xb01cbd1c01e58065, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256R1_3P_edge_case() { let mut data = array![ 0x4, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x7f8bb562ff60a902ef14bcb0, 0xeb9420089fa531db62e806a6, 0xfd028df433dfd5cc, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x6b315ececbb6406837bf51f5, 0x8ee7eb4a7c0f9e162bce3357, 0x4fe342e2fe1a7f9b, 0x0, 0x4, 0x0, 0x0, 0xe443df789558867f5ba91faf7a024204, 0x23a7711a8133287637ebdcd9e87a1613, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0xbce6faada7179e84f3b9cac2fc632550, 0xffffffff00000000ffffffffffffffff, 0x3, 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0x1, 0x100000000000000000000000000000001, 0x33ee7695471a03192ef22266, 0xb449dd8cfd0c3438e14a718c, 0x1fbb33f079b828e2, 0x0, 0xb411f97aeec2eae6044122ec, 0xcdce180b60667260d7ce284e, 0xa73a7381dd3b07c, 0x0, 0x29fa93ff2e088f257810ffaf340cbe2f, 0x67db401fe06eea845a19e61367b76a34, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x44faf735503f8d6a4fd7c1f1541b0e83, 0x108efc1b039167d94064f65615a509dcb, 0x2deb33a0f4a13945d898c296, 0xf8bce6e563a440f277037d81, 0x6b17d1f2e12c4247, 0x0, 0x94cea1313449bf97c840ae0a, 0x711814b583f061e9d431cca9, 0xb01cbd1c01e58065, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xdffcaf62be678f4d3d103700, limb1: 0x4ae0c3b5a4fb0e4e7ee75279, limb2: 0x651ce75927276c9a, limb3: 0x0, }, y: u384 { limb0: 0xb27867c3cd0eb05ed74c5f9c, limb1: 0xd30f6d2e04931e22def1d510, limb2: 0x645a0d9d9776e75f, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0xa68554199c47d08ffb10d4b8, 0x5da4fbfc0e1108a8fd17b448, 0x483ada7726a3c465, 0x0, 0x2, 0x0, 0x0, 0xbaaedce6af48a03bbfd25e8cd0364140, 0xfffffffffffffffffffffffffffffffe, 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0x597aabe663b82f6f04ef2777, 0xa25b0403f1eef75702e84bb7, 0xb7c52588d95c3b9a, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x2dce28d959f2815b16f81798, limb1: 0x55a06295ce870b07029bfcdb, limb2: 0x79be667ef9dcbbac, limb3: 0x0, }, y: u384 { limb0: 0x597aabe663b82f6f04ef2777, limb1: 0xa25b0403f1eef75702e84bb7, limb2: 0xb7c52588d95c3b9a, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_2P_edge_case() { let mut data = array![ 0x3, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0xa68554199c47d08ffb10d4b8, 0x5da4fbfc0e1108a8fd17b448, 0x483ada7726a3c465, 0x0, 0x3, 0x0, 0x0, 0xeb1167b367a9c3787c65c1e582e2e662, 0xf7c1bd874da5e709d4713d60c8a70639, 0xbaaedce6af48a03bbfd25e8cd0364140, 0xfffffffffffffffffffffffffffffffe, 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x100000000000000006d17da9dde38d3aa, 0x100000000000000008e0801a3d001f325, 0x87ea3597eb650e8, 0xe42d003a1f0e89bd, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0x597aabe663b82f6f04ef2777, 0xa25b0403f1eef75702e84bb7, 0xb7c52588d95c3b9a, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x2dce28d959f2815b16f81798, limb1: 0x55a06295ce870b07029bfcdb, limb2: 0x79be667ef9dcbbac, limb3: 0x0, }, y: u384 { limb0: 0x597aabe663b82f6f04ef2777, limb1: 0xa25b0403f1eef75702e84bb7, limb2: 0xb7c52588d95c3b9a, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_SECP256K1_3P_edge_case() { let mut data = array![ 0x4, 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x589fa250d638e35400c12ddf, 0xb3aac19fcb5095808402aa7f, 0xed6de6590d0195d1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0xa68554199c47d08ffb10d4b8, 0x5da4fbfc0e1108a8fd17b448, 0x483ada7726a3c465, 0x0, 0x4, 0x0, 0x0, 0xe443df789558867f5ba91faf7a024204, 0x23a7711a8133287637ebdcd9e87a1613, 0x1846d424c17c627923c6612f48268673, 0xfcbd04c340212ef7cca5a5a19e4d6e3c, 0xbaaedce6af48a03bbfd25e8cd0364140, 0xfffffffffffffffffffffffffffffffe, 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x55909ba28af82ea934a4b85d, 0x4bf448ca5d57fb119c843e0a, 0x6a2275491b991ee3, 0x0, 0x5bf4bf0cefc9553422e60eb0, 0x178d55925d3d72f44783f626, 0xe13a21d7302f8139, 0x0, 0x4bab076cac43472e, 0x896dcc1031d19f2d, 0x100000000000000006f45630d920758e7, 0x13bfcc5670fee7eb, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x40c3f72fa123bad6, 0x461e3a87e8955f53, 0x53ec0e0286c9f6ad, 0x1000000000000000074832ec5bb09d4f6, 0x2dce28d959f2815b16f81798, 0x55a06295ce870b07029bfcdb, 0x79be667ef9dcbbac, 0x0, 0x597aabe663b82f6f04ef2777, 0xa25b0403f1eef75702e84bb7, 0xb7c52588d95c3b9a, 0x0, 0x100000000000000000000000000000001, 0x0, 0x1, 0x0, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x8ae1b945a4bee5df2482580e, limb1: 0x113a509c4213fb90b017895a, limb2: 0xdb53345431b0c359, limb3: 0x0, }, y: u384 { limb0: 0x5f8a05f7d421794bf1c2f718, limb1: 0xf026f2017517996e6dc446ce, limb2: 0xc09762999f005286, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x807131659b7830f3f62c1d14, 0xbe483ba563798323cf6fd061, 0x29c644a5c71da22e, 0x0, 0x2, 0x0, 0x0, 0x14def9dea2f79cd65812631a5cf5d3ec, 0x10000000000000000000000000000000, 0x4, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x100000000000000000000000000000001, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x7f8ece9a6487cf0c09d3e2d9, 0x41b7c45a9c867cdc30902f9e, 0x5639bb5a38e25dd1, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xd617c9aca55c89b025aef35, limb1: 0xf00b8f02f1c20618a9c13fdf, limb2: 0x2a78dd0fd02c0339, limb3: 0x0, }, y: u384 { limb0: 0x7f8ece9a6487cf0c09d3e2d9, limb1: 0x41b7c45a9c867cdc30902f9e, limb2: 0x5639bb5a38e25dd1, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_2P_edge_case() { let mut data = array![ 0x3, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x807131659b7830f3f62c1d14, 0xbe483ba563798323cf6fd061, 0x29c644a5c71da22e, 0x0, 0x3, 0x0, 0x0, 0xb4862b21fb97d43588561712e8e5216a, 0x4b3e865e6f4590b9a164106cf6a659e, 0x14def9dea2f79cd65812631a5cf5d3ec, 0x10000000000000000000000000000000, 0x4, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x1, 0x100000000000000000000000000000001, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x21ef407bea1953254c1bc318a0af2527, 0x1c147c0993c84eed5f426b94b3350045, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x7f8ece9a6487cf0c09d3e2d9, 0x41b7c45a9c867cdc30902f9e, 0x5639bb5a38e25dd1, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xd617c9aca55c89b025aef35, limb1: 0xf00b8f02f1c20618a9c13fdf, limb2: 0x2a78dd0fd02c0339, limb3: 0x0, }, y: u384 { limb0: 0x7f8ece9a6487cf0c09d3e2d9, limb1: 0x41b7c45a9c867cdc30902f9e, limb2: 0x5639bb5a38e25dd1, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_ED25519_3P_edge_case() { let mut data = array![ 0x4, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0x19657783ba5660e255c21849, 0x7ed7474bcea7551fc71e46bc, 0x596c0a76b75f4756, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x807131659b7830f3f62c1d14, 0xbe483ba563798323cf6fd061, 0x29c644a5c71da22e, 0x0, 0x4, 0x0, 0x0, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0xa90f9c3af19922ad9b8a714e61a441c, 0xeb2083e6ce164dba0ff18e0242af9fc3, 0x2fc154703983ca8ea7e9d498c778ea6, 0x14def9dea2f79cd65812631a5cf5d3ec, 0x10000000000000000000000000000000, 0x4, 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xf046f8cd6e5a75fca71dd19b, 0x892b4613ef5c58df4ef692a4, 0x7527fa36f5738847, 0x0, 0x1, 0x100000000000000000000000000000001, 0xf7d884feff5aba51d9990dce, 0x999f1d302046c6266257ff5, 0x7f9caa5ee5815899, 0x0, 0x6d71279424538e87f8ecf2cc, 0x8a8a1d74581da5996a52bbaf, 0x29acff692eccea25, 0x0, 0x211c4f690d00cb3af0b34c381ddf6429, 0x10dbbf233e0f266b14c85329c2440c426, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x3242668a77ced3cb6ca4b87c1b759c91, 0x128e825972592d2a632df711368a1c105, 0xd617c9aca55c89b025aef35, 0xf00b8f02f1c20618a9c13fdf, 0x2a78dd0fd02c0339, 0x0, 0x7f8ece9a6487cf0c09d3e2d9, 0x41b7c45a9c867cdc30902f9e, 0x5639bb5a38e25dd1, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xea1930f7f9c99711b76d5726, limb1: 0xa06d0a2a0011cdaa581c307a, limb2: 0x6a9d379c7dcfb5b6, limb3: 0x0, }, y: u384 { limb0: 0xe529194a47d7db7a9a8b88b1, limb1: 0xebb88d8901d42d55b9966ff5, limb2: 0x2ea083fb0eb0877c, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_1P_edge_case() { let mut data = array![ 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0xf1181294833fc48d823f272c, 0xcf135e7506a45d632d270d45, 0x2, 0x0, 0x2, 0x0, 0x0, 0x97816a916871ca8d3c208c16d87cfd46, 0x30644e72e131a029b85045b68181585d, 0x5, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x100000000000000000000000000000001, 0x1, 0x0, 0x0, 0x0, 0x88a15dfcc0a231066dc0d8d5, 0xe93ce7417adcfaf9fb0cdb02, 0x30644e72e131a026, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x88a15dfcc0a231066dc0d8d5, limb1: 0xe93ce7417adcfaf9fb0cdb02, limb2: 0x30644e72e131a026, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_2P_edge_case() { let mut data = array![ 0x3, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0xf1181294833fc48d823f272c, 0xcf135e7506a45d632d270d45, 0x2, 0x0, 0x3, 0x0, 0x0, 0xb4862b21fb97d43588561712e8e5216a, 0x967d0cae6f4590b9a164106cf6a659e, 0x97816a916871ca8d3c208c16d87cfd46, 0x30644e72e131a029b85045b68181585d, 0x5, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x1, 0x100000000000000000000000000000001, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x5520c252aad219e02bf5055a4ed023b7, 0x197e50b8e7adb6dd93eeede129c12721, 0x1, 0x0, 0x0, 0x0, 0x88a15dfcc0a231066dc0d8d5, 0xe93ce7417adcfaf9fb0cdb02, 0x30644e72e131a026, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x88a15dfcc0a231066dc0d8d5, limb1: 0xe93ce7417adcfaf9fb0cdb02, limb2: 0x30644e72e131a026, limb3: 0x0, }, }, ); } #[test] #[ignore] fn test_msm_GRUMPKIN_3P_edge_case() { let mut data = array![ 0x4, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0xa560a5759c90985fde99aca0, 0xc5b21186cc6dcd0421026513, 0x21fb1f47c6ac55b3, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0xf1181294833fc48d823f272c, 0xcf135e7506a45d632d270d45, 0x2, 0x0, 0x4, 0x0, 0x0, 0x12e0c8b2bad640fb19488dec4f65d4d9, 0x1521f387af19922ad9b8a714e61a441c, 0x5a92118719c78df48f4ff31e78de5857, 0x28fcb26f9c6316b950f244556f25e2a2, 0x97816a916871ca8d3c208c16d87cfd46, 0x30644e72e131a029b85045b68181585d, 0x5, 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x371e7b6a5c01505bd4334e81, 0x2f596ae4492a87c66f7bda1a, 0x9dffb4dcdb94df9, 0x0, 0x1, 0x100000000000000000000000000000001, 0xf47b4ee8eecf8576c38173d8, 0x755d90a26c30d7d6fb33afd3, 0x5e835e05fdb55c5, 0x0, 0x990d5f4767a8d057f8695e4e, 0x5f8dd4e272c268c0d2ce4a39, 0x1704905427d31a82, 0x0, 0x39dea48eef47b3e6bcae980c9112d477, 0x538cc4627274d8f320bf5df15c887356, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10a2e45b33049f11b360c09b6389565b, 0x63f1d0c59d848c415389772b72561b3d, 0x1, 0x0, 0x0, 0x0, 0x88a15dfcc0a231066dc0d8d5, 0xe93ce7417adcfaf9fb0cdb02, 0x30644e72e131a026, 0x0, 0x1, 0x1, ] .span(); let points = Serde::deserialize(ref data).unwrap(); let scalars = Serde::deserialize(ref data).unwrap(); let curve_id = Serde::deserialize(ref data).unwrap(); let res = msm_g1(points, scalars, curve_id, data); assert!( res == G1Point { x: u384 { limb0: 0xf8c1f1ea2f76ef32e8aaa1e5, limb1: 0x4f332469fd3c88e2a2a255c6, limb2: 0x25bea91cb12ea60f, limb3: 0x0, }, y: u384 { limb0: 0x13dd399b7d2ee3c5048e382d, limb1: 0x8d9fd23cff123740ae29ea9a, limb2: 0x8aa44466337bea4, limb3: 0x0, }, }, ); } ================================================ FILE: src/src/tests/autogenerated/pairing_tests.cairo ================================================ use garaga::definitions::{ E12D, G1G2Pair, G1Point, G2Line, G2Point, MillerLoopResultScalingFactor, u288, u384, }; use garaga::groth16::{ multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result, multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result, }; use garaga::pairing_check::{ MPCheckHintBLS12_381, MPCheckHintBN254, multi_pairing_check_bls12_381_2P_2F, multi_pairing_check_bn254_2P_2F, }; #[test] fn test_BN254_mpcheck_2P_2F() { let pair0: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xcdb6d03cb7b9a5409b7efcd8, limb1: 0xd1df87eab84852372b905c9c, limb2: 0x1d0634f3f21e7890, limb3: 0x0, }, y: u384 { limb0: 0xaa1d4f4d3021032564460978, limb1: 0xeb3f1d6ba3b10e2b53dc193b, limb2: 0x24c53532773dce26, limb3: 0x0, }, }, q: G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }, }; let pair1: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0x536c985db33c69f7c242e07a, limb1: 0xfc531bccffafcf1e59d91fb9, limb2: 0x2585e4f8a31664cb, limb3: 0x0, }, y: u384 { limb0: 0x57fa42444057cf0c1d62ae3c, limb1: 0x4f48d341183118d68ea41313, limb2: 0x1d2d2799db056ed1, limb3: 0x0, }, }, q: G2Point { x0: u384 { limb0: 0x335eb0538f718d8e6651eeb1, limb1: 0x635e573808d9d5c7178bdce7, limb2: 0x1314aaf1c372e6d7, limb3: 0x0, }, x1: u384 { limb0: 0x5289f29ccc5acf5e81526673, limb1: 0x2d4aba9e1448a8cc1048d01a, limb2: 0x14c25d3aec745e5a, limb3: 0x0, }, y0: u384 { limb0: 0x10d1d0efd5869ecd23aab8e9, limb1: 0xba7d1de6d86501d49b6a8dab, limb2: 0x397391b7b25e2f, limb3: 0x0, }, y1: u384 { limb0: 0x385a553ea12434f4eda6db36, limb1: 0xb058c1ff7e4c5c7ec7e5859b, limb2: 0x1863ac65eca09e89, limb3: 0x0, }, }, }; let lines = array![ G2Line { r0a0: u288 { limb0: 0x4d347301094edcbfa224d3d5, limb1: 0x98005e68cacde68a193b54e6, limb2: 0x237db2935c4432bc, }, r0a1: u288 { limb0: 0x6b4ba735fba44e801d415637, limb1: 0x707c3ec1809ae9bafafa05dd, limb2: 0x124077e14a7d826a, }, r1a0: u288 { limb0: 0x49a8dc1dd6e067932b6a7e0d, limb1: 0x7676d0000961488f8fbce033, limb2: 0x3b7178c857630da, }, r1a1: u288 { limb0: 0x98c81278efe1e96b86397652, limb1: 0xe3520b9dfa601ead6f0bf9cd, limb2: 0x2b17c2b12c26fdd0, }, }, G2Line { r0a0: u288 { limb0: 0x7e165b3014d84802bf01484e, limb1: 0x3260b32ceced0b1243d4c84e, limb2: 0x2d4b148197812cd9, }, r0a1: u288 { limb0: 0xed50630084c5fc98c14adf76, limb1: 0x8b3e4e11609f5b1ec2a4a3fd, limb2: 0x9449ebaa6581db4, }, r1a0: u288 { limb0: 0x6dbbec1fa71f727fad9c2035, limb1: 0x2d74c51612b1473f7a789efb, limb2: 0x219b1595f2e94586, }, r1a1: u288 { limb0: 0x18b802809d63c96cb122eb63, limb1: 0x971ad93ce0fb9233480bfe98, limb2: 0x1cf3a36431cdb52c, }, }, G2Line { r0a0: u288 { limb0: 0x1b3d578c32d1af5736582972, limb1: 0x204fe74db6b371d37e4615ab, limb2: 0xce69bdf84ed6d6d, }, r0a1: u288 { limb0: 0xfd262357407c3d96bb3ba710, limb1: 0x47d406f500e66ea29c8764b3, limb2: 0x1e23d69196b41dbf, }, r1a0: u288 { limb0: 0x1ec8ee6f65402483ad127f3a, limb1: 0x41d975b678200fce07c48a5e, limb2: 0x2cad36e65bbb6f4f, }, r1a1: u288 { limb0: 0xcfa9b8144c3ea2ab524386f5, limb1: 0xd4fe3a18872139b0287570c3, limb2: 0x54c8bc1b50aa258, }, }, G2Line { r0a0: u288 { limb0: 0xb5ee22ba52a7ed0c533b7173, limb1: 0xbfa13123614ecf9c4853249b, limb2: 0x6567a7f6972b7bb, }, r0a1: u288 { limb0: 0xcf422f26ac76a450359f819e, limb1: 0xc42d7517ae6f59453eaf32c7, limb2: 0x899cb1e339f7582, }, r1a0: u288 { limb0: 0x9f287f4842d688d7afd9cd67, limb1: 0x30af75417670de33dfa95eda, limb2: 0x1121d4ca1c2cab36, }, r1a1: u288 { limb0: 0x7c4c55c27110f2c9a228f7d8, limb1: 0x8f14f6c3a2e2c9d74b347bfe, limb2: 0x83ef274ba7913a5, }, }, G2Line { r0a0: u288 { limb0: 0xea5b6f5d27484414197bb4f9, limb1: 0x85ef928994944d4b53aca242, limb2: 0x31939f149b07350, }, r0a1: u288 { limb0: 0x7b21678cb75a8f7e17321dd1, limb1: 0x2d11f7a520e1fd3ed4dcc693, limb2: 0x271fafb83ad98275, }, r1a0: u288 { limb0: 0xfab5de6d950119972ae0dd12, limb1: 0x8adb80a06ed0111e1d08cb95, limb2: 0xec938dcee485aa3, }, r1a1: u288 { limb0: 0x4fb9c80c9ebcc2aa275a11e4, limb1: 0x21356c79a085c62a4f756bf9, limb2: 0x1370ab0eaf63eafd, }, }, G2Line { r0a0: u288 { limb0: 0xc0f94eb338d27e3d9c3c54bf, limb1: 0xcbc81234f5e7a25b356780b1, limb2: 0x2d7855cb075109f7, }, r0a1: u288 { limb0: 0x284c304021c8efe832d4019, limb1: 0xcf072fe1e6a5712c6939b2e5, limb2: 0x2aebdfbcb148dbd2, }, r1a0: u288 { limb0: 0xd7b47c349d5fa8cbc0c0bdc4, limb1: 0x262a79a0c9001db94d4629e6, limb2: 0x229b6a2be2e077d7, }, r1a1: u288 { limb0: 0x5ac06a263b3dad67c61b9b1a, limb1: 0x218d4cdc4cddee7306803f0c, limb2: 0x2c404c393f42c23c, }, }, G2Line { r0a0: u288 { limb0: 0xfc23a674d089e9cfdefb1db8, limb1: 0x9ddfd61d289b65a9b4254476, limb2: 0x1e2f561324ef4447, }, r0a1: u288 { limb0: 0xf67a6a9e31f6975b220642ea, limb1: 0xccd852893796296e4d1ed330, limb2: 0x94ff1987d19b62, }, r1a0: u288 { limb0: 0x360c2a5aca59996d24cc1947, limb1: 0x66c2d7d0d176a3bc53f386e8, limb2: 0x2cfcc62a17fbeecb, }, r1a1: u288 { limb0: 0x2ddc73389dd9a9e34168d8a9, limb1: 0xae9afc57944748b835cbda0f, limb2: 0x12f0a1f8cf564067, }, }, G2Line { r0a0: u288 { limb0: 0x9e2613c20164688ed46379a, limb1: 0x716db3679a44c686aa59d1ab, limb2: 0x15001844790ca939, }, r0a1: u288 { limb0: 0x6fbc98bc7a182aa3dd0cb359, limb1: 0xc97408d0c1cf3952033b11b0, limb2: 0x1ab481f0cb16916b, }, r1a0: u288 { limb0: 0x7f38f154b08df182e2924e74, limb1: 0xba31b530302528255113573a, limb2: 0x933362e822d9bbb, }, r1a1: u288 { limb0: 0xfe131760a10954277d407df3, limb1: 0x7fa6f47454535d07b1c8ffad, limb2: 0x966415d59cef8df, }, }, G2Line { r0a0: u288 { limb0: 0x9c963c4bdade6ce3d460b077, limb1: 0x1738311feefc76f565e34e8a, limb2: 0x1aae0d6c9e9888ad, }, r0a1: u288 { limb0: 0x9272581fdf80b045c9c3f0a, limb1: 0x3946807b0756e87666798edb, limb2: 0x2bf6eeda2d8be192, }, r1a0: u288 { limb0: 0x3e957661b35995552fb475de, limb1: 0xd8076fa48f93f09d8128a2a8, limb2: 0xb6f87c3f00a6fcf, }, r1a1: u288 { limb0: 0xcf17d6cd2101301246a8f264, limb1: 0x514d04ad989b91e697aa5a0e, limb2: 0x175f17bbd0ad1219, }, }, G2Line { r0a0: u288 { limb0: 0x894bc18cc70ca1987e3b8f9f, limb1: 0xd4bfa535181f0f8659b063e3, limb2: 0x19168d524164f463, }, r0a1: u288 { limb0: 0x850ee8d0e9b58b82719a6e92, limb1: 0x9fc4eb75cbb027c137d48341, limb2: 0x2b2f8a383d944fa0, }, r1a0: u288 { limb0: 0x5451c8974a709483c2b07fbd, limb1: 0xd7e09837b8a2a3b78e7fe525, limb2: 0x347d96be5e7fa31, }, r1a1: u288 { limb0: 0x823f2ba2743ee254e4c18a1e, limb1: 0x6a61af5db035c443ed0f8172, limb2: 0x1e840eee275d1063, }, }, G2Line { r0a0: u288 { limb0: 0x97890ec993740b1ca0337563, limb1: 0x4fa454f0d8b7b9f3e996a148, limb2: 0x2687d9105ae36d86, }, r0a1: u288 { limb0: 0x94553c479c2341dd9d19c228, limb1: 0xf3893568e1c69e8691e6d21d, limb2: 0x176dd970f5c96141, }, r1a0: u288 { limb0: 0x10b35743d178c928ae8988f3, limb1: 0x4e09ad83d2ef00527273723e, limb2: 0x2357f050a2e191c4, }, r1a1: u288 { limb0: 0x4c47ba83a5200a671c9a6e66, limb1: 0x9ed7cd2e0db8b052d78aeccf, limb2: 0x2b778d052020e24f, }, }, G2Line { r0a0: u288 { limb0: 0x38f9cedd0c82018426759a6e, limb1: 0x44c9564dd70a19718df031b9, limb2: 0x2c123a573f011ecf, }, r0a1: u288 { limb0: 0xdc5f6dd6fabcfd365452fd48, limb1: 0x3be2013bcd845c73bef09c2a, limb2: 0x20a73a0d44be878, }, r1a0: u288 { limb0: 0x9d6fc1cc6d53b9b473418843, limb1: 0x179167ea194fa9a3fb5546bf, limb2: 0x122aeeaaf6e42f52, }, r1a1: u288 { limb0: 0x3b7e8d815b2f3ad687c6b33b, limb1: 0xbfacefc007f6e8b61a5b0930, limb2: 0x14d40bc6eff71288, }, }, G2Line { r0a0: u288 { limb0: 0x18d630598e58bb5d0102b30e, limb1: 0x9767e27b02a8da37411a2787, limb2: 0x100a541662b9cd7c, }, r0a1: u288 { limb0: 0x4ca7313df2e168e7e5ea70, limb1: 0xd49cce6abd50b574f31c2d72, limb2: 0x78a2afbf72317e7, }, r1a0: u288 { limb0: 0x6d99388b0a1a67d6b48d87e0, limb1: 0x1d8711d321a193be3333bc68, limb2: 0x27e76de53a010ce1, }, r1a1: u288 { limb0: 0x77341bf4e1605e982fa50abd, limb1: 0xc5cf10db170b4feaaf5f8f1b, limb2: 0x762adef02274807, }, }, G2Line { r0a0: u288 { limb0: 0x3896b4539101a9d082d01df0, limb1: 0x1bdd4fa3c048c10eb04232b4, limb2: 0x2bbc70702a7f5b2d, }, r0a1: u288 { limb0: 0x617716ce0b0fc90781832057, limb1: 0x800927818218483eb3cf9245, limb2: 0x211e4fc4a1ae2c66, }, r1a0: u288 { limb0: 0xe7b44e14a444b645b8c0b11f, limb1: 0x2b07f556a654bd49cd865885, limb2: 0x1866e4634404cecf, }, r1a1: u288 { limb0: 0x48a0768996bd4017ff614ce, limb1: 0x4f0066744ba90bd46ee6e88e, limb2: 0x1de00ce581b3556f, }, }, G2Line { r0a0: u288 { limb0: 0xa137b991ba9048aee9fa0bc7, limb1: 0xf5433785c186cd1100ab6b80, limb2: 0xab519fd7cf8e7f9, }, r0a1: u288 { limb0: 0x90832f45d3398c60aa1a74e2, limb1: 0x17f7ac209532723f22a344b, limb2: 0x23db979f8481c5f, }, r1a0: u288 { limb0: 0x723b0e23c2808a5d1ea6b11d, limb1: 0x3030030d26411f84235c3af5, limb2: 0x122e78da5509eddb, }, r1a1: u288 { limb0: 0xf1718c1e21a9bc3ec822f319, limb1: 0xf5ee6dfa3bd3272b2f09f0c7, limb2: 0x5a29c1e27616b34, }, }, G2Line { r0a0: u288 { limb0: 0x7369b6adc59d1ad1956aa29c, limb1: 0x5a1a92f3dda868e7423f70bd, limb2: 0x13da850286346586, }, r0a1: u288 { limb0: 0x5eedbb4b5f1b8c52d4ff5734, limb1: 0x9988f4f6e06343ab4f5831ad, limb2: 0xfbbd4d49b51a489, }, r1a0: u288 { limb0: 0x9cd983785651ba1c2c06bf74, limb1: 0x21f088328b5920e22e7a73f6, limb2: 0x1e16dd13e77f83f4, }, r1a1: u288 { limb0: 0x44bdd6e622016e7b7287c24f, limb1: 0xb454bfef81527e305bd509e6, limb2: 0x25b37c864eb9335d, }, }, G2Line { r0a0: u288 { limb0: 0xbc1ede480873fceb8739511e, limb1: 0xd5a60533bd0ce7869efbc15, limb2: 0x182c17d793eba74d, }, r0a1: u288 { limb0: 0x83bf38d91876ad8999516bc2, limb1: 0x7756322ea3dc079289d51f2d, limb2: 0x1d0f6156a89a4244, }, r1a0: u288 { limb0: 0x6aba652f197be8f99707b88c, limb1: 0xbf94286c245794ea0f562f32, limb2: 0x25a358967a2ca81d, }, r1a1: u288 { limb0: 0xc028cbff48c01433e8b23568, limb1: 0xd2e791f5772ed43b056beba1, limb2: 0x83eb38dff4960e, }, }, G2Line { r0a0: u288 { limb0: 0xea4e2dfe89a1e44be7ce1e1c, limb1: 0x5a92c01d769c449c202b3214, limb2: 0xff9af539be5c8c9, }, r0a1: u288 { limb0: 0x787ac32ae432e43bed70fb07, limb1: 0x4a33b653a031d4b9f2785ff3, limb2: 0x26614c3211203a55, }, r1a0: u288 { limb0: 0xb191249d1a1f0c8c86ebe4ea, limb1: 0xad273f446b939f4f1f361ebf, limb2: 0xedc66a88aa083a1, }, r1a1: u288 { limb0: 0xdca5c397dab1714ac36c1bc8, limb1: 0x924f9820543a3519c11d3f74, limb2: 0x1ad8a781081d4a96, }, }, G2Line { r0a0: u288 { limb0: 0xc2a2b787d8e718e81970db80, limb1: 0x5372abeaf56844dee60d6198, limb2: 0x131210153a2217d6, }, r0a1: u288 { limb0: 0x70421980313e09a8a0e5a82d, limb1: 0xf75ca1f68f4b8deafb1d3b48, limb2: 0x102113c9b6feb035, }, r1a0: u288 { limb0: 0x4654c11d73bda84873de9b86, limb1: 0xa67601bca2e595339833191a, limb2: 0x1c2b76e439adc8cc, }, r1a1: u288 { limb0: 0x9c53a48cc66c1f4d644105f2, limb1: 0xa17a18867557d96fb7c2f849, limb2: 0x1deb99799bd8b63a, }, }, G2Line { r0a0: u288 { limb0: 0xc32026c56341297fa080790c, limb1: 0xe23ad2ff283399133533b31f, limb2: 0xa6860f5c968f7ad, }, r0a1: u288 { limb0: 0x2966cf259dc612c6a4d8957d, limb1: 0xfba87ea86054f3db5774a08f, limb2: 0xc73408b6a646780, }, r1a0: u288 { limb0: 0x6272ce5976d8eeba08f66b48, limb1: 0x7dfbd78fa06509604c0cec8d, limb2: 0x181ec0eaa6660e45, }, r1a1: u288 { limb0: 0x48af37c1a2343555fbf8a357, limb1: 0xa7b5e1e20e64d6a9a9ce8e61, limb2: 0x1147dcea39a47abd, }, }, G2Line { r0a0: u288 { limb0: 0x9fd5ab512989c347dc77f420, limb1: 0xc1c85ee38ca3eb02a0a92db3, limb2: 0x2134aa9ca8e8d251, }, r0a1: u288 { limb0: 0xe4f274770138210ec97f351c, limb1: 0x95d8dbdcefe97681885f8ca3, limb2: 0x25c205641353bd02, }, r1a0: u288 { limb0: 0x67e5fc30cb9d54c952e30530, limb1: 0xbed1776ffd1f34cef4d280ba, limb2: 0x9bfcdc38d2edfbc, }, r1a1: u288 { limb0: 0x2cdc4960c64fd9f1e1d8c062, limb1: 0x25ab4699c0326eb69704502c, limb2: 0x1a1bfdd2477bfb3, }, }, G2Line { r0a0: u288 { limb0: 0xc01f15fdcbfada9ddb6d29e5, limb1: 0x1c597a278f91d2146e39417b, limb2: 0x1e738c819e505603, }, r0a1: u288 { limb0: 0xc448617c638a5f5a3d7bb80b, limb1: 0xe5c0daa3ccc9d0066e8748e6, limb2: 0x1531822272e52502, }, r1a0: u288 { limb0: 0xe6dcbe5738e474a779a48437, limb1: 0x778679b9709f1160945eb1f4, limb2: 0x1c4c788451e4cdd3, }, r1a1: u288 { limb0: 0x9bb0e3bca45c662cc5a01154, limb1: 0xdcc6384e4ed67039e4f3a54d, limb2: 0x1e8aea6fd2e608bf, }, }, G2Line { r0a0: u288 { limb0: 0x4033c51e6e469818521cd2ae, limb1: 0xb71a4629a4696b2759f8e19e, limb2: 0x4f5744e29c1eb30, }, r0a1: u288 { limb0: 0xa4f47bbc60cb0649dca1c772, limb1: 0x835f427106f4a6b897c6cf23, limb2: 0x17ca6ea4855756bb, }, r1a0: u288 { limb0: 0x7f844a35c7eeadf511e67e57, limb1: 0x8bb54fb0b3688cac8860f10, limb2: 0x1c7258499a6bbebf, }, r1a1: u288 { limb0: 0x10d269c1779f96946e518246, limb1: 0xce6fcef6676d0dacd395dc1a, limb2: 0x2cf4c6ae1b55d87d, }, }, G2Line { r0a0: u288 { limb0: 0xc55a9ab2be5b1c5f99b4afdf, limb1: 0x443b75328adfb9d1d45195be, limb2: 0x568d5a8780d1576, }, r0a1: u288 { limb0: 0x85b522186579e779a3606ede, limb1: 0x1ebb4d198b300f1f7309a38f, limb2: 0x9f9cb82898a523d, }, r1a0: u288 { limb0: 0x731bed2ccf3a6cbf023ed5b, limb1: 0xcf340b50f74cdea1da20612a, limb2: 0x21d63865d400949d, }, r1a1: u288 { 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{ r0a0: u288 { limb0: 0xe2031868c812b8cecacd7a4a, limb1: 0x50546c799ceed3c43c41f4ba, limb2: 0x25cc77c74cbabdbd, }, r0a1: u288 { limb0: 0x295bae77b9ad4b6c97646232, limb1: 0x75621d2aff5e576b7d6fe300, limb2: 0x143043b86b1ca5b4, }, r1a0: u288 { limb0: 0xca3c979fa4d3b18d2f7b1bcc, limb1: 0xdd2c365809773b6e09ccb2b9, limb2: 0x14391c33bfc390d8, }, r1a1: u288 { limb0: 0x5e861ecfb9119d168163c202, limb1: 0xcdbc50774ab2e9bee2b80649, limb2: 0x1fbe4fcdc5c5a57e, }, }, G2Line { r0a0: u288 { limb0: 0xb2236e5462d1e11842039bb5, limb1: 0x8d746dd0bb8bb2a455d505c1, limb2: 0x2fd3f4a905e027ce, }, r0a1: u288 { limb0: 0x3d6d9836d71ddf8e3b741b09, limb1: 0x443f16e368feb4cb20a5a1ab, limb2: 0xb5f19dda13bdfad, }, r1a0: u288 { limb0: 0x4e5612c2b64a1045a590a938, limb1: 0xbca215d075ce5769db2a29d7, limb2: 0x161e651ebdfb5065, }, r1a1: u288 { limb0: 0xc02a55b6685351f24e4bf9c7, limb1: 0x4134240119050f22bc4991c8, limb2: 0x300bd9f8d76bbc11, }, }, G2Line { r0a0: u288 { limb0: 0xe9296a3a3aed4c4143d2e0ba, limb1: 0x7de973514b499b2da739b3e6, limb2: 0x1b4b807986fcdee0, }, r0a1: u288 { limb0: 0xb9295fecce961afe0c5e6dad, limb1: 0xc4e30c322bcae6d526c4de95, limb2: 0x1fee592f513ed6b2, }, r1a0: u288 { limb0: 0x7245f5e5e803d0d448fafe21, limb1: 0xcbdc032ecb3b7a63899c53d0, limb2: 0x1fde9ffc17accfc3, }, r1a1: u288 { limb0: 0x8edcc1b2fdd35c87a7814a87, limb1: 0x99d54b5c2fe171c49aa9cb08, limb2: 0x130ef740e416a6fe, }, }, G2Line { r0a0: u288 { limb0: 0x50cb7f4b087200d53fa86cb2, limb1: 0xff132c0ccf9286b3bc6e72f8, limb2: 0xd1d98c6aa4cbd20, }, r0a1: u288 { limb0: 0x5cb371016b5e5346aa276b94, limb1: 0xb4491b5077bb58bcf9cd8f43, limb2: 0xd51bc57128e720a, }, r1a0: u288 { limb0: 0x397965b705cdb46b061f25e8, limb1: 0xd1ed8b8fa62c5c50b27dc115, limb2: 0x395493fce79da18, }, r1a1: u288 { limb0: 0x8964d77b83faf3ac3f972566, limb1: 0x6c73a21e7e6db17d8f89f9fa, limb2: 0x7ed3c0d414cddf7, }, }, G2Line { r0a0: u288 { limb0: 0xed3ac7bc560f29f1d5148309, limb1: 0xd4bc60d88edc82f6a9336b9a, limb2: 0x1af46a921f0bb17, }, r0a1: u288 { limb0: 0xf5a22ff7d977b6b6acf9f3ca, limb1: 0xad4b2299bff7a855dfde34df, limb2: 0x2176ace7d56a9ff2, }, r1a0: u288 { limb0: 0xdc5d8bbb9566386bdca9619e, limb1: 0x518f514d6bf9082b5e1ca06a, limb2: 0x28162e5d570380f, }, r1a1: u288 { limb0: 0x448f699ecddf33780c7293a, limb1: 0x147b945d1db66b75de1d0e11, limb2: 0x2c3dec42b83ab6d5, }, }, G2Line { r0a0: u288 { limb0: 0x537ecf0916b38aeea21d4e47, limb1: 0x181a00de27ba4be1b380d6c8, limb2: 0x8c2fe2799316543, }, r0a1: u288 { limb0: 0xe68fff5ee73364fff3fe403b, limb1: 0x7b8685c8a725ae79cfac8f99, limb2: 0x7b4be349766aba4, }, r1a0: u288 { limb0: 0xdf7c93c0095545ad5e5361ea, limb1: 0xce316c76191f1e7cd7d03f3, limb2: 0x22ea21f18ddec947, }, r1a1: u288 { limb0: 0xa19620b4c32db68cc1c2ef0c, limb1: 0xffa1e4be3bed5faba2ccbbf4, limb2: 0x16fc78a64c45f518, }, }, G2Line { r0a0: u288 { limb0: 0x2b6af476f520b4bf804415bc, limb1: 0xd949ee7f9e8874698b090fca, limb2: 0x34db5e5ec2180cf, }, r0a1: u288 { limb0: 0x3e06a324f038ac8abcfb28d7, limb1: 0xc2e6375b7a83c0a0145f8942, limb2: 0x2247e79161483763, }, r1a0: u288 { limb0: 0x708773d8ae3a13918382fb9d, limb1: 0xaf83f409556e32aa85ae92bf, limb2: 0x9af0a924ae43ba, }, r1a1: u288 { limb0: 0xa6fded212ff5b2ce79755af7, limb1: 0x55a2adfb2699ef5de6581b21, limb2: 0x2476e83cfe8daa5c, }, }, G2Line { r0a0: u288 { limb0: 0x88da3121b35160882a1c7589, limb1: 0x65804a112b6f3376e944918a, limb2: 0x16dacfb60b1ce19a, }, r0a1: u288 { limb0: 0xeff82aff39cb798ce9b8b0d9, limb1: 0xa90ce85c7d5f232be9d0aa48, limb2: 0x193c05a28703b386, }, r1a0: u288 { limb0: 0x20ad3c10b068e055950db02d, limb1: 0x7f126eebf19b02a0833fe0ce, limb2: 0x297139b7691ecc5, }, r1a1: u288 { limb0: 0x1b6a771c255179179254a975, limb1: 0x6e8c9e35001729b1f77e9eb2, limb2: 0x3e2e494608e33c7, }, }, G2Line { r0a0: u288 { limb0: 0x7f9803672c5c3c3885d9f98a, limb1: 0xde4f0a101b3d8f9ee11d42b2, limb2: 0x20a37cabfbfa257, }, r0a1: u288 { limb0: 0x26838cb91e386068a3da1af1, limb1: 0xee22b598ea3b51661d35cff3, limb2: 0x1919454dad133f1c, }, r1a0: u288 { limb0: 0x7c23a02fb58896140cab4a26, limb1: 0xb61a77a33f73616e4ebaac8a, limb2: 0x98a546ad9b9c556, }, r1a1: u288 { limb0: 0xa4bc65cb502123f8cab8a370, limb1: 0x8be2308b4f0c0dd30f4f47e8, limb2: 0x20ccdec6f5186f9e, }, }, G2Line { r0a0: u288 { limb0: 0x1c4759bcf7c607fe3f839d4d, limb1: 0xea91f311da73327e2ed40785, limb2: 0x2017052c72360f42, }, r0a1: u288 { limb0: 0x38cf8a4368c0709980199fc3, limb1: 0xfc9047885996c19e84d7d4ea, limb2: 0x1795549eb0b97783, }, r1a0: u288 { limb0: 0xb70f7ecfbec0eaf46845e8cc, limb1: 0x9ddf274c2a9f89ea3bc4d66f, limb2: 0xcc6f106abfcf377, }, r1a1: u288 { limb0: 0xf6ff11ce29186237468c2698, limb1: 0x5c629ad27bb61e4826bb1313, limb2: 0x2014c6623f1fb55e, }, }, G2Line { r0a0: u288 { limb0: 0x5c4102ef74201f7de38e0463, limb1: 0xb1ef54e99607be59909009bb, limb2: 0x25ff50f42e66453b, }, r0a1: u288 { limb0: 0x76c0ba1f7c7f207460e65d58, limb1: 0x878854c0c07edabf3d15a5c9, limb2: 0x182311cfea026538, }, r1a0: u288 { limb0: 0xc8bbb32e6a668cf1e33ec2d8, limb1: 0x23c6efb2db33c7221af7e56c, limb2: 0x22c07d0e7f650e9a, }, r1a1: u288 { limb0: 0xadf5b275b9ae0362598bc296, limb1: 0x70f05b3cbfa5ee508c52d108, limb2: 0x2c76c696e1630aa3, }, }, G2Line { r0a0: u288 { limb0: 0xc648054e4b6134bbfd68487f, limb1: 0xdf0506dad3f3d098c13a6386, limb2: 0x26bebeb6f46c2e8c, }, r0a1: u288 { limb0: 0x9d0cdb28a94204776c6e6ba6, limb1: 0x303f02dfe619752b1607951d, limb2: 0x1127d8b17ef2c064, }, r1a0: u288 { limb0: 0xe34ca1188b8db4e4694a696c, limb1: 0x243553602481d9b88ca1211, limb2: 0x1f8ef034831d0132, }, r1a1: u288 { limb0: 0xe3a5dfb1785690dad89ad10c, limb1: 0xd690b583ace24ba033dd23e0, limb2: 0x405d0709e110c03, }, }, G2Line { r0a0: u288 { limb0: 0x9f395ba5aff2b0485d02ad3, limb1: 0xd745a02f5dda7608c1aa5b6c, limb2: 0x2c12ce79338fb06c, }, r0a1: u288 { limb0: 0x6bbfa55a1d9bfb38880150f5, limb1: 0x3a352c8ebceaab1b84fddea8, limb2: 0x1ef234624c2a4dd1, }, r1a0: u288 { limb0: 0xce4d0f18e7500ec5e79f5c9b, limb1: 0x806d4caac7b410b45752f986, limb2: 0x12ec5a5f04110219, }, r1a1: u288 { limb0: 0x1cacd816d2c00f06c10b8405, limb1: 0xfa95cba80a6fa53f6e8fcdbd, limb2: 0xd5b083f527eaaf5, }, }, G2Line { r0a0: u288 { limb0: 0x72cc2cef2785ce4ff4e9b7af, limb1: 0x60ed5b9c207d7f31fb6234ab, limb2: 0x1bb17a4bc7b643ed, }, r0a1: u288 { limb0: 0x9424eb15b502cde7927c7530, limb1: 0xa0e33edbbaa9de8e9c206059, limb2: 0x2b9a3a63bbf4af99, }, r1a0: u288 { limb0: 0x423811cb6386e606cf274a3c, limb1: 0x8adcc0e471ecfe526f56dc39, limb2: 0x9169a8660d14368, }, r1a1: u288 { limb0: 0xf616c863890c3c8e33127931, limb1: 0xcc9414078a6da6989dae6b91, limb2: 0x594d6a7e6b34ab2, }, }, G2Line { r0a0: u288 { limb0: 0x7fb74b75258ad974f27f0b99, limb1: 0x84f19bd902fadad4d0bcd73c, limb2: 0xce721ef63bddc72, }, r0a1: u288 { limb0: 0xaaa754b4283ded9567a7ebe6, limb1: 0x8680b8bb98776864cf0b9a91, limb2: 0x2c654975f8cf5aac, }, r1a0: u288 { limb0: 0x15b404bb99c14804cb871df0, limb1: 0x28f2373909ce28eab3269ad5, limb2: 0x23f0beb80a0dc66f, }, r1a1: u288 { limb0: 0x1a40652ffabc01487ee07368, limb1: 0xfb7d1ac226c315f73ba10295, limb2: 0xd4a4463afd8862a, }, }, G2Line { r0a0: u288 { limb0: 0xf2d619ae78049bf9141c35cf, limb1: 0x717f8b10d469a1ee2d91f191, limb2: 0x2c72c82fa8afe345, }, r0a1: u288 { limb0: 0xb89321223b82a2dc793c0185, limb1: 0x71506a0cf4adb8e51bb7b759, limb2: 0x2c13b92a98651492, }, r1a0: u288 { limb0: 0x4947ef2c89276f77f9d20942, limb1: 0xb454d68685ab6b6976e71ec5, limb2: 0x19a938d0e78a3593, }, r1a1: u288 { limb0: 0xbe883eb119609b489c01c905, limb1: 0xaa06779922047f52feac5ce6, limb2: 0x76977a3015dc164, }, }, G2Line { r0a0: u288 { limb0: 0x43a96a588005043a46aadf2c, limb1: 0xa37b89d8a1784582f0c52126, limb2: 0x22e9ef3f5d4b2297, }, r0a1: u288 { limb0: 0x8c6f6d8474cf6e5a58468a31, limb1: 0xeb1ce6ac75930ef1c79b07e5, limb2: 0xf49839a756c7230, }, r1a0: u288 { limb0: 0x82b84693a656c8e8c1f962fd, limb1: 0x2c1c8918ae80282208b6b23d, limb2: 0x14d3504b5c8d428f, }, r1a1: u288 { limb0: 0x60ef4f4324d5619b60a3bb84, limb1: 0x6d3090caefeedbc33638c77a, limb2: 0x159264c370c89fec, }, }, G2Line { r0a0: u288 { limb0: 0x8fac42bd654a73e6e06cd8cf, limb1: 0xc3830a580c7ae62ca9a58036, limb2: 0xb1a750d7380c19e, }, r0a1: u288 { limb0: 0x4e8496aad8f6ac809fd15dae, limb1: 0xb51505336049b39b3fe98502, limb2: 0xc2e5994cb400618, }, r1a0: u288 { limb0: 0x2fc55d31524d834b260b3051, limb1: 0xe465c3c590247c88422d26c8, limb2: 0x10322a13b180bb0a, }, r1a1: u288 { limb0: 0x25a29688c4e32c67cb1134a8, limb1: 0x651bc8b0deb27bdb5762232f, limb2: 0x117dd3744aca1f64, }, }, G2Line { r0a0: u288 { limb0: 0xee89d2a59689701ecf4a31f2, limb1: 0xefc968d4b47e143fc28040f3, limb2: 0x1a5b2ca3ba6945b3, }, r0a1: u288 { limb0: 0x981810f00669aa9ef6a5c331, limb1: 0x483396ddbc880f5c1a0a0915, limb2: 0x85f453a76b6bc86, }, r1a0: u288 { limb0: 0xe25dfca55ef96a66eb1a716a, limb1: 0xa36d2f86b377aeddc41b101b, limb2: 0x36848c2314fd3a7, }, r1a1: u288 { limb0: 0xac4c5ac54d6c417facda3992, limb1: 0xd0b77b71f704c0930adeef4c, limb2: 0x8c773a6db51d65d, }, }, ] .span(); let hint = MPCheckHintBN254 { lambda_root: E12D { w0: u288 { limb0: 0x195c16df4a0f8f9dcb48bee9, limb1: 0x27f3cb7c50eca75e794d2f14, limb2: 0x14156ca1853095df, }, w1: u288 { limb0: 0xf01d099a6df0a4a55ed21b59, limb1: 0x9fed6b2018946bcc2a8dad06, limb2: 0xdc2a20a6107d4c4, }, w2: u288 { limb0: 0x6c1817c4efa721fc98f69503, limb1: 0xed80f8339cf9e06ff04257cb, limb2: 0x14260c5afb0b1148, }, w3: u288 { limb0: 0xf98323135baab8ae3c766c60, limb1: 0xffefe512eb9448ef436dd090, limb2: 0xafe8a09df07bf3d, }, w4: u288 { limb0: 0x1707d6579371dae20368253c, limb1: 0x7bb02cc2b5dc98aff593681, limb2: 0x114692950f53d4f7, }, w5: u288 { limb0: 0xa9da397fe12d4a3939ce650c, limb1: 0x49646f1e106dc0ee917551f5, limb2: 0x2dd3fca725919631, }, w6: u288 { limb0: 0xd6054be99a9248497b82062a, limb1: 0x2ea3f1b228beff5fd364a127, limb2: 0x1750bd450b85cbd6, }, w7: u288 { limb0: 0x4b83377c168d89b919386546, limb1: 0x26169d3ce55db12ecafd74bc, limb2: 0x1248cfad33a21477, }, w8: u288 { limb0: 0x724e5f5589d549a709b2b5ef, limb1: 0x8816b055888399c99a954b82, limb2: 0x28d156bac04e6493, }, w9: u288 { limb0: 0x56fbb49c235bc75082f5f26e, limb1: 0x56afece475580f453f9126f2, limb2: 0x39e1ab153bd7095, }, w10: u288 { limb0: 0x4fd83597fed1d7e7b9d09e04, limb1: 0x7c7f558d3e74e6617d7f08b5, limb2: 0x14853f940bf5c55, }, w11: u288 { limb0: 0xae3473546aa01a618b78b125, limb1: 0xfee14a3ce2b7af4e1872fe49, limb2: 0xaa480d613601947, }, }, lambda_root_inverse: E12D { w0: u288 { limb0: 0xd4445d3e89123811ede12825, limb1: 0x7794dbccbd7925ea98507cf8, limb2: 0x1d7a9ffbbe137d69, }, w1: u288 { limb0: 0xe7642301653a6307c7467811, limb1: 0x75e5c1fc0ff08be0981a61d8, limb2: 0x1f45aa2ee73f15e2, }, w2: u288 { limb0: 0x9865533968e39b5083fc576e, limb1: 0xc63d81e8d0c1e37c901a5a56, limb2: 0x2446d99f276e4c8b, }, w3: u288 { limb0: 0x31b5aada49be919aaa447cc7, limb1: 0x5131a5f04c3c634c9df3447, limb2: 0x223bd50b771fcaa9, }, w4: u288 { limb0: 0x6aefbf4a9ce706bc36252c47, limb1: 0x4d7ddfacdd59750105dcc37f, limb2: 0x24cfef2958a7c9c, }, w5: u288 { limb0: 0xe9789fb7259c294210f7720e, limb1: 0x4955cb370b0ac66e3e295ea6, limb2: 0x3a974db52b27468, }, w6: u288 { limb0: 0x3fb8266ad697b531de5e2fb6, limb1: 0x41feb355a44845dc30c2a9ae, limb2: 0x160b7346ec9fdd98, }, w7: u288 { limb0: 0xa56b5d534495a358f9c739f, limb1: 0x5f204fa5ce1c9a99c7979911, limb2: 0xe46af84e1cbba80, }, w8: u288 { limb0: 0xa9b51192113e131bd5572a21, limb1: 0x9b9524e9708ac412d3fa05fe, limb2: 0x1f2b5709d0d7c949, }, w9: u288 { limb0: 0x1052a86d50224b92838c5d76, limb1: 0xf690cd9eab121b1f329194c, limb2: 0x8a75eef583ffc3b, }, w10: u288 { limb0: 0x9764f07572ce9593878da9fb, limb1: 0xde7ec74175c125ac7e878050, limb2: 0xef3a64570d17038, }, w11: u288 { limb0: 0x35825f15893ad52a39f54331, limb1: 0x7b87bc78053320664e06d12b, limb2: 0x2a6290607745b58a, }, }, w: MillerLoopResultScalingFactor { w0: u288 { limb0: 0x1, limb1: 0x0, limb2: 0x0 }, w2: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w4: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w6: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w8: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w10: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, }, Ris: array![ E12D { w0: u288 { limb0: 0xf2fa8194a9fdd627525394de, limb1: 0xe1d604e9b0c0efb376aaa3e1, limb2: 0x6e2d5c667e253ff, }, w1: u288 { limb0: 0x9d2d152e532c421b7834a99d, limb1: 0xe2c971b204e63954fbc8ad23, limb2: 0x2dc3c5e55face7c5, }, w2: u288 { limb0: 0xa81940aec94ea9901fcac97d, limb1: 0xea2801041714bcb5d41a0ff, limb2: 0x2ff4750593044152, }, w3: u288 { limb0: 0x55867c1f0779e0422d545f0c, limb1: 0xf76a2af1d6b410d8639501aa, limb2: 0xdab9fd3d1ef5226, }, w4: u288 { limb0: 0x845bfd3e55f70e8272c8fb3, limb1: 0x3ffd60992916c6410e0f5352, limb2: 0x2fea029bdb6a10f5, }, w5: u288 { limb0: 0xc46ce45b66636cb6ba1ee436, limb1: 0xb7d8f5bedbe3c09728563ff0, limb2: 0x2f329aa1c588e3e4, }, w6: u288 { limb0: 0x100fa50e29907ad3283e7b83, limb1: 0xa405ca3722d951cb9a512f1c, limb2: 0x2290e74d07afff26, }, w7: u288 { limb0: 0x7f4ccb1aa1cff1983d7d2ae4, limb1: 0x8be6fdabbb6f2986a20934fe, limb2: 0x6bd6eba6eb034c9, }, w8: u288 { limb0: 0x49149a6939c1e7afec80ee3c, limb1: 0xb3543992e315765cb35d0f7d, limb2: 0x1ca0c85d7f94b5c6, }, w9: u288 { limb0: 0x3e916ca84262a68f9eea11f9, limb1: 0x5ecce1f7718bba441de2df4f, limb2: 0x1f70622e79ccbeb3, }, w10: u288 { limb0: 0x9e62952be0e54c3427ea8aab, limb1: 0xc1ad39913d06e14c6ad3a156, limb2: 0x2492333e1554b6d2, }, w11: u288 { limb0: 0xb40efced523794fd2aa17d4a, limb1: 0xe1f6f435746d944886953830, limb2: 0x2a9baf66b1ec17a, }, }, E12D { w0: u288 { limb0: 0xa1fc4e1e3b65f7f7793d75d7, limb1: 0xae4e796f20d02f00e403c73f, limb2: 0x21c18c15eaf2e543, }, w1: u288 { limb0: 0x3199827390abbe9ca30d6d5e, limb1: 0x730b129db4170c217248713c, limb2: 0x1ea8d6f41a6171e5, }, w2: u288 { limb0: 0x78d14fddb4434f077e2deab0, limb1: 0x9663d11277af92fcfe15e610, limb2: 0x19210af828cd091a, }, w3: u288 { limb0: 0x4de887d39eee6cb04c395b87, limb1: 0xc2ff130aea14a5d78e28cf8d, limb2: 0x2b61bdd91c851524, }, w4: u288 { limb0: 0xf2b2ba244a309375052c4f42, limb1: 0xacf0b149db02d1722805cad4, limb2: 0x1b3d1b4d652e719c, }, w5: u288 { limb0: 0x8f6d0954663be60b848af91b, limb1: 0x4cd56e52e93373b68f6d679d, limb2: 0x2e72ef29d615a4a, }, w6: u288 { limb0: 0xe4d9fbc1e47fc17f958217f, limb1: 0x1866843e972eb31da1b03a09, limb2: 0x17626c9319fd1b0e, }, w7: u288 { limb0: 0x6e90014bb73ec0e94d75f1ae, limb1: 0x8ce846c86c0d98599ea26c73, limb2: 0x1c2a1cb42ebfeca2, }, w8: u288 { limb0: 0x59885f5adfdafec208157d20, limb1: 0xc06108cd50dca18c6f38d6bc, limb2: 0x6cd036a10985c09, }, w9: u288 { limb0: 0x585e0bc54c4d2fe3d596b2e3, limb1: 0x5927149279279dcadf8c97b5, limb2: 0x2b1fa6025f359ad2, }, w10: u288 { limb0: 0x2b7b8c0f7639faad593e8383, limb1: 0xfcf8631ba48c4afe18d80c85, limb2: 0x966e5a47631686f, }, w11: u288 { limb0: 0x69461bc00469ae6f14b23750, limb1: 0xbc63f9e8cb37c1f943bf0690, limb2: 0x1d4e149f8299aa2d, }, }, E12D { w0: u288 { limb0: 0xbfcbda7691d6021a784022d5, limb1: 0xf407b3b09ed4b94542a95f63, limb2: 0x484ab1dd7428e01, }, w1: u288 { limb0: 0xb133cd33b820c39fb9fef059, limb1: 0x254f89192819893523420d52, limb2: 0x181f7e2c71063ffc, }, w2: u288 { limb0: 0x6386c277c18b70fbeccdb0ac, limb1: 0x830322bd75699347acf10beb, limb2: 0x25b122a978cff8b4, }, w3: u288 { limb0: 0x43de51582c42a09b767cb0db, limb1: 0x38fbf88e5df42583be8f94b5, limb2: 0x425b802f131c9cb, }, w4: u288 { limb0: 0x79e8bf369ece3027d02d9b23, limb1: 0xc43d966f8d7269715ebecee4, limb2: 0x10b0ade019bf9b51, }, w5: u288 { limb0: 0x25fb1663997d761c2d966543, limb1: 0xbc90d7df362a1172ac8ad1d7, limb2: 0x1236e39a09e91ce8, }, w6: u288 { limb0: 0x7519170922b5b0bdd65be6a7, limb1: 0x8d728cf7e9203cdde92b6b1a, limb2: 0x1559bd06e06a1748, }, w7: u288 { limb0: 0x3522045a369b7bbb242270df, limb1: 0xd947b9644921f9337a72005e, limb2: 0xdcb748b310acabf, }, w8: u288 { limb0: 0xca82b75883645f8fd56ce314, limb1: 0x48e0e79fa58c59fd9d8355f8, limb2: 0x101f82655362fa7b, }, w9: u288 { limb0: 0x61742edaa0da46b51a3efb80, limb1: 0x20dc1158e04bce1a5dc049e0, limb2: 0x1cf24ce8520c3a8b, }, w10: u288 { limb0: 0x37ffb162df38cdcb561cd489, limb1: 0x16b25873b29fdfb563b16a9f, limb2: 0x2375d4bad02acd4, }, w11: u288 { limb0: 0x2c023248737e318d2195a92, limb1: 0xaca7d0297ea2a7757d8cc9e1, limb2: 0x251260ddb7f1756d, }, }, E12D { w0: u288 { limb0: 0x81fe8c8afe6873cf3f7b5cd, limb1: 0x4ec5d556e1a946d1ddcb069a, limb2: 0xca3291e3f6ef12e, }, w1: u288 { limb0: 0x474f1efbda01f550d6c04a8a, limb1: 0x59446cd0acd4c47c9c9dce4f, limb2: 0x210465e49e0a585b, }, w2: u288 { limb0: 0xad9aeb3a7e41876c9e3ef2d2, limb1: 0xb4967ef0d9e28b41cfb7752e, limb2: 0x1579d33d082372e9, }, w3: u288 { limb0: 0x8897068598400e625d41936c, limb1: 0x3630dc545ed7f6dd2996f95d, limb2: 0xe7b6ee901988b96, }, w4: u288 { limb0: 0x56832f4842ec5db2742798ab, limb1: 0xe2699baf1ca60a52f7018e62, limb2: 0x135c42195434dfb8, }, w5: u288 { limb0: 0x152cc078fbb77283d8258c18, limb1: 0xbf47d56bbf8a81ad6350e169, limb2: 0x1c7c8963acb4f782, }, w6: u288 { limb0: 0xbe58ec496805ce645c12ea57, limb1: 0x3dee712fe63432f75fa00299, limb2: 0x230af637699638ee, }, w7: u288 { limb0: 0xa24d5cf767d2273e5a46a6de, limb1: 0x9d31117f3370645b3f8ba4d3, limb2: 0x20db0eb3812b696a, }, w8: u288 { limb0: 0xb177322e3c461ec3a18fab81, limb1: 0x4e10f0ab4925d0caa9f27a52, limb2: 0x1c467f5ac56d1ba3, }, w9: u288 { limb0: 0x6582d9e0006027351cb08356, limb1: 0x9e577626acb2a07771557dbe, limb2: 0xd7c96fe485899f0, }, w10: u288 { limb0: 0x100017574dd91436dbce587a, limb1: 0xbdda3d96d428123f881648ff, limb2: 0x2b7e0871d76d7562, }, w11: u288 { limb0: 0x534b2d82060ca792890071fb, limb1: 0x28eb9400b69a85997c673f39, limb2: 0x26256194b2d8184d, }, }, E12D { w0: u288 { limb0: 0x7a0590f085219d1e49b1a202, limb1: 0xc263a8319f723136aa0b96a3, limb2: 0x679690afb81dbda, }, w1: u288 { limb0: 0x71b85226100a44d0bf7d832a, limb1: 0x3067f6fbf94ee90ffad1172, limb2: 0x1736140d66ba7277, }, w2: u288 { limb0: 0x623d0ea9bc4d6d56f1f30d4a, limb1: 0x2ab6f8d1d518c5bf6193d719, limb2: 0x9f1bd18e2b9ee3a, }, w3: u288 { limb0: 0x6761411697651fc6c319f2f6, limb1: 0x61d48ed7306e80c3c447cc50, limb2: 0x18b5b8fee4c3bed9, }, w4: u288 { limb0: 0xb09464e6861e5ed9142f517a, limb1: 0x3697362f33ee1b6a2ffca931, limb2: 0x251eca3eb15ae1bb, }, w5: u288 { limb0: 0xb753d0fb3ef0221f38b3777d, limb1: 0x2b3cba72ef077890d91f7d72, limb2: 0xcac0c0d82a467de, }, w6: u288 { limb0: 0xacf131a2e4a8ac99cb66c4c7, limb1: 0xf0ba7668749554c860961672, limb2: 0x2b83f6926886f3ff, }, w7: u288 { limb0: 0xa57b1654a5ea8d73e9cb6916, limb1: 0x37d0bb062363510695f11887, limb2: 0x1025a3438e62a335, }, w8: u288 { limb0: 0xa6e8bde02fc0040222948861, limb1: 0xb3cd895a379088da54e7d665, limb2: 0xf239a541e2db6d9, }, w9: u288 { limb0: 0x150ab124c283da1a24aaa28f, limb1: 0x7b68a368f3df8a541116a40, limb2: 0x29dabc63d0f5e9a1, }, w10: u288 { limb0: 0xfcc3ffb404bd1c0effcc67fc, limb1: 0xa99cc3a1080e8fa3eac0f79d, limb2: 0x16b2ab0f6fefb72b, }, w11: u288 { limb0: 0xf4fab8a30df710b0a7aa23e4, limb1: 0xee08aba39e9b86d66f89b09, limb2: 0x10297d8dba978173, }, }, E12D { w0: u288 { limb0: 0x7f1da8d717c321da92620a38, limb1: 0x1c34d5a41dd1580cad5da4bb, limb2: 0x264c35a795ea35b3, }, w1: u288 { limb0: 0x93ef419e31d7e04fbfe40f26, limb1: 0x8dcee057ceb6a01686e7055a, limb2: 0x1c2f5969c7a2c07e, }, w2: u288 { limb0: 0x8fe175866e96f98fff3a22a0, limb1: 0x9e8081541ccefcb53c7eb2d, limb2: 0x2244e4f0ae949c4, }, w3: u288 { limb0: 0xf44cab93381d8325a2fc894e, limb1: 0x21e4d8a6a1c197c760b4b674, limb2: 0x2e70f85fae87c741, }, w4: u288 { limb0: 0x2b9421d1f4a75279a4a37950, limb1: 0xa40bf928ba237c3b64bd886b, limb2: 0x2181a8053d4d2243, }, w5: u288 { limb0: 0x551eedbb1be148ec878c8497, limb1: 0x63cfbe2727afbb1c9ab904d8, limb2: 0x1201390258b7fa5c, }, w6: u288 { limb0: 0x3413023817ffe912237924bb, limb1: 0xc8ec7546fa50a3a5bf73ef64, limb2: 0x154b10842ab9f08e, }, w7: u288 { limb0: 0x3433f3946abd235f4852671f, limb1: 0x4f0065f08eeb7ee8349bf5b9, limb2: 0x25af5a4af220ec11, }, w8: u288 { limb0: 0xdf980696295073821473e3a9, limb1: 0xe1d5ffff2ee85385ae1d84ed, limb2: 0x998add2cc38123b, }, w9: u288 { limb0: 0xa4460f4fa19d7da44b6d37d6, limb1: 0x21a63d9ac273152908e20cf4, limb2: 0xb43c05ecc1a46d7, }, w10: u288 { limb0: 0xfa2ac15271ea1ea122a7f7c2, limb1: 0x98ccdf1be55f7224639cae5a, limb2: 0x128165600a34f4d8, }, w11: u288 { limb0: 0x880fb407eaa05426a8a3699f, limb1: 0x13b039a6d088cde86bc99280, limb2: 0x25f0ddbe00bfe102, }, }, E12D { w0: u288 { limb0: 0xe79a1a3b581b15c6552fee96, limb1: 0x623169860e532b6833adaed0, limb2: 0xdf2e1bc3f49b17f, }, w1: u288 { limb0: 0x82fbfcc8e320d1a559108ebd, limb1: 0x398449cedc8a6c95fb7efba7, limb2: 0xe3f4dc0728dd65a, }, w2: u288 { limb0: 0xd42e5660c7259f239e94e9e6, limb1: 0x56a59f4335e45444ad6f0ab9, limb2: 0x717e8c6b06e6d07, }, w3: u288 { limb0: 0x959c3512c9bb1d3663382bf5, limb1: 0x25061bc0e8ad631f66c35752, limb2: 0x1be6180a76fe2379, }, w4: u288 { limb0: 0x113a01a95ff0b7344a6ed1fa, limb1: 0xed275900f8b636a554551b04, limb2: 0x1ed20c5fe3160f13, }, w5: u288 { limb0: 0xda5b00dcbf123e7ef0e22ecb, limb1: 0x4712a15f67df4356961b91b0, limb2: 0x191a6e54a247677e, }, w6: u288 { limb0: 0x8727e056ef1f2e00001ee30b, limb1: 0xa5899f981336f6b6ffb14600, limb2: 0x2ba9019a071ff9e7, }, w7: u288 { limb0: 0x430616f2db6ce63405b60234, limb1: 0x38853a1ed4fe555eb90e9387, limb2: 0xeb9cf3c0e1b1390, }, w8: u288 { limb0: 0x48f41979d7ee62a531dc11b1, limb1: 0xbf258b286416b510392d3426, limb2: 0x586a2b2130ac60c, }, w9: u288 { limb0: 0x12a3062d7cf738e164cab726, limb1: 0xd7c481cf0010024424dad92, limb2: 0x240e926f21d6137a, }, w10: u288 { limb0: 0xde116640887cb84fb5764ef7, limb1: 0xced8e2d7611e1b329248dc19, limb2: 0x6b9c04f96a0360e, }, w11: u288 { limb0: 0xc8f83c2f3507e8a16a023597, limb1: 0x7a1d65fb1bc859ac0b9a3af6, limb2: 0x2dbdf00f63e255a2, }, }, E12D { w0: u288 { limb0: 0x9f1833d4ee6e05b2e98eb194, limb1: 0xdf61e89608afbbff54451d49, limb2: 0x7341a57c8351835, }, w1: u288 { limb0: 0x396bde8ca73f5e0e52f1bcc3, limb1: 0xb41de7c6525d9097f89f9874, limb2: 0x1fee062ab770bd4a, }, w2: u288 { limb0: 0xde88c90e56f5efff42fc5ae5, limb1: 0x70eb11756f50d40816fa1a84, limb2: 0x1f35fa63de82bc30, }, w3: u288 { limb0: 0xaacbc7daaefa32f112ff727, limb1: 0x55e72851bb33661f52250a3f, limb2: 0x18c4cc5aa53fa8ab, }, w4: u288 { limb0: 0x4d832925bb29a07f12600b73, limb1: 0x4d648c8bf3aef6e9dc8f3eca, limb2: 0x468982847f8a07e, }, w5: u288 { limb0: 0x6865044fe86fc113321d84b3, limb1: 0x4afb949d44ddc19a50d76746, limb2: 0x1c4878b6bc126ea, }, w6: u288 { limb0: 0xcdb1ec52b0efcf2a333cb03e, limb1: 0x1d47715e046d09a63bd817b5, limb2: 0x47664218590ab80, }, w7: u288 { limb0: 0x9354e8a50050939f807da303, limb1: 0xdd6956fd5c5a1aab21b97b7c, limb2: 0x1bf57342d5e7ec73, }, w8: u288 { limb0: 0xf18eec3aaeee1eea6b00228e, limb1: 0x90405b5368a83b8e3e141abd, limb2: 0x5489f27d98c5a6d, }, w9: u288 { limb0: 0x33372084065e44dcd5edfe77, limb1: 0x9ea7ef66db0f0ff55972dbea, limb2: 0x20d81d5b8dd287c6, }, w10: u288 { limb0: 0xf95c243e1128f75841ac88a8, limb1: 0xe39101c1f545587666fc99c9, limb2: 0x1332f858bc2d9ed6, }, w11: u288 { limb0: 0x3dda3f6e97341fc9cbbe60d7, limb1: 0x7214e1d782068b63e36e074f, limb2: 0x7087cef01dfb965, }, }, E12D { w0: u288 { limb0: 0xee419f4271957570f4b1c32, limb1: 0xee1f110052ca2e56a97efb6c, limb2: 0xad375e8d172d961, }, w1: u288 { limb0: 0x63ebd35fc505842517b7e802, limb1: 0x62c3623a58ae1bd17f9436b7, limb2: 0x249b716ea1290d35, }, w2: u288 { limb0: 0x21b92dabf6e5280c26e361ee, limb1: 0x3c390fa8b8657c4f4fe50e82, limb2: 0x585285292095c27, }, w3: u288 { limb0: 0x755a1f81220bff5c131d7e96, limb1: 0x4df7a8ee45d3302f30ff29a8, limb2: 0x10d1d361cff8aba5, }, w4: u288 { limb0: 0xa2041d8fc2c467e3f1bac97a, limb1: 0x48e7421f5ec41f255b8c45ce, limb2: 0xca996570d833fcf, }, w5: u288 { limb0: 0x2183fed77e39e6b8807abd2c, limb1: 0xda8b0ba5b995978dd002d1ef, limb2: 0x25ba30a10ab4363f, }, w6: u288 { limb0: 0x44a4271d7e7d6e2372deb46f, limb1: 0x6ebe794b43059afaf191747a, limb2: 0x62cd7ea75a47f9d, }, w7: u288 { limb0: 0xb01b410bdd4f7d17faad0b02, limb1: 0x92b6fa71257d0e35216b8d76, limb2: 0x234c010bcace1d9e, }, w8: u288 { limb0: 0x2dba0f00a37d7388eb27942d, limb1: 0xb2148684b3580c6d45dfc7f8, limb2: 0x2286172b9d954df5, }, w9: u288 { limb0: 0xe48a688bec46fdf3a2b3458d, limb1: 0xc0dd157ca14a9dddee9f0749, limb2: 0x29b03a6b1d1d3ec9, }, w10: u288 { limb0: 0x7cf25068f4085c9a3552b26b, limb1: 0x51c51346bf9ee9478e82069a, limb2: 0x1c3b363ed4ad026a, }, w11: u288 { limb0: 0x32055cc475ed2979ba936b5d, limb1: 0x3a76365f65bb11dfa20f6f03, limb2: 0x14e82b52083c1950, }, }, E12D { w0: u288 { limb0: 0x86528ff5d288de551ba82e20, limb1: 0x779518dbb60908f0c9f431, limb2: 0x17e7b0c198e5fbb4, }, w1: u288 { limb0: 0xa6b91b5273ad23056d2b5571, limb1: 0x18283f4038662f9f2d32aa6d, limb2: 0x26250f9c485aaafe, }, w2: u288 { limb0: 0xff4b38ab950cec36907872c, limb1: 0xe8220a80ab1a1ebfb4a6b5ad, limb2: 0x16a38cdcffaa084e, }, w3: u288 { limb0: 0x30fe4c50e7cfb82354077ff9, limb1: 0xd825202a8b56831d4cb461f8, limb2: 0xacbc4404e784841, }, w4: u288 { limb0: 0x2f290a090b14ab72c573f72d, limb1: 0x28fe7dd957a3fea3a48824a3, limb2: 0x8d4fde60889f05e, }, w5: u288 { limb0: 0x78e4ad232628f93493799b05, limb1: 0x853fa0b232ed0e0fe4c72ee8, limb2: 0x1905420adaee585, }, w6: u288 { limb0: 0xf5b5ceac316dae7d4b72f222, limb1: 0xda7b251194b88252808ac1a8, limb2: 0xc2ad9e69e7a3c18, }, w7: u288 { limb0: 0x871823350e01e7c076568b23, limb1: 0xc2fcb7b9ab99f9ea2de64a6f, limb2: 0xcbca7c0f294b05, }, w8: u288 { limb0: 0x58214cf485aa2980892ab270, limb1: 0x38ae8b1a6d563a6e90b57720, limb2: 0xadc0f206a82720c, }, w9: u288 { limb0: 0xe47d85736adce266525b33a5, limb1: 0x75f41b36a691ecb3f1af75f, limb2: 0x2aaaad4a322f5ca2, }, w10: u288 { limb0: 0x449e76f3e507d1e4f79b2b41, limb1: 0xa66a19bfc8476c6ef9730a71, limb2: 0x1c4a7da448d6a424, }, w11: u288 { limb0: 0xaa745ba79deacfc0e958305c, limb1: 0x771b3d2cba2c850277042d9f, limb2: 0x2bbe2dd81ae206bf, }, }, E12D { w0: u288 { limb0: 0x89800871747a5772af0a4a5a, limb1: 0xc77aea4a034bd02c1a52fda4, limb2: 0x7696ff7e1b8f387, }, w1: u288 { limb0: 0xdc9663d006102d510d74c328, limb1: 0xfa5faa547c8a1b45034a3b2, limb2: 0x260faf1bbeb9d987, }, w2: u288 { limb0: 0x1bc1799be4bb7102992ecd13, limb1: 0x94e15f371c06ced1fde0dd3, limb2: 0x665a3a12509ed21, }, w3: u288 { limb0: 0xdcd827948ef109459f3b29fb, limb1: 0xa669670e935b5b5f278378c2, limb2: 0x2d04dee2ca1ba30c, }, w4: u288 { limb0: 0x63cc8b1759ef1e93c126782a, limb1: 0xe01767580df775dd4a40d5e5, limb2: 0x161187b33f992c8b, }, w5: u288 { limb0: 0xfe53c1faf8ba08de077db23f, limb1: 0x6ac9f2dc628f14bdf063327f, limb2: 0xec69da938087b0, }, w6: u288 { limb0: 0xead0bc1f5077694dad55c03f, limb1: 0xd6e68bf4d6cc956adcf2c643, limb2: 0x2dbf0ee9310afb09, }, w7: u288 { limb0: 0x863a0a8f4e19da762f117929, limb1: 0xdcf7e18447603c210882cb78, limb2: 0xdf9e8f70db03ce1, }, w8: u288 { limb0: 0xedf02766e9b8595f63abd18c, limb1: 0x784e4d5d60f519796f01cde8, limb2: 0x8671ab547845137, }, w9: u288 { limb0: 0x5b506c6c1ece6c888adc5d1a, limb1: 0x4ac5204b72b2c1a7db79a319, limb2: 0x1f01964bf79ce370, }, w10: u288 { limb0: 0x50e0979033627a4231737ef9, limb1: 0x9547f6bbfc8dee1f09baa0d9, limb2: 0xc73a07daa4654d3, }, w11: u288 { limb0: 0x152d341606f78da11aad9ad2, limb1: 0xdda73da51b1d63f6e0ba9b3, limb2: 0xf3378aada8698c6, }, }, E12D { w0: u288 { limb0: 0xc8a1ffbcd36ed4cf96782047, limb1: 0xd674cc0260707439a67f952c, limb2: 0x2bf4eb8f91fe5fe, }, w1: u288 { limb0: 0x87b77db32833cadca24eb37e, limb1: 0xf97e1ee9a29b1b3c4719de34, limb2: 0x10126e19d78ecaaa, }, w2: u288 { limb0: 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0x27f9c5cf95c7c1614561860a, limb1: 0x2b6222d4d1199c76ca386b22, limb2: 0x16c8ee50f9adc5ac, }, }, E12D { w0: u288 { limb0: 0x6f3f7d0292c186ae873944f, limb1: 0x35c8a1bf39fa92a9f242fd69, limb2: 0x14b95f826ac74736, }, w1: u288 { limb0: 0x1c8deec644cf2503777cd0e9, limb1: 0xe390b3744ef378a066993673, limb2: 0x1ce103c73af34607, }, w2: u288 { limb0: 0xe51b2b5264cab98b0dce20e3, limb1: 0x12baa9b4a22f7f60f5a9e8a7, limb2: 0x199e6082a24e29fc, }, w3: u288 { limb0: 0x8ccec4fd0f4c40b24c174906, limb1: 0xd0eb4c466b50542bdd1f7ccd, limb2: 0x130c4888c5671589, }, w4: u288 { limb0: 0x841b256a04eb7ee8c763a86, limb1: 0x44dcb7ccff639f5cf00547f6, limb2: 0x43826f4900a3942, }, w5: u288 { limb0: 0x9dd7608e2f8eaab2cf59cf27, limb1: 0x6c531affa90ee4c3e6b1315b, limb2: 0x14c5bbbc9b662751, }, w6: u288 { limb0: 0x40ead5c383741f5e94a372dd, limb1: 0x63456b35874faf8614778b7e, limb2: 0x160428014e84270e, }, w7: u288 { limb0: 0x77ca9da77c9c26fa4eddeffb, limb1: 0xd64c0c2e0baa8971ce138592, limb2: 0x2532dd267a25b4f, }, w8: u288 { limb0: 0x8f0b492fe9cbb6713b3ae0b9, limb1: 0x6cd8f706cbc20ff6c2978d34, limb2: 0x25b8b619c12b4d53, }, w9: u288 { limb0: 0xb9f16df613dc83610524ae59, limb1: 0x999af8cf94fe6e9155b24ee, limb2: 0x2d763001f6ee910a, }, w10: u288 { limb0: 0x72e6293fa1874d4456f6a7ab, limb1: 0xbba9e551a891ac14dc529d7, limb2: 0x2fe56f474f803a1a, }, w11: u288 { limb0: 0xddef305ed66e797eb44cc927, limb1: 0x46cf45a1ffa3be343166c96a, limb2: 0x2c91340e7201c8e7, }, }, E12D { w0: u288 { limb0: 0xacd367bfb3a86503c4696228, limb1: 0xe5bebb9f891e0fcf9bb400df, limb2: 0x1f053bcf8dd0c40e, }, w1: u288 { limb0: 0xaa5f25aba69edf7eb3fbac7f, limb1: 0xa57c44bfb7a813d9565c6f4e, limb2: 0x1cbd2cad199b90af, }, w2: u288 { limb0: 0x1e3561ce4486f49c51c4841, limb1: 0x5d707d777cc267134dcb4a3e, limb2: 0x2d4f1b6b1704fcf8, }, w3: u288 { limb0: 0x8133df3d973205e2a6667b05, limb1: 0xd71333cad7c23d6436f895b1, limb2: 0xb96c7c4d9019afe, }, w4: u288 { limb0: 0x4c82c43fae3e6a4e9ac79773, limb1: 0xd632da8c8fade4bdd6d055b5, limb2: 0x1493c61b79713a9c, }, w5: u288 { limb0: 0x14f7514b5a6375a0ba02dfdd, limb1: 0xdb0492be6d819a64e5c8e869, limb2: 0x29ce11799d8ce7f6, }, w6: u288 { limb0: 0x88e5da8addd545f6e1828516, limb1: 0x59ab28d6dd8eb6ea501d3cb9, limb2: 0xe761374e20c2910, }, w7: u288 { limb0: 0x494bfaefdde4921257b3c8ff, limb1: 0xc560828dcd36efd417e936e7, limb2: 0x19065a582b0bfe84, }, w8: u288 { limb0: 0x54aed757dacfad3714775cd3, limb1: 0xc84bdb236c7d909b5a8a3cfc, limb2: 0x1568bd40a8a5b14d, }, w9: u288 { limb0: 0x5b800e067bb87a8edd6ba6f4, limb1: 0x72fafdbd2943d900f8330a8a, limb2: 0x203214386552455e, }, w10: u288 { limb0: 0x79c850293dd1ed17289f8d7a, limb1: 0x23514882c698d62934f0b85c, limb2: 0x2c8da86af166ec2, }, w11: u288 { limb0: 0x3149423b81d0601bf6983f66, limb1: 0xfdab0d5a898edf32625fdbe6, limb2: 0x81a2800e45aa663, }, }, E12D { w0: u288 { limb0: 0x8b51da2d8c55494918df21dd, limb1: 0xe08f0cc653fff5f77d129809, limb2: 0xac43cdef76e8e2b, }, w1: u288 { limb0: 0xe88d81f8cdf9db6cc3d7a8e3, limb1: 0xbbb798eb9215c4e9215009f5, limb2: 0x2b6e67c7cd78b23c, }, w2: u288 { limb0: 0x95fbbffc4a22fefe6ed6f466, limb1: 0x44b328ca91837bc5f2813bea, limb2: 0x15a0aa861322fe8e, }, w3: u288 { limb0: 0x230d31e951092a571dd5146, limb1: 0x1a87d85d215cd450d2691c01, limb2: 0x273b3d4ad1da0c4f, }, w4: u288 { limb0: 0xe13981b2395738db11f814d4, limb1: 0x96f3b24aa8b0e2286829b356, limb2: 0x17ca1b6c416d0b08, }, w5: u288 { limb0: 0x8a2711890225f3347def3ac, limb1: 0xaff7929a071b6d219ecc0d90, limb2: 0x13ab0ad11f39ed5c, }, w6: u288 { limb0: 0x131141a0e2587df1ed43c57a, limb1: 0xee8de29045aa8df56e7bf4d3, limb2: 0x53d8a8045aced2a, }, w7: u288 { limb0: 0x751db179fd8b0dd97ab90b62, limb1: 0xb24fa4509ea9a05ea3a0820e, limb2: 0x1b94eafd5f42b129, }, w8: u288 { limb0: 0x54d9a3cce32c8d336a38434, limb1: 0x8ef332aae2744817c97aa9fc, limb2: 0x5acd19414989ac9, }, w9: u288 { limb0: 0xdcd805c3441bf8da9f078037, limb1: 0x9d7cef94b46af01f54df6022, limb2: 0x13e81873c53f7de, }, w10: u288 { limb0: 0xd188a8da6b09f460a30ea7d4, limb1: 0x5e7d133426f98ced17f967ed, limb2: 0x2f9622f5e2961afd, }, w11: u288 { limb0: 0x835b65476aa69e0fee8add66, limb1: 0xf7eb0db4196481743f7c8536, limb2: 0x2420247c2eae05, }, }, E12D { w0: u288 { limb0: 0x1b9b3275438def2b14d3d6ec, limb1: 0x215e7ca4b8e610b90aea1fe2, limb2: 0xc57e1f84bab1fde, }, w1: u288 { limb0: 0xa3aa8bb56e04c330c70af082, limb1: 0x762683dea3a91a1813ebbe47, limb2: 0x1db06cf6c01944ef, }, w2: u288 { limb0: 0x6d3534ad1666ff07aef8ee5e, limb1: 0x95034543d303718bdddd0876, limb2: 0x4ffb855d2c5477a, }, w3: u288 { limb0: 0x9de5ea1d4cd7b93d85eef3a3, limb1: 0x7a3b2e8a90f40fbe7afa11b, limb2: 0x286259c2593cd27f, }, w4: u288 { limb0: 0xdb82f137af29e3458455efc4, limb1: 0x8b665e9e0eb3b9c8f027e3c9, limb2: 0x20fefbc49fb31a8e, }, w5: u288 { limb0: 0x6efd0bb670c6350880f786b3, limb1: 0x205615a0185a1b00916d37b7, limb2: 0x6375097bd6ed176, }, w6: u288 { limb0: 0x5e049cdbb227617f099b81d, limb1: 0x7c89c3a84805e47debd2d9b0, limb2: 0x90ad0e891a3872a, }, w7: u288 { limb0: 0x8deade236dc1f483f78b820, limb1: 0xa22016ef71d65892b510b65a, limb2: 0x15b035673845e2ba, }, w8: u288 { limb0: 0x28cce0800fcaeca24e4a1f11, limb1: 0xc873a609eb7443c53cc2146e, limb2: 0xed7bc75055a0bee, }, w9: u288 { limb0: 0xfdb3d8249042253ea50045c3, limb1: 0x1873c79692308a13011bf359, limb2: 0x1a1644f1a3d5b115, }, w10: u288 { limb0: 0x5c988b98ae035a4304a5f88d, limb1: 0x8a2936146d5703d9604e064c, limb2: 0x29b6437df8007dea, }, w11: u288 { limb0: 0x86051e2a2aaadd941e2a9241, limb1: 0xbf728a94603ee43956adbfb9, limb2: 0x2d4db3ebddcfd258, }, }, E12D { w0: u288 { limb0: 0x92acc012d562dfdfb6481b25, limb1: 0x3e64355b8e9e3082f99d33c5, limb2: 0x290b6aea5955f671, }, w1: u288 { limb0: 0xea2dac1a1640a6ac9b9ad377, limb1: 0xe1775d01c8f21468867a89ff, limb2: 0x1cf6cdd23f7ccb8b, }, w2: u288 { limb0: 0xd51e98bf9719380b097ea1fb, limb1: 0xd74149401b7667643b22e27f, limb2: 0x129b599f9eed72c9, }, w3: u288 { limb0: 0x66f868e872b587c8e5a18431, limb1: 0x5ce11b08a6e0fe0e0f9b96f1, limb2: 0xcecf76d78ff36b2, }, w4: u288 { limb0: 0x5ccd6edc479aeaf571c0890d, limb1: 0x91881d482210406422d39529, limb2: 0x2b1eefab1035d22a, }, w5: u288 { limb0: 0x10b346eae6854f264c866223, limb1: 0xece7a4751aad88e0d43ff850, limb2: 0x26ac9d94ac41a06c, }, w6: u288 { limb0: 0xdca528ca6016058cf3e5fae2, limb1: 0x78690b84e775a92f8bc8a4ed, limb2: 0x212be7d16a5f6c89, }, w7: u288 { limb0: 0xf3e83e445c62eeeb7ec84ce0, limb1: 0xdd116e6e8364db0a64b50304, limb2: 0x279d1022cd3e3e1f, }, w8: u288 { limb0: 0x65f73450ca7a1766028a9d92, limb1: 0xf27270b3123129865bf05ad5, limb2: 0x26bc3d97ad8925f4, }, w9: u288 { limb0: 0x944c276de7f91d41bcc4127e, limb1: 0xa89166f745e7e0640866c8db, limb2: 0xe7f920bd863ceb4, }, w10: u288 { limb0: 0xa31d4c6a3bdcbe04860624d4, limb1: 0x7c504b80689c987f9708269e, limb2: 0x27550021cf25c30d, }, w11: u288 { limb0: 0x91cb5c5218981603a881667f, limb1: 0xa0905ee77f1c0e9a5f9de4, limb2: 0xcc2ecbee6addff5, }, }, E12D { w0: u288 { limb0: 0x27ea098c66c31201eefb8430, limb1: 0x289402da5fe4bd14d8ef6edf, limb2: 0x1259961e054d6cd7, }, w1: u288 { limb0: 0xdf5835eb2fd6b73c5dba911a, limb1: 0xca03ca62684adaa9524cea2, limb2: 0x2eb6accd5526bb8c, }, w2: u288 { limb0: 0x30900fcfe01bded79b3d2477, limb1: 0xb279579672976833505fa71d, limb2: 0x162ac340cc3a9243, }, w3: u288 { limb0: 0xea6f09f94f1137fe93d6e281, limb1: 0xabf9e0b69162edef149ff1f3, limb2: 0xff91140a0ef8671, }, w4: u288 { limb0: 0x202e27f741f1e2b81753060e, limb1: 0x26a9a0ce89b8f06fa7d6326, limb2: 0x1c707bf011a33ace, }, w5: u288 { limb0: 0x95578a2c8e1895ac184cabfb, limb1: 0xbb75389aaa763c673982ea8, limb2: 0x607a8649a7b2555, }, w6: u288 { limb0: 0x71d90544c20a5aed5f41931, limb1: 0x16847c43a0cdfc05ebe58815, limb2: 0x4721c3f212088b0, }, w7: u288 { limb0: 0xc360aaad2a45074edfb74e14, limb1: 0x77f564b43fa632bde8eec9d, limb2: 0x250afa706df6d5e2, }, w8: u288 { limb0: 0x8bde53cc45322245c61c9a8b, limb1: 0xbb082994c8f59570001a3550, limb2: 0x27b5ec7a33a77874, }, w9: u288 { limb0: 0xd33f34a1a253f871c0f128e9, limb1: 0x88e401602a88af3bb22d4b4f, limb2: 0x8194f6251e043d8, }, w10: u288 { limb0: 0x37787931890dad2749f4172f, limb1: 0xb781b6da2911d39376770d8a, limb2: 0xf86cba82a2a63ca, }, w11: u288 { limb0: 0xb283d3c5e1df307fbded08de, limb1: 0x845c1e02379ee7fb83ade74d, limb2: 0x113edfefc35c7b27, }, }, E12D { w0: u288 { limb0: 0x800d14c753c40eb876da5bb8, limb1: 0xdd394093deedc4a58300a401, limb2: 0x20bbc62916a1c1c5, }, w1: u288 { limb0: 0x1ff3c025cb5fe163ac6341a1, limb1: 0x3492edb1001d97c57690e3ea, limb2: 0x2af5edbf90641874, }, w2: u288 { limb0: 0xa01ab0362ad9941df67212b5, limb1: 0x1273a4cfacad5b920f984247, limb2: 0x2c8dfd25ae12d28b, }, w3: u288 { limb0: 0xc72f15c7299855613325128d, limb1: 0xa7e25f6a3deaf4f7be35e120, limb2: 0x2607d100cbda5ad, }, w4: u288 { limb0: 0x2e236358d7c29fcbc45476ce, limb1: 0x696b09274ac45b177403228f, limb2: 0x22e618af62719cf3, }, w5: u288 { limb0: 0x81b4d1b3b2d2686cc3a33fac, limb1: 0xf5c5ffadb6ae0769530803d7, limb2: 0xe18f6caa2f9150, }, w6: u288 { limb0: 0x820aefb2f234355503fd73f6, limb1: 0xee49d901c9c66c15af10aafc, limb2: 0x2cf38629461bbcbd, }, w7: u288 { limb0: 0x702e95e8e205ab0d73f4d645, limb1: 0x6cc8a9e2e5bd482c2d970d01, limb2: 0x26c6783eedf68370, }, w8: u288 { limb0: 0xb083a4ca598ff879ef7aa527, limb1: 0x5310d5c6e27bf7bfa6681a70, limb2: 0x29480250c596232a, }, w9: u288 { limb0: 0x6cfaa3e7f9ac2fd8645db473, limb1: 0xb2739d025d0bf248c2d4e1a2, limb2: 0x912e2dc7402cd4f, }, w10: u288 { limb0: 0x2bd49d41f5a3e28554df2631, limb1: 0x8065584c5473ee5f56b0993e, limb2: 0xfb04b567cc1113a, }, w11: u288 { limb0: 0xf5cd0cfcb2e6ff69bf4754a5, limb1: 0xdb8d57f575f0a9e1419111fe, limb2: 0x1d1cea3ff669ce4e, }, }, E12D { w0: u288 { limb0: 0x61d29bcc1a3f6167a79d8c38, limb1: 0x532714800454848152e1c0e0, limb2: 0x132484d6b22372ae, }, w1: u288 { limb0: 0x108ce4183553945caff854, limb1: 0xbd70dd52d149435432ea127f, limb2: 0x189cdc05d04909b0, }, w2: u288 { limb0: 0x5ad21b0a5646ad085f528109, limb1: 0x1a9fc07a354670945f565e9e, limb2: 0x1e93c1c3e4b89488, }, w3: u288 { limb0: 0xa2b07e2a8ba8644821d8d454, limb1: 0xb04d7421f3ac6397e80a92a1, limb2: 0xe2e5a47221b2430, }, w4: u288 { limb0: 0x60e96edf654796d2d1e7ad12, limb1: 0xc053caa606b820b7bc203105, limb2: 0x23de5802449e2d0d, }, w5: u288 { limb0: 0x33531996505d714b68e97cdc, limb1: 0xb2f7f6dacae5650c70369c5, limb2: 0x2b9c8a1bd70d65c8, }, w6: u288 { limb0: 0x29c656ded9d8ede8b14e133a, limb1: 0x3251a0119e1def6470a73ee1, limb2: 0x108ccfd72642f085, }, w7: u288 { limb0: 0x59d63f9e2a5252d394fb3b13, limb1: 0x6af3a4182c974a4a4cb8cb43, limb2: 0x1a0d6334a517c128, }, w8: u288 { limb0: 0x1f9c66a90a3636f14efcc3bb, limb1: 0xbcf2e4dd6a6a18e0f4032755, limb2: 0xf77ce25573b3637, }, w9: u288 { limb0: 0x8629d396f0cbb19e5e5ae3ef, limb1: 0x8999b95d2cef1a967c52155e, limb2: 0x1a651bad046779e8, }, w10: u288 { limb0: 0x4136e2e567c71c7327bb5498, limb1: 0xfc077703802a973be3e1b595, limb2: 0x164eecf7e317e50f, }, w11: u288 { limb0: 0xa675d361f8324c4030afe60, limb1: 0xa5a92a85a22d4b737612f493, limb2: 0x1904c09382a0596a, }, }, E12D { w0: u288 { limb0: 0x7430544030d0c5607d8574fa, limb1: 0x948e3aa4cdc35494aa3d0c22, limb2: 0x149ca9118143d93b, }, w1: u288 { limb0: 0xe2ca69dc59b49107e665c357, limb1: 0xdff3f92ef170aba8ecbfed91, limb2: 0xc0020a7d7b54ee9, }, w2: u288 { limb0: 0x70927630b958392565150156, limb1: 0x50bccd63e76535da30f22410, limb2: 0x85f6272d3683e99, }, w3: u288 { limb0: 0x18b10fe562294e1493d32869, limb1: 0x7e3a83f64e5b06dad1f392f0, limb2: 0x7e60317cbbc746e, }, w4: u288 { limb0: 0x77d3f868cb018f42a51a098f, limb1: 0x3b28392831d5cdaf18471e03, limb2: 0x11b5be48a78a0132, }, w5: u288 { limb0: 0x8d1ce97123cff01dbf56879c, limb1: 0x2f02af85223c497ff5b2e11a, limb2: 0x1d3f1a99dfbd1384, }, w6: u288 { limb0: 0x3fd75ee1c489f88b2fc32243, limb1: 0x737aae095a654f624b6f63f9, limb2: 0x2f4b2b139fdc4fa9, }, w7: u288 { limb0: 0xa450865b8dc8ad706d913ad1, limb1: 0x6568246a5878ce9e6911b5d5, limb2: 0xd1505e942ab53fc, }, w8: u288 { limb0: 0x803cfc36831117d202a58c58, limb1: 0xc6daa54242c30c5d44005261, limb2: 0x27e112ce5019213, }, w9: u288 { limb0: 0x1381248822859f125ce62cd4, limb1: 0xfc617ab7f0e7bc85a514d322, limb2: 0x2a4e7ebc04f2a885, }, w10: u288 { limb0: 0x70e8bced7cd129b4096b8665, limb1: 0x8f4670dd657fde1c37ca0a3d, limb2: 0x9b49f8885959fcd, }, w11: u288 { limb0: 0x20534cc97052c24c0833ee05, limb1: 0xe9fe07db116fc63f2e2a4c5c, limb2: 0x1e017a6b3eebf717, }, }, E12D { w0: u288 { limb0: 0x6e6bdf80500cb854f5dd0bff, limb1: 0xbf9a626b9cbccc283c57700b, limb2: 0x20f5c7f5f71cb22d, }, w1: u288 { limb0: 0xdb32a31be60950339fb1122a, limb1: 0xf752607f2d770dbc152220c2, limb2: 0x119f27829f3f396b, }, w2: u288 { limb0: 0x9d48d334e95302c9d457e824, limb1: 0x71e66184e0c417cc823bcb6d, limb2: 0x230fd13d768e195b, }, w3: u288 { limb0: 0x2cce2b592737976adcdeb399, limb1: 0x6f7e7895cc9ac490802fc64c, limb2: 0x2e34a9c5e37e2c13, }, w4: u288 { limb0: 0x1b78faac53b2579e5036465a, limb1: 0x3dd4cb80488ff8f5cac70df4, limb2: 0x29834f6805b456e1, }, w5: u288 { limb0: 0xbeb6734949c1988a2bab2b43, limb1: 0x2551b72dc3bd9631884c52eb, limb2: 0x2a7502d7a3ab80e4, }, w6: u288 { limb0: 0xc862806b3e7a8b9b9c55054, limb1: 0x874d4d7db6cd2dc1c25218dc, limb2: 0x102e882c30c3623e, }, w7: u288 { limb0: 0xf303abb1515fa0b31a804e39, limb1: 0x240918f6ba89758a1c7d1cfa, limb2: 0x7f3dfb58aa1125b, }, w8: u288 { limb0: 0x3f1cfdf33cad91734b211407, limb1: 0x17c4a8522daa84de4bad7323, limb2: 0x19c76e0eb6c3b0c3, }, w9: u288 { limb0: 0x3a57bba7ae1b75fc6df7c6c0, limb1: 0xac20c3a4dd640432204a0563, limb2: 0x23288051e80e08eb, }, w10: u288 { limb0: 0x5e00c38b0e2a7ce9098d68b0, limb1: 0x66eae940dafebe8c421747aa, limb2: 0x9136eb12adac86f, }, w11: u288 { limb0: 0xf157c33f547ac7f32e5da8f0, limb1: 0xf76a7a02c64558b3145a2909, limb2: 0x260334b73e26b56, }, }, E12D { w0: u288 { limb0: 0xd4841712eb8b92acbedd7923, limb1: 0xdcc6cee17886abdb1007239, limb2: 0x150b39f44b2070e0, }, w1: u288 { limb0: 0x5693a871b5fcffa2aa8b4aaf, limb1: 0xf260475042f99b758ffee0f5, limb2: 0x10a5018f8eb12723, }, w2: u288 { limb0: 0x43308af7aa07017ad6f06355, limb1: 0xc9bed74aa5c3e515055e74bb, limb2: 0x281c1906fc2d8afe, }, w3: u288 { limb0: 0xaa4bf5eb2f5748f9b858b3ac, limb1: 0x903bb70501a35aac3f678acf, limb2: 0x1eb2165addc33abe, }, w4: u288 { limb0: 0xfc14dce79b687ac1377a374f, limb1: 0x18252db25bc6c91e70b57c56, limb2: 0x250aa6edf0514ce, }, w5: u288 { limb0: 0x229282724410b8e16b0f2fa7, limb1: 0x43c0ab0e53479a84a0f564b1, limb2: 0x277ac6336a1a9b7d, }, w6: u288 { limb0: 0xdeed55ef2faf345e53af52ec, limb1: 0x3bce9ebf3a661964cfe37503, limb2: 0x97f9056a20ad491, }, w7: u288 { limb0: 0x5f69ceece471cc3ebd6aa0f8, limb1: 0x32189eba17079bfd1de6d1a9, limb2: 0x12a79a708bf4a5f3, }, w8: u288 { limb0: 0xccbdec684569a23bb8881bd3, limb1: 0xd74a36913d0eb6e13ae1583b, limb2: 0xced65adac6fe081, }, w9: u288 { limb0: 0x37e051b03ff0ee8df34ca1d1, limb1: 0xc09812bdf872a01279ba5ec7, limb2: 0xc1c7be819a2edf5, }, w10: u288 { limb0: 0xdfb1cb3fd176963ae1e316f5, limb1: 0xdfef2969e0f31e316ae3b98, limb2: 0x16ce939a24e83d96, }, w11: u288 { limb0: 0x4def6d08fe4f8a3b36f8e4e4, limb1: 0x25c0237a5c43846680868d, limb2: 0x28301a94744a9062, }, }, E12D { w0: u288 { limb0: 0x51d791055394af3437707fca, limb1: 0x23d9d4f513172857b91ac570, limb2: 0x12d712a33c1350ef, }, w1: u288 { limb0: 0x6ebaf7ae16d5257aa23557c3, limb1: 0x7e85a68783668f379c36a3df, limb2: 0x1b780a9a09031ddc, }, w2: u288 { limb0: 0xfec2358627a9becd5a63e12e, limb1: 0xe9bef5e0c521222e0b7da3b1, limb2: 0x1296f365f4cf82fb, }, w3: u288 { limb0: 0x6cc4cf9d0dad41495180590b, limb1: 0x9f70ac798e90cf1ea4b1c1c8, limb2: 0x87c41a6c59dfc2d, }, w4: u288 { limb0: 0xe8febbc4d69a96df764a0a62, limb1: 0x1fb35aecac9dae22ec85780a, limb2: 0xdf36c808d1b34d, }, w5: u288 { limb0: 0x2e55c0606268af7f04a33d7c, limb1: 0xa3ea362cb853b36d21362864, limb2: 0x2440dcee8b02c1d8, }, w6: u288 { limb0: 0xef7561c98b669e09fef5573b, limb1: 0x9faf5b92dae5c40288b29667, limb2: 0x211a161b16c7393a, }, w7: u288 { limb0: 0x24d4a044898ad07d62fa1828, limb1: 0xf0baabec5df39b859a9a23b6, limb2: 0x26521f9732987047, }, w8: u288 { limb0: 0x7229c3d55422cc60a2776f2c, limb1: 0x22befd3a50a7a7e04032a122, limb2: 0x105baaf5e920b8c2, }, w9: u288 { limb0: 0x4390439b3b081876e13423a3, limb1: 0xb568d6eb2f6f72b6c3159bcc, limb2: 0x169d5ab5a0f60736, }, w10: u288 { limb0: 0x2f0b3c9576e4fd67031ca87d, limb1: 0x22e0bc83c4170a8aa384e3dd, limb2: 0x2872abcaeb098125, }, w11: u288 { limb0: 0xe52e2fb0028f73e921534e74, limb1: 0xf6cfd97c1d181d7750441ac9, limb2: 0x1c56ef8977682024, }, }, E12D { w0: u288 { limb0: 0xae28d327617f61548f759aba, limb1: 0x1401aa78c9ec2231ff346415, limb2: 0x113fb038206ddf58, }, w1: u288 { limb0: 0x42996e09532c7a0cefd8a71e, limb1: 0x69c61eb722a1e7209c4cd611, limb2: 0x13a6cbdff96772d, }, w2: u288 { limb0: 0xbf63f1fcc51ddcc897f42363, limb1: 0x707fca9fe10a26f918b0ca37, limb2: 0x669edeff7d809fe, }, w3: u288 { limb0: 0x8bb34e49a388ddc9b04b2180, limb1: 0x38dcd13822ba4ee2a5cdd793, limb2: 0x1d5dac515eaa51b8, }, w4: u288 { limb0: 0xa0125e6adb1681a41dbbf2d6, limb1: 0x3e2cccd5ac961e1a78aab8ce, limb2: 0x13d6bd7db8c4b48e, }, w5: u288 { limb0: 0x737b7f10bf6822280731a819, limb1: 0x69bd4676e8f1e6a89c10d4e7, limb2: 0x19ba69c1ce404728, }, w6: u288 { limb0: 0x4309f0c42a45a1cd80562659, limb1: 0xdda759df4dc118a6bb9c4ff4, limb2: 0x1fef98dddc22b559, }, w7: u288 { limb0: 0x16e4b900d586497d3c45f6df, limb1: 0x49f7f05337ad0de92e3b353d, limb2: 0x2a317f6bb6771fc4, }, w8: u288 { limb0: 0xdb1d34070b21596c13268b11, limb1: 0xaa74ad91700236cbbbdc34ff, limb2: 0x1f3d2738883aba1b, }, w9: u288 { limb0: 0x5dd4d2f3b2fa8a97fa8ea9f9, limb1: 0x2c5dc834a8f95e902710f4df, limb2: 0x138f968bf21498ba, }, w10: u288 { limb0: 0xabdbabb3b67443c8a7106c79, limb1: 0xb0ae2b75703e953d30907447, limb2: 0x190bab990471c462, }, w11: u288 { limb0: 0xcf34ae390b76e945d679a1ba, limb1: 0x4f4ea018b12e85eefbae6240, limb2: 0x11b6508aaf7e8efa, }, }, E12D { w0: u288 { limb0: 0x1d3d00823688d41dfa0aa2b3, limb1: 0x9b15db2c2993d757e61bb1c0, limb2: 0x2ae11207cfbeafa3, }, w1: u288 { limb0: 0x98d01e898aa5900d5e36c127, limb1: 0x5758a38ee763892c547b2b91, limb2: 0x10637e0aedce350d, }, w2: u288 { limb0: 0x7e29a433af8412d07647248, limb1: 0xa64f271a5fcb6111d0d23fe5, limb2: 0x19b1b1819c206eb3, }, w3: u288 { limb0: 0x76c3391612430b219f11873, limb1: 0x10b12d6e15c51b81da686386, limb2: 0x2e39ee00a0dd8a97, }, w4: u288 { limb0: 0x1a95ae61cf5a0ed10ad477b2, limb1: 0x288278e4057eea5d43aa3a66, limb2: 0xb2bb0125965187e, }, w5: u288 { limb0: 0xdcec59caea988d5ed8354e57, limb1: 0xd9de2dbed0736af7fb5adde9, limb2: 0x139627bfb4249292, }, w6: u288 { limb0: 0xb1a085a9c20d52aff5c6f0be, limb1: 0x9a17337ed73c52ccead8864e, limb2: 0xdcfc8e7b31d6b15, }, w7: u288 { limb0: 0x1ded66fd8aec0a04c911f1a3, limb1: 0x2814204faef35f41e3f1cc8b, limb2: 0x1999b17d88973015, }, w8: u288 { limb0: 0xa9969aafed2e81fe21fceccc, limb1: 0xde819f6c6186b981c324bd60, limb2: 0x2ea9d87f146b9984, }, w9: u288 { limb0: 0xa576384a80333dedf9e88310, limb1: 0x364ad41f1043ed9c6286cf5d, limb2: 0x185381ccca5628e0, }, w10: u288 { limb0: 0xec6a507f1e942bf671d63ab3, limb1: 0xf9ec826df2822a61bc36725, limb2: 0x14ce04de4bbb61da, }, w11: u288 { limb0: 0x168a2628e665ca7591760e15, limb1: 0x115842818d09028abf06552f, limb2: 0x1c7b912d4cec67a3, }, }, E12D { w0: u288 { limb0: 0xf73192b2fe5dc1293422b385, limb1: 0x7c0b272084084d471108c781, limb2: 0x3020dd2bb1971af4, }, w1: u288 { limb0: 0x30a64137b7e95ebfcdab4d96, limb1: 0x229f57d761eeb3876b51cd56, limb2: 0x19a596949310e6ad, }, w2: u288 { limb0: 0x6a8e194198a83adeb7bb2d57, limb1: 0xdd72e054a7572ae9694e527b, limb2: 0x1e166b19fd03f8da, }, w3: u288 { limb0: 0x89955ac52e292b8ef51fee5b, limb1: 0xb4a02290d35f652e34e4160c, limb2: 0x25f5a19aec7507fc, }, w4: u288 { limb0: 0xfd26f66a7e8b7c9b65ccf82f, limb1: 0x885924961e16baba1430bbff, limb2: 0x340f95fa56b75d0, }, w5: u288 { limb0: 0xef273d28469f2f491bbcd40a, limb1: 0xe90efb0fe5cac233218f725e, limb2: 0x2270370eed956191, }, w6: u288 { limb0: 0xca9dcd949b9485cbb6caf5, limb1: 0xf042772fe0b0a8d9ca424d0d, limb2: 0x6d8cd4db60bffeb, }, w7: u288 { limb0: 0x62143619306fd7c0b3b08cc9, limb1: 0xe18c5df14640cc99bb874bd4, limb2: 0x1e30a97ba92bbad6, }, w8: u288 { limb0: 0x25f8c1f28cee5b135d48cdb6, limb1: 0x9acc1820c130cb285092986d, limb2: 0x2f167bb2de542dc7, }, w9: u288 { limb0: 0xdfd9bc4b5d951cf27288f3d8, limb1: 0x20e76c8c514cfc034e8cee6c, limb2: 0x8b4f5acd534d42, }, w10: u288 { limb0: 0x8e677eb53bf14698e8b36257, limb1: 0x9aea99485edddd73910e5d7b, limb2: 0x1973552b29e8f190, }, w11: u288 { limb0: 0xd5b7c92c3679269e6e89fe4d, limb1: 0x571711871632367838fd954f, limb2: 0xca34d2d34fc803f, }, }, E12D { w0: u288 { limb0: 0x5a115fd010369153e97447d6, limb1: 0x30bec73abe3a59b63e145fad, limb2: 0x13cad9f295161d7b, }, w1: u288 { limb0: 0xa241b367a81e2287bcb61b16, limb1: 0x46dcbe36594cfb18595a8f0, limb2: 0xab01b7e5df25989, }, w2: u288 { limb0: 0x958fca463d9bb5661f0b2fd9, limb1: 0xe06657821675ca026783130d, limb2: 0x59ffe9952b66fb9, }, w3: u288 { limb0: 0x574fb844c92111198355d520, limb1: 0xa14dab7a5284adcd16f40ce5, limb2: 0x1806c0e26ec0aee7, }, w4: u288 { limb0: 0xe7172a20883b7e788bde9782, limb1: 0xcf0a0721de528a49cb3dd1c4, limb2: 0x25972b2764f33320, }, w5: u288 { limb0: 0x731c250de9790bc763ae6475, limb1: 0x2a9161ea6cab27c57ed08479, limb2: 0xbba79ad176ebf3d, }, w6: u288 { limb0: 0x1883e2d532d070e92581f205, limb1: 0x3ee4f828dc142213ed8af967, limb2: 0x2e502ad8c56d0a28, }, w7: u288 { limb0: 0x5e8c5fa9891c0aba3c546e3b, limb1: 0xef69eec871a7317eb48f3c4c, limb2: 0x15527229b85df416, }, w8: u288 { limb0: 0xf9d9b27fb6982c16115b072a, limb1: 0x25855f7b17b4ab7d777c5a71, limb2: 0x17b488bbc4482f41, }, w9: u288 { limb0: 0xc8d3bb50e255913069e7e85a, limb1: 0x24471c0093ed7d60d8ec93fe, limb2: 0x1d25a04ef49a8340, }, w10: u288 { limb0: 0x8469405a54b25563e06b7556, limb1: 0x362aa168589a62d47f199abd, limb2: 0x144504d5e88c24cd, }, w11: u288 { limb0: 0x6ecf9040c554795e77fbc3d, limb1: 0xce3f520885d6702426c67484, limb2: 0x1729093a618f3459, }, }, E12D { w0: u288 { limb0: 0x4e76344718fef690a24dad4a, limb1: 0xc77cee5e9c5a4c63dcec6df, limb2: 0x2eabcc53f3044ba2, }, w1: u288 { limb0: 0xff72f26ff560d5c610868418, limb1: 0xcf976dd967e078f76ffa7f14, limb2: 0x2c4c3336767ab0f8, }, w2: u288 { limb0: 0x74290c1a859b6a664515c7ec, limb1: 0x4018fec3da718ea7ce725e7a, limb2: 0x2c0acbaf6d3dda8c, }, w3: u288 { limb0: 0x9e24330df30e289200970ddc, limb1: 0x2c7506954dfbab29debdcc33, limb2: 0x19e88e5ba2f32c9e, }, w4: u288 { limb0: 0x92b81688683664e49ad6c207, limb1: 0x950a1848e1e7bd3bee4e9648, limb2: 0x245fb841e1ea7f20, }, w5: u288 { limb0: 0xc0f5268607b5fb01ab981f8, limb1: 0x92b4bd8b0642eb9b8125e71e, limb2: 0x832b45514154898, }, w6: u288 { limb0: 0x18faa9f18edac485d6a7b190, limb1: 0xc374fb5ae398115c8cc5d4f, limb2: 0x1b89ed6497f7528b, }, w7: u288 { limb0: 0x60c6513ff564579e1988b356, limb1: 0x829048cc61af118a911e5195, limb2: 0x4b67c5750b2a6c8, }, w8: u288 { limb0: 0x2ad1d470e7cbba646712536d, limb1: 0xebf4f74cfd00385bc9700205, limb2: 0x21fb3b56977d6981, }, w9: u288 { limb0: 0xc193efe12433a6a7cd169fd5, limb1: 0x8e27c0d34ce21cff9d29399a, limb2: 0x132d71372731fcc8, }, w10: u288 { limb0: 0x556a4d23d4f86a177341b2e5, limb1: 0x383fea5b5626cc64d9e66b7a, limb2: 0x1ce052cbe93337d, }, w11: u288 { limb0: 0x4e56bc802b5abe09ee095df, limb1: 0x37fb83a829d63d38ea7fe544, limb2: 0x2b3dbc96d14de0ea, }, }, E12D { w0: u288 { limb0: 0x672f14cd0b10414f1a06ab0e, limb1: 0xbc03210758f55bd394a8677b, limb2: 0x1919a01fe8398d6e, }, w1: u288 { limb0: 0x994ec01c61f79b37735fb04e, limb1: 0x9f89038d35f704713d113e7c, limb2: 0x2fb067f3596c6f5d, }, w2: u288 { limb0: 0xc4db13525dd2ebf1798bc011, limb1: 0xd7f230dddfb10272addc3ac5, limb2: 0x129d55618745bdb6, }, w3: u288 { limb0: 0x4df6042036cc4e73caee7fd1, limb1: 0xf39bb2f57992a78b7f562caf, limb2: 0x10b637bffbf9e3b6, }, w4: u288 { limb0: 0xaf7ef004ea70cae206949fe0, limb1: 0x746537a320de6c4a8a3597ea, limb2: 0x2aaeaf029d031dc, }, w5: u288 { limb0: 0xc621594a078899f8c62a9cdb, limb1: 0x89e9884f3bf39f6476b7b0ea, limb2: 0x272b433fbcd53b5c, }, w6: u288 { limb0: 0xed69fdcb268caf1bf4e7be79, limb1: 0xd64e544332ba16059fbe6f21, limb2: 0x453884fd8055fc7, }, w7: u288 { limb0: 0xfcb53a4db14a035bb31b8e42, limb1: 0xcb56190ac6955b4789800190, limb2: 0x1948730c4a6d36a3, }, w8: u288 { limb0: 0xf71fef15f0a4caabc93864d4, limb1: 0x533dd6e3aef09b50136b0424, limb2: 0x26d7908e833342d0, }, w9: u288 { limb0: 0xa7702df86f4ffe60b5fcd8be, limb1: 0x82f85e85117830f257dc4449, limb2: 0x1beb171bf8d70197, }, w10: u288 { limb0: 0x31fc4912bfb5683fe07e25cb, limb1: 0xd283fd947a39cca9cf8bad14, limb2: 0x115ec5f3559e2fc, }, w11: u288 { limb0: 0xa9507d23f9e956aa9f5be47d, limb1: 0x20a327008223620fe131958e, limb2: 0x1e5fc15a15ef1efa, }, }, E12D { w0: u288 { limb0: 0x2a32729f621dc67e38a9e308, limb1: 0x3c7a4c38ab41463dd90d71e6, limb2: 0x164410a5de4f6a31, }, w1: u288 { limb0: 0x7c865da012acb0d622f3e6af, limb1: 0x6efcde33e8cb90fe34763281, limb2: 0x8bb58070cb757b0, }, w2: u288 { limb0: 0x102a4c45e1c7dc9a185096a6, limb1: 0x939ac06cca64b4059b650779, limb2: 0x18d0f097d8f27ead, }, w3: u288 { limb0: 0x5604d370b04f242174dfdc19, limb1: 0x3f2331ab9d6af28b81d598d7, limb2: 0x14096280fdb84ef2, }, w4: u288 { limb0: 0x4412fcdec6354f32bbfff8ab, limb1: 0xb2455bc4da7ee0be75af5185, limb2: 0x1a06f1d06514810a, }, w5: u288 { limb0: 0x5b518b0ce27ac5904af109d2, limb1: 0x505b8452fe08ea12e98c5709, limb2: 0xb8fe7b802f5d89a, }, w6: u288 { limb0: 0xd0c037f851034b765eed83e4, limb1: 0xb208cada98ad38bb65fa1eac, limb2: 0xad14e495078b750, }, w7: u288 { limb0: 0x27c34e9def3b3769635e71be, limb1: 0xb2ec25f739ecf7d9600f51a6, limb2: 0x2865787fdd12b638, }, w8: u288 { limb0: 0x639142ced19d81d2bb7fab2e, limb1: 0x7c2168110de34c92009b4685, limb2: 0x1c898a9a832e3d64, }, w9: u288 { limb0: 0x1f5eb66df1fdc41bf0ce081e, limb1: 0xafbc19ef146651ce2da77852, limb2: 0xe6eac8e4ccd9b71, }, w10: u288 { limb0: 0xf57e46ceab88a82e3a3f41c0, limb1: 0xb9c56b5c009ea3787342009, limb2: 0x2b02ef12c18f1e03, }, w11: u288 { limb0: 0xfb98309dd05609eb835a18ea, limb1: 0x831938e89a1a52e80f384288, limb2: 0x2f28355805f38fcd, }, }, E12D { w0: u288 { limb0: 0xbc95d451e65b0289c2f0d9f4, limb1: 0x29864b5c2006361c7ec32dbc, limb2: 0x231b97e42e88b4ff, }, w1: u288 { limb0: 0x4bc818c5e9f6ed62903ac570, limb1: 0xa6da69d8d95bf6c6529bfd2e, limb2: 0x9e56c349c350628, }, w2: u288 { limb0: 0xed520f5d2e7e426947558231, limb1: 0x407b04e8f131e18a83493135, limb2: 0xa24acdc96970f27, }, w3: u288 { limb0: 0x1d6c5e4e2aeea52567838f68, limb1: 0x3bdb301020d1702216efd42d, limb2: 0x2b59a5b8dcb0422b, }, w4: u288 { limb0: 0xf85e1201fcab94bada581d84, limb1: 0xe0efe6f4951ed52abf8b76af, limb2: 0xa6ae5af3e8d245c, }, w5: u288 { limb0: 0x51002d24f61e489d8c153193, limb1: 0xb32c323348563ffd15f5c33c, limb2: 0x26c4b2966b0b0244, }, w6: u288 { limb0: 0xb16e8f73703c8fc9cbe27a54, limb1: 0xe85c673315e3ff3bd80c385a, limb2: 0x1097084941caa56b, }, w7: u288 { limb0: 0x418c90f7a9ddb4b009516166, limb1: 0x6b3e04040348ba6064a95888, limb2: 0x1109803e56079bbf, }, w8: u288 { limb0: 0xfba73400ff9d91da0d4bb12f, limb1: 0xaa1955281d88ef0e24a3555b, limb2: 0x2eb930dc35c971e5, }, w9: u288 { limb0: 0x5cf265fa7a069ab0faf07634, limb1: 0x1fc2d713371237aca902f86b, limb2: 0x239dbccb24faaa, }, w10: u288 { limb0: 0x2b4f288428a4b9bbe4f2fa4c, limb1: 0x7623c03640928ed49d920ddf, limb2: 0x13201c25a3d33428, }, w11: u288 { limb0: 0x40775c9ff8a831905a097195, limb1: 0x26f944b86fd036f02e3194c7, limb2: 0x28d19be843b3ff3c, }, }, E12D { w0: u288 { limb0: 0x189cb16fa9189ecd4fbb9343, limb1: 0x3b0200dcdda749a4ac7badd1, limb2: 0x127325cd0676619e, }, w1: u288 { limb0: 0x69426bc4ac151ab78084bd46, limb1: 0x6ed73cc76b2e6866f2bb6e99, limb2: 0xa8a06bc3b26bf4d, }, w2: u288 { limb0: 0x773e7d09877a907af19e3b20, limb1: 0xceef25b4bf04c5319d48ec40, limb2: 0x1551ac68039dc2ff, }, w3: u288 { limb0: 0x5109ce5668e51d98d7e472da, limb1: 0x79997b0e4983fd2528c1da6, limb2: 0x47a2e7358f796cc, }, w4: u288 { limb0: 0xab89501874d5d5203a865933, limb1: 0xd17c5b1d843b9ac35877d3b7, limb2: 0x1b0b482637ee8296, }, w5: u288 { limb0: 0x2409320a513ccf12624ea83d, limb1: 0x4e71c7cafee4e2c6029411d3, limb2: 0x3f88321fd8d60cb, }, w6: u288 { limb0: 0xda33ccef60ef4ad0f7de09a4, limb1: 0x896d7cf80ee703d4a76ea589, limb2: 0x26c5d68117d6cd8b, }, w7: u288 { limb0: 0xaae41113d58ca2d0b98fdc40, limb1: 0xb2b5035495fad57c313b39c7, limb2: 0x2332fb21abcde1dc, }, w8: u288 { limb0: 0x2265477f67c8e381757e2444, limb1: 0xff72e21f4c00cdb8045fe56a, limb2: 0xe369c6ccb5e2670, }, w9: u288 { limb0: 0xa47c80b7062c0a20d48497b6, limb1: 0x89c328f7723a88bdc303660f, limb2: 0x233963ef5c38065c, }, w10: u288 { limb0: 0xeaee6b9ebb4333692353011d, limb1: 0xd5b4ec24d21d826b39675fc1, limb2: 0x1ddb842c4860ed55, }, w11: u288 { limb0: 0x905d5ae2cb91239753abae8b, limb1: 0xe05b3862330500c4e491581a, limb2: 0x2a0484f49430b2f4, }, }, E12D { w0: u288 { limb0: 0x322ea1fa72a31dba5d539d3c, limb1: 0x7a42a67f2be67efd3656ce90, limb2: 0x20b10c4394721d38, }, w1: u288 { limb0: 0x8d4223351a2c2e79c68f7016, limb1: 0x7780a8b63715a853e1637024, limb2: 0x4840a61778756f7, }, w2: u288 { limb0: 0xd33364f24b90b7283e555f03, limb1: 0x2725b6c80c1db189e6c6030f, limb2: 0xd0e44a0d823a67e, }, w3: u288 { limb0: 0x882366ae98da604af6b4b252, limb1: 0xb3c7302035df6f08fe1bb60f, limb2: 0x1a9eb767ddd9d0d, }, w4: u288 { limb0: 0xcfbe7c69e24937ff2679bd74, limb1: 0xa52b7b97b50a452b511dc5ec, limb2: 0x1b0e7a47140766b2, }, w5: u288 { limb0: 0x31951de26a27a91be138fa32, limb1: 0x47bc4f53494987139e77af9a, limb2: 0x1149a75ca93cba86, }, w6: u288 { limb0: 0x88cbc9cc41de5834f9fb4004, limb1: 0x5bb1bdd77409a1a3e8607b84, limb2: 0xcec6462b9b83783, }, w7: u288 { limb0: 0xe8cca50626729793c273633c, limb1: 0xa94a00b04453b3af1fcda1e7, limb2: 0xe304d8c44e2ad29, }, w8: u288 { limb0: 0x6d79c62f33ef542ee031b10b, limb1: 0xa853b8626dc0f8edc9dae8a2, limb2: 0x25a442e527fb55ae, }, w9: u288 { limb0: 0xb73c62448fcc061b7461540, limb1: 0xd36efa0f2e61f0bdf4f23d5e, limb2: 0x146329a5e06f73d8, }, w10: u288 { limb0: 0xa78188e4bc75e2262a094916, limb1: 0xe7126a1cbcb03e681a2f9eb0, limb2: 0x22b08cfb6cb34c00, }, w11: u288 { limb0: 0x93651f5e4cfcfd80ebae9e97, limb1: 0x2ad39d6d02435965ab528f04, limb2: 0x162d5418053965e7, }, }, ] .span(), big_Q: array![ u288 { limb0: 0x65737383940f52cb41c10526, limb1: 0xf877e2e11c81d1fe760106bd, limb2: 0x227bda5a9bc6a20e, }, u288 { limb0: 0x1b3e8afea54678452808b494, limb1: 0x9a314566b20243000ffffaeb, limb2: 0x2e7746007ddf67d0, }, u288 { limb0: 0x62312dca7c275ac579aa50b8, limb1: 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0x8319fe8b5dd4bb0fe9a7f86c, limb2: 0x9d1a1848abb76cb, }, u288 { limb0: 0xe126329ee21b76c790e81302, limb1: 0x9abbee7b21ea11a7ba796135, limb2: 0x106b34443f87265b, }, u288 { limb0: 0xcad4ede64aa9f7184a78da58, limb1: 0x195ccfcab97b6f2bc0af932c, limb2: 0xe6149e62bd9cd99, }, u288 { limb0: 0xfca6890b61e4ae37626aea9f, limb1: 0xefd7f6a4e50af11fbb574989, limb2: 0x2708074111d394f4, }, u288 { limb0: 0x3a5685f239bbb7516a9ce4f0, limb1: 0x9e27ca310f6eed7da9da0ae3, limb2: 0x856156f2344cd99, }, u288 { limb0: 0xdc860e4205aac0d4a119db7a, limb1: 0xcab98cf8c47fe661e5e51751, limb2: 0xa6b9ecbecc92920, }, u288 { limb0: 0x421f4f31e89cd635f715f0b2, limb1: 0xf7438c10f4292abac4911cb1, limb2: 0xca7cb6b53e66e2d, }, u288 { limb0: 0xff8730c83666f03b63c82e9a, limb1: 0xbf15a711d60434a18ad0b332, limb2: 0x1e4e0174abb3ff35, }, u288 { limb0: 0xddaa0774bd9d3400487b3332, limb1: 0xa47169b652481e69cdbd586, limb2: 0x1077eff1074d9cf8, }, u288 { limb0: 0xb9d99431843de1c6e03930cf, limb1: 0x48055c4caf106ecdba4ac34, limb2: 0x1d85593859c0a084, }, u288 { limb0: 0x4d70a2f8aadfaef4a1684fc3, limb1: 0x851a661cb719732bb10a8605, limb2: 0x77fb033385f4d55, }, u288 { limb0: 0xa8df36d7fc5dde16f2f92d30, limb1: 0x3828c87739f9975c4679f6e3, limb2: 0x1e49eba589ab9049, }, u288 { limb0: 0x8afb36ffc90cdfb2c394054c, limb1: 0x68e2f7def70b6b68fd976374, limb2: 0x14f9b073519d71ca, }, u288 { limb0: 0x537ea3eac7013cbef6144e1f, limb1: 0x237fb1851dbe67882d4d5c11, limb2: 0x11ebc5003e3b3263, }, u288 { limb0: 0xfcced309e1dd2f53c834728c, limb1: 0xf9516f53eecb333fc95a18e4, limb2: 0x29f5bbf3dd9109e3, }, u288 { limb0: 0x938889c1b734d1489d03cad1, limb1: 0x1db581687ac5c8a9a17ed553, limb2: 0x161ecb984fb856e3, }, u288 { limb0: 0xa268de500efb03f7bea07973, limb1: 0x6c4a37b98bad9ddb8cfbd6d0, limb2: 0x1524755288056cda, }, u288 { limb0: 0x7d4497670d42bbf1c2145bc9, limb1: 0x7abbbc4122653cc6ca902869, limb2: 0x261090fa8aee41bb, }, u288 { limb0: 0x151b2312dc16eaa91f70b86d, limb1: 0xdb244db1311f915d8c6552d1, limb2: 0xf78ff35f48b050e, }, u288 { limb0: 0x583a0c5dabf9c29cb843214e, limb1: 0xd11a9ac8a4d814eab40581, limb2: 0xa40191c26327e38, }, u288 { limb0: 0x42d106709fde0376b3baaf29, limb1: 0xeade8db6e8f2d9a0f908711a, limb2: 0x1bc9aa9ee2ecedc9, }, u288 { limb0: 0xb1e8bdc9ae134a052e65b82f, limb1: 0xe9a3b46a54f1aa42cc41f70d, limb2: 0x2a5ab4034d9620c8, }, u288 { limb0: 0x6cd32ed3f988bd665ae0c4ad, limb1: 0xdba8bd99a74f29cf958bbd93, limb2: 0x30211dca93e1d47e, }, u288 { limb0: 0x7c7eedd9922c46ad005dbc1d, limb1: 0xbef703824144548d2ec5d752, limb2: 0x1d6d3e4b54788235, }, u288 { limb0: 0x3bb2440fa67475f383044802, limb1: 0xe4557d5ab9325d4dbe872115, limb2: 0x672a865f51eb536, }, u288 { limb0: 0x2e915fc6800aa8adc2dc20c3, limb1: 0x46bd6375ff3d31847846dbc2, limb2: 0x2c9d928ee5f7e380, }, u288 { limb0: 0x886a5670bcf95b46c8f20ad9, limb1: 0x77ee46095f8543fad0b9cfc5, limb2: 0x3db727715156be8, }, u288 { limb0: 0xbae6bfa1ab50e3f01425a433, limb1: 0x47856f2553698328e4e579f0, limb2: 0x190d21e247afb41a, }, u288 { limb0: 0xa5d50f00f3e9814c6440dfab, limb1: 0xb6a91c5c710bd62ee2b58fb7, limb2: 0x21aef87938c717b1, }, u288 { limb0: 0xf470603734c27f99d0c0182f, limb1: 0x377ba5790ad04eb84bbd37eb, limb2: 0x1e8b05f3cfda0857, }, u288 { limb0: 0x77d147b35e8a28c9a8f59a25, limb1: 0x475d3713be9110798f8ea60e, limb2: 0xa54c2f08056d9a0, }, ], z: 0x7f997c7ceaaa93d340bc143f505f6d8423271960d6604ea8bf9d8c50dc40977, }; let res = multi_pairing_check_bn254_2P_2F(pair0, pair1, lines, hint); assert!(res.is_ok()); } #[test] fn test_BN254_mpcheck_3P_2F_with_extra_miller_loop_result() { let pair0: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0x5c724369afbc772d02aed58e, limb1: 0x2cd3bc838c66439a3d6160b, limb2: 0x72f26b55fb56be1, limb3: 0x0, }, y: u384 { limb0: 0x772ca79c580e121ca148fe75, limb1: 0xce2f55e418ca01b3d6d1014b, limb2: 0x2884b1dc4e84e30f, limb3: 0x0, }, }, q: G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }, }; let pair1: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0x5c724369afbc772d02aed58e, limb1: 0x2cd3bc838c66439a3d6160b, limb2: 0x72f26b55fb56be1, limb3: 0x0, }, y: u384 { limb0: 0x772ca79c580e121ca148fe75, limb1: 0xce2f55e418ca01b3d6d1014b, limb2: 0x2884b1dc4e84e30f, limb3: 0x0, }, }, q: G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }, }; let pair2: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0x5c724369afbc772d02aed58e, limb1: 0x2cd3bc838c66439a3d6160b, limb2: 0x72f26b55fb56be1, limb3: 0x0, }, y: u384 { limb0: 0x772ca79c580e121ca148fe75, limb1: 0xce2f55e418ca01b3d6d1014b, limb2: 0x2884b1dc4e84e30f, limb3: 0x0, }, }, q: G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }, }; let precomputed_miller_loop_result = E12D { w0: u288 { limb0: 0xfaccb300f066ee143625434e, limb1: 0x12bfc53caae870d85457c4bc, limb2: 0x590ff61397d0dd2, }, w1: u288 { limb0: 0x3d74a2131fff08abcc77f5ff, limb1: 0xcc055f39a02506234d00e8eb, limb2: 0xf706ef44c1d0af1, }, w2: u288 { limb0: 0x4605464626791e8c2d23914a, limb1: 0x7da5ae6eba3609b9a258aeb5, limb2: 0x22a5875254921ffd, }, w3: u288 { limb0: 0xa36080e7d54da24b20b89bf4, limb1: 0x701510a38855b7b7bbcf7e5b, limb2: 0xae461e60176f9fc, }, w4: u288 { limb0: 0x310a2f82381041f00ab0a97b, limb1: 0x4ec0223c3dc06216c285cccb, limb2: 0xaae21f01619c3fa, }, w5: u288 { limb0: 0xa206b95ba090599b7a5e8c2e, limb1: 0xac945c0f61fb2673fb43b2aa, limb2: 0xe203da0f9a03b1a, }, w6: u288 { limb0: 0x280fda652c0775ee0202237c, limb1: 0x4ad4e2c546956c34ec381b30, limb2: 0x1e2de9ed7968cac1, }, w7: u288 { limb0: 0xdff110a40e2837285a53cdc9, limb1: 0x303a0db8cbb989aa911eec40, limb2: 0xf3b13b4d08af03, }, w8: u288 { limb0: 0x622927b875c780e6f64e6abe, limb1: 0xc79a5ba5d705c69b59a88b64, limb2: 0x242bd1109f659686, }, w9: u288 { limb0: 0x47a207ed1fe3501ee8a66a12, limb1: 0x92d2dc829a2f34f4ee684f04, limb2: 0x1f626f25b03417e4, }, w10: u288 { limb0: 0x9cf6ea1c727f2d3d16f4095b, limb1: 0xdca506524d7f4aeb8f093970, limb2: 0x234cc399b032b927, }, w11: u288 { limb0: 0xc04208d92713b2b39e39f93, limb1: 0x339c2266bcf3504782285acc, limb2: 0x8dd178fb6d5acd8, }, }; let lines = array![ G2Line { r0a0: u288 { limb0: 0x13fc2cd2d19c89caf55a13a8, limb1: 0x6a3f58c82d87f618a84e2bf0, limb2: 0x18b4a261a618f14c, }, r0a1: u288 { limb0: 0xa12d7217806e8da77076b27c, limb1: 0x868641e2c5440aefc45ec097, limb2: 0x21a23fb8ecb967b4, }, r1a0: u288 { limb0: 0x9c39813fffc4c7b20cc17a76, limb1: 0xf4a2427d51f32abb183e2860, limb2: 0x2687525f35660d8f, }, r1a1: u288 { limb0: 0xc039aad6d5de6af4f5c6c0bb, limb1: 0x3750d73ecbf7e1bca03d1cf2, limb2: 0xecbbbebf08974c8, }, }, G2Line { r0a0: u288 { limb0: 0x13fc2cd2d19c89caf55a13a8, limb1: 0x6a3f58c82d87f618a84e2bf0, limb2: 0x18b4a261a618f14c, }, r0a1: u288 { limb0: 0xa12d7217806e8da77076b27c, limb1: 0x868641e2c5440aefc45ec097, limb2: 0x21a23fb8ecb967b4, }, r1a0: u288 { limb0: 0x9c39813fffc4c7b20cc17a76, limb1: 0xf4a2427d51f32abb183e2860, limb2: 0x2687525f35660d8f, }, r1a1: u288 { limb0: 0xc039aad6d5de6af4f5c6c0bb, limb1: 0x3750d73ecbf7e1bca03d1cf2, limb2: 0xecbbbebf08974c8, }, }, G2Line { r0a0: u288 { limb0: 0x54759dba6a84024be322e99f, limb1: 0x4e10ecee53f96244ef333ea1, limb2: 0x17afac113b18aedd, }, r0a1: u288 { limb0: 0xc7445875bbb1fe6f68064acb, limb1: 0x31ca03d3bc3d4d6dd322a9f9, limb2: 0xec20eb9f4783875, }, r1a0: u288 { limb0: 0xcc38494d3c5bc464cbbb82d1, limb1: 0xc3ae03392f8e2da27f434230, limb2: 0x9dcfc13abcb9299, }, r1a1: u288 { limb0: 0xa8381fb666422121e2b63c8c, limb1: 0x80ff6e77b58976a0f7444d9e, limb2: 0x21989286f0a82b61, }, }, G2Line { r0a0: u288 { limb0: 0x52cd2431a88ef78ec482ce43, limb1: 0xdb994b0266c17f5e8dded89e, limb2: 0x107cd7f4d3a5c20f, }, r0a1: u288 { limb0: 0xb4e4c1a20d77277f1ecef6b, limb1: 0x3fc13dd5746446d4e724e645, limb2: 0x18ed3b584ac56dfe, }, r1a0: u288 { limb0: 0x3a537f5b220d3afddbd3be9d, limb1: 0xeddb087729b8776323c5b8ee, limb2: 0x1f5e5f61ae8c59e6, }, r1a1: u288 { limb0: 0x4fe2c98dc347d3ceb841acdf, limb1: 0xe6a7f4bdda3390e40c62a288, limb2: 0x2a277c878fe85394, }, }, G2Line { r0a0: u288 { limb0: 0x54759dba6a84024be322e99f, limb1: 0x4e10ecee53f96244ef333ea1, limb2: 0x17afac113b18aedd, }, r0a1: u288 { limb0: 0xc7445875bbb1fe6f68064acb, limb1: 0x31ca03d3bc3d4d6dd322a9f9, limb2: 0xec20eb9f4783875, }, r1a0: u288 { limb0: 0xcc38494d3c5bc464cbbb82d1, limb1: 0xc3ae03392f8e2da27f434230, limb2: 0x9dcfc13abcb9299, }, r1a1: u288 { limb0: 0xa8381fb666422121e2b63c8c, limb1: 0x80ff6e77b58976a0f7444d9e, limb2: 0x21989286f0a82b61, }, }, G2Line { r0a0: u288 { limb0: 0x52cd2431a88ef78ec482ce43, limb1: 0xdb994b0266c17f5e8dded89e, limb2: 0x107cd7f4d3a5c20f, }, r0a1: u288 { limb0: 0xb4e4c1a20d77277f1ecef6b, limb1: 0x3fc13dd5746446d4e724e645, limb2: 0x18ed3b584ac56dfe, }, r1a0: u288 { limb0: 0x3a537f5b220d3afddbd3be9d, limb1: 0xeddb087729b8776323c5b8ee, limb2: 0x1f5e5f61ae8c59e6, }, r1a1: u288 { limb0: 0x4fe2c98dc347d3ceb841acdf, limb1: 0xe6a7f4bdda3390e40c62a288, limb2: 0x2a277c878fe85394, }, }, G2Line { r0a0: u288 { limb0: 0x53e743cfae97f5f975cf49cd, limb1: 0x4a80ced31104872cc46b3fa6, limb2: 0x26af32e1e4b51233, }, r0a1: u288 { limb0: 0x20537276ce9b6d318ea2f567, limb1: 0xf0d44c7024c00ead73f13f53, limb2: 0x13e665e776128b92, }, r1a0: u288 { limb0: 0xad9a173a5d331f5e8221dedc, limb1: 0x11fc759697a8b7533cf8e7fd, limb2: 0x281514af188294d6, }, r1a1: u288 { limb0: 0xcd59e5219230c0937878feff, limb1: 0x85d1c954acb2bf4803a9e200, limb2: 0x4229bcd8d07f251, }, }, G2Line { r0a0: u288 { limb0: 0x53e743cfae97f5f975cf49cd, limb1: 0x4a80ced31104872cc46b3fa6, limb2: 0x26af32e1e4b51233, }, r0a1: u288 { limb0: 0x20537276ce9b6d318ea2f567, limb1: 0xf0d44c7024c00ead73f13f53, limb2: 0x13e665e776128b92, }, r1a0: u288 { limb0: 0xad9a173a5d331f5e8221dedc, limb1: 0x11fc759697a8b7533cf8e7fd, limb2: 0x281514af188294d6, }, r1a1: u288 { limb0: 0xcd59e5219230c0937878feff, limb1: 0x85d1c954acb2bf4803a9e200, limb2: 0x4229bcd8d07f251, }, }, G2Line { r0a0: u288 { limb0: 0xa4e9586d1e24c4e20dafd647, limb1: 0x7f88fb247cdc95b6010d9e1, limb2: 0x2fc2b7b6b4abaf58, }, r0a1: u288 { limb0: 0x9bbcc4481ffe859db49e1d98, limb1: 0x13be783da3c9bea06995338d, limb2: 0x2041db55312bcc8b, }, r1a0: u288 { limb0: 0x89721c899fdfd2776e1d4131, limb1: 0x602e0c14a55d62b055ca8113, limb2: 0x1fbed06b550ce696, }, r1a1: u288 { limb0: 0xfff5deaaf0a2cf3cca44de5c, limb1: 0xd5efcfc87d7bc3cc0d3d9be1, limb2: 0x18106453c47c63f5, }, }, G2Line { r0a0: u288 { limb0: 0x33720aad04d475cab632ceb4, limb1: 0xd7b4eef636fd40d7ad28aaf7, limb2: 0x25e952c734deb4a7, }, r0a1: u288 { limb0: 0x8c407e44689ce2ec6ea22bb3, limb1: 0x10ab4ebbd57974771a9bfe37, limb2: 0xc2d6b95efdcdb61, }, r1a0: u288 { limb0: 0xb03dd6a767461c482dcafa86, limb1: 0xbbde25f51257025e9a28974, limb2: 0x278e5fd00fb1b935, }, r1a1: u288 { limb0: 0x7bbd2c1bbf42867093a08f41, limb1: 0xcc4d5b03ab2a82a219b80b43, limb2: 0x2105554776d3cf89, }, }, G2Line { r0a0: u288 { limb0: 0xa4e9586d1e24c4e20dafd647, limb1: 0x7f88fb247cdc95b6010d9e1, limb2: 0x2fc2b7b6b4abaf58, }, r0a1: u288 { limb0: 0x9bbcc4481ffe859db49e1d98, limb1: 0x13be783da3c9bea06995338d, limb2: 0x2041db55312bcc8b, }, r1a0: u288 { limb0: 0x89721c899fdfd2776e1d4131, limb1: 0x602e0c14a55d62b055ca8113, limb2: 0x1fbed06b550ce696, }, r1a1: u288 { limb0: 0xfff5deaaf0a2cf3cca44de5c, limb1: 0xd5efcfc87d7bc3cc0d3d9be1, limb2: 0x18106453c47c63f5, }, }, G2Line { r0a0: u288 { limb0: 0x33720aad04d475cab632ceb4, limb1: 0xd7b4eef636fd40d7ad28aaf7, limb2: 0x25e952c734deb4a7, }, r0a1: u288 { limb0: 0x8c407e44689ce2ec6ea22bb3, limb1: 0x10ab4ebbd57974771a9bfe37, limb2: 0xc2d6b95efdcdb61, }, r1a0: u288 { limb0: 0xb03dd6a767461c482dcafa86, limb1: 0xbbde25f51257025e9a28974, limb2: 0x278e5fd00fb1b935, }, r1a1: u288 { limb0: 0x7bbd2c1bbf42867093a08f41, limb1: 0xcc4d5b03ab2a82a219b80b43, limb2: 0x2105554776d3cf89, }, }, G2Line { r0a0: u288 { limb0: 0x32e40fb4d2025cd0e82ced6f, limb1: 0xbc0608261a5f898f868a08d8, limb2: 0x282ba090b78fca30, }, r0a1: u288 { limb0: 0xdfe55dec41a63986c6aceff7, limb1: 0x2555dd47b4f4cd057f63d51, limb2: 0xf5a1242bc10ee1f, }, r1a0: u288 { limb0: 0x590c3a14f70d93710ad8d62d, limb1: 0x91b6b9b5a53eb9825ebe4230, limb2: 0x2f3c78d5b1a40d44, }, r1a1: u288 { limb0: 0x7fa2feee5a3d934393f3dcdb, limb1: 0x216af82d8ef724bef3a0cff9, limb2: 0x2a3b1b41079d39de, }, }, G2Line { r0a0: u288 { limb0: 0x32e40fb4d2025cd0e82ced6f, limb1: 0xbc0608261a5f898f868a08d8, limb2: 0x282ba090b78fca30, }, r0a1: u288 { limb0: 0xdfe55dec41a63986c6aceff7, limb1: 0x2555dd47b4f4cd057f63d51, limb2: 0xf5a1242bc10ee1f, }, r1a0: u288 { limb0: 0x590c3a14f70d93710ad8d62d, limb1: 0x91b6b9b5a53eb9825ebe4230, limb2: 0x2f3c78d5b1a40d44, }, r1a1: u288 { limb0: 0x7fa2feee5a3d934393f3dcdb, limb1: 0x216af82d8ef724bef3a0cff9, limb2: 0x2a3b1b41079d39de, }, }, G2Line { r0a0: u288 { limb0: 0x70f807c9bd9cc653569a88c0, limb1: 0xd3bd9e80a4c0879b8c54502f, limb2: 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0xf6d057dbafe03b544a69128f, limb1: 0xe03743865a854f3f554c95b7, limb2: 0x29c21dd74cd29781, }, }, G2Line { r0a0: u288 { limb0: 0xb964e3c6d975ca8cf820a505, limb1: 0x58cf1dfe1e77f86538998d74, limb2: 0x253f8f7c9eb4af1, }, r0a1: u288 { limb0: 0x751409cbae1c0030ee5977d1, limb1: 0xe203b703551126fdae59e500, limb2: 0x2e4d7a2dbc83f9b5, }, r1a0: u288 { limb0: 0x3bb2d7500573a130dfcc7b70, limb1: 0x2e94772d1e8a4db8783ea2f7, limb2: 0xb43fdec6bd93bce, }, r1a1: u288 { limb0: 0xdcad2320f5fe6edb3ee742ff, limb1: 0xdb00d689081d6770c6978582, limb2: 0x6029475ae5587e5, }, }, G2Line { r0a0: u288 { limb0: 0x44ec71963665d6ec8ad74841, limb1: 0x8403830d652edbde8339e929, limb2: 0x100fb102d85f5085, }, r0a1: u288 { limb0: 0xc055c9daf26d35310e7b1e74, limb1: 0x40cdbeaffc8383e3cdc8926, limb2: 0x6fd31831cc5c2e2, }, r1a0: u288 { limb0: 0xad2ce478f7297f6138ae1c8c, limb1: 0x4d31d6f7382542621c5b6e17, limb2: 0x7dbf7c3c0f14e33, }, r1a1: u288 { limb0: 0xe4640196247c27251483088e, limb1: 0x34dea70f9956ebc54e0606ba, limb2: 0x8b41cd44b48eaaa, }, }, G2Line { r0a0: u288 { limb0: 0x44ec71963665d6ec8ad74841, limb1: 0x8403830d652edbde8339e929, limb2: 0x100fb102d85f5085, }, r0a1: u288 { limb0: 0xc055c9daf26d35310e7b1e74, limb1: 0x40cdbeaffc8383e3cdc8926, limb2: 0x6fd31831cc5c2e2, }, r1a0: u288 { limb0: 0xad2ce478f7297f6138ae1c8c, limb1: 0x4d31d6f7382542621c5b6e17, limb2: 0x7dbf7c3c0f14e33, }, r1a1: u288 { limb0: 0xe4640196247c27251483088e, limb1: 0x34dea70f9956ebc54e0606ba, limb2: 0x8b41cd44b48eaaa, }, }, G2Line { r0a0: u288 { limb0: 0xa4dc3d37041029c7b2f1bb9, limb1: 0xf72869e330906647a7d54af8, limb2: 0x705bd30bad6ce42, }, r0a1: u288 { limb0: 0xb00eef39b09348fd65e27aec, limb1: 0xd5e053aa5ae39359fac6cdbc, limb2: 0x90e03f1f820fe9a, }, r1a0: u288 { limb0: 0x7f56704e86148b1a5595647e, limb1: 0xb8e4acc00d27e4eaf2d3de14, limb2: 0x160398dceafe1fbe, }, r1a1: u288 { limb0: 0x7c39f499101722b5d82ceec4, limb1: 0xaf99a11bb8ab6c8134832009, limb2: 0x2d7388a9d5187a36, }, }, G2Line { r0a0: u288 { limb0: 0xa4dc3d37041029c7b2f1bb9, limb1: 0xf72869e330906647a7d54af8, limb2: 0x705bd30bad6ce42, }, r0a1: u288 { limb0: 0xb00eef39b09348fd65e27aec, limb1: 0xd5e053aa5ae39359fac6cdbc, limb2: 0x90e03f1f820fe9a, }, r1a0: u288 { limb0: 0x7f56704e86148b1a5595647e, limb1: 0xb8e4acc00d27e4eaf2d3de14, limb2: 0x160398dceafe1fbe, }, r1a1: u288 { limb0: 0x7c39f499101722b5d82ceec4, limb1: 0xaf99a11bb8ab6c8134832009, limb2: 0x2d7388a9d5187a36, }, }, G2Line { r0a0: u288 { limb0: 0x26743d3c5ceab5151856abc8, limb1: 0x2bc840c6b3375132f6df6c4d, limb2: 0xf20cc4455c9206b, }, r0a1: u288 { limb0: 0x75257f283994114ee03b667e, limb1: 0xb71eada78256c22a8b22564d, limb2: 0x2c4f6002e64db7e4, }, r1a0: u288 { limb0: 0xadeaeea86f50da58c232d0b5, limb1: 0xe988059d0234448257239cec, limb2: 0x23c7423d92bbc634, }, r1a1: u288 { limb0: 0x6afee648e46e570b43f3696d, limb1: 0x9a3f1aae0067f1de3d0a489, limb2: 0xa7256957d6a8ed, }, }, G2Line { r0a0: u288 { limb0: 0x26743d3c5ceab5151856abc8, limb1: 0x2bc840c6b3375132f6df6c4d, limb2: 0xf20cc4455c9206b, }, r0a1: u288 { limb0: 0x75257f283994114ee03b667e, limb1: 0xb71eada78256c22a8b22564d, limb2: 0x2c4f6002e64db7e4, }, r1a0: u288 { limb0: 0xadeaeea86f50da58c232d0b5, limb1: 0xe988059d0234448257239cec, limb2: 0x23c7423d92bbc634, }, r1a1: u288 { limb0: 0x6afee648e46e570b43f3696d, limb1: 0x9a3f1aae0067f1de3d0a489, limb2: 0xa7256957d6a8ed, }, }, G2Line { r0a0: u288 { limb0: 0x9894b9b6df6285e00cb3ef9d, limb1: 0xc7799b231f547596527979f9, limb2: 0x1873cf42f2befcbc, }, r0a1: u288 { limb0: 0xea5b37d753c87bdd55f0ed0, limb1: 0x70d0582e29fd33896e945be5, limb2: 0x273059304eef6b83, }, r1a0: u288 { limb0: 0x1a8c1b6d717a3b41ece55725, limb1: 0x7b31c1b97f15745a6d80ea0d, limb2: 0x2cd26d3a7bbe93e6, }, r1a1: u288 { limb0: 0xe2ad8bc0279b5c304c489ca6, limb1: 0x176d1c945108ce77fcd238cd, limb2: 0xde3c7c3f1c3d01b, }, }, G2Line { r0a0: u288 { limb0: 0x3980a9ac8c34a235d2616212, limb1: 0x84c8a8ab074ce118b68f30e9, limb2: 0x13d1902579c8a95e, }, r0a1: u288 { limb0: 0x84b1be8046674b6544cdbd07, limb1: 0x198c1a70db0768c46ee0879f, limb2: 0xb7e46866f7c1d4f, }, r1a0: u288 { limb0: 0x5aa04f6da050797974642dff, limb1: 0x67018b676db95697c6fc0e94, limb2: 0x174b5365db908344, }, r1a1: u288 { limb0: 0x12ae4d7bff5800094457c75f, limb1: 0xaf7fb1cf0adfdefc0943c20d, limb2: 0x2e168cd37dc90c25, }, }, G2Line { r0a0: u288 { limb0: 0x9894b9b6df6285e00cb3ef9d, limb1: 0xc7799b231f547596527979f9, limb2: 0x1873cf42f2befcbc, }, r0a1: u288 { limb0: 0xea5b37d753c87bdd55f0ed0, limb1: 0x70d0582e29fd33896e945be5, limb2: 0x273059304eef6b83, }, r1a0: u288 { limb0: 0x1a8c1b6d717a3b41ece55725, limb1: 0x7b31c1b97f15745a6d80ea0d, limb2: 0x2cd26d3a7bbe93e6, }, r1a1: u288 { limb0: 0xe2ad8bc0279b5c304c489ca6, limb1: 0x176d1c945108ce77fcd238cd, limb2: 0xde3c7c3f1c3d01b, }, }, G2Line { r0a0: u288 { limb0: 0x3980a9ac8c34a235d2616212, limb1: 0x84c8a8ab074ce118b68f30e9, limb2: 0x13d1902579c8a95e, }, r0a1: u288 { limb0: 0x84b1be8046674b6544cdbd07, limb1: 0x198c1a70db0768c46ee0879f, limb2: 0xb7e46866f7c1d4f, }, r1a0: u288 { limb0: 0x5aa04f6da050797974642dff, limb1: 0x67018b676db95697c6fc0e94, limb2: 0x174b5365db908344, }, r1a1: u288 { limb0: 0x12ae4d7bff5800094457c75f, limb1: 0xaf7fb1cf0adfdefc0943c20d, limb2: 0x2e168cd37dc90c25, }, }, ] .span(); let hint = MPCheckHintBN254 { lambda_root: E12D { w0: u288 { limb0: 0x23ca9e30f07b55b24f193b0f, limb1: 0xe87a29af47945c59bebde6e3, limb2: 0x25202875a18b48d6, }, w1: u288 { limb0: 0x73c45803819fb7aff4be48d4, limb1: 0xbc4e8cdff399f10e04552e9e, limb2: 0xe200b0579a47bb3, }, w2: u288 { limb0: 0xb7e202dd946f1c1e893294f5, limb1: 0x9b242eecb685264d1d38f92, limb2: 0x2743277dfb400b12, }, w3: u288 { limb0: 0x713dcf49af707a72abcdd23f, limb1: 0x297d2b276e1e10592a67e028, limb2: 0x7ce37c37c9a9830, }, w4: u288 { limb0: 0x1a1e7136ddb0226444e3dd93, limb1: 0x10ec67e9ba10af63294f9067, limb2: 0x2209ca34e9632ffe, }, w5: u288 { limb0: 0x282b36f9275c1d75a96b4bba, limb1: 0xcd30a7361a37968571854966, limb2: 0x56824745ec0be7e, }, w6: u288 { limb0: 0xfd161b3f69becd983863c1f8, limb1: 0x9e173cc60a49b16b0ae54cb6, limb2: 0x21c2ff8564f4b359, }, w7: u288 { limb0: 0x83b2b95b17f74a4135c8f0ec, limb1: 0x1d49d1548ca28958a1477f77, limb2: 0x21dfaf1ab1424f7a, }, w8: u288 { limb0: 0x9f42e8c899eb37b1c750776a, limb1: 0x1d527af4bf9944d9cacfc9b6, limb2: 0x2cedae6373f81ff3, }, w9: u288 { limb0: 0x5826957af02c5ff75ecf2f7f, limb1: 0x63de3d3ed13db73b40636e33, limb2: 0x1b4e8f8bab34df27, }, w10: u288 { limb0: 0xe47acbb5fc054b575c4de206, limb1: 0x21c9659455fa7db99219fcb1, limb2: 0x1da51303ee50de45, }, w11: u288 { limb0: 0xfba59dce6d63b61b27c81f88, limb1: 0xdcca144de9ddd923bbb33c4b, limb2: 0x291ee2a6f851083a, }, }, lambda_root_inverse: E12D { w0: u288 { limb0: 0xb5c3eabbd3b1eef8ea5617f4, limb1: 0x11833d922f25b3a34d3fca8f, limb2: 0x13750c425c423ee, }, w1: u288 { limb0: 0x8983bd9d7448c89812be4350, limb1: 0xcc0a0b4ca76d768c80ff8e55, limb2: 0xfb6e764fd741485, }, w2: u288 { limb0: 0x3edb9b44088f29518c1cf962, limb1: 0x3800221baf8e4d5d69808d93, limb2: 0x14d575b46d080633, }, w3: u288 { limb0: 0x132e0ad247c2f54fbe52f5bb, limb1: 0x4b0a3207c00cd30d7bdcf774, limb2: 0x1a93653a38cb2fe4, }, w4: u288 { limb0: 0xad30ef932f284898d3a7a46b, limb1: 0x4163e6658533a807cd45d00d, limb2: 0xddb14c4f82f8631, }, w5: u288 { limb0: 0x6b8e30e4eaa63a9ed81168d8, limb1: 0x313309f6dbce4e865d4fedb1, limb2: 0x2d3f5b1fefcb56f, }, w6: u288 { limb0: 0x4ef02281cc723a6da515811a, limb1: 0x14ff8ed665651ab8ce848f43, limb2: 0x131a42012d97077d, }, w7: u288 { limb0: 0x9378001a32c652b319e017f4, limb1: 0x7adaa3bb782735807171c8ee, limb2: 0x26a3c45ea339b47e, }, w8: u288 { limb0: 0xb45f0d072cee9451b2ef6bcd, limb1: 0xb5c79d9af82faa633c46c783, limb2: 0x288162b64a95050e, }, w9: u288 { limb0: 0xb400e23dbb10336db8e3e567, limb1: 0xf8be889f6826d20f76b01fa, limb2: 0x2a6ee642f39f6ea8, }, w10: u288 { limb0: 0xaa002ca04722ef6e113c90c7, limb1: 0x4a44cfbf7d0d8a113c67d3b8, limb2: 0x1b19f196206d8a99, }, w11: u288 { limb0: 0x3b36e8198a598435a63c262d, limb1: 0x5bd67fccbd394684e1e4c572, limb2: 0x166091a34daab9c1, }, }, w: MillerLoopResultScalingFactor { w0: u288 { limb0: 0x1, limb1: 0x0, limb2: 0x0 }, w2: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w4: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w6: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w8: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, w10: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }, }, Ris: array![ E12D { w0: u288 { limb0: 0xe2f6acee09a64156c15e3478, limb1: 0xed70b0971287f50104248a93, limb2: 0x127703e3d61d8953, }, w1: u288 { limb0: 0x3f33ed733eb4838ff43a064d, limb1: 0x261b3bb5a0d1e3b1fc2eea8d, limb2: 0x1b45799651c4e710, }, w2: u288 { limb0: 0xfef7aacba92a3760281d63cc, limb1: 0xd3c17160fa29274e8fb29068, limb2: 0xd4e6a9fe3bada06, }, w3: u288 { limb0: 0xf8318240f89419438fe2d639, limb1: 0xe998e7c29f76b508e0538e38, limb2: 0xfb03e005dbba59f, }, w4: u288 { limb0: 0x70c9890149ae3e2742c5c731, limb1: 0xe9a6d4fc61f71f5d5ed989d4, limb2: 0x2dad8e036bd59924, }, w5: u288 { limb0: 0xd7b63c2f5eed5c20e605768d, limb1: 0xb0003493ed0492f6fa50f418, limb2: 0x17228fa4697986c7, }, w6: u288 { limb0: 0xa3dc70c11244fb2deda36cb2, limb1: 0xb8fb759606fba9d97587f0e8, limb2: 0x2e2f815e063bb0, }, w7: u288 { limb0: 0x686d29a44e7110ac6c8b9505, limb1: 0x74ac5a716ee1e9d44b50960f, limb2: 0x2152b931c3859503, }, w8: u288 { limb0: 0x5868412c8c818820977a66f0, limb1: 0x2f9e83b27ce0c185c6f1c18f, limb2: 0x14fac55b88d3ce93, }, w9: u288 { limb0: 0xb78d2652e51b3c673a385a19, limb1: 0x795b0f1a23960c7aca666e05, limb2: 0x12a1f27a3602498a, }, w10: u288 { limb0: 0xaccfdbe167c5f15ccbe8a10b, limb1: 0xe7f7a9853750e8e77d47908, limb2: 0x1b9bfc8952b7f369, }, w11: u288 { limb0: 0x149b5924ec95ec9b05da4bf8, limb1: 0x7567100511e744c551a6e4ea, limb2: 0x2b223a2dfd168795, }, }, E12D { w0: u288 { limb0: 0xa72a4848e30642eded615898, limb1: 0xbef543f14f1aad5e18139eb6, limb2: 0x2c7bcf2fddd1e961, }, w1: u288 { limb0: 0x46fd177379d58e372b9b6f07, limb1: 0x517211fbf41f194c331f00e5, limb2: 0x2f5c91ca28636a00, }, w2: u288 { limb0: 0xe41a3ec01dc8bb8501df492e, limb1: 0xd7f7ab9d0f2782f2373b5314, limb2: 0x91712eca3f77452, }, w3: u288 { limb0: 0x133e5c67a8f2690bc04b91b9, limb1: 0x8582c464e09299148f27b703, limb2: 0x249bfada0b86ef33, }, w4: u288 { limb0: 0xeeb02ca00147f12d2e8458f7, limb1: 0xceaae80445f4c7407c02c1da, limb2: 0x25e046234afd2a85, }, w5: u288 { limb0: 0x64b3d4f3d18031d4235862df, limb1: 0x92f83b81871013f01b47013c, limb2: 0x15fe7761fa1f33ac, }, w6: u288 { limb0: 0x3fb298307f41db600150f88c, limb1: 0x3da094ebafc14d7eb2182997, limb2: 0x818cb4e830ba356, }, w7: u288 { limb0: 0x12ef8a22b1bc73ea237df6f6, limb1: 0x9d344aace728adbd489c9720, limb2: 0x821d3466302b0d2, }, w8: u288 { limb0: 0x638f4928fe9fe06b17f5d2db, limb1: 0x596ab928517338096d96b2f6, limb2: 0x29e68f04a0ee89be, }, w9: u288 { limb0: 0x67f1e11e7d4fea0d7745eb44, limb1: 0x105e36bfdc4442638522b7d5, limb2: 0x2593d5a9dac5df2c, }, w10: u288 { limb0: 0x453ddfce74fe7c8b9bc7ea76, limb1: 0x73264637eb39edbe0400abf1, limb2: 0x2f665b3f82c255a5, }, w11: u288 { limb0: 0xa64871f14a5c040bc6216bc1, limb1: 0xc3071982e7657ce273aafe11, limb2: 0x25c2ccc6a7f12699, }, }, E12D { w0: u288 { limb0: 0x8d5b811a09caa58be413ffdb, limb1: 0xaec13af0ff4aa5a9b3dcb582, limb2: 0xb759534e5c8811b, }, w1: u288 { limb0: 0x8bfd162f232d87d70447c4fb, limb1: 0x5b714a61f27eeeb66210a238, limb2: 0x235eb11b01463a62, }, w2: u288 { limb0: 0xa97e216801ac38c907ba52a0, limb1: 0x70ae4f1968af5555df98298f, limb2: 0x95e6702a59e1a6a, }, w3: u288 { limb0: 0x9cd4ed96bdec2348819310c, limb1: 0x4766b2e8e7e732e7970b9689, limb2: 0x149bdcbd6a7afcb9, }, w4: u288 { limb0: 0xbe702be60291c9e6e885e5c3, limb1: 0xe93a545111f29c9592a036c4, limb2: 0x1591e5e82ed4b4dc, }, w5: u288 { limb0: 0x8d199a3abe5faaff7a3bc9f8, limb1: 0x7cc933e5a020b4766ac8a761, limb2: 0x2fe6b400ae57faae, }, w6: u288 { limb0: 0xaec592ab3c28bfe83c215cfa, limb1: 0xac24f84ed0a437939c2000e9, limb2: 0x1f2843afe30b053a, }, w7: u288 { limb0: 0x6d2d0627cede31c8eb85e75e, limb1: 0x7bdddc87f039012eb3b77194, limb2: 0x178660f13401179e, }, w8: u288 { limb0: 0x62368134bd89bd0f837ed4d4, limb1: 0x6dc31aed6fb226f4b4c0f22c, limb2: 0x24e758c4f9d85d63, }, w9: u288 { limb0: 0x2f1d16930c76c2c58ded454a, limb1: 0xd31b8e954fb055fe7ca38da, limb2: 0xdc52b7ecb883c77, }, w10: u288 { limb0: 0x709c6bce583682d54711f158, limb1: 0xb32e399977ba98f1dbf49828, limb2: 0x1ff3ce291ef8cdaa, }, w11: u288 { limb0: 0xfedfcfb5ac3535fd88a15183, limb1: 0xe97e7b5d3bf6635f37dd122d, limb2: 0x22a38c2aae1e8fc9, }, }, E12D { w0: u288 { limb0: 0x4e15598d95c5f7c52c6b9226, limb1: 0x7260273fb797ec0382fc0b74, limb2: 0x1b4722521d49dd9c, }, w1: u288 { limb0: 0x41a84bd4c94bd9e253b5dbe8, limb1: 0x4f06564a6624a9a4b1f4922f, limb2: 0x154f62ec865e8ec2, }, w2: u288 { limb0: 0x25ed47681b082c51b72e1c67, limb1: 0xfdab86c84aa645fdcc31d18d, limb2: 0x824a28773085f87, }, w3: u288 { limb0: 0x725527ec8d20e00f959c8e4b, limb1: 0x5f0a9b28686d3343669aa6dd, limb2: 0x24b7b0049449f95c, }, w4: u288 { limb0: 0xbbe336284924385760066449, limb1: 0xf34b401046c192b98e0b8e64, limb2: 0x22a2832e9e2adf52, }, w5: u288 { limb0: 0x49e39158392c0ff5930f63bd, limb1: 0xdc907401ccc882dbb3d29c09, limb2: 0x135a779eb01ae2a9, }, w6: u288 { limb0: 0x27f79ea3a7d57234b676f496, limb1: 0x75257d3143963669b9c2f6a, limb2: 0x2b202d6fa27717e1, }, w7: u288 { limb0: 0xff147074bd0eb0177d13885d, limb1: 0x75c3a42b9b267b3842b6b4c7, limb2: 0x54de18ae56affbc, }, w8: u288 { limb0: 0xea9ab70d9faddee08a3d721, limb1: 0x2799218b0495f05389162288, limb2: 0x1b188d8d706d0da5, }, w9: u288 { limb0: 0xc78b4fdfd2c7f08de090785a, limb1: 0xb0ed8ae4c9d8f8cf66b189a3, limb2: 0x3ef3e9bb717b0be, }, w10: u288 { limb0: 0xa95f9089c84967d73eeb7c72, limb1: 0xfcc8b694c6dab512b6097cc7, limb2: 0x185f26ab25337e83, }, w11: u288 { limb0: 0x10a59371fd44cdb8de434ac6, limb1: 0x3c17b135fbcb13d74e419dfb, limb2: 0x278311e97f6ef4, }, }, E12D { w0: u288 { limb0: 0xe7df08107e805939ebd064d1, limb1: 0x84eaf0a72178fea0cd7fdda3, limb2: 0x1a3c2d31a8a1ee84, }, w1: u288 { limb0: 0xac6519066bbcb1864ae2773, limb1: 0xc26038949c313989e0054bbe, limb2: 0x28eb7e83ec81a257, }, w2: u288 { limb0: 0x11e340e6c9fe6671a0adb177, limb1: 0x92b97e720c203dfe72f47426, limb2: 0xb846a3ae27eaf33, }, w3: u288 { limb0: 0xe04834e31217e48f0e8eb14e, limb1: 0x8935efe701ea6319c4ec860f, limb2: 0x13f14982cf2bc20c, }, w4: u288 { limb0: 0x82dc6d9f7406f0a279ef8a56, limb1: 0x51d959b05efad385a218b2bb, limb2: 0x103a320e5b6a9452, }, w5: u288 { limb0: 0x2ed59048aebb44b229f7267a, limb1: 0xc8a4f65f52a1922dec503120, limb2: 0x2d8aad0d7b0b6937, }, w6: u288 { limb0: 0xdf4cb0cb215170ff0a6b3c1e, limb1: 0x18ee79ed0b8c2cd754f322a6, limb2: 0xbd8cb5657cc0178, }, w7: u288 { limb0: 0x440e6b453eda236f95430186, limb1: 0x39d4deb16fd3ecee0a714cf7, limb2: 0x26574156175bc55, }, w8: u288 { limb0: 0x1f4caed0971cc3ed8347723d, limb1: 0x28a247d79794bcee6045e924, limb2: 0x2657b147233a6fc4, }, w9: u288 { limb0: 0xf26b32e9d9a108813f659c6b, limb1: 0x876ed468fa80b8be08c0b09b, limb2: 0x10ca44b2c6d4f9da, }, w10: u288 { limb0: 0xa8ab369559d68eb036cd3db, limb1: 0x723fdc5ac4ca2c61a5a1ffe9, limb2: 0x12199d02a50f2c5, }, w11: u288 { limb0: 0x1a376782048bbe32096ddea0, limb1: 0xa715d036367bef48038ea78d, limb2: 0x14e09936f8a93c9e, }, }, E12D { w0: u288 { limb0: 0x5c840d64ee3e008381f3e04, limb1: 0x243b2760acc2f44649a5b24f, limb2: 0x2e6cfbab4b3fed61, }, w1: u288 { limb0: 0x9743d90c3eef67f5cdf72c19, limb1: 0xf3b5548f9d13f9dc940fa4b2, limb2: 0x13b8b4c7ca5ec4a2, }, w2: u288 { limb0: 0xf97c58447c8b03814fa6103f, limb1: 0x30d22f3e8c4c7d8523c76597, limb2: 0x872b0b5d8b48bd1, }, w3: u288 { limb0: 0x78947a908649525b01ca6334, limb1: 0xcfe0ba68f50e623a89171963, limb2: 0x29503e874bbfec29, }, w4: u288 { limb0: 0x1dae9e71040fd1230c92cbb1, limb1: 0x65a3011a3d4b8129b45eaad6, limb2: 0x81795daa56a29d3, }, w5: u288 { limb0: 0xd7376a308b09572a31465eb8, limb1: 0x9a987b8f5f86b01cd050946c, limb2: 0x1b4cef85ace274fe, }, w6: u288 { limb0: 0x121c88496e9a87e389aabc55, limb1: 0x53070d5039789dbe1ff3c5d9, limb2: 0x6f0665bfd35e8c7, }, w7: u288 { limb0: 0xdd9ddf4069428e4d4bdf5f7d, limb1: 0x6dace55e5658b1bf8c3a2093, limb2: 0x29485c58194eed74, }, w8: u288 { limb0: 0x5ee1da4b7149da261bda9305, limb1: 0x7601e480e9a8d7be7979c77e, limb2: 0x14cffa23faf832a0, }, w9: u288 { limb0: 0xb4e59ad341d4b129ba6ce9a2, limb1: 0xaa1fd997e27e7f4f5fab6918, limb2: 0x157b9b49aca1ab9, }, w10: u288 { limb0: 0xfff92978e32c48590140bfab, limb1: 0xe1cc130cb1566161f46fa326, limb2: 0x11f2a66bd21895fe, }, w11: u288 { limb0: 0x4a8d0b05c8ab2197c89b44f2, limb1: 0x48260cd32fd7d0452d9aa26, limb2: 0x1ff38242cb34892c, }, }, E12D { w0: u288 { limb0: 0x20f9010789e7b152257be743, limb1: 0x41355459a9e13ce010e9491c, limb2: 0x175f282d0d7ac03e, }, w1: u288 { limb0: 0xd61a99e14e1f68ea78858dfe, limb1: 0xdb29e70187d87a8d1f4d27a1, limb2: 0x17afeea1b34fc021, }, w2: u288 { limb0: 0x3c9e6fb3d89216edef33a1d7, limb1: 0x3dd931680d2bb7651f688b2a, limb2: 0x13e86a7233e4491b, }, w3: u288 { limb0: 0x377d4b442701faa12601d1f0, limb1: 0xfa864548c3a1a262fd21db8c, limb2: 0x8c5a91f3fe9bf24, }, w4: u288 { limb0: 0xdc1920a9ba58d700bf2b145c, limb1: 0xd46f80f0104c31aa036d6a0b, limb2: 0x1073f44a4d433e6b, }, w5: u288 { limb0: 0xbe5e796a5bd4049ddad323b0, limb1: 0xe7bc4d5004bad605fd02a27, limb2: 0x3028bf8868ed598a, }, w6: u288 { limb0: 0x40b609fabc6888cab7f4019d, limb1: 0x7bcf89f3bd29e5c43d4f02ce, limb2: 0x16a2865923d5b251, }, w7: u288 { limb0: 0x70655717bb0c1ed90589d31c, limb1: 0xd8f6e54cc87b156c80122aad, limb2: 0x1854b621bdf3aa08, }, w8: u288 { limb0: 0x25e6085c5d718fa434af198d, limb1: 0x243092e705cd68fcd328a2a3, limb2: 0xabda9d2c0c69f93, }, w9: u288 { limb0: 0x12d9ff05f7fd76b25f56ee31, limb1: 0xff2e5068668cbd41d6a8d70e, limb2: 0x30318bdd373e291, }, w10: u288 { limb0: 0x5b6d9d5299e67c2427987d3, limb1: 0x60309cea9bcde182039deaf7, limb2: 0x1eeb35c995c1375b, }, w11: u288 { limb0: 0xf6c6a575126d36fb8016d94a, limb1: 0x9a38ec893c85a4a110a3845e, limb2: 0x2992a2b7e6cd37c2, }, }, E12D { w0: u288 { limb0: 0x2513fcc1815172e2acb78c48, limb1: 0xf1fb049b85c85a858e3796f5, limb2: 0x300c791e8d042987, }, w1: u288 { limb0: 0xb5f548909a82f0ce9b151b26, limb1: 0x8087f9db3ad26d11c3dcd0d3, limb2: 0xbe98e54b599db1f, }, w2: u288 { limb0: 0x1e55ee1359e4dacd0a224ac, limb1: 0xc049969cc268c7302cbbb96, limb2: 0x292939420dc4994c, }, w3: u288 { limb0: 0x9a439ef1b4b8a3e5e0d131ee, limb1: 0x5243b76e0bffe1ad4934762b, limb2: 0x10b7c0e8f5e55d8e, }, w4: u288 { limb0: 0x472318a31d61843dc0ac35a3, limb1: 0xfdc8264ebbe6c3255fd45fbd, limb2: 0x23cab8acf199a2a6, }, w5: u288 { limb0: 0x3c5f90aa19be5ca9d586b983, limb1: 0xcba0d66ca2dc42a68f4136fa, limb2: 0x23d949165118abea, }, w6: u288 { limb0: 0x7aff327e17d6666c7f90c4a7, limb1: 0x2f133759ea769762428ca397, limb2: 0x229a3fc5c84e256a, }, w7: u288 { limb0: 0xe2793380656d37b00873ec9a, limb1: 0x1338f4f95cf705ab40325500, limb2: 0xf5ae003d907d6e1, }, w8: u288 { limb0: 0x85c6f4773db45818f2a0edfa, limb1: 0x11b541412c501fd59d939141, limb2: 0x25f1c74f47ddcbbc, }, w9: u288 { limb0: 0x79f213447462cc95732ff6eb, limb1: 0xa2d558f0e0eca18cfa84426, limb2: 0x1ab5af6e2200b5a6, }, w10: u288 { limb0: 0x7bae196bef0db195215adf17, limb1: 0xd0a4b5dc5a11d37222964f4d, limb2: 0x4f26d49b9bc199a, }, w11: u288 { limb0: 0xb16717e715fbc76c3bac66f1, limb1: 0x3ebe263de3e1a89803bc0da8, limb2: 0xfb0595b5b9d8246, }, }, E12D { w0: u288 { limb0: 0x4691a6b6d8442401fdb5fd61, limb1: 0x1a4aa6fd9f3cfbd122b2cd2b, limb2: 0x254267bcadf6ce8b, }, w1: u288 { limb0: 0xe22fbb9f0206f7b3b78be6ee, limb1: 0xf6e0deb6e65d40117da6b2fd, limb2: 0x2a4f1a801c3cd205, }, w2: u288 { limb0: 0x163800b0a0c25286cf11a38b, limb1: 0xac61df59604318c6fcd74d67, limb2: 0x1a9633d30804c9cf, }, w3: u288 { limb0: 0x7333b8203f73c7c30b504051, limb1: 0xa080c3854f1a6a8a917b0366, limb2: 0x276eac4715fb20ca, }, w4: u288 { limb0: 0x399e6af618d4d4f3d6b6df5, limb1: 0xc75b47790bdefc3a4c3f9514, limb2: 0x29d9317f2b639acd, }, w5: u288 { limb0: 0x3c127769d3815a3c70c1ee1e, limb1: 0xfd2b1eee94f11e14c21a9358, limb2: 0x350f2baa271499a, }, w6: u288 { limb0: 0x16ad4469d442f5ad7e3a969b, limb1: 0xa319c77cf65f5ddf06c79804, limb2: 0xfc01932cb22cac6, }, w7: u288 { limb0: 0xd3ec2fe1d535457c02b0abdb, limb1: 0x9336d37bd33818f9e69963f8, limb2: 0x221133208264ed33, }, w8: u288 { limb0: 0xba4ad8aa28c47ead56764d20, limb1: 0x60ea71535c537102ff8591aa, limb2: 0x99bbc9915f4f422, }, w9: u288 { limb0: 0xd10f7b7b93fff77a5af1c82a, limb1: 0x54501ad6471fd3ea73f001d2, limb2: 0x218c4075b09ef652, }, w10: u288 { limb0: 0x6656f1088f37e6bae8831fe4, limb1: 0xd3542728908036bec18ddee4, limb2: 0x16fe23702ee4af80, }, w11: u288 { limb0: 0x8bf6a24658757bdf96918d6d, limb1: 0x1e72bce9091c22a645562e32, limb2: 0x1856aa098aa33d63, }, }, E12D { w0: u288 { limb0: 0x5eaa057c5e9d338929a7ad43, limb1: 0x7ae96e982db7587ba91a1736, limb2: 0x72cb1aafef8fc8e, }, w1: u288 { limb0: 0x1bb7723ff47ccb109a4226ec, limb1: 0x328efe288a27af15b2af6381, limb2: 0x2dccf1917c988cef, }, w2: u288 { limb0: 0xcc638278fb869f3c6930e578, limb1: 0x685535107befb2dbff15dcb0, limb2: 0x1552b4647293ddad, }, w3: u288 { limb0: 0x6a2bab4ed331aeb86499d23f, limb1: 0x3e6ac194919d26afeae1c7e6, limb2: 0xa3bd7d404906b4a, }, w4: u288 { limb0: 0xd0f18a8f6bcb2c54d031eae7, limb1: 0x428e6f2b4d1b1d15ecbfeaf5, limb2: 0x2f7d795e0c7bb871, }, w5: u288 { limb0: 0x9fa385290e5a47297dba3917, limb1: 0xb79650782cdb39ff5a1f208, limb2: 0x15d475f38ea7476b, }, w6: u288 { limb0: 0x7bb49cca7dfd0cb7e3f79b2c, limb1: 0x8c7bac4c06a9d05c2accbd03, limb2: 0x1fa0d8145555736d, }, w7: u288 { limb0: 0xf736aafbbf8cd7e7c4065e91, limb1: 0x43830e9122457788cb86d1ab, limb2: 0x135aa9aaad9954db, }, w8: u288 { limb0: 0xbed546ba0b8744fcb9d52660, limb1: 0xfbc7f3baa7c7119fcce3e80, limb2: 0x15a9f9b27f95df27, }, w9: u288 { limb0: 0xb4f28322f24bab28cefc2b81, limb1: 0xbb67c1a9879e054fb1dd9bd3, limb2: 0x6dc479b44e4a35, }, w10: u288 { limb0: 0xc55900f2e2fcb03d4745b72e, limb1: 0x789b848782d349549f5f1e85, limb2: 0x13a9a01aff27a9ae, }, w11: u288 { limb0: 0xec2faefd68343ff84384d5e8, limb1: 0x1a7cf79c9cfdf71ef2008e74, limb2: 0x29c5f1ef7cfa4e48, }, }, E12D { w0: u288 { limb0: 0x7da07b86a17f90a2b01f070, limb1: 0x32e6cbe8bb76431d030b6541, limb2: 0x169136ca3fcbd52e, }, w1: u288 { limb0: 0x14b5cdc5d62216c47192de8b, limb1: 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0xae856be4ca18bfeeb97256e7, limb2: 0x2ff69682f9db28ad, }, w11: u288 { limb0: 0x8cbe2f6182148a74244954ac, limb1: 0xc968190da741992ceeeac286, limb2: 0x296c04958814178f, }, }, E12D { w0: u288 { limb0: 0xaabe5805d69bcf87faaa0624, limb1: 0x478fadd1e2384b0d94ffd427, limb2: 0x1778a52ea6419cbb, }, w1: u288 { limb0: 0x3a2bb7367f836fd33e72bc42, limb1: 0x9ed4175a04e317113a9bf7cc, limb2: 0x1bd3b89c53bba237, }, w2: u288 { limb0: 0x283ba112d1a901a2963ebce9, limb1: 0xb88b6d8c90c32641cd8de77c, limb2: 0x4330ff81bbf1aaa, }, w3: u288 { limb0: 0xef466974e62e9d7175c4cb8c, limb1: 0x96bfc81d65fe336227113e7d, limb2: 0x231f3ab8575b8204, }, w4: u288 { limb0: 0x6032f7ceed8d763a3c16ca06, limb1: 0xbd357cd0947f134569dd65c, limb2: 0x24d6a3c8b70196e5, }, w5: u288 { limb0: 0x4d47e505d9d4281c38d84f9a, limb1: 0x86fdc9b122276e23bdaef6c4, limb2: 0x2d2a5a3cfec76827, }, w6: u288 { limb0: 0x10764f6301da0139409355eb, limb1: 0x169023ab7ba2af2701d8ee7, limb2: 0xa8fd0478a5bd5b3, }, w7: u288 { limb0: 0x36fbb7632c5e32ac4d439c06, limb1: 0x77e68a927e6bf7b50f468589, limb2: 0xd712970fe77ed33, }, w8: u288 { limb0: 0xc6333c4fb88e300a722635d2, limb1: 0x3bd0a9d311c8a7a2a831fc13, limb2: 0x24a2803265596f98, }, w9: u288 { limb0: 0x602f27f3c41e13f70ec306ac, limb1: 0xa2d9c70458bc21b31e4e8bbb, limb2: 0x2318628ab88e0d2e, }, w10: u288 { limb0: 0x31d07509de71e84d70fc3597, limb1: 0x63a67db560e7854c1b9ffbe6, limb2: 0x24630165d03ca7e4, }, w11: u288 { limb0: 0x7f01293d47393ed8f8faacfd, limb1: 0x693d55d27d34d8d82a45ded6, limb2: 0x2e982efc254e90e2, }, }, E12D { w0: u288 { limb0: 0x7a0151622f32149cc39127, limb1: 0xb7d82d0d7cbfc0854dc18a81, limb2: 0x15121c24c444fb2f, }, w1: u288 { limb0: 0xfe3069d46d030b7bfeb319c7, limb1: 0x92e43b1c259b05e959a29443, limb2: 0x2f82238cefd08b68, }, w2: u288 { limb0: 0xffacb1a6cd1e11dec597ebce, limb1: 0xd482f37e951b21ac15bda39, limb2: 0xd4d51a607e5c451, }, w3: u288 { limb0: 0xc8c7f69a0db529acbb725a01, limb1: 0x56ba1fcd17ca509c764236b9, limb2: 0x266c3b87a040d37e, }, w4: u288 { limb0: 0x4571f5a426917bcc6db587c7, limb1: 0x37b7677a534ffa0b66876d0b, limb2: 0x242bb826f4dad2b9, }, w5: u288 { limb0: 0x3b306aacc86c5e63e826c06, limb1: 0x71a1e66a7cf1dd9abd8f6be3, limb2: 0xf55d9b7d527f5bd, }, w6: u288 { limb0: 0xc2334694e7214460556de85d, limb1: 0x44f339ca483ed2f8e20760e0, limb2: 0x1543c07af87205ef, }, w7: u288 { limb0: 0x193cbdd9bd6c91872b1446e8, limb1: 0x390ed7d90a9e41dd08eb0563, limb2: 0x69314f2882ec9bf, }, w8: u288 { limb0: 0x3e0e5deb39dfbceb0c50cccb, limb1: 0x5359859220ecaaed1bb1d8d5, limb2: 0x2c243e59d1644b8c, }, w9: u288 { limb0: 0x63a83a2e6ee175fe65f5b650, limb1: 0x6d0dae1d5b365f909737b583, limb2: 0x2e16f1774475930e, }, w10: u288 { limb0: 0x4bf38c8f50cf94e94ac2eefe, limb1: 0x91db1898abcd99d2828dcd2b, limb2: 0x2a7826645be14d28, }, w11: u288 { limb0: 0x88d5c83684006468edcfb23a, limb1: 0x52c496f1f5f22ebee63f5006, limb2: 0xf75dc2e7a584b21, }, }, E12D { w0: u288 { limb0: 0x1d5b005c0f05c5913d89d3b8, limb1: 0x1e9c6e293e242c3b4c758f7f, limb2: 0x303cc3f8883df373, }, w1: u288 { limb0: 0x97919a6105618116083ae38, limb1: 0x548b96828190b58631bd017f, limb2: 0xd62fd4a5522751e, }, w2: u288 { limb0: 0xb90c093c24bd6b00dcaef48e, limb1: 0x332793bc6fe8daec55a499e3, limb2: 0x1a62c1adf27dcf4, }, w3: u288 { limb0: 0xed9979bdbc911880b0f2993a, limb1: 0xb9b3d9a78d1ba75a2054dcb6, limb2: 0x1139bc2af9fc7062, }, w4: u288 { limb0: 0xd01ad4e199459d8cfb34022d, limb1: 0xaa55da20d2c29e4f72e8428f, limb2: 0x19408bc263e8c5e3, }, w5: u288 { limb0: 0xe6b6ec6c97330d7bd862275e, limb1: 0xfc7647d2e15333b7f1dc16df, limb2: 0xe8505d43bbb0de1, }, w6: u288 { limb0: 0xac1553394c20ce85bac73bc9, limb1: 0xfd38aa3ace7885aeac4f9c51, limb2: 0x14bf831b8d59488a, }, w7: u288 { limb0: 0xe7b696d082fe6624d2f66473, limb1: 0x19efee72fac6dc76acb45556, limb2: 0x2c27a0376c0c6cd0, }, w8: u288 { limb0: 0x587829d461e3ac5dd4c122b0, limb1: 0x1489d76e7d359134feda6f9d, limb2: 0x2bf00f05d6d34be6, }, w9: u288 { limb0: 0x68c5607a34b7e03c4ad3e625, limb1: 0x34a43c63330e1744beef8754, limb2: 0x56191473aed3f7, }, w10: u288 { limb0: 0x9b9361a588fabd5162e75e94, limb1: 0xbca7aeef2e209ac40e230e6f, limb2: 0x241e1b5b17b02573, }, w11: u288 { limb0: 0x6466ba52d605bf43dcc711a6, limb1: 0x4fd443195501e425d1d0dc3, limb2: 0x2b1b1a35b478f840, }, }, E12D { w0: u288 { limb0: 0x37359d1ca3169479a4787c63, limb1: 0xe6959b34e4552a7091baa5c2, limb2: 0x251e2d6fc02a0dd1, }, w1: u288 { limb0: 0xff5382744072d73ab25ff20d, limb1: 0x899afcd9d3ae5e06050f28f, limb2: 0x69671dfe2d55cc2, }, w2: u288 { limb0: 0x4c5bc5ee2d1c3c29908f93b9, limb1: 0x818cc183be27df97d8e39ad3, limb2: 0x136a07953bb41b63, }, w3: u288 { limb0: 0xc8ba1092a51526df08511ece, limb1: 0xca463cae871d2aa4f117545d, limb2: 0x2ec243402bbea649, }, w4: u288 { limb0: 0x73459af87f990777dd76405b, limb1: 0x9167416ccd1679acd9c0dc19, limb2: 0x25d92fc30a1b3c13, }, w5: u288 { limb0: 0xe7d616bf546a691f57deb700, limb1: 0xb6ee6aefa4852dc03975ecac, limb2: 0xb46a9fae190dacc, }, w6: u288 { limb0: 0xc858c3ec3ca78161afa95440, limb1: 0x88e7ab9779f7b3100a561d0c, limb2: 0x4646ce8e109b9ec, }, w7: u288 { limb0: 0x6078ed80374f164838d05309, limb1: 0x49036f0001a89a5411eacecd, limb2: 0x17d15ad5a21e80c, }, w8: u288 { limb0: 0xfbf54aa1649f1360f628f647, limb1: 0x873566f2575908c732fa2601, limb2: 0x8081b2cbe570dc9, }, w9: u288 { limb0: 0xdd3685fd23d83f41b8fef63b, limb1: 0x570af8337c272785be94352a, limb2: 0x24153962f93d7ca0, }, w10: u288 { limb0: 0x6b6fc38cd84153e3d243c8eb, limb1: 0x70e90d7590bb138f44afe58a, limb2: 0x27de5024e0c84f0c, }, w11: u288 { limb0: 0x3fdd6c208244f367bff5c112, limb1: 0x91e2f705ede749a13823072b, limb2: 0xe1375efaa7677ef, }, }, E12D { w0: u288 { limb0: 0xff28b79435eb24678e3c8eb2, limb1: 0xc0ba0a6fad1811714d5c9c79, limb2: 0x303a480b499d41e7, }, w1: u288 { limb0: 0xfa7877caa1e87cb6765e080, limb1: 0xa17c36fc7d0139b6b04e701b, limb2: 0x100468da3cdddbdf, }, w2: u288 { limb0: 0x556a84f960de5f80740c18f1, limb1: 0xbc003e85b28d9419b1321c41, limb2: 0x2486957161a92fa6, }, w3: u288 { limb0: 0xee123f2e218e5fc7636d043b, limb1: 0x2b4620d525e7c98b54118214, limb2: 0x1ced0e32a4c0e974, }, w4: u288 { limb0: 0xf456e317add8dd976e4f5ec3, limb1: 0xe1f85ddcbcd7b5d860ee1fbe, limb2: 0x20bdfcffe9078da6, }, w5: u288 { limb0: 0xa2e12460aebe22abbb6623d, limb1: 0x3243bd5a49f9c15ce84b992e, limb2: 0xa794ff503d2eb58, }, w6: u288 { limb0: 0xb2013aea1419e59761f6c6b, limb1: 0x18c41d13e9b5ae46b4fbe2c5, limb2: 0x243e8aea6f4bc41f, }, w7: u288 { limb0: 0x834bff6b7ec9caf258fa8481, limb1: 0xd5e3f6fb4e5949909942a836, limb2: 0xf5651e38a53058f, }, w8: u288 { limb0: 0x2392f32d40ef4fdcb8f7bde1, limb1: 0xd92211269e6981a3796f748b, limb2: 0x1cdde6b416be4e91, }, w9: u288 { limb0: 0x627d6f1b96532fc7f042aa71, limb1: 0xbc546773f537f33e8088aa6b, limb2: 0x165110d82726d415, }, w10: u288 { limb0: 0xd218510f5366a09241344258, limb1: 0x5687f91e9d385ff162a2ca58, limb2: 0xa3e9521fd2d3236, }, w11: u288 { limb0: 0x96ab37c321ac8988f874caf6, limb1: 0x1d6deccbe79c563f085d2193, limb2: 0x2f84f7ff1d8e8ee6, }, }, E12D { w0: u288 { limb0: 0x5f32f9a8eeade34241b12810, limb1: 0x133593b9a4a6f381aada074b, limb2: 0x19a32273e388ac99, }, w1: u288 { limb0: 0xbb69e4856293ec3d92e7d805, limb1: 0x14b85538654531e02cc5932f, limb2: 0x2491b31e28bd44cb, }, w2: u288 { limb0: 0x7d82d03af6f8c76c427ba75e, limb1: 0x967b04b92b39941ab44d08d0, limb2: 0x2ed3f4a2944bbc22, }, w3: u288 { limb0: 0xa67689abcb222c5eb04f50c2, limb1: 0xe0d373c25972b07e166bbcea, limb2: 0x1a446eebcb6a1bee, }, w4: u288 { limb0: 0x144f30062c10c29bc8be47e4, limb1: 0x64ff3ba7a156ef19d36084b, limb2: 0x1cc5ff275bd1ad9f, }, w5: u288 { limb0: 0x4056c33c3a351381152ed01f, limb1: 0xb7b9abe58c58333fc5e0adf8, limb2: 0xdc9e6ce6f13cf11, }, w6: u288 { limb0: 0x859bc9e4ea2fc918100b2aac, limb1: 0xc35b40b2582eadc5a1bfe918, limb2: 0x26298d0dffc77744, }, w7: u288 { limb0: 0x291737ba242cd9b07c66d388, limb1: 0x333115d29458501e74089135, limb2: 0x19226600b340c7ad, }, w8: u288 { limb0: 0xee5f0962e034c8abc8d0ba4d, limb1: 0xc7427067383034c39b47f730, limb2: 0x2ae92f519b17a927, }, w9: u288 { limb0: 0xadcd32340a46dbcdcf713132, limb1: 0x14238f7af8998c11c93864c3, limb2: 0x2d78f33e6b135046, }, 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limb2: 0x25aa6ae3c7e3ca0b, }, w4: u288 { limb0: 0xbf23d984a1987abc8698d6fe, limb1: 0xdd4d0bf7124d07e5bdb0ccbf, limb2: 0x120468245f03f2c5, }, w5: u288 { limb0: 0xb7ce1be795587bce1bec22d2, limb1: 0xc1741799c9616ccbda199640, limb2: 0x18e8aabf72cf2545, }, w6: u288 { limb0: 0xcf933e271bebd4985302d609, limb1: 0xe2765fd44c8c12899cdeafec, limb2: 0x2469cab8cca6a721, }, w7: u288 { limb0: 0xf4e8330657ffd4d21e3489ad, limb1: 0xeaa193edb41eca1d92439dff, limb2: 0x2bdca29cc4f5e24f, }, w8: u288 { limb0: 0xc1bbfb6aff365e98d6f377ce, limb1: 0xd798f860fbf687b45aedbcb, limb2: 0x1816a7d7508073be, }, w9: u288 { limb0: 0x1751153c6447e4dd744cb3d6, limb1: 0xb5575d0d3a63675f38f68fb7, limb2: 0xcf079455eea2772, }, w10: u288 { limb0: 0x9103d7708c70e7ca7c1afb54, limb1: 0x269475ce46651c528d3ba3b0, limb2: 0x1612bee0a4422ef0, }, w11: u288 { limb0: 0x7e74e496a46aa542d7ba3398, limb1: 0x38381d151f53772b3c7b6ac5, limb2: 0x2627da3091fe9618, }, }, E12D { w0: u288 { limb0: 0x4a472c78419727c213f1ecb7, limb1: 0x52e7713a969eea3195477e0d, limb2: 0x2452ff1793e9989f, }, w1: u288 { limb0: 0x5af2af840a414c07f88aafe7, limb1: 0x84d438781dc331e9f8dbe5c7, limb2: 0xa08c364dac40aa7, }, w2: u288 { limb0: 0x7544947cd54dce3b7db3f88a, limb1: 0xb21db0825eb2c743a0974622, limb2: 0x99e9f9e14609b3a, }, w3: u288 { limb0: 0x3df463ae1c6f6e33af40b4ed, limb1: 0x6e6bf88773cfb5481ed3a5ef, limb2: 0x18093f68aa581ebb, }, w4: u288 { limb0: 0x2e9083725e6fafe12ada88db, limb1: 0x5c7f7db97c54dd97d496e7dd, limb2: 0x169da8674967384c, }, w5: u288 { limb0: 0xc3e8ae8e4f6250be5ce5700e, limb1: 0x551ed24f2d0023c301973675, limb2: 0x4d06cb38306e620, }, w6: u288 { limb0: 0xd07fd97a4c34b22e94e00333, limb1: 0x44142bc7fa2c3c38bd001770, limb2: 0x26cb2e67195220a9, }, w7: u288 { limb0: 0x4d74de63b523c2d231d42069, limb1: 0xb755b6feb43d9e3b85679a26, limb2: 0x8ef130214a48a61, }, w8: u288 { limb0: 0x92d0adc0007a60452b2b1d1, limb1: 0x6ebdf8fb1be942eae576175e, limb2: 0x1487691fffafabad, }, w9: u288 { limb0: 0x3da0ccf413998d4af4fff3c2, limb1: 0xaae02debc708b689df0b0507, limb2: 0x24db0f80bd712d56, }, w10: u288 { limb0: 0xe0cf1a580089999c4ee222c0, limb1: 0xbf0ae87f88101f422985bd99, limb2: 0x12f407eec0475734, }, w11: u288 { limb0: 0xc8783d4bc08a2731ab3bfa93, limb1: 0x7d26093e383c18102ae4cb0b, limb2: 0x1f96be2222d525ac, }, }, E12D { w0: u288 { limb0: 0xda5fa34846746a819c442983, limb1: 0xb0cda896f70d81847cc85ed8, limb2: 0x16f7dc8dd816b6ef, }, w1: u288 { limb0: 0xd598894ff54bdafbad9f94c6, limb1: 0x67341e698880b16e06df5b4, limb2: 0xe0a2eba838a6862, }, w2: u288 { limb0: 0x2d4fdc3d1173c7dfb46e7170, limb1: 0x4a30acf8b62d37adef886fec, limb2: 0x2f262ecea836ecc8, }, w3: u288 { limb0: 0x4d2de3a485f44ce40095aca, limb1: 0x4f6ebf38f1b4a74b022a98ba, limb2: 0x2b98abba58a8b9c0, }, w4: u288 { limb0: 0x99eec2af9a4b45e84482053a, limb1: 0xdef95a01ab7f2212fd6f0ddf, limb2: 0x20ca7118bbba9b13, }, w5: u288 { limb0: 0xf62ca396c4cd4f9a37c0ec41, limb1: 0xf80e07d6f2016fced6c1a99d, limb2: 0x27e0a522003ad386, }, w6: u288 { limb0: 0x31af536e3dcc88a84fc144d, limb1: 0x48f7d70e0e9d5af9cbaf031, limb2: 0x2f1467cd5d03c065, }, w7: u288 { limb0: 0x4b8a521ef408c203f233db65, limb1: 0x50bfacca6815a45eb7cabce8, limb2: 0x1340f48baad171ef, }, w8: u288 { limb0: 0xb74e02f678431063c3f330c9, limb1: 0x48c8b7fb6de93b918a05dfa3, limb2: 0x19d05aab262398f6, }, w9: u288 { limb0: 0x4e020ba19bfe30be269bc882, limb1: 0x309357da0126dcc065d540a3, limb2: 0x1b5842e9443aad53, }, w10: u288 { limb0: 0xaf0d9cd44dcdb29271788d84, limb1: 0x655b4319e3a14fb30daf866a, limb2: 0x25d96272a676a0a5, }, w11: u288 { limb0: 0xcf12e3f075ae79dd26bf1616, limb1: 0xb383301919d9fa2d99fd0ab3, limb2: 0x229dfa1b1e366c8c, }, }, E12D { w0: u288 { limb0: 0x62979183e1e24b624116a174, limb1: 0xbdba041021322754848f1d61, limb2: 0xa476d754210008a, }, w1: u288 { limb0: 0x4287ad8fa4e3fda207b68f52, limb1: 0xcd665ac9b975b2aff1f8dd08, limb2: 0xfe07d087ed107ab, }, w2: u288 { limb0: 0x308669cfeafff59899fa785e, limb1: 0x829fc34300d1e178417143de, limb2: 0xd874d7418c3b242, }, w3: u288 { limb0: 0x675789df45cb28ed6b2f322, limb1: 0x6829dd797f7f7a6f1fc6bf04, limb2: 0x268ec7b4c8e79e67, }, w4: u288 { limb0: 0x5b0a25b74c83183bc84f5d0e, limb1: 0x6c375c7e4a8f194cfcc07c38, limb2: 0x21dd433dcc0e0ce5, }, w5: u288 { limb0: 0xa042285feb04a253194546ae, limb1: 0x36b0350cc940c7e0f0a1ec94, limb2: 0x2b85fd9d9e053b76, }, w6: u288 { limb0: 0x2b65196fb3229731e0e0639c, limb1: 0x5365707554bc24f77ea1439e, limb2: 0x73310d2feb86b4, }, w7: u288 { limb0: 0xda9afd8f517d9c0088de82a6, limb1: 0x3a334adbafdc8c0fe20dd788, limb2: 0x12bc5ca2182ea4c0, }, w8: u288 { limb0: 0x30f3db4d6495b2ae35511824, limb1: 0x96e95c10e585fe2e57ce7be8, limb2: 0x1fca4754d1120ebf, }, w9: u288 { limb0: 0x411d4e59d273304e5653544, limb1: 0x2b76a536fa12d1623f35eaa5, limb2: 0x1f9ebab7aa9085b1, }, w10: u288 { limb0: 0x21016f80ced8c3d9272193ab, limb1: 0xdd9f7de1487853a3ac2db25b, limb2: 0xfb3e5578686ac87, }, w11: u288 { limb0: 0x7c123e62ef78fe69adf00547, limb1: 0x468ac789efbe486f5b24bdae, limb2: 0x2d5f9d45750a66f9, }, }, E12D { w0: u288 { limb0: 0xf49ddda8e747747083079d37, limb1: 0x68a320e1b5f8a55def8eb451, limb2: 0x1d8d87d7afc034c6, }, w1: u288 { limb0: 0xd0e8f83930e790d0cf7aa4f3, limb1: 0xdc51e7ce79d82f0986e755e3, limb2: 0xb35f2092f80a77a, }, w2: u288 { limb0: 0xd9e56962870a50e84be40dd8, limb1: 0x9f1423b923aef765c9073547, limb2: 0x2407cef32c374634, }, w3: u288 { limb0: 0x8a6e91e2640524e91ca9e5c0, limb1: 0x60cfea5268e4f21f3c9385ba, limb2: 0x2d57872e784ffe8f, }, w4: u288 { limb0: 0x610c92d3030b34c8fe759af4, limb1: 0xccef054c52c61f91aec59117, limb2: 0x2a7fdfb70893c87f, }, w5: u288 { limb0: 0xdc3871296f6b5fb090ff3d84, limb1: 0x7a2b2003194e22958c65aad, limb2: 0x11330e4b772d813, }, w6: u288 { limb0: 0xc2c316717393e539996e2dfa, limb1: 0x6dbced58e49bc602d3ecb633, limb2: 0x2b493ea7f055a49f, }, w7: u288 { limb0: 0x4e7a8676b9ce8022f6546955, limb1: 0x8d4e830787b1fde166a8a9df, limb2: 0x1e95fcd6da158d5f, }, w8: u288 { limb0: 0x61aeabf44d5b761527cd6678, limb1: 0xdd5f062d6ff2ff617a9bade5, limb2: 0x2e9d36256b9199be, }, w9: u288 { limb0: 0x27a4291e6987daf0dbe6e8ae, limb1: 0x84b47163847a8f4d8682775a, limb2: 0x27cdc91e5d2053dc, }, w10: u288 { limb0: 0xef2510a74d7892233c254ea, limb1: 0x7cc4faf9b18401574a7fd4c7, limb2: 0x9da984836efee50, }, w11: u288 { limb0: 0x21081127deea91bde61024b2, limb1: 0xf193ac5ac85dd5ec608e1907, limb2: 0x2a555324963199e5, }, }, E12D { w0: u288 { limb0: 0x231431a681ca1912d93c493c, limb1: 0x7cd5100d863f21b7b69548cf, limb2: 0x6be1a88eb32559b, }, w1: u288 { limb0: 0x26fe843824491895c70e6492, limb1: 0xad3f2925ef00c47f85f0c5cb, limb2: 0x1c25f399327375f2, }, w2: u288 { limb0: 0x1d64a276a7ca6a07f378c73c, limb1: 0x2d2741e0d465bc545054a3d8, limb2: 0x1bf7749bd948c147, }, w3: u288 { limb0: 0xd28017558ebe08c23c711eb, limb1: 0x49b4bfd3c9086160e68f932a, limb2: 0x7c63194c9b2d822, }, w4: u288 { limb0: 0xc66f31af760d6d857ef14191, limb1: 0x3d37853c09dfc5735f6ab95a, limb2: 0x4c9d5f418fc2eca, }, w5: u288 { limb0: 0x9d28f5110dcb53d41cb6a236, limb1: 0x4b42d62aba0e8095600662f9, limb2: 0x222dbbf0d045f1e4, }, w6: u288 { limb0: 0x855491cbc4c074f566c1ff07, limb1: 0x3d2ad6ec1c1b07319336b1c0, limb2: 0x2216d43a7fc3d867, }, w7: u288 { limb0: 0xa2d181effcab2485fd0929b1, limb1: 0xbd1dbcdda521d518016ab038, limb2: 0x17da64f8a088f289, }, w8: u288 { limb0: 0x7e4609531a9a80575e4fc446, limb1: 0x7fc0249541f923b62c80b7ab, limb2: 0x1b1f3ca3a35aed95, }, w9: u288 { limb0: 0x6bde512b2db44cc14aaab80b, limb1: 0x3332a36522218d5054b2df73, limb2: 0x16cc444aacfea675, }, w10: u288 { limb0: 0x9d073f56f1ef70e1409f958f, limb1: 0x11ef505741b46c711501e196, limb2: 0x37e686418823710, }, w11: u288 { limb0: 0x7d2b23008dd91058e4fe64f9, limb1: 0x914180e46029b050930de287, limb2: 0xcae32e2fb03a1cf, }, }, E12D { w0: u288 { limb0: 0xec5d0a0dbf26b9244185606, limb1: 0x2577b931ba5d8d5cde41b68d, limb2: 0x5e96e308db4b280, }, w1: u288 { limb0: 0xbaa744f3269430ce568e50bd, limb1: 0x60f2b1523bf010f9abc7a2c8, limb2: 0x8e4f258d7ed76a4, }, w2: u288 { limb0: 0x2342a9e354749981838268ee, limb1: 0xaf2ecea58318aed3b37f5692, limb2: 0x291525813b88babf, }, w3: u288 { limb0: 0xdc734db514a13e85b5204e5d, limb1: 0x122d47c0509cc9315fcc9d29, limb2: 0x23d67f47908d3e5, }, w4: u288 { limb0: 0x56558781f1a6382f991559cb, limb1: 0xd87862bbd0f987a16c7df25d, limb2: 0x7281838826ccd22, }, w5: u288 { limb0: 0x288fc284a7951c14de8da86e, limb1: 0x69d04a96c38b3cc0548f7544, limb2: 0xf60950d3a14b67b, }, w6: u288 { limb0: 0x318952aeb73d7b08c5fe781b, limb1: 0x901f81c957993437980ea613, limb2: 0x119433627695ee93, }, w7: u288 { limb0: 0x595a69d331001fb9c7a9f006, limb1: 0x1e4cc5c97a405d3e3f5b53fe, limb2: 0x1348746ac61470a, }, w8: u288 { limb0: 0x9c061b99db93b1ebce5d9fe6, limb1: 0x1cfe992ec44f28737dff910b, limb2: 0x2ef11c4ef77570ee, }, w9: u288 { limb0: 0xea82ad0d20f75a7fcb7131a, limb1: 0xa08d4a3e487358d11c698ece, limb2: 0x1b26098d599d7ae1, }, w10: u288 { limb0: 0xc022d7a34d19af209e5bd73e, limb1: 0xe7579941b62b48517495a22, limb2: 0x4624fa9f3c5da9a, }, w11: u288 { limb0: 0xda5e34b4246623fb0f08bbeb, limb1: 0x5b88dd2c5f4e947261dbf571, limb2: 0x14fb70e3a5644ab9, }, }, E12D { w0: u288 { limb0: 0x37435bacb68ebcdf3ca0f9e6, limb1: 0x95680e9183aeea980381c2ff, limb2: 0x2e0b176a2f536c6e, }, w1: u288 { limb0: 0x5d257200e0e3f0f8260548a1, limb1: 0x43ac10e47e02c1a9d08110ee, limb2: 0x656613d14e5d850, }, w2: u288 { limb0: 0x29edc8659226397445adcfd7, limb1: 0x1cb605f25f1232c4b97003b8, limb2: 0x13a6a30088bf9a55, }, w3: u288 { limb0: 0x4837b7e02ab5c97e266a9eb2, limb1: 0xefb32f653bbae6f3eb726d8c, limb2: 0xceb8c4e50028cc4, }, w4: u288 { limb0: 0x17fdc9308535284c68a7ac7d, limb1: 0x8f766d31c197ea65a39bc4ca, limb2: 0x11acbfcb24ad2ba8, }, w5: u288 { limb0: 0x967bd60ae3efddda5dfbec81, limb1: 0xad70c14c97b8c7380a686e0f, limb2: 0x30371ad6bf543c10, }, w6: u288 { limb0: 0xd6adaf61b6d0903807ee7c9a, limb1: 0xee225f52f407d4ac976ef50a, limb2: 0x2bda417303c6e24, }, w7: u288 { limb0: 0x65b3fb8257e7965d755002d2, limb1: 0xfeb9878a646b31e21f1bc4dd, limb2: 0x3fabd669db5667, }, w8: u288 { limb0: 0xc8927e2bf2fd8606dc9b6e85, limb1: 0x9ddb06748b2b5d9c90979f30, limb2: 0x24bbdf3df96e6ea1, }, w9: u288 { limb0: 0xd7eba07d8fb5fcb950830fc7, limb1: 0x1c092ce0a8e62ed5de82e1d8, limb2: 0x7e9c4205bfb999c, }, w10: u288 { limb0: 0x22d58baa6c70b1c140f13e2b, limb1: 0x38546fe262f003b039568289, limb2: 0x13eb0f5e2523f2ca, }, w11: u288 { limb0: 0xe6fdf4239d6fe039730db80e, limb1: 0x81fc600118834bde7b210e33, limb2: 0x23e94c10560dd48f, }, }, E12D { w0: u288 { limb0: 0x126dcabb9c83e55788a421b5, limb1: 0x2e5a8020d31d184d2bd680f8, limb2: 0x176e9e74d5123bec, }, w1: u288 { limb0: 0x732eaa22202d100e390b18ca, limb1: 0x2595de575d6260fc6337efbc, limb2: 0xf59c55b16fb73c0, }, w2: u288 { limb0: 0x8454d677091dc5fd7e035f79, limb1: 0x6a2dd013fb3bc6a2e5003d7, limb2: 0x1c39b76d67404b64, }, w3: u288 { limb0: 0x4fc8609d589ce3d8c239a3dd, limb1: 0xa8f08cf1f22a3c5957b65a22, limb2: 0x241f11fcdd196ec, }, w4: u288 { limb0: 0x67e9b76b6ba40ce55cf6ab86, limb1: 0x8efa4d2d0eabda1157c2bb0d, limb2: 0x252d5836afe72740, }, w5: u288 { limb0: 0x44c643bb39ed068dead8aca2, limb1: 0xa1da68cdcb0915ecad11d33c, limb2: 0x102404f3b319bf2a, }, w6: u288 { limb0: 0xb5b9204c239db4019c1fdb3b, limb1: 0xf9e229ea94fa5218d7c1fc77, limb2: 0x143ceec4f0df474, }, w7: u288 { limb0: 0x453b36a8489031e742fad6a5, limb1: 0x9092027d3685f9f1c9d26cfb, limb2: 0x50420383217b07e, }, w8: u288 { limb0: 0x23c8b1a3576fc3fe496deedc, limb1: 0x17660d0f8467bc551b9d0bdd, limb2: 0x103804c850751821, }, w9: u288 { limb0: 0x1d3bb90042e840d2625d12ea, limb1: 0xf92dc5238204717730ffb1ce, limb2: 0x246eb81f06275fc2, }, w10: u288 { limb0: 0x53509e255bff37a25830dbe3, limb1: 0x985df0466ce0dcec904b0fd7, limb2: 0x908c8217e42cd80, }, w11: u288 { limb0: 0x3e912b9df8245fa466263f73, limb1: 0xaefb85c91fb824510a98d40a, limb2: 0xff2b69e5bfe0481, }, }, E12D { w0: u288 { limb0: 0x56b32d16ca998bb70b7788b2, limb1: 0xb01d382c48614d4ead2ee20f, limb2: 0x9a64fc7378b5983, }, w1: u288 { limb0: 0xa6231f1419290d1fe863d395, limb1: 0xa558113440db59f078ce3064, limb2: 0xae4a839007bf42e, }, w2: u288 { limb0: 0x75ef5211c2b0d3fb68e934fe, limb1: 0x4b999ebd29af21abdebfd167, limb2: 0x1300c3b30e57dd45, }, w3: u288 { limb0: 0x20db161a9639e8681ce22733, limb1: 0x59edc8f158aeb79b697b9c19, limb2: 0xf3607616f05f4f4, }, w4: u288 { limb0: 0x8e0047a94f779f1b616a665e, limb1: 0x7bf323f05fe820cd6b92f8c1, limb2: 0x255f3301a994d38, }, w5: u288 { limb0: 0x7cce5d4463609087e5be3f9b, limb1: 0xf5ba833a41f0ba18432a33f1, limb2: 0x2251cd91d4cb556a, }, w6: u288 { limb0: 0x1c4f0dfbc693f258d4248701, limb1: 0x77e4e4829a6bc521b295a18, limb2: 0xbfac02addd7ca9, }, w7: u288 { limb0: 0xfd7f0f015d04a59f87d0cc26, limb1: 0xe29e4605e3049af9e29c2f97, limb2: 0x2a8c7ce36cd38433, }, w8: u288 { limb0: 0x11d34ee47ec5a24c6604f5fc, limb1: 0x30be471321da0d345f4143f9, limb2: 0x2c5fa2db51bc0d96, }, w9: u288 { limb0: 0x1502abefbd9b920aec4bea87, limb1: 0x9639b012f620a9a4549f90ee, limb2: 0x276a2c92cd4b35c4, }, w10: u288 { limb0: 0xf17b79c9b6aeb4d04783926c, limb1: 0x9c1643fc7f0a9517dab75329, limb2: 0x147a63c2afd56d1a, }, w11: u288 { limb0: 0xe66eec94302fe7c283b5bd88, limb1: 0x727ac48a4b194db5633b8172, limb2: 0x256a4b164497e127, }, }, E12D { w0: u288 { limb0: 0xcf8cd1f2d235c546a64155e1, limb1: 0x49f94fe26f2f8dc3c32b753d, limb2: 0x90af94bddbbae6, }, w1: u288 { limb0: 0x5f46fc7fd14501d9b48e3f00, limb1: 0xd6a0531b22317d46ae0f7263, limb2: 0x29090bfeabc27bd9, }, w2: u288 { limb0: 0x5a83a53c14292881b779531a, limb1: 0xf2ea658491724e9014f110eb, limb2: 0xb760c5729a55ed5, }, w3: u288 { limb0: 0xcf101de6acf2078bfe7b48e4, limb1: 0xbf896390bca819f7001bf1c, limb2: 0x1216bca4050f3d36, }, w4: u288 { limb0: 0x1bc0ecc2ac251eaa5f21d71a, limb1: 0x587b63c9693e42ba2ecbc329, limb2: 0xe831722223e7137, }, w5: u288 { limb0: 0x6f420c9c7b0f3f6216d8b5d7, limb1: 0x2cf500acafedbc3812a974a1, limb2: 0x16c6c0d66ff0e496, }, w6: u288 { limb0: 0x6b80583ddb0da3dc147a8761, limb1: 0xd2ab1ecd4915c94f067bb706, limb2: 0x5becfa1995ffb0b, }, w7: u288 { limb0: 0x735f62f6dc9d27b0c99a7afc, limb1: 0x9b049dab7d2617bd302e6ca1, limb2: 0xc1d8f04d1a37743, }, w8: u288 { limb0: 0x1b6e19f6d80457fbd011fdf8, limb1: 0x60bdc4f77e10fdedb4718dbc, limb2: 0x250fbdefea34c70e, }, w9: u288 { limb0: 0x86a9b4513fb51e5cb981fea3, limb1: 0x3b7f9a4e04823b4667573b4e, limb2: 0x23be804fbf7fc5ba, }, w10: u288 { limb0: 0xd632f7614d5fab9d356c0fd9, limb1: 0x9a02bfc36db366078d9b9289, limb2: 0xc077e1b37c3db7, }, w11: u288 { limb0: 0xb85605ecfcfe3176c018bc6f, limb1: 0x25fddd5b4babdaf0e7ebc66c, limb2: 0x2d126fc19343eb6d, }, }, E12D { w0: u288 { limb0: 0xe0eb79ef697704f9f88009a7, limb1: 0xf84e9fd2b03ff24c279431ef, limb2: 0x1ecafc868da37277, }, w1: u288 { limb0: 0x2ac72b964e5cc678d621ba0b, limb1: 0xb71c8056e530a371916123aa, limb2: 0xa6a0ceb5f1b6d2d, }, w2: u288 { limb0: 0xb6bad8778afe2fef077674ba, limb1: 0x7a16c7fd65c6f7f2e37b1e23, limb2: 0x22a5e8a58f9c582b, }, w3: u288 { limb0: 0xb396d10dfc48fc667c7690c3, limb1: 0x16d22ca57a88a11bca38ff4a, limb2: 0x20ef9698b6d40399, }, w4: u288 { limb0: 0xa2c377682b43313850d5bceb, limb1: 0x278d711737f6ea40b0dce47c, limb2: 0x295158b2625822c, }, w5: u288 { limb0: 0xda0ba60542bf2bcbc9602228, limb1: 0x7cc8b336d9d47520093bb1ba, limb2: 0x300a142a2850796f, }, w6: u288 { limb0: 0x73fc5bdded39397faec57d1a, limb1: 0x93befe8f64a746ca03d89fb8, limb2: 0xd34647249cce294, }, w7: u288 { limb0: 0x949decf431ad41a4c35769a8, limb1: 0xe75de8c12021d75cc1efb433, limb2: 0x1a5f238d6dce3644, }, w8: u288 { limb0: 0xb63f0e9fb3fee04aeace972f, limb1: 0x5764b150d8ed8b5cdfaaee7f, limb2: 0x1154bf9d5bd93772, }, w9: u288 { limb0: 0x954e689968960d0c6a3a5be9, limb1: 0x9f6a3e9cc45fbcb1a92c2433, limb2: 0x403a6d1d9e0e3f3, }, w10: u288 { limb0: 0xe8cb3b0bc09991bdbc73f57b, limb1: 0x7b7e751a540e324065a25619, limb2: 0x2f223fa11d10f5f9, }, w11: u288 { limb0: 0xec0d73c52157b51a5163723, limb1: 0x5b46f935b0ed7732d2de6790, limb2: 0x28dfc542f18824d9, }, }, E12D { w0: u288 { limb0: 0xe2fea35c4a5b28c62048e60a, limb1: 0xaf70594c4748f6aec0400b42, limb2: 0x3ce671704d55a22, }, w1: u288 { limb0: 0x978176f558827db938ce63cb, limb1: 0x5de249f88953aba9e96e95f6, limb2: 0xd03c2c5a6e7a15d, }, w2: u288 { limb0: 0x1d20a8027dff3e64687b0caa, limb1: 0x448f6d039cfcc3132aeb2043, limb2: 0xd84a765a1ed7869, }, w3: u288 { limb0: 0x1703cf57601441d313ce9f6, limb1: 0xb4db90a6e191a4af88fe5033, limb2: 0x678587681e1f62d, }, w4: u288 { limb0: 0x36cff464be8bd512f26bce5c, limb1: 0xb716aac34db1dc56b2294b3d, limb2: 0x1bf3f2db255639d1, }, w5: u288 { limb0: 0xeac83ef4b82b4b763bac4e8b, limb1: 0xf4cde6c8121a2baa622243a6, limb2: 0xb2055633f438f3b, }, w6: u288 { limb0: 0xda63aa46e3f37283a06151c7, limb1: 0x8ee3b65ce2564d4c7b5f483f, limb2: 0x297ecb7fdeba1aa4, }, w7: u288 { limb0: 0xfb59559a190f305cac04eaf9, limb1: 0xa90e8d265b71e75a7341b23f, limb2: 0xcb8a82d979e7ea2, }, w8: u288 { limb0: 0xc58bf182be372c06687de495, limb1: 0xf4cb50f848c1e0e2072c7486, limb2: 0x2b107173b97495a9, }, w9: u288 { limb0: 0xe0eabd65692464ca0dd92b1f, limb1: 0x56abb5cb408d804cc85bf34a, limb2: 0xc80e3c37d6cad8a, }, w10: u288 { limb0: 0x2ee21b700c674b257b1831d7, limb1: 0x3d01c28bcd9b53ad28d0864f, limb2: 0x51f5ebd4bc028b9, }, w11: u288 { limb0: 0x5ec5d4da4056deda36f904a, limb1: 0x168e485c29ffe2be92bd8ea9, limb2: 0x2c51b496555823dc, }, }, E12D { w0: u288 { limb0: 0xa8471dd55603384b42066496, limb1: 0xe46eee6fcaba6ee1116284f5, limb2: 0x2575472a96ec8df, }, w1: u288 { limb0: 0x9b001b2c565f0ddfa573296c, limb1: 0x5debea2a4077e45fd6049d3e, limb2: 0x10ea438a1d19edf5, }, w2: u288 { limb0: 0x459fab1d8fcf4bb48996829, limb1: 0x1beefd7fc2a65a73c031c7f3, limb2: 0xbfde865e2af211d, }, w3: u288 { limb0: 0x127b67ab28f4648ccd7298af, limb1: 0x8d1a33c8a95c07a2d8182b51, limb2: 0x154f5a2a8978766f, }, w4: u288 { limb0: 0xa843c7b6cdbfec70273c7179, limb1: 0x451376ff143138b26508e149, limb2: 0x27ee093ad5b5641d, }, w5: u288 { limb0: 0xe46d7ddc38e93e5d4539397e, limb1: 0x10c546e7762036ef0406b68e, limb2: 0x1e5de28d570d8c23, }, w6: u288 { limb0: 0x1d71841c43b80d2bfc818be0, limb1: 0x9ed8354ed235ab98dcbafdfd, limb2: 0xc7832fd4bcfdd58, }, w7: u288 { limb0: 0x9120a99dcef073912a3fbe11, limb1: 0xc99085975b31be35943fe6de, limb2: 0x19b2aeb3f9a37fc0, }, w8: u288 { limb0: 0xfdd9ded7b646da18595ccac2, limb1: 0x7326e81c5c4d6cd485a95afc, limb2: 0xb12576c70934ed4, }, w9: u288 { limb0: 0x761820abaa0929428358b641, limb1: 0x49c5bd0dedc35fae8f0ae35e, limb2: 0x179d6cc8ca4c2127, }, w10: u288 { limb0: 0x337630f723038a58f57b249a, limb1: 0xb6754ac913be8838812111fe, limb2: 0xc811873605012b5, }, w11: u288 { limb0: 0xd311f807d8869697ae180475, limb1: 0x3184bc6814d397f313fcd460, limb2: 0x335982df9e3c62a, }, }, E12D { w0: u288 { limb0: 0xd43b4f3fddaca664aeb0609a, limb1: 0x4bfc6836c701691c4414eee0, limb2: 0x2fb3fa9c32523106, }, w1: u288 { limb0: 0x8e7ad226defaa97d7f70c6e6, limb1: 0x857e2881a21df90f085e3b8a, limb2: 0xe37b527e826d61c, }, w2: u288 { limb0: 0x30530cf277d3ac15f532bb98, limb1: 0x88cbcea6dfad7de0cfc2ba7d, limb2: 0x2eca3af594e50fbf, }, w3: u288 { limb0: 0xef4cc3ba0de6966b75295de8, limb1: 0xaf8676b848865e67c0f26489, limb2: 0x1460c0fd900d19c, }, w4: u288 { limb0: 0xc01ef62a31ee02de38d89329, limb1: 0x1d525f597b96d81d5254e48e, limb2: 0x14221da9a4fc3c02, }, w5: u288 { limb0: 0xadc48338e7db4e11166052f6, limb1: 0x9e68b555bddbd64621247d0c, limb2: 0x5a77fdfda3d9125, }, w6: u288 { limb0: 0x63d9fa8e08c9954284f16245, limb1: 0xca621cede38d19231a12d63, limb2: 0xd27fe5bd781b034, }, w7: u288 { limb0: 0x77a9046ebfaeabcd937b61aa, limb1: 0xdfa2e67db4bb78ec8cab398f, limb2: 0x1dd3f480cadc51bf, }, w8: u288 { limb0: 0xf65c9e4d2df095b6d942b195, limb1: 0xd6ebcf23f6276b9f4398ca5b, limb2: 0x1685cb6183c850a4, }, w9: u288 { limb0: 0xe5ce6d51f5c7a2aeec8cada, limb1: 0x516cacc2dabd97d328953757, limb2: 0x1974d6cc4195d3f0, }, w10: u288 { limb0: 0xc2dc450c125c4f157be8a0ed, limb1: 0x4de5175e01fcec11f2943446, limb2: 0x94d92ac291aff6d, }, w11: u288 { limb0: 0xab272482c2c48dac7030c6fb, limb1: 0xad02ca14f40e608b78e0d102, limb2: 0x1bb830e6999b29a3, }, }, E12D { w0: u288 { limb0: 0xc83eac5d253a3c206da26863, limb1: 0x1a2947347e60ca31a19b795a, limb2: 0x19d283eb90879408, }, w1: u288 { limb0: 0xfe29e4f1c7f2933ca1484bb7, limb1: 0xa467cb57c5dd3ee90eb9b1fd, limb2: 0x5af95cf457531b6, }, w2: u288 { limb0: 0x5219339ef8753869ba2e72df, limb1: 0xf6edbe19ee9528b014d5c5e4, limb2: 0x17e4d2b93b5a24d6, }, w3: u288 { limb0: 0x702d294fada771a134eda0dd, limb1: 0x6f78dce21c0fa36347352189, limb2: 0x271fd9860e85dc01, }, w4: u288 { limb0: 0xcdae44d3e06c07681ae14c73, limb1: 0xe07fa16b28b87a358d682e14, limb2: 0x1b33f9d4bedad80f, }, w5: u288 { limb0: 0x527e57b7206c1f1abed0556, limb1: 0xc5f02956f7dd77fc77040195, limb2: 0x1917515d732e83cf, }, w6: u288 { limb0: 0x821089dfaa7ef412763e67ff, limb1: 0xfd54fe4da59d3b34626aa0a3, limb2: 0x1f646c3c1ce572a3, }, w7: u288 { limb0: 0x2266b08b3a2f19ef3dfde72f, limb1: 0x8b17232a32f1d284469f812a, limb2: 0x3d46d9f79f4918e, }, w8: u288 { limb0: 0x8bc72d70c71f6a14c2015aec, limb1: 0x3e3b1d0272aeee3c95095070, limb2: 0x1401f32c5bdc074d, }, w9: u288 { limb0: 0x6b9fdcc49f933192fdd316d9, limb1: 0x51b8f8765258f14ff0b91b7f, limb2: 0x2d04765080f5aa72, }, w10: u288 { limb0: 0x282af58df7dd63615218a4db, limb1: 0xdb5b2942254b35298f473dfa, limb2: 0x19371f2e44f2642f, }, w11: u288 { limb0: 0xf656fcc4885e9bac2311a500, limb1: 0xb86e168eccc1490248a1bbcf, limb2: 0x1e94a5f389c1134f, }, }, ] .span(), big_Q: array![ u288 { limb0: 0xcd9ecd0e7e0de83876860721, limb1: 0x7a0e802a360ad60fb6b3ba6, limb2: 0x1f26bff9d463a948, }, u288 { limb0: 0xc45197a61e985bb95c93982, limb1: 0x2b04ba2a8963f7ae0fa62ce7, limb2: 0x2d01448cacdad685, }, u288 { limb0: 0x588f7a63bbaf841b308e5cb1, limb1: 0xa0de63d533eccee6a673d8f6, limb2: 0x1c044a4e0a5d5939, }, u288 { limb0: 0x3499e2c2ef45664c1c7cfc31, limb1: 0x7046243b95e70d66fd128d3d, limb2: 0x1badeff894c418b2, }, u288 { limb0: 0x9d4d9b283dda2d4cf3b482ca, limb1: 0xe8f67766ff9b89e228118e0, limb2: 0x12cf4b1f6ca74656, }, u288 { limb0: 0x7f78b962b9a9586c785bf41d, limb1: 0x942b1fd431968dcb396f0ea6, limb2: 0x21f639eb74937d42, }, u288 { limb0: 0xcf363881046546501cf425ea, limb1: 0x443c6e66796429495be332e5, limb2: 0x14e45de7b5461b27, }, u288 { limb0: 0xf6f3d82bef402316dfeb53e7, limb1: 0xda01fc4dbf0d0280eb89e6ec, limb2: 0x402be40fe8cf55d, }, u288 { limb0: 0x43ff2f5f02c99faf8526decc, limb1: 0x979a21765f207f8c3f88f9f3, limb2: 0x1a50d93e54087d54, }, u288 { limb0: 0xeae0f77e14ad1d010fed4797, limb1: 0x86a3801139a2f3b0ba5ac0, limb2: 0x1c16aa3c3908741d, }, u288 { limb0: 0xdf7f8f09db39050b510740c4, limb1: 0x88a3c866773a26b91a70377c, limb2: 0xf5dcebb0a8eb1bf, }, u288 { limb0: 0xe509b26f0280664ececb3be8, limb1: 0xdb438338837751f01dce4b67, limb2: 0x166a10efa92b6056, }, u288 { limb0: 0x82875b919a173ea8a3511d48, limb1: 0xf9b0528311202cfd6db28337, limb2: 0x1ac72f8b464f7578, }, u288 { limb0: 0x2b0709cd2f982e17d43ce465, limb1: 0x85605341bfd989b9e558a9e8, limb2: 0x29d232336b682435, }, u288 { limb0: 0xe080bdc4d14676d875f5ca74, limb1: 0xef83976d59ee48dab51aed6c, limb2: 0x2597d1c934d909c7, }, u288 { limb0: 0x4e15c1b6fd41bc38a5b7a5e0, limb1: 0x29058fd34d46cbb1d2cd7e9d, limb2: 0x153c756a13e16b87, }, u288 { limb0: 0x110465de721c0a397c95788, limb1: 0x339beb1394a74bf7fac9e22e, limb2: 0x136b97bb54329558, }, u288 { limb0: 0x4cc1dc324e163ccc6884836c, limb1: 0xee91e93251059174573ef629, limb2: 0x2e207e483b0fd5c6, }, u288 { limb0: 0xac5b393cd606a10dd8a89e51, limb1: 0xe2babe1352a2ac60c4f9033c, limb2: 0x300370ae36800f97, }, u288 { limb0: 0xebb8e75229ae08a0e0425b33, limb1: 0x78b9ecf71e5ef222976daa3, limb2: 0x154407d45ce0fcd3, }, u288 { limb0: 0x95119019b9386ee462a8ccd8, limb1: 0x431aba6ef81c2a9699eea450, limb2: 0x4564056387a17b0, }, u288 { limb0: 0x10eadf8480859a90430d0518, limb1: 0x3a4e3e5be0e7dd36aba57ad4, limb2: 0x12f4b351402098eb, }, u288 { limb0: 0xc96e5311b9a34a252ef24927, limb1: 0xc6bce3be0e5ca2a07424c205, limb2: 0x248132cfddd4df2a, }, u288 { limb0: 0x673824c0f93813a2d66d7215, limb1: 0x3e733001aa8c9dde8e5ad458, limb2: 0xba398158cb0eab8, }, u288 { limb0: 0x51a4016794c88913507629c1, limb1: 0x912fd8dee344710fdafb700c, limb2: 0x2ae28b98c05f9f6b, }, u288 { limb0: 0x79a009fe57a9b359b4adb352, limb1: 0x1372ca03aacbb433e1226a55, limb2: 0x12617bd21c0abb52, }, u288 { limb0: 0x7eaf2f952174f82c330b95e8, limb1: 0x4eb90281cfd1dd1c4671b9b, limb2: 0x20bac73e741ffc3e, }, u288 { limb0: 0x982bce06f0d39bb2cdc5accb, limb1: 0xb050fa46b9b7dd28cfa99214, limb2: 0x2af9624e1b305800, }, u288 { limb0: 0x3a27a0a47e34c1af07bee4e5, limb1: 0x4a217069cf62a8cb5dc21be0, limb2: 0x113cf013ea01537b, }, u288 { limb0: 0x397138d3414f0ce30034c150, limb1: 0x78a5fc50efeccd0380f5f953, limb2: 0x2bbf36d098bc85cb, }, u288 { limb0: 0x1dd90e3163d35b29a4df6324, limb1: 0xf4f174473f47e8f6d85260d7, limb2: 0x177ea72f9955fb3f, }, u288 { limb0: 0xf5f2e7bde58014b48317751f, limb1: 0xff017eda0d8456f5c6fbd91f, limb2: 0xbfd8d46a321cd92, }, u288 { limb0: 0x703202d10d086be3180bb09f, limb1: 0x4777e8d0e0172a43f3bc41fd, limb2: 0x86c412c67ea9a24, }, u288 { limb0: 0x828ef41cae766d576be8e58e, limb1: 0xbb9975959f9e49b0d1d47d5e, limb2: 0x214d2c6480221840, }, u288 { limb0: 0xd6fbfa1e1ce00ffa4643b274, limb1: 0xdce6d04cbe36a1f9c1f68d3b, limb2: 0x249a0a2cef1fcf37, }, u288 { limb0: 0xb9fb8ad79768b63fc7a465c4, limb1: 0x47908a6e2af2ba3361c8aaff, limb2: 0x119055b6663e7b1f, }, u288 { limb0: 0x7c1cddcc18521e4581a65fa5, limb1: 0xce811a3bf18b91a42cf807d4, limb2: 0xb9c97707c1dfb5e, }, u288 { limb0: 0x82cf50a98d6a60d98898f, limb1: 0xfb8668942142c8ed097fd49c, limb2: 0xa33341d40ab89c1, }, u288 { limb0: 0x944ad8e61fe850d38033ce23, limb1: 0x33595a089ea014ad58f9bd71, limb2: 0x2e0f1bfcb86fb4c6, }, u288 { limb0: 0x637e01f7ce86989ac3bbc8a0, limb1: 0x103ca90052a9d3cc1071872a, limb2: 0x1afb86c103e88176, }, u288 { limb0: 0x1f082eeca6098eccfcb5f394, limb1: 0xf3456368bf412757e690b18e, limb2: 0xf2df40ce38dfa9f, }, u288 { limb0: 0x334b5616731bda1e93099512, limb1: 0x9da6bbfc03dfb03d67bdf53, limb2: 0x15aa211a87b2137e, }, u288 { limb0: 0xf282c83a11343e347e30120, limb1: 0x4d683ae65f5a7e8f7c4e845d, limb2: 0x244c10d60252be9d, }, u288 { limb0: 0x86cb9a2bc80a9396e05e6a31, limb1: 0x9d91ba4be143eb493f6a7dfd, limb2: 0x22e6cb69f0e48722, }, u288 { limb0: 0xf9ce34ca7f58a460c0ab03e2, limb1: 0xb24fdc31808aa1aa652d2373, limb2: 0x16271dc397abc2d0, }, u288 { limb0: 0x90b7836ac52290f685e38858, limb1: 0x3d6bcd1716684e0f79af6add, limb2: 0x1c1d91fd1b172cf3, }, u288 { limb0: 0x61363d39d930cfa7e7efdbdf, limb1: 0xfd93b569a8206d555229c16a, limb2: 0x1e98a6aa74f629c2, }, u288 { limb0: 0x15ce60589452ecb11866120b, limb1: 0xe50dff8fe0f59568560ff039, limb2: 0x1e280d5a22136a7c, }, u288 { limb0: 0xfc490e9f2a962e6e87d9ea27, limb1: 0xae538485491902fbf60f604d, limb2: 0xba325703cb9d622, }, u288 { limb0: 0x611de88bd1e06877f38545a5, limb1: 0xde29c8fb70cabae4e03fcfc0, limb2: 0x3040033c88c2ee9f, }, u288 { limb0: 0xaae7db4415d65b00609f5931, limb1: 0x125a49ea3b009299fe42e200, limb2: 0x2f27237befc96a46, }, u288 { limb0: 0xbac1d16fd779c3681906273, limb1: 0xe5faff69c63d4509d664660e, limb2: 0x176cc60c39ad7261, }, u288 { limb0: 0x1dff6ba32886a747f4028ce1, limb1: 0x7d3dc0f77f55a160febe9533, limb2: 0x41eb1e2cc9620ef, }, u288 { limb0: 0x6f159369a14c55f116b056a1, limb1: 0x4d6a71d44a9e5f4b416bedaa, limb2: 0x1e7d1caf0a514c8, }, u288 { limb0: 0x3eaae80d65438be521ccaa8f, limb1: 0xb3cb70353f9ab7c9308878e0, limb2: 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0x5d9219cfc8d5ca6ef93f34d, limb2: 0x2b1322f0eff448ec, }, u288 { limb0: 0x4cca24b0b778472065b78f26, limb1: 0xf97924058d24e5673c16c4aa, limb2: 0x185b829c05f1f99c, }, u288 { limb0: 0x3eee6f0043b04acd6bbf71db, limb1: 0x7c8f4c1a93ae3ea5b9ca3414, limb2: 0x1d71ed45dd37c55e, }, u288 { limb0: 0x9e1311913e9c2052a16dca48, limb1: 0xcdcaa853fb8f8267ebdfc69e, limb2: 0x2abcb6f497eeaf02, }, u288 { limb0: 0x79c438d659c0c62ac1fec12, limb1: 0x775044aec0471597922e3111, limb2: 0x6214986f36bba06, }, ], z: 0x690450caee78b3590fe0ce78a9df9ca1987c494b5ca8e9629f81245f1099f16, }; let res = multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result( pair0, pair1, pair2, precomputed_miller_loop_result, lines, hint, ); assert!(res.is_ok()); } #[test] fn test_BLS12_381_mpcheck_2P_2F() { let pair0: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xfe174bb39be8658ef83c8c2d, limb1: 0xdb24ddec0e0c3b63d82efa81, limb2: 0xe360a80121d5ef96fd687003, limb3: 0x59d2a79bda5f8a941d4db9, }, y: u384 { limb0: 0x7f68344f543e52fe891285a9, limb1: 0x6f6992be16bc35f88c471acf, limb2: 0xcebb5ee96e40a033f5d3b798, limb3: 0x2df47e8cdf189985d5085bd, }, }, q: G2Point { x0: u384 { limb0: 0xa805bbefd48056c8c121bdb8, limb1: 0xb4510b647ae3d1770bac0326, limb2: 0x2dc51051c6e47ad4fa403b02, limb3: 0x24aa2b2f08f0a9126080527, }, x1: u384 { limb0: 0x13945d57e5ac7d055d042b7e, limb1: 0xb5da61bbdc7f5049334cf112, limb2: 0x88274f65596bd0d09920b61a, limb3: 0x13e02b6052719f607dacd3a0, }, y0: u384 { limb0: 0x3baca289e193548608b82801, limb1: 0x6d429a695160d12c923ac9cc, limb2: 0xda2e351aadfd9baa8cbdd3a7, limb3: 0xce5d527727d6e118cc9cdc6, }, y1: u384 { limb0: 0x5cec1da1aaa9075ff05f79be, limb1: 0x267492ab572e99ab3f370d27, limb2: 0x2bc28b99cb3e287e85a763af, limb3: 0x606c4a02ea734cc32acd2b0, }, }, }; let pair1: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xde4f62a6588c9401ffefbd3, limb1: 0x9bb5f797ac6d3395b71420b5, limb2: 0xdc39e973aaf31de52219df08, limb3: 0x105dcc4dce3960447d21d3c1, }, y: u384 { limb0: 0xaefd0d854043fd325dd3c34f, limb1: 0x9b63c98d9a7845c52e1e2b0f, limb2: 0x9db0be660d847ccc58358f3f, limb3: 0x17cb6c41f0c4e1a7394ab62a, }, }, q: G2Point { x0: u384 { limb0: 0x3b3d3c305a70960906e6cb09, limb1: 0x40e5bf3ff02d81e98b75703a, limb2: 0x665a5fc010510bd690ddd7b5, limb3: 0x82dc9154807866eb0f36ccb, }, x1: u384 { limb0: 0xe6709deb0dcf81d4285e5e60, limb1: 0xb4dcf956002c4efb974ffcee, limb2: 0x4a6ceebe6375a83dd242851b, limb3: 0xdd18d077ad5bd58dabb18d8, }, y0: u384 { limb0: 0x61535fe1a90bae7e6692f9b0, limb1: 0xc91aa58105d3a281b2e84ddb, limb2: 0x197d3446652372ce5ef50e93, limb3: 0x4a468eb9e206b9833d8e8e2, }, y1: u384 { limb0: 0x27115c334e82ed4be8da6c10, limb1: 0x194fa3bf769a2e5a52535277, limb2: 0x8be8992de81f47ae3341c590, limb3: 0x198fd0ab6249082bf7007d7e, }, }, }; let lines = array![ G2Line { r0a0: u384 { limb0: 0x36701a5831c9fb39250e2ea9, limb1: 0x26ad0ec05ad6440f1df034cf, limb2: 0x67cd27cf7598a85f81c23cd9, limb3: 0x15a76ee3d8d1c3451005d560, }, r0a1: u384 { limb0: 0x9009367bbf6e6aa19488df66, limb1: 0xce5cd2ccda4704dc0e4b92b6, limb2: 0xd7656829a6a71c42deb7dd, limb3: 0x16d96e785c797fb5d6afcb14, }, r1a0: u384 { limb0: 0x9d68b0bdf431a2f53189c109, limb1: 0x70e39167384e44fdaf716fa4, limb2: 0x3768099390a3f9d581d88280, limb3: 0x4c208bdb300097927393e96, }, r1a1: u384 { limb0: 0x68ab4b88cf058f147ba2cda9, limb1: 0xce3b4d4da03cbdac75933b54, limb2: 0x1be2f7e6eaa0f1474cb64c53, limb3: 0x546ca700477f9c2f9def969, }, }, G2Line { r0a0: u384 { limb0: 0x96e0f84058018a4538d64e8b, limb1: 0xdb7b84172cb1e68ddd09eb12, limb2: 0xcf3aaa45c2b370e810ea9361, limb3: 0x14b92565b748c30f253912c6, }, r0a1: u384 { limb0: 0x9cdcddf4728a38086aebcd7, limb1: 0x7b8d9115b96656327dd79780, limb2: 0xbf914addbdcbe307142bf7cc, limb3: 0x3c50d0829bdc305ff694cc9, }, r1a0: u384 { limb0: 0xcc0dbe864e35231bdec2ef76, limb1: 0x4efa339ef551d8f751da95ba, limb2: 0xfde5910a13d5c428549ed3f5, limb3: 0x105e4803f5b8472a138e00b, }, r1a1: u384 { limb0: 0x584879d210eb30bfd6518cf2, limb1: 0xa7c4af01b40d0e68243b050c, limb2: 0xade596dd94a41e4aedec2196, limb3: 0x162a46f819eba8e3b9d215f9, }, }, G2Line { r0a0: u384 { limb0: 0x3717dfec242e39e2ff1f466e, limb1: 0x2e1a47c8b52d2a155331b3bf, limb2: 0xb9705c11a0dc1b7a21290360, limb3: 0x186349066cd6c743642100bc, }, r0a1: u384 { limb0: 0xc653dbae90aec138bdc66689, limb1: 0x84a0e18292766501cc981050, limb2: 0xcb8cbe9f0dad8baba490c814, limb3: 0x49af016994f800024ad3138, }, r1a0: u384 { limb0: 0xaae746564160600e87f79910, limb1: 0x9b0e53f36f1c737506ce80ce, limb2: 0xc88af441fe63a2b5746950e6, limb3: 0x9e6e8335a28c0593fb7797f, }, r1a1: u384 { limb0: 0x3353ff16d642750e655d9250, limb1: 0x1c83cf0f79a4997f9f673aab, limb2: 0x5ec8ef641f38e8160f0fafc8, limb3: 0xd6e97ce3437dbe7066bb16c, }, }, G2Line { r0a0: u384 { limb0: 0xebdfba548549869254397482, limb1: 0x59fe075d9bedf0d74abf57be, limb2: 0xabab1d37873d3366c37fca47, limb3: 0x1538a52f8fae05fcab86cb76, }, r0a1: u384 { limb0: 0x1d682b553c5f64f0dade7dbc, limb1: 0x3ab75e8798604af41cea2a02, limb2: 0xe905b5289633293089e66f7d, limb3: 0x1952802636ce6e28657b087, }, r1a0: u384 { limb0: 0x4634dee1af84530ccf6b310e, limb1: 0x2648d262401e3b709787473a, limb2: 0x17a30eb731c1037d19aa1fdd, limb3: 0x2d6c23a0ffe044c163492a7, }, r1a1: u384 { limb0: 0x9c68a627823ca443a9e945b, limb1: 0xb3c2ff91b20c36d112c61699, limb2: 0xc263985d3095da2f3db9773e, limb3: 0xa1e844c3f1cb15b6b809857, }, }, G2Line { r0a0: u384 { limb0: 0x6a72f085ee4e78bd4c2aef8e, limb1: 0xdec05cffe4a869aed2a64ee8, limb2: 0xd41aa908b1a833b94e768d2, limb3: 0x56ceab5d5d994dee0ca07fc, }, r0a1: u384 { limb0: 0xd23aad6cd3e84e398a4e7bc8, limb1: 0xb343a6878db6ec20bcac1275, limb2: 0x3111e14b674a67295a242cf3, limb3: 0x39b596a976f556e5ea4016a, }, r1a0: u384 { limb0: 0x19fcdcac7feb1f0edbefdbf8, limb1: 0x71bc60f1a68459eb52df6a92, limb2: 0x2827dbba9d5d8516fb557dfb, limb3: 0x4786cc02b147d13e701c1f5, }, r1a1: u384 { limb0: 0xcb7555c0db86510eb99cfadd, limb1: 0x43387d10f8329296e43e6610, limb2: 0xbf6789475132950c583823a, limb3: 0x145f508c63c10d270e027b2b, }, }, G2Line { r0a0: u384 { limb0: 0x61e12a1921e9e0192225eb47, limb1: 0xe7959ccf3ab7897b63eaea0a, limb2: 0x44172872757e4112552dfda0, limb3: 0x140a9f8fd2d77ee9ce9eda9e, }, r0a1: u384 { limb0: 0xc4bd827c5fcc80aeefab436d, limb1: 0xed5133aed1007276d5defd61, limb2: 0xeae0d97e880c76210872600, limb3: 0x12f12f5d73e707622f58355, }, r1a0: u384 { limb0: 0x641d998236970e3d020b53af, limb1: 0xe7cbadbae704bf8e96b8a6b4, limb2: 0x2b9f4df44bf2e79afe0c94f2, limb3: 0x955b0249e73e276cc78deb7, }, r1a1: u384 { limb0: 0xd8ed50e5cdfbf761b34675d9, limb1: 0xd1070d143ecc709daf022bbd, limb2: 0x5df7054bb133a14672778550, limb3: 0x17b953a66b43816b30bac24, }, }, G2Line { r0a0: u384 { limb0: 0x7bd212f8f60967471e995a8e, limb1: 0xec76fa31d0fd358f36ee756e, limb2: 0xa63e06c40964532a724817c3, limb3: 0xd860767952ed2b694b64eea, }, r0a1: u384 { limb0: 0xd18f8b1de21e64c50d3c6fc2, limb1: 0x456cec057d45521c48d0b547, limb2: 0x23fb8276293fac77c9a38c1b, limb3: 0x1469d7cf50d58855fa523aa8, }, r1a0: u384 { limb0: 0x52f1d22ea6bfc23435bf7e3b, limb1: 0x3e2d5122467bf39f2573a57b, limb2: 0x378db9e77f53b5b1e38981da, limb3: 0x1015deb442db265529d8948, }, r1a1: u384 { limb0: 0x73c44618fb7917b2596bd460, limb1: 0x598ee13313073cf3232e1b37, limb2: 0xbd63e58ae4aa477bcd459ef2, limb3: 0x272bfde06aa8302ab8c70d6, }, }, G2Line { r0a0: u384 { limb0: 0x84d7880d9c5ad98d07f1b961, limb1: 0xd5be4b6e58ad745353113073, limb2: 0x592ecc7534e44983a06d755c, limb3: 0x15d60a0d6d8a2e4543194737, }, r0a1: u384 { limb0: 0x9ba63990e4f1ea4875173006, limb1: 0xf84fa98d5f3742b3c571f427, limb2: 0xdd28189a4a2e3a70f78a170e, limb3: 0x1ad5bc82425c66f655a75db, }, r1a0: u384 { limb0: 0x49306522c22ca321950bf155, limb1: 0x369a747f27aa6472ebc5d290, limb2: 0x20d8977cbe5acf112574c70a, limb3: 0xcdc103da1aac9ec5f855b64, }, r1a1: u384 { limb0: 0x74517cbd651af3940075c057, limb1: 0x94d3802d81c93d69eb13518b, limb2: 0x76411c393dd03e5381661629, limb3: 0x16e57b05faef24ef64868a07, }, }, G2Line { r0a0: u384 { limb0: 0xaa72fbca0fc809a3c04cfe63, limb1: 0xb197b948b9fb7b1d17db7811, limb2: 0x912c914d3a6ff39a540a4f3d, limb3: 0x16cacbdaa9c89addb1ab2cbe, }, r0a1: u384 { limb0: 0xbc48a5607d4379fef56b2969, limb1: 0xc1f23a19f0081d7a3e19795d, limb2: 0xd3b68107f121763ac21a3013, limb3: 0x105753740850ad267b13b914, }, r1a0: u384 { limb0: 0x9922c12ecdd8f9f562a9ffbf, limb1: 0xd3ddfb6bca4e7fcf1de87fe4, limb2: 0x43cafb5ca79d345cd7fb414f, limb3: 0xcf76a75d055e5103c1f3bb4, }, r1a1: u384 { limb0: 0xfe0eed2060bf837fabeb633c, limb1: 0x7647ff2029a177beb2026c82, limb2: 0x6c89e5be509cdaa5d0724f48, limb3: 0x18e2495d0e738bcb51e26445, }, }, G2Line { r0a0: u384 { limb0: 0xaf7eb92e30bb53c95dbc4140, limb1: 0x9792c2287a214b5e4a26edb0, limb2: 0x9e2e1f53797f04ffeabc4a20, limb3: 0x11ffc63e88b938e0364be5e7, }, r0a1: u384 { limb0: 0x23f6838c52c8c103f492d019, limb1: 0xc28ff9b5147ad2c6e80ba89, limb2: 0x54862dd590b2cefb84f4884e, limb3: 0x137f181e7bc2d6e0858337e0, }, r1a0: u384 { limb0: 0xf25f4290fc34cdb084e88912, limb1: 0xb45c1d0b4bb37399c6f2f06f, limb2: 0x1c520b9c1f9a27c6dc5ce1f2, limb3: 0x8f5b2f168533ac53479939d, }, r1a1: u384 { limb0: 0x90f6fed4ce70be068a771f84, limb1: 0x6c083f0007d7b530d7bb7762, limb2: 0x621955ba256f0878ab3f71cf, limb3: 0x147b25e183343ffa8070b1c0, }, }, G2Line { r0a0: u384 { limb0: 0xb5abe92a46d0ff04a4205803, limb1: 0xdb760c98b7aad959e5dfc28d, limb2: 0xbea9b6e4adf41fa1060713ee, limb3: 0x75707a467e7543c28370330, }, r0a1: u384 { limb0: 0x8b0715d2f6a16be8d5828197, limb1: 0x598a8a6da7ed2bcc091f594d, limb2: 0x18cfc9c1ee8960c06ff2c240, limb3: 0x14061839f139644bb20e8647, }, r1a0: u384 { limb0: 0xd529f0561fff46258f565dec, limb1: 0x80402f61ae7ce96272aff23b, limb2: 0x883367465c3a4bde2507377a, limb3: 0x14fc234296369891318c6245, }, r1a1: u384 { limb0: 0x9fdc0242b4d20c44b72c8d49, limb1: 0x37e047238dd417acab9ea0c2, limb2: 0xc424c8845919fe27ac23e9, limb3: 0x151e87d65d95c3b1cc9b1de6, }, }, G2Line { r0a0: u384 { limb0: 0x6d3e75c7266836a5f88da38f, limb1: 0x9f0dcd126bc3eb7a57863065, limb2: 0x2dd839b48eaaf3738b6378c3, limb3: 0xaaa2a6bcd21b87d1c17c1d7, }, r0a1: u384 { limb0: 0xd751d74691ccfbf8a2e44893, limb1: 0x39dc71f7d866971a5b34a793, limb2: 0x61f4c7b07c463740fdfa24ca, limb3: 0x7aaec7413e01006276f927b, }, r1a0: u384 { limb0: 0xc02a7ffd3ac8b07a8351a74, limb1: 0x3e5cf07a7c56c9a5eb07e2e4, limb2: 0x3e8a62aa55827a8825e3a32b, limb3: 0x17607fbb8f27884431eb0d0e, }, r1a1: u384 { limb0: 0x67fe51eac141e68a4dc9a759, limb1: 0xa4ffe5ceccd1cdfd737bd38, limb2: 0x3efc4588564baa38aef1502e, limb3: 0x19a6b0517bf3ba0a12058062, }, }, G2Line { r0a0: u384 { limb0: 0x9bd8fa7a943e0e3a924e7492, limb1: 0xad948685eedfe9d3ac7315ff, limb2: 0x8148910d6004895792caa88d, limb3: 0x1deabfaeb3374b50119ecb9, }, r0a1: u384 { limb0: 0xfedf28954ae85d6e9f58c709, limb1: 0x7c01f5d8a4b9368fc9cbb8eb, limb2: 0xbe98bf07cbd25fe6f4ac154f, limb3: 0x7c9b05e8adef4de506459f7, }, r1a0: u384 { limb0: 0x71812aeba8c33457117bfb0, limb1: 0xaf1a11b5a7571775ec17c1, limb2: 0x721e08542ff85e7037b2c02f, limb3: 0x991d1db86230da71efb4475, }, r1a1: u384 { limb0: 0x4122fa433f37c5e6888de07c, limb1: 0x144d977681671d8cd0854c34, limb2: 0x93981673fae1df08d18161aa, limb3: 0x145eae6a49c250f2435d1ec8, }, }, G2Line { r0a0: u384 { limb0: 0x468d577fdfbdbc46e423962d, limb1: 0x5bee3b6cf7059efb0069632a, limb2: 0xc1effa8ed920dfc235de8974, limb3: 0x13d2fffc28b953d3ca80ffa1, }, r0a1: u384 { limb0: 0xdefb34cc5a85aabacaaacdd9, limb1: 0xfac8915a4c4373e6a38752dd, limb2: 0xbe1dce6fa4eaa80db5298aef, limb3: 0xbb539e692a1a2274f4304f4, }, r1a0: u384 { limb0: 0x615c9153f8460e09de46571d, limb1: 0x4f55bef9c25736ce73e4eec3, limb2: 0xbfe37903c95e022709a17263, limb3: 0x1d523a97a76bc409ae24135, }, r1a1: u384 { limb0: 0xeaec0a3f08b499ac07b95ea8, limb1: 0xae9a839b303953da2d3fe15c, limb2: 0x97307b6e3e3abcb8ecd98686, limb3: 0x77101a8f07adfc3ad5c763a, }, }, G2Line { r0a0: u384 { limb0: 0xa8af53d78f2fa38c6e213a84, limb1: 0xc908fd45d36e147e8a3449ea, limb2: 0x9224181cd573d3836b141129, limb3: 0x140090a04158ea562a90ed5, }, r0a1: u384 { limb0: 0x95e6526648a96a5a43488327, limb1: 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}, r1a1: u384 { limb0: 0xed834e1b94dfdd91c8d4311d, limb1: 0xe0efd3a3e73341c128668e23, limb2: 0xad8f2be3d52a01168b375d5d, limb3: 0xa34b7e1dee43f4de567f3e3, }, }, G2Line { r0a0: u384 { limb0: 0xee48f089c7a4594a201092eb, limb1: 0xc9d8a7b7d87389e25b856b97, limb2: 0x74d54bf4748e38d3b2c782b3, limb3: 0x78af2f8549231aa92bba1b3, }, r0a1: u384 { limb0: 0x61acc46ca422be84be4fee75, limb1: 0xf425406455688e07fe496eb2, limb2: 0x1151b627d67176b268c6b18b, limb3: 0x157a7e87571314c4eeffcc64, }, r1a0: u384 { limb0: 0xd95d245c747804a8f3bd59ab, limb1: 0xb3c7108b5d8ce6d797a8ab29, limb2: 0x452fc047d47ec02830b1b9c1, limb3: 0x12ea35020ddc17232447b57c, }, r1a1: u384 { limb0: 0xb027d5b2037b8170fb63b93a, limb1: 0xf317c06fee2a5ef8113fd9d3, limb2: 0xdd1a58fc8de1d70f065c435c, limb3: 0x11d55ce218987319447cc925, }, }, G2Line { r0a0: u384 { limb0: 0xed2bfa7ce99d4f69b850d09c, limb1: 0x5efc2ec9bfecf49ff6bd1417, limb2: 0xf733724aff4a909b6a9579c4, limb3: 0x129d26f7087d748c81d164c8, }, r0a1: u384 { limb0: 0x4fe6ed09a9ce55efa63b7173, limb1: 0xacdf286e6dda680bd7f43d82, limb2: 0x157ceffdd1328af6f6e5b95c, limb3: 0x160cbfb08a54af89dfeb868a, }, r1a0: u384 { limb0: 0x4ec774d0354010b5e861fe21, limb1: 0xe9ed591725d9834344f2c119, limb2: 0x6381097476472bf91dd79d7, limb3: 0xd2c74ef03918d458f67a780, }, r1a1: u384 { limb0: 0x818639c9a397b4bf6f38e3d3, limb1: 0xa7c0dbcc3c17ee84d28afb8e, limb2: 0xe2e3c55da00c29aaff4a0571, limb3: 0x13b5dbdad3c6aeb8219944e7, }, }, G2Line { r0a0: u384 { limb0: 0x1b9ff207335fcb7b28f48654, limb1: 0xaa059fc26f53a4b15d861e5d, limb2: 0x7409e84a31ef57e217e3d45d, limb3: 0x8f022244af0b719146e8cfb, }, r0a1: u384 { limb0: 0x1fa9d79eb0320e586c2d096a, limb1: 0x8fde2d5c9ef41c1612865896, limb2: 0xec88b9f86c99799b380ebac9, limb3: 0x72c117c18b8dfa89321c27c, }, r1a0: u384 { limb0: 0x4570eb295684cad19e7cfded, limb1: 0x2e204f8114c805f866cca868, limb2: 0xba0509fc0eea7cc65c8b3dee, limb3: 0xc7c1e717bb7b078054d3851, }, r1a1: u384 { limb0: 0x25eb9fba51d76d2292c1e2bf, limb1: 0xa43de47dba6db4c3e5c3d8b8, limb2: 0x365ea08af8998db774b8b61e, limb3: 0x6367ffd71d3c44095424fc7, }, }, G2Line { r0a0: u384 { limb0: 0xbc6935d4f6d5d4aa0ec642b, limb1: 0x1d6e2d4d9106b5ecff982a66, limb2: 0x5e8531cb5f36f807288638c1, limb3: 0xa7631b901291f87b31ffb35, }, r0a1: u384 { limb0: 0x65c64711fddc1f635ae6e574, limb1: 0x9e9ea3a84804bd3fb56c4c1e, limb2: 0x91aa460ccbc52472b90ce0b3, limb3: 0x13b3c25d2edef40f806ef614, }, r1a0: u384 { limb0: 0x9b3f8b6844ada64077c6dc45, limb1: 0x78a3cdbb5ad78183e72572d, limb2: 0x34763f876de5f0004af6d3b9, limb3: 0x148f019d0a59b993e259d612, }, r1a1: u384 { limb0: 0x95843db564a4b5a94a1b14c4, limb1: 0x832d5ca2f0420c55f9007f4a, limb2: 0x56047bf28b726775ad1f126a, limb3: 0x13283203fb6b13b007258900, }, }, G2Line { r0a0: u384 { limb0: 0xd8934218abbe5eda42e0374, limb1: 0x4efa70797ab04d5777f18cae, limb2: 0x657bd72dc32622552c01c3a1, limb3: 0x86675ec3781ecc255b9b8f, }, r0a1: u384 { limb0: 0xdb3cdd784259d6f00a05188, limb1: 0x4d7d18f24dc5139d8829c6be, limb2: 0x9067fb6cb2810aa19e5e838d, limb3: 0x99b7b955ea60c02306dd019, }, r1a0: u384 { limb0: 0x9569e6a9a6dfc936dc66c37d, limb1: 0x8ce5600bf62265cce1600d14, limb2: 0xe437be1358f94ae1da7ba693, limb3: 0x26001dbd81fb98024703f0a, }, r1a1: u384 { limb0: 0x38347efb475ef26461922ce8, limb1: 0x434f13930fd2a42336fc5a71, limb2: 0xa611a973d0bf99e3535651af, limb3: 0xf623d241cf8d903d2d48305, }, }, G2Line { r0a0: u384 { limb0: 0x1bcaf5fed0bbcd1a934472b1, limb1: 0xbd468b117d710b48e9e33679, limb2: 0x705c11550a052c1bb8ccc4ea, limb3: 0x6f15de535822689ea86e65e, }, r0a1: u384 { limb0: 0x95d3b31c7228eccaeaf12838, limb1: 0xa92a1590da11c257350bbf1f, limb2: 0xd4e2202f05265990a6557be7, limb3: 0x11f8c21a8309afd4c60ea316, }, r1a0: u384 { limb0: 0xa27a54fe04de2265b2fe96e8, limb1: 0x53dcd9b100331a701e8ba5f9, limb2: 0x57845f6219e44f2109c795e5, limb3: 0x22a93fc0d0171aa6e5a89a2, }, r1a1: u384 { limb0: 0x95504a55dc0699b071a8dd33, limb1: 0x372f0a3e8d642e214174c90a, limb2: 0xcf8e1be4fec9c43ae6e6c879, limb3: 0x112c15cec305822060501913, }, }, G2Line { r0a0: u384 { limb0: 0x7464425eeb75a1d3a3486fba, limb1: 0xd4f0931c31459109811008d1, limb2: 0x5aac0cfc9b43343826136afb, limb3: 0xf16056dd2e8b5f8240d4ac7, }, r0a1: u384 { limb0: 0xee0993ef125a22747400b5ea, limb1: 0x438805278ea9e18b001cf7da, limb2: 0x11c5cbb3ae17332e06f5b415, limb3: 0x134957b7abe963c5d074abc9, }, r1a0: u384 { limb0: 0xacf8eb684fdd044dd83f813e, limb1: 0xcb5dae51f81a4969f0370c67, limb2: 0x491fc4a63ef64f17b8aa0d30, limb3: 0x188b4199d41c95a7991f2d89, }, r1a1: u384 { limb0: 0x1f69582489be9a39cb94c326, limb1: 0xdfa20ef759cc430ed060c20b, limb2: 0xeab00aeca148c6a408bcd34a, limb3: 0xd6a605bcb73c8061942fb57, }, }, G2Line { r0a0: u384 { limb0: 0x1a00fe857129fb0706afc443, limb1: 0x699bd305a05a49e5376fa125, limb2: 0x5123ef38664f302385f6e355, limb3: 0x1138d923f33a7667d3f218ec, }, r0a1: u384 { limb0: 0xa8b0789c07a18e1212c35b42, limb1: 0xe6062cdb7c672277492e486f, limb2: 0x21d77ef2efc7c58cc7f07fa, limb3: 0xe1c4f192a69167da717d052, }, r1a0: u384 { limb0: 0x1083df31373d17c10c6f96ce, limb1: 0x3c0db10e3745399ce144521, limb2: 0x4be19a961fa7762df7e8174f, limb3: 0x157ba9b5969d3125fa86ea07, }, r1a1: u384 { limb0: 0xd3bd3b38817ebc095decab10, limb1: 0x99d4b7d79829b113b4490f45, limb2: 0x205d4e72b9d31001a602b263, limb3: 0x16fedb246b41f78c5a46ac30, }, }, G2Line { r0a0: u384 { limb0: 0xed72eccb4e30eeaf3b992446, limb1: 0x14e0585cd696c72e9adb4736, limb2: 0x7df5eabb84672fab4d4a6e10, limb3: 0x2d6c8112234d7f18ea478ea, }, r0a1: u384 { limb0: 0x95586dac212579b39f39df97, limb1: 0xff0488c63a739029f85aec22, limb2: 0x38ce286aeea4511ddcb23d59, limb3: 0x444323d14c7a3549b9f6b27, }, r1a0: u384 { limb0: 0xac929d1bb6bfa0df5bd0b951, limb1: 0x9a5e39e018083d89aeeaee3d, limb2: 0xc84698d95675ba2c1b93662e, limb3: 0xa82a23fd9338c15ba09139b, }, r1a1: u384 { limb0: 0x8a89d4ebf46cc78b9a67add2, limb1: 0x1761e578b693547ecbf4817f, limb2: 0xbd9d23d081864a636a27dce, limb3: 0x40d68a72ee4363db50d3c92, }, }, G2Line { r0a0: u384 { limb0: 0x5a204b2b8496bf6fd941adbe, limb1: 0x9c069a02ba48bdf34aed625e, limb2: 0x5459c5d76fa5925ae4b04121, limb3: 0x2c12f82e0dcd33df5ac48a7, }, r0a1: u384 { limb0: 0x38870a783f4004476ddafcab, limb1: 0xa98e80effda828b7a2908d37, limb2: 0x8152285afd4302b3b87447d1, limb3: 0x183817defa2bfa474a6e1fdf, }, r1a0: u384 { limb0: 0x6bceb45fb77a9e20a0152815, limb1: 0x20636e0b8ad36f12a65176b1, limb2: 0x7ee4c1a972b5386c1303665e, limb3: 0x71199de43d6e23e8d666f51, }, r1a1: u384 { limb0: 0x4f26920f05c3d38669cade7a, limb1: 0x9028c6ddc1cd21f516bc0d4, limb2: 0xca7680b59d22ca8045eba3d1, limb3: 0xc81627ec1998db363f1c26, }, }, G2Line { r0a0: u384 { limb0: 0xbdda2d3c31051f4071ae2945, limb1: 0xbc66726ddee31b37d058d7e5, limb2: 0x9f4eb741ac78b510ccf452ab, limb3: 0x65fb0c0d47de8795557bd2f, }, r0a1: u384 { limb0: 0xb9c37518dd4a05df7a4d6dc1, limb1: 0xd4ee64da91ea67b8a4525b4, limb2: 0x73a813ffff40ee810a12214b, limb3: 0x7f9fda3fa03c5295720441d, }, r1a0: u384 { limb0: 0xaa6d391bd6b4113145484e4f, limb1: 0x86d3fa56727d8879496d1827, limb2: 0x71223351a13a9577646c0ec3, limb3: 0x5c4513dff602b8ec227f711, }, r1a1: u384 { limb0: 0xb9b127f0cbfc3172bba7a933, limb1: 0x10d730ec07d1e0f84c5c6c34, limb2: 0x693e354e2246bf96f3ebf563, limb3: 0x1163f7e15fbd10f4086aad86, }, }, G2Line { r0a0: u384 { limb0: 0x324f76ca3eb989e9ccb12696, limb1: 0xeb1a302ddcf16336370c347d, limb2: 0xcd35a0d29495cd0999ca03e2, limb3: 0xa74e5ad34004c7e57d2a14e, }, r0a1: u384 { limb0: 0x525e1ef1f8480fcfda387f8b, limb1: 0xaf0c314992fa29dd3e45eeec, limb2: 0xae09cf42c0a53751919fe1b1, limb3: 0x106562358cc0ca813815bb1f, }, r1a0: u384 { limb0: 0x19d180d969228995aa21a1e5, limb1: 0x34f6f5fbd9b098d1b3efd0b, limb2: 0x3533d5af99af7a4dc323297a, limb3: 0x1604dfd23c32fe35ae8fd03, }, r1a1: u384 { limb0: 0x95f9c758ce1e361efe4c0032, limb1: 0x910fa18b85ad81540e31e1ff, limb2: 0x564537d6beb09c576a28d18f, limb3: 0xa483de0527b3738ae218c4c, }, }, ] .span(); let hint = MPCheckHintBLS12_381 { lambda_root_inverse: E12D { w0: u384 { limb0: 0x1d4eab620cf33a8eded7fd2c, limb1: 0x45778308171f9267fab69519, limb2: 0x874b1a6540a5a24a4fd9c68f, limb3: 0x521ad898cee9071ebcbf44d, }, w1: u384 { limb0: 0xa9f581d9c26c7bc732af4135, limb1: 0x5cecf0013c8d5695a1e6a597, limb2: 0x66651ab83510fb89f6b2afe4, limb3: 0x5966d7f6d173ea01e1a5869, }, w2: u384 { limb0: 0x7a64d089a1a115a3eab1a695, limb1: 0xccdc16d44e3cbdf8393eb355, limb2: 0xccd24b9c3e637b240a4100a3, limb3: 0x110012a0987f151e6eacf408, }, w3: u384 { limb0: 0xd7d9acb3a8622465c6b1c0fe, limb1: 0xcdaab0fcd1147d96b5521ac4, limb2: 0xae897c7118bbf9c0479cff61, limb3: 0xfc350acc198fbd5b4d95cfc, }, w4: u384 { limb0: 0x32d5c3bbed4da9a68948c926, limb1: 0x6f68e9017165ef8db1a4f975, limb2: 0x8c36a4b56c817816904d0605, limb3: 0x6d44964cce393f36664dfb7, }, w5: u384 { limb0: 0x9715bc72d9969488889a609f, limb1: 0x2b0c186b4950da2943f4ad01, limb2: 0x9a49542de5fc03a989fe46f8, limb3: 0x86f3ebd100f5f5157bc57f7, }, w6: u384 { limb0: 0x54e14ea09aad1c01c5c5faac, limb1: 0x65bf572081d748820d57d62d, limb2: 0xe04c49ded673151413b8ce9b, limb3: 0x18776284b17c0858f647e075, }, w7: u384 { limb0: 0xd4ff280a7232eada165a4400, limb1: 0xf5bd8e019057fb48dad4ea34, limb2: 0xae5bd1a1ce889e14808c4ee8, limb3: 0x647bb2047c521d397fd0f7, }, w8: u384 { limb0: 0xc8266658d2a03e597cfec8fc, limb1: 0x62aae0152d3543705d87df48, limb2: 0xfc4fae663d5040baacca25a8, limb3: 0xa97b4be53ee479681acc5eb, }, w9: u384 { limb0: 0x45b2fc96a09f2ffc8b84a4dc, limb1: 0x22bbd02e82d79e84d590ca96, limb2: 0xf24bb9b22ece2fe9e392d6ff, limb3: 0x1338aeb075e78cc7505a5d70, }, w10: u384 { limb0: 0xe4354c04ab5208100a0129af, limb1: 0x4675bf96847cb9d629da62d1, limb2: 0xcbb4b845ab04d0a51ea25ee0, limb3: 0xe608702099837e04fc2e999, }, w11: u384 { limb0: 0x3cca5a2ae19eefaf128521, limb1: 0x7a10d38aa97360f22cd213ab, limb2: 0xe8162fd74d36e0786ea6a88c, limb3: 0x12c968f3ea7364e3ee21b8b2, }, }, w: MillerLoopResultScalingFactor { w0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w2: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w4: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w6: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w8: u384 { limb0: 0xf1ca42a0e74df934924892fb, limb1: 0x91e7a80fe41d8f58d83f1513, limb2: 0x8e9a0930581e2c940247cd09, limb3: 0x18bc5b99f39cbf0fd8d08768, }, w10: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, Ris: array![ E12D { w0: u384 { limb0: 0xf63d7acf09f9e238c86f7575, limb1: 0xaf8ac67e915aa56c1f18943c, limb2: 0x1f0d89e52ce00053fb4cd271, limb3: 0x6dcf1ec2bee9d55fd7c7dd0, }, w1: u384 { limb0: 0x8c542fcbddc8a2f30326ff28, limb1: 0x93400f32912e689ef50ff729, limb2: 0x5e397600577a07eddd78a637, limb3: 0x7f05f480f32402899fc238d, }, w2: u384 { limb0: 0xfc8e47f2ce78aed551c79270, limb1: 0xb7505079976315ae30aea8c7, limb2: 0x1397705b5336a8c404e29aba, limb3: 0x71d870e4553f214175e57f7, }, w3: u384 { limb0: 0x32f0ae88611fa10260d597c0, limb1: 0x29a0888f8ce8b899253e37ae, limb2: 0x7123a17956e452893cabef6a, limb3: 0x37df42454ed3974bb2b32f9, }, w4: u384 { limb0: 0xa72f0e1e9c109d242988e116, limb1: 0x54b5dec1284a8c9177b3c945, limb2: 0x815f8322190dde62bdc8a55e, limb3: 0xba703f387adf415b877fd75, }, w5: u384 { limb0: 0x1f07d02f85fc8a875e197521, limb1: 0x5585ddebaf32dc4e03ae577f, limb2: 0x6f8907d9616c496a0f51dbcc, limb3: 0x14068f72159c932c910dd512, }, w6: u384 { limb0: 0xce6bb359366acbb7781372b9, limb1: 0x7c5e8df6083d142e2fd17ccf, limb2: 0x1174df6680c4991d4d20cc80, limb3: 0x17dfc12834ee7334831b24af, }, w7: u384 { limb0: 0x95daa3bc8b9ac34a59ff12f0, limb1: 0xa2349e79dd3de20eea74d8b, limb2: 0x90308dd36ed98b5e1d50a816, limb3: 0x17d3b0da632dabdf4ba0f6c8, }, w8: u384 { limb0: 0x4c5d01ef3358bf5ad26286cc, limb1: 0xed0c77db94e0738119993eb, limb2: 0xfd31f8f2bab3cabf17b82c77, limb3: 0x17ddaa28e29c2317b96c21b7, }, w9: u384 { limb0: 0xea817f28532b8d5198e199dd, limb1: 0x99aeb257fdcdc23c15eb5315, limb2: 0x31387bb67348f155192cf97f, limb3: 0x22b2500baf6ce28a86979f, }, w10: u384 { limb0: 0xb0e382b90ef6654c3bd2e20c, limb1: 0x4d096e4e54120fe17325dec0, limb2: 0xc2d4414912600bfec37d116a, limb3: 0x6524f53a10bd1ed1f7de6ac, }, w11: u384 { limb0: 0x8a680e766390ddaa62af47cd, limb1: 0xf23d641db780ebb70c7fbfbe, limb2: 0x531a0f1fc69bf6acd1695e9a, limb3: 0xebb85352772f284d12c95bf, }, }, E12D { w0: u384 { limb0: 0x46f601ab362202e8276c007d, limb1: 0x586b3c2927dbffdd38a1a44b, limb2: 0x6b07370100418d3fcd5ad5c5, limb3: 0x1727a4684524eb2175d31f50, }, w1: u384 { limb0: 0x73738bbe4943b6aee387caa1, limb1: 0x755dec64232750ca866647b3, limb2: 0x52a64d020d10ab12ab460dd, limb3: 0x57d77a9e8e6cd838edc1e63, }, w2: u384 { limb0: 0x5f2c12da594e423a2108737d, limb1: 0x3aa7e22e27bccb5d4840ac81, limb2: 0x40d4f01ea67f2f082b59dec0, limb3: 0x42e0115d1c7594745490233, }, w3: u384 { limb0: 0x9fe7471a196e8bd9a0db6863, limb1: 0x27379618cb58b0b55c0acff3, limb2: 0x1d61ee1f8c5c6c2e40b633da, limb3: 0x54735182a914667a25226c9, }, w4: u384 { limb0: 0xeb6d788023db42ceefa73d8b, limb1: 0x983e97ed4491a3cda57fabeb, limb2: 0x9449deaf0a40d6de94e8347d, limb3: 0x14276d83ecbbeddabdf9bf5d, }, w5: u384 { limb0: 0x411db147cc5627ef50c9210d, limb1: 0xa34577b4dcbbb76911a90cbb, limb2: 0x5523d4d906c194a134c2695b, limb3: 0xda9195159528161fa4960f2, }, w6: u384 { limb0: 0x7df4506c40e2424b24c6b69b, limb1: 0x934699dcb5cf7eab408dbe02, limb2: 0xf98880b746c6ce0f7f41377d, limb3: 0x9552828c7dcc07d56efc554, }, w7: u384 { limb0: 0x7f232224b4fe0b20245f2fd4, limb1: 0xc9d51a652303decdf4907f6e, limb2: 0x71ae0aeab8e0333d7ff3018, limb3: 0x122dcaa1ba9a8a8613064735, }, w8: u384 { limb0: 0x697c449335ca5f9d21b7f654, limb1: 0xf8a13e81943a4a18f4896097, limb2: 0xde94de861275afae359c3016, limb3: 0x112f00e12354b1ad57581a4d, }, w9: u384 { limb0: 0xfc2ecc6d437c20102b74f4ae, limb1: 0x3fc77a685f0e4ae94092405a, limb2: 0xbd067589e294b4d708407307, limb3: 0x13bbf456483cd4566ed59718, }, w10: u384 { limb0: 0x920a2dc4d6405a69dafd98b8, limb1: 0xaefdccb098674950b928bb5c, limb2: 0x2e93db68f2ed629f9872a3b1, limb3: 0xeef615cd28929e56a59bf2e, }, w11: u384 { limb0: 0x32fb24bfa3edf65997e82785, limb1: 0x11a11c3e6606acd9cd851f81, limb2: 0x55f01d098689453651a335e7, limb3: 0xebec00852daa59ee4861f6c, }, }, E12D { w0: u384 { limb0: 0x49168a1f3a22e43aa9131c14, limb1: 0x6ff87ec4e2647706b3fde592, limb2: 0x9ebb9d7748bb4b630bb9e8ad, limb3: 0x10bbd67a2e6b8bd12ca2a8fc, }, w1: u384 { limb0: 0x4dbbf2265569906a0d24b1bb, limb1: 0x4e4e1893305748d5ffd9fef1, limb2: 0xf13628a4c95b6fc55a9eef6a, limb3: 0x10b832788eae08063407690b, }, w2: u384 { limb0: 0x1acce936e2cf8c477b127acb, limb1: 0xd6ec68233a19bba472836ae0, limb2: 0x45a97406d2a99dc971e2c9eb, limb3: 0x19496c56f34ced68a7cd75ca, }, w3: u384 { limb0: 0x22cc017e588ebe02c9d8944d, limb1: 0x4a12e88d4c855c6e93e88d24, limb2: 0xac08da0adfb221ad320d929c, limb3: 0x925d1d1ef9c0beba6f0a34c, }, w4: u384 { limb0: 0x3de8b6df17b043f047eb3d95, limb1: 0xa0f7fe84c2f3b0c22ea84f0e, limb2: 0x9fc100a34798496f25a17711, limb3: 0x63551db5a468540a882a52a, }, w5: u384 { limb0: 0x6acb9303682c1c8ca5fac965, limb1: 0x5743d3be8818de60a9a1a515, limb2: 0x7df5b7b9df88e4cf55e829b7, limb3: 0x1452bf2c3fe715937d83b5c5, }, w6: u384 { limb0: 0xbe1e1ab9e46108a3da2287de, limb1: 0xe10d9eea83bb012f8e01a28e, limb2: 0x4e0f865fe70bcd3a215ac2d2, limb3: 0x159fe260119fbb98baf253f, }, w7: u384 { limb0: 0xbe7a9434b3beb015897656bd, limb1: 0x6fa097bc9669f5a4c6e33dbe, limb2: 0x7884c156e8281d85d5a0ee4e, limb3: 0x2cf0869f40402c8b1642954, }, w8: u384 { limb0: 0x95cdf327419c78b6710a6c8c, limb1: 0xd3dded1b3595c3ce4312a36a, limb2: 0xc2ccd8f589dd387f86500444, limb3: 0xd2c631a38ce47d9e8f0ee1f, }, w9: u384 { limb0: 0x7e6f24ade84350245ac9e72, limb1: 0xb504394fbc5fc5b04e7a8465, limb2: 0xc8fb3405378036f4c5867363, limb3: 0xcaa4d999eec4b8f23cb8406, }, w10: u384 { limb0: 0xe7e990c95a109a8caa63a02b, limb1: 0xde60f93bdf429d379caaf598, limb2: 0x434f9cece5b000d281057b64, limb3: 0xdca015d5a2e52becd816f7a, }, w11: u384 { limb0: 0x1b9bf5b1707249c394b385b4, limb1: 0x591ab99d664c7bb9537bd1bd, limb2: 0x663ec0365e65c06194887eb1, limb3: 0x6995ffd83bb53d7b9787c81, }, }, E12D { w0: u384 { limb0: 0x4aa7f5d7f85dd4c4af5e97a3, limb1: 0x4c65d12afeff17a68cd917da, limb2: 0x6530b54704b338c9e41d551b, limb3: 0x7f7956e7258b204e6bb76fb, }, w1: u384 { limb0: 0xc3b5ae69e8bc70cc1642be88, limb1: 0x9e9f6a61c9d21a413a15b875, limb2: 0xfb2649c3298b59c310e02346, limb3: 0x61f63de6863a0737ea4c564, }, w2: u384 { limb0: 0xe65eff130e3bf3e78e64a8d5, limb1: 0x3c7415a182a906c0c440ec19, limb2: 0xb16f94ad9149d23b673b8b03, limb3: 0xd54ccfbe6ce28ca435fb866, }, w3: u384 { limb0: 0xd59039e2f71aab9d24fe1f50, limb1: 0x77632f67dd17dd934dcdc3b3, limb2: 0x49405e14816e285681f6d108, limb3: 0x5b0b2403b504c7c3c04fa26, }, w4: u384 { limb0: 0xeef17c2cd5a8e39666056b16, limb1: 0x2a2d7664553675a1cd30ab8, limb2: 0x112482fcc1899b14e6ac805c, limb3: 0x120e02660f9058203246fbf0, }, w5: u384 { limb0: 0x224a2242169998bd45bcfecd, limb1: 0xf40bce68d096dad390d28e98, limb2: 0xd0f1e29a3fe03f4e210140c9, limb3: 0x848bb58f7c097a46b3a03e, }, w6: u384 { limb0: 0x95f2d0acc60f04b266569319, limb1: 0x7dd58a061d1a3e0141a6e2e, limb2: 0x494f27de393ef818bbd4517d, limb3: 0xdc72aced2c6f4a5c4819c14, }, w7: u384 { limb0: 0xd77df88de226de432ab03d2b, limb1: 0x333622e9b8f46b0713f2f072, limb2: 0xea5a83207f896f6abf8ab0e2, limb3: 0x4a715b7a58dc6543add0fc9, }, w8: u384 { limb0: 0xc2816abbab513ff9a9c7b5d1, limb1: 0x82fde4beda8b9e6a5885c858, limb2: 0x1f84be86960bad82590ceca, limb3: 0xc04235cb1fe7822f16be8bc, }, w9: u384 { limb0: 0xedb79bdcbaa9dc247ec2effa, limb1: 0xa269f5787fd2b0bd9ed885f0, limb2: 0x8bf6b02312251b650e69f258, limb3: 0xe44406c2cb2d23cae0a6ab3, }, w10: u384 { limb0: 0x29dfd9eaed5f6ee84dbefdc7, limb1: 0x4efb1890226e01d82c5dd985, limb2: 0x485f10c54276bce940584dc7, limb3: 0x86501a5cf1b338e3103b59e, }, w11: u384 { limb0: 0x7302b90bf0cd9d620156bc89, limb1: 0x7f5499c66dc28fbd4c320700, limb2: 0x34cc18aa5ab46c409e63ff3, limb3: 0x10a91f5f4e43b2f252c415e2, }, }, E12D { w0: u384 { limb0: 0xb719f9dec03ab8f164bb3a6b, limb1: 0x20cb7011e080d653d9dcc756, limb2: 0xe2dbfe688c03d53d6a00fef1, limb3: 0x813beb1246503c45e0f230, }, w1: u384 { limb0: 0xeb0491457c8c6edc155753c1, limb1: 0xd0271cbb54b204bf4b295f5d, limb2: 0xb26e1eb4fab09d1d4faefd5b, limb3: 0x15dd36f07b01019665228060, }, w2: u384 { limb0: 0xbaee8621d18761c3b2904a73, limb1: 0x816d9cac84eb28a5e7d9e25, limb2: 0xcd1c794f2313f6772e45355d, limb3: 0x124a87dab04b19db1b8bd588, }, w3: u384 { limb0: 0xfb0de8939a0760770b40a9cb, limb1: 0x917a039550c37cea059c85e8, limb2: 0xc5edbc8267c1b80ef97cef18, limb3: 0x324f9d878506723c60a4345, }, w4: u384 { limb0: 0x83c439e7eafe348b8671a385, limb1: 0x3bf1e6a663a56bf87b16e6f6, limb2: 0xe5ca68a4b426e6b7c000e7a0, limb3: 0xc7c38ce48b61dd7513469c4, }, w5: u384 { limb0: 0x32bad965995076769d669ace, limb1: 0xd5949cc1627771c51c0bb4d3, limb2: 0x5d34827387c8e3fa45ba7b49, limb3: 0x14a6bccbc3a0c7ead062ac2b, }, w6: u384 { limb0: 0x5221d77a4e1c87eb4fd9fcc5, limb1: 0x9aee6eec1d7ec0ce27a00cea, limb2: 0x8181e5c1b1a7a1b1e6454e58, limb3: 0x16364ed330a5e5ac2211ed9c, }, w7: u384 { limb0: 0xd0db08209c90ad48501b74ca, limb1: 0x6b1f991adece59fe7b2d5db8, limb2: 0x2a617c6295c1be2c062284a1, limb3: 0x15df50360a83866f4fa35544, }, w8: u384 { limb0: 0x4200fde82b3f83f87f7adc25, limb1: 0xba304360e4b83811e874ab86, limb2: 0xc8370b31cae44f74c2d81952, limb3: 0x113787d1e314b4473cc3f55, }, w9: u384 { limb0: 0xe403a7fa1d756ed0dba8fb34, limb1: 0xccf3814c1270f5a1212a245e, limb2: 0xdc74463c46f3f26d79630a77, limb3: 0x3dee0d30b7bb94689c6daee, }, w10: u384 { limb0: 0x3c74ad56a6efcb3c5c1d9c8b, limb1: 0x25d0f254898fb3c093097f4, limb2: 0xf5331098d7ed88bea4215633, limb3: 0x1f45a4472f7628ea0cba303, }, w11: u384 { limb0: 0x7290b9b901cdb657a706a75b, limb1: 0x54d189205a59a1173bb4f663, limb2: 0xe75abfbc13c6d01ac5579e1e, limb3: 0x345cf5c394a7ac50eee7a9f, }, }, E12D { w0: u384 { limb0: 0x344bd25fb7f83d9dfae06f6a, limb1: 0x22fde129b885f0c710ff71ac, limb2: 0x783a03d3f6609e73117cb2d7, limb3: 0xe37e60a61076748d0233945, }, w1: u384 { limb0: 0x29e60bd8298eaf694914bf96, limb1: 0x4d570c1cab177ec2719c02ba, limb2: 0x2b7031090424638824b4463e, limb3: 0xc26aba31fe7a05a5bbc7e8f, }, w2: u384 { limb0: 0x574b39c83abd56863e6172a, limb1: 0xc54b9b6afa11629a99d4636f, limb2: 0xa12f92bcc3f8005b33eec0d, limb3: 0x8d4ad3c7fa6a1b149c19888, }, w3: u384 { limb0: 0x2c11d194c9576b7f466f32d9, limb1: 0x7c55ac60cbb6cb8a927390d5, limb2: 0x57cb35bcc9af97e319be764e, limb3: 0x11c8f585011f475dce234ff7, }, w4: u384 { limb0: 0x33bff81455e77429bd4ee8aa, limb1: 0x1cba0458d1e364c2c64ece45, limb2: 0x8c03288861b89e4335b14d14, limb3: 0x64b8c93dfa5c160f9493484, }, w5: u384 { limb0: 0x2aba92419b5fd3f35844fce4, limb1: 0x429bb226e16a911555eedda0, limb2: 0xc2c54fa7a26bb7296669f9a0, limb3: 0xedb5a603fb61c4588349061, }, w6: u384 { limb0: 0x71a798b6e55ee50c3f59159e, limb1: 0x858e9f261b23e89b180b4c4a, limb2: 0x751305c885f1a21af7ed4e1e, limb3: 0x10964f9f66dc1a6d9df88ce6, }, w7: u384 { limb0: 0x15bad475a51bb3db482ae425, limb1: 0x7254f373bd19c4481767607c, limb2: 0xc11e80391c7c6aaadbfdde61, limb3: 0x15e22e3a46ee30b26a98c6d8, }, w8: u384 { limb0: 0xf78a0e313b61e2ac5105e1a3, limb1: 0x47ec84e1592e649c61bd8776, limb2: 0xe7189f594aba4ccfc6a5a11c, limb3: 0x2f7c3dbf00640bb0148a21b, }, w9: u384 { limb0: 0xc41f29e4dd6b145c6b661df5, limb1: 0x673062ba459b3d042a0cee5f, limb2: 0xcf47a3f2dfef1e55b3e97b8, limb3: 0x19a49c7db5078a54448a9c32, }, w10: u384 { limb0: 0x7da75932777016e386681a3b, limb1: 0x5dfa78392bafdfe2ea984a6e, limb2: 0xfa0b5780b4722ac13170d67, limb3: 0xdca20a45aac899ff8534471, }, w11: u384 { limb0: 0x20d272afe37306d5a752a35c, limb1: 0x3cb6565178072916bd25bcee, limb2: 0x84f886cd8d78cde2acb45c73, limb3: 0x166ebbd52543e9a2ad6f564f, }, }, E12D { w0: u384 { limb0: 0x71bb2c644889a2139f430cad, limb1: 0xf453e8802ab1059d1d517b47, limb2: 0x8e72791f4287dfbb95ce68f5, limb3: 0x19452bfa0813f110ecc74e8f, }, w1: u384 { limb0: 0x2daf0b4287be1963023f46d5, limb1: 0x534ae95e7dd740e2800fd7, limb2: 0xd5e9e2cb66b4ffcb00e4fb35, limb3: 0xca9bc3e4e55c038c84e0b99, }, w2: u384 { limb0: 0x5a1a5909ad03ea711e0f7d50, limb1: 0x4f450184eb018a3bbee2646c, limb2: 0x132d9cf05d2a74ea4af12f6a, limb3: 0xea601cf5926174f615ae34d, }, w3: u384 { limb0: 0x56009030241b25051e7c60ab, limb1: 0x49653a64f27328b24b36a431, limb2: 0xcb3f2876ee487db94d9a8c8e, limb3: 0x176ccfe7df56c88d4d77e6b0, }, w4: u384 { limb0: 0x777b0007ff8949336580dafd, limb1: 0x6240fd408535fd5d5e2a239e, limb2: 0x1a8a6e4d29d8df1d1a44f128, limb3: 0xb900c08323d8fad4afd7461, }, w5: u384 { limb0: 0x4804154f8db931d57b3d4952, limb1: 0x589692071a72e7feaab93c58, limb2: 0x4893fc502e75c3fafb3cffa2, limb3: 0x78ee6e0f71424add9367862, }, w6: u384 { limb0: 0x56f1e165c65d6701d9c8d72d, limb1: 0xc70ec69746317ab3eb2e5b49, limb2: 0xeb1c562f709f33c0e19f16e0, limb3: 0xaed371d73f9f750e9779d14, }, w7: u384 { limb0: 0xa011a3fd58c09a6e7f3f76d2, limb1: 0x5d34d82a867f4d1c3bd46279, limb2: 0xae3b42bb54a050efd9902ac0, limb3: 0x10084af27180873684abfaf8, }, w8: u384 { limb0: 0x8c40fae1d51740fbd0c540ce, limb1: 0x69fff344d5f472a1c52d83c0, limb2: 0x7b8df84c1f122b0449441a27, limb3: 0x142a792323b26d9f32f310d5, }, w9: u384 { limb0: 0x4173f4024c385b2b52eabf19, limb1: 0x4debf14fe4434f2cfa941bd8, limb2: 0x62eba10a2346416ae61c056d, limb3: 0x9baea19f3c57310aa68d30f, }, w10: u384 { limb0: 0x470c9a5918ea3b12844359f1, limb1: 0xf97a14494853215d38d3754f, limb2: 0xd23e9687409056661abb709f, limb3: 0x11394e84e3642ccb7ec05dad, }, w11: u384 { limb0: 0xe732350ab1f36f07bde5c4a7, limb1: 0x265db95a4305a9c4ee911f7a, limb2: 0x330e500f64fd18af7a3c3d78, limb3: 0x114243c10cb4e98eaa22527c, }, }, E12D { w0: u384 { limb0: 0x5c2cfc6a914fa5d7980965e, limb1: 0x80de48670c60e5949512196f, limb2: 0x23d4df1b56009e60e26dc15b, limb3: 0x9129169ad34aad0171a90d1, }, w1: u384 { limb0: 0x1b23a1da94d4d9ad13969f10, limb1: 0x96cb9baefc5a118f384b27d7, limb2: 0xa0992f485a9410d7cce6e205, limb3: 0xbb7b5611649e884b101d9c3, }, w2: u384 { limb0: 0x60891a8a266a27cee0a09a1c, limb1: 0xfd9b045e70482ec052ffd6c, limb2: 0x4a82d989d3fcfda3d23d0789, limb3: 0xbefe911ada4c0fd8150056e, }, w3: u384 { limb0: 0x7109634c22a12f03bc7575, limb1: 0x3560465146565541ff8326a4, limb2: 0x9e4388d110bae139a5146460, limb3: 0x18df1bb4889f0e8436e35316, }, w4: u384 { limb0: 0x38819b839225ab70bb79ae23, limb1: 0x2640a881db6fa15743615201, limb2: 0x61801751cd1a8742d06e98e7, limb3: 0x5b766333766879a731ad833, }, w5: u384 { limb0: 0xe3650f335d56af0a89dd5cf7, limb1: 0x5437795ba9d2867f64f5dc8f, limb2: 0x41358fb12e6a5ed63208bea, limb3: 0x1304e9875fcf1bbe0cf4984f, }, w6: u384 { limb0: 0xe06199520d32463c4895fb76, limb1: 0x239e44a1b7472bb9e3928c3, limb2: 0x3faaa7126afa86e0ccac02b4, limb3: 0xba0b261bef58dc64082d841, }, w7: u384 { limb0: 0x80579b7ecabe4b1c6bd27e7f, limb1: 0xda54e55ee34e1ce69eb01380, limb2: 0xc5e78f1b6a7bb2c57094c127, limb3: 0x3d4150c6b4a01b418d9646c, }, w8: u384 { limb0: 0xb2ecc04591fdd668de2d86e2, limb1: 0xa63ad6aa31101e6c4be44934, limb2: 0x77fa5f8d2026c8f0256fcf43, limb3: 0xea684e10899989d49474ed2, }, w9: u384 { limb0: 0x67f59a72e128d99d7b3a3bdc, limb1: 0x997cb42e388262b6a92cd769, limb2: 0xf23c7a0ea08062d3297e0143, limb3: 0xce8caed0b31565408c2a7e9, }, w10: u384 { limb0: 0x4be943eafe89a30984531544, limb1: 0xa2d077ae492d257ff11bb7ae, limb2: 0xa222ba8de8769fd438c2817, limb3: 0x2255ba650dce97fbed316b2, }, w11: u384 { limb0: 0x4d21bea6b45611509ce730eb, limb1: 0x340fb492f0558334acb4ccf8, limb2: 0x5c3040b88f05c25acb8b35ce, limb3: 0x155847f8080fd6991320f9ca, }, }, E12D { w0: u384 { limb0: 0x25d13b5892adacfaeffe2aea, limb1: 0x2aee4febbea2f40459b107eb, limb2: 0x19c5c4c41dcd61a6f4ba7579, limb3: 0x13241af723624918fd903b28, }, w1: u384 { limb0: 0x8ff9b04334f08e4c49e8ce2, limb1: 0x28c2966f31e0e08817c5cf74, limb2: 0xd60b874eea904a280be515a4, limb3: 0x18f183d3d62072e6b66f4110, }, w2: u384 { limb0: 0xa22500a03ee8ebf353a15614, limb1: 0x279f607a1d94cf8727ad1ac3, limb2: 0x9d5cc495009b0929965f222c, limb3: 0x1029d8c9b14ba02bd2caacfa, }, w3: u384 { limb0: 0xd425541781902201ec22f2a1, limb1: 0x3c388cd7504114ac6bbb4136, limb2: 0xe6bf8d9f49e199cf7eedb194, limb3: 0x11afbc718969caad2d3f7e1b, }, w4: u384 { limb0: 0x4f585eeaad43f01857265b34, limb1: 0x77e04d4ab93fd04750b8072b, limb2: 0xc00bc285a02119ea4c1da23a, limb3: 0x1382db753f8c3905e0e47311, }, w5: u384 { limb0: 0x8e61233422edad3f37a8b352, limb1: 0xd8dc773a6ff4059b9a0a4cb3, limb2: 0xeccbe35b88a061471dd93af5, limb3: 0x104353579926809447957e97, }, w6: u384 { limb0: 0x384c2b731d616e06b9706b87, limb1: 0x6184e0c8e2d7efb1e06154b8, limb2: 0x8167168429698bc7c087ab2a, limb3: 0x194e8c9db8ffa492523d7bdb, }, w7: u384 { limb0: 0xef02a778fe63a32428538720, limb1: 0x93bfb3a65c893583a3688fe, limb2: 0x1175ee9952b07130cc8b3cc9, limb3: 0xb2d14a4629987e71acd5e81, }, w8: u384 { limb0: 0xa816c07b4cc35518ff83c9ab, limb1: 0x1ccdac7487bad56114ab2569, limb2: 0xb390f4a4c15354c6338643b7, limb3: 0xe8e333eb89e659ea821952e, }, w9: u384 { limb0: 0xaeaf2010379242754f5b7f2e, limb1: 0xe2f1bb28b645f9572ab5f6c4, limb2: 0xfe5084401ff0479a6a180942, limb3: 0x18ccc973cf5a7599815ebc7f, }, w10: u384 { limb0: 0xfbcc6f1a1d48a24160749924, limb1: 0xac2ee791fd07a94084c429e, limb2: 0xaaab252962e1102b2892410a, limb3: 0x2c0dbce2c7ff58b3fb2dfa6, }, w11: u384 { limb0: 0xee87fa8cda7e1bd7d4ae31, limb1: 0x5530a68eec71db3821d5eba9, limb2: 0x7c8c0427d82dab63686794e8, limb3: 0xa033e5036049bb12eac6c9b, }, }, E12D { w0: u384 { limb0: 0x3959ad574bcacfbd805a4570, limb1: 0xaab9f932204b35ccad7fb2d7, limb2: 0x6fa101b072d1313611453bf6, limb3: 0x34e294724006c7c710d628b, }, w1: u384 { limb0: 0x155d3e49d0ccb5b95d9e1c27, limb1: 0x1b86b23f1cef30c30980eb2a, limb2: 0x874af95f2c59ddcd93d76006, limb3: 0x1112ad6169cb6e63e65235e, }, w2: u384 { limb0: 0x82ed5ab9afa68983dc9ba552, limb1: 0x9357cfcf9e6e32dd53c8c666, limb2: 0x79a16ac1fb53afd7a079392a, limb3: 0x12a89edea194c648bfaf42e7, }, w3: u384 { limb0: 0x5eca27f7deb3e9c8c10c08f8, limb1: 0x35321bd9e01f65b62ca2aecc, limb2: 0xc5cc73f3e11486f5229b5b4b, limb3: 0x78a5b9ae5119db042c5e071, }, w4: u384 { limb0: 0xf83ea19e58f36dfb00f5ce55, limb1: 0xa9e201136fafc1bff43560d8, limb2: 0x23fd58ab1bf41c10792d7ffd, limb3: 0x4ebec45d01da532c22ab1bb, }, w5: u384 { limb0: 0x684275e8d953a79f60899ccb, limb1: 0xb18e874d63bf59ce2c949011, limb2: 0x457fb3e09f148575e172066c, limb3: 0x150b00dfaa17d829b6dd5c03, }, w6: u384 { limb0: 0xd149a0d4da27002a5642c37b, limb1: 0xa71fea7579ac00de168a813d, limb2: 0x117b36766caa30b7cc54cf39, limb3: 0x5376ad503028c81c1359a67, }, w7: u384 { limb0: 0x60cf60a90b0f985ac2aacdd7, limb1: 0x20ed4c6d121128b29ca8c7f2, limb2: 0x9d9a5f70c09f70c572cdb9f8, limb3: 0x33b86259bf794af7ff4b871, }, w8: u384 { limb0: 0x247e6ab4517b16d9454b428a, limb1: 0xb3647e9f6093737762a5c15b, limb2: 0x4764994dbefe4268f940353, limb3: 0x9e9e48f06256acea0e845ea, }, w9: u384 { limb0: 0x3fa933373fcb565bb588371f, limb1: 0x53babd42743d6d401b70dc45, limb2: 0xc61d4b87a359271a9318d7c6, limb3: 0xadd5ef0316a5b7771a60136, }, w10: u384 { limb0: 0x97038a4a9cdb7d2fcec42361, limb1: 0x59ce5adedbdb2b586a82e8ad, limb2: 0xf22dbf3800a4a169d3c6c7e2, limb3: 0x173f59f580a1bedc1b8f8674, }, w11: u384 { limb0: 0xccc37b11a6abd0b1c43eca61, limb1: 0xc2e453ad058b0159b3bb8b88, limb2: 0x291724dc796ab3a452decb5e, limb3: 0x167c4d498cafbbc0709a910b, }, }, E12D { w0: u384 { limb0: 0xfb6f2dc21108c4b5151f2644, limb1: 0xb62a4d04de63665a00a57773, limb2: 0x1670b2eaf514bfc8fc53ce22, limb3: 0x130f529c90d3b568aca6e087, }, w1: u384 { limb0: 0x19d81dc0086b598004e3bef7, limb1: 0xbc1384c369a618483eaa5567, limb2: 0x6ad960cc8a498524c1ec078, limb3: 0xadf4daf613e0d097995aa8d, }, w2: u384 { limb0: 0xd29b5724f6b6860e8fa58b56, limb1: 0x8b377db541dbbe2b9fa2b31e, limb2: 0xc3478090367667b8c7c40a96, limb3: 0xd8ae4c4ab61a3b7237a8395, }, w3: u384 { limb0: 0x18098cdc0aaa9de5d90d4785, limb1: 0x415b7efa58b50be0b4e2264c, limb2: 0x93e4c08ac1b499e1f0d6f521, limb3: 0xaaf94e53139efb216ce5e0e, }, w4: u384 { limb0: 0xdf4ed64059dec768e050c2f6, limb1: 0xd3c1316e6a8799940ab2d258, limb2: 0x549413f970f60e7dc26655e2, limb3: 0x35a9aeaa9102416916b2e5f, }, w5: u384 { limb0: 0x7442c43542d7f96a0bdc28a, limb1: 0xf422506e4ba33649decea164, limb2: 0x3aebe61dd6543439953778c, limb3: 0xabdb4ce21a40381201b2705, }, w6: u384 { limb0: 0xbe15abd3c348ddad19da6a10, limb1: 0x9e7d94492b6507ff377fb04f, limb2: 0x3bf64c8180bdc3335507a487, limb3: 0xecfb1e3d52594e2d494e792, }, w7: u384 { limb0: 0x5b2b533a56d49245ab6788c6, limb1: 0xd86f1adc31c48edff72fd114, limb2: 0x9ab458995b092274677e207c, limb3: 0x23ca282bada7d44f7cfd31, }, w8: u384 { limb0: 0x3437d71285507fca4851f133, limb1: 0x54ab8dd4a4a49d8ae172e8e0, limb2: 0xdad31a35129c5da141a6a49d, limb3: 0xbc19f605351e55b755d68d7, }, w9: u384 { limb0: 0xa4b79c920e09f351a49d7de5, limb1: 0x984bf5dc7d5fde910df79900, limb2: 0xc5088d8b76f99b9fa536dc41, limb3: 0x12e688e9f1f4fad3711d14c2, }, w10: u384 { limb0: 0x9167cf28f421e605fc529bc1, limb1: 0x245b24732934cfbc08caed20, limb2: 0xc5635e145d2eef79f98fce36, limb3: 0x180e73749e24faf4fcfd3b2, }, w11: u384 { limb0: 0xde97ba398aa3a54028ab5184, limb1: 0xfa8f2784a38b5421adc6b4e4, limb2: 0xe3c7c2b40b1fe9a3e96c2c4, limb3: 0x58f95a0d10e29ba75f4abfd, }, }, E12D { w0: u384 { limb0: 0xf7cb9c74a2c111c0755ef704, limb1: 0x67a7bdc548d00ca24752db6e, limb2: 0x5fc2a7a5510431696ab76c19, limb3: 0x15249501304492c16d83291f, }, w1: u384 { limb0: 0x55f588a277bf5c8a379a1f94, limb1: 0xaecf9b67ff5e644c13cb3993, limb2: 0x6bb2f12ba2cbe23fb8247d67, limb3: 0x3ed46f7421c5162ca6ba24f, }, w2: u384 { limb0: 0x2fb039392e1e9eacfe012783, limb1: 0xcc550086b3d01a606a030eb1, limb2: 0xdfc6d4c564c0695c34dfb6e6, limb3: 0x11edbc923f8ebc5aefd70289, }, w3: u384 { limb0: 0x59e9ad36dff5f9b289a66f0b, limb1: 0xfe0cd6c3385d435faea3fe13, limb2: 0xb1111302e6d8f88878cd2fb2, limb3: 0x1073ed5e414f7f7e3aab4cc9, }, w4: u384 { limb0: 0x6d6ea80c99c8af39666df7b4, limb1: 0x87e26f50b2a298723ca31b49, limb2: 0x95aef7220ca22268bf66ed32, limb3: 0x6cc0c6596529932a385f7f9, }, w5: u384 { limb0: 0xaf8a21cc737ec216405b6b30, limb1: 0x2731f6ef5d655a1368fc7bd1, limb2: 0xd5428f0c318cd5fa09e854c5, limb3: 0xade1e414a93505d63733946, }, w6: u384 { limb0: 0x3fd711e86acf882a1f403cb2, limb1: 0x7c503cfca897c07df4c5cb3b, limb2: 0x46843cb1e9ef833a5869650d, limb3: 0xa033c2879d1aaf7a54d0c45, }, w7: u384 { limb0: 0x2236aa04d4af4cd7a32dc9e2, limb1: 0x480f9dcff78b12a690d0cb8d, limb2: 0x6fa9da69e4a1c1a4fae93140, limb3: 0x4ecc0f925cf79952426f74, }, w8: u384 { limb0: 0x281d06a57030b61135cef166, limb1: 0xb35e03f80e56523abe9bd62d, limb2: 0xbff83152f2b6238494d8da43, limb3: 0x16f23db2174fd855bbc9f573, }, w9: u384 { limb0: 0x2ae34f5f1b961e31cff788e6, limb1: 0xd5208cd2ba55b284bcb6a740, limb2: 0x8def14ec173b046b77cee877, limb3: 0x8b924b8f096c955fa87bdb, }, w10: u384 { limb0: 0xdd1563aa8adc394ba1bb510e, limb1: 0xe6a4f47eafd98a1d57f7618c, limb2: 0xf0fde0fde71032421d34c342, limb3: 0xbe1046e6670770c40f83d9e, }, w11: u384 { limb0: 0x6c23f54e964a04cc93accd7a, limb1: 0xd64796555b1e02e20e137d7a, limb2: 0xd6306e03d1e023aebfd884b0, limb3: 0xeb55ee41c0d9903f5481cfb, }, }, E12D { w0: u384 { limb0: 0x4fd806a0c08d7cb1d8f5576, limb1: 0x947475d806bb8e73d72c6bb1, limb2: 0x58fd15305c66b78a447558b5, limb3: 0xa07c3e28c6576058ea12204, }, w1: u384 { limb0: 0x58244662118b67b83218a6eb, limb1: 0xebb5e2e2db5b9e0a6b3f5b2e, limb2: 0x3e1042fb26fbbae62ffe0728, limb3: 0x15c39aa7cb6464b8bbdd9a54, }, w2: u384 { limb0: 0xf23ae0578867c5ec6121c5a0, limb1: 0x839ffceb9d2fd41b0648690c, limb2: 0x957e160add723e94eea2c76d, limb3: 0x11c8875c282e2bffa22a4025, }, w3: u384 { limb0: 0x436161c822e4491dd8ccef2a, limb1: 0xdeef4e125ba9fdcb262e6af2, limb2: 0x1402cd92e91d2d46e4a5d6ed, limb3: 0xa15d9e59cadf2cd29423a8f, }, w4: u384 { limb0: 0x689749a0ebda6921732143a0, limb1: 0x5baf655dbcffa4154f1278cd, limb2: 0x274b7ef4bb61387d8ae1f60c, limb3: 0x17824661dbd47612ae5a5460, }, w5: u384 { limb0: 0x38248e96afa3964a27770f54, limb1: 0xcdbf91a995b3b0f56e64c291, limb2: 0xd6305f44de865a7dc66ad423, limb3: 0x181c47228172dfa2880b24ee, }, w6: u384 { limb0: 0xf831ce78619934b9c066f9ad, limb1: 0xbb8b831e8ae9c18e7247d2f5, limb2: 0x9e4e8fed49a8161f9a7d6f41, limb3: 0xd6f8228befd39ea769d2e22, }, w7: u384 { limb0: 0x26f6e50a7dae368f03b9203f, limb1: 0xe8254786b607c0c264159695, limb2: 0xf8df238611d760e21a824ae9, limb3: 0xcb9d2a40bc4c198dadc7fc7, }, w8: u384 { limb0: 0xa31618232fc0a276fa8a13bc, limb1: 0xb2e5fd1cbe70792b1ae5be4e, limb2: 0xcad2bef61d3eb16dbe304133, limb3: 0x746908f8e2904c17b88295, }, w9: u384 { limb0: 0xf7fbbcd3a09d95a4b4b4271d, limb1: 0x53013b5b2cb87122125471ff, limb2: 0xb8ada555618e2cdd4bffab84, limb3: 0x9f993ee384df146cd8df4ea, }, w10: u384 { limb0: 0x7d6ce0b7c1cb3e2498f54294, limb1: 0xa261c1bd75d838bfb7082bf4, limb2: 0x4006f75c1d6b50133de4326f, limb3: 0x836a75393f4c32f8c93b0f, }, w11: u384 { limb0: 0x516f6021bc449c6442591c40, limb1: 0x846385bc47d8d5d7462de9de, limb2: 0xa46c395391341a99e731bb63, limb3: 0xe3c1b8abb46081754501420, }, }, E12D { w0: u384 { limb0: 0x7ecbc81a3c1252aed2cb5af1, limb1: 0x3383e4f86811fd96196f89a5, limb2: 0xe681090ab10830dd807c3443, limb3: 0x1ee0f0a189fe6cf9eb5af7f, }, w1: u384 { limb0: 0xedf1f516e56499b6fb02c1c8, limb1: 0xc1f92022dc8805e7d95a1106, limb2: 0xe33f8dab8d7737441529e8ac, limb3: 0x146e3b7474e409260572871b, }, w2: u384 { limb0: 0x9673e873b8a7c3418ebf8d4c, limb1: 0x7a783f69e749f4f29453c545, limb2: 0x69f350e484834de9d8fa34a, limb3: 0xe9ca5bcc844976bf619effc, }, w3: u384 { limb0: 0x5fcf82227a8ea8b3254820c9, limb1: 0xa2bd05419c073d586a41cf6e, limb2: 0xe518de71e6ac729107926d7c, limb3: 0x844ea5cfff361a9705930cc, }, w4: u384 { limb0: 0x429c3618d116a80c181685fa, limb1: 0x486ce09af708401f4a6c7ee6, limb2: 0x15bbecd706ca76d65704416c, limb3: 0x142489c0fe2e40be632effe2, }, w5: u384 { limb0: 0x6c35d18f3e06bc51f762cf95, limb1: 0x6e5f3313f423ad6904300234, limb2: 0xc28cb4900bf47d29c3fbfc30, limb3: 0x18d6a6340f2f9ddc473dcd7e, }, w6: u384 { limb0: 0x77f90efb84d14408e59f1c03, limb1: 0xb049cbfe6bcd8d08b28e8ce9, limb2: 0xbb35bf3bf049671de2d64cff, limb3: 0x173d7f74864e93e2060343f3, }, w7: u384 { limb0: 0x52c3924e0df7f728e4b119c9, limb1: 0xeec6fa434e31cf84d10575b3, limb2: 0x34fc4325ef25b4772cf88be3, limb3: 0x103bdbad7f3c5e4347f78e23, }, w8: u384 { limb0: 0x50b2cfe1dc1c01ae0e5969a, limb1: 0x2a9b3221a11e330465ef0595, limb2: 0x958ce0c16afbe3fc0276051d, limb3: 0xfabbe257f75d65c2add5f22, }, w9: u384 { limb0: 0x6b8eb7bd4aefc50c3c79931, limb1: 0xb8857fda7cc456e68b528569, limb2: 0x95a710c446e6af9dd11f75b3, limb3: 0x15f22d94f0a51b34b4dd51c3, }, w10: u384 { limb0: 0xc47dbd473089bd4709414e0f, limb1: 0xf549310959600107d2281325, limb2: 0x909324fa4a1e59755e5aca2c, limb3: 0x12f9ee461775892889de4320, }, w11: u384 { limb0: 0xd8dd2af7e3ae6a18cd4251d3, limb1: 0x41f1e4e4c3e7daf40c677808, limb2: 0x4748497b4e11c79b39dce7e3, limb3: 0x53e7ea7549b6f013ee9cb12, }, }, E12D { w0: u384 { limb0: 0x7380438f87399c7e3609ef99, limb1: 0xae251f1bb307841b8e3b97ff, limb2: 0x10586f0049d74ac499bb10f1, limb3: 0x15d69ce6494624b9dfaf148a, }, w1: u384 { limb0: 0xe70f2186c12698f57901bcc, limb1: 0x6853377d8eb10f90ffcddf81, limb2: 0x7fe7ce6260e8ccacd34aa93a, limb3: 0x11c3d29b6bed3f8ec66ccf9e, }, w2: u384 { limb0: 0x8de574f1fa8df34dd4436614, limb1: 0x3d2468e8d3fe2f1b89bb129a, limb2: 0xe5c565c90b6e45bf3d6ef92a, limb3: 0x2fdec231c7a259d6b274cc7, }, w3: u384 { limb0: 0x381afcca5edd7ab2c2ee55d3, limb1: 0xdb0d28a944c5b5e6f1de9d1a, limb2: 0xca789736a75cd4847472db80, limb3: 0xb8857429befc7d11918d904, }, w4: u384 { limb0: 0x8aae77fae75932fd56ef1ed3, limb1: 0x1dcb6c6eff6602f4efc533c2, limb2: 0xb0853b8091023746c6956eb4, limb3: 0x158e6193740bfac3349cae31, }, w5: u384 { limb0: 0xae2e48564c4d12a418a56403, limb1: 0x668c45ed4e3b77890ca488d, limb2: 0x758af6b95f421af2b9e80dda, limb3: 0x829bbd81deb660c5c410ebc, }, w6: u384 { limb0: 0x2b33f8be265845893a4d2cdf, limb1: 0xadab60575595c27d3a695f56, limb2: 0x2bb38114e26dcff01b3c7a, limb3: 0xb15f5d3fcb62c5c1cb0103d, }, w7: u384 { limb0: 0xf547b3d2ddb97a0ec597c1e4, limb1: 0x4dfe359dcb7415317a0d96c6, limb2: 0x4db32c68ccb2fff63d900b3a, limb3: 0xf40331313d149fd78f8999f, }, w8: u384 { limb0: 0xe1859718ba67a65d2f7dd9e1, limb1: 0x7f66d368473637540d2de335, limb2: 0x94d70dd4d71f90a6b8996edd, limb3: 0x7f11bf976be5160fff2b5e8, }, w9: u384 { limb0: 0xcb043aa483655ca971eb708, limb1: 0xc6514161d25e989cfe0eb910, limb2: 0x4b03463f10bd5486a5150bf6, limb3: 0x19207d670b11d96e63c9c7f3, }, w10: u384 { limb0: 0x518d10761529279fc06a4e8, limb1: 0x64139e4ea8660ee98b864aea, limb2: 0x1aa32f01ce8213c10b08030c, limb3: 0x15064a81f43178365db85227, }, w11: u384 { limb0: 0x14ddb10fd846711efe04e524, limb1: 0x34676af4100eeb93fc894295, limb2: 0x2bbf7682b985b2187e2ad98c, limb3: 0xb2c84517ed0cae95c0fd980, }, }, E12D { w0: u384 { limb0: 0x7053639bdef1a630ad4f5af6, limb1: 0x739c43473d55a600db56c9ab, limb2: 0x6a2e59a43b3e0b5a88499b12, limb3: 0xe1d00aa3380a50f80ff85d2, }, w1: u384 { limb0: 0x3f2e33d1598a70be6cb11313, limb1: 0x1486afa60b15b33b54cfb747, limb2: 0x81bf2a71d10300239b7aaf1f, limb3: 0x9b35119c385fc20a0386282, }, w2: u384 { limb0: 0x31d6979bfefd74931a576d6, limb1: 0x90a0c3530607355c33b0fd0c, limb2: 0x65fba06248d03e088f1d48a, limb3: 0x11395dbf5901f9d349f3b984, }, w3: u384 { limb0: 0x4291c385689ad964bc8bf72a, limb1: 0xb0737aaac176737a1ecf6ac3, limb2: 0xce8664f73ce5a6aaf0f10ca7, limb3: 0xb6a7d5c46340b57ed0472e5, }, w4: u384 { limb0: 0xd4e72b1d919d76e6f7c68488, limb1: 0xec2f0d04a7a2f7d4d7a31590, limb2: 0x4112c57e0a9dcfedf038c956, limb3: 0x1928f6565ead905c25593eb9, }, w5: u384 { limb0: 0x92b1d18299192443eab3cf31, limb1: 0x363339f1c99447dbe74383f3, limb2: 0xdcac6005cc60106f88576c3a, limb3: 0x261463ad40df4e97165053e, }, w6: u384 { limb0: 0x45616d4a15bc7f5c57750089, limb1: 0x19ac60bbc57465009e3dcb1b, limb2: 0x7ceb498d022dfcfcae9aec60, limb3: 0x19c44919e9fa2e772d9dccf7, }, w7: u384 { limb0: 0x74d7db77e3c5ea2003e6de14, limb1: 0x7f694b25adcf375071dc2f54, limb2: 0xf3d7f4f1a8dcb8d0debb2bcd, limb3: 0x14c0504bbd68a3b627e1d579, }, w8: u384 { limb0: 0xbf696e7d082490ab2a810909, limb1: 0xdce3d8459c86e173b9b814d9, limb2: 0x7d35e60fe95d54b4297c06ea, limb3: 0xe0428d15a83059ac75d4252, }, w9: u384 { limb0: 0xf15b4e3caed564cfc1168aa8, limb1: 0xfa6ecde037cb585b65aa3b52, limb2: 0xe2a2b5aede3c734d6530056f, limb3: 0x14109312a06f6c1e8250362, }, w10: u384 { limb0: 0x9f4a8b4546befff0a6481af8, limb1: 0xdce5e22b5ea0a42e8928c84a, limb2: 0xe59648247bf7715701129ca8, limb3: 0x1209e1d34b0c1d14ec7839cf, }, w11: u384 { limb0: 0xf2a74f539bad5a4682af3491, limb1: 0x93097b4ae591134223d3a872, limb2: 0xd33d11a3041a2bd1bbd4cfce, limb3: 0x43584ae57d4f086e437d219, }, }, E12D { w0: u384 { limb0: 0xccd3861f8b36806faafb781d, limb1: 0x6dda1400a7c6d4456935dd83, limb2: 0x20b444358405090025a9b7cf, limb3: 0xf54e285bf8f9c32d389d6db, }, w1: u384 { limb0: 0xe9b4bf3d1c5b280abc31ebfc, limb1: 0xd862307b44fcf93aae7b11ba, limb2: 0xe232ba534a45a34a7432f6ea, limb3: 0x82261cd3aeaa85fbe4c96df, }, w2: u384 { limb0: 0x2c7b8a630170b7f631239855, limb1: 0x853e2961c8b4130c85116507, limb2: 0xbf9ce9a53e945b9c6d7b5f1b, limb3: 0x145d89cb83700774a22db1bc, }, w3: u384 { limb0: 0xa74c5c7e5df8d3667adf1671, limb1: 0x52de2b913d78406ec8f99a, limb2: 0xc812988870f9f7517c79ff58, limb3: 0xb223e7cfbc3fc377b1fe75d, }, w4: u384 { limb0: 0x8cfdf31674b93a20c992a24b, limb1: 0x8f21312988d7da962d321bc0, limb2: 0x2dbf0528a791ea0d5f981e13, limb3: 0x15aac1f8e330eff4e20ab3fe, }, w5: u384 { limb0: 0xf685ec483cea983d1a69a4d7, limb1: 0xb82b746d8797df323095a302, limb2: 0x534715a12884e752ec62c600, limb3: 0x1639bc27f80a1b9be7937efa, }, w6: u384 { limb0: 0x2bfbdf97d360b348dc75d028, limb1: 0x3e93c81c56c9d7703ac2d15, limb2: 0x3ecb33be37dc97e5a75ba27, limb3: 0x14ec70fdfe7e62ee63fd9e82, }, w7: u384 { limb0: 0xecabff100ee999721d0aeedb, limb1: 0x408694288104b8240aefef54, limb2: 0xae05168387150e2c1c0b069b, limb3: 0xf14bd4f7226a16796796e6b, }, w8: u384 { limb0: 0x779e398587211c93d2d419af, limb1: 0xf33f48e9339556264944ed85, limb2: 0x641e8d0911a2129916d623a9, limb3: 0xda22254161644c0d73135b3, }, w9: u384 { limb0: 0x97edd0906ebc8269feff2745, limb1: 0x9faf40b4f990563dbb8b6a9b, limb2: 0x55e5557db5d8f738aca6cfce, limb3: 0xf13fb2d9a5e619a1e10167d, }, w10: u384 { limb0: 0x7fc2ba107c37bf200a3d128e, limb1: 0x9bb0216dec247ae73a8d8f46, limb2: 0x1ddfeeb377abfa6a56ce7bd7, limb3: 0x152f629874880c14a7fc9709, }, w11: u384 { limb0: 0x29793cf627b6c775b761a603, limb1: 0x2d71f3cf25ee0423e7c54f3c, limb2: 0x8470327513832374e529222e, limb3: 0xd8a7063ea9e13a1184eb587, }, }, E12D { w0: u384 { limb0: 0xc98374fb3b44c0e6942ba4a3, limb1: 0x67de3f6c038ef1323a6aa322, limb2: 0xb2277b3b25524d61527bacd7, limb3: 0x14d40787156e7ebfa93f6f99, }, w1: u384 { limb0: 0xced08def20a48570ef18bf4, limb1: 0xdb6983a66359c51f2ab71327, limb2: 0xe099b96500cdab825f87b7fd, limb3: 0x14e67481e4aec8ffb05fbb17, }, w2: u384 { limb0: 0x7f465e87c522bb9f7df6a9f9, limb1: 0xda4ccc6d47457fd8073dac50, limb2: 0x52533bf52010ae930ae384f3, limb3: 0x36f4d9a630f659ee0049940, }, w3: u384 { limb0: 0x9458ec32cf854cf87179a081, limb1: 0x3708fddeb7317f93acfb1b9, limb2: 0x45e25f7a68c0c63865dc7169, limb3: 0x17cc7f665ab618af9bb8ed0a, }, w4: u384 { limb0: 0x85fbbd958c9517c58a72f4eb, limb1: 0xeb94429d923c8f57aa64659d, limb2: 0x53d22d4278caae28dee0ab98, limb3: 0x77749f245b0607f9a8266dc, }, w5: u384 { limb0: 0x4a9e638a04d4cdefa92a921b, limb1: 0xa751ed26127bdae0471e4d66, limb2: 0xcaa20c710aaaf86cf3509376, limb3: 0x754e574bc910d618dc31dea, }, w6: u384 { limb0: 0x5d9f22fb58b20cb89b60a7a2, limb1: 0xa2d39e0d29c61b355f9f8221, limb2: 0x5b42ad2b0cdd40f198fb4933, limb3: 0x146b356a1037d82e3fd60a35, }, w7: u384 { limb0: 0x8c8f7c35ea3ba1960632cbb2, limb1: 0x88989dfeb7c7f7c108812866, limb2: 0x5d65fb080c6c9703c3de7da3, limb3: 0x17f80c85d8708e2c4e0f76db, }, w8: u384 { limb0: 0xe72c663563a2683a88282047, limb1: 0x9f896928b8f68240ae87318d, limb2: 0xae2fe9dae790ab09f051d396, limb3: 0x103c85e204ea356a1df02170, }, w9: u384 { limb0: 0x8b2a42e00385585058c6871d, limb1: 0xca757495dd55992019b0532e, limb2: 0xddc38038d9b6c6b0c1191c19, limb3: 0x456598325b3e07c16f6cb90, }, w10: u384 { limb0: 0xc0a98bdc8196fd8b9bf4edf2, limb1: 0x971354e815f09e434646dc35, limb2: 0x8848e0035a10ca071f522483, limb3: 0xea464fda93a90c2f0c6cbc, }, w11: u384 { limb0: 0x125314c8b22d6dc1d849816f, limb1: 0x81596b8b1354b4a79eff397b, limb2: 0x6fd4eae90dc4ca7a020c0d58, limb3: 0x633d54eba634239e2224280, }, }, E12D { w0: u384 { limb0: 0x7664507d65379e09b0cc8081, limb1: 0xa7214a05165e9dd1cb822746, limb2: 0xdaa4b32cd1894fcb5869da3e, limb3: 0x11dd5a0d713ff9a4216dc02, }, w1: u384 { limb0: 0x72c884220671860deab6fe4c, limb1: 0xf7edb308d081aad11737b2aa, limb2: 0x179a550ac8de7988cb51745f, limb3: 0x18c92348bd738ff79eb51da6, }, w2: u384 { limb0: 0xd0997e854e959e9fcf50612a, limb1: 0x731bde68fbe33e65958e25a5, limb2: 0x5c75550140147ca50f03f4c1, limb3: 0x1724f1c48007969b733593aa, }, w3: u384 { limb0: 0x8cdd8173b838cbfa5e716055, limb1: 0x7cce9c3704cca203a84d1eaf, limb2: 0x609798ba1aa28ffaff08d41, limb3: 0x17815ba1eca35154689bbbd, }, w4: u384 { limb0: 0x1c7e64b6dbfeaca240b5ce1c, limb1: 0x334cf124f9c76e1e2c54997f, limb2: 0x64e29de5338a04c86a571534, limb3: 0x4322d1d2e68ad82e5576014, }, w5: u384 { limb0: 0x8e8720162d72df7b82b54ddc, limb1: 0xf9a9d4e498d4932f72861daf, limb2: 0xa62955f8bf4d62ab5326d370, limb3: 0xe10f22c8698bbbb16ce96ab, }, w6: u384 { limb0: 0x7e12194ea7c3af3ca1f4627e, limb1: 0x57c3921b26b0c0f8ae782c80, limb2: 0x7807e0e72a965c15e92a3692, limb3: 0x10d5c83fc7687bdeda2fa6a9, }, w7: u384 { limb0: 0x6c3118b5d18f2ba8f3358410, limb1: 0xdbd08498b72968ac4f865556, limb2: 0x1606bcc23a2fefcd7b98b187, limb3: 0x1836f088bafe98f9f35b628d, }, w8: u384 { limb0: 0xb3ec8857a717227fd2e410c7, limb1: 0xf71681b713d44faee8ccade2, limb2: 0x1a889225d6c3ae543975d7ab, limb3: 0x4042e6058ba0ed258215db8, }, w9: u384 { limb0: 0x92dca3c8ef22f5c5ad68411e, limb1: 0xea04b401e31bd03c03f45391, limb2: 0xf274818f73907b389eee6555, limb3: 0x110981e160f9a1144b049f6d, }, w10: u384 { limb0: 0x7809289b28677816d3d20f51, limb1: 0x2b325b38281ca3d9447717a8, limb2: 0x750a16aae8cec71a981e64f9, limb3: 0x4c4bb16a4d45dbfcdd6de82, }, w11: u384 { limb0: 0xa19d86a548a59b31bee7330d, limb1: 0xbab4358db8efdc356098935c, limb2: 0xecf4b1e2071637cfa269d441, limb3: 0xfdc8efae68b158880892941, }, }, E12D { w0: u384 { limb0: 0x731a6668a56fb2e638b5386d, limb1: 0x2f6050b816d5da56d8b4aeac, limb2: 0x9f8cc60a1825ed2bc48ced64, limb3: 0x14d27ab7d2dd9d4dfc62f9b4, }, w1: u384 { limb0: 0x36e235511e3aba57cd7a4166, limb1: 0x651418ba41dd7e611da499af, limb2: 0xa2443f20594fb2be6da75cc3, limb3: 0xe5b76d2ac4d96fc0a324e20, }, w2: u384 { limb0: 0xd9a45f081496460d0c0ed0ac, limb1: 0x2e77975aa2352664d6adb2e4, limb2: 0x2faa41b81ca6013a7f61b19a, limb3: 0x486d9ef9a7963973b526016, }, w3: u384 { limb0: 0xa30b18466742d1c3215c7ca9, limb1: 0x76bb8e0f21ed01073e7cd26d, limb2: 0x72e300f6162dfb4f824322b3, limb3: 0x170086077deae464de32c314, }, w4: u384 { limb0: 0xb98779fe717a76947ffc64a8, limb1: 0x22829a2223d7a3c1e115868, limb2: 0xfd92daccd29c35d6e9891f91, limb3: 0xc8cd313b3bac470a84c06c, }, w5: u384 { limb0: 0xd7fb2ab79ade8db9f0753816, limb1: 0xc8e90a86892a3f9973f3a709, limb2: 0x439586d8958df5477546a8c9, limb3: 0x11c5062a433f8a665d2fec03, }, w6: u384 { limb0: 0xec349f8ca4e9628ef8ad1d0f, limb1: 0x41ed7cebf144cf0991fd449f, limb2: 0x83fd7077e122719cd9a150db, limb3: 0x4f4f8cab62516e0bd8eed4, }, w7: u384 { limb0: 0xd65b0369dac2474a3360256c, limb1: 0x73aa7477aa55f747c118bde4, limb2: 0x166c215a026d96f815575905, limb3: 0x19ef4018eacc8cec0d7c2952, }, w8: u384 { limb0: 0xaf93f1012698bd074cae6d2a, limb1: 0xf1dd95a8d7d4c5624dc77fab, limb2: 0x22ad91dc94c520bed552ce68, limb3: 0x7149e3ea5cbb31d49fa48d4, }, w9: u384 { limb0: 0x309be21144e9429149f5ea74, limb1: 0x5a23ebfb744401c93d028104, limb2: 0x1328c0e96b3dc98cf9ca2178, limb3: 0x4a0a0910ab2af1883e3bd42, }, w10: u384 { limb0: 0xd096a251af3d32c676bb4288, limb1: 0x81a2455886a5de7de17a3a3d, limb2: 0x785780c752a0fec2ab697d7f, limb3: 0x424eb933d2f578926758c8c, }, w11: u384 { limb0: 0x9bbf4ea4c5f12c0f3a80655a, limb1: 0x6c3952358a56be8b39ffc122, limb2: 0xaabdbf346cb1e900c6fa6ef7, limb3: 0xfc816c836e1f58f9bc2ee34, }, }, E12D { w0: u384 { limb0: 0x423f069d338c478ec1af9c39, limb1: 0x29b54a9a019077a85febd5b1, limb2: 0xd6c54429887f79c4f5e8537e, limb3: 0x2d645e495b1ae162900aa5d, }, w1: u384 { limb0: 0x15924967d61c029186ecddf3, limb1: 0xad51150b9a239c5f6107f3e, limb2: 0xc131c14b453f056fdeb354d0, limb3: 0x7ce2f5cee25ccf4630a4da6, }, w2: u384 { limb0: 0x24cffdd2b4963236469c595b, limb1: 0x1cedb62a0a9a9d19ec0ef73b, limb2: 0xc83e7dc874bd3671d4079d93, limb3: 0x54f10b385a7cc18a25a48e9, }, w3: u384 { limb0: 0x51156a1330e11e4107978c65, limb1: 0x126d680056df9e678c923a15, limb2: 0xc88a5e31000b304a279d33c3, limb3: 0x5add5bf0e3de07507b300e9, }, w4: u384 { limb0: 0xaabb4da106a561c89da6e640, limb1: 0x67706e7ff291eb8350fe823f, limb2: 0xa2a5b3a4109b157167daed75, limb3: 0x3a53fba9d2b86d5617419bd, }, w5: u384 { limb0: 0x49f0d1228f3483ea001e89c, limb1: 0x2904017f1a05647ad6b814bc, limb2: 0x32c50c7b36360c7072b97c5e, limb3: 0x4a4b35d842e9157f9452ef4, }, w6: u384 { limb0: 0xe910ff959aa337ba694b3103, limb1: 0x1eb7de8661a5aa726957afc5, limb2: 0xf46dc87d119c3f6b7bc26c47, limb3: 0x16d4d3eee5db3369b1cd5095, }, w7: u384 { limb0: 0x2b2ebbf8ed056759bb5ad089, limb1: 0xc997a5c29ff182751a7a4a1f, limb2: 0xd4255d635200af86412c0d3c, limb3: 0x133e3849f5abe45d50ebd4f3, }, w8: u384 { limb0: 0xc646891ae42a453618bf6946, limb1: 0x6cdba6a4c36531001a999ba9, limb2: 0x4f8028f68a1b39ea09f81c8c, limb3: 0x5a4a8424db89080f7ef2d4c, }, w9: u384 { limb0: 0xcfad8c2e4174ad2ae083acd8, limb1: 0x11fa7404e0d60cc8429a7206, limb2: 0x16f6645ea542f26a2bbb02c2, limb3: 0xe221955c928cb0869ff1e7e, }, w10: u384 { limb0: 0xa55f4a4e3b44b7435f37266c, limb1: 0xde3c9ef2eb0e12ebacbf789b, limb2: 0xec729141e4b14e595a75e170, limb3: 0x9d7eb5a60f56f8c5b9cc908, }, w11: u384 { limb0: 0x51393b6db9309927d8ab8093, limb1: 0x81b817c741b2485a83aade8b, limb2: 0x45548c3f24b4ce607a7498a1, limb3: 0x1329d0b6119a0a2fb95f1365, }, }, E12D { w0: u384 { limb0: 0x22d7122b0c05411b942f9640, limb1: 0x1bcc87de4a309fbcf7df22c1, limb2: 0x3dbff192e88552ff01ec54f2, limb3: 0x16453c594411bc9614273cb, }, w1: u384 { limb0: 0x3cdd3cbd9b5ef16b0ab5d12e, limb1: 0xc9b831682cc9f7562631eb82, limb2: 0xd8c0b4a326e6d711af1c6fcc, limb3: 0x15999f5b65933e477e527ca2, }, w2: u384 { limb0: 0x8e1e5c76737a52e34970f54a, limb1: 0x13e660457b4680094701954, limb2: 0x8ef5bfc33edf509615dba422, limb3: 0xaf25c6ba9a9da6f8d1d8d84, }, w3: u384 { limb0: 0xc6158c9388e8d4cdf213db7, limb1: 0x99bf0fc5cd55777088191fa4, limb2: 0xca9fb43a85b157663614f5e7, limb3: 0xe19f5a790b81946863c09, }, w4: u384 { limb0: 0xaaf5ae0abc93c789d2f553f5, limb1: 0xb0e4d0b4161db236bfdded84, limb2: 0xcb1b789e885ae9f7603d7597, limb3: 0x173a004b4ac0b6990ce57848, }, w5: u384 { limb0: 0xb8270359d997a568b9ca2d, limb1: 0x6c3f97a0095424bac05918c8, limb2: 0x4fc75521f68391b186c98d69, limb3: 0x179c925b368a6922c052109a, }, w6: u384 { limb0: 0x4a64cd8043d641ec589cbced, limb1: 0xc32ad31f1e72fbf5ad938a1d, limb2: 0x394ab548e7bbdcecd04cfa57, limb3: 0x1903183cfe25996781a6f138, }, w7: u384 { limb0: 0x95d6117e159fd5a627fbf3c8, limb1: 0x8bb75a8e2cca90dca43db09d, limb2: 0x52ac5959acb24c2975de0b46, limb3: 0xc733099ca61082513b739d0, }, w8: u384 { limb0: 0xc254c0d7ebcfb3e456d4db70, limb1: 0x841731cd2f31e3eb6dc2cb83, limb2: 0xbd575ed553cf9d9f4fe2d195, limb3: 0xb9b6dbbc6b7b7a3872452d6, }, w9: u384 { limb0: 0xc35f21cbc3ac37bfefbb62b, limb1: 0x6d0f6d5a72fb9754dd45e03e, limb2: 0x115c5b6547d1b15f1ab880c8, limb3: 0x49fc712ba5a255dbc3c3734, }, w10: u384 { limb0: 0x455d3b2f4797212bc3a8eb2a, limb1: 0xcb84367fab4cc67d4a608ee7, limb2: 0x27c5381bf627b1f6770fb730, limb3: 0xda5838799c2b92a9a46f93b, }, w11: u384 { limb0: 0xe377b673276f66aed0431e2e, limb1: 0x22424ab805248189df3bbc60, limb2: 0xe8df0a999d7ea73c0e5c21c6, limb3: 0xa1a1a982e74b25c855c6630, }, }, E12D { w0: u384 { limb0: 0xd8de7c0a020c2bfab98f462b, limb1: 0x4259e1a06cc5c0d48aa4b7b5, limb2: 0xa600cfba72cd0eefd68378ca, limb3: 0x16d21a98b960ac0a3ce99480, }, w1: u384 { limb0: 0x9c441104f663c6cfd27a21f, limb1: 0xa2538fbacb469c18af6f6d36, limb2: 0xaca0084cb5ce246d9e004b86, limb3: 0x1818d39bf51f5701a630cd13, }, w2: u384 { limb0: 0x83662e661b082815e9b3291e, limb1: 0x953c223a59774cd045bb2e72, limb2: 0xd965efa4e0a2b9c6d63ed7bc, limb3: 0x75910bff00e3ebfb430ea1d, }, w3: u384 { limb0: 0x21f101851b5e6a66fe5fb3cc, limb1: 0x2078ad4044a6e58b48b2fcad, limb2: 0xb95b15546d0fb95d6af37e7f, limb3: 0xc85bc26e7c69777a5b73186, }, w4: u384 { limb0: 0x2813b1a799ef66155d7a5ff5, limb1: 0x706d19aaf61ac615d8d7a776, limb2: 0x35b48c7bae00bb479924c911, limb3: 0x113f0545928ec85fc72b3b83, }, w5: u384 { limb0: 0x29ac845c79e1955587d53a3f, limb1: 0xb889fc1aef4cf20aff2f8c4f, limb2: 0x50fef6b1712a33cba0703bf4, limb3: 0x149cfd613a758a131850b749, }, w6: u384 { limb0: 0xa74862c7c240e22184bb0faa, limb1: 0xe185dab81bd7e850ecfe6e7e, limb2: 0x579166b24e863176b906fc26, limb3: 0x4d862301cdecd83870cf1d3, }, w7: u384 { limb0: 0xd63ac2c17c787ffef5f67ac5, limb1: 0x490f34bd28d97037038b425c, limb2: 0x8eaaea7d3e9970844eca0bb7, limb3: 0x12ff4861711d4f5fc6c7df52, }, w8: u384 { limb0: 0xa77d513840181e6049eb2cfd, limb1: 0x29144762781008597f248817, limb2: 0x29ddbf8ae66b47d99b8f144b, limb3: 0x33b700fe7d54ab6cc6366d8, }, w9: u384 { limb0: 0x7c605b80a783b29fbdb7913a, limb1: 0x8b972070a4c66018b2157c13, limb2: 0x9b41fbff0b39b434d4fc621e, limb3: 0x3642078114e5416bdd1743b, }, w10: u384 { limb0: 0xb65736f5f91bc2870134be37, limb1: 0xe433e5c3d68b7ae3c424715a, limb2: 0x9fd29af8fc74edec039d14b7, limb3: 0x77405e5599759db17b993e5, }, w11: u384 { limb0: 0x5ebf0ff64d839d1b21510f03, limb1: 0x2ecb8cc84c90c881b6abd4f4, limb2: 0x1cce59b581d9b2b04bdce6c0, limb3: 0x13c54e92b75b47920c1bc23c, }, }, E12D { w0: u384 { limb0: 0xd230ba8192574b8f0d2e8d0d, limb1: 0x8d46a7f9896bc752e15f2bd1, limb2: 0x4c46523f3eaeb3d3c195cc64, limb3: 0x9a8c180064d8e4aa41a3fb8, }, w1: u384 { limb0: 0x6b41258f53e02a3f4f4080b9, limb1: 0xae4efe95de593debca9447c8, limb2: 0x53fa98259797f7b69a5a740c, limb3: 0x1e723f2e6d538ec35ab098a, }, w2: u384 { limb0: 0xa82549fa15fa37278e37e54f, limb1: 0xf3e4bcc528ef5b1739c54e51, limb2: 0x23325e087bd1e6be95bc9c2, limb3: 0x3d06b79028ddad39882372, }, w3: u384 { limb0: 0xb8692892001c9cb56b90952c, limb1: 0x733b4da305705ade344a3621, limb2: 0xdfe666914d66fb6ab1d4c9bf, limb3: 0x89317029155d09a628dc7ad, }, w4: u384 { limb0: 0x92116763fe48fd34e5fcde4c, limb1: 0xbc96d0f997ba650008ac0eac, limb2: 0x770993a8f2ddc97a352efec4, limb3: 0x1584ba5015a2629d14debb7d, }, w5: u384 { limb0: 0xfcfe8c0df558699103baf566, limb1: 0x5435e711fabc8e56bf54699b, limb2: 0xeb0c73e7b22d70352bb5a564, limb3: 0x343483df7a88d987c69408a, }, w6: u384 { limb0: 0x384d80fe4e9e50d65ceae168, limb1: 0x74f4dcd19aed7592bc9593ab, limb2: 0xe493540b588ffd977f4ee0ca, limb3: 0x23ed7611ed958da6db24d3b, }, w7: u384 { limb0: 0x2eec2f1a902b21208d2243b1, limb1: 0x3ff398adc2bf7b18affd6970, limb2: 0xfe74e53e674476aad89727fe, limb3: 0x17adfbe5a9f0d328bed1b1d5, }, w8: u384 { limb0: 0xb3c26226f8db87e4acd22a19, limb1: 0x74b1ff048bb0cee38198e560, limb2: 0xf91b63c44856aa5995195c7a, limb3: 0x57ae60555c4dfbb9f119dd0, }, w9: u384 { limb0: 0x391b35c3b492a2b733913137, limb1: 0x1b718fb7d4529435ea05e0ff, limb2: 0x7628c94eae8736f7066faa73, limb3: 0x12482498758030e4cf058fa1, }, w10: u384 { limb0: 0x6fe096b1a72856d5ff144f61, limb1: 0xe7e8e20c91eb503e936201d3, limb2: 0xa873f6f582a8c5e528b7e017, limb3: 0xac11b393a2ca9b81f52d7e2, }, w11: u384 { limb0: 0xbbcfbb7847f1fc7f5c887867, limb1: 0x8ca064238b30c902565c58f4, limb2: 0x3b342400e4bf64f5cfe303f8, limb3: 0x141881c8cb4ac57fdd2421d0, }, }, E12D { w0: u384 { limb0: 0x57c1e0a314f410d7c80f0d6c, limb1: 0x188efa3af0e9a15ae09a39a6, limb2: 0x8549ddd8cee9cc24a76927f5, limb3: 0x828abb514c39b36af5e5e59, }, w1: u384 { limb0: 0x86b5e60ab6d06ad115373349, limb1: 0x30ec5eab948a288e962221e0, limb2: 0xa5ece7da90052d41645094dc, limb3: 0x292b0c29d2ca5076acaa1f7, }, w2: u384 { limb0: 0x53fa181062874a0e2952a6bd, limb1: 0x139aea9f3d57245a94f247b8, limb2: 0x13e918fdbed0933c9e1e4691, limb3: 0x129ab8b6bedb190996697c6c, }, w3: u384 { limb0: 0x8c94450ce70b11a241947381, limb1: 0xa6c255e7d67f8a5466c2d100, limb2: 0xa28b8d54a0eb9220bda7f20b, limb3: 0x9645f3081882f29208bc4ca, }, w4: u384 { limb0: 0xdb6f564cc32943107d116638, limb1: 0xd9799a7f993d67fe769b8272, limb2: 0x861d137dc34f59e9b52ea65d, limb3: 0x10da20caed9c13858e34bfd5, }, w5: u384 { limb0: 0x223bada77c016723d852006d, limb1: 0x95041b73eafb915659a2fff7, limb2: 0x36b777b400b7e9e299363ccd, limb3: 0x17c8527995c3f0b83cbe83b, }, w6: u384 { limb0: 0x387c0822da34f6001fe9f474, limb1: 0x7ca208b866f7d21734a55544, limb2: 0x7415b9fff8e87b99635abfd3, limb3: 0xcae06be69307d97643444a3, }, w7: u384 { limb0: 0x7826924ebf635fa31599f2d8, limb1: 0x255b41d4dcc5e9df82f2bc5, limb2: 0x742046a3d48ba8fd2ded46fa, limb3: 0x14e1a77687c2fafa04ad3cc5, }, w8: u384 { limb0: 0xd1861303b32847e9dfa309b, limb1: 0x95643d858f4ab818e1429eb4, limb2: 0xf5f69835e9e3219e541e489a, limb3: 0x106791b088d3043aec789d2, }, w9: u384 { limb0: 0x3fbf8473656db45761cd4577, limb1: 0x95dfb9c6f2581b80ca9c6e0d, limb2: 0x19cdeb22dd3af66c09886e0, limb3: 0x46d1856bcf6eb442eaa0dd1, }, w10: u384 { limb0: 0xfc5db242d9eef89d6b2b0ead, limb1: 0xa441afa00af0ebf9e4a5566d, limb2: 0x737340b78921c31e7d6b998b, limb3: 0x152c1e8a7645e37878c00117, }, w11: u384 { limb0: 0x707b12110eb67f3f3e25082d, limb1: 0xadfe406a34710c9b1f1a67f9, limb2: 0xcf700552ca3b4a453710e271, limb3: 0x1329ce5688848746b4cdb9c6, }, }, E12D { w0: u384 { limb0: 0x63ea02a83316ced86cff7bc3, limb1: 0xad3cc1665ec97ed103bf2a97, limb2: 0x66e914ba49a82240606bef39, limb3: 0xbe1aae2e0755468744c9cf8, }, w1: u384 { limb0: 0xdd0988f0f7381759cede6cf1, limb1: 0x8c668cf30f6b849f93e18738, limb2: 0x17677bd95c25553069f8d3bb, limb3: 0x213b88bd1d59c856f22c57a, }, w2: u384 { limb0: 0x468ebd74785e502a030b2d64, limb1: 0x99e6500a6eec17b7582c46de, limb2: 0xca602fa99428bb3096ed2234, limb3: 0x221c7127baba56f36027a78, }, w3: u384 { limb0: 0xecf5c97a4baeeec96686a951, limb1: 0x8a858ecbe3f7428c1e485263, limb2: 0x7a93d3d522c174fc7563ce8, limb3: 0x6b458b1280095fbd58dced3, }, w4: u384 { limb0: 0xf7235d01c69ea79eb8c3f3c8, limb1: 0x1e8d53af3b6a8c0d384dba87, limb2: 0x7219df5572fc6a5fb03c3640, limb3: 0x4a28cd8ddddd35c4a2bc756, }, w5: u384 { limb0: 0xea22308af0e9f3e49bc2073, limb1: 0xe16fb20226994cd501b48956, limb2: 0x8b5463f6a25ad49ef766f7c9, limb3: 0x920549318b13fd2a55438e, }, w6: u384 { limb0: 0x72d478cbbd10de13e7840523, limb1: 0x61148bd13cf2cd5f974ef513, limb2: 0x14fc5faacaf5f306eca036dd, limb3: 0xd5c18cfe88ef2a96785e79, }, w7: u384 { limb0: 0xedaaa07fbc739502463ef449, limb1: 0x8756dc3df79501b08bcfd30a, limb2: 0x41db0294140d03ab93ac331a, limb3: 0x2faf35b55c223051329f5f9, }, w8: u384 { limb0: 0xf4ddf6770b28a0e39c42e1, limb1: 0x1bc579527a6d36ebcb9c1e43, limb2: 0xd8d3dda24eb2d5c51e94fbf7, limb3: 0x1929169f16f2bb1805258a1f, }, w9: u384 { limb0: 0xb7c17acd08c863c5de00ab8e, limb1: 0xd061e541ab904021cb7415f3, limb2: 0x4e4103b8a474b65ca3b96404, limb3: 0x43f042bfe3512474ab82a6, }, w10: u384 { limb0: 0xdf4f7f352c2231ba350a5e09, limb1: 0x436f7c965c9cba8884ee1f92, limb2: 0x8820c54c22fc9835d6d63889, limb3: 0x137b29d6f48df1e1e6a859e3, }, w11: u384 { limb0: 0x213101a3e3c1d0de36762bb2, limb1: 0x2841a7df27a0c7cd8324b382, limb2: 0xf3aa170a745fb830cf57da1e, limb3: 0x34d8b8302b0f58d9d5a85e4, }, }, E12D { w0: u384 { limb0: 0xc102bc3e2c1431657103a4a8, limb1: 0x3aba49ff88c4ee3806b04d0d, limb2: 0x985c1f9d4156682f0c5aef65, limb3: 0xc0561c0e6c3d1cc794c57dd, }, w1: u384 { limb0: 0x9c02003f65c233b63f5d57df, limb1: 0x675a9896c5ebc6c86acfe082, limb2: 0xf10e29c84b756a49c862026e, limb3: 0x397c60ac478f6f3d04dd211, }, w2: u384 { limb0: 0xde0ab514224b0a09d4470108, limb1: 0x30cffe24a16eef64a4e3f8d9, limb2: 0x250e573cf0cdc9d0474a96a5, limb3: 0x320c97808c919b6bc77a6b9, }, w3: u384 { limb0: 0x22e1478aaa8dbef5b7eb5c75, limb1: 0xd73e5649b061e7dec320410, limb2: 0x9e5973e5c196af20a9522b87, limb3: 0x888405f1b7e02f51d25e4cc, }, w4: u384 { limb0: 0x7d63d9cb91c7e6ecea27bd0f, limb1: 0xafd606d67aec5132495aea6e, limb2: 0x89d9cc366cd70849bf7a6c5a, limb3: 0x6a1cdcfbb9094ed585438, }, w5: u384 { limb0: 0xc63d5979f095ce42b97ffe02, limb1: 0xf0b1958f676e488a85a463d3, limb2: 0x579f2806dc3a11e99b548e2c, limb3: 0xd3efe9be9e8ed6f0311f48a, }, w6: u384 { limb0: 0x241c2c02a7a3ed68c8347454, limb1: 0x3c2e082d9d49bc403f20af15, limb2: 0xffb91438b7adbf0fd03b8452, limb3: 0x9f4a8a1c2bd71edd80fc8fa, }, w7: u384 { limb0: 0x7a09864d807d30f8134e35af, limb1: 0x4909a61fde584e8a97843962, limb2: 0xb0ae7df0ca31783cdef766ec, limb3: 0xab6c21fb130ff409a076e98, }, w8: u384 { limb0: 0xa4cf4a4bfb9a8696346ae5f2, limb1: 0xf441ab330a1a48b023ea4b16, limb2: 0xccbedbb5d89afd778ebbe2c6, limb3: 0xba098deb3929c27bad2d7cf, }, w9: u384 { limb0: 0x15ecdee09158e723e156143a, limb1: 0x2d88661ce3e7ed32f1813f83, limb2: 0x9268f857661e69f43c1006e9, limb3: 0x1baab7bc3df8b069e7921d3, }, w10: u384 { limb0: 0x8851dedab1e371b332830bb3, limb1: 0xe53bc821c7dd0054d6f6f857, limb2: 0x46240f19ae951bc875a2c8d5, limb3: 0xe7507265782567bc614a60b, }, w11: u384 { limb0: 0x9cace8682481da13c90f59c7, limb1: 0x79b9f6744c3fa34fa7ff5e2c, limb2: 0xa95279fc2041e30178a37645, limb3: 0x1201d399c1c8c0f103f8acf8, }, }, E12D { w0: u384 { limb0: 0xfe58f82f5a9a9486897fd7e1, limb1: 0x2f004eba229cefab93da839d, limb2: 0x3002f2bb83b58880f0d25efa, limb3: 0x122600e61fb5e8a8f3a87752, }, w1: u384 { limb0: 0xdcc4e4defac8110561f0b81f, limb1: 0xe4595573f7563e76b39ecf25, limb2: 0xe9a4f842ebb4b0f21e7e6904, limb3: 0x1b7035165596268ab55405, }, w2: u384 { limb0: 0xe2a1e6ad130b5dec5a307b9c, limb1: 0xa0715f0bb37946dee0717185, limb2: 0x89926a4a4bd27b0dcb987e4, limb3: 0xfa2213bf1fa84f02b4f4886, }, w3: u384 { limb0: 0xf7a4cd53187cf70d56c22d5b, limb1: 0xe27c4a45b50546e7d688b66b, limb2: 0xfffbb1435cd3e4d84e85fca7, limb3: 0xeef721f1ff2d893b897c350, }, w4: u384 { limb0: 0xf91449f591421e2ef6a486e7, limb1: 0xeeef2201ee263b14b45d18e4, limb2: 0xbd80060590e3e6b8ea5c51c9, limb3: 0x265aec09b58dacbb7a04b17, }, w5: u384 { limb0: 0xa799249a4b8a0bf74c5885dc, limb1: 0xf3369cf6149d51d50c53050f, limb2: 0x94e0a1d05c1748dbf29dcddb, limb3: 0x1025ab4a8aff8453c776f76, }, w6: u384 { limb0: 0xab0a9cbc3226d768b05be455, limb1: 0xda1ec9b71b4492481506fcd7, limb2: 0xdc657a6b18a8b49f20be7022, limb3: 0x16501c8c3d498fdd182c68da, }, w7: u384 { limb0: 0xda69756ffc4c2cc6785aea22, limb1: 0xf61431a0fb779cd2dcd9d576, limb2: 0x13bf99c01ad490a1b53665f8, limb3: 0x18af034f82f45856ec965578, }, w8: u384 { limb0: 0xd266c249f052d3f201c1b0d2, limb1: 0x13da63c60e3566cc4f009ccc, limb2: 0x3333fc6cdb72a6194cde21f6, limb3: 0x1604d59edc49752480de7888, }, w9: u384 { limb0: 0x440a479dbe693668b173c604, limb1: 0xe7aa2e5dcfda7aacf9e06a79, limb2: 0x659ba8b7e2702424fd322b71, limb3: 0x15f91e27f1ea647ab5b891a2, }, w10: u384 { limb0: 0x7d84e72876d78a543b85f35, limb1: 0x41d7a06e4188086be325658c, limb2: 0x4a3001b914f7fb1079e14d4e, limb3: 0x167fc4dc25373f64678594d7, }, w11: u384 { limb0: 0x82563c053c16182776849317, limb1: 0x6700ae4d019967f052b9feec, limb2: 0x78546ed88fbe3f4cb7f7a30c, limb3: 0x534411f7b6d38c591965d08, }, }, E12D { w0: u384 { limb0: 0x43cfc7d230ced51564ac1d27, limb1: 0x3f27df63705e89b5887f6ef6, limb2: 0xed962f37b246373dbe286875, limb3: 0x1153ae983b4bebeb96cee574, }, w1: u384 { limb0: 0x796edbbce52298f87a09de3c, limb1: 0x28594a3a94d2643da1f44c88, limb2: 0x1122679cf2a223c7641eba1, limb3: 0xec358db63b010a5f0195832, }, w2: u384 { limb0: 0x65114260981734bbd0c401dc, limb1: 0xaece96d8df427dc37661c427, limb2: 0xee18de1e045a8e8f278623ac, limb3: 0x119fd094c25c6ad221e4b923, }, w3: u384 { limb0: 0x2260aed58c6f1839b18780e0, limb1: 0xff136cb3f7910868a9bd9f6b, limb2: 0xa8eac3560aa6f0b6e9ce27f9, limb3: 0x147713d9a2ed668c5f769433, }, w4: u384 { limb0: 0xbfa0b51b9f28c1f41615b31a, limb1: 0xafe3bdfe46e1df691c9e4a8b, limb2: 0x8ec87ae1766b9944f1d28933, limb3: 0x173b1e22848118b6d362da12, }, w5: u384 { limb0: 0x3cb1473e40e34bac4f045ec0, limb1: 0xffe3bde303763828c46764b2, limb2: 0x2b156470816c102ef2910681, limb3: 0xff3da5b54bbef112da2264a, }, w6: u384 { limb0: 0xe700fcac3096a1a6fd859886, limb1: 0x31262c27298b10b8d1a8355, limb2: 0x7a0c2177d76d700ef9d473a0, limb3: 0xf68f4e6113a631c0da8e2fa, }, w7: u384 { limb0: 0x74b654d838f7a245bee7f39f, limb1: 0x665df41d4d1641df03af8d97, limb2: 0xd3ddeee4890b0c01b82e54c5, limb3: 0x12c5046f460d2c4e5b4384dc, }, w8: u384 { limb0: 0xfccdc5d4095fc526da571897, limb1: 0x83b7338c59475d4d75e801d, limb2: 0x402d5fd5dae3ea66188e61c0, limb3: 0xa4242530cd7992d10545d7f, }, w9: u384 { limb0: 0x8f330139a313def3b14a4191, limb1: 0xbbc6ef1fb35d0f418f9f78b5, limb2: 0xbb0532bb79ba32741aed8541, limb3: 0xece0fdc026b4f6a1a0e84ea, }, w10: u384 { limb0: 0xcd423bcb1fbc2198f7bfc5bc, limb1: 0xb2829a2104116480290ac2de, limb2: 0xbab0876e094583ff5a08ffe5, limb3: 0x9566104e8e04e6378963df0, }, w11: u384 { limb0: 0xcbcb4e81ebceca9d4be2280f, limb1: 0x46236f243dc5d2907d7cb0e6, limb2: 0x886438c7d5394b0df090d49c, limb3: 0x1736df2c975b470c28a0dfb8, }, }, E12D { w0: u384 { limb0: 0x41aaffbd4ffbc921fa99dafc, limb1: 0xe10f7c7325899560c7dc1a15, limb2: 0xc24436ca6dd16b7441353e1a, limb3: 0x768fbbaedb7eb6fa18ee62a, }, w1: u384 { limb0: 0xa237ae4d25932d4ea5316730, limb1: 0x2d696a5048a33ad2fe17b0fd, limb2: 0x2748a8d213d462a9afaf75d1, limb3: 0x1537e87dbfb1af57898e5a44, }, w2: u384 { limb0: 0x77e95072df611554c6efed5a, limb1: 0xb1a40cdb1e3fd9dc0c2f0268, limb2: 0xafa4361c57a92f48e272fd3c, limb3: 0x19670062e69cf3c129c6037b, }, w3: u384 { limb0: 0x35569a07f433ce179f869383, limb1: 0x2da70c3d64dc95f2a35dc5da, limb2: 0x5b6e4b1ebc196d9275e65fcd, limb3: 0xf527e45157446612739f8ea, }, w4: u384 { limb0: 0x52794dcb5d3a71e191ca9117, limb1: 0x1081a05756e17821c1a6b318, limb2: 0x7806bbf278080f55a756ac75, limb3: 0xa02c71394733385a722a842, }, w5: u384 { limb0: 0x488205f5f0ed76726dc2e4a8, limb1: 0x2156776174a8c26fcb09988, limb2: 0x48ed81cc7d76f82b1770c797, limb3: 0x581d27120bc189525f2a93d, }, w6: u384 { limb0: 0x5bd47af3f999778815753987, limb1: 0xb6749ec4bc2deb56879c4187, limb2: 0x12f25e541c1a97a1a04db98a, limb3: 0x29634e7d8dbbf051cac5686, }, w7: u384 { limb0: 0xb63879d6fdc4ddd1f14e0d7e, limb1: 0x5502d042b5ca2ca1fd1c87d, limb2: 0xde0a342fb21dec963cb42765, limb3: 0x9e6bd948d174830a6c0bdb5, }, w8: u384 { limb0: 0xbab8115cffcdaa9e9ffdd880, limb1: 0x507a287e0529113ee7c9872a, limb2: 0x8c9a7d3cd5caf1cbf71ea4f, limb3: 0x171c19b44ea2abed89e0eee7, }, w9: u384 { limb0: 0x3bdbf8f85ceba757f787a73f, limb1: 0x55e0e28688c74db104715a2d, limb2: 0x1d8c0545ec4eb386da5973c, limb3: 0xc12462e516c1d11b83d70c0, }, w10: u384 { limb0: 0x589e9e0e262699811b884e88, limb1: 0x849f9b1f3bfbecd0815d022, limb2: 0x72e87be328e66292abc0bfa0, limb3: 0xc20248f3856e6b79db43f4f, }, w11: u384 { limb0: 0xa0d3c01dc5b590235ed2b4a8, limb1: 0x36a65d97aa5e2789abe72557, limb2: 0x4dc3c2f633d2e2bf574872ac, limb3: 0x9b01ee1082798777c0ba5ce, }, }, E12D { w0: u384 { limb0: 0x3f8f38e60deac05c2621e24f, limb1: 0xd09553fa481657f8340e5069, limb2: 0xc4822e62b67cb0f3512ed972, limb3: 0x8fdd89171a3d99d824644e3, }, w1: u384 { limb0: 0x9f974bcce04ca7c552cefc61, limb1: 0x7d1e97af057c4e8bd1237e3a, limb2: 0xf6c412a8f240fdb471a4e6e8, limb3: 0x12798c3ef22db33c453af285, }, w2: u384 { limb0: 0x351067948f68705deef729f0, limb1: 0xdac1ded2ce3421f0f1c2a824, limb2: 0x8d9e3cebc0f199ce2dba4472, limb3: 0x37aca41f4d506c7b78e5a97, }, w3: u384 { limb0: 0xb7ff11075c5dfb0889eb8cf9, limb1: 0xdd6620d6caebf6d2c4bc9fe4, limb2: 0x78ebf44c90eb026aef8a4723, limb3: 0x11df205507286f5912bb28f9, }, w4: u384 { limb0: 0x2184c9e357e8fc5938e9f91e, limb1: 0xf6b93e6931861792051e41e8, limb2: 0xfa6774f07bec91d5b9056ac0, limb3: 0x5fd1e8fcb66b2024f4770cb, }, w5: u384 { limb0: 0xd34e1ed35b4acef37cdfcfcf, limb1: 0x3a3af4aade2ca0b690f8b745, limb2: 0xf18dd5095a8e61ebe9ec15c0, limb3: 0x14ac25a5dd1932d42434e64f, }, w6: u384 { limb0: 0x8deb2453cc29535af302a32a, limb1: 0x47377a569ca788bd447d51a, limb2: 0x7473f95b420a7a96033055b2, limb3: 0x1368da24ff42c9dbaddd1fd9, }, w7: u384 { limb0: 0x8a006d92f0f659b5879128c, limb1: 0x91a706c5249b0611411ef8, limb2: 0x476806b8ff9f387448c2283f, limb3: 0x86486211f2b7a69d85e6cc, }, w8: u384 { limb0: 0x359fb6053a482fd881477b73, limb1: 0x2e56ddae282b251bd26dc277, limb2: 0x9cc9414eb0de5930e18c2aef, limb3: 0xba5c3dae029b3461c4d83e3, }, w9: u384 { limb0: 0xd0329a1bee072189c5ee820d, limb1: 0x606c86092ed3d4c42466d4ed, limb2: 0xf05b66e3549519f50780d211, limb3: 0x9a4267bb540004634129449, }, w10: u384 { limb0: 0x7aac5888cca570c157bf526f, limb1: 0x37f49ebc8a648980697e0e77, limb2: 0xf97e721d54c47e0de9076619, limb3: 0x142cb1de4579b0555e3da41c, }, w11: u384 { limb0: 0x1ed3e34a9c2bf2a76e006e02, limb1: 0x295f1656ab393d271edff1c6, limb2: 0x5420889deecb1a07595e00d9, limb3: 0x4283e729218065b6577b5e2, }, }, E12D { w0: u384 { limb0: 0x5075209593337486e18df46d, limb1: 0xf0356df4c7181711fc91a827, limb2: 0xd97a31f91df154f5bb5851cc, limb3: 0x171ad2856e94d72ca9a24f15, }, w1: u384 { limb0: 0xff1d933543c728b07bca89f9, limb1: 0xccef75c4f943b25f9239cb2d, limb2: 0x5c4ebc877307706d280a3dbb, limb3: 0x1eb968438d74e489e2b3144, }, w2: u384 { limb0: 0x8cc0fc5028083749c6f1aba5, limb1: 0xf1a9d3c2e0265d84355ba0f4, limb2: 0x335a9d47fd282d5dce169790, limb3: 0x10f93b957c6f10e331c414bc, }, w3: u384 { limb0: 0x46ec651152db5023c9f201ed, limb1: 0xfb6d11467392f49bb22c65c9, limb2: 0xa591f73affc1eab979a3e88b, limb3: 0x826052b7ce51942a2ef191e, }, w4: u384 { limb0: 0x33ba6d3afeb674e23e5875d0, limb1: 0x59f23b1c3550f6e384c0f685, limb2: 0xda5c8ec47b003492848f9ced, limb3: 0x1693006cebfdda8888546ed4, }, w5: u384 { limb0: 0xd6d0c83bf1cad49129736afe, limb1: 0x9649be7e294be8399af5d37f, limb2: 0x4aa71b90ad07b5b8a36e6c12, limb3: 0x35aec40aaf79e7d69ccbee7, }, w6: u384 { limb0: 0xdb5a92f23380dee1624ece55, limb1: 0x5134a328c29fbe8f507b8e9, limb2: 0xc945ce072ddf331a76668f54, limb3: 0x16394a30abe069b9227e1c33, }, w7: u384 { limb0: 0xa23da0b9f52799a68dc93f24, limb1: 0x87cdda8d4a6217959ec51377, limb2: 0x57249de4c45419d6599ad204, limb3: 0x42312785159ea4b25189b90, }, w8: u384 { limb0: 0xbf4121cb4d006fe76a80ea73, limb1: 0x7572811c50bd43f4651663cc, limb2: 0xe1efd672ed967d2245b943d8, limb3: 0x1787f0a67f549962e9c14900, }, w9: u384 { limb0: 0x46eeec468b79d350dd499738, limb1: 0x2ea49c3b0d31b16e48774d10, limb2: 0x310dc8b2a2ce05fee1740e93, limb3: 0xc87d0f3e5646d57ba0f3aa3, }, w10: u384 { limb0: 0x342ee816cba104cc57c6c72f, limb1: 0x786438adbb7043c5ca348854, limb2: 0x493f49c69d99c3d0ab1ba333, limb3: 0x14f90bf3e332bc9472da656d, }, w11: u384 { limb0: 0xc34c780a191b063eee244f53, limb1: 0x4e65b486457bf36ded6b97be, limb2: 0xbfc811de2f4a72e871385095, limb3: 0x8e6f83135818adcffa10fb9, }, }, E12D { w0: u384 { limb0: 0xb672236717111ed916845c5d, limb1: 0xe05ed5f5b63130ce5ed7ce8d, limb2: 0xeb31d1721af0fc01c6a57a35, limb3: 0x39032c279eab78dcba6e6ed, }, w1: u384 { limb0: 0xb5fd928b359354dc3322587b, limb1: 0xe23b26cd9dcb026a63d7bd14, limb2: 0xe0c70e5315487d5185137fc0, limb3: 0x350b47980276bd086fb0081, }, w2: u384 { limb0: 0x35f10b2645a702ea20eb8a58, limb1: 0x8daf440feacc4167bd29f29f, limb2: 0x8aa066da8142908fd9dd00b9, limb3: 0xd808b595dfc641171a4589a, }, w3: u384 { limb0: 0x1a92f884e524af5ef9c51b4f, limb1: 0xa420b70bacb14c6241ffde9b, limb2: 0x5f3bbe9b0ed979e4a113a09f, limb3: 0x9362ed73e972e33f186b81e, }, w4: u384 { limb0: 0xc38fa3335d37ad7b433afc9a, limb1: 0x233c0caa5edcf5a96d0e9df4, limb2: 0x1bd45454abb2f3b001e563ff, limb3: 0x12ccd66a1baf7b9f617dc713, }, w5: u384 { limb0: 0x113ef84207dd50c3add3fb08, limb1: 0x803162a58c79355e6436964e, limb2: 0x27dbde708a2b5bcd71d8a803, limb3: 0x111e309aec4985bdbc80882c, }, w6: u384 { limb0: 0xbd293026b3eb9df6867cb268, limb1: 0xe20ee1bf24af986d5cd083f7, limb2: 0x5ef64ec24565ce144c3829bf, limb3: 0x11dd5ad08abb5b561a3f55a9, }, w7: u384 { limb0: 0xfbabf0ed3f8a0d795e246760, limb1: 0xe9f3f24bc74110c7a273f445, limb2: 0x55201b84cd4c2ed4db4b827c, limb3: 0x7581bdc02eb21512e4e5199, }, w8: u384 { limb0: 0x50990b07d3ad07f5cda1df83, limb1: 0x632286f3bbfcad27346d18bc, limb2: 0x57ddc3d0b6196616acbbf690, limb3: 0x12cb2e180657e981fd9f6793, }, w9: u384 { limb0: 0xb4a25977ccb83376385bcc3f, limb1: 0x409e0fc5843535e7b6ed163e, limb2: 0x7ee8e7148fce7871fc278d1e, limb3: 0x10956002d20d7414b33e971d, }, w10: u384 { limb0: 0xd2cad3667d7c91db4583301f, limb1: 0xce857381a82611c73427cf30, limb2: 0xd7519dec35afa6c62fdf1a93, limb3: 0x457e7d9af1ed868a22feb53, }, w11: u384 { limb0: 0xc5f0ce046d88cc73490b1ba2, limb1: 0xfa220bea70edb53dc7864606, limb2: 0x2918cf7c1e8cc362d0e91f41, limb3: 0x12c017f62533b0ecd49a3ec7, }, }, E12D { w0: u384 { limb0: 0x4518aac78144e2db1d690fe4, limb1: 0x8ee22fb09c4090a1c02db65, limb2: 0x8a5c9ae4cbcaac8abb408bf2, limb3: 0x9651c5934720322443f5a11, }, w1: u384 { limb0: 0x6494b375c23dfcce21c4995e, limb1: 0x41ecb011428f2cb8862ef588, limb2: 0xf99f42bcd9191bca26998f29, limb3: 0xaa56757b8a17fc161800337, }, w2: u384 { limb0: 0x49ed4b52c0e1957338585f16, limb1: 0xec9df95dec8748f334e0f2e1, limb2: 0x7de0ae19ffdac0ccb39246a2, limb3: 0xfb3acdb8486b68439e30548, }, w3: u384 { limb0: 0xfef29938a4d46b29fc1ab8ec, limb1: 0xb4893ab6f86df3d65f57ba5c, limb2: 0xd0404e3bd8ec3026aa989c65, limb3: 0x271d6ebc660acd8d80a0656, }, w4: u384 { limb0: 0x61ae001710978b805f2424d7, limb1: 0x641045bf7c449640c468a29e, limb2: 0x36471cc643cd1ac29df0fecb, limb3: 0x133f2d50d17aae7195255662, }, w5: u384 { limb0: 0x9ce3fa0f813dfdc1e58f1ba3, limb1: 0xda6067cb476596387621fd0c, limb2: 0xc4e9614cae2d4dbdedf3b5c9, limb3: 0x85036d8b38d3ec0fcf70a7c, }, w6: u384 { limb0: 0xfd1f35878f06df50b774ff5c, limb1: 0x50feeff3c2321474b6452db4, limb2: 0x9f7493a63e0d85a47fd3e297, limb3: 0x62dc9eb788448f8540cd8dc, }, w7: u384 { limb0: 0xc4a0867d87c7ad51322cb810, limb1: 0xd8ef0e23b67744060ef9dfb7, limb2: 0x40fd187e3a88eb2b97cfbeb2, limb3: 0xaa2506dbbb4b40e1160280f, }, w8: u384 { limb0: 0xc1dcb7d5d062a5a166387c7c, limb1: 0x6562c45c946f18353a39c690, limb2: 0xf6e93d09b449f23d816feb2c, limb3: 0x11fcfa1ad45d21f75f769cea, }, w9: u384 { limb0: 0xc01a508042b05e97a5f4713b, limb1: 0x34d0b623b7a887b7b8cd2b48, limb2: 0x3bdf0590b650cf2abd0cb69e, limb3: 0xd40ad6f197e440c5d882cfb, }, w10: u384 { limb0: 0xda450f4ec50e45a1aa05c7df, limb1: 0x8ed297199f1e04707e165a6f, limb2: 0x9953fd6d893f944489b6f265, limb3: 0x151f722a9d71cdbbc3f64572, }, w11: u384 { limb0: 0xab94a633f81012d0aa0a1123, limb1: 0x1fee996f53b99d7f880cd81f, limb2: 0x2eba0e596f0cb217540a9f6f, limb3: 0x6a3beb6e5c4d83dac52cd9c, }, }, E12D { w0: u384 { limb0: 0xe0bce0d55a595944dab6dbfa, limb1: 0x6a8646a7ccf054a613ef1054, limb2: 0xba8e1f16cf4e8c395896994c, limb3: 0x162d381237a930f8b29e736a, }, w1: u384 { limb0: 0xf1f266735451b2d2d7f1d30a, limb1: 0xa7218efef53e9dffab65229c, limb2: 0xb7c5e4dc5293bd7f9783effc, limb3: 0x11b0811580e449f355565e71, }, w2: u384 { limb0: 0x80d5d222072028933b28d7b2, limb1: 0xee7584721937fe2ab48078cb, limb2: 0x4df768bf695ffd52b0fd1c32, limb3: 0x1855a6b25e83bf66d4356b58, }, w3: u384 { limb0: 0x3a3df0e6083bf4bbe71e8c4f, limb1: 0x4fb213df213dbee762ab39c7, limb2: 0xca84e456f84ba4f61d280ed2, limb3: 0xcfc546b353f4c6f5d27dbe7, }, w4: u384 { limb0: 0x9cfab6d9fafadbd0e1c42893, limb1: 0xb5fb4e768002cba4b920caed, limb2: 0x506afea26fc4c7c654f4e050, limb3: 0x1583e33fd9048512c2a5c9fe, }, w5: u384 { limb0: 0xb3811bd3567d02c9c8ffb739, limb1: 0xcd49c3a01653b401503ab6c0, limb2: 0x56c65a37847a8f7251aa3148, limb3: 0x900ced571b08ea59f466697, }, w6: u384 { limb0: 0x3db7e62a39526ebeabbc5d95, limb1: 0x2a409338985dd19e8c1439bf, limb2: 0xce7718a40c9c26112265bf75, limb3: 0x105d6bb94f794d207e8dccf2, }, w7: u384 { limb0: 0x4a9921138c1b9724c664dad0, limb1: 0xe16e3e800231777a1b18f5e0, limb2: 0x406d5a7ed31a84b8c7e805b, limb3: 0x119e145f07bc6e23006475a8, }, w8: u384 { limb0: 0x91390ea551d00747d4835f37, limb1: 0xe8dded89909fe1429974f19, limb2: 0x36fc694a2d1a3d77ceb70cfa, limb3: 0x19f915fd54dfc09d92f03acf, }, w9: u384 { limb0: 0xb10a5bb15622ec5835700d8, limb1: 0x989765daca6c7f7b3a9cee46, limb2: 0xeb8d07dda116e084c5d9987f, limb3: 0x4b16db66ec480015be50763, }, w10: u384 { limb0: 0x1a0cb2b253062c1b6714614c, limb1: 0x1346a04f437bbb3430c7afbc, limb2: 0x9ee70f56486f1312034e6782, limb3: 0x8c8bfb66fadd2f5708f4ac0, }, w11: u384 { limb0: 0x8e4fa36170fcf1446bb898c0, limb1: 0x4b7035e4e8270f856e5671ed, limb2: 0x8cacdde4a419ed5e07bccd6f, limb3: 0xe892aa8d03b1e9dec74558a, }, }, ] .span(), big_Q: array![ u384 { limb0: 0x445d6baafba8450dd13ed7b1, limb1: 0x290c9657f4f55cea043fdd38, limb2: 0x9325259addf718d6d8287cff, limb3: 0x1d9331cfa3c9e50315038fa, }, u384 { limb0: 0x4b3082298a1e64aeadf6bf90, limb1: 0x4073d7bf69cf718d0056a5c6, limb2: 0xe00ddf4c12751e4cfccfd895, limb3: 0x259e13c714da7cdadc58791, }, u384 { limb0: 0x3a1c999d4db095eb59dcab4, limb1: 0x2d7de69e089b90aaa2d37e93, limb2: 0xf1be9d13ca73d61ed6817074, limb3: 0x97c9b09076cb34cee98515a, }, u384 { limb0: 0xa2c1efb24769a664c8b5fd35, limb1: 0x83a2af13670211bb0d69e600, limb2: 0xb1257a3a2c065750ddb409ba, limb3: 0x8c516dd5cc0af28b42feb7a, }, u384 { limb0: 0xb842c53b0590a848831e42f9, limb1: 0xb19e34913aff2326ef7a4358, limb2: 0x326f8de9bd1da5637f27ecc9, limb3: 0xdd6b998d03b616754dd2745, }, u384 { limb0: 0x6b61729e36ac7dc6f5114f96, limb1: 0xd67d641943aaa49b670230b0, limb2: 0xa2742c61b2099b163d2f67a2, limb3: 0xaff98133b5513c388c77286, }, u384 { limb0: 0x6c662edd7ccaf9aff500ed55, limb1: 0xd9aff80b364e3e5ab855a905, limb2: 0x286b7ac3c97fda4c95bd5fc0, limb3: 0xa2a508ed4fbf2d5ed430d8a, }, u384 { limb0: 0x7d3c3e63daa6a1ba97034b14, limb1: 0xa274ec2fe88d6f6509fed56d, limb2: 0xd2e7878eda9439d8d344d66a, limb3: 0xce409e0c30a390acd5cb44c, }, u384 { limb0: 0x217d423b495dc5ae1a3ebb46, limb1: 0xbad9b357090039ce2657b4ac, limb2: 0x4b7d3dbf36446dbb89dc0a97, limb3: 0x14dbe2f3ac60d09cf4d130b8, }, u384 { limb0: 0xcb0e3cb62edd80a81422c3f, limb1: 0x284dd7b6213f74f850e5a00, limb2: 0xee16b1f7b204b3379109d597, limb3: 0x159214b5b6cdbe70787026a1, }, u384 { limb0: 0x890f89db0a2e6271f1c5b430, limb1: 0x28bec49f958bb579f22ab228, limb2: 0x4ae230efdbd46047ad515117, limb3: 0x19a91b845ba6892ce3bef339, }, u384 { limb0: 0x738e91e3ecfbd258f8fe8a6e, limb1: 0xf796d5a8506ed71d63fec016, limb2: 0x4c4e70198951e55aa23495c, limb3: 0x14cca87e427a70b85b070c0f, }, u384 { limb0: 0x1573dafb3e3cc8f7087e2baa, limb1: 0xc24144c0ef7d7c40d7cc7a28, limb2: 0xe7ec035065fef9dfdf8f89a3, limb3: 0x106c1926f28babab7d8c16cb, }, u384 { limb0: 0x22081492011aae7272771a1b, limb1: 0x5c9f5077ca48e0ee885c6ffe, limb2: 0x529b91af0e34992c4e6bcc84, limb3: 0xcc8121d3536a7a113bca097, }, u384 { limb0: 0xaf6cc43bbd7f160a7e936e79, limb1: 0x2492c5c3c94b513a864cf1e1, limb2: 0x413026ea3fcfee76f31caa1d, limb3: 0x9f639d622d22ffab05ccfb4, }, u384 { limb0: 0xa877cd8f36cb3fad2288d537, limb1: 0x6d098c614d17493d58c3c12a, limb2: 0xd3a0579b4b38d611668682d5, limb3: 0xe77527e6087815c6f095c7a, }, u384 { limb0: 0xfa0ce8e766acf11630ac4ed1, limb1: 0x12148dd86cbeb22d385c029b, limb2: 0xcc1cb77fabb58425e96a9996, limb3: 0x10239f2110b3cbb1f9fa2ec9, }, u384 { limb0: 0x750d10e2bd02a6c51086cab4, limb1: 0x9d29bb0591e7f1a185d6a776, limb2: 0x6f9be5ccb0ab1c3fe3d823d6, limb3: 0x18a3598c016c5e90fc1c8f93, }, u384 { limb0: 0x9283ce36ff033ab356f55ba, limb1: 0xf6fccbb17c45b9432dd6ca1f, limb2: 0xfa06112ff2521c21241b2f4c, limb3: 0x1778d3acef5459b9a2e97de3, }, u384 { limb0: 0x67ebade07e5471b202335db2, limb1: 0xfc73e15d09d8a445fc192c6a, limb2: 0x496a96cc7341206bc41eb57c, limb3: 0x11c3434c4f2c87f3e8015fa1, }, u384 { limb0: 0xc68e6c66eeb7b465b7a91053, limb1: 0x8d32cd1f66e178c5551f52ab, limb2: 0x6607f3d6497797b353046088, limb3: 0x14c3d0025036e6b347df5690, }, u384 { limb0: 0x70b5f2016163fb80daf98105, limb1: 0x53531c225664a31d885c9f09, limb2: 0x972f54744c8910194d46b123, limb3: 0x2dff63e76a655c07087f97c, }, u384 { limb0: 0xe6301609c8d5798ee22c1634, limb1: 0xab940f7cc6a16e27f73d7bf1, limb2: 0xd83458215932fa14abc055f3, limb3: 0xb092a78ebfefa3b0e719d2a, }, u384 { limb0: 0xa9f81870938647e39e5a22e3, limb1: 0x6c8ece4ae0c4af6863738aa4, limb2: 0xccf0c9038baa5c9ea8f6a27c, limb3: 0x3d1f8e8e7891e4c79a2b0a1, }, u384 { limb0: 0x3971f6e183c521ccc4c00f1b, limb1: 0x1c4c8c97c639b207b8334f11, limb2: 0xe680de4e5fb8abf302d2f58b, limb3: 0x17be4592af7a922cca9c9fc3, }, u384 { limb0: 0x87c35e39141341ca2e0d8508, limb1: 0x3e32e84fe81062ada2274c5e, limb2: 0x7f158c23738383ccea5ed387, limb3: 0x2acdbe9122d2488cffaad06, }, u384 { limb0: 0x53e7b760e7074537bf97d1b1, limb1: 0xbddef09a5d237ab04bc1758a, limb2: 0x796e09ce6356693c2c754faf, limb3: 0x190c405bbe626263a60ac287, }, u384 { limb0: 0x259984eb9d3cbf91b1e9a850, limb1: 0x86793adaf8b0d344f2beaabb, limb2: 0x7756383d853d7f737c71c33a, limb3: 0x19714a1835930d5c7f5cd913, }, u384 { limb0: 0xc5ae3086a997b7d18c2d4b28, limb1: 0x13ad293d82c1ac29f38ffe23, limb2: 0x31b2e0aa3407a25ed34c91f8, limb3: 0xa8f492b622aaefbdc4da524, }, u384 { limb0: 0x557ec346c69c378c38506f20, limb1: 0x29c46724103db6643eccd29c, limb2: 0xc5397b60e6ac233c35673a04, limb3: 0x19b827ff25ac18face681427, }, u384 { limb0: 0x140a82fed9826ee3a61c5da9, limb1: 0x1b69c21c770397907d5a8576, limb2: 0xb189950ab3596e8822c02df1, limb3: 0xb3fd0ef8640d326a5093267, }, u384 { limb0: 0xf584f2222babbd504f512a06, limb1: 0xb5c7167d437b911cdb124a20, limb2: 0x9d31759b776236e702a59c4, limb3: 0x5620a9e0b882123b8c43352, }, u384 { limb0: 0xb47cc9d50f5c044ef3fc54ff, limb1: 0xce9e44ddec479c872583193b, limb2: 0x1278be54a9143510810a44e2, limb3: 0x14c158919eb2b2b17ae59dcb, }, u384 { limb0: 0x6510443a881532d33252a377, limb1: 0xab07a032dad31a1fd281ece1, limb2: 0x8268c9bec54ed78904bd2ec3, limb3: 0x19b2d416d9612fc5f1270b6, }, u384 { limb0: 0xb09728c1e17000e2a3adca0f, limb1: 0x7484c18a5ae8b6cb9e65a9ca, limb2: 0x9eb0da27d0ddd54d0bff2cdd, limb3: 0x59e4c1fc0b81222a58f48af, }, u384 { limb0: 0xb3d5cfcc42af3d890070a1f6, limb1: 0x633a89c63d397a8dbd0dc25, limb2: 0xad82bbba57b2be1082e3235f, limb3: 0x12d31cdd24655dd244b0404f, }, u384 { limb0: 0x122ff70798de075749ce2d26, limb1: 0xd5b4963a1b98a82c73786fbf, limb2: 0x372484de20675fa54dc2cf9f, limb3: 0x2a445bfa7323e30a092f5b, }, u384 { limb0: 0x77f0cb8771beabc8ea2c4272, limb1: 0xe0b49b26fb8aeb933a750769, limb2: 0x84abeca7fef536bdd473ab51, limb3: 0x14851f0a498cd44b8afb6001, }, u384 { limb0: 0x6a468d6d89d57fe33804ff0, limb1: 0xc4e66bc6e60b089dae3d5ad7, limb2: 0xd3ab3db43c216558e8c77290, limb3: 0x40f13e37975ec01631d71f3, }, u384 { limb0: 0x85425db02fcadd803a092e2e, limb1: 0x28638cae2487483c84297b8f, limb2: 0x945bfcd8bee8582abc15e530, limb3: 0x13c56cdb8fcf524429af5173, }, u384 { limb0: 0xc6d332dc2c22eff4ac31e3f7, limb1: 0xab10f60e98c90fa3ec89aef0, limb2: 0xde024ec2857f5a84fc6db8c4, limb3: 0x2964e03f7fc83afe59cde96, }, u384 { limb0: 0xd4925da47f5e2e95b67a3ced, limb1: 0x6e6d8b1e0d6a29fe41045062, limb2: 0xd27a4e1e277668d8bda45b13, limb3: 0xbdf5a29b9faecbc2d3177d6, }, u384 { limb0: 0x434c8372e10401e48ec2429f, limb1: 0x69d82c824fdc0d3805790867, limb2: 0xe7ed7a57583b5216053c9db9, limb3: 0x17f4f9de7e48979601c1c2a2, }, u384 { limb0: 0xa0d11eb6a504d256679608e5, limb1: 0x29c90c255da6fbb5cfc4495f, limb2: 0xca47b1abd20a31804f8930db, limb3: 0xbbd83ec78a6166ef36aa1fb, }, u384 { limb0: 0x7289808af814df23d6c89d00, limb1: 0x43453d1ce5e8e05dbb839b05, limb2: 0xa97d31b161062d0943e6f9a6, limb3: 0x9c04f649cb1a2e07c8773e8, }, u384 { limb0: 0x20586d603e1ddff39a084aed, limb1: 0xf31785a3ac061168a03aa547, limb2: 0xf814cb5325da93c4f837d4b2, limb3: 0x81783db43513c9c522bbc62, }, u384 { limb0: 0x6fbdc21a5be36a2e3010fbfa, limb1: 0x6bc5468e17f4418d53ebd302, limb2: 0x601c35ccaad0d6f3e1b3a8ac, limb3: 0x1973786c55c0ba2f6b87f117, }, u384 { limb0: 0x78aebf2ddcc087a32daa8eca, limb1: 0xb61ae20d301ccd65afcbde1b, limb2: 0xa3a00d31127efee85171b8a8, limb3: 0x37fe11b1a206af95bb12277, }, u384 { limb0: 0x812d7f20aca719c4e96ef68c, limb1: 0xb793866373bb9784eca7769f, limb2: 0x77d685e75d4c729ee2f5aa1e, limb3: 0x96bae5729b3ff540ca2e986, }, u384 { limb0: 0xb68666a1db42879ded98f557, limb1: 0x9dd8d5a6b735fd37f11c7d0a, limb2: 0xdccd06cb933682744b6edec1, limb3: 0x13f9cffbe7dfca805ca43c1c, }, u384 { limb0: 0x3b0007fe2df3aa78e4d00825, limb1: 0x87f41fa9a1e246c025a48aae, limb2: 0x13bd23d6f9969a42cbf12ad5, limb3: 0x329bcac3396e175891f5e45, }, u384 { limb0: 0x2fd7716c4a48ac8b434706b3, limb1: 0xd21d16d7856b1674f1dc39ae, limb2: 0xb43394cda9fe62e8d377d54, limb3: 0x8ad7cfe0094ae811e0a3063, }, u384 { limb0: 0x58cf88bebce17edd906ae443, limb1: 0x94a46cad8c18eade64faded7, limb2: 0xae14dd193ff4541d23d85e17, limb3: 0x13360e00eb699cc99be490e9, }, u384 { limb0: 0x1a7e23cb5791836fe922268d, limb1: 0xde8655a6b4507b002bd271b7, limb2: 0x4710dbc3fdb420049b6c64fa, limb3: 0x2db26a62c747dc5bdd7b775, }, u384 { limb0: 0xebeafa29827e65bb15878c9d, limb1: 0x14681e2120d0cd6e6336c9e3, limb2: 0x5485292282ed8e1294af5d54, limb3: 0xa26f69d8c76f9c959e41210, }, u384 { limb0: 0xcc466e1b38a8dff604c867f8, limb1: 0x16c8fe03017f1c81ae02d22, limb2: 0xa179039f6497c0a5fc60b563, limb3: 0x19066a33a7e3ed1118e61830, }, u384 { limb0: 0xc346d0995967c29aa92807b9, limb1: 0x85f1f66d99d64af8bf82b8b0, limb2: 0x8187274b1c52c1da8f724a15, limb3: 0x18ba38267c30aba28957f941, }, u384 { limb0: 0x646086cb2ac155e1ec929d86, limb1: 0x531e5f581431c7586f5e2110, limb2: 0x93f08aaaa048fa9e4bfcad79, limb3: 0x19451eb73b51d2550bf756d1, }, u384 { limb0: 0xe873237c87e085a9d92c285c, limb1: 0xc005d71145372f35f6e41051, limb2: 0x53d935a5d3983508180a8b39, limb3: 0x29b1bb36952f26c9ab9cb09, }, u384 { limb0: 0x801be88517a11ef1b6fd18a3, limb1: 0x9e2732f2abe69238df87e036, limb2: 0xcd6b60dca61b24f8bd2a8142, limb3: 0x28b7a065b5815f550404fd3, }, u384 { limb0: 0x917514fee5ea2267d6e33cd5, limb1: 0xcc67cdf72598354987d6755f, limb2: 0x25a5303b6c2af70c314ce7a5, limb3: 0x19e3c56d8709c7c04df676ae, }, u384 { limb0: 0x26bfe1899ae9dfd5b4da3b4, limb1: 0x969e22add3fd0aab63ad293, limb2: 0x48b187c212b3c7a4e7921c71, limb3: 0x672ed7e345d5f8a631c3304, }, u384 { limb0: 0xd20189c1a4bb67316333ae21, limb1: 0xc954417d074501388e7f6f86, limb2: 0xb5bd8dfb4efa8691c82c5800, limb3: 0x222584ecf600b97d162905e, }, u384 { limb0: 0xe60621f5521bd7ad8ad8b96c, limb1: 0x22475963b9bc603f561d5380, limb2: 0xf7ac4167352d3fc0b99fdf27, limb3: 0x150dd6bc480b181487774516, }, u384 { limb0: 0x7ca855b1cb1b28d86747f5a7, limb1: 0x53c0147cb1c13d8013522d02, limb2: 0x8ec52bfd40787ffbff320a9b, limb3: 0x182a5b33ef92df1c12447743, }, u384 { limb0: 0x9114a84f9bf4bd50874294fb, limb1: 0x5c0ae0681a57917c99e1426d, limb2: 0x6ad9a76609db5dc5c675c791, limb3: 0x19c1ec699482671fcaf1b19c, }, u384 { limb0: 0x2a3fd6b81e91f29b4d984e09, limb1: 0x50d301fab9c7d2f4779f90b1, limb2: 0xe6c8ccba191f1a279aee7e85, limb3: 0x136aa0c1143935a5e1a88ffc, }, u384 { limb0: 0x80a7670da417aa6f772cbfde, limb1: 0x61a344bfe57ffda8583dce50, limb2: 0xaeff7716b9b0e2a62feb3444, limb3: 0x2d4acc5a6afcbbdd3ec1106, }, u384 { limb0: 0x676c32bbca3e50f9280e1061, limb1: 0x721511fc5f703e9ee9cc8da7, limb2: 0xe4c28b279f46d1cae3f54872, limb3: 0x15d485af475c1ec9dbe78064, }, u384 { limb0: 0xed174e0ba434acd83711140, limb1: 0x42582904c61a29492ae17412, limb2: 0x3a8c7681f1eea64ae9caf7e9, limb3: 0x114f3cbdcbb37059a0b84f27, }, u384 { limb0: 0xad20ab5616fdbbbc85cff83d, limb1: 0x6b942863e803e855a12ae040, limb2: 0x49b20e2216eeafa9f267a636, limb3: 0xe96b66c6575d66a4ca5151d, }, u384 { limb0: 0x39ee6f5f837a2777769add11, limb1: 0x6da3d6ae14650170b03ee541, limb2: 0x5b568a3fc770bbc64a7abe0f, limb3: 0x2eb487d6806532733c3d5fc, }, u384 { limb0: 0xcbd78245c1111c2acf1cef7d, limb1: 0x2911da3ac9da565e05474a87, limb2: 0xb674717dd54246d1432893f7, limb3: 0x17d72d4450da66be3e21d845, }, u384 { limb0: 0xe8768aa2b9f49c1c9b179f7d, limb1: 0x8e87b8af5558360512405719, limb2: 0x2156d221f1eb0cd2ed4dea1a, limb3: 0x100512b562db61ca04587345, }, u384 { limb0: 0x2c7c6d4b54613235e5cfdbd8, limb1: 0xba509a15aba288f06e03b94b, limb2: 0x90018281875bf77714f47bd7, limb3: 0x68ccc6e229baf5e85a3eb3a, }, u384 { limb0: 0x2fe1317b1246c3d092d82bdd, limb1: 0xea756691cedf3b7369b482a5, limb2: 0x4eb31426855d031dede7aca0, limb3: 0x19285fe3057c4fff419fa3c4, }, u384 { limb0: 0xa3e0fe5805b346066bc4765c, limb1: 0xe6925e5999a25ae2beffa0d, limb2: 0xc009e4bb5bedc77b372b3277, limb3: 0x7940eb50b0ca5cc3b3bfe6d, }, u384 { limb0: 0x893e34d59249b8ef88b06c0c, limb1: 0x5e5488f21489b1d42d4febd7, limb2: 0xab8d85a40ac50c5467e84a53, limb3: 0x130cf982003e63a5c952d9a3, }, u384 { limb0: 0x859ef9e375fa2adec571eed0, limb1: 0xb90ec8bfa8bd1f80c7e76d4, limb2: 0x8f340c9d3ba7ceeac975a64, limb3: 0xd081f665e8f9b330e06062b, }, u384 { limb0: 0x7b665812578a7a35233cb10, limb1: 0x4424006d3b8b0e80e45cce9d, limb2: 0xd8dcfef05921b7a43d2e5a2a, limb3: 0x134f53443d962f815cb5ed9d, }, u384 { limb0: 0xc834d23469e835f617f80a52, limb1: 0x5efea47890e7f384560bcf1e, limb2: 0xc90a7871da96e44eaf467fb3, limb3: 0xe142bddd0e6505216e1da4, }, ], z: 0x73e890d1574ee2b2f3ca3ceae9c940462f46109b37cd53e4f1b245027a6ccfa, }; let res = multi_pairing_check_bls12_381_2P_2F(pair0, pair1, lines, hint); assert!(res.is_ok()); } #[test] fn test_BLS12_381_mpcheck_3P_2F_with_extra_miller_loop_result() { let pair0: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xe4f817e54aede0613c17035c, limb1: 0xdff1f15010392a6da1f95a6, limb2: 0xbed78d3d341e911d49f15454, limb3: 0x18154782ce0913b21588066d, }, y: u384 { limb0: 0x3d77d61326ef5a9a5a681757, limb1: 0xd3070afd4f0e121de7fcee60, limb2: 0xdf9ef4088763fe611fb85858, limb3: 0x11a612bdd0bc09562856a70, }, }, q: G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }, }; let pair1: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xe4f817e54aede0613c17035c, limb1: 0xdff1f15010392a6da1f95a6, limb2: 0xbed78d3d341e911d49f15454, limb3: 0x18154782ce0913b21588066d, }, y: u384 { limb0: 0x3d77d61326ef5a9a5a681757, limb1: 0xd3070afd4f0e121de7fcee60, limb2: 0xdf9ef4088763fe611fb85858, limb3: 0x11a612bdd0bc09562856a70, }, }, q: G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }, }; let pair2: G1G2Pair = G1G2Pair { p: G1Point { x: u384 { limb0: 0xe4f817e54aede0613c17035c, limb1: 0xdff1f15010392a6da1f95a6, limb2: 0xbed78d3d341e911d49f15454, limb3: 0x18154782ce0913b21588066d, }, y: u384 { limb0: 0x3d77d61326ef5a9a5a681757, limb1: 0xd3070afd4f0e121de7fcee60, limb2: 0xdf9ef4088763fe611fb85858, limb3: 0x11a612bdd0bc09562856a70, }, }, q: G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }, }; let precomputed_miller_loop_result = E12D { w0: u384 { limb0: 0xb911c83d732e7d278eca2b2, limb1: 0x371bde647281b4f0753c7b54, limb2: 0x32f3136b6412048dad82afcf, limb3: 0x276d8a09b1ef471d61e1fe9, }, w1: u384 { limb0: 0x2d08819331e98c628ad7e6a4, limb1: 0xf78975823557a6eaed403568, limb2: 0xd357bcaa08f3bcf837b69302, limb3: 0x84dc8eb534426c70fdeb97a, }, w2: u384 { limb0: 0xd8ab7356837a3539e775e8a4, limb1: 0xeac85ffce2bc7b2518fb953c, limb2: 0xdb2e7f9897c5d9aac15601e7, limb3: 0xad1ecf602d65fe881eaa6e0, }, w3: u384 { limb0: 0xb4bbd298bab0e4881a5ebb34, limb1: 0x14d8b2b539c52b38e862bb30, limb2: 0xc1ba1386389c858a2803bf51, limb3: 0xc44713fa939be012d57473a, }, w4: u384 { limb0: 0x8c8a60ac405578242750266c, limb1: 0x1f6ed0fc4768c4d33ae5bde9, limb2: 0x74356664cf5f284c5d9047dd, limb3: 0x17d27924032bad1b96b038a7, }, w5: u384 { limb0: 0xdca890b5c14238be57f05981, limb1: 0x5d5411099e394511d4bf5f21, limb2: 0x529d5c8a74ead9d439593056, limb3: 0x252d46d43966352b46ef871, }, w6: u384 { limb0: 0x1e65e90c6094915aaef973cd, limb1: 0x606ac452167328657347b203, limb2: 0x6198bb2924ef03ae600f7222, limb3: 0xdb2280eeda7144c402dfe7f, }, w7: u384 { limb0: 0x71c5034bc18b6d1c45a03c30, limb1: 0x31f94b4bb159c235c039f752, limb2: 0xdf1e1ed1387d8c002c5f3a20, limb3: 0x190ab4a19e1f1b981b892bae, }, w8: u384 { limb0: 0xf00e883b8262021a004b9fc8, limb1: 0x369f48c0083f000e7eeec362, limb2: 0x9170f7ea386763607860320a, limb3: 0x16e03a19b04611cdff78c5fd, }, w9: u384 { limb0: 0xf3b76b5dfdcf84760b96fa0c, limb1: 0x4ba7b263cc869557904c59cf, limb2: 0xbed73f63ea723c5eca33d491, limb3: 0x128d8d88c3c8616ff326a554, }, w10: u384 { limb0: 0x4380616825a3a723a4dc2b5c, limb1: 0x712262fd5e7ddfa653a4708e, limb2: 0x303031f5c1bf5e2f73d4750a, limb3: 0x36d2ef1d9b923357234e298, }, w11: u384 { limb0: 0xbe53e886831d35b55f343069, limb1: 0x34b2a5b11f48e46a872245a2, limb2: 0x6afab08a2bc52479f09c105f, limb3: 0x329f18e7852fa05613e9204, }, }; let lines = array![ G2Line { r0a0: u384 { limb0: 0xa5165654d48ad38da89955b2, limb1: 0x36388a52d2379c53735285c1, limb2: 0xb1cba90b5a7d592a905913f6, limb3: 0xf04eef4de6a895d29865a33, }, r0a1: u384 { limb0: 0x11170525e014139da401da13, limb1: 0xdfc4d38dc6621f61b8834990, limb2: 0xb86906ab9966ab43169ba396, limb3: 0x104b8a575e67290a4d8e5d0, }, r1a0: u384 { limb0: 0x2fddaa92e366f11a886242bb, limb1: 0xf7255a5c3e06de681d21207f, limb2: 0x544afd5f8c149ed0980ad33f, limb3: 0x18ff3a5ad5398470eec050cd, }, r1a1: u384 { limb0: 0x5ebc8ff3cef71a1b2b0ce5d9, limb1: 0xf4093ee74d1a5714b4562355, limb2: 0xe6d400f1614d23e5b0b3831f, limb3: 0x4e3cba1ec100020f137797e, }, }, G2Line { r0a0: u384 { limb0: 0xcf94aa0961ba244fb7b34f8, limb1: 0x9eedbbaadfb34c820b7b9046, limb2: 0xdfdb0674b62b2c9622a321e9, limb3: 0x18745455fc3b957175dbaaab, }, r0a1: u384 { limb0: 0xb18b9b496c7e76d19d0476a3, limb1: 0x532e40e737e71a727e36699d, limb2: 0x1173a4db0c906464c9c6dfe5, limb3: 0x14436970af87927ca25ab397, }, r1a0: u384 { limb0: 0x2b8bedf7ace9601914137555, limb1: 0x8e5a6616ba6b5a7c0a4b60cc, limb2: 0xeed2fb7a6b6951d08720afd2, limb3: 0x6e20b841803b78a54cb51f0, }, r1a1: u384 { limb0: 0xe2f3cc1d38637307df479c33, limb1: 0x553fbfecff64b0f8513ea53, limb2: 0xc35e934c2f0dd0dfc36fb764, limb3: 0xfe253f73265563f5da37bf0, }, }, G2Line { r0a0: u384 { limb0: 0xa5165654d48ad38da89955b2, limb1: 0x36388a52d2379c53735285c1, limb2: 0xb1cba90b5a7d592a905913f6, limb3: 0xf04eef4de6a895d29865a33, }, r0a1: u384 { limb0: 0x11170525e014139da401da13, limb1: 0xdfc4d38dc6621f61b8834990, limb2: 0xb86906ab9966ab43169ba396, limb3: 0x104b8a575e67290a4d8e5d0, }, r1a0: u384 { limb0: 0x2fddaa92e366f11a886242bb, limb1: 0xf7255a5c3e06de681d21207f, limb2: 0x544afd5f8c149ed0980ad33f, limb3: 0x18ff3a5ad5398470eec050cd, }, r1a1: u384 { limb0: 0x5ebc8ff3cef71a1b2b0ce5d9, limb1: 0xf4093ee74d1a5714b4562355, limb2: 0xe6d400f1614d23e5b0b3831f, limb3: 0x4e3cba1ec100020f137797e, }, }, G2Line { r0a0: u384 { limb0: 0xcf94aa0961ba244fb7b34f8, limb1: 0x9eedbbaadfb34c820b7b9046, limb2: 0xdfdb0674b62b2c9622a321e9, limb3: 0x18745455fc3b957175dbaaab, }, r0a1: u384 { limb0: 0xb18b9b496c7e76d19d0476a3, limb1: 0x532e40e737e71a727e36699d, limb2: 0x1173a4db0c906464c9c6dfe5, limb3: 0x14436970af87927ca25ab397, }, r1a0: u384 { limb0: 0x2b8bedf7ace9601914137555, limb1: 0x8e5a6616ba6b5a7c0a4b60cc, limb2: 0xeed2fb7a6b6951d08720afd2, limb3: 0x6e20b841803b78a54cb51f0, }, r1a1: u384 { limb0: 0xe2f3cc1d38637307df479c33, limb1: 0x553fbfecff64b0f8513ea53, limb2: 0xc35e934c2f0dd0dfc36fb764, limb3: 0xfe253f73265563f5da37bf0, }, }, G2Line { r0a0: u384 { limb0: 0xf63d5adf98504eb919404838, limb1: 0x322c7fec39e0dbb7e3fab671, limb2: 0x66a7d9554b938f680e363589, limb3: 0x168b865e60bf25b5f80efdba, }, r0a1: u384 { limb0: 0xa19475051f484344fbfcb94, limb1: 0xecab432b31e20fd481ef1641, limb2: 0x9aef0e4871833b8e86498442, limb3: 0xbfbebd5fe20e6b34cd10d52, }, r1a0: u384 { limb0: 0x3034c4ead4a9ecca97ef227f, limb1: 0x3ff722abdd9b1b4fb2ed76a2, limb2: 0x89478f4e3e947df714a9fb5e, limb3: 0xf7d15d762bc99988f9d789d, }, r1a1: u384 { limb0: 0xe7309c91453760cefb576bc9, limb1: 0xc04e0c62e92a4efd0f9d9c3b, limb2: 0xada0f0a505209353f4b17f24, limb3: 0x185b2e9615659da43b50282e, }, }, G2Line { r0a0: u384 { limb0: 0xf63d5adf98504eb919404838, limb1: 0x322c7fec39e0dbb7e3fab671, limb2: 0x66a7d9554b938f680e363589, limb3: 0x168b865e60bf25b5f80efdba, }, r0a1: u384 { limb0: 0xa19475051f484344fbfcb94, limb1: 0xecab432b31e20fd481ef1641, limb2: 0x9aef0e4871833b8e86498442, limb3: 0xbfbebd5fe20e6b34cd10d52, }, r1a0: u384 { limb0: 0x3034c4ead4a9ecca97ef227f, limb1: 0x3ff722abdd9b1b4fb2ed76a2, limb2: 0x89478f4e3e947df714a9fb5e, limb3: 0xf7d15d762bc99988f9d789d, }, r1a1: u384 { limb0: 0xe7309c91453760cefb576bc9, limb1: 0xc04e0c62e92a4efd0f9d9c3b, limb2: 0xada0f0a505209353f4b17f24, limb3: 0x185b2e9615659da43b50282e, }, }, G2Line { r0a0: u384 { limb0: 0xacd0c846fbba57a06a86174d, limb1: 0xb3559bb08ff796c300ff2163, limb2: 0xb7ebbcfa41b1f30d02874a61, limb3: 0x7a87f7612c63af0969932c, }, r0a1: u384 { limb0: 0xd4f55c22c625dddb92b73bd7, limb1: 0x681facc4bfa2b130fcf3dacd, limb2: 0x3bd92d164662bbb7f99c1b5a, limb3: 0x12ac7263968961adecde567f, }, r1a0: u384 { limb0: 0x81f5ef562d3dfd1fe4780fbf, limb1: 0xcb396419628f7f02f0f0e2f8, limb2: 0x3012e01dd8fc025163ad5e2a, limb3: 0x1c053f246178e26fa6d3dea, }, r1a1: u384 { limb0: 0xc81f62215d8116e0b580ac54, limb1: 0xef2e48f58ffbbafac5b2b827, limb2: 0xe22598ad9700d53d0ab24440, limb3: 0xeec459ce4be55ed92aa3f08, }, }, G2Line { r0a0: u384 { limb0: 0x628192ce61515a10db139388, limb1: 0xdf2fbc87bd9658e30ab5ca96, limb2: 0x81420786279bf4a2c17ecbee, limb3: 0x7cd8317980fac457217aa73, }, r0a1: u384 { limb0: 0xad2f18fc2c832eedc6828d6a, limb1: 0x2c62b1d26ffe93fb41fbf6a6, limb2: 0x54a6928b6b6cb48d95627389, limb3: 0x155b45f029858968773bd77a, }, r1a0: u384 { limb0: 0x3a4649b4ea519194273b8413, limb1: 0x39ed13d914c220a2a8621253, limb2: 0xb2c2fe85ccf72ab37ef6d3e8, limb3: 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0xaa05f45202de8ae127c3d64b, limb3: 0x105819b4d71c03790bfeb092, }, r0a1: u384 { limb0: 0xdbca0a627c296fe7aad607f1, limb1: 0x7a8255ce902319b92cd065be, limb2: 0x7b50bc220077a52b59ce5307, limb3: 0xf9e05915fae54c347b88c1e, }, r1a0: u384 { limb0: 0x2cac98351a30b0b82a54b79e, limb1: 0xed07531e9f2463331277b6f3, limb2: 0x12b3ebca243e04ae826f6c33, limb3: 0x12969325aa2fdc65900e8a68, }, r1a1: u384 { limb0: 0xb0799b5a24a5ceb48429df27, limb1: 0x2ee6d0a37a7ddc7798f3bc77, limb2: 0x63ec626451e43c56ff92bafb, limb3: 0x50818d39d6234b4dc233a38, }, }, G2Line { r0a0: u384 { limb0: 0xb67cc5f083f96e39a134d194, limb1: 0xaf9e780b6c4a7184061027d7, limb2: 0xdcda4477070e92cdf3397d43, limb3: 0x6a696f2522cc9af3d082748, }, r0a1: u384 { limb0: 0x392c02806e22eca0d48618e7, limb1: 0x8aba49a57d2d347b3df198c6, limb2: 0x754cc050d1a93ac3f85ce805, limb3: 0xe759f363f34e4784dc65a71, }, r1a0: u384 { limb0: 0xd34741277335bd3799ea321e, limb1: 0xdd6641b8fbd73a1428f041ea, limb2: 0xe38c8915296a5c201145b868, limb3: 0x105d879c98b5261f00ea9de9, }, r1a1: u384 { limb0: 0x5c96d186d5a39ffc6149aefc, limb1: 0xe4f274d1b18b7edb57fc9918, limb2: 0xea1f8cfaa190965fbae29234, limb3: 0x110e5f288f9b57423dcde8a7, }, }, G2Line { r0a0: u384 { limb0: 0xb67cc5f083f96e39a134d194, limb1: 0xaf9e780b6c4a7184061027d7, limb2: 0xdcda4477070e92cdf3397d43, limb3: 0x6a696f2522cc9af3d082748, }, r0a1: u384 { limb0: 0x392c02806e22eca0d48618e7, limb1: 0x8aba49a57d2d347b3df198c6, limb2: 0x754cc050d1a93ac3f85ce805, limb3: 0xe759f363f34e4784dc65a71, }, r1a0: u384 { limb0: 0xd34741277335bd3799ea321e, limb1: 0xdd6641b8fbd73a1428f041ea, limb2: 0xe38c8915296a5c201145b868, limb3: 0x105d879c98b5261f00ea9de9, }, r1a1: u384 { limb0: 0x5c96d186d5a39ffc6149aefc, limb1: 0xe4f274d1b18b7edb57fc9918, limb2: 0xea1f8cfaa190965fbae29234, limb3: 0x110e5f288f9b57423dcde8a7, }, }, G2Line { r0a0: u384 { limb0: 0xfd988b3fefee9bec8d580624, limb1: 0xea8b268179a0cff5e5a733de, limb2: 0xc3261de3bb0dae36dd3a12d1, limb3: 0xe0311c57778716dd26ec448, }, r0a1: u384 { limb0: 0xbd3bb91f6aebae19c756f359, limb1: 0x8ddb3cfc5cbb0a427decde5c, limb2: 0xa3ee67368948da84ef76cc9c, limb3: 0x386b903ec5f7b21375b440b, }, r1a0: u384 { limb0: 0xf101c44cc5023657f2d800ce, limb1: 0xe3c33e1823e3fbd36e6ec7f3, limb2: 0xb72b4d93169a4b6f53c98bd8, limb3: 0xfe4e73b7283c84a94493193, }, r1a1: u384 { limb0: 0x72d680350e90ad8a1b951514, limb1: 0xbcc457b76fcdb17ec8734b67, limb2: 0xc2f60e7bf5f241b7e5cee4a0, limb3: 0x16aaebbc648697f433c2261d, }, }, G2Line { r0a0: u384 { limb0: 0xfd988b3fefee9bec8d580624, limb1: 0xea8b268179a0cff5e5a733de, limb2: 0xc3261de3bb0dae36dd3a12d1, limb3: 0xe0311c57778716dd26ec448, }, r0a1: u384 { limb0: 0xbd3bb91f6aebae19c756f359, limb1: 0x8ddb3cfc5cbb0a427decde5c, limb2: 0xa3ee67368948da84ef76cc9c, limb3: 0x386b903ec5f7b21375b440b, }, r1a0: u384 { limb0: 0xf101c44cc5023657f2d800ce, limb1: 0xe3c33e1823e3fbd36e6ec7f3, limb2: 0xb72b4d93169a4b6f53c98bd8, limb3: 0xfe4e73b7283c84a94493193, }, r1a1: u384 { limb0: 0x72d680350e90ad8a1b951514, limb1: 0xbcc457b76fcdb17ec8734b67, limb2: 0xc2f60e7bf5f241b7e5cee4a0, limb3: 0x16aaebbc648697f433c2261d, }, }, G2Line { r0a0: u384 { limb0: 0x6f85133f411d25e0b5f35e4e, limb1: 0xc638badc6521e71c561777f7, limb2: 0x8353d2452d7ab56d813e41e4, limb3: 0x10bc8e7f6b5289bdc1c5fa9f, }, r0a1: u384 { limb0: 0xab5f1742cb30521d01daacc0, limb1: 0x9e56c445377075119d1596a4, limb2: 0xa72211611536639fe4976d69, limb3: 0x11f238149a22f79fa16cb32b, }, r1a0: u384 { limb0: 0x8367fe7274231c74704c80ff, limb1: 0xa8e2ad1a7f0c36a34b48cd88, limb2: 0x7faca91a72963d25472465c, limb3: 0x1311fd26e3b83c10952fb826, }, r1a1: u384 { limb0: 0xae246df1f149439c747384f1, limb1: 0x68a615ee2f9d7f8d56f2174b, limb2: 0xf64d48e37e9111200271d2ee, limb3: 0x2daa9898e27bc3d9ce26195, }, }, G2Line { r0a0: u384 { limb0: 0x6f85133f411d25e0b5f35e4e, limb1: 0xc638badc6521e71c561777f7, limb2: 0x8353d2452d7ab56d813e41e4, limb3: 0x10bc8e7f6b5289bdc1c5fa9f, }, r0a1: u384 { limb0: 0xab5f1742cb30521d01daacc0, limb1: 0x9e56c445377075119d1596a4, limb2: 0xa72211611536639fe4976d69, limb3: 0x11f238149a22f79fa16cb32b, }, r1a0: u384 { limb0: 0x8367fe7274231c74704c80ff, limb1: 0xa8e2ad1a7f0c36a34b48cd88, limb2: 0x7faca91a72963d25472465c, limb3: 0x1311fd26e3b83c10952fb826, }, r1a1: u384 { limb0: 0xae246df1f149439c747384f1, limb1: 0x68a615ee2f9d7f8d56f2174b, limb2: 0xf64d48e37e9111200271d2ee, limb3: 0x2daa9898e27bc3d9ce26195, }, }, G2Line { r0a0: u384 { limb0: 0x293cdab968151d9a88ba8197, limb1: 0x91e20a097317fbf539a50489, limb2: 0x60d594dea296004ee2824b62, limb3: 0x190b7e72bd6ee0ed0faf4962, }, r0a1: u384 { limb0: 0xb5b5a519c745663a2d0a6a22, limb1: 0xe8d8005fede56d9bb7f102ac, limb2: 0x1534acc00cf17be37afd327d, limb3: 0xb3c34b4025f50c09d86ccf1, }, r1a0: u384 { limb0: 0x8a28c9f5c487242be3157d10, limb1: 0x35adb9f220d3910e8e7e628a, limb2: 0x8a53a50706970f599abb8b1, limb3: 0x1813805985492b229d25c9c0, }, r1a1: u384 { limb0: 0x53f421abc7375d7ef5f4ea15, limb1: 0x3453e28c8b88718a6bd2122c, limb2: 0x181dbbb6144062890a582400, limb3: 0xe27d7ff293c8253269fc184, }, }, G2Line { r0a0: u384 { limb0: 0x293cdab968151d9a88ba8197, limb1: 0x91e20a097317fbf539a50489, limb2: 0x60d594dea296004ee2824b62, limb3: 0x190b7e72bd6ee0ed0faf4962, }, r0a1: u384 { limb0: 0xb5b5a519c745663a2d0a6a22, limb1: 0xe8d8005fede56d9bb7f102ac, limb2: 0x1534acc00cf17be37afd327d, limb3: 0xb3c34b4025f50c09d86ccf1, }, r1a0: u384 { limb0: 0x8a28c9f5c487242be3157d10, limb1: 0x35adb9f220d3910e8e7e628a, limb2: 0x8a53a50706970f599abb8b1, limb3: 0x1813805985492b229d25c9c0, }, r1a1: u384 { limb0: 0x53f421abc7375d7ef5f4ea15, limb1: 0x3453e28c8b88718a6bd2122c, limb2: 0x181dbbb6144062890a582400, limb3: 0xe27d7ff293c8253269fc184, }, }, G2Line { r0a0: u384 { limb0: 0x788ac954b6de3b9ef5a6c12c, limb1: 0xe13873c4ba9728c89be70b9a, limb2: 0x5d6b9d45c0985f271595d4c9, limb3: 0x1954917fe709faff9865ebc3, }, r0a1: u384 { limb0: 0x93fca181f0664865a2fc75fe, limb1: 0x535e2e42a4a967f7ca763127, limb2: 0xce90cca6dfec0e2e8fae9e3, limb3: 0xd086b29c92aaddb7245299d, }, r1a0: u384 { limb0: 0x4ef1ed09cae08920a78f3bd7, limb1: 0x6714e095d8cc53e3829f2b5a, limb2: 0x9022123e8d70a0049ccb62a6, limb3: 0xef311f53ea87dc5da3ddd33, }, r1a1: u384 { limb0: 0xbc5ec58d4c68ebde3ce5d6af, limb1: 0x91f1285170fbc3c4d812f3aa, limb2: 0x13eec60eefd5588477e432d8, limb3: 0x74a34dc5c8359340c5fe4f1, }, }, G2Line { r0a0: u384 { limb0: 0x788ac954b6de3b9ef5a6c12c, limb1: 0xe13873c4ba9728c89be70b9a, limb2: 0x5d6b9d45c0985f271595d4c9, limb3: 0x1954917fe709faff9865ebc3, }, r0a1: u384 { limb0: 0x93fca181f0664865a2fc75fe, limb1: 0x535e2e42a4a967f7ca763127, limb2: 0xce90cca6dfec0e2e8fae9e3, limb3: 0xd086b29c92aaddb7245299d, }, r1a0: u384 { limb0: 0x4ef1ed09cae08920a78f3bd7, limb1: 0x6714e095d8cc53e3829f2b5a, limb2: 0x9022123e8d70a0049ccb62a6, limb3: 0xef311f53ea87dc5da3ddd33, }, r1a1: u384 { limb0: 0xbc5ec58d4c68ebde3ce5d6af, limb1: 0x91f1285170fbc3c4d812f3aa, limb2: 0x13eec60eefd5588477e432d8, limb3: 0x74a34dc5c8359340c5fe4f1, }, }, G2Line { r0a0: u384 { limb0: 0x46d409dd77b17a23fc402a34, limb1: 0x26d0e70f78ec18c019c2f074, limb2: 0x98d531c6d1b75c297e5f3c9, limb3: 0x3a571d848cc57291ff2ffa, }, r0a1: u384 { limb0: 0x9220d2160322f603fa59c76, limb1: 0xf7811520cd515d496363e693, limb2: 0x2c5614352975026f33861c37, limb3: 0x17644f4fbe80675d0953c99d, }, r1a0: u384 { limb0: 0x4aaca6cc8c9d33c63c0f1d1b, limb1: 0xe45b1fa9442911a2857ec8fa, limb2: 0x32c9f0ff272cf03afd720f7d, limb3: 0x1e0242dad0177697c8a0aff, }, r1a1: u384 { limb0: 0x728463c48b5aea9ca697e90b, limb1: 0x7b8f08b990bfcb2db30c3193, limb2: 0x7232cfafe8d7566719d9c4af, limb3: 0x5f1c40f1c28ca2cf8f83994, }, }, G2Line { r0a0: u384 { limb0: 0x46d409dd77b17a23fc402a34, limb1: 0x26d0e70f78ec18c019c2f074, limb2: 0x98d531c6d1b75c297e5f3c9, limb3: 0x3a571d848cc57291ff2ffa, }, r0a1: u384 { limb0: 0x9220d2160322f603fa59c76, limb1: 0xf7811520cd515d496363e693, limb2: 0x2c5614352975026f33861c37, limb3: 0x17644f4fbe80675d0953c99d, }, r1a0: u384 { limb0: 0x4aaca6cc8c9d33c63c0f1d1b, limb1: 0xe45b1fa9442911a2857ec8fa, limb2: 0x32c9f0ff272cf03afd720f7d, limb3: 0x1e0242dad0177697c8a0aff, }, r1a1: u384 { limb0: 0x728463c48b5aea9ca697e90b, limb1: 0x7b8f08b990bfcb2db30c3193, limb2: 0x7232cfafe8d7566719d9c4af, limb3: 0x5f1c40f1c28ca2cf8f83994, }, }, G2Line { r0a0: u384 { limb0: 0xf6913070c37af578aa1b9a37, limb1: 0x664781917f37151d3a0d627a, limb2: 0x9d5cd2ddf7dd66c044a101e6, limb3: 0x13cc21b4e1f7c288d1b899ad, }, r0a1: u384 { limb0: 0x5607928bdfad47c77f840a3, limb1: 0xdd3d8bf376d25ba8b3a926aa, limb2: 0x35c034874a2ccd33ec0fedad, limb3: 0x176b6eb4cbcedd0416d8b2e9, }, r1a0: u384 { limb0: 0x1f81c4f93cff2721578a1cd7, limb1: 0x7908a9522938e77f3e279a41, limb2: 0x7fdc79ff7c835d873ab01ed2, limb3: 0x11e3d19be097dc7e63b49b10, }, r1a1: u384 { limb0: 0x235b99292b27c9efd6a59ff4, limb1: 0x82cb49f680a93e6e718e3689, limb2: 0x710cd7d6390eca09a291ad52, limb3: 0xf60ffe1a70c2771c44ee20f, }, }, G2Line { r0a0: u384 { limb0: 0xf6913070c37af578aa1b9a37, limb1: 0x664781917f37151d3a0d627a, limb2: 0x9d5cd2ddf7dd66c044a101e6, limb3: 0x13cc21b4e1f7c288d1b899ad, }, r0a1: u384 { limb0: 0x5607928bdfad47c77f840a3, limb1: 0xdd3d8bf376d25ba8b3a926aa, limb2: 0x35c034874a2ccd33ec0fedad, limb3: 0x176b6eb4cbcedd0416d8b2e9, }, r1a0: u384 { limb0: 0x1f81c4f93cff2721578a1cd7, limb1: 0x7908a9522938e77f3e279a41, limb2: 0x7fdc79ff7c835d873ab01ed2, limb3: 0x11e3d19be097dc7e63b49b10, }, r1a1: u384 { limb0: 0x235b99292b27c9efd6a59ff4, limb1: 0x82cb49f680a93e6e718e3689, limb2: 0x710cd7d6390eca09a291ad52, limb3: 0xf60ffe1a70c2771c44ee20f, }, }, G2Line { r0a0: u384 { limb0: 0x8b2d5026a69128c8dcd7fa01, limb1: 0xa28af7e6845ec126ce674de3, limb2: 0x74618fcee9375eaffe329a57, limb3: 0xd495764b344945c1bbf2528, }, r0a1: u384 { limb0: 0xc7191fe7d9c67d8956440c8e, limb1: 0x9886e12a6f751b086c256b4e, limb2: 0x2d800e1229e7acc62268ce86, limb3: 0x8a1766c3924e9fe41995f27, }, r1a0: u384 { limb0: 0xe95730415bdae7fa69798292, limb1: 0x550a77eda4e6fd2f0bea1e69, limb2: 0xad91cd00e401b4c4d699ac6, limb3: 0x147171fe6dce69e5291e5d4, }, r1a1: u384 { limb0: 0x3950881f65abb4ae1b59bbca, limb1: 0x588580a38b689b30f05b80bd, limb2: 0x77cb4489a340d3748044c17c, limb3: 0xda658ea95a6fefe83fa39d1, }, }, G2Line { r0a0: u384 { limb0: 0x8b2d5026a69128c8dcd7fa01, limb1: 0xa28af7e6845ec126ce674de3, limb2: 0x74618fcee9375eaffe329a57, limb3: 0xd495764b344945c1bbf2528, }, r0a1: u384 { limb0: 0xc7191fe7d9c67d8956440c8e, limb1: 0x9886e12a6f751b086c256b4e, limb2: 0x2d800e1229e7acc62268ce86, limb3: 0x8a1766c3924e9fe41995f27, }, r1a0: u384 { limb0: 0xe95730415bdae7fa69798292, limb1: 0x550a77eda4e6fd2f0bea1e69, limb2: 0xad91cd00e401b4c4d699ac6, limb3: 0x147171fe6dce69e5291e5d4, }, r1a1: u384 { limb0: 0x3950881f65abb4ae1b59bbca, limb1: 0x588580a38b689b30f05b80bd, limb2: 0x77cb4489a340d3748044c17c, limb3: 0xda658ea95a6fefe83fa39d1, }, }, G2Line { r0a0: u384 { limb0: 0xfb36382a07a0546177544af4, limb1: 0x98af0f0579819a56ea21677c, limb2: 0xaba237656261d369d5d808d6, limb3: 0xc9fb6adc6528d40d93c0da4, }, r0a1: u384 { limb0: 0x5c117b9250db1f77095f3f80, limb1: 0xda15f91e9282ff6deb2a2558, limb2: 0xaa820f7393229d9126ae7b62, limb3: 0x110c5e918c554c126361e32e, }, r1a0: u384 { limb0: 0xac056d30f948e924aa511f05, limb1: 0x31318c843660bb21180267e1, limb2: 0xb22b2d85ae7080079ab0bc7e, limb3: 0x14941dda97edcedd3d32ad23, }, r1a1: u384 { limb0: 0x876fd0749511e318e84cc37e, limb1: 0x71b4a1c6b941f0bd7731cf3a, limb2: 0x54e1fb48d3305bd534e5132f, limb3: 0x262c905d8278be2f7a9d1ea, }, }, G2Line { r0a0: u384 { limb0: 0xfb36382a07a0546177544af4, limb1: 0x98af0f0579819a56ea21677c, limb2: 0xaba237656261d369d5d808d6, limb3: 0xc9fb6adc6528d40d93c0da4, }, r0a1: u384 { limb0: 0x5c117b9250db1f77095f3f80, limb1: 0xda15f91e9282ff6deb2a2558, limb2: 0xaa820f7393229d9126ae7b62, limb3: 0x110c5e918c554c126361e32e, }, r1a0: u384 { limb0: 0xac056d30f948e924aa511f05, limb1: 0x31318c843660bb21180267e1, limb2: 0xb22b2d85ae7080079ab0bc7e, limb3: 0x14941dda97edcedd3d32ad23, }, r1a1: u384 { limb0: 0x876fd0749511e318e84cc37e, limb1: 0x71b4a1c6b941f0bd7731cf3a, limb2: 0x54e1fb48d3305bd534e5132f, limb3: 0x262c905d8278be2f7a9d1ea, }, }, ] .span(); let hint = MPCheckHintBLS12_381 { lambda_root_inverse: E12D { w0: u384 { limb0: 0x8bdaa3278720844c37567039, limb1: 0xd2f1409607d64c54b73d78aa, limb2: 0x2f6a4e683585d4ccc465352a, limb3: 0x105016815aeab4c1b10cba42, }, w1: u384 { limb0: 0xf14f1369d17825c133efc2d6, limb1: 0xece7f8c4810788c9023c2ad2, limb2: 0x8a7a3dca8c8fe5ccf68c0b23, limb3: 0xe11367a38a9da9df3424073, }, w2: u384 { limb0: 0xbf3c140b105713ed07834b4a, limb1: 0x31325aee1b1dbae62f7c153, limb2: 0xf1712c06213e43c0272585dc, limb3: 0x13e42c3e0801ac2144a06fb, }, w3: u384 { limb0: 0x713b362105bba1e8fcbb94a0, limb1: 0x7336f37c2c0d759c4ff697bf, limb2: 0xc61d5ab0a8dc2dffbaa7e2dc, limb3: 0xc759210484ca64b6a064096, }, w4: u384 { limb0: 0xdb2b0eb950e9144b7f2f02fa, limb1: 0x83f2d1513c7ce01407cbcbeb, limb2: 0x3acef2763be703fa77d90506, limb3: 0xd6a3922a006a5ac269f1105, }, w5: u384 { limb0: 0xd7a563e564895cf2511754e1, limb1: 0xc5ec4b01df1cb55da421916c, limb2: 0x6a17068bd9eb8099e645e126, limb3: 0xde779332fd6d9f465b20e6a, }, w6: u384 { limb0: 0x62b4676a303984e5006cae4a, limb1: 0xf48de62916116cc249eda468, limb2: 0x30355b613eab563b9cb9b14a, limb3: 0x92dc96c5c90e4a4e20a4cc8, }, w7: u384 { limb0: 0x2adef7cf0ce5e70667934f1c, limb1: 0x49df16aef14c96dda3795592, limb2: 0x90675022b9d62cbd8685978d, limb3: 0xe6467206b01d8ecaea8fdd, }, w8: u384 { limb0: 0x5a0918f6778263817954d908, limb1: 0xf1cea39accc8cc574af25807, limb2: 0xeb067bfcab205abe6c371677, limb3: 0x33f8a5722e1821e1f8c5f4a, }, w9: u384 { limb0: 0x5bec5a38ecbb7806f62dcc79, limb1: 0xcf4fd2a6884e312f05ffe06b, limb2: 0x59da93e49907f3bcb160ed13, limb3: 0x130fe108a81a7753e3f765d5, }, w10: u384 { limb0: 0x675bac7aed2b433f922616d3, limb1: 0x2f2f405981e6aca41db75f4d, limb2: 0x5c5e051f326dbaef7f17399b, limb3: 0xcd24160fefddfaa66c9468a, }, w11: u384 { limb0: 0x82d362ba811d62d7264e9909, limb1: 0x6e0c09afc5dbcf4dffd7fc05, limb2: 0x30ce07f0ccb46385c2b2b40a, limb3: 0x17f2b41158bbf2cb53644eae, }, }, w: MillerLoopResultScalingFactor { w0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w2: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w4: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w6: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, w8: u384 { limb0: 0x79b43033d2c6148ace378dd, limb1: 0xc6a64d7c9213ad89ad6e2940, limb2: 0x6935c3e1b9cf1af588eafb63, limb3: 0x66ba50e8c99edbeedf33b87, }, w10: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, Ris: array![ E12D { w0: u384 { limb0: 0x5e87a33f78e1f9158930afbe, limb1: 0xb03343f0ba8a9f2239714f7b, limb2: 0x9b36f2ea6a63c232dd98cdfc, limb3: 0x12fa722de4e2d3218998c810, }, w1: u384 { limb0: 0xc9f693551a877941adc4d9e5, limb1: 0x55a0971be122dcda5e5c3c8, limb2: 0x7c004df041a155e3b48cdf91, limb3: 0x959ea623e7d5b6f547c34aa, }, w2: u384 { limb0: 0x7b00e2956467ad946b1cbad4, limb1: 0xb3dddc7d363c4618d35bbfd0, limb2: 0x67f8fcf4c55fc2cd48e50cff, limb3: 0x155823e0d57749245ea41a2d, }, w3: u384 { limb0: 0xac48c31201b554c29ed60ab6, limb1: 0xd5f6cd8404db4fba9b6b1908, limb2: 0x2a12dd0e1ba2a2c71c111daa, limb3: 0xeec9f4d9359e16042385ce1, }, w4: u384 { limb0: 0x612b6944bb47d6ef40f0a521, limb1: 0x8d9728d2c62f0e796f49eef1, limb2: 0xef1cf82ad9649cdaf92b4dad, limb3: 0x16338f7d8ffc1e1319fc335b, }, w5: u384 { limb0: 0x9ea8de19e0e2a79e3da646e8, limb1: 0x71979065bb38d55f71156ee4, limb2: 0x8f7025473478c1bc198be805, limb3: 0x187985494ec2b58fdcbde38d, }, w6: u384 { limb0: 0x96686495d190b64a7ea79e6e, limb1: 0x89a11b76e803f02eb0d472b0, limb2: 0x6528eebe102cbb5374fe497f, limb3: 0xd3cc49ff4fec483e733e76d, }, w7: u384 { limb0: 0x82a3ef2511fe244c62bd5677, limb1: 0x52f0c10aafffafc1cf866828, limb2: 0x3cfe5bcd4718b63e76a65b17, limb3: 0x2e63847fb6ea974a63e85df, }, w8: u384 { limb0: 0xe04c4235ae17a9fab047b993, limb1: 0x9ade428b70a43c53f180123c, limb2: 0x892fce8b94f415a31260f4a5, limb3: 0x14939c716e672d2e4f93049d, }, w9: u384 { limb0: 0x2076170f69cca61e8266cf77, limb1: 0xa94c356ff22eb446d1816afa, limb2: 0x7b5ee869ff77574fbd075e32, limb3: 0x18c4c735d8759f9d05c97b53, }, w10: u384 { limb0: 0x87b2d06f00ce9210f880f777, limb1: 0x270fa1aa87ff48d0c7029e08, limb2: 0xd7a0a067fdef49ae272a9cee, limb3: 0x2670fa59b1931a9f41abca2, }, w11: u384 { limb0: 0x1d6670cd3b34ffaf62d4d572, limb1: 0x2a6da26183af5ba37e45e771, limb2: 0x2a68a3421c934fb0eb0a917c, limb3: 0x51f182c87581744f24c2335, }, }, E12D { w0: u384 { limb0: 0xa5f19f0768085bfad6e01cd4, limb1: 0xdb5ba1fd09ac91a4ae47652f, limb2: 0x2b13b3f3a78d5dc5c4d512a1, limb3: 0x8ce9c32b58bdfd51336a482, }, w1: u384 { limb0: 0xe2f45c49eb706f9f80de75ea, limb1: 0x2f2a290fef99d780bdbb0c7a, limb2: 0xde3a67d7d6bc965776584229, limb3: 0xddda4d389f0c2b9300d301a, }, w2: u384 { limb0: 0x48376e71dfcc68f658e47c4c, limb1: 0xcac6cb5c19f8d13b4df976d, limb2: 0x84384bb472feb3909e7ed3f8, limb3: 0xa4c6d75fd40944d23efad65, }, w3: u384 { limb0: 0x5706ae17c1b9f75e69a7e787, limb1: 0xc7cec8901103a5ee7bbd04d7, limb2: 0x8ddb584192f1250140b1ee3, limb3: 0x13d733d54618baa778469263, }, w4: u384 { limb0: 0x9050e16d385573cfaaf7154a, limb1: 0x82794a915ed9862237629b23, limb2: 0xa64cea16d0c28ec3f2bf97df, limb3: 0xa9ea911e3c1f16f11159bbe, }, w5: u384 { limb0: 0x7e65b51d042ee4735403a47b, limb1: 0x319fb8dfee0f546bd682f411, limb2: 0xc23d64d72ebcfddc3ea548e2, limb3: 0x111a1b915b3b25c5b9ec5052, }, w6: u384 { limb0: 0x7bd1cf57624895a0b3032653, limb1: 0x4961831e7409f7db175def7a, limb2: 0xb306db9676eef0f14180f0b4, limb3: 0x125ee887fc0eef7011ad0bbb, }, w7: u384 { limb0: 0x116cbb348fef5002aab5a1a0, limb1: 0xb1c8c7d1d9cff958a4004f0c, limb2: 0xb84a0ac8e21027d24b14ddc4, limb3: 0x1169229cdff8901d09902cb5, }, w8: u384 { limb0: 0x1046697d16f72172bef7ed16, limb1: 0xdb516839f9a0cbcbcc73b40b, limb2: 0xda4b81ca7038c6e7899437b4, limb3: 0x898ffff0cbbee98eed4ddfa, }, w9: u384 { limb0: 0xc57fc0dc768cc4566d475c1c, limb1: 0xcd5963a848c0b4c0417f5a2e, limb2: 0x73ecaffe0aae8b6dbac48037, limb3: 0x79fd45ff01f26c32e1a83da, }, w10: u384 { limb0: 0x1d5fdcdedff07d7317cb5f87, limb1: 0xfed3411e06c703dee8b6e5c7, limb2: 0xb5edc0395ade200d535f84ab, limb3: 0x3b6c9db7c2bec65f7929ef8, }, w11: u384 { limb0: 0x835a3107a27c76602bb8a4e9, limb1: 0x9f1a745144ee7c13c69cd736, limb2: 0xad8ace8310aa4a6b8e6fd789, limb3: 0x142320e4351ea7b89b1ea055, }, }, E12D { w0: u384 { limb0: 0xe94b430873c2411e6cd80043, limb1: 0xe30be01010b7d9c627c228d, limb2: 0x51c2c7c9b4365780e79dc3c0, limb3: 0x6f3bceeb9b996819b8ca685, }, w1: u384 { limb0: 0x95c356530e86a107434237b9, limb1: 0x4aa9d2df5c497600a1e350a1, limb2: 0x59381ea2332d5b1974e07ee9, limb3: 0x3049a4a61599e5e8113f1fe, }, w2: u384 { limb0: 0xae504a32d9b39dfef2a23777, limb1: 0xd9da3a1a5469845953c6d4d7, limb2: 0x207cdf567143514f2d7f3fc8, limb3: 0x12974191549a6a396beba2bf, }, w3: u384 { limb0: 0xa112cd0e530a494b22dfca4f, limb1: 0x18ea6ce26c166e7a7d78de70, limb2: 0x9cb0e03de354d7bf6282702a, limb3: 0x909b63c04423c5894538c19, }, w4: u384 { limb0: 0x686333c3d129ac16d5d0ad66, limb1: 0xb15463f680076cd25cc96a52, limb2: 0x208b9c263e7d649bb3ac2736, limb3: 0x48c5ece6bb71a9d77de1d17, }, w5: u384 { limb0: 0x57e69dc9f02cc1dde9971341, limb1: 0xa7297c6bef065a6a9b542e82, limb2: 0xc886c7dab888b9c5b38236bc, limb3: 0xdebc617818a9847334705f1, }, w6: u384 { limb0: 0xe6056f10696a9817a2425aec, limb1: 0xeb0c85f199cd35e58fe7cbcf, limb2: 0xa246425777e777880b8a125d, limb3: 0xda706ead9599d92c2d65149, }, w7: u384 { limb0: 0x9bf16e33aedf71df2d4615be, limb1: 0xefff1d4d74d22cd6cfaa0d54, limb2: 0x8f7e66896dad6c69fb46b6a0, limb3: 0x6025284a12405855f01f281, }, w8: u384 { limb0: 0xc7aa07b19da3addbc2b2a7ac, limb1: 0x89af564addcf5ac140968e42, limb2: 0xb0f94c85c9d1a1140317c3f9, limb3: 0x16ffce50f413f24cc8399c64, }, w9: u384 { limb0: 0xc11681d83427ac2c574dd74e, limb1: 0xa76eee7857186b0aeae75d7e, limb2: 0xeccab02a3412fbf189e977ac, limb3: 0x184a0251d3a98256bf42b0eb, }, w10: u384 { limb0: 0x2c07fdd1036592df4a6f3498, limb1: 0x10f649a440ac4b37266f2219, limb2: 0x22a63f7af99b416d9bb930a5, limb3: 0x115fdf891425fbf6a4362dd6, }, w11: u384 { limb0: 0x411ed4c1110386e3d69aaad8, limb1: 0xc92f854a1d0559c20cdf125e, limb2: 0x948d25f76bb996b92261cdc2, limb3: 0xe201b9e13565fa18bba4420, }, }, E12D { w0: u384 { limb0: 0x2ee816637d0ff936afb8192a, limb1: 0x771b55e7479b197971b078f1, limb2: 0x809429f842e6085d43c2dfd8, limb3: 0x12623c6450560ceb87d1c6ad, }, w1: u384 { limb0: 0xeb6d6091ca6ac5b35b99eba4, limb1: 0xa6a7a574ab4b881d5074fc7d, limb2: 0x43a56d15e2274855ea77e5a1, limb3: 0x16be7b0f604c838b37f1e747, }, w2: u384 { limb0: 0x555b0c9f5c07106cbb3f5fc5, limb1: 0xef42d2fe6dacaee0528364c4, limb2: 0xbd41cc43f3df8706302622af, limb3: 0xe2dcea4824247cacbfc4297, }, w3: u384 { limb0: 0x93fb255d08dc8e71b39fb796, limb1: 0x1da87c5554ed815d4aac7141, limb2: 0xbaf8fdb0836e7741b324217f, limb3: 0x19e568ec730b0d8fd4db5525, }, w4: u384 { limb0: 0x200e327ef349bbef548d1776, limb1: 0xb2d456abe3bf1e04b5899611, limb2: 0xae05f54f4449a81f4604671, limb3: 0x162689b2975c2604e0a4685c, }, w5: u384 { limb0: 0xc6b02b729ad74be636166fc8, limb1: 0x2cfefc55cda91fd7a951573a, limb2: 0x8867af21f665b7a7fd8a6f02, limb3: 0x176cd52f992ba8fed217c160, }, w6: u384 { limb0: 0x6c354775c20d8791793669d2, limb1: 0xf380243d419f9aec61c9e9e4, limb2: 0x24ab6a5a78f417f251ab18b2, limb3: 0x19f302018bfc588d7199c144, }, w7: u384 { limb0: 0x52f43e2d2f77df98fb709a0c, limb1: 0x294172d5620df7163a2e150e, limb2: 0xf24eacdd84d1f5d70b8b68c1, limb3: 0x162d18d8dab6547e5a096d2f, }, w8: u384 { limb0: 0x892c129896da39f99f72f0e2, limb1: 0x2c40af61fe531cc67546a683, limb2: 0xbccbe0a4026db352047dffba, limb3: 0x8a6b4810628e934e1415956, }, w9: u384 { limb0: 0xa206e84f0a4d23df6ff06511, limb1: 0x8cbf6576156d7285ec9f1b68, limb2: 0x116d55d1a59d130f52984060, limb3: 0x15d4804fc77d3471b7bf1405, }, w10: u384 { limb0: 0x531e0c7406043a22ea3e34ad, limb1: 0x8d1faf249e41a0a2e8ac800f, limb2: 0xad7bce015e4d3978fb0cdda1, limb3: 0xf30f8063668661ca0ebd8c2, }, w11: u384 { limb0: 0x1533da47d1c4ea429dfd2495, limb1: 0x1c5bdfdd4dc1b9d6e11ffb51, limb2: 0x853362ef8f300727f4ea8d73, limb3: 0x2619aecebc65f8daf270bae, }, }, E12D { w0: u384 { limb0: 0x616ca54bea5ef71f6286e9db, limb1: 0x6ce5a76d2b62972a2ab13707, limb2: 0x32b53a08c2162aa1ee95a837, limb3: 0x128bfd33226c297592d19ded, }, w1: u384 { limb0: 0xcc4facfcbbb91a1e3c3a9aba, limb1: 0xa590e0a709daa71b0d6fd371, limb2: 0x906ab38c0a9cfc5bd91564f2, limb3: 0x14da16be5a21292efdfabb0c, }, w2: u384 { limb0: 0x81a973e5217a805d0f888a36, limb1: 0x58274f5c6f509cde4b0f4e5a, limb2: 0xc2440a9e7e7a7a859779f0ba, limb3: 0x14521550f97d6648241075e6, }, w3: u384 { limb0: 0xb2a9bd1fcaf992c0021668eb, limb1: 0x9ccf56b74f1ab26b6d6ab9be, limb2: 0x816fe549db002a04eedb9e09, limb3: 0x169e5ef8091dccbfaa89609f, }, w4: u384 { limb0: 0x71582a7c30020dc2781a23de, limb1: 0xfa09bff3c0432c74e8fb9782, limb2: 0xc060bc37bb18f1f165fe9f21, limb3: 0xd0d60bbfe488a8943c7382, }, w5: u384 { limb0: 0xe51c7d600a303222b1443dd5, limb1: 0x2c421d1581bad4b1ce684362, limb2: 0x240e5e597ff47e268342bc08, limb3: 0x2ae81d2fb3dbf1912e36c66, }, w6: u384 { limb0: 0xf0cc1dc4593248465748b59c, limb1: 0x9a31a99ab145a54bccce7dea, limb2: 0xed2c2e4617c78555f7d61215, limb3: 0x5e6d735233a245b22780211, }, w7: u384 { limb0: 0x88de0b5fd8db35069051139b, limb1: 0x52bcf4adb04aae5a93d1eb1a, limb2: 0x5860e277e6ce67cd26925a08, limb3: 0x1541095aedd2a87a36fce5cb, }, w8: u384 { limb0: 0xb79b773a3df8822db5cc474e, limb1: 0x17206d8a558c6ec7b445f402, limb2: 0x5aeeec6a9815c02665ce217e, limb3: 0x10abc052332b3bb7fc3fadd4, }, w9: u384 { limb0: 0xeaa86f676206f32bf7169228, limb1: 0x4432637a0bd250d8204fafdb, limb2: 0xc1396d9dfe01fbec380c12d9, limb3: 0xeae8fbe6d882b3953e92e72, }, w10: u384 { limb0: 0xf618e52b9429f1e88d3f1251, limb1: 0x1c25dcfe5d75ecd687176354, limb2: 0xf37879c40f1da5f52a2cdb38, limb3: 0x81232dec101c7c15928ab21, }, w11: u384 { limb0: 0x40b603d2425b79cd710ee557, limb1: 0xdbb0b89a3646397437da8f84, limb2: 0x60e361e4ee2f67acda38b14e, limb3: 0x88d292cadc4d714c0f31fc7, }, }, E12D { w0: u384 { limb0: 0xfde925b26590efd93b29dc21, limb1: 0x79fa334e9e39f1cf6d597f85, limb2: 0x351ca1e01bd6f669cfc33a39, limb3: 0xaacd403561cecaae25da3e8, }, w1: u384 { limb0: 0xfbf49b1ca286c7f34ca70db4, limb1: 0x52ae3e3ca34e2a102d3e8acb, limb2: 0xee70f348286b4f214b7e2a44, limb3: 0x19adc6e6dd23e9b87918f0d3, }, w2: u384 { limb0: 0x360cc29b8f16a161f0bb5695, limb1: 0xe23f0c483bc3484ccfbbf75, limb2: 0x544f00069e83cfa220de35a4, limb3: 0x145f89ec3fbc9c19593fae68, }, w3: u384 { limb0: 0x32d82fd5786426e4f0249f0e, limb1: 0xaac0cc9febb225961afd999e, limb2: 0xbfd0b5657b2f0e275599ec2d, limb3: 0x64ea70d1faa0e80ec792a74, }, w4: u384 { limb0: 0x836319c6483c95a22c9308b9, limb1: 0x9d0fcdd8c80002b659c474b7, limb2: 0xc44e2984149175f867392f06, limb3: 0x13fdf1738cceefd7c77fccba, }, w5: u384 { limb0: 0x38b69c65caedae1d60f4a6b, limb1: 0x476a63341944240588cd40a, limb2: 0x2c822ad9edb35cdb9398c48a, limb3: 0xfbd30b4e1561b17fad5975c, }, w6: u384 { limb0: 0xaa5dda2031d51398be5cdaa, limb1: 0x838072096046591839743da0, limb2: 0x4b2dbad7c26ef3e750e7e8da, limb3: 0xeda6a14042c9d4e7bf9b02f, }, w7: u384 { limb0: 0xfcc892c0fbf45ec567cf21aa, limb1: 0xad6b081ad539e5b3f081e6ea, limb2: 0x9e60e7c195d26421d13f4687, limb3: 0xe642044d3f37f6ea8897f42, }, w8: u384 { limb0: 0x9d04e86c9b4834f0738e451a, limb1: 0xd9105203107ce7a46d995976, limb2: 0x9706b8693910cb373cb60d32, limb3: 0x14d8f8c68cdab040e35a108a, }, w9: u384 { limb0: 0x9210fb0d45f1817d93bd99fc, limb1: 0x23c86949a3759639599da994, limb2: 0xdda9c2a5d34994981322c82b, limb3: 0xb4dc029e7276741f11943fc, }, w10: u384 { limb0: 0xe89745492c1f82b80e23c8d0, limb1: 0xb9c873781b1837885be73f64, limb2: 0x77070c688a2a77abbe11888, limb3: 0x86daf906e8a95c38a3b481b, }, w11: u384 { limb0: 0x72251fa4e076caba8d7e2596, limb1: 0xe91daee82b59abd08a9cb5ac, limb2: 0xc5e4c8122cacedd33cea5be8, limb3: 0x2fb080bcdfe8c56c90fca2c, }, }, E12D { w0: u384 { limb0: 0x6cdf3812d7d2ec500440d2bb, limb1: 0xcde664d9abf0e6043be0c188, limb2: 0x16e42aa6f1a259a62ebff4b, limb3: 0x144527f2e63badeffe2607e, }, w1: u384 { limb0: 0xc82526bfc5a307f2b9e9e30b, limb1: 0xdf63ab3c0f39d7908dde39ce, limb2: 0x257aa1bc6dc3a1e2b2cb1136, limb3: 0x4f7492f6a900520c078efba, }, w2: u384 { limb0: 0x5ae59b52a5576a972231e4f4, limb1: 0x6fdf79c79aaa7ee533f448ae, limb2: 0x9a6dd69f434272d73d12bd40, limb3: 0xbaa39a35a43b44bce2325d5, }, w3: u384 { limb0: 0xe504a48ed83f8bcd77382d00, limb1: 0x1fdb6ea298ac1c3c0af7522d, limb2: 0x56227bf372218d4677e592a8, limb3: 0xcaec0e91d882a292e585313, }, w4: u384 { limb0: 0x4f8be2e79b7ba3a3ac9da613, limb1: 0x7219bc5c36dcdeea294b1d83, limb2: 0x9f27e9cd48a9ee4d3e2c6383, limb3: 0x308909137cc1584e7cb9186, }, w5: u384 { limb0: 0x7834a99d69b1f3e2b42bdcd3, limb1: 0x300aced389ad9948ca1d8c39, limb2: 0xfe3f888a08ed761acee1b1c, limb3: 0xdd41de0f3e2890eefbaaf79, }, w6: u384 { limb0: 0xca9ab9a1739b5f5137d4ac40, limb1: 0x9ba2e33a23bc2b27e91bc510, limb2: 0xdc366bc48c0a8720af349c88, limb3: 0xc940b71841009914f7f29dd, }, w7: u384 { limb0: 0x7711c3dd44d84334bd207762, limb1: 0xba355253aea149c9d273461c, limb2: 0x8a45011ad06e5acfea138ae1, limb3: 0xd1b7d2bb8587892435f528e, }, w8: u384 { limb0: 0xd5c10f3e091a9acaf0886474, limb1: 0x626c2a14805abbb07cae8876, limb2: 0x66356be50aa68d09b54f071c, limb3: 0x3f1c0a601bbe3f6575e7477, }, w9: u384 { limb0: 0xfb4552ccdf1883dbe077d13e, limb1: 0xd8b4b21222a465176a4c7744, limb2: 0x7347818431aab5489408c638, limb3: 0xf9d77cf7abe38162019e8df, }, w10: u384 { limb0: 0x81aadeeb9df873401f32a628, limb1: 0xb93520f726c2d052f5b116d5, limb2: 0xd00b2c5d62680f3fc93d9a6, limb3: 0x17b559291ebbfe6e0574534c, }, w11: u384 { limb0: 0x9ad70ac80ce3b8527270dc24, limb1: 0x5fbd9b265250614247c4f157, limb2: 0xf0322eaaa789d68a0f83c8f6, limb3: 0x1323275b562dca758c81b1d4, }, }, E12D { w0: u384 { limb0: 0xaba7980a06ebfac9ddd04a09, limb1: 0x26ef9c306f336efa100b11ba, limb2: 0x40393c1afce51c8f52083a5b, limb3: 0x88c312a356277e9545f6421, }, w1: u384 { limb0: 0x50fe671710174daa78e31dcf, limb1: 0x5a2428575d62b8bbdc6bdce1, limb2: 0x18dbe1b6cdb06e3ecd5497b2, limb3: 0x63e9335b2697eb47a466830, }, w2: u384 { limb0: 0x243fcb55d2e8070937b2e5f2, limb1: 0xb3f0fd54bf8cd30335f72fb8, limb2: 0xdc36b46d1bd1ccd2d5c317e6, limb3: 0x54fa05e31dcddca0b10647b, }, w3: u384 { limb0: 0x178a369ede0d5f33b4088124, limb1: 0x688173ffe450814fda34adaf, limb2: 0x679b60cfa4fa68f7064b124, limb3: 0x5c210fb56be682d3515a22c, }, w4: u384 { limb0: 0x80e33e3e2bde4084c4ecc31b, limb1: 0xcc13974ef64aef9cde3aa9f3, limb2: 0x9f66e9c5ad97d198a2226f6d, limb3: 0x25b15dff2c6064ec8a6bc71, }, w5: u384 { limb0: 0xfefac90d2c27ea76fadfbdb6, limb1: 0xe6bcda36951c314c5fd2ca9d, limb2: 0x6b32e67596b531b9529cf2e9, limb3: 0x652300a58d5cd6e4e248a96, }, w6: u384 { limb0: 0xb39dcebf1162dc60631b50e, limb1: 0x9a904262c61ce054c078710b, limb2: 0xcc950e9965a1b3d7a42d94ac, limb3: 0x83f7f8554815facc18fdac1, }, w7: u384 { limb0: 0x4628f9c8fe8de0ab7b878521, limb1: 0xd4e2dc674f4251bb6dcab9c7, limb2: 0x5e6b8ac26ebd553eca2d6af9, limb3: 0xa69e14fdd6b8c0a24bc8494, }, w8: u384 { limb0: 0xdcddcf1a486e8fa5de038782, limb1: 0xda495c8e9a173872cff839fe, limb2: 0xd503a115971a590b4ca5c531, limb3: 0x140f92b94c08399b9f00c46, }, w9: u384 { limb0: 0xf45410cf50b2db223627396f, limb1: 0x518dc7a16e20322edfd1dff7, limb2: 0xb0ad958b70aea0c767e3cf28, limb3: 0x8d2d63cfd448ce80af04fbf, }, w10: u384 { limb0: 0xa26f24a5d5acdbebb6ae2597, limb1: 0xa754c3d093f65f02627ef393, limb2: 0xc700c9fe30406f4b29029911, limb3: 0x13f157503df37670cdec5bb5, }, w11: u384 { limb0: 0xf73127358c0f9e89e02146ec, limb1: 0xee6055a98cfdb3d7bbfb9469, limb2: 0x5e382cbaff9a0c1e152cfde9, limb3: 0xd2db85a3b0103b4fd8b4beb, }, }, E12D { w0: u384 { limb0: 0xb0034c0dc0470e3bd056c655, limb1: 0x68739ef9acf49ed16185f94b, limb2: 0xe5397364df8b3c4eccbd060e, limb3: 0x12bc87cbeb825883cab4c21f, }, w1: u384 { limb0: 0x9a4f283376c9c46e6f449d80, limb1: 0x3f034aefed75e2faacf1d862, limb2: 0x7716ffd86a4f3673375706fb, limb3: 0x3346cfcd71ef93e7f3e58ec, }, w2: u384 { limb0: 0x752d55436d4f77575db3ba3a, limb1: 0x4b21615ce3a76f38e73528e1, limb2: 0x2a79467dd6ca41febd836ed5, limb3: 0xe7558f44fcb9ba3b991a46d, }, w3: u384 { limb0: 0x90b74252285317a40a980d51, limb1: 0xf625a1046957406fd64d36a3, limb2: 0xdd287597f3eb9e33e82d2677, limb3: 0x19d79ac4ee250bd2e0f365fd, }, w4: u384 { limb0: 0xe7b8ebf0928a50cdc097ca80, limb1: 0x1c75acb67a4fbd8038084a85, limb2: 0x6700cd4270fb401157a956ef, limb3: 0x11c418010389f02167f7d294, }, w5: u384 { limb0: 0xe7311b3c007c2ffeaf935df6, limb1: 0x3a969f26bacb20feb532ccae, limb2: 0xad9c7997e6a29e0dae2f57c1, limb3: 0x31d45316bbd38e161892ba1, }, w6: u384 { limb0: 0xb836ac5fff285b97a9cfaf8a, limb1: 0x11e79fa6603cfd51966395a6, limb2: 0x241907be43b9b971573a8e1, limb3: 0x50b992346863b906e942433, }, w7: u384 { limb0: 0x77884fb393767a1d533c0b8a, limb1: 0x75a3dfc2b4ed6292b7de2d3, limb2: 0x8db56997d672b7b27505e3ff, limb3: 0xfd375b7c1ed070088edeb4b, }, w8: u384 { limb0: 0x217ce46babc14c3e6f804698, limb1: 0x8d2f38976a56c1930e0f9ef2, limb2: 0x206cf46bdd9bb85ec1788dfb, limb3: 0x69879bad0032e0b666ef550, }, w9: u384 { limb0: 0xfa6e30d2ab6ea25256a7006d, limb1: 0xad6c71121a695eeb476a4cbe, limb2: 0x9ded25624cae3f7bfed45fa7, limb3: 0xbdc0cac28fed44c8a9974a6, }, w10: u384 { limb0: 0x5f32e37fb43e4fbcd4382886, limb1: 0x25a8be4ff2142fae23203a90, limb2: 0x141071f19b469cc0cdbf36e4, limb3: 0x152a566ca9d531e91f06c8d3, }, w11: u384 { limb0: 0xa9e30bf7189793c3dae917d9, limb1: 0xcecc2f8cf114f38941cc16e7, limb2: 0x55a8efcb2983963fd1c5d7ea, limb3: 0xe0d3178bc1e4a9281acc39d, }, }, E12D { w0: u384 { limb0: 0x85d69f2d431d2c6f1afe22b3, limb1: 0xeb3b3ba1d64653e590a78169, limb2: 0xf2df045d48326a6371a5bffa, limb3: 0x120ea922564a9885abce0f6e, }, w1: u384 { limb0: 0x5de8b63bf3968b010da3bef4, limb1: 0xd788608863c1a08d747106fa, limb2: 0xde6d5d9aae8e97f0c2158038, limb3: 0x1832c580f19d3f73da7dd439, }, w2: u384 { limb0: 0xf2a1d0325fe6caa419acdc37, limb1: 0x90897834506f8faa6976e0b9, limb2: 0x200e730ee8dba54a64266bdb, limb3: 0x3f427d2880d6471c9b2cec4, }, w3: u384 { limb0: 0x854fb7b9e02882e8e2d3461e, limb1: 0xc7211649b2fbdb298e6b4935, limb2: 0xaa8bc4976bc2349ad9bb313c, limb3: 0x1557211bab3b60506b310219, }, w4: u384 { limb0: 0x485d0305732c8c1f4d6b6f2a, limb1: 0xfed07e935e4f20dda4935b1, limb2: 0x2504416e43da5cbf988bf0c, limb3: 0xfd13a11b696f3d323002b0a, }, w5: u384 { limb0: 0xb39dcfe5381fa64cbe569124, limb1: 0xfcc10e3db88ee4c11ab8b90c, limb2: 0x7f3dc79e449233c3c05cd4cc, limb3: 0x1a68d8218a4a298083c7ac2, }, w6: u384 { limb0: 0x402d97fd8c450137963dc715, limb1: 0xbaabab131fbf75f84b8c4d09, limb2: 0xeac1634a2ef470848b63e082, limb3: 0x18020a7c33b6e6def47b23a7, }, w7: u384 { limb0: 0x40747eb2ed38084318c5fd6a, limb1: 0x79c80f12fd1e9512f4c815d1, limb2: 0x3a48a5fc5d3e961ef0543995, limb3: 0x5c22e5ce258b23d32382246, }, w8: u384 { limb0: 0x58fdf5cf39bed59b75a08248, limb1: 0xf73f318ea3a19e93473249fa, limb2: 0x302354c7cec45c0f4e22be73, limb3: 0x45dc87c70a7f4551180d0af, }, w9: u384 { limb0: 0xea611623da31b1471f9b932, limb1: 0x32719fa75ff0141d7348d0e9, limb2: 0xb45905063c07e8c33fb9b2e9, limb3: 0x687c2df9d7f663be99d9468, }, w10: u384 { limb0: 0xf1d27eab29c68003c6c210e1, limb1: 0xb8843060c4bc968cb7982d1b, limb2: 0xeea7620d6be4c290ade9a4fa, limb3: 0x18fe77343f6e8206f89b9744, }, w11: u384 { limb0: 0xa444a56f7e397cfafb6930c8, limb1: 0xdae564fe2862cf1cdcad16c0, limb2: 0xbc4f53f2efefa51fdfac4891, limb3: 0x551ab423ade813eabb16804, }, }, E12D { w0: u384 { limb0: 0x5e957ccda4f73f9215fb110d, limb1: 0xdc36a49661989b5a3b5d79ee, limb2: 0xdec6eba0b4700511ff1300cc, limb3: 0x124c0cd615ff328b360ee2b9, }, w1: u384 { limb0: 0xb236047e323f07b02f2ec515, limb1: 0x583e5738966fa3a8aad40f7f, limb2: 0xccd1bc05a2119220b4544232, limb3: 0x780b2230acf081408bbcdda, }, w2: u384 { limb0: 0x260e2e2d6b359ac7810e7275, limb1: 0xbd1696a0a3bd92fa7fc31844, limb2: 0x742ff3c39bf81cbb48fa4a4b, limb3: 0xfe258a1791cd92b4ef3e60e, }, w3: u384 { limb0: 0x54d88d0d9b96f02414851b3f, limb1: 0x55334650ffc5ec8e900a1d3b, limb2: 0xad3cb70cc267b5f757f7cef6, limb3: 0x794700e48a5eb285c05ed22, }, w4: u384 { limb0: 0x1b66b0589fd79fc234125121, limb1: 0xbda857f94889f518fe44cf86, limb2: 0x9370106e7bd9937a478134d4, limb3: 0x167eb12b6b3572f0a3aca9d2, }, w5: u384 { limb0: 0x375981f086e8cb4ef19fc188, limb1: 0xbdbe1a3fc397484a93a2b29c, limb2: 0x7a02a3f5fa8210e8f14b2276, limb3: 0xc67f4b31546be3553dd2985, }, w6: u384 { limb0: 0x600f009107ab2a1da4997be, limb1: 0x69994acdcbfbe38056baf6f5, limb2: 0x11ccdd90a6781a41f22c760f, limb3: 0x13c5f50c127cb29bc0d17999, }, w7: u384 { limb0: 0xffe9f03f0aa94835f9525c88, limb1: 0xfdde4a867496327c5043cc57, limb2: 0x3f6144c573c696e50855fc1, limb3: 0x6b94fcad15ff18a3c2f248f, }, w8: u384 { limb0: 0x8884346bdd2a3341fc7322cd, limb1: 0x93ab61c19fa719030de7cc2a, limb2: 0xc757ba65e13b170ca901db80, limb3: 0x100f6a0711ba91a6f1b251b2, }, w9: u384 { limb0: 0x12a6e600d76166876d9b3f52, limb1: 0x414068fe6847dd8ebae8539, limb2: 0xa76a533d9740918d76a56dcd, limb3: 0x5dc91d58b53e3e96acd6def, }, w10: u384 { limb0: 0x718ec50c1dac99c6d874f4e7, limb1: 0x16d6a04ccba7bbefb03d6951, limb2: 0xeb4c2625dd73b31f645168c4, limb3: 0x6afd115d3d01e4b290b84e5, }, w11: u384 { limb0: 0x52b5c082cd25730db3a34738, limb1: 0x6967f7eb2ca4e4a712dc0131, limb2: 0x5c5e6c3183d02ccca35ce987, limb3: 0x757bb566047196e238a8b26, }, }, E12D { w0: u384 { limb0: 0x7c9854d25a3cb0be4d2f40d7, limb1: 0x43fd00e1f4a86259c11e88ef, limb2: 0xe994cfcb5001b763f7901bb1, limb3: 0x86155b09edadffde4dfbbd7, }, w1: u384 { limb0: 0x304a578df65f91fee6b573c4, limb1: 0xec0472b755f143bbb562ab87, limb2: 0x7277a095088372ca3f0a1d27, limb3: 0x197e53f43b82cae3374c44d8, }, w2: u384 { limb0: 0xe11977e635d061e6b989c868, limb1: 0x1e500845921807459e23651b, limb2: 0xbec3e77afae83a1c5ea6abfb, limb3: 0x14e286717a22a735ed2bc0ee, }, w3: u384 { limb0: 0xa1e676b1afa2d9ce1870874d, limb1: 0x7091d51696fde538628c1f6a, limb2: 0x96df8da6c99457376c4a33a9, limb3: 0x8e98a801b4c9ab4aa5d063f, }, w4: u384 { limb0: 0xc02c8f24e55e6d222f17ca30, limb1: 0x76dd4ee9d6b6332479504760, limb2: 0x197e8f329510abb24930400a, limb3: 0x16a154ff6848bf4bfdb82d9, }, w5: u384 { limb0: 0xbba922639ae8bf28d410a19c, limb1: 0x3086e9cd8bb7de09c46ea5d1, limb2: 0x38963f320b7441e9d6a77a5a, limb3: 0x12abf3a5df31ef34b735b45b, }, w6: u384 { limb0: 0x8a1312c4fa12d188aa5a2fc5, limb1: 0xc1a534c21fe8d43d46d061c4, limb2: 0x19cca041bdb84797c38dd77c, limb3: 0x90f272bc677afbf4ea47fdb, }, w7: u384 { limb0: 0x742fc53d89d385243fcac586, limb1: 0x9f1522d5dee448f1ea0bd110, limb2: 0xa6e48bd6c1d03e300f33a7be, limb3: 0x14f218097b54f125db0fa277, }, w8: u384 { limb0: 0x4e8d1c9d0611bff11b73be65, limb1: 0x1d75932dc0fd9604caeee1db, limb2: 0xc738ab9f0ad9baad911e4207, limb3: 0x6e45511232a9e5d4095e985, }, w9: u384 { limb0: 0xd52cce486c7f42104e9f3b7a, limb1: 0x58b30b3f567ae170e66d8aa9, limb2: 0x5e34ff47bd1c3c1eeda2872d, limb3: 0xe250f5f3302568adb516219, }, w10: u384 { limb0: 0x7c9a5e6eca301db139ad106, limb1: 0xc2b3cc3e715be6a7efe28f96, limb2: 0xd6d1ca55ddaaf9abf16efb04, limb3: 0x10c5de68ac532bc3f398aed4, }, w11: u384 { limb0: 0x5256c2f9aaa56fdfffc2caff, limb1: 0x90c30061f644a4c3d03f5830, limb2: 0x851db2eca15852453ab2d70e, limb3: 0x201ae57b8bd651a9a211245, }, }, E12D { w0: u384 { limb0: 0x107a402a8e5fd3d6694e2491, limb1: 0x2fcd3a87cd5349af3c857428, limb2: 0x5e7694bbf0930a85be56591b, limb3: 0x7d93547fc3384cad47215e5, }, w1: u384 { limb0: 0x2d9484d3a15699a7a1f5cdb8, limb1: 0xf1552b9e00277c8adf417bff, limb2: 0x797fa3b98f9243d4b02d9431, limb3: 0xee3f7dfe449d9914888e159, }, w2: u384 { limb0: 0x8cb567b9cd6c029b00fc4e41, limb1: 0xa86ba8941e760df1c880b78e, limb2: 0xe39f860fa3f881c589990047, limb3: 0xcd133ff0a3d963a38f16788, }, w3: u384 { limb0: 0x6e71601b16aa6640cfd5d5de, limb1: 0x1e4d16be3edc7039f570f547, limb2: 0xe015353d569f8688f394214f, limb3: 0x59546e8ca3e361bfa7f3414, }, w4: u384 { limb0: 0xcba11f8010fcb1b7018d4942, limb1: 0x1936e2410861c27516ef1950, limb2: 0xba1a67208cba4d4c43b6eb14, limb3: 0xf3d199823dda0ca4ce0f913, }, w5: u384 { limb0: 0x4141a8ab05e48332c7a97101, limb1: 0xc11b08f6a7ade95596c91b9d, limb2: 0xc60f61f46ada4e329659dad5, limb3: 0xc713a291ca63d714b43b773, }, w6: u384 { limb0: 0xfd82de6406270dbaa131943c, limb1: 0xd30c660ecf76e1ca4ca5df67, limb2: 0x7a3ac1af7f68fe980f73984f, limb3: 0x51b9df004712c0a919c1021, }, w7: u384 { limb0: 0xca9fe85418e99c70b24bfbc9, limb1: 0x6c09ab753fa1bd7e5eb72928, limb2: 0x29ac58579f2e59649b78e304, limb3: 0x19bd14410529841d8976139b, }, w8: u384 { limb0: 0x24dbe1d4f02d7ef87c2cb830, limb1: 0x16bd5c02c49e80904866a252, limb2: 0xaf1a9309f3303d6c367356ea, limb3: 0x1e19bba8cf8459f8f4dfd36, }, w9: u384 { limb0: 0x2d779d40ef68e8d88e174d50, limb1: 0x3e8cddfef78f63c6b4492711, limb2: 0xcc77ab33895f03cb0526a45f, limb3: 0x125fdd8cf5eb4cbf87136c28, }, w10: u384 { limb0: 0xdc1c3be866980e02cb6c6552, limb1: 0xa95aa3b3e5bd3b4f9e44b20d, limb2: 0xb044b29c621e7b2dad2234c1, limb3: 0xce6623d2aafe10b6e17cfdf, }, w11: u384 { limb0: 0x60124efd5e01a25ae6df0508, limb1: 0x721f5b9120ddb48b58c45e92, limb2: 0x1dd4bdf5f24d952ff670777d, limb3: 0x19f4d3c0a17c210e64fdc0d0, }, }, E12D { w0: u384 { limb0: 0x840e3de720a4548f1da7be6e, limb1: 0x3ac07781ccebe03234a3c070, limb2: 0x60a15844dc5503c9619d9185, limb3: 0xabb0efbdafc1bf8dba79909, }, w1: u384 { limb0: 0x35e738bdafcef08554231156, limb1: 0x152ec5c04b5d82140676dcb, limb2: 0x92b8cdb4123580d2823f3463, limb3: 0x6c6271bd78c3dc0ad928081, }, w2: u384 { limb0: 0xc0885cc50b00d5788f6bfe71, limb1: 0xe0e2e4020c8e3d3aad0bb4fc, limb2: 0xa03d4b3f246f40eb91edbd0a, limb3: 0x2ad754c710d3c5a0a9c8aa7, }, w3: u384 { limb0: 0x150f44c02d8d2ece9cc20e89, limb1: 0xbe88ea3462b0ac825a3f7683, limb2: 0x392c7bdfbcadea15c9ec3776, limb3: 0xcf868bdeb3044866e335299, }, w4: u384 { limb0: 0x5e373df33b60f49f245eeeae, limb1: 0x32ccc0c3ab265f108c87af10, limb2: 0x24b304890cb346fddc8baecb, limb3: 0xa5602cbb5588e7a5347043, }, w5: u384 { limb0: 0x79a45fc3a6b3476edccb39ef, limb1: 0x699737a3f0a37ccbf1351d50, limb2: 0x628e055199d024aaae669c51, limb3: 0xb7a54344f41ac4806f963c, }, w6: u384 { limb0: 0x56763ce8241e2e4c4ebbfdf, limb1: 0xc7e7f096be44dfd4045256dc, limb2: 0x59d483ad26bd43de0be0f89b, limb3: 0x115650afb40f7cc9bfc41d67, }, w7: u384 { limb0: 0xf761296c383bc157c0dc74d2, limb1: 0xf7ae69719276fa4a8f45a7b1, limb2: 0x9519a049398c825b8591fd3e, limb3: 0x116c67cb21786e95c1a81a42, }, w8: u384 { limb0: 0xf88348b16f829f538445e4ae, limb1: 0x5c59ddf4cb31896b683c0532, limb2: 0x34a2ed13f5d41b79207f2bb2, limb3: 0xf05b669ee27d19d64a44624, }, w9: u384 { limb0: 0x60c0435be32f160a839128b2, limb1: 0x5da4368729030e6e45435c2, limb2: 0xc3225b269d34d229f0daabe4, limb3: 0x16bd338ab123444102821db2, }, w10: u384 { limb0: 0xbe99f7a76adf1a39fcd16614, limb1: 0x455ad4d2c342a9150c205cdf, limb2: 0x6c7129df025ad6c248cc3e23, limb3: 0x117d45dac2232adcc3a58865, }, w11: u384 { limb0: 0xe7227b87d84291616d163423, limb1: 0x62f024ba3b1eeea3201b342a, limb2: 0xdba6e933ce41754f118a7c3, limb3: 0xb03ee9bfce34be38e903aa0, }, }, E12D { w0: u384 { limb0: 0xacbe4cc978644dd3b66d1251, limb1: 0x8b0827e7f460731253c48669, limb2: 0xce9fb3a4b707ceedf9e4ccd5, limb3: 0x13601ecdfe890ac5b6394083, }, w1: u384 { limb0: 0xf7595a279ff9c75a51e66dfd, limb1: 0xc142b5880c07598137eae9b6, limb2: 0x7a5bc2021f658c6a85627610, limb3: 0x132b8e30cfd8515a3df346f7, }, w2: u384 { limb0: 0xf6ba0f17bd64a508a34ff8cf, limb1: 0x74707c027b3fe929fc806de9, limb2: 0x22d365a315971b9f0c206a82, limb3: 0x19dbbd0c7f94d1f4ee79356, }, w3: u384 { limb0: 0x3f626447ce3814e02b1ec0d7, limb1: 0x5c8f6f2fcf4e7e35083554c4, limb2: 0x8dbaacc8bf9b1754dfc5c7a, limb3: 0xb35d9b7d542e11dc9367339, }, w4: u384 { limb0: 0xe625bd4cf03325a6336ecd5d, limb1: 0xc3e56498d973b972df22643, limb2: 0x4da8a81d2cb2053b00ea8fcd, limb3: 0xa642ca8b89b6a1c4e9877db, }, w5: u384 { limb0: 0x90a8380dd53bc5b94dbe3c0f, limb1: 0x2903c25cab059c295574f591, limb2: 0xb2377f88137b3e6b90d7ef37, limb3: 0xb7c1e72e24735bde787a674, }, w6: u384 { limb0: 0x4773b12414a16ce9d033310f, limb1: 0x9df89f470a41a445b7748c4e, limb2: 0xa96cdf868e25c1dfa2eae25a, limb3: 0x160d60066e34bef4bf67e8ba, }, w7: u384 { limb0: 0x97741dddbadcd502d93d1ada, limb1: 0x91f945eb520c5683d7d835be, limb2: 0x3acf7014131ff4db19eab525, limb3: 0xeefb54325e312a77579cfb4, }, w8: u384 { limb0: 0x9d6c29377b2addb30bb07eb6, limb1: 0x99fdbae79fab5cf167aff047, limb2: 0x5ade5a8e1c7b6bc090eab03b, limb3: 0x11d79b9562108c1f05e613e1, }, w9: u384 { limb0: 0x2a7b85423fcc9846cbd9fe8f, limb1: 0xd29258a1f3d53096b5ef7341, limb2: 0x6962bcbf5cd737335faf272c, limb3: 0xbcf4003e7213cf0a16d92a8, }, w10: u384 { limb0: 0x283fa69586ab328da624f05a, limb1: 0xe538df54e03534989f032f90, limb2: 0x8def2c7d92aeadbb57db8dd5, limb3: 0x1023a83a0bc5f302bc4918a8, }, w11: u384 { limb0: 0xf0dd374565f0c70e62ab7914, limb1: 0xdfb1156b56c464fa271bea64, limb2: 0xfb31d547c72f0e06b7e95d05, limb3: 0x199fffdc2a5a3333d46c2722, }, }, E12D { w0: u384 { limb0: 0x8f76261cf238884bdcac039c, limb1: 0xf1a631914c8ee95d8d563038, limb2: 0x7ad15fcf82a1de05d7ca78c4, limb3: 0x17d503bf7c0186f31fb87cac, }, w1: u384 { limb0: 0x12c73d43b1d6e5e93cffbda9, limb1: 0xc8f8aebf2cdb43903aaf1fa8, limb2: 0x5f1bb59cf75e973628df5a3c, limb3: 0x133637214037ed72a089671b, }, w2: u384 { limb0: 0x99b289b7c895e0389505ae3e, limb1: 0x807d96bb7abc61490b0b2ae9, limb2: 0xe901e5c6b224704f999bc014, limb3: 0xb1762e3a5ab01513e934471, }, w3: u384 { limb0: 0xc2991401ebd01d353eff0e10, limb1: 0x3f78a46de2ae77e99130d6c4, limb2: 0xe8076c850bd55b9dc399ef14, limb3: 0x1959a68b64e006097eedd9ca, }, w4: u384 { limb0: 0x31f962a10ef81a0e881e9412, limb1: 0xed29acc9384952f5e68bda38, limb2: 0x5ad6682fe35e6be9e495e035, limb3: 0x53290025191e515d71e6a4f, }, w5: u384 { limb0: 0x1826298b7042b45f2484b705, limb1: 0xf7754a63c6f36ead9c0722a6, limb2: 0x3e19ea5d2569e83b367df44e, limb3: 0x117cde4851820ba5a6d323a7, }, w6: u384 { limb0: 0xb2c4b66f8d495051b1e92716, limb1: 0xebf594dc49b44c3275b03925, limb2: 0x3e1e370a07e830d358d9d527, limb3: 0x17f0f608ef7e255a7740e438, }, w7: u384 { limb0: 0xf7eb9970e3d485405ed26e6f, limb1: 0x55504e6108e307d4c105fb01, limb2: 0x37e5a48b0089379bc4d3a960, limb3: 0x15542f45dbe73bde5df32e74, }, w8: u384 { limb0: 0xfc2e20fbd6973e5782d582f7, limb1: 0xb0d924870a4c93a0ee8de35d, limb2: 0x554637f24083718a82311c10, limb3: 0x12764367f85796814078b42, }, w9: u384 { limb0: 0x8fd5bd83ed527a4d26c45fe3, limb1: 0x43b7d218d10ff081da67bf2b, limb2: 0xf9fc937c157ca5ee08088e73, limb3: 0x119362054157e7dc5658fc69, }, w10: u384 { limb0: 0xcd2d08d72116be874d6ee56d, limb1: 0x77c4f1eefb4d35ef0221d5b0, limb2: 0xacf3b9162ffc9c289bbf6928, limb3: 0x2e08e8400c38ac22655b3d3, }, w11: u384 { limb0: 0xf4d15b649f3d55ead568462e, limb1: 0xb567200eda805f6453c250d7, limb2: 0x7be6abfce3538971d5c5f487, limb3: 0x9d5f5b42216ceaf147ac21a, }, }, E12D { w0: u384 { limb0: 0xd347ed30451ff201af63eeca, limb1: 0xad5110b2aeba89322b006323, limb2: 0xf82434189453d69149a0c0a6, limb3: 0x80326dc5e35502bbce7ac6c, }, w1: u384 { limb0: 0xc83c82247fb95b58a4ee3810, limb1: 0x31a8674c7e68d35d98762cae, limb2: 0x9cfbb7fec0c26829164628ce, limb3: 0x16bbaaedd62985c32f4e076, }, w2: u384 { limb0: 0x2fa6372a48bfbaadfa13763e, limb1: 0x5e40bda6de39b49e34b6cddb, limb2: 0x112c3d354dca6adf2dca4bbd, limb3: 0x31f3d996a2adee764770117, }, w3: u384 { limb0: 0xff3ed33234b352e29be10777, limb1: 0xa48ea598a7173580b764c4b2, limb2: 0x4f673c656ed817dd15a35331, limb3: 0x2789ee0833b95e2a631106b, }, w4: u384 { limb0: 0x9ac4d1b96cb51db76fdbee0b, limb1: 0x803a0ddd0255fcf6dab7617c, limb2: 0xd6b0af076d77742457695aff, limb3: 0x43761452a76341901155087, }, w5: u384 { limb0: 0xbe44dbd432d048dd243c8bc3, limb1: 0x98d9d4bdc6a8954684fcdf2d, limb2: 0xcfba6c2b4124b837319047eb, limb3: 0x8a9e73497aafaafe182bc19, }, w6: u384 { limb0: 0x8a3b064f566cf7a95dbe7548, limb1: 0x3a7f64c477a6e83e434ce861, limb2: 0x9ba7cae92f44149908673e10, limb3: 0x45103051f125fedb866d95b, }, w7: u384 { limb0: 0x5ee818e7234e7272ec07f3d1, limb1: 0xdd4bc27187a7d422aa6df86c, limb2: 0xcbb7f78d9fe849c55f5caf73, limb3: 0x1862b91a119174f1c7aff149, }, w8: u384 { limb0: 0xd08c79a7c7850cbda627d11c, limb1: 0x9d4f4f86dbf4a4ac0d4606f2, limb2: 0xd464fb70944a1feb5e7f92f0, limb3: 0xd5b0522da04c9aeca0608e6, }, w9: u384 { limb0: 0x3dbd70f614fc2d3eb4edbcb8, limb1: 0xcc386604b029681e5d5de15a, limb2: 0xa03d1c9d026d090768bf5861, limb3: 0x55ff5a76816f6d652fd986a, }, w10: u384 { limb0: 0x9d633d1f35aea7549904415e, limb1: 0xb6d0d361ca6497edc9faa721, limb2: 0x6d5289bb547465b3be8c6ad9, limb3: 0x985850e8cd4013c4b6d95cc, }, w11: u384 { limb0: 0x7cb50dc102dcb28e77742892, limb1: 0xe2437d8286205ad782d6b72e, limb2: 0xda1f62195f31b4783bab661d, limb3: 0x15ecca5677df076e39049bb8, }, }, E12D { w0: u384 { limb0: 0x9d72d5db64cb7507239422e0, limb1: 0x264e7e57b7260676a8bb7688, limb2: 0x7344113fcc925f1d30d06dcb, limb3: 0x18de0ecba8fd3371b8aa34ca, }, w1: u384 { limb0: 0x1861183cc4b2f46d87979e5c, limb1: 0x6e0a01a25c6ebaf9464e11e, limb2: 0x7f2de4bc5dd520e1c25ddd85, limb3: 0xe800e85c928ae4a62b295f1, }, w2: u384 { limb0: 0x947b7670a81523ba7d89ed92, limb1: 0x14b12adacd332e3d09706640, limb2: 0x11e97f9c6bc126a2f82ea1e6, limb3: 0x10624939def344ec8c1b3cf4, }, w3: u384 { limb0: 0x3b6a7bcdd62aecc44c37866d, limb1: 0x4f090d678ea45519842d182d, limb2: 0xcebc7bf7f3c10bfd2e6639e9, limb3: 0x1631faf829d85ac9c61de59f, }, w4: u384 { limb0: 0x559cd524045548ae86151607, limb1: 0x6e006893ba4aa3699195e31e, limb2: 0xdc1c446eeecc785b43fb9a22, limb3: 0x123202194c62a4c9baccb009, }, w5: u384 { limb0: 0x11fcaa3dba1a600b6010182f, limb1: 0xf01f5f9fdeb3c498d7b7cb06, limb2: 0x882cc64b2d18415e180078fa, limb3: 0x8b267ee888fef3cd7927dfb, }, w6: u384 { limb0: 0xd6b28085df279d9394b5a7fa, limb1: 0x763cd39e04067be6fdf56c8, limb2: 0xe6dc2b118d1a64282a465791, limb3: 0xf5493b733d5896bc5700fd3, }, w7: u384 { limb0: 0x90a1f465c6e97bcd81222eee, limb1: 0x7149530fb2e4319be2323f28, limb2: 0xc88a2ea7d5e7ff07ca2ad206, limb3: 0x162bb34dcd7e91a975c63630, }, w8: u384 { limb0: 0x170a35595a61d913f682b57c, limb1: 0xf2c9e682be5246c93b4e6ec3, limb2: 0x2bf4029c422908fa4563de, limb3: 0x641187d200dfd28e8e82aa4, }, w9: u384 { limb0: 0x6fa76ba0131b78d2942cadad, limb1: 0x3bb0f673c1a7b42445c6acb0, limb2: 0x60a06dde4ec45da8ec121095, limb3: 0x20100c6e96666951b26138c, }, w10: u384 { limb0: 0xf0b483b7fa8c7e7af338816b, limb1: 0x56d359ad26375fcae41714a3, limb2: 0x873b27b4fa0b116a18158d0c, limb3: 0x12e72267a31cafa207dd8dbc, }, w11: u384 { limb0: 0x77cdf664971600615baaec2c, limb1: 0x26bf00719aa6690f5b19075, limb2: 0xdc51ab3277d503c215650c3e, limb3: 0xc0f9441d20276e0db93c8e5, }, }, E12D { w0: u384 { limb0: 0x49b8bc0bba1b3b3e63506f5f, limb1: 0x69ae08affd3b257cc0d8bdc, limb2: 0x721d9ad5b76a8ba8f139dd3a, limb3: 0xf8ac0fbc40271dc9a22eff8, }, w1: u384 { limb0: 0xe9e8035fd0a006b598845454, limb1: 0xdcc25fc32ad1942d93a350ee, limb2: 0xfd77a0ec6e37dc33615964d1, limb3: 0xb75169082563e4c6f1be90, }, w2: u384 { limb0: 0xefd32d50a707ddbd100ee51b, limb1: 0x810cdffcb09eae39f48aa1e1, limb2: 0xa18a7cf96101b979a65ff7bb, limb3: 0x6cd39500720118321f2738a, }, w3: u384 { limb0: 0x26986ba695a566d0262b9ee7, limb1: 0xaab9e0bdc5aed6c48fa8efda, limb2: 0x72f6704bebcf7ac9af380ed6, limb3: 0xe16ceb416196f23bc2560a1, }, w4: u384 { limb0: 0x7762c889e40661d695e0dffc, limb1: 0xb8bc925ae8124f3b8c369b23, limb2: 0xb522ccf634c91621e1559f97, limb3: 0x5bacf21780b28756242dcc3, }, w5: u384 { limb0: 0xf90a60c0d778d09b834b48c3, limb1: 0x3c87554e9260971b487713e2, limb2: 0x71220ad4dba9858bfc12ccac, limb3: 0x16db742f5078344568720d98, }, w6: u384 { limb0: 0x485a9dcceae19bdbf2dc0cfc, limb1: 0x8e2f65401be2d31c093c53c, limb2: 0x8238a47a96eb2cde2677e2b0, limb3: 0x6039568233497b9222dfbf5, }, w7: u384 { limb0: 0x6f64078fdd7a425f4436d862, limb1: 0x64d28a2586ab1e7f2bf280f4, limb2: 0x1f66c4e09e8145a306b09bea, limb3: 0x813c1ecd8822f2944b930ae, }, w8: u384 { limb0: 0x4060ce7fd6ea39ae7a74236c, limb1: 0xd45a1c125ec3bc1614862318, limb2: 0xa88ab4b47d71797470a4ca95, limb3: 0x68574f8aed261828f2ba0a2, }, w9: u384 { limb0: 0xc994b57f3410a4503912f0db, limb1: 0x76871514e839d62296d23629, limb2: 0x2fde71411b384900f656ab6c, limb3: 0xdeebb1943725d48b9cdc7cb, }, w10: u384 { limb0: 0xf3ef74f709c6cb45c21cd12e, limb1: 0xd720f3876bdd542b86eeeb58, limb2: 0xb85aea0cd816c09909b4d88c, limb3: 0xa3ce54f3ee833e0bae2cb1c, }, w11: u384 { limb0: 0xf8c6ec38f3b7f955775e2832, limb1: 0x716a5e0f39967a70c5bd78be, limb2: 0x61f2e36cf96f821d6a3287d1, limb3: 0xf19ea07493d608bae66bea0, }, }, E12D { w0: u384 { limb0: 0x83b19eadcea71010d1565cfa, limb1: 0x4825e294172616ab26e7eb20, limb2: 0x54d4259a351535c9cbd1c6a4, limb3: 0x241d155f21449ca4b5addf7, }, w1: u384 { limb0: 0xde3e245c2756d991ab554365, limb1: 0xded567d010568eb5ba3ce705, limb2: 0x327429176a50f14bdc580858, limb3: 0x156807de27314670790e7ca0, }, w2: u384 { limb0: 0x66bb95d7a4d98dfc50ec8fb1, limb1: 0xc3c8058f329d30723233d845, limb2: 0xd30b40aaa7eebcb481e5f715, limb3: 0x6af8fbe105e0796a8e398ed, }, w3: u384 { limb0: 0xa940b949eb2388785b224608, limb1: 0x1cec59486fc6a5cd144a91de, limb2: 0x11402b75ed1bcd6cd14590ec, limb3: 0x7f1086112d77b89f7582269, }, w4: u384 { limb0: 0x8f257f0a1e6796e78b8f951e, limb1: 0x48f84ddb963cadbfe5e55521, limb2: 0x6e427ce34296e0997e34bb67, limb3: 0x1358d67c804b33fcd6dccd26, }, w5: u384 { limb0: 0xf29a7dc92df446d59d0ae4e5, limb1: 0x823d3505088601b6a6610c21, limb2: 0xec67638c41976d4b1caf835e, limb3: 0x15c8e64bbf555ac7f232789, }, w6: u384 { limb0: 0x658317131159794cfb897b2a, limb1: 0x3efb5096028939e901d050eb, limb2: 0xb364141abe4f342b2d342e4c, limb3: 0x697dece994d9f1cfd79f309, }, w7: u384 { limb0: 0xaadcb5f26d03fad4f28df12c, limb1: 0x492f0e081e52c8c88fce9f44, limb2: 0x29717b344f24a9ce5704183b, limb3: 0x77175c6d4b377dbafe0e4fe, }, w8: u384 { limb0: 0xea668960f018818ab2dc143e, limb1: 0xd1b189a93d737c7c9df377b2, limb2: 0xc326f49a444ae09fe755412b, limb3: 0x9347fcd49e2293efb0a78de, }, w9: u384 { limb0: 0x17514b18815a49976674c5f2, limb1: 0xeadf8c7afaddb62cb39d0e85, limb2: 0xb3bad6f772ce35db00653f13, limb3: 0x17fd638fda925abc9867be18, }, w10: u384 { limb0: 0x824d407e1486549861a4f9b1, limb1: 0xd708e8188307765b7e7b5c71, limb2: 0xb458d64fdc3cfcae7d504007, limb3: 0x11376135f9107c7d85f2d49a, }, w11: u384 { limb0: 0xdd930da650b850fd475ab204, limb1: 0x6d1c787f7452a96d6fe58ed2, limb2: 0x77fc37156b99d375a7d16ca6, limb3: 0x2c52abc9192f9453d49eab3, }, }, E12D { w0: u384 { limb0: 0xa1f4bb4ceda1931c829fab23, limb1: 0x804ffc41249665a2790a0228, limb2: 0x1de01e71f91960ccaf6c410c, limb3: 0x81b2c2ac7a57744e8e9b410, }, w1: u384 { limb0: 0x130433d5494eebebcfd9df94, limb1: 0x99364cbac719f5f41ddfa380, limb2: 0x3f29270ecf71851f43731a20, limb3: 0x1145c70e232f053297295621, }, w2: u384 { limb0: 0xec442113c386176b32efde95, limb1: 0x7bd862d3003678d9531d9c1e, limb2: 0xfc594d12f8c8b42b2e4d6b90, limb3: 0xeeb75363b656d3ec3fa9b09, }, w3: u384 { limb0: 0x222852bc2d918bd1ac5f63f, limb1: 0xfe7d5faeb604de77c643a175, limb2: 0xc65d389008dc614c33e685b9, limb3: 0x180b7b07d9590c95ef7c4d32, }, w4: u384 { limb0: 0x970068a4b9eec3828487ea39, limb1: 0xd9327df1470019283e338516, limb2: 0x5952d080bc8bc07c9a246b5f, limb3: 0x188de0056afd14bfc26980e5, }, w5: u384 { limb0: 0x1f95997064e7188584c76d47, limb1: 0xba3e7e6239cb59b9630224f1, limb2: 0xd02ab63f0952c3a26ac56788, limb3: 0x6c3f71d101f157a0eb5e8c3, }, w6: u384 { limb0: 0xcf705d3f30333b45aeb056b0, limb1: 0x3ded81674542b511276368b0, limb2: 0x1a953a0af3d55e115c95e424, limb3: 0x12c2bb84d66b242ac047d7a9, }, w7: u384 { limb0: 0x1d84fb17c565be3824c9eb81, limb1: 0x983f3cef4c3580414e1c63d8, limb2: 0xc6f813385e3fce4ae1a9f4c7, limb3: 0x175fdf9433765408fdfc601a, }, w8: u384 { limb0: 0x6c61ac267d1db760fbeaf92f, limb1: 0x20b3d2e50bab22ff0da90069, limb2: 0x54860d69bdb67b696fced45c, limb3: 0x15f95850b768b8a0f63b96d5, }, w9: u384 { limb0: 0x3fa62e0c86ad1d63fbae241f, limb1: 0xb30f2dea012c94c9c26d22f, limb2: 0x61befc67d0413374617f46f8, limb3: 0x4078076119540c4a20693eb, }, w10: u384 { limb0: 0x25e4fe7a019eedeaa28ff1b, limb1: 0x9324c0e779bd0c9fcd27f7e8, limb2: 0x24d326b0d8a8c42d982f21c1, limb3: 0xdfcf7aef0bf4098ae68b1cd, }, w11: u384 { limb0: 0xfe63a0539935bee31d38ec22, limb1: 0xd033b49fee05e4d97bd6842c, limb2: 0x78d04ec2b510789e14ee988f, limb3: 0x17aba0964ab1ddcdf413639a, }, }, E12D { w0: u384 { limb0: 0x278d77a81d602afd5a52947, limb1: 0xcb5c30044228bb45093b0d90, limb2: 0x8e471498d8a8be03dade312b, limb3: 0x19beee76172ad8aa02dbf3dc, }, w1: u384 { limb0: 0x7c77ce05c4c305a7dc0e5b4d, limb1: 0x7bd3f5e81744c8fbff1e9d10, limb2: 0x30ea7f32e968b9454c93c8ca, limb3: 0x13642c30cde1dbf6af429fd5, }, w2: u384 { limb0: 0x595b8c57681cead9648c7acb, limb1: 0x689d10dae2cc8e703e53a0e, limb2: 0x29ae6fb08dc277565e3505c9, limb3: 0xcf96b5bf70d0ccc001f3322, }, w3: u384 { limb0: 0xd1b554ed5518219199f34526, limb1: 0x26ac3af216434fe1ed48aa17, limb2: 0xc07d051d9daf7c6e095e8aa3, limb3: 0xd6c203b2d9e77cc0cd40bb1, }, w4: u384 { limb0: 0xab65021306a36284149c06e7, limb1: 0x4e3f42db62b95d309ced3670, limb2: 0x76fb0b0b7954df85d0d8c050, limb3: 0x5101d7e82eade26493678b6, }, w5: u384 { limb0: 0x7a6b2765b8a9ccbaaad5c828, limb1: 0x7f4e8febb620ef2bc2d7a407, limb2: 0xd30c4bf4b5860ebfbf7e3b9d, limb3: 0x14d20e5825a0cf0631c843de, }, w6: u384 { limb0: 0x84f1594b851f0ddca968e8c5, limb1: 0x3a6491a30f5721041f7581c6, limb2: 0x9169d487e761ae399b754ba9, limb3: 0x530b8c30d14555dddbf8776, }, w7: u384 { limb0: 0x57ad58f9bd5592d446a6b748, limb1: 0x135c76ec36e730bf679e1619, limb2: 0x549cc33448758c73223137e8, limb3: 0x55d3b3769b18c8c17597c38, }, w8: u384 { limb0: 0xcb42d1d43cdf605892d0b23e, limb1: 0x2197b1bc85e160f4865d08ef, limb2: 0x37c01be0fe47d2cce9adbb3e, limb3: 0x1553b94e1939110d4b99fc57, }, w9: u384 { limb0: 0x6fbad2a03ba0aa5de69f43d3, limb1: 0x765a3a8b3a2f959e767ed7e9, limb2: 0x4316e351dc01ca2da29b0710, limb3: 0x8183e742bf50ac5b25c5617, }, w10: u384 { limb0: 0xae282d2b795b5314b7f53f0d, limb1: 0x7a64af990d741c0fe71b0b64, limb2: 0x4fecda665a2e9c0826568d87, limb3: 0x914cd3723446a757562b82a, }, w11: u384 { limb0: 0xdb326552a864fae27e34e3c0, limb1: 0xbfd09d5d1e29af9e9d992c5b, limb2: 0xd6d7663d363167d6317a28f6, limb3: 0xe66725a5996b856981dbff3, }, }, E12D { w0: u384 { limb0: 0x925f1548a2586b3c83acb844, limb1: 0x353b125c82d3547bb22e873e, limb2: 0x66e1c1174e42b65d840ce5a4, limb3: 0x16fbfde31f733d31881cdfff, }, w1: u384 { limb0: 0xf48a04b2ecb65b0ec1ee74a7, limb1: 0xd3ce0c326344e634d721fb34, limb2: 0xa30496b2da7fb2ea97b754d9, limb3: 0x107d126f58ec9e97c6cc8e71, }, w2: u384 { limb0: 0xd2ffb5a8958fd358b9a0db9b, limb1: 0x402808c39b52369ae59fd83a, limb2: 0x3fe0960e8aa72beb2fa961d9, limb3: 0x166dc226ccb9eff556343907, }, w3: u384 { limb0: 0x8df0689b8854be488ecb991, limb1: 0x4795a4cc43a8d4530c1ad931, limb2: 0xb3bc8527ab33e10f80cfde20, limb3: 0xba7ae8be240e9d11a287d8b, }, w4: u384 { limb0: 0x7f368c6c241b048fb218dbb8, limb1: 0xa2476498a10081bfa027924e, limb2: 0x56b88e4492e6f0c99fa165f0, limb3: 0x18a38fa4ee9f26ba78fec53c, }, w5: u384 { limb0: 0xe98903321b25313c95f003dc, limb1: 0x31f82952f9329bd9368402e7, limb2: 0x54ae4abaa3d2432318e04599, limb3: 0x128f6b10489dc4631361966f, }, w6: u384 { limb0: 0xd6c9252e840a0651da685774, limb1: 0x20c689e5be6b3d7db49e75c1, limb2: 0x49de02ce0f57209e965aab87, limb3: 0xb84356ad3a02a7a23840580, }, w7: u384 { limb0: 0x4feb2265d9e9cfe5347bcdef, limb1: 0xdbf93707cc036c505a681a7f, limb2: 0x991dae2fc5278d2e4c49b442, limb3: 0x581e622fe997190ffcaff05, }, w8: u384 { limb0: 0x4fed4adee961344d7de4ce04, limb1: 0xa2179aa116019af6aab8119, limb2: 0x390cfa09d93c9cf5d45a6f51, limb3: 0x301f95a1cad02ce95b9e7f4, }, w9: u384 { limb0: 0x839f077e7f1268f3969297a, limb1: 0xc6678bdf10aac686ea78af9e, limb2: 0xbded8a9b29e5e041ebcc7d56, limb3: 0x16f210725bf2a00ce33bb7ad, }, w10: u384 { limb0: 0xa0b68df81c8f7dce35651343, limb1: 0x948b8def6ecf0f2c1235607b, limb2: 0x9cacf2c2c4cebabc980ba63c, limb3: 0x88eb934296e671e6ca4b0bd, }, w11: u384 { limb0: 0x5d277be91e70605270b0736c, limb1: 0x31a5c600c967c11668a20a8e, limb2: 0x8ca866246a7e7d273c67c89c, limb3: 0x1717a1fd9cd5ec3784a48c7e, }, }, E12D { w0: u384 { limb0: 0xc0cf5bb3ddf86547fe00b03f, limb1: 0x261d5fdf16216b0b5b2fd0af, limb2: 0x5090c7ece64dea3b6ef1fe9c, limb3: 0x127241b7afea2d881250e65, }, w1: u384 { limb0: 0x6e263d81f4a3f1c877c39333, limb1: 0x1410d9bf499e755eea959c02, limb2: 0x6ae0b4fa4bdabd77d6114c95, limb3: 0x18b34ace95b722dd2f0913af, }, w2: u384 { limb0: 0x9e798a325b9b9324627d90a7, limb1: 0xe44be7d37275a6b9307a4d70, limb2: 0x60a94c03db1b4341044162b0, limb3: 0xc5e0af70498faeb66e96c7e, }, w3: u384 { limb0: 0x62c3ec64962f4b5dfd4957e2, limb1: 0x175b2e34bc0b79de8b26e5ac, limb2: 0xd00c44dfe200edc1823d4127, limb3: 0x1f9c390217fc2eab214ec8f, }, w4: u384 { limb0: 0xca1db3d196ebee4afcb49439, limb1: 0x76c891130d535411b8d13bae, limb2: 0x1346242621dc20c966481630, limb3: 0x62a4a8737ee4ed122146323, }, w5: u384 { limb0: 0xd89259ce24c1bc3c80b4c31b, limb1: 0x6916e85ee261583718b5be9c, limb2: 0x614b567f265ccea1c3bf6c88, limb3: 0xd63901d756cb9c4f6e4ebf, }, w6: u384 { limb0: 0x2854083be3f609fb5747a0a4, limb1: 0xf9363f130c8a061ad4454dca, limb2: 0x99fa1036b41a93c9bb5f04a5, limb3: 0x10be26b58c1e20556bf90eca, }, w7: u384 { limb0: 0xcaa7afbc5dd33d0090d478eb, limb1: 0x33bac5729659b2886831c90e, limb2: 0x8c228f55fb3b16a6089cfc9b, limb3: 0x1425aa18228f951444e69bbe, }, w8: u384 { limb0: 0xbd8aa0ce83f76fa3d6195952, limb1: 0xa49e1c3f96658b0c6984d0e4, limb2: 0xdfc5f4d167ad19270de11602, limb3: 0xe8f8eb7f390acecb765644f, }, w9: u384 { limb0: 0x7fa94e38426b019637ed329d, limb1: 0x8a030e40d455c8eeb294aee7, limb2: 0x62c6e010ad31dc3e8cdfd551, limb3: 0x8d9ba6f08f065d3d6b80ab7, }, w10: u384 { limb0: 0x6b2cb77e359c675839c57ed8, limb1: 0x4ece0febc3fb31c9c799768f, limb2: 0x20e25d25010860a327da0640, limb3: 0x12eb1699559e1e7b06f3d0b, }, w11: u384 { limb0: 0x5fcbf346dc790bb6c9e48356, limb1: 0x8e7801394a1a49b06320bbd9, limb2: 0x7ac8d93c05e1831764f8daf5, limb3: 0x102edca82e8f1857ed209bd, }, }, E12D { w0: u384 { limb0: 0xb15ad72f4fcb2591d1abc46c, limb1: 0x74d4a9d3481b818b70fdb5eb, limb2: 0xf8210ae9f2b7df0516a267ba, limb3: 0xd5a2800ca938c6f7c3113fb, }, w1: u384 { limb0: 0x38b065590c2e60fe7f44767f, limb1: 0x7eecabf14ae695b8a3360ed8, limb2: 0x9985104a902c20936ea57238, limb3: 0x124695215443652ba7e6cf22, }, w2: u384 { limb0: 0x1f9841b55fe2c623f1078c67, limb1: 0xb9c8a90b95c1f3344984344d, limb2: 0x2a340ad73875dff79e1352ff, limb3: 0x18bd138bc116843c32beff0, }, w3: u384 { limb0: 0x56c68b860cbcfc33006bdf0d, limb1: 0x52813de6808192f9b0c7811b, limb2: 0x4fc72a2832a54a2c1377aef, limb3: 0xc240bb809dfa30523851f3, }, w4: u384 { limb0: 0xaf85594768f62ada3aff44ff, limb1: 0xff3854a044fc5e69851ba430, limb2: 0xb47e8573d120728f31c90440, limb3: 0xcaf2c186c804f855cfa2c4d, }, w5: u384 { limb0: 0x4e380f88b214dbbab34dbebb, limb1: 0xa77d375a8f3582d99d8e771c, limb2: 0x7ff0478d6f4c30522d5cf061, limb3: 0xeda4fddf15c6de3928a7494, }, w6: u384 { limb0: 0x53c092ef68bc25c37d25fe15, limb1: 0x3fd91dbc6dc8c4ce23ddfec8, limb2: 0x2f533a2c53b9bc59f7da808b, limb3: 0x54ea204f43fc3cc511e2771, }, w7: u384 { limb0: 0x874484b23512d69c64456edc, limb1: 0x4bae99896f81ad7e8b33986f, limb2: 0x315ae13e8f7eef39bb5fc6f3, limb3: 0x2e3ddb5c86a0d7ffa46ce19, }, w8: u384 { limb0: 0x6ec7f3337526ebcca0cd7a9f, limb1: 0xd48463f9f2d1f19c3853fbb8, limb2: 0x7e348340df28aef8d2b5b0d, limb3: 0x7180eed89e074ef58739ed8, }, w9: u384 { limb0: 0xbe6bdfc582a702b560a6e04d, limb1: 0x592fe00300d974cb544bb609, limb2: 0x5585618cce120a0ca8ae3b06, limb3: 0xd8b2fbd00859855d8059c04, }, w10: u384 { limb0: 0x14bf3cd112d125e4e25a3e65, limb1: 0x811a1021fa6981370e82b3d3, limb2: 0x2458fd0cced7cade1c669de9, limb3: 0x7c3ff3ae5fd17f6a1ce0359, }, w11: u384 { limb0: 0xf1c60ca1b056ed5abf67e04d, limb1: 0xbc819ca227d2d48d19f96458, limb2: 0xb390024831387ab08e67c776, limb3: 0x5f4a62df64a479d75594956, }, }, E12D { w0: u384 { limb0: 0xf65ce3527d75962dfe24a3f9, limb1: 0x91e01eaad05aadc43322e7bc, limb2: 0x1749b8efc10800f0117b9ada, limb3: 0x63f0bc72657931f9c4c0ec6, }, w1: u384 { limb0: 0xb0a176acec5241ab58a92fe4, limb1: 0xfff6673048e856befecc052f, limb2: 0x3aabf57172cbeea4e5656e93, limb3: 0xf8b8f049c1f37ea1b91f865, }, w2: u384 { limb0: 0x591f822c01335afd1788ae6c, limb1: 0xacb21dac6272701a054407c5, limb2: 0x27c93a2906618dc8eac1c17, limb3: 0x135348203e2ab3a8030bab8e, }, w3: u384 { limb0: 0x83f8664aa234b6ef1bee1838, limb1: 0xfbe202c883895731f698255b, limb2: 0xb8ab5bee5b71245380d5a22b, limb3: 0xdd0f12d1fb706b63a83e4f6, }, w4: u384 { limb0: 0x6c00eabfeaa8a1e18d743643, limb1: 0x35082c7740b28bed8c2911c4, limb2: 0x705d87b2509c7563f2f9cd83, limb3: 0x355565388006efda83748a9, }, w5: u384 { limb0: 0x721da2148c278de04ea6b48, limb1: 0x1223b5e9df2c7ce207e3cb29, limb2: 0x9fd921169ebea2d627e0e2b4, limb3: 0xca348e51467605b1891750f, }, w6: u384 { limb0: 0x567eebe72695309b8b9fa49a, limb1: 0x9b2ed7c13fcd5218178f6c36, limb2: 0x69db0caedd82eb26178db3bb, limb3: 0x10b37cb311f6f5db3cf04ead, }, w7: u384 { limb0: 0x1c36184bcddcb3bef030a967, limb1: 0x30f09d8bdcd920ef630b29da, limb2: 0xd99cd4ca8ee16996294d6867, limb3: 0x14b4ecde21559c315401a904, }, w8: u384 { limb0: 0xbff20fece07ace4ed15c0801, limb1: 0x8c641efedb23644ab9dac1b6, limb2: 0x65ed2f82940530717a3a8f6, limb3: 0xd6faee36c1be2a6bd80aad3, }, w9: u384 { limb0: 0xa45919c319e86e4c7cf0a9aa, limb1: 0x2c3b3dbcd368facc0fa8a97d, limb2: 0x18bb74bd046abb617241aa0a, limb3: 0xe6a08b13a47fee0dea5d182, }, w10: u384 { limb0: 0xad46273f102a1a28b7ea1210, limb1: 0xbd6857d74c142f5b0750a4c, limb2: 0xa179b4418056dce93b5d5ebe, limb3: 0x8edde64f71a1e7a8d5c256b, }, w11: u384 { limb0: 0x40c84a2231765e3ccdd1fee2, limb1: 0xe23fa47d96e3019174e1e708, limb2: 0xda247b93ca36f321d7e891a8, limb3: 0xf3dec99dae8597e09aa6441, }, }, E12D { w0: u384 { limb0: 0x5c071fe7249396da8890e55b, limb1: 0x88bf9396d97ac96c8ca065b9, limb2: 0xaa1bd31d7ac0d0063932745b, limb3: 0x4f008c1e4e917d1a0388386, }, w1: u384 { limb0: 0xde583cfef9c2b34ea6b3a860, limb1: 0xe79957b07ce9cf7cc9d7b0fd, limb2: 0xf9e5d92728e5fee33eb8a4c8, limb3: 0x7921cbfbdf11fda5479b251, }, w2: u384 { limb0: 0x7fcb1d0ad133dcac3db9691a, limb1: 0x8b34904f9f4147431e803592, limb2: 0xaa188d2c64f4ffae74679611, limb3: 0x6311dfa9565d635c03e0855, }, w3: u384 { limb0: 0xc6e8d1386e240defd0c8b358, limb1: 0xd916b51af6ef639109f7f064, limb2: 0x84f668ddc480ae7a6282e8bd, limb3: 0x14514e50d271db4c38f25c17, }, w4: u384 { limb0: 0xc05129d365f445bca7481a4c, limb1: 0x732f03651202c5d590aef375, limb2: 0x861a12d79020a018d52dfb3e, limb3: 0xf5779b069bb04e8aa65b1b0, }, w5: u384 { limb0: 0x49e85a71966f4085bb96a561, limb1: 0xa90812c10e7c338efd62e260, limb2: 0xb4dc3c8f6b473eeff051c55, limb3: 0xf162180ccd92f8be4baba3, }, w6: u384 { limb0: 0x1fc53cda9e145b9f2fc0958, limb1: 0xbc91a2f7fe6c04e89954a778, limb2: 0x713a21c6c35bc119e06027c9, limb3: 0xb945c61f5ef234c3f61368b, }, w7: u384 { limb0: 0xfc851571d35721bd06ad24ba, limb1: 0xb0cc8ed633947c99cc26b4bc, limb2: 0xa96709e905b2f0a160cc731, limb3: 0x13bb465d841c0df6abe9d8e6, }, w8: u384 { limb0: 0xf420c15aaa99c651e4dcf96f, limb1: 0x27cf47ecb908e16bb29a5fd, limb2: 0x5c212064d3152d60db688c4, limb3: 0xf132a5857b7a6c50640125c, }, w9: u384 { limb0: 0xd596517bf0328136d09b30d, limb1: 0x731fc3434888560bb4aa0036, limb2: 0x89171b1a244c1520a1e52cb7, limb3: 0x13a4065c684afc1509831b34, }, w10: u384 { limb0: 0x62b192ba8953068ad2beeb13, limb1: 0xf55df8dc4798f0c1303be1fa, limb2: 0x5586b58227a76995ce18ab1c, limb3: 0x1765d0dd29b138f1e15317a2, }, w11: u384 { limb0: 0x194160a75b09ead5c093d1f, limb1: 0x55458b207983cc60044cd893, limb2: 0x2ec1346ee6df706c64efdd21, limb3: 0x1889fe7577e0886013ee76a3, }, }, E12D { w0: u384 { limb0: 0x83a64d1fbd12b2105fd006de, limb1: 0x1fed0ced58ffc1247b300226, limb2: 0x40c7a77d43046a8dc496e8f7, limb3: 0x1273d35b2a7041c0c8e09fa9, }, w1: u384 { limb0: 0xd1bc518cb9f97989e4518323, limb1: 0xfda16e1ba8f5eee22baff865, limb2: 0x2282715ec39be7c1d9c05abf, limb3: 0x14ca6298addcce08172693e7, }, w2: u384 { limb0: 0x581296f543f611452833a9af, limb1: 0x8f7d57a9ccf015a529c0274f, limb2: 0xf4cec85b20feb49320169086, limb3: 0x7294cb9fc3914e72a74f677, }, w3: u384 { limb0: 0xa0d1c30484f8d800aa47cf33, limb1: 0x7896af58662828a8134758f5, limb2: 0xf8bf1ed82532b434dd6745f9, limb3: 0x1480045d9cc01e11e67e1744, }, w4: u384 { limb0: 0xab14069003747ce311deeda8, limb1: 0x46aee3ebf1505f27b11a43d7, limb2: 0x441e3585d1d14f573a862938, limb3: 0xa693eb56c06023e67761b5c, }, w5: u384 { limb0: 0x3b5aa1d13ac4ae07439068e1, limb1: 0x6bb8a4c24c1d85a23c028385, limb2: 0x356f653ce96361ec3cb08dd8, limb3: 0x19470f3488d1b42c710e0403, }, w6: u384 { limb0: 0xc6d25ab33b45985888bbb03d, limb1: 0x2026eb4eebc11b2af25c91fe, limb2: 0x84aec238c5ba5499a91244ed, limb3: 0x16ff44f85dcd5017d4f39ab0, }, w7: u384 { limb0: 0x6357ebc232777ec4f0019a51, limb1: 0xb2cf574426b91619de6260c7, limb2: 0xf3c73b5a7864f2a9e9df5921, limb3: 0xac8b2e81bf45ba782379164, }, w8: u384 { limb0: 0x78111c1a35a4b111e381ee5b, limb1: 0x87cbda1cc35fd4ffab98097f, limb2: 0x3785ba57e275cc071106468c, limb3: 0x887d372d0e2fe0e53316176, }, w9: u384 { limb0: 0x4a426c4f5b404cf8f9058f36, limb1: 0x6f4e2e0c8dca076756efa639, limb2: 0x574294ee9354db253276ffb9, limb3: 0x16453113da3cd9edc0f268cd, }, w10: u384 { limb0: 0x980837e72a53e6da4c4922bd, limb1: 0xb4f32169b47b9f2ab0864b73, limb2: 0x85967069c73e3c636b70e667, limb3: 0xe5e15629c61068bb9a3bf3, }, w11: u384 { limb0: 0x6b4e751b6afbfdc1286e2037, limb1: 0x2dceab2a8fec6a14f9f2a926, limb2: 0x67ac3d207965577ee1e47a15, limb3: 0x16526e02b5ea0131ca58ab70, }, }, E12D { w0: u384 { limb0: 0x17309de18596c600420fa7f1, limb1: 0x6ecfdc0a3cc31fcaf8050eac, limb2: 0x609fdb67c2d4bbd1da92d235, limb3: 0x17a9bc9c95045b9efdc7f8db, }, w1: u384 { limb0: 0x1c460122fcd6b6ece46d69fe, limb1: 0xcddd726c39b803c9d61e2ff4, limb2: 0xb314bb778d464e80e5137e80, limb3: 0x15f7cda48b321f00b848ba73, }, w2: u384 { limb0: 0xdc79881f76b18acaeca0693a, limb1: 0x5ced5bc216155207131869a5, limb2: 0x25abd10b17bb130a7edae34, limb3: 0xdc3c019b632e3991d4a6b8a, }, w3: u384 { limb0: 0xbfb097d9e966f087325bf903, limb1: 0x3fb4262eebf93492bbe3ff8b, limb2: 0x997195ae28496678b778b068, limb3: 0xb656130b375669e276ed9f1, }, w4: u384 { limb0: 0xc537baabbac6f92b3d4c43ee, limb1: 0xeee6011b5932150b96520428, limb2: 0x1632d8218fb9bf323d52bc24, limb3: 0x1206adf0e4af46155081e668, }, w5: u384 { limb0: 0xf12a97149fe018fa0dd0605f, limb1: 0x27ce7eaabf9c6f26f66d2e41, limb2: 0x869e24a6417b5fbecfb2ae7c, limb3: 0x15359c4c6224b1be86a615b0, }, w6: u384 { limb0: 0xc56549e245c6bbf68d09bc30, limb1: 0x90446e06fd1130455ef711ac, limb2: 0x343d611550a4e05dc84d901a, limb3: 0x198fe7d93aad83e5f503de9f, }, w7: u384 { limb0: 0xb0c7c0f44e04ee29115cb4e8, limb1: 0xd222e0c76f9d55a44b4eaea2, limb2: 0x9ec62b435c34f660f31beca1, limb3: 0x5b9706e9f1da4dd9d3cc2e5, }, w8: u384 { limb0: 0xf05234158a8a37dc15fec48a, limb1: 0x31d75743addea81c0d768a59, limb2: 0x460db2475e22f9cd60b2af15, limb3: 0x9c8e0f3693a433d950421f2, }, w9: u384 { limb0: 0x17b4ab8ab4d7825f202b8075, limb1: 0x6cb9c1f003024631fa0a9500, limb2: 0xfa9afda884aaff4eb0ff2eee, limb3: 0x92e1623974d20acee9fa952, }, w10: u384 { limb0: 0x6c311178704be9f7e65ec330, limb1: 0x432fab41537509fdc218bc65, limb2: 0x12ee9a3189d387cff951a877, limb3: 0x19a486fdde7a19ec3f4ea4ae, }, w11: u384 { limb0: 0x848acd4e5e19ac8787ce01e, limb1: 0xe23b95c772890cc36eb7edd7, limb2: 0xa78e19bb81ea2fefc9e5ee40, limb3: 0x98b9fa87c52256357e6ce9d, }, }, E12D { w0: u384 { limb0: 0xb1832e7be4513791a1b5a318, limb1: 0xdab8acfabf82ff15fabe8bde, limb2: 0xd1448ba915158cf8dd685915, limb3: 0x8a3480406ef8ab208c666da, }, w1: u384 { limb0: 0x7dc6f41df1fa7200a0e5046, limb1: 0x82afd83d6d865f579b9d987a, limb2: 0x3010fccb8d335ce1762c467c, limb3: 0x12d4daf068c14b93bf91349a, }, w2: u384 { limb0: 0x53b9d0922336710ddf03e6e9, limb1: 0xa2f7a6a8b7ea63dc7d3e5ce8, limb2: 0x2bc0e8f29fedb1969d4e5f70, limb3: 0x19f8ad2a13f5789efa24f88d, }, w3: u384 { limb0: 0x7fc2bba69df28a5e59bcf7e2, limb1: 0x93d61d335ab812d0fb5713ef, limb2: 0x86810bcd2b84909a86b9b8c2, limb3: 0x5c4bd6acfb17dbb0de99e92, }, w4: u384 { limb0: 0xabc6617ab0841c6fdd54cf71, limb1: 0x496bdff2baf9ba636d2800ca, limb2: 0xb46135c83828d48109162fc3, limb3: 0xbe70db79d790397b600b4a7, }, w5: u384 { limb0: 0x3aa09c6a57d7e89443f7196f, limb1: 0xd3c78490ef6a135ba4118eda, limb2: 0xd35cf1052a2161b3d1d9311e, limb3: 0x3a504798d0df370f6dc9e00, }, w6: u384 { limb0: 0x946105209210749c1ad130ec, limb1: 0xe6944ce1875edfee81ba5ac, limb2: 0xe803f442e26a40d80220321b, limb3: 0xa69d4ea6d1551c43e86ec33, }, w7: u384 { limb0: 0x7725777b6dd3a778505d129, limb1: 0xcf8f223a0ba7f0d56314005, limb2: 0x50b6542d68bb7e41cbac597d, limb3: 0x6773d995348c78185a125af, }, w8: u384 { limb0: 0x47dd4b505ece4e63c6a42ab9, limb1: 0x47b66fcf40b4579f8e7dafa8, limb2: 0xe1e00a837a5913248e2bc9ec, limb3: 0x122e42c9101c0f785e0bf0ac, }, w9: u384 { limb0: 0x320bc6a9543249df447ca30b, limb1: 0xae128dc852cdae534003d880, limb2: 0x2acf697d73ce229710a1db6f, limb3: 0x169fa56b9fe0085cd1ec32e7, }, w10: u384 { limb0: 0x9c3dc69b716e4c8b8a63f106, limb1: 0x7b7677044476f901b21ea7b4, limb2: 0x42e2af7bb87210cb120f41a7, limb3: 0x179117c4bf7aeed19202d38a, }, w11: u384 { limb0: 0x578af2d1c50886a02d13c7eb, limb1: 0x1d251a678674e497bfa5141e, limb2: 0xd5efc634d0cb4c7c1807787d, limb3: 0x60538a49b6f95d8179548d1, }, }, E12D { w0: u384 { limb0: 0x14663ec8aaf41e9dac839168, limb1: 0x8320d3931ce0be5febdaa063, limb2: 0xe8a54f2801c82ff94d4af442, limb3: 0x1537d76fdb6fcc5e66d13c05, }, w1: u384 { limb0: 0xc408aeca0ef982f1d4919f16, limb1: 0xacf15993d11ed9b848098954, limb2: 0xe710b0aeaf54ebc0e4f53ef, limb3: 0x1172e3f6d60f5b8f8275f3a3, }, w2: u384 { limb0: 0x807779f90c7ea090ec58037b, limb1: 0xfa1c670f3d46124c0962b69f, limb2: 0x812e66dc9ca6554d3d5fb28e, limb3: 0xede7d1b272245097eeab0ea, }, w3: u384 { limb0: 0xfac578f3346be762844bd2ec, limb1: 0x994ad6bbf2b2282021651555, limb2: 0x20bd8715803ee77607e72467, limb3: 0x7606e734900bc75f36d5948, }, w4: u384 { limb0: 0xc1ca06dc742aede8e3ed91c5, limb1: 0x71d50ee0f44520e8b6e60d54, limb2: 0xd0e04e25c2746017e5d029b8, limb3: 0xd44f1471bc3b841396c63ee, }, w5: u384 { limb0: 0x8863d4db6f58c06706c68dc, limb1: 0xcd8010d2fe2689df15faab2c, limb2: 0xe0bcfa9b2100aa2f75a3064b, limb3: 0x198af1ae7a81661000298cf3, }, w6: u384 { limb0: 0x584eba278a62b05b865d0046, limb1: 0xfd3905d4620e04d59c9f9db3, limb2: 0xb3a6714f1f875f49e045d5fd, limb3: 0x109ae235efe54330fbaa8ef9, }, w7: u384 { limb0: 0x41056d92722bdd9ef745bb95, limb1: 0xa49b528aa11e35ff72e1fde6, limb2: 0x9a18ff2224ff861ac716668c, limb3: 0x47387893d8d042ea3a4f516, }, w8: u384 { limb0: 0x6f24529271fb5203cfe12902, limb1: 0x310663d10c2acea99de8b04, limb2: 0xb5e0fae90872f9a49eaded38, limb3: 0xd4cdc64cb2b7e85aa244f97, }, w9: u384 { limb0: 0x99ed80f6330c7657ae9b36fa, limb1: 0xb4ecf4f1f9cc32690999e417, limb2: 0xd6a74b7ae48b6f4307720772, limb3: 0xd55e06f38a04ecb830f50ec, }, w10: u384 { limb0: 0x824deee4997b239c579cdfdf, limb1: 0x64de788297270c01860e025d, limb2: 0x2c570777664a58e9ed48b38e, limb3: 0x9845b19e98f1ec8238c635f, }, w11: u384 { limb0: 0x13e8cac3d7640ddbb717cd3b, limb1: 0x2bb8aa759817d4f5a47fd7b0, limb2: 0xa1d374b7e02465a35189b692, limb3: 0x351a9dec88d73a12476d425, }, }, E12D { w0: u384 { limb0: 0xc5619e330db7753690d3e4d7, limb1: 0x47612532deb6199b29ae01f0, limb2: 0x526a20bf47a55f080f9bad08, limb3: 0xcda6894283305a7ae037814, }, w1: u384 { limb0: 0xd01df400ca021228f79039cf, limb1: 0x5079235d8e615126f16b88a7, limb2: 0x6b29bb389bdfc6cfc202e4df, limb3: 0x4c469f79ecbf88cf78fba60, }, w2: u384 { limb0: 0x392c76f20e657cca0412ccd2, limb1: 0x8a03a9b1522a799165f5ce90, limb2: 0x3f1c10daef22f593d0c939e7, limb3: 0x114680f68ccb81f99a98d2e3, }, w3: u384 { limb0: 0x1a5d475778ed021bbba71dff, limb1: 0x3c1dcef8127eb06e3d386b6d, limb2: 0xa18b55a60be13efc53be2643, limb3: 0x430d7536307562e71e3b624, }, w4: u384 { limb0: 0x33b945b9e91a613f214c281d, limb1: 0x5246a0bb4a3b5e88b2a556f7, limb2: 0x76952d20fa901063986b5af1, limb3: 0x30dc626b4efb4dcf45dda85, }, w5: u384 { limb0: 0xc91f47f926bf741f50167758, limb1: 0xb283412e7dec1abf2af4b54c, limb2: 0x819210cc10240985a197b6fd, limb3: 0x148983abd0919160ca75ab3a, }, w6: u384 { limb0: 0x3ae52b385b8d7ccd1149b186, limb1: 0xc2fdad714d3b4f3b44c34b05, limb2: 0xa2594e80b8a3d876c89a7dd2, limb3: 0x17e8e95e2e4453a999120f47, }, w7: u384 { limb0: 0x4143d9f9eae7ba680e4ce790, limb1: 0xc6428a7db6bcfe2c09ff2784, limb2: 0xb6c49338a7f200baf9ba7b62, limb3: 0x110a8b846f24a8e5a48f8df8, }, w8: u384 { limb0: 0xec6894f7048d74cc521cfa9e, limb1: 0x7a74baa8349402edd473262e, limb2: 0xa587bd8ba9d0db61105a9bfb, limb3: 0x1542de51d10ad154d14d1ab1, }, w9: u384 { limb0: 0x623d3472956a6fd9dfb57f1c, limb1: 0xbc706464f02579b27b176261, limb2: 0x5fbba85d07f3b4037c86332c, limb3: 0x389948fb6649d454eaafd78, }, w10: u384 { limb0: 0x3d6160146d3ee8bd841a82d8, limb1: 0xe798a563e2e9319cc47c6e26, limb2: 0x534d22ca0ba24f883387c567, limb3: 0x8724e1114e6e80541a91631, }, w11: u384 { limb0: 0x274eb7f12825b047a3a3289c, limb1: 0x64eaa3423e2a707806fe1205, limb2: 0xf84ab17d32acb39a3dd6c673, limb3: 0x127600c6ca9df9612df7b2e5, }, }, E12D { w0: u384 { limb0: 0x3796de51981f6024fd06174e, limb1: 0x94d83a402696f8c183f7eaa0, limb2: 0xc9225b2cfd7c3d5c24574a05, limb3: 0x10c73e67a277a6aae451031d, }, w1: u384 { limb0: 0xf896b5516da8d004534d0d5e, limb1: 0x13d040c8b2eb76307a8963e2, limb2: 0x4106bcea580d4e5cdbac42fb, limb3: 0x194bcf981b8ad069b42ef14f, }, w2: u384 { limb0: 0xa01d5085551a704cf0fc81f8, limb1: 0x6f550724287ce9ccd035e27c, limb2: 0x4ff8a38afc93789bc77d11e3, limb3: 0x15387fd205f34ad531fb7495, }, w3: u384 { limb0: 0x2d86600edfa521e03bd1e1c7, limb1: 0x91911144ee37f4bda9841ae8, limb2: 0x7013dc289771aae3049aa557, limb3: 0x1264774c7cad53e0ce2c2512, }, w4: u384 { limb0: 0x7b8d55a4e9537ae0138637b9, limb1: 0xaedbff15cf4e9d82355484c4, limb2: 0xfa1e2235cecbef2155df3ba, limb3: 0x151f2f232b2c641091433b1f, }, w5: u384 { limb0: 0x72ec4e504cfb5f2b309e1b1b, limb1: 0xb307889291791d9836f74c5c, limb2: 0xcc60fb54fe4ebb3c834028fa, limb3: 0x73d28c074b6d0a9bbb93a6e, }, w6: u384 { limb0: 0x42714ec1b398c2646a44fc8c, limb1: 0xf9c8174e936e14a688589f9b, limb2: 0x74f6aaa1b47f90087951593c, limb3: 0xf56e6232d6c70f9bfc19e5e, }, w7: u384 { limb0: 0xe304f2b0d829f6d2faa65947, limb1: 0xa26f23153498cde40f054342, limb2: 0xfba50877ef63e16fa824a815, limb3: 0x1256debfa10663438ea50adf, }, w8: u384 { limb0: 0xc757cecbeefd79b47270e6b5, limb1: 0x3fb9d4754903dc457f7597dd, limb2: 0x8a9f050e1077482a52f7bef7, limb3: 0xb1d0a3d278779c2252b7aa7, }, w9: u384 { limb0: 0x5092b50f667acdababf052a9, limb1: 0x67c7132abfda100e74791ab9, limb2: 0x679b7be1175e7dab6bbf7b8c, limb3: 0x769778649047c85b6580077, }, w10: u384 { limb0: 0xfd8979bca7fe4209f707b3a6, limb1: 0x9ec62bedcbf628a3ceb18d29, limb2: 0x319886ca998f583080ae6e1b, limb3: 0x381d855df46f8b4c2c9d6a2, }, w11: u384 { limb0: 0x5724976349a32d6f327568bb, limb1: 0x17fdebce21bdc92e64f8196b, limb2: 0xeac82f3bc4b86e5d8147ef45, limb3: 0x131358e92a4dd1ca0ddb2c80, }, }, E12D { w0: u384 { limb0: 0x35716cc42b7f43a8fc723ebf, limb1: 0x22fadd338e2c25972f85dda1, limb2: 0x46872acb9511d7767537705b, limb3: 0x155d2de74effe44cf4798599, }, w1: u384 { limb0: 0x376ac4e9b575568e825c5a73, limb1: 0x2769ef9a9f77e879b6b8a6ec, limb2: 0xa666a8e2ee113b3b4567435a, limb3: 0xc6b84a04fd0d0f116ad9e5a, }, w2: u384 { limb0: 0x59d60284544cb1eaec05d203, limb1: 0xd6cf07d6abaf48adde29bad7, limb2: 0xf08eaf520c0bc5fe6b8eb966, limb3: 0x8207e1ac978f7a918c110a2, }, w3: u384 { limb0: 0xbbdf9ed2369c8b7b97583800, limb1: 0xb649e54a0e1787927560a57f, limb2: 0xa914d51f826065538792be78, limb3: 0x16b5820f317d590fbb5896f6, }, w4: u384 { limb0: 0x43ec6635aeecccb9d2c29f78, limb1: 0x8e2372e1b0e3678817be3069, limb2: 0xd78c8144a0ea302301b30a98, limb3: 0x17a61c387bd1ad61e28354de, }, w5: u384 { limb0: 0x4c34bc4845eec9fe3a68d75b, limb1: 0x314780d022648ad56cb24a5, limb2: 0x585a32f768086f1fdd9a8da, limb3: 0x1324f29ce3b3d74e74b08b03, }, w6: u384 { limb0: 0x223401b4185f66cb102dc565, limb1: 0x46f3ebee9b04e69f007f8111, limb2: 0xf8ae83de384f52416b6be2, limb3: 0x13727dee2bab50f43deaa793, }, w7: u384 { limb0: 0xdafd089f3c769cddeb63c576, limb1: 0x4329764ad1958fba5407edb3, limb2: 0x832c80c10c3981b2d197d42f, limb3: 0x14a64986d3b0dbbf0297eac8, }, w8: u384 { limb0: 0xeec166dc39802b9c81e08f7, limb1: 0x61a05c9d1447aba4d0279bbb, limb2: 0x5a891acf231010014c92af9d, limb3: 0x42193c8d6a9bccd990e962e, }, w9: u384 { limb0: 0xdbe5765f57be1a326f0b78bd, limb1: 0x3417ea0001ea3efb8c6de325, limb2: 0x80dfc16ab0411f7cb6727faa, limb3: 0x19415881fac9b97f02c3a6f8, }, w10: u384 { limb0: 0x6440e9bb2320475c39624871, limb1: 0xc39741e3212573abf24cd446, limb2: 0xddb817e1e7237e88f9285a4d, limb3: 0x98fa9061f0a765886c03c21, }, w11: u384 { limb0: 0x91b97eb11b2b9466c4781b02, limb1: 0x98c2e0826cece826f5d1e2a, limb2: 0xffdc08767b9c38eb95323f94, limb3: 0xdb9012a8490308dfbd1ec31, }, }, E12D { w0: u384 { limb0: 0x3942fef601ca6d254a68858b, limb1: 0xea9499ac5e6f2d267cf812f6, limb2: 0x1ddc6c2df9859ff4f2adf48d, limb3: 0x2f04749264cbba7320d82c7, }, w1: u384 { limb0: 0xea370966790afa13e5a15b8b, limb1: 0xcf600ddedf1922470eb6c8f4, limb2: 0xcc3b2095a20acd637561e075, limb3: 0x1099a2649fcc6f0876de42f4, }, w2: u384 { limb0: 0xf7c03af81a901c952bb74ab0, limb1: 0x73344a8772689f0e65751dc, limb2: 0xad18a2477643704a0385cf67, limb3: 0x6d8fdc35189573632dcc97, }, w3: u384 { limb0: 0xc40e849145b8a6ac81ba9633, limb1: 0xaf7eee8a3d8b2ce1ee4f3450, limb2: 0xeb5dc70d8393cddf4b749d5e, limb3: 0x3a16616e0857c168005f567, }, w4: u384 { limb0: 0xa46376638fd600b1522df0eb, limb1: 0xd54238ba273db8846de529d5, limb2: 0x5c999239af48c2ee8edebd55, limb3: 0x4573d87029391d0d65f209d, }, w5: u384 { limb0: 0x320028c1a7a461ad9eb19b21, limb1: 0x3b1235187099e3e7eccea674, limb2: 0xc63359900cf9bea379c7c265, limb3: 0x181ece5056a99b30368a01f7, }, w6: u384 { limb0: 0x67c40b01d45218cb7c9261ed, limb1: 0x5f12224f9bc6f6b0f758ed7c, limb2: 0xfe65e99f9dba2b226f3bdb14, limb3: 0xefb00660b8c006503becde6, }, w7: u384 { limb0: 0x98835c191b00687892a50c84, limb1: 0xd4ce327a1cde229daaf91062, limb2: 0x41b55aa7f2b569fbe90125b3, limb3: 0xb5ddb3660a32eb070881b79, }, w8: u384 { limb0: 0xdf1e95ef6d2b993d5a1909e8, limb1: 0xa22871054afc0a86111e80ac, limb2: 0x65699d8354776199ea73ba7e, limb3: 0xad1800f05ab0f5361037f95, }, w9: u384 { limb0: 0x332c0317051a794c9dea2cbf, limb1: 0xf8a485eae6c2e410a7f79c41, limb2: 0xffb6acfadd9e81a1d72f7ab5, limb3: 0x4af742d5ef004df236eac2, }, w10: u384 { limb0: 0x6e7cd75aecd367d01b025d90, limb1: 0xea672964fdc59edd7195d82a, limb2: 0x9ef714a07f2ab07c12d493, limb3: 0x11a59352336ea017c4cf99eb, }, w11: u384 { limb0: 0x499742508d3b02cee2ce2e5f, limb1: 0x2a7cd0175d28e3847c94e3a7, limb2: 0xba1633b10be308ed90e705de, limb3: 0x144cf257dd87eb064641dc1d, }, }, ] .span(), big_Q: array![ u384 { limb0: 0x1bd71287e4906779ed3d3a26, limb1: 0xd6ea2055c878317e8e522dd4, limb2: 0xf4fe9582467798093d5d263c, limb3: 0x11c2da419a6a8b9d227ad990, }, u384 { limb0: 0xc4b64371b43a0cbbaf9d662e, limb1: 0xab2cfb720c7749414576a711, limb2: 0x92a2a7b9b8fe2b36c9da54d2, limb3: 0xd7d0a6b6ef80b6d591b0389, }, u384 { limb0: 0xfd068547a7981576f0c4eab4, limb1: 0xe3208a0cd42c834c885e3eba, limb2: 0xc9230cd9a7fe97e5b519d330, limb3: 0x8c3edee1458190d7fc7671f, }, u384 { limb0: 0xfec91f076649b9094b9dfb07, limb1: 0xa86247f16a24f3301ca06ee1, limb2: 0xfe14f3967c8dd011c2464c84, limb3: 0xe55d8db7f7697b9b674fb85, }, u384 { limb0: 0xa6b137189875f80342ffbaa2, limb1: 0xe37567e386092f9fb4b918e, limb2: 0x76317540dbdb5389182fdb22, limb3: 0x19535a1856bd170c6b1566d2, }, u384 { limb0: 0x9349bd150ea103338810c7eb, limb1: 0x194631f44c64118bf4948d01, limb2: 0xcddf00a5a0e0129f7c0dacf, limb3: 0x1585b63aca5869287d76ccca, }, u384 { limb0: 0xf213beca10de71d6d4bfdd63, limb1: 0x9321b3ed32e293a3d811f88b, limb2: 0x4ce2b9fe3580484b72432cbd, limb3: 0x49fc76b104fb5d550c0ce19, }, u384 { limb0: 0x9b78043b0ef59cdd195fc3e2, limb1: 0xe30e5a40e2f5d9b79d51644, limb2: 0x906317a8fb233964738a7ba6, limb3: 0x7f49e99f37b4d2d1b603da6, }, u384 { limb0: 0xc28def775de8d2f0de39828b, limb1: 0x3d548f753a65e3a014768533, limb2: 0x7715613c11ffdca201f853ad, limb3: 0x7d643af409084b57b822d69, }, u384 { limb0: 0xe0e29a0dc136aae59457c606, limb1: 0xf7d71f6b5d87524d0d943d23, limb2: 0x111166fadfc7e3a266cc28bb, limb3: 0x6af8bddb724e98e205c5283, }, u384 { limb0: 0x2697ad39910ece7d8ed5b9a, limb1: 0x7d1911eb0968e4d5eb165c0b, limb2: 0xbb4b11231e556addef54e9d6, limb3: 0x11446940cd2b7dc0d38a7ded, }, u384 { limb0: 0xef35f0e98cf3fc950bef6b82, limb1: 0xfb650be4f7bf7a60f0e3c3f0, limb2: 0x8243d4126588d55da730f0, limb3: 0x692a7966594961c2db69273, }, u384 { limb0: 0x9a390157a11eb1b42aea41bc, limb1: 0x8023ef1036cf8cf57aceff7, limb2: 0xe9a14efd71cb83b6a03bd56a, limb3: 0x171031a4b2549f628d8f557, }, u384 { limb0: 0x5fb64070f77ec2efbd1e2f60, limb1: 0x7aedac149757093b7a21fb, limb2: 0xc734391d5f1f79153379a5c4, limb3: 0x2e4431bd67ad7971fd3853c, }, u384 { limb0: 0xed6981f8f4f6e017d40251f, limb1: 0xd1ef4609f089a1fc18e6bbb9, limb2: 0xdf4659d17b22be624a57a90f, limb3: 0xebec9788a27d3a42ef67f66, }, u384 { limb0: 0xb4309c259a5e1310b40d0a24, limb1: 0xf20ffbdc1d69b685c69a1f90, limb2: 0xc8614f276879f6797faea9f2, limb3: 0xa01435953aeaef80b73e664, }, u384 { limb0: 0xe962fea520fd3cfee77322f6, limb1: 0xea0db9db4549cfbd7e654519, limb2: 0xf2f15d706dd410f74601a948, limb3: 0xb43c39da3af0262718248a9, }, u384 { limb0: 0x89af2659aec46adcbc283eb0, limb1: 0x44e22f284d8f97e7b188b4c8, limb2: 0x8f012c6f8148af4043497b90, limb3: 0x568db4fa914b292333eba0, }, u384 { limb0: 0x96fc87f0735f521fa9b6ac33, limb1: 0xb5ff33870a9f925b1ea88009, limb2: 0x7674aa497c8cf7b309ef0c5f, limb3: 0x15c240ff0b84df67ba9be747, }, u384 { limb0: 0x3858d615f050e01af6284057, limb1: 0x7052ee4a1956878719d6285d, limb2: 0x8dea5552ecfa9cc7ae5bca13, limb3: 0xc05db0ea0bfb4247a01845d, }, u384 { limb0: 0x4a0e85645dfccdbdca3a819b, limb1: 0x95ceafd93712eaa349882f33, limb2: 0x11a9b8209be7b8bda0f8bac5, limb3: 0x1187a1136ee5fc0651af6f6, }, u384 { limb0: 0xd3d4b65f6177627644271dce, limb1: 0x190991c48a2642418882b846, limb2: 0xe25f3fa16699fc7b12981b44, limb3: 0x14d3886d451365cd2ab9629f, }, u384 { limb0: 0x9dd3c016b1cda4f9a3d8dabe, limb1: 0xa1dc52d9783032e16103ff29, limb2: 0x2eeb760dfccd32e7a74e496f, limb3: 0xb0dd812d5b993d258a429f2, }, u384 { limb0: 0xc8b6b1d68bc9818f99b76bfe, limb1: 0xdadfc4ddb28936a746a4af8, limb2: 0x806e1b074865fed25de96d6c, limb3: 0x181d8d37ffb1f532bd5aa33d, }, u384 { limb0: 0x1d6e65950828510762179474, limb1: 0x7108c95801c369b0c7551ee0, limb2: 0xbeb1e03936499685cd2f0150, limb3: 0x94df4f30a2fffb4042894c7, }, u384 { limb0: 0x983c632a3e1a5947b7c7ce7d, limb1: 0x2be8a2b39940f29c12c6cd3f, limb2: 0x587797cc44e4124149751541, limb3: 0x30de53dc59c8860b9c16f7f, }, u384 { limb0: 0xeaf612b94d0bc60deb981119, limb1: 0x3b9840081665e52e3bb40328, limb2: 0xc465e07048a44b2ae6654163, limb3: 0x11c10d0e95e42b0240c50e62, }, u384 { limb0: 0xab55890011ebbaefa3538ccc, limb1: 0x5e688af48008d385303ff84b, limb2: 0x9a1e17509b5c09ca03249f9a, limb3: 0xef5fd5c3f8fe0595b598a3d, }, u384 { limb0: 0x191cf20ea760df983e8b0b72, limb1: 0x6d8cd162272dbbd1c6fff8b4, limb2: 0xaa4f764ac0b0d6f68fdbf162, limb3: 0xd84adfad72ed9e456fa601b, }, u384 { limb0: 0xd9880e4da287586fe3129b1a, limb1: 0x66e9a0d449b088f203a3ec47, limb2: 0xd84ecaf86584177be6450249, limb3: 0x3642d36fa62f740e86db979, }, u384 { limb0: 0xb4a17111e89cb47a754013b4, limb1: 0xb42368b0f282cf82e2c6cca6, limb2: 0x2a6ad63690743b24f3539bdd, limb3: 0x19658ec275b7492d1dfe64ac, }, u384 { limb0: 0x24ee1f851f58a051cd009256, limb1: 0xf9f8f3cc7d416c74a2689447, limb2: 0x7243778aab332312a96edeed, limb3: 0x191189f043eab9fb823e6b07, }, u384 { limb0: 0xae250e76dbd459da5fa132b3, limb1: 0x22355b40a8ab9531239d43f5, limb2: 0x6eb78f695a56c09d76521bf2, limb3: 0x1731d8fd2184ba4105a4a229, }, u384 { limb0: 0x671dcb205f5f18d66b176193, limb1: 0xb4756273e2d3f131ef547396, limb2: 0xb4e704610e05e40aceabf3e2, limb3: 0xe10b93d6de58686874163f6, }, u384 { limb0: 0x39638c7cf8c5ba660d53968c, limb1: 0xbc5fd36fc0bc3338f748b7a5, limb2: 0x5cb957768b2d2991b2f16ae3, limb3: 0x675685ab77f59ec1cf3447e, }, u384 { limb0: 0xb1dc8051918f43cd46dff901, limb1: 0x7c7757704dbf37b25a368fa5, limb2: 0xda3a570871cc0e84780027d, limb3: 0x6f3551123964dd05e1dafb0, }, u384 { limb0: 0x1d45fe61b35a80a2c80f592b, limb1: 0xa06d85ecc6b734969e9a0eb6, limb2: 0xbd560c030fd6d54a4a8c949e, limb3: 0x3bbdce254a4f9d715fbc81c, }, u384 { limb0: 0x3ca2ceab38f0421274b7534c, limb1: 0xf0ff90132756fbb051d8aa4b, limb2: 0x58859f8404a55bd454a5de1f, limb3: 0x9ea264eb37003ba2e196965, }, u384 { limb0: 0xb6820f9ae8020c0aa809da67, limb1: 0x8d2b765aaa3cdb50b34b1f08, limb2: 0x750249d318beb2125df15f87, limb3: 0x1edaf94fccb23ffa7f389c, }, u384 { limb0: 0x55862e3259ef6862f16ecec7, limb1: 0x7b91a3f930b0944742923ed7, limb2: 0x557d1688f2f93b98dc4b982, limb3: 0xe28648e51b39571ad532a88, }, u384 { limb0: 0x12f090e45f01ae193958c82b, limb1: 0x9037ff4c808f2367d58be5f0, limb2: 0x1bb112b91dcab6bb8fcda4d, limb3: 0x170ec6a92ff5df984ccdc533, }, u384 { limb0: 0x156d184f364ebb691c75f987, limb1: 0x6d770effc0f532318505945, limb2: 0xc8356e86afaddca62c1cc1ab, limb3: 0xcb3ee3182c3597c54eb338, }, u384 { limb0: 0xf417b27304e057bd07c46d86, limb1: 0x7e62858cbc2377e17eb40f95, limb2: 0x36954cb5ded007d2c6ca51fb, limb3: 0x4c09d37e7aeaf8b9747dce, }, u384 { limb0: 0x50fa90d805efe8914ff46ae4, limb1: 0x6ddee6e60ae8b0c12747584c, limb2: 0x931d47a2d99037715a8d213d, limb3: 0x16bc62f391ef098c5d89402a, }, u384 { limb0: 0x1552e86382234328310450ad, limb1: 0xd78438385562436267a9fe86, limb2: 0xc9d9e66c1b636e4182c42420, limb3: 0x1783646f20e293896acf90d5, }, u384 { limb0: 0x1d42fec0e646e25e77f86995, limb1: 0x137cca27775b396c26faf443, limb2: 0xe365d3c83d9c421ee1254536, limb3: 0x472b2f78d789bf9b1f2762d, }, u384 { limb0: 0x35876d82ee0d92db0478774f, limb1: 0xa8b9224db7d15be474909274, limb2: 0xad9143269ca1da1b85fc863, limb3: 0x112e2c7730637568391bd4ae, }, u384 { limb0: 0x6a0bd1f7640cbe4488273abd, limb1: 0xa11e780f3e28bdd9131da09, limb2: 0x2c35554e941b0f5de2f5c418, limb3: 0x69d31175d11988c85135109, }, u384 { limb0: 0x7f71caf4e001e1b0568f3e5, limb1: 0x92233912d20c5526fa8d42cb, limb2: 0xb162077f59fa7ac2e8cb7bf7, limb3: 0x1622697802fff915cc1e1080, }, u384 { limb0: 0xf56fd5b7f9ffd0fa52929a2a, limb1: 0xdc74cbb063c5f4a0d7b15de4, limb2: 0x449b4e9b45d4412680b742a0, limb3: 0x12d88dedc3deebd154388d55, }, u384 { limb0: 0xad8617f926733972028e1f5d, limb1: 0x55fbcaf8e6fb0c2f362206a9, limb2: 0xb81429cd318e1e736cce078d, limb3: 0x6f9c101123ba0139453231f, }, u384 { limb0: 0xd775ebee2c86b41f644f03c2, limb1: 0x531c4d620f411d55b1a94de3, limb2: 0xc155f42f31ccd7954ba6583a, limb3: 0x1387c3f8aede859d1d5b3fe4, }, u384 { limb0: 0xc86e265466fd08932ca64167, limb1: 0x88cdb047a6d4264c3cc2523e, limb2: 0xa0d9953a4266dd1d27e7a588, limb3: 0x609de67c510183f4752cba9, }, u384 { limb0: 0x59017b9249d2fcb894edec36, limb1: 0x4c8d817ddb8ecac7145a1cfe, limb2: 0x8248676e83742fa4c9460307, limb3: 0x1f84a9b31ce0a25340ef65a, }, u384 { limb0: 0xd4e57f2873f7f6cb353910c0, limb1: 0xd488f5b670d47eb81231935b, limb2: 0xc7bd11e77d109294836796bf, limb3: 0xe66dac679006b99972ead25, }, u384 { limb0: 0xc5e72ca4699a899f05679a5d, limb1: 0x2e4d56bead2c9e839241aba2, limb2: 0x5f925cd8319353aad49014a0, limb3: 0x24259652398e68d250ae008, }, u384 { limb0: 0xf94f6c9ff7c59b13c738f95f, limb1: 0x3bff0eb04836ec96a66c4618, limb2: 0x5de5f0fb1fc22054ea2768c4, limb3: 0x18b8c769a9325f433df2b3c8, }, u384 { limb0: 0xfa6cd0021653c7f8b700eb81, limb1: 0x1c3bef5f0deb705a4cfd07c, limb2: 0x3e148cd9648dbe6962737f37, limb3: 0x8c48c803b9df61d5d0f4335, }, u384 { limb0: 0x2d13228fc43fa72174e1d79d, limb1: 0x8ceee96560e7839948fd73f5, limb2: 0x7a1ff60936ba067ecf2be4e7, limb3: 0x55e59f6b053aedc954e2f64, }, u384 { limb0: 0xa7c35f69c4142f10400830bc, limb1: 0x24262150bc21dff0b6696005, limb2: 0xfce95af53cd4ddfaa700bce1, limb3: 0x11bec78b5abb2ab6854178a, }, u384 { limb0: 0x19a5ee954c07b7281089a8e6, limb1: 0xd40256b77a93b72bb5531d26, limb2: 0xadf2b131573cb69c0ae34da1, limb3: 0x16074d4792a0789dc26c48f1, }, u384 { limb0: 0xc697db24f748b0859934c9a3, limb1: 0x74969ae8603e2a72639c65c5, limb2: 0xe62e7354ec8af2959199abfe, limb3: 0x4a6f9c7648e14a2039a345f, }, u384 { limb0: 0x1b7d1e1cd9070f82a05a1151, limb1: 0x7b4bdbb15ecfa8352bf3cd5, limb2: 0xb0f6cde11169747ceec1f223, limb3: 0x50af2df26d997326dea9c7d, }, u384 { limb0: 0xd7db3a18448433fb1c4bb1d9, limb1: 0xcfdd5e74ee538dccaf44e51a, limb2: 0xba81ec9b76bf3b70626faa1f, limb3: 0x1b2ac611094f4ac2ef0cb43, }, u384 { limb0: 0x36f4653ad3f0f0630d32acf3, limb1: 0x1127cda884fd049cf5d17efb, limb2: 0x458693ee9c4582a3f9af1391, limb3: 0x1752b89881cf24240c3822d, }, u384 { limb0: 0xa52a317d238eb3eb0ff813f6, limb1: 0xa06066005cbc71d651de16eb, limb2: 0xc5b6eb4edc413750b81522e5, limb3: 0x16c66a2b3916bb88e9c219f1, }, u384 { limb0: 0xf39b6ed97d58a4149909d14e, limb1: 0xbaa4b842f39d06692eff2cd5, limb2: 0xe0d48869ae01117461e5a9ff, limb3: 0x1766de5097c23481915e97dd, }, u384 { limb0: 0xc0da9a67da5938ac5c763fc7, limb1: 0x82bc876fa2ed871c19c33af5, limb2: 0x2ba919e7c8369424a77fe5f5, limb3: 0x4ef14b10234db8ba75cf2d6, }, u384 { limb0: 0xc0f0246d30f910f7f4f7bacc, limb1: 0xa4e2b9ce9a30a297d83a0796, limb2: 0xaf667e1daa0e7696f9802aac, limb3: 0x163125067faa7ae61d3ff47f, }, u384 { limb0: 0x5cf5fda1c4d762853036b498, limb1: 0x7cd7e6647f670b4d0c2b6905, limb2: 0x88bd728ea76b8c9fe62759e2, limb3: 0xf92379c473f637bdadf46d6, }, u384 { limb0: 0x17fb595f33d4288f509c18f7, limb1: 0x76bc6f78fd2c0a0eba1f4c20, limb2: 0x160547d489f3e681f1b6fa64, limb3: 0x1330acf4ae3feafbf7aafe3b, }, u384 { limb0: 0x8d5df3e5ea678ee71e59cd1a, limb1: 0xbe91049490dfd32e6ad7a807, limb2: 0xf78eb313f65393a1a3398681, limb3: 0x16cbd3644701e09fcabd2594, }, u384 { limb0: 0x6e09472504dd5d81bce3b334, limb1: 0x41468f5dec22b70c3722d5cc, limb2: 0x374a4f7fe05f282dc2be1d52, limb3: 0xf815461ed5859eae9bb0e8b, }, u384 { limb0: 0xdd2ffdb4aba3e50f719dba69, limb1: 0x2e420ef25ff984065f707276, limb2: 0xd47eff4408dd3bdad9d78007, limb3: 0xfdee00bf00506d168704e7d, }, u384 { limb0: 0x45f6b066bbb7f0cb3c3c233e, limb1: 0xcb2d60923f67fdcee0ccb02f, limb2: 0x311b087540790fbef7288bec, limb3: 0x152f310fa6ad50b6a026dff8, }, u384 { limb0: 0x476fcbc57effe3f4a65cd4dc, limb1: 0x4e05361ceef3f561aa29e14, limb2: 0x1e4c75e1332e0af3f9a9ff9f, limb3: 0x8875888546de92902edb37a, }, u384 { limb0: 0x55f3a0cf8ed908c42e96d5be, limb1: 0xb83d0572643dd6c39126a152, limb2: 0xb2d2325f1ecdc8a4e76a4901, limb3: 0x15f5e61b210c26915de8e31f, }, u384 { limb0: 0xa43c056ead4885b2e99e75ec, limb1: 0x24de1ff766c475543e9c08ea, limb2: 0x146b120194e009008241f009, limb3: 0xd12952df98f8b8411a9ffd1, }, u384 { limb0: 0xc36c37c1fb558da5cd73cf40, limb1: 0xac52aa4a715d2825185d2ae8, limb2: 0xd1b77b6a984e9ea14a5c8ba0, limb3: 0x9267a9326170d966179a68a, }, u384 { limb0: 0x2c89cfc4db7cf43a294f8f8a, limb1: 0xeeaddf051f0015ba50ec2338, limb2: 0xde7aa569ac55a5bc8d4363c1, limb3: 0xc203f318f1bee0a7226ae73, }, u384 { limb0: 0xda5c952362d08ba865626193, limb1: 0xbbeb49ffbbf97b67c903ff69, limb2: 0xf3e184149e42b4d2dd6a5946, limb3: 0x9dd3738ac39100a3ac4c162, }, u384 { limb0: 0x56a4fa61ca2b466dc01250da, limb1: 0x63bf3d66be728d50924bc624, limb2: 0xee30c430bdd97d34263b0b28, limb3: 0xc53aab22b677ec2d4aa6710, }, u384 { limb0: 0xa074bedc692500027bedb6d3, limb1: 0x3a537d5b75de7ef92b7688cb, limb2: 0x246b5825593b5b9d56a4d9d3, limb3: 0x113c2003c37b1eb947676645, }, u384 { limb0: 0xe2af5a83acd48d45e355ac92, limb1: 0xe768b9a9dbf88555c0f48458, limb2: 0x7a72521d4206efcf74f38493, limb3: 0x14677be8d18e0941c802144e, }, u384 { limb0: 0xa974f39ec059cbedcbdc7662, limb1: 0x28a5f36c96f7b5889b559318, limb2: 0x8f0b8fe25fe2545fb6858c97, limb3: 0x951deb7764c5542e25187c9, }, u384 { limb0: 0x94a5bef76599825c390182a0, limb1: 0x778d1517e3063378cdf51734, limb2: 0x7971f91f1002849ab158bd47, limb3: 0x17a9ace9cd4d35468504f957, }, u384 { limb0: 0x96d64f9432d239fb26cdf3cc, limb1: 0x3125e568352713de99062560, limb2: 0xc34e0e636e67217f2181de15, limb3: 0x12bf8fb33bbe5c5ba6a55268, }, u384 { limb0: 0x3729d178812e993cb3d59ff2, limb1: 0x7164060bd545db0f5e55e9f0, limb2: 0xc5eb7111ea2fa2d19ed6634c, limb3: 0xb50481d3c4a6f38480415c3, }, u384 { limb0: 0xd4496c2106c96bdbc6a5235c, limb1: 0x52d7c52ddf53c605aa610286, limb2: 0x2a8d5d11ba94d192d58b0c6f, limb3: 0x119e88de0eef3cf393d8d315, }, u384 { limb0: 0xebae8c783f077fd3c2fba31, limb1: 0x9b868a30413b925f51c33114, limb2: 0x53b5d13cbde84dd58cf4e713, limb3: 0xfecf474b851e762145a27ca, }, u384 { limb0: 0x7fad2c76d54e6ac3c73eda24, limb1: 0x7428d7731e6ad0732f6b0067, limb2: 0x611f5cd79e2c44710a59f166, limb3: 0x16c032a5f08ce4f07fe6c985, }, u384 { limb0: 0xe3825ea9fcfdededa3e156be, limb1: 0x93f814ed177fcaad9542f2ce, limb2: 0x74e5e08dfc2d39d9cbe41bd4, limb3: 0x14ccd9031b038e809755fe62, }, u384 { limb0: 0x541c62f55d52bed742659afb, limb1: 0x9588890d2ba337d20a53f942, limb2: 0x5a1f5b14da9474238b147bb4, limb3: 0x7a691b3ee7c2e5c0c51c8f5, }, u384 { limb0: 0x9d12d194ef6623a00266d1dc, limb1: 0x1f5b2f36e044c804845e63f8, limb2: 0x1b5eac5cee412396c2688c55, limb3: 0x73c653497a9f8b9683aec46, }, u384 { limb0: 0xff839b6315bb41548d0f065b, limb1: 0x39d44131b83a688dea580cf1, limb2: 0x6a4a6ba320b991421349ced7, limb3: 0x15d23e4230faf11b2d12a1f7, }, u384 { limb0: 0x6761fee71ab41ad98ca781fb, limb1: 0xafe1a079c3e99036534f3b73, limb2: 0xda73c296967b61b3bbf4549, limb3: 0xbfab60cf853b369dcaf4e83, }, u384 { limb0: 0x8179f1752883102ceb7aa69e, limb1: 0xa13caa48cfe29a2a6846f284, limb2: 0x3e296b59646aec40a2e7f7f5, limb3: 0xc672f3083b9812dc0ad1d0e, }, u384 { limb0: 0xabf6b28f2c7b09f7211ff2aa, limb1: 0x1b81548b8b84cdc8196a89b, limb2: 0x48d81c0549c1cd98cd89cd7a, limb3: 0x150a4a35d24be72173ac1335, }, u384 { limb0: 0x2cd54ac23ec0fb5d623cb2c9, limb1: 0xfe8d0101b4fae5f0a71b59c2, limb2: 0x935cf0170abc1d88e0e2fb07, limb3: 0xe2dc487c52a2f677e1efec9, }, u384 { limb0: 0x29c949ec89d4ed04f794429a, limb1: 0xf1258b9d7e7d8bb80fb58b9a, limb2: 0x4d5ff9db250e0cfe18b02497, limb3: 0x10e30a2eac74c41f16474f61, }, u384 { limb0: 0x80b766999bafe7554b1ba789, limb1: 0xceab56251f7fe2864df2ce3b, limb2: 0x1f56382d890248035810f2bd, limb3: 0x7b06a1bffe3bfdea07ba2d2, }, u384 { limb0: 0x67cf0f0cedb32104ed3ec1f6, limb1: 0x9dcfa86edb05f376a6de76ef, limb2: 0x6a593cc2d259710819d92dd5, limb3: 0xd6c135c5615705b299a78e2, }, u384 { limb0: 0x8e18746f53c857e8a8383a74, limb1: 0x3dddf8b75512376fc42c2458, limb2: 0x4bdb6f1386a9f883b40de577, limb3: 0xcae1edbc64c45c95fc152b1, }, u384 { limb0: 0xed4a4581e83c76e945c984ca, limb1: 0xdae5b71fdc78f94ee5b097b0, limb2: 0xbc3d1b1b38b6d13d1629f2ec, limb3: 0x16b1a4eb022c1381f056fb61, }, u384 { limb0: 0x6a2cdf284ea9d17e237e14e4, limb1: 0xa029c79c09561485e46ea2a1, limb2: 0x82cd28ab9dc6e2ffab6e2a25, limb3: 0xca4c79a420395c8919f51ab, }, ], z: 0x52ef92c6fb1c4777cdbad00b49ca5611928c145e716dfccbc705fdd4a0b02f9, }; let res = multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result( pair0, pair1, pair2, precomputed_miller_loop_result, lines, hint, ); assert!(res.is_ok()); } ================================================ FILE: src/src/tests/autogenerated/rsa_tests.cairo ================================================ use core::serde::Serde; use garaga::signatures::rsa::{ RSA2048PublicKey, RSA2048SignatureWithHint, is_valid_rsa2048_sha256_signature, is_valid_rsa2048_signature_assuming_encoded_message, }; #[test] fn test_rsa2048_positive_seed_0() { let mut rsa_sig_with_hints_serialized = array![ 0x766ad7a96b6a74dcb0d4ee21, 0x3c31169ffb4c539d20a19c30, 0x4813ed39e65994f370938d52, 0x19c0d08706b4597638cc3e30, 0xc7e80539ead20295baaa808a, 0x299992cbadae99aeb97422ae, 0xb226c9a7b454cef99bca662d, 0xbf70d4a08cf48ed827e59567, 0x7f746d2d77af83b2122fa87b, 0x9aa92b2128d9725d8656dd96, 0x3b526db14be8de881d9d16f0, 0x60ef9dd9b7346128d4904a2d, 0xc956b02d42c83dcd03152b6a, 0x417242ec1b72b9d2c28b3a8e, 0x31094b84fe9156b6d0462fe, 0xaee058ad4254ba267bfa369f, 0x236079af55b0b25854deb6d, 0x1e371829465e97bdc783fbc4, 0x308ac6dcf29aabb20d05c85e, 0x250ca4cbef9a5ded24279a60, 0xc2667b7be6ec40e1236d59df, 0x92c2ffdd, 0x0, 0x0, 0xccd4d72e904d8d17594ab5f7, 0x39711006ced57a24b0b3ddc, 0x2ccfe85722998e88ce696503, 0xbb4d033f6bc441dd1a08890f, 0x126b5e07fd274f3c18f28ad6, 0x6d1e293c0af656e2d1d56a47, 0x311e4ff1497cc51e1df029af, 0x9b5c4fd21b926c416bee361d, 0xc2763b9d1cc4af2edb1ed69b, 0x38c872d56da6fbe02f39f2b1, 0xbf55fbbf55d4cc74e2b1257b, 0xe6128d2cb2c59820b674fdd2, 0xa13fdbe9e48e2bf32e68a32f, 0xa91b93a068472e0dda54fb2d, 0xddb762befe90bd234be8b786, 0x8de87eebcd0e03fcc11febb2, 0x58c09101bebc3bd1c58c0616, 0x7ebe6e4cc8aee40772b501ec, 0x8e478ff6dd4c4a4422e8f182, 0x10d134c96c1d30ec1c29823c, 0x5dda7fcba4eb273a149eb833, 0x5c6704f1, 0x0, 0x0, 0xa9dc684ea7a072c583378bdc, 0x234eebfb13b9f83dbedc9689, 0x46f68cddc2dbc0748d995ad3, 0x4338acea2099179babc1f7ab, 0xcc0fca21384a6773f735d8eb, 0x5cc17f9d3c9d8636229c1adf, 0x5af4b70e86e1d9ebcec76328, 0x73474b28f23261bbc278997f, 0x60b65df1d9c6c2025877cbc7, 0xe5f371b392daa99d60dc68f5, 0x6d459b8018d80c189e4fb2db, 0x3b782f2fb21f91af6f955e29, 0xe58e194ead8b059afb9cc6e5, 0x714a92db56aaef13c5eb239d, 0xd17462b734aae256a7c053bb, 0xc7364388960d6831d60e8379, 0xa6e642a3822390a909108133, 0xbb3455c47c1d625f04473e54, 0x473a8914fd186b8c2f53bd98, 0x56cb778707e253d5bcd9c897, 0xb212545df5bc302598e61647, 0x879e816f, 0x0, 0x0, 0xf11082a78e2349176eefb845, 0xa2c474b18dd8215e6ce79a2, 0xaf8397d226331e6fe0287b82, 0x2021be0dbe82e1d87ff0464a, 0xf9f671cbb480c9ad30e96b04, 0xbf0341d821907bf2d1714934, 0xc4133dd8b0fbec701c6bce5b, 0xab8a9912700daed15fb14efb, 0x6408b84f7f8cfcc466adb647, 0xed064d750384670cdc484c57, 0x10d17bd4d1d8b673945244cf, 0x3661fd2009f806b98f962802, 0x3ded8d1c80a858c317f106ea, 0x69490720cdaa41dd567bfd75, 0xa2e9da91a7303beb4b22e507, 0x63d845332aea5d5d79157f21, 0x1ba1ef9812c965e541b8c9e7, 0xadd80c35198e137ffef51c0c, 0xec2ddf921bd92a5be54e75d5, 0x9f260f9358d8c772581bc666, 0x49cb9677cbc1c13c5b5a6b46, 0x3a2d6680, 0x0, 0x0, 0x61ae0775f0594f0d3ec84d6c, 0xcdf82c4368c89d619ad6c4ec, 0x16634f8f537349438fbf800f, 0x18bb5fd323098da014d9e4e9, 0x3de3d2b1c1ce83174249eac3, 0xe04e43c5856d447e64fb2c49, 0x8315c17c23405e47aa9dfdaa, 0xdd3e2d06e6755e5877139c96, 0x1de63f44a100a924034140b4, 0xd1c1be2c6c01be2cb6165113, 0xb3f8ef010376c8d557dd3a74, 0x5330b322e6537546d099577, 0x50feacf7ef56d00d299880d8, 0xde8af60590cff5c21c9021e0, 0xc719c781d43d99eac9c9a446, 0xa03f627aea3b9c54fe08cb8b, 0x2fe3ddee1358fa008dcfbd75, 0x183d0552096beeda805632ba, 0xead565b3a9fd13f32d94abbf, 0x8aa3b518bf3670dc8a44dce5, 0x7ce23145e486815f1397916a, 0x836001e1, 0x0, 0x0, 0xa50443039d3dd37156158183, 0x383a7d1fe53348285bdd2f37, 0x3e634aab243fc03bdd9548c9, 0xf63f0748d8ca9bc50034c997, 0x5cc782e51c7c576b5cb62457, 0x767abde2f4d3fc3d27c8dc12, 0xc55ace8470f37a3727c4cdb6, 0xa970e7780d86111b86e8184c, 0x3b930d12e10453014f602550, 0xe86920884a33c79d586e5b08, 0xe1c35a842d9968776b9a5756, 0x2d87248120b10947502a05c9, 0xce2325942bb6cfc89ac9a16d, 0x3023e567a6aeaa0e56e67c5f, 0x931367e2e28f64cf5e67881b, 0x5086944531c4016e1b638c8f, 0x2041352d23b8eb7553c90821, 0x45e38d7e09438b118b8c8797, 0xd15618e1fa2be214b20a2b62, 0x613c5bc02562fac980d54ff6, 0x3547852fb77b7ad22f7a3809, 0x7599fbf7, 0x0, 0x0, 0x25772373859fcc1ff880a9ad, 0xb3d1a77be83203586116cc33, 0x249ddde6a735af8d54f76e5d, 0x126236052ece65c16a4f8147, 0xc14108cea2b89f8bd216819b, 0x31e5b9cd08617bfbebc340ec, 0xc533488c6e32cee86b51bb65, 0x3427cbf5c389545877454003, 0x5f471a99ed38c12709340c97, 0x782d84eec1f578cf6332df12, 0xcff0e44dab2705c3df8ed43b, 0x828932cdc82c07604ed8aa16, 0x3f3c04ef18aff4f15ecac8a6, 0xb00f3fd36e39d0b3ba293f0e, 0x98e9053c9079b132080e1433, 0x8ae039670f1f588d49b0ead0, 0x84e04057fe631a9950e3741e, 0xf0975e0d1d87294c0779e4a5, 0x9af5116c3122c9454c33abf9, 0xfc8e70dd2f1882948bfaa669, 0xc4110d0bb3e3fe5bd4aa3849, 0x63ed1112, 0x0, 0x0, 0xdde6339489f82be2a548914, 0xa6129a46e7fa08cf79fe8795, 0x4ecf9c35860837ca5cc9964c, 0xce764f24f9a04630792a3962, 0xb037bf199470e6de572c42bd, 0x956ff3546d57ee943af1668f, 0x9677e96ffddc8fb4befbe60b, 0xcc50d5f30da8488eda5e2c68, 0x5c1aee3bac6f9bfcb475b589, 0x417cbaff0027179506246182, 0x4884fa40151152ccfb8f2361, 0x5fad486584738fb532be17dd, 0xdafafed3e1c4cd027bba63c0, 0x7f443066f06aa1556dd9abb5, 0x4b627b9936231df8ae4b77a0, 0x84fb2d5a4f24cfe981dbfad0, 0xb876a978d779736ade0abc08, 0x5e6ecdc675a0b2c27e3a310, 0x68b895aa08ce6e80cc24b677, 0x933d588163cd237a200f2ec6, 0xdf366116dbf8e636789c8917, 0x440972fb, 0x0, 0x0, 0x4c43909d3df7aa01fc8f9b55, 0x573f92547eed486eaecf4fc4, 0x706df3b0fa507cf78864078e, 0x72beedac7c3f62c50da7858, 0x7b01b47908dafa52fa8f40ca, 0x42c7fe0d226b199ff3a8b27a, 0x2cd291e0f2b7259731ca1103, 0x9936fd0d86cce4683dbd3593, 0x6fa4eae97809921e2e8f1c29, 0x61bcf43cb948de83f418604c, 0x4be8bf5f7aa4f97164b57e28, 0xb2cac9559ad2a26568d798c7, 0xc9e3f5b00702b0a067b7ce6d, 0x42738b954118f7fc09daf06e, 0x936703c37dcc919aeabbf3c2, 0x8234f4da6b15efc32f91b03a, 0x51016906f1aba3d0051cc8d8, 0x29c616b65059e5257568c86a, 0x9e7959ef4cbfa69866c3ae8b, 0xad55fa216ca080ce5f33515a, 0x4010f7d945e56f9faaaeed47, 0x59c35b15, 0x0, 0x0, 0xbd7ab4dca711f0d929017d0a, 0xf6e1b23766720a08df2e064b, 0xf743a47b9ef21525e4a3851f, 0x2e9e91630551f14e278d959f, 0x450e114a827f3fe74024242e, 0x768f0b12f0fca0e28cad2d5, 0x6f7551b524fa35f7afb69fb0, 0x503e453c615811e1bce63aea, 0x89d3c0aa219ca344b32b4a69, 0x9847c02179a77916a0aad3d0, 0x363a2da6bb7cc920afd971f9, 0x105756bde27aa2e4a1654eed, 0x782316203cc0dd1bde9739bb, 0x729e9df0a4384508f628312a, 0x7c58ad79ca4ff22633b6c393, 0xc25e962083bee700b96ce224, 0x4b99b07dcff3f811dd6d63e2, 0xa07af35bb0745dd4de9d5dc1, 0x2362f99b653a6d200acdcf4c, 0x7ed1f7a32c6633f50a1a6d1f, 0xc67831f8385e2ebf6c0e15ce, 0x36e6be8d, 0x0, 0x0, 0xaf2e85f517483d20277d9fef, 0xa6c8e9ef245c3cfbe92f5583, 0xae0e652d9bfd555164f5dde9, 0xac463ea67f143f6b90484d24, 0x292d0d6d7a0f61537e241903, 0x1dbd26b03b4c300939500257, 0x38f5405d2d4eb07f94eb4174, 0xebed3bea8633f2024a17fa8b, 0xd8029bd940f48c17be9061cd, 0xdb881dc57fa541995190cffb, 0x28dbb1531a44706a35f17fe9, 0x47ad149d189b70df6962e01d, 0xe56b6feae22bea7827cf0aef, 0xca565c0873f303db366b4122, 0x18739e8523299686923d88f7, 0xe4c0c42cd30512c887141263, 0xd6664b534d1f54775647116d, 0xccdd2182bb113823e3c8cae, 0x5351a577848f05aa228c7e, 0x12209ca46ab63bc8985be0c5, 0xe39f22696539616774a946cf, 0x857b13e2, 0x0, 0x0, 0xb4b75cf7190e9fb150c78ed, 0xebb37162b1d1a0cc8ed4e70, 0x2e90eaa6bca468a75954af94, 0x921837f27c919b98ea12bd7a, 0x938d23cf452c57690e41acd9, 0xeaeb0bbd339278e588377648, 0xea059eb1bcb1327413df220f, 0xf3d015ee9a83e173bbfe05db, 0x6eca8ea01474071813e0575f, 0x478da59c5392a7c4859552b0, 0xd53538319b99b57602230736, 0xdfa5ccd9411adccaae6481fe, 0xfbb3284f1a46aab145b14e97, 0x54ac3cb4084ce72b420b1440, 0xfc0030ee568632dc99eb3e3e, 0x67838dcc7ffababee905e4cb, 0x1dccbde1880631c960965f05, 0xd92ae551a3b09f2b1914b2c9, 0xb92dfcad76ba37636909b5ba, 0x6d02704ea436775eb9eba0a1, 0x1239f0c36942aa41d0fdb583, 0x7966d36b, 0x0, 0x0, 0x2f0370e0de67e0e0204d494, 0x41e6a7ffb185c93fc567919f, 0x33b32ddef77fc52a3e1b5a8c, 0xff9cdac2a8555b74120dd0a6, 0x374fe9884c8e839da4c5b64e, 0x765771b2daeb10f3e43d714e, 0x6e482c50677c27f548576bb4, 0x1ba9ee7076cc48c2028e07d0, 0x2d544810350024a0c1b4d179, 0xb8f7bf71b996e3c125d6df41, 0xe1527c84c71956afc34f6845, 0x8c339e263df547b486a303c1, 0xd671bf4705270e96c2dcecf6, 0x8e2ab787b0d997e2c435288d, 0x5aa9c5acfa39c50a3921e905, 0x99a4f9d3b39672a4ef023e78, 0x299824406248082c032f9e88, 0x5cce13392a9c02c95f51a627, 0x8ad6ee4d053df429a6f03f9d, 0xdcf0e7cafb7fd7f3c7f87d80, 0x9aebea38b3e33b2b482c8a04, 0x8bf92cbb, 0x0, 0x0, 0x9f7d6f589e82e9756cb90734, 0x1efc494737c83d8d1e5555e6, 0xdc14db376bb2abe4ad6c5145, 0x6350095e5153267e0f7cccd6, 0x2f11b257bb2b86998a1c4fe1, 0x1b0f01fffa4cb3d342c3331d, 0x45f2b93d6b87e6c14c8bdb25, 0xe0443287f9111fd56efb078b, 0x1560ccb1b67cd638d2ab63d1, 0x48598e67a7c87a38e45761f0, 0x42e95914d4ce2835d31ffdff, 0x39b5c97ac03b49dc9f8f6118, 0x1264a7647a6a15794f811a46, 0x83c3d06dbfb2b86373c10c27, 0x930c355b5fa314b6b1620102, 0x22692e942620240d77d0c6a9, 0x7b8897708cd33be40719d6e3, 0x7df5c691973b2ebe3fad0373, 0x6703a5c064a846c40c588c44, 0x2ae4b8ea5e745d2f0c269bbe, 0xfe723d71902007fbc8a70662, 0x857fbb68, 0x0, 0x0, 0xa5af2060ca06c184e5892fdc, 0xddc0a0a99021868d6da0893d, 0x24b56567184dc2acbcf5c73e, 0x160ef95f8c1f209f220add52, 0x2534d4dbc6d040d83fdb27e, 0xe9975a62f1ec391cc7426ae, 0x491ed56f50664e259b8ebad8, 0x7fd81ec116d12e3df8c35dc6, 0x2a894fd7972edf7865cc64f0, 0xcc22be61d6c9dcd87bbd11f7, 0xfd08aef895fe6b35568a1478, 0xf859f2778a321a7653ef2225, 0xf76ab371c23da4e6581b30ba, 0xeb87317e55dee41753d04513, 0x65f710857dc2c2200f569276, 0xda8ec2912b42abfb71ff2aa0, 0xef0a6b1ecc8548494c574227, 0x91b537e4d720dfa8b9997cd2, 0x7c31d1185eca8ca5c6625a84, 0xb78354ea69a8e98692057c26, 0x8d1da54563cc19a1f35e8c2f, 0x639a0b16, 0x0, 0x0, 0xa875570c9d0284f771cce145, 0x591c0201ab939b39b4e90b8e, 0x637eda8b6d46c7f37c41ba1a, 0x4108ec753bdbd2b8355b71da, 0x3e09320343a531c8f224f413, 0x1b9bf7cf3daf215cb444a32d, 0x41ce25a20127e9fb2c094c62, 0xace162be846660ab7dbdf99c, 0x2b033b29ca496f3fd509fddb, 0x9d4c1e14a408995d3f7c5bbb, 0xa66dc01cfd2bd5f969dd2e4f, 0x627f37970e930fadd339ee01, 0xc9aff619c84d5b4d8397cab8, 0xae250d0978d29cc49ab124fa, 0x2a5d7e131b5b9e30a46c41eb, 0xd55d087936c566f14dde0f46, 0x69846557a74460713cac372f, 0x8d8ab518931b5aa875a9d0b2, 0x27710e2b2af85a3b75ea264e, 0x1d3109d2d289a899712e2dd, 0x61383d251a5299190b540559, 0x4398936f, 0x0, 0x0, 0x747e4b323bf2a87bb86f552b, 0xf7f2ab1dff8cc754dcdca592, 0x1f34a08fd4c07735a767dc51, 0xe746b680a62bfed15401f9d5, 0x97f4eb618871a00cde3631cb, 0x8339d6fbea40aa941ad85327, 0x90c5edb34de4570c96a5a8f0, 0xefd960fb4e9b509a7e987b10, 0xc05807b47e82a5d7c3825160, 0x314c4c6704487c24b8f15709, 0xc392683af214f5f11cf3b479, 0x948c6d20cd304068c11bdd9, 0x3c78b7c1b58f7f9a72fe71d9, 0x9c5e03c8abda7529065625d5, 0x1a01ea030d11b96aebb1a48b, 0x8c7d949a55df28049f8611b0, 0x9e8bf8c8d36ba12e7aa228ac, 0xb9fce7d6eefc436c65b5c89b, 0xf8136f55dfb42a001616e769, 0xeeb08cb097dcaeb0f5243d31, 0x94d23cd76a90197b1a55f77c, 0x260e3765, 0x0, 0x0, 0xcd3ba7bd04a31b040366053b, 0xe6f10c837922880344fc9e38, 0x5d689eba02224e76eb42b684, 0x6e7643cf0b82715749e94cc3, 0xd140b4dfeb987b80865ec722, 0xe94da4823df0f77f53fbe6b0, 0xa1464b2c1b416476e7472812, 0x94a7a32cff9f1d73f72e09ae, 0x4e74a3c7d9049e7e96cc9ea, 0x1110951d3cc54cf1cf14d94f, 0x67cea4b746527cab8d59000, 0x36179b0c462d4f5cf76e42a2, 0x1742726164e268484e912ab, 0x22709f163ff2cd135caf2445, 0xf81d959cb2c9f991011eaaab, 0xf4f1c1cc347528cd1a4e1e62, 0x4664c8151c0d996bd9f0420f, 0xc086ba3be97b7ee3105c59c4, 0x9672fb601d8e57065a40c748, 0x6f878822fca3f1d46f3a48d0, 0xbde69f62a7e1eb664ba1aa3c, 0x9de2bd9, 0x0, 0x0, 0x4482aeb75faa1cb499c00e9e, 0x8b344a97e26bd3b78fdf7075, 0xad4d20ca51614ca72be40048, 0xaf5d2f7ebfb641ff1b918596, 0xb6d8ec60ccce46edc936e0cb, 0x690e2923dae76b1c1a8a60a2, 0x85c2e3ef5f249cd3e100bbac, 0x4d9a6bc3931d8bac5d9ac6ee, 0x169d730a5e2e1b69821c527b, 0xc15ca47f3a1729e6c2a9ea74, 0x474fa9cf9bd7331ec6810757, 0xd422d04149b9b0debce1cb01, 0xb7efd18fc08f89555d4c11b0, 0x269d2078f1960a85fc421a70, 0x46b5771a2f9d3510c9c3769e, 0xb623a42327ee23cbcb526328, 0xbe8a45ec511d7a54c64fde80, 0x3328dfafc42b91b1c69e10fb, 0x264c1e6be83c39fecf98268d, 0x25408a50e9b65f70f5df411a, 0x41334cb48418bdccbe5c4a47, 0x5c88a46, 0x0, 0x0, 0x25316546d55f7e0dcbe6a3ac, 0xeacfb5cea96b8a320936b33c, 0x6f6812d56f2c9d3dad9d17dd, 0x684a95ba1fa821ea81a11556, 0x1641c404477985dffd7cc386, 0x871d716b23e46bc3b4cf9c86, 0x8fb05800ce27e75c87859c5f, 0xf74b57029f2826c3d32008f1, 0xd5b3c939cbb451990b332659, 0x3a958ecf6774f75eef392e66, 0x5faf5e626a2d5c1986e4531e, 0x8579929032fe8da13ad1017a, 0xf19fd7bd978667567947badb, 0x658966b7546c960300b13096, 0xaf6c205a1a8f1b46855a36e1, 0xc1c3e6045b8b25a219c1335c, 0xf0fa6ff6bf56bcbb0116f9cf, 0xbd84e957d385047457f5b35f, 0x9421fc8ca5d0f21eaa8a7af2, 0xddb3c45dacbe09d2b201c3ce, 0xd931044489e3194da19542cb, 0x3a57c4, 0x0, 0x0, 0x9c2e41e8b5c429114a80a858, 0x5a966e31657c7f8c4b03d19a, 0xf6d631a3b323e9d2d0bf9577, 0x5344cc9641e9b5f74f7112af, 0xe429d282cbf83a3a6b9d4cbd, 0xb7113a43b4dd22a6685afcef, 0x27da7f0630345d55a449bef0, 0x20d6e5d82e5c8e25fee2526f, 0xd4713cd17ed740c4e73e65e6, 0xcc3bcbff28c0d7c447d07124, 0x23305fe2dee2774c0c4edcdb, 0xd281cfaeed124f6cb215f85e, 0x9601c6e2be06ccdd44830d12, 0xe8c75f8ea6aff1231d173084, 0x590ebc020ac0a24a9767b4b3, 0xb8a534f177c2d240170ae8b4, 0x792877e41b28f602a3a9af96, 0x187312ca50914f7652ece934, 0x2d4a3f443efdb605e7461262, 0x1d7d53cf6231accf900fe2f3, 0xbc39ae48093f0259794962a7, 0x18f99fdb, 0x0, 0x0, 0xffa9482e842897e00f682bfd, 0x834c8268bdfe3fe9126289d7, 0x285ef56cdea1beface4af9b9, 0xdf26308909c6236175c8b94b, 0xd0f05616288f3037160caaf6, 0xe037d0024d1c561b107d4d59, 0xb53d73e81fea4422d6277248, 0xe198cc789000080db790ae73, 0x4a534c95b61cf17c5ba235bc, 0x908c97c0440dc62088b9a69e, 0x7ae47a71e12de983ef98db45, 0xf8562cc339b439ad34d2fc63, 0x2eb470ce422fcb4897856278, 0xd00c1f59bbf2e4200912498b, 0x46cd5901f82298f50f8f37e0, 0xda394bd5a6faa8c6f98d178d, 0x9489f43f270c6bd97a56f14e, 0xba345afd6fa08c5b66103257, 0x172117c1bd860df49c7f68f0, 0x693100c5b36bc3d8210615b0, 0x2c8d3dcfb83ac31efe164c, 0x4400815, 0x0, 0x0, 0x6505fa9f69a8798873dcbca3, 0x540522659d27e26b155741a5, 0xb2cbbe014d7b317df5281b60, 0x3159a1e8a255736027c15b00, 0xec172ec870f4885861fa715, 0x450108025ca4fdd95d3ea4be, 0xa7ca5bc05077bd9a6fe4f01e, 0xdeea885ab4bfc82189ac2b72, 0x9468616b7bb8b2d1eb378868, 0x56276a0966928b08971684af, 0xd16a3d10a6032348f539e2f7, 0xde3dc7466c581674d211cdfb, 0x5440706286f05e61df345166, 0x1cea89c8227619129efbe254, 0xf84c4b9dcc9de5cfdd1b745f, 0x7439a70edf670ccdb8757ce, 0x9a9d2a2044ce0c63c7749a64, 0xd575c9cb73c6f9d36bb8d1d7, 0x5a9ee0be1abbe2291846dc4b, 0xee674484c468ac3848193a80, 0xef5f5b67e32d2ec4ebb4cde5, 0x3080adc, 0x0, 0x0, 0xf6183ed40d6aeb397805b3da, 0x8ceb48f0508ff239d7bd175b, 0x9f0b273513d427b0a7d38648, 0x82b3956877f67e15e22f2b4a, 0xdbcdf5049103c9c7b7ee4bb5, 0xa4880f67b985ed22f3b7ca29, 0xccc0bac7846da5cc7c7ec380, 0x26fada19f84b75c2954ff0d5, 0x607e2a4f32863fead642e8c6, 0xd81931fe7d0a479f060e12a4, 0xdb46e7ef3efca9bef3b7728, 0xedba7c2de2c90177fc3f4840, 0x956ce80fa9fdea3dcc2a6ff3, 0x5a8e76cc6a2b0143634b7489, 0xff054f521cf0d1a934283a01, 0xbef59d14565d6ba48d073ae4, 0x650b2d52c1122a56007b90a, 0x7c76c9af9f608addb1afc04f, 0x2ba9ee990da5b1a115506e61, 0x56ffc7c840d5cb87a0d64779, 0xfdad49c955958334a75424e1, 0x100788, 0x0, 0x0, 0x40f427e784fe2b4a9eaef4af, 0x2f0795ae8e0911ef1df50341, 0x90df7762e822199b4e8f9dd8, 0x3a0b913a4eaf581bb478be28, 0x207103d33ce1e0b8493a8cd4, 0x8656a65ce57b0b8a4dd5622, 0x7f95bcb4d175408d176f192c, 0x3e7c781e0afc6ece0cd3fc3f, 0x399d9626316a4a703009d68a, 0xa406d4c272643c0e932ccfb, 0xbd7c66e6c97d1c5db9fa9355, 0x8eed69ec5068d7cb399c4ffa, 0x79fabd0f06e0921e6cb79d77, 0x8cbbba1bc258146680adf88d, 0x16fcaf5768364d146bb355ad, 0x225fe736e47e97ed2f956d95, 0x70d015c5a2328fda9308b98, 0x673d4d765ad984ed15b17de0, 0x1e5a5778fc5a30396b36b904, 0xe49771bd3a3478f09574b1ea, 0x35c5a852b2225574a7952926, 0x353afb31, 0x0, 0x0, 0xba3c64ce6140f14718d0875d, 0xaea551a60be2bda2d6bf6db3, 0xe8a0282d2347aeeb81e33e89, 0xb8c1ab53b1e38117bc833379, 0xf028317bd0b9336aac1c8012, 0x3c856cf187839e9d21dfc4c3, 0x880a5e18613966ff8cdd7cd8, 0x79a454208ea16d30679cf088, 0xf3ef14e5fbbed7488440d7ea, 0x418e97737d58665881d8462, 0xf4fc8d9df7440e8998f035ce, 0xdb8e672415f226facf42e72d, 0xe589c0b91168de2021f13fa8, 0xa3085040132adf68a6e77dad, 0x94431ba64e4a6e6b83409212, 0x26e5b535fb3ed44b9a28e8b5, 0x52ce3fd32264c1d47149801e, 0x9c8ef28bf945bc77a227b011, 0xabb4c1b5e2a27b69704cac21, 0xcf74f58df7e45d4826769eea, 0xb2159f7de25a0c030219cee2, 0x134e7fac, 0x0, 0x0, 0xebd8d90c934d17dd720426a4, 0x33bea95aa8ad5797da6c4efc, 0x7fac880279bd173527763ac2, 0xd909e429bd1b54225afb9391, 0xcd2c7929287c08f6773cc15b, 0x3dcde19b61dd92d44568e30c, 0xc4fe323e9fcabf11e0fef9f9, 0x2c768c0140cad8de1b3f8295, 0x5ec06f9a55af974795824dd4, 0x71249dd9d21a50f8a5dbc25, 0x9c236dd1615cc0a9f1cfed04, 0xba5a73986d84f4435169a34a, 0xa02b96c267abf2aa37dde261, 0xc2e354265ebf226db4ead96b, 0xe5ce9a686d3e5e30e5e7d927, 0xaa9aa8ff79b86b3c71463e0f, 0xc7573536e36cb43693dbd891, 0x23b6e4c59c0de1ac968462d9, 0xb20bf031108b4e72afefe016, 0x21e962fb9134282b48547ad, 0xa710aa758ef9c12b377d9d41, 0x66af5f92, 0x0, 0x0, 0xfcbe8e8bc2857c63648e74c7, 0x3c387f8020a8e593e0b552fc, 0x8ad201a4b3f0ad06ca1cad3b, 0x89172fbe0f87df535688ccce, 0xa60fd06f89622f8e0ab0e81f, 0x9d95dfbbdbfb83d920f26406, 0x3100ae331c6bcdbd5bab2863, 0x1cd23a1e15830352e125d568, 0x6d486ad849053b6f55603009, 0x119e3472ed62abc0075a2f7c, 0x66cc98c72d2681a98920289f, 0xd6eb1f2dc51f8afa59605173, 0x6c3fa021ab66060a374d7ea0, 0x723138898370b39a75ee7b1a, 0xe92d868e3a8be03af9568450, 0xf2f5f837b5321258e6bc92be, 0x27361dd77e44ebee906a0ebd, 0x7003f43a6806ccd3b189ba18, 0x97b5b27be13f5b8425e2472, 0x855e2bd2e42c6b36bb09545b, 0x7aeebee267ae270f26abcff0, 0x47d88976, 0x0, 0x0, 0x8b00c396084b4115f3b0969, 0xfc60246f4f9cfb7e951de468, 0x8022a8e11b4f620d48a3ae49, 0xd273b3ebe223884b92885a5f, 0x5f57fa057af4248d7576fa82, 0x5e57e11d3c9f89b7cc0e4431, 0xbc5bcef6f56876529e294838, 0x32c32a62b1db35b064a7a2da, 0x35bd10f3388759eb1c787e1d, 0x63c601309b69160147d3db35, 0xb1f8bdc3cb3cfd5528610a71, 0xcf31a9f03bdfed10e2e83e2d, 0xa80331587c59ced241357ea0, 0x54ba8bd269e3759998fb3358, 0xc67a073c9bfd12d1c69480cd, 0x6990cb91da39aacae8f6ce2d, 0x3073b77341d7f8914f23e232, 0x39fb609d816e019cc062f795, 0x6c58563224905c46dfc15b2e, 0x1fa29a5d77347775bad7e2d, 0x35100e5348a3d6577246b271, 0x1cd09ea0, 0x0, 0x0, 0x254f1d592f204e7e1117be57, 0x637fe9b28ec4e1f1fdb5fab3, 0xfde99837ed06ee649f6a5eb9, 0xba50e700e7ce0dd5d699c0ff, 0xb89b6c7dbb34bf4c0741c2e8, 0x2c77cbafe161b05a3f5ccf95, 0xc147dafe9d4dd839dc184d0d, 0x78ca47ed2f48eabc1b8afe82, 0x368de7c0d41674796d946bf9, 0x88a0432c9a758fd891670603, 0xb356dffba421f23219149c12, 0xc0df0de9addab73f0c677b23, 0x87fb6390c845a00a2b8c2549, 0x9b188ebfb7e3b513d5ea61d3, 0x7733b7d80a0c1f1fb3b87794, 0x308c820f6a5ab36f0492ce8b, 0x5be8d42b69166421dda3b512, 0xd55839cff5548d24ad1cace1, 0xb3cd437bd0293cff21b2402a, 0x516f98df61b6536f450f3a71, 0xf3eec531c8051639aeb8eb9b, 0x5a84fc9, 0x0, 0x0, 0x3693b7dcdad0fb1d8dae21da, 0xaa2d5a7fee71d0e906cab278, 0x5261e8b980d9f82cf85a741e, 0x805979217bb90514988dc3a1, 0x3c6a195de3e6163393f551c8, 0x25a79dcd01f7db4a73a32bdc, 0xa7176752a77cd24ee908f424, 0x4b7dd5151993ff88a4c03c25, 0x5dcf4916e368e17734f83d70, 0x2e5f1a6e9dde29cbc71f3d81, 0xf3552a7a1a4bd98489ccd41, 0x9ef5fdc24b5f5aaf500cf09f, 0xcae76c7fc41ae096aab9df71, 0x579928c3ee25c5800351522c, 0xd5e2ee4cf7c598422d6ae639, 0xd5508e83d4ad6c99e73208d7, 0x7523da007c5afd2a33842db4, 0xb293a4cb6cfef6673c866725, 0x8b23e76640f41d8d279e3da1, 0xb6493b8f9d86cd0c7a64ca1e, 0x6bf55177b0690d6f60230935, 0x8d7f18f0, 0x0, 0x0, 0xcf9b94648da0dc88d439cb42, 0xb19c1b4ed7e72d465dc45fc3, 0xe22642c00a0c25f6a008c710, 0x6dbbd01b909f016773fb145f, 0xef242bc362f4d1468c82e39, 0xe34317b99d8a82bea65e106b, 0xbc454454e26d6db44e7963ed, 0xedecd51a67f3162e0c834c5e, 0xdc830b6c09e84e9eae0a9ca7, 0xbad8f2a473274a65401c1dd5, 0x992e8052530e7b5c61f9a3d5, 0xd5315b554e0bcb21a5ace36, 0x6b83a662e5b7114044086c25, 0xff316e31ab82abcec0cc162b, 0x8c98f344a4995dbd05e66a77, 0xe81a043b3a0e65a2659c0f30, 0xb36df7f95fd54501774f350b, 0xd5e3f5af9878cda0a39a3de5, 0xe6056818952b06acb4c81ed4, 0xe54abb01d005ca29cf99a131, 0xd209bc96061f13ab6005f749, 0x886b8d88, 0x0, 0x0, 0xeb52f6df556abbdd63bf5e22, 0xaed60e75dae57df80b34ec39, 0x70fcd3e27df287e5753b20d7, 0x128b5971e45761158b8f3dcf, 0x16bb42b3873e00053132b0c4, 0x8b0245e9a0219afeafd79a79, 0xdb9e91446865bc1fc657888a, 0x25a871a4d2ab4269bbea7ac9, 0x3ddca061ceff660108ef52d4, 0xa7e61c5901838a28c34d99cd, 0x7544f5dbb3defa0163d7f17c, 0xca241d14cc49fae4a772b7f5, 0xbe29d28849a5e324aee3408c, 0x836767d43077526f48faa2a8, 0x8cd32c65af954bc68d0e493f, 0x7892b889609b1f9e6f0d79c2, 0x278ce3abbff2f5263777664b, 0x81cd003b95994a5b17a7a683, 0x9c86115d81e0632d5fc3c81a, 0x997516ed4cc19a8a483d09d3, 0x1e179242d56cd19e4f7aa60c, 0x451e7279, 0x0, 0x0, 0x1fe5390dd58ec47ccaca6165, 0xee0376fd38d66576b38407b, 0xcf065c5ede16b9078ed8b950, 0xe401e1dba006c46264e08784, 0x52c0f066ccb0e51a2836dada, 0x964e301923a41c67dc6b472c, 0x3031e417f447570565032bc9, 0x50c821279b44dc3b5b074a72, 0xcd5a7aedb746388d9305d94b, 0xe93818f4b95a48f01baaa16e, 0x9d558ad11e2bea56a6739a4a, 0x8f98e3a980cc27f5514501f9, 0x1b5009bfd2a8cf3f3dbb7737, 0x6ebe9ac5b62d601eab9605fc, 0xba78365c99e325914055aca7, 0x62889d4b8f17ddedd15ad267, 0x1fee7dce2fad2700f8aa8817, 0x5b2a16de45abfaa3ca0f804d, 0x348b77de9a9e9fdd39057b1b, 0x2d4143c1cd9b408801ac0932, 0xa3cf55f17eb11d4fb32b9426, 0x208d6195, 0x0, 0x0, 0xfc49e873313de2978312887f, 0x5fbe773faa24320f70e6ea6b, 0x4256b86e9528473bdd9e6ace, 0xd74f172dbdba542bc9ecda9, 0x96924c9de06632dece3702de, 0x69358eb612656ca3198158e2, 0x6d79a01613661779c78e0032, 0x4e3bad2411014a48f1259b42, 0xd8871b2ea785f687de8c7952, 0x4be6a0fccf274cf898f145fe, 0x17c2c3616f78801493116b78, 0x940f2f0ed4e8f04ff92ffadd, 0x9b5d10dd4a3522d51f93be51, 0x1556a11712de4fac4f6f42a6, 0x895f21afa42c4af48861ce0f, 0x226800704f911bf97dfd3f55, 0xe51750defa8db7ae997056cc, 0xe037899ffa2f92560d0555c1, 0xd2e12a9746629d0f3e5d14bf, 0xa960a9ca8b8dd7220eb506db, 0x66bbd4ab5e553d07fecab1bc, 0x3307cd8a, 0x0, 0x0, 0x67f2457b8c831d56a9929a0d, 0x96e370441e52fae5bbcae56d, 0xa93ed687236fc53206e0419a, 0x7fe79b87578b0d38b0d1c317, 0xf48d8398df15059bb792f949, 0x2514308d75b0450ea06b07c6, 0xe85e7668282416c14df6e0b7, 0x703fae82d76ba4de92480e44, 0xd86b0d011d4e5e495c06d796, 0xb329a5d9c0778130705ba25f, 0xbe8a7bef6b49924124bf136d, 0x719510f51704a78a4b63090f, 0x3be3feb5ceb690d534e57107, 0xd0a2d35b72ad6978b8bde8b3, 0x936079a39d638c5c33d6eadd, 0xe177aa16d66b4356a9f9bce2, 0x9a626604f2f0d249417e0ea9, 0x6be7c6bd4f517bd69fece5bf, 0x923735990296cdfb6fae17d6, 0xc1b535aee17900ed24102daa, 0xf2431179faa78ff59fd6503a, 0x202114b4, 0x0, 0x0, 0xa9dc684ea7a072c583378bdc, 0x234eebfb13b9f83dbedc9689, 0x46f68cddc2dbc0748d995ad3, 0x4338acea2099179babc1f7ab, 0xcc0fca21384a6773f735d8eb, 0x5cc17f9d3c9d8636229c1adf, 0x5af4b70e86e1d9ebcec76328, 0x73474b28f23261bbc278997f, 0x60b65df1d9c6c2025877cbc7, 0xe5f371b392daa99d60dc68f5, 0x6d459b8018d80c189e4fb2db, 0x3b782f2fb21f91af6f955e29, 0xe58e194ead8b059afb9cc6e5, 0x714a92db56aaef13c5eb239d, 0xd17462b734aae256a7c053bb, 0xc7364388960d6831d60e8379, 0xa6e642a3822390a909108133, 0xbb3455c47c1d625f04473e54, 0x473a8914fd186b8c2f53bd98, 0x56cb778707e253d5bcd9c897, 0xb212545df5bc302598e61647, 0x879e816f, 0x0, 0x0, ] .span(); let public_key = Serde::::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let rsa_with_hints = Serde::< RSA2048SignatureWithHint, >::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_rsa2048_signature_assuming_encoded_message( @rsa_with_hints, @public_key, ); assert!(is_valid); } #[test] fn test_rsa2048_tampered_message_seed_0() { let mut rsa_sig_with_hints_serialized = array![ 0x766ad7a96b6a74dcb0d4ee21, 0x3c31169ffb4c539d20a19c30, 0x4813ed39e65994f370938d52, 0x19c0d08706b4597638cc3e30, 0xc7e80539ead20295baaa808a, 0x299992cbadae99aeb97422ae, 0xb226c9a7b454cef99bca662d, 0xbf70d4a08cf48ed827e59567, 0x7f746d2d77af83b2122fa87b, 0x9aa92b2128d9725d8656dd96, 0x3b526db14be8de881d9d16f0, 0x60ef9dd9b7346128d4904a2d, 0xc956b02d42c83dcd03152b6a, 0x417242ec1b72b9d2c28b3a8e, 0x31094b84fe9156b6d0462fe, 0xaee058ad4254ba267bfa369f, 0x236079af55b0b25854deb6d, 0x1e371829465e97bdc783fbc4, 0x308ac6dcf29aabb20d05c85e, 0x250ca4cbef9a5ded24279a60, 0xc2667b7be6ec40e1236d59df, 0x92c2ffdd, 0x0, 0x0, 0xccd4d72e904d8d17594ab5f7, 0x39711006ced57a24b0b3ddc, 0x2ccfe85722998e88ce696503, 0xbb4d033f6bc441dd1a08890f, 0x126b5e07fd274f3c18f28ad6, 0x6d1e293c0af656e2d1d56a47, 0x311e4ff1497cc51e1df029af, 0x9b5c4fd21b926c416bee361d, 0xc2763b9d1cc4af2edb1ed69b, 0x38c872d56da6fbe02f39f2b1, 0xbf55fbbf55d4cc74e2b1257b, 0xe6128d2cb2c59820b674fdd2, 0xa13fdbe9e48e2bf32e68a32f, 0xa91b93a068472e0dda54fb2d, 0xddb762befe90bd234be8b786, 0x8de87eebcd0e03fcc11febb2, 0x58c09101bebc3bd1c58c0616, 0x7ebe6e4cc8aee40772b501ec, 0x8e478ff6dd4c4a4422e8f182, 0x10d134c96c1d30ec1c29823c, 0x5dda7fcba4eb273a149eb833, 0x5c6704f1, 0x0, 0x0, 0xa9dc684ea7a072c583378bdd, 0x234eebfb13b9f83dbedc9689, 0x46f68cddc2dbc0748d995ad3, 0x4338acea2099179babc1f7ab, 0xcc0fca21384a6773f735d8eb, 0x5cc17f9d3c9d8636229c1adf, 0x5af4b70e86e1d9ebcec76328, 0x73474b28f23261bbc278997f, 0x60b65df1d9c6c2025877cbc7, 0xe5f371b392daa99d60dc68f5, 0x6d459b8018d80c189e4fb2db, 0x3b782f2fb21f91af6f955e29, 0xe58e194ead8b059afb9cc6e5, 0x714a92db56aaef13c5eb239d, 0xd17462b734aae256a7c053bb, 0xc7364388960d6831d60e8379, 0xa6e642a3822390a909108133, 0xbb3455c47c1d625f04473e54, 0x473a8914fd186b8c2f53bd98, 0x56cb778707e253d5bcd9c897, 0xb212545df5bc302598e61647, 0x879e816f, 0x0, 0x0, 0xf11082a78e2349176eefb845, 0xa2c474b18dd8215e6ce79a2, 0xaf8397d226331e6fe0287b82, 0x2021be0dbe82e1d87ff0464a, 0xf9f671cbb480c9ad30e96b04, 0xbf0341d821907bf2d1714934, 0xc4133dd8b0fbec701c6bce5b, 0xab8a9912700daed15fb14efb, 0x6408b84f7f8cfcc466adb647, 0xed064d750384670cdc484c57, 0x10d17bd4d1d8b673945244cf, 0x3661fd2009f806b98f962802, 0x3ded8d1c80a858c317f106ea, 0x69490720cdaa41dd567bfd75, 0xa2e9da91a7303beb4b22e507, 0x63d845332aea5d5d79157f21, 0x1ba1ef9812c965e541b8c9e7, 0xadd80c35198e137ffef51c0c, 0xec2ddf921bd92a5be54e75d5, 0x9f260f9358d8c772581bc666, 0x49cb9677cbc1c13c5b5a6b46, 0x3a2d6680, 0x0, 0x0, 0x61ae0775f0594f0d3ec84d6c, 0xcdf82c4368c89d619ad6c4ec, 0x16634f8f537349438fbf800f, 0x18bb5fd323098da014d9e4e9, 0x3de3d2b1c1ce83174249eac3, 0xe04e43c5856d447e64fb2c49, 0x8315c17c23405e47aa9dfdaa, 0xdd3e2d06e6755e5877139c96, 0x1de63f44a100a924034140b4, 0xd1c1be2c6c01be2cb6165113, 0xb3f8ef010376c8d557dd3a74, 0x5330b322e6537546d099577, 0x50feacf7ef56d00d299880d8, 0xde8af60590cff5c21c9021e0, 0xc719c781d43d99eac9c9a446, 0xa03f627aea3b9c54fe08cb8b, 0x2fe3ddee1358fa008dcfbd75, 0x183d0552096beeda805632ba, 0xead565b3a9fd13f32d94abbf, 0x8aa3b518bf3670dc8a44dce5, 0x7ce23145e486815f1397916a, 0x836001e1, 0x0, 0x0, 0xa50443039d3dd37156158183, 0x383a7d1fe53348285bdd2f37, 0x3e634aab243fc03bdd9548c9, 0xf63f0748d8ca9bc50034c997, 0x5cc782e51c7c576b5cb62457, 0x767abde2f4d3fc3d27c8dc12, 0xc55ace8470f37a3727c4cdb6, 0xa970e7780d86111b86e8184c, 0x3b930d12e10453014f602550, 0xe86920884a33c79d586e5b08, 0xe1c35a842d9968776b9a5756, 0x2d87248120b10947502a05c9, 0xce2325942bb6cfc89ac9a16d, 0x3023e567a6aeaa0e56e67c5f, 0x931367e2e28f64cf5e67881b, 0x5086944531c4016e1b638c8f, 0x2041352d23b8eb7553c90821, 0x45e38d7e09438b118b8c8797, 0xd15618e1fa2be214b20a2b62, 0x613c5bc02562fac980d54ff6, 0x3547852fb77b7ad22f7a3809, 0x7599fbf7, 0x0, 0x0, 0x25772373859fcc1ff880a9ad, 0xb3d1a77be83203586116cc33, 0x249ddde6a735af8d54f76e5d, 0x126236052ece65c16a4f8147, 0xc14108cea2b89f8bd216819b, 0x31e5b9cd08617bfbebc340ec, 0xc533488c6e32cee86b51bb65, 0x3427cbf5c389545877454003, 0x5f471a99ed38c12709340c97, 0x782d84eec1f578cf6332df12, 0xcff0e44dab2705c3df8ed43b, 0x828932cdc82c07604ed8aa16, 0x3f3c04ef18aff4f15ecac8a6, 0xb00f3fd36e39d0b3ba293f0e, 0x98e9053c9079b132080e1433, 0x8ae039670f1f588d49b0ead0, 0x84e04057fe631a9950e3741e, 0xf0975e0d1d87294c0779e4a5, 0x9af5116c3122c9454c33abf9, 0xfc8e70dd2f1882948bfaa669, 0xc4110d0bb3e3fe5bd4aa3849, 0x63ed1112, 0x0, 0x0, 0xdde6339489f82be2a548914, 0xa6129a46e7fa08cf79fe8795, 0x4ecf9c35860837ca5cc9964c, 0xce764f24f9a04630792a3962, 0xb037bf199470e6de572c42bd, 0x956ff3546d57ee943af1668f, 0x9677e96ffddc8fb4befbe60b, 0xcc50d5f30da8488eda5e2c68, 0x5c1aee3bac6f9bfcb475b589, 0x417cbaff0027179506246182, 0x4884fa40151152ccfb8f2361, 0x5fad486584738fb532be17dd, 0xdafafed3e1c4cd027bba63c0, 0x7f443066f06aa1556dd9abb5, 0x4b627b9936231df8ae4b77a0, 0x84fb2d5a4f24cfe981dbfad0, 0xb876a978d779736ade0abc08, 0x5e6ecdc675a0b2c27e3a310, 0x68b895aa08ce6e80cc24b677, 0x933d588163cd237a200f2ec6, 0xdf366116dbf8e636789c8917, 0x440972fb, 0x0, 0x0, 0x4c43909d3df7aa01fc8f9b55, 0x573f92547eed486eaecf4fc4, 0x706df3b0fa507cf78864078e, 0x72beedac7c3f62c50da7858, 0x7b01b47908dafa52fa8f40ca, 0x42c7fe0d226b199ff3a8b27a, 0x2cd291e0f2b7259731ca1103, 0x9936fd0d86cce4683dbd3593, 0x6fa4eae97809921e2e8f1c29, 0x61bcf43cb948de83f418604c, 0x4be8bf5f7aa4f97164b57e28, 0xb2cac9559ad2a26568d798c7, 0xc9e3f5b00702b0a067b7ce6d, 0x42738b954118f7fc09daf06e, 0x936703c37dcc919aeabbf3c2, 0x8234f4da6b15efc32f91b03a, 0x51016906f1aba3d0051cc8d8, 0x29c616b65059e5257568c86a, 0x9e7959ef4cbfa69866c3ae8b, 0xad55fa216ca080ce5f33515a, 0x4010f7d945e56f9faaaeed47, 0x59c35b15, 0x0, 0x0, 0xbd7ab4dca711f0d929017d0a, 0xf6e1b23766720a08df2e064b, 0xf743a47b9ef21525e4a3851f, 0x2e9e91630551f14e278d959f, 0x450e114a827f3fe74024242e, 0x768f0b12f0fca0e28cad2d5, 0x6f7551b524fa35f7afb69fb0, 0x503e453c615811e1bce63aea, 0x89d3c0aa219ca344b32b4a69, 0x9847c02179a77916a0aad3d0, 0x363a2da6bb7cc920afd971f9, 0x105756bde27aa2e4a1654eed, 0x782316203cc0dd1bde9739bb, 0x729e9df0a4384508f628312a, 0x7c58ad79ca4ff22633b6c393, 0xc25e962083bee700b96ce224, 0x4b99b07dcff3f811dd6d63e2, 0xa07af35bb0745dd4de9d5dc1, 0x2362f99b653a6d200acdcf4c, 0x7ed1f7a32c6633f50a1a6d1f, 0xc67831f8385e2ebf6c0e15ce, 0x36e6be8d, 0x0, 0x0, 0xaf2e85f517483d20277d9fef, 0xa6c8e9ef245c3cfbe92f5583, 0xae0e652d9bfd555164f5dde9, 0xac463ea67f143f6b90484d24, 0x292d0d6d7a0f61537e241903, 0x1dbd26b03b4c300939500257, 0x38f5405d2d4eb07f94eb4174, 0xebed3bea8633f2024a17fa8b, 0xd8029bd940f48c17be9061cd, 0xdb881dc57fa541995190cffb, 0x28dbb1531a44706a35f17fe9, 0x47ad149d189b70df6962e01d, 0xe56b6feae22bea7827cf0aef, 0xca565c0873f303db366b4122, 0x18739e8523299686923d88f7, 0xe4c0c42cd30512c887141263, 0xd6664b534d1f54775647116d, 0xccdd2182bb113823e3c8cae, 0x5351a577848f05aa228c7e, 0x12209ca46ab63bc8985be0c5, 0xe39f22696539616774a946cf, 0x857b13e2, 0x0, 0x0, 0xb4b75cf7190e9fb150c78ed, 0xebb37162b1d1a0cc8ed4e70, 0x2e90eaa6bca468a75954af94, 0x921837f27c919b98ea12bd7a, 0x938d23cf452c57690e41acd9, 0xeaeb0bbd339278e588377648, 0xea059eb1bcb1327413df220f, 0xf3d015ee9a83e173bbfe05db, 0x6eca8ea01474071813e0575f, 0x478da59c5392a7c4859552b0, 0xd53538319b99b57602230736, 0xdfa5ccd9411adccaae6481fe, 0xfbb3284f1a46aab145b14e97, 0x54ac3cb4084ce72b420b1440, 0xfc0030ee568632dc99eb3e3e, 0x67838dcc7ffababee905e4cb, 0x1dccbde1880631c960965f05, 0xd92ae551a3b09f2b1914b2c9, 0xb92dfcad76ba37636909b5ba, 0x6d02704ea436775eb9eba0a1, 0x1239f0c36942aa41d0fdb583, 0x7966d36b, 0x0, 0x0, 0x2f0370e0de67e0e0204d494, 0x41e6a7ffb185c93fc567919f, 0x33b32ddef77fc52a3e1b5a8c, 0xff9cdac2a8555b74120dd0a6, 0x374fe9884c8e839da4c5b64e, 0x765771b2daeb10f3e43d714e, 0x6e482c50677c27f548576bb4, 0x1ba9ee7076cc48c2028e07d0, 0x2d544810350024a0c1b4d179, 0xb8f7bf71b996e3c125d6df41, 0xe1527c84c71956afc34f6845, 0x8c339e263df547b486a303c1, 0xd671bf4705270e96c2dcecf6, 0x8e2ab787b0d997e2c435288d, 0x5aa9c5acfa39c50a3921e905, 0x99a4f9d3b39672a4ef023e78, 0x299824406248082c032f9e88, 0x5cce13392a9c02c95f51a627, 0x8ad6ee4d053df429a6f03f9d, 0xdcf0e7cafb7fd7f3c7f87d80, 0x9aebea38b3e33b2b482c8a04, 0x8bf92cbb, 0x0, 0x0, 0x9f7d6f589e82e9756cb90734, 0x1efc494737c83d8d1e5555e6, 0xdc14db376bb2abe4ad6c5145, 0x6350095e5153267e0f7cccd6, 0x2f11b257bb2b86998a1c4fe1, 0x1b0f01fffa4cb3d342c3331d, 0x45f2b93d6b87e6c14c8bdb25, 0xe0443287f9111fd56efb078b, 0x1560ccb1b67cd638d2ab63d1, 0x48598e67a7c87a38e45761f0, 0x42e95914d4ce2835d31ffdff, 0x39b5c97ac03b49dc9f8f6118, 0x1264a7647a6a15794f811a46, 0x83c3d06dbfb2b86373c10c27, 0x930c355b5fa314b6b1620102, 0x22692e942620240d77d0c6a9, 0x7b8897708cd33be40719d6e3, 0x7df5c691973b2ebe3fad0373, 0x6703a5c064a846c40c588c44, 0x2ae4b8ea5e745d2f0c269bbe, 0xfe723d71902007fbc8a70662, 0x857fbb68, 0x0, 0x0, 0xa5af2060ca06c184e5892fdc, 0xddc0a0a99021868d6da0893d, 0x24b56567184dc2acbcf5c73e, 0x160ef95f8c1f209f220add52, 0x2534d4dbc6d040d83fdb27e, 0xe9975a62f1ec391cc7426ae, 0x491ed56f50664e259b8ebad8, 0x7fd81ec116d12e3df8c35dc6, 0x2a894fd7972edf7865cc64f0, 0xcc22be61d6c9dcd87bbd11f7, 0xfd08aef895fe6b35568a1478, 0xf859f2778a321a7653ef2225, 0xf76ab371c23da4e6581b30ba, 0xeb87317e55dee41753d04513, 0x65f710857dc2c2200f569276, 0xda8ec2912b42abfb71ff2aa0, 0xef0a6b1ecc8548494c574227, 0x91b537e4d720dfa8b9997cd2, 0x7c31d1185eca8ca5c6625a84, 0xb78354ea69a8e98692057c26, 0x8d1da54563cc19a1f35e8c2f, 0x639a0b16, 0x0, 0x0, 0xa875570c9d0284f771cce145, 0x591c0201ab939b39b4e90b8e, 0x637eda8b6d46c7f37c41ba1a, 0x4108ec753bdbd2b8355b71da, 0x3e09320343a531c8f224f413, 0x1b9bf7cf3daf215cb444a32d, 0x41ce25a20127e9fb2c094c62, 0xace162be846660ab7dbdf99c, 0x2b033b29ca496f3fd509fddb, 0x9d4c1e14a408995d3f7c5bbb, 0xa66dc01cfd2bd5f969dd2e4f, 0x627f37970e930fadd339ee01, 0xc9aff619c84d5b4d8397cab8, 0xae250d0978d29cc49ab124fa, 0x2a5d7e131b5b9e30a46c41eb, 0xd55d087936c566f14dde0f46, 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.span(); let public_key = Serde::::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let rsa_with_hints = Serde::< RSA2048SignatureWithHint, >::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_rsa2048_signature_assuming_encoded_message( @rsa_with_hints, @public_key, ); assert!(!is_valid); } #[test] fn test_rsa2048_tampered_limb_seed_0() { let mut rsa_sig_with_hints_serialized = array![ 0x766ad7a96b6a74dcb0d4ee21, 0x3c31169ffb4c539d20a19c30, 0x4813ed39e65994f370938d52, 0x19c0d08706b4597638cc3e30, 0xc7e80539ead20295baaa808a, 0x299992cbadae99aeb97422ae, 0xb226c9a7b454cef99bca662d, 0xbf70d4a08cf48ed827e59567, 0x7f746d2d77af83b2122fa87b, 0x9aa92b2128d9725d8656dd96, 0x3b526db14be8de881d9d16f0, 0x60ef9dd9b7346128d4904a2d, 0xc956b02d42c83dcd03152b6a, 0x417242ec1b72b9d2c28b3a8e, 0x31094b84fe9156b6d0462fe, 0xaee058ad4254ba267bfa369f, 0x236079af55b0b25854deb6d, 0x1e371829465e97bdc783fbc4, 0x308ac6dcf29aabb20d05c85e, 0x250ca4cbef9a5ded24279a60, 0xc2667b7be6ec40e1236d59df, 0x92c2ffdd, 0x0, 0x0, 0xccd4d72e904d8d17594ab5f7, 0x39711006ced57a24b0b3ddc, 0x2ccfe85722998e88ce696503, 0xbb4d033f6bc441dd1a08890f, 0x126b5e07fd274f3c18f28ad6, 0x6d1e293c0af656e2d1d56a47, 0x311e4ff1497cc51e1df029af, 0x9b5c4fd21b926c416bee361d, 0xc2763b9d1cc4af2edb1ed69b, 0x38c872d56da6fbe02f39f2b1, 0xbf55fbbf55d4cc74e2b1257b, 0xe6128d2cb2c59820b674fdd2, 0xa13fdbe9e48e2bf32e68a32f, 0xa91b93a068472e0dda54fb2d, 0xddb762befe90bd234be8b786, 0x8de87eebcd0e03fcc11febb2, 0x58c09101bebc3bd1c58c0616, 0x7ebe6e4cc8aee40772b501ec, 0x8e478ff6dd4c4a4422e8f182, 0x10d134c96c1d30ec1c29823c, 0x5dda7fcba4eb273a149eb833, 0x5c6704f1, 0x0, 0x0, 0xa9dc684ea7a072c583378bdc, 0x234eebfb13b9f83dbedc9689, 0x46f68cddc2dbc0748d995ad3, 0x4338acea2099179babc1f7ab, 0xcc0fca21384a6773f735d8eb, 0x5cc17f9d3c9d8636229c1adf, 0x5af4b70e86e1d9ebcec76328, 0x73474b28f23261bbc278997f, 0x60b65df1d9c6c2025877cbc7, 0xe5f371b392daa99d60dc68f5, 0x6d459b8018d80c189e4fb2db, 0x3b782f2fb21f91af6f955e29, 0xe58e194ead8b059afb9cc6e5, 0x714a92db56aaef13c5eb239d, 0xd17462b734aae256a7c053bb, 0xc7364388960d6831d60e8379, 0xa6e642a3822390a909108133, 0xbb3455c47c1d625f04473e54, 0x473a8914fd186b8c2f53bd98, 0x56cb778707e253d5bcd9c897, 0xb212545df5bc302598e61647, 0x879e816f, 0x0, 0x0, 0xf11082a78e2349176eefb845, 0xa2c474b18dd8215e6ce79a3, 0xaf8397d226331e6fe0287b82, 0x2021be0dbe82e1d87ff0464a, 0xf9f671cbb480c9ad30e96b04, 0xbf0341d821907bf2d1714934, 0xc4133dd8b0fbec701c6bce5b, 0xab8a9912700daed15fb14efb, 0x6408b84f7f8cfcc466adb647, 0xed064d750384670cdc484c57, 0x10d17bd4d1d8b673945244cf, 0x3661fd2009f806b98f962802, 0x3ded8d1c80a858c317f106ea, 0x69490720cdaa41dd567bfd75, 0xa2e9da91a7303beb4b22e507, 0x63d845332aea5d5d79157f21, 0x1ba1ef9812c965e541b8c9e7, 0xadd80c35198e137ffef51c0c, 0xec2ddf921bd92a5be54e75d5, 0x9f260f9358d8c772581bc666, 0x49cb9677cbc1c13c5b5a6b46, 0x3a2d6680, 0x0, 0x0, 0x61ae0775f0594f0d3ec84d6c, 0xcdf82c4368c89d619ad6c4ec, 0x16634f8f537349438fbf800f, 0x18bb5fd323098da014d9e4e9, 0x3de3d2b1c1ce83174249eac3, 0xe04e43c5856d447e64fb2c49, 0x8315c17c23405e47aa9dfdaa, 0xdd3e2d06e6755e5877139c96, 0x1de63f44a100a924034140b4, 0xd1c1be2c6c01be2cb6165113, 0xb3f8ef010376c8d557dd3a74, 0x5330b322e6537546d099577, 0x50feacf7ef56d00d299880d8, 0xde8af60590cff5c21c9021e0, 0xc719c781d43d99eac9c9a446, 0xa03f627aea3b9c54fe08cb8b, 0x2fe3ddee1358fa008dcfbd75, 0x183d0552096beeda805632ba, 0xead565b3a9fd13f32d94abbf, 0x8aa3b518bf3670dc8a44dce5, 0x7ce23145e486815f1397916a, 0x836001e1, 0x0, 0x0, 0xa50443039d3dd37156158183, 0x383a7d1fe53348285bdd2f37, 0x3e634aab243fc03bdd9548c9, 0xf63f0748d8ca9bc50034c997, 0x5cc782e51c7c576b5cb62457, 0x767abde2f4d3fc3d27c8dc12, 0xc55ace8470f37a3727c4cdb6, 0xa970e7780d86111b86e8184c, 0x3b930d12e10453014f602550, 0xe86920884a33c79d586e5b08, 0xe1c35a842d9968776b9a5756, 0x2d87248120b10947502a05c9, 0xce2325942bb6cfc89ac9a16d, 0x3023e567a6aeaa0e56e67c5f, 0x931367e2e28f64cf5e67881b, 0x5086944531c4016e1b638c8f, 0x2041352d23b8eb7553c90821, 0x45e38d7e09438b118b8c8797, 0xd15618e1fa2be214b20a2b62, 0x613c5bc02562fac980d54ff6, 0x3547852fb77b7ad22f7a3809, 0x7599fbf7, 0x0, 0x0, 0x25772373859fcc1ff880a9ad, 0xb3d1a77be83203586116cc33, 0x249ddde6a735af8d54f76e5d, 0x126236052ece65c16a4f8147, 0xc14108cea2b89f8bd216819b, 0x31e5b9cd08617bfbebc340ec, 0xc533488c6e32cee86b51bb65, 0x3427cbf5c389545877454003, 0x5f471a99ed38c12709340c97, 0x782d84eec1f578cf6332df12, 0xcff0e44dab2705c3df8ed43b, 0x828932cdc82c07604ed8aa16, 0x3f3c04ef18aff4f15ecac8a6, 0xb00f3fd36e39d0b3ba293f0e, 0x98e9053c9079b132080e1433, 0x8ae039670f1f588d49b0ead0, 0x84e04057fe631a9950e3741e, 0xf0975e0d1d87294c0779e4a5, 0x9af5116c3122c9454c33abf9, 0xfc8e70dd2f1882948bfaa669, 0xc4110d0bb3e3fe5bd4aa3849, 0x63ed1112, 0x0, 0x0, 0xdde6339489f82be2a548914, 0xa6129a46e7fa08cf79fe8795, 0x4ecf9c35860837ca5cc9964c, 0xce764f24f9a04630792a3962, 0xb037bf199470e6de572c42bd, 0x956ff3546d57ee943af1668f, 0x9677e96ffddc8fb4befbe60b, 0xcc50d5f30da8488eda5e2c68, 0x5c1aee3bac6f9bfcb475b589, 0x417cbaff0027179506246182, 0x4884fa40151152ccfb8f2361, 0x5fad486584738fb532be17dd, 0xdafafed3e1c4cd027bba63c0, 0x7f443066f06aa1556dd9abb5, 0x4b627b9936231df8ae4b77a0, 0x84fb2d5a4f24cfe981dbfad0, 0xb876a978d779736ade0abc08, 0x5e6ecdc675a0b2c27e3a310, 0x68b895aa08ce6e80cc24b677, 0x933d588163cd237a200f2ec6, 0xdf366116dbf8e636789c8917, 0x440972fb, 0x0, 0x0, 0x4c43909d3df7aa01fc8f9b55, 0x573f92547eed486eaecf4fc4, 0x706df3b0fa507cf78864078e, 0x72beedac7c3f62c50da7858, 0x7b01b47908dafa52fa8f40ca, 0x42c7fe0d226b199ff3a8b27a, 0x2cd291e0f2b7259731ca1103, 0x9936fd0d86cce4683dbd3593, 0x6fa4eae97809921e2e8f1c29, 0x61bcf43cb948de83f418604c, 0x4be8bf5f7aa4f97164b57e28, 0xb2cac9559ad2a26568d798c7, 0xc9e3f5b00702b0a067b7ce6d, 0x42738b954118f7fc09daf06e, 0x936703c37dcc919aeabbf3c2, 0x8234f4da6b15efc32f91b03a, 0x51016906f1aba3d0051cc8d8, 0x29c616b65059e5257568c86a, 0x9e7959ef4cbfa69866c3ae8b, 0xad55fa216ca080ce5f33515a, 0x4010f7d945e56f9faaaeed47, 0x59c35b15, 0x0, 0x0, 0xbd7ab4dca711f0d929017d0a, 0xf6e1b23766720a08df2e064b, 0xf743a47b9ef21525e4a3851f, 0x2e9e91630551f14e278d959f, 0x450e114a827f3fe74024242e, 0x768f0b12f0fca0e28cad2d5, 0x6f7551b524fa35f7afb69fb0, 0x503e453c615811e1bce63aea, 0x89d3c0aa219ca344b32b4a69, 0x9847c02179a77916a0aad3d0, 0x363a2da6bb7cc920afd971f9, 0x105756bde27aa2e4a1654eed, 0x782316203cc0dd1bde9739bb, 0x729e9df0a4384508f628312a, 0x7c58ad79ca4ff22633b6c393, 0xc25e962083bee700b96ce224, 0x4b99b07dcff3f811dd6d63e2, 0xa07af35bb0745dd4de9d5dc1, 0x2362f99b653a6d200acdcf4c, 0x7ed1f7a32c6633f50a1a6d1f, 0xc67831f8385e2ebf6c0e15ce, 0x36e6be8d, 0x0, 0x0, 0xaf2e85f517483d20277d9fef, 0xa6c8e9ef245c3cfbe92f5583, 0xae0e652d9bfd555164f5dde9, 0xac463ea67f143f6b90484d24, 0x292d0d6d7a0f61537e241903, 0x1dbd26b03b4c300939500257, 0x38f5405d2d4eb07f94eb4174, 0xebed3bea8633f2024a17fa8b, 0xd8029bd940f48c17be9061cd, 0xdb881dc57fa541995190cffb, 0x28dbb1531a44706a35f17fe9, 0x47ad149d189b70df6962e01d, 0xe56b6feae22bea7827cf0aef, 0xca565c0873f303db366b4122, 0x18739e8523299686923d88f7, 0xe4c0c42cd30512c887141263, 0xd6664b534d1f54775647116d, 0xccdd2182bb113823e3c8cae, 0x5351a577848f05aa228c7e, 0x12209ca46ab63bc8985be0c5, 0xe39f22696539616774a946cf, 0x857b13e2, 0x0, 0x0, 0xb4b75cf7190e9fb150c78ed, 0xebb37162b1d1a0cc8ed4e70, 0x2e90eaa6bca468a75954af94, 0x921837f27c919b98ea12bd7a, 0x938d23cf452c57690e41acd9, 0xeaeb0bbd339278e588377648, 0xea059eb1bcb1327413df220f, 0xf3d015ee9a83e173bbfe05db, 0x6eca8ea01474071813e0575f, 0x478da59c5392a7c4859552b0, 0xd53538319b99b57602230736, 0xdfa5ccd9411adccaae6481fe, 0xfbb3284f1a46aab145b14e97, 0x54ac3cb4084ce72b420b1440, 0xfc0030ee568632dc99eb3e3e, 0x67838dcc7ffababee905e4cb, 0x1dccbde1880631c960965f05, 0xd92ae551a3b09f2b1914b2c9, 0xb92dfcad76ba37636909b5ba, 0x6d02704ea436775eb9eba0a1, 0x1239f0c36942aa41d0fdb583, 0x7966d36b, 0x0, 0x0, 0x2f0370e0de67e0e0204d494, 0x41e6a7ffb185c93fc567919f, 0x33b32ddef77fc52a3e1b5a8c, 0xff9cdac2a8555b74120dd0a6, 0x374fe9884c8e839da4c5b64e, 0x765771b2daeb10f3e43d714e, 0x6e482c50677c27f548576bb4, 0x1ba9ee7076cc48c2028e07d0, 0x2d544810350024a0c1b4d179, 0xb8f7bf71b996e3c125d6df41, 0xe1527c84c71956afc34f6845, 0x8c339e263df547b486a303c1, 0xd671bf4705270e96c2dcecf6, 0x8e2ab787b0d997e2c435288d, 0x5aa9c5acfa39c50a3921e905, 0x99a4f9d3b39672a4ef023e78, 0x299824406248082c032f9e88, 0x5cce13392a9c02c95f51a627, 0x8ad6ee4d053df429a6f03f9d, 0xdcf0e7cafb7fd7f3c7f87d80, 0x9aebea38b3e33b2b482c8a04, 0x8bf92cbb, 0x0, 0x0, 0x9f7d6f589e82e9756cb90734, 0x1efc494737c83d8d1e5555e6, 0xdc14db376bb2abe4ad6c5145, 0x6350095e5153267e0f7cccd6, 0x2f11b257bb2b86998a1c4fe1, 0x1b0f01fffa4cb3d342c3331d, 0x45f2b93d6b87e6c14c8bdb25, 0xe0443287f9111fd56efb078b, 0x1560ccb1b67cd638d2ab63d1, 0x48598e67a7c87a38e45761f0, 0x42e95914d4ce2835d31ffdff, 0x39b5c97ac03b49dc9f8f6118, 0x1264a7647a6a15794f811a46, 0x83c3d06dbfb2b86373c10c27, 0x930c355b5fa314b6b1620102, 0x22692e942620240d77d0c6a9, 0x7b8897708cd33be40719d6e3, 0x7df5c691973b2ebe3fad0373, 0x6703a5c064a846c40c588c44, 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0x7fe79b87578b0d38b0d1c317, 0xf48d8398df15059bb792f949, 0x2514308d75b0450ea06b07c6, 0xe85e7668282416c14df6e0b7, 0x703fae82d76ba4de92480e44, 0xd86b0d011d4e5e495c06d796, 0xb329a5d9c0778130705ba25f, 0xbe8a7bef6b49924124bf136d, 0x719510f51704a78a4b63090f, 0x3be3feb5ceb690d534e57107, 0xd0a2d35b72ad6978b8bde8b3, 0x936079a39d638c5c33d6eadd, 0xe177aa16d66b4356a9f9bce2, 0x9a626604f2f0d249417e0ea9, 0x6be7c6bd4f517bd69fece5bf, 0x923735990296cdfb6fae17d6, 0xc1b535aee17900ed24102daa, 0xf2431179faa78ff59fd6503a, 0x202114b4, 0x0, 0x0, 0xa9dc684ea7a072c583378bdc, 0x234eebfb13b9f83dbedc9689, 0x46f68cddc2dbc0748d995ad3, 0x4338acea2099179babc1f7ab, 0xcc0fca21384a6773f735d8eb, 0x5cc17f9d3c9d8636229c1adf, 0x5af4b70e86e1d9ebcec76328, 0x73474b28f23261bbc278997f, 0x60b65df1d9c6c2025877cbc7, 0xe5f371b392daa99d60dc68f5, 0x6d459b8018d80c189e4fb2db, 0x3b782f2fb21f91af6f955e29, 0xe58e194ead8b059afb9cc6e5, 0x714a92db56aaef13c5eb239d, 0xd17462b734aae256a7c053bb, 0xc7364388960d6831d60e8379, 0xa6e642a3822390a909108133, 0xbb3455c47c1d625f04473e54, 0x473a8914fd186b8c2f53bd98, 0x56cb778707e253d5bcd9c897, 0xb212545df5bc302598e61647, 0x879e816f, 0x0, 0x0, ] .span(); let public_key = Serde::::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializePk'); let rsa_with_hints = Serde::< RSA2048SignatureWithHint, >::deserialize(ref rsa_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_rsa2048_signature_assuming_encoded_message( @rsa_with_hints, @public_key, ); assert!(!is_valid); } #[test] fn test_rsa2048_sha256_positive_seed_0() { let mut rsa_sha256_serialized = array![ 0x766ad7a96b6a74dcb0d4ee21, 0x3c31169ffb4c539d20a19c30, 0x4813ed39e65994f370938d52, 0x19c0d08706b4597638cc3e30, 0xc7e80539ead20295baaa808a, 0x299992cbadae99aeb97422ae, 0xb226c9a7b454cef99bca662d, 0xbf70d4a08cf48ed827e59567, 0x7f746d2d77af83b2122fa87b, 0x9aa92b2128d9725d8656dd96, 0x3b526db14be8de881d9d16f0, 0x60ef9dd9b7346128d4904a2d, 0xc956b02d42c83dcd03152b6a, 0x417242ec1b72b9d2c28b3a8e, 0x31094b84fe9156b6d0462fe, 0xaee058ad4254ba267bfa369f, 0x236079af55b0b25854deb6d, 0x1e371829465e97bdc783fbc4, 0x308ac6dcf29aabb20d05c85e, 0x250ca4cbef9a5ded24279a60, 0xc2667b7be6ec40e1236d59df, 0x92c2ffdd, 0x0, 0x0, 0x7f4adbc1493730e14321c70, 0x849a3d79f6c117d6751bab75, 0xdef1d75dc88702eca86351bd, 0x6aef5c1c105f674fd757aa13, 0x6124f02cbef475f1cc85d17a, 0x28803427b3731834a879e9d, 0x6cd15cf1679c35f246588d95, 0xab5a6c049666f9c22ba7d277, 0x12e89c90c000260d5490da8e, 0x25b9bbfa6c68c42f721bbe6f, 0x454e04965f51a38d060dd0fe, 0x39a9a0136648523e13fcf263, 0xce9e095c0a64109949379439, 0xd1e4d94562299517fe80da9f, 0x76f07578746961dc58bcc72b, 0x3dbe6daa287ba6415eec8541, 0x14ec3fafe6b952ef2b91f61e, 0x6d4444f0f7c59726a2fd5f33, 0x87d945fb5629131f7d73deb2, 0x980707f11d31be5557efb7c0, 0xa9c4105d7512a9dc58a59c77, 0x8f5855e2, 0x0, 0x0, 0x63daf4f0614487a857aa397, 0x4cee11531104e6d3321a6137, 0x500042073e6d1148bd2559c, 0xd0609608648016503040201, 0xffffffffffffffff00303130, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1ffff, 0x0, 0x0, 0xdba5a28d104571ccaf78c101, 0xde0117f8864376d17e88e2c9, 0x31387d8bbe690ba05421b41, 0xf673c108d61081ff7c953c48, 0xd9c9a2123806b51703d5777f, 0xe265a231a3561308fbb49d4c, 0x2ea20b01ec074f116aabcff2, 0xbd76cb54c0d3d67ad6dc8504, 0x62d001857ed90fd9c70f8fa2, 0x5212b17c0cf2b3ab8c00191e, 0x21666c4a4c652d1f4a5d52b3, 0x98a34f392a569608d8d8493c, 0xc65cd9cc53784a7c308283f7, 0x62f1d8f077885369d37c61a3, 0x9d63ecf92c1e9b9fab5ff7d7, 0xcefd87f373eac3a6af12fd2f, 0xa5f6a5771df42c025f4b0519, 0xc02c4eab0d7cfda3ab49183d, 0xdba201748a5570a32f3e6bba, 0xca3a6619ca8b60d71bdf8553, 0x34ae8309fd18234a383d2dc6, 0x8c0208b0, 0x0, 0x0, 0x9c87939cedb6fe6f3814e1df, 0xd8cd896842147c97a0490ea0, 0x213d73b8263f2f958f6663f4, 0x690232c0e0f0144d0685acac, 0xc84a114f20611bafc7bd30ee, 0x33c2ba1feafcfdb7d10cf679, 0xed8dc5f9755ef64c81b46f28, 0xa96ed77ae8898078d8bb61b7, 0x73a8776c045f5d0f7680a2bd, 0x847647dae5acf8e1b03e809, 0x463c09c16101b921ea54c4be, 0x768425bba132d55771bc78ca, 0x6e0434cfde716fd7c0ceb8b2, 0x917544da08a8b9ee878b2381, 0x9466aab26d29e7d673a164a7, 0x97cdb9d7322c80ed8d3ed134, 0x16ef46e3b67f627176ca26d8, 0xea77601794d88428cdda4f3d, 0x8664168215ef6f0f6d47c112, 0xb59493de236379caad223952, 0xc864adcd34c308060e25c4a1, 0x27880312, 0x0, 0x0, 0x1b078c215f7e30839506357a, 0xe8eeade9f2e28e0526abd509, 0x609e1db5293846d19cfd6c09, 0xda08942f4ec9833d381430bd, 0x5a39cdcfe8d9f409c73fd30c, 0xdecdb3cf727a5e776e3ce4b2, 0xf5f1c4449ed6addde3e69a97, 0xd987cbe3706bf8a2de4d75d9, 0xe1435f64a565ba527abaa25c, 0xeae4659f4f7a72a4ca8aa299, 0x457e02417fce6e0177fd025, 0x7b1d76c4aa928c4018f2687e, 0xae05806571542e12952af007, 0xfba852a24c29037dc76c8f92, 0x6486e47652c434421a6d65cc, 0x6d7626f77de17de67266bb40, 0x9cd5342b860a920e13c22b26, 0x954a74eb36626d553555d51d, 0x338c190d3c06429be7ae25e7, 0xae387d46cf8b86579ecfad40, 0x5e06aabdd4c3f2e971a0ed67, 0xaa5e56a, 0x0, 0x0, 0x3ca35f4ae5d007a57d956f87, 0xd58e44fec8e6f1e32edaae6e, 0x9036137ecb69e1ce77a61039, 0x14dd6aa90c2bdf6ce5739734, 0x10d71cbfb2aa3539aa1f56bb, 0x10f45a90aabecd18b6af19cc, 0x3a01e721289d1a8a630bc18c, 0x57c15ae4a7fc259d1eeac0d9, 0xb3e2f6623abcf9c36592977f, 0xbaa0551bed2b298958bc096a, 0x125e26df65683a7f9f496247, 0x131e1cc18846a946c21be7ce, 0x2bf4cbee40d1e4585d9983fc, 0x29612d8f2af44c050e7a6e47, 0x98d94d7b506f22f348d7b218, 0x710fdb924a0d2bd2fda56c0, 0xdd6d98342fe4f67cb05ee54f, 0x596a30326a952e6191185a6f, 0x9e6b2e0fa8aaa896014d67e9, 0x2e1d0c4aaa2cc51004adab21, 0x11879893708f3aebaf96f3e0, 0x41fd2ad7, 0x0, 0x0, 0xddc793d0f6ded76302697a39, 0xb22b4ba096bbdcedab9c16db, 0x73616c77e6e46b41f6af5bc9, 0x3ba104f3aced59dedaef1865, 0x2cc05918fb50406e83e92eff, 0x6ad12e22614f551de7c81293, 0xdefa3e8456b59a6371d910fd, 0x554cdf2c7105b45fc800d838, 0x793a679a65d68b07844e02d9, 0x1ec761c49dabab9424955eb9, 0xae7084bbd6f9337cf0aa7a5a, 0xa7fc8e7eff7a3c4b4e8c03fe, 0xb8aac4ca75210e6ea5c7ab4, 0xebbe07edb0b8334436abfb55, 0x883a0d104e6b72e1f32262cf, 0xff52ab49429dc49bf41aba2c, 0x25f95ac11682b4b14b4b4119, 0x7490f57a7dbb06fcfd03f72d, 0x90cd6913f9ebfb549d76df3a, 0xf77a906a9f1a245c92c07403, 0xffa77bde9d5166a772b0cfde, 0x1dabba6f, 0x0, 0x0, 0x5afffd9f52773bcd134e99d8, 0xcc416ef0789bac74567880f3, 0xad42778193d4679231d5f473, 0xf4f26773d02609d7633a2a61, 0xa0c22952edad9f723658f6f4, 0x93c8922499bda3bf71a994f2, 0x6f7eae52dfef16bf8ff3a67a, 0xdd467265cc3850970deba314, 0x7e8563c73bb63cdec42c041b, 0xa185c8df07c535191a340cd6, 0x6fa32662bf558974fac76df, 0x292f85f6ba2c832ee39c5ab7, 0x12a6486c242536e088258404, 0x4df8eefd4cf775f72e9ca5b9, 0x61020f7671b569c1dbe31db4, 0x1a111d0b8ce4c16d87231063, 0x57bc87bfbd8acde04a824ff8, 0xc5dcb21e8da06528633eda2, 0x9231631a3351430f2dbe84b0, 0x2b372f1d9cddade685602ff7, 0xa91f085b78fa241f56866b0d, 0x6cc4b091, 0x0, 0x0, 0x2de4528e7b943ad0b8c9f5f, 0xdea1d1df4ba169dc5a1a5776, 0xf11c9b5150d95e3f0c89ff40, 0x527cc16aae8858f5a5e4f31e, 0x448f9057581c58075994e074, 0x231063986b1cbb4bd563afd, 0x344db7ab3a2d40cec1b173a8, 0xc542682483c9d71617d2eb3d, 0x9ef98379499e539ec46f7074, 0x32e52b7738d5b58cacfc4dbe, 0xf7610b5ccb8c9c6b661a1c16, 0xc05f2c6e95d529d28382d2bf, 0x4038236c2163c7e6357585dd, 0xe3daf988dac9558969621182, 0x9873f618ff4254711dad9732, 0x3643e7c051e76dcb6518b3d0, 0x4a851f8ec41c3c830bacaddf, 0x223c145bf38736959511709c, 0x39e9b0b61980a5143db18fdb, 0x1a773aea976c808bbe1d9bf3, 0x157499a5cadea1cef829beed, 0x509c4f0b, 0x0, 0x0, 0x62852df9189fdd33a81d0901, 0x255b693e36a6c6c541ab1d7d, 0xce7cd3bd2a1a06275a258a5d, 0x1f66e4feae610347d0e0f77e, 0xba53b3e84326580d7f22858d, 0x78882c1f8d3fa0a1bc9a81ae, 0xdf99db3c39601ef65bfc1f0f, 0x496c687a779ddce8b94b6a33, 0x74378f794ffcbe7e38a80cc3, 0xc723ca3c7897199395ccb800, 0xa8f18815b946f95745fe430, 0xa2c332eb85dbebfdf5d21dd9, 0xf9f881512200e348e82a0f3a, 0xda431a30a0c8dd24f4410246, 0x62c6db75c3fc7b1dd0283ae6, 0x97023b40f4b8c97815ff92fe, 0xa2396d228e7807eb2b1bd67c, 0x410dc34640be2ca8dc373e80, 0xef567bc33ad8c2bde671e4fc, 0x75fee92add7a75af0f0eea88, 0x59ab3b009a3fef41785a844b, 0x41f8a5c7, 0x0, 0x0, 0xf8a571c5e36fd078f3ea0d88, 0xf8417b317828b6b8d59117c1, 0x2d5bfe87ca678aa61a804879, 0x7f60a51495bdb47fa2d00682, 0x3e84116b6dfefcc443ef929c, 0x4c73b96a37578eb1e3482db4, 0x55524215b93774818d8af3bb, 0x545bd195e8fe68d6f4c0c2fa, 0x18725691b86ccfd9f50b66a9, 0x6f5dc884624a880ced3a4606, 0xa5badaa83d8a7485cc1543b5, 0x7f49cc75e4a6186e6bc9b00b, 0xdd54decc49065e13394e739d, 0x10dc460007aa0bea87a3bdc9, 0xc9d8bf28956b4dc557d7b0da, 0x394f1b90b12d42bcd86d862e, 0x15e44894ede73370d08e59ad, 0x94414117d8025428f35dcf01, 0x9b0242480d2a9c54411d44c3, 0xd87b5eeae928debb12590061, 0x16f5649b2ce3e9b8d13710d, 0x1da7aa12, 0x0, 0x0, 0x906592b0bc16f5269c2ae379, 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0x99552eb3ebd2167dba704a47, 0x2f85bb7fdb8bb6ef6d7082f5, 0x59e12c5dab3d653e8d5dcae, 0x5efb1e847dac8f3c75e6b2dc, 0x5653b10a46f38289a303c60a, 0xb55b7ad35a60ee01b2a06c4a, 0x2fc9d6cc476812629f0690b4, 0x127881a109554756878eb900, 0xb64d4a9c25bc64493e8b83e7, 0x6f8220072f19c81354045b30, 0xc4b84f9f5cbfad17bb05e85f, 0x41e819c22d4771ec5f50b372, 0x6afd6a56fd002341db9aecd7, 0x8195c45613d4712c1545e7e, 0x581e31f3, 0x0, 0x0, 0x1039be0899a914834427fdaf, 0x46898826a20e11ccfcc9a6b9, 0x35ff691ea831f633237de7fd, 0xae796ca123ba5798fa00d076, 0x83e345f46082ea55b5e73ffb, 0x2c1051210027ac1a408050d8, 0xd9e8bdc02a581e56669179d0, 0xfb7f2e57b366f4297774790b, 0x9704009b7358e08261ab6a04, 0x38ede9f905cb13659162d038, 0xb27aab1efb2051983cbdcee0, 0xfdd5ea62b0b31a4c2516e8b9, 0xa4829e1cd351862e9e452ab6, 0x291f2bea88892dbe735d13b, 0xce6527df3fd6ee2cca7903ac, 0x3499269dbc455e3d447b0f5d, 0x8a245660e949239c73fa705d, 0x32794bbd8aadb6cf5290c426, 0xe68dda773520f0a862d1907c, 0x1f0329b4a262b8f4bbf513ef, 0x824202b9d0f6adc0d9791bc7, 0x168affea, 0x0, 0x0, 0x85e053b71672165b770143d9, 0x1435d4d955c76f51109fa271, 0x596f2aa4c7304743cec7e970, 0x81967cb23d3345f3da0d6483, 0xcd4ad402a7d80575069686e9, 0x9b9d2cc7150a4c07e8676a2c, 0x34dfc8eab0f7d59bcff3728e, 0xe035a0fd9108c35b2d8c53ac, 0xb5565a2c22c8b7ebc1dd0359, 0x503c2ed493799d64966c78a1, 0x9a59a23e1521bdcd93f1bd2e, 0xbafc90ae21f0818a58aa0c3c, 0x1ad7ca23fddbf265a8f7468b, 0x18dbd08c4b9e816d53551b57, 0xaea8b0fb268ba1a879fa3ead, 0xcc9019294c7af9ba8ea52429, 0x81243fc6681f4cc437df5791, 0x1c3973da8c348624795b1b35, 0x6213f497373385d11b004a0b, 0x3a15e382fec94f43fedb9fba, 0xdf2658a450ca87bc2b772dfa, 0x1604a62a, 0x0, 0x0, 0x63daf4f0614487a857aa397, 0x4cee11531104e6d3321a6137, 0x500042073e6d1148bd2559c, 0xd0609608648016503040201, 0xffffffffffffffff00303130, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0xffffffffffffffffffffffff, 0x1ffff, 0x0, 0x0, 0x0, 0x68656c6c6f20676172616761, 0xc, ] .span(); let public_key = Serde::::deserialize(ref rsa_sha256_serialized) .expect('FailToDeserializePk'); let rsa_with_hints = Serde::::deserialize(ref rsa_sha256_serialized) .expect('FailToDeserializeSig'); let message = Serde::::deserialize(ref rsa_sha256_serialized) .expect('FailToDeserializeMsg'); let is_valid = is_valid_rsa2048_sha256_signature(@rsa_with_hints, @public_key, @message); assert!(is_valid); } ================================================ FILE: src/src/tests/autogenerated/schnorr_tests.cairo ================================================ use garaga::core::circuit::u288IntoCircuitInputValue; use garaga::definitions::G1Point; use garaga::signatures::schnorr::{ SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash, }; #[test] #[ignore] // Ignored for auto-benchmarks fn test_schnorr_BN254() { let mut sch_sig_with_hints_serialized = array![ 0x5c724369afbc772d02aed58e, 0x2cd3bc838c66439a3d6160b, 0x72f26b55fb56be1, 0x0, 0xf14522f0e41279fa3733fed2, 0xea20efd268b756a9c0b06945, 0x7df9c9692acbd19, 0x0, 0x536c985db33c69f7c242e07a, 0xfc531bccffafcf1e59d91fb9, 0x2585e4f8a31664cb, 0x0, 0x88be2ce9ce62b465354a3799fa203a0f, 0x153a203b4df3737a1b3372ac547e5fbc, 0x12e0c8b2bad640fb19488dec4f65d4da, 0x1521f387af19922ad9b8a714e61a441c, 0x18, 0x2c40cb132c58c1528d9f95d4, 0x363f4c34cb9e9ec70646c9a0, 0x283fe6ad6138b4db, 0x0, 0x10969c686e4b6ba132f856ea, 0x9a84e9b2de29941e85990dd8, 0xce8c7dd9d8b7727, 0x0, 0x15f0bf1ccf4e04fd, 0x100000000000000004d15cba927fede3d, 0x100000000000000003fda8089c1ac8853, 0x8309133f4f176e9e, 0x2c41289f2cce1b1d98bc1c58, 0x877a1e0880ae4ac2e8cb9898, 0x1f1f91048403230b, 0x0, 0x51b26382cce36f83e9330566, 0x9303c191ab170a86a28c3ddd, 0x122b07c7aa481cb, 0x0, 0x100000000000000003a941ddef107f2c9, 0x10000000000000000002a2b771d1d6d88, 0x6f26862a18f2c12b, 0x44028f462731bd, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 0); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_schnorr_BLS12_381() { let mut sch_sig_with_hints_serialized = array![ 0xe4f817e54aede0613c17035c, 0xdff1f15010392a6da1f95a6, 0xbed78d3d341e911d49f15454, 0x18154782ce0913b21588066d, 0x73dc29ec930fa565a5979354, 0x9429c7a3a7a2e40636af119e, 0x63acb8cedd134d23d3ccba66, 0x18e6b0be5c742604e8963d45, 0xde4f62a6588c9401ffefbd3, 0x9bb5f797ac6d3395b71420b5, 0xdc39e973aaf31de52219df08, 0x105dcc4dce3960447d21d3c1, 0xb83ced7922696854920e4dce5618fd79, 0x1efa0c12855ed037f8665a14d0c63ba1, 0x12e0c8b2bad640fb19488dec4f65d4da, 0x2a43e70faf19922ad9b8a714e61a441c, 0x18, 0x99c33ff58fea7052bbb086a1, 0x1c359e13cb837e312dddb499, 0xedbe35427d90e4bb5ebcdf77, 0xb985b53c974e161da07a472, 0xde25a39170f2c0507b5ed860, 0x994e3ae48dce086260b85782, 0x7b22ea9577da0309f37f3ef9, 0x10ea8776b9541b0999d8d9cd, 0x22dbd86bddefd4d2, 0x100000000000000002092233c9decb8ff, 0xcd1dbee71ada39b7, 0x9322462863de7845, 0x95784ad2a24613cafab3e5ce, 0xdcf21fab1f76105f40e47606, 0x53de1e9b25d4c163c91db04c, 0x11a0b3d6dba83f3db716cb0e, 0x79e7b489b946a83ef4db5c0, 0x3b050ac62a98e6a19f9fe1c6, 0x93e750c788c6bfeb8566333a, 0x457b247b6591483d8dbf18b, 0x100000000000000008af4c254e183b405, 0x100000000000000004cbee0df44e8382c, 0x10000000000000000946f8bb609f9ba7d, 0x100000000000000004e77077ba28bdfd6, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 1); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_schnorr_SECP256R1() { let mut sch_sig_with_hints_serialized = array![ 0x113c8d620e3745e45e4389b8, 0x85b8ff52d905fd02fe191c3f, 0xf5d132d685201517, 0x0, 0x60c0ba1b358f375b2362662e, 0x6abfc829d93e09aa5174ec04, 0x7bc4637aca93cb5a, 0x0, 0xd3ff147ff0ee4213f51f677d, 0x431366a7732a6e4a6b942255, 0x9fe743b25d39a591, 0x0, 0x227664fcd18152d34168f6ded74ab915, 0x69b292ba7d07a7c252d76438f5ee7ec1, 0xe443df789558867f5ba91faf7a024205, 0x23a7711a8133287637ebdcd9e87a1613, 0x14, 0xe7048fa08ff83c48faafa01e, 0x4f5e1916e57a6dbf63c36e8d, 0x72872d18857fcd24, 0x0, 0x701ae40e4ba5a9f2e60e57ea, 0xadfda7abf39a0913191769f6, 0x2de1ee879affd779, 0x0, 0x434ebc818522df6c3a48fdeffa4bc338, 0x187026bb983fceb4a56a5ca9e9c969631, 0x40ab24bf96ae6fa731d65b90, 0x3d2d6da80d5ca858290e1409, 0x953b9901eec6e415, 0x0, 0x553919b2bd1f42bea69d67f3, 0x320dbca9f723841d3be6dcf9, 0x936046f4cb8c4595, 0x0, 0x3de0ac20b2665b5ee208e66433aaac05, 0x67db401fe06eea845a19e61367b76a34, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 3); assert!(is_valid); } #[test] fn test_schnorr_SECP256K1() { let mut sch_sig_with_hints_serialized = array![ 0x393dead57bc85a6e9bb44a70, 0x64d4b065b3ede27cf9fb9e5c, 0xda670c8c69a8ce0a, 0x0, 0x789872895ad7121175bd78f8, 0xc0deb0b56fb251e8fb5d0a8d, 0x3f10d670dc3297c2, 0x0, 0xfdfdc509f368ba4395773d3a, 0x8de2b60b577a13d0f83b578e, 0xc2dd970269530ba2, 0x0, 0x2cad564f3e93c6683bd94b5438ce08f0, 0xcbbfcb3b677e87eff66c9a804800a3b3, 0xe443df789558867f5ba91faf7a024205, 0x23a7711a8133287637ebdcd9e87a1613, 0x18, 0x594f9cb2a86a873bb8d4ccbd, 0xfee1700bc5d2111958ae798c, 0x4d99e99571d0a61e, 0x0, 0xf284daf0aabffcef1939ef8, 0x91753b141fbe90ddcb717736, 0x3233811221bd1d30, 0x0, 0x100000000000000000a9b06fa280b530a, 0x1000000000000000040415040c7a17610, 0x100000000000000002e35f1582f3234ce, 0x100000000000000008f635c9bcb2eefe1, 0x79a64775d37621de2372f3cb, 0xd3aa1d3b8418f14398df80f2, 0x2430232b1b17cb55, 0x0, 0x895249ed4eaf972102b5c3f5, 0xd35f2675285d8568f81ef0d, 0x1fbd9931c3f2bbf8, 0x0, 0x10000000000000000baf06a7a3e4aa015, 0x1000000000000000075adffb9c0d2b742, 0x100000000000000006f45630d920758e7, 0x13bfcc5670fee7eb, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 2); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_schnorr_ED25519() { let mut sch_sig_with_hints_serialized = array![ 0x7238f02b9f20e09c2181a557, 0x2cedcc5b0be371c337fd7e9e, 0x41f3bbeb280fe8a2, 0x0, 0xfb9073291a58a0358e22e52, 0x76d4b9ec10a3a720b1096d5b, 0xad805c90a8c77b8, 0x0, 0x82e4a33f8e4e5881e791d86b, 0xbcb062435ae8ec5fdaeac4bf, 0x179e1bae9e0f9f34, 0x0, 0xa84dfdd6e617589384812f69a2d349c1, 0xa968f5c0a623e3b190de39304eb726a, 0x12e0c8b2bad640fb19488dec4f65d4da, 0xa90f9c3af19922ad9b8a714e61a441c, 0x14, 0x5cba1348511e21f20cd92c86, 0x63fd89d574978c8364a33dc6, 0x7a1a075dacc03bb1, 0x0, 0xe16c3afd3bd9d2a736b5cb70, 0xd954e7aefbda0297b7855a5, 0x3285ce7a8018f502, 0x0, 0x3315e27d27a210cb7baa18b5f3f0f9b3, 0x10f773711dcf75ce59993cf26c4f5ebf9, 0xfbd811bae294558352d2ca8f, 0xc6b9c22af47b1e43d21ba644, 0x5c18972e38278425, 0x0, 0x6a687b6263384a17569caeb3, 0x4166dd87f125393bd27679eb, 0x13a8e31e947075f3, 0x0, 0x2ed8419cedf331ec3d387ed44220284f, 0xdbbf233e0f266b14c85329c2440c426, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 4); assert!(is_valid); } #[test] #[ignore] // Ignored for auto-benchmarks fn test_schnorr_GRUMPKIN() { let mut sch_sig_with_hints_serialized = array![ 0x86b402ce02e7c7ca81f13d51, 0x39493672733a9289a36020c1, 0x7f40d91dc5413d3, 0x0, 0x429af526e7e0a5381bccb180, 0x88f6dad23856d096b8b80e2e, 0x2684532513785230, 0x0, 0x20669ef12954f8e3bbc8b4d3, 0x396a6f7243c27ce553121ee3, 0x11438ca2ec259aed, 0x0, 0x7c7059f6158e689893dd21a94f41e410, 0x2454f3702220747f9b72cc1f2d34af71, 0x12e0c8b2bad640fb19488dec4f65d4da, 0x1521f387af19922ad9b8a714e61a441c, 0x14, 0x1619e977386f5b086cdc8857, 0x9ee9c3131ed8c4e6fb8d3b10, 0x2a23881e074bdeda, 0x0, 0x783572bfbbe358723c90aaab, 0xf40d2176448bb22e9cbc031d, 0x2be35fe4dd3f44fb, 0x0, 0x51cf7b3d0715b44af5d2f31cb1fd7677, 0x15838663fe7e8f8c16583cabb5df7308, 0xa8fc937f9ebc90a8a9a2cf09, 0x6c2d666bea9386f60b1a46c2, 0x2244eddd508f6f81, 0x0, 0x5ec6d01c41cedc947662556b, 0x4a7cb97d69bce744b75607b3, 0x2e39c1ad41f66954, 0x0, 0x19ae1fd3832d250c6410c5e4cb759edf, 0x538cc4627274d8f320bf5df15c887356, ] .span(); let public_key = Serde::::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializePk'); let sch_with_hints = Serde::< SchnorrSignatureWithHint, >::deserialize(ref sch_sig_with_hints_serialized) .expect('FailToDeserializeSig'); let is_valid = is_valid_schnorr_signature_assuming_hash(sch_with_hints, public_key, 5); assert!(is_valid); } ================================================ FILE: src/src/tests/autogenerated/tower_pairing_tests.cairo ================================================ use core::num::traits::One; use garaga::circuits::tower_circuits::{run_BLS12_381_E12T_MUL_circuit, run_BN254_E12T_MUL_circuit}; use garaga::definitions::{E12T, G1Point, G2Point, u384}; use garaga::ec_ops::G1PointImpl; use garaga::ec_ops_g2::G2PointImpl; use garaga::single_pairing_tower::{ final_exp_bls12_381_tower, final_exp_bn254_tower, miller_loop_bls12_381_tower, miller_loop_bn254_tower, }; #[test] fn test_tower_pairing_BN254_1P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, y: u384 { limb0: 0x2, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }; p0.assert_on_curve_excluding_infinity(0); let q0: G2Point = G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }; q0.assert_on_curve_excluding_infinity(0); let (tmp0) = miller_loop_bn254_tower(p0, q0); let (res) = run_BN254_E12T_MUL_circuit(tmp0, res); let final = final_exp_bn254_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x898578b55e1f63739d870e95, limb1: 0xda01bde280a3ed6f87e5feb, limb2: 0x262b253feda94cfe, limb3: 0x0, }, c0b0a1: u384 { limb0: 0x918ed66b49d34b48efb8a4a, limb1: 0xa1b1f823879abbd397c4dea, limb2: 0x2e02d2cc795a200, limb3: 0x0, }, c0b1a0: u384 { limb0: 0x87ecb1fc4e135402fdbd1de0, limb1: 0xa5b1ad44b31977935fd29573, limb2: 0x13a9f2d6e29b128d, limb3: 0x0, }, c0b1a1: u384 { limb0: 0x699ce630b130b08a6ea1162b, limb1: 0x4b31984a74e68659c4b420bd, limb2: 0x40ba9fa500f1a5c, limb3: 0x0, }, c0b2a0: u384 { limb0: 0x211ce30bf5e3eeaef89eafdb, limb1: 0xbe359d7f9873f052478f590b, limb2: 0xafc2f3fd870678f, limb3: 0x0, }, c0b2a1: u384 { limb0: 0xcc5a8243f9cddbd2d98dd1f0, limb1: 0xbdc662d929e645cadda9a712, limb2: 0x1c54a530398c9064, limb3: 0x0, }, c1b0a0: u384 { limb0: 0xfd4b7aef5c0d58c5dc2429fe, limb1: 0x23794a0d856f92591ba990ec, limb2: 0x95c0fbf5d5a1ac0, limb3: 0x0, }, c1b0a1: u384 { limb0: 0x590cb4a60f8215d4b99f2b4a, limb1: 0xa31dc10f7b4053c9e9ad9ebb, limb2: 0x14d3d6ca72d8a950, limb3: 0x0, }, c1b1a0: u384 { limb0: 0x43c585fdfaf545838ca7429, limb1: 0x89dc206b4b91c85759dc1a23, limb2: 0x1dc0e7bbc3d70e66, limb3: 0x0, }, c1b1a1: u384 { limb0: 0xac16cc1b7ab2cd3ed5e22b97, limb1: 0x98a855ffc837d2a75ab90d61, limb2: 0xb53320e5a6488cb, limb3: 0x0, }, c1b2a0: u384 { limb0: 0xc42a9c0f9bd7fddaf5ebd723, limb1: 0x6c91476ef36cd1d318ce07ba, limb2: 0x13a8afd3085dae4c, limb3: 0x0, }, c1b2a1: u384 { limb0: 0x43940c383e5314859e762c97, limb1: 0xb601f3730a3afa965ceee1b3, limb2: 0xf97b5221474526, limb3: 0x0, }, }, ); } #[test] fn test_tower_pairing_BN254_2P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0xcdb6d03cb7b9a5409b7efcd8, limb1: 0xd1df87eab84852372b905c9c, limb2: 0x1d0634f3f21e7890, limb3: 0x0, }, y: u384 { limb0: 0xaa1d4f4d3021032564460978, limb1: 0xeb3f1d6ba3b10e2b53dc193b, limb2: 0x24c53532773dce26, limb3: 0x0, }, }; p0.assert_on_curve_excluding_infinity(0); let q0: G2Point = G2Point { x0: u384 { limb0: 0xf75edadd46debd5cd992f6ed, limb1: 0x426a00665e5c4479674322d4, limb2: 0x1800deef121f1e76, limb3: 0x0, }, x1: u384 { limb0: 0x35a9e71297e485b7aef312c2, limb1: 0x7260bfb731fb5d25f1aa4933, limb2: 0x198e9393920d483a, limb3: 0x0, }, y0: u384 { limb0: 0xc43d37b4ce6cc0166fa7daa, limb1: 0x4aab71808dcb408fe3d1e769, limb2: 0x12c85ea5db8c6deb, limb3: 0x0, }, y1: u384 { limb0: 0x70b38ef355acdadcd122975b, limb1: 0xec9e99ad690c3395bc4b3133, limb2: 0x90689d0585ff075, limb3: 0x0, }, }; q0.assert_on_curve_excluding_infinity(0); let (tmp0) = miller_loop_bn254_tower(p0, q0); let (res) = run_BN254_E12T_MUL_circuit(tmp0, res); let p1: G1Point = G1Point { x: u384 { limb0: 0x536c985db33c69f7c242e07a, limb1: 0xfc531bccffafcf1e59d91fb9, limb2: 0x2585e4f8a31664cb, limb3: 0x0, }, y: u384 { limb0: 0x57fa42444057cf0c1d62ae3c, limb1: 0x4f48d341183118d68ea41313, limb2: 0x1d2d2799db056ed1, limb3: 0x0, }, }; p1.assert_on_curve_excluding_infinity(0); let q1: G2Point = G2Point { x0: u384 { limb0: 0x335eb0538f718d8e6651eeb1, limb1: 0x635e573808d9d5c7178bdce7, limb2: 0x1314aaf1c372e6d7, limb3: 0x0, }, x1: u384 { limb0: 0x5289f29ccc5acf5e81526673, limb1: 0x2d4aba9e1448a8cc1048d01a, limb2: 0x14c25d3aec745e5a, limb3: 0x0, }, y0: u384 { limb0: 0x10d1d0efd5869ecd23aab8e9, limb1: 0xba7d1de6d86501d49b6a8dab, limb2: 0x397391b7b25e2f, limb3: 0x0, }, y1: u384 { limb0: 0x385a553ea12434f4eda6db36, limb1: 0xb058c1ff7e4c5c7ec7e5859b, limb2: 0x1863ac65eca09e89, limb3: 0x0, }, }; q1.assert_on_curve_excluding_infinity(0); let (tmp1) = miller_loop_bn254_tower(p1, q1); let (res) = run_BN254_E12T_MUL_circuit(tmp1, res); let final = final_exp_bn254_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, ); } #[test] fn test_tower_pairing_BN254_3P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0x5c724369afbc772d02aed58e, limb1: 0x2cd3bc838c66439a3d6160b, limb2: 0x72f26b55fb56be1, limb3: 0x0, }, y: u384 { limb0: 0x772ca79c580e121ca148fe75, limb1: 0xce2f55e418ca01b3d6d1014b, limb2: 0x2884b1dc4e84e30f, limb3: 0x0, }, }; p0.assert_on_curve_excluding_infinity(0); let q0: G2Point = G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }; q0.assert_on_curve_excluding_infinity(0); let (tmp0) = miller_loop_bn254_tower(p0, q0); let (res) = run_BN254_E12T_MUL_circuit(tmp0, res); let p1: G1Point = G1Point { x: u384 { limb0: 0x5c724369afbc772d02aed58e, limb1: 0x2cd3bc838c66439a3d6160b, limb2: 0x72f26b55fb56be1, limb3: 0x0, }, y: u384 { limb0: 0x772ca79c580e121ca148fe75, limb1: 0xce2f55e418ca01b3d6d1014b, limb2: 0x2884b1dc4e84e30f, limb3: 0x0, }, }; p1.assert_on_curve_excluding_infinity(0); let q1: G2Point = G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }; q1.assert_on_curve_excluding_infinity(0); let (tmp1) = miller_loop_bn254_tower(p1, q1); let (res) = run_BN254_E12T_MUL_circuit(tmp1, res); let p2: G1Point = G1Point { x: u384 { limb0: 0x8dcb6db105ead17484cff544, limb1: 0x95151f1c65bf4c2e698b5634, limb2: 0xc83f07e39979c6a, limb3: 0x0, }, y: u384 { limb0: 0x38cf77eafd4a4fdd9e46575, limb1: 0x3cf1e428854a9a0e559814bc, limb2: 0x15571140da88fd37, limb3: 0x0, }, }; p2.assert_on_curve_excluding_infinity(0); let q2: G2Point = G2Point { x0: u384 { limb0: 0xa30b422f34656d6c94e40be, limb1: 0x83069b5050fd7194c7e35d0c, limb2: 0xf0e8184945e8d34, limb3: 0x0, }, x1: u384 { limb0: 0xde9079ee8fa5e15901dfef27, limb1: 0xdb602cf367841e5047ffab14, limb2: 0x1752c7b6b35af45, limb3: 0x0, }, y0: u384 { limb0: 0x4dafbd7f615fd2aa9f5a0acc, limb1: 0x35c8bbffe201ffd56deb5dea, limb2: 0xa822a5ba029a283, limb3: 0x0, }, y1: u384 { limb0: 0xec6d9e4fafec17b8404c0341, limb1: 0x17fe961ad4b8ee3bf2ade626, limb2: 0x1228147f83e3ea5, limb3: 0x0, }, }; q2.assert_on_curve_excluding_infinity(0); let (tmp2) = miller_loop_bn254_tower(p2, q2); let (res) = run_BN254_E12T_MUL_circuit(tmp2, res); let final = final_exp_bn254_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, ); } #[test] fn test_tower_pairing_BLS12_381_1P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0xf97a1aeffb3af00adb22c6bb, limb1: 0xa14e3a3f171bac586c55e83f, limb2: 0x4fa9ac0fc3688c4f9774b905, limb3: 0x17f1d3a73197d7942695638c, }, y: u384 { limb0: 0xa2888ae40caa232946c5e7e1, limb1: 0xdb18cb2c04b3edd03cc744, limb2: 0x741d8ae4fcf5e095d5d00af6, limb3: 0x8b3f481e3aaa0f1a09e30ed, }, }; p0.assert_on_curve_excluding_infinity(1); let q0: G2Point = G2Point { x0: u384 { limb0: 0xa805bbefd48056c8c121bdb8, limb1: 0xb4510b647ae3d1770bac0326, limb2: 0x2dc51051c6e47ad4fa403b02, limb3: 0x24aa2b2f08f0a9126080527, }, x1: u384 { limb0: 0x13945d57e5ac7d055d042b7e, limb1: 0xb5da61bbdc7f5049334cf112, limb2: 0x88274f65596bd0d09920b61a, limb3: 0x13e02b6052719f607dacd3a0, }, y0: u384 { limb0: 0x3baca289e193548608b82801, limb1: 0x6d429a695160d12c923ac9cc, limb2: 0xda2e351aadfd9baa8cbdd3a7, limb3: 0xce5d527727d6e118cc9cdc6, }, y1: u384 { limb0: 0x5cec1da1aaa9075ff05f79be, limb1: 0x267492ab572e99ab3f370d27, limb2: 0x2bc28b99cb3e287e85a763af, limb3: 0x606c4a02ea734cc32acd2b0, }, }; q0.assert_on_curve_excluding_infinity(1); let (tmp0) = miller_loop_bls12_381_tower(p0, q0); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp0, res); let final = final_exp_bls12_381_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x839c508a84305aaca1789b6, limb1: 0x3dd8e90ce98db3e7b6d194f6, limb2: 0x68d0d727272d441befa15c50, limb3: 0x1250ebd871fc0a92a7b2d831, }, c0b0a1: u384 { limb0: 0x50439f1d59882a98eaa0170f, limb1: 0xaf5af689452eafabf1a8943e, limb2: 0xa532348868a84045483c92b7, limb3: 0x89a1c5b46e5110b86750ec6, }, c0b1a0: u384 { limb0: 0x9396b38c881c4c849ec23e87, limb1: 0x16da0e22a5031b54ddff5730, limb2: 0x689ce34c0378a68e72a6b3b2, limb3: 0x1368bb445c7c2d209703f239, }, c0b1a1: u384 { limb0: 0x579973b1315021ec3c19934f, limb1: 0x7c90d8bd66065b1fffe51d7a, limb2: 0x5a50512937e0794e1e65a761, limb3: 0x193502b86edb8857c273fa07, }, c0b2a0: u384 { limb0: 0xbbaad8431dad1c1fb597aaa5, limb1: 0x185203fcca589ac719c34dff, limb2: 0x4dc4007cfbf2f8da752f7c74, limb3: 0x1b2f522473d171391125ba8, }, c0b2a1: u384 { limb0: 0xa35c8ca78beae9624045b4b6, limb1: 0x8061e55cceba478b23f7daca, limb2: 0x7a45b84546da634b8f6be14a, limb3: 0x18107154f25a764bd3c7993, }, c1b0a0: u384 { limb0: 0x86a8703e0f948226e47ee89d, limb1: 0xdea54d43b2b73f2cbb12d583, limb2: 0xc3d5a04dc88784fbb3d0b2db, limb3: 0x19f26337d205fb469cd6bd15, }, c1b0a1: u384 { limb0: 0xff02f0b8102ae1c2d5d5ab1a, limb1: 0xa7d2809d61bfe02e1bfd1b68, limb2: 0xa771b6ffd5857baaf222eb95, limb3: 0x6fba23eb7c5af0d9f80940c, }, c1b1a0: u384 { limb0: 0x1e32fac91b93b47333e2ba57, limb1: 0x7d0d15ff7b984e8978ef4888, limb2: 0x3b0b0ec5c81a93b330ee1a67, limb3: 0x11b8b424cd48bf38fcef6808, }, c1b1a1: u384 { limb0: 0xa09ffdd9be2291a0c25a99a2, limb1: 0x20c806ad360829107ba810c5, limb2: 0x6ce5771cc6a0e9786ab59733, limb3: 0x3350f55a7aefcd3c31b4fcb, }, c1b2a0: u384 { limb0: 0x66245cb9108f0242d0fe3ef, limb1: 0x1c7cdba7b3872629a4fafc05, limb2: 0x728ffd21a189e87935a95405, limb3: 0x4c581234d086a9902249b64, }, c1b2a1: u384 { limb0: 0xafe47e1efde449383b676631, limb1: 0xdeff686bfd6df543d48eaa24, limb2: 0xd01a7ec73baca4d72ca93544, limb3: 0xf41e58663bf08cf068672cb, }, }, ); } #[test] fn test_tower_pairing_BLS12_381_2P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0xfe174bb39be8658ef83c8c2d, limb1: 0xdb24ddec0e0c3b63d82efa81, limb2: 0xe360a80121d5ef96fd687003, limb3: 0x59d2a79bda5f8a941d4db9, }, y: u384 { limb0: 0x7f68344f543e52fe891285a9, limb1: 0x6f6992be16bc35f88c471acf, limb2: 0xcebb5ee96e40a033f5d3b798, limb3: 0x2df47e8cdf189985d5085bd, }, }; p0.assert_on_curve_excluding_infinity(1); let q0: G2Point = G2Point { x0: u384 { limb0: 0xa805bbefd48056c8c121bdb8, limb1: 0xb4510b647ae3d1770bac0326, limb2: 0x2dc51051c6e47ad4fa403b02, limb3: 0x24aa2b2f08f0a9126080527, }, x1: u384 { limb0: 0x13945d57e5ac7d055d042b7e, limb1: 0xb5da61bbdc7f5049334cf112, limb2: 0x88274f65596bd0d09920b61a, limb3: 0x13e02b6052719f607dacd3a0, }, y0: u384 { limb0: 0x3baca289e193548608b82801, limb1: 0x6d429a695160d12c923ac9cc, limb2: 0xda2e351aadfd9baa8cbdd3a7, limb3: 0xce5d527727d6e118cc9cdc6, }, y1: u384 { limb0: 0x5cec1da1aaa9075ff05f79be, limb1: 0x267492ab572e99ab3f370d27, limb2: 0x2bc28b99cb3e287e85a763af, limb3: 0x606c4a02ea734cc32acd2b0, }, }; q0.assert_on_curve_excluding_infinity(1); let (tmp0) = miller_loop_bls12_381_tower(p0, q0); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp0, res); let p1: G1Point = G1Point { x: u384 { limb0: 0xde4f62a6588c9401ffefbd3, limb1: 0x9bb5f797ac6d3395b71420b5, limb2: 0xdc39e973aaf31de52219df08, limb3: 0x105dcc4dce3960447d21d3c1, }, y: u384 { limb0: 0xaefd0d854043fd325dd3c34f, limb1: 0x9b63c98d9a7845c52e1e2b0f, limb2: 0x9db0be660d847ccc58358f3f, limb3: 0x17cb6c41f0c4e1a7394ab62a, }, }; p1.assert_on_curve_excluding_infinity(1); let q1: G2Point = G2Point { x0: u384 { limb0: 0x3b3d3c305a70960906e6cb09, limb1: 0x40e5bf3ff02d81e98b75703a, limb2: 0x665a5fc010510bd690ddd7b5, limb3: 0x82dc9154807866eb0f36ccb, }, x1: u384 { limb0: 0xe6709deb0dcf81d4285e5e60, limb1: 0xb4dcf956002c4efb974ffcee, limb2: 0x4a6ceebe6375a83dd242851b, limb3: 0xdd18d077ad5bd58dabb18d8, }, y0: u384 { limb0: 0x61535fe1a90bae7e6692f9b0, limb1: 0xc91aa58105d3a281b2e84ddb, limb2: 0x197d3446652372ce5ef50e93, limb3: 0x4a468eb9e206b9833d8e8e2, }, y1: u384 { limb0: 0x27115c334e82ed4be8da6c10, limb1: 0x194fa3bf769a2e5a52535277, limb2: 0x8be8992de81f47ae3341c590, limb3: 0x198fd0ab6249082bf7007d7e, }, }; q1.assert_on_curve_excluding_infinity(1); let (tmp1) = miller_loop_bls12_381_tower(p1, q1); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp1, res); let final = final_exp_bls12_381_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, ); } #[test] fn test_tower_pairing_BLS12_381_3P() { let mut res: E12T = One::one(); let p0: G1Point = G1Point { x: u384 { limb0: 0xe4f817e54aede0613c17035c, limb1: 0xdff1f15010392a6da1f95a6, limb2: 0xbed78d3d341e911d49f15454, limb3: 0x18154782ce0913b21588066d, }, y: u384 { limb0: 0x3d77d61326ef5a9a5a681757, limb1: 0xd3070afd4f0e121de7fcee60, limb2: 0xdf9ef4088763fe611fb85858, limb3: 0x11a612bdd0bc09562856a70, }, }; p0.assert_on_curve_excluding_infinity(1); let q0: G2Point = G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }; q0.assert_on_curve_excluding_infinity(1); let (tmp0) = miller_loop_bls12_381_tower(p0, q0); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp0, res); let p1: G1Point = G1Point { x: u384 { limb0: 0xe4f817e54aede0613c17035c, limb1: 0xdff1f15010392a6da1f95a6, limb2: 0xbed78d3d341e911d49f15454, limb3: 0x18154782ce0913b21588066d, }, y: u384 { limb0: 0x3d77d61326ef5a9a5a681757, limb1: 0xd3070afd4f0e121de7fcee60, limb2: 0xdf9ef4088763fe611fb85858, limb3: 0x11a612bdd0bc09562856a70, }, }; p1.assert_on_curve_excluding_infinity(1); let q1: G2Point = G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }; q1.assert_on_curve_excluding_infinity(1); let (tmp1) = miller_loop_bls12_381_tower(p1, q1); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp1, res); let p2: G1Point = G1Point { x: u384 { limb0: 0x6b2dbb412523879f8e3a96a0, limb1: 0x6daa411c3d8c33de611bc2fe, limb2: 0x38ff9a4921f13749974e4731, limb3: 0x2b2fcedd1d05f99449b4884, }, y: u384 { limb0: 0x845744e5af99690d2a360ec2, limb1: 0x56b0c0147f0ee90a5c1b6e41, limb2: 0xdee769045aef4994aab4b4fc, limb3: 0x32b985c03cd5519d41d0cbb, }, }; p2.assert_on_curve_excluding_infinity(1); let q2: G2Point = G2Point { x0: u384 { limb0: 0x30d2fddc2fa171cdd4d31a55, limb1: 0x92fab4f255a20d09700542e5, limb2: 0x4d92a8c02d22b8cea4ff21ab, limb3: 0x120a838699abaae7ed948194, }, x1: u384 { limb0: 0x51cd5fdc71cf4557ef606935, limb1: 0x92e1b13e2c93fc9957b17841, limb2: 0x6143a906b63b7f3476ad6819, limb3: 0x158186f6f2dd04cfa4e78547, }, y0: u384 { limb0: 0x9f1c7dcdbe4574f05d0c093b, limb1: 0xcde395f3ee4e353cf25a2e21, limb2: 0x6a44c4a6d642c3dd98128703, limb3: 0x2bd32fdfe26d866771e2180, }, y1: u384 { limb0: 0x7060005397ea11f7e9a26050, limb1: 0xeb8540654b533da9b594fc27, limb2: 0xfc83cf9d283b7231df1db3f9, limb3: 0x7ff9623d918ca12e0ff6cce, }, }; q2.assert_on_curve_excluding_infinity(1); let (tmp2) = miller_loop_bls12_381_tower(p2, q2); let (res) = run_BLS12_381_E12T_MUL_circuit(tmp2, res); let final = final_exp_bls12_381_tower(res); assert_eq!( final, E12T { c0b0a0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c0b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b0a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b1a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a0: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, c1b2a1: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }, }, ); } #[test] fn test_tower_final_exp_BN254() { let input = E12T { c0b0a0: u384 { limb0: 0x9558867f5ba91faf7a024204, limb1: 0x37ebdcd9e87a1613e443df78, limb2: 0x8e9dc4681332876, limb3: 0x0, }, c0b0a1: u384 { limb0: 0xfb97d43588561712e8e5216a, limb1: 0x9a164106cf6a659eb4862b21, limb2: 0x967d0cae6f4590b, limb3: 0x0, }, c0b1a0: u384 { limb0: 0xbad640fb19488dec4f65d4d9, limb1: 0xd9b8a714e61a441c12e0c8b2, limb2: 0x1521f387af19922a, limb3: 0x0, }, c0b1a1: u384 { limb0: 0x19c78df48f4ff31e78de5857, limb1: 0x50f244556f25e2a25a921187, limb2: 0x28fcb26f9c6316b9, limb3: 0x0, }, c0b2a0: u384 { limb0: 0xf77383c13458a748e9bb17bc, limb1: 0x71545a137a1d50068d723104, limb2: 0x215ddba6dd84f39e, limb3: 0x0, }, c0b2a1: u384 { limb0: 0xce164dba0ff18e0242af9fc3, limb1: 0xea7e9d498c778ea6eb2083e6, limb2: 0x5f82a8f03983ca8, limb3: 0x0, }, c1b0a0: u384 { limb0: 0x66194cb1d71037d1b83e90ec, limb1: 0xc8f8e3d0d3290a4cb5d32b16, limb2: 0x28045af9ab0c1681, limb3: 0x0, }, c1b0a1: u384 { limb0: 0x7e5b1e7f9ca5499d004ae545, limb1: 0x55485822de1b372ad3fbf47a, limb2: 0x2ebce25e3e70f16a, limb3: 0x0, }, c1b1a0: u384 { limb0: 0xded733e8b421eaeb534097ca, limb1: 0xeac1c14f30e9c5cc101fbccc, limb2: 0xe30658b9148624f, limb3: 0x0, }, c1b1a1: u384 { limb0: 0xf7b0b7d2cda8056c3d15eef7, limb1: 0x8b0163c1cd9d2b7d247a8333, limb2: 0x5d67b7072ae2244, limb3: 0x0, }, c1b2a0: u384 { limb0: 0x51ef1922fe43c49e149818d1, limb1: 0xff7b118e820865d6e005b860, limb2: 0x1f507980eece328b, limb3: 0x0, }, c1b2a1: u384 { limb0: 0x8d1fd9b74d2b9deb1beb3711, limb1: 0x1ff39849b4e1357d4a84eb03, limb2: 0x154bc8ce8c25166a, limb3: 0x0, }, }; let res = final_exp_bn254_tower(input); assert_eq!( res, E12T { c0b0a0: u384 { limb0: 0xdbc3eb4cffd298b3fa7d5a31, limb1: 0x9c46ca08e6740e40f6588c03, limb2: 0x1e656501517e97b6, limb3: 0x0, }, c0b0a1: u384 { limb0: 0x5c5f9021ddc05b4e8e458180, limb1: 0xfc9ac0db94ad84f883101197, limb2: 0x10d35fc577ab954a, limb3: 0x0, }, c0b1a0: u384 { limb0: 0x8338823c5e5ac5cd9c54b10c, limb1: 0x1749d62236197afa5b52b1b2, limb2: 0xc2fb8c574d4a2aa, limb3: 0x0, }, c0b1a1: u384 { limb0: 0x3fed1e7b4d562acb92ab1a7c, limb1: 0x215c21048e64e6366563b7bd, limb2: 0x56befad9198c47f, limb3: 0x0, }, c0b2a0: u384 { limb0: 0x2e357f74fb161fde82246aaf, limb1: 0x30461114e53b7faeeabde969, limb2: 0x160bd4f153a876cc, limb3: 0x0, }, c0b2a1: u384 { limb0: 0x9953d9fc7152b696a117f008, limb1: 0x3260659f2890ee7e7fef447, limb2: 0x2c09cd97bcdf915f, limb3: 0x0, }, c1b0a0: u384 { limb0: 0x68db7596dac15cee7f675e5b, limb1: 0xd64fc7fa279a306f05a4f7bb, limb2: 0x1badb5f4113cf175, limb3: 0x0, }, c1b0a1: u384 { limb0: 0xd43446d44724e68a5d3e0ce0, limb1: 0x1ad7eb734406471bac65ff96, limb2: 0x15027bc7d1c7191b, limb3: 0x0, }, c1b1a0: u384 { limb0: 0x75668ecaf7e92d7d38d72226, limb1: 0x2f055eefa07fed95961aa90e, limb2: 0x231ea84923202c33, limb3: 0x0, }, c1b1a1: u384 { limb0: 0x5d2ac3131b5214c54a04b4ca, limb1: 0x5a879571728f9d6a335a11b6, limb2: 0x1a88b1de9b27f1fe, limb3: 0x0, }, c1b2a0: u384 { limb0: 0x1c3137fb1e4efedec89693d5, limb1: 0x90787e810e0d14fcd37605c5, limb2: 0x27a6e50c674c3d45, limb3: 0x0, }, c1b2a1: u384 { limb0: 0x36b1cc116e2ac5e8f8918e00, limb1: 0xcb7e94a03ed3261502d9cf46, limb2: 0xbec9af879f51f8, limb3: 0x0, }, }, ); } #[test] fn test_tower_final_exp_BLS12_381() { let input = E12T { c0b0a0: u384 { limb0: 0x4da5e709d4713d60c8a70639, limb1: 0x5ba91faf7a024204f7c1bd87, limb2: 0xe87a1613e443df789558867f, limb3: 0x474ee238133287637ebdcd9, }, c0b0a1: u384 { limb0: 0xc17c627923c6612f48268673, limb1: 0xcca5a5a19e4d6e3c1846d424, limb2: 0xe8e5216afcbd04c340212ef7, limb3: 0x1690c564fb97d43588561712, }, c0b1a0: u384 { limb0: 0xe6f4590b9a164106cf6a659e, limb1: 0x19488dec4f65d4d9259f4329, limb2: 0xe61a441c12e0c8b2bad640fb, limb3: 0xa90f9c3af19922ad9b8a714, }, c0b1a1: u384 { limb0: 0x19c78df48f4ff31e78de5857, limb1: 0x50f244556f25e2a25a921187, limb2: 0xe9bb17bca3f2c9bf9c6316b9, limb3: 0x11ae4620f77383c13458a748, }, c0b2a0: u384 { limb0: 0xdd84f39e71545a137a1d5006, limb1: 0xff18e0242af9fc385776e9a, limb2: 0x8c778ea6eb2083e6ce164dba, limb3: 0x2fc154703983ca8ea7e9d49, }, c0b2a1: u384 { limb0: 0x3e70f16a55485822de1b372a, limb1: 0xb421eaeb534097cabaf3897a, limb2: 0x30e9c5cc101fbcccded733e8, limb3: 0x71832c59148624feac1c14f, }, c1b0a0: u384 { limb0: 0xeece328bff7b118e820865d6, limb1: 0x4d2b9deb1beb37117d41e602, limb2: 0xb4e1357d4a84eb038d1fd9b7, limb3: 0xaa5e4678c25166a1ff39849, }, c1b0a1: u384 { limb0: 0x8a5006c1ec188efbd080e66e, limb1: 0xcca74147f6be1f723405095c, limb2: 0x966e12778c1745a79a6a5f92, limb3: 0x2eea66d71eacd0549a3e80e, }, c1b1a0: u384 { limb0: 0x6288e1a5cc45782198a6416d, limb1: 0x3dfabc08935ddd725129fb7c, limb2: 0x307bf3262f1205544a5308cc, limb3: 0x10e1c2b2fcd81b5d24bace4, }, c1b1a1: u384 { limb0: 0xa81ad477fb3675b89cdeb3e6, limb1: 0x11af923d79fdef7c42930b33, limb2: 0xc1f254b8adc0da7a16febaa0, limb3: 0x4c91dc7e07405eb215663ab, }, c1b2a0: u384 { limb0: 0x151665705b7c709acb175a5a, limb1: 0x1d878f9f9cdf5a865306f3f5, limb2: 0xa1515607964a870c7c879b74, limb3: 0x6179561d857010255d44936, }, c1b2a1: u384 { limb0: 0xbb42e0b20426465e3e37952d, limb1: 0xb490b6081dfc83524562be7f, limb2: 0xcb69ca385f3f563838701a14, limb3: 0xda2ddc3552116dd2ba4b180, }, }; let res = final_exp_bls12_381_tower(input); assert_eq!( res, E12T { c0b0a0: u384 { limb0: 0xc47661ee2c6ec195b6465492, limb1: 0x6923c966026d1a5202d2547f, limb2: 0x3ca333e30f3750a593c5dd62, limb3: 0x16211c8f3af6c885d6e7aae7, }, c0b0a1: u384 { limb0: 0x18ef376237b7b85323d0d503, limb1: 0x6e98bbb5ebf752814d657668, limb2: 0xf72474b60f257f5566c184d6, limb3: 0x6298b60c51ccfdaa550d764, }, c0b1a0: u384 { limb0: 0x348c2c399e7bd6de56256576, limb1: 0xf4a77fefb18543958b97e185, limb2: 0x5d0aab75be4368260e7d2ed9, limb3: 0x158469853e297d165ee80a77, }, c0b1a1: u384 { limb0: 0x72f3c5aec1469c18e1fdbce1, limb1: 0x51ddbb4388643f1a6efaf631, limb2: 0x34f1e1e014398ac114bd5c0, limb3: 0x10e831545a67da3f9fdf361a, }, c0b2a0: u384 { limb0: 0xf0e118cc2ee8a943979abc0c, limb1: 0x6e7b8556c21ea7bb63547b6d, limb2: 0x4479c64648fd5135f004569a, limb3: 0x9c3267b433303abded9ab0, }, c0b2a1: u384 { limb0: 0xe5fa5528617a7773128a3a1f, limb1: 0x6be496fac02353edcae1c79e, limb2: 0x4f9bbd2d6d5199cbf179da1f, limb3: 0x17f02c9ce45af7421efccde, }, c1b0a0: u384 { limb0: 0xd2192367be40c767eecd94f0, limb1: 0x5a094323a3c2b121fc6db025, limb2: 0xe70f56b994092e1f7d106f54, limb3: 0x12ac5958b941614ac10d5ff6, }, c1b0a1: u384 { limb0: 0x96dcae9f5d11d83ff8ee58e0, limb1: 0x1539f36298c543196ff7521, limb2: 0xf4f41990abca0c681a3221f6, limb3: 0x11aa8e62757ec2cbf6c16ffc, }, c1b1a0: u384 { limb0: 0xffb243b8fb10435f6ea824db, limb1: 0x1bda384d4058fd317cf9270f, limb2: 0x3f176c05329fa1b37897428a, limb3: 0x9ffc940d1185cb35015aa48, }, c1b1a1: u384 { limb0: 0x74d71b12604949416f2e7fad, limb1: 0x84b612cd1cafbc9b8af3e707, limb2: 0xe4855dd3d16e5ae18223225e, limb3: 0x801946300201b84e305ee6, }, c1b2a0: u384 { limb0: 0xbb3b943ceffbff6187a09c3a, limb1: 0x8c71050ce550d5e89695deb2, limb2: 0x2fd70aa73c133a3e0e483ef2, limb3: 0x7f835c51a9434870d20cedf, }, c1b2a1: u384 { limb0: 0xcb5beb0bdcff8c233260205d, limb1: 0x987fe621d66e1a6dca01005b, limb2: 0xf19f8ff647ec05851ed472a9, limb3: 0x9f783e3dcba8af017c07469, }, }, ); } ================================================ FILE: src/src/tests/calldata_tests.cairo ================================================ use crate::utils::calldata::deserialize_full_proof_with_hints_bls12_381; #[test] fn test_deserialize_full_proof_with_hints_bls12_381() { // garaga calldata --system groth16 --proof // hydra/garaga/starknet/groth16_contract_generator/examples/proof_bls.json --vk // hydra/garaga/starknet/groth16_contract_generator/examples/vk_bls.json --format array let mut serialized = array![ 77971247423532365748231213480, 68566630218281092565267874044, 69218241659544231899447836734, 5210713370446757553310648104, 29975532048713345346728513874, 60131236376572367113577691315, 66829595643973230840624156168, 851093425154653346347584866, 36988298159079040949455438986, 57841331206497126486942833902, 78394969930433492883730279315, 5168616600757658063044848131, 71996036696940156226136278626, 39908840363606579425569960997, 37427347626246260567577938253, 7711402467582346430323174384, 61866231490764965852336666920, 1485446282956182122235189114, 24505774892507781812596026670, 166936301920675049843325984, 14142961460712467494187312601, 59336570766763966042896958993, 33125257106653746636063844303, 6336617002331687822928929267, 76208108071419754504567488535, 67522218240854508687713598507, 60778260558056083193758028786, 6994315738203844514307689821, 39109476850504384255101416373, 4563203902324250838004362280, 74008827421754500938243422144, 4588649057457317000305384776, 1, 162188267535021012914933874695527094689, 74351682113781394910510902205804837421, 32194719649307445341132812807, 7279752730359835541367473802, 47710710288577935245284447693, 1419950009495443211853955399, 3647836096884217263029835403, 56321839293630983331949256555, 48457408484169336698114154298, 4033250274037303739812601995, 37791419294239366654696089744, 70998552777774589024396988311, 39915671134059625140321314026, 3809343904542700736033250473, 33829996627126998929524224821, 61676065104950018712089150876, 68439794587965551511766573689, 2865007045925431983911439426, 27112224452789409282270111183, 66906936443170431587936776481, 29509391152443426525913329789, 2942044231372461502017727018, 31524594061511080573222581436, 14986353866705479312904394863, 71972723636501966110222074452, 5344092690743570953559106774, 4765507480019605351198077835, 14908496520367678240933103306, 24908591596218651556279785125, 3944092145422224742714103693, 8429801903301466479642247085, 16057780532905072011846247931, 17399093308238050206590708045, 5139994617788050452861167220, 73754063866928330632151581570, 73714290802177719414194343911, 22445364163983035216803177788, 6366889707934883191084004393, 3491039030479184294747549822, 51732121100147969073250799890, 27386944946323904500348273181, 4385913456436807188041388171, 63406929780934892902085432865, 13024244925354710667504340948, 9818759060015048768231121209, 3940387827675730450538662159, 9498746512908964047922834279, 53170642112366515401625025220, 54395118314665947463893798725, 1288128069358204676876048440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43248345015923410511418527918, 2339359598397411241327981188, 73890304341590518017447068133, 6484088522357121612563628351, 0, 0, 0, 0, 35, 30027838756051553592474048858, 54101158246873281893268851782, 16252313257754462986798756494, 6730039006201148461101016722, 59166942355452517793514621311, 29611964699459785437591579035, 8519817219883889074793807703, 5634861121456970087752773730, 31628006324283734577903836259, 10539101379075759086036605267, 14510051136041346261035086002, 1788279434461014558870064366, 50538859019818205318127166575, 24101814558253546467372316153, 36861647121021098091587437350, 2109509723737426726090214104, 50995296157422730826447535567, 34115639409343349990007173687, 39889791167462707668956600355, 7139454304258571058057145968, 5677486451271889915150751900, 49381072058996141057339648450, 45236818714965917096073435257, 5410014512167636985502543724, 52851369230184844446011095835, 26956742559940204615504752861, 10586594386753721807366226964, 5285237918858329369750056736, 72491064846101162851502169694, 16357430162813483087252302988, 2776322324062868736865069294, 7691450961040902460162854352, 28070630466005464928724117413, 64187001067926917335528887714, 46788419336828522044462049855, 4382033612830061984319085754, 8034583862966778503247220961, 56096742313325232975868774585, 68585550580565240665212971182, 4476353455202817151691083445, 310085044230562831031036615, 60617887746516426241306123887, 37826463078236280791329443240, 1011833944445122731301232013, 9746904122117636655601728898, 27966741000383526869167288219, 21209996526299107239973360442, 3103923575483653836603642308, 72934753446937741447647845012, 47190295587938652246440505693, 63247625434314253446260470906, 4162213667224368104349214158, 44116566986492106261260643145, 36663164458555541551023132397, 21443211471927538917929059805, 29364840375223351024347720, 69133722904601054637541361174, 5824483258086841476910730082, 68503634142372854073292211203, 1937841124855622741132428093, 16342922410047931143944537196, 65970020997323617011530981603, 35057865146334572145945070096, 3451750236012488220190472699, 4311306230156727887087261132, 8695412623966263837937733798, 77176357502616542704656042128, 6101454099849957954515297657, 26622917829487454213461225101, 58605703673705566057178169233, 33113413176132064837543231640, 995773979584154924305479998, 31053677400349199753754451188, 40713559952895299870148850462, 62418803868553690327027026698, 93382446560968940373702036, 37712776509346478393543844243, 49864030905083736886253329472, 50632088155738237480407451318, 4206148787912257087329709277, 63375650005341941504168657969, 29297861299097956601364333997, 33763825508232552291739922496, 1985797962564307174288266194, 66696036047918564881956507309, 77167968750690188742636584677, 65054228210931679861446554657, 285937451162313357308376487, 73651724253810292011419259430, 70485925834587700255097149228, 77910644048681279676827387407, 5794027271286644917142723998, 14033893853278077343078387793, 33280173313783426060203760416, 48372060495225247258877841260, 3603717336592238868900693842, 35456068715660483094487770530, 16554550064157054487441106354, 14326732948379501626951591875, 3698282433453704050453631894, 19146564924553830738333216240, 25020931864070774283275229299, 22211845828645492626018913178, 5083210263577039175223654275, 41952074144039335942222955181, 55663683689078188645088175554, 60496493342305037524741110278, 4304619539671921717172032133, 50858649693567842098042385967, 52165707910425217246618470427, 41339315330087377357294597117, 6539089028599035740094380703, 72053127906157009580161741600, 22157559310014076427322619430, 70125657965596091683801708562, 3022877841189616397537213489, 6934534485162623435238541802, 47165543872991109029877011528, 2566259322647998968241017753, 7067362300862537521110073710, 35413603792063749196537285749, 11933166219420367971739694184, 40765194826541066033934446797, 7129410806727453756625011822, 29662307088543837149206305134, 65727977531111266904340756978, 42496286358276282218467101201, 7747883663466642582384665508, 17669369957595764186984839002, 40677642819188609359029355170, 59164559721383814161088328323, 6448449646684808231497776519, 25619368862892179391009855646, 26381527199732177089152363916, 14850373154740658284833360333, 1076564188815688551187118834, 32887175812143566285910166960, 13249683844989241745607228921, 36456117534193488400480016588, 170141990863262138143052988, 61760824788503155462102203539, 67320570476006959596849012803, 7766127653453634897585163528, 5812689405665018357313789116, 28344794854282756958093754, 5269947778693928801263573956, 53963701928114333840090271243, 4234461668157274586969416989, 20644958011919486212644357036, 26027812993954453814277748447, 275941194480212844069522943, 3538313684263000688182076336, 32801747500662710107225666753, 72682974215035517456530493687, 11581356430328319373161672017, 4533402135467029581720881425, 44058220463589537079385810011, 9333160639543932900599272247, 34172223003063687035350629785, 4794543240810738112240156944, 66965669599092548335505382683, 7238580231678608477454713965, 594337166918393597453047263, 573384765934888290368105125, 5298611690427555842434593544, 72410071650016602831108419020, 62739255899796079018370306360, 7849113008352889379633423443, 25258471464787299307135994029, 55762491168129233861203453862, 34626239502635003182102731944, 4480270938899930929063085116, 38884223664535909069137747383, 60280836569594947747629168214, 32856950205705764745608993213, 2392129868089939474880361662, 37838992250108998686527194786, 37288434055699776877846613558, 7949422721057160329636737842, 8036696326455776379012768983, 827077001344265445859285175, 13012960033941055488017688611, 25173972490487079546640335690, 1925414097850431151291670446, 58595610619929099032787293815, 59496529594755496148283316365, 13875217823643943649398141619, 7372094443240058558285115189, 15308212201423385157221091191, 32595930911053677946031331419, 61379406643649190572985248884, 2996375498768731539234628958, 46936883038348260351614004847, 75148696570210889440602146167, 25106178939001538254192127116, 7167710891023322575832224224, 100723146502372083165311896, 55751937316279468177742802836, 13871905808263810908577369544, 3737876825512892199597660458, 63816212289840684036461122375, 17733810278901303208048721488, 3351835079747659573922533568, 3046359189407291089286136161, 13044104993142686637496395172, 9282845231912569956252516712, 5761562488028695340583952910, 5921232933352375862448457265, 21518340125394465148399554843, 5982470152449697525125353289, 57053181264227943937678085503, 6292711021140480762840428167, 20076579190065982979764971926, 53780374660066758165656920782, 36805613003594702952829511499, 6547759856425411111890981980, 47512071241281773216035110875, 56022529648726063889428729621, 30858618567768404792580768416, 5757919197631638054742627364, 15669019961284650462106553953, 66639617563672338978768140574, 8082266105417603982291825844, 4564626181978619405084267045, 26009201212564438460739797336, 64572665731556470248113629014, 59252263505414064169597193741, 7883562242748919475083180284, 56470253812221414253305276776, 4498045693294739345032368018, 8301015289726367266397191053, 5348409005514905968887450762, 51387389277124520529090934476, 56941222593669910106396786388, 42622730933944117660047364473, 173196935167601629026012489, 41345835421790350935003416835, 21667287315177218504729214260, 22489091250914396077676341317, 2742300185381864076197017486, 47167411505437997622504473369, 38171590942991972995898002181, 45230515905390045720039559055, 6190428625729966894895772964, 22421896522252105799597726706, 22767691098362212992825587837, 8272539897093289253906939946, 6624376755118367265034331918, 15661111081153176052555263530, 76520770728514633564622590654, 7514263970502628885483842834, 4161399108172689732299496968, 60499668660768151028227772386, 47180509148512048563055856732, 54947867068696841243448279979, 3892308014696337859766042527, 52579604138530131332831897276, 23848195015190911842220533856, 23144083113629883183090117996, 8039822788758490597926641553, 29984552573156797877940033032, 66562098176719407889244652079, 49437533671009460826493634846, 1156205892955632813090181532, 50340753975243539886466578963, 71600268508272898437620580476, 7749173236713132109818996799, 937217378878921200898898681, 61530787830163118334408183838, 46718403155930865835143965039, 3360479066512207989279511115, 1242095274119975861215890980, 25631398301122740779039338607, 8684240449838525915272645580, 56524280049856107750242803162, 447558878172142624222306080, 36697831213375122858015827821, 31628650890081021735794393291, 10505167761437020089256195553, 7979550648404801060728402084, 15222854946553811809213857382, 362368517711213651621254492, 74279206026608922070481420749, 3092794960790330037616934773, 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0xcd3ecab431257f8b80b8dc77 0x154e8dd3aac3d42c 0x0 0x100000000000000005c19a465cc7cbb28 0x3378cd034f0d9ebb 0x24df6021ce19cb18 0x9c6a591e71b87b32 0x970e2d83fd3ed91e6df39f2c 0x85294ea4088b8c3ca50dcf1e 0x3a237bdbf87287c 0x0 0xd13f9298545a1d77942e20d7 0xa85510aa9d5e7b357755b5d6 0x15c764c1c5380102 0x0 0x100000000000000003aa0eb9486eaea7c 0x100000000000000003ed064b9068afd7b 0x100000000000000004e76be5e17f551d8 0x100000000000000008d717becec440328 ================================================ FILE: src/src/tests/sha512_tests.cairo ================================================ use garaga::hashes::sha_512::{Word64WordOperations, sha512}; fn get_lorem_ipsum() -> Array { let mut input: Array = array![ 0x4C, 0x6F, 0x72, 0x65, 0x6D, 0x20, 0x69, 0x70, 0x73, 0x75, 0x6D, 0x2C, 0x20, 0x6F, 0x72, 0x20, 0x6C, 0x73, 0x69, 0x70, 0x73, 0x75, 0x6D, 0x20, 0x61, 0x73, 0x20, 0x69, 0x74, 0x20, 0x69, 0x73, 0x20, 0x73, 0x6F, 0x6D, 0x65, 0x74, 0x69, 0x6D, 0x65, 0x73, 0x20, 0x6B, 0x6E, 0x6F, 0x77, 0x6E, 0x2C, 0x20, 0x69, 0x73, 0x20, 0x64, 0x75, 0x6D, 0x6D, 0x79, 0x20, 0x74, 0x65, 0x78, 0x74, 0x20, 0x75, 0x73, 0x65, 0x64, 0x20, 0x69, 0x6E, 0x20, 0x6C, 0x61, 0x79, 0x69, 0x6E, 0x67, 0x20, 0x6F, 0x75, 0x74, 0x20, 0x70, 0x72, 0x69, 0x6E, 0x74, 0x2C, 0x20, 0x67, 0x72, 0x61, 0x70, 0x68, 0x69, 0x63, 0x20, 0x6F, 0x72, 0x20, 0x77, 0x65, 0x62, 0x20, 0x64, 0x65, 0x73, 0x69, 0x67, 0x6E, 0x73, 0x2E, 0x20, 0x54, 0x68, 0x65, 0x20, 0x70, 0x61, 0x73, 0x73, 0x61, 0x67, 0x65, 0x20, 0x69, 0x73, 0x20, 0x61, 0x74, 0x74, 0x72, 0x69, 0x62, 0x75, 0x74, 0x65, 0x64, 0x20, 0x74, 0x6F, 0x20, 0x61, 0x6E, 0x20, 0x75, 0x6E, 0x6B, 0x6E, 0x6F, 0x77, 0x6E, 0x20, 0x74, 0x79, 0x70, 0x65, 0x73, 0x65, 0x74, 0x74, 0x65, 0x72, 0x20, 0x69, 0x6E, 0x20, 0x74, 0x68, 0x65, 0x20, 0x31, 0x35, 0x74, 0x68, 0x20, 0x63, 0x65, 0x6E, 0x74, 0x75, 0x72, 0x79, 0x20, 0x77, 0x68, 0x6F, 0x20, 0x69, 0x73, 0x20, 0x74, 0x68, 0x6F, 0x75, 0x67, 0x68, 0x74, 0x20, 0x74, 0x6F, 0x20, 0x68, 0x61, 0x76, 0x65, 0x20, 0x73, 0x63, 0x72, 0x61, 0x6D, 0x62, 0x6C, 0x65, 0x64, 0x20, 0x70, 0x61, 0x72, 0x74, 0x73, 0x20, 0x6F, 0x66, 0x20, 0x43, 0x69, 0x63, 0x65, 0x72, 0x6F, 0x27, 0x73, 0x20, 0x44, 0x65, 0x20, 0x46, 0x69, 0x6E, 0x69, 0x62, 0x75, 0x73, 0x20, 0x42, 0x6F, 0x6E, 0x6F, 0x72, 0x75, 0x6D, 0x20, 0x65, 0x74, 0x20, 0x4D, 0x61, 0x6C, 0x6F, 0x72, 0x75, 0x6D, 0x20, 0x66, 0x6F, 0x72, 0x20, 0x75, 0x73, 0x65, 0x20, 0x69, 0x6E, 0x20, 0x61, 0x20, 0x74, 0x79, 0x70, 0x65, 0x20, 0x73, 0x70, 0x65, 0x63, 0x69, 0x6D, 0x65, 0x6E, 0x20, 0x62, 0x6F, 0x6F, 0x6B, 0x2E, 0x20, 0x49, 0x74, 0x20, 0x75, 0x73, 0x75, 0x61, 0x6C, 0x6C, 0x79, 0x20, 0x62, 0x65, 0x67, 0x69, 0x6E, 0x73, 0x20, 0x77, 0x69, 0x74, 0x68, ]; input } #[test] fn test_sha512_lorem_ipsum() { let msg = get_lorem_ipsum(); let res = sha512(msg).span(); assert_eq!( res, array![ 0xd5, 0xa2, 0xe1, 0x4e, 0xf4, 0x20, 0xf8, 0x2d, 0x68, 0x2b, 0x19, 0xc3, 0xd0, 0x70, 0xf4, 0x81, 0x14, 0xcb, 0xb9, 0x74, 0x7c, 0x7d, 0xb1, 0x15, 0xce, 0xa5, 0x41, 0x3e, 0xf8, 0xcb, 0x8f, 0xba, 0xc6, 0x90, 0x17, 0xc5, 0x17, 0x0f, 0x01, 0xc4, 0x77, 0xb3, 0xdf, 0x3d, 0xfb, 0x34, 0xd3, 0x50, 0x8f, 0xa0, 0xb2, 0xb1, 0x37, 0xd4, 0xcb, 0x54, 0x60, 0x9e, 0x63, 0x3d, 0x14, 0x45, 0x82, 0xc9, ] .span(), ); } #[test] fn test_sha512_size_one() { let mut arr: Array = array![49]; let res = sha512(arr).span(); assert_eq!( res, array![ 0x4d, 0xff, 0x4e, 0xa3, 0x40, 0xf0, 0xa8, 0x23, 0xf1, 0x5d, 0x3f, 0x4f, 0x01, 0xab, 0x62, 0xea, 0xe0, 0xe5, 0xda, 0x57, 0x9c, 0xcb, 0x85, 0x1f, 0x8d, 0xb9, 0xdf, 0xe8, 0x4c, 0x58, 0xb2, 0xb3, 0x7b, 0x89, 0x90, 0x3a, 0x74, 0x0e, 0x1e, 0xe1, 0x72, 0xda, 0x79, 0x3a, 0x6e, 0x79, 0xd5, 0x60, 0xe5, 0xf7, 0xf9, 0xbd, 0x05, 0x8a, 0x12, 0xa2, 0x80, 0x43, 0x3e, 0xd6, 0xfa, 0x46, 0x51, 0x0a, ] .span(), ); } #[test] fn test_size_zero() { let msg = array![]; let res = sha512(msg).span(); assert_eq!( res, array![ 0xcf, 0x83, 0xe1, 0x35, 0x7e, 0xef, 0xb8, 0xbd, 0xf1, 0x54, 0x28, 0x50, 0xd6, 0x6d, 0x80, 0x07, 0xd6, 0x20, 0xe4, 0x05, 0x0b, 0x57, 0x15, 0xdc, 0x83, 0xf4, 0xa9, 0x21, 0xd3, 0x6c, 0xe9, 0xce, 0x47, 0xd0, 0xd1, 0x3c, 0x5d, 0x85, 0xf2, 0xb0, 0xff, 0x83, 0x18, 0xd2, 0x87, 0x7e, 0xec, 0x2f, 0x63, 0xb9, 0x31, 0xbd, 0x47, 0x41, 0x7a, 0x81, 0xa5, 0x38, 0x32, 0x7a, 0xf9, 0x27, 0xda, 0x3e, ] .span(), ); } ================================================ FILE: src/src/tests/sp1_groth_16_tests.cairo ================================================ use garaga::apps::sp1::{deserialize_full_proof_with_hints_sp1, verify_groth16_sp1}; use snforge_std::fs::{FileTrait, read_txt}; #[test] fn test_verify_sp1_groth16_proof_bn254() { let file = FileTrait::new("src/tests/proof_calldata.txt"); let calldata = read_txt(@file).span(); assert(main(calldata).is_ok(), 'Proof verification failed'); } #[executable] pub fn main(full_proof_with_hints: Span) -> Result, felt252> { let fph = deserialize_full_proof_with_hints_sp1(full_proof_with_hints); return verify_groth16_sp1(fph); } ================================================ FILE: src/src/utils/calldata.cairo ================================================ use core::circuit::u384; use corelib_imports::bounded_int::downcast; pub use garaga::definitions::{E12D, G1Point, G2Point, MillerLoopResultScalingFactor, u288}; pub use garaga::groth16::{Groth16Proof, Groth16ProofRaw}; pub use garaga::pairing_check::{MPCheckHintBLS12_381, MPCheckHintBN254}; #[derive(Drop)] pub struct FullProofWithHintsBN254 { pub groth16_proof: Groth16Proof, pub mpcheck_hint: MPCheckHintBN254, pub msm_hint: Span, } #[derive(Drop, Debug)] pub struct FullProofWithHintsBLS12_381 { pub groth16_proof: Groth16Proof, pub mpcheck_hint: MPCheckHintBLS12_381, pub msm_hint: Span, } const U288_N_LIMBS: usize = 3; const U384_N_LIMBS: usize = 4; #[inline(always)] fn downcast_u288(l0: felt252, l1: felt252, l2: felt252) -> u288 { u288 { limb0: downcast(l0).unwrap(), limb1: downcast(l1).unwrap(), limb2: downcast(l2).unwrap(), } } #[inline(always)] fn downcast_u384(l0: felt252, l1: felt252, l2: felt252, l3: felt252) -> u384 { u384 { limb0: downcast(l0).unwrap(), limb1: downcast(l1).unwrap(), limb2: downcast(l2).unwrap(), limb3: downcast(l3).unwrap(), } } #[inline(always)] pub fn _deserialize_groth16_proof_points(ref serialized: Span) -> Groth16ProofRaw { let [ a_x_l0, a_x_l1, a_x_l2, a_x_l3, a_y_l0, a_y_l1, a_y_l2, a_y_l3, b_x0_l0, b_x0_l1, b_x0_l2, b_x0_l3, b_x1_l0, b_x1_l1, b_x1_l2, b_x1_l3, b_y0_l0, b_y0_l1, b_y0_l2, b_y0_l3, b_y1_l0, b_y1_l1, b_y1_l2, b_y1_l3, c_x_l0, c_x_l1, c_x_l2, c_x_l3, c_y_l0, c_y_l1, c_y_l2, c_y_l3, ] = (*serialized .multi_pop_front::<32>() .unwrap()) .unbox(); let a = G1Point { x: downcast_u384(a_x_l0, a_x_l1, a_x_l2, a_x_l3), y: downcast_u384(a_y_l0, a_y_l1, a_y_l2, a_y_l3), }; let b = G2Point { x0: downcast_u384(b_x0_l0, b_x0_l1, b_x0_l2, b_x0_l3), x1: downcast_u384(b_x1_l0, b_x1_l1, b_x1_l2, b_x1_l3), y0: downcast_u384(b_y0_l0, b_y0_l1, b_y0_l2, b_y0_l3), y1: downcast_u384(b_y1_l0, b_y1_l1, b_y1_l2, b_y1_l3), }; let c = G1Point { x: downcast_u384(c_x_l0, c_x_l1, c_x_l2, c_x_l3), y: downcast_u384(c_y_l0, c_y_l1, c_y_l2, c_y_l3), }; return Groth16ProofRaw { a: a, b: b, c: c }; } #[inline(always)] pub fn _deserialize_E12D_u288(ref serialized: Span) -> E12D { let [ w0l0, w0l1, w0l2, w1l0, w1l1, w1l2, w2l0, w2l1, w2l2, w3l0, w3l1, w3l2, w4l0, w4l1, w4l2, w5l0, w5l1, w5l2, w6l0, w6l1, w6l2, w7l0, w7l1, w7l2, w8l0, w8l1, w8l2, w9l0, w9l1, w9l2, w10l0, w10l1, w10l2, w11l0, w11l1, w11l2, ] = (*serialized .multi_pop_front::<36>() .unwrap()) .unbox(); E12D { w0: downcast_u288(w0l0, w0l1, w0l2), w1: downcast_u288(w1l0, w1l1, w1l2), w2: downcast_u288(w2l0, w2l1, w2l2), w3: downcast_u288(w3l0, w3l1, w3l2), w4: downcast_u288(w4l0, w4l1, w4l2), w5: downcast_u288(w5l0, w5l1, w5l2), w6: downcast_u288(w6l0, w6l1, w6l2), w7: downcast_u288(w7l0, w7l1, w7l2), w8: downcast_u288(w8l0, w8l1, w8l2), w9: downcast_u288(w9l0, w9l1, w9l2), w10: downcast_u288(w10l0, w10l1, w10l2), w11: downcast_u288(w11l0, w11l1, w11l2), } } #[inline(always)] pub fn deserialize_full_proof_with_hints_bn254( mut serialized: Span, ) -> FullProofWithHintsBN254 { let groth16_proof_raw = _deserialize_groth16_proof_points(ref serialized); let n_public_inputs: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mut public_inputs = array![]; for _ in 0..n_public_inputs { public_inputs .append( u256 { low: (*serialized.pop_front().unwrap()).try_into().unwrap(), high: (*serialized.pop_front().unwrap()).try_into().unwrap(), }, ); } let groth16_proof = Groth16Proof { raw: groth16_proof_raw, public_inputs: public_inputs.span(), }; let mpcheck_hint = _deserialize_mpcheck_hint_bn254(ref serialized); let msm_hint = serialized; return FullProofWithHintsBN254 { groth16_proof, mpcheck_hint, msm_hint }; } #[inline(always)] pub fn _deserialize_mpcheck_hint_bn254(ref serialized: Span) -> MPCheckHintBN254 { let lambda_root = _deserialize_E12D_u288(ref serialized); let lambda_root_inverse = _deserialize_E12D_u288(ref serialized); let [ w0_l0, w0_l1, w0_l2, w2_l0, w2_l1, w2_l2, w4_l0, w4_l1, w4_l2, w6_l0, w6_l1, w6_l2, w8_l0, w8_l1, w8_l2, w10_l0, w10_l1, w10_l2, ] = (*serialized .multi_pop_front::<18>() .unwrap()) .unbox(); // full_len -= 18; // assert(full_len == serialized.len(), 'F'); let w = MillerLoopResultScalingFactor { w0: downcast_u288(w0_l0, w0_l1, w0_l2), w2: downcast_u288(w2_l0, w2_l1, w2_l2), w4: downcast_u288(w4_l0, w4_l1, w4_l2), w6: downcast_u288(w6_l0, w6_l1, w6_l2), w8: downcast_u288(w8_l0, w8_l1, w8_l2), w10: downcast_u288(w10_l0, w10_l1, w10_l2), }; // usize_assert_eq(mpcheck_hint.Ris.len(), 34); // 34 * 12 * 3 = 1224 let mut ris_slice = serialized.slice(1, 1224); // println!("ris_slice.len(): {}", ris_slice.len()); let end = serialized.len(); serialized = serialized.slice(1225, end - 1224 - 1); // println!("serialized.len(): {}", serialized.len()); let mut Ris = array![]; while let Option::Some(ri) = ris_slice.multi_pop_front::<36>() { let [ w0l0, w0l1, w0l2, w1l0, w1l1, w1l2, w2l0, w2l1, w2l2, w3l0, w3l1, w3l2, w4l0, w4l1, w4l2, w5l0, w5l1, w5l2, w6l0, w6l1, w6l2, w7l0, w7l1, w7l2, w8l0, w8l1, w8l2, w9l0, w9l1, w9l2, w10l0, w10l1, w10l2, w11l0, w11l1, w11l2, ] = (*ri) .unbox(); Ris .append( E12D { w0: downcast_u288(w0l0, w0l1, w0l2), w1: downcast_u288(w1l0, w1l1, w1l2), w2: downcast_u288(w2l0, w2l1, w2l2), w3: downcast_u288(w3l0, w3l1, w3l2), w4: downcast_u288(w4l0, w4l1, w4l2), w5: downcast_u288(w5l0, w5l1, w5l2), w6: downcast_u288(w6l0, w6l1, w6l2), w7: downcast_u288(w7l0, w7l1, w7l2), w8: downcast_u288(w8l0, w8l1, w8l2), w9: downcast_u288(w9l0, w9l1, w9l2), w10: downcast_u288(w10l0, w10l1, w10l2), w11: downcast_u288(w11l0, w11l1, w11l2), }, ) } // usize_assert_eq(mpcheck_hint.big_Q.len(), 190); let mut big_q_slice = serialized.slice(1, 190 * 3); let end = serialized.len(); serialized = serialized.slice(190 * 3 + 1, end - 190 * 3 - 1); let mut big_q = array![]; while let Option::Some(q) = big_q_slice.multi_pop_front::<3>() { let [l0, l1, l2] = (*q).unbox(); big_q.append(downcast_u288(l0, l1, l2)) } let z = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mpcheck_hint = MPCheckHintBN254 { lambda_root: lambda_root, lambda_root_inverse: lambda_root_inverse, w: w, Ris: Ris.span(), big_Q: big_q, z: z, }; return mpcheck_hint; } pub fn deserialize_mpcheck_hint_bls12_381(ref serialized: Span) -> MPCheckHintBLS12_381 { let [ w0l0, w0l1, w0l2, w0l3, w1l0, w1l1, w1l2, w1l3, w2l0, w2l1, w2l2, w2l3, w3l0, w3l1, w3l2, w3l3, w4l0, w4l1, w4l2, w4l3, w5l0, w5l1, w5l2, w5l3, w6l0, w6l1, w6l2, w6l3, w7l0, w7l1, w7l2, w7l3, w8l0, w8l1, w8l2, w8l3, w9l0, w9l1, w9l2, w9l3, w10l0, w10l1, w10l2, w10l3, w11l0, w11l1, w11l2, w11l3, ] = (*serialized .multi_pop_front::<48>() .unwrap()) .unbox(); let lambda_root_inverse = E12D { w0: downcast_u384(w0l0, w0l1, w0l2, w0l3), w1: downcast_u384(w1l0, w1l1, w1l2, w1l3), w2: downcast_u384(w2l0, w2l1, w2l2, w2l3), w3: downcast_u384(w3l0, w3l1, w3l2, w3l3), w4: downcast_u384(w4l0, w4l1, w4l2, w4l3), w5: downcast_u384(w5l0, w5l1, w5l2, w5l3), w6: downcast_u384(w6l0, w6l1, w6l2, w6l3), w7: downcast_u384(w7l0, w7l1, w7l2, w7l3), w8: downcast_u384(w8l0, w8l1, w8l2, w8l3), w9: downcast_u384(w9l0, w9l1, w9l2, w9l3), w10: downcast_u384(w10l0, w10l1, w10l2, w10l3), w11: downcast_u384(w11l0, w11l1, w11l2, w11l3), }; let [ w0_l0, w0_l1, w0_l2, w0_l3, w2_l0, w2_l1, w2_l2, w2_l3, w4_l0, w4_l1, w4_l2, w4_l3, w6_l0, w6_l1, w6_l2, w6_l3, w8_l0, w8_l1, w8_l2, w8_l3, w10_l0, w10_l1, w10_l2, w10_l3, ] = (*serialized .multi_pop_front::<24>() .unwrap()) .unbox(); let w = MillerLoopResultScalingFactor { w0: downcast_u384(w0_l0, w0_l1, w0_l2, w0_l3), w2: downcast_u384(w2_l0, w2_l1, w2_l2, w2_l3), w4: downcast_u384(w4_l0, w4_l1, w4_l2, w4_l3), w6: downcast_u384(w6_l0, w6_l1, w6_l2, w6_l3), w8: downcast_u384(w8_l0, w8_l1, w8_l2, w8_l3), w10: downcast_u384(w10_l0, w10_l1, w10_l2, w10_l3), }; // assert!(hint.Ris.len() == 35, "Wrong Number of Ris for BLS12-381 3-Pairs Paring check"); // 35 * 12 * 4 = 1680 let end_ris = 1680; let mut ris_slice = serialized.slice(1, end_ris); let end = serialized.len(); serialized = serialized.slice(end_ris + 1, end - end_ris - 1); let mut Ris = array![]; while let Option::Some(ri) = ris_slice.multi_pop_front::<48>() { let [ w0l0, w0l1, w0l2, w0l3, w1l0, w1l1, w1l2, w1l3, w2l0, w2l1, w2l2, w2l3, w3l0, w3l1, w3l2, w3l3, w4l0, w4l1, w4l2, w4l3, w5l0, w5l1, w5l2, w5l3, w6l0, w6l1, w6l2, w6l3, w7l0, w7l1, w7l2, w7l3, w8l0, w8l1, w8l2, w8l3, w9l0, w9l1, w9l2, w9l3, w10l0, w10l1, w10l2, w10l3, w11l0, w11l1, w11l2, w11l3, ] = (*ri) .unbox(); Ris .append( E12D { w0: downcast_u384(w0l0, w0l1, w0l2, w0l3), w1: downcast_u384(w1l0, w1l1, w1l2, w1l3), w2: downcast_u384(w2l0, w2l1, w2l2, w2l3), w3: downcast_u384(w3l0, w3l1, w3l2, w3l3), w4: downcast_u384(w4l0, w4l1, w4l2, w4l3), w5: downcast_u384(w5l0, w5l1, w5l2, w5l3), w6: downcast_u384(w6l0, w6l1, w6l2, w6l3), w7: downcast_u384(w7l0, w7l1, w7l2, w7l3), w8: downcast_u384(w8l0, w8l1, w8l2, w8l3), w9: downcast_u384(w9l0, w9l1, w9l2, w9l3), w10: downcast_u384(w10l0, w10l1, w10l2, w10l3), w11: downcast_u384(w11l0, w11l1, w11l2, w11l3), }, ) } let big_q_len: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let biq_len_n_limbs = big_q_len * 4; let mut big_q_slice = serialized.slice(0, biq_len_n_limbs); serialized = serialized.slice(biq_len_n_limbs, serialized.len() - biq_len_n_limbs); let mut big_q = array![]; while let Option::Some(q) = big_q_slice.multi_pop_front::<4>() { let [l0, l1, l2, l3] = (*q).unbox(); big_q.append(downcast_u384(l0, l1, l2, l3)) } let z = *serialized.pop_front().unwrap(); let mpcheck_hint = MPCheckHintBLS12_381 { lambda_root_inverse: lambda_root_inverse, w: w, Ris: Ris.span(), big_Q: big_q, z: z, }; return mpcheck_hint; } pub fn deserialize_full_proof_with_hints_bls12_381( mut serialized: Span, ) -> FullProofWithHintsBLS12_381 { let groth16_proof_raw = _deserialize_groth16_proof_points(ref serialized); let n_public_inputs: u32 = (*serialized.pop_front().unwrap()).try_into().unwrap(); let mut public_inputs = array![]; for _ in 0..n_public_inputs { public_inputs .append( u256 { low: (*serialized.pop_front().unwrap()).try_into().unwrap(), high: (*serialized.pop_front().unwrap()).try_into().unwrap(), }, ); } // full_len -= (1 + 2 * n_public_inputs); // assert(full_len == serialized.len(), 'C'); let groth16_proof = Groth16Proof { raw: groth16_proof_raw, public_inputs: public_inputs.span(), }; // Deserialize mpcheck_hint let mpcheck_hint = deserialize_mpcheck_hint_bls12_381(ref serialized); let msm_hint = serialized; return FullProofWithHintsBLS12_381 { groth16_proof, mpcheck_hint, msm_hint }; } ================================================ FILE: src/src/utils/hashing.cairo ================================================ use core::circuit::u384; pub use core::poseidon::hades_permutation; use garaga::definitions::{E12D, G1G2Pair, G1Point, MillerLoopResultScalingFactor, u288}; pub const TWO_POW_96: felt252 = 79228162514264337593543950336; #[derive(Copy, Drop)] pub struct PoseidonState { pub s0: felt252, pub s1: felt252, pub s2: felt252, } #[inline(always)] pub fn hash_u384(elmt: u384, base: felt252, s: PoseidonState) -> PoseidonState { let in_1 = s.s0 + elmt.limb0.into() + base * elmt.limb1.into(); let in_2 = s.s1 + elmt.limb2.into() + base * elmt.limb3.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); return PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; } #[inline(always)] pub fn hash_u288(elmt: u288, base: felt252, s: PoseidonState) -> PoseidonState { let in_1 = s.s0 + elmt.limb0.into() + base * elmt.limb1.into(); let in_2 = s.s1 + elmt.limb2.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); return PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; } #[inline(always)] pub fn hash_quadruple_u288( elmt0: u288, elmt1: u288, elmt2: u288, elmt3: u288, base: felt252, s: PoseidonState, ) -> PoseidonState { let in_1 = s.s0 + elmt0.limb0.into() + base * elmt0.limb1.into(); let in_2 = s.s1 + elmt0.limb2.into() + base * elmt1.limb0.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); let in_1 = _s0 + elmt1.limb1.into() + base * elmt1.limb2.into(); let in_2 = _s1 + elmt2.limb0.into() + base * elmt2.limb1.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); let in_1 = _s0 + elmt2.limb2.into() + base * elmt3.limb0.into(); let in_2 = _s1 + elmt3.limb1.into() + base * elmt3.limb2.into(); let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2); return PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; } // Apply sponge construction to a transcript of u384 elements #[inline(always)] pub fn hash_u384_transcript(transcript: Span, mut s: PoseidonState) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 for elmt in transcript { s = hash_u384(*elmt, base, s); } return s; } #[inline(always)] pub fn hash_u288_transcript(transcript: Span, mut s: PoseidonState) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let (n_quadruples, rest) = DivRem::div_rem(transcript.len(), 4); let n_quadruples_index = n_quadruples * 4; let mut transcript_quadruples = transcript.slice(0, n_quadruples_index); while let Some(fours) = transcript_quadruples.multi_pop_front::<4>() { let [elmt0, elmt1, elmt2, elmt3] = fours.unbox(); let _s = hash_quadruple_u288(elmt0, elmt1, elmt2, elmt3, base, s); s = _s; } let mut rest_transcript = transcript.slice(n_quadruples_index, rest); for elmt in rest_transcript { s = hash_u288(*elmt, base, s); } return s; } // Apply sponge construction to a E12D element from an initial state (s0, s1, s2) pub fn hash_E12D_u384(elmt: E12D, mut s: PoseidonState) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let _s = hash_u384(elmt.w0, base, s); let _s = hash_u384(elmt.w1, base, _s); let _s = hash_u384(elmt.w2, base, _s); let _s = hash_u384(elmt.w3, base, _s); let _s = hash_u384(elmt.w4, base, _s); let _s = hash_u384(elmt.w5, base, _s); let _s = hash_u384(elmt.w6, base, _s); let _s = hash_u384(elmt.w7, base, _s); let _s = hash_u384(elmt.w8, base, _s); let _s = hash_u384(elmt.w9, base, _s); let _s = hash_u384(elmt.w10, base, _s); let _s = hash_u384(elmt.w11, base, _s); return _s; } pub fn hash_E12D_u288(elmt: E12D, mut s: PoseidonState) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let _s = hash_quadruple_u288(elmt.w0, elmt.w1, elmt.w2, elmt.w3, base, s); let _s = hash_quadruple_u288(elmt.w4, elmt.w5, elmt.w6, elmt.w7, base, _s); let _s = hash_quadruple_u288(elmt.w8, elmt.w9, elmt.w10, elmt.w11, base, _s); return _s; } // Hash a E12D element known to be 1 pub fn hash_E12D_one_u384(s: PoseidonState) -> PoseidonState { let in_1 = s.s0 + 1; let in_2 = s.s1; let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); // 1 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 2 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 3 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 4 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 5 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 6 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 7 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 8 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 9 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 10 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 11 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 12 return PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; } // Hash a E12D element known to be 1 pub fn hash_E12D_one_u288(s: PoseidonState) -> PoseidonState { let in_1 = s.s0 + 1; let in_2 = s.s1; let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s.s2); // 1 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 2 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 3 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 4 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 5 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 6 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 7 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 8 let (_s0, _s1, _s2) = hades_permutation(_s0, _s1, _s2); // 9 return PoseidonState { s0: _s0, s1: _s1, s2: _s2 }; } // Apply sponge construction to a MillerLoopResultScalingFactor element from an initial state (s0, // s1, s2) #[inline(always)] pub fn hash_MillerLoopResultScalingFactor_u384( elmt: MillerLoopResultScalingFactor, s: PoseidonState, ) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let _s = hash_u384(elmt.w0, base, s); let _s = hash_u384(elmt.w2, base, _s); let _s = hash_u384(elmt.w4, base, _s); let _s = hash_u384(elmt.w6, base, _s); let _s = hash_u384(elmt.w8, base, _s); let _s = hash_u384(elmt.w10, base, _s); return _s; } #[inline(always)] pub fn hash_MillerLoopResultScalingFactor_u288( elmt: MillerLoopResultScalingFactor, s: PoseidonState, ) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let _s = hash_quadruple_u288(elmt.w0, elmt.w2, elmt.w4, elmt.w6, base, s); let _s = hash_u288(elmt.w8, base, _s); let _s = hash_u288(elmt.w10, base, _s); return _s; } // Apply sponge construction to a sequence of E12D elements from an initial state (s0, s1, s2) #[inline(always)] pub fn hash_E12D_u384_transcript( transcript: Span>, mut s: PoseidonState, ) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 for elmt in transcript { let elmt = *elmt; let _s = hash_u384(elmt.w0, base, s); let _s = hash_u384(elmt.w1, base, _s); let _s = hash_u384(elmt.w2, base, _s); let _s = hash_u384(elmt.w3, base, _s); let _s = hash_u384(elmt.w4, base, _s); let _s = hash_u384(elmt.w5, base, _s); let _s = hash_u384(elmt.w6, base, _s); let _s = hash_u384(elmt.w7, base, _s); let _s = hash_u384(elmt.w8, base, _s); let _s = hash_u384(elmt.w9, base, _s); let _s = hash_u384(elmt.w10, base, _s); let _s = hash_u384(elmt.w11, base, _s); s = _s; } return s; } #[inline(always)] pub fn hash_E12D_u288_transcript( transcript: Span>, mut s: PoseidonState, ) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 for elmt in transcript { let elmt = *elmt; let _s = hash_quadruple_u288(elmt.w0, elmt.w1, elmt.w2, elmt.w3, base, s); let _s = hash_quadruple_u288(elmt.w4, elmt.w5, elmt.w6, elmt.w7, base, _s); let _s = hash_quadruple_u288(elmt.w8, elmt.w9, elmt.w10, elmt.w11, base, _s); s = _s; } return s; } // Apply sponge construction to a pair of G1 and G2 points from an initial state (s0, s1, s2) // #[inline(always)] pub fn hash_G1G2Pair(pair: G1G2Pair, s: PoseidonState) -> PoseidonState { let base: felt252 = TWO_POW_96; // 2**96 let _s = hash_u384(pair.p.x, base, s); let _s = hash_u384(pair.p.y, base, _s); let _s = hash_u384(pair.q.x0, base, _s); let _s = hash_u384(pair.q.x1, base, _s); let _s = hash_u384(pair.q.y0, base, _s); let _s = hash_u384(pair.q.y1, base, _s); return _s; } pub fn hash_G1Point(point: G1Point) -> felt252 { let base: felt252 = TWO_POW_96; // 2**96 let in_1: felt252 = point.x.limb0.into() + base * point.x.limb1.into(); let in_2: felt252 = point.x.limb2.into() + base * point.x.limb3.into(); let (s0, s1, s2) = hades_permutation(in_1, in_2, 2); let in_1 = s0 + point.y.limb0.into() + base * point.y.limb1.into(); let in_2 = s1 + point.y.limb2.into() + base * point.y.limb3.into(); let (s0, _, _) = hades_permutation(in_1, in_2, s2); return s0; } ================================================ FILE: src/src/utils/neg_3.cairo ================================================ use core::circuit::u384; use corelib_imports::bounded_int::{ AddHelper, BoundedInt, DivRemHelper, UnitInt, bounded_int, upcast, }; use garaga::definitions::get_min_one; const STARK_MINUS_1_HALF: u256 = 180925139433306560684866139154753505281553607665798349986546028067936010240; // (STARK-1)//2 // Returns the sign of a felt252. // num is considered positive if num <= (STARK-1)//2 // num is considered negative if num > (STARK-1)//2 pub fn sign(num: felt252) -> felt252 { if num.into() <= STARK_MINUS_1_HALF { return 1; } else { return -1; } } // Maps a sign returned by sign() to a u384 modulo the prime of a given curve index. pub fn sign_to_u384(sign: felt252, curve_index: usize) -> u384 { if (sign == -1) { return get_min_one(curve_index); } else { return u384 { limb0: 1, limb1: 0, limb2: 0, limb3: 0 }; } } pub fn u256_array_to_low_high_epns( scalars: Span, scalars_digits_decompositions: Option, Span)>>, ) -> (Array<(felt252, felt252, felt252, felt252)>, Array<(felt252, felt252, felt252, felt252)>) { let mut epns_low: Array<(felt252, felt252, felt252, felt252)> = ArrayTrait::new(); let mut epns_high: Array<(felt252, felt252, felt252, felt252)> = ArrayTrait::new(); match scalars_digits_decompositions { Option::None(_) => { for scalar in scalars { epns_low.append(scalar_to_epns(*scalar.low)); epns_high.append(scalar_to_epns(*scalar.high)); } }, Option::Some(decompositions) => { let mut i = 0; for scalar in scalars { match decompositions.get(i) { Option::Some(decompositions) => { let (decomposition_low, decomposition_high) = decompositions.unbox(); epns_low .append(scalar_to_epns_with_digits(*scalar.low, *decomposition_low)); epns_high .append(scalar_to_epns_with_digits(*scalar.high, *decomposition_high)); }, Option::None(_) => { epns_low.append(scalar_to_epns(*scalar.low)); epns_high.append(scalar_to_epns(*scalar.high)); }, } i += 1; } }, } return (epns_low, epns_high); } pub fn u128_array_to_epns( scalars: Span, scalars_digits_decompositions: Option>>, ) -> Array<(felt252, felt252, felt252, felt252)> { let mut epns: Array<(felt252, felt252, felt252, felt252)> = ArrayTrait::new(); match scalars_digits_decompositions { Option::None(_) => { for scalar in scalars { epns.append(scalar_to_epns(*scalar)); } }, Option::Some(decompositions) => { let mut i = 0; for scalar in scalars { match decompositions.get(i) { Option::Some(decomposition) => { let decomposition = decomposition.unbox(); epns.append(scalar_to_epns_with_digits(*scalar, *decomposition)); }, Option::None(_) => { epns.append(scalar_to_epns(*scalar)); }, } i += 1; } }, } return epns; } const THREE: felt252 = 3; const THREE_NZ_TYPED: NonZero> = 3; const POW128_DIV_3: felt252 = 113427455640312821154458202477256070485; // ((2^128-1) // 3) const POW128: felt252 = 0x100000000000000000000000000000000; impl DivRemU128By3 of DivRemHelper, UnitInt> { type DivT = BoundedInt<0, { POW128_DIV_3 }>; type RemT = BoundedInt<0, { THREE - 1 }>; } impl AddOneHelper of AddHelper, BoundedInt<0, 1>> { type Result = BoundedInt<0, { POW128_DIV_3 + 1 }>; } // From a 128 bit scalar, returns the positive and negative multiplicities of the scalar in base // (-3) // scalar = sum(digits[i] * (-3)^i for i in [0, 81]) // scalar = sum_p - sum_n // Where sum_p = sum(digits[i] * (-3)^i for i in [0, 81] if digits[i]==1) // And sum_n = sum(digits[i] * (-3)^i for i in [0, 81] if digits[i]==-1) // Returns (abs(sum_p), abs(sum_n), p_sign, n_sign) pub fn scalar_to_epns(mut _scalar: u128) -> (felt252, felt252, felt252, felt252) { let mut sum_p: felt252 = 0; let mut sum_n: felt252 = 0; let mut base_power: felt252 = 1; // Init to (-3)^0 let mut scalar: BoundedInt<0, { POW128 - 1 }> = upcast(_scalar); while scalar != 0 { let (q0, r0) = bounded_int::div_rem(scalar, THREE_NZ_TYPED); let r0: felt252 = r0.into(); if r0 == 0 { scalar = upcast(q0); } else if r0 == 2 { scalar = upcast(bounded_int::add(q0, 1)); sum_n += base_power; } else { scalar = upcast(q0); sum_p += base_power; } base_power = base_power * (-3); let (q1, r1) = bounded_int::div_rem(scalar, THREE_NZ_TYPED); let r1: felt252 = r1.into(); if r1 == 0 { scalar = upcast(q1); } else if r1 == 2 { scalar = upcast(bounded_int::add(q1, 1)); sum_p += base_power; } else { scalar = upcast(q1); sum_n += base_power; } base_power = base_power * (-3); } let sign_p = sign(sum_p); let sign_n = sign(sum_n); return (sign_p * sum_p, sign_n * sum_n, sign_p, sign_n); } pub fn scalar_to_epns_with_digits( scalar: u128, mut digits: Span, ) -> (felt252, felt252, felt252, felt252) { assert!(digits.len() <= 82, "The number of digits must be <= 82 for u128"); let mut sum_p = 0; let mut sum_n = 0; let mut base_power = 1; // Init to (-3)^0 while let Option::Some(digit) = digits.pop_front() { let digit = *digit; if digit != 0 { if digit == 1 { sum_p += base_power; } else { sum_n += base_power; } } base_power = base_power * (-3); } assert!( scalar.into() == sum_p - sum_n, "The scalar must be equal to the sum of the positive and negative digits", ); let sign_p = sign(sum_p); let sign_n = sign(sum_n); return (sign_p * sum_p, sign_n * sum_n, sign_p, sign_n); } #[cfg(test)] mod tests { use super::scalar_to_epns; #[test] fn test_scalar_to_epns() { let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns(12); assert_eq!(sum_p, 9); assert_eq!(sum_n, 3); assert_eq!(sign_p, 1); assert_eq!(sign_n, -1); let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns(35); assert_eq!(sum_p, 9); assert_eq!(sum_n, 26); assert_eq!(sign_p, 1); assert_eq!(sign_n, -1); let (sum_p, sum_n, _, _) = scalar_to_epns(0); assert_eq!(sum_p, 0); assert_eq!(sum_n, 0); let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns( 170141183460469231731687303715884105728, ); //2**127 assert_eq!(sum_p, 164253760949568696627221936579612523510); assert_eq!(sum_n, 5887422510900535104465367136271582218); //using STARK field assert_eq!(sign_p, 1); assert_eq!(sign_n, -1); let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns( 85070591730234615865843651857942052864, ); //2 **126 assert_eq!(sum_p, 97865891762673628272143863189949020615); assert_eq!(sum_n, 12795300032439012406300211332006967751); assert_eq!(sign_p, 1); assert_eq!(sign_n, 1); let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns( 85070591730234615865843651857942052874, ); //2 **126 + 10 assert_eq!(sum_p, 97865891762673628272143863189949020623); assert_eq!(sum_n, 12795300032439012406300211332006967749); assert_eq!(sign_p, 1); assert_eq!(sign_n, 1); } #[test] fn test_scalar_to_epns_single() { let (sum_p, sum_n, sign_p, sign_n) = scalar_to_epns( 170141183460469231731687303715884105728, ); //2**127 assert_eq!(sum_p, 164253760949568696627221936579612523510); assert_eq!(sum_n, 5887422510900535104465367136271582218); assert_eq!(sign_p, 1); assert_eq!(sign_n, -1); } } ================================================ FILE: tests/benchmarks_compiled.py ================================================ import inspect import pandas as pd from tabulate import tabulate from garaga.curves import CurveID from hydra.garaga.precompiled_circuits.all_circuits import ALL_CAIRO_CIRCUITS def benchmark_all_cairo_circuits(): """ For each circuit class in ALL_CAIRO_CIRCUITS: - Instantiate the circuit (with any params, for each listed curve_id). - Safe-construct them by removing any kwargs that aren't accepted by their __init__. - finalize the circuit (if not already done). - gather the summary info (MULMOD, ADDMOD, etc.). Then we mark circuits as "GENERIC" if they have the same MULMOD/ADDMOD on multiple curves. """ results = [] for circuit_id, circuit_info in ALL_CAIRO_CIRCUITS.items(): # If no curve_ids present, default to [BN254, BLS12_381] curve_ids = circuit_info.get("curve_ids", [CurveID.BN254, CurveID.BLS12_381]) # If params is None, turn that into a list of length 1 containing None params_list = circuit_info["params"] or [None] circuit_class = circuit_info["class"] # Use inspect to see valid parameters on the circuit class's __init__ init_signature = inspect.signature(circuit_class.__init__) valid_params = set(init_signature.parameters.keys()) for curve_id in curve_ids: for param in params_list: # Build default kwargs kwargs = { "name": f"{circuit_class.__name__}_bench", "curve_id": curve_id.value, "auto_run": True, "compilation_mode": 1, } # Possibly update with param dict if isinstance(param, dict): kwargs.update(param) # Remove any keys the constructor doesn't accept safe_kwargs = {k: v for k, v in kwargs.items() if k in valid_params} # Now instantiate the circuit safely circuit_instance = circuit_class(**safe_kwargs) # Summarize summary = circuit_instance.circuit.summarize() # Build row for DataFrame, including separate columns for the class, param, curve row = { "circuit_class": circuit_class.__name__, "param": str(param) if param else "", "curve_id": curve_id.name, "MULMOD": summary.get("MULMOD", 0), "ADDMOD": summary.get("ADDMOD", 0), } results.append(row) # Create a DataFrame df = pd.DataFrame(results) # If you want to compute a simple "~steps" metric: costs = {"MULMOD": 8, "ADDMOD": 4} def compute_steps(row): return sum(row[op] * wt for op, wt in costs.items()) df["~steps"] = df.apply(compute_steps, axis=1) # Sort by ~steps first df.sort_values(by="~steps", inplace=True, ignore_index=True) # 1) Group by (circuit_class, param, MULMOD, ADDMOD). # 2) If multiple distinct curves appear in a group, mark curve_id as "GENERIC". df["curve_id"] = df.groupby(["circuit_class", "param", "MULMOD", "ADDMOD"])[ "curve_id" ].transform(lambda g: "GENERIC" if g.nunique() > 1 else g) # Drop duplicates, so "GENERIC" appears only once per group df_unique = df.drop_duplicates( subset=["circuit_class", "param", "MULMOD", "ADDMOD", "curve_id"], keep="first" ) print("\n===== Benchmark Summaries (Filtered) =====\n") print(tabulate(df_unique, headers="keys", tablefmt="github", showindex=False)) if __name__ == "__main__": benchmark_all_cairo_circuits() ================================================ FILE: tests/benchmarks_manual.py ================================================ import random from random import randint from garaga.algebra import ModuloCircuitElement from garaga.curves import CURVES, STARK, Curve, CurveID, PyFelt, get_base_field from garaga.extension_field_modulo_circuit import ExtensionFieldModuloCircuit, WriteOps from garaga.hints import neg_3 from garaga.hints.ecip import zk_ecip_hint from garaga.hints.io import padd_function_felt, split_128 from garaga.hints.tower_backup import E12 from garaga.points import G1G2Pair, G1Point, G2Point, direct_to_tower from garaga.precompiled_circuits.ec import BasicEC, DerivePointFromX, ECIPCircuits from garaga.precompiled_circuits.final_exp import FinalExpTorusCircuit, test_final_exp from garaga.precompiled_circuits.multi_miller_loop import MultiMillerLoopCircuit random.seed(0) def test_extf_mul(curve_id: CurveID, extension_degree: int): curve: Curve = CURVES[curve_id.value] p = curve.p X = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] Y = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] circuit = ExtensionFieldModuloCircuit( f"Fp{extension_degree} MUL", curve_id=curve_id.value, extension_degree=extension_degree, hash_input=False, ) X = circuit.write_elements(X, WriteOps.INPUT) Y = circuit.write_elements(Y, WriteOps.INPUT) circuit.extf_mul([X, Y], extension_degree) circuit.finalize_circuit() return circuit.summarize(), circuit.ops_counter def test_extf_square(curve_id: CurveID, extension_degree: int): curve: Curve = CURVES[curve_id.value] p = curve.p X = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] circuit = ExtensionFieldModuloCircuit( f"Fp{extension_degree} SQUARE", curve_id=curve_id.value, extension_degree=extension_degree, hash_input=False, ) X = circuit.write_elements(X, WriteOps.INPUT) circuit.extf_mul([X, X], extension_degree) circuit.finalize_circuit() return circuit.summarize(), circuit.ops_counter def test_extf_mul_circuit_full(curve_id: CurveID, extension_degree: int): curve: Curve = CURVES[curve_id.value] p = curve.p X = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] circuit = ExtensionFieldModuloCircuit( f"{curve_id.name}_mul_zpow_verif_Fp{extension_degree}", curve_id=curve_id.value, extension_degree=extension_degree, ) X = circuit.write_elements(X, WriteOps.INPUT) circuit.extf_mul(X, X, extension_degree) circuit.finalize_circuit() circuit.values_segment = circuit.values_segment.non_interactive_transform() circuit.print_value_segment() return circuit.summarize(), circuit.ops_counter def test_square_torus_amortized(curve_id: CurveID, extension_degree: int): curve: Curve = CURVES[curve_id.value] p = curve.p X = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] circuit = FinalExpTorusCircuit( f"Fp{extension_degree} SQUARE_TORUS", curve_id=curve_id.value, extension_degree=extension_degree, hash_input=False, ) X = circuit.write_elements(X, WriteOps.INPUT) circuit.square_torus(X) circuit.finalize_circuit() return circuit.summarize(), circuit.ops_counter def test_mul_torus(curve_id: CurveID, extension_degree: int): curve: Curve = CURVES[curve_id.value] p = curve.p X = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] Y = [PyFelt(randint(0, p - 1), p) for _ in range(extension_degree)] circuit = FinalExpTorusCircuit( f"Fp{extension_degree} MUL_TORUS", curve_id=curve_id.value, extension_degree=extension_degree, hash_input=False, ) X = circuit.write_elements(X, WriteOps.INPUT) Y = circuit.write_elements(Y, WriteOps.INPUT) circuit.mul_torus(X, Y) circuit.finalize_circuit() return circuit.summarize(), circuit.ops_counter def test_final_exp_circuit(curve_id: CurveID): part1, part2 = test_final_exp(curve_id) summ1 = part1.summarize() summ1["circuit"] = summ1["circuit"] summ2 = part2.summarize() summ2["circuit"] = summ2["circuit"] # part1.print_value_segment() # part1.compile_circuit() summ = { "circuit": summ1["circuit"], "MULMOD": summ1["MULMOD"] + summ2["MULMOD"], "ADDMOD": summ1["ADDMOD"] + summ2["ADDMOD"], "ASSERT_EQ": summ1["ASSERT_EQ"] + summ2["ASSERT_EQ"], "POSEIDON": summ1["POSEIDON"] + summ2["POSEIDON"], "RLC": summ1["RLC"] + summ2["RLC"], } ops_counter = { key: part1.ops_counter.get(key) + part2.ops_counter.get(key) for key in set(part1.ops_counter) | set(part2.ops_counter) if key != "Circuit" } ops_counter["Circuit"] = part1.ops_counter["Circuit"] return summ, ops_counter def test_miller_n(curve_id, n): order = CURVES[curve_id.value].n field = get_base_field(curve_id.value) pair_list = [] pairs = [] for k in range(n): n1, n2 = randint(1, order), randint(1, order) p1, p2 = G1Point.get_nG(curve_id, n1), G2Point.get_nG(curve_id, n2) pair_list.append(G1G2Pair(p1, p2)) pairs.extend([p1.x, p1.y, p2.x[0], p2.x[1], p2.y[0], p2.y[1]]) c = MultiMillerLoopCircuit(f"Miller n={n} {curve_id.name}", curve_id.value, n) c.write_p_and_q_raw([field(x) for x in pairs]) f = c.miller_loop(n_pairs=n) f_tower = E12( direct_to_tower([x.felt for x in f], curve_id.value, 12), curve_id.value ) cofactor = CURVES[curve_id.value].final_exp_cofactor f = f_tower ** ( cofactor * (CURVES[curve_id.value].p ** 12 - 1) // CURVES[curve_id.value].n ) res = G1G2Pair.pair(pair_list).value_coeffs c.finalize_circuit() for i, (rg, fv) in enumerate(zip(res, f.value_coeffs)): assert rg == fv, f"Mismatch at index {i}: {rg=} != {fv=}, {curve_id} {n}" return c.summarize(), c.ops_counter def test_derive_point_from_x(curve_id: CurveID): field = get_base_field(curve_id.value) c = DerivePointFromX( "Derive Point From X", curve_id.value, ) x = c.write_element(field(randint(0, STARK - 1))) a = c.write_element(field(CURVES[curve_id.value].a)) b = c.write_element(field(CURVES[curve_id.value].b)) g = c.write_element(field(CURVES[curve_id.value].fp_generator)) c._derive_point_from_x(x, a, b, g) return c.summarize(), None def test_msm_n_points(curve_id: CurveID, n: int): order = CURVES[curve_id.value].n field = get_base_field(curve_id.value) points_g1 = [G1Point.get_nG(curve_id, i + 1) for i in range(n)] points_values = [(p.x, p.y) for p in points_g1] scalars = [randint(1, order) for _ in range(n)] scalars_split = [split_128(s) for s in scalars] scalars_low, scalars_high = zip(*scalars_split) circuit: ECIPCircuits = ECIPCircuits(f"MSM {n} points", curve_id.value) A0 = G1Point.gen_random_point(curve_id) # A0 = G1Point( # 18428833980079511615272996143804193211436754676692982772704777987001013940329, # 11912813278234620045155380611021998667623598196864500681264424672047345567217, # curve_id, # ) A0: tuple(ModuloCircuitElement, ModuloCircuitElement) = ( circuit.write_element(field(A0.x)), circuit.write_element(field(A0.y)), ) A_weirstrass = circuit.write_element(field(CURVES[curve_id.value].a)) m_A0, b_A0, xA0, yA0, xA2, yA2, coeff0, coeff2 = ( circuit._slope_intercept_same_point(A0, A_weirstrass) ) points = [ (circuit.write_element(field(x)), circuit.write_element(field(y))) for x, y in points_values ] def msm_inner(points, scalars): epns = [ neg_3.positive_negative_multiplicities(neg_3.neg_3_base_le(s)) for s in scalars ] first_B = points[0] if isinstance(first_B, G1Point): points_g1 = points elif isinstance(first_B, tuple): if isinstance(first_B[0], int): points_g1 = [G1Point(B[0], B[1], curve_id) for B in points] else: points_g1 = [G1Point(B[0].value, B[1].value, curve_id) for B in points] else: raise ValueError("Invalid Bs type") Q, SumDlog = zk_ecip_hint(points_g1, scalars) rhs_acc = circuit.write_element(field(0)) for index, (point, epn) in enumerate(zip(points, epns)): # print(f"RHS INDEX : {index}") ep = circuit.write_element(field(abs(epn[0]))) en = circuit.write_element(field(abs(epn[1]))) p_sign = circuit.write_element(field(epn[0] // abs(epn[0]))) n_sign = circuit.write_element(field(epn[1] // abs(epn[1]))) rhs_acc = circuit._accumulate_eval_point_challenge_signed_same_point( rhs_acc, (m_A0, b_A0), xA0, point, ep, en, p_sign, n_sign ) # print(f"\trhs_acc_intermediate: {rhs_acc.value}") Q = (Q.x, Q.y) if Q != (0, 0): Q = (circuit.write_element(field(Q[0])), circuit.write_element(field(Q[1]))) rhs_acc = circuit._RHS_finalize_acc(rhs_acc, (m_A0, b_A0), xA0, Q) a_num, a_den, b_num, b_den = padd_function_felt(SumDlog, n) a_num, a_den, b_num, b_den = ( circuit.write_elements([field(x) for x in a_num], WriteOps.INPUT), circuit.write_elements([field(x) for x in a_den], WriteOps.INPUT), circuit.write_elements([field(x) for x in b_num], WriteOps.INPUT), circuit.write_elements([field(x) for x in b_den], WriteOps.INPUT), ) lhs = circuit._eval_function_challenge_dupl( (xA0, yA0), (xA2, yA2), coeff0, coeff2, a_num, a_den, b_num, b_den ) assert lhs.value == rhs_acc.value, f"{lhs.value} != {rhs_acc.value}" if Q == (0, 0): return G1Point.infinity(curve_id) return G1Point(Q[0].value, Q[1].value, curve_id) # print(f"\tlhs: {lhs.value}") # print(f"\trhs_acc_final: {rhs_acc.value}") Q_low = msm_inner(points, scalars_low) Q_high = msm_inner(points, scalars_high) Q_shift = msm_inner( [ ( circuit.write_element(field(Q_high.x)), circuit.write_element(field(Q_high.y)), ) ], [2**128], ) scalar_mul_low = G1Point.msm(points_g1, scalars_low) scalar_mul_high = G1Point.msm(points_g1, scalars_high) scalar_mul = G1Point.msm(points_g1, scalars) assert Q_low == scalar_mul_low, f"{Q_low} != {scalar_mul_low}" assert Q_high == scalar_mul_high, f"{Q_high} != {scalar_mul_high}" assert Q_high.scalar_mul(2**128) == Q_shift assert Q_low.add(Q_shift) == scalar_mul basic_ec = BasicEC("Basic EC", curve_id.value) final_res = basic_ec.add_points( basic_ec.write_elements([field(Q_low.x), field(Q_low.y)], WriteOps.INPUT), basic_ec.write_elements([field(Q_shift.x), field(Q_shift.y)], WriteOps.INPUT), ) assert G1Point(final_res[0].value, final_res[1].value, curve_id) == Q_low.add( Q_shift ) ec_summary = basic_ec.summarize() circuit.values_segment = circuit.values_segment.non_interactive_transform() summary = circuit.summarize() summary["MULMOD"] = summary["MULMOD"] + ec_summary["MULMOD"] summary["ADDMOD"] = summary["ADDMOD"] + ec_summary["ADDMOD"] summary["POSEIDON"] = n * 2 # N points summary["POSEIDON"] += n * 2 # N scalars (spliited in low_high) summary["POSEIDON"] += 3 * 2 # 3 Q result points summary["POSEIDON"] += 2 * (4 * n + 10) # 2 * Total # of coefficients in SumDlogDiv summary["POSEIDON"] += ( 4 + 10 ) # Total # of coefficients in SumDlogDivShifted (1 point MSM) return summary, None if __name__ == "__main__": import pandas as pd from tabulate import tabulate pd.set_option("display.max_rows", None) # None means show all rows pd.set_option("display.max_columns", None) # None means show all columns pd.set_option("display.width", None) # None means auto-detect the display width pd.set_option("display.max_colwidth", None) # None means show full width of columns builtin_ops_data = [] builtin_ops_data.append( { "circuit": "BLS12FinalExp Fp12 Karabina No EXTF Trick", "MULMOD": 7774, "ADDMOD": 26038 + 16964, # ADD + SUBS. "ASSERT_EQ": 0, "POSEIDON": 0, "RLC": 0, } ) final_exp_data = {CurveID.BN254: None, CurveID.BLS12_381: None} sub_circuit_count = [] # print(f"Running...") for curveID in [CurveID.BN254, CurveID.BLS12_381]: builtin_ops, sub_circuits = test_final_exp_circuit(curveID) builtin_ops_data.append(builtin_ops) final_exp_data[curveID] = builtin_ops sub_circuit_count.append(sub_circuits) # Sub circuits. Same values for both curves for test_func, curve_id, ext_degree in [ (test_extf_square, CurveID.BLS12_381, 12), (test_mul_torus, CurveID.BLS12_381, 6), (test_square_torus_amortized, CurveID.BLS12_381, 6), (test_extf_mul, CurveID.BLS12_381, 12), ]: builtin_ops, _ = test_func(curve_id, ext_degree) builtin_ops_data.append(builtin_ops) for test_func, curve_id in [ (test_derive_point_from_x, CurveID.BN254), ]: builtin_ops, _ = test_func(curve_id) builtin_ops_data.append(builtin_ops) for n in [1, 2, 3]: for curve_id in [CurveID.BLS12_381, CurveID.BN254]: # print(f"Running {curve_id} {n}") builtin_ops, sub_circuits = test_miller_n(curve_id, n) builtin_ops_data.append(builtin_ops) builtin_ops_data.append( { "circuit": f"MultiPairing {n=} {curve_id.name}", "MULMOD": builtin_ops["MULMOD"] + final_exp_data[curve_id]["MULMOD"], "ADDMOD": builtin_ops["ADDMOD"] + final_exp_data[curve_id]["ADDMOD"], "ASSERT_EQ": builtin_ops["ASSERT_EQ"] + final_exp_data[curve_id]["ASSERT_EQ"], "POSEIDON": builtin_ops["POSEIDON"] + final_exp_data[curve_id]["POSEIDON"], "RLC": builtin_ops["RLC"] + final_exp_data[curve_id]["RLC"], } ) sub_circuit_count.append(sub_circuits) for n in [1, 2, 3, 10, 50]: builtin_ops, _ = test_msm_n_points(CurveID.BN254, n) builtin_ops_data.append(builtin_ops) df = pd.DataFrame(builtin_ops_data) costs = [ { "OP": "MULMOD", "Weight in steps": 8, "Comment": "Equivalent cost of a*b % p with the modulo builtin in VM steps", }, { "OP": "ADDMOD", "Weight in steps": 4, "Comment": "Equivalent cost of a+b % p with the modulo builtin in VM steps", }, { "OP": "ASSERT_EQ", "Weight in steps": 2, "Comment": "Equivalent cost of a==b % p with the modulo builtin in VM steps", }, { "OP": "POSEIDON", "Weight in steps": 16, "Comment": "Cost of hashing the first 3 limbs of 384 bits emulated field element with Poseidon", }, { "OP": "RLC", "Weight in steps": 28, "Comment": "Cost of writing a field element to the value segment and retrieving random coefficients", }, ] def get_poseidon_cost(curve_name: CurveID) -> int: poseidon_costs = { CurveID.BN254: 14, CurveID.BLS12_381: 17, } return poseidon_costs.get(curve_name, 0) # Default to 0 if curve_name not found def calculate_row_cost(row): total_cost = 0 for _row in costs: op, weight = _row["OP"], _row["Weight in steps"] if "POSEIDON" in op: # Dynamically adjust Poseidon cost based on the 'circuit' column for curve_id in CurveID: if curve_id.name in row["circuit"]: weight = get_poseidon_cost(curve_id) break # Stop checking once the first matching CurveID is found total_cost += row[op] * weight return total_cost # Apply the function to each row to calculate the total cost df["~steps"] = df.apply(calculate_row_cost, axis=1) pd.set_option("display.colheader_justify", "center") print("\n\n") costs = [cost for cost in costs if cost["OP"] != "POSEIDON"] costs.extend( [ { "OP": "POSEIDON 4 LIMBS", "Weight in steps": 17, "Comment": "Cost of hashing the 4 limbs of 384 bits emulated field element with Poseidon", }, ] ) df_costs = pd.DataFrame(costs) print(tabulate(df_costs, headers="keys", tablefmt="github", showindex=False)) print("\n") df.sort_values(by="~steps", inplace=True) print( tabulate( df, headers="keys", tablefmt="github", showindex=False, floatfmt=".2f", ) ) df_sub_circuits = ( pd.DataFrame(sub_circuit_count) .set_index("Circuit") .fillna(0) .astype(int) .transpose() ) # print("\n") # print( # tabulate( # df_sub_circuits, # headers="keys", # tablefmt="github", # showindex=True, # ) # ) # print("\n") ================================================ FILE: tests/conftest.py ================================================ import os from pathlib import Path # Configure Hypothesis to store all its data in the .cargo/hypothesis directory build_path = Path(__file__).parent.parent / ".cargo" / "hypothesis" build_path.mkdir( parents=True, exist_ok=True ) # Ensure the .cargo/hypothesis directory exists # Set the environment variable before importing hypothesis os.environ["HYPOTHESIS_STORAGE_DIRECTORY"] = str(build_path) from hypothesis import settings from hypothesis.database import DirectoryBasedExampleDatabase # Also set the database for good measure settings.register_profile("default", database=DirectoryBasedExampleDatabase(build_path)) settings.load_profile("default") pytest_plugins = [ "tests.contracts_e2e.fixtures.accounts", "tests.contracts_e2e.fixtures.clients", "tests.contracts_e2e.fixtures.devnet", ] ================================================ FILE: tests/contracts_e2e/__init__.py ================================================ ================================================ FILE: tests/contracts_e2e/e2e_test.py ================================================ from pathlib import Path import pytest from starknet_py.contract import ( Contract, ContractFunction, InvokeResult, PreparedFunctionInvokeV3, ) from starknet_py.hash.address import compute_address from starknet_py.hash.utils import pedersen_hash from starknet_py.net.account.account import Account, BaseAccount from starknet_py.net.client_errors import ContractNotFoundError from garaga.curves import ProofSystem from garaga.hints.io import to_int from garaga.precompiled_circuits.zk_honk import honk_proof_from_bytes from garaga.starknet.cli.smart_contract_project import ( Groth16SmartContract, SmartContractProject, ) from garaga.starknet.groth16_contract_generator.generator import ECIP_OPS_CLASS_HASH from garaga.starknet.groth16_contract_generator.parsing_utils import ( find_item_from_key_patterns, ) from garaga.starknet.honk_contract_generator.calldata import ( HonkVk, get_ultra_flavor_honk_calldata_from_vk_and_proof, ) from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_encrypt_to_calldata, drand_round_to_calldata, ) CONTRACTS_PATH = Path("src/contracts") CONTRACTS_PATH_AUTOGENERATED = CONTRACTS_PATH / "autogenerated" GROTH16_EXAMPLES_PATH = Path( "hydra/garaga/starknet/groth16_contract_generator/examples" ) NOIR_EXAMPLES_PATH = Path("hydra/garaga/starknet/honk_contract_generator/examples") ALL_GROTH16_CONTRACTS = [ { "contract_project": Groth16SmartContract( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "sp1_verifier_bn254", vk_path=GROTH16_EXAMPLES_PATH / "vk_sp1.json", ), "proof_path": GROTH16_EXAMPLES_PATH / "proof_sp1.json", }, { "contract_project": Groth16SmartContract( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "risc0_verifier_bn254", vk_path=GROTH16_EXAMPLES_PATH / "vk_risc0.json", ), "proof_path": GROTH16_EXAMPLES_PATH / "proof_risc0.json", }, { "contract_project": Groth16SmartContract( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "groth16_example_bls12_381", vk_path=GROTH16_EXAMPLES_PATH / "vk_bls.json", ), "proof_path": GROTH16_EXAMPLES_PATH / "proof_bls.json", }, { "contract_project": Groth16SmartContract( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "groth16_example_bn254", vk_path=GROTH16_EXAMPLES_PATH / "vk_bn254.json", ), "proof_path": GROTH16_EXAMPLES_PATH / "proof_bn254.json", }, ] ECIP_CONTRACT = SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "universal_ecip" ) DEPLOYER_ADDRESS = 0x41A78E741E5AF2FEC34B695679BC6891742439F7AFB8484ECD7766661AD02BF async def get_contract_if_exists( account: Account, contract_address: int ) -> Contract | None: try: res = await Contract.from_address(contract_address, account) return res except ContractNotFoundError: return None @pytest.mark.asyncio @pytest.mark.parametrize("contract_info", ALL_GROTH16_CONTRACTS) async def test_groth16_contracts(account_devnet: BaseAccount, contract_info: dict): account = account_devnet contract_project: Groth16SmartContract = contract_info["contract_project"] proof_path: Path = contract_info["proof_path"] print(f"ACCOUNT {hex(account.address)}, NONCE {await account.get_nonce()}") for i in range(2): print(f"\n\nROUND {i}") # Declare the ECIP contract ecip_class_hash, _ = await ECIP_CONTRACT.declare_class_hash(account) assert ( ecip_class_hash == ECIP_OPS_CLASS_HASH ), f"ECIP hardcoded class hash is not up to date, got {hex(ecip_class_hash)}, expected {hex(ECIP_OPS_CLASS_HASH)}" # Declare the groth16 contract groth16_class_hash, groth16_abi = await contract_project.declare_class_hash( account ) print(f"Declared contract class hash: {hex(groth16_class_hash)}") # Deploy the groth16 contract precomputed_address = compute_address( class_hash=groth16_class_hash, constructor_calldata=[], salt=pedersen_hash(to_int(account.address), 1), deployer_address=DEPLOYER_ADDRESS, ) try_contract = await get_contract_if_exists(account, precomputed_address) if try_contract is None: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=groth16_class_hash, abi=groth16_abi, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=1, cairo_version=1, ) await deploy_result.wait_for_acceptance() contract = deploy_result.deployed_contract else: print(f"Contract already deployed at {hex(precomputed_address)}") contract = try_contract print(f"Deployed contract address: {hex(contract.address)}") print(f"Deployed contract: {contract.functions}") function_call: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) prepare_invoke = PreparedFunctionInvokeV3( to_addr=function_call.contract_data.address, calldata=contract_project.generate_calldata( proof_path=proof_path, public_inputs_path=None ), selector=function_call.get_selector(function_call.name), _contract_data=function_call.contract_data, _client=function_call.client, _account=function_call.account, _payload_transformer=function_call._payload_transformer, resource_bounds=None, ) invoke_result: InvokeResult = await prepare_invoke.invoke(auto_estimate=True) await invoke_result.wait_for_acceptance() print(f"Invoke result : {invoke_result.status}") receipt = await account.client.get_transaction_receipt(invoke_result.hash) print( f"Execution resources: {contract_project.smart_contract_folder} \n{receipt.execution_resources}" ) @pytest.mark.asyncio @pytest.mark.parametrize( "contract_info", [ { "contract_project": SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "drand_quicknet" ) }, ], ) async def test_drand_contract(account_devnet: BaseAccount, contract_info: dict): account = account_devnet contract_project: SmartContractProject = contract_info["contract_project"] print(f"ACCOUNT {hex(account.address)}, NONCE {await account.get_nonce()}") drand_class_hash, drand_abi = await contract_project.declare_class_hash(account) print(f"Declared contract class hash: {hex(drand_class_hash)}") # Deploy the drand contract precomputed_address = compute_address( class_hash=drand_class_hash, constructor_calldata=[], salt=pedersen_hash(to_int(account.address), 1), deployer_address=DEPLOYER_ADDRESS, ) try_contract = await get_contract_if_exists(account, precomputed_address) if try_contract is None: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=drand_class_hash, abi=drand_abi, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=1, cairo_version=1, ) await deploy_result.wait_for_acceptance() contract = deploy_result.deployed_contract else: print(f"Contract already deployed at {hex(precomputed_address)}") contract = try_contract print(f"Deployed contract address: {hex(contract.address)}") print(f"Deployed contract: {contract.functions}") function_call: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) for drand_round in range(1, 5): prepare_invoke = PreparedFunctionInvokeV3( to_addr=function_call.contract_data.address, calldata=drand_round_to_calldata(drand_round), selector=function_call.get_selector(function_call.name), _contract_data=function_call.contract_data, _client=function_call.client, _account=function_call.account, _payload_transformer=function_call._payload_transformer, resource_bounds=None, ) invoke_result: InvokeResult = await prepare_invoke.invoke(auto_estimate=True) await invoke_result.wait_for_acceptance() @pytest.mark.asyncio @pytest.mark.parametrize( "contract_info", [ { "verifier_project": SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "drand_quicknet" ), "decrypt_project": SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "drand_decrypt_quicknet" ), }, ], ) async def test_drand_decrypt_contract(account_devnet: BaseAccount, contract_info: dict): account = account_devnet # Step 1: Declare the verifier class (not deployed) and generate decrypt constants verifier_project: SmartContractProject = contract_info["verifier_project"] verifier_class_hash, _ = await verifier_project.declare_class_hash(account) print(f"Declared verifier class hash: {hex(verifier_class_hash)}") from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( generate_drand_decrypt_constants, ) decrypt_project: SmartContractProject = contract_info["decrypt_project"] generate_drand_decrypt_constants( verifier_class_hash, decrypt_project.smart_contract_folder ) # Step 2: Declare and deploy the decrypt contract decrypt_class_hash, decrypt_abi = await decrypt_project.declare_class_hash(account) precomputed_address = compute_address( class_hash=decrypt_class_hash, constructor_calldata=[], salt=pedersen_hash(to_int(account.address), 2), deployer_address=DEPLOYER_ADDRESS, ) try_contract = await get_contract_if_exists(account, precomputed_address) if try_contract is None: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=decrypt_class_hash, abi=decrypt_abi, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=2, cairo_version=1, ) await deploy_result.wait_for_acceptance() contract = deploy_result.deployed_contract else: contract = try_contract print(f"Deployed decrypt contract at: {hex(contract.address)}") print(f"Functions: {contract.functions}") verify_fn: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) decrypt_fn: ContractFunction = find_item_from_key_patterns( contract.functions, ["decrypt"] ) # Step 3: Verify round 1 via library_call invoke = PreparedFunctionInvokeV3( to_addr=verify_fn.contract_data.address, calldata=drand_round_to_calldata(1), selector=verify_fn.get_selector(verify_fn.name), _contract_data=verify_fn.contract_data, _client=verify_fn.client, _account=verify_fn.account, _payload_transformer=verify_fn._payload_transformer, resource_bounds=None, ) result = await invoke.invoke(auto_estimate=True) await result.wait_for_acceptance() print("Round 1 verified via library_call") # Step 4: Decrypt for round 1 (signature already stored) decrypt_calldata = drand_encrypt_to_calldata( 1, b"0000000000000000", b"0000000000000000" ) invoke = PreparedFunctionInvokeV3( to_addr=decrypt_fn.contract_data.address, calldata=decrypt_calldata, selector=decrypt_fn.get_selector(decrypt_fn.name), _contract_data=decrypt_fn.contract_data, _client=decrypt_fn.client, _account=decrypt_fn.account, _payload_transformer=decrypt_fn._payload_transformer, resource_bounds=None, ) result = await invoke.invoke(auto_estimate=True) await result.wait_for_acceptance() print("Round 1 decrypted (stored sig)") # Step 5: Decrypt for round 2 (combined: verify inline + decrypt) encrypt_cd = drand_encrypt_to_calldata(2, b"0000000000000000", b"0000000000000000") verify_cd = drand_round_to_calldata(2) combined_data = encrypt_cd[1:] + verify_cd[1:] combined_calldata = [len(combined_data)] + combined_data invoke = PreparedFunctionInvokeV3( to_addr=decrypt_fn.contract_data.address, calldata=combined_calldata, selector=decrypt_fn.get_selector(decrypt_fn.name), _contract_data=decrypt_fn.contract_data, _client=decrypt_fn.client, _account=decrypt_fn.account, _payload_transformer=decrypt_fn._payload_transformer, resource_bounds=None, ) result = await invoke.invoke(auto_estimate=True) await result.wait_for_acceptance() print("Round 2 verified + decrypted in one tx") HONK_CONTRACTS = [ { "contract_project": SmartContractProject( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "noir_ultra_keccak_zk_honk_example", ), "vk_path": NOIR_EXAMPLES_PATH / "vk_ultra_keccak.bin", "public_inputs_path": NOIR_EXAMPLES_PATH / "public_inputs_ultra_keccak.bin", "proof_path": NOIR_EXAMPLES_PATH / "proof_ultra_keccak_zk.bin", "system": ProofSystem.UltraKeccakZKHonk, }, ] @pytest.mark.asyncio @pytest.mark.parametrize("contract_info", HONK_CONTRACTS) async def test_honk_contracts(account_devnet: BaseAccount, contract_info: dict): account = account_devnet contract_project: SmartContractProject = contract_info["contract_project"] vk_path: Path = contract_info["vk_path"] proof_path: Path = contract_info["proof_path"] public_inputs_path: Path = contract_info["public_inputs_path"] system: ProofSystem = contract_info["system"] vk = HonkVk.from_bytes(open(vk_path, "rb").read()) proof = honk_proof_from_bytes( open(proof_path, "rb").read(), open(public_inputs_path, "rb").read(), vk, system ) print(f"ACCOUNT {hex(account.address)}, NONCE {await account.get_nonce()}") # Declare the honk contract honk_class_hash, honk_abi = await contract_project.declare_class_hash(account) print(f"Declared contract class hash: {hex(honk_class_hash)}") # Deploy the honk contract precomputed_address = compute_address( class_hash=honk_class_hash, constructor_calldata=[], salt=pedersen_hash(to_int(account.address), 1), deployer_address=DEPLOYER_ADDRESS, ) try_contract = await get_contract_if_exists(account, precomputed_address) if try_contract is None: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=honk_class_hash, abi=honk_abi, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=1, cairo_version=1, ) await deploy_result.wait_for_acceptance() contract = deploy_result.deployed_contract else: print(f"Contract already deployed at {hex(precomputed_address)}") contract = try_contract print(f"Deployed contract address: {hex(contract.address)}") print(f"Deployed contract: {contract.functions}") function_call: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) prepare_invoke = PreparedFunctionInvokeV3( to_addr=function_call.contract_data.address, calldata=get_ultra_flavor_honk_calldata_from_vk_and_proof( vk=vk, proof=proof, system=system ), selector=function_call.get_selector(function_call.name), _contract_data=function_call.contract_data, _client=function_call.client, _account=function_call.account, _payload_transformer=function_call._payload_transformer, resource_bounds=None, ) invoke_result: InvokeResult = await prepare_invoke.invoke(auto_estimate=True) await invoke_result.wait_for_acceptance() print(f"Invoke result : {invoke_result.status}") receipt = await account.client.get_transaction_receipt(invoke_result.hash) print( f"Execution resources: {contract_project.smart_contract_folder} \n{receipt.execution_resources}\n" ) @pytest.mark.asyncio async def test_risc0_sample_app(account_devnet: BaseAccount): account = account_devnet lib_contract_project = Groth16SmartContract( smart_contract_folder=CONTRACTS_PATH_AUTOGENERATED / "risc0_verifier_bn254", vk_path=GROTH16_EXAMPLES_PATH / "vk_risc0.json", ) contract_project = SmartContractProject( smart_contract_folder=CONTRACTS_PATH / "risc0_sample_app" / "fibonacci_sequencer", ) proof_path = CONTRACTS_PATH / "risc0_sample_app" / "fibonacci_prover" / "proof.json" src_path = ( CONTRACTS_PATH / "risc0_sample_app" / "fibonacci_sequencer" / "src" / "lib.cairo" ) print(f"ACCOUNT {hex(account.address)}, NONCE {await account.get_nonce()}") # Declare the ECIP contract ecip_class_hash, _ = await ECIP_CONTRACT.declare_class_hash(account) assert ( ecip_class_hash == ECIP_OPS_CLASS_HASH ), f"ECIP hardcoded class hash is not up to date, got {hex(ecip_class_hash)}, expected {hex(ECIP_OPS_CLASS_HASH)}" # Declare the risc0 verifier contract lib_groth16_class_hash, _ = await lib_contract_project.declare_class_hash(account) print(f"Declared contract class hash: {hex(lib_groth16_class_hash)}") assert ( hex(lib_groth16_class_hash) in open(src_path).read() ), f"risc0_verifier_bn254 hardcoded class hash is not up to date, expected {hex(lib_groth16_class_hash)}" # Declare the risc0 sample app contract groth16_class_hash, groth16_abi = await contract_project.declare_class_hash(account) print(f"Declared contract class hash: {hex(groth16_class_hash)}") # Deploy the risc0 sample app contract precomputed_address = compute_address( class_hash=groth16_class_hash, constructor_calldata=[], salt=pedersen_hash(to_int(account.address), 1), deployer_address=DEPLOYER_ADDRESS, ) try_contract = await get_contract_if_exists(account, precomputed_address) if try_contract is None: deploy_result = await Contract.deploy_contract_v3( account=account, class_hash=groth16_class_hash, abi=groth16_abi, deployer_address=DEPLOYER_ADDRESS, auto_estimate=True, salt=1, cairo_version=1, ) await deploy_result.wait_for_acceptance() contract = deploy_result.deployed_contract else: print(f"Contract already deployed at {hex(precomputed_address)}") contract = try_contract print(f"Deployed contract address: {hex(contract.address)}") print(f"Deployed contract: {contract.functions}") function_call: ContractFunction = find_item_from_key_patterns( contract.functions, ["verify"] ) prepare_invoke = PreparedFunctionInvokeV3( to_addr=function_call.contract_data.address, calldata=lib_contract_project.generate_calldata( proof_path=proof_path, public_inputs_path=None ), selector=function_call.get_selector(function_call.name), _contract_data=function_call.contract_data, _client=function_call.client, _account=function_call.account, _payload_transformer=function_call._payload_transformer, resource_bounds=None, ) invoke_result: InvokeResult = await prepare_invoke.invoke(auto_estimate=True) await invoke_result.wait_for_acceptance() print(f"Invoke result : {invoke_result.status}") receipt = await account.client.get_transaction_receipt(invoke_result.hash) print(receipt.execution_resources) ================================================ FILE: tests/contracts_e2e/fixtures/__init__.py ================================================ ================================================ FILE: tests/contracts_e2e/fixtures/accounts.py ================================================ # pylint: disable=redefined-outer-name from dataclasses import dataclass from typing import List, Optional, Tuple import pytest import pytest_asyncio from starknet_py.contract import Contract from starknet_py.hash.address import compute_address from starknet_py.net.account.account import Account from starknet_py.net.account.base_account import BaseAccount from starknet_py.net.client_models import PriceUnit from starknet_py.net.full_node_client import FullNodeClient from starknet_py.net.http_client import HttpMethod, RpcHttpClient from starknet_py.net.models import AddressRepresentation, StarknetChainId from starknet_py.net.signer.key_pair import KeyPair from tests.contracts_e2e.fixtures.constants import ( DEVNET_PRE_DEPLOYED_ACCOUNT_ADDRESS, DEVNET_PRE_DEPLOYED_ACCOUNT_PRIVATE_KEY, MAX_RESOURCE_BOUNDS, ) from tests.contracts_e2e.utils import ( AccountToBeDeployedDetails, _get_random_private_key_unsafe, _new_address, get_deploy_account_transaction, prepay_account, ) @dataclass class AccountPrerequisites: address: AddressRepresentation salt: int calldata: list[int] key_pair: KeyPair async def devnet_account_details( client: FullNodeClient, class_hash: int, devnet, ) -> Tuple[str, str]: """ Deploys an Account and adds fee tokens to its balance (only on devnet). """ private_key = _get_random_private_key_unsafe() key_pair = KeyPair.from_private_key(private_key) salt = 1 address = compute_address( class_hash=class_hash, constructor_calldata=[key_pair.public_key], salt=salt, deployer_address=0, ) await mint_token_on_devnet(devnet, address, int(1e30), PriceUnit.WEI.value) await mint_token_on_devnet(devnet, address, int(1e30), PriceUnit.FRI.value) deploy_account_tx = await get_deploy_account_transaction( address=address, key_pair=key_pair, salt=salt, class_hash=class_hash, client=client, ) account = Account( address=address, client=client, key_pair=key_pair, chain=StarknetChainId.SEPOLIA, ) res = await account.client.deploy_account(deploy_account_tx) await account.client.wait_for_tx(res.transaction_hash) return hex(address), hex(key_pair.private_key) async def mint_token_on_devnet(url: str, address: int, amount: int, unit: str): http_client = RpcHttpClient(url) await http_client.request( http_method=HttpMethod.POST, address=f"{url}/mint", payload={"address": hex(address), "amount": amount, "unit": unit}, ) @pytest.fixture(name="account_devnet", scope="package") def full_node_account(client_devnet: FullNodeClient) -> BaseAccount: """ Returns a new Account created with FullNodeClient. """ address = DEVNET_PRE_DEPLOYED_ACCOUNT_ADDRESS private_key = DEVNET_PRE_DEPLOYED_ACCOUNT_PRIVATE_KEY return Account( address=address, client=client_devnet, key_pair=KeyPair.from_private_key(int(private_key, 0)), chain=StarknetChainId.SEPOLIA, ) @dataclass class AccountToBeDeployedDetailsFactory: class_hash: int eth_fee_contract: Contract strk_fee_contract: Contract async def get( self, *, class_hash: Optional[int] = None, calldata: Optional[List[int]] = None, ) -> AccountToBeDeployedDetails: key_pair = KeyPair.from_private_key(_get_random_private_key_unsafe()) calldata = calldata if calldata is not None else [] class_hash = class_hash if class_hash is not None else self.class_hash if calldata == []: calldata = [key_pair.public_key] address, salt = _new_address( class_hash=class_hash, calldata=calldata, ) await prepay_account( address=address, eth_fee_contract=self.eth_fee_contract, strk_fee_contract=self.strk_fee_contract, ) return address, key_pair, salt, class_hash @pytest_asyncio.fixture(scope="package") async def deploy_account_details_factory( account_with_validate_deploy_class_hash: int, eth_fee_contract: Contract, strk_fee_contract: Contract, ) -> AccountToBeDeployedDetailsFactory: """ Returns AccountToBeDeployedDetailsFactory. The Factory's get() method returns: address, key_pair, salt and class_hash of the account with validate deploy. Prefunds the address with enough tokens to allow for deployment. """ return AccountToBeDeployedDetailsFactory( class_hash=account_with_validate_deploy_class_hash, eth_fee_contract=eth_fee_contract, strk_fee_contract=strk_fee_contract, ) @pytest.fixture(scope="package") def pre_deployed_account_with_validate_deploy(client) -> BaseAccount: """ Returns an Account pre-deployed on specified network. Used to deploy other accounts. """ address = DEVNET_PRE_DEPLOYED_ACCOUNT_ADDRESS private_key = DEVNET_PRE_DEPLOYED_ACCOUNT_PRIVATE_KEY return Account( address=address, client=client, key_pair=KeyPair.from_private_key(int(private_key, 16)), chain=StarknetChainId.SEPOLIA, ) @pytest_asyncio.fixture(scope="function") async def argent_account_v040_data( argent_account_v040_class_hash, eth_fee_contract: Contract, strk_fee_contract: Contract, ) -> AccountPrerequisites: key_pair = KeyPair.from_private_key(_get_random_private_key_unsafe()) # Based on ABI definition documentation constructor_calldata = [ 0, key_pair.public_key, 1, ] address, salt = _new_address(argent_account_v040_class_hash, constructor_calldata) await prepay_account( address=address, eth_fee_contract=eth_fee_contract, strk_fee_contract=strk_fee_contract, ) return AccountPrerequisites(address, salt, constructor_calldata, key_pair) @pytest_asyncio.fixture(scope="package") async def argent_account_v040( argent_account_v040_class_hash, eth_fee_contract: Contract, strk_fee_contract: Contract, client, ) -> BaseAccount: key_pair = KeyPair.from_private_key(_get_random_private_key_unsafe()) # Based on ABI definition documentation constructor_calldata = [ 0, key_pair.public_key, 1, ] address, salt = _new_address(argent_account_v040_class_hash, constructor_calldata) await prepay_account( address=address, eth_fee_contract=eth_fee_contract, strk_fee_contract=strk_fee_contract, ) deploy_result = await Account.deploy_account_v3( address=address, class_hash=argent_account_v040_class_hash, salt=salt, key_pair=key_pair, client=client, constructor_calldata=constructor_calldata, resource_bounds=MAX_RESOURCE_BOUNDS, ) await deploy_result.wait_for_acceptance() return deploy_result.account ================================================ FILE: tests/contracts_e2e/fixtures/clients.py ================================================ import pytest from starknet_py.net.full_node_client import FullNodeClient from tests.contracts_e2e.fixtures.constants import SEPOLIA_RPC_URL @pytest.fixture(name="client_devnet", scope="package") def create_full_node_client_devnet(devnet) -> FullNodeClient: return FullNodeClient(node_url=devnet + "/rpc") @pytest.fixture(name="client_sepolia", scope="package") def create_full_node_client_sepolia() -> FullNodeClient: return FullNodeClient(node_url=SEPOLIA_RPC_URL) ================================================ FILE: tests/contracts_e2e/fixtures/constants.py ================================================ import os from pathlib import Path from dotenv import load_dotenv from starknet_py.net.client_models import ResourceBounds, ResourceBoundsMapping load_dotenv(dotenv_path=Path(os.path.dirname(__file__)) / "../test-variables.env") def _get_env_or_throw(env_name: str) -> str: env = os.getenv(key=env_name) if env is None: raise ValueError( f"{env_name} environmental variable is not set. " f"Update it manually or set it in `starknet_py/tests/e2e/test-variables.env` file. " f"More info here: https://starknetpy.readthedocs.io/en/latest/development.html#setup" ) return env def _get_env_lambda(env_name): return lambda: _get_env_or_throw(env_name) # -------------------------------- SEPOLIA TESTNET ------------------------------------- SEPOLIA_ACCOUNT_PRIVATE_KEY = _get_env_lambda("SEPOLIA_ACCOUNT_PRIVATE_KEY") SEPOLIA_ACCOUNT_ADDRESS = _get_env_lambda("SEPOLIA_ACCOUNT_ADDRESS") SEPOLIA_RPC_URL = _get_env_lambda("SEPOLIA_RPC_URL") EMPTY_CONTRACT_ADDRESS_SEPOLIA = ( "0x06524771cb912945bf2db355b5a12355ca2e2ff05e15ee35366336a602293f2d" ) # ----------------------------------------------------------------------------- DEVNET_PRE_DEPLOYED_ACCOUNT_ADDRESS = ( "0x260a8311b4f1092db620b923e8d7d20e76dedcc615fb4b6fdf28315b81de201" ) DEVNET_PRE_DEPLOYED_ACCOUNT_PRIVATE_KEY = "0xc10662b7b247c7cecf7e8a30726cff12" STRK_FEE_CONTRACT_ADDRESS = ( "0x04718f5a0fc34cc1af16a1cdee98ffb20c31f5cd61d6ab07201858f4287c938d" ) STRK_CLASS_HASH = "0x04ad3c1dc8413453db314497945b6903e1c766495a1e60492d44da9c2a986e4b" MAX_RESOURCE_BOUNDS_L1 = ResourceBounds( max_amount=int(1e5), max_price_per_unit=int(1e13) ) MAX_RESOURCE_BOUNDS = ResourceBoundsMapping( l1_gas=ResourceBounds(max_amount=int(1e5), max_price_per_unit=int(1e13)), l2_gas=ResourceBounds(max_amount=int(1e10), max_price_per_unit=int(1e20)), l1_data_gas=ResourceBounds(max_amount=int(1e5), max_price_per_unit=int(1e13)), ) MAX_RESOURCE_BOUNDS_SEPOLIA = ResourceBoundsMapping( l1_gas=ResourceBounds(max_amount=int(1e4), max_price_per_unit=int(1e15)), l2_gas=ResourceBounds(max_amount=int(1e6), max_price_per_unit=int(1e10)), l1_data_gas=ResourceBounds(max_amount=int(1e4), max_price_per_unit=int(1e15)), ) MOCK_DIR = Path(os.path.dirname(__file__)) / "../mock" TYPED_DATA_DIR = MOCK_DIR / "typed_data" CONTRACTS_DIR = MOCK_DIR / "contracts" CONTRACTS_COMPILED_V0_DIR = MOCK_DIR / "contracts_compiled" # PRECOMPILED_CONTRACTS are contracts compiled with various Sierras # They are mainly used to verify if we compute class_hash for older Sierras correctly PRECOMPILED_CONTRACTS_DIR = MOCK_DIR / "precompiled_contracts" CONTRACTS_V2_COMPILED = MOCK_DIR / "contracts_v2/target/dev" CONTRACTS_V2_ARTIFACTS_MAP = ( CONTRACTS_V2_COMPILED / "contracts_v2.starknet_artifacts.json" ) CONTRACTS_V1_COMPILED = MOCK_DIR / "contracts_v1/target/dev" CONTRACTS_V1_ARTIFACTS_MAP = ( CONTRACTS_V1_COMPILED / "contracts_v1.starknet_artifacts.json" ) ================================================ FILE: tests/contracts_e2e/fixtures/devnet.py ================================================ import socket import subprocess import time from contextlib import closing from pathlib import Path from typing import Generator, List import pytest from tests.contracts_e2e.fixtures.constants import SEPOLIA_RPC_URL def get_available_port() -> int: with closing(socket.socket(socket.AF_INET, socket.SOCK_STREAM)) as sock: sock.bind(("", 0)) sock.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1) return sock.getsockname()[1] def start_devnet(fork_mode: bool = False): devnet_port = get_available_port() start_devnet_command = get_start_devnet_command(devnet_port, fork_mode=fork_mode) # pylint: disable=consider-using-with proc = subprocess.Popen(start_devnet_command) time.sleep(5) return devnet_port, proc def get_start_devnet_command(devnet_port: int, fork_mode: bool = False) -> List[str]: devnet_path = Path(__file__).parent.parent / "devnet" / "bin" / "starknet-devnet" start_command = [ str(devnet_path), "--port", str(devnet_port), "--accounts", # deploys specified number of accounts str(1), "--seed", # generates same accounts each time str(1), "--state-archive-capacity", "full", "--block-generation-on", "transaction", "--initial-balance", "1000000000000000000000000000000000000000000000000000000000000000000", ] if fork_mode: start_command.extend( [ "--fork-network", str(SEPOLIA_RPC_URL()), ] ) return start_command @pytest.fixture(scope="package") def devnet() -> Generator[str, None, None]: """ Runs devnet instance once per module and returns it's address. """ devnet_port, proc = start_devnet() yield f"http://localhost:{devnet_port}" proc.kill() @pytest.fixture(scope="package") def devnet_forking_mode() -> Generator[str, None, None]: """ Runs devnet instance once per module and returns its address. """ devnet_port, proc = start_devnet(fork_mode=True) yield f"http://localhost:{devnet_port}" proc.kill() ================================================ FILE: tests/contracts_e2e/install_devnet.sh ================================================ #!/bin/bash set -e DEVNET_INSTALL_DIR="$(git rev-parse --show-toplevel)/tests/contracts_e2e/devnet/bin" DEVNET_REPO="https://github.com/0xSpaceShard/starknet-devnet" DEVNET_VERSION="v0.5.1" require_cmd() { if ! command -v "$1" >/dev/null 2>&1; then echo "$1 is not available" echo "Please install $1 and run the script again" exit 1 fi } get_architecture() { local _ostype _cputype _arch _clibtype _ostype="$(uname -s)" _cputype="$(uname -m)" _clibtype="gnu" if [ "$_ostype" = Linux ] && ldd --_requested_version 2>&1 | grep -q 'musl'; then _clibtype="musl" fi if [ "$_ostype" = Darwin ] && [ "$_cputype" = i386 ] && sysctl hw.optional.x86_64 | grep -q ': 1'; then _cputype=x86_64 fi case "$_ostype" in Linux) _ostype=unknown-linux-$_clibtype ;; Darwin) _ostype=apple-darwin ;; *) err "unsupported OS type: $_ostype" ;; esac case "$_cputype" in aarch64 | arm64) _cputype=aarch64 ;; x86_64 | x86-64 | x64 | amd64) _cputype=x86_64 ;; *) err "unknown CPU type: $_cputype" ;; esac _arch="${_cputype}-${_ostype}" RETVAL="$_arch" } require_cmd curl require_cmd tar get_architecture SYSTEM_TRIPLET="$RETVAL" mkdir -p "${DEVNET_INSTALL_DIR}" curl -L "${DEVNET_REPO}/releases/download/${DEVNET_VERSION}/starknet-devnet-${SYSTEM_TRIPLET}.tar.gz" | tar -xz -C "${DEVNET_INSTALL_DIR}" || exit 1 echo "All done!" exit 0 ================================================ FILE: tests/contracts_e2e/test-variables.env.template ================================================ SEPOLIA_RPC_URL=URL SEPOLIA_ACCOUNT_PRIVATE_KEY=0xabcdef SEPOLIA_ACCOUNT_ADDRESS=0xfedcba SEPOLIA = ================================================ FILE: tests/contracts_e2e/utils.py ================================================ import random from typing import List, Tuple from starknet_py.constants import EC_ORDER from starknet_py.contract import Contract from starknet_py.hash.address import compute_address from starknet_py.net.account.account import Account from starknet_py.net.client import Client from starknet_py.net.http_client import HttpClient, HttpMethod from starknet_py.net.models import DeployAccountV3, StarknetChainId from starknet_py.net.signer.key_pair import KeyPair from starknet_py.net.udc_deployer.deployer import _get_random_salt from tests.contracts_e2e.fixtures.constants import MAX_RESOURCE_BOUNDS AccountToBeDeployedDetails = Tuple[int, KeyPair, int, int] def _new_address( class_hash: int, calldata: List[int], ): salt = _get_random_salt() return ( compute_address( salt=salt, class_hash=class_hash, constructor_calldata=calldata, deployer_address=0, ), salt, ) async def prepay_account( *, address: int, eth_fee_contract: Contract, strk_fee_contract: Contract, ): """ Transfer fees from system contracts (ETH and STRK) to address specified. :param address: Address of the account to send funds to. :param eth_fee_contract: Contract for prefunding deployments in ETH. :param strk_fee_contract: Contract for prefunding deployments in STRK. """ transfer_wei_res = await eth_fee_contract.functions["transfer"].invoke_v3( recipient=address, amount=int(1e40), resource_bounds=MAX_RESOURCE_BOUNDS ) await transfer_wei_res.wait_for_acceptance() transfer_fri_res = await strk_fee_contract.functions["transfer"].invoke_v3( recipient=address, amount=int(1e40), resource_bounds=MAX_RESOURCE_BOUNDS ) await transfer_fri_res.wait_for_acceptance() async def get_deploy_account_transaction( *, address: int, key_pair: KeyPair, salt: int, class_hash: int, client: Client ) -> DeployAccountV3: """ Get a signed DeployAccount transaction from provided details """ account = Account( address=address, client=client, key_pair=key_pair, chain=StarknetChainId.SEPOLIA, ) return await account.sign_deploy_account_v3( class_hash=class_hash, contract_address_salt=salt, constructor_calldata=[key_pair.public_key], resource_bounds=MAX_RESOURCE_BOUNDS, ) def _get_random_private_key_unsafe() -> int: """ Returns a private key in the range [1, EC_ORDER). This is not a safe way of generating private keys and should be used only in tests. """ return random.randint(1, EC_ORDER - 1) async def create_empty_block(http_client: HttpClient) -> None: url = http_client.url[:-4] if http_client.url.endswith("/rpc") else http_client.url await http_client.request( address=f"{url}/create_block", http_method=HttpMethod.POST, ) ================================================ FILE: tests/ed25519_test_vectors.json ================================================ [ { "secret_key": "9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60", "public_key": "d75a980182b10ab7d54bfed3c964073a0ee172f3daa62325af021a68f707511a", "message": "", "signed": "e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e065224901555fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b", "signature": "e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e065224901555fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b" }, { "secret_key": "4ccd089b28ff96da9db6c346ec114e0f5b8a319f35aba624da8cf6ed4fb8a6fb", "public_key": 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"signature": "0aab4c900501b3e24d7cdf4663326a3a87df5e4843b2cbdb67cbf6e460fec350aa5371b1508f9f4528ecea23c436d94b5e8fcd4f681e30a6ac00a9704a188a03" } ] ================================================ FILE: tests/hydra/algebra/test_polynomial.py ================================================ import pytest from garaga.algebra import BaseField, Polynomial from garaga.curves import CURVES, CurveID # List of curve IDs to test p = CURVES[CurveID.SECP256K1.value].p zero = Polynomial.zero(p) @pytest.mark.parametrize("degree_x", [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) @pytest.mark.parametrize("degree_y", [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) def test_xgcd(degree_x: int, degree_y: int): field = BaseField(p) x_coeffs = [field.random() for _ in range(degree_x + 1)] y_coeffs = [field.random() for _ in range(degree_y + 1)] x = Polynomial(x_coeffs) y = Polynomial(y_coeffs) a, b, g = Polynomial.xgcd(x, y) assert a * x + b * y == g assert x % g == zero assert y % g == zero @pytest.mark.parametrize("degree", [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) def test_lagrange_interpolation(degree: int): field = BaseField(p) # Define domain and values for interpolation domain = [field(i) for i in range(1, degree + 2)] values = [field(i * i) for i in range(1, degree + 2)] # Perform Lagrange interpolation interpolated_poly = Polynomial.lagrange_interpolation(p, domain, values) # Check that the polynomial evaluates correctly at the domain points for x, y in zip(domain, values): assert interpolated_poly.evaluate(x) == y # Additional checks for edge cases domain_edge = [field(0)] values_edge = [field(7)] interpolated_poly_edge = Polynomial.lagrange_interpolation( p, domain_edge, values_edge ) assert interpolated_poly_edge.evaluate(domain_edge[0]) == values_edge[0] # Check for larger set of points domain_large = [field(i) for i in range(1, 11)] values_large = [field(i * i) for i in range(1, 11)] interpolated_poly_large = Polynomial.lagrange_interpolation( p, domain_large, values_large ) for x, y in zip(domain_large, values_large): assert interpolated_poly_large.evaluate(x) == y ================================================ FILE: tests/hydra/algebra/test_pyfelt.py ================================================ import pytest from garaga.algebra import PyFelt # Define a prime number for the finite field p = 101 def test_pyfelt_addition(): a = PyFelt(10, p) b = PyFelt(20, p) c = 30 assert a + b == PyFelt(30, p) assert a + c == PyFelt(40, p) assert c + a == PyFelt(40, p) def test_pyfelt_subtraction(): a = PyFelt(10, p) b = PyFelt(20, p) c = 5 assert a - b == PyFelt(-10 % p, p) assert a - c == PyFelt(5, p) assert c - a == PyFelt(-5 % p, p) def test_pyfelt_multiplication(): a = PyFelt(10, p) b = PyFelt(20, p) c = 2 assert a * b == PyFelt(200 % p, p) assert a * c == PyFelt(20, p) assert c * a == PyFelt(20, p) def test_pyfelt_division(): a = PyFelt(10, p) c = PyFelt(1, p) assert a / c == a with pytest.raises(ValueError): a / PyFelt(0, p) def test_pyfelt_negation(): a = PyFelt(10, p) assert -a == PyFelt(-10 % p, p) def test_pyfelt_inversion(): a = PyFelt(10, p) inv_a = a.__inv__() assert a * inv_a == PyFelt(1, p) with pytest.raises(ValueError): PyFelt(0, p).__inv__() def test_pyfelt_exponentiation(): a = PyFelt(10, p) assert a**3 == PyFelt(1000 % p, p) assert a**0 == PyFelt(1, p) def test_pyfelt_equality(): a = PyFelt(10, p) b = PyFelt(10, p) c = PyFelt(20, p) assert a == b assert a != c assert a == 10 assert a != 20 def test_pyfelt_comparison(): a = PyFelt(10, p) b = PyFelt(20, p) c = 15 assert a < b assert a <= b assert b > a assert b >= a assert a < c assert a <= c assert b > c assert b >= c def test_pyfelt_quadratic_residue(): a = PyFelt(4, p) b = PyFelt(99, p) assert a.is_quad_residue() assert not b.is_quad_residue() def test_pyfelt_sqrt(): a = PyFelt(4, p) b = PyFelt(99, p) assert a.sqrt() == PyFelt(2, p) with pytest.raises(ValueError): print(b.sqrt()) def test_pyfelt_repr(): a = PyFelt(10, p) assert repr(a) == "PyFelt(10, 0x65)" def test_pyfelt_invalid_operations(): a = PyFelt(10, p) with pytest.raises(Exception): a + "invalid" with pytest.raises(Exception): a - "invalid" with pytest.raises(Exception): a * "invalid" with pytest.raises(Exception): a / "invalid" with pytest.raises(Exception): a == "invalid" with pytest.raises(Exception): a < "invalid" with pytest.raises(Exception): a <= "invalid" with pytest.raises(Exception): a > "invalid" with pytest.raises(Exception): a >= "invalid" if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/algebra/test_tower_final_exp.py ================================================ import time import pytest from garaga.curves import CurveID from garaga.hints.tower_backup import E12, get_base_field @pytest.mark.parametrize("curve_id", [CurveID.BN254.value, CurveID.BLS12_381.value]) def test_tower_final_exp(curve_id): e12 = E12.random(curve_id) start = time.time() e12t = e12.final_exp(use_rust=False) end = time.time() print(f"Python final_exp time: {end - start}") start = time.time() e12t_rust = e12.final_exp(use_rust=True) end = time.time() print(f"Rust final_exp time: {end - start}") assert e12t == e12t_rust @pytest.mark.parametrize("curve_id", [CurveID.BN254.value, CurveID.BLS12_381.value]) def test_tower_final_exp_zero_numerator(curve_id): field = get_base_field(curve_id) for _ in range(5): e12 = E12.from_direct( [ field.zero(), field.random(), field.zero(), field.random(), field.zero(), field.random(), field.zero(), field.random(), field.zero(), field.random(), field.zero(), field.random(), ], curve_id, ) e12t_rust = e12.final_exp(use_rust=True) assert e12t_rust == E12.one(curve_id) ================================================ FILE: tests/hydra/circuits/test_ec.py ================================================ import pytest from garaga.curves import CURVES, CurveID, get_base_field from garaga.modulo_circuit import WriteOps from garaga.points import G1Point, G2Point from garaga.precompiled_circuits.ec import BasicEC, BasicECG2 @pytest.mark.parametrize("curve_id", [CurveID.BLS12_381]) def test_double_point_g1(curve_id: CurveID): g = G1Point.get_nG(curve_id, 1) circuit = BasicEC("test", 1) gxys = circuit.write_elements(g.to_pyfelt_list(), WriteOps.INPUT) field = get_base_field(CurveID.BLS12_381) A = CURVES[CurveID.BLS12_381.value].a a = circuit.write_element(field(A)) resx, resy = circuit.double_point(gxys, a) got = G1Point( resx.value, resy.value, curve_id, ) expected = G1Point.get_nG(CurveID.BLS12_381, 2) assert got == expected, f"{got} != {expected}" @pytest.mark.parametrize("curve_id", [CurveID.BLS12_381]) def test_add_point_g1(curve_id: CurveID): g = G1Point.get_nG(curve_id, 1) h = G1Point.get_nG(curve_id, 2) circuit = BasicEC("test", 1) gxys = circuit.write_elements(g.to_pyfelt_list(), WriteOps.INPUT) hxys = circuit.write_elements(h.to_pyfelt_list(), WriteOps.INPUT) resx, resy = circuit.add_points(gxys, hxys) got = G1Point( resx.value, resy.value, curve_id, ) expected = G1Point.get_nG(curve_id, 3) assert got == expected, f"{got} != {expected}" @pytest.mark.parametrize("curve_id", [CurveID.BLS12_381]) def test_double_point_g2(curve_id: CurveID): # Arrange g = G2Point.get_nG(CurveID.BLS12_381, 1) circuit = BasicECG2("test", 1) gxys = circuit.write_elements(g.to_pyfelt_list(), WriteOps.INPUT) # Act resx, resy = circuit.double_point_a_eq_0((gxys[0:2], gxys[2:4])) # Assert got = G2Point( (resx[0].value, resx[1].value), (resy[0].value, resy[1].value), CurveID.BLS12_381, ) expected = G2Point.get_nG(CurveID.BLS12_381, 2) assert got == expected, f"{got} != {expected}" @pytest.mark.parametrize("curve_id", [CurveID.BLS12_381]) def test_add_point_g2(curve_id: CurveID): # Arrange g = G2Point.get_nG(curve_id, 1) h = G2Point.get_nG(curve_id, 2) circuit = BasicECG2("test", 1) gxys = circuit.write_elements(g.to_pyfelt_list(), WriteOps.INPUT) hxys = circuit.write_elements(h.to_pyfelt_list(), WriteOps.INPUT) # Act resx, resy = circuit.add_points((gxys[0:2], gxys[2:4]), (hxys[0:2], hxys[2:4])) # Assert got = G2Point( (resx[0].value, resx[1].value), (resy[0].value, resy[1].value), CurveID.BLS12_381, ) expected = G2Point.get_nG(curve_id, 3) assert got == expected, f"{got} != {expected}" ================================================ FILE: tests/hydra/circuits/test_honk.py ================================================ import pytest import garaga.hints.io as io from garaga.curves import ProofSystem from garaga.hints.keccak256 import keccak_256 from garaga.points import G1G2Pair from garaga.precompiled_circuits.zk_honk import ( CURVES, G2_POINT_KZG_1, G2_POINT_KZG_2, CurveID, G1Point, HonkVk, ZKHonkProof, ZKHonkTranscript, ZKHonkVerifierCircuits, get_msm_points_from_vk_and_proof, honk_proof_from_bytes, ) PATH = "hydra/garaga/starknet/honk_contract_generator/examples" def convert_pairing_points_to_g1( pairing_point_object: list[int], ) -> tuple[G1Point, G1Point]: """Convert the 16 field element pairing point object to two G1 points (lhs, rhs). Each point is encoded as 4 68-bit limbs for x and 4 68-bit limbs for y. """ def decode_coord(limbs): return limbs[0] | (limbs[1] << 68) | (limbs[2] << 136) | (limbs[3] << 204) lhs_x = decode_coord(pairing_point_object[0:4]) lhs_y = decode_coord(pairing_point_object[4:8]) rhs_x = decode_coord(pairing_point_object[8:12]) rhs_y = decode_coord(pairing_point_object[12:16]) lhs = G1Point(x=lhs_x, y=lhs_y, curve_id=CurveID.BN254) rhs = G1Point(x=rhs_x, y=rhs_y, curve_id=CurveID.BN254) return lhs, rhs def generate_recursion_separator( pairing_point_object: list[int], acc_lhs: G1Point, acc_rhs: G1Point ) -> int: """Generate the recursion separator by hashing the proof and accumulator points. Matches Solidity's generateRecursionSeparator function. """ proof_lhs, proof_rhs = convert_pairing_points_to_g1(pairing_point_object) # Hash 8 uint256 values: proofLhs.x, proofLhs.y, proofRhs.x, proofRhs.y, accLhs.x, accLhs.y, accRhs.x, accRhs.y data = b"" data += proof_lhs.x.to_bytes(32, "big") data += proof_lhs.y.to_bytes(32, "big") data += proof_rhs.x.to_bytes(32, "big") data += proof_rhs.y.to_bytes(32, "big") data += acc_lhs.x.to_bytes(32, "big") data += acc_lhs.y.to_bytes(32, "big") data += acc_rhs.x.to_bytes(32, "big") data += acc_rhs.y.to_bytes(32, "big") hash_result = keccak_256(data).digest() # Convert to field element (mod p) FR = CURVES[CurveID.GRUMPKIN.value].p return int.from_bytes(hash_result, "big") % FR @pytest.mark.parametrize( "proof_path, system", [ (f"{PATH}/proof_ultra_keccak_zk.bin", ProofSystem.UltraKeccakZKHonk), ], ) def test_verify_honk_proof(proof_path: str, system: ProofSystem): vk: HonkVk = HonkVk.from_bytes(open(f"{PATH}/vk_ultra_keccak.bin", "rb").read()) proof: ZKHonkProof = honk_proof_from_bytes( open(proof_path, "rb").read(), open(f"{PATH}/public_inputs_ultra_keccak.bin", "rb").read(), vk, system, ) tp = ZKHonkTranscript.from_proof(vk, proof, system) circuit: ZKHonkVerifierCircuits = ZKHonkVerifierCircuits( name="test", log_n=vk.log_circuit_size ) vk_circuit = vk.to_circuit_elements(circuit) proof_circuit = proof.to_circuit_elements(circuit) tp = tp.to_circuit_elements(circuit) public_input_delta = circuit.compute_public_input_delta( public_inputs=proof_circuit.public_inputs, pairing_point_object=proof_circuit.pairing_point_object, beta=tp.beta, gamma=tp.gamma, ) vanishing_check, diff_check = circuit.check_evals_consistency( proof_circuit.libra_evaluation, proof_circuit.libra_poly_evals, tp.gemini_r, tp.sum_check_u_challenges, ) assert vanishing_check.value != 0 assert diff_check.value == 0 rlc_check, check = circuit.verify_sum_check( libra_sum=proof_circuit.libra_sum, sumcheck_univariates=proof_circuit.sumcheck_univariates, sumcheck_evaluations=(proof_circuit.sumcheck_evaluations), libra_evaluation=proof_circuit.libra_evaluation, beta=tp.beta, gamma=tp.gamma, public_inputs_delta=public_input_delta, eta=tp.eta, eta_two=tp.etaTwo, eta_three=tp.etaThree, libra_challenge=tp.libra_challenge, sum_check_u_challenges=tp.sum_check_u_challenges, gate_challenge=tp.gate_challenge, alpha=tp.alpha, log_n=vk.log_circuit_size, base_rlc=circuit.write_element(1234), ) assert rlc_check.value == 0 assert check.value == 0 print(f"Pub input delta: {io.int_to_u384(public_input_delta, as_hex=False)}") scalars = circuit.compute_shplemini_msm_scalars( proof_circuit.sumcheck_evaluations, proof_circuit.gemini_masking_eval, proof_circuit.gemini_a_evaluations, proof_circuit.libra_poly_evals, tp.gemini_r, tp.rho, tp.shplonk_z, tp.shplonk_nu, tp.sum_check_u_challenges, ) print([scalar.value if scalar else scalar for scalar in scalars]) print(len(scalars)) points = get_msm_points_from_vk_and_proof(vk, proof) for i, (p, s) in enumerate(zip(points, scalars)): if s: print(i, hex(s.value)) P_0 = G1Point.msm(points=points, scalars=[scalar.value for scalar in scalars]) P_1 = -proof.kzg_quotient # Extract the points from pairing_point_object P_0_other, P_1_other = convert_pairing_points_to_g1(proof.pairing_point_object) print(f"P_0_other: x={hex(P_0_other.x)}, y={hex(P_0_other.y)}") print(f"P_1_other: x={hex(P_1_other.x)}, y={hex(P_1_other.y)}") # Generate recursion separator recursion_separator = generate_recursion_separator( proof.pairing_point_object, P_0, P_1 ) print(f"Recursion separator: {hex(recursion_separator)}") # Aggregate: P_0_final = recursionSeparator * P_0 + P_0_other # P_1_final = recursionSeparator * P_1 + P_1_other P_0_final = P_0.scalar_mul(recursion_separator).add(P_0_other) P_1_final = P_1.scalar_mul(recursion_separator).add(P_1_other) print(f"P_0_final: x={hex(P_0_final.x)}, y={hex(P_0_final.y)}") print(f"P_1_final: x={hex(P_1_final.x)}, y={hex(P_1_final.y)}") # Final pairing check with aggregated points pairs = [G1G2Pair(P_0_final, G2_POINT_KZG_1), G1G2Pair(P_1_final, G2_POINT_KZG_2)] pairing_result = G1G2Pair.pair(pairs).value_coeffs print(f"Pairing result WITH recursion aggregation: {pairing_result[:3]}...") assert ( pairing_result == [1] + [0] * 11 ), "Pairing check failed with recursion aggregation" @pytest.mark.parametrize( "proof_path, system", [ (f"{PATH}/proof_ultra_keccak_zk.bin", ProofSystem.UltraKeccakZKHonk), ], ) def test_check_evals_consistency(proof_path: str, system: ProofSystem): vk: HonkVk = HonkVk.from_bytes(open(f"{PATH}/vk_ultra_keccak.bin", "rb").read()) proof = honk_proof_from_bytes( open(proof_path, "rb").read(), open(f"{PATH}/public_inputs_ultra_keccak.bin", "rb").read(), vk, system, ) tp = ZKHonkTranscript.from_proof(vk, proof, system) circuit = ZKHonkVerifierCircuits(name="test", log_n=vk.log_circuit_size) proof_circuit = proof.to_circuit_elements(circuit) tp = tp.to_circuit_elements(circuit) vanishing_check_expected, diff_check_expected = circuit.check_evals_consistency( proof_circuit.libra_evaluation, proof_circuit.libra_poly_evals, tp.gemini_r, tp.sum_check_u_challenges, ) vanishing_check, diff_check = circuit.check_evals_consistency_split( proof_circuit.libra_evaluation, proof_circuit.libra_poly_evals, tp.gemini_r, tp.sum_check_u_challenges, ) assert vanishing_check.value == vanishing_check_expected.value assert diff_check.value == diff_check_expected.value ================================================ FILE: tests/hydra/circuits/test_multi_miller_loop.py ================================================ import copy import pytest from garaga.curves import CurveID from garaga.hints.extf_mul import nondeterministic_extension_field_mul_divmod from garaga.modulo_circuit import WriteOps from garaga.points import G1Point, G2Point from garaga.precompiled_circuits.multi_miller_loop import ( MultiMillerLoopCircuit, precompute_lines, ) @pytest.fixture( params=[ (CurveID.BN254, 1), (CurveID.BLS12_381, 1), (CurveID.BN254, 2), (CurveID.BLS12_381, 2), (CurveID.BN254, 3), (CurveID.BLS12_381, 3), (CurveID.BN254, 4), (CurveID.BLS12_381, 4), ] ) def circuit_and_points( request, ) -> tuple[MultiMillerLoopCircuit, list[G1Point], list[G2Point]]: curve_id, n_pairs = request.param def init_miller_loop_circuit() -> ( tuple[MultiMillerLoopCircuit, list[G1Point], list[G2Point]] ): circuit = MultiMillerLoopCircuit( name="test", curve_id=curve_id.value, n_pairs=n_pairs, hash_input=False ) Ps = [G1Point.gen_random_point(curve_id) for _ in range(n_pairs)] Qs = [G2Point.gen_random_point(curve_id) for _ in range(n_pairs)] circuit.write_p_and_q(Ps, Qs) return circuit, Ps, Qs return init_miller_loop_circuit() def test_precomputed_and_without_precompute_gives_same_output( circuit_and_points: tuple[MultiMillerLoopCircuit, list[G1Point], list[G2Point]], ): circuit0, Ps, Qs = circuit_and_points n_pairs = len(Ps) f0 = circuit0.miller_loop(n_pairs) f0 = [fi.felt for fi in f0] circuit1 = copy.deepcopy(circuit0) circuit1.precompute_lines = True circuit1.precomputed_lines = circuit1.write_elements( precompute_lines(Qs), WriteOps.INPUT ) circuit1._precomputed_lines_generator = ( circuit1._create_precomputed_lines_generator() ) circuit1.n_points_precomputed_lines = n_pairs f1 = circuit1.miller_loop(n_pairs) f1 = [fi.felt for fi in f1] assert f0 == f1 def test_partially_precomputed_and_without_precompute_gives_same_output( circuit_and_points: tuple[MultiMillerLoopCircuit, list[G1Point], list[G2Point]], ): circuit0, Ps, Qs = circuit_and_points n_pairs = len(Ps) f0 = circuit0.miller_loop(n_pairs) f0 = [fi.felt for fi in f0] circuit1 = copy.deepcopy(circuit0) circuit1.precompute_lines = True circuit1.precomputed_lines = circuit1.write_elements( precompute_lines(Qs[: n_pairs // 2]), WriteOps.INPUT ) circuit1._precomputed_lines_generator = ( circuit1._create_precomputed_lines_generator() ) circuit1.n_points_precomputed_lines = n_pairs // 2 f1 = circuit1.miller_loop(n_pairs) f1 = [fi.felt for fi in f1] assert f0 == f1 def test_prod_miller_loop_equals_multi_miller_loop( circuit_and_points: tuple[MultiMillerLoopCircuit, list[G1Point], list[G2Point]], ): circuit_multi, Ps, Qs = circuit_and_points curve_id = circuit_multi.curve_id n_pairs = len(Ps) f0 = circuit_multi.miller_loop(n_pairs) f0 = [fi.felt for fi in f0] fis = [] for i in range(n_pairs): circuit_prod_i = MultiMillerLoopCircuit( name="test", curve_id=curve_id, n_pairs=1, hash_input=False ) circuit_prod_i.write_p_and_q(Ps[i : i + 1], Qs[i : i + 1]) f_i = circuit_prod_i.miller_loop(1) fis.append(f_i) _, R = nondeterministic_extension_field_mul_divmod(fis, curve_id, 12) assert f0 == R ================================================ FILE: tests/hydra/hints/test_ecip.py ================================================ import random import pytest from garaga.curves import CURVES, CurveID, PairingCurve from garaga.hints.ecip import verify_ecip, zk_ecip_hint from garaga.points import G1Point, G2Point # Define the curves to be tested curves = list(CurveID) @pytest.mark.parametrize("curve_id", curves) @pytest.mark.parametrize("msm_size", range(1, 3)) def test_verify_ecip(curve_id, msm_size): curve = CURVES[curve_id.value] order = curve.n # Test for G1 points Bs_G1 = [G1Point.get_nG(curve_id, 1) for _ in range(msm_size)] scalars = [random.randint(1, order - 1) for _ in range(msm_size)] Q, sum_dlog = zk_ecip_hint(Bs_G1, scalars, use_rust=False) Q_rust, sum_dlog_rust = zk_ecip_hint(Bs_G1, scalars, use_rust=True) assert Q == Q_rust, f"Q: {Q}, \nQ_rust: {Q_rust}" assert ( sum_dlog == sum_dlog_rust ), f"sum_dlog: {sum_dlog}, \nsum_dlog_rust: {sum_dlog_rust}" assert verify_ecip(Bs_G1, scalars, Q=Q_rust, sum_dlog=sum_dlog_rust) # Test for G2 points if the curve supports pairing if isinstance(CURVES[curve_id.value], PairingCurve): Bs_G2 = [G2Point.gen_random_point(curve_id) for _ in range(msm_size)] assert verify_ecip(Bs_G2, scalars) @pytest.mark.parametrize("curve_id", curves) @pytest.mark.parametrize("msm_size", range(0, 3)) def test_verify_ecip_edge_cases(curve_id, msm_size): curve = CURVES[curve_id.value] order = curve.n # Test for G1 points Bs_G1 = [G1Point.gen_random_point(curve_id) for _ in range(msm_size)] + [ G1Point.infinity(curve_id) ] scalars = [0] + [random.randint(1, order - 1) for _ in range(msm_size)] assert verify_ecip(Bs_G1, scalars) # Test for G2 points if the curve supports pairing if isinstance(CURVES[curve_id.value], PairingCurve): Bs_G2 = [G2Point.gen_random_point(curve_id) for _ in range(msm_size)] + [ G2Point.infinity(curve_id) ] assert verify_ecip(Bs_G2, scalars) if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/hints/test_eisenstein.py ================================================ import pytest from hypothesis import given, settings from hypothesis import strategies as st from hydra.garaga.hints.eisenstein import EisensteinInteger, half_gcd # --- Hypothesis Strategies --- # Define reasonable bounds for generated integers to avoid excessively long tests # Using 64-bit range as a starting point, adjust if needed based on performance/coverage MAX_BITS = 64 min_int = -(2 ** (MAX_BITS - 1)) max_int = 2 ** (MAX_BITS - 1) - 1 MAX_EXAMPLES = 50 # Strategy for generating individual integers integer_strategy = st.integers(min_value=min_int, max_value=max_int) # Strategy for generating EisensteinInteger instances eisenstein_integer_strategy = st.builds( EisensteinInteger, a0=integer_strategy, a1=integer_strategy ) # Strategy for generating non-zero EisensteinInteger instances (for division) non_zero_eisenstein_integer_strategy = eisenstein_integer_strategy.filter( lambda x: not x.is_zero() ) # --- Test Constants --- ZERO = EisensteinInteger(0, 0) ONE = EisensteinInteger(1, 0) # --- Test Functions --- @settings(max_examples=MAX_EXAMPLES) # Adjust number of examples as needed @given(eisenstein_integer_strategy) def test_neg_twice_invariant(a: EisensteinInteger): """Test that negating twice returns the original number: -(-a) == a""" assert -(-a) == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy) def test_conj_twice_invariant(a: EisensteinInteger): """Test that conjugating twice returns the original number: conj(conj(a)) == a""" assert a.conjugate().conjugate() == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy, eisenstein_integer_strategy) def test_add_sub_invariant(a: EisensteinInteger, b: EisensteinInteger): """Test that adding then subtracting the same number is invariant: (a + b) - b == a""" assert (a + b) - b == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy, eisenstein_integer_strategy) def test_sub_add_invariant(a: EisensteinInteger, b: EisensteinInteger): """Test that subtracting then adding the same number is invariant: (a - b) + b == a""" assert (a - b) + b == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy) def test_add_zero_invariant(a: EisensteinInteger): """Test that adding zero is invariant: a + 0 == a""" assert a + ZERO == a assert ZERO + a == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy) def test_mul_one_invariant(a: EisensteinInteger): """Test that multiplying by one is invariant: a * 1 == a""" assert a * ONE == a assert ONE * a == a @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy) def test_mul_zero(a: EisensteinInteger): """Test that multiplying by zero results in zero: a * 0 == 0""" assert a * ZERO == ZERO assert ZERO * a == ZERO @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy, eisenstein_integer_strategy) def test_add_commutative(a: EisensteinInteger, b: EisensteinInteger): """Test addition commutativity: a + b == b + a""" assert a + b == b + a @settings(max_examples=MAX_EXAMPLES) @given( eisenstein_integer_strategy, eisenstein_integer_strategy, eisenstein_integer_strategy, ) def test_add_associative( a: EisensteinInteger, b: EisensteinInteger, c: EisensteinInteger ): """Test addition associativity: (a + b) + c == a + (b + c)""" assert (a + b) + c == a + (b + c) @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy, eisenstein_integer_strategy) def test_mul_commutative(a: EisensteinInteger, b: EisensteinInteger): """Test multiplication commutativity: a * b == b * a""" assert a * b == b * a @settings(max_examples=MAX_EXAMPLES) @given( eisenstein_integer_strategy, eisenstein_integer_strategy, eisenstein_integer_strategy, ) def test_mul_associative( a: EisensteinInteger, b: EisensteinInteger, c: EisensteinInteger ): """Test multiplication associativity: (a * b) * c == a * (b * c)""" assert (a * b) * c == a * (b * c) @settings(max_examples=MAX_EXAMPLES) @given( eisenstein_integer_strategy, eisenstein_integer_strategy, eisenstein_integer_strategy, ) def test_distributive(a: EisensteinInteger, b: EisensteinInteger, c: EisensteinInteger): """Test distributivity: a * (b + c) == (a * b) + (a * c)""" assert a * (b + c) == (a * b) + (a * c) assert (b + c) * a == (b * a) + (c * a) # Right distributivity @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy, eisenstein_integer_strategy) def test_sub_definition(a: EisensteinInteger, b: EisensteinInteger): """Test subtraction definition: a - b == a + (-b)""" assert a - b == a + (-b) @settings(max_examples=MAX_EXAMPLES) @given(eisenstein_integer_strategy) def test_norm_positive(a: EisensteinInteger): """Test that the norm is always non-negative: norm(a) >= 0""" assert a.norm() >= 0 @settings( max_examples=MAX_EXAMPLES ) # Reduced examples, increased deadline for performance @given(eisenstein_integer_strategy, non_zero_eisenstein_integer_strategy) def test_half_gcd(a: EisensteinInteger, b: EisensteinInteger): """ Test the half_gcd identity: w = a*u + b*v Where (w, v, u) is the result of half_gcd(a, b). Handles the case where b might become zero during the process. """ # half_gcd might raise ZeroDivisionError if b is zero initially or becomes zero # in an unexpected way, although the internal check should prevent this normally. try: w, v, u = half_gcd(a, b) # Verify the Bézout-like identity returned by half_gcd assert a * u + b * v == w except ZeroDivisionError: # This case might occur if the input 'b' leads to division by zero internally, # which shouldn't happen with the non_zero strategy and internal checks, # but we catch it defensively. pytest.skip( "Skipping test case due to potential division by zero in half_gcd internals." ) except Exception as e: # Catch any other unexpected exceptions pytest.fail(f"half_gcd raised an unexpected exception: {e}") # You might want to add specific edge case tests manually as well def test_specific_cases(): z1 = EisensteinInteger(3, 2) z2 = EisensteinInteger(1, -1) assert z1 + z2 == EisensteinInteger(4, 1) assert z1 * z2 == EisensteinInteger(5, 1) assert z1.norm() == 7 assert z2.norm() == 3 q, r = z1.quo_rem(z2) assert z1 == z2 * q + r # Test half_gcd with a specific case from the original Python example a_int = EisensteinInteger(0, 1) b_int = EisensteinInteger(-3, 19999) w, v, u = half_gcd(a_int, b_int) assert a_int * u + b_int * v == w def test_zero_division(): a = EisensteinInteger(5, 2) with pytest.raises(ZeroDivisionError): a.quo_rem(ZERO) with pytest.raises(ZeroDivisionError): a // ZERO with pytest.raises(ZeroDivisionError): a % ZERO # half_gcd(a, ZERO) should ideally handle this gracefully or be caught by tests # Let's see how the current implementation handles it try: w, v, u = half_gcd(a, ZERO) # If b is zero, the loop condition `b_run.norm() >= limit` might be false initially # The result should be (a, 0, 1) according to standard extended Euclidean Alg. conventions? # Let's check what the code *actually* does. # The loop `while b_run.norm() >= limit:` will not run if b_run is zero. # It returns `b_run, v_, u_` initialized as `(b, 1, 0)` before loop. # So it should return (ZERO, 1, 0) assert w == ZERO assert v == ONE # Initial v_ assert u == ZERO # Initial u_ # Let's check the identity a*u + b*v == w # a*0 + 0*1 == 0 -> Correct except ZeroDivisionError: pytest.fail("half_gcd(a, ZERO) raised ZeroDivisionError unexpectedly") except Exception as e: pytest.fail(f"half_gcd(a, ZERO) raised an unexpected exception: {e}") def test_half_gcd_a_zero(): b = EisensteinInteger(3, 5) # half_gcd(0, b) try: w, v, u = half_gcd(ZERO, b) # Initialization: a_run=0, b_run=b, u=1, v=0, u_=0, v_=1 # limit = isqrt(0) = 0 # Loop condition: b.norm() >= 0 (true if b != 0) # Inside loop: quotient, remainder = a_run.quo_rem(b_run) -> 0.quo_rem(b) # 0 // b = 0, 0 % b = 0 # quotient = 0, remainder = 0 # next_u_ = u - quotient * u_ = 1 - 0*0 = 1 # next_v_ = v - quotient * v_ = 0 - 0*1 = 0 # a_run = b_run = b # b_run = remainder = 0 # u = u_ = 0 # v = v_ = 1 # u_ = next_u_ = 1 # v_ = next_v_ = 0 # Loop condition: b_run.norm() (0) >= limit (0) -> true? No, condition is >= limit, should be false if limit=0. # Let's re-read loop: `while b_run.norm() >= limit:` # If limit is 0, loop runs as long as norm is non-negative. Needs a b_run.is_zero() check. # The code *has* `if b_run.is_zero(): break` # So, in the first iteration: a_run=0, b_run=b. limit=0. norm(b) >= 0. # quo=0, rem=0. # next_u_=1, next_v_=0 # a_run becomes b. b_run becomes 0. u becomes 0, v becomes 1. u_ becomes 1, v_ becomes 0. # Next iteration: b_run is 0. Break. # Return b_run, v_, u_ -> (0, 0, 1) assert w == ZERO assert v == ZERO # Final v_ assert u == ONE # Final u_ # Check identity: a*u + b*v == w # 0*1 + b*0 == 0 -> Correct except ZeroDivisionError: pytest.fail("half_gcd(ZERO, b) raised ZeroDivisionError unexpectedly") except Exception as e: pytest.fail(f"half_gcd(ZERO, b) raised an unexpected exception: {e}") ================================================ FILE: tests/hydra/hints/test_fake_glv.py ================================================ import random import pytest from garaga.curves import CURVES, CurveID from garaga.hints.fake_glv import ( half_gcd_eisenstein_hint, scalar_mul_fake_glv, scalar_mul_glv_and_fake_glv, ) from garaga.points import G1Point GLV_FAKE_GLV_CURVES = [ CurveID(k) for k, v in CURVES.items() if v.is_endomorphism_available() ] FAKE_GLV_CURVES = [ CurveID(k) for k, v in CURVES.items() if not v.is_endomorphism_available() ] @pytest.mark.parametrize("curve_id", GLV_FAKE_GLV_CURVES) def test_half_gcd_eisenstein_hint(curve_id): curve = CURVES[curve_id.value] eigen_value = curve.eigen_value order = curve.n max_bit_length = curve.n.bit_length() // 4 + 9 print(f"max_bit_length: {max_bit_length}") for _ in range(10000): scalar = random.randint(1, order) u1, u2, v1, v2 = half_gcd_eisenstein_hint(order, scalar, eigen_value) # assert (scalar * (v1 + eigen_value * v2) + u1 + eigen_value * u2) % order == 0 assert abs(u1).bit_length() <= max_bit_length assert abs(u2).bit_length() <= max_bit_length assert abs(v1).bit_length() <= max_bit_length assert abs(v2).bit_length() <= max_bit_length @pytest.mark.parametrize("curve_id", GLV_FAKE_GLV_CURVES) def test_glv_fake_glv(curve_id): curve = CURVES[curve_id.value] random_point = G1Point.get_nG(curve_id, 1) # for _ in range(100): # scalar = random.randint(1, curve.n) # _ = scalar_mul_glv_and_fake_glv(random_point, scalar) scalar = curve.n - 2 _ = scalar_mul_glv_and_fake_glv(random_point, scalar) # for _ in range(100): # _ = scalar_mul_glv_and_fake_glv(random_point, scalar) # scalar -= 1 def test_glv_fake_glv_bls12_381_2(): curve = CURVES[CurveID.BLS12_381.value] n_failed = 0 n_passed = 0 for _ in range(10): try: point = G1Point.gen_random_point_not_in_subgroup(CurveID.BLS12_381) scalar = random.randint(1, 2**63) expected_point = point.scalar_mul(scalar) print(f"expected_point: {expected_point}") _ = scalar_mul_glv_and_fake_glv(point, scalar) n_passed += 1 except AssertionError as e: print(f"Assertion error for scalar = {e}") n_failed += 1 print(f"n_failed: {n_failed}, n_passed: {n_passed}") # _ = scalar_mul_glv_and_fake_glv(point, scalar) assert not point.is_in_prime_order_subgroup_generic() print(f"point nisg: {point}") def test_glv_fake_glv_bls12_381_3(): curve = CURVES[CurveID.BLS12_381.value] n_failed = 0 n_passed = 0 for _ in range(100): try: point = G1Point.gen_random_point(CurveID.BLS12_381) scalar = random.randint(1, curve.n) _ = scalar_mul_glv_and_fake_glv(point, scalar) n_passed += 1 except AssertionError as e: print(f"Assertion error for scalar = {scalar}") n_failed += 1 print(f"n_failed: {n_failed}, n_passed: {n_passed}") # _ = scalar_mul_glv_and_fake_glv(point, scalar) @pytest.mark.parametrize("curve_id", FAKE_GLV_CURVES) def test_scalar_mul_fake_glv(curve_id): curve = CURVES[curve_id.value] G = G1Point.get_nG(curve_id, 1) infinity_point = G1Point.infinity(curve_id) n = curve.n test_cases = [ # Point, Scalar, Description (G, 0, "Generator * 0"), (G, 1, "Generator * 1"), (G, 2, "Generator * 2"), (G, n - 1, "Generator * (n-1)"), (G, n, "Generator * n"), (infinity_point, 5, "Infinity * 5"), (infinity_point, 0, "Infinity * 0"), ] # Add a random point case random_point = G1Point.gen_random_point(curve_id) test_cases.extend( [ (random_point, 0, "Random * 0"), (random_point, 1, "Random * 1"), (random_point, n, "Random * n"), ] ) print(f"\nTesting Curve: {curve_id.name}") for point, scalar, desc in test_cases: print(f" Case: {desc} (P={point}, s={scalar})") expected = point.scalar_mul(scalar) actual = scalar_mul_fake_glv(point, scalar) assert actual == expected, f"Mismatch for {desc}" # Test more random points and scalars num_random_tests = 10 print(f" Running {num_random_tests} random tests...") for i in range(num_random_tests): point = G1Point.gen_random_point(curve_id) scalar = random.randint(1, n) # print(f" Random Test {i+1}: P={point}, s={scalar}") # Optional: verbose logging expected = point.scalar_mul(scalar) actual = scalar_mul_fake_glv(point, scalar) assert ( actual == expected ), f"Mismatch for random test {i+1} (P={point}, s={scalar})" print(f" {num_random_tests} random tests passed.") # Test random scalars for each bit length up to n.bit_length() print(f" Running tests for scalar bit lengths 1 to {n.bit_length()}...") for k in range(1, n.bit_length() + 1, 4): # Generate a scalar with exactly k bits if k == 1: scalar = 1 # Only possible 1-bit scalar > 0 else: lower_bound = 1 << (k - 1) upper_bound = (1 << k) - 1 scalar = random.randint(lower_bound, upper_bound) # Ensure scalar is less than n (important for high bit lengths) scalar = scalar % n if scalar == 0: # Avoid scalar 0 if it happens by modulo scalar = 1 # Or continue; let's test with 1 in this rare case point_to_test = G # Use generator for consistency # print(f" Bit Length {k}: s={scalar}") # Optional: verbose logging expected = point_to_test.scalar_mul(scalar) actual = scalar_mul_fake_glv(point_to_test, scalar) assert actual == expected, f"Mismatch for scalar bit length {k} (s={scalar})" print(f" Scalar bit length tests passed.") ================================================ FILE: tests/hydra/hints/test_final_exp_witness.py ================================================ import random import pytest from garaga.algebra import get_sparsity from garaga.curves import CURVES, CurveID from garaga.hints.multi_miller_witness import ( get_final_exp_witness, get_lambda, get_miller_loop_output, ) from garaga.hints.tower_backup import E6, E12 from garaga.precompiled_circuits.multi_pairing_check import ( MultiPairingCheckCircuit, WriteOps, get_max_Q_degree, get_pairing_check_input, ) @pytest.mark.parametrize("seed", range(4)) @pytest.mark.parametrize("curve_id", [CurveID.BN254, CurveID.BLS12_381]) def test_final_exp_witness(seed, curve_id): random.seed(seed) ONE = E12.one(curve_id.value) λ = get_lambda(curve_id) q = CURVES[curve_id.value].p r = CURVES[curve_id.value].n h = (q**12 - 1) // r # Test correct case f_correct = get_miller_loop_output(curve_id=curve_id, will_be_one=True) root_correct_rust, w_full_correct_rust = get_final_exp_witness( curve_id.value, f_correct, use_rust=True ) root_correct_python, w_full_correct_python = get_final_exp_witness( curve_id.value, f_correct, use_rust=False ) # Compare Rust and Python implementations assert ( root_correct_rust == root_correct_python ), "Roots should match between Rust and Python implementations" assert ( w_full_correct_rust == w_full_correct_python ), "Scaling factors should match between Rust and Python implementations" e6_subfield = E12( [E6.random(curve_id.value), E6.zero(curve_id.value)], curve_id.value ) scaling_factor_sparsity = get_sparsity(e6_subfield.to_direct()) scaling_factor = w_full_correct_rust.to_direct() # Assert sparsity is correct: for every index where the sparsity is 0, the coefficient must 0 in scaling factor for i in range(len(scaling_factor_sparsity)): if scaling_factor_sparsity[i] == 0: assert scaling_factor[i].value == 0 # Therefore scaling factor lies in Fp6 assert f_correct**h == ONE, "f^h should equal 1 for correct case" assert ( f_correct * w_full_correct_rust == root_correct_rust**λ ), "f * w_full should equal root**λ for correct case" # Test incorrect case f_incorrect = get_miller_loop_output(curve_id=curve_id, will_be_one=False) root_incorrect_rust, w_full_incorrect_rust = get_final_exp_witness( curve_id.value, f_incorrect, use_rust=True ) root_incorrect_python, w_full_incorrect_python = get_final_exp_witness( curve_id.value, f_incorrect, use_rust=False ) # Compare Rust and Python implementations assert ( root_incorrect_rust == root_incorrect_python ), "Roots should match between Rust and Python implementations" assert ( w_full_incorrect_rust == w_full_incorrect_python ), "Scaling factors should match between Rust and Python implementations" assert f_incorrect**h != ONE, "f^h should not equal 1 for incorrect case" assert ( f_incorrect * w_full_incorrect_rust != root_incorrect_rust**λ ), "f * w_full should not equal root**λ for incorrect case" print(f"{seed}-th check ok") @pytest.mark.parametrize("curve_id", [CurveID.BN254, CurveID.BLS12_381]) @pytest.mark.parametrize("n_pairs", [2, 3, 4, 5]) @pytest.mark.parametrize("include_m", [False, True]) def test_mpcheck(curve_id: CurveID, n_pairs: int, include_m: bool): c = MultiPairingCheckCircuit(name="mock", curve_id=curve_id.value, n_pairs=n_pairs) circuit_input, m = get_pairing_check_input(curve_id, n_pairs, include_m=include_m) c.write_p_and_q_raw(circuit_input) M = c.write_elements(m, WriteOps.INPUT) if m is not None else None c.multi_pairing_check(n_pairs, M) # Check done implicitely here c.finalize_circuit() def total_cost(c): summ = c.summarize() summ["total_steps_cost"] = ( summ["MULMOD"] * 8 + summ["ADDMOD"] * 4 + summ["ASSERT_EQ"] * 2 + summ["POSEIDON"] * 17 + summ["RLC"] * 28 ) return summ cost = total_cost(c) q_max_degree = max([q.degree() for q in c.accumulate_poly_instructions[0].Qis]) # Assertions assert q_max_degree <= get_max_Q_degree(curve_id.value, n_pairs) print(f"\nTest {curve_id.name} {n_pairs=} {'with m' if include_m else 'without m'}") print(f"Total cost: {cost}") print(f"Q max degree: {q_max_degree}") ================================================ FILE: tests/hydra/hints/test_frobenius.py ================================================ import pytest from garaga.curves import CurveID from garaga.hints.frobenius import generate_frobenius_maps, get_frobenius_maps @pytest.mark.parametrize("curve_id", [CurveID.BN254.value, CurveID.BLS12_381.value]) @pytest.mark.parametrize("extension_degree", [6, 12]) @pytest.mark.parametrize("frob_power", [1, 2, 3]) def test_get_frobenius_maps(curve_id, extension_degree, frob_power): k_expressions, constants_list = get_frobenius_maps( curve_id, extension_degree, frob_power ) k_expressions_gen, constants_list_gen = generate_frobenius_maps( curve_id, extension_degree, frob_power ) assert k_expressions == k_expressions_gen, f"{k_expressions} != {k_expressions_gen}" assert constants_list == constants_list_gen ================================================ FILE: tests/hydra/hints/test_neg3.py ================================================ import random import pytest from garaga.hints.neg_3 import neg_3_base_le, positive_negative_multiplicities @pytest.fixture def test_params(): return list(range(128)) + [random.randint(0, 2**128) for _ in range(128)] def test_neg_3_base_le(test_params): for integer in test_params: assert ( sum((-3) ** i * x for i, x in enumerate(neg_3_base_le(integer))) == integer ) def test_positive_negative_multiplicities(test_params): for integer in test_params: ep, en = positive_negative_multiplicities(neg_3_base_le(integer)) assert integer == ep - en if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/starknet/test_calldata.py ================================================ import random import pytest from garaga.curves import CURVES, CurveID from garaga.points import G1Point from garaga.precompiled_circuits.multi_pairing_check import get_pairing_check_input from garaga.starknet.tests_and_calldata_generators.drand_calldata import ( drand_encrypt_to_calldata, drand_round_to_calldata, ) from garaga.starknet.tests_and_calldata_generators.mpcheck import MPCheckCalldataBuilder from garaga.starknet.tests_and_calldata_generators.msm import MSMCalldataBuilder # Define the curves to be tested curves = list(CurveID) @pytest.mark.parametrize("curve_id", [CurveID.BN254, CurveID.BLS12_381]) @pytest.mark.parametrize("mpc_size", [2, 3]) @pytest.mark.parametrize("n_fixed_g2", [2]) @pytest.mark.parametrize("include_m", [True, False]) def test_mpc_calldata_builder( curve_id, mpc_size, n_fixed_g2, include_m, ): pairs, public_pair = get_pairing_check_input( curve_id=curve_id, n_pairs=mpc_size, include_m=include_m, return_pairs=True, ) mpc = MPCheckCalldataBuilder( curve_id=curve_id, pairs=pairs, n_fixed_g2=n_fixed_g2, public_pair=public_pair, ) calldata_py = mpc.serialize_to_calldata(use_rust=False) calldata_rs = mpc.serialize_to_calldata(use_rust=True) assert len(calldata_py) == len(calldata_rs) assert calldata_py == calldata_rs @pytest.mark.parametrize("curve_id", curves) @pytest.mark.parametrize("msm_size", [1, 2]) @pytest.mark.parametrize("include_points_and_scalars", [True, False]) @pytest.mark.parametrize("serialize_as_pure_felt252_array", [True, False]) def test_msm_calldata_builder( curve_id, msm_size, include_points_and_scalars, serialize_as_pure_felt252_array, ): curve = CURVES[curve_id.value] order = curve.n scalar_limit = order points = [G1Point.gen_random_point(curve_id) for _ in range(msm_size)] scalars = [random.randint(0, scalar_limit - 1) for _ in range(msm_size)] msm = MSMCalldataBuilder( points=points, scalars=scalars, curve_id=curve_id, ) calldata1 = msm.serialize_to_calldata( include_points_and_scalars=include_points_and_scalars, serialize_as_pure_felt252_array=serialize_as_pure_felt252_array, use_rust=False, ) calldata2 = msm.serialize_to_calldata( include_points_and_scalars=include_points_and_scalars, serialize_as_pure_felt252_array=serialize_as_pure_felt252_array, use_rust=True, ) assert calldata1 == calldata2 @pytest.mark.parametrize("round_number", [1, 2, 3]) def test_drand_randomness_to_calldata( round_number, ): calldata1 = drand_round_to_calldata( round_number, use_rust=False, ) calldata2 = drand_round_to_calldata( round_number, use_rust=True, ) assert calldata1 == calldata2 @pytest.mark.parametrize("round_number", [1, 2, 3]) @pytest.mark.parametrize( "message", [b"0000000000000000", b"1234567890abcdef", b"fedababafecacaca"] ) @pytest.mark.parametrize("randomness", [b"0000000000000000", b"dead00013000beef"]) def test_drand_encrypt_to_round_calldata( round_number, message, randomness, ): calldata1 = drand_encrypt_to_calldata( round_number, message, randomness, use_rust=False, ) calldata2 = drand_encrypt_to_calldata( round_number, message, randomness, use_rust=True, ) assert calldata1 == calldata2 if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/starknet/test_groth16_vk_proof_parsing.py ================================================ import pytest from garaga.starknet.groth16_contract_generator.calldata import ( groth16_calldata_from_vk_and_proof, ) from garaga.starknet.groth16_contract_generator.parsing_utils import ( Groth16Proof, Groth16VerifyingKey, ) PATH = "hydra/garaga/starknet/groth16_contract_generator/examples" @pytest.mark.parametrize( "vk_path", [ f"{PATH}/snarkjs_vk_bn254.json", f"{PATH}/snarkjs_vk_bls12381.json", f"{PATH}/vk_bn254.json", f"{PATH}/vk_bls.json", f"{PATH}/gnark_vk_bn254.json", f"{PATH}/vk_risc0.json", f"{PATH}/vk_sp1.json", ], ) def test_vk_parsing(vk_path: str): vk = Groth16VerifyingKey.from_json(vk_path) print(vk) # if vk_path == f"{PATH}/vk_sp1.json": # print("[") # for e in vk.flatten(): # print(f'"{hex(e)[2:]}",') # print("]") @pytest.mark.parametrize( "proof_path", [ f"{PATH}/proof_bn254.json", f"{PATH}/proof_bls.json", f"{PATH}/proof_risc0.json", f"{PATH}/proof_sp1.json", ], ) def test_proof_parsing(proof_path: str): proof = Groth16Proof.from_json(proof_path) print(proof) @pytest.mark.parametrize( "proof_path, pub_inputs_path", [ (f"{PATH}/snarkjs_proof_bn254.json", f"{PATH}/snarkjs_public_bn254.json"), (f"{PATH}/snarkjs_proof_bls12381.json", f"{PATH}/snarkjs_public_bls12381.json"), (f"{PATH}/gnark_proof_bn254.json", f"{PATH}/gnark_public_bn254.json"), ], ) def test_proof_parsing_with_public_input(proof_path: str, pub_inputs_path: str): proof = Groth16Proof.from_json(proof_path, pub_inputs_path) print(proof) @pytest.mark.parametrize( "proof_path, vk_path, pub_inputs_path", [ (f"{PATH}/proof_bn254.json", f"{PATH}/vk_bn254.json", None), (f"{PATH}/proof_bls.json", f"{PATH}/vk_bls.json", None), ( f"{PATH}/gnark_proof_bn254.json", f"{PATH}/gnark_vk_bn254.json", f"{PATH}/gnark_public_bn254.json", ), ( f"{PATH}/snarkjs_proof_bn254.json", f"{PATH}/snarkjs_vk_bn254.json", f"{PATH}/snarkjs_public_bn254.json", ), (f"{PATH}/proof_risc0.json", f"{PATH}/vk_risc0.json", None), (f"{PATH}/proof_sp1.json", f"{PATH}/vk_sp1.json", None), ], ) def test_calldata_generation( proof_path: str, vk_path: str, pub_inputs_path: str | None ): import time vk = Groth16VerifyingKey.from_json(vk_path) proof = Groth16Proof.from_json(proof_path, pub_inputs_path) start = time.time() calldata = groth16_calldata_from_vk_and_proof(vk, proof, use_rust=False) end = time.time() print(f"Python time: {end - start}") start = time.time() calldata_rust = groth16_calldata_from_vk_and_proof(vk, proof, use_rust=True) end = time.time() print(f"Rust time: {end - start}") assert calldata == calldata_rust ================================================ FILE: tests/hydra/starknet/test_honk_vk_proof_parsing.py ================================================ import pytest from garaga.curves import ProofSystem from garaga.precompiled_circuits.zk_honk import HonkVk, honk_proof_from_bytes from garaga.starknet.honk_contract_generator.calldata import ( get_ultra_flavor_honk_calldata_from_vk_and_proof, ) PATH = "hydra/garaga/starknet/honk_contract_generator/examples" @pytest.mark.parametrize( "vk_path, vk_hash_path", [ (f"{PATH}/vk_ultra_keccak.bin", f"{PATH}/vk_hash_ultra_keccak.bin"), ], ) def test_vk_parsing(vk_path: str, vk_hash_path: str): vk = HonkVk.from_bytes(open(vk_path, "rb").read()) vk_hash_expected = int.from_bytes(open(vk_hash_path, "rb").read(), "big") assert ( vk.vk_hash == vk_hash_expected ), f"vk_hash: {hex(vk.vk_hash)} != vk_hash_expected: {hex(vk_hash_expected)}" print(vk) @pytest.mark.parametrize( "proof_path, public_inputs_path, vk_path, system", [ ( f"{PATH}/proof_ultra_keccak_zk.bin", f"{PATH}/public_inputs_ultra_keccak.bin", f"{PATH}/vk_ultra_keccak.bin", ProofSystem.UltraKeccakZKHonk, ), ], ) def test_proof_parsing( proof_path: str, public_inputs_path: str, vk_path: str, system: ProofSystem, ): vk = HonkVk.from_bytes(open(vk_path, "rb").read()) proof = honk_proof_from_bytes( open(proof_path, "rb").read(), open(public_inputs_path, "rb").read(), vk, system ) print(proof) @pytest.mark.parametrize( "proof_path, public_inputs_path, vk_path, system", [ ( f"{PATH}/proof_ultra_keccak_zk.bin", f"{PATH}/public_inputs_ultra_keccak.bin", f"{PATH}/vk_ultra_keccak.bin", ProofSystem.UltraKeccakZKHonk, ), ], ) def test_calldata_generation( proof_path: str, public_inputs_path: str, vk_path: str, system: ProofSystem, ): import time vk = HonkVk.from_bytes(open(vk_path, "rb").read()) proof = honk_proof_from_bytes( open(proof_path, "rb").read(), open(public_inputs_path, "rb").read(), vk, system ) start = time.time() calldata = get_ultra_flavor_honk_calldata_from_vk_and_proof( vk, proof, system, use_rust=False ) end = time.time() print(f"Python time: {end - start}") start = time.time() calldata_rust = get_ultra_flavor_honk_calldata_from_vk_and_proof( vk, proof, system, use_rust=True ) end = time.time() print(f"Rust time: {end - start}") assert calldata == calldata_rust ================================================ FILE: tests/hydra/starknet/test_signatures_calldata.py ================================================ import json import pytest from garaga.curves import CurveID from garaga.starknet.tests_and_calldata_generators.signatures import ( ECDSASignature, EdDSA25519Signature, RSA2048Signature, SchnorrSignature, ) # Define the curves to be tested curves = list(CurveID) @pytest.mark.parametrize("curve_id", curves) @pytest.mark.parametrize("prepend_public_key", [True, False]) def test_schnorr_calldata_builder(curve_id, prepend_public_key): """Test that Python and Rust implementations of Schnorr signature calldata match""" for _ in range(3): # Test 3 random samples # Generate a random valid signature sig = SchnorrSignature.sample(curve_id) # Get calldata from Python implementation calldata1 = sig.serialize_with_hints( use_rust=False, prepend_public_key=prepend_public_key ) # Get calldata from Rust implementation calldata2 = sig.serialize_with_hints( use_rust=True, prepend_public_key=prepend_public_key ) assert ( calldata1 == calldata2 ), f"Mismatch in Schnorr calldata for curve {curve_id.name}" @pytest.mark.parametrize("curve_id", curves) @pytest.mark.parametrize("prepend_public_key", [True, False]) def test_ecdsa_calldata_builder(curve_id, prepend_public_key): """Test that Python and Rust implementations of ECDSA signature calldata match""" for _ in range(4): # Test 4 random samples # Generate a random valid signature sig = ECDSASignature.sample(curve_id) # Get calldata from Python implementation calldata1 = sig.serialize_with_hints( use_rust=False, prepend_public_key=prepend_public_key ) # Get calldata from Rust implementation calldata2 = sig.serialize_with_hints( use_rust=True, prepend_public_key=prepend_public_key ) assert ( calldata1 == calldata2 ), f"Mismatch in ECDSA calldata for curve {curve_id.name}" @pytest.mark.parametrize("prepend_public_key", [True, False]) def test_eddsa_25519_signatures(prepend_public_key, full=False): with open("tests/ed25519_test_vectors.json", "r") as f: test_vectors = json.load(f) if full: test_vectors = test_vectors else: test_vectors = test_vectors[0:96] for i, test_vector in enumerate(test_vectors): signature = EdDSA25519Signature.from_json(test_vector) assert signature.is_valid(), f"Signature {i} is invalid" calldata_py = signature.serialize_with_hints( use_rust=False, prepend_public_key=prepend_public_key ) calldata_rust = signature.serialize_with_hints( use_rust=True, prepend_public_key=prepend_public_key ) assert ( calldata_py == calldata_rust ), f"Mismatch in EdDSA calldata for test vector {i}" @pytest.mark.parametrize("prepend_public_key", [True, False]) def test_rsa2048_calldata_lengths(prepend_public_key): signature = RSA2048Signature.sample(seed=0) calldata = signature.serialize_with_hints( use_rust=False, prepend_public_key=prepend_public_key ) expected_len = 888 if prepend_public_key else 864 assert len(calldata) == expected_len def test_rsa2048_calldata_public_key_prefix(): signature = RSA2048Signature.sample(seed=0) full = signature.serialize_with_hints(use_rust=False, prepend_public_key=True) public_key = signature.serialize_public_key() witness = signature.serialize_signature_with_hints() assert full[: len(public_key)] == public_key assert full[len(public_key) :] == witness @pytest.mark.parametrize("prepend_public_key", [True, False]) def test_rsa2048_calldata_builder(prepend_public_key): """Test that Python and Rust implementations of RSA-2048 calldata match""" for seed in range(3): sig = RSA2048Signature.sample(seed=seed) calldata_py = sig.serialize_with_hints( use_rust=False, prepend_public_key=prepend_public_key ) calldata_rs = sig.serialize_with_hints( use_rust=True, prepend_public_key=prepend_public_key ) assert ( calldata_py == calldata_rs ), f"Mismatch in RSA-2048 calldata for seed {seed}" @pytest.mark.parametrize("prepend_public_key", [True, False]) @pytest.mark.parametrize("message", [b"hello garaga", b"", b"a" * 100, b"\x00\x01\x02"]) def test_rsa2048_sha256_calldata_builder(prepend_public_key, message): """Test that Python and Rust implementations of RSA-2048 SHA-256 calldata match""" sig = RSA2048Signature.from_sha256_message(message, seed=0) calldata_py = sig.serialize_sha256_with_hints( message=message, use_rust=False, prepend_public_key=prepend_public_key, ) calldata_rs = sig.serialize_sha256_with_hints( message=message, use_rust=True, prepend_public_key=prepend_public_key, ) assert ( calldata_py == calldata_rs ), f"Mismatch in RSA-2048 SHA-256 calldata for message {message!r}" if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/test_bls18_381_map_to_curve.py ================================================ from garaga.modulo_circuit import WriteOps from garaga.precompiled_circuits.map_to_curve import MapToCurveG1, MapToCurveG2 def test_bls18_381_map_to_curve_g2_non_quadratic(): circuit = MapToCurveG2("test", 1) circuit.set_consts() field = circuit.write_elements( [ circuit.field( 3741944764571472160006322193608041966151877622471123223277469611910821820061028054244113212685535996904839352799402 ), circuit.field( 2076377621229436486953902801269393160218977179950230047408992877427440885760409779221205731516804245080380194857867 ), ], WriteOps.INPUT, ) g1x, div, num_x1, zeta_u2 = circuit.map_to_curve_part_1(field) # Assert intermediate results assert ( g1x[0].emulated_felt.value == 953996773580150187658453355749387256203585747550541475689949001565592017941792784008487857020741875161940439358169 ) assert ( g1x[1].emulated_felt.value == 1091041959624877033265075916985653082630429384881674462548287154185532968300913190673468388150241943339667076518253 ) assert ( div[0].emulated_felt.value == 1271124738425673168909051490409346544806999942963856749219399676853245141674638476952210593612982147617933716830990 ) assert ( div[1].emulated_felt.value == 2707549614030537572533166896762785147996244686855330285575235995466755739337470183080976608052299087222211278178288 ) assert ( num_x1[0].emulated_felt.value == 3368717908425370587121521256961562283349295337955434359453978866874955592536159067888255032927442968748123109596151 ) assert ( num_x1[1].emulated_felt.value == 3415444388557434595807082624117973727069974003779938583652094445339905219350042585004730694719550642891646061378068 ) assert ( zeta_u2[0].emulated_felt.value == 2066503771099735372725208757434934470387642893685367231392552060087408173898621033802030119021772665098131312925308 ) assert ( zeta_u2[1].emulated_felt.value == 1011496392125783422068061997226415746244229915320831072846626167000664891392171563621675612638222437312051389941143 ) x_affine, y, field = circuit.compute_initial_coordinates_non_quadratic( field, g1x, div, num_x1, zeta_u2 ) y_affine, qfield, qy = circuit.adjust_y_sign(y, field) # Assert final results assert ( x_affine[0].emulated_felt.value == 2006413752686223508612366075043722458232321744863932880413784802489452766740742045984482044248764924205010366531647 ) assert ( x_affine[1].emulated_felt.value == 2103918733930157635900741069076788853417130098910518594897125230089087553459780427160470339353748226243766968776215 ) assert ( y_affine[0].emulated_felt.value == 2345181275451808874246097791768578660839971403546046193253448677984295781774410213317345275973043584946083029690838 ) assert ( y_affine[1].emulated_felt.value == 491718355885353185704655750809656447183587281146662745649897882009019112506313662303269809992594062560315039747134 ) def test_bls18_381_map_to_curve_g2_quadratic(): circuit = MapToCurveG2("test", 1) circuit.set_consts() field = circuit.write_elements( [ circuit.field( 1556800727266659224486307223710983989761661593776178353933175239605467918853638579207638742450628877266610077644019 ), circuit.field( 2231413721970278425038638834062370180699174210864795385441649994565282274875534254514118105433862522641883533654145 ), ], WriteOps.INPUT, ) g1x, div, num_x1, zeta_u2 = circuit.map_to_curve_part_1(field) # Assert intermediate results assert ( g1x[0].emulated_felt.value == 1741461048819108320601120926297383578798673393844727619465122674954412335152552581570073244593349691385858884173583 ) assert ( g1x[1].emulated_felt.value == 622728400870450638897257156989331087788861565586056105959821305999301052577755232615332472975146795773248285518397 ) assert ( div[0].emulated_felt.value == 245484112468371472016059514225945212312552892410862615098545961349697995155733061412689120985823985643121008707443 ) assert ( div[1].emulated_felt.value == 2710033076136311888860218740720521072952923210029411465485968205608170799418483286817121694092479356648635501832540 ) assert ( num_x1[0].emulated_felt.value == 678813894361393103360103286141952477825674360176586850375556142934890501990305386551122112060089003594179575462051 ) assert ( num_x1[1].emulated_felt.value == 481031161552380994425457621530411412945970154876090436018460806513725659192179414613944042534095739563026661110941 ) assert ( zeta_u2[0].emulated_felt.value == 2605347211487192472869035898066121846694525878433542755302801455037350149869786867270039608133704248908541829065188 ) assert ( zeta_u2[1].emulated_felt.value == 2186733141282187687524429079326838649285331456588145172920951615849025076744838489106511432055390831654029460361575 ) x_affine, y, field = circuit.compute_initial_coordinates_quadratic( field, g1x, div, num_x1 ) y_affine, qfield, qy = circuit.adjust_y_sign(y, field) # Assert final results assert ( x_affine[0].emulated_felt.value == 2843075373688611471290556504186176053275483247291128525980163517764803526616259371130035811825227707920936817728741 ) assert ( x_affine[1].emulated_felt.value == 3661712616179456093275454398202160102594067191736010383603184812959944211042529505618295008186663134429283699505891 ) assert ( y_affine[0].emulated_felt.value == 2229899020770589661585214900480830515873415727829711460134445858387853696109925143060238999266818473086058450471795 ) assert ( y_affine[1].emulated_felt.value == 3127664777588830509127251096086955764006894160737524705993294599144750103128110100147816255502757346871240956727581 ) def test_bls18_381_map_to_curve_g1_quadratic(): circuit = MapToCurveG1("test", 1) circuit.set_consts() field = circuit.write_element( circuit.field( 2231413721970278425038638834062370180699174210864795385441649994565282274875534254514118105433862522641883533654145 ) ) g1x, div, num_x1, zeta_u2 = circuit.map_to_curve_part_1(field) # Assert intermediate results assert ( g1x.emulated_felt.value == 2597611908074869266676097344052780591254059561619989704088799034359084350987704445977946845985385140941235233170571 ) assert ( div.emulated_felt.value == 2805237479025562283149334731040192757369528037210657601602127558394884972035943561694397352660127862349210615463142 ) assert ( num_x1.emulated_felt.value == 357516532893183420527219030989999274866612035539674613298479245292141662614414253856542640697610990033784993055353 ) assert ( zeta_u2.emulated_felt.value == 1458720157247399937074920312179320190319011370446888399995409372377477911247349655187476411795089883075347478260790 ) x_affine, y_initial, field = circuit.compute_initial_coordinates_quadratic( field, g1x, div, num_x1 ) y_affine, qy, qfield = circuit.adjust_y_sign(y_initial, field) # Assert final results assert ( x_affine.emulated_felt.value == 821680820282835312240647697969669528662337868557420531415876216710180320418897646214379495222032594074174798424202 ) assert ( y_affine.emulated_felt.value == 2810929796268343801118836101228108033947242316820103062127644703467142871560955216144508646104360230898984292110363 ) def test_bls18_381_map_to_curve_g1_non_quadratic(): circuit = MapToCurveG1("test", 1) circuit.set_consts() field = circuit.write_element( circuit.field( 1556800727266659224486307223710983989761661593776178353933175239605467918853638579207638742450628877266610077644019 ) ) g1x, div, num_x1, zeta_u2 = circuit.map_to_curve_part_1(field) # Assert intermediate results assert ( g1x.emulated_felt.value == 341972610627912974245460429393853020244324285563375868527372516439156668443097006714852415949547549919046535667616 ) assert ( div.emulated_felt.value == 437377489188823988571636230286582387258102034988413032009071756963827842481400269867189494736241034037731549310834 ) assert ( num_x1.emulated_felt.value == 859079108276904279242178106413495842276094320054147243681841678369946208284556898300157013329362279916993343726889 ) assert ( zeta_u2.emulated_felt.value == 3595463469902610153619251584554498156597029272564817168764456841515827675239496939601340079478403412813212271353518 ) x_affine, y_initial, field = circuit.compute_initial_coordinates_non_quadratic( field, g1x, div, num_x1, zeta_u2 ) y_affine, qy, qfield = circuit.adjust_y_sign(y_initial, field) # Assert final results assert ( x_affine.emulated_felt.value == 1412853964218444964438936699552956047210482383152224645596624291427056376487356261681298103080878386132407858666637 ) assert ( y_affine.emulated_felt.value == 752734926215712395741522221355891264404138695398702662135908094550118515106801651502315795564392519475687558113863 ) ================================================ FILE: tests/hydra/test_cofactor_clearing.py ================================================ import garaga.modulo_circuit_structs as structs from garaga.curves import CURVES, PyFelt from garaga.modulo_circuit import WriteOps from hydra.garaga.precompiled_circuits.cofactor_clearing import ( FastG2CofactorClearing, G1CofactorClearing, SlowG2CofactorClearing, ) def test_cofactor_clearing(): # Initialize circuit circuit = FastG2CofactorClearing(name="cofactor_clearing", curve_id=1) # Input values values = [ PyFelt( 3789617024712504402204306620295003375951143917889162928515122476381982967144814366712031831841518399614182231387665, CURVES[1].p, ), PyFelt( 1467567314213963969852279817989131104935039564231603908576814773321528757289376676761397368853965316423532584391899, CURVES[1].p, ), PyFelt( 1292375129422168617658520396283100687686347104559592203462491249161639006037671760603453326853098986903549775136448, CURVES[1].p, ), PyFelt( 306655960768766438834866368706782505873384691666290681181893693450298456233972904889955517117016529975705729523733, CURVES[1].p, ), ] # Write struct and get coordinates px0, px1, py0, py1 = circuit.write_struct( structs.G2PointCircuit("G2", values), WriteOps.INPUT ) # Run cofactor clearing result = circuit.clear_cofactor(([px0, px1], [py0, py1])) print(result) # Assert x coordinates assert ( result[0][0].emulated_felt.value == 3553105769882656599146811322193073462254184878577379981354181602459568891247079537874757677386646278295787021209189 ) assert ( result[0][1].emulated_felt.value == 214383232028397026483172293507406653308736549333914058501039576182920645751681896937109061242049824624418352241545 ) # Assert y coordinates assert ( result[1][0].emulated_felt.value == 3739747178790495019675321498823208242976352322769291665915571365507822310651678949551185523146598688776619260961478 ) assert ( result[1][1].emulated_felt.value == 2892856738085945244799268348340138656888776287206503012318583837503972113824639536543638524553710065178322083313320 ) # Test slow cofactor clearing produces same results slow_circuit = SlowG2CofactorClearing(name="slow_co_clear", curve_id=1) # Write struct and get coordinates slow_px0, slow_px1, slow_py0, slow_py1 = slow_circuit.write_struct( structs.G2PointCircuit("G2", values), WriteOps.INPUT ) # Run slow cofactor clearing slow_result = slow_circuit.clear_cofactor( ([slow_px0, slow_px1], [slow_py0, slow_py1]) ) # Assert results match fast implementation assert slow_result[0][0].emulated_felt.value == result[0][0].emulated_felt.value assert slow_result[0][1].emulated_felt.value == result[0][1].emulated_felt.value assert slow_result[1][0].emulated_felt.value == result[1][0].emulated_felt.value assert slow_result[1][1].emulated_felt.value == result[1][1].emulated_felt.value def test_cofactor_clearing_g1(): circuit = G1CofactorClearing(name="cofactor_clearing", curve_id=1) val_x = circuit.write_element( circuit.field( 3789617024712504402204306620295003375951143917889162928515122476381982967144814366712031831841518399614182231387665 ) ) val_y = circuit.write_element( circuit.field( 1292375129422168617658520396283100687686347104559592203462491249161639006037671760603453326853098986903549775136448 ) ) x, y = circuit.clear_cofactor((val_x, val_y)) assert ( x.emulated_felt.value == 124653168926536040050712523694358620626733702681766514335826706855268535061758110145263289951074346182616444645930 ) assert ( y.emulated_felt.value == 1763117104256928975303050316870512727100973588519940064853641891041664131774050255702157308774582078610333186925605 ) ================================================ FILE: tests/hydra/test_drand.py ================================================ import hashlib import random import pytest import requests from garaga.curves import CurveID from garaga.drand.client import ( BASE_URLS, DrandNetwork, digest_func, get_randomness, print_all_chain_info, ) from garaga.drand.tlock import decrypt_at_round, encrypt_for_round from garaga.points import G1G2Pair, G2Point from garaga.signature import hash_to_curve @pytest.mark.parametrize("round_number", list(range(1, 5)) + list(range(1000, 1005))) def test_drand_sig_verification(round_number: int): chain_infos = print_all_chain_info() network = DrandNetwork.quicknet chain = chain_infos[network] round = get_randomness(chain.hash, round_number) print(f"Randomness for round {round_number}:", round) sha256 = hashlib.sha256() sha256.update(bytes.fromhex(round.signature)) print("randomness", sha256.hexdigest()) print("random beacon", hex(round.randomness)) msg_point = hash_to_curve( digest_func(round.round_number), CurveID.BLS12_381, "sha256" ) print("message", msg_point) assert ( G1G2Pair.pair( [ G1G2Pair( p=round.signature_point, q=G2Point.get_nG(CurveID.BLS12_381, 1) ), G1G2Pair(p=msg_point, q=-chain.public_key), ], curve_id=CurveID.BLS12_381, ).value_coeffs == [1] + [0] * 11 ), "Signature verification failed" @pytest.mark.parametrize("round", list(range(1, 5)) + list(range(1000, 1005))) def test_tlock_encrypt_decrypt(round: int): random.seed(42) chain_infos = print_all_chain_info() network = DrandNetwork.quicknet chain = chain_infos[network] master = chain.public_key msg = random.randbytes(16) ciph = encrypt_for_round(master, round, msg) chain = chain_infos[network] beacon = get_randomness(chain.hash, round) signature_at_round = beacon.signature_point msg_decrypted = decrypt_at_round(signature_at_round, ciph) assert msg_decrypted == msg @pytest.mark.parametrize("round", list(range(1, 5))) def test_tlock_encrypt_same_message_gives_different_ciphertexts(round: int): random.seed(42) chain_infos = print_all_chain_info() network = DrandNetwork.quicknet chain = chain_infos[network] master = chain.public_key msg = b"0123456789abcdef" ciph1 = encrypt_for_round(master, round, msg) ciph2 = encrypt_for_round(master, round, msg) assert ciph1.U != ciph2.U assert ciph1.V != ciph2.V assert ciph1.W != ciph2.W chain = chain_infos[network] beacon = get_randomness(chain.hash, round) signature_at_round = beacon.signature_point msg_decrypted1 = decrypt_at_round(signature_at_round, ciph1) msg_decrypted2 = decrypt_at_round(signature_at_round, ciph2) assert msg_decrypted1 == msg assert msg_decrypted2 == msg def test_all_base_urls_return_chains(): for url in BASE_URLS: try: response = requests.get(f"{url}/chains") response.raise_for_status() chains = response.json() # Check that both default and quicknet chains are present expected_chains = {network.value for network in DrandNetwork} found_chains = set(chains) assert expected_chains.issubset( found_chains ), f"URL {url} missing chains: {expected_chains - found_chains}" print(f"✓ {url} returned all expected chains") except Exception as e: print(f"✗ {url} failed: {str(e)}") continue ================================================ FILE: tests/hydra/test_extension_field_modulo_circuit.py ================================================ import random import pytest from garaga.algebra import PyFelt from garaga.curves import CurveID from garaga.extension_field_modulo_circuit import ExtensionFieldModuloCircuit from garaga.modulo_circuit import ModuloCircuitElement, WriteOps @pytest.fixture( params=[ (CurveID.BN254, 6), (CurveID.BLS12_381, 6), (CurveID.BN254, 12), (CurveID.BLS12_381, 12), ] ) def circuit(request) -> tuple[ExtensionFieldModuloCircuit, list[ModuloCircuitElement]]: curve_id, extension_degree = request.param def init_z_circuit( z: int = 2, ) -> tuple[ExtensionFieldModuloCircuit, list[ModuloCircuitElement]]: c = ExtensionFieldModuloCircuit( name="test", curve_id=curve_id.value, extension_degree=extension_degree ) c.create_powers_of_Z(c.field(z)) X = c.write_elements( [PyFelt(i + 1, c.field.p) for i in range(extension_degree)], operation=WriteOps.INPUT, ) return c, X return init_z_circuit() def test_eval(circuit: tuple[ExtensionFieldModuloCircuit, list[ModuloCircuitElement]]): c, X = circuit X_of_z = c.eval_poly_in_precomputed_Z(X) assert ( X_of_z.value == sum((i + 1) * 2**i for i in range(c.extension_degree)) % c.field.p ) assert len(c.z_powers) == c.extension_degree def generate_random_sparsity( extension_degree: int, num_cases: int = 32 ) -> list[list[int]]: sparsities = [ [random.choice([0, 1, 2]) for _ in range(extension_degree)] for _ in range(num_cases) ] for sparsity in sparsities: if all(x == 0 for x in sparsity): # Make sure there is at least one non-zero element somewhere sparsity[random.randint(0, extension_degree - 1)] = random.choice([1, 2]) return sparsities def test_eval_sparse( circuit: tuple[ExtensionFieldModuloCircuit, list[ModuloCircuitElement]], ): c, X = circuit sparsities = generate_random_sparsity(c.extension_degree) for sparsity in sparsities: X_of_z = c.eval_poly_in_precomputed_Z(X, sparsity=sparsity) assert ( X_of_z.value == ( sum((i + 1) * 2**i for i, s in enumerate(sparsity) if s == 1) + sum(2**i for i, s in enumerate(sparsity) if s == 2) ) % c.field.p ) if __name__ == "__main__": pytest.main() ================================================ FILE: tests/hydra/test_g1_point.py ================================================ import pytest from garaga.curves import CURVES, CurveID, TwistedEdwardsCurve, is_generator from garaga.points import G1Point # List of curve IDs to test curve_ids = list(CurveID) @pytest.mark.parametrize("curve_id", [CurveID.ED25519]) def test_weierstrass_to_twistededwards_and_back(curve_id): curve: TwistedEdwardsCurve = CURVES[curve_id.value] # Define a point in Weierstrass form x_weierstrass = curve.Gx y_weierstrass = curve.Gy x_twisted, y_twisted = curve.to_twistededwards(x_weierstrass, y_weierstrass) x_weierstrass_back, y_weierstrass_back = curve.to_weierstrass(x_twisted, y_twisted) assert x_weierstrass == x_weierstrass_back assert y_weierstrass == y_weierstrass_back @pytest.mark.parametrize("curve_id", curve_ids) def test_fp_generator(curve_id): if curve_id == CurveID.BLS12_381: pytest.skip( "Skipping test for curve BLS12_381, it's a bit too slow to factorize p-1, but already tested. Uncomment to convince yourself." ) g = CURVES[curve_id.value].fp_generator p = CURVES[curve_id.value].p assert is_generator(g, p) @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_equality(curve_id): p1 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p2 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p3 = p1.add(p2) assert p1 == p2 assert p1 != p3 @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_infinity(curve_id): inf = G1Point.infinity(curve_id) assert inf.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_on_curve(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) assert p.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_not_on_curve(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p.y = 3 # Modify y to make it not on the curve assert not p.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p.scalar_mul(2) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_addition(curve_id): p1 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p2 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p1.add(p2) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_addition_with_negative_point(curve_id): p1 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p2 = -p1 result = p1.add(p2) assert result.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_negation(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) neg_p = -p assert neg_p.is_on_curve() assert p.add(neg_p).is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_msm(curve_id): p1 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) p2 = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) points = [p1, p2] scalars = [2, 3] result = G1Point.msm(points, scalars) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_gen_random_point(curve_id): p = G1Point.gen_random_point(curve_id) assert p.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_gen_random_point_not_in_subgroup(curve_id): if CURVES[curve_id.value].h == 1: pytest.skip(f"Skipping test for curve {curve_id} because the cofactor is 1") p = G1Point.gen_random_point_not_in_subgroup(curve_id, force_gen=True) assert p.is_on_curve() assert not p.is_in_prime_order_subgroup_generic() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_to_cairo_1(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) cairo_repr = p.to_cairo_1() assert isinstance(cairo_repr, str) @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_doubling(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) doubled = p.add(p) assert doubled.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_addition_vs_doubling(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) doubled = p.add(p) scalar_mul_2 = p.scalar_mul(2) assert doubled == scalar_mul_2 @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_msm_vs_scalar_mul(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) scalar = 3 msm_result = G1Point.msm([p], [scalar]) scalar_mul_result = p.scalar_mul(scalar) assert msm_result == scalar_mul_result # Edge case tests for scalar multiplication @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_zero(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p.scalar_mul(0) assert result.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_one(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p.scalar_mul(1) assert result == p @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_negative(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p.scalar_mul(-1) assert result == -p @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_large(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) large_scalar = 10**18 result = p.scalar_mul(large_scalar) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_invalid(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) with pytest.raises(TypeError): p.scalar_mul("invalid_scalar") @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_order(curve_id): p = G1Point(CURVES[curve_id.value].Gx, CURVES[curve_id.value].Gy, curve_id) result = p.scalar_mul(CURVES[curve_id.value].n) assert result.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g1point_scalar_mul_larger_than_order(curve_id): # Generate 10 random points on the curve random_points = [G1Point.gen_random_point(curve_id) for _ in range(10)] for p in random_points: result = p.scalar_mul(CURVES[curve_id.value].n + 1) assert result == p @pytest.mark.parametrize("curve_id", curve_ids) def test_is_in_subgroup(curve_id): for _ in range(10): p = G1Point.gen_random_point(curve_id) assert p.is_in_prime_order_subgroup() assert p.is_in_prime_order_subgroup_generic() if CURVES[curve_id.value].h != 1: p = G1Point.gen_random_point_not_in_subgroup(curve_id) assert not p.is_in_prime_order_subgroup() assert not p.is_in_prime_order_subgroup_generic() ================================================ FILE: tests/hydra/test_g2_point.py ================================================ import random import pytest from garaga.curves import CURVES, CurveID from garaga.points import G2Point # List of curve IDs to test curve_ids = [CurveID.BN254, CurveID.BLS12_381] def get_g2_generator_point(curve_id): return G2Point(CURVES[curve_id.value].G2x, CURVES[curve_id.value].G2y, curve_id) @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_equality(curve_id): p1 = get_g2_generator_point(curve_id) p2 = get_g2_generator_point(curve_id) p3 = p1.add(p2) assert p1 == p2 assert p1 != p3 @pytest.mark.parametrize("curve_id", curve_ids) def test_ng2(curve_id): p = get_g2_generator_point(curve_id) nG = G2Point.get_nG(curve_id, 1) assert nG == p @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_infinity(curve_id): inf = G2Point.infinity(curve_id) assert inf.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_on_curve(curve_id): p = get_g2_generator_point(curve_id) assert p.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_not_on_curve(curve_id): with pytest.raises(ValueError): _ = G2Point((1, 2), (3, 4), curve_id) @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(2) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_addition(curve_id): p1 = get_g2_generator_point(curve_id) p2 = get_g2_generator_point(curve_id) result = p1.add(p2) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_negation(curve_id): p = get_g2_generator_point(curve_id) neg_p = -p assert neg_p.is_on_curve() assert p.add(neg_p).is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_msm(curve_id): p1 = get_g2_generator_point(curve_id) p2 = get_g2_generator_point(curve_id) points = [p1, p2] scalars = [2, 3] result = G2Point.msm(points, scalars) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_gen_random_point(curve_id): p = G2Point.gen_random_point(curve_id) assert p.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_zero(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(0) assert result.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_one(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(1) assert result == p @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_negative(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(-1) assert result == -p @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_large(curve_id): p = get_g2_generator_point(curve_id) large_scalar = 10**18 result = p.scalar_mul(large_scalar) assert result.is_on_curve() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_invalid(curve_id): p = get_g2_generator_point(curve_id) with pytest.raises(TypeError): p.scalar_mul("invalid_scalar") @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_order(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(CURVES[curve_id.value].n) assert result.is_infinity() @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_larger_than_order(curve_id): p = get_g2_generator_point(curve_id) result = p.scalar_mul(CURVES[curve_id.value].n + 1) assert result == p @pytest.mark.parametrize("curve_id", curve_ids) def test_g2point_scalar_mul_larger_than_order_random_points(curve_id): # Generate 10 random points on the curve random_points = [G2Point.gen_random_point(curve_id) for _ in range(10)] # Shuffle the points random.shuffle(random_points) for p in random_points: result = p.scalar_mul(CURVES[curve_id.value].n + 1) assert result == p @pytest.mark.parametrize("curve_id", curve_ids) def test_is_in_subgroup(curve_id): for _ in range(10): p = G2Point.gen_random_point(curve_id) assert p.is_in_prime_order_subgroup() assert p.is_in_prime_order_subgroup_generic() if CURVES[curve_id.value].h != 1: p = G2Point.gen_random_point_not_in_subgroup(curve_id) assert not p.is_in_prime_order_subgroup() assert not p.is_in_prime_order_subgroup_generic() ================================================ FILE: tests/hydra/test_isogeny.py ================================================ from garaga.modulo_circuit import WriteOps from hydra.garaga.precompiled_circuits.isogeny import IsogenyG1, IsogenyG2 def test_isogeny_g2(): # Initialize circuit circuit = IsogenyG2("isogeny", 1) # BLS12-381 # Input coordinates field_x = circuit.write_elements( [ circuit.field( 169519152402139697623491793754012113789032894758910773796231348501731795490199910990796174115277871812568749679080 ), circuit.field( 1728095456082680609005278389175634228411286941580472237217092659287996601824281397719739792814994738024437208024916 ), ], WriteOps.INPUT, ) field_y = circuit.write_elements( [ circuit.field( 921899175962300040840420456901482071750200770271137541308616448315528969776376924836021205171957295791079922974103 ), circuit.field( 3684633599184560222490700115577520911020962810206788383522966831012065752604210815152740734710545831758791724608234 ), ], WriteOps.INPUT, ) # Run isogeny calculation x_affine, y_affine = circuit.run_isogeny(field_x, field_y) # Expected values for x_affine coordinates expected_x = [ 3789617024712504402204306620295003375951143917889162928515122476381982967144814366712031831841518399614182231387665, 1467567314213963969852279817989131104935039564231603908576814773321528757289376676761397368853965316423532584391899, ] # Expected values for y_affine coordinates expected_y = [ 1292375129422168617658520396283100687686347104559592203462491249161639006037671760603453326853098986903549775136448, 306655960768766438834866368706782505873384691666290681181893693450298456233972904889955517117016529975705729523733, ] # Assert x coordinates match assert len(x_affine) == 2, "Expected x_affine to have 2 coordinates" assert ( x_affine[0].emulated_felt.value == expected_x[0] ), "First x coordinate doesn't match" assert ( x_affine[1].emulated_felt.value == expected_x[1] ), "Second x coordinate doesn't match" # Assert y coordinates match assert len(y_affine) == 2, "Expected y_affine to have 2 coordinates" assert ( y_affine[0].emulated_felt.value == expected_y[0] ), "First y coordinate doesn't match" assert ( y_affine[1].emulated_felt.value == expected_y[1] ), "Second y coordinate doesn't match" def test_isogeny_g1(): circuit = IsogenyG1("isogeny", 1) # BLS12-381 field_x = circuit.write_element( circuit.field( 1412853964218444964438936699552956047210482383152224645596624291427056376487356261681298103080878386132407858666637 ) ) field_y = circuit.write_element( circuit.field( 752734926215712395741522221355891264404138695398702662135908094550118515106801651502315795564392519475687558113863 ) ) x_affine, y_affine = circuit.run_isogeny(field_x, field_y) assert ( x_affine.emulated_felt.value == 446982818448762443925483450503077743305378332574765060957007466897598303326699997098749910515002846743254056890542 ) assert ( y_affine.emulated_felt.value == 3454829136341282129428339331123792952068649713505379945415096993679155752159553081385690994340465600247693047311369 ) ================================================ FILE: tests/hydra/test_poseidon_hash.py ================================================ import time import pytest from garaga import garaga_rs from garaga.precompiled_circuits.poseidon_bn254 import poseidon_hash def test_poseidon_hash_bn254(): # Test with valid inputs x = 1 y = 2 expected = 0x115CC0F5E7D690413DF64C6B9662E9CF2A3617F2743245519E19607A4417189A tr0 = time.time() for _ in range(20): result = garaga_rs.poseidon_hash_bn254(x, y) tr1 = time.time() print(f"Garaga RS time: {tr1 - tr0} seconds") assert result == expected tp0 = time.time() for _ in range(20): result = poseidon_hash(x, y) tp1 = time.time() print(f"Garaga Python time: {tp1 - tp0} seconds") assert result.value == expected # Test different inputs give different results result2 = garaga_rs.poseidon_hash_bn254(2, 1) assert result != result2 # Test with large numbers x_large = 2**255 - 1 y_large = 2**255 - 2 result = garaga_rs.poseidon_hash_bn254(x_large, y_large) assert isinstance(result, int) assert len(hex(result)[2:]) <= 64 # Result should be within field size # Test invalid inputs with pytest.raises((OverflowError, ValueError)): garaga_rs.poseidon_hash_bn254(-1, 1) # Negative numbers not allowed ================================================ FILE: tests/hydra/test_rsa_rns.py ================================================ import math from garaga.rsa_rns import ( BASE, CHANNEL_MODULI, CHUNK_LIMBS, CRT_EXACTNESS_BOUND, PKCS1_SHA256_DIGEST_INFO_PREFIX, RSA_PUBLIC_EXPONENT, RSA_REDUCTION_COUNT, RNSContext, generate_rsa2048_sha256_witness, generate_rsa2048_witness, is_valid_rsa2048_witness, modular_exponentiation_with_proof, pkcs1_v1_5_encode_sha256, ) from garaga.starknet.tests_and_calldata_generators.signatures import RSA2048Signature def eval_chunks_mod(chunks: tuple[int, ...], step: int, modulus: int) -> int: """Horner evaluation of chunk polynomial at step, reduced modulo modulus.""" acc = 0 for chunk in reversed(chunks): acc = (acc * step + chunk) % modulus return acc def test_rsa_channel_moduli_are_pairwise_coprime(): for i, lhs in enumerate(CHANNEL_MODULI): assert lhs > 1 for j, rhs in enumerate(CHANNEL_MODULI[i + 1 :], start=i + 1): assert ( math.gcd(lhs, rhs) == 1 ), f"channel moduli {i} and {j} are not coprime" def test_rsa_chunk_steps_match_chunk_radix_mod_channel_moduli(): expected_steps = [pow(BASE, CHUNK_LIMBS, p) for p in CHANNEL_MODULI] assert expected_steps == [ 5880, 9624, 24728, 32024, 38504, 45624, 48200, 55592, 57224, 64488, 71448, ] def test_rsa_chunk_horner_evaluation_matches_residues(): ctx = RNSContext(CHANNEL_MODULI) steps = [pow(BASE, CHUNK_LIMBS, p) for p in CHANNEL_MODULI] for seed in range(3): sample = RSA2048Signature.sample(seed=seed) encoded_values = [ sample.modulus, sample.signature, sample.expected_message, sample.reductions[0].quotient, sample.reductions[0].remainder, sample.reductions[-1].quotient, sample.reductions[-1].remainder, ] for encoded_value in encoded_values: horner_residues = tuple( eval_chunks_mod(encoded_value.chunks, step, modulus) for step, modulus in zip(steps, CHANNEL_MODULI) ) assert horner_residues == ctx.residues_from_limbs(encoded_value.limbs) def test_rsa_context_exactness_bound(): ctx = RNSContext(CHANNEL_MODULI) assert ctx.M > CRT_EXACTNESS_BOUND def test_rsa_sample_is_valid(): sample = RSA2048Signature.sample(seed=0) assert sample.is_valid() assert len(sample.reductions) == RSA_REDUCTION_COUNT assert len(sample.serialize_public_key()) == 24 assert len(sample.serialize_signature_with_hints()) == 864 assert len(sample.serialize()) == 888 def test_rsa_verification_path_uses_expected_reductions(): ctx = RNSContext(CHANNEL_MODULI) bundle = generate_rsa2048_witness(seed=0) verified_message, reduction_count = modular_exponentiation_with_proof( ctx, bundle.signature.value, RSA_PUBLIC_EXPONENT, bundle.modulus.value, ) assert reduction_count == RSA_REDUCTION_COUNT assert verified_message == bundle.expected_message.value def test_rsa_tampered_residue_is_invalid(): assert not RSA2048Signature.tampered_residue_sample(seed=0).is_valid() def test_rsa_tampered_limb_is_invalid(): assert not RSA2048Signature.tampered_limb_sample(seed=0).is_valid() def test_rsa_tampered_expected_message_is_invalid(): assert not RSA2048Signature.tampered_expected_message_sample(seed=0).is_valid() def test_pkcs1_v1_5_encode_sha256_structure(): message_hash = bytes(range(32)) encoded = pkcs1_v1_5_encode_sha256(message_hash) encoded_bytes = encoded.to_bytes(256, byteorder="big") # 0x00 || 0x01 || PS(0xFF × 202) || 0x00 || DigestInfo(19) || Hash(32) = 256 assert encoded_bytes[0] == 0x00 assert encoded_bytes[1] == 0x01 assert encoded_bytes[2:204] == b"\xff" * 202 assert encoded_bytes[204] == 0x00 assert encoded_bytes[205:224] == PKCS1_SHA256_DIGEST_INFO_PREFIX assert encoded_bytes[224:256] == message_hash def test_rsa2048_sha256_witness_is_valid(): bundle = generate_rsa2048_sha256_witness(b"hello garaga", seed=0) assert is_valid_rsa2048_witness(bundle) assert len(bundle.reductions) == RSA_REDUCTION_COUNT # Verify the expected message is a valid PKCS#1 v1.5 encoding import hashlib message_hash = hashlib.sha256(b"hello garaga").digest() expected = pkcs1_v1_5_encode_sha256(message_hash) assert bundle.expected_message.value == expected def test_rsa2048_sha256_byte_array_serialization(): """Test that ByteArray serialization matches Cairo's format.""" from garaga.starknet.tests_and_calldata_generators.signatures import ( _serialize_byte_array, ) # Empty cd = _serialize_byte_array(b"") assert cd == [0, 0, 0] # Short message (< 31 bytes) cd = _serialize_byte_array(b"hello") assert cd[0] == 0 # 0 full words assert cd[1] == int.from_bytes(b"hello", "big") # pending word assert cd[2] == 5 # pending len # Exactly 31 bytes data = bytes(range(31)) cd = _serialize_byte_array(data) assert cd[0] == 1 # 1 full word assert cd[1] == int.from_bytes(data[:31], "big") assert cd[2] == 0 # pending = 0 assert cd[3] == 0 # pending len = 0 # 65 bytes = 2 full words + 3 pending data = bytes([0xCD] * 65) cd = _serialize_byte_array(data) assert cd[0] == 2 assert len(cd) == 5 assert cd[4] == 3 # pending len ================================================ FILE: tools/addchain/bls12_381_e.acc ================================================ _10 = 2*1 _11 = 1 + _10 _101 = _10 + _11 _111 = _10 + _101 _1001 = _10 + _111 _1011 = _10 + _1001 _1101 = _10 + _1011 _1111 = _10 + _1101 _10001 = _10 + _1111 _10011 = _10 + _10001 _10101 = _10 + _10011 _10111 = _10 + _10101 _11001 = _10 + _10111 _11011 = _10 + _11001 _11101 = _10 + _11011 _11111 = _10 + _11101 _100001 = _10 + _11111 _100011 = _10 + _100001 _100101 = _10 + _100011 _100111 = _10 + _100101 _101001 = _10 + _100111 _101011 = _10 + _101001 _101101 = _10 + _101011 _101111 = _10 + _101101 _110001 = _10 + _101111 _110011 = _10 + _110001 _110101 = _10 + _110011 _110111 = _10 + _110101 _111001 = _10 + _110111 _111011 = _10 + _111001 _111101 = _10 + _111011 _111111 = _10 + _111101 _1000001 = _10 + _111111 _1000011 = _10 + _1000001 _1000101 = _10 + _1000011 _1000111 = _10 + _1000101 _1001001 = _10 + _1000111 _1001011 = _10 + _1001001 _1001101 = _10 + _1001011 _1001111 = _10 + _1001101 _1010001 = _10 + _1001111 _1010011 = _10 + _1010001 _1010101 = _10 + _1010011 _1010111 = _10 + _1010101 _1011001 = _10 + _1010111 _1011011 = _10 + _1011001 _1011101 = _10 + _1011011 _1011111 = _10 + _1011101 _1100001 = _10 + _1011111 _1100011 = _10 + _1100001 _1100101 = _10 + _1100011 _1100111 = _10 + _1100101 _1101001 = _10 + _1100111 _1101011 = _10 + _1101001 _1101101 = _10 + _1101011 _1101111 = _10 + _1101101 _1110001 = _10 + _1101111 _1110011 = _10 + _1110001 _1110101 = _10 + _1110011 _1110111 = _10 + _1110101 _1111001 = _10 + _1110111 _1111011 = _10 + _1111001 _1111101 = _10 + _1111011 _1111111 = _10 + _1111101 _11111110 = 2*_1111111 _11111111 = 1 + _11111110 x9 = 2*_11111111 + 1 i69 = _1110001 + x9 x10 = 2*x9 + 1 i72 = 2*i69 x11 = 2*x10 + 1 i95 = ((i72 << 2 + _101001) << 8 + _100011) << 9 i118 = ((_1100101 + i95) << 7 + _1100101) << 13 + _1101011 i140 = ((i118 << 7 + _1010111) << 4 + _101) << 9 i163 = ((_101 + i140) << 13 + _1110111) << 7 + _10001 i188 = ((i163 << 9 + _100001) << 7 + _100001) << 7 i214 = ((_101011 + i188) << 7 + _11) << 16 + _111001 i242 = ((i214 << 8 + _101001) << 8 + _111011) << 10 i258 = ((_1010011 + i242) << 7 + _1001001) << 6 + _101001 i286 = ((i258 << 9 + _1010111) << 7 + _1101) << 10 i306 = ((_1100011 + i286) << 7 + _101011) << 10 + _1110111 i331 = ((i306 << 7 + _1110001) << 7 + _11101) << 9 i349 = ((_1000111 + i331) << 8 + _1011101) << 7 + _1101 i380 = ((i349 << 9 + _110101) << 10 + _1111001) << 10 i400 = ((_110101 + i380) << 10 + _1101111) << 7 + _1101101 i428 = ((i400 << 8 + _1111) << 11 + _1011011) << 7 i449 = ((_1110111 + i428) << 8 + _101011) << 10 + _1000011 i473 = ((i449 << 7 + _1010111) << 6 + _100101) << 9 i489 = ((_1010001 + i473) << 5 + _1011) << 8 + _1001 i518 = ((i489 << 12 + _1001011) << 8 + _1010001) << 7 i537 = ((_1101111 + i518) << 8 + _1010001) << 8 + _1110111 i562 = ((i537 << 8 + _1001001) << 5 + _11101) << 10 i578 = ((_101111 + i562) << 8 + _1001101) << 5 + _10001 i609 = ((i578 << 9 + _1011101) << 13 + _110011) << 7 i627 = ((_110001 + i609) << 6 + _11011) << 9 + _1100111 i651 = ((i627 << 7 + _1101) << 10 + _1000111) << 5 i672 = ((_10001 + i651) << 10 + _1000001) << 8 + _1100011 i699 = ((i672 << 10 + _1111011) << 8 + _1001101) << 7 i715 = ((_1110101 + i699) << 9 + _1000011) << 4 + _1101 i742 = ((i715 << 14 + _1010101) << 6 + _111101) << 5 i764 = ((_111 + i742) << 10 + _110111) << 9 + _1101001 i789 = ((i764 << 7 + _1100101) << 3 + _11) << 13 i807 = ((_1010011 + i789) << 4 + _11) << 11 + _11001 i833 = ((i807 << 9 + _100111) << 8 + _1111011) << 7 i855 = ((_1100111 + i833) << 2 + _11) << 17 + x11 i882 = ((i855 << 7 + _101111) << 10 + _1101011) << 8 i902 = ((_1001111 + i882) << 7 + _111001) << 10 + _11111111 i928 = ((i902 << 8 + _100111) << 8 + _110011) << 8 i946 = ((_10111 + i928) << 6 + _1101) << 9 + _11011 i971 = ((i946 << 9 + _110101) << 6 + _11101) << 8 i992 = ((_100011 + i971) << 10 + _110001) << 8 + _10101 i1018 = ((i992 << 10 + _1010001) << 7 + _111111) << 7 i1039 = ((_101101 + i1018) << 9 + _11011) << 9 + _101111 i1063 = ((i1039 << 8 + _1001001) << 6 + _111001) << 8 i1081 = ((_110111 + i1063) << 8 + _1010101) << 7 + _1111001 i1101 = ((i1081 << 6 + _111011) << 8 + _1100011) << 4 i1123 = ((_1101 + i1101) << 13 + _1111011) << 6 + _110001 i1147 = ((i1123 << 8 + _1101101) << 7 + _1000001) << 7 i1163 = ((_1100001 + i1147) << 6 + _111011) << 7 + _100111 i1193 = ((i1163 << 8 + _10011) << 11 + _1111111) << 9 i1210 = ((_1001101 + i1193) << 6 + _101011) << 8 + _1011011 i1233 = ((i1210 << 7 + _1110111) << 7 + _1001011) << 7 i1254 = ((_110101 + i1233) << 8 + _1011111) << 10 + _1101111 i1283 = ((i1254 << 7 + _101101) << 5 + _111) << 15 i1297 = ((_1000001 + i1283) << 8 + _1110001) << 3 + 1 i1331 = ((i1297 << 15 + _110001) << 8 + _1100001) << 9 i1351 = ((_1111011 + i1331) << 7 + _10011) << 10 + _1011101 i1372 = ((i1351 << 8 + _1110111) << 5 + _10111) << 6 i1395 = ((_1011 + i1372) << 6 + _11) << 14 + x11 i1415 = ((2*i1395 + 1) << 8 + _1011001) << 9 i1437 = ((_1110101 + i1415) << 9 + _1111011) << 10 + _1101011 i1459 = ((i1437 << 8 + _100101) << 3 + 1) << 9 i1480 = ((_11111111 + i1459) << 11 + _101011) << 7 + _110011 i1503 = ((i1480 << 7 + _111111) << 7 + _101011) << 7 i1529 = ((_100101 + i1503) << 13 + _1000001) << 10 + _1001101 i1553 = ((i1529 << 8 + _1100101) << 8 + _1010101) << 6 i1573 = ((_100101 + i1553) << 9 + _1010001) << 8 + _1011101 i1599 = ((i1573 << 6 + _111011) << 8 + _1011111) << 10 i1617 = ((_1011101 + i1599) << 7 + _1001111) << 8 + _1111001 i1642 = ((i1617 << 8 + _1100001) << 7 + _1010111) << 8 i1662 = ((_1001001 + i1642) << 7 + _1000111) << 10 + _1001001 i1695 = ((i1662 << 12 + _1011101) << 9 + _1110101) << 10 i1713 = ((_111101 + i1695) << 8 + _111011) << 7 + _111101 i1735 = ((i1713 << 6 + _11011) << 9 + _1101011) << 5 i1758 = ((_11011 + i1735) << 10 + _1001011) << 10 + _1001001 i1782 = ((i1758 << 4 + _1111) << 11 + _1000011) << 7 i1803 = ((_10101 + i1782) << 9 + _111001) << 9 + _1000011 i1829 = ((i1803 << 5 + _10011) << 10 + _1011001) << 9 i1846 = ((_1110011 + i1829) << 8 + _1100001) << 6 + _110011 i1875 = ((i1846 << 9 + _110001) << 7 + _101101) << 11 i1898 = ((_1100111 + i1875) << 8 + _1011011) << 12 + _1101101 i1927 = ((i1898 << 11 + _1000011) << 7 + _1110111) << 9 i1945 = ((_1101001 + i1927) << 4 + _1011) << 11 + _1100011 i1967 = ((i1945 << 4 + _1001) << 11 + _1001111) << 5 i1986 = ((_10111 + i1967) << 6 + _1001) << 10 + _1001011 i2009 = ((i1986 << 8 + _1011011) << 4 + _1001) << 9 i2029 = ((_100101 + i2009) << 10 + _11111111) << 7 + _101011 i2057 = ((i2029 << 10 + _1111) << 10 + _1011011) << 6 i2075 = ((_111001 + i2057) << 9 + _1101001) << 6 + _101111 i2100 = ((i2075 << 7 + _10011) << 9 + _1110011) << 7 i2125 = ((_1110011 + i2100) << 10 + _101101) << 12 + _1110001 i2153 = ((i2125 << 6 + _11) << 12 + _1101101) << 8 i2171 = ((_110011 + i2153) << 6 + _10111) << 9 + _1011011 i2199 = ((i2171 << 10 + _1000111) << 7 + _1111011) << 9 i2220 = ((_1111111 + i2199) << 11 + _1110001) << 7 + _1101111 i2244 = ((i2220 << 9 + _1001101) << 7 + _1000111) << 6 i2264 = ((_1011 + i2244) << 11 + _1010001) << 6 + _11001 i2289 = ((i2264 << 10 + _1101001) << 8 + _1010111) << 5 i2309 = ((_10111 + i2289) << 6 + _101) << 11 + _1010011 i2333 = ((i2309 << 6 + _110101) << 5 + _1101) << 11 i2354 = ((_110101 + i2333) << 8 + _11001) << 10 + _1111011 i2378 = ((i2354 << 8 + _1110111) << 6 + _1011) << 8 i2398 = ((_11001 + i2378) << 9 + _11111111) << 8 + _1011111 i2427 = ((i2398 << 6 + _1111) << 13 + _1100001) << 8 i2444 = ((_1100001 + i2427) << 5 + _11001) << 9 + _1101001 i2470 = ((i2444 << 9 + _1010111) << 3 + _111) << 12 i2487 = ((_1000011 + i2470) << 6 + _100011) << 8 + _1011111 i2519 = ((i2487 << 10 + _111011) << 10 + _101011) << 10 i2538 = ((_11111111 + i2519) << 9 + _111101) << 7 + _11111 i2566 = ((i2538 << 7 + _11001) << 9 + _10101) << 10 i2586 = ((_1111001 + i2566) << 9 + _1010101) << 8 + _10101 i2609 = ((i2586 << 9 + _1110001) << 5 + _1001) << 7 i2631 = ((_1011 + i2609) << 12 + _1011101) << 7 + _1000011 i2658 = ((i2631 << 9 + _1011001) << 9 + _1100101) << 7 i2679 = ((_1010111 + i2658) << 10 + _11111) << 8 + _11111 i2703 = ((i2679 << 7 + _10111) << 10 + _1110011) << 5 i2725 = ((_10111 + i2703) << 9 + _100101) << 10 + _1011101 i2749 = ((i2725 << 4 + _1111) << 11 + _1010011) << 7 i2771 = ((_1000001 + i2749) << 9 + _1111001) << 10 + _1100101 i2799 = ((2*i2771 + 1) << 17 + _1000001) << 8 i2815 = ((_1011101 + i2799) << 7 + _1010101) << 6 + _111011 i2842 = ((i2815 << 8 + _1100011) << 5 + _11011) << 12 i2861 = ((_1101011 + i2842) << 8 + _1101111) << 8 + _1000111 i2882 = ((i2861 << 2 + 1) << 10 + x9) << 7 i2900 = ((_101101 + i2882) << 3 + _11) << 12 + _1110111 i2929 = ((i2900 << 6 + 1) << 12 + _100111) << 9 i2949 = ((_1010001 + i2929) << 6 + _110011) << 11 + _1100011 i2971 = ((i2949 << 6 + _101111) << 11 + _1110011) << 3 i2990 = ((_111 + i2971) << 11 + _1010111) << 5 + _11101 i3017 = ((i2990 << 9 + _1110011) << 5 + _1101) << 11 i3037 = ((x9 + i3017) << 6 + _10011) << 11 + _1101011 i3061 = ((i3037 << 7 + _1110111) << 6 + _10011) << 9 i3081 = ((_1101111 + i3061) << 10 + _1100011) << 7 + _1000111 i3099 = 2*((i3081 << 3 + _111) << 12 + _1111001) i3125 = ((1 + i3099) << 15 + _111101) << 8 + _1101111 i3152 = ((i3125 << 5 + _1101) << 10 + _1011001) << 10 i3172 = ((_1101011 + i3152) << 6 + _110111) << 11 + _10011 i3200 = ((i3172 << 12 + _1111011) << 8 + _1100001) << 6 i3220 = ((_10101 + i3200) << 9 + _1011011) << 8 + _1010111 i3243 = ((i3220 << 5 + _11101) << 8 + _100001) << 8 i3262 = ((_1101101 + i3243) << 8 + _1001101) << 8 + _100101 i3286 = 2*((i3262 << 12 + _1111101) << 9 + _1000011) i3309 = ((1 + i3286) << 11 + x10) << 9 + _1110111 i3330 = ((i3309 << 7 + _101011) << 8 + _1110101) << 4 i3350 = ((_1111 + i3330) << 10 + _1000101) << 7 + _111101 i3373 = ((i3350 << 9 + _1101101) << 6 + _110101) << 6 i3395 = ((_11101 + i3373) << 8 + _101) << 11 + _1001101 i3420 = ((i3395 << 9 + _1000111) << 2 + _11) << 12 i3435 = ((_1110111 + i3420) << 6 + _111011) << 6 + _10101 i3462 = ((i3435 << 9 + _100001) << 7 + _101101) << 9 i3480 = ((_1101001 + i3462) << 7 + _101001) << 8 + _101101 i3505 = ((i3480 << 8 + _1000101) << 4 + _1001) << 11 i3522 = ((_1111001 + i3505) << 7 + _110001) << 7 + _100011 i3551 = ((i3522 << 12 + _1011001) << 4 + _1101) << 11 i3568 = ((_1100011 + i3551) << 5 + _11111) << 9 + _111001 i3592 = ((i3568 << 8 + _1010011) << 7 + _1100011) << 7 i3609 = ((_101101 + i3592) << 8 + _1101111) << 6 + _100111 i3637 = ((i3609 << 8 + _1000101) << 9 + _100001) << 9 i3657 = ((_1010111 + i3637) << 7 + _1101101) << 10 + _1100001 i3682 = ((i3657 << 10 + _100101) << 7 + _101111) << 6 i3704 = ((_11111 + i3682) << 9 + _101101) << 10 + _1101001 i3728 = ((i3704 << 7 + _101101) << 8 + _1110111) << 7 i3746 = ((_100011 + i3728) << 8 + _1000111) << 7 + _110101 i3769 = ((i3746 << 8 + _1110101) << 7 + _1010001) << 6 i3785 = ((_101001 + i3769) << 6 + _10001) << 7 + _10111 i3811 = ((i3785 << 9 + _1110011) << 8 + _110001) << 7 i3831 = ((_100101 + i3811) << 8 + _1010011) << 9 + _1100111 i3857 = ((i3831 << 7 + _1000011) << 10 + _1111011) << 7 i3879 = ((_101 + i3857) << 12 + _1111001) << 7 + _1101011 i3902 = ((i3879 << 6 + _110011) << 9 + _10101) << 6 i3928 = ((_101 + i3902) << 13 + _10111) << 10 + _1011101 i3953 = ((i3928 << 5 + _1001) << 12 + _100001) << 6 i3977 = ((_1001 + i3953) << 9 + _11111) << 12 + _1111101 i4010 = ((i3977 << 10 + _1011101) << 12 + _1111101) << 9 i4029 = ((_1001001 + i4010) << 7 + _101011) << 9 + _100111 i4058 = ((i4029 << 9 + _11011) << 9 + _1100011) << 9 i4075 = ((_1010101 + i4058) << 6 + _110001) << 8 + _1101101 i4098 = ((i4075 << 7 + _110101) << 8 + _1000111) << 6 i4120 = ((_101011 + i4098) << 10 + _11011) << 9 + _101011 i4145 = ((i4120 << 5 + _101) << 8 + _111) << 10 i4169 = ((_11101 + i4145) << 10 + _1110011) << 11 + _101001 i4194 = ((i4169 << 7 + _111011) << 14 + _101111) << 2 i4218 = ((1 + i4194) << 14 + _1011111) << 7 + _1101101 i4243 = ((i4218 << 7 + _1110101) << 4 + _101) << 12 i4262 = ((_110001 + i4243) << 5 + _1101) << 11 + _1011001 i4286 = ((i4262 << 7 + _1011011) << 6 + _110011) << 9 i4311 = ((_110101 + i4286) << 15 + _1100001) << 7 + _101001 i4336 = ((i4311 << 9 + _1001011) << 7 + _110011) << 7 i4354 = ((_10101 + i4336) << 6 + _1101) << 9 + _101001 i4382 = ((i4354 << 9 + _1010011) << 9 + _1111111) << 8 i4400 = ((_1010101 + i4382) << 5 + _10101) << 10 + _1000111 i4424 = ((i4400 << 8 + _110101) << 4 + _101) << 10 i4444 = ((_111001 + i4424) << 8 + _11001) << 9 + _1011101 i4471 = ((i4444 << 7 + _1101101) << 11 + _1110001) << 7 i4491 = ((_1100001 + i4471) << 2 + _11) << 15 + _1010001 i4515 = ((i4491 << 5 + _1101) << 8 + _10011) << 9 i4532 = ((_1010011 + i4515) << 7 + _1110101) << 7 + _1010111 i4561 = ((i4532 << 8 + _1010001) << 8 + _101101) << 11 i4580 = ((_1100101 + i4561) << 7 + _101111) << 9 + _111011 i4605 = ((i4580 << 6 + _11111) << 6 + _1011) << 11 i4619 = ((_1000001 + i4605) << 7 + _1101001) << 4 + _1011 i4646 = ((i4619 << 10 + _1111101) << 3 + 1) << 12 i4665 = ((_111001 + i4646) << 9 + _1000101) << 7 + _1111011 i4688 = ((i4665 << 7 + _1110011) << 6 + _100011) << 8 i4704 = ((_1001001 + i4688) << 8 + _1011101) << 5 + _101 i4731 = ((i4704 << 11 + _1111011) << 5 + _10101) << 9 i4747 = ((_1000011 + i4731) << 5 + _10101) << 8 + _100101 i4778 = ((i4747 << 6 + _10011) << 8 + _110111) << 15 i4797 = ((_1011011 + i4778) << 4 + _111) << 12 + x9 i4822 = ((i4797 << 8 + _1111101) << 8 + _1010111) << 7 return (_1011011 + i4822) << 10 + _100011 ================================================ FILE: tools/addchain/bls12_381_h3_s.acc ================================================ _10 = 2*1 _11 = 1 + _10 _101 = _10 + _11 _111 = _10 + _101 _1001 = _10 + _111 _1011 = _10 + _1001 _1101 = _10 + _1011 _1111 = _10 + _1101 _10001 = _10 + _1111 _10011 = _10 + _10001 _10101 = _10 + _10011 _10111 = _10 + _10101 _11001 = _10 + _10111 _11011 = _10 + _11001 _11101 = _10 + _11011 _11111 = _10 + _11101 _100001 = _10 + _11111 _100011 = _10 + _100001 _100101 = _10 + _100011 _100110 = 1 + _100101 _100111 = 1 + _100110 _101001 = _10 + _100111 _101011 = _10 + _101001 _101101 = _10 + _101011 _110001 = _1011 + _100110 _110011 = _10 + _110001 _110101 = _10 + _110011 _110111 = _10 + _110101 _111001 = _10 + _110111 _111011 = _10 + _111001 _111101 = _10 + _111011 _111111 = _10 + _111101 _1000001 = _10 + _111111 _1000011 = _10 + _1000001 _1000101 = _10 + _1000011 _1000111 = _10 + _1000101 _1001001 = _10 + _1000111 _1001011 = _10 + _1001001 _1001101 = _10 + _1001011 _1001111 = _10 + _1001101 _1010001 = _10 + _1001111 _1010011 = _10 + _1010001 _1010101 = _10 + _1010011 _1010111 = _10 + _1010101 _1011001 = _10 + _1010111 _1011011 = _10 + _1011001 _1011101 = _10 + _1011011 _1011111 = _10 + _1011101 _1100001 = _10 + _1011111 _1100011 = _10 + _1100001 _1100101 = _10 + _1100011 _1100111 = _10 + _1100101 _1101001 = _10 + _1100111 _1101011 = _10 + _1101001 _1101101 = _10 + _1101011 _1101111 = _10 + _1101101 _1110001 = _10 + _1101111 _1110011 = _10 + _1110001 _1110101 = _10 + _1110011 _1110111 = _10 + _1110101 _1111001 = _10 + _1110111 _1111011 = _10 + _1111001 _1111101 = _10 + _1111011 _1111111 = _10 + _1111101 _10000001 = _10 + _1111111 _10000011 = _10 + _10000001 _10000101 = _10 + _10000011 _10000111 = _10 + _10000101 _10001001 = _10 + _10000111 _10001011 = _10 + _10001001 _10001101 = _10 + _10001011 _10001111 = _10 + _10001101 _10010001 = _10 + _10001111 _10010011 = _10 + _10010001 _10010101 = _10 + _10010011 _10010111 = _10 + _10010101 _10011001 = _10 + _10010111 _10011011 = _10 + _10011001 _10011101 = _10 + _10011011 _10011111 = _10 + _10011101 _10100001 = _10 + _10011111 _10100011 = _10 + _10100001 _10100101 = _10 + _10100011 _10100111 = _10 + _10100101 _10101001 = _10 + _10100111 _10101011 = _10 + _10101001 _10101101 = _10 + _10101011 _10101111 = _10 + _10101101 _10110001 = _10 + _10101111 _10110011 = _10 + _10110001 _10110101 = _10 + _10110011 _10110111 = _10 + _10110101 _10111001 = _10 + _10110111 _10111011 = _10 + _10111001 _10111101 = _10 + _10111011 _10111111 = _10 + _10111101 _11000001 = _10 + _10111111 _11000011 = _10 + _11000001 _11000101 = _10 + _11000011 _11000111 = _10 + _11000101 _11001001 = _10 + _11000111 _11001011 = _10 + _11001001 _11001101 = _10 + _11001011 _11001111 = _10 + _11001101 _11010001 = _10 + _11001111 _11010011 = _10 + _11010001 _11010101 = _10 + _11010011 _11010111 = _10 + _11010101 _11011001 = _10 + _11010111 _11011011 = _10 + _11011001 _11011101 = _10 + _11011011 _11011111 = _10 + _11011101 _11100001 = _10 + _11011111 _11100011 = _10 + _11100001 _11100101 = _10 + _11100011 _11100111 = _10 + _11100101 _11101001 = _10 + _11100111 _11101011 = _10 + _11101001 _11101101 = _10 + _11101011 _11101111 = _10 + _11101101 _11110101 = _100110 + _11001111 _11110111 = _10 + _11110101 _11111001 = _10 + _11110111 _11111101 = _100110 + _11010111 _11111111 = _10 + _11111101 i145 = ((_110001 + _11111111) << 7 + _11001101) << 10 + _10100111 i172 = ((i145 << 9 + _1001011) << 8 + _1011001) << 8 i199 = ((_100001 + i172) << 10 + _10111) << 14 + _1111101 i228 = ((i199 << 11 + _1000111) << 9 + _11111101) << 7 i248 = ((_1101011 + i228) << 10 + _11011001) << 7 + _1011111 i274 = ((i248 << 8 + _1101011) << 9 + _1001111) << 7 i295 = ((_101001 + i274) << 10 + _10100011) << 8 + _11101011 i321 = ((i295 << 9 + _11011011) << 6 + _111111) << 9 i342 = ((_100111 + i321) << 9 + _1011001) << 9 + _11000101 i368 = ((i342 << 7 + _1101111) << 9 + _10010011) << 8 i388 = ((_10001001 + i368) << 9 + _11101001) << 8 + _1010011 i417 = ((i388 << 3 + _11) << 15 + _1110101) << 9 i437 = ((_10110111 + i417) << 5 + _10001) << 12 + _10010111 i463 = ((i437 << 9 + _10101001) << 9 + _10100111) << 6 i486 = ((_10101 + i463) << 9 + _10101) << 11 + _10101011 i513 = ((i486 << 4 + _101) << 13 + _10001101) << 8 i530 = ((_10100011 + i513) << 8 + _11011101) << 6 + _10011 i560 = ((i530 << 11 + _1101111) << 8 + _101001) << 9 i582 = ((_1001101 + i560) << 11 + _10111001) << 8 + _11000011 i606 = ((i582 << 9 + _11100111) << 10 + _11010011) << 3 i630 = ((_101 + i606) << 13 + _10110011) << 8 + _11011101 i661 = ((i630 << 8 + _1000011) << 12 + _10101111) << 9 i679 = ((_10010001 + i661) << 9 + _10000001) << 6 + _100101 i708 = ((i679 << 8 + _100101) << 10 + _1100111) << 9 i727 = ((_1100001 + i708) << 9 + _10110101) << 7 + _110011 i755 = ((i727 << 8 + _101101) << 10 + _1101101) << 8 i776 = ((_1110111 + i755) << 9 + _1101011) << 9 + _11001011 i806 = ((i776 << 4 + _1001) << 9 + _10011) << 15 i826 = ((_11000011 + i806) << 10 + _10001001) << 7 + _1011101 i855 = ((i826 << 9 + _10011111) << 8 + _1100111) << 10 i876 = ((_11100101 + i855) << 9 + _10101111) << 9 + _10001111 i904 = ((i876 << 7 + _110001) << 9 + _1110111) << 10 i925 = ((_1100011 + i904) << 9 + _1010101) << 9 + _11110111 i955 = ((i925 << 10 + _10100011) << 10 + _11110101) << 8 i978 = ((_11101111 + i955) << 12 + _11100001) << 8 + _10000001 i1010 = ((i978 << 5 + _10101) << 11 + _1111101) << 14 i1029 = ((_11101001 + i1010) << 7 + _1110011) << 9 + _11000101 i1057 = ((i1029 << 11 + _1001011) << 9 + _10101011) << 6 i1081 = ((_111011 + i1057) << 11 + _111101) << 10 + _10011101 i1108 = ((i1081 << 8 + _10000011) << 8 + _11010111) << 9 i1129 = ((_11010001 + i1108) << 8 + _11011001) << 10 + _10101001 i1157 = ((i1129 << 5 + _10011) << 12 + _11010011) << 9 i1176 = ((_10101101 + i1157) << 8 + _11110101) << 8 + _10000101 i1201 = ((i1176 << 7 + _1111011) << 8 + _1110001) << 8 i1222 = ((_1111011 + i1201) << 9 + _11010001) << 9 + _11111101 i1250 = ((i1222 << 7 + _1101101) << 8 + _1111011) << 11 i1270 = ((_11101111 + i1250) << 8 + _11101101) << 9 + _11111001 i1299 = ((i1270 << 10 + _10000011) << 8 + _11110111) << 9 i1322 = ((_101101 + i1299) << 8 + _100101) << 12 + _1111101 i1354 = ((i1322 << 10 + _1001011) << 11 + _11011001) << 9 i1376 = ((_100101 + i1354) << 10 + _10001011) << 9 + _11101111 i1399 = ((i1376 << 8 + _1010111) << 8 + _1010111) << 5 i1423 = ((_111 + i1399) << 12 + _1001001) << 9 + _10000111 i1449 = ((i1423 << 7 + _1111111) << 7 + _11011) << 10 i1470 = ((_1111011 + i1449) << 10 + _10011101) << 8 + _11011001 i1499 = ((i1470 << 6 + _11001) << 11 + _10111101) << 10 i1522 = ((_1111101 + i1499) << 12 + _11010001) << 8 + _11010011 i1548 = ((i1522 << 8 + _11000011) << 8 + _10010011) << 8 i1563 = ((_10011001 + i1548) << 7 + _1110111) << 5 + _1011 i1599 = ((i1563 << 18 + _10001101) << 9 + _10101101) << 7 i1618 = ((_1100101 + i1599) << 8 + _1001001) << 8 + _1111111 i1651 = ((i1618 << 10 + _10010101) << 10 + _100011) << 11 i1672 = ((_11100111 + i1651) << 7 + _1101111) << 11 + _1000001 i1701 = ((i1672 << 9 + _10100011) << 10 + _10010111) << 8 i1720 = ((_11101001 + i1701) << 9 + _1111101) << 7 + _110011 i1752 = ((i1720 << 8 + _110101) << 12 + _1010011) << 10 i1775 = ((_1101001 + i1752) << 9 + _1000001) << 11 + _11001111 i1801 = ((i1775 << 6 + _110001) << 10 + _11010011) << 8 i1825 = ((_11001011 + i1801) << 13 + _11101001) << 8 + _10010111 i1852 = ((i1825 << 7 + _1111011) << 10 + _11001001) << 8 i1874 = ((_11111101 + i1852) << 7 + _1011011) << 12 + _1010111 i1906 = ((i1874 << 11 + _11101) << 9 + _110001) << 10 i1925 = ((_10111001 + i1906) << 8 + _10011001) << 8 + _10110101 i1954 = ((i1925 << 11 + _10100011) << 7 + _1010101) << 9 i1971 = ((_11001011 + i1954) << 9 + _10110111) << 5 + _10001 i2003 = ((i1971 << 11 + _1101011) << 9 + _100011) << 10 i2023 = ((_11110111 + i2003) << 10 + _1011101) << 7 + _11011 i2052 = ((i2023 << 10 + _1001001) << 6 + _11001) << 11 i2076 = ((_10011011 + i2052) << 8 + _1100111) << 13 + _11001001 i2102 = ((i2076 << 8 + _11110111) << 8 + _11100101) << 8 i2127 = ((_10111011 + i2102) << 7 + _111001) << 15 + _11101011 i2153 = ((i2127 << 9 + _11010011) << 6 + _10001) << 9 i2178 = ((_110111 + i2153) << 10 + _11101001) << 12 + _11100011 i2205 = ((i2178 << 7 + _1010011) << 9 + _10101111) << 9 i2237 = ((_10001 + i2205) << 20 + _11111111) << 9 + _11111001 i2267 = ((i2237 << 8 + _10011111) << 8 + _101001) << 12 i2287 = ((_10110011 + i2267) << 7 + _1011101) << 10 + _10111111 i2312 = ((i2287 << 8 + _11111101) << 8 + _11011001) << 7 i2333 = ((_1011111 + i2312) << 8 + _100011) << 10 + _10011101 i2357 = ((i2333 << 8 + _11101001) << 10 + _10101001) << 4 i2381 = ((_111 + i2357) << 14 + _10010101) << 7 + _101011 i2407 = ((i2381 << 9 + _1111111) << 5 + _1011) << 10 i2428 = ((_101101 + i2407) << 11 + _1000101) << 7 + _11101 i2458 = ((i2428 << 11 + _10101111) << 4 + _11) << 13 i2482 = ((_110111 + i2458) << 10 + _10110011) << 11 + _1100111 i2514 = ((i2482 << 10 + _1101001) << 9 + _101011) << 11 i2536 = ((_1101001 + i2514) << 8 + _1100011) << 11 + _10011001 i2564 = ((i2536 << 4 + _1101) << 15 + _1111011) << 7 i2586 = ((_11011 + i2564) << 8 + _10101) << 11 + _10111101 i2612 = ((i2586 << 6 + _110011) << 7 + _11111) << 11 i2633 = ((_11100101 + i2612) << 8 + _111001) << 10 + _10101111 i2661 = ((i2633 << 8 + _10000111) << 7 + _110011) << 11 i2685 = ((_11100101 + i2661) << 10 + _11010111) << 11 + _10000001 i2715 = ((i2685 << 6 + _110001) << 12 + _11100001) << 10 i2737 = ((_1011111 + i2715) << 9 + _11001101) << 10 + _1111011 i2767 = ((i2737 << 8 + _1100011) << 8 + _110101) << 12 i2789 = ((_10101111 + i2767) << 8 + _10010011) << 11 + _11011001 i2815 = ((i2789 << 9 + _1100111) << 10 + _10101101) << 5 i2839 = ((_11011 + i2815) << 11 + _101101) << 10 + _1001111 i2866 = ((i2839 << 9 + _11110101) << 7 + _1111001) << 9 i2888 = ((_10110001 + i2866) << 3 + _101) << 16 + _10011111 i2912 = ((i2888 << 7 + _1011101) << 6 + _11001) << 9 i2934 = ((_100011 + i2912) << 10 + _10111101) << 9 + _1001011 i2960 = ((i2934 << 6 + _10011) << 12 + _11111001) << 6 i2982 = ((_101001 + i2960) << 13 + _10001101) << 6 + _111011 i3017 = ((i2982 << 11 + _10001001) << 15 + _11111001) << 7 i3042 = ((_111011 + i3017) << 9 + _10101) << 13 + _10111011 i3071 = ((i3042 << 9 + _11001011) << 4 + _1111) << 14 i3096 = ((_10001001 + i3071) << 13 + _10011011) << 9 + _100111 i3123 = ((i3096 << 10 + _11110101) << 7 + _1110111) << 8 i3146 = ((_1100001 + i3123) << 10 + _11111111) << 10 + _1011001 i3174 = ((i3146 << 9 + _11001101) << 7 + _1000011) << 10 i3193 = ((_11000111 + i3174) << 8 + _10110001) << 8 + _11001011 i3221 = ((i3193 << 5 + _10001) << 8 + _11001) << 13 i3241 = ((_1101101 + i3221) << 9 + _10000011) << 8 + _11000011 i3269 = ((i3241 << 9 + _11101001) << 9 + _10011111) << 8 i3288 = ((_10110011 + i3269) << 3 + _11) << 13 + _1000001 i3317 = ((i3288 << 10 + _1010011) << 8 + _1010111) << 9 i3340 = ((_1000101 + i3317) << 11 + _11001001) << 9 + _1000101 i3366 = ((i3340 << 8 + _1010001) << 3 + _11) << 13 i3386 = ((_1001011 + i3366) << 9 + _1000101) << 8 + _1110011 i3414 = ((i3386 << 10 + _10110101) << 9 + _10101101) << 7 i3433 = ((_1010001 + i3414) << 12 + _10001111) << 4 + _1101 i3463 = ((i3433 << 12 + _10000111) << 7 + _100111) << 9 i3485 = ((_1110101 + i3463) << 9 + _1000001) << 10 + _11111101 i3514 = ((i3485 << 9 + _11000001) << 8 + _1011011) << 10 i3534 = ((_1101001 + i3514) << 9 + _10000001) << 8 + _11000111 i3564 = ((i3534 << 8 + _10000011) << 8 + _10110011) << 12 i3580 = ((_10011111 + i3564) << 8 + _1000101) << 5 + _1011 i3611 = ((i3580 << 11 + _1111001) << 10 + _11000011) << 8 i3633 = ((_10011111 + i3611) << 11 + _10001) << 8 + _101 i3663 = ((i3633 << 13 + _1100001) << 7 + _100001) << 8 i3684 = ((_100011 + i3663) << 10 + _10011111) << 8 + _1101001 i3712 = ((i3684 << 7 + _100101) << 10 + _11110111) << 9 i3733 = ((_1110001 + i3712) << 9 + _101001) << 9 + _11001 i3766 = ((i3733 << 14 + _11011001) << 10 + _10101101) << 7 i3789 = ((_100111 + i3766) << 9 + _11101) << 11 + _11101111 i3814 = ((i3789 << 9 + _11100001) << 8 + _11010001) << 6 i3838 = ((_100101 + i3814) << 11 + _11011001) << 10 + _11101001 i3864 = ((i3838 << 8 + _11111111) << 8 + _11110111) << 8 i3884 = ((_10101111 + i3864) << 5 + _10101) << 12 + _10100001 i3910 = ((i3884 << 8 + _11010101) << 9 + _10000001) << 7 i3932 = ((_1010001 + i3910) << 9 + _1101101) << 10 + _1000011 i3958 = ((i3932 << 8 + _1010011) << 8 + _1001101) << 8 i3980 = ((_1100011 + i3958) << 11 + _11111101) << 8 + _11100001 i4013 = ((i3980 << 12 + _11001111) << 5 + _1101) << 14 i4033 = ((_10100101 + i4013) << 7 + _1001111) << 10 + _10110111 i4065 = ((i4033 << 12 + _11100111) << 11 + _11100001) << 7 i4087 = ((_1010101 + i4065) << 8 + _11011) << 11 + _11101011 i4116 = ((i4087 << 8 + _10110101) << 8 + _100111) << 11 i4136 = ((_11001011 + i4116) << 9 + _10110001) << 8 + _10001011 i4162 = ((i4136 << 4 + _1111) << 7 + _101) << 13 i4181 = ((_10111001 + i4162) << 8 + _10101101) << 8 + _10100111 i4208 = ((i4181 << 8 + _10010101) << 9 + _11110101) << 8 i4227 = ((_11001001 + i4208) << 8 + _10101101) << 8 + _1101001 i4263 = ((i4227 << 17 + _1100001) << 8 + _1001011) << 9 i4284 = ((_10001 + i4263) << 11 + _11001001) << 7 + _111111 i4316 = ((i4284 << 14 + _11111001) << 8 + _11101011) << 8 i4344 = ((_1101011 + i4316) << 12 + _10001111) << 13 + _1000011 i4375 = ((i4344 << 8 + _1011001) << 10 + _1101011) << 11 i4389 = ((_11110111 + i4375) << 7 + _1111001) << 4 + _101 i4421 = ((i4389 << 12 + _100001) << 7 + _10101) << 11 i4440 = ((_10001001 + i4421) << 8 + _10111011) << 8 + _1000101 i4475 = ((i4440 << 11 + _110101) << 12 + _11001) << 10 i4493 = ((_1011111 + i4475) << 8 + _1111101) << 7 + _100001 i4523 = ((i4493 << 11 + _11101011) << 6 + _111111) << 11 i4545 = ((_10010111 + i4523) << 10 + _1010001) << 9 + _11110101 i4565 = ((i4545 << 6 + _110011) << 10 + _10101001) << 2 i4590 = ((1 + i4565) << 16 + _10100011) << 6 + _111111 i4620 = ((i4590 << 7 + _10001) << 10 + _1100011) << 11 i4638 = ((_1101111 + i4620) << 9 + _10000101) << 6 + _100111 i4665 = ((i4638 << 13 + _111111) << 10 + _11011101) << 2 i4687 = ((1 + i4665) << 14 + _1000101) << 5 + _1111 i4719 = ((i4687 << 14 + _10000111) << 8 + _11110101) << 8 i4741 = ((_11011001 + i4719) << 8 + _11011111) << 11 + _11000011 i4767 = ((i4741 << 7 + _1111101) << 9 + _10001011) << 8 i4787 = ((_1010011 + i4767) << 9 + _1000001) << 8 + _110011 i4814 = ((i4787 << 11 + _1111001) << 9 + _11100001) << 5 i4836 = ((_11101 + i4814) << 12 + _10000101) << 7 + _1010111 i4867 = ((i4836 << 10 + _11010101) << 11 + _11011001) << 8 i4886 = ((_11011111 + i4867) << 4 + _111) << 12 + _10001 return ((i4886 << 7 + _1001) << 8 + _1111) << 4 ================================================ FILE: tools/addchain/bn254_exp.acc ================================================ _10 = 2*1 _11 = 1 + _10 _101 = _10 + _11 _111 = _10 + _101 _1001 = _10 + _111 _1011 = _10 + _1001 _1101 = _10 + _1011 _1111 = _10 + _1101 _10001 = _10 + _1111 _10011 = _10 + _10001 _10101 = _10 + _10011 _10111 = _10 + _10101 _11001 = _10 + _10111 _11011 = _10 + _11001 _11101 = _10 + _11011 _11111 = _10 + _11101 _100001 = _10 + _11111 _100011 = _10 + _100001 _100101 = _10 + _100011 _100111 = _10 + _100101 _101001 = _10 + _100111 _101011 = _10 + _101001 _101101 = _10 + _101011 _101111 = _10 + _101101 _110001 = _10 + _101111 _110011 = _10 + _110001 _110101 = _10 + _110011 _110111 = _10 + _110101 _111001 = _10 + _110111 _111011 = _10 + _111001 _111101 = _10 + _111011 _111111 = _10 + _111101 _1000001 = _10 + _111111 _1000011 = _10 + _1000001 _1000101 = _10 + _1000011 _1000111 = _10 + _1000101 _1001001 = _10 + _1000111 _1001011 = _10 + _1001001 _1001101 = _10 + _1001011 _1001111 = _10 + _1001101 _1010001 = _10 + _1001111 _1010011 = _10 + _1010001 _1010101 = _10 + _1010011 _1010111 = _10 + _1010101 _1011001 = _10 + _1010111 _1011011 = _10 + _1011001 _1011101 = _10 + _1011011 _1011111 = _10 + _1011101 _1100001 = _10 + _1011111 _1100011 = _10 + _1100001 _1100101 = _10 + _1100011 _1100111 = _10 + _1100101 _1101001 = _10 + _1100111 _1101011 = _10 + _1101001 _1101101 = _10 + _1101011 _1101111 = _10 + _1101101 _1110001 = _10 + _1101111 _1110011 = _10 + _1110001 _1110101 = _10 + _1110011 _1110111 = _10 + _1110101 _1111001 = _10 + _1110111 _1111011 = _10 + _1111001 _1111101 = _10 + _1111011 _1111111 = _10 + _1111101 _11111110 = 2*_1111111 _11111111 = 1 + _11111110 i81 = ((_1111101 + _11111111) << 4 + _10111) << 8 + _100001 i105 = ((i81 << 7 + _111001) << 9 + _1001011) << 6 i125 = ((_100111 + i105) << 9 + _1001001) << 8 + _101001 i150 = ((i125 << 8 + _1110101) << 7 + _1001111) << 8 i168 = ((_1001011 + i150) << 6 + _101001) << 9 + _1011001 i192 = ((i168 << 6 + _11001) << 4 + 1) << 12 i209 = ((_110111 + i192) << 6 + _10011) << 8 + _10101 i236 = ((i209 << 9 + _1110001) << 9 + _1011111) << 7 i256 = ((_1101 + i236) << 9 + _110101) << 8 + _1000101 i281 = ((i256 << 6 + _101101) << 11 + _110001) << 6 i307 = ((_11111 + i281) << 17 + _1010111) << 6 + _110011 i337 = ((i307 << 6 + _11011) << 12 + _11111111) << 10 i356 = ((_10101 + i337) << 7 + _10101) << 9 + _1110011 i384 = ((i356 << 10 + _1000101) << 8 + _100001) << 8 i399 = ((_1100111 + i384) << 6 + _101011) << 6 + _10011 i427 = ((i399 << 8 + _111011) << 9 + _11111) << 9 i437 = (2*(_11111111 + i427) + 1) << 6 + _111 i466 = ((i437 << 11 + _1001011) << 6 + _110001) << 10 i484 = ((_1100111 + i466) << 7 + _1001101) << 8 + _1100111 i510 = ((i484 << 6 + _11011) << 9 + _110111) << 9 i527 = ((_1111011 + i510) << 4 + _1101) << 10 + _1101111 i557 = ((i527 << 5 + _11011) << 13 + _101111) << 10 i577 = ((_1110011 + i557) << 10 + _1000101) << 7 + _1000011 i598 = ((i577 << 7 + _1010101) << 6 + _11111) << 6 i613 = ((_1001 + i598) << 10 + _100101) << 2 + 1 i644 = ((i613 << 9 + _11111111) << 9 + _1110111) << 11 i661 = ((_1100011 + i644) << 6 + _110011) << 8 + _1110011 i684 = ((i661 << 7 + _1000101) << 7 + _1110001) << 7 i700 = ((_1001111 + i684) << 9 + _1000101) << 4 + _11 i727 = ((i700 << 12 + _1001101) << 3 + _101) << 10 i746 = ((_1101 + i727) << 10 + _1001011) << 6 + _110001 i772 = ((i746 << 8 + _110111) << 8 + _110011) << 8 i790 = (2*(_1001011 + i772) + 1) << 14 + _1101011 i815 = ((i790 << 8 + _1000111) << 5 + _10101) << 10 i834 = ((_1000101 + i815) << 6 + _11101) << 10 + _100111 i856 = ((i834 << 5 + _1101) << 10 + _100011) << 5 i876 = ((_1011 + i856) << 9 + _110111) << 8 + _1010011 i900 = ((i876 << 7 + _1000001) << 7 + _110101) << 8 i925 = ((_1101101 + i900) << 11 + _1111101) << 11 + _1010101 i953 = ((i925 << 7 + _1001111) << 9 + _1000111) << 10 i971 = ((_1111011 + i953) << 8 + _1100111) << 7 + _1011011 i996 = ((i971 << 8 + _1011111) << 7 + _101001) << 8 i1012 = ((_110001 + i996) << 5 + _1101) << 8 + _10011 i1037 = ((i1012 << 9 + _1001101) << 6 + _110101) << 8 i1055 = ((_1101111 + i1037) << 8 + _1110101) << 7 + _101001 i1081 = ((i1055 << 10 + _1001101) << 7 + _1010001) << 7 i1098 = ((_1111101 + i1081) << 5 + _10101) << 9 + _100111 i1125 = ((i1098 << 7 + _11111) << 8 + _110111) << 10 i1144 = ((_101111 + i1125) << 8 + _1000111) << 8 + _1111101 i1169 = ((i1144 << 5 + _10001) << 12 + _110101) << 6 i1189 = ((_11011 + i1169) << 10 + _1110101) << 7 + _1010111 i1217 = ((i1189 << 7 + _111101) << 12 + _1101011) << 7 i1236 = ((_101111 + i1217) << 8 + _1001001) << 8 + _1001011 i1267 = ((i1236 << 12 + _1100001) << 10 + _100011) << 7 i1287 = ((_100111 + i1267) << 10 + _1011011) << 7 + _1001001 i1309 = ((i1287 << 7 + _1101111) << 7 + _1101011) << 6 i1329 = ((_10001 + i1309) << 8 + _111011) << 9 + _1010001 i1351 = ((i1329 << 7 + _1100011) << 8 + _1001101) << 5 i1374 = ((_10111 + i1351) << 13 + _1111001) << 7 + _1011001 i1398 = ((i1374 << 7 + _1010101) << 7 + _1101001) << 8 i1417 = ((_110011 + i1398) << 6 + _1011) << 10 + _1001011 i1444 = ((i1417 << 8 + _1111101) << 4 + _101) << 13 i1463 = ((_1100101 + i1444) << 7 + _1000101) << 9 + _100111 i1491 = ((i1463 << 8 + _1101101) << 10 + _1001011) << 8 i1509 = ((_1000011 + i1491) << 9 + _110101) << 6 + _10111 i1539 = ((i1509 << 9 + _110111) << 9 + _111101) << 10 i1558 = ((_101011 + i1539) << 2 + 1) << 14 + _1111101 i1585 = ((i1558 << 7 + _1101) << 10 + _101111) << 8 i1610 = ((_1110001 + i1585) << 15 + _1011101) << 7 + _1101001 i1637 = ((i1610 << 6 + _11001) << 9 + _101011) << 10 i1654 = (2*(_1001111 + i1637) + 1) << 13 + _1011001 i1678 = ((i1654 << 4 + _1111) << 9 + _111011) << 9 i1695 = ((_1011011 + i1678) << 6 + _110011) << 8 + _1101 i1725 = ((i1695 << 10 + _1101011) << 7 + _1010001) << 11 i1746 = ((_1111001 + i1725) << 6 + _100011) << 12 + _1111111 i1769 = ((i1746 << 8 + _1000111) << 7 + _1010001) << 6 i1788 = ((_110101 + i1769) << 8 + _1011001) << 8 + _110111 i1812 = ((i1788 << 10 + _1110011) << 6 + _101011) << 6 i1834 = ((_11111 + i1812) << 8 + _101101) << 11 + _1111001 i1863 = ((i1834 << 9 + _10111) << 10 + _1000111) << 8 i1880 = ((_1011001 + i1863) << 5 + _11011) << 9 + _1000001 i1907 = ((i1880 << 2 + _11) << 16 + _1100011) << 7 i1923 = ((_1001001 + i1907) << 7 + _1100111) << 6 + _110111 i1950 = ((i1923 << 8 + _1111011) << 10 + _1100111) << 7 i1971 = ((_11011 + i1950) << 6 + _111) << 12 + _101101 i1994 = ((i1971 << 8 + _1001001) << 7 + _1101111) << 6 i2016 = ((_110011 + i1994) << 10 + _100101) << 9 + _1101001 i2041 = ((i2016 << 7 + _1110101) << 6 + _10101) << 10 i2060 = ((_1100001 + i2041) << 7 + _1000101) << 9 + _110101 i2085 = ((i2060 << 5 + _1101) << 11 + _1100111) << 7 i2103 = ((_1010011 + i2085) << 6 + _100001) << 9 + _1000111 i2129 = ((i2103 << 5 + _11011) << 9 + _1100011) << 10 i2146 = ((_1001011 + i2129) << 7 + _1110011) << 7 + _101111 i2167 = ((i2146 << 6 + _11101) << 9 + _1010111) << 4 i2195 = ((1 + i2167) << 16 + _101111) << 9 + _100011 i2220 = ((i2195 << 7 + _11101) << 8 + _111111) << 8 i2238 = ((_1011101 + i2220) << 6 + _10001) << 9 + _1100011 i2264 = ((i2238 << 7 + _1101111) << 8 + _1001001) << 9 i2283 = ((_10011 + i2264) << 9 + _1111011) << 7 + _1110111 i2308 = ((i2283 << 7 + _1110101) << 7 + _1101111) << 9 i2327 = ((_10001 + i2308) << 8 + _100111) << 8 + _1001011 i2351 = ((i2327 << 5 + _10101) << 9 + _1110101) << 8 i2371 = ((_1010011 + i2351) << 7 + _1101111) << 10 + _1010011 i2402 = ((i2371 << 13 + _1010111) << 9 + _1010001) << 7 i2420 = ((_1111101 + i2402) << 7 + _110001) << 8 + _1001001 i2446 = (2*(i2420 << 7 + _1001101) + 1) << 16 i2465 = ((_111011 + i2446) << 8 + _1010011) << 8 + _1111011 i2492 = ((i2465 << 8 + _1011111) << 8 + _111001) << 9 i2511 = ((_100001 + i2492) << 8 + _1100101) << 8 + _1010011 i2542 = ((i2511 << 9 + _1010111) << 9 + _1001) << 11 i2562 = ((_10111 + i2542) << 9 + _1111111) << 8 + _1010111 i2585 = ((i2562 << 6 + _110001) << 8 + _1010001) << 7 i2607 = ((_1100101 + i2585) << 7 + _1011001) << 12 + _1000011 i2635 = ((i2607 << 6 + _110111) << 11 + _1110111) << 9 i2656 = ((_110111 + i2635) << 6 + _1111) << 12 + _1000011 i2679 = ((i2656 << 7 + _1101101) << 5 + _10111) << 9 i2691 = 2*((_101001 + i2679) << 8 + _1110001) + 1 i2720 = ((i2691 << 14 + _1100001) << 6 + _111101) << 7 i2740 = ((_110101 + i2720) << 11 + _1110001) << 6 + _111011 i2770 = ((i2740 << 9 + _1110011) << 12 + _1000101) << 7 i2788 = ((_101101 + i2770) << 6 + _10101) << 9 + _1001001 i2811 = ((i2788 << 4 + _1001) << 10 + _1100011) << 7 i2829 = ((_1011001 + i2811) << 5 + _11111) << 10 + _1101011 i2853 = ((i2829 << 6 + _11011) << 9 + _110001) << 7 i2866 = 2*((_11111 + i2853) << 9 + _1101111) + 1 i2896 = ((i2866 << 12 + _111011) << 8 + _110101) << 8 i2915 = ((_1000101 + i2896) << 7 + _11101) << 9 + _1111101 i2941 = ((i2915 << 9 + _1001011) << 6 + _10011) << 9 i2957 = ((_1110001 + i2941) << 6 + _111101) << 7 + _10111 i2984 = ((i2957 << 9 + _111011) << 8 + _100111) << 8 i3001 = ((_1001101 + i2984) << 6 + _110011) << 8 + _1001111 i3025 = ((i3001 << 8 + _1001001) << 6 + _100111) << 8 i3040 = ((_1110011 + i3025) << 5 + _10011) << 7 + _10101 i3065 = ((i3040 << 9 + _1111001) << 7 + _1101001) << 7 i3085 = ((_1111011 + i3065) << 8 + _101101) << 9 + _1000001 i3110 = ((i3085 << 8 + _111001) << 8 + _1011101) << 7 i3126 = ((_1111011 + i3110) << 5 + _10001) << 8 + _110111 i3150 = ((i3126 << 8 + _1000101) << 6 + _101111) << 8 i3168 = ((_1101011 + i3150) << 2 + _11) << 13 + _1110011 i3191 = ((i3168 << 7 + _1000001) << 5 + _10011) << 9 i3207 = ((_1111101 + i3191) << 7 + _1010011) << 6 + _110011 i3232 = ((i3207 << 8 + _1010011) << 5 + _1011) << 10 i3251 = ((_1110101 + i3232) << 10 + _1101111) << 6 + _110001 i3282 = ((i3251 << 12 + _100011) << 9 + _1011011) << 8 i3299 = ((_1001011 + i3282) << 6 + _100111) << 8 + _1100011 i3324 = ((i3299 << 7 + _1011111) << 7 + _1101101) << 9 i3341 = ((_10001 + i3324) << 10 + _1101001) << 4 + _1111 i3372 = ((i3341 << 12 + _100101) << 8 + _1000001) << 9 i3391 = ((_1100111 + i3372) << 9 + _1010111) << 7 + _1000001 i3415 = ((i3391 << 2 + _11) << 11 + _11111111) << 9 i3433 = ((_1111101 + i3415) << 5 + _1101) << 10 + _1101111 i3456 = ((i3433 << 6 + _11001) << 8 + _11001) << 7 i3477 = ((_111 + i3456) << 11 + _100101) << 7 + _11 return i3477 << 5 ================================================ FILE: tools/addchain/bn254_exp0.acc ================================================ _10 = 2*1 _11 = 1 + _10 _101 = _10 + _11 _111 = _10 + _101 _1001 = _10 + _111 _1011 = _10 + _1001 _1101 = _10 + _1011 _1111 = _10 + _1101 _10001 = _10 + _1111 _10011 = _10 + _10001 _10101 = _10 + _10011 _10111 = _10 + _10101 _11001 = _10 + _10111 _11011 = _10 + _11001 _11101 = _10 + _11011 _11111 = _10 + _11101 _100001 = _10 + _11111 _100011 = _10 + _100001 _100101 = _10 + _100011 _100111 = _10 + _100101 _101001 = _10 + _100111 _101011 = _10 + _101001 _101101 = _10 + _101011 _101111 = _10 + _101101 _110001 = _10 + _101111 _110011 = _10 + _110001 _110101 = _10 + _110011 _110111 = _10 + _110101 _111001 = _10 + _110111 _111011 = _10 + _111001 _111101 = _10 + _111011 _111111 = _10 + _111101 _1000001 = _10 + _111111 _1000011 = _10 + _1000001 _1000101 = _10 + _1000011 _1000111 = _10 + _1000101 _1001001 = _10 + _1000111 _1001011 = _10 + _1001001 _1001101 = _10 + _1001011 _1001111 = _10 + _1001101 _1010001 = _10 + _1001111 _1010011 = _10 + _1010001 _1010101 = _10 + _1010011 _1010111 = _10 + _1010101 _1011001 = _10 + _1010111 _1011011 = _10 + _1011001 _1011101 = _10 + _1011011 _1011111 = _10 + _1011101 _1100001 = _10 + _1011111 _1100011 = _10 + _1100001 _1100101 = _10 + _1100011 _1100111 = _10 + _1100101 _1101001 = _10 + _1100111 _1101011 = _10 + _1101001 _1101101 = _10 + _1101011 _1101111 = _10 + _1101101 _1110001 = _10 + _1101111 _1110011 = _10 + _1110001 _1110101 = _10 + _1110011 _1110111 = _10 + _1110101 _1111001 = _10 + _1110111 _1111011 = _10 + _1111001 _1111101 = _10 + _1111011 _1111111 = _10 + _1111101 _11100010 = _1100011 + _1111111 _11111111 = _11101 + _11100010 i67 = 2*_11100010 x9 = _111011 + i67 i94 = ((i67 << 10 + _1010101) << 7 + _1100001) << 7 i118 = ((_1000011 + i94) << 8 + _111011) << 13 + _101011 i146 = ((i118 << 8 + _1101111) << 8 + _110111) << 10 i165 = ((_1010111 + i146) << 11 + _1110111) << 5 + _1011 i191 = ((i165 << 6 + _101) << 10 + _111001) << 8 i212 = ((_100101 + i191) << 5 + _11) << 13 + _1100011 i243 = ((i212 << 10 + _111) << 11 + _1011011) << 8 i261 = ((_1100001 + i243) << 4 + _1111) << 11 + _110101 i287 = ((i261 << 6 + _10111) << 9 + _1010101) << 9 i308 = ((_10011 + i287) << 9 + _100001) << 9 + _100011 i334 = ((i308 << 9 + _1100001) << 8 + _101101) << 7 i359 = ((_1011 + i334) << 13 + _1100011) << 9 + _100111 i384 = ((i359 << 9 + _1101001) << 5 + _10001) << 9 i402 = ((_100101 + i384) << 9 + _1010001) << 6 + _100011 i426 = ((i402 << 9 + _1100001) << 9 + _1001011) << 4 i445 = ((_1101 + i426) << 7 + _1101) << 9 + _101001 i469 = ((i445 << 8 + _1101001) << 5 + _10011) << 9 i489 = ((_1111101 + i469) << 9 + _1111101) << 8 + _1110101 i515 = ((i489 << 7 + _111011) << 10 + _100011) << 7 i532 = ((_111001 + i515) << 5 + _1101) << 9 + _111 i561 = ((i532 << 11 + _11111111) << 8 + _1111001) << 8 i576 = ((_1010111 + i561) << 5 + _11101) << 7 + _1001 i602 = ((i576 << 10 + _1011001) << 7 + _1111001) << 7 i625 = ((_11001 + i602) << 9 + _101101) << 11 + _111101 i649 = ((i625 << 6 + _10011) << 6 + _101) << 10 i671 = ((_10111 + i649) << 11 + _1101101) << 8 + _1111001 i696 = ((i671 << 9 + _1000001) << 7 + _1101101) << 7 i716 = ((_1100111 + i696) << 7 + _10001) << 10 + _1100011 i737 = ((i716 << 6 + _100111) << 8 + _1101101) << 5 i762 = ((_11101 + i737) << 8 + _10101) << 14 + _1111001 i787 = ((i762 << 7 + _1001011) << 8 + _1000011) << 8 i805 = ((_1011101 + i787) << 9 + _110111) << 6 + _10001 i830 = ((i805 << 6 + _1111) << 10 + _1010101) << 7 i847 = ((_1011001 + i830) << 8 + _1011111) << 6 + _1001 i872 = ((i847 << 5 + _11) << 11 + _110111) << 7 i887 = ((_100101 + i872) << 5 + _1011) << 7 + _1011 i913 = ((i887 << 10 + _1011011) << 6 + _10101) << 8 i936 = ((_111001 + i913) << 8 + _1001001) << 12 + _1110111 i965 = ((i936 << 10 + _101111) << 8 + _10001) << 9 i984 = ((_1010011 + i965) << 7 + _1111011) << 9 + _1010001 i1004 = ((i984 << 6 + _10011) << 9 + _1010111) << 3 i1023 = ((_111 + i1004) << 10 + _110001) << 6 + _11101 i1051 = ((i1023 << 11 + x9) << 8 + _1011011) << 7 i1071 = ((_1010001 + i1051) << 7 + _1101111) << 10 + _111011 i1099 = ((i1071 << 9 + _1111001) << 6 + _101001) << 11 i1118 = ((_101111 + i1099) << 9 + _1011001) << 7 + _1000001 i1143 = ((i1118 << 9 + _1000011) << 7 + _111101) << 7 i1162 = ((_111001 + i1143) << 4 + _11) << 12 + _1100101 i1187 = ((i1162 << 4 + _1001) << 11 + _110011) << 8 i1205 = ((_1100101 + i1187) << 4 + _1101) << 11 + _1101011 i1231 = ((i1205 << 7 + _1010101) << 8 + _11111) << 9 i1248 = ((_1100101 + i1231) << 5 + _1011) << 9 + _111011 i1272 = ((i1248 << 8 + _1010111) << 7 + _100101) << 7 i1292 = ((_110001 + i1272) << 8 + _1110011) << 9 + _1111011 i1317 = ((i1292 << 9 + _1010011) << 5 + _10011) << 9 i1336 = ((_1111001 + i1317) << 6 + _10001) << 10 + _1111001 i1357 = ((i1336 << 7 + _1001101) << 7 + _1110001) << 5 i1382 = ((_11011 + i1357) << 9 + _1001001) << 13 + _1100111 i1407 = ((i1382 << 8 + _1110011) << 6 + _101011) << 9 i1423 = ((_100111 + i1407) << 7 + _101001) << 6 + _11101 i1458 = ((i1423 << 8 + _111001) << 14 + _1101001) << 11 i1478 = ((_1100011 + i1458) << 8 + _110111) << 9 + _1001111 i1498 = ((i1478 << 4 + _11) << 12 + _1010011) << 2 i1519 = ((_11 + i1498) << 12 + _1110101) << 6 + _110111 i1544 = ((i1519 << 10 + _1010101) << 7 + _1011101) << 6 i1559 = ((_111011 + i1544) << 8 + _1100111) << 4 + _111 i1594 = ((i1559 << 12 + _111) << 10 + _11101) << 11 i1610 = ((_1001111 + i1594) << 8 + _1010011) << 5 + _10101 i1636 = ((i1610 << 10 + _1001111) << 11 + _1010111) << 3 i1658 = ((_101 + i1636) << 11 + _1011001) << 8 + _101101 i1680 = ((i1658 << 8 + _1001111) << 7 + _1001111) << 5 i1700 = ((_1011 + i1680) << 10 + _1111001) << 7 + _1000101 i1727 = ((i1700 << 7 + _1001101) << 9 + _111011) << 9 i1744 = ((_1000111 + i1727) << 7 + _1000111) << 7 + _1011001 i1766 = ((i1744 << 6 + _101001) << 8 + _1101101) << 6 i1784 = ((_100101 + i1766) << 9 + _1000111) << 6 + _110101 i1812 = ((i1784 << 9 + _1100111) << 7 + _110001) << 10 i1828 = ((_1101111 + i1812) << 7 + _1101001) << 6 + _100011 i1854 = ((i1828 << 6 + _10011) << 10 + _1000111) << 8 i1876 = ((_1110001 + i1854) << 12 + _100011) << 7 + _101 i1918 = ((i1876 << 20 + _111011) << 11 + _10001) << 9 i1937 = ((_1011001 + i1918) << 6 + _110001) << 10 + _110101 i1962 = ((i1937 << 8 + _110111) << 4 + _111) << 11 i1978 = ((_1001101 + i1962) << 7 + _1000011) << 6 + _101111 i2002 = ((i1978 << 8 + _1000001) << 7 + _1110001) << 7 i2019 = ((_1111001 + i2002) << 7 + _1001101) << 7 + _101001 i2043 = ((i2019 << 10 + _1010111) << 6 + _111011) << 6 i2061 = ((_11111 + i2043) << 8 + _110001) << 7 + _110001 i2084 = ((i2061 << 8 + _1010111) << 2 + 1) << 11 i2103 = ((_10111 + i2084) << 9 + _1000011) << 7 + _1011001 i2126 = ((i2103 << 7 + _1011011) << 5 + _11101) << 9 i2144 = ((_101001 + i2126) << 8 + _1110011) << 7 + _1100011 i2173 = ((i2144 << 9 + _1110111) << 8 + _1010011) << 10 i2184 = 2*((_1110001 + i2173) << 7 + _1110001) + 1 i2216 = ((i2184 << 14 + _111101) << 9 + _1110001) << 7 i2233 = ((_1001011 + i2216) << 7 + _111001) << 7 + _11111 i2259 = ((i2233 << 10 + _1100111) << 7 + _1101111) << 7 i2280 = ((_1011011 + i2259) << 10 + x9) << 8 + _1100101 i2305 = ((i2280 << 7 + _1110011) << 6 + _100001) << 10 i2327 = ((_101011 + i2305) << 13 + _1000101) << 6 + _1011 i2354 = ((i2327 << 10 + _110111) << 7 + _100111) << 8 i2374 = ((_1100101 + i2354) << 7 + _1100101) << 10 + _1011111 i2402 = ((i2374 << 12 + _1000011) << 7 + _1110001) << 7 i2421 = ((_1011101 + i2402) << 8 + _1011011) << 8 + _1101111 i2446 = ((i2421 << 5 + _11101) << 9 + _10011) << 9 i2461 = ((_1111001 + i2446) << 5 + _10101) << 7 + _10111 i2494 = ((i2461 << 11 + _100101) << 10 + _101) << 10 i2519 = ((_110011 + i2494) << 8 + _101001) << 14 + _1100111 i2543 = ((i2519 << 9 + _1000011) << 4 + _1001) << 9 i2561 = ((_110101 + i2543) << 8 + _1010011) << 7 + _1100011 i2586 = ((i2561 << 5 + _1001) << 6 + _101) << 12 i2614 = ((_11011 + i2586) << 13 + _101) << 12 + _1101101 i2641 = ((i2614 << 4 + _101) << 14 + _1000001) << 7 i2658 = ((_111011 + i2641) << 6 + _10011) << 8 + _11011 i2684 = ((i2658 << 8 + _10111) << 9 + _1010001) << 7 i2702 = ((_111001 + i2684) << 8 + _1010101) << 7 + _1000111 i2726 = ((i2702 << 4 + _1011) << 10 + _1000101) << 8 i2741 = ((_1011101 + i2726) << 6 + _110001) << 6 + _11011 i2767 = ((i2741 << 9 + _1000111) << 9 + _1100001) << 6 i2792 = ((_111111 + i2767) << 9 + _1101011) << 13 + _111011 i2820 = ((i2792 << 8 + _1111101) << 6 + _11101) << 12 i2837 = ((_1110101 + i2820) << 2 + _11) << 12 + _1101001 i2862 = ((i2837 << 8 + _110101) << 8 + _1001101) << 7 i2878 = ((_1110101 + i2862) << 8 + _1011001) << 5 + _10111 i2910 = ((i2878 << 8 + _11) << 13 + _1011101) << 9 i2932 = ((_1011101 + i2910) << 10 + _1111111) << 9 + _1010111 i2956 = ((i2932 << 8 + _1110001) << 4 + _1001) << 10 i2972 = ((_1101001 + i2956) << 6 + _11001) << 7 + _1001 i3000 = ((i2972 << 9 + _100011) << 7 + _101001) << 10 i3019 = ((_11111 + i3000) << 9 + _1010111) << 7 + _1000101 i3046 = ((i3019 << 7 + _100011) << 11 + _1111101) << 7 i3065 = ((_1000001 + i3046) << 7 + _1111011) << 9 + _1010111 i3094 = ((i3065 << 14 + _1001101) << 8 + _1001101) << 5 i3115 = ((_1111 + i3094) << 8 + _11011) << 10 + _1111101 i3140 = ((i3115 << 7 + _100111) << 9 + _1101111) << 7 i3160 = ((_101001 + i3140) << 9 + _1010101) << 8 + _1110111 i3182 = ((i3160 << 7 + _1000111) << 6 + _100101) << 7 i3202 = ((_111101 + i3182) << 5 + _1001) << 12 + _1111001 i3225 = ((i3202 << 5 + _10101) << 9 + _1000111) << 7 i3243 = ((_1010011 + i3225) << 7 + _1001111) << 8 + _1100011 i3266 = ((i3243 << 7 + _1101101) << 6 + _10111) << 8 i3284 = ((_110111 + i3266) << 7 + _111111) << 8 + _1011001 i3309 = ((i3284 << 7 + _1011011) << 8 + _101111) << 8 i3326 = ((_1010001 + i3309) << 4 + _1101) << 10 + _1001111 i3354 = ((i3326 << 7 + _1100011) << 8 + _1000011) << 11 i3369 = ((_1111011 + i3354) << 3 + _11) << 9 + _11111111 i3396 = ((i3369 << 12 + _1000111) << 7 + _11111) << 6 i3421 = ((_111 + i3396) << 11 + _1110001) << 11 + _10101 i3449 = ((i3421 << 12 + _1101001) << 5 + _10011) << 9 i3470 = ((_111101 + i3449) << 11 + _1100001) << 7 + _1100101 return 2*i3470 + 1 ================================================ FILE: tools/addchain/bn254_r_m_d_inv.acc ================================================ _10 = 2*1 _11 = 1 + _10 _100 = 1 + _11 _101 = 1 + _100 _111 = _10 + _101 _1001 = _10 + _111 _1011 = _10 + _1001 _1101 = _10 + _1011 _1111 = _10 + _1101 _10001 = _10 + _1111 _10011 = _10 + _10001 _10101 = _10 + _10011 _10111 = _10 + _10101 _11001 = _10 + _10111 _11011 = _10 + _11001 _11101 = _10 + _11011 _11111 = _10 + _11101 _100001 = _10 + _11111 _100011 = _10 + _100001 _100101 = _10 + _100011 _100111 = _10 + _100101 _101001 = _10 + _100111 _101011 = _10 + _101001 _101101 = _10 + _101011 _101111 = _10 + _101101 _110001 = _10 + _101111 _110011 = _10 + _110001 _110101 = _10 + _110011 _110111 = _10 + _110101 _111001 = _10 + _110111 _111011 = _10 + _111001 _111101 = _10 + _111011 _111111 = _10 + _111101 _1000001 = _10 + _111111 _1000011 = _10 + _1000001 _1000101 = _10 + _1000011 _1000111 = _10 + _1000101 _1001001 = _10 + _1000111 _1001011 = _10 + _1001001 _1001101 = _10 + _1001011 _1001111 = _10 + _1001101 _1010001 = _10 + _1001111 _1010011 = _10 + _1010001 _1010101 = _10 + _1010011 _1010111 = _10 + _1010101 _1011001 = _10 + _1010111 _1011011 = _10 + _1011001 _1011101 = _10 + _1011011 _1011111 = _10 + _1011101 _1100001 = _10 + _1011111 _1100011 = _10 + _1100001 _1100101 = _10 + _1100011 _1100111 = _10 + _1100101 _1101001 = _10 + _1100111 _1101011 = _10 + _1101001 _1101101 = _10 + _1101011 _1101111 = _10 + _1101101 _1110001 = _10 + _1101111 _1110011 = _10 + _1110001 _1110101 = _10 + _1110011 _1110111 = _10 + _1110101 _1111001 = _10 + _1110111 _1111011 = _10 + _1111001 _1111101 = _10 + _1111011 _1111111 = _10 + _1111101 _10000001 = _10 + _1111111 _10000011 = _10 + _10000001 _10000101 = _10 + _10000011 _10000111 = _10 + _10000101 _10001001 = _10 + _10000111 _10001011 = _10 + _10001001 _10001101 = _10 + _10001011 _10001111 = _10 + _10001101 _10010001 = _10 + _10001111 _10010011 = _10 + _10010001 _10010101 = _10 + _10010011 _10010111 = _10 + _10010101 _10011001 = _10 + _10010111 _10011011 = _10 + _10011001 _10011101 = _10 + _10011011 _10011111 = _10 + _10011101 _10100001 = _10 + _10011111 _10100011 = _10 + _10100001 _10100101 = _10 + _10100011 _10100111 = _10 + _10100101 _10101001 = _10 + _10100111 _10101011 = _10 + _10101001 _10101101 = _10 + _10101011 _10101111 = _10 + _10101101 _10110001 = _10 + _10101111 _10110011 = _10 + _10110001 _10110101 = _10 + _10110011 _10110111 = _10 + _10110101 _10111001 = _10 + _10110111 _10111011 = _10 + _10111001 _10111101 = _10 + _10111011 _10111111 = _10 + _10111101 _11000001 = _10 + _10111111 _11000011 = _10 + _11000001 _11000101 = _10 + _11000011 _11000111 = _10 + _11000101 _11001001 = _10 + _11000111 _11001011 = _10 + _11001001 _11001101 = _10 + _11001011 _11001111 = _10 + _11001101 _11010001 = _10 + _11001111 _11010011 = _10 + _11010001 _11010111 = _100 + _11010011 _11011001 = _10 + _11010111 _11011011 = _10 + _11011001 _11011101 = _10 + _11011011 _11011111 = _10 + _11011101 _11100001 = _10 + _11011111 _11100011 = _10 + _11100001 _11100101 = _10 + _11100011 _11100111 = _10 + _11100101 _11101001 = _10 + _11100111 _11101011 = _10 + _11101001 _11101101 = _10 + _11101011 _11101111 = _10 + _11101101 _11110001 = _10 + _11101111 _11110011 = _10 + _11110001 _11110101 = _10 + _11110011 _11110111 = _10 + _11110101 _11111001 = _10 + _11110111 _11111011 = _10 + _11111001 _11111101 = _10 + _11111011 _11111111 = _10 + _11111101 i146 = ((_11 + _11111111) << 7 + _10100011) << 8 + _11010011 i174 = ((i146 << 9 + _1110011) << 9 + _10101001) << 8 i199 = ((_101011 + i174) << 11 + _100011) << 11 + _11100011 i229 = ((i199 << 8 + _10011011) << 8 + _11000001) << 12 i255 = ((_11110111 + i229) << 9 + _10000111) << 14 + _10100001 i278 = ((i255 << 5 + _11101) << 9 + _10101) << 7 i298 = ((_1011 + i278) << 10 + _100011) << 7 + _11111 i330 = ((i298 << 12 + _10111111) << 8 + _1000011) << 10 i352 = ((_1011111 + i330) << 8 + _1100001) << 11 + _11111111 i387 = ((i352 << 10 + _11011001) << 10 + _10001) << 13 i411 = ((_1000111 + i387) << 6 + _10111) << 15 + _1101101 i441 = ((i411 << 12 + _11100011) << 7 + _1111011) << 9 i461 = ((_11111011 + i441) << 8 + _11111011) << 9 + _10101011 i490 = ((i461 << 11 + _10111111) << 9 + _10011011) << 7 i508 = ((_1100111 + i490) << 8 + _1101111) << 7 + _101111 i537 = ((i508 << 10 + _11000011) << 6 + _11011) << 11 i560 = ((_10111111 + i537) << 9 + _10010101) << 11 + _10100101 i587 = ((i560 << 9 + _1001101) << 9 + _1100001) << 7 i609 = ((_110111 + i587) << 7 + _10111) << 12 + _11101 i638 = ((i609 << 11 + _11100111) << 6 + _100111) << 10 i660 = ((_100111 + i638) << 12 + _10110011) << 7 + _1111101 i686 = ((i660 << 12 + _10100101) << 8 + _11110011) << 4 i710 = ((_1001 + i686) << 13 + _10001011) << 8 + _1001101 i737 = ((i710 << 5 + _1001) << 12 + _10100011) << 8 i755 = ((_10001101 + i737) << 7 + _1010101) << 8 + _1001001 i788 = ((i755 << 5 + _1011) << 13 + _1001001) << 13 i806 = ((_10110011 + i788) << 8 + _11001101) << 7 + _1010011 i838 = ((i806 << 11 + _1101111) << 10 + _10000001) << 9 i860 = ((_10111011 + i838) << 11 + _11100111) << 8 + _11101011 i884 = ((i860 << 2 + _11) << 13 + _1010101) << 7 i912 = ((_101101 + i884) << 12 + _10101011) << 13 + _111011 i937 = ((i912 << 7 + _11101) << 7 + _1111) << 9 i962 = ((_10011 + i937) << 10 + _100001) << 12 + _101011 i993 = ((i962 << 10 + _11100011) << 10 + _10111011) << 9 i1013 = ((_11001111 + i993) << 10 + _10101101) << 7 + _1001111 i1041 = ((i1013 << 10 + _11110011) << 8 + _10001001) << 8 i1060 = ((_10011101 + i1041) << 8 + _10001001) << 8 + _1101011 i1092 = ((i1060 << 7 + _111011) << 12 + _1000101) << 11 i1116 = ((_10011011 + i1092) << 10 + _111001) << 11 + _10111011 i1151 = ((i1116 << 11 + _10111011) << 10 + _11011011) << 12 i1173 = ((_10011111 + i1151) << 12 + _11100111) << 7 + _1000111 i1204 = ((i1173 << 9 + _10001111) << 10 + _11110001) << 10 i1223 = ((_10001001 + i1204) << 8 + _10000011) << 8 + _10001001 i1250 = ((i1223 << 6 + _100111) << 11 + _10011011) << 8 i1273 = ((_11101001 + i1250) << 13 + _1110111) << 7 + _100011 i1304 = ((i1273 << 11 + _1100001) << 9 + _11110111) << 9 i1324 = ((_1011011 + i1304) << 10 + _11100001) << 7 + _1100011 i1352 = ((i1324 << 9 + _11010001) << 8 + _11000111) << 9 i1378 = ((_10010101 + i1352) << 14 + _11010001) << 9 + _1001101 i1409 = ((i1378 << 8 + _1010001) << 12 + _1011011) << 9 i1430 = ((_1101111 + i1409) << 8 + _111101) << 10 + _1010011 i1460 = ((i1430 << 12 + _10101101) << 8 + _10011011) << 8 i1485 = ((_10100001 + i1460) << 8 + _10001111) << 14 + _1111101 i1511 = ((i1485 << 7 + _100011) << 9 + _1000111) << 8 i1532 = ((_1100001 + i1511) << 9 + _1110011) << 9 + _11110001 i1559 = ((i1532 << 7 + _1100111) << 10 + _11101101) << 8 i1579 = ((_1101101 + i1559) << 8 + _11001) << 9 + _110001 i1613 = ((i1579 << 9 + _1000011) << 10 + _1000011) << 13 i1640 = ((_11001101 + i1613) << 12 + _1110001) << 12 + _10101011 i1666 = ((i1640 << 4 + _1011) << 12 + _10111011) << 8 i1685 = ((_11011011 + i1666) << 7 + _1010101) << 9 + _11101101 i1712 = ((i1685 << 8 + _11001011) << 7 + _1111101) << 10 i1732 = ((_11100101 + i1712) << 7 + _1101011) << 10 + _10101101 i1759 = ((i1732 << 8 + _1000001) << 9 + _11001011) << 8 i1778 = ((_11001011 + i1759) << 3 + _111) << 13 + _11011111 i1809 = ((i1778 << 8 + _100011) << 12 + _11100111) << 9 i1827 = ((_10001111 + i1809) << 6 + _110101) << 9 + _1111111 i1854 = ((i1827 << 10 + _10111101) << 8 + _10001101) << 7 i1877 = ((_1101011 + i1854) << 10 + _11101101) << 10 + _10001111 i1900 = ((i1877 << 9 + _11110101) << 8 + _11000111) << 4 i1922 = ((_1111 + i1900) << 12 + _10110111) << 7 + _10001 i1945 = ((i1922 << 12 + _11101001) << 6 + _111101) << 3 i1970 = ((1 + i1945) << 14 + _1101011) << 8 + _111011 i1997 = ((i1970 << 11 + _11011001) << 7 + _1100001) << 7 i2018 = ((_110001 + i1997) << 10 + _11000111) << 8 + _11110111 i2044 = ((i2018 << 6 + _11011) << 12 + _10110011) << 6 i2067 = ((_11111 + i2044) << 11 + _1101101) << 9 + _10110011 i2093 = ((i2067 << 8 + _11010001) << 5 + _10011) << 11 i2112 = ((_10001001 + i2093) << 5 + _11001) << 11 + _11011111 i2138 = ((i2112 << 8 + _11001001) << 8 + _11111001) << 8 i2160 = ((_10101111 + i2138) << 11 + _10111001) << 8 + _1001001 i2189 = ((i2160 << 10 + _11100111) << 9 + _10111101) << 8 i2210 = ((_11101011 + i2189) << 8 + _1111001) << 10 + _1100001 i2238 = ((i2210 << 9 + _11010111) << 10 + _10100011) << 7 i2258 = ((_1111101 + i2238) << 9 + _11000011) << 8 + _1001001 i2284 = ((i2258 << 9 + _1000001) << 12 + _11001001) << 3 i2312 = ((_111 + i2284) << 18 + _10011001) << 7 + _1010111 i2340 = ((i2312 << 9 + _11100001) << 8 + _11110101) << 9 i2359 = ((_10011011 + i2340) << 8 + _10000011) << 8 + _1001101 i2387 = ((i2359 << 8 + _100111) << 9 + _1100001) << 9 i2409 = ((_10100011 + i2387) << 8 + _1000011) << 11 + _10001 i2451 = ((i2409 << 18 + _1111001) << 9 + _111001) << 13 i2469 = ((_11101011 + i2451) << 7 + _1011101) << 8 + _1001101 i2491 = ((i2469 << 10 + _10000111) << 8 + _11001001) << 2 i2515 = ((_11 + i2491) << 13 + _1011011) << 8 + _1010101 i2544 = ((i2515 << 9 + _100011) << 9 + _111101) << 9 i2568 = ((_10001 + i2544) << 14 + _10010011) << 7 + _1001101 i2599 = ((i2568 << 3 + 1) << 18 + _110011) << 8 i2618 = ((_110011 + i2599) << 10 + _10100111) << 6 + _11011 i2648 = ((i2618 << 8 + _11101) << 12 + _10101111) << 8 i2671 = ((_101101 + i2648) << 10 + _10101111) << 10 + _11100101 i2696 = ((i2671 << 7 + _110111) << 10 + _10110001) << 6 i2716 = ((_101101 + i2696) << 11 + _10001001) << 6 + _1001 i2749 = ((i2716 << 9 + _11101) << 12 + _101011) << 10 i2769 = ((_100001 + i2749) << 11 + _10001111) << 6 + _101001 i2800 = ((i2769 << 12 + _10111101) << 8 + _10111011) << 9 i2820 = ((_101101 + i2800) << 10 + _10101001) << 7 + _1110011 i2849 = ((i2820 << 9 + _10000001) << 7 + _101011) << 11 i2869 = ((_10110101 + i2849) << 8 + _1110101) << 9 + _10001101 i2895 = ((i2869 << 8 + _11111001) << 8 + _1110101) << 8 i2918 = ((_1111 + i2895) << 6 + _11) << 14 + _1011111 i2939 = ((i2918 << 5 + _1111) << 11 + _1100101) << 3 i2968 = ((_11 + i2939) << 13 + _1011011) << 13 + _10001001 i2994 = ((i2968 << 8 + _10000111) << 8 + _10100001) << 8 i3013 = ((_11001101 + i2994) << 8 + _1000111) << 8 + _1101111 i3042 = ((i3013 << 11 + _10010001) << 8 + _1011001) << 8 i3064 = ((_100001 + i3042) << 9 + _1101001) << 10 + _11010011 i3092 = ((i3064 << 8 + _11110011) << 8 + _110111) << 10 i3114 = ((_101111 + i3092) << 11 + _11100001) << 8 + _10000111 i3140 = ((i3114 << 5 + _10111) << 12 + _10111111) << 7 i3165 = ((_1110011 + i3140) << 10 + _11110111) << 12 + _10110011 i3191 = ((i3165 << 8 + _10111111) << 7 + _1010011) << 9 i3212 = ((_1100101 + i3191) << 9 + _10000001) << 9 + _10101101 i3239 = ((i3212 << 6 + _11011) << 11 + _10111101) << 8 i3258 = ((_11100001 + i3239) << 7 + _1111001) << 9 + _1110111 i3287 = ((i3258 << 10 + _11111001) << 6 + _10011) << 11 i3308 = ((_11110101 + i3287) << 7 + _100101) << 11 + _11101111 i3344 = ((i3308 << 11 + _1100111) << 10 + _1110001) << 13 i3365 = ((_1100011 + i3344) << 12 + _11110111) << 6 + _111011 i3399 = ((i3365 << 12 + _10010001) << 7 + _1110101) << 13 i3418 = ((_11100101 + i3399) << 7 + _1010111) << 9 + _1100111 i3444 = ((i3418 << 9 + _11110101) << 9 + _1010011) << 6 i3470 = ((_10001 + i3444) << 9 + _101101) << 14 + _1101001 i3497 = ((i3470 << 9 + _10100101) << 4 + _101) << 12 i3515 = ((_1010001 + i3497) << 3 + 1) << 12 + _11011 i3551 = ((i3515 << 14 + _11011001) << 12 + _1101011) << 8 i3570 = ((_1101111 + i3551) << 9 + _10110111) << 7 + _110001 i3604 = ((i3570 << 10 + _11110111) << 8 + _11111111) << 14 i3623 = ((_10101001 + i3604) << 9 + _11010001) << 7 + _1011011 i3650 = ((i3623 << 9 + _10100111) << 4 + _1111) << 12 i3676 = ((_100101 + i3650) << 15 + _10011111) << 8 + _11001011 i3706 = ((i3676 << 9 + _11000101) << 8 + _11101111) << 11 i3726 = ((_11101101 + i3706) << 6 + _100101) << 11 + _10001011 i3753 = ((i3726 << 7 + _1010001) << 9 + _1011001) << 9 i3771 = ((_10001001 + i3753) << 8 + _11101011) << 7 + _1000101 i3804 = ((i3771 << 11 + _1010011) << 8 + _1001111) << 12 i3825 = ((_1101111 + i3804) << 10 + _11111101) << 8 + _1100111 i3852 = ((i3825 << 8 + _1000001) << 3 + _11) << 14 i3867 = ((_10101101 + i3852) << 8 + _10011001) << 4 + _1011 i3895 = ((i3867 << 14 + _11110011) << 8 + _10101001) << 4 i3919 = ((_1101 + i3895) << 11 + _110111) << 10 + _11011111 i3946 = ((i3919 << 9 + _10010011) << 6 + _10101) << 10 i3967 = ((_1101001 + i3946) << 12 + _10011011) << 6 + _110111 i3998 = ((i3967 << 10 + _11000111) << 6 + _11011) << 13 i4017 = ((_11010111 + i3998) << 7 + _1001001) << 9 + _11100011 i4047 = ((i4017 << 8 + _11101) << 11 + _11111011) << 9 i4063 = ((_10111111 + i4047) << 8 + _10100011) << 5 + _1101 i4093 = ((i4063 << 11 + _1110001) << 9 + _10111101) << 8 i4113 = ((_10111011 + i4093) << 9 + _10001101) << 8 + _10100001 i4143 = ((i4113 << 9 + _11111001) << 11 + _10111111) << 8 i4168 = ((_11111001 + i4143) << 5 + _111) << 17 + _10001001 i4191 = ((i4168 << 4 + _1001) << 12 + _1111001) << 5 i4217 = ((_1001 + i4191) << 14 + _10111101) << 9 + _11111111 i4245 = ((i4217 << 8 + _10101011) << 8 + _10101101) << 10 i4267 = ((_101111 + i4245) << 11 + _110011) << 8 + _101101 i4294 = ((i4267 << 9 + _1100001) << 9 + _10111001) << 7 i4317 = ((_100001 + i4294) << 12 + _11110001) << 8 + _10101101 i4345 = ((i4317 << 11 + _10111011) << 7 + _1111011) << 8 i4366 = ((_1101101 + i4345) << 10 + _10100101) << 8 + _1110111 i4396 = ((i4366 << 11 + _11100101) << 4 + _111) << 13 i4418 = ((_1100011 + i4396) << 9 + _111111) << 10 + _10010011 i4446 = ((i4418 << 9 + _11111011) << 8 + _1111111) << 9 i4462 = ((_10010101 + i4446) << 8 + _10010101) << 5 + _10011 i4495 = ((i4462 << 11 + _1101101) << 8 + _1000111) << 12 i4514 = ((_11000001 + i4495) << 8 + _1101111) << 8 + _1100001 i4543 = ((i4514 << 10 + _10011101) << 8 + _11000001) << 9 i4562 = ((_1010011 + i4543) << 7 + _111111) << 9 + _101001 i4589 = ((i4562 << 10 + _11010001) << 9 + _11110111) << 6 i4609 = ((_111001 + i4589) << 4 + _11) << 13 + _1001001 i4637 = ((i4609 << 8 + _1010001) << 9 + _11101011) << 9 i4658 = ((_10100101 + i4637) << 10 + _11100101) << 8 + _10001 i4686 = ((i4658 << 11 + _10011011) << 8 + _10001011) << 7 i4706 = ((_1111111 + i4686) << 7 + _100011) << 10 + _1101011 i4732 = ((i4706 << 9 + _10010001) << 5 + _10011) << 10 i4760 = ((_10001 + i4732) << 17 + _10000101) << 8 + _11001111 i4787 = ((i4760 << 7 + _1000111) << 9 + _11011011) << 9 i4806 = ((_10011101 + i4787) << 6 + _101101) << 10 + _111001 i4834 = ((i4806 << 10 + _11111) << 9 + _110011) << 7 i4863 = ((_10101 + i4834) << 11 + _1111) << 15 + _11111011 i4889 = ((i4863 << 7 + _1001101) << 6 + _11001) << 11 i4914 = ((_11110111 + i4889) << 13 + _1111111) << 9 + _10000011 i4942 = ((i4914 << 10 + _11100011) << 10 + _11010011) << 6 i4959 = ((_111011 + i4942) << 10 + _11111111) << 4 + _1001 i4991 = ((i4959 << 12 + _10111111) << 8 + _110001) << 10 i5010 = ((_11001111 + i4991) << 6 + _111111) << 10 + _11011 i5033 = ((i5010 << 11 + _11110001) << 7 + _1111111) << 3 i5060 = ((_11 + i5033) << 13 + _1010001) << 11 + _11101111 i5088 = ((i5060 << 6 + _101111) << 11 + _11010111) << 9 i5109 = ((_10101101 + i5088) << 11 + _11011001) << 7 + _1011101 i5134 = ((i5109 << 9 + _10101011) << 8 + _10010111) << 6 i5161 = ((_100101 + i5134) << 12 + _11001101) << 12 + _10000011 i5192 = ((i5161 << 7 + _1101011) << 10 + _10110011) << 12 i5209 = ((_1100001 + i5192) << 9 + _1001001) << 5 + _1011 i5243 = ((i5209 << 12 + _11100101) << 8 + _110111) << 12 i5264 = ((_11111111 + i5243) << 9 + _11110001) << 9 + _11101101 i5291 = ((i5264 << 9 + _11100111) << 7 + _1100101) << 9 i5314 = ((_1101011 + i5291) << 4 + _11) << 16 + _11001011 i5341 = ((i5314 << 7 + _1010101) << 10 + _10100111) << 8 i5359 = ((_10100001 + i5341) << 4 + _1111) << 11 + _1011101 i5388 = ((i5359 << 10 + _10111101) << 10 + _11111101) << 7 i5406 = ((_1011011 + i5388) << 8 + _1011111) << 7 + _110101 i5435 = ((i5406 << 10 + _10110001) << 8 + _11010011) << 9 i5457 = ((_11011011 + i5435) << 10 + _11101101) << 9 + _1010011 i5485 = ((i5457 << 3 + _11) << 13 + _1001111) << 10 i5506 = ((_1010101 + i5485) << 9 + _10100011) << 9 + _11110111 i5530 = ((i5506 << 8 + _11110011) << 7 + _1011011) << 7 i5547 = ((_111011 + i5530) << 10 + _11010111) << 4 + _1011 i5576 = ((i5547 << 12 + _1000101) << 11 + _11110111) << 4 i5600 = ((_1001 + i5576) << 13 + _11001111) << 8 + _11001011 i5631 = ((i5600 << 9 + _10010111) << 9 + _10101) << 11 i5650 = ((_10011111 + i5631) << 9 + _11011101) << 7 + _1101011 i5676 = ((i5650 << 7 + _100011) << 10 + _10111001) << 7 i5697 = ((_1001011 + i5676) << 8 + _110011) << 10 + _11100011 i5725 = ((i5697 << 8 + _11001001) << 9 + _10011011) << 9 i5744 = ((_10100111 + i5725) << 8 + _11001011) << 8 + _10011001 i5773 = ((i5744 << 7 + _11111) << 11 + _11110111) << 9 i5793 = ((_11100101 + i5773) << 9 + _11010111) << 8 + _10011001 i5821 = ((i5793 << 6 + _11101) << 12 + _11101011) << 8 i5844 = ((_1111001 + i5821) << 9 + _10110111) << 11 + _10100001 i5867 = ((i5844 << 9 + _10111001) << 8 + _11001001) << 4 i5890 = ((_1011 + i5867) << 13 + _11110101) << 7 + _1001001 i5917 = ((i5890 << 8 + _1011101) << 6 + _10111) << 11 i5939 = ((_10010101 + i5917) << 9 + _1011101) << 10 + _11110101 i5969 = ((i5939 << 5 + _1001) << 11 + _1110111) << 12 i5985 = ((_10110011 + i5969) << 8 + _10110101) << 5 + _10111 i6017 = ((i5985 << 12 + _11011111) << 10 + _11111011) << 8 i6037 = ((_10101011 + i6017) << 8 + _11010001) << 9 + _10000011 i6066 = ((i6037 << 9 + _11011111) << 11 + _1010111) << 7 i6088 = ((_110001 + i6066) << 5 + _111) << 14 + _11011111 i6112 = ((i6088 << 6 + _101101) << 9 + _1101101) << 7 i6137 = ((_110111 + i6112) << 9 + _10001) << 13 + _11100011 i6161 = ((i6137 << 8 + _10010001) << 5 + _11001) << 9 i6182 = ((_101101 + i6161) << 10 + _1011101) << 8 + _1110101 i6208 = ((i6182 << 10 + _10101001) << 11 + _10000101) << 3 i6235 = ((_111 + i6208) << 10 + _10101) << 14 + _101001 i6263 = ((i6235 << 10 + _1100001) << 9 + _10010011) << 7 i6283 = ((_100111 + i6263) << 10 + _10111111) << 7 + _1111101 i6314 = ((i6283 << 12 + _11101111) << 9 + _1111101) << 8 return _10111 + i6314 ================================================ FILE: tools/addchain/gen_rust_addchain.py ================================================ #!/usr/bin/env python3 from __future__ import annotations from dataclasses import dataclass from pathlib import Path from typing import List, Tuple ACC_DIR = Path(__file__).resolve().parent OUTPUT_FILE = ( ACC_DIR.parent / "garaga_rs" / "src" / "pairing" / "final_exp_witness" / "addchain_pow_generated.rs" ) CHAINS: List[Tuple[str, str, str]] = [ ("bn254_exp.acc", "bn254", "pow_exp"), ("bn254_exp0.acc", "bn254", "pow_exp0"), ("bn254_r_m_d_inv.acc", "bn254", "pow_r_m_d_inv"), ("bls12_381_h3_s.acc", "bls12_381", "pow_h3_s"), ("bls12_381_e.acc", "bls12_381", "pow_e"), ] @dataclass(frozen=True) class Var: name: str @dataclass(frozen=True) class Add: left: "Expr" right: "Expr" @dataclass(frozen=True) class Shift: value: "Expr" amount: int Expr = Var | Add | Shift @dataclass(frozen=True) class Token: kind: str value: str | int def tokenize(expr: str) -> List[Token]: tokens: List[Token] = [] i = 0 while i < len(expr): ch = expr[i] if ch.isspace(): i += 1 continue if expr.startswith("<<", i): tokens.append(Token("SYMBOL", "<<")) i += 2 continue if ch.isdigit(): j = i + 1 while j < len(expr) and expr[j].isdigit(): j += 1 tokens.append(Token("NUMBER", int(expr[i:j]))) i = j continue if ch.isalpha() or ch == "_": j = i + 1 while j < len(expr) and (expr[j].isalnum() or expr[j] == "_"): j += 1 tokens.append(Token("NAME", expr[i:j])) i = j continue if ch in "+*()": tokens.append(Token("SYMBOL", ch)) i += 1 continue raise ValueError(f"Unexpected character {ch!r} in {expr!r}") return tokens class Parser: def __init__(self, tokens: List[Token]) -> None: self.tokens = tokens self.pos = 0 def _peek(self) -> Token | None: if self.pos >= len(self.tokens): return None return self.tokens[self.pos] def _peek_next(self) -> Token | None: if self.pos + 1 >= len(self.tokens): return None return self.tokens[self.pos + 1] def _match(self, kind: str, value: str | None = None) -> bool: tok = self._peek() if tok is None or tok.kind != kind: return False if value is not None and tok.value != value: return False self.pos += 1 return True def _expect(self, kind: str, value: str | None = None) -> Token: tok = self._peek() if ( tok is None or tok.kind != kind or (value is not None and tok.value != value) ): raise ValueError( f"Expected {kind} {value or ''} at {self.pos}, got {tok!r}" ) self.pos += 1 return tok def parse(self) -> Expr: expr = self._parse_expr() if self._peek() is not None: raise ValueError(f"Unexpected trailing tokens at {self.pos}") return expr def _parse_expr(self) -> Expr: expr = self._parse_chain() while self._match("SYMBOL", "+"): rhs = self._parse_chain() expr = Add(expr, rhs) return expr def _parse_chain(self) -> Expr: expr = self._parse_term() while self._match("SYMBOL", "<<"): amount = self._expect("NUMBER").value if not isinstance(amount, int): raise ValueError("Shift amount must be integer") expr = Shift(expr, amount) if self._match("SYMBOL", "+"): rhs = self._parse_term() expr = Add(expr, rhs) return expr def _parse_term(self) -> Expr: tok = self._peek() if tok and tok.kind == "NUMBER" and tok.value == 2: if self._peek_next() and self._peek_next().kind == "SYMBOL": if self._peek_next().value == "*": self._expect("NUMBER", None) self._expect("SYMBOL", "*") atom = self._parse_atom() return Shift(atom, 1) return self._parse_atom() def _parse_atom(self) -> Expr: if self._match("SYMBOL", "("): expr = self._parse_expr() self._expect("SYMBOL", ")") return expr tok = self._peek() if tok is None: raise ValueError("Unexpected end of expression") if tok.kind == "NAME": self.pos += 1 return Var(str(tok.value)) if tok.kind == "NUMBER": self.pos += 1 if tok.value != 1: raise ValueError(f"Unsupported literal {tok.value}") return Var("1") raise ValueError(f"Unexpected token {tok!r}") def parse_expr(expr: str) -> Expr: tokens = tokenize(expr) return Parser(tokens).parse() def load_chain(path: Path) -> Tuple[List[Tuple[str, Expr]], Expr]: defs: List[Tuple[str, Expr]] = [] return_expr: Expr | None = None for raw_line in path.read_text(encoding="utf-8").splitlines(): line = raw_line.strip() if not line: continue if line.startswith("return"): expr = line[len("return") :].strip() return_expr = parse_expr(expr) continue name, expr = line.split("=", 1) defs.append((name.strip(), parse_expr(expr.strip()))) if return_expr is None: raise ValueError(f"{path} missing return expression") return defs, return_expr class Emitter: def __init__(self) -> None: self.temp_counter = 0 def _temp(self) -> str: name = f"t{self.temp_counter}" self.temp_counter += 1 return name def emit_expr(self, expr: Expr, lines: List[str]) -> str: if isinstance(expr, Var): if expr.name == "1": return "base" return expr.name if isinstance(expr, Add): left = self.emit_expr(expr.left, lines) right = self.emit_expr(expr.right, lines) temp = self._temp() lines.append(f"let {temp} = &{left} * &{right};") return temp if isinstance(expr, Shift): value = self.emit_expr(expr.value, lines) temp = self._temp() lines.append(f"let {temp} = square_n(&{value}, {expr.amount});") return temp raise TypeError(f"Unknown expr type {expr}") def emit_assignment(self, name: str, expr: Expr, indent: str) -> str: self.temp_counter = 0 lines: List[str] = [] result = self.emit_expr(expr, lines) if not lines: return f"{indent}let {name} = {result}.clone();" lines.append(result) inner = "\n".join(f"{indent} {line}" for line in lines) return f"{indent}let {name} = {{\n{inner}\n{indent}}};" def emit_chain_function(name: str, defs: List[Tuple[str, Expr]], ret: Expr) -> str: emitter = Emitter() indent = " " body_lines: List[str] = [f"{indent}let base = base.clone();"] for var, expr in defs: body_lines.append(emitter.emit_assignment(var, expr, indent)) body_lines.append(emitter.emit_assignment("result", ret, indent)) body_lines.append(f"{indent}result") return "\n".join(body_lines) def main() -> int: header_lines = [ "// AUTO-GENERATED: DO NOT EDIT BY HAND.", "// Generated by tools/addchain/gen_rust_addchain.py from:", ] for acc_name, _, _ in CHAINS: header_lines.append(f"// - tools/addchain/{acc_name}") header = "\n".join(header_lines) blocks: List[str] = [ header, "", "use lambdaworks_math::field::element::FieldElement;", "use lambdaworks_math::field::traits::IsField;", "", "fn square_n(x: &FieldElement, n: usize) -> FieldElement {", " let mut t = x.clone();", " for _ in 0..n {", " t = t.square();", " }", " t", "}", "", "pub mod bn254 {", " use super::square_n;", " use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField;", " use lambdaworks_math::field::element::FieldElement;", "", ] for acc_name, module, func_name in CHAINS: acc_path = ACC_DIR / acc_name defs, ret = load_chain(acc_path) if module != "bn254": continue blocks.append(f" /// Generated from tools/addchain/{acc_name}") blocks.append( f" pub fn {func_name}(base: &FieldElement) -> FieldElement {{" ) blocks.append(emit_chain_function(func_name, defs, ret)) blocks.append(" }") blocks.append("") blocks.append("}") blocks.append("") blocks.append("pub mod bls12_381 {") blocks.append(" use super::square_n;") blocks.append( " use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField;" ) blocks.append(" use lambdaworks_math::field::element::FieldElement;") blocks.append("") for acc_name, module, func_name in CHAINS: acc_path = ACC_DIR / acc_name defs, ret = load_chain(acc_path) if module != "bls12_381": continue blocks.append(f" /// Generated from tools/addchain/{acc_name}") blocks.append( f" pub fn {func_name}(base: &FieldElement) -> FieldElement {{" ) blocks.append(emit_chain_function(func_name, defs, ret)) blocks.append(" }") blocks.append("") blocks.append("}") blocks.append("") OUTPUT_FILE.write_text("\n".join(blocks), encoding="utf-8") return 0 if __name__ == "__main__": raise SystemExit(main()) ================================================ FILE: tools/garaga_rs/Cargo.toml ================================================ [package] name = "garaga_rs" version = "1.1.0" edition = "2021" # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html [lib] name = "garaga_rs" crate-type = ["cdylib", "rlib"] [features] # By default, we don't include any bindings - pure Rust library mode # This allows users to import garaga_rs without pulling in pyo3 or wasm-bindgen default = [] # Enable Python bindings (for maturin builds) python = ["dep:pyo3"] # Enable WASM bindings (for wasm-pack builds) wasm = ["dep:wasm-bindgen", "dep:js-sys"] [dev-dependencies] #proptest = "1.6.0" #proptest-arbitrary-interop = "0.1" test-strategy = "0.4.0" # WASM-specific dev dependencies - only included when target is wasm32 [target.'cfg(target_arch = "wasm32")'.dev-dependencies] wasm-bindgen-test = "0.3" # Platform-specific optional dependencies: # These ensure the right bindings are available only when needed and on the right platform # Python bindings - only available when: # 1. Not on wasm32 target AND # 2. "python" feature is enabled (e.g., when building with maturin) [target.'cfg(not(target_arch = "wasm32"))'.dependencies] pyo3 = { version = "0.28", features = ["extension-module", "num-bigint"], optional = true } # WASM bindings - only available when: # 1. On wasm32 target AND # 2. "wasm" feature is enabled (e.g., when building with wasm-pack) [target.'cfg(target_arch = "wasm32")'.dependencies] wasm-bindgen = { version = "0.2", optional = true } js-sys = { version = "0.3", optional = true } [dependencies] getrandom = { version = "0.3.1", features = ["wasm_js"] } num-bigint = "0.4" num-integer = "0.1" num-traits = "0.2" hex = "0.4" sha2 = "0.10" sha3 = "0.10" lazy_static = "1.4" rand = "0.9.0" starknet-types-core = { version = "1.0", default-features = false, features = ["curve"] } lambdaworks-crypto = { git = "https://github.com/lambdaclass/lambdaworks.git", rev="be4a329" } lambdaworks-math = { git = "https://github.com/lambdaclass/lambdaworks.git", rev="be4a329" } arbitrary = "1.0" thiserror = "2.0.11" itertools = "0.14" rayon = "1.8" ================================================ FILE: tools/garaga_rs/src/algebra/extf_mul.rs ================================================ use crate::algebra::polynomial::{pad_with_zero_coefficients_to_length, Polynomial}; use crate::definitions::{get_irreducible_poly, CurveParamsProvider}; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; // Returns (Q(X), R(X)) such that Π(Pi)(X) = Q(X) * P_irr(X) + R(X), for a given curve and extension degree. // R(X) is the result of the multiplication in the extension field. // Q(X) is used for verification. pub fn nondeterministic_extension_field_mul_divmod>( ext_degree: usize, ps: Vec>, ) -> (Polynomial, Polynomial) { let mut z_poly = Polynomial::one(); for poly in ps { z_poly = z_poly.mul_with_ref(&poly); } let p_irr = get_irreducible_poly(ext_degree); let (z_polyq, mut z_polyr) = z_poly.divmod(&p_irr); assert!(z_polyr.coefficients.len() <= ext_degree); // Extend polynomial with 0 coefficients to match the expected length. if z_polyr.coefficients.len() < ext_degree { pad_with_zero_coefficients_to_length(&mut z_polyr, ext_degree); } (z_polyq, z_polyr) } pub fn nondeterministic_extension_field_div( x: Polynomial, y: Polynomial, ext_degree: usize, ) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { let a = direct_to_tower(&x.get_coefficients_ext_degree(ext_degree), ext_degree); let b = direct_to_tower(&y.get_coefficients_ext_degree(ext_degree), ext_degree); let div = tower_div(&a, &b, ext_degree); Polynomial::new(tower_to_direct(&div, ext_degree)) } pub fn tower_to_direct(x: &[FieldElement], ext_degree: usize) -> Vec> where F: IsPrimeField + CurveParamsProvider, { assert_eq!(x.len(), ext_degree); let nr_a0 = &FieldElement::::from(F::get_curve_params().nr_a0); match ext_degree { 2 => x.to_vec(), 6 => vec![ &x[0] - nr_a0 * &x[1], &x[2] - nr_a0 * &x[3], &x[4] - nr_a0 * &x[5], x[1].clone(), x[3].clone(), x[5].clone(), ], 12 => vec![ &x[0] - nr_a0 * &x[1], &x[6] - nr_a0 * &x[7], &x[2] - nr_a0 * &x[3], &x[8] - nr_a0 * &x[9], &x[4] - nr_a0 * &x[5], &x[10] - nr_a0 * &x[11], x[1].clone(), x[7].clone(), x[3].clone(), x[9].clone(), x[5].clone(), x[11].clone(), ], _ => panic!("Unsupported extension degree"), } } pub fn direct_to_tower(x: &[FieldElement], ext_degree: usize) -> Vec> where F: IsPrimeField + CurveParamsProvider, { assert_eq!(x.len(), ext_degree); let nr_a0 = &FieldElement::::from(F::get_curve_params().nr_a0); match ext_degree { 2 => x.to_vec(), 6 => vec![ &x[0] + nr_a0 * &x[3], x[3].clone(), &x[1] + nr_a0 * &x[4], x[4].clone(), &x[2] + nr_a0 * &x[5], x[5].clone(), ], 12 => vec![ &x[0] + nr_a0 * &x[6], x[6].clone(), &x[2] + nr_a0 * &x[8], x[8].clone(), &x[4] + nr_a0 * &x[10], x[10].clone(), &x[1] + nr_a0 * &x[7], x[7].clone(), &x[3] + nr_a0 * &x[9], x[9].clone(), &x[5] + nr_a0 * &x[11], x[11].clone(), ], _ => panic!("Unsupported extension degree"), } } pub fn tower_mul( a: &[FieldElement], b: &[FieldElement], ext_degree: usize, ) -> Vec> where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { assert_eq!(a.len(), ext_degree); assert_eq!(b.len(), ext_degree); match ext_degree { 2 => { let a = to_e2(a.to_vec().try_into().unwrap()); let b = to_e2(b.to_vec().try_into().unwrap()); let c = a * b; from_e2(c).to_vec() } 6 => { let a = to_e6(a.to_vec().try_into().unwrap()); let b = to_e6(b.to_vec().try_into().unwrap()); let c = a * b; from_e6(c).to_vec() } 12 => { let a = to_e12(a.to_vec().try_into().unwrap()); let b = to_e12(b.to_vec().try_into().unwrap()); let c = a * b; from_e12(c).to_vec() } _ => panic!("Unsupported extension degree"), } } pub fn tower_div( a: &[FieldElement], b: &[FieldElement], ext_degree: usize, ) -> Vec> where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { assert_eq!(a.len(), ext_degree); assert_eq!(b.len(), ext_degree); match ext_degree { 2 => { let a = to_e2(a.to_vec().try_into().unwrap()); let b = to_e2(b.to_vec().try_into().unwrap()); let c = (a / b).unwrap(); from_e2(c).to_vec() } 6 => { let a = to_e6(a.to_vec().try_into().unwrap()); let b = to_e6(b.to_vec().try_into().unwrap()); let c = (a / b).unwrap(); from_e6(c).to_vec() } 12 => { let a = to_e12(a.to_vec().try_into().unwrap()); let b = to_e12(b.to_vec().try_into().unwrap()); let c = (a / b).unwrap(); from_e12(c).to_vec() } _ => panic!("Unsupported extension degree"), } } pub fn tower_inv(a: &[FieldElement], ext_degree: usize) -> Vec> where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { let mut one = vec![FieldElement::from(0); ext_degree]; one[0] = FieldElement::from(1); tower_div(&one, a, ext_degree) } pub fn to_e2(v: [FieldElement; 2]) -> FieldElement where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]>, { FieldElement::new(v) } pub fn to_e6(v: [FieldElement; 6]) -> FieldElement where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]>, { let [v0, v1, v2, v3, v4, v5] = v; FieldElement::new([to_e2([v0, v1]), to_e2([v2, v3]), to_e2([v4, v5])]) } pub fn to_e12(v: [FieldElement; 12]) -> FieldElement where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { let [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11] = v; FieldElement::new([ to_e6([v0, v1, v2, v3, v4, v5]), to_e6([v6, v7, v8, v9, v10, v11]), ]) } pub fn from_e2(v: FieldElement) -> [FieldElement; 2] where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]>, { let [v0, v1] = v.to_subfield_vec().try_into().unwrap(); [v0, v1] } pub fn from_e6(v: FieldElement) -> [FieldElement; 6] where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]>, { let [a1, a2, a3] = v.to_subfield_vec().try_into().unwrap(); let [v0, v1] = from_e2(a1); let [v2, v3] = from_e2(a2); let [v4, v5] = from_e2(a3); [v0, v1, v2, v3, v4, v5] } pub fn from_e12(v: FieldElement) -> [FieldElement; 12] where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, { let [a0, a1] = v.to_subfield_vec().try_into().unwrap(); let [v0, v1, v2, v3, v4, v5] = from_e6(a0); let [v6, v7, v8, v9, v10, v11] = from_e6(a1); [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11] } pub fn e2_conjugate(a: FieldElement) -> FieldElement where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let [x, y] = from_e2(a); to_e2([x, -y]) } #[cfg(test)] mod tests { use super::*; use crate::definitions::{BLS12381PrimeField, BN254PrimeField}; #[test] fn test_nondeterministic_extension_field_mul_divmod_1() { let ps = [ [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ], [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ], [ "0x1", "0x3049ed443e0ee79060270c9094ac6390a5c1ab3db65328a47174c6c33f6bd5f2", "0x0", "0xa279a60d390f263fa2b23afda6a2160c7af52ea6fdddb7ffe26ded0e216c821", "0x0", "0x0", "0x0", "0x146bccf3dc47e8eedf574326c5188ea8e4978a568116c9aa5b8517cdeb0e1f38", "0x0", "0x10b71d55b795eb0c1590286e48c412e3434b0def1afddfc8840541b6936825fd", "0x0", "0x0", ], [ "0x1", "0x10b80d23f4e55970de219c8bb6cc99af9ca48837a7da389ff6e02693c8912bf3", "0x0", "0x1999e3b5911b71ef05b218f5be987ba6f43afb6a702ffca89c7a6643b411046f", "0x0", "0x0", "0x0", "0x2a00794e593076aab0ec5e6283a9ed0ddbe6ef97af88861febd351722d50802a", "0x0", "0x22583e5a131ce5504fbb720b2081781441eeb10978efac409e27787d1fa359b6", "0x0", "0x0", ], ]; let q = [ "0xe894c747efef08ab122e832492446abf3359cf28786e81ab3a81a74fce2c75b", "0x0", "0x221a77eeae1aacc77e771d8440e698d3b8d2447bb8de2a046cf8c063f7523fb7", "0x0", "0x1d9393fe1dfd5bf8174a7b2086cdc6288de8ee5409946e58d5385d342633aa56", "0x0", "0x122377527927c40e63ddc4c9ef6a51a864d1e6575602045f81ddf7ae83afc4c3", ]; let r = [ "0x11d12be7502f97a642a86eb73802fe0fe4772283c9e66f3d535534c22390e0ca", "0x109dabf551c2a0d785f86365c9f7a4e2aae4c8e3f5bb96b72c3461402f80049e", "0x15e06e6b765f21da4c21d50705a9bf0f72ba0283f93e75a896235fa107d4ca4d", "0x23c17e1664ac6452ffdd3ca599029d07bbea4e54e00dd8289aa145149627cc90", "0x751d37ad50cc00d6245f08ca81ce16f9a3714c3efe87c95ae8e132234b5dd07", "0x0", "0x1535e3c0e51be5f14093e8501425031896dfb26ec8759e3409e44e94d81e17cf", "0xe07f7cf5446bf6fd7f35bd2c741235928fd0f5cc82d853d0b37dd293fe1a21b", "0x2eae2d9b2332fb1f1c3617826ac6ede574d04ed01692a36b9743fc604b3f3bf", "0x2ab0d3ce9813032acfb54c2e7c43299edb854672b7bc17be60c2e1cda8e826c", "0x1f316d8807400efe60a15b7e5311a9031439eb344c0d84fb80044f8786d59de4", "0x0", ]; let ps = ps .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xq = q .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xr = r .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let (q, r) = nondeterministic_extension_field_mul_divmod(12, ps); let q = q.coefficients; let r = r.coefficients; assert_eq!(q, xq); assert_eq!(r, xr); } #[test] fn test_nondeterministic_extension_field_mul_divmod_2() { let ps = [ [ "0x1d7a9ffbbe137d697794dbccbd7925ea98507cf8d4445d3e89123811ede12825", "0x1f45aa2ee73f15e275e5c1fc0ff08be0981a61d8e7642301653a6307c7467811", "0x2446d99f276e4c8bc63d81e8d0c1e37c901a5a569865533968e39b5083fc576e", "0x223bd50b771fcaa905131a5f04c3c634c9df344731b5aada49be919aaa447cc7", "0x24cfef2958a7c9c4d7ddfacdd59750105dcc37f6aefbf4a9ce706bc36252c47", "0x3a974db52b274684955cb370b0ac66e3e295ea6e9789fb7259c294210f7720e", "0x160b7346ec9fdd9841feb355a44845dc30c2a9ae3fb8266ad697b531de5e2fb6", "0xe46af84e1cbba805f204fa5ce1c9a99c79799110a56b5d534495a358f9c739f", "0x1f2b5709d0d7c9499b9524e9708ac412d3fa05fea9b51192113e131bd5572a21", "0x8a75eef583ffc3b0f690cd9eab121b1f329194c1052a86d50224b92838c5d76", "0xef3a64570d17038de7ec74175c125ac7e8780509764f07572ce9593878da9fb", "0x2a6290607745b58a7b87bc78053320664e06d12b35825f15893ad52a39f54331", ], [ "0x14156ca1853095df27f3cb7c50eca75e794d2f14195c16df4a0f8f9dcb48bee9", "0xdc2a20a6107d4c49fed6b2018946bcc2a8dad06f01d099a6df0a4a55ed21b59", "0x14260c5afb0b1148ed80f8339cf9e06ff04257cb6c1817c4efa721fc98f69503", "0xafe8a09df07bf3dffefe512eb9448ef436dd090f98323135baab8ae3c766c60", "0x114692950f53d4f707bb02cc2b5dc98aff5936811707d6579371dae20368253c", "0x2dd3fca72591963149646f1e106dc0ee917551f5a9da397fe12d4a3939ce650c", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ], ]; let q = [ "0x13e8e196ed7970229c16369f6f62a54fe9848ec0abbb56e77355358805db92a6", "0x29aa20be8afc3104b3211fb1c2636e3291bca41e1276bdbbb485917fae34c150", "0xcbdf387c0036815f944eeedb8a3ed8babb406326444cbed0df3e47fc7a3f440", "0xcc614e3d877550dc9bb19f8dfdc513f2f8fed01d3a180a2a9e475c9a29f6d96", "0x1a6e474f0a5394b39bd15f2390e0cfa64391cb4ffc5d435a63028ac3c744d064", "0x8fc0b38f1129ab34ebd5a5888f0711adecaecc7aa5312cc62508d51da03aa1e", "0xff9b26cf44e068601c663a62662f0ef698166a3410d4f36a68b2e46800daa6e", "0xf4ec161da901a5ab3f6088ede93acdbf15f0c18b653b9f7146d132c6d4111c5", "0x1843faa07a91bed2c949f1b3f126e0ae88d429bf7d37b5e00696b22be53ac607", "0x1c151df931008732415af45f4616affed9e0e64976e66cc5e2e57c799ddfa646", "0x1526c80d7045ccb0ae04a7cf1de7a2519ad52f885c7b9acb7bed0d027459433", ]; let r = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let ps = ps .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xq = q .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xr = r .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let (q, r) = nondeterministic_extension_field_mul_divmod(12, ps); let q = q.coefficients; let r = r.coefficients; assert_eq!(q, xq); assert_eq!(r, xr); } #[test] fn test_nondeterministic_extension_field_mul_divmod_3() { let ps = [ ["0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0"], ["0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0"], ["0x183a80ffaffb035552f419948ba0d8b0148bb90e6bcbb072eece2a095bc3205571aa45062fb615d5204db9b0c13f16e4", "0x0", "0x141ce6d849b3b3ffd366962219920de592e0ea7888507ff651543f3d3a8c57b5778f9afcad1c00079fa2fc01d02a31de", "0x1", "0x0", "0x0", "0x12b7ea026b36040c682213ecc6663b4f916612568d3ceaa4876f9acffd4c8fb349a27daa5d44ff45bb92b5007dd00a56", "0x0", "0xead53480ba83b742644a3d8bfd432993007ed23c1a85090c6434e1ddd4dc8f16f8f6673fda2e538f5e9e9599b6062bc", "0x0", "0x0", "0x0"], ["0x9cbaaa39d75e767a38004c5e4e834cda92fe4fff0759cdfb078c61cff1349b3342fb6a19dc7ce19412c60791e787332", "0x0", "0x16422cfd0179e176be2c6e27226f61c162e6b3a7051f9e20ca33a1c7e99bd8cd5877aff6a82f042819707e2978027054", "0x1", "0x0", "0x0", "0x12138c3d7561ca85c9104207590388d773edbd1c46ecd9a2c1361c65ba39f487ff39a9d5edbbd942ee1bd5aae5fba357", "0x0", "0x709ac70c47538c5c9b0049aed2d39ed130b9053cd39a2c8534dfa6cb7ae9a6e13d78c0d5c7382ae146e085e91eeb43c", "0x0", "0x0", "0x0"], ["0x9f80115619172e4eaaf3a62b7d000cc462cff591e011ff8c39ec0595d8b263320711ed10ee74568947c52ac80f129bc", "0x0", "0x31679196cf9cc8a93705f2bb6cbcbb0e7b0196b962472706b416552474f667dd33b2d50a9800ac99110e7750e1d1618", "0x1", "0x0", "0x0", "0x4569b6e40372c16710ab2e2f85b80033cfab50f70f991c76de84083a53f47d14e26fa59b9a8fc74f8b95bcefb1f92fb", "0x0", "0x11efd369477790f94456f4fc5baea8c480249c8f56623b31e444435bd1e8b39e757ca81b8d19b958d6b425a17c15ec7f", "0x0", "0x0", "0x0"], ["0x142105c43e7e33dbcc983f7b693970ae4ea601a5c627832343932cf6f182d6ef712a0d4b0cfbfb92da1e505c39cf5bc0", "0x0", "0x83e650c23da50b57d95f2ef421a27900ff6e0f98249dd136de37c6c48fa04f830455843af17f7b00406d3ee2534e65d", "0x1", "0x0", "0x0", "0x15ad49314f1e2bbf517f7d37bb828abdedefb77d9e7762477bac0436451e74e9131399b84307d62da5495a0f3708b9cb", "0x0", "0x195ed72d7f572bb7dc0a78b45f824d75e155eb0dc7430f1544193109d75e4dbf5167d465a21b346c1ece84d7938e7107", "0x0", "0x0", "0x0"], ]; let q = ["0x15b1a92444c003fd30d2759337ee1d2b521d89eb3e8d5f9c89def701a70b9e590d409ee54018189157fb5b83fbc6e281", "0x3b383b5cd40d3b067def58412145c9dabdd2b59b7cd1cf07f832e97d05219ca794c099ba76477110a811e0a886fb833", "0xadbf541db6df55a263938da2e0ae43b6c9217f748fc8d2e668133cc88eec729e76b65fc361a4b58266ae0c46b5d3b7e", "0x19da2ede02f3dc475518f4df24b7478c26ef3e18edce534e307f24161b09dd2f287fe8a27c63bd9f145b2a3f782eb0d1", "0x13f314681f4f7af49a1de550de5c171c36fa385ab2c0ecdbc73aee60cf8374ab43795b72d38f3e3bfe70505932163789", "0x12426b3d3990b9b961f1686e6274f1b97fbd3646512c80a0e5ee05c2ff5193709e760abbb6c676531078a768bedd7124", "0x10c8f0fec5ead5f4d5d7bb706d5e3da8f609a48a4da086ee82bc3b9d27ef5e52af16c8b309cf88c0d433985fc56b1e42", "0x5cb67da1dd940f40ecffb3f4683b6f6253fc005fbd345d5fa74ed9b0c33de90b875699040e7a4298059eb58baced6bf", "0xecffb82dcfdf5bdf438503c919684f0cfe228611387f6b404c7fdd0d0a4c1f2615e65450f4cc416f27038f083bc5e9c", "0x44b8912d0d9311ae5eb2205969a85d426b3d6c5d58cd3db35ffe118abb24510c503b91a0c476274832acc12327506d8", "0x151de551fd53045ea8127ed3887126378157871289970127638dcf0214f26b2c946216c5e4418a0b5b8e19e14984714b", "0x1b9bcc051f541e88e9377684505f5ded93b7d350b427ec2ba79970220ad2f6f781be5559762b1789038fe7c8f1d8fd7", "0x539e9ef4cfe0c1c409c6b724f8420997dcd0d0e0b8c12d44a883d8188fc1f8802753128bcb3533c154c449e4986e2d7", "0x10e1aafbcaeb68abb0fa69263c5a78ffea85c3fcee39a9ea478f3e7953407c81d32bb8808bde55c8c2b4fd37a4aeea73", "0x17b51d4ffaf4e7cb1b66757d4658959ee4492146684bac3062740594c753d58362c79d57ba6a46323404ea6219f70a51", "0xc0084a4d0393cd3768c8733ac77addd268dd86fcd3de379a08aab70a1a96c8bad202694ab0cc9e9dd401bf576ccc0ac", "0x14fdce739f217fefb6716848b5618143fdfb07de6c348ce5d0dcaaf3d3dfb07f8bc0883376eb80ccdc7db9ca23acee1c", "0x0", "0x2b05f7876fe128e401cd7f696383c57f638f58d1dd09fdcbd0d28ff4561e9e3f3a90da3b62783914f74a2bce9c76cfc", "0x0", "0x186ebefaece7849868ec8c230d6c288155e9f9376c0e6db3e75dbd02d80456323a4bfd6ea33441ab580942a3fe2f9364"]; let r = ["0xc71fb5b76cf57e5c7c9dbbd201062289f97dedce8bbb72d15abaec86c40039d3b4f3fccb7338ff3e7701b7f6619769b", "0x129a0a7e9efe3f397b5dbcae1f22f39c0cbcf4d183ead8de682a7571560cc28f2c13ecc7628b11dda4fcc3eaef203a45", "0x162ca20e57a4ad07f919b85c9975acd11d5f0cddd22192ebc465e5a89a0546be2ec98581fcda54c808aa8790189addd6", "0x10a05ef6bc41b1ac2ba68a585a4c7016589ffad9c5412bf00fd0f50f8ac9ea3d9a7db639e62eae3ca960447fb588a60b", "0x16dbc5bd5769b32d94959f3a71085f5adc66454928e158caeecda06706afd32cea844001820431c1f3534760c01c3ce5", "0x199988fcc386f48448a34d747599bd68a9bb4993cc0e6d2434e9182475096fe323352ae743be4cec47278fbbb8d52f52", "0x189109c92dac219f6b362d169e4ca995bbd0536c8727610f0f361f3490e9d41a94c69d397c1401b31b5a973bc393f3b1", "0x19ea64dde64bbb01d1072ca0532cbe26f8227deaf22155b2ba4bacf79ec45d43bbecca1bb35c6efdd163d6d7ff862979", "0xd9b819680b2cfa830393d2a883cbf07d691020e2a01580c62c9bb1869a1c40317ab6b0df57ff873f2b4bc93d71985e5", "0x704a7bc9193e53c9dde39b3a0a34d0e76345261a4caa612bb3ee39b3715a0d649760f83a32b24cc4b37fe549e80afde", "0x117957ce838607a66a58785c7af8af5a2d3a1832a559f19b20af84c9a5e968cabea23dd6815968b93234b9b34f8108e1", "0xae22d05bd7cd226ba438387b13606f1ad88319c787ccdcec28ab4de6e9bd5fd1ede497ebb746c3313cd6655b961689d"]; let ps = ps .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xq = q .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xr = r .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let (q, r) = nondeterministic_extension_field_mul_divmod(12, ps); let q = q.coefficients; let r = r.coefficients; assert_eq!(q, xq); assert_eq!(r, xr); } #[test] fn nondeterministic_extension_field_div_1() { let x = [ "0x2f6a437ba87bf892de86475ec2155dd6bf2acf7ddb7ad74c028c1a0bd146a17d", "0xc2fc4dd8bf1d0a89f2a486ff97fe6ba7ef3267310f51196b7463fd620b3b35a", ]; let y = [ "0x2590bd4bb718dbd69556e3011b96811fc7a3ced21887a6f699cd9802cdf4fb54", "0x120d13a0b0bfe0ebd93d335ad218672b78966266e1671de6ab59b5b9a2452eb6", ]; let z = [ "0x237db2935c4432bc98005e68cacde68a193b54e64d347301094edcbfa224d3d5", "0x124077e14a7d826a707c3ec1809ae9bafafa05dd6b4ba735fba44e801d415637", ]; let x = Polynomial::new( x.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let y = Polynomial::new( y.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xz = z .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; let z = nondeterministic_extension_field_div::< BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(x, y, 2); let z = z.coefficients; assert_eq!(z, xz); } #[test] fn nondeterministic_extension_field_div_2() { let x = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let y = [ "0x14156ca1853095df27f3cb7c50eca75e794d2f14195c16df4a0f8f9dcb48bee9", "0xdc2a20a6107d4c49fed6b2018946bcc2a8dad06f01d099a6df0a4a55ed21b59", "0x14260c5afb0b1148ed80f8339cf9e06ff04257cb6c1817c4efa721fc98f69503", "0xafe8a09df07bf3dffefe512eb9448ef436dd090f98323135baab8ae3c766c60", "0x114692950f53d4f707bb02cc2b5dc98aff5936811707d6579371dae20368253c", "0x2dd3fca72591963149646f1e106dc0ee917551f5a9da397fe12d4a3939ce650c", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ]; let z = [ "0x1d7a9ffbbe137d697794dbccbd7925ea98507cf8d4445d3e89123811ede12825", "0x1f45aa2ee73f15e275e5c1fc0ff08be0981a61d8e7642301653a6307c7467811", "0x2446d99f276e4c8bc63d81e8d0c1e37c901a5a569865533968e39b5083fc576e", "0x223bd50b771fcaa905131a5f04c3c634c9df344731b5aada49be919aaa447cc7", "0x24cfef2958a7c9c4d7ddfacdd59750105dcc37f6aefbf4a9ce706bc36252c47", "0x3a974db52b274684955cb370b0ac66e3e295ea6e9789fb7259c294210f7720e", "0x160b7346ec9fdd9841feb355a44845dc30c2a9ae3fb8266ad697b531de5e2fb6", "0xe46af84e1cbba805f204fa5ce1c9a99c79799110a56b5d534495a358f9c739f", "0x1f2b5709d0d7c9499b9524e9708ac412d3fa05fea9b51192113e131bd5572a21", "0x8a75eef583ffc3b0f690cd9eab121b1f329194c1052a86d50224b92838c5d76", "0xef3a64570d17038de7ec74175c125ac7e8780509764f07572ce9593878da9fb", "0x2a6290607745b58a7b87bc78053320664e06d12b35825f15893ad52a39f54331", ]; let x = Polynomial::new( x.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let y = Polynomial::new( y.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xz = z .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; let z = nondeterministic_extension_field_div::< BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(x, y, 12); let z = z.coefficients; assert_eq!(z, xz); } #[test] fn nondeterministic_extension_field_div_3() { let x = ["0xcebfbdf0b4abf3a47cd17cf6b889effc2af960568f453fe4b87e955f8a854ba4df986c2aa1974e16b32c53379d3e81f", "0x8acd6cd869315ed3703b767ffdbb324a2e3f13b6352bdcb503496ebf38b120e3b623f3a913c43356e4431c1e9ca9332"]; let y = ["0x19cbaa4ee4fadc2319939b8db45c6a355bfb3755197ba74eda8534d2a2c1a2592475939877594513c326a90c11705002", "0xc0d89405d4e69986559a56057851733967c50fd0b4ec75e4ce92556ae5d33567e6e1a4eb9d83b4355520ebfe0bef37c"]; let z = ["0x15a76ee3d8d1c3451005d56067cd27cf7598a85f81c23cd926ad0ec05ad6440f1df034cf36701a5831c9fb39250e2ea9", "0x16d96e785c797fb5d6afcb1400d7656829a6a71c42deb7ddce5cd2ccda4704dc0e4b92b69009367bbf6e6aa19488df66"]; let x = Polynomial::new( x.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let y = Polynomial::new( y.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xz = z .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree6ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; let z = nondeterministic_extension_field_div::< BLS12381PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(x, y, 2); let z = z.coefficients; assert_eq!(z, xz); } } ================================================ FILE: tools/garaga_rs/src/algebra/g1g2pair.rs ================================================ use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::definitions::{CurveParamsProvider, FieldElement}; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; #[derive(Debug, Clone)] pub struct G1G2Pair where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]>, { pub g1: G1Point, pub g2: G2Point, } impl G1G2Pair where F: IsPrimeField + IsSubFieldOf + CurveParamsProvider, E2: IsField; 2]>, { pub fn new(g1: G1Point, g2: G2Point) -> Self { Self { g1, g2 } } pub fn flatten(&self) -> Vec> { let mut elements = vec![]; let (x, y) = self.g1.get_coords(); elements.push(x[0].clone()); elements.push(y[0].clone()); let (x, y) = self.g2.get_coords(); elements.push(x[0].clone()); elements.push(x[1].clone()); elements.push(y[0].clone()); elements.push(y[1].clone()); elements } } ================================================ FILE: tools/garaga_rs/src/algebra/g1point.rs ================================================ use crate::definitions::{CurveParamsProvider, FieldElement}; use lambdaworks_math::field::traits::IsPrimeField; use num_bigint::{BigInt, BigUint, Sign}; #[derive(Debug, Clone)] pub struct G1Point { pub x: FieldElement, pub y: FieldElement, pub iso_point: bool, } impl G1Point { pub fn is_infinity(&self) -> bool { let zero = FieldElement::zero(); self.x.eq(&zero) && self.y.eq(&zero) } pub fn representative(&self) -> String { format!( "({:?}, {:?})", self.x.representative().to_string(), self.y.representative().to_string() ) } } impl> G1Point { pub fn get_coords(&self) -> ([FieldElement; 1], [FieldElement; 1]) { ([self.x.clone()], [self.y.clone()]) } pub fn new(x: FieldElement, y: FieldElement, iso_point: bool) -> Result { let point = Self { x, y, iso_point }; if !point.is_infinity() && !point.is_on_curve() { return Err(format!( "Point ({:?}, {:?}) is not on the curve", point.x.representative().to_string(), point.y.representative().to_string(), )); } Ok(point) } pub fn new_unchecked(x: FieldElement, y: FieldElement, iso_point: bool) -> Self { Self { x, y, iso_point } } pub fn add(&self, other: &G1Point) -> G1Point { assert!(self.iso_point == other.iso_point); if self.is_infinity() { return other.clone(); } if other.is_infinity() { return self.clone(); } if self.x == other.x && self.y != other.y { return Self::new_unchecked( FieldElement::::zero(), FieldElement::::zero(), self.iso_point, ); } let lambda = if self.eq(other) { let curve_params = F::get_curve_params(); let alpha = if self.iso_point { let swu_params = curve_params.swu_params.unwrap(); swu_params.a } else { curve_params.a }; let numerator = FieldElement::::from(3_u64) * &self.x.square() + alpha; let denominator = FieldElement::::from(2_u64) * &self.y; numerator / denominator } else { (&other.y - &self.y) / (&other.x - &self.x) } .unwrap(); let x3 = &lambda.square() - &self.x - &other.x; let y3 = &lambda * &(self.x.clone() - &x3) - &self.y; Self::new_unchecked(x3, y3, self.iso_point) } pub fn neg(&self) -> Self { if self.is_infinity() { self.clone() } else { Self::new_unchecked(self.x.clone(), -self.y.clone(), self.iso_point) } } pub fn scalar_mul_neg_3(&self) -> G1Point { let double_point = self.add(self); let triple_point = self.add(&double_point); triple_point.neg() } pub fn scalar_mul(&self, scalar: BigInt) -> G1Point { if self.is_infinity() { return self.clone(); } if scalar == BigInt::ZERO { return Self::new_unchecked( FieldElement::::zero(), FieldElement::::zero(), self.iso_point, ); } let mut result = Self::new_unchecked( FieldElement::::zero(), FieldElement::::zero(), self.iso_point, ); let mut base = self.clone(); //println!("scalar mul scalar: {:?}", scalar); let sign = scalar.sign(); let abs_scalar = match sign { Sign::Plus => scalar, Sign::Minus => -scalar, _ => scalar, }; let mut scalar: BigUint = abs_scalar.to_biguint().unwrap(); while scalar > BigUint::ZERO { if &scalar & BigUint::from(1_u64) != BigUint::ZERO { result = result.add(&base); } base = base.add(&base); scalar >>= 1; } if sign == num_bigint::Sign::Minus { result = result.neg(); } result } pub fn is_on_curve(&self) -> bool { if self.is_infinity() { return true; } let curve_params = F::get_curve_params(); let (a, b) = if self.iso_point { let swu_params = curve_params.swu_params.unwrap(); (swu_params.a, swu_params.b) } else { (curve_params.a, curve_params.b) }; self.y.square() == self.x.clone().square() * self.x.clone() + a * self.x.clone() + b } pub fn print(&self) { println!( "G1Point: x = {:?}, y = {:?}", self.x.representative().to_string(), self.y.representative().to_string() ); } pub fn generator() -> Self { let curve_params = F::get_curve_params(); let generator_x = curve_params.g_x; let generator_y = curve_params.g_y; G1Point::new(generator_x, generator_y, false).unwrap() } pub fn msm(points: &[Self], scalars: &[BigUint]) -> Self { assert!(!points.is_empty()); assert_eq!(points.len(), scalars.len()); let mut result = points[0].scalar_mul(scalars[0].clone().into()); for i in 1..points.len() { result = result.add(&points[i].scalar_mul(scalars[i].clone().into())); } result } pub fn new_infinity() -> Self { G1Point::new_unchecked(FieldElement::::zero(), FieldElement::::zero(), false) } } impl PartialEq for G1Point { fn eq(&self, other: &Self) -> bool { self.x == other.x && self.y == other.y } } ================================================ FILE: tools/garaga_rs/src/algebra/g2point.rs ================================================ use crate::algebra::extf_mul::{from_e2, to_e2}; use crate::definitions::{CurveParamsProvider, FieldElement}; use crate::io::biguint_to_u256; use lambdaworks_math::elliptic_curve::short_weierstrass::traits::IsShortWeierstrass; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; use num_bigint::{BigInt, BigUint, Sign}; #[derive(Debug, Clone)] pub struct G2Point where F: IsPrimeField + IsSubFieldOf, E2: IsField; 2]>, { pub x: FieldElement, pub y: FieldElement, } impl G2Point where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { pub fn get_coords(&self) -> ([FieldElement; 2], [FieldElement; 2]) { (from_e2(self.x.clone()), from_e2(self.y.clone())) } pub fn representative(&self) -> String { let ([x0, x1], [y0, y1]) = self.get_coords(); format!( "G2Point: X = ({:?}, {:?}), Y = ({:?}, {:?})", x0.representative().to_string(), x1.representative().to_string(), y0.representative().to_string(), y1.representative().to_string() ) } pub fn new(x: [FieldElement; 2], y: [FieldElement; 2]) -> Result { let x = to_e2(x); let y = to_e2(y); let point = Self { x, y }; if !point.is_infinity() && !point.is_on_curve() { let x = from_e2(point.x); let y = from_e2(point.y); return Err(format!( "Point (({:?}, {:?}), ({:?}, {:?})) is not on the curve", x[0].representative().to_string(), x[1].representative().to_string(), y[0].representative().to_string(), y[1].representative().to_string(), )); } Ok(point) } pub fn new_unchecked(x: FieldElement, y: FieldElement) -> Self { Self { x, y } } pub fn is_infinity(&self) -> bool { let zero = to_e2([FieldElement::zero(), FieldElement::zero()]); self.x.eq(&zero) && self.y.eq(&zero) } pub fn neg(&self) -> Self { if self.is_infinity() { self.clone() } else { G2Point::new_unchecked(self.x.clone(), -self.y.clone()) } } pub fn is_on_curve(&self) -> bool { if self.is_infinity() { return true; } let curve_params = F::get_curve_params(); let a = curve_params.a; let b = to_e2([curve_params.b20, curve_params.b21]); self.y.square() == self.x.clone().square() * self.x.clone() + a * self.x.clone() + b } pub fn generator() -> Self { let curve_params = F::get_curve_params(); let generator_x = curve_params .g2_x .expect("G2 generator coordinates not defined for this curve"); let generator_y = curve_params .g2_y .expect("G2 generator coordinates not defined for this curve"); G2Point::new(generator_x, generator_y).unwrap() } pub fn compute_doubling_slope(a: &Self) -> FieldElement { let [x, y] = &from_e2(a.x.clone()); let num = to_e2([ (x + y) * (x - y) * FieldElement::::from(3), x * y * FieldElement::::from(6), ]); (num / (&a.y + &a.y)).unwrap() } pub fn compute_adding_slope(a: &Self, b: &Self) -> FieldElement { ((&a.y - &b.y) / (&a.x - &b.x)).unwrap() } pub fn new_infinity() -> Self { let zero = to_e2([FieldElement::zero(), FieldElement::zero()]); G2Point::new_unchecked(zero.clone(), zero) } pub fn add(&self, other: &G2Point) -> G2Point where C: IsShortWeierstrass, { g2_point_add::(self.clone(), other.clone()) } pub fn scalar_mul(&self, scalar: BigInt) -> G2Point where C: IsShortWeierstrass, { if self.is_infinity() { return self.clone(); } if scalar == BigInt::ZERO { return Self::new_infinity(); } let base = self.clone(); let sign = scalar.sign(); let abs_scalar = match sign { Sign::Plus => scalar, Sign::Minus => -scalar, _ => scalar, }; let scalar: BigUint = abs_scalar.to_biguint().unwrap(); let mut result = g2_point_scalar_mul::(base, scalar); if sign == num_bigint::Sign::Minus { result = result.neg(); } result } } fn g2_point_add(a: G2Point, b: G2Point) -> G2Point where F: IsPrimeField + IsSubFieldOf + CurveParamsProvider, E2: IsField; 2]>, C: IsShortWeierstrass, { use lambdaworks_math::cyclic_group::IsGroup; use lambdaworks_math::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; use lambdaworks_math::elliptic_curve::traits::FromAffine; let a = ShortWeierstrassProjectivePoint::::from_affine(a.x, a.y).unwrap(); let b = ShortWeierstrassProjectivePoint::::from_affine(b.x, b.y).unwrap(); let c = a.operate_with(&b).to_affine(); if c.z() == &FieldElement::zero() { G2Point::new_infinity() } else { let x = c.x().value().clone(); let y = c.y().value().clone(); G2Point::new(x, y).unwrap() } } fn g2_point_scalar_mul(a: G2Point, k: BigUint) -> G2Point where F: IsPrimeField + IsSubFieldOf + CurveParamsProvider, E2: IsField; 2]>, C: IsShortWeierstrass, { use lambdaworks_math::cyclic_group::IsGroup; use lambdaworks_math::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; use lambdaworks_math::elliptic_curve::traits::FromAffine; let a = ShortWeierstrassProjectivePoint::::from_affine(a.x, a.y).unwrap(); let c = a.operate_with_self(biguint_to_u256(&k)).to_affine(); if c.z() == &FieldElement::zero() { G2Point::new_infinity() } else { let x = c.x().value().clone(); let y = c.y().value().clone(); G2Point::new(x, y).unwrap() } } ================================================ FILE: tools/garaga_rs/src/algebra/polynomial.rs ================================================ use crate::definitions::FieldElement; use lambdaworks_math::field::traits::IsPrimeField; #[derive(Debug, Clone)] pub struct Polynomial { pub coefficients: Vec>, // Cache the degree to avoid recomputing it degree: isize, } impl Polynomial { pub fn get_coefficients_ext_degree(&self, ext_degree: usize) -> Vec> { assert!(self.coefficients.len() <= ext_degree); let mut coefficients = self.coefficients.clone(); coefficients.resize(ext_degree, FieldElement::zero()); coefficients } pub fn new(mut coefficients: Vec>) -> Self { // Find the position of the last non-zero coefficient let last_non_zero = coefficients .iter() .rposition(|x| *x != FieldElement::zero()); // Truncate the vector to remove trailing zeros let degree = if let Some(pos) = last_non_zero { coefficients.truncate(pos + 1); pos as isize } else { // All coefficients are zero, return a zero polynomial coefficients = vec![FieldElement::zero()]; -1 }; Self { coefficients, degree, } } pub fn print_as_sage_poly(&self) -> String { let var_name = 'x'; if self.degree == -1 { return String::new(); } let mut string = String::new(); let zero = FieldElement::::zero(); for (i, coeff) in self.coefficients.iter().rev().enumerate() { if *coeff == zero { continue; } let coeff_str = coeff.representative().to_string(); if i == self.coefficients.len() - 1 { string.push_str(&coeff_str); } else if i == self.coefficients.len() - 2 { string.push_str(&format!("{}*{} + ", coeff_str, var_name)); } else { string.push_str(&format!( "{}*{}^{} + ", coeff_str, var_name, self.coefficients.len() - 1 - i )); } } string } #[inline] pub fn degree(&self) -> isize { // Use cached degree value self.degree } pub fn evaluate(&self, x: &FieldElement) -> FieldElement { // Use Horner's method for polynomial evaluation if self.degree == -1 { return FieldElement::zero(); } let mut result = self.coefficients[self.degree as usize].clone(); for i in (0..self.degree as usize).rev() { result = &result * x + &self.coefficients[i]; } result } pub fn leading_coefficient(&self) -> FieldElement { if self.degree == -1 { return FieldElement::zero(); } self.coefficients[self.degree as usize].clone() } pub fn zero() -> Self { Self { coefficients: vec![FieldElement::::zero()], degree: -1, } } pub fn one() -> Self { Self { coefficients: vec![FieldElement::::one()], degree: 0, } } pub fn mul_with_ref(&self, other: &Polynomial) -> Polynomial { if self.degree == -1 || other.degree == -1 { return Polynomial::zero(); } let result_len = (self.degree + other.degree + 1) as usize; let mut result_coeffs = vec![FieldElement::::zero(); result_len]; for (i, self_coeff) in self.coefficients.iter().enumerate() { for (j, other_coeff) in other.coefficients.iter().enumerate() { result_coeffs[i + j] += self_coeff * other_coeff; } } // We already know the degree, so construct directly let degree = self.degree + other.degree; Polynomial { coefficients: result_coeffs, degree, } } pub fn divmod(self, denominator: &Self) -> (Self, Self) { let den_deg = denominator.degree; if den_deg == -1 { panic!("Division by zero polynomial"); } let num_deg = self.degree; let mut remainder = self.clone(); if num_deg < den_deg { return (Polynomial::zero(), self); } let mut quotient_coeffs = vec![FieldElement::::zero(); (num_deg - den_deg + 1) as usize]; let denom_lead_inv = denominator.leading_coefficient().inv().unwrap(); let mut rem_deg = num_deg; while rem_deg >= den_deg { let shift = rem_deg - den_deg; let coefficient = &remainder.coefficients[rem_deg as usize] * &denom_lead_inv; quotient_coeffs[shift as usize] = coefficient.clone(); let subtractee = denominator .scale_by_coeff(&coefficient) .shift(shift as usize); remainder = remainder - subtractee; rem_deg = remainder.degree; } let degree = num_deg - den_deg; let quotient = Polynomial { coefficients: quotient_coeffs, degree, }; (quotient, remainder) } pub fn shift(&self, shift: usize) -> Self { if self.degree == -1 { return Polynomial::zero(); } let mut shifted_coeffs = vec![FieldElement::::zero(); shift]; shifted_coeffs.extend(self.coefficients.clone()); Self { coefficients: shifted_coeffs, degree: self.degree + shift as isize, } } pub fn divfloor(&self, denominator: &Self) -> Self { let (quotient, _remainder) = self.clone().divmod(denominator); quotient } pub fn differentiate(&self) -> Self { if self.degree <= 0 { return Polynomial::zero(); } let new_deg = self.degree - 1; let mut new_coeffs = vec![FieldElement::::zero(); new_deg as usize + 1]; for i in 1..=self.degree as usize { let u_64 = i as u64; let degree = &FieldElement::::from(u_64); new_coeffs[i - 1] = &self.coefficients[i] * degree; } Polynomial { coefficients: new_coeffs, degree: new_deg, } } pub fn xgcd(&self, other: &Polynomial) -> (Polynomial, Polynomial, Polynomial) { let mut old_r = self.clone(); let mut r = other.clone(); let mut old_s = Polynomial::one(); let mut s = Polynomial::zero(); let mut old_t = Polynomial::zero(); let mut t = Polynomial::one(); while r.degree != -1 { let quotient = old_r.clone().div_with_ref(&r); let new_r = old_r - quotient.clone().mul_with_ref(&r); old_r = r; r = new_r; let new_s = old_s - quotient.clone().mul_with_ref(&s); old_s = s; s = new_s; let new_t = old_t - quotient.clone().mul_with_ref(&t); old_t = t; t = new_t; } let lcinv = old_r.leading_coefficient().inv().unwrap(); ( old_s.scale_by_coeff(&lcinv), old_t.scale_by_coeff(&lcinv), old_r.scale_by_coeff(&lcinv), ) } pub fn div_with_ref(self, dividend: &Self) -> Self { let (quotient, _remainder) = self.divmod(dividend); quotient } pub fn scale_by_coeff(&self, coeff: &FieldElement) -> Polynomial { if *coeff == FieldElement::zero() { return Polynomial::zero(); } if self.degree == -1 { return Polynomial::zero(); } let scaled_coeffs = self.coefficients.iter().map(|c| c * coeff).collect(); // Degree remains the same when scaling by non-zero coefficient Polynomial { coefficients: scaled_coeffs, degree: self.degree, } } } pub fn pad_with_zero_coefficients_to_length(pa: &mut Polynomial, n: usize) { if pa.coefficients.len() < n { pa.coefficients.resize(n, FieldElement::zero()); // Degree doesn't change when adding trailing zeros } } pub fn pad_with_zero_coefficients( pa: &Polynomial, pb: &Polynomial, ) -> (Polynomial, Polynomial) { let mut pa = pa.clone(); let mut pb = pb.clone(); if pa.coefficients.len() > pb.coefficients.len() { pad_with_zero_coefficients_to_length(&mut pb, pa.coefficients.len()); } else { pad_with_zero_coefficients_to_length(&mut pa, pb.coefficients.len()); } (pa, pb) } impl std::ops::Add<&Polynomial> for &Polynomial { type Output = Polynomial; fn add(self, a_polynomial: &Polynomial) -> Self::Output { let (pa, pb) = pad_with_zero_coefficients(self, a_polynomial); // Calculate new coefficients let mut new_coefficients = Vec::with_capacity(pa.coefficients.len()); for (x, y) in pa.coefficients.iter().zip(pb.coefficients.iter()) { new_coefficients.push(x + y); } // Find max degree - this is a potential optimization spot if we find this is slow let degree = if self.degree > a_polynomial.degree { self.degree } else if self.degree < a_polynomial.degree { a_polynomial.degree } else { // If degrees are equal, we need to check if leading terms cancel out let mut max_deg = self.degree; // Find the actual degree by scanning backward for first non-zero term while max_deg >= 0 && new_coefficients[max_deg as usize] == FieldElement::::zero() { max_deg -= 1; } max_deg }; // If degree is -1, ensure we have a single zero if degree == -1 { Polynomial::zero() } else { // Trim the vector to actual degree + 1 new_coefficients.truncate(degree as usize + 1); Polynomial { coefficients: new_coefficients, degree, } } } } impl std::ops::Add for Polynomial { type Output = Polynomial; fn add(self, other: Polynomial) -> Polynomial { // Fast path for zeros if self.degree == -1 { return other; } if other.degree == -1 { return self; } let (mut longer, shorter, longer_deg) = if self.degree >= other.degree { (self.coefficients, other.coefficients, self.degree) } else { (other.coefficients, self.coefficients, other.degree) }; // Add shorter polynomial terms to longer one for (i, coeff) in shorter.into_iter().enumerate() { longer[i] += coeff; } // Check if the degree has changed due to cancellations let mut actual_deg = longer_deg; while actual_deg >= 0 && longer[actual_deg as usize] == FieldElement::::zero() { actual_deg -= 1; } if actual_deg == -1 { Polynomial::zero() } else { longer.truncate(actual_deg as usize + 1); Polynomial { coefficients: longer, degree: actual_deg, } } } } impl std::ops::Neg for &Polynomial { type Output = Polynomial; fn neg(self) -> Polynomial { if self.degree == -1 { return Polynomial::zero(); } Polynomial { coefficients: self.coefficients.iter().map(|c| -c).collect(), degree: self.degree, } } } impl std::ops::Neg for Polynomial { type Output = Polynomial; fn neg(self) -> Polynomial { -&self } } impl std::ops::Sub for Polynomial { type Output = Polynomial; fn sub(self, other: Polynomial) -> Polynomial { // Fast path for zeros if self.degree == -1 { return -other; } if other.degree == -1 { return self; } self + (-other) } } impl PartialEq for Polynomial { fn eq(&self, other: &Self) -> bool { // Quick check based on degree if self.degree != other.degree { return false; } // If both are zero polynomials if self.degree == -1 { return true; } // Compare coefficients for i in 0..=self.degree as usize { if self.coefficients[i] != other.coefficients[i] { return false; } } true } } impl std::ops::Mul<&Polynomial> for &Polynomial { type Output = Polynomial; fn mul(self, factor: &Polynomial) -> Polynomial { self.mul_with_ref(factor) } } impl std::ops::Mul> for Polynomial { type Output = Polynomial; fn mul(self, factor: Polynomial) -> Polynomial { &self * &factor } } impl std::ops::Mul> for &Polynomial { type Output = Polynomial; fn mul(self, factor: Polynomial) -> Polynomial { self * &factor } } impl std::ops::Mul<&Polynomial> for Polynomial { type Output = Polynomial; fn mul(self, factor: &Polynomial) -> Polynomial { &self * factor } } ================================================ FILE: tools/garaga_rs/src/algebra/rational_function.rs ================================================ use crate::algebra::polynomial::Polynomial; use crate::definitions::FieldElement; use lambdaworks_math::field::traits::IsPrimeField; #[derive(Debug, Clone)] pub struct RationalFunction { pub numerator: Polynomial, pub denominator: Polynomial, } impl RationalFunction { pub fn new(numerator: Polynomial, denominator: Polynomial) -> Self { Self { numerator, denominator, } } pub fn simplify(&self) -> RationalFunction { let (_, _, gcd) = self.numerator.xgcd(&self.denominator); let num_simplified = self.numerator.clone().div_with_ref(&gcd); let den_simplified = self.denominator.clone().div_with_ref(&gcd); RationalFunction::new( num_simplified.scale_by_coeff(&self.denominator.leading_coefficient().inv().unwrap()), den_simplified.scale_by_coeff(&den_simplified.leading_coefficient().inv().unwrap()), ) } pub fn evaluate(&self, x: FieldElement) -> FieldElement { (self.numerator.evaluate(&x.clone()) / self.denominator.evaluate(&x.clone())).unwrap() } pub fn scale_by_coeff(&self, coeff: FieldElement) -> RationalFunction { RationalFunction::new( self.numerator.scale_by_coeff(&coeff), self.denominator.clone(), ) } } impl std::ops::Add for RationalFunction { type Output = RationalFunction; fn add(self, other: RationalFunction) -> RationalFunction { let num_1: Polynomial = self.numerator.clone() * other.denominator.clone(); let num_2 = other.numerator.clone() * self.denominator.clone(); let num = num_1 + num_2; let den: Polynomial = self.denominator.clone() * other.denominator.clone(); RationalFunction::new(num, den).simplify() } } #[derive(Debug, Clone)] pub struct FunctionFelt { pub a: RationalFunction, pub b: RationalFunction, } impl FunctionFelt { pub fn new(a: RationalFunction, b: RationalFunction) -> Self { Self { a, b } } pub fn simplify(&self) -> FunctionFelt { FunctionFelt::new(self.a.simplify(), self.b.simplify()) } pub fn evaluate(&self, x: FieldElement, y: &FieldElement) -> FieldElement { self.a.evaluate(x.clone()) + y * self.b.evaluate(x.clone()) } pub fn scale_by_coeff(&self, coeff: FieldElement) -> FunctionFelt { FunctionFelt::new( self.a.scale_by_coeff(coeff.clone()), self.b.scale_by_coeff(coeff), ) } // def print_as_sage_poly(self, var: str = "x") -> str: // return f"(({self.b.numerator.print_as_sage_poly(var)}) / ({self.b.denominator.print_as_sage_poly(var)}) * y + ({self.a.numerator.print_as_sage_poly(var)} / ({self.a.denominator.print_as_sage_poly(var)})" pub fn print_as_sage_poly(&self) -> String { format!( "(({}) / ({}) * y + ({}) / ({})", self.b.numerator.print_as_sage_poly(), self.b.denominator.print_as_sage_poly(), self.a.numerator.print_as_sage_poly(), self.a.denominator.print_as_sage_poly() ) } } impl std::ops::Add for FunctionFelt { type Output = FunctionFelt; fn add(self, other: FunctionFelt) -> FunctionFelt { FunctionFelt { a: self.a + other.a, b: self.b + other.b, } } } ================================================ FILE: tools/garaga_rs/src/calldata/drand_calldata.rs ================================================ use crate::algebra::g1g2pair::G1G2Pair; use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::algebra::polynomial::Polynomial; use crate::algebra::rational_function::RationalFunction; use crate::calldata::mpc_calldata; use crate::definitions::{BLS12381PrimeField, CurveID, CurveParamsProvider, FieldElement}; use crate::io::{ element_from_biguint, element_from_bytes_be, element_to_biguint, field_element_to_u384_limbs, }; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField as BLS12381Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField as BLS12381Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree6ExtensionField as BLS12381Degree6ExtensionField; use lambdaworks_math::field::traits::{IsPrimeField, LegendreSymbol}; use lambdaworks_math::traits::ByteConversion; use num_bigint::{BigInt, BigUint}; use num_traits::Num; use sha2::{Digest, Sha256}; pub fn drand_calldata_builder(values: &[BigUint]) -> Result, String> { if values.len() != 3 { return Err(format!("Invalid data array length: {}", values.len())); } let round_number: usize = (&values[0]) .try_into() .map_err(|e| format!("Invalid round number: {}", e))?; let randomness = { let bytes = values[1].to_bytes_be(); if bytes.len() > 32 { return Err(format!("Invalid randomness array length: {}", bytes.len())); } let mut padded_bytes = [0; 32]; let len = bytes.len(); padded_bytes[32 - len..].copy_from_slice(&bytes); padded_bytes }; let signature = { let bytes = values[2].to_bytes_be(); // Only supports G1 compressed points as per Quicknet if bytes.len() > 48 { return Err(format!("Invalid signature array length: {}", bytes.len())); } let mut padded_bytes = [0; 48]; let len = bytes.len(); padded_bytes[48 - len..].copy_from_slice(&bytes); deserialize_bls_point(&padded_bytes)? }; let round = RandomnessBeacon { round_number, randomness, signature, previous_signature: None, }; drand_randomness_to_calldata(round) } pub fn drand_randomness_to_calldata(round: RandomnessBeacon) -> Result, String> { let chain = get_chain_info(get_chain_hash(DrandNetwork::Quicknet))?; let round_number = round.round_number.try_into().unwrap(); let message = digest_func(round_number); let msg_point = hash_to_curve(message, "sha256")?; let sig_pt = round.signature.g1_point().unwrap().clone(); let hash_to_curve_hint = build_hash_to_curve_hint(message)?.to_calldata()?; let pairs = [ G1G2Pair::new(sig_pt.clone(), G2Point::generator()), G1G2Pair::new(msg_point, chain.public_key.g2_point().unwrap().neg()), ]; let mpc_data = { mpc_calldata::calldata_builder::< false, BLS12381PrimeField, BLS12381Degree2ExtensionField, BLS12381Degree6ExtensionField, BLS12381Degree12ExtensionField, >(&pairs, 2, &None)? }; let size = 1 + 4 + 4 + hash_to_curve_hint.len() + mpc_data.len(); let mut call_data = vec![size.into()]; call_data.push(round_number.into()); call_data.extend(field_element_to_u384_limbs(&sig_pt.x).map(BigUint::from)); call_data.extend(field_element_to_u384_limbs(&sig_pt.y).map(BigUint::from)); call_data.extend(hash_to_curve_hint); call_data.extend(mpc_data); assert!(call_data.len() == 1 + size); Ok(call_data) } pub fn drand_round_to_calldata(round_number: usize) -> Result, String> { let round_number = round_number.try_into().map_err(|err| format!("{}", err))?; let round = get_randomness(get_chain_hash(DrandNetwork::Quicknet), round_number); drand_randomness_to_calldata(round) } pub fn digest_func(round_number: u64) -> [u8; 32] { let bytes = round_number.to_be_bytes(); let digest = Sha256::digest(bytes); digest.into() } pub fn hash_to_curve(message: [u8; 32], hash_name: &str) -> Result, String> where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let [felt0, felt1] = hash_to_field::(message, 2, hash_name)? .try_into() .unwrap(); let pt0 = map_to_curve(felt0); let pt1 = map_to_curve(felt1); assert!(pt0.iso_point, "Point {:?} is not an iso point", pt0); assert!(pt1.iso_point, "Point {:?} is not an iso point", pt1); let curve_params = F::get_curve_params(); let cofactor = match curve_params.curve_id { CurveID::BLS12_381 => { let x = BigInt::from(curve_params.x); let n: BigInt = curve_params.n.into(); (BigInt::from(1) - (&x % &n)) % &n } _ => BigInt::from(curve_params.h), }; let sum = pt0.add(&pt1); assert!(sum.iso_point, "Point {:?} is not an iso point", sum); Ok(apply_isogeny(sum).scalar_mul(cofactor)) } fn map_to_curve(field_element: FieldElement) -> G1Point where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let curve_params = F::get_curve_params(); let swu_params = curve_params.swu_params.unwrap(); let a = swu_params.a; let b = swu_params.b; let z = swu_params.z; let u = field_element; let zeta_u2 = &z * (&u * &u); let ta = (&zeta_u2 * &zeta_u2) + &zeta_u2; let num_x1 = &b * (&ta + FieldElement::::from(1)); let div = if ta == FieldElement::from(0) { &a * &z } else { &a * -ta }; let num2_x1 = &num_x1 * &num_x1; let div2 = &div * ÷ let div3 = &div2 * ÷ assert!(div3 != FieldElement::from(0)); let num_gx1 = (&num2_x1 + &a * &div2) * &num_x1 + &b * &div3; let num_x2 = &zeta_u2 * &num_x1; let gx1 = (&num_gx1 / &div3).unwrap(); let gx1_square = is_quad_residue(&gx1); let y1 = if gx1_square { let y1 = max_sqrt(&gx1); assert!(&y1 * &y1 == gx1); y1 } else { let y1 = max_sqrt(&(&z * &gx1)); assert!(&y1 * &y1 == &z * &gx1); y1 }; let y2 = &zeta_u2 * &u * &y1; let num_x = if gx1_square { num_x1 } else { num_x2 }; let y = if gx1_square { y1.clone() } else { y2.clone() }; let x_affine = (&num_x / &div).unwrap(); let y_flag = element_to_biguint(&y) % BigUint::from(2usize) == element_to_biguint(&u) % BigUint::from(2usize); let y_affine = if !y_flag { -y.clone() } else { y.clone() }; G1Point::new(x_affine, y_affine, true).unwrap() } fn hash_to_field( message: [u8; 32], count: usize, hash_name: &str, ) -> Result>, String> where F: IsPrimeField, FieldElement: ByteConversion, { let len_per_elem = get_len_per_elem::(None); let output = match hash_name { "sha256" => hash_to_bytes::(message, count, len_per_elem), _ => return Err(format!("Unsupported hash function: {}", hash_name)), }; Ok(output .into_iter() .map(|v| element_from_bytes_be(&v)) .collect()) } fn hash_to_bytes(message: [u8; 32], count: usize, len_per_elem: usize) -> Vec> { let len_in_bytes = count * len_per_elem; assert!( len_in_bytes < (1 << 16), "Length should be smaller than 2^16" ); let mut expander = ExpanderXmd::::new(DST, len_per_elem); let uniform_bytes = expander.expand_message_xmd(&message, len_in_bytes.try_into().unwrap()); let mut output = vec![]; for i in (0..len_in_bytes).step_by(len_per_elem) { output.push(uniform_bytes[i..i + len_per_elem].to_vec()); } output } /* This function computes the length in bytes that a hash function should output for hashing an element of type `Field`. :param sec_param: The security parameter. :return: The length in bytes. */ fn get_len_per_elem(sec_param: Option) -> usize where F: IsPrimeField, { let sec_param = sec_param.unwrap_or(128); let base_field_size_in_bits = F::field_bit_size(); let base_field_size_with_security_padding_in_bits = base_field_size_in_bits + sec_param; base_field_size_with_security_padding_in_bits.div_ceil(8) } fn is_quad_residue(element: &FieldElement) -> bool { if element == &FieldElement::from(0) { true } else { element.legendre_symbol() == LegendreSymbol::One } } fn min_sqrt(element: &FieldElement) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { let (sqrt1, sqrt2) = element.sqrt().unwrap(); if element_to_biguint(&sqrt1) < element_to_biguint(&sqrt2) { sqrt1 } else { sqrt2 } } fn max_sqrt(element: &FieldElement) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { let (sqrt1, sqrt2) = element.sqrt().unwrap(); if element_to_biguint(&sqrt1) > element_to_biguint(&sqrt2) { sqrt1 } else { sqrt2 } } pub trait Hasher: Clone { fn new() -> Self; fn reset(&mut self); fn update(&mut self, bytes: &[u8]); fn digest_size(&self) -> usize; fn digest(&self) -> Vec; } #[derive(Clone)] pub struct Sha256Hasher { data: Vec, } impl Hasher for Sha256Hasher { fn new() -> Self { Self { data: vec![] } } fn reset(&mut self) { self.data = vec![]; } fn update(&mut self, bytes: &[u8]) { self.data.extend_from_slice(bytes); } fn digest_size(&self) -> usize { 32 } fn digest(&self) -> Vec { Sha256::digest(&self.data).to_vec() } } const G1_DOMAIN: &[u8] = b"BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_"; const DST: &[u8] = G1_DOMAIN; const LONG_DST_PREFIX: &[u8] = b"H2C-OVERSIZE-DST-"; const MAX_DST_LENGTH: usize = 255; pub struct ExpanderXmd { pub hasher: H, pub dst: Vec, pub block_size: usize, } impl ExpanderXmd { fn new(dst: &[u8], block_size: usize) -> Self { Self { hasher: H::new(), dst: dst.to_vec(), block_size, } } fn construct_dst_prime(&self) -> Vec { let mut dst_prime = if self.dst.len() > MAX_DST_LENGTH { let mut hasher_copy = self.hasher.clone(); hasher_copy.update(LONG_DST_PREFIX); hasher_copy.update(&self.dst); hasher_copy.digest() } else { self.dst.clone() }; dst_prime.push(dst_prime.len().try_into().unwrap()); dst_prime } fn expand_message_xmd(&mut self, msg: &[u8], n: u16) -> Vec { let mut uniform_bytes = vec![]; let b_len = self.hasher.digest_size(); let ell = Into::::into(n).div_ceil(b_len); assert!( ell <= 255, "The ratio of desired output to the output size of hash function is too large!" ); let dst_prime = self.construct_dst_prime(); let z_pad = vec![0u8; self.block_size]; let lib_str: [u8; 2] = n.to_be_bytes(); self.hasher.update(&z_pad); self.hasher.update(msg); let mut lib_str_dst_prime = lib_str.to_vec(); lib_str_dst_prime.push(0); lib_str_dst_prime.extend_from_slice(&dst_prime); self.hasher.update(&lib_str_dst_prime); let b0 = self.hasher.digest(); let mut hasher = self.hasher.clone(); hasher.reset(); hasher.update(&b0); let mut one_dst_prime = vec![1]; one_dst_prime.extend_from_slice(&dst_prime); hasher.update(&one_dst_prime); let mut bi = hasher.digest(); uniform_bytes.extend_from_slice(&bi); for i in 2..ell + 1 { let b0_xor_bi = b0 .iter() .zip(bi.iter()) .map(|(&x, &y)| x ^ y) .collect::>(); let mut hasher = self.hasher.clone(); hasher.reset(); hasher.update(&b0_xor_bi); let mut bytes_i_dst_prime = vec![i.try_into().unwrap()]; bytes_i_dst_prime.extend_from_slice(&dst_prime); hasher.update(&bytes_i_dst_prime); bi = hasher.digest(); uniform_bytes.extend_from_slice(&bi); } uniform_bytes[0..n.into()].to_vec() } } fn apply_isogeny(pt: G1Point) -> G1Point where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { assert!(pt.iso_point, "Point {:?} is not an iso point", pt); let (x_rational, y_rational) = get_isogeny_to_g1_map::(); let x_affine = x_rational.evaluate(pt.x.clone()); let y_affine = y_rational.evaluate(pt.x) * pt.y; G1Point::new(x_affine, y_affine, false).unwrap() } fn get_isogeny_to_g1_map() -> (RationalFunction, RationalFunction) where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let curve_params = F::get_curve_params(); match curve_params.curve_id { CurveID::BLS12_381 => { let f1 = RationalFunction::new( Polynomial::new( [ BigUint::from_str_radix("11A05F2B1E833340B809101DD99815856B303E88A2D7005FF2627B56CDB4E2C85610C2D5F2E62D6EAEAC1662734649B7", 16).unwrap(), BigUint::from_str_radix("17294ED3E943AB2F0588BAB22147A81C7C17E75B2F6A8417F565E33C70D1E86B4838F2A6F318C356E834EEF1B3CB83BB", 16).unwrap(), BigUint::from_str_radix("D54005DB97678EC1D1048C5D10A9A1BCE032473295983E56878E501EC68E25C958C3E3D2A09729FE0179F9DAC9EDCB0", 16).unwrap(), BigUint::from_str_radix("1778E7166FCC6DB74E0609D307E55412D7F5E4656A8DBF25F1B33289F1B330835336E25CE3107193C5B388641D9B6861", 16).unwrap(), BigUint::from_str_radix("E99726A3199F4436642B4B3E4118E5499DB995A1257FB3F086EEB65982FAC18985A286F301E77C451154CE9AC8895D9", 16).unwrap(), BigUint::from_str_radix("1630C3250D7313FF01D1201BF7A74AB5DB3CB17DD952799B9ED3AB9097E68F90A0870D2DCAE73D19CD13C1C66F652983", 16).unwrap(), BigUint::from_str_radix("D6ED6553FE44D296A3726C38AE652BFB11586264F0F8CE19008E218F9C86B2A8DA25128C1052ECADDD7F225A139ED84", 16).unwrap(), BigUint::from_str_radix("17B81E7701ABDBE2E8743884D1117E53356DE5AB275B4DB1A682C62EF0F2753339B7C8F8C8F475AF9CCB5618E3F0C88E", 16).unwrap(), BigUint::from_str_radix("80D3CF1F9A78FC47B90B33563BE990DC43B756CE79F5574A2C596C928C5D1DE4FA295F296B74E956D71986A8497E317", 16).unwrap(), BigUint::from_str_radix("169B1F8E1BCFA7C42E0C37515D138F22DD2ECB803A0C5C99676314BAF4BB1B7FA3190B2EDC0327797F241067BE390C9E", 16).unwrap(), BigUint::from_str_radix("10321DA079CE07E272D8EC09D2565B0DFA7DCCDDE6787F96D50AF36003B14866F69B771F8C285DECCA67DF3F1605FB7B", 16).unwrap(), BigUint::from_str_radix("6E08C248E260E70BD1E962381EDEE3D31D79D7E22C837BC23C0BF1BC24C6B68C24B1B80B64D391FA9C8BA2E8BA2D229", 16).unwrap(), ].iter().map(element_from_biguint).collect() ), Polynomial::new( [ BigUint::from_str_radix("8CA8D548CFF19AE18B2E62F4BD3FA6F01D5EF4BA35B48BA9C9588617FC8AC62B558D681BE343DF8993CF9FA40D21B1C", 16).unwrap(), BigUint::from_str_radix("12561A5DEB559C4348B4711298E536367041E8CA0CF0800C0126C2588C48BF5713DAA8846CB026E9E5C8276EC82B3BFF", 16).unwrap(), BigUint::from_str_radix("B2962FE57A3225E8137E629BFF2991F6F89416F5A718CD1FCA64E00B11ACEACD6A3D0967C94FEDCFCC239BA5CB83E19", 16).unwrap(), BigUint::from_str_radix("3425581A58AE2FEC83AAFEF7C40EB545B08243F16B1655154CCA8ABC28D6FD04976D5243EECF5C4130DE8938DC62CD8", 16).unwrap(), BigUint::from_str_radix("13A8E162022914A80A6F1D5F43E7A07DFFDFC759A12062BB8D6B44E833B306DA9BD29BA81F35781D539D395B3532A21E", 16).unwrap(), BigUint::from_str_radix("E7355F8E4E667B955390F7F0506C6E9395735E9CE9CAD4D0A43BCEF24B8982F7400D24BC4228F11C02DF9A29F6304A5", 16).unwrap(), BigUint::from_str_radix("772CAACF16936190F3E0C63E0596721570F5799AF53A1894E2E073062AEDE9CEA73B3538F0DE06CEC2574496EE84A3A", 16).unwrap(), BigUint::from_str_radix("14A7AC2A9D64A8B230B3F5B074CF01996E7F63C21BCA68A81996E1CDF9822C580FA5B9489D11E2D311F7D99BBDCC5A5E", 16).unwrap(), BigUint::from_str_radix("A10ECF6ADA54F825E920B3DAFC7A3CCE07F8D1D7161366B74100DA67F39883503826692ABBA43704776EC3A79A1D641", 16).unwrap(), BigUint::from_str_radix("95FC13AB9E92AD4476D6E3EB3A56680F682B4EE96F7D03776DF533978F31C1593174E4B4B7865002D6384D168ECDD0A", 16).unwrap(), BigUint::from_str_radix("1", 16).unwrap(), ].iter().map(element_from_biguint).collect() ), ); let f2 = RationalFunction::new( Polynomial::new( [ BigUint::from_str_radix("90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33", 16).unwrap(), BigUint::from_str_radix("134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696", 16).unwrap(), BigUint::from_str_radix("cc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6", 16).unwrap(), BigUint::from_str_radix("1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb", 16).unwrap(), BigUint::from_str_radix("8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb", 16).unwrap(), BigUint::from_str_radix("16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0", 16).unwrap(), BigUint::from_str_radix("4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2", 16).unwrap(), BigUint::from_str_radix("987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29", 16).unwrap(), BigUint::from_str_radix("9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587", 16).unwrap(), BigUint::from_str_radix("e1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30", 16).unwrap(), BigUint::from_str_radix("19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132", 16).unwrap(), BigUint::from_str_radix("18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e", 16).unwrap(), BigUint::from_str_radix("b182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8", 16).unwrap(), BigUint::from_str_radix("245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133", 16).unwrap(), BigUint::from_str_radix("5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b", 16).unwrap(), BigUint::from_str_radix("15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604", 16).unwrap(), ].iter().map(element_from_biguint).collect() ), Polynomial::new( [ BigUint::from_str_radix("16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1", 16).unwrap(), BigUint::from_str_radix("1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d", 16).unwrap(), BigUint::from_str_radix("58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2", 16).unwrap(), BigUint::from_str_radix("16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416", 16).unwrap(), BigUint::from_str_radix("be0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d", 16).unwrap(), BigUint::from_str_radix("8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac", 16).unwrap(), BigUint::from_str_radix("166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c", 16).unwrap(), BigUint::from_str_radix("16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9", 16).unwrap(), BigUint::from_str_radix("1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a", 16).unwrap(), BigUint::from_str_radix("167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55", 16).unwrap(), BigUint::from_str_radix("4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8", 16).unwrap(), BigUint::from_str_radix("accbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092", 16).unwrap(), BigUint::from_str_radix("ad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc", 16).unwrap(), BigUint::from_str_radix("2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7", 16).unwrap(), BigUint::from_str_radix("e0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f", 16).unwrap(), BigUint::from_str_radix("1", 16).unwrap(), ].iter().map(element_from_biguint).collect() ), ); (f1, f2) } curve_id => unimplemented!("Isogeny for curve {:?} is not implemented", curve_id), } } pub struct MapToCurveHint { pub gx1_is_square: bool, pub y1: FieldElement, pub y_flag: bool, } impl MapToCurveHint { fn to_calldata(&self) -> Vec { let mut call_data = vec![]; call_data.push(self.gx1_is_square.into()); call_data.extend(field_element_to_u384_limbs(&self.y1).map(BigUint::from)); call_data.push(self.y_flag.into()); call_data } } pub struct HashToCurveHint { pub f0_hint: MapToCurveHint, pub f1_hint: MapToCurveHint, } impl HashToCurveHint { fn to_calldata(&self) -> Result, String> { let mut call_data = vec![]; call_data.extend(self.f0_hint.to_calldata()); call_data.extend(self.f1_hint.to_calldata()); Ok(call_data) } } fn build_hash_to_curve_hint(message: [u8; 32]) -> Result { let [felt0, felt1] = hash_to_field::(message, 2, "sha256")? .try_into() .unwrap(); let f0_hint = build_map_to_curve_hint(felt0); let f1_hint = build_map_to_curve_hint(felt1); Ok(HashToCurveHint { f0_hint, f1_hint }) } fn build_map_to_curve_hint(u: FieldElement) -> MapToCurveHint { let curve_params = BLS12381PrimeField::get_curve_params(); let swu_params = curve_params.swu_params.unwrap(); let a = swu_params.a; let b = swu_params.b; let z = swu_params.z; let zeta_u2 = &z * (&u * &u); let ta = (&zeta_u2 * &zeta_u2) + &zeta_u2; let num_x1 = &b * (&ta + FieldElement::::from(1)); let div = if ta == FieldElement::from(0) { &a * &z } else { &a * -ta }; let num2_x1 = &num_x1 * &num_x1; let div2 = &div * ÷ let div3 = &div2 * ÷ assert!(div3 != FieldElement::from(0)); let num_gx1 = (&num2_x1 + &a * &div2) * &num_x1 + &b * &div3; let gx1 = (&num_gx1 / &div3).unwrap(); let gx1_square = is_quad_residue(&gx1); let y1 = if gx1_square { let y1 = max_sqrt(&gx1); assert!(&y1 * &y1 == gx1); y1 } else { let y1 = max_sqrt(&(&z * &gx1)); assert!(&y1 * &y1 == &z * &gx1); y1 }; let y2 = &zeta_u2 * &u * &y1; let y = if gx1_square { y1.clone() } else { y2 }; let y_flag = element_to_biguint(&y) % BigUint::from(2usize) == element_to_biguint(&u) % BigUint::from(2usize); MapToCurveHint { gx1_is_square: gx1_square, y1, y_flag, } } pub fn get_base_urls() -> Vec<&'static str> { vec![ "https://drand.cloudflare.com", "https://api.drand.sh", "https://api2.drand.sh", "https://api3.drand.sh", ] } pub enum DrandNetwork { Default, Quicknet, } pub fn get_chain_hash(network: DrandNetwork) -> [u8; 32] { match network { DrandNetwork::Default => { from_hex("8990e7a9aaed2ffed73dbd7092123d6f289930540d7651336225dc172e51b2ce") } DrandNetwork::Quicknet => { from_hex("52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971") } } } pub enum CurvePoint { G1Point(G1Point), G2Point(G2Point), } impl CurvePoint { pub fn g1_point(&self) -> Option<&G1Point> { match self { Self::G1Point(point) => Some(point), _ => None, } } pub fn g2_point(&self) -> Option<&G2Point> { match self { Self::G2Point(point) => Some(point), _ => None, } } } pub fn deserialize_bls_point(s_string: &[u8]) -> Result { let m_byte = s_string[0] & 0xE0; if [0x20, 0x60, 0xE0].contains(&m_byte) { return Err("Invalid encoding".to_string()); } let c_bit = (m_byte & 0x80) >> 7; // Compression bit let i_bit = (m_byte & 0x40) >> 6; // Infinity bit let s_bit = (m_byte & 0x20) >> 5; // Sign bit let mut s_string = s_string.to_vec(); s_string[0] &= 0x1F; if i_bit == 1 { if !s_string.iter().all(|&b| b == 0) { return Err("Invalid encoding for point at infinity".to_string()); } let point = if [48, 96].contains(&s_string.len()) { CurvePoint::G1Point(G1Point::new_infinity()) } else { CurvePoint::G2Point(G2Point::new_infinity()) }; return Ok(point); } if c_bit == 0 { if s_string.len() == 96 { // G1 point (uncompressed) let x = element_from_bytes_be(&s_string[..48]); let y = element_from_bytes_be(&s_string[48..]); return Ok(CurvePoint::G1Point(G1Point::new(x, y, false)?)); } if s_string.len() == 192 { // G2 point (uncompressed) let x0 = element_from_bytes_be(&s_string[..48]); let x1 = element_from_bytes_be(&s_string[48..96]); let y0 = element_from_bytes_be(&s_string[96..144]); let y1 = element_from_bytes_be(&s_string[144..]); return Ok(CurvePoint::G2Point(G2Point::new([x0, x1], [y0, y1])?)); } Err(format!( "Invalid length for uncompressed point: {}", s_string.len() )) } else { // C_bit == 1 if s_string.len() == 48 { // G1 point (compressed) let x = element_from_bytes_be(&s_string); let y2 = &x * &x * &x + FieldElement::from(4); let y = if s_bit == 1 { max_sqrt(&y2) } else { min_sqrt(&y2) }; return Ok(CurvePoint::G1Point(G1Point::new(x, y, false)?)); } if s_string.len() == 96 { // G2 point (compressed) unimplemented!("Decoding of compressed G2 points not yet supported"); } Err(format!( "Invalid length for compressed point: {}", s_string.len() )) } } pub struct NetworkInfo { pub public_key: CurvePoint, pub period: usize, pub genesis_time: usize, pub hash: [u8; 32], pub group_hash: [u8; 32], pub scheme_id: String, pub beacon_id: DrandNetwork, } pub fn get_chain_info(chain_hash: [u8; 32]) -> Result { let network = if chain_hash == get_chain_hash(DrandNetwork::Default) { DrandNetwork::Default } else if chain_hash == get_chain_hash(DrandNetwork::Quicknet) { DrandNetwork::Quicknet } else { return Err(format!("Unknown chain hash: {:?}", chain_hash)); }; let info = match network { DrandNetwork::Default => { let x = FieldElement::from_hex_unchecked("68f005eb8e6e4ca0a47c8a77ceaa5309a47978a7c71bc5cce96366b5d7a569937c529eeda66c7293784a9402801af31"); let y = FieldElement::from_hex_unchecked("26fa5eef143aaa17c53b3c150d96a18051b718531af576803cfb9acf29b8774a8184e63c62da81ddf4d76fb0a65895c"); NetworkInfo { public_key: CurvePoint::G1Point(G1Point::new(x, y, false).unwrap()), period: 30, genesis_time: 1595431050, hash: chain_hash, group_hash: from_hex( "176f93498eac9ca337150b46d21dd58673ea4e3581185f869672e59fa4cb390a", ), scheme_id: "pedersen-bls-chained".to_string(), beacon_id: DrandNetwork::Default, } } DrandNetwork::Quicknet => { let x = [ FieldElement::from_hex_unchecked("d1fec758c921cc22b0e17e63aaf4bcb5ed66304de9cf809bd274ca73bab4af5a6e9c76a4bc09e76eae8991ef5ece45a"), FieldElement::from_hex_unchecked("3cf0f2896adee7eb8b5f01fcad3912212c437e0073e911fb90022d3e760183c8c4b450b6a0a6c3ac6a5776a2d106451"), ]; let y = [ FieldElement::from_hex_unchecked("e5db2b6bfbb01c867749cadffca88b36c24f3012ba09fc4d3022c5c37dce0f977d3adb5d183c7477c442b1f04515273"), FieldElement::from_hex_unchecked("1a714f2edb74119a2f2b0d5a7c75ba902d163700a61bc224ededd8e63aef7be1aaf8e93d7a9718b047ccddb3eb5d68b"), ]; NetworkInfo { public_key: CurvePoint::G2Point(G2Point::new(x, y).unwrap()), period: 3, genesis_time: 1692803367, hash: chain_hash, group_hash: from_hex( "f477d5c89f21a17c863a7f937c6a6d15859414d2be09cd448d4279af331c5d3e", ), scheme_id: "bls-unchained-g1-rfc9380".to_string(), beacon_id: DrandNetwork::Quicknet, } } }; Ok(info) } pub struct RandomnessBeacon { pub round_number: usize, pub randomness: [u8; 32], pub signature: CurvePoint, pub previous_signature: Option, } fn from_hex(hex: &str) -> [u8; 32] { assert!(hex.len() == 64); let mut bytes = [0u8; 32]; for i in 0..32 { bytes[i] = u8::from_str_radix(&hex[2 * i..2 * (i + 1)], 16).unwrap(); } bytes } fn get_randomness(chain_hash: [u8; 32], round_number: u64) -> RandomnessBeacon { /* hardcoded for testing */ if chain_hash == get_chain_hash(DrandNetwork::Quicknet) { match round_number { 1 => { let x = FieldElement::from_hex_unchecked("155e7cb2d5c613ee0b2e28d6750aabbb78c39dcc96bd9d38c2c2e12198df95571de8e8e402a0cc48871c7089a2b3af4b"); let y = FieldElement::from_hex_unchecked("0fbb74ee8788264320f2501b0fa0dd56363bcec5ce4b113b2bf1de6e331116c79191af99234824f03aeb10ab1c4c7771"); return RandomnessBeacon { round_number: round_number.try_into().unwrap(), randomness: from_hex( "1466a6cd24e327188770752f6134001c64d6efcc590ccc26b721611ad96f165a", ), signature: CurvePoint::G1Point(G1Point::new(x, y, false).unwrap()), previous_signature: None, }; } 2 => { let x = FieldElement::from_hex_unchecked("16b6a585449b66eb12e875b64fcbab3799861a00e4dbf092d99e969a5eac57dd3f798acf61e705fe4f093db926626807"); let y = FieldElement::from_hex_unchecked("15ff2dfd0adad43e0219d11f00f14d4e14cb0d8292bd2c0a8ec634c1b402c2a067fc5d9c53aa2aa0aab8214ca1fce58c"); return RandomnessBeacon { round_number: round_number.try_into().unwrap(), randomness: from_hex( "5782d6987841c654515a0e72b2d1ebb4e741234042c37cb19608ae50d93fb60c", ), signature: CurvePoint::G1Point(G1Point::new(x, y, false).unwrap()), previous_signature: None, }; } 3 => { let x = FieldElement::from_hex_unchecked("13fab6df720b68cc47175f2c777e86d84187caab5770906f515ff1099cb01e4deaa027075d860823e49477b93c72bd64"); let y = FieldElement::from_hex_unchecked("18a83e0a35ee138a879bebc1ac56ab46832bf67deaa63061fb98c8d35333557003c4cde8c2b5320ce2be2073a12b6112"); return RandomnessBeacon { round_number: round_number.try_into().unwrap(), randomness: from_hex( "7ef4621ace1c6da4eb2eee7cd901f81385bca5b189771ec0f08d0d2566dd1a21", ), signature: CurvePoint::G1Point(G1Point::new(x, y, false).unwrap()), previous_signature: None, }; } _ => (), } } unimplemented!("Not to be used in production"); } #[cfg(test)] mod tests { use super::*; #[test] fn test_drand_round_to_calldata_1() { let _ = drand_round_to_calldata(1).unwrap(); } #[test] fn test_drand_round_to_calldata_2() { let _ = drand_round_to_calldata(2).unwrap(); } #[test] fn test_drand_round_to_calldata_3() { let _ = drand_round_to_calldata(3).unwrap(); } } ================================================ FILE: tools/garaga_rs/src/calldata/drand_tlock_calldata.rs ================================================ use crate::algebra::extf_mul::from_e2; use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::calldata::drand_calldata::{ digest_func, get_chain_hash, get_chain_info, hash_to_curve, DrandNetwork, }; use crate::definitions::{BLS12381PrimeField, CurveParamsProvider, FieldElement}; use crate::io::field_element_to_u384_limbs; use crate::pairing::final_exp_witness::{bls12_381_final_exp_witness, to_bls}; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField as BLS12381Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField as BLS12381Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::pairing::BLS12381AtePairing; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::twist::BLS12381TwistCurve; use lambdaworks_math::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; use lambdaworks_math::elliptic_curve::traits::{FromAffine, IsPairing}; use num_bigint::BigUint; use sha2::{Digest, Sha256}; pub fn drand_tlock_encrypt_calldata_builder(values: &[BigUint]) -> Result, String> { if values.len() != 3 { return Err(format!("Invalid data array length: {}", values.len())); } let round_number: usize = (&values[0]) .try_into() .map_err(|e| format!("Invalid round number: {}", e))?; let message = { let bytes = values[1].to_bytes_be(); if bytes.len() > 16 { return Err(format!("Invalid message array length: {}", bytes.len())); } let mut padded_bytes = [0; 16]; let len = bytes.len(); padded_bytes[16 - len..].copy_from_slice(&bytes); padded_bytes }; let randomness = { let bytes = values[2].to_bytes_be(); if bytes.len() > 16 { return Err(format!("Invalid randomness array length: {}", bytes.len())); } let mut padded_bytes = [0; 16]; let len = bytes.len(); padded_bytes[16 - len..].copy_from_slice(&bytes); padded_bytes }; let chain = get_chain_info(get_chain_hash(DrandNetwork::Quicknet))?; let public_key = chain.public_key.g2_point().unwrap().clone(); let cipher_text = encrypt_for_round(public_key, round_number, message, randomness)?; let cipher_text_hint = cipher_text.to_calldata(); let size = 1 + cipher_text_hint.len(); let mut call_data = vec![size.into()]; call_data.push(round_number.into()); call_data.extend(cipher_text_hint); assert!(call_data.len() == 1 + size); Ok(call_data) } pub struct CipherText { pub u: G2Point, pub v: [u8; 16], pub w: [u8; 16], } impl CipherText { pub fn to_calldata(&self) -> Vec { let u_x = from_e2(self.u.x.clone()); let u_y = from_e2(self.u.y.clone()); let mut call_data = vec![]; call_data.extend(field_element_to_u384_limbs(&u_x[0]).map(BigUint::from)); call_data.extend(field_element_to_u384_limbs(&u_x[1]).map(BigUint::from)); call_data.extend(field_element_to_u384_limbs(&u_y[0]).map(BigUint::from)); call_data.extend(field_element_to_u384_limbs(&u_y[1]).map(BigUint::from)); for b in self.v { call_data.push(b.into()); } for b in self.w { call_data.push(b.into()); } call_data } } pub fn encrypt_for_round( public_key: G2Point, round_number: usize, message: [u8; 16], sigma: [u8; 16], ) -> Result { let round_number = round_number.try_into().unwrap(); let msg_at_round = digest_func(round_number); let pt_at_round = hash_to_curve::(msg_at_round, "sha256")?; let gid = bls12381_single_pairing(pt_at_round, public_key)?; let r = { let mut bytes = vec![]; bytes.extend(b"IBE-H3"); bytes.extend(sigma); bytes.extend(message); let output = sha256_digest(&bytes); BigUint::from_bytes_le(&expand_message_drand(&output, 32)) }; let r = { let curve_params = BLS12381PrimeField::get_curve_params(); r % curve_params.n }; let u = G2Point::generator().scalar_mul::(r.clone().into()); let r_gid = bls12_381_final_exp_witness::pow_custom(&gid, &r); let r_gid_serialized = { let mut bytes = vec![]; let mut values = to_bls(r_gid); values.reverse(); for value in values { let mut padded_value_bytes = [0u8; 48]; let value_bytes = value.to_bytes_be(); let len = value_bytes.len(); assert!(len <= 48); padded_value_bytes[48 - len..].copy_from_slice(&value_bytes); bytes.extend(padded_value_bytes); } bytes }; let r_gid_hash: [u8; 16] = { let mut bytes = vec![]; bytes.extend(b"IBE-H2"); bytes.extend(r_gid_serialized); let output = sha256_digest(&bytes); output[..16].to_vec().try_into().unwrap() }; let v: [u8; 16] = { let bytes = sigma .into_iter() .zip(r_gid_hash) .map(|(a, b)| a ^ b) .collect::>(); bytes.try_into().unwrap() }; let sigma_hash: [u8; 16] = { let mut bytes = vec![]; bytes.extend(b"IBE-H4"); bytes.extend(sigma); let output = sha256_digest(&bytes); output[..16].to_vec().try_into().unwrap() }; let w: [u8; 16] = { let bytes = message .into_iter() .zip(sigma_hash) .map(|(a, b)| a ^ b) .collect::>(); bytes.try_into().unwrap() }; Ok(CipherText { u, v, w }) } fn bls12381_single_pairing( g1_point: G1Point, g2_point: G2Point, ) -> Result, String> { let g1_point = ShortWeierstrassProjectivePoint::from_affine(g1_point.x, g1_point.y) .map_err(|err| format!("{:?}", err))?; let g2_point = ShortWeierstrassProjectivePoint::from_affine(g2_point.x, g2_point.y) .map_err(|err| format!("{:?}", err))?; let product = BLS12381AtePairing::compute_batch(&[(&g1_point, &g2_point)]) .map_err(|err| format!("{:?}", err))?; Ok(product) } fn expand_message_drand(msg: &[u8], buf_size: usize) -> Vec { assert!(buf_size <= 32); const BITS_TO_MASK_FOR_BLS12381: usize = 1; let curve_params = BLS12381PrimeField::get_curve_params(); let order = curve_params.n; for i in 1..65536 { let i: u16 = i.try_into().unwrap(); let hash_result = { let mut bytes = vec![]; bytes.extend(i.to_le_bytes()); bytes.extend(msg); sha256_digest(&bytes) }; let hash_result = { let mut bytes = hash_result; bytes[0] >>= BITS_TO_MASK_FOR_BLS12381; bytes }; let reversed_hash = { let mut bytes = hash_result; bytes.reverse(); bytes }; let scalar = &BigUint::from_bytes_le(&reversed_hash) % ℴ if scalar != BigUint::from(0usize) { return reversed_hash[..buf_size].to_vec(); } } panic!("You are insanely unlucky and should have been hit by a meteor before now"); } fn sha256_digest(data: &[u8]) -> [u8; 32] { Sha256::digest(data).into() } pub fn get_drand_round_at(genesis_time: usize, period: usize, time: usize) -> usize { assert!(time >= genesis_time); (time - genesis_time) / period + 1 } pub fn get_drand_round_time(genesis_time: usize, period: usize, round_number: usize) -> usize { assert!(round_number >= 1); genesis_time + period * (round_number - 1) } #[cfg(test)] mod tests { use super::*; #[test] fn test_encrypt_for_round_1() { let chain = get_chain_info(get_chain_hash(DrandNetwork::Quicknet)).unwrap(); let public_key = chain.public_key.g2_point().unwrap().clone(); let cypher_text = encrypt_for_round(public_key, 1, *b"1234567890abcdef", *b"deaf00013000beef").unwrap(); let expected_v = [ 211, 169, 110, 124, 57, 249, 177, 59, 54, 206, 185, 125, 242, 220, 74, 184, ]; let expected_w = [ 60, 105, 170, 165, 30, 223, 128, 199, 37, 162, 104, 106, 18, 148, 250, 43, ]; assert_eq!(cypher_text.v, expected_v); assert_eq!(cypher_text.w, expected_w); } } ================================================ FILE: tools/garaga_rs/src/calldata/full_proof_with_hints/groth16.rs ================================================ // use crate::algebra::g1g2pair::G1G2Pair; use crate::calldata::mpc_calldata::mpc_calldata_builder; use crate::calldata::msm_calldata::msm_calldata_builder; use crate::calldata::G1PointBigUint; use crate::calldata::G2PointBigUint; use crate::constants::{get_risc0_constants, SP1_VERIFIER_HASH, SP1_VERIFIER_VERSION}; use crate::definitions::{ BLS12381PrimeField, BN254PrimeField, CurveID, CurveParamsProvider, FieldElement, }; use crate::io::{ biguint_split, element_to_biguint, field_elements_from_big_uints, parse_g1_points_from_flattened_field_elements_list, }; use hex; use lambdaworks_math::field::traits::IsPrimeField; use lambdaworks_math::traits::ByteConversion; use num_bigint::{BigInt, BigUint, Sign}; use num_traits::Num; use sha2::{Digest, Sha256}; use starknet_types_core::felt::Felt; pub struct Groth16Proof { pub a: G1PointBigUint, pub b: G2PointBigUint, pub c: G1PointBigUint, pub public_inputs: Vec, pub image_id_journal_risc0: Option<(Vec, Vec)>, // Only used for risc0 proofs pub vkey_public_values_sp1: Option<(Vec, Vec)>, // Only used for sp1 proofs } impl Groth16Proof { pub fn flatten(&self) -> Vec { let mut result = Vec::new(); result.extend(self.a.flatten()); result.extend(self.b.flatten()); result.extend(self.c.flatten()); result } pub fn from( values: Vec, image_id_journal_risc0: Option<(Vec, Vec)>, vkey_public_values_sp1: Option<(Vec, Vec)>, ) -> Self { let a = G1PointBigUint::from(values[0..2].to_vec()); let b = G2PointBigUint::from(values[2..6].to_vec()); let c = G1PointBigUint::from(values[6..8].to_vec()); let public_inputs = values[8..].to_vec(); Groth16Proof { a, b, c, public_inputs, image_id_journal_risc0, vkey_public_values_sp1, } } pub fn serialize_to_calldata(&self) -> Vec { let mut cd: Vec = vec![]; // Serialize a.x, a.y, b.x[0], b.x[1], b.y[0], b.y[1], c.x, c.y directly // This matches the Python: cd.extend(io.bigint_split(self.a.x)) etc. for v in [ &self.a.x, &self.a.y, &self.b.x0, &self.b.x1, &self.b.y0, &self.b.y1, &self.c.x, &self.c.y, ] { cd.extend(biguint_split::<4, 96>(v).iter().map(|&x| BigUint::from(x))); } let risc0_mode = self.image_id_journal_risc0.is_some(); let _sp1_mode = self.vkey_public_values_sp1.is_some(); if risc0_mode && !_sp1_mode { // Risc0 mode. // Public inputs will be reconstructed from image id and journal. let (image_id, journal) = self.image_id_journal_risc0.as_ref().unwrap(); let image_id_u256 = BigUint::from_bytes_be(image_id); let image_id_u256_split = biguint_split::<8, 32>(&image_id_u256).map(BigUint::from); let image_id_u256_split_reversed: Vec = image_id_u256_split.iter().rev().cloned().collect(); // Span of u32, length 8. cd.push(BigUint::from(8u64)); cd.extend(image_id_u256_split_reversed); // Span of u8, length depends on input cd.push(BigUint::from(journal.len())); cd.extend(journal.iter().map(|&x| BigUint::from(x))); } else if _sp1_mode && !risc0_mode { // SP1 mode - matches Python implementation exactly let (_vkey, public_values) = self.vkey_public_values_sp1.as_ref().unwrap(); // public_inputs[0] is the vkey as BigUint - serialize as 2 limbs of 128 bits // This matches Python: cd.extend(io.bigint_split(self.public_inputs[0], 2, 2**128)) let vkey_int = &self.public_inputs[0]; // This should already be the vkey as BigUint let vkey_limbs = biguint_split::<2, 128>(vkey_int); cd.extend(vkey_limbs.iter().map(|&x| BigUint::from(x))); // Serialize public_values (public_inputs_sp1) as u32 array // This matches Python SP1 serialization exactly let n_bytes = public_values.len(); assert_eq!( n_bytes % 32, 0, "SP1 public inputs must be a multiple of 32 bytes" ); let n_words = n_bytes / 32; // Add number of words first (matches Python: cd.append(n_words)) cd.push(BigUint::from(n_words)); // Then serialize as u32 values (matches Python: for i in range(0, n_bytes, 4): cd.append(int.from_bytes(...))) for i in (0..n_bytes).step_by(4) { let word = u32::from_be_bytes([ public_values[i], public_values[i + 1], public_values[i + 2], public_values[i + 3], ]); cd.push(BigUint::from(word)); } } else if risc0_mode && _sp1_mode { panic!("Cannot have both RISC0 and SP1 modes enabled"); } else { // Normal mode. cd.push(BigUint::from(self.public_inputs.len())); for pub_input in &self.public_inputs { cd.extend( biguint_split::<2, 128>(pub_input) .iter() .map(|&x| BigUint::from(x)), ); } } cd } pub fn from_risc0(seal: Vec, image_id: Vec, journal: Vec) -> Self { assert!(image_id.len() <= 32, "image_id must be 32 bytes"); let (control_root, bn254_control_id) = get_risc0_constants(); let (control_root_0, control_root_1) = risc0_utils::split_digest(&control_root); let proof = &seal[4..]; let mut hasher = Sha256::new(); hasher.update(&journal); let journal_digest = hasher.finalize(); let claim_digest = risc0_utils::ok_digest(&image_id, &journal_digest); let claim_digest_biguint = BigUint::from_bytes_be(&claim_digest); let (claim0, claim1) = risc0_utils::split_digest(&claim_digest_biguint); Groth16Proof { a: G1PointBigUint { x: BigUint::from_bytes_be(&proof[0..32]), y: BigUint::from_bytes_be(&proof[32..64]), }, b: G2PointBigUint { x0: BigUint::from_bytes_be(&proof[96..128]), x1: BigUint::from_bytes_be(&proof[64..96]), y0: BigUint::from_bytes_be(&proof[160..192]), y1: BigUint::from_bytes_be(&proof[128..160]), }, c: G1PointBigUint { x: BigUint::from_bytes_be(&proof[192..224]), y: BigUint::from_bytes_be(&proof[224..256]), }, public_inputs: vec![ control_root_0, control_root_1, claim0, claim1, bn254_control_id, ], image_id_journal_risc0: Some((image_id, journal)), vkey_public_values_sp1: None, } } pub fn from_sp1(vkey: Vec, public_values: Vec, proof: Vec) -> Self { // Skip the first 4 bytes (selector) let selector = &proof[..4]; let proof = &proof[4..]; // Validate SP1 verifier version by checking selector against expected hash let expected_selector = hex::decode(&SP1_VERIFIER_HASH[2..]).unwrap()[..4].to_vec(); if selector != expected_selector { panic!( "Invalid SP1 proof version. Expected {:02x}{:02x}{:02x}{:02x} for version {}, got {:02x}{:02x}{:02x}{:02x}\nPlease use SP1 verifier version {} or contact garaga developers to update the SP1 verifier version.", expected_selector[0], expected_selector[1], expected_selector[2], expected_selector[3], SP1_VERIFIER_VERSION, selector[0], selector[1], selector[2], selector[3], SP1_VERIFIER_VERSION ); } // sha256(public_values) % 2**253 assert!( public_values.len().is_multiple_of(32), "public_values must be a multiple of 32 bytes" ); let pub_input_hash = BigUint::from_bytes_be(&Sha256::digest(&public_values)); // 2^253 as BigUint to avoid overflow let modulus = BigUint::from(2u64).pow(253); let pub_input_hash = pub_input_hash % modulus; let mut public_inputs_sp1 = Vec::new(); for i in 0..public_values.len() / 32 { let public_input = BigUint::from_bytes_be(&public_values[i * 32..(i + 1) * 32]); public_inputs_sp1.push(public_input); } Groth16Proof { a: G1PointBigUint { x: BigUint::from_bytes_be(&proof[0..32]), y: BigUint::from_bytes_be(&proof[32..64]), }, b: G2PointBigUint { x0: BigUint::from_bytes_be(&proof[96..128]), x1: BigUint::from_bytes_be(&proof[64..96]), y0: BigUint::from_bytes_be(&proof[160..192]), y1: BigUint::from_bytes_be(&proof[128..160]), }, c: G1PointBigUint { x: BigUint::from_bytes_be(&proof[192..224]), y: BigUint::from_bytes_be(&proof[224..256]), }, public_inputs: vec![BigUint::from_bytes_be(&vkey), pub_input_hash], image_id_journal_risc0: None, vkey_public_values_sp1: Some((vkey, public_values)), } } } #[derive(Debug, PartialEq)] pub struct Groth16VerificationKey { pub alpha: G1PointBigUint, pub beta: G2PointBigUint, pub gamma: G2PointBigUint, pub delta: G2PointBigUint, pub ic: Vec, } impl Groth16VerificationKey { pub fn from(values: Vec) -> Self { let alpha = G1PointBigUint::from(values[0..2].to_vec()); let beta = G2PointBigUint::from(values[2..6].to_vec()); let gamma = G2PointBigUint::from(values[6..10].to_vec()); let delta = G2PointBigUint::from(values[10..14].to_vec()); let ic = values[14..] .chunks(2) .map(|chunk| G1PointBigUint::from(chunk.to_vec())) .collect(); Groth16VerificationKey { alpha, beta, gamma, delta, ic, } } } pub fn get_sp1_vk() -> Groth16VerificationKey { let vk_hex = [ "2d4d9aa7e302d9df41749d5507949d05dbea33fbb16c643b22f599a2be6df2e2", "14bedd503c37ceb061d8ec60209fe345ce89830a19230301f076caff004d1926", "e187847ad4c798374d0d6732bf501847dd68bc0e071241e0213bc7fc13db7ab", "967032fcbf776d1afc985f88877f182d38480a653f2decaa9794cbc3bf3060c", "1739c1b1a457a8c7313123d24d2f9192f896b7c63eea05a9d57f06547ad0cec8", "304cfbd1e08a704a99f5e847d93f8c3caafddec46b7a0d379da69a4d112346a7", "1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa", "90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", "3ff41f4ba0c37fe2caf27354d28e4b8f83d3b76777a63b327d736bffb0122ed", "1cc7cb8de715675f21f01ecc9b46d236e0865e0cc020024521998269845f74e6", "17387b4b9cf03927909b4f1c3d80fcd6865afc4a264a04499f7e2f6df690dd85", "2ed3b19b5eb39db0d19a3d72dcd590ac85a971def614f4fd11b56b3c5e53c44c", "26091e1cafb0ad8a4ea0a694cd3743ebf524779233db734c451d28b58aa9758e", "9ff50a6b8b11c3ca6fdb2690a124f8ce25489fefa65a3e782e7ba70b66690e", "61c3fd0fd3da25d2607c227d090cca750ed36c6ec878755e537c1c48951fb4c", "fa17ae9c2033379df7b5c65eff0e107055e9a273e6119a212dd09eb51707219", "4eab241388a79817fe0e0e2ead0b2ec4ffdec51a16028dee020634fd129e71c", "7236256d21c60d02f0bdbf95cff83e03ea9e16fca56b18d5544b0889a65c1f5", ]; Groth16VerificationKey::from( vk_hex .iter() .map(|s| BigUint::from_str_radix(s, 16).unwrap()) .collect::>(), ) } pub fn get_groth16_calldata_felt( proof: &Groth16Proof, vk: &Groth16VerificationKey, curve_id: CurveID, ) -> Result, String> { let calldata = get_groth16_calldata(proof, vk, curve_id)?; Ok(calldata.into_iter().map(Felt::from).collect()) } pub fn get_groth16_calldata( proof: &Groth16Proof, vk: &Groth16VerificationKey, curve_id: CurveID, ) -> Result, String> { let mut calldata: Vec = Vec::new(); let risc0_mode = proof.image_id_journal_risc0.is_some(); let _sp1_mode = proof.vkey_public_values_sp1.is_some(); // Calculate vk_x let vk_x = calculate_vk_x(vk, &proof.public_inputs, curve_id); // MPC calldata let mut mpc_values: Vec = vec![]; mpc_values.extend(vk_x.flatten()); mpc_values.extend(vk.gamma.flatten()); mpc_values.extend(proof.c.flatten()); mpc_values.extend(vk.delta.flatten()); mpc_values.extend(proof.a.neg(curve_id).flatten()); mpc_values.extend(proof.b.flatten()); let mut mpc_public_pair: Vec = vec![]; mpc_public_pair.extend(vk.alpha.flatten()); mpc_public_pair.extend(vk.beta.flatten()); let mpc_calldata = mpc_calldata_builder(curve_id as usize, &mpc_values, 2, &mpc_public_pair)?; // MSM calldata let msm_calldata = match risc0_mode { false => msm_calldata_builder( &vk.ic .iter() .skip(1) .flat_map(|point| vec![point.x.clone(), point.y.clone()]) .collect::>(), &proof.public_inputs, curve_id as usize, false, true, )?, true => msm_calldata_builder( &[ vk.ic[3].x.clone(), vk.ic[3].y.clone(), vk.ic[4].x.clone(), vk.ic[4].y.clone(), ], &[ proof.public_inputs[2].clone(), proof.public_inputs[3].clone(), ], curve_id as usize, false, true, )?, }; calldata.push(BigUint::from(0u64)); // Len Placeholder. calldata.extend(proof.serialize_to_calldata()); calldata.extend(mpc_calldata); calldata.extend(msm_calldata); // Update length calldata[0] = BigUint::from(calldata.len() - 1); Ok(calldata) } fn calculate_vk_x( vk: &Groth16VerificationKey, pub_inputs: &[BigUint], curve_id: CurveID, ) -> G1PointBigUint { match curve_id { CurveID::BN254 => vk_x_handle_curve::(vk, pub_inputs), CurveID::BLS12_381 => vk_x_handle_curve::(vk, pub_inputs), _ => panic!("Unsupported curve ID for vk_x"), } } fn vk_x_handle_curve(vk: &Groth16VerificationKey, pub_inputs: &[BigUint]) -> G1PointBigUint where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { // Parse IC points from BigUint to FieldElement let ic_elements = field_elements_from_big_uints::( &vk.ic .iter() .flat_map(|point| vec![point.x.clone(), point.y.clone()]) .collect::>(), ); let ic_points = parse_g1_points_from_flattened_field_elements_list(&ic_elements).unwrap(); // Start with IC[0] let mut vk_x = ic_points[0].clone(); // Compute IC[0] + pub_input_i * IC[i] for each public input for (i, pub_input) in pub_inputs.iter().enumerate() { let pub_input_bigint = BigInt::from_biguint(Sign::Plus, pub_input.clone()); let scaled_ic = ic_points[i + 1].scalar_mul(pub_input_bigint); vk_x = vk_x.add(&scaled_ic); } // Convert G1Point back to G1PointBigUint G1PointBigUint { x: element_to_biguint(&vk_x.x), y: element_to_biguint(&vk_x.y), } } pub mod risc0_utils { use super::Groth16VerificationKey; use hex; use num_bigint::BigUint; use num_traits::Num; use sha2::{Digest, Sha256}; pub fn get_risc0_vk() -> Groth16VerificationKey { let vk_hex = [ "2d4d9aa7e302d9df41749d5507949d05dbea33fbb16c643b22f599a2be6df2e2", "14bedd503c37ceb061d8ec60209fe345ce89830a19230301f076caff004d1926", "e187847ad4c798374d0d6732bf501847dd68bc0e071241e0213bc7fc13db7ab", "967032fcbf776d1afc985f88877f182d38480a653f2decaa9794cbc3bf3060c", "1739c1b1a457a8c7313123d24d2f9192f896b7c63eea05a9d57f06547ad0cec8", "304cfbd1e08a704a99f5e847d93f8c3caafddec46b7a0d379da69a4d112346a7", "1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa", "90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", "1aa085ff28179a12d922dba0547057ccaae94b9d69cfaa4e60401fea7f3e0333", "3b03cd5effa95ac9bee94f1f5ef907157bda4812ccf0b4c91f42bb629f83a1c", "1e60f31fcbf757e837e867178318832d0b2d74d59e2fea1c7142df187d3fc6d3", "110c10134f200b19f6490846d518c9aea868366efb7228ca5c91d2940d030762", "12ac9a25dcd5e1a832a9061a082c15dd1d61aa9c4d553505739d0f5d65dc3be4", "25aa744581ebe7ad91731911c898569106ff5a2d30f3eee2b23c60ee980acd4", "707b920bc978c02f292fae2036e057be54294114ccc3c8769d883f688a1423f", "2e32a094b7589554f7bc357bf63481acd2d55555c203383782a4650787ff6642", "bca36e2cbe6394b3e249751853f961511011c7148e336f4fd974644850fc347", "2ede7c9acf48cf3a3729fa3d68714e2a8435d4fa6db8f7f409c153b1fcdf9b8b", "1b8af999dbfbb3927c091cc2aaf201e488cbacc3e2c6b6fb5a25f9112e04f2a7", "2b91a26aa92e1b6f5722949f192a81c850d586d81a60157f3e9cf04f679cccd6", "2b5f494ed674235b8ac1750bdfd5a7615f002d4a1dcefeddd06eda5a076ccd0d", "2fe520ad2020aab9cbba817fcbb9a863b8a76ff88f14f912c5e71665b2ad5e82", "f1c3c0d5d9da0fa03666843cde4e82e869ba5252fce3c25d5940320b1c4d493", "214bfcff74f425f6fe8c0d07b307482d8bc8bb2f3608f68287aa01bd0b69e809", ]; Groth16VerificationKey::from( vk_hex .iter() .map(|s| BigUint::from_str_radix(s, 16).unwrap()) .collect::>(), ) } pub fn split_digest(digest: &BigUint) -> (BigUint, BigUint) { // Convert to bytes, ensure 32 bytes, and reverse let mut bytes = digest.to_bytes_be(); bytes.resize(32, 0); bytes.reverse(); // Split into two 128-bit parts let lower = BigUint::from_bytes_be(&bytes[0..16]); let upper = BigUint::from_bytes_be(&bytes[16..32]); (upper, lower) } struct ExitCode { system: u32, user: u32, } struct Output { journal_digest: Vec, assumptions_digest: Vec, } impl Output { fn digest(&self) -> Vec { let mut hasher = Sha256::new(); hasher.update(Sha256::digest(b"risc0.Output")); hasher.update(&self.journal_digest); hasher.update(&self.assumptions_digest); hasher.update((2u16 << 8).to_be_bytes()); hasher.finalize().to_vec() } } struct ReceiptClaim { pre_state_digest: Vec, post_state_digest: Vec, exit_code: ExitCode, input: Vec, output: Vec, tag_digest: Vec, } impl ReceiptClaim { fn digest(&self) -> Vec { let mut hasher = Sha256::new(); hasher.update(&self.tag_digest); hasher.update(&self.input); hasher.update(&self.pre_state_digest); hasher.update(&self.post_state_digest); hasher.update(&self.output); hasher.update((self.exit_code.system << 24).to_be_bytes()); hasher.update((self.exit_code.user << 24).to_be_bytes()); hasher.update((4u16 << 8).to_be_bytes()); hasher.finalize().to_vec() } } pub fn ok_digest(image_id: &[u8], journal_digest: &[u8]) -> Vec { let system_state_zero_digest = hex::decode("A3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2") .unwrap(); let output = Output { journal_digest: journal_digest.to_vec(), assumptions_digest: vec![0; 32], }; let receipt_claim = ReceiptClaim { pre_state_digest: image_id.to_vec(), post_state_digest: system_state_zero_digest, exit_code: ExitCode { system: 0, user: 0 }, input: vec![0; 32], output: output.digest(), tag_digest: Sha256::digest(b"risc0.ReceiptClaim").to_vec(), }; receipt_claim.digest() } } #[cfg(test)] mod test_groth16_calldata { use super::risc0_utils::{ok_digest, split_digest}; use super::Groth16Proof; use hex; use num_bigint::BigUint; use sha2::{Digest, Sha256}; #[test] fn test_ok_digest_1() { let image_id = vec![ 0xd0, 0x1c, 0x15, 0xaf, 0xa7, 0x68, 0xa0, 0x5b, 0x21, 0x3a, 0x9e, 0x5f, 0xcd, 0xcc, 0x57, 0x24, 0xa2, 0x94, 0x7e, 0x00, 0x09, 0x8c, 0x7e, 0xc3, 0x4c, 0xcb, 0xe2, 0x94, 0x6b, 0xbc, 0x00, 0x13, ]; let journal = vec![ 0x6a, 0x75, 0x73, 0x74, 0x20, 0x61, 0x20, 0x73, 0x69, 0x6d, 0x70, 0x6c, 0x65, 0x20, 0x72, 0x65, 0x63, 0x65, 0x69, 0x70, 0x74, ]; let journal_digest = Sha256::digest(&journal); let digest = ok_digest(&image_id, &journal_digest); let (claim0, claim1) = split_digest(&BigUint::from_bytes_be(&digest)); assert_eq!( hex::encode(digest), "e58e40abecebcfa4af85692fca5ed77d4ccb4b3f640f5e684e4faf3a36b0c4e0" ); assert_eq!( hex::encode(claim0.to_bytes_be()), "7dd75eca2f6985afa4cfebecab408ee5" ); assert_eq!( hex::encode(claim1.to_bytes_be()), "e0c4b0363aaf4f4e685e0f643f4bcb4c" ); } #[test] fn test_ok_digest_2() { let image_id = vec![ 0x07, 0x9f, 0x23, 0xf1, 0x3e, 0xa8, 0x1b, 0xde, 0x11, 0xa9, 0x49, 0x12, 0xba, 0xdf, 0xe8, 0xd9, 0x2d, 0x5b, 0xe1, 0x13, 0x4b, 0x2c, 0x99, 0x1b, 0x99, 0x55, 0xe9, 0xc1, 0x89, 0x41, 0xba, 0x69, ]; let journal: Vec = vec![0x01, 0x00, 0x00, 0x78]; let journal_digest = Sha256::digest(&journal); let digest = ok_digest(&image_id, &journal_digest); let (claim0, claim1) = split_digest(&BigUint::from_bytes_be(&digest)); assert_eq!( hex::encode(claim0.to_bytes_be()), "d284212f0d87311c45e710301d86639f" ); assert_eq!( hex::encode(claim1.to_bytes_be()), "8875bcad22cdcfda1e2878df4e414108" ); } #[test] #[should_panic(expected = "Invalid SP1 proof version")] fn test_from_sp1_invalid_selector() { // Create test data with invalid selector (wrong first 4 bytes) let vkey = vec![0u8; 32]; let public_values = vec![0u8; 64]; // Must be multiple of 32 let mut proof = vec![0xde, 0xad, 0xbe, 0xef]; // Invalid selector proof.extend(vec![0u8; 252]); // Add remaining proof data // This should panic with our error message Groth16Proof::from_sp1(vkey, public_values, proof); } } ================================================ FILE: tools/garaga_rs/src/calldata/full_proof_with_hints/zk_honk.rs ================================================ use crate::algebra::g1g2pair::G1G2Pair; use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::calldata::mpc_calldata; use crate::calldata::msm_calldata; use crate::calldata::G1PointBigUint; use crate::definitions::BN254PrimeField; use crate::definitions::CurveID; use crate::definitions::FieldElement; use crate::definitions::GrumpkinPrimeField; use crate::definitions::Stark252PrimeField; use crate::io::{element_from_biguint, element_to_biguint, field_element_to_u256_limbs}; use lambdaworks_crypto::hash::poseidon::starknet::PoseidonCairoStark252; use lambdaworks_crypto::hash::poseidon::Poseidon; use lambdaworks_math::field::errors::FieldError; use lambdaworks_math::field::traits::IsPrimeField; use lambdaworks_math::traits::ByteConversion; use num_bigint::BigUint; use sha3::{Digest, Keccak256}; pub const NUMBER_OF_SUBRELATIONS: usize = 28; pub const NUMBER_OF_ALPHAS: usize = NUMBER_OF_SUBRELATIONS - 1; pub const NUMBER_OF_ENTITIES: usize = 41; pub const NUMBER_UNSHIFTED: usize = 36; pub const NUMBER_TO_BE_SHIFTED: usize = 5; pub const SHIFTED_COMMITMENTS_START: usize = 30; pub const MAX_LOG_N: usize = 23; pub const MAX_CIRCUIT_SIZE: usize = 1 << MAX_LOG_N; pub const PAIRING_POINT_OBJECT_LENGTH: usize = 16; pub const CONST_PROOF_SIZE_LOG_N: usize = 28; pub const NUM_WITNESS_ENTITIES: usize = 8; pub const NUM_ELEMENTS_COMM: usize = 2; pub const NUM_ELEMENTS_FR: usize = 1; /// Calculate expected proof size based on log_circuit_size pub fn calculate_proof_size(log_circuit_size: usize) -> usize { let mut proof_size = NUM_WITNESS_ENTITIES * NUM_ELEMENTS_COMM; // 16 proof_size += NUM_ELEMENTS_COMM * 4; // 8 (Libra concat, grand sum, quotient comms + Gemini masking) proof_size += log_circuit_size * ZK_BATCHED_RELATION_PARTIAL_LENGTH * NUM_ELEMENTS_FR; // sumcheck univariates proof_size += NUMBER_OF_ENTITIES * NUM_ELEMENTS_FR; // 41 (sumcheck evaluations) proof_size += NUM_ELEMENTS_FR * 3; // 3 (Libra sum, claimed eval, Gemini masking eval) proof_size += log_circuit_size * NUM_ELEMENTS_FR; // Gemini a evaluations proof_size += LIBRA_EVALUATIONS * NUM_ELEMENTS_FR; // 4 (libra evaluations) proof_size += (log_circuit_size - 1) * NUM_ELEMENTS_COMM; // Gemini Fold commitments proof_size += NUM_ELEMENTS_COMM * 2; // 4 (Shplonk Q and KZG W) proof_size += PAIRING_POINT_OBJECT_LENGTH; // 16 (pairing inputs) proof_size } pub const ZK_BATCHED_RELATION_PARTIAL_LENGTH: usize = 9; pub const SUBGROUP_SIZE: usize = 256; pub const LIBRA_COMMITMENTS: usize = 3; pub const LIBRA_EVALUATIONS: usize = 4; pub const LIBRA_UNIVARIATES_LENGTH: usize = 9; // Number of G1 points in the VK pub const VK_NUM_POINTS: usize = 28; pub struct HonkVerificationKey { pub log_circuit_size: usize, pub public_inputs_size: usize, pub public_inputs_offset: usize, pub qm: G1PointBigUint, pub qc: G1PointBigUint, pub ql: G1PointBigUint, pub qr: G1PointBigUint, pub qo: G1PointBigUint, pub q4: G1PointBigUint, pub q_lookup: G1PointBigUint, pub q_arith: G1PointBigUint, pub q_delta_range: G1PointBigUint, pub q_elliptic: G1PointBigUint, pub q_memory: G1PointBigUint, pub q_nnf: G1PointBigUint, pub q_poseidon2_external: G1PointBigUint, pub q_poseidon2_internal: G1PointBigUint, pub s1: G1PointBigUint, pub s2: G1PointBigUint, pub s3: G1PointBigUint, pub s4: G1PointBigUint, pub id1: G1PointBigUint, pub id2: G1PointBigUint, pub id3: G1PointBigUint, pub id4: G1PointBigUint, pub t1: G1PointBigUint, pub t2: G1PointBigUint, pub t3: G1PointBigUint, pub t4: G1PointBigUint, pub lagrange_first: G1PointBigUint, pub lagrange_last: G1PointBigUint, pub vk_hash: BigUint, } impl HonkVerificationKey { pub fn from_bytes(vk_bytes: &[u8]) -> Result { // VK format: 3 * 32 bytes for log_circuit_size, public_inputs_size, public_inputs_offset // then 28 * 64 bytes for G1 points let expected_len = 3 * 32 + VK_NUM_POINTS * 64; if vk_bytes.len() != expected_len { return Err(format!( "Invalid input length: {} (expected {})", vk_bytes.len(), expected_len )); } // Compute vk_hash using keccak256, then mod by BN254 curve order let vk_hash_bytes = Keccak256::digest(vk_bytes); let vk_hash_full = BigUint::from_bytes_be(&vk_hash_bytes); // BN254 curve order (n) let bn254_n = BigUint::parse_bytes( b"30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001", 16, ) .unwrap(); let vk_hash = vk_hash_full % bn254_n; // Parse header fields (32 bytes each) let log_circuit_size = BigUint::from_bytes_be(&vk_bytes[0..32]); let public_inputs_size = BigUint::from_bytes_be(&vk_bytes[32..64]); let public_inputs_offset = BigUint::from_bytes_be(&vk_bytes[64..96]); let log_circuit_size: usize = log_circuit_size .try_into() .map_err(|e: num_bigint::TryFromBigIntError| e.to_string())?; let public_inputs_size: usize = public_inputs_size .try_into() .map_err(|e: num_bigint::TryFromBigIntError| e.to_string())?; let public_inputs_offset: usize = public_inputs_offset .try_into() .map_err(|e: num_bigint::TryFromBigIntError| e.to_string())?; if public_inputs_offset != 1 { return Err(format!( "Invalid public inputs offset: {}", public_inputs_offset )); } if log_circuit_size > CONST_PROOF_SIZE_LOG_N { return Err(format!("Invalid log circuit size: {}", log_circuit_size)); } if public_inputs_size < PAIRING_POINT_OBJECT_LENGTH { return Err(format!( "Invalid public inputs size: {}", public_inputs_size )); } // Parse G1 points (64 bytes each: 32 for x, 32 for y) let mut cursor = 96; let mut points = vec![]; for _ in 0..VK_NUM_POINTS { let x = BigUint::from_bytes_be(&vk_bytes[cursor..cursor + 32]); let y = BigUint::from_bytes_be(&vk_bytes[cursor + 32..cursor + 64]); points.push(G1PointBigUint { x, y }); cursor += 64; } let [qm, qc, ql, qr, qo, q4, q_lookup, q_arith, q_delta_range, q_elliptic, q_memory, q_nnf, q_poseidon2_external, q_poseidon2_internal, s1, s2, s3, s4, id1, id2, id3, id4, t1, t2, t3, t4, lagrange_first, lagrange_last] = points.try_into().unwrap(); Ok(Self { log_circuit_size, public_inputs_size, public_inputs_offset, qm, qc, ql, qr, qo, q4, q_lookup, q_arith, q_delta_range, q_elliptic, q_memory, q_nnf, q_poseidon2_external, q_poseidon2_internal, s1, s2, s3, s4, id1, id2, id3, id4, t1, t2, t3, t4, lagrange_first, lagrange_last, vk_hash, }) } } pub trait Hasher { fn reset(&mut self); fn digest_as_bytes(&self) -> Vec; fn update_bytes(&mut self, data: &[u8]); fn digest(&self) -> BigUint { let bytes = self.digest_as_bytes(); BigUint::from_bytes_be(&bytes) } fn digest_reset(&mut self) -> Vec { let result = self.digest_as_bytes(); self.reset(); result } fn update(&mut self, value: &BigUint) { // Pad to 32 bytes let mut bytes = value.to_bytes_be(); while bytes.len() < 32 { bytes.insert(0, 0); } self.update_bytes(&bytes); } fn update_point(&mut self, point: &G1PointBigUint) { self.update(&point.x); self.update(&point.y); } } pub struct KeccakHasher { data: Vec, } impl Default for KeccakHasher { fn default() -> Self { Self::new() } } impl KeccakHasher { pub fn new() -> Self { KeccakHasher { data: vec![] } } } impl Hasher for KeccakHasher { fn reset(&mut self) { self.data = vec![]; } fn update_bytes(&mut self, data: &[u8]) { self.data.extend_from_slice(data); } fn digest_as_bytes(&self) -> Vec { let hash = Keccak256::digest(&self.data); let hash_int = BigUint::from_bytes_be(&hash); // Reduce modulo Grumpkin field prime (same as BN254 curve order) let grumpkin_p = BigUint::parse_bytes( b"30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001", 16, ) .unwrap(); let reduced = hash_int % grumpkin_p; // Convert back to 32 bytes let mut bytes = reduced.to_bytes_be(); while bytes.len() < 32 { bytes.insert(0, 0); } bytes } } pub struct ZKHonkProof { pub public_inputs: Vec, pub pairing_point_object: [BigUint; PAIRING_POINT_OBJECT_LENGTH], pub w1: G1PointBigUint, pub w2: G1PointBigUint, pub w3: G1PointBigUint, pub w4: G1PointBigUint, pub z_perm: G1PointBigUint, pub lookup_read_counts: G1PointBigUint, pub lookup_read_tags: G1PointBigUint, pub lookup_inverses: G1PointBigUint, pub libra_commitments: [G1PointBigUint; 3], pub libra_sum: BigUint, pub sumcheck_univariates: [[BigUint; ZK_BATCHED_RELATION_PARTIAL_LENGTH]; CONST_PROOF_SIZE_LOG_N], pub sumcheck_evaluations: [BigUint; NUMBER_OF_ENTITIES], pub libra_evaluation: BigUint, pub gemini_masking_poly: G1PointBigUint, pub gemini_masking_eval: BigUint, pub gemini_fold_comms: [G1PointBigUint; CONST_PROOF_SIZE_LOG_N - 1], pub gemini_a_evaluations: [BigUint; CONST_PROOF_SIZE_LOG_N], pub libra_poly_evals: [BigUint; 4], pub shplonk_q: G1PointBigUint, pub kzg_quotient: G1PointBigUint, } impl ZKHonkProof { pub fn from_bytes( proof_bytes: &[u8], public_inputs_bytes: &[u8], log_circuit_size: usize, ) -> Result { let expected_proof_size = calculate_proof_size(log_circuit_size); if proof_bytes.len() != 32 * expected_proof_size { return Err(format!( "Invalid proof bytes length: {} (expected {})", proof_bytes.len(), 32 * expected_proof_size )); } let mut values = vec![]; for i in (0..).step_by(32).take(expected_proof_size) { values.push(BigUint::from_bytes_be(&proof_bytes[i..i + 32])); } if !public_inputs_bytes.len().is_multiple_of(32) { return Err(format!( "Invalid public input bytes length: {}", public_inputs_bytes.len() )); } let public_inputs_size = public_inputs_bytes.len() / 32; let mut public_inputs = vec![]; for i in (0..).step_by(32).take(public_inputs_size) { public_inputs.push(BigUint::from_bytes_be(&public_inputs_bytes[i..i + 32])); } Self::from(values, public_inputs, log_circuit_size) } pub fn from( values: Vec, public_inputs: Vec, log_circuit_size: usize, ) -> Result { let expected_proof_size = calculate_proof_size(log_circuit_size); if values.len() != expected_proof_size { return Err(format!( "Invalid proof length: {} (expected {})", values.len(), expected_proof_size )); } let mut offset = 0; // Parse pairing point object let pairing_point_object: [BigUint; PAIRING_POINT_OBJECT_LENGTH] = values [offset..offset + PAIRING_POINT_OBJECT_LENGTH] .to_vec() .try_into() .unwrap(); offset += PAIRING_POINT_OBJECT_LENGTH; fn parse_g1_proof_point(values: [BigUint; 2]) -> G1PointBigUint { let [x, y] = values; G1PointBigUint { x, y } } // Parse 9 G1 points: w1, w2, w3, lookup_read_counts, lookup_read_tags, w4, lookup_inverses, z_perm, libra_commitment_0 let mut points = vec![]; for i in (offset..).step_by(2).take(9) { points.push(parse_g1_proof_point( values[i..i + 2].to_vec().try_into().unwrap(), )); } offset += 9 * 2; let [w1, w2, w3, lookup_read_counts, lookup_read_tags, w4, lookup_inverses, z_perm, libra_commitment_0] = points.try_into().unwrap(); let libra_sum = values[offset].clone(); offset += 1; // Parse sumcheck univariates let mut sumcheck_univariates = vec![]; for i in (offset..) .step_by(ZK_BATCHED_RELATION_PARTIAL_LENGTH) .take(log_circuit_size) { sumcheck_univariates.push( values[i..i + ZK_BATCHED_RELATION_PARTIAL_LENGTH] .to_vec() .try_into() .unwrap(), ); } // Fill rest with zeros while sumcheck_univariates.len() < CONST_PROOF_SIZE_LOG_N { sumcheck_univariates.push([0u8; ZK_BATCHED_RELATION_PARTIAL_LENGTH].map(BigUint::from)); } let sumcheck_univariates: [[BigUint; ZK_BATCHED_RELATION_PARTIAL_LENGTH]; CONST_PROOF_SIZE_LOG_N] = sumcheck_univariates.try_into().unwrap(); offset += log_circuit_size * ZK_BATCHED_RELATION_PARTIAL_LENGTH; // Parse sumcheck evaluations let sumcheck_evaluations: [BigUint; NUMBER_OF_ENTITIES] = values [offset..offset + NUMBER_OF_ENTITIES] .to_vec() .try_into() .unwrap(); offset += NUMBER_OF_ENTITIES; let libra_evaluation = values[offset].clone(); offset += 1; // Parse libra_commitment_1, libra_commitment_2, gemini_masking_poly let mut points = vec![]; for i in (offset..).step_by(2).take(3) { points.push(parse_g1_proof_point( values[i..i + 2].to_vec().try_into().unwrap(), )); } offset += 3 * 2; let [libra_commitment_1, libra_commitment_2, gemini_masking_poly] = points.try_into().unwrap(); let libra_commitments = [libra_commitment_0, libra_commitment_1, libra_commitment_2]; let gemini_masking_eval = values[offset].clone(); offset += 1; // Parse gemini fold comms let mut gemini_fold_comms = vec![]; for i in (offset..).step_by(2).take(log_circuit_size - 1) { gemini_fold_comms.push(parse_g1_proof_point( values[i..i + 2].to_vec().try_into().unwrap(), )); } // Fill rest with dummy points while gemini_fold_comms.len() < CONST_PROOF_SIZE_LOG_N - 1 { gemini_fold_comms.push(G1PointBigUint { x: BigUint::from(0u8), y: BigUint::from(0u8), }); } let gemini_fold_comms: [G1PointBigUint; CONST_PROOF_SIZE_LOG_N - 1] = gemini_fold_comms.try_into().unwrap(); offset += (log_circuit_size - 1) * 2; // Parse gemini a evaluations let mut gemini_a_evaluations = values[offset..offset + log_circuit_size].to_vec(); // Fill rest with zeros while gemini_a_evaluations.len() < CONST_PROOF_SIZE_LOG_N { gemini_a_evaluations.push(BigUint::from(0u8)); } let gemini_a_evaluations: [BigUint; CONST_PROOF_SIZE_LOG_N] = gemini_a_evaluations.try_into().unwrap(); offset += log_circuit_size; let libra_poly_evals: [BigUint; 4] = values[offset..offset + 4].to_vec().try_into().unwrap(); offset += 4; // Parse shplonk_q, kzg_quotient let mut points = vec![]; for i in (offset..).step_by(2).take(2) { points.push(parse_g1_proof_point( values[i..i + 2].to_vec().try_into().unwrap(), )); } let [shplonk_q, kzg_quotient] = points.try_into().unwrap(); offset += 2 * 2; assert_eq!(offset, expected_proof_size); Ok(Self { public_inputs, pairing_point_object, w1, w2, w3, w4, z_perm, lookup_read_counts, lookup_read_tags, lookup_inverses, libra_commitments, libra_sum, sumcheck_univariates, sumcheck_evaluations, libra_evaluation, gemini_masking_poly, gemini_masking_eval, gemini_fold_comms, gemini_a_evaluations, libra_poly_evals, shplonk_q, kzg_quotient, }) } } pub struct ZKHonkTranscript { pub eta: BigUint, pub eta_two: BigUint, pub eta_three: BigUint, pub beta: BigUint, pub gamma: BigUint, pub alpha: BigUint, pub gate_challenge: BigUint, pub libra_challenge: BigUint, pub sumcheck_u_challenges: [BigUint; CONST_PROOF_SIZE_LOG_N], pub rho: BigUint, pub gemini_r: BigUint, pub shplonk_nu: BigUint, pub shplonk_z: BigUint, } impl ZKHonkTranscript { pub fn from_proof( vk: &HonkVerificationKey, proof: &ZKHonkProof, ) -> Result< ( Self, FieldElement, FieldElement, ), String, > { if proof.public_inputs.len() != vk.public_inputs_size - PAIRING_POINT_OBJECT_LENGTH { return Err(format!( "Public inputs length mismatch: proof {}, vk {}", proof.public_inputs.len(), vk.public_inputs_size - PAIRING_POINT_OBJECT_LENGTH )); } Ok(compute_zk_transcript(vk, proof, KeccakHasher::new())) } } pub fn get_zk_honk_calldata( proof: &ZKHonkProof, vk: &HonkVerificationKey, ) -> Result, String> { let (transcript, transcript_state, _) = ZKHonkTranscript::from_proof(vk, proof)?; fn element_on_curve(element: &BigUint) -> FieldElement { element_from_biguint(element) } fn g1_point_on_curve(point: &G1PointBigUint) -> Result, String> { G1Point::new( element_from_biguint(&point.x), element_from_biguint(&point.y), false, ) } let public_inputs: Vec> = proof.public_inputs.iter().map(element_on_curve).collect(); let pairing_point_object: Vec> = proof .pairing_point_object .iter() .map(element_on_curve) .collect(); let w1 = g1_point_on_curve(&proof.w1)?; let w2 = g1_point_on_curve(&proof.w2)?; let w3 = g1_point_on_curve(&proof.w3)?; let w4 = g1_point_on_curve(&proof.w4)?; let z_perm = g1_point_on_curve(&proof.z_perm)?; let lookup_read_counts = g1_point_on_curve(&proof.lookup_read_counts)?; let lookup_read_tags = g1_point_on_curve(&proof.lookup_read_tags)?; let lookup_inverses = g1_point_on_curve(&proof.lookup_inverses)?; let libra_commitments: Vec> = proof .libra_commitments .iter() .map(g1_point_on_curve) .collect::, _>>()?; let libra_sum = element_on_curve(&proof.libra_sum); let sumcheck_univariates: Vec>> = proof .sumcheck_univariates .iter() .map(|v| v.iter().map(element_on_curve).collect()) .collect(); let sumcheck_evaluations: [FieldElement; NUMBER_OF_ENTITIES] = proof .sumcheck_evaluations .iter() .map(element_on_curve) .collect::>() .try_into() .unwrap(); let libra_evaluation = element_on_curve(&proof.libra_evaluation); let gemini_masking_poly = g1_point_on_curve(&proof.gemini_masking_poly)?; let gemini_masking_eval = element_on_curve(&proof.gemini_masking_eval); let gemini_fold_comms: Vec> = proof .gemini_fold_comms .iter() .map(g1_point_on_curve) .collect::, _>>()?; let gemini_a_evaluations: [FieldElement; CONST_PROOF_SIZE_LOG_N] = proof .gemini_a_evaluations .iter() .map(element_on_curve) .collect::>() .try_into() .unwrap(); let libra_poly_evals: [FieldElement; 4] = proof .libra_poly_evals .iter() .map(element_on_curve) .collect::>() .try_into() .unwrap(); let shplonk_q = g1_point_on_curve(&proof.shplonk_q)?; let kzg_quotient = g1_point_on_curve(&proof.kzg_quotient)?; let qm = g1_point_on_curve(&vk.qm)?; let qc = g1_point_on_curve(&vk.qc)?; let ql = g1_point_on_curve(&vk.ql)?; let qr = g1_point_on_curve(&vk.qr)?; let qo = g1_point_on_curve(&vk.qo)?; let q4 = g1_point_on_curve(&vk.q4)?; let q_lookup = g1_point_on_curve(&vk.q_lookup)?; let q_arith = g1_point_on_curve(&vk.q_arith)?; let q_delta_range = g1_point_on_curve(&vk.q_delta_range)?; let q_elliptic = g1_point_on_curve(&vk.q_elliptic)?; let q_memory = g1_point_on_curve(&vk.q_memory)?; let q_nnf = g1_point_on_curve(&vk.q_nnf)?; let q_poseidon2_external = g1_point_on_curve(&vk.q_poseidon2_external)?; let q_poseidon2_internal = g1_point_on_curve(&vk.q_poseidon2_internal)?; let s1 = g1_point_on_curve(&vk.s1)?; let s2 = g1_point_on_curve(&vk.s2)?; let s3 = g1_point_on_curve(&vk.s3)?; let s4 = g1_point_on_curve(&vk.s4)?; let id1 = g1_point_on_curve(&vk.id1)?; let id2 = g1_point_on_curve(&vk.id2)?; let id3 = g1_point_on_curve(&vk.id3)?; let id4 = g1_point_on_curve(&vk.id4)?; let t1 = g1_point_on_curve(&vk.t1)?; let t2 = g1_point_on_curve(&vk.t2)?; let t3 = g1_point_on_curve(&vk.t3)?; let t4 = g1_point_on_curve(&vk.t4)?; let lagrange_first = g1_point_on_curve(&vk.lagrange_first)?; let lagrange_last = g1_point_on_curve(&vk.lagrange_last)?; let sumcheck_u_challenges: [FieldElement; CONST_PROOF_SIZE_LOG_N] = transcript .sumcheck_u_challenges .iter() .map(element_on_curve) .collect::>() .try_into() .unwrap(); let rho = element_on_curve(&transcript.rho); let gemini_r = element_on_curve(&transcript.gemini_r); let shplonk_nu = element_on_curve(&transcript.shplonk_nu); let shplonk_z = element_on_curve(&transcript.shplonk_z); let consistent = check_evals_consistency( &libra_evaluation, &libra_poly_evals, &gemini_r, &sumcheck_u_challenges, vk.log_circuit_size, ) .map_err(|e| format!("Field error: {:?}", e))?; if !consistent { return Err("Consistency check failed".to_string()); } let scalars = extract_msm_scalars( vk.log_circuit_size, compute_shplemini_msm_scalars( vk.log_circuit_size, &sumcheck_evaluations, &gemini_masking_eval, &gemini_a_evaluations, &libra_poly_evals, &gemini_r, &rho, &shplonk_z, &shplonk_nu, &sumcheck_u_challenges, ) .map_err(|e| format!("Field error: {:?}", e))?, ); let mut scalars_msm = scalars; // Swap last two scalars let len = scalars_msm.len(); if len >= 2 { scalars_msm.swap(len - 1, len - 2); } // Place first scalar just after the vk_lagrange_last point (index 28) if !scalars_msm.is_empty() { let first_scalar = scalars_msm.remove(0); scalars_msm.insert(28, first_scalar); } let proof_data = { let mut call_data = vec![]; let call_data_ref = &mut call_data; fn push(call_data_ref: &mut Vec, value: T) where BigUint: From, { call_data_ref.push(value.into()); } fn push_element(call_data_ref: &mut Vec, element: &FieldElement) where F: IsPrimeField, FieldElement: ByteConversion, { let limbs = field_element_to_u256_limbs(element); for limb in limbs { push(call_data_ref, limb); } } fn push_elements( call_data_ref: &mut Vec, elements: &[FieldElement], prepend_length: bool, ) { if prepend_length { push(call_data_ref, elements.len()); } for element in elements { push_element(call_data_ref, element); } } fn push_point(call_data_ref: &mut Vec, point: &G1Point) { push_element(call_data_ref, &point.x); push_element(call_data_ref, &point.y); } push_elements(call_data_ref, &public_inputs, true); push_elements(call_data_ref, &pairing_point_object, true); push_point(call_data_ref, &w1); push_point(call_data_ref, &w2); push_point(call_data_ref, &w3); push_point(call_data_ref, &w4); push_point(call_data_ref, &z_perm); push_point(call_data_ref, &lookup_read_counts); push_point(call_data_ref, &lookup_read_tags); push_point(call_data_ref, &lookup_inverses); push(call_data_ref, libra_commitments.len()); for point in &libra_commitments { push_point(call_data_ref, point); } push_element(call_data_ref, &libra_sum); push_elements( call_data_ref, &(0..vk.log_circuit_size) .flat_map(|i| sumcheck_univariates[i].clone()) .collect::>(), true, ); push_elements(call_data_ref, &sumcheck_evaluations, true); push_element(call_data_ref, &libra_evaluation); push_point(call_data_ref, &gemini_masking_poly); push_element(call_data_ref, &gemini_masking_eval); push(call_data_ref, vk.log_circuit_size - 1); for point in &gemini_fold_comms[..vk.log_circuit_size - 1] { push_point(call_data_ref, point); } push_elements( call_data_ref, &gemini_a_evaluations[..vk.log_circuit_size], true, ); push_elements(call_data_ref, &libra_poly_evals, true); push_point(call_data_ref, &shplonk_q); push_point(call_data_ref, &kzg_quotient); call_data }; let mut points = vec![ qm, // 0 qc, // 1 ql, // 2 qr, // 3 qo, // 4 q4, // 5 q_lookup, // 6 q_arith, // 7 q_delta_range, // 8 q_elliptic, // 9 q_memory, // 10 q_nnf, // 11 q_poseidon2_external, // 12 q_poseidon2_internal, // 13 s1, // 14 s2, // 15 s3, // 16 s4, // 17 id1, // 18 id2, // 19 id3, // 20 id4, // 21 t1, // 22 t2, // 23 t3, // 24 t4, // 25 lagrange_first, // 26 lagrange_last, // 27 gemini_masking_poly, // 28 w1, // 29 w2, // 30 w3, // 31 w4, // 32 z_perm, // 33 lookup_inverses, // 34 lookup_read_counts, // 35 lookup_read_tags, // 36 ]; points.extend(gemini_fold_comms[0..vk.log_circuit_size - 1].to_vec()); points.extend(libra_commitments); points.push(kzg_quotient.clone()); points.push(G1Point::generator()); let two = FieldElement::::one().double(); let vk_hash_element: FieldElement = element_from_biguint(&vk.vk_hash); let mut state = [vk_hash_element, transcript_state, two]; PoseidonCairoStark252::hades_permutation(&mut state); let msm_data = msm_calldata::calldata_builder(&points, &scalars_msm, CurveID::BN254 as usize, false, true); let p_0 = G1Point::msm(&points, &scalars_msm).add(&shplonk_q); let p_1 = kzg_quotient.neg(); let g2_point_kzg_1 = G2Point::generator(); let g2_point_kzg_2 = G2Point::new( [ FieldElement::from_hex_unchecked( "0118C4D5B837BCC2BC89B5B398B5974E9F5944073B32078B7E231FEC938883B0", ), FieldElement::from_hex_unchecked( "260E01B251F6F1C7E7FF4E580791DEE8EA51D87A358E038B4EFE30FAC09383C1", ), ], [ FieldElement::from_hex_unchecked( "22FEBDA3C0C0632A56475B4214E5615E11E6DD3F96E6CEA2854A87D4DACC5E55", ), FieldElement::from_hex_unchecked( "04FC6369F7110FE3D25156C1BB9A72859CF2A04641F99BA4EE413C80DA6A5FE4", ), ], )?; let pairs = [ G1G2Pair::new(p_0, g2_point_kzg_1), G1G2Pair::new(p_1, g2_point_kzg_2), ]; let mpc_data = { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; mpc_calldata::calldata_builder::< true, BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&pairs, 2, &None)? }; let size = proof_data.len() + msm_data.len() + mpc_data.len(); let mut call_data = vec![size.into()]; call_data.extend(proof_data); call_data.extend(msm_data); call_data.extend(mpc_data); Ok(call_data) } #[allow(clippy::needless_range_loop)] fn compute_zk_transcript( vk: &HonkVerificationKey, proof: &ZKHonkProof, mut hasher: T, ) -> ( ZKHonkTranscript, FieldElement, FieldElement, ) { fn split(ch: &[u8]) -> [BigUint; 2] { let ch_int = BigUint::from_bytes_be(ch); let mask = (BigUint::from(1u8) << 128) - 1u8; let low_128 = &ch_int & &mask; let high_128 = &ch_int >> 128; [low_128, high_128] } // Round 0: vk_hash, public_inputs, pairing_point_object, w1, w2, w3 hasher.update(&vk.vk_hash); for pub_input in &proof.public_inputs { hasher.update(pub_input); } for pub_input in &proof.pairing_point_object { hasher.update(pub_input); } hasher.update_point(&proof.w1); hasher.update_point(&proof.w2); hasher.update_point(&proof.w3); let ch0 = hasher.digest_reset(); let [eta, eta_two] = split(&ch0); hasher.update_bytes(&ch0); let ch0 = hasher.digest_reset(); let [eta_three, _] = split(&ch0); // Round 1: ch0, lookup_read_counts, lookup_read_tags, w4 hasher.update_bytes(&ch0); hasher.update_point(&proof.lookup_read_counts); hasher.update_point(&proof.lookup_read_tags); hasher.update_point(&proof.w4); let ch1 = hasher.digest_reset(); let [beta, gamma] = split(&ch1); // Round 2: ch1, lookup_inverses, z_perm -> alpha hasher.update_bytes(&ch1); hasher.update_point(&proof.lookup_inverses); hasher.update_point(&proof.z_perm); let ch2 = hasher.digest_reset(); let [alpha, _] = split(&ch2); // Round 3: Gate challenge hasher.update_bytes(&ch2); let ch3 = hasher.digest_reset(); let [gate_challenge, _] = split(&ch3); // Round 3.5: Libra challenge hasher.update_bytes(&ch3); hasher.update_point(&proof.libra_commitments[0]); hasher.update(&proof.libra_sum); let ch3 = hasher.digest_reset(); let [libra_challenge, _] = split(&ch3); // Round 4: Sumcheck u challenges let mut sumcheck_u_challenges = [0u8; CONST_PROOF_SIZE_LOG_N].map(BigUint::from); let mut ch4 = ch3; for i in 0..vk.log_circuit_size { hasher.update_bytes(&ch4); for j in 0..ZK_BATCHED_RELATION_PARTIAL_LENGTH { hasher.update(&proof.sumcheck_univariates[i][j]); } ch4 = hasher.digest_reset(); let [challenge, _] = split(&ch4); sumcheck_u_challenges[i] = challenge; } // Rho challenge hasher.update_bytes(&ch4); for i in 0..NUMBER_OF_ENTITIES { hasher.update(&proof.sumcheck_evaluations[i]); } hasher.update(&proof.libra_evaluation); hasher.update_point(&proof.libra_commitments[1]); hasher.update_point(&proof.libra_commitments[2]); hasher.update_point(&proof.gemini_masking_poly); hasher.update(&proof.gemini_masking_eval); let c5 = hasher.digest_reset(); let [rho, _] = split(&c5); // Gemini R hasher.update_bytes(&c5); for i in 0..vk.log_circuit_size - 1 { hasher.update_point(&proof.gemini_fold_comms[i]); } let c6 = hasher.digest_reset(); let [gemini_r, _] = split(&c6); // Shplonk Nu hasher.update_bytes(&c6); for i in 0..vk.log_circuit_size { hasher.update(&proof.gemini_a_evaluations[i]); } for i in 0..4 { hasher.update(&proof.libra_poly_evals[i]); } let c7 = hasher.digest_reset(); let [shplonk_nu, _] = split(&c7); // Shplonk Z hasher.update_bytes(&c7); hasher.update_point(&proof.shplonk_q); let c8 = hasher.digest_reset(); let [shplonk_z_low, shplonk_z_high] = split(&c8); let mut state: [FieldElement; 3] = [ element_from_biguint(&shplonk_z_low), element_from_biguint(&shplonk_z_high), FieldElement::one().double(), ]; PoseidonCairoStark252::hades_permutation(&mut state); let [s0, s1, _] = state; ( ZKHonkTranscript { eta, eta_two, eta_three, beta, gamma, alpha, gate_challenge, libra_challenge, sumcheck_u_challenges, rho, gemini_r, shplonk_nu, shplonk_z: shplonk_z_low, }, s0, s1, ) } #[allow(clippy::needless_range_loop, clippy::too_many_arguments)] fn compute_shplemini_msm_scalars( log_circuit_size: usize, sumcheck_evaluations: &[FieldElement; NUMBER_OF_ENTITIES], gemini_masking_eval: &FieldElement, gemini_a_evaluations: &[FieldElement; CONST_PROOF_SIZE_LOG_N], libra_poly_evals: &[FieldElement; 4], gemini_r: &FieldElement, rho: &FieldElement, shplonk_z: &FieldElement, shplonk_nu: &FieldElement, sumcheck_u_challenges: &[FieldElement; CONST_PROOF_SIZE_LOG_N], ) -> Result< [Option; NUMBER_UNSHIFTED + CONST_PROOF_SIZE_LOG_N + LIBRA_COMMITMENTS + 3], FieldError, > { let powers_of_evaluations_challenge = { let mut values = vec![]; let mut value = *gemini_r; for _ in 0..log_circuit_size { values.push(value); value = value * value; } values }; let mut pos_inverted_denominator = (shplonk_z - powers_of_evaluations_challenge[0]).inv()?; let mut neg_inverted_denominator = (shplonk_z + powers_of_evaluations_challenge[0]).inv()?; let mut scalars = { const NONE: Option> = None; let mut values = [NONE; NUMBER_UNSHIFTED + CONST_PROOF_SIZE_LOG_N + LIBRA_COMMITMENTS + 3]; for i in 0..values.len() { values[i] = Some(FieldElement::zero()); } values }; let unshifted_scalar = pos_inverted_denominator + (shplonk_nu * neg_inverted_denominator); let unshifted_scalar_neg = -unshifted_scalar; let shifted_scalar_neg = -(gemini_r.inv()? * (pos_inverted_denominator - (shplonk_nu * neg_inverted_denominator))); scalars[0] = Some(FieldElement::one()); let mut batched_evaluation = *gemini_masking_eval; let mut batching_challenge = *rho; scalars[1] = Some(unshifted_scalar_neg); for i in 0..NUMBER_UNSHIFTED { scalars[i + 2] = Some(unshifted_scalar_neg * batching_challenge); batched_evaluation += sumcheck_evaluations[i] * batching_challenge; batching_challenge *= rho; } for i in 0..NUMBER_TO_BE_SHIFTED { let scalar_offset = i + SHIFTED_COMMITMENTS_START; let evaluation_offset = i + NUMBER_UNSHIFTED; scalars[scalar_offset] = Some(scalars[scalar_offset].unwrap() + (shifted_scalar_neg * batching_challenge)); batched_evaluation += sumcheck_evaluations[evaluation_offset] * batching_challenge; // skip last round: if i < NUMBER_TO_BE_SHIFTED - 1 { batching_challenge *= rho; } } // computeFoldPosEvaluations let fold_pos_evaluations = { let mut values = vec![FieldElement::from(0); CONST_PROOF_SIZE_LOG_N]; let mut batched_eval_accumulator = batched_evaluation; for i in (0..log_circuit_size).rev() { let challenge_power = &powers_of_evaluations_challenge[i]; let u = &sumcheck_u_challenges[i]; let eval_neg = &gemini_a_evaluations[i]; let term = challenge_power * (FieldElement::::one() - u); let batched_eval_round_acc = (FieldElement::::from(2) * challenge_power * batched_eval_accumulator) - (eval_neg * (term - u)); let den = term + u; batched_eval_accumulator = batched_eval_round_acc * den.inv()?; values[i] = batched_eval_accumulator; } values }; let mut constant_term_accumulator = fold_pos_evaluations[0] * pos_inverted_denominator; constant_term_accumulator += gemini_a_evaluations[0] * shplonk_nu * neg_inverted_denominator; let mut batching_challenge = shplonk_nu * shplonk_nu; let boundary = NUMBER_UNSHIFTED + 2; for i in 0..log_circuit_size - 1 { pos_inverted_denominator = (shplonk_z - powers_of_evaluations_challenge[i + 1]).inv()?; neg_inverted_denominator = (shplonk_z + powers_of_evaluations_challenge[i + 1]).inv()?; let scaling_factor_pos = batching_challenge * pos_inverted_denominator; let scaling_factor_neg = batching_challenge * shplonk_nu * neg_inverted_denominator; scalars[boundary + i] = Some(-(scaling_factor_neg + scaling_factor_pos)); let mut accum_contribution = scaling_factor_neg * gemini_a_evaluations[i + 1]; accum_contribution += scaling_factor_pos * fold_pos_evaluations[i + 1]; constant_term_accumulator += accum_contribution; batching_challenge *= shplonk_nu * shplonk_nu; } let boundary = boundary + log_circuit_size - 1; let subgroup_generator = FieldElement::::from_hex_unchecked( "07B0C561A6148404F086204A9F36FFB0617942546750F230C893619174A57A76", ); let denom_0 = (FieldElement::::from(1) / (shplonk_z - gemini_r)).unwrap(); let denom_1 = (FieldElement::::from(1) / (shplonk_z - subgroup_generator * gemini_r)) .unwrap(); let denominators = [denom_0, denom_1, denom_0, denom_0]; let mut batching_scalars = vec![]; batching_challenge *= shplonk_nu * shplonk_nu; for i in 0..LIBRA_EVALUATIONS { let scaling_factor = denominators[i] * batching_challenge; batching_scalars.push(-scaling_factor); // skip last step: if i < LIBRA_EVALUATIONS - 1 { batching_challenge *= shplonk_nu; } constant_term_accumulator += scaling_factor * libra_poly_evals[i]; } scalars[boundary] = Some(batching_scalars[0]); scalars[boundary + 1] = Some(batching_scalars[1] + batching_scalars[2]); scalars[boundary + 2] = Some(batching_scalars[3]); scalars[boundary + 3] = Some(constant_term_accumulator); scalars[boundary + 4] = Some(*shplonk_z); Ok(scalars .into_iter() .map(|v| v.map(|e| element_to_biguint(&e))) .collect::>() .try_into() .unwrap()) } fn check_evals_consistency( libra_evaluation: &FieldElement, libra_poly_evals: &[FieldElement; 4], gemini_r: &FieldElement, sumcheck_u_challenges: &[FieldElement; CONST_PROOF_SIZE_LOG_N], log_circuit_size: usize, ) -> Result { let vanishing_poly_eval = gemini_r.pow(SUBGROUP_SIZE) - FieldElement::::from(1); if vanishing_poly_eval == FieldElement::::from(0) { return Ok(false); } let mut challenge_poly_lagrange = vec![FieldElement::::from(0); SUBGROUP_SIZE]; challenge_poly_lagrange[0] = FieldElement::::from(1); for (round, u_challenge) in sumcheck_u_challenges .iter() .enumerate() .take(log_circuit_size) { let curr_idx = 1 + LIBRA_UNIVARIATES_LENGTH * round; challenge_poly_lagrange[curr_idx] = FieldElement::::from(1); for idx in curr_idx + 1..curr_idx + LIBRA_UNIVARIATES_LENGTH { challenge_poly_lagrange[idx] = challenge_poly_lagrange[idx - 1] * u_challenge; } } let subgroup_generator_inverse = FieldElement::::from_hex_unchecked( "204bd3277422fad364751ad938e2b5e6a54cf8c68712848a692c553d0329f5d6", ); let mut root_power = FieldElement::::from(1); let mut challenge_poly_eval = FieldElement::::from(0); let mut denominators = vec![FieldElement::::from(0); SUBGROUP_SIZE]; for idx in 0..SUBGROUP_SIZE { denominators[idx] = root_power * gemini_r - FieldElement::::from(1); denominators[idx] = denominators[idx].inv()?; challenge_poly_eval += challenge_poly_lagrange[idx] * denominators[idx]; // skip last step: if idx < SUBGROUP_SIZE - 1 { root_power *= subgroup_generator_inverse; } } let numerator = vanishing_poly_eval * FieldElement::::from(SUBGROUP_SIZE as u64).inv()?; challenge_poly_eval *= numerator; let lagrange_first = denominators[0] * numerator; let lagrange_last = denominators[SUBGROUP_SIZE - 1] * numerator; let mut diff = lagrange_first * libra_poly_evals[2]; diff += (gemini_r - subgroup_generator_inverse) * (libra_poly_evals[1] - libra_poly_evals[2] - libra_poly_evals[0] * challenge_poly_eval); diff = diff + lagrange_last * (libra_poly_evals[2] - libra_evaluation) - vanishing_poly_eval * libra_poly_evals[3]; if diff != FieldElement::::from(0) { return Ok(false); } Ok(true) } fn extract_msm_scalars( log_circuit_size: usize, scalars: [Option; NUMBER_UNSHIFTED + CONST_PROOF_SIZE_LOG_N + LIBRA_COMMITMENTS + 3], ) -> Vec { // Remove first element (==1) // scalars[1..NUMBER_UNSHIFTED+2] are the unshifted/shifted scalars // scalars[NUMBER_UNSHIFTED+2..NUMBER_UNSHIFTED+2+log_n-1] are gemini fold comm scalars // scalars[NUMBER_UNSHIFTED+2+log_n-1..NUMBER_UNSHIFTED+2+log_n-1+5] are libra + final scalars let gemini_end = NUMBER_UNSHIFTED + 2 + log_circuit_size - 1; let libra_start = gemini_end; let libra_end = libra_start + 5; // 3 libra + constant_term + shplonk_z [&scalars[1..gemini_end], &scalars[libra_start..libra_end]] .concat() .into_iter() .flatten() .collect() } ================================================ FILE: tools/garaga_rs/src/calldata/mod.rs ================================================ pub mod drand_calldata; pub mod drand_tlock_calldata; pub mod full_proof_with_hints { pub mod groth16; pub mod zk_honk; } pub mod mpc_calldata; pub mod msm_calldata; pub mod signatures; use crate::definitions::{get_modulus_from_curve_id, CurveID}; use num_bigint::BigUint; #[derive(Debug, PartialEq)] pub struct G1PointBigUint { pub x: BigUint, pub y: BigUint, } #[derive(Debug, PartialEq)] pub struct G2PointBigUint { pub x0: BigUint, pub x1: BigUint, pub y0: BigUint, pub y1: BigUint, } impl G1PointBigUint { pub fn neg(&self, curve_id: CurveID) -> Self { let modulus = get_modulus_from_curve_id(curve_id); G1PointBigUint { x: self.x.clone(), y: &modulus - &self.y, } } pub fn flatten(&self) -> Vec { vec![self.x.clone(), self.y.clone()] } pub fn from(values: Vec) -> Self { G1PointBigUint { x: values[0].clone(), y: values[1].clone(), } } } impl G2PointBigUint { pub fn flatten(&self) -> Vec { vec![ self.x0.clone(), self.x1.clone(), self.y0.clone(), self.y1.clone(), ] } pub fn from(values: Vec) -> Self { G2PointBigUint { x0: values[0].clone(), x1: values[1].clone(), y0: values[2].clone(), y1: values[3].clone(), } } } ================================================ FILE: tools/garaga_rs/src/calldata/mpc_calldata.rs ================================================ use crate::algebra::g1g2pair::G1G2Pair; use crate::algebra::polynomial::Polynomial; use crate::definitions::{CurveID, CurveParamsProvider, Stark252PrimeField}; use crate::io::{ element_from_bytes_be, field_element_to_u288_limbs, field_element_to_u384_limbs, field_elements_from_big_uints, parse_g1_g2_pairs_from_flattened_field_elements_list, }; use crate::pairing::multi_miller_loop::miller_loop; use crate::pairing::multi_pairing_check::{get_max_q_degree, multi_pairing_check}; use crate::poseidon_transcript::CairoPoseidonTranscript; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; use lambdaworks_math::traits::ByteConversion; use num_bigint::BigUint; pub fn mpc_calldata_builder( curve_id: usize, values1: &[BigUint], n_fixed_g2: usize, values2: &[BigUint], ) -> Result, String> { if !values1.len().is_multiple_of(6) { return Err("Pairs values length must be a multiple of 6".to_string()); } let n_pairs = values1.len() / 6; if n_pairs < 2 { return Err("A minimum number of 2 pairs is required".to_string()); } if !values2.is_empty() && values2.len() != 6 { return Err("Public pair values length must be 0 or 6".to_string()); } if n_fixed_g2 > n_pairs { return Err("Fixed G2 count must be less than or equal to pairs count".to_string()); } let curve_id = CurveID::try_from(curve_id)?; match curve_id { CurveID::BN254 => { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::BN254PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; handle_curve::< true, BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(values1, n_fixed_g2, values2) } CurveID::BLS12_381 => { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::BLS12381PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree6ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; handle_curve::< false, BLS12381PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(values1, n_fixed_g2, values2) } _ => Err("Unsupported curve".to_string()), } } fn handle_curve( values1: &[BigUint], n_fixed_g2: usize, values2: &[BigUint], ) -> Result, String> where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { let elements = field_elements_from_big_uints::(values1); let pairs = parse_g1_g2_pairs_from_flattened_field_elements_list(&elements)?; let public_pair = if values2.len() == 6 { let elements = field_elements_from_big_uints::(values2); let pairs = parse_g1_g2_pairs_from_flattened_field_elements_list(&elements)?; Some(pairs[0].clone()) } else { None }; calldata_builder::(&pairs, n_fixed_g2, &public_pair) } fn extra_miller_loop_result(public_pair: &G1G2Pair) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { miller_loop( std::slice::from_ref(&public_pair.g1), std::slice::from_ref(&public_pair.g2), ) } #[allow(clippy::type_complexity)] fn multi_pairing_check_result( pairs: &[G1G2Pair], m: &Option>, ) -> ( Polynomial, Option>, Polynomial, Vec>, Vec>, Vec>, ) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { assert!(pairs.len() >= 2); let mut p = vec![]; let mut q = vec![]; for pair in pairs { p.push(pair.g1.clone()); q.push(pair.g2.clone()); } let (f, lambda_root, lambda_root_inverse, scaling_factor, qis, ris) = multi_pairing_check(&p, &q, m); let curve_id = F::get_curve_params().curve_id; let ris = match curve_id { CurveID::BN254 => ris[1..].to_vec(), CurveID::BLS12_381 => ris, _ => unimplemented!(), }; ( f, lambda_root, lambda_root_inverse, scaling_factor, qis, ris, ) } #[allow(clippy::too_many_arguments)] fn hash_hints_and_get_base_random_rlc_coeff( pairs: &[G1G2Pair], n_fixed_g2: usize, curve_id: CurveID, three_limbs_only: bool, lambda_root: &Option>, lambda_root_inverse: &Polynomial, scaling_factor: &[FieldElement], ris: &[Polynomial], m: Option>, ) -> (FieldElement, CairoPoseidonTranscript) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, FieldElement: ByteConversion, { let curve_name = match curve_id { CurveID::BN254 => "BN254", CurveID::BLS12_381 => "BLS12_381", _ => unimplemented!(), }; let init_hash_text = format!("MPCHECK_{}_{}P_{}F", curve_name, pairs.len(), n_fixed_g2); let init_hash_hex = "0x".to_owned() + &init_hash_text .as_bytes() .iter() .fold(String::new(), |mut acc, byte| { use std::fmt::Write; write!(&mut acc, "{:02X}", byte).unwrap(); acc }); let init_hash = FieldElement::from_hex(&init_hash_hex).unwrap(); let mut transcript = CairoPoseidonTranscript::new(init_hash); for pair in pairs { let pairs_elements_flat = pair.flatten(); transcript.hash_emulated_field_elements(&pairs_elements_flat, None, false); } // println!( // "RS transcript.state1: {:?}", // transcript.state[0].representative().to_string() // ); if let Some(lambda_root) = lambda_root { assert_eq!(curve_id, CurveID::BN254); transcript.hash_emulated_field_elements( &lambda_root.get_coefficients_ext_degree(12), None, three_limbs_only, ); } transcript.hash_emulated_field_elements( &lambda_root_inverse.get_coefficients_ext_degree(12), None, three_limbs_only, ); transcript.hash_emulated_field_elements(scaling_factor, None, three_limbs_only); for ri in ris { transcript.hash_emulated_field_elements( &ri.get_coefficients_ext_degree(12), None, three_limbs_only, ); } if let Some(m) = m { transcript.hash_emulated_field_elements( &m.get_coefficients_ext_degree(12), None, three_limbs_only, ); } ( element_from_bytes_be(&transcript.state[1].to_bytes_be()), transcript, ) } fn compute_big_q_coeffs( n_pairs: usize, qis: &[Polynomial], ris_len: usize, c1: &FieldElement, ) -> Vec> where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let curve_id = F::get_curve_params().curve_id; let extra_n = match curve_id { CurveID::BN254 => 1, CurveID::BLS12_381 => 0, _ => unimplemented!(), }; let n_relations_with_ci = ris_len + extra_n; let (mut ci, mut big_q) = (FieldElement::one(), Polynomial::::zero()); for i in (0..n_relations_with_ci).rev() { big_q = big_q + (&qis[i] * &Polynomial::new(vec![ci.clone()])); ci *= c1; } let big_q_expected_len = get_max_q_degree(curve_id, n_pairs) + 1; let mut big_q_coeffs = big_q.coefficients; while big_q_coeffs.len() < big_q_expected_len { big_q_coeffs.push(FieldElement::from(0)); } big_q_coeffs } fn hash_big_q_and_get_z( big_q: &[FieldElement], n_pairs: usize, n_fixed_g2: usize, three_limbs_only: bool, c1: &FieldElement, ) -> FieldElement where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, FieldElement: ByteConversion, { let init_hash_text = init_hash_label::(n_pairs, n_fixed_g2, true); let mut new_transcript = new_transcript_from_text(init_hash_text); seed_transcript_with_base_rlc::(&mut new_transcript, c1, three_limbs_only); new_transcript.hash_emulated_field_elements(big_q, None, three_limbs_only); new_transcript.state[0] } #[allow(clippy::type_complexity)] fn build_mpcheck_hint( pairs: &[G1G2Pair], n_fixed_g2: usize, public_pair: &Option>, ) -> ( Polynomial, Option>, Polynomial, Vec>, Vec>, Vec>, FieldElement, ) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { let n_pairs = pairs.len(); assert!(n_pairs >= 2); assert!(n_fixed_g2 <= n_pairs); let curve_id = F::get_curve_params().curve_id; let three_limbs_only: bool = !matches!(curve_id, CurveID::BLS12_381); let m = public_pair .as_ref() .map(|public_pair| extra_miller_loop_result(public_pair)); let (f, lambda_root, lambda_root_inverse, scaling_factor, qis, ris) = multi_pairing_check_result(pairs, &m); let (c1, _transcript) = hash_hints_and_get_base_random_rlc_coeff( pairs, n_fixed_g2, curve_id, three_limbs_only, &lambda_root, &lambda_root_inverse, &scaling_factor, &ris, m, ); let big_q_coeffs = compute_big_q_coeffs(n_pairs, &qis, ris.len(), &c1); let z = hash_big_q_and_get_z::(&big_q_coeffs, n_pairs, n_fixed_g2, three_limbs_only, &c1); // Assert last Ri is 1 assert_eq!(ris[ris.len() - 1], Polynomial::one()); // Skip last Ri as it is known to be 1 for pairing checks let ris = ris[..ris.len() - 1].to_vec(); ( f, lambda_root, lambda_root_inverse, scaling_factor, ris, big_q_coeffs, z, ) } fn init_hash_label>( n_pairs: usize, n_fixed_g2: usize, second_stage: bool, ) -> String { let curve_name = match F::get_curve_params().curve_id { CurveID::BN254 => "BN254", CurveID::BLS12_381 => "BLS12_381", _ => unreachable!(), }; if second_stage { format!("MPCHECK_{}_{}P_{}F_II", curve_name, n_pairs, n_fixed_g2) } else { format!("MPCHECK_{}_{}P_{}F", curve_name, n_pairs, n_fixed_g2) } } fn seed_transcript_with_base_rlc( transcript: &mut CairoPoseidonTranscript, c1: &FieldElement, three_limbs_only: bool, ) where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { transcript.hash_emulated_field_elements(std::slice::from_ref(c1), None, three_limbs_only); } fn new_transcript_from_text(init_hash_text: String) -> CairoPoseidonTranscript { let init_hash_hex = "0x".to_owned() + &init_hash_text .as_bytes() .iter() .fold(String::new(), |mut acc, byte| { use std::fmt::Write; write!(&mut acc, "{:02X}", byte).unwrap(); acc }); let init_hash = FieldElement::from_hex(&init_hash_hex).unwrap(); CairoPoseidonTranscript::new(init_hash) } pub fn calldata_builder( pairs: &[G1G2Pair], n_fixed_g2: usize, public_pair: &Option>, ) -> Result, String> where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { let (f, lambda_root, lambda_root_inverse, scaling_factor, ris, big_q_coeffs, z) = build_mpcheck_hint(pairs, n_fixed_g2, public_pair); if f != Polynomial::one() { return Err("Pairing check is not == 1".to_string()); } let mut call_data = vec![]; let call_data_ref = &mut call_data; fn push(call_data_ref: &mut Vec, value: T) where BigUint: From, { call_data_ref.push(value.into()); } fn push_element( call_data_ref: &mut Vec, element: &FieldElement, ) where F: IsPrimeField, FieldElement: ByteConversion, { if USE_288 { let limbs = field_element_to_u288_limbs(element); for limb in limbs { push(call_data_ref, limb); } } else { let limbs = field_element_to_u384_limbs(element); for limb in limbs { push(call_data_ref, limb); } } } fn push_elements( call_data_ref: &mut Vec, elements: &[FieldElement], prepend_length: bool, ) where F: IsPrimeField, FieldElement: ByteConversion, { if prepend_length { push(call_data_ref, elements.len()); } for element in elements { push_element::(call_data_ref, element); } } if let Some(lambda_root) = lambda_root { push_elements::( call_data_ref, &lambda_root.get_coefficients_ext_degree(12), false, ); } push_elements::( call_data_ref, &lambda_root_inverse.get_coefficients_ext_degree(12), false, ); push_elements::(call_data_ref, &scaling_factor, false); push(call_data_ref, ris.len()); for ri in ris { push_elements::(call_data_ref, &ri.get_coefficients_ext_degree(12), false); } push_elements::(call_data_ref, &big_q_coeffs, true); push(call_data_ref, BigUint::from_bytes_be(&z.to_bytes_be())); Ok(call_data) } ================================================ FILE: tools/garaga_rs/src/calldata/msm_calldata.rs ================================================ use crate::algebra::g1point::G1Point; use crate::definitions::{ BLS12381PrimeField, BN254PrimeField, CurveParamsProvider, FieldElement, GrumpkinPrimeField, SECP256K1PrimeField, SECP256R1PrimeField, X25519PrimeField, }; use crate::hints::fake_glv::{get_fake_glv_hint, get_glv_fake_glv_hint}; use crate::io::{ element_to_biguint, field_element_to_u288_limbs, field_element_to_u384_limbs, field_elements_from_big_uints, parse_g1_points_from_flattened_field_elements_list, scalar_to_limbs, }; use lambdaworks_math::{field::traits::IsPrimeField, traits::ByteConversion}; use num_bigint::BigUint; use crate::definitions::CurveID; pub fn msm_calldata_builder( values: &[BigUint], scalars: &[BigUint], curve_id: usize, include_points_and_scalars: bool, serialize_as_pure_felt252_array: bool, ) -> Result, String> { if values.len() != 2 * scalars.len() { return Err("Values length must be twice the scalars length".to_string()); } let curve_id = CurveID::try_from(curve_id)?; match curve_id { CurveID::BN254 => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), CurveID::BLS12_381 => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), CurveID::SECP256K1 => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), CurveID::SECP256R1 => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), CurveID::X25519 => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), CurveID::GRUMPKIN => handle_curve::( values, scalars, curve_id as usize, include_points_and_scalars, serialize_as_pure_felt252_array, ), } } fn handle_curve( values: &[BigUint], scalars: &[BigUint], curve_id: usize, include_points_and_scalars: bool, serialize_as_pure_felt252_array: bool, ) -> Result, String> where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let elements = field_elements_from_big_uints::(values); let points = parse_g1_points_from_flattened_field_elements_list(&elements)?; let limit = &F::get_curve_params().n; if !scalars.iter().all(|x| x < limit) { return Err("Scalar value must be less than the curve order".to_string()); } Ok(calldata_builder::( &points, scalars, curve_id, include_points_and_scalars, serialize_as_pure_felt252_array, )) } #[allow(non_snake_case)] pub fn calldata_builder>( points: &[G1Point], scalars: &[BigUint], curve_id: usize, include_points_and_scalars: bool, serialize_as_pure_felt252_array: bool, ) -> Vec where FieldElement: ByteConversion, { let mut scalars_low = vec![]; let mut scalars_high = vec![]; for scalar in scalars { let [low, high] = scalar_to_limbs(scalar); scalars_low.push(BigUint::from(low)); scalars_high.push(BigUint::from(high)); } let mut call_data = vec![]; let call_data_ref = &mut call_data; fn push(call_data_ref: &mut Vec, value: T) where BigUint: From, { call_data_ref.push(value.into()); } fn push_element(call_data_ref: &mut Vec, element: &FieldElement, use_288: bool) where F: IsPrimeField, FieldElement: ByteConversion, { if use_288 { let limbs = field_element_to_u288_limbs(element); for limb in limbs { push(call_data_ref, limb); } } else { let limbs = field_element_to_u384_limbs(element); for limb in limbs { push(call_data_ref, limb); } } } if serialize_as_pure_felt252_array { // placeholder, actual length is updated at the end push(call_data_ref, 0usize); } if include_points_and_scalars { // points { push(call_data_ref, points.len()); for point in points { push_element(call_data_ref, &point.x, false); push_element(call_data_ref, &point.y, false); } } // scalars { push(call_data_ref, scalars.len()); for i in 0..scalars.len() { push(call_data_ref, scalars_low[i].clone()); push(call_data_ref, scalars_high[i].clone()); } } // curve id push(call_data_ref, curve_id); } // Hint for (pt, scalar) in points.iter().zip(scalars.iter()) { match curve_id { 0..=2 => { let (Q, u1, u2, v1, v2) = get_glv_fake_glv_hint(pt, scalar).unwrap(); push_element(call_data_ref, &Q.x, false); push_element(call_data_ref, &Q.y, false); push(call_data_ref, u1); push(call_data_ref, u2); push(call_data_ref, v1); push(call_data_ref, v2); } _ => { let scalar = if scalar == &BigUint::from(0u64) { BigUint::from(1u64) } else { scalar.clone() }; let (Q, u1, u2) = get_fake_glv_hint(pt, &scalar).unwrap(); push_element(call_data_ref, &Q.x, false); push_element(call_data_ref, &Q.y, false); push(call_data_ref, u1); push(call_data_ref, u2); } } } if serialize_as_pure_felt252_array { // updates overall length call_data[0] = (call_data.len() - 1).into(); } call_data } #[allow(dead_code)] fn sqrt(value: &FieldElement) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { let (root1, root2) = value.sqrt().expect("there is no root"); if element_to_biguint(&root1) < element_to_biguint(&root2) { root1 } else { root2 } } #[cfg(test)] mod tests {} ================================================ FILE: tools/garaga_rs/src/calldata/signatures.rs ================================================ use crate::algebra::g1point::G1Point; use crate::definitions::{ get_modulus_from_curve_id, BLS12381PrimeField, BN254PrimeField, CurveParamsProvider, GrumpkinPrimeField, SECP256K1PrimeField, SECP256R1PrimeField, ToWeierstrassCurve, X25519PrimeField, }; use crate::calldata::msm_calldata::msm_calldata_builder; use crate::io::{biguint_split, element_from_biguint, element_to_biguint}; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::unsigned_integer::element::U256; use num_bigint::BigUint; use num_traits::{One, Zero}; use sha2::{Digest, Sha256, Sha512}; use crate::definitions::CurveID; // Fix the get_curve_order function to use FieldElement pub fn get_curve_order(curve_id: CurveID) -> BigUint { match curve_id { CurveID::BLS12_381 => BLS12381PrimeField::get_curve_params().n, CurveID::BN254 => BN254PrimeField::get_curve_params().n, CurveID::SECP256K1 => SECP256K1PrimeField::get_curve_params().n, CurveID::SECP256R1 => SECP256R1PrimeField::get_curve_params().n, CurveID::X25519 => X25519PrimeField::get_curve_params().n, CurveID::GRUMPKIN => GrumpkinPrimeField::get_curve_params().n, } } /// Build calldata for Schnorr signature verification /// /// Arguments: /// * `rx` - x-coordinate of R point /// * `s` - signature value /// * `e` - challenge hash /// * `px` - public key x-coordinate /// * `py` - public key y-coordinate /// * `prepend_public_key` - whether to prepend the public key to the calldata /// * `curve_id` - curve identifier pub fn schnorr_calldata_builder( rx: BigUint, s: BigUint, e: BigUint, px: BigUint, py: BigUint, prepend_public_key: bool, curve_id: usize, ) -> Result, String> { let mut cd = Vec::new(); if prepend_public_key { cd.extend(biguint_split::<4, 96>(&px).map(BigUint::from)); cd.extend(biguint_split::<4, 96>(&py).map(BigUint::from)); } // Add base signature components cd.extend(biguint_split::<4, 96>(&rx).map(BigUint::from)); cd.extend(biguint_split::<2, 128>(&s).map(BigUint::from)); cd.extend(biguint_split::<2, 128>(&e).map(BigUint::from)); // Calculate e_neg = -e mod n let curve_id = CurveID::try_from(curve_id)?; let n = get_curve_order(curve_id); let e_neg = n - e; // Add MSM calldata for sG + (-e)P let msm_cd = msm_calldata_builder( &[ match curve_id { CurveID::BN254 => element_to_biguint(&BN254PrimeField::get_curve_params().g_x), CurveID::BLS12_381 => { element_to_biguint(&BLS12381PrimeField::get_curve_params().g_x) } CurveID::SECP256K1 => { element_to_biguint(&SECP256K1PrimeField::get_curve_params().g_x) } CurveID::SECP256R1 => { element_to_biguint(&SECP256R1PrimeField::get_curve_params().g_x) } CurveID::X25519 => element_to_biguint(&X25519PrimeField::get_curve_params().g_x), CurveID::GRUMPKIN => { element_to_biguint(&GrumpkinPrimeField::get_curve_params().g_x) } }, match curve_id { CurveID::BN254 => element_to_biguint(&BN254PrimeField::get_curve_params().g_y), CurveID::BLS12_381 => { element_to_biguint(&BLS12381PrimeField::get_curve_params().g_y) } CurveID::SECP256K1 => { element_to_biguint(&SECP256K1PrimeField::get_curve_params().g_y) } CurveID::SECP256R1 => { element_to_biguint(&SECP256R1PrimeField::get_curve_params().g_y) } CurveID::X25519 => element_to_biguint(&X25519PrimeField::get_curve_params().g_y), CurveID::GRUMPKIN => { element_to_biguint(&GrumpkinPrimeField::get_curve_params().g_y) } }, px, py, ], &[s, e_neg], curve_id as usize, false, true, )?; cd.extend(msm_cd); Ok(cd) } /// Build calldata for ECDSA signature verification /// /// Arguments: /// * `r` - signature r value /// * `s` - signature s value /// * `v` - recovery parameter (0 or 1) /// * `px` - public key x-coordinate /// * `py` - public key y-coordinate /// * `z` - message hash /// * `prepend_public_key` - whether to prepend the public key to the calldata /// * `curve_id` - curve identifier #[allow(clippy::too_many_arguments)] pub fn ecdsa_calldata_builder( r: BigUint, s: BigUint, v: u8, px: BigUint, py: BigUint, z: BigUint, prepend_public_key: bool, curve_id: usize, ) -> Result, String> { let mut cd = Vec::new(); if prepend_public_key { cd.extend(biguint_split::<4, 96>(&px).map(BigUint::from)); cd.extend(biguint_split::<4, 96>(&py).map(BigUint::from)); } // Add base signature components cd.extend(biguint_split::<4, 96>(&r).map(BigUint::from)); cd.extend(biguint_split::<2, 128>(&s).map(BigUint::from)); cd.push(BigUint::from(v)); cd.extend(biguint_split::<2, 128>(&z).map(BigUint::from)); // Calculate s_inv, u1, u2 let curve_id = CurveID::try_from(curve_id)?; let n = get_curve_order(curve_id); let s_inv = s.modpow(&(n.clone() - BigUint::from(2u32)), &n); let u1 = (z * &s_inv) % &n; let u2 = (r * &s_inv) % &n; // Add MSM calldata for u1*G + u2*P let msm_cd = msm_calldata_builder( &[ match curve_id { CurveID::BN254 => element_to_biguint(&BN254PrimeField::get_curve_params().g_x), CurveID::BLS12_381 => { element_to_biguint(&BLS12381PrimeField::get_curve_params().g_x) } CurveID::SECP256K1 => { element_to_biguint(&SECP256K1PrimeField::get_curve_params().g_x) } CurveID::SECP256R1 => { element_to_biguint(&SECP256R1PrimeField::get_curve_params().g_x) } CurveID::X25519 => element_to_biguint(&X25519PrimeField::get_curve_params().g_x), CurveID::GRUMPKIN => { element_to_biguint(&GrumpkinPrimeField::get_curve_params().g_x) } }, match curve_id { CurveID::BN254 => element_to_biguint(&BN254PrimeField::get_curve_params().g_y), CurveID::BLS12_381 => { element_to_biguint(&BLS12381PrimeField::get_curve_params().g_y) } CurveID::SECP256K1 => { element_to_biguint(&SECP256K1PrimeField::get_curve_params().g_y) } CurveID::SECP256R1 => { element_to_biguint(&SECP256R1PrimeField::get_curve_params().g_y) } CurveID::X25519 => element_to_biguint(&X25519PrimeField::get_curve_params().g_y), CurveID::GRUMPKIN => { element_to_biguint(&GrumpkinPrimeField::get_curve_params().g_y) } }, px, py, ], &[u1, u2], curve_id as usize, false, true, )?; cd.extend(msm_cd); Ok(cd) } pub fn eddsa_calldata_builder( ry_twisted: BigUint, s: BigUint, py_twisted: BigUint, msg: Vec, prepend_public_key: bool, ) -> Result, String> { let mut cd = Vec::new(); let max_value = BigUint::from(1u64) << 256; if ry_twisted >= max_value { return Err("Invalid Ry value".to_string()); } if py_twisted >= max_value { return Err("Invalid Py value".to_string()); } if s >= max_value { return Err("Invalid s value".to_string()); } if prepend_public_key { cd.extend(biguint_split::<2, 128>(&py_twisted).map(BigUint::from)); } cd.extend(biguint_split::<2, 128>(&ry_twisted).map(BigUint::from)); cd.extend(biguint_split::<2, 128>(&s).map(BigUint::from)); cd.push(BigUint::from(msg.len() as u64)); for byte in msg.clone() { cd.push(BigUint::from(byte as u64)); } let mut hasher = Sha512::new(); let ry_bytes = ry_twisted.to_bytes_le(); let py_bytes = py_twisted.to_bytes_le(); // Ensure the byte arrays are of length 32 let ry_bytes_padded = if ry_bytes.len() < 32 { let mut padded = vec![0; 32]; padded[..ry_bytes.len()].copy_from_slice(&ry_bytes); padded } else { ry_bytes }; let py_bytes_padded = if py_bytes.len() < 32 { let mut padded = vec![0; 32]; padded[..py_bytes.len()].copy_from_slice(&py_bytes); padded } else { py_bytes }; hasher.update(&ry_bytes_padded); hasher.update(&py_bytes_padded); hasher.update(msg); let hash = hasher.finalize(); let hash_biguint = BigUint::from_bytes_le(&hash); fn xrecover(y_twisted: FieldElement) -> FieldElement { let d_twisted = FieldElement::::from_hex( "52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3", ) .unwrap(); let i = FieldElement::::from_hex( "2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0", ) .unwrap(); let y_sq = y_twisted.square(); let xx = ((y_sq - FieldElement::::one()) / (d_twisted * y_sq + FieldElement::::one())) .unwrap(); // exp =(p+3) // 8 let exp = U256::from_hex("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe") .unwrap(); let x = xx.pow(exp); let x = if x.square() != xx { x * i } else { x }; let is_even = element_to_biguint(&x) % 2_u32 == BigUint::zero(); if is_even { x } else { -x } } fn decode_point( compressed_point_le: BigUint, ) -> ( FieldElement, FieldElement, ) { let two_pow_255: BigUint = BigUint::from(1u64) << 255; let sign_bit: BigUint = compressed_point_le.clone() / two_pow_255.clone(); let y_twisted = compressed_point_le % two_pow_255; let y_twisted = element_from_biguint(&y_twisted); let x_twisted = xrecover(y_twisted); let x_twisted = if element_to_biguint(&x_twisted.clone()) % 2_u32 != sign_bit { -x_twisted } else { x_twisted }; (x_twisted, y_twisted) } let (r_point_x_twisted, r_point_y_twisted) = decode_point(ry_twisted); let (p_point_x_twisted, p_point_y_twisted) = decode_point(py_twisted); let (r_point_x_weierstrass, r_point_y_weierstrass) = X25519PrimeField::to_weirstrass(r_point_x_twisted, r_point_y_twisted); let (p_point_x_weierstrass, p_point_y_weierstrass) = X25519PrimeField::to_weirstrass(p_point_x_twisted, p_point_y_twisted); let _p_pt = G1Point::new(p_point_x_weierstrass, p_point_y_weierstrass, false).expect("Invalid point P"); let _r_pt = G1Point::new(r_point_x_weierstrass, r_point_y_weierstrass, false).expect("Invalid point R"); let gx = element_to_biguint(&X25519PrimeField::get_curve_params().g_x); let modulus = get_modulus_from_curve_id(CurveID::X25519); let neg_gy = modulus - element_to_biguint(&X25519PrimeField::get_curve_params().g_y); let h = hash_biguint % get_curve_order(CurveID::X25519); let values = &[ gx, neg_gy, element_to_biguint(&p_point_x_weierstrass), element_to_biguint(&p_point_y_weierstrass), ]; let scalars = &[s, h]; let msm_cd = msm_calldata_builder(values, scalars, CurveID::X25519 as usize, false, true)?; cd.extend(msm_cd); cd.extend(biguint_split::<2, 128>(&element_to_biguint(&r_point_x_twisted)).map(BigUint::from)); cd.extend(biguint_split::<2, 128>(&element_to_biguint(&p_point_x_twisted)).map(BigUint::from)); Ok(cd) } /// PKCS#1 v1.5 SHA-256 DigestInfo prefix (DER-encoded AlgorithmIdentifier + NULL param). /// RFC 8017, Section 9.2, Note 1. const PKCS1_SHA256_DIGEST_INFO_PREFIX: [u8; 19] = [ 0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20, ]; /// Encode a SHA-256 hash as a PKCS#1 v1.5 padded integer (RFC 8017, Section 9.2). /// /// Constructs: 0x00 || 0x01 || PS(0xFF × 202) || 0x00 || DigestInfo || H fn pkcs1_v1_5_encode_sha256(message_hash: &[u8; 32]) -> BigUint { let mut encoded = vec![0x00, 0x01]; encoded.extend(std::iter::repeat_n(0xff, 202)); encoded.push(0x00); encoded.extend_from_slice(&PKCS1_SHA256_DIGEST_INFO_PREFIX); encoded.extend_from_slice(message_hash); BigUint::from_bytes_be(&encoded) } /// Serialize a Cairo `ByteArray` as felt252 calldata. /// /// Layout: [num_full_words, word_0, ..., word_{n-1}, pending_word, pending_word_len] /// Each full word is 31 bytes. The pending word is 0-30 bytes. fn serialize_byte_array(data: &[u8]) -> Vec { let full_word_count = data.len() / 31; let pending_len = data.len() % 31; let mut cd = Vec::new(); cd.push(BigUint::from(full_word_count as u64)); for i in 0..full_word_count { let start = i * 31; let word = BigUint::from_bytes_be(&data[start..start + 31]); cd.push(word); } if pending_len > 0 { let pending = BigUint::from_bytes_be(&data[full_word_count * 31..]); cd.push(pending); } else { cd.push(BigUint::zero()); } cd.push(BigUint::from(pending_len as u64)); cd } /// Build calldata for RSA-2048 SHA-256 signature verification. /// /// Computes SHA-256(message), builds PKCS#1 v1.5 encoding, generates /// the RSA reduction witnesses, and appends the ByteArray-serialized message. /// /// Arguments: /// * `signature` - RSA signature s in [0, modulus) /// * `message` - Raw message bytes /// * `modulus` - RSA-2048 modulus n /// * `prepend_public_key` - Whether to prepend n to the calldata pub fn rsa_2048_sha256_calldata_builder( signature: BigUint, message: &[u8], modulus: BigUint, prepend_public_key: bool, ) -> Result, String> { let hash: [u8; 32] = Sha256::digest(message) .as_slice() .try_into() .map_err(|_| "SHA-256 digest failed")?; let expected_message = pkcs1_v1_5_encode_sha256(&hash); let mut cd = rsa_2048_calldata_builder(signature, expected_message, modulus, prepend_public_key)?; cd.extend(serialize_byte_array(message)); Ok(cd) } /// Serialize a 2048-bit integer to 24 calldata elements (96-bit words). /// /// Layout: 6 chunks of 4 words each. The first 5 chunks hold 384 bits, /// the last chunk holds 128 bits (top 2 words are zero). fn serialize_rsa2048_integer(x: &BigUint) -> Vec { biguint_split::<24, 96>(x) .iter() .map(|&w| BigUint::from(w)) .collect() } /// Build calldata for RSA-2048 signature verification. /// /// Computes s^{65537} mod n via square-and-multiply, generating 17 /// reduction witnesses (quotient, remainder) that certify each step. /// /// Arguments: /// * `signature` - RSA signature s in [0, modulus) /// * `expected_message` - Expected result m = s^{65537} mod n /// * `modulus` - RSA-2048 modulus n /// * `prepend_public_key` - Whether to prepend n to the calldata pub fn rsa_2048_calldata_builder( signature: BigUint, expected_message: BigUint, modulus: BigUint, prepend_public_key: bool, ) -> Result, String> { if modulus.bits() > 2048 || modulus <= BigUint::one() { return Err("modulus must be a positive integer fitting in 2048 bits".into()); } if signature >= modulus { return Err("signature must be less than modulus".into()); } if expected_message >= modulus { return Err("expected_message must be less than modulus".into()); } // Verify s^{65537} ≡ m (mod n) let e = BigUint::from(65537u32); if signature.modpow(&e, &modulus) != expected_message { return Err("signature^65537 mod modulus does not equal expected_message".into()); } // Square-and-multiply for e = 65537 = 2^16 + 1: // 16 squarings followed by 1 multiplication = 17 reductions. let mut acc = signature.clone(); let mut witnesses: Vec<(BigUint, BigUint)> = Vec::with_capacity(17); for _ in 0..16 { let product = &acc * &acc; let quotient = &product / &modulus; let remainder = &product % &modulus; witnesses.push((quotient, remainder.clone())); acc = remainder; } let product = &acc * &signature; let quotient = &product / &modulus; let remainder = &product % &modulus; witnesses.push((quotient, remainder)); // Serialize to calldata let mut cd = Vec::new(); if prepend_public_key { cd.extend(serialize_rsa2048_integer(&modulus)); } cd.extend(serialize_rsa2048_integer(&signature)); cd.extend(serialize_rsa2048_integer(&expected_message)); for (q, r) in &witnesses { cd.extend(serialize_rsa2048_integer(q)); cd.extend(serialize_rsa2048_integer(r)); } Ok(cd) } #[cfg(test)] mod tests { use super::*; #[test] fn test_pkcs1_v1_5_encode_sha256_structure() { let hash = [0u8; 32]; let encoded = pkcs1_v1_5_encode_sha256(&hash); let encoded_bytes = encoded.to_bytes_be(); // Pad to 256 bytes (leading 0x00 is dropped by BigUint) let mut padded = vec![0u8; 256 - encoded_bytes.len()]; padded.extend_from_slice(&encoded_bytes); assert_eq!(padded[0], 0x00); assert_eq!(padded[1], 0x01); assert!(padded[2..204].iter().all(|&b| b == 0xff)); assert_eq!(padded[204], 0x00); assert_eq!(&padded[205..224], &PKCS1_SHA256_DIGEST_INFO_PREFIX); assert_eq!(&padded[224..256], &hash); } #[test] fn test_serialize_byte_array_empty() { let cd = serialize_byte_array(b""); // [0 full words, pending_word=0, pending_word_len=0] assert_eq!(cd.len(), 3); assert_eq!(cd[0], BigUint::zero()); assert_eq!(cd[1], BigUint::zero()); assert_eq!(cd[2], BigUint::zero()); } #[test] fn test_serialize_byte_array_short() { let msg = b"hello"; let cd = serialize_byte_array(msg); // 5 bytes < 31, so 0 full words, pending = "hello", pending_len = 5 assert_eq!(cd.len(), 3); assert_eq!(cd[0], BigUint::zero()); // 0 full words assert_eq!(cd[1], BigUint::from_bytes_be(msg)); // pending word assert_eq!(cd[2], BigUint::from(5u32)); // pending len } #[test] fn test_serialize_byte_array_exact_word() { let msg = vec![0xABu8; 31]; // exactly one full word let cd = serialize_byte_array(&msg); // 1 full word, pending = 0, pending_len = 0 assert_eq!(cd.len(), 4); assert_eq!(cd[0], BigUint::one()); // 1 full word assert_eq!(cd[1], BigUint::from_bytes_be(&msg)); // word_0 assert_eq!(cd[2], BigUint::zero()); // pending = 0 assert_eq!(cd[3], BigUint::zero()); // pending_len = 0 } #[test] fn test_serialize_byte_array_multi() { let msg = vec![0xCDu8; 65]; // 2 full words (62 bytes) + 3 pending let cd = serialize_byte_array(&msg); assert_eq!(cd.len(), 5); // num_full + word0 + word1 + pending + pending_len assert_eq!(cd[0], BigUint::from(2u32)); assert_eq!(cd[4], BigUint::from(3u32)); // pending_len } #[test] fn test_rsa_2048_sha256_calldata_pkcs_encoding() { let hash: [u8; 32] = Sha256::digest(b"hello garaga").into(); let expected_message = pkcs1_v1_5_encode_sha256(&hash); let em_bytes = expected_message.to_bytes_be(); let mut padded = vec![0u8; 256 - em_bytes.len()]; padded.extend_from_slice(&em_bytes); assert_eq!(&padded[224..256], &hash); } } ================================================ FILE: tools/garaga_rs/src/constants.rs ================================================ //! Auto-generated constants file from constants.json. Do not edit manually. use num_bigint::BigUint; use num_traits::Num; // RISC0 Constants // https://github.com/risc0/risc0-ethereum/blob/v2.2.2/contracts/src/groth16/ControlID.sol // release v2.2.2 pub fn get_risc0_constants() -> (BigUint, BigUint) { let risc0_control_root = BigUint::from_str_radix( "CE52BF56033842021AF3CF6DB8A50D1B7535C125A34F1A22C6FDCF002C5A1529", 16, ) .unwrap(); let risc0_bn254_control_id = BigUint::from_str_radix( "04446E66D300EB7FB45C9726BB53C793DDA407A62E9601618BB43C5C14657AC0", 16, ) .unwrap(); (risc0_control_root, risc0_bn254_control_id) } // SP1 Constants // https://github.com/succinctlabs/sp1-contracts/blob/main/contracts/src/v5.0.0/SP1VerifierGroth16.sol pub const SP1_VERIFIER_VERSION: &str = "v5.0.0"; pub const SP1_VERIFIER_HASH: &str = "0xa4594c59bbc142f3b81c3ecb7f50a7c34bc9af7c4c444b5d48b795427e285913"; // Additional RISC0 constants for internal use pub const RISC0_SYSTEM_STATE_ZERO_DIGEST: &str = "0xA3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2"; pub const RISC0_TAG_DIGEST: &str = "0xcb1fefcd1f2d9a64975cbbbf6e161e2914434b0cbb9960b84df5d717e86b48af"; pub const RISC0_OUTPUT_TAG: &str = "0x77eafeb366a78b47747de0d7bb176284085ff5564887009a5be63da32d3559d4"; ================================================ FILE: tools/garaga_rs/src/crypto/digest.rs ================================================ use core::fmt; // use arbitrary::Arbitrary; // use bfieldcodec_derive::BFieldCodec; // use get_size2::GetSize; // use itertools::Itertools; // use num_traits::Zero; // use rand::distr::Distribution; // use rand::distr::StandardUniform; // use rand::Rng; // use serde::Deserialize; // use serde::Deserializer; // use serde::Serialize; // use serde::Serializer; // use crate::crypto::poseidon_bn254::poseidon_hash_bn254; use crate::crypto::poseidon_bn254::poseidon_hash_bn254; use crate::definitions::{FieldElement, GrumpkinPrimeField, Random}; // use crate::error::TryFromDigestError; // use crate::error::TryFromHexDigestError; // use crate::math::b_field_element::BFieldElement; // use crate::prelude::Tip5; /// A trait defining the hash function interface pub trait HashFunction: Clone + Copy + fmt::Debug + PartialEq { /// The type of elements being hashed type Element: Clone + Copy + PartialEq + Eq + Default + fmt::Debug + From; /// Hash two elements together fn hash_pair(left: &Self::Element, right: &Self::Element) -> Self::Element; fn hash_single(element: &Self::Element) -> Self::Element; fn random() -> Self::Element; } // /// A fixed-size array of BFieldElements // #[derive(Clone, Copy, Debug, PartialEq, Eq)] // pub struct Tip5Element([BFieldElement; 5]); // /// Implementation for Tip5 hash function // pub struct Tip5Hash; // impl HashFunction for Tip5Hash { // type Element = Tip5Element; // fn hash_pair(left: &Self::Element, right: &Self::Element) -> Self::Element { // let result = Tip5::hash_pair(&left.0, &right.0); // Tip5Element(result.try_into().unwrap()) // } // } /// Implementation for Poseidon BN254 hash function #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)] pub struct PoseidonBn254Hash; impl HashFunction for PoseidonBn254Hash { type Element = FieldElement; fn hash_pair(left: &Self::Element, right: &Self::Element) -> Self::Element { poseidon_hash_bn254(left, right) } fn hash_single(element: &Self::Element) -> Self::Element { let zero = FieldElement::::zero(); poseidon_hash_bn254(element, &zero) } fn random() -> Self::Element { FieldElement::::random() } } /// Generate a vector of n random digests for the given hash function type pub fn random_elements(n: usize) -> Vec> { (0..n).map(|_| Digest::new(H::random())).collect() } /// A fixed-size digest for hash functions #[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)] pub struct Digest where H::Element: Clone + Copy + PartialEq + Eq + fmt::Debug, { pub data: H::Element, } impl Digest { /// The number of bytes in a digest. // pub const BYTES: usize = BFieldElement::BYTES; /// The all-zero digest. pub(crate) fn all_zero() -> Self { Self { data: H::Element::default(), } } pub const fn value(self) -> H::Element { self.data } pub const fn new(element: H::Element) -> Self { Self { data: element } } /// Hash this digest using the specified hash function H pub fn hash_pair(left: &Self, right: &Self) -> Self { Self { data: H::hash_pair(&left.data, &right.data), } } pub fn to_element(self) -> H::Element { self.data } pub fn from_element(element: H::Element) -> Self { Self { data: element } } } impl Default for Digest { fn default() -> Self { Self::all_zero() } } impl fmt::Display for Digest { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{:?}", self.data) } } // impl fmt::LowerHex for Digest { // fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { // let bytes = <[u8; Self::BYTES]>::from(*self); // write!(f, "{}", hex::encode(bytes)) // } // } // impl fmt::UpperHex for Digest { // fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { // let bytes = <[u8; Self::BYTES]>::from(*self); // write!(f, "{}", hex::encode_upper(bytes)) // } // } // impl Distribution> for StandardUniform { // fn sample(&self, rng: &mut R) -> Digest { // Digest::new(rng.random()) // } // } // impl FromStr for Digest { // type Err = TryFromDigestError; // fn from_str(string: &str) -> Result { // let bfes: Vec<_> = string // .split(',') // .map(str::parse::) // .try_collect()?; // let invalid_len_err = Self::Err::InvalidLength(bfes.len()); // let digest_innards = bfes.try_into().map_err(|_| invalid_len_err)?; // Ok(Digest { // data: digest_innards, // }) // } // } #[derive(Debug)] pub struct TryFromDigestError; #[derive(Debug)] pub struct TryFromHexDigestError; // impl TryFrom> for Digest { // type Error = TryFromDigestError; // fn try_from(value: Vec) -> Result { // Digest::try_from(&value as &[H::Element]) // } // } // impl From> for Vec { // fn from(val: Digest) -> Self { // val.data.to_vec() // } // } // impl From> for [u8; BFieldElement::BYTES] { // fn from(Digest { data }: Digest) -> Self { // // This needs to be implemented based on how you want to serialize your Element type // unimplemented!("Implement byte serialization for Element type") // } // } // impl TryFrom<[u8; BFieldElement::BYTES]> for Digest { // type Error = TryFromDigestError; // fn try_from(bytes: [u8; BFieldElement::BYTES]) -> Result { // // This needs to be implemented based on how you want to deserialize your Element type // unimplemented!("Implement byte deserialization for Element type") // } // } // impl TryFrom for Digest // where // H::Element: TryFrom, // { // type Error = TryFromDigestError; // fn try_from(value: BigUint) -> Result { // let mut remaining = value; // let mut digest_innards = H::Element::ZERO; // let modulus: BigUint = BFieldElement::P.into(); // for digest_element in &mut digest_innards { // let element = u64::try_from(remaining.clone() % modulus.clone()).unwrap(); // *digest_element = H::Element::new(element); // remaining /= modulus.clone(); // } // if !remaining.is_zero() { // return Err(Self::Error::Overflow); // } // Ok(Self { // data: digest_innards, // }) // } // } // impl From> for BigUint // where // H::Element: Into, // { // fn from(digest: Digest) -> Self { // let Digest { data } = digest; // let mut ret = BigUint::zero(); // let modulus: BigUint = BFieldElement::P.into(); // for i in (0..BFieldElement::BYTES).rev() { // ret *= modulus.clone(); // let digest_element: BigUint = data[i].value().into(); // ret += digest_element; // } // ret // } // } // impl Digest { // /// Encode digest as hex. // /// // /// Since `Digest` also implements [`LowerHex`][lo] and [`UpperHex`][up], it is // /// possible to `{:x}`-format directly, _e.g._, `print!("{digest:x}")`. // /// // /// [lo]: fmt::LowerHex // /// [up]: fmt::UpperHex // pub fn to_hex(self) -> String { // format!("{self:x}") // } // /// Decode hex string to [`Digest`]. Must not include leading "0x". // pub fn try_from_hex(data: impl AsRef<[u8]>) -> Result { // let slice = hex::decode(data)?; // Ok(Self::try_from(&slice as &[u8])?) // } // } // we implement Serialize so that we can serialize as hex for human readable // formats like JSON but use default serializer for other formats likes bincode // impl Serialize for Digest // where // H::Element: Serialize, // { // fn serialize(&self, serializer: S) -> Result // where // S: Serializer, // { // if serializer.is_human_readable() { // self.to_hex().serialize(serializer) // } else { // self.data.serialize(serializer) // } // } // } // we impl Deserialize so that we can deserialize as hex for human readable // formats like JSON but use default deserializer for other formats like bincode // impl<'de, H: HashFunction> Deserialize<'de> for Digest // where // H::Element: Deserialize<'de>, // { // fn deserialize(deserializer: D) -> Result // where // D: Deserializer<'de>, // { // if deserializer.is_human_readable() { // let hex_string = String::deserialize(deserializer)?; // Self::try_from_hex(hex_string).map_err(serde::de::Error::custom) // } else { // Ok(Self::new(H::Element::deserialize(deserializer)?)) // } // } // } // Implement conversion between Digest and FieldElement for PoseidonBn254 impl From> for FieldElement { fn from(_digest: Digest) -> Self { // Implement conversion logic here // This might need to be adjusted based on your specific requirements unimplemented!("Need to implement conversion from Digest to FieldElement") } } impl From> for Digest { fn from(_field: FieldElement) -> Self { // Implement conversion logic here // This might need to be adjusted based on your specific requirements unimplemented!("Need to implement conversion from FieldElement to Digest") } } // // Keep existing implementations but make them generic over H // impl PartialOrd for Digest { // fn partial_cmp(&self, other: &Self) -> Option { // self.data.partial_cmp(&other.data) // } // } // impl Ord for Digest { // fn cmp(&self, other: &Self) -> std::cmp::Ordering { // self.data.cmp(&other.data) // } // } // impl GetSize for Digest // where // H::Element: GetSize, // { // fn get_stack_size() -> usize { // std::mem::size_of::() // } // fn get_heap_size(&self) -> usize { // self.data.get_heap_size() // } // } // impl fmt::Display for Tip5Element { // fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { // write!(f, "{:?}", self.0) // } // } // // Implement conversion between array and Tip5Element // impl From<[BFieldElement; 5]> for Tip5Element { // fn from(array: [BFieldElement; 5]) -> Self { // Self(array) // } // } // impl From for [BFieldElement; 5] { // fn from(element: Tip5Element) -> Self { // element.0 // } // } // // Add AsRef for convenient slice access // impl AsRef<[BFieldElement]> for Tip5Element { // fn as_ref(&self) -> &[BFieldElement] { // &self.0 // } // } // // Add AsMut for convenient mutable slice access // impl AsMut<[BFieldElement]> for Tip5Element { // fn as_mut(&mut self) -> &mut [BFieldElement] { // &mut self.0 // } // } // // Add these impls // impl From> for H::Element { // fn from(digest: Digest) -> Self { // digest.data // } // } impl AsRef for Digest { fn as_ref(&self) -> &H::Element { &self.data } } impl<'a, H: HashFunction> arbitrary::Arbitrary<'a> for Digest { fn arbitrary(_u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result { Ok(Self::new(H::random())) } } // #[cfg(test)] // pub(crate) mod digest_tests { // use num_traits::One; // use proptest::collection::vec; // use proptest::prelude::Arbitrary as ProptestArbitrary; // use proptest::prelude::*; // use proptest_arbitrary_interop::arb; // use test_strategy::proptest; // use super::*; // // use crate::prelude::*; // impl ProptestArbitrary for Digest { // type Parameters = (); // fn arbitrary_with(_args: Self::Parameters) -> Self::Strategy { // arb().prop_map(|d| d).no_shrink().boxed() // } // type Strategy = BoxedStrategy; // } // /// Test helper struct for corrupting digests. Primarily used for negative tests. // #[derive(Debug, Clone, PartialEq, Eq, test_strategy::Arbitrary)] // pub(crate) struct DigestCorruptor; // impl DigestCorruptor { // pub fn corrupt_digest(&self, digest: Digest) -> Digest { // // Generate a new random digest different from the input // loop { // let new_digest = Digest::new(H::random()); // if new_digest != digest { // return new_digest; // } // } // } // } // // mod serde_test { // // use super::hex_test::hex_examples; // // use super::*; // // mod json_test { // // use super::*; // // #[test] // // fn serialize() -> Result<(), serde_json::Error> { // // for (digest, hex) in hex_examples() { // // assert_eq!(serde_json::to_string(&digest)?, format!("\"{}\"", hex)); // // } // // Ok(()) // // } // // #[test] // // fn deserialize() -> Result<(), serde_json::Error> { // // for (digest, hex) in hex_examples() { // // let json_hex = format!("\"{}\"", hex); // // let digest_deserialized: Digest = serde_json::from_str::(&json_hex)?; // // assert_eq!(digest_deserialized, digest); // // } // // Ok(()) // // } // // } // // mod bincode_test { // // use super::*; // // fn bincode_examples() -> Vec<(Digest, [u8; Digest::BYTES])> { // // vec![ // // (Digest::default(), [0u8; Digest::BYTES]), // // ( // // Digest::new(bfe_array![0, 1, 10, 15, 255]), // // [ // // 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, // // 0, 15, 0, 0, 0, 0, 0, 0, 0, 255, 0, 0, 0, 0, 0, 0, 0, // // ], // // ), // // ] // // } // // #[test] // // fn serialize() { // // for (digest, bytes) in bincode_examples() { // // assert_eq!(bincode::serialize(&digest).unwrap(), bytes); // // } // // } // // #[test] // // fn deserialize() { // // for (digest, bytes) in bincode_examples() { // // assert_eq!(bincode::deserialize::(&bytes).unwrap(), digest); // // } // // } // // } // // } // } ================================================ FILE: tools/garaga_rs/src/crypto/merkle_tree.rs ================================================ use crate::crypto::digest::{Digest, HashFunction}; use arbitrary::{Arbitrary, Unstructured}; use itertools::Itertools; use lazy_static::lazy_static; // use rayon::prelude::*; use std::collections::hash_map::Entry::*; use std::collections::*; use std::fmt::Debug; use std::result; use thiserror::Error; // Add this import // use crate::prelude::*; const DEFAULT_PARALLELIZATION_CUTOFF: usize = 512; lazy_static! { static ref PARALLELIZATION_CUTOFF: usize = std::env::var("TWENTY_FIRST_MERKLE_TREE_PARALLELIZATION_CUTOFF") .ok() .and_then(|v| v.parse().ok()) .unwrap_or(DEFAULT_PARALLELIZATION_CUTOFF); } /// Enforces that all compilation targets have a consistent [`MAX_TREE_HEIGHT`]. /// In particular, if `usize` has more than 32 bits, the maximum height of a /// Merkle tree is limited as if only 32 bits were available. If `usize` has /// less than 32 bits, compilation will fail. /// /// Using a type other than `usize` could enable a higher maximum height, but /// would require a different storage mechanism for the Merkle tree's nodes: /// indexing into a `Vec<_>` can only be done with `usize`. const MAX_NUM_NODES: usize = 1 << (32 - 1); const MAX_NUM_LEAFS: usize = MAX_NUM_NODES / 2; /// The maximum height of a Merkle tree. pub const MAX_TREE_HEIGHT: usize = MAX_NUM_LEAFS.ilog2() as usize; type Result = result::Result; /// A [Merkle tree][merkle_tree] is a binary tree of [digests](Digest) that is /// used to efficiently prove the inclusion of items in a set. Set inclusion can /// be verified through an [inclusion proof](MerkleTreeInclusionProof). /// /// The used hash function is [`Tip5`]. /// /// [merkle_tree]: https://en.wikipedia.org/wiki/Merkle_tree #[derive(Debug, Clone, PartialEq, Eq)] pub struct MerkleTree { nodes: Vec>, } /// A full inclusion proof for the leafs at the supplied indices, including the /// leafs themselves. The proof is relative to some [Merkle tree](MerkleTree), /// which is not necessarily (and generally cannot be) known in its entirety by /// the verifier. #[derive(Debug, Clone, PartialEq, Eq, Default)] pub struct MerkleTreeInclusionProof { /// The stated height of the Merkle tree this proof is relative to. pub tree_height: usize, /// The leafs the proof is about, _i.e._, the revealed leafs. /// /// Purposefully not a [`HashMap`] to preserve order of the keys, which is /// relevant for [`into_authentication_paths`][paths]. /// /// [paths]: MerkleTreeInclusionProof::into_authentication_paths pub indexed_leafs: Vec<(usize, Digest)>, /// The proof's witness: de-duplicated authentication structure for the /// leafs this proof is about. See [`authentication_structure`][auth_structure] /// for details. /// /// [auth_structure]: MerkleTree::authentication_structure pub authentication_structure: Vec>, } /// Helper struct for verifying inclusion of items in a Merkle tree. /// /// Continuing the example from [`authentication_structure`][auth_structure], /// the partial tree for leafs 0 and 2, _i.e._, nodes 8 and 10 respectively, /// with nodes [11, 9, 3] from the authentication structure is: /// /// ```markdown /// ──── _ ──── /// ╱ ╲ /// _ 3 /// ╱ ╲ /// ╱ ╲ /// _ _ /// ╱ ╲ ╱ ╲ /// 8 9 10 11 /// ``` /// /// [auth_structure]: MerkleTree::authentication_structure #[derive(Debug, Clone, PartialEq, Eq, Default)] pub(crate) struct PartialMerkleTree { tree_height: usize, leaf_indices: Vec, nodes: HashMap>, } impl MerkleTree { /// The index of the root node. /// /// If you need to read the root, try [`root()`](Self::root) instead. pub(crate) const ROOT_INDEX: usize = 1; /// Build a MerkleTree with the given leafs. /// /// [`MerkleTree::par_new`] is equivalent and usually faster. /// /// # Errors /// /// - If the number of leafs is zero. /// - If the number of leafs is not a power of two. pub fn sequential_new(leafs: &[Digest]) -> Result { let mut nodes = Self::initialize_merkle_tree_nodes(leafs)?; for i in (MerkleTree::::ROOT_INDEX..leafs.len()).rev() { nodes[i] = Digest::::from_element(H::hash_pair(&nodes[i * 2].data, &nodes[i * 2 + 1].data)); } Ok(MerkleTree { nodes }) } /// Build a MerkleTree with the given leafs. /// /// Uses [`rayon`] to parallelize Merkle tree construction. If the use of /// [`rayon`] is not an option in your context, use /// [`MerkleTree::sequential_new`], which is equivalent but usually slower. /// /// # Errors /// /// - If the number of leafs is zero. /// - If the number of leafs is not a power of two. pub fn par_new(leafs: &[Digest]) -> Result { let mut nodes = Self::initialize_merkle_tree_nodes(leafs)?; // (not) parallel let mut num_nodes_on_this_level = leafs.len(); while num_nodes_on_this_level >= *PARALLELIZATION_CUTOFF { num_nodes_on_this_level /= 2; let node_indices_on_this_level = num_nodes_on_this_level..2 * num_nodes_on_this_level; let nodes_on_this_level = node_indices_on_this_level .clone() .map(|i| { Digest::::from_element(H::hash_pair( &nodes[i * 2].data, &nodes[i * 2 + 1].data, )) }) .collect::>(); nodes[node_indices_on_this_level].copy_from_slice(&nodes_on_this_level); } // sequential let num_remaining_nodes = num_nodes_on_this_level; for i in (MerkleTree::::ROOT_INDEX..num_remaining_nodes).rev() { nodes[i] = Digest::::from_element(H::hash_pair(&nodes[i * 2].data, &nodes[i * 2 + 1].data)); } Ok(MerkleTree { nodes }) } /// Helps to kick off Merkle tree construction. Sets up the Merkle tree's /// internal nodes if (and only if) it is possible to construct a Merkle /// tree with the given leafs. fn initialize_merkle_tree_nodes(leafs: &[Digest]) -> Result>> { if leafs.is_empty() { return Err(MerkleTreeError::TooFewLeafs); } let num_leafs = leafs.len(); if !num_leafs.is_power_of_two() { return Err(MerkleTreeError::IncorrectNumberOfLeafs); } if num_leafs > MAX_NUM_LEAFS { return Err(MerkleTreeError::TreeTooHigh); } let mut nodes = vec![Digest::::default(); 2 * num_leafs]; nodes[num_leafs..].copy_from_slice(leafs); Ok(nodes) } /// Given a list of leaf indices, return the indices of exactly those nodes that /// are needed to prove (or verify) that the indicated leafs are in the Merkle /// tree. // This function is not defined as a method (taking self as argument) since it's // needed by the verifier, who does not have access to the Merkle tree. fn authentication_structure_node_indices( num_leafs: usize, leaf_indices: &[usize], ) -> Result> { // The set of indices of nodes that need to be included in the authentications // structure. In principle, every node of every authentication path is needed. // The root is never needed. Hence, it is not considered below. let mut node_is_needed = HashSet::new(); // The set of indices of nodes that can be computed from other nodes in the // authentication structure or the leafs that are explicitly supplied during // verification. Every node on the direct path from the leaf to the root can // be computed by the very nature of "authentication path". let mut node_can_be_computed = HashSet::new(); for &leaf_index in leaf_indices { if leaf_index >= num_leafs { return Err(MerkleTreeError::LeafIndexInvalid { num_leafs }); } let mut node_index = leaf_index + num_leafs; while node_index > Self::ROOT_INDEX { let sibling_index = node_index ^ 1; node_can_be_computed.insert(node_index); node_is_needed.insert(sibling_index); node_index /= 2; } } let set_difference = node_is_needed.difference(&node_can_be_computed).copied(); Ok(set_difference.sorted_unstable().rev()) } /// Generate a de-duplicated authentication structure for the given leaf indices. /// If a single index is supplied, the authentication structure is the /// authentication path for the indicated leaf. /// /// For example, consider the following Merkle tree. /// /// ```markdown /// ──── 1 ──── ╮ /// ╱ ╲ │ /// 2 3 │ /// ╱ ╲ ╱ ╲ ├╴ node indices /// ╱ ╲ ╱ ╲ │ /// 4 5 6 7 │ /// ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ │ /// 8 9 10 11 12 13 14 15 ╯ /// /// 0 1 2 3 4 5 6 7 ←── leaf indices /// ``` /// /// The authentication path for leaf 2, _i.e._, node 10, is nodes [11, 4, 3]. /// /// The authentication structure for leafs 0 and 2, _i.e._, nodes 8 and 10 /// respectively, is nodes [11, 9, 3]. /// Note how: /// - Node 3 is included only once, even though the individual authentication /// paths for leafs 0 and 2 both include node 3. This is one part of the /// de-duplication. /// - Node 4 is not included at all, even though the authentication path for /// leaf 2 requires the node: node 4 can be computed from nodes 8 and 9; /// the former is supplied explicitly during [verification][verify], /// the latter is included in the authentication structure. /// This is the other part of the de-duplication. /// /// [verify]: MerkleTreeInclusionProof::verify pub fn authentication_structure(&self, leaf_indices: &[usize]) -> Result>> { let num_leafs = self.num_leafs(); let indices = Self::authentication_structure_node_indices(num_leafs, leaf_indices)?; let auth_structure = indices.map(|idx| self.nodes[idx]).collect(); Ok(auth_structure) } pub fn root(&self) -> Digest { self.nodes[Self::ROOT_INDEX] } pub fn num_leafs(&self) -> usize { let node_count = self.nodes.len(); debug_assert!(node_count.is_power_of_two()); node_count / 2 } pub fn height(&self) -> usize { let leaf_count = self.num_leafs(); debug_assert!(leaf_count.is_power_of_two()); leaf_count.ilog2() as usize } /// All nodes of the Merkle tree. pub fn nodes(&self) -> &[Digest] { &self.nodes } /// The node at the given node index, if it exists. pub fn node(&self, index: usize) -> Option> { self.nodes.get(index).copied() } /// All leafs of the Merkle tree. pub fn leafs(&self) -> &[Digest] { let first_leaf = self.nodes.len() / 2; &self.nodes[first_leaf..] } /// The leaf at the given index, if it exists. pub fn leaf(&self, index: usize) -> Option> { let first_leaf_index = self.nodes.len() / 2; self.nodes.get(first_leaf_index + index).copied() } pub fn indexed_leafs(&self, indices: &[usize]) -> Result)>> { let num_leafs = self.num_leafs(); let invalid_index = MerkleTreeError::LeafIndexInvalid { num_leafs }; let maybe_indexed_leaf = |&i| self.leaf(i).ok_or(invalid_index).map(|leaf| (i, leaf)); indices.iter().map(maybe_indexed_leaf).collect() } /// A full inclusion proof for the leafs at the supplied indices, including the /// leafs. Generally, using [`authentication_structure`][auth_structure] is /// preferable. Use this method only if the verifier needs explicit access to the /// leafs, _i.e._, cannot compute them from other information. /// /// [auth_structure]: Self::authentication_structure pub fn inclusion_proof_for_leaf_indices( &self, indices: &[usize], ) -> Result> { let proof = MerkleTreeInclusionProof { tree_height: self.height(), indexed_leafs: self.indexed_leafs(indices)?, authentication_structure: self.authentication_structure(indices)?, }; Ok(proof) } // fn test_tree_of_height(tree_height: usize) -> Self { // let num_leafs = 1 << tree_height; // let leafs = (0..num_leafs) // .map(|i| Digest::new(H::random())) // .collect_vec(); // let tree = Self::par_new(&leafs).unwrap(); // assert!(leafs.iter().all_unique()); // tree // } } impl<'a, H: HashFunction> Arbitrary<'a> for MerkleTree { fn arbitrary(u: &mut Unstructured<'a>) -> arbitrary::Result { let height = u.int_in_range(0..=13)?; let num_leafs = 1 << height; let leaf_digests: arbitrary::Result> = (0..num_leafs).map(|_| u.arbitrary()).collect(); let tree = Self::par_new(&leaf_digests?).unwrap(); Ok(tree) } } impl MerkleTreeInclusionProof { fn leaf_indices(&self) -> impl Iterator { self.indexed_leafs.iter().map(|(index, _)| index) } fn is_trivial(&self) -> bool { self.indexed_leafs.is_empty() && self.authentication_structure.is_empty() } /// Verify that the given root digest is the root of a Merkle tree that contains /// the indicated leafs. pub fn verify(self, expected_root: Digest) -> bool { if self.is_trivial() { return true; } let Ok(partial_tree) = PartialMerkleTree::try_from(self) else { return false; }; let Ok(computed_root) = partial_tree.root() else { return false; }; computed_root == expected_root } /// Transform the inclusion proof into a list of authentication paths. /// /// This corresponds to a decompression of the authentication structure. /// In some contexts, it is easier to deal with individual authentication paths /// than with the de-duplicated authentication structure. /// /// Continuing the example from [`authentication_structure`][auth_structure], /// the authentication structure for leafs 0 and 2, _i.e._, nodes 8 and 10 /// respectively, is nodes [11, 9, 3]. /// /// The authentication path /// - for leaf 0 is [9, 5, 3], and /// - for leaf 2 is [11, 4, 3]. /// /// ```markdown /// ──── 1 ──── /// ╱ ╲ /// 2 3 /// ╱ ╲ ╱ ╲ /// ╱ ╲ ╱ ╲ /// 4 5 6 7 /// ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ /// 8 9 10 11 12 13 14 15 /// ``` /// /// [auth_structure]: MerkleTree::authentication_structure pub fn into_authentication_paths(self) -> Result>>> { let partial_tree = PartialMerkleTree::try_from(self)?; partial_tree.into_authentication_paths() } } impl PartialMerkleTree { pub fn root(&self) -> Result> { self.nodes .get(&MerkleTree::::ROOT_INDEX) .copied() .ok_or(MerkleTreeError::RootNotFound) } fn node(&self, index: usize) -> Result> { self.nodes .get(&index) .copied() .ok_or(MerkleTreeError::MissingNodeIndex(index)) } fn num_leafs(&self) -> Result { if self.tree_height > MAX_TREE_HEIGHT { return Err(MerkleTreeError::TreeTooHigh); } Ok(1 << self.tree_height) } /// Compute all computable digests of the partial Merkle tree, modifying self. /// Returns an error if self is either /// - incomplete, _i.e._, does not contain all the nodes required to compute /// the root, or /// - not minimal, _i.e._, if it contains nodes that can be computed from other /// nodes. pub fn fill(&mut self) -> Result<()> { let mut parent_node_indices = self.first_layer_parent_node_indices()?; for _ in 0..self.tree_height { for &parent_node_index in &parent_node_indices { self.insert_digest_for_index(parent_node_index)?; } parent_node_indices = Self::move_indices_one_layer_up(parent_node_indices); } Ok(()) } /// Any parent node index is included only once. This guarantees that the number /// of hash operations is minimal. fn first_layer_parent_node_indices(&self) -> Result> { let num_leafs = self.num_leafs()?; let leaf_to_parent_node_index = |&leaf_index| (leaf_index + num_leafs) / 2; let parent_node_indices = self.leaf_indices.iter().map(leaf_to_parent_node_index); let mut parent_node_indices = parent_node_indices.collect_vec(); parent_node_indices.sort_unstable(); parent_node_indices.dedup(); Ok(parent_node_indices) } fn insert_digest_for_index(&mut self, parent_index: usize) -> Result<()> { let (left_child, right_child) = self.children_of_node(parent_index)?; let parent_digest = Digest::::from_element(H::hash_pair(&left_child.data, &right_child.data)); match self.nodes.insert(parent_index, parent_digest) { Some(_) => Err(MerkleTreeError::SpuriousNodeIndex(parent_index)), None => Ok(()), } } fn children_of_node(&self, parent_index: usize) -> Result<(Digest, Digest)> { let left_child_index = parent_index * 2; let right_child_index = left_child_index ^ 1; let left_child = self.node(left_child_index)?; let right_child = self.node(right_child_index)?; Ok((left_child, right_child)) } /// Indices are deduplicated to guarantee minimal number of hash operations. fn move_indices_one_layer_up(mut indices: Vec) -> Vec { indices.iter_mut().for_each(|i| *i /= 2); indices.dedup(); indices } /// Collect all individual authentication paths for the indicated leafs. fn into_authentication_paths(self) -> Result>>> { self.leaf_indices .iter() .map(|&i| self.authentication_path_for_index(i)) .collect() } /// Given a single leaf index and a partial Merkle tree, collect the /// authentication path for the indicated leaf. /// /// Fails if the partial Merkle tree does not contain the entire /// authentication path. fn authentication_path_for_index(&self, leaf_index: usize) -> Result>> { let num_leafs = self.num_leafs()?; let mut authentication_path = vec![]; let mut node_index = leaf_index + num_leafs; while node_index > MerkleTree::::ROOT_INDEX { let sibling_index = node_index ^ 1; let sibling = self.node(sibling_index)?; authentication_path.push(sibling); node_index /= 2; } Ok(authentication_path) } } impl TryFrom> for PartialMerkleTree { type Error = MerkleTreeError; fn try_from(proof: MerkleTreeInclusionProof) -> Result { let leaf_indices = proof.leaf_indices().copied().collect(); let mut partial_tree = PartialMerkleTree { tree_height: proof.tree_height, leaf_indices, nodes: HashMap::new(), }; let num_leafs = partial_tree.num_leafs()?; if partial_tree.leaf_indices.iter().any(|&i| i >= num_leafs) { return Err(MerkleTreeError::LeafIndexInvalid { num_leafs }); } let node_indices = MerkleTree::::authentication_structure_node_indices( num_leafs, &partial_tree.leaf_indices, )?; if proof.authentication_structure.len() != node_indices.len() { return Err(MerkleTreeError::AuthenticationStructureLengthMismatch); } let mut nodes: HashMap<_, _> = node_indices .zip_eq(proof.authentication_structure) .collect(); for (leaf_index, leaf_digest) in proof.indexed_leafs { let node_index = leaf_index + num_leafs; if let Vacant(entry) = nodes.entry(node_index) { entry.insert(leaf_digest); } else if nodes[&node_index] != leaf_digest { return Err(MerkleTreeError::RepeatedLeafDigestMismatch); } } partial_tree.nodes = nodes; partial_tree.fill()?; Ok(partial_tree) } } #[derive(Debug, Clone, Copy, PartialEq, Eq, Error)] pub enum MerkleTreeError { #[error("All leaf indices must be valid, i.e., less than {num_leafs}.")] LeafIndexInvalid { num_leafs: usize }, #[error("The length of the supplied authentication structure must match the expected length.")] AuthenticationStructureLengthMismatch, #[error("Leaf digests of repeated indices must be identical.")] RepeatedLeafDigestMismatch, #[error("The partial tree must be minimal. Node {0} was supplied but can be computed.")] SpuriousNodeIndex(usize), #[error("The partial tree must contain all necessary information. Node {0} is missing.")] MissingNodeIndex(usize), #[error("Could not compute the root. Maybe no leaf indices were supplied?")] RootNotFound, #[error("Too few leafs to build a Merkle tree.")] TooFewLeafs, #[error("The number of leafs must be a power of two.")] IncorrectNumberOfLeafs, #[error("Tree height must not exceed {MAX_TREE_HEIGHT}.")] TreeTooHigh, } // #[cfg(test)] // pub mod merkle_tree_test { // use crate::crypto::digest::*; // use crate::definitions::{FieldElement, GrumpkinPrimeField}; // use proptest::collection::vec; // use proptest::prelude::*; // use proptest_arbitrary_interop::arb; // use test_strategy::proptest; // use super::*; // use crate::crypto::digest::digest_tests::DigestCorruptor; // impl MerkleTree { // fn test_tree_of_height(tree_height: usize) -> Self { // let num_leafs = 1 << tree_height; // let leafs = (0..num_leafs) // .map(|i| Digest::new(FieldElement::::from(i))) // .collect_vec(); // let tree = Self::par_new(&leafs).unwrap(); // assert!(leafs.iter().all_unique()); // tree // } // } // impl PartialMerkleTree { // fn dummy_nodes_for_indices( // node_indices: &[usize], // ) -> HashMap> { // node_indices // .iter() // .map(|&i| (i, FieldElement::::from(i as u64))) // .map(|(i, leaf)| (i, Digest::new(PoseidonBn254Hash::hash_single(&leaf)))) // .collect() // } // } // /// Test helper to deduplicate generation of Merkle trees. // #[derive(Debug, Clone, test_strategy::Arbitrary)] // pub(crate) struct MerkleTreeToTest { // #[strategy(arb())] // pub tree: MerkleTree, // #[strategy(vec(0..#tree.num_leafs(), 0..#tree.num_leafs()))] // pub selected_indices: Vec, // } // impl MerkleTreeToTest { // fn has_non_trivial_proof(&self) -> bool { // !self.selected_indices.is_empty() // } // fn proof(&self) -> MerkleTreeInclusionProof { // // test helper – unwrap is fine // self.tree // .inclusion_proof_for_leaf_indices(&self.selected_indices) // .unwrap() // } // } // #[test] // fn building_merkle_tree_from_empty_list_of_digests_fails_with_expected_error() { // let maybe_tree = MerkleTree::::par_new(&[]); // let err = maybe_tree.unwrap_err(); // assert_eq!(MerkleTreeError::TooFewLeafs, err); // } // #[test] // fn merkle_tree_with_one_leaf_has_expected_height_and_number_of_leafs() { // let digest = Digest::::default(); // let tree = MerkleTree::::par_new(&[digest]).unwrap(); // assert_eq!(1, tree.num_leafs()); // assert_eq!(0, tree.height()); // } // #[proptest] // fn building_merkle_tree_from_one_digest_makes_that_digest_the_root( // digest: Digest, // ) { // let tree = MerkleTree::par_new(&[digest]).unwrap(); // assert_eq!(digest, tree.root()); // } // #[proptest] // fn building_merkle_tree_from_list_of_digests_with_incorrect_number_of_leafs_fails( // #[filter(!#num_leafs.is_power_of_two())] // #[strategy(1_usize..1 << 13)] // num_leafs: usize, // ) { // let digest = Digest::::default(); // let digests = vec![digest; num_leafs]; // let maybe_tree = MerkleTree::::par_new(&digests); // let err = maybe_tree.unwrap_err(); // assert_eq!(MerkleTreeError::IncorrectNumberOfLeafs, err); // } // #[proptest] // fn merkle_tree_construction_strategies_behave_identically_on_random_input( // leafs: Vec>, // ) { // let sequential = MerkleTree::sequential_new(&leafs); // let parallel = MerkleTree::par_new(&leafs); // prop_assert_eq!(sequential, parallel); // } // #[proptest] // fn merkle_tree_construction_strategies_produce_identical_trees( // #[strategy(0_usize..10)] _tree_height: usize, // #[strategy(vec(arb(), 1 << #_tree_height))] leafs: Vec>, // ) { // let sequential = MerkleTree::sequential_new(&leafs)?; // let parallel = MerkleTree::par_new(&leafs)?; // prop_assert_eq!(sequential, parallel); // } // #[proptest(cases = 100)] // fn accessing_number_of_leafs_and_height_never_panics( // #[strategy(arb())] merkle_tree: MerkleTree, // ) { // let _ = merkle_tree.num_leafs(); // let _ = merkle_tree.height(); // } // #[proptest(cases = 50)] // fn trivial_proof_can_be_verified( // #[strategy(arb())] merkle_tree: MerkleTree, // ) { // let proof = merkle_tree.inclusion_proof_for_leaf_indices(&[]).unwrap(); // prop_assert!(proof.authentication_structure.is_empty()); // let verdict = proof.verify(merkle_tree.root()); // prop_assert!(verdict); // } // #[proptest(cases = 40)] // fn honestly_generated_authentication_structure_can_be_verified(test_tree: MerkleTreeToTest) { // let proof = test_tree.proof(); // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(verdict); // } // #[proptest(cases = 30)] // fn corrupt_root_leads_to_verification_failure( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // corruptor: DigestCorruptor, // ) { // let bad_root = corruptor.corrupt_digest(test_tree.tree.root()); // let proof = test_tree.proof(); // let verdict = proof.verify(bad_root); // prop_assert!(!verdict); // } // #[proptest(cases = 20)] // fn corrupt_authentication_structure_leads_to_verification_failure( // #[filter(!#test_tree.proof().authentication_structure.is_empty())] // test_tree: MerkleTreeToTest, // #[strategy(Just(#test_tree.proof().authentication_structure.len()))] // _num_auth_structure_entries: usize, // #[strategy(vec(0..#_num_auth_structure_entries, 1..=#_num_auth_structure_entries))] // indices_to_corrupt: Vec, // #[strategy(vec(any::(), #indices_to_corrupt.len()))] // digest_corruptors: Vec, // ) { // let mut proof = test_tree.proof(); // for (i, digest_corruptor) in indices_to_corrupt.into_iter().zip_eq(digest_corruptors) { // proof.authentication_structure[i] = // digest_corruptor.corrupt_digest(proof.authentication_structure[i]); // } // if proof == test_tree.proof() { // let reject_reason = "corruption must change authentication structure".into(); // return Err(TestCaseError::Reject(reject_reason)); // } // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(!verdict); // } // #[proptest(cases = 30)] // fn corrupt_leaf_digests_lead_to_verification_failure( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // #[strategy(Just(#test_tree.proof().indexed_leafs.len()))] _n_leafs: usize, // #[strategy(vec(0..#_n_leafs, 1..=#_n_leafs))] leafs_to_corrupt: Vec, // #[strategy(vec(any::(), #leafs_to_corrupt.len()))] digest_corruptors: Vec< // DigestCorruptor, // >, // ) { // let mut proof = test_tree.proof(); // for (&i, digest_corruptor) in leafs_to_corrupt.iter().zip_eq(&digest_corruptors) { // let (leaf_index, leaf_digest) = proof.indexed_leafs[i]; // let corrupt_digest = digest_corruptor.corrupt_digest(leaf_digest); // proof.indexed_leafs[i] = (leaf_index, corrupt_digest); // } // if proof == test_tree.proof() { // let reject_reason = "corruption must change leaf digests".into(); // return Err(TestCaseError::Reject(reject_reason)); // } // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(!verdict); // } // #[proptest(cases = 30)] // fn removing_leafs_from_proof_leads_to_verification_failure( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // #[strategy(Just(#test_tree.proof().indexed_leafs.len()))] _n_leafs: usize, // #[strategy(vec(0..#_n_leafs, 1..=#_n_leafs))] leaf_indices_to_remove: Vec, // ) { // let mut proof = test_tree.proof(); // let leafs_to_keep = proof // .indexed_leafs // .iter() // .filter(|(i, _)| !leaf_indices_to_remove.contains(i)); // proof.indexed_leafs = leafs_to_keep.copied().collect(); // if proof == test_tree.proof() { // let reject_reason = "removing leafs must change proof".into(); // return Err(TestCaseError::Reject(reject_reason)); // } // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(!verdict); // } // #[proptest(cases = 30)] // fn checking_set_inclusion_of_items_not_in_set_leads_to_verification_failure( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // #[strategy(vec(0..#test_tree.tree.num_leafs(), 1..=#test_tree.tree.num_leafs()))] // spurious_indices: Vec, // #[strategy(vec(any::>(), #spurious_indices.len()))] // spurious_digests: Vec>, // ) { // let spurious_leafs = spurious_indices // .into_iter() // .zip_eq(spurious_digests) // .collect_vec(); // let mut proof = test_tree.proof(); // proof.indexed_leafs.extend(spurious_leafs); // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(!verdict); // } // #[proptest(cases = 30)] // fn honestly_generated_proof_with_duplicate_leafs_can_be_verified( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // #[strategy(Just(#test_tree.proof().indexed_leafs.len()))] _n_leafs: usize, // #[strategy(vec(0..#_n_leafs, 1..=#_n_leafs))] indices_to_duplicate: Vec, // ) { // let mut proof = test_tree.proof(); // let duplicate_leafs = indices_to_duplicate // .into_iter() // .map(|i| proof.indexed_leafs[i]) // .collect_vec(); // proof.indexed_leafs.extend(duplicate_leafs); // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(verdict); // } // #[proptest(cases = 40)] // fn incorrect_tree_height_leads_to_verification_failure( // #[filter(#test_tree.has_non_trivial_proof())] test_tree: MerkleTreeToTest, // #[strategy(0..=MAX_TREE_HEIGHT)] // #[filter(#test_tree.tree.height() != #incorrect_height)] // incorrect_height: usize, // ) { // let mut proof = test_tree.proof(); // proof.tree_height = incorrect_height; // let verdict = proof.verify(test_tree.tree.root()); // prop_assert!(!verdict); // } // #[proptest(cases = 20)] // fn honestly_generated_proof_with_all_leafs_revealed_can_be_verified( // #[strategy(arb())] tree: MerkleTree, // ) { // let leaf_indices = (0..tree.num_leafs()).collect_vec(); // let proof = tree // .inclusion_proof_for_leaf_indices(&leaf_indices) // .unwrap(); // let verdict = proof.verify(tree.root()); // prop_assert!(verdict); // } // #[proptest(cases = 30)] // fn requesting_inclusion_proof_for_nonexistent_leaf_fails_with_expected_error( // #[strategy(arb())] tree: MerkleTree, // #[filter(#leaf_indices.iter().any(|&i| i > #tree.num_leafs()))] leaf_indices: Vec, // ) { // let maybe_proof = tree.inclusion_proof_for_leaf_indices(&leaf_indices); // let err = maybe_proof.unwrap_err(); // let num_leafs = tree.num_leafs(); // assert_eq!(MerkleTreeError::LeafIndexInvalid { num_leafs }, err); // } // #[test] // fn authentication_paths_of_extremely_small_tree_use_expected_digests() { // // _ 1_ // // / \ // // 2 3 // // / \ / \ // // 4 5 6 7 // // // // 0 1 2 3 <- leaf indices // let tree = MerkleTree::test_tree_of_height(2); // let auth_path_with_nodes = |indices: [usize; 2]| indices.map(|i| tree.nodes[i]).to_vec(); // let auth_path_for_leaf = |index| tree.authentication_structure(&[index]).unwrap(); // assert_eq!(auth_path_with_nodes([5, 3]), auth_path_for_leaf(0)); // assert_eq!(auth_path_with_nodes([4, 3]), auth_path_for_leaf(1)); // assert_eq!(auth_path_with_nodes([7, 2]), auth_path_for_leaf(2)); // assert_eq!(auth_path_with_nodes([6, 2]), auth_path_for_leaf(3)); // } // #[test] // fn authentication_paths_of_very_small_tree_use_expected_digests() { // // ──── 1 ──── // // ╱ ╲ // // 2 3 // // ╱ ╲ ╱ ╲ // // ╱ ╲ ╱ ╲ // // 4 5 6 7 // // ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ // // 8 9 10 11 12 13 14 15 // // // // 0 1 2 3 4 5 6 7 <- leaf indices // let tree = MerkleTree::test_tree_of_height(3); // let auth_path_with_nodes = |indices: [usize; 3]| indices.map(|i| tree.nodes[i]).to_vec(); // let auth_path_for_leaf = |index| tree.authentication_structure(&[index]).unwrap(); // assert_eq!(auth_path_with_nodes([9, 5, 3]), auth_path_for_leaf(0)); // assert_eq!(auth_path_with_nodes([8, 5, 3]), auth_path_for_leaf(1)); // assert_eq!(auth_path_with_nodes([11, 4, 3]), auth_path_for_leaf(2)); // assert_eq!(auth_path_with_nodes([10, 4, 3]), auth_path_for_leaf(3)); // assert_eq!(auth_path_with_nodes([13, 7, 2]), auth_path_for_leaf(4)); // assert_eq!(auth_path_with_nodes([12, 7, 2]), auth_path_for_leaf(5)); // assert_eq!(auth_path_with_nodes([15, 6, 2]), auth_path_for_leaf(6)); // assert_eq!(auth_path_with_nodes([14, 6, 2]), auth_path_for_leaf(7)); // } // #[proptest(cases = 10)] // fn each_leaf_can_be_verified_individually(test_tree: MerkleTreeToTest) { // let tree = test_tree.tree; // for (leaf_index, &leaf) in tree.leafs().iter().enumerate() { // let authentication_path = tree.authentication_structure(&[leaf_index]).unwrap(); // let proof = MerkleTreeInclusionProof { // tree_height: tree.height(), // indexed_leafs: [(leaf_index, leaf)].into(), // authentication_structure: authentication_path, // }; // let verdict = proof.verify(tree.root()); // prop_assert!(verdict); // } // } // #[test] // fn partial_merkle_tree_built_from_authentication_structure_contains_expected_nodes() { // let merkle_tree = MerkleTree::test_tree_of_height(3); // let proof = merkle_tree // .inclusion_proof_for_leaf_indices(&[0, 2]) // .unwrap(); // let partial_tree = PartialMerkleTree::try_from(proof).unwrap(); // // ──── 1 ──── // // ╱ ╲ // // 2 3 // // ╱ ╲ // // ╱ ╲ // // 4 5 // // ╱ ╲ ╱ ╲ // // 8 9 10 11 // // // // 0 2 <-- opened_leaf_indices // let expected_node_indices = vec![1, 2, 3, 4, 5, 8, 9, 10, 11]; // let node_indices = partial_tree.nodes.keys().copied().sorted().collect_vec(); // assert_eq!(expected_node_indices, node_indices); // } // #[test] // fn manually_constructed_partial_tree_can_be_filled() { // // ──── _ ─── // // ╱ ╲ // // _ 3 // // ╱ ╲ // // ╱ ╲ // // _ _ // // ╱ ╲ ╱ ╲ // // 8 9 10 11 // // // // 0 2 <-- opened_leaf_indices // let node_indices = [3, 8, 9, 10, 11]; // let mut partial_tree = PartialMerkleTree { // tree_height: 3, // leaf_indices: vec![0, 2], // nodes: PartialMerkleTree::dummy_nodes_for_indices(&node_indices), // }; // partial_tree.fill().unwrap(); // } // #[test] // fn trying_to_compute_root_of_partial_tree_with_necessary_node_missing_gives_expected_error() { // // ──── _ ──── // // ╱ ╲ // // _ _ (!) // // ╱ ╲ // // ╱ ╲ // // _ _ // // ╱ ╲ ╱ ╲ // // 8 9 10 11 // // // // 0 2 <-- opened_leaf_indices // let node_indices = [8, 9, 10, 11]; // let mut partial_tree = PartialMerkleTree { // tree_height: 3, // leaf_indices: vec![0, 2], // nodes: PartialMerkleTree::dummy_nodes_for_indices(&node_indices), // }; // let err = partial_tree.fill().unwrap_err(); // assert_eq!(MerkleTreeError::MissingNodeIndex(3), err); // } // #[test] // fn trying_to_compute_root_of_partial_tree_with_redundant_node_gives_expected_error() { // // ──── _ ──── // // ╱ ╲ // // 2 (!) 3 // // ╱ ╲ // // ╱ ╲ // // _ _ // // ╱ ╲ ╱ ╲ // // 8 9 10 11 // // // // 0 2 <-- opened_leaf_indices // let node_indices = [2, 3, 8, 9, 10, 11]; // let mut partial_tree = PartialMerkleTree { // tree_height: 3, // leaf_indices: vec![0, 2], // nodes: PartialMerkleTree::dummy_nodes_for_indices(&node_indices), // }; // let err = partial_tree.fill().unwrap_err(); // assert_eq!(MerkleTreeError::SpuriousNodeIndex(2), err); // } // #[test] // fn converting_authentication_structure_to_authentication_paths_results_in_expected_paths() { // const TREE_HEIGHT: usize = 3; // let merkle_tree = MerkleTree::test_tree_of_height(TREE_HEIGHT); // let proof = merkle_tree // .inclusion_proof_for_leaf_indices(&[0, 2]) // .unwrap(); // let auth_paths = proof.into_authentication_paths().unwrap(); // let auth_path_with_nodes = // |indices: [usize; TREE_HEIGHT]| indices.map(|i| merkle_tree.nodes[i]).to_vec(); // let expected_path_0 = auth_path_with_nodes([9, 5, 3]); // let expected_path_1 = auth_path_with_nodes([11, 4, 3]); // let expected_paths = vec![expected_path_0, expected_path_1]; // assert_eq!(expected_paths, auth_paths); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/mmr_accumulator.rs ================================================ use std::collections::HashMap; use std::fmt::Debug; // use arbitrary::Arbitrary; // use get_size2::GetSize; use itertools::Itertools; // use serde::Deserialize; // use serde::Serialize; use super::mmr_trait::LeafMutation; use super::shared_basic; use super::TOO_MANY_LEAFS_ERR; use crate::crypto::digest::Digest; use crate::crypto::digest::HashFunction; use crate::crypto::mmr::mmr_membership_proof::MmrMembershipProof; use crate::crypto::mmr::mmr_trait::Mmr; use crate::crypto::mmr::shared_advanced; // use crate::prelude::*; #[derive(Debug, Clone, PartialEq, Eq)] // Serialize, Deserialize, , GetSize)] pub struct MmrAccumulator { leaf_count: u64, peaks: Vec>, } impl MmrAccumulator { pub fn init(peaks: Vec>, leaf_count: u64) -> Self { Self { leaf_count, peaks } } pub fn new_from_leafs(digests: Vec>) -> Self { let mut mmra = MmrAccumulator { leaf_count: 0, peaks: vec![], }; for digest in digests { mmra.append(digest); } mmra } /// Is `self` self-consistent? That is, is it possible to have the claimed /// number of leafs given the number of peaks? pub(crate) fn is_consistent(&self) -> bool { let num_peaks = u32::try_from(self.peaks.len()).expect(TOO_MANY_LEAFS_ERR); num_peaks == self.num_leafs().count_ones() } } impl Mmr for MmrAccumulator { /// Calculate a commitment to the entire MMR. fn bag_peaks(&self) -> Digest { bag_peaks(&self.peaks, self.leaf_count) } /// Return the Merkle tree roots of the Merkle trees that this MMR consists /// of. fn peaks(&self) -> Vec> { self.peaks.clone() } /// Returns true iff there are no leafs in the MMR. fn is_empty(&self) -> bool { self.leaf_count == 0 } /// Return the number of leafs in the MMR. fn num_leafs(&self) -> u64 { self.leaf_count } /// Add a leaf to the MMR. Returns the membership proof of the newly added /// leaf. fn append(&mut self, new_leaf: Digest) -> MmrMembershipProof { let (new_peaks, membership_proof) = shared_basic::calculate_new_peaks_from_append( self.leaf_count, self.peaks.clone(), new_leaf, ); self.peaks = new_peaks; self.leaf_count += 1; membership_proof } /// Mutate an existing leaf. It is the caller's responsibility that the /// membership proof is valid. If the membership proof is wrong, the MMR /// will end up in a broken state. fn mutate_leaf(&mut self, leaf_mutation: LeafMutation) { self.peaks = shared_basic::calculate_new_peaks_from_leaf_mutation( &self.peaks, self.leaf_count, leaf_mutation.new_leaf, leaf_mutation.leaf_index, &leaf_mutation.membership_proof, ) } /// Mutate multiple leafs in the MMR. Takes a list of membership proofs /// that will be updated accordingly. Meaning that the provided membership /// proofs will be valid for the new MMR, provided they were valid before /// the update was applied. /// Panics if `membership_proofs` and `membership_proof_leaf_indices` do not have /// the same length, or if a leaf index is out-of-bounds for the MMR. fn batch_mutate_leaf_and_update_mps( &mut self, membership_proofs: &mut [&mut MmrMembershipProof], membership_proof_leaf_indices: &[u64], mut mutation_data: Vec>, ) -> Vec { assert_eq!( membership_proofs.len(), membership_proof_leaf_indices.len(), "Lists must have same length. Got: {} and {}", membership_proofs.len(), membership_proof_leaf_indices.len() ); assert!( membership_proof_leaf_indices .iter() .all(|x| *x < self.leaf_count), "All leaf indices must be in-bounds. Got indices [{}] and leaf_count = {}", membership_proof_leaf_indices.iter().join(", "), self.leaf_count ); // Calculate all derivable paths let mut new_ap_digests: HashMap> = HashMap::new(); // Calculate the derivable digests from a number of leaf mutations and their // associated authentication paths. Notice that all authentication paths // are only valid *prior* to any updates. They get invalidated (unless updated) // throughout the updating as their neighbor leaf digests change values. // The hash map `new_ap_digests` takes care of that. while let Some(LeafMutation { leaf_index, new_leaf, membership_proof, }) = mutation_data.pop() { let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_index); let former_value = new_ap_digests.insert(node_index, new_leaf); assert!( former_value.is_none(), "Duplicated leaf indices are not allowed in membership proof updater" ); let mut acc_hash: Digest = new_leaf.to_owned(); for (count, &hash) in membership_proof.authentication_path.iter().enumerate() { // If sibling node is something that has already been calculated, we use that // hash digest. Otherwise, we use the one in our authentication path. let (right_ancestor_count, height) = shared_advanced::right_lineage_length_and_own_height(node_index); let is_right_child = right_ancestor_count != 0; if is_right_child { let left_sibling_index = shared_advanced::left_sibling(node_index, height); let sibling_hash: Digest = new_ap_digests .get(&left_sibling_index) .copied() .unwrap_or(hash); acc_hash = Digest::::from_element(H::hash_pair(&sibling_hash.data, &acc_hash.data)); // Find parent node index node_index += 1; } else { let right_sibling_index = shared_advanced::right_sibling(node_index, height); let sibling_hash: Digest = new_ap_digests .get(&right_sibling_index) .copied() .unwrap_or(hash); acc_hash = Digest::::from_element(H::hash_pair(&acc_hash.data, &sibling_hash.data)); // Find parent node index node_index += 1 << (height + 1); } // The last hash calculated is the peak hash // This is not inserted in the hash map, as it will never be in any // authentication path if count < membership_proof.authentication_path.len() - 1 { new_ap_digests.insert(node_index, acc_hash); } } // Update the peak let (_, peak_index) = shared_basic::leaf_index_to_mt_index_and_peak_index(leaf_index, self.num_leafs()); self.peaks[peak_index as usize] = acc_hash; } // Update all the supplied membership proofs let mut modified_membership_proof_indices: Vec = vec![]; for (i, (membership_proof, mp_leaf_index)) in membership_proofs .iter_mut() .zip(membership_proof_leaf_indices) .enumerate() { let ap_indices = membership_proof.get_node_indices(*mp_leaf_index); // Some of the hashes in `membership_proof` might need to be updated. We can // loop over `authentication_path_indices` and check if the element is // contained `deducible_hashes`. If it is, then the appropriate element in // `membership_proof.authentication_path` needs to be replaced with an element // from `deducible_hashes`. for (digest, authentication_path_indices) in membership_proof .authentication_path .iter_mut() .zip(ap_indices.into_iter()) { // Any number of hashes can be updated in the authentication path, since // we're modifying multiple leafs in the MMR // Since this function returns the indices of the modified membership proofs, // a check if the new digest is actually different from the previous value is // needed. if new_ap_digests.contains_key(&authentication_path_indices) && *digest != new_ap_digests[&authentication_path_indices] { *digest = new_ap_digests[&authentication_path_indices]; modified_membership_proof_indices.push(i); } } } modified_membership_proof_indices.dedup(); modified_membership_proof_indices } /// `true` if the `new_peaks` input matches the calculated new MMR peaks /// resulting from the provided appends and mutations. Can panic if initial /// state is not a valid MMR. fn verify_batch_update( &self, new_peaks: &[Digest], appended_leafs: &[Digest], leaf_mutations: Vec>, ) -> bool { let mut manipulated_leaf_indices = leaf_mutations.iter().map(|x| x.leaf_index); if !manipulated_leaf_indices.clone().all_unique() { return false; } if manipulated_leaf_indices.any(|idx| idx >= self.leaf_count) { return false; } // Reverse the leaf mutation vectors, since we want to apply them using `pop` let ( mut leaf_mutation_indices, mut leaf_mutation_target_values, mut updated_membership_proofs, ): (Vec<_>, Vec<_>, Vec<_>) = leaf_mutations .into_iter() .rev() .map(|m| (m.leaf_index, m.new_leaf, m.membership_proof)) .multiunzip(); let mut running_peaks = self.peaks.clone(); while let Some(membership_proof) = updated_membership_proofs.pop() { let new_leaf_value = leaf_mutation_target_values.pop().unwrap(); let leaf_index_mutated_leaf = leaf_mutation_indices.pop().unwrap(); // TODO: Should we verify the membership proof here? // Calculate the new peaks after mutating a leaf running_peaks = shared_basic::calculate_new_peaks_from_leaf_mutation( &running_peaks, self.leaf_count, new_leaf_value, leaf_index_mutated_leaf, &membership_proof, ); // TODO: Replace this with the new batch updater `batch_update_from_batch_leaf_mutation` // Update all remaining membership proofs with this leaf mutation let leaf_mutation = LeafMutation::new(leaf_index_mutated_leaf, new_leaf_value, membership_proof); MmrMembershipProof::batch_update_from_leaf_mutation( &mut updated_membership_proofs, &leaf_mutation_indices, leaf_mutation, ); } for (append_count, &leaf_to_append) in (0..).zip(appended_leafs) { let (calculated_new_peaks, _) = shared_basic::calculate_new_peaks_from_append( self.leaf_count + append_count, running_peaks, leaf_to_append, ); running_peaks = calculated_new_peaks; } running_peaks == new_peaks } fn to_accumulator(&self) -> MmrAccumulator { self.to_owned() } } /// Follows the description on /// /// to calculate a root from a list of peaks and the size of the MMR. pub(crate) fn bag_peaks(peaks: &[Digest], leaf_count: u64) -> Digest { // use `hash_10` over `hash` or `hash_varlen` to simplify hashing in Triton VM let leaf_count_elem = H::Element::from(leaf_count); let hashed_leaf_count = Digest::::from_element(H::hash_single(&leaf_count_elem)); peaks.iter().rev().fold(hashed_leaf_count, |acc, &peak| { Digest::::from_element(H::hash_pair(&peak.data, &acc.data)) }) } pub mod util { // use itertools::Itertools; use super::super::shared_advanced::right_lineage_length_from_node_index; use super::super::shared_basic::leaf_index_to_mt_index_and_peak_index; use super::*; use crate::crypto::digest::random_elements; /// Get an MMR accumulator with a requested number of leafs, and requested leaf /// digests at specified indices. Also returns the MMR membership proofs for the /// specified leafs. pub fn mmra_with_mps( leaf_count: u64, specified_leafs: Vec<(u64, Digest)>, ) -> (MmrAccumulator, Vec>) { assert!( specified_leafs.iter().map(|&(idx, _)| idx).all_unique(), "Specified leaf indices must be unique" ); // initial_setup let mut peaks: Vec> = random_elements::(leaf_count.count_ones() as usize); if specified_leafs.is_empty() { return (MmrAccumulator::init(peaks, leaf_count), vec![]); } let (first_leaf_index, first_specified_digest) = specified_leafs[0]; let (first_mt_index, first_peak_index) = leaf_index_to_mt_index_and_peak_index(first_leaf_index, leaf_count); // Change peaks such that the 1st specification belongs in the MMR let first_mt_height = (first_mt_index + 1).next_power_of_two().ilog2() - 1; let first_ap: Vec> = random_elements(first_mt_height as usize); let first_mp = MmrMembershipProof::new(first_ap); let original_node_indices = first_mp.get_node_indices(first_leaf_index); let mut derivable_node_values: HashMap> = HashMap::default(); let mut first_acc_hash = first_specified_digest; for (height, node_index_in_path) in first_mp .get_direct_path_indices(first_leaf_index) .into_iter() .enumerate() { derivable_node_values.insert(node_index_in_path, first_acc_hash); if first_mp.authentication_path.len() > height { if right_lineage_length_from_node_index(node_index_in_path) != 0 { first_acc_hash = Digest::::from_element(H::hash_pair( &first_mp.authentication_path[height].data, &first_acc_hash.data, )); } else { first_acc_hash = Digest::::from_element(H::hash_pair( &first_acc_hash.data, &first_mp.authentication_path[height].data, )); } } } // Update root peaks[first_peak_index as usize] = first_acc_hash; let mut all_ap_elements: HashMap> = original_node_indices .into_iter() .zip_eq(first_mp.authentication_path.clone()) .collect(); let mut all_mps = vec![first_mp]; let mut all_leaf_indices = vec![first_leaf_index]; let mut all_leafs = vec![first_specified_digest]; for (new_leaf_index, new_leaf) in specified_leafs.into_iter().skip(1) { let (new_leaf_mt_index, _new_leaf_peaks_index) = leaf_index_to_mt_index_and_peak_index(new_leaf_index, leaf_count); let height_of_new_mt = (new_leaf_mt_index + 1).next_power_of_two().ilog2() - 1; let mut new_mp = MmrMembershipProof::new(random_elements(height_of_new_mt as usize)); let new_node_indices = new_mp.get_node_indices(new_leaf_index); for (height, new_node_index) in new_node_indices.iter().enumerate() { if all_ap_elements.contains_key(new_node_index) { // AP element may not be mutated new_mp.authentication_path[height] = all_ap_elements[new_node_index]; } else if derivable_node_values.contains_key(new_node_index) { // AP element must refer to both old and new leaf new_mp.authentication_path[height] = derivable_node_values[new_node_index]; } } let new_peaks = shared_basic::calculate_new_peaks_from_leaf_mutation( &peaks, leaf_count, new_leaf, new_leaf_index, &new_mp, ); assert!(new_mp.verify(new_leaf_index, new_leaf, &new_peaks, leaf_count)); let leaf_mutations = vec![LeafMutation::new(new_leaf_index, new_leaf, new_mp.clone())]; let mutated = MmrMembershipProof::batch_update_from_batch_leaf_mutation( &mut all_mps.iter_mut().collect_vec(), &all_leaf_indices, leaf_mutations, ); // Sue me for muta in mutated.iter() { let mp = &all_mps[*muta]; let mp_leaf_index = all_leaf_indices[*muta]; for (hght, idx) in mp.get_node_indices(mp_leaf_index).iter().enumerate() { all_ap_elements.insert(*idx, mp.authentication_path[hght]); } } // Update derivable node values let mut acc_hash = new_leaf; for (height, node_index_in_path) in new_mp .get_direct_path_indices(new_leaf_index) .into_iter() .enumerate() { if height == new_mp.get_direct_path_indices(new_leaf_index).len() - 1 { break; } derivable_node_values.insert(node_index_in_path, acc_hash); if right_lineage_length_from_node_index(node_index_in_path) != 0 { acc_hash = Digest::::from_element(H::hash_pair( &new_mp.authentication_path[height].data, &acc_hash.data, )); } else { acc_hash = Digest::::from_element(H::hash_pair( &acc_hash.data, &new_mp.authentication_path[height].data, )); } } // Update all_ap_elements for (node_index, ap_element) in new_node_indices .into_iter() .zip_eq(new_mp.authentication_path.clone().into_iter()) { all_ap_elements.insert(node_index, ap_element); } all_mps.push(new_mp); peaks = new_peaks; all_leafs.push(new_leaf); all_leaf_indices.push(new_leaf_index); } (MmrAccumulator::init(peaks, leaf_count), all_mps) } } use arbitrary::Arbitrary; impl<'a, H: HashFunction> Arbitrary<'a> for MmrAccumulator { fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result { let num_leafs = u.arbitrary::()? >> 1; // num_leafs can be at most 63 bits let peaks = (0..num_leafs.count_ones()) .map(|_| Digest::arbitrary(u)) .try_collect()?; Ok(MmrAccumulator::init(peaks, num_leafs)) } } // #[cfg(test)] // mod accumulator_mmr_tests { // use std::cmp; // use insta::assert_snapshot; // use itertools::izip; // use itertools::Itertools; // use num_traits::ConstZero; // use proptest::collection::vec; // use proptest::prop_assert_eq; // use proptest_arbitrary_interop::arb; // use rand::distr::Uniform; // use rand::prelude::*; // use rand::random; // use test_strategy::proptest; // use super::*; // use crate::math::b_field_element::BFieldElement; // use crate::math::other::random_elements; // use crate::math::tip5::Tip5; // use crate::mock::mmr::get_mock_ammr_from_digests; // use crate::mock::mmr::MockMmr; // impl From for MmrAccumulator { // fn from(ammr: MockMmr) -> Self { // MmrAccumulator { // leaf_count: ammr.num_leafs(), // peaks: ammr.peaks(), // } // } // } // impl From<&MockMmr> for MmrAccumulator { // fn from(ammr: &MockMmr) -> Self { // MmrAccumulator { // leaf_count: ammr.num_leafs(), // peaks: ammr.peaks(), // } // } // } // #[test] // fn conversion_test() { // let leaf_hashes: Vec = random_elements(3); // let mock_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes); // let accumulator_mmr = MmrAccumulator::from(mock_mmr.clone()); // assert_eq!(mock_mmr.peaks(), accumulator_mmr.peaks()); // assert_eq!(mock_mmr.bag_peaks(), accumulator_mmr.bag_peaks()); // assert_eq!(mock_mmr.is_empty(), accumulator_mmr.is_empty()); // assert!(!mock_mmr.is_empty()); // assert_eq!(mock_mmr.num_leafs(), accumulator_mmr.num_leafs()); // assert_eq!(3, accumulator_mmr.num_leafs()); // } // #[test] // fn verify_batch_update_single_append_test() { // let leaf_hashes_start: Vec = random_elements(3); // let appended_leaf: Digest = random(); // let mut leaf_hashes_end: Vec = leaf_hashes_start.clone(); // leaf_hashes_end.push(appended_leaf); // let accumulator_mmr_start: MmrAccumulator = // MmrAccumulator::new_from_leafs(leaf_hashes_start); // let accumulator_mmr_end: MmrAccumulator = MmrAccumulator::new_from_leafs(leaf_hashes_end); // let leafs_were_appended = accumulator_mmr_start.verify_batch_update( // &accumulator_mmr_end.peaks(), // &[appended_leaf], // vec![], // ); // assert!(leafs_were_appended); // } // #[test] // fn verify_batch_update_single_mutate_test() { // let leaf0: Digest = random(); // let leaf1: Digest = random(); // let leaf2: Digest = random(); // let leaf3: Digest = random(); // let leaf4: Digest = random(); // let leaf_hashes_start: Vec = vec![leaf0, leaf1, leaf2, leaf4]; // let leaf_hashes_end: Vec = vec![leaf0, leaf1, leaf2, leaf3]; // let accumulator_mmr_start: MmrAccumulator = // MmrAccumulator::new_from_leafs(leaf_hashes_start.clone()); // let archive_mmr_start: MockMmr = get_mock_ammr_from_digests(leaf_hashes_start); // let leaf_index_3 = 3; // let membership_proof = archive_mmr_start.prove_membership(leaf_index_3); // let accumulator_mmr_end: MmrAccumulator = MmrAccumulator::new_from_leafs(leaf_hashes_end); // { // let appended_leafs = []; // let leaf_mutations = vec![LeafMutation::new( // leaf_index_3, // leaf3, // membership_proof.clone(), // )]; // assert!(accumulator_mmr_start.verify_batch_update( // &accumulator_mmr_end.peaks(), // &appended_leafs, // leaf_mutations, // )); // } // // Verify that repeated mutations are disallowed // { // let appended_leafs = []; // let leaf_mutations = vec![ // LeafMutation::new(leaf_index_3, leaf3, membership_proof.clone()), // LeafMutation::new(leaf_index_3, leaf3, membership_proof), // ]; // assert!(!accumulator_mmr_start.verify_batch_update( // &accumulator_mmr_end.peaks(), // &appended_leafs, // leaf_mutations, // )); // } // } // #[test] // fn verify_batch_update_two_append_test() { // let leaf_hashes_start: Vec = random_elements(3); // let appended_leafs: Vec = random_elements(2); // let leaf_hashes_end: Vec = // [leaf_hashes_start.clone(), appended_leafs.clone()].concat(); // let accumulator_mmr_start: MmrAccumulator = // MmrAccumulator::new_from_leafs(leaf_hashes_start); // let accumulator_mmr_end: MmrAccumulator = MmrAccumulator::new_from_leafs(leaf_hashes_end); // let leafs_were_appended = accumulator_mmr_start.verify_batch_update( // &accumulator_mmr_end.peaks(), // &appended_leafs, // vec![], // ); // assert!(leafs_were_appended); // } // #[test] // fn verify_batch_update_two_mutate_test() { // let leaf14: Digest = random(); // let leaf15: Digest = random(); // let leaf16: Digest = random(); // let leaf17: Digest = random(); // let leaf20: Digest = random(); // let leaf21: Digest = random(); // let leaf_hashes_start: Vec = vec![leaf14, leaf15, leaf16, leaf17]; // let leaf_hashes_end: Vec = vec![leaf14, leaf20, leaf16, leaf21]; // let accumulator_mmr_start: MmrAccumulator = // MmrAccumulator::new_from_leafs(leaf_hashes_start.clone()); // let archive_mmr_start: MockMmr = get_mock_ammr_from_digests(leaf_hashes_start); // let leaf_index_1 = 1; // let leaf_index_3 = 3; // let membership_proof1 = archive_mmr_start.prove_membership(leaf_index_1); // let membership_proof3 = archive_mmr_start.prove_membership(leaf_index_3); // let accumulator_mmr_end: MmrAccumulator = MmrAccumulator::new_from_leafs(leaf_hashes_end); // let leaf_mutations = vec![ // LeafMutation::new(leaf_index_1, leaf20, membership_proof1), // LeafMutation::new(leaf_index_3, leaf21, membership_proof3), // ]; // assert!(accumulator_mmr_start.verify_batch_update( // &accumulator_mmr_end.peaks(), // &[], // leaf_mutations // )); // } // #[test] // fn batch_mutate_leaf_and_update_mps_test() { // let mut rng = rand::rng(); // for mmr_leaf_count in 1..100 { // let initial_leaf_digests: Vec = random_elements(mmr_leaf_count); // let mut mmra: MmrAccumulator = // MmrAccumulator::new_from_leafs(initial_leaf_digests.clone()); // let mut ammr: MockMmr = get_mock_ammr_from_digests(initial_leaf_digests.clone()); // let mut ammr_copy: MockMmr = get_mock_ammr_from_digests(initial_leaf_digests.clone()); // let mutated_leaf_count = rng.random_range(0..mmr_leaf_count); // let all_indices: Vec = (0..mmr_leaf_count as u64).collect(); // // Pick indices for leafs that are being mutated // let mut all_indices_mut0 = all_indices.clone(); // let mut mutated_leaf_indices: Vec = vec![]; // for _ in 0..mutated_leaf_count { // let leaf_index = // all_indices_mut0.remove(rng.random_range(0..all_indices_mut0.len())); // mutated_leaf_indices.push(leaf_index); // } // // Pick membership proofs that we want to update // let membership_proof_count = rng.random_range(0..mmr_leaf_count); // let mut all_indices_mut1 = all_indices.clone(); // let mut membership_proof_indices: Vec = vec![]; // for _ in 0..membership_proof_count { // let leaf_index = // all_indices_mut1.remove(rng.random_range(0..all_indices_mut1.len())); // membership_proof_indices.push(leaf_index); // } // // Calculate the terminal leafs, as they look after the batch leaf mutation // // that we are preparing to execute // let new_leafs: Vec = random_elements(mutated_leaf_count); // let mut terminal_leafs: Vec = initial_leaf_digests; // for (i, new_leaf) in mutated_leaf_indices.iter().zip(new_leafs.iter()) { // new_leaf.clone_into(&mut terminal_leafs[*i as usize]); // } // // Calculate the leafs digests associated with the membership proofs, as they look // // *after* the batch leaf mutation // let mut terminal_leafs_for_mps: Vec = vec![]; // for i in membership_proof_indices.iter() { // terminal_leafs_for_mps.push(terminal_leafs[*i as usize]); // } // // Construct the mutation data // let all_mps = mutated_leaf_indices // .iter() // .map(|i| ammr.prove_membership(*i)) // .collect_vec(); // let mutation_data: Vec = new_leafs // .into_iter() // .zip(mutated_leaf_indices) // .zip(all_mps.iter()) // .map(|((leaf, leaf_index), mp)| LeafMutation::new(leaf_index, leaf, mp.clone())) // .collect_vec(); // assert_eq!(mutated_leaf_count, mutation_data.len()); // let original_membership_proofs: Vec = membership_proof_indices // .iter() // .map(|i| ammr.prove_membership(*i)) // .collect(); // // Do the update on both MMRs // let mut mmra_mps = original_membership_proofs.clone(); // let mut ammr_mps = original_membership_proofs.clone(); // let mutated_mps_mmra = mmra.batch_mutate_leaf_and_update_mps( // &mut mmra_mps.iter_mut().collect::>(), // &membership_proof_indices, // mutation_data.clone(), // ); // let mutated_mps_ammr = ammr.batch_mutate_leaf_and_update_mps( // &mut ammr_mps.iter_mut().collect::>(), // &membership_proof_indices, // mutation_data.clone(), // ); // assert_eq!(mutated_mps_mmra, mutated_mps_ammr); // // Verify that both MMRs end up with same peaks // assert_eq!(mmra.peaks(), ammr.peaks()); // // Verify that membership proofs from AMMR and MMRA are equal // assert_eq!(membership_proof_count, mmra_mps.len()); // assert_eq!(membership_proof_count, ammr_mps.len()); // assert_eq!(ammr_mps, mmra_mps); // // Verify that all membership proofs still work // assert!(mmra_mps // .iter() // .zip(terminal_leafs_for_mps.iter()) // .zip(membership_proof_indices.iter()) // .all(|((mp, &leaf), leaf_index)| mp.verify( // *leaf_index, // leaf, // &mmra.peaks(), // mmra.num_leafs() // ))); // // Manually construct an MMRA from the new data and verify that peaks and leaf // // count matches // assert!( // mutated_leaf_count == 0 || ammr_copy.peaks() != ammr.peaks(), // "If mutated leaf count is non-zero, at least on peaks must be different" // ); // mutation_data.into_iter().for_each( // |LeafMutation { // leaf_index, // new_leaf, // .. // }| { // ammr_copy.mutate_leaf_raw(leaf_index, new_leaf); // }, // ); // assert_eq!( // ammr_copy.peaks(), // ammr.peaks(), // "Mutation though batch mutation function must transform the MMR \ // like a list of individual leaf mutations" // ); // } // } // #[test] // fn verify_batch_update_pbt() { // type H = Tip5; // for start_size in 1..18 { // let leaf_hashes_start: Vec = random_elements(start_size); // let local_hash = |x: u128| H::hash_varlen(&[BFieldElement::new(x as u64)]); // let bad_digests: Vec = (12..12 + start_size) // .map(|x| local_hash(x as u128)) // .collect(); // let bad_mmr: MockMmr = get_mock_ammr_from_digests(bad_digests.clone()); // let bad_membership_proof: MmrMembershipProof = bad_mmr.prove_membership(0); // let bad_membership_proof_digest = bad_digests[0]; // let bad_leaf: Digest = local_hash(8765432165123u128); // let mock_mmr_init: MockMmr = get_mock_ammr_from_digests(leaf_hashes_start.clone()); // let accumulator_mmr = MmrAccumulator::new_from_leafs(leaf_hashes_start.clone()); // for append_size in 0..18 { // let appends: Vec = (2000..2000 + append_size).map(local_hash).collect(); // let mutate_count = cmp::min(12, start_size); // for mutate_size in 0..mutate_count { // let new_leaf_values: Vec = (13..13 + mutate_size) // .map(|x| local_hash(x as u128)) // .collect(); // // Ensure that indices are unique since batch updating cannot update // // the same leaf twice in one go // let mutated_indices: Vec = rand::rng() // .sample_iter(Uniform::new(0, start_size as u64).unwrap()) // .take(mutate_size) // .sorted() // .unique() // .collect(); // // Create the expected MMRs // let mut leaf_hashes_mutated = leaf_hashes_start.clone(); // for (index, new_leaf) in izip!(mutated_indices.clone(), new_leaf_values.clone()) // { // leaf_hashes_mutated[index as usize] = new_leaf; // } // for appended_digest in appends.iter() { // leaf_hashes_mutated.push(appended_digest.to_owned()); // } // // let mutated_mock_mmr = // // MockMmr::::new(leaf_hashes_mutated.clone()); // let mutated_mock_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_hashes_mutated.clone()); // let mutated_accumulator_mmr = // MmrAccumulator::new_from_leafs(leaf_hashes_mutated); // let expected_new_peaks_from_archival = mutated_mock_mmr.peaks(); // let expected_new_peaks_from_accumulator = mutated_accumulator_mmr.peaks(); // assert_eq!( // expected_new_peaks_from_archival, // expected_new_peaks_from_accumulator // ); // // Create the inputs to the method call // let all_mps = mutated_indices // .iter() // .map(|i| mock_mmr_init.prove_membership(*i)) // .collect_vec(); // let mut leaf_mutations: Vec = new_leaf_values // .clone() // .into_iter() // .zip(mutated_indices.iter()) // .zip(all_mps.iter()) // .map(|((leaf, leaf_index), mp)| { // LeafMutation::new(*leaf_index, leaf, mp.clone()) // }) // .collect_vec(); // assert!(accumulator_mmr.verify_batch_update( // &expected_new_peaks_from_accumulator, // &appends, // leaf_mutations.clone() // )); // assert!(mock_mmr_init.verify_batch_update( // &expected_new_peaks_from_accumulator, // &appends, // leaf_mutations.clone() // )); // // Negative tests // let mut bad_appends = appends.clone(); // if append_size > 0 && mutate_size > 0 { // // bad append vector // bad_appends[(mutated_indices[0] % append_size as u64) as usize] = bad_leaf; // assert!(!accumulator_mmr.verify_batch_update( // &expected_new_peaks_from_accumulator, // &bad_appends, // leaf_mutations.clone() // )); // // Bad membership proof // let bad_index = mutated_indices[0] as usize % mutated_indices.len(); // leaf_mutations[bad_index].new_leaf = bad_membership_proof_digest; // assert!(!accumulator_mmr.verify_batch_update( // &expected_new_peaks_from_accumulator, // &appends, // leaf_mutations.clone() // )); // leaf_mutations[mutated_indices[0] as usize % mutated_indices.len()] // .membership_proof = bad_membership_proof.clone(); // assert!(!accumulator_mmr.verify_batch_update( // &expected_new_peaks_from_accumulator, // &appends, // leaf_mutations // )); // } // } // } // } // } // #[test] // fn mmra_serialization_test() { // // You could argue that this test doesn't belong here, as it tests the behavior of // // an imported library. I included it here, though, because the setup seems a bit clumsy // // to me so far. // type H = Tip5; // type Mmr = MmrAccumulator; // let mut mmra: Mmr = MmrAccumulator::new_from_leafs(vec![]); // mmra.append(H::hash(&BFieldElement::ZERO)); // let json = serde_json::to_string(&mmra).unwrap(); // let s_back = serde_json::from_str::(&json).unwrap(); // assert_eq!(mmra.bag_peaks(), s_back.bag_peaks()); // assert_eq!(1, mmra.num_leafs()); // } // #[test] // fn get_size_test() { // type Mmr = MmrAccumulator; // // 10 digests produces an MMRA with two peaks // let digests: Vec = random_elements(10); // let mmra: Mmr = MmrAccumulator::new_from_leafs(digests); // println!("mmra.get_size() = {}", mmra.get_size()); // // Sanity check of measured size in RAM // assert!(mmra.get_size() > 2 * std::mem::size_of::()); // // For some reason this failed on GitHub's server when only multiplied by 4. This worked // // consistently on my machine with `4`. It's probably because of a different architecture. // // So the number was just increased to 100. See: // // https://github.com/Neptune-Crypto/twenty-first/actions/runs/4928129170/jobs/8806086355 // assert!(mmra.get_size() < 100 * std::mem::size_of::()); // } // #[test] // fn test_mmr_accumulator_decode() { // for _ in 0..100 { // let num_leafs = rand::random_range(0..100); // let leafs = random_elements(num_leafs); // let mmra = MmrAccumulator::new_from_leafs(leafs); // let encoded = mmra.encode(); // let decoded = *MmrAccumulator::decode(&encoded).unwrap(); // assert_eq!(mmra, decoded); // } // } // #[test] // #[should_panic(expected = "Lists must have same length. Got: 0 and 3")] // fn test_diff_len_lists_batch_mutate_leaf_and_update_mps() { // // Checks that batch_mutate_leaf_and_update_mps panics when passed differing length lists // // differing length lists // let mut mock_membership_proofs: Vec = vec![]; // let membership_proof_leaf_indices = vec![1, 2, 3]; // // This should trigger the panic due to the lengths mismatch // let mut mmra: MmrAccumulator = MmrAccumulator::new_from_leafs(vec![]); // mmra.batch_mutate_leaf_and_update_mps( // mock_membership_proofs // .iter_mut() // .collect::>() // .as_mut_slice(), // &membership_proof_leaf_indices, // vec![], // ); // } // #[proptest] // fn arbitrary_mmra_has_consistent_num_leafs_and_peaks( // #[strategy(arb::())] mmra: MmrAccumulator, // ) { // prop_assert_eq!(mmra.peaks().len(), mmra.num_leafs().count_ones() as usize); // } // #[proptest(cases = 20)] // fn mmra_with_mps_produces_valid_output( // #[strategy(0..u64::MAX / 2)] mmr_leaf_count: u64, // #[strategy(0usize..10)] _num_revealed_leafs: usize, // #[strategy(vec(0u64..#mmr_leaf_count, #_num_revealed_leafs))] // mmr_revealed_leaf_indices: Vec, // ) { // let indexed_leafs_input: Vec<(u64, Digest)> = mmr_revealed_leaf_indices // .iter() // .map(|idx| (*idx, random())) // .collect_vec(); // let (mmra, mmr_mps) = util::mmra_with_mps(mmr_leaf_count, indexed_leafs_input.clone()); // for (mmr_mp, (mmr_leaf_index, leaf)) in // mmr_mps.into_iter().zip_eq(indexed_leafs_input.iter()) // { // mmr_mp.verify(*mmr_leaf_index, *leaf, &mmra.peaks(), mmra.num_leafs()); // } // } // #[test] // fn computing_mmr_root_for_no_leafs_produces_some_digest() { // MmrAccumulator::new_from_leafs(vec![]).bag_peaks(); // } // #[test] // fn bag_peaks_snapshot() { // let mut rng = StdRng::seed_from_u64(0x92ca758afeec6d29); // let empty_mmr = MmrAccumulator::new_from_leafs(vec![]); // assert_snapshot!(empty_mmr.bag_peaks().0[0], @"00941080798860502477"); // let one_leaf_mmr = MmrAccumulator::new_from_leafs(vec![rng.random()]); // assert_snapshot!(one_leaf_mmr.bag_peaks().0[0], @"16030278140236594076"); // let two_leafs_mmr = MmrAccumulator::new_from_leafs(vec![rng.random()]); // assert_snapshot!(two_leafs_mmr.bag_peaks().0[0], @"09405464453414142998"); // let ten_peaks: [Digest; 10] = rng.random(); // let ten_peak_mmr = MmrAccumulator::init(ten_peaks.to_vec(), 0b11_1111_1111); // assert_snapshot!(ten_peak_mmr.bag_peaks().0[0], @"03780783030734820370"); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/mmr_membership_proof.rs ================================================ use std::collections::hash_map::RandomState; use std::collections::hash_set::Intersection; use std::collections::HashMap; use std::collections::HashSet; use std::fmt::Debug; use std::iter::FromIterator; // use arbitrary::Arbitrary; // use get_size2::GetSize; use itertools::Itertools; // use serde::Deserialize; // use serde::Serialize; use super::mmr_trait::LeafMutation; use super::shared_advanced; use super::shared_basic; use super::TOO_MANY_LEAFS_ERR; use crate::crypto::digest::{Digest, HashFunction}; use crate::crypto::merkle_tree::MerkleTree; // use crate::error::U32_TO_USIZE_ERR; // use crate::error::USIZE_TO_U64_ERR; // use crate::prelude::*; #[derive(Debug, Clone, Eq, PartialEq)] // Serialize, Deserialize, GetSize, Arbitrary)] pub struct MmrMembershipProof { pub authentication_path: Vec>, } impl MmrMembershipProof { pub fn new(authentication_path: Vec>) -> Self { Self { authentication_path, } } /// Verify a membership proof for an MMR. pub fn verify( &self, leaf_index: u64, leaf_hash: Digest, peaks: &[Digest], num_leafs: u64, ) -> bool { if leaf_index >= num_leafs { // out of bounds return false; } let (mut mt_index, peak_index) = shared_basic::leaf_index_to_mt_index_and_peak_index(leaf_index, num_leafs); let expected_peak_count = num_leafs.count_ones(); let actual_peak_count = u32::try_from(peaks.len()).expect(TOO_MANY_LEAFS_ERR); if expected_peak_count != actual_peak_count { return false; } let merkle_tree_height = u64::from(mt_index.ilog2()); let auth_path_len = u64::try_from(self.authentication_path.len()) .expect("Authentication path length is too large"); if merkle_tree_height != auth_path_len { return false; } let mut current_node = leaf_hash; for &sibling in &self.authentication_path { let current_node_is_left_sibling = mt_index % 2 == 0; current_node = if current_node_is_left_sibling { Digest::::from_element(H::hash_pair(¤t_node.data, &sibling.data)) } else { Digest::::from_element(H::hash_pair(&sibling.data, ¤t_node.data)) }; mt_index /= 2; } debug_assert_eq!(MerkleTree::::ROOT_INDEX as u64, mt_index); let peak_index = usize::try_from(peak_index).expect("Peak index is too large"); peaks[peak_index] == current_node } /// Return the node indices for the authentication path in this membership proof pub(crate) fn get_node_indices(&self, leaf_index: u64) -> Vec { let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_index); let mut node_indices = vec![]; for _ in 0..self.authentication_path.len() { let (right_ancestor_count, height) = shared_advanced::right_lineage_length_and_own_height(node_index); let is_right_child = right_ancestor_count != 0; if is_right_child { node_indices.push(shared_advanced::left_sibling(node_index, height)); // parent of right child is +1 node_index += 1; } else { node_indices.push(shared_advanced::right_sibling(node_index, height)); // parent of left child: node_index += 1 << (height + 1); } } node_indices } /// Return the node indices for the hash values that can be derived from this proof, /// including the node index for the leaf itself. pub(crate) fn get_direct_path_indices(&self, leaf_index: u64) -> Vec { let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_index); let mut node_indices = vec![node_index]; for _ in 0..self.authentication_path.len() { node_index = shared_advanced::parent(node_index); node_indices.push(node_index); } node_indices } /// Return the node index of the peak that the membership proof is pointing /// to, as well as this peak's height. fn get_peak_index_and_height(&self, leaf_index: u64) -> (u64, u32) { ( *self.get_direct_path_indices(leaf_index).last().unwrap(), self.authentication_path.len() as u32, ) } /// Update a membership proof with a `verify_append` proof. Returns `true` if an /// authentication path has been mutated, false otherwise. pub fn update_from_append( &mut self, membership_proof_leaf_index: u64, old_mmr_leaf_count: u64, new_mmr_leaf: Digest, old_mmr_peaks: &[Digest], ) -> bool { // 1. Get index of authentication paths's peak // 2. Get node indices for nodes added by the append // 3. Check if authentication path's peak's parent is present in the added nodes // (peak can only be left child) // a. If not, then we are done, return from method // 4. Get the indices that auth path must be extended with // 5. Get all derivable node digests, store in hash map // a. Get the node digests from the previous peaks // b. Get the node digests that can be calculated by hashing from the new leaf // 6. Push required digests to the authentication path // 1 let (own_old_peak_index, own_old_peak_height) = self.get_peak_index_and_height(membership_proof_leaf_index); // 2 let added_node_indices = shared_advanced::node_indices_added_by_append(old_mmr_leaf_count); // 3 // Any peak is a left child, so we don't have to check if it's a right or left child. // This means we can use a faster method to find the parent index than the generic method. let peak_parent_index = own_old_peak_index + (1 << (own_old_peak_height + 1)); // 3a if !added_node_indices.contains(&peak_parent_index) { return false; } // 4 Get node indices of missing digests let new_peak_index: u64 = *added_node_indices.last().unwrap(); let new_node_count: u64 = shared_advanced::num_leafs_to_num_nodes(old_mmr_leaf_count + 1); let node_indices_for_missing_digests: Vec = shared_advanced::get_authentication_path_node_indices( own_old_peak_index, new_peak_index, new_node_count, ) .unwrap(); // 5 collect all derivable peaks in a hashmap indexed by node index // 5.a, collect all node hash digests that are present in the old peaks // The keys in the hash map are node indices let mut known_digests: HashMap> = HashMap::new(); let (_old_mmr_peak_heights, old_mmr_peak_indices) = shared_advanced::get_peak_heights_and_peak_node_indices(old_mmr_leaf_count); for (old_peak_index, old_peak_digest) in old_mmr_peak_indices.iter().zip(old_mmr_peaks.iter()) { known_digests.insert(*old_peak_index, old_peak_digest.to_owned()); } // 5.b collect all node hash digests that are derivable from `new_leaf` and // `old_peaks`. These are the digests of `new_leaf`'s path to the root. // break out of loop once *one* digest is found this way since that will // always suffice. let mut acc_hash = new_mmr_leaf.to_owned(); for (node_index, &old_peak_digest) in added_node_indices.iter().zip(old_mmr_peaks.iter().rev()) { known_digests.insert(*node_index, acc_hash.to_owned()); // peaks are always left children, so we don't have to check for that acc_hash = Digest::::from_element(H::hash_pair(&old_peak_digest.data, &acc_hash.data)); // once we encounter the first of the needed accumulator indices, // we can break. Just like we could in the update for the leaf update // membership proof update. // The reason for this break is that the authentication path consists of // commits to disjoint sets, so anything that can be derived from a // hash that is part of the missing digests cannot possible be an // element in an authentication path if node_indices_for_missing_digests.contains(node_index) { break; } } // 6 for missing_digest_node_index in node_indices_for_missing_digests { self.authentication_path .push(known_digests[&missing_digest_node_index]); } true } /// Batch update multiple membership proofs. /// Returns the indices of the membership proofs that were modified where index refers /// to the order in which the membership proofs were given to this function. /// Panics if `membership_proofs` and `membership_proof_leaf_indices` do not have /// the same length, or if a leaf index is out-of-bounds for the MMR. pub fn batch_update_from_append( membership_proofs: &mut [&mut Self], membership_proof_leaf_indices: &[u64], old_leaf_count: u64, new_leaf: Digest, old_peaks: &[Digest], ) -> Vec { assert_eq!( membership_proofs.len(), membership_proof_leaf_indices.len(), "Lists must have same length. Got: {} and {}", membership_proofs.len(), membership_proof_leaf_indices.len() ); assert!( membership_proof_leaf_indices .iter() .all(|x| *x < old_leaf_count), "All leaf indices must be in-bounds. Got indices [{}] and old_leaf_count = {}", membership_proof_leaf_indices.iter().join(", "), old_leaf_count ); // 1. Get node indices for nodes added by the append // a. If length of this list is one, newly added leaf was a left child. Return. // 2. Get all derivable node digests, store in hash map let added_node_indices = shared_advanced::node_indices_added_by_append(old_leaf_count); if added_node_indices.len() == 1 { return vec![]; } // 2 collect all derivable peaks in a hashmap indexed by node index // 2.a, collect all node hash digests that are present in the old peaks // The keys in the hash map are node indices let mut known_digests: HashMap> = HashMap::new(); let (_old_peak_heights, old_peak_indices) = shared_advanced::get_peak_heights_and_peak_node_indices(old_leaf_count); for (old_peak_index, old_peak_digest) in old_peak_indices.iter().zip(old_peaks.iter()) { known_digests.insert(*old_peak_index, old_peak_digest.to_owned()); } // 2.b collect all node hash digests that are derivable from `new_leaf` and // `old_peaks`. These are the digests of `new_leaf`'s path to the root. let mut acc_hash = new_leaf.to_owned(); for ((count, node_index), &old_peak_digest) in added_node_indices .iter() .enumerate() .zip(old_peaks.iter().rev()) { known_digests.insert(*node_index, acc_hash.to_owned()); // The last index in `added_node_indices` is the new peak // and the 2nd last will hash to the digest of the new peak, // so we can skip the last two values from this list if count == added_node_indices.len() - 2 { break; } // peaks are always left children, so we don't have to check for that acc_hash = Digest::::from_element(H::hash_pair(&old_peak_digest.data, &acc_hash.data)); } // Loop over all membership proofs and insert missing hashes for each let mut modified: Vec = vec![]; let new_peak_index: u64 = *added_node_indices.last().unwrap(); let new_node_count: u64 = shared_advanced::num_leafs_to_num_nodes(old_leaf_count + 1); for (i, (membership_proof, mp_leaf_index)) in membership_proofs .iter_mut() .zip(membership_proof_leaf_indices) .enumerate() { let (old_peak_index, old_peak_height) = membership_proof.get_peak_index_and_height(*mp_leaf_index); // Any peak is a left child, so we don't have to check if it's a right or left child. // This means we can use a faster method to find the parent index than the generic // method. let peak_parent_index = old_peak_index + (1 << (old_peak_height + 1)); if !added_node_indices.contains(&peak_parent_index) { continue; } modified.push(i); let node_indices_for_missing_digests: Vec = shared_advanced::get_authentication_path_node_indices( old_peak_index, new_peak_index, new_node_count, ) .unwrap(); // Sanity check debug_assert!( !node_indices_for_missing_digests.is_empty(), "authentication path must be missing digests at this point" ); for missing_digest_node_index in node_indices_for_missing_digests { membership_proof .authentication_path .push(known_digests[&missing_digest_node_index]); } } modified } /// Update a membership proof with a `leaf_mutation` data structure. In /// other words: Given a valid MMR membership proof for an MMR, calculate /// the updated MMR membership proof after one of the MMR's leafs have been /// changed. pub fn update_from_leaf_mutation( &mut self, own_mp_leaf_index: u64, leaf_mutation: &LeafMutation, ) -> bool { let affected_node_indices: HashSet = leaf_mutation.affected_node_indices().into_iter().collect(); let own_node_ap_indices = self.get_node_indices(own_mp_leaf_index); let own_node_indices_hash_set: HashSet = HashSet::from_iter(own_node_ap_indices.clone()); let mut intersection: Intersection = own_node_indices_hash_set.intersection(&affected_node_indices); // If intersection is empty no change is needed let Some(&intersection_index) = intersection.next() else { return false; }; // Sanity check, should always be true, since `intersection` can at most // contain *one* element. assert!(intersection.next().is_none()); // If intersection is **not** empty, we need to calculate all deducible node hashes from the // `leaf_mutation_membership_proof`, until we meet the intersecting node. let mut deducible_hashes: HashMap> = HashMap::new(); let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_mutation.leaf_index); deducible_hashes.insert(node_index, leaf_mutation.new_leaf); let mut acc_hash: Digest = leaf_mutation.new_leaf; // Calculate hashes from the bottom towards the peak. Break when // the intersecting node is reached. for &hash in leaf_mutation.membership_proof.authentication_path.iter() { // It's not necessary to calculate all the way to the root since, // the intersection set has a size of at most one. // So we can break the loop when we find a `node_index` that // is equal to the intersection index. This way we same some // hash calculations here. if intersection_index == node_index { break; } let (acc_right_ancestor_count, acc_height) = shared_advanced::right_lineage_length_and_own_height(node_index); if acc_right_ancestor_count != 0 { acc_hash = Digest::::from_element(H::hash_pair(&hash.data, &acc_hash.data)); // parent of right child is +1 node_index += 1; } else { acc_hash = Digest::::from_element(H::hash_pair(&acc_hash.data, &hash.data)); // parent of left child: node_index += 1 << (acc_height + 1); }; deducible_hashes.insert(node_index, acc_hash); } // Some of the hashes in `self` need to be updated. We can loop over // `own_node_indices` and check if the element is contained `deducible_hashes`. // If it is, then the appropriate element in `self.authentication_path` needs to // be replaced with an element from `deducible_hashes`. for (digest, own_node_index) in self .authentication_path .iter_mut() .zip(own_node_ap_indices.into_iter()) { if !deducible_hashes.contains_key(&own_node_index) { continue; } *digest = deducible_hashes[&own_node_index]; } true } /// Update multiple membership proofs with a `leaf_mutation` proof. For the /// `leaf_mutation_membership_proof` parameter, it doesn't matter if you use the /// old or new membership proof associated with the leaf mutation, as they are /// the same before and after the leaf mutation. /// /// Returns the indices of the membership proofs that were modified where index refers /// to the order in which the membership proofs were given to this function. /// Panics if `membership_proofs` and `membership_proof_leaf_indices` do not have /// the same length. pub fn batch_update_from_leaf_mutation( membership_proofs: &mut [Self], membership_proof_leaf_indices: &[u64], leaf_mutation: LeafMutation, ) -> Vec { assert_eq!( membership_proofs.len(), membership_proof_leaf_indices.len(), "Lists must have same length. Got: {} and {}", membership_proofs.len(), membership_proof_leaf_indices.len() ); // 1. Calculate all hashes that are deducible from the leaf update // 2. Iterate through all membership proofs and update digests that // are deducible from the leaf update proof. // Calculate hashes from the bottom towards the peak. Break before we // calculate the hash of the peak, since peaks are never included in // authentication paths let mut deducible_hashes: HashMap> = HashMap::new(); let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_mutation.leaf_index); deducible_hashes.insert(node_index, leaf_mutation.new_leaf); let mut acc_hash: Digest = leaf_mutation.new_leaf; for (count, &hash) in leaf_mutation .membership_proof .authentication_path .iter() .enumerate() { // Do not calculate the last hash as it will always be a peak which // are never included in the authentication path if count == leaf_mutation.membership_proof.authentication_path.len() - 1 { break; } let (right_ancestor_count, acc_height) = shared_advanced::right_lineage_length_and_own_height(node_index); if right_ancestor_count != 0 { // node is right child acc_hash = Digest::::from_element(H::hash_pair(&hash.data, &acc_hash.data)); // parent of right child is +1 node_index += 1; } else { // node is left child acc_hash = Digest::::from_element(H::hash_pair(&acc_hash.data, &hash.data)); // parent of left child: node_index += 1 << (acc_height + 1); }; deducible_hashes.insert(node_index, acc_hash); } let mut modified_membership_proofs: Vec = vec![]; for (i, (membership_proof, mp_leaf_index)) in membership_proofs .iter_mut() .zip(membership_proof_leaf_indices) .enumerate() { let ap_indices = membership_proof.get_node_indices(*mp_leaf_index); // Some of the hashes in `membership_proof` might need to be updated. We can loop over // `authentication_path_indices` and check if the element is contained // `deducible_hashes`. // If it is, then the appropriate element in `membership_proof.authentication_path` // needs to be replaced with an element from `deducible_hashes`. for (digest, authentication_path_indices) in membership_proof .authentication_path .iter_mut() .zip(ap_indices.into_iter()) { // Maximum 1 digest can be updated in each authentication path // so if that is encountered, we might as well break and go to // the next membership proof // Since this function returns the indices of the modified membership proofs, // a check if the new digest is actually different from the previous value is // needed. if deducible_hashes.contains_key(&authentication_path_indices) && *digest != deducible_hashes[&authentication_path_indices] { *digest = deducible_hashes[&authentication_path_indices]; modified_membership_proofs.push(i as u64); break; } } } modified_membership_proofs } /// batch_update_from_batch_leaf_mutation /// Update a batch of own membership proofs given a batch of /// authenticated leaf modifications. It is the caller's res- /// ponsibility to ensure that the authentication paths are /// valid; if not, the updated membership proofs will become /// invalid as well. /// @params /// - membership_proofs -- own membership proofs, to be updated /// - authentication_paths_and_leafs -- membership proofs of the mutated /// leafs, and the new leaf values /// /// Returns those indices into the slice of membership proofs that were updated. pub fn batch_update_from_batch_leaf_mutation( membership_proofs: &mut [&mut Self], membership_proof_leaf_indices: &[u64], mut leaf_mutations: Vec>, ) -> Vec { assert_eq!( membership_proofs.len(), membership_proof_leaf_indices.len(), "Lists must have same length. Got: {} and {}", membership_proofs.len(), membership_proof_leaf_indices.len() ); // Calculate all derivable paths let mut new_ap_digests: HashMap> = HashMap::new(); // Calculate the derivable digests from a number of leaf mutations and their // associated authentication paths. Notice that all authentication paths // are only valid *prior* to any updates. They get invalidated (unless updated) // throughout the updating as their neighbor leaf digests change values. // The hash map `new_ap_digests` takes care of that. while let Some(LeafMutation { leaf_index, new_leaf, membership_proof, }) = leaf_mutations.pop() { let mut node_index = shared_advanced::leaf_index_to_node_index(leaf_index); let former_value = new_ap_digests.insert(node_index, new_leaf); assert!( former_value.is_none(), "Duplicated leafs are not allowed in membership proof updater" ); let mut acc_hash: Digest = new_leaf.to_owned(); for (i, &hash) in membership_proof.authentication_path.iter().enumerate() { // Do not calculate the last hash as it will always be a peak which // are never included in the authentication path if i == membership_proof.authentication_path.len() - 1 { break; } // If sibling node is something that has already been calculated, we use that // hash digest. Otherwise, we use the one in our authentication path. let (right_ancestor_count, height) = shared_advanced::right_lineage_length_and_own_height(node_index); if right_ancestor_count != 0 { let left_sibling_index = shared_advanced::left_sibling(node_index, height); let sibling_hash: Digest = new_ap_digests .get(&left_sibling_index) .copied() .unwrap_or(hash); acc_hash = Digest::::from_element(H::hash_pair(&sibling_hash.data, &acc_hash.data)); // Find parent node index node_index += 1; } else { let right_sibling_index = shared_advanced::right_sibling(node_index, height); let sibling_hash: Digest = new_ap_digests .get(&right_sibling_index) .copied() .unwrap_or(hash); acc_hash = Digest::::from_element(H::hash_pair(&acc_hash.data, &sibling_hash.data)); // Find parent node index node_index += 1 << (height + 1); } new_ap_digests.insert(node_index, acc_hash); } } let mut modified_membership_proof_indices: Vec = vec![]; for (i, (membership_proof, mp_leaf_index)) in membership_proofs .iter_mut() .zip(membership_proof_leaf_indices) .enumerate() { let ap_indices = membership_proof.get_node_indices(*mp_leaf_index); // Some of the hashes in `membership_proof` might need to be updated. We can // loop over `authentication_path_indices` and check if the element is contained // `deducible_hashes`. If it is, then the appropriate element in // `membership_proof.authentication_path` needs to be replaced with an element // from `deducible_hashes`. for (digest, authentication_path_indices) in membership_proof .authentication_path .iter_mut() .zip(ap_indices.into_iter()) { // Any number of hashes can be updated in the authentication path, since // we're modifying multiple leafs in the MMR // Since this function returns the indices of the modified membership proofs, // a check if the new digest is actually different from the previous value is // needed. if new_ap_digests.contains_key(&authentication_path_indices) && *digest != new_ap_digests[&authentication_path_indices] { modified_membership_proof_indices.push(i); *digest = new_ap_digests[&authentication_path_indices]; } } } modified_membership_proof_indices.dedup(); modified_membership_proof_indices } } // #[cfg(test)] // mod mmr_membership_proof_test { // use itertools::Itertools; // use proptest_arbitrary_interop::arb; // use rand::random; // use rand::Rng; // use test_strategy::proptest; // use super::*; // use crate::math::b_field_element::BFieldElement; // use crate::math::digest::Digest; // use crate::math::other::random_elements; // use crate::math::tip5::Tip5; // use crate::mock::mmr::get_mock_ammr_from_digests; // use crate::mock::mmr::MockMmr; // use crate::util_types::mmr::mmr_accumulator::util::mmra_with_mps; // use crate::util_types::mmr::mmr_accumulator::MmrAccumulator; // use crate::util_types::mmr::mmr_trait::Mmr; // #[test] // fn equality_and_hash_test() { // type H = Tip5; // let mut rng = rand::rng(); // let some_digest: Digest = rng.random(); // let other_digest: Digest = rng.random(); // // Assert that both membership proofs and their digests are equal // let mp0 = MmrMembershipProof::new(vec![]); // let mp1 = MmrMembershipProof::new(vec![]); // assert_eq!(mp0, mp1); // assert_eq!(H::hash(&mp0), H::hash(&mp1)); // let mp2 = MmrMembershipProof::new(vec![some_digest]); // let mp3 = MmrMembershipProof::new(vec![some_digest]); // assert_eq!(mp2, mp3); // assert_eq!(H::hash(&mp2), H::hash(&mp3)); // assert_ne!(mp0, mp2); // assert_ne!(H::hash(&mp0), H::hash(&mp2)); // let mp4 = MmrMembershipProof::new(vec![other_digest]); // assert_ne!(mp2, mp4); // assert_ne!(H::hash(&mp2), H::hash(&mp4)); // let mp5 = MmrMembershipProof::new(vec![some_digest, other_digest]); // let mp6 = MmrMembershipProof::new(vec![other_digest, some_digest]); // assert_eq!(mp5, mp5); // assert_eq!(H::hash(&mp5), H::hash(&mp5)); // assert_ne!(mp5, mp6); // assert_ne!(H::hash(&mp5), H::hash(&mp6)); // assert_ne!(mp0, mp5); // assert_ne!(H::hash(&mp0), H::hash(&mp5)); // assert_ne!(mp2, mp5); // assert_ne!(H::hash(&mp2), H::hash(&mp5)); // assert_ne!(mp4, mp5); // assert_ne!(H::hash(&mp4), H::hash(&mp5)); // } // #[test] // fn get_node_indices_simple_test() { // const LEAF_INDEX: u64 = 4; // let leaf_hashes: Vec = random_elements(8); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes); // let membership_proof = archival_mmr.prove_membership(LEAF_INDEX); // assert_eq!( // vec![9, 13, 7], // membership_proof.get_node_indices(LEAF_INDEX) // ); // assert_eq!( // vec![8, 10, 14, 15], // membership_proof.get_direct_path_indices(LEAF_INDEX) // ); // } // #[test] // fn get_peak_index_simple_test() { // type H = Tip5; // let mut mmr_size = 7; // let leaf_digests: Vec = random_elements(mmr_size); // let mut archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_digests); // let mut expected_peak_indices_and_heights: Vec<(u64, u32)> = // vec![(7, 2), (7, 2), (7, 2), (7, 2), (10, 1), (10, 1), (11, 0)]; // for (leaf_index, expected_peak_index) in // (0..mmr_size as u64).zip(expected_peak_indices_and_heights.into_iter()) // { // let membership_proof = archival_mmr.prove_membership(leaf_index); // assert_eq!( // expected_peak_index, // membership_proof.get_peak_index_and_height(leaf_index) // ); // } // // Increase size to 8 and verify that the peaks are now different // mmr_size = 8; // let leaf_hash: Digest = H::hash(&1337u64); // archival_mmr.append(leaf_hash); // expected_peak_indices_and_heights = vec![(15, 3); mmr_size]; // for (leaf_index, expected_peak_index) in // (0..mmr_size as u64).zip(expected_peak_indices_and_heights.into_iter()) // { // let membership_proof = archival_mmr.prove_membership(leaf_index); // assert_eq!( // expected_peak_index, // membership_proof.get_peak_index_and_height(leaf_index) // ); // } // // Increase size to 9 and verify that the peaks are now different // mmr_size = 9; // let another_leaf_hash: Digest = H::hash(&13337u64); // archival_mmr.append(another_leaf_hash); // expected_peak_indices_and_heights = vec![ // (15, 3), // (15, 3), // (15, 3), // (15, 3), // (15, 3), // (15, 3), // (15, 3), // (15, 3), // (16, 0), // ]; // for (leaf_index, expected_peak_index) in // (0..mmr_size as u64).zip(expected_peak_indices_and_heights.into_iter()) // { // let membership_proof = archival_mmr.prove_membership(leaf_index); // assert_eq!( // expected_peak_index, // membership_proof.get_peak_index_and_height(leaf_index) // ); // } // } // #[proptest(cases = 10)] // fn mmr_verification_if_leaf_index_is_out_of_bounds( // #[strategy(0..=121usize)] leaf_count: usize, // ) { // let leafs: Vec = random_elements(leaf_count); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leafs.clone()); // let peaks = archival_mmr.peaks(); // for (i, leaf) in leafs.into_iter().enumerate() { // let leaf_index = i as u64; // let mp = archival_mmr.prove_membership(leaf_index); // assert!(mp.verify(leaf_index, leaf, &peaks, leaf_count as u64)); // let bad_leaf_index = leaf_index + leaf_count as u64; // assert!(!mp.verify(bad_leaf_index, leaf, &peaks, leaf_count as u64)); // } // } // #[test] // fn mmr_verify_does_not_crash_on_too_short_peaks_list_unit() { // let mmr_mp = MmrMembershipProof::new(vec![Default::default()]); // assert!(!mmr_mp.verify(0, Default::default(), &[], 2)); // } // #[proptest(cases = 10)] // fn mmr_verification_with_wrong_length_of_peak_list( // #[strategy(0..=1_000_000u64)] leaf_count: u64, // #[strategy(0..=#leaf_count)] leaf_index: u64, // #[strategy(arb())] leaf: Digest, // ) { // let (mmra, mps) = mmra_with_mps(leaf_count, vec![(leaf_index, leaf)]); // let mp = mps[0].clone(); // let peaks_list = mmra.peaks(); // assert!(mp.verify(leaf_index, leaf, &peaks_list, leaf_count)); // let one_too_few = if peaks_list.is_empty() { // return Ok(()); // } else { // &peaks_list[..peaks_list.len() - 1] // }; // assert!(!mp.verify(leaf_index, leaf, one_too_few, leaf_count)); // let one_too_many = [peaks_list.clone(), vec![Digest::default()]].concat(); // assert!(!mp.verify(leaf_index, leaf, &one_too_many, leaf_count)); // } // #[test] // fn update_batch_membership_proofs_from_leaf_mutations_new_test() { // type H = Tip5; // let total_leaf_count = 8; // let leaf_hashes: Vec = random_elements(total_leaf_count); // let mut archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let mut membership_proofs: Vec = vec![]; // for i in 0..total_leaf_count { // let leaf_index = i as u64; // membership_proofs.push(archival_mmr.prove_membership(leaf_index)); // } // let new_leaf2: Digest = H::hash(&133337u64); // let new_leaf3: Digest = H::hash(&12345678u64); // let mutation_membership_proof_old2 = archival_mmr.prove_membership(2); // let mutation_membership_proof_old3 = archival_mmr.prove_membership(3); // archival_mmr.mutate_leaf_raw(2, new_leaf2); // archival_mmr.mutate_leaf_raw(3, new_leaf3); // for (mp_leaf_index, mp) in membership_proofs.iter_mut().enumerate() { // let leaf_mutation = // LeafMutation::new(2, new_leaf2, mutation_membership_proof_old2.clone()); // mp.update_from_leaf_mutation(mp_leaf_index as u64, &leaf_mutation); // } // for (mp_leaf_index, mp) in membership_proofs.iter_mut().enumerate() { // let leaf_mutation = // LeafMutation::new(3, new_leaf3, mutation_membership_proof_old3.clone()); // mp.update_from_leaf_mutation(mp_leaf_index as u64, &leaf_mutation); // } // let mut updated_leaf_hashes = leaf_hashes; // updated_leaf_hashes[2] = new_leaf2; // updated_leaf_hashes[3] = new_leaf3; // for (mp_leaf_index, (mp, &leaf_hash)) in membership_proofs // .iter() // .zip(&updated_leaf_hashes) // .enumerate() // { // mp.verify( // mp_leaf_index as u64, // leaf_hash, // &archival_mmr.peaks(), // archival_mmr.num_leafs(), // ); // } // } // #[test] // fn batch_update_from_batch_leaf_mutation_total_replacement_test() { // let total_leaf_count = 268; // let leaf_hashes_init: Vec = random_elements(total_leaf_count); // let archival_mmr_init: MockMmr = get_mock_ammr_from_digests(leaf_hashes_init); // let leaf_hashes_final: Vec = random_elements(total_leaf_count); // let archival_mmr_final: MockMmr = get_mock_ammr_from_digests(leaf_hashes_final.clone()); // let mp_leaf_indices = 0..total_leaf_count as u64; // let mut membership_proofs: Vec = mp_leaf_indices // .clone() // .map(|leaf_index| archival_mmr_init.prove_membership(leaf_index)) // .collect(); // let membership_proofs_clone = membership_proofs.clone(); // let leaf_mutations: Vec = leaf_hashes_final // .clone() // .into_iter() // .zip(mp_leaf_indices.clone()) // .zip(membership_proofs_clone) // .map(|((leaf, leaf_index), mp)| LeafMutation::new(leaf_index, leaf, mp)) // .collect(); // let changed_values = MmrMembershipProof::batch_update_from_batch_leaf_mutation( // &mut membership_proofs.iter_mut().collect::>(), // &mp_leaf_indices.clone().collect_vec(), // leaf_mutations, // ); // // This assert only works if `total_leaf_count` is an even number since there // // otherwise is a membership proof that's an empty authentication path, and that // // does not change // assert_eq!( // (0..total_leaf_count).collect::>(), // changed_values, // "All membership proofs must be indicated as changed" // ); // for ((mp, final_leaf_hash), leaf_index) in membership_proofs // .into_iter() // .zip(leaf_hashes_final) // .zip(mp_leaf_indices) // { // assert!(mp.verify( // leaf_index, // final_leaf_hash, // &archival_mmr_final.peaks(), // total_leaf_count as u64 // )); // } // } // #[test] // fn batch_update_from_batch_leaf_mutation_test() { // let total_leaf_count = 34; // let mut leaf_hashes: Vec = random_elements(total_leaf_count); // let mut archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let mut rng = rand::rng(); // for modified_leaf_count in 0..=total_leaf_count { // // Pick a set of membership proofs that we want to batch-update // let own_membership_proof_count = rng.random_range(0..total_leaf_count); // let mut all_leaf_indices: Vec = (0..total_leaf_count as u64).collect(); // let mut own_mp_leaf_indices = vec![]; // let mut own_membership_proofs: Vec = vec![]; // for _ in 0..own_membership_proof_count { // let leaf_index = // all_leaf_indices.remove(rng.random_range(0..all_leaf_indices.len())); // own_membership_proofs.push(archival_mmr.prove_membership(leaf_index)); // own_mp_leaf_indices.push(leaf_index); // } // // Set the new leafs and their associated authentication paths for the mutation // // argument // let new_leafs: Vec = random_elements(modified_leaf_count); // let mut all_leaf_indices_new: Vec = (0..total_leaf_count as u64).collect(); // let mut authentication_paths: Vec = vec![]; // let mut mutated_leaf_leaf_indices = vec![]; // for _ in 0..modified_leaf_count { // let leaf_index = // all_leaf_indices_new.remove(rng.random_range(0..all_leaf_indices_new.len())); // authentication_paths.push(archival_mmr.prove_membership(leaf_index)); // mutated_leaf_leaf_indices.push(leaf_index); // } // // let the magic start // let original_mps = own_membership_proofs.clone(); // let mutation_argument: Vec = authentication_paths // .into_iter() // .zip(new_leafs.clone().into_iter()) // .zip(mutated_leaf_leaf_indices.iter()) // .map(|((mp, leaf), leaf_idx)| LeafMutation::new(*leaf_idx, leaf, mp)) // .collect(); // let updated_mp_indices_0 = MmrMembershipProof::batch_update_from_batch_leaf_mutation( // &mut own_membership_proofs.iter_mut().collect::>(), // &own_mp_leaf_indices, // mutation_argument.clone(), // ); // // update MMR // for (i, mutated_leaf_index) in mutated_leaf_leaf_indices.iter().enumerate() { // leaf_hashes[*mutated_leaf_index as usize] = new_leafs[i]; // archival_mmr.mutate_leaf_raw(*mutated_leaf_index, new_leafs[i]); // } // // Let's verify that `batch_mutate_leaf_and_update_mps` from the // // MmrAccumulator agrees // let mut mmra: MmrAccumulator = (&archival_mmr).into(); // let mut mps_copy = original_mps; // let updated_mp_indices_1 = mmra.batch_mutate_leaf_and_update_mps( // &mut mps_copy.iter_mut().collect::>(), // &own_mp_leaf_indices, // mutation_argument, // ); // assert_eq!(own_membership_proofs, mps_copy); // assert_eq!(mmra.peaks(), archival_mmr.peaks()); // assert_eq!(updated_mp_indices_0, updated_mp_indices_1); // // test that all updated membership proofs are valid under the updated MMR // (0..own_membership_proof_count) // .zip(own_mp_leaf_indices) // .for_each(|(i, own_leaf_index)| { // let membership_proof = own_membership_proofs[i].clone(); // assert!(membership_proof.verify( // own_leaf_index, // leaf_hashes[own_leaf_index as usize], // &archival_mmr.peaks(), // archival_mmr.num_leafs(), // )); // }); // } // } // #[test] // fn batch_update_from_leaf_mutation_no_change_return_value_test() { // // This test verifies that the return value indicating changed membership proofs is empty // // even though the mutations affect the membership proofs. The reason it is empty is that // // the resulting membership proof digests are unchanged, since the leaf hashes mutations // // are the identity operators. In other words: the leafs don't change. // let total_leaf_count = 8; // let (leaf_hashes, mut membership_proofs) = make_populated_archival_mmr(total_leaf_count); // let own_leaf_indices = (0..total_leaf_count as u64).collect_vec(); // for leaf_index in own_leaf_indices.iter() { // let leaf_mutation_membership_proof = membership_proofs[*leaf_index as usize].clone(); // let new_leaf = leaf_hashes[*leaf_index as usize]; // let leaf_mutation = // LeafMutation::new(*leaf_index, new_leaf, leaf_mutation_membership_proof); // let ret = MmrMembershipProof::batch_update_from_leaf_mutation( // &mut membership_proofs, // &own_leaf_indices, // leaf_mutation, // ); // // the return value must be empty since no membership proof has changed // assert!(ret.is_empty()); // } // let membership_proofs_clone = membership_proofs.clone(); // let membership_proofs_init_and_new_leafs: Vec = leaf_hashes // .clone() // .into_iter() // .zip(membership_proofs_clone) // .zip(own_leaf_indices.iter()) // .map(|((leaf, mp), leaf_idx)| LeafMutation::new(*leaf_idx, leaf, mp)) // .collect(); // let ret = MmrMembershipProof::batch_update_from_batch_leaf_mutation( // &mut membership_proofs.iter_mut().collect::>(), // &own_leaf_indices, // membership_proofs_init_and_new_leafs.clone(), // ); // // the return value must be empty since no membership proof has changed // assert!(ret.is_empty()); // // Let's test the exact same for the MMR accumulator scheme // let mut mmra: MmrAccumulator = MmrAccumulator::new_from_leafs(leaf_hashes); // let ret_from_acc = mmra.batch_mutate_leaf_and_update_mps( // &mut membership_proofs.iter_mut().collect::>(), // &own_leaf_indices, // membership_proofs_init_and_new_leafs, // ); // assert!(ret_from_acc.is_empty()); // } // fn make_populated_archival_mmr( // total_leaf_count: usize, // ) -> (Vec, Vec) { // let leaf_hashes: Vec = random_elements(total_leaf_count); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let mut membership_proofs: Vec = vec![]; // for i in 0..total_leaf_count { // let leaf_index = i as u64; // membership_proofs.push(archival_mmr.prove_membership(leaf_index)); // } // (leaf_hashes, membership_proofs) // } // #[test] // fn update_batch_membership_proofs_from_batch_leaf_mutations_test() { // let total_leaf_count = 8; // let leaf_hashes: Vec = random_elements(total_leaf_count); // let mut archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes); // let modified_leaf_count: usize = 8; // let mut membership_proofs: Vec = vec![]; // let mut own_mp_leaf_indices = vec![]; // for i in 0..modified_leaf_count { // let leaf_index = i as u64; // membership_proofs.push(archival_mmr.prove_membership(leaf_index)); // own_mp_leaf_indices.push(leaf_index); // } // let new_leafs: Vec = random_elements(modified_leaf_count); // for i in 0..modified_leaf_count { // let leaf_mutation_membership_proof = membership_proofs[i].clone(); // let new_leaf = new_leafs[i]; // let leaf_mutation = // LeafMutation::new(i as u64, new_leaf, leaf_mutation_membership_proof); // MmrMembershipProof::batch_update_from_leaf_mutation( // &mut membership_proofs, // &own_mp_leaf_indices, // leaf_mutation, // ); // } // (0..modified_leaf_count).for_each(|i| { // let leaf_index = i as u64; // archival_mmr.mutate_leaf_raw(leaf_index, new_leafs[i]); // }); // for (i, (mp, mp_leaf_idx)) in membership_proofs // .into_iter() // .zip_eq(own_mp_leaf_indices) // .enumerate() // { // assert!(mp.verify( // mp_leaf_idx, // new_leafs[i], // &archival_mmr.peaks(), // archival_mmr.num_leafs() // )); // } // } // #[test] // fn update_membership_proof_from_leaf_mutation_test() { // type H = Tip5; // let leaf_hashes: Vec = random_elements(8); // let new_leaf: Digest = H::hash(&133337u64); // let mut accumulator_mmr = MmrAccumulator::new_from_leafs(leaf_hashes.clone()); // assert_eq!(8, accumulator_mmr.num_leafs()); // let mut an_archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let original_archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let own_leaf_leaf_index = 4; // let mut membership_proof = an_archival_mmr.prove_membership(own_leaf_leaf_index); // // 1. Update a leaf in both the accumulator MMR and in the archival MMR // let old_peaks = an_archival_mmr.peaks(); // let mutated_leaf_leaf_index = 2; // let membership_proof_for_manipulated_leaf = // an_archival_mmr.prove_membership(mutated_leaf_leaf_index); // an_archival_mmr.mutate_leaf_raw(mutated_leaf_leaf_index, new_leaf); // let leaf_mutation = LeafMutation::new( // mutated_leaf_leaf_index, // new_leaf, // membership_proof_for_manipulated_leaf, // ); // accumulator_mmr.mutate_leaf(leaf_mutation.clone()); // assert_eq!(an_archival_mmr.peaks(), accumulator_mmr.peaks()); // let new_peaks_1 = an_archival_mmr.peaks(); // assert_ne!( // new_peaks_1, old_peaks, // "Peaks must change when leaf is mutated" // ); // let real_membership_proof_from_archival = // an_archival_mmr.prove_membership(own_leaf_leaf_index); // let archival_peaks = an_archival_mmr.peaks(); // assert_eq!( // new_peaks_1, archival_peaks, // "peaks returned from `get_peaks` must match that returned with membership proof" // ); // // 2. Verify that the proof fails but that the one from archival works // assert!(!membership_proof.verify( // own_leaf_leaf_index, // new_leaf, // &new_peaks_1, // accumulator_mmr.num_leafs() // )); // assert!(membership_proof.verify( // own_leaf_leaf_index, // leaf_hashes[own_leaf_leaf_index as usize], // &old_peaks, // accumulator_mmr.num_leafs() // )); // assert!(real_membership_proof_from_archival.verify( // own_leaf_leaf_index, // leaf_hashes[own_leaf_leaf_index as usize], // &new_peaks_1, // accumulator_mmr.num_leafs() // )); // // 3. Update the membership proof with the membership method // membership_proof.update_from_leaf_mutation(own_leaf_leaf_index, &leaf_mutation); // // 4. Verify that the proof now succeeds // assert!(membership_proof.verify( // own_leaf_leaf_index, // leaf_hashes[own_leaf_leaf_index as usize], // &new_peaks_1, // accumulator_mmr.num_leafs() // )); // // 5. test batch update from leaf update // let all_leaf_indices = (0..8u64).collect_vec(); // for leaf_index_mutated in all_leaf_indices.iter() { // let mut archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let mut mps: Vec = vec![]; // for j in all_leaf_indices.iter() { // mps.push(original_archival_mmr.prove_membership(*j)); // } // let original_mps = mps.clone(); // let leaf_mutation_membership_proof = archival_mmr.prove_membership(*leaf_index_mutated); // archival_mmr.mutate_leaf_raw(*leaf_index_mutated, new_leaf); // let new_peaks_2 = archival_mmr.peaks(); // let new_leaf_mutation = LeafMutation::new( // *leaf_index_mutated, // new_leaf, // leaf_mutation_membership_proof, // ); // let modified = MmrMembershipProof::batch_update_from_leaf_mutation( // &mut mps, // &all_leaf_indices, // new_leaf_mutation, // ); // // when updating data index i, all authentication paths are updated // // *except* for element i. // let mut expected_modified = all_leaf_indices.clone(); // expected_modified.remove(*leaf_index_mutated as usize); // assert_eq!(expected_modified, modified); // for j in all_leaf_indices.iter() { // let our_leaf = if *leaf_index_mutated == *j { // new_leaf // } else { // leaf_hashes[*j as usize] // }; // assert!(mps[*j as usize].verify(*j, our_leaf, &new_peaks_2, 8)); // // Verify that original membership proofs are no longer valid // // For size = 8, all membership proofs except the one for element 0 // // will be updated since this MMR only contains a single peak. // // An updated leaf (0 in this case) retains its authentication path after // // the update. But all other leafs pointing to the same MMR will have updated // // authentication paths. // if j == leaf_index_mutated { // assert!( // original_mps[*j as usize].verify(*j, our_leaf, &new_peaks_2, 8), // "original membership proof must be valid when j = i" // ); // } else { // assert!( // !original_mps[*j as usize].verify(*j, our_leaf, &new_peaks_2, 8), // "original membership proof must be invalid when j != i" // ); // } // } // } // } // #[test] // fn update_membership_proof_from_leaf_mutation_big_test() { // // Build MMR from leaf count 0 to 22, and loop through *each* // // leaf index for MMR, modifying its membership proof with a // // leaf update. // for leaf_count in 0..=22 { // let leaf_hashes: Vec = random_elements(leaf_count); // let new_leaf: Digest = random(); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // // Loop over all leaf indices that we want to modify in the MMR // for i in 0..leaf_count { // let leaf_index_i = i as u64; // let leaf_mutation_membership_proof = archival_mmr.prove_membership(leaf_index_i); // let mut modified_archival_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_hashes.clone()); // modified_archival_mmr.mutate_leaf_raw(leaf_index_i, new_leaf); // let new_peaks = modified_archival_mmr.peaks(); // // Loop over all leaf indices want a membership proof of, for modification // for j in 0..leaf_count { // let leaf_index_j = j as u64; // let mut membership_proof: MmrMembershipProof = // archival_mmr.prove_membership(leaf_index_j); // let original_membership_roof = membership_proof.clone(); // let leaf_mutation = LeafMutation::new( // leaf_index_i, // new_leaf, // leaf_mutation_membership_proof.clone(), // ); // let membership_proof_was_mutated = // membership_proof.update_from_leaf_mutation(leaf_index_j, &leaf_mutation); // let our_leaf = if leaf_index_i == leaf_index_j { // new_leaf // } else { // leaf_hashes[leaf_index_j as usize] // }; // assert!(membership_proof.verify( // leaf_index_j, // our_leaf, // &new_peaks, // leaf_count as u64 // )); // // If membership proof was mutated, the original proof must fail // if membership_proof_was_mutated { // assert!(!original_membership_roof.verify( // leaf_index_j, // our_leaf, // &new_peaks, // leaf_count as u64 // )); // } // // Verify that modified membership proof matches that which can be // // fetched from the modified archival MMR // assert_eq!( // modified_archival_mmr.prove_membership(leaf_index_j), // membership_proof // ); // } // } // } // } // #[test] // fn update_membership_proof_from_append_simple_with_bit_mmra() { // let original_leaf_count = (1 << 35) + (1 << 7) - 1; // let specified_count = 40; // let mut rng = rand::rng(); // let mut specified_indices: HashSet = HashSet::default(); // for _ in 0..specified_count { // specified_indices.insert(rng.random_range(0..original_leaf_count)); // } // // Ensure that at least *one* MP will be mutated upon insertion of a new leaf // specified_indices.insert(original_leaf_count - 1); // let collected_values = specified_indices.len(); // let specified_leafs: Vec<(u64, Digest)> = specified_indices // .clone() // .into_iter() // .zip_eq(random_elements(collected_values)) // .collect_vec(); // let (mut mmra, mut mps) = mmra_with_mps(original_leaf_count, specified_leafs.clone()); // let new_leaf: Digest = random(); // let old_peaks = mmra.peaks(); // mmra.append(new_leaf); // assert!(!mps // .iter() // .zip_eq(specified_leafs.iter()) // .all(|(mp, (leaf_index, leaf))| mp.verify( // *leaf_index, // *leaf, // &mmra.peaks(), // mmra.num_leafs() // ))); // MmrMembershipProof::batch_update_from_append( // &mut mps.iter_mut().collect_vec(), // &specified_indices.into_iter().collect_vec(), // original_leaf_count, // new_leaf, // &old_peaks, // ); // assert!(mps // .iter() // .zip_eq(specified_leafs.iter()) // .all(|(mp, (leaf_index, leaf))| mp.verify( // *leaf_index, // *leaf, // &mmra.peaks(), // mmra.num_leafs() // ))); // } // #[test] // fn update_membership_proof_from_append_simple() { // type H = Tip5; // let leaf_count = 7; // let leaf_hashes: Vec = random_elements(leaf_count); // let new_leaf: Digest = H::hash(&133337u64); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // for i in 0..leaf_count { // let leaf_index = i as u64; // let mut membership_proof = archival_mmr.prove_membership(leaf_index); // let old_peaks = archival_mmr.peaks(); // let mut appended_archival_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_hashes.clone()); // // let mut appended_archival_mmr = archival_mmr.clone(); // appended_archival_mmr.append(new_leaf); // let new_peaks = appended_archival_mmr.peaks(); // // Verify that membership proof fails before update and succeeds after // // for the case of leaf_count 7, **all** membership proofs have to be // // updated to be valid, so they should all fail prior to the update. // let last_leaf_index = leaf_count as u64; // assert!(!membership_proof.verify( // leaf_index, // leaf_hashes[leaf_index as usize], // &new_peaks, // last_leaf_index + 1 // )); // membership_proof.update_from_append(leaf_index, last_leaf_index, new_leaf, &old_peaks); // assert!(membership_proof.verify( // leaf_index, // leaf_hashes[leaf_index as usize], // &new_peaks, // last_leaf_index + 1 // )); // // Verify that the appended Arhival MMR produces the same membership proof // // as the one we got by updating the old membership proof // assert_eq!( // appended_archival_mmr.prove_membership(leaf_index), // membership_proof // ); // } // } // #[test] // fn update_membership_proof_from_append_big_tests() { // for leaf_count in 0..68u64 { // // 1. Build a MockMmr with a variable amount of leafs // let leaf_digests: Vec = random_elements(leaf_count as usize); // let new_leaf_digest: Digest = random(); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_digests.clone()); // // For every valid data index // for leaf_index in 0..leaf_count { // // 2. Create an equivalent MockMmr, but with `new_leaf_digest` appended // let mut appended_archival_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_digests.clone()); // appended_archival_mmr.append(new_leaf_digest); // let new_peaks = appended_archival_mmr.peaks(); // // 3. Create membership proof for MockMmr from before `new_leaf_digest` // let original_membership_proof = archival_mmr.prove_membership(leaf_index); // // 4. Update (a copy of) membership proof and verify it // let mut updated_membership_proof = original_membership_proof.clone(); // let is_updated_membership_proof_changed = updated_membership_proof // .update_from_append( // leaf_index, // leaf_count, // new_leaf_digest, // &archival_mmr.peaks(), // ); // let updated_membership_proof_verifies = updated_membership_proof.verify( // leaf_index, // leaf_digests[leaf_index as usize], // &new_peaks, // leaf_count + 1, // ); // assert!(updated_membership_proof_verifies); // // 5. Assert that original membership proof fails iff a change was indicated // let original_membership_proof_verifies = original_membership_proof.verify( // leaf_index, // leaf_digests[leaf_index as usize], // &new_peaks, // leaf_count + 1, // ); // if is_updated_membership_proof_changed { // assert!(!original_membership_proof_verifies,); // } else { // assert!(original_membership_proof_verifies,); // } // // 6. Assert that updating an old membership proof is equivalent to getting a // // proof for an appended MockMmr // assert_eq!( // updated_membership_proof, // appended_archival_mmr.prove_membership(leaf_index) // ); // } // // 7. Test batch update of membership proofs... // let old_peaks = archival_mmr.peaks(); // let mp_leaf_indices = (0..leaf_count).collect_vec(); // let original_membership_proofs = mp_leaf_indices // .iter() // .map(|leaf_index| archival_mmr.prove_membership(*leaf_index)) // .collect_vec(); // // ...first by asserting that all leafs are members... // for (membership_proof, leaf_index) in original_membership_proofs // .iter() // .zip(mp_leaf_indices.iter()) // { // let membership_proof_verifies_before_batch_update = membership_proof.verify( // *leaf_index, // leaf_digests[*leaf_index as usize], // &old_peaks, // leaf_count, // ); // assert!(membership_proof_verifies_before_batch_update); // } // // ...and then create an equivalent MockMmr, but with `new_leaf_digest` appended... // let mut appended_archival_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_digests.clone()); // appended_archival_mmr.append(new_leaf_digest); // let new_peaks = appended_archival_mmr.peaks(); // let mut mutated_membership_proofs = original_membership_proofs.clone(); // // ...run batch_update_from_append()... // let indices_of_mutated_membership_proofs: Vec = // MmrMembershipProof::batch_update_from_append( // &mut mutated_membership_proofs.iter_mut().collect_vec(), // &mp_leaf_indices, // leaf_count, // new_leaf_digest, // &old_peaks, // ); // // ...and assert that mutated membership proofs with new peaks verify! // for (leaf_index, mutated_membership_proof) in // mutated_membership_proofs.iter().enumerate() // { // let mutated_membership_proof_verifies_with_new_peaks = mutated_membership_proof // .verify( // leaf_index as u64, // leaf_digests[leaf_index], // &new_peaks, // leaf_count + 1, // ); // assert!(mutated_membership_proof_verifies_with_new_peaks); // } // // Finally, assert that original membership proofs only work if they're not mutated. // for (leaf_index, original_membership_proof) in // original_membership_proofs.iter().enumerate() // { // let original_membership_proof_verifies = original_membership_proof.verify( // leaf_index as u64, // leaf_digests[leaf_index], // &new_peaks, // leaf_count + 1, // ); // if indices_of_mutated_membership_proofs.contains(&leaf_index) { // assert!(!original_membership_proof_verifies) // } else { // assert!(original_membership_proof_verifies); // } // } // } // } // #[test] // fn update_membership_proof_from_append_big_tip5() { // type H = Tip5; // // Build MMR from leaf count 0 to 9, and loop through *each* // // leaf index for MMR, modifying its membership proof with an // // append update. // for leaf_count in 0..9 { // let leaf_hashes: Vec = random_elements(leaf_count); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let new_leaf = H::hash(&BFieldElement::new(13333337)); // for i in 0..leaf_count { // let leaf_index = i as u64; // let leaf_count_index = leaf_count as u64; // let original_membership_proof = archival_mmr.prove_membership(leaf_index); // let mut appended_archival_mmr: MockMmr = // get_mock_ammr_from_digests(leaf_hashes.clone()); // appended_archival_mmr.append(new_leaf); // let new_peaks = appended_archival_mmr.peaks(); // // Update membership proof and verify that it succeeds // let mut membership_proof_mutated = original_membership_proof.clone(); // let mutated = membership_proof_mutated.update_from_append( // leaf_index, // leaf_count_index, // new_leaf, // &archival_mmr.peaks(), // ); // assert!(membership_proof_mutated.verify( // leaf_index, // leaf_hashes[i], // &new_peaks, // leaf_count_index + 1 // )); // // If membership proof mutated, then the old proof must be invalid // if mutated { // assert!(!original_membership_proof.verify( // leaf_index, // leaf_hashes[i], // &new_peaks, // leaf_count_index + 1 // )); // } // // Verify that the appended Arhival MMR produces the same membership proof // // as the one we got by updating the old membership proof // assert_eq!( // appended_archival_mmr.prove_membership(leaf_index), // membership_proof_mutated // ); // } // } // } // #[test] // fn serialization_test() { // // You could argue that this test doesn't belong here, as it tests the behavior of // // an imported library. I included it here, though, because the setup seems a bit clumsy // // to me so far. // let leaf_index = 1; // let leaf_count = 3; // let leaf_hashes: Vec = random_elements(leaf_count); // let archival_mmr: MockMmr = get_mock_ammr_from_digests(leaf_hashes.clone()); // let mp: MmrMembershipProof = archival_mmr.prove_membership(1); // let json = serde_json::to_string(&mp).unwrap(); // let s_back = serde_json::from_str::(&json).unwrap(); // assert!(s_back.verify( // leaf_index, // leaf_hashes[leaf_index as usize], // &archival_mmr.peaks(), // leaf_count as u64 // )); // } // #[test] // fn test_decode_mmr_membership_proof() { // let mut rng = rand::rng(); // for _ in 0..100 { // let num_leafs = 2 + rng.random_range(0..1000); // let leaf_hashes = random_elements(num_leafs); // let archival_mmr = get_mock_ammr_from_digests(leaf_hashes); // let leaf_index = rng.random_range(0..num_leafs) as u64; // let mp = archival_mmr.prove_membership(leaf_index); // let mp_encoded = mp.encode(); // let mp_decoded = *MmrMembershipProof::decode(&mp_encoded).unwrap(); // assert_eq!(mp, mp_decoded); // } // } // #[test] // #[should_panic(expected = "Lists must have same length. Got: 0 and 3")] // fn test_diff_len_lists_batch_update_from_append() { // // Checks that batch_update_from_append() panics when passed differing length lists // // different length lists // let mut mock_membership_proofs: Vec = vec![]; // let mock_membership_proof_leaf_indices: Vec = vec![0, 1, 2]; // // This should panic due to mismatched lengths // MmrMembershipProof::batch_update_from_append( // &mut mock_membership_proofs.iter_mut().collect_vec(), // &mock_membership_proof_leaf_indices, // 3, // random(), // &[], // ); // } // #[test] // #[should_panic(expected = "Lists must have same length. Got: 0 and 3")] // fn test_diff_len_lists_batch_update_from_leaf_mutation() { // // Checks that batch_update_from_leaf_mutation() panics when passed differing length lists // // differing length lists // let mut mock_membership_proofs: Vec = vec![]; // let mock_membership_proof_leaf_indices: Vec = vec![0, 1, 2]; // // other mock input params // let membership_proof = MmrMembershipProof::new(vec![random()]); // let mock_leaf_mutation = LeafMutation::new(0, random(), membership_proof); // // This should panic due to mismatched lengths // MmrMembershipProof::batch_update_from_leaf_mutation( // &mut mock_membership_proofs, // &mock_membership_proof_leaf_indices, // mock_leaf_mutation, // ); // } // #[test] // #[should_panic(expected = "Lists must have same length. Got: 0 and 3")] // fn test_diff_len_lists_batch_update_from_batch_leaf_mutation() { // // Checks that batch_update_from_batch_leaf_mutation() panics when passed // // differing length lists // // differing length lists // let mut mock_membership_proofs: Vec = vec![]; // let mock_membership_proof_leaf_indices: Vec = vec![0, 1, 2]; // // other mock input params // let membership_proof = MmrMembershipProof::new(vec![random()]); // let mock_leaf_mutation = LeafMutation::new(0, random(), membership_proof); // let mock_leaf_mutations = vec![mock_leaf_mutation; 3]; // // This should panic due to mismatched lengths // MmrMembershipProof::batch_update_from_batch_leaf_mutation( // &mut mock_membership_proofs.iter_mut().collect::>(), // &mock_membership_proof_leaf_indices, // mock_leaf_mutations, // ); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/mmr_successor_proof.rs ================================================ // use arbitrary::Arbitrary; use super::mmr_accumulator::MmrAccumulator; use super::mmr_trait::Mmr; use super::shared_basic::leaf_index_to_mt_index_and_peak_index; // use crate::error::USIZE_TO_U64_ERR; // use crate::prelude::*; use super::super::digest::{Digest, HashFunction}; use crate::crypto::merkle_tree::MerkleTree; /// Asserts that one [MMR Accumulator] is the descendant of another, *i.e.*, /// that the second can be obtained by appending a set of leafs to the first. It /// consists of an authentication path connecting the relevant old peaks to the /// new peaks. /// /// [MMR Accumulator]: MmrAccumulator #[derive(Debug, Clone)] pub struct MmrSuccessorProof { pub paths: Vec>, } impl MmrSuccessorProof { /// Compute a new `MmrSuccessorProof` given the starting MMR accumulator (MMRA) /// and a list of digests to be appended. /// /// # Panics /// /// This function will panic if the number of leafs in the MMRA is greater than /// or equal to 2^63. /// /// This function may panic if the passed-in MMRA is inconsistent, that is, has /// fewer peaks than is possible for its claimed number of leafs. // // For an introduction to the inner workings of this function, see // [`Self::verify_internal`]. pub fn new_from_batch_append(mmra: &MmrAccumulator, new_leafs: &[Digest]) -> Self { if mmra.num_leafs() == 0 { // any MMR is a successor to the empty MMR – nothing to check, nothing to prove return Self { paths: vec![] }; } let height_of_lowest_peak = mmra.num_leafs().trailing_zeros(); let num_leafs_in_lowest_peak = 1 << height_of_lowest_peak; if new_leafs.len() < num_leafs_in_lowest_peak { // the new leafs do not affect the old peaks return Self { paths: vec![] }; } let leafs_in_initial_right_tree = &new_leafs[..num_leafs_in_lowest_peak]; let initial_right_tree = MerkleTree::par_new(leafs_in_initial_right_tree) .expect("internal error: should be able to build Merkle tree"); let num_total_leafs = mmra.num_leafs() + u64::try_from(new_leafs.len()).expect("USIZE_TO_U64_ERR"); let first_new_leaf_index = mmra.num_leafs(); let (mut merkle_tree_index, _) = leaf_index_to_mt_index_and_peak_index(first_new_leaf_index, num_total_leafs); let height_of_new_peak = merkle_tree_index.ilog2(); merkle_tree_index >>= height_of_lowest_peak; let mut current_node = initial_right_tree.root(); let mut paths = vec![current_node]; let mut old_peaks = mmra.peaks().into_iter(); let mut first_unused_new_leaf_idx = num_leafs_in_lowest_peak; let merkle_tree_root_index = u64::try_from(MerkleTree::::ROOT_INDEX).expect("USIZE_TO_U64_ERR"); while merkle_tree_index > merkle_tree_root_index { let current_node_is_left_sibling = merkle_tree_index % 2 == 0; current_node = if current_node_is_left_sibling { let current_height = height_of_new_peak - merkle_tree_index.ilog2(); let num_leafs_in_right_tree = 1 << current_height; let indices_of_leafs_in_right_tree = first_unused_new_leaf_idx..first_unused_new_leaf_idx + num_leafs_in_right_tree; let leafs_in_right_tree = &new_leafs[indices_of_leafs_in_right_tree]; let right_tree = MerkleTree::par_new(leafs_in_right_tree) .expect("internal error: should be able to build Merkle tree"); first_unused_new_leaf_idx += num_leafs_in_right_tree; paths.push(right_tree.root()); Digest::::from_element(H::hash_pair( ¤t_node.to_element(), &right_tree.root().to_element(), )) } else { let left_sibling = old_peaks .next_back() .expect("Merkle Mountain Range Accumulator should be consistent"); Digest::::from_element(H::hash_pair( &left_sibling.to_element(), ¤t_node.to_element(), )) }; merkle_tree_index /= 2; } debug_assert_eq!(merkle_tree_root_index, merkle_tree_index); Self { paths } } /// Verify that the `old` [`MmrAccumulator`] is a predecessor of the `new` one. pub fn verify(&self, old: &MmrAccumulator, new: &MmrAccumulator) -> bool { self.verify_internal(old, new).is_ok() } /// Like [`Self::verify`], but with failure reasons instead of a `bool` to /// increase testability. // // An explanation of the algorithm follows. As an example, take the following // Merkle Mountain Range with 42 = 101010₂ leafs. Peaks are marked with `·`s. // // · // ╭───────────────┴───────────────╮ // ╭───────┴───────╮ ╭───────┴───────╮ · // ╭───┴───╮ ╭───┴───╮ ╭───┴───╮ ╭───┴───╮ ╭───┴───╮ // ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ · // ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ // // Adding 8 leafs to it results in the following new Merkle Mountain Range with // 50 = 110010₂ leafs. The addition is drawn boxy and bold. The elements of the // required authentication path are marked with `x`es. The new peaks are marked // with `○`. The one peak that's both old and new is marked `⊙`. // // ⊙ // ╭─────────┴─────────╮ ○ // ┄┄┴┄┄ ╭───────┴───────╮ ·━━━━━━━┻━━━━━━━┓ // ╭───┴───╮ ╭───┴───╮ ╭───┴───╮ ┏━━━┻━━━x // ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ·━┻━x ┏━┻━┓ ○ // ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ┏┻┓ ┏┻┓ ┏┻┓ ┏┻┓ // // The new MMR Accumulator (the one with 50 leafs) is a successor to the old // MMR Accumulator (the one with 42 leafs) if all of the following are true: // - Both MMR Accumulators are self-consistent. // - The new MMR Accumulator has more or equal the number of leafs as the old // one. // - All “shared peaks” are identical. In the example, only the highest peak is // shared. // - The first unshared peak in the new MMR Accumulator is a Merkle tree that // contains all remaining old peaks. In the example, the second new peak // contains the second and third old peaks. // // All subsequent new peaks are irrelevant for verification. In the example, // this is only the smallest peak of the new MMR Accumulator. // // To re-compute the first unshared peak in the new MMR Accumulator, // - start the Merkle tree authentication from the correct height, that is, from // the height of the smallest old peak; // - for any left sibling, use an old peak; and // - for any right sibling, use an element of the authentication path. fn verify_internal( &self, old: &MmrAccumulator, new: &MmrAccumulator, ) -> Result<(), Error> { if !old.is_consistent() { return Err(Error::InconsistentOldMmr); } if !new.is_consistent() { return Err(Error::InconsistentNewMmr); } let verify_auth_path_is_empty = || { if self.paths.is_empty() { Ok(()) } else { Err(Error::AuthenticationPathTooLong) } }; match old.num_leafs() { 0 => return verify_auth_path_is_empty(), // any MMR is a successor to the empty MMR n if n < new.num_leafs() => (), // nominal case, continued below n if n == new.num_leafs() => { // treated separately to simplify logic in nominal case return if old.peaks() == new.peaks() { verify_auth_path_is_empty() } else { Err(Error::DifferentSharedPeak) }; } _ => return Err(Error::OldHasMoreLeafsThanNew), }; let index_of_first_unverified_leaf = old.num_leafs(); let (merkle_tree_index, num_unchanged_peaks) = leaf_index_to_mt_index_and_peak_index(index_of_first_unverified_leaf, new.num_leafs()); let mut old_peaks = old.peaks().into_iter(); let mut new_peaks = new.peaks().into_iter(); for _ in 0..num_unchanged_peaks { let old_peak = old_peaks.next().ok_or(Error::MissingOldPeak)?; let new_peak = new_peaks.next().ok_or(Error::MissingNewPeak)?; if old_peak != new_peak { return Err(Error::DifferentSharedPeak); } } let height_of_lowest_old_peak = old.num_leafs().trailing_zeros(); let num_leafs_in_lowest_old_peak = 1 << height_of_lowest_old_peak; let num_new_leafs = new.num_leafs() - old.num_leafs(); if num_new_leafs < num_leafs_in_lowest_old_peak { // the new leafs don't affect the old peaks return verify_auth_path_is_empty(); } let mut auth_path = self.paths.iter(); let mut current_node = *auth_path.next().ok_or(Error::AuthenticationPathTooShort)?; let mut merkle_tree_index = merkle_tree_index >> height_of_lowest_old_peak; let merkle_tree_root_index = u64::try_from(MerkleTree::::ROOT_INDEX).expect("USIZE_TO_U64_ERR"); while merkle_tree_index > merkle_tree_root_index { let current_node_is_left_sibling = merkle_tree_index % 2 == 0; current_node = if current_node_is_left_sibling { let &right_sibling = auth_path.next().ok_or(Error::AuthenticationPathTooShort)?; Digest::::from_element(H::hash_pair( ¤t_node.to_element(), &right_sibling.to_element(), )) } else { let left_sibling = old_peaks.next_back().ok_or(Error::MissingOldPeak)?; Digest::::from_element(H::hash_pair( &left_sibling.to_element(), ¤t_node.to_element(), )) }; merkle_tree_index /= 2; } debug_assert_eq!(0, old_peaks.len()); if auth_path.len() > 0 { return Err(Error::AuthenticationPathTooLong); } let first_unshared_peak = new_peaks.next().ok_or(Error::MissingNewPeak)?; if current_node != first_unshared_peak { return Err(Error::DifferentUnsharedPeak); } Ok(()) } } #[derive(Debug, Copy, Clone, Eq, PartialEq, Hash, thiserror::Error)] // , Arbitrary)] enum Error { #[error("the new MMRA must not take away any leafs")] OldHasMoreLeafsThanNew, #[error("the old MMRA must be self-consistent")] InconsistentOldMmr, #[error("the new MMRA must be self-consistent")] InconsistentNewMmr, #[error("the old MMRA has too few peaks – is it consistent?")] MissingOldPeak, #[error("the new MMRA has too few peaks – is it consistent?")] MissingNewPeak, #[error("the authentication path contains too few elements")] AuthenticationPathTooShort, #[error("the authentication path contains spurious elements")] AuthenticationPathTooLong, #[error("a peak that should be shared between old and new MMRA is unequal")] DifferentSharedPeak, #[error("the first peak that's unshared between old and new MMRA is not as claimed")] DifferentUnsharedPeak, } // #[cfg(test)] // mod test { // use std::ops::Range; // use itertools::Itertools; // use proptest::prelude::*; // use proptest_arbitrary_interop::arb; // use test_strategy::proptest; // use super::*; // use crate::math::digest::digest_tests::DigestCorruptor; // /// A type exclusive to testing. Simplifies construction and verification of // /// [`MmrSuccessorProof`]s. // #[derive(Debug, Clone)] // struct MmrSuccessorRelation { // old: MmrAccumulator, // new: MmrAccumulator, // proof: MmrSuccessorProof, // } // impl MmrSuccessorRelation { // fn new(old_leafs: Vec, new_leafs: Vec) -> Self { // let old = MmrAccumulator::new_from_leafs(old_leafs.clone()); // let proof = MmrSuccessorProof::new_from_batch_append(&old, &new_leafs); // let new = MmrAccumulator::new_from_leafs([old_leafs, new_leafs].concat()); // Self { old, new, proof } // } // fn new_with_numbered_leafs(num_old_leafs: u64, num_new_leafs: u64) -> Self { // let numbered_leafs = |r: Range<_>| r.map(|leaf| Tip5::hash(&leaf)).collect(); // let old_leafs = numbered_leafs(0..num_old_leafs); // let new_leafs = numbered_leafs(num_old_leafs..num_old_leafs + num_new_leafs); // Self::new(old_leafs, new_leafs) // } // fn verify(&self) -> Result<(), Error> { // self.proof.verify_internal(&self.old, &self.new) // } // } // impl<'a> arbitrary::Arbitrary<'a> for MmrSuccessorRelation { // fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result { // let mut leafs = |upper_bound| -> Result, _> { // let num_leafs = u.int_in_range(0..=upper_bound)?; // (0..num_leafs).map(|_| u.arbitrary()).collect() // }; // Ok(Self::new(leafs(1 << 8)?, leafs(1 << 8)?)) // } // } // impl proptest::arbitrary::Arbitrary for MmrSuccessorRelation { // type Parameters = (); // fn arbitrary_with(_: Self::Parameters) -> Self::Strategy { // arb().boxed() // } // type Strategy = BoxedStrategy; // } // #[test] // fn append_nothing_to_empty_mmra() { // let relation = MmrSuccessorRelation::new_with_numbered_leafs(0, 0); // assert_eq!(0, relation.proof.paths.len()); // relation.verify().unwrap(); // } // #[test] // fn append_one_thing_to_empty_mmra() { // let relation = MmrSuccessorRelation::new_with_numbered_leafs(0, 1); // assert_eq!(0, relation.proof.paths.len()); // relation.verify().unwrap(); // } // #[test] // fn append_leafs_without_influence_on_existing_peaks() { // let relation = MmrSuccessorRelation::new_with_numbered_leafs(1 << 3, 3); // assert_eq!(0, relation.proof.paths.len()); // relation.verify().unwrap(); // } // /// 42 = 101010₂ gives nice gaps between peaks, the additional 8 leafs fill some // /// of them nicely and adds a non-trivial new peak that's irrelevant for // /// verification. // /// // /// See the figure below, where the old Merkle Mountain Range is drawn rounded // /// and thin, the addition boxy and bold. The elements of the authentication // /// path are marked with `x`es, the “old peaks” required for authentication are // /// marked with `·`s. // /// // /// ```markdown // /// ╭─────────┴─────────╮ // /// ┄┄┴┄┄ ╭───────┴───────╮ ·━━━━━━━┻━━━━━━━┓ // /// ╭───┴───╮ ╭───┴───╮ ╭───┴───╮ ┏━━━┻━━━x // /// ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ╭─┴─╮ ·━┻━x ┏━┻━┓ // /// ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ╭┴╮ ┏┻┓ ┏┻┓ ┏┻┓ ┏┻┓ // /// ``` // #[test] // fn append_8_leafs_to_mmra_with_42_leafs() { // let relation = MmrSuccessorRelation::new_with_numbered_leafs(42, 8); // assert_eq!(2, relation.proof.paths.len()); // let first_merkle_tree_leafs = [42_u64, 43].map(|i| Tip5::hash(&i)); // let first_merkle_tree = MerkleTree::par_new(&first_merkle_tree_leafs).unwrap(); // assert_eq!(first_merkle_tree.root(), relation.proof.paths[0]); // let second_merkle_tree_leafs = [44_u64, 45, 46, 47].map(|i| Tip5::hash(&i)); // let second_merkle_tree = MerkleTree::par_new(&second_merkle_tree_leafs).unwrap(); // assert_eq!(second_merkle_tree.root(), relation.proof.paths[1]); // relation.verify().unwrap(); // } // #[test] // fn unit_tests() { // for (n, m) in (0..18).cartesian_product(0..18) { // dbg!((n, m)); // let relation = MmrSuccessorRelation::new_with_numbered_leafs(n, m); // relation.verify().unwrap(); // } // } // #[proptest] // fn arbitrary_mmr_successor_relation_holds(relation: MmrSuccessorRelation) { // relation.verify()?; // } // #[proptest] // fn verification_fails_if_old_mmr_is_inconsistent( // mut relation: MmrSuccessorRelation, // wrong_num_leafs: u64, // ) { // prop_assume!(wrong_num_leafs != relation.old.num_leafs()); // relation.old = MmrAccumulator::init(relation.old.peaks(), wrong_num_leafs); // prop_assert_eq!(Err(Error::InconsistentOldMmr), relation.verify()); // } // #[proptest] // fn verification_fails_if_new_mmr_is_inconsistent( // mut relation: MmrSuccessorRelation, // wrong_num_leafs: u64, // ) { // prop_assume!(wrong_num_leafs != relation.new.num_leafs()); // relation.new = MmrAccumulator::init(relation.new.peaks(), wrong_num_leafs); // prop_assert_eq!(Err(Error::InconsistentNewMmr), relation.verify()); // } // #[proptest] // fn verification_fails_if_old_mmra_has_more_leafs_than_new_mmra( // #[filter(#relation.old != #relation.new)] mut relation: MmrSuccessorRelation, // ) { // std::mem::swap(&mut relation.old, &mut relation.new); // prop_assert_eq!(Err(Error::OldHasMoreLeafsThanNew), relation.verify()); // } // #[proptest] // fn verification_fails_if_old_mmra_has_swapped_peaks( // #[filter(#relation.old.peaks().len() >= 2)] mut relation: MmrSuccessorRelation, // #[strategy(0..#relation.old.peaks().len())] first_swap_idx: usize, // #[strategy(0..#relation.old.peaks().len())] second_swap_idx: usize, // ) { // prop_assume!(first_swap_idx != second_swap_idx); // let mut wrong_peaks = relation.old.peaks(); // wrong_peaks.swap(first_swap_idx, second_swap_idx); // relation.old = MmrAccumulator::init(wrong_peaks, relation.old.num_leafs()); // prop_assert!(matches!( // relation.verify(), // Err(Error::DifferentSharedPeak) | Err(Error::DifferentUnsharedPeak) // )); // } // /// Because some peaks of the new MMRA might be irrelevant for the successor // /// relation, it is impossible to swap arbitrary peaks and guarantee a // /// verification failure. However, if the old MMRA is non-empty, the first // /// peak of the new MMRA is always relevant. // #[proptest] // fn verification_fails_if_new_mmra_has_first_peak_swapped_out( // #[filter(#relation.old.num_leafs() > 0)] // #[filter(#relation.new.peaks().len() >= 2)] // mut relation: MmrSuccessorRelation, // #[strategy(1..#relation.new.peaks().len())] swap_idx: usize, // ) { // let mut wrong_peaks = relation.new.peaks(); // wrong_peaks.swap(0, swap_idx); // relation.new = MmrAccumulator::init(wrong_peaks, relation.new.num_leafs()); // prop_assert!(matches!( // relation.verify(), // Err(Error::DifferentSharedPeak) | Err(Error::DifferentUnsharedPeak) // )); // } // #[proptest(cases = 50)] // fn verification_fails_if_authentication_path_is_corrupt( // #[filter(!#relation.proof.paths.is_empty())] mut relation: MmrSuccessorRelation, // #[strategy(0..#relation.proof.paths.len())] corruption_idx: usize, // corruptor: DigestCorruptor, // ) { // let auth_path = &mut relation.proof.paths; // auth_path[corruption_idx] = corruptor.corrupt_digest(auth_path[corruption_idx])?; // prop_assert!(matches!( // relation.verify(), // Err(Error::DifferentSharedPeak) | Err(Error::DifferentUnsharedPeak) // )); // } // #[proptest] // fn verification_fails_if_authentication_path_has_too_few_elements( // #[filter(!#relation.proof.paths.is_empty())] mut relation: MmrSuccessorRelation, // #[strategy(0..#relation.proof.paths.len())] deletion_idx: usize, // ) { // relation.proof.paths.remove(deletion_idx); // prop_assert_eq!(Err(Error::AuthenticationPathTooShort), relation.verify()); // } // #[proptest] // fn verification_fails_if_authentication_path_has_too_many_elements( // mut relation: MmrSuccessorRelation, // #[strategy(arb())] spurious_element: Digest, // ) { // relation.proof.paths.push(spurious_element); // prop_assert_eq!(Err(Error::AuthenticationPathTooLong), relation.verify()); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/mmr_trait.rs ================================================ use super::mmr_accumulator::MmrAccumulator; use super::mmr_membership_proof::MmrMembershipProof; use crate::crypto::digest::{Digest, HashFunction}; /// A wrapper for the data needed to change the value of a leaf in an MMR when /// only the MMR-accumulator is known, i.e., only the peaks and the leaf-count /// are known. #[derive(Debug, Clone)] pub struct LeafMutation { /// The leaf-index of the leaf being mutated. If the MMR is viewed as a /// commitment to a list, then this is simply the (0-indexed) list-index /// into that list. pub leaf_index: u64, /// The new leaf value, after the mutation has been applied. pub new_leaf: Digest, /// MMR membership proof (authentication path) both before *and* after the /// leaf has been mutated. An authentication path is a commitment to all /// other leafs in the Merkle tree than the one it is a membership proof /// for. pub membership_proof: MmrMembershipProof, } impl LeafMutation { pub fn new( leaf_index: u64, new_leaf: Digest, membership_proof: MmrMembershipProof, ) -> Self { Self { leaf_index, new_leaf, membership_proof, } } /// Returns the node indices into the MMR of the nodes that are mutated by /// this leaf-mutation. pub fn affected_node_indices(&self) -> Vec { self.membership_proof .get_direct_path_indices(self.leaf_index) } } /// A “Merkle Mountain Range” (MMR) is a data structure for storing lists of /// hashes. Similar to [Merkle trees](crate::prelude::MerkleTree), they enable /// efficient set inclusion proofs. Unlike Merkle trees, the number of leafs of /// an MMR is not required to be a power of 2. /// /// One valid perspective of this data structure is to see it as a list of /// Merkle trees. Each of the Merkle tree's roots is one peak of the MMR. /// In order to keep the number of peaks to a minimum, any two Merkle trees of /// the same height are merged, which results in a single tree that has one /// additional “tier”, _i.e._, it's height is one more than that of the two /// trees that got merged. /// /// # Example /// /// The following is a Merkle Mountain Range, annotated with both node and leaf /// indices: /// /// ```markdown /// ──── 15 ─── ╮ /// ╱ ╲ │ /// 7 14 22 │ /// ╱ ╲ ╱ ╲ ╱ ╲ ├╴ node indices /// ╱ ╲ ╱ ╲ ╱ ╲ │ /// 3 6 10 13 18 21 │ /// ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ │ /// 1 2 4 5 8 9 11 12 16 17 19 20 21 ╯ /// /// 0 1 2 3 4 5 6 7 8 9 10 11 12 ←── leaf indices /// ``` /// /// Adding another leaf to the above MMR will result in the following MMR: /// /// ```markdown /// ──── 15 ─── /// ╱ ╲ /// 7 14 22 /// ╱ ╲ ╱ ╲ ╱ ╲ /// ╱ ╲ ╱ ╲ ╱ ╲ /// 3 6 10 13 18 21 25 /// ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ /// 1 2 4 5 8 9 11 12 16 17 19 20 21 23 24 /// /// 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 /// ``` /// /// Note how the new leaf with index 13, which by itself is a Merkle tree of /// height 0, was merged with its neighboring Merkle tree of equal height, /// resulting in a new Merkle tree of height 1 (the nodes 23, 24, and 25). /// /// Adding two more leafs to this MMR results in a single Merkle tree of height /// four. /// /// # Counterexample /// /// The following is **not** a valid Merkle Mountain Range, since it contains /// trees of equal height. /// /// ```markdown /// _ _ /// ╱ ╲ ╱ ╲ /// ╱ ╲ ╱ ╲ /// _ _ _ _ _ _ /// ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ /// _ _ _ _ _ _ _ _ _ _ _ _ /// ``` /// /// # Terminology /// /// Similar to Merkle trees, Merkle Mountain Ranges have “leafs” and “nodes”. /// Any leaf is a node, but the reverse is not true. Note that the indexing /// scheme for the nodes does not follow that of a Merkle tree – see /// [this][mt_proof] explanation for Merkle tree indexing. /// /// A single Merkle tree's root is one “peak” of the MMR. The number of peaks in /// the MMR equals the number of Merkle trees it is made out of. Because of the /// 1-to-1 mapping between peaks and Merkle trees, the “peak index” uniquely /// identifies any one Merkle tree. /// /// When selecting for a single Merkle tree within a Merkle Mountain Range, the /// usual Merkel tree indexing is used to identify nodes. This is called the /// “Merkle tree index” and is usually only meaningful in combination with a /// peak index, for example like [here][mt_peak_idx]. /// /// [mt_proof]: crate::util_types::merkle_tree::MerkleTree::authentication_structure /// [mt_peak_idx]: crate::util_types::mmr::shared_basic::leaf_index_to_mt_index_and_peak_index pub trait Mmr { /// A single digest committing to the entire MMR. fn bag_peaks(&self) -> Digest; /// The peaks of the MMR, _i.e._, the roots of the Merkle trees that constitute /// the MMR. fn peaks(&self) -> Vec>; /// `true` iff the MMR has no leafs. fn is_empty(&self) -> bool; /// The number of leafs in the MMR. fn num_leafs(&self) -> u64; /// Append a hash digest to the MMR. fn append(&mut self, new_leaf: Digest) -> MmrMembershipProof; /// Mutate an existing leaf. It is the caller's responsibility that the /// membership proof is valid. If the membership proof is wrong, the MMR /// will end up in a broken state. fn mutate_leaf(&mut self, leaf_mutation: LeafMutation); /// Batch mutate an MMR while updating a list of membership proofs. Returns the /// indices of the membership proofs that have changed as a result of this /// operation. fn batch_mutate_leaf_and_update_mps( &mut self, membership_proofs: &mut [&mut MmrMembershipProof], membership_proof_leaf_indices: &[u64], mutation_data: Vec>, ) -> Vec; /// `true` iff a list of leaf mutations and a list of appends results in the expected /// `new_peaks`. fn verify_batch_update( &self, new_peaks: &[Digest], appended_leafs: &[Digest], leaf_mutations: Vec>, ) -> bool; /// Derive an MMR accumulator, which contains only peaks and the number of /// leafs. fn to_accumulator(&self) -> MmrAccumulator; } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/shared_advanced.rs ================================================ use super::shared_basic::*; /// Get (index, height) of leftmost ancestor /// This ancestor does *not* have to be in the MMR /// This algorithm finds the closest $2^n - 1$ that's bigger than /// or equal to `node_index`. #[inline] pub fn leftmost_ancestor(node_index: u64) -> (u64, u32) { if node_index.leading_zeros() == 0 { return (u64::MAX, 63); } let height = node_index.ilog2(); let index = (1 << (height + 1)) - 1; (index, height) } /// Traversing from this node upwards, count how many of the ancestor (including itself) /// is a right child. Also returns node's height. pub fn right_lineage_length_and_own_height(node_index: u64) -> (u32, u32) { let (mut candidate, mut candidate_height) = leftmost_ancestor(node_index); // leftmost ancestor is always a left node, so count starts at 0. let mut right_ancestor_count = 0; loop { if candidate == node_index { return (right_ancestor_count, candidate_height); } let left_child = left_child(candidate, candidate_height); let candidate_is_right_child = left_child < node_index; if candidate_is_right_child { candidate = right_child(candidate); right_ancestor_count += 1; } else { candidate = left_child; right_ancestor_count = 0; }; candidate_height -= 1; } } pub fn right_lineage_length_from_node_index(node_index: u64) -> u32 { let bit_width = u64::BITS - node_index.leading_zeros(); let npo2 = 1u128 << bit_width; let dist = (npo2 - (node_index as u128)) as u64; if (bit_width as u64) < dist { right_lineage_length_from_node_index(node_index - (1 << (bit_width - 1)) + 1) } else { (dist - 1) as u32 } } /// Convert from leaf index to node index. /// /// Crashes if `leaf_index` exceeds 63 bits. pub fn leaf_index_to_node_index(leaf_index: u64) -> u64 { let hamming_weight = leaf_index.count_ones() as u64; 2 * leaf_index - hamming_weight + 1 } /// Get the node_index of the parent #[inline] pub fn parent(node_index: u64) -> u64 { let (right_ancestor_count, height) = right_lineage_length_and_own_height(node_index); if right_ancestor_count != 0 { node_index + 1 } else { node_index + (1 << (height + 1)) } } /// Get the node index of the left sibling, given the right sibling's node index /// and the height of the layer on which it lives. #[inline] pub fn left_sibling(node_index: u64, height: u32) -> u64 { node_index - (1 << (height + 1)) + 1 } /// Get the node index of the right sibling, given the left sibling's node index /// and the height of the layer on which it lives. #[inline] pub fn right_sibling(node_index: u64, height: u32) -> u64 { node_index + (1 << (height + 1)) - 1 } /// The number of nodes in an MMR with `leaf_count` leafs. pub fn num_leafs_to_num_nodes(num_leafs: u64) -> u64 { let hamming_weight = num_leafs.count_ones() as u64; 2 * num_leafs - hamming_weight } /// Return the indices of the nodes added by an append, including the (node index /// of the) peak that this append gave rise to and (that of) the new leaf. pub fn node_indices_added_by_append(old_leaf_count: u64) -> Vec { let mut node_index = leaf_index_to_node_index(old_leaf_count); let mut added_node_indices = vec![node_index]; let mut right_count = right_lineage_length_from_node_index(node_index); while right_count != 0 { // a right child's parent is found by adding 1 to the node index node_index += 1; added_node_indices.push(node_index); right_count -= 1; } added_node_indices } /// Get the node indices of the authentication path starting from the specified /// leaf, to its peak. /// /// # Panics /// /// Panics if the leaf index is out-of-bounds. pub fn auth_path_node_indices(num_leafs: u64, leaf_index: u64) -> Vec { assert!( leaf_index < num_leafs, "Leaf index out-of-bounds: {leaf_index}/{num_leafs}" ); let (mut merkle_tree_index, _) = leaf_index_to_mt_index_and_peak_index(leaf_index, num_leafs); let mut node_index = leaf_index_to_node_index(leaf_index); let mut height = 0; let tree_height = u64::BITS - merkle_tree_index.leading_zeros() - 1; let mut ret = Vec::with_capacity(tree_height as usize); while merkle_tree_index > 1 { let is_left_sibling = merkle_tree_index & 1 == 0; let height_pow = 1u64 << (height + 1); let as_1_or_minus_1: u64 = (2 * (is_left_sibling as i64) - 1) as u64; let signed_height_pow = height_pow.wrapping_mul(as_1_or_minus_1); let sibling = node_index .wrapping_add(signed_height_pow) .wrapping_sub(as_1_or_minus_1); node_index += 1 << ((height + 1) * is_left_sibling as u32); ret.push(sibling); merkle_tree_index >>= 1; height += 1; } debug_assert_eq!(tree_height, ret.len() as u32, "Allocation must be optimal"); ret } /// Get the node indices of the authentication path hash digest needed /// to calculate the digest of `peak_node_index` from `start_node_index` pub fn get_authentication_path_node_indices( start_node_index: u64, peak_node_index: u64, node_count: u64, ) -> Option> { let mut authentication_path_node_indices = vec![]; let mut node_index = start_node_index; while node_index <= node_count && node_index != peak_node_index { // TODO: Consider if this function can be written better, or discard // it entirely. let (right_ancestor_count, height) = right_lineage_length_and_own_height(node_index); let sibling_node_index: u64; if right_ancestor_count != 0 { sibling_node_index = left_sibling(node_index, height); // parent of right child is +1 node_index += 1; } else { sibling_node_index = right_sibling(node_index, height); // parent of left child: node_index += 1 << (height + 1); } authentication_path_node_indices.push(sibling_node_index); } if node_index == peak_node_index { Some(authentication_path_node_indices) } else { None } } /// Return a list of the peak heights for a given leaf count. /// /// # Examples /// /// ``` // /// use twenty_first::util_types::mmr::shared_advanced::get_peak_heights; // /// assert_eq!(get_peak_heights(0b1010), vec![3, 1]); // /// assert_eq!(get_peak_heights(0b1011), vec![3, 1, 0]); // /// ``` pub fn get_peak_heights(leaf_count: u64) -> Vec { // In an MMR, the peak heights directly correspond the leaf count's bit decomposition. That is, // the indices of the bits that are set in the binary representation of the leaf count are the // peaks' heights. let Some(num_bits_in_leaf_count) = leaf_count.checked_ilog2() else { return vec![]; }; let mut indices_of_set_bits = vec![]; for bit_index in 0..=num_bits_in_leaf_count { let bit_mask = 1 << bit_index; let is_set_bit_in_leaf_count = bit_mask & leaf_count != 0; if is_set_bit_in_leaf_count { indices_of_set_bits.push(bit_index); } } // put highest index first indices_of_set_bits.reverse(); indices_of_set_bits } /// Given the number of leafs in the MMR, return one vector representing the heights /// of the peaks, and another vector representing their MMR node indices. pub fn get_peak_heights_and_peak_node_indices(leaf_count: u64) -> (Vec, Vec) { if leaf_count == 0 { return (vec![], vec![]); } let node_index_of_rightmost_leaf = leaf_index_to_node_index(leaf_count - 1); let node_count = num_leafs_to_num_nodes(leaf_count); let (mut top_peak, mut top_height) = leftmost_ancestor(node_index_of_rightmost_leaf); if top_peak > node_count { top_peak = left_child(top_peak, top_height); top_height -= 1; } let mut heights: Vec = vec![top_height]; let mut node_indices: Vec = vec![top_peak]; let mut height = top_height; let mut candidate = right_sibling(top_peak, height); 'outer: while height > 0 { '_inner: while candidate > node_count && height > 0 { candidate = left_child(candidate, height); height -= 1; if candidate <= node_count { heights.push(height); node_indices.push(candidate); candidate = right_sibling(candidate, height); continue 'outer; } } } (heights, node_indices) } /// Convert from node index to leaf index in log(size) time pub fn node_index_to_leaf_index(node_index: u64) -> Option { let (_right, own_height) = right_lineage_length_and_own_height(node_index); if own_height != 0 { return None; } let (mut node, mut node_height) = leftmost_ancestor(node_index); let mut leaf_index = 0; while node_height > 0 { let left_child = left_child(node, node_height); if node_index <= left_child { node = left_child; node_height -= 1; } else { node = right_child(node); node_height -= 1; leaf_index += 1 << node_height; } } Some(leaf_index) } // #[cfg(test)] // mod mmr_test { // use proptest::prelude::Just; // use proptest::prop_assert_eq; // use rand::RngCore; // use test_strategy::proptest; // use super::*; // use crate::prelude::Digest; // use crate::prelude::MmrMembershipProof; // #[test] // fn leaf_index_to_node_index_test() { // assert_eq!(1, leaf_index_to_node_index(0)); // assert_eq!(2, leaf_index_to_node_index(1)); // assert_eq!(4, leaf_index_to_node_index(2)); // assert_eq!(5, leaf_index_to_node_index(3)); // assert_eq!(8, leaf_index_to_node_index(4)); // assert_eq!(9, leaf_index_to_node_index(5)); // assert_eq!(11, leaf_index_to_node_index(6)); // assert_eq!(12, leaf_index_to_node_index(7)); // assert_eq!(16, leaf_index_to_node_index(8)); // assert_eq!(17, leaf_index_to_node_index(9)); // assert_eq!(19, leaf_index_to_node_index(10)); // assert_eq!(20, leaf_index_to_node_index(11)); // assert_eq!(23, leaf_index_to_node_index(12)); // assert_eq!(24, leaf_index_to_node_index(13)); // assert_eq!(26, leaf_index_to_node_index(14)); // assert_eq!(27, leaf_index_to_node_index(15)); // assert_eq!(32, leaf_index_to_node_index(16)); // assert_eq!(33, leaf_index_to_node_index(17)); // assert_eq!(35, leaf_index_to_node_index(18)); // assert_eq!(36, leaf_index_to_node_index(19)); // assert_eq!(39, leaf_index_to_node_index(20)); // assert_eq!(40, leaf_index_to_node_index(21)); // } // #[test] // fn node_indices_added_by_append_test() { // assert_eq!(vec![1], node_indices_added_by_append(0)); // assert_eq!(vec![2, 3], node_indices_added_by_append(1)); // assert_eq!(vec![4], node_indices_added_by_append(2)); // assert_eq!(vec![5, 6, 7], node_indices_added_by_append(3)); // assert_eq!(vec![8], node_indices_added_by_append(4)); // assert_eq!(vec![9, 10], node_indices_added_by_append(5)); // assert_eq!(vec![11], node_indices_added_by_append(6)); // assert_eq!(vec![12, 13, 14, 15], node_indices_added_by_append(7)); // assert_eq!(vec![16], node_indices_added_by_append(8)); // assert_eq!(vec![17, 18], node_indices_added_by_append(9)); // assert_eq!(vec![19], node_indices_added_by_append(10)); // assert_eq!(vec![20, 21, 22], node_indices_added_by_append(11)); // assert_eq!(vec![23], node_indices_added_by_append(12)); // assert_eq!(vec![24, 25], node_indices_added_by_append(13)); // assert_eq!(vec![26], node_indices_added_by_append(14)); // assert_eq!(vec![27, 28, 29, 30, 31], node_indices_added_by_append(15)); // assert_eq!(vec![32], node_indices_added_by_append(16)); // assert_eq!(vec![33, 34], node_indices_added_by_append(17)); // assert_eq!(vec![35], node_indices_added_by_append(18)); // assert_eq!(vec![36, 37, 38], node_indices_added_by_append(19)); // assert_eq!( // vec![58, 59, 60, 61, 62, 63], // node_indices_added_by_append(31) // ); // assert_eq!(vec![64], node_indices_added_by_append(32)); // } // #[test] // fn leaf_index_node_index_pbt() { // let mut rng = rand::rng(); // for _ in 0..10_000 { // let rand = rng.next_u32(); // let inversion_result = node_index_to_leaf_index(leaf_index_to_node_index(rand as u64)); // let inversion = inversion_result.unwrap(); // assert_eq!(rand, inversion as u32); // } // } // #[test] // fn right_ancestor_count_test() { // assert_eq!((0, 0), right_lineage_length_and_own_height(1)); // 0b1 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(2)); // 0b10 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(3)); // 0b11 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(4)); // 0b100 => 0 // assert_eq!((2, 0), right_lineage_length_and_own_height(5)); // 0b101 => 2 // assert_eq!((1, 1), right_lineage_length_and_own_height(6)); // 0b110 => 1 // assert_eq!((0, 2), right_lineage_length_and_own_height(7)); // 0b111 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(8)); // 0b1000 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(9)); // 0b1001 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(10)); // 0b1010 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(11)); // 0b1011 => 0 // assert_eq!((3, 0), right_lineage_length_and_own_height(12)); // 0b1100 => 3 // assert_eq!((2, 1), right_lineage_length_and_own_height(13)); // 0b1101 => 2 // assert_eq!((1, 2), right_lineage_length_and_own_height(14)); // 0b1110 => 1 // assert_eq!((0, 3), right_lineage_length_and_own_height(15)); // 0b1111 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(16)); // 0b10000 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(17)); // 0b10001 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(18)); // 0b10010 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(19)); // 0b10011 => 0 // assert_eq!((2, 0), right_lineage_length_and_own_height(20)); // 0b10100 => 2 // assert_eq!((1, 1), right_lineage_length_and_own_height(21)); // 0b10101 => 1 // assert_eq!((0, 2), right_lineage_length_and_own_height(22)); // 0b10110 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(23)); // 0b10111 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(24)); // 0b11000 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(25)); // 0b11001 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(26)); // 0b11010 => 0 // assert_eq!((4, 0), right_lineage_length_and_own_height(27)); // 0b11011 => 4 // assert_eq!((3, 1), right_lineage_length_and_own_height(28)); // 0b11100 => 3 // assert_eq!((2, 2), right_lineage_length_and_own_height(29)); // 0b11101 => 2 // assert_eq!((1, 3), right_lineage_length_and_own_height(30)); // 0b11110 => 1 // assert_eq!((0, 4), right_lineage_length_and_own_height(31)); // 0b11111 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(32)); // 0b100000 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(33)); // 0b100001 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(34)); // 0b100010 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(35)); // 0b100011 => 0 // assert_eq!((2, 0), right_lineage_length_and_own_height(36)); // 0b100100 => 2 // assert_eq!((1, 1), right_lineage_length_and_own_height(37)); // 0b100101 => 1 // assert_eq!((0, 2), right_lineage_length_and_own_height(38)); // 0b100110 => 0 // assert_eq!((0, 0), right_lineage_length_and_own_height(39)); // 0b100111 => 0 // assert_eq!((1, 0), right_lineage_length_and_own_height(40)); // 0b101000 => 1 // assert_eq!((0, 1), right_lineage_length_and_own_height(41)); // 0b101001 => 0 // assert_eq!( // (61, 1), // right_lineage_length_and_own_height(u64::MAX / 2 - 61) // ); // 0b111...11 => 0 // assert_eq!( // (3, 59), // right_lineage_length_and_own_height(u64::MAX / 2 - 3) // ); // 0b111...11 => 0 // assert_eq!( // (2, 60), // right_lineage_length_and_own_height(u64::MAX / 2 - 2) // ); // 0b111...11 => 0 // assert_eq!( // (1, 61), // right_lineage_length_and_own_height(u64::MAX / 2 - 1) // ); // 0b111...11 => 0 // assert_eq!((0, 62), right_lineage_length_and_own_height(u64::MAX / 2)); // 0b111...11 => 0 // } // #[proptest] // fn right_lineage_length_property(#[strategy(0u64..(1<<63))] leaf_index: u64) { // let rll = right_lineage_length_from_leaf_index(leaf_index); // let rac = right_lineage_length_and_own_height(leaf_index_to_node_index(leaf_index)).0; // prop_assert_eq!(rac, rll); // } // #[test] // fn leftmost_ancestor_test() { // assert_eq!((1, 0), leftmost_ancestor(1)); // assert_eq!((3, 1), leftmost_ancestor(2)); // assert_eq!((3, 1), leftmost_ancestor(3)); // assert_eq!((7, 2), leftmost_ancestor(4)); // assert_eq!((7, 2), leftmost_ancestor(5)); // assert_eq!((7, 2), leftmost_ancestor(6)); // assert_eq!((7, 2), leftmost_ancestor(7)); // assert_eq!((15, 3), leftmost_ancestor(8)); // assert_eq!((15, 3), leftmost_ancestor(9)); // assert_eq!((15, 3), leftmost_ancestor(10)); // assert_eq!((15, 3), leftmost_ancestor(11)); // assert_eq!((15, 3), leftmost_ancestor(12)); // assert_eq!((15, 3), leftmost_ancestor(13)); // assert_eq!((15, 3), leftmost_ancestor(14)); // assert_eq!((15, 3), leftmost_ancestor(15)); // assert_eq!((31, 4), leftmost_ancestor(16)); // } // #[test] // fn left_sibling_test() { // assert_eq!(3, left_sibling(6, 1)); // assert_eq!(1, left_sibling(2, 0)); // assert_eq!(4, left_sibling(5, 0)); // assert_eq!(15, left_sibling(30, 3)); // assert_eq!(22, left_sibling(29, 2)); // assert_eq!(7, left_sibling(14, 2)); // } // #[test] // fn node_index_to_leaf_index_test() { // assert_eq!(Some(0), node_index_to_leaf_index(1)); // assert_eq!(Some(1), node_index_to_leaf_index(2)); // assert_eq!(None, node_index_to_leaf_index(3)); // assert_eq!(Some(2), node_index_to_leaf_index(4)); // assert_eq!(Some(3), node_index_to_leaf_index(5)); // assert_eq!(None, node_index_to_leaf_index(6)); // assert_eq!(None, node_index_to_leaf_index(7)); // assert_eq!(Some(4), node_index_to_leaf_index(8)); // assert_eq!(Some(5), node_index_to_leaf_index(9)); // assert_eq!(None, node_index_to_leaf_index(10)); // assert_eq!(Some(6), node_index_to_leaf_index(11)); // assert_eq!(Some(7), node_index_to_leaf_index(12)); // assert_eq!(None, node_index_to_leaf_index(13)); // assert_eq!(None, node_index_to_leaf_index(14)); // assert_eq!(None, node_index_to_leaf_index(15)); // assert_eq!(Some(8), node_index_to_leaf_index(16)); // assert_eq!(Some(9), node_index_to_leaf_index(17)); // assert_eq!(None, node_index_to_leaf_index(18)); // assert_eq!(Some(10), node_index_to_leaf_index(19)); // assert_eq!(Some(11), node_index_to_leaf_index(20)); // assert_eq!(None, node_index_to_leaf_index(21)); // assert_eq!(None, node_index_to_leaf_index(22)); // } // #[test] // fn leaf_count_to_node_count_test() { // let node_counts: Vec = vec![ // 0, 1, 3, 4, 7, 8, 10, 11, 15, 16, 18, 19, 22, 23, 25, 26, 31, 32, 34, 35, 38, 39, 41, // 42, 46, 47, 49, 50, 53, 54, 56, 57, 63, 64, // ]; // for (i, node_count) in node_counts.iter().enumerate() { // assert_eq!(*node_count, num_leafs_to_num_nodes(i as u64)); // } // } // #[test] // fn get_peak_heights_and_peak_node_indices_test() { // type TestCase = (u64, (Vec, Vec)); // let leaf_count_and_expected: Vec = vec![ // (0, (vec![], vec![])), // (1, (vec![0], vec![1])), // (2, (vec![1], vec![3])), // (3, (vec![1, 0], vec![3, 4])), // (4, (vec![2], vec![7])), // (5, (vec![2, 0], vec![7, 8])), // (6, (vec![2, 1], vec![7, 10])), // (7, (vec![2, 1, 0], vec![7, 10, 11])), // (8, (vec![3], vec![15])), // (9, (vec![3, 0], vec![15, 16])), // (10, (vec![3, 1], vec![15, 18])), // (11, (vec![3, 1, 0], vec![15, 18, 19])), // (12, (vec![3, 2], vec![15, 22])), // (13, (vec![3, 2, 0], vec![15, 22, 23])), // (14, (vec![3, 2, 1], vec![15, 22, 25])), // (15, (vec![3, 2, 1, 0], vec![15, 22, 25, 26])), // (16, (vec![4], vec![31])), // (17, (vec![4, 0], vec![31, 32])), // (18, (vec![4, 1], vec![31, 34])), // (19, (vec![4, 1, 0], vec![31, 34, 35])), // ]; // for (leaf_count, (expected_heights, expected_indices)) in leaf_count_and_expected { // assert_eq!( // (expected_heights.clone(), expected_indices), // get_peak_heights_and_peak_node_indices(leaf_count) // ); // assert_eq!(expected_heights, get_peak_heights(leaf_count)); // } // } // #[test] // fn get_authentication_path_node_indices_test() { // type Interval = (u64, u64, u64); // type TestCase = (Interval, Option>); // let start_end_node_count_expected: Vec = vec![ // ((1, 31, 31), Some(vec![2, 6, 14, 30])), // ((2, 31, 31), Some(vec![1, 6, 14, 30])), // ((3, 31, 31), Some(vec![6, 14, 30])), // ((4, 31, 31), Some(vec![5, 3, 14, 30])), // ((21, 31, 31), Some(vec![18, 29, 15])), // ((21, 31, 32), Some(vec![18, 29, 15])), // ((32, 32, 32), Some(vec![])), // ((1, 32, 32), None), // ]; // for ((start, end, node_count), expected) in start_end_node_count_expected { // assert_eq!( // expected, // get_authentication_path_node_indices(start, end, node_count) // ); // } // } // #[test] // #[should_panic(expected = "Leaf index out-of-bounds: 5/5")] // fn auth_path_indices_out_of_bounds_unit_test() { // auth_path_node_indices(5, 5); // } // #[proptest] // fn auth_path_indices_prop( // #[strategy(0u64..(u64::MAX>>1))] _num_leafs: u64, // #[strategy(0u64..(#_num_leafs))] leaf_index: u64, // #[strategy(Just(auth_path_node_indices(#_num_leafs, #leaf_index)))] node_indices: Vec, // ) { // let mp = MmrMembershipProof { // authentication_path: vec![Digest::default(); node_indices.len()], // }; // prop_assert_eq!(mp.get_node_indices(leaf_index), node_indices); // } // #[test] // fn auth_path_indices_unit_test() { // assert_eq!(vec![2, 6, 14, 30], auth_path_node_indices(16, 0)); // assert_eq!(vec![1, 6, 14, 30], auth_path_node_indices(16, 1)); // assert_eq!(vec![5, 3, 14, 30], auth_path_node_indices(16, 2)); // assert_eq!(vec![4, 3, 14, 30], auth_path_node_indices(16, 3)); // assert_eq!(vec![9, 13, 7, 30], auth_path_node_indices(16, 4)); // assert_eq!(vec![8, 13, 7, 30], auth_path_node_indices(16, 5)); // assert_eq!(vec![12, 10, 7, 30], auth_path_node_indices(16, 6)); // assert_eq!(vec![11, 10, 7, 30], auth_path_node_indices(16, 7)); // assert_eq!(vec![17, 21, 29, 15], auth_path_node_indices(16, 8)); // assert_eq!(vec![16, 21, 29, 15], auth_path_node_indices(16, 9)); // assert_eq!(vec![20, 18, 29, 15], auth_path_node_indices(16, 10)); // assert_eq!(vec![19, 18, 29, 15], auth_path_node_indices(16, 11)); // assert_eq!(vec![24, 28, 22, 15], auth_path_node_indices(16, 12)); // assert_eq!(vec![23, 28, 22, 15], auth_path_node_indices(16, 13)); // assert_eq!(vec![27, 25, 22, 15], auth_path_node_indices(16, 14)); // assert_eq!(vec![26, 25, 22, 15], auth_path_node_indices(16, 15)); // assert_eq!(Vec::::new(), auth_path_node_indices(1, 0)); // assert_eq!(vec![2], auth_path_node_indices(2, 0)); // assert_eq!(vec![1], auth_path_node_indices(2, 1)); // let mut expected = vec![]; // for i in 1..63 { // expected.push((1u64 << (i + 1)) - 2); // assert_eq!( // expected, // auth_path_node_indices(1 << i, 0), // "must match for i={i}" // ); // } // } // #[proptest] // fn right_lineage_length_from_node_index_does_not_crash(node_index: u64) { // right_lineage_length_from_node_index(node_index); // } // #[proptest] // fn leftmost_ancestor_does_not_crash(node_index: u64) { // leftmost_ancestor(node_index); // } // #[proptest] // fn right_lineage_length_and_own_height_does_not_crash(node_index: u64) { // right_lineage_length_and_own_height(node_index); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/mmr/shared_basic.rs ================================================ // use crate::prelude::*; use crate::crypto::digest::{Digest, HashFunction}; use crate::crypto::merkle_tree::MerkleTree; use crate::crypto::mmr::mmr_membership_proof::MmrMembershipProof; pub(crate) const USIZE_TO_U64_ERR: &str = "internal error: type `usize` should have at most 64 bits"; pub(crate) const U32_TO_USIZE_ERR: &str = "internal error: type `usize` should have at least 32 bits"; #[inline] pub fn left_child(node_index: u64, height: u32) -> u64 { node_index - (1 << height) } #[inline] pub fn right_child(node_index: u64) -> u64 { node_index - 1 } /// Given the leaf index in the MMR as well as the number of leafs in the MMR, /// compute that leaf's Merkle tree index and its peak index. /// /// For an explanation of the terminology, see [`Mmr`]. /// /// # Panics /// /// - if the leaf index is larger than or equal to the number of leafs #[inline] pub fn leaf_index_to_mt_index_and_peak_index(leaf_index: u64, num_leafs: u64) -> (u64, u32) { // This algorithm works by first identifying how high the local Merkle tree is. This is // the Merkle tree that the leaf with `leaf_index` is part of. Then it finds the peak // index which identifies which of the N Merkle trees the leaf is part of. // // The height of local tree is the lowest index (from least significant) of the bits where // there is a discrepancy between `leaf_index` and `num_leafs`. The discrepant bits can // be identified with a xor. // // The bit-decomposition of `num_leafs` shows the height of the involved Merkle trees. // The number of ones in this bit-decomposition is the number of Merkle trees in the MMR; // the index of each one (counting from least-significant bit) is the height of that // Merkle tree. So counting the ones before and after the discrepancy bit reveals which // Merkle tree the leaf is in. This value is called "peak index" since we have a list // of digests that are the peaks of the MMR, and the peak index shows which element of // that list is the Merkle root that its authentication path refers to. assert!( leaf_index < num_leafs, "Leaf index must be strictly smaller than the number of leafs" ); // get node index, as if this was a Merkle tree let discrepancies = leaf_index ^ num_leafs; let local_mt_height = discrepancies.ilog2(); let local_mt_num_leafs = 1 << local_mt_height; let remainder_bitmask = local_mt_num_leafs - 1; let local_leaf_index = remainder_bitmask & leaf_index; let mt_node_index = local_leaf_index + local_mt_num_leafs; // peak index let num_peaks = num_leafs.count_ones(); let num_peaks_smaller_or_equal_own_peak = (num_leafs & remainder_bitmask).count_ones(); // subtract one to go from cardinal to ordinal let peak_index = num_peaks - num_peaks_smaller_or_equal_own_peak - 1; (mt_node_index, peak_index) } #[inline] /// The number of parents that need to be added when a new leaf is inserted. pub fn right_lineage_length_from_leaf_index(leaf_index: u64) -> u32 { leaf_index.trailing_ones() } /// Return the new peaks of the MMR after adding `new_leaf` as well as the membership /// proof for the added leaf. /// /// # Panics /// /// - if the `old_peaks` and the `old_num_leafs` are inconsistent pub fn calculate_new_peaks_from_append( old_num_leafs: u64, old_peaks: Vec>, new_leaf: Digest, ) -> (Vec>, MmrMembershipProof) { assert_eq!( old_peaks.len(), usize::try_from(old_num_leafs.count_ones()).expect(U32_TO_USIZE_ERR) ); let mut peaks = old_peaks; peaks.push(new_leaf); let mut authentication_path = vec![]; for _ in 0..right_lineage_length_from_leaf_index(old_num_leafs) { let in_progress_peak = peaks.pop().unwrap(); let previous_peak = peaks.pop().unwrap(); authentication_path.push(previous_peak); peaks.push(Digest::::from_element(H::hash_pair( &previous_peak.data, &in_progress_peak.data, ))); } (peaks, MmrMembershipProof::new(authentication_path)) } /// Calculate a new peak list given the mutation of a leaf /// The new peak list will only (max) have *one* element different /// from `old_peaks` /// /// # Panics /// /// Panics if the `membership_proof`'s authentication path is of insufficient /// length. This can only happen if the `membership_proof` is invalid (but /// there are other ways in which it can be invalid, too). pub fn calculate_new_peaks_from_leaf_mutation( old_peaks: &[Digest], num_leafs: u64, new_leaf: Digest, leaf_index: u64, membership_proof: &MmrMembershipProof, ) -> Vec> { let merkle_tree_root_index = u64::try_from(MerkleTree::::ROOT_INDEX).expect(USIZE_TO_U64_ERR); let (mut acc_mt_index, peak_index) = leaf_index_to_mt_index_and_peak_index(leaf_index, num_leafs); let mut acc_hash = new_leaf; let mut authentication_path = membership_proof.authentication_path.iter(); while acc_mt_index > merkle_tree_root_index { let &ap_element = authentication_path.next().unwrap(); let accumulator_is_left_child = acc_mt_index % 2 == 0; if accumulator_is_left_child { acc_hash = Digest::::from_element(H::hash_pair(&acc_hash.data, &ap_element.data)); } else { acc_hash = Digest::::from_element(H::hash_pair(&ap_element.data, &acc_hash.data)); } acc_mt_index /= 2; } debug_assert_eq!(merkle_tree_root_index, acc_mt_index); let mut calculated_peaks: Vec> = old_peaks.to_vec(); calculated_peaks[peak_index as usize] = acc_hash; calculated_peaks } // #[cfg(test)] // mod mmr_test { // use proptest::collection::vec; // use proptest_arbitrary_interop::arb; // use test_strategy::proptest; // use super::*; // #[test] // fn right_lineage_length_from_leaf_index_test() { // assert_eq!(0, right_lineage_length_from_leaf_index(0)); // assert_eq!(1, right_lineage_length_from_leaf_index(1)); // assert_eq!(0, right_lineage_length_from_leaf_index(2)); // assert_eq!(2, right_lineage_length_from_leaf_index(3)); // assert_eq!(0, right_lineage_length_from_leaf_index(4)); // assert_eq!(1, right_lineage_length_from_leaf_index(5)); // assert_eq!(0, right_lineage_length_from_leaf_index(6)); // assert_eq!(3, right_lineage_length_from_leaf_index(7)); // assert_eq!(0, right_lineage_length_from_leaf_index(8)); // assert_eq!(1, right_lineage_length_from_leaf_index(9)); // assert_eq!(0, right_lineage_length_from_leaf_index(10)); // assert_eq!(32, right_lineage_length_from_leaf_index((1 << 32) - 1)); // assert_eq!(63, right_lineage_length_from_leaf_index((1 << 63) - 1)); // } // #[test] // fn leaf_index_to_mt_index_test() { // // 1 leaf // assert_eq!((1, 0), leaf_index_to_mt_index_and_peak_index(0, 1)); // // 2 leafs // assert_eq!((2, 0), leaf_index_to_mt_index_and_peak_index(0, 2)); // assert_eq!((3, 0), leaf_index_to_mt_index_and_peak_index(1, 2)); // // 3 leafs // assert_eq!((2, 0), leaf_index_to_mt_index_and_peak_index(0, 3)); // assert_eq!((3, 0), leaf_index_to_mt_index_and_peak_index(1, 3)); // assert_eq!((1, 1), leaf_index_to_mt_index_and_peak_index(2, 3)); // // 4 leafs // assert_eq!((4, 0), leaf_index_to_mt_index_and_peak_index(0, 4)); // assert_eq!((5, 0), leaf_index_to_mt_index_and_peak_index(1, 4)); // assert_eq!((6, 0), leaf_index_to_mt_index_and_peak_index(2, 4)); // assert_eq!((7, 0), leaf_index_to_mt_index_and_peak_index(3, 4)); // // 14 leafs // assert_eq!((8, 0), leaf_index_to_mt_index_and_peak_index(0, 14)); // assert_eq!((9, 0), leaf_index_to_mt_index_and_peak_index(1, 14)); // assert_eq!((10, 0), leaf_index_to_mt_index_and_peak_index(2, 14)); // assert_eq!((11, 0), leaf_index_to_mt_index_and_peak_index(3, 14)); // assert_eq!((12, 0), leaf_index_to_mt_index_and_peak_index(4, 14)); // assert_eq!((13, 0), leaf_index_to_mt_index_and_peak_index(5, 14)); // assert_eq!((14, 0), leaf_index_to_mt_index_and_peak_index(6, 14)); // assert_eq!((15, 0), leaf_index_to_mt_index_and_peak_index(7, 14)); // assert_eq!((4, 1), leaf_index_to_mt_index_and_peak_index(8, 14)); // assert_eq!((5, 1), leaf_index_to_mt_index_and_peak_index(9, 14)); // assert_eq!((6, 1), leaf_index_to_mt_index_and_peak_index(10, 14)); // assert_eq!((7, 1), leaf_index_to_mt_index_and_peak_index(11, 14)); // assert_eq!((7, 1), leaf_index_to_mt_index_and_peak_index(11, 14)); // // 22 leafs // assert_eq!((16, 0), leaf_index_to_mt_index_and_peak_index(0, 23)); // assert_eq!((17, 0), leaf_index_to_mt_index_and_peak_index(1, 23)); // assert_eq!((18, 0), leaf_index_to_mt_index_and_peak_index(2, 23)); // assert_eq!((19, 0), leaf_index_to_mt_index_and_peak_index(3, 23)); // assert_eq!((30, 0), leaf_index_to_mt_index_and_peak_index(14, 23)); // assert_eq!((31, 0), leaf_index_to_mt_index_and_peak_index(15, 23)); // assert_eq!((4, 1), leaf_index_to_mt_index_and_peak_index(16, 23)); // assert_eq!((5, 1), leaf_index_to_mt_index_and_peak_index(17, 23)); // assert_eq!((6, 1), leaf_index_to_mt_index_and_peak_index(18, 23)); // assert_eq!((7, 1), leaf_index_to_mt_index_and_peak_index(19, 23)); // assert_eq!((2, 2), leaf_index_to_mt_index_and_peak_index(20, 23)); // assert_eq!((3, 2), leaf_index_to_mt_index_and_peak_index(21, 23)); // assert_eq!((1, 3), leaf_index_to_mt_index_and_peak_index(22, 23)); // // 32 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 32)); // } // // 33 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 33)); // } // assert_eq!((1, 1), leaf_index_to_mt_index_and_peak_index(32, 33)); // // 34 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 34)); // } // assert_eq!((2, 1), leaf_index_to_mt_index_and_peak_index(32, 34)); // assert_eq!((3, 1), leaf_index_to_mt_index_and_peak_index(33, 34)); // // 35 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 35)); // } // assert_eq!((2, 1), leaf_index_to_mt_index_and_peak_index(32, 35)); // assert_eq!((3, 1), leaf_index_to_mt_index_and_peak_index(33, 35)); // assert_eq!((1, 2), leaf_index_to_mt_index_and_peak_index(34, 35)); // // 36 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 36)); // } // assert_eq!((4, 1), leaf_index_to_mt_index_and_peak_index(32, 36)); // assert_eq!((5, 1), leaf_index_to_mt_index_and_peak_index(33, 36)); // assert_eq!((6, 1), leaf_index_to_mt_index_and_peak_index(34, 36)); // assert_eq!((7, 1), leaf_index_to_mt_index_and_peak_index(35, 36)); // // 37 leafs // for i in 0..32 { // assert_eq!((32 + i, 0), leaf_index_to_mt_index_and_peak_index(i, 37)); // } // assert_eq!((4, 1), leaf_index_to_mt_index_and_peak_index(32, 37)); // assert_eq!((5, 1), leaf_index_to_mt_index_and_peak_index(33, 37)); // assert_eq!((6, 1), leaf_index_to_mt_index_and_peak_index(34, 37)); // assert_eq!((7, 1), leaf_index_to_mt_index_and_peak_index(35, 37)); // assert_eq!((1, 2), leaf_index_to_mt_index_and_peak_index(36, 37)); // for i in (10..63).map(|x| 1 << x) { // assert_eq!((14 + i, 0), leaf_index_to_mt_index_and_peak_index(14, i)); // assert_eq!((3, 2), leaf_index_to_mt_index_and_peak_index(i + 9, i + 11)); // assert_eq!( // (1, 3), // leaf_index_to_mt_index_and_peak_index(i + 10, i + 11) // ); // } // } // #[test] // fn peak_index_test() { // let peak_index = |leaf_index, num_leafs| { // let (_, peak_index) = leaf_index_to_mt_index_and_peak_index(leaf_index, num_leafs); // peak_index // }; // assert_eq!(0, peak_index(0, 1)); // assert_eq!(0, peak_index(0, 2)); // assert_eq!(0, peak_index(1, 2)); // assert_eq!(0, peak_index(0, 3)); // assert_eq!(0, peak_index(1, 3)); // assert_eq!(1, peak_index(2, 3)); // assert_eq!(0, peak_index(0, 4)); // assert_eq!(0, peak_index(1, 4)); // assert_eq!(0, peak_index(2, 4)); // assert_eq!(0, peak_index(3, 4)); // assert_eq!(0, peak_index(0, 5)); // assert_eq!(0, peak_index(1, 5)); // assert_eq!(0, peak_index(2, 5)); // assert_eq!(0, peak_index(3, 5)); // assert_eq!(1, peak_index(4, 5)); // assert_eq!(0, peak_index(0, 7)); // assert_eq!(0, peak_index(1, 7)); // assert_eq!(0, peak_index(2, 7)); // assert_eq!(0, peak_index(3, 7)); // assert_eq!(1, peak_index(4, 7)); // assert_eq!(1, peak_index(5, 7)); // assert_eq!(2, peak_index(6, 7)); // assert_eq!(0, peak_index(0, (1 << 32) - 1)); // assert_eq!(0, peak_index(1, (1 << 32) - 1)); // assert_eq!(0, peak_index((0b01 << 31) - 1, (0b10 << 31) - 1)); // assert_eq!(1, peak_index(0b01 << 31, (0b10 << 31) - 1)); // assert_eq!(1, peak_index((0b011 << 30) - 1, (0b100 << 30) - 1)); // assert_eq!(2, peak_index(0b011 << 30, (0b100 << 30) - 1)); // assert_eq!(1, peak_index((0b0101 << 29) - 1, (0b1000 << 29) - 1)); // assert_eq!(2, peak_index((0b0111 << 29) - 1, (0b1000 << 29) - 1)); // } // #[test] // fn merkle_tree_and_peak_indices_can_be_computed_for_large_mmrs() { // leaf_index_to_mt_index_and_peak_index(0, u64::MAX); // leaf_index_to_mt_index_and_peak_index(u64::MAX - 1, u64::MAX); // } // #[proptest] // fn right_lineage_length_from_leaf_index_does_not_crash( // #[strategy(0..=u64::MAX >> 1)] leaf_index: u64, // ) { // right_lineage_length_from_leaf_index(leaf_index); // } // #[proptest] // fn calculate_new_peaks_from_append_does_not_crash( // #[strategy(0..u64::MAX >> 1)] old_num_leafs: u64, // #[strategy(vec(arb(), #old_num_leafs.count_ones() as usize))] old_peaks: Vec, // #[strategy(arb())] new_leaf: Digest, // ) { // calculate_new_peaks_from_append(old_num_leafs, old_peaks, new_leaf); // } // #[test] // fn calculate_new_peaks_from_append_to_empty_mmra_does_not_crash() { // calculate_new_peaks_from_append(0, vec![], rand::random()); // } // } ================================================ FILE: tools/garaga_rs/src/crypto/poseidon_bn254.rs ================================================ use crate::definitions::{FieldElement, GrumpkinPrimeField}; use lazy_static::lazy_static; type F = GrumpkinPrimeField; // Poseidon hash parameters. const T: usize = 3; // Width of the state const N_ROUNDS_F: usize = 8; // Number of full rounds const N_ROUNDS_P: usize = 57; // Number of partial rounds // Precompute and cache the Poseidon constants. lazy_static! { static ref POSEIDON_C_VEC: Vec> = POSEIDON_C .iter() .copied() .map(FieldElement::from_hex_unchecked) .collect(); static ref POSEIDON_M_MAT: Vec>> = POSEIDON_M .iter() .map(|row| row .iter() .copied() .map(FieldElement::from_hex_unchecked) .collect()) .collect(); static ref POSEIDON_P_MAT: Vec>> = POSEIDON_P .iter() .map(|row| row .iter() .copied() .map(FieldElement::from_hex_unchecked) .collect()) .collect(); static ref POSEIDON_S_VEC: Vec> = POSEIDON_S .iter() .copied() .map(FieldElement::from_hex_unchecked) .collect(); } /// Computes the Poseidon hash for BN254 given two inputs. pub fn poseidon_hash_bn254(x: &FieldElement, y: &FieldElement) -> FieldElement { let mut state = vec![FieldElement::zero(), *x, *y]; // Initial Ark state = ark(&state, &POSEIDON_C_VEC, 0); // First half of full rounds. for r in 0..(N_ROUNDS_F / 2 - 1) { state = state.iter().map(sigma).collect(); state = ark(&state, &POSEIDON_C_VEC, (r + 1) * T); state = mix(&state, &POSEIDON_M_MAT); } // Middle round. state = state.iter().map(sigma).collect(); state = ark(&state, &POSEIDON_C_VEC, (N_ROUNDS_F / 2) * T); state = mix(&state, &POSEIDON_P_MAT); // Partial rounds. for r in 0..N_ROUNDS_P { state[0] = sigma(&state[0]); let mut new_state = vec![state[0] + POSEIDON_C_VEC[(N_ROUNDS_F / 2 + 1) * T + r]]; new_state.extend_from_slice(&state[1..]); state = mix_s(&new_state, &POSEIDON_S_VEC, r); } // Second half of full rounds. for r in 0..(N_ROUNDS_F / 2 - 1) { state = state.iter().map(sigma).collect(); state = ark( &state, &POSEIDON_C_VEC, (N_ROUNDS_F / 2 + 1) * T + N_ROUNDS_P + r * T, ); state = mix(&state, &POSEIDON_M_MAT); } // Final round. state = state.iter().map(sigma).collect(); mix_last(&state, &POSEIDON_M_MAT) } // --- Utility functions --- fn sigma(value: &FieldElement) -> FieldElement { // Computes x^5 = x^2 * x^2 * x. let x2 = value * value; let x4 = x2 * x2; x4 * value } fn ark( state: &[FieldElement], constants: &[FieldElement], offset: usize, ) -> Vec> { state .iter() .enumerate() .map(|(i, s)| s + constants[i + offset]) .collect() } fn mix(state: &[FieldElement], matrix: &[Vec>]) -> Vec> { (0..T) .map(|i| { state .iter() .enumerate() .fold(FieldElement::zero(), |acc, (j, s)| acc + (matrix[j][i] * s)) }) .collect() } fn mix_last(state: &[FieldElement], matrix: &[Vec>]) -> FieldElement { state .iter() .enumerate() .fold(FieldElement::zero(), |acc, (j, s)| acc + (matrix[j][0] * s)) } fn mix_s( state: &[FieldElement], s_constants: &[FieldElement], r: usize, ) -> Vec> { let mut result = vec![state .iter() .enumerate() .fold(FieldElement::zero(), |acc, (i, s)| { acc + (s_constants[(T * 2 - 1) * r + i] * s) })]; for i in 1..T { result.push(state[i] + (state[0] * s_constants[(T * 2 - 1) * r + T + i - 1])); } result } // --- Poseidon constant definitions (unchanged) --- const POSEIDON_M: [[&str; 3]; 3] = [ [ "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771", "0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7", ], [ "0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0", "0x2e2419f9ec02ec394c9871c832963dc1b89d743c8c7b964029b2311687b1fe23", "0x176cc029695ad02582a70eff08a6fd99d057e12e58e7d7b6b16cdfabc8ee2911", ], [ "0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736d", "0x101071f0032379b697315876690f053d148d4e109f5fb065c8aacc55a0f89bfa", "0x19a3fc0a56702bf417ba7fee3802593fa644470307043f7773279cd71d25d5e0", ], ]; const POSEIDON_P: [[&str; 3]; 3] = [ [ "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x1e6f20a11d1e31e43f83dcedddb9a0236203f5f24ae72c925a8a79a66831f51d", "0x1bd8c528472e57bdc722a141f8785694484f426725403ae24084e3027e782467", ], [ "0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0", "0x2d51ba82c8073c6d6bacf1ad5e56655b7143625b0a9e9c3190527a1a5f05079a", "0x1b07d6d51e6f7e97e0ab10fc2e51ea83ce0611f940ff0731b5f927fe8d6a77c9", ], [ "0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736d", "0x11e12a40d262ae88e8376f62d19edf43093cdef1ccf34d985a3e53f0bc5765a0", "0x221c170e4d02a2479c6f3e47b5ff55781574f980d89038308a3ef37cce8463bd", ], ]; const POSEIDON_S: [&str; 285] = [ "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x3f0815ab463f1b76ee25a9b8768b3231a89752f427f4f063ab718e707576b31", "0x15648bf46f60d82954c7e33029b3617357012a3d3b1d34c8e008859f1dbfb317", "0x127e00c2253de07818ca7f2eafdd7564d05ea850cf61f1daa0cfefbf7fbfba85", "0x66365afd18a41ef9382fc0b1d265cb4d3ce470a8cbbb878f7d48051630747bd", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x219d14f823513140dc69a96f7fe7e086f4fa24c84e57dcf2b099715c4404aae7", "0x3a30bfbbf2cb86d4a6a63a8050d91f9f14f4d33696d37ebaefa9ac2302132d5", "0x2121bbcdeaa33a35b0270fb7d5c9f94edad5a84d74b06e3385104b0b41935bcc", "0x196b544fbeb0a792cfbb82c289e579b7cd5580c2e338a389d053ef8b3d10e70e", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2809c3a1547c0cee89c1db270ef479c26973ec73edb4bd4e7d907ea0202f560f", "0x11c34446b083ef92ca157585a02b8b342a4c67175b31f4b5d40d4e96dfc5c8f1", "0x253ea0b33a8bf3b2367c030e3289cbe0f6242ad7709d90b86d9d8026e2e39925", 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"0x1d82bedccd2bc8a06e3742e720b7fec2ea72182f11c0c60d135c811152aa4b60", "0x480064d4b3eb0ada5e9a3e7d05930b7c3397fd6b94d481314bd1c690a17c979", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x10a892763b3cca9ef7593fbb1140edc8c8e4580568560cf41867f7464fb0c11a", "0xb5ec64548ea841ac921f9b2553680785978b315667ae4714dde4cd7f4de8b91", "0x10554aca4e348e5949761bd7131dfaebd78010edd030e1a9ce3c65c9db931d46", "0x15be66f38d86b0998b93655462b1f475b9be9de306e150d4ac648fab3db0cff6", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x176ad3600fd3491182d182957ffad01bf6c26e9d4ab0c23caaf308e427d3dbe8", "0x2b6f355b3dbf65f09335001d705ac125e3beb20f4fc11bd3ce82b5cf0af2e6f2", "0x1c85c06a6d5d40d81d7c89edefb32d1a8448c51288fa296b6de9ff788c77451", "0x20e1e876c4746a0cbd9a51d76b2e25f82361c389e43f7d1f51a70aaac2460d79", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x20e46219f684186d2a024b637bc35a29ee3b08ce737701392d987dda9217fa08", "0x2ea7279db9f2aa0f654e987907277c24480766367a8bd90e28be0f2ed6091367", "0x136be2a7f18924c9362096d472bc75ca0969dc077c9171b1641be95091780f74", "0x1ca2033501baa3f73067c4300fb0f51119ed5736fbc8f1f6c924baf0df5a0e9e", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0xa82f199c2505277ecaa75e495f34e3525824f7a4a9d9fa1da810832b48a50c7", "0xecf10485307b4bae92fefb0d7f7782a9f37a2722e7ed9eb7925a2dea580b7d5", "0x7b642138dfd6a6dd12aa22f08a8296d68615c8478f13af16aebbbb339a3936b", "0x1d9dda43a25593ffd2256d34921fb86ed70e760ba76d61e9cbc3b6dd0f1a2150", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2f1af228520c8b751dc91136c91c6bccd5367eb08213d392958ce2fd3d7d2fce", "0x1fecfe833ad540455c6d6c1ab3de4abae61ada625a1a2b6b18551a45a6cde123", "0x18fc8e608c735b2b3b0d7583460227575657ff8a77abe637bdd3ad28e4a23c88", "0x28f740bc1182e9706ebf03cb3f53aba8a43ce0b618783a5586388a7547faa815", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x47998cc0af5a26b94ad301e4b998d29e960a4851cfd13822bed35b7146966a4", "0x1b5f1525b31db911dda43e415e1b9a3a9725c7b52e880ee130a14a692b777b70", "0x275a83fa5d19b4535f65e965a90eac9bf770ae9bd1d7b1af945fa57ed5c8de6e", "0x2e8789257ed2cbcccb430568e49bc9dc2a563359808c9897ce3e40a6f6a27aa8", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x927f46cfe80feefeb2721a4c09e9d17f60c34500dcd6e41e2925a39c8e2c7c1", "0x1f868ae04832a5dbc37619bfe6ab6a97fd8fb2cfbc1ecf9e0e484bbfe7698101", "0x9d7a11e27d2f53109b73f745b2defed65d94ba80f308fb19ce6d56c9b45eff4", "0x282d857cfe8da3b5104e1c2823fb7c5b9a7b25924fda5995b0c351aa2b879dff", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x20ba8a9fcec815b13f349ff830ae663b27576e135c0744f6987fb0f6ff49c217", "0x11b6afc91e32f1ca4589fba12e657d226d57b471ddd2ab1b66a8ae4dcbfb136e", "0x2e666402ac9cc588316e335c7d93db344788eec2c72ddf3f908141736cebc3be", "0x17522e0e9e64f795a202a110e283faad7057aec5c9ed9a1a74920f2794f18595", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2d2ed17f7a1f3ee9e20b470cad4cc7319e6adb40e2ff24b7878cb9878edbd3b9", "0x1a81efb19d7e1edaa96fa276e89e85d08f75e54a8136f4d73c937da16c7bf9f4", "0x27ff57c1ca847e57210a7b44e52e5630f299c5f451c7a0d515a16bb3bd33e237", "0x1c1a8e22230abcd13c5be96031bfa167840d117b3c6a5a0a11be26a7f5fb1a94", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2a1c3f15d4927c843627a9cd533e4250d81e7774d2c32b59d5836f9c19a5657", "0x2ddbb7239eb904d81c52499b37cb4be1af0373a10ac112e185acb219899357e4", "0xdff198393085a754e0d6faec54be81d8edf8bc25edadab48a86fad6da0afb60", "0x10d50c2473146bbc76275fcc589d038dec8db28728789f28b6d5f504bd1645ca", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x61e8328fb5593f92a53dfd40e1022e6231ba45948506282536b08b4476c1538", "0x1b589243847198ded90b644bee31ac58067debf3f07d3c51cfa5a0dd9f6d9784", "0x4b00c0da1f851e59863b053bd4c6087190f0bdcced99d5ce6f67a420a3bd1f7", "0x239941a46c2b93d9126a70163009a7ac27f8a8d42e35018b3bec8cdcb5ddfd67", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x204f26ca7993b03ac2c35377cb0a3712bfc9bc3ec0bfecb4e87ef6814acf2ea2", "0x85aff9c7fdadba039d832d8be165a1e5747cf7308d515e348ef117e926d721c", "0x249042a8dc111f27c4ae9db044c0b0b3f10e57d05e093158efd375df00ea2068", "0x6e799bcdf2b4a74542854f3029803e2f84550665203327b3e0825977413e96b", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x1cb3caed4bffb6aca9f4d2c002921bc3fffed333cae12085c612496183b87996", "0xb47e9755fae480128a128bfd4faa6a3dd6ea03cab566889dcd99e84d310d51c", "0xc7e4cea365c2061920a0c9fd2c360a6506293bc024fd1ca3f0bb730da886a4f", "0x21da1f701bac77bcbbaa30d964d6f6f63dbe1b20d9d6988c8dcd7ba4187215df", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x9ae612e8ba1ca1370905fb67899d10db86b47bd19965b6edd1a9486e3c6cc55", "0x262e1e0b56cac47fc150f284491190e6aab75445b0c99373fe1f7a0e3b95cf3d", "0x234bf4a7dce7587c2c87c293e3bb7c9e2a7bfa5f29fd4ddeaa5d3f67491d34bd", "0x2f6cbac694c886b02d0a527cac744fb658d2690e213d7432eee67f6cb69f70c2", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x22accb18b7c49b4b7bb8c9fdf78b7aded52aa1842fff818d9a3300876dec3ad9", "0x81e2f0652f898c6d659f22d2c77be302eabd9182a0b3d3cbf623a1df7f8f2fc", "0x12c0a25e70d006eccea3ada75d669b8c534b962890f3ffc016b3186ad675b935", "0x10ef9c23848128cc2fd6fc869df24d7ab56efd349edd56f49f8d4f2381df3259", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x2161cd280772819dd4a81262b71df1bcc2c1d41b9491e0620bda347962b240f0", "0x2cebb0ae5108318eb406590041b5248292533364f799bc41b7f4fdd12cb8d38a", "0x2b2092f86b5979a7fe4f7c22d9561f3bf2852283a656880fb759e08709a0a62f", "0x1566b3402d774b8c08146188425a442450cfc900cf643e7382b2d8507a065fed", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x11a316aa31607f268fb4c56d6c57ba01627c3635fccf8d3d1a163e601d1a0173", "0xde7ee069c934256b782648b560e595408a5e8434644609152e353d9c2874e44", "0x2d36f4029245704cc84df0297708c5e5845c36ae706c72e67128b8949eab1af", "0x1b8cc326b5ee160f53198c217fb34e899bde46cd82dabdc284d7951d546f858", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x27625da0f73ea07110689fb2187b71694cbf9203fd4ddf8a96ece85407550ebb", "0x1cd8338a3e5b1ad7cdc0da581a6950f6dea349c3edda06cb99ba025b94e4790d", "0x5ea02d65b209f6da763856c94b6438c78a8aed8d3e67e877a10a84072741a56", "0x9f7cb68d4e388f85366cfcf284a895d8b6250ced627e810817743ce03330a55", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x18c6230ddc0f896827b043f5e58dbd1aec13995a202e4ebcdfeb969e9d5c1212", "0x73a6114b997285e1a91c0a0fdccdaa8452e4f07bfd2e1a10578232096db6dcd", "0x2e78746340b2a6d222c6a1fc0838adf5fe013f39b1660ce7a3e7742b2f37be7f", "0x7aa27e7150baddd06303ad8e5e4bf4249b7ea846553def28e675259d3e5c851", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0xb66fdec210ea4eabf623d2712cf4d9fa90273ccb4643f680cbc98345715ead8", "0x2fb6a29d9f394a589b633b8a4d6be51c9c0601ce0b140be641acea41c49aa5e3", "0x29025cc66fd041c4fc845e9c1c2cd1288569fb243d049bd675a69dc889b2ce2a", "0x150963f0aca9bcbe4126214ab9c627a6f7ed731cfa695168b85d534b17be3f48", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0xed59780302257663f72c1bfc6656eb7b5bca2e47bec0d5798a08a32a61a8a65", "0x7e19cb8a893369b3d30ae188c767f391c11888a3000debfc8d30c06143cc084", "0x600c7d2b6946345e5f1eeeafb5eb8ec2b6ecfe528d2c052cd860afb4a3aa272", "0x596083b6c972bc13022a1f33d6523b4773f2cd0a480e19ea0125119f0385705", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0x210b5c36f27a07d97f98b9d8663d85db2e64513099a8e1ef6db21043631e24c4", "0x13bb2764bf1475cfc7bb9f3d563c5cc201c2489874e9159326a8f4930b7883f9", "0x202cf557d625c26080eb082862a76757287872b181e89997219e4b7576e24d30", "0xe561c3f8bd4f76e76d49e97142d220601fbc5a03d905a4728ea1f95fd8824b2", "0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118b", "0xde20097480e7555471785de07bd9809d57dd859bbe827307c33ae9ed7890597", "0x72f2a6287fb984bb810df8c5788eebcfd2825613cb72bb80cde8edd76d2e97d", "0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771", "0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7", ]; const POSEIDON_C: [&str; 81] = [ "0xee9a592ba9a9518d05986d656f40c2114c4993c11bb29938d21d47304cd8e6e", "0xf1445235f2148c5986587169fc1bcd887b08d4d00868df5696fff40956e864", "0x8dff3487e8ac99e1f29a058d0fa80b930c728730b7ab36ce879f3890ecf73f5", "0x84d520e4e5bb469e1f9075cb7c490efa59565eedae2d00ca8ef88ceea2b0197", "0x2d15d982d99577fa33da56722416fd734b3e667a2f9f15d8eb3e767ae0fd811e", "0xed2538844aba161cf1578a43cf0364e91601f6536a5996d0efbe65632c41b6d", "0x2600c27d879fbca186e739e6363c71cf804c877d829b735dcc3e3af02955e60a", "0x28f8bd44a583cbaa475bd15396430e7ccb99a5517440dfd970058558282bf2c5", "0x9cd7d4c380dc5488781aad012e7eaef1ed314d7f697a5572d030c55df153221", "0x11bb6ee1291aabb206120ecaace460d24b6713febe82234951e2bee7d0f855f5", "0x2d74e8fa0637d9853310f3c0e3fae1d06f171580f5b8fd05349cadeecfceb230", "0x2735e4ec9d39bdffac9bef31bacba338b1a09559a511a18be4b4d316ed889033", "0xf03c1e9e0895db1a5da6312faa78e971106c33f826e08dcf617e24213132dfd", "0x17094cd297bf827caf92920205b719c18741090b8f777811848a7e9ead6778c4", "0xdb8f419c21f92461fc2b3219465798348df90d4178042c81ba7d4b4d559e2b8", "0x243443613f64ffa417427ed5933fcfbc66809db60b9ca1724a22709ceceeece2", "0x22af49fbfd5d7e9fcd256c25c07d3dd8ecbbae6deecd03aa04bb191fada75411", "0x14fbd37fa8ad6e4e0c78a20d93c7230c4677f797b4327323f7f7c097c19420e0", "0x15a9298bbb882534d4b2c9fbc6e4ef4189420c4eb3f3e1ea22faa7e18b5ae625", "0x2f7de75f23ddaaa5221323ebceb2f2ac83eef92e854e75434c2f1d90562232bc", "0x36a4432a868283b78a315e84c4ae5aeca216f2ff9e9b2e623584f7479cd5c27", "0x2180d7786a8cf810e277218ab14a11e5e39f3c962f11e860ae1c5682c797de5c", "0xa268ef870736eebd0cb55be640d73ee3778990484cc03ce53572377eefff8e4", "0x1eefefe11c0be4664f2999031f15994829e982e8c90e09069df9bae16809a5b2", "0x27e87f033bd1e0a89ca596e8cb77fe3a4b8fb93d9a1129946571a3c3cf244c52", "0x1498a3e6599fe243321f57d6c5435889979c4f9d2a3e184d21451809178ee39", "0x27c0a41f4cb9fe67e9dd4d7ce33707f74d5d6bcc235bef108dea1bbebde507aa", "0x1f75230908b141b46637238b120fc770f4f4ae825d5004c16a7c91fe1dae280f", "0x25f99a9198e923167bba831b15fffd2d7b97b3a089808d4eb1f0a085bee21656", "0x101bc318e9ea5920d0f6acdc2bb526593d3d56ec8ed14c67622974228ba900c6", "0x1a175607067d517397c1334ecb019754ebc0c852a3cf091ec1ccc43207a83c76", "0xf02f0e6d25f9ea3deb245f3e8c381ee6b2eb380ba4af5c1c4d89770155df37b", "0x151d757acc8237af08d8a6677203ec9692565de456ae789ff358b3163b393bc9", "0x256cd9577cea143049e0a1fe0068dd20084980ee5b757890a79d13a3a624fad4", "0x513abaff6195ea48833b13da50e0884476682c3fbdd195497b8ae86e1937c61", "0x1d9570dc70a205f36f610251ee6e2e8039246e84e4ac448386d19dbac4e4a655", "0x18f1a5194755b8c5d5d7f1bf8aaa6f56effb012dd784cf5e044eec50b29fc9d4", "0x266b53b615ef73ac866512c091e4a4f2fa4bb0af966ef420d88163238eebbca8", "0x2d63234c9207438aa42b8de27644c02268304dfeb8c89a1a3f4fd6e8344ae0f7", "0x2ab30fbe51ee49bc7b3adde219a6f0b5fbb976205ef8df7e0021daee6f55c693", "0x1aee6d4b3ebe9366dcb9cce48969d4df1dc42abcd528b270068d9207fa6a45c9", "0x1891aeab71e34b895a79452e5864ae1d11f57646c60bb34aa211d123f6095219", "0x24492b5f95c0b0876437e94b4101c69118e16b2657771bd3a7caab01c818aa4b", "0x1752161b3350f7e1b3b2c8663a0d642964628213d66c10ab2fddf71bcfde68f", "0xab676935722e2f67cfb84938e614c6c2f445b8d148de54368cfb8f90a00f3a7", "0xb0f72472b9a2f5f45bc730117ed9ae5683fc2e6e227e3d4fe0da1f7aa348189", "0x16aa6f9273acd5631c201d1a52fc4f8acaf2b2152c3ae6df13a78a513edcd369", "0x2f60b987e63614eb13c324c1d8716eb0bf62d9b155d23281a45c08d52435cd60", "0x18d24ae01dde92fd7606bb7884554e9df1cb89b042f508fd9db76b7cc1b21212", "0x4fc3bf76fe31e2f8d776373130df79d18c3185fdf1593960715d4724cffa586", "0xd18f6b53fc69546cfdd670b41732bdf6dee9e06b21260c6b5d26270468dbf82", "0xba4231a918f13acec11fbafa17c5223f1f70b4cdb045036fa5d7045bd10e24", "0x7b458b2e00cd7c6100985301663e7ec33c826da0635ff1ebedd0dd86120b4c8", "0x1c35c2d96db90f4f6058e76f15a0c8286bba24e2ed40b16cec39e9fd7baa5799", "0x1d12bea3d8c32a5d766568f03dd1ecdb0a4f589abbef96945e0dde688e292050", "0xd953e20022003270525f9a73526e9889c995bb62fdea94313db405a61300286", "0x29f053ec388795d786a40bec4c875047f06ff0b610b4040a760e33506d2671e1", "0x4188e33735f46b14a4952a98463bc12e264d5f446e0c3f64b9679caaae44fc2", "0x149ec28846d4f438a84f1d0529431bb9e996a408b7e97eb3bf1735cdbe96f68f", "0xde20fae0af5188bca24b5f63630bad47aeafd98e651922d148cce1c5fdddee8", "0x12d650e8f790b1253ea94350e722ad2f7d836c234b8660edf449fba6984c6709", "0x22ab53aa39f34ad30ea96717ba7446aafdadbc1a8abe28d78340dfc4babb8f6c", "0x26503e8d4849bdf5450dabea7907bc3de0de109871dd776904a129db9149166c", "0x1d5e7a0e2965dffa00f5454f5003c5c8ec34b23d897e7fc4c8064035b0d33850", "0xee3d8daa098bee012d96b7ec48448c6bc9a6aefa544615b9cb3c7bbd07104cb", "0x1bf282082a04979955d30754cd4d9056fa9ef7a7175703d91dc232b5f98ead00", "0x7ae1344abfc6c2ce3e951bc316bee49971645f16b693733a0272173ee9ad461", "0x217e3a247827c376ec21b131d511d7dbdc98a36b7a47d97a5c8e89762ee80488", "0x215ffe584b0eb067a003d438e2fbe28babe1e50efc2894117509b616addc30ee", "0x1e770fc8ecbfdc8692dcedc597c4ca0fbec19b84e33da57412a92d1d3ce3ec20", "0x2f6243cda919bf4c9f1e3a8a6d66a05742914fc19338b3c0e50e828f69ff6d1f", "0x246efddc3117ecd39595d0046f44ab303a195d0e9cc89345d3c03ff87a11b693", "0x53e8d9b3ea5b8ed4fe006f139cbc4e0168b1c89a918dfbe602bc62cec6adf1", "0x1b894a2f45cb96647d910f6a710d38b7eb4f261beefff135aec04c1abe59427b", "0xaeb1554e266693d8212652479107d5fdc077abf88651f5a42553d54ec242cc0", "0x16a735f6f7209d24e6888680d1781c7f04ba7d71bd4b7d0e11faf9da8d9ca28e", "0x487b8b7fab5fc8fd7c13b4df0543cd260e4bcbb615b19374ff549dcf073d41b", "0x1e75b9d2c2006307124bea26b0772493cfb5d512068c3ad677fdf51c92388793", "0x5120e3d0e28003c253b46d5ff77d272ae46fa1e239d1c6c961dcb02da3b388f", "0xda5feb534576492b822e8763240119ac0900a053b171823f890f5fd55d78372", "0x2e211b39a023031a22acc1a1f5f3bb6d8c2666a6379d9d2c40cc8f78b7bd9abe", ]; #[cfg(test)] mod tests { use super::*; #[test] fn test_poseidon_bn254() { let x = FieldElement::from_hex_unchecked("1"); let y = FieldElement::from_hex_unchecked("2"); let z = poseidon_hash_bn254(&x, &y); assert_eq!( z, FieldElement::from_hex_unchecked( "115cc0f5e7d690413df64c6b9662e9cf2a3617f2743245519e19607a4417189a" ) ); } } ================================================ FILE: tools/garaga_rs/src/definitions.rs ================================================ use crate::algebra::polynomial::Polynomial; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::BLS12381PrimeField as BLSPF; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::BN254PrimeField as BNPF; use lambdaworks_math::field::element::FieldElement as Felt; use lambdaworks_math::field::fields::fft_friendly::stark_252_prime_field::Stark252PrimeField as StrkPF; use lambdaworks_math::field::fields::montgomery_backed_prime_fields::{ IsModulus, MontgomeryBackendPrimeField, }; use lambdaworks_math::field::traits::IsPrimeField; use lambdaworks_math::traits::ByteConversion; use lambdaworks_math::unsigned_integer::element::U256; use num_bigint::BigInt; use num_bigint::BigUint; use num_traits::Num; use std::cmp::PartialEq; use std::collections::HashMap; use crate::io::{biguint_from_hex, element_from_biguint}; #[derive(Debug, Clone, Copy, PartialEq, Eq)] pub enum CurveID { BN254 = 0, BLS12_381 = 1, SECP256K1 = 2, SECP256R1 = 3, X25519 = 4, GRUMPKIN = 5, } impl TryFrom for CurveID { type Error = String; fn try_from(value: u8) -> Result { match value { 0 => Ok(CurveID::BN254), 1 => Ok(CurveID::BLS12_381), 2 => Ok(CurveID::SECP256K1), 3 => Ok(CurveID::SECP256R1), 4 => Ok(CurveID::X25519), 5 => Ok(CurveID::GRUMPKIN), _ => Err(format!("Invalid curve ID: {}", value)), } } } impl TryFrom for CurveID { type Error = String; fn try_from(value: usize) -> Result { match value { 0 => Ok(CurveID::BN254), 1 => Ok(CurveID::BLS12_381), 2 => Ok(CurveID::SECP256K1), 3 => Ok(CurveID::SECP256R1), 4 => Ok(CurveID::X25519), 5 => Ok(CurveID::GRUMPKIN), _ => Err(format!("Invalid curve ID: {}", value)), } } } pub type FieldElement = Felt; pub type BN254PrimeField = BNPF; pub type BLS12381PrimeField = BLSPF; pub type Stark252PrimeField = StrkPF; pub const SECP256K1_PRIME_FIELD_ORDER: U256 = U256::from_hex_unchecked("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"); #[derive(Clone, Debug, Copy)] pub struct SECP256K1FieldModulus; impl IsModulus for SECP256K1FieldModulus { const MODULUS: U256 = SECP256K1_PRIME_FIELD_ORDER; } pub type SECP256K1PrimeField = MontgomeryBackendPrimeField; pub const SECP256R1_PRIME_FIELD_ORDER: U256 = U256::from_hex_unchecked("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"); #[derive(Clone, Debug)] pub struct SECP256R1FieldModulus; impl IsModulus for SECP256R1FieldModulus { const MODULUS: U256 = SECP256R1_PRIME_FIELD_ORDER; } pub type SECP256R1PrimeField = MontgomeryBackendPrimeField; pub const X25519_PRIME_FIELD_ORDER: U256 = U256::from_hex_unchecked("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"); #[derive(Clone, Debug, Copy)] pub struct X25519FieldModulus; impl IsModulus for X25519FieldModulus { const MODULUS: U256 = X25519_PRIME_FIELD_ORDER; } pub type X25519PrimeField = MontgomeryBackendPrimeField; pub const GRUMPKIN_PRIME_FIELD_ORDER: U256 = U256::from_hex_unchecked("30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001"); #[derive(Clone, Debug, Copy, Hash)] pub struct GrumpkinFieldModulus; impl IsModulus for GrumpkinFieldModulus { const MODULUS: U256 = GRUMPKIN_PRIME_FIELD_ORDER; } pub type GrumpkinPrimeField = MontgomeryBackendPrimeField; /// A trait to generate random field elements. pub trait Random { fn random() -> Self; } impl Random for FieldElement where FieldElement: ByteConversion, { fn random() -> Self { use rand::Rng; let mut rng = rand::rng(); let bits = F::field_bit_size(); let bytes = bits.div_ceil(8); // Round up to nearest byte let random_bytes: Vec = (0..bytes).map(|_| rng.random()).collect(); let random_num = BigUint::from_bytes_be(&random_bytes); // Try to convert to field element element_from_biguint::(&random_num) } } pub struct CurveParams { pub curve_id: CurveID, pub a: FieldElement, pub b: FieldElement, pub b20: FieldElement, pub b21: FieldElement, pub g_x: FieldElement, pub g_y: FieldElement, pub g2_x: Option<[FieldElement; 2]>, // Only for pairing curves pub g2_y: Option<[FieldElement; 2]>, // Only for pairing curves pub n: BigUint, // Order of the curve pub h: u32, // Cofactor pub x: i128, pub fp_generator: FieldElement, pub irreducible_polys: HashMap, pub loop_counter: &'static [i8], pub nr_a0: u64, // E2 non residue pub eigen_value: Option, // Endomorphism eigenvalue pub swu_params: Option>, } pub struct SWUParams { pub a: FieldElement, pub b: FieldElement, pub z: FieldElement, } pub fn get_irreducible_poly>( ext_degree: usize, ) -> Polynomial { let coeffs = (F::get_curve_params().irreducible_polys)[&ext_degree]; fn lift(c: i8) -> FieldElement { if c >= 0 { FieldElement::from(c as u64) } else { -FieldElement::from(-c as u64) } } Polynomial::new(coeffs.iter().map(|x| lift::(*x)).collect()) } /// A trait that provides curve parameters for a specific field type. pub trait CurveParamsProvider { fn get_curve_params() -> CurveParams; } /// A trait to convert a BigUint into a FieldElement. pub trait FromBigUint { fn from_biguint(num: BigUint) -> FieldElement; } impl CurveParamsProvider for SECP256K1PrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::SECP256K1, a: FieldElement::zero(), b: FieldElement::from_hex_unchecked("7"), b20: FieldElement::zero(), // Provide appropriate values here b21: FieldElement::zero(), // Provide appropriate values here g_x: FieldElement::from_hex_unchecked( "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", ), g_y: FieldElement::from_hex_unchecked( "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", ), g2_x: None, g2_y: None, n: BigUint::from_str_radix( "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16, ) .unwrap(), h: 1, x: 0, // Replace with actual 'x' fp_generator: FieldElement::from(3), irreducible_polys: HashMap::from([]), // Provide appropriate values here loop_counter: &[], // Provide appropriate values here nr_a0: 0, // Provide appropriate values here eigen_value: Some( BigInt::from_str_radix( "5363AD4CC05C30E0A5261C028812645A122E22EA20816678DF02967C1B23BD72", 16, ) .unwrap(), ), swu_params: None, } } } impl CurveParamsProvider for SECP256R1PrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::SECP256R1, a: FieldElement::from_hex_unchecked( "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", ), b: FieldElement::from_hex_unchecked( "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", ), b20: FieldElement::zero(), // Provide appropriate values here b21: FieldElement::zero(), // Provide appropriate values here g_x: FieldElement::from_hex_unchecked( "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", ), g_y: FieldElement::from_hex_unchecked( "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5", ), g2_x: None, g2_y: None, n: BigUint::from_str_radix( "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", 16, ) .unwrap(), h: 1, x: 0, // Replace with actual 'x' fp_generator: FieldElement::from(6), irreducible_polys: HashMap::from([]), // Provide appropriate values here loop_counter: &[], // Provide appropriate values here nr_a0: 0, // Provide appropriate values here eigen_value: None, // SECP256R1 does not have a known endomorphism eigenvalue for GLV swu_params: None, } } } impl CurveParamsProvider for X25519PrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::X25519, a: FieldElement::from_hex_unchecked( "0x5d4eacd3a5b9bee63197e10d617b3dd66bb8b65d0ca52af7ac71e18ef8bc172d", ), b: FieldElement::from_hex_unchecked( "0x1d11b29bcfd0b3e0550ddb06105780d5f54831976b9fbc329004ebc1f364b2a4", ), b20: FieldElement::zero(), // Provide appropriate values here b21: FieldElement::zero(), // Provide appropriate values here g_x: FieldElement::from_hex_unchecked( "2a78dd0fd02c0339f00b8f02f1c20618a9c13fdf0d617c9aca55c89b025aef35", ), g_y: FieldElement::from_hex_unchecked( "29c644a5c71da22ebe483ba563798323cf6fd061807131659b7830f3f62c1d14", ), g2_x: None, g2_y: None, n: BigUint::from_str_radix( "1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16, ) .unwrap(), h: 8, x: 0, // Replace with actual 'x' fp_generator: FieldElement::from(6), irreducible_polys: HashMap::from([]), // Provide appropriate values here loop_counter: &[], // Provide appropriate values here nr_a0: 0, // Provide appropriate values here eigen_value: None, // X25519 (Edwards/Montgomery) does not typically use this type of endomorphism swu_params: None, } } } impl CurveParamsProvider for GrumpkinPrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::GRUMPKIN, a: FieldElement::from_hex_unchecked("0"), b: FieldElement::from_hex_unchecked( "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffff0", ), b20: FieldElement::zero(), b21: FieldElement::zero(), g_x: FieldElement::from_hex_unchecked("0x1"), g_y: FieldElement::from_hex_unchecked( "0x2CF135E7506A45D632D270D45F1181294833FC48D823F272C", ), g2_x: None, g2_y: None, n: BigUint::from_str_radix( "30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD47", 16, ) .unwrap(), h: 1, x: 0, // Replace with actual 'x' fp_generator: FieldElement::from(5), irreducible_polys: HashMap::from([]), // Provide appropriate values here loop_counter: &[], // Provide appropriate values here nr_a0: 0, // Provide appropriate values here eigen_value: None, // Grumpkin does not have a known endomorphism eigenvalue for GLV swu_params: None, } } } impl CurveParamsProvider for BN254PrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::BN254, a: FieldElement::zero(), b: FieldElement::from(3), b20: FieldElement::from_hex_unchecked( "2B149D40CEB8AAAE81BE18991BE06AC3B5B4C5E559DBEFA33267E6DC24A138E5", ), b21: FieldElement::from_hex_unchecked( "009713B03AF0FED4CD2CAFADEED8FDF4A74FA084E52D1852E4A2BD0685C315D2", ), g_x: FieldElement::from_hex_unchecked("1"), // Replace with actual 'g_x' g_y: FieldElement::from_hex_unchecked("2"), // Replace with actual 'g_y' g2_x: Some([ FieldElement::from_hex_unchecked( "1800DEEF121F1E76426A00665E5C4479674322D4F75EDADD46DEBD5CD992F6ED", ), FieldElement::from_hex_unchecked( "198E9393920D483A7260BFB731FB5D25F1AA493335A9E71297E485B7AEF312C2", ), ]), g2_y: Some([ FieldElement::from_hex_unchecked( "12C85EA5DB8C6DEB4AAB71808DCB408FE3D1E7690C43D37B4CE6CC0166FA7DAA", ), FieldElement::from_hex_unchecked( "090689D0585FF075EC9E99AD690C3395BC4B313370B38EF355ACDADCD122975B", ), ]), n: BigUint::from_str_radix( "30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001", 16, ) .unwrap(), h: 1, // Replace with actual 'h' x: 0x44E992B44A6909F1, fp_generator: FieldElement::from(3), irreducible_polys: HashMap::from([ (6, [82, 0, 0, -18, 0, 0, 1].as_slice()), (12, [82, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1].as_slice()), ]), loop_counter: &[ 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, ], nr_a0: 9, eigen_value: Some( BigInt::from_str_radix("B3C4D79D41A917585BFC41088D8DAAA78B17EA66B99C90DD", 16) .unwrap(), ), swu_params: None, } } } impl CurveParamsProvider for BLS12381PrimeField { fn get_curve_params() -> CurveParams { CurveParams { curve_id: CurveID::BLS12_381, a: FieldElement::zero(), b: FieldElement::from(4), b20: FieldElement::from_hex_unchecked("4"), b21: FieldElement::from_hex_unchecked("4"), g_x: FieldElement::from_hex_unchecked("17F1D3A73197D7942695638C4FA9AC0FC3688C4F9774B905A14E3A3F171BAC586C55E83FF97A1AEFFB3AF00ADB22C6BB"), // Replace with actual 'g_x' g_y: FieldElement::from_hex_unchecked("08B3F481E3AAA0F1A09E30ED741D8AE4FCF5E095D5D00AF600DB18CB2C04B3EDD03CC744A2888AE40CAA232946C5E7E1"), // Replace with actual 'g_y' g2_x: Some([ FieldElement::from_hex_unchecked("24AA2B2F08F0A91260805272DC51051C6E47AD4FA403B02B4510B647AE3D1770BAC0326A805BBEFD48056C8C121BDB8"), // Replace with actual 'g2_x.0' FieldElement::from_hex_unchecked("13E02B6052719F607DACD3A088274F65596BD0D09920B61AB5DA61BBDC7F5049334CF11213945D57E5AC7D055D042B7E"), // Replace with actual 'g2_x.1' ]), g2_y: Some([ FieldElement::from_hex_unchecked("CE5D527727D6E118CC9CDC6DA2E351AADFD9BAA8CBDD3A76D429A695160D12C923AC9CC3BACA289E193548608B82801"), // Replace with actual 'g2_y.0' FieldElement::from_hex_unchecked("606C4A02EA734CC32ACD2B02BC28B99CB3E287E85A763AF267492AB572E99AB3F370D275CEC1DA1AAA9075FF05F79BE"), // Replace with actual 'g2_y.1' ]), n: BigUint::from_str_radix( "73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001", 16, ) .unwrap(), h: 1, // Replace with actual 'h' x: -0xD201000000010000, fp_generator: FieldElement::from(3), irreducible_polys: HashMap::from([ (6, [2, 0, 0, -2, 0, 0, 1].as_slice()), (12, [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1].as_slice()), ]), loop_counter: &[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, ], nr_a0: 1, eigen_value: Some( BigInt::from_str_radix("AC45A4010001A40200000000FFFFFFFF", 16).unwrap(), ), swu_params: Some(SWUParams { a: FieldElement::from_hex_unchecked("144698A3B8E9433D693A02C96D4982B0EA985383EE66A8D8E8981AEFD881AC98936F8DA0E0F97F5CF428082D584C1D"), b: FieldElement::from_hex_unchecked("12E2908D11688030018B12E8753EEE3B2016C1F0F24F4070A0B9C14FCEF35EF55A23215A316CEAA5D1CC48E98E172BE0"), z: FieldElement::from_hex_unchecked("B"), }), } } } pub trait ToWeierstrassCurve { fn to_weirstrass( x_twisted: FieldElement, y_twisted: FieldElement, ) -> ( FieldElement, FieldElement, ); } pub trait ToTwistedEdwardsCurve { fn to_twistededwards( x_weierstrass: FieldElement, y_weierstrass: FieldElement, ) -> ( FieldElement, FieldElement, ); } impl ToWeierstrassCurve for X25519PrimeField { fn to_weirstrass( x_twisted: FieldElement, y_twisted: FieldElement, ) -> ( FieldElement, FieldElement, ) { let a = element_from_biguint::(&biguint_from_hex( "0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC", )); // Replace with actual a_twisted let d = element_from_biguint::(&biguint_from_hex( "0x52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3", )); // Replace with actual d_twisted let x = (FieldElement::::from(5) * a + a * y_twisted - FieldElement::::from(5) * d * y_twisted - d) * (FieldElement::::from(12) - FieldElement::::from(12) * y_twisted) .inv() .unwrap(); let y = (a + a * y_twisted - d * y_twisted - d) * (FieldElement::::from(4) * x_twisted - FieldElement::::from(4) * x_twisted * y_twisted) .inv() .unwrap(); (x, y) } } impl ToTwistedEdwardsCurve for X25519PrimeField { fn to_twistededwards( x_weierstrass: FieldElement, y_weierstrass: FieldElement, ) -> ( FieldElement, FieldElement, ) { let a = element_from_biguint::(&biguint_from_hex( "0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC", )); // Replace with actual a_twisted let d = element_from_biguint::(&biguint_from_hex( "0x52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3", )); // Replace with actual d_twisted let y = (FieldElement::::from(5) * a - FieldElement::::from(12) * x_weierstrass - d) * (-FieldElement::::from(12) * x_weierstrass - a + FieldElement::::from(5) * d) .inv() .unwrap(); let x = (a + a * y - d * y - d) * (FieldElement::::from(4) * y_weierstrass - FieldElement::::from(4) * y_weierstrass * y) .inv() .unwrap(); (x, y) } } pub fn get_modulus_from_curve_id(curve_id: CurveID) -> BigUint { match curve_id { CurveID::BN254 => biguint_from_hex("0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD47"), CurveID::BLS12_381 => biguint_from_hex("0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAB"), CurveID::SECP256K1 => biguint_from_hex("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"), CurveID::SECP256R1 => biguint_from_hex("0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"), CurveID::X25519 => biguint_from_hex("0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED"), CurveID::GRUMPKIN => biguint_from_hex("0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001"), } } #[cfg(test)] mod tests { use super::{CurveParamsProvider, ToTwistedEdwardsCurve, ToWeierstrassCurve, X25519PrimeField}; #[test] fn test_to_weierstrass_and_back() { let curve = X25519PrimeField::get_curve_params(); let x_weirstrass = curve.g_x; let y_weirstrass = curve.g_y; let (x_twisted, y_twisted) = X25519PrimeField::to_twistededwards(x_weirstrass.clone(), y_weirstrass.clone()); let (x_weirstrass_back, y_weirstrass_back) = X25519PrimeField::to_weirstrass(x_twisted, y_twisted); assert_eq!(x_weirstrass, x_weirstrass_back); assert_eq!(y_weirstrass, y_weirstrass_back); } } ================================================ FILE: tools/garaga_rs/src/ecip/core.rs ================================================ use crate::algebra::polynomial::Polynomial; use crate::definitions::FieldElement; use lambdaworks_math::field::traits::IsPrimeField; use lambdaworks_math::traits::ByteConversion; use crate::algebra::g1point::G1Point; use crate::algebra::rational_function::{FunctionFelt, RationalFunction}; use crate::definitions::{ BLS12381PrimeField, BN254PrimeField, CurveParamsProvider, GrumpkinPrimeField, SECP256K1PrimeField, SECP256R1PrimeField, X25519PrimeField, }; use crate::ecip::ff::FF; use crate::io::{ field_elements_from_big_uints, field_elements_to_big_uints, parse_g1_points_from_flattened_field_elements_list, }; use num_bigint::{BigInt, BigUint, ToBigInt}; pub fn zk_ecip_hint( points: Vec, scalars: Vec, curve_id: usize, ) -> Result<[Vec; 5], String> { match curve_id { 0 => handle_curve::(points, scalars, field_elements_from_big_uints), 1 => handle_curve::(points, scalars, field_elements_from_big_uints), 2 => handle_curve::(points, scalars, field_elements_from_big_uints), 3 => handle_curve::(points, scalars, field_elements_from_big_uints), 4 => handle_curve::(points, scalars, field_elements_from_big_uints), 5 => handle_curve::(points, scalars, field_elements_from_big_uints), _ => Err(String::from("Invalid curve ID")), } } fn handle_curve( values: Vec, scalars: Vec, parse_fn: fn(&[BigUint]) -> Vec>, ) -> Result<[Vec; 5], String> where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let elements = parse_fn(&values); let points = parse_g1_points_from_flattened_field_elements_list(&elements)?; let (q, sum_dlog) = run_ecip(&points, &scalars); Ok(prepare_result(&q, &sum_dlog)) } fn construct_digits_vectors>( list: &[BigUint], ) -> Vec> { let mut dss_ = Vec::new(); for scalar_biguint in list { let neg_3_digits = neg_3_base_le(scalar_biguint); dss_.push(neg_3_digits); } let max_len = dss_.iter().map(|ds| ds.len()).max().unwrap(); dss_.iter_mut().for_each(|ds| { while ds.len() < max_len { ds.push(0); } }); // Transpose the matrix let mut dss = Vec::new(); for i in 0..max_len { let ds: Vec<_> = dss_.iter().map(|d| d[i]).collect(); dss.push(ds); } dss } pub fn neg_3_base_le(scalar: &BigUint) -> Vec { if scalar == &BigUint::from(0u32) { return vec![0]; } let mut iscalar = scalar.to_bigint().unwrap(); let mut digits = Vec::new(); let three = BigInt::from(3); let one = BigInt::from(1); let min_one = BigInt::from(-1); let zero = BigInt::from(0); let two = BigInt::from(2); while iscalar != zero { let mut remainder = iscalar.clone() % three.clone(); if remainder < zero { remainder += three.clone(); } if remainder == two { remainder = min_one.clone(); iscalar += one.clone(); } digits.push(remainder.try_into().unwrap()); iscalar = -floor_division(iscalar.clone(), three.clone()); // Use floor division } digits } fn floor_division(a: BigInt, b: BigInt) -> BigInt { let div = &a / &b; let rem = &a % &b; if (rem != BigInt::from(0)) && ((rem < BigInt::from(0)) != (b < BigInt::from(0))) { div - BigInt::from(1) } else { div } } pub fn run_ecip(points: &[G1Point], scalars: &[BigUint]) -> (G1Point, FunctionFelt) where F: IsPrimeField + CurveParamsProvider, { let dss = construct_digits_vectors::(scalars); // println!("Running ecip"); let (q, divisors) = ecip_functions(points, dss); // println!("Calculating dlogs"); let dlogs: Vec<_> = divisors.iter().map(|d| dlog(d.clone())).collect(); let mut sum_dlog = dlogs[0].clone(); let minus_three = FieldElement::::zero() - FieldElement::::from(3); let mut neg_3_power = FieldElement::::one(); for dlog in dlogs.iter().skip(1) { neg_3_power *= minus_three.clone(); sum_dlog = sum_dlog + dlog.clone().scale_by_coeff(neg_3_power.clone()); } // let sum_dlog = sum_dlog.simplify(); (q, sum_dlog) } fn prepare_result(q: &G1Point, sum_dlog: &FunctionFelt) -> [Vec; 5] where F: IsPrimeField, FieldElement: ByteConversion, { let q_list = &[q.x.clone(), q.y.clone()]; let a_num_list = &sum_dlog.a.numerator.coefficients; let a_den_list = &sum_dlog.a.denominator.coefficients; let b_num_list = &sum_dlog.b.numerator.coefficients; let b_den_list = &sum_dlog.b.denominator.coefficients; [ field_elements_to_big_uints(q_list), field_elements_to_big_uints(a_num_list), field_elements_to_big_uints(a_den_list), field_elements_to_big_uints(b_num_list), field_elements_to_big_uints(b_den_list), ] } // Equivalent to line(p, p.neg()), converted to a polynomial fn line_p_p_neg>(p: &G1Point) -> FF { if p.is_infinity() { // 1 + 0 * y. return FF::new(vec![Polynomial::new(vec![FieldElement::one()])]); } // (-px + x) + 0 * y FF::new(vec![Polynomial::new(vec![-&p.x, FieldElement::one()])]) } // Equivalent to (line(a, a.neg()) * line(b, b.neg())).to_poly() fn mul_line_line_p_p_neg(p: &G1Point, q: &G1Point) -> Polynomial { if p.is_infinity() { // 1 if q.is_infinity() { // 1 Polynomial::one() } else { // -qx + X Polynomial::new(vec![-&q.x, FieldElement::one()]) } } else if q.is_infinity() { // -px + X Polynomial::new(vec![-&p.x, FieldElement::one()]) } else { // (-px+X) * (-qx+X) = px*qx -px * X - qx* X + X^2 = px*qx -(px + qx)X + X^2 Polynomial::new(vec![&p.x * &q.x, -&p.x - &q.x, FieldElement::one()]) } } fn line>(p: &G1Point, q: &G1Point) -> FF { if p.is_infinity() { if q.is_infinity() { return FF::new(vec![Polynomial::new(vec![FieldElement::one()])]); } else { let qx = q.x.clone(); return FF::new(vec![Polynomial::new(vec![-qx, FieldElement::one()])]); } } if q.is_infinity() { let px = p.x.clone(); return FF::new(vec![Polynomial::new(vec![-px, FieldElement::one()])]); } let px = p.x.clone(); let py = p.y.clone(); let three: FieldElement = FieldElement::from(3); if p == q { let m = (three * &px.square() + F::get_curve_params().a) / (py.double()); let m = m.unwrap(); let b = py - &m * px; return FF::new(vec![ Polynomial::new(vec![-b, -m]), Polynomial::new(vec![FieldElement::one()]), ]); } if p == &q.neg() { return FF::new(vec![Polynomial::new(vec![-px, FieldElement::one()])]); } let qx = q.x.clone(); let qy = q.y.clone(); let m = (py - &qy) / (px - &qx); let m = m.unwrap(); let b = qy - &m * qx; FF::new(vec![ Polynomial::new(vec![-b, -m]), Polynomial::new(vec![FieldElement::one()]), ]) } fn construct_function>(ps: Vec>) -> FF { if ps.is_empty() { return FF::new(vec![Polynomial::new(vec![FieldElement::one()])]); } let mut xs: Vec<(G1Point, FF)> = ps.iter().map(|p| (p.clone(), line_p_p_neg(p))).collect(); while xs.len() != 1 { let mut xs2: Vec<(G1Point, FF)> = Vec::new(); let x0 = if !xs.len().is_multiple_of(2) { let x0 = xs[0].clone(); xs.remove(0); Some(x0) } else { None }; for n in 0..(xs.len() / 2) { let (a, a_num) = &xs[2 * n]; let (b, b_num) = &xs[2 * n + 1]; let a_num_b_num = a_num * b_num; let line_ab = line(a, b); let product = a_num_b_num * line_ab; let num = product.reduce(); let den = mul_line_line_p_p_neg(a, b); let d = num.div_by_poly(&den); xs2.push((a.add(b), d)); } if let Some(x0) = x0 { xs2.push(x0); } xs = xs2; } assert!(xs[0].0.is_infinity(), "xs[0] is not infinity"); xs.last().unwrap().1.normalize() } fn row_function>( ds: Vec, ps: &[G1Point], q: G1Point, ) -> (FF, G1Point) { let one = 1; let minus_one = -1; let digits_points: Vec> = ds .iter() .zip(ps.iter()) .map(|(&d, p)| { if d == one { p.clone() } else if d == minus_one { p.neg() } else { G1Point::new_infinity() } }) .collect(); let sum_digits_points = digits_points .iter() .cloned() .reduce(|x, y| x.add(&y)) .unwrap(); let q2 = q.scalar_mul_neg_3().add(&sum_digits_points); let q_neg = q.neg(); // Pre-allocate with exact capacity to avoid reallocations let mut div = Vec::with_capacity(4 + digits_points.len()); // Push negated points without cloning div.push(q_neg.clone()); // Only clone once div.push(q_neg.clone()); div.push(q_neg.clone()); div.push(q2.neg()); // Extend with non-infinity points directly to avoid double filtering div.extend(digits_points.iter().filter(|p| !p.is_infinity()).cloned()); let d = construct_function(div); (d, q2) } fn ecip_functions>( bs: &[G1Point], dss: Vec>, ) -> (G1Point, Vec>) { let mut dss = dss; dss.reverse(); let mut q = G1Point::new_infinity(); let mut divisors: Vec> = Vec::new(); for ds in dss.iter() { let (div, new_q) = row_function(ds.clone(), bs, q); divisors.push(div); q = new_q; } divisors.reverse(); (q, divisors) } fn dlog>(d: FF) -> FunctionFelt { let d = d.reduce(); assert!( d.coeffs.len() == 2, "D has {} coeffs: {:?}", d.coeffs.len(), d.coeffs ); let dx = FF::new(vec![ d.coeffs[0].differentiate(), d.coeffs[1].differentiate(), ]); let dy = d.coeffs[1].clone(); let two_y = FF::::new(vec![ Polynomial::::zero(), Polynomial::new(vec![FieldElement::::from(2)]), ]); let poly = dy.clone() * Polynomial::::new(vec![ F::get_curve_params().a, FieldElement::zero(), FieldElement::from(3), ]); let u = dx * two_y.clone() + FF::new(vec![poly, Polynomial::zero()]); let v = two_y * d; let num = (u * v.clone().neg_y()).reduce(); let den_ff = (v.clone() * v.neg_y()).reduce(); assert!( den_ff.coeffs[1].degree() == -1, "Den[1] is not zero: {:?}", den_ff.coeffs[1].degree() ); let den = den_ff.coeffs[0].clone(); let den_lead_inv = den.leading_coefficient().inv().unwrap(); let (_, _, gcd_0) = Polynomial::xgcd(&num.coeffs[0], &den); let (_, _, gcd_1) = Polynomial::xgcd(&num.coeffs[1], &den); let a_num = num.coeffs[0].divfloor(&gcd_0); let a_den = den.divfloor(&gcd_0); let b_num = num.coeffs[1].divfloor(&gcd_1); let b_den = den.divfloor(&gcd_1); FunctionFelt { a: RationalFunction::new( a_num.scale_by_coeff(&den_lead_inv), a_den.scale_by_coeff(&a_den.leading_coefficient().inv().unwrap()), ), b: RationalFunction::new( b_num.scale_by_coeff(&den_lead_inv), b_den.scale_by_coeff(&b_den.leading_coefficient().inv().unwrap()), ), } } ================================================ FILE: tools/garaga_rs/src/ecip/ff.rs ================================================ use crate::algebra::polynomial::Polynomial; use crate::definitions::FieldElement; use lambdaworks_math::field::traits::IsPrimeField; use std::ops::{Add, Mul}; use crate::definitions::CurveParamsProvider; #[derive(Debug, Clone)] pub struct FF { pub coeffs: Vec>, } impl> FF { pub fn new(coeffs: Vec>) -> Self { FF { coeffs } } pub fn degree(&self) -> usize { self.coeffs.len() - 1 } pub fn neg_y(self) -> FF { if self.coeffs.len() < 2 { self } else { let mut coeff_neg = self.coeffs.clone(); for i in (1..coeff_neg.len()).step_by(2) { coeff_neg[i] = -&coeff_neg[i]; } FF { coeffs: coeff_neg } } } pub fn reduce(&self) -> FF { match self.coeffs.len() { 0 => FF { coeffs: vec![Polynomial::zero(), Polynomial::zero()], }, 1 => FF { coeffs: vec![self.coeffs[0].clone(), Polynomial::zero()], }, _ => { let mut deg_0_coeff = self.coeffs[0].clone(); let mut deg_1_coeff = self.coeffs[1].clone(); let curve_params = F::get_curve_params(); let a = curve_params.a; let b = curve_params.b; let mut y2 = Polynomial::new(vec![b, a, FieldElement::zero(), FieldElement::one()]); for (i, poly) in self.coeffs.iter().enumerate().skip(2) { if i % 2 == 0 { deg_0_coeff = deg_0_coeff + poly * &y2; } else { deg_1_coeff = deg_1_coeff + poly * &y2; y2 = &y2 * &y2; } } FF { coeffs: vec![deg_0_coeff, deg_1_coeff], } } } } pub fn normalize(&self) -> FF { let coeff = self.coeffs[0].coefficients[0].clone(); let inv_coeff: FieldElement = coeff.inv().unwrap(); FF { coeffs: self .coeffs .iter() .map(|c| c.scale_by_coeff(&inv_coeff)) .collect(), } } pub fn to_poly(&self) -> Polynomial { assert!(self.coeffs.len() == 1); self.coeffs[0].clone() } pub fn div_by_poly(&self, poly: &Polynomial) -> FF { let coeffs: Vec> = self .coeffs .iter() .map(|c| c.clone().div_with_ref(poly)) .collect(); // println!("Final coefficients after division: {:?}", coeffs); FF { coeffs } } pub fn print_as_sage_poly(&self) -> String { let mut string = String::new(); let coeffs = &self.coeffs; for (i, p) in coeffs.iter().rev().enumerate() { let coeff_str = p.print_as_sage_poly(); if i == coeffs.len() - 1 { if coeff_str.is_empty() { string.truncate(string.len().saturating_sub(2)); } else { string.push_str(&coeff_str); } } else if i == coeffs.len() - 2 { string.push_str(&format!("({})*y + ", coeff_str)); } else { string.push_str(&format!("({})*y^{} + ", coeff_str, coeffs.len() - i - 1)); } } string } } impl> Add for FF { type Output = Self; fn add(self, other: Self) -> Self::Output { let max_degree = self.coeffs.len().max(other.coeffs.len()); let mut coeffs = vec![Polynomial::zero(); max_degree]; for i in 0..self.coeffs.len() { coeffs[i] = &coeffs[i] + &self.coeffs[i]; } for i in 0..other.coeffs.len() { coeffs[i] = &coeffs[i] + &other.coeffs[i]; } FF::new(coeffs) } } impl> Mul for FF { type Output = Self; fn mul(self, other: Self) -> Self::Output { let max_degree = self.coeffs.len() + other.coeffs.len() - 1; let mut coeffs = vec![Polynomial::zero(); max_degree]; if self.coeffs.is_empty() || other.coeffs.is_empty() { return FF::new(vec![Polynomial::zero()]); } for (i, self_poly) in self.coeffs.iter().enumerate() { for (j, other_poly) in other.coeffs.iter().enumerate() { let product = self_poly * other_poly; coeffs[i + j] = &coeffs[i + j] + &product; } } FF::new(coeffs) } } impl> Mul for &FF { type Output = FF; fn mul(self, other: Self) -> Self::Output { let max_degree = self.coeffs.len() + other.coeffs.len() - 1; let mut coeffs = vec![Polynomial::zero(); max_degree]; if self.coeffs.is_empty() || other.coeffs.is_empty() { return FF::new(vec![Polynomial::zero()]); } for (i, self_poly) in self.coeffs.iter().enumerate() { for (j, other_poly) in other.coeffs.iter().enumerate() { let product = self_poly * other_poly; coeffs[i + j] = &coeffs[i + j] + &product; } } FF::new(coeffs) } } ================================================ FILE: tools/garaga_rs/src/frobenius.rs ================================================ use crate::algebra::polynomial::Polynomial; use crate::definitions::CurveID; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::IsPrimeField; use std::collections::HashMap; type FrobeniusMap = HashMap)>>>; pub fn frobenius( frobenius_maps: &FrobeniusMap, x: &Polynomial, frob_power: usize, ext_degree: usize, ) -> Polynomial { let frobenius_map = frobenius_maps.get(&frob_power).unwrap(); assert!(x.coefficients.len() <= ext_degree); let mut frob = vec![]; for coeffs in frobenius_map.iter().take(x.coefficients.len()) { let mut v = FieldElement::from(0); for (index, constant) in coeffs { v += constant * &x.coefficients[*index]; } frob.push(v); } Polynomial::new(frob) } // returns only the indices required by multi_pairing_check (bn254: 1, 2, 3; bls12-381: 1) pub fn get_frobenius_maps_ext_degree_12(curve_id: CurveID) -> FrobeniusMap { match curve_id { CurveID::BN254 => HashMap::from([ (1, vec![ vec![ (0, FieldElement::from_hex("1").unwrap()), (6, FieldElement::from_hex("12").unwrap()), ], vec![ (1, FieldElement::from_hex("1d8c8daef3eee1e81b2522ec5eb28ded6895e1cdfde6a43f5daa971f3fa65955").unwrap()), (7, FieldElement::from_hex("217e400dc9351e774e34e2ac06ead4000d14d1e242b29c567e9c385ce480a71a").unwrap()), ], vec![ (2, FieldElement::from_hex("242b719062f6737b8481d22c6934ce844d72f250fd28d102c0d147b2f4d521a7").unwrap()), (8, FieldElement::from_hex("359809094bd5c8e1b9c22d81246ffc2e794e17643ac198484b8d9094aa82536").unwrap()), ], vec![ (3, FieldElement::from_hex("21436d48fcb50cc60dd4ef1e69a0c1f0dd2949fa6df7b44cbb259ef7cb58d5ed").unwrap()), (9, FieldElement::from_hex("18857a58f3b5bb3038a4311a86919d9c7c6c15f88a4f4f0831364cf35f78f771").unwrap()), ], vec![ (4, FieldElement::from_hex("2c84bbad27c3671562b7adefd44038ab3c0bbad96fc008e7d6998c82f7fc048b").unwrap()), (10, FieldElement::from_hex("c33b1c70e4fd11b6d1eab6fcd18b99ad4afd096a8697e0c9c36d8ca3339a7b5").unwrap()), ], vec![ (5, FieldElement::from_hex("1b007294a55accce13fe08bea73305ff6bdac77c5371c546d428780a6e3dcfa8").unwrap()), (11, FieldElement::from_hex("215d42e7ac7bd17cefe88dd8e6965b3adae92c974f501fe811493d72543a3977").unwrap()), ], vec![ (6, FieldElement::from_hex("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap()), ], vec![ (1, FieldElement::from_hex("246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac").unwrap()), (7, FieldElement::from_hex("12d7c0c3ed42be419d2b22ca22ceca702eeb88c36a8b264dde75f4f798d6a3f2").unwrap()), ], vec![ (2, FieldElement::from_hex("16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2").unwrap()), (8, FieldElement::from_hex("c38dce27e3b2cae33ce738a184c89d94a0e78406b48f98a7b4f4463e3a7dba0").unwrap()), ], vec![ (3, FieldElement::from_hex("7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3").unwrap()), (9, FieldElement::from_hex("f20e129e47c9363aa7b569817e0966cba582096fa7a164080faed1f0d24275a").unwrap()), ], vec![ (4, FieldElement::from_hex("2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126").unwrap()), (10, FieldElement::from_hex("3df92c5b96e3914559897c6ad411fb25b75afb7f8b1c1a56586ff93e080f8bc").unwrap()), ], vec![ (5, FieldElement::from_hex("12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b").unwrap()), (11, FieldElement::from_hex("1563dbde3bd6d35ba4523cf7da4e525e2ba6a3151500054667f8140c6a3f2d9f").unwrap()), ], ]), (2, vec![ vec![ (0, FieldElement::from_hex("1").unwrap()), ], vec![ (1, FieldElement::from_hex("30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49").unwrap()), ], vec![ (2, FieldElement::from_hex("30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48").unwrap()), ], vec![ (3, FieldElement::from_hex("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap()), ], vec![ (4, FieldElement::from_hex("59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe").unwrap()), ], vec![ (5, FieldElement::from_hex("59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff").unwrap()), ], vec![ (6, FieldElement::from_hex("1").unwrap()), ], vec![ (7, FieldElement::from_hex("30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49").unwrap()), ], vec![ (8, FieldElement::from_hex("30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48").unwrap()), ], vec![ (9, FieldElement::from_hex("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap()), ], vec![ (10, FieldElement::from_hex("59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe").unwrap()), ], vec![ (11, FieldElement::from_hex("59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff").unwrap()), ], ]), (3, vec![ vec![ (0, FieldElement::from_hex("1").unwrap()), (6, FieldElement::from_hex("12").unwrap()), ], vec![ (1, FieldElement::from_hex("13d0c369615f7bb0b2bdfa8fef85fa07122bde8d67dfc8fabd3581ad840ddd76").unwrap()), (7, FieldElement::from_hex("18a0f4219f4fdff6fc2bf531eb331a053a35744cac285af5685d3f90eacf7a66").unwrap()), ], vec![ (2, FieldElement::from_hex("c3a5e9c462a654779c3e050c9ca2a428908a81264e2b5a5bf22f67654883ae6").unwrap()), (8, FieldElement::from_hex("2ce02aa5f9bf8cd65bdd2055c255cf9d9e08c1d9345582cc92fd973c74bd77f4").unwrap()), ], vec![ (3, FieldElement::from_hex("f20e129e47c9363aa7b569817e0966cba582096fa7a164080faed1f0d24275a").unwrap()), (9, FieldElement::from_hex("17ded419ed7be4f97fac149bfaefbac11b155498de227b850aea3f23790405d6").unwrap()), ], vec![ (4, FieldElement::from_hex("1bfe7b214c0294242fb81a8dccd8a9b4441d64f34150a79753fb0cd31cc99cc0").unwrap()), (10, FieldElement::from_hex("697b9c523e0390ed15da0ec97a9b8346513297b9efaf0f0f1a228f0d5662fbd").unwrap()), ], vec![ (5, FieldElement::from_hex("7a0e052f2b1c443b5186d6ac4c723b85d3f78a3182d2db0c413901c32b0c6fe").unwrap()), (11, FieldElement::from_hex("1b76a37fba85f3cd5dc79824a3792597356c892c39c0d06b220500933945267f").unwrap()), ], vec![ (6, FieldElement::from_hex("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap()), ], vec![ (1, FieldElement::from_hex("abf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101").unwrap()), (7, FieldElement::from_hex("1c938b097fd2247905924b2691fb5e5685558c04009201927eeb0a69546f1fd1").unwrap()), ], vec![ (2, FieldElement::from_hex("4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de").unwrap()), (8, FieldElement::from_hex("2429efd69b073ae23e8c6565b7b72e1b0e78c27f038f14e77cfd95a083f4c261").unwrap()), ], vec![ (3, FieldElement::from_hex("28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64").unwrap()), (9, FieldElement::from_hex("21436d48fcb50cc60dd4ef1e69a0c1f0dd2949fa6df7b44cbb259ef7cb58d5ed").unwrap()), ], vec![ (4, FieldElement::from_hex("23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f").unwrap()), (10, FieldElement::from_hex("1465d351952f0c0588982b28b4a8aea95364059e272122f5e8257f43bbb36087").unwrap()), ], vec![ (5, FieldElement::from_hex("16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499").unwrap()), (11, FieldElement::from_hex("28c36e1fee7fdbe60337d84bbcba34a53a41f1ee50449cdc780cfbfaa5cc3649").unwrap()), ], ]), ]), CurveID::BLS12_381 => HashMap::from([ (1, vec![ vec![ (0, FieldElement::from_hex("1").unwrap()), (6, FieldElement::from_hex("2").unwrap()), ], vec![ (1, FieldElement::from_hex("18089593cbf626353947d5b1fd0c6d66bb34bc7585f5abdf8f17b50e12c47d65ce514a7c167b027b600febdb244714c5").unwrap()), (7, FieldElement::from_hex("18089593cbf626353947d5b1fd0c6d66bb34bc7585f5abdf8f17b50e12c47d65ce514a7c167b027b600febdb244714c5").unwrap()), ], vec![ (2, FieldElement::from_hex("5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff").unwrap()), ], vec![ (9, FieldElement::from_hex("d5e1c086ffe8016d063c6dad7a2fffc9072bb5785a686bcefeedc2e0124838bdccf325ee5d80be9902109f7dbc79812").unwrap()), ], vec![ (4, FieldElement::from_hex("1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad").unwrap()), (10, FieldElement::from_hex("1a0111ea397fe6998ce8d956845e1033efa3bf761f6622e9abc9802928bfc912627c4fd7ed3ffffb5dfb00000001aaaf").unwrap()), ], vec![ (5, FieldElement::from_hex("b659fb20274bfb1be8ff4d69163c08be7302c4818171fdd17d5be9b1d380acd8c747cdc4aff0e653631f5d3000f022c").unwrap()), (11, FieldElement::from_hex("b659fb20274bfb1be8ff4d69163c08be7302c4818171fdd17d5be9b1d380acd8c747cdc4aff0e653631f5d3000f022c").unwrap()), ], vec![ (6, FieldElement::from_hex("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa").unwrap()), ], vec![ (1, FieldElement::from_hex("fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3").unwrap()), (7, FieldElement::from_hex("1f87c566d89c06511d3d204463f3f70a9428f0f6d8f66dfd8191d92e3ec78be505ab5829ad8fd8459ef1424dbb895e6").unwrap()), ], vec![ (2, FieldElement::from_hex("1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac").unwrap()), (8, FieldElement::from_hex("1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac").unwrap()), ], vec![ (3, FieldElement::from_hex("6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09").unwrap()), ], vec![ (10, FieldElement::from_hex("5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe").unwrap()), ], vec![ (5, FieldElement::from_hex("144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995").unwrap()), (11, FieldElement::from_hex("e9b7238370b26e88c8bb2dfb1e7ec4b7d471f3cdb6df2e24f5b1405d978eb56923783226654f19a83cd0a2cfff0a87f").unwrap()), ], ]), ]), _ => unimplemented!(), } } ================================================ FILE: tools/garaga_rs/src/hints/eisenstein.rs ================================================ use num_bigint::BigInt; use num_traits::{One, Signed, Zero}; /// Axial coordinates of the 6 unit directions in the hexagonal lattice. const NEIGHBOURS: [(i32, i32); 6] = [(1, 0), (0, 1), (-1, 1), (-1, 0), (0, -1), (1, -1)]; /// Symmetric integer rounding ⌊(z + d/2) / d⌋ valid for *any* sign of `z`. fn round_nearest(z: &BigInt, d: &BigInt) -> BigInt { debug_assert!(*d > BigInt::zero()); let half = d >> 1; // d / 2 if *z >= BigInt::zero() { (z + &half) / d } else { let quotient: BigInt = ((-z) + &half) / d; -quotient } } /* Represents an Eisenstein integer z = a0 + a1*ω, where ω = exp(2πi/3). ω satisfies ω^2 + ω + 1 = 0. Uses Python's built-in arbitrary-precision integers. Attributes: a0: The integer coefficient of 1. a1: The integer coefficient of ω. */ #[derive(Clone, Debug, Eq, PartialEq)] pub struct EisensteinInteger { pub a0: BigInt, pub a1: BigInt, } impl EisensteinInteger { /*Initializes an EisensteinInteger.*/ pub fn new(a0: BigInt, a1: BigInt) -> Self { Self { a0, a1 } } /*Sets the value of self to the value of other. Returns self.*/ pub fn set(&mut self, other: &Self) -> &Self { self.a0 = other.a0.clone(); self.a1 = other.a1.clone(); self } /*Sets the value of self to zero. Returns self.*/ pub fn set_zero(&mut self) -> &Self { self.a0 = BigInt::zero(); self.a1 = BigInt::zero(); self } /*Sets the value of self to one. Returns self.*/ pub fn set_one(&mut self) -> &Self { self.a0 = BigInt::one(); self.a1 = BigInt::zero(); self } /* Computes the complex conjugate. conj(a0 + a1*ω) = (a0 - a1) - a1*ω */ pub fn conjugate(&self) -> Self { Self::new(&self.a0 - &self.a1, -&self.a1) } /* Computes the norm N(self). N(a0 + a1*ω) = a0^2 + a1^2 - a0*a1 The norm is always non-negative. */ pub fn norm(&self) -> BigInt { &self.a0.pow(2) + &self.a1.pow(2) - &self.a0 * &self.a1 } /* Performs Euclidean division self / y using rounding to the NEAREST Eisenstein integer. This method guarantees norm(remainder) < norm(divisor). Args: y: The divisor (must be non-zero). Returns: A tuple (quotient, remainder). Raises: ZeroDivisionError: If y is zero. TypeError: If y is not an EisensteinInteger. */ /* ---------- Euclidean division in ℤ[ω] ---------- */ pub fn quo_rem(&self, y: &Self) -> Result<[Self; 2], String> { if y.is_zero() { return Err("division by zero EisensteinInteger".into()); } let nrm = y.norm(); // positive let num = self * &y.conjugate(); // still integer-only // first guess by independent symmetric rounding let mut q0 = round_nearest(&num.a0, &nrm); let mut q1 = round_nearest(&num.a1, &nrm); let mut q = Self::new(q0.clone(), q1.clone()); // Calculate product first, then subtract its reference let qy = &q * y; let mut r = self - &qy; // walk the neighbourhood until N(r) < N(y) (≤ 2 iterations) while r.norm() >= nrm { let mut best_q = None; let mut best_r = None; let mut best_n2 = r.norm(); // current (worst) remainder for (dp, dq) in NEIGHBOURS.iter() { let cand_q = Self::new(&q0 + dp, &q1 + dq); // Calculate product first, then subtract its reference let cand_qy = &cand_q * y; let cand_r = self - &cand_qy; let cand_n2 = cand_r.norm(); if cand_n2 < best_n2 { best_q = Some(cand_q); best_r = Some(cand_r); best_n2 = cand_n2; } } q = best_q.expect("Euclidean property violated"); r = best_r.unwrap(); q0 = q.a0.clone(); q1 = q.a1.clone(); // centre for 2nd lap } Ok([q, r]) } } impl std::fmt::Display for EisensteinInteger { /*Returns a user-friendly string representation (e.g., '3 + 2*ω').*/ fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { if self.a1.is_zero() { write!(f, "{}", self.a0) } else { let a0_str = if !self.a0.is_zero() { format!("{}", self.a0) } else { "".into() }; let a1_str = if self.a1 == BigInt::one() { "ω".into() } else if self.a1 == (-1).into() { "-ω".into() } else { format!("{}*ω", self.a1) }; if a0_str.is_empty() { write!(f, "{}", a1_str) } else { let sign = if self.a1 > BigInt::zero() { " + " } else { " - " }; let a1_abs_str = if self.a1.abs() == BigInt::one() { "ω".into() } else { format!("{}*ω", self.a1.abs()) }; write!(f, "{}{}{}", a0_str, sign, a1_abs_str) } } } } impl std::ops::Neg for EisensteinInteger { type Output = Self; /*Computes the negation -self.*/ fn neg(self) -> Self::Output { Self { a0: -self.a0, a1: -self.a1, } } } impl std::ops::Add for EisensteinInteger { type Output = Self; /*Computes the sum self + other.*/ fn add(self, other: Self) -> Self::Output { &self + &other } } impl<'a> std::ops::Add<&'a EisensteinInteger> for &'a EisensteinInteger { type Output = EisensteinInteger; /*Computes the sum self + other.*/ fn add(self, other: Self) -> Self::Output { EisensteinInteger::new(&self.a0 + &other.a0, &self.a1 + &other.a1) } } impl std::ops::Sub for EisensteinInteger { type Output = Self; /*Computes the difference self - other.*/ fn sub(self, other: Self) -> Self::Output { &self - &other } } impl<'a> std::ops::Sub<&'a EisensteinInteger> for &'a EisensteinInteger { type Output = EisensteinInteger; /*Computes the difference self - other.*/ fn sub(self, other: Self) -> Self::Output { EisensteinInteger::new(&self.a0 - &other.a0, &self.a1 - &other.a1) } } impl std::ops::Mul for EisensteinInteger { type Output = Self; /* Computes the product self * other. Supports multiplication by another EisensteinInteger. Uses the identity (x0+x1ω)(y0+y1ω) = (x0y0 - x1y1) + (x0y1 + x1y0 - x1y1)ω. */ fn mul(self, other: Self) -> Self::Output { &self * &other } } impl<'a> std::ops::Mul<&'a EisensteinInteger> for &'a EisensteinInteger { type Output = EisensteinInteger; /* Computes the product self * other. Supports multiplication by another EisensteinInteger. Uses the identity (x0+x1ω)(y0+y1ω) = (x0y0 - x1y1) + (x0y1 + x1y0 - x1y1)ω. */ fn mul(self, other: Self) -> Self::Output { let (x0, x1) = (&self.a0, &self.a1); let (y0, y1) = (&other.a0, &other.a1); let res_a0 = x0 * y0 - x1 * y1; let res_a1 = x0 * y1 + x1 * y0 - x1 * y1; EisensteinInteger::new(res_a0, res_a1) } } impl std::ops::Mul for EisensteinInteger { type Output = Self; /*Computes the product self * int.*/ fn mul(self, other: BigInt) -> Self::Output { &self * &other } } impl<'a> std::ops::Mul<&'a BigInt> for &'a EisensteinInteger { type Output = EisensteinInteger; /*Computes the product self * int.*/ fn mul(self, other: &BigInt) -> Self::Output { other * self } } impl std::ops::Mul for BigInt { type Output = EisensteinInteger; /*Computes the product int * self.*/ fn mul(self, other: EisensteinInteger) -> Self::Output { &self * &other } } impl<'a> std::ops::Mul<&'a EisensteinInteger> for &'a BigInt { type Output = EisensteinInteger; /*Computes the product int * self.*/ fn mul(self, other: &EisensteinInteger) -> Self::Output { EisensteinInteger::new(self * &other.a0, self * &other.a1) } } impl std::ops::Div for EisensteinInteger { type Output = Self; /*Computes the quotient self // other using Euclidean rounding division.*/ fn div(self, other: Self) -> Self::Output { &self / &other } } impl<'a> std::ops::Div<&'a EisensteinInteger> for &'a EisensteinInteger { type Output = EisensteinInteger; /*Computes the quotient self // other using Euclidean rounding division.*/ fn div(self, other: Self) -> Self::Output { let [q, _] = self.quo_rem(other).unwrap(); q } } impl std::ops::Rem for EisensteinInteger { type Output = Self; /*Computes the remainder self % other using Euclidean rounding division.*/ fn rem(self, other: Self) -> Self::Output { &self % &other } } impl<'a> std::ops::Rem<&'a EisensteinInteger> for &'a EisensteinInteger { type Output = EisensteinInteger; /*Computes the remainder self % other using Euclidean rounding division.*/ fn rem(self, other: Self) -> Self::Output { let [_, r] = self.quo_rem(other).unwrap(); r } } impl Zero for EisensteinInteger { fn zero() -> Self { Self::new(BigInt::zero(), BigInt::zero()) } /*Checks if the value is zero.*/ fn is_zero(&self) -> bool { self.a0.is_zero() && self.a1.is_zero() } } impl One for EisensteinInteger { fn one() -> Self { Self::new(BigInt::one(), BigInt::zero()) } } /* Computes the partial GCD result using the Half-GCD approach based on norm reduction. Args: a: The first EisensteinInteger. b: The second EisensteinInteger. Returns: A tuple (w, v, u) such that w = a*u + b*v and norm(w) is approximately less than sqrt(norm(a)). The identity w = a*u + b*v always holds. Raises: TypeError: If inputs are not EisensteinInteger instances. ValueError: If the norm of 'a' is unexpectedly negative. RuntimeError: If the algorithm takes an excessive number of iterations. */ pub fn half_gcd( a: &EisensteinInteger, b: &EisensteinInteger, ) -> Result<[EisensteinInteger; 3], String> { // Initialize variables for the Extended Euclidean Algorithm let mut a_run = a.clone(); let mut b_run = b.clone(); let mut u = EisensteinInteger::one(); // Use class constant copies let mut v = EisensteinInteger::zero(); let mut u_ = EisensteinInteger::zero(); let mut v_ = EisensteinInteger::one(); // Invariants: a_run = a*u + b*v, b_run = a*u_ + b*v_ let norm_a = a.norm(); if norm_a < BigInt::zero() { return Err("Norm of input 'a' cannot be negative".into()); } // Calculate the termination threshold let limit = norm_a.sqrt(); // Loop while the norm of the 'smaller' value (b_run) is >= the limit let mut iteration = 0; let max_iterations = 20000; // Safety limit while b_run.norm() >= limit { if iteration > max_iterations { return Err(format!( "HalfGCD exceeded {} iterations for a={}, b={}", max_iterations, a, b )); } if b_run.is_zero() { break; // GCD is a_run } let [quotient, remainder] = match a_run.quo_rem(&b_run) { Ok(result) => result, _ => break, // Should ideally not happen if b_run.is_zero() check works }; // Update coefficients let next_u_ = u - "ient * &u_; let next_v_ = v - "ient * &v_; // Update state (a_run, b_run) = (b_run, remainder); (u, u_) = (u_, next_u_); (v, v_) = (v_, next_v_); iteration += 1; } // Return the final state corresponding to the Go implementation's return values // (b_run, v_, u_) which satisfy b_run = a*u_ + b*v_ Ok([b_run, v_, u_]) } #[allow(unused_imports)] mod tests { use super::*; #[test] fn test_01() -> Result<(), String> { let z1 = EisensteinInteger::new(3.into(), 2.into()); // 3 + 2ω let z2 = EisensteinInteger::new(1.into(), (-1).into()); // 1 - ω println!("z1 = {}", z1); println!("z2 = {}", z2); println!("z1 + z2 = {}", &z1 + &z2); println!("z1 - z2 = {}", &z1 - &z2); println!("z1 * z2 = {}", &z1 * &z2); println!("Norm(z1) = {}", z1.norm()); println!("Conj(z1) = {}", z1.conjugate()); println!("-z1 = {}", -z1.clone()); let [q, r] = z1.quo_rem(&z2)?; println!("z1 // z2 = {}", q); println!("z1 % z2 = {}", r); println!("Check: z2 * q + r = {}, Expected: {}", &(&z2 * &q) + &r, z1); assert_eq!(&(&z2 * &q) + &r, z1); // Half GCD example let a = EisensteinInteger::new(10.into(), 3.into()); let b = EisensteinInteger::new(3.into(), 1.into()); println!("\nHalf GCD for a = {}, b = {}", a, b); let [w, v_res, u_res] = half_gcd(&a, &b)?; println!(" w = {}", w); println!(" v = {}", v_res); println!(" u = {}", u_res); let check = &a * &u_res + &b * &v_res; println!(" Check: a*u + b*v = {}, Expected w: {}", check, w); println!(" Norm(w) = {}, Limit = {}", w.norm(), a.norm().sqrt()); assert_eq!(check, w); // a = EisensteinInteger(8+7j * (math.sqrt(3)/2 + 0.5j)) # Approximate large number let a_int = EisensteinInteger::new(13.into(), 14.into()); // Example large int coeffs let b_int = EisensteinInteger::new(5.into(), 3.into()); println!("\nHalf GCD for a = {}, b = {}", a_int, b_int); let [w, v_res, u_res] = half_gcd(&a_int, &b_int)?; println!(" w = {}", w); println!(" v = {}", v_res); println!(" u = {}", u_res); let check = &a_int * &u_res + &b_int * &v_res; println!(" Check: a*u + b*v = {}, Expected w: {}", check, w); println!(" Norm(w) = {}, Limit = {}", w.norm(), a_int.norm().sqrt()); assert_eq!(check, w); Ok(()) } } ================================================ FILE: tools/garaga_rs/src/hints/fake_glv.rs ================================================ use crate::algebra::g1point::G1Point; use crate::definitions::CurveParamsProvider; use crate::hints::eisenstein; use lambdaworks_math::field::traits::IsPrimeField; use num_bigint::{BigInt, BigUint, Sign, ToBigInt}; use num_integer::Integer; use num_traits::Signed; /* Represents a 2D lattice basis (V1, V2) derived from GLV decomposition. Attributes: V1: First basis vector [v11, v12]. V2: Second basis vector [v21, v22], chosen to be short. Det: Determinant of the lattice basis (v11*v22 - v12*v21). b1: Rounding coefficient derived from V2, used in scalar decomposition. b2: Rounding coefficient derived from V1, used in scalar decomposition. */ struct Lattice { v1: [BigInt; 2], v2: [BigInt; 2], det: BigInt, b1: BigInt, b2: BigInt, } /* Computes the first vector of a GLV lattice basis for a given modulus and input. This is a Python adaptation of a Go function likely used for cryptographic scalar multiplication optimizations (GLV method). Args: modu (int): The modulus (often the group order `r`). input_val (int): The input value (often the eigenvalue `lambda`). Returns: Tuple[int, int]: The components (v11, |v12|) of the first basis vector V1. */ pub fn half_gcd(modu: &BigInt, input_val: &BigInt) -> Result<[BigInt; 2], String> { let lattice = precompute_lattice(modu, input_val)?; let output0 = lattice.v1[0].clone(); let output1 = lattice.v1[1].clone(); // The GLV decomposition often requires the absolute value of the second component. Ok([output0, output1.abs()]) } /* Computes a short 2D lattice basis related to parameters (r, lambda). Uses a variant of the Extended Euclidean Algorithm to find short vectors (v1, v2) such that v1 = [a, b] and v2 = [c, d] satisfy a + b*lambda = 0 (mod r) and c + d*lambda = 0 (mod r). See https://www.iacr.org/archive/crypto2001/21390189.pdf (Algorithm 3.7) Args: r (int): The modulus. lam (int): The lambda value (e.g., eigenvalue in GLV). Returns: Lattice: An object containing the lattice basis vectors (V1, V2), determinant (Det), and rounding coefficients (b1, b2). Raises: ValueError: If intermediate steps lead to division by zero (e.g., lam=0 mod r) or if the final determinant is zero. */ fn precompute_lattice(r: &BigInt, lam: &BigInt) -> Result { // Extended Euclidean Algorithm State: [[value, s_coeff, t_coeff], ...] // We maintain two states [ri, si, ti] such that ri = si*r + ti*lambda let mut euclidean_state = [ [r.clone(), 1.into(), 0.into()], // Corresponds to r = 1*r + 0*lambda [lam.clone(), 0.into(), 1.into()], // Corresponds to lam = 0*r + 1*lambda ]; // Compute the integer square root of r as the termination threshold let sqrt_r = r.sqrt(); // Run Euclidean algorithm until the remainder (state[1][0]) is smaller than sqrt(r) while euclidean_state[1][0].abs() >= sqrt_r { let [current_rem, s_curr, t_curr] = euclidean_state[1].clone(); let [prev_rem, s_prev, t_prev] = euclidean_state[0].clone(); if current_rem == 0.into() { // This occurs if lambda is a multiple of r or lambda is 0. return Err("Division by zero in Euclidean algorithm. Check inputs r and lam.".into()); } let quotient = prev_rem.div_floor(¤t_rem); let next_rem = prev_rem.mod_floor(¤t_rem); // Update coefficients using the identity: R_next = R_prev - q * R_curr // where R represents [rem, s, t] let s_next = &s_prev - &s_curr * "ient; let t_next = &t_prev - &t_curr * "ient; // Shift states: current becomes previous, new becomes current euclidean_state[0] = [current_rem, s_curr, t_curr]; euclidean_state[1] = [next_rem, s_next, t_next]; } // One final step to potentially find a shorter vector combination let [current_rem, _s_curr, t_curr] = euclidean_state[1].clone(); let [prev_rem, _s_prev, t_prev] = euclidean_state[0].clone(); if current_rem == 0.into() { return Err( "Division by zero in Euclidean algorithm final step. Check inputs r and lam.".into(), ); } let quotient = prev_rem.div_floor(¤t_rem); // Calculate the next potential remainder and t-coefficient let final_rem = prev_rem.mod_floor(¤t_rem); let final_t = &t_prev - &t_curr * "ient; // First basis vector: V1 = [current_rem, -t_curr] // Satisfies current_rem + (-t_curr)*lambda = 0 mod r (since current_rem = s_curr*r + t_curr*lambda) let v1_list = [current_rem.clone(), -t_curr]; // Candidate vectors for the second basis vector V2 // Candidate 1: [prev_rem, -t_prev] let cand1 = [prev_rem.clone(), -t_prev]; // Candidate 2: [final_rem, -final_t] let cand2 = [final_rem.clone(), -final_t]; // Choose the shorter candidate vector based on squared Euclidean norm (||v||^2 = x^2 + y^2) let norm1_sq = cand1[0].pow(2) + cand1[1].pow(2); let norm2_sq = cand2[0].pow(2) + cand2[1].pow(2); let v2_list = if norm1_sq > norm2_sq { cand2 } else { cand1 }; // Calculate the determinant of the chosen basis {V1, V2} let det = &v1_list[0] * &v2_list[1] - &v1_list[1] * &v2_list[0]; if det == 0.into() { // Basis vectors are linearly dependent, which shouldn't happen for typical inputs. return Err("Lattice determinant is zero. Input parameters might be unsuitable.".into()); } /* Computes round(a / b), rounding ties away from zero. Equivalent to standard mathematical rounding, differs from Python's default round() which rounds ties to the nearest even number. Needed to potentially match specific Go implementation behavior. */ fn round_half_away_from_zero(a: &BigInt, b: &BigInt) -> Result { if *b == 0.into() { return Err("Division by zero in rounding.".into()); } // Perform division using absolute values let (mut quotient, remainder) = a.abs().div_rem(&b.abs()); // Check if the remainder is large enough to round up (away from zero) if remainder * 2 >= b.abs() { quotient += 1; } // Restore the sign based on the original signs of a and b if (*a < 0.into()) != (*b < 0.into()) { Ok(-quotient) // Result is negative } else { Ok(quotient) // Result is positive } } // Compute rounding coefficients b1, b2 used in scalar decomposition // n is calculated to ensure 2^n is sufficiently larger than |det|, // potentially matching Go's fixed-size integer/word alignment logic. // The `+ 32 >> 6 << 6` part aligns the bit length to a multiple of 64. let n_bit_length = std::cmp::max(&1.into(), &det).bits(); // Use max(1,...) for robustness if det=0 (though checked above) let n = 2 * (((n_bit_length + 32) >> 6) << 6); // Calculate b1 = round(2^n * V2[1] / det) let b1 = round_half_away_from_zero(&(&v2_list[1] << n), &det)?; // Calculate b2 = round(2^n * V1[1] / det) let b2 = round_half_away_from_zero(&(&v1_list[1] << n), &det)?; // Return the results structured in the Lattice dataclass Ok(Lattice { v1: v1_list, v2: v2_list, det, b1, b2, }) } /* Splits a scalar s into components (u, v) using a precomputed GLV lattice. Based on the approach described in https://www.iacr.org/archive/crypto2001/21390189.pdf, this function finds a vector (u, v) such that s = u + v*lambda (mod r), where lambda and r are the parameters used to generate the lattice l. The vector (u, v) is typically chosen such that u and v have smaller magnitudes than s. Args: s: The scalar to split. l: The precomputed Lattice object containing basis V1, V2, determinant Det, and rounding coefficients b1, b2. Returns: A tuple (u, v) representing the scalar decomposition. */ fn split_scalar(s: &BigInt, l: &Lattice) -> [BigInt; 2] { // Calculate intermediate values k1, k2 using the scalar and rounding coefficients let mut k1 = s * &l.b1; let mut k2 = -(s * &l.b2); // Determine the shift amount 'n' used during lattice precomputation // This should match the logic in precompute_lattice let n_bit_length = std::cmp::max(1.into(), l.det.clone()).bits(); let n = 2 * (((n_bit_length + 32) >> 6) << 6); // Right-shift k1 and k2 to effectively divide by 2^n, // approximating division by the determinant Det. // This gives the integer coefficients for the closest lattice vector approximation. k1 >>= n; k2 >>= n; // Calculate the lattice vector w = k1*V1 + k2*V2 let w_vec0 = &k1 * &l.v1[0] + &k2 * &l.v2[0]; let w_vec1 = &k1 * &l.v1[1] + &k2 * &l.v2[1]; // Calculate the final decomposition (u, v) // u = s - w[0] // v = -w[1] let u = s - &w_vec0; let v = -w_vec1; [u, v] } pub fn half_gcd_eisenstein_hint( modulus: &BigInt, scalar: &BigInt, eigen_value: &BigInt, ) -> Result<[BigInt; 4], String> { let glv_basis = precompute_lattice(modulus, eigen_value)?; let r = eisenstein::EisensteinInteger::new(glv_basis.v1[0].clone(), glv_basis.v1[1].clone()); let scalar = if scalar % modulus == modulus - 1 { BigInt::from(1) } else { scalar.clone() }; let sp = split_scalar(&scalar, &glv_basis); let s = eisenstein::EisensteinInteger::new(sp[0].clone(), sp[1].clone()); // in-circuit we check that Q - [s]P = 0 or equivalently Q + [-s]P = 0 // so here we return -s instead of s. let s = -s; // println!("r: {}, \ns: {}", r, s); let [w, v_res, _] = eisenstein::half_gcd(&r, &s)?; // Note : outputs can be negative. Ok([ w.a0.clone(), w.a1.clone(), v_res.a0.clone(), v_res.a1.clone(), ]) } fn encode_value(value: &BigInt) -> BigUint { // Corresponds to Python: abs(value) + 2**128 if value < 0 else value let power_128_bigint: BigInt = BigInt::from(1) << 128; let power_128_biguint = power_128_bigint.to_biguint().unwrap(); // Safe because 2^128 > 0 if value.sign() == Sign::Minus { // Convert `value.abs()` (BigInt) to BigUint before adding power_128 (BigUint) value.abs().to_biguint().unwrap() + power_128_biguint } else { // value is non-negative, safe to convert to BigUint value.to_biguint().unwrap() } } fn encode_glv_fake_glv_hint(u1: &BigInt, u2: &BigInt, v1: &BigInt, v2: &BigInt) -> [BigUint; 4] { // Re-use the standalone encode_value function [ encode_value(u1), encode_value(u2), encode_value(v1), encode_value(v2), ] } /// Corresponds to Python `get_glv_fake_glv_hint`. /// Computes the GLV hint components (u1, u2, v1, v2) encoded for Cairo, and the scalar multiplication result Q. pub fn get_glv_fake_glv_hint( point: &G1Point, scalar: &BigUint, ) -> Result<(G1Point, BigUint, BigUint, BigUint, BigUint), String> where F: IsPrimeField + CurveParamsProvider, { let curve_params = F::get_curve_params(); let curve_n_bigint = curve_params.n.to_bigint().unwrap(); let scalar_bigint = scalar.to_bigint().unwrap(); // Get eigen_value from curve_params let eigen_value = match &curve_params.eigen_value { Some(ev) => ev, None => { return Err(format!( "Curve {:?} does not have a known endomorphism eigenvalue or is not supported here.", curve_params.curve_id )); } }; // Call half_gcd_eisenstein_hint to get raw u1, u2, v1, v2 let hint_result = half_gcd_eisenstein_hint(&curve_n_bigint, &scalar_bigint, eigen_value)?; let [u1_raw, u2_raw, v1_raw, v2_raw] = hint_result; // Encode the results for Cairo compatibility let encoded_hints = encode_glv_fake_glv_hint(&u1_raw, &u2_raw, &v1_raw, &v2_raw); let [u1_encoded, u2_encoded, v1_encoded, v2_encoded] = encoded_hints; // Compute Q = [scalar]P let q = point.scalar_mul(scalar_bigint.clone()); // Assumes G1Point::scalar_mul takes BigInt Ok((q, u1_encoded, u2_encoded, v1_encoded, v2_encoded)) } pub fn get_fake_glv_hint( point: &G1Point, scalar: &BigUint, ) -> Result<(G1Point, BigUint, BigUint), String> where F: IsPrimeField + CurveParamsProvider, { let curve_params = F::get_curve_params(); let curve_n_bigint = curve_params.n.to_bigint().unwrap(); let scalar_bigint = scalar.to_bigint().unwrap(); // Check if the curve has an endomorphism; if so, this hint shouldn't be used. if curve_params.eigen_value.is_some() { return Err(format!( "Curve {:?} has an endomorphism, use get_glv_fake_glv_hint instead", curve_params.curve_id )); } // Call precompute_lattice using the scalar as the 'lambda' parameter, // mimicking the Python implementation. let glv_basis = precompute_lattice(&curve_n_bigint, &scalar_bigint)?; let s1 = &glv_basis.v1[0]; let s2 = &glv_basis.v1[1]; // Assertions from Python code converted to Rust checks if (s1 + &scalar_bigint * s2).mod_floor(&curve_n_bigint) != BigInt::from(0) { return Err("Assertion failed: (s1 + scalar * s2) % curve.n != 0".to_string()); } // Check s1 > 0 and s2 != 0 if !(s1.sign() == Sign::Plus && s2.sign() != Sign::NoSign) { return Err("Assertion failed: !(s1 > 0 and s2 != 0)".to_string()); } // Compute Q = [scalar]P let q = point.scalar_mul(scalar_bigint.clone()); // Convert s1 (known positive) to BigUint let s1_biguint = s1.to_biguint().unwrap(); // Encode s2 let s2_encoded = encode_value(s2); Ok((q, s1_biguint, s2_encoded)) } #[allow(unused_imports)] mod tests { use super::*; use num_traits::Num; use rand::Rng; use std::str::FromStr; #[test] fn test_bn254() -> Result<(), String> { let mut rng = rand::rng(); for _ in 0..100 { let scalar = rng.random::().into(); let curve_n = BigInt::from_str_radix( "30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000001", 16, ) .unwrap(); let eigen_value = BigInt::from_str_radix("B3C4D79D41A917585BFC41088D8DAAA78B17EA66B99C90DD", 16) .unwrap(); let [u1, u2, v1, v2] = half_gcd_eisenstein_hint(&curve_n, &scalar, &eigen_value)?; assert!( (&scalar * (&v1 + &eigen_value * &v2) + &u1 + &eigen_value * &u2) .mod_floor(&curve_n) == 0.into() ); } Ok(()) } #[test] fn test_bls12_381() -> Result<(), String> { use rand::Rng; let mut rng = rand::rng(); for _ in 0..100 { let scalar = rng.random::().into(); let curve_n = BigInt::from_str_radix( "73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001", 16, ) .unwrap(); let eigen_value = BigInt::from_str_radix("AC45A4010001A40200000000FFFFFFFF", 16).unwrap(); let [u1, u2, v1, v2] = half_gcd_eisenstein_hint(&curve_n, &scalar, &eigen_value)?; assert!( (&scalar * (&v1 + &eigen_value * &v2) + &u1 + &eigen_value * &u2) .mod_floor(&curve_n) == 0.into() ); } Ok(()) } #[test] fn test_secp256k1() -> Result<(), String> { use rand::Rng; let mut rng = rand::rng(); for _ in 0..100 { let scalar = rng.random::().into(); let curve_n = BigInt::from_str_radix( "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16, ) .unwrap(); let eigen_value = BigInt::from_str_radix( "5363AD4CC05C30E0A5261C028812645A122E22EA20816678DF02967C1B23BD72", 16, ) .unwrap(); let [u1, u2, v1, v2] = half_gcd_eisenstein_hint(&curve_n, &scalar, &eigen_value)?; assert!( (&scalar * (&v1 + &eigen_value * &v2) + &u1 + &eigen_value * &u2) .mod_floor(&curve_n) == 0.into() ); } Ok(()) } } ================================================ FILE: tools/garaga_rs/src/io.rs ================================================ use crate::algebra::{ g1g2pair::G1G2Pair, g1point::G1Point, g2point::G2Point, rational_function::FunctionFelt, }; use crate::definitions::{CurveParamsProvider, FieldElement, Stark252PrimeField}; use lambdaworks_math::{ field::traits::{IsField, IsPrimeField, IsSubFieldOf}, traits::ByteConversion, }; use num_bigint::BigUint; use lambdaworks_math::unsigned_integer::element::U256; pub fn biguint_to_u256(x: &BigUint) -> U256 { U256::from_hex_unchecked(&x.to_str_radix(16)) } pub fn parse_g1_points_from_flattened_field_elements_list( values: &[FieldElement], ) -> Result>, String> where F: IsPrimeField + CurveParamsProvider, { values .chunks(2) .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone(), false)) .collect::, _>>() } pub fn parse_g1_g2_pairs_from_flattened_field_elements_list( values: &[FieldElement], ) -> Result>, String> where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { values .chunks(6) .map(|chunk| { let g1 = G1Point::new(chunk[0].clone(), chunk[1].clone(), false)?; let g2 = G2Point::new( [chunk[2].clone(), chunk[3].clone()], [chunk[4].clone(), chunk[5].clone()], )?; Ok(G1G2Pair::new(g1, g2)) }) .collect::, _>>() } pub fn field_elements_from_big_uints(values: &[BigUint]) -> Vec> where F: IsPrimeField, FieldElement: ByteConversion, { values.iter().map(element_from_biguint).collect() } pub fn element_from_biguint(value: &BigUint) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { element_from_bytes_be(&value.to_bytes_be()) } pub fn element_from_bytes_be(bytes: &[u8]) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { let length = F::field_bit_size().div_ceil(8); if bytes.len() > length { let x = BigUint::from_bytes_be(bytes); let p = biguint_from_hex(&F::modulus_minus_one().to_string()) + 1usize; return element_from_bytes_be(&(x % p).to_bytes_be()); } let pad_length = length - bytes.len(); let mut padded_bytes = vec![0u8; pad_length]; padded_bytes.extend(bytes); FieldElement::from_bytes_be(&padded_bytes).unwrap() // must never fail } pub fn field_elements_to_big_uints(values: &[FieldElement]) -> Vec where F: IsPrimeField, FieldElement: ByteConversion, { values.iter().map(element_to_biguint).collect() } pub fn element_to_biguint(x: &FieldElement) -> BigUint where F: IsPrimeField, FieldElement: ByteConversion, { BigUint::from_bytes_be(&x.to_bytes_be()) } pub fn felt252_to_element(x: &FieldElement) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { element_from_bytes_be(&x.to_bytes_be()) } pub fn padd_function_felt( f: &FunctionFelt, n: usize, batched: bool, ) -> [Vec>; 4] { fn pad_vec(v: &mut Vec>, n: usize) { assert!(v.len() <= n); while v.len() < n { v.push((0u64).into()); } } let mut a_num = f.a.numerator.coefficients.clone(); let mut a_den = f.a.denominator.coefficients.clone(); let mut b_num = f.b.numerator.coefficients.clone(); let mut b_den = f.b.denominator.coefficients.clone(); let extra_padding = if batched { 2 } else { 0 }; pad_vec(&mut a_num, n + 1 + extra_padding); pad_vec(&mut a_den, n + 2 + extra_padding); pad_vec(&mut b_num, n + 2 + extra_padding); pad_vec(&mut b_den, n + 5 + extra_padding); [a_num, a_den, b_num, b_den] } pub fn u128_from_bytes_be(bytes: &[u8]) -> u128 { assert!(bytes.len() <= 16); let mut v = 0; for byte in bytes { v = (v << 8) | (*byte as u128); } v } pub fn u128_to_bytes_be(v: u128) -> Vec { let mut bytes = vec![]; let mut v = v; while v > 0 { bytes.push(v as u8); v >>= 8; } bytes.reverse(); bytes } pub fn element_from_u128(value: u128) -> FieldElement where F: IsPrimeField, FieldElement: ByteConversion, { element_from_bytes_be(&u128_to_bytes_be(value)) } pub fn field_element_to_u256_limbs(x: &FieldElement) -> [u128; 2] where F: IsPrimeField, FieldElement: ByteConversion, { byte_slice_split::<2, 128>(&x.to_bytes_be()) } pub fn field_element_to_u288_limbs(x: &FieldElement) -> [u128; 3] where F: IsPrimeField, FieldElement: ByteConversion, { byte_slice_split::<3, 96>(&x.to_bytes_be()) } pub fn field_element_to_u384_limbs(x: &FieldElement) -> [u128; 4] where F: IsPrimeField, FieldElement: ByteConversion, { byte_slice_split::<4, 96>(&x.to_bytes_be()) } pub fn scalar_to_limbs(x: &BigUint) -> [u128; 2] { byte_slice_split::<2, 128>(&x.to_bytes_be()) } pub fn biguint_split(x: &BigUint) -> [u128; N] { byte_slice_split::(&x.to_bytes_be()) } pub fn byte_slice_split(bytes: &[u8]) -> [u128; N] { assert!(SIZE <= 128 && SIZE.is_multiple_of(8)); assert!(bytes.len() <= N * SIZE / 8); let mut bytes = bytes; let mut limbs = [0u128; N]; for limb in limbs.iter_mut().take(N) { let index = bytes.len().saturating_sub(SIZE / 8); let slice = &bytes[index..]; *limb = u128_from_bytes_be(slice); bytes = &bytes[..index]; } limbs } pub fn biguint_from_hex(hex: &str) -> BigUint { let mut s = hex; if let Some(stripped) = s.strip_prefix("0x") { s = stripped; } BigUint::parse_bytes(s.as_bytes(), 16).unwrap_or_else(|| panic!("invalid hex string: {}", hex)) } #[cfg(test)] mod tests { use super::{biguint_from_hex, element_from_biguint, FieldElement}; use crate::definitions::{ BLS12381PrimeField, BN254PrimeField, SECP256K1PrimeField, SECP256R1PrimeField, Stark252PrimeField, X25519PrimeField, }; #[test] fn test_element_from_hex() { let s = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"; let x = biguint_from_hex(s); { let s = "6D89F71CAB8351F47AB1EFF0A417FF6B5E71911D44501FBF32CFC5B538AFA88"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } { let s = "2CB5D3A884E56C4FAB7CD07EE4E16BC15EFEBB5D396D7CF82383087033108464532383FA8EAFF4E967D3988A62B6C9C"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } { let s = "1000007A2000E90A0"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } { let s = "4FFFFFFFDFFFFFFFFFFFFFFFEFFFFFFFBFFFFFFFF0000000000000002"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } { let s = "5A3"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } { let s = "7FFD4AB5E008810FFFFFFFFFF6F800000000001330FFFFFFFFFFD737E000400"; let one = element_from_biguint::(&x); assert_eq!(one, FieldElement::from_hex(s).unwrap()); } } } ================================================ FILE: tools/garaga_rs/src/lib.rs ================================================ pub mod algebra { pub mod extf_mul; pub mod g1g2pair; pub mod g1point; pub mod g2point; pub mod polynomial; pub mod rational_function; } pub mod calldata; pub mod constants; pub mod crypto { pub mod mmr { pub mod mmr_accumulator; pub mod mmr_membership_proof; pub mod mmr_successor_proof; pub mod mmr_trait; pub mod shared_advanced; pub mod shared_basic; pub const TOO_MANY_LEAFS_ERR: &str = "internal error: Merkle Mountain Ranges should have at most 2^63 leafs"; } pub mod digest; pub mod merkle_tree; #[allow(dead_code)] pub mod poseidon_bn254; } pub mod definitions; pub mod ecip { pub mod core; pub mod ff; } pub mod frobenius; pub mod io; pub mod pairing { pub mod final_exp_witness; pub mod multi_miller_loop; pub mod multi_pairing_check; } pub mod poseidon_transcript; pub mod hints { pub mod eisenstein; pub mod fake_glv; } // automatically excludes python bindings on wasm32-unknown-unknown (pyo3 not supported) #[cfg(all(feature = "python", not(target_arch = "wasm32")))] pub mod python_bindings; // only include wasm bindings when both wasm feature is enabled AND on wasm32 target #[cfg(all(feature = "wasm", target_arch = "wasm32"))] pub mod wasm_bindings; ================================================ FILE: tools/garaga_rs/src/pairing/final_exp_witness/addchain_pow_generated.rs ================================================ // AUTO-GENERATED: DO NOT EDIT BY HAND. // Generated by tools/addchain/gen_rust_addchain.py from: // - tools/addchain/bn254_exp.acc // - tools/addchain/bn254_exp0.acc // - tools/addchain/bn254_r_m_d_inv.acc // - tools/addchain/bls12_381_h3_s.acc // - tools/addchain/bls12_381_e.acc use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::IsField; fn square_n(x: &FieldElement, n: usize) -> FieldElement { let mut t = x.clone(); for _ in 0..n { t = t.square(); } t } pub mod bn254 { use super::square_n; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::field::element::FieldElement; /// Generated from tools/addchain/bn254_exp.acc pub fn pow_exp( base: &FieldElement, ) -> FieldElement { let base = base.clone(); let _10 = { let t0 = square_n(&base, 1); t0 }; let _11 = { let t0 = &base * &_10; t0 }; let _101 = { let t0 = &_10 * &_11; t0 }; let _111 = { let t0 = &_10 * &_101; t0 }; let _1001 = { let t0 = &_10 * &_111; t0 }; let _1011 = { let t0 = &_10 * &_1001; t0 }; let _1101 = { let t0 = &_10 * &_1011; t0 }; let _1111 = { let t0 = &_10 * &_1101; t0 }; let _10001 = { let t0 = &_10 * &_1111; t0 }; let _10011 = { let t0 = &_10 * &_10001; t0 }; let _10101 = { let t0 = &_10 * &_10011; t0 }; let _10111 = { let t0 = &_10 * &_10101; t0 }; let _11001 = { let t0 = &_10 * &_10111; t0 }; let _11011 = { let t0 = &_10 * &_11001; t0 }; let _11101 = { let t0 = &_10 * &_11011; t0 }; let _11111 = { let t0 = &_10 * &_11101; t0 }; let _100001 = { let t0 = &_10 * &_11111; t0 }; let _100011 = { let t0 = &_10 * &_100001; t0 }; let _100101 = { let t0 = &_10 * &_100011; t0 }; let _100111 = { let t0 = &_10 * &_100101; t0 }; let _101001 = { let t0 = &_10 * &_100111; t0 }; let _101011 = { let t0 = &_10 * &_101001; t0 }; let _101101 = { let t0 = &_10 * &_101011; t0 }; let _101111 = { let t0 = &_10 * &_101101; t0 }; let _110001 = { let t0 = &_10 * &_101111; t0 }; let _110011 = { let t0 = &_10 * &_110001; t0 }; let _110101 = { let t0 = &_10 * &_110011; t0 }; let _110111 = { let t0 = &_10 * &_110101; t0 }; let _111001 = { let t0 = &_10 * &_110111; t0 }; let _111011 = { let t0 = &_10 * &_111001; t0 }; let _111101 = { let t0 = &_10 * &_111011; t0 }; let _111111 = { let t0 = &_10 * &_111101; t0 }; let _1000001 = { let t0 = &_10 * &_111111; t0 }; let _1000011 = { let t0 = &_10 * &_1000001; t0 }; let _1000101 = { let t0 = &_10 * &_1000011; t0 }; let _1000111 = { let t0 = &_10 * &_1000101; t0 }; let _1001001 = { let t0 = &_10 * &_1000111; t0 }; let _1001011 = { let t0 = &_10 * &_1001001; t0 }; let _1001101 = { let t0 = &_10 * &_1001011; t0 }; let _1001111 = { let t0 = &_10 * &_1001101; t0 }; let _1010001 = { let t0 = &_10 * &_1001111; t0 }; let _1010011 = { let t0 = &_10 * &_1010001; t0 }; let _1010101 = { let t0 = &_10 * &_1010011; t0 }; let _1010111 = { let t0 = &_10 * &_1010101; t0 }; let _1011001 = { let t0 = &_10 * &_1010111; t0 }; let _1011011 = { let t0 = &_10 * &_1011001; t0 }; let _1011101 = { let t0 = &_10 * &_1011011; t0 }; let _1011111 = { let t0 = &_10 * &_1011101; t0 }; let _1100001 = { let t0 = &_10 * &_1011111; t0 }; let _1100011 = { let t0 = &_10 * &_1100001; t0 }; let _1100101 = { let t0 = &_10 * &_1100011; t0 }; let _1100111 = { let t0 = &_10 * &_1100101; t0 }; let _1101001 = { let t0 = &_10 * &_1100111; t0 }; let _1101011 = { let t0 = &_10 * &_1101001; t0 }; let _1101101 = { let t0 = &_10 * &_1101011; t0 }; let _1101111 = { let t0 = &_10 * &_1101101; t0 }; let _1110001 = { let t0 = &_10 * &_1101111; t0 }; let _1110011 = { let t0 = &_10 * &_1110001; t0 }; let _1110101 = { let t0 = &_10 * &_1110011; t0 }; let _1110111 = { let t0 = &_10 * &_1110101; t0 }; let _1111001 = { let t0 = &_10 * &_1110111; t0 }; let _1111011 = { let t0 = &_10 * &_1111001; t0 }; let _1111101 = { let t0 = &_10 * &_1111011; t0 }; let _1111111 = { let t0 = &_10 * &_1111101; t0 }; let _11111110 = { let t0 = square_n(&_1111111, 1); t0 }; let _11111111 = { let t0 = &base * &_11111110; t0 }; let i81 = { let t0 = &_1111101 * &_11111111; let t1 = square_n(&t0, 4); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_100001; t4 }; let i105 = { let t0 = square_n(&i81, 7); let t1 = &t0 * &_111001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1001011; let t4 = square_n(&t3, 6); t4 }; let i125 = { let t0 = &_100111 * &i105; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_101001; t4 }; let i150 = { let t0 = square_n(&i125, 8); let t1 = &t0 * &_1110101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 8); t4 }; let i168 = { let t0 = &_1001011 * &i150; let t1 = square_n(&t0, 6); let t2 = &t1 * &_101001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1011001; t4 }; let i192 = { let t0 = square_n(&i168, 6); let t1 = &t0 * &_11001; let t2 = square_n(&t1, 4); let t3 = &t2 * &base; let t4 = square_n(&t3, 12); t4 }; let i209 = { let t0 = &_110111 * &i192; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10101; t4 }; let i236 = { let t0 = square_n(&i209, 9); let t1 = &t0 * &_1110001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1011111; let t4 = square_n(&t3, 7); t4 }; let i256 = { let t0 = &_1101 * &i236; let t1 = square_n(&t0, 9); let t2 = &t1 * &_110101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1000101; t4 }; let i281 = { let t0 = square_n(&i256, 6); let t1 = &t0 * &_101101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 6); t4 }; let i307 = { let t0 = &_11111 * &i281; let t1 = square_n(&t0, 17); let t2 = &t1 * &_1010111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110011; t4 }; let i337 = { let t0 = square_n(&i307, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11111111; let t4 = square_n(&t3, 10); t4 }; let i356 = { let t0 = &_10101 * &i337; let t1 = square_n(&t0, 7); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1110011; t4 }; let i384 = { let t0 = square_n(&i356, 10); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 8); t4 }; let i399 = { let t0 = &_1100111 * &i384; let t1 = square_n(&t0, 6); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_10011; t4 }; let i427 = { let t0 = square_n(&i399, 8); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11111; let t4 = square_n(&t3, 9); t4 }; let i437 = { let t0 = &_11111111 * &i427; let t1 = square_n(&t0, 1); let t2 = &t1 * &base; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111; t4 }; let i466 = { let t0 = square_n(&i437, 11); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 10); t4 }; let i484 = { let t0 = &_1100111 * &i466; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100111; t4 }; let i510 = { let t0 = square_n(&i484, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 9); t4 }; let i527 = { let t0 = &_1111011 * &i510; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101111; t4 }; let i557 = { let t0 = square_n(&i527, 5); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 13); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 10); t4 }; let i577 = { let t0 = &_1110011 * &i557; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000011; t4 }; let i598 = { let t0 = square_n(&i577, 7); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11111; let t4 = square_n(&t3, 6); t4 }; let i613 = { let t0 = &_1001 * &i598; let t1 = square_n(&t0, 10); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 2); let t4 = &t3 * &base; t4 }; let i644 = { let t0 = square_n(&i613, 9); let t1 = &t0 * &_11111111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 11); t4 }; let i661 = { let t0 = &_1100011 * &i644; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110011; t4 }; let i684 = { let t0 = square_n(&i661, 7); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 7); t4 }; let i700 = { let t0 = &_1001111 * &i684; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 4); let t4 = &t3 * &_11; t4 }; let i727 = { let t0 = square_n(&i700, 12); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 3); let t3 = &t2 * &_101; let t4 = square_n(&t3, 10); t4 }; let i746 = { let t0 = &_1101 * &i727; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1001011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110001; t4 }; let i772 = { let t0 = square_n(&i746, 8); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 8); t4 }; let i790 = { let t0 = &_1001011 * &i772; let t1 = square_n(&t0, 1); let t2 = &t1 * &base; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1101011; t4 }; let i815 = { let t0 = square_n(&i790, 8); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 10); t4 }; let i834 = { let t0 = &_1000101 * &i815; let t1 = square_n(&t0, 6); let t2 = &t1 * &_11101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_100111; t4 }; let i856 = { let t0 = square_n(&i834, 5); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 5); t4 }; let i876 = { let t0 = &_1011 * &i856; let t1 = square_n(&t0, 9); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010011; t4 }; let i900 = { let t0 = square_n(&i876, 7); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 8); t4 }; let i925 = { let t0 = &_1101101 * &i900; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1111101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1010101; t4 }; let i953 = { let t0 = square_n(&i925, 7); let t1 = &t0 * &_1001111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 10); t4 }; let i971 = { let t0 = &_1111011 * &i953; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011011; t4 }; let i996 = { let t0 = square_n(&i971, 8); let t1 = &t0 * &_1011111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101001; let t4 = square_n(&t3, 8); t4 }; let i1012 = { let t0 = &_110001 * &i996; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10011; t4 }; let i1037 = { let t0 = square_n(&i1012, 9); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 8); t4 }; let i1055 = { let t0 = &_1101111 * &i1037; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101001; t4 }; let i1081 = { let t0 = square_n(&i1055, 10); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 7); t4 }; let i1098 = { let t0 = &_1111101 * &i1081; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100111; t4 }; let i1125 = { let t0 = square_n(&i1098, 7); let t1 = &t0 * &_11111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 10); t4 }; let i1144 = { let t0 = &_101111 * &i1125; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1111101; t4 }; let i1169 = { let t0 = square_n(&i1144, 5); let t1 = &t0 * &_10001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 6); t4 }; let i1189 = { let t0 = &_11011 * &i1169; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1110101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1010111; t4 }; let i1217 = { let t0 = square_n(&i1189, 7); let t1 = &t0 * &_111101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 7); t4 }; let i1236 = { let t0 = &_101111 * &i1217; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001011; t4 }; let i1267 = { let t0 = square_n(&i1236, 12); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 7); t4 }; let i1287 = { let t0 = &_100111 * &i1267; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001001; t4 }; let i1309 = { let t0 = square_n(&i1287, 7); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 6); t4 }; let i1329 = { let t0 = &_10001 * &i1309; let t1 = square_n(&t0, 8); let t2 = &t1 * &_111011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1010001; t4 }; let i1351 = { let t0 = square_n(&i1329, 7); let t1 = &t0 * &_1100011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001101; let t4 = square_n(&t3, 5); t4 }; let i1374 = { let t0 = &_10111 * &i1351; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011001; t4 }; let i1398 = { let t0 = square_n(&i1374, 7); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101001; let t4 = square_n(&t3, 8); t4 }; let i1417 = { let t0 = &_110011 * &i1398; let t1 = square_n(&t0, 6); let t2 = &t1 * &_1011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001011; t4 }; let i1444 = { let t0 = square_n(&i1417, 8); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_101; let t4 = square_n(&t3, 13); t4 }; let i1463 = { let t0 = &_1100101 * &i1444; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100111; t4 }; let i1491 = { let t0 = square_n(&i1463, 8); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1001011; let t4 = square_n(&t3, 8); t4 }; let i1509 = { let t0 = &_1000011 * &i1491; let t1 = square_n(&t0, 9); let t2 = &t1 * &_110101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_10111; t4 }; let i1539 = { let t0 = square_n(&i1509, 9); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 10); t4 }; let i1558 = { let t0 = &_101011 * &i1539; let t1 = square_n(&t0, 2); let t2 = &t1 * &base; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1111101; t4 }; let i1585 = { let t0 = square_n(&i1558, 7); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 8); t4 }; let i1610 = { let t0 = &_1110001 * &i1585; let t1 = square_n(&t0, 15); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101001; t4 }; let i1637 = { let t0 = square_n(&i1610, 6); let t1 = &t0 * &_11001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 10); t4 }; let i1654 = { let t0 = &_1001111 * &i1637; let t1 = square_n(&t0, 1); let t2 = &t1 * &base; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1011001; t4 }; let i1678 = { let t0 = square_n(&i1654, 4); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_111011; let t4 = square_n(&t3, 9); t4 }; let i1695 = { let t0 = &_1011011 * &i1678; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101; t4 }; let i1725 = { let t0 = square_n(&i1695, 10); let t1 = &t0 * &_1101011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 11); t4 }; let i1746 = { let t0 = &_1111001 * &i1725; let t1 = square_n(&t0, 6); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1111111; t4 }; let i1769 = { let t0 = square_n(&i1746, 8); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 6); t4 }; let i1788 = { let t0 = &_110101 * &i1769; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_110111; t4 }; let i1812 = { let t0 = square_n(&i1788, 10); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 6); t4 }; let i1834 = { let t0 = &_11111 * &i1812; let t1 = square_n(&t0, 8); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1111001; t4 }; let i1863 = { let t0 = square_n(&i1834, 9); let t1 = &t0 * &_10111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 8); t4 }; let i1880 = { let t0 = &_1011001 * &i1863; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1000001; t4 }; let i1907 = { let t0 = square_n(&i1880, 2); let t1 = &t0 * &_11; let t2 = square_n(&t1, 16); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 7); t4 }; let i1923 = { let t0 = &_1001001 * &i1907; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1100111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110111; t4 }; let i1950 = { let t0 = square_n(&i1923, 8); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1100111; let t4 = square_n(&t3, 7); t4 }; let i1971 = { let t0 = &_11011 * &i1950; let t1 = square_n(&t0, 6); let t2 = &t1 * &_111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_101101; t4 }; let i1994 = { let t0 = square_n(&i1971, 8); let t1 = &t0 * &_1001001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101111; let t4 = square_n(&t3, 6); t4 }; let i2016 = { let t0 = &_110011 * &i1994; let t1 = square_n(&t0, 10); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1101001; t4 }; let i2041 = { let t0 = square_n(&i2016, 7); let t1 = &t0 * &_1110101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 10); t4 }; let i2060 = { let t0 = &_1100001 * &i2041; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_110101; t4 }; let i2085 = { let t0 = square_n(&i2060, 5); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1100111; let t4 = square_n(&t3, 7); t4 }; let i2103 = { let t0 = &_1010011 * &i2085; let t1 = square_n(&t0, 6); let t2 = &t1 * &_100001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1000111; t4 }; let i2129 = { let t0 = square_n(&i2103, 5); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 10); t4 }; let i2146 = { let t0 = &_1001011 * &i2129; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101111; t4 }; let i2167 = { let t0 = square_n(&i2146, 6); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 4); t4 }; let i2195 = { let t0 = &base * &i2167; let t1 = square_n(&t0, 16); let t2 = &t1 * &_101111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100011; t4 }; let i2220 = { let t0 = square_n(&i2195, 7); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_111111; let t4 = square_n(&t3, 8); t4 }; let i2238 = { let t0 = &_1011101 * &i2220; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1100011; t4 }; let i2264 = { let t0 = square_n(&i2238, 7); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001001; let t4 = square_n(&t3, 9); t4 }; let i2283 = { let t0 = &_10011 * &i2264; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1110111; t4 }; let i2308 = { let t0 = square_n(&i2283, 7); let t1 = &t0 * &_1110101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101111; let t4 = square_n(&t3, 9); t4 }; let i2327 = { let t0 = &_10001 * &i2308; let t1 = square_n(&t0, 8); let t2 = &t1 * &_100111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001011; t4 }; let i2351 = { let t0 = square_n(&i2327, 5); let t1 = &t0 * &_10101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 8); t4 }; let i2371 = { let t0 = &_1010011 * &i2351; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1010011; t4 }; let i2402 = { let t0 = square_n(&i2371, 13); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 7); t4 }; let i2420 = { let t0 = &_1111101 * &i2402; let t1 = square_n(&t0, 7); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001001; t4 }; let i2446 = { let t0 = square_n(&i2420, 7); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 1); let t3 = &t2 * &base; let t4 = square_n(&t3, 16); t4 }; let i2465 = { let t0 = &_111011 * &i2446; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1111011; t4 }; let i2492 = { let t0 = square_n(&i2465, 8); let t1 = &t0 * &_1011111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_111001; let t4 = square_n(&t3, 9); t4 }; let i2511 = { let t0 = &_100001 * &i2492; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010011; t4 }; let i2542 = { let t0 = square_n(&i2511, 9); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 11); t4 }; let i2562 = { let t0 = &_10111 * &i2542; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010111; t4 }; let i2585 = { let t0 = square_n(&i2562, 6); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 7); t4 }; let i2607 = { let t0 = &_1100101 * &i2585; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1000011; t4 }; let i2635 = { let t0 = square_n(&i2607, 6); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 9); t4 }; let i2656 = { let t0 = &_110111 * &i2635; let t1 = square_n(&t0, 6); let t2 = &t1 * &_1111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1000011; t4 }; let i2679 = { let t0 = square_n(&i2656, 7); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10111; let t4 = square_n(&t3, 9); t4 }; let i2691 = { let t0 = &_101001 * &i2679; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 1); let t4 = &t3 * &base; t4 }; let i2720 = { let t0 = square_n(&i2691, 14); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 7); t4 }; let i2740 = { let t0 = &_110101 * &i2720; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111011; t4 }; let i2770 = { let t0 = square_n(&i2740, 9); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1000101; let t4 = square_n(&t3, 7); t4 }; let i2788 = { let t0 = &_101101 * &i2770; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1001001; t4 }; let i2811 = { let t0 = square_n(&i2788, 4); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 7); t4 }; let i2829 = { let t0 = &_1011001 * &i2811; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101011; t4 }; let i2853 = { let t0 = square_n(&i2829, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 7); t4 }; let i2866 = { let t0 = &_11111 * &i2853; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 1); let t4 = &t3 * &base; t4 }; let i2896 = { let t0 = square_n(&i2866, 12); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 8); t4 }; let i2915 = { let t0 = &_1000101 * &i2896; let t1 = square_n(&t0, 7); let t2 = &t1 * &_11101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1111101; t4 }; let i2941 = { let t0 = square_n(&i2915, 9); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i2957 = { let t0 = &_1110001 * &i2941; let t1 = square_n(&t0, 6); let t2 = &t1 * &_111101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10111; t4 }; let i2984 = { let t0 = square_n(&i2957, 9); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 8); t4 }; let i3001 = { let t0 = &_1001101 * &i2984; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001111; t4 }; let i3025 = { let t0 = square_n(&i3001, 8); let t1 = &t0 * &_1001001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 8); t4 }; let i3040 = { let t0 = &_1110011 * &i3025; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10101; t4 }; let i3065 = { let t0 = square_n(&i3040, 9); let t1 = &t0 * &_1111001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101001; let t4 = square_n(&t3, 7); t4 }; let i3085 = { let t0 = &_1111011 * &i3065; let t1 = square_n(&t0, 8); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1000001; t4 }; let i3110 = { let t0 = square_n(&i3085, 8); let t1 = &t0 * &_111001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011101; let t4 = square_n(&t3, 7); t4 }; let i3126 = { let t0 = &_1111011 * &i3110; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_110111; t4 }; let i3150 = { let t0 = square_n(&i3126, 8); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 8); t4 }; let i3168 = { let t0 = &_1101011 * &i3150; let t1 = square_n(&t0, 2); let t2 = &t1 * &_11; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1110011; t4 }; let i3191 = { let t0 = square_n(&i3168, 7); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i3207 = { let t0 = &_1111101 * &i3191; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1010011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110011; t4 }; let i3232 = { let t0 = square_n(&i3207, 8); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1011; let t4 = square_n(&t3, 10); t4 }; let i3251 = { let t0 = &_1110101 * &i3232; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110001; t4 }; let i3282 = { let t0 = square_n(&i3251, 12); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 8); t4 }; let i3299 = { let t0 = &_1001011 * &i3282; let t1 = square_n(&t0, 6); let t2 = &t1 * &_100111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100011; t4 }; let i3324 = { let t0 = square_n(&i3299, 7); let t1 = &t0 * &_1011111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 9); t4 }; let i3341 = { let t0 = &_10001 * &i3324; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1101001; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1111; t4 }; let i3372 = { let t0 = square_n(&i3341, 12); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000001; let t4 = square_n(&t3, 9); t4 }; let i3391 = { let t0 = &_1100111 * &i3372; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000001; t4 }; let i3415 = { let t0 = square_n(&i3391, 2); let t1 = &t0 * &_11; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11111111; let t4 = square_n(&t3, 9); t4 }; let i3433 = { let t0 = &_1111101 * &i3415; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101111; t4 }; let i3456 = { let t0 = square_n(&i3433, 6); let t1 = &t0 * &_11001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 7); t4 }; let i3477 = { let t0 = &_111 * &i3456; let t1 = square_n(&t0, 11); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11; t4 }; let result = { let t0 = square_n(&i3477, 5); t0 }; result } /// Generated from tools/addchain/bn254_exp0.acc pub fn pow_exp0( base: &FieldElement, ) -> FieldElement { let base = base.clone(); let _10 = { let t0 = square_n(&base, 1); t0 }; let _11 = { let t0 = &base * &_10; t0 }; let _101 = { let t0 = &_10 * &_11; t0 }; let _111 = { let t0 = &_10 * &_101; t0 }; let _1001 = { let t0 = &_10 * &_111; t0 }; let _1011 = { let t0 = &_10 * &_1001; t0 }; let _1101 = { let t0 = &_10 * &_1011; t0 }; let _1111 = { let t0 = &_10 * &_1101; t0 }; let _10001 = { let t0 = &_10 * &_1111; t0 }; let _10011 = { let t0 = &_10 * &_10001; t0 }; let _10101 = { let t0 = &_10 * &_10011; t0 }; let _10111 = { let t0 = &_10 * &_10101; t0 }; let _11001 = { let t0 = &_10 * &_10111; t0 }; let _11011 = { let t0 = &_10 * &_11001; t0 }; let _11101 = { let t0 = &_10 * &_11011; t0 }; let _11111 = { let t0 = &_10 * &_11101; t0 }; let _100001 = { let t0 = &_10 * &_11111; t0 }; let _100011 = { let t0 = &_10 * &_100001; t0 }; let _100101 = { let t0 = &_10 * &_100011; t0 }; let _100111 = { let t0 = &_10 * &_100101; t0 }; let _101001 = { let t0 = &_10 * &_100111; t0 }; let _101011 = { let t0 = &_10 * &_101001; t0 }; let _101101 = { let t0 = &_10 * &_101011; t0 }; let _101111 = { let t0 = &_10 * &_101101; t0 }; let _110001 = { let t0 = &_10 * &_101111; t0 }; let _110011 = { let t0 = &_10 * &_110001; t0 }; let _110101 = { let t0 = &_10 * &_110011; t0 }; let _110111 = { let t0 = &_10 * &_110101; t0 }; let _111001 = { let t0 = &_10 * &_110111; t0 }; let _111011 = { let t0 = &_10 * &_111001; t0 }; let _111101 = { let t0 = &_10 * &_111011; t0 }; let _111111 = { let t0 = &_10 * &_111101; t0 }; let _1000001 = { let t0 = &_10 * &_111111; t0 }; let _1000011 = { let t0 = &_10 * &_1000001; t0 }; let _1000101 = { let t0 = &_10 * &_1000011; t0 }; let _1000111 = { let t0 = &_10 * &_1000101; t0 }; let _1001001 = { let t0 = &_10 * &_1000111; t0 }; let _1001011 = { let t0 = &_10 * &_1001001; t0 }; let _1001101 = { let t0 = &_10 * &_1001011; t0 }; let _1001111 = { let t0 = &_10 * &_1001101; t0 }; let _1010001 = { let t0 = &_10 * &_1001111; t0 }; let _1010011 = { let t0 = &_10 * &_1010001; t0 }; let _1010101 = { let t0 = &_10 * &_1010011; t0 }; let _1010111 = { let t0 = &_10 * &_1010101; t0 }; let _1011001 = { let t0 = &_10 * &_1010111; t0 }; let _1011011 = { let t0 = &_10 * &_1011001; t0 }; let _1011101 = { let t0 = &_10 * &_1011011; t0 }; let _1011111 = { let t0 = &_10 * &_1011101; t0 }; let _1100001 = { let t0 = &_10 * &_1011111; t0 }; let _1100011 = { let t0 = &_10 * &_1100001; t0 }; let _1100101 = { let t0 = &_10 * &_1100011; t0 }; let _1100111 = { let t0 = &_10 * &_1100101; t0 }; let _1101001 = { let t0 = &_10 * &_1100111; t0 }; let _1101011 = { let t0 = &_10 * &_1101001; t0 }; let _1101101 = { let t0 = &_10 * &_1101011; t0 }; let _1101111 = { let t0 = &_10 * &_1101101; t0 }; let _1110001 = { let t0 = &_10 * &_1101111; t0 }; let _1110011 = { let t0 = &_10 * &_1110001; t0 }; let _1110101 = { let t0 = &_10 * &_1110011; t0 }; let _1110111 = { let t0 = &_10 * &_1110101; t0 }; let _1111001 = { let t0 = &_10 * &_1110111; t0 }; let _1111011 = { let t0 = &_10 * &_1111001; t0 }; let _1111101 = { let t0 = &_10 * &_1111011; t0 }; let _1111111 = { let t0 = &_10 * &_1111101; t0 }; let _11100010 = { let t0 = &_1100011 * &_1111111; t0 }; let _11111111 = { let t0 = &_11101 * &_11100010; t0 }; let i67 = { let t0 = square_n(&_11100010, 1); t0 }; let x9 = { let t0 = &_111011 * &i67; t0 }; let i94 = { let t0 = square_n(&i67, 10); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 7); t4 }; let i118 = { let t0 = &_1000011 * &i94; let t1 = square_n(&t0, 8); let t2 = &t1 * &_111011; let t3 = square_n(&t2, 13); let t4 = &t3 * &_101011; t4 }; let i146 = { let t0 = square_n(&i118, 8); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 10); t4 }; let i165 = { let t0 = &_1010111 * &i146; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1110111; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1011; t4 }; let i191 = { let t0 = square_n(&i165, 6); let t1 = &t0 * &_101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_111001; let t4 = square_n(&t3, 8); t4 }; let i212 = { let t0 = &_100101 * &i191; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1100011; t4 }; let i243 = { let t0 = square_n(&i212, 10); let t1 = &t0 * &_111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 8); t4 }; let i261 = { let t0 = &_1100001 * &i243; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_110101; t4 }; let i287 = { let t0 = square_n(&i261, 6); let t1 = &t0 * &_10111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010101; let t4 = square_n(&t3, 9); t4 }; let i308 = { let t0 = &_10011 * &i287; let t1 = square_n(&t0, 9); let t2 = &t1 * &_100001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100011; t4 }; let i334 = { let t0 = square_n(&i308, 9); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_101101; let t4 = square_n(&t3, 7); t4 }; let i359 = { let t0 = &_1011 * &i334; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1100011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100111; t4 }; let i384 = { let t0 = square_n(&i359, 9); let t1 = &t0 * &_1101001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10001; let t4 = square_n(&t3, 9); t4 }; let i402 = { let t0 = &_100101 * &i384; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_100011; t4 }; let i426 = { let t0 = square_n(&i402, 9); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1001011; let t4 = square_n(&t3, 4); t4 }; let i445 = { let t0 = &_1101 * &i426; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_101001; t4 }; let i469 = { let t0 = square_n(&i445, 8); let t1 = &t0 * &_1101001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i489 = { let t0 = &_1111101 * &i469; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110101; t4 }; let i515 = { let t0 = square_n(&i489, 7); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 7); t4 }; let i532 = { let t0 = &_111001 * &i515; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_111; t4 }; let i561 = { let t0 = square_n(&i532, 11); let t1 = &t0 * &_11111111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 8); t4 }; let i576 = { let t0 = &_1010111 * &i561; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001; t4 }; let i602 = { let t0 = square_n(&i576, 10); let t1 = &t0 * &_1011001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 7); t4 }; let i625 = { let t0 = &_11001 * &i602; let t1 = square_n(&t0, 9); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_111101; t4 }; let i649 = { let t0 = square_n(&i625, 6); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101; let t4 = square_n(&t3, 10); t4 }; let i671 = { let t0 = &_10111 * &i649; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1101101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1111001; t4 }; let i696 = { let t0 = square_n(&i671, 9); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 7); t4 }; let i716 = { let t0 = &_1100111 * &i696; let t1 = square_n(&t0, 7); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1100011; t4 }; let i737 = { let t0 = square_n(&i716, 6); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 5); t4 }; let i762 = { let t0 = &_11101 * &i737; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1111001; t4 }; let i787 = { let t0 = square_n(&i762, 7); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 8); t4 }; let i805 = { let t0 = &_1011101 * &i787; let t1 = square_n(&t0, 9); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_10001; t4 }; let i830 = { let t0 = square_n(&i805, 6); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1010101; let t4 = square_n(&t3, 7); t4 }; let i847 = { let t0 = &_1011001 * &i830; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_1001; t4 }; let i872 = { let t0 = square_n(&i847, 5); let t1 = &t0 * &_11; let t2 = square_n(&t1, 11); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 7); t4 }; let i887 = { let t0 = &_100101 * &i872; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011; t4 }; let i913 = { let t0 = square_n(&i887, 10); let t1 = &t0 * &_1011011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 8); t4 }; let i936 = { let t0 = &_111001 * &i913; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1110111; t4 }; let i965 = { let t0 = square_n(&i936, 10); let t1 = &t0 * &_101111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10001; let t4 = square_n(&t3, 9); t4 }; let i984 = { let t0 = &_1010011 * &i965; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1111011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1010001; t4 }; let i1004 = { let t0 = square_n(&i984, 6); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 3); t4 }; let i1023 = { let t0 = &_111 * &i1004; let t1 = square_n(&t0, 10); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_11101; t4 }; let i1051 = { let t0 = square_n(&i1023, 11); let t1 = &t0 * &x9; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 7); t4 }; let i1071 = { let t0 = &_1010001 * &i1051; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_111011; t4 }; let i1099 = { let t0 = square_n(&i1071, 9); let t1 = &t0 * &_1111001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101001; let t4 = square_n(&t3, 11); t4 }; let i1118 = { let t0 = &_101111 * &i1099; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000001; t4 }; let i1143 = { let t0 = square_n(&i1118, 9); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 7); t4 }; let i1162 = { let t0 = &_111001 * &i1143; let t1 = square_n(&t0, 4); let t2 = &t1 * &_11; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1100101; t4 }; let i1187 = { let t0 = square_n(&i1162, 4); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 8); t4 }; let i1205 = { let t0 = &_1100101 * &i1187; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1101011; t4 }; let i1231 = { let t0 = square_n(&i1205, 7); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11111; let t4 = square_n(&t3, 9); t4 }; let i1248 = { let t0 = &_1100101 * &i1231; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_111011; t4 }; let i1272 = { let t0 = square_n(&i1248, 8); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_100101; let t4 = square_n(&t3, 7); t4 }; let i1292 = { let t0 = &_110001 * &i1272; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1111011; t4 }; let i1317 = { let t0 = square_n(&i1292, 9); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i1336 = { let t0 = &_1111001 * &i1317; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1111001; t4 }; let i1357 = { let t0 = square_n(&i1336, 7); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 5); t4 }; let i1382 = { let t0 = &_11011 * &i1357; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1100111; t4 }; let i1407 = { let t0 = square_n(&i1382, 8); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 9); t4 }; let i1423 = { let t0 = &_100111 * &i1407; let t1 = square_n(&t0, 7); let t2 = &t1 * &_101001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_11101; t4 }; let i1458 = { let t0 = square_n(&i1423, 8); let t1 = &t0 * &_111001; let t2 = square_n(&t1, 14); let t3 = &t2 * &_1101001; let t4 = square_n(&t3, 11); t4 }; let i1478 = { let t0 = &_1100011 * &i1458; let t1 = square_n(&t0, 8); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1001111; t4 }; let i1498 = { let t0 = square_n(&i1478, 4); let t1 = &t0 * &_11; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 2); t4 }; let i1519 = { let t0 = &_11 * &i1498; let t1 = square_n(&t0, 12); let t2 = &t1 * &_1110101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110111; t4 }; let i1544 = { let t0 = square_n(&i1519, 10); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1011101; let t4 = square_n(&t3, 6); t4 }; let i1559 = { let t0 = &_111011 * &i1544; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100111; let t3 = square_n(&t2, 4); let t4 = &t3 * &_111; t4 }; let i1594 = { let t0 = square_n(&i1559, 12); let t1 = &t0 * &_111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 11); t4 }; let i1610 = { let t0 = &_1001111 * &i1594; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010011; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10101; t4 }; let i1636 = { let t0 = square_n(&i1610, 10); let t1 = &t0 * &_1001111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 3); t4 }; let i1658 = { let t0 = &_101 * &i1636; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_101101; t4 }; let i1680 = { let t0 = square_n(&i1658, 8); let t1 = &t0 * &_1001111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 5); t4 }; let i1700 = { let t0 = &_1011 * &i1680; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000101; t4 }; let i1727 = { let t0 = square_n(&i1700, 7); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_111011; let t4 = square_n(&t3, 9); t4 }; let i1744 = { let t0 = &_1000111 * &i1727; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011001; t4 }; let i1766 = { let t0 = square_n(&i1744, 6); let t1 = &t0 * &_101001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 6); t4 }; let i1784 = { let t0 = &_100101 * &i1766; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110101; t4 }; let i1812 = { let t0 = square_n(&i1784, 9); let t1 = &t0 * &_1100111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 10); t4 }; let i1828 = { let t0 = &_1101111 * &i1812; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_100011; t4 }; let i1854 = { let t0 = square_n(&i1828, 6); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 8); t4 }; let i1876 = { let t0 = &_1110001 * &i1854; let t1 = square_n(&t0, 12); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101; t4 }; let i1918 = { let t0 = square_n(&i1876, 20); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10001; let t4 = square_n(&t3, 9); t4 }; let i1937 = { let t0 = &_1011001 * &i1918; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_110101; t4 }; let i1962 = { let t0 = square_n(&i1937, 8); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 4); let t3 = &t2 * &_111; let t4 = square_n(&t3, 11); t4 }; let i1978 = { let t0 = &_1001101 * &i1962; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1000011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_101111; t4 }; let i2002 = { let t0 = square_n(&i1978, 8); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 7); t4 }; let i2019 = { let t0 = &_1111001 * &i2002; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101001; t4 }; let i2043 = { let t0 = square_n(&i2019, 10); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111011; let t4 = square_n(&t3, 6); t4 }; let i2061 = { let t0 = &_11111 * &i2043; let t1 = square_n(&t0, 8); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110001; t4 }; let i2084 = { let t0 = square_n(&i2061, 8); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 2); let t3 = &t2 * &base; let t4 = square_n(&t3, 11); t4 }; let i2103 = { let t0 = &_10111 * &i2084; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011001; t4 }; let i2126 = { let t0 = square_n(&i2103, 7); let t1 = &t0 * &_1011011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 9); t4 }; let i2144 = { let t0 = &_101001 * &i2126; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1100011; t4 }; let i2173 = { let t0 = square_n(&i2144, 9); let t1 = &t0 * &_1110111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 10); t4 }; let i2184 = { let t0 = &_1110001 * &i2173; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 1); let t4 = &t3 * &base; t4 }; let i2216 = { let t0 = square_n(&i2184, 14); let t1 = &t0 * &_111101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 7); t4 }; let i2233 = { let t0 = &_1001011 * &i2216; let t1 = square_n(&t0, 7); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11111; t4 }; let i2259 = { let t0 = square_n(&i2233, 10); let t1 = &t0 * &_1100111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101111; let t4 = square_n(&t3, 7); t4 }; let i2280 = { let t0 = &_1011011 * &i2259; let t1 = square_n(&t0, 10); let t2 = &t1 * &x9; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100101; t4 }; let i2305 = { let t0 = square_n(&i2280, 7); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 10); t4 }; let i2327 = { let t0 = &_101011 * &i2305; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_1011; t4 }; let i2354 = { let t0 = square_n(&i2327, 10); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 8); t4 }; let i2374 = { let t0 = &_1100101 * &i2354; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1100101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1011111; t4 }; let i2402 = { let t0 = square_n(&i2374, 12); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 7); t4 }; let i2421 = { let t0 = &_1011101 * &i2402; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101111; t4 }; let i2446 = { let t0 = square_n(&i2421, 5); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i2461 = { let t0 = &_1111001 * &i2446; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10111; t4 }; let i2494 = { let t0 = square_n(&i2461, 11); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_101; let t4 = square_n(&t3, 10); t4 }; let i2519 = { let t0 = &_110011 * &i2494; let t1 = square_n(&t0, 8); let t2 = &t1 * &_101001; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1100111; t4 }; let i2543 = { let t0 = square_n(&i2519, 9); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 9); t4 }; let i2561 = { let t0 = &_110101 * &i2543; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1100011; t4 }; let i2586 = { let t0 = square_n(&i2561, 5); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_101; let t4 = square_n(&t3, 12); t4 }; let i2614 = { let t0 = &_11011 * &i2586; let t1 = square_n(&t0, 13); let t2 = &t1 * &_101; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1101101; t4 }; let i2641 = { let t0 = square_n(&i2614, 4); let t1 = &t0 * &_101; let t2 = square_n(&t1, 14); let t3 = &t2 * &_1000001; let t4 = square_n(&t3, 7); t4 }; let i2658 = { let t0 = &_111011 * &i2641; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11011; t4 }; let i2684 = { let t0 = square_n(&i2658, 8); let t1 = &t0 * &_10111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 7); t4 }; let i2702 = { let t0 = &_111001 * &i2684; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000111; t4 }; let i2726 = { let t0 = square_n(&i2702, 4); let t1 = &t0 * &_1011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1000101; let t4 = square_n(&t3, 8); t4 }; let i2741 = { let t0 = &_1011101 * &i2726; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_11011; t4 }; let i2767 = { let t0 = square_n(&i2741, 9); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 6); t4 }; let i2792 = { let t0 = &_111111 * &i2767; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101011; let t3 = square_n(&t2, 13); let t4 = &t3 * &_111011; t4 }; let i2820 = { let t0 = square_n(&i2792, 8); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 12); t4 }; let i2837 = { let t0 = &_1110101 * &i2820; let t1 = square_n(&t0, 2); let t2 = &t1 * &_11; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1101001; t4 }; let i2862 = { let t0 = square_n(&i2837, 8); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001101; let t4 = square_n(&t3, 7); t4 }; let i2878 = { let t0 = &_1110101 * &i2862; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10111; t4 }; let i2910 = { let t0 = square_n(&i2878, 8); let t1 = &t0 * &_11; let t2 = square_n(&t1, 13); let t3 = &t2 * &_1011101; let t4 = square_n(&t3, 9); t4 }; let i2932 = { let t0 = &_1011101 * &i2910; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1111111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1010111; t4 }; let i2956 = { let t0 = square_n(&i2932, 8); let t1 = &t0 * &_1110001; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 10); t4 }; let i2972 = { let t0 = &_1101001 * &i2956; let t1 = square_n(&t0, 6); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001; t4 }; let i3000 = { let t0 = square_n(&i2972, 9); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101001; let t4 = square_n(&t3, 10); t4 }; let i3019 = { let t0 = &_11111 * &i3000; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000101; t4 }; let i3046 = { let t0 = square_n(&i3019, 7); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1111101; let t4 = square_n(&t3, 7); t4 }; let i3065 = { let t0 = &_1000001 * &i3046; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1111011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1010111; t4 }; let i3094 = { let t0 = square_n(&i3065, 14); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001101; let t4 = square_n(&t3, 5); t4 }; let i3115 = { let t0 = &_1111 * &i3094; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1111101; t4 }; let i3140 = { let t0 = square_n(&i3115, 7); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1101111; let t4 = square_n(&t3, 7); t4 }; let i3160 = { let t0 = &_101001 * &i3140; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110111; t4 }; let i3182 = { let t0 = square_n(&i3160, 7); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100101; let t4 = square_n(&t3, 7); t4 }; let i3202 = { let t0 = &_111101 * &i3182; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1111001; t4 }; let i3225 = { let t0 = square_n(&i3202, 5); let t1 = &t0 * &_10101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 7); t4 }; let i3243 = { let t0 = &_1010011 * &i3225; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100011; t4 }; let i3266 = { let t0 = square_n(&i3243, 7); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10111; let t4 = square_n(&t3, 8); t4 }; let i3284 = { let t0 = &_110111 * &i3266; let t1 = square_n(&t0, 7); let t2 = &t1 * &_111111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1011001; t4 }; let i3309 = { let t0 = square_n(&i3284, 7); let t1 = &t0 * &_1011011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 8); t4 }; let i3326 = { let t0 = &_1010001 * &i3309; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001111; t4 }; let i3354 = { let t0 = square_n(&i3326, 7); let t1 = &t0 * &_1100011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 11); t4 }; let i3369 = { let t0 = &_1111011 * &i3354; let t1 = square_n(&t0, 3); let t2 = &t1 * &_11; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11111111; t4 }; let i3396 = { let t0 = square_n(&i3369, 12); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_11111; let t4 = square_n(&t3, 6); t4 }; let i3421 = { let t0 = &_111 * &i3396; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10101; t4 }; let i3449 = { let t0 = square_n(&i3421, 12); let t1 = &t0 * &_1101001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i3470 = { let t0 = &_111101 * &i3449; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1100001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1100101; t4 }; let result = { let t0 = square_n(&i3470, 1); let t1 = &t0 * &base; t1 }; result } /// Generated from tools/addchain/bn254_r_m_d_inv.acc pub fn pow_r_m_d_inv( base: &FieldElement, ) -> FieldElement { let base = base.clone(); let _10 = { let t0 = square_n(&base, 1); t0 }; let _11 = { let t0 = &base * &_10; t0 }; let _100 = { let t0 = &base * &_11; t0 }; let _101 = { let t0 = &base * &_100; t0 }; let _111 = { let t0 = &_10 * &_101; t0 }; let _1001 = { let t0 = &_10 * &_111; t0 }; let _1011 = { let t0 = &_10 * &_1001; t0 }; let _1101 = { let t0 = &_10 * &_1011; t0 }; let _1111 = { let t0 = &_10 * &_1101; t0 }; let _10001 = { let t0 = &_10 * &_1111; t0 }; let _10011 = { let t0 = &_10 * &_10001; t0 }; let _10101 = { let t0 = &_10 * &_10011; t0 }; let _10111 = { let t0 = &_10 * &_10101; t0 }; let _11001 = { let t0 = &_10 * &_10111; t0 }; let _11011 = { let t0 = &_10 * &_11001; t0 }; let _11101 = { let t0 = &_10 * &_11011; t0 }; let _11111 = { let t0 = &_10 * &_11101; t0 }; let _100001 = { let t0 = &_10 * &_11111; t0 }; let _100011 = { let t0 = &_10 * &_100001; t0 }; let _100101 = { let t0 = &_10 * &_100011; t0 }; let _100111 = { let t0 = &_10 * &_100101; t0 }; let _101001 = { let t0 = &_10 * &_100111; t0 }; let _101011 = { let t0 = &_10 * &_101001; t0 }; let _101101 = { let t0 = &_10 * &_101011; t0 }; let _101111 = { let t0 = &_10 * &_101101; t0 }; let _110001 = { let t0 = &_10 * &_101111; t0 }; let _110011 = { let t0 = &_10 * &_110001; t0 }; let _110101 = { let t0 = &_10 * &_110011; t0 }; let _110111 = { let t0 = &_10 * &_110101; t0 }; let _111001 = { let t0 = &_10 * &_110111; t0 }; let _111011 = { let t0 = &_10 * &_111001; t0 }; let _111101 = { let t0 = &_10 * &_111011; t0 }; let _111111 = { let t0 = &_10 * &_111101; t0 }; let _1000001 = { let t0 = &_10 * &_111111; t0 }; let _1000011 = { let t0 = &_10 * &_1000001; t0 }; let _1000101 = { let t0 = &_10 * &_1000011; t0 }; let _1000111 = { let t0 = &_10 * &_1000101; t0 }; let _1001001 = { let t0 = &_10 * &_1000111; t0 }; let _1001011 = { let t0 = &_10 * &_1001001; t0 }; let _1001101 = { let t0 = &_10 * &_1001011; t0 }; let _1001111 = { let t0 = &_10 * &_1001101; t0 }; let _1010001 = { let t0 = &_10 * &_1001111; t0 }; let _1010011 = { let t0 = &_10 * &_1010001; t0 }; let _1010101 = { let t0 = &_10 * &_1010011; t0 }; let _1010111 = { let t0 = &_10 * &_1010101; t0 }; let _1011001 = { let t0 = &_10 * &_1010111; t0 }; let _1011011 = { let t0 = &_10 * &_1011001; t0 }; let _1011101 = { let t0 = &_10 * &_1011011; t0 }; let _1011111 = { let t0 = &_10 * &_1011101; t0 }; let _1100001 = { let t0 = &_10 * &_1011111; t0 }; let _1100011 = { let t0 = &_10 * &_1100001; t0 }; let _1100101 = { let t0 = &_10 * &_1100011; t0 }; let _1100111 = { let t0 = &_10 * &_1100101; t0 }; let _1101001 = { let t0 = &_10 * &_1100111; t0 }; let _1101011 = { let t0 = &_10 * &_1101001; t0 }; let _1101101 = { let t0 = &_10 * &_1101011; t0 }; let _1101111 = { let t0 = &_10 * &_1101101; t0 }; let _1110001 = { let t0 = &_10 * &_1101111; t0 }; let _1110011 = { let t0 = &_10 * &_1110001; t0 }; let _1110101 = { let t0 = &_10 * &_1110011; t0 }; let _1110111 = { let t0 = &_10 * &_1110101; t0 }; let _1111001 = { let t0 = &_10 * &_1110111; t0 }; let _1111011 = { let t0 = &_10 * &_1111001; t0 }; let _1111101 = { let t0 = &_10 * &_1111011; t0 }; let _1111111 = { let t0 = &_10 * &_1111101; t0 }; let _10000001 = { let t0 = &_10 * &_1111111; t0 }; let _10000011 = { let t0 = &_10 * &_10000001; t0 }; let _10000101 = { let t0 = &_10 * &_10000011; t0 }; let _10000111 = { let t0 = &_10 * &_10000101; t0 }; let _10001001 = { let t0 = &_10 * &_10000111; t0 }; let _10001011 = { let t0 = &_10 * &_10001001; t0 }; let _10001101 = { let t0 = &_10 * &_10001011; t0 }; let _10001111 = { let t0 = &_10 * &_10001101; t0 }; let _10010001 = { let t0 = &_10 * &_10001111; t0 }; let _10010011 = { let t0 = &_10 * &_10010001; t0 }; let _10010101 = { let t0 = &_10 * &_10010011; t0 }; let _10010111 = { let t0 = &_10 * &_10010101; t0 }; let _10011001 = { let t0 = &_10 * &_10010111; t0 }; let _10011011 = { let t0 = &_10 * &_10011001; t0 }; let _10011101 = { let t0 = &_10 * &_10011011; t0 }; let _10011111 = { let t0 = &_10 * &_10011101; t0 }; let _10100001 = { let t0 = &_10 * &_10011111; t0 }; let _10100011 = { let t0 = &_10 * &_10100001; t0 }; let _10100101 = { let t0 = &_10 * &_10100011; t0 }; let _10100111 = { let t0 = &_10 * &_10100101; t0 }; let _10101001 = { let t0 = &_10 * &_10100111; t0 }; let _10101011 = { let t0 = &_10 * &_10101001; t0 }; let _10101101 = { let t0 = &_10 * &_10101011; t0 }; let _10101111 = { let t0 = &_10 * &_10101101; t0 }; let _10110001 = { let t0 = &_10 * &_10101111; t0 }; let _10110011 = { let t0 = &_10 * &_10110001; t0 }; let _10110101 = { let t0 = &_10 * &_10110011; t0 }; let _10110111 = { let t0 = &_10 * &_10110101; t0 }; let _10111001 = { let t0 = &_10 * &_10110111; t0 }; let _10111011 = { let t0 = &_10 * &_10111001; t0 }; let _10111101 = { let t0 = &_10 * &_10111011; t0 }; let _10111111 = { let t0 = &_10 * &_10111101; t0 }; let _11000001 = { let t0 = &_10 * &_10111111; t0 }; let _11000011 = { let t0 = &_10 * &_11000001; t0 }; let _11000101 = { let t0 = &_10 * &_11000011; t0 }; let _11000111 = { let t0 = &_10 * &_11000101; t0 }; let _11001001 = { let t0 = &_10 * &_11000111; t0 }; let _11001011 = { let t0 = &_10 * &_11001001; t0 }; let _11001101 = { let t0 = &_10 * &_11001011; t0 }; let _11001111 = { let t0 = &_10 * &_11001101; t0 }; let _11010001 = { let t0 = &_10 * &_11001111; t0 }; let _11010011 = { let t0 = &_10 * &_11010001; t0 }; let _11010111 = { let t0 = &_100 * &_11010011; t0 }; let _11011001 = { let t0 = &_10 * &_11010111; t0 }; let _11011011 = { let t0 = &_10 * &_11011001; t0 }; let _11011101 = { let t0 = &_10 * &_11011011; t0 }; let _11011111 = { let t0 = &_10 * &_11011101; t0 }; let _11100001 = { let t0 = &_10 * &_11011111; t0 }; let _11100011 = { let t0 = &_10 * &_11100001; t0 }; let _11100101 = { let t0 = &_10 * &_11100011; t0 }; let _11100111 = { let t0 = &_10 * &_11100101; t0 }; let _11101001 = { let t0 = &_10 * &_11100111; t0 }; let _11101011 = { let t0 = &_10 * &_11101001; t0 }; let _11101101 = { let t0 = &_10 * &_11101011; t0 }; let _11101111 = { let t0 = &_10 * &_11101101; t0 }; let _11110001 = { let t0 = &_10 * &_11101111; t0 }; let _11110011 = { let t0 = &_10 * &_11110001; t0 }; let _11110101 = { let t0 = &_10 * &_11110011; t0 }; let _11110111 = { let t0 = &_10 * &_11110101; t0 }; let _11111001 = { let t0 = &_10 * &_11110111; t0 }; let _11111011 = { let t0 = &_10 * &_11111001; t0 }; let _11111101 = { let t0 = &_10 * &_11111011; t0 }; let _11111111 = { let t0 = &_10 * &_11111101; t0 }; let i146 = { let t0 = &_11 * &_11111111; let t1 = square_n(&t0, 7); let t2 = &t1 * &_10100011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11010011; t4 }; let i174 = { let t0 = square_n(&i146, 9); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101001; let t4 = square_n(&t3, 8); t4 }; let i199 = { let t0 = &_101011 * &i174; let t1 = square_n(&t0, 11); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11100011; t4 }; let i229 = { let t0 = square_n(&i199, 8); let t1 = &t0 * &_10011011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11000001; let t4 = square_n(&t3, 12); t4 }; let i255 = { let t0 = &_11110111 * &i229; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000111; let t3 = square_n(&t2, 14); let t4 = &t3 * &_10100001; t4 }; let i278 = { let t0 = square_n(&i255, 5); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 7); t4 }; let i298 = { let t0 = &_1011 * &i278; let t1 = square_n(&t0, 10); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11111; t4 }; let i330 = { let t0 = square_n(&i298, 12); let t1 = &t0 * &_10111111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 10); t4 }; let i352 = { let t0 = &_1011111 * &i330; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11111111; t4 }; let i387 = { let t0 = square_n(&i352, 10); let t1 = &t0 * &_11011001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10001; let t4 = square_n(&t3, 13); t4 }; let i411 = { let t0 = &_1000111 * &i387; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 15); let t4 = &t3 * &_1101101; t4 }; let i441 = { let t0 = square_n(&i411, 12); let t1 = &t0 * &_11100011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 9); t4 }; let i461 = { let t0 = &_11111011 * &i441; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11111011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10101011; t4 }; let i490 = { let t0 = square_n(&i461, 11); let t1 = &t0 * &_10111111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10011011; let t4 = square_n(&t3, 7); t4 }; let i508 = { let t0 = &_1100111 * &i490; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101111; t4 }; let i537 = { let t0 = square_n(&i508, 10); let t1 = &t0 * &_11000011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11011; let t4 = square_n(&t3, 11); t4 }; let i560 = { let t0 = &_10111111 * &i537; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10010101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10100101; t4 }; let i587 = { let t0 = square_n(&i560, 9); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 7); t4 }; let i609 = { let t0 = &_110111 * &i587; let t1 = square_n(&t0, 7); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_11101; t4 }; let i638 = { let t0 = square_n(&i609, 11); let t1 = &t0 * &_11100111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 10); t4 }; let i660 = { let t0 = &_100111 * &i638; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10110011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1111101; t4 }; let i686 = { let t0 = square_n(&i660, 12); let t1 = &t0 * &_10100101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11110011; let t4 = square_n(&t3, 4); t4 }; let i710 = { let t0 = &_1001 * &i686; let t1 = square_n(&t0, 13); let t2 = &t1 * &_10001011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001101; t4 }; let i737 = { let t0 = square_n(&i710, 5); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10100011; let t4 = square_n(&t3, 8); t4 }; let i755 = { let t0 = &_10001101 * &i737; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001001; t4 }; let i788 = { let t0 = square_n(&i755, 5); let t1 = &t0 * &_1011; let t2 = square_n(&t1, 13); let t3 = &t2 * &_1001001; let t4 = square_n(&t3, 13); t4 }; let i806 = { let t0 = &_10110011 * &i788; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11001101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1010011; t4 }; let i838 = { let t0 = square_n(&i806, 11); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10000001; let t4 = square_n(&t3, 9); t4 }; let i860 = { let t0 = &_10111011 * &i838; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11100111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11101011; t4 }; let i884 = { let t0 = square_n(&i860, 2); let t1 = &t0 * &_11; let t2 = square_n(&t1, 13); let t3 = &t2 * &_1010101; let t4 = square_n(&t3, 7); t4 }; let i912 = { let t0 = &_101101 * &i884; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10101011; let t3 = square_n(&t2, 13); let t4 = &t3 * &_111011; t4 }; let i937 = { let t0 = square_n(&i912, 7); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111; let t4 = square_n(&t3, 9); t4 }; let i962 = { let t0 = &_10011 * &i937; let t1 = square_n(&t0, 10); let t2 = &t1 * &_100001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_101011; t4 }; let i993 = { let t0 = square_n(&i962, 10); let t1 = &t0 * &_11100011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10111011; let t4 = square_n(&t3, 9); t4 }; let i1013 = { let t0 = &_11001111 * &i993; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10101101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001111; t4 }; let i1041 = { let t0 = square_n(&i1013, 10); let t1 = &t0 * &_11110011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10001001; let t4 = square_n(&t3, 8); t4 }; let i1060 = { let t0 = &_10011101 * &i1041; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10001001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101011; t4 }; let i1092 = { let t0 = square_n(&i1060, 7); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1000101; let t4 = square_n(&t3, 11); t4 }; let i1116 = { let t0 = &_10011011 * &i1092; let t1 = square_n(&t0, 10); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10111011; t4 }; let i1151 = { let t0 = square_n(&i1116, 11); let t1 = &t0 * &_10111011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11011011; let t4 = square_n(&t3, 12); t4 }; let i1173 = { let t0 = &_10011111 * &i1151; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11100111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000111; t4 }; let i1204 = { let t0 = square_n(&i1173, 9); let t1 = &t0 * &_10001111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11110001; let t4 = square_n(&t3, 10); t4 }; let i1223 = { let t0 = &_10001001 * &i1204; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10000011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10001001; t4 }; let i1250 = { let t0 = square_n(&i1223, 6); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10011011; let t4 = square_n(&t3, 8); t4 }; let i1273 = { let t0 = &_11101001 * &i1250; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1110111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_100011; t4 }; let i1304 = { let t0 = square_n(&i1273, 11); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 9); t4 }; let i1324 = { let t0 = &_1011011 * &i1304; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11100001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1100011; t4 }; let i1352 = { let t0 = square_n(&i1324, 9); let t1 = &t0 * &_11010001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11000111; let t4 = square_n(&t3, 9); t4 }; let i1378 = { let t0 = &_10010101 * &i1352; let t1 = square_n(&t0, 14); let t2 = &t1 * &_11010001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1001101; t4 }; let i1409 = { let t0 = square_n(&i1378, 8); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 9); t4 }; let i1430 = { let t0 = &_1101111 * &i1409; let t1 = square_n(&t0, 8); let t2 = &t1 * &_111101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1010011; t4 }; let i1460 = { let t0 = square_n(&i1430, 12); let t1 = &t0 * &_10101101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10011011; let t4 = square_n(&t3, 8); t4 }; let i1485 = { let t0 = &_10100001 * &i1460; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10001111; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1111101; t4 }; let i1511 = { let t0 = square_n(&i1485, 7); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 8); t4 }; let i1532 = { let t0 = &_1100001 * &i1511; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11110001; t4 }; let i1559 = { let t0 = square_n(&i1532, 7); let t1 = &t0 * &_1100111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11101101; let t4 = square_n(&t3, 8); t4 }; let i1579 = { let t0 = &_1101101 * &i1559; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_110001; t4 }; let i1613 = { let t0 = square_n(&i1579, 9); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 13); t4 }; let i1640 = { let t0 = &_11001101 * &i1613; let t1 = square_n(&t0, 12); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10101011; t4 }; let i1666 = { let t0 = square_n(&i1640, 4); let t1 = &t0 * &_1011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10111011; let t4 = square_n(&t3, 8); t4 }; let i1685 = { let t0 = &_11011011 * &i1666; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11101101; t4 }; let i1712 = { let t0 = square_n(&i1685, 8); let t1 = &t0 * &_11001011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111101; let t4 = square_n(&t3, 10); t4 }; let i1732 = { let t0 = &_11100101 * &i1712; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10101101; t4 }; let i1759 = { let t0 = square_n(&i1732, 8); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11001011; let t4 = square_n(&t3, 8); t4 }; let i1778 = { let t0 = &_11001011 * &i1759; let t1 = square_n(&t0, 3); let t2 = &t1 * &_111; let t3 = square_n(&t2, 13); let t4 = &t3 * &_11011111; t4 }; let i1809 = { let t0 = square_n(&i1778, 8); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11100111; let t4 = square_n(&t3, 9); t4 }; let i1827 = { let t0 = &_10001111 * &i1809; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1111111; t4 }; let i1854 = { let t0 = square_n(&i1827, 10); let t1 = &t0 * &_10111101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10001101; let t4 = square_n(&t3, 7); t4 }; let i1877 = { let t0 = &_1101011 * &i1854; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10001111; t4 }; let i1900 = { let t0 = square_n(&i1877, 9); let t1 = &t0 * &_11110101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11000111; let t4 = square_n(&t3, 4); t4 }; let i1922 = { let t0 = &_1111 * &i1900; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10110111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10001; t4 }; let i1945 = { let t0 = square_n(&i1922, 12); let t1 = &t0 * &_11101001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 3); t4 }; let i1970 = { let t0 = &base * &i1945; let t1 = square_n(&t0, 14); let t2 = &t1 * &_1101011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_111011; t4 }; let i1997 = { let t0 = square_n(&i1970, 11); let t1 = &t0 * &_11011001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 7); t4 }; let i2018 = { let t0 = &_110001 * &i1997; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11000111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11110111; t4 }; let i2044 = { let t0 = square_n(&i2018, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10110011; let t4 = square_n(&t3, 6); t4 }; let i2067 = { let t0 = &_11111 * &i2044; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1101101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10110011; t4 }; let i2093 = { let t0 = square_n(&i2067, 8); let t1 = &t0 * &_11010001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 11); t4 }; let i2112 = { let t0 = &_10001001 * &i2093; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11011111; t4 }; let i2138 = { let t0 = square_n(&i2112, 8); let t1 = &t0 * &_11001001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11111001; let t4 = square_n(&t3, 8); t4 }; let i2160 = { let t0 = &_10101111 * &i2138; let t1 = square_n(&t0, 11); let t2 = &t1 * &_10111001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001001; t4 }; let i2189 = { let t0 = square_n(&i2160, 10); let t1 = &t0 * &_11100111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10111101; let t4 = square_n(&t3, 8); t4 }; let i2210 = { let t0 = &_11101011 * &i2189; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1100001; t4 }; let i2238 = { let t0 = square_n(&i2210, 9); let t1 = &t0 * &_11010111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10100011; let t4 = square_n(&t3, 7); t4 }; let i2258 = { let t0 = &_1111101 * &i2238; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11000011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001001; t4 }; let i2284 = { let t0 = square_n(&i2258, 9); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11001001; let t4 = square_n(&t3, 3); t4 }; let i2312 = { let t0 = &_111 * &i2284; let t1 = square_n(&t0, 18); let t2 = &t1 * &_10011001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1010111; t4 }; let i2340 = { let t0 = square_n(&i2312, 9); let t1 = &t0 * &_11100001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11110101; let t4 = square_n(&t3, 9); t4 }; let i2359 = { let t0 = &_10011011 * &i2340; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10000011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001101; t4 }; let i2387 = { let t0 = square_n(&i2359, 8); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 9); t4 }; let i2409 = { let t0 = &_10100011 * &i2387; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1000011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10001; t4 }; let i2451 = { let t0 = square_n(&i2409, 18); let t1 = &t0 * &_1111001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_111001; let t4 = square_n(&t3, 13); t4 }; let i2469 = { let t0 = &_11101011 * &i2451; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001101; t4 }; let i2491 = { let t0 = square_n(&i2469, 10); let t1 = &t0 * &_10000111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11001001; let t4 = square_n(&t3, 2); t4 }; let i2515 = { let t0 = &_11 * &i2491; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010101; t4 }; let i2544 = { let t0 = square_n(&i2515, 9); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 9); t4 }; let i2568 = { let t0 = &_10001 * &i2544; let t1 = square_n(&t0, 14); let t2 = &t1 * &_10010011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001101; t4 }; let i2599 = { let t0 = square_n(&i2568, 3); let t1 = &t0 * &base; let t2 = square_n(&t1, 18); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 8); t4 }; let i2618 = { let t0 = &_110011 * &i2599; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10100111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_11011; t4 }; let i2648 = { let t0 = square_n(&i2618, 8); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10101111; let t4 = square_n(&t3, 8); t4 }; let i2671 = { let t0 = &_101101 * &i2648; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10101111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11100101; t4 }; let i2696 = { let t0 = square_n(&i2671, 7); let t1 = &t0 * &_110111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10110001; let t4 = square_n(&t3, 6); t4 }; let i2716 = { let t0 = &_101101 * &i2696; let t1 = square_n(&t0, 11); let t2 = &t1 * &_10001001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_1001; t4 }; let i2749 = { let t0 = square_n(&i2716, 9); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 10); t4 }; let i2769 = { let t0 = &_100001 * &i2749; let t1 = square_n(&t0, 11); let t2 = &t1 * &_10001111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_101001; t4 }; let i2800 = { let t0 = square_n(&i2769, 12); let t1 = &t0 * &_10111101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10111011; let t4 = square_n(&t3, 9); t4 }; let i2820 = { let t0 = &_101101 * &i2800; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10101001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1110011; t4 }; let i2849 = { let t0 = square_n(&i2820, 9); let t1 = &t0 * &_10000001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 11); t4 }; let i2869 = { let t0 = &_10110101 * &i2849; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10001101; t4 }; let i2895 = { let t0 = square_n(&i2869, 8); let t1 = &t0 * &_11111001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 8); t4 }; let i2918 = { let t0 = &_1111 * &i2895; let t1 = square_n(&t0, 6); let t2 = &t1 * &_11; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1011111; t4 }; let i2939 = { let t0 = square_n(&i2918, 5); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1100101; let t4 = square_n(&t3, 3); t4 }; let i2968 = { let t0 = &_11 * &i2939; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 13); let t4 = &t3 * &_10001001; t4 }; let i2994 = { let t0 = square_n(&i2968, 8); let t1 = &t0 * &_10000111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10100001; let t4 = square_n(&t3, 8); t4 }; let i3013 = { let t0 = &_11001101 * &i2994; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101111; t4 }; let i3042 = { let t0 = square_n(&i3013, 11); let t1 = &t0 * &_10010001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 8); t4 }; let i3064 = { let t0 = &_100001 * &i3042; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11010011; t4 }; let i3092 = { let t0 = square_n(&i3064, 8); let t1 = &t0 * &_11110011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 10); t4 }; let i3114 = { let t0 = &_101111 * &i3092; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11100001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10000111; t4 }; let i3140 = { let t0 = square_n(&i3114, 5); let t1 = &t0 * &_10111; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10111111; let t4 = square_n(&t3, 7); t4 }; let i3165 = { let t0 = &_1110011 * &i3140; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11110111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10110011; t4 }; let i3191 = { let t0 = square_n(&i3165, 8); let t1 = &t0 * &_10111111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 9); t4 }; let i3212 = { let t0 = &_1100101 * &i3191; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10101101; t4 }; let i3239 = { let t0 = square_n(&i3212, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10111101; let t4 = square_n(&t3, 8); t4 }; let i3258 = { let t0 = &_11100001 * &i3239; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1110111; t4 }; let i3287 = { let t0 = square_n(&i3258, 10); let t1 = &t0 * &_11111001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 11); t4 }; let i3308 = { let t0 = &_11110101 * &i3287; let t1 = square_n(&t0, 7); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11101111; t4 }; let i3344 = { let t0 = square_n(&i3308, 11); let t1 = &t0 * &_1100111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 13); t4 }; let i3365 = { let t0 = &_1100011 * &i3344; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11110111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111011; t4 }; let i3399 = { let t0 = square_n(&i3365, 12); let t1 = &t0 * &_10010001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 13); t4 }; let i3418 = { let t0 = &_11100101 * &i3399; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1010111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1100111; t4 }; let i3444 = { let t0 = square_n(&i3418, 9); let t1 = &t0 * &_11110101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 6); t4 }; let i3470 = { let t0 = &_10001 * &i3444; let t1 = square_n(&t0, 9); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1101001; t4 }; let i3497 = { let t0 = square_n(&i3470, 9); let t1 = &t0 * &_10100101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_101; let t4 = square_n(&t3, 12); t4 }; let i3515 = { let t0 = &_1010001 * &i3497; let t1 = square_n(&t0, 3); let t2 = &t1 * &base; let t3 = square_n(&t2, 12); let t4 = &t3 * &_11011; t4 }; let i3551 = { let t0 = square_n(&i3515, 14); let t1 = &t0 * &_11011001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 8); t4 }; let i3570 = { let t0 = &_1101111 * &i3551; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10110111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110001; t4 }; let i3604 = { let t0 = square_n(&i3570, 10); let t1 = &t0 * &_11110111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11111111; let t4 = square_n(&t3, 14); t4 }; let i3623 = { let t0 = &_10101001 * &i3604; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11010001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011011; t4 }; let i3650 = { let t0 = square_n(&i3623, 9); let t1 = &t0 * &_10100111; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1111; let t4 = square_n(&t3, 12); t4 }; let i3676 = { let t0 = &_100101 * &i3650; let t1 = square_n(&t0, 15); let t2 = &t1 * &_10011111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11001011; t4 }; let i3706 = { let t0 = square_n(&i3676, 9); let t1 = &t0 * &_11000101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11101111; let t4 = square_n(&t3, 11); t4 }; let i3726 = { let t0 = &_11101101 * &i3706; let t1 = square_n(&t0, 6); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10001011; t4 }; let i3753 = { let t0 = square_n(&i3726, 7); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 9); t4 }; let i3771 = { let t0 = &_10001001 * &i3753; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11101011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000101; t4 }; let i3804 = { let t0 = square_n(&i3771, 11); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 12); t4 }; let i3825 = { let t0 = &_1101111 * &i3804; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11111101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100111; t4 }; let i3852 = { let t0 = square_n(&i3825, 8); let t1 = &t0 * &_1000001; let t2 = square_n(&t1, 3); let t3 = &t2 * &_11; let t4 = square_n(&t3, 14); t4 }; let i3867 = { let t0 = &_10101101 * &i3852; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10011001; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1011; t4 }; let i3895 = { let t0 = square_n(&i3867, 14); let t1 = &t0 * &_11110011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10101001; let t4 = square_n(&t3, 4); t4 }; let i3919 = { let t0 = &_1101 * &i3895; let t1 = square_n(&t0, 11); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11011111; t4 }; let i3946 = { let t0 = square_n(&i3919, 9); let t1 = &t0 * &_10010011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 10); t4 }; let i3967 = { let t0 = &_1101001 * &i3946; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10011011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110111; t4 }; let i3998 = { let t0 = square_n(&i3967, 10); let t1 = &t0 * &_11000111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11011; let t4 = square_n(&t3, 13); t4 }; let i4017 = { let t0 = &_11010111 * &i3998; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11100011; t4 }; let i4047 = { let t0 = square_n(&i4017, 8); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11111011; let t4 = square_n(&t3, 9); t4 }; let i4063 = { let t0 = &_10111111 * &i4047; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10100011; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1101; t4 }; let i4093 = { let t0 = square_n(&i4063, 11); let t1 = &t0 * &_1110001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10111101; let t4 = square_n(&t3, 8); t4 }; let i4113 = { let t0 = &_10111011 * &i4093; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10001101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10100001; t4 }; let i4143 = { let t0 = square_n(&i4113, 9); let t1 = &t0 * &_11111001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10111111; let t4 = square_n(&t3, 8); t4 }; let i4168 = { let t0 = &_11111001 * &i4143; let t1 = square_n(&t0, 5); let t2 = &t1 * &_111; let t3 = square_n(&t2, 17); let t4 = &t3 * &_10001001; t4 }; let i4191 = { let t0 = square_n(&i4168, 4); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 5); t4 }; let i4217 = { let t0 = &_1001 * &i4191; let t1 = square_n(&t0, 14); let t2 = &t1 * &_10111101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11111111; t4 }; let i4245 = { let t0 = square_n(&i4217, 8); let t1 = &t0 * &_10101011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10101101; let t4 = square_n(&t3, 10); t4 }; let i4267 = { let t0 = &_101111 * &i4245; let t1 = square_n(&t0, 11); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_101101; t4 }; let i4294 = { let t0 = square_n(&i4267, 9); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10111001; let t4 = square_n(&t3, 7); t4 }; let i4317 = { let t0 = &_100001 * &i4294; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10101101; t4 }; let i4345 = { let t0 = square_n(&i4317, 11); let t1 = &t0 * &_10111011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 8); t4 }; let i4366 = { let t0 = &_1101101 * &i4345; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10100101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110111; t4 }; let i4396 = { let t0 = square_n(&i4366, 11); let t1 = &t0 * &_11100101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_111; let t4 = square_n(&t3, 13); t4 }; let i4418 = { let t0 = &_1100011 * &i4396; let t1 = square_n(&t0, 9); let t2 = &t1 * &_111111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10010011; t4 }; let i4446 = { let t0 = square_n(&i4418, 9); let t1 = &t0 * &_11111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1111111; let t4 = square_n(&t3, 9); t4 }; let i4462 = { let t0 = &_10010101 * &i4446; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10010101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10011; t4 }; let i4495 = { let t0 = square_n(&i4462, 11); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 12); t4 }; let i4514 = { let t0 = &_11000001 * &i4495; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100001; t4 }; let i4543 = { let t0 = square_n(&i4514, 10); let t1 = &t0 * &_10011101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11000001; let t4 = square_n(&t3, 9); t4 }; let i4562 = { let t0 = &_1010011 * &i4543; let t1 = square_n(&t0, 7); let t2 = &t1 * &_111111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_101001; t4 }; let i4589 = { let t0 = square_n(&i4562, 10); let t1 = &t0 * &_11010001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 6); t4 }; let i4609 = { let t0 = &_111001 * &i4589; let t1 = square_n(&t0, 4); let t2 = &t1 * &_11; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1001001; t4 }; let i4637 = { let t0 = square_n(&i4609, 8); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11101011; let t4 = square_n(&t3, 9); t4 }; let i4658 = { let t0 = &_10100101 * &i4637; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11100101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10001; t4 }; let i4686 = { let t0 = square_n(&i4658, 11); let t1 = &t0 * &_10011011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10001011; let t4 = square_n(&t3, 7); t4 }; let i4706 = { let t0 = &_1111111 * &i4686; let t1 = square_n(&t0, 7); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101011; t4 }; let i4732 = { let t0 = square_n(&i4706, 9); let t1 = &t0 * &_10010001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 10); t4 }; let i4760 = { let t0 = &_10001 * &i4732; let t1 = square_n(&t0, 17); let t2 = &t1 * &_10000101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11001111; t4 }; let i4787 = { let t0 = square_n(&i4760, 7); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11011011; let t4 = square_n(&t3, 9); t4 }; let i4806 = { let t0 = &_10011101 * &i4787; let t1 = square_n(&t0, 6); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_111001; t4 }; let i4834 = { let t0 = square_n(&i4806, 10); let t1 = &t0 * &_11111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 7); t4 }; let i4863 = { let t0 = &_10101 * &i4834; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1111; let t3 = square_n(&t2, 15); let t4 = &t3 * &_11111011; t4 }; let i4889 = { let t0 = square_n(&i4863, 7); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 11); t4 }; let i4914 = { let t0 = &_11110111 * &i4889; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1111111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10000011; t4 }; let i4942 = { let t0 = square_n(&i4914, 10); let t1 = &t0 * &_11100011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11010011; let t4 = square_n(&t3, 6); t4 }; let i4959 = { let t0 = &_111011 * &i4942; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11111111; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1001; t4 }; let i4991 = { let t0 = square_n(&i4959, 12); let t1 = &t0 * &_10111111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 10); t4 }; let i5010 = { let t0 = &_11001111 * &i4991; let t1 = square_n(&t0, 6); let t2 = &t1 * &_111111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11011; t4 }; let i5033 = { let t0 = square_n(&i5010, 11); let t1 = &t0 * &_11110001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111111; let t4 = square_n(&t3, 3); t4 }; let i5060 = { let t0 = &_11 * &i5033; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11101111; t4 }; let i5088 = { let t0 = square_n(&i5060, 6); let t1 = &t0 * &_101111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11010111; let t4 = square_n(&t3, 9); t4 }; let i5109 = { let t0 = &_10101101 * &i5088; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11011001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011101; t4 }; let i5134 = { let t0 = square_n(&i5109, 9); let t1 = &t0 * &_10101011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10010111; let t4 = square_n(&t3, 6); t4 }; let i5161 = { let t0 = &_100101 * &i5134; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11001101; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10000011; t4 }; let i5192 = { let t0 = square_n(&i5161, 7); let t1 = &t0 * &_1101011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10110011; let t4 = square_n(&t3, 12); t4 }; let i5209 = { let t0 = &_1100001 * &i5192; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1011; t4 }; let i5243 = { let t0 = square_n(&i5209, 12); let t1 = &t0 * &_11100101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 12); t4 }; let i5264 = { let t0 = &_11111111 * &i5243; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11110001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11101101; t4 }; let i5291 = { let t0 = square_n(&i5264, 9); let t1 = &t0 * &_11100111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1100101; let t4 = square_n(&t3, 9); t4 }; let i5314 = { let t0 = &_1101011 * &i5291; let t1 = square_n(&t0, 4); let t2 = &t1 * &_11; let t3 = square_n(&t2, 16); let t4 = &t3 * &_11001011; t4 }; let i5341 = { let t0 = square_n(&i5314, 7); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10100111; let t4 = square_n(&t3, 8); t4 }; let i5359 = { let t0 = &_10100001 * &i5341; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1011101; t4 }; let i5388 = { let t0 = square_n(&i5359, 10); let t1 = &t0 * &_10111101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11111101; let t4 = square_n(&t3, 7); t4 }; let i5406 = { let t0 = &_1011011 * &i5388; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110101; t4 }; let i5435 = { let t0 = square_n(&i5406, 10); let t1 = &t0 * &_10110001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11010011; let t4 = square_n(&t3, 9); t4 }; let i5457 = { let t0 = &_11011011 * &i5435; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11101101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1010011; t4 }; let i5485 = { let t0 = square_n(&i5457, 3); let t1 = &t0 * &_11; let t2 = square_n(&t1, 13); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 10); t4 }; let i5506 = { let t0 = &_1010101 * &i5485; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10100011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11110111; t4 }; let i5530 = { let t0 = square_n(&i5506, 8); let t1 = &t0 * &_11110011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 7); t4 }; let i5547 = { let t0 = &_111011 * &i5530; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11010111; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1011; t4 }; let i5576 = { let t0 = square_n(&i5547, 12); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 4); t4 }; let i5600 = { let t0 = &_1001 * &i5576; let t1 = square_n(&t0, 13); let t2 = &t1 * &_11001111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11001011; t4 }; let i5631 = { let t0 = square_n(&i5600, 9); let t1 = &t0 * &_10010111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 11); t4 }; let i5650 = { let t0 = &_10011111 * &i5631; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11011101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101011; t4 }; let i5676 = { let t0 = square_n(&i5650, 7); let t1 = &t0 * &_100011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10111001; let t4 = square_n(&t3, 7); t4 }; let i5697 = { let t0 = &_1001011 * &i5676; let t1 = square_n(&t0, 8); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11100011; t4 }; let i5725 = { let t0 = square_n(&i5697, 8); let t1 = &t0 * &_11001001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10011011; let t4 = square_n(&t3, 9); t4 }; let i5744 = { let t0 = &_10100111 * &i5725; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11001011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10011001; t4 }; let i5773 = { let t0 = square_n(&i5744, 7); let t1 = &t0 * &_11111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 9); t4 }; let i5793 = { let t0 = &_11100101 * &i5773; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11010111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10011001; t4 }; let i5821 = { let t0 = square_n(&i5793, 6); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11101011; let t4 = square_n(&t3, 8); t4 }; let i5844 = { let t0 = &_1111001 * &i5821; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10110111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10100001; t4 }; let i5867 = { let t0 = square_n(&i5844, 9); let t1 = &t0 * &_10111001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11001001; let t4 = square_n(&t3, 4); t4 }; let i5890 = { let t0 = &_1011 * &i5867; let t1 = square_n(&t0, 13); let t2 = &t1 * &_11110101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1001001; t4 }; let i5917 = { let t0 = square_n(&i5890, 8); let t1 = &t0 * &_1011101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10111; let t4 = square_n(&t3, 11); t4 }; let i5939 = { let t0 = &_10010101 * &i5917; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11110101; t4 }; let i5969 = { let t0 = square_n(&i5939, 5); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 12); t4 }; let i5985 = { let t0 = &_10110011 * &i5969; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10110101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10111; t4 }; let i6017 = { let t0 = square_n(&i5985, 12); let t1 = &t0 * &_11011111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11111011; let t4 = square_n(&t3, 8); t4 }; let i6037 = { let t0 = &_10101011 * &i6017; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11010001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10000011; t4 }; let i6066 = { let t0 = square_n(&i6037, 9); let t1 = &t0 * &_11011111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 7); t4 }; let i6088 = { let t0 = &_110001 * &i6066; let t1 = square_n(&t0, 5); let t2 = &t1 * &_111; let t3 = square_n(&t2, 14); let t4 = &t3 * &_11011111; t4 }; let i6112 = { let t0 = square_n(&i6088, 6); let t1 = &t0 * &_101101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 7); t4 }; let i6137 = { let t0 = &_110111 * &i6112; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 13); let t4 = &t3 * &_11100011; t4 }; let i6161 = { let t0 = square_n(&i6137, 8); let t1 = &t0 * &_10010001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 9); t4 }; let i6182 = { let t0 = &_101101 * &i6161; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110101; t4 }; let i6208 = { let t0 = square_n(&i6182, 10); let t1 = &t0 * &_10101001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10000101; let t4 = square_n(&t3, 3); t4 }; let i6235 = { let t0 = &_111 * &i6208; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 14); let t4 = &t3 * &_101001; t4 }; let i6263 = { let t0 = square_n(&i6235, 10); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10010011; let t4 = square_n(&t3, 7); t4 }; let i6283 = { let t0 = &_100111 * &i6263; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10111111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1111101; t4 }; let i6314 = { let t0 = square_n(&i6283, 12); let t1 = &t0 * &_11101111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1111101; let t4 = square_n(&t3, 8); t4 }; let result = { let t0 = &_10111 * &i6314; t0 }; result } } pub mod bls12_381 { use super::square_n; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; use lambdaworks_math::field::element::FieldElement; /// Generated from tools/addchain/bls12_381_h3_s.acc pub fn pow_h3_s( base: &FieldElement, ) -> FieldElement { let base = base.clone(); let _10 = { let t0 = square_n(&base, 1); t0 }; let _11 = { let t0 = &base * &_10; t0 }; let _101 = { let t0 = &_10 * &_11; t0 }; let _111 = { let t0 = &_10 * &_101; t0 }; let _1001 = { let t0 = &_10 * &_111; t0 }; let _1011 = { let t0 = &_10 * &_1001; t0 }; let _1101 = { let t0 = &_10 * &_1011; t0 }; let _1111 = { let t0 = &_10 * &_1101; t0 }; let _10001 = { let t0 = &_10 * &_1111; t0 }; let _10011 = { let t0 = &_10 * &_10001; t0 }; let _10101 = { let t0 = &_10 * &_10011; t0 }; let _10111 = { let t0 = &_10 * &_10101; t0 }; let _11001 = { let t0 = &_10 * &_10111; t0 }; let _11011 = { let t0 = &_10 * &_11001; t0 }; let _11101 = { let t0 = &_10 * &_11011; t0 }; let _11111 = { let t0 = &_10 * &_11101; t0 }; let _100001 = { let t0 = &_10 * &_11111; t0 }; let _100011 = { let t0 = &_10 * &_100001; t0 }; let _100101 = { let t0 = &_10 * &_100011; t0 }; let _100110 = { let t0 = &base * &_100101; t0 }; let _100111 = { let t0 = &base * &_100110; t0 }; let _101001 = { let t0 = &_10 * &_100111; t0 }; let _101011 = { let t0 = &_10 * &_101001; t0 }; let _101101 = { let t0 = &_10 * &_101011; t0 }; let _110001 = { let t0 = &_1011 * &_100110; t0 }; let _110011 = { let t0 = &_10 * &_110001; t0 }; let _110101 = { let t0 = &_10 * &_110011; t0 }; let _110111 = { let t0 = &_10 * &_110101; t0 }; let _111001 = { let t0 = &_10 * &_110111; t0 }; let _111011 = { let t0 = &_10 * &_111001; t0 }; let _111101 = { let t0 = &_10 * &_111011; t0 }; let _111111 = { let t0 = &_10 * &_111101; t0 }; let _1000001 = { let t0 = &_10 * &_111111; t0 }; let _1000011 = { let t0 = &_10 * &_1000001; t0 }; let _1000101 = { let t0 = &_10 * &_1000011; t0 }; let _1000111 = { let t0 = &_10 * &_1000101; t0 }; let _1001001 = { let t0 = &_10 * &_1000111; t0 }; let _1001011 = { let t0 = &_10 * &_1001001; t0 }; let _1001101 = { let t0 = &_10 * &_1001011; t0 }; let _1001111 = { let t0 = &_10 * &_1001101; t0 }; let _1010001 = { let t0 = &_10 * &_1001111; t0 }; let _1010011 = { let t0 = &_10 * &_1010001; t0 }; let _1010101 = { let t0 = &_10 * &_1010011; t0 }; let _1010111 = { let t0 = &_10 * &_1010101; t0 }; let _1011001 = { let t0 = &_10 * &_1010111; t0 }; let _1011011 = { let t0 = &_10 * &_1011001; t0 }; let _1011101 = { let t0 = &_10 * &_1011011; t0 }; let _1011111 = { let t0 = &_10 * &_1011101; t0 }; let _1100001 = { let t0 = &_10 * &_1011111; t0 }; let _1100011 = { let t0 = &_10 * &_1100001; t0 }; let _1100101 = { let t0 = &_10 * &_1100011; t0 }; let _1100111 = { let t0 = &_10 * &_1100101; t0 }; let _1101001 = { let t0 = &_10 * &_1100111; t0 }; let _1101011 = { let t0 = &_10 * &_1101001; t0 }; let _1101101 = { let t0 = &_10 * &_1101011; t0 }; let _1101111 = { let t0 = &_10 * &_1101101; t0 }; let _1110001 = { let t0 = &_10 * &_1101111; t0 }; let _1110011 = { let t0 = &_10 * &_1110001; t0 }; let _1110101 = { let t0 = &_10 * &_1110011; t0 }; let _1110111 = { let t0 = &_10 * &_1110101; t0 }; let _1111001 = { let t0 = &_10 * &_1110111; t0 }; let _1111011 = { let t0 = &_10 * &_1111001; t0 }; let _1111101 = { let t0 = &_10 * &_1111011; t0 }; let _1111111 = { let t0 = &_10 * &_1111101; t0 }; let _10000001 = { let t0 = &_10 * &_1111111; t0 }; let _10000011 = { let t0 = &_10 * &_10000001; t0 }; let _10000101 = { let t0 = &_10 * &_10000011; t0 }; let _10000111 = { let t0 = &_10 * &_10000101; t0 }; let _10001001 = { let t0 = &_10 * &_10000111; t0 }; let _10001011 = { let t0 = &_10 * &_10001001; t0 }; let _10001101 = { let t0 = &_10 * &_10001011; t0 }; let _10001111 = { let t0 = &_10 * &_10001101; t0 }; let _10010001 = { let t0 = &_10 * &_10001111; t0 }; let _10010011 = { let t0 = &_10 * &_10010001; t0 }; let _10010101 = { let t0 = &_10 * &_10010011; t0 }; let _10010111 = { let t0 = &_10 * &_10010101; t0 }; let _10011001 = { let t0 = &_10 * &_10010111; t0 }; let _10011011 = { let t0 = &_10 * &_10011001; t0 }; let _10011101 = { let t0 = &_10 * &_10011011; t0 }; let _10011111 = { let t0 = &_10 * &_10011101; t0 }; let _10100001 = { let t0 = &_10 * &_10011111; t0 }; let _10100011 = { let t0 = &_10 * &_10100001; t0 }; let _10100101 = { let t0 = &_10 * &_10100011; t0 }; let _10100111 = { let t0 = &_10 * &_10100101; t0 }; let _10101001 = { let t0 = &_10 * &_10100111; t0 }; let _10101011 = { let t0 = &_10 * &_10101001; t0 }; let _10101101 = { let t0 = &_10 * &_10101011; t0 }; let _10101111 = { let t0 = &_10 * &_10101101; t0 }; let _10110001 = { let t0 = &_10 * &_10101111; t0 }; let _10110011 = { let t0 = &_10 * &_10110001; t0 }; let _10110101 = { let t0 = &_10 * &_10110011; t0 }; let _10110111 = { let t0 = &_10 * &_10110101; t0 }; let _10111001 = { let t0 = &_10 * &_10110111; t0 }; let _10111011 = { let t0 = &_10 * &_10111001; t0 }; let _10111101 = { let t0 = &_10 * &_10111011; t0 }; let _10111111 = { let t0 = &_10 * &_10111101; t0 }; let _11000001 = { let t0 = &_10 * &_10111111; t0 }; let _11000011 = { let t0 = &_10 * &_11000001; t0 }; let _11000101 = { let t0 = &_10 * &_11000011; t0 }; let _11000111 = { let t0 = &_10 * &_11000101; t0 }; let _11001001 = { let t0 = &_10 * &_11000111; t0 }; let _11001011 = { let t0 = &_10 * &_11001001; t0 }; let _11001101 = { let t0 = &_10 * &_11001011; t0 }; let _11001111 = { let t0 = &_10 * &_11001101; t0 }; let _11010001 = { let t0 = &_10 * &_11001111; t0 }; let _11010011 = { let t0 = &_10 * &_11010001; t0 }; let _11010101 = { let t0 = &_10 * &_11010011; t0 }; let _11010111 = { let t0 = &_10 * &_11010101; t0 }; let _11011001 = { let t0 = &_10 * &_11010111; t0 }; let _11011011 = { let t0 = &_10 * &_11011001; t0 }; let _11011101 = { let t0 = &_10 * &_11011011; t0 }; let _11011111 = { let t0 = &_10 * &_11011101; t0 }; let _11100001 = { let t0 = &_10 * &_11011111; t0 }; let _11100011 = { let t0 = &_10 * &_11100001; t0 }; let _11100101 = { let t0 = &_10 * &_11100011; t0 }; let _11100111 = { let t0 = &_10 * &_11100101; t0 }; let _11101001 = { let t0 = &_10 * &_11100111; t0 }; let _11101011 = { let t0 = &_10 * &_11101001; t0 }; let _11101101 = { let t0 = &_10 * &_11101011; t0 }; let _11101111 = { let t0 = &_10 * &_11101101; t0 }; let _11110101 = { let t0 = &_100110 * &_11001111; t0 }; let _11110111 = { let t0 = &_10 * &_11110101; t0 }; let _11111001 = { let t0 = &_10 * &_11110111; t0 }; let _11111101 = { let t0 = &_100110 * &_11010111; t0 }; let _11111111 = { let t0 = &_10 * &_11111101; t0 }; let i145 = { let t0 = &_110001 * &_11111111; let t1 = square_n(&t0, 7); let t2 = &t1 * &_11001101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10100111; t4 }; let i172 = { let t0 = square_n(&i145, 9); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 8); t4 }; let i199 = { let t0 = &_100001 * &i172; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 14); let t4 = &t3 * &_1111101; t4 }; let i228 = { let t0 = square_n(&i199, 11); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11111101; let t4 = square_n(&t3, 7); t4 }; let i248 = { let t0 = &_1101011 * &i228; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11011001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011111; t4 }; let i274 = { let t0 = square_n(&i248, 8); let t1 = &t0 * &_1101011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 7); t4 }; let i295 = { let t0 = &_101001 * &i274; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10100011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11101011; t4 }; let i321 = { let t0 = square_n(&i295, 9); let t1 = &t0 * &_11011011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111111; let t4 = square_n(&t3, 9); t4 }; let i342 = { let t0 = &_100111 * &i321; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1011001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11000101; t4 }; let i368 = { let t0 = square_n(&i342, 7); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10010011; let t4 = square_n(&t3, 8); t4 }; let i388 = { let t0 = &_10001001 * &i368; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11101001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010011; t4 }; let i417 = { let t0 = square_n(&i388, 3); let t1 = &t0 * &_11; let t2 = square_n(&t1, 15); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 9); t4 }; let i437 = { let t0 = &_10110111 * &i417; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10010111; t4 }; let i463 = { let t0 = square_n(&i437, 9); let t1 = &t0 * &_10101001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10100111; let t4 = square_n(&t3, 6); t4 }; let i486 = { let t0 = &_10101 * &i463; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10101011; t4 }; let i513 = { let t0 = square_n(&i486, 4); let t1 = &t0 * &_101; let t2 = square_n(&t1, 13); let t3 = &t2 * &_10001101; let t4 = square_n(&t3, 8); t4 }; let i530 = { let t0 = &_10100011 * &i513; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11011101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_10011; t4 }; let i560 = { let t0 = square_n(&i530, 11); let t1 = &t0 * &_1101111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_101001; let t4 = square_n(&t3, 9); t4 }; let i582 = { let t0 = &_1001101 * &i560; let t1 = square_n(&t0, 11); let t2 = &t1 * &_10111001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11000011; t4 }; let i606 = { let t0 = square_n(&i582, 9); let t1 = &t0 * &_11100111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11010011; let t4 = square_n(&t3, 3); t4 }; let i630 = { let t0 = &_101 * &i606; let t1 = square_n(&t0, 13); let t2 = &t1 * &_10110011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11011101; t4 }; let i661 = { let t0 = square_n(&i630, 8); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_10101111; let t4 = square_n(&t3, 9); t4 }; let i679 = { let t0 = &_10010001 * &i661; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_100101; t4 }; let i708 = { let t0 = square_n(&i679, 8); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1100111; let t4 = square_n(&t3, 9); t4 }; let i727 = { let t0 = &_1100001 * &i708; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10110101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110011; t4 }; let i755 = { let t0 = square_n(&i727, 8); let t1 = &t0 * &_101101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 8); t4 }; let i776 = { let t0 = &_1110111 * &i755; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11001011; t4 }; let i806 = { let t0 = square_n(&i776, 4); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 15); t4 }; let i826 = { let t0 = &_11000011 * &i806; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10001001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1011101; t4 }; let i855 = { let t0 = square_n(&i826, 9); let t1 = &t0 * &_10011111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1100111; let t4 = square_n(&t3, 10); t4 }; let i876 = { let t0 = &_11100101 * &i855; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10101111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10001111; t4 }; let i904 = { let t0 = square_n(&i876, 7); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 10); t4 }; let i925 = { let t0 = &_1100011 * &i904; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11110111; t4 }; let i955 = { let t0 = square_n(&i925, 10); let t1 = &t0 * &_10100011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11110101; let t4 = square_n(&t3, 8); t4 }; let i978 = { let t0 = &_11101111 * &i955; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11100001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10000001; t4 }; let i1010 = { let t0 = square_n(&i978, 5); let t1 = &t0 * &_10101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1111101; let t4 = square_n(&t3, 14); t4 }; let i1029 = { let t0 = &_11101001 * &i1010; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11000101; t4 }; let i1057 = { let t0 = square_n(&i1029, 11); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101011; let t4 = square_n(&t3, 6); t4 }; let i1081 = { let t0 = &_111011 * &i1057; let t1 = square_n(&t0, 11); let t2 = &t1 * &_111101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10011101; t4 }; let i1108 = { let t0 = square_n(&i1081, 8); let t1 = &t0 * &_10000011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11010111; let t4 = square_n(&t3, 9); t4 }; let i1129 = { let t0 = &_11010001 * &i1108; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11011001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10101001; t4 }; let i1157 = { let t0 = square_n(&i1129, 5); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11010011; let t4 = square_n(&t3, 9); t4 }; let i1176 = { let t0 = &_10101101 * &i1157; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11110101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10000101; t4 }; let i1201 = { let t0 = square_n(&i1176, 7); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 8); t4 }; let i1222 = { let t0 = &_1111011 * &i1201; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11010001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11111101; t4 }; let i1250 = { let t0 = square_n(&i1222, 7); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 11); t4 }; let i1270 = { let t0 = &_11101111 * &i1250; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11101101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11111001; t4 }; let i1299 = { let t0 = square_n(&i1270, 10); let t1 = &t0 * &_10000011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 9); t4 }; let i1322 = { let t0 = &_101101 * &i1299; let t1 = square_n(&t0, 8); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1111101; t4 }; let i1354 = { let t0 = square_n(&i1322, 10); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11011001; let t4 = square_n(&t3, 9); t4 }; let i1376 = { let t0 = &_100101 * &i1354; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10001011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11101111; t4 }; let i1399 = { let t0 = square_n(&i1376, 8); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 5); t4 }; let i1423 = { let t0 = &_111 * &i1399; let t1 = square_n(&t0, 12); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_10000111; t4 }; let i1449 = { let t0 = square_n(&i1423, 7); let t1 = &t0 * &_1111111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_11011; let t4 = square_n(&t3, 10); t4 }; let i1470 = { let t0 = &_1111011 * &i1449; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10011101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11011001; t4 }; let i1499 = { let t0 = square_n(&i1470, 6); let t1 = &t0 * &_11001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_10111101; let t4 = square_n(&t3, 10); t4 }; let i1522 = { let t0 = &_1111101 * &i1499; let t1 = square_n(&t0, 12); let t2 = &t1 * &_11010001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11010011; t4 }; let i1548 = { let t0 = square_n(&i1522, 8); let t1 = &t0 * &_11000011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10010011; let t4 = square_n(&t3, 8); t4 }; let i1563 = { let t0 = &_10011001 * &i1548; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1110111; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1011; t4 }; let i1599 = { let t0 = square_n(&i1563, 18); let t1 = &t0 * &_10001101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101101; let t4 = square_n(&t3, 7); t4 }; let i1618 = { let t0 = &_1100101 * &i1599; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1111111; t4 }; let i1651 = { let t0 = square_n(&i1618, 10); let t1 = &t0 * &_10010101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 11); t4 }; let i1672 = { let t0 = &_11100111 * &i1651; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1000001; t4 }; let i1701 = { let t0 = square_n(&i1672, 9); let t1 = &t0 * &_10100011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10010111; let t4 = square_n(&t3, 8); t4 }; let i1720 = { let t0 = &_11101001 * &i1701; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110011; t4 }; let i1752 = { let t0 = square_n(&i1720, 8); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 10); t4 }; let i1775 = { let t0 = &_1101001 * &i1752; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000001; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11001111; t4 }; let i1801 = { let t0 = square_n(&i1775, 6); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11010011; let t4 = square_n(&t3, 8); t4 }; let i1825 = { let t0 = &_11001011 * &i1801; let t1 = square_n(&t0, 13); let t2 = &t1 * &_11101001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10010111; t4 }; let i1852 = { let t0 = square_n(&i1825, 7); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11001001; let t4 = square_n(&t3, 8); t4 }; let i1874 = { let t0 = &_11111101 * &i1852; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1010111; t4 }; let i1906 = { let t0 = square_n(&i1874, 11); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 10); t4 }; let i1925 = { let t0 = &_10111001 * &i1906; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10011001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10110101; t4 }; let i1954 = { let t0 = square_n(&i1925, 11); let t1 = &t0 * &_10100011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010101; let t4 = square_n(&t3, 9); t4 }; let i1971 = { let t0 = &_11001011 * &i1954; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10110111; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10001; t4 }; let i2003 = { let t0 = square_n(&i1971, 11); let t1 = &t0 * &_1101011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 10); t4 }; let i2023 = { let t0 = &_11110111 * &i2003; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11011; t4 }; let i2052 = { let t0 = square_n(&i2023, 10); let t1 = &t0 * &_1001001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 11); t4 }; let i2076 = { let t0 = &_10011011 * &i2052; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100111; let t3 = square_n(&t2, 13); let t4 = &t3 * &_11001001; t4 }; let i2102 = { let t0 = square_n(&i2076, 8); let t1 = &t0 * &_11110111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11100101; let t4 = square_n(&t3, 8); t4 }; let i2127 = { let t0 = &_10111011 * &i2102; let t1 = square_n(&t0, 7); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 15); let t4 = &t3 * &_11101011; t4 }; let i2153 = { let t0 = square_n(&i2127, 9); let t1 = &t0 * &_11010011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10001; let t4 = square_n(&t3, 9); t4 }; let i2178 = { let t0 = &_110111 * &i2153; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11101001; let t3 = square_n(&t2, 12); let t4 = &t3 * &_11100011; t4 }; let i2205 = { let t0 = square_n(&i2178, 7); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101111; let t4 = square_n(&t3, 9); t4 }; let i2237 = { let t0 = &_10001 * &i2205; let t1 = square_n(&t0, 20); let t2 = &t1 * &_11111111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11111001; t4 }; let i2267 = { let t0 = square_n(&i2237, 8); let t1 = &t0 * &_10011111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_101001; let t4 = square_n(&t3, 12); t4 }; let i2287 = { let t0 = &_10110011 * &i2267; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10111111; t4 }; let i2312 = { let t0 = square_n(&i2287, 8); let t1 = &t0 * &_11111101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11011001; let t4 = square_n(&t3, 7); t4 }; let i2333 = { let t0 = &_1011111 * &i2312; let t1 = square_n(&t0, 8); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10011101; t4 }; let i2357 = { let t0 = square_n(&i2333, 8); let t1 = &t0 * &_11101001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10101001; let t4 = square_n(&t3, 4); t4 }; let i2381 = { let t0 = &_111 * &i2357; let t1 = square_n(&t0, 14); let t2 = &t1 * &_10010101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101011; t4 }; let i2407 = { let t0 = square_n(&i2381, 9); let t1 = &t0 * &_1111111; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1011; let t4 = square_n(&t3, 10); t4 }; let i2428 = { let t0 = &_101101 * &i2407; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11101; t4 }; let i2458 = { let t0 = square_n(&i2428, 11); let t1 = &t0 * &_10101111; let t2 = square_n(&t1, 4); let t3 = &t2 * &_11; let t4 = square_n(&t3, 13); t4 }; let i2482 = { let t0 = &_110111 * &i2458; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10110011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1100111; t4 }; let i2514 = { let t0 = square_n(&i2482, 10); let t1 = &t0 * &_1101001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 11); t4 }; let i2536 = { let t0 = &_1101001 * &i2514; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10011001; t4 }; let i2564 = { let t0 = square_n(&i2536, 4); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 15); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 7); t4 }; let i2586 = { let t0 = &_11011 * &i2564; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10111101; t4 }; let i2612 = { let t0 = square_n(&i2586, 6); let t1 = &t0 * &_110011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_11111; let t4 = square_n(&t3, 11); t4 }; let i2633 = { let t0 = &_11100101 * &i2612; let t1 = square_n(&t0, 8); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10101111; t4 }; let i2661 = { let t0 = square_n(&i2633, 8); let t1 = &t0 * &_10000111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 11); t4 }; let i2685 = { let t0 = &_11100101 * &i2661; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11010111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10000001; t4 }; let i2715 = { let t0 = square_n(&i2685, 6); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11100001; let t4 = square_n(&t3, 10); t4 }; let i2737 = { let t0 = &_1011111 * &i2715; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11001101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1111011; t4 }; let i2767 = { let t0 = square_n(&i2737, 8); let t1 = &t0 * &_1100011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 12); t4 }; let i2789 = { let t0 = &_10101111 * &i2767; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10010011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11011001; t4 }; let i2815 = { let t0 = square_n(&i2789, 9); let t1 = &t0 * &_1100111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10101101; let t4 = square_n(&t3, 5); t4 }; let i2839 = { let t0 = &_11011 * &i2815; let t1 = square_n(&t0, 11); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001111; t4 }; let i2866 = { let t0 = square_n(&i2839, 9); let t1 = &t0 * &_11110101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 9); t4 }; let i2888 = { let t0 = &_10110001 * &i2866; let t1 = square_n(&t0, 3); let t2 = &t1 * &_101; let t3 = square_n(&t2, 16); let t4 = &t3 * &_10011111; t4 }; let i2912 = { let t0 = square_n(&i2888, 7); let t1 = &t0 * &_1011101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 9); t4 }; let i2934 = { let t0 = &_100011 * &i2912; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10111101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1001011; t4 }; let i2960 = { let t0 = square_n(&i2934, 6); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11111001; let t4 = square_n(&t3, 6); t4 }; let i2982 = { let t0 = &_101001 * &i2960; let t1 = square_n(&t0, 13); let t2 = &t1 * &_10001101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111011; t4 }; let i3017 = { let t0 = square_n(&i2982, 11); let t1 = &t0 * &_10001001; let t2 = square_n(&t1, 15); let t3 = &t2 * &_11111001; let t4 = square_n(&t3, 7); t4 }; let i3042 = { let t0 = &_111011 * &i3017; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 13); let t4 = &t3 * &_10111011; t4 }; let i3071 = { let t0 = square_n(&i3042, 9); let t1 = &t0 * &_11001011; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1111; let t4 = square_n(&t3, 14); t4 }; let i3096 = { let t0 = &_10001001 * &i3071; let t1 = square_n(&t0, 13); let t2 = &t1 * &_10011011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100111; t4 }; let i3123 = { let t0 = square_n(&i3096, 10); let t1 = &t0 * &_11110101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 8); t4 }; let i3146 = { let t0 = &_1100001 * &i3123; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11111111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1011001; t4 }; let i3174 = { let t0 = square_n(&i3146, 9); let t1 = &t0 * &_11001101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 10); t4 }; let i3193 = { let t0 = &_11000111 * &i3174; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11001011; t4 }; let i3221 = { let t0 = square_n(&i3193, 5); let t1 = &t0 * &_10001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 13); t4 }; let i3241 = { let t0 = &_1101101 * &i3221; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11000011; t4 }; let i3269 = { let t0 = square_n(&i3241, 9); let t1 = &t0 * &_11101001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10011111; let t4 = square_n(&t3, 8); t4 }; let i3288 = { let t0 = &_10110011 * &i3269; let t1 = square_n(&t0, 3); let t2 = &t1 * &_11; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1000001; t4 }; let i3317 = { let t0 = square_n(&i3288, 10); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 9); t4 }; let i3340 = { let t0 = &_1000101 * &i3317; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11001001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1000101; t4 }; let i3366 = { let t0 = square_n(&i3340, 8); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 3); let t3 = &t2 * &_11; let t4 = square_n(&t3, 13); t4 }; let i3386 = { let t0 = &_1001011 * &i3366; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110011; t4 }; let i3414 = { let t0 = square_n(&i3386, 10); let t1 = &t0 * &_10110101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101101; let t4 = square_n(&t3, 7); t4 }; let i3433 = { let t0 = &_1010001 * &i3414; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10001111; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1101; t4 }; let i3463 = { let t0 = square_n(&i3433, 12); let t1 = &t0 * &_10000111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 9); t4 }; let i3485 = { let t0 = &_1110101 * &i3463; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11111101; t4 }; let i3514 = { let t0 = square_n(&i3485, 9); let t1 = &t0 * &_11000001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 10); t4 }; let i3534 = { let t0 = &_1101001 * &i3514; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11000111; t4 }; let i3564 = { let t0 = square_n(&i3534, 8); let t1 = &t0 * &_10000011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10110011; let t4 = square_n(&t3, 12); t4 }; let i3580 = { let t0 = &_10011111 * &i3564; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1011; t4 }; let i3611 = { let t0 = square_n(&i3580, 11); let t1 = &t0 * &_1111001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11000011; let t4 = square_n(&t3, 8); t4 }; let i3633 = { let t0 = &_10011111 * &i3611; let t1 = square_n(&t0, 11); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_101; t4 }; let i3663 = { let t0 = square_n(&i3633, 13); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 8); t4 }; let i3684 = { let t0 = &_100011 * &i3663; let t1 = square_n(&t0, 10); let t2 = &t1 * &_10011111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101001; t4 }; let i3712 = { let t0 = square_n(&i3684, 7); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 9); t4 }; let i3733 = { let t0 = &_1110001 * &i3712; let t1 = square_n(&t0, 9); let t2 = &t1 * &_101001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11001; t4 }; let i3766 = { let t0 = square_n(&i3733, 14); let t1 = &t0 * &_11011001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10101101; let t4 = square_n(&t3, 7); t4 }; let i3789 = { let t0 = &_100111 * &i3766; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11101111; t4 }; let i3814 = { let t0 = square_n(&i3789, 9); let t1 = &t0 * &_11100001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11010001; let t4 = square_n(&t3, 6); t4 }; let i3838 = { let t0 = &_100101 * &i3814; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11011001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11101001; t4 }; let i3864 = { let t0 = square_n(&i3838, 8); let t1 = &t0 * &_11111111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11110111; let t4 = square_n(&t3, 8); t4 }; let i3884 = { let t0 = &_10101111 * &i3864; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10100001; t4 }; let i3910 = { let t0 = square_n(&i3884, 8); let t1 = &t0 * &_11010101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10000001; let t4 = square_n(&t3, 7); t4 }; let i3932 = { let t0 = &_1010001 * &i3910; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1000011; t4 }; let i3958 = { let t0 = square_n(&i3932, 8); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001101; let t4 = square_n(&t3, 8); t4 }; let i3980 = { let t0 = &_1100011 * &i3958; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11111101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11100001; t4 }; let i4013 = { let t0 = square_n(&i3980, 12); let t1 = &t0 * &_11001111; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1101; let t4 = square_n(&t3, 14); t4 }; let i4033 = { let t0 = &_10100101 * &i4013; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_10110111; t4 }; let i4065 = { let t0 = square_n(&i4033, 12); let t1 = &t0 * &_11100111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11100001; let t4 = square_n(&t3, 7); t4 }; let i4087 = { let t0 = &_1010101 * &i4065; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11101011; t4 }; let i4116 = { let t0 = square_n(&i4087, 8); let t1 = &t0 * &_10110101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 11); t4 }; let i4136 = { let t0 = &_11001011 * &i4116; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10001011; t4 }; let i4162 = { let t0 = square_n(&i4136, 4); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101; let t4 = square_n(&t3, 13); t4 }; let i4181 = { let t0 = &_10111001 * &i4162; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10101101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10100111; t4 }; let i4208 = { let t0 = square_n(&i4181, 8); let t1 = &t0 * &_10010101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11110101; let t4 = square_n(&t3, 8); t4 }; let i4227 = { let t0 = &_11001001 * &i4208; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10101101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101001; t4 }; let i4263 = { let t0 = square_n(&i4227, 17); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001011; let t4 = square_n(&t3, 9); t4 }; let i4284 = { let t0 = &_10001 * &i4263; let t1 = square_n(&t0, 11); let t2 = &t1 * &_11001001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_111111; t4 }; let i4316 = { let t0 = square_n(&i4284, 14); let t1 = &t0 * &_11111001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11101011; let t4 = square_n(&t3, 8); t4 }; let i4344 = { let t0 = &_1101011 * &i4316; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10001111; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1000011; t4 }; let i4375 = { let t0 = square_n(&i4344, 8); let t1 = &t0 * &_1011001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 11); t4 }; let i4389 = { let t0 = &_11110111 * &i4375; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 4); let t4 = &t3 * &_101; t4 }; let i4421 = { let t0 = square_n(&i4389, 12); let t1 = &t0 * &_100001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 11); t4 }; let i4440 = { let t0 = &_10001001 * &i4421; let t1 = square_n(&t0, 8); let t2 = &t1 * &_10111011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1000101; t4 }; let i4475 = { let t0 = square_n(&i4440, 11); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_11001; let t4 = square_n(&t3, 10); t4 }; let i4493 = { let t0 = &_1011111 * &i4475; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1111101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_100001; t4 }; let i4523 = { let t0 = square_n(&i4493, 11); let t1 = &t0 * &_11101011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111111; let t4 = square_n(&t3, 11); t4 }; let i4545 = { let t0 = &_10010111 * &i4523; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11110101; t4 }; let i4565 = { let t0 = square_n(&i4545, 6); let t1 = &t0 * &_110011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_10101001; let t4 = square_n(&t3, 2); t4 }; let i4590 = { let t0 = &base * &i4565; let t1 = square_n(&t0, 16); let t2 = &t1 * &_10100011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111111; t4 }; let i4620 = { let t0 = square_n(&i4590, 7); let t1 = &t0 * &_10001; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 11); t4 }; let i4638 = { let t0 = &_1101111 * &i4620; let t1 = square_n(&t0, 9); let t2 = &t1 * &_10000101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_100111; t4 }; let i4665 = { let t0 = square_n(&i4638, 13); let t1 = &t0 * &_111111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_11011101; let t4 = square_n(&t3, 2); t4 }; let i4687 = { let t0 = &base * &i4665; let t1 = square_n(&t0, 14); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_1111; t4 }; let i4719 = { let t0 = square_n(&i4687, 14); let t1 = &t0 * &_10000111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_11110101; let t4 = square_n(&t3, 8); t4 }; let i4741 = { let t0 = &_11011001 * &i4719; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11011111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11000011; t4 }; let i4767 = { let t0 = square_n(&i4741, 7); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10001011; let t4 = square_n(&t3, 8); t4 }; let i4787 = { let t0 = &_1010011 * &i4767; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_110011; t4 }; let i4814 = { let t0 = square_n(&i4787, 11); let t1 = &t0 * &_1111001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_11100001; let t4 = square_n(&t3, 5); t4 }; let i4836 = { let t0 = &_11101 * &i4814; let t1 = square_n(&t0, 12); let t2 = &t1 * &_10000101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1010111; t4 }; let i4867 = { let t0 = square_n(&i4836, 10); let t1 = &t0 * &_11010101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_11011001; let t4 = square_n(&t3, 8); t4 }; let i4886 = { let t0 = &_11011111 * &i4867; let t1 = square_n(&t0, 4); let t2 = &t1 * &_111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_10001; t4 }; let result = { let t0 = square_n(&i4886, 7); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1111; let t4 = square_n(&t3, 4); t4 }; result } /// Generated from tools/addchain/bls12_381_e.acc pub fn pow_e( base: &FieldElement, ) -> FieldElement { let base = base.clone(); let _10 = { let t0 = square_n(&base, 1); t0 }; let _11 = { let t0 = &base * &_10; t0 }; let _101 = { let t0 = &_10 * &_11; t0 }; let _111 = { let t0 = &_10 * &_101; t0 }; let _1001 = { let t0 = &_10 * &_111; t0 }; let _1011 = { let t0 = &_10 * &_1001; t0 }; let _1101 = { let t0 = &_10 * &_1011; t0 }; let _1111 = { let t0 = &_10 * &_1101; t0 }; let _10001 = { let t0 = &_10 * &_1111; t0 }; let _10011 = { let t0 = &_10 * &_10001; t0 }; let _10101 = { let t0 = &_10 * &_10011; t0 }; let _10111 = { let t0 = &_10 * &_10101; t0 }; let _11001 = { let t0 = &_10 * &_10111; t0 }; let _11011 = { let t0 = &_10 * &_11001; t0 }; let _11101 = { let t0 = &_10 * &_11011; t0 }; let _11111 = { let t0 = &_10 * &_11101; t0 }; let _100001 = { let t0 = &_10 * &_11111; t0 }; let _100011 = { let t0 = &_10 * &_100001; t0 }; let _100101 = { let t0 = &_10 * &_100011; t0 }; let _100111 = { let t0 = &_10 * &_100101; t0 }; let _101001 = { let t0 = &_10 * &_100111; t0 }; let _101011 = { let t0 = &_10 * &_101001; t0 }; let _101101 = { let t0 = &_10 * &_101011; t0 }; let _101111 = { let t0 = &_10 * &_101101; t0 }; let _110001 = { let t0 = &_10 * &_101111; t0 }; let _110011 = { let t0 = &_10 * &_110001; t0 }; let _110101 = { let t0 = &_10 * &_110011; t0 }; let _110111 = { let t0 = &_10 * &_110101; t0 }; let _111001 = { let t0 = &_10 * &_110111; t0 }; let _111011 = { let t0 = &_10 * &_111001; t0 }; let _111101 = { let t0 = &_10 * &_111011; t0 }; let _111111 = { let t0 = &_10 * &_111101; t0 }; let _1000001 = { let t0 = &_10 * &_111111; t0 }; let _1000011 = { let t0 = &_10 * &_1000001; t0 }; let _1000101 = { let t0 = &_10 * &_1000011; t0 }; let _1000111 = { let t0 = &_10 * &_1000101; t0 }; let _1001001 = { let t0 = &_10 * &_1000111; t0 }; let _1001011 = { let t0 = &_10 * &_1001001; t0 }; let _1001101 = { let t0 = &_10 * &_1001011; t0 }; let _1001111 = { let t0 = &_10 * &_1001101; t0 }; let _1010001 = { let t0 = &_10 * &_1001111; t0 }; let _1010011 = { let t0 = &_10 * &_1010001; t0 }; let _1010101 = { let t0 = &_10 * &_1010011; t0 }; let _1010111 = { let t0 = &_10 * &_1010101; t0 }; let _1011001 = { let t0 = &_10 * &_1010111; t0 }; let _1011011 = { let t0 = &_10 * &_1011001; t0 }; let _1011101 = { let t0 = &_10 * &_1011011; t0 }; let _1011111 = { let t0 = &_10 * &_1011101; t0 }; let _1100001 = { let t0 = &_10 * &_1011111; t0 }; let _1100011 = { let t0 = &_10 * &_1100001; t0 }; let _1100101 = { let t0 = &_10 * &_1100011; t0 }; let _1100111 = { let t0 = &_10 * &_1100101; t0 }; let _1101001 = { let t0 = &_10 * &_1100111; t0 }; let _1101011 = { let t0 = &_10 * &_1101001; t0 }; let _1101101 = { let t0 = &_10 * &_1101011; t0 }; let _1101111 = { let t0 = &_10 * &_1101101; t0 }; let _1110001 = { let t0 = &_10 * &_1101111; t0 }; let _1110011 = { let t0 = &_10 * &_1110001; t0 }; let _1110101 = { let t0 = &_10 * &_1110011; t0 }; let _1110111 = { let t0 = &_10 * &_1110101; t0 }; let _1111001 = { let t0 = &_10 * &_1110111; t0 }; let _1111011 = { let t0 = &_10 * &_1111001; t0 }; let _1111101 = { let t0 = &_10 * &_1111011; t0 }; let _1111111 = { let t0 = &_10 * &_1111101; t0 }; let _11111110 = { let t0 = square_n(&_1111111, 1); t0 }; let _11111111 = { let t0 = &base * &_11111110; t0 }; let x9 = { let t0 = square_n(&_11111111, 1); let t1 = &t0 * &base; t1 }; let i69 = { let t0 = &_1110001 * &x9; t0 }; let x10 = { let t0 = square_n(&x9, 1); let t1 = &t0 * &base; t1 }; let i72 = { let t0 = square_n(&i69, 1); t0 }; let x11 = { let t0 = square_n(&x10, 1); let t1 = &t0 * &base; t1 }; let i95 = { let t0 = square_n(&i72, 2); let t1 = &t0 * &_101001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 9); t4 }; let i118 = { let t0 = &_1100101 * &i95; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1100101; let t3 = square_n(&t2, 13); let t4 = &t3 * &_1101011; t4 }; let i140 = { let t0 = square_n(&i118, 7); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 4); let t3 = &t2 * &_101; let t4 = square_n(&t3, 9); t4 }; let i163 = { let t0 = &_101 * &i140; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1110111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10001; t4 }; let i188 = { let t0 = square_n(&i163, 9); let t1 = &t0 * &_100001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 7); t4 }; let i214 = { let t0 = &_101011 * &i188; let t1 = square_n(&t0, 7); let t2 = &t1 * &_11; let t3 = square_n(&t2, 16); let t4 = &t3 * &_111001; t4 }; let i242 = { let t0 = square_n(&i214, 8); let t1 = &t0 * &_101001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_111011; let t4 = square_n(&t3, 10); t4 }; let i258 = { let t0 = &_1010011 * &i242; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_101001; t4 }; let i286 = { let t0 = square_n(&i258, 9); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1101; let t4 = square_n(&t3, 10); t4 }; let i306 = { let t0 = &_1100011 * &i286; let t1 = square_n(&t0, 7); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1110111; t4 }; let i331 = { let t0 = square_n(&i306, 7); let t1 = &t0 * &_1110001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 9); t4 }; let i349 = { let t0 = &_1000111 * &i331; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101; t4 }; let i380 = { let t0 = square_n(&i349, 9); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 10); t4 }; let i400 = { let t0 = &_110101 * &i380; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101101; t4 }; let i428 = { let t0 = square_n(&i400, 8); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 7); t4 }; let i449 = { let t0 = &_1110111 * &i428; let t1 = square_n(&t0, 8); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1000011; t4 }; let i473 = { let t0 = square_n(&i449, 7); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100101; let t4 = square_n(&t3, 9); t4 }; let i489 = { let t0 = &_1010001 * &i473; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1001; t4 }; let i518 = { let t0 = square_n(&i489, 12); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 7); t4 }; let i537 = { let t0 = &_1101111 * &i518; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1110111; t4 }; let i562 = { let t0 = square_n(&i537, 8); let t1 = &t0 * &_1001001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 10); t4 }; let i578 = { let t0 = &_101111 * &i562; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1001101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_10001; t4 }; let i609 = { let t0 = square_n(&i578, 9); let t1 = &t0 * &_1011101; let t2 = square_n(&t1, 13); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 7); t4 }; let i627 = { let t0 = &_110001 * &i609; let t1 = square_n(&t0, 6); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1100111; t4 }; let i651 = { let t0 = square_n(&i627, 7); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 5); t4 }; let i672 = { let t0 = &_10001 * &i651; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1000001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1100011; t4 }; let i699 = { let t0 = square_n(&i672, 10); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1001101; let t4 = square_n(&t3, 7); t4 }; let i715 = { let t0 = &_1110101 * &i699; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000011; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1101; t4 }; let i742 = { let t0 = square_n(&i715, 14); let t1 = &t0 * &_1010101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111101; let t4 = square_n(&t3, 5); t4 }; let i764 = { let t0 = &_111 * &i742; let t1 = square_n(&t0, 10); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1101001; t4 }; let i789 = { let t0 = square_n(&i764, 7); let t1 = &t0 * &_1100101; let t2 = square_n(&t1, 3); let t3 = &t2 * &_11; let t4 = square_n(&t3, 13); t4 }; let i807 = { let t0 = &_1010011 * &i789; let t1 = square_n(&t0, 4); let t2 = &t1 * &_11; let t3 = square_n(&t2, 11); let t4 = &t3 * &_11001; t4 }; let i833 = { let t0 = square_n(&i807, 9); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 7); t4 }; let i855 = { let t0 = &_1100111 * &i833; let t1 = square_n(&t0, 2); let t2 = &t1 * &_11; let t3 = square_n(&t2, 17); let t4 = &t3 * &x11; t4 }; let i882 = { let t0 = square_n(&i855, 7); let t1 = &t0 * &_101111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 8); t4 }; let i902 = { let t0 = &_1001111 * &i882; let t1 = square_n(&t0, 7); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_11111111; t4 }; let i928 = { let t0 = square_n(&i902, 8); let t1 = &t0 * &_100111; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 8); t4 }; let i946 = { let t0 = &_10111 * &i928; let t1 = square_n(&t0, 6); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_11011; t4 }; let i971 = { let t0 = square_n(&i946, 9); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_11101; let t4 = square_n(&t3, 8); t4 }; let i992 = { let t0 = &_100011 * &i971; let t1 = square_n(&t0, 10); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10101; t4 }; let i1018 = { let t0 = square_n(&i992, 10); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_111111; let t4 = square_n(&t3, 7); t4 }; let i1039 = { let t0 = &_101101 * &i1018; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_101111; t4 }; let i1063 = { let t0 = square_n(&i1039, 8); let t1 = &t0 * &_1001001; let t2 = square_n(&t1, 6); let t3 = &t2 * &_111001; let t4 = square_n(&t3, 8); t4 }; let i1081 = { let t0 = &_110111 * &i1063; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1111001; t4 }; let i1101 = { let t0 = square_n(&i1081, 6); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 4); t4 }; let i1123 = { let t0 = &_1101 * &i1101; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1111011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110001; t4 }; let i1147 = { let t0 = square_n(&i1123, 8); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1000001; let t4 = square_n(&t3, 7); t4 }; let i1163 = { let t0 = &_1100001 * &i1147; let t1 = square_n(&t0, 6); let t2 = &t1 * &_111011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_100111; t4 }; let i1193 = { let t0 = square_n(&i1163, 8); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1111111; let t4 = square_n(&t3, 9); t4 }; let i1210 = { let t0 = &_1001101 * &i1193; let t1 = square_n(&t0, 6); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1011011; t4 }; let i1233 = { let t0 = square_n(&i1210, 7); let t1 = &t0 * &_1110111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1001011; let t4 = square_n(&t3, 7); t4 }; let i1254 = { let t0 = &_110101 * &i1233; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101111; t4 }; let i1283 = { let t0 = square_n(&i1254, 7); let t1 = &t0 * &_101101; let t2 = square_n(&t1, 5); let t3 = &t2 * &_111; let t4 = square_n(&t3, 15); t4 }; let i1297 = { let t0 = &_1000001 * &i1283; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 3); let t4 = &t3 * &base; t4 }; let i1331 = { let t0 = square_n(&i1297, 15); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 9); t4 }; let i1351 = { let t0 = &_1111011 * &i1331; let t1 = square_n(&t0, 7); let t2 = &t1 * &_10011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1011101; t4 }; let i1372 = { let t0 = square_n(&i1351, 8); let t1 = &t0 * &_1110111; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10111; let t4 = square_n(&t3, 6); t4 }; let i1395 = { let t0 = &_1011 * &i1372; let t1 = square_n(&t0, 6); let t2 = &t1 * &_11; let t3 = square_n(&t2, 14); let t4 = &t3 * &x11; t4 }; let i1415 = { let t0 = square_n(&i1395, 1); let t1 = &t0 * &base; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 9); t4 }; let i1437 = { let t0 = &_1110101 * &i1415; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101011; t4 }; let i1459 = { let t0 = square_n(&i1437, 8); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 3); let t3 = &t2 * &base; let t4 = square_n(&t3, 9); t4 }; let i1480 = { let t0 = &_11111111 * &i1459; let t1 = square_n(&t0, 11); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110011; t4 }; let i1503 = { let t0 = square_n(&i1480, 7); let t1 = &t0 * &_111111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 7); t4 }; let i1529 = { let t0 = &_100101 * &i1503; let t1 = square_n(&t0, 13); let t2 = &t1 * &_1000001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001101; t4 }; let i1553 = { let t0 = square_n(&i1529, 8); let t1 = &t0 * &_1100101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010101; let t4 = square_n(&t3, 6); t4 }; let i1573 = { let t0 = &_100101 * &i1553; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1011101; t4 }; let i1599 = { let t0 = square_n(&i1573, 6); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1011111; let t4 = square_n(&t3, 10); t4 }; let i1617 = { let t0 = &_1011101 * &i1599; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1001111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1111001; t4 }; let i1642 = { let t0 = square_n(&i1617, 8); let t1 = &t0 * &_1100001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 8); t4 }; let i1662 = { let t0 = &_1001001 * &i1642; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001001; t4 }; let i1695 = { let t0 = square_n(&i1662, 12); let t1 = &t0 * &_1011101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 10); t4 }; let i1713 = { let t0 = &_111101 * &i1695; let t1 = square_n(&t0, 8); let t2 = &t1 * &_111011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_111101; t4 }; let i1735 = { let t0 = square_n(&i1713, 6); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1101011; let t4 = square_n(&t3, 5); t4 }; let i1758 = { let t0 = &_11011 * &i1735; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1001011; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001001; t4 }; let i1782 = { let t0 = square_n(&i1758, 4); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 7); t4 }; let i1803 = { let t0 = &_10101 * &i1782; let t1 = square_n(&t0, 9); let t2 = &t1 * &_111001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1000011; t4 }; let i1829 = { let t0 = square_n(&i1803, 5); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 9); t4 }; let i1846 = { let t0 = &_1110011 * &i1829; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1100001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_110011; t4 }; let i1875 = { let t0 = square_n(&i1846, 9); let t1 = &t0 * &_110001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101101; let t4 = square_n(&t3, 11); t4 }; let i1898 = { let t0 = &_1100111 * &i1875; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1101101; t4 }; let i1927 = { let t0 = square_n(&i1898, 11); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 9); t4 }; let i1945 = { let t0 = &_1101001 * &i1927; let t1 = square_n(&t0, 4); let t2 = &t1 * &_1011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1100011; t4 }; let i1967 = { let t0 = square_n(&i1945, 4); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1001111; let t4 = square_n(&t3, 5); t4 }; let i1986 = { let t0 = &_10111 * &i1967; let t1 = square_n(&t0, 6); let t2 = &t1 * &_1001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1001011; t4 }; let i2009 = { let t0 = square_n(&i1986, 8); let t1 = &t0 * &_1011011; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 9); t4 }; let i2029 = { let t0 = &_100101 * &i2009; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11111111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101011; t4 }; let i2057 = { let t0 = square_n(&i2029, 10); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1011011; let t4 = square_n(&t3, 6); t4 }; let i2075 = { let t0 = &_111001 * &i2057; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1101001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_101111; t4 }; let i2100 = { let t0 = square_n(&i2075, 7); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1110011; let t4 = square_n(&t3, 7); t4 }; let i2125 = { let t0 = &_1110011 * &i2100; let t1 = square_n(&t0, 10); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1110001; t4 }; let i2153 = { let t0 = square_n(&i2125, 6); let t1 = &t0 * &_11; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1101101; let t4 = square_n(&t3, 8); t4 }; let i2171 = { let t0 = &_110011 * &i2153; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1011011; t4 }; let i2199 = { let t0 = square_n(&i2171, 10); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 9); t4 }; let i2220 = { let t0 = &_1111111 * &i2199; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1110001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101111; t4 }; let i2244 = { let t0 = square_n(&i2220, 9); let t1 = &t0 * &_1001101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 6); t4 }; let i2264 = { let t0 = &_1011 * &i2244; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1010001; let t3 = square_n(&t2, 6); let t4 = &t3 * &_11001; t4 }; let i2289 = { let t0 = square_n(&i2264, 10); let t1 = &t0 * &_1101001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 5); t4 }; let i2309 = { let t0 = &_10111 * &i2289; let t1 = square_n(&t0, 6); let t2 = &t1 * &_101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1010011; t4 }; let i2333 = { let t0 = square_n(&i2309, 6); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1101; let t4 = square_n(&t3, 11); t4 }; let i2354 = { let t0 = &_110101 * &i2333; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1111011; t4 }; let i2378 = { let t0 = square_n(&i2354, 8); let t1 = &t0 * &_1110111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_1011; let t4 = square_n(&t3, 8); t4 }; let i2398 = { let t0 = &_11001 * &i2378; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11111111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1011111; t4 }; let i2427 = { let t0 = square_n(&i2398, 6); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 13); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 8); t4 }; let i2444 = { let t0 = &_1100001 * &i2427; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1101001; t4 }; let i2470 = { let t0 = square_n(&i2444, 9); let t1 = &t0 * &_1010111; let t2 = square_n(&t1, 3); let t3 = &t2 * &_111; let t4 = square_n(&t3, 12); t4 }; let i2487 = { let t0 = &_1000011 * &i2470; let t1 = square_n(&t0, 6); let t2 = &t1 * &_100011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1011111; t4 }; let i2519 = { let t0 = square_n(&i2487, 10); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_101011; let t4 = square_n(&t3, 10); t4 }; let i2538 = { let t0 = &_11111111 * &i2519; let t1 = square_n(&t0, 9); let t2 = &t1 * &_111101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_11111; t4 }; let i2566 = { let t0 = square_n(&i2538, 7); let t1 = &t0 * &_11001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 10); t4 }; let i2586 = { let t0 = &_1111001 * &i2566; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_10101; t4 }; let i2609 = { let t0 = square_n(&i2586, 9); let t1 = &t0 * &_1110001; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 7); t4 }; let i2631 = { let t0 = &_1011 * &i2609; let t1 = square_n(&t0, 12); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000011; t4 }; let i2658 = { let t0 = square_n(&i2631, 9); let t1 = &t0 * &_1011001; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100101; let t4 = square_n(&t3, 7); t4 }; let i2679 = { let t0 = &_1010111 * &i2658; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_11111; t4 }; let i2703 = { let t0 = square_n(&i2679, 7); let t1 = &t0 * &_10111; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1110011; let t4 = square_n(&t3, 5); t4 }; let i2725 = { let t0 = &_10111 * &i2703; let t1 = square_n(&t0, 9); let t2 = &t1 * &_100101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1011101; t4 }; let i2749 = { let t0 = square_n(&i2725, 4); let t1 = &t0 * &_1111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1010011; let t4 = square_n(&t3, 7); t4 }; let i2771 = { let t0 = &_1000001 * &i2749; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1100101; t4 }; let i2799 = { let t0 = square_n(&i2771, 1); let t1 = &t0 * &base; let t2 = square_n(&t1, 17); let t3 = &t2 * &_1000001; let t4 = square_n(&t3, 8); t4 }; let i2815 = { let t0 = &_1011101 * &i2799; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1010101; let t3 = square_n(&t2, 6); let t4 = &t3 * &_111011; t4 }; let i2842 = { let t0 = square_n(&i2815, 8); let t1 = &t0 * &_1100011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_11011; let t4 = square_n(&t3, 12); t4 }; let i2861 = { let t0 = &_1101011 * &i2842; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1000111; t4 }; let i2882 = { let t0 = square_n(&i2861, 2); let t1 = &t0 * &base; let t2 = square_n(&t1, 10); let t3 = &t2 * &x9; let t4 = square_n(&t3, 7); t4 }; let i2900 = { let t0 = &_101101 * &i2882; let t1 = square_n(&t0, 3); let t2 = &t1 * &_11; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1110111; t4 }; let i2929 = { let t0 = square_n(&i2900, 6); let t1 = &t0 * &base; let t2 = square_n(&t1, 12); let t3 = &t2 * &_100111; let t4 = square_n(&t3, 9); t4 }; let i2949 = { let t0 = &_1010001 * &i2929; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1100011; t4 }; let i2971 = { let t0 = square_n(&i2949, 6); let t1 = &t0 * &_101111; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1110011; let t4 = square_n(&t3, 3); t4 }; let i2990 = { let t0 = &_111 * &i2971; let t1 = square_n(&t0, 11); let t2 = &t1 * &_1010111; let t3 = square_n(&t2, 5); let t4 = &t3 * &_11101; t4 }; let i3017 = { let t0 = square_n(&i2990, 9); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_1101; let t4 = square_n(&t3, 11); t4 }; let i3037 = { let t0 = &x9 * &i3017; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1101011; t4 }; let i3061 = { let t0 = square_n(&i3037, 7); let t1 = &t0 * &_1110111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i3081 = { let t0 = &_1101111 * &i3061; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1100011; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1000111; t4 }; let i3099 = { let t0 = square_n(&i3081, 3); let t1 = &t0 * &_111; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1111001; let t4 = square_n(&t3, 1); t4 }; let i3125 = { let t0 = &base * &i3099; let t1 = square_n(&t0, 15); let t2 = &t1 * &_111101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101111; t4 }; let i3152 = { let t0 = square_n(&i3125, 5); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1011001; let t4 = square_n(&t3, 10); t4 }; let i3172 = { let t0 = &_1101011 * &i3152; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110111; let t3 = square_n(&t2, 11); let t4 = &t3 * &_10011; t4 }; let i3200 = { let t0 = square_n(&i3172, 12); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1100001; let t4 = square_n(&t3, 6); t4 }; let i3220 = { let t0 = &_10101 * &i3200; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1011011; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1010111; t4 }; let i3243 = { let t0 = square_n(&i3220, 5); let t1 = &t0 * &_11101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 8); t4 }; let i3262 = { let t0 = &_1101101 * &i3243; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1001101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_100101; t4 }; let i3286 = { let t0 = square_n(&i3262, 12); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1000011; let t4 = square_n(&t3, 1); t4 }; let i3309 = { let t0 = &base * &i3286; let t1 = square_n(&t0, 11); let t2 = &t1 * &x10; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1110111; t4 }; let i3330 = { let t0 = square_n(&i3309, 7); let t1 = &t0 * &_101011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1110101; let t4 = square_n(&t3, 4); t4 }; let i3350 = { let t0 = &_1111 * &i3330; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_111101; t4 }; let i3373 = { let t0 = square_n(&i3350, 9); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 6); let t3 = &t2 * &_110101; let t4 = square_n(&t3, 6); t4 }; let i3395 = { let t0 = &_11101 * &i3373; let t1 = square_n(&t0, 8); let t2 = &t1 * &_101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1001101; t4 }; let i3420 = { let t0 = square_n(&i3395, 9); let t1 = &t0 * &_1000111; let t2 = square_n(&t1, 2); let t3 = &t2 * &_11; let t4 = square_n(&t3, 12); t4 }; let i3435 = { let t0 = &_1110111 * &i3420; let t1 = square_n(&t0, 6); let t2 = &t1 * &_111011; let t3 = square_n(&t2, 6); let t4 = &t3 * &_10101; t4 }; let i3462 = { let t0 = square_n(&i3435, 9); let t1 = &t0 * &_100001; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101101; let t4 = square_n(&t3, 9); t4 }; let i3480 = { let t0 = &_1101001 * &i3462; let t1 = square_n(&t0, 7); let t2 = &t1 * &_101001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_101101; t4 }; let i3505 = { let t0 = square_n(&i3480, 8); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1001; let t4 = square_n(&t3, 11); t4 }; let i3522 = { let t0 = &_1111001 * &i3505; let t1 = square_n(&t0, 7); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_100011; t4 }; let i3551 = { let t0 = square_n(&i3522, 12); let t1 = &t0 * &_1011001; let t2 = square_n(&t1, 4); let t3 = &t2 * &_1101; let t4 = square_n(&t3, 11); t4 }; let i3568 = { let t0 = &_1100011 * &i3551; let t1 = square_n(&t0, 5); let t2 = &t1 * &_11111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_111001; t4 }; let i3592 = { let t0 = square_n(&i3568, 8); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 7); t4 }; let i3609 = { let t0 = &_101101 * &i3592; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1101111; let t3 = square_n(&t2, 6); let t4 = &t3 * &_100111; t4 }; let i3637 = { let t0 = square_n(&i3609, 8); let t1 = &t0 * &_1000101; let t2 = square_n(&t1, 9); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 9); t4 }; let i3657 = { let t0 = &_1010111 * &i3637; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1100001; t4 }; let i3682 = { let t0 = square_n(&i3657, 10); let t1 = &t0 * &_100101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 6); t4 }; let i3704 = { let t0 = &_11111 * &i3682; let t1 = square_n(&t0, 9); let t2 = &t1 * &_101101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1101001; t4 }; let i3728 = { let t0 = square_n(&i3704, 7); let t1 = &t0 * &_101101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1110111; let t4 = square_n(&t3, 7); t4 }; let i3746 = { let t0 = &_100011 * &i3728; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1000111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_110101; t4 }; let i3769 = { let t0 = square_n(&i3746, 8); let t1 = &t0 * &_1110101; let t2 = square_n(&t1, 7); let t3 = &t2 * &_1010001; let t4 = square_n(&t3, 6); t4 }; let i3785 = { let t0 = &_101001 * &i3769; let t1 = square_n(&t0, 6); let t2 = &t1 * &_10001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_10111; t4 }; let i3811 = { let t0 = square_n(&i3785, 9); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110001; let t4 = square_n(&t3, 7); t4 }; let i3831 = { let t0 = &_100101 * &i3811; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1010011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1100111; t4 }; let i3857 = { let t0 = square_n(&i3831, 7); let t1 = &t0 * &_1000011; let t2 = square_n(&t1, 10); let t3 = &t2 * &_1111011; let t4 = square_n(&t3, 7); t4 }; let i3879 = { let t0 = &_101 * &i3857; let t1 = square_n(&t0, 12); let t2 = &t1 * &_1111001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101011; t4 }; let i3902 = { let t0 = square_n(&i3879, 6); let t1 = &t0 * &_110011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 6); t4 }; let i3928 = { let t0 = &_101 * &i3902; let t1 = square_n(&t0, 13); let t2 = &t1 * &_10111; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1011101; t4 }; let i3953 = { let t0 = square_n(&i3928, 5); let t1 = &t0 * &_1001; let t2 = square_n(&t1, 12); let t3 = &t2 * &_100001; let t4 = square_n(&t3, 6); t4 }; let i3977 = { let t0 = &_1001 * &i3953; let t1 = square_n(&t0, 9); let t2 = &t1 * &_11111; let t3 = square_n(&t2, 12); let t4 = &t3 * &_1111101; t4 }; let i4010 = { let t0 = square_n(&i3977, 10); let t1 = &t0 * &_1011101; let t2 = square_n(&t1, 12); let t3 = &t2 * &_1111101; let t4 = square_n(&t3, 9); t4 }; let i4029 = { let t0 = &_1001001 * &i4010; let t1 = square_n(&t0, 7); let t2 = &t1 * &_101011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_100111; t4 }; let i4058 = { let t0 = square_n(&i4029, 9); let t1 = &t0 * &_11011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1100011; let t4 = square_n(&t3, 9); t4 }; let i4075 = { let t0 = &_1010101 * &i4058; let t1 = square_n(&t0, 6); let t2 = &t1 * &_110001; let t3 = square_n(&t2, 8); let t4 = &t3 * &_1101101; t4 }; let i4098 = { let t0 = square_n(&i4075, 7); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1000111; let t4 = square_n(&t3, 6); t4 }; let i4120 = { let t0 = &_101011 * &i4098; let t1 = square_n(&t0, 10); let t2 = &t1 * &_11011; let t3 = square_n(&t2, 9); let t4 = &t3 * &_101011; t4 }; let i4145 = { let t0 = square_n(&i4120, 5); let t1 = &t0 * &_101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_111; let t4 = square_n(&t3, 10); t4 }; let i4169 = { let t0 = &_11101 * &i4145; let t1 = square_n(&t0, 10); let t2 = &t1 * &_1110011; let t3 = square_n(&t2, 11); let t4 = &t3 * &_101001; t4 }; let i4194 = { let t0 = square_n(&i4169, 7); let t1 = &t0 * &_111011; let t2 = square_n(&t1, 14); let t3 = &t2 * &_101111; let t4 = square_n(&t3, 2); t4 }; let i4218 = { let t0 = &base * &i4194; let t1 = square_n(&t0, 14); let t2 = &t1 * &_1011111; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1101101; t4 }; let i4243 = { let t0 = square_n(&i4218, 7); let t1 = &t0 * &_1110101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_101; let t4 = square_n(&t3, 12); t4 }; let i4262 = { let t0 = &_110001 * &i4243; let t1 = square_n(&t0, 5); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 11); let t4 = &t3 * &_1011001; t4 }; let i4286 = { let t0 = square_n(&i4262, 7); let t1 = &t0 * &_1011011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 9); t4 }; let i4311 = { let t0 = &_110101 * &i4286; let t1 = square_n(&t0, 15); let t2 = &t1 * &_1100001; let t3 = square_n(&t2, 7); let t4 = &t3 * &_101001; t4 }; let i4336 = { let t0 = square_n(&i4311, 9); let t1 = &t0 * &_1001011; let t2 = square_n(&t1, 7); let t3 = &t2 * &_110011; let t4 = square_n(&t3, 7); t4 }; let i4354 = { let t0 = &_10101 * &i4336; let t1 = square_n(&t0, 6); let t2 = &t1 * &_1101; let t3 = square_n(&t2, 9); let t4 = &t3 * &_101001; t4 }; let i4382 = { let t0 = square_n(&i4354, 9); let t1 = &t0 * &_1010011; let t2 = square_n(&t1, 9); let t3 = &t2 * &_1111111; let t4 = square_n(&t3, 8); t4 }; let i4400 = { let t0 = &_1010101 * &i4382; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 10); let t4 = &t3 * &_1000111; t4 }; let i4424 = { let t0 = square_n(&i4400, 8); let t1 = &t0 * &_110101; let t2 = square_n(&t1, 4); let t3 = &t2 * &_101; let t4 = square_n(&t3, 10); t4 }; let i4444 = { let t0 = &_111001 * &i4424; let t1 = square_n(&t0, 8); let t2 = &t1 * &_11001; let t3 = square_n(&t2, 9); let t4 = &t3 * &_1011101; t4 }; let i4471 = { let t0 = square_n(&i4444, 7); let t1 = &t0 * &_1101101; let t2 = square_n(&t1, 11); let t3 = &t2 * &_1110001; let t4 = square_n(&t3, 7); t4 }; let i4491 = { let t0 = &_1100001 * &i4471; let t1 = square_n(&t0, 2); let t2 = &t1 * &_11; let t3 = square_n(&t2, 15); let t4 = &t3 * &_1010001; t4 }; let i4515 = { let t0 = square_n(&i4491, 5); let t1 = &t0 * &_1101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_10011; let t4 = square_n(&t3, 9); t4 }; let i4532 = { let t0 = &_1010011 * &i4515; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1110101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1010111; t4 }; let i4561 = { let t0 = square_n(&i4532, 8); let t1 = &t0 * &_1010001; let t2 = square_n(&t1, 8); let t3 = &t2 * &_101101; let t4 = square_n(&t3, 11); t4 }; let i4580 = { let t0 = &_1100101 * &i4561; let t1 = square_n(&t0, 7); let t2 = &t1 * &_101111; let t3 = square_n(&t2, 9); let t4 = &t3 * &_111011; t4 }; let i4605 = { let t0 = square_n(&i4580, 6); let t1 = &t0 * &_11111; let t2 = square_n(&t1, 6); let t3 = &t2 * &_1011; let t4 = square_n(&t3, 11); t4 }; let i4619 = { let t0 = &_1000001 * &i4605; let t1 = square_n(&t0, 7); let t2 = &t1 * &_1101001; let t3 = square_n(&t2, 4); let t4 = &t3 * &_1011; t4 }; let i4646 = { let t0 = square_n(&i4619, 10); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 3); let t3 = &t2 * &base; let t4 = square_n(&t3, 12); t4 }; let i4665 = { let t0 = &_111001 * &i4646; let t1 = square_n(&t0, 9); let t2 = &t1 * &_1000101; let t3 = square_n(&t2, 7); let t4 = &t3 * &_1111011; t4 }; let i4688 = { let t0 = square_n(&i4665, 7); let t1 = &t0 * &_1110011; let t2 = square_n(&t1, 6); let t3 = &t2 * &_100011; let t4 = square_n(&t3, 8); t4 }; let i4704 = { let t0 = &_1001001 * &i4688; let t1 = square_n(&t0, 8); let t2 = &t1 * &_1011101; let t3 = square_n(&t2, 5); let t4 = &t3 * &_101; t4 }; let i4731 = { let t0 = square_n(&i4704, 11); let t1 = &t0 * &_1111011; let t2 = square_n(&t1, 5); let t3 = &t2 * &_10101; let t4 = square_n(&t3, 9); t4 }; let i4747 = { let t0 = &_1000011 * &i4731; let t1 = square_n(&t0, 5); let t2 = &t1 * &_10101; let t3 = square_n(&t2, 8); let t4 = &t3 * &_100101; t4 }; let i4778 = { let t0 = square_n(&i4747, 6); let t1 = &t0 * &_10011; let t2 = square_n(&t1, 8); let t3 = &t2 * &_110111; let t4 = square_n(&t3, 15); t4 }; let i4797 = { let t0 = &_1011011 * &i4778; let t1 = square_n(&t0, 4); let t2 = &t1 * &_111; let t3 = square_n(&t2, 12); let t4 = &t3 * &x9; t4 }; let i4822 = { let t0 = square_n(&i4797, 8); let t1 = &t0 * &_1111101; let t2 = square_n(&t1, 8); let t3 = &t2 * &_1010111; let t4 = square_n(&t3, 7); t4 }; let result = { let t0 = &_1011011 * &i4822; let t1 = square_n(&t0, 10); let t2 = &t1 * &_100011; t2 }; result } } ================================================ FILE: tools/garaga_rs/src/pairing/final_exp_witness/bls12_381_final_exp_witness.rs ================================================ use super::addchain_pow_generated::bls12_381 as bls12_addchain; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; use lambdaworks_math::field::element::FieldElement; use num_bigint::BigUint; pub fn pow_custom( base: &FieldElement, exponent: &BigUint, ) -> FieldElement { if exponent == &BigUint::from(0u64) { return FieldElement::::one(); } if exponent == &BigUint::from(1u64) { return base.clone(); } let mut result = FieldElement::::one(); let temp = base.clone(); let exponent_bytes = exponent.to_bytes_be(); for byte in exponent_bytes { for i in (0..8).rev() { result = result.square(); if (byte >> i) & 1 == 1 { result = &result * &temp; } } } result } /// Takes a miller loop output and returns root, shift such that /// root ** lam = shift * mlo, if and only if mlo ** h == 1. pub fn get_final_exp_witness( mlo: FieldElement, ) -> ( FieldElement, FieldElement, ) { // Calculate shift and root let shift = bls12_addchain::pow_h3_s(&mlo); let root = bls12_addchain::pow_e(&(&shift * &mlo)); (root, shift) } #[cfg(test)] mod tests { use super::*; use crate::definitions::BLS12381PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::{ Degree2ExtensionField, Degree6ExtensionField, }; use num_bigint::BigUint; use num_traits::Num; fn sample_element() -> FieldElement { FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ FieldElement::::from_hex_unchecked("2"), FieldElement::::zero(), ]), FieldElement::::zero(), FieldElement::::zero(), ]), FieldElement::::zero(), ]) } #[test] fn addchain_matches_pow_custom() { let base = sample_element(); let h3_s = BigUint::from_str_radix(H3_S, 16).unwrap(); let e = BigUint::from_str_radix(E, 16).unwrap(); assert_eq!(bls12_addchain::pow_h3_s(&base), pow_custom(&base, &h3_s)); assert_eq!(bls12_addchain::pow_e(&base), pow_custom(&base, &e)); } const H3_S: &str = "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"; const E: &str = "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"; } ================================================ FILE: tools/garaga_rs/src/pairing/final_exp_witness/bn254_final_exp_witness.rs ================================================ use super::addchain_pow_generated::bn254 as bn254_addchain; use crate::definitions::BN254PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::{ Degree12ExtensionField, Degree2ExtensionField, Degree6ExtensionField, }; use lambdaworks_math::field::element::FieldElement; /// Algorithm for computing λ residues over BN254 curve /// Input: Output of a Miller loop f /// Output: (c, wi) such that c ** λ = f * wi pub fn get_final_exp_witness( f: FieldElement, ) -> ( FieldElement, FieldElement, ) { let w = get_27th_root(); let mut c = f.clone(); let mut ws = FieldElement::::one(); if bn254_addchain::pow_exp(&c) != FieldElement::::one() { c = &c * &w; ws = &ws * &w; if bn254_addchain::pow_exp(&c) != FieldElement::::one() { c = &c * &w; ws = &ws * &w; } } c = bn254_addchain::pow_r_m_d_inv(&c); (find_cube_root(c, w), ws) } fn get_27th_root() -> FieldElement { FieldElement::::new([ FieldElement::::new([ FieldElement::::zero(), FieldElement::::zero(), FieldElement::::new([ FieldElement::::from_hex_unchecked( "1223c9e5932f55ff4c5bb93e3ae400abc8ff620b6cd0ba64515fe1909e9f8e51", ), FieldElement::::from_hex_unchecked( "279a0a9dbd98089c184dac0e71909eb223ea52bfc24790f6d545aed52a2fbdb8", ), ]), ]), FieldElement::::zero(), ]) } fn find_cube_root( a: FieldElement, w: FieldElement, ) -> FieldElement { let a_inv = a.inv().unwrap(); let we = bn254_addchain::pow_exp0(&w); let mut x = bn254_addchain::pow_exp0(&a); let mut t = pow_3_ord(&(&x.pow(3u64) * &a_inv)); while t != 0 { x = &x * &we; t = pow_3_ord(&(&x.pow(3u64) * &a_inv)); } x } fn pow_3_ord(a: &FieldElement) -> usize { let mut a = a.clone(); let mut t = 0; while a != FieldElement::::one() { a = a.pow(3u64); t += 1; } t } #[cfg(test)] mod tests { use super::*; use num_bigint::BigUint; use num_traits::Num; // Optimized implementation of exponentiation using square-and-multiply algorithm // with binary representation scanning fn pow_custom( base: &FieldElement, exponent: &BigUint, ) -> FieldElement { if exponent == &BigUint::from(0u64) { return FieldElement::::one(); } if exponent == &BigUint::from(1u64) { return base.clone(); } let mut result = FieldElement::::one(); let temp = base.clone(); // Use bytes directly instead of string conversion for better performance let exponent_bytes = exponent.to_bytes_be(); for byte in exponent_bytes { for i in (0..8).rev() { result = result.square(); if (byte >> i) & 1 == 1 { result = &result * &temp; } } } result } fn sample_element() -> FieldElement { FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ FieldElement::::from_hex_unchecked("2"), FieldElement::::zero(), ]), FieldElement::::zero(), FieldElement::::zero(), ]), FieldElement::::zero(), ]) } #[test] fn addchain_matches_pow_custom() { let base = sample_element(); let exp = BigUint::from_str_radix(EXP, 16).unwrap(); let exp0 = BigUint::from_str_radix(EXP0, 16).unwrap(); let r_m_d_inv = BigUint::from_str_radix(R_M_D_INV, 16).unwrap(); assert_eq!(bn254_addchain::pow_exp(&base), pow_custom(&base, &exp)); assert_eq!(bn254_addchain::pow_exp0(&base), pow_custom(&base, &exp0)); assert_eq!( bn254_addchain::pow_r_m_d_inv(&base), pow_custom(&base, &r_m_d_inv) ); } // (q ** k - 1) / 3 const EXP: &str = "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"; // (s + 1) / 3 const EXP0: &str = "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"; // r_inv * m_dash_inv const R_M_D_INV: &str = "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"; } ================================================ FILE: tools/garaga_rs/src/pairing/final_exp_witness/mod.rs ================================================ #[allow(clippy::all)] pub mod addchain_pow_generated; pub mod bls12_381_final_exp_witness; pub mod bn254_final_exp_witness; use crate::definitions::{BLS12381PrimeField, BN254PrimeField}; use crate::io::{element_from_biguint, element_to_biguint}; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254; use lambdaworks_math::field::element::FieldElement; use num_bigint::BigUint; pub fn to_bn(v: FieldElement) -> [BigUint; 12] { let [c0, c1] = v.value(); let [c0b0, c0b1, c0b2] = c0.value(); let [c1b0, c1b1, c1b2] = c1.value(); let [c0b0a0, c0b0a1] = c0b0.value(); let [c0b1a0, c0b1a1] = c0b1.value(); let [c0b2a0, c0b2a1] = c0b2.value(); let [c1b0a0, c1b0a1] = c1b0.value(); let [c1b1a0, c1b1a1] = c1b1.value(); let [c1b2a0, c1b2a1] = c1b2.value(); [ element_to_biguint(c0b0a0), element_to_biguint(c0b0a1), element_to_biguint(c0b1a0), element_to_biguint(c0b1a1), element_to_biguint(c0b2a0), element_to_biguint(c0b2a1), element_to_biguint(c1b0a0), element_to_biguint(c1b0a1), element_to_biguint(c1b1a0), element_to_biguint(c1b1a1), element_to_biguint(c1b2a0), element_to_biguint(c1b2a1), ] } pub fn to_bls( v: FieldElement, ) -> [BigUint; 12] { let [c0, c1] = v.value(); let [c0b0, c0b1, c0b2] = c0.value(); let [c1b0, c1b1, c1b2] = c1.value(); let [c0b0a0, c0b0a1] = c0b0.value(); let [c0b1a0, c0b1a1] = c0b1.value(); let [c0b2a0, c0b2a1] = c0b2.value(); let [c1b0a0, c1b0a1] = c1b0.value(); let [c1b1a0, c1b1a1] = c1b1.value(); let [c1b2a0, c1b2a1] = c1b2.value(); [ element_to_biguint(c0b0a0), element_to_biguint(c0b0a1), element_to_biguint(c0b1a0), element_to_biguint(c0b1a1), element_to_biguint(c0b2a0), element_to_biguint(c0b2a1), element_to_biguint(c1b0a0), element_to_biguint(c1b0a1), element_to_biguint(c1b1a0), element_to_biguint(c1b1a1), element_to_biguint(c1b2a0), element_to_biguint(c1b2a1), ] } pub fn get_final_exp_witness(curve_id: usize, f: [BigUint; 12]) -> ([BigUint; 12], [BigUint; 12]) { let [f_0, f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, f_10, f_11] = f; if curve_id == 0 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::{Degree12ExtensionField, Degree6ExtensionField, Degree2ExtensionField}; let f = FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_0), element_from_biguint::(&f_1), ]), FieldElement::::new([ element_from_biguint::(&f_2), element_from_biguint::(&f_3), ]), FieldElement::::new([ element_from_biguint::(&f_4), element_from_biguint::(&f_5), ]), ]), FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_6), element_from_biguint::(&f_7), ]), FieldElement::::new([ element_from_biguint::(&f_8), element_from_biguint::(&f_9), ]), FieldElement::::new([ element_from_biguint::(&f_10), element_from_biguint::(&f_11), ]), ]), ]); let (c, wi) = bn254_final_exp_witness::get_final_exp_witness(f); return (to_bn(c), to_bn(wi)); } if curve_id == 1 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::{Degree12ExtensionField, Degree6ExtensionField, Degree2ExtensionField}; let f = FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_0), element_from_biguint::(&f_1), ]), FieldElement::::new([ element_from_biguint::(&f_2), element_from_biguint::(&f_3), ]), FieldElement::::new([ element_from_biguint::(&f_4), element_from_biguint::(&f_5), ]), ]), FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_6), element_from_biguint::(&f_7), ]), FieldElement::::new([ element_from_biguint::(&f_8), element_from_biguint::(&f_9), ]), FieldElement::::new([ element_from_biguint::(&f_10), element_from_biguint::(&f_11), ]), ]), ]); let (c, wi) = bls12_381_final_exp_witness::get_final_exp_witness(f); return (to_bls(c), to_bls(wi)); } panic!("Curve ID {} not supported", curve_id); } #[cfg(test)] mod tests { use super::*; use crate::definitions::{BLS12381PrimeField, BN254PrimeField, FieldElement}; use crate::io::element_to_biguint; #[test] fn get_final_exp_witness_1() { let x = [ "0x1783da1d016c7d380bab8db21a4f525528f83278c6254b13db77fe8107a60be8", "0x4416c4d771078798075d9cc460c7e56f7f542684531e2ee2edbac2c6ebbdbaa", "0xaea0397220f7c7c61e7177abe59b7dfae731041bb381ea6993f45b251ae79ce", "0x29b9c51055891c1a3b737806faf180242ad61412f5085b626fc947d8aee4d4c5", "0xa6cd400de616117bc7c37de0c125e55223b735265eca4e175be078132ad0392", "0x28c17a415e6aab151f632943c971274916c89f88e0826a7ad992060e110cf9a8", "0x218f7d922f219475c106f110a215a256f4c6853d96d4691f93ef8def3553244d", "0x18ba4cb6edcb80bdd3f053158786731fd54bd02afc16a4d65e82d41ee8f71269", "0x3ade11ccef2e9df15c2b9fa6144b5c707dd49b92fb62a4382f3c2e94ac20c84", "0x201b5f896062f80674ac89dc04ef8753139fbf37db26c3c7c9614977f007260d", "0x11f27b345af3ee8d876267a812b60c46c3868500f2e402d0493bc689dd6c5277", "0x2cde97e8c9b263ffbcb53d46c4ed015fdeeb692d8fbf301ad8dc0c1e656d5c27", ]; let y = [ "0x245ada43681e3fbfea7633e5b99e404689d12f34fdc497e0c8b1e9d7c0e70147", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x5fa554b43f992af3cafd815d8f8599a376aad62d4b1d5ce72258252c571032", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x1cd18658560e13f8683504c35d79e2f868d084e0e5a1b8af88d272078bbdb360", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0x212503c88e25ac77cdc82120a45b9d5886f287f15e649d4f8488d7e2b856b2fa", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x2b8d7a45d0b0b47e0c1f391b0bacd25e7f882f16085c7c9099e4ba82d71bf23e", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x2cd3e748118f3965ceaf7fd505e039f23e7d6d69f8ceb25d288d1f797012a4cb", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ]; let z = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let x = x .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let xy = y .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let xz = z .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let (y, z) = get_final_exp_witness(0, x.try_into().unwrap()); assert_eq!(y.to_vec(), xy); assert_eq!(z.to_vec(), xz); } #[test] fn get_final_exp_witness_2() { let x = ["0x189edeac1525a5256ae8c76a82b4df330e0fdac10c95d7fb5f01e6c6b243a52cc62f55f9b74e8bcef7cf857ec72dce93", "0x1c5cc475a78741fb935272142f80370ecc6a698ef863d33e5e187f3cd4fcdb91c49236aafcce6c2b7e91ff0678305ee", "0x38f22b3f8377694c4b17bbea3afd26c71d6c07f64c4661a0d8d77bc9f8f1752bfcbe1e3c6ab95b6eb522fa601ea9305", "0x431d707ff3a55977c4868bc4de8c336ecf67b804ac90c2c739ff85161bbe9a730e3021edaed5902502eb385ea4cc50c", "0x14a833d75d7614710c13c79f3df94ae7d9fa9ec20fa02356381fd6755be5a71ca30e230a1bece62346f0bcfa0f10c949", "0x12bd3ae4a4aca5e0db13fd94c2c2b0127ee3d7d9491d3fa7faa9fb6046a0543f1092c5761636021e091d1a18beeccfba", "0x8577fff37edfad39505f3c47bd6df6fdd80d5f75aff4efd05edf11725abf6458c140d50d4b33c0560aaed4d8167373b", "0x71ad85945ebc453009cb5cf204e41fa0caf2075fc94cf9a57b2460ca293b6eb5c12df3ceb0d17ca563eb044181077c", "0xe17d78c3c7663a52347558b81f589708ad2e84bd32830f61b9d25f1d8f2fe668f9548e4f6bc8a2a6cbf63f72e538a1", "0x15b2f2eca1e3e6c52dc3e40ccdef2f63d0085c459442bdbf592cb6df02973c4f21c96db9ee3d7084d33b0699d260eb06", "0x110cf0e03683bd834bf62dfa7717e01f244814560f4bd540f96ab24703ecc763272a2594a640383e1496b1d6cbdd032f", "0xc54fb45e0131b724250f6b3cf02d8287133dd162bf106ab6ed3d3101b20f9045c77b25ad127a0e193d95f573796e10"]; let y = ["0x12deecbe6648e28516e35daa1e0c318027b97f93995f24274523f4382c02ce6aacce3efefec37100737f82dfe340a4d3", "0xb417c5f4b0e31cdc36e64f4220554380793013c3a3a18557ce659630295c5e67e4cc6131699b575e3435a2c495d3d34", "0x21b2745b9213155921a4e4f1f78aa93aacf1acab10c8f49685f617c0c881fd11ccb4a00d6198229a0f329755fdaa894", "0x174ce865876ea77ee960d6a7b9eada1e4b8afab93489903fbed3dd36c52f4b70fc0d52418a67418ee47875805d80b77d", "0x11307f8213b5a5cf011068461c937525fcc1bac74e8440a0011e899805c83143f52e11e2540f90027da0a3795bdbc359", "0x1976eebc878d175bc93678c0985755703c9866091b78ec8bef5f8948f3b6fa174a284c65e9913a4346aa72b17c319aa", "0xa35d36af451eb622dc96a60848761402315cca37f2fa9e861fb1ac89348be93bf05793ed4ac0c9fd9de3befa4f2577c", "0x36837217109690a2f7f6cd5df81e0f5d49597d200624b374626abf6d941253feb172c215a05d52f76a75caf3b6ea5d2", "0x3f0bccdc44d95bf26b464dcc1a586b8521061565c1ee05cfba8cb30479aaf08448f6451ea7fdc3fff0efd54f27ec0fb", "0xb98f31f1bce837a3fee2cd18f3d43a542e2b386b893be959d87e1541dd78939de6b6e3050e52f17111ab805cf5c0434", "0x177f4b467a8559f03d1ce53454a64dd7a5fdc0e2a0d2cb6593184986d2dcc78dab7bf8e95a1e41b3ed044ebe3aa84c2f", "0xb26abddfd9c70b423b180f3ea13c507dbe3396e795d2f2f8a303718e823dfb73f1073bdf99057642a29280f237244ef"]; let z = ["0x0", "0x0", "0x18bc5b99f39cbf0fd8d087688e9a0930581e2c940247cd0991e7a80fe41d8f58d83f1513f1ca42a0e74df934924892fb", "0x18bc5b99f39cbf0fd8d087688e9a0930581e2c940247cd0991e7a80fe41d8f58d83f1513f1ca42a0e74df934924892fb", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0"]; let x = x .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let xy = y .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let xz = z .into_iter() .map(|v| element_to_biguint(&FieldElement::::from_hex(v).unwrap())) .collect::>(); let (y, z) = get_final_exp_witness(1, x.try_into().unwrap()); assert_eq!(y.to_vec(), xy); assert_eq!(z.to_vec(), xz); } } ================================================ FILE: tools/garaga_rs/src/pairing/multi_miller_loop.rs ================================================ use crate::algebra::extf_mul::{ e2_conjugate, nondeterministic_extension_field_div, nondeterministic_extension_field_mul_divmod, }; use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::algebra::polynomial::Polynomial; use crate::definitions::{CurveID, CurveParamsProvider}; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; use lambdaworks_math::traits::ByteConversion; // Replaces elements in a list by zero where sparsity is not set // e.g. [1 2 3 4] [T F T F] => [1 0 3 0] pub fn replace_by_zero_elements_given_sparsity( elmts: &[FieldElement], sparsity: &[bool], ) -> Vec> { assert_eq!(sparsity.len(), elmts.len()); let mut result = vec![]; for i in 0..elmts.len() { result.push(if sparsity[i] { elmts[i].clone() } else { FieldElement::from(0) }); } result } // Removes elements from a list where sparsity is not set, it compacts the list // e.g. [1 2 3 4] [T F T F] => [1 3] pub fn remove_and_compact_elements_given_sparsity( elmts: &[FieldElement], sparsity: &[bool], ) -> Vec> { assert_eq!(sparsity.len(), elmts.len()); let mut result = vec![]; for i in 0..elmts.len() { if sparsity[i] { result.push(elmts[i].clone()); } } result } pub fn extf_mul( ps: Vec>, r_sparsity: Option>, qis: Option<&mut Vec>>, ris: Option<&mut Vec>>, ) -> Polynomial where F: IsPrimeField + CurveParamsProvider, { let (q, r) = nondeterministic_extension_field_mul_divmod(12, ps); let mut r = r.get_coefficients_ext_degree(12); if let Some(r_sparsity) = r_sparsity { r = replace_by_zero_elements_given_sparsity(&r, &r_sparsity); } let r = Polynomial::new(r); if let Some(qis) = qis { qis.push(q) } if let Some(ris) = ris { ris.push(r.clone()) } r } pub fn extf_inv( y: &Polynomial, qis: Option<&mut Vec>>, ris: Option<&mut Vec>>, ) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { let one = Polynomial::one(); let y_inv = nondeterministic_extension_field_div(one, y.clone(), 12); let (q, r) = nondeterministic_extension_field_mul_divmod(12, vec![y_inv.clone(), y.clone()]); let r = Polynomial::new(r.coefficients); // removes trailing zero coefficients assert_eq!(r, Polynomial::one()); if let Some(qis) = qis { qis.push(q) } if let Some(ris) = ris { ris.push(r) } y_inv } pub fn conjugate_e12d(f: Polynomial) -> Polynomial { let e12d = f.get_coefficients_ext_degree(12); Polynomial::new(vec![ e12d[0].clone(), -&e12d[1], e12d[2].clone(), -&e12d[3], e12d[4].clone(), -&e12d[5], e12d[6].clone(), -&e12d[7], e12d[8].clone(), -&e12d[9], e12d[10].clone(), -&e12d[11], ]) } pub fn precompute_consts( p: &[G1Point], ) -> (Vec>, Vec>) { let mut y_inv = vec![]; let mut x_neg_over_y = vec![]; for point in p { y_inv.push(point.y.inv().unwrap()); x_neg_over_y.push(-&(&point.x / &point.y).unwrap()); } (y_inv, x_neg_over_y) } fn build_sparse_line_eval( r0: &FieldElement, r1: &FieldElement, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { use crate::algebra::extf_mul::from_e2; let curve_id = F::get_curve_params().curve_id; let [r0x, r0y] = from_e2(r0.clone()); let [r1x, r1y] = from_e2(r1.clone()); let coefficients = match curve_id { CurveID::BN254 => vec![ FieldElement::from(1), &(&r0x + &(&-FieldElement::::from(9) * &r0y)) * x_neg_over_y, FieldElement::from(0), &(&r1x + &(&-FieldElement::::from(9) * &r1y)) * y_inv, FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), &r0y * x_neg_over_y, FieldElement::from(0), &r1y * y_inv, FieldElement::from(0), FieldElement::from(0), ], CurveID::BLS12_381 => vec![ &(&r1x - &r1y) * y_inv, FieldElement::from(0), &(&r0x - &r0y) * x_neg_over_y, FieldElement::from(1), FieldElement::from(0), FieldElement::from(0), &r1y * y_inv, FieldElement::from(0), &r0y * x_neg_over_y, FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), ], _ => unimplemented!(), }; Polynomial::new(coefficients) } pub fn add_step( qa: &G2Point, qb: &G2Point, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> (G2Point, Polynomial) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let λ = G2Point::compute_adding_slope(qa, qb); let xr = &(&λ * &λ) - &(&qa.x + &qb.x); let yr = &(&λ * &(&qa.x - &xr)) - &qa.y; let p = G2Point::new_unchecked(xr, yr); let line_r0 = λ.clone(); let line_r1 = &(&λ * &qa.x) - &qa.y; let line = build_sparse_line_eval(&line_r0, &line_r1, y_inv, x_neg_over_y); (p, line) } pub fn line_compute_step( qa: &G2Point, qb: &G2Point, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let λ = G2Point::compute_adding_slope(qa, qb); let line_r0 = λ.clone(); let line_r1 = &(&λ * &qa.x) - &qa.y; build_sparse_line_eval(&line_r0, &line_r1, y_inv, x_neg_over_y) } pub fn double_step( q: &G2Point, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> (G2Point, Polynomial) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let λ = G2Point::compute_doubling_slope(q); let xr = &(&λ * &λ) - &(&q.x + &q.x); let yr = &(&λ * &(&q.x - &xr)) - &q.y; let p = G2Point::new_unchecked(xr, yr); let line_r0 = λ.clone(); let line_r1 = &(&λ * &q.x) - &q.y; let line = build_sparse_line_eval(&line_r0, &line_r1, y_inv, x_neg_over_y); (p, line) } pub fn double_and_add_step( qa: &G2Point, qb: &G2Point, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> (G2Point, Polynomial, Polynomial) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let λ1 = G2Point::compute_adding_slope(qa, qb); let x3 = &(&λ1 * &λ1) - &(&qa.x + &qb.x); let line1_r0 = λ1.clone(); let line1_r1 = &(&λ1 * &qa.x) - &qa.y; let num = &qa.y + &qa.y; let den = &x3 - &qa.x; let λ2 = -&(&λ1 + &(&num / &den).unwrap()); let x4 = &(&(&λ2 * &λ2) - &qa.x) - &x3; let y4 = &(&λ2 * &(&qa.x - &x4)) - &qa.y; let p = G2Point::new_unchecked(x4, y4); let line2_r0 = λ2.clone(); let line2_r1 = &(&λ2 * &qa.x) - &qa.y; let line1 = build_sparse_line_eval(&line1_r0, &line1_r1, y_inv, x_neg_over_y); let line2 = build_sparse_line_eval(&line2_r0, &line2_r1, y_inv, x_neg_over_y); (p, line1, line2) } pub fn triple_step( q: &G2Point, y_inv: &FieldElement, x_neg_over_y: &FieldElement, ) -> (G2Point, Polynomial, Polynomial) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let λ1 = G2Point::compute_doubling_slope(q); let line1_r0 = λ1.clone(); let line1_r1 = &(&λ1 * &q.x) - &q.y; let x2 = &(&λ1 * &λ1) - &(&q.x + &q.x); let λ2 = &(((&q.y + &q.y) / &(&q.x - &x2)).unwrap()) - &λ1; let line2_r0 = λ2.clone(); let line2_r1 = &(&λ2 * &q.x) - &q.y; let xr = &(&λ2 * &λ2) - &(&q.x + &x2); let yr = &(&λ2 * &(&q.x - &xr)) - &q.y; let p = G2Point::new_unchecked(xr, yr); let line1 = build_sparse_line_eval(&line1_r0, &line1_r1, y_inv, x_neg_over_y); let line2 = build_sparse_line_eval(&line2_r0, &line2_r1, y_inv, x_neg_over_y); (p, line1, line2) } fn bit_0_case( f: &Polynomial, q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_points.push(t); } let new_f = extf_mul(new_lines, None, None, None); (new_f, new_points) } fn bit_1_init_case( f: &Polynomial, q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = triple_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_lines.push(l2); new_points.push(t); } let new_f = extf_mul(new_lines, None, None, None); (new_f, new_points) } fn bit_1_case( f: &Polynomial, q: &[G2Point], q_select: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = double_and_add_step(&q[k], &q_select[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_lines.push(l2); new_points.push(t); } let new_f = extf_mul(new_lines, None, None, None); (new_f, new_points) } pub fn bn254_finalize_step( qs: &[G2Point], q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], ) -> Vec> where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { use crate::algebra::extf_mul::to_e2; let nr1p2 = to_e2([ FieldElement::::from_hex( "2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d", ) .unwrap(), FieldElement::::from_hex( "16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2", ) .unwrap(), ]); let nr1p3 = to_e2([ FieldElement::::from_hex( "63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a", ) .unwrap(), FieldElement::::from_hex( "7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3", ) .unwrap(), ]); let nr2p2 = FieldElement::::from_hex( "30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48", ) .unwrap(); let nr2p3 = -FieldElement::::from_hex( "30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46", ) .unwrap(); let mut lines = vec![]; for k in 0..q.len() { let q1x = nr1p2.clone() * e2_conjugate(q[k].x.clone()); let q1y = nr1p3.clone() * e2_conjugate(q[k].y.clone()); let q2x = nr2p2.clone() * q[k].x.clone(); let q2y = nr2p3.clone() * q[k].y.clone(); let (t, line1) = add_step( &qs[k], &G2Point::new_unchecked(q1x, q1y), &y_inv[k], &x_neg_over_y[k], ); lines.push(line1); let line2 = line_compute_step( &t, &G2Point::new_unchecked(q2x, q2y), &y_inv[k], &x_neg_over_y[k], ); lines.push(line2); } lines } pub fn miller_loop(p: &[G1Point], q: &[G2Point]) -> Polynomial where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { assert_eq!(p.len(), q.len()); let (y_inv, x_neg_over_y) = precompute_consts(p); let loop_counter = &F::get_curve_params().loop_counter; let mut f = Polynomial::new(vec![ FieldElement::from(1), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), FieldElement::from(0), ]); let mut qs; let mut q_neg = vec![]; if loop_counter.contains(&-1) { for point in q { q_neg.push(point.neg()); } } let start_index = loop_counter.len() - 2; if loop_counter[start_index] == 1 { (f, qs) = bit_1_init_case(&f, q, &y_inv, &x_neg_over_y); } else if loop_counter[start_index] == 0 { (f, qs) = bit_0_case(&f, q, &y_inv, &x_neg_over_y); } else { unimplemented!(); } for i in (0..start_index).rev() { if loop_counter[i] == 0 { (f, qs) = bit_0_case(&f, &qs, &y_inv, &x_neg_over_y); } else if loop_counter[i] == 1 || loop_counter[i] == -1 { let mut q_selects = vec![]; for k in 0..q.len() { q_selects.push(if loop_counter[i] == 1 { q[k].clone() } else { q_neg[k].clone() }); } (f, qs) = bit_1_case(&f, &qs, &q_selects, &y_inv, &x_neg_over_y); } else { unimplemented!(); } } let curve_id = F::get_curve_params().curve_id; match curve_id { CurveID::BN254 => { let mut lines = bn254_finalize_step(&qs, q, &y_inv, &x_neg_over_y); lines.insert(0, f); f = extf_mul(lines, None, None, None); } CurveID::BLS12_381 => { f = conjugate_e12d(f); } _ => unimplemented!(), } f } #[cfg(test)] mod tests { use super::*; use crate::algebra::extf_mul::{from_e2, to_e2}; use crate::definitions::{BLS12381PrimeField, BN254PrimeField}; #[test] fn test_extf_mul_1() { let p = [ [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ], [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ], [ "0x1", "0x3049ed443e0ee79060270c9094ac6390a5c1ab3db65328a47174c6c33f6bd5f2", "0x0", "0xa279a60d390f263fa2b23afda6a2160c7af52ea6fdddb7ffe26ded0e216c821", "0x0", "0x0", "0x0", "0x146bccf3dc47e8eedf574326c5188ea8e4978a568116c9aa5b8517cdeb0e1f38", "0x0", "0x10b71d55b795eb0c1590286e48c412e3434b0def1afddfc8840541b6936825fd", "0x0", "0x0", ], [ "0x1", "0x10b80d23f4e55970de219c8bb6cc99af9ca48837a7da389ff6e02693c8912bf3", "0x0", "0x1999e3b5911b71ef05b218f5be987ba6f43afb6a702ffca89c7a6643b411046f", "0x0", "0x0", "0x0", "0x2a00794e593076aab0ec5e6283a9ed0ddbe6ef97af88861febd351722d50802a", "0x0", "0x22583e5a131ce5504fbb720b2081781441eeb10978efac409e27787d1fa359b6", "0x0", "0x0", ], ]; let xf = [ "0x11d12be7502f97a642a86eb73802fe0fe4772283c9e66f3d535534c22390e0ca", "0x109dabf551c2a0d785f86365c9f7a4e2aae4c8e3f5bb96b72c3461402f80049e", "0x15e06e6b765f21da4c21d50705a9bf0f72ba0283f93e75a896235fa107d4ca4d", "0x23c17e1664ac6452ffdd3ca599029d07bbea4e54e00dd8289aa145149627cc90", "0x751d37ad50cc00d6245f08ca81ce16f9a3714c3efe87c95ae8e132234b5dd07", "0x0", "0x1535e3c0e51be5f14093e8501425031896dfb26ec8759e3409e44e94d81e17cf", "0xe07f7cf5446bf6fd7f35bd2c741235928fd0f5cc82d853d0b37dd293fe1a21b", "0x2eae2d9b2332fb1f1c3617826ac6ede574d04ed01692a36b9743fc604b3f3bf", "0x2ab0d3ce9813032acfb54c2e7c43299edb854672b7bc17be60c2e1cda8e826c", "0x1f316d8807400efe60a15b7e5311a9031439eb344c0d84fb80044f8786d59de4", "0x0", ]; let p: Vec> = p .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let f = extf_mul(p, None, None, None); assert_eq!(f, xf); } #[test] fn test_extf_mul_2() { let p = [["0xc71fb5b76cf57e5c7c9dbbd201062289f97dedce8bbb72d15abaec86c40039d3b4f3fccb7338ff3e7701b7f6619769b", "0x129a0a7e9efe3f397b5dbcae1f22f39c0cbcf4d183ead8de682a7571560cc28f2c13ecc7628b11dda4fcc3eaef203a45", "0x162ca20e57a4ad07f919b85c9975acd11d5f0cddd22192ebc465e5a89a0546be2ec98581fcda54c808aa8790189addd6", "0x10a05ef6bc41b1ac2ba68a585a4c7016589ffad9c5412bf00fd0f50f8ac9ea3d9a7db639e62eae3ca960447fb588a60b", "0x16dbc5bd5769b32d94959f3a71085f5adc66454928e158caeecda06706afd32cea844001820431c1f3534760c01c3ce5", "0x199988fcc386f48448a34d747599bd68a9bb4993cc0e6d2434e9182475096fe323352ae743be4cec47278fbbb8d52f52", "0x189109c92dac219f6b362d169e4ca995bbd0536c8727610f0f361f3490e9d41a94c69d397c1401b31b5a973bc393f3b1", "0x19ea64dde64bbb01d1072ca0532cbe26f8227deaf22155b2ba4bacf79ec45d43bbecca1bb35c6efdd163d6d7ff862979", "0xd9b819680b2cfa830393d2a883cbf07d691020e2a01580c62c9bb1869a1c40317ab6b0df57ff873f2b4bc93d71985e5", "0x704a7bc9193e53c9dde39b3a0a34d0e76345261a4caa612bb3ee39b3715a0d649760f83a32b24cc4b37fe549e80afde", "0x117957ce838607a66a58785c7af8af5a2d3a1832a559f19b20af84c9a5e968cabea23dd6815968b93234b9b34f8108e1", "0xae22d05bd7cd226ba438387b13606f1ad88319c787ccdcec28ab4de6e9bd5fd1ede497ebb746c3313cd6655b961689d"], ["0xc71fb5b76cf57e5c7c9dbbd201062289f97dedce8bbb72d15abaec86c40039d3b4f3fccb7338ff3e7701b7f6619769b", "0x129a0a7e9efe3f397b5dbcae1f22f39c0cbcf4d183ead8de682a7571560cc28f2c13ecc7628b11dda4fcc3eaef203a45", "0x162ca20e57a4ad07f919b85c9975acd11d5f0cddd22192ebc465e5a89a0546be2ec98581fcda54c808aa8790189addd6", "0x10a05ef6bc41b1ac2ba68a585a4c7016589ffad9c5412bf00fd0f50f8ac9ea3d9a7db639e62eae3ca960447fb588a60b", "0x16dbc5bd5769b32d94959f3a71085f5adc66454928e158caeecda06706afd32cea844001820431c1f3534760c01c3ce5", "0x199988fcc386f48448a34d747599bd68a9bb4993cc0e6d2434e9182475096fe323352ae743be4cec47278fbbb8d52f52", "0x189109c92dac219f6b362d169e4ca995bbd0536c8727610f0f361f3490e9d41a94c69d397c1401b31b5a973bc393f3b1", "0x19ea64dde64bbb01d1072ca0532cbe26f8227deaf22155b2ba4bacf79ec45d43bbecca1bb35c6efdd163d6d7ff862979", "0xd9b819680b2cfa830393d2a883cbf07d691020e2a01580c62c9bb1869a1c40317ab6b0df57ff873f2b4bc93d71985e5", "0x704a7bc9193e53c9dde39b3a0a34d0e76345261a4caa612bb3ee39b3715a0d649760f83a32b24cc4b37fe549e80afde", "0x117957ce838607a66a58785c7af8af5a2d3a1832a559f19b20af84c9a5e968cabea23dd6815968b93234b9b34f8108e1", "0xae22d05bd7cd226ba438387b13606f1ad88319c787ccdcec28ab4de6e9bd5fd1ede497ebb746c3313cd6655b961689d"], ["0xed2ad16fd30c6bae9d4659d084faa4e8bbce72d77ce2867a8ccd2916078758f11a33bf3f6acad21af21aafd4dbe67c1", "0x0", "0x143159d9a3967261ec92e14b1108686052cbe30a24c1142a087b498252aaef8b03b69ea297bc174eb69de56e7a594cfa", "0x1", "0x0", "0x0", "0xd2c6c6d4383235e52ea373e1add3c36becb732dbd0fae843b6a12f2841cfa4243dd3bead4e582e60c1e81c3f4db03bb", "0x0", "0x5dd1d6911248fb5ef5a2e4f99c1f90767186060eda81b7f490cc99583db6989183cc9884244bc5b62a507c413c93e2e", "0x0", "0x0", "0x0"], ["0x4ca59a9615490d4871ae113788793a0ef5c6dbbfb2602731932d16dd279f227782505589090120984a32f00d5c17317", "0x0", "0x9649308cd68a27b4e25e3702dab91e62890a1fb24fa7318b413f60fc7b95245612a76f802df69650a6d78458addb193", "0x1", "0x0", "0x0", "0x6d3c6b1903e1d11b99026fac6088b42737e0e7cddf5e95d20f6b7b05c13589063d20aefc27a91c014a7b5f49957ff", "0x0", "0xc9fb3306280d86d70eb3b713248de91c6d4ef90148d3c2300b3d6b19df197e00e70af98bcd050a431a8c58b53832815", "0x0", "0x0", "0x0"]]; let xf = ["0x1913c7c566f59082bc8178020dbab618db967238ea9cd35f30a48e8f4e37b31fa826f2ce8023e3f492da64e7fc430262", "0xe88184d680a3c04ed182e6b263c806982325a7601dab1e928ee1cf7c98a702c77ef44f6202e8049b3eb05d0d530416d", "0x133b8d475abdbde6aa5ce6524599001bdebe394bd4b3c7a7c62a4c736176f27fabcb165d0e9db88c3aa8af04ac87b690", "0xff88e1756ceadda3075ef7ac6f1764de912e15b03a34e439b837bfa984174e90399e3fbda93a12cc209b1ed1469ab6f", "0xa2e5dd0e5330c07becfea58e47106140d177f1b1241de5c1e752050408f4970ed1275db43a9c3cc8b4f393a72148638", "0x1124c5ec5de53991b87616d2e433c3387e4ea68342f9713bcf93e2be0ff2b07e03ff0091e0ff71ae050db38a10394cca", "0x47203ee35055ffa8e288c3da40c9831b46d6c7b911ea92ee62d4af79903c75831bb79321155920b413155ca1f2424bf", "0x180ccf08a53eb9416fc958429dfea456e5e802217f5f5ecc44653622720256512e4c7f01efa251cd28065c103db44f11", "0xf4e1f72f26c9590b43bc7b7c45fff374a786d462f2dc275bc0812c9a26969ce0bd7d8fc5a90a9fa47cb7f40320d6418", "0x134043dade475ebc5c796603d3ae7161f7f06e07e968716ea64520685e44705bd9221f8d7d7b0b9e2d131576fdb3af44", "0x19ceec83acdc521e6a9dbf17392e097e01a2685cc2c9d7f3f1430e22221070d222e599ac3e9142d486383eec146b8dac", "0x7ca2e9db2452cc19c71ff5049bdd024819954fb83f0f903169da844e8fe4a584031b750f0678f8661f1c1e1f4653a84"]; let p: Vec> = p .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let f = extf_mul(p, None, None, None); assert_eq!(f, xf); } #[test] fn test_extf_inv_1() { let c = [ "0x14156ca1853095df27f3cb7c50eca75e794d2f14195c16df4a0f8f9dcb48bee9", "0xdc2a20a6107d4c49fed6b2018946bcc2a8dad06f01d099a6df0a4a55ed21b59", "0x14260c5afb0b1148ed80f8339cf9e06ff04257cb6c1817c4efa721fc98f69503", "0xafe8a09df07bf3dffefe512eb9448ef436dd090f98323135baab8ae3c766c60", "0x114692950f53d4f707bb02cc2b5dc98aff5936811707d6579371dae20368253c", "0x2dd3fca72591963149646f1e106dc0ee917551f5a9da397fe12d4a3939ce650c", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ]; let xi = [[ "0x13e8e196ed7970229c16369f6f62a54fe9848ec0abbb56e77355358805db92a6", "0x29aa20be8afc3104b3211fb1c2636e3291bca41e1276bdbbb485917fae34c150", "0xcbdf387c0036815f944eeedb8a3ed8babb406326444cbed0df3e47fc7a3f440", "0xcc614e3d877550dc9bb19f8dfdc513f2f8fed01d3a180a2a9e475c9a29f6d96", "0x1a6e474f0a5394b39bd15f2390e0cfa64391cb4ffc5d435a63028ac3c744d064", "0x8fc0b38f1129ab34ebd5a5888f0711adecaecc7aa5312cc62508d51da03aa1e", "0xff9b26cf44e068601c663a62662f0ef698166a3410d4f36a68b2e46800daa6e", "0xf4ec161da901a5ab3f6088ede93acdbf15f0c18b653b9f7146d132c6d4111c5", "0x1843faa07a91bed2c949f1b3f126e0ae88d429bf7d37b5e00696b22be53ac607", "0x1c151df931008732415af45f4616affed9e0e64976e66cc5e2e57c799ddfa646", "0x1526c80d7045ccb0ae04a7cf1de7a2519ad52f885c7b9acb7bed0d027459433", ]]; let xj = [[ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]]; let xc = [ "0x1d7a9ffbbe137d697794dbccbd7925ea98507cf8d4445d3e89123811ede12825", "0x1f45aa2ee73f15e275e5c1fc0ff08be0981a61d8e7642301653a6307c7467811", "0x2446d99f276e4c8bc63d81e8d0c1e37c901a5a569865533968e39b5083fc576e", "0x223bd50b771fcaa905131a5f04c3c634c9df344731b5aada49be919aaa447cc7", "0x24cfef2958a7c9c4d7ddfacdd59750105dcc37f6aefbf4a9ce706bc36252c47", "0x3a974db52b274684955cb370b0ac66e3e295ea6e9789fb7259c294210f7720e", "0x160b7346ec9fdd9841feb355a44845dc30c2a9ae3fb8266ad697b531de5e2fb6", "0xe46af84e1cbba805f204fa5ce1c9a99c79799110a56b5d534495a358f9c739f", "0x1f2b5709d0d7c9499b9524e9708ac412d3fa05fea9b51192113e131bd5572a21", "0x8a75eef583ffc3b0f690cd9eab121b1f329194c1052a86d50224b92838c5d76", "0xef3a64570d17038de7ec74175c125ac7e8780509764f07572ce9593878da9fb", "0x2a6290607745b58a7b87bc78053320664e06d12b35825f15893ad52a39f54331", ]; let c = c .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let c = Polynomial::new(c); let xc = Polynomial::new( xc.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; let c = extf_inv::< BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&c, Some(&mut i), Some(&mut j)); assert_eq!(c, xc); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_precompute_consts_1() { let p = [ ( "0x1d0634f3f21e7890d1df87eab84852372b905c9ccdb6d03cb7b9a5409b7efcd8", "0x24c53532773dce26eb3f1d6ba3b10e2b53dc193baa1d4f4d3021032564460978", ), ( "0x2585e4f8a31664cbfc531bccffafcf1e59d91fb9536c985db33c69f7c242e07a", "0x1d2d2799db056ed14f48d341183118d68ea4131357fa42444057cf0c1d62ae3c", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let xy = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xx = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let (y, x) = precompute_consts(&p); assert_eq!(y.to_vec(), xy); assert_eq!(x.to_vec(), xx); } #[test] fn test_precompute_consts_2() { let p = [("0x59d2a79bda5f8a941d4db9e360a80121d5ef96fd687003db24ddec0e0c3b63d82efa81fe174bb39be8658ef83c8c2d", "0x2df47e8cdf189985d5085bdcebb5ee96e40a033f5d3b7986f6992be16bc35f88c471acf7f68344f543e52fe891285a9"), ("0x105dcc4dce3960447d21d3c1dc39e973aaf31de52219df089bb5f797ac6d3395b71420b50de4f62a6588c9401ffefbd3", "0x17cb6c41f0c4e1a7394ab62a9db0be660d847ccc58358f3f9b63c98d9a7845c52e1e2b0faefd0d854043fd325dd3c34f")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let xy = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xx = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let (y, x) = precompute_consts(&p); assert_eq!(y.to_vec(), xy); assert_eq!(x.to_vec(), xx); } #[test] fn test_build_sparse_line_eval_1() { let r0 = [ "0x237db2935c4432bc98005e68cacde68a193b54e64d347301094edcbfa224d3d5", "0x124077e14a7d826a707c3ec1809ae9bafafa05dd6b4ba735fba44e801d415637", ]; let r1 = [ "0x3b7178c857630da7676d0000961488f8fbce03349a8dc1dd6e067932b6a7e0d", "0x2b17c2b12c26fdd0e3520b9dfa601ead6f0bf9cd98c81278efe1e96b86397652", ]; let y = "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8"; let x = "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb"; let xl = [ "0x1", "0x3049ed443e0ee79060270c9094ac6390a5c1ab3db65328a47174c6c33f6bd5f2", "0x0", "0xa279a60d390f263fa2b23afda6a2160c7af52ea6fdddb7ffe26ded0e216c821", "0x0", "0x0", "0x0", "0x146bccf3dc47e8eedf574326c5188ea8e4978a568116c9aa5b8517cdeb0e1f38", "0x0", "0x10b71d55b795eb0c1590286e48c412e3434b0def1afddfc8840541b6936825fd", "0x0", "0x0", ]; let r0 = r0 .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let r1 = r1 .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xl = Polynomial::new( xl.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let r0: [FieldElement; 2] = r0.try_into().unwrap(); let r1: [FieldElement; 2] = r1.try_into().unwrap(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let r0 = to_e2::(r0); let r1 = to_e2::(r1); let y = FieldElement::::from_hex(y).unwrap(); let x = FieldElement::::from_hex(x).unwrap(); let l = build_sparse_line_eval(&r0, &r1, &y, &x); assert_eq!(l, xl); } #[test] fn test_build_sparse_line_eval_2() { let r0 = ["0x56ceab5d5d994dee0ca07fc0d41aa908b1a833b94e768d2dec05cffe4a869aed2a64ee86a72f085ee4e78bd4c2aef8e", "0x39b596a976f556e5ea4016a3111e14b674a67295a242cf3b343a6878db6ec20bcac1275d23aad6cd3e84e398a4e7bc8"]; let r1 = ["0x4786cc02b147d13e701c1f52827dbba9d5d8516fb557dfb71bc60f1a68459eb52df6a9219fcdcac7feb1f0edbefdbf8", "0x145f508c63c10d270e027b2b0bf6789475132950c583823a43387d10f8329296e43e6610cb7555c0db86510eb99cfadd"]; let y = "0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb"; let x = "0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046"; let xl = ["0xed2ad16fd30c6bae9d4659d084faa4e8bbce72d77ce2867a8ccd2916078758f11a33bf3f6acad21af21aafd4dbe67c1", "0x0", "0x143159d9a3967261ec92e14b1108686052cbe30a24c1142a087b498252aaef8b03b69ea297bc174eb69de56e7a594cfa", "0x1", "0x0", "0x0", "0xd2c6c6d4383235e52ea373e1add3c36becb732dbd0fae843b6a12f2841cfa4243dd3bead4e582e60c1e81c3f4db03bb", "0x0", "0x5dd1d6911248fb5ef5a2e4f99c1f90767186060eda81b7f490cc99583db6989183cc9884244bc5b62a507c413c93e2e", "0x0", "0x0", "0x0"]; let r0 = r0 .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let r1 = r1 .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xl = Polynomial::new( xl.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let r0: [FieldElement; 2] = r0.try_into().unwrap(); let r1: [FieldElement; 2] = r1.try_into().unwrap(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let r0 = to_e2::(r0); let r1 = to_e2::(r1); let y = FieldElement::::from_hex(y).unwrap(); let x = FieldElement::::from_hex(x).unwrap(); let l = build_sparse_line_eval(&r0, &r1, &y, &x); assert_eq!(l, xl); } #[test] fn test_bit_0_case_1() { let f = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let q = [ ( "0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa", "0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", ), ( "0x1314aaf1c372e6d7635e573808d9d5c7178bdce7335eb0538f718d8e6651eeb1", "0x14c25d3aec745e5a2d4aba9e1448a8cc1048d01a5289f29ccc5acf5e81526673", "0x397391b7b25e2fba7d1de6d86501d49b6a8dab10d1d0efd5869ecd23aab8e9", "0x1863ac65eca09e89b058c1ff7e4c5c7ec7e5859b385a553ea12434f4eda6db36", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let xf = [ "0x11d12be7502f97a642a86eb73802fe0fe4772283c9e66f3d535534c22390e0ca", "0x109dabf551c2a0d785f86365c9f7a4e2aae4c8e3f5bb96b72c3461402f80049e", "0x15e06e6b765f21da4c21d50705a9bf0f72ba0283f93e75a896235fa107d4ca4d", "0x23c17e1664ac6452ffdd3ca599029d07bbea4e54e00dd8289aa145149627cc90", "0x751d37ad50cc00d6245f08ca81ce16f9a3714c3efe87c95ae8e132234b5dd07", "0x0", "0x1535e3c0e51be5f14093e8501425031896dfb26ec8759e3409e44e94d81e17cf", "0xe07f7cf5446bf6fd7f35bd2c741235928fd0f5cc82d853d0b37dd293fe1a21b", "0x2eae2d9b2332fb1f1c3617826ac6ede574d04ed01692a36b9743fc604b3f3bf", "0x2ab0d3ce9813032acfb54c2e7c43299edb854672b7bc17be60c2e1cda8e826c", "0x1f316d8807400efe60a15b7e5311a9031439eb344c0d84fb80044f8786d59de4", "0x0", ]; let xp = [ ( "0x27dc7234fd11d3e8c36c59277c3e6f149d5cd3cfa9a62aee49f8130962b4b3b9", "0x203e205db4f19b37b60121b83a7333706db86431c6d835849957ed8c3928ad79", "0x4bb53b8977e5f92a0bc372742c4830944a59b4fe6b1c0466e2a6dad122b5d2e", "0x195e8aa5b7827463722b8c153931579d3505566b4edf48d498e185f0509de152", ), ( "0x19092b3d714b3bb6599b735386dd05eab401e72057bab79773a6de8f5693387b", "0x1acb3fbdde3ce471791558747f0e52b1b7a708834dc533393bcfc2af317703ee", "0x258d7966e4b36382460549a44d5cbe96fbe1c412e36f25218438f72d7d387077", "0x2a58bf6a639ae104439ba4e8db873938a26fcd5bd0b68beb20c44705d9820860", ), ]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let (f, p) = bit_0_case::(&f, &q, &y, &x); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); } #[test] fn test_bit_0_case_2() { let f = ["0xc71fb5b76cf57e5c7c9dbbd201062289f97dedce8bbb72d15abaec86c40039d3b4f3fccb7338ff3e7701b7f6619769b", "0x129a0a7e9efe3f397b5dbcae1f22f39c0cbcf4d183ead8de682a7571560cc28f2c13ecc7628b11dda4fcc3eaef203a45", "0x162ca20e57a4ad07f919b85c9975acd11d5f0cddd22192ebc465e5a89a0546be2ec98581fcda54c808aa8790189addd6", "0x10a05ef6bc41b1ac2ba68a585a4c7016589ffad9c5412bf00fd0f50f8ac9ea3d9a7db639e62eae3ca960447fb588a60b", "0x16dbc5bd5769b32d94959f3a71085f5adc66454928e158caeecda06706afd32cea844001820431c1f3534760c01c3ce5", "0x199988fcc386f48448a34d747599bd68a9bb4993cc0e6d2434e9182475096fe323352ae743be4cec47278fbbb8d52f52", "0x189109c92dac219f6b362d169e4ca995bbd0536c8727610f0f361f3490e9d41a94c69d397c1401b31b5a973bc393f3b1", "0x19ea64dde64bbb01d1072ca0532cbe26f8227deaf22155b2ba4bacf79ec45d43bbecca1bb35c6efdd163d6d7ff862979", "0xd9b819680b2cfa830393d2a883cbf07d691020e2a01580c62c9bb1869a1c40317ab6b0df57ff873f2b4bc93d71985e5", "0x704a7bc9193e53c9dde39b3a0a34d0e76345261a4caa612bb3ee39b3715a0d649760f83a32b24cc4b37fe549e80afde", "0x117957ce838607a66a58785c7af8af5a2d3a1832a559f19b20af84c9a5e968cabea23dd6815968b93234b9b34f8108e1", "0xae22d05bd7cd226ba438387b13606f1ad88319c787ccdcec28ab4de6e9bd5fd1ede497ebb746c3313cd6655b961689d"]; let q = [("0x122915c824a0857e2ee414a3dccb23ae691ae54329781315a0c75df1c04d6d7a50a030fc866f09d516020ef82324afae", "0x9380275bbc8e5dcea7dc4dd7e0550ff2ac480905396eda55062650f8d251c96eb480673937cc6d9d6a44aaa56ca66dc", "0xb21da7955969e61010c7a1abc1a6f0136961d1e3b20b1a7326ac738fef5c721479dfd948b52fdf2455e44813ecfd892", "0x8f239ba329b3967fe48d718a36cfe5f62a7e42e0bf1c1ed714150a166bfbd6bcf6b3b58b975b9edea56d53f23a0e849"), ("0x893227b499dab30e15b606ec3c375f9fabf7fbb574b9b11c9eefbe33fae82066297e23c518f59e74d5cf646cec6464f", "0x10578234a81819d1ebb3d77b03a128f3165642386fff1b0a74ad73c139425703a991ce459cdc1995351adff98061f0ea", "0x16efa85752a02d4358a92eb3b577c1e27a02ec36000c44403159baf7022541a02104b633549e05b774e1b76343a8e661", "0xaf65df48a519d9209257e3df9fb0a1bd3491799091df954380242592db0bead0ddd62dbe33aeeaf1d4a63bdbc4c6008")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let xf = ["0x1913c7c566f59082bc8178020dbab618db967238ea9cd35f30a48e8f4e37b31fa826f2ce8023e3f492da64e7fc430262", "0xe88184d680a3c04ed182e6b263c806982325a7601dab1e928ee1cf7c98a702c77ef44f6202e8049b3eb05d0d530416d", "0x133b8d475abdbde6aa5ce6524599001bdebe394bd4b3c7a7c62a4c736176f27fabcb165d0e9db88c3aa8af04ac87b690", "0xff88e1756ceadda3075ef7ac6f1764de912e15b03a34e439b837bfa984174e90399e3fbda93a12cc209b1ed1469ab6f", "0xa2e5dd0e5330c07becfea58e47106140d177f1b1241de5c1e752050408f4970ed1275db43a9c3cc8b4f393a72148638", "0x1124c5ec5de53991b87616d2e433c3387e4ea68342f9713bcf93e2be0ff2b07e03ff0091e0ff71ae050db38a10394cca", "0x47203ee35055ffa8e288c3da40c9831b46d6c7b911ea92ee62d4af79903c75831bb79321155920b413155ca1f2424bf", "0x180ccf08a53eb9416fc958429dfea456e5e802217f5f5ecc44653622720256512e4c7f01efa251cd28065c103db44f11", "0xf4e1f72f26c9590b43bc7b7c45fff374a786d462f2dc275bc0812c9a26969ce0bd7d8fc5a90a9fa47cb7f40320d6418", "0x134043dade475ebc5c796603d3ae7161f7f06e07e968716ea64520685e44705bd9221f8d7d7b0b9e2d131576fdb3af44", "0x19ceec83acdc521e6a9dbf17392e097e01a2685cc2c9d7f3f1430e22221070d222e599ac3e9142d486383eec146b8dac", "0x7ca2e9db2452cc19c71ff5049bdd024819954fb83f0f903169da844e8fe4a584031b750f0678f8661f1c1e1f4653a84"]; let xp = [("0x19e384121b7d70927c49e6d044fd8517c36bc6ed2813a8956dd64f049869e8a77f7e46930240e6984abe26fa6a89658f", "0x3f4b4e761936d90fd5f55f99087138a07a69755ad4a46e4dd1c2cfe6d11371e1cc033111a0595e3bba98d0f538db451", "0x17a31a4fccfb5f768a2157517c77a4f8aaf0dee8f260d96e02e1175a8754d09600923beae02a019afc327b65a2fdbbfc", "0x88bb5832f4a4a452edda646ebaa2853a54205d56329960b44b2450070734724a74daaa401879bad142132316e9b3401"), ("0x1604bd06ba18d6d65bdd88e22c26eaef8a620a1a9fefe016d00eac356f9ceda8bc8eee5e46f9f4736ab22cff0e8cb9e8", "0x3e5755e9bfc250ff0a03efea22428a36a247504e613980918dc5319efb7f66b10d5fe2e7e86af7e014e1456aeaeac5f", "0x5655a99f7ff904c1e41382c25ff0360d9c51d0e331bfb1e38f5dd41c6909caaf6e313f47f727922109bf8c3204fe274", "0x62ec2ed9b207f63e0d9899ed11f9a125b472586b65bb77b8a04d5d446d15a8701ba5c361a07cd85e0743f5ae2e95a9f")]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_0_case::(&f, &q, &y, &x); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); } #[test] fn test_bit_1_init_case_1() { let f = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let q = [("0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8", "0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e", "0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801", "0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be"), ("0x82dc9154807866eb0f36ccb665a5fc010510bd690ddd7b540e5bf3ff02d81e98b75703a3b3d3c305a70960906e6cb09", "0xdd18d077ad5bd58dabb18d84a6ceebe6375a83dd242851bb4dcf956002c4efb974ffceee6709deb0dcf81d4285e5e60", "0x4a468eb9e206b9833d8e8e2197d3446652372ce5ef50e93c91aa58105d3a281b2e84ddb61535fe1a90bae7e6692f9b0", "0x198fd0ab6249082bf7007d7e8be8992de81f47ae3341c590194fa3bf769a2e5a5253527727115c334e82ed4be8da6c10")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let xf = ["0xc71fb5b76cf57e5c7c9dbbd201062289f97dedce8bbb72d15abaec86c40039d3b4f3fccb7338ff3e7701b7f6619769b", "0x129a0a7e9efe3f397b5dbcae1f22f39c0cbcf4d183ead8de682a7571560cc28f2c13ecc7628b11dda4fcc3eaef203a45", "0x162ca20e57a4ad07f919b85c9975acd11d5f0cddd22192ebc465e5a89a0546be2ec98581fcda54c808aa8790189addd6", "0x10a05ef6bc41b1ac2ba68a585a4c7016589ffad9c5412bf00fd0f50f8ac9ea3d9a7db639e62eae3ca960447fb588a60b", "0x16dbc5bd5769b32d94959f3a71085f5adc66454928e158caeecda06706afd32cea844001820431c1f3534760c01c3ce5", "0x199988fcc386f48448a34d747599bd68a9bb4993cc0e6d2434e9182475096fe323352ae743be4cec47278fbbb8d52f52", "0x189109c92dac219f6b362d169e4ca995bbd0536c8727610f0f361f3490e9d41a94c69d397c1401b31b5a973bc393f3b1", "0x19ea64dde64bbb01d1072ca0532cbe26f8227deaf22155b2ba4bacf79ec45d43bbecca1bb35c6efdd163d6d7ff862979", "0xd9b819680b2cfa830393d2a883cbf07d691020e2a01580c62c9bb1869a1c40317ab6b0df57ff873f2b4bc93d71985e5", "0x704a7bc9193e53c9dde39b3a0a34d0e76345261a4caa612bb3ee39b3715a0d649760f83a32b24cc4b37fe549e80afde", "0x117957ce838607a66a58785c7af8af5a2d3a1832a559f19b20af84c9a5e968cabea23dd6815968b93234b9b34f8108e1", "0xae22d05bd7cd226ba438387b13606f1ad88319c787ccdcec28ab4de6e9bd5fd1ede497ebb746c3313cd6655b961689d"]; let xp = [("0x122915c824a0857e2ee414a3dccb23ae691ae54329781315a0c75df1c04d6d7a50a030fc866f09d516020ef82324afae", "0x9380275bbc8e5dcea7dc4dd7e0550ff2ac480905396eda55062650f8d251c96eb480673937cc6d9d6a44aaa56ca66dc", "0xb21da7955969e61010c7a1abc1a6f0136961d1e3b20b1a7326ac738fef5c721479dfd948b52fdf2455e44813ecfd892", "0x8f239ba329b3967fe48d718a36cfe5f62a7e42e0bf1c1ed714150a166bfbd6bcf6b3b58b975b9edea56d53f23a0e849"), ("0x893227b499dab30e15b606ec3c375f9fabf7fbb574b9b11c9eefbe33fae82066297e23c518f59e74d5cf646cec6464f", "0x10578234a81819d1ebb3d77b03a128f3165642386fff1b0a74ad73c139425703a991ce459cdc1995351adff98061f0ea", "0x16efa85752a02d4358a92eb3b577c1e27a02ec36000c44403159baf7022541a02104b633549e05b774e1b76343a8e661", "0xaf65df48a519d9209257e3df9fb0a1bd3491799091df954380242592db0bead0ddd62dbe33aeeaf1d4a63bdbc4c6008")]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_1_init_case::(&f, &q, &y, &x); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); } #[test] fn test_bit_1_case_1() { let f = [ "0x11d12be7502f97a642a86eb73802fe0fe4772283c9e66f3d535534c22390e0ca", "0x109dabf551c2a0d785f86365c9f7a4e2aae4c8e3f5bb96b72c3461402f80049e", "0x15e06e6b765f21da4c21d50705a9bf0f72ba0283f93e75a896235fa107d4ca4d", "0x23c17e1664ac6452ffdd3ca599029d07bbea4e54e00dd8289aa145149627cc90", "0x751d37ad50cc00d6245f08ca81ce16f9a3714c3efe87c95ae8e132234b5dd07", "0x0", "0x1535e3c0e51be5f14093e8501425031896dfb26ec8759e3409e44e94d81e17cf", "0xe07f7cf5446bf6fd7f35bd2c741235928fd0f5cc82d853d0b37dd293fe1a21b", "0x2eae2d9b2332fb1f1c3617826ac6ede574d04ed01692a36b9743fc604b3f3bf", "0x2ab0d3ce9813032acfb54c2e7c43299edb854672b7bc17be60c2e1cda8e826c", "0x1f316d8807400efe60a15b7e5311a9031439eb344c0d84fb80044f8786d59de4", "0x0", ]; let q = [ ( "0x27dc7234fd11d3e8c36c59277c3e6f149d5cd3cfa9a62aee49f8130962b4b3b9", "0x203e205db4f19b37b60121b83a7333706db86431c6d835849957ed8c3928ad79", "0x4bb53b8977e5f92a0bc372742c4830944a59b4fe6b1c0466e2a6dad122b5d2e", "0x195e8aa5b7827463722b8c153931579d3505566b4edf48d498e185f0509de152", ), ( "0x19092b3d714b3bb6599b735386dd05eab401e72057bab79773a6de8f5693387b", "0x1acb3fbdde3ce471791558747f0e52b1b7a708834dc533393bcfc2af317703ee", "0x258d7966e4b36382460549a44d5cbe96fbe1c412e36f25218438f72d7d387077", "0x2a58bf6a639ae104439ba4e8db873938a26fcd5bd0b68beb20c44705d9820860", ), ]; let s = [ ( "0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "0x1d9befcd05a5323e6da4d435f3b617cdb3af83285c2df711ef39c01571827f9d", "0x275dc4a288d1afb3cbb1ac09187524c7db36395df7be3b99e673b13a075a65ec", ), ( "0x1314aaf1c372e6d7635e573808d9d5c7178bdce7335eb0538f718d8e6651eeb1", "0x14c25d3aec745e5a2d4aba9e1448a8cc1048d01a5289f29ccc5acf5e81526673", "0x302adae1297f41f9fdd327cfa91c5688fc16dce6579ff99d6699ed49b4d2445e", "0x1800a20cf49101a007f783b70334fbdecf9be4f63017754e9afc5721ead62211", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let xf = [ "0x44e300afb5d8c9fe4ed7556cdf91d67bae6f78cdd7b5afdb2d62ae76d668cf9", "0x2d6f11dc8d07f13fae893dc146f477a28fdcbe346b5536270b156027e060cbb6", "0x1d6149797ffea4e32ec9ad26f54081fc57e62a50c0657a81f91fe7e5b0ee93d0", "0x297f8335441b111054cbff68ca424972bff570bcb8b05d4876e93c92fe0b6ff0", "0x7aedbe74e081653144a40e4713c7d64ce54773908e447526ec741ff71182e8d", "0x164a744315557a2bcc0654ff50e4d8a2ee66dd2a5046c3a93c677b5d76febcf5", "0x2b1a554f7baf8c4b91a81e797d2cafbc401bd86d331a29d9309ced81b8b81c26", "0x197d1963b67e5a1ffff3e87eca2bc07326ce5e0b7be87d82a1f0ed18c864f08c", "0x1bf49bd642edf7a1b83ca6efc6293abfcf04bdc29066ceb99b02c0e71bd454f0", "0x243aef64db80f1e463301ece27afe624978d8bfc8033b3470b14731fd488561f", "0x2c2632c4740be43538ff3ac49b28b87df2ae5ebe6c5f5853b62815d62cb02e1e", "0x4a1156582f27dbbb55d2203377de72269bee7a13ed0105a8a6f2e434c3bcc6d", ]; let xp = [ ( "0x6064e784db10e9051e52826e192715e8d7e478cb09a5e0012defa0694fbc7f5", "0x1014772f57bb9742735191cd5dcfe4ebbc04156b6878a0a7c9824f32ffb66e85", "0x58e1d5681b5b9e0074b0f9c8d2c68a069b920d74521e79765036d57666c5597", "0x21e2335f3354bb7922ffcc2f38d3323dd9453ac49b55441452aeaca147711b2", ), ( "0xbddb1ea5c182ba12d0762b9c85ebd180541e0b153ca85ff24489f09cb0d44a7", "0x2170b47e91296dad38a19f370fa3368b1f333b8f05e5018b7a38af0a045be237", "0x760488b80e6b5dd63b4b7422f5609df112bf8a63604449ae3020c63ad8e2489", "0x1c937b1f996ef4397c744c8b2503cf644feb5b6d8b7f77237a7b8a2bcb98583a", ), ]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let s = s .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let (f, p) = bit_1_case::(&f, &q, &s, &y, &x); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); } #[test] fn test_bit_1_case_2() { let f = ["0x1913c7c566f59082bc8178020dbab618db967238ea9cd35f30a48e8f4e37b31fa826f2ce8023e3f492da64e7fc430262", "0xe88184d680a3c04ed182e6b263c806982325a7601dab1e928ee1cf7c98a702c77ef44f6202e8049b3eb05d0d530416d", "0x133b8d475abdbde6aa5ce6524599001bdebe394bd4b3c7a7c62a4c736176f27fabcb165d0e9db88c3aa8af04ac87b690", "0xff88e1756ceadda3075ef7ac6f1764de912e15b03a34e439b837bfa984174e90399e3fbda93a12cc209b1ed1469ab6f", "0xa2e5dd0e5330c07becfea58e47106140d177f1b1241de5c1e752050408f4970ed1275db43a9c3cc8b4f393a72148638", "0x1124c5ec5de53991b87616d2e433c3387e4ea68342f9713bcf93e2be0ff2b07e03ff0091e0ff71ae050db38a10394cca", "0x47203ee35055ffa8e288c3da40c9831b46d6c7b911ea92ee62d4af79903c75831bb79321155920b413155ca1f2424bf", "0x180ccf08a53eb9416fc958429dfea456e5e802217f5f5ecc44653622720256512e4c7f01efa251cd28065c103db44f11", "0xf4e1f72f26c9590b43bc7b7c45fff374a786d462f2dc275bc0812c9a26969ce0bd7d8fc5a90a9fa47cb7f40320d6418", "0x134043dade475ebc5c796603d3ae7161f7f06e07e968716ea64520685e44705bd9221f8d7d7b0b9e2d131576fdb3af44", "0x19ceec83acdc521e6a9dbf17392e097e01a2685cc2c9d7f3f1430e22221070d222e599ac3e9142d486383eec146b8dac", "0x7ca2e9db2452cc19c71ff5049bdd024819954fb83f0f903169da844e8fe4a584031b750f0678f8661f1c1e1f4653a84"]; let q = [("0x19e384121b7d70927c49e6d044fd8517c36bc6ed2813a8956dd64f049869e8a77f7e46930240e6984abe26fa6a89658f", "0x3f4b4e761936d90fd5f55f99087138a07a69755ad4a46e4dd1c2cfe6d11371e1cc033111a0595e3bba98d0f538db451", "0x17a31a4fccfb5f768a2157517c77a4f8aaf0dee8f260d96e02e1175a8754d09600923beae02a019afc327b65a2fdbbfc", "0x88bb5832f4a4a452edda646ebaa2853a54205d56329960b44b2450070734724a74daaa401879bad142132316e9b3401"), ("0x1604bd06ba18d6d65bdd88e22c26eaef8a620a1a9fefe016d00eac356f9ceda8bc8eee5e46f9f4736ab22cff0e8cb9e8", "0x3e5755e9bfc250ff0a03efea22428a36a247504e613980918dc5319efb7f66b10d5fe2e7e86af7e014e1456aeaeac5f", "0x5655a99f7ff904c1e41382c25ff0360d9c51d0e331bfb1e38f5dd41c6909caaf6e313f47f727922109bf8c3204fe274", "0x62ec2ed9b207f63e0d9899ed11f9a125b472586b65bb77b8a04d5d446d15a8701ba5c361a07cd85e0743f5ae2e95a9f")]; let s = [("0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8", "0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e", "0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801", "0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be"), ("0x82dc9154807866eb0f36ccb665a5fc010510bd690ddd7b540e5bf3ff02d81e98b75703a3b3d3c305a70960906e6cb09", "0xdd18d077ad5bd58dabb18d84a6ceebe6375a83dd242851bb4dcf956002c4efb974ffceee6709deb0dcf81d4285e5e60", "0x4a468eb9e206b9833d8e8e2197d3446652372ce5ef50e93c91aa58105d3a281b2e84ddb61535fe1a90bae7e6692f9b0", "0x198fd0ab6249082bf7007d7e8be8992de81f47ae3341c590194fa3bf769a2e5a5253527727115c334e82ed4be8da6c10")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let xf = ["0x1a009648cc19099f6492fffcdbb1fbed70f61197872a6cbe7e8dda188a5d86701784d71b61130b358bf54a34a90ef1b9", "0x12a81cb61e9b5488fd7cdce673b05acb85475e23b8a68a787721d157650449c422c2903f1f40bab857321ca2aa7ad526", "0x9f9613378d1e258091b5642054bd71a71b047398ae80810d638e9376ae6e45487b41b4d0e5f766f5213b574c27049a1", "0xa211beb012676eacf4c5b94424d3691722b63d3d4493933ffac06589780f351522a8581a194c0663460652181577475", "0x7cdae4413bdf98e6ddbde01882644efcf0cda6141b28ae006abaea3bd405dfcece6208283faef1dad7be06019612c51", "0x1000cb1d25ade5a4224ab93d088ac6a9c5a26cb42b515b71b62ea00d23d39580d75fc848b3ed14fe32b393cd2aa77a29", "0xdfa1993791bd8119033f1734210190856724381a8c45726a9f0f2639f7d5d6b088f4771ae23235234d8108f4beb088", "0x3defca275c0c70ef01a514491daac5461b809ecd6890ef97bafc8e603d20c8e1c75650097bcbc9aaf67428bff100652", "0x62dde56c4a01536859050695f6b9236a150fe6cc3bfd1cfe15921706a387e20dc210c1e0d186abb3a2bcbf8c468135d", "0x15c7bab248f754a557cbaac90c4dda45383bdb5d55cc267955f7b12c32aadcce7f967fcc20f5e803369dfbb63332db60", "0x16a53e4e17f1ba363ae7d2374caaf5b1c11876e4979c1d9ad8f6503f3e2bc05b4fecb1c25d4639d2664929ce90b9552f", "0xb943117f90666049d9ca925443e630eb956afcd48a48f44b90da802913f096aad69e0be1318bff8e88512eaa1f1e13d"]; let xp = [("0x152110e866f1a6e8c5348f6e005dbd93de671b7d0fbfa04d6614bcdd27a3cb2a70f0deacb3608ba95226268481a0be7c", "0xbf78a97086750eb166986ed8e428ca1d23ae3bbf8b2ee67451d7dd84445311e8bc8ab558b0bc008199f577195fc39b7", "0x845be51ad0d708657bfb0da8eec64cd7779c50d90b59a3ac6a2045cad0561d654af9a84dd105cea5409d2adf286b561", "0xa298f69fd652551e12219252baacab101768fc6651309450e49c7d3bb52b7547f218d12de64961aa7f059025b8e0cb5"), ("0xbfa363ea499e05a429d9af2a73ba635e0ff3825edddacfab8afc6b9188700c835282a2c4c7effe70dc61c557b8d90e1", "0x5c3fefe5849b36814f32ce71dee6eba467b220e1b53f01421b9ec6d23209f6206e864539ddaa327b085ad8d78a8589b", "0x17b304f1c4f58afee1ecd75f1570b13da2ee02dfc5731f82ac55d5b6d011ce70ae42061b3d205cbe49efdfcd8d2c04b4", "0x101d88f38de6be9d7eb2c074905585f487715b3e6d8179a066ba56988207caa28f7a5f1ba2f7abd01e200ac71d198282")]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let s = s .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_1_case::(&f, &q, &s, &y, &x); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); } } ================================================ FILE: tools/garaga_rs/src/pairing/multi_pairing_check.rs ================================================ use crate::algebra::extf_mul::{direct_to_tower, tower_inv, tower_mul, tower_to_direct}; use crate::algebra::g1point::G1Point; use crate::algebra::g2point::G2Point; use crate::algebra::polynomial::Polynomial; use crate::definitions::{CurveID, CurveParamsProvider}; use crate::frobenius::{frobenius, get_frobenius_maps_ext_degree_12}; use crate::pairing::multi_miller_loop::{ bn254_finalize_step, conjugate_e12d, double_and_add_step, double_step, extf_inv, extf_mul, miller_loop, precompute_consts, remove_and_compact_elements_given_sparsity, triple_step, }; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::field::traits::{IsField, IsPrimeField, IsSubFieldOf}; use lambdaworks_math::traits::ByteConversion; pub fn get_max_q_degree(curve_id: CurveID, n_pairs: usize) -> usize { let line_degree = match curve_id { CurveID::BN254 => 9, CurveID::BLS12_381 => 8, _ => unimplemented!(), }; let f_degree = 11; let lambda_root_degree = 11; match curve_id { CurveID::BN254 => { // Largest degree happens in bit_10 case where we do (f*f*C * Π_n_pairs(line)^2 * Π_n_pairs(line)) 4 * f_degree + 2 * lambda_root_degree + 4 * line_degree * n_pairs + line_degree * n_pairs - 12 } CurveID::BLS12_381 => { // Largest Q happens in bit_00 case where we do (f*f* Π_n_pairs(line)^2 * Π_n_pairs(line) 4 * f_degree + 2 * line_degree * n_pairs + line_degree * n_pairs - 12 } _ => unimplemented!(), } } fn get_final_exp_witness(f: &[FieldElement]) -> (Vec>, Vec>) where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { use crate::io::{element_from_biguint, element_to_biguint}; let f = f.iter().map(element_to_biguint).collect::>(); let curve_id = F::get_curve_params().curve_id; let (c, wi) = crate::pairing::final_exp_witness::get_final_exp_witness( curve_id as usize, f.try_into().unwrap(), ); let c = c.iter().map(element_from_biguint).collect::>(); let wi = wi.iter().map(element_from_biguint).collect::>(); (c, wi) } pub fn get_root_and_scaling_factor( p: &[G1Point], q: &[G2Point], m: &Option>, ) -> (Polynomial, Vec>, Vec) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { assert!(p.len() >= 2); let f = miller_loop(p, q); let mut f = direct_to_tower(&f.get_coefficients_ext_degree(12), 12); if let Some(m) = m { let m = direct_to_tower(&m.get_coefficients_ext_degree(12), 12); f = tower_mul(&f, &m, 12); } let (lambda_root, scaling_factor) = get_final_exp_witness(&f); let curve_id = F::get_curve_params().curve_id; let lambda_root_or_inv = match curve_id { CurveID::BN254 => lambda_root, CurveID::BLS12_381 => tower_inv(&lambda_root, 12), _ => unimplemented!(), }; let lambda_root = Polynomial::new(tower_to_direct(&lambda_root_or_inv, 12)); let scaling_factor = tower_to_direct(&scaling_factor, 12); let scaling_factor_sparsity = vec![ true, false, true, false, true, false, true, false, true, false, true, false, ]; for i in 0..scaling_factor.len() { if !scaling_factor_sparsity[i] { assert_eq!(scaling_factor[i], FieldElement::from(0)); } } (lambda_root, scaling_factor, scaling_factor_sparsity) } fn bit_0_case( f: &Polynomial, q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_points.push(t); } let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_points) } fn bit_00_case( f: &Polynomial, q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone(), f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1.clone()); new_lines.push(l1); new_points.push(t); } let mut new_new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&new_points[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_new_points.push(t); } let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_new_points) } fn bit_1_init_case( f: &Polynomial, q: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], c: &Polynomial, qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone(), c.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = triple_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_lines.push(l2); new_points.push(t); } let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_points) } #[allow(clippy::too_many_arguments)] fn bit_1_case( f: &Polynomial, q: &[G2Point], q_select: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], c_or_c_inv: &Polynomial, qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone(), c_or_c_inv.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = double_and_add_step(&q[k], &q_select[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_lines.push(l2); new_points.push(t); } let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_points) } #[allow(clippy::too_many_arguments)] fn bit_01_case( f: &Polynomial, q: &[G2Point], q_select: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], c_or_c_inv: &Polynomial, qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone(), f.clone(), f.clone()]; let mut new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&q[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1.clone()); new_lines.push(l1); new_points.push(t); } let mut new_new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = double_and_add_step(&new_points[k], &q_select[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_lines.push(l2); new_new_points.push(t); } new_lines.push(c_or_c_inv.clone()); let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_new_points) } #[allow(clippy::too_many_arguments)] fn bit_10_case( f: &Polynomial, q: &[G2Point], q_select: &[G2Point], y_inv: &[FieldElement], x_neg_over_y: &[FieldElement], c_or_c_inv: &Polynomial, qis: &mut Vec>, ris: &mut Vec>, ) -> (Polynomial, Vec>) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]>, { let mut new_lines = vec![f.clone(), f.clone(), f.clone(), f.clone()]; new_lines.push(c_or_c_inv.clone()); new_lines.push(c_or_c_inv.clone()); let mut new_points = vec![]; for k in 0..q.len() { let (t, l1, l2) = double_and_add_step(&q[k], &q_select[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1.clone()); new_lines.push(l1); new_lines.push(l2.clone()); new_lines.push(l2); new_points.push(t); } let mut new_new_points = vec![]; for k in 0..q.len() { let (t, l1) = double_step(&new_points[k], &y_inv[k], &x_neg_over_y[k]); new_lines.push(l1); new_new_points.push(t); } let new_f = extf_mul(new_lines, None, Some(qis), Some(ris)); (new_f, new_new_points) } #[allow(clippy::type_complexity)] pub fn multi_pairing_check( p: &[G1Point], q: &[G2Point], m: &Option>, ) -> ( Polynomial, Option>, Polynomial, Vec>, Vec>, Vec>, ) where F: IsPrimeField + CurveParamsProvider + IsSubFieldOf, E2: IsField; 2]> + IsSubFieldOf, E6: IsField; 3]> + IsSubFieldOf, E12: IsField; 2]>, FieldElement: ByteConversion, { assert_eq!(p.len(), q.len()); // let n_pairs: usize = p.len(); let (y_inv, x_neg_over_y) = precompute_consts(p); let loop_counter = &F::get_curve_params().loop_counter; let (mut qis, mut ris) = (vec![], vec![]); let (c_or_c_inv, scaling_factor, scaling_factor_sparsity) = get_root_and_scaling_factor(p, q, m); let w = Polynomial::new(scaling_factor.clone()); let compact_scaling_factor = remove_and_compact_elements_given_sparsity(&scaling_factor, &scaling_factor_sparsity); let lambda_root; let lambda_root_inverse; let c; let c_inv; let curve_id = F::get_curve_params().curve_id; match curve_id { CurveID::BLS12_381 => { lambda_root = None; lambda_root_inverse = c_or_c_inv.clone(); c = None; c_inv = conjugate_e12d(lambda_root_inverse.clone()); } CurveID::BN254 => { lambda_root = Some(c_or_c_inv.clone()); lambda_root_inverse = extf_inv(&c_or_c_inv, Some(&mut qis), Some(&mut ris)); c = Some(c_or_c_inv.clone()); c_inv = lambda_root_inverse.clone(); } _ => unimplemented!(), } let mut f = c_inv.clone(); let mut qs; let mut q_neg = vec![]; if loop_counter.contains(&-1) { for point in q { q_neg.push(point.neg()); } } let start_index = loop_counter.len() - 2; if loop_counter[start_index] == 1 { (f, qs) = bit_1_init_case(&f, q, &y_inv, &x_neg_over_y, &c_inv, &mut qis, &mut ris); } else if loop_counter[start_index] == 0 { (f, qs) = bit_0_case(&f, q, &y_inv, &x_neg_over_y, &mut qis, &mut ris); } else { unimplemented!(); } let mut i: i32 = (start_index - 1) as i32; while i >= 0 { let idx = i as usize; if loop_counter[idx] == 0 { if idx > 0 { let next_bit = loop_counter[idx - 1]; if next_bit == 0 { // 00 case let (new_f, new_points) = bit_00_case(&f, &qs, &y_inv, &x_neg_over_y, &mut qis, &mut ris); f = new_f; qs = new_points; i -= 1; // Skip next bit } else if (next_bit == 1 || next_bit == -1) && F::get_curve_params().curve_id == CurveID::BN254 { // 01 or 0(-1) case let q_select: Vec> = qs .iter() .enumerate() .map(|(k, _)| { if next_bit == 1 { q[k].clone() } else { q_neg[k].clone() } }) .collect(); let c_or_c_inv = if next_bit == 1 { &c_inv } else { c.as_ref().unwrap() }; let (new_f, new_points) = bit_01_case( &f, &qs, &q_select, &y_inv, &x_neg_over_y, c_or_c_inv, &mut qis, &mut ris, ); f = new_f; qs = new_points; i -= 1; // Skip next bit } else { // Single 0 (BLS only) let (new_f, new_points) = bit_0_case(&f, &qs, &y_inv, &x_neg_over_y, &mut qis, &mut ris); f = new_f; qs = new_points; } } else { // Single 0 at the end let (new_f, new_points) = bit_0_case(&f, &qs, &y_inv, &x_neg_over_y, &mut qis, &mut ris); f = new_f; qs = new_points; } } else if loop_counter[idx] == 1 || loop_counter[idx] == -1 { let q_select: Vec> = qs .iter() .enumerate() .map(|(k, _)| { if loop_counter[idx] == 1 { q[k].clone() } else { q_neg[k].clone() } }) .collect(); let c_or_c_inv = if loop_counter[idx] == 1 { &c_inv } else { &c.clone().unwrap() }; if idx > 0 && loop_counter[idx - 1] == 0 && F::get_curve_params().curve_id == CurveID::BN254 { // 10 or (-1)0 case let (new_f, new_points) = bit_10_case( &f, &qs, &q_select, &y_inv, &x_neg_over_y, c_or_c_inv, &mut qis, &mut ris, ); f = new_f; qs = new_points; i -= 1; // Skip next bit } else if idx == 0 || F::get_curve_params().curve_id == CurveID::BLS12_381 { // Single ±1 at the end let (new_f, new_points) = bit_1_case( &f, &qs, &q_select, &y_inv, &x_neg_over_y, c_or_c_inv, &mut qis, &mut ris, ); f = new_f; qs = new_points; } else { panic!("Bit {} not implemented", loop_counter[idx]); } } else { panic!("Bit {} not implemented", loop_counter[idx]); } i -= 1; } let final_r_sparsity = Some(vec![ true, false, false, false, false, false, false, false, false, false, false, false, ]); let frobenius_maps = get_frobenius_maps_ext_degree_12(curve_id); match curve_id { CurveID::BN254 => { let mut lines = bn254_finalize_step(&qs, q, &y_inv, &x_neg_over_y); lines.insert(0, f); f = extf_mul(lines, None, Some(&mut qis), Some(&mut ris)); let c_inv_frob_1 = frobenius(&frobenius_maps, &c_inv, 1, 12); let c_frob_2 = frobenius(&frobenius_maps, c.as_ref().unwrap(), 2, 12); let c_inv_frob_3 = frobenius(&frobenius_maps, &c_inv, 3, 12); let mut ps = vec![f, w, c_inv_frob_1, c_frob_2, c_inv_frob_3]; if m.is_some() { ps.push(m.clone().unwrap()); } f = extf_mul(ps, final_r_sparsity, Some(&mut qis), Some(&mut ris)); } CurveID::BLS12_381 => { let c_inv_frob_1 = frobenius(&frobenius_maps, &c_inv, 1, 12); f = conjugate_e12d(f); let w = conjugate_e12d(w); let c_inv_frob_1 = conjugate_e12d(c_inv_frob_1); let mut ps = vec![f, w, c_inv_frob_1]; if m.is_some() { ps.push(m.clone().unwrap()); } f = extf_mul(ps, final_r_sparsity, Some(&mut qis), Some(&mut ris)); } _ => unimplemented!(), } ( f, lambda_root, lambda_root_inverse, compact_scaling_factor, qis, ris, ) } #[cfg(test)] mod tests { use super::*; use crate::algebra::extf_mul::from_e2; use crate::definitions::{BLS12381PrimeField, BN254PrimeField}; #[test] fn test_get_root_and_scaling_factor_1() { let p = [ ( "0x1d0634f3f21e7890d1df87eab84852372b905c9ccdb6d03cb7b9a5409b7efcd8", "0x24c53532773dce26eb3f1d6ba3b10e2b53dc193baa1d4f4d3021032564460978", ), ( "0x2585e4f8a31664cbfc531bccffafcf1e59d91fb9536c985db33c69f7c242e07a", "0x1d2d2799db056ed14f48d341183118d68ea4131357fa42444057cf0c1d62ae3c", ), ]; let q = [ ( "0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa", "0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", ), ( "0x1314aaf1c372e6d7635e573808d9d5c7178bdce7335eb0538f718d8e6651eeb1", "0x14c25d3aec745e5a2d4aba9e1448a8cc1048d01a5289f29ccc5acf5e81526673", "0x397391b7b25e2fba7d1de6d86501d49b6a8dab10d1d0efd5869ecd23aab8e9", "0x1863ac65eca09e89b058c1ff7e4c5c7ec7e5859b385a553ea12434f4eda6db36", ), ]; let c = [ "0x14156ca1853095df27f3cb7c50eca75e794d2f14195c16df4a0f8f9dcb48bee9", "0xdc2a20a6107d4c49fed6b2018946bcc2a8dad06f01d099a6df0a4a55ed21b59", "0x14260c5afb0b1148ed80f8339cf9e06ff04257cb6c1817c4efa721fc98f69503", "0xafe8a09df07bf3dffefe512eb9448ef436dd090f98323135baab8ae3c766c60", "0x114692950f53d4f707bb02cc2b5dc98aff5936811707d6579371dae20368253c", "0x2dd3fca72591963149646f1e106dc0ee917551f5a9da397fe12d4a3939ce650c", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ]; let f = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let xs = [ true, false, true, false, true, false, true, false, true, false, true, false, ]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let xc = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = f .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; let (c, f, s) = get_root_and_scaling_factor::< BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&p, &q, &None); assert_eq!(c, xc); assert_eq!(f.to_vec(), xf); assert_eq!(s.to_vec(), xs); } #[test] fn test_get_root_and_scaling_factor_2() { let p = [ ( "0x72f26b55fb56be102cd3bc838c66439a3d6160b5c724369afbc772d02aed58e", "0x2884b1dc4e84e30fce2f55e418ca01b3d6d1014b772ca79c580e121ca148fe75", ), ( "0x72f26b55fb56be102cd3bc838c66439a3d6160b5c724369afbc772d02aed58e", "0x2884b1dc4e84e30fce2f55e418ca01b3d6d1014b772ca79c580e121ca148fe75", ), ( "0x72f26b55fb56be102cd3bc838c66439a3d6160b5c724369afbc772d02aed58e", "0x2884b1dc4e84e30fce2f55e418ca01b3d6d1014b772ca79c580e121ca148fe75", ), ]; let q = [ ( "0xf0e8184945e8d3483069b5050fd7194c7e35d0c0a30b422f34656d6c94e40be", "0x1752c7b6b35af45db602cf367841e5047ffab14de9079ee8fa5e15901dfef27", "0xa822a5ba029a28335c8bbffe201ffd56deb5dea4dafbd7f615fd2aa9f5a0acc", "0x1228147f83e3ea517fe961ad4b8ee3bf2ade626ec6d9e4fafec17b8404c0341", ), ( "0xf0e8184945e8d3483069b5050fd7194c7e35d0c0a30b422f34656d6c94e40be", "0x1752c7b6b35af45db602cf367841e5047ffab14de9079ee8fa5e15901dfef27", "0xa822a5ba029a28335c8bbffe201ffd56deb5dea4dafbd7f615fd2aa9f5a0acc", "0x1228147f83e3ea517fe961ad4b8ee3bf2ade626ec6d9e4fafec17b8404c0341", ), ( "0xf0e8184945e8d3483069b5050fd7194c7e35d0c0a30b422f34656d6c94e40be", "0x1752c7b6b35af45db602cf367841e5047ffab14de9079ee8fa5e15901dfef27", "0xa822a5ba029a28335c8bbffe201ffd56deb5dea4dafbd7f615fd2aa9f5a0acc", "0x1228147f83e3ea517fe961ad4b8ee3bf2ade626ec6d9e4fafec17b8404c0341", ), ]; let m = [ "0x590ff61397d0dd212bfc53caae870d85457c4bcfaccb300f066ee143625434e", "0xf706ef44c1d0af1cc055f39a02506234d00e8eb3d74a2131fff08abcc77f5ff", "0x22a5875254921ffd7da5ae6eba3609b9a258aeb54605464626791e8c2d23914a", "0xae461e60176f9fc701510a38855b7b7bbcf7e5ba36080e7d54da24b20b89bf4", "0xaae21f01619c3fa4ec0223c3dc06216c285cccb310a2f82381041f00ab0a97b", "0xe203da0f9a03b1aac945c0f61fb2673fb43b2aaa206b95ba090599b7a5e8c2e", "0x1e2de9ed7968cac14ad4e2c546956c34ec381b30280fda652c0775ee0202237c", "0xf3b13b4d08af03303a0db8cbb989aa911eec40dff110a40e2837285a53cdc9", "0x242bd1109f659686c79a5ba5d705c69b59a88b64622927b875c780e6f64e6abe", "0x1f626f25b03417e492d2dc829a2f34f4ee684f0447a207ed1fe3501ee8a66a12", "0x234cc399b032b927dca506524d7f4aeb8f0939709cf6ea1c727f2d3d16f4095b", "0x8dd178fb6d5acd8339c2266bcf3504782285acc0c04208d92713b2b39e39f93", ]; let c = [ "0x25202875a18b48d6e87a29af47945c59bebde6e323ca9e30f07b55b24f193b0f", "0xe200b0579a47bb3bc4e8cdff399f10e04552e9e73c45803819fb7aff4be48d4", "0x2743277dfb400b1209b242eecb685264d1d38f92b7e202dd946f1c1e893294f5", "0x7ce37c37c9a9830297d2b276e1e10592a67e028713dcf49af707a72abcdd23f", "0x2209ca34e9632ffe10ec67e9ba10af63294f90671a1e7136ddb0226444e3dd93", "0x56824745ec0be7ecd30a7361a37968571854966282b36f9275c1d75a96b4bba", "0x21c2ff8564f4b3599e173cc60a49b16b0ae54cb6fd161b3f69becd983863c1f8", "0x21dfaf1ab1424f7a1d49d1548ca28958a1477f7783b2b95b17f74a4135c8f0ec", "0x2cedae6373f81ff31d527af4bf9944d9cacfc9b69f42e8c899eb37b1c750776a", "0x1b4e8f8bab34df2763de3d3ed13db73b40636e335826957af02c5ff75ecf2f7f", "0x1da51303ee50de4521c9659455fa7db99219fcb1e47acbb5fc054b575c4de206", "0x291ee2a6f851083adcca144de9ddd923bbb33c4bfba59dce6d63b61b27c81f88", ]; let f = [ "0x1", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", ]; let xs = [ true, false, true, false, true, false, true, false, true, false, true, false, ]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let m = Polynomial::new( m.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xc = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = f .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree6ExtensionField; let (c, f, s) = get_root_and_scaling_factor::< BN254PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&p, &q, &Some(m)); assert_eq!(c, xc); assert_eq!(f.to_vec(), xf); assert_eq!(s.to_vec(), xs); } #[test] fn test_get_root_and_scaling_factor_3() { let p = [("0x59d2a79bda5f8a941d4db9e360a80121d5ef96fd687003db24ddec0e0c3b63d82efa81fe174bb39be8658ef83c8c2d", "0x2df47e8cdf189985d5085bdcebb5ee96e40a033f5d3b7986f6992be16bc35f88c471acf7f68344f543e52fe891285a9"), ("0x105dcc4dce3960447d21d3c1dc39e973aaf31de52219df089bb5f797ac6d3395b71420b50de4f62a6588c9401ffefbd3", "0x17cb6c41f0c4e1a7394ab62a9db0be660d847ccc58358f3f9b63c98d9a7845c52e1e2b0faefd0d854043fd325dd3c34f")]; let q = [("0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8", "0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e", "0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801", "0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be"), ("0x82dc9154807866eb0f36ccb665a5fc010510bd690ddd7b540e5bf3ff02d81e98b75703a3b3d3c305a70960906e6cb09", "0xdd18d077ad5bd58dabb18d84a6ceebe6375a83dd242851bb4dcf956002c4efb974ffceee6709deb0dcf81d4285e5e60", "0x4a468eb9e206b9833d8e8e2197d3446652372ce5ef50e93c91aa58105d3a281b2e84ddb61535fe1a90bae7e6692f9b0", "0x198fd0ab6249082bf7007d7e8be8992de81f47ae3341c590194fa3bf769a2e5a5253527727115c334e82ed4be8da6c10")]; let c = ["0x521ad898cee9071ebcbf44d874b1a6540a5a24a4fd9c68f45778308171f9267fab695191d4eab620cf33a8eded7fd2c", "0x5966d7f6d173ea01e1a586966651ab83510fb89f6b2afe45cecf0013c8d5695a1e6a597a9f581d9c26c7bc732af4135", "0x110012a0987f151e6eacf408ccd24b9c3e637b240a4100a3ccdc16d44e3cbdf8393eb3557a64d089a1a115a3eab1a695", "0xfc350acc198fbd5b4d95cfcae897c7118bbf9c0479cff61cdaab0fcd1147d96b5521ac4d7d9acb3a8622465c6b1c0fe", "0x6d44964cce393f36664dfb78c36a4b56c817816904d06056f68e9017165ef8db1a4f97532d5c3bbed4da9a68948c926", "0x86f3ebd100f5f5157bc57f79a49542de5fc03a989fe46f82b0c186b4950da2943f4ad019715bc72d9969488889a609f", "0x18776284b17c0858f647e075e04c49ded673151413b8ce9b65bf572081d748820d57d62d54e14ea09aad1c01c5c5faac", "0x647bb2047c521d397fd0f7ae5bd1a1ce889e14808c4ee8f5bd8e019057fb48dad4ea34d4ff280a7232eada165a4400", "0xa97b4be53ee479681acc5ebfc4fae663d5040baacca25a862aae0152d3543705d87df48c8266658d2a03e597cfec8fc", "0x1338aeb075e78cc7505a5d70f24bb9b22ece2fe9e392d6ff22bbd02e82d79e84d590ca9645b2fc96a09f2ffc8b84a4dc", "0xe608702099837e04fc2e999cbb4b845ab04d0a51ea25ee04675bf96847cb9d629da62d1e4354c04ab5208100a0129af", "0x12c968f3ea7364e3ee21b8b2e8162fd74d36e0786ea6a88c7a10d38aa97360f22cd213ab003cca5a2ae19eefaf128521"]; let f = ["0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x18bc5b99f39cbf0fd8d087688e9a0930581e2c940247cd0991e7a80fe41d8f58d83f1513f1ca42a0e74df934924892fb", "0x0", "0x0", "0x0"]; let xs = [ true, false, true, false, true, false, true, false, true, false, true, false, ]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let xc = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = f .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree6ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; let (c, f, s) = get_root_and_scaling_factor::< BLS12381PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&p, &q, &None); assert_eq!(c, xc); assert_eq!(f.to_vec(), xf); assert_eq!(s.to_vec(), xs); } #[test] fn test_get_root_and_scaling_factor_4() { let p = [("0x18154782ce0913b21588066dbed78d3d341e911d49f154540dff1f15010392a6da1f95a6e4f817e54aede0613c17035c", "0x11a612bdd0bc09562856a70df9ef4088763fe611fb85858d3070afd4f0e121de7fcee603d77d61326ef5a9a5a681757"), ("0x18154782ce0913b21588066dbed78d3d341e911d49f154540dff1f15010392a6da1f95a6e4f817e54aede0613c17035c", "0x11a612bdd0bc09562856a70df9ef4088763fe611fb85858d3070afd4f0e121de7fcee603d77d61326ef5a9a5a681757"), ("0x18154782ce0913b21588066dbed78d3d341e911d49f154540dff1f15010392a6da1f95a6e4f817e54aede0613c17035c", "0x11a612bdd0bc09562856a70df9ef4088763fe611fb85858d3070afd4f0e121de7fcee603d77d61326ef5a9a5a681757")]; let q = [("0x120a838699abaae7ed9481944d92a8c02d22b8cea4ff21ab92fab4f255a20d09700542e530d2fddc2fa171cdd4d31a55", "0x158186f6f2dd04cfa4e785476143a906b63b7f3476ad681992e1b13e2c93fc9957b1784151cd5fdc71cf4557ef606935", "0x2bd32fdfe26d866771e21806a44c4a6d642c3dd98128703cde395f3ee4e353cf25a2e219f1c7dcdbe4574f05d0c093b", "0x7ff9623d918ca12e0ff6ccefc83cf9d283b7231df1db3f9eb8540654b533da9b594fc277060005397ea11f7e9a26050"), ("0x120a838699abaae7ed9481944d92a8c02d22b8cea4ff21ab92fab4f255a20d09700542e530d2fddc2fa171cdd4d31a55", "0x158186f6f2dd04cfa4e785476143a906b63b7f3476ad681992e1b13e2c93fc9957b1784151cd5fdc71cf4557ef606935", "0x2bd32fdfe26d866771e21806a44c4a6d642c3dd98128703cde395f3ee4e353cf25a2e219f1c7dcdbe4574f05d0c093b", "0x7ff9623d918ca12e0ff6ccefc83cf9d283b7231df1db3f9eb8540654b533da9b594fc277060005397ea11f7e9a26050"), ("0x120a838699abaae7ed9481944d92a8c02d22b8cea4ff21ab92fab4f255a20d09700542e530d2fddc2fa171cdd4d31a55", "0x158186f6f2dd04cfa4e785476143a906b63b7f3476ad681992e1b13e2c93fc9957b1784151cd5fdc71cf4557ef606935", "0x2bd32fdfe26d866771e21806a44c4a6d642c3dd98128703cde395f3ee4e353cf25a2e219f1c7dcdbe4574f05d0c093b", "0x7ff9623d918ca12e0ff6ccefc83cf9d283b7231df1db3f9eb8540654b533da9b594fc277060005397ea11f7e9a26050")]; let m = ["0x276d8a09b1ef471d61e1fe932f3136b6412048dad82afcf371bde647281b4f0753c7b540b911c83d732e7d278eca2b2", "0x84dc8eb534426c70fdeb97ad357bcaa08f3bcf837b69302f78975823557a6eaed4035682d08819331e98c628ad7e6a4", "0xad1ecf602d65fe881eaa6e0db2e7f9897c5d9aac15601e7eac85ffce2bc7b2518fb953cd8ab7356837a3539e775e8a4", "0xc44713fa939be012d57473ac1ba1386389c858a2803bf5114d8b2b539c52b38e862bb30b4bbd298bab0e4881a5ebb34", "0x17d27924032bad1b96b038a774356664cf5f284c5d9047dd1f6ed0fc4768c4d33ae5bde98c8a60ac405578242750266c", "0x252d46d43966352b46ef871529d5c8a74ead9d4395930565d5411099e394511d4bf5f21dca890b5c14238be57f05981", "0xdb2280eeda7144c402dfe7f6198bb2924ef03ae600f7222606ac452167328657347b2031e65e90c6094915aaef973cd", "0x190ab4a19e1f1b981b892baedf1e1ed1387d8c002c5f3a2031f94b4bb159c235c039f75271c5034bc18b6d1c45a03c30", "0x16e03a19b04611cdff78c5fd9170f7ea386763607860320a369f48c0083f000e7eeec362f00e883b8262021a004b9fc8", "0x128d8d88c3c8616ff326a554bed73f63ea723c5eca33d4914ba7b263cc869557904c59cff3b76b5dfdcf84760b96fa0c", "0x36d2ef1d9b923357234e298303031f5c1bf5e2f73d4750a712262fd5e7ddfa653a4708e4380616825a3a723a4dc2b5c", "0x329f18e7852fa05613e92046afab08a2bc52479f09c105f34b2a5b11f48e46a872245a2be53e886831d35b55f343069"]; let c = ["0x105016815aeab4c1b10cba422f6a4e683585d4ccc465352ad2f1409607d64c54b73d78aa8bdaa3278720844c37567039", "0xe11367a38a9da9df34240738a7a3dca8c8fe5ccf68c0b23ece7f8c4810788c9023c2ad2f14f1369d17825c133efc2d6", "0x13e42c3e0801ac2144a06fbf1712c06213e43c0272585dc031325aee1b1dbae62f7c153bf3c140b105713ed07834b4a", "0xc759210484ca64b6a064096c61d5ab0a8dc2dffbaa7e2dc7336f37c2c0d759c4ff697bf713b362105bba1e8fcbb94a0", "0xd6a3922a006a5ac269f11053acef2763be703fa77d9050683f2d1513c7ce01407cbcbebdb2b0eb950e9144b7f2f02fa", "0xde779332fd6d9f465b20e6a6a17068bd9eb8099e645e126c5ec4b01df1cb55da421916cd7a563e564895cf2511754e1", "0x92dc96c5c90e4a4e20a4cc830355b613eab563b9cb9b14af48de62916116cc249eda46862b4676a303984e5006cae4a", "0xe6467206b01d8ecaea8fdd90675022b9d62cbd8685978d49df16aef14c96dda37955922adef7cf0ce5e70667934f1c", "0x33f8a5722e1821e1f8c5f4aeb067bfcab205abe6c371677f1cea39accc8cc574af258075a0918f6778263817954d908", "0x130fe108a81a7753e3f765d559da93e49907f3bcb160ed13cf4fd2a6884e312f05ffe06b5bec5a38ecbb7806f62dcc79", "0xcd24160fefddfaa66c9468a5c5e051f326dbaef7f17399b2f2f405981e6aca41db75f4d675bac7aed2b433f922616d3", "0x17f2b41158bbf2cb53644eae30ce07f0ccb46385c2b2b40a6e0c09afc5dbcf4dffd7fc0582d362ba811d62d7264e9909"]; let f = ["0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x0", "0x66ba50e8c99edbeedf33b876935c3e1b9cf1af588eafb63c6a64d7c9213ad89ad6e2940079b43033d2c6148ace378dd", "0x0", "0x0", "0x0"]; let xs = [ true, false, true, false, true, false, true, false, true, false, true, false, ]; let p = p .into_iter() .map(|(x, y)| { G1Point::new( FieldElement::::from_hex(x).unwrap(), FieldElement::::from_hex(y).unwrap(), false, ) .unwrap() }) .collect::>(); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let m = Polynomial::new( m.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xc = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = f .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree6ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; let (c, f, s) = get_root_and_scaling_factor::< BLS12381PrimeField, Degree2ExtensionField, Degree6ExtensionField, Degree12ExtensionField, >(&p, &q, &Some(m)); assert_eq!(c, xc); assert_eq!(f.to_vec(), xf); assert_eq!(s.to_vec(), xs); } #[test] fn test_bit_0_case_1() { let f = [ "0x1d7a9ffbbe137d697794dbccbd7925ea98507cf8d4445d3e89123811ede12825", "0x1f45aa2ee73f15e275e5c1fc0ff08be0981a61d8e7642301653a6307c7467811", "0x2446d99f276e4c8bc63d81e8d0c1e37c901a5a569865533968e39b5083fc576e", "0x223bd50b771fcaa905131a5f04c3c634c9df344731b5aada49be919aaa447cc7", "0x24cfef2958a7c9c4d7ddfacdd59750105dcc37f6aefbf4a9ce706bc36252c47", "0x3a974db52b274684955cb370b0ac66e3e295ea6e9789fb7259c294210f7720e", "0x160b7346ec9fdd9841feb355a44845dc30c2a9ae3fb8266ad697b531de5e2fb6", "0xe46af84e1cbba805f204fa5ce1c9a99c79799110a56b5d534495a358f9c739f", "0x1f2b5709d0d7c9499b9524e9708ac412d3fa05fea9b51192113e131bd5572a21", "0x8a75eef583ffc3b0f690cd9eab121b1f329194c1052a86d50224b92838c5d76", "0xef3a64570d17038de7ec74175c125ac7e8780509764f07572ce9593878da9fb", "0x2a6290607745b58a7b87bc78053320664e06d12b35825f15893ad52a39f54331", ]; let q = [ ( "0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa", "0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b", ), ( "0x1314aaf1c372e6d7635e573808d9d5c7178bdce7335eb0538f718d8e6651eeb1", "0x14c25d3aec745e5a2d4aba9e1448a8cc1048d01a5289f29ccc5acf5e81526673", "0x397391b7b25e2fba7d1de6d86501d49b6a8dab10d1d0efd5869ecd23aab8e9", "0x1863ac65eca09e89b058c1ff7e4c5c7ec7e5859b385a553ea12434f4eda6db36", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let xf = [ "0x6e2d5c667e253ffe1d604e9b0c0efb376aaa3e1f2fa8194a9fdd627525394de", "0x2dc3c5e55face7c5e2c971b204e63954fbc8ad239d2d152e532c421b7834a99d", "0x2ff47505930441520ea2801041714bcb5d41a0ffa81940aec94ea9901fcac97d", "0xdab9fd3d1ef5226f76a2af1d6b410d8639501aa55867c1f0779e0422d545f0c", "0x2fea029bdb6a10f53ffd60992916c6410e0f53520845bfd3e55f70e8272c8fb3", "0x2f329aa1c588e3e4b7d8f5bedbe3c09728563ff0c46ce45b66636cb6ba1ee436", "0x2290e74d07afff26a405ca3722d951cb9a512f1c100fa50e29907ad3283e7b83", "0x6bd6eba6eb034c98be6fdabbb6f2986a20934fe7f4ccb1aa1cff1983d7d2ae4", "0x1ca0c85d7f94b5c6b3543992e315765cb35d0f7d49149a6939c1e7afec80ee3c", "0x1f70622e79ccbeb35ecce1f7718bba441de2df4f3e916ca84262a68f9eea11f9", "0x2492333e1554b6d2c1ad39913d06e14c6ad3a1569e62952be0e54c3427ea8aab", "0x2a9baf66b1ec17ae1f6f435746d944886953830b40efced523794fd2aa17d4a", ]; let xp = [ ( "0x27dc7234fd11d3e8c36c59277c3e6f149d5cd3cfa9a62aee49f8130962b4b3b9", "0x203e205db4f19b37b60121b83a7333706db86431c6d835849957ed8c3928ad79", "0x4bb53b8977e5f92a0bc372742c4830944a59b4fe6b1c0466e2a6dad122b5d2e", "0x195e8aa5b7827463722b8c153931579d3505566b4edf48d498e185f0509de152", ), ( "0x19092b3d714b3bb6599b735386dd05eab401e72057bab79773a6de8f5693387b", "0x1acb3fbdde3ce471791558747f0e52b1b7a708834dc533393bcfc2af317703ee", "0x258d7966e4b36382460549a44d5cbe96fbe1c412e36f25218438f72d7d387077", "0x2a58bf6a639ae104439ba4e8db873938a26fcd5bd0b68beb20c44705d9820860", ), ]; let xi = [[ "0x11a253cbe22e3132c161d5e3e3343657bbd9cf3475b824786b01f9b6b2954451", "0x15c7110a9b8d99717d5b36a5ace0ec208511247742b718857d387d03646e962a", "0xce691f6829cbf96477c2680a0b89f055de1342852e78bf44a00a771618a2fb9", "0x1dbb1eac7562ccccd643bd095a91457d40cdc83000932991e9eb0d518a123ac8", "0x334cb5ce87c27266ceb11f14868d44bc2b0d0642fe2d03cccf424afcde8fb8f", "0x2fad54548575eabff6e9ff91ccec2fd782accb81b070e6920fff020ab182dcab", "0x205830d2f4414548e1226815b77fa991c4ad82698e2714e9fe8186d3eb02a938", "0x20e43c4e7765ce864bc67ee78d7ee54a77de4888351a6f55e1014a7ba6b7db7d", "0xf5529f07c581dfe555a1997f4037a95be74e5a845fbe8ef3bfee3bfa46bafee", "0x2fdbcae39c35e9916e344eca4617e328542adda118c9c7647a66752f0f9312be", "0x22cece7898caa51dc9b45b37d3bcab7bee6bf46a8bb62a59772f9bfba17143c7", "0x237133eb50789ad88140f3acabdd1e0eb4f1a5ba81f2dbcf40379242cfcbcebc", "0xd6bc07c1405393e2a04f16c95d908468731b135ec8df7280a411bbf74bc2a97", "0x1c8f529ca5c5f3db100755ee2b62b30fbac4ee36be96a2991bb5c5df10409f30", "0x29692f0b8e65ae15c851e5558aba62671dbbad538149b59ada944f8913daab87", "0x2091081625469e0549f3ad0902bb68b780db24524a08fcab699a012dead87cb5", "0x15420ca5e286164b842ccdd5ede9c9d488836ae7e4250735d913bc865c686ffd", "0x2910950b8c5e2f956ea34c9f80bedc007437f5be8a2d391182d57cc107d44ceb", "0xcddf598527c71f4c6fe7f3a63f2a6088c35d97703d6a457935d29e9e80f32eb", "0x26ffdefe8388fcb1b412d6d5da117ad677c3d01634e46a148db9582257e95966", "0xd6ab9f93f6f075e4d50a47dfd2b76c7891b8a7d309beb55e52ff2573ee2f439", "0x488ebca58142b146b8891ec91c9eb2f7dd13a31d648eb3b58337aa3f473f7c", "0x4a5388ce5bbca66cb7b57f8d1ef6d825f32ba5dee832d7120c24de5db34b0d1", "0x6d4d58288e64b3cc7248a086e64f07c9edd468fe1339b6475c6cabe949e4492", "0x27a0872bf114a6aff047a0c387c16408308894a8586b2ceca263af44b9e5e2ad", "0x212c049231594608761ee58f620b6744e388ff939835e413e987b16a53ac10ee", "0xd6fb3a414a6bf136a738e599e89ac51c2bc026a344b709e78b931803d9eb471", "0x2d5fd74719cbc5e3b6e5d5acbe6d908e436163e27df30a584573e7beecee6a8c", "0x2b238a056fc7b2b14b73eaef6efba5a7fb9ac70d230379d1c72d70fa80ec5f83", ]]; let xj = [[ "0x6e2d5c667e253ffe1d604e9b0c0efb376aaa3e1f2fa8194a9fdd627525394de", "0x2dc3c5e55face7c5e2c971b204e63954fbc8ad239d2d152e532c421b7834a99d", "0x2ff47505930441520ea2801041714bcb5d41a0ffa81940aec94ea9901fcac97d", "0xdab9fd3d1ef5226f76a2af1d6b410d8639501aa55867c1f0779e0422d545f0c", "0x2fea029bdb6a10f53ffd60992916c6410e0f53520845bfd3e55f70e8272c8fb3", "0x2f329aa1c588e3e4b7d8f5bedbe3c09728563ff0c46ce45b66636cb6ba1ee436", "0x2290e74d07afff26a405ca3722d951cb9a512f1c100fa50e29907ad3283e7b83", "0x6bd6eba6eb034c98be6fdabbb6f2986a20934fe7f4ccb1aa1cff1983d7d2ae4", "0x1ca0c85d7f94b5c6b3543992e315765cb35d0f7d49149a6939c1e7afec80ee3c", "0x1f70622e79ccbeb35ecce1f7718bba441de2df4f3e916ca84262a68f9eea11f9", "0x2492333e1554b6d2c1ad39913d06e14c6ad3a1569e62952be0e54c3427ea8aab", "0x2a9baf66b1ec17ae1f6f435746d944886953830b40efced523794fd2aa17d4a", ]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let (f, p) = bit_0_case::(&f, &q, &y, &x, &mut i, &mut j); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_0_case_2() { let f = ["0x6dcf1ec2bee9d55fd7c7dd01f0d89e52ce00053fb4cd271af8ac67e915aa56c1f18943cf63d7acf09f9e238c86f7575", "0x7f05f480f32402899fc238d5e397600577a07eddd78a63793400f32912e689ef50ff7298c542fcbddc8a2f30326ff28", "0x71d870e4553f214175e57f71397705b5336a8c404e29abab7505079976315ae30aea8c7fc8e47f2ce78aed551c79270", "0x37df42454ed3974bb2b32f97123a17956e452893cabef6a29a0888f8ce8b899253e37ae32f0ae88611fa10260d597c0", "0xba703f387adf415b877fd75815f8322190dde62bdc8a55e54b5dec1284a8c9177b3c945a72f0e1e9c109d242988e116", "0x14068f72159c932c910dd5126f8907d9616c496a0f51dbcc5585ddebaf32dc4e03ae577f1f07d02f85fc8a875e197521", "0x17dfc12834ee7334831b24af1174df6680c4991d4d20cc807c5e8df6083d142e2fd17ccfce6bb359366acbb7781372b9", "0x17d3b0da632dabdf4ba0f6c890308dd36ed98b5e1d50a8160a2349e79dd3de20eea74d8b95daa3bc8b9ac34a59ff12f0", "0x17ddaa28e29c2317b96c21b7fd31f8f2bab3cabf17b82c770ed0c77db94e0738119993eb4c5d01ef3358bf5ad26286cc", "0x22b2500baf6ce28a86979f31387bb67348f155192cf97f99aeb257fdcdc23c15eb5315ea817f28532b8d5198e199dd", "0x6524f53a10bd1ed1f7de6acc2d4414912600bfec37d116a4d096e4e54120fe17325dec0b0e382b90ef6654c3bd2e20c", "0xebb85352772f284d12c95bf531a0f1fc69bf6acd1695e9af23d641db780ebb70c7fbfbe8a680e766390ddaa62af47cd"]; let q = [("0x122915c824a0857e2ee414a3dccb23ae691ae54329781315a0c75df1c04d6d7a50a030fc866f09d516020ef82324afae", "0x9380275bbc8e5dcea7dc4dd7e0550ff2ac480905396eda55062650f8d251c96eb480673937cc6d9d6a44aaa56ca66dc", "0xb21da7955969e61010c7a1abc1a6f0136961d1e3b20b1a7326ac738fef5c721479dfd948b52fdf2455e44813ecfd892", "0x8f239ba329b3967fe48d718a36cfe5f62a7e42e0bf1c1ed714150a166bfbd6bcf6b3b58b975b9edea56d53f23a0e849"), ("0x893227b499dab30e15b606ec3c375f9fabf7fbb574b9b11c9eefbe33fae82066297e23c518f59e74d5cf646cec6464f", "0x10578234a81819d1ebb3d77b03a128f3165642386fff1b0a74ad73c139425703a991ce459cdc1995351adff98061f0ea", "0x16efa85752a02d4358a92eb3b577c1e27a02ec36000c44403159baf7022541a02104b633549e05b774e1b76343a8e661", "0xaf65df48a519d9209257e3df9fb0a1bd3491799091df954380242592db0bead0ddd62dbe33aeeaf1d4a63bdbc4c6008")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let xf = ["0x1727a4684524eb2175d31f506b07370100418d3fcd5ad5c5586b3c2927dbffdd38a1a44b46f601ab362202e8276c007d", "0x57d77a9e8e6cd838edc1e63052a64d020d10ab12ab460dd755dec64232750ca866647b373738bbe4943b6aee387caa1", "0x42e0115d1c759474549023340d4f01ea67f2f082b59dec03aa7e22e27bccb5d4840ac815f2c12da594e423a2108737d", "0x54735182a914667a25226c91d61ee1f8c5c6c2e40b633da27379618cb58b0b55c0acff39fe7471a196e8bd9a0db6863", "0x14276d83ecbbeddabdf9bf5d9449deaf0a40d6de94e8347d983e97ed4491a3cda57fabebeb6d788023db42ceefa73d8b", "0xda9195159528161fa4960f25523d4d906c194a134c2695ba34577b4dcbbb76911a90cbb411db147cc5627ef50c9210d", "0x9552828c7dcc07d56efc554f98880b746c6ce0f7f41377d934699dcb5cf7eab408dbe027df4506c40e2424b24c6b69b", "0x122dcaa1ba9a8a8613064735071ae0aeab8e0333d7ff3018c9d51a652303decdf4907f6e7f232224b4fe0b20245f2fd4", "0x112f00e12354b1ad57581a4dde94de861275afae359c3016f8a13e81943a4a18f4896097697c449335ca5f9d21b7f654", "0x13bbf456483cd4566ed59718bd067589e294b4d7084073073fc77a685f0e4ae94092405afc2ecc6d437c20102b74f4ae", "0xeef615cd28929e56a59bf2e2e93db68f2ed629f9872a3b1aefdccb098674950b928bb5c920a2dc4d6405a69dafd98b8", "0xebec00852daa59ee4861f6c55f01d098689453651a335e711a11c3e6606acd9cd851f8132fb24bfa3edf65997e82785"]; let xp = [("0x19e384121b7d70927c49e6d044fd8517c36bc6ed2813a8956dd64f049869e8a77f7e46930240e6984abe26fa6a89658f", "0x3f4b4e761936d90fd5f55f99087138a07a69755ad4a46e4dd1c2cfe6d11371e1cc033111a0595e3bba98d0f538db451", "0x17a31a4fccfb5f768a2157517c77a4f8aaf0dee8f260d96e02e1175a8754d09600923beae02a019afc327b65a2fdbbfc", "0x88bb5832f4a4a452edda646ebaa2853a54205d56329960b44b2450070734724a74daaa401879bad142132316e9b3401"), ("0x1604bd06ba18d6d65bdd88e22c26eaef8a620a1a9fefe016d00eac356f9ceda8bc8eee5e46f9f4736ab22cff0e8cb9e8", "0x3e5755e9bfc250ff0a03efea22428a36a247504e613980918dc5319efb7f66b10d5fe2e7e86af7e014e1456aeaeac5f", "0x5655a99f7ff904c1e41382c25ff0360d9c51d0e331bfb1e38f5dd41c6909caaf6e313f47f727922109bf8c3204fe274", "0x62ec2ed9b207f63e0d9899ed11f9a125b472586b65bb77b8a04d5d446d15a8701ba5c361a07cd85e0743f5ae2e95a9f")]; let xi = [["0x4058ae506a6ea2d9acf5767ef521a39416357fba20e7c319ff4bc05fead6c03a9f34ff39427dd30ca948256f8f5e776", "0x15124e81cc29571ada5ab8d3c9d55f5f083502a4b884a87ea770d7087dce6fc1a4143063e431ab1965a326d6cc5cf28e", "0x190d1a256dc8cad275af59ea8f7d203c3bb8c8a34b2078662bbfd23e7e7294f4afd91a8877df524ca96a0a34ec4fc2d4", "0x18881b4d655fddc0574a3f3cbcbfb2ff8dc94eed30e46b6ae7144979716438563e9ba0cf2a2973a17db83db2e5314407", "0xc65c65aa02e44da35031c6b340fc9709367a561d0bf13a144f325beeba0e0f837e91b5218aac9eb1f28c196c093af1d", "0x10fcc3d0cbcae26707dc37c424fa4c3a37744fbaad96c6df4b766075ccfb1f59f458be55d30259657664f11127121f3c", "0x110c58ec3d55cc3593e958640c42d93f05c964469be251ad45a2e7af7646ff0daba3ef5e5618ece1e61f64fdab4dd60a", "0x173e8e07ef932c01bcc0be6e316728d8acdaebb34d0630aabc5960f155c3dc7c94efff23d3a81c5545aed40de3353b24", "0x167b41861a4cf1f89dd265419cffa76667283a684802d8543352088a297ffac030708ca3205c22ff262b4c32af064100", "0x3b4fa4dc3a053fbc445810c88a8198298b1dad990acb6b4ebb7058fa77a680751dd9ac9bb42ae39582ad6ad7647e2d9", "0xa14179662d3280fa96471af03be7fc5feaca5fbbdd79f0eef4b1e354fc4ae6e4fddf497eeb8f3ad8613273537c80c08", "0xf8242af4b8ae30e76ded4ea3db45d278d4782604e03214436fd0ea18d6f45914fd8d25937ae6c7af57f6c1fa36a075a", "0x1859b038205c8a50cb4f91f15b8828a0c649fd9bd316b0d42bef6398bcb47ec124b1c884dd3c52f08396e95ffa0d2048", "0x15ce69cc39bf81686ea6b3e18bd550a9d570a14a9e397c6c1fefad6e5efd209e994f31f93bdad0f5a85cdf7eb8f71f1e", "0x46f25b1914231273bef92307b4a85cf4f558882c65c35cc36e685ba343e66314e03f1a97b91cb45be155085e29255a8", "0x85450ffae0bf84261ee380b516b33ea88e49cca061f6ccc4818232d9a845081eadd269b1d6c86ac42b4a6c88ba177b8", "0x49d9c4120a63a738795739519c8463107763e61e1aadf534ab6477567e6d327c56c45cb93e9be10a894cab32d9186a9", "0x48aba2f406cc53ac0c9d572d6fd9e99ca649a8d2ce390771d4264c0766a974bf4fc6b3222d6596a946a8187ae404004", "0xb3d9d9f100e451e2ff5d3ff32d211a539a0d90f190e3cc0ccf0d2d44ba805072589b66c7f53c916463cdda53fb33bd0", "0x115caccb0b82e44cf7079fd95d8b6cb506de5e6a67f28c6a5ae713497742697960f5e9dc08d75cacc6f0ea6e4f29e76c", "0x1674a25b64d278d9c8747d1d1a532686bce60ab496ba0ba83a26e3d30942f1ef3c7aa05187a258032ee573659693d6e2", "0x14d18d8c6242d9c3b2cfcf95da5628e94694fec1d40f64e432f1a4e79f9b96ed40b3d9cd602855fde8e8f6527570af27", "0x161fb4586486c4828d6de3f6b1da13867f8db7916355427d8573b8891ec2f2e533e4988d374bf52f0868f45e89b47410", "0x1075865248624b63a4b59a293747451724956b8517187e9554770f9c5551534815ff969dcb1857ce1ab2093cf9c9a8b8", "0x9f685cfe49c968d8c596d9f647ec9a2c5b8b45ae16fef8d7cc9ccd858f5b66fc526c01589a93fadef83efc0b865661c", "0x366861d36b3781daea9909bcde600135486e55965744c33f0f88e1a74f270b402fe2a1eb34bd412007a7501bcc0a1e", "0xe53938fd56c7fdf34c21c1b011fb083c02fb12b440c859f910ff0671a8348d38bac8380d170b07f8dd6e50ac18a8dc8"]]; let xj = [["0x1727a4684524eb2175d31f506b07370100418d3fcd5ad5c5586b3c2927dbffdd38a1a44b46f601ab362202e8276c007d", "0x57d77a9e8e6cd838edc1e63052a64d020d10ab12ab460dd755dec64232750ca866647b373738bbe4943b6aee387caa1", "0x42e0115d1c759474549023340d4f01ea67f2f082b59dec03aa7e22e27bccb5d4840ac815f2c12da594e423a2108737d", "0x54735182a914667a25226c91d61ee1f8c5c6c2e40b633da27379618cb58b0b55c0acff39fe7471a196e8bd9a0db6863", "0x14276d83ecbbeddabdf9bf5d9449deaf0a40d6de94e8347d983e97ed4491a3cda57fabebeb6d788023db42ceefa73d8b", "0xda9195159528161fa4960f25523d4d906c194a134c2695ba34577b4dcbbb76911a90cbb411db147cc5627ef50c9210d", "0x9552828c7dcc07d56efc554f98880b746c6ce0f7f41377d934699dcb5cf7eab408dbe027df4506c40e2424b24c6b69b", "0x122dcaa1ba9a8a8613064735071ae0aeab8e0333d7ff3018c9d51a652303decdf4907f6e7f232224b4fe0b20245f2fd4", "0x112f00e12354b1ad57581a4dde94de861275afae359c3016f8a13e81943a4a18f4896097697c449335ca5f9d21b7f654", "0x13bbf456483cd4566ed59718bd067589e294b4d7084073073fc77a685f0e4ae94092405afc2ecc6d437c20102b74f4ae", "0xeef615cd28929e56a59bf2e2e93db68f2ed629f9872a3b1aefdccb098674950b928bb5c920a2dc4d6405a69dafd98b8", "0xebec00852daa59ee4861f6c55f01d098689453651a335e711a11c3e6606acd9cd851f8132fb24bfa3edf65997e82785"]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_0_case::(&f, &q, &y, &x, &mut i, &mut j); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_00_case_1() { let f = [ "0x9f8f3a5142813065834851b0abdb02873b62058c141808bf3d908c4616492b3", "0x2e48eb414b93a0b30e2c3f393d3ed30b098663d73b820a07ba724a9917378495", "0xbdf45af1f5b4215f808a4d7ad54cfeb6d8eba26084098a37010e1038db40961", "0xf6c4c18f9d9acdf9b467c9e83e6ad6cb145da60900ccb524892622686c3b558", "0x8c23916cee1cbeefa7be656ef56e78fce55e743b2a38810a29073d9d799fbd6", "0x1d16044d319830664057b4957d214455b93b6279e9b5f5ac08dc3072186dc4f3", "0x17f1f10e76b4e9fdb704ceb895c3924cf4727927b0ad3ee897b0f656eabd71b5", "0x1095b03dcb74d1b11d583e19e6bc9ac57db13a0c4f04625b02e3e1bf6d387c36", "0x2d67c398ad69288c687f6f86108390a0cf2dd20821c4399cc18b975d04242497", "0x2955c5cde10bd61dadcf00e62f844d042fa55c88603e3fe991e6720bd794401c", "0x2ecbad3d0674a417f39baea2524cc0790b3ba9673433d6d3c30f1ede92e895d6", "0x11b947c4a0acbee9a2eb50c665bf7a12292ea3bc4cb8e0bfc2f34d527970ee48", ]; let q = [ ( "0x23ad66f3a7cca9dc75049635faebd124316244b91de5fb2764cd151572a905f7", "0x9edaf0698a8c56f51139588acc094cee3c37d427bb6d2eab830aae529097d1", "0x1ad4f87d3b4375a39988ac099b042b1e7c0c715678e4c2bea8905f607cf950f8", "0x2700e8a29b7bb45f3022a18a07bdc66d0254559e17cce64e3b4ad21578fcf410", ), ( "0x2c261e6771e418f02c5225132405065a249033d6f8799261934c3c9f9b3d33f7", "0x270394a3fc58d9e321fcdfb8fffd764208a6caea73d65f24bba0cc1ae0d3750f", "0x2cb21d611ecd44169370fcad2b3dcb1d757f0e468ed4cc0d6c680d0d89c3214e", "0x1a737173a08f49638e4b84b0fbe900d1831d55c6097a45af5af1ec1eaedb5726", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let xf = [ "0x17774e3e8a23ff734ca1598a87bc0412dd8d117f26c62ee7e94dcb29e0357bb1", "0x1982b56c3e0bcdc9c994b0437e4dc0b9527821ca7809068c62de431b5489c670", "0x2872b0c088da975ca497c1a9c18ef0ef3993ddfd09077dade5d72d1ad3abd8fd", "0x2969378a0cfddacbdbcbcc93eb8642d2dc8167a467acef3ecbb15eee40139640", "0x193581cebff836c6d2319b0bfd91255bddcef3eba4383bb93d17ceefd6953d3c", "0x26457780a6d80fcc0f23a463b42645f7fec8e6f0a0008e4410656947089801c1", "0x24e212fee032cb7c7409ae15eaa0aa0311a810586db2f6f180a6b0cab54e0502", "0x260d3e40114b8d2ecb09e3f0e4fcd13eece95b0a7d7b5ce96bac14f5cb32d71b", "0x1b1a5d98ae47d8520d89e8c8fa73dbf28988f9670c62aa77588361bf2193aa0c", "0x19139c8f3a190fa873462ce2dd5f25690f00ec110f4b62996e365f3421a3259b", "0x2143f989b60bcfb4a9887cd610decf67818b14bd709d865aa40c7a52986a5e5a", "0x2d87bf0c00e24b175e5363e0de0a1c9ed68f160c43ca0093e2dca54f07586b65", ]; let xp = [ ( "0x126a285e45fa024002aa806848f10e5b2c64a25c6af0163612ef34379fd72584", "0x1303baa20971befe5aa7458c1164eac4a10108c8abbcd37a1e09d83ee94bdbd5", "0x37dedb5d778240b5f237eaa4160f20981e0ed5d24f832e9eb07004e1a722d0c", "0x1305fcc05ab211db0fd12d1f8f1f894726dc7bdbfedeab57b33af11d81279c2b", ), ( "0xdded79e4d972e50343575387abeef8a0e3c874b791e2c9491e583ed9d1dfd82", "0x2e89537cdf57a51d5d306241c3360b78ab60e5fdbca2bebaae6544d0a9fb6d9a", "0x1f661619c64b414dfbf50599d40cee296e40fee522ff41a1039e9b21d41a37e6", "0x15de46c6b8e5286908252cdc6a905536304a49b95b386e8139797409df7a1527", ), ]; let xi = [[ "0x1b0a3a3d5e555ec6d6bda084d0fad0138fd60d139e23540b5d4a49b45ac56587", "0xc191bad21244bcb105c57c9b4967e036b3b7e3ea1ec8778a8a9371f58d430b1", "0x1f4207ade61d68bb73fe79838db33e1b17e3857b7fe958ab082c04ac63561f87", "0x3ce267d6ec699ef2f104643b6bb6ab6ddfddc83763b2647a99f23941c324142", "0x1b3e7e2fbe90dcaf67c060a52268ee3bf1384274580bfab77a2f986369216fa7", "0x1f4204f30004aaa5ec1e9e3b9e81d05ba8672bb8db19e9a79df837073a2d493b", "0x1c6b68ae31ec29d4014068f482fbe495e277fd1016cf0ca4883e1fe6da155abb", "0x2e2e0e7f32035eddd17a6b3e42c6e311081ee61f8a7372f76c9920109d008214", "0x243ce082e4280ebbfb5b3c1f2175052d62978b43133d9f61b38790b33222f17e", "0x15bc2bb4c2356e76895c57bf67b8d4a2964bb0dbe972a7b446800dfdfe24e6ee", "0xea059ff364db12717381403450f58d590818fff46c46fc0aebdabbb0624ace7", "0xe292bee9383249aeaef594757561443d0fea89fdca0b2e9bb1cb2b9979c6466", "0x14b41af439343d54bd5aa01e3ac5dbf852fe6ae591dbd86765e376787ee3cc0d", "0x1dd42fe7d2d0f14e414514edb81e5f7578d0ad524267c77457f5dc16dc8dfa2e", "0x1099b52fd7afa1cb074293cca265168ad673ef7ae209f473fd17bea6e168a5bb", "0x17fcc96a8db4a93d6470aab33710e1c9b38fb564679c8849635a53b896ddaa01", "0x278f744a391cfa66ca77f51e8aac097db3f4589a7a7438207fcbe7734ee67a89", "0x9c274d0e18f401ed95a636f9b7e688ea30c8fd32edb8a2b498ed95e6f0d3678", "0x298bf2d5da37d9694cd289309a1a3cfb5977aef139b51f6b5586e6e7969c6676", "0x23b4dbd772dad9320234a772dad888faf4054fac8cbc73f2078dff2825e9f7dc", "0x7e4100c82537ac9286ff99c1eff62318a12c18c63c9f10e59b02531e40b9d4e", "0x194fb153c621bb05efe4a0b8ab9ecbd016865ece06cd81862bf80faba6fbb041", "0x1df7ec45772db3f999295ff6bdd8333535b1b4b96b19ca3fae0237ba3d883a8e", "0x2b0249411af1423381825db72aa8373b35a5687f4d553fff50bad5dee900a989", "0x208bb01a1c668e48ac1c862f3daef64529f2bd36ee2ae50aede8a66d7c8be06d", "0x2a920d7def469f8e332dc14d6554d260fb8bf21775a45e9550c9cffbf1583f4f", "0x9711d36060019a300a8c5ae3d121b0c5350c00adda85e86ce4bf0ce175cb30a", "0x5f9cfb1ea6bf7c0053f7f71df63c007829252cad120c40181eed11520f8ef3a", "0x8d951ab724ffc54a8b9c5cb73e77a4ef38a0aaebad1b66e954b54d50e61026b", "0x2e2c1f50d0f642d878adf4e06190b5d9f44daf16706f494a71168aacc05d0590", "0x2513136cc9d436edca83a981b22b66862cf71e478b09f93d38a2898f80938ae8", "0xb811f4b5506117dce1adff60d3b331d796cc4b2900897db300d641be0ba59bd", "0x2058f15a7df528cc1d8460287e3a0c5cd66116f98bf8d36fae19f595ba683131", "0x2fd9e7a48c6d265a6d76368ae6762f2a3cbac6594ca02481cf295198e65ad723", "0x25e61d1cdb9d0efa3dfb7a705f9a2f1d649e113b072bc835776080dc692da4ff", "0x688733a105f7f2bbf8f1e99f24a881e4f9e1e1a79551cc40d3038e796b23aee", "0x14a5bcaf7f082ae94ba1c357ed865c5e73864a7e2a1a5ad55a6e6f20f1b4f88e", "0x1afa85300fbc30626fec5727e2b13b4522eea1731747644bc408319746646fbd", "0x2b51d05dd1a610997be175ce8d95064e1bdc83b535da2d8ebfcc58f36e8999c", "0x1211e87fd861a4ff60aca71a116f379e6d014ebd50cc4b9de88bd476a28a6cd7", "0x16a28d23e4e16eb5f46935a6a6c078810254eaca76f3adb24788543bffb6dce1", "0x1a9cb5868564b268952c4cff2c1588cbc95f867cfb112d2634b78f6939b1089c", "0x167e0bf6a4329f36deb8c0f66377e8706c2c62686b635ec8e7b965a465d765c7", "0x1d48e9c952fdd47498442beb72ed468cd0bd1aaa797482777fa0b45df9391e29", "0x2be24efdb917338d46cc5776eaa4fd1eec584b3e55c612c754279f2350072ef7", "0x12e7dd26b099490c1682623afbfab964afc23f7b18c77df371b233564c1c75d5", "0xf872fd57889ff7b68b0206ca3080fde59c7d2c71b043b8fef8ea9d4e7fdfaf1", "0x1a305a6ee976d6d5bb781eb230f24fc1e944ab44caead8b97939ead5b206d56e", "0x110248593cb658c9dad10ab6ff442f60c708d63144366926c74ece34926b667d", "0x2911a9443b7c8e59996bbbfeec60928da492646304d750b48e054150f21ae7c7", "0xae050eee5defe765dd9f066e7714f97441b6c7a1da9a169b9ed7cdb0124da8a", "0x1b43e5c7e755e6e22a0bcb8ff95e247bb6ba30d845e27c3c6a65088b7d9f8651", "0xf68c7b436f14e3dead7e8c7de3c0b4af4dc7d36f922766893a2e9559c8610d2", "0xb085935a1ae2fb12dd4aeff87d34da6ea8f1f03cff8cc20ee66e036613a6b08", "0x2b39ad399267003696ecd758fb89cc0a1c49551ff69da652404564d56a3d3481", "0x144b43003888f26443fa2dc2c7354749117b746a05f8e3ef4a4abaf0afb60600", "0xa90bbac85af36a606d100f71b9b1c9f2c705906a83e659ef457c7e952ed0b28", "0xfacd123f0294b69dd2508b485842d1cda5cba41270ad7dfbb9fc97f5bb0547f", "0x4e6285a710a4dd253ba29e1b0f6ccfc1209b236b01367c612e546bc683c293b", "0x1b6948fd0b32c3feb50d66c5ae5685587ac7ffcf1aff3e3601a31201a424db7f", "0x4f662e8e1fc8523907b3e887990ab29087bf2f1e7ba12e4ccbf06b474894d81", "0x2bf8a1279f19a68c96de2f2115fcf8d0828cca0491c10cb1b97ab200a8499fe", "0x65e1427c6c0a7f1c4e20cddea99611b66a4668966b788dd590f6469679c47b3", "0x91660f9429fc5f9985030ea064d3d7aaf2234eee7320c1c730c08a8413869a8", "0x87e9d609a0f6c29d4e57bf4a3e1743f6b698486d689569033a5f987a24347fd", "0x2c5528aca016c80f5aea6e50df4ba106b830de16871528264bcf3bfeb5bffceb", "0x1a94deec61949e75978d9c94826b8bfa8e6f4a20751f5a17374694d5aa93e715", "0x60845a0f779048ec9a712ce5da33a370b785401d838b6d92e1177ff7113265d", "0x1fd4046339acb4631e26777abde4a0de9d2bb27cc226dcf6c03ca1520366c8eb", "0x1943e7070264148ca273df06a7bcd984ba03497dc86cd5480e0c072a1c2bfda9", "0x2cf34e981d2335162e7a8c523110a9ac4042df6181038ebd4080ffb5100e1751", "0x13230369b80fe2e6c83adae77dbb3d8d7b6ac03073afb55b45dc2e9360de216f", "0xe4e4fff31c6a7b4dbe201ce9b4271bf28e1f52ea3e5ceef05dbf29db763e65", "0x1a630eb03a920cf31ed396a0b1f900fb699350244c6b8790c12e0dd9241470fe", "0x1644c6bd2f50746f3d469743b173655b5665ea0eb77070785efce560b681463a", "0x2935c80cbd7a4336883fb448ee6750c75ff4037f996f2040e2bc0bb2066f17ba", "0x2ee3eb795e73b84f1d042b472b98b5f884ce32b5bc36b05787d33831a504fd80", "0x22ca9da95fc7621796cff16d5a7538d711eb230aca1667afb948910b2aa767a8", "0x2d529009c37ddf423d9264df6743990d63604bb168cbdef2bc6a99e886fe8452", "0x2407471f7d9339927a72aac4a02eb1f2b2999a6892f5869a54587f4842100434", "0x66103e919367b340c163e96eadbd09c01b616f075baa12d999c5af10af900e7", "0x28c276632422a69e7dc41ed859375de537917402930e3c3733df4fa8e30df41f", "0x2f088812877deb6674478c892a6277820b4836151bc7bca42f4af5cc1135d160", "0x1340222ea17d6c3ae591db414b6ba52c14881e2595e9be814df595cd038d6628", "0x18514fbb98af7b4ef58db81dd0d1e195a1e3e6d094856f2c457dd19b6c6fa9cc", "0x70d71dc0012610f06b23ffae222632103d468d952e2c274848c3d28f4f66d3f", "0x5358f254bd79cfcb37aea816e287d08f86b324fd9ea61beea1eff33ee3eb374", ]]; let xj = [[ "0x17774e3e8a23ff734ca1598a87bc0412dd8d117f26c62ee7e94dcb29e0357bb1", "0x1982b56c3e0bcdc9c994b0437e4dc0b9527821ca7809068c62de431b5489c670", "0x2872b0c088da975ca497c1a9c18ef0ef3993ddfd09077dade5d72d1ad3abd8fd", "0x2969378a0cfddacbdbcbcc93eb8642d2dc8167a467acef3ecbb15eee40139640", "0x193581cebff836c6d2319b0bfd91255bddcef3eba4383bb93d17ceefd6953d3c", "0x26457780a6d80fcc0f23a463b42645f7fec8e6f0a0008e4410656947089801c1", "0x24e212fee032cb7c7409ae15eaa0aa0311a810586db2f6f180a6b0cab54e0502", "0x260d3e40114b8d2ecb09e3f0e4fcd13eece95b0a7d7b5ce96bac14f5cb32d71b", "0x1b1a5d98ae47d8520d89e8c8fa73dbf28988f9670c62aa77588361bf2193aa0c", "0x19139c8f3a190fa873462ce2dd5f25690f00ec110f4b62996e365f3421a3259b", "0x2143f989b60bcfb4a9887cd610decf67818b14bd709d865aa40c7a52986a5e5a", "0x2d87bf0c00e24b175e5363e0de0a1c9ed68f160c43ca0093e2dca54f07586b65", ]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let (f, p) = bit_00_case::(&f, &q, &y, &x, &mut i, &mut j); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_00_case_2() { let f = ["0x10bbd67a2e6b8bd12ca2a8fc9ebb9d7748bb4b630bb9e8ad6ff87ec4e2647706b3fde59249168a1f3a22e43aa9131c14", "0x10b832788eae08063407690bf13628a4c95b6fc55a9eef6a4e4e1893305748d5ffd9fef14dbbf2265569906a0d24b1bb", "0x19496c56f34ced68a7cd75ca45a97406d2a99dc971e2c9ebd6ec68233a19bba472836ae01acce936e2cf8c477b127acb", "0x925d1d1ef9c0beba6f0a34cac08da0adfb221ad320d929c4a12e88d4c855c6e93e88d2422cc017e588ebe02c9d8944d", "0x63551db5a468540a882a52a9fc100a34798496f25a17711a0f7fe84c2f3b0c22ea84f0e3de8b6df17b043f047eb3d95", "0x1452bf2c3fe715937d83b5c57df5b7b9df88e4cf55e829b75743d3be8818de60a9a1a5156acb9303682c1c8ca5fac965", "0x159fe260119fbb98baf253f4e0f865fe70bcd3a215ac2d2e10d9eea83bb012f8e01a28ebe1e1ab9e46108a3da2287de", "0x2cf0869f40402c8b16429547884c156e8281d85d5a0ee4e6fa097bc9669f5a4c6e33dbebe7a9434b3beb015897656bd", "0xd2c631a38ce47d9e8f0ee1fc2ccd8f589dd387f86500444d3dded1b3595c3ce4312a36a95cdf327419c78b6710a6c8c", "0xcaa4d999eec4b8f23cb8406c8fb3405378036f4c5867363b504394fbc5fc5b04e7a846507e6f24ade84350245ac9e72", "0xdca015d5a2e52becd816f7a434f9cece5b000d281057b64de60f93bdf429d379caaf598e7e990c95a109a8caa63a02b", "0x6995ffd83bb53d7b9787c81663ec0365e65c06194887eb1591ab99d664c7bb9537bd1bd1b9bf5b1707249c394b385b4"]; let q = [("0x152110e866f1a6e8c5348f6e005dbd93de671b7d0fbfa04d6614bcdd27a3cb2a70f0deacb3608ba95226268481a0be7c", "0xbf78a97086750eb166986ed8e428ca1d23ae3bbf8b2ee67451d7dd84445311e8bc8ab558b0bc008199f577195fc39b7", "0x845be51ad0d708657bfb0da8eec64cd7779c50d90b59a3ac6a2045cad0561d654af9a84dd105cea5409d2adf286b561", "0xa298f69fd652551e12219252baacab101768fc6651309450e49c7d3bb52b7547f218d12de64961aa7f059025b8e0cb5"), ("0xbfa363ea499e05a429d9af2a73ba635e0ff3825edddacfab8afc6b9188700c835282a2c4c7effe70dc61c557b8d90e1", "0x5c3fefe5849b36814f32ce71dee6eba467b220e1b53f01421b9ec6d23209f6206e864539ddaa327b085ad8d78a8589b", "0x17b304f1c4f58afee1ecd75f1570b13da2ee02dfc5731f82ac55d5b6d011ce70ae42061b3d205cbe49efdfcd8d2c04b4", "0x101d88f38de6be9d7eb2c074905585f487715b3e6d8179a066ba56988207caa28f7a5f1ba2f7abd01e200ac71d198282")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let xf = ["0x7f7956e7258b204e6bb76fb6530b54704b338c9e41d551b4c65d12afeff17a68cd917da4aa7f5d7f85dd4c4af5e97a3", "0x61f63de6863a0737ea4c564fb2649c3298b59c310e023469e9f6a61c9d21a413a15b875c3b5ae69e8bc70cc1642be88", "0xd54ccfbe6ce28ca435fb866b16f94ad9149d23b673b8b033c7415a182a906c0c440ec19e65eff130e3bf3e78e64a8d5", "0x5b0b2403b504c7c3c04fa2649405e14816e285681f6d10877632f67dd17dd934dcdc3b3d59039e2f71aab9d24fe1f50", "0x120e02660f9058203246fbf0112482fcc1899b14e6ac805c02a2d7664553675a1cd30ab8eef17c2cd5a8e39666056b16", "0x848bb58f7c097a46b3a03ed0f1e29a3fe03f4e210140c9f40bce68d096dad390d28e98224a2242169998bd45bcfecd", "0xdc72aced2c6f4a5c4819c14494f27de393ef818bbd4517d07dd58a061d1a3e0141a6e2e95f2d0acc60f04b266569319", "0x4a715b7a58dc6543add0fc9ea5a83207f896f6abf8ab0e2333622e9b8f46b0713f2f072d77df88de226de432ab03d2b", "0xc04235cb1fe7822f16be8bc01f84be86960bad82590ceca82fde4beda8b9e6a5885c858c2816abbab513ff9a9c7b5d1", "0xe44406c2cb2d23cae0a6ab38bf6b02312251b650e69f258a269f5787fd2b0bd9ed885f0edb79bdcbaa9dc247ec2effa", "0x86501a5cf1b338e3103b59e485f10c54276bce940584dc74efb1890226e01d82c5dd98529dfd9eaed5f6ee84dbefdc7", "0x10a91f5f4e43b2f252c415e2034cc18aa5ab46c409e63ff37f5499c66dc28fbd4c3207007302b90bf0cd9d620156bc89"]; let xp = [("0x76147fc1a30a666d36b43fa11419b6fa517b642c143cc2ad863426f2c7832c9c9fb62fd3c6f9dc94801523782f9b37b", "0x12f4b28115b81c38e3bbf17cf69059247c386ecccbaed914cbf1417f24431096f49191365acd1aafeffe8c4489a89415", "0x164aaf1243752293eb1376a3448bc1941c8b25df7cfd0bcb708514d7f477439817f367d8ffbf02b95629d336e7da1574", "0xe46ddd6615bd3583b69fe7156087f35ed4b8896375ccd7f52459f56836fa38e0b596d289800df74c3a361e813b24550"), ("0x86fe5ccf8266e2300ca10c33b1c74cfa6cb698664f6c984cc2545f9c89af0520d755ca7ffdbc37d75f20fff15e4518", "0x18c767f073bb43219f813ed472efb42787e62706503974e6c49c10fd5a41e617f592da748faf3e3d7139b54f8accc080", "0x558b3b314565e03cfdec488e39e9c099eebea93016d9e1e3a93bec47068d4dad9910792eb85c8382bc646aede853bff", "0xcd8cc6ed38c417768827084f4d1e22c516dbaf1a90f29c2249210c3476f70251f1923bca1422ba5f9f4f6db107339ec")]; let xi = [["0x11ba967b8fcf46c439d636b9e14c3edd68e62dc6cc493f4e1a7c214779913dd40e5ebc6bfbae882c56c11ff73e7bed8f", "0xcc9f9862097d6f31f2781f916f394a4d9a06009f54f616d9d5c5a517a880391ed02b8f871d1004a5a305453e0c4075b", "0x1a66a98e21ca07db0b1b7d6b7bf65921c7dfce0cc9b25efcdd5e7c1b8e492ffff9dfedb9b32b3affb827c5478907357", "0xc82b7ea20f3578f7eb67a4d7e966e54e595b2ecf91e2a4210f76656817e35952cac71e75199e7fb161f85d569406353", "0x189640b74e901e4042df77f784cc7381c43e27d3da200ce86f47f308a6ea37932bd16fbab80fa131c37d8b429d7598b6", "0x6f14945ff075b3221a66ee8ad672b31c0f85429ab90d7a9c8bf557813fa0efbfe25e5f49f87ffcd4956e178a119492a", "0xf5628335e48c424da2650414f0baf02b9e296d9efebc881f597af374dbe634ddb199eda9ac5ac7c4d76150b6243e95e", "0x1443dc581cbc60dd4197b6f74799d7cebe9cb6bc1932d2f117a6687849f319f20c6c51637f416117f896c0826f70c6a3", "0x5ecc867bb9640bab6c57f5446f435a473568f31dcd5ed8e20f1097f4e3a5c98b9d2fd9170309e54f0d23595241e9ab4", "0xb35142bf853116f48afac573549d09794c7b8d4ca101d4a64fd850cd7a72385486e7c965e9b58910c237a0b61dfb0d1", "0x495f2d46c6fe317c3557f02ad66976d933fcf31aed50fd27207d34b5546dc367a479be3a9dc0d748ee958dbdf4c3dc6", "0x4b87f6f948320dd3accbcc1653d67f9ee8a8495695c52c0463544a7775a58518a607e074453f8663e7b0ad8ea07e21c", "0x65810cc51bcd92db40f079a885a7657d113367ef6b2321380496cb4e94e4c6189b9c80b51107ba437417a83bec3670d", "0x13dddbb670491725aec1646c87db2e3fea286661dd0dc9f62ceba6b063eda63672d8ecc5180785f602438e64bbcd1f17", "0x108542e68466c8e6c016bba69375a0ae187a4e357d15853dfe777e2cad3467f288b83356dd39d2af46db6ad97d56c658", "0xb39e319c9be2be6e28c6d4fa1e3a62a586467af5fa17e602acfa253883982c30bef0ae4bd9af5afa14c357da2dee047", "0x83070c328cf2393b9c0e28a6863343a05d51d75e8a1a489998663833a08663e952bab23b09696d397cbd542f7af429a", "0x78d9252259df0ecdad5e05685c241525043ce26007d819f5c211e8384f6fa9929e8a7f6a7fbe43f15a46544fc8b46ec", "0x9534112d11f8c6657e1eb94a03d1694c7ecfc2d833e8b9b32555d40b8cce7ed08b6cde4c0a8a1a481d509a142dada65", "0x17fb2d3043728a3c9f4f7eb7147eefa2ae79f8ecec711064d1a396f10625c33e2e67085d1f974f1c283e084505347b11", "0x1527d49f0223c4632d2978541c5e7d8d51a7283bd1985381512c5dd8b2103e51c61667251be7e073a48da118fd27232b", "0x181fc8ed425ead408c6162e73014b441098305a952c7b215beb11798b894b948772a699f7560657e0791f7353df0fd5d", "0xd2a54509e10e5665e61510098a424a76631a524e26b5d033d53575a81d77565c865023853d8778c869559a08cadb589", "0x6a3a81c3d7ec179f1becd1274efb578b65b64466ff53b9b9f7f990ce828624ba8fecf97cfd459b2b24c0b02eb315b01", "0x2ccba8aa6af85b297f41cf199aaf4a3f0650cdc229e926e25ff6133b52e12964907bf7c1ab807fa1c1a27077f82fcf4", "0x13f701cb63206a749cc4547b34fc3542d8be923cd0e05a141f5238f8b32ba5f381d59fd53cc11dc73a6988109694725b", "0x104a7d09036552a18da7875dab655b8e25de43d2f2fb359d2c1000ccaeeef04fad656589265f4c04113e798a73c20330", "0x930275466d564f686f7319a6a4727f3d02c510a942f72381b77c9ab13b2adffadee2bcceb4aa896dcebb7b064442c07", "0x23a127089f836b5408e8988a0b92a096caf8d05ee8447312f063af45c922bd8723c158b1562c936e4fb1b53aa43d1e1", "0x8287b7ae5eed694cc39d607c7b7d971612d1bbf700af830baa9494e633b6fb89c2413f8a8ad726c8e283eb3c1be71d2", "0xd3abe3cb1df8ab5cb11d076cd758cb1432c326ddd72aa2a71227a94ed7229680b089254776d3b94a3dce697af042639", "0x160189e110bda3353ae5682c644795d63233a1fa07a574d48ba2836408c15cceb02f98d62856a3d1cf7a6642db52fca8", "0x8ea0f4b667ddae4e4a277bae882943a2111525e96173e9285514b6fdf91ca60123fe4de5f1d49ed1385231a5e71b28b", "0xa791a01fb8b16a02152ebc641bd7a3a6509f18b2581db4aefb73a72fddd79466a905fa8d0e5e7f5ad2c593d095627e", "0x870ad87f645720a0ba982b6466f9a581ed89af7cc0080c7f1d114536877e26b953f26804458cf3fd67cc53be9bae575", "0x3811a0a51b11eeaa5e4de1b43984feb40668a0c62c5530b738dafbdba6c9e815cc4cf952c6207ebfc6b46b2a788c065", "0x4abffc61e058a798cb893b106afd6642a9a5b9c9d190ec6b7e7b7736ae7f55a249a0b111e77724efa62ffa005d60c1b", "0x15001106717bc45a513b6146a10459901cff726c93d0d1e631079bee82eefa9155dbd411db488636973beb7098c9c4b4", "0xab0519a411e6eff310339690c65e26a5fe9b219c8c6945c187f8770c76c54868e294fa116e256a599fad06fe2083152", "0x520c7b90cf5c98118a54b28000fa41595bd4268ae83a9bdb5577168577387d851618625ecc43910bbab4c61a021591", "0xc65eacc9be6245d73eed5b34f8ac954da859308e4b75dbf9c2d3112091ab90f36538189e6273259d778197bb7ce6818", "0x71c5b1b76aba5f951b840c414510b8a36729740fbb935ee17a89d02a9118d4b299f7f704c2814db96c58b5c3e8e4d32", "0xbd28e1ac6c5e1fc4c3c997bfdc3b364690a7fe355062b0cfeb9891f24d1e1098dd536b4174c486ab9acd77c6aff88a4", "0x19adf3b54e4ede32e8529051b0da99c4ab475a13ae3aec8ce601154c65a333d3db61523e885303ec600017b7628ea4cb", "0x1414c8b51b998f78adf2545657e79e04c5e6713c798ba7fbea1b3100eec83d020178ee760d4aa7cfe33d5c9a82591444", "0x5251cc2093d6ace28beccc75ba85b076a4f82043696c3596f25482780c5d16de2d89576fd654eed140266533553b456", "0x44adc21c8b70388f0d70a25d9da68a9b1c99e5db0339827f45d676d966ecd70d51c17e99be1eaebe4256435ec7b2cb3", "0xd2764ffdd4aafbec5111e3502e485297b41c4eb78cd1aca40b15b39ff5f15d0164e59d271a9765179d78100e190c08a", "0xf495343ff43c6582b39c72d7c8451702f9f60ec9e718c09d10a9e93bb138cc69c9674cae87e3dc51c9782830fe3a1c3", "0x813353910401dd8201039268d018a7dcfd8666549fe5f94c51374ef5a37e15c8477d0a60e906c0fb761eae9eb6a3ca1", "0x18a61359e28c306f78bc965891d78d017ddd72a45062b72cf8dce528b0f32dae65e85266779e83ffe2250308e69dd641", "0x14d41d8887c59da2b7cddc906b83183a8d3c745d247eaf6bfc04e806c4696d177ba228233cea1f2adf60e9a125821564", "0x27b4eb6686078e08e0b2c5cea6c4e60bfbbc7839ac73c47ab312a1959c261cf2c2949031a36cfe5624595eb1105eb9f", "0x157440aa6437f627e6177f5e1f009a2cd4f844beedd80029b7b2caf076b31974a103ec4f7bc04326b50da3d2abbd1093", "0xdbfeadd899ed34a01cfd537096e630c70209c4bcfd61188dbe39b7dd19dbe13774820c247de3fec5143e4d23a89d0dd", "0x10431edbc907726e8f1471a35aad7df33f528ed82b927926cca56c54d70c84c511feb40d5f76da3ccc22e3b9a4fc7003", "0x742a7bab4d10cf49e492e363988c6faeb8320a3d46913f3b89907afdb9ce12df2e0674a5e4661193657916509398d3f", "0x49def4922bc54ec02e8412e5265310b6e778071fa1083980ecc1034ccd3dc724ef66584834e9dddc689900aaa044ef3", "0x138f41302d6034a1952188cab929eb75a81d1c8a1adea5099537ed125d6fbf33a330b83096d3145b90919d5e3c992255", "0x6ebb5f7da78c6138fa6834af37751887cdc9cee7518dd38ccc4ee0b5611195a70a401db0e755ba00b56b76f6c9f94a6", "0x126c7803e4974596968a4f04cb60c0ce1b2e259bc760a8e439eb3279905d908a6dd94746750996f969b08d93a2e524d1", "0xa6d898382d6eda6ac3e11fec169f84e17f16397e41b2df42707046ef7fe2ebd592c79977881f70b7bfe829d66d5765b", "0x137218011633b381bd89a97e55763aa251d63568f442799981da6f8735a7dfa1ee0402830ab83afdc84348871ac16e37", "0x2760e0d91fe71d8b4b54e9c65b91e89f5a4ea2a3e3bae93c0bb37ac9b28c8a3390e2a572a56ed9859d027d5500e54ca", "0x14addd1e3595e48b0d69ff071fad7e8decea0154410b54843d8bbece5c0fb194c9ff11e548e3d85022533f0124485c6e", "0xc922489ee0d82dd82e9c9fa32fafb8653984c6847bb45d09429a64bcf8b483c5925582f20b95b4f3386708fb12e1972", "0x124198bd68cdd64d11b74a28e390a36b2b76eefed0a9692cb7f68cfccfd03a91cf4770e6b584334aade210bb1addc2af", "0x12c5e08cba713e18995f1fe5c2941ce6812ba3af7597767d5f9846f4f4484302ca7aeff43ccceff055fbb5045467a5a0", "0x48529961f0804ff9d586c6fce3865111121f620920b5f5c8fe5260d8abad708978027fff404c819fb03d0b1a57fb212", "0x9900bc240091764a11f90800c16626daa8ea09d84ee80ef30eae8f0c2b73a2b0e502a90225fd77e61fe5514c02661bb", "0x21cb6d48e3869a917ea7f7c2c8348bca2f28ee8858ef05dc213b7b3866858eb1d2ff273bd9a7e9094f7395f08cd2494", "0xf310752dd0682895f38102bd06e233884d4c1f9a90fbbd0ebd2ed6970b4009373bc13eeae85e57e4ff71e10d363aebd", "0xb521644578cf2ac7c7427e6bb83a50d771124be587383ca5243a7aa37061cadd7de09dbfdc0e4b3e0733fb33927f485", "0x378f671119170c553acd6df72c0aec702f32dd9c90fd959bada99fc7650e9e121d1a933c2089e03112b40be116ebe3d", "0x1054ee4ca3b1d8523e0e4d82bc512f8e057e843968d57185220906c270ff8dc90a9e903f928967422ff4775a65934653", "0x3c7dacef5d95a76e46ce2f737eea2116d95ac0afa8cedca27dbe830464e9fe9cdc82be6709bafe101a4cfea5286dba5", "0x1534470261aa9852854998dfa667ff1d2fcccb490e54d4b41be562e7a9bc3f5f5772a676d94523b83ce39b61d635a25c", "0x8dec854c0b36dbd59a59a4b391e5bbf8d7dd6a66c21362acf590035182f517da887406fe26bf7bea657269ea5e33c1d", "0xad646d6e77d25c4825dd9bf177d4d4b5b2efd71c31e5977ce2156daafde511c63b6830d944b87697dc19bb9cc0b4bfc", "0x20c0214d819311198ddf2f073f3ec68bc3762fe0299707152bd06a9daadddb87f4c0b5edbc90da730abf7bb2407cef8", "0x1569c15b058a27e1957b7302e1ee92036f14d15f5389f63a875e5e2b5d53f7c48defe9eb7dedd9939e905f7f3dc950a4"]]; let xj = [["0x7f7956e7258b204e6bb76fb6530b54704b338c9e41d551b4c65d12afeff17a68cd917da4aa7f5d7f85dd4c4af5e97a3", "0x61f63de6863a0737ea4c564fb2649c3298b59c310e023469e9f6a61c9d21a413a15b875c3b5ae69e8bc70cc1642be88", "0xd54ccfbe6ce28ca435fb866b16f94ad9149d23b673b8b033c7415a182a906c0c440ec19e65eff130e3bf3e78e64a8d5", "0x5b0b2403b504c7c3c04fa2649405e14816e285681f6d10877632f67dd17dd934dcdc3b3d59039e2f71aab9d24fe1f50", "0x120e02660f9058203246fbf0112482fcc1899b14e6ac805c02a2d7664553675a1cd30ab8eef17c2cd5a8e39666056b16", "0x848bb58f7c097a46b3a03ed0f1e29a3fe03f4e210140c9f40bce68d096dad390d28e98224a2242169998bd45bcfecd", "0xdc72aced2c6f4a5c4819c14494f27de393ef818bbd4517d07dd58a061d1a3e0141a6e2e95f2d0acc60f04b266569319", "0x4a715b7a58dc6543add0fc9ea5a83207f896f6abf8ab0e2333622e9b8f46b0713f2f072d77df88de226de432ab03d2b", "0xc04235cb1fe7822f16be8bc01f84be86960bad82590ceca82fde4beda8b9e6a5885c858c2816abbab513ff9a9c7b5d1", "0xe44406c2cb2d23cae0a6ab38bf6b02312251b650e69f258a269f5787fd2b0bd9ed885f0edb79bdcbaa9dc247ec2effa", "0x86501a5cf1b338e3103b59e485f10c54276bce940584dc74efb1890226e01d82c5dd98529dfd9eaed5f6ee84dbefdc7", "0x10a91f5f4e43b2f252c415e2034cc18aa5ab46c409e63ff37f5499c66dc28fbd4c3207007302b90bf0cd9d620156bc89"]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_00_case::( &f, &q, &y, &x, &mut i, &mut j, ); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_1_init_case_1() { let f = ["0x521ad898cee9071ebcbf44d874b1a6540a5a24a4fd9c68f45778308171f9267fab695191d4eab620cf33a8eded7fd2c", "0x146aa46acc68a7fa2d014f4cdce6921f2f664ffafcd262db0a43e29fba239f8e7cc55a67075e7e25f7928438cd506976", "0x110012a0987f151e6eacf408ccd24b9c3e637b240a4100a3ccdc16d44e3cbdf8393eb3557a64d089a1a115a3eab1a695", "0xa3dc13d77e6eac496424ab994c230664bbb51c4abe8135d998621a4259c788d6959e539d97a534c119cdb9a394de9ad", "0x6d44964cce393f36664dfb78c36a4b56c817816904d06056f68e9017165ef8db1a4f97532d5c3bbed4da9a68948c926", "0x1191d32d29708748f35f4fbea90258a97e7b47db6986cbc73c24ba35ad601bfadab752fd1a3e438ce0686b7777654a0c", "0x18776284b17c0858f647e075e04c49ded673151413b8ce9b65bf572081d748820d57d62d54e14ea09aad1c01c5c5faac", "0x199c96383503947d119bd6be94efdb3595eead7072f8c3d67173449f6658fadb43d715c9dc54d7f547cc1525e9a566ab", "0xa97b4be53ee479681acc5ebfc4fae663d5040baacca25a862aae0152d3543705d87df48c8266658d2a03e597cfec8fc", "0x6c86339c39859d2fac14a4550fff32535a91b9b0ff23bc04475027273d9579f491b35686ba10369195fd003747b05cf", "0xe608702099837e04fc2e999cbb4b845ab04d0a51ea25ee04675bf96847cb9d629da62d1e4354c04ab5208100a0129af", "0x737a8f64f0c81b65cf9ef035b357d0017406b0c84de6a32ed1fff164d3d9531f1d9ec53b11735a58f1d611050ed258a"]; let q = [("0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8", "0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e", "0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801", "0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be"), ("0x82dc9154807866eb0f36ccb665a5fc010510bd690ddd7b540e5bf3ff02d81e98b75703a3b3d3c305a70960906e6cb09", "0xdd18d077ad5bd58dabb18d84a6ceebe6375a83dd242851bb4dcf956002c4efb974ffceee6709deb0dcf81d4285e5e60", "0x4a468eb9e206b9833d8e8e2197d3446652372ce5ef50e93c91aa58105d3a281b2e84ddb61535fe1a90bae7e6692f9b0", "0x198fd0ab6249082bf7007d7e8be8992de81f47ae3341c590194fa3bf769a2e5a5253527727115c334e82ed4be8da6c10")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let c = ["0x521ad898cee9071ebcbf44d874b1a6540a5a24a4fd9c68f45778308171f9267fab695191d4eab620cf33a8eded7fd2c", "0x146aa46acc68a7fa2d014f4cdce6921f2f664ffafcd262db0a43e29fba239f8e7cc55a67075e7e25f7928438cd506976", "0x110012a0987f151e6eacf408ccd24b9c3e637b240a4100a3ccdc16d44e3cbdf8393eb3557a64d089a1a115a3eab1a695", "0xa3dc13d77e6eac496424ab994c230664bbb51c4abe8135d998621a4259c788d6959e539d97a534c119cdb9a394de9ad", "0x6d44964cce393f36664dfb78c36a4b56c817816904d06056f68e9017165ef8db1a4f97532d5c3bbed4da9a68948c926", "0x1191d32d29708748f35f4fbea90258a97e7b47db6986cbc73c24ba35ad601bfadab752fd1a3e438ce0686b7777654a0c", "0x18776284b17c0858f647e075e04c49ded673151413b8ce9b65bf572081d748820d57d62d54e14ea09aad1c01c5c5faac", "0x199c96383503947d119bd6be94efdb3595eead7072f8c3d67173449f6658fadb43d715c9dc54d7f547cc1525e9a566ab", "0xa97b4be53ee479681acc5ebfc4fae663d5040baacca25a862aae0152d3543705d87df48c8266658d2a03e597cfec8fc", "0x6c86339c39859d2fac14a4550fff32535a91b9b0ff23bc04475027273d9579f491b35686ba10369195fd003747b05cf", "0xe608702099837e04fc2e999cbb4b845ab04d0a51ea25ee04675bf96847cb9d629da62d1e4354c04ab5208100a0129af", "0x737a8f64f0c81b65cf9ef035b357d0017406b0c84de6a32ed1fff164d3d9531f1d9ec53b11735a58f1d611050ed258a"]; let xf = ["0x6dcf1ec2bee9d55fd7c7dd01f0d89e52ce00053fb4cd271af8ac67e915aa56c1f18943cf63d7acf09f9e238c86f7575", "0x7f05f480f32402899fc238d5e397600577a07eddd78a63793400f32912e689ef50ff7298c542fcbddc8a2f30326ff28", "0x71d870e4553f214175e57f71397705b5336a8c404e29abab7505079976315ae30aea8c7fc8e47f2ce78aed551c79270", "0x37df42454ed3974bb2b32f97123a17956e452893cabef6a29a0888f8ce8b899253e37ae32f0ae88611fa10260d597c0", "0xba703f387adf415b877fd75815f8322190dde62bdc8a55e54b5dec1284a8c9177b3c945a72f0e1e9c109d242988e116", "0x14068f72159c932c910dd5126f8907d9616c496a0f51dbcc5585ddebaf32dc4e03ae577f1f07d02f85fc8a875e197521", "0x17dfc12834ee7334831b24af1174df6680c4991d4d20cc807c5e8df6083d142e2fd17ccfce6bb359366acbb7781372b9", "0x17d3b0da632dabdf4ba0f6c890308dd36ed98b5e1d50a8160a2349e79dd3de20eea74d8b95daa3bc8b9ac34a59ff12f0", "0x17ddaa28e29c2317b96c21b7fd31f8f2bab3cabf17b82c770ed0c77db94e0738119993eb4c5d01ef3358bf5ad26286cc", "0x22b2500baf6ce28a86979f31387bb67348f155192cf97f99aeb257fdcdc23c15eb5315ea817f28532b8d5198e199dd", "0x6524f53a10bd1ed1f7de6acc2d4414912600bfec37d116a4d096e4e54120fe17325dec0b0e382b90ef6654c3bd2e20c", "0xebb85352772f284d12c95bf531a0f1fc69bf6acd1695e9af23d641db780ebb70c7fbfbe8a680e766390ddaa62af47cd"]; let xp = [("0x122915c824a0857e2ee414a3dccb23ae691ae54329781315a0c75df1c04d6d7a50a030fc866f09d516020ef82324afae", "0x9380275bbc8e5dcea7dc4dd7e0550ff2ac480905396eda55062650f8d251c96eb480673937cc6d9d6a44aaa56ca66dc", "0xb21da7955969e61010c7a1abc1a6f0136961d1e3b20b1a7326ac738fef5c721479dfd948b52fdf2455e44813ecfd892", "0x8f239ba329b3967fe48d718a36cfe5f62a7e42e0bf1c1ed714150a166bfbd6bcf6b3b58b975b9edea56d53f23a0e849"), ("0x893227b499dab30e15b606ec3c375f9fabf7fbb574b9b11c9eefbe33fae82066297e23c518f59e74d5cf646cec6464f", "0x10578234a81819d1ebb3d77b03a128f3165642386fff1b0a74ad73c139425703a991ce459cdc1995351adff98061f0ea", "0x16efa85752a02d4358a92eb3b577c1e27a02ec36000c44403159baf7022541a02104b633549e05b774e1b76343a8e661", "0xaf65df48a519d9209257e3df9fb0a1bd3491799091df954380242592db0bead0ddd62dbe33aeeaf1d4a63bdbc4c6008")]; let xi = [["0xe8899bf2d1f2f54c552427835589cd2828d33eb1fef81e5382af6e33a32d19e7436939b3a0aca3000826ee5f29f7a41", "0x163cc7d50f58e7fd58c4467784a7f6848c725dbed14ffa37ceb2664733594beecc9e8e74e15b88e3df1df249b1ee10e7", "0x5456b23a25e181f03ecaf790566ee2ae3f9a7c9aace97c5f51b1822a9d2e8b0ceb672afdc6811f64c2a47bf3b14a670", "0x148cc9dcaebdde0fa4b641ce52ac847504136c550836467c59fdc151741f4e8e8bb6dac0275c34709e7f843f60afe9dc", "0xef2dcf1a1af1d85290833bdc8d333eae4a2416662a7f8d1f171df42ba46755601670b356942900157a4a691278e838a", "0x76ec0b906fec3e2548ddafd05cbe92834d9f67602526598cf63790c56effc25547b035723461181b30bb7f402c48ad5", "0x1893ea72d489bb198282ce86062a8f7d79862b680b0dc9a96d0e0c06024a12ae4269cff7afad6d3c5475405e2884021", "0x380676d535bcc75c2ff6b216b5bc81b5725b2aff21e124d93fd6315a2248700c21be8f775d2bf696c927decf4af8b7f", "0x1ee362659422cdf7cb061e82acac95cc7cb4cf73f02e0c49bc166bbc125ee67ee92e8111ee26b7a8624e906fdba11be", "0x16cc42e3d79053697cf26dfaa74a55c8546d3a08ecefd2b6c0c7ffc2eaf861068d95bba66b1eb9b4daca7ac05c61305d", "0xa9cf5030f0c62f73281fad2c97854ff91e3e22ad09abdb334743ed5de591bba3496cdf30a3357f360fad1f2d109b7ff", "0x1343b69e1140100f3dc3aedcdbfcc4363709747a511a3d8b576f2a210c59a8378ee1acf6ad57126d9da7e4f2099902dc", "0x463f6de4e5ef5d7b704ab2fb2eaf6ba225d334c2080f688657bf8eba8cfdd7d090b35bd45a8d09f1fd5e3ef3a8ce079", "0x114fb86f02da46f189d2db73a0c8a258472caa22d95d35ff3ea1f72cc98d310000e5e3451cef06cbc702937b1ef2fa9c", "0x123daf0320a5fe89b20346dc0f6f518d5ae7cad91197b2d9838bbc04ed0c6681dfb816e4cb8f5f763e05be29aabfa3b4", "0x4ebdb59fa847ba75e7fba78eca31af430c4ce13b8b845d6f1cb144eb550379e57b248c2cf134622a17a72daec5a175d", "0x12bc3e0a8465166f229da4dea0b0698e143efd397b0421810c07ba2caa14590a92641f141e42823cd0d4be8161d8a0cf", "0xc841c20248b8989103512b3c9b44da503c1aa5e941109fd849821197ba666bca1daddba36e8f615fdf46b8f74148576", "0xef637fc86371e1f3f24608bc1ab79884f9ead6afb9102b802ab14471b2298f46c5ce6718c8fb1861e7f0ca584df38e8", "0x8a18906704d81bbe407f0003945c43f7f0827f9dfb606caa563c62390ced3f07a091ee47c69d5c38505445ab5404686", "0xb41a7c5f385e5e11370c7febebccc6c906f7dd9351bc99f3c47b45f89c740383b21ccda4e78a74e1f02df5685fec579", "0x18152c8ebc343acf58014d9f9b8f3f44379b2ef18c288b1a2413e416d3e4e97f18c9eea2a988bafe4b405e9b1e6a1068", "0xd9bec30500bf612262f752ac2c2981be010f17e60f210b21978f498af139b2601f81df384f7891155dc524028a9c85a", "0x3677bf0ef760a7e32576dd0376c00d6c2619cc2a4ed7246a57d7c2f5bdab6ea17d8cc25736f9435d795542853f87851", "0x1a8e6daeeec4175a6a74f5e40f57ca05149fcbdbbc9d4dcba25bff52377e27bdeaa64591b6b4d05b6ec5a6aaad93bb5", "0xb1d85cbda8e37689d68ac73b63a2c4c62582bead16d0572003865fe6a85e8e49f37374ae25acf5584962cc0e85f502d", "0xc85c01b9b42b297feb1a34cc0aefb3739f44df44f6409865738862a7b741741e29841860c40e51d4f154ec443783197", "0xbb3b12dc3cfc717a4612174b132d1c2e06b1ff648cd27d00e2e15247de13695aa784234aa6ad5f62976e220f2802f7c", "0x4a4c14b30188c9e4b26e5362872eb13784c6c7effa2a3de7bb05c6c2c3277d2426a62a490d49d2930e8c6787507b4fe", "0xfd9b096dc81d49c0f30145d2d462c986462656d2fea44782020eae45c9ecfed514d15a91907c933f2cff180d01230f7", "0x1050d223a7ae09664142e67d8bcf631d8e8270c7cf379f55da84fb35756ec93aac7062850e88a2d80a9f8c6eabcde61a", "0x10d6c35de0dbf0832bfac6901fc2f4cebfe769d251c1d018f15709279f7378f5611951d66f04935523f8d3e6bbcfc40a", "0x17502e841d1c751f97992599ab672fd7b4406353102a50e13849da6a584f2defc35cb436546b6ad48a39fdad2448a82e", "0xaaf33baa4db7f6edb87dd9cd7311bd39069a840fa8d8dd49e58df12f3714d71eb7c83e43fa5423d80d01c7fb35712d9", "0x5d0f763804e8e4e17c6e29ff93ceb128a5c6e46c3a6688ed3285727b387018fa11003d39c8d5356b83f5a050f2ba23f", "0x210f7ce0277ee88f4bdfb77a38d8333eaf3ee9aa8d846351042248be09dcbea0fe06622a82d2a52e2f15942cecf7868", "0x7009a78d046a4223d6918822cbc00c0523696f78e85d7883cacccc3eb781350c85fcf0f278738b86441a6806e2556d4", "0x6c2041bd2df5687640ef195e8677a03c150050f4bbe304da55ea4c4a1036aeafb73cff23a63f3fe06d9480947e55a52", "0x4d9c72a03be12a88b76831d01a353ee068c09f96fdaec74eb60a38c08bd5ad8c393119a1b3227b4ac72455594358da1", "0x13f228eb5b3f295c64e9ddf2250879b623441c0db2f2617b3b85df938f2427a7190d721d87254067019582785dd6964f", "0x23d5b1edc9d5bf13fd5dde686530cae59ad34f32962a43efc58eb582cf3f69d9360706533a5a3043913f97b1f01bc4d", "0x15fba452e8ffcd78d21f4ded67b9c9eac394df22928fd62ea7d3375de41fa486f272a3e7c9dbfe15d4344718257ee00d", "0x119e8db942cd3373ead2539dc6c19d97c28ace94de92e80a71e49ca831646f45cce63f39ab8dbc4063e136195ba9df9e", "0x54872800533a260494090d1f316a5b6aae9fa22843ba6b76ce5f7db72189c29195731167868ce96342dcb9a1d676c67", "0x190ec7594c543f6a6279c47fb997f36649b16583c9493ec0e80fbe17d6b32b6f6a025a31625357d868db93889fa9bc83", "0x1076cb0dfadbeeba2605e596436f69349532cd836fc10b9997fb9a5f1f5b73eee3b055b5cebaa2435c9ff0f8146d07b4", "0x74d333f32f240ba7aafdb1572a94d228ade7d6bb45b67654606f8d98c05b2b091cfc71957338186d26c9bdbfb03d775", "0x10d9f3c7dacc7ef8b7b60f7474d5329b95c597c4083e626a618690793228b1f358623c4c5772ecd80b3c9ac273608279", "0x8dbb8728b6da5f245cd61eb18a4a34d1382b0a44c1ed8c88c3f620b14fe9211f61d69c5cc9529da708a50e3a97aa176", "0xc12777fe64bffb84d4d0c6c409519da77a081bfb05bce0c326aad71c243b134577ef7921fd3927bf956ac0d7704f7ea", "0xcb09aa163755c68a0e912444b03f8c2c26284f784b191ceecc23922c1c6b67a2e0b86d26c8d31f2bca44df1a40628e5", "0x32281704643a5a864ec2140874d8a97299d4a552d31df0f92c3e07c745b074f42c3ffe54e7d95c0b0ce5552e684a43a", "0x15f0a4d8bae8b018138c36b4021e8b66465477f4bbbad73cd44ce790b461f3cb3b3030a39599a4db7f147ba2c75a4ec3", "0xa505444671788b4d171af1972edb140da8569c5beab9becbb9ede13407cb096491558679fc1746bd66e36b53e7c5340"]]; let xj = [["0x6dcf1ec2bee9d55fd7c7dd01f0d89e52ce00053fb4cd271af8ac67e915aa56c1f18943cf63d7acf09f9e238c86f7575", "0x7f05f480f32402899fc238d5e397600577a07eddd78a63793400f32912e689ef50ff7298c542fcbddc8a2f30326ff28", "0x71d870e4553f214175e57f71397705b5336a8c404e29abab7505079976315ae30aea8c7fc8e47f2ce78aed551c79270", "0x37df42454ed3974bb2b32f97123a17956e452893cabef6a29a0888f8ce8b899253e37ae32f0ae88611fa10260d597c0", "0xba703f387adf415b877fd75815f8322190dde62bdc8a55e54b5dec1284a8c9177b3c945a72f0e1e9c109d242988e116", "0x14068f72159c932c910dd5126f8907d9616c496a0f51dbcc5585ddebaf32dc4e03ae577f1f07d02f85fc8a875e197521", "0x17dfc12834ee7334831b24af1174df6680c4991d4d20cc807c5e8df6083d142e2fd17ccfce6bb359366acbb7781372b9", "0x17d3b0da632dabdf4ba0f6c890308dd36ed98b5e1d50a8160a2349e79dd3de20eea74d8b95daa3bc8b9ac34a59ff12f0", "0x17ddaa28e29c2317b96c21b7fd31f8f2bab3cabf17b82c770ed0c77db94e0738119993eb4c5d01ef3358bf5ad26286cc", "0x22b2500baf6ce28a86979f31387bb67348f155192cf97f99aeb257fdcdc23c15eb5315ea817f28532b8d5198e199dd", "0x6524f53a10bd1ed1f7de6acc2d4414912600bfec37d116a4d096e4e54120fe17325dec0b0e382b90ef6654c3bd2e20c", "0xebb85352772f284d12c95bf531a0f1fc69bf6acd1695e9af23d641db780ebb70c7fbfbe8a680e766390ddaa62af47cd"]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let c = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_1_init_case::( &f, &q, &y, &x, &c, &mut i, &mut j, ); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_1_case_1() { let f = [ "0x6e2d5c667e253ffe1d604e9b0c0efb376aaa3e1f2fa8194a9fdd627525394de", "0x2dc3c5e55face7c5e2c971b204e63954fbc8ad239d2d152e532c421b7834a99d", "0x2ff47505930441520ea2801041714bcb5d41a0ffa81940aec94ea9901fcac97d", "0xdab9fd3d1ef5226f76a2af1d6b410d8639501aa55867c1f0779e0422d545f0c", "0x2fea029bdb6a10f53ffd60992916c6410e0f53520845bfd3e55f70e8272c8fb3", "0x2f329aa1c588e3e4b7d8f5bedbe3c09728563ff0c46ce45b66636cb6ba1ee436", "0x2290e74d07afff26a405ca3722d951cb9a512f1c100fa50e29907ad3283e7b83", "0x6bd6eba6eb034c98be6fdabbb6f2986a20934fe7f4ccb1aa1cff1983d7d2ae4", "0x1ca0c85d7f94b5c6b3543992e315765cb35d0f7d49149a6939c1e7afec80ee3c", "0x1f70622e79ccbeb35ecce1f7718bba441de2df4f3e916ca84262a68f9eea11f9", "0x2492333e1554b6d2c1ad39913d06e14c6ad3a1569e62952be0e54c3427ea8aab", "0x2a9baf66b1ec17ae1f6f435746d944886953830b40efced523794fd2aa17d4a", ]; let q = [ ( "0x27dc7234fd11d3e8c36c59277c3e6f149d5cd3cfa9a62aee49f8130962b4b3b9", "0x203e205db4f19b37b60121b83a7333706db86431c6d835849957ed8c3928ad79", "0x4bb53b8977e5f92a0bc372742c4830944a59b4fe6b1c0466e2a6dad122b5d2e", "0x195e8aa5b7827463722b8c153931579d3505566b4edf48d498e185f0509de152", ), ( "0x19092b3d714b3bb6599b735386dd05eab401e72057bab79773a6de8f5693387b", "0x1acb3fbdde3ce471791558747f0e52b1b7a708834dc533393bcfc2af317703ee", "0x258d7966e4b36382460549a44d5cbe96fbe1c412e36f25218438f72d7d387077", "0x2a58bf6a639ae104439ba4e8db873938a26fcd5bd0b68beb20c44705d9820860", ), ]; let s = [ ( "0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed", "0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2", "0x1d9befcd05a5323e6da4d435f3b617cdb3af83285c2df711ef39c01571827f9d", "0x275dc4a288d1afb3cbb1ac09187524c7db36395df7be3b99e673b13a075a65ec", ), ( "0x1314aaf1c372e6d7635e573808d9d5c7178bdce7335eb0538f718d8e6651eeb1", "0x14c25d3aec745e5a2d4aba9e1448a8cc1048d01a5289f29ccc5acf5e81526673", "0x302adae1297f41f9fdd327cfa91c5688fc16dce6579ff99d6699ed49b4d2445e", "0x1800a20cf49101a007f783b70334fbdecf9be4f63017754e9afc5721ead62211", ), ]; let y = [ "0x1ab9de59fc825e8b5326694c7d82556785cb9cbfd0d0a11721d1972c21c411f8", "0x16a475582082ae3616c808acd62684170d9fa7bf234110353e9cbceca19d2c69", ]; let x = [ "0x27783160c70b7ac760cff888c621846a7ed80e50c7ea8a7a718a4ad8a50886fb", "0x10a6d46618419682152a25b5f819b22c2e572d1f670d12026a18c384248dad2f", ]; let c = [ "0x14156ca1853095df27f3cb7c50eca75e794d2f14195c16df4a0f8f9dcb48bee9", "0xdc2a20a6107d4c49fed6b2018946bcc2a8dad06f01d099a6df0a4a55ed21b59", "0x14260c5afb0b1148ed80f8339cf9e06ff04257cb6c1817c4efa721fc98f69503", "0xafe8a09df07bf3dffefe512eb9448ef436dd090f98323135baab8ae3c766c60", "0x114692950f53d4f707bb02cc2b5dc98aff5936811707d6579371dae20368253c", "0x2dd3fca72591963149646f1e106dc0ee917551f5a9da397fe12d4a3939ce650c", "0x1750bd450b85cbd62ea3f1b228beff5fd364a127d6054be99a9248497b82062a", "0x1248cfad33a2147726169d3ce55db12ecafd74bc4b83377c168d89b919386546", "0x28d156bac04e64938816b055888399c99a954b82724e5f5589d549a709b2b5ef", "0x39e1ab153bd709556afece475580f453f9126f256fbb49c235bc75082f5f26e", "0x14853f940bf5c557c7f558d3e74e6617d7f08b54fd83597fed1d7e7b9d09e04", "0xaa480d613601947fee14a3ce2b7af4e1872fe49ae3473546aa01a618b78b125", ]; let xf = [ "0x9cc2ac2feb91b788f180b7f837ff5880af2d8a7b2cbc2078ddbfaa7de025ab5", "0x2b4691bfa6539beb28208698d947d559a85b25c7a591428b92ebd2a21abec753", "0x27b1bda2ff2bbe089cd77810447ab3747db696a3f6ef1e002aa95b3c440d8421", "0xfc2973e1356ebf52ddb6a5f96f0380df66dfe01de4cd7d7910730b235b46414", "0x96dc0c72aa87605c1be1f3b6812a70f1d4dbdefd725e7a84302d8aa32e80fcf", "0xea15f5754762638499ad8458f796af631ece5e5aa4b56d786db49e831390ace", "0x103abf47dccc2f4d223ede9edcf039bf49c1ec61174d95d075fd3727469afe66", "0x26e4a5a33276fc3166bb1e1310597230fbd36c03a6cf05749310487c359ed5e3", "0x65373ec7b46d26577bdfb0a69f8df530bdd64ae3b63b728ddcc7c24ba04ea22", "0x51b781e90fe55d3767d00d134cad0d2879f07054f31198ee15d57679a07cceb", "0x880237565c157f17a67f4f4d74fd3acd28c325e1d25747ef4e9d6c1a688457c", "0x1c718116af5b9bfe4b9a0f502db2b1916a717feb5c1a016cca2b0b70d3882c4", ]; let xp = [ ( "0x6064e784db10e9051e52826e192715e8d7e478cb09a5e0012defa0694fbc7f5", "0x1014772f57bb9742735191cd5dcfe4ebbc04156b6878a0a7c9824f32ffb66e85", "0x58e1d5681b5b9e0074b0f9c8d2c68a069b920d74521e79765036d57666c5597", "0x21e2335f3354bb7922ffcc2f38d3323dd9453ac49b55441452aeaca147711b2", ), ( "0xbddb1ea5c182ba12d0762b9c85ebd180541e0b153ca85ff24489f09cb0d44a7", "0x2170b47e91296dad38a19f370fa3368b1f333b8f05e5018b7a38af0a045be237", "0x760488b80e6b5dd63b4b7422f5609df112bf8a63604449ae3020c63ad8e2489", "0x1c937b1f996ef4397c744c8b2503cf644feb5b6d8b7f77237a7b8a2bcb98583a", ), ]; let xi = [[ "0xa79ee9efbaa87e84974d0064a9b0a54517dd0e329163c9af0ca337787769c76", "0x2e6655c0294cbfc67c5eafdd31ccb9a5bfd1bd6f6d00d86b27ee6f0f45132db9", "0x223aa77e00ac43da1cb9698a9bcd76dd0d4dc9e9f3361c19fbdfc575f825dfcd", "0xba550ec81fdab48e83ae063002c0a4363f06d42bc9fb8cd9c54bb9a738583fd", "0xc46766575f8ded7a90993cd70cc42210d77233b92ac51af1b37d71fdc9f03a5", "0x1d93b6b19feee096b780bf18a2084117c9fc934df72b39b9856368f6d621b7e0", "0xf790c1fea05178b7f9de1aabfb394cfafdc45716ffdb752bedf419215896403", "0x2e7f87004e656e2f0a90f87cc58103f6dbc75f156feb6e940594809f32468890", "0x1b7de56671644ff780c45f087d0b1b8f2c9603c7748e99bf81ac39475092049e", "0x1d4f78206e251a9dcef0c173c33a2860153e783ab6fdfca8734f90b9695e7825", "0x271eefd32b948443ea242ffa8d1f3c281c64272c21580c03d60b46b9cefd3903", "0x26d01c1ee109d33051f2f49f318c80672f843c74b859e1bb3249b20dc11f559d", "0x45f8774c96e9d51f4d665cffa0f9ac1b8cb75fa4ef193ed5e67609288bb62c8", "0x191b686c256a3b826b6f99ff6dfb1f7cb22f02515655b308d60bc4563459264c", "0x170eba3d98078d3d7cdadabf7e2eb4e24aed94351ef9de5ca685e544cc958cc9", "0x99c99ebce93adddeba403ffecc8c37691bf52cddce48fb2092b99baa9c37fc1", "0xa794d503fc1a9aaa6ed5c70d1452971e44ce9e14c4e33d728ca3aa71a139bac", "0xda34cb75f019e7077721004cef3c0ed836d7a62ac54f203f01a7ea5caeba2c9", "0x15284512bc0074e4ae175a7a86cca36b516e4ee6230ebcd426435f215cd7e1ba", "0xa4370b540cdf6a3ba34992e9b9c4c715119fe0f3307eff2a746493af08ff459", "0x14536aa2d190a0ceae4599fce6f4e99835d08b23d98e5217c654d41d8035cdca", "0x383c83dc474b9cb3d2f2b2bf0cbfc2713bd31e45cf8d30e4989451d3c929897", "0x23d8e6b10a662363f1b4711ed89c7f057c63679d41f3aa7e215cce1c65afeb3e", "0xcaaaa24187a70d233875111d0cdb09351153eada98914d9de99eee6a5ab5193", "0x182fcae609a86cdc19e81d291fae341048bedef4988ce4b3290e7997f9f71a80", "0x1f9a679a7a9aa2f6bbc8b2b7ca097db3784e7014d77a6e4b495ed3a6f2a4f727", "0x297aab9149267a69d02e8a75a50eae577160b740b19c2eae326fe2e8411a2818", "0x1b7b271c51f6252ad920dd621b69da3c60606c5ce9d8029ccbc807548c882cea", "0xb55add16f95fca8c970b0ae91796ce3fca1f40869b7ce250b5893f118080586", "0x29b43ab30d36fb285b38dd37771d6d998397e2f6a89ae62246af45d79e14becc", "0x23d92b8079583f2a528fcabe2d23eaaaad7e52a42d5e8b6eee647dc1d4d6e274", "0x138492ccab0224206a5c568fb3e7e73859e9f8f5e72da7654418a584284f5960", "0x2af93e8c93e9bd75f1cd46b9906b58634677b179a97288f27ef07b1b5fc9d8dd", "0x20fc268e39b33c7617497bdc3e7bd939a45e832ed413bb408b7d79230ce4f60b", "0xb9dc0788d376ac77f442031ac7bde522955a9eef3395343a6d3edce03b4a829", "0x15e9ec57703b3c37f621b98b75e94b0885b27936d94b8ae29f78c9f1adc0ed1e", "0xce8e0c66aeabaf7877a971e4043ac96f34f540c7b5aa6e074fe17407c48b071", "0x24567171e46bb99f25f932f8924da00f057613de43e23523768a838f3e06a3f1", "0xf4465460c7ff15d8a5adb5af8645cba61d4b9fcbe36a81476207fcc031e40a5", "0x1b8eea0e13a9845eadf38c4778cdb5a43d81cb0747a31d1b8d940ea59b149951", "0x13577c9318b6a3919ab6701bab529507e4b5300312ef2d6f1f958a42be9c2eb", "0x2d03f66a7b412e0bd1630dd126a66b046e6bbd16ea1ae05fb3ac8c34c176cc95", "0x2b8d2b6aad77b369fd5d502a8b00b8b6247fcacf16b1ae354c57901d6b3eb934", "0x8b452b0ab3e4d897e1fec5b90f0450ef9036e4966049120832a980ea5a83d29", "0x6af107effff47a9e2609ca233e81e6bde4bcaaca497a816c0645d039241c7d0", "0x26ac80e013f793ef90929288be4f84d3be8f3ba373e8fdc2897ec1d500fa86f0", "0x29c9bcac9752160d466ece56a3066fd4ddfde6dac1d7dd2ffc43e264bbe46fdf", "0x22181cddd7f75ec3e11f54f23e4a4488d762d3e0d06911a076cc0ffa57a57094", "0x1dbb2fde8644a40b897c3b8c87426d37c2ac98507eb2c2321d53c07c1120eae", "0x2be613f72c50ce45878c294c553e1d9b3929f33466f99cfca6b61dd0b38714f7", "0x2673bef40c708e61da5540d99a69ea7a04777ca491b53359bc19d7131cb0a73", "0x185efbfcab081123f13ac188e539580aa7ba31fcb1fd1464ecc52c4c597534bd", "0xa98fb59b21fd4a2619712941a0a1ef57964e02ec3892e46422442c6cdc0766f", "0x965417e5cc262886ba34dfc81b0dbce0ad7ec0f1703ae45608792577b69793f", "0x9fffdbf32bec4ef94ba958e1b1ec8b5da5701ffe9c9e039794fda3d60b97296", "0x1788f44b56ed3ededf77708e0a2e1e5523368c5731c1366fab9d6dba253525d0", "0x2d62c0f8a2c995ccce46c16747f8c800ce5d8f00cfb013448883f0f2c37d076c", "0x2487fc89973ad2a53dc502d6826c03bd8a129d37efbd987c0c8c2d224dbb0fe0", ]]; let xj = [[ "0x9cc2ac2feb91b788f180b7f837ff5880af2d8a7b2cbc2078ddbfaa7de025ab5", "0x2b4691bfa6539beb28208698d947d559a85b25c7a591428b92ebd2a21abec753", "0x27b1bda2ff2bbe089cd77810447ab3747db696a3f6ef1e002aa95b3c440d8421", "0xfc2973e1356ebf52ddb6a5f96f0380df66dfe01de4cd7d7910730b235b46414", "0x96dc0c72aa87605c1be1f3b6812a70f1d4dbdefd725e7a84302d8aa32e80fcf", "0xea15f5754762638499ad8458f796af631ece5e5aa4b56d786db49e831390ace", "0x103abf47dccc2f4d223ede9edcf039bf49c1ec61174d95d075fd3727469afe66", "0x26e4a5a33276fc3166bb1e1310597230fbd36c03a6cf05749310487c359ed5e3", "0x65373ec7b46d26577bdfb0a69f8df530bdd64ae3b63b728ddcc7c24ba04ea22", "0x51b781e90fe55d3767d00d134cad0d2879f07054f31198ee15d57679a07cceb", "0x880237565c157f17a67f4f4d74fd3acd28c325e1d25747ef4e9d6c1a688457c", "0x1c718116af5b9bfe4b9a0f502db2b1916a717feb5c1a016cca2b0b70d3882c4", ]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let s = s .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let c = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField; let (f, p) = bit_1_case::( &f, &q, &s, &y, &x, &c, &mut i, &mut j, ); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } #[test] fn test_bit_1_case_2() { let f = ["0x1727a4684524eb2175d31f506b07370100418d3fcd5ad5c5586b3c2927dbffdd38a1a44b46f601ab362202e8276c007d", "0x57d77a9e8e6cd838edc1e63052a64d020d10ab12ab460dd755dec64232750ca866647b373738bbe4943b6aee387caa1", "0x42e0115d1c759474549023340d4f01ea67f2f082b59dec03aa7e22e27bccb5d4840ac815f2c12da594e423a2108737d", "0x54735182a914667a25226c91d61ee1f8c5c6c2e40b633da27379618cb58b0b55c0acff39fe7471a196e8bd9a0db6863", "0x14276d83ecbbeddabdf9bf5d9449deaf0a40d6de94e8347d983e97ed4491a3cda57fabebeb6d788023db42ceefa73d8b", "0xda9195159528161fa4960f25523d4d906c194a134c2695ba34577b4dcbbb76911a90cbb411db147cc5627ef50c9210d", "0x9552828c7dcc07d56efc554f98880b746c6ce0f7f41377d934699dcb5cf7eab408dbe027df4506c40e2424b24c6b69b", "0x122dcaa1ba9a8a8613064735071ae0aeab8e0333d7ff3018c9d51a652303decdf4907f6e7f232224b4fe0b20245f2fd4", "0x112f00e12354b1ad57581a4dde94de861275afae359c3016f8a13e81943a4a18f4896097697c449335ca5f9d21b7f654", "0x13bbf456483cd4566ed59718bd067589e294b4d7084073073fc77a685f0e4ae94092405afc2ecc6d437c20102b74f4ae", "0xeef615cd28929e56a59bf2e2e93db68f2ed629f9872a3b1aefdccb098674950b928bb5c920a2dc4d6405a69dafd98b8", "0xebec00852daa59ee4861f6c55f01d098689453651a335e711a11c3e6606acd9cd851f8132fb24bfa3edf65997e82785"]; let q = [("0x19e384121b7d70927c49e6d044fd8517c36bc6ed2813a8956dd64f049869e8a77f7e46930240e6984abe26fa6a89658f", "0x3f4b4e761936d90fd5f55f99087138a07a69755ad4a46e4dd1c2cfe6d11371e1cc033111a0595e3bba98d0f538db451", "0x17a31a4fccfb5f768a2157517c77a4f8aaf0dee8f260d96e02e1175a8754d09600923beae02a019afc327b65a2fdbbfc", "0x88bb5832f4a4a452edda646ebaa2853a54205d56329960b44b2450070734724a74daaa401879bad142132316e9b3401"), ("0x1604bd06ba18d6d65bdd88e22c26eaef8a620a1a9fefe016d00eac356f9ceda8bc8eee5e46f9f4736ab22cff0e8cb9e8", "0x3e5755e9bfc250ff0a03efea22428a36a247504e613980918dc5319efb7f66b10d5fe2e7e86af7e014e1456aeaeac5f", "0x5655a99f7ff904c1e41382c25ff0360d9c51d0e331bfb1e38f5dd41c6909caaf6e313f47f727922109bf8c3204fe274", "0x62ec2ed9b207f63e0d9899ed11f9a125b472586b65bb77b8a04d5d446d15a8701ba5c361a07cd85e0743f5ae2e95a9f")]; let s = [("0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8", "0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e", "0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801", "0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be"), ("0x82dc9154807866eb0f36ccb665a5fc010510bd690ddd7b540e5bf3ff02d81e98b75703a3b3d3c305a70960906e6cb09", "0xdd18d077ad5bd58dabb18d84a6ceebe6375a83dd242851bb4dcf956002c4efb974ffceee6709deb0dcf81d4285e5e60", "0x4a468eb9e206b9833d8e8e2197d3446652372ce5ef50e93c91aa58105d3a281b2e84ddb61535fe1a90bae7e6692f9b0", "0x198fd0ab6249082bf7007d7e8be8992de81f47ae3341c590194fa3bf769a2e5a5253527727115c334e82ed4be8da6c10")]; let y = ["0x6ce420ceafa50ff15baa710e1633d7893404a18b69ef5316a81b182dadbe66bb0ef4fe49ffa578c7698795e6d4a12cb", "0xf45ba6de68a0f1ab26ba5fac564f3f21a75239243fae800e2a8665fd9699e2795c674834c6ce016370aee9e4a1d38d1"]; let x = ["0x7f2db8fbcf121365e92ce3d77bf5d9a3537b5422e894c09e00053ace96a5403a8db66fbe03950e93033c5874bbe8046", "0xb190c99770f69f3e912d3ef69f63e082a05a1e63b50eb9a5de3e07b14aed7eded07b2f2b3c42c7e365d2a47945fc285"]; let c = ["0x521ad898cee9071ebcbf44d874b1a6540a5a24a4fd9c68f45778308171f9267fab695191d4eab620cf33a8eded7fd2c", "0x146aa46acc68a7fa2d014f4cdce6921f2f664ffafcd262db0a43e29fba239f8e7cc55a67075e7e25f7928438cd506976", "0x110012a0987f151e6eacf408ccd24b9c3e637b240a4100a3ccdc16d44e3cbdf8393eb3557a64d089a1a115a3eab1a695", "0xa3dc13d77e6eac496424ab994c230664bbb51c4abe8135d998621a4259c788d6959e539d97a534c119cdb9a394de9ad", "0x6d44964cce393f36664dfb78c36a4b56c817816904d06056f68e9017165ef8db1a4f97532d5c3bbed4da9a68948c926", "0x1191d32d29708748f35f4fbea90258a97e7b47db6986cbc73c24ba35ad601bfadab752fd1a3e438ce0686b7777654a0c", "0x18776284b17c0858f647e075e04c49ded673151413b8ce9b65bf572081d748820d57d62d54e14ea09aad1c01c5c5faac", "0x199c96383503947d119bd6be94efdb3595eead7072f8c3d67173449f6658fadb43d715c9dc54d7f547cc1525e9a566ab", "0xa97b4be53ee479681acc5ebfc4fae663d5040baacca25a862aae0152d3543705d87df48c8266658d2a03e597cfec8fc", "0x6c86339c39859d2fac14a4550fff32535a91b9b0ff23bc04475027273d9579f491b35686ba10369195fd003747b05cf", "0xe608702099837e04fc2e999cbb4b845ab04d0a51ea25ee04675bf96847cb9d629da62d1e4354c04ab5208100a0129af", "0x737a8f64f0c81b65cf9ef035b357d0017406b0c84de6a32ed1fff164d3d9531f1d9ec53b11735a58f1d611050ed258a"]; let xf = ["0x10bbd67a2e6b8bd12ca2a8fc9ebb9d7748bb4b630bb9e8ad6ff87ec4e2647706b3fde59249168a1f3a22e43aa9131c14", "0x10b832788eae08063407690bf13628a4c95b6fc55a9eef6a4e4e1893305748d5ffd9fef14dbbf2265569906a0d24b1bb", "0x19496c56f34ced68a7cd75ca45a97406d2a99dc971e2c9ebd6ec68233a19bba472836ae01acce936e2cf8c477b127acb", "0x925d1d1ef9c0beba6f0a34cac08da0adfb221ad320d929c4a12e88d4c855c6e93e88d2422cc017e588ebe02c9d8944d", "0x63551db5a468540a882a52a9fc100a34798496f25a17711a0f7fe84c2f3b0c22ea84f0e3de8b6df17b043f047eb3d95", "0x1452bf2c3fe715937d83b5c57df5b7b9df88e4cf55e829b75743d3be8818de60a9a1a5156acb9303682c1c8ca5fac965", "0x159fe260119fbb98baf253f4e0f865fe70bcd3a215ac2d2e10d9eea83bb012f8e01a28ebe1e1ab9e46108a3da2287de", "0x2cf0869f40402c8b16429547884c156e8281d85d5a0ee4e6fa097bc9669f5a4c6e33dbebe7a9434b3beb015897656bd", "0xd2c631a38ce47d9e8f0ee1fc2ccd8f589dd387f86500444d3dded1b3595c3ce4312a36a95cdf327419c78b6710a6c8c", "0xcaa4d999eec4b8f23cb8406c8fb3405378036f4c5867363b504394fbc5fc5b04e7a846507e6f24ade84350245ac9e72", "0xdca015d5a2e52becd816f7a434f9cece5b000d281057b64de60f93bdf429d379caaf598e7e990c95a109a8caa63a02b", "0x6995ffd83bb53d7b9787c81663ec0365e65c06194887eb1591ab99d664c7bb9537bd1bd1b9bf5b1707249c394b385b4"]; let xp = [("0x152110e866f1a6e8c5348f6e005dbd93de671b7d0fbfa04d6614bcdd27a3cb2a70f0deacb3608ba95226268481a0be7c", "0xbf78a97086750eb166986ed8e428ca1d23ae3bbf8b2ee67451d7dd84445311e8bc8ab558b0bc008199f577195fc39b7", "0x845be51ad0d708657bfb0da8eec64cd7779c50d90b59a3ac6a2045cad0561d654af9a84dd105cea5409d2adf286b561", "0xa298f69fd652551e12219252baacab101768fc6651309450e49c7d3bb52b7547f218d12de64961aa7f059025b8e0cb5"), ("0xbfa363ea499e05a429d9af2a73ba635e0ff3825edddacfab8afc6b9188700c835282a2c4c7effe70dc61c557b8d90e1", "0x5c3fefe5849b36814f32ce71dee6eba467b220e1b53f01421b9ec6d23209f6206e864539ddaa327b085ad8d78a8589b", "0x17b304f1c4f58afee1ecd75f1570b13da2ee02dfc5731f82ac55d5b6d011ce70ae42061b3d205cbe49efdfcd8d2c04b4", "0x101d88f38de6be9d7eb2c074905585f487715b3e6d8179a066ba56988207caa28f7a5f1ba2f7abd01e200ac71d198282")]; let xi = [["0xfa0a76861031f74c3397565d1db68d2963758855de5ff1cffb69bf13a0ea4371279ac1efa65710c7f4a97919a78ff59", "0x510accb9026da5f06a82195a8b978613fda96cf96aed978cca28a204a199cedc7d167de9ed320732d244e33e99e023", "0x15c6dd3afd26f1e0be2ddbb1b37dbc396c0d3cf212cf9f913d234eff2e573adf0c3801e3e2b0000295bed5df8256241d", "0xe4b5650a1764134020a30d8b7db861be3d99eabc16f3be0c3ccd04aedd3396d12f676011cc534280d11de2c32174054", "0x92b6ac1f5ee0d203bb67f480484b3bc8e1ae220dd231a7e8551aa0f1870337992bbe9468d227d075a169fac1df2c8cd", "0xa2f8871f36609c163c8f4fdc40e2a9e929064409ecf1f5f97663ddab6050fe1d57588d8b03f2a4fbec819cecb39deb3", "0x174392a02f5845ab761133e81929786093fd6dde47f00acabcabaa7df89d108873e342125536e31efb1bdddd7093573f", "0x19b7370d6e64482d5a63c2e296b9d58c27367b340d071f0b83753b977eec6d95847ab64f51e8b2b2b86a21700fc1036a", "0x16aafd26dece43d80d70cdcb43e12f92b10667ba3c079f4714bb254dc4a87dea3329e95692ebb10341473208df09ace0", "0x100e7e1d58af9be477931364d058b55599df02466821b9b708aa273e764a0a70bc05a73457f377972563f1bcb81f11d5", "0x170d56bd6ad6c4de225b80b20ccedbdb8e8df8a04779caa0e1556af352cc3ecd056532fae73625550ca6b183fcf0a096", "0xece7f85c875c8e55edec040d13de2bdaa6d2857da5d6a015778afa6331abd58894791f3c3518c9f45ba74c620b46d41", "0x1607bb82f6dd503070001a627a4af4c14804ba89eebaf68263f9bd809f9e0c8a864dc9830ae4cdf08fcc98ca8b40946b", "0xc5768744b07f71ca9929c2eb4d1c6e7ef588be129d03e364b9a6de5363e625c35120c6457e55c9869ac77c4e68ec86", "0xaf6c9e178fb5b59b567c04cdd4aa040aab8de72fe49c1446bf5199cd13161196a9b6d91fc8ae08fe1bf7d3298713131", "0x124afd78e247a139b8cb3bb39508823c22f7e82b5c7efebe5dbb5362fd9518cc0f978862a5a6b9fa8b69845e104c6d02", "0x5d6e665e77ca1f94e0e0d1167ab09c74e1968c6c237e04da4e30581076651295154a4a5e87f457561b6d5018e45ce0", "0x10f8bc2e981e2fb9c2d3523c3133480686050d777200627b7b4618d52460a7c5e77052ebe7840f526ec51d5936e353e4", "0x10fd3968a035eb5802605b0a1a74fad870dc523e869a8a387f0c54254a837be577e145bb93f66ea2c68eda44071f2cfe", "0xf5f7384635978f87c75314add179a7da2ac4f123d1ddb75c53595c04078a212534b0a21504085f4df62156608d80212", "0x8341b253d9c0094bf3d43fdb03c965eda9e5aa299cf380e3dcf9029d38e858d3a7295bff01cb5715e8e33baa9b6977f", "0x165960db1dfc8f1762170585bd7070d53f454c1f6a9ca49e3d45d8496a5ead89adbebd3c0aa9ea01394b672c4aa894ea", "0x131c0b3cd87830c0b91ea8df14129a2cddff268498079d99e38d2be315ac4fdbcff0f825e13ba9e4a9432d4b60167f2b", "0x2f9b19cd56d9d4ca715391183b5f6e03d281b33be0c460dfabb5e0dd022bc55693304f1cc256b54eb812efd68a36d37", "0x14c0070279d9be555722b667e01e5f500d8eadbba9f5e7cdb91d46924827f5268656e8866e285c2fb4c1e51bb61a0177", "0xcb3a116c5f6723d33a71594caa68ec1c8b6c5f5dfe1b9f0a41d9a60242cdb2df01904a42c125d77f7bdb03b900abe5b", "0x18d59a51db9f1248df991f56a7d48b8e6ea57f000d4c84b0d72a74ee646c2d8925e6196f2a77660e4a77608bddc25f9", "0x19af59a0c7b6682c578e96b27ca0f1b9e253245d818e0c1edecddd98bc6f97d027b28f31dd23c32125316145dca9de58", "0x153c39704769fc40669f0a815152cb1551adbd773c24127acfeda50a2c9c12771b77af68528b524ef497a42076d31c87", "0xe2d3b3118f05cb799343c422605fb005e2e739eceaf0cfd73b770bc5d5deb4edfcac88256e8acfa2647a337312e6e65", "0x1a0100e060db5cdfcd5066fe802535e18f96907085a2952bf7a6e0dc14be04f669df6608c60262347bfa0f198a5ce318", "0xce0cebc0ca92c4c756a3d5b1d1ec42da974ff6e0e2d0c7171c3aaea7ffa0757c0fedb1761d9c4d8d9b289069dd41250", "0x160d326dedc18b7005ca481307404f7f274d900494d7e3fe5b15bec1cb78f3e4a79b19745e6323506dd9f231ae866779", "0x1af4ed07df74414ca87f776e4dd643c8bd7349cbc1e6c2de84a20743369bbb016a5993f0e66568235d44f58d9cbc38b", "0x8d0a11ab066bfc13b257f2b9b860457a3b944f78951b2f7cf3887e22bf75516749ccc5d4f91c14ffefb1cbd92409b1d", "0x23d98a00873b026887cf7eb45508774de78d2412c09f564e43093f04699ad31d05bc73d28126b35f23596da726b644", "0x14207774abb793f1d52aa7c8ac936076506a86a651134cb8ba65d95740b2f8a3ae1afe5ebe0e886326111ce837d6effc", "0xb33f8a80d98e787229da96e781febf5660519e6b448c2239665b43ca641e9c68bee7f63a1807b15d7d271945312c3c1", "0x1428ec16f781182ad72b3bf06f6218cd798f16b662c2393581b47b697b8af05a28c5da63394c737343ecb50c9d27438b", "0x17532398aac71a6c4741eee86041daa073963428b809a020bb2b83b43242f0ed2c169504a1f3007389361a1d5d78774e", "0x44224d63e381d69226405fdbafedfdd5da9456f6c4e155f82570869b69aba03a38400086f0eb8432f2d1d216b69bdd1", "0x21e0297c72148c86aa36a059f19b04c75c95e8c7344026cea29241eff3bece2d7e44645183d2b081bc846ba0cf97e16", "0x503b980fe1358a7f87af5c7eb65b389a0188da60c45be6a540bacb5b66075c991276fa6383d987e5f94ee897417a0f5", "0xc9035d2db00a9ae5f26b4adc44f00d813bb51f8726987918aa26d0eafab97c243e43cf15ab4fcb3ec97b8fca39ddb07", "0x1688460ce66c019b531545c1dab18ade5626fe61eac71df48814c0f5921d48deaab89097cb728efb319b71d29cfc8cbe", "0xb74bc33f01fbf84ebb3d80025cc8b60a2c00cb34b70ffa2903f38c7648c3c5173cae4df4d36646947688488dc6423fd", "0xb0fdff8ae056ea274693d443ed2b2abec5cbd272f090cba71b45adeda28670bb64b26968c1dea90077a422656379b4c", "0x1da52b1ef7183381d3f1557bf9cb515b38124b3f3247400248735e18ebae90b0dfe82b3ab03e48b9f61d5bdfa0885ee", "0x1062e0ee97214d084babe14f0717c2e37f30332e837499400ac3afe77017dff007f0b72ed14a05c96e435a3ef2764d11", "0x16d97325a47795dd4153640facfdf98323eebd53fe8cb69190d6fea3a2790f8ad0e608966bfeb4baf4c415a5f62d654", "0x70e8df7511e1f3476b3fe23002d2c68e9a436310c1e0d4cc099aa5909358e6bb1bbf8e1e10c2917053795568c5c3f67", "0x2e7db1c975008709135824f015babb80e570cdadd85ef1314f376d102036ce3774efc376c0cfdc73201659d99037ba9", "0x1341d5d6806f9bb5bb82898a095128304b1715d59315e7733d82f7fe91c7906d87b76d4fd03825e24eea1ea2e60ce145", "0xdcec9030cb633c339a6db2ed9639197e426e4768c74ece2ac97d78a778ebd7955f47161e041812a516257489e1a357f"]]; let xj = [["0x10bbd67a2e6b8bd12ca2a8fc9ebb9d7748bb4b630bb9e8ad6ff87ec4e2647706b3fde59249168a1f3a22e43aa9131c14", "0x10b832788eae08063407690bf13628a4c95b6fc55a9eef6a4e4e1893305748d5ffd9fef14dbbf2265569906a0d24b1bb", "0x19496c56f34ced68a7cd75ca45a97406d2a99dc971e2c9ebd6ec68233a19bba472836ae01acce936e2cf8c477b127acb", "0x925d1d1ef9c0beba6f0a34cac08da0adfb221ad320d929c4a12e88d4c855c6e93e88d2422cc017e588ebe02c9d8944d", "0x63551db5a468540a882a52a9fc100a34798496f25a17711a0f7fe84c2f3b0c22ea84f0e3de8b6df17b043f047eb3d95", "0x1452bf2c3fe715937d83b5c57df5b7b9df88e4cf55e829b75743d3be8818de60a9a1a5156acb9303682c1c8ca5fac965", "0x159fe260119fbb98baf253f4e0f865fe70bcd3a215ac2d2e10d9eea83bb012f8e01a28ebe1e1ab9e46108a3da2287de", "0x2cf0869f40402c8b16429547884c156e8281d85d5a0ee4e6fa097bc9669f5a4c6e33dbebe7a9434b3beb015897656bd", "0xd2c631a38ce47d9e8f0ee1fc2ccd8f589dd387f86500444d3dded1b3595c3ce4312a36a95cdf327419c78b6710a6c8c", "0xcaa4d999eec4b8f23cb8406c8fb3405378036f4c5867363b504394fbc5fc5b04e7a846507e6f24ade84350245ac9e72", "0xdca015d5a2e52becd816f7a434f9cece5b000d281057b64de60f93bdf429d379caaf598e7e990c95a109a8caa63a02b", "0x6995ffd83bb53d7b9787c81663ec0365e65c06194887eb1591ab99d664c7bb9537bd1bd1b9bf5b1707249c394b385b4"]]; let f = Polynomial::new( f.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let q = q .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let s = s .into_iter() .map(|(x1, y1, x2, y2)| { G2Point::new( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) .unwrap() }) .collect::>(); let y = y .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let x = x .into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(); let c = Polynomial::new( c.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xf = Polynomial::new( xf.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ); let xp = xp .into_iter() .map(|(x1, y1, x2, y2)| { ( [ FieldElement::::from_hex(x1).unwrap(), FieldElement::::from_hex(y1).unwrap(), ], [ FieldElement::::from_hex(x2).unwrap(), FieldElement::::from_hex(y2).unwrap(), ], ) }) .collect::>(); let xi = xi .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let xj = xj .into_iter() .map(|v| { Polynomial::new( v.into_iter() .map(|v| FieldElement::::from_hex(v).unwrap()) .collect::>(), ) }) .collect::>(); let mut i = vec![]; let mut j = vec![]; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField; let (f, p) = bit_1_case::( &f, &q, &s, &y, &x, &c, &mut i, &mut j, ); let p = p .into_iter() .map(|g| (from_e2(g.x), from_e2(g.y))) .collect::>(); assert_eq!(f, xf); assert_eq!(p, xp); assert_eq!(i, xi); assert_eq!(j, xj); } } ================================================ FILE: tools/garaga_rs/src/poseidon_transcript.rs ================================================ use crate::definitions::{FieldElement, Stark252PrimeField}; use crate::io::{biguint_split, element_from_u128, field_element_to_u384_limbs}; use lambdaworks_crypto::hash::poseidon::{starknet::PoseidonCairoStark252, Poseidon}; use lambdaworks_math::{field::traits::IsPrimeField, traits::ByteConversion}; use num_bigint::BigUint; const BASE_96_FELT252: FieldElement = FieldElement::from_hex_unchecked("0x1000000000000000000000000"); pub struct CairoPoseidonTranscript { pub init_hash: FieldElement, pub state: [FieldElement; 3], } fn biguint_split_1_128(x: &BigUint) -> [FieldElement; 1] { let limbs = biguint_split::<1, 128>(x); [element_from_u128(limbs[0])] } fn biguint_split_2_128(x: &BigUint) -> [FieldElement; 2] { let limbs = biguint_split::<2, 128>(x); [element_from_u128(limbs[0]), element_from_u128(limbs[1])] } impl CairoPoseidonTranscript { pub fn new(init_hash: FieldElement) -> Self { let mut state = [FieldElement::zero(), FieldElement::zero(), init_hash]; PoseidonCairoStark252::hades_permutation(&mut state); Self { init_hash, state } } pub fn continuable_hash(&self) -> FieldElement { self.state[0] } pub fn rlc_coeff(&mut self) -> FieldElement { self.state[1] } pub fn update_sponge_state( &mut self, x: FieldElement, y: FieldElement, ) { self.state[0] += x; self.state[1] += y; PoseidonCairoStark252::hades_permutation(&mut self.state); } fn hash_u384_limbs(&mut self, limbs: [u128; 4]) { // Private function. // Should be called from hash_emulated_field_element to guarantee the limbs fits in u96 let elems: [FieldElement; 4] = [ element_from_u128(limbs[0]), element_from_u128(limbs[1]), element_from_u128(limbs[2]), element_from_u128(limbs[3]), ]; self.state[0] += elems[0] + BASE_96_FELT252 * elems[1]; self.state[1] += elems[2] + BASE_96_FELT252 * elems[3]; PoseidonCairoStark252::hades_permutation(&mut self.state) } pub fn hash_emulated_field_element(&mut self, element: &FieldElement) where F: IsPrimeField, FieldElement: ByteConversion, { let limbs = field_element_to_u384_limbs(element); self.hash_u384_limbs(limbs); } pub fn hash_emulated_field_elements( &mut self, xs: &[FieldElement], sparsity: Option<&[bool]>, three_limbs_only: bool, ) where F: IsPrimeField, FieldElement: ByteConversion, { let mut xs_filtered: Vec> = vec![]; if let Some(sparsity) = sparsity { assert_eq!(xs.len(), sparsity.len()); for i in 0..xs.len() { if sparsity[i] { xs_filtered.push(xs[i].clone()); } } } else { xs_filtered = xs.to_vec(); } if three_limbs_only { let (n_quadruples, rest) = (xs_filtered.len() / 4, xs_filtered.len() % 4); for i in 0..n_quadruples { self.hash_quadruple_u288(&xs_filtered[i * 4..(i + 1) * 4]); } for i in 0..rest { self.hash_emulated_field_element(&xs_filtered[n_quadruples * 4 + i]); } } else { for x in xs_filtered { self.hash_emulated_field_element(&x); } } } pub fn hash_quadruple_u288(&mut self, xs: &[FieldElement]) where F: IsPrimeField, FieldElement: ByteConversion, { assert_eq!( xs.len(), 4, "hash_quadruple_u288 requires exactly 4 elements" ); // Split each element into 3 limbs of 96 bits and convert to FieldElements let mut elems: Vec<[FieldElement; 3]> = Vec::with_capacity(4); for x in xs { let x_bytes = x.to_bytes_be(); let x_biguint = BigUint::from_bytes_be(&x_bytes); let x_limbs = biguint_split::<3, 96>(&x_biguint); elems.push([ element_from_u128::(x_limbs[0]), element_from_u128::(x_limbs[1]), element_from_u128::(x_limbs[2]), ]); } // First permutation: s0 + x[0][0] + BASE*x[0][1], s1 + x[0][2] + BASE*x[1][0], s2 self.state[0] += elems[0][0] + BASE_96_FELT252 * elems[0][1]; self.state[1] += elems[0][2] + BASE_96_FELT252 * elems[1][0]; PoseidonCairoStark252::hades_permutation(&mut self.state); // Second permutation: s0 + x[1][1] + BASE*x[1][2], s1 + x[2][0] + BASE*x[2][1], s2 self.state[0] += elems[1][1] + BASE_96_FELT252 * elems[1][2]; self.state[1] += elems[2][0] + BASE_96_FELT252 * elems[2][1]; PoseidonCairoStark252::hades_permutation(&mut self.state); // Third permutation: s0 + x[2][2] + BASE*x[3][0], s1 + x[3][1] + BASE*x[3][2], s2 self.state[0] += elems[2][2] + BASE_96_FELT252 * elems[3][0]; self.state[1] += elems[3][1] + BASE_96_FELT252 * elems[3][2]; PoseidonCairoStark252::hades_permutation(&mut self.state); } pub fn hash_u128(&mut self, x: &BigUint) -> FieldElement { let elems = biguint_split_1_128(x); self.state[0] += elems[0]; PoseidonCairoStark252::hades_permutation(&mut self.state); self.state[0] } pub fn hash_u256(&mut self, x: &BigUint) -> FieldElement { let elems = biguint_split_2_128(x); self.state[0] += elems[0]; self.state[1] += elems[1]; PoseidonCairoStark252::hades_permutation(&mut self.state); self.state[0] } pub fn hash_u128_multi(&mut self, xs: &[BigUint]) -> FieldElement { for x in xs { self.hash_u128(x); } self.state[0] } pub fn hash_u256_multi(&mut self, xs: &[BigUint]) -> FieldElement { for x in xs { self.hash_u256(x); } self.state[0] } // fn hash_biguint( // &mut self, // x: &BigUint, // ) -> ( // FieldElement, // FieldElement, // ) { // let elems = biguint_split_4_96(x); // self.state[0] += elems[0] + BASE_96_FELT252 * elems[1]; // self.state[1] += elems[2] + BASE_96_FELT252 * elems[3]; // PoseidonCairoStark252::hades_permutation(&mut self.state); // (self.state[0], self.state[1]) // } // // TODO unused, should remove? // pub fn hash_biguint_limbs_multi(&mut self, xs: &[BigUint], sparsity: Option<&[bool]>) { // if let Some(sparsity) = sparsity { // assert_eq!(xs.len(), sparsity.len()); // for i in 0..xs.len() { // if sparsity[i] { // self.hash_biguint(&xs[i]); // } // } // } else { // for x in xs { // self.hash_biguint(x); // } // } // } } #[cfg(test)] mod tests { use super::CairoPoseidonTranscript; use crate::definitions::FieldElement; use num_bigint::BigUint; #[test] fn test_hash_u256() { let values = vec![ "11104976625974322414992515260237855724255768622271447502939221706321239646163926750529079402619769361141474851372384", "3967829709048026487667605767879663147330695847448860299062651717898165991149219471605164102628080243401554871141161", "20542379293379792421624641272746453190479316725484729966518436208854994615297484525229284199372356175508316843532962", "17650899844399818850216658397857397433150932740144581357248968616099085471799047373874018729030516138169880851496140", "23153291335322918391032655582853912472568833796263669034103198103796686482485894027826714525281391374850320336394313", "32367456268301553665798368340615053510284603246272143427825701218738172825017097170094900631328955480180538273877253", ]; let values = values .iter() .map(|s| BigUint::parse_bytes(s.as_bytes(), 10).unwrap()) .collect::>(); let mut transcript = CairoPoseidonTranscript::new(FieldElement::one()); for value in values { transcript.hash_u256(&(value % (BigUint::from(1usize) << 256))); } let expected_res: lambdaworks_math::field::element::FieldElement> = transcript.continuable_hash(); assert_eq!( expected_res, FieldElement::from_hex( "2a4b9382c92e77909659d0406c152da22c176cc4d7109e3fc32aff80da50bf9" ) .unwrap() ); } } ================================================ FILE: tools/garaga_rs/src/python_bindings/drand_calldata.rs ================================================ use super::*; #[pyfunction] pub fn drand_calldata_builder(py: Python, py_list1: &Bound<'_, PyList>) -> PyResult> { let values1 = py_list1 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let result = crate::calldata::drand_calldata::drand_calldata_builder(&values1) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } #[pyfunction] pub fn drand_tlock_encrypt_calldata_builder( py: Python, py_list1: &Bound<'_, PyList>, ) -> PyResult> { let values1 = py_list1 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let result = crate::calldata::drand_tlock_calldata::drand_tlock_encrypt_calldata_builder(&values1) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/ecip.rs ================================================ use super::*; use crate::ecip; #[pyfunction] pub fn zk_ecip_hint( py: Python, flattened_g1_points_list: &Bound<'_, PyList>, scalars_list: &Bound<'_, PyList>, curve_id: usize, ) -> PyResult> { let list_values = flattened_g1_points_list .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let list_scalars = scalars_list .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let v = ecip::core::zk_ecip_hint(list_values, list_scalars, curve_id) .map_err(PyErr::new::)?; let inner_lists: Vec<_> = v .into_iter() .map(|x| PyList::new(py, x)) .collect::>()?; let py_list = PyList::new(py, inner_lists)?; Ok(py_list.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/extf_mul.rs ================================================ use crate::algebra::extf_mul; use crate::algebra::polynomial::Polynomial; use crate::definitions::{CurveID, CurveParamsProvider}; use crate::io::field_elements_from_big_uints; use super::*; #[pyfunction] pub fn nondeterministic_extension_field_mul_divmod( py: Python, curve_id: usize, ext_degree: usize, py_list: &Bound<'_, PyList>, ) -> PyResult> { let list_coeffs = py_list .into_iter() .map(|x| x.extract()) .collect::>, _>>()?; let curve_id = CurveID::try_from(curve_id).unwrap(); match curve_id { CurveID::BN254 => { handle_extension_field_mul_divmod::(py, ext_degree, list_coeffs) } CurveID::BLS12_381 => { handle_extension_field_mul_divmod::(py, ext_degree, list_coeffs) } _ => panic!("Curve ID {} not supported", curve_id as usize), } } fn handle_extension_field_mul_divmod( py: Python, ext_degree: usize, list_coeffs: Vec>, ) -> PyResult> where F: IsPrimeField + CurveParamsProvider, FieldElement: ByteConversion, { let mut ps = Vec::new(); for coeffs in list_coeffs { let coeffs = field_elements_from_big_uints::(&coeffs); ps.push(Polynomial::new(coeffs)); } let (z_polyq, z_polyr) = extf_mul::nondeterministic_extension_field_mul_divmod(ext_degree, ps); let q = z_polyq .coefficients .into_iter() .map(|x| BigUint::from_bytes_be(&x.to_bytes_be())) .collect::>(); let r = z_polyr .coefficients .into_iter() .map(|x| BigUint::from_bytes_be(&x.to_bytes_be())) .collect::>(); let q_list = PyList::new(py, q)?; let r_list = PyList::new(py, r)?; let py_tuple = PyTuple::new(py, [q_list, r_list])?; Ok(py_tuple.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/final_exp_witness.rs ================================================ use super::*; #[pyfunction] pub fn get_final_exp_witness( py: Python, curve_id: usize, py_list: &Bound<'_, PyList>, ) -> PyResult> { let f_0: BigUint = py_list.get_item(0)?.extract()?; let f_1: BigUint = py_list.get_item(1)?.extract()?; let f_2: BigUint = py_list.get_item(2)?.extract()?; let f_3: BigUint = py_list.get_item(3)?.extract()?; let f_4: BigUint = py_list.get_item(4)?.extract()?; let f_5: BigUint = py_list.get_item(5)?.extract()?; let f_6: BigUint = py_list.get_item(6)?.extract()?; let f_7: BigUint = py_list.get_item(7)?.extract()?; let f_8: BigUint = py_list.get_item(8)?.extract()?; let f_9: BigUint = py_list.get_item(9)?.extract()?; let f_10: BigUint = py_list.get_item(10)?.extract()?; let f_11: BigUint = py_list.get_item(11)?.extract()?; let f = [f_0, f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, f_10, f_11]; let (c, wi) = crate::pairing::final_exp_witness::get_final_exp_witness(curve_id, f); let c_list = PyList::new(py, c)?; let wi_list = PyList::new(py, wi)?; let py_tuple = PyTuple::new(py, [c_list, wi_list])?; Ok(Py::from(py_tuple)) } ================================================ FILE: tools/garaga_rs/src/python_bindings/g2.rs ================================================ use super::*; use crate::io::{biguint_to_u256, element_from_biguint}; use lambdaworks_math::cyclic_group::IsGroup; use lambdaworks_math::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; use lambdaworks_math::elliptic_curve::traits::FromAffine; #[pyfunction] pub fn g2_add( py: Python, curve_id: usize, py_tuple_1: &Bound<'_, PyTuple>, py_tuple_2: &Bound<'_, PyTuple>, ) -> PyResult> { let a_0: BigUint = py_tuple_1.get_item(0)?.extract()?; let a_1: BigUint = py_tuple_1.get_item(1)?.extract()?; let a_2: BigUint = py_tuple_1.get_item(2)?.extract()?; let a_3: BigUint = py_tuple_1.get_item(3)?.extract()?; let b_0: BigUint = py_tuple_2.get_item(0)?.extract()?; let b_1: BigUint = py_tuple_2.get_item(1)?.extract()?; let b_2: BigUint = py_tuple_2.get_item(2)?.extract()?; let b_3: BigUint = py_tuple_2.get_item(3)?.extract()?; if curve_id == CURVE_BN254 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::BN254PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::twist::BN254TwistCurve; let a = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&a_0), element_from_biguint::(&a_1), ]), FieldElement::new([ element_from_biguint::(&a_2), element_from_biguint::(&a_3), ]), ) .unwrap(); let b = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); let c = a.operate_with(&b); let c_affine = c.to_affine(); let [[x0, x1], [y0, y1]] = match c_affine.z() == &FieldElement::zero() { true => [ &[FieldElement::zero(), FieldElement::zero()], &[FieldElement::zero(), FieldElement::zero()], ], false => [c_affine.x().value(), c_affine.y().value()], }; let py_tuple = PyTuple::new( py, [ element_to_biguint::(x0), element_to_biguint::(x1), element_to_biguint::(y0), element_to_biguint::(y1), ], ); return Ok(py_tuple?.into()); } if curve_id == CURVE_BLS12_381 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::twist::BLS12381TwistCurve; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::BLS12381PrimeField; let a = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&a_0), element_from_biguint::(&a_1), ]), FieldElement::new([ element_from_biguint::(&a_2), element_from_biguint::(&a_3), ]), ) .unwrap(); let b = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); let c = a.operate_with(&b); let c_affine = c.to_affine(); let [[x0, x1], [y0, y1]] = match c_affine.z() == &FieldElement::zero() { true => [ &[FieldElement::zero(), FieldElement::zero()], &[FieldElement::zero(), FieldElement::zero()], ], false => [c_affine.x().value(), c_affine.y().value()], }; let py_tuple = PyTuple::new( py, [ element_to_biguint::(x0), element_to_biguint::(x1), element_to_biguint::(y0), element_to_biguint::(y1), ], ); return Ok(py_tuple?.into()); } panic!("Curve ID {} not supported", curve_id); } #[pyfunction] pub fn g2_scalar_mul( py: Python, curve_id: usize, py_tuple_1: &Bound<'_, PyTuple>, py_int_2: &Bound<'_, PyInt>, ) -> PyResult> { let a_0: BigUint = py_tuple_1.get_item(0)?.extract()?; let a_1: BigUint = py_tuple_1.get_item(1)?.extract()?; let a_2: BigUint = py_tuple_1.get_item(2)?.extract()?; let a_3: BigUint = py_tuple_1.get_item(3)?.extract()?; let k: BigUint = py_int_2.extract()?; if curve_id == CURVE_BN254 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::BN254PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::twist::BN254TwistCurve; let a = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&a_0), element_from_biguint::(&a_1), ]), FieldElement::new([ element_from_biguint::(&a_2), element_from_biguint::(&a_3), ]), ) .unwrap(); let c = a.operate_with_self(biguint_to_u256(&k)); let c_affine = c.to_affine(); let [[x0, x1], [y0, y1]] = match c_affine.z() == &FieldElement::zero() { true => [ &[FieldElement::zero(), FieldElement::zero()], &[FieldElement::zero(), FieldElement::zero()], ], false => [c_affine.x().value(), c_affine.y().value()], }; let py_tuple = PyTuple::new( py, [ element_to_biguint::(x0), element_to_biguint::(x1), element_to_biguint::(y0), element_to_biguint::(y1), ], ); return Ok(py_tuple?.into()); } if curve_id == CURVE_BLS12_381 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::BLS12381PrimeField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::twist::BLS12381TwistCurve; let a = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&a_0), element_from_biguint::(&a_1), ]), FieldElement::new([ element_from_biguint::(&a_2), element_from_biguint::(&a_3), ]), ) .unwrap(); let c = a.operate_with_self(biguint_to_u256(&k)); let c_affine = c.to_affine(); let [[x0, x1], [y0, y1]] = match c_affine.z() == &FieldElement::zero() { true => [ &[FieldElement::zero(), FieldElement::zero()], &[FieldElement::zero(), FieldElement::zero()], ], false => [c_affine.x().value(), c_affine.y().value()], }; let py_tuple = PyTuple::new( py, [ element_to_biguint::(x0), element_to_biguint::(x1), element_to_biguint::(y0), element_to_biguint::(y1), ], ); return Ok(py_tuple?.into()); } panic!("Curve ID {} not supported", curve_id); } ================================================ FILE: tools/garaga_rs/src/python_bindings/groth16_calldata.rs ================================================ use super::*; use crate::calldata::full_proof_with_hints::groth16; use crate::calldata::full_proof_with_hints::groth16::{Groth16Proof, Groth16VerificationKey}; use crate::definitions::CurveID; use pyo3::prelude::*; use pyo3::types::PyList; #[pyfunction(signature = (proof, vk, curve_id, image_id=None, journal=None, public_inputs_sp1=None, vkey=None))] pub fn get_groth16_calldata( py: Python, proof: &Bound<'_, PyList>, vk: &Bound<'_, PyList>, curve_id: usize, image_id: Option<&[u8]>, journal: Option<&[u8]>, public_inputs_sp1: Option<&[u8]>, vkey: Option<&[u8]>, ) -> PyResult> { let proof_values = proof .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let vk_values = vk .into_iter() .map(|x| x.extract()) .collect::, _>>()?; // Handle RISC0 optional parameters let image_id_journal_risc0 = if let (Some(image_id), Some(journal)) = (image_id, journal) { Some((image_id.to_vec(), journal.to_vec())) } else { None }; let verifying_key = Groth16VerificationKey::from(vk_values); // Handle SP1 optional parameters let vkey_public_values_sp1 = if let (Some(vkey), Some(public_inputs_sp1)) = (vkey, public_inputs_sp1) { assert!(verifying_key == groth16::get_sp1_vk()); Some((vkey.to_vec(), public_inputs_sp1.to_vec())) } else { None }; let result = groth16::get_groth16_calldata( &Groth16Proof::from(proof_values, image_id_journal_risc0, vkey_public_values_sp1), &verifying_key, CurveID::try_from(curve_id).map_err(PyErr::new::)?, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/hades_permutation.rs ================================================ use super::*; #[pyfunction] pub fn hades_permutation( py: Python, py_value_1: &Bound<'_, PyBytes>, py_value_2: &Bound<'_, PyBytes>, py_value_3: &Bound<'_, PyBytes>, ) -> PyResult> { let byte_slice_1: &[u8] = py_value_1.as_bytes(); let byte_slice_2: &[u8] = py_value_2.as_bytes(); let byte_slice_3: &[u8] = py_value_3.as_bytes(); let mut state: Vec> = vec![ FieldElement::::from_bytes_be(byte_slice_1) .expect("Unable to convert first param from bytes to FieldElement"), FieldElement::::from_bytes_be(byte_slice_2) .expect("Unable to convert second param from bytes to FieldElement"), FieldElement::::from_bytes_be(byte_slice_3) .expect("Unable to convert third param from bytes to FieldElement"), ]; PoseidonCairoStark252::hades_permutation(&mut state); let py_tuple = PyTuple::new( py, state.iter().map(|fe| { let fe_bytes = fe.to_bytes_be(); PyBytes::new(py, &fe_bytes) }), ); Ok(py_tuple?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/mod.rs ================================================ pub mod drand_calldata; pub mod ecip; pub mod extf_mul; pub mod final_exp_witness; pub mod g2; pub mod groth16_calldata; pub mod hades_permutation; pub mod mpc_calldata; pub mod msm; pub mod pairing; pub mod signatures; pub mod zk_honk_calldata; use lambdaworks_crypto::hash::poseidon::{starknet::PoseidonCairoStark252, Poseidon}; use lambdaworks_math::{field::traits::IsPrimeField, traits::ByteConversion}; use crate::crypto::poseidon_bn254::poseidon_hash_bn254 as core_poseidon_hash_bn254; use crate::definitions::{ BLS12381PrimeField, BN254PrimeField, FieldElement, GrumpkinPrimeField, Stark252PrimeField, }; use crate::io::{element_from_biguint, element_to_biguint}; use num_bigint::BigUint; use pyo3::{ conversion::IntoPyObject, prelude::*, types::{PyBytes, PyInt, PyList, PyTuple}, }; const CURVE_BN254: usize = 0; const CURVE_BLS12_381: usize = 1; #[pyfunction] pub fn poseidon_hash_bn254( py: Python, x: &Bound<'_, PyInt>, y: &Bound<'_, PyInt>, ) -> PyResult> { let x_biguint: BigUint = x.extract()?; let y_biguint: BigUint = y.extract()?; let x_fe = element_from_biguint::(&x_biguint); let y_fe = element_from_biguint::(&y_biguint); let result = core_poseidon_hash_bn254(&x_fe, &y_fe); let result_biguint = element_to_biguint(&result); Ok(result_biguint.into_pyobject(py)?.into()) } #[pymodule] fn garaga_rs(m: &Bound<'_, PyModule>) -> PyResult<()> { m.add_function(wrap_pyfunction!(g2::g2_add, m)?)?; m.add_function(wrap_pyfunction!(g2::g2_scalar_mul, m)?)?; m.add_function(wrap_pyfunction!(pairing::multi_pairing, m)?)?; m.add_function(wrap_pyfunction!(pairing::multi_miller_loop, m)?)?; m.add_function(wrap_pyfunction!( final_exp_witness::get_final_exp_witness, m )?)?; m.add_function(wrap_pyfunction!(hades_permutation::hades_permutation, m)?)?; m.add_function(wrap_pyfunction!( extf_mul::nondeterministic_extension_field_mul_divmod, m )?)?; m.add_function(wrap_pyfunction!(ecip::zk_ecip_hint, m)?)?; m.add_function(wrap_pyfunction!(msm::msm_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!(mpc_calldata::mpc_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!(groth16_calldata::get_groth16_calldata, m)?)?; m.add_function(wrap_pyfunction!(zk_honk_calldata::get_zk_honk_calldata, m)?)?; m.add_function(wrap_pyfunction!(signatures::schnorr_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!(signatures::ecdsa_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!(signatures::eddsa_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!(signatures::rsa_2048_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!( signatures::rsa_2048_sha256_calldata_builder, m )?)?; m.add_function(wrap_pyfunction!(poseidon_hash_bn254, m)?)?; m.add_function(wrap_pyfunction!(pairing::final_exp, m)?)?; m.add_function(wrap_pyfunction!(drand_calldata::drand_calldata_builder, m)?)?; m.add_function(wrap_pyfunction!( drand_calldata::drand_tlock_encrypt_calldata_builder, m )?)?; Ok(()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/mpc_calldata.rs ================================================ use super::*; #[pyfunction] pub fn mpc_calldata_builder( py: Python, curve_id: usize, py_list1: &Bound<'_, PyList>, n_fixed_g2: usize, py_list2: &Bound<'_, PyList>, ) -> PyResult> { let values1 = py_list1 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let values2 = py_list2 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let result = crate::calldata::mpc_calldata::mpc_calldata_builder( curve_id, &values1, n_fixed_g2, &values2, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/msm.rs ================================================ use super::*; #[pyfunction] #[allow(clippy::too_many_arguments)] pub fn msm_calldata_builder( py: Python, py_list1: &Bound<'_, PyList>, py_list2: &Bound<'_, PyList>, curve_id: usize, include_points_and_scalars: bool, serialize_as_pure_felt252_array: bool, ) -> PyResult> { let values = py_list1 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let scalars = py_list2 .into_iter() .map(|x| x.extract()) .collect::, _>>()?; let result = crate::calldata::msm_calldata::msm_calldata_builder( &values, &scalars, curve_id, include_points_and_scalars, serialize_as_pure_felt252_array, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/pairing.rs ================================================ use super::*; use crate::definitions::{BLS12381PrimeField, BN254PrimeField}; use crate::io::element_from_biguint; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::curve::BN254Curve; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::twist::BN254TwistCurve; use lambdaworks_math::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; use lambdaworks_math::elliptic_curve::traits::FromAffine; use lambdaworks_math::elliptic_curve::{ short_weierstrass::curves::bn_254::pairing::BN254AtePairing, traits::IsPairing, }; use itertools::Itertools; use lambdaworks_math::cyclic_group::IsGroup; use lambdaworks_math::field::element::FieldElement; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254; use lambdaworks_math::unsigned_integer::element::U256; use crate::pairing::final_exp_witness::{to_bls, to_bn}; #[pyfunction] pub fn multi_pairing( py: Python, curve_id: usize, py_list_1: &Bound<'_, PyList>, ) -> PyResult> { assert!(py_list_1.len() % 6 == 0, "invalid length"); if curve_id == CURVE_BN254 { let pairs = py_list_1 .iter() .chunks(6) .into_iter() .map(|chunk| { let [a_0, a_1, b_0, b_1, b_2, b_3] = chunk .map(|item| item.extract::().unwrap()) .collect::>() .try_into() .unwrap(); let ap = ShortWeierstrassProjectivePoint::::from_affine( element_from_biguint::(&a_0), element_from_biguint::(&a_1), ) .unwrap(); let bp = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); (ap, bp) }) .collect::>(); let cx = BN254AtePairing::compute_batch(&pairs.iter().map(|(a, b)| (a, b)).collect::>()) .unwrap(); let cx = match cx == FieldElement::one() { true => cx, false => { let final_exp_cofactor = U256::from_hex_unchecked("3bec47df15e307c81ea96b02d9d9e38d2e5d4e223ddedaf4"); cx.pow(final_exp_cofactor) } }; let py_list = PyList::new(py, to_bn(cx)); return Ok(py_list?.into()); } if curve_id == CURVE_BLS12_381 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::{ curve::BLS12381Curve, pairing::BLS12381AtePairing, twist::BLS12381TwistCurve, }; let pairs = py_list_1 .iter() .chunks(6) .into_iter() .map(|chunk| { let [a_0, a_1, b_0, b_1, b_2, b_3] = chunk .map(|item| item.extract::().unwrap()) .collect::>() .try_into() .unwrap(); let ap = ShortWeierstrassProjectivePoint::::from_affine( element_from_biguint::(&a_0), element_from_biguint::(&a_1), ) .unwrap(); let bp = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); (ap, bp) }) .collect::>(); let cx = BLS12381AtePairing::compute_batch( &pairs.iter().map(|(a, b)| (a, b)).collect::>(), ) .unwrap(); let py_list = PyList::new(py, to_bls(cx)); return Ok(py_list?.into()); } panic!("Curve ID {} not supported", curve_id); } #[pyfunction] pub fn multi_miller_loop( py: Python, curve_id: usize, py_list_1: &Bound<'_, PyList>, ) -> PyResult> { assert!(py_list_1.len() % 6 == 0, "invalid length"); if curve_id == CURVE_BN254 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree12ExtensionField; let pairs = py_list_1 .iter() .chunks(6) .into_iter() .map(|chunk| { let [a_0, a_1, b_0, b_1, b_2, b_3] = chunk .map(|item| item.extract::().unwrap()) .collect::>() .try_into() .unwrap(); let ap = ShortWeierstrassProjectivePoint::::from_affine( element_from_biguint::(&a_0), element_from_biguint::(&a_1), ) .unwrap(); let bp = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); (ap, bp) }) .collect::>(); let mut result = FieldElement::::one(); for (p, q) in pairs { // We don't need to check if p is in the subgroup because the subgroup oF G1 is G1. // See https://hackmd.io/@jpw/bn254#Subgroup-checks. if !q.is_in_subgroup() { return Err(PyErr::new::( "Point not in subgroup", )); } if !p.is_neutral_element() && !q.is_neutral_element() { let p = p.to_affine(); let q = q.to_affine(); result *= bn_254::pairing::miller_optimized(&p, &q); } } let py_list = PyList::new(py, to_bn(result)); return Ok(py_list?.into()); } if curve_id == CURVE_BLS12_381 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree12ExtensionField; use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::{ curve::BLS12381Curve, twist::BLS12381TwistCurve, }; let pairs = py_list_1 .iter() .chunks(6) .into_iter() .map(|chunk| { let [a_0, a_1, b_0, b_1, b_2, b_3] = chunk .map(|item| item.extract::().unwrap()) .collect::>() .try_into() .unwrap(); let ap = ShortWeierstrassProjectivePoint::::from_affine( element_from_biguint::(&a_0), element_from_biguint::(&a_1), ) .unwrap(); let bp = ShortWeierstrassProjectivePoint::::from_affine( FieldElement::new([ element_from_biguint::(&b_0), element_from_biguint::(&b_1), ]), FieldElement::new([ element_from_biguint::(&b_2), element_from_biguint::(&b_3), ]), ) .unwrap(); (ap, bp) }) .collect::>(); let mut result = FieldElement::::one(); for (p, q) in pairs { // We don't need to check if p is in the subgroup because the subgroup oF G1 is G1. // See https://hackmd.io/@jpw/bn254#Subgroup-checks. if !q.is_in_subgroup() { return Err(PyErr::new::( "Point not in subgroup", )); } if !p.is_neutral_element() && !q.is_neutral_element() { let p = p.to_affine(); let q = q.to_affine(); result *= bls12_381::pairing::miller(&q, &p); } } let py_list = PyList::new(py, to_bls(result)); return Ok(py_list?.into()); } panic!("Curve ID {} not supported", curve_id); } #[pyfunction] pub fn final_exp( py: Python, curve_id: usize, py_list_1: &Bound<'_, PyList>, ) -> PyResult> { assert!(py_list_1.len() == 12, "invalid length"); let [f_0, f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, f_10, f_11] = py_list_1.extract::<[BigUint; 12]>().unwrap(); if curve_id == 0 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::{Degree12ExtensionField, Degree6ExtensionField, Degree2ExtensionField}; let f = FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_0), element_from_biguint::(&f_1), ]), FieldElement::::new([ element_from_biguint::(&f_2), element_from_biguint::(&f_3), ]), FieldElement::::new([ element_from_biguint::(&f_4), element_from_biguint::(&f_5), ]), ]), FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_6), element_from_biguint::(&f_7), ]), FieldElement::::new([ element_from_biguint::(&f_8), element_from_biguint::(&f_9), ]), FieldElement::::new([ element_from_biguint::(&f_10), element_from_biguint::(&f_11), ]), ]), ]); let final_exp = bn_254::pairing::final_exponentiation_optimized(&f); let fx = match final_exp == FieldElement::one() { true => final_exp, false => { let final_exp_cofactor = U256::from_hex_unchecked("3bec47df15e307c81ea96b02d9d9e38d2e5d4e223ddedaf4"); final_exp.pow(final_exp_cofactor) } }; let py_list = PyList::new(py, to_bn(fx)); return Ok(py_list?.into()); } if curve_id == 1 { use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::{Degree12ExtensionField, Degree6ExtensionField, Degree2ExtensionField}; let f = FieldElement::::new([ FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_0), element_from_biguint::(&f_1), ]), FieldElement::::new([ element_from_biguint::(&f_2), element_from_biguint::(&f_3), ]), FieldElement::::new([ element_from_biguint::(&f_4), element_from_biguint::(&f_5), ]), ]), FieldElement::::new([ FieldElement::::new([ element_from_biguint::(&f_6), element_from_biguint::(&f_7), ]), FieldElement::::new([ element_from_biguint::(&f_8), element_from_biguint::(&f_9), ]), FieldElement::::new([ element_from_biguint::(&f_10), element_from_biguint::(&f_11), ]), ]), ]); let fx = bls12_381::pairing::final_exponentiation(&f); let py_list = PyList::new(py, to_bls(fx)); return Ok(py_list?.into()); } panic!("Curve ID {} not supported", curve_id); } ================================================ FILE: tools/garaga_rs/src/python_bindings/signatures.rs ================================================ use super::*; #[pyfunction] pub fn schnorr_calldata_builder( py: Python, rx: &Bound<'_, PyInt>, s: &Bound<'_, PyInt>, e: &Bound<'_, PyInt>, px: &Bound<'_, PyInt>, py_coord: &Bound<'_, PyInt>, prepend_public_key: bool, curve_id: usize, ) -> PyResult> { let rx: BigUint = rx.extract()?; let s: BigUint = s.extract()?; let e: BigUint = e.extract()?; let px: BigUint = px.extract()?; let py_coord: BigUint = py_coord.extract()?; let result = crate::calldata::signatures::schnorr_calldata_builder( rx, s, e, px, py_coord, prepend_public_key, curve_id, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } #[pyfunction] pub fn ecdsa_calldata_builder( py: Python, r: &Bound<'_, PyInt>, s: &Bound<'_, PyInt>, v: u8, px: &Bound<'_, PyInt>, py_coord: &Bound<'_, PyInt>, z: &Bound<'_, PyInt>, prepend_public_key: bool, curve_id: usize, ) -> PyResult> { let r: BigUint = r.extract()?; let s: BigUint = s.extract()?; let px: BigUint = px.extract()?; let py_coord: BigUint = py_coord.extract()?; let z: BigUint = z.extract()?; let result = crate::calldata::signatures::ecdsa_calldata_builder( r, s, v, px, py_coord, z, prepend_public_key, curve_id, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } #[pyfunction] pub fn eddsa_calldata_builder( py: Python, rx: &Bound<'_, PyInt>, s: &Bound<'_, PyInt>, py_coord: &Bound<'_, PyInt>, msg: &Bound<'_, PyBytes>, prepend_public_key: bool, ) -> PyResult> { let rx: BigUint = rx.extract()?; let s: BigUint = s.extract()?; let py_coord: BigUint = py_coord.extract()?; let msg: Vec = msg.extract()?; let result = crate::calldata::signatures::eddsa_calldata_builder( rx, s, py_coord, msg, prepend_public_key, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } #[pyfunction] pub fn rsa_2048_calldata_builder( py: Python, signature: &Bound<'_, PyInt>, expected_message: &Bound<'_, PyInt>, modulus: &Bound<'_, PyInt>, prepend_public_key: bool, ) -> PyResult> { let signature: BigUint = signature.extract()?; let expected_message: BigUint = expected_message.extract()?; let modulus: BigUint = modulus.extract()?; let result = crate::calldata::signatures::rsa_2048_calldata_builder( signature, expected_message, modulus, prepend_public_key, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } #[pyfunction] pub fn rsa_2048_sha256_calldata_builder( py: Python, signature: &Bound<'_, PyInt>, message: &Bound<'_, PyBytes>, modulus: &Bound<'_, PyInt>, prepend_public_key: bool, ) -> PyResult> { let signature: BigUint = signature.extract()?; let message: Vec = message.extract()?; let modulus: BigUint = modulus.extract()?; let result = crate::calldata::signatures::rsa_2048_sha256_calldata_builder( signature, &message, modulus, prepend_public_key, ) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/python_bindings/zk_honk_calldata.rs ================================================ use super::*; use crate::calldata::full_proof_with_hints::zk_honk; use crate::calldata::full_proof_with_hints::zk_honk::{HonkVerificationKey, ZKHonkProof}; use pyo3::prelude::*; use pyo3::types::PyList; #[pyfunction] pub fn get_zk_honk_calldata( py: Python, proof: &Bound<'_, PyBytes>, public_inputs: &Bound<'_, PyBytes>, vk: &Bound<'_, PyBytes>, ) -> PyResult> { let proof_bytes = proof.as_bytes(); let public_inputs_bytes = public_inputs.as_bytes(); let vk_bytes = vk.as_bytes(); let vk = HonkVerificationKey::from_bytes(vk_bytes) .map_err(PyErr::new::)?; let proof = ZKHonkProof::from_bytes(proof_bytes, public_inputs_bytes, vk.log_circuit_size) .map_err(PyErr::new::)?; let result = zk_honk::get_zk_honk_calldata(&proof, &vk) .map_err(PyErr::new::)?; let py_list = PyList::new(py, result); Ok(py_list?.into()) } ================================================ FILE: tools/garaga_rs/src/wasm_bindings.rs ================================================ use crate::calldata::full_proof_with_hints::groth16; use crate::calldata::full_proof_with_hints::groth16::{Groth16Proof, Groth16VerificationKey}; use crate::calldata::full_proof_with_hints::zk_honk; use crate::calldata::full_proof_with_hints::zk_honk::{HonkVerificationKey, ZKHonkProof}; use crate::calldata::{G1PointBigUint, G2PointBigUint}; use crate::crypto::poseidon_bn254::poseidon_hash_bn254; use crate::definitions::CurveID; use crate::definitions::{ GrumpkinPrimeField, ToTwistedEdwardsCurve, ToWeierstrassCurve, X25519PrimeField, }; use crate::io::{element_from_biguint, element_to_biguint}; use js_sys::{Array, Uint8Array}; use num_bigint::BigUint; use num_traits::Num; use wasm_bindgen::prelude::*; // Import the Num trait #[wasm_bindgen] pub fn drand_calldata_builder(values: Vec) -> Result, JsValue> { let values: Vec = values .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; let result = crate::calldata::drand_calldata::drand_calldata_builder(&values) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn drand_tlock_encrypt_calldata_builder(values: Vec) -> Result, JsValue> { let values: Vec = values .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; let result = crate::calldata::drand_tlock_calldata::drand_tlock_encrypt_calldata_builder(&values) .map_err(|e| JsValue::from_str(&e.to_string()))?; let result: Vec = result; Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn msm_calldata_builder( values: Vec, scalars: Vec, curve_id: usize, include_points_and_scalars: bool, serialize_as_pure_felt252_array: bool, ) -> Result, JsValue> { let values: Vec = values .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; let scalars: Vec = scalars .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; // Ensure msm_calldata_builder returns a Result type let result = crate::calldata::msm_calldata::msm_calldata_builder( &values, &scalars, curve_id, include_points_and_scalars, serialize_as_pure_felt252_array, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn mpc_calldata_builder( curve_id: usize, values1: Vec, n_fixed_g2: usize, values2: Vec, ) -> Result, JsValue> { let values1: Vec = values1 .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; let values2: Vec = values2 .into_iter() .map(jsvalue_to_biguint) .collect::, _>>()?; // Ensure msm_calldata_builder returns a Result type let result = crate::calldata::mpc_calldata::mpc_calldata_builder( curve_id, &values1, n_fixed_g2, &values2, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn schnorr_calldata_builder( rx: JsValue, s: JsValue, e: JsValue, px: JsValue, py: JsValue, prepend_public_key: bool, curve_id: usize, ) -> Result, JsValue> { let rx: BigUint = jsvalue_to_biguint(rx)?; let s: BigUint = jsvalue_to_biguint(s)?; let e: BigUint = jsvalue_to_biguint(e)?; let px: BigUint = jsvalue_to_biguint(px)?; let py: BigUint = jsvalue_to_biguint(py)?; let result = crate::calldata::signatures::schnorr_calldata_builder( rx, s, e, px, py, prepend_public_key, curve_id, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn ecdsa_calldata_builder( r: JsValue, s: JsValue, v: usize, px: JsValue, py: JsValue, z: JsValue, prepend_public_key: bool, curve_id: usize, ) -> Result, JsValue> { let r: BigUint = jsvalue_to_biguint(r)?; let s: BigUint = jsvalue_to_biguint(s)?; let v: u8 = v .try_into() .map_err(|_| JsValue::from_str("Failed to convert value to u8"))?; let px: BigUint = jsvalue_to_biguint(px)?; let py: BigUint = jsvalue_to_biguint(py)?; let z: BigUint = jsvalue_to_biguint(z)?; let result = crate::calldata::signatures::ecdsa_calldata_builder( r, s, v, px, py, z, prepend_public_key, curve_id, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn eddsa_calldata_builder( ry_twisted: JsValue, s: JsValue, py_twisted: JsValue, msg: JsValue, prepend_public_key: bool, ) -> Result, JsValue> { let r: BigUint = jsvalue_to_biguint(ry_twisted)?; let s: BigUint = jsvalue_to_biguint(s)?; let py: BigUint = jsvalue_to_biguint(py_twisted)?; let msg: Vec = msg.dyn_into::().map(|arr| arr.to_vec())?; let result = crate::calldata::signatures::eddsa_calldata_builder(r, s, py, msg, prepend_public_key) .map_err(|e| JsValue::from_str(&e.to_string()))?; // Handle error here let result: Vec = result; // Ensure result is of type Vec Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn rsa_2048_calldata_builder( signature: JsValue, expected_message: JsValue, modulus: JsValue, prepend_public_key: bool, ) -> Result, JsValue> { let signature: BigUint = jsvalue_to_biguint(signature)?; let expected_message: BigUint = jsvalue_to_biguint(expected_message)?; let modulus: BigUint = jsvalue_to_biguint(modulus)?; let result = crate::calldata::signatures::rsa_2048_calldata_builder( signature, expected_message, modulus, prepend_public_key, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } #[wasm_bindgen] pub fn rsa_2048_sha256_calldata_builder( signature: JsValue, message: JsValue, modulus: JsValue, prepend_public_key: bool, ) -> Result, JsValue> { let signature: BigUint = jsvalue_to_biguint(signature)?; let message: Vec = message .dyn_into::() .map(|arr| arr.to_vec()) .map_err(|_| JsValue::from_str("message must be a Uint8Array"))?; let modulus: BigUint = jsvalue_to_biguint(modulus)?; let result = crate::calldata::signatures::rsa_2048_sha256_calldata_builder( signature, &message, modulus, prepend_public_key, ) .map_err(|e| JsValue::from_str(&e.to_string()))?; Ok(result.into_iter().map(biguint_to_jsvalue).collect()) } fn jsvalue_to_biguint(v: JsValue) -> Result { let s = (JsValue::from_str("") + v) .as_string() .ok_or_else(|| JsValue::from_str("Failed to convert JsValue to string"))?; let (number_str, radix) = if s.starts_with("0x") || s.starts_with("0X") { // It's a hexadecimal string; remove the '0x' prefix (&s[2..], 16) } else { // Assume it's a decimal string (s.as_str(), 10) }; BigUint::from_str_radix(number_str, radix) .map_err(|_| JsValue::from_str("Failed to convert string to BigUint")) } fn biguint_to_jsvalue(v: BigUint) -> JsValue { JsValue::bigint_from_str(&v.to_string()) } // Helper function to get a property from an object fn get_property(obj: &js_sys::Object, key: &str) -> Result { js_sys::Reflect::get(obj, &JsValue::from_str(key)) } #[allow(dead_code)] fn set_property(obj: &js_sys::Object, key: &str, value: &JsValue) -> Result<(), JsValue> { let success = js_sys::Reflect::set(obj, &JsValue::from_str(key), value)?; if !success { return Err(JsValue::from_str(&format!( "Failed to set property: {}", key ))); } Ok(()) } // Parsing helper for G1PointBigUint fn parse_g1_point(value: JsValue) -> Result { let obj = value .dyn_into::() .map_err(|_| JsValue::from_str("Failed to parse G1PointBigUint"))?; let x = jsvalue_to_biguint(get_property(&obj, "x")?)?; let y = jsvalue_to_biguint(get_property(&obj, "y")?)?; Ok(G1PointBigUint { x, y }) } #[allow(dead_code)] fn jsvalue_from_g1_point(point: &G1PointBigUint, curve_id: usize) -> Result { let point_obj = js_sys::Object::new(); set_property(&point_obj, "x", &biguint_to_jsvalue(point.x.clone()))?; set_property(&point_obj, "y", &biguint_to_jsvalue(point.y.clone()))?; set_property(&point_obj, "curveId", &curve_id.into())?; Ok(point_obj.into()) } // Parsing helper for G2PointBigUint fn parse_g2_point(value: JsValue) -> Result { let obj = value .dyn_into::() .map_err(|_| JsValue::from_str("Failed to parse G2PointBigUint"))?; let x_tuple = get_property(&obj, "x")? .dyn_into::() .map_err(|_| JsValue::from_str("x is not an array"))?; let y_tuple = get_property(&obj, "y")? .dyn_into::() .map_err(|_| JsValue::from_str("y is not an array"))?; let x0 = jsvalue_to_biguint(x_tuple.get(0))?; let x1 = jsvalue_to_biguint(x_tuple.get(1))?; let y0 = jsvalue_to_biguint(y_tuple.get(0))?; let y1 = jsvalue_to_biguint(y_tuple.get(1))?; Ok(G2PointBigUint { x0, x1, y0, y1 }) } // Parsing helper for an array of BigUint fn parse_biguint_array(value: JsValue) -> Result, JsValue> { let array = value .dyn_into::() .map_err(|_| JsValue::from_str("public_inputs is not an array"))?; array .iter() .map(|v| { // let s = v // .as_string() // .ok_or_else(|| JsValue::from_str("public_inputs element is not a string"))?; // Parse the string into BigUint using the helper function jsvalue_to_biguint(v) }) .collect() } #[allow(dead_code)] fn jsvalue_from_biguint_array(values: &[BigUint]) -> Result { let values = values .iter() .cloned() .map(biguint_to_jsvalue) .collect::>(); Ok(values.into()) } // Parses an array of G1 points from JsValue fn parse_g1_point_array(value: JsValue) -> Result, JsValue> { let array = value .dyn_into::() .map_err(|_| JsValue::from_str("ic is not an array"))?; let mut points = Vec::new(); for i in 0..array.length() { let point = parse_g1_point(array.get(i))?; points.push(point); } Ok(points) } #[allow(dead_code)] fn jsvalue_from_g1_point_array( points: &[G1PointBigUint], curve_id: usize, ) -> Result { let points = points .iter() .map(|point| jsvalue_from_g1_point(point, curve_id)) .collect::, _>>()?; Ok(points.into()) } // Optional parsing helper for Uint8Array #[allow(dead_code)] fn _parse_optional_uint8_array(value: JsValue) -> Option> { value.dyn_into::().ok().map(|arr| arr.to_vec()) } #[wasm_bindgen] pub fn to_weirstrass(x_twisted: JsValue, y_twisted: JsValue) -> Result, JsValue> { let x_twisted_biguint = jsvalue_to_biguint(x_twisted).unwrap(); let x_twisted = element_from_biguint::(&x_twisted_biguint); let y_twisted_biguint = jsvalue_to_biguint(y_twisted).unwrap(); let y_twisted = element_from_biguint::(&y_twisted_biguint); let result = crate::definitions::X25519PrimeField::to_weirstrass(x_twisted, y_twisted); let x_weirstrass = element_to_biguint::(&result.0); let y_weirstrass = element_to_biguint::(&result.1); let result = vec![ biguint_to_jsvalue(x_weirstrass), biguint_to_jsvalue(y_weirstrass), ]; Ok(result) } #[wasm_bindgen] pub fn to_twistededwards( x_weirstrass: JsValue, y_weirstrass: JsValue, ) -> Result, JsValue> { let x_weirstrass_biguint = jsvalue_to_biguint(x_weirstrass).unwrap(); let x_weirstrass = element_from_biguint::(&x_weirstrass_biguint); let y_weirstrass_biguint = jsvalue_to_biguint(y_weirstrass).unwrap(); let y_weirstrass = element_from_biguint::(&y_weirstrass_biguint); let result = crate::definitions::X25519PrimeField::to_twistededwards(x_weirstrass, y_weirstrass); let x_twisted = element_to_biguint::(&result.0); let y_twisted = element_to_biguint::(&result.1); let result = vec![biguint_to_jsvalue(x_twisted), biguint_to_jsvalue(y_twisted)]; Ok(result) } #[wasm_bindgen] pub fn get_groth16_calldata( proof_js: JsValue, vk_js: JsValue, curve_id_js: JsValue, ) -> Result, JsValue> { let proof_obj = proof_js .dyn_into::() .map_err(|_| JsValue::from_str("proof_js is not an object"))?; let property = get_property(&proof_obj, "a")?; let a = parse_g1_point(property)?; let b = parse_g2_point(get_property(&proof_obj, "b")?)?; let c = parse_g1_point(get_property(&proof_obj, "c")?)?; let public_inputs = parse_biguint_array(get_property(&proof_obj, "publicInputs")?)?; // Parse RISC0 data if present let image_id_journal_risc0 = match get_property(&proof_obj, "imageIdJournalRisc0") { Ok(value) if !value.is_undefined() && !value.is_null() => { let risc0_obj = value .dyn_into::() .map_err(|_| JsValue::from_str("imageIdJournalRisc0 is not an object"))?; let image_id = get_property(&risc0_obj, "imageId")? .dyn_into::() .map(|arr| arr.to_vec()) .map_err(|_| JsValue::from_str("imageId is not a Uint8Array"))?; let journal = get_property(&risc0_obj, "journal")? .dyn_into::() .map(|arr| arr.to_vec()) .map_err(|_| JsValue::from_str("journal is not a Uint8Array"))?; Some((image_id, journal)) } _ => None, }; // Parse SP1 data if present let vkey_public_values_sp1 = match get_property(&proof_obj, "vkeyPublicValuesSp1") { Ok(value) if !value.is_undefined() && !value.is_null() => { let sp1_obj = value .dyn_into::() .map_err(|_| JsValue::from_str("vkeyPublicValuesSp1 is not an object"))?; let vkey = get_property(&sp1_obj, "vkey")? .dyn_into::() .map(|arr| arr.to_vec()) .map_err(|_| JsValue::from_str("vkey is not a Uint8Array"))?; let public_values = get_property(&sp1_obj, "publicValues")? .dyn_into::() .map(|arr| arr.to_vec()) .map_err(|_| JsValue::from_str("publicValues is not a Uint8Array"))?; Some((vkey, public_values)) } _ => None, }; let proof = Groth16Proof { a, b, c, public_inputs, image_id_journal_risc0, vkey_public_values_sp1, }; let vk_obj = vk_js .dyn_into::() .map_err(|_| JsValue::from_str("vk_js is not an object"))?; let alpha = parse_g1_point(get_property(&vk_obj, "alpha")?)?; let beta = parse_g2_point(get_property(&vk_obj, "beta")?)?; let gamma = parse_g2_point(get_property(&vk_obj, "gamma")?)?; let delta = parse_g2_point(get_property(&vk_obj, "delta")?)?; let ic = parse_g1_point_array(get_property(&vk_obj, "ic")?)?; let vk = Groth16VerificationKey { alpha, beta, gamma, delta, ic, }; //Parse curve_id_js into usize let curve_id_num = curve_id_js .as_f64() .ok_or_else(|| JsValue::from_str("curve_id_js is not a number"))? as usize; // Convert usize to CurveID using TryFrom let curve_id = CurveID::try_from(curve_id_num).map_err(|e| JsValue::from_str(&e))?; let groth16_calldata_biguint = groth16::get_groth16_calldata(&proof, &vk, curve_id); let groth16_calldata_js = groth16_calldata_biguint? .into_iter() .map(biguint_to_jsvalue) .collect::>(); Ok(groth16_calldata_js) } #[wasm_bindgen] pub fn get_zk_honk_calldata( proof_js: JsValue, public_inputs_js: JsValue, vk_js: JsValue, ) -> Result, JsValue> { let proof_bytes = proof_js.dyn_into::().map(|arr| arr.to_vec())?; let public_inputs_bytes = public_inputs_js .dyn_into::() .map(|arr| arr.to_vec())?; let vk_bytes = vk_js.dyn_into::().map(|arr| arr.to_vec())?; let vk = HonkVerificationKey::from_bytes(&vk_bytes).map_err(|s| JsValue::from_str(&s))?; let proof = ZKHonkProof::from_bytes(&proof_bytes, &public_inputs_bytes, vk.log_circuit_size) .map_err(|s| JsValue::from_str(&s))?; let honk_calldata_biguint = zk_honk::get_zk_honk_calldata(&proof, &vk); let honk_calldata_js = honk_calldata_biguint? .into_iter() .map(biguint_to_jsvalue) .collect::>(); Ok(honk_calldata_js) } #[wasm_bindgen] pub fn poseidon_hash(x: JsValue, y: JsValue) -> Result { // Convert hex strings to field elements, handling potential errors let x_biguint = jsvalue_to_biguint(x).map_err(|_| JsValue::from_str("Failed to parse x input as hex"))?; let x_fe = element_from_biguint::(&x_biguint); let y_biguint = jsvalue_to_biguint(y).map_err(|_| JsValue::from_str("Failed to parse y input as hex"))?; let y_fe = element_from_biguint::(&y_biguint); // Compute hash let result = poseidon_hash_bn254(&x_fe, &y_fe); let res_biguint = element_to_biguint::(&result); // Convert result to hex string Ok(biguint_to_jsvalue(res_biguint)) } #[allow(dead_code)] #[cfg(test)] mod tests { use super::*; use crate::definitions::CurveParamsProvider; use js_sys::Object; use num_bigint::BigUint; use wasm_bindgen_test::wasm_bindgen_test; // This test runs only in wasm32-unknown-unknown targets // wasm-pack test --node --release --no-default-features #[wasm_bindgen_test] pub fn test_biguint_marshalling() { let v = 31415usize; assert_eq!( jsvalue_to_biguint(biguint_to_jsvalue(BigUint::from(v))).unwrap(), BigUint::from(v) ); } #[wasm_bindgen_test] pub fn test_to_weierstrass_and_back() { let curve = X25519PrimeField::get_curve_params(); let x_weirstrass = curve.g_x; let y_weirstrass = curve.g_y; let (x_twisted, y_twisted) = X25519PrimeField::to_twistededwards(x_weirstrass.clone(), y_weirstrass.clone()); let (x_weirstrass_back, y_weirstrass_back) = X25519PrimeField::to_weirstrass(x_twisted, y_twisted); assert_eq!(x_weirstrass, x_weirstrass_back); assert_eq!(y_weirstrass, y_weirstrass_back); } #[wasm_bindgen_test] pub fn test_to_twistededwards_and_back_from_js() { let curve = X25519PrimeField::get_curve_params(); let x_weirstrass = curve.g_x; let y_weirstrass = curve.g_y; let x_weirstrass_js = biguint_to_jsvalue(element_to_biguint::(&x_weirstrass)); let y_weirstrass_js = biguint_to_jsvalue(element_to_biguint::(&y_weirstrass)); let result_js = to_twistededwards(x_weirstrass_js, y_weirstrass_js).unwrap(); assert_eq!(result_js.len(), 2); let x_twisted_js = result_js.get(0).unwrap(); let y_twisted_js = result_js.get(1).unwrap(); let x_twisted_biguint = jsvalue_to_biguint(x_twisted_js.clone()).unwrap(); let y_twisted_biguint = jsvalue_to_biguint(y_twisted_js.clone()).unwrap(); let x_twisted = element_from_biguint::(&x_twisted_biguint); let y_twisted = element_from_biguint::(&y_twisted_biguint); let (x_weirstrass_back, y_weirstrass_back) = X25519PrimeField::to_weirstrass(x_twisted, y_twisted); assert_eq!(x_weirstrass, x_weirstrass_back); assert_eq!(y_weirstrass, y_weirstrass_back); } #[wasm_bindgen_test] pub fn test_get_groth16_calldata() { let proof_js = mock_proof_js(); assert!(proof_js.is_object(), "Failed to parse proof"); let vk_js = mock_vk_js(); assert!(vk_js.is_object(), "Failed to parse Verifying Key"); let curve_id_js = JsValue::from_f64(0.0); let result = get_groth16_calldata(proof_js, vk_js, curve_id_js); assert!( result.is_ok(), "Expected successful result, got {:?}", result ); let result_values = result.unwrap(); // Add specific assertions here to validate expected output structure or content assert!( !result_values.is_empty(), "Expected non-empty result values" ); } // Mock helper to create G1 and G2 points as JsValues fn mock_g1_point(x: &str, y: &str) -> JsValue { let obj = Object::new(); js_sys::Reflect::set(&obj, &JsValue::from_str("x"), &JsValue::from_str(x)).unwrap(); js_sys::Reflect::set(&obj, &JsValue::from_str("y"), &JsValue::from_str(y)).unwrap(); obj.into() } fn mock_g2_point(x0: &str, x1: &str, y0: &str, y1: &str) -> JsValue { let obj = Object::new(); let x_tuple = Array::of2(&JsValue::from_str(x0), &JsValue::from_str(x1)); let y_tuple = Array::of2(&JsValue::from_str(y0), &JsValue::from_str(y1)); js_sys::Reflect::set(&obj, &JsValue::from_str("x"), &x_tuple).unwrap(); js_sys::Reflect::set(&obj, &JsValue::from_str("y"), &y_tuple).unwrap(); obj.into() } fn mock_proof_js() -> JsValue { let obj = Object::new(); js_sys::Reflect::set( &obj, &JsValue::from_str("a"), &mock_g1_point( "0x2abaae3dd6e4c662f5e071bca525a26d21e2400d01d02c87bce2e8363285990a", "0x24211ff0aa742a6dd1651aadce6f72757beb89de2cff83a6162de7c15674c2", ), ) .unwrap(); js_sys::Reflect::set( &obj, &JsValue::from_str("b"), &mock_g2_point( "0x2335f1564c154d7a2ec5d11faf6d991a205bef2858f1687976d0a46502f5224a", "0x223af0bb0912d8ebc535ed489d06cd01fcf4a8ab4596cc28164edf9041d97080", "0x182e8fd86a44983de1d1d9dc4f12f134535b75d39f7aeb21adbf57e1a32ee603", "0xecb11668a0dd5d5031b0837e62ba14222b45718dc101c1278f44a9ed823c16b", ), ) .unwrap(); js_sys::Reflect::set( &obj, &JsValue::from_str("c"), &mock_g1_point( "0x290243624a4c11868e7cb0c0f7cfd690dac08e4205d19795b0a8f686dddcdfd6", "0x15de00cc8af159fbdbdc802592e83e1ac61a8026b97e8889b8c5def59ec50b16", ), ) .unwrap(); let public_inputs = Array::new(); public_inputs.push(&JsValue::from_str( "0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474", )); js_sys::Reflect::set(&obj, &JsValue::from_str("publicInputs"), &public_inputs).unwrap(); obj.into() } fn mock_vk_js() -> JsValue { let obj = Object::new(); js_sys::Reflect::set( &obj, &JsValue::from_str("alpha"), &mock_g1_point( "0xef3cb41414ad20b4fc5891f6b41a263d9f0c0509ee5ab16f866ff6a33fb9e73", "0x1b30646c7d96cf7830a42b1f2f7c0527c38601f1030674b0f14cf7c67de5027b", ), ) .unwrap(); js_sys::Reflect::set( &obj, &JsValue::from_str("beta"), &mock_g2_point( "0x21f7077b68f4faa9dcbfdc868e9a0b5c76eb0d62b919772a83b34a8bc1108489", "0x8693a2418c12721dddb0d4f9f3811645c372de7400061b6c6cebc4b3b799bb2", "0x3062e0c71d392fb15f33a8d7f87bf689709cb28f87d554e29dc92d92d1b0ce46", "0x4976fda5a1cd2a69e5b4fd77116cf638be2063a3359e40d8f3e8ec0c90ffd90", ), ) .unwrap(); js_sys::Reflect::set( &obj, &JsValue::from_str("gamma"), &mock_g2_point( "0x3541dacedd860ef884359c76cc9c6b81d289d3389e732f5f87195d15a4ce637", "0x2eb7d1fa8416da97272d9cc4aa2e71146c83c13be313e222b376d9a9da02f080", "0x8dce093ad7f7fe20efcb8bbb160b0f2ecb7cd98a7d48b949e86c8b00eef73f9", "0x29a4b793edc639746eb4af5910b954a713c49174d917839a146ea15cd7493f1d", ), ) .unwrap(); js_sys::Reflect::set( &obj, &JsValue::from_str("delta"), &mock_g2_point( "0x34fc9ba8eba1e49185580c9ee198f6cac8bc78463d786683ef471af4434acdc", "0x17f115a16975c6f261912be284ecae3a3f0899bb161153d19ebc7f594246b9b0", "0x17fd1ad43bbc8ef931c92abab72ef0ed83a3c195b4dbc7294e1eacf59b3e2054", "0x1bd7d75bf918b6766ff9481052ddb780a4cc43da055b6e98c187b34ca3e7cd1b", ), ) .unwrap(); let ic_array = Array::new(); ic_array.push(&mock_g1_point( "0x124e30bf4dff3ae9c9da665a8bebfd01ce6489a462587fa0f6c879156e7390bc", "0x1fdc3a96cea49b085e101dd2383fdc600dcb4a3450c0471724e1b022791c7532", )); ic_array.push(&mock_g1_point( "0x164668f89d9d6c6126a8465790ba44ddb5716750edaa0ed100691cceb974c6a1", "0x1d9c7309625ec7cf153290e7b5c8497412386c61f3d9d0426a702f368be936da", )); js_sys::Reflect::set(&obj, &JsValue::from_str("ic"), &ic_array).unwrap(); obj.into() } #[wasm_bindgen_test] fn test_poseidon_hash() { // Test with valid inputs let x_js = JsValue::from_str("1"); let y_js = JsValue::from_str("2"); let result = poseidon_hash(x_js, y_js); let expected_js = biguint_to_jsvalue( BigUint::from_str_radix( "115CC0F5E7D690413DF64C6B9662E9CF2A3617F2743245519E19607A4417189A", 16, ) .unwrap(), ); assert_eq!(result.unwrap(), expected_js); } } ================================================ FILE: tools/make/bytecode_check.sh ================================================ #!/bin/bash # Store the original working directory SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" PROJECT_ROOT="$(cd "$SCRIPT_DIR/../.." && pwd)" cd "$PROJECT_ROOT/src/contracts" echo "----------------------------------------" get_target_dir() { local contract_folder_path=$1 local metadata local target_dir # Get absolute path of the contract folder local abs_contract_path="$PROJECT_ROOT/src/contracts/$contract_folder_path" # Change to the contract directory and run scarb metadata metadata=$(cd "$abs_contract_path" && scarb metadata --format-version 1 2>/dev/null) if [[ $? -ne 0 ]] || [[ -z "$metadata" ]]; then return 1 fi # Extract the target_dir from the JSON output target_dir=$(echo "$metadata" | jq -r '.target_dir' 2>/dev/null) if [[ -z "$target_dir" ]] || [[ "$target_dir" == "null" ]]; then return 1 fi # The target_dir from metadata is usually an absolute path to the workspace target # We need to append "/dev" to get the dev build directory if [[ "$target_dir" == */ ]]; then echo "${target_dir}dev" else echo "${target_dir}/dev" fi } # Function to build and check bytecode length check_bytecode_length() { local contract_dir=$1 local target_dir local abs_contract_path="$PROJECT_ROOT/src/contracts/$contract_dir" target_dir=$(get_target_dir "$contract_dir") if [[ $? -ne 0 ]] || [[ -z "$target_dir" ]]; then echo "Error: Could not determine target directory for $contract_dir" echo "----------------------------------------" return 1 fi # echo "target_dir: $target_dir" cd "$abs_contract_path" scarb build # Find the compiled contract class JSON file # Find the files that start with the base name of the contract directory and end with "compiled_contract_class.json", with anything in between # ex : target/dev/groth16_example_bls12_381_Groth16VerifierBLS12_381.compiled_contract_class.json compiled_file=$(find "$target_dir" -type f -name "$(basename "$contract_dir")*.compiled_contract_class.json" -print -quit 2>/dev/null) if [[ -f "$compiled_file" ]]; then bytecode_length=$(jq '.bytecode | length' "$compiled_file" 2>/dev/null) if [[ -n "$bytecode_length" ]] && [[ "$bytecode_length" != "null" ]]; then # Color the output: use green for the bytecode length line echo -e "\e[32mBytecode length [$contract_dir] = $bytecode_length\e[0m" else echo "Error: Could not read bytecode length from $compiled_file" fi echo "----------------------------------------" else echo "Compiled contract class JSON not found in $contract_dir" echo "Searched in: $target_dir" echo "Pattern: $(basename "$contract_dir")*.compiled_contract_class.json" echo "----------------------------------------" fi } # List of contract directories contracts=( "autogenerated/groth16_example_bn254" "autogenerated/groth16_example_bls12_381" "autogenerated/noir_ultra_keccak_zk_honk_example" "universal_ecip" "drand_quicknet" "autogenerated/risc0_verifier_bn254" ) # Run sequentially - this is reliable and fast enough for contract in "${contracts[@]}"; do check_bytecode_length "$contract" done ================================================ FILE: tools/make/bytecode_check_max_log_n.sh ================================================ #!/bin/bash echo "Cleaning up max log n contracts" rm -rf src/contracts/autogenerated/ultra_keccak_zk_honk_max_log_n echo "Generating max log n contracts" python hydra/garaga/starknet/honk_contract_generator/generator_honk.py --max-log-n cd src/contracts echo "----------------------------------------" echo "Checking bytecode length" # Maximum allowed bytecode length MAX_BYTECODE_LENGTH=81290 # Adjust this value as needed # Function to get bytecode length get_bytecode_length() { local contract_dir=$1 local bytecode_length=0 cd "$contract_dir" || return 1 # Redirect scarb build output to /dev/null to avoid mixing with our output scarb build > /dev/null 2>&1 # Find the compiled contract class JSON file compiled_file=$(find ./target/dev -name '*.compiled_contract_class.json' -print -quit) if [[ -f "$compiled_file" ]]; then bytecode_length=$(jq '.bytecode | length' "$compiled_file") else echo "Error: Compiled contract class JSON not found in $contract_dir" >&2 cd ../ return 1 fi cd ../ echo "$bytecode_length" return 0 } # Function to print bytecode length print_bytecode_length() { local contract_dir=$1 local length=$2 echo -e "\e[32mBytecode length [$contract_dir] = $length (max: $MAX_BYTECODE_LENGTH)\e[0m" echo "----------------------------------------" } # List of contract directories contracts=( "autogenerated/ultra_keccak_zk_honk_max_log_n" ) # Check each contract results=() for contract in "${contracts[@]}"; do length=$(get_bytecode_length "$contract") if [ $? -eq 0 ]; then print_bytecode_length "$contract" "$length" results+=("$length") else echo "Error checking bytecode length for $contract" >&2 exit 1 fi done # Check if all bytecode lengths are below the limit all_below_limit=true for length in "${results[@]}"; do if [ "$length" -gt "$MAX_BYTECODE_LENGTH" ]; then all_below_limit=false break fi done rm -rf autogenerated/ultra_keccak_zk_honk_max_log_n # Return true/false based on the check if [ "$all_below_limit" = true ]; then echo "true" exit 0 else echo "false" exit 1 fi ================================================ FILE: tools/make/check_sierra_size.py ================================================ import json data = json.load( open("src/cairo/target/dev/garaga_contracts_Garaga.contract_class.json") ) print(len(data["sierra_program"])) ================================================ FILE: tools/make/ci_cairo.sh ================================================ #!/bin/bash source $(dirname "$0")/common.sh run_ci_workflow ".github/workflows/cairo.yml" ================================================ FILE: tools/make/ci_e2e.sh ================================================ #!/bin/bash source $(dirname "$0")/common.sh run_ci_workflow ".github/workflows/e2e.yml" ================================================ FILE: tools/make/ci_hydra.sh ================================================ #!/bin/bash source $(dirname "$0")/common.sh run_ci_workflow ".github/workflows/hydra.yml" ================================================ FILE: tools/make/ci_wasm.sh ================================================ #!/bin/bash source $(dirname "$0")/common.sh run_ci_workflow ".github/workflows/wasm.yml" ================================================ FILE: tools/make/common.sh ================================================ #!/bin/bash # Function to check for 'act' or 'gh act' and execute the appropriate command run_ci_workflow() { local workflow_file=$1 if command -v act &> /dev/null then act -W $workflow_file --secret-file .secrets elif command -v gh &> /dev/null && gh act --version &> /dev/null then gh act -W $workflow_file --secret-file .secrets else echo "Error: Neither 'act' nor 'gh act' command found. Please install one of them to proceed." exit 1 fi } ================================================ FILE: tools/make/constants.json ================================================ { "risc0": { "control_root": "0xCE52BF56033842021AF3CF6DB8A50D1B7535C125A34F1A22C6FDCF002C5A1529", "bn254_control_id": "0x04446E66D300EB7FB45C9726BB53C793DDA407A62E9601618BB43C5C14657AC0", "system_state_zero_digest": "0xA3ACC27117418996340B84E5A90F3EF4C49D22C79E44AAD822EC9C313E1EB8E2", "tag_digest": "0xcb1fefcd1f2d9a64975cbbbf6e161e2914434b0cbb9960b84df5d717e86b48af", "output_tag": "0x77eafeb366a78b47747de0d7bb176284085ff5564887009a5be63da32d3559d4" }, "sp1": { "verifier_version": "v5.0.0", "verifier_hash": "0xa4594c59bbc142f3b81c3ecb7f50a7c34bc9af7c4c444b5d48b795427e285913" }, "release_info": { "garaga_version": "1.1.0", "risc0_release": "v2.2.2", "cairo_version": "2.16.1", "starknet_foundry_version": "0.57.0" }, "noir": { "bb_version": "3.0.0-nightly.20251104", "bbup_version": "3.0.0-nightly.20251104", "nargo_version": "1.0.0-beta.16" } } ================================================ FILE: tools/make/generate_constants.py ================================================ #!/usr/bin/env python3 """ Generate language-specific constants from constants.json and sync version numbers across files. """ import json import logging import os import re import subprocess import sys from dataclasses import dataclass from pathlib import Path from typing import Any, Dict, Optional, Protocol from garaga.starknet.groth16_contract_generator.parsing_utils import Groth16VerifyingKey class FormatterProtocol(Protocol): """Protocol for code formatters.""" def format_file(self, file_path: str, cwd: Optional[str] = None) -> bool: """Format a file. Returns True if successful, False otherwise.""" ... class SubprocessFormatter: """Formatter that uses external subprocess commands.""" def __init__(self, cmd: list[str], name: str): self.cmd = cmd self.name = name def format_file(self, file_path: str, cwd: Optional[str] = None) -> bool: """Format a file using subprocess command.""" print(f"Formatting {file_path} with {self.name}") try: cmd = self.cmd + [file_path] subprocess.run(cmd, check=True, capture_output=True, text=True, cwd=cwd) logger.info(f"Successfully formatted with {self.name}") return True except subprocess.CalledProcessError as e: logger.warning(f"{self.name} formatting failed: {e.stderr}") return False except FileNotFoundError: logger.warning(f"{self.name} not found - skipping formatting") return False except Exception as e: logger.warning(f"Unexpected error running {self.name}: {e}") return False from rich.logging import RichHandler # Configure logging with rich for color-based level printing logging.basicConfig( level=logging.INFO, format="%(asctime)s - %(name)s - %(levelname)s - %(message)s", handlers=[ RichHandler(), ], ) logger = logging.getLogger(__name__) class ConstantsError(Exception): """Base exception for constants generation errors.""" class VKError(ConstantsError): """Raised when verification key processing fails.""" @dataclass(frozen=True) class UpdateConfig: """Configuration for version update operations.""" name: str pattern: str replacement: str description: str = "" version_key: str = ( "garaga_version" # Default to garaga_version for backward compatibility ) def apply_update(self, content: str, version: str) -> tuple[str, bool]: """Apply the update to content and return (new_content, changed).""" replacement = self.replacement.replace("{version}", version) new_content = re.sub(self.pattern, replacement, content) return new_content, content != new_content @dataclass(frozen=True) class VKConfig: """Configuration for verification key updates.""" name: str json_filename: str function_name: str def get_json_path(self, project_root: Path) -> Path: return ( project_root / "hydra" / "garaga" / "starknet" / "groth16_contract_generator" / "examples" / self.json_filename ) def get_function_pattern(self) -> str: """Generate the regex pattern for this VK function.""" return ( f"(pub fn {self.function_name}\\(\\) -> Groth16VerificationKey \\{{\\s*let vk_hex = \\[)" "([\\s\\S]*?)" "(\\];\\s*Groth16VerificationKey::from\\([\\s\\S]*?\\}\\s*\\})" ) # VK Configurations - simplified with pattern generation SP1_VK_CONFIG = VKConfig( name="SP1", json_filename="vk_sp1.json", function_name="get_sp1_vk", ) RISC0_VK_CONFIG = VKConfig( name="RISC0", json_filename="vk_risc0.json", function_name="get_risc0_vk", ) @dataclass(frozen=True) class PathConfig: """Configuration for all file paths used in the script.""" project_root: Path @property def python_output(self) -> Path: return self.project_root / "hydra" / "garaga" / "starknet" / "constants.py" @property def rust_output(self) -> Path: return self.project_root / "tools" / "garaga_rs" / "src" / "constants.rs" @property def typescript_output(self) -> Path: return ( self.project_root / "tools" / "npm" / "garaga_ts" / "src" / "constants.ts" ) @property def readme_path(self) -> Path: return self.project_root / "docs" / "PYPI_README.md" @property def pyproject_path(self) -> Path: return self.project_root / "pyproject.toml" @property def garaga_rs_cargo_path(self) -> Path: return self.project_root / "tools" / "garaga_rs" / "Cargo.toml" @property def package_json_path(self) -> Path: return self.project_root / "tools" / "npm" / "garaga_ts" / "package.json" @property def npm_readme_path(self) -> Path: return self.project_root / "tools" / "npm" / "garaga_ts" / "README.md" @property def noir_smart_contract_docs_path(self) -> Path: return ( self.project_root / "docs" / "gitbook" / "smart-contract-generators" / "noir.md" ) @property def groth16_rust_file(self) -> Path: return ( self.project_root / "tools" / "garaga_rs" / "src" / "calldata" / "full_proof_with_hints" / "groth16.rs" ) # File path to update config mappings VERSION_UPDATES = [ ( "PYPI README", "readme_path", UpdateConfig( name="PYPI README", pattern=r"(pip\s+install\s+garaga==)[\d]+\.[\d]+\.[\d]+(?:[\w\-\.]*)?", replacement=r"\g<1>{version}", description="pip install commands", ), ), ( "pyproject.toml", "pyproject_path", UpdateConfig( name="pyproject.toml", pattern=r'(version\s*=\s*["\'])[\d]+\.[\d]+\.[\d]+(?:[\w\-\.]*)?(["\'])', replacement=r"\g<1>{version}\g<2>", description="Python package version", ), ), ( "Cargo.toml", "garaga_rs_cargo_path", UpdateConfig( name="Cargo.toml", pattern=r'(\[package\].*?^version\s*=\s*["\'])[\d]+\.[\d]+\.[\d]+(?:[\w\-\.]*)?(["\'])', replacement=r"\g<1>{version}\g<2>", description="Rust package version", ), ), ( "package.json", "package_json_path", UpdateConfig( name="package.json", pattern=r'("version"\s*:\s*["\'])[\d]+\.[\d]+\.[\d]+(?:[\w\-\.]*)?(["\'])', replacement=r"\g<1>{version}\g<2>", description="NPM package version", ), ), ( "npm README", "npm_readme_path", UpdateConfig( name="npm README", pattern=r"(📋 \*\*For complete API documentation.*?)v[\d]+\.[\d]+\.[\d]+(?:[\w\-\.]*)?(/tools/npm/garaga_ts/src/node/api\.ts)", replacement=r"\g<1>v{version}\g<2>", description="API documentation links", ), ), ( "Noir version in smart contract docs", "noir_smart_contract_docs_path", UpdateConfig( name="Noir version in smart contract docs", pattern=r"(\* Noir\s+)[\d]+\.[\d]+\.[\d]+[-\w\.]*(\s+\(install with `noirup --version\s+)[\d]+\.[\d]+\.[\d]+[-\w\.]*(`\s+or `npm i @noir-lang/noir_js@)[\d]+\.[\d]+\.[\d]+[-\w\.]*(`\s*\))", replacement=r"\g<1>{version}\g<2>{version}\g<3>{version}\g<4>", description="Noir version in smart contract generator documentation", version_key="nargo_version", ), ), ( "BB version in smart contract docs", "noir_smart_contract_docs_path", UpdateConfig( name="BB version in smart contract docs", pattern=r"(\* Barretenberg\s+)[\d]+\.[\d]+\.[\d]+[-\w\.]*(\s+\(install with `bbup --version\s+)[\d]+\.[\d]+\.[\d]+[-\w\.]*(`\s+or `npm i @aztec/bb\.js@)[\d]+\.[\d]+\.[\d]+[-\w\.]*(`\s+\))", replacement=r"\g<1>{version}\g<2>{version}\g<3>{version}\g<4>", description="Barretenberg version in smart contract generator documentation", version_key="bb_version", ), ), ] VK_UPDATES = [ ("SP1 VK in Rust", SP1_VK_CONFIG), ("RISC0 VK in Rust", RISC0_VK_CONFIG), ] def load_constants() -> Dict[str, Any]: """Load constants from the centralized JSON file.""" constants_file = Path(__file__).parent / "constants.json" try: if not constants_file.exists(): raise ConstantsError(f"Constants file not found: {constants_file}") with open(constants_file, "r") as f: constants = json.load(f) # Basic validation required_keys = ["risc0", "sp1", "release_info", "noir"] missing_keys = [key for key in required_keys if key not in constants] if missing_keys: raise ConstantsError( f"Missing required keys in constants.json: {missing_keys}" ) logger.info(f"Successfully loaded constants from {constants_file}") return constants except (json.JSONDecodeError, IOError) as e: raise ConstantsError(f"Failed to load constants from {constants_file}: {e}") except Exception as e: raise ConstantsError(f"Unexpected error loading constants: {e}") @dataclass(frozen=True) class LanguageConfig: """Configuration for language-specific code generation.""" name: str comment_prefix: str constant_template: str formatter: FormatterProtocol # Language-specific configurations COMMON_FILE_HEADER = ( "Auto-generated constants file from constants.json. Do not edit manually." ) LANGUAGE_CONFIGS = [ LanguageConfig( name="Python", comment_prefix="#", constant_template="{name} = {value}", formatter=SubprocessFormatter(["black"], "black"), ), LanguageConfig( name="Rust", comment_prefix="//", constant_template="pub const {name}: &str = {value};", formatter=SubprocessFormatter(["cargo", "fmt", "--"], "cargo fmt"), ), LanguageConfig( name="TypeScript", comment_prefix="//", constant_template="export const {name}: string = {value};", formatter=SubprocessFormatter( ["npx", "prettier", "--write"], "prettier (ensure it's installed)" ), ), ] def hex_to_uint8array_literal(hex_str: str) -> str: """Convert a hex string like '0xABCD...' to 'new Uint8Array([0xAB, 0xCD, ...])'.""" raw = hex_str.removeprefix("0x").removeprefix("0X") byte_values = [f"0x{raw[i:i+2].upper()}" for i in range(0, len(raw), 2)] # Format in rows of 16 for readability rows = [] for i in range(0, len(byte_values), 16): rows.append(" " + ", ".join(byte_values[i : i + 16])) return "new Uint8Array([\n" + ",\n".join(rows) + "\n])" def safe_read_file(file_path: str) -> str: """Safely read a file with proper error handling.""" try: with open(file_path, "r", encoding="utf-8") as f: return f.read() except IOError as e: raise ConstantsError(f"Failed to read {file_path}: {e}") def safe_write_file(file_path: str, content: str) -> None: """Safely write to a file with proper error handling.""" try: os.makedirs(os.path.dirname(file_path), exist_ok=True) with open(file_path, "w", encoding="utf-8") as f: f.write(content) except IOError as e: raise ConstantsError(f"Failed to write {file_path}: {e}") def generate_unified_constants( constants: Dict[str, Any], config: LanguageConfig ) -> str: """Generate constants file content using unified template.""" # Build content sections lines = [] # File header if config.name == "Python": lines.extend(['"""', COMMON_FILE_HEADER, '"""', ""]) elif config.name == "TypeScript": lines.extend( ["/**", " * " + COMMON_FILE_HEADER.replace("\n", "\n * "), " */", ""] ) else: # Rust lines.extend([f"//! {line}" for line in COMMON_FILE_HEADER.split("\n")] + [""]) # Add Rust-specific imports if config.name == "Rust": lines.extend(["use num_bigint::BigUint;", "use num_traits::Num;", ""]) # RISC0 section risc0_info = constants["risc0"] release_version = constants["release_info"]["risc0_release"] lines.extend( [ f"{config.comment_prefix} RISC0 Constants", f"{config.comment_prefix} https://github.com/risc0/risc0-ethereum/blob/{release_version}/contracts/src/groth16/ControlID.sol", f"{config.comment_prefix} release {release_version}", ] ) if config.name == "Rust": lines.extend( [ "pub fn get_risc0_constants() -> (BigUint, BigUint) {", f' let risc0_control_root = BigUint::from_str_radix("{risc0_info["control_root"][2:]}", 16).unwrap();', f' let risc0_bn254_control_id = BigUint::from_str_radix("{risc0_info["bn254_control_id"][2:]}", 16).unwrap();', " (risc0_control_root, risc0_bn254_control_id)", "}", ] ) elif config.name == "TypeScript": lines.extend( [ f'export const RISC0_CONTROL_ROOT = BigInt("{risc0_info["control_root"]}");', f'export const RISC0_BN254_CONTROL_ID = BigInt("{risc0_info["bn254_control_id"]}");', ] ) else: # Python lines.extend( [ f'RISC0_CONTROL_ROOT = {risc0_info["control_root"]}', f'RISC0_BN254_CONTROL_ID = {risc0_info["bn254_control_id"]}', ] ) lines.append("") # SP1 section sp1_info = constants["sp1"] lines.extend( [ f"{config.comment_prefix} SP1 Constants", f"{config.comment_prefix} https://github.com/succinctlabs/sp1-contracts/blob/main/contracts/src/{sp1_info['verifier_version']}/SP1VerifierGroth16.sol", ] ) if config.name == "Python": lines.extend( [ f'SP1_VERIFIER_VERSION = "{sp1_info["verifier_version"]}"', f'SP1_VERIFIER_HASH = bytes.fromhex("{sp1_info["verifier_hash"][2:]}")', ] ) elif config.name == "TypeScript": lines.extend( [ f'export const SP1_VERIFIER_VERSION = "{sp1_info["verifier_version"]}";', f'export const SP1_VERIFIER_HASH = "{sp1_info["verifier_hash"]}";', ] ) else: # Rust lines.extend( [ f'pub const SP1_VERIFIER_VERSION: &str = "{sp1_info["verifier_version"]}";', f'pub const SP1_VERIFIER_HASH: &str = "{sp1_info["verifier_hash"]}";', ] ) lines.append("") # Additional constants lines.extend( [ f"{config.comment_prefix} Additional RISC0 constants for internal use", ] ) if config.name == "Python": lines.extend( [ f'RISC0_SYSTEM_STATE_ZERO_DIGEST = "{risc0_info["system_state_zero_digest"]}"', f'RISC0_TAG_DIGEST = "{risc0_info["tag_digest"]}"', f'RISC0_OUTPUT_TAG = "{risc0_info["output_tag"]}"', f'RISC0_RELEASE_VERSION = "{constants["release_info"]["risc0_release"]}"', ] ) elif config.name == "TypeScript": lines.extend( [ f'export const RISC0_SYSTEM_STATE_ZERO_DIGEST = {hex_to_uint8array_literal(risc0_info["system_state_zero_digest"])};', f'export const RISC0_TAG_DIGEST = "{risc0_info["tag_digest"]}";', f'export const RISC0_OUTPUT_TAG = "{risc0_info["output_tag"]}";', ] ) else: # Rust lines.extend( [ f'pub const RISC0_SYSTEM_STATE_ZERO_DIGEST: &str = "{risc0_info["system_state_zero_digest"]}";', f'pub const RISC0_TAG_DIGEST: &str = "{risc0_info["tag_digest"]}";', f'pub const RISC0_OUTPUT_TAG: &str = "{risc0_info["output_tag"]}";', ] ) if config.name == "Python": release_info = constants["release_info"] noir_info = constants["noir"] lines.extend( [ "", f"{config.comment_prefix} Version info", f'CAIRO_VERSION = "{release_info["cairo_version"]}"', f'STARKNET_FOUNDRY_VERSION = "{release_info["starknet_foundry_version"]}"', f'BB_VERSION = "{noir_info["bb_version"]}"', f'BBUP_VERSION = "{noir_info["bbup_version"]}"', f'NARGO_VERSION = "{noir_info["nargo_version"]}"', ] ) return "\n".join(lines) + "\n" def generate_language_constants( constants: Dict[str, Any], config: LanguageConfig, output_path: str ) -> None: """Generate constants file for a specific language.""" try: content = generate_unified_constants(constants, config) safe_write_file(output_path, content) # Format if formatter available if config.formatter: cwd = os.path.dirname(output_path) if config.name == "Rust" else None config.formatter.format_file(output_path, cwd) logger.info(f"Generated {config.name} constants: {output_path}") except Exception as e: raise ConstantsError(f"Failed to generate {config.name} constants: {e}") def generate_constants_by_language( constants: Dict[str, Any], language: str, output_path: str ): """Generate constants file for a specific language by name.""" # Find language config config = next((cfg for cfg in LANGUAGE_CONFIGS if cfg.name == language), None) if not config: raise ConstantsError(f"Unknown language: {language}") generate_language_constants(constants, config, output_path) def update_file_version(file_path: str, config: UpdateConfig, version: str) -> bool: """Generic file version update function.""" try: if not Path(file_path).exists(): logger.warning(f"{config.name} file not found: {file_path}") return False content = safe_read_file(file_path) new_content, changed = config.apply_update(content, version) if not changed: logger.info(f"No {config.name} update needed (already {version})") return True safe_write_file(file_path, new_content) logger.info(f"Updated {config.name} to version {version}") return True except Exception as e: raise ConstantsError(f"Failed to update {config.name}: {e}") def update_vk_in_rust( project_root: Path, groth16_rust_file: str, config: VKConfig ) -> bool: """Update verification key function in Rust with values from JSON.""" try: # Load and parse VK vk_path = config.get_json_path(project_root) if not vk_path.exists(): raise ConstantsError(f"{config.name} VK file not found at {vk_path}") try: vk = Groth16VerifyingKey.from_json(vk_path) logger.info(f"Successfully loaded {config.name} VK from {vk_path}") except Exception as e: raise VKError(f"Failed to parse {config.name} VK: {e}") # Process VK data hex_values = [hex(value)[2:] for value in vk.flatten()] # Format hex array hex_lines = [] for i in range(0, len(hex_values), 4): line_values = hex_values[i : i + 4] formatted_line = " " + ", ".join(f'"{val}"' for val in line_values) hex_lines.append(formatted_line) new_hex_array = ",\n".join(hex_lines) + "," # Update file content = safe_read_file(groth16_rust_file) match = re.search(config.get_function_pattern(), content) if not match: raise VKError(f"Could not find {config.name} VK function pattern") new_content = re.sub( config.get_function_pattern(), f"\\g<1>\n{new_hex_array}\n \\g<3>", content, ) if content == new_content: logger.info(f"No {config.name} VK update needed - already current") return True safe_write_file(groth16_rust_file, new_content) logger.info( f"Updated {config.name} verification key ({len(hex_values)} values)" ) # Format with cargo rust_config = next( (cfg for cfg in LANGUAGE_CONFIGS if cfg.name == "Rust"), None ) if rust_config: rust_config.formatter.format_file( groth16_rust_file, os.path.dirname(groth16_rust_file) ) return True except (VKError, ConstantsError): raise except Exception as e: raise VKError(f"Unexpected error updating {config.name} VK: {e}") finally: if str(project_root / "hydra") in sys.path: sys.path.remove(str(project_root / "hydra")) def report_results(all_results: list[tuple[str, bool]]) -> int: """Report operation results and return exit code.""" failed = [result for result in all_results if not result[1]] successful = [result for result in all_results if result[1]] logger.info( f"Operations completed: {len(successful)}/{len(all_results)} successful" ) if successful: logger.info("Successful operations:") for result in successful: logger.info(f" ✓ {result[0]}") if failed: logger.warning("Failed operations:") for result in failed: logger.warning(f" ✗ {result[0]}") logger.warning(f"{len(failed)} operations failed") return 1 else: logger.info("All constants files and version references updated successfully!") return 0 def generate_all_constants(constants: Dict[str, Any], paths: PathConfig) -> None: """Generate constants files for all languages.""" generate_constants_by_language(constants, "Python", str(paths.python_output)) generate_constants_by_language(constants, "Rust", str(paths.rust_output)) generate_constants_by_language( constants, "TypeScript", str(paths.typescript_output) ) logger.info("Successfully generated all constants files") def update_all_versions( constants: Dict[str, Any], paths: PathConfig ) -> list[tuple[str, bool]]: """Update version references across all files.""" results = [] for mapping in VERSION_UPDATES: try: file_path = str(getattr(paths, mapping[1])) config = mapping[2] # Get the appropriate version based on the version_key if config.version_key == "nargo_version": version = constants["noir"]["nargo_version"] elif config.version_key == "bb_version": version = constants["noir"]["bb_version"] else: version = constants["release_info"]["garaga_version"] success = update_file_version(file_path, config, version) results.append((mapping[0], success)) if success: logger.info(f"Successfully updated {mapping[0]}") else: logger.warning(f"No updates needed for {mapping[0]}") except Exception as e: logger.error(f"Failed to update {mapping[0]}: {e}") results.append((mapping[0], False)) return results def update_verification_keys(paths: PathConfig) -> list[tuple[str, bool]]: """Update verification keys in Rust code.""" results = [] for mapping in VK_UPDATES: try: success = update_vk_in_rust( paths.project_root, str(paths.groth16_rust_file), mapping[1], ) results.append((mapping[0], success)) if success: logger.info(f"Successfully updated {mapping[0]}") except (VKError, ConstantsError) as e: logger.error(f"Failed to update {mapping[0]}: {e}") results.append((mapping[0], False)) except Exception as e: logger.error(f"Unexpected error updating {mapping[0]}: {e}") results.append((mapping[0], False)) return results def main(): """Main function to generate all constants files and update version references.""" try: logger.info("Starting constants generation and version updates...") # Load and validate constants constants = load_constants() # Define output paths project_root = Path(__file__).parent.parent.parent paths = PathConfig(project_root) # Generate constants files generate_all_constants(constants, paths) # Update version references and verification keys logger.info("Updating version references...") version_results = update_all_versions(constants, paths) logger.info("Updating verification keys...") vk_results = update_verification_keys(paths) # Report results and return appropriate exit code all_results = version_results + vk_results return report_results(all_results) except ConstantsError as e: logger.error(f"Constants error: {e}") return 1 except Exception as e: logger.error(f"Unexpected error in main: {e}") return 1 if __name__ == "__main__": exit_code = main() sys.exit(exit_code) ================================================ FILE: tools/make/rewrite.sh ================================================ #!/bin/bash set -e clean_dirs() { rm -rf src/src/circuits/*.cairo rm -rf src/contracts/autogenerated/* } run_generators() { python hydra/garaga/starknet/honk_contract_generator/generator_honk.py python hydra/garaga/precompiled_circuits/all_circuits.py python hydra/garaga/starknet/groth16_contract_generator/generator.py python hydra/garaga/starknet/groth16_contract_generator/generator_risc0.py python hydra/garaga/starknet/groth16_contract_generator/generator_sp1.py } clean_dirs start_time=$(date +%s) if [ "$1" = "no-tests" ]; then run_generators else rm -rf src/src/tests/autogenerated/* run_generators python hydra/garaga/starknet/tests_and_calldata_generators/test_writer.py fi elapsed=$(($(date +%s) - start_time)) echo "Total time taken: ${elapsed} seconds" ================================================ FILE: tools/make/setup.sh ================================================ #!/bin/bash set -euo pipefail PYTHON_VERSION_TARGET="3.14" # Function to install GNU parallel install_parallel() { case "$OSTYPE" in linux-gnu*) # Linux if command -v apt-get >/dev/null; then # Debian/Ubuntu sudo apt-get install -y parallel elif command -v dnf >/dev/null; then # Fedora sudo dnf install -y parallel else echo "Unsupported Linux distribution for automatic parallel installation." exit 1 fi ;; darwin*) # macOS if command -v brew >/dev/null; then brew install parallel else echo "Homebrew is not installed. Please install Homebrew and try again." exit 1 fi ;; *) echo "Unsupported operating system for automatic parallel installation." exit 1 ;; esac } # Function to install GMP (required by fastecdsa) install_gmp() { case "$OSTYPE" in linux-gnu*) if command -v apt-get >/dev/null; then sudo apt-get install -y libgmp-dev elif command -v dnf >/dev/null; then sudo dnf install -y gmp-devel else echo "Unsupported Linux distribution for automatic GMP installation." echo "Please install GMP manually: https://pypi.org/project/fastecdsa/#installing" exit 1 fi ;; darwin*) if command -v brew >/dev/null; then brew install gmp else echo "Homebrew is not installed. Please install Homebrew and try again." exit 1 fi ;; *) echo "Unsupported operating system for automatic GMP installation." echo "Please install GMP manually: https://gmplib.org/" exit 1 ;; esac } # Function to install cmake (required by crypto-cpp-py) install_cmake() { case "$OSTYPE" in linux-gnu*) if command -v apt-get >/dev/null; then sudo apt-get install -y cmake elif command -v dnf >/dev/null; then sudo dnf install -y cmake else echo "Unsupported Linux distribution for automatic cmake installation." exit 1 fi ;; darwin*) if command -v brew >/dev/null; then brew install cmake else echo "Homebrew is not installed. Please install Homebrew and try again." exit 1 fi ;; *) echo "Unsupported operating system for automatic cmake installation." exit 1 ;; esac } # Ensure uv is available (installs if missing) ensure_uv() { if command -v uv >/dev/null 2>&1; then return 0 fi echo "Installing uv..." curl -LsSf https://astral.sh/uv/install.sh | sh export PATH="$HOME/.local/bin:$PATH" } # Find or install a suitable Python version (3.10-3.14) find_python() { # If PYTHON_VERSION env var is set, use that specific version if [ -n "${PYTHON_VERSION:-}" ]; then PYTHON_VERSION_TARGET="$PYTHON_VERSION" fi # Try to find it on PATH first for version in $PYTHON_VERSION_TARGET 3.14 3.13 3.12 3.11 3.10; do if command -v "python${version}" >/dev/null 2>&1; then echo "python${version}" return 0 fi done # Fall back to python3 if it's in the right version range if command -v python3 >/dev/null 2>&1; then local py_version py_version=$(python3 -c "import sys; print(f'{sys.version_info.major}.{sys.version_info.minor}')") case "$py_version" in 3.10|3.11|3.12|3.13|3.14) echo "python3" return 0 ;; esac fi # Not found — use uv to install it echo "Python ${PYTHON_VERSION_TARGET} not found. Installing via uv..." >&2 ensure_uv uv python install "$PYTHON_VERSION_TARGET" >&2 local uv_python uv_python=$(uv python find "$PYTHON_VERSION_TARGET" 2>/dev/null || true) if [ -n "$uv_python" ]; then echo "$uv_python" return 0 fi return 1 } # Check if existing venv is valid and matches expected Python version range venv_is_valid() { [ -f "venv/bin/python" ] || return 1 local py_version py_version=$(venv/bin/python -c "import sys; print(f'{sys.version_info.major}.{sys.version_info.minor}')" 2>/dev/null) || return 1 case "$py_version" in 3.10|3.11|3.12|3.13|3.14) return 0 ;; *) return 1 ;; esac } # Check if parallel is installed, if not, attempt to install it if ! command -v parallel >/dev/null; then echo "GNU parallel not found. Attempting to install..." install_parallel else echo "GNU parallel is already installed." fi # Check if GMP is installed (required by fastecdsa) gmp_found=false case "$OSTYPE" in linux-gnu*) # Check for the development headers (gmp.h), not just the runtime library if [ -f /usr/include/gmp.h ] \ || pkg-config --exists gmp 2>/dev/null; then gmp_found=true fi ;; darwin*) # Use formula-specific prefix (works even if formula is unlinked) if command -v brew >/dev/null 2>&1; then GMP_PREFIX=$(brew --prefix gmp 2>/dev/null || true) if [ -n "$GMP_PREFIX" ] && [ -f "${GMP_PREFIX}/include/gmp.h" ]; then gmp_found=true fi fi ;; esac if [ "$gmp_found" = false ]; then echo "GMP not found. Attempting to install (required by fastecdsa)..." install_gmp else echo "GMP is already installed." fi # Check if cmake is installed (required by crypto-cpp-py) if ! command -v cmake >/dev/null; then echo "cmake not found. Attempting to install (required by crypto-cpp-py)..." install_cmake else echo "cmake is already installed." fi ensure_uv if venv_is_valid; then echo "Existing venv is valid ($(venv/bin/python --version)). Updating dependencies..." else # Clean up broken/outdated venv if [ -d "venv" ]; then echo "Removing invalid venv..." rm -rf venv fi # Find a suitable Python version (installs via uv if needed) PYTHON_CMD=$(find_python || true) if [ -z "$PYTHON_CMD" ]; then echo "No suitable Python version found and uv install failed." echo "Please install Python 3.10 through 3.14 manually." exit 1 fi echo "Using Python: $PYTHON_CMD ($($PYTHON_CMD --version))" # Create virtual environment using uv (no venv module needed) if ! uv venv --python "$PYTHON_CMD" venv; then echo "Failed to create virtual environment" exit 1 fi echo 'export PYTHONPATH="$PWD/hydra:$PWD:${PYTHONPATH:-}"' >> venv/bin/activate echo 'export PYTHONPYCACHEPREFIX="$PWD/venv/build/__pycache__"' >> venv/bin/activate fi echo "PROJECT_ROOT=$PWD" > .env echo "PYTHONPATH=$PWD/hydra" >> .env # For vscode python path when running in integrated terminal. source venv/bin/activate # On macOS, ensure compiler can find Homebrew-installed GMP if [[ "$OSTYPE" == darwin* ]] && command -v brew >/dev/null; then GMP_PREFIX=$(brew --prefix gmp 2>/dev/null || true) if [ -n "$GMP_PREFIX" ] && [ -d "${GMP_PREFIX}/include" ]; then export CFLAGS="-I${GMP_PREFIX}/include ${CFLAGS:-}" export LDFLAGS="-L${GMP_PREFIX}/lib ${LDFLAGS:-}" fi fi # Allow crypto-cpp-py's bundled googletest to build with newer cmake (>= 4.x) export CMAKE_POLICY_VERSION_MINIMUM=3.5 # crypto-cpp-py hardcodes a -target flag that conflicts with cmake's auto-detected # -mmacosx-version-min on macOS; suppress the resulting -Werror to let it build. if [[ "$OSTYPE" == darwin* ]]; then export CXXFLAGS="-Wno-overriding-option ${CXXFLAGS:-}" fi uv pip compile pyproject.toml --extra dev --output-file tools/make/requirements.txt -q uv pip install -r tools/make/requirements.txt # Install the commit hooks (black, isort) pre-commit install echo "Compiling garaga_rs Rust extension..." # Create target directory with proper permissions in the correct location mkdir -p .cargo/garaga_rs/target chmod 755 .cargo/garaga_rs/target # Build the Rust extension with Python feature enabled maturin develop --release --features python echo "All done!" # Check Scarb version and print warning if it's not cd src/ # To use the .tool-versions file with asdf. scarb_version=$(scarb --version 2>/dev/null || true) if ! echo "$scarb_version" | grep -q "2.16.1"; then echo "Warning: Scarb is not installed or its version is not 2.16.1." echo "Got: ${scarb_version:-}" echo "Please install Scarb 2.16.1 before continuing. https://docs.swmansion.com/scarb/download.html" fi ================================================ FILE: tools/make/steps.sh ================================================ cd src/cairo scarb test -f test_BN254_mpcheck_3P_2F --print-resource-usage ================================================ FILE: tools/make/test_contracts.sh ================================================ #!/usr/bin/env bash # Script to run snforge test in all autogenerated contract folders # Usage: ./tools/make/test_contracts.sh set -e # Get the directory where this script is located SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" # Get the repository root (two levels up from script location) REPO_ROOT="$(cd "$SCRIPT_DIR/../.." && pwd)" # Path to autogenerated contracts AUTOGEN_DIR="$REPO_ROOT/src/contracts/autogenerated" # Check if the autogenerated directory exists if [ ! -d "$AUTOGEN_DIR" ]; then echo "Error: Autogenerated directory not found at $AUTOGEN_DIR" exit 1 fi echo "Running snforge test in all autogenerated contract folders..." echo "========================================================" echo "" # Track success/failure FAILED_TESTS=() PASSED_TESTS=() # Iterate through each subdirectory in autogenerated for dir in "$AUTOGEN_DIR"/*/ ; do if [ -d "$dir" ]; then folder_name=$(basename "$dir") echo "Testing: $folder_name" echo "----------------------------------------" # Change to the directory and run snforge test if (cd "$dir" && snforge test); then PASSED_TESTS+=("$folder_name") echo "✓ $folder_name: PASSED" else FAILED_TESTS+=("$folder_name") echo "✗ $folder_name: FAILED" fi echo "" fi done # Print summary echo "========================================================" echo "Test Summary" echo "========================================================" echo "Passed: ${#PASSED_TESTS[@]}" for test in "${PASSED_TESTS[@]}"; do echo " ✓ $test" done if [ ${#FAILED_TESTS[@]} -gt 0 ]; then echo "" echo "Failed: ${#FAILED_TESTS[@]}" for test in "${FAILED_TESTS[@]}"; do echo " ✗ $test" done exit 1 else echo "" echo "All tests passed!" exit 0 fi ================================================ FILE: tools/make/update_bench_in_readme.py ================================================ import re import subprocess def run_benchmarks(): try: # Run benchmarks.py and capture its output result = subprocess.run( ["python", "tests/benchmarks.py"], capture_output=True, text=True, check=True, ) return result.stdout except subprocess.CalledProcessError as e: print(f"Error running benchmarks: {e.stderr}") return None def update_readme(benchmarks_markdown): if benchmarks_markdown is None: print("Skipping README update due to benchmark error.") return # Read the current README.md content with open("README.md", "r", encoding="utf-8") as file: readme_contents = file.read() # Define a pattern to find the Benchmarks section # Adjust the pattern as necessary to match your README's structure pattern = r"(## Benchmarks\n)(.*?)(\n## )" replacement = r"\1" + benchmarks_markdown + r"\3" # Replace the Benchmarks section with the new benchmarks updated_readme = re.sub(pattern, replacement, readme_contents, flags=re.DOTALL) # Write the updated README back to disk with open("README.md", "w", encoding="utf-8") as file: file.write(updated_readme) if __name__ == "__main__": benchmarks_markdown = run_benchmarks() update_readme(benchmarks_markdown) print(f"README updated with benchmarks: {benchmarks_markdown}") ================================================ FILE: tools/make/update_risc0_class_hash.sh ================================================ #!/bin/bash set -e SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" PROJECT_ROOT="$(cd "$SCRIPT_DIR/../.." && pwd)" RISC0_VERIFIER_DIR="$PROJECT_ROOT/src/contracts/autogenerated/risc0_verifier_bn254" FIBONACCI_SEQUENCER_FILE="$PROJECT_ROOT/src/contracts/risc0_sample_app/fibonacci_sequencer/src/lib.cairo" echo "Computing class hash for Risc0Groth16VerifierBN254..." OUTPUT=$(cd "$RISC0_VERIFIER_DIR" && sncast utils class-hash --contract-name Risc0Groth16VerifierBN254) CLASS_HASH=$(echo "$OUTPUT" | grep "Class Hash:" | awk '{print $3}') if [ -z "$CLASS_HASH" ]; then echo "Error: Could not parse class hash from sncast output: $OUTPUT" exit 1 fi # Strip leading zeros for Cairo format (0x0708... -> 0x708...) CAIRO_CLASS_HASH=$(echo "$CLASS_HASH" | sed 's/^0x0*/0x/') echo "Class hash: $CAIRO_CLASS_HASH" # Portable sed -i (macOS requires '' suffix, Linux does not) sed -i.bak "s|^\([[:space:]]*\)0x[0-9a-fA-F]\{1,64\};|\1$CAIRO_CLASS_HASH;|" "$FIBONACCI_SEQUENCER_FILE" rm -f "${FIBONACCI_SEQUENCER_FILE}.bak" scarb fmt "$FIBONACCI_SEQUENCER_FILE" echo "Updated RISC_ZERO_VERIFIER_CLASS_HASH in fibonacci_sequencer." ================================================ FILE: tools/make/wasm-test-gen.sh ================================================ cd tools/npm/integration-test-suite rm -rf node_modules package-lock.json && npm cache clean --force && npm install garaga.tgz # Uses turbo to build all packages first, then run test-generate sequentially # (--concurrency 1 because web packages share port 8080) npm run test-generate ================================================ FILE: tools/make/wasm.sh ================================================ #!/bin/bash start_docker() { local os_type=$1 echo "Attempting to start Docker daemon..." case "$os_type" in "macos") echo "Please start Docker Desktop manually for macOS" echo "Cannot automatically start Docker Desktop due to security restrictions" exit 1 ;; "fedora") read -p "Docker daemon is not running. Would you like to start it? (y/N) " response if [[ "$response" =~ ^[Yy]$ ]]; then if command -v sudo >/dev/null 2>&1; then echo "Starting Docker daemon..." sudo systemctl start docker # Wait for Docker to be ready echo "Waiting for Docker to be ready..." sleep 3 else echo "Error: sudo is not available. Please start Docker manually:" echo "sudo systemctl start docker" exit 1 fi else echo "Please start Docker manually when ready" exit 1 fi ;; "debian") read -p "Docker daemon is not running. Would you like to start it? (y/N) " response if [[ "$response" =~ ^[Yy]$ ]]; then if command -v sudo >/dev/null 2>&1; then echo "Starting Docker daemon..." sudo systemctl start docker # Wait for Docker to be ready echo "Waiting for Docker to be ready..." sleep 3 else echo "Error: sudo is not available. Please start Docker manually:" echo "sudo systemctl start docker" exit 1 fi else echo "Please start Docker manually when ready" exit 1 fi ;; *) echo "Unsupported operating system. Please start Docker daemon manually" exit 1 ;; esac } check_docker() { if ! docker info >/dev/null 2>&1; then echo "Docker daemon is not running." # Detect OS and try to start Docker if [[ "$OSTYPE" == "darwin"* ]]; then start_docker "macos" elif [ -f /etc/fedora-release ]; then start_docker "fedora" elif [ -f /etc/debian_version ] || [ -f /etc/lsb-release ]; then start_docker "debian" else echo "Unsupported operating system. Please start Docker daemon manually" exit 1 fi # Double check if Docker started successfully if ! docker info >/dev/null 2>&1; then echo "Failed to start Docker daemon" exit 1 fi fi echo "Docker daemon is running" } # Check if Docker is running and start if needed check_docker cd tools/npm/garaga_ts docker compose up --build cd ../integration-test-suite GARAGA_VERSION=$(jq -r '.release_info.garaga_version' ../../make/constants.json) cp ../garaga_ts/garaga-$GARAGA_VERSION.tgz garaga.tgz npm install garaga.tgz ================================================ FILE: tools/noir/Makefile ================================================ # ============================================================================== # Solidity Verifier Debugging # ============================================================================== # Run the Solidity ZK Honk verifier with the test proof and log variables. # This is useful for comparing intermediate values with the Python implementation. # # Prerequisites: # 1. Install Foundry: curl -L https://foundry.paradigm.xyz | bash && foundryup # 2. Install forge-std: forge install foundry-rs/forge-std --no-commit # # Usage: # make sol-verify-debug # Run with full logging # make sol-verify-debug-detailed # Run with detailed proof parsing # # To add custom logging, edit tools/noir/hello/target/contract_ultra_keccak_zk.sol: # 1. Add: import "forge-std/console.sol"; # 2. Add: console.log("varName:", value); or console.log("Fr:", Fr.unwrap(frValue)); # 3. Run: make sol-verify-debug # # See tools/noir/hello/README.md for more details. # ============================================================================== sol-verify-debug: @echo "=== Running Solidity ZK Honk Verifier Test ===" @echo "See tools/noir/hello/README.md for how to add custom logging" @echo "" cd hello && forge test -vv --match-test testVerifyProof sol-verify-debug-verbose: @echo "=== Running Solidity ZK Honk Verifier Test (verbose) ===" cd hello && forge test -vvvv --match-test testVerifyProof sol-verify-debug-detailed: @echo "=== Running Detailed Proof Parsing Test ===" cd hello && forge test -vv --match-test testVerifyProofWithDetailedLogging sol-verify-setup: @echo "=== Setting up Foundry for Solidity testing ===" @if [ -d "hello/lib/forge-std" ]; then \ echo "forge-std already installed"; \ else \ cd hello && forge install foundry-rs/forge-std --no-git; \ fi @echo "Setup complete! Now run: make sol-verify-debug" ================================================ FILE: tools/noir/hello/Nargo.toml ================================================ [package] name = "hello" type = "bin" authors = [""] [dependencies] ================================================ FILE: tools/noir/hello/Prover.toml ================================================ x = "1" y = "2" ================================================ FILE: tools/noir/hello/src/main.nr ================================================ fn main(x: u64, y: pub u64) { assert(x != y); } #[test] fn test_main() { main(1, 2); // Uncomment to make test fail // main(1, 1); } ================================================ FILE: tools/noir/run.sh ================================================ reset() { rm -rf hello/ nargo new hello cd hello nargo check cat << EOF > Prover.toml x = "1" y = "2" EOF nargo execute witness cd ../ } # Setup Foundry for testing the generated Solidity verifier setup_foundry() { cd hello # Create foundry.toml configuration cat << 'EOF' > foundry.toml # Foundry configuration for testing the Honk verifier [profile.default] src = "target" out = "out" libs = ["lib"] test = "test" # Enable optimizer for faster execution optimizer = true optimizer_runs = 200 # Increase memory limit for large proof verification memory_limit = 134217728 # 128MB # Show more output verbosity = 3 # EVM version evm_version = "cancun" # Allow reading binary files for proof verification tests fs_permissions = [{ access = "read", path = "./target" }] [fuzz] runs = 256 EOF # Create test directory mkdir -p test # Create the Foundry test file cat << 'EOF' > test/VerifierTest.t.sol // SPDX-License-Identifier: MIT pragma solidity ^0.8.27; import "forge-std/Test.sol"; import "forge-std/console.sol"; // Import the verifier contract import "../target/contract_ultra_keccak_zk.sol"; /** * @title VerifierTest * @notice Test contract for debugging the ZK Honk verifier * @dev This test loads the proof from binary files and verifies it, * logging intermediate values for comparison with Python implementation. * * HOW TO RUN: * From the project root: * make sol-verify-debug * * Or manually from tools/noir/hello/: * forge test -vvvv --match-test testVerifyProof * * HOW TO ADD MORE LOGGING: * 1. Import console.sol in the contract you want to debug * 2. Add console.log() calls, e.g.: * console.log("variableName:", value); * console.log("Fr value:", Fr.unwrap(someField)); * 3. Run with -vvvv for maximum verbosity */ contract VerifierTest is Test { HonkVerifier verifier; function setUp() public { verifier = new HonkVerifier(); console.log("=== Verifier deployed ==="); console.log("VK_HASH:", VK_HASH); console.log("N:", N); console.log("LOG_N:", LOG_N); console.log("NUMBER_OF_PUBLIC_INPUTS:", NUMBER_OF_PUBLIC_INPUTS); } function testVerifyProof() public { console.log("\n=== Loading proof and public inputs ==="); // Load proof bytes from file bytes memory proofBytes = vm.readFileBinary("target/proof_ultra_keccak_zk.bin"); console.log("Proof length (bytes):", proofBytes.length); console.log("Proof length (field elements):", proofBytes.length / 32); // Load public inputs from file bytes memory pubInputsBytes = vm.readFileBinary("target/public_inputs_ultra_keccak_zk.bin"); console.log("Public inputs length (bytes):", pubInputsBytes.length); // Parse public inputs into bytes32 array uint256 numPubInputs = pubInputsBytes.length / 32; console.log("Number of public inputs:", numPubInputs); bytes32[] memory publicInputs = new bytes32[](numPubInputs); for (uint256 i = 0; i < numPubInputs; i++) { bytes32 val; uint256 offset = i * 32; assembly { val := mload(add(add(pubInputsBytes, 32), offset)) } publicInputs[i] = val; console.log("publicInput[%d]:", i); console.logBytes32(val); } console.log("\n=== Calling verify() ==="); // Call verify and check result bool result = verifier.verify(proofBytes, publicInputs); console.log("\n=== Result ==="); console.log("Verification result:", result); assertTrue(result, "Proof verification failed!"); } /** * @notice Test with manual proof parsing to log intermediate values * @dev Uncomment and modify this to debug specific parts of the proof */ function testVerifyProofWithDetailedLogging() public { console.log("\n=== Detailed Proof Parsing ==="); bytes memory proofBytes = vm.readFileBinary("target/proof_ultra_keccak_zk.bin"); bytes memory pubInputsBytes = vm.readFileBinary("target/public_inputs_ultra_keccak_zk.bin"); // Parse first few elements of proof (pairing point object) console.log("\n--- Pairing Point Object (first 16 field elements) ---"); for (uint256 i = 0; i < 16; i++) { uint256 val; uint256 offset = i * 32; assembly { val := mload(add(add(proofBytes, 32), offset)) } console.log("pairingPointObject[%d]:", i); console.log(" hex:", val); } // Parse commitment points (after pairing point object) console.log("\n--- Wire Commitments ---"); uint256 baseOffset = 16 * 32; // After pairing point object // W1 uint256 w1x; uint256 w1y; assembly { w1x := mload(add(add(proofBytes, 32), baseOffset)) w1y := mload(add(add(proofBytes, 64), baseOffset)) } console.log("W1.x:", w1x); console.log("W1.y:", w1y); // W2 uint256 w2x; uint256 w2y; assembly { w2x := mload(add(add(proofBytes, 32), add(baseOffset, 64))) w2y := mload(add(add(proofBytes, 64), add(baseOffset, 64))) } console.log("W2.x:", w2x); console.log("W2.y:", w2y); // W3 uint256 w3x; uint256 w3y; assembly { w3x := mload(add(add(proofBytes, 32), add(baseOffset, 128))) w3y := mload(add(add(proofBytes, 64), add(baseOffset, 128))) } console.log("W3.x:", w3x); console.log("W3.y:", w3y); // Now verify uint256 numPubInputs = pubInputsBytes.length / 32; bytes32[] memory publicInputs = new bytes32[](numPubInputs); for (uint256 i = 0; i < numPubInputs; i++) { bytes32 val; uint256 offset = i * 32; assembly { val := mload(add(add(pubInputsBytes, 32), offset)) } publicInputs[i] = val; } bool result = verifier.verify(proofBytes, publicInputs); console.log("\nVerification result:", result); assertTrue(result, "Proof verification failed!"); } } EOF # Install forge-std if not already present if [ ! -d "lib/forge-std" ]; then echo "Installing forge-std..." forge install foundry-rs/forge-std --no-git fi cd ../ echo "Foundry setup complete!" } reset BB_PATH="bb" echo "nargo version : $(nargo --version)" # See constants.json for recommended nargo version echo "bb version : $($BB_PATH --version)" # See constants.json for recommended bb version SCRIPT_PATH=$(dirname $(realpath $0)) HONK_FIXTURES_PATH="$SCRIPT_PATH/../../hydra/garaga/starknet/honk_contract_generator/examples" run_noir_proof_ultra_keccak_zk() { cd hello local suffix="_ultra_keccak_zk" mkdir -p target/proof${suffix}/ $BB_PATH prove -s ultra_honk --oracle_hash keccak --write_vk -b target/hello.json -w target/witness.gz -o target/proof${suffix}/ mv -f target/proof${suffix}/public_inputs target/public_inputs${suffix}.bin mv -f target/proof${suffix}/proof target/proof${suffix}.bin mv -f target/proof${suffix}/vk target/vk${suffix}.bin mv -f target/proof${suffix}/vk_hash target/vk_hash${suffix}.bin # Copy and replace proof.bin to HONK_FIXTURES_PATH/ (no renaming) cp target/proof${suffix}.bin $HONK_FIXTURES_PATH/ rmdir target/proof${suffix}/ if $BB_PATH verify -s ultra_honk --oracle_hash keccak -i target/public_inputs${suffix}.bin -p target/proof${suffix}.bin -k target/vk${suffix}.bin; then echo "ok $suffix" else echo "Verification failed $suffix" fi $BB_PATH write_solidity_verifier -s ultra_honk -k target/vk${suffix}.bin -o target/contract${suffix}.sol cd ../ } echo $'\n ultra keccak zk honk' # reset run_noir_proof_ultra_keccak_zk echo $'\n' # Print sha256 hash of of .sol files : for file in hello/target/*.sol; do echo $(md5sum $file) done # Print sha256 hash of of .bin files : for file in hello/target/*.bin; do echo $(md5sum $file) done # Setup Foundry for testing the Solidity verifier echo $'\n Setting up Foundry...' setup_foundry ================================================ FILE: tools/noir/transcript.py ================================================ x = """received: circuit_size: 32 received: public_input_size: 1 received: pub_inputs_offset: 1 received: public_input_0: 0x0000000000000000000000000000000000000000000000000000000000000002 received: W_L: { 0x2465e9ff1629df572d7ae9fd1b9bd98946560392b669c03f9a4a496ae7e4cace, 0x17bce8fc74ab3b9430b6485da928ea6951ebee411689e29dc324843ee1708142 } received: W_R: { 0x0eb93267e664634c1ae1a608b81785cfec11669ee95a1dbc6386717066310cb1, 0x23169272f91d323ced584549d31020c12f7cbf314c309c0ee105c3bbfef28399 } received: W_O: { 0x0d394ffb5eb2d33c6a2540db125d27fb60665db10ae3f80d91eb189b318d7d58, 0x0a325d606966d0ecbf514d787c3440de179ff8427f66be54fcabe05420fc14d0 } received: LOOKUP_READ_COUNTS: { 0x0ddfdbbdefc4ac1580ed38e12cfa490d9d719a8b9f020ad3642d60fe704e696f, 0x0ff3e0896bdea021253b3d360fa6788289fe9754ce48cd01b7be96a861b5e157 } received: LOOKUP_READ_TAGS: { 0x0ddfdbbdefc4ac1580ed38e12cfa490d9d719a8b9f020ad3642d60fe704e696f, 0x0ff3e0896bdea021253b3d360fa6788289fe9754ce48cd01b7be96a861b5e157 } received: W_4: { 0x0ca7365a8a7d92bd713e8625cde47db105835a557cf68ce01414ede87a1ce97b, 0x26bf12dceab316d64651db4ea03663d3d9478d6ea9a1f20bbe215561e139c7f7 } received: LOOKUP_INVERSES: { 0x1fad315eb3f489658734a3aff63bfb846255a077783e50444d60ac2b104b1ad4, 0x1067a4d8157c660c69e7022dd32ab0e30dd9987dae02f54e15edab896b9469a2 } received: Z_PERM: { 0x069b493db1ad1bcb140505bc5a806d425af4e78b20794bc813a7669eba382a02, 0x2d6c35a33c91dd52432099ee20f87ed823919ed60347a56b4678b3a485e58197 } challenge: Sumcheck:gate_challenge_0: 0x00000000000000000000000000000000c172dd2450a5c43df9f45a102035f4aa challenge: Sumcheck:gate_challenge_1: 0x00000000000000000000000000000000d9e8e31dd1bf34b1fd2c8dc378718bad challenge: Sumcheck:gate_challenge_2: 0x000000000000000000000000000000003b18273b302fc3f7e291bde9e8f657af challenge: Sumcheck:gate_challenge_3: 0x0000000000000000000000000000000063851884d3d82ee17736f752da9bac35 challenge: Sumcheck:gate_challenge_4: 0x00000000000000000000000000000000f209bde7aca3c49f2cadbe4dca83dde9 challenge: Sumcheck:gate_challenge_5: 0x0000000000000000000000000000000069f14a768158343825c27a938fbf36b5 challenge: Sumcheck:gate_challenge_6: 0x00000000000000000000000000000000ec589c20c082a8bbc2a5358dffcbb029 challenge: Sumcheck:gate_challenge_7: 0x00000000000000000000000000000000cbc709637c971ff0235b30e22631d7c4 challenge: Sumcheck:gate_challenge_8: 0x00000000000000000000000000000000b21375f2d73fe9a9b9a0bc6ec2572958 challenge: Sumcheck:gate_challenge_9: 0x00000000000000000000000000000000245b66aebdb626945436091e17da60ac challenge: Sumcheck:gate_challenge_10: 0x0000000000000000000000000000000062d7e222920e40d2706978b2e032cef5 challenge: Sumcheck:gate_challenge_11: 0x00000000000000000000000000000000d7f22806ba3855643a24874eacad3416 challenge: Sumcheck:gate_challenge_12: 0x00000000000000000000000000000000471214514009909e9ab6cb05b004dcd2 challenge: Sumcheck:gate_challenge_13: 0x00000000000000000000000000000000c5ea117fcb3a2986a4a0a3b2524e8cda challenge: Sumcheck:gate_challenge_14: 0x00000000000000000000000000000000c83493ac2556971a3705619eb92a536f challenge: Sumcheck:gate_challenge_15: 0x00000000000000000000000000000000c5830917428e1bac8ddffd2455fd95a4 challenge: Sumcheck:gate_challenge_16: 0x00000000000000000000000000000000c285c631c4c8da6a4878d427ab0ee02e challenge: Sumcheck:gate_challenge_17: 0x00000000000000000000000000000000bf75c5b1da0b6a57af698f776b4739ab challenge: Sumcheck:gate_challenge_18: 0x00000000000000000000000000000000276eccfb8e82d126f2c292d9708dd761 challenge: Sumcheck:gate_challenge_19: 0x000000000000000000000000000000009476a0a387149c8d1b78a58476b9efff challenge: Sumcheck:gate_challenge_20: 0x000000000000000000000000000000007ffa377781a42d05905df51f7fe83dff challenge: Sumcheck:gate_challenge_21: 0x00000000000000000000000000000000be0897e28f22aaf3c50014d76d49f4a0 challenge: Sumcheck:gate_challenge_22: 0x0000000000000000000000000000000062bcad183fec3655f642f8bd33895c5f challenge: Sumcheck:gate_challenge_23: 0x000000000000000000000000000000002cd23571aaa192e5525b3f440c21946d challenge: Sumcheck:gate_challenge_24: 0x00000000000000000000000000000000abc55392a196f776e4e6c843c9076946 challenge: Sumcheck:gate_challenge_25: 0x00000000000000000000000000000000609cc20bb22f811a3c24e0c1f20deb03 challenge: Sumcheck:gate_challenge_26: 0x0000000000000000000000000000000015356ea3058bd02736fc6ee7fae12b0d challenge: Sumcheck:gate_challenge_27: 0x00000000000000000000000000000000dee13f4571cd5267161d943456bc803b challenge: Sumcheck:u_0: 0x00000000000000000000000000000000e61948888da551fcbd6481a7af8cf0c0 challenge: Sumcheck:u_1: 0x000000000000000000000000000000001bc9a638f9f0e48211e06f74fdc4ee30 challenge: Sumcheck:u_2: 0x00000000000000000000000000000000b0494ceda348dd1ad61845b2820bb7a4 challenge: Sumcheck:u_3: 0x00000000000000000000000000000000e1a0fcc92b7bfa7d75edec03b2500e70 challenge: Sumcheck:u_4: 0x0000000000000000000000000000000049f16b7a01ed1d92bea9852b447cbbfa challenge: Sumcheck:u_5: 0x00000000000000000000000000000000b05ec1b687b95e039f37a9c102b6faa1 challenge: Sumcheck:u_6: 0x0000000000000000000000000000000093f8c2d82054794f1d9bc5016a00093f challenge: Sumcheck:u_7: 0x0000000000000000000000000000000059690cf79013abb0d194ec0d621435cb challenge: Sumcheck:u_8: 0x00000000000000000000000000000000b092f424ff1f2dc7e55a9aec2bcd1b6a challenge: Sumcheck:u_9: 0x00000000000000000000000000000000b41ba16fc7d5b8771894145a6a4a3653 challenge: Sumcheck:u_10: 0x00000000000000000000000000000000b7b0adaf7d801bae84bb10e77898104f challenge: Sumcheck:u_11: 0x00000000000000000000000000000000dcc650724f78f5544d9e4104c0c66049 challenge: Sumcheck:u_12: 0x000000000000000000000000000000009372338e1b74cefc0a9297fb6c9cdf2f challenge: Sumcheck:u_13: 0x00000000000000000000000000000000e7caf286270a5faab65e811c41b651ec challenge: Sumcheck:u_14: 0x00000000000000000000000000000000c3ecafac87e8f09ca2d644596fdf1843 challenge: Sumcheck:u_15: 0x00000000000000000000000000000000680091c031e3e54068f30b1abbba4032 challenge: Sumcheck:u_16: 0x00000000000000000000000000000000e923e5d1a9f802c0de0263b0847a98a7 challenge: Sumcheck:u_17: 0x0000000000000000000000000000000001e082dbe7f823be4a12dc7fc18ff4ba challenge: Sumcheck:u_18: 0x00000000000000000000000000000000f97bd808c15fcecef5eafa333438370b challenge: Sumcheck:u_19: 0x00000000000000000000000000000000dfdcaff7ed6c257079dce44b5d1ad9d1 challenge: Sumcheck:u_20: 0x000000000000000000000000000000004cc20354eac16fac6ebafb10cd388f45 challenge: Sumcheck:u_21: 0x00000000000000000000000000000000d0c31e08a9ca0944d44537b854c011da challenge: Sumcheck:u_22: 0x0000000000000000000000000000000065969933912dedee841ad8a92c062c7b challenge: Sumcheck:u_23: 0x000000000000000000000000000000009ee2e4b83c5e0156a4902309cc087a9a challenge: Sumcheck:u_24: 0x0000000000000000000000000000000011e8bfbd21b91ca1bee77a21bbc35be8 challenge: Sumcheck:u_25: 0x0000000000000000000000000000000010a6c496ccd27e38f0b8649a9470389f challenge: Sumcheck:u_26: 0x0000000000000000000000000000000048effcc28eda12ce3859196ddc398c76 challenge: Sumcheck:u_27: 0x00000000000000000000000000000000c44b6fe342b5502bf9b7416f1f257b2e challenge: rho: 0x00000000000000000000000000000000a4bb7935b0320a044f9a06e7ce23f501 received: Gemini:FOLD_1: { 0x0030f6ead299b812a9d0e34913e4897baa11cec4f4364333bd02c3ddb15b2796, 0x0e2c88de5ecff9e5e57f587f11a581f95e8311abc9cbc8b79f71f5043aa54178 } received: Gemini:FOLD_2: { 0x24c191be28e3c61bc03e45da0e82ef589a4e35476322229e437e049dbdf633a9, 0x190ea556eee073ab057011ff249806fce345419ce1c38dc47e6eac312132d8c0 } received: Gemini:FOLD_3: { 0x0dca2271951c15f10fe1bd6b142ae96d710cbe11e7f67b885ba8cf553f9b7a89, 0x222d3b8adfc808eccc9b6be870295d686f2f78a47a20070faa67ac921a0d62ec } received: Gemini:FOLD_4: { 0x03518fba7088a6f8103d8bc2f72a67a68cff759c9e8e70071a0c0d67a89bd684, 0x2796e48e3909df2b389f68123329adb1994e35d6faad76671de81ead27b3bef0 } received: Gemini:FOLD_5: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_6: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_7: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_8: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_9: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_10: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_11: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_12: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_13: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_14: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_15: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_16: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_17: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_18: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_19: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_20: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_21: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_22: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_23: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_24: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_25: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_26: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } received: Gemini:FOLD_27: { 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002 } challenge: Gemini:r: 0x000000000000000000000000000000007f80d41613ee8455f306ecb97366f6fb received: Gemini:a_1: 0x06d88005bac7d50eaf47b0321f0075d0892f453254935ef79c503047f177ac3c received: Gemini:a_2: 0x1f22b729740dcd28043721670fa5c3f6ec7c6e8f7150848eb590a57bb2c774a1 received: Gemini:a_3: 0x27af7bd3cb339be63a51d2305fc2ddf2c887b0a59511ec160aacec44308c9ffd received: Gemini:a_4: 0x16368d4a8fc2dee62530847567ad8d75ecd96aaa541c487628f56c47c5bb1771 received: Gemini:a_5: 0x0e405cd6caac953006162d7c72468986e014792ee1e09e041c69bea39def7c6d received: Gemini:a_6: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_7: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_8: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_9: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_10: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_11: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_12: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_13: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_14: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_15: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_16: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_17: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_18: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_19: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_20: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_21: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_22: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_23: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_24: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_25: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_26: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_27: 0x0000000000000000000000000000000000000000000000000000000000000000 received: Gemini:a_28: 0x0000000000000000000000000000000000000000000000000000000000000000 challenge: Shplonk:nu: 0x000000000000000000000000000000009f8c2321fe0106bf29aaadc94f24dea6 received: Shplonk:Q: { 0x1e3ce2491c516e0e06eaa5dcad936bce2677c1867be2aeb5720375ffc79b6e21, 0x0d1133764157bc108c1e4e201a02968887c77e16afdbb635b2729af6424c9e9e } challenge: Shplonk:z: 0x00000000000000000000000000000000d704d217bac677a48ad056c8aa8f9e44 received: KZG:W: { 0x1068dd1d211c8b30fdbfa561f69a4d062daa8998dd609fd7de22ed5babb86c4b, 0x216af708e0184bcac66514720a6bffaa7fee53f2f7ae34dc374df8ede0c3c09b } """ # print(x) # Initialize an empty list to store the processed data processed_data = [] lines = x.strip().split("\n") # Iterate over each line # Iterate over each line # ... existing code ... # Initialize an empty dictionary to store the processed data processed_data = {} lines = x.strip().split("\n") # Iterate over each line for line in lines: # Split the line into key and value based on the first occurrence of ': ' print(f"Processing line: {line}") parts = line.split(": ", 2) print(f"Parts: {parts}") op, key, value = parts print(f"Op: {op}, Key: {key}, Value: {value}") # Print the processed data to verify print(processed_data) import os cwd = os.path.dirname(os.path.abspath(__file__)) proof_bytes: bytes = open(f"{cwd}/hello/target/proof_ultra_keccak.bin", "rb").read() vk_bytes: bytes = open(f"{cwd}/hello/target/vk_ultra_keccak.bin", "rb").read() # print(proof_bytes.hex()) proof = [ 0x0000000000000000000000000000000000000000000000000000000000000020, 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000001, 0x0000000000000000000000000000000000000000000000000000000000000002, 0x0000000000000000000000000000008946560392B669C03F9A4A496AE7E4CACE, 0x00000000000000000000000000000000002465E9FF1629DF572D7AE9FD1B9BD9, 0x0000000000000000000000000000006951EBEE411689E29DC324843EE1708142, 0x000000000000000000000000000000000017BCE8FC74AB3B9430B6485DA928EA, 0x000000000000000000000000000000CFEC11669EE95A1DBC6386717066310CB1, 0x00000000000000000000000000000000000EB93267E664634C1AE1A608B81785, 0x000000000000000000000000000000C12F7CBF314C309C0EE105C3BBFEF28399, 0x000000000000000000000000000000000023169272F91D323CED584549D31020, 0x000000000000000000000000000000FB60665DB10AE3F80D91EB189B318D7D58, 0x00000000000000000000000000000000000D394FFB5EB2D33C6A2540DB125D27, 0x000000000000000000000000000000DE179FF8427F66BE54FCABE05420FC14D0, 0x00000000000000000000000000000000000A325D606966D0ECBF514D787C3440, 0x0000000000000000000000000000000D9D719A8B9F020AD3642D60FE704E696F, 0x00000000000000000000000000000000000DDFDBBDEFC4AC1580ED38E12CFA49, 0x0000000000000000000000000000008289FE9754CE48CD01B7BE96A861B5E157, 0x00000000000000000000000000000000000FF3E0896BDEA021253B3D360FA678, 0x0000000000000000000000000000000D9D719A8B9F020AD3642D60FE704E696F, 0x00000000000000000000000000000000000DDFDBBDEFC4AC1580ED38E12CFA49, 0x0000000000000000000000000000008289FE9754CE48CD01B7BE96A861B5E157, 0x00000000000000000000000000000000000FF3E0896BDEA021253B3D360FA678, 0x000000000000000000000000000000B105835A557CF68CE01414EDE87A1CE97B, 0x00000000000000000000000000000000000CA7365A8A7D92BD713E8625CDE47D, 0x000000000000000000000000000000D3D9478D6EA9A1F20BBE215561E139C7F7, 0x000000000000000000000000000000000026BF12DCEAB316D64651DB4EA03663, 0x000000000000000000000000000000846255A077783E50444D60AC2B104B1AD4, 0x00000000000000000000000000000000001FAD315EB3F489658734A3AFF63BFB, 0x000000000000000000000000000000E30DD9987DAE02F54E15EDAB896B9469A2, 0x00000000000000000000000000000000001067A4D8157C660C69E7022DD32AB0, 0x000000000000000000000000000000425AF4E78B20794BC813A7669EBA382A02, 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0x0000000000000000000000000000000000000000000000000000000000000000, 0x000000000000000000000000000000CE2677C1867BE2AEB5720375FFC79B6E21, 0x00000000000000000000000000000000001E3CE2491C516E0E06EAA5DCAD936B, 0x0000000000000000000000000000008887C77E16AFDBB635B2729AF6424C9E9E, 0x00000000000000000000000000000000000D1133764157BC108C1E4E201A0296, 0x000000000000000000000000000000062DAA8998DD609FD7DE22ED5BABB86C4B, 0x00000000000000000000000000000000001068DD1D211C8B30FDBFA561F69A4D, 0x000000000000000000000000000000AA7FEE53F2F7AE34DC374DF8EDE0C3C09B, 0x0000000000000000000000000000000000216AF708E0184BCAC66514720A6BFF, ] print(len(proof)) # Assert it's a multiple of 32 bytes # assert len(proof) % 32 == 0, f"Proof is not a multiple of 32 bytes: {len(proof)}" def deserialize_ultraproof(proof: bytes) -> list[int]: # Extract # of field elements from the first 4 bytes : num_field_elements = int.from_bytes(proof[:4], "big") assert len(proof[4:]) % 32 == 0 # Deserialize the rest of the proof return [int.from_bytes(proof[i : i + 32], "big") for i in range(4, len(proof), 32)] assert deserialize_ultraproof(proof_bytes) == proof from garaga.precompiled_circuits.zk_honk import HonkProof, HonkTranscript, HonkVk for i, elmt in enumerate(proof): print(f"element {i}: {hex(elmt)}") pproof = HonkProof.from_bytes(proof_bytes) # print(pproof) transcript = HonkTranscript.from_proof(pproof) # print(transcript) print(vk_bytes) print(vk_bytes.hex()) vk = HonkVk.from_bytes(vk_bytes) print(f"vk: {vk}") # print(pproof) print(vk.serialize_to_cairo()) ================================================ FILE: tools/npm/garaga_ts/.gitignore ================================================ /node_modules /dist /*.tgz /coverage ================================================ FILE: tools/npm/garaga_ts/Dockerfile ================================================ # This file (along with docker-compose.yml) helps creating reproducible builds # - It must be manually triggered whenever the Rust code is changed # - It will update the code generated under src/wasm/pkg # Usage: docker compose up --build && docker compose down FROM rust:1.87.0 RUN cargo install --locked wasm-pack@0.13.1 RUN curl -L https://bit.ly/n-install | bash -s -- -y 20.17.0 ENV HOME="/root/" ENV N_PREFIX="$HOME/n" ENV PATH="$HOME/n/bin/:$PATH" WORKDIR /garaga/tools/npm/garaga_ts CMD npm ci --ignore-scripts && npm run build && npm pack && ./fix-chown.sh ../.. ================================================ FILE: tools/npm/garaga_ts/README.md ================================================ # Garaga 🐺 State-of-the-art Elliptic Curve operations and SNARKS verification for Cairo & Starknet in TypeScript/JavaScript. ## Quick Start ```bash npm install garaga ``` ```bash yarn add garaga ``` **Requirements:** Node.js >= 18.0.0 ## What is Garaga? Garaga provides optimized cryptographic primitives for TypeScript/JavaScript: - **Elliptic Curve Operations** - High-performance curve arithmetic - **SNARK Verification** - Groth16, Noir Honk proof systems - **Pairing-Based Cryptography** - BN254, BLS12-381 curves - **Starknet Integration** - Generate calldata for Cairo contracts ## Basic Usage ```typescript import { init, msmCalldataBuilder, getGroth16CallData, CurveId } from 'garaga'; // Initialize WASM module await init(); // Multi-scalar multiplication const calldata = msmCalldataBuilder(points, scalars, CurveId.BN254); // Groth16 proof verification calldata const groth16Calldata = getGroth16CallData(proof, verifyingKey, CurveId.BN254); ``` ## Key Features ✅ **TypeScript Support** - Full type definitions included ✅ **WASM Performance** - Rust-powered cryptographic operations ✅ **Multiple Curves** - BN254, BLS12-381 support ✅ **Proof Systems** - Groth16, Noir Honk verification ✅ **Starknet Ready** - Generate calldata for Cairo contracts ✅ **Drand Integration** - Verifiable randomness support ## Available Functions 📋 **For complete API documentation with examples, see:** [API Reference](https://github.com/keep-starknet-strange/garaga/blob/v1.1.0/tools/npm/garaga_ts/src/node/api.ts) - `msmCalldataBuilder()` - Multi-scalar multiplication calldata generation - `mpcCalldataBuilder()` - Multi-pairing check calldata generation - `schnorrCalldataBuilder()` - Schnorr signature verification calldata - `ecdsaCalldataBuilder()` - ECDSA signature verification calldata - `eddsaCalldataBuilder()` - EdDSA signature verification calldata - `toWeirstrass()` - Convert from Twisted Edwards to Weierstrass coordinates - `toTwistedEdwards()` - Convert from Weierstrass to Twisted Edwards coordinates - `getGroth16CallData()` - Generate Groth16 proof verification calldata - `getZKHonkCallData()` - Generate Noir ZK Honk proof verification calldata - `fetchAndGetDrandCallData()` - Fetch Drand randomness and generate calldata - `poseidonHashBN254()` - Compute Poseidon hash on BN254 curve - and more... See the api reference (link above) for more details. ## Building from Source For development or custom builds: ```bash git clone https://github.com/keep-starknet-strange/garaga.git cd tools/npm/garaga_ts npm ci && npm run build ``` **Docker build (recommended):** ```bash docker compose up --build npm install ./garaga-.tgz ``` ## Documentation & Links - 📖 **Documentation**: [garaga.gitbook.io](https://garaga.gitbook.io/) - 🔧 **GitHub**: [github.com/keep-starknet-strange/garaga](https://github.com/keep-starknet-strange/garaga) - 📦 **NPM**: [npmjs.com/package/garaga](https://www.npmjs.com/package/garaga) - 🐛 **Issues**: [Report bugs](https://github.com/keep-starknet-strange/garaga/issues) ## Requirements - Node.js >= 18.0.0 - For building: Rust + wasm-pack ## License MIT License - see [LICENSE](https://github.com/keep-starknet-strange/garaga/blob/main/LICENSE) ================================================ FILE: tools/npm/garaga_ts/babel.config.cjs ================================================ module.exports = { presets: [ '@babel/preset-env', '@babel/preset-typescript', ], }; ================================================ FILE: tools/npm/garaga_ts/docker-compose.yml ================================================ # This file (along with Dockerfile) helps creating reproducible builds # - It must be manually triggered whenever the Rust code is changed # - It will update the code generated under src/wasm/pkg # Usage: docker compose up --build && docker compose down services: app: platform: linux/amd64 build: . volumes: - "../../..:/garaga" ================================================ FILE: tools/npm/garaga_ts/fix-chown.sh ================================================ #!/bin/sh # This script will apply the current folder ownership to its contents recursively # It is useful to fix up the ownership of files handled by a docker container FOLDER="${1:-$(dirname "$0")}" UID=$(stat -c "%u" "$FOLDER") GID=$(stat -c "%g" "$FOLDER") chown -R "$UID:$GID" "$FOLDER" ================================================ FILE: tools/npm/garaga_ts/jest.config.ts ================================================ module.exports= { preset: 'ts-jest', testEnvironment: 'node', testMatch: ['**/tests/**/*.test.ts'], moduleFileExtensions: ['ts', 'js'], // transform: { // '^.+\\.ts$': 'ts-jest' // }, collectCoverage: true, collectCoverageFrom: ['src/**/*.ts'], transform: { '^.+\\.(ts|tsx|js|jsx)$': 'babel-jest', }, }; ================================================ FILE: tools/npm/garaga_ts/patch.wasm.cjs ================================================ // This script will patch a 'wasm-pack --target web' output folder // towards a platform agnostic build const fs = require('fs'); const path = require('path'); function patch() { // package folder const pkgFolder = path.join(__dirname, 'src/wasm/pkg'); // package file name/path const jsonName = 'package.json'; const jsonFile = path.join(pkgFolder, jsonName); // package name const pkgName = JSON.parse(fs.readFileSync(jsonFile, 'utf8'))['name']; // other files const gitignoreName = '.gitignore'; const gitignoreFile = path.join(pkgFolder, gitignoreName); const jsName = pkgName + '.js'; const jsFile = path.join(pkgFolder, jsName); const wasmName = pkgName + '_bg.wasm'; const wasmFile = path.join(pkgFolder, wasmName); const wasmjsName = pkgName + '_bg.wasm.js'; const wasmjsFile = path.join(pkgFolder, wasmjsName); const wasmtsName = pkgName + '_bg.wasm.d.ts'; const wasmtsFile = path.join(pkgFolder, wasmtsName); // patches .js file: // - replaces the default WASM load behavior via URL by error (cjs compatibility) { const input = fs.readFileSync(jsFile, 'utf8'); const output = input .replaceAll('module_or_path = new URL(\'' + wasmName + '\', import.meta.url)', 'throw new Error()'); fs.writeFileSync(jsFile, output, 'utf8'); } // encodes .wasm file as .wasm.js: // - creates .wasm.js exporting the binary contents of the .wasm file { const input = fs.readFileSync(wasmFile).toString('base64'); const output = 'export default \'data:application/wasm;base64,' + input + '\';'; fs.writeFileSync(wasmjsFile, output, 'utf8'); } // overwrites .wasm.d.ts file: // - updates .wasm.d.ts with the type signature of the .wasm.js file { const output = 'declare const wasm_module_base64: string;' + '\n' + 'export default wasm_module_base64;'; fs.writeFileSync(wasmtsFile, output, 'utf8'); } // cleans up now obsolete files: // - removes .gitignore and .wasm files { fs.rmSync(gitignoreFile); fs.rmSync(wasmFile); } } patch(); ================================================ FILE: tools/npm/garaga_ts/rollup.config.js ================================================ import typescript from '@rollup/plugin-typescript'; import dts from 'rollup-plugin-dts'; export default [ { input: './src/node/index.ts', output: [ { file: 'dist/index.cjs', format: 'cjs', sourcemap: true, }, { file: 'dist/index.mjs', format: 'esm', sourcemap: true, }, ], external: ['fs', 'crypto', 'path', 'util', 'os', 'stream', 'buffer'], plugins: [typescript()], }, { input: './src/node/index.ts', output: { file: 'dist/index.d.ts', format: 'esm', sourcemap: false, }, external: ['fs', 'crypto', 'path', 'util', 'os', 'stream', 'buffer'], plugins: [typescript(), dts()], }, ]; ================================================ FILE: tools/npm/garaga_ts/src/constants.ts ================================================ /** * Auto-generated constants file from constants.json. Do not edit manually. */ // RISC0 Constants // https://github.com/risc0/risc0-ethereum/blob/v2.2.2/contracts/src/groth16/ControlID.sol // release v2.2.2 export const RISC0_CONTROL_ROOT = BigInt( "0xCE52BF56033842021AF3CF6DB8A50D1B7535C125A34F1A22C6FDCF002C5A1529", ); export const RISC0_BN254_CONTROL_ID = BigInt( "0x04446E66D300EB7FB45C9726BB53C793DDA407A62E9601618BB43C5C14657AC0", ); // SP1 Constants // https://github.com/succinctlabs/sp1-contracts/blob/main/contracts/src/v5.0.0/SP1VerifierGroth16.sol export const SP1_VERIFIER_VERSION = "v5.0.0"; export const SP1_VERIFIER_HASH = "0xa4594c59bbc142f3b81c3ecb7f50a7c34bc9af7c4c444b5d48b795427e285913"; // Additional RISC0 constants for internal use export const RISC0_SYSTEM_STATE_ZERO_DIGEST = new Uint8Array([ 0xa3, 0xac, 0xc2, 0x71, 0x17, 0x41, 0x89, 0x96, 0x34, 0x0b, 0x84, 0xe5, 0xa9, 0x0f, 0x3e, 0xf4, 0xc4, 0x9d, 0x22, 0xc7, 0x9e, 0x44, 0xaa, 0xd8, 0x22, 0xec, 0x9c, 0x31, 0x3e, 0x1e, 0xb8, 0xe2, ]); export const RISC0_TAG_DIGEST = "0xcb1fefcd1f2d9a64975cbbbf6e161e2914434b0cbb9960b84df5d717e86b48af"; export const RISC0_OUTPUT_TAG = "0x77eafeb366a78b47747de0d7bb176284085ff5564887009a5be63da32d3559d4"; ================================================ FILE: tools/npm/garaga_ts/src/node/api.ts ================================================ // This files provides a ts-like interface for garaga_rs import { drand_calldata_builder, drand_tlock_encrypt_calldata_builder, msm_calldata_builder, mpc_calldata_builder, schnorr_calldata_builder, ecdsa_calldata_builder, eddsa_calldata_builder, rsa_2048_calldata_builder, rsa_2048_sha256_calldata_builder, to_twistededwards, to_weirstrass, get_groth16_calldata, get_zk_honk_calldata, poseidon_hash, } from '../wasm/pkg/garaga_rs'; import { CurveId } from './definitions'; import { Groth16Proof, Groth16VerifyingKey } from './starknet/groth16ContractGenerator/parsingUtils'; export { parseGroth16ProofFromJson, parseGroth16ProofFromObject, parseGroth16VerifyingKeyFromJson, parseGroth16VerifyingKeyFromObject, } from './starknet/groth16ContractGenerator/parsingUtils'; export type { Groth16Proof, Groth16VerifyingKey, } from './starknet/groth16ContractGenerator/parsingUtils'; /** * Represents a point on an elliptic curve in affine coordinates (x, y) */ export type G1Point = [bigint, bigint]; /** * Represents a point on a twisted elliptic curve over an extension field * Format: [[x0, x1], [y0, y1]] where x = x0 + x1*i and y = y0 + y1*i */ export type G2Point = [[bigint, bigint], [bigint, bigint]]; /** * Represents a pairing of G1 and G2 points for pairing-based cryptography */ export type G1G2Pair = [G1Point, G2Point]; function flatten(data: bigint[][]): bigint[] { return data.reduce((values, item) => values.concat(item), []); } function pairToList(pair: G1G2Pair): bigint[] { const [[x1, y1], [[x2a, x2b], [y2a, y2b]]] = pair; return [x1, y1, x2a, x2b, y2a, y2b]; } /** * Configuration options for MSM (Multi-Scalar Multiplication) calldata builder */ export type MsmCalldataBuilderOptons = Partial<{ /** Whether to include the original points and scalars in the output */ includePointsAndScalars: boolean; /** Whether to serialize the output as a pure felt252 array for Cairo compatibility */ serializeAsPureFelt252Array: boolean; }>; /** * Builds calldata for Multi-Scalar Multiplication (MSM) operations. * MSM computes the sum of scalar multiplications: Σ(scalar_i * point_i) * * @param points - Array of G1 points to be multiplied * @param scalars - Array of scalar values for multiplication * @param curveId - Identifier for the elliptic curve (e.g., BN254, BLS12_381) * @param options - Configuration options for the MSM operation * @returns Array of bigint values representing the MSM calldata * * @example * ```typescript * const points: G1Point[] = [[1n, 2n], [3n, 4n]]; * const scalars = [5n, 6n]; * const calldata = msmCalldataBuilder(points, scalars, CurveId.BN254); * ``` */ export function msmCalldataBuilder(points: G1Point[], scalars: bigint[], curveId: CurveId, options: MsmCalldataBuilderOptons = {}): bigint[] { const values = flatten(points); const includePointsAndScalars = options.includePointsAndScalars ?? true; const serializeAsPureFelt252Array = options.serializeAsPureFelt252Array ?? false; return msm_calldata_builder(values, scalars, curveId, includePointsAndScalars, serializeAsPureFelt252Array); } /** * Builds calldata for Multi-Pairing Check (MPC) operations. * MPC verifies that a set of pairing equations hold: e(G1_i, G2_i) = 1 * * @param curveId - Identifier for the elliptic curve * @param pairs - Array of G1-G2 point pairs for pairing * @param nFixedG2 - Number of fixed G2 points in the pairing * @param publicPair - Optional additional public pairing for verification * @returns Array of bigint values representing the MPC calldata * * @example * ```typescript * const pairs: G1G2Pair[] = [[[1n, 2n], [[3n, 4n], [5n, 6n]]]]; * const calldata = mpcCalldataBuilder(CurveId.BN254, pairs, 1); * ``` */ export function mpcCalldataBuilder(curveId: CurveId, pairs: G1G2Pair[], nFixedG2: number, publicPair?: G1G2Pair): bigint[] { const values1 = flatten(pairs.map(pairToList)); const values2 = publicPair === undefined ? [] : pairToList(publicPair); return mpc_calldata_builder(curveId, values1, nFixedG2, values2); } /** * Builds calldata for Schnorr signature verification. * Schnorr signatures provide a simple and efficient digital signature scheme. * * @param rx - X-coordinate of the signature point R * @param s - Signature scalar value * @param e - Challenge hash value * @param px - X-coordinate of the public key point * @param py - Y-coordinate of the public key point * @param prependPublickey - Whether to include the public key in the calldata. * When true, prepends (px, py) coordinates to the output. * When false, only includes signature data (rx, s, e). * Set to false when the public key is provided separately to the Cairo contract, * useful for verifying multiple signatures with the same public key. * @param curveId - Identifier for the elliptic curve * @returns Array of bigint values representing the Schnorr verification calldata * * @example * ```typescript * // With public key included (default behavior for single verification) * const calldata = schnorrCalldataBuilder( * 0x123n, // rx * 0x456n, // s * 0x789n, // e * 0xabcn, // px * 0xdefn, // py * true, // prependPublickey * CurveId.BN254 * ); * * // Without public key (when provided separately to contract) * const calldataNoKey = schnorrCalldataBuilder( * 0x123n, // rx * 0x456n, // s * 0x789n, // e * 0xabcn, // px * 0xdefn, // py * false, // prependPublickey * CurveId.BN254 * ); * ``` */ export function schnorrCalldataBuilder(rx: bigint, s: bigint, e: bigint, px: bigint, py: bigint, prependPublickey: boolean, curveId: CurveId): bigint[] { return schnorr_calldata_builder(rx, s, e, px, py, prependPublickey, curveId); } /** * Builds calldata for ECDSA signature verification. * ECDSA is the standard elliptic curve digital signature algorithm. * * @param r - R component of the ECDSA signature * @param s - S component of the ECDSA signature * @param v - Recovery ID (0 or 1) for public key recovery * @param px - X-coordinate of the public key point * @param py - Y-coordinate of the public key point * @param z - Hash of the signed message * @param prependPublickey - Whether to include the public key in the calldata. * When true, prepends (px, py) coordinates to the output. * When false, only includes signature data (r, s, v, z). * Set to false when the public key is provided separately to the Cairo contract, * useful for verifying multiple signatures with the same public key. * @param curveId - Identifier for the elliptic curve * @returns Array of bigint values representing the ECDSA verification calldata * * @example * ```typescript * // With public key included (default behavior for single verification) * const calldata = ecdsaCalldataBuilder( * 0x123n, // r * 0x456n, // s * 0, // v * 0x789n, // px * 0xabcn, // py * 0xdefn, // z (message hash) * true, // prependPublickey * CurveId.SECP256K1 * ); * * // Without public key (when provided separately to contract) * const calldataNoKey = ecdsaCalldataBuilder( * 0x123n, // r * 0x456n, // s * 0, // v * 0x789n, // px * 0xabcn, // py * 0xdefn, // z (message hash) * false, // prependPublickey * CurveId.SECP256K1 * ); * ``` */ export function ecdsaCalldataBuilder(r: bigint, s: bigint, v: number, px: bigint, py: bigint, z: bigint, prependPublickey: boolean, curveId: CurveId): bigint[] { return ecdsa_calldata_builder(r, s, v, px, py, z, prependPublickey, curveId); } /** * Builds calldata for EdDSA signature verification for Ed25519. * EdDSA provides deterministic signatures with strong security properties. * * @param ry_twisted_le - Y-coordinate of signature point R in twisted Edwards form (little-endian) * @param s - Signature scalar value * @param py_twisted_le - Y-coordinate of public key in twisted Edwards form (little-endian) * @param msg - Raw message bytes that were signed * @param prependPublickey - Whether to include the public key in the calldata. * When true, prepends py_twisted_le to the output. * When false, only includes signature data (ry_twisted_le, s, msg). * Set to false when the public key is provided separately to the Cairo contract, * useful for verifying multiple signatures with the same public key. * @returns Array of bigint values representing the EdDSA verification calldata * * @example * ```typescript * const message = new Uint8Array([1, 2, 3, 4]); * * // With public key included (default behavior for single verification) * const calldata = eddsaCalldataBuilder( * 0x123n, // ry_twisted_le * 0x456n, // s * 0x789n, // py_twisted_le * message, * true // prependPublickey * ); * * // Without public key (when provided separately to contract) * const calldataNoKey = eddsaCalldataBuilder( * 0x123n, // ry_twisted_le * 0x456n, // s * 0x789n, // py_twisted_le * message, * false // prependPublickey * ); * ``` */ export function eddsaCalldataBuilder(ry_twisted_le: bigint, s: bigint, py_twisted_le: bigint, msg: Uint8Array, prependPublickey: boolean): bigint[] { return eddsa_calldata_builder(ry_twisted_le, s, py_twisted_le, msg, prependPublickey); } /** * Builds calldata for RSA-2048 signature verification. * Computes s^{65537} mod n via square-and-multiply with 17 certified reductions. * * @param signature - RSA signature value s * @param expectedMessage - Expected result m = s^{65537} mod n * @param modulus - RSA-2048 modulus n * @param prependPublicKey - Whether to include the modulus in the calldata. * When true, prepends n to the output (24 elements). * When false, only includes signature, message, and reduction witnesses. * @returns Array of bigint values representing the RSA verification calldata * * @example * ```typescript * const calldata = rsa2048CalldataBuilder( * signature, // RSA signature * expectedMessage, // s^65537 mod n * modulus, // RSA-2048 modulus * true // include modulus in calldata * ); * ``` */ export function rsa2048CalldataBuilder(signature: bigint, expectedMessage: bigint, modulus: bigint, prependPublicKey: boolean): bigint[] { return rsa_2048_calldata_builder(signature, expectedMessage, modulus, prependPublicKey); } /** * Builds calldata for RSA-2048 SHA-256 full on-chain signature verification. * Computes SHA-256(message), constructs the PKCS#1 v1.5 encoding, generates * RSA reduction witnesses, and appends the ByteArray-serialized message. * * @param signature - RSA signature value s * @param message - Raw message bytes to verify * @param modulus - RSA-2048 modulus n * @param prependPublicKey - Whether to include the modulus in the calldata. * When true, prepends n to the output (24 elements). * When false, only includes signature, message, and reduction witnesses. * @returns Array of bigint values representing the RSA SHA-256 verification calldata * * @example * ```typescript * const message = new TextEncoder().encode("hello garaga"); * const calldata = rsa2048Sha256CalldataBuilder( * signature, // RSA signature * message, // raw message bytes * modulus, // RSA-2048 modulus * true // include modulus in calldata * ); * ``` */ export function rsa2048Sha256CalldataBuilder(signature: bigint, message: Uint8Array, modulus: bigint, prependPublicKey: boolean): bigint[] { return rsa_2048_sha256_calldata_builder(signature, message, modulus, prependPublicKey); } /** * Converts a point from twisted Edwards form to Weierstrass form for Ed25519. * This is useful for interoperability between different curve representations. * * @param x_twisted - X-coordinate in twisted Edwards form * @param y_twisted - Y-coordinate in twisted Edwards form * @returns Tuple of [x_weierstrass, y_weierstrass] coordinates * @throws Error if the conversion fails or produces invalid results * * @example * ```typescript * const [x_w, y_w] = toWeirstrass(0x123n, 0x456n); * console.log(`Weierstrass form: (${x_w}, ${y_w})`); * ``` */ export function toWeirstrass(x_twisted: bigint, y_twisted: bigint): [bigint, bigint] { const result = to_weirstrass(x_twisted, y_twisted); if (result.length !== 2) { throw new Error('Invalid result length'); } return [result[0], result[1]]; } /** * Converts a point from Weierstrass form to twisted Edwards form for Ed25519. * This is useful for interoperability between different curve representations. * * @param x_weierstrass - X-coordinate in Weierstrass form * @param y_weierstrass - Y-coordinate in Weierstrass form * @returns Tuple of [x_twisted, y_twisted] coordinates * @throws Error if the conversion fails or produces invalid results * * @example * ```typescript * const [x_t, y_t] = toTwistedEdwards(0x789n, 0xabcn); * console.log(`Twisted Edwards form: (${x_t}, ${y_t})`); * ``` */ export function toTwistedEdwards(x_weierstrass: bigint, y_weierstrass: bigint): [bigint, bigint] { const result = to_twistededwards(x_weierstrass, y_weierstrass); if (result.length !== 2) { throw new Error('Invalid result length'); } return [result[0], result[1]]; } /** * Generates calldata for Groth16 zero-knowledge proof verification. * Groth16 is a succinct non-interactive zero-knowledge proof system. * * @param proof - The Groth16 proof containing points A, B, C and public inputs * @param verifyingKey - The verification key containing curve points for verification * @param curveId - Identifier for the elliptic curve used in the proof * @returns Array of bigint values representing the complete verification calldata * * @example * ```typescript * const proof: Groth16Proof = { * a: [0x123n, 0x456n], * b: [[0x789n, 0xabcn], [0xdefn, 0x111n]], * c: [0x222n, 0x333n], * publicInputs: [0x444n, 0x555n] * }; * const calldata = getGroth16CallData(proof, verifyingKey, CurveId.BN254); * ``` */ export function getGroth16CallData(proof: Groth16Proof, verifyingKey: Groth16VerifyingKey, curveId: CurveId): bigint[] { return get_groth16_calldata(proof, verifyingKey, curveId); } /** * Generates calldata for ZK-Honk zero-knowledge proof verification. * ZK-Honk provides zero-knowledge properties on top of the Honk system. * * @param proof - Raw ZK proof bytes from the ZK-Honk prover * @param publicInputs - Public input bytes for the circuit * @param verifyingKey - Verification key bytes for the specific circuit * @returns Array of bigint values representing the complete verification calldata * * @example * ```typescript * const zkProofBytes = new Uint8Array([...]); * const publicInputsBytes = new Uint8Array([...]); * const vkBytes = new Uint8Array([...]); * const calldata = getZKHonkCallData(zkProofBytes, publicInputsBytes, vkBytes); * ``` */ export function getZKHonkCallData(proof: Uint8Array, publicInputs: Uint8Array, verifyingKey: Uint8Array): bigint[] { return get_zk_honk_calldata(proof, publicInputs, verifyingKey); } /** * Default base URLs for accessing drand randomness beacons */ const DRAND_BASE_URLS = [ 'https://drand.cloudflare.com', 'https://api.drand.sh', 'https://api2.drand.sh', 'https://api3.drand.sh', ]; /** * Hash identifier for the drand quicknet chain */ const DRAND_QUICKNET_HASH = '52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971'; /** * Represents a randomness beacon from the drand network */ type DrandRandomnessBeacon = { /** The round number of this randomness beacon */ round: number; /** The random value generated for this round */ randomness: bigint; /** The BLS signature proving the randomness */ signature: bigint; }; /** * Fetches drand randomness and generates verification calldata in one step. * This is a convenience function that combines fetching and calldata generation. * * @param roundNumber - The specific round to fetch, or 'latest' for the most recent * @param chainHash - Hash identifier of the drand chain (defaults to quicknet) * @param baseUrls - Array of drand API endpoints to try * @returns Promise resolving to calldata array for verifying the drand randomness * * @example * ```typescript * // Fetch latest randomness and generate calldata * const calldata = await fetchAndGetDrandCallData(); * * // Fetch specific round * const roundCalldata = await fetchAndGetDrandCallData(12345); * ``` */ export async function fetchAndGetDrandCallData(roundNumber: number | 'latest' = 'latest', chainHash = DRAND_QUICKNET_HASH, baseUrls = DRAND_BASE_URLS): Promise { return getDrandCallData(await fetchDrandRandomness(roundNumber, chainHash, baseUrls)); } /** * Generates calldata for drand randomness beacon verification. * This prepares the data needed to verify a drand signature on-chain. * * @param beacon - The drand randomness beacon containing round, randomness, and signature * @returns Array of bigint values representing the verification calldata * * @example * ```typescript * const beacon = { * round: 12345, * randomness: 0x123456789n, * signature: 0xabcdef123n * }; * const calldata = getDrandCallData(beacon); * ``` */ export function getDrandCallData({ round, randomness, signature }: DrandRandomnessBeacon): bigint[] { return drand_calldata_builder([round, randomness, signature]); } /** * Encrypts a message using drand tlock encryption for a specific round and returns calldata. * The message can only be decrypted once the drand beacon for that round is published. * * @param roundNumber - The drand round number to encrypt for * @param message - 16-byte message to encrypt * @param randomness - 16-byte randomness for encryption * @returns Array of bigint values representing the tlock encryption calldata */ export function encryptToDrandRoundAndGetCallData(roundNumber: number, message: Uint8Array, randomness: Uint8Array): bigint[] { if (message.length != 16) throw new Error('Message size should be 16'); if (randomness.length != 16) throw new Error('Randomness size should be 16'); const messageValue = message.reduce((acc: bigint, b: number) => (acc << 8n) | BigInt(b), 0n); const randomnessValue = randomness.reduce((acc: bigint, b: number) => (acc << 8n) | BigInt(b), 0n); return drand_tlock_encrypt_calldata_builder([roundNumber, messageValue, randomnessValue]); } /** * Fetches randomness data from the drand distributed randomness beacon network. * Tries multiple endpoints for reliability and returns the first successful response. * * @param roundNumber - The specific round to fetch, or 'latest' for the most recent * @param chainHash - Hash identifier of the drand chain to query * @param baseUrls - Array of drand API endpoints to attempt * @returns Promise resolving to the randomness beacon data * @throws Error if all endpoints fail or return invalid data * * @example * ```typescript * // Fetch latest round * const latest = await fetchDrandRandomness(); * * // Fetch specific round * const round12345 = await fetchDrandRandomness(12345); * * // Use custom endpoints * const custom = await fetchDrandRandomness('latest', 'custom-hash', ['https://custom-drand.com']); * ``` */ export async function fetchDrandRandomness(roundNumber: number | 'latest' = 'latest', chainHash = DRAND_QUICKNET_HASH, baseUrls = DRAND_BASE_URLS): Promise { if (baseUrls.length == 0) { throw new Error('No base url provided'); } const endpoint = '/' + chainHash + '/public/' + roundNumber; const promises = baseUrls.map((baseUrl) => fetch(baseUrl + endpoint)); let response; try { response = await Promise.any(promises); } catch (e) { throw new Error('All urls failed: ' + e); } const data = await response?.json(); if (!data || !data.round || !data.randomness || !data.signature) { throw new Error('Unexpected response: ' + JSON.stringify(data)); } const round = Number(data.round); const randomness = BigInt('0x' + data.randomness.replace(/^0x/i, '')); const signature = BigInt('0x' + data.signature.replace(/^0x/i, '')); return { round, randomness, signature }; } /** * Computes the Poseidon hash function over the BN254 curve. * Poseidon is a cryptographic hash function optimized for zero-knowledge circuits. * * @param x - First input field element * @param y - Second input field element * @returns The Poseidon hash result as a bigint * @throws Error if the hash computation fails or inputs are invalid * * @example * ```typescript * const hash = poseidonHashBN254(1n, 2n); * console.log(`Poseidon(1, 2) = ${hash.toString(16)}`); * * // Expected output for (1, 2): * // 115CC0F5E7D690413DF64C6B9662E9CF2A3617F2743245519E19607A4417189A * ``` */ export function poseidonHashBN254(x: bigint, y: bigint): bigint { try { const result = poseidon_hash(x, y); if (typeof result === 'bigint') { return result; } throw new Error('Invalid result from poseidon_hash'); } catch (error) { throw new Error(`Failed to compute Poseidon hash: ${error}`); } } ================================================ FILE: tools/npm/garaga_ts/src/node/definitions.ts ================================================ // const N_LIMBS: number = 4 // const BASE: number = 2**96 // const STARK: bigint = BigInt("0x800000000000011000000000000000000000000000000000000000000000001"); // const BN254_ID: number = 0 // const BLS12_381_ID: number = 1 // const SECP256K1_ID: number = 2 // const SECP256R1_ID: number = 3 // const ED25519_ID: number = 4 export enum CurveId { BN254 = 0, BLS12_381 = 1, SECP256K1 = 2, SECP256R1 = 3, ED25519 = 4, } export interface G1Point { x: bigint; y: bigint; curveId: CurveId } export interface G2Point { x: [bigint, bigint]; y: [bigint, bigint]; curveId: CurveId } export interface G1G2Pair { p: G1Point; q: G2Point; curveId: CurveId } interface WeiertrassCurve { cairoZeroNamespaceName: string, curveId: CurveId, p: bigint, n: bigint, h: bigint, a?: bigint, b?: bigint, fpGenerator: bigint, Gx: bigint, Gy: bigint, } interface PairingCurve extends WeiertrassCurve { x: bigint, irreduciblePolys: Record, nrA0: bigint, nrA1: bigint, b20: bigint, b21: bigint, loopCounter: number[], lineFunctionSparcity: number[], finalExpCofactor: bigint, G2x: [bigint, bigint], G2y: [bigint, bigint], } interface TwistedEdwardsCurve extends WeiertrassCurve { aTwisted: bigint, dTwisted: bigint } export const findValueInStringToCurveId = (s: string): CurveId | null =>{ // Find the value of the Curve ID in the string if(s.toLowerCase() === "bn128"){ return CurveId.BN254; } if(s.toLowerCase() === "bls12381"){ return CurveId.BLS12_381; } let curveId: CurveId | null = null; Object.entries(CurveId).forEach(([key, value]) => { if(s.toLowerCase().includes(key.toLowerCase()) || key.toLowerCase().includes(s.toLowerCase())){ curveId = CurveId[key as keyof typeof CurveId]; return; } }); return curveId; } export const jy00 = (value: bigint): number[] => { /** * This is a minimum-Hamming-Weight left-to-right recoding. * It outputs signed {-1, 0, 1} bits from MSB to LSB * with minimal Hamming Weight to minimize operations * in Miller Loops and vartime scalar multiplications * * - Optimal Left-to-Right Binary Signed-Digit Recoding * Joye, Yen, 2000 * https://marcjoye.github.io/papers/JY00sd2r.pdf */ const bit = (value: bigint, index: number): bigint => { return (value >> BigInt(index)) & 1n; }; let bi = 0n, bi1 = 0n, ri = 0n, ri1 = 0n, ri2 = 0n; const bits = value.toString(2).length; const recoded: number[] = []; for (let i = bits; i >= 0; i--) { if (i === bits) { ri1 = bit(value, bits - 1); ri2 = bit(value, bits - 2); } else { bi = bi1; ri = ri1; ri1 = ri2; ri2 = i >= 2 ? bit(value, i - 2) : 0n; } bi1 = (bi + ri1 + ri2) >> 1n; recoded.push(Number(-2n * bi + ri + bi1)); // Cast bigint result to number } return recoded; } export const CURVES: Record = { [CurveId.BN254]: { cairoZeroNamespaceName: "bn254", curveId: CurveId.BN254, p: BigInt("0x30644E72E131A029B85045B68181585D97816A916871CA8D3C208C16D87CFD47"), n: BigInt("0x44E992B44A6909F1"), h: BigInt(1), irreduciblePolys: { 6: [82, 0, 0, -18, 0, 0, 1], 12: [82, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1], }, nrA0: BigInt(9), nrA1: BigInt(1), a: BigInt(0), b: BigInt(3), b20: BigInt("0x2B149D40CEB8AAAE81BE18991BE06AC3B5B4C5E559DBEFA33267E6DC24A138E5"), b21: BigInt("0x9713B03AF0FED4CD2CAFADEED8FDF4A74FA084E52D1852E4A2BD0685C315D2"), loopCounter: jy00(BigInt(6) * BigInt("0x44E992B44A6909F1") + BigInt(2)).reverse(), lineFunctionSparcity: [2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0 ,0], finalExpCofactor: BigInt("1469306990098747947464455738335385361638823152381947992820"), fpGenerator: BigInt(3), Gx: BigInt("0x1"), Gy: BigInt("0x2"), G2x: [BigInt("0x1800DEEF121F1E76426A00665E5C4479674322D4F75EDADD46DEBD5CD992F6ED"), BigInt("0x198E9393920D483A7260BFB731FB5D25F1AA493335A9E71297E485B7AEF312C2")], G2y: [BigInt("0x12C85EA5DB8C6DEB4AAB71808DCB408FE3D1E7690C43D37B4CE6CC0166FA7DAA"), BigInt("0x90689D0585FF075EC9E99AD690C3395BC4B313370B38EF355ACDADCD122975B")] }, [CurveId.BLS12_381]: { cairoZeroNamespaceName: "bls", curveId: CurveId.BLS12_381, p: BigInt("0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAB"), n: BigInt("0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001"), x: -BigInt("0xD201000000010000"), h: BigInt("0x396C8C005555E1568C00AAAB0000AAAB"), irreduciblePolys: { 6: [2, 0, 0, -2, 0, 0, 1], 12: [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1], }, nrA0: BigInt(1), nrA1: BigInt(1), a: BigInt(0), b: BigInt(4), b20: BigInt(4), b21: BigInt(4), loopCounter: BigInt("0xD201000000010000").toString(2).slice(0).split("").reverse().map(x => parseInt(x, 10)), lineFunctionSparcity: [1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0], finalExpCofactor: BigInt(3), fpGenerator: BigInt(3), Gx: BigInt("0x17F1D3A73197D7942695638C4FA9AC0FC3688C4F9774B905A14E3A3F171BAC586C55E83FF97A1AEFFB3AF00ADB22C6BB"), Gy: BigInt("0x08B3F481E3AAA0F1A09E30ED741D8AE4FCF5E095D5D00AF600DB18CB2C04B3EDD03CC744A2888AE40CAA232946C5E7E1"), G2x: [ BigInt("0x24AA2B2F08F0A91260805272DC51051C6E47AD4FA403B02B4510B647AE3D1770BAC0326A805BBEFD48056C8C121BDB8"), BigInt("0x13E02B6052719F607DACD3A088274F65596BD0D09920B61AB5DA61BBDC7F5049334CF11213945D57E5AC7D055D042B7E") ], G2y: [ BigInt("0xCE5D527727D6E118CC9CDC6DA2E351AADFD9BAA8CBDD3A76D429A695160D12C923AC9CC3BACA289E193548608B82801"), BigInt("0x606C4A02EA734CC32ACD2B02BC28B99CB3E287E85A763AF267492AB572E99AB3F370D275CEC1DA1AAA9075FF05F79BE") ] }, [CurveId.SECP256K1]: { cairoZeroNamespaceName: "secp256r1", curveId: CurveId.SECP256K1, p: BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"), n: BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141"), h: BigInt(1), a: BigInt(0), b: BigInt(7), fpGenerator: BigInt(2), Gx: BigInt("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"), Gy: BigInt("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8") }, [CurveId.SECP256R1]: { cairoZeroNamespaceName: "secp256r1", curveId: CurveId.SECP256R1, p: BigInt("0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"), n: BigInt("0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"), h: BigInt(1), a: BigInt("0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"), b: BigInt("0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"), fpGenerator: BigInt(6), Gx: BigInt("0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"), Gy: BigInt("0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5") }, [CurveId.ED25519]: { cairoZeroNamespaceName: "ED25519", curveId: CurveId.ED25519, p: BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED"), n: BigInt("0x1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED"), h: BigInt(8), dTwisted: BigInt("0x52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3"), aTwisted: BigInt("0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC"), fpGenerator: BigInt(6), Gx: BigInt("0x216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A"), Gy: BigInt("0x6666666666666666666666666666666666666666666666666666666666666658") } } ================================================ FILE: tools/npm/garaga_ts/src/node/hints/io.ts ================================================ export const toBigInt = (value: string | bigint | number | Uint8Array): bigint => { //Convert a string or integer to an integer. Supports hexadecimal and decimal strings. if (typeof value === 'string') { value = value.trim(); try { return BigInt(value); } catch (e) { if (value.toLowerCase().startsWith('0x')) { throw new Error(`Invalid hexadecimal value: ${value}`); } else { throw new Error(`Invalid decimal value: ${value}`); } } } else if (typeof value === 'bigint') { return value; } else if (typeof value === 'number') { if (Number.isInteger(value)) { return BigInt(value); } else { throw new TypeError(`Expected integer number, got non-integer number: ${value}`); } } else if (value instanceof Uint8Array) { let result = BigInt(0); for (const byte of value) { result = (result << 8n) + BigInt(byte); } return result; } else { throw new TypeError( `Expected string, number, or Uint8Array, got ${typeof value}` ); } } export const toHexStr = (value: string | number | bigint): string => { if (typeof value === 'string') { value = value.trim(); const intValue = BigInt(value); return ('0x' + intValue.toString(16)).toLowerCase(); } else if (typeof value === 'number' || typeof value === 'bigint') { const intValue = BigInt(value); return ('0x' + intValue.toString(16)).toLowerCase(); } else { throw new TypeError(`Expected string, number integer, or bigint, got ${typeof value}`); } } export const hexStringToBytes = (hexString: string): Uint8Array => { if (hexString.toLowerCase().startsWith('0x')) { hexString = hexString.slice(2); } if (hexString.length % 2 !== 0) { hexString = '0' + hexString; } const bytes = new Uint8Array(hexString.length / 2); for (let i = 0; i < bytes.length; i++) { const byte = hexString.slice(i * 2, i * 2 + 2); bytes[i] = parseInt(byte, 16); } return bytes; } export const bitLength = (x: bigint): number => { if (x === 0n || x === -0n) { return 0; } let bits = 0; let n = x < 0n ? -x : x; // Handle negative numbers while (n > 0n) { n >>= 1n; bits++; } return bits; } export const split128 = (a: bigint): [bigint, bigint] => { try { console.log("a bigint", a); const MAX_UINT256 = 115792089237316195423570985008687907853269984665640564039457584007913129639936n; const MASK_128 = BigInt((1n << 128n) - 1n); if (a < 0n || a >= MAX_UINT256) { throw new Error(`Value ${a} is too large to fit in a u256`); } const low = a & MASK_128; const high = a >> BigInt(128); return [low, high]; } catch (err) { console.log("ERR split 128: ", err); throw new Error("ERROR split 128") } } export const modInverse = (a: bigint, p: bigint): bigint => { let m0 = p; let y = BigInt(0), x = BigInt(1); if (p === BigInt(1)) { return BigInt(0); } while (a > BigInt(1)) { // q is quotient let q = a / p; let t = p; // p is remainder now, process same as Euclid's algorithm p = a % p; a = t; t = y; // Update x and y y = x - q * y; x = t; } // Make x positive if (x < BigInt(0)) { x = x + m0; } return x; } ================================================ FILE: tools/npm/garaga_ts/src/node/index.ts ================================================ export * from './api'; // exports "ts" interface export * from '../wasm/pkg/garaga_rs'; // export "raw" interface export { CurveId } from './definitions'; import pkg_init from '../wasm/pkg/garaga_rs'; import module_or_path from '../wasm/pkg/garaga_rs_bg.wasm'; export function init(): ReturnType { return pkg_init({ module_or_path }); } ================================================ FILE: tools/npm/garaga_ts/src/node/starknet/groth16ContractGenerator/parsingUtils.ts ================================================ import { CURVES, CurveId, G1Point, G2Point, findValueInStringToCurveId } from "../../definitions"; import * as fs from 'fs'; import { bitLength, hexStringToBytes, modInverse, split128, toBigInt, toHexStr } from "../../hints/io"; import { createHash } from 'crypto'; import { RISC0_CONTROL_ROOT, RISC0_BN254_CONTROL_ID, RISC0_SYSTEM_STATE_ZERO_DIGEST, SP1_VERIFIER_HASH, SP1_VERIFIER_VERSION } from "../../../constants"; //https://github.com/risc0/risc0-ethereum/blob/main/contracts/src/groth16/ControlID.sol export interface Groth16Proof { a: G1Point, b: G2Point, c: G1Point, publicInputs: bigint[], curveId?: CurveId, imageIdJournalRisc0?: { imageId: Uint8Array, journal: Uint8Array }, vkeyPublicValuesSp1?: { vkey: Uint8Array, publicValues: Uint8Array } } export interface Groth16VerifyingKey { alpha: G1Point, beta: G2Point, gamma: G2Point, delta: G2Point, ic: G1Point[] } interface Output { journalDigest: Uint8Array; assumptionsDigest: Uint8Array; } interface ExitCode { system: number; user: number; } interface ReceiptClaim { preStateDigest: Uint8Array; postStateDigest: Uint8Array; exitCode: ExitCode; input: Uint8Array; output: Uint8Array; tagDigest?: Uint8Array; } export class KeyPatternNotFoundError extends Error { constructor(message: string) { super(message); this.name = "KeyPatternNotFoundError"; } } export const parseGroth16VerifyingKeyFromJson = (filePath: string): Groth16VerifyingKey => { try { const data: any = JSON.parse(fs.readFileSync(filePath, 'utf8')); return parseGroth16VerifyingKeyFromObject(data); } catch (err) { throw new Error(`Failed to parse Groth16 verifying key from ${filePath}: ${err}`); } } export const parseGroth16VerifyingKeyFromObject = (data: any): Groth16VerifyingKey => { try { const curveId = tryGuessingCurveIdFromJson(data); let verifyingKey: any; try { verifyingKey = findItemFromKeyPatterns(data, ["verifying_key"]) } catch (err) { verifyingKey = data; } try { const alpha = tryParseG1PointFromKey(verifyingKey, ['alpha'], curveId); const beta = tryParseG2PointFromKey(verifyingKey, ['beta'], curveId); const gamma = tryParseG2PointFromKey(verifyingKey, ['gamma'], curveId); const delta = tryParseG2PointFromKey(verifyingKey, ['delta'], curveId); if (curveId !== null && curveId !== undefined) { const ic: G1Point[] = findItemFromKeyPatterns(verifyingKey, ['ic']).map((point: any) => { const g1Point = tryParseG1Point(point, curveId) return g1Point; }); const vk: Groth16VerifyingKey = { alpha, beta, gamma, delta, ic } if (checkGroth16VerifyingKey(vk)) { return vk; } throw new Error(`Invalid Groth16 verifying key: ${vk}`); } throw new Error("Curve ID not provided"); } catch (err) { // Gnark case const g1Points = findItemFromKeyPatterns(verifyingKey, ['g1']); const g2Points = findItemFromKeyPatterns(verifyingKey, ['g2']); const alpha = tryParseG1PointFromKey(g1Points, ['alpha'], curveId); const beta = tryParseG2PointFromKey(g2Points, ['beta'], curveId); const gamma = tryParseG2PointFromKey(g2Points, ['gamma'], curveId); const delta = tryParseG2PointFromKey(g2Points, ['delta'], curveId); if (curveId !== null && curveId !== undefined) { const ic: G1Point[] = findItemFromKeyPatterns(g1Points, ['K']).map((point: any) => tryParseG1Point(point, curveId)); const vk = { alpha, beta, gamma, delta, ic } if (checkGroth16VerifyingKey(vk)) { return vk; } } throw new Error("Curve ID not provided"); } } catch (err) { throw new Error(`Failed to parse Groth16 verifying key from object: ${err}`); } } export const parseGroth16ProofFromJson = (proofPath: string, publicInputsPath?: string | null): Groth16Proof => { try { const data: any = JSON.parse(fs.readFileSync(proofPath, 'utf8')); let publicInputs: any = null; if (publicInputsPath && publicInputsPath !== null && publicInputsPath !== undefined) { try { publicInputs = JSON.parse(fs.readFileSync(publicInputsPath, 'utf8')); } catch (err) { throw new Error(`Invalid public inputs format: ${publicInputsPath}`); } } return parseGroth16ProofFromObject(data, publicInputs); } catch (err) { throw new Error(`Failed to parse Groth16 proof from ${proofPath}: ${err}`); } } export const parseGroth16ProofFromObject = (data: any, publicInputsData?: bigint[] | object): Groth16Proof => { try { let curveId = tryGuessingCurveIdFromJson(data); let proof: any = null; try { proof = findItemFromKeyPatterns(data, ['proof']); } catch (err) { proof = data } // Try RISC0 parsing first try { const sealHex = toHexStr(findItemFromKeyPatterns(data, ['seal'])); const imageIdHex = toHexStr(findItemFromKeyPatterns(data, ['image_id'])); const journalHex = toHexStr(findItemFromKeyPatterns(data, ['journal'])); const sealBytes = hexStringToBytes(sealHex); const imageIdBytes = hexStringToBytes(imageIdHex); const journalBytes = hexStringToBytes(journalHex); return createGroth16ProofFromRisc0(sealBytes, imageIdBytes, journalBytes) } catch (err) { // Continue to SP1 parsing } // Try SP1 parsing second try { const sp1VkeyHex = findItemFromKeyPatterns(data, ['vkey']); const sp1PublicValuesHex = findItemFromKeyPatterns(data, ['publicValues']); const sp1ProofHex = findItemFromKeyPatterns(data, ['proof']); let vkeyBytes: Uint8Array; let publicValuesBytes: Uint8Array; let proofBytes: Uint8Array; // Handle hex strings directly to preserve leading zeros if (typeof sp1VkeyHex === 'string') { vkeyBytes = hexStringToBytes(sp1VkeyHex); } else { vkeyBytes = hexStringToBytes(toHexStr(sp1VkeyHex)); } if (typeof sp1PublicValuesHex === 'string') { publicValuesBytes = hexStringToBytes(sp1PublicValuesHex); } else { publicValuesBytes = hexStringToBytes(toHexStr(sp1PublicValuesHex)); } if (typeof sp1ProofHex === 'string') { proofBytes = hexStringToBytes(sp1ProofHex); } else { proofBytes = hexStringToBytes(toHexStr(sp1ProofHex)); } return createGroth16ProofFromSp1(vkeyBytes, publicValuesBytes, proofBytes); } catch (err) { // Continue to regular proof parsing } let publicInputs: bigint[] = []; if (publicInputsData && publicInputsData !== null && publicInputsData !== undefined) { if (typeof publicInputsData === 'object' && !Array.isArray(publicInputsData)) { // If it's an object, convert it to a list (array) of its values publicInputs = Object.values(publicInputsData).map( (value: any) => toBigInt(value) ); } else if (Array.isArray(publicInputsData)) { publicInputs = publicInputsData.map((value: any) => toBigInt(value)); } else { throw new Error(`Invalid public inputs format: ${publicInputsData}`); } } else { try { publicInputs = findItemFromKeyPatterns(data, ['public']); } catch (err) { } } const a = tryParseG1PointFromKey(proof, ['a', 'Ar'], curveId); const b = tryParseG2PointFromKey(proof, ['b', 'Bs'], curveId); const c = tryParseG1PointFromKey(proof, ['c', 'Krs'], curveId); const returnProof = { a, b, c, publicInputs: publicInputs } if (checkGroth16Proof(returnProof)) { return returnProof; } throw new Error(`Invalid Groth16 proof: ${returnProof}`); } catch (err) { throw new Error(`Failed to parse Groth16 proof from object: ${err}`); } } export const createGroth16ProofFromRisc0 = (seal: Uint8Array, imageId: Uint8Array, journalBytes: Uint8Array, controlRoot: bigint = RISC0_CONTROL_ROOT, bn254ControlId: bigint = RISC0_BN254_CONTROL_ID): Groth16Proof => { if (imageId.length > 32) { throw new Error("imageId must be 32 bytes") } const [controlRoot0, controlRoot1] = splitDigest(controlRoot); const proof = seal.slice(4); const journal_digest = createHash("sha256").update(journalBytes).digest(); const claimDigest = digestReceiptClaim(ok(imageId, journal_digest)); const [claim0, claim1] = splitDigest(claimDigest); const groth16Proof: Groth16Proof = { a: { x: toBigInt(proof.slice(0, 32)), y: toBigInt(proof.slice(32, 64)), curveId: CurveId.BN254 }, b: { x: [ toBigInt(proof.slice(96, 128)), toBigInt(proof.slice(64, 96)) ], y: [ toBigInt(proof.slice(160, 192)), toBigInt(proof.slice(128, 160)) ], curveId: CurveId.BN254 }, c: { x: toBigInt(proof.slice(192, 224)), y: toBigInt(proof.slice(224, 256)), curveId: CurveId.BN254 }, publicInputs: [ controlRoot0, controlRoot1, claim0, claim1, bn254ControlId ], imageIdJournalRisc0: { imageId, journal: journalBytes } } if (checkGroth16Proof(groth16Proof)) { return groth16Proof; } throw new Error(`Invalid Groth16 proof: ${groth16Proof}`); } export const checkGroth16Proof = (proof: Groth16Proof): boolean => { return proof.a.curveId === proof.b.curveId && proof.b.curveId === proof.c.curveId; } export const checkGroth16VerifyingKey = (vk: Groth16VerifyingKey): boolean => { if (vk.ic.length <= 1) { return false; } //check if ic points are different for (let i = 0; i < vk.ic.length; i++) { for (let j = i + 1; j < vk.ic.length; j++) { if (vk.ic[i]?.x === vk.ic[j]?.x && vk.ic[i]?.y === vk.ic[j]?.y && vk.ic[i]?.curveId === vk.ic[j]?.curveId) { return false; } } if (vk.ic[i]?.curveId !== vk.alpha.curveId) { return false; } } return vk.alpha.curveId === vk.beta.curveId && vk.beta.curveId === vk.gamma.curveId && vk.gamma.curveId === vk.delta.curveId; } // Helper: concatenate multiple Uint8Arrays const concatBytes = (...arrays: Uint8Array[]): Uint8Array => { const totalLength = arrays.reduce((sum, arr) => sum + arr.length, 0); const result = new Uint8Array(totalLength); let offset = 0; for (const arr of arrays) { result.set(arr, offset); offset += arr.length; } return result; }; // Helper: write uint32 as big-endian bytes const uint32ToBE = (value: number): Uint8Array => { const arr = new Uint8Array(4); new DataView(arr.buffer).setUint32(0, value, false); return arr; }; // Helper: write uint16 as big-endian bytes const uint16ToBE = (value: number): Uint8Array => { const arr = new Uint8Array(2); new DataView(arr.buffer).setUint16(0, value, false); return arr; }; // Helper: encode string to bytes const stringToBytes = (str: string): Uint8Array => new TextEncoder().encode(str); // Helper: bytes to hex string const bytesToHex = (bytes: Uint8Array): string => Array.from(bytes).map(b => b.toString(16).padStart(2, '0')).join(''); const digestReceiptClaim = (receipt: ReceiptClaim): Uint8Array => { const { tagDigest, input, preStateDigest, postStateDigest, output, exitCode } = receipt; const systemExitCodeBytes = uint32ToBE(exitCode.system << 24); const userExitCodeBytes = uint32ToBE(exitCode.user << 24); const twoBytes = uint16ToBE(4 << 8); const data = concatBytes( tagDigest!, input, preStateDigest, postStateDigest, output, systemExitCodeBytes, userExitCodeBytes, twoBytes ); return createHash('sha256').update(data).digest(); } function ok(imageId: Uint8Array, journalDigest: Uint8Array): ReceiptClaim { const exitCode: ExitCode = { system: 0, user: 0 }; const output: Output = { journalDigest, assumptionsDigest: new Uint8Array(32) }; return { tagDigest: createHash('sha256').update(stringToBytes("risc0.ReceiptClaim")).digest(), preStateDigest: imageId, postStateDigest: RISC0_SYSTEM_STATE_ZERO_DIGEST, exitCode, input: new Uint8Array(32), output: digestOutput(output), }; } const digestOutput = (output: Output): Uint8Array => { const { journalDigest, assumptionsDigest } = output; const tagDigest = createHash('sha256').update(stringToBytes("risc0.Output")).digest(); const twoBytes = uint16ToBE(512); const combined = concatBytes( tagDigest, journalDigest, assumptionsDigest, twoBytes ); return createHash('sha256').update(combined).digest(); } const reverseByteOrderUint256 = (value: bigint | Uint8Array): bigint => { let valueBytes: Uint8Array; if (typeof value === 'bigint') { const hexString = value.toString(16).padStart(64, '0'); valueBytes = hexStringToBytes(hexString); } else { valueBytes = new Uint8Array(32); valueBytes.set(value.slice(0, 32), 0); } const reversedBytes = valueBytes.slice().reverse(); return BigInt('0x' + bytesToHex(reversedBytes)); } const splitDigest = (digest: bigint | Uint8Array): [bigint, bigint] => { const reversedDigest = reverseByteOrderUint256(digest); return split128(reversedDigest); } export const tryGuessingCurveIdFromJson = (data: Object): CurveId | null => { try { const curveId = findValueInStringToCurveId(findItemFromKeyPatterns(data, ['curve'])); return curveId; } catch (err) { let x: bigint | null = null; for (let value in iterateNestedDictToArray(data)) { try { x = toBigInt(value); break; } catch (err) { continue; } } if (x == null || x == undefined) { throw new Error("No integer found in the JSON data."); } if (bitLength(x) > 256) { return CurveId.BLS12_381; } else { return CurveId.BN254; } } } const iterateNestedDictToArray = (d: any): any[] => { const result: any[] = []; for (const key in d) { if (Object.prototype.hasOwnProperty.call(d, key)) { const value = d[key]; if (value && typeof value === 'object' && !Array.isArray(value)) { // Recursively collect values from nested objects result.push(...iterateNestedDictToArray(value)); } else { // Add the value to the result array result.push(value); } } } return result; } const findItemFromKeyPatterns = (data: { [key: string]: any }, keyPatterns: string[]): any => { let bestMatch = null; let bestScore = -1; let bestMatchFound: boolean = false; Object.keys(data).forEach(key => { keyPatterns.forEach(pattern => { if (key.toLowerCase() == pattern.toLowerCase()) { bestMatch = data[key]; bestMatchFound = true; } else if (!bestMatchFound && key.trim().toLowerCase().includes(pattern.trim().toLowerCase())) { //count number of matching character const re = new RegExp(pattern.toLowerCase(), 'g'); const occurences = key.toLowerCase().match(re); const score = occurences ? occurences.length : 0; if (score > bestScore) { bestScore = score; bestMatch = data[key]; } } }); }); if (bestMatch !== null) { return bestMatch; } throw new KeyPatternNotFoundError(`No key found with patterns ${keyPatterns}`); } export const getPFromCurveId = (curveId: CurveId): bigint => { return CURVES[curveId].p; } const projToAffine = (x: string | number | bigint | Uint8Array, y: string | number | bigint | Uint8Array, z: string | number | bigint | Uint8Array, curveId: CurveId): G1Point => { let xBigInt = toBigInt(x); let yBigInt = toBigInt(y); let zBigInt = toBigInt(z); const p = getPFromCurveId(curveId); zBigInt = modInverse(zBigInt, p); xBigInt = xBigInt * zBigInt % p; yBigInt = yBigInt * zBigInt % p; return { x: xBigInt, y: yBigInt, curveId } } const tryParseG1PointFromKey = (data: any, keyPatterns: string[], curveId: CurveId | null): G1Point => { const point = findItemFromKeyPatterns(data, keyPatterns); if (curveId === null || curveId === undefined) { throw new Error("Curve ID not provided"); } return tryParseG1Point(point, curveId); } const tryParseG1Point = (point: any, curveId: CurveId): G1Point => { if (typeof point === "object" && !Array.isArray(point)) { const x = toBigInt(findItemFromKeyPatterns(point, ["x"])) const y = toBigInt(findItemFromKeyPatterns(point, ["y"])) return { x, y, curveId } } else if (Array.isArray(point)) { if (point.length == 2) { return { x: toBigInt(point[0]), y: toBigInt(point[1]), curveId } } else if (point.length == 3) { return projToAffine(point[0], point[1], point[2], curveId); } throw new Error(`Invalid point: ${point}`); } else { throw new Error(`Invalid point: ${point}`); } } const tryParseG2PointFromKey = (data: any, keyPatterns: string[], curveId: CurveId | null): G2Point => { const point = findItemFromKeyPatterns(data, keyPatterns); if (curveId === null || curveId === undefined) { throw new Error("Curve ID not provided"); } return tryParseG2Point(point, curveId); } const tryParseG2Point = (point: any, curveId: CurveId): G2Point => { if (typeof point === "object" && !Array.isArray(point)) { const xG2 = findItemFromKeyPatterns(point, ["x"]); const yG2 = findItemFromKeyPatterns(point, ["y"]); if (typeof xG2 === "object" && typeof yG2 === "object" && !Array.isArray(xG2) && !Array.isArray(yG2)) { return { x: [ toBigInt(findItemFromKeyPatterns(xG2, ["a0"])), toBigInt(findItemFromKeyPatterns(xG2, ["a1"])) ], y: [ toBigInt(findItemFromKeyPatterns(yG2, ["a0"])), toBigInt(findItemFromKeyPatterns(yG2, ["a1"])) ], curveId: curveId }; } else if (Array.isArray(xG2) && Array.isArray(yG2)) { return { x: [toBigInt(xG2[0]), toBigInt(xG2[1])], y: [toBigInt(yG2[0]), toBigInt(yG2[1])], curveId: curveId }; } else { throw new Error(`Invalid point: ${point}`); } } else if (Array.isArray(point)) { let supposedX, supposedY; if (point.length === 2) { supposedX = point[0]; supposedY = point[1]; } else if (point.length === 3) { const check = [ toBigInt(point[2][0]), toBigInt(point[2][1]) ]; if (check[0] !== 1n || check[1] !== 0n) { throw new Error("Non standard projective coordinates"); } supposedX = point[0]; supposedY = point[1]; } if (Array.isArray(supposedX)) { if (supposedX.length !== 2) { throw new Error(`Invalid fp2 coordinates: ${supposedX}`); } supposedX = [toBigInt(supposedX[0]), toBigInt(supposedX[1])]; } if (Array.isArray(supposedY)) { if (supposedY.length !== 2) { throw new Error(`Invalid fp2 coordinates: ${supposedY}`); } supposedY = [toBigInt(supposedY[0]), toBigInt(supposedY[1])]; } return { x: supposedX, y: supposedY, curveId: curveId }; } else { throw new Error(`Invalid point: ${point}`); } } export const createGroth16ProofFromSp1 = (vkey: Uint8Array, publicValues: Uint8Array, proof: Uint8Array): Groth16Proof => { // SP1 version checking - first 4 bytes should match expected hash const sp1VerifierHashBytes = hexStringToBytes(SP1_VERIFIER_HASH); const selector = proof.slice(0, 4); const expectedSelector = sp1VerifierHashBytes.slice(0, 4); if (!selector.every((byte, index) => byte === expectedSelector[index])) { throw new Error(`Invalid SP1 proof version. Expected ${Array.from(expectedSelector).map(b => b.toString(16).padStart(2, '0')).join('')} for version ${SP1_VERIFIER_VERSION}, got ${Array.from(selector).map(b => b.toString(16).padStart(2, '0')).join('')}`); } if (publicValues.length % 32 !== 0) { throw new Error("SP1 public values must be a multiple of 32 bytes"); } // Hash public values and take mod 2^253 const pubInputHash = createHash("sha256").update(publicValues).digest(); const power253 = 1n << 253n; // 2^253 using bit shift const pubInputHashBigInt = toBigInt(pubInputHash) % power253; const actualProof = proof.slice(4); const groth16Proof: Groth16Proof = { a: { x: toBigInt(actualProof.slice(0, 32)), y: toBigInt(actualProof.slice(32, 64)), curveId: CurveId.BN254 }, b: { x: [ toBigInt(actualProof.slice(96, 128)), toBigInt(actualProof.slice(64, 96)) ], y: [ toBigInt(actualProof.slice(160, 192)), toBigInt(actualProof.slice(128, 160)) ], curveId: CurveId.BN254 }, c: { x: toBigInt(actualProof.slice(192, 224)), y: toBigInt(actualProof.slice(224, 256)), curveId: CurveId.BN254 }, publicInputs: [ toBigInt(vkey), pubInputHashBigInt ], vkeyPublicValuesSp1: { vkey, publicValues } }; if (checkGroth16Proof(groth16Proof)) { return groth16Proof; } throw new Error(`Invalid SP1 Groth16 proof: ${groth16Proof}`); }; ================================================ FILE: tools/npm/garaga_ts/src/node/starknet/honkContractGenerator/parsingUtils.ts ================================================ export enum HonkFlavor { KECCAK = 0, STARKNET = 1, } ================================================ FILE: tools/npm/garaga_ts/src/wasm/pkg/garaga_rs.d.ts ================================================ /* tslint:disable */ /* eslint-disable */ export function drand_calldata_builder(values: any[]): any[]; export function drand_tlock_encrypt_calldata_builder(values: any[]): any[]; export function msm_calldata_builder(values: any[], scalars: any[], curve_id: number, include_points_and_scalars: boolean, serialize_as_pure_felt252_array: boolean): any[]; export function mpc_calldata_builder(curve_id: number, values1: any[], n_fixed_g2: number, values2: any[]): any[]; export function schnorr_calldata_builder(rx: any, s: any, e: any, px: any, py: any, prepend_public_key: boolean, curve_id: number): any[]; export function ecdsa_calldata_builder(r: any, s: any, v: number, px: any, py: any, z: any, prepend_public_key: boolean, curve_id: number): any[]; export function eddsa_calldata_builder(ry_twisted: any, s: any, py_twisted: any, msg: any, prepend_public_key: boolean): any[]; export function rsa_2048_calldata_builder(signature: any, expected_message: any, modulus: any, prepend_public_key: boolean): any[]; export function rsa_2048_sha256_calldata_builder(signature: any, message: any, modulus: any, prepend_public_key: boolean): any[]; export function to_weirstrass(x_twisted: any, y_twisted: any): any[]; export function to_twistededwards(x_weirstrass: any, y_weirstrass: any): any[]; export function get_groth16_calldata(proof_js: any, vk_js: any, curve_id_js: any): any[]; export function get_zk_honk_calldata(proof_js: any, public_inputs_js: any, vk_js: any): any[]; export function poseidon_hash(x: any, y: any): any; export type InitInput = RequestInfo | URL | Response | BufferSource | WebAssembly.Module; export interface InitOutput { readonly memory: WebAssembly.Memory; readonly drand_calldata_builder: (a: number, b: number) => [number, number, number, number]; readonly drand_tlock_encrypt_calldata_builder: (a: number, b: number) => [number, number, number, number]; readonly msm_calldata_builder: (a: number, b: number, c: number, d: number, e: number, f: number, g: number) => [number, number, number, number]; readonly mpc_calldata_builder: (a: number, b: number, c: number, d: number, e: number, f: number) => [number, number, number, number]; readonly schnorr_calldata_builder: (a: any, b: any, c: any, d: any, e: any, f: number, g: number) => [number, number, number, number]; readonly ecdsa_calldata_builder: (a: any, b: any, c: number, d: any, e: any, f: any, g: number, h: number) => [number, number, number, number]; readonly eddsa_calldata_builder: (a: any, b: any, c: any, d: any, e: number) => [number, number, number, number]; readonly rsa_2048_calldata_builder: (a: any, b: any, c: any, d: number) => [number, number, number, number]; readonly rsa_2048_sha256_calldata_builder: (a: any, b: any, c: any, d: number) => [number, number, number, number]; readonly to_weirstrass: (a: any, b: any) => [number, number, number, number]; readonly to_twistededwards: (a: any, b: any) => [number, number, number, number]; readonly get_groth16_calldata: (a: any, b: any, c: any) => [number, number, number, number]; readonly get_zk_honk_calldata: (a: any, b: any, c: any) => [number, number, number, number]; readonly poseidon_hash: (a: any, b: any) => [number, number, number]; readonly __wbindgen_exn_store: (a: number) => void; readonly __externref_table_alloc: () => number; readonly __wbindgen_export_2: WebAssembly.Table; readonly __wbindgen_malloc: (a: number, b: number) => number; readonly __wbindgen_realloc: (a: number, b: number, c: number, d: number) => number; readonly __externref_table_dealloc: (a: number) => void; readonly __externref_drop_slice: (a: number, b: number) => void; readonly __wbindgen_free: (a: number, b: number, c: number) => void; readonly __wbindgen_start: () => void; } export type SyncInitInput = BufferSource | WebAssembly.Module; /** * Instantiates the given `module`, which can either be bytes or * a precompiled `WebAssembly.Module`. * * @param {{ module: SyncInitInput }} module - Passing `SyncInitInput` directly is deprecated. * * @returns {InitOutput} */ export function initSync(module: { module: SyncInitInput } | SyncInitInput): InitOutput; /** * If `module_or_path` is {RequestInfo} or {URL}, makes a request and * for everything else, calls `WebAssembly.instantiate` directly. * * @param {{ module_or_path: InitInput | Promise }} module_or_path - Passing `InitInput` directly is deprecated. * * @returns {Promise} */ export default function __wbg_init (module_or_path?: { module_or_path: InitInput | Promise } | InitInput | Promise): Promise; ================================================ FILE: tools/npm/garaga_ts/src/wasm/pkg/garaga_rs.js ================================================ let wasm; function addToExternrefTable0(obj) { const idx = wasm.__externref_table_alloc(); wasm.__wbindgen_export_2.set(idx, obj); return idx; } function handleError(f, args) { try { return f.apply(this, args); } catch (e) { const idx = addToExternrefTable0(e); wasm.__wbindgen_exn_store(idx); } } const cachedTextDecoder = (typeof TextDecoder !== 'undefined' ? new TextDecoder('utf-8', { ignoreBOM: true, fatal: true }) : { decode: () => { throw Error('TextDecoder not available') } } ); if (typeof TextDecoder !== 'undefined') { cachedTextDecoder.decode(); }; let cachedUint8ArrayMemory0 = null; function getUint8ArrayMemory0() { if (cachedUint8ArrayMemory0 === null || cachedUint8ArrayMemory0.byteLength === 0) { cachedUint8ArrayMemory0 = new Uint8Array(wasm.memory.buffer); } return cachedUint8ArrayMemory0; } function getStringFromWasm0(ptr, len) { ptr = ptr >>> 0; return cachedTextDecoder.decode(getUint8ArrayMemory0().subarray(ptr, ptr + len)); } function debugString(val) { // primitive types const type = typeof val; if (type == 'number' || type == 'boolean' || val == null) { return `${val}`; } if (type == 'string') { return `"${val}"`; } if (type == 'symbol') { const description = val.description; if (description == null) { return 'Symbol'; } else { return `Symbol(${description})`; } } if (type == 'function') { const name = val.name; if (typeof name == 'string' && name.length > 0) { return `Function(${name})`; } else { return 'Function'; } } // objects if (Array.isArray(val)) { const length = val.length; let debug = '['; if (length > 0) { debug += debugString(val[0]); } for(let i = 1; i < length; i++) { debug += ', ' + debugString(val[i]); } debug += ']'; return debug; } // Test for built-in const builtInMatches = /\[object ([^\]]+)\]/.exec(toString.call(val)); let className; if (builtInMatches && builtInMatches.length > 1) { className = builtInMatches[1]; } else { // Failed to match the standard '[object ClassName]' return toString.call(val); } if (className == 'Object') { // we're a user defined class or Object // JSON.stringify avoids problems with cycles, and is generally much // easier than looping through ownProperties of `val`. try { return 'Object(' + JSON.stringify(val) + ')'; } catch (_) { return 'Object'; } } // errors if (val instanceof Error) { return `${val.name}: ${val.message}\n${val.stack}`; } // TODO we could test for more things here, like `Set`s and `Map`s. return className; } let WASM_VECTOR_LEN = 0; const cachedTextEncoder = (typeof TextEncoder !== 'undefined' ? new TextEncoder('utf-8') : { encode: () => { throw Error('TextEncoder not available') } } ); const encodeString = (typeof cachedTextEncoder.encodeInto === 'function' ? function (arg, view) { return cachedTextEncoder.encodeInto(arg, view); } : function (arg, view) { const buf = cachedTextEncoder.encode(arg); view.set(buf); return { read: arg.length, written: buf.length }; }); function passStringToWasm0(arg, malloc, realloc) { if (realloc === undefined) { const buf = cachedTextEncoder.encode(arg); const ptr = malloc(buf.length, 1) >>> 0; getUint8ArrayMemory0().subarray(ptr, ptr + buf.length).set(buf); WASM_VECTOR_LEN = buf.length; return ptr; } let len = arg.length; let ptr = malloc(len, 1) >>> 0; const mem = getUint8ArrayMemory0(); let offset = 0; for (; offset < len; offset++) { const code = arg.charCodeAt(offset); if (code > 0x7F) break; mem[ptr + offset] = code; } if (offset !== len) { if (offset !== 0) { arg = arg.slice(offset); } ptr = realloc(ptr, len, len = offset + arg.length * 3, 1) >>> 0; const view = getUint8ArrayMemory0().subarray(ptr + offset, ptr + len); const ret = encodeString(arg, view); offset += ret.written; ptr = realloc(ptr, len, offset, 1) >>> 0; } WASM_VECTOR_LEN = offset; return ptr; } let cachedDataViewMemory0 = null; function getDataViewMemory0() { if (cachedDataViewMemory0 === null || cachedDataViewMemory0.buffer.detached === true || (cachedDataViewMemory0.buffer.detached === undefined && cachedDataViewMemory0.buffer !== wasm.memory.buffer)) { cachedDataViewMemory0 = new DataView(wasm.memory.buffer); } return cachedDataViewMemory0; } function isLikeNone(x) { return x === undefined || x === null; } function passArrayJsValueToWasm0(array, malloc) { const ptr = malloc(array.length * 4, 4) >>> 0; for (let i = 0; i < array.length; i++) { const add = addToExternrefTable0(array[i]); getDataViewMemory0().setUint32(ptr + 4 * i, add, true); } WASM_VECTOR_LEN = array.length; return ptr; } function takeFromExternrefTable0(idx) { const value = wasm.__wbindgen_export_2.get(idx); wasm.__externref_table_dealloc(idx); return value; } function getArrayJsValueFromWasm0(ptr, len) { ptr = ptr >>> 0; const mem = getDataViewMemory0(); const result = []; for (let i = ptr; i < ptr + 4 * len; i += 4) { result.push(wasm.__wbindgen_export_2.get(mem.getUint32(i, true))); } wasm.__externref_drop_slice(ptr, len); return result; } /** * @param {any[]} values * @returns {any[]} */ export function drand_calldata_builder(values) { const ptr0 = passArrayJsValueToWasm0(values, wasm.__wbindgen_malloc); const len0 = WASM_VECTOR_LEN; const ret = wasm.drand_calldata_builder(ptr0, len0); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v2 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v2; } /** * @param {any[]} values * @returns {any[]} */ export function drand_tlock_encrypt_calldata_builder(values) { const ptr0 = passArrayJsValueToWasm0(values, wasm.__wbindgen_malloc); const len0 = WASM_VECTOR_LEN; const ret = wasm.drand_tlock_encrypt_calldata_builder(ptr0, len0); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v2 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v2; } /** * @param {any[]} values * @param {any[]} scalars * @param {number} curve_id * @param {boolean} include_points_and_scalars * @param {boolean} serialize_as_pure_felt252_array * @returns {any[]} */ export function msm_calldata_builder(values, scalars, curve_id, include_points_and_scalars, serialize_as_pure_felt252_array) { const ptr0 = passArrayJsValueToWasm0(values, wasm.__wbindgen_malloc); const len0 = WASM_VECTOR_LEN; const ptr1 = passArrayJsValueToWasm0(scalars, wasm.__wbindgen_malloc); const len1 = WASM_VECTOR_LEN; const ret = wasm.msm_calldata_builder(ptr0, len0, ptr1, len1, curve_id, include_points_and_scalars, serialize_as_pure_felt252_array); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v3 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v3; } /** * @param {number} curve_id * @param {any[]} values1 * @param {number} n_fixed_g2 * @param {any[]} values2 * @returns {any[]} */ export function mpc_calldata_builder(curve_id, values1, n_fixed_g2, values2) { const ptr0 = passArrayJsValueToWasm0(values1, wasm.__wbindgen_malloc); const len0 = WASM_VECTOR_LEN; const ptr1 = passArrayJsValueToWasm0(values2, wasm.__wbindgen_malloc); const len1 = WASM_VECTOR_LEN; const ret = wasm.mpc_calldata_builder(curve_id, ptr0, len0, n_fixed_g2, ptr1, len1); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v3 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v3; } /** * @param {any} rx * @param {any} s * @param {any} e * @param {any} px * @param {any} py * @param {boolean} prepend_public_key * @param {number} curve_id * @returns {any[]} */ export function schnorr_calldata_builder(rx, s, e, px, py, prepend_public_key, curve_id) { const ret = wasm.schnorr_calldata_builder(rx, s, e, px, py, prepend_public_key, curve_id); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} r * @param {any} s * @param {number} v * @param {any} px * @param {any} py * @param {any} z * @param {boolean} prepend_public_key * @param {number} curve_id * @returns {any[]} */ export function ecdsa_calldata_builder(r, s, v, px, py, z, prepend_public_key, curve_id) { const ret = wasm.ecdsa_calldata_builder(r, s, v, px, py, z, prepend_public_key, curve_id); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} ry_twisted * @param {any} s * @param {any} py_twisted * @param {any} msg * @param {boolean} prepend_public_key * @returns {any[]} */ export function eddsa_calldata_builder(ry_twisted, s, py_twisted, msg, prepend_public_key) { const ret = wasm.eddsa_calldata_builder(ry_twisted, s, py_twisted, msg, prepend_public_key); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} signature * @param {any} expected_message * @param {any} modulus * @param {boolean} prepend_public_key * @returns {any[]} */ export function rsa_2048_calldata_builder(signature, expected_message, modulus, prepend_public_key) { const ret = wasm.rsa_2048_calldata_builder(signature, expected_message, modulus, prepend_public_key); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} signature * @param {any} message * @param {any} modulus * @param {boolean} prepend_public_key * @returns {any[]} */ export function rsa_2048_sha256_calldata_builder(signature, message, modulus, prepend_public_key) { const ret = wasm.rsa_2048_sha256_calldata_builder(signature, message, modulus, prepend_public_key); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} x_twisted * @param {any} y_twisted * @returns {any[]} */ export function to_weirstrass(x_twisted, y_twisted) { const ret = wasm.to_weirstrass(x_twisted, y_twisted); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} x_weirstrass * @param {any} y_weirstrass * @returns {any[]} */ export function to_twistededwards(x_weirstrass, y_weirstrass) { const ret = wasm.to_twistededwards(x_weirstrass, y_weirstrass); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} proof_js * @param {any} vk_js * @param {any} curve_id_js * @returns {any[]} */ export function get_groth16_calldata(proof_js, vk_js, curve_id_js) { const ret = wasm.get_groth16_calldata(proof_js, vk_js, curve_id_js); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} proof_js * @param {any} public_inputs_js * @param {any} vk_js * @returns {any[]} */ export function get_zk_honk_calldata(proof_js, public_inputs_js, vk_js) { const ret = wasm.get_zk_honk_calldata(proof_js, public_inputs_js, vk_js); if (ret[3]) { throw takeFromExternrefTable0(ret[2]); } var v1 = getArrayJsValueFromWasm0(ret[0], ret[1]).slice(); wasm.__wbindgen_free(ret[0], ret[1] * 4, 4); return v1; } /** * @param {any} x * @param {any} y * @returns {any} */ export function poseidon_hash(x, y) { const ret = wasm.poseidon_hash(x, y); if (ret[2]) { throw takeFromExternrefTable0(ret[1]); } return takeFromExternrefTable0(ret[0]); } async function __wbg_load(module, imports) { if (typeof Response === 'function' && module instanceof Response) { if (typeof WebAssembly.instantiateStreaming === 'function') { try { return await WebAssembly.instantiateStreaming(module, imports); } catch (e) { if (module.headers.get('Content-Type') != 'application/wasm') { console.warn("`WebAssembly.instantiateStreaming` failed because your server does not serve Wasm with `application/wasm` MIME type. Falling back to `WebAssembly.instantiate` which is slower. Original error:\n", e); } else { throw e; } } } const bytes = await module.arrayBuffer(); return await WebAssembly.instantiate(bytes, imports); } else { const instance = await WebAssembly.instantiate(module, imports); if (instance instanceof WebAssembly.Instance) { return { instance, module }; } else { return instance; } } } function __wbg_get_imports() { const imports = {}; imports.wbg = {}; imports.wbg.__wbg_buffer_609cc3eee51ed158 = function(arg0) { const ret = arg0.buffer; return ret; }; imports.wbg.__wbg_get_67b2ba62fc30de12 = function() { return handleError(function (arg0, arg1) { const ret = Reflect.get(arg0, arg1); return ret; }, arguments) }; imports.wbg.__wbg_get_b9b93047fe3cf45b = function(arg0, arg1) { const ret = arg0[arg1 >>> 0]; return ret; }; imports.wbg.__wbg_instanceof_Object_7f2dcef8f78644a4 = function(arg0) { let result; try { result = arg0 instanceof Object; } catch (_) { result = false; } const ret = result; return ret; }; imports.wbg.__wbg_instanceof_Uint8Array_17156bcf118086a9 = function(arg0) { let result; try { result = arg0 instanceof Uint8Array; } catch (_) { result = false; } const ret = result; return ret; }; imports.wbg.__wbg_isArray_a1eab7e0d067391b = function(arg0) { const ret = Array.isArray(arg0); return ret; }; imports.wbg.__wbg_length_a446193dc22c12f8 = function(arg0) { const ret = arg0.length; return ret; }; imports.wbg.__wbg_length_e2d2a49132c1b256 = function(arg0) { const ret = arg0.length; return ret; }; imports.wbg.__wbg_new_a12002a7f91c75be = function(arg0) { const ret = new Uint8Array(arg0); return ret; }; imports.wbg.__wbg_set_65595bdd868b3009 = function(arg0, arg1, arg2) { arg0.set(arg1, arg2 >>> 0); }; imports.wbg.__wbindgen_add = function(arg0, arg1) { const ret = arg0 + arg1; return ret; }; imports.wbg.__wbindgen_bigint_from_str = function(arg0, arg1) { const ret = BigInt(getStringFromWasm0(arg0, arg1)); return ret; }; imports.wbg.__wbindgen_debug_string = function(arg0, arg1) { const ret = debugString(arg1); const ptr1 = passStringToWasm0(ret, wasm.__wbindgen_malloc, wasm.__wbindgen_realloc); const len1 = WASM_VECTOR_LEN; getDataViewMemory0().setInt32(arg0 + 4 * 1, len1, true); getDataViewMemory0().setInt32(arg0 + 4 * 0, ptr1, true); }; imports.wbg.__wbindgen_init_externref_table = function() { const table = wasm.__wbindgen_export_2; const offset = table.grow(4); table.set(0, undefined); table.set(offset + 0, undefined); table.set(offset + 1, null); table.set(offset + 2, true); table.set(offset + 3, false); ; }; imports.wbg.__wbindgen_is_null = function(arg0) { const ret = arg0 === null; return ret; }; imports.wbg.__wbindgen_is_undefined = function(arg0) { const ret = arg0 === undefined; return ret; }; imports.wbg.__wbindgen_memory = function() { const ret = wasm.memory; return ret; }; imports.wbg.__wbindgen_number_get = function(arg0, arg1) { const obj = arg1; const ret = typeof(obj) === 'number' ? obj : undefined; getDataViewMemory0().setFloat64(arg0 + 8 * 1, isLikeNone(ret) ? 0 : ret, true); getDataViewMemory0().setInt32(arg0 + 4 * 0, !isLikeNone(ret), true); }; imports.wbg.__wbindgen_string_get = function(arg0, arg1) { const obj = arg1; const ret = typeof(obj) === 'string' ? obj : undefined; var ptr1 = isLikeNone(ret) ? 0 : passStringToWasm0(ret, wasm.__wbindgen_malloc, wasm.__wbindgen_realloc); var len1 = WASM_VECTOR_LEN; getDataViewMemory0().setInt32(arg0 + 4 * 1, len1, true); getDataViewMemory0().setInt32(arg0 + 4 * 0, ptr1, true); }; imports.wbg.__wbindgen_string_new = function(arg0, arg1) { const ret = getStringFromWasm0(arg0, arg1); return ret; }; imports.wbg.__wbindgen_throw = function(arg0, arg1) { throw new Error(getStringFromWasm0(arg0, arg1)); }; return imports; } function __wbg_init_memory(imports, memory) { } function __wbg_finalize_init(instance, module) { wasm = instance.exports; __wbg_init.__wbindgen_wasm_module = module; cachedDataViewMemory0 = null; cachedUint8ArrayMemory0 = null; wasm.__wbindgen_start(); return wasm; } function initSync(module) { if (wasm !== undefined) return wasm; if (typeof module !== 'undefined') { if (Object.getPrototypeOf(module) === Object.prototype) { ({module} = module) } else { console.warn('using deprecated parameters for `initSync()`; pass a single object instead') } } const imports = __wbg_get_imports(); __wbg_init_memory(imports); if (!(module instanceof WebAssembly.Module)) { module = new WebAssembly.Module(module); } const instance = new WebAssembly.Instance(module, imports); return __wbg_finalize_init(instance, module); } async function __wbg_init(module_or_path) { if (wasm !== undefined) return wasm; if (typeof module_or_path !== 'undefined') { if (Object.getPrototypeOf(module_or_path) === Object.prototype) { ({module_or_path} = module_or_path) } else { console.warn('using deprecated parameters for the initialization function; pass a single object instead') } } if (typeof module_or_path === 'undefined') { throw new Error(); } const imports = __wbg_get_imports(); if (typeof module_or_path === 'string' || (typeof Request === 'function' && module_or_path instanceof Request) || (typeof URL === 'function' && module_or_path instanceof URL)) { module_or_path = fetch(module_or_path); } __wbg_init_memory(imports); const { instance, module } = await __wbg_load(await module_or_path, imports); return __wbg_finalize_init(instance, module); } export { initSync }; export default __wbg_init; ================================================ FILE: tools/npm/garaga_ts/src/wasm/pkg/garaga_rs_bg.wasm.d.ts ================================================ declare const wasm_module_base64: string; export default wasm_module_base64; ================================================ FILE: tools/npm/garaga_ts/src/wasm/pkg/garaga_rs_bg.wasm.js ================================================ export default 'data:application/wasm;base64,AGFzbQEAAAABoQM0YAJ/fwBgA39/fwBgAn9/AX9gA39/fwF/YAF/AGAEf39/fwBgAAR/f39/YAV/f39/fwBgAX8Bf2ABbwF/YAV/f39/fwF/YAAAYAZ/f39/f38AYAABf2ACf28AYAh/f39/f39/fwBgA39/fwF+YAR/f39/AX9gAn9/AW9gAm9vAW9gAW8Bb2AJf39/f39/f39/AGAHf39/f39/fwBgCn9/f39/f39/f38AYAZ/f39/f38Bf2AHf39/f39/fwF/YARvb29/BH9/f39gA29vbwR/f39/YAJ/fwR/f39/YAJvbwR/f39/YAADf39/YAJvfwFvYANvb38AYAABb2ADf39+AGACf34AYAN/fn4AYAF8AXxgC39/f39/f39/f39/AX9gBX9+fn5+AGAIb29/b29vf38Ef39/f2AHf39/f39/fwR/f39/YAdvb29vb39/BH9/f39gBn9/f39/fwR/f39/YAVvb29vfwR/f39/YAJvbwN/f39gBX9/fX9/AGAEf31/fwBgBX9/fn9/AGAEf35/fwBgBX9/fH9/AGAEf3x/fwACrAUVA3diZxVfX3diaW5kZ2VuX3N0cmluZ19uZXcAEgN3YmcOX193YmluZGdlbl9hZGQAEwN3YmcVX193YmluZGdlbl9zdHJpbmdfZ2V0AA4Dd2JnGl9fd2JpbmRnZW5fYmlnaW50X2Zyb21fc3RyABIDd2JnF19fd2JpbmRnZW5faXNfdW5kZWZpbmVkAAkDd2JnEl9fd2JpbmRnZW5faXNfbnVsbAAJA3diZxVfX3diaW5kZ2VuX251bWJlcl9nZXQADgN3YmcaX193YmdfZ2V0X2I5YjkzMDQ3ZmUzY2Y0NWIAHwN3YmcdX193YmdfbGVuZ3RoX2UyZDJhNDkxMzJjMWIyNTYACQN3YmcaX193YmdfZ2V0XzY3YjJiYTYyZmMzMGRlMTIAEwN3YmceX193YmdfaXNBcnJheV9hMWVhYjdlMGQwNjczOTFiAAkDd2JnKF9fd2JnX2luc3RhbmNlb2ZfT2JqZWN0XzdmMmRjZWY4Zjc4NjQ0YTQACQN3YmcdX193YmdfYnVmZmVyXzYwOWNjM2VlZTUxZWQxNTgAFAN3YmcaX193YmdfbmV3X2ExMjAwMmE3ZjkxYzc1YmUAFAN3YmcaX193Ymdfc2V0XzY1NTk1YmRkODY4YjMwMDkAIAN3YmcdX193YmdfbGVuZ3RoX2E0NDYxOTNkYzIyYzEyZjgACQN3YmcsX193YmdfaW5zdGFuY2VvZl9VaW50OEFycmF5XzE3MTU2YmNmMTE4MDg2YTkACQN3YmcXX193YmluZGdlbl9kZWJ1Z19zdHJpbmcADgN3YmcQX193YmluZGdlbl90aHJvdwAAA3diZxFfX3diaW5kZ2VuX21lbW9yeQAhA3diZx9fX3diaW5kZ2VuX2luaXRfZXh0ZXJucmVmX3RhYmxlAAsD9QTzBAEAAQEHAQAPAQAABwQBAQUFBAEHDAAHAQEAAAAFBwEAAQEHAQEEAQEABAEBBwcBAAEEABUEBAABABUFBwEBCAEEAQABAQEBAQAAARYAAQAFAAABAAAIBQEEAQEBAAAAAQQAAQcBAQUBAQEBAQEAAQEAAQEAAQEBBAEBAAwBAQEBAQEBAQcBAQEBAQAAAQUFAAUAAQEHAAcBAAEAAAEBAAAAAAAAAAABBQEAAAEHAQAFBAAFAAABAAAAIgUXBQ8BAAECAgABFw8BAQAAAAEADQEBAAAABQABBQEBAQEFAAABAAEAAAAAAQEBAQEBAAEBFgAAAQEYAQEBAAAAAAABBAADAAEAAAIBAQEBAgEAAgAFAgEBAAEAAwMAAAABAQEAAAUAAQABBAAjAQAEBQEBAAACBQABAQEEASQFBQQAAAICAAEAAAAAAAAAAwIAAgICAgAMJRAQGQQABwIBAAgAAgAAAAAAAQQABAABAgEBCg0BAQIEBwEAAQEKAQAAAQACAgEBBAcAAAAAAAQAAQUAAAAABAEAACYEAA0AABkADAgAAAACBQIACAIAAAQAAQICAgIAAAInBwICAgICAgIIAQACBAQAAQQAAgIIAgICAgICBAICAQAFAgMCBAMLAwQEBAsDAAICAgIAAAEEASgEAgICAAIpKgICAgIKKwICAgAFBQIFLAIEBBoaAhsbCBwcHR0CAgAtABECAgQCGAICAgICAgIKLgcwMgQEBAQEAgUCAwQNAQICBAQCEQEDAgcCAgICAgQAAAACAgIACAgIBQEBAQIEAgICAgICAgICAgICAgICCwECAgACAgACAwAACAgICAQLAnABnAGcAW8AgAEFAwEAEgYJAX8BQYCAwAALB8UEGAZtZW1vcnkCABZkcmFuZF9jYWxsZGF0YV9idWlsZGVyAKIEJGRyYW5kX3Rsb2NrX2VuY3J5cHRfY2FsbGRhdGFfYnVpbGRlcgCjBBRtc21fY2FsbGRhdGFfYnVpbGRlcgCIBBRtcGNfY2FsbGRhdGFfYnVpbGRlcgCPBBhzY2hub3JyX2NhbGxkYXRhX2J1aWxkZXIAiQQWZWNkc2FfY2FsbGRhdGFfYnVpbGRlcgCBBBZlZGRzYV9jYWxsZGF0YV9idWlsZGVyAJgEGXJzYV8yMDQ4X2NhbGxkYXRhX2J1aWxkZXIAnAQgcnNhXzIwNDhfc2hhMjU2X2NhbGxkYXRhX2J1aWxkZXIAnQQNdG9fd2VpcnN0cmFzcwCkBBF0b190d2lzdGVkZWR3YXJkcwClBBRnZXRfZ3JvdGgxNl9jYWxsZGF0YQCfBBRnZXRfemtfaG9ua19jYWxsZGF0YQCgBA1wb3NlaWRvbl9oYXNoAKkEFF9fd2JpbmRnZW5fZXhuX3N0b3JlANgEF19fZXh0ZXJucmVmX3RhYmxlX2FsbG9jAK0DE19fd2JpbmRnZW5fZXhwb3J0XzIBARFfX3diaW5kZ2VuX21hbGxvYwCZBBJfX3diaW5kZ2VuX3JlYWxsb2MAqwQZX19leHRlcm5yZWZfdGFibGVfZGVhbGxvYwCrAxZfX2V4dGVybnJlZl9kcm9wX3NsaWNlAJIDD19fd2JpbmRnZW5fZnJlZQDPBBBfX3diaW5kZ2VuX3N0YXJ0ABQJvQIBAEEBC5sBlAPzBIMEvwTLA8AE0APcA9oD0QPBBKIC9gTnBNYB7QOxBNQExgTsA+EC7ATpBMIErwSLBMAE0wTdA5AEkQSSBO4EywS3A9ME6wTEBPAExgTsA+IC6gTfA9UDsgSEBPsD+gOMBI0E6wP/AvkDrQSzBOkC6ALvBNMEuQOTA8YE7APfAu0E4AOWBOEDxgTsA+MC8QS/A88D2gOuBM4DvwTNA9cDzAPyBOIDtATjA4UEvwTABJoC1QT0BKwEtgTGBOwD5AL1BLUE5AOKBMYE0wS3BLgEsgO6BLgEsATFBMMEugS6BLkEvAS7BNUEzASfAocE+gTmA4ME5wOeBNsDxgTvA/MC+wTaBNkE3AT9A9sE/AS9BMgDigOpA4MFxgT2A+4C/QT+BNEE3QTeBKUCvAOGA6wC+AOABQwBNgrqj27zBLeHAgIIfyZ+IwBB8CdrIgMkAAJAAkACQAJAAkACQAJAIAJB4ABqIgVBwI3FAEEwEPEDBEAgAUHgAGoiBkHAjcUAQTAQ8QNFDQIgAikDMCEZIAIpAzghFiACKQNAIRcgAikDSCEVIAIpA1AhEyACKQNYIRFBiAEhBANAIANB4BtqIAEgBGopAwAiDkIAIBFCABDJAyADQfAbaiAOQgAgE0IAEMkDIANBgBxqIA5CACAVQgAQyQMgA0GQHGogDkIAIBdCABDJAyADQaAcaiAOQgAgFkIAEMkDIANBsBxqIA5CACAZQgAQyQMgA0HQG2ogAykD4BsiEiAUfCIcQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgA0HAG2ogDkIAQv//z4rr///VHkIAEMkDIANBsBtqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0GgG2ogDkIAQr+llJzP8NK75ABCABDJAyADQZAbaiAOQgBC19mumuT26Y3LAEIAEMkDIANBgBtqIA5CAEKazf/Lo73EgBpCABDJAyADKQOIGyADKQOwHCIOIA18IhogAykDqBwgAykDoBwiDSAQfCIYIA1UrXwgGCADKQOYHCALIAMpA5AcIgt8IhAgC1StfCAQIAMpA4gcIAMpA4AcIgsgDHwiDCALVK18IAwgAykD+BsgAykD8BsiCyAPfCINIAtUrXwgDSADKQPoGyASIBxWrXx8IgsgDVStfHwiDyAMVK18fCIMIBBUrXx8Ig0gGFStfHwiGyADKQOAG3wiGCAbVK18IBggAykDmBsgDSADKQOQG3wiECANVK18IBAgAykDqBsgDCADKQOgG3wiEiAMVK18IBIgAykDuBsgDyADKQOwG3wiDCAPVK18IAwgAykDyBsgCyADKQPAGyILfCINIAtUrXwgDSADKQPYGyADKQPQGyILIBx8IAtUrXx8IhQgDVStfHwiDyAMVK18fCIMIBJUrXx8IgsgEFStfHwiECAYVK18IBogG1atIAMpA7gcIA4gGlatfHx8IQ0gBEEIayIEQdgARw0ACyANQprN/8ujvcSAGlgNAQwECyADQbgfaiABQShqKQMANwMAIANBsB9qIAFBIGopAwA3AwAgA0GoH2ogAUEYaikDADcDACADQaAfaiABQRBqKQMANwMAIANBmB9qIAFBCGopAwA3AwAgA0HIH2ogAUE4aikDADcDACADQdAfaiABQUBrKQMANwMAIANB2B9qIAFByABqKQMANwMAIANB4B9qIAFB0ABqKQMANwMAIANB6B9qIAFB2ABqKQMANwMAIAMgASkDADcDkB8gAyABKQMwNwPAHyADQZggaiABQYgBaikDADcDACADQZAgaiABQYABaikDADcDACADQYggaiABQfgAaikDADcDACADQYAgaiABQfAAaikDADcDACADQfgfaiABQegAaikDADcDACADIAEpA2A3A/AfIAAgA0GQH2pBkAH8CgAADAULIA1Cms3/y6O9xIAaUQ0BIA8hDiAMIRIgCyERIBAhEwwDCyADQcggaiACQShqKQMANwMAIANBwCBqIAJBIGopAwA3AwAgA0G4IGogAkEYaikDADcDACADQbAgaiACQRBqKQMANwMAIANBqCBqIAJBCGopAwA3AwAgA0HYIGogAkEwaiIBQQhqKQMANwMAIANB4CBqIAFBEGopAwA3AwAgA0HoIGogAUEYaikDADcDACADQfAgaiABQSBqKQMANwMAIANB+CBqIAFBKGopAwA3AwAgAyACKQMANwOgICADIAEpAwA3A9AgIANBqCFqIAVBKGopAwA3AwAgA0GgIWogBUEgaikDADcDACADQZghaiAFQRhqKQMANwMAIANBkCFqIAVBEGopAwA3AwAgA0GIIWogBUEIaikDADcDACADIAUpAwA3A4AhIAAgA0GgIGpBkAH8CgAADAMLIBBC19mumuT26Y3LAFYNAAJAIBBC19mumuT26Y3LAFIEQCAPIQ4gDCESIAshESAQIRMMAQsgC0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhEyALQr+llJzP8NK75ABSBEAgDyEOIAwhEiALIREMAQsgDEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhESAMQqTsw7WP1LSY5wBSBEAgDyEOIAwhEgwBCyAPQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRIgD0L//8+K6///1R5SBEAgDyEODAELQv//z4rr///VHiEOIBRCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQ0MAQsgD0L//8+K6///1R59IhMgFEKr1f7///+//7l/VK0iEn0hDiAMQqTsw7WP1LSY5wB9IhEgD0L//8+K6///1R5UIBIgE1ZyrSIPfSESIAtCv6WUnM/w0rvkAH0iEyAMQqTsw7WP1LSY5wBUIA8gEVZyrSIPfSERIBBC19mumuT26Y3LAH0iDCALQr+llJzP8NK75ABUIA8gE1ZyrSILfSETIA0gEELX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDSAUQtWqgYCAgMCAxgB8IRQLIAMgFDcD6BwgAyAONwPgHCADIBI3A9gcIAMgETcD0BwgAyATNwPIHCADIA03A8AcIAFBMGohByABKQMwISogASkDOCErIAEpA0AhLCABKQNIIS0gASkDUCEuIAEpA1ghL0GIASEEQgAhDUIAIRBCACELQgAhDEIAIQ9CACEUA0AgA0GgGmogAiAEaikDACIOQgAgL0IAEMkDIANBsBpqIA5CACAuQgAQyQMgA0HAGmogDkIAIC1CABDJAyADQdAaaiAOQgAgLEIAEMkDIANB4BpqIA5CACArQgAQyQMgA0HwGmogDkIAICpCABDJAyADQZAaaiADKQOgGiISIBR8IhdC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQYAaaiAOQgBC///Piuv//9UeQgAQyQMgA0HwGWogDkIAQqTsw7WP1LSY5wBCABDJAyADQeAZaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB0BlqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HAGWogDkIAQprN/8ujvcSAGkIAEMkDIAMpA8gZIAMpA/AaIg4gDXwiFSADKQPoGiADKQPgGiINIBB8IhAgDVStfCAQIAMpA9gaIAsgAykD0BoiC3wiESALVK18IBEgAykDyBogAykDwBoiCyAMfCIMIAtUrXwgDCADKQO4GiADKQOwGiILIA98Ig0gC1StfCANIAMpA6gaIBIgF1atfHwiCyANVK18fCIPIAxUrXx8IgwgEVStfHwiDSAQVK18fCITIAMpA8AZfCIQIBNUrXwgECAQIAMpA9gZIA0gAykD0Bl8IhEgDVStfCARIAMpA+gZIAwgAykD4Bl8IhIgDFStfCASIAMpA/gZIA8gAykD8Bl8IgwgD1StfCAMIAMpA4gaIAsgAykDgBoiC3wiDSALVK18IA0gAykDmBogAykDkBoiCyAXfCALVK18fCIUIA1UrXx8Ig8gDFStfHwiDCASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykD+BogDiAVVq18fHwhDSAEQQhrIgRB2ABHDQALAkACQCANQprN/8ujvcSAGlYNACANQprN/8ujvcSAGlIEQCAPIQ4gDCESIAshESAQIRMMAgsgEELX2a6a5PbpjcsAVg0AAkAgEELX2a6a5PbpjcsAUgRAIA8hDiAMIRIgCyERIBAhEwwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACETIAtCv6WUnM/w0rvkAFIEQCAPIQ4gDCESIAshEQwBCyAMQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACERIAxCpOzDtY/UtJjnAFIEQCAPIQ4gDCESDAELIA9C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhEiAPQv//z4rr///VHlIEQCAPIQ4MAQtC///Piuv//9UeIQ4gFEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDQwBCyAPQv//z4rr///VHn0iEyAUQqvV/v///7//uX9UrSISfSEOIAxCpOzDtY/UtJjnAH0iESAPQv//z4rr///VHlQgEiATVnKtIg99IRIgC0K/pZScz/DSu+QAfSITIAxCpOzDtY/UtJjnAFQgDyARVnKtIg99IREgEELX2a6a5PbpjcsAfSIMIAtCv6WUnM/w0rvkAFQgDyATVnKtIgt9IRMgDSAQQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSENIBRC1aqBgICAwIDGAHwhFAsgAyAUNwOYHSADIA43A5AdIAMgEjcDiB0gAyARNwOAHSADIBM3A/gcIAMgDTcD8BwgAikDACEZIAIpAwghFiACKQMQIRcgAikDGCEVIAIpAyAhEyACKQMoIRFBiAEhBEIAIQ1CACEQQgAhC0IAIQxCACEPQgAhFANAIANB4BhqIAEgBGopAwAiDkIAIBFCABDJAyADQfAYaiAOQgAgE0IAEMkDIANBgBlqIA5CACAVQgAQyQMgA0GQGWogDkIAIBdCABDJAyADQaAZaiAOQgAgFkIAEMkDIANBsBlqIA5CACAZQgAQyQMgA0HQGGogAykD4BgiEiAUfCIcQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgA0HAGGogDkIAQv//z4rr///VHkIAEMkDIANBsBhqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0GgGGogDkIAQr+llJzP8NK75ABCABDJAyADQZAYaiAOQgBC19mumuT26Y3LAEIAEMkDIANBgBhqIA5CAEKazf/Lo73EgBpCABDJAyADKQOIGCADKQOwGSIOIA18IhogAykDqBkgAykDoBkiDSAQfCIYIA1UrXwgGCADKQOYGSALIAMpA5AZIgt8IhAgC1StfCAQIAMpA4gZIAMpA4AZIgsgDHwiDCALVK18IAwgAykD+BggAykD8BgiCyAPfCINIAtUrXwgDSADKQPoGCASIBxWrXx8IgsgDVStfHwiDyAMVK18fCIMIBBUrXx8Ig0gGFStfHwiGyADKQOAGHwiGCAbVK18IBggAykDmBggDSADKQOQGHwiECANVK18IBAgAykDqBggDCADKQOgGHwiEiAMVK18IBIgAykDuBggDyADKQOwGHwiDCAPVK18IAwgAykDyBggCyADKQPAGCILfCINIAtUrXwgDSADKQPYGCADKQPQGCILIBx8IAtUrXx8IhQgDVStfHwiDyAMVK18fCIMIBJUrXx8IgsgEFStfHwiECAYVK18IBogG1atIAMpA7gZIA4gGlatfHx8IQ0gBEEIayIEQdgARw0ACwJAAkAgDUKazf/Lo73EgBpWDQAgDUKazf/Lo73EgBpSBEAgDyEOIAwhEiALIREgECETDAILIBBC19mumuT26Y3LAFYNAAJAIBBC19mumuT26Y3LAFIEQCAPIQ4gDCESIAshESAQIRMMAQsgC0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhEyALQr+llJzP8NK75ABSBEAgDyEOIAwhEiALIREMAQsgDEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhESAMQqTsw7WP1LSY5wBSBEAgDyEOIAwhEgwBCyAPQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRIgD0L//8+K6///1R5SBEAgDyEODAELQv//z4rr///VHiEOIBRCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQ0MAQsgD0L//8+K6///1R59IhMgFEKr1f7///+//7l/VK0iEn0hDiAMQqTsw7WP1LSY5wB9IhEgD0L//8+K6///1R5UIBIgE1ZyrSIPfSESIAtCv6WUnM/w0rvkAH0iEyAMQqTsw7WP1LSY5wBUIA8gEVZyrSIPfSERIBBC19mumuT26Y3LAH0iDCALQr+llJzP8NK75ABUIA8gE1ZyrSILfSETIA0gEELX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDSAUQtWqgYCAgMCAxgB8IRQLIAMgFDcDyB0gAyAONwPAHSADIBI3A7gdIAMgETcDsB0gAyATNwOoHSADIA03A6AdIAJBiAFqIQUgASkDACEwIAEpAwghJiABKQMQISIgASkDGCEjIAEpAyAhICABKQMoISFBACEEQgAhFEIAIQ9CACEMQgAhC0IAIRBCACENA0AgA0GgF2ogBCAFaikDACIOQgAgIUIAEMkDIANBsBdqIA5CACAgQgAQyQMgA0HAF2ogDkIAICNCABDJAyADQdAXaiAOQgAgIkIAEMkDIANB4BdqIA5CACAmQgAQyQMgA0HwF2ogDkIAIDBCABDJAyADQZAXaiADKQOgFyISIBR8IhdC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQYAXaiAOQgBC///Piuv//9UeQgAQyQMgA0HwFmogDkIAQqTsw7WP1LSY5wBCABDJAyADQeAWaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB0BZqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HAFmogDkIAQprN/8ujvcSAGkIAEMkDIAMpA8gWIAMpA/AXIg4gDXwiFSADKQPoFyADKQPgFyINIBB8IhAgDVStfCAQIAMpA9gXIAsgAykD0BciC3wiESALVK18IBEgAykDyBcgAykDwBciCyAMfCIMIAtUrXwgDCADKQO4FyADKQOwFyILIA98Ig0gC1StfCANIAMpA6gXIBIgF1atfHwiCyANVK18fCIPIAxUrXx8IgwgEVStfHwiDSAQVK18fCITIAMpA8AWfCIQIBNUrXwgECAQIAMpA9gWIA0gAykD0BZ8IhEgDVStfCARIAMpA+gWIAwgAykD4BZ8IhIgDFStfCASIAMpA/gWIA8gAykD8BZ8IgwgD1StfCAMIAMpA4gXIAsgAykDgBciC3wiDSALVK18IA0gAykDmBcgAykDkBciCyAXfCALVK18fCIUIA1UrXx8Ig8gDFStfHwiDCASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykD+BcgDiAVVq18fHwhDSAEQQhrIgRBUEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AIA1Cms3/y6O9xIAaUgRAIA8hDiAMIRIgCyERIBAhEwwCCyAQQtfZrprk9umNywBWDQACQCAQQtfZrprk9umNywBSBEAgDyEOIAwhEiALIREgECETDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRMgC0K/pZScz/DSu+QAUgRAIA8hDiAMIRIgCyERDAELIAxCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIREgDEKk7MO1j9S0mOcAUgRAIA8hDiAMIRIMAQsgD0L//8+K6///1R5WDQFCpOzDtY/UtJjnACESIA9C///Piuv//9UeUgRAIA8hDgwBC0L//8+K6///1R4hDiAUQqrV/v///7//uX9WDQELQprN/8ujvcSAGiENDAELIA9C///Piuv//9UefSITIBRCq9X+////v/+5f1StIhJ9IQ4gDEKk7MO1j9S0mOcAfSIRIA9C///Piuv//9UeVCASIBNWcq0iD30hEiALQr+llJzP8NK75AB9IhMgDEKk7MO1j9S0mOcAVCAPIBFWcq0iD30hESAQQtfZrprk9umNywB9IgwgC0K/pZScz/DSu+QAVCAPIBNWcq0iC30hEyANIBBC19mumuT26Y3LAFQgCyAMVnKtfUKazf/Lo73EgBp9IQ0gFELVqoGAgIDAgMYAfCEUCyADIBQ3A/gdIAMgDjcD8B0gAyASNwPoHSADIBE3A+AdIAMgEzcD2B0gAyANNwPQHQJAAkACQCADQaAdaiADQdAdaiIIQTAQ8QMEQCADQeglaiIJIANB6BxqKQMANwMAIANB4CVqIgQgA0HgHGopAwA3AwAgA0HYJWoiBiADQdgcaikDADcDACADQdAlaiIHIANB0BxqKQMANwMAIANByCVqIgUgA0HIHGopAwA3AwAgAyADKQPAHDcDwCUgA0GAHmogA0HAJWoiCiADQfAcahCDAiAJIANByB1qKQMANwMAIAQgA0HAHWopAwA3AwAgBiADQbgdaikDADcDACAHIANBsB1qKQMANwMAIAUgA0GoHWopAwA3AwAgAyADKQOgHTcDwCUgAkGIAWohAiADQaAjaiAKIAgQgwIgASkDYCEZIAEpA2ghFiABKQNwIRcgASkDeCEVIAEpA4ABIRMgASkDiAEhEUEAIQFCACEUQgAhD0IAIQxCACELQgAhEEIAIQ0DQCADQeAVaiABIAJqKQMAIg5CACARQgAQyQMgA0HwFWogDkIAIBNCABDJAyADQYAWaiAOQgAgFUIAEMkDIANBkBZqIA5CACAXQgAQyQMgA0GgFmogDkIAIBZCABDJAyADQbAWaiAOQgAgGUIAEMkDIANB0BVqIAMpA+AVIhIgFHwiHEL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIANBwBVqIA5CAEL//8+K6///1R5CABDJAyADQbAVaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANBoBVqIA5CAEK/pZScz/DSu+QAQgAQyQMgA0GQFWogDkIAQtfZrprk9umNywBCABDJAyADQYAVaiAOQgBCms3/y6O9xIAaQgAQyQMgAykDiBUgAykDsBYiDiANfCIaIAMpA6gWIAMpA6AWIg0gEHwiGCANVK18IBggAykDmBYgCyADKQOQFiILfCIQIAtUrXwgECADKQOIFiADKQOAFiILIAx8IgwgC1StfCAMIAMpA/gVIAMpA/AVIgsgD3wiDSALVK18IA0gAykD6BUgEiAcVq18fCILIA1UrXx8Ig8gDFStfHwiDCAQVK18fCINIBhUrXx8IhsgAykDgBV8IhggG1StfCAYIAMpA5gVIA0gAykDkBV8IhAgDVStfCAQIAMpA6gVIAwgAykDoBV8IhIgDFStfCASIAMpA7gVIA8gAykDsBV8IgwgD1StfCAMIAMpA8gVIAsgAykDwBUiC3wiDSALVK18IA0gAykD2BUgAykD0BUiCyAcfCALVK18fCIUIA1UrXx8Ig8gDFStfHwiDCASVK18fCILIBBUrXx8IhAgGFStfCAaIBtWrSADKQO4FiAOIBpWrXx8fCENIAFBCGsiAUFQRw0ACyANQprN/8ujvcSAGlYNAiANQprN/8ujvcSAGlENASAPIQ4gDCESIAshESAQIRMMAwsCQAJAAkACQAJAAkACQAJAAkAgA0HAHGogA0HwHGpBMBDxA0UEQCAHQcCNxQBBMBDxAw0BCyADQYAnakIANwMAIANB+CZqQgA3AwAgA0HwJmpCADcDACADQegmakIANwMAIANB4CZqQgA3AwAgA0GQJ2pBgJHFACkDADcDACADQZgnakGIkcUAKQMANwMAIANBoCdqQZCRxQApAwA3AwAgA0GoJ2pBmJHFACkDADcDACADQbAnakGgkcUAKQMANwMAIANCADcD2CYgA0H4kMUAKQMANwOIJyADQeAnakIANwMAIANB2CdqQgA3AwAgA0HQJ2pCADcDACADQcgnakIANwMAIANBwCdqQgA3AwAgA0IANwO4JyADQcAlaiADQdgmahDyAiADKALAJUEBRg0BIAAgA0HIJWpBkAH8CgAADAwLIAZBwI3FAEEwEPEDBEBBKCEEQgAhFEIAIQ9CACEMQgAhC0IAIRBCACENA0AgA0GgC2ogASAEaikDACIOQgAgIUIAEMkDIANBsAtqIA5CACAgQgAQyQMgA0HAC2ogDkIAICNCABDJAyADQdALaiAOQgAgIkIAEMkDIANB4AtqIA5CACAmQgAQyQMgA0HwC2ogDkIAIDBCABDJAyADQZALaiADKQOgCyISIBR8IhdC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQYALaiAOQgBC///Piuv//9UeQgAQyQMgA0HwCmogDkIAQqTsw7WP1LSY5wBCABDJAyADQeAKaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB0ApqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HACmogDkIAQprN/8ujvcSAGkIAEMkDIAMpA8gKIAMpA/ALIg4gDXwiFSADKQPoCyADKQPgCyINIBB8IhAgDVStfCAQIAMpA9gLIAsgAykD0AsiC3wiESALVK18IBEgAykDyAsgAykDwAsiCyAMfCIMIAtUrXwgDCADKQO4CyADKQOwCyILIA98Ig0gC1StfCANIAMpA6gLIBIgF1atfHwiCyANVK18fCIPIAxUrXx8IgwgEVStfHwiDSAQVK18fCITIAMpA8AKfCIQIBNUrXwgECAQIAMpA9gKIA0gAykD0Ap8IhEgDVStfCARIAMpA+gKIAwgAykD4Ap8IhIgDFStfCASIAMpA/gKIA8gAykD8Ap8IgwgD1StfCAMIAMpA4gLIAsgAykDgAsiC3wiDSALVK18IA0gAykDmAsgAykDkAsiCyAXfCALVK18fCIUIA1UrXx8Ig8gDFStfHwiDCASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykD+AsgDiAVVq18fHwhDSAEQQhrIgRBeEcNAAsgDUKazf/Lo73EgBpWDQcgDUKazf/Lo73EgBpRDQIMAwsgA0HoJWogAUEoaikDADcDACADQeAlaiABQSBqKQMANwMAIANB2CVqIAFBGGopAwA3AwAgA0HQJWogAUEQaikDADcDACADQcglaiABQQhqKQMANwMAIANB+CVqIAdBCGopAwA3AwAgA0GAJmogB0EQaikDADcDACADQYgmaiAHQRhqKQMANwMAIANBkCZqIAdBIGopAwA3AwAgA0GYJmogB0EoaikDADcDACADIAEpAwA3A8AlIAMgBykDADcD8CUgA0HIJmogBkEoaikDADcDACADQcAmaiAGQSBqKQMANwMAIANBuCZqIAZBGGopAwA3AwAgA0GwJmogBkEQaikDADcDACADQagmaiAGQQhqKQMANwMAIAMgBikDADcDoCYgACADQcAlakGQAfwKAAAMCwtBkI3FAEErIANB7ydqQYCNxQBBsJLFABDKAwALIBBC19mumuT26Y3LAFYNBCAQQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ0MAQsgC0K/pZScz/DSu+QAVg0EQtfZrprk9umNywAhEyALQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ0MAgsgDEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhESAMQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ0MAwsgD0L//8+K6///1R5WDQRCpOzDtY/UtJjnACESIA9C///Piuv//9UeUQ0DQprN/8ujvcSAGiENIA8hDgwFCyAQIRMLIAshEQsgDCESIA8hDgwCC0L//8+K6///1R4hDiAUQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ0MAQsgD0L//8+K6///1R59IhMgFEKr1f7///+//7l/VK0iEn0hDiAMQqTsw7WP1LSY5wB9IhEgD0L//8+K6///1R5UIBIgE1ZyrSIPfSESIAtCv6WUnM/w0rvkAH0iEyAMQqTsw7WP1LSY5wBUIA8gEVZyrSIPfSERIBBC19mumuT26Y3LAH0iDCALQr+llJzP8NK75ABUIA8gE1ZyrSILfSETIA0gEELX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDSAUQtWqgYCAgMCAxgB8IRQLIAMgDjcD0CEgAyAUNwPYISADIBI3A8ghIAMgETcDwCEgAyATNwO4ISADIA03A7AhQprN/8ujvcSAGiEPIA1CAYYgEyATIBN8IhNWIBMgESARfCIQIBFUIBAgEiASfCIMIBJUIAwgDCAOIA58IgsgDlQgCyAUIBR8Ig0gFFStfCIRIAtUcq18IgxWcq18IhIgEFRyrXwiDiATVHKthCITIQsCQAJAAkAgE0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEPIA4iC0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDyASIgtCv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQ8gDCILQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQ8gESILQv//z4rr///VHlINAEKr1f7///+//7l/IQ8gDSILQqvV/v///7//uX9RDQELIAsgD1oNACARIQsgDCERIBIhDCAOIRAMAQsgEUL//8+K6///1R59IhAgDUKr1f7///+//7l/VK0iD30hCyAMQqTsw7WP1LSY5wB9IhUgEUL//8+K6///1R5UIA8gEFZyrSIPfSERIBJCv6WUnM/w0rvkAH0iECAMQqTsw7WP1LSY5wBUIA8gFVZyrSIPfSEMIA5C19mumuT26Y3LAH0iFSASQr+llJzP8NK75ABUIA8gEFZyrSIPfSEQIBMgDkLX2a6a5PbpjcsAVCAPIBVWcq19QprN/8ujvcSAGn0hEyANQtWqgYCAgMCAxgB8IQ0LIAMgDTcD6CUgAyALNwPgJSADIBE3A9glIAMgDDcD0CUgAyAQNwPIJSADIBM3A8AlIANB4CFqIgUgA0HAJWoiAiADQbAhahC9AkEoIQQgA0HoJWpCADcDACADQeAlakIANwMAIANB2CVqQgA3AwAgA0HQJWpCADcDACADQcglakIANwMAIANCADcDwCUgA0HYJmoiByACIAYQuwEgAiAHIAYQuwEgA0GQImogAiAFEL0CIAMpA5AiIRkgAykDmCIhFiADKQOgIiEXIAMpA6giIRUgAykDsCIhEyADKQO4IiERQgAhFEIAIQ9CACEMQgAhC0IAIRBCACENA0AgA0HgCWogA0GQImogBGopAwAiDkIAIBFCABDJAyADQfAJaiAOQgAgE0IAEMkDIANBgApqIA5CACAVQgAQyQMgA0GQCmogDkIAIBdCABDJAyADQaAKaiAOQgAgFkIAEMkDIANBsApqIA5CACAZQgAQyQMgA0HQCWogAykD4AkiEiAUfCIcQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgA0HACWogDkIAQv//z4rr///VHkIAEMkDIANBsAlqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0GgCWogDkIAQr+llJzP8NK75ABCABDJAyADQZAJaiAOQgBC19mumuT26Y3LAEIAEMkDIANBgAlqIA5CAEKazf/Lo73EgBpCABDJAyADKQOICSADKQOwCiIOIA18IhogAykDqAogAykDoAoiDSAQfCIYIA1UrXwgGCADKQOYCiALIAMpA5AKIgt8IhAgC1StfCAQIAMpA4gKIAMpA4AKIgsgDHwiDCALVK18IAwgAykD+AkgAykD8AkiCyAPfCINIAtUrXwgDSADKQPoCSASIBxWrXx8IgsgDVStfHwiDyAMVK18fCIMIBBUrXx8Ig0gGFStfHwiGyADKQOACXwiGCAbVK18IBggAykDmAkgDSADKQOQCXwiECANVK18IBAgAykDqAkgDCADKQOgCXwiEiAMVK18IBIgAykDuAkgDyADKQOwCXwiDCAPVK18IAwgAykDyAkgCyADKQPACSILfCINIAtUrXwgDSADKQPYCSADKQPQCSILIBx8IAtUrXx8IhQgDVStfHwiDyAMVK18fCIMIBJUrXx8IgsgEFStfHwiECAYVK18IBogG1atIAMpA7gKIA4gGlatfHx8IQ0gBEEIayIEQXhHDQALAkACQCANQprN/8ujvcSAGlYNAAJAAkACQAJAIA1Cms3/y6O9xIAaUg0AIBBC19mumuT26Y3LAFYNBCAQQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ0MAQsgC0K/pZScz/DSu+QAVg0EQtfZrprk9umNywAhEyALQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ0MAgsgDEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhESAMQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ0MAwsgD0L//8+K6///1R5WDQRCpOzDtY/UtJjnACESIA9C///Piuv//9UeUQ0DQprN/8ujvcSAGiENIA8hDgwFCyAQIRMLIAshEQsgDCESIA8hDgwCC0L//8+K6///1R4hDiAUQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ0MAQsgD0L//8+K6///1R59IhMgFEKr1f7///+//7l/VK0iEn0hDiAMQqTsw7WP1LSY5wB9IhEgD0L//8+K6///1R5UIBIgE1ZyrSIPfSESIAtCv6WUnM/w0rvkAH0iEyAMQqTsw7WP1LSY5wBUIA8gEVZyrSIPfSERIBBC19mumuT26Y3LAH0iDCALQr+llJzP8NK75ABUIA8gE1ZyrSILfSETIA0gEELX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDSAUQtWqgYCAgMCAxgB8IRQLIAMgFDcD6CIgAyAONwPgIiADIBI3A9giIAMgETcD0CIgAyATNwPIIiADIA03A8AiIAFBiAFqIQJBACEEQgAhDUIAIQ9CACEMQgAhC0IAIRBCACEUA0AgA0GgCGogAiAEaikDACIOQgAgL0IAEMkDIANBsAhqIA5CACAuQgAQyQMgA0HACGogDkIAIC1CABDJAyADQdAIaiAOQgAgLEIAEMkDIANB4AhqIA5CACArQgAQyQMgA0HwCGogDkIAICpCABDJAyADQZAIaiADKQOgCCISIA18IhdC/f/z/8////mJf34iDUIAQqvV/v///7//uX9CABDJAyADQYAIaiANQgBC///Piuv//9UeQgAQyQMgA0HwB2ogDUIAQqTsw7WP1LSY5wBCABDJAyADQeAHaiANQgBCv6WUnM/w0rvkAEIAEMkDIANB0AdqIA1CAELX2a6a5PbpjcsAQgAQyQMgA0HAB2ogDUIAQprN/8ujvcSAGkIAEMkDIAMpA8gHIAMpA/AIIg4gFHwiFSADKQPoCCADKQPgCCINIBB8IhAgDVStfCAQIAMpA9gIIAsgAykD0AgiC3wiESALVK18IBEgAykDyAggAykDwAgiCyAMfCIMIAtUrXwgDCADKQO4CCADKQOwCCILIA98Ig0gC1StfCANIAMpA6gIIBIgF1atfHwiCyANVK18fCIPIAxUrXx8IgwgEVStfHwiDSAQVK18fCITIAMpA8AHfCIQIBNUrXwgECAQIAMpA9gHIA0gAykD0Ad8IhEgDVStfCARIAMpA+gHIAwgAykD4Ad8IhIgDFStfCASIAMpA/gHIA8gAykD8Ad8IgwgD1StfCAMIAMpA4gIIAsgAykDgAgiC3wiDSALVK18IA0gDSADKQOYCCADKQOQCCILIBd8IAtUrXx8Ig1WrXx8Ig8gDFStfHwiDCASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykD+AggDiAVVq18fHwhFCAEQQhrIgRBUEcNAAsCQAJAIBRCms3/y6O9xIAaVg0AAkACQAJAAkAgFEKazf/Lo73EgBpSDQAgEELX2a6a5PbpjcsAVg0EIBBC19mumuT26Y3LAFIEQEKazf/Lo73EgBohFAwBCyALQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEXIAtCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohFAwCCyAMQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEYIAxCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohFAwDCyAPQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIR4gD0L//8+K6///1R5RDQNCms3/y6O9xIAaIRQgDyEfDAULIBAhFwsgCyEYCyAMIR4gDyEfDAILQv//z4rr///VHiEfIA1CqtX+////v/+5f1YNAEKazf/Lo73EgBohFAwBCyAPQv//z4rr///VHn0iESANQqvV/v///7//uX9UrSIOfSEfIAxCpOzDtY/UtJjnAH0iEiAPQv//z4rr///VHlQgDiARVnKtIg59IR4gC0K/pZScz/DSu+QAfSIPIAxCpOzDtY/UtJjnAFQgDiASVnKtIg59IRggEELX2a6a5PbpjcsAfSIMIAtCv6WUnM/w0rvkAFQgDiAPVnKtIgt9IRcgFCAQQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSEUIA1C1aqBgICAwIDGAHwhDQsgAyANNwOYIyADIB83A5AjIAMgHjcDiCMgAyAYNwOAIyADIBc3A/giIAMgFDcD8CJBKCEEQgAhEEIAIRVCACEOQgAhEUIAIQxCACELA0AgA0HgBmogA0HwImogBGopAwAiD0IAIA1CABDJAyADQfAGaiAPQgAgH0IAEMkDIANBgAdqIA9CACAeQgAQyQMgA0GQB2ogD0IAIBhCABDJAyADQaAHaiAPQgAgF0IAEMkDIANBsAdqIA9CACAUQgAQyQMgA0HQBmogAykD4AYiEiAQfCIbQv3/8//P///5iX9+Ig9CAEKr1f7///+//7l/QgAQyQMgA0HABmogD0IAQv//z4rr///VHkIAEMkDIANBsAZqIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0GgBmogD0IAQr+llJzP8NK75ABCABDJAyADQZAGaiAPQgBC19mumuT26Y3LAEIAEMkDIANBgAZqIA9CAEKazf/Lo73EgBpCABDJAyADKQOIBiADKQOwByIPIAt8IhkgAykDqAcgAykDoAciCyAMfCITIAtUrXwgEyADKQOYByADKQOQByILIBF8IhEgC1StfCARIAMpA4gHIAMpA4AHIgsgDnwiDiALVK18IA4gAykD+AYgAykD8AYiCyAVfCIMIAtUrXwgDCADKQPoBiASIBtWrXx8IgsgDFStfHwiECAOVK18fCIOIBFUrXx8IgwgE1StfHwiFiADKQOABnwiEyAWVK18IBMgAykDmAYgDCADKQOQBnwiESAMVK18IBEgESADKQOoBiAOIAMpA6AGfCISIA5UrXwgEiADKQO4BiAQIAMpA7AGfCIOIBBUrXwgDiADKQPIBiALIAMpA8AGIgt8IgwgC1StfCAMIAMpA9gGIAMpA9AGIgsgG3wgC1StfHwiECAMVK18fCIVIA5UrXx8Ig4gElStfHwiEVatfHwiDCATVK18IBYgGVStIAMpA7gHIA8gGVatfHx8IQsgBEEIayIEQXhHDQALAkACQCALQprN/8ujvcSAGlYNAAJAAkACQAJAIAtCms3/y6O9xIAaUg0AIAxC19mumuT26Y3LAFYNBCAMQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQsMAQsgEUK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhEyARQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQsMAgsgDkKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhDyAOQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQsMAwsgFUL//8+K6///1R5WDQRCpOzDtY/UtJjnACEbIBVC///Piuv//9UeUQ0DQprN/8ujvcSAGiELIBUhEgwFCyAMIRMLIBEhDwsgDiEbIBUhEgwCC0L//8+K6///1R4hEiAQQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQsMAQsgFUL//8+K6///1R59IhMgEEKr1f7///+//7l/VK0iD30hEiAOQqTsw7WP1LSY5wB9IhYgFUL//8+K6///1R5UIA8gE1ZyrSIPfSEbIBFCv6WUnM/w0rvkAH0iEyAOQqTsw7WP1LSY5wBUIA8gFlZyrSIOfSEPIAxC19mumuT26Y3LAH0iFSARQr+llJzP8NK75ABUIA4gE1ZyrSIOfSETIAsgDELX2a6a5PbpjcsAVCAOIBVWcq19QprN/8ujvcSAGn0hCyAQQtWqgYCAgMCAxgB8IRALIAMgEDcDyCMgAyASNwPAIyADIBs3A7gjIAMgDzcDsCMgAyATNwOoIyADIAs3A6AjQSghBEIAIRBCACEVQgAhDkIAIRFCACEMQgAhCwNAIANBoAVqIANBoCNqIARqKQMAIg9CACANQgAQyQMgA0GwBWogD0IAIB9CABDJAyADQcAFaiAPQgAgHkIAEMkDIANB0AVqIA9CACAYQgAQyQMgA0HgBWogD0IAIBdCABDJAyADQfAFaiAPQgAgFEIAEMkDIANBkAVqIAMpA6AFIhIgEHwiG0L9//P/z///+Yl/fiIPQgBCq9X+////v/+5f0IAEMkDIANBgAVqIA9CAEL//8+K6///1R5CABDJAyADQfAEaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANB4ARqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0HQBGogD0IAQtfZrprk9umNywBCABDJAyADQcAEaiAPQgBCms3/y6O9xIAaQgAQyQMgAykDyAQgAykD8AUiDyALfCIZIAMpA+gFIAMpA+AFIgsgDHwiEyALVK18IBMgAykD2AUgAykD0AUiCyARfCIRIAtUrXwgESADKQPIBSADKQPABSILIA58Ig4gC1StfCAOIAMpA7gFIAMpA7AFIgsgFXwiDCALVK18IAwgAykDqAUgEiAbVq18fCILIAxUrXx8IhAgDlStfHwiDiARVK18fCIMIBNUrXx8IhYgAykDwAR8IhMgFlStfCATIAMpA9gEIAwgAykD0AR8IhEgDFStfCARIBEgAykD6AQgDiADKQPgBHwiEiAOVK18IBIgAykD+AQgECADKQPwBHwiDiAQVK18IA4gAykDiAUgCyADKQOABSILfCIMIAtUrXwgDCADKQOYBSADKQOQBSILIBt8IAtUrXx8IhAgDFStfHwiFSAOVK18fCIOIBJUrXx8IhFWrXx8IgwgE1StfCAWIBlUrSADKQP4BSAPIBlWrXx8fCELIARBCGsiBEF4Rw0ACwJAAkAgC0Kazf/Lo73EgBpWDQACQAJAAkACQCALQprN/8ujvcSAGlINACAMQtfZrprk9umNywBWDQQgDELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiELDAELIBFCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRMgEUK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiELDAILIA5CpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRQgDkKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiELDAMLIBVC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhDyAVQv//z4rr///VHlENA0Kazf/Lo73EgBohCyAVIQ0MBQsgDCETCyARIRQLIA4hDyAVIQ0MAgtC///Piuv//9UeIQ0gEEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiELDAELIBVC///Piuv//9UefSISIBBCq9X+////v/+5f1StIg99IQ0gDkKk7MO1j9S0mOcAfSIXIBVC///Piuv//9UeVCAPIBJWcq0iEn0hDyARQr+llJzP8NK75AB9IhMgDkKk7MO1j9S0mOcAVCASIBdWcq0iDn0hFCAMQtfZrprk9umNywB9IhIgEUK/pZScz/DSu+QAVCAOIBNWcq0iDn0hEyALIAxC19mumuT26Y3LAFQgDiASVnKtfUKazf/Lo73EgBp9IQsgEELVqoGAgIDAgMYAfCEQC0Kazf/Lo73EgBohDiATIBN8IhcgE1QgFyAUIBR8IhUgFFQgFSAPIA98IgwgD1QgDCANIA0gDXwiDVYgDSAQIBB8IhMgEFStfCIRIA1Ucq18IhIgDFRyrXwiDCAVVHKtfCIPIBdUcq0gC0IBhoQiFCENAkACQAJAIBRCms3/y6O9xIAaUg0AQtfZrprk9umNywAhDiAPIg1C19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQ4gDCINQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEOIBIiDUKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEOIBEiDUL//8+K6///1R5SDQBCq9X+////v/+5fyEOIBMiDUKr1f7///+//7l/UQ0BCyANIA5aDQAgESENIBIhECAMIQsgDyEMDAELIBFC///Piuv//9UefSIQIBNCq9X+////v/+5f1StIgt9IQ0gEkKk7MO1j9S0mOcAfSIOIBFC///Piuv//9UeVCALIBBWcq0iC30hECAMQr+llJzP8NK75AB9IhEgEkKk7MO1j9S0mOcAVCALIA5Wcq0iDn0hCyAPQtfZrprk9umNywB9IhIgDEK/pZScz/DSu+QAVCAOIBFWcq0iDn0hDCAUIA9C19mumuT26Y3LAFQgDiASVnKtfUKazf/Lo73EgBp9IRQgE0LVqoGAgIDAgMYAfCETC0Kazf/Lo73EgBohDyAUQgGGIAwgDHwiESAMVCARIAsgC3wiDiALVCAOIBAgEHwiDCAQVCAMIA0gDXwiCyANVCALIBMgE3wiFCATVK18IhIgC1RyrXwiCyAMVHKtfCIMIA5Ucq18Ig4gEVRyrYQiEyENAkACQAJAIBNCms3/y6O9xIAaUg0AQtfZrprk9umNywAhDyAOIg1C19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQ8gDCINQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEPIAsiDUKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEPIBIiDUL//8+K6///1R5SDQBCq9X+////v/+5fyEPIBQiDUKr1f7///+//7l/UQ0BCyANIA9aDQAgEiENIAshECAMIQsgDiEMDAELIBJC///Piuv//9UefSIRIBRCq9X+////v/+5f1StIg99IQ0gC0Kk7MO1j9S0mOcAfSIVIBJC///Piuv//9UeVCAPIBFWcq0iD30hECAMQr+llJzP8NK75AB9IhEgC0Kk7MO1j9S0mOcAVCAPIBVWcq0iD30hCyAOQtfZrprk9umNywB9IhIgDEK/pZScz/DSu+QAVCAPIBFWcq0iD30hDCATIA5C19mumuT26Y3LAFQgDyASVnKtfUKazf/Lo73EgBp9IRMgFELVqoGAgIDAgMYAfCEUC0Kazf/Lo73EgBohDiAMIAx8IhUgDFQgFSALIAt8IhEgC1QgESAQIBB8IgwgEFQgDCANIA18IgsgDVQgCyAUIBR8IiUgFFStfCISIAtUcq18Ig8gDFRyrXwiDCARVHKtfCILIBVUcq0gE0IBhoQiKSENAkACQAJAIClCms3/y6O9xIAaUg0AQtfZrprk9umNywAhDiALIg1C19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQ4gDCINQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEOIA8iDUKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEOIBIiDUL//8+K6///1R5SDQBCq9X+////v/+5fyEOICUiDUKr1f7///+//7l/UQ0BCyANIA5aDQAgEiEnIA8hKCAMISQgCyEdDAELIBJC///Piuv//9UefSIRICVCq9X+////v/+5f1StIg19IScgD0Kk7MO1j9S0mOcAfSIOIBJC///Piuv//9UeVCANIBFWcq0iDX0hKCAMQr+llJzP8NK75AB9IhIgD0Kk7MO1j9S0mOcAVCANIA5Wcq0iDX0hJCALQtfZrprk9umNywB9Ig4gDEK/pZScz/DSu+QAVCANIBJWcq0iDX0hHSApIAtC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9ISkgJULVqoGAgIDAgMYAfCElC0HYACEEQgAhFEIAIQ9CACEMQgAhC0IAIRBCACENA0AgA0HgA2ogASAEaikDACIOQgAgIUIAEMkDIANB8ANqIA5CACAgQgAQyQMgA0GABGogDkIAICNCABDJAyADQZAEaiAOQgAgIkIAEMkDIANBoARqIA5CACAmQgAQyQMgA0GwBGogDkIAIDBCABDJAyADQdADaiADKQPgAyISIBR8IhdC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQcADaiAOQgBC///Piuv//9UeQgAQyQMgA0GwA2ogDkIAQqTsw7WP1LSY5wBCABDJAyADQaADaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBkANqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0GAA2ogDkIAQprN/8ujvcSAGkIAEMkDIAMpA4gDIAMpA7AEIg4gDXwiFSADKQOoBCADKQOgBCINIBB8IhAgDVStfCAQIAMpA5gEIAsgAykDkAQiC3wiESALVK18IBEgAykDiAQgAykDgAQiCyAMfCIMIAtUrXwgDCADKQP4AyADKQPwAyILIA98Ig0gC1StfCANIAMpA+gDIBIgF1atfHwiCyANVK18fCIPIAxUrXx8IgwgEVStfHwiDSAQVK18fCITIAMpA4ADfCIQIBNUrXwgECAQIAMpA5gDIA0gAykDkAN8IhEgDVStfCARIAMpA6gDIAwgAykDoAN8IhIgDFStfCASIAMpA7gDIA8gAykDsAN8IgwgD1StfCAMIAMpA8gDIAsgAykDwAMiC3wiDSALVK18IA0gAykD2AMgAykD0AMiCyAXfCALVK18fCIUIA1UrXx8Ig8gDFStfHwiDCASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykDuAQgDiAVVq18fHwhDSAEQQhrIgRBKEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AAkACQAJAAkAgDUKazf/Lo73EgBpSDQAgEELX2a6a5PbpjcsAVg0EIBBC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDQwBCyALQr+llJzP8NK75ABWDQRC19mumuT26Y3LACETIAtCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDQwCCyAMQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACERIAxCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDQwDCyAPQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRIgD0L//8+K6///1R5RDQNCms3/y6O9xIAaIQ0gDyEODAULIBAhEwsgCyERCyAMIRIgDyEODAILQv//z4rr///VHiEOIBRCqtX+////v/+5f1YNAEKazf/Lo73EgBohDQwBCyAPQv//z4rr///VHn0iEyAUQqvV/v///7//uX9UrSISfSEOIAxCpOzDtY/UtJjnAH0iESAPQv//z4rr///VHlQgEiATVnKtIg99IRIgC0K/pZScz/DSu+QAfSITIAxCpOzDtY/UtJjnAFQgDyARVnKtIg99IREgEELX2a6a5PbpjcsAfSIMIAtCv6WUnM/w0rvkAFQgDyATVnKtIgt9IRMgDSAQQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSENIBRC1aqBgICAwIDGAHwhFAsgAyAUNwPoJSADIA43A+AlIAMgEjcD2CUgAyARNwPQJSADIBM3A8glIAMgDTcDwCUgA0HQI2ogA0HAJWogA0HwImoQuwFCms3/y6O9xIAaIQ4gAykD2CMiCyALfCIRIAtUIBEgAykD4CMiCyALfCIPIAtUIA8gAykD6CMiCyALfCIMIAtUIAwgAykD8CMiCyALfCINIAtUIA0gAykD+CMiCyALfCITIAtUrXwiEiANVHKtfCILIAxUcq18IgwgD1RyrXwiDyARVHKtIAMpA9AjQgGGhCIUIQ0CQAJAAkAgFEKazf/Lo73EgBpSDQBC19mumuT26Y3LACEOIA8iDULX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDiAMIg1Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQ4gCyINQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQ4gEiINQv//z4rr///VHlINAEKr1f7///+//7l/IQ4gEyINQqvV/v///7//uX9RDQELIA0gDloNACASIQ0gCyEQIAwhCyAPIQwMAQsgEkL//8+K6///1R59IhEgE0Kr1f7///+//7l/VK0iDn0hDSALQqTsw7WP1LSY5wB9IhUgEkL//8+K6///1R5UIA4gEVZyrSIOfSEQIAxCv6WUnM/w0rvkAH0iESALQqTsw7WP1LSY5wBUIA4gFVZyrSIOfSELIA9C19mumuT26Y3LAH0iEiAMQr+llJzP8NK75ABUIA4gEVZyrSIOfSEMIBQgD0LX2a6a5PbpjcsAVCAOIBJWcq19QprN/8ujvcSAGn0hFCATQtWqgYCAgMCAxgB8IRMLQprN/8ujvcSAGiEOIAwgDHwiFSAMVCAVIAsgC3wiESALVCARIBAgEHwiDCAQVCAMIA0gDXwiCyANVCALIBMgE3wiGCATVK18IhIgC1RyrXwiDyAMVHKtfCIMIBFUcq18IgsgFVRyrSAUQgGGhCIfIQ0CQAJAAkAgH0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEOIAsiDULX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDiAMIg1Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQ4gDyINQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQ4gEiINQv//z4rr///VHlINAEKr1f7///+//7l/IQ4gGCINQqvV/v///7//uX9RDQELIA0gDloNACALIR4gDCEbIA8hISASISMMAQsgEkL//8+K6///1R59IhEgGEKr1f7///+//7l/VK0iDX0hIyAPQqTsw7WP1LSY5wB9Ig4gEkL//8+K6///1R5UIA0gEVZyrSINfSEhIAxCv6WUnM/w0rvkAH0iEiAPQqTsw7WP1LSY5wBUIA0gDlZyrSINfSEbIAtC19mumuT26Y3LAH0iDiAMQr+llJzP8NK75ABUIA0gElZyrSINfSEeIB8gC0LX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hHyAYQtWqgYCAgMCAxgB8IRgLQprN/8ujvcSAGiEMIB4gHnwiDyAeVCAPIBsgG3wiDiAbVCAOIA4gISAhfCINICFUIA0gIyAjfCILICNUIAsgGCAYfCIUIBhUrXwiECALVHKtfCIRIA1Ucq18Ig5Wcq18Ig0gD1RyrSAfQgGGhCITIQsCQAJAAkAgE0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEMIA0iC0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDCAOIgtCv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQwgESILQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQwgECILQv//z4rr///VHlINAEKr1f7///+//7l/IQwgFCILQqvV/v///7//uX9RDQELIAsgDFoNACANIQsgDiEMIBEhDyAQIRIMAQsgEEL//8+K6///1R59Ig8gFEKr1f7///+//7l/VK0iC30hEiARQqTsw7WP1LSY5wB9IgwgEEL//8+K6///1R5UIAsgD1ZyrSILfSEPIA5Cv6WUnM/w0rvkAH0iECARQqTsw7WP1LSY5wBUIAsgDFZyrSILfSEMIA1C19mumuT26Y3LAH0iESAOQr+llJzP8NK75ABUIAsgEFZyrSIOfSELIBMgDULX2a6a5PbpjcsAVCAOIBFWcq19QprN/8ujvcSAGn0hEyAUQtWqgYCAgMCAxgB8IRQLIAMgFDcDqCQgAyASNwOgJCADIA83A5gkIAMgDDcDkCQgAyALNwOIJCADIBM3A4AkIANBsCRqIANBwCJqIANBgCRqEIMCQSghBCADKQOwJCEaIAMpA7gkIRkgAykDwCQhFiADKQPIJCEXIAMpA9AkIRMgAykD2CQhEUIAIQ9CACEVQgAhDEIAIQtCACEQQgAhEgNAIANBoAJqIANB8CJqIARqKQMAIg1CACARQgAQyQMgA0GwAmogDUIAIBNCABDJAyADQcACaiANQgAgF0IAEMkDIANB0AJqIA1CACAWQgAQyQMgA0HgAmogDUIAIBlCABDJAyADQfACaiANQgAgGkIAEMkDIANBkAJqIA8gAykDoAIiD3wiIkL9//P/z///+Yl/fiINQgBCq9X+////v/+5f0IAEMkDIANBgAJqIA1CAEL//8+K6///1R5CABDJAyADQfABaiANQgBCpOzDtY/UtJjnAEIAEMkDIANB4AFqIA1CAEK/pZScz/DSu+QAQgAQyQMgA0HQAWogDUIAQtfZrprk9umNywBCABDJAyADQcABaiANQgBCms3/y6O9xIAaQgAQyQMgAykDyAEgAykD8AIiDiASfCIgIAMpA+gCIAMpA+ACIg0gEHwiECANVK18IBAgAykD2AIgCyADKQPQAiILfCISIAtUrXwgEiADKQPIAiADKQPAAiILIAx8IgwgC1StfCAMIAMpA7gCIAMpA7ACIgsgFXwiDSALVK18IA0gAykDqAIgDyAiVq18fCILIA1UrXx8Ig8gDFStfHwiDCASVK18fCINIBBUrXx8IhQgAykDwAF8IhwgFFStfCAcIAMpA9gBIA0gAykD0AF8IhAgDVStfCAQIAMpA+gBIAwgAykD4AF8IhIgDFStfCASIAMpA/gBIA8gAykD8AF8IgwgD1StfCAMIAMpA4gCIAsgAykDgAIiC3wiDSALVK18IA0gAykDmAIgAykDkAIiCyAifCALVK18fCIPIA1UrXx8IhUgDFStfHwiDCASVK18fCILIBBUrXx8IhAgHFStfCAUICBUrSADKQP4AiAOICBWrXx8fCESIARBCGsiBEF4Rw0ACwJAAkAgEkKazf/Lo73EgBpWDQACQAJAAkACQCASQprN/8ujvcSAGlINACAQQtfZrprk9umNywBWDQQgEELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiESDAELIAtCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRkgC0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiESDAILIAxCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAISAgDEKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiESDAMLIBVC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhGiAVQv//z4rr///VHlENA0Kazf/Lo73EgBohEiAVIRwMBQsgECEZCyALISALIAwhGiAVIRwMAgtC///Piuv//9UeIRwgD0Kq1f7///+//7l/Vg0AQprN/8ujvcSAGiESDAELIBVC///Piuv//9UefSIOIA9Cq9X+////v/+5f1StIg19IRwgDEKk7MO1j9S0mOcAfSIRIBVC///Piuv//9UeVCANIA5Wcq0iDX0hGiALQr+llJzP8NK75AB9Ig4gDEKk7MO1j9S0mOcAVCANIBFWcq0iDH0hICAQQtfZrprk9umNywB9Ig0gC0K/pZScz/DSu+QAVCAMIA5Wcq0iC30hGSASIBBC19mumuT26Y3LAFQgCyANVnKtfUKazf/Lo73EgBp9IRIgD0LVqoGAgIDAgMYAfCEPC0HYACEEQgAhFEIAIRVCACEMQgAhC0IAIRBCACENA0AgA0HgAGogASAEaikDACIOQgAgL0IAEMkDIANB8ABqIA5CACAuQgAQyQMgA0GAAWogDkIAIC1CABDJAyADQZABaiAOQgAgLEIAEMkDIANBoAFqIA5CACArQgAQyQMgA0GwAWogDkIAICpCABDJAyADQdAAaiADKQNgIhEgFHwiFEL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIANBQGsgDkIAQv//z4rr///VHkIAEMkDIANBMGogDkIAQqTsw7WP1LSY5wBCABDJAyADQSBqIA5CAEK/pZScz/DSu+QAQgAQyQMgA0EQaiAOQgBC19mumuT26Y3LAEIAEMkDIAMgDkIAQprN/8ujvcSAGkIAEMkDIAMpAwggAykDsAEiDiANfCIWIAMpA6gBIAMpA6ABIg0gEHwiEyANVK18IBMgAykDmAEgCyADKQOQASILfCIQIAtUrXwgECADKQOIASADKQOAASILIAx8IgwgC1StfCAMIAMpA3ggAykDcCILIBV8Ig0gC1StfCANIAMpA2ggESAUVq18fCILIA1UrXx8IhUgDFStfHwiDCAQVK18fCINIBNUrXx8IhcgAykDAHwiEyAXVK18IBMgAykDGCANIAMpAxB8IhAgDVStfCAQIAMpAyggDCADKQMgfCIRIAxUrXwgESADKQM4IBUgAykDMHwiDCAVVK18IAwgAykDSCALIAMpA0AiC3wiDSALVK18IA0gAykDWCADKQNQIgsgFHwgC1StfHwiFCANVK18fCIVIAxUrXx8IgwgEVStfHwiCyAQVK18fCIQIBNUrXwgFiAXVq0gAykDuAEgDiAWVq18fHwhDSAEQQhrIgRBKEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AAkACQAJAAkAgDUKazf/Lo73EgBpSDQAgEELX2a6a5PbpjcsAVg0EIBBC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDQwBCyALQr+llJzP8NK75ABWDQRC19mumuT26Y3LACETIAtCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDQwCCyAMQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACERIAxCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDQwDCyAVQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRYgFUL//8+K6///1R5RDQNCms3/y6O9xIAaIQ0gFSEODAULIBAhEwsgCyERCyAMIRYgFSEODAILQv//z4rr///VHiEOIBRCqtX+////v/+5f1YNAEKazf/Lo73EgBohDQwBCyAVQv//z4rr///VHn0iFyAUQqvV/v///7//uX9UrSIRfSEOIAxCpOzDtY/UtJjnAH0iEyAVQv//z4rr///VHlQgESAXVnKtIhF9IRYgC0K/pZScz/DSu+QAfSIVIAxCpOzDtY/UtJjnAFQgESATVnKtIhN9IREgEELX2a6a5PbpjcsAfSIMIAtCv6WUnM/w0rvkAFQgEyAVVnKtIgt9IRMgDSAQQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSENIBRC1aqBgICAwIDGAHwhFAsgAyAUNwPoJSADIA43A+AlIAMgFjcD2CUgAyARNwPQJSADIBM3A8glIAMgDTcDwCUgA0HgJGogA0HAJWogA0GgI2oQuwFCms3/y6O9xIAaIRUgAykD6CQiCyALfCIQIAtUIBAgAykD8CQiCyALfCIOIAtUIA4gAykD+CQiCyALfCIMIAtUIAwgAykDgCUiCyALfCINIAtUIA0gAykDiCUiCyALfCITIAtUrXwiFiANVHKtfCIXIAxUcq18IhEgDlRyrXwiDiAQVHKtIAMpA+AkQgGGhCIUIQ0CQAJAAkAgFEKazf/Lo73EgBpSDQBC19mumuT26Y3LACEVIA4iDULX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhFSARIg1Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIRUgFyINQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIRUgFiINQv//z4rr///VHlINAEKr1f7///+//7l/IRUgEyINQqvV/v///7//uX9RDQELIA0gFVoNACAOIQ0gESEQIBchCyAWIQwMAQsgFkL//8+K6///1R59Ig0gE0Kr1f7///+//7l/VK0iC30hDCAXQqTsw7WP1LSY5wB9IhAgFkL//8+K6///1R5UIAsgDVZyrSINfSELIBFCv6WUnM/w0rvkAH0iFiAXQqTsw7WP1LSY5wBUIA0gEFZyrSINfSEQIA5C19mumuT26Y3LAH0iFSARQr+llJzP8NK75ABUIA0gFlZyrSIRfSENIBQgDkLX2a6a5PbpjcsAVCARIBVWcq19QprN/8ujvcSAGn0hFCATQtWqgYCAgMCAxgB8IRMLQprN/8ujvcSAGiEWIBRCAYYgDSANfCIiIA1UICIgECAQfCIOIBBUIA4gCyALfCINIAtUIA0gDCAMfCILIAxUIAsgEyATfCIUIBNUrXwiFyALVHKtfCIVIA1Ucq18IhEgDlRyrXwiDiAiVHKthCITIQ0CQAJAAkAgE0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEWIA4iDULX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhFiARIg1Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIRYgFSINQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIRYgFyINQv//z4rr///VHlINAEKr1f7///+//7l/IRYgFCINQqvV/v///7//uX9RDQELIA0gFloNACAOIQ0gESEQIBUhCyAXIQwMAQsgF0L//8+K6///1R59Ig0gFEKr1f7///+//7l/VK0iC30hDCAVQqTsw7WP1LSY5wB9IhAgF0L//8+K6///1R5UIAsgDVZyrSINfSELIBFCv6WUnM/w0rvkAH0iFyAVQqTsw7WP1LSY5wBUIA0gEFZyrSINfSEQIA5C19mumuT26Y3LAH0iFSARQr+llJzP8NK75ABUIA0gF1ZyrSIRfSENIBMgDkLX2a6a5PbpjcsAVCARIBVWcq19QprN/8ujvcSAGn0hEyAUQtWqgYCAgMCAxgB8IRQLQprN/8ujvcSAGiEOIA0gDXwiFiANVCAWIBAgECAQfCIQViAQIBAgCyALfCIRIAtUIBEgDCAMfCILIAxUIAsgFCAUfCINIBRUrXwiFyALVHKtfCIVIBFUcq18IhBWcq18IgwgFlRyrSATQgGGhCITIQsCQAJAAkAgE0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEOIAwiC0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDiAQIgtCv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQ4gFSILQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQ4gFyILQv//z4rr///VHlINAEKr1f7///+//7l/IQ4gDSILQqvV/v///7//uX9RDQELIAsgDloNACAMIQsgECERIBUhDiAXIRYMAQsgF0L//8+K6///1R59Ig4gDUKr1f7///+//7l/VK0iC30hFiAVQqTsw7WP1LSY5wB9IhEgF0L//8+K6///1R5UIAsgDlZyrSILfSEOIBBCv6WUnM/w0rvkAH0iFyAVQqTsw7WP1LSY5wBUIAsgEVZyrSILfSERIAxC19mumuT26Y3LAH0iFSAQQr+llJzP8NK75ABUIAsgF1ZyrSIQfSELIBMgDELX2a6a5PbpjcsAVCAQIBVWcq19QprN/8ujvcSAGn0hEyANQtWqgYCAgMCAxgB8IQ0LIAMgDTcDuCUgAyAWNwOwJSADIA43A6glIAMgETcDoCUgAyALNwOYJSADIBM3A5AlQprN/8ujvcSAGiEMIBkgGXwiEyAZVCATICAgIHwiDiAgVCAOIA4gGiAafCINIBpUIA0gHCAcfCILIBxUIAsgDyAPfCIUIA9UrXwiECALVHKtfCIRIA1Ucq18Ig5Wcq18Ig0gE1RyrSASQgGGhCITIQsCQAJAAkAgE0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEMIA0iC0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDCAOIgtCv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQwgESILQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQwgECILQv//z4rr///VHlINAEKr1f7///+//7l/IQwgFCILQqvV/v///7//uX9RDQELIAsgDFoNACANIQsgDiEMIBEhDyAQIRIMAQsgEEL//8+K6///1R59Ig8gFEKr1f7///+//7l/VK0iC30hEiARQqTsw7WP1LSY5wB9IgwgEEL//8+K6///1R5UIAsgD1ZyrSILfSEPIA5Cv6WUnM/w0rvkAH0iECARQqTsw7WP1LSY5wBUIAsgDFZyrSILfSEMIA1C19mumuT26Y3LAH0iESAOQr+llJzP8NK75ABUIAsgEFZyrSIOfSELIBMgDULX2a6a5PbpjcsAVCAOIBFWcq19QprN/8ujvcSAGn0hEyAUQtWqgYCAgMCAxgB8IRQLIAMgGDcD6CUgAyAjNwPgJSADICE3A9glIAMgGzcD0CUgAyAeNwPIJSADIB83A8AlIANB2CZqIgIgA0HAJWoiASADQbAkahCDAiABIANBkCJqIAIQuwEgA0GIJ2ogASADQZAlahCDAiADICU3A+AnIAMgJzcD2CcgAyAoNwPQJyADICQ3A8gnIAMgHTcDwCcgAyApNwO4JyADIBQ3A4AnIAMgEjcD+CYgAyAPNwPwJiADIAw3A+gmIAMgCzcD4CYgAyATNwPYJiABIAIQ8gIgAygCwCUEQEGQjcUAQSsgA0HvJ2pBgI3FAEGgksUAEMoDAAsgACADQcglakGQAfwKAAAMAwsgEELX2a6a5PbpjcsAVg0AAkAgEELX2a6a5PbpjcsAUgRAIA8hDiAMIRIgCyERIBAhEwwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACETIAtCv6WUnM/w0rvkAFIEQCAPIQ4gDCESIAshEQwBCyAMQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACERIAxCpOzDtY/UtJjnAFIEQCAPIQ4gDCESDAELIA9C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhEiAPQv//z4rr///VHlIEQCAPIQ4MAQtC///Piuv//9UeIQ4gFEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDQwBCyAPQv//z4rr///VHn0iEyAUQqvV/v///7//uX9UrSISfSEOIAxCpOzDtY/UtJjnAH0iESAPQv//z4rr///VHlQgEiATVnKtIg99IRIgC0K/pZScz/DSu+QAfSITIAxCpOzDtY/UtJjnAFQgDyARVnKtIg99IREgEELX2a6a5PbpjcsAfSIMIAtCv6WUnM/w0rvkAFQgDyATVnKtIgt9IRMgDSAQQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSENIBRC1aqBgICAwIDGAHwhFAsgAyAUNwPYHiADIA43A9AeIAMgEjcDyB4gAyARNwPAHiADIBM3A7geIAMgDTcDsB5BKCEBIAMpA4AeIRggAykDiB4hGSADKQOQHiEWIAMpA5geIRcgAykDoB4hEyADKQOoHiERQgAhC0IAIRVCACESQgAhD0IAIQxCACEQA0AgA0GgFGogA0GAHmogAWopAwAiDUIAIBFCABDJAyADQbAUaiANQgAgE0IAEMkDIANBwBRqIA1CACAXQgAQyQMgA0HQFGogDUIAIBZCABDJAyADQeAUaiANQgAgGUIAEMkDIANB8BRqIA1CACAYQgAQyQMgA0GQFGogAykDoBQiDiALfCIUQv3/8//P///5iX9+IgtCAEKr1f7///+//7l/QgAQyQMgA0GAFGogC0IAQv//z4rr///VHkIAEMkDIANB8BNqIAtCAEKk7MO1j9S0mOcAQgAQyQMgA0HgE2ogC0IAQr+llJzP8NK75ABCABDJAyADQdATaiALQgBC19mumuT26Y3LAEIAEMkDIANBwBNqIAtCAEKazf/Lo73EgBpCABDJAyADKQPIEyADKQPwFCINIBB8IhwgAykD6BQgAykD4BQiCyAMfCIbIAtUrXwgGyADKQPYFCADKQPQFCILIA98IhAgC1StfCAQIAMpA8gUIAMpA8AUIgsgEnwiDyALVK18IA8gAykDuBQgAykDsBQiCyAVfCIMIAtUrXwgDCADKQOoFCAOIBRWrXx8IgsgDFStfHwiEiAPVK18fCIOIBBUrXx8IgwgG1StfHwiGiADKQPAE3wiGyAaVK18IBsgAykD2BMgDCADKQPQE3wiECAMVK18IBAgAykD6BMgDiADKQPgE3wiDyAOVK18IA8gAykD+BMgEiADKQPwE3wiDiASVK18IA4gAykDiBQgCyADKQOAFCILfCIMIAtUrXwgDCADKQOYFCADKQOQFCILIBR8IAtUrXx8IgsgDFStfHwiFSAOVK18fCISIA9UrXx8Ig8gEFStfHwiDCAbVK18IBogHFStIAMpA/gUIA0gHFatfHx8IRAgAUEIayIBQXhHDQALAkACQCAQQprN/8ujvcSAGlYNACAQQprN/8ujvcSAGlIEQCAVIRsgEiEhIA8hHiAMIR8MAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIBUhGyASISEgDyEeIAwhHwwBCyAPQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEfIA9Cv6WUnM/w0rvkAFIEQCAVIRsgEiEhIA8hHgwBCyASQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEeIBJCpOzDtY/UtJjnAFIEQCAVIRsgEiEhDAELIBVC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhISAVQv//z4rr///VHlIEQCAVIRsMAQtC///Piuv//9UeIRsgC0Kq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEAwBCyAVQv//z4rr///VHn0iESALQqvV/v///7//uX9UrSINfSEbIBJCpOzDtY/UtJjnAH0iDiAVQv//z4rr///VHlQgDSARVnKtIg19ISEgD0K/pZScz/DSu+QAfSIRIBJCpOzDtY/UtJjnAFQgDSAOVnKtIg19IR4gDELX2a6a5PbpjcsAfSIOIA9Cv6WUnM/w0rvkAFQgDSARVnKtIg19IR8gECAMQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSEQIAtC1aqBgICAwIDGAHwhCwtBKCEBIAMpA6AjISYgAykDqCMhIiADKQOwIyElIAMpA7gjISMgAykDwCMhICADKQPIIyEnQgAhDUIAIRFCACEMQgAhFUIAIRZCACEUA0AgA0HgEmogA0GgI2ogAWopAwAiDkIAICdCABDJAyADQfASaiAOQgAgIEIAEMkDIANBgBNqIA5CACAjQgAQyQMgA0GQE2ogDkIAICVCABDJAyADQaATaiAOQgAgIkIAEMkDIANBsBNqIA5CACAmQgAQyQMgA0HQEmogAykD4BIiDyANfCIaQv3/8//P///5iX9+Ig1CAEKr1f7///+//7l/QgAQyQMgA0HAEmogDUIAQv//z4rr///VHkIAEMkDIANBsBJqIA1CAEKk7MO1j9S0mOcAQgAQyQMgA0GgEmogDUIAQr+llJzP8NK75ABCABDJAyADQZASaiANQgBC19mumuT26Y3LAEIAEMkDIANBgBJqIA1CAEKazf/Lo73EgBpCABDJAyADKQOIEiADKQOwEyIOIBR8IhggAykDqBMgAykDoBMiDSAWfCIXIA1UrXwgFyADKQOYEyADKQOQEyINIBV8IhMgDVStfCATIAMpA4gTIAMpA4ATIg0gDHwiEiANVK18IBIgAykD+BIgAykD8BIiDSARfCIMIA1UrXwgDCADKQPoEiAPIBpWrXx8Ig0gDFStfHwiESASVK18fCIPIBNUrXx8IgwgF1StfHwiGSADKQOAEnwiFyAZVK18IBcgAykDmBIgDCADKQOQEnwiEyAMVK18IBMgAykDqBIgDyADKQOgEnwiEiAPVK18IBIgAykDuBIgESADKQOwEnwiDyARVK18IA8gAykDyBIgDSADKQPAEiINfCIMIA1UrXwgDCADKQPYEiADKQPQEiINIBp8IA1UrXx8Ig0gDFStfHwiESAPVK18fCIMIBJUrXx8IhUgE1StfHwiFiAXVK18IBggGVatIAMpA7gTIA4gGFatfHx8IRQgAUEIayIBQXhHDQALAkACQCAUQprN/8ujvcSAGlYNACAUQprN/8ujvcSAGlIEQCARIRcgDCEYIBUhGiAWIRwMAgsgFkLX2a6a5PbpjcsAVg0AAkAgFkLX2a6a5PbpjcsAUgRAIBEhFyAMIRggFSEaIBYhHAwBCyAVQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEcIBVCv6WUnM/w0rvkAFIEQCARIRcgDCEYIBUhGgwBCyAMQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEaIAxCpOzDtY/UtJjnAFIEQCARIRcgDCEYDAELIBFC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhGCARQv//z4rr///VHlIEQCARIRcMAQtC///Piuv//9UeIRcgDUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohFAwBCyARQv//z4rr///VHn0iDyANQqvV/v///7//uX9UrSIOfSEXIAxCpOzDtY/UtJjnAH0iEiARQv//z4rr///VHlQgDiAPVnKtIg59IRggFUK/pZScz/DSu+QAfSIPIAxCpOzDtY/UtJjnAFQgDiASVnKtIgx9IRogFkLX2a6a5PbpjcsAfSIOIBVCv6WUnM/w0rvkAFQgDCAPVnKtIgx9IRwgFCAWQtfZrprk9umNywBUIAwgDlZyrX1Cms3/y6O9xIAafSEUIA1C1aqBgICAwIDGAHwhDQsgAyANNwP4IyADIBc3A/AjIAMgGDcD6CMgAyAaNwPgIyADIBw3A9gjIAMgFDcD0CNBKCEBQgAhFkIAIRJCACEPQgAhDEIAIRUDQCADQaARaiADQdAjaiABaikDACIOQgAgJ0IAEMkDIANBsBFqIA5CACAgQgAQyQMgA0HAEWogDkIAICNCABDJAyADQdARaiAOQgAgJUIAEMkDIANB4BFqIA5CACAiQgAQyQMgA0HwEWogDkIAICZCABDJAyADQZARaiADKQOgESIRIBZ8IihC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQYARaiAOQgBC///Piuv//9UeQgAQyQMgA0HwEGogDkIAQqTsw7WP1LSY5wBCABDJAyADQeAQaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB0BBqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HAEGogDkIAQprN/8ujvcSAGkIAEMkDIAMpA8gQIAMpA/ARIg4gFXwiJCADKQPoESAMIAMpA+ARIgx8IhUgDFStfCAVIAMpA9gRIAMpA9ARIgwgD3wiEyAMVK18IBMgAykDyBEgAykDwBEiDCASfCISIAxUrXwgEiADKQO4ESADKQOwESIMIB18Ig8gDFStfCAPIAMpA6gRIBEgKFatfHwiDCAPVK18fCIWIBJUrXx8IhIgE1StfHwiDyAVVK18fCIZIAMpA8AQfCIVIBlUrXwgFSADKQPYECAPIAMpA9AQfCITIA9UrXwgEyADKQPoECASIAMpA+AQfCIRIBJUrXwgESADKQP4ECAWIAMpA/AQfCISIBZUrXwgEiADKQOIESAMIAMpA4ARIgx8Ig8gDFStfCAPIAMpA5gRIAMpA5ARIgwgKHwgDFStfHwiFiAPVK18fCIdIBJUrXx8IhIgEVStfHwiDyATVK18fCIMIBVUrXwgGSAkVK0gAykD+BEgDiAkVq18fHwhFSABQQhrIgFBeEcNAAsCQAJAIBVCms3/y6O9xIAaVg0AIBVCms3/y6O9xIAaUgRAIB0hDiASIRkgDyERIAwhEwwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgHSEOIBIhGSAPIREgDCETDAELIA9Cv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRMgD0K/pZScz/DSu+QAUgRAIB0hDiASIRkgDyERDAELIBJCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIREgEkKk7MO1j9S0mOcAUgRAIB0hDiASIRkMAQsgHUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEZIB1C///Piuv//9UeUgRAIB0hDgwBC0L//8+K6///1R4hDiAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEVDAELIB1C///Piuv//9UefSIZIBZCq9X+////v/+5f1StIhF9IQ4gEkKk7MO1j9S0mOcAfSITIB1C///Piuv//9UeVCARIBlWcq0iEX0hGSAPQr+llJzP8NK75AB9Ih0gEkKk7MO1j9S0mOcAVCARIBNWcq0iE30hESAMQtfZrprk9umNywB9IhIgD0K/pZScz/DSu+QAVCATIB1Wcq0iD30hEyAVIAxC19mumuT26Y3LAFQgDyASVnKtfUKazf/Lo73EgBp9IRUgFkLVqoGAgIDAgMYAfCEWCyADIBY3A6gkIAMgDjcDoCQgAyAZNwOYJCADIBE3A5AkIAMgEzcDiCQgAyAVNwOAJEEoIQFCACEdQgAhGUIAIRJCACEPQgAhDEIAIREDQCADQeAPaiADQdAdaiABaikDACIOQgAgDUIAEMkDIANB8A9qIA5CACAXQgAQyQMgA0GAEGogDkIAIBhCABDJAyADQZAQaiAOQgAgGkIAEMkDIANBoBBqIA5CACAcQgAQyQMgA0GwEGogDkIAIBRCABDJAyADQdAPaiADKQPgDyITIB18Ih1C/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQcAPaiAOQgBC///Piuv//9UeQgAQyQMgA0GwD2ogDkIAQqTsw7WP1LSY5wBCABDJAyADQaAPaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBkA9qIA5CAELX2a6a5PbpjcsAQgAQyQMgA0GAD2ogDkIAQprN/8ujvcSAGkIAEMkDIAMpA4gPIAMpA7AQIg4gEXwiJCADKQOoECAMIAMpA6AQIgx8IhUgDFStfCAVIAMpA5gQIAMpA5AQIgwgD3wiESAMVK18IBEgAykDiBAgAykDgBAiDCASfCISIAxUrXwgEiADKQP4DyADKQPwDyIMIBl8Ig8gDFStfCAPIAMpA+gPIBMgHVatfHwiDCAPVK18fCIZIBJUrXx8IhIgEVStfHwiDyAVVK18fCIWIAMpA4APfCIVIBZUrXwgFSADKQOYDyAPIAMpA5APfCITIA9UrXwgEyADKQOoDyASIAMpA6APfCIRIBJUrXwgESADKQO4DyAZIAMpA7APfCISIBlUrXwgEiADKQPIDyAMIAMpA8APIgx8Ig8gDFStfCAPIAMpA9gPIAMpA9APIgwgHXwgDFStfHwiHSAPVK18fCIZIBJUrXx8IhIgEVStfHwiDyATVK18fCIMIBVUrXwgFiAkVK0gAykDuBAgDiAkVq18fHwhESABQQhrIgFBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIBkhFyASIRggDyEaIAwhHAwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgGSEXIBIhGCAPIRogDCEcDAELIA9Cv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRwgD0K/pZScz/DSu+QAUgRAIBkhFyASIRggDyEaDAELIBJCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRogEkKk7MO1j9S0mOcAUgRAIBkhFyASIRgMAQsgGUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEYIBlC///Piuv//9UeUgRAIBkhFwwBC0L//8+K6///1R4hFyAdQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIBlC///Piuv//9UefSITIB1Cq9X+////v/+5f1StIg19IRcgEkKk7MO1j9S0mOcAfSIOIBlC///Piuv//9UeVCANIBNWcq0iDX0hGCAPQr+llJzP8NK75AB9IhMgEkKk7MO1j9S0mOcAVCANIA5Wcq0iDX0hGiAMQtfZrprk9umNywB9Ig4gD0K/pZScz/DSu+QAVCANIBNWcq0iDX0hHCARIAxC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IREgHULVqoGAgIDAgMYAfCEdCyADIB03A9gkIAMgFzcD0CQgAyAYNwPIJCADIBo3A8AkIAMgHDcDuCQgAyARNwOwJEEoIQFCACEUQgAhDkIAIQxCACEVQgAhFkIAIQ0DQCADQaAOaiADQbAeaiABaikDACIPQgAgC0IAEMkDIANBsA5qIA9CACAbQgAQyQMgA0HADmogD0IAICFCABDJAyADQdAOaiAPQgAgHkIAEMkDIANB4A5qIA9CACAfQgAQyQMgA0HwDmogD0IAIBBCABDJAyADQZAOaiADKQOgDiISIBR8IhRC/f/z/8////mJf34iD0IAQqvV/v///7//uX9CABDJAyADQYAOaiAPQgBC///Piuv//9UeQgAQyQMgA0HwDWogD0IAQqTsw7WP1LSY5wBCABDJAyADQeANaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB0A1qIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HADWogD0IAQprN/8ujvcSAGkIAEMkDIAMpA8gNIAMpA/AOIg8gDXwiJCADKQPoDiADKQPgDiINIBZ8IhkgDVStfCAZIAMpA9gOIAMpA9AOIg0gFXwiFiANVK18IBYgAykDyA4gAykDwA4iDSAMfCITIA1UrXwgEyADKQO4DiADKQOwDiINIA58IgwgDVStfCAMIAMpA6gOIBIgFFatfHwiDSAMVK18fCIVIBNUrXx8Ig4gFlStfHwiDCAZVK18fCIZIAMpA8ANfCIWIBlUrXwgFiAWIAMpA9gNIAwgAykD0A18IhMgDFStfCATIAMpA+gNIA4gAykD4A18IhIgDlStfCASIAMpA/gNIBUgAykD8A18Ig4gFVStfCAOIA4gAykDiA4gDSADKQOADiINfCIMIA1UrXwgDCADKQOYDiADKQOQDiINIBR8IA1UrXx8IhQgDFStfHwiDlatfHwiDCASVK18fCIVIBNUrXx8IhZWrXwgGSAkVK0gAykD+A4gDyAkVq18fHwhDSABQQhrIgFBeEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AIA1Cms3/y6O9xIAaUgRAIA4hCyAMIQ8gFSEQIBYhEwwCCyAWQtfZrprk9umNywBWDQACQCAWQtfZrprk9umNywBSBEAgDiELIAwhDyAVIRAgFiETDAELIBVCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRMgFUK/pZScz/DSu+QAUgRAIA4hCyAMIQ8gFSEQDAELIAxCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRAgDEKk7MO1j9S0mOcAUgRAIA4hCyAMIQ8MAQsgDkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEPIA5C///Piuv//9UeUgRAIA4hCwwBC0L//8+K6///1R4hCyAUQqrV/v///7//uX9WDQELQprN/8ujvcSAGiENDAELIA5C///Piuv//9UefSISIBRCq9X+////v/+5f1StIg99IQsgDEKk7MO1j9S0mOcAfSIQIA5C///Piuv//9UeVCAPIBJWcq0iDn0hDyAVQr+llJzP8NK75AB9IhIgDEKk7MO1j9S0mOcAVCAOIBBWcq0iDH0hECAWQtfZrprk9umNywB9Ig4gFUK/pZScz/DSu+QAVCAMIBJWcq0iDH0hEyANIBZC19mumuT26Y3LAFQgDCAOVnKtfUKazf/Lo73EgBp9IQ0gFELVqoGAgIDAgMYAfCEUCyADIBQ3A+glIAMgCzcD4CUgAyAPNwPYJSADIBA3A9AlIAMgEzcDyCUgAyANNwPAJUKazf/Lo73EgBohFiADQdgmaiADQcAlaiADQYAkahCDAiAcIBx8IhIgHFQgEiAaIBp8IgwgGlQgDCAMIBggGHwiDSAYVCANIBcgF3wiCyAXVCALIB0gHXwiFCAdVK18Ig8gC1RyrXwiDiANVHKtfCIMVnKtfCINIBJUcq0gEUIBhoQiEyELAkACQAJAIBNCms3/y6O9xIAaUg0AQtfZrprk9umNywAhFiANIgtC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIRYgDCILQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEWIA4iC0Kk7MO1j9S0mOcAUg0AQv//z4rr///VHiEWIA8iC0L//8+K6///1R5SDQBCq9X+////v/+5fyEWIBQiC0Kr1f7///+//7l/UQ0BCyALIBZaDQAgDyELIA4hFiAMIRUgDSEQDAELIA9C///Piuv//9UefSIQIBRCq9X+////v/+5f1StIhJ9IQsgDkKk7MO1j9S0mOcAfSIRIA9C///Piuv//9UeVCAQIBJUcq0iD30hFiAMQr+llJzP8NK75AB9IhIgDkKk7MO1j9S0mOcAVCAPIBFWcq0iD30hFSANQtfZrprk9umNywB9Ig4gDEK/pZScz/DSu+QAVCAPIBJWcq0iDH0hECATIA1C19mumuT26Y3LAFQgDCAOVnKtfUKazf/Lo73EgBp9IRMgFELVqoGAgIDAgMYAfCEUCyADIBQ3A+glIAMgCzcD4CUgAyAWNwPYJSADIBU3A9AlIAMgEDcDyCUgAyATNwPAJSADQeAeaiADQdgmaiADQcAlahCDAkEoIQFCACEUQgAhD0IAIRZCACELQgAhEEIAIQ0DQCADQeAMaiADQeAeaiABaikDACIMQgAgJ0IAEMkDIANB8AxqIAxCACAgQgAQyQMgA0GADWogDEIAICNCABDJAyADQZANaiAMQgAgJUIAEMkDIANBoA1qIAxCACAiQgAQyQMgA0GwDWogDEIAICZCABDJAyADQdAMaiADKQPgDCIOIBR8IhdC/f/z/8////mJf34iDEIAQqvV/v///7//uX9CABDJAyADQcAMaiAMQgBC///Piuv//9UeQgAQyQMgA0GwDGogDEIAQqTsw7WP1LSY5wBCABDJAyADQaAMaiAMQgBCv6WUnM/w0rvkAEIAEMkDIANBkAxqIAxCAELX2a6a5PbpjcsAQgAQyQMgA0GADGogDEIAQprN/8ujvcSAGkIAEMkDIAMpA4gMIAMpA7ANIgwgDXwiFSADKQOoDSADKQOgDSINIBB8IhAgDVStfCAQIAMpA5gNIAsgAykDkA0iC3wiESALVK18IBEgAykDiA0gAykDgA0iCyAWfCISIAtUrXwgEiADKQP4DCADKQPwDCILIA98Ig0gC1StfCANIAMpA+gMIA4gF1atfHwiCyANVK18fCIPIBJUrXx8Ig4gEVStfHwiDSAQVK18fCITIAMpA4AMfCIQIBNUrXwgECAQIAMpA5gMIA0gAykDkAx8IhEgDVStfCARIAMpA6gMIA4gAykDoAx8IhIgDlStfCASIAMpA7gMIA8gAykDsAx8Ig4gD1StfCAOIAMpA8gMIAsgAykDwAwiC3wiDSALVK18IA0gAykD2AwgAykD0AwiCyAXfCALVK18fCIUIA1UrXx8Ig8gDlStfHwiFiASVK18fCILIBFUrXx8IhBWrXwgEyAVVK0gAykDuA0gDCAVVq18fHwhDSABQQhrIgFBeEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AIA1Cms3/y6O9xIAaUgRAIA8hESAWIQ4gCyEMIBAhEwwCCyAQQtfZrprk9umNywBWDQACQCAQQtfZrprk9umNywBSBEAgDyERIBYhDiALIQwgECETDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRMgC0K/pZScz/DSu+QAUgRAIA8hESAWIQ4gCyEMDAELIBZCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQwgFkKk7MO1j9S0mOcAUgRAIA8hESAWIQ4MAQsgD0L//8+K6///1R5WDQFCpOzDtY/UtJjnACEOIA9C///Piuv//9UeUgRAIA8hEQwBC0L//8+K6///1R4hESAUQqrV/v///7//uX9WDQELQprN/8ujvcSAGiENDAELIA9C///Piuv//9UefSIOIBRCq9X+////v/+5f1StIgx9IREgFkKk7MO1j9S0mOcAfSISIA9C///Piuv//9UeVCAMIA5Wcq0iDH0hDiALQr+llJzP8NK75AB9IhMgFkKk7MO1j9S0mOcAVCAMIBJWcq0iEn0hDCAQQtfZrprk9umNywB9Ig8gC0K/pZScz/DSu+QAVCASIBNWcq0iC30hEyANIBBC19mumuT26Y3LAFQgCyAPVnKtfUKazf/Lo73EgBp9IQ0gFELVqoGAgIDAgMYAfCEUCyADIBQ3A4AnIAMgETcD+CYgAyAONwPwJiADIAw3A+gmIAMgEzcD4CYgAyANNwPYJiADQcAlaiICIANBsCRqIANB4B5qEIMCIANB4CRqIgQgA0GAHmogAhC7ASADQeglaiADQZgdaikDADcDACADQeAlaiADQZAdaikDADcDACADQdglaiADQYgdaikDADcDACADQdAlaiADQYAdaikDADcDACADQcglaiIBIANB+BxqKQMANwMAIAMgAykD8Bw3A8AlIANBkCVqIgYgA0GAJGoiBSACELsBIANBiCdqIAQgBhCDAiADQbgnaiAFIANBsB5qELsBIAIgA0HYJmoQ8gIgAygCwCUNASAAIAFBkAH8CgAACyADQfAnaiQADwtBkI3FAEErIANB7ydqQYCNxQBBwJLFABDKAwALr9oBAgl/KX4jAEHQKGsiAiQAIAJBoB1qECYCQAJAAkACQAJAAkACQCACKALAIEEBcQRAIAIpA6AhIS4gAikDmCEhLyACKQOQISEwIAIpA4ghITEgAikDgCEhMiACKQP4ICEzIAIpA/AgISIgAikD6CAhIyACKQPgICEkIAIpA9ggISUgAikD0CAhJiACKQPIICEnQSghAyACQegjaiACQdAhaikDADcDACACQeAjaiACQcghaikDADcDACACQdgjaiACQcAhaikDADcDACACQdAjaiACQbghaikDADcDACACQcgjaiACQbAhaikDADcDACACIAIpA6ghNwPAIyABKQMAIRMgASkDCCEVIAEpAxAhFiABKQMYIRcgASkDICEYIAEpAyghGQNAIAJBwBxqIAEgA2opAwAiDUIAIBlCABDJAyACQdAcaiANQgAgGEIAEMkDIAJB4BxqIA1CACAXQgAQyQMgAkHwHGogDUIAIBZCABDJAyACQYAdaiANQgAgFUIAEMkDIAJBkB1qIA1CACATQgAQyQMgAkGwHGogFCACKQPAHCIUfCISQgBCAEL9//P/z///+Yl/EMkDIAJBoBxqIAIpA7gcIg1CAEKr1f7///+//7l/QgAQyQMgAkGQHGogDUIAQv//z4rr///VHkIAEMkDIAJBgBxqIA1CAEKk7MO1j9S0mOcAQgAQyQMgAkHwG2ogDUIAQr+llJzP8NK75ABCABDJAyACQeAbaiANQgBC19mumuT26Y3LAEIAEMkDIAJB0BtqIA1CAEKazf/Lo73EgBpCABDJAyACKQPYGyACKQOQHSIaIA98Ig0gAikDiB0gAikDgB0iDyARfCIQIA9UrXwgECACKQP4HCACKQPwHCIPIA58Ig4gD1StfCAOIAIpA+gcIAIpA+AcIg8gDHwiDCAPVK18IAwgAikD2BwgAikD0BwiDyALfCILIA9UrXwgCyACKQPIHCASIBRUrXx8IhEgC1StfHwiCyAMVK18fCIMIA5UrXx8Ig4gEFStfHwiECACKQPQG3wiDyAQVK18IA8gAikD6BsgDiAOIAIpA+AbfCIOVq18IA4gDiACKQP4GyAMIAwgAikD8Bt8IgxWrXwgDCAMIAIpA4gcIAsgCyACKQOAHHwiC1atfCALIAsgAikDmBwgAikDkBwiFCARfCIRIBRUrXwgESACKQOoHCASIAIpA6AcIhJ8IBJUrXx8IhQgEVStfHwiC1atfHwiDFatfHwiDlatfHwiESAPVK18IA0gEFatIAIpA5gdIA0gGlStfHx8IQ8gA0EIayIDQXhHDQALIA9Cms3/y6O9xIAaVg0GIA9Cms3/y6O9xIAaUQ0BDAILQYzgwAAQ6AQACyARQtfZrprk9umNywBWDQQgEULX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEPDAELIA5Cv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRUgDkK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEPDAILIAxCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRAgDEKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEPDAMLIAtC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhEiALQv//z4rr///VHlENA0Kazf/Lo73EgBohDyALIQ0MBQsgESEVCyAOIRALIAwhEiALIQ0MAgtC///Piuv//9UeIQ0gFEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEPDAELIAtC///Piuv//9UefSISIBRCq9X+////v/+5f1StIhB9IQ0gDEKk7MO1j9S0mOcAfSITIAtC///Piuv//9UeVCAQIBJWcq0iC30hEiAOQr+llJzP8NK75AB9IhUgDEKk7MO1j9S0mOcAVCALIBNWcq0iC30hECARQtfZrprk9umNywB9IgwgDkK/pZScz/DSu+QAVCALIBVWcq0iC30hFSAPIBFC19mumuT26Y3LAFQgCyAMVnKtfUKazf/Lo73EgBp9IQ8gFELVqoGAgIDAgMYAfCEUCyACIBQ3A5gnIAIgDTcDkCcgAiASNwOIJyACIBA3A4AnIAIgFTcD+CYgAiAPNwPwJkEoIQMgAikDwCMhKCACKQPIIyEpIAIpA9AjISogAikD2CMhKyACKQPgIyEsIAIpA+gjIS1CACEPQgAhC0IAIQxCACEOQgAhEUIAIRQDQCACQfAaaiACQfAmaiADaikDACINQgAgLUIAEMkDIAJBgBtqIA1CACAsQgAQyQMgAkGQG2ogDUIAICtCABDJAyACQaAbaiANQgAgKkIAEMkDIAJBsBtqIA1CACApQgAQyQMgAkHAG2ogDUIAIChCABDJAyACQeAaaiAPIAIpA/AaIg98IhJCAEIAQv3/8//P///5iX8QyQMgAkHQGmogAikD6BoiDUIAQqvV/v///7//uX9CABDJAyACQcAaaiANQgBC///Piuv//9UeQgAQyQMgAkGwGmogDUIAQqTsw7WP1LSY5wBCABDJAyACQaAaaiANQgBCv6WUnM/w0rvkAEIAEMkDIAJBkBpqIA1CAELX2a6a5PbpjcsAQgAQyQMgAkGAGmogDUIAQprN/8ujvcSAGkIAEMkDIAIpA4gaIAIpA8AbIhMgFHwiDSACKQO4GyARIAIpA7AbIhF8IhAgEVStfCAQIAIpA6gbIAIpA6AbIhEgDnwiDiARVK18IA4gAikDmBsgAikDkBsiESAMfCIMIBFUrXwgDCACKQOIGyACKQOAGyIRIAt8IgsgEVStfCALIAIpA/gaIA8gElatfHwiDyALVK18fCILIAxUrXx8IgwgDlStfHwiDiAQVK18fCIQIAIpA4AafCIRIBBUrXwgESARIAIpA5gaIA4gDiACKQOQGnwiDlatfCAOIA4gAikDqBogDCAMIAIpA6AafCIMVq18IAwgDCACKQO4GiALIAsgAikDsBp8IgtWrXwgCyALIAIpA8gaIAIpA8AaIhUgD3wiDyAVVK18IA8gDyACKQPYGiASIAIpA9AaIhJ8IBJUrXx8Ig9WrXx8IgtWrXx8IgxWrXx8Ig5WrXx8IhFWrXwgDSAQVq0gAikDyBsgDSATVK18fHwhFCADQQhrIgNBeEcNAAsCQAJAIBRCms3/y6O9xIAaVg0AAkACQAJAAkAgFEKazf/Lo73EgBpSDQAgEULX2a6a5PbpjcsAVg0EIBFC19mumuT26Y3LAFIEQEKazf/Lo73EgBohFAwBCyAOQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEWIA5Cv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohFAwCCyAMQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEbIAxCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohFAwDCyALQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRggC0L//8+K6///1R5RDQNCms3/y6O9xIAaIRQgCyEaDAULIBEhFgsgDiEbCyAMIRggCyEaDAILQv//z4rr///VHiEaIA9CqtX+////v/+5f1YNAEKazf/Lo73EgBohFAwBCyALQv//z4rr///VHn0iDSAPQqvV/v///7//uX9UrSISfSEaIAxCpOzDtY/UtJjnAH0iECALQv//z4rr///VHlQgDSASVHKtIgt9IRggDkK/pZScz/DSu+QAfSINIAxCpOzDtY/UtJjnAFQgCyAQVnKtIgt9IRsgEULX2a6a5PbpjcsAfSIMIA5Cv6WUnM/w0rvkAFQgCyANVnKtIgt9IRYgFCARQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSEUIA9C1aqBgICAwIDGAHwhDwsgAiAPNwOYJCACIBo3A5AkIAIgGDcDiCQgAiAbNwOAJCACIBY3A/gjIAIgFDcD8CNBKCEDQgAhEUIAIRNCACENQgAhEEIAIQxCACEOA0AgAkGgGWogAkHwI2ogA2opAwAiC0IAIA9CABDJAyACQbAZaiALQgAgGkIAEMkDIAJBwBlqIAtCACAYQgAQyQMgAkHQGWogC0IAIBtCABDJAyACQeAZaiALQgAgFkIAEMkDIAJB8BlqIAtCACAUQgAQyQMgAkGQGWogESACKQOgGSIRfCISQgBCAEL9//P/z///+Yl/EMkDIAJBgBlqIAIpA5gZIgtCAEKr1f7///+//7l/QgAQyQMgAkHwGGogC0IAQv//z4rr///VHkIAEMkDIAJB4BhqIAtCAEKk7MO1j9S0mOcAQgAQyQMgAkHQGGogC0IAQr+llJzP8NK75ABCABDJAyACQcAYaiALQgBC19mumuT26Y3LAEIAEMkDIAJBsBhqIAtCAEKazf/Lo73EgBpCABDJAyACKQO4GCACKQPwGSIZIA58IgsgAikD6BkgAikD4BkiDiAMfCIMIA5UrXwgDCAMIAIpA9gZIBAgAikD0BkiEHwiDiAQVK18IA4gDiACKQPIGSACKQPAGSIQIA18Ig0gEFStfCANIA0gAikDuBkgEyACKQOwGSITfCIQIBNUrXwgECAQIAIpA6gZIBEgElatfHwiEFatfHwiDVatfHwiDlatfHwiDFatfHwiFSACKQOwGHwiFyAVVK18IBcgAikDyBggDCAMIAIpA8AYfCIMVq18IAwgAikD2BggDiAOIAIpA9AYfCIOVq18IA4gAikD6BggDSANIAIpA+AYfCINVq18IA0gAikD+BggAikD8BgiESAQfCIQIBFUrXwgECACKQOIGSASIAIpA4AZIhJ8IBJUrXx8IhEgEFStfHwiEyANVK18fCINIA5UrXx8IhAgDFStfHwiDCAXVK18IAsgFVatIAIpA/gZIAsgGVStfHx8IQ4gA0EIayIDQXhHDQALAkACQCAOQprN/8ujvcSAGlYNAAJAAkACQAJAIA5Cms3/y6O9xIAaUg0AIAxC19mumuT26Y3LAFYNBCAMQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ4MAQsgEEK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhFSAQQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ4MAgsgDUKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhCyANQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ4MAwsgE0L//8+K6///1R5WDQRCpOzDtY/UtJjnACEXIBNC///Piuv//9UeUQ0DQprN/8ujvcSAGiEOIBMhEgwFCyAMIRULIBAhCwsgDSEXIBMhEgwCC0L//8+K6///1R4hEiARQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ4MAQsgE0L//8+K6///1R59IgsgEUKr1f7///+//7l/VK0iFX0hEiANQqTsw7WP1LSY5wB9IhkgE0L//8+K6///1R5UIAsgFVRyrSILfSEXIBBCv6WUnM/w0rvkAH0iEyANQqTsw7WP1LSY5wBUIAsgGVZyrSINfSELIAxC19mumuT26Y3LAH0iGSAQQr+llJzP8NK75ABUIA0gE1ZyrSINfSEVIA4gDELX2a6a5PbpjcsAVCANIBlWcq19QprN/8ujvcSAGn0hDiARQtWqgYCAgMCAxgB8IRELQprN/8ujvcSAGiEQIBUgFnwiEyAVVCATIAsgG3wiDSALVCANIA0gFyAYfCIMIBdUIAwgDCASIBp8IgsgElQgCyALIA8gEXwiFyARVK18IgtWcq18IgxWcq18Ig1Wcq18IhIgE1RyrSAOIBR8fCIcIQ8CQAJAAkAgHEKazf/Lo73EgBpSDQBC19mumuT26Y3LACEQIBIiD0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhECANIg9Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIRAgDCIPQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIRAgCyIPQv//z4rr///VHlINAEKr1f7///+//7l/IRAgFyIPQqvV/v///7//uX9RDQELIA8gEFoNACASIRYgDSEbIAwhGCALIRkMAQsgC0L//8+K6///1R59Ig4gF0Kr1f7///+//7l/VK0iEH0hGSAMQqTsw7WP1LSY5wB9Ig8gC0L//8+K6///1R5UIA4gEFRyrSILfSEYIA1Cv6WUnM/w0rvkAH0iDiAMQqTsw7WP1LSY5wBUIAsgD1ZyrSILfSEbIBJC19mumuT26Y3LAH0iDCANQr+llJzP8NK75ABUIAsgDlZyrSILfSEWIBwgEkLX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hHCAXQtWqgYCAgMCAxgB8IRcLIAIgGTcDwCQgAiAXNwPIJCACIBg3A7gkIAIgGzcDsCQgAiAWNwOoJCACIBw3A6AkQprN/8ujvcSAGiEMIBwgFkLt2NuS+tLGg9wAfCILIBZUIAsgG0LFrsmCt4qW5/cAfCIOIBtUIA4gGEK6sZ2e9YqmpN8AfCISIBhUIBIgGUL+/8/fw/7/hRR9Ig0gGVQgDSANIBdC/f+LgICAwIT2AHwiFCAXVK18Ig1Wcq18IhAgElRyrXwiDyAOVHKtfCIRIAtUcq18QpPJg9S/2Jf7FXwiFSEOAkACQAJAIBVCms3/y6O9xIAaUg0AQtfZrprk9umNywAhDCARIg5C19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQwgDyIOQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEMIBAiDkKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEMIA0iDkL//8+K6///1R5SDQBCq9X+////v/+5fyEMIBQiDkKr1f7///+//7l/UQ0BCyAMIA5YDQAgESEOIA8hDCAQIQsgDSESDAELIA1C///Piuv//9UefSILIBRCq9X+////v/+5f1StIgx9IRIgEEKk7MO1j9S0mOcAfSIOIA1C///Piuv//9UeVCALIAxUcq0iDH0hCyAPQr+llJzP8NK75AB9Ig0gEEKk7MO1j9S0mOcAVCAMIA5Wcq0iDn0hDCARQtfZrprk9umNywB9IhAgD0K/pZScz/DSu+QAVCANIA5Ucq0iDX0hDiAVIBFC19mumuT26Y3LAFQgDSAQVnKtfUKazf/Lo73EgBp9IRUgFELVqoGAgIDAgMYAfCEUCyACIBQ3A5gnIAIgEjcDkCcgAiALNwOIJyACIAw3A4AnIAIgDjcD+CYgAiAVNwPwJkEoIQNCACEPQgAhEUIAIQxCACELQgAhEkIAIQ4DQCACQdAXaiACQfAmaiADaikDACINQgAgLkIAEMkDIAJB4BdqIA1CACAvQgAQyQMgAkHwF2ogDUIAIDBCABDJAyACQYAYaiANQgAgMUIAEMkDIAJBkBhqIA1CACAyQgAQyQMgAkGgGGogDUIAIDNCABDJAyACQcAXaiACKQPQFyITIA58Ig1CAEIAQv3/8//P///5iX8QyQMgAkGwF2ogAikDyBciDkIAQqvV/v///7//uX9CABDJAyACQaAXaiAOQgBC///Piuv//9UeQgAQyQMgAkGQF2ogDkIAQqTsw7WP1LSY5wBCABDJAyACQYAXaiAOQgBCv6WUnM/w0rvkAEIAEMkDIAJB8BZqIA5CAELX2a6a5PbpjcsAQgAQyQMgAkHgFmogDkIAQprN/8ujvcSAGkIAEMkDIAIpA+gWIAIpA6AYIhUgD3wiECACKQOYGCACKQOQGCIPIBF8Ig4gD1StfCAOIA4gAikDiBggAikDgBgiDyAMfCIMIA9UrXwgDCAMIAIpA/gXIAIpA/AXIg8gC3wiCyAPVK18IAsgCyACKQPoFyACKQPgFyIPIBJ8IhIgD1StfCASIBIgAikD2BcgDSATVK18fCISVq18fCILVq18fCIMVq18fCIOVq18fCIPIAIpA+AWfCIRIA9UrXwgESARIAIpA/gWIA4gAikD8BZ8IhMgDlStfCATIAIpA4gXIAwgDCACKQOAF3wiDFatfCAMIAIpA5gXIAsgCyACKQOQF3wiC1atfCALIAIpA6gXIBIgAikDoBciEnwiDiASVK18IA4gDiACKQO4FyANIAIpA7AXIg18IA1UrXx8Ig5WrXx8IhIgC1StfHwiCyAMVK18fCIMIBNUrXx8IhFWrXwgDyAQVK0gAikDqBggECAVVK18fHwhDyADQQhrIgNBeEcNAAsCQAJAIA9Cms3/y6O9xIAaVg0AAkACQAJAAkAgD0Kazf/Lo73EgBpSDQAgEULX2a6a5PbpjcsAVg0EIBFC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDwwBCyAMQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEaIAxCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDwwCCyALQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEdIAtCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDwwDCyASQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIR8gEkL//8+K6///1R5RDQNCms3/y6O9xIAaIQ8gEiEeDAULIBEhGgsgDCEdCyALIR8gEiEeDAILQv//z4rr///VHiEeIA5CqtX+////v/+5f1YNAEKazf/Lo73EgBohDwwBCyASQv//z4rr///VHn0iDSAOQqvV/v///7//uX9UrSIQfSEeIAtCpOzDtY/UtJjnAH0iEyASQv//z4rr///VHlQgDSAQVHKtIg19IR8gDEK/pZScz/DSu+QAfSISIAtCpOzDtY/UtJjnAFQgDSATVnKtIgt9IR0gEULX2a6a5PbpjcsAfSINIAxCv6WUnM/w0rvkAFQgCyASVnKtIgt9IRogDyARQtfZrprk9umNywBUIAsgDVZyrX1Cms3/y6O9xIAafSEPIA5C1aqBgICAwIDGAHwhDgsgAiAONwP4JCACIB43A/AkIAIgHzcD6CQgAiAdNwPgJCACIBo3A9gkIAIgDzcD0CRBKCEDIAJBmCdqIgdCADcDACACQZAnaiIFQgA3AwAgAkGIJ2oiBEIANwMAIAJBgCdqIghCADcDACACQfgmaiIGQgA3AwAgAkIANwPwJgJAAkACQAJAAkACQCACQaAkaiACQfAmaiIJQTAQ8QMEQCAHIAJByCRqKQMANwMAIAUgAkHAJGopAwA3AwAgBCACQbgkaikDADcDACAIIAJBsCRqKQMANwMAIAYgAkGoJGopAwA3AwAgAiACKQOgJDcD8CYgAiAJQfiewABBMBDxAwR+Qv//z4rr///VHiACKQOQJyILfSIMIAIpA5gnIg1Cq9X+////v/+5f1atIhJ9IRlCpOzDtY/UtJjnACACKQOIJyIQfSIRIAwgElQgC0L//8+K6///1R5Wcq0iC30hGEK/pZScz/DSu+QAIAIpA4AnIgx9IhIgCyARViAQQqTsw7WP1LSY5wBWcq0iC30hG0LX2a6a5PbpjcsAIAIpA/gmIhB9IhEgCyASViAMQr+llJzP8NK75ABWcq0iC30hFkKazf/Lo73EgBogAikD8CYgCyARViAQQtfZrprk9umNywBWcq18fSEcQqvV/v///7//uX8gDX0FIBcLNwOwKCACIBk3A6goIAIgGDcDoCggAiAbNwOYKCACIBY3A5AoIAIgHDcDiChCACEUQgAhDEIAIRBCACENQgAhE0IAIREDQCACQYAWaiACQYgoaiADaikDACILQgAgIkIAEMkDIAJBkBZqIAtCACAjQgAQyQMgAkGgFmogC0IAICRCABDJAyACQbAWaiALQgAgJUIAEMkDIAJBwBZqIAtCACAmQgAQyQMgAkHQFmogC0IAICdCABDJAyACQfAVaiACKQOAFiIVIBF8IhJCAEIAQv3/8//P///5iX8QyQMgAkHgFWogAikD+BUiC0IAQqvV/v///7//uX9CABDJAyACQdAVaiALQgBC///Piuv//9UeQgAQyQMgAkHAFWogC0IAQqTsw7WP1LSY5wBCABDJAyACQbAVaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJBoBVqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkGQFWogC0IAQprN/8ujvcSAGkIAEMkDIAIpA5gVIAIpA9AWIhcgFHwiCyACKQPIFiACKQPAFiIRIAx8IgwgEVStfCAMIAwgAikDuBYgAikDsBYiESAQfCIQIBFUrXwgECAQIAIpA6gWIAIpA6AWIhEgDXwiDSARVK18IA0gDSACKQOYFiATIAIpA5AWIhN8IhEgE1StfCARIBEgAikDiBYgEiAVVK18fCIRVq18fCINVq18fCIQVq18fCIMVq18fCIVIAIpA5AVfCIWIBVUrXwgFiACKQOoFSAMIAwgAikDoBV8IgxWrXwgDCACKQO4FSAQIBAgAikDsBV8IhBWrXwgECACKQPIFSANIA0gAikDwBV8Ig1WrXwgDSACKQPYFSACKQPQFSITIBF8IhEgE1StfCARIBEgAikD6BUgEiACKQPgFSISfCASVK18fCIRVq18fCITIA1UrXx8Ig0gEFStfHwiECAMVK18fCIMIBZUrXwgCyAVVq0gAikD2BYgCyAXVK18fHwhFCADQQhrIgNBeEcNAAsgFEKazf/Lo73EgBpYDQEMBQtCACEUQgAhDEIAIRBCACENQgAhE0IAIREDQCACQbAUaiACQcAjaiADaikDACILQgAgIkIAEMkDIAJBwBRqIAtCACAjQgAQyQMgAkHQFGogC0IAICRCABDJAyACQeAUaiALQgAgJUIAEMkDIAJB8BRqIAtCACAmQgAQyQMgAkGAFWogC0IAICdCABDJAyACQaAUaiACKQOwFCIVIBF8IhJCAEIAQv3/8//P///5iX8QyQMgAkGQFGogAikDqBQiC0IAQqvV/v///7//uX9CABDJAyACQYAUaiALQgBC///Piuv//9UeQgAQyQMgAkHwE2ogC0IAQqTsw7WP1LSY5wBCABDJAyACQeATaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJB0BNqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkHAE2ogC0IAQprN/8ujvcSAGkIAEMkDIAIpA8gTIAIpA4AVIhcgFHwiCyACKQP4FCACKQPwFCIRIAx8IgwgEVStfCAMIAwgAikD6BQgAikD4BQiESAQfCIQIBFUrXwgECAQIAIpA9gUIAIpA9AUIhEgDXwiDSARVK18IA0gDSACKQPIFCATIAIpA8AUIhN8IhEgE1StfCARIBEgAikDuBQgEiAVVK18fCIRVq18fCINVq18fCIQVq18fCIMVq18fCIVIAIpA8ATfCIWIBVUrXwgFiACKQPYEyAMIAwgAikD0BN8IgxWrXwgDCACKQPoEyAQIBAgAikD4BN8IhBWrXwgECACKQP4EyANIA0gAikD8BN8Ig1WrXwgDSACKQOIFCACKQOAFCITIBF8IhEgE1StfCARIBEgAikDmBQgEiACKQOQFCISfCASVK18fCIRVq18fCITIA1UrXx8Ig0gEFStfHwiECAMVK18fCIMIBZUrXwgCyAVVq0gAikDiBUgCyAXVK18fHwhFCADQQhrIgNBeEcNAAsgFEKazf/Lo73EgBpYDQEMAgsCQAJAAkACQCAUQprN/8ujvcSAGlINACAMQtfZrprk9umNywBWDQcgDELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEUDAELIBBCv6WUnM/w0rvkAFYNB0LX2a6a5PbpjcsAIRggEEK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEUDAILIA1CpOzDtY/UtJjnAFYNB0K/pZScz/DSu+QAIRkgDUKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEUDAMLIBNC///Piuv//9UeVg0HQqTsw7WP1LSY5wAhGyATQv//z4rr///VHlENA0Kazf/Lo73EgBohFCATIRUMCAsgDCEYCyAQIRkLIA0hGyATIRUMBQtC///Piuv//9UeIRUgEUKq1f7///+//7l/Vg0DDAILAkACQAJAAkAgFEKazf/Lo73EgBpSDQAgDELX2a6a5PbpjcsAVg0EIAxC19mumuT26Y3LAFIEQEKazf/Lo73EgBohFAwBCyAQQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEYIBBCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohFAwCCyANQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEZIA1CpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohFAwDCyATQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRsgE0L//8+K6///1R5RDQNCms3/y6O9xIAaIRQgEyEVDAcLIAwhGAsgECEZCyANIRsgEyEVDAQLQv//z4rr///VHiEVIBFCqtX+////v/+5f1gNAQsgE0L//8+K6///1R59IgsgEUKr1f7///+//7l/VK0iEn0hFSANQqTsw7WP1LSY5wB9IhYgE0L//8+K6///1R5UIAsgElRyrSILfSEbIBBCv6WUnM/w0rvkAH0iEiANQqTsw7WP1LSY5wBUIAsgFlZyrSILfSEZIAxC19mumuT26Y3LAH0iDSAQQr+llJzP8NK75ABUIAsgElZyrSILfSEYIBQgDELX2a6a5PbpjcsAVCALIA1Wcq19QprN/8ujvcSAGn0hFCARQtWqgYCAgMCAxgB8IREMAgtCms3/y6O9xIAaIRQMAQsgE0L//8+K6///1R59IgsgEUKr1f7///+//7l/VK0iEn0hFSANQqTsw7WP1LSY5wB9IhYgE0L//8+K6///1R5UIAsgElRyrSILfSEbIBBCv6WUnM/w0rvkAH0iEiANQqTsw7WP1LSY5wBUIAsgFlZyrSILfSEZIAxC19mumuT26Y3LAH0iDSAQQr+llJzP8NK75ABUIAsgElZyrSILfSEYIBQgDELX2a6a5PbpjcsAVCALIA1Wcq19QprN/8ujvcSAGn0hFCARQtWqgYCAgMCAxgB8IRELIAIgETcDqCUgAiAVNwOgJSACIBs3A5glIAIgGTcDkCUgAiAYNwOIJSACIBQ3A4AlQSghA0IAIRNCACENQgAhC0IAIRJCACEWQgAhHANAIAJB4BJqIAJB0CRqIANqKQMAIgxCACAOQgAQyQMgAkHwEmogDEIAIB5CABDJAyACQYATaiAMQgAgH0IAEMkDIAJBkBNqIAxCACAdQgAQyQMgAkGgE2ogDEIAIBpCABDJAyACQbATaiAMQgAgD0IAEMkDIAJB0BJqIAIpA+ASIhcgHHwiEEIAQgBC/f/z/8////mJfxDJAyACQcASaiACKQPYEiIMQgBCq9X+////v/+5f0IAEMkDIAJBsBJqIAxCAEL//8+K6///1R5CABDJAyACQaASaiAMQgBCpOzDtY/UtJjnAEIAEMkDIAJBkBJqIAxCAEK/pZScz/DSu+QAQgAQyQMgAkGAEmogDEIAQtfZrprk9umNywBCABDJAyACQfARaiAMQgBCms3/y6O9xIAaQgAQyQMgAikD+BEgAikDsBMiICATfCIMIAIpA6gTIAIpA6ATIhMgDXwiDSATVK18IA0gDSACKQOYEyACKQOQEyITIAt8IgsgE1StfCALIAsgAikDiBMgAikDgBMiEyASfCISIBNUrXwgEiASIAIpA/gSIBYgAikD8BIiFnwiEyAWVK18IBMgAikD6BIgECAXVK18fCIWIBNUrXx8IhJWrXx8IgtWrXx8Ig1WrXx8IhMgAikD8BF8IhcgE1StfCAXIAIpA4gSIA0gDSACKQOAEnwiDVatfCANIAIpA5gSIAsgCyACKQOQEnwiC1atfCALIAIpA6gSIBIgEiACKQOgEnwiElatfCASIAIpA7gSIAIpA7ASIiEgFnwiFiAhVK18IBYgAikDyBIgECACKQPAEiIQfCAQVK18fCIcIBZUrXx8IhYgElStfHwiEiALVK18fCILIA1UrXx8Ig0gF1StfCAMIBNWrSACKQO4EyAMICBUrXx8fCETIANBCGsiA0F4Rw0ACwJAAkAgE0Kazf/Lo73EgBpWDQACQAJAAkACQCATQprN/8ujvcSAGlINACANQtfZrprk9umNywBWDQQgDULX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiETDAELIAtCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIR4gC0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiETDAILIBJCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIR8gEkKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiETDAMLIBZC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhISAWQv//z4rr///VHlENA0Kazf/Lo73EgBohEyAWISAMBQsgDSEeCyALIR8LIBIhISAWISAMAgtC///Piuv//9UeISAgHEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiETDAELIBZC///Piuv//9UefSIMIBxCq9X+////v/+5f1StIg59ISAgEkKk7MO1j9S0mOcAfSIQIBZC///Piuv//9UeVCAMIA5Ucq0iDH0hISALQr+llJzP8NK75AB9Ig4gEkKk7MO1j9S0mOcAVCAMIBBWcq0iDH0hHyANQtfZrprk9umNywB9IhIgC0K/pZScz/DSu+QAVCAMIA5Wcq0iC30hHiATIA1C19mumuT26Y3LAFQgCyASVnKtfUKazf/Lo73EgBp9IRMgHELVqoGAgIDAgMYAfCEcC0EoIQNCACEPQgAhDEIAIRBCACENQgAhF0IAIQ4DQCACQZARaiACQYAlaiADaikDACILQgAgEUIAEMkDIAJBoBFqIAtCACAVQgAQyQMgAkGwEWogC0IAIBtCABDJAyACQcARaiALQgAgGUIAEMkDIAJB0BFqIAtCACAYQgAQyQMgAkHgEWogC0IAIBRCABDJAyACQYARaiACKQOQESIWIA58Ig5CAEIAQv3/8//P///5iX8QyQMgAkHwEGogAikDiBEiC0IAQqvV/v///7//uX9CABDJAyACQeAQaiALQgBC///Piuv//9UeQgAQyQMgAkHQEGogC0IAQqTsw7WP1LSY5wBCABDJAyACQcAQaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJBsBBqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkGgEGogC0IAQprN/8ujvcSAGkIAEMkDIAIpA6gQIAIpA+ARIhogD3wiCyACKQPYESACKQPQESISIAx8IgwgElStfCAMIAwgAikDyBEgECACKQPAESIQfCISIBBUrXwgEiASIAIpA7gRIAIpA7ARIhAgDXwiDSAQVK18IA0gDSACKQOoESACKQOgESIPIBd8IhAgD1StfCAQIBAgAikDmBEgDiAWVK18fCIQVq18fCINVq18fCISVq18fCIMVq18fCIPIAIpA6AQfCIWIA9UrXwgFiACKQO4ECAMIAwgAikDsBB8IgxWrXwgDCACKQPIECASIBIgAikDwBB8IhJWrXwgEiACKQPYECANIA0gAikD0BB8Ig1WrXwgDSACKQPoECACKQPgECIXIBB8IhAgF1StfCAQIAIpA/gQIA4gAikD8BAiDnwgDlStfHwiDiAQVK18fCIXIA1UrXx8Ig0gElStfHwiECAMVK18fCIMIBZUrXwgCyAPVq0gAikD6BEgCyAaVK18fHwhDyADQQhrIgNBeEcNAAsCQAJAIA9Cms3/y6O9xIAaVg0AAkACQAJAAkAgD0Kazf/Lo73EgBpSDQAgDELX2a6a5PbpjcsAVg0EIAxC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDwwBCyAQQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEaIBBCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDwwCCyANQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEYIA1CpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDwwDCyAXQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRkgF0L//8+K6///1R5RDQNCms3/y6O9xIAaIQ8gFyEdDAULIAwhGgsgECEYCyANIRkgFyEdDAILQv//z4rr///VHiEdIA5CqtX+////v/+5f1YNAEKazf/Lo73EgBohDwwBCyAXQv//z4rr///VHn0iCyAOQqvV/v///7//uX9UrSISfSEdIA1CpOzDtY/UtJjnAH0iESAXQv//z4rr///VHlQgCyASVHKtIgt9IRkgEEK/pZScz/DSu+QAfSISIA1CpOzDtY/UtJjnAFQgCyARVnKtIgt9IRggDELX2a6a5PbpjcsAfSINIBBCv6WUnM/w0rvkAFQgCyASVnKtIgt9IRogDyAMQtfZrprk9umNywBUIAsgDVZyrX1Cms3/y6O9xIAafSEPIA5C1aqBgICAwIDGAHwhDgsgAiAONwPYJSACIB03A9AlIAIgGTcDyCUgAiAYNwPAJSACIBo3A7glIAIgDzcDsCVBKCEDQgAhEUIAIQxCACEQQgAhDUIAIRdCACEUA0AgAkHAD2ogAkGAJWogA2opAwAiC0IAIA5CABDJAyACQdAPaiALQgAgHUIAEMkDIAJB4A9qIAtCACAZQgAQyQMgAkHwD2ogC0IAIBhCABDJAyACQYAQaiALQgAgGkIAEMkDIAJBkBBqIAtCACAPQgAQyQMgAkGwD2ogAikDwA8iFSAUfCISQgBCAEL9//P/z///+Yl/EMkDIAJBoA9qIAIpA7gPIgtCAEKr1f7///+//7l/QgAQyQMgAkGQD2ogC0IAQv//z4rr///VHkIAEMkDIAJBgA9qIAtCAEKk7MO1j9S0mOcAQgAQyQMgAkHwDmogC0IAQr+llJzP8NK75ABCABDJAyACQeAOaiALQgBC19mumuT26Y3LAEIAEMkDIAJB0A5qIAtCAEKazf/Lo73EgBpCABDJAyACKQPYDiACKQOQECIbIBF8IgsgAikDiBAgAikDgBAiESAMfCIMIBFUrXwgDCAMIAIpA/gPIAIpA/APIhEgEHwiECARVK18IBAgECACKQPoDyACKQPgDyIRIA18Ig0gEVStfCANIA0gAikD2A8gAikD0A8iFiAXfCIRIBZUrXwgESACKQPIDyASIBVUrXx8IhYgEVStfHwiDVatfHwiEFatfHwiDFatfHwiESACKQPQDnwiFSARVK18IBUgAikD6A4gDCAMIAIpA+AOfCIMVq18IAwgAikD+A4gECAQIAIpA/AOfCIQVq18IBAgAikDiA8gDSANIAIpA4APfCINVq18IA0gAikDmA8gAikDkA8iFyAWfCIWIBdUrXwgFiACKQOoDyASIAIpA6APIhJ8IBJUrXx8IhQgFlStfHwiFyANVK18fCINIBBUrXx8IhAgDFStfHwiDCAVVK18IAsgEVatIAIpA5gQIAsgG1StfHx8IREgA0EIayIDQXhHDQALAkACQCARQprN/8ujvcSAGlYNAAJAAkACQAJAIBFCms3/y6O9xIAaUg0AIAxC19mumuT26Y3LAFYNBCAMQtfZrprk9umNywBSBEBCms3/y6O9xIAaIREMAQsgEEK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhFSAQQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIREMAgsgDUKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhDyANQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIREMAwsgF0L//8+K6///1R5WDQRCpOzDtY/UtJjnACELIBdC///Piuv//9UeUQ0DQprN/8ujvcSAGiERIBchDgwFCyAMIRULIBAhDwsgDSELIBchDgwCC0L//8+K6///1R4hDiAUQqrV/v///7//uX9WDQBCms3/y6O9xIAaIREMAQsgF0L//8+K6///1R59IgsgFEKr1f7///+//7l/VK0iEn0hDiANQqTsw7WP1LSY5wB9Ig8gF0L//8+K6///1R5UIAsgElRyrSISfSELIBBCv6WUnM/w0rvkAH0iFSANQqTsw7WP1LSY5wBUIA8gElRyrSINfSEPIAxC19mumuT26Y3LAH0iEiAQQr+llJzP8NK75ABUIA0gFVZyrSINfSEVIBEgDELX2a6a5PbpjcsAVCANIBJWcq19QprN/8ujvcSAGn0hESAUQtWqgYCAgMCAxgB8IRQLIAIgFDcDiCYgAiAONwOAJiACIAs3A/glIAIgDzcD8CUgAiAVNwPoJSACIBE3A+AlQSghAyACQZgnakIANwMAIAJBkCdqQgA3AwAgAkGIJ2pCADcDACACQYAnakIANwMAIAJB+CZqQgA3AwAgAkIANwPwJgJAAkACQAJAAkACQAJAIAJB4CVqIAJB8CZqQTAQ8QMEQEIAIQ9CACERQgAhDkIAIQxCACELQgAhFANAIAJB8A1qIAJBsCVqIANqKQMAIg1CACAiQgAQyQMgAkGADmogDUIAICNCABDJAyACQZAOaiANQgAgJEIAEMkDIAJBoA5qIA1CACAlQgAQyQMgAkGwDmogDUIAICZCABDJAyACQcAOaiANQgAgJ0IAEMkDIAJB4A1qIAIpA/ANIhUgFHwiEkIAQgBC/f/z/8////mJfxDJAyACQdANaiACKQPoDSINQgBCq9X+////v/+5f0IAEMkDIAJBwA1qIA1CAEL//8+K6///1R5CABDJAyACQbANaiANQgBCpOzDtY/UtJjnAEIAEMkDIAJBoA1qIA1CAEK/pZScz/DSu+QAQgAQyQMgAkGQDWogDUIAQtfZrprk9umNywBCABDJAyACQYANaiANQgBCms3/y6O9xIAaQgAQyQMgAikDiA0gAikDwA4iFiAPfCINIAIpA7gOIAIpA7AOIg8gEXwiECAPVK18IBAgAikDqA4gAikDoA4iDyAOfCIOIA9UrXwgDiACKQOYDiACKQOQDiIPIAx8IgwgD1StfCAMIAIpA4gOIAIpA4AOIg8gC3wiCyAPVK18IAsgAikD+A0gEiAVVK18fCIRIAtUrXx8IgsgDFStfHwiDCAOVK18fCIOIBBUrXx8IhAgAikDgA18Ig8gEFStfCAPIAIpA5gNIA4gDiACKQOQDXwiDlatfCAOIA4gAikDqA0gDCAMIAIpA6ANfCIMVq18IAwgDCACKQO4DSALIAsgAikDsA18IgtWrXwgCyALIAIpA8gNIAIpA8ANIhUgEXwiESAVVK18IBEgAikD2A0gEiACKQPQDSISfCASVK18fCIUIBFUrXx8IgtWrXx8IgxWrXx8Ig5WrXx8IhEgD1StfCANIBBWrSACKQPIDiANIBZUrXx8fCEPIANBCGsiA0F4Rw0ACyAPQprN/8ujvcSAGlYNBiAPQprN/8ujvcSAGlENAQwCC0GsqsAAQS9BnODAABD+AwALIBFC19mumuT26Y3LAFYNBCARQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ8MAQsgDkK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhFSAOQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ8MAgsgDEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhECAMQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ8MAwsgC0L//8+K6///1R5WDQRCpOzDtY/UtJjnACENIAtC///Piuv//9UeUQ0DQprN/8ujvcSAGiEPIAshEgwFCyARIRULIA4hEAsgDCENIAshEgwCC0L//8+K6///1R4hEiAUQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ8MAQsgC0L//8+K6///1R59Ig0gFEKr1f7///+//7l/VK0iEH0hEiAMQqTsw7WP1LSY5wB9IhUgC0L//8+K6///1R5UIA0gEFRyrSILfSENIA5Cv6WUnM/w0rvkAH0iFiAMQqTsw7WP1LSY5wBUIAsgFVZyrSILfSEQIBFC19mumuT26Y3LAH0iDCAOQr+llJzP8NK75ABUIAsgFlZyrSILfSEVIA8gEULX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDyAUQtWqgYCAgMCAxgB8IRQLQprN/8ujvcSAGiEMIBUgHnwiESAeVCARIBAgH3wiECAfVCAQIA0gIXwiDiAhVCAOIA4gEiAgfCILICBUIAsgCyAUIBx8IhYgHFStfCILVnKtfCIOVnKtfCINIBBUcq18IhIgEVRyrSAPIBN8fCIcIQ8CQAJAAkAgHEKazf/Lo73EgBpSDQBC19mumuT26Y3LACEMIBIiD0LX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhDCANIg9Cv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQwgDiIPQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQwgCyIPQv//z4rr///VHlINAEKr1f7///+//7l/IQwgFiIPQqvV/v///7//uX9RDQELIAwgD1gNACALIRkgDiEYIA0hGiASIQ0MAQsgC0L//8+K6///1R59IgwgFkKr1f7///+//7l/VK0iEH0hGSAOQqTsw7WP1LSY5wB9Ig8gC0L//8+K6///1R5UIAwgEFRyrSILfSEYIA1Cv6WUnM/w0rvkAH0iDCAOQqTsw7WP1LSY5wBUIAsgD1ZyrSILfSEaIBJC19mumuT26Y3LAH0iDiANQr+llJzP8NK75ABUIAsgDFZyrSILfSENIBwgEkLX2a6a5PbpjcsAVCALIA5Wcq19QprN/8ujvcSAGn0hHCAWQtWqgYCAgMCAxgB8IRYLQSghA0IAIRJCACERQgAhDkIAIQxCACETQgAhCwNAIAJBoAxqIAJB0CRqIANqKQMAIhBCACAWQgAQyQMgAkGwDGogEEIAIBlCABDJAyACQcAMaiAQQgAgGEIAEMkDIAJB0AxqIBBCACAaQgAQyQMgAkHgDGogEEIAIA1CABDJAyACQfAMaiAQQgAgHEIAEMkDIAJBkAxqIAIpA6AMIhUgC3wiEEIAQgBC/f/z/8////mJfxDJAyACQYAMaiACKQOYDCILQgBCq9X+////v/+5f0IAEMkDIAJB8AtqIAtCAEL//8+K6///1R5CABDJAyACQeALaiALQgBCpOzDtY/UtJjnAEIAEMkDIAJB0AtqIAtCAEK/pZScz/DSu+QAQgAQyQMgAkHAC2ogC0IAQtfZrprk9umNywBCABDJAyACQbALaiALQgBCms3/y6O9xIAaQgAQyQMgAikDuAsgAikD8AwiFyASfCISIAIpA+gMIAIpA+AMIg8gEXwiCyAPVK18IAsgCyACKQPYDCACKQPQDCIPIA58Ig4gD1StfCAOIA4gAikDyAwgAikDwAwiDyAMfCIMIA9UrXwgDCAMIAIpA7gMIAIpA7AMIhEgE3wiDyARVK18IA8gAikDqAwgECAVVK18fCITIA9UrXx8IgxWrXx8Ig5WrXx8IgtWrXx8Ig8gAikDsAt8IhEgD1StfCARIBEgAikDyAsgCyACKQPAC3wiFSALVK18IBUgAikD2AsgDiAOIAIpA9ALfCIOVq18IA4gAikD6AsgDCAMIAIpA+ALfCIMVq18IAwgAikD+AsgEyACKQPwCyITfCILIBNUrXwgCyALIAIpA4gMIBAgAikDgAwiEHwgEFStfHwiC1atfHwiEyAMVK18fCIMIA5UrXx8Ig4gFVStfHwiEVatfCAPIBJUrSACKQP4DCASIBdUrXx8fCESIANBCGsiA0F4Rw0ACwJAAkAgEkKazf/Lo73EgBpWDQACQAJAAkACQCASQprN/8ujvcSAGlINACARQtfZrprk9umNywBWDQQgEULX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiESDAELIA5Cv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRYgDkK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiESDAILIAxCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRkgDEKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiESDAMLIBNC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhGiATQv//z4rr///VHlENA0Kazf/Lo73EgBohEiATIRgMBQsgESEWCyAOIRkLIAwhGiATIRgMAgtC///Piuv//9UeIRggC0Kq1f7///+//7l/Vg0AQprN/8ujvcSAGiESDAELIBNC///Piuv//9UefSINIAtCq9X+////v/+5f1StIhB9IRggDEKk7MO1j9S0mOcAfSIPIBNC///Piuv//9UeVCANIBBUcq0iDX0hGiAOQr+llJzP8NK75AB9IhAgDEKk7MO1j9S0mOcAVCANIA9Wcq0iDH0hGSARQtfZrprk9umNywB9Ig0gDkK/pZScz/DSu+QAVCAMIBBWcq0iDH0hFiASIBFC19mumuT26Y3LAFQgDCANVnKtfUKazf/Lo73EgBp9IRIgC0LVqoGAgIDAgMYAfCELC0EoIQNCACEPQgAhEUIAIQ5CACEMQgAhE0IAIRQDQCACQdAKaiACQeAlaiADaikDACINQgAgLkIAEMkDIAJB4ApqIA1CACAvQgAQyQMgAkHwCmogDUIAIDBCABDJAyACQYALaiANQgAgMUIAEMkDIAJBkAtqIA1CACAyQgAQyQMgAkGgC2ogDUIAIDNCABDJAyACQcAKaiACKQPQCiIVIBR8IhBCAEIAQv3/8//P///5iX8QyQMgAkGwCmogAikDyAoiDUIAQqvV/v///7//uX9CABDJAyACQaAKaiANQgBC///Piuv//9UeQgAQyQMgAkGQCmogDUIAQqTsw7WP1LSY5wBCABDJAyACQYAKaiANQgBCv6WUnM/w0rvkAEIAEMkDIAJB8AlqIA1CAELX2a6a5PbpjcsAQgAQyQMgAkHgCWogDUIAQprN/8ujvcSAGkIAEMkDIAIpA+gJIAIpA6ALIhcgD3wiDSACKQOYCyARIAIpA5ALIhF8Ig8gEVStfCAPIA8gAikDiAsgAikDgAsiESAOfCIOIBFUrXwgDiAOIAIpA/gKIAIpA/AKIhEgDHwiDCARVK18IAwgDCACKQPoCiATIAIpA+AKIhN8IhEgE1StfCARIAIpA9gKIBAgFVStfHwiEyARVK18fCIMVq18fCIOVq18fCIPVq18fCIVIAIpA+AJfCIRIBVUrXwgESARIAIpA/gJIA8gDyACKQPwCXwiD1atfCAPIAIpA4gKIA4gDiACKQOACnwiDlatfCAOIAIpA5gKIAwgDCACKQOQCnwiDFatfCAMIAIpA6gKIAIpA6AKIhQgE3wiEyAUVK18IBMgAikDuAogECACKQOwCiIQfCAQVK18fCIUIBNUrXx8IhMgDFStfHwiDCAOVK18fCIOIA9UrXx8IhFWrXwgDSAVVq0gAikDqAsgDSAXVK18fHwhDyADQQhrIgNBeEcNAAsCQAJAIA9Cms3/y6O9xIAaVg0AAkACQAJAAkAgD0Kazf/Lo73EgBpSDQAgEULX2a6a5PbpjcsAVg0EIBFC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDwwBCyAOQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEVIA5Cv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDwwCCyAMQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEQIAxCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDwwDCyATQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIQ0gE0L//8+K6///1R5RDQNCms3/y6O9xIAaIQ8gEyEXDAULIBEhFQsgDiEQCyAMIQ0gEyEXDAILQv//z4rr///VHiEXIBRCqtX+////v/+5f1YNAEKazf/Lo73EgBohDwwBCyATQv//z4rr///VHn0iDSAUQqvV/v///7//uX9UrSIQfSEXIAxCpOzDtY/UtJjnAH0iFSATQv//z4rr///VHlQgDSAQVHKtIhB9IQ0gDkK/pZScz/DSu+QAfSITIAxCpOzDtY/UtJjnAFQgECAVVnKtIgx9IRAgEULX2a6a5PbpjcsAfSIdIA5Cv6WUnM/w0rvkAFQgDCATVnKtIgx9IRUgDyARQtfZrprk9umNywBUIAwgHVZyrX1Cms3/y6O9xIAafSEPIBRC1aqBgICAwIDGAHwhFAtCms3/y6O9xIAaIQwgFSAWfCIOIBZUIA4gECAZfCIRIBlUIBEgESANIBp8IhAgGlQgECAQIBcgGHwiDSAYVCANIA0gCyAUfCIUIAtUrXwiDVZyrXwiEFZyrXwiEVZyrXwiEyAOVHKtIA8gEnx8IhUhDgJAAkACQCAVQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIQwgEyIOQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEMIBEiDkK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhDCAQIg5CpOzDtY/UtJjnAFINAEL//8+K6///1R4hDCANIg5C///Piuv//9UeUg0AQqvV/v///7//uX8hDCAUIg5Cq9X+////v/+5f1ENAQsgDCAOWA0AIBMhDiARIQwgECELIA0hEgwBCyANQv//z4rr///VHn0iCyAUQqvV/v///7//uX9UrSIMfSESIBBCpOzDtY/UtJjnAH0iDiANQv//z4rr///VHlQgCyAMVHKtIgx9IQsgEUK/pZScz/DSu+QAfSINIBBCpOzDtY/UtJjnAFQgDCAOVnKtIg59IQwgE0LX2a6a5PbpjcsAfSIQIBFCv6WUnM/w0rvkAFQgDSAOVHKtIg19IQ4gFSATQtfZrprk9umNywBUIA0gEFZyrX1Cms3/y6O9xIAafSEVIBRC1aqBgICAwIDGAHwhFAsgAiAUNwO4JiACIBI3A7AmIAIgCzcDqCYgAiAMNwOgJiACIA43A5gmIAIgFTcDkCYgAkHwJmoiBiACQZAmaiACQeAlahBMAn8CQAJAAkACQAJAAkACQAJAAkACQCACKALwJkEBRwRAQSghAyACQegmaiACQaAnaikDADcDACACQeAmaiACQZgnaiIHKQMANwMAIAJB2CZqIAJBkCdqIgUpAwA3AwAgAkHQJmogAkGIJ2oiBCkDADcDACACQcgmaiACQYAnaiIIKQMANwMAIAIgAikD+CY3A8AmIAdCADcDACAFQgA3AwAgBEIANwMAIAhCADcDACACQfgmakIANwMAIAJCADcD8CYCQCACQcAmaiIEIAZBMBDxA0UNACAEEPECQf8BcUECRg0AQgAhD0IAIRFCACEOQgAhDEIAIQtCACEUA0AgAkGACWogAkHAJmogA2opAwAiDUIAIC1CABDJAyACQZAJaiANQgAgLEIAEMkDIAJBoAlqIA1CACArQgAQyQMgAkGwCWogDUIAICpCABDJAyACQcAJaiANQgAgKUIAEMkDIAJB0AlqIA1CACAoQgAQyQMgAkHwCGogAikDgAkiEyAUfCISQgBCAEL9//P/z///+Yl/EMkDIAJB4AhqIAIpA/gIIg1CAEKr1f7///+//7l/QgAQyQMgAkHQCGogDUIAQv//z4rr///VHkIAEMkDIAJBwAhqIA1CAEKk7MO1j9S0mOcAQgAQyQMgAkGwCGogDUIAQr+llJzP8NK75ABCABDJAyACQaAIaiANQgBC19mumuT26Y3LAEIAEMkDIAJBkAhqIA1CAEKazf/Lo73EgBpCABDJAyACKQOYCCACKQPQCSIVIA98Ig0gAikDyAkgAikDwAkiDyARfCIQIA9UrXwgECACKQO4CSACKQOwCSIPIA58Ig4gD1StfCAOIAIpA6gJIAIpA6AJIg8gDHwiDCAPVK18IAwgAikDmAkgAikDkAkiDyALfCILIA9UrXwgCyACKQOICSASIBNUrXx8IhEgC1StfHwiCyAMVK18fCIMIA5UrXx8Ig4gEFStfHwiECACKQOQCHwiDyAQVK18IA8gAikDqAggDiAOIAIpA6AIfCIOVq18IA4gDiACKQO4CCAMIAwgAikDsAh8IgxWrXwgDCAMIAIpA8gIIAsgCyACKQPACHwiC1atfCALIAsgAikD2AggAikD0AgiEyARfCIRIBNUrXwgESACKQPoCCASIAIpA+AIIhJ8IBJUrXx8IhQgEVStfHwiC1atfHwiDFatfHwiDlatfHwiESAPVK18IA0gEFatIAIpA9gJIA0gFVStfHx8IQ8gA0EIayIDQXhHDQALIA9Cms3/y6O9xIAaVg0KIA9Cms3/y6O9xIAaUQ0FDAYLIAJBiChqIAJBwCZqEKECIAIpA4goIRMgAikDkCghFSACKQOYKCEWIAIpA6AoIRcgAikDqCghGCACKQOwKCEZQgAhD0IAIRFCACEOQgAhDEIAIQtCACEUA0AgAkGQBGogAkGIKGogA2opAwAiDUIAIBlCABDJAyACQaAEaiANQgAgGEIAEMkDIAJBsARqIA1CACAXQgAQyQMgAkHABGogDUIAIBZCABDJAyACQdAEaiANQgAgFUIAEMkDIAJB4ARqIA1CACATQgAQyQMgAkGABGogFCACKQOQBCIUfCISQgBCAEL9//P/z///+Yl/EMkDIAJB8ANqIAIpA4gEIg1CAEKr1f7///+//7l/QgAQyQMgAkHgA2ogDUIAQv//z4rr///VHkIAEMkDIAJB0ANqIA1CAEKk7MO1j9S0mOcAQgAQyQMgAkHAA2ogDUIAQr+llJzP8NK75ABCABDJAyACQbADaiANQgBC19mumuT26Y3LAEIAEMkDIAJBoANqIA1CAEKazf/Lo73EgBpCABDJAyACKQOoAyACKQPgBCIaIA98Ig0gAikD2AQgAikD0AQiDyARfCIQIA9UrXwgECACKQPIBCACKQPABCIPIA58Ig4gD1StfCAOIAIpA7gEIAIpA7AEIg8gDHwiDCAPVK18IAwgAikDqAQgAikDoAQiDyALfCILIA9UrXwgCyACKQOYBCASIBRUrXx8IhEgC1StfHwiCyAMVK18fCIMIA5UrXx8Ig4gEFStfHwiECACKQOgA3wiDyAQVK18IA8gAikDuAMgDiAOIAIpA7ADfCIOVq18IA4gDiACKQPIAyAMIAwgAikDwAN8IgxWrXwgDCAMIAIpA9gDIAsgCyACKQPQA3wiC1atfCALIAsgAikD6AMgAikD4AMiFCARfCIRIBRUrXwgESACKQP4AyASIAIpA/ADIhJ8IBJUrXx8IhQgEVStfHwiC1atfHwiDFatfHwiDlatfHwiESAPVK18IA0gEFatIAIpA+gEIA0gGlStfHx8IQ8gA0EIayIDQXhHDQALIA9Cms3/y6O9xIAaWA0BDAILIAIgAikDgCc3A5AoIAIgAikD+CY3A4goQYSdwABBKyACQYgoakH4q8AAQczgwAAQygMACyAPQprN/8ujvcSAGlIEQCALIQ0gDCESIA4hECARIRUMAgsgEULX2a6a5PbpjcsAVg0AIBFC19mumuT26Y3LAFIEQCALIQ0gDCESIA4hECARIRVCms3/y6O9xIAaIQ8MAgsgDkK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhFSAOQr+llJzP8NK75ABSBEAgCyENIAwhEiAOIRBCms3/y6O9xIAaIQ8MAgsgDEKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhECAMQqTsw7WP1LSY5wBSBEAgCyENIAwhEkKazf/Lo73EgBohDwwCCyALQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIRIgC0L//8+K6///1R5SBEAgCyENQprN/8ujvcSAGiEPDAILQv//z4rr///VHiENIBRCqtX+////v/+5f1YNAEKazf/Lo73EgBohDwwBCyALQv//z4rr///VHn0iEiAUQqvV/v///7//uX9UrSIQfSENIAxCpOzDtY/UtJjnAH0iEyALQv//z4rr///VHlQgECASVnKtIgt9IRIgDkK/pZScz/DSu+QAfSIVIAxCpOzDtY/UtJjnAFQgCyATVnKtIgt9IRAgEULX2a6a5PbpjcsAfSIMIA5Cv6WUnM/w0rvkAFQgCyAVVnKtIgt9IRUgDyARQtfZrprk9umNywBUIAsgDFZyrX1Cms3/y6O9xIAafSEPIBRC1aqBgICAwIDGAHwhFAsgAiAUNwOYJyACIA03A5AnIAIgEjcDiCcgAiAQNwOAJyACIBU3A/gmIAIgDzcD8CYgAkHwJmogAkHAJmpBMBDxAwRAQaSrwABBIkG84MAAEP4DAAsgAkHQJ2ogAkGwKGopAwA3AwAgAkHIJ2ogAkGoKGopAwA3AwAgAkHAJ2ogAkGgKGopAwA3AwAgAkG4J2ogAkGYKGopAwA3AwAgAkGwJ2ogAkGQKGopAwA3AwAgAiACKQOIKDcDqCdBAQwHCyARQtfZrprk9umNywBWDQQgEULX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEPDAELIA5Cv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRUgDkK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEPDAILIAxCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRAgDEKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEPDAMLIAtC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhEiALQv//z4rr///VHlENA0Kazf/Lo73EgBohDyALIQ0MBQsgESEVCyAOIRALIAwhEiALIQ0MAgtC///Piuv//9UeIQ0gFEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEPDAELIAtC///Piuv//9UefSISIBRCq9X+////v/+5f1StIhB9IQ0gDEKk7MO1j9S0mOcAfSITIAtC///Piuv//9UeVCAQIBJWcq0iC30hEiAOQr+llJzP8NK75AB9IhUgDEKk7MO1j9S0mOcAVCALIBNWcq0iC30hECARQtfZrprk9umNywB9IgwgDkK/pZScz/DSu+QAVCALIBVWcq0iC30hFSAPIBFC19mumuT26Y3LAFQgCyAMVnKtfUKazf/Lo73EgBp9IQ8gFELVqoGAgIDAgMYAfCEUCyACIBQ3A5gnIAIgDTcDkCcgAiASNwOIJyACIBA3A4AnIAIgFTcD+CYgAiAPNwPwJiACQdgnaiACQfAmahChAkEoIQMgAikD2CchEyACKQPgJyEVIAIpA+gnIRYgAikD8CchFyACKQP4JyEYIAIpA4AoIRlCACEPQgAhEUIAIQ5CACEMQgAhC0IAIRQDQCACQbAHaiACQdgnaiADaikDACINQgAgGUIAEMkDIAJBwAdqIA1CACAYQgAQyQMgAkHQB2ogDUIAIBdCABDJAyACQeAHaiANQgAgFkIAEMkDIAJB8AdqIA1CACAVQgAQyQMgAkGACGogDUIAIBNCABDJAyACQaAHaiAUIAIpA7AHIhR8IhJCAEIAQv3/8//P///5iX8QyQMgAkGQB2ogAikDqAciDUIAQqvV/v///7//uX9CABDJAyACQYAHaiANQgBC///Piuv//9UeQgAQyQMgAkHwBmogDUIAQqTsw7WP1LSY5wBCABDJAyACQeAGaiANQgBCv6WUnM/w0rvkAEIAEMkDIAJB0AZqIA1CAELX2a6a5PbpjcsAQgAQyQMgAkHABmogDUIAQprN/8ujvcSAGkIAEMkDIAIpA8gGIAIpA4AIIhogD3wiDSACKQP4ByACKQPwByIPIBF8IhAgD1StfCAQIAIpA+gHIAIpA+AHIg8gDnwiDiAPVK18IA4gAikD2AcgAikD0AciDyAMfCIMIA9UrXwgDCACKQPIByACKQPAByIPIAt8IgsgD1StfCALIAIpA7gHIBIgFFStfHwiESALVK18fCILIAxUrXx8IgwgDlStfHwiDiAQVK18fCIQIAIpA8AGfCIPIBBUrXwgDyACKQPYBiAOIA4gAikD0AZ8Ig5WrXwgDiAOIAIpA+gGIAwgDCACKQPgBnwiDFatfCAMIAwgAikD+AYgCyALIAIpA/AGfCILVq18IAsgCyACKQOIByACKQOAByIUIBF8IhEgFFStfCARIAIpA5gHIBIgAikDkAciEnwgElStfHwiFCARVK18fCILVq18fCIMVq18fCIOVq18fCIRIA9UrXwgDSAQVq0gAikDiAggDSAaVK18fHwhDyADQQhrIgNBeEcNAAsCQAJAIA9Cms3/y6O9xIAaVg0AIA9Cms3/y6O9xIAaUgRAIAwhEiAOIRAgESEVIAshDQwCCyARQtfZrprk9umNywBWDQACQAJAIBFC19mumuT26Y3LAFIEQCAMIRIgDiEQIBEhFQwBCyAOQr+llJzP8NK75ABWDQJC19mumuT26Y3LACEVIA5Cv6WUnM/w0rvkAFIEQCAMIRIgDiEQDAELIAxCpOzDtY/UtJjnAFYNAkK/pZScz/DSu+QAIRAgDEKk7MO1j9S0mOcAUgRAIAwhEgwBCyALQv//z4rr///VHlYNAkKk7MO1j9S0mOcAIRIgC0L//8+K6///1R5RDQELQprN/8ujvcSAGiEPIAshDQwCC0L//8+K6///1R4hDSAUQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ8MAQsgC0L//8+K6///1R59IhIgFEKr1f7///+//7l/VK0iEH0hDSAMQqTsw7WP1LSY5wB9IhMgC0L//8+K6///1R5UIBAgElZyrSILfSESIA5Cv6WUnM/w0rvkAH0iFSAMQqTsw7WP1LSY5wBUIAsgE1ZyrSILfSEQIBFC19mumuT26Y3LAH0iDCAOQr+llJzP8NK75ABUIAsgFVZyrSILfSEVIA8gEULX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDyAUQtWqgYCAgMCAxgB8IRQLIAIgFDcDsCggAiANNwOoKCACIBI3A6AoIAIgEDcDmCggAiAVNwOQKCACIA83A4goQSghA0IAIQ9CACERQgAhDkIAIQxCACELQgAhFANAIAJB4AVqIAJBwCZqIANqKQMAIg1CACAtQgAQyQMgAkHwBWogDUIAICxCABDJAyACQYAGaiANQgAgK0IAEMkDIAJBkAZqIA1CACAqQgAQyQMgAkGgBmogDUIAIClCABDJAyACQbAGaiANQgAgKEIAEMkDIAJB0AVqIAIpA+AFIhMgFHwiEkIAQgBC/f/z/8////mJfxDJAyACQcAFaiACKQPYBSINQgBCq9X+////v/+5f0IAEMkDIAJBsAVqIA1CAEL//8+K6///1R5CABDJAyACQaAFaiANQgBCpOzDtY/UtJjnAEIAEMkDIAJBkAVqIA1CAEK/pZScz/DSu+QAQgAQyQMgAkGABWogDUIAQtfZrprk9umNywBCABDJAyACQfAEaiANQgBCms3/y6O9xIAaQgAQyQMgAikD+AQgAikDsAYiFSAPfCINIAIpA6gGIAIpA6AGIg8gEXwiECAPVK18IBAgAikDmAYgAikDkAYiDyAOfCIOIA9UrXwgDiACKQOIBiACKQOABiIPIAx8IgwgD1StfCAMIAIpA/gFIAIpA/AFIg8gC3wiCyAPVK18IAsgAikD6AUgEiATVK18fCIRIAtUrXx8IgsgDFStfHwiDCAOVK18fCIOIBBUrXx8IhAgAikD8AR8Ig8gEFStfCAPIAIpA4gFIA4gDiACKQOABXwiDlatfCAOIA4gAikDmAUgDCAMIAIpA5AFfCIMVq18IAwgDCACKQOoBSALIAsgAikDoAV8IgtWrXwgCyALIAIpA7gFIAIpA7AFIhMgEXwiESATVK18IBEgAikDyAUgEiACKQPABSISfCASVK18fCIUIBFUrXx8IgtWrXx8IgxWrXx8Ig5WrXx8IhEgD1StfCANIBBWrSACKQO4BiANIBVUrXx8fCEPIANBCGsiA0F4Rw0ACwJAAkAgD0Kazf/Lo73EgBpWDQAgD0Kazf/Lo73EgBpSBEAgCyENIAwhEiAOIRAgESEVDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCALIQ0gDCESIA4hECARIRUMAQsgDkK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhFSAOQr+llJzP8NK75ABSBEAgCyENIAwhEiAOIRAMAQsgDEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhECAMQqTsw7WP1LSY5wBSBEAgCyENIAwhEgwBCyALQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRIgC0L//8+K6///1R5SBEAgCyENDAELQv//z4rr///VHiENIBRCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQ8MAQsgC0L//8+K6///1R59IhIgFEKr1f7///+//7l/VK0iEH0hDSAMQqTsw7WP1LSY5wB9IhMgC0L//8+K6///1R5UIBAgElZyrSILfSESIA5Cv6WUnM/w0rvkAH0iFSAMQqTsw7WP1LSY5wBUIAsgE1ZyrSILfSEQIBFC19mumuT26Y3LAH0iDCAOQr+llJzP8NK75ABUIAsgFVZyrSILfSEVIA8gEULX2a6a5PbpjcsAVCALIAxWcq19QprN/8ujvcSAGn0hDyAUQtWqgYCAgMCAxgB8IRQLIAIgFDcDmCcgAiANNwOQJyACIBI3A4gnIAIgEDcDgCcgAiAVNwP4JiACIA83A/AmIAJBiChqIAJB8CZqQTAQ8QMEQEHsqsAAQShBrODAABD+AwALIAJB0CdqIAJBgChqKQMANwMAIAJByCdqIAJB+CdqKQMANwMAIAJBwCdqIAJB8CdqKQMANwMAIAJBuCdqIAJB6CdqKQMANwMAIAJBsCdqIAJB4CdqKQMANwMAIAIgAikD2Cc3A6gnQQALIQdBKCEDIAIpA/AjIRMgAikD+CMhFSACKQOAJCEWIAIpA4gkIRcgAikDkCQhGCACKQOYJCEZQgAhFEIAIRFCACEOQgAhDEIAIQtCACEPA0AgAkHAAmogASADaikDACINQgAgGUIAEMkDIAJB0AJqIA1CACAYQgAQyQMgAkHgAmogDUIAIBdCABDJAyACQfACaiANQgAgFkIAEMkDIAJBgANqIA1CACAVQgAQyQMgAkGQA2ogDUIAIBNCABDJAyACQbACaiAPIAIpA8ACIg98IhJCAEIAQv3/8//P///5iX8QyQMgAkGgAmogAikDuAIiDUIAQqvV/v///7//uX9CABDJAyACQZACaiANQgBC///Piuv//9UeQgAQyQMgAkGAAmogDUIAQqTsw7WP1LSY5wBCABDJAyACQfABaiANQgBCv6WUnM/w0rvkAEIAEMkDIAJB4AFqIA1CAELX2a6a5PbpjcsAQgAQyQMgAkHQAWogDUIAQprN/8ujvcSAGkIAEMkDIAIpA9gBIBQgAikDkAMiFHwiDSACKQOIAyARIAIpA4ADIhF8IhAgEVStfCAQIAIpA/gCIAIpA/ACIhEgDnwiDiARVK18IA4gAikD6AIgAikD4AIiESAMfCIMIBFUrXwgDCACKQPYAiACKQPQAiIRIAt8IgsgEVStfCALIAIpA8gCIA8gElatfHwiDyALVK18fCILIAxUrXx8IgwgDlStfHwiDiAQVK18fCIQIAIpA9ABfCIRIBBUrXwgESARIAIpA+gBIA4gDiACKQPgAXwiDlatfCAOIA4gAikD+AEgDCAMIAIpA/ABfCIMVq18IAwgDCACKQOIAiALIAsgAikDgAJ8IgtWrXwgCyALIAIpA5gCIAIpA5ACIhogD3wiDyAaVK18IA8gDyACKQOoAiASIAIpA6ACIhJ8IBJUrXx8Ig9WrXx8IgtWrXx8IgxWrXx8Ig5WrXx8IhFWrXwgDSAQVq0gAikDmAMgDSAUVK18fHwhFCADQQhrIgNBeEcNAAsCQAJAIBRCms3/y6O9xIAaVg0AIBRCms3/y6O9xIAaUgRAIAshEiAMIRUgDiEXIBEhFgwCCyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgCyESIAwhFSAOIRcgESEWDAELIA5Cv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRYgDkK/pZScz/DSu+QAUgRAIAshEiAMIRUgDiEXDAELIAxCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRcgDEKk7MO1j9S0mOcAUgRAIAshEiAMIRUMAQsgC0L//8+K6///1R5WDQFCpOzDtY/UtJjnACEVIAtC///Piuv//9UeUgRAIAshEgwBC0L//8+K6///1R4hEiAPQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEUDAELIAtC///Piuv//9UefSINIA9Cq9X+////v/+5f1StIhB9IRIgDEKk7MO1j9S0mOcAfSITIAtC///Piuv//9UeVCANIBBUcq0iC30hFSAOQr+llJzP8NK75AB9Ig0gDEKk7MO1j9S0mOcAVCALIBNWcq0iC30hFyARQtfZrprk9umNywB9IgwgDkK/pZScz/DSu+QAVCALIA1Wcq0iC30hFiAUIBFC19mumuT26Y3LAFQgCyAMVnKtfUKazf/Lo73EgBp9IRQgD0LVqoGAgIDAgMYAfCEPC0EoIQNCACEOQgAhDEIAIRBCACENQgAhE0IAIREDQCACQfAAaiACQagnaiADaikDACILQgAgD0IAEMkDIAJBgAFqIAtCACASQgAQyQMgAkGQAWogC0IAIBVCABDJAyACQaABaiALQgAgF0IAEMkDIAJBsAFqIAtCACAWQgAQyQMgAkHAAWogC0IAIBRCABDJAyACQeAAaiACKQNwIhggEXwiEUIAQgBC/f/z/8////mJfxDJAyACQdAAaiACKQNoIgtCAEKr1f7///+//7l/QgAQyQMgAkFAayALQgBC///Piuv//9UeQgAQyQMgAkEwaiALQgBCpOzDtY/UtJjnAEIAEMkDIAJBIGogC0IAQr+llJzP8NK75ABCABDJAyACQRBqIAtCAELX2a6a5PbpjcsAQgAQyQMgAiALQgBCms3/y6O9xIAaQgAQyQMgAikDCCACKQPAASIaIA58IgsgAikDuAEgAikDsAEiDiAMfCIMIA5UrXwgDCAMIAIpA6gBIBAgAikDoAEiEHwiDiAQVK18IA4gDiACKQOYASACKQOQASIQIA18Ig0gEFStfCANIA0gAikDiAEgEyACKQOAASITfCIQIBNUrXwgECAQIAIpA3ggESAYVK18fCIQVq18fCINVq18fCIOVq18fCIMVq18fCIYIAIpAwB8IhkgGFStfCAZIAIpAxggDCAMIAIpAxB8IgxWrXwgDCACKQMoIA4gDiACKQMgfCIOVq18IA4gAikDOCANIA0gAikDMHwiDVatfCANIAIpA0ggAikDQCITIBB8IhAgE1StfCAQIAIpA1ggESACKQNQIhF8IBFUrXx8IhEgEFStfHwiEyANVK18fCINIA5UrXx8IhAgDFStfHwiDCAZVK18IAsgGFatIAIpA8gBIAsgGlStfHx8IQ4gA0EIayIDQXhHDQALAkACQCAOQprN/8ujvcSAGlYNACAOQprN/8ujvcSAGlIEQCATIQ8gDSELIBAhFCAMIRUMAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIBMhDyANIQsgECEUIAwhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCATIQ8gDSELIBAhFAwBCyANQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEUIA1CpOzDtY/UtJjnAFIEQCATIQ8gDSELDAELIBNC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhCyATQv//z4rr///VHlIEQCATIQ8MAQtC///Piuv//9UeIQ8gEUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDgwBCyATQv//z4rr///VHn0iCyARQqvV/v///7//uX9UrSISfSEPIA1CpOzDtY/UtJjnAH0iFSATQv//z4rr///VHlQgCyASVHKtIhJ9IQsgEEK/pZScz/DSu+QAfSITIA1CpOzDtY/UtJjnAFQgEiAVVnKtIg19IRQgDELX2a6a5PbpjcsAfSISIBBCv6WUnM/w0rvkAFQgDSATVnKtIg19IRUgDiAMQtfZrprk9umNywBUIA0gElZyrX1Cms3/y6O9xIAafSEOIBFC1aqBgICAwIDGAHwhEQsCQCAHRQRAIAIgETcDmCcgAiAPNwOQJyACIAs3A4gnIAIgFDcDgCcgAiAVNwP4JiACIA43A/AmDAELIAJBmCdqIAJB0CdqKQMANwMAIAJBkCdqIAJByCdqKQMANwMAIAJBiCdqIAJBwCdqKQMANwMAIAJBgCdqIAJBuCdqKQMANwMAIAJB+CZqIAJBsCdqKQMANwMAIAIgAikDqCc3A/AmCyACQcQoaiIGIAJB8CZqENgCQQAhAyACQZAoaiIFQdyawAAoAgAiBDYCACACQdSawAApAgAiCzcDiCggAkGIKGoiCUHIm8AAEKUDIAIoAowoQQI2AgAgAkHgJ2oiCEEBNgIAIAIgAikDiCg3A9gnIAJBuChqIAYgAkHYJ2oiChDtASAGIAEQ2AIgBSAENgIAIAIgCzcDiCggCUHIm8AAEKUDIAIoAowoQQI2AgAgCEEBNgIAIAIgAikDiCg3A9gnIAkgBiAKEO0BIAIoAowoIQEgAigCvCghBSACKALAKCIEIAIoApAoRgRAIAUgASAEQQJ0EPEDRSEDCyACKAKIKCIEBEAgASAEQQJ0EN8ECyACKAK4KCIBBEAgBSABQQJ0EN8ECyAAIAc6ADAgACACKQOoJzcDACAAIAM6ADEgAEEIaiACQbAnaikDADcDACAAQRBqIAJBuCdqKQMANwMAIABBGGogAkHAJ2opAwA3AwAgAEEgaiACQcgnaikDADcDACAAQShqIAJB0CdqKQMANwMAIAIoAqwjIgAEQCACKAKwIyAAQQJ0EN8ECwJAIAIoAqQdIgBFDQAgACAAQQxsQRNqQXhxIgFqQQlqIgBFDQAgAigCoB0gAWsgABDfBAsgAigCoCAiAEGAgICAeEYgAEVyRQRAIAIoAqQgIABBAnQQ3wQLIAJB0ChqJAALj6ABAgJ/Kn4jAEHAHmsiAyQAIANBoB5qIgRB5I/CAEHCABCVAyADQYAdaiAEEPUCIAMoAqAeIgQEQCADKAKkHiAEQQJ0EN8ECyADQaAeaiIEQaaQwgBBwgAQlQMgA0GgHWogBBD1AiADKAKgHiIEBEAgAygCpB4gBEECdBDfBAsgA0HwHGogAykDmB0iKEIAQr4BQgAQyQMgA0HgHGogAykD8BwiCUKblK/D8rWo3oZ/fiIFQgBCbUIAEMkDIANB0BxqIAVCAEJ/QgAQyQMgA0HAHGogBUIAQv///////////wBCABDJAyADQbAcaiADKQOQHSIpQgBCvgFCABDJAyADQaAcaiADKQPQHCIFIAMpA/gcfCIGIAMpA+gcIAMpA+AcIgggCUJ+g3wgCFStfHwiCSADKQOwHHwiCEKblK/D8rWo3oZ/fiIHQgBCbUIAEMkDIANBkBxqIAdCAEJ/QgAQyQMgA0GAHGogB0IAQv///////////wBCABDJAyADQfAbaiADKQOIHSIqQgBCvgFCABDJAyADQeAbaiADKQOQHCIHIAMpA7gcIAggCVStfCIMIAUgBiAJVq0gAykD2BwiCiAFIAZWrXx8Ig58Igt8IhJ8IgUgAykDqBwgAykDoBwiBiAIfCAGVK18fCIGIAMpA/AbfCIJQpuUr8Pytajehn9+IghCAEJtQgAQyQMgA0HQG2ogCEIAQn9CABDJAyADQcAbaiAIQgBC////////////AEIAEMkDIANBsBtqIAMpA4AdIitCAEK+AUIAEMkDIANBoBtqIAMpA9AbIgggByAMIBJWrSISIAogCyAOVK18IgsgAykDwBx8Ig18Igx8IgogBSAGVq0gAykDmBwiDyAFIAdUrXx8fCIFIAMpA/gbIAYgCVatfHwiEHwiBiADKQPoGyAJIAMpA+AbIgl8IAlUrXx8IgkgAykDsBt8IgdCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyADQZAbaiAOQgBCf0IAEMkDIANBgBtqIA5CAEL///////////8AQgAQyQMCQAJAIAMpA4gbIAMpA8gbIAMpA4gcIAMpA4AcIhEgAykDyBwgCyANVq18fCIOIBFUrXwgDiAOIAwgElStfCIOVq18IA4gBSAKVK0gDyAKIAxUrXx8fCIMIA5UrXwiDiADKQPAG3wiCiAOVK18IAogDCAFIBBWrXwiBSAMVK18IgwgClStfCAMIAMpA9gbIgogBSAFIAh8IgVWrXwgBSAFIAYgCVatIAogBiAIVK18fHwiBVatfHwiBiAMVK18IgwgAykDgBt8IgggDFStfCAIIAYgBSADKQO4GyAHIAlUrXx8IgwgBVStfCIFIAZUrXwiCSAIVK18IAkgAykDmBsiCCAFIAUgAykDkBsiBnwiBVatfCAFIAggBiAGIAx8IgZWrXwgBiADKQOoGyADKQOgGyIIIAd8IAhUrXx8IgogBlStfHwiBiAFVK18fCIIIAlUrXwiC0IAWQRAIAtC////////////AFIgCkJtVHIgBiAIg0J/UnINAQsgBkIBfCIFIApCbVStIgd9IQkgCEIBfCIMIAZCf1IgBSAHVHKtIgZ9IQUgCyAIQn9SIAYgDFZyrX1C////////////AH0hCyAKQhN8IQoMAQsgCCEFIAYhCQsgA0HwGmogAikDGCIdQgAgKEIAEMkDIANBsBpqIB1CACApQgAQyQMgA0GgGmogHUIAICpCABDJAyADQZAaaiAdQgAgK0IAEMkDIANB4BpqIAMpA/AaIgdCm5Svw/K1qN6Gf34iBkIAQm1CABDJAyADQdAaaiAGQgBCf0IAEMkDIANBwBpqIAZCAEL///////////8AQgAQyQMgA0GAGmogAikDECIeQgAgKEIAEMkDIANBwBlqIB5CACApQgAQyQMgA0GwGWogHkIAICpCABDJAyADQaAZaiAeQgAgK0IAEMkDIANB8BlqIAMpA9AaIgYgAykD+BoiEiADKQOwGnwiDXwiCCADKQPoGiAHIAMpA+AaIgx8IAxUrXx8IgcgAykDgBp8IgxCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyADQeAZaiAOQgBCf0IAEMkDIANB0BlqIA5CAEL///////////8AQgAQyQMgA0GQGWogAikDCCIfQgAgKEIAEMkDIANB0BhqIB9CACApQgAQyQMgA0HAGGogH0IAICpCABDJAyADQbAYaiAfQgAgK0IAEMkDIANBgBlqIAMpA4gaIAcgDFatfCITIAMpA8AZfCIOIAYgAykDuBogDSASVK18IhAgAykDoBp8IhJ8Ig0gByAIVK0gAykD2BoiFCAGIAhWrXx8fCIVfCIGIAMpA+AZIhZ8IgggAykD+BkgAykD8BkiByAMfCAHVK18fCIHIAMpA5AZfCIMQpuUr8Pytajehn9+Ig9CAEJtQgAQyQMgA0HwGGogD0IAQn9CABDJAyADQeAYaiAPQgBC////////////AEIAEMkDIANBoBhqIAIpAwAiIEIAIChCABDJAyADQeAXaiAgQgAgKUIAEMkDIANB0BdqICBCACAqQgAQyQMgA0HAF2ogIEIAICtCABDJAyADQZAYaiADKQOYGSAHIAxWrXwiFyADKQPQGHwiDyAWIAMpA6gaIBAgElatfCIYIAMpA5AafCIQIAMpA8AafCIRIA0gFVatIBQgDSASVK18fHwiEiADKQOwGXwiDSAGIA5UrSADKQPIGSAOIBNUrXx8fCIOfCITIAcgCFStIAMpA+gZIhUgBiAIVq18fHwiFnwiBiADKQPwGCIZfCIIIAMpA4gZIAMpA4AZIgcgDHwgB1StfHwiByADKQOgGHwiDEKblK/D8rWo3oZ/fiIUQgBCbUIAEMkDIANBgBhqIBRCAEJ/QgAQyQMgA0HwF2ogFEIAQv///////////wBCABDJAwJAIAMpA/gXIAMpA+gYIAMpA9gZIBEgElatIAMpA8gaIBAgEVatfHwiFCADKQOYGiAQIBhUrXx8IhAgAykDoBl8IhEgDSAOVq0gAykDuBkgDSASVK18fHwiEiADKQPQGXwiDSASVK18IA0gEyAWVq0gFSAOIBNWrXx8fCIOIA1UrXwiEyARIBJWrSADKQOoGSAQIBFWrXx8IhEgECAUVK18IhR8IhIgAykDsBh8Ig0gAykDyBggDiAOIAMpA8AYfCIOVq18IA4gDiAGIA9UrSADKQPYGCAPIBdUrXx8fCIOVq18fCIPIAMpA+AYfCIQIA9UrXwgECADKQP4GCIVIA4gDiAZfCIOVq18IA4gByAIVK0gFSAGIAhWrXx8fCIVIA5UrXx8IgYgEFStfCIQIA0gD1atIAMpA7gYIA0gElStfHwiDyASIBNUrSARIBRWrXx8IhF8IgggAykDwBd8Ig4gAykD2BcgBiAGIAMpA9AXfCIGVq18IAYgBiADKQPoFyADKQOoGCAHIAxWrXwiEiADKQPgF3wiByASVK18IAcgByAVfCIHVq18fCIGVq18fCISIAMpA/AXfCINIBJUrXwgDSADKQOIGCITIAYgBiADKQOAGCIUfCIGVq18IAYgEyAHIAcgFHwiB1atfCAHIAMpA5gYIAwgAykDkBgiDHwgDFStfHwiISAHVK18fCIaIAZUrXx8IiIgDVStfCIGIA4gElatIAMpA8gXIAggDlatfHwiByAIIBBUrSAPIBFWrXx8Igh8IiYgBlQgByAIVnIgJkIAU3IiBEUEQCAmIQwgGiIOICIiB4NCf1IgISISQm1UciAMQv///////////wBScg0BCyAaQgF8IgYgIUJtVK0iCH0hDiAiQgF8IgwgGkJ/UiAGIAhUcq0iBn0hByAmICJCf1IgBiAMVnKtfUL///////////8AfSEMICFCE3whEgsgCyAMfCINIAUgB3wiBiAFVCAGIAYgCSAOfCIFIAlUIAUgBSAKIBJ8IgwgClStfCIFVnKtfCIGVnKtfCEIAkACQCAIIA1UIAsgDVZyDQBC////////////ACELIAgiB0L///////////8AUQRAQn8hCUL///////////8AIQ4gBkJ/UgRAIAUhEiAGIQkMAwsgBUJ/UgRAIAUhEgwDC0JtIQsgDCIHQm1RDQELIAcgC1oNACAFIRIgBiEJIAghDgwBCyAFQgF8IgkgDEJtVK0iB30hEiAGQgF8IgogBUJ/UiAHIAlWcq0iBX0hCSAIIAZCf1IgBSAKVnKtfUL///////////8AfSEOIAxCE3whDAsgA0GAF2ogAykDuB0iF0IAQr4BQgAQyQMgA0HwFmogAykDgBciCEKblK/D8rWo3oZ/fiIFQgBCbUIAEMkDIANB4BZqIAVCAEJ/QgAQyQMgA0HwFWogBUIAQv///////////wBCABDJAyADQZAXaiADKQOwHSIYQgBCvgFCABDJAyADQdAWaiADKQPgFiIFIAMpA4gXfCIGIAMpA/gWIAMpA/AWIgcgCEJ+g3wgB1StfHwiCCADKQOQF3wiB0KblK/D8rWo3oZ/fiIKQgBCbUIAEMkDIANBwBZqIApCAEJ/QgAQyQMgA0GAFmogCkIAQv///////////wBCABDJAyADQaAXaiADKQOoHSIZQgBCvgFCABDJAyADQbAWaiADKQPAFiIKIAMpA5gXIAcgCFStfCILIAUgBiAIVq0gAykD6BYiDSAFIAZWrXx8Ig98IhB8IhF8IgUgAykD2BYgAykD0BYiBiAHfCAGVK18fCIGIAMpA6AXfCIIQpuUr8Pytajehn9+IgdCAEJtQgAQyQMgA0GgFmogB0IAQn9CABDJAyADQZAWaiAHQgBC////////////AEIAEMkDIANBsBdqIAMpA6AdIhxCAEK+AUIAEMkDIANB4BVqIAMpA6AWIgcgCiALIBFWrSIRIA0gDyAQVq18IhAgAykD8BV8IhN8Igt8Ig0gBSAGVq0gAykDyBYiFCAFIApUrXx8fCIFIAMpA6gXIAYgCFatfHwiFXwiBiADKQO4FiAIIAMpA7AWIgh8IAhUrXx8IgggAykDsBd8IgpCm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQdAVaiAPQgBCf0IAEMkDIANBwBVqIA9CAEL///////////8AQgAQyQMCQAJAIAMpA8gVIAMpA5gWIAMpA4gWIAMpA4AWIhYgAykD+BUgECATVq18fCIPIBZUrXwgDyAPIAsgEVStfCIPVq18IA8gBSANVK0gFCALIA1WrXx8fCILIA9UrXwiDyADKQOQFnwiDSAPVK18IA0gCyAFIBVWrXwiBSALVK18IgsgDVStfCALIAMpA6gWIg0gBSAFIAd8IgVWrXwgBSAFIAYgCFatIA0gBiAHVK18fHwiBVatfHwiBiALVK18IgsgAykDwBV8IgcgC1StfCAHIAYgBSADKQO4FyAIIApWrXx8IgsgBVStfCIFIAZUrXwiCCAHVK18IAggCCADKQPYFSIHIAUgBSADKQPQFSIGfCIFVq18IAUgByAGIAYgC3wiBlatfCAGIAMpA+gVIAMpA+AVIgcgCnwgB1StfHwiCiAGVK18fCIGIAVUrXx8IghWrXwiC0IAWQRAIAtC////////////AFIgCkJtVHIgBiAIg0J/UnINAQsgBkIBfCIHIApCbVStIg19IQUgCEIBfCIPIAZCf1IgByANVHKtIgZ9IQcgCyAIQn9SIAYgD1ZyrX1C////////////AH0hCyAKQhN8IQoMAQsgCCEHIAYhBQsgA0GwFWogCkIAIB1CABDJAyADQcAUaiAFQgAgHUIAEMkDIANB0BNqIAdCACAdQgAQyQMgA0HgEmogC0IAIB1CABDJAyADQaAVaiADKQOwFSINQpuUr8Pytajehn9+IgZCAEJtQgAQyQMgA0GQFWogBkIAQn9CABDJAyADQYAVaiAGQgBC////////////AEIAEMkDIANB8BRqIApCACAeQgAQyQMgA0GAFGogBUIAIB5CABDJAyADQZATaiAHQgAgHkIAEMkDIANBoBJqIAtCACAeQgAQyQMgA0GwFGogAykDkBUiBiADKQO4FSIRIAMpA8AUfCITfCIIIAMpA6gVIA0gAykDoBUiD3wgD1StfHwiDSADKQPwFHwiD0KblK/D8rWo3oZ/fiIQQgBCbUIAEMkDIANBoBRqIBBCAEJ/QgAQyQMgA0GQFGogEEIAQv///////////wBCABDJAyADQeAUaiAKQgAgH0IAEMkDIANB8BNqIAVCACAfQgAQyQMgA0GAE2ogB0IAIB9CABDJAyADQZASaiALQgAgH0IAEMkDIANBwBNqIAMpA/gUIA0gD1atfCIVIAMpA4AUfCIQIAYgAykDyBQgESATVq18IhYgAykD0BN8IhF8IhMgCCANVq0gAykDmBUiGyAGIAhWrXx8fCIlfCIGIAMpA6AUIiN8IgggAykDuBQgAykDsBQiDSAPfCANVK18fCINIAMpA+AUfCIPQpuUr8Pytajehn9+IhRCAEJtQgAQyQMgA0GwE2ogFEIAQn9CABDJAyADQaATaiAUQgBC////////////AEIAEMkDIANB0BRqIApCACAgQgAQyQMgA0HgE2ogBUIAICBCABDJAyADQfASaiAHQgAgIEIAEMkDIANBgBJqIAtCACAgQgAQyQMgA0HQEmogAykD6BQgDSAPVq18IiQgAykD8BN8IgUgIyADKQPYEyARIBZUrXwiFiADKQPgEnwiByADKQOAFXwiCiATICVWrSAbIBEgE1atfHx8IgsgAykDkBN8IhEgBiAQVK0gAykDiBQgECAVVK18fHwiEHwiEyAIIA1WrSADKQOoFCIVIAYgCFatfHx8Iht8IgYgAykDsBMiJXwiCCADKQPIEyADKQPAEyINIA98IA1UrXx8Ig0gAykD0BR8Ig9Cm5Svw/K1qN6Gf34iFEIAQm1CABDJAyADQcASaiAUQgBCf0IAEMkDIANBsBJqIBRCAEL///////////8AQgAQyQMCQAJAIAMpA7gSIAMpA6gTIAMpA5gUIAogC1atIAMpA4gVIAcgClatfHwiFCADKQPoEiAHIBZUrXx8IgcgAykDoBJ8IgogECARVK0gAykDmBMgCyARVq18fHwiCyADKQOQFHwiESALVK18IBEgEyAbVq0gFSAQIBNWrXx8fCIQIBFUrXwiESAKIAtWrSADKQOoEiAHIApWrXx8IhMgByAUVK18IhR8IgcgAykDkBJ8IgogAykDiBMgECADKQOAE3wiCyAQVK18IAsgBSAGVq0gAykD+BMgBSAkVK18fHwiBSALVK18fCILIAMpA6ATfCIQIAtUrXwgECADKQO4EyIVIAUgBSAlfCIFVq18IAUgCCANVq0gFSAGIAhWrXx8fCIIIAVUrXx8IgUgEFStfCIQIAogC1atIAMpA5gSIAcgClatfHwiFSAHIBFUrSATIBRWrXx8IhF8IgcgAykDgBJ8IgogAykD+BIgBSAFIAMpA/ASfCIFVq18IAUgBSADKQPoEyADKQPYFCANIA9WrXwiCyADKQPgE3wiBiALVK18IAYgBiAIfCIGVq18fCIFVq18fCINIAMpA7ASfCIIIA1UrXwgCCAIIAMpA8gSIgsgBSAFIAMpA8ASIhN8IgVWrXwgBSALIAYgBiATfCIGVq18IAYgAykD2BIgAykD0BIiCyAPfCALVK18fCILIAZUrXx8IgYgBVStfHwiCFatfCIFIAogDVatIAMpA4gSIAcgClatfHwiDSAHIBBUrSARIBVUrXx8Igd8IgogBVQgByANVHIgCkIAU3JFBEAgBiAIg0J/UiALQm1UciAKQv///////////wBScg0BCyAGQgF8IgcgC0JtVK0iDX0hBSAIQgF8Ig8gBkJ/UiAHIA1Ucq0iBn0hByAKIAhCf1IgBiAPVnKtfUL///////////8AfSEKIAtCE3whCwwBCyAIIQcgBiEFCwJ+AkACQCAKIgYgDiIIUg0AIAciBiAJIghSDQAgBSEGIBIiCCAFUg0AIAwiCCALIgZRDQELIAYgCFgNACAFIBJUIAUgEn0iBSALIAxUrSIGVHKtIgggByAJfSISQn+FfCINIAYgBUJ/hXwiBiALIAx9IgxCbVatIgtUrSIPfSEFIA0gD1QhAiAGIAt9IQYgByAJVCAIIBJWcq0gDiAKfXxC////////////AHwhB0JtIAx9DAELIBIgBX0iCCALIAxWrSINfSEGIAkgB30iDyAIIA1UIAUgElZyrSIIfSEFIAggD1YgByAJVnIhAiAOIAp9IQcgDCALfQshCiAHIAKtfSIJIQcCfwJAAkAgCSAcIgxSDQAgBSIHIBkiDFINACAGIgcgGCIMUg0AIAoiByAXIgxRDQELIAcgDFoNACAYIAZ9IgggCiAXVq0iB1QgBiAYVnKtIgYgGSAFfSIMQn+FfCIOIAhCf4UgB3wiCCAXIAp9IgdCbVatIgpUrSILfSEjIAggCn0hJCAFIBlWIAYgDFZyrSAJIBx9fEL///////////8AfCETQm0gB30hJSALIA5WDAELIAYgGH0iCCAKIBdUrSIHfSEkIAUgGX0iDCAGIBhUIAcgCFZyrSIGfSEjIAkgHH0hEyAKIBd9ISUgBSAZVCAGIAxWcgshAiADQcARaiAdQgBCyANCABDJAyADQbARaiADKQPAESIJQpuUr8Pytajehn9+IgVCAEJtQgAQyQMgA0GgEWogBUIAQn9CABDJAyADQbAQaiAFQgBC////////////AEIAEMkDIANB0BFqIB5CAELIA0IAEMkDIANBkBFqIAMpA6ARIgUgAykDyBF8IgYgAykDuBEgAykDsBEiCCAJQniDfCAIVK18fCIJIAMpA9ARfCIIQpuUr8Pytajehn9+IgdCAEJtQgAQyQMgA0GAEWogB0IAQn9CABDJAyADQcAQaiAHQgBC////////////AEIAEMkDIANB4BFqIB9CAELIA0IAEMkDIANB8BBqIAMpA4ARIgcgAykD2BEgCCAJVK18IgwgBSAGIAlWrSADKQOoESIKIAUgBlatfHwiDnwiC3wiEnwiBSADKQOYESADKQOQESIGIAh8IAZUrXx8IgYgAykD4BF8IglCm5Svw/K1qN6Gf34iCEIAQm1CABDJAyADQeAQaiAIQgBCf0IAEMkDIANB0BBqIAhCAEL///////////8AQgAQyQMgA0HwEWogIEIAQsgDQgAQyQMgA0GgEGogAykD4BAiCCAHIAwgElatIhIgCiALIA5UrXwiCyADKQOwEHwiDXwiDHwiCiAFIAZWrSADKQOIESIPIAUgB1StfHx8IgUgAykD6BEgBiAJVq18fCIQfCIGIAMpA/gQIAkgAykD8BAiCXwgCVStfHwiCSADKQPwEXwiB0KblK/D8rWo3oZ/fiIOQgBCbUIAEMkDIANBkBBqIA5CAEJ/QgAQyQMgA0GAEGogDkIAQv///////////wBCABDJAwJAAkAgAykDiBAgAykD2BAgAykDyBAgAykDwBAiESADKQO4ECALIA1WrXx8Ig4gEVStfCAOIA4gDCASVK18Ig5WrXwgDiAFIApUrSAPIAogDFStfHx8IgwgDlStfCIOIAMpA9AQfCIKIA5UrXwgCiAMIAUgEFatfCIFIAxUrXwiDCAKVK18IAwgAykD6BAiCiAFIAUgCHwiBVatfCAFIAUgBiAJVq0gCiAGIAhUrXx8fCIFVq18fCIGIAxUrXwiDCADKQOAEHwiCCAMVK18IAggBiAFIAMpA/gRIAcgCVStfHwiDCAFVK18IgUgBlStfCIJIAhUrXwgCSADKQOYECIIIAUgBSADKQOQECIGfCIFVq18IAUgCCAGIAYgDHwiBlatfCAGIAMpA6gQIAMpA6AQIgggB3wgCFStfHwiCiAGVK18fCIGIAVUrXx8IgggCVStfCILQgBZBEAgC0L///////////8AUiAKQm1UciAGIAiDQn9Scg0BCyAGQgF8IgkgCkJtVK0iB30hBSAIQgF8IgwgBkJ/UiAHIAlWcq0iBn0hCSALIAhCf1IgBiAMVnKtfUL///////////8AfSELIApCE3whCgwBCyAIIQkgBiEFC0LIAyEMIAMCfiAFIAuEQgBSIApCyANWckUEQEIAIQdCACEOQgAgCVANARoLIAUgCkLIA1StIgZUrSIIIAlCf4V8IgcgBiAFQn+FfCIFIApCtgN9QhJUrSIGVK0iDH0hDiAIIAlWrSALfSAHIAxUrX1C////////////AHwhB0K1AyEMIAUgBn0LNwPQHSADIA43A8gdIAMgBzcDwB0gAyAMIAp9NwPYHQJAAkAgA0HAHWpB6NHBAEEgEPEDBEAgEyACrX0hLCADQfAdakIANwMAIANB6B1qQgA3AwAgA0IANwPgHSADQgE3A/gdIANBmB5qIANB2B1qKQMANwMAIANBkB5qIANB0B1qKQMANwMAIANBiB5qIANByB1qKQMANwMAIAMgAykDwB03A4AeIANBuB5qQeDRwQApAwA3AwAgA0GwHmpB2NHBACkDADcDACADQageakHQ0cEAKQMANwMAIANByNHBACkDADcDoB4CQCADQYAeaiADQeAdakEgEPEDRQRAQqQLIQxCACEKQgAhEEIAIREMAQtCpAshDCADKQOYHiEFIAMpA4AeIQ4gAykDkB4hFSADKQOIHiEGQgAhB0IAIRRCACETQgAhC0IAIRFCACEQQgAhCkJtIQlC////////////ACESQn8hCEJ/IRYDQCADQaAeaiADQeAdakEgEPEDRQRAIAshCiATIRAgFCERIAchDAwCCyAFp0EBcUUEQANAIBVCP4YgBUIBiIQhBQJ+IAynQQFxRQRAIBFCP4YgDEIBiIQhDCAQQj+GIBFCAYiEIREgCkI/hiAQQgGIhAwBCyAQQgF9Ig8gEUIAUiARQgF9Ig0gDEITfSIbIAxUrXwiDCANVHKtfCINQj+GIAxCAYiEIREgDEI/hiAbQgGIhCEMIAogEEIAUiANIA9Ucq18Qv///////////wB8IgpCP4YgDUIBiIQLIRAgDkI/hiAGQj+GIBVCAYiEIRUgDkIBiCEOIApCAYghCiAGQgGIhCEGIAVCAYNQDQALIAMgBjcDiB4gAyAVNwOQHgsgAyAONwOAHiADIAU3A5geIAmnQQFxRQRAA0AgFkI/hiAJQgGIhCEJAn4gB0IBg1BFBEAgE0IBfSIPIBRCAFIgFEIBfSINIAdCE30iGyAHVK18IgcgDVRyrXwiDUI/hiAHQgGIhCEUIAdCP4YgG0IBiIQhByALIBNCAFIgDSAPVHKtfEL///////////8AfCILQj+GIA1CAYiEDAELIBRCP4YgB0IBiIQhByATQj+GIBRCAYiEIRQgC0I/hiATQgGIhAshEyASQj+GIAhCP4YgFkIBiIQhFiASQgGIIRIgC0IBiCELIAhCAYiEIQggCUIBg1ANAAsgAyAINwOoHiADIBY3A7AeCyADIAk3A7geIAMgEjcDoB4gDiEPAkACQAJAAkACQCASIg0gDlINACAIIQ0gBiEPIAYgCFINACAVIg8gFiINUg0AIAkhDSAFIQ8gBSAJUQ0BCyANIA9YDQAgAyAJIAV9Ig03A7geIAMgFiAVfSIbIAUgCVatIgl9Ig83A7AeIAMgCCAGfSInIAkgG1YgFSAWVnKtIgl9Ihs3A6geIAMgEiAOfSAJICdWIAYgCFZyrX0iEjcDoB4CQAJAIAoiCCALIglSDQAgECIIIBMiCVINACARIgggFCIJUg0AIAchCSAHIAwiCFENAQsgCCAJVg0CCyALIAp9IBMgEH0iJyAUIBF9Ii0gByAMVK0iLlQgESAUVnKtIhRUIBAgE1ZyrX0hCyAHIAx9IQcgDyEWIBshCCANIQkgJyAUfSETIC0gLn0hFAwDCyADIAUgCX0iDTcDmB4gAyAVIBZ9IhsgBSAJVK0iBX0iDzcDkB4gAyAGIAh9IicgFSAWVCAFIBtWcq0iBX0iFTcDiB4gAyAOIBJ9IAYgCFQgBSAnVnKtfSIONwOAHgJAAkAgCiIFIAsiBlINACAQIgUgEyIGUg0AIBEiBSAUIgZSDQAgDCIFIAciBlENAQsgBSAGVA0CCyAKIAt9IBAgE1QgECATfSIQIBEgFFQgESAUfSIRIAcgDFatIhtUcq0iJ1RyrX0hCiAMIAd9IQwgFSEGIA8hFSANIQUgECAnfSEQIBEgG30hEQwCCyALQn9CACAQQn+FIgkgEUJ/hSIIIAxCbVatIgtUrSIWVBsgCn18IBMgCSAWfSITfCIJIBNUIAkgCCALfSILIBR8IgggC1QgCEJtIAx9IgsgB3wiByALVK18IhQgCFRyrXwiEyAJVHKtfEL///////////8AfCELIA8hFiAbIQggDSEJDAELIAogC30gE0J/hSIFIBRCf4UiBiAHQm1WrSIKVK0iG1StfSAQIAUgG30iEHwiBSAQVCAFIAYgCn0iCiARfCIGIApUIAZCbSAHfSIKIAx8IgwgClStfCIRIAZUcq18IhAgBVRyrXxC////////////AHwhCiAVIQYgDyEVIA0hBQsgA0GAHmogA0HgHWpBIBDxAw0ACwsgA0HwD2ogDEIAICVCABDJAyADQbAPaiAMQgAgJEIAEMkDIANBoA9qIAxCACAjQgAQyQMgA0GQD2ogDEIAICxCABDJAyADQeAPaiADKQPwDyIJQpuUr8Pytajehn9+IgVCAEJtQgAQyQMgA0HQD2ogBUIAQn9CABDJAyADQcAPaiAFQgBC////////////AEIAEMkDIANBgA9qIBFCACAlQgAQyQMgA0HADmogEUIAICRCABDJAyADQbAOaiARQgAgI0IAEMkDIANBoA5qIBFCACAsQgAQyQMgA0HwDmogAykD0A8iBSADKQP4DyIMIAMpA7APfCIOfCIGIAMpA+gPIAkgAykD4A8iCHwgCFStfHwiCSADKQOAD3wiCEKblK/D8rWo3oZ/fiIHQgBCbUIAEMkDIANB4A5qIAdCAEJ/QgAQyQMgA0HQDmogB0IAQv///////////wBCABDJAyADQZAOaiAQQgAgJUIAEMkDIANB0A1qIBBCACAkQgAQyQMgA0HADWogEEIAICNCABDJAyADQbANaiAQQgAgLEIAEMkDIANBgA5qIAMpA4gPIAggCVStfCINIAMpA8AOfCIHIAUgAykDuA8gDCAOVq18IhIgAykDoA98Igx8Ig4gBiAJVq0gAykD2A8iDyAFIAZWrXx8fCIQfCIFIAMpA+AOIhF8IgYgAykD+A4gAykD8A4iCSAIfCAJVK18fCIJIAMpA5AOfCIIQpuUr8Pytajehn9+IgtCAEJtQgAQyQMgA0HwDWogC0IAQn9CABDJAyADQeANaiALQgBC////////////AEIAEMkDIANBoA1qIApCACAlQgAQyQMgA0HgDGogCkIAICRCABDJAyADQdAMaiAKQgAgI0IAEMkDIANBwAxqIApCACAsQgAQyQMgA0GQDWogAykDmA4gCCAJVK18IhMgAykD0A18IgogESADKQOoDyAMIBJUrXwiFCADKQOQD3wiCyADKQPAD3wiEiAOIBBWrSAPIAwgDlatfHx8IgwgAykDsA58Ig4gBSAHVK0gAykDyA4gByANVK18fHwiB3wiDSAGIAlWrSADKQPoDiIQIAUgBlatfHx8IhF8IgUgAykD8A0iFXwiBiADKQOIDiADKQOADiIJIAh8IAlUrXx8IgkgAykDoA18IghCm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQYANaiAPQgBCf0IAEMkDIANB8AxqIA9CAEL///////////8AQgAQyQMgAykD+AwgAykD6A0gAykD2A4gDCASVK0gAykDyA8gCyASVq18fCIPIAMpA5gPIAsgFFStfHwiCyADKQOgDnwiEiAHIA5UrSADKQO4DiAMIA5WrXx8fCIMIAMpA9AOfCIOIAxUrXwgDiANIBFWrSAQIAcgDVatfHx8IgcgDlStfCINIAwgElStIAMpA6gOIAsgElatfHwiEiALIA9UrXwiD3wiDCADKQOwDXwiDiADKQPIDSAHIAcgAykDwA18IgdWrXwgByAHIAUgClStIAMpA9gNIAogE1StfHx8IgdWrXx8IgogAykD4A18IgsgClStfCALIAMpA/gNIhAgByAHIBV8IgdWrXwgByAGIAlWrSAQIAUgBlatfHx8IhAgB1StfHwiBSALVK18IgsgCiAOVK0gAykDuA0gDCAOVq18fCIOIAwgDVStIA8gElStfHwiEnwiByADKQPADHwiDCADKQPYDCAFIAUgAykD0Ax8IgVWrXwgBSAFIAMpA+gMIAMpA6gNIAggCVStfCIJIAMpA+AMfCIGIAlUrXwgBiAGIBB8IgZWrXx8IgVWrXx8IgkgAykD8Ax8IgogCVStfCAKIAMpA4gNIg0gBSAFIAMpA4ANIg98IgVWrXwgBSAFIA0gBiAGIA98IgZWrXwgBiADKQOYDSAIIAMpA5ANIgh8IAhUrXx8IiMgBlStfHwiBVatfHwiBiAKVK18IgggCSAMVK0gAykDyAwgByAMVq18fCIJIAcgC1StIA4gElatfHwiB3wiJCAIVCAHIAlUciAkQgBTckUEQCAFIAaDQn9SICNCbVRyICRC////////////AFJyDQILIAVCAXwiCSAjQm1UrSIIfSEbIAZCAXwiByAFQn9SIAggCVZyrSIFfSElICQgBkJ/UiAFIAdWcq19Qv///////////wB9ISQgI0ITfCEjDAILIANCAjcDoB5BjPfBAEErIANBoB5qQfz2wQBB+JDCABDKAwALIAYhJSAFIRsLAkACQCAERQRAIBogIoNCf1IgIUJtVHIgJkL///////////8AUnINAQsgGkIBfCIFICFCbVStIgZ9IQsgIkIBfCIJIBpCf1IgBSAGVHKtIgV9IQogJiAiQn9SIAUgCVZyrX1C////////////AH0hJiAhQhN8ISEMAQsgIiEKIBohCwsgJiArfCIFIAogKnwiCSAqVCAJIAkgCyApfCIGIClUIAYgBiAhICh8IgwgKFStfCIGVnKtfCIJVnKtfCEIAkACQCAFICtUIAUgCFZyDQBC////////////ACEHIAgiBUL///////////8AUQRAQn8hB0L///////////8AIQUgCUJ/UgRAIAYhDiAJIQcMAwsgBkJ/UgRAIAYhDgwDC0JtIQcgDCIFQm1RDQELIAUgB1oNACAGIQ4gCSEHIAghBQwBCyAGQgF8IgUgDEJtVK0iB30hDiAJQgF8IgogBkJ/UiAFIAdUcq0iBX0hByAIIAlCf1IgBSAKVnKtfUL///////////8AfSEFIAxCE3whDAsgA0HwCmogF0IAIB1CABDJAyADQbAKaiAYQgAgHUIAEMkDIANB8AlqIBlCACAdQgAQyQMgA0GwCWogHEIAIB1CABDJAyADQeAKaiADKQPwCiIIQpuUr8Pytajehn9+IgZCAEJtQgAQyQMgA0HQCmogBkIAQn9CABDJAyADQcAKaiAGQgBC////////////AEIAEMkDIANBsAtqIBdCACAeQgAQyQMgA0GgC2ogGEIAIB5CABDJAyADQZALaiAZQgAgHkIAEMkDIANBgAtqIBxCACAeQgAQyQMgA0GgCmogAykD0AoiBiADKQP4CiISIAMpA7AKfCINfCIJIAMpA+gKIAggAykD4AoiCnwgClStfHwiCCADKQOwC3wiCkKblK/D8rWo3oZ/fiILQgBCbUIAEMkDIANBkApqIAtCAEJ/QgAQyQMgA0GACmogC0IAQv///////////wBCABDJAyADQfALaiAXQgAgH0IAEMkDIANB4AtqIBhCACAfQgAQyQMgA0HQC2ogGUIAIB9CABDJAyADQcALaiAcQgAgH0IAEMkDIANB4AlqIAMpA7gLIAggClatfCITIAMpA6ALfCILIAYgAykDuAogDSASVK18IhAgAykD8Al8IhJ8Ig0gCCAJVK0gAykD2AoiFCAGIAlWrXx8fCIVfCIGIAMpA5AKIhZ8IgkgAykDqAogAykDoAoiCCAKfCAIVK18fCIIIAMpA/ALfCIKQpuUr8Pytajehn9+Ig9CAEJtQgAQyQMgA0HQCWogD0IAQn9CABDJAyADQcAJaiAPQgBC////////////AEIAEMkDIANBsAxqIBdCACAgQgAQyQMgA0GgDGogGEIAICBCABDJAyADQZAMaiAZQgAgIEIAEMkDIANBgAxqIBxCACAgQgAQyQMgA0GgCWogAykD+AsgCCAKVq18IhogAykD4At8Ig8gFiADKQP4CSAQIBJWrXwiIiADKQOwCXwiECADKQPACnwiESANIBVWrSAUIA0gElStfHx8IhIgAykDkAt8Ig0gBiALVK0gAykDqAsgCyATVK18fHwiC3wiEyAIIAlUrSADKQOYCiIVIAYgCVatfHx8IhZ8IgYgAykD0AkiIXwiCSADKQPoCSADKQPgCSIIIAp8IAhUrXx8IgggAykDsAx8IgpCm5Svw/K1qN6Gf34iFEIAQm1CABDJAyADQZAJaiAUQgBCf0IAEMkDIANBgAlqIBRCAEL///////////8AQgAQyQMCQAJAIAMpA4gJIAMpA8gJIAMpA4gKIBEgElatIAMpA8gKIBAgEVatfHwiFCADKQO4CSAQICJUrXx8IhAgAykDgAt8IhEgCyANVK0gAykDmAsgDSASVK18fHwiEiADKQOACnwiDSASVK18IA0gEyAWVq0gFSALIBNWrXx8fCILIA1UrXwiEyARIBJWrSADKQOICyAQIBFWrXx8IhEgECAUVK18IhR8IhIgAykDwAt8Ig0gAykD2AsgCyALIAMpA9ALfCILVq18IAsgCyAGIA9UrSADKQPoCyAPIBpUrXx8fCILVq18fCIPIAMpA8AJfCIQIA9UrXwgECADKQPYCSIVIAsgCyAhfCILVq18IAsgCyAIIAlUrSAVIAYgCVatfHx8IgtWrXx8IgYgEFStfCIQIA0gD1atIAMpA8gLIA0gElStfHwiFSASIBNUrSARIBRWrXx8IhF8IgkgAykDgAx8IhIgAykDmAwgBiAGIAMpA5AMfCIGVq18IAYgBiADKQOoDCADKQO4DCAIIApWrXwiDSADKQOgDHwiCCANVK18IAggCCALfCIIVq18fCIGVq18fCINIAMpA4AJfCIPIA1UrXwgDyADKQOYCSILIAYgBiADKQOQCSITfCIGVq18IAYgBiALIAggCCATfCIIVq18IAggAykDqAkgCiADKQOgCSIKfCAKVK18fCILIAhUrXx8IgZWrXx8IgggD1StfCIPIA0gElStIAMpA4gMIAkgElatfHwiEiAJIBBUrSARIBVUrXx8Igl8IgogD1QgCSASVHIgCkIAU3JFBEAgBiAIg0J/UiALQm1UciAKQv///////////wBScg0BCyAGQgF8IgkgC0JtVK0iDX0hEiAIQgF8Ig8gBkJ/UiAJIA1Ucq0iBn0hCSAKIAhCf1IgBiAPVnKtfUL///////////8AfSEKIAtCE3whCwwBCyAIIQkgBiESCyAFIQgCfgJAAkAgBSAKIgZSDQAgByEIIAkiBiAHUg0AIA4iCCASIgZSDQAgDCIIIAsiBlENAQsgBiAIWA0AIBIgDn0iBiALIAxUrSIIVCAOIBJWcq0iEiAJIAd9Ig1Cf4V8Ig8gCCAGQn+FfCIGIAsgDH0iCEJtVq0iDFStIgt9IQ4gCyAPViECIAYgDH0hBiANIBJUIAcgCVZyrSAFIAp9fEL///////////8AfCEHQm0gCH0MAQsgDiASfSIIIAsgDFatIg19IQYgByAJfSIPIA4gElQgCCANVHKtIgh9IQ4gByAJVCAIIA9WciECIAUgCn0hByAMIAt9CyEKIAcgAq19IgUhBwJ+AkACQCAFIBwiDFINACAOIgcgGSIMUg0AIAYiByAYIgxSDQAgCiIHIBciDFENAQsgByAMWg0AIBggBn0iCSAKIBdWrSIIVCAGIBhWcq0iBiAZIA59IgdCf4V8IgwgCUJ/hSAIfCIJIBcgCn0iCEJtVq0iClStIgt9IRggCyAMViEEIAkgCn0hISAOIBlWIAYgB1ZyrSAFIBx9fEL///////////8AfCENQm0gCH0MAQsgBiAYfSIJIAogF1StIgh9ISEgDiAZfSIHIAYgGFQgCCAJVnKtIgZ9IRggDiAZVCAGIAdWciEEIAUgHH0hDSAKIBd9CyEZIANB8AhqIAEpAxhCAEKYAUIAEMkDIANB4AhqIAMpA/AIIglCm5Svw/K1qN6Gf34iBUIAQm1CABDJAyADQdAIaiAFQgBCf0IAEMkDIANBwAhqIAVCAEL///////////8AQgAQyQMgA0GwCGogASkDEEIAQpgBQgAQyQMgA0GgCGogAykD0AgiBSADKQP4CHwiBiADKQPoCCADKQPgCCIIIAlCeIN8IAhUrXx8IgkgAykDsAh8IghCm5Svw/K1qN6Gf34iB0IAQm1CABDJAyADQZAIaiAHQgBCf0IAEMkDIANBgAhqIAdCAEL///////////8AQgAQyQMgA0HwB2ogASkDCEIAQpgBQgAQyQMgA0HgB2ogAykDkAgiByADKQO4CCAIIAlUrXwiDCAFIAYgCVatIAMpA9gIIgogBSAGVq18fCIOfCILfCISfCIFIAMpA6gIIAMpA6AIIgYgCHwgBlStfHwiBiADKQPwB3wiCUKblK/D8rWo3oZ/fiIIQgBCbUIAEMkDIANB0AdqIAhCAEJ/QgAQyQMgA0HAB2ogCEIAQv///////////wBCABDJAyADQbAHaiABKQMAQgBCmAFCABDJAyADQaAHaiADKQPQByIIIAcgDCASVq0iEiAKIAsgDlStfCILIAMpA8AIfCIPfCIMfCIKIAUgBlatIAMpA5gIIhAgBSAHVK18fHwiBSADKQP4ByAGIAlWrXx8IhF8IgYgAykD6AcgCSADKQPgByIJfCAJVK18fCIJIAMpA7AHfCIHQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgA0GQB2ogDkIAQn9CABDJAyADQYAHaiAOQgBC////////////AEIAEMkDAkACQAJ+AkACQCADKQOIByADKQPIByADKQOICCADKQOACCITIAMpA8gIIAsgD1atfHwiDiATVK18IA4gDiAMIBJUrXwiDlatfCAOIAUgClStIBAgCiAMVK18fHwiDCAOVK18Ig4gAykDwAd8IgogDlStfCAKIAwgBSARVq18IgUgDFStfCIMIApUrXwgDCADKQPYByIKIAUgBSAIfCIFVq18IAUgBSAGIAlWrSAKIAYgCFStfHx8IgVWrXx8IgYgDFStfCIMIAMpA4AHfCIIIAxUrXwgCCAGIAUgAykDuAcgByAJVK18fCIMIAVUrXwiBSAGVK18IgYgCFStfCAGIAMpA5gHIgggBSAFIAMpA5AHIgl8IgVWrXwgBSAIIAkgCSAMfCIJVq18IAkgAykDqAcgAykDoAciCCAHfCAIVK18fCIHIAlUrXx8IgogBVStfHwiDCAGVK18IgtCAFMiAUUEQCAKIAyDIQUgC0L///////////8AUiAHQm1Ucg0BIAchBiAKIQggDCEOIAshEiAFQn9SDQILIApCAXwiECAHQm1UrSIFfSEIIAxCAXwiFSAKQn9SIAUgEFZyrSIFfSEOIAtC////////////AH0iFiAMQn9SIAUgFVZyrX0hEiAHQhN8IQYgBiABDQIaIAogDIMhBQwBCyAHIQYgCiEIIAwhDiALIRILIAtC////////////AFIgB0JtVHIgBUJ/UnINASAMQgF8IRUgCkIBfCEQQgAhFiAHQhN8CyEFIBUgCkJ/UiAQIAdCbVStIgdUcq0iCn0hCSAWIAxCf1IgCiAVVnKtfSELIBAgB30hCgwBCyAMIQkgByEFCyADQfAGaiAFQgAgHUIAEMkDIANBgAZqIApCACAdQgAQyQMgA0GQBWogCUIAIB1CABDJAyADQaAEaiALQgAgHUIAEMkDIANB4AZqIAMpA/AGIg9Cm5Svw/K1qN6Gf34iB0IAQm1CABDJAyADQdAGaiAHQgBCf0IAEMkDIANBwAZqIAdCAEL///////////8AQgAQyQMgA0GwBmogBUIAIB5CABDJAyADQcAFaiAKQgAgHkIAEMkDIANB0ARqIAlCACAeQgAQyQMgA0HgA2ogC0IAIB5CABDJAyADQfAFaiADKQPQBiIHIAMpA/gGIhMgAykDgAZ8IhR8IgwgAykD6AYgDyADKQPgBiIQfCAQVK18fCIPIAMpA7AGfCIQQpuUr8Pytajehn9+IhFCAEJtQgAQyQMgA0HgBWogEUIAQn9CABDJAyADQdAFaiARQgBC////////////AEIAEMkDIANBoAZqIAVCACAfQgAQyQMgA0GwBWogCkIAIB9CABDJAyADQcAEaiAJQgAgH0IAEMkDIANB0ANqIAtCACAfQgAQyQMgA0GABWogAykDuAYgDyAQVq18IhYgAykDwAV8IhEgByADKQOIBiATIBRWrXwiFyADKQOQBXwiE3wiFCAMIA9WrSADKQPYBiIcIAcgDFatfHx8Ihp8IgcgAykD4AUiInwiDCADKQP4BSADKQPwBSIPIBB8IA9UrXx8Ig8gAykDoAZ8IhBCm5Svw/K1qN6Gf34iFUIAQm1CABDJAyADQfAEaiAVQgBCf0IAEMkDIANB4ARqIBVCAEL///////////8AQgAQyQMgA0GQBmogBUIAICBCABDJAyADQaAFaiAKQgAgIEIAEMkDIANBsARqIAlCACAgQgAQyQMgA0HAA2ogC0IAICBCABDJAyADQZAEaiADKQOoBiAPIBBWrXwiJiADKQOwBXwiBSAiIAMpA5gFIBMgF1StfCIXIAMpA6AEfCIJIAMpA8AGfCIKIBQgGlatIBwgEyAUVq18fHwiCyADKQPQBHwiEyAHIBFUrSADKQPIBSARIBZUrXx8fCIRfCIUIAwgD1atIAMpA+gFIhYgByAMVq18fHwiHHwiByADKQPwBCIafCIMIAMpA4gFIAMpA4AFIg8gEHwgD1StfHwiDyADKQOQBnwiEEKblK/D8rWo3oZ/fiIVQgBCbUIAEMkDIANBgARqIBVCAEJ/QgAQyQMgA0HwA2ogFUIAQv///////////wBCABDJAwJAAkAgAykD+AMgAykD6AQgAykD2AUgCiALVq0gAykDyAYgCSAKVq18fCIVIAMpA6gEIAkgF1StfHwiCSADKQPgA3wiCiARIBNUrSADKQPYBCALIBNWrXx8fCILIAMpA9AFfCITIAtUrXwgEyAUIBxWrSAWIBEgFFatfHx8IhEgE1StfCITIAogC1atIAMpA+gDIAkgClatfHwiFCAJIBVUrXwiFXwiCSADKQPQA3wiCiADKQPIBCARIAMpA8AEfCILIBFUrXwgCyAFIAdWrSADKQO4BSAFICZUrXx8fCIFIAtUrXx8IgsgAykD4AR8IhEgC1StfCARIAMpA/gEIhYgBSAFIBp8IgVWrXwgBSAMIA9WrSAWIAcgDFatfHx8IhYgBVStfHwiBSARVK18IhEgCiALVq0gAykD2AMgCSAKVq18fCIXIAkgE1StIBQgFVatfHwiE3wiByADKQPAA3wiDCADKQO4BCAFIAUgAykDsAR8IgVWrXwgBSAFIAMpA6gFIAMpA5gGIA8gEFatfCIKIAMpA6AFfCIJIApUrXwgCSAJIBZ8IglWrXx8IgVWrXx8IgogAykD8AN8Ig8gClStfCAPIAMpA4gEIgsgBSAFIAMpA4AEIhR8IgVWrXwgBSAFIAsgCSAJIBR8IglWrXwgCSADKQOYBCADKQOQBCILIBB8IAtUrXx8IgsgCVStfHwiBVatfHwiCSAPVK18Ig8gCiAMVK0gAykDyAMgByAMVq18fCIMIAcgEVStIBMgF1StfHwiB3wiCiAPVCAHIAxUciAKQgBTckUEQCAFIAmDQn9SIAtCbVRyIApC////////////AFJyDQELIAVCAXwiDCALQm1UrSIPfSEHIAlCAXwiECAFQn9SIAwgD1RyrSIFfSEMIAogCUJ/UiAFIBBWcq19Qv///////////wB9IQogC0ITfCELDAELIAkhDCAFIQcLAn4CQAJAIAoiBSASIglSDQAgDCIFIA4iCVINACAHIgUgCCIJUg0AIAsiBSAGIglRDQELIAUgCVgNACAHIAhUIAcgCH0iBSAGIAtWrSIJVHKtIgggDCAOfSIPQn+FfCIQIAkgBUJ/hXwiBSALIAZ9IgZCbVatIglUrSILfSEHIAsgEFYhAiAFIAl9IQVCbSAGfSELIAwgDlQgCCAPVnKtIBIgCn18Qv///////////wB8DAELIAggB30iCSAGIAtUrSIPfSEFIA4gDH0iECAJIA9UIAcgCFZyrSIJfSEHIAkgEFYgDCAOVnIhAiAGIAt9IQsgEiAKfQshCiADIAs3A9gdIAMgBTcD0B0gAyAHNwPIHSADIAogAq19NwPAHQJAAkAgA0HAHWpB6NHBAEEgEPEDBEAgDSAErX0hHCADQfAdakIANwMAIANB6B1qQgA3AwAgA0IANwPgHSADQgE3A/gdIANBmB5qIANB2B1qKQMANwMAIANBkB5qIANB0B1qKQMANwMAIANBiB5qIANByB1qKQMANwMAIAMgAykDwB03A4AeIANBuB5qQeDRwQApAwA3AwAgA0GwHmpB2NHBACkDADcDACADQageakHQ0cEAKQMANwMAIANByNHBACkDADcDoB4CQCADQYAeaiADQeAdakEgEPEDRQRAQqQLIQxCACEKQgAhEEIAIREMAQtCpAshDCADKQOYHiEFIAMpA4AeIQ4gAykDkB4hFSADKQOIHiEGQgAhB0IAIRRCACETQgAhC0IAIRFCACEQQgAhCkJtIQlC////////////ACESQn8hCEJ/IRYDQCADQaAeaiADQeAdakEgEPEDRQRAIAshCiATIRAgFCERIAchDAwCCyAFp0EBcUUEQANAIBVCP4YgBUIBiIQhBQJ+IAynQQFxRQRAIBFCP4YgDEIBiIQhDCAQQj+GIBFCAYiEIREgCkI/hiAQQgGIhAwBCyAQQgF9Ig8gEUIAUiARQgF9Ig0gDEITfSIXIAxUrXwiDCANVHKtfCINQj+GIAxCAYiEIREgDEI/hiAXQgGIhCEMIAogEEIAUiANIA9Ucq18Qv///////////wB8IgpCP4YgDUIBiIQLIRAgDkI/hiAGQj+GIBVCAYiEIRUgDkIBiCEOIApCAYghCiAGQgGIhCEGIAVCAYNQDQALIAMgBjcDiB4gAyAVNwOQHgsgAyAONwOAHiADIAU3A5geIAmnQQFxRQRAA0AgFkI/hiAJQgGIhCEJAn4gB0IBg1BFBEAgE0IBfSIPIBRCAFIgFEIBfSINIAdCE30iFyAHVK18IgcgDVRyrXwiDUI/hiAHQgGIhCEUIAdCP4YgF0IBiIQhByALIBNCAFIgDSAPVHKtfEL///////////8AfCILQj+GIA1CAYiEDAELIBRCP4YgB0IBiIQhByATQj+GIBRCAYiEIRQgC0I/hiATQgGIhAshEyASQj+GIAhCP4YgFkIBiIQhFiASQgGIIRIgC0IBiCELIAhCAYiEIQggCUIBg1ANAAsgAyAINwOoHiADIBY3A7AeCyADIAk3A7geIAMgEjcDoB4gDiEPAkACQAJAAkACQCASIg0gDlINACAIIQ0gBiEPIAYgCFINACAVIg8gFiINUg0AIAkhDSAFIQ8gBSAJUQ0BCyANIA9YDQAgAyAJIAV9Ig03A7geIAMgFiAVfSIXIAUgCVatIgl9Ig83A7AeIAMgCCAGfSIaIAkgF1YgFSAWVnKtIgl9Ihc3A6geIAMgEiAOfSAJIBpWIAYgCFZyrX0iEjcDoB4CQAJAIAoiCCALIglSDQAgECIIIBMiCVINACARIgggFCIJUg0AIAchCSAHIAwiCFENAQsgCCAJVg0CCyALIAp9IBMgEH0iGiAUIBF9IiIgByAMVK0iJlQgESAUVnKtIhRUIBAgE1ZyrX0hCyAHIAx9IQcgDyEWIBchCCANIQkgGiAUfSETICIgJn0hFAwDCyADIAUgCX0iDTcDmB4gAyAVIBZ9IhcgBSAJVK0iBX0iDzcDkB4gAyAGIAh9IhogFSAWVCAFIBdWcq0iBX0iFTcDiB4gAyAOIBJ9IAYgCFQgBSAaVnKtfSIONwOAHgJAAkAgCiIFIAsiBlINACAQIgUgEyIGUg0AIBEiBSAUIgZSDQAgDCIFIAciBlENAQsgBSAGVA0CCyAKIAt9IBAgE1QgECATfSIQIBEgFFQgESAUfSIRIAcgDFatIhdUcq0iGlRyrX0hCiAMIAd9IQwgFSEGIA8hFSANIQUgECAafSEQIBEgF30hEQwCCyALQn9CACAQQn+FIgkgEUJ/hSIIIAxCbVatIgtUrSIWVBsgCn18IBMgCSAWfSITfCIJIBNUIAkgCCALfSILIBR8IgggC1QgCEJtIAx9IgsgB3wiByALVK18IhQgCFRyrXwiEyAJVHKtfEL///////////8AfCELIA8hFiAXIQggDSEJDAELIAogC30gE0J/hSIFIBRCf4UiBiAHQm1WrSIKVK0iF1StfSAQIAUgF30iEHwiBSAQVCAFIAYgCn0iCiARfCIGIApUIAZCbSAHfSIKIAx8IgwgClStfCIRIAZUcq18IhAgBVRyrXxC////////////AHwhCiAVIQYgDyEVIA0hBQsgA0GAHmogA0HgHWpBIBDxAw0ACwsgA0GwA2ogDEIAIBlCABDJAyADQfACaiAMQgAgIUIAEMkDIANB4AJqIAxCACAYQgAQyQMgA0HQAmogDEIAIBxCABDJAyADQaADaiADKQOwAyIJQpuUr8Pytajehn9+IgVCAEJtQgAQyQMgA0GQA2ogBUIAQn9CABDJAyADQYADaiAFQgBC////////////AEIAEMkDIANBwAJqIBFCACAZQgAQyQMgA0GAAmogEUIAICFCABDJAyADQfABaiARQgAgGEIAEMkDIANB4AFqIBFCACAcQgAQyQMgA0GwAmogAykDkAMiBSADKQO4AyIMIAMpA/ACfCIOfCIGIAMpA6gDIAkgAykDoAMiCHwgCFStfHwiCSADKQPAAnwiCEKblK/D8rWo3oZ/fiIHQgBCbUIAEMkDIANBoAJqIAdCAEJ/QgAQyQMgA0GQAmogB0IAQv///////////wBCABDJAyADQdABaiAQQgAgGUIAEMkDIANBkAFqIBBCACAhQgAQyQMgA0GAAWogEEIAIBhCABDJAyADQfAAaiAQQgAgHEIAEMkDIANBwAFqIAMpA8gCIAggCVStfCINIAMpA4ACfCIHIAUgAykD+AIgDCAOVq18IhIgAykD4AJ8Igx8Ig4gBiAJVq0gAykDmAMiDyAFIAZWrXx8fCIQfCIFIAMpA6ACIhF8IgYgAykDuAIgAykDsAIiCSAIfCAJVK18fCIJIAMpA9ABfCIIQpuUr8Pytajehn9+IgtCAEJtQgAQyQMgA0GwAWogC0IAQn9CABDJAyADQaABaiALQgBC////////////AEIAEMkDIANB4ABqIApCACAZQgAQyQMgA0EgaiAKQgAgIUIAEMkDIANBEGogCkIAIBhCABDJAyADIApCACAcQgAQyQMgA0HQAGogAykD2AEgCCAJVK18IhMgAykDkAF8IgogESADKQPoAiAMIBJUrXwiFCADKQPQAnwiCyADKQOAA3wiEiAOIBBWrSAPIAwgDlatfHx8IgwgAykD8AF8Ig4gBSAHVK0gAykDiAIgByANVK18fHwiB3wiDSAGIAlWrSADKQOoAiIQIAUgBlatfHx8IhF8IgUgAykDsAEiFXwiBiADKQPIASADKQPAASIJIAh8IAlUrXx8IgkgAykDYHwiCEKblK/D8rWo3oZ/fiIPQgBCbUIAEMkDIANBQGsgD0IAQn9CABDJAyADQTBqIA9CAEL///////////8AQgAQyQMgAykDOCADKQOoASADKQOYAiAMIBJUrSADKQOIAyALIBJWrXx8Ig8gAykD2AIgCyAUVK18fCILIAMpA+ABfCISIAcgDlStIAMpA/gBIAwgDlatfHx8IgwgAykDkAJ8Ig4gDFStfCAOIA0gEVatIBAgByANVq18fHwiByAOVK18Ig0gDCASVK0gAykD6AEgCyASVq18fCISIAsgD1StfCIPfCIMIAMpA3B8Ig4gAykDiAEgByAHIAMpA4ABfCIHVq18IAcgByAFIApUrSADKQOYASAKIBNUrXx8fCIHVq18fCIKIAMpA6ABfCILIApUrXwgCyADKQO4ASIQIAcgByAVfCIHVq18IAcgBiAJVq0gECAFIAZWrXx8fCIQIAdUrXx8IgUgC1StfCILIAogDlStIAMpA3ggDCAOVq18fCIRIAwgDVStIA8gElStfHwiEnwiByADKQMAfCIMIAMpAxggBSAFIAMpAxB8IgVWrXwgBSAFIAMpAyggAykDaCAIIAlUrXwiCSADKQMgfCIGIAlUrXwgBiAGIBB8IgZWrXx8IgVWrXx8IgkgAykDMHwiDiAJVK18IA4gAykDSCIKIAUgBSADKQNAIg18IgVWrXwgBSAKIAYgBiANfCIGVq18IAYgAykDWCAIIAMpA1AiCHwgCFStfHwiCiAGVK18fCIGIAVUrXx8IgggDlStfCIFIAkgDFStIAMpAwggByAMVq18fCIJIAcgC1StIBEgElatfHwiB3wiCyAFVCAHIAlUciALQgBTckUEQCAGIAiDQn9SIApCbVRyIAtC////////////AFJyDQILIAZCAXwiBSAKQm1UrSIHfSEJIAhCAXwiDCAGQn9SIAUgB1RyrSIGfSEFIAsgCEJ/UiAGIAxWcq19Qv///////////wB9IQsgCkITfCEKDAILIANCAjcDoB5BjPfBAEErIANBoB5qQfz2wQBB6JDCABDKAwALIAghBSAGIQkLIAAgCjcDOCAAIAk3AzAgACAFNwMoIAAgCzcDICAAICM3AxggACAbNwMQIAAgJTcDCCAAICQ3AwAgA0HAHmokAAv/wwECB38kfiMAQZAwayIDJAAgAyACNgLMKyADQQw2AsgrAkACQAJAAkACQAJAIAJBDEYEQCADQdArahAhIANBgCtqIAMpA/AtIgpCAEKJ9auctYu/lnNCABDJAyADQfAqaiADKQOAKyIMQgBCAEKJx5mkrvCB6Yd/EMkDIANB4CpqIAMpA/gqIgtCAELH+vPD7YKjkDxCABDJAyADQdAqaiALQgBCjZXHw5bS2sCXf0IAEMkDIANB8ClqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0GQKWogC0IAQqnAxomuzpOyMEIAEMkDIANBkCtqIApCAEL7g5SinaLG87V/QgAQyQMgA0HAKmogAykD0CoiECADKQOIK3wiDyADKQPoKiAMIAMpA+AqIgt8IAtUrXx8IgwgAykDkCt8Ig1CAEIAQonHmaSu8IHph38QyQMgA0GwKmogAykDyCoiC0IAQsf688PtgqOQPEIAEMkDIANBoCpqIAtCAEKNlcfDltLawJd/QgAQyQMgA0GQKmogC0IAQt2whYzotpGouH9CABDJAyADQYAqaiALQgBCqcDGia7Ok7IwQgAQyQMgA0GgK2ogCkIAQvb/hdLw38fVxwBCABDJAyADQeApaiADKQOgKiIUIAMpA5grIAwgDVatfCIOIAwgD1StIAMpA9gqIA8gEFStfHwiECADKQPwKXwiEnwiEXwiDyADKQO4KiADKQOwKiILIA18IAtUrXx8IgwgAykDoCt8Ig1CAEIAQonHmaSu8IHph38QyQMgA0HQKWogAykD6CkiC0IAQsf688PtgqOQPEIAEMkDIANBwClqIAtCAEKNlcfDltLawJd/QgAQyQMgA0GwKWogC0IAQt2whYzotpGouH9CABDJAyADQaApaiALQgBCqcDGia7Ok7IwQgAQyQMgA0GwK2ogCkIAQp/q4NWc7qfsBkIAEMkDIANBgClqIAMpA8ApIhcgDiARVq0iDiADKQP4KSAQIBJWrXwiEiADKQOQKXwiEXwiCyADKQOQKnwiECAMIA9UrSADKQOoKiAPIBRUrXx8fCIPIAMpA6grIAwgDVatfHwiE3wiDCADKQPYKSADKQPQKSIKIA18IApUrXx8Ig0gAykDsCt8IhRCAEIAQonHmaSu8IHph38QyQMgA0HwKGogAykDiCkiCkIAQsf688PtgqOQPEIAEMkDIANB4ChqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQKGogCkIAQt2whYzotpGouH9CABDJAyADQcAoaiAKQgBCqcDGia7Ok7IwQgAQyQMCQCADKQPIKCADKQOoKSADKQOIKiADKQOAKiIWIAMpA5gpIBEgElStfHwiCiAWVK18IAogCiALIA5UrXwiDlatfCAOIA4gDyAQVK0gAykDmCogCyAQVq18fHwiClatfCIQIAMpA6ApfCILIBBUrXwgCyALIAogCiAPIBNWrXwiD1atfCIKVq18IAogCiADKQO4KSAPIA8gAykDsCl8IgtWrXwgCyALIAwgDVatIAMpA8gpIAwgF1StfHx8Ig9WrXx8IgtWrXwiDCADKQPAKHwiCiAMVK18IAogCyALIA8gAykDuCsgDSAUVq18fCINIA9UrXwiC1atfCIPIApUrXwgDyADKQPYKCALIAsgAykD0Ch8IgxWrXwgDCAMIAMpA+goIA0gAykD4CgiC3wiCiALVK18IAogAykD+CggAykD8CgiCyAUfCALVK18fCITIApUrXx8IgpWrXx8IhkgD1StfCIaQqnAxomuzpOyMFQEQCAKIRQMAQsCQCAZQt2whYzotpGouH9WDQAgGULdsIWM6LaRqLh/UgRAIAohFEKpwMaJrs6TsjAhGgwCCyAKQo2Vx8OW0trAl39WDQACQCAKQo2Vx8OW0trAl39SBEAgCiEUDAELQo2Vx8OW0trAl38hFCATQsf688PtgqOQPFoNAQtC3bCFjOi2kai4fyEZQqnAxomuzpOyMCEaDAELIApC8+q4vOmtpb/oAHwiCyATQsf688PtgqOQPFStIg99IRQgGUKjz/rzl8nu18cAfCIMIApCjZXHw5bS2sCXf1QgCyAPVHKtIgp9IRkgGiAKIAxWrX1CqcDGia7Ok7IwfSEaIBNCx/rzw+2Co5A8fSETCyADKAL8LyIFBEAgAygCgDAgBUECdBDfBAsCQCADKAK0LSIFRQ0AIAUgBUEMbEETakF4cSIEakEJaiIFRQ0AIAMoArAtIARrIAUQ3wQLIAMoAuAtIgVBgICAgHhGIAVFckUEQCADKALkLSAFQQJ0EN8ECwJAAkACQAJAIAMoAsgrQQJrDgsBAAAAAgAAAAAAAwALIANBADYC4CsgA0EBNgLUKyADQYiJwAA2AtArIANCBDcC2CsgA0HQK2pBwIrAABCoBAALIAJB////P0sgAkEFdCIHQfj///8HS3INAyAHRQRAQQghBEEAIQIMCQtB0c7FAC0AABpBCCEGIAdBCBDWBCIERQ0DIAJFBEBBACECDAkLQQAhBiACIQUDQCAGIAdGDQkgBCAGaiIIIAEgBmoiCSkDADcDACAIQRhqIAlBGGopAwA3AwAgCEEQaiAJQRBqKQMANwMAIAhBCGogCUEIaikDADcDACAGQSBqIQYgBUEBayIFDQALDAgLQdHOxQAtAAAaQcABQQgQ1gQiBEUNBiADKALMKyICRQ0DAkACQCACQQNLBEAgA0GwDWogASkDeCIKQgAgE0IAEMkDIANBoAxqIApCACAUQgAQyQMgA0GQC2ogCkIAIBlCABDJAyADQYAKaiAKQgAgGkIAEMkDIANBoA1qIAMpA7ANIg9CAEIAQonHmaSu8IHph38QyQMgA0GQDWogAykDqA0iCkIAQsf688PtgqOQPEIAEMkDIANBgA1qIApCAEKNlcfDltLawJd/QgAQyQMgA0HwDGogCkIAQt2whYzotpGouH9CABDJAyADQeAMaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HQDGogASkDcCIKQgAgE0IAEMkDIANBwAtqIApCACAUQgAQyQMgA0GwCmogCkIAIBlCABDJAyADQaAJaiAKQgAgGkIAEMkDIANBkAxqIAMpA4ANIhIgAykDuA0iECADKQOgDHwiDnwiCyADKQOYDSAPIAMpA5ANIgp8IApUrXx8Ig8gAykD0Ax8IgxCAEIAQonHmaSu8IHph38QyQMgA0GADGogAykDmAwiCkIAQsf688PtgqOQPEIAEMkDIANB8AtqIApCAEKNlcfDltLawJd/QgAQyQMgA0HgC2ogCkIAQt2whYzotpGouH9CABDJAyADQdALaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HADGogASkDaCIKQgAgE0IAEMkDIANBsAtqIApCACAUQgAQyQMgA0GgCmogCkIAIBlCABDJAyADQZAJaiAKQgAgGkIAEMkDIANBgAtqIAMpA9gMIAwgD1StfCIYIAMpA8ALfCINIAMpA6gMIA4gEFStfCIXIAMpA5ALfCIQIAMpA/AMfCIOIAsgD1atIAMpA4gNIAsgElStfHx8IhV8IgsgAykD8At8Ig8gAykDiAwgAykDgAwiCiAMfCAKVK18fCIMIAMpA8AMfCISQgBCAEKJx5mkrvCB6Yd/EMkDIANB8ApqIAMpA4gLIgpCAELH+vPD7YKjkDxCABDJAyADQeAKaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0ApqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HACmogCkIAQqnAxomuzpOyMEIAEMkDIANBsAxqIAEpA2AiCkIAIBNCABDJAyADQaALaiAKQgAgFEIAEMkDIANBkApqIApCACAZQgAQyQMgA0GACWogCkIAIBpCABDJAyADQfAJaiADKQPIDCAMIBJWrXwiICADKQOwC3wiESADKQOYCyAQIBdUrXwiHiADKQOACnwiFyADKQPgDHwiFiAOIBVWrSADKQP4DCAOIBBUrXx8fCIQIAMpA7AKfCIOIAsgDVStIAMpA8gLIA0gGFStfHx8Ig0gAykD4At8IhggDCAPVK0gAykD+AsgCyAPVq18fHwiFXwiCyADKQPgCnwiDyADKQP4CiADKQPwCiIKIBJ8IApUrXx8IgwgAykDsAx8IhJCAEIAQonHmaSu8IHph38QyQMgA0HgCWogAykD+AkiCkIAQsf688PtgqOQPEIAEMkDIANB0AlqIApCAEKNlcfDltLawJd/QgAQyQMgA0HACWogCkIAQt2whYzotpGouH9CABDJAyADQbAJaiAKQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA7gJIAMpA8gKIAMpA9gLIBAgFlStIAMpA+gMIBYgF1StfHwgAykDiAogFyAeVK18fCIXIAMpA6AJfCIKIA0gDlStIAMpA7gKIA4gEFStfHx8IhAgAykD0At8Ig4gEFStfCAOIBUgGFStIAMpA+gLIA0gGFatfHx8Ig0gDlStfCAKIBBWrSADKQOoCSAKIBdUrXx8fCIXIAMpA5AJfCIKIAMpA6gKIA0gDSADKQOgCnwiEFatfCAQIBAgCyARVK0gAykDuAsgESAgVK18fHwiDVatfHwiECADKQPACnwiDiAQVK18IA4gAykD2AogDSANIAMpA9AKfCIRVq18IBEgESAMIA9UrSADKQPoCiALIA9WrXx8fCINVq18fCILIA5UrXwgCiAQVq0gAykDmAkgCiAXVK18fHwiESADKQOACXwiDyADKQOYCiALIAMpA5AKfCIKIAtUrXwgCiAKIAMpA6gLIAMpA7gMIAwgElatfCIMIAMpA6ALfCILIAxUrXwgCyALIA18IgxWrXx8IgtWrXx8Ig0gAykDsAl8IhAgDVStfCAQIAMpA8gJIAsgCyADKQPACXwiDlatfCAOIA4gAykD2AkgDCAMIAMpA9AJfCIKVq18IAogAykD6AkgAykD4AkiCyASfCALVK18fCIcIApUrXx8IgpWrXx8IgsgEFStfCANIA9UrSADKQOICSAPIBFUrXx8fCIbQqnAxomuzpOyMFYNAAJAIBtCqcDGia7Ok7IwUQRAIAtC3bCFjOi2kai4f1YNAiALQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRsLIAshECAKIQ8MAgsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hECAKQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRsgCiEPDAILQo2Vx8OW0trAl38hDyAcQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhGwwBCyAKQvPquLzpraW/6AB8IgwgHELH+vPD7YKjkDxUrSINfSEPIAtCo8/685fJ7tfHAHwiDiAKQo2Vx8OW0trAl39UIAwgDVRyrSIKfSEQIBsgC0LdsIWM6LaRqLh/VCAKIA5Wcq19QqnAxomuzpOyMH0hGyAcQsf688PtgqOQPH0hHAtCqcDGia7Ok7IwIQogASkDCCIMIBB8IgsgDFQgCyAPIAEpAxAiD3wiDCAPVCAMIAwgASkDGCIPIBx8IhAgD1StfCIPVnKtfCIMIAtUcq0gASkDACAbfHwiHCELAkAgHEKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEKIAwiC0LdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hCiAPIgtCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhCiAQIgtCx/rzw+2Co5A8UQ0CCyAKIAtYDQEgDCENIA8hEQwCC0EDIAJBwInAABDZAwALIA9C8+q4vOmtpb/oAHwiCiAQQsf688PtgqOQPFStIgt9IREgDEKjz/rzl8nu18cAfCIOIA9CjZXHw5bS2sCXf1QgCiALVHKtIgp9IQ0gHCAMQt2whYzotpGouH9UIAogDlZyrX1CqcDGia7Ok7IwfSEcIBBCx/rzw+2Co5A8fSEQCwJAAkAgAkEERwRAIANBgAhqIAEpA5gBIgpCACATQgAQyQMgA0GQCGogCkIAIBRCABDJAyADQaAIaiAKQgAgGUIAEMkDIANBsAhqIApCACAaQgAQyQMgA0HwB2ogAykDgAgiD0IAQgBCiceZpK7wgemHfxDJAyADQeAHaiADKQP4ByIKQgBCx/rzw+2Co5A8QgAQyQMgA0HQB2ogCkIAQo2Vx8OW0trAl39CABDJAyADQcAHaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBsAdqIApCAEKpwMaJrs6TsjBCABDJAyADQfAGaiABKQOQASIKQgAgE0IAEMkDIANBgAdqIApCACAUQgAQyQMgA0GQB2ogCkIAIBlCABDJAyADQaAHaiAKQgAgGkIAEMkDIANB4AZqIAMpA9AHIhYgAykDiAgiEiADKQOQCHwiF3wiCyADKQPoByAPIAMpA+AHIgp8IApUrXx8Ig8gAykD8AZ8IgxCAEIAQonHmaSu8IHph38QyQMgA0HQBmogAykD6AYiCkIAQsf688PtgqOQPEIAEMkDIANBwAZqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwBmogCkIAQt2whYzotpGouH9CABDJAyADQaAGaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HgBWogASkDiAEiCkIAIBNCABDJAyADQfAFaiAKQgAgFEIAEMkDIANBgAZqIApCACAZQgAQyQMgA0GQBmogCkIAIBpCABDJAyADQdAFaiADKQP4BiAMIA9UrXwiHiADKQOAB3wiDiADKQOYCCASIBdWrXwiFSADKQOgCHwiEiADKQPAB3wiFyALIA9WrSADKQPYByALIBZUrXx8fCIifCILIAMpA8AGfCIPIAMpA9gGIAMpA9AGIgogDHwgClStfHwiDCADKQPgBXwiFkIAQgBCiceZpK7wgemHfxDJAyADQcAFaiADKQPYBSIKQgBCx/rzw+2Co5A8QgAQyQMgA0GwBWogCkIAQo2Vx8OW0trAl39CABDJAyADQdAEaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwARqIApCAEKpwMaJrs6TsjBCABDJAyADQcAIaiABKQOAASIKQgAgE0IAEMkDIANB0AhqIApCACAUQgAQyQMgA0HgCGogCkIAIBlCABDJAyADQfAIaiAKQgAgGkIAEMkDIANBoAVqIAMpA+gFIAwgFlatfCInIAMpA/AFfCIYIAMpA6gIIBIgFVStfCIkIAMpA7AIfCIVIAMpA7AHfCIgIBcgIlatIAMpA8gHIBIgF1atfHx8IhIgAykDkAd8IhcgCyAOVK0gAykDiAcgDiAeVK18fHwiDiADKQOwBnwiHiAMIA9UrSADKQPIBiALIA9WrXx8fCIifCILIAMpA7AFfCIPIAMpA8gFIAMpA8AFIgogFnwgClStfHwiDCADKQPACHwiFkIAQgBCiceZpK7wgemHfxDJAyADQZAFaiADKQOoBSIKQgBCx/rzw+2Co5A8QgAQyQMgA0GABWogCkIAQo2Vx8OW0trAl39CABDJAyADQfAEaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4ARqIApCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD6AQgAykDyAQgAykDqAYgEiAgVK0gAykDuAcgFSAgVq18fCADKQO4CCAVICRUrXx8IhUgAykDoAd8IgogDiAXVK0gAykDmAcgEiAXVq18fHwiEiADKQOgBnwiFyASVK18IBcgHiAiVq0gAykDuAYgDiAeVq18fHwiDiAXVK18IAogElatIAMpA6gHIAogFVStfHx8IhUgAykDkAZ8IgogAykDiAYgDiAOIAMpA4AGfCISVq18IBIgEiALIBhUrSADKQP4BSAYICdUrXx8fCIOVq18fCISIAMpA8AEfCIXIBJUrXwgFyADKQPYBCAOIA4gAykD0AR8IhhWrXwgGCAYIAwgD1StIAMpA7gFIAsgD1atfHx8Ig5WrXx8IgsgF1StfCAKIBJWrSADKQOYBiAKIBVUrXx8fCIXIAMpA/AIfCIKIAMpA+gIIAsgCyADKQPgCHwiD1atfCAPIA8gAykD2AggAykDyAggDCAWVq18IgwgAykD0Ah8IgsgDFStfCALIAsgDnwiDFatfHwiC1atfHwiDiADKQPgBHwiDyAOVK18IA8gDyADKQP4BCALIAsgAykD8AR8IhJWrXwgEiASIAMpA4gFIAwgDCADKQOABXwiC1atfCALIAMpA5gFIAMpA5AFIgwgFnwgDFStfHwiGyALVK18fCILVq18fCIPVq18IAogDlatIAMpA/gIIAogF1StfHx8IhJCqcDGia7Ok7IwVg0AAkAgEkKpwMaJrs6TsjBRBEAgD0LdsIWM6LaRqLh/Vg0CIA9C3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhEgsgDyEKIAshDgwCCyALQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEKIAtCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhEiALIQ4MAgtCjZXHw5bS2sCXfyEOIBtCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCESDAELIAtC8+q4vOmtpb/oAHwiCiAbQsf688PtgqOQPFStIgx9IQ4gD0Kjz/rzl8nu18cAfCIXIAtCjZXHw5bS2sCXf1QgCiAMVHKtIgt9IQogEiAPQt2whYzotpGouH9UIAsgF1ZyrX1CqcDGia7Ok7IwfSESIBtCx/rzw+2Co5A8fSEbC0KpwMaJrs6TsjAhFyAKIAEpAygiC3wiDyALVCAPIAEpAzAiCiAOfCIMIApUIAwgDCABKQM4IgogG3wiCyAKVK18IgpWcq18Ig4gD1RyrSABKQMgIBJ8fCIbIQ8CQCAbQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRcgDiIPQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEXIAoiD0KNlcfDltLawJd/Ug0AQsf688PtgqOQPCEXIAshDyALQsf688PtgqOQPFENAgsgDyAXWg0BIA4hDCAKIRgMAgtBBEEEQdCJwAAQ2QMACyAKQvPquLzpraW/6AB8Ig8gC0LH+vPD7YKjkDxUrSIMfSEYIA5Co8/685fJ7tfHAHwiEiAKQo2Vx8OW0trAl39UIAwgD1ZyrSIKfSEMIBsgDkLdsIWM6LaRqLh/VCAKIBJWcq19QqnAxomuzpOyMH0hGyALQsf688PtgqOQPH0hCwsgAkEGTwRAIANBwANqIAEpA7gBIgpCACATQgAQyQMgA0HQA2ogCkIAIBRCABDJAyADQeADaiAKQgAgGUIAEMkDIANB8ANqIApCACAaQgAQyQMgA0GwA2ogAykDwAMiDkIAQgBCiceZpK7wgemHfxDJAyADQaADaiADKQO4AyIKQgBCx/rzw+2Co5A8QgAQyQMgA0GQA2ogCkIAQo2Vx8OW0trAl39CABDJAyADQYADaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB8AJqIApCAEKpwMaJrs6TsjBCABDJAyADQbACaiABKQOwASIKQgAgE0IAEMkDIANBwAJqIApCACAUQgAQyQMgA0HQAmogCkIAIBlCABDJAyADQeACaiAKQgAgGkIAEMkDIANBoAJqIAMpA5ADIiAgAykDyAMiFiADKQPQA3wiFXwiDyADKQOoAyAOIAMpA6ADIgp8IApUrXx8Ig4gAykDsAJ8IhJCAEIAQonHmaSu8IHph38QyQMgA0GQAmogAykDqAIiCkIAQsf688PtgqOQPEIAEMkDIANBgAJqIApCAEKNlcfDltLawJd/QgAQyQMgA0HwAWogCkIAQt2whYzotpGouH9CABDJAyADQeABaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GgAWogASkDqAEiCkIAIBNCABDJAyADQbABaiAKQgAgFEIAEMkDIANBwAFqIApCACAZQgAQyQMgA0HQAWogCkIAIBpCABDJAyADQZABaiADKQO4AiAOIBJWrXwiIiADKQPAAnwiFyADKQPYAyAVIBZUrXwiHiADKQPgA3wiFiADKQOAA3wiFSAOIA9UrSADKQOYAyAPICBUrXx8fCInfCIPIAMpA4ACfCIOIAMpA5gCIAMpA5ACIgogEnwgClStfHwiEiADKQOgAXwiIEIAQgBCiceZpK7wgemHfxDJAyADQYABaiADKQOYASIKQgBCx/rzw+2Co5A8QgAQyQMgA0HwAGogCkIAQo2Vx8OW0trAl39CABDJAyADQRBqIApCAELdsIWM6LaRqLh/QgAQyQMgAyAKQgBCqcDGia7Ok7IwQgAQyQMgA0GABGogASkDoAEiCkIAIBNCABDJAyADQZAEaiAKQgAgFEIAEMkDIANBoARqIApCACAZQgAQyQMgA0GwBGogCkIAIBpCABDJAyADQeAAaiADKQOoASASICBWrXwiJCADKQOwAXwiFCADKQPoAyAWIB5UrXwiKCADKQPwA3wiEyADKQPwAnwiHiAVICdWrSADKQOIAyAVIBZUrXx8fCIWIAMpA9ACfCIVIA8gF1StIAMpA8gCIBcgIlStfHx8IhcgAykD8AF8IiIgDiASVq0gAykDiAIgDiAPVK18fHwiJ3wiDyADKQNwfCIOIAMpA4gBIAMpA4ABIgogIHwgClStfHwiEiADKQOABHwiIEIAQgBCiceZpK7wgemHfxDJAyADQdAAaiADKQNoIgpCAELH+vPD7YKjkDxCABDJAyADQUBrIApCAEKNlcfDltLawJd/QgAQyQMgA0EwaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBIGogCkIAQqnAxomuzpOyMEIAEMkDAkACQCADKQMoIAMpAwggAykD6AEgFiAeVK0gAykD+AIgEyAeVq18fCADKQP4AyATIChUrXx8Ih4gAykD4AJ8IgogFSAXVq0gAykD2AIgFSAWVK18fHwiEyADKQPgAXwiFiATVK18IBYgIiAnVq0gAykD+AEgFyAiVq18fHwiFyAWVK18IAogE1atIAMpA+gCIAogHlStfHx8IhUgAykD0AF8IgogAykDyAEgFyAXIAMpA8ABfCITVq18IBMgDyAUVK0gAykDuAEgFCAkVK18fHwiFCATVK18fCIXIAMpAwB8IhMgF1StfCATIAMpAxggFCAUIAMpAxB8IhZWrXwgFiAOIBJWrSADKQN4IA4gD1StfHx8Ig4gFlStfHwiDyATVK18IAogF1atIAMpA9gBIAogFVStfHx8IhYgAykDsAR8IhQgAykDqAQgDyADKQOgBHwiCiAPVK18IAogCiADKQOYBCADKQOIBCASICBWrXwiEiADKQOQBHwiDyASVK18IA8gDiAPfCIOVq18fCIPVq18fCISIAMpAyB8IhcgElStfCAXIBcgAykDOCAPIA8gAykDMHwiE1atfCATIBMgAykDSCAOIA4gAykDQHwiClatfCAKIAMpA1ggAykDUCIPICB8IA9UrXx8IhkgClStfHwiClatfHwiDlatfCASIBRUrSADKQO4BCAUIBZUrXx8fCITQqnAxomuzpOyMFYNAAJAIBNCqcDGia7Ok7IwUQRAIA5C3bCFjOi2kai4f1YNAiAOQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRMLIA4hFCAKIQ8MAgsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hFCAKQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRMgCiEPDAILQo2Vx8OW0trAl38hDyAZQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhEwwBCyAKQvPquLzpraW/6AB8IhQgGULH+vPD7YKjkDxUrSISfSEPIA5Co8/685fJ7tfHAHwiFyAKQo2Vx8OW0trAl39UIBIgFFZyrSIKfSEUIBMgDkLdsIWM6LaRqLh/VCAKIBdWcq19QqnAxomuzpOyMH0hEyAZQsf688PtgqOQPH0hGQsgAUHgAGohAiABQYABaiEFIAFBoAFqIQZCqcDGia7Ok7IwIQogASkDQCATfCAUIAEpA0giFHwiDiAUVCAOIA4gDyABKQNQIg98IhQgD1QgFCAUIAEpA1giDyAZfCITIA9UrXwiD1ZyrXwiFFZyrXwiGSESAkACQAJAIBlCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hCiAUIhJC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQogDyISQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQogEyISQsf688PtgqOQPFENAQsgCiASWA0AIBQhEiAPIQoMAQsgD0Lz6ri86a2lv+gAfCIOIBNCx/rzw+2Co5A8VK0iEn0hCiAUQqPP+vOXye7XxwB8IhcgD0KNlcfDltLawJd/VCAOIBJUcq0iD30hEiAZIBRC3bCFjOi2kai4f1QgDyAXVnKtfUKpwMaJrs6TsjB9IRkgE0LH+vPD7YKjkDx9IRMLIAQgEzcDmAEgBCAKNwOQASAEIBI3A4gBIAQgGTcDgAEgBCAQNwMYIAQgETcDECAEIA03AwggBCAcNwMAIAQgBikDADcDoAEgBCACKQMANwMgIARBqAFqIAZBCGopAwA3AwAgBEGwAWogBkEQaikDADcDACAEQbgBaiAGQRhqKQMANwMAIARBKGogAkEIaikDADcDACAEQTBqIAJBEGopAwA3AwAgBEE4aiACQRhqKQMANwMAIAQgCzcDWCAEIBg3A1AgBCAMNwNIIAQgGzcDQCAEIAUpAwA3A2AgBEHoAGogBUEIaikDADcDACAEQfAAaiAFQRBqKQMANwMAIARB+ABqIAVBGGopAwA3AwBBBiECDAgLQQUgAkHgicAAENkDAAtB0c7FAC0AABpBgANBCBDWBCIERQ0EIAMoAswrIgJFDQMCQAJAIAJBBksEQCADQbAoaiABKQPYASIKQgAgE0IAEMkDIANBoCdqIApCACAUQgAQyQMgA0GQJmogCkIAIBlCABDJAyADQYAlaiAKQgAgGkIAEMkDIANBoChqIAMpA7AoIg9CAEIAQonHmaSu8IHph38QyQMgA0GQKGogAykDqCgiCkIAQsf688PtgqOQPEIAEMkDIANBgChqIApCAEKNlcfDltLawJd/QgAQyQMgA0HwJ2ogCkIAQt2whYzotpGouH9CABDJAyADQeAnaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HQJ2ogASkD0AEiCkIAIBNCABDJAyADQcAmaiAKQgAgFEIAEMkDIANBsCVqIApCACAZQgAQyQMgA0GgJGogCkIAIBpCABDJAyADQZAnaiADKQOAKCISIAMpA7goIhAgAykDoCd8Ig58IgsgAykDmCggDyADKQOQKCIKfCAKVK18fCIPIAMpA9AnfCIMQgBCAEKJx5mkrvCB6Yd/EMkDIANBgCdqIAMpA5gnIgpCAELH+vPD7YKjkDxCABDJAyADQfAmaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB4CZqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HQJmogCkIAQqnAxomuzpOyMEIAEMkDIANBwCdqIAEpA8gBIgpCACATQgAQyQMgA0GwJmogCkIAIBRCABDJAyADQaAlaiAKQgAgGUIAEMkDIANBkCRqIApCACAaQgAQyQMgA0GAJmogAykD2CcgDCAPVK18IhggAykDwCZ8Ig0gAykDqCcgDiAQVK18IhcgAykDkCZ8IhAgAykD8Cd8Ig4gCyAPVq0gAykDiCggCyASVK18fHwiFXwiCyADKQPwJnwiDyADKQOIJyADKQOAJyIKIAx8IApUrXx8IgwgAykDwCd8IhJCAEIAQonHmaSu8IHph38QyQMgA0HwJWogAykDiCYiCkIAQsf688PtgqOQPEIAEMkDIANB4CVqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQJWogCkIAQt2whYzotpGouH9CABDJAyADQcAlaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GwJ2ogASkDwAEiCkIAIBNCABDJAyADQaAmaiAKQgAgFEIAEMkDIANBkCVqIApCACAZQgAQyQMgA0GAJGogCkIAIBpCABDJAyADQfAkaiADKQPIJyAMIBJWrXwiICADKQOwJnwiESADKQOYJiAQIBdUrXwiHiADKQOAJXwiFyADKQPgJ3wiFiAOIBVWrSADKQP4JyAOIBBUrXx8fCIQIAMpA7AlfCIOIAsgDVStIAMpA8gmIA0gGFStfHx8Ig0gAykD4CZ8IhggDCAPVK0gAykD+CYgCyAPVq18fHwiFXwiCyADKQPgJXwiDyADKQP4JSADKQPwJSIKIBJ8IApUrXx8IgwgAykDsCd8IhJCAEIAQonHmaSu8IHph38QyQMgA0HgJGogAykD+CQiCkIAQsf688PtgqOQPEIAEMkDIANB0CRqIApCAEKNlcfDltLawJd/QgAQyQMgA0HAJGogCkIAQt2whYzotpGouH9CABDJAyADQbAkaiAKQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA7gkIAMpA8glIAMpA9gmIBAgFlStIAMpA+gnIBYgF1StfHwgAykDiCUgFyAeVK18fCIXIAMpA6AkfCIKIA0gDlStIAMpA7glIA4gEFStfHx8IhAgAykD0CZ8Ig4gEFStfCAOIBUgGFStIAMpA+gmIA0gGFatfHx8Ig0gDlStfCAKIBBWrSADKQOoJCAKIBdUrXx8fCIXIAMpA5AkfCIKIAMpA6glIA0gDSADKQOgJXwiEFatfCAQIBAgCyARVK0gAykDuCYgESAgVK18fHwiDVatfHwiECADKQPAJXwiDiAQVK18IA4gAykD2CUgDSANIAMpA9AlfCIRVq18IBEgESAMIA9UrSADKQPoJSALIA9WrXx8fCINVq18fCILIA5UrXwgCiAQVq0gAykDmCQgCiAXVK18fHwiDiADKQOAJHwiCiADKQOYJSALIAsgAykDkCV8Ig9WrXwgDyAPIAMpA6gmIAMpA7gnIAwgElatfCIMIAMpA6AmfCILIAxUrXwgCyALIA18IgxWrXx8IgtWrXx8Ig0gAykDsCR8Ig8gDVStfCAPIA8gAykDyCQgCyALIAMpA8AkfCIQVq18IBAgECADKQPYJCAMIAwgAykD0CR8IgtWrXwgCyADKQPoJCADKQPgJCIMIBJ8IAxUrXx8IhwgC1StfHwiC1atfHwiD1atfCAKIA1WrSADKQOIJCAKIA5UrXx8fCIbQqnAxomuzpOyMFYNAAJAIBtCqcDGia7Ok7IwUQRAIA9C3bCFjOi2kai4f1YNAiAPQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRsLIA8hECALIQoMAgsgC0KNlcfDltLawJd/Vg0AQt2whYzotpGouH8hECALQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRsgCyEKDAILQo2Vx8OW0trAl38hCiAcQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhGwwBCyALQvPquLzpraW/6AB8IgwgHELH+vPD7YKjkDxUrSINfSEKIA9Co8/685fJ7tfHAHwiDiALQo2Vx8OW0trAl39UIAwgDVRyrSILfSEQIBsgD0LdsIWM6LaRqLh/VCALIA5Wcq19QqnAxomuzpOyMH0hGyAcQsf688PtgqOQPH0hHAtCqcDGia7Ok7IwIQsgASkDCCIPIBB8Ig0gD1QgDSANIAogASkDECIKfCIMIApUIAwgDCABKQMYIgogHHwiDyAKVK18IgpWcq18IgxWcq0gASkDACAbfHwiHCEQAkAgHEKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyELIAwiEELdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hCyAKIhBCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhCyAPIhBCx/rzw+2Co5A8UQ0CCyALIBBYDQEgDCEgIAohHgwCC0EGIAJBgIrAABDZAwALIApC8+q4vOmtpb/oAHwiCyAPQsf688PtgqOQPFStIg19IR4gDEKjz/rzl8nu18cAfCIQIApCjZXHw5bS2sCXf1QgCyANVHKtIgp9ISAgHCAMQt2whYzotpGouH9UIAogEFZyrX1CqcDGia7Ok7IwfSEcIA9Cx/rzw+2Co5A8fSEPCwJAAkAgAkEJTwRAIANBgCNqIAEpA5gCIgpCACATQgAQyQMgA0GQI2ogCkIAIBRCABDJAyADQaAjaiAKQgAgGUIAEMkDIANBsCNqIApCACAaQgAQyQMgA0HwImogAykDgCMiDEIAQgBCiceZpK7wgemHfxDJAyADQeAiaiADKQP4IiIKQgBCx/rzw+2Co5A8QgAQyQMgA0HQImogCkIAQo2Vx8OW0trAl39CABDJAyADQcAiaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBsCJqIApCAEKpwMaJrs6TsjBCABDJAyADQfAhaiABKQOQAiIKQgAgE0IAEMkDIANBgCJqIApCACAUQgAQyQMgA0GQImogCkIAIBlCABDJAyADQaAiaiAKQgAgGkIAEMkDIANB4CFqIAMpA9AiIhEgAykDiCMiDiADKQOQI3wiEnwiCyADKQPoIiAMIAMpA+AiIgp8IApUrXx8IgwgAykD8CF8Ig1CAEIAQonHmaSu8IHph38QyQMgA0HQIWogAykD6CEiCkIAQsf688PtgqOQPEIAEMkDIANBwCFqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwIWogCkIAQt2whYzotpGouH9CABDJAyADQaAhaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HgIGogASkDiAIiCkIAIBNCABDJAyADQfAgaiAKQgAgFEIAEMkDIANBgCFqIApCACAZQgAQyQMgA0GQIWogCkIAIBpCABDJAyADQdAgaiADKQP4ISAMIA1WrXwiFSADKQOAInwiECADKQOYIyAOIBJWrXwiFiADKQOgI3wiDiADKQPAInwiEiALIAxWrSADKQPYIiALIBFUrXx8fCIifCILIAMpA8AhfCIMIAMpA9ghIAMpA9AhIgogDXwgClStfHwiDSADKQPgIHwiEUIAQgBCiceZpK7wgemHfxDJAyADQcAgaiADKQPYICIKQgBCx/rzw+2Co5A8QgAQyQMgA0GwIGogCkIAQo2Vx8OW0trAl39CABDJAyADQdAfaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwB9qIApCAEKpwMaJrs6TsjBCABDJAyADQcAjaiABKQOAAiIKQgAgE0IAEMkDIANB0CNqIApCACAUQgAQyQMgA0HgI2ogCkIAIBlCABDJAyADQfAjaiAKQgAgGkIAEMkDIANBoCBqIAMpA+ggIA0gEVatfCInIAMpA/AgfCIXIAMpA6gjIA4gFlStfCIkIAMpA7AjfCIWIAMpA7AifCIYIBIgIlatIAMpA8giIA4gElatfHx8Ig4gAykDkCJ8IhIgCyAQVK0gAykDiCIgECAVVK18fHwiECADKQOwIXwiFSAMIA1WrSADKQPIISALIAxWrXx8fCIifCILIAMpA7AgfCIMIAMpA8ggIAMpA8AgIgogEXwgClStfHwiDSADKQPAI3wiEUIAQgBCiceZpK7wgemHfxDJAyADQZAgaiADKQOoICIKQgBCx/rzw+2Co5A8QgAQyQMgA0GAIGogCkIAQo2Vx8OW0trAl39CABDJAyADQfAfaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4B9qIApCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD6B8gAykDyB8gAykDqCEgDiAYVK0gAykDuCIgFiAYVq18fCADKQO4IyAWICRUrXx8IhYgAykDoCJ8IgogECASVK0gAykDmCIgDiASVq18fHwiDiADKQOgIXwiEiAOVK18IBIgFSAiVq0gAykDuCEgECAVVq18fHwiECASVK18IAogDlatIAMpA6giIAogFlStfHx8IhYgAykDkCF8IgogAykDiCEgECAQIAMpA4AhfCIOVq18IA4gDiALIBdUrSADKQP4ICAXICdUrXx8fCIQVq18fCIOIAMpA8AffCISIA5UrXwgEiADKQPYHyAQIBAgAykD0B98IhdWrXwgFyAMIA1WrSADKQO4ICALIAxWrXx8fCIMIBdUrXx8IgsgElStfCAKIA5WrSADKQOYISAKIBZUrXx8fCIXIAMpA/AjfCIQIAMpA+gjIAsgAykD4CN8IgogC1StfCAKIAogAykD2CMgAykDyCMgDSARVq18Ig0gAykD0CN8IgsgDVStfCALIAsgDHwiDFatfHwiC1atfHwiDSADKQPgH3wiDiANVK18IA4gDiADKQP4HyALIAsgAykD8B98IhJWrXwgEiASIAMpA4ggIAwgDCADKQOAIHwiClatfCAKIAMpA5ggIAMpA5AgIgsgEXwgC1StfHwiGyAKVK18fCIKVq18fCIMVq18IA0gEFStIAMpA/gjIBAgF1StfHx8IhJCqcDGia7Ok7IwVg0AAkAgEkKpwMaJrs6TsjBRBEAgDELdsIWM6LaRqLh/Vg0CIAxC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhEgsgDCELIAohFwwCCyAKQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyELIApCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhEiAKIRcMAgtCjZXHw5bS2sCXfyEXIBtCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCESDAELIApC8+q4vOmtpb/oAHwiCyAbQsf688PtgqOQPFStIg19IRcgDEKjz/rzl8nu18cAfCIQIApCjZXHw5bS2sCXf1QgCyANVHKtIgp9IQsgEiAMQt2whYzotpGouH9UIAogEFZyrX1CqcDGia7Ok7IwfSESIBtCx/rzw+2Co5A8fSEbC0KpwMaJrs6TsjAhCiABKQNIIgwgC3wiCyAMVCALIAEpA1AiDCAXfCINIAxUIA0gDSABKQNYIgwgG3wiFyAMVK18IgxWcq18Ig0gC1RyrSABKQNAIBJ8fCIbIQsCQCAbQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IQogDSILQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEKIAwiC0KNlcfDltLawJd/Ug0AQsf688PtgqOQPCEKIBciC0LH+vPD7YKjkDxRDQILIAogC1gNASANISIgDCEnDAILQQggAkGQisAAENkDAAsgDELz6ri86a2lv+gAfCIKIBdCx/rzw+2Co5A8VK0iC30hJyANQqPP+vOXye7XxwB8IhAgDEKNlcfDltLawJd/VCAKIAtUcq0iCn0hIiAbIA1C3bCFjOi2kai4f1QgCiAQVnKtfUKpwMaJrs6TsjB9IRsgF0LH+vPD7YKjkDx9IRcLAkACQCACQQtPBEAgA0HAHmogASkD2AIiCkIAIBNCABDJAyADQdAeaiAKQgAgFEIAEMkDIANB4B5qIApCACAZQgAQyQMgA0HwHmogCkIAIBpCABDJAyADQbAeaiADKQPAHiIMQgBCAEKJx5mkrvCB6Yd/EMkDIANBoB5qIAMpA7geIgpCAELH+vPD7YKjkDxCABDJAyADQZAeaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBgB5qIApCAELdsIWM6LaRqLh/QgAQyQMgA0HwHWogCkIAQqnAxomuzpOyMEIAEMkDIANBsB1qIAEpA9ACIgpCACATQgAQyQMgA0HAHWogCkIAIBRCABDJAyADQdAdaiAKQgAgGUIAEMkDIANB4B1qIApCACAaQgAQyQMgA0GgHWogAykDkB4iESADKQPIHiIOIAMpA9AefCISfCILIAMpA6geIAwgAykDoB4iCnwgClStfHwiDCADKQOwHXwiDUIAQgBCiceZpK7wgemHfxDJAyADQZAdaiADKQOoHSIKQgBCx/rzw+2Co5A8QgAQyQMgA0GAHWogCkIAQo2Vx8OW0trAl39CABDJAyADQfAcaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4BxqIApCAEKpwMaJrs6TsjBCABDJAyADQaAcaiABKQPIAiIKQgAgE0IAEMkDIANBsBxqIApCACAUQgAQyQMgA0HAHGogCkIAIBlCABDJAyADQdAcaiAKQgAgGkIAEMkDIANBkBxqIAMpA7gdIAwgDVatfCIkIAMpA8AdfCIQIAMpA9geIA4gElatfCIYIAMpA+AefCIOIAMpA4AefCISIAsgDFatIAMpA5geIAsgEVStfHx8Iih8IgsgAykDgB18IgwgAykDmB0gAykDkB0iCiANfCAKVK18fCINIAMpA6AcfCIRQgBCAEKJx5mkrvCB6Yd/EMkDIANBgBxqIAMpA5gcIgpCAELH+vPD7YKjkDxCABDJAyADQfAbaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBkBtqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GAG2ogCkIAQqnAxomuzpOyMEIAEMkDIANBgB9qIAEpA8ACIgpCACATQgAQyQMgA0GQH2ogCkIAIBRCABDJAyADQaAfaiAKQgAgGUIAEMkDIANBsB9qIApCACAaQgAQyQMgA0HgG2ogAykDqBwgDSARVq18IiMgAykDsBx8IhYgAykD6B4gDiAYVK18IikgAykD8B58IhggAykD8B18IhUgEiAoVq0gAykDiB4gDiASVq18fHwiDiADKQPQHXwiEiALIBBUrSADKQPIHSAQICRUrXx8fCIQIAMpA/AcfCIkIAwgDVatIAMpA4gdIAsgDFatfHx8Iih8IgsgAykD8Bt8IgwgAykDiBwgAykDgBwiCiARfCAKVK18fCINIAMpA4AffCIRQgBCAEKJx5mkrvCB6Yd/EMkDIANB0BtqIAMpA+gbIgpCAELH+vPD7YKjkDxCABDJAyADQcAbaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsBtqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgG2ogCkIAQqnAxomuzpOyMEIAEMkDAkACQCADKQOoGyADKQOIGyADKQPoHCAOIBVUrSADKQP4HSAVIBhUrXx8IAMpA/geIBggKVStfHwiGCADKQPgHXwiCiAQIBJUrSADKQPYHSAOIBJWrXx8fCIOIAMpA+AcfCISIA5UrXwgEiAkIChWrSADKQP4HCAQICRWrXx8fCIQIBJUrXwgCiAOVq0gAykD6B0gCiAYVK18fHwiGCADKQPQHHwiCiADKQPIHCAQIBAgAykDwBx8Ig5WrXwgDiAOIAsgFlStIAMpA7gcIBYgI1StfHx8IhBWrXx8Ig4gAykDgBt8IhIgDlStfCASIAMpA5gbIBAgECADKQOQG3wiFlatfCAWIBYgDCANVq0gAykD+BsgCyAMVq18fHwiEFatfHwiCyASVK18IAogDlatIAMpA9gcIAogGFStfHx8IhYgAykDsB98IgogAykDqB8gCyALIAMpA6AffCIMVq18IAwgDCADKQOYHyADKQOIHyANIBFWrXwiDSADKQOQH3wiCyANVK18IAsgCyAQfCINVq18fCILVq18fCIQIAMpA6AbfCIMIBBUrXwgDCAMIAMpA7gbIAsgCyADKQOwG3wiDlatfCAOIA4gAykDyBsgDSANIAMpA8AbfCILVq18IAsgAykD2BsgAykD0BsiDSARfCANVK18fCISIAtUrXx8IgtWrXx8IgxWrXwgCiAQVq0gAykDuB8gCiAWVK18fHwiEEKpwMaJrs6TsjBWDQACQCAQQqnAxomuzpOyMFEEQCAMQt2whYzotpGouH9WDQIgDELdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCEQCyAMIQogCyEODAILIAtCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IQogC0KNlcfDltLawJd/UgRAQqnAxomuzpOyMCEQIAshDgwCC0KNlcfDltLawJd/IQ4gEkLH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIRAMAQsgC0Lz6ri86a2lv+gAfCIKIBJCx/rzw+2Co5A8VK0iDX0hDiAMQqPP+vOXye7XxwB8IhEgC0KNlcfDltLawJd/VCAKIA1Ucq0iC30hCiAQIAxC3bCFjOi2kai4f1QgCyARVnKtfUKpwMaJrs6TsjB9IRAgEkLH+vPD7YKjkDx9IRILQqnAxomuzpOyMCEWIAEpA4gBIgsgCnwiCiALVCAKIAEpA5ABIgsgDnwiDCALVCAMIAwgASkDmAEiCyASfCIOIAtUrXwiC1ZyrXwiDCAKVHKtIAEpA4ABIBB8fCISIQoCQCASQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRYgDCIKQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEWIAsiCkKNlcfDltLawJd/Ug0AQsf688PtgqOQPCEWIA4iCkLH+vPD7YKjkDxRDQILIAogFloNASAMISQgCyEoDAILQQogAkGgisAAENkDAAsgC0Lz6ri86a2lv+gAfCIKIA5Cx/rzw+2Co5A8VK0iDX0hKCAMQqPP+vOXye7XxwB8IhAgC0KNlcfDltLawJd/VCAKIA1Ucq0iCn0hJCASIAxC3bCFjOi2kai4f1QgCiAQVnKtfUKpwMaJrs6TsjB9IRIgDkLH+vPD7YKjkDx9IQ4LIANBgBpqIAEpA/gBIgpCACATQgAQyQMgA0GQGmogCkIAIBRCABDJAyADQaAaaiAKQgAgGUIAEMkDIANBsBpqIApCACAaQgAQyQMgA0HwGWogAykDgBoiDEIAQgBCiceZpK7wgemHfxDJAyADQeAZaiADKQP4GSIKQgBCx/rzw+2Co5A8QgAQyQMgA0HQGWogCkIAQo2Vx8OW0trAl39CABDJAyADQcAZaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBsBlqIApCAEKpwMaJrs6TsjBCABDJAyADQfAYaiABKQPwASIKQgAgE0IAEMkDIANBgBlqIApCACAUQgAQyQMgA0GQGWogCkIAIBlCABDJAyADQaAZaiAKQgAgGkIAEMkDIANB4BhqIAMpA9AZIhggAykDiBoiESADKQOQGnwiFnwiCyADKQPoGSAMIAMpA+AZIgp8IApUrXx8IgwgAykD8Bh8Ig1CAEIAQonHmaSu8IHph38QyQMgA0HQGGogAykD6BgiCkIAQsf688PtgqOQPEIAEMkDIANBwBhqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwGGogCkIAQt2whYzotpGouH9CABDJAyADQaAYaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HgF2ogASkD6AEiCkIAIBNCABDJAyADQfAXaiAKQgAgFEIAEMkDIANBgBhqIApCACAZQgAQyQMgA0GQGGogCkIAIBpCABDJAyADQdAXaiADKQP4GCAMIA1WrXwiISADKQOAGXwiECADKQOYGiARIBZWrXwiIyADKQOgGnwiESADKQPAGXwiFiALIAxWrSADKQPYGSALIBhUrXx8fCIdfCILIAMpA8AYfCIMIAMpA9gYIAMpA9AYIgogDXwgClStfHwiDSADKQPgF3wiGEIAQgBCiceZpK7wgemHfxDJAyADQcAXaiADKQPYFyIKQgBCx/rzw+2Co5A8QgAQyQMgA0GwF2ogCkIAQo2Vx8OW0trAl39CABDJAyADQdAWaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwBZqIApCAEKpwMaJrs6TsjBCABDJAyADQcAaaiABKQPgASIKQgAgE0IAEMkDIANB0BpqIApCACAUQgAQyQMgA0HgGmogCkIAIBlCABDJAyADQfAaaiAKQgAgGkIAEMkDIANBoBdqIAMpA+gXIA0gGFatfCIfIAMpA/AXfCIVIAMpA6gaIBEgI1StfCIlIAMpA7AafCIjIAMpA7AZfCIpIBYgHVatIAMpA8gZIBEgFlatfHx8IhEgAykDkBl8IhYgCyAQVK0gAykDiBkgECAhVK18fHwiECADKQOwGHwiISAMIA1WrSADKQPIGCALIAxWrXx8fCIdfCILIAMpA7AXfCIMIAMpA8gXIAMpA8AXIgogGHwgClStfHwiDSADKQPAGnwiGEIAQgBCiceZpK7wgemHfxDJAyADQZAXaiADKQOoFyIKQgBCx/rzw+2Co5A8QgAQyQMgA0GAF2ogCkIAQo2Vx8OW0trAl39CABDJAyADQfAWaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4BZqIApCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD6BYgAykDyBYgAykDqBggESApVK0gAykDuBkgIyApVq18fCADKQO4GiAjICVUrXx8IiMgAykDoBl8IgogECAWVK0gAykDmBkgESAWVq18fHwiESADKQOgGHwiFiARVK18IBYgHSAhVK0gAykDuBggECAhVq18fHwiECAWVK18IAogEVatIAMpA6gZIAogI1StfHx8IiMgAykDkBh8IgogAykDiBggECAQIAMpA4AYfCIRVq18IBEgESALIBVUrSADKQP4FyAVIB9UrXx8fCIQVq18fCIRIAMpA8AWfCIWIBFUrXwgFiADKQPYFiAQIBAgAykD0BZ8IhVWrXwgFSAVIAwgDVatIAMpA7gXIAsgDFatfHx8IhBWrXx8IgsgFlStfCAKIBFWrSADKQOYGCAKICNUrXx8fCIjIAMpA/AafCIMIAMpA+gaIAsgAykD4Bp8IgogC1StfCAKIAogAykD2BogAykDyBogDSAYVq18Ig0gAykD0Bp8IgsgDVStfCALIAsgEHwiDVatfHwiC1atfHwiESADKQPgFnwiFiARVK18IBYgFiADKQP4FiALIAsgAykD8BZ8IhVWrXwgFSAVIAMpA4gXIA0gDSADKQOAF3wiClatfCAKIAMpA5gXIAMpA5AXIgsgGHwgC1StfHwiECAKVK18fCIKVq18fCINVq18IAwgEVatIAMpA/gaIAwgI1StfHx8IgtCqcDGia7Ok7IwVg0AAkAgC0KpwMaJrs6TsjBRBEAgDULdsIWM6LaRqLh/Vg0CIA1C3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhCwsgDSEWIAohDAwCCyAKQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEWIApCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhCyAKIQwMAgtCjZXHw5bS2sCXfyEMIBBCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCELDAELIApC8+q4vOmtpb/oAHwiESAQQsf688PtgqOQPFStIhZ9IQwgDUKjz/rzl8nu18cAfCIYIApCjZXHw5bS2sCXf1QgESAWVHKtIgp9IRYgCyANQt2whYzotpGouH9UIAogGFZyrX1CqcDGia7Ok7IwfSELIBBCx/rzw+2Co5A8fSEQC0KpwMaJrs6TsjAhESABKQMoIgogFnwiDSAKVCANIAwgASkDMCIKfCIMIApUIAwgDCABKQM4IgogEHwiFiAKVK18IgpWcq18IgwgDVRyrSABKQMgIAt8fCIQIQ0CQAJAAkAgEEKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyERIAwiDULdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hESAKIg1CjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhESAWIg1Cx/rzw+2Co5A8UQ0BCyANIBFaDQAgDCEjIAohKQwBCyAKQvPquLzpraW/6AB8IgsgFkLH+vPD7YKjkDxUrSINfSEpIAxCo8/685fJ7tfHAHwiESAKQo2Vx8OW0trAl39UIAsgDVRyrSIKfSEjIBAgDELdsIWM6LaRqLh/VCAKIBFWcq19QqnAxomuzpOyMH0hECAWQsf688PtgqOQPH0hFgsgA0HAFWogASkDuAIiCkIAIBNCABDJAyADQdAVaiAKQgAgFEIAEMkDIANB4BVqIApCACAZQgAQyQMgA0HwFWogCkIAIBpCABDJAyADQbAVaiADKQPAFSIMQgBCAEKJx5mkrvCB6Yd/EMkDIANBoBVqIAMpA7gVIgpCAELH+vPD7YKjkDxCABDJAyADQZAVaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBgBVqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HwFGogCkIAQqnAxomuzpOyMEIAEMkDIANBsBRqIAEpA7ACIgpCACATQgAQyQMgA0HAFGogCkIAIBRCABDJAyADQdAUaiAKQgAgGUIAEMkDIANB4BRqIApCACAaQgAQyQMgA0GgFGogAykDkBUiISADKQPIFSIYIAMpA9AVfCIVfCILIAMpA6gVIAwgAykDoBUiCnwgClStfHwiDCADKQOwFHwiDUIAQgBCiceZpK7wgemHfxDJAyADQZAUaiADKQOoFCIKQgBCx/rzw+2Co5A8QgAQyQMgA0GAFGogCkIAQo2Vx8OW0trAl39CABDJAyADQfATaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4BNqIApCAEKpwMaJrs6TsjBCABDJAyADQaATaiABKQOoAiIKQgAgE0IAEMkDIANBsBNqIApCACAUQgAQyQMgA0HAE2ogCkIAIBlCABDJAyADQdATaiAKQgAgGkIAEMkDIANBkBNqIAMpA7gUIAwgDVatfCImIAMpA8AUfCIRIAMpA9gVIBUgGFStfCIfIAMpA+AVfCIYIAMpA4AVfCIVIAsgDFatIAMpA5gVIAsgIVStfHx8Iip8IgsgAykDgBR8IgwgAykDmBQgAykDkBQiCiANfCAKVK18fCINIAMpA6ATfCIhQgBCAEKJx5mkrvCB6Yd/EMkDIANBgBNqIAMpA5gTIgpCAELH+vPD7YKjkDxCABDJAyADQfASaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBkBJqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GAEmogCkIAQqnAxomuzpOyMEIAEMkDIANBgBZqIAEpA6ACIgpCACATQgAQyQMgA0GQFmogCkIAIBRCABDJAyADQaAWaiAKQgAgGUIAEMkDIANBsBZqIApCACAaQgAQyQMgA0HgEmogAykDqBMgDSAhVq18IisgAykDsBN8Ih0gAykD6BUgGCAfVK18IiwgAykD8BV8Ih8gAykD8BR8IiUgFSAqVq0gAykDiBUgFSAYVK18fHwiGCADKQPQFHwiFSALIBFUrSADKQPIFCARICZUrXx8fCIRIAMpA/ATfCImIAwgDVatIAMpA4gUIAsgDFatfHx8Iip8IgsgAykD8BJ8IgwgAykDiBMgAykDgBMiCiAhfCAKVK18fCINIAMpA4AWfCIhQgBCAEKJx5mkrvCB6Yd/EMkDIANB0BJqIAMpA+gSIgpCAELH+vPD7YKjkDxCABDJAyADQcASaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsBJqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgEmogCkIAQqnAxomuzpOyMEIAEMkDAkACQCADKQOoEiADKQOIEiADKQPoEyAYICVUrSADKQP4FCAfICVWrXx8IAMpA/gVIB8gLFStfHwiHyADKQPgFHwiCiARIBVUrSADKQPYFCAVIBhUrXx8fCIYIAMpA+ATfCIVIBhUrXwgFSAmICpWrSADKQP4EyARICZWrXx8fCIRIBVUrXwgCiAYVq0gAykD6BQgCiAfVK18fHwiHyADKQPQE3wiCiADKQPIEyARIBEgAykDwBN8IhhWrXwgGCAYIAsgHVStIAMpA7gTIB0gK1StfHx8IhFWrXx8IhggAykDgBJ8IhUgGFStfCAVIAMpA5gSIBEgESADKQOQEnwiHVatfCAdIB0gDCANVq0gAykD+BIgCyAMVq18fHwiEVatfHwiCyAVVK18IAogGFatIAMpA9gTIAogH1StfHx8IhUgAykDsBZ8IgogAykDqBYgCyALIAMpA6AWfCIMVq18IAwgDCADKQOYFiADKQOIFiANICFWrXwiDSADKQOQFnwiCyANVK18IAsgCyARfCINVq18fCILVq18fCIRIAMpA6ASfCIYIBFUrXwgGCAYIAMpA7gSIAsgAykDsBJ8IgwgC1StfCAMIAwgAykDyBIgDSANIAMpA8ASfCINVq18IA0gDSADKQPYEiADKQPQEiILICF8IAtUrXx8IgtWrXx8IgxWrXx8IhhWrXwgCiARVq0gAykDuBYgCiAVVK18fHwiCkKpwMaJrs6TsjBWDQACQCAKQqnAxomuzpOyMFEEQCAYQt2whYzotpGouH9WDQIgGELdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCEKCyAYIREgDCENDAILIAxCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IREgDEKNlcfDltLawJd/UgRAQqnAxomuzpOyMCEKIAwhDQwCC0KNlcfDltLawJd/IQ0gC0LH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQoMAQsgDELz6ri86a2lv+gAfCIRIAtCx/rzw+2Co5A8VK0iFX0hDSAYQqPP+vOXye7XxwB8IiEgDEKNlcfDltLawJd/VCARIBVUcq0iDH0hESAKIBhC3bCFjOi2kai4f1QgDCAhVnKtfUKpwMaJrs6TsjB9IQogC0LH+vPD7YKjkDx9IQsLQqnAxomuzpOyMCEYIBEgASkDaCIVfCIMIBVUIAwgDSABKQNwIhF8IhUgEVQgFSAVIAsgASkDeCIRfCINIBFUrXwiEVZyrXwiFSAMVHKtIAEpA2AgCnx8IgshDAJAAkACQCALQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRggFSIMQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEYIBEiDEKNlcfDltLawJd/Ug0AQsf688PtgqOQPCEYIA0iDELH+vPD7YKjkDxRDQELIAwgGFoNACAVIRggESEhDAELIBFC8+q4vOmtpb/oAHwiCiANQsf688PtgqOQPFStIgx9ISEgFUKjz/rzl8nu18cAfCIdIBFCjZXHw5bS2sCXf1QgCiAMVHKtIgp9IRggCyAVQt2whYzotpGouH9UIAogHVZyrX1CqcDGia7Ok7IwfSELIA1Cx/rzw+2Co5A8fSENCyACQQtHBEAgA0GAEWogASkD+AIiCkIAIBNCABDJAyADQZARaiAKQgAgFEIAEMkDIANBoBFqIApCACAZQgAQyQMgA0GwEWogCkIAIBpCABDJAyADQfAQaiADKQOAESIRQgBCAEKJx5mkrvCB6Yd/EMkDIANB4BBqIAMpA/gQIgpCAELH+vPD7YKjkDxCABDJAyADQdAQaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBwBBqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GwEGogCkIAQqnAxomuzpOyMEIAEMkDIANB8A9qIAEpA/ACIgpCACATQgAQyQMgA0GAEGogCkIAIBRCABDJAyADQZAQaiAKQgAgGUIAEMkDIANBoBBqIApCACAaQgAQyQMgA0HgD2ogAykD0BAiJiADKQOIESIfIAMpA5ARfCIlfCIMIAMpA+gQIBEgAykD4BAiCnwgClStfHwiESADKQPwD3wiFUIAQgBCiceZpK7wgemHfxDJAyADQdAPaiADKQPoDyIKQgBCx/rzw+2Co5A8QgAQyQMgA0HAD2ogCkIAQo2Vx8OW0trAl39CABDJAyADQbAPaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBoA9qIApCAEKpwMaJrs6TsjBCABDJAyADQeAOaiABKQPoAiIKQgAgE0IAEMkDIANB8A5qIApCACAUQgAQyQMgA0GAD2ogCkIAIBlCABDJAyADQZAPaiAKQgAgGkIAEMkDIANB0A5qIAMpA/gPIBEgFVatfCIqIAMpA4AQfCIdIAMpA5gRIB8gJVatfCIrIAMpA6ARfCIfIAMpA8AQfCIlIAwgEVatIAMpA9gQIAwgJlStfHx8Iix8IgwgAykDwA98IhEgAykD2A8gAykD0A8iCiAVfCAKVK18fCIVIAMpA+AOfCImQgBCAEKJx5mkrvCB6Yd/EMkDIANBwA5qIAMpA9gOIgpCAELH+vPD7YKjkDxCABDJAyADQbAOaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0A1qIApCAELdsIWM6LaRqLh/QgAQyQMgA0HADWogCkIAQqnAxomuzpOyMEIAEMkDIANBwBFqIAEpA+ACIgpCACATQgAQyQMgA0HQEWogCkIAIBRCABDJAyADQeARaiAKQgAgGUIAEMkDIANB8BFqIApCACAaQgAQyQMgA0GgDmogAykD6A4gFSAmVq18Ii0gAykD8A58IhQgAykDqBEgHyArVK18IisgAykDsBF8IhMgAykDsBB8IhkgJSAsVq0gAykDyBAgHyAlVq18fHwiGiADKQOQEHwiHyAMIB1UrSADKQOIECAdICpUrXx8fCIdIAMpA7APfCIlIBEgFVatIAMpA8gPIAwgEVatfHx8Iip8IgwgAykDsA58IhEgAykDyA4gAykDwA4iCiAmfCAKVK18fCIVIAMpA8ARfCImQgBCAEKJx5mkrvCB6Yd/EMkDIANBkA5qIAMpA6gOIgpCAELH+vPD7YKjkDxCABDJAyADQYAOaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB8A1qIApCAELdsIWM6LaRqLh/QgAQyQMgA0HgDWogCkIAQqnAxomuzpOyMEIAEMkDAkACQCADKQPoDSADKQPIDSADKQOoDyAZIBpWrSADKQO4ECATIBlWrXx8IAMpA7gRIBMgK1StfHwiKyADKQOgEHwiCiAdIB9UrSADKQOYECAaIB9WrXx8fCITIAMpA6APfCIZIBNUrXwgGSAZICUgKlatIAMpA7gPIB0gJVatfHx8IhpWrXwgCiATVq0gAykDqBAgCiArVK18fHwiHSADKQOQD3wiCiADKQOIDyAaIAMpA4APfCITIBpUrXwgEyAMIBRUrSADKQP4DiAUIC1UrXx8fCIUIBNUrXx8IhMgAykDwA18IhkgE1StfCAZIAMpA9gNIBQgFCADKQPQDXwiGlatfCAaIBEgFVatIAMpA7gOIAwgEVatfHx8IhEgGlStfHwiDCAZVK18IAogE1atIAMpA5gPIAogHVStfHx8Ih0gAykD8BF8IhQgAykD6BEgDCADKQPgEXwiCiAMVK18IAogCiADKQPYESADKQPIESAVICZWrXwiEyADKQPQEXwiDCATVK18IAwgDCARfCIRVq18fCIMVq18fCITIAMpA+ANfCIVIBNUrXwgFSAVIAMpA/gNIAwgDCADKQPwDXwiGlatfCAaIBogAykDiA4gESARIAMpA4AOfCIKVq18IAogAykDmA4gAykDkA4iDCAmfCAMVK18fCIZIApUrXx8IgpWrXx8IhFWrXwgEyAUVK0gAykD+BEgFCAdVK18fHwiE0KpwMaJrs6TsjBWDQACQCATQqnAxomuzpOyMFEEQCARQt2whYzotpGouH9WDQIgEULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCETCyARIRQgCiEMDAILIApCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IRQgCkKNlcfDltLawJd/UgRAQqnAxomuzpOyMCETIAohDAwCC0KNlcfDltLawJd/IQwgGULH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIRMMAQsgCkLz6ri86a2lv+gAfCIUIBlCx/rzw+2Co5A8VK0iFX0hDCARQqPP+vOXye7XxwB8IhogCkKNlcfDltLawJd/VCAUIBVUcq0iCn0hFCATIBFC3bCFjOi2kai4f1QgCiAaVnKtfUKpwMaJrs6TsjB9IRMgGULH+vPD7YKjkDx9IRkLIAFBwAFqIQIgAUGAAmohBSABQcACaiEGIAFB4AFqIQcgAUGgAmohCCABQeACaiEJQqnAxomuzpOyMCERIAEpA6ABIBN8IBQgASkDqAEiE3wiCiATVCAKIAwgASkDsAEiDHwiFCAMVCAUIBQgASkDuAEiDCAZfCITIAxUrXwiDFZyrXwiFCAKVHKtfCIZIQoCQAJAAkAgGUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyERIBQiCkLdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hESAMIgpCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhESATIgpCx/rzw+2Co5A8UQ0BCyAKIBFaDQAgFCEKIAwhEQwBCyAMQvPquLzpraW/6AB8IgogE0LH+vPD7YKjkDxUrSIVfSERIBRCo8/685fJ7tfHAHwiGiAMQo2Vx8OW0trAl39UIAogFVRyrSIMfSEKIBkgFELdsIWM6LaRqLh/VCAMIBpWcq19QqnAxomuzpOyMH0hGSATQsf688PtgqOQPH0hEwsgBCATNwPYAiAEIBE3A9ACIAQgCjcDyAIgBCAZNwPAAiAEIA83AxggBCAeNwMQIAQgIDcDCCAEIBw3AwAgBCAJKQMANwPgAiAEIAIpAwA3AyAgBEHoAmogCUEIaikDADcDACAEQfACaiAJQRBqKQMANwMAIARB+AJqIAlBGGopAwA3AwAgBEEoaiACQQhqKQMANwMAIARBMGogAkEQaikDADcDACAEQThqIAJBGGopAwA3AwAgBCAXNwNYIAQgJzcDUCAEICI3A0ggBCAbNwNAIAQgDjcDmAEgBCAoNwOQASAEICQ3A4gBIAQgEjcDgAEgBCAFKQMANwNgIARB6ABqIAVBCGopAwA3AwAgBEHwAGogBUEQaikDADcDACAEQfgAaiAFQRhqKQMANwMAIAQgBikDADcDoAEgBEGoAWogBkEIaikDADcDACAEQbABaiAGQRBqKQMANwMAIARBuAFqIAZBGGopAwA3AwAgBCAWNwPYASAEICk3A9ABIAQgIzcDyAEgBCAQNwPAASAEQfgBaiAHQRhqKQMANwMAIARB8AFqIAdBEGopAwA3AwAgBEHoAWogB0EIaikDADcDACAEIAcpAwA3A+ABIAQgDTcDmAIgBCAhNwOQAiAEIBg3A4gCIAQgCzcDgAIgBEG4AmogCEEYaikDADcDACAEQbACaiAIQRBqKQMANwMAIARBqAJqIAhBCGopAwA3AwAgBCAIKQMANwOgAkEMIQIMBwtBC0ELQbCKwAAQ2QMACyADQQA2AtArIANBzCtqIANByCtqIANB0CtqQaCJwAAQlwQACyAGIAdBuIXAABDIBAALQQBBAEGwicAAENkDAAtBAEEAQfCJwAAQ2QMAC0EIQYADEP8EAAtBCEHAARD/BAALIAAgAjYCCCAAIAQ2AgQgACACNgIAIANBkDBqJAAL778BAgZ/JH4jAEHQMmsiBSQAIAVBgC1qECEgBS0AuDEhCiAFKAKsMSIGBEAgBSgCsDEgBkECdBDfBAsCQCAFKALkLiIGRQ0AIAYgBkEMbEETakF4cSIHakEJaiIGRQ0AIAUoAuAuIAdrIAYQ3wQLIAUoApAvIgZBgICAgHhGIAZFckUEQCAFKAKULyAGQQJ0EN8ECyAFQYgtaiABQQhqKQMANwMAIAVBkC1qIAFBEGopAwA3AwAgBUGYLWogAUEYaikDADcDACAFQaAtaiABKQMgNwMAIAVBqC1qIAFBKGopAwA3AwAgBUGwLWogAUEwaikDADcDACAFQbgtaiABQThqKQMANwMAIAUgASkDADcDgC0gBUHEMmogBUGALWoQrwMgBSgCyDIhASAFKALEMiEGAkACQAJAAkACQCAFKALMMiIHQQJGBEAgASkDOCEUIAEpAzAhFSABKQMoIRkgASkDICEoIAEpAxghECABKQMQIRIgASkDCCENIAEoAgQhByABKAIAIQggBgRAIAEgBkEFdBDfBAsgBUGILWogAkEIaikDADcDACAFQZAtaiACQRBqKQMANwMAIAVBmC1qIAJBGGopAwA3AwAgBUGgLWogAikDIDcDACAFQagtaiACQShqKQMANwMAIAVBsC1qIAJBMGopAwA3AwAgBUG4LWogAkE4aikDADcDACAFIAIpAwA3A4AtIAVBxDJqIAVBgC1qEK8DIAUoAsgyIQEgBSgCxDIhAiAFKALMMiIGQQJHDQEgASkDOCEWIAEpAzAhGiABKQMoIRggASkDICEnIAEpAxghDyABKQMQISUgASkDCCEjIAEoAgQhBiABKAIAIQkgAgRAIAEgAkEFdBDfBAsCQAJAAkAgCg4CAQIAC0HUusIAQQ9B5LrCABD+AwALQdHOxQAtAAAaQYADQQgQ1gQiAUUNBUL3/7WI5PmRg3YhGyAFQvf/tYjk+ZGDdjcDmC1CkaDvmN3p254vIRcgBUKRoO+Y3enbni83A5AtQtGNg8rj78yhKSERIAVC0Y2DyuPvzKEpNwOILULXsI6/ip3myh0hDCAFQtewjr+KnebKHTcDgC0gBUGALWpBuLPCAEEgEPEDBEBC0o+4yqOxrecSIQxC+/TXqrno/qHoACEXQtD6vbuJiZGNxgAhG0KMo4LChMfEho9/IRELIAVB8BpqIBtCACAUQgAQyQMgBUGQGmogF0IAIBRCABDJAyAFQYAaaiARQgAgFEIAEMkDIAVB8BlqIAxCACAUQgAQyQMgBUHgGmogBSkD8BoiE0IAQgBCiceZpK7wgemHfxDJAyAFQdAaaiAFKQPoGiILQgBCx/rzw+2Co5A8QgAQyQMgBUHAGmogC0IAQo2Vx8OW0trAl39CABDJAyAFQbAaaiALQgBC3bCFjOi2kai4f0IAEMkDIAVBoBpqIAtCAEKpwMaJrs6TsjBCABDJAyAFQeAZaiAbQgAgFUIAEMkDIAVBgBlqIBdCACAVQgAQyQMgBUHwGGogEUIAIBVCABDJAyAFQeAYaiAMQgAgFUIAEMkDIAVB0BlqIAUpA8AaIh8gBSkD+BoiHCAFKQOQGnwiInwiDiAFKQPYGiATIAUpA9AaIgt8IAtUrXx8IhMgBSkD4Bl8IiRCAEIAQonHmaSu8IHph38QyQMgBUHAGWogBSkD2BkiC0IAQsf688PtgqOQPEIAEMkDIAVBsBlqIAtCAEKNlcfDltLawJd/QgAQyQMgBUGgGWogC0IAQt2whYzotpGouH9CABDJAyAFQZAZaiALQgBCqcDGia7Ok7IwQgAQyQMgBUHQGGogG0IAIBlCABDJAyAFQfAXaiAXQgAgGUIAEMkDIAVB4BdqIBFCACAZQgAQyQMgBUHQF2ogDEIAIBlCABDJAyAFQcAYaiAFKQPoGSATICRWrXwiHSAFKQOAGXwiICAFKQOYGiAcICJWrXwiHiAFKQOAGnwiHCAFKQOwGnwiIiAOIBNWrSAFKQPIGiAOIB9UrXx8fCIhfCIOIAUpA7AZfCITIAUpA8gZIAUpA8AZIgsgJHwgC1StfHwiJCAFKQPQGHwiH0IAQgBCiceZpK7wgemHfxDJAyAFQbAYaiAFKQPIGCILQgBCx/rzw+2Co5A8QgAQyQMgBUGgGGogC0IAQo2Vx8OW0trAl39CABDJAyAFQZAYaiALQgBC3bCFjOi2kai4f0IAEMkDIAVBgBhqIAtCAEKpwMaJrs6TsjBCABDJAyAFQcAXaiAbQgAgKEIAEMkDIAVB4BZqIBdCACAoQgAQyQMgBUHQFmogEUIAIChCABDJAyAFQcAWaiAMQgAgKEIAEMkDIAVBsBdqIAUpA9gYIB8gJFStfCImIAUpA/AXfCIRIAUpA4gaIBwgHlStfCIeIAUpA/AZfCIMIAUpA6AafCIXICEgIlStIAUpA7gaIBwgIlatfHx8IhsgBSkD8Bh8IhwgDiAgVK0gBSkDiBkgHSAgVq18fHwiICAFKQOgGXwiIiATICRWrSAFKQO4GSAOIBNWrXx8fCIdfCIOIAUpA6AYfCITIAUpA7gYIAUpA7AYIgsgH3wgC1StfHwiJCAFKQPAF3wiH0IAQgBCiceZpK7wgemHfxDJAyAFQaAXaiAFKQO4FyILQgBCx/rzw+2Co5A8QgAQyQMgBUGQF2ogC0IAQo2Vx8OW0trAl39CABDJAyAFQYAXaiALQgBC3bCFjOi2kai4f0IAEMkDIAVB8BZqIAtCAEKpwMaJrs6TsjBCABDJAwJAAkAgBSkD+BYgBSkD2BcgBSkD6BggBSkD+BkgDCAeVK18Ih4gBSkD4Bh8IgsgHlStfCALIAsgFyAbVq0gBSkDqBogDCAXVq18fHwiC1atfCALIAsgHCAgVq0gBSkD+BggGyAcVq18fHwiC1atfCIXIAUpA9AXfCIMIBdUrXwgDCAMIAUpA5gZIAsgCyAFKQOQGXwiC1atfCALIAsgHSAiVK0gBSkDqBkgICAiVq18fHwiC1atfHwiDFatfCAMIAUpA+gXIAsgCyAFKQPgF3wiC1atfCALIAsgDiARVK0gBSkD+BcgESAmVK18fHwiC1atfHwiESAMVK18IiAgBSkDwBZ8IgwgBSkDiBggESARIAUpA4AYfCIRVq18IBEgBSkDmBggCyALIAUpA5AYfCILVq18IAsgEyAkVq0gBSkDqBggDiATVq18fHwiFyALVK18fCILIBFUrXx8Ig4gBSkD2BYgCyALIAUpA9AWfCILVq18IAsgCyAFKQPoFiAFKQPIFyAfICRUrXwiGyAFKQPgFnwiESAbVK18IBEgESAXfCIRVq18fCILVq18fCIXIAUpA/AWfCITIBdUrXwgEyAFKQOIFyALIAsgBSkDgBd8IgtWrXwgCyALIAUpA5gXIBEgESAFKQOQF3wiEVatfCARIAUpA6gXIAUpA6AXIhsgH3wgG1StfHwiGyARVK18fCILVq18fCIRIBNUrXwgDiAXVq0gDCAOVq0gBSkDyBYgDCAgVK18fHx8IhdCqcDGia7Ok7IwVg0AAkAgF0KpwMaJrs6TsjBRBEAgEULdsIWM6LaRqLh/Vg0CIBFC3bCFjOi2kai4f1IEQCALIQwgESEOQqnAxomuzpOyMCEXDAQLIAtCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQ4gC0KNlcfDltLawJd/UQ0BIAshDEKpwMaJrs6TsjAhFwwDCyALIQwgESEODAILQo2Vx8OW0trAl38hDCAbQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhFwwBCyALQvPquLzpraW/6AB8Ig4gG0LH+vPD7YKjkDxUrSITfSEMIBFCo8/685fJ7tfHAHwiJCALQo2Vx8OW0trAl39UIA4gE1RyrSILfSEOIBcgEULdsIWM6LaRqLh/VCALICRWcq19QqnAxomuzpOyMH0hFyAbQsf688PtgqOQPH0hGwtCqcDGia7Ok7IwIQsgDSAOfCIRIA1UIBEgDCASfCIOIBJUIA4gDiAQIBt8IgwgEFStfCIOVnKtfCIQIBFUcq0gCK0gB61CIIaEIBd8fCINIRECQAJAAkAgDUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyELIBAiEULdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hCyAOIhFCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhCyAMIREgDELH+vPD7YKjkDxRDQELIAsgEVgNACAOIRMgECELDAELIA5C8+q4vOmtpb/oAHwiCyAMQsf688PtgqOQPFStIhF9IRMgEEKjz/rzl8nu18cAfCIXIA5CjZXHw5bS2sCXf1QgCyARVHKtIhF9IQsgDSAQQt2whYzotpGouH9UIBEgF1ZyrX1CqcDGia7Ok7IwfSENIAxCx/rzw+2Co5A8fSEMCyAFQbAWaiAEKQMYIiBCACAMQgAQyQMgBUGgFWogIEIAIBNCABDJAyAFQZAUaiAgQgAgC0IAEMkDIAVBgBNqICBCACANQgAQyQMgBUGgFmogBSkDsBYiF0IAQgBCiceZpK7wgemHfxDJAyAFQZAWaiAFKQOoFiIRQgBCx/rzw+2Co5A8QgAQyQMgBUGAFmogEUIAQo2Vx8OW0trAl39CABDJAyAFQfAVaiARQgBC3bCFjOi2kai4f0IAEMkDIAVB4BVqIBFCAEKpwMaJrs6TsjBCABDJAyAFQdAVaiAEKQMQIhxCACAMQgAQyQMgBUHAFGogHEIAIBNCABDJAyAFQbATaiAcQgAgC0IAEMkDIAVBoBJqIBxCACANQgAQyQMgBUGQFWogBSkDgBYiHyAFKQO4FiIbIAUpA6AVfCIkfCIOIAUpA5gWIBcgBSkDkBYiEXwgEVStfHwiFyAFKQPQFXwiEEIAQgBCiceZpK7wgemHfxDJAyAFQYAVaiAFKQOYFSIRQgBCx/rzw+2Co5A8QgAQyQMgBUHwFGogEUIAQo2Vx8OW0trAl39CABDJAyAFQeAUaiARQgBC3bCFjOi2kai4f0IAEMkDIAVB0BRqIBFCAEKpwMaJrs6TsjBCABDJAyAFQcAVaiAEKQMIIiJCACAMQgAQyQMgBUGwFGogIkIAIBNCABDJAyAFQaATaiAiQgAgC0IAEMkDIAVBkBJqICJCACANQgAQyQMgBUGAFGogBSkD2BUgECAXVK18Ih4gBSkDwBR8IhIgBSkDqBUgGyAkVq18IiEgBSkDkBR8IhsgBSkD8BV8IiQgDiAXVq0gBSkDiBYgDiAfVK18fHwiJnwiDiAFKQPwFHwiFyAFKQOIFSAFKQOAFSIRIBB8IBFUrXx8IhAgBSkDwBV8Ih1CAEIAQonHmaSu8IHph38QyQMgBUHwE2ogBSkDiBQiEUIAQsf688PtgqOQPEIAEMkDIAVB4BNqIBFCAEKNlcfDltLawJd/QgAQyQMgBUHQE2ogEUIAQt2whYzotpGouH9CABDJAyAFQcATaiARQgBCqcDGia7Ok7IwQgAQyQMgBUGwFWogBCkDACIfQgAgDEIAEMkDIAVBoBRqIB9CACATQgAQyQMgBUGQE2ogH0IAIAtCABDJAyAFQYASaiAfQgAgDUIAEMkDIAVB8BJqIAUpA8gVIBAgHVatfCIpIAUpA7AUfCIRIAUpA5gUIBsgIVStfCIhIAUpA4ATfCIMIAUpA+AVfCINICQgJlatIAUpA/gVIBsgJFatfHx8IhsgBSkDsBN8IhMgDiASVK0gBSkDyBQgEiAeVK18fHwiEiAFKQPgFHwiJCAQIBdUrSAFKQP4FCAOIBdWrXx8fCIefCIOIAUpA+ATfCIXIAUpA/gTIAUpA/ATIgsgHXwgC1StfHwiECAFKQOwFXwiHUIAQgBCiceZpK7wgemHfxDJAyAFQeASaiAFKQP4EiILQgBCx/rzw+2Co5A8QgAQyQMgBUHQEmogC0IAQo2Vx8OW0trAl39CABDJAyAFQcASaiALQgBC3bCFjOi2kai4f0IAEMkDIAVBsBJqIAtCAEKpwMaJrs6TsjBCABDJAwJAAkAgBSkDuBIgBSkDyBMgBSkD2BQgDSAbVq0gBSkD6BUgDCANVq18fCAFKQOIEyAMICFUrXx8IiEgBSkDoBJ8IgsgEiATVK0gBSkDuBMgEyAbVK18fHwiDCAFKQPQFHwiDSAMVK18IA0gHiAkVK0gBSkD6BQgEiAkVq18fHwiEiANVK18IAsgDFatIAUpA6gSIAsgIVStfHx8Ig0gBSkDkBJ8IgsgBSkDqBMgEiAFKQOgE3wiDCASVK18IAwgDiARVK0gBSkDuBQgESApVK18fHwiESAMVK18fCIMIAUpA8ATfCISIAxUrXwgEiAFKQPYEyARIBEgBSkD0BN8IhFWrXwgESAQIBdUrSAFKQPoEyAOIBdWrXx8fCIOIBFUrXx8IhEgElStfCALIAxWrSAFKQOYEiALIA1UrXx8fCISIAUpA4ASfCIMIAUpA5gTIBEgBSkDkBN8IgsgEVStfCALIAsgBSkDqBQgBSkDuBUgECAdVq18IhcgBSkDoBR8IhEgF1StfCARIA4gEXwiEVatfHwiC1atfHwiFyAFKQOwEnwiDiAXVK18IA4gDiAFKQPIEiALIAsgBSkDwBJ8IgtWrXwgCyALIAUpA9gSIBEgESAFKQPQEnwiEVatfCARIAUpA+gSIAUpA+ASIhAgHXwgEFStfHwiGyARVK18fCILVq18fCIOVq18IAwgF1atIAUpA4gSIAwgElStfHx8IiRCqcDGia7Ok7IwVg0AAkAgJEKpwMaJrs6TsjBRBEAgDkLdsIWM6LaRqLh/Vg0CIA5C3bCFjOi2kai4f1IEQCALIREgDiEXQqnAxomuzpOyMCEkDAQLIAtCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IRcgC0KNlcfDltLawJd/UQ0BIAshEUKpwMaJrs6TsjAhJAwDCyALIREgDiEXDAILQo2Vx8OW0trAl38hESAbQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhJAwBCyALQvPquLzpraW/6AB8IgwgG0LH+vPD7YKjkDxUrSIXfSERIA5Co8/685fJ7tfHAHwiECALQo2Vx8OW0trAl39UIAwgF1RyrSILfSEXICQgDkLdsIWM6LaRqLh/VCALIBBWcq19QqnAxomuzpOyMH0hJCAbQsf688PtgqOQPH0hGwtC9/+1iOT5kYN2IQ0gBUL3/7WI5PmRg3Y3A5gtQpGg75jd6dueLyEMIAVCkaDvmN3p254vNwOQLULRjYPK4+/MoSkhEyAFQtGNg8rj78yhKTcDiC1C17COv4qd5sodIQsgBULXsI6/ip3myh03A4AtIAVBgC1qQbizwgBBIBDxAwRAQoyjgsKEx8SGj38hE0L79Nequej+oegAIQxC0Pq9u4mJkY3GACENQtKPuMqjsa3nEiELCyAFQfARaiANQgAgFkIAEMkDIAVBkBFqIAxCACAWQgAQyQMgBUGAEWogE0IAIBZCABDJAyAFQfAQaiALQgAgFkIAEMkDIAVB4BFqIAUpA/ARIhJCAEIAQonHmaSu8IHph38QyQMgBUHQEWogBSkD6BEiDkIAQsf688PtgqOQPEIAEMkDIAVBwBFqIA5CAEKNlcfDltLawJd/QgAQyQMgBUGwEWogDkIAQt2whYzotpGouH9CABDJAyAFQaARaiAOQgBCqcDGia7Ok7IwQgAQyQMgBUHgEGogDUIAIBpCABDJAyAFQYAQaiAMQgAgGkIAEMkDIAVB8A9qIBNCACAaQgAQyQMgBUHgD2ogC0IAIBpCABDJAyAFQdAQaiAFKQPAESIpIAUpA/gRIiEgBSkDkBF8IiZ8IhAgBSkD2BEgEiAFKQPQESIOfCAOVK18fCISIAUpA+AQfCIdQgBCAEKJx5mkrvCB6Yd/EMkDIAVBwBBqIAUpA9gQIg5CAELH+vPD7YKjkDxCABDJAyAFQbAQaiAOQgBCjZXHw5bS2sCXf0IAEMkDIAVBoBBqIA5CAELdsIWM6LaRqLh/QgAQyQMgBUGQEGogDkIAQqnAxomuzpOyMEIAEMkDIAVB0A9qIA1CACAYQgAQyQMgBUHwDmogDEIAIBhCABDJAyAFQeAOaiATQgAgGEIAEMkDIAVB0A5qIAtCACAYQgAQyQMgBUHAD2ogBSkD6BAgEiAdVq18IiogBSkDgBB8Ih4gBSkDmBEgISAmVq18IisgBSkDgBF8IiEgBSkDsBF8IiYgECASVq0gBSkDyBEgECApVK18fHwiLHwiECAFKQOwEHwiEiAFKQPIECAFKQPAECIOIB18IA5UrXx8Ih0gBSkD0A98IilCAEIAQonHmaSu8IHph38QyQMgBUGwD2ogBSkDyA8iDkIAQsf688PtgqOQPEIAEMkDIAVBoA9qIA5CAEKNlcfDltLawJd/QgAQyQMgBUGQD2ogDkIAQt2whYzotpGouH9CABDJAyAFQYAPaiAOQgBCqcDGia7Ok7IwQgAQyQMgBUHADmogDUIAICdCABDJAyAFQeANaiAMQgAgJ0IAEMkDIAVB0A1qIBNCACAnQgAQyQMgBUHADWogC0IAICdCABDJAyAFQbAOaiAFKQPYDyAdIClWrXwiLSAFKQPwDnwiDiAFKQOIESAhICtUrXwiKyAFKQPwEHwiDCAFKQOgEXwiDSAmICxWrSAFKQO4ESAhICZWrXx8fCITIAUpA/APfCIhIBAgHlStIAUpA4gQIB4gKlStfHx8Ih4gBSkDoBB8IiYgEiAdVq0gBSkDuBAgECASVq18fHwiKnwiECAFKQOgD3wiEiAFKQO4DyAFKQOwDyILICl8IAtUrXx8Ih0gBSkDwA58IilCAEIAQonHmaSu8IHph38QyQMgBUGgDmogBSkDuA4iC0IAQsf688PtgqOQPEIAEMkDIAVBkA5qIAtCAEKNlcfDltLawJd/QgAQyQMgBUGADmogC0IAQt2whYzotpGouH9CABDJAyAFQfANaiALQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAUpA/gNIAUpA9gOIAUpA+gPIAUpA/gQIAwgK1StfCIrIAUpA+APfCILICtUrXwgCyALIA0gE1atIAUpA6gRIAwgDVatfHx8IgtWrXwgCyALIB4gIVStIAUpA/gPIBMgIVatfHx8IgtWrXwiDSAFKQPQDnwiDCANVK18IAwgDCAFKQOYECALIAsgBSkDkBB8IgtWrXwgCyALICYgKlatIAUpA6gQIB4gJlatfHx8IgtWrXx8IgxWrXwgDCAFKQPoDiALIAsgBSkD4A58IgtWrXwgCyALIA4gEFatIAUpA/gOIA4gLVStfHx8IgtWrXx8Ig4gDFStfCIeIAUpA8ANfCIMIAUpA4gPIA4gDiAFKQOAD3wiDlatfCAOIAUpA5gPIAsgCyAFKQOQD3wiC1atfCALIBIgHVatIAUpA6gPIBAgElatfHx8IhAgC1StfHwiCyAOVK18fCISIAUpA9gNIAsgCyAFKQPQDXwiC1atfCALIAsgBSkD6A0gBSkDyA4gHSApVq18Ig0gBSkD4A18Ig4gDVStfCAOIA4gEHwiDlatfHwiC1atfHwiEyAFKQPwDXwiECATVK18IBAgECAFKQOIDiALIAsgBSkDgA58IgtWrXwgCyAFKQOYDiAOIA4gBSkDkA58Ig5WrXwgDiAFKQOoDiAFKQOgDiINICl8IA1UrXx8Ig0gDlStfHwiDiALVK18fCIQVq18IBIgE1atIAwgElatIAUpA8gNIAwgHlStfHx8fCIMQqnAxomuzpOyMFYNAAJAIAxCqcDGia7Ok7IwUQRAIBBC3bCFjOi2kai4f1YNAiAQQt2whYzotpGouH9SBEAgDiELIBAhEkKpwMaJrs6TsjAhDAwECyAOQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyESIA5CjZXHw5bS2sCXf1ENASAOIQtCqcDGia7Ok7IwIQwMAwsgDiELIBAhEgwCC0KNlcfDltLawJd/IQsgDULH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQwMAQsgDkLz6ri86a2lv+gAfCISIA1Cx/rzw+2Co5A8VK0iE30hCyAQQqPP+vOXye7XxwB8Ih0gDkKNlcfDltLawJd/VCASIBNUcq0iDn0hEiAMIBBC3bCFjOi2kai4f1QgDiAdVnKtfUKpwMaJrs6TsjB9IQwgDULH+vPD7YKjkDx9IQ0LQqnAxomuzpOyMCEOIBIgI3wiEiAjVCASIBIgCyAlfCIQICVUIBAgECANIA98IgsgD1StfCIQVnKtfCISVnKtIAmtIAatQiCGhCAMfHwiEyEMAkACQAJAIBNCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hDiASIgxC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQ4gECIMQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQ4gCyEMIAtCx/rzw+2Co5A8UQ0BCyAMIA5aDQAgECEMIBIhDgwBCyAQQvPquLzpraW/6AB8Ig4gC0LH+vPD7YKjkDxUrSINfSEMIBJCo8/685fJ7tfHAHwiDyAQQo2Vx8OW0trAl39UIA0gDlZyrSIQfSEOIBMgEkLdsIWM6LaRqLh/VCAPIBBUcq19QqnAxomuzpOyMH0hEyALQsf688PtgqOQPH0hCwsgBUGwDWogAykDGCIlQgAgC0IAEMkDIAVBoAxqICVCACAMQgAQyQMgBUGQC2ogJUIAIA5CABDJAyAFQYAKaiAlQgAgE0IAEMkDIAVBoA1qIAUpA7ANIg1CAEIAQonHmaSu8IHph38QyQMgBUGQDWogBSkDqA0iEEIAQsf688PtgqOQPEIAEMkDIAVBgA1qIBBCAEKNlcfDltLawJd/QgAQyQMgBUHwDGogEEIAQt2whYzotpGouH9CABDJAyAFQeAMaiAQQgBCqcDGia7Ok7IwQgAQyQMgBUHQDGogAykDECIjQgAgC0IAEMkDIAVBwAtqICNCACAMQgAQyQMgBUGwCmogI0IAIA5CABDJAyAFQaAJaiAjQgAgE0IAEMkDIAVBkAxqIAUpA4ANIh4gBSkDuA0iJiAFKQOgDHwiKXwiEiAFKQOYDSANIAUpA5ANIhB8IBBUrXx8Ig0gBSkD0Ax8Ig9CAEIAQonHmaSu8IHph38QyQMgBUGADGogBSkDmAwiEEIAQsf688PtgqOQPEIAEMkDIAVB8AtqIBBCAEKNlcfDltLawJd/QgAQyQMgBUHgC2ogEEIAQt2whYzotpGouH9CABDJAyAFQdALaiAQQgBCqcDGia7Ok7IwQgAQyQMgBUHADGogAykDCCIdQgAgC0IAEMkDIAVBsAtqIB1CACAMQgAQyQMgBUGgCmogHUIAIA5CABDJAyAFQZAJaiAdQgAgE0IAEMkDIAVBgAtqIAUpA9gMIA0gD1atfCIrIAUpA8ALfCIhIAUpA6gMICYgKVatfCIsIAUpA5ALfCImIAUpA/AMfCIpIA0gElStIAUpA4gNIBIgHlStfHx8Ii18IhIgBSkD8At8Ig0gBSkDiAwgBSkDgAwiECAPfCAQVK18fCIPIAUpA8AMfCIqQgBCAEKJx5mkrvCB6Yd/EMkDIAVB8ApqIAUpA4gLIhBCAELH+vPD7YKjkDxCABDJAyAFQeAKaiAQQgBCjZXHw5bS2sCXf0IAEMkDIAVB0ApqIBBCAELdsIWM6LaRqLh/QgAQyQMgBUHACmogEEIAQqnAxomuzpOyMEIAEMkDIAVBsAxqIAMpAwAiHkIAIAtCABDJAyAFQaALaiAeQgAgDEIAEMkDIAVBkApqIB5CACAOQgAQyQMgBUGACWogHkIAIBNCABDJAyAFQfAJaiAFKQPIDCAPICpWrXwiLiAFKQOwC3wiDiAFKQOYCyAmICxUrXwiLCAFKQOACnwiDCAFKQPgDHwiECApIC1WrSAFKQP4DCAmIClWrXx8fCITIAUpA7AKfCImIBIgIVStIAUpA8gLICEgK1StfHx8IiEgBSkD4At8IikgDSAPVq0gBSkD+AsgDSASVK18fHwiK3wiEiAFKQPgCnwiDSAFKQP4CiAFKQPwCiILICp8IAtUrXx8Ig8gBSkDsAx8IipCAEIAQonHmaSu8IHph38QyQMgBUHgCWogBSkD+AkiC0IAQsf688PtgqOQPEIAEMkDIAVB0AlqIAtCAEKNlcfDltLawJd/QgAQyQMgBUHACWogC0IAQt2whYzotpGouH9CABDJAyAFQbAJaiALQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAUpA7gJIAUpA8gKIAUpA9gLIBAgE1atIAUpA+gMIAwgEFatfHwgBSkDiAogDCAsVK18fCIsIAUpA6AJfCILICEgJlStIAUpA7gKIBMgJlatfHx8IgwgBSkD0At8IhAgDFStfCAQIBAgKSArVq0gBSkD6AsgISApVq18fHwiEFatfCALIAxWrSAFKQOoCSALICxUrXx8fCITIAUpA5AJfCILIAUpA6gKIBAgBSkDoAp8IgwgEFStfCAMIA4gElatIAUpA7gLIA4gLlStfHx8Ig4gDFStfHwiDCAFKQPACnwiECAMVK18IBAgBSkD2AogDiAOIAUpA9AKfCIOVq18IA4gDSAPVq0gBSkD6AogDSASVK18fHwiEiAOVK18fCIOIBBUrXwgCyAMVq0gBSkDmAkgCyATVK18fHwiDSAFKQOACXwiCyAFKQOYCiAOIA4gBSkDkAp8Ig5WrXwgDiAOIAUpA6gLIAUpA7gMIA8gKlatfCIQIAUpA6ALfCIMIBBUrXwgDCAMIBJ8IgxWrXx8Ig5WrXx8IhAgBSkDsAl8IhIgEFStfCASIAUpA8gJIA4gDiAFKQPACXwiDlatfCAOIA4gBSkD2AkgDCAMIAUpA9AJfCIMVq18IAwgBSkD6AkgBSkD4AkiDyAqfCAPVK18fCITIAxUrXx8Ig5WrXx8IgwgElStfCALIBBWrSAFKQOICSALIA1UrXx8fCILQqnAxomuzpOyMFYNAAJAIAtCqcDGia7Ok7IwUQRAIAxC3bCFjOi2kai4f1YNAiAMQt2whYzotpGouH9SBEAgDiEQIAwhEkKpwMaJrs6TsjAhCwwECyAOQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyESIA5CjZXHw5bS2sCXf1ENASAOIRBCqcDGia7Ok7IwIQsMAwsgDiEQIAwhEgwCC0KNlcfDltLawJd/IRAgE0LH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQsMAQsgDkLz6ri86a2lv+gAfCISIBNCx/rzw+2Co5A8VK0iDX0hECAMQqPP+vOXye7XxwB8Ig8gDkKNlcfDltLawJd/VCANIBJWcq0iDn0hEiALIAxC3bCFjOi2kai4f1QgDiAPVnKtfUKpwMaJrs6TsjB9IQsgE0LH+vPD7YKjkDx9IRMLIAVBsAdqICBCACAUQgAQyQMgBUHwB2ogIEIAIBVCABDJAyAFQbAIaiAgQgAgGUIAEMkDIAVB8AhqICBCACAoQgAQyQMgBUGgB2ogBSkDsAciDUIAQgBCiceZpK7wgemHfxDJAyAFQZAHaiAFKQOoByIOQgBCx/rzw+2Co5A8QgAQyQMgBUGAB2ogDkIAQo2Vx8OW0trAl39CABDJAyAFQfAGaiAOQgBC3bCFjOi2kai4f0IAEMkDIAVB4AZqIA5CAEKpwMaJrs6TsjBCABDJAyAFQdAGaiAcQgAgFEIAEMkDIAVB4AdqIBxCACAVQgAQyQMgBUGgCGogHEIAIBlCABDJAyAFQeAIaiAcQgAgKEIAEMkDIAVBwAZqIAUpA4AHIiEgBSkDuAciHCAFKQPwB3wiJnwiDCAFKQOYByANIAUpA5AHIg58IA5UrXx8Ig0gBSkD0AZ8Ig9CAEIAQonHmaSu8IHph38QyQMgBUGwBmogBSkDyAYiDkIAQsf688PtgqOQPEIAEMkDIAVBoAZqIA5CAEKNlcfDltLawJd/QgAQyQMgBUGQBmogDkIAQt2whYzotpGouH9CABDJAyAFQYAGaiAOQgBCqcDGia7Ok7IwQgAQyQMgBUHwBWogIkIAIBRCABDJAyAFQdAHaiAiQgAgFUIAEMkDIAVBkAhqICJCACAZQgAQyQMgBUHQCGogIkIAIChCABDJAyAFQeAFaiAFKQPYBiANIA9WrXwiKSAFKQPgB3wiICAFKQP4ByAcICZWrXwiJiAFKQOwCHwiHCAFKQPwBnwiIiAMIA1WrSAFKQOIByAMICFUrXx8fCIqfCIMIAUpA6AGfCINIAUpA7gGIAUpA7AGIg4gD3wgDlStfHwiDyAFKQPwBXwiIUIAQgBCiceZpK7wgemHfxDJAyAFQdAFaiAFKQPoBSIOQgBCx/rzw+2Co5A8QgAQyQMgBUHABWogDkIAQo2Vx8OW0trAl39CABDJAyAFQbAFaiAOQgBC3bCFjOi2kai4f0IAEMkDIAVBoAVqIA5CAEKpwMaJrs6TsjBCABDJAyAFQZAFaiAfQgAgFEIAEMkDIAVBwAdqIB9CACAVQgAQyQMgBUGACGogH0IAIBlCABDJAyAFQcAIaiAfQgAgKEIAEMkDIAVBgAVqIAUpA/gFIA8gIVatfCIrIAUpA9AHfCIUIAUpA7gIIBwgJlStfCImIAUpA/AIfCIVIAUpA+AGfCIZICIgKlatIAUpA/gGIBwgIlatfHx8IiggBSkDoAh8IhwgDCAgVK0gBSkD6AcgICApVK18fHwiICAFKQOQBnwiIiANIA9WrSAFKQOoBiAMIA1WrXx8fCIpfCIMIAUpA8AFfCINIAUpA9gFIAUpA9AFIg4gIXwgDlStfHwiDyAFKQOQBXwiH0IAQgBCiceZpK7wgemHfxDJAyAFQfAEaiAFKQOIBSIOQgBCx/rzw+2Co5A8QgAQyQMgBUHgBGogDkIAQo2Vx8OW0trAl39CABDJAyAFQdAEaiAOQgBC3bCFjOi2kai4f0IAEMkDIAVBwARqIA5CAEKpwMaJrs6TsjBCABDJAwJAAkAgBSkDyAQgBSkDqAUgBSkDiAYgGSAoVq0gBSkD6AYgFSAZVq18fCAFKQP4CCAVICZUrXx8IiEgBSkD4Ah8Ig4gHCAgVq0gBSkDqAggHCAoVK18fHwiFSAFKQOABnwiGSAVVK18IBkgGSAiIClWrSAFKQOYBiAgICJWrXx8fCIZVq18IA4gFVatIAUpA+gIIA4gIVStfHx8IiggBSkD0Ah8Ig4gBSkDmAggGSAFKQOQCHwiFSAZVK18IBUgDCAUVK0gBSkD2AcgFCArVK18fHwiFCAVVK18fCIVIAUpA6AFfCIZIBVUrXwgGSAFKQO4BSAUIBQgBSkDsAV8IhRWrXwgFCAUIA0gD1atIAUpA8gFIAwgDVatfHx8IhRWrXx8IgwgGVStfCAOIBVWrSAFKQPYCCAOIChUrXx8fCIVIAUpA8AIfCIOIAUpA4gIIAwgDCAFKQOACHwiDFatfCAMIAwgBSkDyAcgBSkDmAUgDyAfVq18Ig8gBSkDwAd8Ig0gD1StfCANIA0gFHwiDVatfHwiDFatfHwiFCAFKQPABHwiDyAUVK18IA8gDyAFKQPYBCAMIAwgBSkD0AR8IgxWrXwgDCAFKQPoBCANIA0gBSkD4AR8Ig1WrXwgDSAFKQP4BCAFKQPwBCIZIB98IBlUrXx8IiggDVStfHwiDSAMVK18fCIPVq18IA4gFFatIAUpA8gIIA4gFVStfHx8IhlCqcDGia7Ok7IwVg0AAkAgGUKpwMaJrs6TsjBRBEAgD0LdsIWM6LaRqLh/Vg0CIA9C3bCFjOi2kai4f1IEQCANIQwgDyEOQqnAxomuzpOyMCEZDAQLIA1CjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQ4gDUKNlcfDltLawJd/UQ0BIA0hDEKpwMaJrs6TsjAhGQwDCyANIQwgDyEODAILQo2Vx8OW0trAl38hDCAoQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhGQwBCyANQvPquLzpraW/6AB8Ig4gKELH+vPD7YKjkDxUrSIUfSEMIA9Co8/685fJ7tfHAHwiFSANQo2Vx8OW0trAl39UIA4gFFRyrSINfSEOIBkgD0LdsIWM6LaRqLh/VCANIBVWcq19QqnAxomuzpOyMH0hGSAoQsf688PtgqOQPH0hKAsgBUHwAmogJUIAIBZCABDJAyAFQbADaiAlQgAgGkIAEMkDIAVB8ANqICVCACAYQgAQyQMgBUGwBGogJUIAICdCABDJAyAFQeACaiAFKQPwAiIUQgBCAEKJx5mkrvCB6Yd/EMkDIAVB0AJqIAUpA+gCIg1CAELH+vPD7YKjkDxCABDJAyAFQcACaiANQgBCjZXHw5bS2sCXf0IAEMkDIAVBsAJqIA1CAELdsIWM6LaRqLh/QgAQyQMgBUGgAmogDUIAQqnAxomuzpOyMEIAEMkDIAVBkAJqICNCACAWQgAQyQMgBUGgA2ogI0IAIBpCABDJAyAFQeADaiAjQgAgGEIAEMkDIAVBoARqICNCACAnQgAQyQMgBUGAAmogBSkDwAIiHCAFKQP4AiIjIAUpA7ADfCIgfCIPIAUpA9gCIBQgBSkD0AIiDXwgDVStfHwiFCAFKQOQAnwiFUIAQgBCiceZpK7wgemHfxDJAyAFQfABaiAFKQOIAiINQgBCx/rzw+2Co5A8QgAQyQMgBUHgAWogDUIAQo2Vx8OW0trAl39CABDJAyAFQdABaiANQgBC3bCFjOi2kai4f0IAEMkDIAVBwAFqIA1CAEKpwMaJrs6TsjBCABDJAyAFQbABaiAdQgAgFkIAEMkDIAVBkANqIB1CACAaQgAQyQMgBUHQA2ogHUIAIBhCABDJAyAFQZAEaiAdQgAgJ0IAEMkDIAVBoAFqIAUpA5gCIBQgFVatfCIiIAUpA6ADfCIlIAUpA7gDICAgI1StfCIfIAUpA/ADfCIjIAUpA7ACfCIgIA8gFFatIAUpA8gCIA8gHFStfHx8Ih18Ig8gBSkD4AF8IhQgBSkD+AEgBSkD8AEiDSAVfCANVK18fCIVIAUpA7ABfCIcQgBCAEKJx5mkrvCB6Yd/EMkDIAVBkAFqIAUpA6gBIg1CAELH+vPD7YKjkDxCABDJAyAFQYABaiANQgBCjZXHw5bS2sCXf0IAEMkDIAVB8ABqIA1CAELdsIWM6LaRqLh/QgAQyQMgBUHgAGogDUIAQqnAxomuzpOyMEIAEMkDIAVB0ABqIB5CACAWQgAQyQMgBUGAA2ogHkIAIBpCABDJAyAFQcADaiAeQgAgGEIAEMkDIAVBgARqIB5CACAnQgAQyQMgBUFAayAFKQO4ASAVIBxWrXwiHiAFKQOQA3wiFiAFKQP4AyAfICNWrXwiHyAFKQOwBHwiGiAFKQOgAnwiGCAdICBUrSAFKQO4AiAgICNUrXx8fCInIAUpA+ADfCIjIA8gJVStIAUpA6gDICIgJVatfHx8IiUgBSkD0AF8IiAgFCAVVq0gBSkD6AEgDyAUVq18fHwiInwiDyAFKQOAAXwiFCAFKQOYASAFKQOQASINIBx8IA1UrXx8IhUgBSkDUHwiHEIAQgBCiceZpK7wgemHfxDJAyAFQTBqIAUpA0giDUIAQsf688PtgqOQPEIAEMkDIAVBIGogDUIAQo2Vx8OW0trAl39CABDJAyAFQRBqIA1CAELdsIWM6LaRqLh/QgAQyQMgBSANQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAUpAwggBSkDaCAFKQPIASAYICdWrSAFKQOoAiAYIBpUrXx8IAUpA7gEIBogH1StfHwiHyAFKQOgBHwiDSAjICVWrSAFKQPoAyAjICdUrXx8fCIaIAUpA8ABfCIYIBpUrXwgGCAYICAgIlatIAUpA9gBICAgJVStfHx8IhhWrXwgDSAaVq0gBSkDqAQgDSAfVK18fHwiJyAFKQOQBHwiDSAFKQPYAyAYIAUpA9ADfCIaIBhUrXwgGiAPIBZUrSAFKQOYAyAWIB5UrXx8fCIWIBpUrXx8IhogBSkDYHwiGCAaVK18IBggBSkDeCAWIBYgBSkDcHwiFlatfCAWIBYgFCAVVq0gBSkDiAEgDyAUVq18fHwiFlatfHwiDyAYVK18IA0gGlatIAUpA5gEIA0gJ1StfHx8IhggBSkDgAR8Ig0gBSkDyAMgDyAPIAUpA8ADfCIPVq18IA8gDyAFKQOIAyAFKQNYIBUgHFatfCIVIAUpA4ADfCIUIBVUrXwgFCAUIBZ8IhRWrXx8Ig9WrXx8IhogBSkDAHwiFSAaVK18IBUgFSAFKQMYIA8gDyAFKQMQfCIPVq18IA8gBSkDKCAUIBQgBSkDIHwiFFatfCAUIAUpAzggBSkDMCIWIBx8IBZUrXx8IhYgFFStfHwiFCAPVK18fCIVVq18IA0gGlatIAUpA4gEIA0gGFStfHx8IhpCqcDGia7Ok7IwVg0AAkAgGkKpwMaJrs6TsjBRBEAgFULdsIWM6LaRqLh/Vg0CIBVC3bCFjOi2kai4f1IEQCAUIQ8gFSENQqnAxomuzpOyMCEaDAQLIBRCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQ0gFEKNlcfDltLawJd/UQ0BIBQhD0KpwMaJrs6TsjAhGgwDCyAUIQ8gFSENDAILQo2Vx8OW0trAl38hDyAWQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhGgwBCyAUQvPquLzpraW/6AB8Ig0gFkLH+vPD7YKjkDxUrSIYfSEPIBVCo8/685fJ7tfHAHwiJyAUQo2Vx8OW0trAl39UIA0gGFRyrSIUfSENIBogFULdsIWM6LaRqLh/VCAUICdWcq19QqnAxomuzpOyMH0hGiAWQsf688PtgqOQPH0hFgsgAUIANwPgAiABQgA3A0AgASAbNwM4IAEgETcDMCABIBc3AyggASAkNwMgIAFCnZu8rNzx0K5TNwMYIAFCvZacro/lurwKNwMQIAFCrIzlw/ftqLfmADcDCCABQq++n9CZ+J2FDjcDACABIBM3A3ggASAQNwNwIAEgEjcDaCABIAs3A2AgAUH4AmpCADcDACABQfACakIANwMAIAFB6AJqQgA3AwAgAUHIAGpCADcDACABQdAAakIANwMAIAFB2ABqQgA3AwAgAUGAAWpBAEHgAPwLACABQgA3A4ACIAEgKDcD+AEgASAMNwPwASABIA43A+gBIAEgGTcD4AEgAUGIAmpCADcDACABQZACakIANwMAIAFBmAJqQgA3AwAgAUIANwPAAiABIBY3A7gCIAEgDzcDsAIgASANNwOoAiABIBo3A6ACIAFByAJqQgA3AwAgAUHQAmpCADcDACABQdgCakIANwMADAQLQdHOxQAtAAAaQYADQQgQ1gQiAUUNAiAJrSAGrUIghoQiDiERAn4CQAJAIA4gJyIXUg0AIBghFyAjIhEgGFINACAaIRcgJSIRIBpSDQAgFiEXIA8iESAWUQ0BCyARIBdaDQBC3bCFjOi2kai4fyAYICN9IhEgGiAlVCAaICV9IgsgDyAWVq0iDFRyrSIXfSIbfSITIAsgDH0iC0KNlcfDltLawJd/VkKNlcfDltLawJd/IAt9IgsgFiAPfSIPQsf688PtgqOQPFatIiVUcq0iJH0hDCATICRUIBtC3bCFjOi2kai4f1ZyIQIgCyAlfSELQsf688PtgqOQPCAPfSEPIBggI1QgESAXVHKtIA4gJ318QqnAxomuzpOyMHwMAQsgJSAafSIRIA8gFlStIgx9IQsgIyAYfSIXIAwgEVYgGiAlVnKtIhF9IQwgESAXViAYICNWciECIA8gFn0hDyAOICd9CyEXIAVBsCxqIAMpAxgiG0IAIA9CABDJAyAFQaAraiAbQgAgC0IAEMkDIAVBkCpqIBtCACAMQgAQyQMgBUHwLGogG0IAIBcgAq19IhFCABDJAyAFQaAsaiAFKQOwLCITQgBCAEKJx5mkrvCB6Yd/EMkDIAVBkCxqIAUpA6gsIg5CAELH+vPD7YKjkDxCABDJAyAFQYAsaiAOQgBCjZXHw5bS2sCXf0IAEMkDIAVB8CtqIA5CAELdsIWM6LaRqLh/QgAQyQMgBUHgK2ogDkIAQqnAxomuzpOyMEIAEMkDIAVB0CtqIAMpAxAiJUIAIA9CABDJAyAFQcAqaiAlQgAgC0IAEMkDIAVBsClqICVCACAMQgAQyQMgBUHgLGogJUIAIBFCABDJAyAFQZAraiAFKQOALCIgIAUpA7gsIiIgBSkDoCt8Ih98IhcgBSkDmCwgEyAFKQOQLCIOfCAOVK18fCITIAUpA9ArfCIkQgBCAEKJx5mkrvCB6Yd/EMkDIAVBgCtqIAUpA5grIg5CAELH+vPD7YKjkDxCABDJAyAFQfAqaiAOQgBCjZXHw5bS2sCXf0IAEMkDIAVB4CpqIA5CAELdsIWM6LaRqLh/QgAQyQMgBUHQKmogDkIAQqnAxomuzpOyMEIAEMkDIAVBwCtqIAMpAwgiI0IAIA9CABDJAyAFQbAqaiAjQgAgC0IAEMkDIAVB0ChqICNCACAMQgAQyQMgBUHQLGogI0IAIBFCABDJAyAFQYAqaiAFKQPYKyATICRWrXwiHiAFKQPAKnwiHCAFKQOoKyAfICJUrXwiISAFKQOQKnwiIiAFKQPwK3wiHyATIBdUrSAFKQOILCAXICBUrXx8fCImfCIXIAUpA/AqfCITIAUpA4grIAUpA4ArIg4gJHwgDlStfHwiJCAFKQPAK3wiHUIAQgBCiceZpK7wgemHfxDJAyAFQfApaiAFKQOIKiIOQgBCx/rzw+2Co5A8QgAQyQMgBUHgKWogDkIAQo2Vx8OW0trAl39CABDJAyAFQdApaiAOQgBC3bCFjOi2kai4f0IAEMkDIAVBwClqIA5CAEKpwMaJrs6TsjBCABDJAyAFQbAraiADKQMAIiBCACAPQgAQyQMgBUGgKmogIEIAIAtCABDJAyAFQcAoaiAgQgAgDEIAEMkDIAVBwCxqICBCACARQgAQyQMgBUGgKWogBSkDyCsgHSAkVK18IikgBSkDsCp8IhEgBSkDmCogISAiVq18IiEgBSkD8Cx8Ig4gBSkD4Ct8IgwgHyAmVq0gBSkD+CsgHyAiVK18fHwiDyAFKQOwKXwiIiAXIBxUrSAFKQPIKiAcIB5UrXx8fCIcIAUpA+AqfCIfIBMgJFatIAUpA/gqIBMgF1StfHx8Ih58IhcgBSkD4Cl8IhMgBSkD+CkgBSkD8CkiCyAdfCALVK18fCIkIAUpA7ArfCIdQgBCAEKJx5mkrvCB6Yd/EMkDIAVBkClqIAUpA6gpIgtCAELH+vPD7YKjkDxCABDJAyAFQYApaiALQgBCjZXHw5bS2sCXf0IAEMkDIAVB8ChqIAtCAELdsIWM6LaRqLh/QgAQyQMgBUHgKGogC0IAQqnAxomuzpOyMEIAEMkDAkACQCAFKQPoKCAFKQPIKSAFKQPYKiAMIA9WrSAFKQPoKyAMIA5UrXx8IAUpA/gsIA4gIVStfHwiISAFKQPgLHwiCyAcICJUrSAFKQO4KSAPICJWrXx8fCIOIAUpA9AqfCIMIA5UrXwgDCAMIB4gH1StIAUpA+gqIBwgH1atfHx8IgxWrXwgCyAOVq0gBSkD6CwgCyAhVK18fHwiDyAFKQPQLHwiCyAFKQPYKCAMIAUpA9AofCIOIAxUrXwgDiARIBdWrSAFKQO4KiARIClUrXx8fCIRIA5UrXx8Ig4gBSkDwCl8IgwgDlStfCAMIAUpA9gpIBEgESAFKQPQKXwiEVatfCARIBMgJFatIAUpA+gpIBMgF1StfHx8IhMgEVStfHwiESAMVK18IAsgDlatIAUpA9gsIAsgD1StfHx8IhwgBSkDwCx8IhcgBSkDyCggESAFKQPAKHwiCyARVK18IAsgCyAFKQOoKiAFKQO4KyAdICRUrXwiDiAFKQOgKnwiESAOVK18IBEgESATfCIRVq18fCILVq18fCIPIAUpA+AofCIMIA9UrXwgDCAMIAUpA/goIAsgCyAFKQPwKHwiC1atfCALIAsgBSkDiCkgESARIAUpA4ApfCIRVq18IBEgBSkDmCkgBSkDkCkiDiAdfCAOVK18fCIOIBFUrXx8IgtWrXx8IgxWrXwgDyAXVK0gBSkDyCwgFyAcVK18fHwiJEKpwMaJrs6TsjBWDQACQCAkQqnAxomuzpOyMFEEQCAMQt2whYzotpGouH9WDQIgDELdsIWM6LaRqLh/UgRAIAshESAMIRdCqcDGia7Ok7IwISQMBAsgC0KNlcfDltLawJd/Vg0CQt2whYzotpGouH8hFyALQo2Vx8OW0trAl39RDQEgCyERQqnAxomuzpOyMCEkDAMLIAshESAMIRcMAgtCjZXHw5bS2sCXfyERIA5Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEkDAELIAtC8+q4vOmtpb/oAHwiFyAOQsf688PtgqOQPFStIg99IREgDEKjz/rzl8nu18cAfCITIAtCjZXHw5bS2sCXf1QgDyAXVnKtIgt9IRcgJCAMQt2whYzotpGouH9UIAsgE1ZyrX1CqcDGia7Ok7IwfSEkIA5Cx/rzw+2Co5A8fSEOCyAIrSAHrUIghoQiDyELAn8CQAJAIA8gKCIMUg0AIBkiDCANIgtSDQAgFSIMIBIiC1INACAUIgwgECILUQ0BCyALIAxaDQBC3bCFjOi2kai4fyAZIA19IhMgFSASfSILIBAgFFatIgxUIBIgFVZyrSISfSIcfSIiIAsgDH0iC0KNlcfDltLawJd/VkKNlcfDltLawJd/IAt9IgwgFCAQfSIQQsf688PtgqOQPFatIh9Ucq0iHX0hCyAMIB99IQwgDSAZViASIBNWcq0gDyAofXxCqcDGia7Ok7IwfCEPQsf688PtgqOQPCAQfSETIB0gIlYgHELdsIWM6LaRqLh/VnIMAQsgEiAVfSILIBAgFFStIhN9IQwgDSAZfSIcIAsgE1QgEiAVVHKtIhJ9IQsgDyAofSEPIBAgFH0hEyANIBlUIBIgHFZyCyECIAVB8CdqIAQpAxgiHEIAIBNCABDJAyAFQeAmaiAcQgAgDEIAEMkDIAVB0CVqIBxCACALQgAQyQMgBUGwKGogHEIAIA8gAq19IhBCABDJAyAFQeAnaiAFKQPwJyIPQgBCAEKJx5mkrvCB6Yd/EMkDIAVB0CdqIAUpA+gnIhJCAELH+vPD7YKjkDxCABDJAyAFQcAnaiASQgBCjZXHw5bS2sCXf0IAEMkDIAVBsCdqIBJCAELdsIWM6LaRqLh/QgAQyQMgBUGgJ2ogEkIAQqnAxomuzpOyMEIAEMkDIAVBkCdqIAQpAxAiIkIAIBNCABDJAyAFQYAmaiAiQgAgDEIAEMkDIAVB8CRqICJCACALQgAQyQMgBUGgKGogIkIAIBBCABDJAyAFQdAmaiAFKQPAJyIpIAUpA/gnIiEgBSkD4CZ8IiZ8Ig0gBSkD2CcgDyAFKQPQJyISfCASVK18fCIPIAUpA5AnfCIdQgBCAEKJx5mkrvCB6Yd/EMkDIAVBwCZqIAUpA9gmIhJCAELH+vPD7YKjkDxCABDJAyAFQbAmaiASQgBCjZXHw5bS2sCXf0IAEMkDIAVBoCZqIBJCAELdsIWM6LaRqLh/QgAQyQMgBUGQJmogEkIAQqnAxomuzpOyMEIAEMkDIAVBgCdqIAQpAwgiH0IAIBNCABDJAyAFQfAlaiAfQgAgDEIAEMkDIAVBkCRqIB9CACALQgAQyQMgBUGQKGogH0IAIBBCABDJAyAFQcAlaiAFKQOYJyAPIB1WrXwiKyAFKQOAJnwiHiAFKQPoJiAhICZWrXwiLCAFKQPQJXwiISAFKQOwJ3wiJiANIA9WrSAFKQPIJyANIClUrXx8fCItfCINIAUpA7AmfCIPIAUpA8gmIAUpA8AmIhIgHXwgElStfHwiKSAFKQOAJ3wiKkIAQgBCiceZpK7wgemHfxDJAyAFQbAlaiAFKQPIJSISQgBCx/rzw+2Co5A8QgAQyQMgBUGgJWogEkIAQo2Vx8OW0trAl39CABDJAyAFQZAlaiASQgBC3bCFjOi2kai4f0IAEMkDIAVBgCVqIBJCAEKpwMaJrs6TsjBCABDJAyAFQfAmaiAEKQMAIh1CACATQgAQyQMgBUHgJWogHUIAIAxCABDJAyAFQYAkaiAdQgAgC0IAEMkDIAVBgChqIB1CACAQQgAQyQMgBUHgJGogBSkDiCcgKSAqVq18Ii4gBSkD8CV8IgwgBSkD2CUgISAsVK18IiwgBSkDsCh8IhAgBSkDoCd8IhIgJiAtVq0gBSkDuCcgISAmVq18fHwiEyAFKQPwJHwiISANIB5UrSAFKQOIJiAeICtUrXx8fCIeIAUpA6AmfCImIA8gKVatIAUpA7gmIA0gD1atfHx8Iit8Ig0gBSkDoCV8Ig8gBSkDuCUgBSkDsCUiCyAqfCALVK18fCIpIAUpA/AmfCIqQgBCAEKJx5mkrvCB6Yd/EMkDIAVB0CRqIAUpA+gkIgtCAELH+vPD7YKjkDxCABDJAyAFQcAkaiALQgBCjZXHw5bS2sCXf0IAEMkDIAVBsCRqIAtCAELdsIWM6LaRqLh/QgAQyQMgBUGgJGogC0IAQqnAxomuzpOyMEIAEMkDAkACQCAFKQOoJCAFKQOIJSAFKQOYJiASIBNWrSAFKQOoJyAQIBJWrXx8IAUpA7goIBAgLFStfHwiLCAFKQOgKHwiCyAeICFUrSAFKQP4JCATICFWrXx8fCIQIAUpA5AmfCISIBBUrXwgEiASICYgK1atIAUpA6gmIB4gJlatfHx8IhJWrXwgCyAQVq0gBSkDqCggCyAsVK18fHwiEyAFKQOQKHwiCyAFKQOYJCASIAUpA5AkfCIQIBJUrXwgECAMIA1WrSAFKQP4JSAMIC5UrXx8fCIMIBBUrXx8IhAgBSkDgCV8IhIgEFStfCASIAUpA5glIAwgDCAFKQOQJXwiDFatfCAMIA8gKVatIAUpA6glIA0gD1atfHx8Ig0gDFStfHwiDCASVK18IAsgEFatIAUpA5goIAsgE1StfHx8Ig8gBSkDgCh8IgsgBSkDiCQgDCAMIAUpA4AkfCIMVq18IAwgDCAFKQPoJSAFKQP4JiApICpWrXwiEiAFKQPgJXwiECASVK18IBAgDSAQfCIQVq18fCIMVq18fCISIAUpA6AkfCINIBJUrXwgDSANIAUpA7gkIAwgDCAFKQOwJHwiDFatfCAMIAwgBSkDyCQgECAQIAUpA8AkfCIQVq18IBAgBSkD2CQgBSkD0CQiEyAqfCATVK18fCITIBBUrXx8IgxWrXx8Ig1WrXwgCyASVq0gBSkDiCggCyAPVK18fHwiC0KpwMaJrs6TsjBWDQACQCALQqnAxomuzpOyMFEEQCANQt2whYzotpGouH9WDQIgDULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCELCyANIRAgDCESDAILIAxCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IRAgDEKNlcfDltLawJd/UgRAQqnAxomuzpOyMCELIAwhEgwCC0KNlcfDltLawJd/IRIgE0LH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQsMAQsgDELz6ri86a2lv+gAfCIQIBNCx/rzw+2Co5A8VK0iD30hEiANQqPP+vOXye7XxwB8Ih4gDEKNlcfDltLawJd/VCAPIBBWcq0iDH0hECALIA1C3bCFjOi2kai4f1QgDCAeVnKtfUKpwMaJrs6TsjB9IQsgE0LH+vPD7YKjkDx9IRMLIAVB8CNqIBtCACAWQgAQyQMgBUHgImogG0IAIBpCABDJAyAFQdAhaiAbQgAgGEIAEMkDIAVBwCBqIBtCACAnQgAQyQMgBUHgI2ogBSkD8CMiD0IAQgBCiceZpK7wgemHfxDJAyAFQdAjaiAFKQPoIyIMQgBCx/rzw+2Co5A8QgAQyQMgBUHAI2ogDEIAQo2Vx8OW0trAl39CABDJAyAFQbAjaiAMQgBC3bCFjOi2kai4f0IAEMkDIAVBoCNqIAxCAEKpwMaJrs6TsjBCABDJAyAFQZAjaiAlQgAgFkIAEMkDIAVBgCJqICVCACAaQgAQyQMgBUHwIGogJUIAIBhCABDJAyAFQeAfaiAlQgAgJ0IAEMkDIAVB0CJqIAUpA8AjIiEgBSkD+CMiHiAFKQPgInwiJnwiDSAFKQPYIyAPIAUpA9AjIgx8IAxUrXx8Ig8gBSkDkCN8IhtCAEIAQonHmaSu8IHph38QyQMgBUHAImogBSkD2CIiDEIAQsf688PtgqOQPEIAEMkDIAVBsCJqIAxCAEKNlcfDltLawJd/QgAQyQMgBUGgImogDEIAQt2whYzotpGouH9CABDJAyAFQZAiaiAMQgBCqcDGia7Ok7IwQgAQyQMgBUGAI2ogI0IAIBZCABDJAyAFQfAhaiAjQgAgGkIAEMkDIAVB4CBqICNCACAYQgAQyQMgBUHQH2ogI0IAICdCABDJAyAFQcAhaiAFKQOYIyAPIBtWrXwiKSAFKQOAInwiJSAFKQPoIiAeICZWrXwiJiAFKQPQIXwiIyAFKQOwI3wiHiANIA9WrSAFKQPIIyANICFUrXx8fCIqfCINIAUpA7AifCIPIAUpA8giIAUpA8AiIgwgG3wgDFStfHwiGyAFKQOAI3wiIUIAQgBCiceZpK7wgemHfxDJAyAFQbAhaiAFKQPIISIMQgBCx/rzw+2Co5A8QgAQyQMgBUGgIWogDEIAQo2Vx8OW0trAl39CABDJAyAFQZAhaiAMQgBC3bCFjOi2kai4f0IAEMkDIAVBgCFqIAxCAEKpwMaJrs6TsjBCABDJAyAFQfAiaiAgQgAgFkIAEMkDIAVB4CFqICBCACAaQgAQyQMgBUHQIGogIEIAIBhCABDJAyAFQcAfaiAgQgAgJ0IAEMkDIAVBsCBqIAUpA4gjIBsgIVatfCIrIAUpA/AhfCIWIAUpA9ghICMgJlStfCImIAUpA8AgfCIaIAUpA6AjfCIYIB4gKlatIAUpA7gjIB4gI1StfHx8IicgBSkD8CB8IiMgDSAlVK0gBSkDiCIgJSApVK18fHwiJSAFKQOgInwiICAPIBtWrSAFKQO4IiANIA9WrXx8fCIpfCINIAUpA6AhfCIPIAUpA7ghIAUpA7AhIgwgIXwgDFStfHwiGyAFKQPwInwiHkIAQgBCiceZpK7wgemHfxDJAyAFQaAgaiAFKQO4ICIMQgBCx/rzw+2Co5A8QgAQyQMgBUGQIGogDEIAQo2Vx8OW0trAl39CABDJAyAFQYAgaiAMQgBC3bCFjOi2kai4f0IAEMkDIAVB8B9qIAxCAEKpwMaJrs6TsjBCABDJAwJAAkAgBSkD+B8gBSkDiCEgBSkDmCIgGCAnVq0gBSkDqCMgGCAaVK18fCAFKQPIICAaICZUrXx8IiEgBSkD4B98IgwgIyAlVq0gBSkD+CAgIyAnVK18fHwiGiAFKQOQInwiGCAaVK18IBggGCAgIClWrSAFKQOoIiAgICVUrXx8fCIYVq18IAwgGlatIAUpA+gfIAwgIVStfHx8IicgBSkD0B98IgwgBSkD6CAgGCAFKQPgIHwiGiAYVK18IBogDSAWVK0gBSkD+CEgFiArVK18fHwiFiAaVK18fCIaIAUpA4AhfCIYIBpUrXwgGCAFKQOYISAWIBYgBSkDkCF8IhZWrXwgFiAWIA8gG1atIAUpA6ghIA0gD1atfHx8IhZWrXx8Ig0gGFStfCAMIBpWrSAFKQPYHyAMICdUrXx8fCIYIAUpA8AffCIMIAUpA9ggIA0gDSAFKQPQIHwiDVatfCANIA0gBSkD6CEgBSkD+CIgGyAeVq18IhsgBSkD4CF8Ig8gG1StfCAPIA8gFnwiD1atfHwiDVatfHwiGyAFKQPwH3wiFiAbVK18IBYgFiAFKQOIICANIA0gBSkDgCB8Ig1WrXwgDSANIAUpA5ggIA8gDyAFKQOQIHwiD1atfCAPIAUpA6ggIAUpA6AgIhogHnwgGlStfHwiGiAPVK18fCINVq18fCIWVq18IAwgG1atIAUpA8gfIAwgGFStfHx8Ig9CqcDGia7Ok7IwVg0AAkAgD0KpwMaJrs6TsjBRBEAgFkLdsIWM6LaRqLh/Vg0CIBZC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhDwsgFiEMIA0hGwwCCyANQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEMIA1CjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhDyANIRsMAgtCjZXHw5bS2sCXfyEbIBpCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEPDAELIA1C8+q4vOmtpb/oAHwiDCAaQsf688PtgqOQPFStIhh9IRsgFkKjz/rzl8nu18cAfCInIA1CjZXHw5bS2sCXf1QgDCAYVHKtIg19IQwgDyAWQt2whYzotpGouH9UIA0gJ1ZyrX1CqcDGia7Ok7IwfSEPIBpCx/rzw+2Co5A8fSEaCyAFQbAfaiAcQgAgFEIAEMkDIAVBoB5qIBxCACAVQgAQyQMgBUGQHWogHEIAIBlCABDJAyAFQYAcaiAcQgAgKEIAEMkDIAVBoB9qIAUpA7AfIhhCAEIAQonHmaSu8IHph38QyQMgBUGQH2ogBSkDqB8iDUIAQsf688PtgqOQPEIAEMkDIAVBgB9qIA1CAEKNlcfDltLawJd/QgAQyQMgBUHwHmogDUIAQt2whYzotpGouH9CABDJAyAFQeAeaiANQgBCqcDGia7Ok7IwQgAQyQMgBUHQHmogIkIAIBRCABDJAyAFQcAdaiAiQgAgFUIAEMkDIAVBsBxqICJCACAZQgAQyQMgBUGgG2ogIkIAIChCABDJAyAFQZAeaiAFKQOAHyIcIAUpA7gfIiMgBSkDoB58IiB8IhYgBSkDmB8gGCAFKQOQHyINfCANVK18fCIYIAUpA9AefCInQgBCAEKJx5mkrvCB6Yd/EMkDIAVBgB5qIAUpA5geIg1CAELH+vPD7YKjkDxCABDJAyAFQfAdaiANQgBCjZXHw5bS2sCXf0IAEMkDIAVB4B1qIA1CAELdsIWM6LaRqLh/QgAQyQMgBUHQHWogDUIAQqnAxomuzpOyMEIAEMkDIAVBwB5qIB9CACAUQgAQyQMgBUGwHWogH0IAIBVCABDJAyAFQaAcaiAfQgAgGUIAEMkDIAVBkBtqIB9CACAoQgAQyQMgBUGAHWogBSkD2B4gGCAnVq18IiIgBSkDwB18IiUgBSkDqB4gICAjVK18Ih8gBSkDkB18IiMgBSkD8B58IiAgFiAYVq0gBSkDiB8gFiAcVK18fHwiHnwiFiAFKQPwHXwiGCAFKQOIHiAFKQOAHiINICd8IA1UrXx8IicgBSkDwB58IhxCAEIAQonHmaSu8IHph38QyQMgBUHwHGogBSkDiB0iDUIAQsf688PtgqOQPEIAEMkDIAVB4BxqIA1CAEKNlcfDltLawJd/QgAQyQMgBUHQHGogDUIAQt2whYzotpGouH9CABDJAyAFQcAcaiANQgBCqcDGia7Ok7IwQgAQyQMgBUGwHmogHUIAIBRCABDJAyAFQaAdaiAdQgAgFUIAEMkDIAVBkBxqIB1CACAZQgAQyQMgBUGAG2ogHUIAIChCABDJAyAFQfAbaiAFKQPIHiAcICdUrXwiHSAFKQOwHXwiFCAFKQOYHSAfICNWrXwiHyAFKQOAHHwiFSAFKQPgHnwiGSAeICBUrSAFKQP4HiAgICNUrXx8fCIoIAUpA7AcfCIjIBYgJVStIAUpA8gdICIgJVatfHx8IiUgBSkD4B18IiAgGCAnVq0gBSkD+B0gFiAYVq18fHwiInwiFiAFKQPgHHwiGCAFKQP4HCAFKQPwHCINIBx8IA1UrXx8IicgBSkDsB58IhxCAEIAQonHmaSu8IHph38QyQMgBUHgG2ogBSkD+BsiDUIAQsf688PtgqOQPEIAEMkDIAVB0BtqIA1CAEKNlcfDltLawJd/QgAQyQMgBUHAG2ogDUIAQt2whYzotpGouH9CABDJAyAFQbAbaiANQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAUpA7gbIAUpA8gcIAUpA9gdIBkgKFatIAUpA+geIBUgGVatfHwgBSkDiBwgFSAfVK18fCIfIAUpA6AbfCINICMgJVatIAUpA7gcICMgKFStfHx8IhUgBSkD0B18IhkgFVStfCAZIBkgICAiVq0gBSkD6B0gICAlVK18fHwiGVatfCANIBVWrSAFKQOoGyANIB9UrXx8fCIoIAUpA5AbfCINIAUpA6gcIBkgBSkDoBx8IhUgGVStfCAVIBQgFlatIAUpA7gdIBQgHVStfHx8IhQgFVStfHwiFSAFKQPAHHwiGSAVVK18IBkgBSkD2BwgFCAUIAUpA9AcfCIUVq18IBQgGCAnVq0gBSkD6BwgFiAYVq18fHwiFiAUVK18fCIUIBlUrXwgDSAVVq0gBSkDmBsgDSAoVK18fHwiGCAFKQOAG3wiDSAFKQOYHCAUIBQgBSkDkBx8IhRWrXwgFCAUIAUpA6gdIAUpA7geIBwgJ1StfCIZIAUpA6AdfCIVIBlUrXwgFSAVIBZ8IhVWrXx8IhRWrXx8IhkgBSkDsBt8IhYgGVStfCAWIAUpA8gbIBQgFCAFKQPAG3wiFFatfCAUIBQgBSkD2BsgFSAVIAUpA9AbfCIVVq18IBUgBSkD6BsgBSkD4BsiKCAcfCAoVK18fCIoIBVUrXx8IhRWrXx8IhUgFlStfCANIBlWrSAFKQOIGyANIBhUrXx8fCIWQqnAxomuzpOyMFYNAAJAIBZCqcDGia7Ok7IwUQRAIBVC3bCFjOi2kai4f1YNAiAVQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRYLIBUhGSAUIQ0MAgsgFEKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hGSAUQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRYgFCENDAILQo2Vx8OW0trAl38hDSAoQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhFgwBCyAUQvPquLzpraW/6AB8IhkgKELH+vPD7YKjkDxUrSIYfSENIBVCo8/685fJ7tfHAHwiJyAUQo2Vx8OW0trAl39UIBggGVZyrSIUfSEZIBYgFULdsIWM6LaRqLh/VCAUICdWcq19QqnAxomuzpOyMH0hFiAoQsf688PtgqOQPH0hKAsgAUIANwPgAiABQgA3AyAgASAONwMYIAEgETcDECABIBc3AwggASAkNwMAIAFCnZu8rNzx0K5TNwN4IAFCvZacro/lurwKNwNwIAFCrIzlw/ftqLfmADcDaCABQq++n9CZ+J2FDjcDYCABIBM3A1ggASASNwNQIAEgEDcDSCABIAs3A0AgAUH4AmpCADcDACABQfACakIANwMAIAFB6AJqQgA3AwAgAUEoakIANwMAIAFBMGpCADcDACABQThqQgA3AwAgAUG4AWpCADcDACABQbABakIANwMAIAFBqAFqQgA3AwAgAUGgAWpCADcDACABQZgBakIANwMAIAFBkAFqQgA3AwAgAUGIAWpCADcDACABQgA3A4ABIAEgGjcD2AEgASAbNwPQASABIAw3A8gBIAEgDzcDwAEgAUIANwPgASABQegBakIANwMAIAFB8AFqQgA3AwAgAUH4AWpCADcDACABICg3A5gCIAEgDTcDkAIgASAZNwOIAiABIBY3A4ACIAFB2AJqQgA3AwAgAUHQAmpCADcDACABQcgCakIANwMAIAFBwAJqQgA3AwAgAUG4AmpCADcDACABQbACakIANwMAIAFBqAJqQgA3AwAgAUIANwOgAgwDCyAFIAc2AswyIAUgATYCyDIgBSAGNgLEMgwECyAFIAY2AswyIAUgATYCyDIgBSACNgLEMgwDC0EIQYADEP8EAAtBDCECAkACfyABQeACakHYw8IAQSAQ8QMEQEELIQRBDAwBCyABQcACakHYw8IAQSAQ8QMEQEEKIQRBCwwBCyABQaACakHYw8IAQSAQ8QMEQEEJIQRBCgwBCyABQYACakHYw8IAQSAQ8QMEQEEIIQRBCQwBCyABQeABakHYw8IAQSAQ8QMEQEEHIQRBCAwBCyABQcABakHYw8IAQSAQ8QMEQEEGIQRBBwwBCyABQaABakHYw8IAQSAQ8QMEQEEFIQRBBgwBCyABQYABakHYw8IAQSAQ8QMEQEEEIQRBBQwBCyABQeAAakHYw8IAQSAQ8QMEQEEDIQRBBAwBCyABQUBrQdjDwgBBIBDxAwRAQQIhBEEDDAELIAFBIGpB2MPCAEEgEPEDBEBBASEEQQIMAQsgAUHYw8IAQSAQ8QMEQEEAIQRBAQwBC0HRzsUALQAAGkEgQQgQ1gQiAkUNASACQgA3AwAgAkEYakIANwMAIAJBEGpCADcDACACQQhqQgA3AwAgAUGAAxDfBEF/IQQgAiEBQQEhAkEBCyEDIAAgBDYCDCAAIAM2AgggACABNgIEIAAgAjYCACAFQdAyaiQADwtBCEEgEP8EAAtBCEGAAxD/BAALQYCLwABBKyAFQcQyakHwisAAQaSNwAAQygMAC4ezAQIHfxN+IwBBsDFrIgMkACADIAI2AswrIANBDDYCyCsCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIAJBDEYEQCADQdArahAhIANBgCtqIAMpA/AtIgpCAEKJ9auctYu/lnNCABDJAyADQfAqaiADKQOAKyINQgBCAEKJx5mkrvCB6Yd/EMkDIANB4CpqIAMpA/gqIgtCAELH+vPD7YKjkDxCABDJAyADQdAqaiALQgBCjZXHw5bS2sCXf0IAEMkDIANB8ClqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0GQKWogC0IAQqnAxomuzpOyMEIAEMkDIANBkCtqIApCAEL7g5SinaLG87V/QgAQyQMgA0HAKmogAykD0CoiDyADKQOIK3wiEiADKQPoKiANIAMpA+AqIgt8IAtUrXx8Ig0gAykDkCt8Ig5CAEIAQonHmaSu8IHph38QyQMgA0GwKmogAykDyCoiC0IAQsf688PtgqOQPEIAEMkDIANBoCpqIAtCAEKNlcfDltLawJd/QgAQyQMgA0GQKmogC0IAQt2whYzotpGouH9CABDJAyADQYAqaiALQgBCqcDGia7Ok7IwQgAQyQMgA0GgK2ogCkIAQvb/hdLw38fVxwBCABDJAyADQeApaiADKQOgKiIRIAMpA5grIA0gDlatfCIMIA0gElStIAMpA9gqIA8gElatfHwiDyADKQPwKXwiFHwiF3wiEiADKQO4KiADKQOwKiILIA58IAtUrXx8Ig0gAykDoCt8Ig5CAEIAQonHmaSu8IHph38QyQMgA0HQKWogAykD6CkiC0IAQsf688PtgqOQPEIAEMkDIANBwClqIAtCAEKNlcfDltLawJd/QgAQyQMgA0GwKWogC0IAQt2whYzotpGouH9CABDJAyADQaApaiALQgBCqcDGia7Ok7IwQgAQyQMgA0GwK2ogCkIAQp/q4NWc7qfsBkIAEMkDIANBgClqIAMpA8ApIhAgDCAXVq0iDCADKQP4KSAPIBRWrXwiFCADKQOQKXwiF3wiCyADKQOQKnwiDyANIBJUrSADKQOoKiARIBJWrXx8fCISIAMpA6grIA0gDlatfHwiE3wiDSADKQPYKSADKQPQKSIKIA58IApUrXx8Ig4gAykDsCt8IhFCAEIAQonHmaSu8IHph38QyQMgA0HwKGogAykDiCkiCkIAQsf688PtgqOQPEIAEMkDIANB4ChqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQKGogCkIAQt2whYzotpGouH9CABDJAyADQcAoaiAKQgBCqcDGia7Ok7IwQgAQyQMCQCADKQPIKCADKQOoKSADKQOIKiADKQOAKiIWIAMpA5gpIBQgF1atfHwiCiAWVK18IAogCiALIAxUrXwiDFatfCAMIAwgDyASVq0gAykDmCogCyAPVq18fHwiClatfCIPIAMpA6ApfCILIA9UrXwgCyALIAogCiASIBNWrXwiElatfCIKVq18IAogCiADKQO4KSASIBIgAykDsCl8IgtWrXwgCyALIA0gDlatIAMpA8gpIA0gEFStfHx8IhJWrXx8IgtWrXwiDSADKQPAKHwiCiANVK18IAogCyALIBIgAykDuCsgDiARVq18fCIOIBJUrXwiC1atfCISIApUrXwgEiADKQPYKCALIAsgAykD0Ch8Ig1WrXwgDSANIAMpA+goIA4gAykD4CgiC3wiCiALVK18IAogAykD+CggAykD8CgiCyARfCALVK18fCIRIApUrXx8IgpWrXx8IhQgElStfCIXQqnAxomuzpOyMFQEQCAKIRIMAQsCQCAUQt2whYzotpGouH9WDQAgFELdsIWM6LaRqLh/UgRAIAohEkKpwMaJrs6TsjAhFwwCCyAKQo2Vx8OW0trAl39WDQACQCAKQo2Vx8OW0trAl39SBEAgCiESDAELQo2Vx8OW0trAl38hEiARQsf688PtgqOQPFoNAQtC3bCFjOi2kai4fyEUQqnAxomuzpOyMCEXDAELIApC8+q4vOmtpb/oAHwiCyARQsf688PtgqOQPFStIg19IRIgFEKjz/rzl8nu18cAfCIOIApCjZXHw5bS2sCXf1QgCyANVHKtIgp9IRQgFyAKIA5WrX1CqcDGia7Ok7IwfSEXIBFCx/rzw+2Co5A8fSERCyADKAL8LyIFBEAgAygCgDAgBUECdBDfBAsCQCADKAK0LSIFRQ0AIAUgBUEMbEETakF4cSIEakEJaiIFRQ0AIAMoArAtIARrIAUQ3wQLIAMoAuAtIgVBgICAgHhGIAVFckUEQCADKALkLSAFQQJ0EN8ECwJAAkACQAJAIAMoAsgrQQJrDgsBAAAAAgAAAAAAAwALIANBADYC4CsgA0EBNgLUKyADQYiJwAA2AtArIANCBDcC2CsgA0HQK2pBkInAABCoBAALIAJB////P0sgAkEFdCIHQfj///8HS3INAyAHRQRAQQghBEEAIQIMFwtB0c7FAC0AABpBCCEGIAdBCBDWBCIERQ0DIAJFBEBBACECDBcLQQAhBiACIQUDQCAGIAdGDRcgBCAGaiIIIAEgBmoiCSkDADcDACAIQRhqIAlBGGopAwA3AwAgCEEQaiAJQRBqKQMANwMAIAhBCGogCUEIaikDADcDACAGQSBqIQYgBUEBayIFDQALDBYLQdHOxQAtAAAaQcABQQgQ1gQiBEUNFCADKALMKyICRQ0DIAJBAUYNBCADQbANaiABKQM4IgpCACARQgAQyQMgA0GgDGogCkIAIBJCABDJAyADQZALaiAKQgAgFEIAEMkDIANBgApqIApCACAXQgAQyQMgA0GgDWogAykDsA0iDUIAQgBCiceZpK7wgemHfxDJAyADQZANaiADKQOoDSIKQgBCx/rzw+2Co5A8QgAQyQMgA0GADWogCkIAQo2Vx8OW0trAl39CABDJAyADQfAMaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4AxqIApCAEKpwMaJrs6TsjBCABDJAyADQdAMaiABKQMwIgpCACARQgAQyQMgA0HAC2ogCkIAIBJCABDJAyADQbAKaiAKQgAgFEIAEMkDIANBoAlqIApCACAXQgAQyQMgA0GQDGogAykDgA0iEyADKQO4DSIMIAMpA6AMfCIQfCILIAMpA5gNIA0gAykDkA0iCnwgClStfHwiDSADKQPQDHwiDkIAQgBCiceZpK7wgemHfxDJAyADQYAMaiADKQOYDCIKQgBCx/rzw+2Co5A8QgAQyQMgA0HwC2ogCkIAQo2Vx8OW0trAl39CABDJAyADQeALaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB0AtqIApCAEKpwMaJrs6TsjBCABDJAyADQcAMaiABKQMoIgpCACARQgAQyQMgA0GwC2ogCkIAIBJCABDJAyADQaAKaiAKQgAgFEIAEMkDIANBkAlqIApCACAXQgAQyQMgA0GAC2ogAykD2AwgDSAOVq18IhggAykDwAt8Ig8gAykDqAwgDCAQVq18IhUgAykDkAt8IgwgAykD8Ax8IhAgCyANVq0gAykDiA0gCyATVK18fHwiGXwiCyADKQPwC3wiDSADKQOIDCADKQOADCIKIA58IApUrXx8Ig4gAykDwAx8IhNCAEIAQonHmaSu8IHph38QyQMgA0HwCmogAykDiAsiCkIAQsf688PtgqOQPEIAEMkDIANB4ApqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQCmogCkIAQt2whYzotpGouH9CABDJAyADQcAKaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GwDGogASkDICIKQgAgEUIAEMkDIANBoAtqIApCACASQgAQyQMgA0GQCmogCkIAIBRCABDJAyADQYAJaiAKQgAgF0IAEMkDIANB8AlqIAMpA8gMIA4gE1atfCIbIAMpA7ALfCIWIAMpA5gLIAwgFVStfCIcIAMpA4AKfCIVIAMpA+AMfCIaIBAgGVatIAMpA/gMIAwgEFatfHx8IgwgAykDsAp8IhAgCyAPVK0gAykDyAsgDyAYVK18fHwiDyADKQPgC3wiGCANIA5WrSADKQP4CyALIA1WrXx8fCIZfCILIAMpA+AKfCINIAMpA/gKIAMpA/AKIgogE3wgClStfHwiDiADKQOwDHwiE0IAQgBCiceZpK7wgemHfxDJAyADQeAJaiADKQP4CSIKQgBCx/rzw+2Co5A8QgAQyQMgA0HQCWogCkIAQo2Vx8OW0trAl39CABDJAyADQcAJaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBsAlqIApCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDuAkgAykDyAogAykD2AsgDCAaVK0gAykD6AwgFSAaVq18fCADKQOICiAVIBxUrXx8IhUgAykDoAl8IgogDyAQVK0gAykDuAogDCAQVq18fHwiDCADKQPQC3wiECAMVK18IBAgGCAZVq0gAykD6AsgDyAYVq18fHwiDyAQVK18IAogDFatIAMpA6gJIAogFVStfHx8IhUgAykDkAl8IgogAykDqAogDyAPIAMpA6AKfCIMVq18IAwgDCALIBZUrSADKQO4CyAWIBtUrXx8fCIPVq18fCIMIAMpA8AKfCIQIAxUrXwgECADKQPYCiAPIA8gAykD0Ap8IhZWrXwgFiAWIA0gDlatIAMpA+gKIAsgDVatfHx8Ig9WrXx8IgsgEFStfCAKIAxWrSADKQOYCSAKIBVUrXx8fCIWIAMpA4AJfCIKIAMpA5gKIAsgCyADKQOQCnwiDVatfCANIA0gAykDqAsgAykDuAwgDiATVq18Ig4gAykDoAt8IgsgDlStfCALIAsgD3wiDlatfHwiC1atfHwiDCADKQOwCXwiECAMVK18IBAgECADKQPICSALIAsgAykDwAl8Ig9WrXwgDyADKQPYCSAOIA4gAykD0Al8IgtWrXwgCyALIAMpA+gJIAMpA+AJIg0gE3wgDVStfHwiDVatfHwiDiAPVK18fCIPVq18IAogDFatIAMpA4gJIAogFlStfHx8IgxCqcDGia7Ok7IwVg0AAkAgDEKpwMaJrs6TsjBRBEAgD0LdsIWM6LaRqLh/Vg0CIA9C3bCFjOi2kai4f1IEQCAOIQogDyELQqnAxomuzpOyMCEMDAQLIA5CjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQsgDkKNlcfDltLawJd/UQ0BIA4hCkKpwMaJrs6TsjAhDAwDCyAOIQogDyELDAILQo2Vx8OW0trAl38hCiANQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhDAwBCyAOQvPquLzpraW/6AB8IgsgDULH+vPD7YKjkDxUrSIQfSEKIA9Co8/685fJ7tfHAHwiEyAOQo2Vx8OW0trAl39UIAsgEFRyrSIOfSELIAwgD0LdsIWM6LaRqLh/VCAOIBNWcq19QqnAxomuzpOyMH0hDCANQsf688PtgqOQPH0hDQsgAyANNwPoKyADIAo3A+ArIAMgCzcD2CsgAyAMNwPQKyADQfAwaiABIANB0CtqEMICIAMoAswrIgJBAk0NBSACQQNGDQYgA0GACGogASkDeCIKQgAgEUIAEMkDIANBkAhqIApCACASQgAQyQMgA0GgCGogCkIAIBRCABDJAyADQbAIaiAKQgAgF0IAEMkDIANB8AdqIAMpA4AIIg1CAEIAQonHmaSu8IHph38QyQMgA0HgB2ogAykD+AciCkIAQsf688PtgqOQPEIAEMkDIANB0AdqIApCAEKNlcfDltLawJd/QgAQyQMgA0HAB2ogCkIAQt2whYzotpGouH9CABDJAyADQbAHaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwBmogASkDcCIKQgAgEUIAEMkDIANBgAdqIApCACASQgAQyQMgA0GQB2ogCkIAIBRCABDJAyADQaAHaiAKQgAgF0IAEMkDIANB4AZqIAMpA9AHIhMgAykDiAgiDCADKQOQCHwiEHwiCyADKQPoByANIAMpA+AHIgp8IApUrXx8Ig0gAykD8AZ8Ig5CAEIAQonHmaSu8IHph38QyQMgA0HQBmogAykD6AYiCkIAQsf688PtgqOQPEIAEMkDIANBwAZqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwBmogCkIAQt2whYzotpGouH9CABDJAyADQaAGaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HgBWogASkDaCIKQgAgEUIAEMkDIANB8AVqIApCACASQgAQyQMgA0GABmogCkIAIBRCABDJAyADQZAGaiAKQgAgF0IAEMkDIANB0AVqIAMpA/gGIA0gDlatfCIYIAMpA4AHfCIPIAMpA5gIIAwgEFatfCIVIAMpA6AIfCIMIAMpA8AHfCIQIAsgDVatIAMpA9gHIAsgE1StfHx8Ihl8IgsgAykDwAZ8Ig0gAykD2AYgAykD0AYiCiAOfCAKVK18fCIOIAMpA+AFfCITQgBCAEKJx5mkrvCB6Yd/EMkDIANBwAVqIAMpA9gFIgpCAELH+vPD7YKjkDxCABDJAyADQbAFaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0ARqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HABGogCkIAQqnAxomuzpOyMEIAEMkDIANBwAhqIAEpA2AiCkIAIBFCABDJAyADQdAIaiAKQgAgEkIAEMkDIANB4AhqIApCACAUQgAQyQMgA0HwCGogCkIAIBdCABDJAyADQaAFaiADKQPoBSAOIBNWrXwiGyADKQPwBXwiFiADKQOoCCAMIBVUrXwiHCADKQOwCHwiFSADKQOwB3wiGiAQIBlWrSADKQPIByAMIBBWrXx8fCIMIAMpA5AHfCIQIAsgD1StIAMpA4gHIA8gGFStfHx8Ig8gAykDsAZ8IhggDSAOVq0gAykDyAYgCyANVq18fHwiGXwiCyADKQOwBXwiDSADKQPIBSADKQPABSIKIBN8IApUrXx8Ig4gAykDwAh8IhNCAEIAQonHmaSu8IHph38QyQMgA0GQBWogAykDqAUiCkIAQsf688PtgqOQPEIAEMkDIANBgAVqIApCAEKNlcfDltLawJd/QgAQyQMgA0HwBGogCkIAQt2whYzotpGouH9CABDJAyADQeAEaiAKQgBCqcDGia7Ok7IwQgAQyQMgAUFAayECAkACQCADKQPoBCADKQPIBCADKQOoBiAMIBpUrSADKQO4ByAVIBpWrXx8IAMpA7gIIBUgHFStfHwiFSADKQOgB3wiCiAPIBBUrSADKQOYByAMIBBWrXx8fCIMIAMpA6AGfCIQIAxUrXwgECAYIBlWrSADKQO4BiAPIBhWrXx8fCIPIBBUrXwgCiAMVq0gAykDqAcgCiAVVK18fHwiFSADKQOQBnwiCiADKQOIBiAPIA8gAykDgAZ8IgxWrXwgDCAMIAsgFlStIAMpA/gFIBYgG1StfHx8Ig9WrXx8IgwgAykDwAR8IhAgDFStfCAQIAMpA9gEIA8gDyADKQPQBHwiFlatfCAWIBYgDSAOVq0gAykDuAUgCyANVq18fHwiD1atfHwiCyAQVK18IAogDFatIAMpA5gGIAogFVStfHx8IhYgAykD8Ah8IgogAykD6AggCyALIAMpA+AIfCINVq18IA0gDSADKQPYCCADKQPICCAOIBNWrXwiDiADKQPQCHwiCyAOVK18IAsgCyAPfCIOVq18fCILVq18fCIMIAMpA+AEfCIQIAxUrXwgECAQIAMpA/gEIAsgCyADKQPwBHwiD1atfCAPIAMpA4gFIA4gDiADKQOABXwiC1atfCALIAsgAykDmAUgAykDkAUiDSATfCANVK18fCINVq18fCIOIA9UrXx8Ig9WrXwgCiAMVq0gAykD+AggCiAWVK18fHwiDEKpwMaJrs6TsjBWDQACQCAMQqnAxomuzpOyMFEEQCAPQt2whYzotpGouH9WDQIgD0LdsIWM6LaRqLh/UgRAIA4hCiAPIQtCqcDGia7Ok7IwIQwMBAsgDkKNlcfDltLawJd/Vg0CQt2whYzotpGouH8hCyAOQo2Vx8OW0trAl39RDQEgDiEKQqnAxomuzpOyMCEMDAMLIA4hCiAPIQsMAgtCjZXHw5bS2sCXfyEKIA1Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEMDAELIA5C8+q4vOmtpb/oAHwiCyANQsf688PtgqOQPFStIhB9IQogD0Kjz/rzl8nu18cAfCITIA5CjZXHw5bS2sCXf1QgCyAQVHKtIg59IQsgDCAPQt2whYzotpGouH9UIA4gE1ZyrX1CqcDGia7Ok7IwfSEMIA1Cx/rzw+2Co5A8fSENCyADIA03A+grIAMgCjcD4CsgAyALNwPYKyADIAw3A9ArIANBkDFqIAIgA0HQK2oQwgIgAygCzCsiAkEETQ0HIAJBBUcEQCABQSBqIQIgAUHgAGohBSADQcADaiABKQO4ASIKQgAgEUIAEMkDIANB0ANqIApCACASQgAQyQMgA0HgA2ogCkIAIBRCABDJAyADQfADaiAKQgAgF0IAEMkDIANBsANqIAMpA8ADIg1CAEIAQonHmaSu8IHph38QyQMgA0GgA2ogAykDuAMiCkIAQsf688PtgqOQPEIAEMkDIANBkANqIApCAEKNlcfDltLawJd/QgAQyQMgA0GAA2ogCkIAQt2whYzotpGouH9CABDJAyADQfACaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GwAmogASkDsAEiCkIAIBFCABDJAyADQcACaiAKQgAgEkIAEMkDIANB0AJqIApCACAUQgAQyQMgA0HgAmogCkIAIBdCABDJAyADQaACaiADKQOQAyITIAMpA8gDIgwgAykD0AN8IhB8IgsgAykDqAMgDSADKQOgAyIKfCAKVK18fCINIAMpA7ACfCIOQgBCAEKJx5mkrvCB6Yd/EMkDIANBkAJqIAMpA6gCIgpCAELH+vPD7YKjkDxCABDJAyADQYACaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB8AFqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HgAWogCkIAQqnAxomuzpOyMEIAEMkDIANBoAFqIAEpA6gBIgpCACARQgAQyQMgA0GwAWogCkIAIBJCABDJAyADQcABaiAKQgAgFEIAEMkDIANB0AFqIApCACAXQgAQyQMgA0GQAWogAykDuAIgDSAOVq18IhYgAykDwAJ8Ig8gAykD2AMgDCAQVq18IhUgAykD4AN8IgwgAykDgAN8IhAgCyANVq0gAykDmAMgCyATVK18fHwiGnwiCyADKQOAAnwiDSADKQOYAiADKQOQAiIKIA58IApUrXx8Ig4gAykDoAF8IhNCAEIAQonHmaSu8IHph38QyQMgA0GAAWogAykDmAEiCkIAQsf688PtgqOQPEIAEMkDIANB8ABqIApCAEKNlcfDltLawJd/QgAQyQMgA0EQaiAKQgBC3bCFjOi2kai4f0IAEMkDIAMgCkIAQqnAxomuzpOyMEIAEMkDIANBgARqIAEpA6ABIgpCACARQgAQyQMgA0GQBGogCkIAIBJCABDJAyADQaAEaiAKQgAgFEIAEMkDIANBsARqIApCACAXQgAQyQMgA0HgAGogAykDqAEgDiATVq18IhggAykDsAF8IhIgAykD6AMgDCAVVK18IhUgAykD8AN8IhEgAykD8AJ8IhQgECAaVq0gAykDiAMgDCAQVq18fHwiDCADKQPQAnwiFyALIA9UrSADKQPIAiAPIBZUrXx8fCIPIAMpA/ABfCIQIA0gDlatIAMpA4gCIAsgDVatfHx8IhZ8IgsgAykDcHwiDSADKQOIASADKQOAASIKIBN8IApUrXx8Ig4gAykDgAR8IhNCAEIAQonHmaSu8IHph38QyQMgA0HQAGogAykDaCIKQgBCx/rzw+2Co5A8QgAQyQMgA0FAayAKQgBCjZXHw5bS2sCXf0IAEMkDIANBMGogCkIAQt2whYzotpGouH9CABDJAyADQSBqIApCAEKpwMaJrs6TsjBCABDJAyABQYABaiEGIAFBoAFqIQECQAJAIAMpAyggAykDCCADKQPoASAMIBRUrSADKQP4AiARIBRWrXx8IAMpA/gDIBEgFVStfHwiFCADKQPgAnwiCiAPIBdUrSADKQPYAiAMIBdWrXx8fCIRIAMpA+ABfCIMIBFUrXwgDCAQIBZWrSADKQP4ASAPIBBWrXx8fCIPIAxUrXwgCiARVq0gAykD6AIgCiAUVK18fHwiFCADKQPQAXwiCiADKQPIASAPIA8gAykDwAF8IhFWrXwgESALIBJUrSADKQO4ASASIBhUrXx8fCISIBFUrXx8Ig8gAykDAHwiESAPVK18IBEgAykDGCASIBIgAykDEHwiDFatfCAMIA0gDlatIAMpA3ggCyANVq18fHwiDSAMVK18fCILIBFUrXwgCiAPVq0gAykD2AEgCiAUVK18fHwiDCADKQOwBHwiEiADKQOoBCALIAMpA6AEfCIKIAtUrXwgCiAKIAMpA5gEIAMpA4gEIA4gE1atfCIOIAMpA5AEfCILIA5UrXwgCyALIA18Ig1WrXx8IgtWrXx8Ig4gAykDIHwiDyAOVK18IA8gAykDOCALIAsgAykDMHwiEVatfCARIBEgAykDSCANIA0gAykDQHwiClatfCAKIAMpA1ggAykDUCILIBN8IAtUrXx8IhQgClStfHwiClatfHwiCyAPVK18IA4gElStIAMpA7gEIAwgElatfHx8IhFCqcDGia7Ok7IwVg0AAkAgEUKpwMaJrs6TsjBRBEAgC0LdsIWM6LaRqLh/Vg0CIAtC3bCFjOi2kai4f1IEQCAKIRIgCyENQqnAxomuzpOyMCERDAQLIApCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQ0gCkKNlcfDltLawJd/UQ0BIAohEkKpwMaJrs6TsjAhEQwDCyAKIRIgCyENDAILQo2Vx8OW0trAl38hEiAUQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhEQwBCyAKQvPquLzpraW/6AB8Ig0gFELH+vPD7YKjkDxUrSIOfSESIAtCo8/685fJ7tfHAHwiDyAKQo2Vx8OW0trAl39UIA0gDlRyrSIKfSENIBEgC0LdsIWM6LaRqLh/VCAKIA9Wcq19QqnAxomuzpOyMH0hESAUQsf688PtgqOQPH0hFAsgAyAUNwPoKyADIBI3A+ArIAMgDTcD2CsgAyARNwPQKyAEQUBrIAYgA0HQK2oQwgIgBEH4AGogAkEYaikDADcDACAEQfAAaiACQRBqKQMANwMAIARB6ABqIAJBCGopAwA3AwAgBCACKQMANwNgIAQgBSkDADcDgAEgBEGIAWogBUEIaikDADcDACAEQZABaiAFQRBqKQMANwMAIARBmAFqIAVBGGopAwA3AwAgBCABKQMANwOgASAEQagBaiABQQhqKQMANwMAIARBsAFqIAFBEGopAwA3AwAgBEG4AWogAUEYaikDADcDACAEQRhqIANBiDFqKQMANwMAIARBEGogA0GAMWopAwA3AwAgBEEIaiADQfgwaikDADcDACAEIAMpA/AwNwMAIARBOGogA0GoMWopAwA3AwAgBEEwaiADQaAxaikDADcDACAEQShqIANBmDFqKQMANwMAIAQgAykDkDE3AyBBBiECDBYLQQVBBUGch8AAENkDAAtB0c7FAC0AABpBgANBCBDWBCIERQ0SIAMoAswrIgJFDQcgAkEBRg0IIANBsChqIAEpAzgiCkIAIBFCABDJAyADQaAnaiAKQgAgEkIAEMkDIANBkCZqIApCACAUQgAQyQMgA0GAJWogCkIAIBdCABDJAyADQaAoaiADKQOwKCINQgBCAEKJx5mkrvCB6Yd/EMkDIANBkChqIAMpA6goIgpCAELH+vPD7YKjkDxCABDJAyADQYAoaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB8CdqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HgJ2ogCkIAQqnAxomuzpOyMEIAEMkDIANB0CdqIAEpAzAiCkIAIBFCABDJAyADQcAmaiAKQgAgEkIAEMkDIANBsCVqIApCACAUQgAQyQMgA0GgJGogCkIAIBdCABDJAyADQZAnaiADKQOAKCITIAMpA7goIgwgAykDoCd8IhB8IgsgAykDmCggDSADKQOQKCIKfCAKVK18fCINIAMpA9AnfCIOQgBCAEKJx5mkrvCB6Yd/EMkDIANBgCdqIAMpA5gnIgpCAELH+vPD7YKjkDxCABDJAyADQfAmaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB4CZqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HQJmogCkIAQqnAxomuzpOyMEIAEMkDIANBwCdqIAEpAygiCkIAIBFCABDJAyADQbAmaiAKQgAgEkIAEMkDIANBoCVqIApCACAUQgAQyQMgA0GQJGogCkIAIBdCABDJAyADQYAmaiADKQPYJyANIA5WrXwiGCADKQPAJnwiDyADKQOoJyAMIBBWrXwiFSADKQOQJnwiDCADKQPwJ3wiECALIA1WrSADKQOIKCALIBNUrXx8fCIZfCILIAMpA/AmfCINIAMpA4gnIAMpA4AnIgogDnwgClStfHwiDiADKQPAJ3wiE0IAQgBCiceZpK7wgemHfxDJAyADQfAlaiADKQOIJiIKQgBCx/rzw+2Co5A8QgAQyQMgA0HgJWogCkIAQo2Vx8OW0trAl39CABDJAyADQdAlaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwCVqIApCAEKpwMaJrs6TsjBCABDJAyADQbAnaiABKQMgIgpCACARQgAQyQMgA0GgJmogCkIAIBJCABDJAyADQZAlaiAKQgAgFEIAEMkDIANBgCRqIApCACAXQgAQyQMgA0HwJGogAykDyCcgDiATVq18IhsgAykDsCZ8IhYgAykDmCYgDCAVVK18IhwgAykDgCV8IhUgAykD4Cd8IhogECAZVq0gAykD+CcgDCAQVq18fHwiDCADKQOwJXwiECALIA9UrSADKQPIJiAPIBhUrXx8fCIPIAMpA+AmfCIYIA0gDlatIAMpA/gmIAsgDVatfHx8Ihl8IgsgAykD4CV8Ig0gAykD+CUgAykD8CUiCiATfCAKVK18fCIOIAMpA7AnfCITQgBCAEKJx5mkrvCB6Yd/EMkDIANB4CRqIAMpA/gkIgpCAELH+vPD7YKjkDxCABDJAyADQdAkaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBwCRqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GwJGogCkIAQqnAxomuzpOyMEIAEMkDAkACQCADKQO4JCADKQPIJSADKQPYJiAMIBpUrSADKQPoJyAVIBpWrXx8IAMpA4glIBUgHFStfHwiFSADKQOgJHwiCiAPIBBUrSADKQO4JSAMIBBWrXx8fCIMIAMpA9AmfCIQIAxUrXwgECAYIBlWrSADKQPoJiAPIBhWrXx8fCIPIBBUrXwgCiAMVq0gAykDqCQgCiAVVK18fHwiFSADKQOQJHwiCiADKQOoJSAPIA8gAykDoCV8IgxWrXwgDCAMIAsgFlStIAMpA7gmIBYgG1StfHx8Ig9WrXx8IgwgAykDwCV8IhAgDFStfCAQIAMpA9glIA8gDyADKQPQJXwiFlatfCAWIBYgDSAOVq0gAykD6CUgCyANVq18fHwiD1atfHwiCyAQVK18IAogDFatIAMpA5gkIAogFVStfHx8IhYgAykDgCR8IgogAykDmCUgCyALIAMpA5AlfCINVq18IA0gDSADKQOoJiADKQO4JyAOIBNWrXwiDiADKQOgJnwiCyAOVK18IAsgCyAPfCIOVq18fCILVq18fCIMIAMpA7AkfCIQIAxUrXwgECAQIAMpA8gkIAsgCyADKQPAJHwiD1atfCAPIAMpA9gkIA4gDiADKQPQJHwiC1atfCALIAsgAykD6CQgAykD4CQiDSATfCANVK18fCINVq18fCIOIA9UrXx8Ig9WrXwgCiAMVq0gAykDiCQgCiAWVK18fHwiDEKpwMaJrs6TsjBWDQACQCAMQqnAxomuzpOyMFEEQCAPQt2whYzotpGouH9WDQIgD0LdsIWM6LaRqLh/UgRAIA4hCiAPIQtCqcDGia7Ok7IwIQwMBAsgDkKNlcfDltLawJd/Vg0CQt2whYzotpGouH8hCyAOQo2Vx8OW0trAl39RDQEgDiEKQqnAxomuzpOyMCEMDAMLIA4hCiAPIQsMAgtCjZXHw5bS2sCXfyEKIA1Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEMDAELIA5C8+q4vOmtpb/oAHwiCyANQsf688PtgqOQPFStIhB9IQogD0Kjz/rzl8nu18cAfCITIA5CjZXHw5bS2sCXf1QgCyAQVHKtIg59IQsgDCAPQt2whYzotpGouH9UIA4gE1ZyrX1CqcDGia7Ok7IwfSEMIA1Cx/rzw+2Co5A8fSENCyADIA03A+grIAMgCjcD4CsgAyALNwPYKyADIAw3A9ArIANBkDBqIAEgA0HQK2oQwgIgAygCzCsiAkEGTQ0JIAJBB0YNCiADQYAjaiABKQP4ASIKQgAgEUIAEMkDIANBkCNqIApCACASQgAQyQMgA0GgI2ogCkIAIBRCABDJAyADQbAjaiAKQgAgF0IAEMkDIANB8CJqIAMpA4AjIg1CAEIAQonHmaSu8IHph38QyQMgA0HgImogAykD+CIiCkIAQsf688PtgqOQPEIAEMkDIANB0CJqIApCAEKNlcfDltLawJd/QgAQyQMgA0HAImogCkIAQt2whYzotpGouH9CABDJAyADQbAiaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwIWogASkD8AEiCkIAIBFCABDJAyADQYAiaiAKQgAgEkIAEMkDIANBkCJqIApCACAUQgAQyQMgA0GgImogCkIAIBdCABDJAyADQeAhaiADKQPQIiITIAMpA4gjIgwgAykDkCN8IhB8IgsgAykD6CIgDSADKQPgIiIKfCAKVK18fCINIAMpA/AhfCIOQgBCAEKJx5mkrvCB6Yd/EMkDIANB0CFqIAMpA+ghIgpCAELH+vPD7YKjkDxCABDJAyADQcAhaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsCFqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgIWogCkIAQqnAxomuzpOyMEIAEMkDIANB4CBqIAEpA+gBIgpCACARQgAQyQMgA0HwIGogCkIAIBJCABDJAyADQYAhaiAKQgAgFEIAEMkDIANBkCFqIApCACAXQgAQyQMgA0HQIGogAykD+CEgDSAOVq18IhggAykDgCJ8Ig8gAykDmCMgDCAQVq18IhUgAykDoCN8IgwgAykDwCJ8IhAgCyANVq0gAykD2CIgCyATVK18fHwiGXwiCyADKQPAIXwiDSADKQPYISADKQPQISIKIA58IApUrXx8Ig4gAykD4CB8IhNCAEIAQonHmaSu8IHph38QyQMgA0HAIGogAykD2CAiCkIAQsf688PtgqOQPEIAEMkDIANBsCBqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQH2ogCkIAQt2whYzotpGouH9CABDJAyADQcAfaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HAI2ogASkD4AEiCkIAIBFCABDJAyADQdAjaiAKQgAgEkIAEMkDIANB4CNqIApCACAUQgAQyQMgA0HwI2ogCkIAIBdCABDJAyADQaAgaiADKQPoICAOIBNWrXwiGyADKQPwIHwiFiADKQOoIyAMIBVUrXwiHCADKQOwI3wiFSADKQOwInwiGiAQIBlWrSADKQPIIiAMIBBWrXx8fCIMIAMpA5AifCIQIAsgD1StIAMpA4giIA8gGFStfHx8Ig8gAykDsCF8IhggDSAOVq0gAykDyCEgCyANVq18fHwiGXwiCyADKQOwIHwiDSADKQPIICADKQPAICIKIBN8IApUrXx8Ig4gAykDwCN8IhNCAEIAQonHmaSu8IHph38QyQMgA0GQIGogAykDqCAiCkIAQsf688PtgqOQPEIAEMkDIANBgCBqIApCAEKNlcfDltLawJd/QgAQyQMgA0HwH2ogCkIAQt2whYzotpGouH9CABDJAyADQeAfaiAKQgBCqcDGia7Ok7IwQgAQyQMgAUHAAWohAgJAAkAgAykD6B8gAykDyB8gAykDqCEgDCAaVK0gAykDuCIgFSAaVq18fCADKQO4IyAVIBxUrXx8IhUgAykDoCJ8IgogDyAQVK0gAykDmCIgDCAQVq18fHwiDCADKQOgIXwiECAMVK18IBAgGCAZVq0gAykDuCEgDyAYVq18fHwiDyAQVK18IAogDFatIAMpA6giIAogFVStfHx8IhUgAykDkCF8IgogAykDiCEgDyAPIAMpA4AhfCIMVq18IAwgDCALIBZUrSADKQP4ICAWIBtUrXx8fCIPVq18fCIMIAMpA8AffCIQIAxUrXwgECADKQPYHyAPIA8gAykD0B98IhZWrXwgFiAWIA0gDlatIAMpA7ggIAsgDVatfHx8Ig9WrXx8IgsgEFStfCAKIAxWrSADKQOYISAKIBVUrXx8fCIWIAMpA/AjfCIKIAMpA+gjIAsgCyADKQPgI3wiDVatfCANIA0gAykD2CMgAykDyCMgDiATVq18Ig4gAykD0CN8IgsgDlStfCALIAsgD3wiDlatfHwiC1atfHwiDCADKQPgH3wiECAMVK18IBAgECADKQP4HyALIAsgAykD8B98Ig9WrXwgDyADKQOIICAOIA4gAykDgCB8IgtWrXwgCyALIAMpA5ggIAMpA5AgIg0gE3wgDVStfHwiDVatfHwiDiAPVK18fCIPVq18IAogDFatIAMpA/gjIAogFlStfHx8IgxCqcDGia7Ok7IwVg0AAkAgDEKpwMaJrs6TsjBRBEAgD0LdsIWM6LaRqLh/Vg0CIA9C3bCFjOi2kai4f1IEQCAOIQogDyELQqnAxomuzpOyMCEMDAQLIA5CjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQsgDkKNlcfDltLawJd/UQ0BIA4hCkKpwMaJrs6TsjAhDAwDCyAOIQogDyELDAILQo2Vx8OW0trAl38hCiANQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhDAwBCyAOQvPquLzpraW/6AB8IgsgDULH+vPD7YKjkDxUrSIQfSEKIA9Co8/685fJ7tfHAHwiEyAOQo2Vx8OW0trAl39UIAsgEFRyrSIOfSELIAwgD0LdsIWM6LaRqLh/VCAOIBNWcq19QqnAxomuzpOyMH0hDCANQsf688PtgqOQPH0hDQsgAyANNwPoKyADIAo3A+ArIAMgCzcD2CsgAyAMNwPQKyADQbAwaiACIANB0CtqEMICIAMoAswrIgJBAk0NCyACQQNGDQwgA0HAHmogASkDeCIKQgAgEUIAEMkDIANB0B5qIApCACASQgAQyQMgA0HgHmogCkIAIBRCABDJAyADQfAeaiAKQgAgF0IAEMkDIANBsB5qIAMpA8AeIg1CAEIAQonHmaSu8IHph38QyQMgA0GgHmogAykDuB4iCkIAQsf688PtgqOQPEIAEMkDIANBkB5qIApCAEKNlcfDltLawJd/QgAQyQMgA0GAHmogCkIAQt2whYzotpGouH9CABDJAyADQfAdaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GwHWogASkDcCIKQgAgEUIAEMkDIANBwB1qIApCACASQgAQyQMgA0HQHWogCkIAIBRCABDJAyADQeAdaiAKQgAgF0IAEMkDIANBoB1qIAMpA5AeIhMgAykDyB4iDCADKQPQHnwiEHwiCyADKQOoHiANIAMpA6AeIgp8IApUrXx8Ig0gAykDsB18Ig5CAEIAQonHmaSu8IHph38QyQMgA0GQHWogAykDqB0iCkIAQsf688PtgqOQPEIAEMkDIANBgB1qIApCAEKNlcfDltLawJd/QgAQyQMgA0HwHGogCkIAQt2whYzotpGouH9CABDJAyADQeAcaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GgHGogASkDaCIKQgAgEUIAEMkDIANBsBxqIApCACASQgAQyQMgA0HAHGogCkIAIBRCABDJAyADQdAcaiAKQgAgF0IAEMkDIANBkBxqIAMpA7gdIA0gDlatfCIYIAMpA8AdfCIPIAMpA9geIAwgEFatfCIVIAMpA+AefCIMIAMpA4AefCIQIAsgDVatIAMpA5geIAsgE1StfHx8Ihl8IgsgAykDgB18Ig0gAykDmB0gAykDkB0iCiAOfCAKVK18fCIOIAMpA6AcfCITQgBCAEKJx5mkrvCB6Yd/EMkDIANBgBxqIAMpA5gcIgpCAELH+vPD7YKjkDxCABDJAyADQfAbaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBkBtqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GAG2ogCkIAQqnAxomuzpOyMEIAEMkDIANBgB9qIAEpA2AiCkIAIBFCABDJAyADQZAfaiAKQgAgEkIAEMkDIANBoB9qIApCACAUQgAQyQMgA0GwH2ogCkIAIBdCABDJAyADQeAbaiADKQOoHCAOIBNWrXwiGyADKQOwHHwiFiADKQPoHiAMIBVUrXwiHCADKQPwHnwiFSADKQPwHXwiGiAQIBlWrSADKQOIHiAMIBBWrXx8fCIMIAMpA9AdfCIQIAsgD1StIAMpA8gdIA8gGFStfHx8Ig8gAykD8Bx8IhggDSAOVq0gAykDiB0gCyANVq18fHwiGXwiCyADKQPwG3wiDSADKQOIHCADKQOAHCIKIBN8IApUrXx8Ig4gAykDgB98IhNCAEIAQonHmaSu8IHph38QyQMgA0HQG2ogAykD6BsiCkIAQsf688PtgqOQPEIAEMkDIANBwBtqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwG2ogCkIAQt2whYzotpGouH9CABDJAyADQaAbaiAKQgBCqcDGia7Ok7IwQgAQyQMgAUFAayECAkACQCADKQOoGyADKQOIGyADKQPoHCAMIBpUrSADKQP4HSAVIBpWrXx8IAMpA/geIBUgHFStfHwiFSADKQPgHXwiCiAPIBBUrSADKQPYHSAMIBBWrXx8fCIMIAMpA+AcfCIQIAxUrXwgECAYIBlWrSADKQP4HCAPIBhWrXx8fCIPIBBUrXwgCiAMVq0gAykD6B0gCiAVVK18fHwiFSADKQPQHHwiCiADKQPIHCAPIA8gAykDwBx8IgxWrXwgDCAMIAsgFlStIAMpA7gcIBYgG1StfHx8Ig9WrXx8IgwgAykDgBt8IhAgDFStfCAQIAMpA5gbIA8gDyADKQOQG3wiFlatfCAWIBYgDSAOVq0gAykD+BsgCyANVq18fHwiD1atfHwiCyAQVK18IAogDFatIAMpA9gcIAogFVStfHx8IhYgAykDsB98IgogAykDqB8gCyALIAMpA6AffCINVq18IA0gDSADKQOYHyADKQOIHyAOIBNWrXwiDiADKQOQH3wiCyAOVK18IAsgCyAPfCIOVq18fCILVq18fCIMIAMpA6AbfCIQIAxUrXwgECAQIAMpA7gbIAsgCyADKQOwG3wiD1atfCAPIAMpA8gbIA4gDiADKQPAG3wiC1atfCALIAsgAykD2BsgAykD0BsiDSATfCANVK18fCINVq18fCIOIA9UrXx8Ig9WrXwgCiAMVq0gAykDuB8gCiAWVK18fHwiDEKpwMaJrs6TsjBWDQACQCAMQqnAxomuzpOyMFEEQCAPQt2whYzotpGouH9WDQIgD0LdsIWM6LaRqLh/UgRAIA4hCiAPIQtCqcDGia7Ok7IwIQwMBAsgDkKNlcfDltLawJd/Vg0CQt2whYzotpGouH8hCyAOQo2Vx8OW0trAl39RDQEgDiEKQqnAxomuzpOyMCEMDAMLIA4hCiAPIQsMAgtCjZXHw5bS2sCXfyEKIA1Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEMDAELIA5C8+q4vOmtpb/oAHwiCyANQsf688PtgqOQPFStIhB9IQogD0Kjz/rzl8nu18cAfCITIA5CjZXHw5bS2sCXf1QgCyAQVHKtIg59IQsgDCAPQt2whYzotpGouH9UIA4gE1ZyrX1CqcDGia7Ok7IwfSEMIA1Cx/rzw+2Co5A8fSENCyADIA03A+grIAMgCjcD4CsgAyALNwPYKyADIAw3A9ArIANB0DBqIAIgA0HQK2oQwgIgAygCzCsiAkEITQ0NIAJBCUYNDiADQYAaaiABKQO4AiIKQgAgEUIAEMkDIANBkBpqIApCACASQgAQyQMgA0GgGmogCkIAIBRCABDJAyADQbAaaiAKQgAgF0IAEMkDIANB8BlqIAMpA4AaIg1CAEIAQonHmaSu8IHph38QyQMgA0HgGWogAykD+BkiCkIAQsf688PtgqOQPEIAEMkDIANB0BlqIApCAEKNlcfDltLawJd/QgAQyQMgA0HAGWogCkIAQt2whYzotpGouH9CABDJAyADQbAZaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwGGogASkDsAIiCkIAIBFCABDJAyADQYAZaiAKQgAgEkIAEMkDIANBkBlqIApCACAUQgAQyQMgA0GgGWogCkIAIBdCABDJAyADQeAYaiADKQPQGSITIAMpA4gaIgwgAykDkBp8IhB8IgsgAykD6BkgDSADKQPgGSIKfCAKVK18fCINIAMpA/AYfCIOQgBCAEKJx5mkrvCB6Yd/EMkDIANB0BhqIAMpA+gYIgpCAELH+vPD7YKjkDxCABDJAyADQcAYaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsBhqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgGGogCkIAQqnAxomuzpOyMEIAEMkDIANB4BdqIAEpA6gCIgpCACARQgAQyQMgA0HwF2ogCkIAIBJCABDJAyADQYAYaiAKQgAgFEIAEMkDIANBkBhqIApCACAXQgAQyQMgA0HQF2ogAykD+BggDSAOVq18IhggAykDgBl8Ig8gAykDmBogDCAQVq18IhUgAykDoBp8IgwgAykDwBl8IhAgCyANVq0gAykD2BkgCyATVK18fHwiGXwiCyADKQPAGHwiDSADKQPYGCADKQPQGCIKIA58IApUrXx8Ig4gAykD4Bd8IhNCAEIAQonHmaSu8IHph38QyQMgA0HAF2ogAykD2BciCkIAQsf688PtgqOQPEIAEMkDIANBsBdqIApCAEKNlcfDltLawJd/QgAQyQMgA0HQFmogCkIAQt2whYzotpGouH9CABDJAyADQcAWaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HAGmogASkDoAIiCkIAIBFCABDJAyADQdAaaiAKQgAgEkIAEMkDIANB4BpqIApCACAUQgAQyQMgA0HwGmogCkIAIBdCABDJAyADQaAXaiADKQPoFyAOIBNWrXwiGyADKQPwF3wiFiADKQOoGiAMIBVUrXwiHCADKQOwGnwiFSADKQOwGXwiGiAQIBlWrSADKQPIGSAMIBBWrXx8fCIMIAMpA5AZfCIQIAsgD1StIAMpA4gZIA8gGFStfHx8Ig8gAykDsBh8IhggDSAOVq0gAykDyBggCyANVq18fHwiGXwiCyADKQOwF3wiDSADKQPIFyADKQPAFyIKIBN8IApUrXx8Ig4gAykDwBp8IhNCAEIAQonHmaSu8IHph38QyQMgA0GQF2ogAykDqBciCkIAQsf688PtgqOQPEIAEMkDIANBgBdqIApCAEKNlcfDltLawJd/QgAQyQMgA0HwFmogCkIAQt2whYzotpGouH9CABDJAyADQeAWaiAKQgBCqcDGia7Ok7IwQgAQyQMgAUGAAmohAgJAAkAgAykD6BYgAykDyBYgAykDqBggDCAaVK0gAykDuBkgFSAaVq18fCADKQO4GiAVIBxUrXx8IhUgAykDoBl8IgogDyAQVK0gAykDmBkgDCAQVq18fHwiDCADKQOgGHwiECAMVK18IBAgGCAZVq0gAykDuBggDyAYVq18fHwiDyAQVK18IAogDFatIAMpA6gZIAogFVStfHx8IhUgAykDkBh8IgogAykDiBggDyAPIAMpA4AYfCIMVq18IAwgDCALIBZUrSADKQP4FyAWIBtUrXx8fCIPVq18fCIMIAMpA8AWfCIQIAxUrXwgECADKQPYFiAPIA8gAykD0BZ8IhZWrXwgFiAWIA0gDlatIAMpA7gXIAsgDVatfHx8Ig9WrXx8IgsgEFStfCAKIAxWrSADKQOYGCAKIBVUrXx8fCIWIAMpA/AafCIKIAMpA+gaIAsgCyADKQPgGnwiDVatfCANIA0gAykD2BogAykDyBogDiATVq18Ig4gAykD0Bp8IgsgDlStfCALIAsgD3wiDlatfHwiC1atfHwiDCADKQPgFnwiECAMVK18IBAgECADKQP4FiALIAsgAykD8BZ8Ig9WrXwgDyADKQOIFyAOIA4gAykDgBd8IgtWrXwgCyALIAMpA5gXIAMpA5AXIg0gE3wgDVStfHwiDVatfHwiDiAPVK18fCIPVq18IAogDFatIAMpA/gaIAogFlStfHx8IgxCqcDGia7Ok7IwVg0AAkAgDEKpwMaJrs6TsjBRBEAgD0LdsIWM6LaRqLh/Vg0CIA9C3bCFjOi2kai4f1IEQCAOIQogDyELQqnAxomuzpOyMCEMDAQLIA5CjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQsgDkKNlcfDltLawJd/UQ0BIA4hCkKpwMaJrs6TsjAhDAwDCyAOIQogDyELDAILQo2Vx8OW0trAl38hCiANQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhDAwBCyAOQvPquLzpraW/6AB8IgsgDULH+vPD7YKjkDxUrSIQfSEKIA9Co8/685fJ7tfHAHwiEyAOQo2Vx8OW0trAl39UIAsgEFRyrSIOfSELIAwgD0LdsIWM6LaRqLh/VCAOIBNWcq19QqnAxomuzpOyMH0hDCANQsf688PtgqOQPH0hDQsgAyANNwPoKyADIAo3A+ArIAMgCzcD2CsgAyAMNwPQKyADQfAwaiACIANB0CtqEMICIAMoAswrIgJBBE0NDyACQQVGDRAgA0HAFWogASkDuAEiCkIAIBFCABDJAyADQdAVaiAKQgAgEkIAEMkDIANB4BVqIApCACAUQgAQyQMgA0HwFWogCkIAIBdCABDJAyADQbAVaiADKQPAFSINQgBCAEKJx5mkrvCB6Yd/EMkDIANBoBVqIAMpA7gVIgpCAELH+vPD7YKjkDxCABDJAyADQZAVaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBgBVqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HwFGogCkIAQqnAxomuzpOyMEIAEMkDIANBsBRqIAEpA7ABIgpCACARQgAQyQMgA0HAFGogCkIAIBJCABDJAyADQdAUaiAKQgAgFEIAEMkDIANB4BRqIApCACAXQgAQyQMgA0GgFGogAykDkBUiEyADKQPIFSIMIAMpA9AVfCIQfCILIAMpA6gVIA0gAykDoBUiCnwgClStfHwiDSADKQOwFHwiDkIAQgBCiceZpK7wgemHfxDJAyADQZAUaiADKQOoFCIKQgBCx/rzw+2Co5A8QgAQyQMgA0GAFGogCkIAQo2Vx8OW0trAl39CABDJAyADQfATaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4BNqIApCAEKpwMaJrs6TsjBCABDJAyADQaATaiABKQOoASIKQgAgEUIAEMkDIANBsBNqIApCACASQgAQyQMgA0HAE2ogCkIAIBRCABDJAyADQdATaiAKQgAgF0IAEMkDIANBkBNqIAMpA7gUIA0gDlatfCIYIAMpA8AUfCIPIAMpA9gVIAwgEFatfCIVIAMpA+AVfCIMIAMpA4AVfCIQIAsgDVatIAMpA5gVIAsgE1StfHx8Ihl8IgsgAykDgBR8Ig0gAykDmBQgAykDkBQiCiAOfCAKVK18fCIOIAMpA6ATfCITQgBCAEKJx5mkrvCB6Yd/EMkDIANBgBNqIAMpA5gTIgpCAELH+vPD7YKjkDxCABDJAyADQfASaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBkBJqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GAEmogCkIAQqnAxomuzpOyMEIAEMkDIANBgBZqIAEpA6ABIgpCACARQgAQyQMgA0GQFmogCkIAIBJCABDJAyADQaAWaiAKQgAgFEIAEMkDIANBsBZqIApCACAXQgAQyQMgA0HgEmogAykDqBMgDiATVq18IhsgAykDsBN8IhYgAykD6BUgDCAVVK18IhwgAykD8BV8IhUgAykD8BR8IhogECAZVq0gAykDiBUgDCAQVq18fHwiDCADKQPQFHwiECALIA9UrSADKQPIFCAPIBhUrXx8fCIPIAMpA/ATfCIYIA0gDlatIAMpA4gUIAsgDVatfHx8Ihl8IgsgAykD8BJ8Ig0gAykDiBMgAykDgBMiCiATfCAKVK18fCIOIAMpA4AWfCITQgBCAEKJx5mkrvCB6Yd/EMkDIANB0BJqIAMpA+gSIgpCAELH+vPD7YKjkDxCABDJAyADQcASaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsBJqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgEmogCkIAQqnAxomuzpOyMEIAEMkDIAFBgAFqIQICQAJAIAMpA6gSIAMpA4gSIAMpA+gTIAwgGlStIAMpA/gUIBUgGlatfHwgAykD+BUgFSAcVK18fCIVIAMpA+AUfCIKIA8gEFStIAMpA9gUIAwgEFatfHx8IgwgAykD4BN8IhAgDFStfCAQIBggGVatIAMpA/gTIA8gGFatfHx8Ig8gEFStfCAKIAxWrSADKQPoFCAKIBVUrXx8fCIVIAMpA9ATfCIKIAMpA8gTIA8gDyADKQPAE3wiDFatfCAMIAwgCyAWVK0gAykDuBMgFiAbVK18fHwiD1atfHwiDCADKQOAEnwiECAMVK18IBAgAykDmBIgDyAPIAMpA5ASfCIWVq18IBYgFiANIA5WrSADKQP4EiALIA1WrXx8fCIPVq18fCILIBBUrXwgCiAMVq0gAykD2BMgCiAVVK18fHwiFiADKQOwFnwiCiADKQOoFiALIAsgAykDoBZ8Ig1WrXwgDSANIAMpA5gWIAMpA4gWIA4gE1atfCIOIAMpA5AWfCILIA5UrXwgCyALIA98Ig5WrXx8IgtWrXx8IgwgAykDoBJ8IhAgDFStfCAQIBAgAykDuBIgCyALIAMpA7ASfCIPVq18IA8gAykDyBIgDiAOIAMpA8ASfCILVq18IAsgCyADKQPYEiADKQPQEiINIBN8IA1UrXx8Ig1WrXx8Ig4gD1StfHwiD1atfCAKIAxWrSADKQO4FiAKIBZUrXx8fCIMQqnAxomuzpOyMFYNAAJAIAxCqcDGia7Ok7IwUQRAIA9C3bCFjOi2kai4f1YNAiAPQt2whYzotpGouH9SBEAgDiEKIA8hC0KpwMaJrs6TsjAhDAwECyAOQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyELIA5CjZXHw5bS2sCXf1ENASAOIQpCqcDGia7Ok7IwIQwMAwsgDiEKIA8hCwwCC0KNlcfDltLawJd/IQogDULH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQwMAQsgDkLz6ri86a2lv+gAfCILIA1Cx/rzw+2Co5A8VK0iEH0hCiAPQqPP+vOXye7XxwB8IhMgDkKNlcfDltLawJd/VCALIBBUcq0iDn0hCyAMIA9C3bCFjOi2kai4f1QgDiATVnKtfUKpwMaJrs6TsjB9IQwgDULH+vPD7YKjkDx9IQ0LIAMgDTcD6CsgAyAKNwPgKyADIAs3A9grIAMgDDcD0CsgA0GQMWogAiADQdArahDCAiADKALMKyICQQpNDREgAkELRwRAIAFBIGohAiABQeABaiEFIAFB4ABqIQYgAUGgAmohByABQaABaiEIIANBgBFqIAEpA/gCIgpCACARQgAQyQMgA0GQEWogCkIAIBJCABDJAyADQaARaiAKQgAgFEIAEMkDIANBsBFqIApCACAXQgAQyQMgA0HwEGogAykDgBEiDUIAQgBCiceZpK7wgemHfxDJAyADQeAQaiADKQP4ECIKQgBCx/rzw+2Co5A8QgAQyQMgA0HQEGogCkIAQo2Vx8OW0trAl39CABDJAyADQcAQaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBsBBqIApCAEKpwMaJrs6TsjBCABDJAyADQfAPaiABKQPwAiIKQgAgEUIAEMkDIANBgBBqIApCACASQgAQyQMgA0GQEGogCkIAIBRCABDJAyADQaAQaiAKQgAgF0IAEMkDIANB4A9qIAMpA9AQIhMgAykDiBEiDCADKQOQEXwiEHwiCyADKQPoECANIAMpA+AQIgp8IApUrXx8Ig0gAykD8A98Ig5CAEIAQonHmaSu8IHph38QyQMgA0HQD2ogAykD6A8iCkIAQsf688PtgqOQPEIAEMkDIANBwA9qIApCAEKNlcfDltLawJd/QgAQyQMgA0GwD2ogCkIAQt2whYzotpGouH9CABDJAyADQaAPaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HgDmogASkD6AIiCkIAIBFCABDJAyADQfAOaiAKQgAgEkIAEMkDIANBgA9qIApCACAUQgAQyQMgA0GQD2ogCkIAIBdCABDJAyADQdAOaiADKQP4DyANIA5WrXwiFiADKQOAEHwiDyADKQOYESAMIBBWrXwiFSADKQOgEXwiDCADKQPAEHwiECALIA1WrSADKQPYECALIBNUrXx8fCIafCILIAMpA8APfCINIAMpA9gPIAMpA9APIgogDnwgClStfHwiDiADKQPgDnwiE0IAQgBCiceZpK7wgemHfxDJAyADQcAOaiADKQPYDiIKQgBCx/rzw+2Co5A8QgAQyQMgA0GwDmogCkIAQo2Vx8OW0trAl39CABDJAyADQdANaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwA1qIApCAEKpwMaJrs6TsjBCABDJAyADQcARaiABKQPgAiIKQgAgEUIAEMkDIANB0BFqIApCACASQgAQyQMgA0HgEWogCkIAIBRCABDJAyADQfARaiAKQgAgF0IAEMkDIANBoA5qIAMpA+gOIA4gE1atfCIYIAMpA/AOfCISIAMpA6gRIAwgFVStfCIVIAMpA7ARfCIRIAMpA7AQfCIUIBAgGlatIAMpA8gQIAwgEFatfHx8IgwgAykDkBB8IhcgCyAPVK0gAykDiBAgDyAWVK18fHwiDyADKQOwD3wiECANIA5WrSADKQPIDyALIA1WrXx8fCIWfCILIAMpA7AOfCINIAMpA8gOIAMpA8AOIgogE3wgClStfHwiDiADKQPAEXwiE0IAQgBCiceZpK7wgemHfxDJAyADQZAOaiADKQOoDiIKQgBCx/rzw+2Co5A8QgAQyQMgA0GADmogCkIAQo2Vx8OW0trAl39CABDJAyADQfANaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4A1qIApCAEKpwMaJrs6TsjBCABDJAyABQcACaiEJIAFB4AJqIQECQAJAIAMpA+gNIAMpA8gNIAMpA6gPIAwgFFStIAMpA7gQIBEgFFatfHwgAykDuBEgESAVVK18fCIUIAMpA6AQfCIKIA8gF1StIAMpA5gQIAwgF1atfHx8IhEgAykDoA98IgwgEVStfCAMIBAgFlatIAMpA7gPIA8gEFatfHx8Ig8gDFStfCAKIBFWrSADKQOoECAKIBRUrXx8fCIUIAMpA5APfCIKIAMpA4gPIA8gDyADKQOAD3wiEVatfCARIAsgElStIAMpA/gOIBIgGFStfHx8IhIgEVStfHwiDyADKQPADXwiESAPVK18IBEgAykD2A0gEiASIAMpA9ANfCIMVq18IAwgDSAOVq0gAykDuA4gCyANVq18fHwiDSAMVK18fCILIBFUrXwgCiAPVq0gAykDmA8gCiAUVK18fHwiDCADKQPwEXwiEiADKQPoESALIAMpA+ARfCIKIAtUrXwgCiAKIAMpA9gRIAMpA8gRIA4gE1atfCIOIAMpA9ARfCILIA5UrXwgCyALIA18Ig1WrXx8IgtWrXx8Ig4gAykD4A18Ig8gDlStfCAPIAMpA/gNIAsgCyADKQPwDXwiEVatfCARIBEgAykDiA4gDSANIAMpA4AOfCIKVq18IAogAykDmA4gAykDkA4iCyATfCALVK18fCIUIApUrXx8IgpWrXx8IgsgD1StfCAOIBJUrSADKQP4ESAMIBJWrXx8fCIRQqnAxomuzpOyMFYNAAJAIBFCqcDGia7Ok7IwUQRAIAtC3bCFjOi2kai4f1YNAiALQt2whYzotpGouH9SBEAgCiESIAshDUKpwMaJrs6TsjAhEQwECyAKQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyENIApCjZXHw5bS2sCXf1ENASAKIRJCqcDGia7Ok7IwIREMAwsgCiESIAshDQwCC0KNlcfDltLawJd/IRIgFELH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIREMAQsgCkLz6ri86a2lv+gAfCINIBRCx/rzw+2Co5A8VK0iDn0hEiALQqPP+vOXye7XxwB8Ig8gCkKNlcfDltLawJd/VCANIA5Ucq0iCn0hDSARIAtC3bCFjOi2kai4f1QgCiAPVnKtfUKpwMaJrs6TsjB9IREgFELH+vPD7YKjkDx9IRQLIAMgFDcD6CsgAyASNwPgKyADIA03A9grIAMgETcD0CsgBEGgAWogCSADQdArahDCAiAEQdgBaiACQRhqKQMANwMAIARB0AFqIAJBEGopAwA3AwAgBEHIAWogAkEIaikDADcDACAEIAIpAwA3A8ABIAQgBSkDADcD4AEgBEHoAWogBUEIaikDADcDACAEQfABaiAFQRBqKQMANwMAIARB+AFqIAVBGGopAwA3AwAgBCAGKQMANwOAAiAEQYgCaiAGQQhqKQMANwMAIARBkAJqIAZBEGopAwA3AwAgBEGYAmogBkEYaikDADcDACAEQbgCaiAHQRhqKQMANwMAIARBsAJqIAdBEGopAwA3AwAgBEGoAmogB0EIaikDADcDACAEIAcpAwA3A6ACIARB2AJqIAhBGGopAwA3AwAgBEHQAmogCEEQaikDADcDACAEQcgCaiAIQQhqKQMANwMAIAQgCCkDADcDwAIgBEH4AmogAUEYaikDADcDACAEQfACaiABQRBqKQMANwMAIARB6AJqIAFBCGopAwA3AwAgBCABKQMANwPgAiAEQRhqIANBqDBqKQMANwMAIARBEGogA0GgMGopAwA3AwAgBEEIaiADQZgwaikDADcDACAEIAMpA5AwNwMAIARBOGogA0HIMGopAwA3AwAgBEEwaiADQcAwaikDADcDACAEQShqIANBuDBqKQMANwMAIAQgAykDsDA3AyAgBEHYAGogA0HoMGopAwA3AwAgBEHQAGogA0HgMGopAwA3AwAgBEHIAGogA0HYMGopAwA3AwAgBCADKQPQMDcDQCAEQfgAaiADQYgxaikDADcDACAEQfAAaiADQYAxaikDADcDACAEQegAaiADQfgwaikDADcDACAEIAMpA/AwNwNgIARBmAFqIANBqDFqKQMANwMAIARBkAFqIANBoDFqKQMANwMAIARBiAFqIANBmDFqKQMANwMAIAQgAykDkDE3A4ABQQwhAgwVC0ELQQtB3IjAABDZAwALIANBADYC0CsgA0HMK2ogA0HIK2ogA0HQK2pBvIbAABCXBAALIAYgB0G4hcAAEMgEAAtBAEEAQcyGwAAQ2QMAC0EBQQFB3IbAABDZAwALQQIgAkHshsAAENkDAAtBA0EDQfyGwAAQ2QMAC0EEIAJBjIfAABDZAwALQQBBAEGsh8AAENkDAAtBAUEBQbyHwAAQ2QMAC0EGIAJBzIfAABDZAwALQQdBB0Hch8AAENkDAAtBAiACQeyHwAAQ2QMAC0EDQQNB/IfAABDZAwALQQggAkGMiMAAENkDAAtBCUEJQZyIwAAQ2QMAC0EEIAJBrIjAABDZAwALQQVBBUG8iMAAENkDAAtBCiACQcyIwAAQ2QMAC0EIQYADEP8EAAtBCEHAARD/BAALIAAgAjYCCCAAIAQ2AgQgACACNgIAIANBsDFqJAAL76sBAgd/Fn4jAEGQJWsiAiQAIAJB4BZqECYCQAJAAkAgAigCgBpBAXEEQEEoIQMgAkGoHWogAkGwGmopAwA3AwAgAkGgHWogAkGoGmopAwA3AwAgAkGYHWogAkGgGmopAwA3AwAgAkGQHWogAkGYGmopAwA3AwAgAkGIHWogAkGQGmopAwA3AwAgAiACKQOIGjcDgB0gAkHYHWogAkHgGmopAwA3AwAgAkHQHWogAkHYGmopAwA3AwAgAkHIHWogAkHQGmopAwA3AwAgAkHAHWogAkHIGmopAwA3AwAgAkG4HWogAkHAGmopAwA3AwAgAiACKQO4GjcDsB0gAkGIHmogAkGQG2opAwA3AwAgAkGAHmogAkGIG2opAwA3AwAgAkH4HWogAkGAG2opAwA3AwAgAkHwHWogAkH4GmopAwA3AwAgAkHoHWogAkHwGmopAwA3AwAgAiACKQPoGjcD4B0gAkG4HmogAUEoaikDACISNwMAIAJBsB5qIAFBIGopAwAiEzcDACACQageaiABQRhqKQMAIhU3AwAgAkGgHmogAUEQaikDACIXNwMAIAJBmB5qIAFBCGopAwAiGDcDACACIAEpAwAiGTcDkB4DQCACQYAWaiACQZAeaiADaikDACIKQgAgEkIAEMkDIAJBkBZqIApCACATQgAQyQMgAkGgFmogCkIAIBVCABDJAyACQbAWaiAKQgAgF0IAEMkDIAJBwBZqIApCACAYQgAQyQMgAkHQFmogCkIAIBlCABDJAyACQfAVaiACKQOAFiIUIBB8Ig9CAEIAQv3/8//P///5iX8QyQMgAkHgFWogAikD+BUiCkIAQqvV/v///7//uX9CABDJAyACQdAVaiAKQgBC///Piuv//9UeQgAQyQMgAkHAFWogCkIAQqTsw7WP1LSY5wBCABDJAyACQbAVaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJBoBVqIApCAELX2a6a5PbpjcsAQgAQyQMgAkGQFWogCkIAQprN/8ujvcSAGkIAEMkDIAIpA5gVIBEgAikD0BYiEXwiCiACKQPIFiAMIAIpA8AWIgx8Ig0gDFStfCANIAIpA7gWIAIpA7AWIgwgC3wiCyAMVK18IAsgAikDqBYgAikDoBYiDCAJfCIJIAxUrXwgCSAJIAIpA5gWIAIpA5AWIgwgDnwiDiAMVK18IA4gAikDiBYgDyAUVK18fCIQIA5UrXx8IglWrXx8Ig4gC1StfHwiCyANVK18fCINIAIpA5AVfCIUIA1UrXwgFCACKQOoFSALIAsgAikDoBV8IgtWrXwgCyALIAIpA7gVIA4gAikDsBV8IgwgDlStfCAMIAIpA8gVIAkgCSACKQPAFXwiCVatfCAJIAIpA9gVIBAgAikD0BUiEHwiDiAQVK18IA4gAikD6BUgDyACKQPgFSIPfCAPVK18fCIQIA5UrXx8Ig4gCVStfHwiCSAMVK18fCILVq18fCIMIBRUrXwgCiANVq0gAikD2BYgCiARVK18fHwhESADQQhrIgNBeEcNAAsgEUKazf/Lo73EgBpWDQIgEUKazf/Lo73EgBpRDQEgDiEKIAkhFCALIQ8gDCESDAMLQZyqwAAQ6AQACyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDiEKIAkhFCALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA4hCiAJIRQgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA4hCiAJIRQMAQsgDkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA5C///Piuv//9UeUgRAIA4hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA5C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIg19IQogCUKk7MO1j9S0mOcAfSISIA5C///Piuv//9UeVCANIA9Wcq0iDn0hFCALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAOIBJWcq0iCX0hDyAMQtfZrprk9umNywB9Ig4gC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAOVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgCjcDmCQgAiAUNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQcAeaiACQeAdaiACQfgjahCyAUEoIQMgAikDwB4hEiACKQPIHiETIAIpA9AeIRUgAikD2B4hFyACKQPgHiEYIAIpA+geIRlCACERQgAhDEIAIQtCACEJQgAhDkIAIRADQCACQbAUaiACQcAeaiADaikDACIKQgAgGUIAEMkDIAJBwBRqIApCACAYQgAQyQMgAkHQFGogCkIAIBdCABDJAyACQeAUaiAKQgAgFUIAEMkDIAJB8BRqIApCACATQgAQyQMgAkGAFWogCkIAIBJCABDJAyACQaAUaiACKQOwFCIUIBB8Ig9CAEIAQv3/8//P///5iX8QyQMgAkGQFGogAikDqBQiCkIAQqvV/v///7//uX9CABDJAyACQYAUaiAKQgBC///Piuv//9UeQgAQyQMgAkHwE2ogCkIAQqTsw7WP1LSY5wBCABDJAyACQeATaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJB0BNqIApCAELX2a6a5PbpjcsAQgAQyQMgAkHAE2ogCkIAQprN/8ujvcSAGkIAEMkDIAIpA8gTIBEgAikDgBUiEXwiCiACKQP4FCAMIAIpA/AUIgx8Ig0gDFStfCANIAIpA+gUIAIpA+AUIgwgC3wiCyAMVK18IAsgAikD2BQgAikD0BQiDCAJfCIJIAxUrXwgCSAJIAIpA8gUIAIpA8AUIgwgDnwiDiAMVK18IA4gAikDuBQgDyAUVK18fCIQIA5UrXx8IglWrXx8Ig4gC1StfHwiCyANVK18fCINIAIpA8ATfCIUIA1UrXwgFCACKQPYEyALIAsgAikD0BN8IgtWrXwgCyALIAIpA+gTIA4gAikD4BN8IgwgDlStfCAMIAIpA/gTIAkgCSACKQPwE3wiCVatfCAJIAIpA4gUIBAgAikDgBQiEHwiDiAQVK18IA4gAikDmBQgDyACKQOQFCIPfCAPVK18fCIQIA5UrXx8Ig4gCVStfHwiCSAMVK18fCILVq18fCIMIBRUrXwgCiANVq0gAikDiBUgCiARVK18fHwhESADQQhrIgNBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIA4hCiAJIRQgCyEPIAwhEgwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDiEKIAkhFCALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA4hCiAJIRQgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA4hCiAJIRQMAQsgDkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA5C///Piuv//9UeUgRAIA4hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA5C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIg19IQogCUKk7MO1j9S0mOcAfSISIA5C///Piuv//9UeVCANIA9Wcq0iDn0hFCALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAOIBJWcq0iCX0hDyAMQtfZrprk9umNywB9Ig4gC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAOVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgCjcDmCQgAiAUNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQfAeaiIFIAJB+CNqIgYgAkHAHmoQvQIgAkL9/4uAgIDAhPYANwOgJCACQoKAsKC8gYD6azcDmCQgAkK6sZ2e9YqmpN8ANwOQJCACQsWuyYK3ipbn9wA3A4gkIAJC7djbkvrSxoPcADcDgCQgAkKTyYPUv9iX+xU3A/gjIAJB4CRqIgEgBSAGEL0CIAJBoB9qIAJBsB1qIAEQsgFBKCEDIAJBoCRqQgA3AwAgAkGYJGpCADcDACACQZAkakIANwMAIAJBiCRqQgA3AwAgAkGAJGpCADcDACACQgA3A/gjAkAgBSAGQTAQ8QMEQCACKQOYHyESIAIpA5AfIQkgAikDiB8hCyACKQOAHyENIAIpA/geIQwgAikD8B4hEAJAIAVB+J7AAEEwEPEDRQRAIAwhDyANIQogCyEOIAkhFAwBC0L//8+K6///1R4gCX0iCiASQqvV/v///7//uX9WrSIOfSEUQqTsw7WP1LSY5wAgC30iDyAKIA5UIAlC///Piuv//9UeVnKtIgp9IQ5Cv6WUnM/w0rvkACANfSIJIAogD1YgC0Kk7MO1j9S0mOcAVnKtIgt9IQpC19mumuT26Y3LACAMfSITIAkgC1QgDUK/pZScz/DSu+QAVnKtIgl9IQ9Cms3/y6O9xIAaIAkgE1YgDELX2a6a5PbpjcsAVnKtIBB8fSEQQqvV/v///7//uX8gEn0hEgsgAiASNwOgJCACIBQ3A5gkIAIgDjcDkCQgAiAKNwOIJCACIA83A4AkIAIgEDcD+CMgAkHQH2ogAkGAHWogAkH4I2oQsgEMAQsgAikDgB0hEiACKQOIHSETIAIpA5AdIRUgAikDmB0hFyACKQOgHSEYIAIpA6gdIRlCACERQgAhDEIAIQtCACEJQgAhDkIAIRADQCACQeASaiACQeAdaiADaikDACIKQgAgGUIAEMkDIAJB8BJqIApCACAYQgAQyQMgAkGAE2ogCkIAIBdCABDJAyACQZATaiAKQgAgFUIAEMkDIAJBoBNqIApCACATQgAQyQMgAkGwE2ogCkIAIBJCABDJAyACQdASaiACKQPgEiIUIBB8Ig9CAEIAQv3/8//P///5iX8QyQMgAkHAEmogAikD2BIiCkIAQqvV/v///7//uX9CABDJAyACQbASaiAKQgBC///Piuv//9UeQgAQyQMgAkGgEmogCkIAQqTsw7WP1LSY5wBCABDJAyACQZASaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJBgBJqIApCAELX2a6a5PbpjcsAQgAQyQMgAkHwEWogCkIAQprN/8ujvcSAGkIAEMkDIAIpA/gRIBEgAikDsBMiEXwiCiACKQOoEyAMIAIpA6ATIgx8Ig0gDFStfCANIAIpA5gTIAIpA5ATIgwgC3wiCyAMVK18IAsgAikDiBMgAikDgBMiDCAJfCIJIAxUrXwgCSAJIAIpA/gSIAIpA/ASIgwgDnwiDiAMVK18IA4gAikD6BIgDyAUVK18fCIQIA5UrXx8IglWrXx8Ig4gC1StfHwiCyANVK18fCINIAIpA/ARfCIUIA1UrXwgFCACKQOIEiALIAsgAikDgBJ8IgtWrXwgCyALIAIpA5gSIA4gAikDkBJ8IgwgDlStfCAMIAIpA6gSIAkgCSACKQOgEnwiCVatfCAJIAIpA7gSIBAgAikDsBIiEHwiDiAQVK18IA4gAikDyBIgDyACKQPAEiIPfCAPVK18fCIQIA5UrXx8Ig4gCVStfHwiCSAMVK18fCILVq18fCIMIBRUrXwgCiANVq0gAikDuBMgCiARVK18fHwhESADQQhrIgNBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIA4hCiAJIRQgCyEPIAwhEgwCCyAMQtfZrprk9umNywBWDQAgDELX2a6a5PbpjcsAUgRAIA4hCiAJIRQgCyEPIAwhEkKazf/Lo73EgBohEQwCCyALQr+llJzP8NK75ABWDQBC19mumuT26Y3LACESIAtCv6WUnM/w0rvkAFIEQCAOIQogCSEUIAshD0Kazf/Lo73EgBohEQwCCyAJQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACEPIAlCpOzDtY/UtJjnAFIEQCAOIQogCSEUQprN/8ujvcSAGiERDAILIA5C///Piuv//9UeVg0AQqTsw7WP1LSY5wAhFCAOQv//z4rr///VHlIEQCAOIQpCms3/y6O9xIAaIREMAgtC///Piuv//9UeIQogEEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiERDAELIA5C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIg19IQogCUKk7MO1j9S0mOcAfSISIA5C///Piuv//9UeVCANIA9Wcq0iDn0hFCALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAOIBJWcq0iCX0hDyAMQtfZrprk9umNywB9Ig4gC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAOVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A/gfIAIgCjcD8B8gAiAUNwPoHyACIA83A+AfIAIgEjcD2B8gAiARNwPQHwtBKCEDIAIpA6AfIRIgAikDqB8hEyACKQOwHyEVIAIpA7gfIRcgAikDwB8hGCACKQPIHyEZQgAhEUIAIQxCACELQgAhCUIAIQ5CACEQA0AgAkGQEWogAkGgH2ogA2opAwAiCkIAIBlCABDJAyACQaARaiAKQgAgGEIAEMkDIAJBsBFqIApCACAXQgAQyQMgAkHAEWogCkIAIBVCABDJAyACQdARaiAKQgAgE0IAEMkDIAJB4BFqIApCACASQgAQyQMgAkGAEWogAikDkBEiFCAQfCIPQgBCAEL9//P/z///+Yl/EMkDIAJB8BBqIAIpA4gRIgpCAEKr1f7///+//7l/QgAQyQMgAkHgEGogCkIAQv//z4rr///VHkIAEMkDIAJB0BBqIApCAEKk7MO1j9S0mOcAQgAQyQMgAkHAEGogCkIAQr+llJzP8NK75ABCABDJAyACQbAQaiAKQgBC19mumuT26Y3LAEIAEMkDIAJBoBBqIApCAEKazf/Lo73EgBpCABDJAyACKQOoECARIAIpA+ARIhF8IgogAikD2BEgDCACKQPQESIMfCINIAxUrXwgDSACKQPIESACKQPAESIMIAt8IgsgDFStfCALIAIpA7gRIAIpA7ARIgwgCXwiCSAMVK18IAkgCSACKQOoESACKQOgESIMIA58Ig4gDFStfCAOIAIpA5gRIA8gFFStfHwiECAOVK18fCIJVq18fCIOIAtUrXx8IgsgDVStfHwiDSACKQOgEHwiFCANVK18IBQgAikDuBAgCyALIAIpA7AQfCILVq18IAsgCyACKQPIECAOIAIpA8AQfCIMIA5UrXwgDCACKQPYECAJIAkgAikD0BB8IglWrXwgCSACKQPoECAQIAIpA+AQIhB8Ig4gEFStfCAOIAIpA/gQIA8gAikD8BAiD3wgD1StfHwiECAOVK18fCIOIAlUrXx8IgkgDFStfHwiC1atfHwiDCAUVK18IAogDVatIAIpA+gRIAogEVStfHx8IREgA0EIayIDQXhHDQALAkACQCARQprN/8ujvcSAGlYNACARQprN/8ujvcSAGlIEQCAOIQogCSEUIAshDyAMIRIMAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIA4hCiAJIRQgCyEPIAwhEgwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACESIAtCv6WUnM/w0rvkAFIEQCAOIQogCSEUIAshDwwBCyAJQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEPIAlCpOzDtY/UtJjnAFIEQCAOIQogCSEUDAELIA5C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCAOQv//z4rr///VHlIEQCAOIQoMAQtC///Piuv//9UeIQogEEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEQwBCyAOQv//z4rr///VHn0iDyAQQqvV/v///7//uX9UrSINfSEKIAlCpOzDtY/UtJjnAH0iEiAOQv//z4rr///VHlQgDSAPVnKtIg59IRQgC0K/pZScz/DSu+QAfSINIAlCpOzDtY/UtJjnAFQgDiASVnKtIgl9IQ8gDELX2a6a5PbpjcsAfSIOIAtCv6WUnM/w0rvkAFQgCSANVnKtIgl9IRIgESAMQtfZrprk9umNywBUIAkgDlZyrX1Cms3/y6O9xIAafSERIBBC1aqBgICAwIDGAHwhEAsgAiAQNwOoICACIAo3A6AgIAIgFDcDmCAgAiAPNwOQICACIBI3A4ggIAIgETcDgCBBKCEDIAIpA9AfIRIgAikD2B8hEyACKQPgHyEVIAIpA+gfIRcgAikD8B8hGCACKQP4HyEZQgAhEEIAIQxCACELQgAhCUIAIQ5CACERA0AgAkHAD2ogAkHQH2ogA2opAwAiCkIAIBlCABDJAyACQdAPaiAKQgAgGEIAEMkDIAJB4A9qIApCACAXQgAQyQMgAkHwD2ogCkIAIBVCABDJAyACQYAQaiAKQgAgE0IAEMkDIAJBkBBqIApCACASQgAQyQMgAkGwD2ogAikDwA8iFCARfCIPQgBCAEL9//P/z///+Yl/EMkDIAJBoA9qIAIpA7gPIgpCAEKr1f7///+//7l/QgAQyQMgAkGQD2ogCkIAQv//z4rr///VHkIAEMkDIAJBgA9qIApCAEKk7MO1j9S0mOcAQgAQyQMgAkHwDmogCkIAQr+llJzP8NK75ABCABDJAyACQeAOaiAKQgBC19mumuT26Y3LAEIAEMkDIAJB0A5qIApCAEKazf/Lo73EgBpCABDJAyACKQPYDiAQIAIpA5AQIhB8IgogAikDiBAgDCACKQOAECIMfCINIAxUrXwgDSACKQP4DyACKQPwDyIMIAt8IgsgDFStfCALIAIpA+gPIAIpA+APIgwgCXwiCSAMVK18IAkgCSACKQPYDyACKQPQDyIMIA58Ig4gDFStfCAOIAIpA8gPIA8gFFStfHwiESAOVK18fCIJVq18fCIOIAtUrXx8IgsgDVStfHwiDSACKQPQDnwiFCANVK18IBQgAikD6A4gCyALIAIpA+AOfCILVq18IAsgCyACKQP4DiAOIAIpA/AOfCIMIA5UrXwgDCACKQOIDyAJIAkgAikDgA98IglWrXwgCSACKQOYDyARIAIpA5APIhF8Ig4gEVStfCAOIAIpA6gPIA8gAikDoA8iD3wgD1StfHwiESAOVK18fCIOIAlUrXx8IgkgDFStfHwiC1atfHwiDCAUVK18IAogDVatIAIpA5gQIAogEFStfHx8IRAgA0EIayIDQXhHDQALAkACQCAQQprN/8ujvcSAGlYNACAQQprN/8ujvcSAGlIEQCAOIRQgCSESIAshEyAMIRUMAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIA4hFCAJIRIgCyETIAwhFQwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIAtCv6WUnM/w0rvkAFIEQCAOIRQgCSESIAshEwwBCyAJQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIAlCpOzDtY/UtJjnAFIEQCAOIRQgCSESDAELIA5C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhEiAOQv//z4rr///VHlIEQCAOIRQMAQtC///Piuv//9UeIRQgEUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEAwBCyAOQv//z4rr///VHn0iCiARQqvV/v///7//uX9UrSIPfSEUIAlCpOzDtY/UtJjnAH0iDSAOQv//z4rr///VHlQgCiAPVHKtIgp9IRIgC0K/pZScz/DSu+QAfSIOIAlCpOzDtY/UtJjnAFQgCiANVnKtIgp9IRMgDELX2a6a5PbpjcsAfSIJIAtCv6WUnM/w0rvkAFQgCiAOVnKtIgp9IRUgECAMQtfZrprk9umNywBUIAkgClRyrX1Cms3/y6O9xIAafSEQIBFC1aqBgICAwIDGAHwhEQsgAiARNwPYICACIBQ3A9AgIAIgEjcDyCAgAiATNwPAICACIBU3A7ggIAIgEDcDsCBBKCEDQgAhC0IAIQlCACEPQgAhCkIAIQ1CACEMA0AgAkHwDWogAkHQH2ogA2opAwAiDkIAIBFCABDJAyACQYAOaiAOQgAgFEIAEMkDIAJBkA5qIA5CACASQgAQyQMgAkGgDmogDkIAIBNCABDJAyACQbAOaiAOQgAgFUIAEMkDIAJBwA5qIA5CACAQQgAQyQMgAkHgDWogAikD8A0iFyAMfCIMQgBCAEL9//P/z///+Yl/EMkDIAJB0A1qIAIpA+gNIg5CAEKr1f7///+//7l/QgAQyQMgAkHADWogDkIAQv//z4rr///VHkIAEMkDIAJBsA1qIA5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgDWogDkIAQr+llJzP8NK75ABCABDJAyACQZANaiAOQgBC19mumuT26Y3LAEIAEMkDIAJBgA1qIA5CAEKazf/Lo73EgBpCABDJAyACKQOIDSACKQPADiIZIAt8Ig4gAikDuA4gAikDsA4iCyAJfCIJIAtUrXwgCSAJIAIpA6gOIA8gAikDoA4iD3wiCyAPVK18IAsgCyACKQOYDiACKQOQDiIPIAp8IgogD1StfCAKIAogAikDiA4gDSACKQOADiINfCIPIA1UrXwgDyAPIAIpA/gNIAwgF1StfHwiD1atfHwiClatfHwiC1atfHwiCVatfHwiFyACKQOADXwiGCAXVK18IBggAikDmA0gCSAJIAIpA5ANfCIJVq18IAkgAikDqA0gCyALIAIpA6ANfCILVq18IAsgAikDuA0gCiAKIAIpA7ANfCIKVq18IAogAikDyA0gAikDwA0iDSAPfCIPIA1UrXwgDyACKQPYDSACKQPQDSINIAx8IA1UrXx8IgwgD1StfHwiDSAKVK18fCIKIAtUrXx8Ig8gCVStfHwiCSAYVK18IA4gF1atIAIpA8gOIA4gGVStfHx8IQsgA0EIayIDQXhHDQALAkACQCALQprN/8ujvcSAGlYNACALQprN/8ujvcSAGlIEQCANIREgCiEOIA8hECAJIRIMAgsgCULX2a6a5PbpjcsAVg0AAkAgCULX2a6a5PbpjcsAUgRAIA0hESAKIQ4gDyEQIAkhEgwBCyAPQr+llJzP8NK75ABWDQFC19mumuT26Y3LACESIA9Cv6WUnM/w0rvkAFIEQCANIREgCiEOIA8hEAwBCyAKQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEQIApCpOzDtY/UtJjnAFIEQCANIREgCiEODAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhDiANQv//z4rr///VHlIEQCANIREMAQtC///Piuv//9UeIREgDEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohCwwBCyANQv//z4rr///VHn0iDiAMQqvV/v///7//uX9UrSIUfSERIApCpOzDtY/UtJjnAH0iEiANQv//z4rr///VHlQgDiAUVHKtIg19IQ4gD0K/pZScz/DSu+QAfSIUIApCpOzDtY/UtJjnAFQgDSASVnKtIgp9IRAgCULX2a6a5PbpjcsAfSINIA9Cv6WUnM/w0rvkAFQgCiAUVnKtIgp9IRIgCyAJQtfZrprk9umNywBUIAogDVZyrX1Cms3/y6O9xIAafSELIAxC1aqBgICAwIDGAHwhDAsgAiAMNwOIISACIBE3A4AhIAIgDjcD+CAgAiAQNwPwICACIBI3A+ggIAIgCzcD4CBBKCEDIAJBoCRqQgA3AwAgAkGYJGpCADcDACACQZAkakIANwMAIAJBiCRqQgA3AwAgAkGAJGpCADcDACACQgA3A/gjAkACQAJAIAJB4CBqIAJB+CNqQTAQ8QMEQCACKQOAHSESIAIpA4gdIRMgAikDkB0hFSACKQOYHSEXIAIpA6AdIRggAikDqB0hGUIAIRFCACEMQgAhC0IAIQlCACEOQgAhEANAIAJBoAxqIAJBsCBqIANqKQMAIgpCACAZQgAQyQMgAkGwDGogCkIAIBhCABDJAyACQcAMaiAKQgAgF0IAEMkDIAJB0AxqIApCACAVQgAQyQMgAkHgDGogCkIAIBNCABDJAyACQfAMaiAKQgAgEkIAEMkDIAJBkAxqIAIpA6AMIhQgEHwiD0IAQgBC/f/z/8////mJfxDJAyACQYAMaiACKQOYDCIKQgBCq9X+////v/+5f0IAEMkDIAJB8AtqIApCAEL//8+K6///1R5CABDJAyACQeALaiAKQgBCpOzDtY/UtJjnAEIAEMkDIAJB0AtqIApCAEK/pZScz/DSu+QAQgAQyQMgAkHAC2ogCkIAQtfZrprk9umNywBCABDJAyACQbALaiAKQgBCms3/y6O9xIAaQgAQyQMgAikDuAsgESACKQPwDCIRfCIKIAIpA+gMIAwgAikD4AwiDHwiDSAMVK18IA0gAikD2AwgAikD0AwiDCALfCILIAxUrXwgCyACKQPIDCACKQPADCIMIAl8IgkgDFStfCAJIAkgAikDuAwgAikDsAwiDCAOfCIOIAxUrXwgDiACKQOoDCAPIBRUrXx8IhAgDlStfHwiCVatfHwiDiALVK18fCILIA1UrXx8Ig0gAikDsAt8IhQgDVStfCAUIAIpA8gLIAsgCyACKQPAC3wiC1atfCALIAsgAikD2AsgDiACKQPQC3wiDCAOVK18IAwgAikD6AsgCSAJIAIpA+ALfCIJVq18IAkgAikD+AsgECACKQPwCyIQfCIOIBBUrXwgDiACKQOIDCAPIAIpA4AMIg98IA9UrXx8IhAgDlStfHwiDiAJVK18fCIJIAxUrXx8IgtWrXx8IgwgFFStfCAKIA1WrSACKQP4DCAKIBFUrXx8fCERIANBCGsiA0F4Rw0ACyARQprN/8ujvcSAGlYNAiARQprN/8ujvcSAGlENASAOIRQgCSEKIAshDyAMIRIMAwtBrKrAAEEvQdyqwAAQ/gMACyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDiEUIAkhCiALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA4hFCAJIQogCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA4hFCAJIQoMAQsgDkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEKIA5C///Piuv//9UeUgRAIA4hFAwBC0L//8+K6///1R4hFCAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA5C///Piuv//9UefSIKIBBCq9X+////v/+5f1StIg99IRQgCUKk7MO1j9S0mOcAfSINIA5C///Piuv//9UeVCAKIA9Ucq0iDn0hCiALQr+llJzP8NK75AB9IhIgCUKk7MO1j9S0mOcAVCANIA5Ucq0iCX0hDyAMQtfZrprk9umNywB9Ig4gC0K/pZScz/DSu+QAVCAJIBJWcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAOVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgFDcDmCQgAiAKNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQeAkaiIBIAJBgCBqIAJB+CNqEL0CIAJBgCNqIAEgAkGgH2oQsgFBKCEDIAIpA7AdIRIgAikDuB0hEyACKQPAHSEVIAIpA8gdIRcgAikD0B0hGCACKQPYHSEZQgAhEUIAIQxCACELQgAhCUIAIQ5CACEQA0AgAkHQCmogAkHgIGogA2opAwAiCkIAIBlCABDJAyACQeAKaiAKQgAgGEIAEMkDIAJB8ApqIApCACAXQgAQyQMgAkGAC2ogCkIAIBVCABDJAyACQZALaiAKQgAgE0IAEMkDIAJBoAtqIApCACASQgAQyQMgAkHACmogAikD0AoiFCAQfCIPQgBCAEL9//P/z///+Yl/EMkDIAJBsApqIAIpA8gKIgpCAEKr1f7///+//7l/QgAQyQMgAkGgCmogCkIAQv//z4rr///VHkIAEMkDIAJBkApqIApCAEKk7MO1j9S0mOcAQgAQyQMgAkGACmogCkIAQr+llJzP8NK75ABCABDJAyACQfAJaiAKQgBC19mumuT26Y3LAEIAEMkDIAJB4AlqIApCAEKazf/Lo73EgBpCABDJAyACKQPoCSARIAIpA6ALIhF8IgogAikDmAsgDCACKQOQCyIMfCINIAxUrXwgDSACKQOICyACKQOACyIMIAt8IgsgDFStfCALIAIpA/gKIAIpA/AKIgwgCXwiCSAMVK18IAkgCSACKQPoCiACKQPgCiIMIA58Ig4gDFStfCAOIAIpA9gKIA8gFFStfHwiECAOVK18fCIJVq18fCIOIAtUrXx8IgsgDVStfHwiDSACKQPgCXwiFCANVK18IBQgAikD+AkgCyALIAIpA/AJfCILVq18IAsgCyACKQOICiAOIAIpA4AKfCIMIA5UrXwgDCACKQOYCiAJIAkgAikDkAp8IglWrXwgCSACKQOoCiAQIAIpA6AKIhB8Ig4gEFStfCAOIAIpA7gKIA8gAikDsAoiD3wgD1StfHwiECAOVK18fCIOIAlUrXx8IgkgDFStfHwiC1atfHwiDCAUVK18IAogDVatIAIpA6gLIAogEVStfHx8IREgA0EIayIDQXhHDQALAkACQCARQprN/8ujvcSAGlYNACARQprN/8ujvcSAGlIEQCAOIRQgCSEKIAshDyAMIRIMAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIA4hFCAJIQogCyEPIAwhEgwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACESIAtCv6WUnM/w0rvkAFIEQCAOIRQgCSEKIAshDwwBCyAJQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEPIAlCpOzDtY/UtJjnAFIEQCAOIRQgCSEKDAELIA5C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhCiAOQv//z4rr///VHlIEQCAOIRQMAQtC///Piuv//9UeIRQgEEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEQwBCyAOQv//z4rr///VHn0iCiAQQqvV/v///7//uX9UrSIPfSEUIAlCpOzDtY/UtJjnAH0iDSAOQv//z4rr///VHlQgCiAPVHKtIg59IQogC0K/pZScz/DSu+QAfSISIAlCpOzDtY/UtJjnAFQgDSAOVHKtIgl9IQ8gDELX2a6a5PbpjcsAfSIOIAtCv6WUnM/w0rvkAFQgCSASVnKtIgl9IRIgESAMQtfZrprk9umNywBUIAkgDlZyrX1Cms3/y6O9xIAafSERIBBC1aqBgICAwIDGAHwhEAsgAiAQNwOgJCACIBQ3A5gkIAIgCjcDkCQgAiAPNwOIJCACIBI3A4AkIAIgETcD+CMgAkGQIWogAkGAI2ogAkH4I2oQvQJBKCEDIAIpA8AeIRMgAikDyB4hESACKQPQHiEVIAIpA9geIRcgAikD4B4hECACKQPoHiEYQgAhDkIAIQxCACELQgAhCUIAIQ1CACEUA0AgAkGACWogAkGgH2ogA2opAwAiCkIAIBhCABDJAyACQZAJaiAKQgAgEEIAEMkDIAJBoAlqIApCACAXQgAQyQMgAkGwCWogCkIAIBVCABDJAyACQcAJaiAKQgAgEUIAEMkDIAJB0AlqIApCACATQgAQyQMgAkHwCGogFCACKQOACSIUfCIPQgBCAEL9//P/z///+Yl/EMkDIAJB4AhqIAIpA/gIIgpCAEKr1f7///+//7l/QgAQyQMgAkHQCGogCkIAQv//z4rr///VHkIAEMkDIAJBwAhqIApCAEKk7MO1j9S0mOcAQgAQyQMgAkGwCGogCkIAQr+llJzP8NK75ABCABDJAyACQaAIaiAKQgBC19mumuT26Y3LAEIAEMkDIAJBkAhqIApCAEKazf/Lo73EgBpCABDJAyACKQOYCCACKQPQCSIZIA58IgogAikDyAkgDCACKQPACSIMfCIOIAxUrXwgDiAOIAIpA7gJIAIpA7AJIgwgC3wiCyAMVK18IAsgCyACKQOoCSACKQOgCSIMIAl8IgkgDFStfCAJIAkgAikDmAkgAikDkAkiDCANfCINIAxUrXwgDSANIAIpA4gJIA8gFFStfHwiDVatfHwiCVatfHwiC1atfHwiDlatfHwiEiACKQOQCHwiDCASVK18IAwgDCACKQOoCCAOIA4gAikDoAh8Ig5WrXwgDiACKQO4CCALIAsgAikDsAh8IgtWrXwgCyACKQPICCAJIAkgAikDwAh8IglWrXwgCSACKQPYCCACKQPQCCIUIA18Ig0gFFStfCANIAIpA+gIIA8gAikD4AgiD3wgD1StfHwiFCANVK18fCINIAlUrXx8IgkgC1StfHwiCyAOVK18fCIMVq18IAogElatIAIpA9gJIAogGVStfHx8IQ4gA0EIayIDQXhHDQALAkACQCAOQprN/8ujvcSAGlYNACAOQprN/8ujvcSAGlIEQCANIRUgCSEXIAshGCAMIRkMAgsgDELX2a6a5PbpjcsAVg0AAkAgDELX2a6a5PbpjcsAUgRAIA0hFSAJIRcgCyEYIAwhGQwBCyALQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEZIAtCv6WUnM/w0rvkAFIEQCANIRUgCSEXIAshGAwBCyAJQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEYIAlCpOzDtY/UtJjnAFIEQCANIRUgCSEXDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFyANQv//z4rr///VHlIEQCANIRUMAQtC///Piuv//9UeIRUgFEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDgwBCyANQv//z4rr///VHn0iCiAUQqvV/v///7//uX9UrSIPfSEVIAlCpOzDtY/UtJjnAH0iEiANQv//z4rr///VHlQgCiAPVHKtIgp9IRcgC0K/pZScz/DSu+QAfSIPIAlCpOzDtY/UtJjnAFQgCiASVnKtIgp9IRggDELX2a6a5PbpjcsAfSIJIAtCv6WUnM/w0rvkAFQgCiAPVnKtIgp9IRkgDiAMQtfZrprk9umNywBUIAkgClRyrX1Cms3/y6O9xIAafSEOIBRC1aqBgICAwIDGAHwhFAsgAkH4I2oiBiACQZAhaiACQeAgahBMAn8CQAJAAkACQAJAAkAgAigC+CNBAUcEQCACQeghaiACQagkaikDADcDACACQeAhaiACQaAkaiIBKQMANwMAIAJB2CFqIAJBmCRqIgMpAwA3AwAgAkHQIWogAkGQJGoiBykDADcDACACQcghaiACQYgkaiIEKQMANwMAIAIgAikDgCQ3A8AhIAFCADcDACADQgA3AwAgB0IANwMAIARCADcDACACQYAkakIANwMAIAJCADcD+CMCQCACQcAhaiIBIAZBMBDxA0UNACABEPECQf8BcUECRg0AQSghAyACKQPgHSEWIAIpA+gdIRogAikD8B0hGyACKQP4HSEcIAIpA4AeIR0gAikDiB4hHkIAIRFCACEMQgAhC0IAIQlCACENQgAhEANAIAJBsAdqIAJBwCFqIANqKQMAIgpCACAeQgAQyQMgAkHAB2ogCkIAIB1CABDJAyACQdAHaiAKQgAgHEIAEMkDIAJB4AdqIApCACAbQgAQyQMgAkHwB2ogCkIAIBpCABDJAyACQYAIaiAKQgAgFkIAEMkDIAJBoAdqIAIpA7AHIhIgEHwiD0IAQgBC/f/z/8////mJfxDJAyACQZAHaiACKQOoByIKQgBCq9X+////v/+5f0IAEMkDIAJBgAdqIApCAEL//8+K6///1R5CABDJAyACQfAGaiAKQgBCpOzDtY/UtJjnAEIAEMkDIAJB4AZqIApCAEK/pZScz/DSu+QAQgAQyQMgAkHQBmogCkIAQtfZrprk9umNywBCABDJAyACQcAGaiAKQgBCms3/y6O9xIAaQgAQyQMgAikDyAYgESACKQOACCIRfCIKIAIpA/gHIAIpA/AHIhMgDHwiDCATVK18IAwgAikD6AcgAikD4AciEyALfCILIBNUrXwgCyALIAIpA9gHIAIpA9AHIhMgCXwiCSATVK18IAkgCSACKQPIByACKQPAByITIA18Ig0gE1StfCANIAIpA7gHIA8gElStfHwiECANVK18fCIJVq18fCILVq18fCINIAxUrXx8IhIgAikDwAZ8IgwgElStfCAMIAwgAikD2AYgDSACKQPQBnwiEyANVK18IBMgAikD6AYgCyALIAIpA+AGfCILVq18IAsgAikD+AYgCSAJIAIpA/AGfCIJVq18IAkgAikDiAcgECACKQOAByIQfCINIBBUrXwgDSACKQOYByAPIAIpA5AHIg98IA9UrXx8IhAgDVStfHwiDSAJVK18fCIJIAtUrXx8IgsgE1StfHwiDFatfCAKIBJWrSACKQOICCAKIBFUrXx8fCERIANBCGsiA0F4Rw0ACyARQprN/8ujvcSAGlYNBiARQprN/8ujvcSAGlENBSANIQogCSETIAshDyAMIRIMBwsgAkHgJGogAkHAIWoQoQJBKCEDIAIpA+AkIRYgAikD6CQhGiACKQPwJCEbIAIpA/gkIRwgAikDgCUhHSACKQOIJSEeQgAhEUIAIQxCACELQgAhCUIAIQ1CACEQA0AgAkHAAmogAkHgJGogA2opAwAiCkIAIB5CABDJAyACQdACaiAKQgAgHUIAEMkDIAJB4AJqIApCACAcQgAQyQMgAkHwAmogCkIAIBtCABDJAyACQYADaiAKQgAgGkIAEMkDIAJBkANqIApCACAWQgAQyQMgAkGwAmogAikDwAIiEiAQfCIPQgBCAEL9//P/z///+Yl/EMkDIAJBoAJqIAIpA7gCIgpCAEKr1f7///+//7l/QgAQyQMgAkGQAmogCkIAQv//z4rr///VHkIAEMkDIAJBgAJqIApCAEKk7MO1j9S0mOcAQgAQyQMgAkHwAWogCkIAQr+llJzP8NK75ABCABDJAyACQeABaiAKQgBC19mumuT26Y3LAEIAEMkDIAJB0AFqIApCAEKazf/Lo73EgBpCABDJAyACKQPYASARIAIpA5ADIhF8IgogAikDiAMgAikDgAMiEyAMfCIMIBNUrXwgDCACKQP4AiACKQPwAiITIAt8IgsgE1StfCALIAsgAikD6AIgAikD4AIiEyAJfCIJIBNUrXwgCSAJIAIpA9gCIAIpA9ACIhMgDXwiDSATVK18IA0gAikDyAIgDyASVK18fCIQIA1UrXx8IglWrXx8IgtWrXx8Ig0gDFStfHwiEiACKQPQAXwiDCASVK18IAwgDCACKQPoASANIAIpA+ABfCITIA1UrXwgEyACKQP4ASALIAsgAikD8AF8IgtWrXwgCyACKQOIAiAJIAkgAikDgAJ8IglWrXwgCSACKQOYAiAQIAIpA5ACIhB8Ig0gEFStfCANIAIpA6gCIA8gAikDoAIiD3wgD1StfHwiECANVK18fCINIAlUrXx8IgkgC1StfHwiCyATVK18fCIMVq18IAogElatIAIpA5gDIAogEVStfHx8IREgA0EIayIDQXhHDQALIBFCms3/y6O9xIAaWA0BDAILIAIgAikDiCQ3A+gkIAIgAikDgCQ3A+AkQYSdwABBKyACQeAkakH4q8AAQZiswAAQygMACyARQprN/8ujvcSAGlIEQCANIQogCSETIAshDyAMIRIMAgsgDELX2a6a5PbpjcsAVg0AIAxC19mumuT26Y3LAFIEQCANIQogCSETIAshDyAMIRJCms3/y6O9xIAaIREMAgsgC0K/pZScz/DSu+QAVg0AQtfZrprk9umNywAhEiALQr+llJzP8NK75ABSBEAgDSEKIAkhEyALIQ9Cms3/y6O9xIAaIREMAgsgCUKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhDyAJQqTsw7WP1LSY5wBSBEAgDSEKIAkhE0Kazf/Lo73EgBohEQwCCyANQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIRMgDUL//8+K6///1R5SBEAgDSEKQprN/8ujvcSAGiERDAILQv//z4rr///VHiEKIBBCqtX+////v/+5f1YNAEKazf/Lo73EgBohEQwBCyANQv//z4rr///VHn0iDyAQQqvV/v///7//uX9UrSISfSEKIAlCpOzDtY/UtJjnAH0iFiANQv//z4rr///VHlQgDyASVHKtIg99IRMgC0K/pZScz/DSu+QAfSINIAlCpOzDtY/UtJjnAFQgDyAWVnKtIgl9IQ8gDELX2a6a5PbpjcsAfSIWIAtCv6WUnM/w0rvkAFQgCSANVnKtIgl9IRIgESAMQtfZrprk9umNywBUIAkgFlZyrX1Cms3/y6O9xIAafSERIBBC1aqBgICAwIDGAHwhEAsgAiAQNwOgJCACIAo3A5gkIAIgEzcDkCQgAiAPNwOIJCACIBI3A4AkIAIgETcD+CMgAkH4I2ogAkHAIWpBMBDxAwRAQaSrwABBIkHIq8AAEP4DAAsgAkGYImogAkGIJWopAwA3AwAgAkGQImogAkGAJWopAwA3AwAgAkGIImogAkH4JGopAwA3AwAgAkGAImogAkHwJGopAwA3AwAgAkH4IWogAkHoJGopAwA3AwAgAiACKQPgJDcD8CFBAQwDCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDSEKIAkhEyALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA0hCiAJIRMgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA0hCiAJIRMMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACETIA1C///Piuv//9UeUgRAIA0hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA1C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIhJ9IQogCUKk7MO1j9S0mOcAfSIWIA1C///Piuv//9UeVCAPIBJUcq0iD30hEyALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAPIBZWcq0iCX0hDyAMQtfZrprk9umNywB9IhYgC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAWVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgCjcDmCQgAiATNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQYAjaiACQfgjahChAkEoIQMgAikDgCMhFiACKQOIIyEaIAIpA5AjIRsgAikDmCMhHCACKQOgIyEdIAIpA6gjIR5CACERQgAhDEIAIQtCACEJQgAhDUIAIRADQCACQeAFaiACQYAjaiADaikDACIKQgAgHkIAEMkDIAJB8AVqIApCACAdQgAQyQMgAkGABmogCkIAIBxCABDJAyACQZAGaiAKQgAgG0IAEMkDIAJBoAZqIApCACAaQgAQyQMgAkGwBmogCkIAIBZCABDJAyACQdAFaiACKQPgBSISIBB8Ig9CAEIAQv3/8//P///5iX8QyQMgAkHABWogAikD2AUiCkIAQqvV/v///7//uX9CABDJAyACQbAFaiAKQgBC///Piuv//9UeQgAQyQMgAkGgBWogCkIAQqTsw7WP1LSY5wBCABDJAyACQZAFaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJBgAVqIApCAELX2a6a5PbpjcsAQgAQyQMgAkHwBGogCkIAQprN/8ujvcSAGkIAEMkDIAIpA/gEIBEgAikDsAYiEXwiCiACKQOoBiACKQOgBiITIAx8IgwgE1StfCAMIAIpA5gGIAIpA5AGIhMgC3wiCyATVK18IAsgCyACKQOIBiACKQOABiITIAl8IgkgE1StfCAJIAkgAikD+AUgAikD8AUiEyANfCINIBNUrXwgDSACKQPoBSAPIBJUrXx8IhAgDVStfHwiCVatfHwiC1atfHwiDSAMVK18fCISIAIpA/AEfCIMIBJUrXwgDCAMIAIpA4gFIA0gAikDgAV8IhMgDVStfCATIAIpA5gFIAsgCyACKQOQBXwiC1atfCALIAIpA6gFIAkgCSACKQOgBXwiCVatfCAJIAIpA7gFIBAgAikDsAUiEHwiDSAQVK18IA0gAikDyAUgDyACKQPABSIPfCAPVK18fCIQIA1UrXx8Ig0gCVStfHwiCSALVK18fCILIBNUrXx8IgxWrXwgCiASVq0gAikDuAYgCiARVK18fHwhESADQQhrIgNBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIA0hCiAJIRMgCyEPIAwhEgwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDSEKIAkhEyALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA0hCiAJIRMgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA0hCiAJIRMMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACETIA1C///Piuv//9UeUgRAIA0hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA1C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIhJ9IQogCUKk7MO1j9S0mOcAfSIWIA1C///Piuv//9UeVCAPIBJUcq0iD30hEyALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAPIBZWcq0iCX0hDyAMQtfZrprk9umNywB9IhYgC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAWVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A4glIAIgCjcDgCUgAiATNwP4JCACIA83A/AkIAIgEjcD6CQgAiARNwPgJEEoIQMgAikD4B0hFiACKQPoHSEaIAIpA/AdIRsgAikD+B0hHCACKQOAHiEdIAIpA4geIR5CACERQgAhDEIAIQtCACEJQgAhDUIAIRADQCACQZAEaiACQcAhaiADaikDACIKQgAgHkIAEMkDIAJBoARqIApCACAdQgAQyQMgAkGwBGogCkIAIBxCABDJAyACQcAEaiAKQgAgG0IAEMkDIAJB0ARqIApCACAaQgAQyQMgAkHgBGogCkIAIBZCABDJAyACQYAEaiACKQOQBCISIBB8Ig9CAEIAQv3/8//P///5iX8QyQMgAkHwA2ogAikDiAQiCkIAQqvV/v///7//uX9CABDJAyACQeADaiAKQgBC///Piuv//9UeQgAQyQMgAkHQA2ogCkIAQqTsw7WP1LSY5wBCABDJAyACQcADaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJBsANqIApCAELX2a6a5PbpjcsAQgAQyQMgAkGgA2ogCkIAQprN/8ujvcSAGkIAEMkDIAIpA6gDIBEgAikD4AQiEXwiCiACKQPYBCACKQPQBCITIAx8IgwgE1StfCAMIAIpA8gEIAIpA8AEIhMgC3wiCyATVK18IAsgCyACKQO4BCACKQOwBCITIAl8IgkgE1StfCAJIAkgAikDqAQgAikDoAQiEyANfCINIBNUrXwgDSACKQOYBCAPIBJUrXx8IhAgDVStfHwiCVatfHwiC1atfHwiDSAMVK18fCISIAIpA6ADfCIMIBJUrXwgDCAMIAIpA7gDIA0gAikDsAN8IhMgDVStfCATIAIpA8gDIAsgCyACKQPAA3wiC1atfCALIAIpA9gDIAkgCSACKQPQA3wiCVatfCAJIAIpA+gDIBAgAikD4AMiEHwiDSAQVK18IA0gAikD+AMgDyACKQPwAyIPfCAPVK18fCIQIA1UrXx8Ig0gCVStfHwiCSALVK18fCILIBNUrXx8IgxWrXwgCiASVq0gAikD6AQgCiARVK18fHwhESADQQhrIgNBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIA0hCiAJIRMgCyEPIAwhEgwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDSEKIAkhEyALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA0hCiAJIRMgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA0hCiAJIRMMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACETIA1C///Piuv//9UeUgRAIA0hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA1C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIhJ9IQogCUKk7MO1j9S0mOcAfSIWIA1C///Piuv//9UeVCAPIBJUcq0iD30hEyALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAPIBZWcq0iCX0hDyAMQtfZrprk9umNywB9IhYgC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAWVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgCjcDmCQgAiATNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQeAkaiACQfgjakEwEPEDBEBB7KrAAEEoQZSrwAAQ/gMACyACQZgiaiACQagjaikDADcDACACQZAiaiACQaAjaikDADcDACACQYgiaiACQZgjaikDADcDACACQYAiaiACQZAjaikDADcDACACQfghaiACQYgjaikDADcDACACIAIpA4AjNwPwIUEACyEBQSghAyACKQPAHiEWIAIpA8geIRogAikD0B4hGyACKQPYHiEcIAIpA+AeIR0gAikD6B4hHkIAIRFCACEMQgAhC0IAIQlCACENQgAhEANAIAJB8ABqIAJBkB5qIANqKQMAIgpCACAeQgAQyQMgAkGAAWogCkIAIB1CABDJAyACQZABaiAKQgAgHEIAEMkDIAJBoAFqIApCACAbQgAQyQMgAkGwAWogCkIAIBpCABDJAyACQcABaiAKQgAgFkIAEMkDIAJB4ABqIAIpA3AiEiAQfCIPQgBCAEL9//P/z///+Yl/EMkDIAJB0ABqIAIpA2giCkIAQqvV/v///7//uX9CABDJAyACQUBrIApCAEL//8+K6///1R5CABDJAyACQTBqIApCAEKk7MO1j9S0mOcAQgAQyQMgAkEgaiAKQgBCv6WUnM/w0rvkAEIAEMkDIAJBEGogCkIAQtfZrprk9umNywBCABDJAyACIApCAEKazf/Lo73EgBpCABDJAyACKQMIIBEgAikDwAEiEXwiCiACKQO4ASACKQOwASITIAx8IgwgE1StfCAMIAIpA6gBIAIpA6ABIhMgC3wiCyATVK18IAsgCyACKQOYASACKQOQASITIAl8IgkgE1StfCAJIAkgAikDiAEgAikDgAEiEyANfCINIBNUrXwgDSACKQN4IA8gElStfHwiECANVK18fCIJVq18fCILVq18fCINIAxUrXx8IhIgAikDAHwiDCASVK18IAwgDCACKQMYIA0gAikDEHwiEyANVK18IBMgAikDKCALIAsgAikDIHwiC1atfCALIAIpAzggCSAJIAIpAzB8IglWrXwgCSACKQNIIBAgAikDQCIQfCINIBBUrXwgDSACKQNYIA8gAikDUCIPfCAPVK18fCIQIA1UrXx8Ig0gCVStfHwiCSALVK18fCILIBNUrXx8IgxWrXwgCiASVq0gAikDyAEgCiARVK18fHwhESADQQhrIgNBeEcNAAsCQAJAIBFCms3/y6O9xIAaVg0AIBFCms3/y6O9xIAaUgRAIA0hCiAJIRMgCyEPIAwhEgwCCyAMQtfZrprk9umNywBWDQACQCAMQtfZrprk9umNywBSBEAgDSEKIAkhEyALIQ8gDCESDAELIAtCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRIgC0K/pZScz/DSu+QAUgRAIA0hCiAJIRMgCyEPDAELIAlCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQ8gCUKk7MO1j9S0mOcAUgRAIA0hCiAJIRMMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACETIA1C///Piuv//9UeUgRAIA0hCgwBC0L//8+K6///1R4hCiAQQqrV/v///7//uX9WDQELQprN/8ujvcSAGiERDAELIA1C///Piuv//9UefSIPIBBCq9X+////v/+5f1StIhJ9IQogCUKk7MO1j9S0mOcAfSIWIA1C///Piuv//9UeVCAPIBJUcq0iD30hEyALQr+llJzP8NK75AB9Ig0gCUKk7MO1j9S0mOcAVCAPIBZWcq0iCX0hDyAMQtfZrprk9umNywB9IhYgC0K/pZScz/DSu+QAVCAJIA1Wcq0iCX0hEiARIAxC19mumuT26Y3LAFQgCSAWVnKtfUKazf/Lo73EgBp9IREgEELVqoGAgIDAgMYAfCEQCyACIBA3A6AkIAIgCjcDmCQgAiATNwOQJCACIA83A4gkIAIgEjcDgCQgAiARNwP4IyACQaAiaiIDIAJB+CNqIAJB8CFqELIBIAJBqCNqAn8gAUUEQCACIBQ3A/giIAIgFTcD8CIgAiAXNwPoIiACIBg3A+AiIAIgGTcD2CIgAiAONwPQIiADDAELIAJB+CJqIAJByB9qKQMANwMAIAJB8CJqIAJBwB9qKQMANwMAIAJB6CJqIAJBuB9qKQMANwMAIAJB4CJqIAJBsB9qKQMANwMAIAJB2CJqIAJBqB9qKQMANwMAIAIgAikDoB83A9AiIAJB8CFqCyIDQShqKQMANwMAIAJBoCNqIANBIGopAwA3AwAgAkGYI2ogA0EYaikDADcDACACQZAjaiADQRBqKQMANwMAIAJBiCNqIANBCGopAwA3AwAgAiADKQMANwOAIyACQfgjaiACQdAiaiACQdAfahBMIAIoAvgjQQFGBEAgAiACKQOIJDcD6CQgAiACKQOAJDcD4CRBhJ3AAEErIAJB4CRqQfirwABBiKzAABDKAwALIAJB2CNqIAJBqCRqKQMANwMAIAJB0CNqIAJBoCRqKQMANwMAIAJByCNqIAJBmCRqKQMANwMAIAJBwCNqIAJBkCRqKQMANwMAIAJBuCNqIAJBiCRqKQMANwMAIAIgAikDgCQ3A7AjIAJB7CNqIgggAkGAI2oQ2AJBACEDIAJBgCRqIgFB3JrAACgCACIHNgIAIAJB1JrAACkCACIKNwP4IyACQfgjaiIFQcibwAAQpQMgAigC/CNBAjYCACACQegkaiIEQQE2AgAgAiACKQP4IzcD4CQgAkHgI2ogCCACQeAkaiIGEO0BIAggAkGQHmoQ2AIgASAHNgIAIAIgCjcD+CMgBUHIm8AAEKUDIAIoAvwjQQI2AgAgBEEBNgIAIAIgAikD+CM3A+AkIAUgCCAGEO0BIAIoAvwjIQEgAigC5CMhByACKALoIyIEIAIoAoAkRgRAIAcgASAEQQJ0EPEDRSEDCyACKAL4IyIEBEAgASAEQQJ0EN8ECyACKALgIyIBBEAgByABQQJ0EN8ECyACKQOoIyESIAIpA6AjIQkgAikDmCMhCyACKQOQIyENIAIpA4gjIQwgAikDgCMhEAJAAkAgAw0AIAJBgCNqQfiewABBMBDxA0UNAEL//8+K6///1R4gCX0iCiASQqvV/v///7//uX9WrSIOfSEPQqTsw7WP1LSY5wAgC30iFCAKIA5UIAlC///Piuv//9UeVnKtIgl9IQpCv6WUnM/w0rvkACANfSITIAkgFFYgC0Kk7MO1j9S0mOcAVnKtIgl9IQ5C19mumuT26Y3LACAMfSILIAkgE1YgDUK/pZScz/DSu+QAVnKtIgl9IRRCms3/y6O9xIAaIAkgC1YgDELX2a6a5PbpjcsAVnKtIBB8fSEQQqvV/v///7//uX8gEn0hEgwBCyAMIRQgDSEOIAshCiAJIQ8LIAIgEjcDiCUgAiAPNwOAJSACIAo3A/gkIAIgDjcD8CQgAiAUNwPoJCACIBA3A+AkIAJB+CNqIgEgAkGwI2ogAkHgJGpBARAxIAItANgkQQJHBEAgACABQegA/AoAACACKALsHCIABEAgAigC8BwgAEECdBDfBAsCQCACKALkFiIARQ0AIAAgAEEMbEETakF4cSIBakEJaiIARQ0AIAIoAuAWIAFrIAAQ3wQLIAIoAuAZIgBBgICAgHhGIABFckUEQCACKALkGSAAQQJ0EN8ECyACQZAlaiQADwsgAkHoJGogAkGAJGooAgA2AgAgAiACKQP4IzcD4CRBhJ3AAEErIAJB4CRqQdirwABB6KvAABDKAwALraoCAiJ/CH4jAEGwCWsiCCQAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIARBAXQgAkYEQCAIIAU2AqAJAkACQAJAAkACQAJAIAUOBgcAAQIDBAULQQEhCQwGC0ECIQkMBQtBAyEJDAQLQQQhCQwDC0EFIQkgCEEFOgCUBwwCCyAIQQE2AgQgCEHImsEANgIAIAhCATcCDCAIIAhBoAlqrUKAgICA4AGENwOoBiAIIAhBqAZqNgIIIAhBkAdqIAgQ0gIgCC0AlAchCSAIKAKQByIFQYCAgIB4Rg0BIAAgCCgAlQc2AAkgAEEMaiAIQZgHaigAADYAACAAIAk6AAggACAFNgIEIABBATYCAAwCC0HRzsUALQAAGkEuQQEQ1gQiAQRAIABBLjYCDCAAIAE2AgggAEKBgICA4AU3AgAgAUEmakHqksEAKQAANwAAIAFBIGpB5JLBACkAADcAACABQRhqQdySwQApAAA3AAAgAUEQakHUksEAKQAANwAAIAFBCGpBzJLBACkAADcAACABQcSSwQApAAA3AAAMAgsMAgsCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgCUH/AXFBAWsOBQECAwQFAAtBACEJIAJB////P0sgAkEFdCIFQfj///8HS3INFgJ/IAVFBEBBCCEQQQAMAQtB0c7FAC0AABpBCCEJIAVBCBDWBCIQRQ0XIAILIQogAgRAIBAhBSACIQkDQCAIIAEQ9wIgBUEYaiAIQRhqKQMANwMAIAVBEGogCEEQaikDADcDACAFQQhqIAhBCGopAwA3AwAgBSAIKQMANwMAIAVBIGohBSABQQxqIQEgCUEBayIJDQALCyAIQYCAgIB4NgKoBiAIQQI2AgggCCACNgIEIAggEDYCACAIIAhBqAZqNgIMIAhBkAdqIAgQjwECQCAIKAKoBiIBQYCAgIB4RwRAIAgoArAGIQIgCCgCrAYhAyAIKAKQByIEBEAgCCgClAcgBEHIAGwQ3wQLIAAgAjYCDCAAIAM2AgggACABNgIEIABBATYCAAwBCyAIKAKYByENIAgoApQHIRIgCCgCkAchBSAIECECQCAEBEAgAyAEQQxsaiEPIAgoArAEIgxBBGshESAIKAK0BCILQQJ0IQIgAyEJA0ACQCALIAkoAggiAUcEQCABIAtPDQQMAQsgCSgCBEEEayEOIAIhAQJAA0AgAUUNASABIBFqIRMgASAOaiABQQRrIQEoAgAiFCATKAIAIhNGDQALIBMgFEsNAQwECyABRQ0DCyAJQQxqIgkgD0cNAAsLIABBBGogEiANIAMgBCAGIAcQYCAAQQA2AgAgCCgCrAQiAARAIAgoArAEIABBAnQQ3wQLIAhB4AFqEP8DIAgoApACIgBBgICAgHhGIABFckUEQCAIKAKUAiAAQQJ0EN8ECyAFRQ0BIBIgBUHIAGwQ3wQMAQtB0c7FAC0AABpBLkEBENYEIgFFDRYgAEEuNgIMIAAgATYCCCAAQoGAgIDgBTcCACABQSZqQZiTwQApAAA3AAAgAUEgakGSk8EAKQAANwAAIAFBGGpBipPBACkAADcAACABQRBqQYKTwQApAAA3AAAgAUEIakH6ksEAKQAANwAAIAFB8pLBACkAADcAACAIKAKsBCIABEAgDCAAQQJ0EN8ECyAIQeABahD/AyAIKAKQAiIAQYCAgIB4RiAARXJFBEAgCCgClAIgAEECdBDfBAsgBUUNACASIAVByABsEN8ECyAKRQ0UIBAgCkEFdBDfBAwUCyACrUIwfiIqpyEFQQAhCSAqQiCIpyAFQfj///8HS3INFQJ/IAVFBEBBCCESQQAMAQtB0c7FAC0AABpBCCEJIAVBCBDWBCISRQ0WIAILIREgAgRAIBIhBSACIQkDQCAIIAEQ9gIgBUEoaiAIQShqKQMANwMAIAVBIGogCEEgaikDADcDACAFQRhqIAhBGGopAwA3AwAgBUEQaiAIQRBqKQMANwMAIAVBCGogCEEIaikDADcDACAFIAgpAwA3AwAgBUEwaiEFIAFBDGohASAJQQFrIgkNAAsLIAhBgICAgHg2AqgGIAhBAjYCCCAIIAI2AgQgCCASNgIAIAggCEGoBmo2AgwgCEGQB2ogCBCPAiAIKAKoBiIBQYCAgIB4RwRAIAgoArAGIQIgCCgCrAYhAyAIKAKQByIEBEAgCCgClAcgBEHoAGwQ3wQLIAAgAjYCDCAAIAM2AgggACABNgIEIABBATYCAAwTCyADIARBDGxqIQ8gCCgCmAchCyAIKAKUByEKIAgoApAHIQ0gCBAmAkAgBARAIAgoApAGIhBBBGshDCAIKAKUBiIFQQJ0IQIgAyEJA0ACQCAFIAkoAggiAUcEQCABIAVPDQQMAQsgCSgCBEEEayEOIAIhAQJAA0AgAUUNASABIAxqIRMgASAOaiABQQRrIQEoAgAiFCATKAIAIhNGDQALIBMgFEsNAQwECyABRQ0DCyAJQQxqIgkgD0cNAAsLQQAhECAIQQA2ArAIIAhCgICAgMAANwKoCCAIQQA2ArwIIAhCgICAgMAANwK0CCAEBEAgA0EMaiEBIAhBmAdqIQlBrPzAACgCACEMQaT8wAApAgAhLiADIQUDQCABIQIgCEGQB2ogBRDiASAIKQOoByEqIAgpA6AHISwgCCkDmAchKyAIKQOQByEtIAkgDDYCACAIIC43A5AHICsgLYRQRQRAQQEhAUEAIQUDQCAIKAKQByABQQFrRgRAIAhBkAdqQaj9wAAQpQMLIAgoApQHIAVqIC0+AgAgK0IghiAtQoCAgIAQVCEOICtQIRMgBUEEaiEFICtCIIghKyAIIAE2ApgHIAFBAWohASAtQiCIhCEtIA4gE3FFDQALCyAIQcgIaiIFIAkoAgA2AgAgCCAIKQOQBzcDwAggCCgCsAgiASAIKAKoCEYEQCAIQagIakGclMEAEJ8DCyAIKAKsCCABQQxsaiIOIAgpA8AINwIAIA5BCGogBSgCADYCACAIIAFBAWo2ArAIIAkgDDYCACAIIC43A5AHICogLIRQRQRAQQEhAUEAIQUDQCAIKAKQByABQQFrRgRAIAhBkAdqQaj9wAAQpQMLIAgoApQHIAVqICw+AgAgKkIghiAsQoCAgIAQVCEOICpQIRMgBUEEaiEFICpCIIghKiAIIAE2ApgHIAFBAWohASAsQiCIhCEsIA4gE3FFDQALCyAIQdgIaiIFIAkoAgA2AgAgCCAIKQOQBzcD0AggCCgCvAgiASAIKAK0CEYEQCAIQbQIakGslMEAEJ8DCyAIKAK4CCABQQxsaiIOIAgpA9AINwIAIA5BCGogBSgCADYCACAIIAFBAWo2ArwIIAJBAEEMIAIgD0YiDhtqIQEgAiEFIA5FDQALCyAIQQA2AugIIAhCgICAgMAANwLgCCAHDQUMEgtB0c7FAC0AABpBLkEBENYEIgFFDRQgAEEuNgIMIAAgATYCCCAAQoGAgIDgBTcCACABQSZqQZiTwQApAAA3AAAgAUEgakGSk8EAKQAANwAAIAFBGGpBipPBACkAADcAACABQRBqQYKTwQApAAA3AAAgAUEIakH6ksEAKQAANwAAIAFB8pLBACkAADcAACAIKAKMBiIABEAgECAAQQJ0EN8ECyAIEP8DIAgoAoADIgBBgICAgHhGIABFckUEQCAIKAKEAyAAQQJ0EN8ECyANRQ0SIAogDUHoAGwQ3wQMEgtBACEJIAJB////P0sgAkEFdCIFQfj///8HS3INFAJ/IAVFBEBBCCESQQAMAQtB0c7FAC0AABpBCCEJIAVBCBDWBCISRQ0VIAILIRQgAgRAIBIhBSACIQkDQCMAQRBrIg0kAAJAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASEQQQFBARDWBCIKRQ0DIApBADoAACAIIApBARCBAQwBCyANQQRqIAFBCBCwAiANKAIIIQoCQCANKAIMIg9BAkkNACAKIA9qIQxBACEQIA9BAXYiEUEBRwRAIA9BAWshCyARQf7///8HcSEOA0AgCiALaiIRLQAAIRMgESAKIBBqIhEtAAA6AAAgESATOgAAIAwgEEF+c2oiEy0AACEYIBMgEUEBaiIRLQAAOgAAIBEgGDoAACALQQJrIQsgDiAQQQJqIhBHDQALCyAPQQJxRQ0AIAogEGoiCy0AACERIAsgDCAQQX9zaiIQLQAAOgAAIBAgEToAAAsgDSgCBCEQIAggCiAPEIEBIBBFDQELIAogEBDfBAsgDUEQaiQADAELQQFBARD/BAALIAVBGGogCEEYaikDADcDACAFQRBqIAhBEGopAwA3AwAgBUEIaiAIQQhqKQMANwMAIAUgCCkDADcDACAFQSBqIQUgAUEMaiEBIAlBAWsiCQ0ACwsgCEGAgICAeDYCqAYgCEECNgIIIAggAjYCBCAIIBI2AgAgCCAIQagGajYCDCAIQZAHaiEJIwBB0AJrIgEkACABQYACaiAIIAgoAgwQgAICQAJAIAEtAMACIgVBA0YNACABQfgBaiICIAFBuAJqKQMANwMAIAFB8AFqIhAgAUGwAmopAwA3AwAgAUHoAWoiCiABQagCaikDADcDACABQeABaiILIAFBoAJqKQMANwMAIAFB2AFqIg0gAUGYAmopAwA3AwAgAUHQAWoiDyABQZACaikDADcDACABQcgBaiIMIAFBiAJqKQMANwMAIAEgASkDgAI3A8ABIAEgASgAwQI2AnggASABQcQCaigAADYAeyAFQQJGDQAgAUHYAGogAikDADcDACABQdAAaiAQKQMANwMAIAFByABqIAopAwA3AwAgAUFAayALKQMANwMAIAFBOGogDSkDADcDACABQTBqIA8pAwA3AwAgAUEoaiAMKQMANwMAIAEgASkDwAE3AyAgASABKAJ4NgIYIAEgASgAezYAGwJAIAgoAgwoAgBBgICAgHhHDQAgCCgCBEUNACAIKAIIRQ0gC0HRzsUALQAAGkGgAkEIENYEIgJFDSAgAiABKQMgNwMAIAIgBToAQCACIAEoAhg2AEEgAkHEAGogASgAGzYAACACQThqIAFB2ABqKQMANwMAIAJBMGogAUHQAGopAwA3AwAgAkEoaiABQcgAaikDADcDACACQSBqIAFBQGspAwA3AwAgAkEYaiABQThqKQMANwMAIAJBEGogAUEwaikDADcDACACQQhqIAFBKGopAwA3AwAgAUEBNgIUIAEgAjYCECABQQQ2AgwgAUHoAGogCEEIaikCADcDACABIAgpAgA3A2AgAUGAAmogAUHgAGogASgCbBCAAgJAIAEtAMACIgVBA0YNAEGJASEKIAFBwQJqIg1BA2ohD0EBIRADQCABQfgBaiILIAFBuAJqKQMANwMAIAFB8AFqIgwgAUGwAmopAwA3AwAgAUHoAWoiESABQagCaikDADcDACABQeABaiIOIAFBoAJqKQMANwMAIAFB2AFqIhMgAUGYAmopAwA3AwAgAUHQAWoiGCABQZACaikDADcDACABQcgBaiIWIAFBiAJqKQMANwMAIAEgASkDgAI3A8ABIAEgDSgAADYCuAEgASAPKAAANgC7ASAFQQJGDQEgAUGwAWoiFyALKQMANwMAIAFBqAFqIgsgDCkDADcDACABQaABaiIMIBEpAwA3AwAgAUGYAWoiESAOKQMANwMAIAFBkAFqIg4gEykDADcDACABQYgBaiITIBgpAwA3AwAgAUGAAWoiGCAWKQMANwMAIAEgASkDwAE3A3ggASABKAK4ATYCcCABIAEoALsBNgBzIAEoAgwgEEYEQAJAIAEoAmwoAgBBgICAgHhHDQAgASgCZEUNACABKAJoRQ0jCyABQQxqIBBBAUEIQcgAEIgDIAEoAhAhAgsgGCkDACEqIBMpAwAhLCAOKQMAISsgESkDACEtIAwpAwAhLiALKQMAIS8gFykDACEwIAEpA3ghMSACIApqIgtBAWsgBToAACALQcEAayIFIDE3AwAgCyABKAJwNgAAIAtBA2ogASgAczYAACAFQThqIDA3AwAgBUEwaiAvNwMAIAVBKGogLjcDACAFQSBqIC03AwAgBUEYaiArNwMAIAVBEGogLDcDACAFQQhqICo3AwAgASAQQQFqIhA2AhQgAUGAAmogAUHgAGogASgCbBCAAiAKQcgAaiEKIAEtAMACIgVBA0cNAAsLIAlBCGogAUEUaigCADYCACAJIAEpAgw3AgAMAQsgCUEANgIIIAlCgICAgIABNwIACyABQdACaiQAIAgoAqgGIgFBgICAgHhHBEAgCCgCsAYhAiAIKAKsBiEDIAgoApAHIgQEQCAIKAKUByAEQcgAbBDfBAsgACACNgIMIAAgAzYCCCAAIAE2AgQgAEEBNgIADBALIAMgBEEMbGohDSAIKAKYByELIAgoApQHIQogCCgCkAchESAIEFUCQCAEBEAgCCgCsAQiEEEEayEPIAgoArQEIgVBAnQhAiADIQkDQAJAIAUgCSgCCCIBRwRAIAEgBU8NBAwBCyAJKAIEQQRrIQwgAiEBAkADQCABRQ0BIAEgD2ohDiABIAxqIAFBBGshASgCACITIA4oAgAiDkYNAAsgDiATSw0BDAQLIAFFDQMLIAlBDGoiCSANRw0ACwtBACEQIAhBADYCsAggCEKAgICAwAA3AqgIIAhBADYCvAggCEKAgICAwAA3ArQIIAQEQCADQQxqIQEgCEGYB2ohCUGs/MAAKAIAIQ9BpPzAACkCACEuIAMhBQNAIAEhAiAIQZAHaiAFEOIBIAgpA6gHISogCCkDoAchLCAIKQOYByErIAgpA5AHIS0gCSAPNgIAIAggLjcDkAcgKyAthFBFBEBBASEBQQAhBQNAIAgoApAHIAFBAWtGBEAgCEGQB2pBqP3AABClAwsgCCgClAcgBWogLT4CACArQiCGIC1CgICAgBBUIQwgK1AhDiAFQQRqIQUgK0IgiCErIAggATYCmAcgAUEBaiEBIC1CIIiEIS0gDCAOcUUNAAsLIAhByAhqIgUgCSgCADYCACAIIAgpA5AHNwPACCAIKAKwCCIBIAgoAqgIRgRAIAhBqAhqQZyUwQAQnwMLIAgoAqwIIAFBDGxqIgwgCCkDwAg3AgAgDEEIaiAFKAIANgIAIAggAUEBajYCsAggCSAPNgIAIAggLjcDkAcgKiAshFBFBEBBASEBQQAhBQNAIAgoApAHIAFBAWtGBEAgCEGQB2pBqP3AABClAwsgCCgClAcgBWogLD4CACAqQiCGICxCgICAgBBUIQwgKlAhDiAFQQRqIQUgKkIgiCEqIAggATYCmAcgAUEBaiEBICxCIIiEISwgDCAOcUUNAAsLIAhB2AhqIgUgCSgCADYCACAIIAgpA5AHNwPQCCAIKAK8CCIBIAgoArQIRgRAIAhBtAhqQayUwQAQnwMLIAgoArgIIAFBDGxqIgwgCCkD0Ag3AgAgDEEIaiAFKAIANgIAIAggAUEBajYCvAggAkEAQQwgAiANRiIMG2ohASACIQUgDEUNAAsLIAhBADYC6AggCEKAgICAwAA3AuAIIAcNBQwPC0HRzsUALQAAGkEuQQEQ1gQiAUUNEyAAQS42AgwgACABNgIIIABCgYCAgOAFNwIAIAFBJmpBmJPBACkAADcAACABQSBqQZKTwQApAAA3AAAgAUEYakGKk8EAKQAANwAAIAFBEGpBgpPBACkAADcAACABQQhqQfqSwQApAAA3AAAgAUHyksEAKQAANwAAIAgoAqwEIgAEQCAQIABBAnQQ3wQLIAhB4AFqEP8DIAgoApACIgBBgICAgHhGIABFckUEQCAIKAKUAiAAQQJ0EN8ECyARRQ0PIAogEUHIAGwQ3wQMDwtBACEJIAJB////P0sgAkEFdCIFQfj///8HS3INEwJ/IAVFBEBBCCEQQQAMAQtB0c7FAC0AABpBCCEJIAVBCBDWBCIQRQ0UIAILIRggAgRAIBAhBSACIQkDQCMAQRBrIg0kAAJAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASESQQFBARDWBCIKRQ0DIApBADoAACAIIApBARCJAQwBCyANQQRqIAFBCBCwAiANKAIIIQoCQCANKAIMIg9BAkkNACAKIA9qIQxBACESIA9BAXYiEUEBRwRAIA9BAWshCyARQf7///8HcSEOA0AgCiALaiIRLQAAIRMgESAKIBJqIhEtAAA6AAAgESATOgAAIAwgEkF+c2oiEy0AACEUIBMgEUEBaiIRLQAAOgAAIBEgFDoAACALQQJrIQsgDiASQQJqIhJHDQALCyAPQQJxRQ0AIAogEmoiCy0AACERIAsgDCASQX9zaiISLQAAOgAAIBIgEToAAAsgDSgCBCESIAggCiAPEIkBIBJFDQELIAogEhDfBAsgDUEQaiQADAELQQFBARD/BAALIAVBGGogCEEYaikDADcDACAFQRBqIAhBEGopAwA3AwAgBUEIaiAIQQhqKQMANwMAIAUgCCkDADcDACAFQSBqIQUgAUEMaiEBIAlBAWsiCQ0ACwsgCEGAgICAeDYCqAYgCEECNgIIIAggAjYCBCAIIBA2AgAgCCAIQagGajYCDCAIQZAHaiEJIwBB0AJrIgEkACABQYACaiAIIAgoAgwQ/gECQAJAIAEtAMACIgVBA0YNACABQfgBaiICIAFBuAJqKQMANwMAIAFB8AFqIhIgAUGwAmopAwA3AwAgAUHoAWoiCiABQagCaikDADcDACABQeABaiILIAFBoAJqKQMANwMAIAFB2AFqIg0gAUGYAmopAwA3AwAgAUHQAWoiDyABQZACaikDADcDACABQcgBaiIMIAFBiAJqKQMANwMAIAEgASkDgAI3A8ABIAEgASgAwQI2AnggASABQcQCaigAADYAeyAFQQJGDQAgAUHYAGogAikDADcDACABQdAAaiASKQMANwMAIAFByABqIAopAwA3AwAgAUFAayALKQMANwMAIAFBOGogDSkDADcDACABQTBqIA8pAwA3AwAgAUEoaiAMKQMANwMAIAEgASkDwAE3AyAgASABKAJ4NgIYIAEgASgAezYAGwJAIAgoAgwoAgBBgICAgHhHDQAgCCgCBEUNACAIKAIIRQ0fC0HRzsUALQAAGkGgAkEIENYEIgJFDR8gAiABKQMgNwMAIAIgBToAQCACIAEoAhg2AEEgAkHEAGogASgAGzYAACACQThqIAFB2ABqKQMANwMAIAJBMGogAUHQAGopAwA3AwAgAkEoaiABQcgAaikDADcDACACQSBqIAFBQGspAwA3AwAgAkEYaiABQThqKQMANwMAIAJBEGogAUEwaikDADcDACACQQhqIAFBKGopAwA3AwAgAUEBNgIUIAEgAjYCECABQQQ2AgwgAUHoAGogCEEIaikCADcDACABIAgpAgA3A2AgAUGAAmogAUHgAGogASgCbBD+AQJAIAEtAMACIgVBA0YNAEGJASEKIAFBwQJqIg1BA2ohD0EBIRIDQCABQfgBaiILIAFBuAJqKQMANwMAIAFB8AFqIgwgAUGwAmopAwA3AwAgAUHoAWoiESABQagCaikDADcDACABQeABaiIOIAFBoAJqKQMANwMAIAFB2AFqIhMgAUGYAmopAwA3AwAgAUHQAWoiFCABQZACaikDADcDACABQcgBaiIWIAFBiAJqKQMANwMAIAEgASkDgAI3A8ABIAEgDSgAADYCuAEgASAPKAAANgC7ASAFQQJGDQEgAUGwAWoiFyALKQMANwMAIAFBqAFqIgsgDCkDADcDACABQaABaiIMIBEpAwA3AwAgAUGYAWoiESAOKQMANwMAIAFBkAFqIg4gEykDADcDACABQYgBaiITIBQpAwA3AwAgAUGAAWoiFCAWKQMANwMAIAEgASkDwAE3A3ggASABKAK4ATYCcCABIAEoALsBNgBzIAEoAgwgEkYEQAJAIAEoAmwoAgBBgICAgHhHDQAgASgCZEUNACABKAJoRQ0iCyABQQxqIBJBAUEIQcgAEIgDIAEoAhAhAgsgFCkDACEqIBMpAwAhLCAOKQMAISsgESkDACEtIAwpAwAhLiALKQMAIS8gFykDACEwIAEpA3ghMSACIApqIgtBAWsgBToAACALQcEAayIFIDE3AwAgCyABKAJwNgAAIAtBA2ogASgAczYAACAFQThqIDA3AwAgBUEwaiAvNwMAIAVBKGogLjcDACAFQSBqIC03AwAgBUEYaiArNwMAIAVBEGogLDcDACAFQQhqICo3AwAgASASQQFqIhI2AhQgAUGAAmogAUHgAGogASgCbBD+ASAKQcgAaiEKIAEtAMACIgVBA0cNAAsLIAlBCGogAUEUaigCADYCACAJIAEpAgw3AgAMAQsgCUEANgIIIAlCgICAgIABNwIACyABQdACaiQAIAgoAqgGIgFBgICAgHhHBEAgCCgCsAYhAiAIKAKsBiEDIAgoApAHIgQEQCAIKAKUByAEQcgAbBDfBAsgACACNgIMIAAgAzYCCCAAIAE2AgQgAEEBNgIADA0LIAMgBEEMbGohDSAIKAKYByEKIAgoApQHIRIgCCgCkAchEyAIED4CQCAEBEAgCCgCsAQiC0EEayEPIAgoArQEIgVBAnQhAiADIQkDQAJAIAUgCSgCCCIBRwRAIAEgBU8NBAwBCyAJKAIEQQRrIQwgAiEBAkADQCABRQ0BIAEgD2ohESABIAxqIAFBBGshASgCACIOIBEoAgAiEUYNAAsgDiARSQ0BDAQLIAFFDQMLIAlBDGoiCSANRw0ACwtBACEJIAhBADYCvAggCEKAgICAwAA3ArQIIAhBADYCyAggCEKAgICAwAA3AsAIIAQEQCADQQxqIQEgCEGYB2ohC0Gs/MAAKAIAIQ9BpPzAACkCACEuIAMhBQNAIAEhAiAIQZAHaiAFEOIBIAgpA6gHISogCCkDoAchLCAIKQOYByErIAgpA5AHIS0gCyAPNgIAIAggLjcDkAcgKyAthFBFBEBBASEBQQAhBQNAIAgoApAHIAFBAWtGBEAgCEGQB2pBqP3AABClAwsgCCgClAcgBWogLT4CACArQiCGIC1CgICAgBBUIQwgK1AhESAFQQRqIQUgK0IgiCErIAggATYCmAcgAUEBaiEBIC1CIIiEIS0gDCARcUUNAAsLIAhB2AhqIgUgCygCADYCACAIIAgpA5AHNwPQCCAIKAK8CCIBIAgoArQIRgRAIAhBtAhqQZyUwQAQnwMLIAgoArgIIAFBDGxqIgwgCCkD0Ag3AgAgDEEIaiAFKAIANgIAIAggAUEBajYCvAggCyAPNgIAIAggLjcDkAcgKiAshFBFBEBBASEBQQAhBQNAIAgoApAHIAFBAWtGBEAgCEGQB2pBqP3AABClAwsgCCgClAcgBWogLD4CACAqQiCGICxCgICAgBBUIQwgKlAhESAFQQRqIQUgKkIgiCEqIAggATYCmAcgAUEBaiEBICxCIIiEISwgDCARcUUNAAsLIAhB6AhqIgUgCygCADYCACAIIAgpA5AHNwPgCCAIKALICCIBIAgoAsAIRgRAIAhBwAhqQayUwQAQnwMLIAgoAsQIIAFBDGxqIgwgCCkD4Ag3AgAgDEEIaiAFKAIANgIAIAggAUEBajYCyAggAkEAQQwgAiANRiIMG2ohASACIQUgDEUNAAsLIAhBADYC+AggCEKAgICAwAA3AvAIIAcNBQwMC0HRzsUALQAAGkEuQQEQ1gQiAUUNEiAAQS42AgwgACABNgIIIABCgYCAgOAFNwIAIAFBJmpBmJPBACkAADcAACABQSBqQZKTwQApAAA3AAAgAUEYakGKk8EAKQAANwAAIAFBEGpBgpPBACkAADcAACABQQhqQfqSwQApAAA3AAAgAUHyksEAKQAANwAAIAgoAqwEIgAEQCALIABBAnQQ3wQLIAhB4AFqEP8DIAgoApACIgBBgICAgHhGIABFckUEQCAIKAKUAiAAQQJ0EN8ECyATRQ0MIBIgE0HIAGwQ3wQMDAtBACEJIAJB////P0sgAkEFdCIFQfj///8HS3INEgJ/IAVFBEBBCCEQQQAMAQtB0c7FAC0AABpBCCEJIAVBCBDWBCIQRQ0TIAILIRggAgRAIBAhBSACIQkDQCAIIAEQ9QIgBUEYaiAIQRhqKQMANwMAIAVBEGogCEEQaikDADcDACAFQQhqIAhBCGopAwA3AwAgBSAIKQMANwMAIAVBIGohBSABQQxqIQEgCUEBayIJDQALCyAIQYCAgIB4NgKoBiAIQQI2AgggCCACNgIEIAggEDYCACAIIAhBqAZqNgIMIAhBkAdqIQkjAEHQAmsiASQAIAFBgAJqIAggCCgCDBD9AQJAAkAgAS0AwAIiBUEDRg0AIAFB+AFqIgIgAUG4AmopAwA3AwAgAUHwAWoiEiABQbACaikDADcDACABQegBaiIKIAFBqAJqKQMANwMAIAFB4AFqIgsgAUGgAmopAwA3AwAgAUHYAWoiDSABQZgCaikDADcDACABQdABaiIPIAFBkAJqKQMANwMAIAFByAFqIgwgAUGIAmopAwA3AwAgASABKQOAAjcDwAEgASABKADBAjYCeCABIAFBxAJqKAAANgB7IAVBAkYNACABQdgAaiACKQMANwMAIAFB0ABqIBIpAwA3AwAgAUHIAGogCikDADcDACABQUBrIAspAwA3AwAgAUE4aiANKQMANwMAIAFBMGogDykDADcDACABQShqIAwpAwA3AwAgASABKQPAATcDICABIAEoAng2AhggASABKAB7NgAbAkAgCCgCDCgCAEGAgICAeEcNACAIKAIERQ0AIAgoAghFDR4LQdHOxQAtAAAaQaACQQgQ1gQiAkUNHiACIAEpAyA3AwAgAiAFOgBAIAIgASgCGDYAQSACQcQAaiABKAAbNgAAIAJBOGogAUHYAGopAwA3AwAgAkEwaiABQdAAaikDADcDACACQShqIAFByABqKQMANwMAIAJBIGogAUFAaykDADcDACACQRhqIAFBOGopAwA3AwAgAkEQaiABQTBqKQMANwMAIAJBCGogAUEoaikDADcDACABQQE2AhQgASACNgIQIAFBBDYCDCABQegAaiAIQQhqKQIANwMAIAEgCCkCADcDYCABQYACaiABQeAAaiABKAJsEP0BAkAgAS0AwAIiBUEDRg0AQYkBIQogAUHBAmoiDUEDaiEPQQEhEgNAIAFB+AFqIgsgAUG4AmopAwA3AwAgAUHwAWoiDCABQbACaikDADcDACABQegBaiIRIAFBqAJqKQMANwMAIAFB4AFqIg4gAUGgAmopAwA3AwAgAUHYAWoiEyABQZgCaikDADcDACABQdABaiIUIAFBkAJqKQMANwMAIAFByAFqIhYgAUGIAmopAwA3AwAgASABKQOAAjcDwAEgASANKAAANgK4ASABIA8oAAA2ALsBIAVBAkYNASABQbABaiIXIAspAwA3AwAgAUGoAWoiCyAMKQMANwMAIAFBoAFqIgwgESkDADcDACABQZgBaiIRIA4pAwA3AwAgAUGQAWoiDiATKQMANwMAIAFBiAFqIhMgFCkDADcDACABQYABaiIUIBYpAwA3AwAgASABKQPAATcDeCABIAEoArgBNgJwIAEgASgAuwE2AHMgASgCDCASRgRAAkAgASgCbCgCAEGAgICAeEcNACABKAJkRQ0AIAEoAmhFDSELIAFBDGogEkEBQQhByAAQiAMgASgCECECCyAUKQMAISogEykDACEsIA4pAwAhKyARKQMAIS0gDCkDACEuIAspAwAhLyAXKQMAITAgASkDeCExIAIgCmoiC0EBayAFOgAAIAtBwQBrIgUgMTcDACALIAEoAnA2AAAgC0EDaiABKABzNgAAIAVBOGogMDcDACAFQTBqIC83AwAgBUEoaiAuNwMAIAVBIGogLTcDACAFQRhqICs3AwAgBUEQaiAsNwMAIAVBCGogKjcDACABIBJBAWoiEjYCFCABQYACaiABQeAAaiABKAJsEP0BIApByABqIQogAS0AwAIiBUEDRw0ACwsgCUEIaiABQRRqKAIANgIAIAkgASkCDDcCAAwBCyAJQQA2AgggCUKAgICAgAE3AgALIAFB0AJqJAAgCCgCqAYiAUGAgICAeEcEQCAIKAKwBiECIAgoAqwGIQMgCCgCkAciBARAIAgoApQHIARByABsEN8ECyAAIAI2AgwgACADNgIIIAAgATYCBCAAQQE2AgAMCgsgAyAEQQxsaiENIAgoApgHIQogCCgClAchEiAIKAKQByETIAgQSQJAIAQEQCAIKAKwBCILQQRrIQ8gCCgCtAQiBUECdCECIAMhCQNAAkAgBSAJKAIIIgFHBEAgASAFTw0EDAELIAkoAgRBBGshDCACIQECQANAIAFFDQEgASAPaiERIAEgDGogAUEEayEBKAIAIg4gESgCACIRRg0ACyAOIBFJDQEMBAsgAUUNAwsgCUEMaiIJIA1HDQALC0EAIQkgCEEANgK8CCAIQoCAgIDAADcCtAggCEEANgLICCAIQoCAgIDAADcCwAggBARAIANBDGohASAIQZgHaiELQaz8wAAoAgAhD0Gk/MAAKQIAIS4gAyEFA0AgASECIAhBkAdqIAUQ4gEgCCkDqAchKiAIKQOgByEsIAgpA5gHISsgCCkDkAchLSALIA82AgAgCCAuNwOQByArIC2EUEUEQEEBIQFBACEFA0AgCCgCkAcgAUEBa0YEQCAIQZAHakGo/cAAEKUDCyAIKAKUByAFaiAtPgIAICtCIIYgLUKAgICAEFQhDCArUCERIAVBBGohBSArQiCIISsgCCABNgKYByABQQFqIQEgLUIgiIQhLSAMIBFxRQ0ACwsgCEHYCGoiBSALKAIANgIAIAggCCkDkAc3A9AIIAgoArwIIgEgCCgCtAhGBEAgCEG0CGpBnJTBABCfAwsgCCgCuAggAUEMbGoiDCAIKQPQCDcCACAMQQhqIAUoAgA2AgAgCCABQQFqNgK8CCALIA82AgAgCCAuNwOQByAqICyEUEUEQEEBIQFBACEFA0AgCCgCkAcgAUEBa0YEQCAIQZAHakGo/cAAEKUDCyAIKAKUByAFaiAsPgIAICpCIIYgLEKAgICAEFQhDCAqUCERIAVBBGohBSAqQiCIISogCCABNgKYByABQQFqIQEgLEIgiIQhLCAMIBFxRQ0ACwsgCEHoCGoiBSALKAIANgIAIAggCCkDkAc3A+AIIAgoAsgIIgEgCCgCwAhGBEAgCEHACGpBrJTBABCfAwsgCCgCxAggAUEMbGoiDCAIKQPgCDcCACAMQQhqIAUoAgA2AgAgCCABQQFqNgLICCACQQBBDCACIA1GIgwbaiEBIAIhBSAMRQ0ACwsgCEEANgL4CCAIQoCAgIDAADcC8AggBw0FDAkLQdHOxQAtAAAaQS5BARDWBCIBRQ0RIABBLjYCDCAAIAE2AgggAEKBgICA4AU3AgAgAUEmakGYk8EAKQAANwAAIAFBIGpBkpPBACkAADcAACABQRhqQYqTwQApAAA3AAAgAUEQakGCk8EAKQAANwAAIAFBCGpB+pLBACkAADcAACABQfKSwQApAAA3AAAgCCgCrAQiAARAIAsgAEECdBDfBAsgCEHgAWoQ/wMgCCgCkAIiAEGAgICAeEYgAEVyRQRAIAgoApQCIABBAnQQ3wQLIBNFDQkgEiATQcgAbBDfBAwJC0EAIQkgAkH///8/SyACQQV0IgVB+P///wdLcg0RAn8gBUUEQEEIIRBBAAwBC0HRzsUALQAAGkEIIQkgBUEIENYEIhBFDRIgAgshGCACBEAgECEFIAIhCQNAIAggARD0AiAFQRhqIAhBGGopAwA3AwAgBUEQaiAIQRBqKQMANwMAIAVBCGogCEEIaikDADcDACAFIAgpAwA3AwAgBUEgaiEFIAFBDGohASAJQQFrIgkNAAsLIAhBgICAgHg2AqgGIAhBAjYCCCAIIAI2AgQgCCAQNgIAIAggCEGoBmo2AgwgCEGQB2ohCSMAQdACayIBJAAgAUGAAmogCCAIKAIMEP8BAkACQCABLQDAAiIFQQNGDQAgAUH4AWoiAiABQbgCaikDADcDACABQfABaiISIAFBsAJqKQMANwMAIAFB6AFqIgogAUGoAmopAwA3AwAgAUHgAWoiCyABQaACaikDADcDACABQdgBaiINIAFBmAJqKQMANwMAIAFB0AFqIg8gAUGQAmopAwA3AwAgAUHIAWoiDCABQYgCaikDADcDACABIAEpA4ACNwPAASABIAEoAMECNgJ4IAEgAUHEAmooAAA2AHsgBUECRg0AIAFB2ABqIAIpAwA3AwAgAUHQAGogEikDADcDACABQcgAaiAKKQMANwMAIAFBQGsgCykDADcDACABQThqIA0pAwA3AwAgAUEwaiAPKQMANwMAIAFBKGogDCkDADcDACABIAEpA8ABNwMgIAEgASgCeDYCGCABIAEoAHs2ABsCQCAIKAIMKAIAQYCAgIB4Rw0AIAgoAgRFDQAgCCgCCEUNHQtB0c7FAC0AABpBoAJBCBDWBCICRQ0dIAIgASkDIDcDACACIAU6AEAgAiABKAIYNgBBIAJBxABqIAEoABs2AAAgAkE4aiABQdgAaikDADcDACACQTBqIAFB0ABqKQMANwMAIAJBKGogAUHIAGopAwA3AwAgAkEgaiABQUBrKQMANwMAIAJBGGogAUE4aikDADcDACACQRBqIAFBMGopAwA3AwAgAkEIaiABQShqKQMANwMAIAFBATYCFCABIAI2AhAgAUEENgIMIAFB6ABqIAhBCGopAgA3AwAgASAIKQIANwNgIAFBgAJqIAFB4ABqIAEoAmwQ/wECQCABLQDAAiIFQQNGDQBBiQEhCiABQcECaiINQQNqIQ9BASESA0AgAUH4AWoiCyABQbgCaikDADcDACABQfABaiIMIAFBsAJqKQMANwMAIAFB6AFqIhEgAUGoAmopAwA3AwAgAUHgAWoiDiABQaACaikDADcDACABQdgBaiITIAFBmAJqKQMANwMAIAFB0AFqIhQgAUGQAmopAwA3AwAgAUHIAWoiFiABQYgCaikDADcDACABIAEpA4ACNwPAASABIA0oAAA2ArgBIAEgDygAADYAuwEgBUECRg0BIAFBsAFqIhcgCykDADcDACABQagBaiILIAwpAwA3AwAgAUGgAWoiDCARKQMANwMAIAFBmAFqIhEgDikDADcDACABQZABaiIOIBMpAwA3AwAgAUGIAWoiEyAUKQMANwMAIAFBgAFqIhQgFikDADcDACABIAEpA8ABNwN4IAEgASgCuAE2AnAgASABKAC7ATYAcyABKAIMIBJGBEACQCABKAJsKAIAQYCAgIB4Rw0AIAEoAmRFDQAgASgCaEUNIAsgAUEMaiASQQFBCEHIABCIAyABKAIQIQILIBQpAwAhKiATKQMAISwgDikDACErIBEpAwAhLSAMKQMAIS4gCykDACEvIBcpAwAhMCABKQN4ITEgAiAKaiILQQFrIAU6AAAgC0HBAGsiBSAxNwMAIAsgASgCcDYAACALQQNqIAEoAHM2AAAgBUE4aiAwNwMAIAVBMGogLzcDACAFQShqIC43AwAgBUEgaiAtNwMAIAVBGGogKzcDACAFQRBqICw3AwAgBUEIaiAqNwMAIAEgEkEBaiISNgIUIAFBgAJqIAFB4ABqIAEoAmwQ/wEgCkHIAGohCiABLQDAAiIFQQNHDQALCyAJQQhqIAFBFGooAgA2AgAgCSABKQIMNwIADAELIAlBADYCCCAJQoCAgICAATcCAAsgAUHQAmokACAIKAKoBiIBQYCAgIB4RwRAIAgoArAGIQIgCCgCrAYhAyAIKAKQByIEBEAgCCgClAcgBEHIAGwQ3wQLIAAgAjYCDCAAIAM2AgggACABNgIEIABBATYCAAwHCyADIARBDGxqIQ0gCCgCmAchCiAIKAKUByESIAgoApAHIRMgCBA6AkAgBARAIAgoArAEIgtBBGshDyAIKAK0BCIFQQJ0IQIgAyEJA0ACQCAFIAkoAggiAUcEQCABIAVPDQQMAQsgCSgCBEEEayEMIAIhAQJAA0AgAUUNASABIA9qIREgASAMaiABQQRrIQEoAgAiDiARKAIAIhFGDQALIA4gEUkNAQwECyABRQ0DCyAJQQxqIgkgDUcNAAsLQQAhCSAIQQA2ArwIIAhCgICAgMAANwK0CCAIQQA2AsgIIAhCgICAgMAANwLACCAEBEAgA0EMaiEBIAhBmAdqIQtBrPzAACgCACEPQaT8wAApAgAhLiADIQUDQCABIQIgCEGQB2ogBRDiASAIKQOoByEqIAgpA6AHISwgCCkDmAchKyAIKQOQByEtIAsgDzYCACAIIC43A5AHICsgLYRQRQRAQQEhAUEAIQUDQCAIKAKQByABQQFrRgRAIAhBkAdqQaj9wAAQpQMLIAgoApQHIAVqIC0+AgAgK0IghiAtQoCAgIAQVCEMICtQIREgBUEEaiEFICtCIIghKyAIIAE2ApgHIAFBAWohASAtQiCIhCEtIAwgEXFFDQALCyAIQdgIaiIFIAsoAgA2AgAgCCAIKQOQBzcD0AggCCgCvAgiASAIKAK0CEYEQCAIQbQIakGclMEAEJ8DCyAIKAK4CCABQQxsaiIMIAgpA9AINwIAIAxBCGogBSgCADYCACAIIAFBAWo2ArwIIAsgDzYCACAIIC43A5AHICogLIRQRQRAQQEhAUEAIQUDQCAIKAKQByABQQFrRgRAIAhBkAdqQaj9wAAQpQMLIAgoApQHIAVqICw+AgAgKkIghiAsQoCAgIAQVCEMICpQIREgBUEEaiEFICpCIIghKiAIIAE2ApgHIAFBAWohASAsQiCIhCEsIAwgEXFFDQALCyAIQegIaiIFIAsoAgA2AgAgCCAIKQOQBzcD4AggCCgCyAgiASAIKALACEYEQCAIQcAIakGslMEAEJ8DCyAIKALECCABQQxsaiIMIAgpA+AINwIAIAxBCGogBSgCADYCACAIIAFBAWo2AsgIIAJBAEEMIAIgDUYiDBtqIQEgAiEFIAxFDQALCyAIQQA2AvgIIAhCgICAgMAANwLwCCAHDQUMBgtB0c7FAC0AABpBLkEBENYEIgFFDRAgAEEuNgIMIAAgATYCCCAAQoGAgIDgBTcCACABQSZqQZiTwQApAAA3AAAgAUEgakGSk8EAKQAANwAAIAFBGGpBipPBACkAADcAACABQRBqQYKTwQApAAA3AAAgAUEIakH6ksEAKQAANwAAIAFB8pLBACkAADcAACAIKAKsBCIABEAgCyAAQQJ0EN8ECyAIQeABahD/AyAIKAKQAiIAQYCAgIB4RiAARXJFBEAgCCgClAIgAEECdBDfBAsgE0UNBiASIBNByABsEN8EDAYLIAhB4AhqQbyUwQAQnwMgCCgC5AgiAUGk/MAAKQIANwIAIAFBCGpBrPzAACgCADYCAEEBIRAgCEEBNgLoCAwMCyAIQeAIakG8lMEAEJ8DIAgoAuQIIgFBpPzAACkCADcCACABQQhqQaz8wAAoAgA2AgBBASEQIAhBATYC6AgMCQsgCEHwCGpBvJTBABCfAyAIKAL0CCIBQaT8wAApAgA3AgAgAUEIakGs/MAAKAIANgIAQQEhCSAIQQE2AvgIDAYLIAhB8AhqQbyUwQAQnwMgCCgC9AgiAUGk/MAAKQIANwIAIAFBCGpBrPzAACgCADYCAEEBIQkgCEEBNgL4CAwDCyAIQfAIakG8lMEAEJ8DIAgoAvQIIgFBpPzAACkCADcCACABQQhqQaz8wAAoAgA2AgBBASEJIAhBATYC+AgLIAYEQCAIQZgHaiIBQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAKBEAgCEGQB2pBmP3AABClAyAIKAKUByAKNgIAIAhBATYCmAcLIAhBsAZqIAEoAgA2AgAgCCAIKQOQBzcDqAYgCCgC8AggCUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCAJQQxsaiIBIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgAgCCAJQQFqNgL4CCAKBEAgEiAKQcgAbGohAiASIQEDQCAIQfAIaiIFIAEQswEgBSABQSBqELMBIAFByABqIgEgAkcNAAsLIAhBmAdqQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAEBEAgCEGQB2pBmP3AABClAyAIKAKUByAENgIAIAhBATYCmAcLIAhBsAZqIgIgCEGYB2ooAgA2AgAgCCAIKQOQBzcDqAYgCCgC+AgiASAIKALwCEYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWoiATYC+AgCQCAERQ0AQQQhAkEAIQUCQANAIAUgCCgCvAgiAU8NEiAIKAK4CCACaiIJQQRqKAIAIgtBAnQhAUEAIQYgC0H/////A0sgAUH8////B0tyDREgCSgCACENAn8gAUUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQYgAUEEENYEIglFDRIgCwshDyABBEAgCSANIAH8CgAACyAIKAL4CCIBIAgoAvAIRgRAIAhB8AhqQbyUwQAQnwMLIAgoAvQIIAFBDGxqIgYgCzYCCCAGIAk2AgQgBiAPNgIAIAggAUEBajYC+AggCCgCyAgiASAFSwRAIAgoAsQIIAJqIglBBGooAgAiC0ECdCEBQQAhBiALQf////8DSyABQfz///8HS3INAiAJKAIAIQ0CfyABRQRAQQQhCUEADAELQdHOxQAtAAAaQQQhBiABQQQQ1gQiCUUNAyALCyEPIAEEQCAJIA0gAfwKAAALIAgoAvgIIgEgCCgC8AhGBEAgCEHwCGpBvJTBABCfAwsgCCgC9AggAUEMbGoiBiALNgIIIAYgCTYCBCAGIA82AgAgCCABQQFqIgE2AvgIIAJBDGohAiAEIAVBAWoiBUcNAQwDCwsMDwsMDwsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBBTYCACAIQbAGaiICQQE2AgAgCCAIKQOQBzcDqAYgCCgC8AggAUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWo2AvgICwJAIAQgCiAEIApJGyIERQ0AIANBCGohBSAIQcgGaiEeIAhB5AdqIRYgCEHYB2ohFyASIQIDQAJAIAUoAgAiAQRAQQAhBgJAIAFB/////wNLIAFBAnQiA0H8////B0tyRQRAIAVBBGsoAgAhCkHRzsUALQAAGkEEIQYgA0EEENYEIgkNAQsMFAsgAwRAIAkgCiAD/AoAAAsgCCABNgKICSAIIAk2AoQJIAggATYCgAkMAQsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBATYCACAIQYgJakEBNgIAIAggCCkDkAc3A4AJCyAIQZAHaiEPIAhBgAlqIQ0jAEGgB2siASQAIAEQOkEBIQZBBCEJQQQhA0EBIQogASgCtAQiCwRAQdHOxQAtAAAaIAEoArAEIQwgC0ECdCIKQQQQ1gQiA0UNGSAKBEAgAyAMIAr8CgAAC0ECIQoLIAFB1wRqQQA6AAAgAUEAOwDVBCABIAo6ANQEIAEgCzYC0AQgASADNgLMBCABIAs2AsgEIA0oAggiDARAQdHOxQAtAAAaIA0oAgQhBiAMQQJ0IgNBBBDWBCIJRQ0aIAMEQCAJIAYgA/wKAAALQQIhBgsgAUHnBGpBADoAACABQQA7AOUEIAEgBjoA5AQgASAMNgLgBCABIAk2AtwEIAEgDDYC2AQCQAJAIAEoApACQYCAgIB4RwRAIAFBAjYC3AUgAUHI4cIANgLYBSABQgE3AuQFIAEgAUG4BGqtQoCAgIDgC4Q3A+gEIAEgAUHoBGo2AuAFIA8gAUHYBWoQ0gIgD0GAgICAeDYCSAwBCyABQdgFaiIDIAFByARqIgsgAUHYBGoiDRA8IAFB0AZqIgogAUHkBWooAgA2AgAgASABKQLcBTcDyAYgASgC2AUiEUGAgICAeEcEQCABQfgEaiIZIAFB6AVqQeAA/AoAACABQfQEaiAKKAIANgIAIAEgETYC6AQgASABKQPIBjcC7AQgAyANIBkQlwIgAUHIBmoiCiABQegEaiADEPQBIAMgCiALEIEDIAEtAOQFIQMgASgC2AUiCgRAIAEoAtwFIApBAnQQ3wQLIAEoAsgGIgoEQCABKALMBiAKQQJ0EN8ECwJAIANBAUcEQEHRzsUALQAAGkEzIQZBM0EBENYEIgNFDR8gA0EvakGH4sIAKAAANgAAIANBKGpBgOLCACkAADcAACADQSBqQfjhwgApAAA3AAAgA0EYakHw4cIAKQAANwAAIANBEGpB6OHCACkAADcAACADQQhqQeDhwgApAAA3AAAgA0HY4cIAKQAANwAADAELAkAgAS0A9ARBAkYEQCABLQCEBUEBRw0BC0HRzsUALQAAGkEnIQZBJ0EBENYEIgNFDSAgA0EfakGq4sIAKQAANwAAIANBGGpBo+LCACkAADcAACADQRBqQZviwgApAAA3AAAgA0EIakGT4sIAKQAANwAAIANBi+LCACkAADcAAAwBCyAMQQJ0IQsCQCAMRQRAQQQhCgwBC0HRzsUALQAAGiALQQQQ1gQiCkUNIQsgCwRAIAogCSAL/AoAAAsgASAGOgDkBSABIAw2AuAFIAEgCjYC3AUgASAMNgLYBSABQdgGaiEGIAFB2AVqIQ1BACEKQQAhESMAQfABayIDJAACQAJAAkACQAJAIAJB6NHBAEEgEPEDRQRAIAJBIGoiDkHo0cEAQSAQ8QNFDQELAkACQCANLQAMIhpBAUcEQCADQRBqQgA3AwAgA0EYakIANwMAIANBIGpCADcDACADQShqQgA3AwAgA0EwakIANwMAIANBOGpCADcDACADQUBrQgA3AwAgA0IANwMIIAMgAi0AQCIOOgBIIANBiAFqIAJBOGopAwA3AwAgA0GAAWogAkEwaikDADcDACADQfgAaiACQShqKQMANwMAIANB2ABqIAJBCGopAwA3AwAgA0HgAGogAkEQaikDADcDACADQegAaiACQRhqKQMANwMAIAMgDjoAkAEgAyACKQMgNwNwIAMgAikDADcDUCANKAIEIRsgDSgCACEcQQQhDiAaDgMBAgECCyAGQgA3AwAgBkEIakIANwMAIAZBEGpCADcDACAGQRhqQgA3AwAgBkEgakIANwMAIAZBKGpCADcDACAGQTBqQgA3AwAgBkE4akIANwMADAMLIA0oAggiCkECdCENIApB/////wNLIA1B/P///wdLcg0DIA0Ef0HRzsUALQAAGkEEIREgDUEEENYEIg5FDQQgCgVBAAshESANRQ0AIA4gGyAN/AoAAAsgCkUNA0Hg98EAKAIAIR8gA0GgAWohIEHY98EAKQIAISoDQCAgIB82AgAgAyAqNwOYASADQZgBakHM+MEAEKUDIAMoApwBQQE2AgAgAygCnAEhFCADKAKYASEdAn8gCkEBRwRAQdHOxQAtAAAaQQRBBBDWBCINRQ0qIA0gFCgCACIVNgIAIBUgDigCAHEMAQtB0c7FAC0AABpBBEEEENYEIg1FDSkgDSAOKAIAIhU2AgAgFSAUKAIAcQshFSANIBU2AgAgHQRAIBQgHUECdBDfBAsgDUEEEN8EIBUEQCADQZgBaiINIANBCGoiFCADQdAAahA1IBQgDUHIAPwKAAALIANBmAFqIhQgA0HQAGoiDSANEDUgDSAUQcgA/AoAACADIAo2AqABIAMgDjYCnAEgAyARNgKYAQJAAkAgEUGAgICAeEcNACAOKAIIDQAgA0EANgLsASADQoCAgIDAADcC5AEMAQsgA0HkAWogA0GYAWpBAEEBEOwBCyADKALkASERIAMoAugBIQ4gAygC7AEiCg0ACwwDCyAGIA4pAwA3AyAgBiACKQMANwMAIAZBOGogDkEYaikDADcDACAGQTBqIA5BEGopAwA3AwAgBkEoaiAOQQhqKQMANwMAIAZBCGogAkEIaikDADcDACAGQRBqIAJBEGopAwA3AwAgBkEYaiACQRhqKQMANwMACyAGIAItAEA6AEAgDSgCACIGRQ0CIA0oAgQgBkECdBDfBAwCCyARIA1B+IHAABDIBAALIBpFBEAgA0GYAWohCgJAAkAgA0EIaiINQejRwQBBIBDxA0UEQCANQSBqIhRB6NHBAEEgEPEDRQ0BCyANKQM4IS4gDSkDMCEqIA0pAyghLCANKQMgIS8CQCANQSBqQejRwQBBIBDxA0UEQCAsISsgKiEtDAELQpHh5c2HifqZKCAqfSIrIC5CgYCAgL+y/fDDAFatIjB9IS1C3bCFjOi2kai4fyAsfSIxICsgMFQgKkKR4eXNh4n6mShWcq0iKn0hK0KpwMaJrs6TsjAgKiAxViAsQt2whYzotpGouH9Wcq0gL3x9IS9CgYCAgL+y/fDDACAufSEuCyAKIC43AzggCiAtNwMwIAogKzcDKCAKIC83AyAgCiANKQMANwMADAELIAogFCkDADcDICAKIA0pAwA3AwAgCkE4aiAUQRhqKQMANwMAIApBMGogFEEQaikDADcDACAKQShqIBRBCGopAwA3AwALIApBCGogDUEIaikDADcDACAKQRBqIA1BEGopAwA3AwAgCkEYaiANQRhqKQMANwMAIAogDS0AQDoAQCANIApByAD8CgAACyAGIANBCGpByAD8CgAAIBEEQCAOIBFBAnQQ3wQLIBxFDQAgGyAcQQJ0EN8ECyADQfABaiQAQQQhCkEAIQZBACENAkACQAJAIAEtAPQEQQFrDgICAQALQbTiwgAQ6AQACyABKALwBCIGQQJ0IQMgBkH/////A0sgA0H8////B0tyDSIgASgC7AQhESADBH9B0c7FAC0AABpBBCENIANBBBDWBCIKRQ0jIAYFQQALIQ0gA0UNACAKIBEgA/wKAAALIAFBrAZqIBkQ5wEgAUHYBWoiAyABQdgGakHIAPwKAAAgASAGNgKoBiABIAo2AqQGIAEgDTYCoAYgDyADQeAA/AoAACABQegEahCmAyAMBEAgCSALEN8ECwwDCyAPQYCAgIB4NgJIIA8gBjYCCCAPIAM2AgQgDyAGNgIAIAFB6ARqEKYDDAELIA8gASkDyAY3AgAgD0GAgICAeDYCSCAPQQhqIAooAgA2AgALIAwEQCAJIAxBAnQQ3wQLCyABKALIBCIDBEAgASgCzAQgA0ECdBDfBAsgASgCrAQiAwRAIAEoArAEIANBAnQQ3wQLAkAgASgC5AEiA0UNACADIANBDGxBE2pBeHEiBmpBCWoiA0UNACABKALgASAGayADEN8ECyABKAKQAiIDQYCAgIB4RiADRXJFBEAgASgClAIgA0ECdBDfBAsgAUGgB2okACAIKALYB0GAgICAeEcEQCAIQagGaiIBIA9ByAD8CgAAIAhBmAlqIgYgF0EIaigCADYCACAIQagJaiIJIBZBCGooAgA2AgAgCCAXKQIANwOQCSAIIBYpAgA3A6AJIAhB8AhqIgMgARCzASADIB4QswEgCCgC+AgiASAIKALwCEYEQCADQbyUwQAQnwMLIAgoAvQIIAFBDGxqIgMgCCkDkAk3AgAgA0EIaiAGKAIANgIAIAggAUEBaiIDNgL4CCAIKALwCCADRgRAIAhB8AhqQbyUwQAQnwMLIAgoAvQIIANBDGxqIgMgCCkDoAk3AgAgA0EIaiAJKAIANgIAIAggAUECajYC+AggCCgCgAkiAQRAIAgoAoQJIAFBAnQQ3wQLIAJByABqIQIgBUEMaiEFIARBAWsiBA0BDAILCwwRCwJAIAcEQCAIKAL4CCEBIAhBmAdqQaz8wAAoAgAiAjYCACAIQaT8wAApAgAiKjcDkAcCQCABQQFrIgFFBEAgCEGwBmogAjYCACAIICo3A6gGDAELIAhBkAdqQZj9wAAQpQMgCCgClAcgATYCACAIQbAGakEBNgIAIAggCCkDkAc3A6gGIAgoAvgIRQ0CCyAIKAL0CCIBKAIAIgIEQCABKAIEIAJBAnQQ3wQLIAEgCCkDqAY3AgAgAUEIaiAIQbAGaigCADYCAAsgACAIKQLwCDcCBCAAQQxqIAhB+AhqKAIANgIAIAhBwAhqEPMDIAgoAsAIIgEEQCAIKALECCABQQxsEN8ECyAIQbQIahDzAyAIKAK0CCIBBEAgCCgCuAggAUEMbBDfBAsgAEEANgIAIAgoAqwEIgAEQCAIKAKwBCAAQQJ0EN8ECyAIQeABahD/AyAIKAKQAiIAQYCAgIB4RiAARXJFBEAgCCgClAIgAEECdBDfBAsgE0UNASASIBNByABsEN8EDAELDBELIBhFDQggECAYQQV0EN8EDAgLIAYEQCAIQZgHaiIBQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAKBEAgCEGQB2pBmP3AABClAyAIKAKUByAKNgIAIAhBATYCmAcLIAhBsAZqIAEoAgA2AgAgCCAIKQOQBzcDqAYgCCgC8AggCUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCAJQQxsaiIBIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgAgCCAJQQFqNgL4CCAKBEAgEiAKQcgAbGohAiASIQEDQCAIQfAIaiIFIAEQtAEgBSABQSBqELQBIAFByABqIgEgAkcNAAsLIAhBmAdqQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAEBEAgCEGQB2pBmP3AABClAyAIKAKUByAENgIAIAhBATYCmAcLIAhBsAZqIgIgCEGYB2ooAgA2AgAgCCAIKQOQBzcDqAYgCCgC+AgiASAIKALwCEYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWoiATYC+AgCQCAERQ0AQQQhAkEAIQUCQANAIAUgCCgCvAgiAU8NECAIKAK4CCACaiIJQQRqKAIAIgtBAnQhAUEAIQYgC0H/////A0sgAUH8////B0tyDQ8gCSgCACENAn8gAUUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQYgAUEEENYEIglFDRAgCwshDyABBEAgCSANIAH8CgAACyAIKAL4CCIBIAgoAvAIRgRAIAhB8AhqQbyUwQAQnwMLIAgoAvQIIAFBDGxqIgYgCzYCCCAGIAk2AgQgBiAPNgIAIAggAUEBajYC+AggCCgCyAgiASAFSwRAIAgoAsQIIAJqIglBBGooAgAiC0ECdCEBQQAhBiALQf////8DSyABQfz///8HS3INAiAJKAIAIQ0CfyABRQRAQQQhCUEADAELQdHOxQAtAAAaQQQhBiABQQQQ1gQiCUUNAyALCyEPIAEEQCAJIA0gAfwKAAALIAgoAvgIIgEgCCgC8AhGBEAgCEHwCGpBvJTBABCfAwsgCCgC9AggAUEMbGoiBiALNgIIIAYgCTYCBCAGIA82AgAgCCABQQFqIgE2AvgIIAJBDGohAiAEIAVBAWoiBUcNAQwDCwsMDQsMDQsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBBDYCACAIQbAGaiICQQE2AgAgCCAIKQOQBzcDqAYgCCgC8AggAUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWo2AvgICwJAIAQgCiAEIApJGyIERQ0AIANBCGohBSAIQcgGaiEeIAhB5AdqIRYgCEHYB2ohFyASIQIDQAJAIAUoAgAiAQRAQQAhBgJAIAFB/////wNLIAFBAnQiA0H8////B0tyRQRAIAVBBGsoAgAhCkHRzsUALQAAGkEEIQYgA0EEENYEIgkNAQsMEgsgAwRAIAkgCiAD/AoAAAsgCCABNgKICSAIIAk2AoQJIAggATYCgAkMAQsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBATYCACAIQYgJakEBNgIAIAggCCkDkAc3A4AJCyAIQZAHaiEPIAhBgAlqIQ0jAEGgB2siASQAIAEQSUEBIQZBBCEJQQQhA0EBIQogASgCtAQiCwRAQdHOxQAtAAAaIAEoArAEIQwgC0ECdCIKQQQQ1gQiA0UNFyAKBEAgAyAMIAr8CgAAC0ECIQoLIAFB1wRqQQA6AAAgAUEAOwDVBCABIAo6ANQEIAEgCzYC0AQgASADNgLMBCABIAs2AsgEIA0oAggiDARAQdHOxQAtAAAaIA0oAgQhBiAMQQJ0IgNBBBDWBCIJRQ0YIAMEQCAJIAYgA/wKAAALQQIhBgsgAUHnBGpBADoAACABQQA7AOUEIAEgBjoA5AQgASAMNgLgBCABIAk2AtwEIAEgDDYC2AQCQAJAIAEoApACQYCAgIB4RwRAIAFBAjYC3AUgAUHI4cIANgLYBSABQgE3AuQFIAEgAUG4BGqtQoCAgIDgC4Q3A+gEIAEgAUHoBGo2AuAFIA8gAUHYBWoQ0gIgD0GAgICAeDYCSAwBCyABQdgFaiIDIAFByARqIgsgAUHYBGoiDRA8IAFB0AZqIgogAUHkBWooAgA2AgAgASABKQLcBTcDyAYgASgC2AUiEUGAgICAeEcEQCABQfgEaiIZIAFB6AVqQeAA/AoAACABQfQEaiAKKAIANgIAIAEgETYC6AQgASABKQPIBjcC7AQgAyANIBkQlwIgAUHIBmoiCiABQegEaiADEPQBIAMgCiALEIEDIAEtAOQFIQMgASgC2AUiCgRAIAEoAtwFIApBAnQQ3wQLIAEoAsgGIgoEQCABKALMBiAKQQJ0EN8ECwJAIANBAUcEQEHRzsUALQAAGkEzIQZBM0EBENYEIgNFDR0gA0EvakGH4sIAKAAANgAAIANBKGpBgOLCACkAADcAACADQSBqQfjhwgApAAA3AAAgA0EYakHw4cIAKQAANwAAIANBEGpB6OHCACkAADcAACADQQhqQeDhwgApAAA3AAAgA0HY4cIAKQAANwAADAELAkAgAS0A9ARBAkYEQCABLQCEBUEBRw0BC0HRzsUALQAAGkEnIQZBJ0EBENYEIgNFDR4gA0EfakGq4sIAKQAANwAAIANBGGpBo+LCACkAADcAACADQRBqQZviwgApAAA3AAAgA0EIakGT4sIAKQAANwAAIANBi+LCACkAADcAAAwBCyAMQQJ0IQsCQCAMRQRAQQQhCgwBC0HRzsUALQAAGiALQQQQ1gQiCkUNHwsgCwRAIAogCSAL/AoAAAsgASAGOgDkBSABIAw2AuAFIAEgCjYC3AUgASAMNgLYBSABQdgGaiEGIAFB2AVqIQ5BACERIwBBkAJrIgMkAAJAAkACQAJAAkAgAkHo0cEAQSAQ8QNFBEAgAkEgaiIKQejRwQBBIBDxA0UNAQsCQAJAIA4tAAwiGkEBRwRAIANBEGpCADcDACADQRhqQgA3AwAgA0EgakIANwMAIANBKGpCADcDACADQTBqQgA3AwAgA0E4akIANwMAIANBQGtCADcDACADQgA3AwggAyACLQBAIgo6AEggA0GIAWogAkE4aikDADcDACADQYABaiACQTBqKQMANwMAIANB+ABqIAJBKGopAwA3AwAgA0HYAGogAkEIaikDADcDACADQeAAaiACQRBqKQMANwMAIANB6ABqIAJBGGopAwA3AwAgAyAKOgCQASADIAIpAyA3A3AgAyACKQMANwNQIA4oAgQhGyAOKAIAIRxBBCEKQQAhDSAaDgMBAgECCyAGQgA3AwAgBkEIakIANwMAIAZBEGpCADcDACAGQRhqQgA3AwAgBkEgakIANwMAIAZBKGpCADcDACAGQTBqQgA3AwAgBkE4akIANwMADAMLIA4oAggiEUECdCEOIBFB/////wNLIA5B/P///wdLcg0DIA4Ef0HRzsUALQAAGkEEIQ0gDkEEENYEIgpFDQQgEQVBAAshDSAORQ0AIAogGyAO/AoAAAsgEUUNA0Hg98EAKAIAIR8gA0GgAWohIEHY98EAKQIAISoDQCAgIB82AgAgAyAqNwOYASADQZgBakHM+MEAEKUDIAMoApwBQQE2AgAgAygCnAEhFCADKAKYASEdAn8gEUEBRwRAQdHOxQAtAAAaQQRBBBDWBCIORQ0oIA4gFCgCACIVNgIAIBUgCigCAHEMAQtB0c7FAC0AABpBBEEEENYEIg5FDScgDiAKKAIAIhU2AgAgFSAUKAIAcQshFSAOIBU2AgAgHQRAIBQgHUECdBDfBAsgDkEEEN8EIBUEQCADQZgBaiIOIANBCGoiFCADQdAAahAzIBQgDkHIAPwKAAALIANBmAFqIhQgA0HQAGoiDiAOEDMgDiAUQcgA/AoAACADIBE2AqABIAMgCjYCnAEgAyANNgKYAQJAAkAgDUGAgICAeEcNACAKKAIIDQAgA0EANgKMAiADQoCAgIDAADcChAIMAQsgA0GEAmogA0GYAWpBAEEBEOwBCyADKAKEAiENIAMoAogCIQogAygCjAIiEQ0ACwwDCyAGIAopAwA3AyAgBiACKQMANwMAIAZBOGogCkEYaikDADcDACAGQTBqIApBEGopAwA3AwAgBkEoaiAKQQhqKQMANwMAIAZBCGogAkEIaikDADcDACAGQRBqIAJBEGopAwA3AwAgBkEYaiACQRhqKQMANwMACyAGIAItAEA6AEAgDigCACIGRQ0CIA4oAgQgBkECdBDfBAwCCyANIA5B+IHAABDIBAALIBpFBEACQAJAIANBCGpB6NHBAEEgEPEDRQRAIANBKGpB6NHBAEEgEPEDRQ0BCyADKQNAISogAykDOCEsIAMpAzAhKyADKQMoIS0gA0EoakHo0cEAQSAQ8QNFDQEgLEJ/hSIuICpCbVatIi99ISwgK0J/hSIwIC4gL1StIi59IStCf0IAIC4gMFYbIC19Qv///////////wB8IS1CbSAqfSEqDAELIAMpA0AhKiADKQM4ISwgAykDMCErIAMpAyghLQsgAyAtNwMoIAMgKzcDMCADICw3AzggAyAqNwNACyAGIANBCGpByAD8CgAAIA0EQCAKIA1BAnQQ3wQLIBxFDQAgGyAcQQJ0EN8ECyADQZACaiQAQQQhCkEAIQZBACENAkACQAJAIAEtAPQEQQFrDgICAQALQbTiwgAQ6AQACyABKALwBCIGQQJ0IQMgBkH/////A0sgA0H8////B0tyDSAgASgC7AQhESADBH9B0c7FAC0AABpBBCENIANBBBDWBCIKRQ0hIAYFQQALIQ0gA0UNACAKIBEgA/wKAAALIAFBrAZqIBkQ5wEgAUHYBWoiAyABQdgGakHIAPwKAAAgASAGNgKoBiABIAo2AqQGIAEgDTYCoAYgDyADQeAA/AoAACABQegEahCmAyAMBEAgCSALEN8ECwwDCyAPQYCAgIB4NgJIIA8gBjYCCCAPIAM2AgQgDyAGNgIAIAFB6ARqEKYDDAELIA8gASkDyAY3AgAgD0GAgICAeDYCSCAPQQhqIAooAgA2AgALIAwEQCAJIAxBAnQQ3wQLCyABKALIBCIDBEAgASgCzAQgA0ECdBDfBAsgASgCrAQiAwRAIAEoArAEIANBAnQQ3wQLAkAgASgC5AEiA0UNACADIANBDGxBE2pBeHEiBmpBCWoiA0UNACABKALgASAGayADEN8ECyABKAKQAiIDQYCAgIB4RiADRXJFBEAgASgClAIgA0ECdBDfBAsgAUGgB2okACAIKALYB0GAgICAeEcEQCAIQagGaiIBIA9ByAD8CgAAIAhBmAlqIgYgF0EIaigCADYCACAIQagJaiIJIBZBCGooAgA2AgAgCCAXKQIANwOQCSAIIBYpAgA3A6AJIAhB8AhqIgMgARC0ASADIB4QtAEgCCgC+AgiASAIKALwCEYEQCADQbyUwQAQnwMLIAgoAvQIIAFBDGxqIgMgCCkDkAk3AgAgA0EIaiAGKAIANgIAIAggAUEBaiIDNgL4CCAIKALwCCADRgRAIAhB8AhqQbyUwQAQnwMLIAgoAvQIIANBDGxqIgMgCCkDoAk3AgAgA0EIaiAJKAIANgIAIAggAUECajYC+AggCCgCgAkiAQRAIAgoAoQJIAFBAnQQ3wQLIAJByABqIQIgBUEMaiEFIARBAWsiBA0BDAILCwwPCwJAIAcEQCAIKAL4CCEBIAhBmAdqQaz8wAAoAgAiAjYCACAIQaT8wAApAgAiKjcDkAcCQCABQQFrIgFFBEAgCEGwBmogAjYCACAIICo3A6gGDAELIAhBkAdqQZj9wAAQpQMgCCgClAcgATYCACAIQbAGakEBNgIAIAggCCkDkAc3A6gGIAgoAvgIRQ0CCyAIKAL0CCIBKAIAIgIEQCABKAIEIAJBAnQQ3wQLIAEgCCkDqAY3AgAgAUEIaiAIQbAGaigCADYCAAsgACAIKQLwCDcCBCAAQQxqIAhB+AhqKAIANgIAIAhBwAhqEPMDIAgoAsAIIgEEQCAIKALECCABQQxsEN8ECyAIQbQIahDzAyAIKAK0CCIBBEAgCCgCuAggAUEMbBDfBAsgAEEANgIAIAgoAqwEIgAEQCAIKAKwBCAAQQJ0EN8ECyAIQeABahD/AyAIKAKQAiIAQYCAgIB4RiAARXJFBEAgCCgClAIgAEECdBDfBAsgE0UNASASIBNByABsEN8EDAELDA8LIBhFDQYgECAYQQV0EN8EDAYLIAYEQCAIQZgHaiIBQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAKBEAgCEGQB2pBmP3AABClAyAIKAKUByAKNgIAIAhBATYCmAcLIAhBsAZqIAEoAgA2AgAgCCAIKQOQBzcDqAYgCCgC8AggCUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCAJQQxsaiIBIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgAgCCAJQQFqNgL4CCAKBEAgEiAKQcgAbGohAiASIQEDQCAIQfAIaiIFIAEQtQEgBSABQSBqELUBIAFByABqIgEgAkcNAAsLIAhBmAdqQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAEBEAgCEGQB2pBmP3AABClAyAIKAKUByAENgIAIAhBATYCmAcLIAhBsAZqIgIgCEGYB2ooAgA2AgAgCCAIKQOQBzcDqAYgCCgC+AgiASAIKALwCEYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWoiATYC+AgCQCAERQ0AQQQhAkEAIQUCQANAIAUgCCgCvAgiAU8NDiAIKAK4CCACaiIJQQRqKAIAIgtBAnQhAUEAIQYgC0H/////A0sgAUH8////B0tyDQ0gCSgCACENAn8gAUUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQYgAUEEENYEIglFDQ4gCwshDyABBEAgCSANIAH8CgAACyAIKAL4CCIBIAgoAvAIRgRAIAhB8AhqQbyUwQAQnwMLIAgoAvQIIAFBDGxqIgYgCzYCCCAGIAk2AgQgBiAPNgIAIAggAUEBajYC+AggCCgCyAgiASAFSwRAIAgoAsQIIAJqIglBBGooAgAiC0ECdCEBQQAhBiALQf////8DSyABQfz///8HS3INAiAJKAIAIQ0CfyABRQRAQQQhCUEADAELQdHOxQAtAAAaQQQhBiABQQQQ1gQiCUUNAyALCyEPIAEEQCAJIA0gAfwKAAALIAgoAvgIIgEgCCgC8AhGBEAgCEHwCGpBvJTBABCfAwsgCCgC9AggAUEMbGoiBiALNgIIIAYgCTYCBCAGIA82AgAgCCABQQFqIgE2AvgIIAJBDGohAiAEIAVBAWoiBUcNAQwDCwsMCwsMCwsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBAzYCACAIQbAGaiICQQE2AgAgCCAIKQOQBzcDqAYgCCgC8AggAUYEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCABQQxsaiIFIAgpA6gGNwIAIAVBCGogAigCADYCACAIIAFBAWo2AvgICwJAIAQgCiAEIApJGyIERQ0AIANBCGohBSAIQcgGaiEeIAhB5AdqIRYgCEHYB2ohFyASIQIDQAJAIAUoAgAiAQRAQQAhBgJAIAFB/////wNLIAFBAnQiA0H8////B0tyRQRAIAVBBGsoAgAhCkHRzsUALQAAGkEEIQYgA0EEENYEIgkNAQsMEAsgAwRAIAkgCiAD/AoAAAsgCCABNgKICSAIIAk2AoQJIAggATYCgAkMAQsgCEGYB2pBrPzAACgCADYCACAIQaT8wAApAgA3A5AHIAhBkAdqQZj9wAAQpQMgCCgClAdBATYCACAIQYgJakEBNgIAIAggCCkDkAc3A4AJCyAIQZAHaiEPIAhBgAlqIQ0jAEGgB2siASQAIAEQPkEBIQZBBCEJQQQhA0EBIQogASgCtAQiCwRAQdHOxQAtAAAaIAEoArAEIQwgC0ECdCIKQQQQ1gQiA0UNFSAKBEAgAyAMIAr8CgAAC0ECIQoLIAFB1wRqQQA6AAAgAUEAOwDVBCABIAo6ANQEIAEgCzYC0AQgASADNgLMBCABIAs2AsgEIA0oAggiDARAQdHOxQAtAAAaIA0oAgQhBiAMQQJ0IgNBBBDWBCIJRQ0WIAMEQCAJIAYgA/wKAAALQQIhBgsgAUHnBGpBADoAACABQQA7AOUEIAEgBjoA5AQgASAMNgLgBCABIAk2AtwEIAEgDDYC2AQCQAJAIAEoApACQYCAgIB4RwRAIAFBAjYC3AUgAUHI4cIANgLYBSABQgE3AuQFIAEgAUG4BGqtQoCAgIDgC4Q3A+gEIAEgAUHoBGo2AuAFIA8gAUHYBWoQ0gIgD0GAgICAeDYCSAwBCyABQdgFaiIDIAFByARqIgsgAUHYBGoiDRA8IAFB0AZqIgogAUHkBWooAgA2AgAgASABKQLcBTcDyAYgASgC2AUiEUGAgICAeEcEQCABQfgEaiIZIAFB6AVqQeAA/AoAACABQfQEaiAKKAIANgIAIAEgETYC6AQgASABKQPIBjcC7AQgAyANIBkQlwIgAUHIBmoiCiABQegEaiADEPQBIAMgCiALEIEDIAEtAOQFIQMgASgC2AUiCgRAIAEoAtwFIApBAnQQ3wQLIAEoAsgGIgoEQCABKALMBiAKQQJ0EN8ECwJAIANBAUcEQEHRzsUALQAAGkEzIQZBM0EBENYEIgNFDRsgA0EvakGH4sIAKAAANgAAIANBKGpBgOLCACkAADcAACADQSBqQfjhwgApAAA3AAAgA0EYakHw4cIAKQAANwAAIANBEGpB6OHCACkAADcAACADQQhqQeDhwgApAAA3AAAgA0HY4cIAKQAANwAADAELAkAgAS0A9ARBAkYEQCABLQCEBUEBRw0BC0HRzsUALQAAGkEnIQZBJ0EBENYEIgNFDRwgA0EfakGq4sIAKQAANwAAIANBGGpBo+LCACkAADcAACADQRBqQZviwgApAAA3AAAgA0EIakGT4sIAKQAANwAAIANBi+LCACkAADcAAAwBCyAMQQJ0IQsCQCAMRQRAQQQhCgwBC0HRzsUALQAAGiALQQQQ1gQiCkUNHQsgCwRAIAogCSAL/AoAAAsgASAGOgDkBSABIAw2AuAFIAEgCjYC3AUgASAMNgLYBSABQdgGaiEGIAFB2AVqIQ5BACERIwBBkAJrIgMkAAJAAkACQAJAAkAgAkHo0cEAQSAQ8QNFBEAgAkEgaiIKQejRwQBBIBDxA0UNAQsCQAJAIA4tAAwiGkEBRwRAIANBEGpCADcDACADQRhqQgA3AwAgA0EgakIANwMAIANBKGpCADcDACADQTBqQgA3AwAgA0E4akIANwMAIANBQGtCADcDACADQgA3AwggAyACLQBAIgo6AEggA0GIAWogAkE4aikDADcDACADQYABaiACQTBqKQMANwMAIANB+ABqIAJBKGopAwA3AwAgA0HYAGogAkEIaikDADcDACADQeAAaiACQRBqKQMANwMAIANB6ABqIAJBGGopAwA3AwAgAyAKOgCQASADIAIpAyA3A3AgAyACKQMANwNQIA4oAgQhGyAOKAIAIRxBBCEKQQAhDSAaDgMBAgECCyAGQgA3AwAgBkEIakIANwMAIAZBEGpCADcDACAGQRhqQgA3AwAgBkEgakIANwMAIAZBKGpCADcDACAGQTBqQgA3AwAgBkE4akIANwMADAMLIA4oAggiEUECdCEOIBFB/////wNLIA5B/P///wdLcg0DIA4Ef0HRzsUALQAAGkEEIQ0gDkEEENYEIgpFDQQgEQVBAAshDSAORQ0AIAogGyAO/AoAAAsgEUUNA0Hg98EAKAIAIR8gA0GgAWohIEHY98EAKQIAISoDQCAgIB82AgAgAyAqNwOYASADQZgBakHM+MEAEKUDIAMoApwBQQE2AgAgAygCnAEhFCADKAKYASEdAn8gEUEBRwRAQdHOxQAtAAAaQQRBBBDWBCIORQ0mIA4gFCgCACIVNgIAIBUgCigCAHEMAQtB0c7FAC0AABpBBEEEENYEIg5FDSUgDiAKKAIAIhU2AgAgFSAUKAIAcQshFSAOIBU2AgAgHQRAIBQgHUECdBDfBAsgDkEEEN8EIBUEQCADQZgBaiIOIANBCGoiFCADQdAAahA7IBQgDkHIAPwKAAALIANBmAFqIhQgA0HQAGoiDiAOEDsgDiAUQcgA/AoAACADIBE2AqABIAMgCjYCnAEgAyANNgKYAQJAAkAgDUGAgICAeEcNACAKKAIIDQAgA0EANgKMAiADQoCAgIDAADcChAIMAQsgA0GEAmogA0GYAWpBAEEBEOwBCyADKAKEAiENIAMoAogCIQogAygCjAIiEQ0ACwwDCyAGIAopAwA3AyAgBiACKQMANwMAIAZBOGogCkEYaikDADcDACAGQTBqIApBEGopAwA3AwAgBkEoaiAKQQhqKQMANwMAIAZBCGogAkEIaikDADcDACAGQRBqIAJBEGopAwA3AwAgBkEYaiACQRhqKQMANwMACyAGIAItAEA6AEAgDigCACIGRQ0CIA4oAgQgBkECdBDfBAwCCyANIA5B+IHAABDIBAALIBpFBEACQAJAIANBCGpB6NHBAEEgEPEDRQRAIANBKGpB6NHBAEEgEPEDRQ0BCyADKQNAIS0gAykDOCErIAMpAzAhKiADKQMoIS4gA0EoakHo0cEAQSAQ8QNFBEAgKiEsDAILQgAgKn0iLyArQv////8PVq0iMH0hLEKBgICAcCAqQgBSIC8gMFRyrSAufH0hLkL/////DyArfSErIC1Cf4UhLQwBCyADKQNAIS0gAykDOCErIAMpAzAhLCADKQMoIS4LIAMgLjcDKCADICw3AzAgAyArNwM4IAMgLTcDQAsgBiADQQhqQcgA/AoAACANBEAgCiANQQJ0EN8ECyAcRQ0AIBsgHEECdBDfBAsgA0GQAmokAEEEIQpBACEGQQAhDQJAAkACQCABLQD0BEEBaw4CAgEAC0G04sIAEOgEAAsgASgC8AQiBkECdCEDIAZB/////wNLIANB/P///wdLcg0eIAEoAuwEIREgAwR/QdHOxQAtAAAaQQQhDSADQQQQ1gQiCkUNHyAGBUEACyENIANFDQAgCiARIAP8CgAACyABQawGaiAZEOcBIAFB2AVqIgMgAUHYBmpByAD8CgAAIAEgBjYCqAYgASAKNgKkBiABIA02AqAGIA8gA0HgAPwKAAAgAUHoBGoQpgMgDARAIAkgCxDfBAsMAwsgD0GAgICAeDYCSCAPIAY2AgggDyADNgIEIA8gBjYCACABQegEahCmAwwBCyAPIAEpA8gGNwIAIA9BgICAgHg2AkggD0EIaiAKKAIANgIACyAMBEAgCSAMQQJ0EN8ECwsgASgCyAQiAwRAIAEoAswEIANBAnQQ3wQLIAEoAqwEIgMEQCABKAKwBCADQQJ0EN8ECwJAIAEoAuQBIgNFDQAgAyADQQxsQRNqQXhxIgZqQQlqIgNFDQAgASgC4AEgBmsgAxDfBAsgASgCkAIiA0GAgICAeEYgA0VyRQRAIAEoApQCIANBAnQQ3wQLIAFBoAdqJAAgCCgC2AdBgICAgHhHBEAgCEGoBmoiASAPQcgA/AoAACAIQZgJaiIGIBdBCGooAgA2AgAgCEGoCWoiCSAWQQhqKAIANgIAIAggFykCADcDkAkgCCAWKQIANwOgCSAIQfAIaiIDIAEQtQEgAyAeELUBIAgoAvgIIgEgCCgC8AhGBEAgA0G8lMEAEJ8DCyAIKAL0CCABQQxsaiIDIAgpA5AJNwIAIANBCGogBigCADYCACAIIAFBAWoiAzYC+AggCCgC8AggA0YEQCAIQfAIakG8lMEAEJ8DCyAIKAL0CCADQQxsaiIDIAgpA6AJNwIAIANBCGogCSgCADYCACAIIAFBAmo2AvgIIAgoAoAJIgEEQCAIKAKECSABQQJ0EN8ECyACQcgAaiECIAVBDGohBSAEQQFrIgQNAQwCCwsMDQsCQCAHBEAgCCgC+AghASAIQZgHakGs/MAAKAIAIgI2AgAgCEGk/MAAKQIAIio3A5AHAkAgAUEBayIBRQRAIAhBsAZqIAI2AgAgCCAqNwOoBgwBCyAIQZAHakGY/cAAEKUDIAgoApQHIAE2AgAgCEGwBmpBATYCACAIIAgpA5AHNwOoBiAIKAL4CEUNAgsgCCgC9AgiASgCACICBEAgASgCBCACQQJ0EN8ECyABIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgALIAAgCCkC8Ag3AgQgAEEMaiAIQfgIaigCADYCACAIQcAIahDzAyAIKALACCIBBEAgCCgCxAggAUEMbBDfBAsgCEG0CGoQ8wMgCCgCtAgiAQRAIAgoArgIIAFBDGwQ3wQLIABBADYCACAIKAKsBCIABEAgCCgCsAQgAEECdBDfBAsgCEHgAWoQ/wMgCCgCkAIiAEGAgICAeEYgAEVyRQRAIAgoApQCIABBAnQQ3wQLIBNFDQEgEiATQcgAbBDfBAwBCwwNCyAYRQ0EIBAgGEEFdBDfBAwECyAGBEAgCEGYB2oiAUGs/MAAKAIANgIAIAhBpPzAACkCADcDkAcgCwRAIAhBkAdqQZj9wAAQpQMgCCgClAcgCzYCACAIQQE2ApgHCyAIQbAGaiABKAIANgIAIAggCCkDkAc3A6gGIAgoAuAIIBBGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggEEEMbGoiASAIKQOoBjcCACABQQhqIAhBsAZqKAIANgIAIAggEEEBajYC6AggCwRAIAogC0HIAGxqIQIgCiEBA0AgCEHgCGoiBSABELYBIAUgAUEgahC2ASABQcgAaiIBIAJHDQALCyAIQZgHakGs/MAAKAIANgIAIAhBpPzAACkCADcDkAcgBARAIAhBkAdqQZj9wAAQpQMgCCgClAcgBDYCACAIQQE2ApgHCyAIQbAGaiICIAhBmAdqKAIANgIAIAggCCkDkAc3A6gGIAgoAugIIgEgCCgC4AhGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggAUEMbGoiBSAIKQOoBjcCACAFQQhqIAIoAgA2AgAgCCABQQFqIgE2AugIAkAgBEUNAEEEIQJBACEFAkADQCAFIAgoArAIIgFPDQwgCCgCrAggAmoiCUEEaigCACIBQQJ0IRBBACEGIAFB/////wNLIBBB/P///wdLcg0QIAkoAgAhDQJ/IBBFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEGIBBBBBDWBCIJRQ0RIAELIQ8gEARAIAkgDSAQ/AoAAAsgCCgC6AgiBiAIKALgCEYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCAGQQxsaiIQIAE2AgggECAJNgIEIBAgDzYCACAIIAZBAWo2AugIIAgoArwIIgEgBUsEQCAIKAK4CCACaiIJQQRqKAIAIgFBAnQhEEEAIQYgAUH/////A0sgEEH8////B0tyDQIgCSgCACENAn8gEEUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQYgEEEEENYEIglFDQMgAQshDyAQBEAgCSANIBD8CgAACyAIKALoCCIGIAgoAuAIRgRAIAhB4AhqQbyUwQAQnwMLIAgoAuQIIAZBDGxqIhAgATYCCCAQIAk2AgQgECAPNgIAIAggBkEBaiIBNgLoCCACQQxqIQIgBCAFQQFqIgVHDQEMAwsLDAkLDA4LIAhBmAdqQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAIQZAHakGY/cAAEKUDIAgoApQHQQI2AgAgCEGwBmoiAkEBNgIAIAggCCkDkAc3A6gGIAgoAuAIIAFGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggAUEMbGoiBSAIKQOoBjcCACAFQQhqIAIoAgA2AgAgCCABQQFqIhA2AugICyAEIAsgBCALSRsiCQRAIAhByAZqISQgCEH8B2ohGCAIQfAHaiEWIAhB5AdqIRcgCEHYB2ohGSAKIQUDQCAIQZAHaiEPIwBB4AZrIgEkACABEFVBASEEQQQhBkEEIRBBASELIAEoArQEIgIEQEHRzsUALQAAGiABKAKwBCENIAJBAnQiC0EEENYEIhBFDRcgCwRAIBAgDSAL/AoAAAtBAiELCyABQdcEakEAOgAAIAFBADsA1QQgASALOgDUBCABIAI2AtAEIAEgEDYCzAQgASACNgLIBAJAAkACQCADKAIIIgIEQEHRzsUALQAAGiADKAIEIRAgAkECdCIEQQQQ1gQiBkUNASAEBEAgBiAQIAT8CgAAC0ECIQQLIAFB5wRqQQA6AAAgAUEAOwDlBCABIAQ6AOQEIAEgAjYC4AQgASAGNgLcBCABIAI2AtgEAkACQAJAAkAgASgCkAIiEEGAgICAeEcEQCABQegFaiABQcgEaiABQdgEaiABQZACahBPIAFBsAVqIgIgAUH0BWooAgA2AgAgASABKQLsBTcDqAUgASgC6AUiDkGAgICAeEcNAiAPIAEpA6gFNwIAIA9BgICAgHg2AkggD0EIaiACKAIANgIADAELIAFBAjYC7AUgAUGA4cIANgLoBSABQgE3AvQFIAEgAUG4BGqtQoCAgIDgC4Q3A6gFIAEgAUGoBWo2AvAFIA8gAUHoBWoQ0gIgD0GAgICAeDYCSAsgASgC2AQiAgRAIAEoAtwEIAJBAnQQ3wQLIAEoAsgEIgIEQCABKALMBCACQQJ0EN8ECyABKAKsBCICBEAgASgCsAQgAkECdBDfBAsCQCABKALkASICRQ0AIAIgAkEMbEETakF4cSIEakEJaiICRQ0AIAEoAuABIARrIAIQ3wQLIAEoApACIhBBgICAgHhHDQEMAgsgAUGQBWogAUGgBmopAgA3AwAgAUGIBWoiBCABQZgGaikCADcDACABQYAFaiABQZAGaikCADcDACABQfgEaiIGIAFBiAZqKQIANwMAIAFB8ARqIAFBgAZqKQIANwMAIAEgASkC+AU3A+gEIAFBpAVqIAIoAgA2AgAgASABKQOoBTcCnAUgASAONgKYBSAEKAIAIRogBigCACEbIAEoAowFISUgASgC/AQhJiABKALsBCEnIAEoAugEIRwgAUGoBWogAUGYBWoQ5wEgAUG0BWoiHSABQegEahDnASABQcAFaiIVIAYQ5wEgAUHMBWoiHiAEEOcBIAEoAuAEIgZBAnQhAkEAIQsgBkH/////A0sgAkH8////B0tyDQMgASgC3AQhDSABLQDkBCEMAn8gAkUEQEEEIQRBAAwBC0HRzsUALQAAGkEEIQsgAkEEENYEIgRFDQQgBgshCyACBEAgBCANIAL8CgAACyABIAw6AOQFIAEgBjYC4AUgASAENgLcBSABIAs2AtgFIAFB6AVqIQQgAUHYBWohDEEAIQ0jAEGQAmsiAiQAAkACQAJAAkACQCAFQejRwQBBIBDxA0UEQCAFQSBqIgZB6NHBAEEgEPEDRQ0BCwJAAkAgDC0ADCIfQQFHBEAgAkEQakIANwMAIAJBGGpCADcDACACQSBqQgA3AwAgAkEoakIANwMAIAJBMGpCADcDACACQThqQgA3AwAgAkFAa0IANwMAIAJCADcDCCACIAUtAEAiBjoASCACQYgBaiAFQThqKQMANwMAIAJBgAFqIAVBMGopAwA3AwAgAkH4AGogBUEoaikDADcDACACQdgAaiAFQQhqKQMANwMAIAJB4ABqIAVBEGopAwA3AwAgAkHoAGogBUEYaikDADcDACACIAY6AJABIAIgBSkDIDcDcCACIAUpAwA3A1AgDCgCBCEgIAwoAgAhIkEEIQZBACELIB8OAwECAQILIARCADcDACAEQQhqQgA3AwAgBEEQakIANwMAIARBGGpCADcDACAEQSBqQgA3AwAgBEEoakIANwMAIARBMGpCADcDACAEQThqQgA3AwAMAwsgDCgCCCINQQJ0IQwgDUH/////A0sgDEH8////B0tyDQMgDAR/QdHOxQAtAAAaQQQhCyAMQQQQ1gQiBkUNBCANBUEACyELIAxFDQAgBiAgIAz8CgAACyANRQ0DQeD3wQAoAgAhKCACQaABaiEpQdj3wQApAgAhKgNAICkgKDYCACACICo3A5gBIAJBmAFqQcz4wQAQpQMgAigCnAFBATYCACACKAKcASETIAIoApgBISMCfyANQQFHBEBB0c7FAC0AABpBBEEEENYEIgxFDSUgDCATKAIAIiE2AgAgISAGKAIAcQwBC0HRzsUALQAAGkEEQQQQ1gQiDEUNJCAMIAYoAgAiITYCACAhIBMoAgBxCyEhIAwgITYCACAjBEAgEyAjQQJ0EN8ECyAMQQQQ3wQgIQRAIAJBmAFqIgwgAkEIaiITIAJB0ABqEDkgEyAMQcgA/AoAAAsgAkGYAWoiEyACQdAAaiIMIAwQOSAMIBNByAD8CgAAIAIgDTYCoAEgAiAGNgKcASACIAs2ApgBAkACQCALQYCAgIB4Rw0AIAYoAggNACACQQA2AowCIAJCgICAgMAANwKEAgwBCyACQYQCaiACQZgBakEAQQEQ7AELIAIoAoQCIQsgAigCiAIhBiACKAKMAiINDQALDAMLIAQgBikDADcDICAEIAUpAwA3AwAgBEE4aiAGQRhqKQMANwMAIARBMGogBkEQaikDADcDACAEQShqIAZBCGopAwA3AwAgBEEIaiAFQQhqKQMANwMAIARBEGogBUEQaikDADcDACAEQRhqIAVBGGopAwA3AwALIAQgBS0AQDoAQCAMKAIAIgZFDQIgDCgCBCAGQQJ0EN8EDAILIAsgDEH4gcAAEMgEAAsgH0UEQAJAAkAgAkEIakHo0cEAQSAQ8QNFBEAgAkEoakHo0cEAQSAQ8QNFDQELIAIpA0AhKiACKQM4ISwgAikDMCErIAIpAyghLSACQShqQejRwQBBIBDxA0UNASAsQn+FIi4gKkKv+P//b1atIi99ISwgK0J/hSIwIC4gL1StIi59ISsgLUJ/hSAuIDBWrX0hLUKv+P//byAqfSEqDAELIAIpA0AhKiACKQM4ISwgAikDMCErIAIpAyghLQsgAiAtNwMoIAIgKzcDMCACICw3AzggAiAqNwNACyAEIAJBCGpByAD8CgAAIAsEQCAGIAtBAnQQ3wQLICJFDQAgICAiQQJ0EN8ECyACQZACaiQAIAFBuAZqIAFBsAVqKAIANgIAIAFBxAZqIB1BCGooAgA2AgAgAUHQBmogFUEIaigCADYCACABQdwGaiAeQQhqKAIANgIAIAEgASkCqAU3A7AGIAEgHSkCADcCvAYgASAVKQIANwPIBiABIB4pAgA3AtQGIA8gBEH4APwKAAAgGgRAICUgGkECdBDfBAsgGwRAICYgG0ECdBDfBAsgHARAICcgHEECdBDfBAsgDgRAIAEoApwFIA5BAnQQ3wQLIAEoAtgEIgIEQCABKALcBCACQQJ0EN8ECyABKALIBCICBEAgASgCzAQgAkECdBDfBAsgASgCrAQiAgRAIAEoArAEIAJBAnQQ3wQLIAEoAuQBIgJFDQAgAiACQQxsQRNqQXhxIgRqQQlqIgJFDQAgASgC4AEgBGsgAhDfBAsgEEUNACABKAKUAiAQQQJ0EN8ECyABQeAGaiQADAILQQQgBEH4gcAAEMgEAAsgCyACQfiBwAAQyAQACyAIKALYB0GAgICAeEYNDyAIQagGaiIBIAhBkAdqQcgA/AoAACAIQfgIaiIEIBlBCGooAgA2AgAgCEGICWoiBiAXQQhqKAIANgIAIAhBmAlqIhAgFkEIaigCADYCACAIQagJaiILIBhBCGooAgA2AgAgCCAZKQIANwPwCCAIIBcpAgA3A4AJIAggFikCADcDkAkgCCAYKQIANwOgCSAIQeAIaiICIAEQtgEgAiAkELYBIAgoAugIIgEgCCgC4AhGBEAgAkG8lMEAEJ8DCyAIKALkCCABQQxsaiICIAgpA/AINwIAIAJBCGogBCgCADYCACAIIAFBAWoiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA4AJNwIAIAJBCGogBigCADYCACAIIAFBAmoiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA5AJNwIAIAJBCGogECgCADYCACAIIAFBA2oiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA6AJNwIAIAJBCGogCygCADYCACAIIAFBBGoiEDYC6AggBUHIAGohBSADQQxqIQMgCUEBayIJDQALCwJAIAcEQCAIQZgHakGs/MAAKAIAIgE2AgAgCEGk/MAAKQIAIio3A5AHAkAgEEEBayICRQRAIAhBsAZqIAE2AgAgCCAqNwOoBgwBCyAIQZAHakGY/cAAEKUDIAgoApQHIAI2AgAgCEGwBmpBATYCACAIIAgpA5AHNwOoBiAIKALoCEUNAgsgCCgC5AgiASgCACICBEAgASgCBCACQQJ0EN8ECyABIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgALIAAgCCkC4Ag3AgQgAEEMaiAIQegIaigCADYCACAIQbQIahDzAyAIKAK0CCIBBEAgCCgCuAggAUEMbBDfBAsgCEGoCGoQ8wMgCCgCqAgiAQRAIAgoAqwIIAFBDGwQ3wQLIABBADYCACAIKAKsBCIABEAgCCgCsAQgAEECdBDfBAsgCEHgAWoQ/wMgCCgCkAIiAEGAgICAeEYgAEVyRQRAIAgoApQCIABBAnQQ3wQLIBFFDQEgCiARQcgAbBDfBAwBCwwLCyAURQ0CIBIgFEEFdBDfBAwCCyAGBEAgCEGYB2oiAUGs/MAAKAIANgIAIAhBpPzAACkCADcDkAcgCwRAIAhBkAdqQZj9wAAQpQMgCCgClAcgCzYCACAIQQE2ApgHCyAIQbAGaiABKAIANgIAIAggCCkDkAc3A6gGIAgoAuAIIBBGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggEEEMbGoiASAIKQOoBjcCACABQQhqIAhBsAZqKAIANgIAIAggEEEBajYC6AggCwRAIAogC0HoAGxqIQIgCiEBA0AgCEHgCGoiBSABELcBIAUgAUEwahC3ASABQegAaiIBIAJHDQALCyAIQZgHakGs/MAAKAIANgIAIAhBpPzAACkCADcDkAcgBARAIAhBkAdqQZj9wAAQpQMgCCgClAcgBDYCACAIQQE2ApgHCyAIQbAGaiICIAhBmAdqKAIANgIAIAggCCkDkAc3A6gGIAgoAugIIgEgCCgC4AhGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggAUEMbGoiBSAIKQOoBjcCACAFQQhqIAIoAgA2AgAgCCABQQFqIgE2AugIAkAgBEUNAEEEIQJBACEFAkADQCAFIAgoArAIIgFPDQogCCgCrAggAmoiCUEEaigCACIBQQJ0IRBBACEGIAFB/////wNLIBBB/P///wdLcg0OIAkoAgAhDwJ/IBBFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEGIBBBBBDWBCIJRQ0PIAELIQwgEARAIAkgDyAQ/AoAAAsgCCgC6AgiBiAIKALgCEYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCAGQQxsaiIQIAE2AgggECAJNgIEIBAgDDYCACAIIAZBAWo2AugIIAgoArwIIgEgBUsEQCAIKAK4CCACaiIJQQRqKAIAIgFBAnQhEEEAIQYgAUH/////A0sgEEH8////B0tyDQIgCSgCACEPAn8gEEUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQYgEEEEENYEIglFDQMgAQshDCAQBEAgCSAPIBD8CgAACyAIKALoCCIGIAgoAuAIRgRAIAhB4AhqQbyUwQAQnwMLIAgoAuQIIAZBDGxqIhAgATYCCCAQIAk2AgQgECAMNgIAIAggBkEBaiIBNgLoCCACQQxqIQIgBCAFQQFqIgVHDQEMAwsLDAcLDAwLIAhBmAdqQaz8wAAoAgA2AgAgCEGk/MAAKQIANwOQByAIQZAHakGY/cAAEKUDIAgoApQHQQE2AgAgCEGwBmoiAkEBNgIAIAggCCkDkAc3A6gGIAgoAuAIIAFGBEAgCEHgCGpBvJTBABCfAwsgCCgC5AggAUEMbGoiBSAIKQOoBjcCACAFQQhqIAIoAgA2AgAgCCABQQFqIhA2AugICyAEIAsgBCALSRsiCQRAIAhB2AZqIR0gCEGcCGohDiAIQZAIaiETIAhBhAhqIRQgCEH4B2ohGCAKIQUDQCAIQZAHaiECIwBB4AhrIgEkACABECZBASEEQQQhBkEEIRBBASELIAEoApQGIg8EQEHRzsUALQAAGiABKAKQBiEMIA9BAnQiC0EEENYEIhBFDRUgCwRAIBAgDCAL/AoAAAtBAiELCyABQbcGakEAOgAAIAFBADsAtQYgASALOgC0BiABIA82ArAGIAEgEDYCrAYgASAPNgKoBgJAAkACQCADKAIIIhAEQEHRzsUALQAAGiADKAIEIQsgEEECdCIEQQQQ1gQiBkUNASAEBEAgBiALIAT8CgAAC0ECIQQLIAFBxwZqQQA6AAAgAUEAOwDFBiABIAQ6AMQGIAEgEDYCwAYgASAGNgK8BiABIBA2ArgGAkACQAJAAkAgASgCgAMiEEGAgICAeEcEQCABQcgHaiABQagGaiABQbgGaiABQYADahBPIAFBkAdqIgQgAUHUB2ooAgA2AgAgASABKQLMBzcDiAcgASgCyAciD0GAgICAeEcNAiACIAEpA4gHNwIAIAJBgICAgHg2AmggAkEIaiAEKAIANgIADAELIAFBAjYCzAcgAUGA4cIANgLIByABQgE3AtQHIAEgAUGYBmqtQoCAgIDgC4Q3A4gHIAEgAUGIB2o2AtAHIAIgAUHIB2oQ0gIgAkGAgICAeDYCaAsgASgCuAYiAgRAIAEoArwGIAJBAnQQ3wQLIAEoAqgGIgIEQCABKAKsBiACQQJ0EN8ECyABKAKMBiICBEAgASgCkAYgAkECdBDfBAsCQCABKAIEIgJFDQAgAiACQQxsQRNqQXhxIgRqQQlqIgJFDQAgASgCACAEayACEN8ECyABKAKAAyIQQYCAgIB4Rw0BDAILIAFB8AZqIAFBgAhqKQIANwMAIAFB6AZqIgYgAUH4B2opAgA3AwAgAUHgBmogAUHwB2opAgA3AwAgAUHYBmoiCyABQegHaikCADcDACABQdAGaiABQeAHaikCADcDACABIAEpAtgHNwPIBiABQYQHaiAEKAIANgIAIAEgASkDiAc3AvwGIAEgDzYC+AYgBigCACEWIAsoAgAhFyABKALsBiEVIAEoAtwGIR4gASgCzAYhHyABKALIBiEZIAFBiAdqIAFB+AZqEOcBIAFBlAdqIhogAUHIBmoQ5wEgAUGgB2oiGyALEOcBIAFBrAdqIhwgBhDnASABKALABiIMQQJ0IQZBACELIAxB/////wNLIAZB/P///wdLcg0DIAEoArwGISAgAS0AxAYhIgJ/IAZFBEBBBCEEQQAMAQtB0c7FAC0AABpBBCELIAZBBBDWBCIERQ0EIAwLIQsgBgRAIAQgICAG/AoAAAsgASAiOgDEByABIAw2AsAHIAEgBDYCvAcgASALNgK4ByABQcgHaiIEIAUgAUG4B2oQpwEgAUG4CGogAUGQB2ooAgA2AgAgAUHECGogGkEIaigCADYCACABQdAIaiAbQQhqKAIANgIAIAFB3AhqIBxBCGooAgA2AgAgASABKQKIBzcDsAggASAaKQIANwK8CCABIBspAgA3A8gIIAEgHCkCADcC1AggAiAEQZgB/AoAACAWBEAgFSAWQQJ0EN8ECyAXBEAgHiAXQQJ0EN8ECyAZBEAgHyAZQQJ0EN8ECyAPBEAgASgC/AYgD0ECdBDfBAsgASgCuAYiAgRAIAEoArwGIAJBAnQQ3wQLIAEoAqgGIgIEQCABKAKsBiACQQJ0EN8ECyABKAKMBiICBEAgASgCkAYgAkECdBDfBAsgASgCBCICRQ0AIAIgAkEMbEETakF4cSIEakEJaiICRQ0AIAEoAgAgBGsgAhDfBAsgEEUNACABKAKEAyAQQQJ0EN8ECyABQeAIaiQADAILQQQgBEH4gcAAEMgEAAsgCyAGQfiBwAAQyAQACyAIKAL4B0GAgICAeEYNDSAIQagGaiIBIAhBkAdqQegA/AoAACAIQfgIaiIEIBhBCGooAgA2AgAgCEGICWoiBiAUQQhqKAIANgIAIAhBmAlqIhAgE0EIaigCADYCACAIQagJaiILIA5BCGooAgA2AgAgCCAYKQIANwPwCCAIIBQpAgA3A4AJIAggEykCADcDkAkgCCAOKQIANwOgCSAIQeAIaiICIAEQtwEgAiAdELcBIAgoAugIIgEgCCgC4AhGBEAgAkG8lMEAEJ8DCyAIKALkCCABQQxsaiICIAgpA/AINwIAIAJBCGogBCgCADYCACAIIAFBAWoiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA4AJNwIAIAJBCGogBigCADYCACAIIAFBAmoiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA5AJNwIAIAJBCGogECgCADYCACAIIAFBA2oiAjYC6AggCCgC4AggAkYEQCAIQeAIakG8lMEAEJ8DCyAIKALkCCACQQxsaiICIAgpA6AJNwIAIAJBCGogCygCADYCACAIIAFBBGoiEDYC6AggBUHoAGohBSADQQxqIQMgCUEBayIJDQALCwJAIAcEQCAIQZgHakGs/MAAKAIAIgE2AgAgCEGk/MAAKQIAIio3A5AHAkAgEEEBayICRQRAIAhBsAZqIAE2AgAgCCAqNwOoBgwBCyAIQZAHakGY/cAAEKUDIAgoApQHIAI2AgAgCEGwBmpBATYCACAIIAgpA5AHNwOoBiAIKALoCEUNAgsgCCgC5AgiASgCACICBEAgASgCBCACQQJ0EN8ECyABIAgpA6gGNwIAIAFBCGogCEGwBmooAgA2AgALIAAgCCkC4Ag3AgQgAEEMaiAIQegIaigCADYCACAIQbQIahDzAyAIKAK0CCIBBEAgCCgCuAggAUEMbBDfBAsgCEGoCGoQ8wMgCCgCqAgiAQRAIAgoAqwIIAFBDGwQ3wQLIABBADYCACAIKAKMBiIABEAgCCgCkAYgAEECdBDfBAsgCBD/AyAIKAKAAyIAQYCAgIB4RiAARXJFBEAgCCgChAMgAEECdBDfBAsgDUUNASAKIA1B6ABsEN8EDAELDAkLIBFFDQAgEiARQTBsEN8ECyAIQbAJaiQADwtBAUEuQayDwQAQyAQACyAJIAVBvIrBABDIBAALIAUgAUGMlMEAENkDAAsgBiABQfiBwAAQyAQACyAFIAFB/JPBABDZAwALIAYgA0H4gcAAEMgEAAsgCEGwBmogCEGYB2ooAgA2AgAgCCAIKQOQBzcDqAZB1P7AAEErIAhBqAZqQZCFwQBB3JPBABDKAwALQQBBAEHMk8EAENkDAAsgBiAQQfiBwAAQyAQACyAIQbAGaiAIQZgHaigCADYCACAIIAgpA5AHNwOoBkHU/sAAQSsgCEGoBmpBkIXBAEHsk8EAEMoDAAtBtJvCABCaBAALQQhBoAJBkJbCABDIBAALQQQgCkH4gcAAEMgEAAtBBCADQfiBwAAQyAQAC0EBQTNB1NjCABDIBAALQQFBJ0HU2MIAEMgEAAtBBCALQfiBwAAQyAQACyANIANB+IHAABDIBAALQQRBBEH4gcAAEMgEAAuVkwECH38DfiMAQdAWayIDJAAgA0GAE2ogASACEFYgAygCjBMhBCADKAKIEyEBIAMoAoQTIQICQAJAAkAgAygCgBNBAUYEQCAAQQI6AGAgACAENgIIIAAgATYCBCAAIAI2AgAMAQsCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIARBAkYEQCABKAIEIQQgASgCACEFIANBoAtqIAFBCGpB2AD8CgAAIAIEQCABIAJBMGwQ3wQLIANBsAJqIgEgA0GgC2pB2AD8CgAAIANBEGogA0G4AmopAwA3AwAgA0EYaiADQcACaikDADcDACADQSBqIANByAJqKQMANwMAIANBKGogA0HQAmopAwA3AwAgA0E4aiADQeACaikDADcDACADQUBrIANB6AJqKQMANwMAIANByABqIANB8AJqKQMANwMAIANB0ABqIANB+AJqKQMANwMAIANB2ABqIANBgANqKQMANwMAIAMgBDYCBCADIAU2AgAgAyADKQOwAjcDCCADIAMpA9gCNwMwIANB4ABqIAMQGyADQcgBaiADQTBqEBsgAy0AwAFFDQEgAy0AqAJFDQIgARAmAkACQAJAIAMtAMgIIhtBAUYEQCADKQPwBCEiAkAgAykD+AQiI0IAUwRAIANBqAtqQdyawAAoAgA2AgAgA0HUmsAAKQIANwOgC0IAICJ9ISRCACAjICJCAFKtfH0hIkEAIQJBASEEA0AgAygCoAsgBEEBa0YEQCADQaALakHYm8AAEKUDCyADKAKkCyACaiAkPgIAICJCIIYgJEKAgICAEFQhASAiUCEFIAJBBGohAiAiQiCIISIgAyAENgKoCyAEQQFqIQQgJEIgiIQhJCABIAVxRQ0ACyADQdAJaiADQagLaigCADYCACADIAMpA6ALNwPICSADQQA6ANQJDAELICIgI4RQBEAgA0HQCWpBzJrAACkCADcDACADQcSawAApAgA3A8gJDAELIANBqAtqQdyawAAoAgA2AgAgA0HUmsAAKQIANwOgC0EAIQJBASEEA0AgAygCoAsgBEEBa0YEQCADQaALakHYm8AAEKUDCyADKAKkCyACaiAiPgIAICNCIIYgIkKAgICAEFQhASAjUCEFIAJBBGohAiAjQiCIISMgAyAENgKoCyAEQQFqIQQgIkIgiIQhIiABIAVxRQ0ACyADQdAJaiADQagLaigCADYCACADIAMpA6ALNwPICSADQQI6ANQJCyADKALECA0BIAMoAsAIIAMoArwIIQEgA0HIEWpBzJrAACkCADcDACADQcSawAApAgA3A8ARIAFFDQIgAUECdBDfBAwCCyADKAK4CCIBRQRAIANB2AhqQcyawAApAgA3AwAgA0HEmsAAKQIANwPQCAwDCyADQagLakHcmsAAKAIANgIAIANB1JrAACkCADcDoAsgA0GgC2pByJvAABClAyADKAKkCyABNgIAIANB2AhqQQE2AgAgAyADKQOgCzcD0AggA0ECOgDcCAwCCyADQcgRaiADQbwIaiIBQQhqKAIANgIAIANBAjoAzBEgAyABKQIANwPAEQsgA0GoC2oiBEHcmsAAKAIANgIAIANB1JrAACkCADcDoAsgA0GgC2oiBUHIm8AAEKUDIAMoAqQLQQE2AgAgAygCpAshAiADKAKgCyEBIAUgA0HICWogA0HAEWoQwgECQAJAAkACQAJAAkACQCADLQCsCw4CAgABCyADQQI6AIwTIANBATYCiBMgAyACNgKEEyADIAE2AoATIAMoAqALIgFFDQUgAygCpAsgAUECdBDfBAwFCwJ/IAMoAqgLIgRBAUYEQCACKAIAIgQgAygCpAsoAgAiBUYNAyAEIAVLIAQgBUlrDAELIARFIARBAUtrC0H/AXEOAgECAwsgA0EBNgKoFiADIAI2AqQWIAMgATYCoBYgA0HoCGogBCgCADYCACADIAMpAqALIiI3A+AIAn8gIqcgAUsEQCADQYgTaiADQagLaigCADYCACADIAMpAqALNwOAEyADQfAVaiADQYATaiADQaAWaiIBEMoBIAEMAQsgA0EBNgKIEyADIAI2AoQTIAMgATYCgBMgA0HwFWogA0GAE2ogA0HgCGoiARDKASABCyIBKAIAIgIEQCABKAIEIAJBAnQQ3wQLIAMoAvgVRQRAIANBiBNqIANB+BVqKAIANgIAIANBAToAjBMgAyADKQLwFTcDgBMMBAsgA0GIE2ogA0H4FWooAgA2AgAgA0ECOgCMEyADIAMpAvAVNwOAEwwDCyADQYgTakHMmsAAKQIANwMAIANBxJrAACkCADcDgBMgAygCoAsiBARAIAMoAqQLIARBAnQQ3wQLIAFFDQIgAiABQQJ0EN8EDAILIANBATYCqBYgAyACNgKkFiADIAE2AqAWIANB6AhqIANBqAtqKAIANgIAIAMgAykCoAs3A+AIIANB8BVqIANBoBZqIANB4AhqEIcCIAMoAuAIIgEEQCADKALkCCABQQJ0EN8ECyADQYgTaiADQfgVaigCACIBNgIAIAMgAykC8BU3A4ATIANBAkEBIAEbOgCMEwwBCyADQagWaiADQagLaigCADYCACADIAMpAqALNwOgFiADQQE2AugIIAMgAjYC5AggAyABNgLgCCADQfAVaiADQaAWaiADQeAIahCHAiADKALgCCIBBEAgAygC5AggAUECdBDfBAsgA0GIE2ogA0H4FWooAgAiATYCACADIAMpAvAVNwOAEyADIAFFOgCMEwsgA0HQCGogA0GAE2ogA0HAEWoQwgEgAygCgBMiAQRAIAMoAoQTIAFBAnQQ3wQLIAMoAsARIgEEQCADKALEESABQQJ0EN8ECyADKALICSIBRQ0AIAMoAswJIAFBAnQQ3wQLIANB4AhqIgEgA0HgAGogA0HIAWoQJyADLQDACUUNAyADQcgJaiABQegA/AoAACADLQCoCkUNBCADQaALahAmIAMtALgRIgFBAUcNBSADQYATaiIFQcCwwABB4ABBEBDxASADKAKAE0GAgICAeEYNBiADQZgVaiIGIANBiBNqIgEoAgA2AgAgAyADKQKAEzcDkBUgBUGgscAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDQcgA0GoFWoiByABKAIANgIAIAMgAykCgBM3A6AVIAVBgLLAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0IIANBuBVqIgggASgCADYCACADIAMpAoATNwOwFSAFQd+ywABB4ABBEBDxASADKAKAE0GAgICAeEYNCSADQcgVaiIJIAEoAgA2AgAgAyADKQKAEzcDwBUgBUG/s8AAQd8AQRAQ8QEgAygCgBNBgICAgHhGDQogA0HYFWoiCiABKAIANgIAIAMgAykCgBM3A9AVIAVBnrTAAEHgAEEQEPEBIAMoAoATQYCAgIB4Rg0LIANB6BVqIgsgASgCADYCACADIAMpAoATNwPgFSAFQf60wABB3wBBEBDxASADKAKAE0GAgICAeEYNDCADQbgKaiIMIAEoAgA2AgAgAyADKQKAEzcDsAogBUHdtcAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDQ0gA0HYCmoiDSABKAIANgIAIAMgAykCgBM3A9AKIAVBvbbAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0OIANB+ApqIg8gASgCADYCACADIAMpAoATNwPwCiAFQZy3wABB4ABBEBDxASADKAKAE0GAgICAeEYNDyADQfgVaiIOIAEoAgA2AgAgAyADKQKAEzcD8BUgBUH8t8AAQeAAQRAQ8QEgAygCgBNBgICAgHhGDRAgA0GoFmoiESABKAIANgIAIAMgAykCgBM3A6AWIANBwBFqIgJB3LjAAEHfAEEQEPEBIAMoAsARQYCAgIB4Rg0RIANBjBRqIANByBFqIgQoAgA2AgAgASAGKAIANgIAIANBlBNqIAcoAgA2AgAgA0GgE2ogCCgCADYCACADIAMpAsARNwKEFCADIAMpA5AVNwOAEyADIAMpA6AVNwKMEyADIAMpA7AVNwOYEyADQawTaiAJKAIANgIAIAMgAykDwBU3AqQTIANBuBNqIAooAgA2AgAgAyADKQPQFTcDsBMgA0HEE2ogCygCADYCACADIAMpA+AVNwK8EyADQdATaiAMKAIANgIAIAMgAykDsAo3A8gTIANB3BNqIA0oAgA2AgAgAyADKQPQCjcC1BMgA0HoE2ogDygCADYCACADIAMpA/AKNwPgEyADQfQTaiAOKAIANgIAIAMgAykD8BU3AuwTIANBgBRqIBEoAgA2AgAgAyADKQOgFjcD+BNB0c7FAC0AABoCfwJAQcAEQQgQ1gQiAQRAQQwhESACIAUQ9gIgAUEoaiADQegRaiIFKQMANwMAIAFBIGogA0HgEWoiBikDADcDACABQRhqIANB2BFqIgcpAwA3AwAgAUEQaiADQdARaiIIKQMANwMAIAFBCGogBCkDADcDACABIAMpA8ARNwMAIAIgA0GME2oQ9gIgAUHYAGogBSkDADcDACABQdAAaiAGKQMANwMAIAFByABqIAcpAwA3AwAgAUFAayAIKQMANwMAIAFBOGogBCkDADcDACABIAMpA8ARNwMwIAIgA0GYE2oQ9gIgAUGIAWogBSkDADcDACABQYABaiAGKQMANwMAIAFB+ABqIAcpAwA3AwAgAUHwAGogCCkDADcDACABQegAaiAEKQMANwMAIAEgAykDwBE3A2AgAiADQaQTahD2AiABQbgBaiAFKQMANwMAIAFBsAFqIAYpAwA3AwAgAUGoAWogBykDADcDACABQaABaiAIKQMANwMAIAFBmAFqIAQpAwA3AwAgASADKQPAETcDkAEgAiADQbATahD2AiABQegBaiAFKQMANwMAIAFB4AFqIAYpAwA3AwAgAUHYAWogBykDADcDACABQdABaiAIKQMANwMAIAFByAFqIAQpAwA3AwAgASADKQPAETcDwAEgAiADQbwTahD2AiABQZgCaiAFKQMANwMAIAFBkAJqIAYpAwA3AwAgAUGIAmogBykDADcDACABQYACaiAIKQMANwMAIAFB+AFqIAQpAwA3AwAgASADKQPAETcD8AEgAiADQcgTahD2AiABQcgCaiAFKQMANwMAIAFBwAJqIAYpAwA3AwAgAUG4AmogBykDADcDACABQbACaiAIKQMANwMAIAFBqAJqIAQpAwA3AwAgASADKQPAETcDoAIgAiADQdQTahD2AiABQfgCaiAFKQMANwMAIAFB8AJqIAYpAwA3AwAgAUHoAmogBykDADcDACABQeACaiAIKQMANwMAIAFB2AJqIAQpAwA3AwAgASADKQPAETcD0AIgAiADQeATahD2AiABQagDaiAFKQMANwMAIAFBoANqIAYpAwA3AwAgAUGYA2ogBykDADcDACABQZADaiAIKQMANwMAIAFBiANqIAQpAwA3AwAgASADKQPAETcDgAMgAiADQewTahD2AiABQdgDaiAFKQMANwMAIAFB0ANqIAYpAwA3AwAgAUHIA2ogBykDADcDACABQcADaiAIKQMANwMAIAFBuANqIAQpAwA3AwAgASADKQPAETcDsAMgAiADQfgTahD2AiABQYgEaiAFKQMANwMAIAFBgARqIAYpAwA3AwAgAUH4A2ogBykDADcDACABQfADaiAIKQMANwMAIAFB6ANqIAQpAwA3AwAgASADKQPAETcD4AMgAiADQYQUahD2AiABQbgEaiAFKQMANwMAIAFBsARqIAYpAwA3AwAgAUGoBGogBykDADcDACABQaAEaiAIKQMANwMAIAFBmARqIAQpAwA3AwAgASADKQPAETcDkAQgAUGQBGpB+MPCAEEwEPEDRQ0BQQshD0EMDAILQQhBwARBpK3AABDIBAALIAFB4ANqQfjDwgBBMBDxAwRAQQohD0ELDAELIAFBsANqQfjDwgBBMBDxAwRAQQkhD0EKDAELIAFBgANqQfjDwgBBMBDxAwRAQQghD0EJDAELIAFB0AJqQfjDwgBBMBDxAwRAQQchD0EIDAELIAFBoAJqQfjDwgBBMBDxAwRAQQYhD0EHDAELIAFB8AFqQfjDwgBBMBDxAwRAQQUhD0EGDAELIAFBwAFqQfjDwgBBMBDxAwRAQQQhD0EFDAELIAFBkAFqQfjDwgBBMBDxAwRAQQMhD0EEDAELIAFB4ABqQfjDwgBBMBDxAwRAQQIhD0EDDAELIAFBMGpB+MPCAEEwEPEDBEBBASEPQQIMAQsgAUH4w8IAQTAQ8QMEf0EABUHRzsUALQAAGkEwQQgQ1gQiAkUNQiACQgA3AwAgAkEoakIANwMAIAJBIGpCADcDACACQRhqQgA3AwAgAkEQakIANwMAIAJBCGpCADcDACABQcAEEN8EQQEhESACIQFBfwshD0EBCyEZIANBwBFqIgZBu7nAAEHfAEEQEPEBIAMoAsARQYCAgIB4Rg0SIANBmBVqIgcgA0HIEWoiBSICKAIANgIAIAMgAykCwBE3A5AVIAZBmrrAAEHgAEEQEPEBIAMoAsARQYCAgIB4Rg0TIANBqBVqIgggAigCADYCACADIAMpAsARNwOgFSAGQfq6wABB3wBBEBDxASADKALAEUGAgICAeEYNFCADQbgVaiIJIAUoAgA2AgAgAyADKQLAETcDsBUgBkHZu8AAQd8AQRAQ8QEgAygCwBFBgICAgHhGDRUgA0HIFWoiCiACKAIANgIAIAMgAykCwBE3A8AVIAZBuLzAAEHgAEEQEPEBIAMoAsARQYCAgIB4Rg0WIANB2BVqIgsgAigCADYCACADIAMpAsARNwPQFSAGQZi9wABB3wBBEBDxASADKALAEUGAgICAeEYNFyADQegVaiIMIAIoAgA2AgAgAyADKQLAETcD4BUgBkH3vcAAQd8AQRAQ8QEgAygCwBFBgICAgHhGDRggA0G4CmoiDSACKAIANgIAIAMgAykCwBE3A7AKIAZB1r7AAEHgAEEQEPEBIAMoAsARQYCAgIB4Rg0ZIANB2ApqIg4gAigCADYCACADIAMpAsARNwPQCiAGQba/wABB3wBBEBDxASADKALAEUGAgICAeEYNGiADQfgKaiISIAIoAgA2AgAgAyADKQLAETcD8AogBkGVwMAAQd8AQRAQ8QEgAygCwBFBgICAgHhGDRsgA0H4FWoiECACKAIANgIAIAMgAykCwBE3A/AVIANBoBZqIgJB9MDAAEEBQRAQ8QEgAygCoBZBgICAgHhGDRwgA0HAEmogA0GoFmoiBCgCADYCACAFIAcoAgA2AgAgA0HUEWogCCgCADYCACADQeARaiAJKAIANgIAIAMgAykCoBY3A7gSIAMgAykDkBU3A8ARIAMgAykDoBU3AswRIAMgAykDsBU3A9gRIANB7BFqIAooAgA2AgAgAyADKQPAFTcC5BEgA0H4EWogCygCADYCACADIAMpA9AVNwPwESADQYQSaiAMKAIANgIAIAMgAykD4BU3AvwRIANBkBJqIA0oAgA2AgAgAyADKQOwCjcDiBIgA0GcEmogDigCADYCACADIAMpA9AKNwKUEiADQagSaiASKAIANgIAIAMgAykD8Ao3A6ASIANBtBJqIBAoAgA2AgAgAyADKQPwFTcCrBJB0c7FAC0AABoCfwJAQZAEQQgQ1gQiBQRAIAIgBhD2AiAFQShqIANByBZqIgYpAwA3AwAgBUEgaiADQcAWaiIHKQMANwMAIAVBGGogA0G4FmoiCCkDADcDACAFQRBqIANBsBZqIgkpAwA3AwAgBUEIaiAEKQMANwMAIAUgAykDoBY3AwAgAiADQcwRahD2AiAFQdgAaiAGKQMANwMAIAVB0ABqIAcpAwA3AwAgBUHIAGogCCkDADcDACAFQUBrIAkpAwA3AwAgBUE4aiAEKQMANwMAIAUgAykDoBY3AzAgAiADQdgRahD2AiAFQYgBaiAGKQMANwMAIAVBgAFqIAcpAwA3AwAgBUH4AGogCCkDADcDACAFQfAAaiAJKQMANwMAIAVB6ABqIAQpAwA3AwAgBSADKQOgFjcDYCACIANB5BFqEPYCIAVBuAFqIAYpAwA3AwAgBUGwAWogBykDADcDACAFQagBaiAIKQMANwMAIAVBoAFqIAkpAwA3AwAgBUGYAWogBCkDADcDACAFIAMpA6AWNwOQASACIANB8BFqEPYCIAVB6AFqIAYpAwA3AwAgBUHgAWogBykDADcDACAFQdgBaiAIKQMANwMAIAVB0AFqIAkpAwA3AwAgBUHIAWogBCkDADcDACAFIAMpA6AWNwPAASACIANB/BFqEPYCIAVBmAJqIAYpAwA3AwAgBUGQAmogBykDADcDACAFQYgCaiAIKQMANwMAIAVBgAJqIAkpAwA3AwAgBUH4AWogBCkDADcDACAFIAMpA6AWNwPwASACIANBiBJqEPYCIAVByAJqIAYpAwA3AwAgBUHAAmogBykDADcDACAFQbgCaiAIKQMANwMAIAVBsAJqIAkpAwA3AwAgBUGoAmogBCkDADcDACAFIAMpA6AWNwOgAiACIANBlBJqEPYCIAVB+AJqIAYpAwA3AwAgBUHwAmogBykDADcDACAFQegCaiAIKQMANwMAIAVB4AJqIAkpAwA3AwAgBUHYAmogBCkDADcDACAFIAMpA6AWNwPQAiACIANBoBJqEPYCIAVBqANqIAYpAwA3AwAgBUGgA2ogBykDADcDACAFQZgDaiAIKQMANwMAIAVBkANqIAkpAwA3AwAgBUGIA2ogBCkDADcDACAFIAMpA6AWNwOAAyACIANBrBJqEPYCIAVB2ANqIAYpAwA3AwAgBUHQA2ogBykDADcDACAFQcgDaiAIKQMANwMAIAVBwANqIAkpAwA3AwAgBUG4A2ogBCkDADcDACAFIAMpA6AWNwOwAyACIANBuBJqEPYCIAVBiARqIAYpAwA3AwAgBUGABGogBykDADcDACAFQfgDaiAIKQMANwMAIAVB8ANqIAkpAwA3AwAgBUHoA2ogBCkDADcDACAFIAMpA6AWNwPgA0ELIRIgBUHgA2pB+MPCAEEwEPEDRQ0BQQohDkELDAILQQhBkARBpK3AABDIBAALIAVBsANqQfjDwgBBMBDxAwRAQQkhDkEKDAELIAVBgANqQfjDwgBBMBDxAwRAQQghDkEJDAELIAVB0AJqQfjDwgBBMBDxAwRAQQchDkEIDAELIAVBoAJqQfjDwgBBMBDxAwRAQQYhDkEHDAELIAVB8AFqQfjDwgBBMBDxAwRAQQUhDkEGDAELIAVBwAFqQfjDwgBBMBDxAwRAQQQhDkEFDAELIAVBkAFqQfjDwgBBMBDxAwRAQQMhDkEEDAELIAVB4ABqQfjDwgBBMBDxAwRAQQIhDkEDDAELIAVBMGpB+MPCAEEwEPEDBEBBASEOQQIMAQsgBUH4w8IAQTAQ8QMEf0EABUHRzsUALQAAGkEwQQgQ1gQiAkUNQiACQgA3AwAgAkEoakIANwMAIAJBIGpCADcDACACQRhqQgA3AwAgAkEQakIANwMAIAJBCGpCADcDACAFQZAEEN8EQQEhEiACIQVBfwshDkEBCyEaIAMoAsARIgIEQCADKALEESACQQJ0EN8ECyADKALMESICBEAgAygC0BEgAkECdBDfBAsgAygC2BEiAgRAIAMoAtwRIAJBAnQQ3wQLIAMoAuQRIgIEQCADKALoESACQQJ0EN8ECyADKALwESICBEAgAygC9BEgAkECdBDfBAsgAygC/BEiAgRAIAMoAoASIAJBAnQQ3wQLIAMoAogSIgIEQCADKAKMEiACQQJ0EN8ECyADKAKUEiICBEAgAygCmBIgAkECdBDfBAsgAygCoBIiAgRAIAMoAqQSIAJBAnQQ3wQLIAMoAqwSIgIEQCADKAKwEiACQQJ0EN8ECyADKAK4EiICBEAgAygCvBIgAkECdBDfBAsgAygCgBMiAgRAIAMoAoQTIAJBAnQQ3wQLIAMoAowTIgIEQCADKAKQEyACQQJ0EN8ECyADKAKYEyICBEAgAygCnBMgAkECdBDfBAsgAygCpBMiAgRAIAMoAqgTIAJBAnQQ3wQLIAMoArATIgIEQCADKAK0EyACQQJ0EN8ECyADKAK8EyICBEAgAygCwBMgAkECdBDfBAsgAygCyBMiAgRAIAMoAswTIAJBAnQQ3wQLIAMoAtQTIgIEQCADKALYEyACQQJ0EN8ECyADKALgEyICBEAgAygC5BMgAkECdBDfBAsgAygC7BMiAgRAIAMoAvATIAJBAnQQ3wQLIAMoAvgTIgIEQCADKAL8EyACQQJ0EN8ECyADKAKEFCICBEAgAygCiBQgAkECdBDfBAsgA0GAE2oiAkH1wMAAQd8AQRAQ8QEgAygCgBNBgICAgHhGDR0gA0HYFGoiByADQYgTaiIGIgQoAgA2AgAgAyADKQKAEzcD0BQgAkHUwcAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDR4gA0HoFGoiCCAEKAIANgIAIAMgAykCgBM3A+AUIAJBtMLAAEHeAEEQEPEBIAMoAoATQYCAgIB4Rg0fIANB+BRqIgkgBigCADYCACADIAMpAoATNwPwFCACQZLDwABB3wBBEBDxASADKAKAE0GAgICAeEYNICADQYgVaiIKIAQoAgA2AgAgAyADKQKAEzcDgBUgAkHxw8AAQd8AQRAQ8QEgAygCgBNBgICAgHhGDSEgA0GYFWoiCyAEKAIANgIAIAMgAykCgBM3A5AVIAJB0MTAAEHgAEEQEPEBIAMoAoATQYCAgIB4Rg0iIANBqBVqIgwgBCgCADYCACADIAMpAoATNwOgFSACQbDFwABB3wBBEBDxASADKAKAE0GAgICAeEYNIyADQbgVaiINIAQoAgA2AgAgAyADKQKAEzcDsBUgAkGPxsAAQd8AQRAQ8QEgAygCgBNBgICAgHhGDSQgA0HIFWoiECAEKAIANgIAIAMgAykCgBM3A8AVIAJB7sbAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0lIANB2BVqIhMgBCgCADYCACADIAMpAoATNwPQFSACQc3HwABB3wBBEBDxASADKAKAE0GAgICAeEYNJiADQegVaiIUIAQoAgA2AgAgAyADKQKAEzcD4BUgAkGsyMAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDScgA0G4CmoiFSAEKAIANgIAIAMgAykCgBM3A7AKIAJBjMnAAEHgAEEQEPEBIAMoAoATQYCAgIB4Rg0oIANB2ApqIhYgBCgCADYCACADIAMpAoATNwPQCiACQezJwABB3wBBEBDxASADKAKAE0GAgICAeEYNKSADQfgKaiIXIAQoAgA2AgAgAyADKQKAEzcD8AogAkHLysAAQd8AQRAQ8QEgAygCgBNBgICAgHhGDSogA0H4FWoiGCAEKAIANgIAIAMgAykCgBM3A/AVIAJBqsvAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0rIANBqBZqIgQgBigCADYCACADIAMpAoATNwOgFiACQYnMwABB4ABBEBDxASADKAKAE0GAgICAeEYNLCADQfwSaiAGKAIANgIAIANByBFqIAcoAgA2AgAgA0HUEWogCCgCADYCACADQeARaiAJKAIANgIAIAMgAykCgBM3AvQSIAMgAykD0BQ3A8ARIAMgAykD4BQ3AswRIAMgAykD8BQ3A9gRIANB7BFqIAooAgA2AgAgAyADKQOAFTcC5BEgA0H4EWogCygCADYCACADIAMpA5AVNwPwESADQYQSaiAMKAIANgIAIAMgAykDoBU3AvwRIANBkBJqIA0oAgA2AgAgAyADKQOwFTcDiBIgA0GcEmogECgCADYCACADIAMpA8AVNwKUEiADQagSaiATKAIANgIAIAMgAykD0BU3A6ASIANBtBJqIBQoAgA2AgAgAyADKQPgFTcCrBIgA0HAEmogFSgCADYCACADIAMpA7AKNwO4EiADQcwSaiAWKAIANgIAIAMgAykD0Ao3AsQSIANB2BJqIBcoAgA2AgAgAyADKQPwCjcD0BIgA0HkEmogGCgCADYCACADIAMpA/AVNwLcEiADQfASaiAEKAIANgIAIAMgAykDoBY3A+gSQdHOxQAtAAAaAn8CQEGABkEIENYEIgQEQCACIANBwBFqEPYCIARBKGogA0GoE2oiBykDADcDACAEQSBqIANBoBNqIggpAwA3AwAgBEEYaiADQZgTaiIJKQMANwMAIARBEGogA0GQE2oiCikDADcDACAEQQhqIAYpAwA3AwAgBCADKQOAEzcDACACIANBzBFqEPYCIARB2ABqIAcpAwA3AwAgBEHQAGogCCkDADcDACAEQcgAaiAJKQMANwMAIARBQGsgCikDADcDACAEQThqIAYpAwA3AwAgBCADKQOAEzcDMCACIANB2BFqEPYCIARBiAFqIAcpAwA3AwAgBEGAAWogCCkDADcDACAEQfgAaiAJKQMANwMAIARB8ABqIAopAwA3AwAgBEHoAGogBikDADcDACAEIAMpA4ATNwNgIAIgA0HkEWoQ9gIgBEG4AWogBykDADcDACAEQbABaiAIKQMANwMAIARBqAFqIAkpAwA3AwAgBEGgAWogCikDADcDACAEQZgBaiAGKQMANwMAIAQgAykDgBM3A5ABIAIgA0HwEWoQ9gIgBEHoAWogBykDADcDACAEQeABaiAIKQMANwMAIARB2AFqIAkpAwA3AwAgBEHQAWogCikDADcDACAEQcgBaiAGKQMANwMAIAQgAykDgBM3A8ABIAIgA0H8EWoQ9gIgBEGYAmogBykDADcDACAEQZACaiAIKQMANwMAIARBiAJqIAkpAwA3AwAgBEGAAmogCikDADcDACAEQfgBaiAGKQMANwMAIAQgAykDgBM3A/ABIAIgA0GIEmoQ9gIgBEHIAmogBykDADcDACAEQcACaiAIKQMANwMAIARBuAJqIAkpAwA3AwAgBEGwAmogCikDADcDACAEQagCaiAGKQMANwMAIAQgAykDgBM3A6ACIAIgA0GUEmoQ9gIgBEH4AmogBykDADcDACAEQfACaiAIKQMANwMAIARB6AJqIAkpAwA3AwAgBEHgAmogCikDADcDACAEQdgCaiAGKQMANwMAIAQgAykDgBM3A9ACIAIgA0GgEmoQ9gIgBEGoA2ogBykDADcDACAEQaADaiAIKQMANwMAIARBmANqIAkpAwA3AwAgBEGQA2ogCikDADcDACAEQYgDaiAGKQMANwMAIAQgAykDgBM3A4ADIAIgA0GsEmoQ9gIgBEHYA2ogBykDADcDACAEQdADaiAIKQMANwMAIARByANqIAkpAwA3AwAgBEHAA2ogCikDADcDACAEQbgDaiAGKQMANwMAIAQgAykDgBM3A7ADIAIgA0G4EmoQ9gIgBEGIBGogBykDADcDACAEQYAEaiAIKQMANwMAIARB+ANqIAkpAwA3AwAgBEHwA2ogCikDADcDACAEQegDaiAGKQMANwMAIAQgAykDgBM3A+ADIAIgA0HEEmoQ9gIgBEG4BGogBykDADcDACAEQbAEaiAIKQMANwMAIARBqARqIAkpAwA3AwAgBEGgBGogCikDADcDACAEQZgEaiAGKQMANwMAIAQgAykDgBM3A5AEIAIgA0HQEmoQ9gIgBEHoBGogBykDADcDACAEQeAEaiAIKQMANwMAIARB2ARqIAkpAwA3AwAgBEHQBGogCikDADcDACAEQcgEaiAGKQMANwMAIAQgAykDgBM3A8AEIAIgA0HcEmoQ9gIgBEGYBWogBykDADcDACAEQZAFaiAIKQMANwMAIARBiAVqIAkpAwA3AwAgBEGABWogCikDADcDACAEQfgEaiAGKQMANwMAIAQgAykDgBM3A/AEIAIgA0HoEmoQ9gIgBEHIBWogBykDADcDACAEQcAFaiAIKQMANwMAIARBuAVqIAkpAwA3AwAgBEGwBWogCikDADcDACAEQagFaiAGKQMANwMAIAQgAykDgBM3A6AFIAIgA0H0EmoQ9gIgBEH4BWogBykDADcDACAEQfAFaiAIKQMANwMAIARB6AVqIAkpAwA3AwAgBEHgBWogCikDADcDACAEQdgFaiAGKQMANwMAIAQgAykDgBM3A9AFIARB0AVqQfjDwgBBMBDxA0UNAUEQIQdBECEIQQ8MAgtBCEGABkGkrcAAEMgEAAsgBEGgBWpB+MPCAEEwEPEDBEBBDyEIQRAhB0EODAELIARB8ARqQfjDwgBBMBDxAwRAQQ4hCEEQIQdBDQwBCyAEQcAEakH4w8IAQTAQ8QMEQEENIQhBECEHQQwMAQsgBEGQBGpB+MPCAEEwEPEDBEBBDCEIQRAhB0ELDAELIARB4ANqQfjDwgBBMBDxAwRAQQshCEEQIQdBCgwBCyAEQbADakH4w8IAQTAQ8QMEQEEKIQhBECEHQQkMAQsgBEGAA2pB+MPCAEEwEPEDBEBBCSEIQRAhB0EIDAELIARB0AJqQfjDwgBBMBDxAwRAQQghCEEQIQdBBwwBCyAEQaACakH4w8IAQTAQ8QMEQEEHIQhBECEHQQYMAQsgBEHwAWpB+MPCAEEwEPEDBEBBBiEIQRAhB0EFDAELIARBwAFqQfjDwgBBMBDxAwRAQQUhCEEQIQdBBAwBCyAEQZABakH4w8IAQTAQ8QMEQEEEIQhBECEHQQMMAQsgBEHgAGpB+MPCAEEwEPEDBEBBAyEIQRAhB0ECDAELIARBMGpB+MPCAEEwEPEDBEBBAiEIQRAhB0EBDAELIARB+MPCAEEwEPEDBEBBASEIQRAhB0EADAELQdHOxQAtAAAaQTBBCBDWBCICRQ1BIAJCADcDACACQShqQgA3AwAgAkEgakIANwMAIAJBGGpCADcDACACQRBqQgA3AwAgAkEIakIANwMAIARBgAYQ3wRBASEHIAIhBEEBIQhBfwshEyADQYATaiIKQenMwABB4ABBEBDxASADKAKAE0GAgICAeEYNLSADQcgUaiILIANBiBNqIgIoAgA2AgAgAyADKQKAEzcDwBQgCkHJzcAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDS4gA0HYFGoiDCACKAIANgIAIAMgAykCgBM3A9AUIApBqc7AAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0vIANB6BRqIg0gAigCADYCACADIAMpAoATNwPgFCAKQYjPwABB4ABBEBDxASADKAKAE0GAgICAeEYNMCADQfgUaiIQIAIoAgA2AgAgAyADKQKAEzcD8BQgCkHoz8AAQd8AQRAQ8QEgAygCgBNBgICAgHhGDTEgA0GIFWoiFCACKAIANgIAIAMgAykCgBM3A4AVIApBx9DAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg0yIANBmBVqIhUgAigCADYCACADIAMpAoATNwOQFSAKQabRwABB4ABBEBDxASADKAKAE0GAgICAeEYNMyADQagVaiIWIAIoAgA2AgAgAyADKQKAEzcDoBUgCkGG0sAAQeAAQRAQ8QEgAygCgBNBgICAgHhGDTQgA0G4FWoiFyACKAIANgIAIAMgAykCgBM3A7AVIApB5tLAAEHgAEEQEPEBIAMoAoATQYCAgIB4Rg01IANByBVqIhggAigCADYCACADIAMpAoATNwPAFSAKQcbTwABB4ABBEBDxASADKAKAE0GAgICAeEYNNiADQdgVaiIcIAIoAgA2AgAgAyADKQKAEzcD0BUgCkGm1MAAQd8AQRAQ8QEgAygCgBNBgICAgHhGDTcgA0HoFWoiHSACKAIANgIAIAMgAykCgBM3A+AVIApBhdXAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg04IANBuApqIh4gAigCADYCACADIAMpAoATNwOwCiAKQeTVwABB3wBBEBDxASADKAKAE0GAgICAeEYNOSADQdgKaiIfIAIoAgA2AgAgAyADKQKAEzcD0AogCkHD1sAAQd8AQRAQ8QEgAygCgBNBgICAgHhGDTogA0H4CmoiICACKAIANgIAIAMgAykCgBM3A/AKIApBotfAAEHfAEEQEPEBIAMoAoATQYCAgIB4Rg07IANB+BVqIiEgAigCADYCACADIAMpAoATNwPwFSADQaAWaiIGQfTAwABBAUEQEPEBIAMoAqAWQYCAgIB4Rg08IANBvBRqIANBqBZqIgkoAgA2AgAgAiALKAIANgIAIANBlBNqIAwoAgA2AgAgA0GgE2ogDSgCADYCACADIAMpAqAWNwK0FCADIAMpA8AUNwOAEyADIAMpA9AUNwKMEyADIAMpA+AUNwOYEyADQawTaiAQKAIANgIAIAMgAykD8BQ3AqQTIANBuBNqIBQoAgA2AgAgAyADKQOAFTcDsBMgA0HEE2ogFSgCADYCACADIAMpA5AVNwK8EyADQdATaiAWKAIANgIAIAMgAykDoBU3A8gTIANB3BNqIBcoAgA2AgAgAyADKQOwFTcC1BMgA0HoE2ogGCgCADYCACADIAMpA8AVNwPgEyADQfQTaiAcKAIANgIAIAMgAykD0BU3AuwTIANBgBRqIB0oAgA2AgAgAyADKQPgFTcD+BMgA0GMFGogHigCADYCACADIAMpA7AKNwKEFCADQZgUaiAfKAIANgIAIAMgAykD0Ao3A5AUIANBpBRqICAoAgA2AgAgAyADKQPwCjcCnBQgA0GwFGogISgCADYCACADIAMpA/AVNwOoFEHRzsUALQAAGgJ/AkBBgAZBCBDWBCICBEAgBiAKEPYCIAJBKGogA0HIFmoiCikDADcDACACQSBqIANBwBZqIgspAwA3AwAgAkEYaiADQbgWaiIMKQMANwMAQRAhECACQRBqIANBsBZqIg0pAwA3AwAgAkEIaiAJKQMANwMAIAIgAykDoBY3AwAgBiADQYwTahD2AiACQdgAaiAKKQMANwMAIAJB0ABqIAspAwA3AwAgAkHIAGogDCkDADcDACACQUBrIA0pAwA3AwAgAkE4aiAJKQMANwMAIAIgAykDoBY3AzAgBiADQZgTahD2AiACQYgBaiAKKQMANwMAIAJBgAFqIAspAwA3AwAgAkH4AGogDCkDADcDACACQfAAaiANKQMANwMAIAJB6ABqIAkpAwA3AwAgAiADKQOgFjcDYCAGIANBpBNqEPYCIAJBuAFqIAopAwA3AwAgAkGwAWogCykDADcDACACQagBaiAMKQMANwMAIAJBoAFqIA0pAwA3AwAgAkGYAWogCSkDADcDACACIAMpA6AWNwOQASAGIANBsBNqEPYCIAJB6AFqIAopAwA3AwAgAkHgAWogCykDADcDACACQdgBaiAMKQMANwMAIAJB0AFqIA0pAwA3AwAgAkHIAWogCSkDADcDACACIAMpA6AWNwPAASAGIANBvBNqEPYCIAJBmAJqIAopAwA3AwAgAkGQAmogCykDADcDACACQYgCaiAMKQMANwMAIAJBgAJqIA0pAwA3AwAgAkH4AWogCSkDADcDACACIAMpA6AWNwPwASAGIANByBNqEPYCIAJByAJqIAopAwA3AwAgAkHAAmogCykDADcDACACQbgCaiAMKQMANwMAIAJBsAJqIA0pAwA3AwAgAkGoAmogCSkDADcDACACIAMpA6AWNwOgAiAGIANB1BNqEPYCIAJB+AJqIAopAwA3AwAgAkHwAmogCykDADcDACACQegCaiAMKQMANwMAIAJB4AJqIA0pAwA3AwAgAkHYAmogCSkDADcDACACIAMpA6AWNwPQAiAGIANB4BNqEPYCIAJBqANqIAopAwA3AwAgAkGgA2ogCykDADcDACACQZgDaiAMKQMANwMAIAJBkANqIA0pAwA3AwAgAkGIA2ogCSkDADcDACACIAMpA6AWNwOAAyAGIANB7BNqEPYCIAJB2ANqIAopAwA3AwAgAkHQA2ogCykDADcDACACQcgDaiAMKQMANwMAIAJBwANqIA0pAwA3AwAgAkG4A2ogCSkDADcDACACIAMpA6AWNwOwAyAGIANB+BNqEPYCIAJBiARqIAopAwA3AwAgAkGABGogCykDADcDACACQfgDaiAMKQMANwMAIAJB8ANqIA0pAwA3AwAgAkHoA2ogCSkDADcDACACIAMpA6AWNwPgAyAGIANBhBRqEPYCIAJBuARqIAopAwA3AwAgAkGwBGogCykDADcDACACQagEaiAMKQMANwMAIAJBoARqIA0pAwA3AwAgAkGYBGogCSkDADcDACACIAMpA6AWNwOQBCAGIANBkBRqEPYCIAJB6ARqIAopAwA3AwAgAkHgBGogCykDADcDACACQdgEaiAMKQMANwMAIAJB0ARqIA0pAwA3AwAgAkHIBGogCSkDADcDACACIAMpA6AWNwPABCAGIANBnBRqEPYCIAJBmAVqIAopAwA3AwAgAkGQBWogCykDADcDACACQYgFaiAMKQMANwMAIAJBgAVqIA0pAwA3AwAgAkH4BGogCSkDADcDACACIAMpA6AWNwPwBCAGIANBqBRqEPYCIAJByAVqIAopAwA3AwAgAkHABWogCykDADcDACACQbgFaiAMKQMANwMAIAJBsAVqIA0pAwA3AwAgAkGoBWogCSkDADcDACACIAMpA6AWNwOgBSAGIANBtBRqEPYCIAJB+AVqIAopAwA3AwAgAkHwBWogCykDADcDACACQegFaiAMKQMANwMAIAJB4AVqIA0pAwA3AwAgAkHYBWogCSkDADcDACACIAMpA6AWNwPQBSACQdAFakH4w8IAQTAQ8QNFDQFBDyEGQRAMAgtBCEGABkGkrcAAEMgEAAsgAkGgBWpB+MPCAEEwEPEDBEBBDiEGQQ8MAQsgAkHwBGpB+MPCAEEwEPEDBEBBDSEGQQ4MAQsgAkHABGpB+MPCAEEwEPEDBEBBDCEGQQ0MAQsgAkGQBGpB+MPCAEEwEPEDBEBBCyEGQQwMAQsgAkHgA2pB+MPCAEEwEPEDBEBBCiEGQQsMAQsgAkGwA2pB+MPCAEEwEPEDBEBBCSEGQQoMAQsgAkGAA2pB+MPCAEEwEPEDBEBBCCEGQQkMAQsgAkHQAmpB+MPCAEEwEPEDBEBBByEGQQgMAQsgAkGgAmpB+MPCAEEwEPEDBEBBBiEGQQcMAQsgAkHwAWpB+MPCAEEwEPEDBEBBBSEGQQYMAQsgAkHAAWpB+MPCAEEwEPEDBEBBBCEGQQUMAQsgAkGQAWpB+MPCAEEwEPEDBEBBAyEGQQQMAQsgAkHgAGpB+MPCAEEwEPEDBEBBAiEGQQMMAQsgAkEwakH4w8IAQTAQ8QMEQEEBIQZBAgwBCyACQfjDwgBBMBDxAwR/QQAFQdHOxQAtAAAaQTBBCBDWBCIGRQ1CIAZCADcDACAGQShqQgA3AwAgBkEgakIANwMAIAZBGGpCADcDACAGQRBqQgA3AwAgBkEIakIANwMAIAJBgAYQ3wRBASEQIAYhAkF/CyEGQQELIQogA0GAE2oQywIgA0HAEWoQywIgAygCrBEiCQRAIAMoArARIAlBAnQQ3wQLAkAgAygCpAsiCUUNACAJIAlBDGxBE2pBeHEiC2pBCWoiCUUNACADKAKgCyALayAJEN8ECyADKAKgDiIJQYCAgIB4RiAJRXJFBEAgAygCpA4gCUECdBDfBAsgAyAONgLMCiADIBo2AsgKIAMgBTYCxAogAyASNgLACiADIA82ArwKIAMgGTYCuAogAyABNgK0CiADIBE2ArAKIAMgBjYC7AogAyAKNgLoCiADIAI2AuQKIAMgEDYC4AogAyATNgLcCiADIAg2AtgKIAMgBDYC1AogAyAHNgLQCiADQagTaiIRIANB8AlqIgQpAwA3AwAgA0GgE2oiEiADQegJaiIFKQMANwMAIANBmBNqIhAgA0HgCWoiBikDADcDACADQZATaiIZIANB2AlqIgcpAwA3AwAgA0GIE2oiGiADQdAJaiIIKQMANwMAIAMgAykDyAk3A4ATIANByBZqIhMgBCkDADcDACADQcAWaiIUIAUpAwA3AwAgA0G4FmoiFSAGKQMANwMAIANBsBZqIhYgBykDADcDACADQagWaiIXIAgpAwA3AwAgAyADKQPICTcDoBYgA0HwFWoiCSADQbAKaiADQaAWaiIKEJYBIANBwBFqIgEgA0HACmogA0GAE2oiCxCWASADQaALaiICIAkgARBMIAMoAqALQQFGDUEgA0GYC2ogA0HQC2oiGCkDADcDACADQZALaiADQcgLaiIMKQMANwMAIANBiAtqIANBwAtqIg0pAwA3AwAgA0GAC2ogA0G4C2oiDykDADcDACADQfgKaiADQbALaiIOKQMANwMAIAMgAykDqAs3A/AKIBEgBCkDADcDACASIAUpAwA3AwAgECAGKQMANwMAIBkgBykDADcDACAaIAgpAwA3AwAgAyADKQPICTcDgBMgEyAEKQMANwMAIBQgBSkDADcDACAVIAYpAwA3AwAgFiAHKQMANwMAIBcgCCkDADcDACADIAMpA8gJNwOgFiAJIANB0ApqIAoQlgEgASADQeAKaiALEJYBIAIgCSABEEwgAygCoAtBAUYNQSADQegRaiAYKQMANwMAIANB4BFqIAwpAwA3AwAgA0HYEWogDSkDADcDACADQdARaiAPKQMANwMAIANByBFqIA4pAwA3AwAgAyADKQOoCzcDwBEgDCADQaAKaikDADcDACANIANBmApqKQMANwMAIA8gA0GQCmopAwA3AwAgDiADQYgKaikDADcDACADQagLaiIEIANBgApqKQMANwMAIAMgAykD+Ak3A6ALIAogASACELIBIAIgA0HwCmogCkEAEDEgAy0AgAxBAkYNPSALIAJB6AD8CgAAIAMoAtAKIgEEQCADKALUCiABQTBsEN8ECyADKALgCiIBBEAgAygC5AogAUEwbBDfBAsgAygCsAoiAQRAIAMoArQKIAFBMGwQ3wQLIAMoAsAKIgEEQCADKALECiABQTBsEN8ECyADQagLaiADQdgIaikDADcDACADIAMpA9AINwOgCyAAIANBgBNqIANBoAtqEKcBIBtBAUYNPiADKAK8CCIARQ0+IAMoAsAIIABBAnQQ3wQMPgsgAyAENgKIEyADIAE2AoQTIAMgAjYCgBNBhJ3AAEErIANBgBNqQfypwABBjKrAABDKAwALIANBAjYCpAsgA0G8qcAANgKgCyADQgE3AqwLIAMgA0HgAGqtQoCAgICAAoQ3A7ACIAMgA0GwAmo2AqgLIANBoAtqQcypwAAQqAQACyADQQI2AqQLIANBvKnAADYCoAsgA0IBNwKsCyADIANByAFqrUKAgICAgAKENwOwAiADIANBsAJqNgKoCyADQaALakHcqcAAEKgEAAsgA0ECNgKkCyADQbypwAA2AqALIANCATcCrAsgAyADQeAIaq1CgICAgIAChDcDgBMgAyADQYATajYCqAsgA0GgC2pB7KnAABCoBAALIANBAjYCpAsgA0G8qcAANgKgCyADQgE3AqwLIAMgA0HICWqtQoCAgICAAoQ3A4ATIAMgA0GAE2o2AqgLIANBoAtqQaCwwAAQqAQACyADIAE6AKAWIANBAjYChBMgA0G838AANgKAEyADQgE3AowTIAMgA0GgFmqtQoCAgICQAoQ3A8ARIAMgA0HAEWo2AogTIANBgBNqQczfwAAQqAQACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEH03sAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABB5N7AABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQdTewAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEHE3sAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABBtN7AABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQaTewAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEGU3sAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABBhN7AABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQfTdwAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEHk3cAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABB1N3AABDKAwALIAMgAy0AxBE6AIATQYSdwABBKyADQYATakGE2MAAQcTdwAAQygMACyADIAMtAMQROgCgFkGEncAAQSsgA0GgFmpBhNjAAEG03cAAEMoDAAsgAyADLQDEEToAoBZBhJ3AAEErIANBoBZqQYTYwABBpN3AABDKAwALIAMgAy0AxBE6AKAWQYSdwABBKyADQaAWakGE2MAAQZTdwAAQygMACyADIAMtAMQROgCgFkGEncAAQSsgA0GgFmpBhNjAAEGE3cAAEMoDAAsgAyADLQDEEToAoBZBhJ3AAEErIANBoBZqQYTYwABB9NzAABDKAwALIAMgAy0AxBE6AKAWQYSdwABBKyADQaAWakGE2MAAQeTcwAAQygMACyADIAMtAMQROgCgFkGEncAAQSsgA0GgFmpBhNjAAEHU3MAAEMoDAAsgAyADLQDEEToAoBZBhJ3AAEErIANBoBZqQYTYwABBxNzAABDKAwALIAMgAy0AxBE6AKAWQYSdwABBKyADQaAWakGE2MAAQbTcwAAQygMACyADIAMtAMQROgCgFkGEncAAQSsgA0GgFmpBhNjAAEGk3MAAEMoDAAsgAyADLQCkFjoAwBFBhJ3AAEErIANBwBFqQYTYwABBlNzAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQYTcwAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEH028AAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABB5NvAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQdTbwAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEHE28AAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABBtNvAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQaTbwAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEGU28AAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABBhNvAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQfTawAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEHk2sAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABB1NrAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQcTawAAQygMACyADIAMtAIQTOgDAEUGEncAAQSsgA0HAEWpBhNjAAEG02sAAEMoDAAsgAyADLQCEEzoAwBFBhJ3AAEErIANBwBFqQYTYwABBpNrAABDKAwALIAMgAy0AhBM6AMARQYSdwABBKyADQcARakGE2MAAQZTawAAQygMACyADIAMtAIQTOgCgFkGEncAAQSsgA0GgFmpBhNjAAEGE2sAAEMoDAAsgAyADLQCEEzoAoBZBhJ3AAEErIANBoBZqQYTYwABB9NnAABDKAwALIAMgAy0AhBM6AKAWQYSdwABBKyADQaAWakGE2MAAQeTZwAAQygMACyADIAMtAIQTOgCgFkGEncAAQSsgA0GgFmpBhNjAAEHU2cAAEMoDAAsgAyADLQCEEzoAoBZBhJ3AAEErIANBoBZqQYTYwABBxNnAABDKAwALIAMgAy0AhBM6AKAWQYSdwABBKyADQaAWakGE2MAAQbTZwAAQygMACyADIAMtAIQTOgCgFkGEncAAQSsgA0GgFmpBhNjAAEGk2cAAEMoDAAsgAyADLQCEEzoAoBZBhJ3AAEErIANBoBZqQYTYwABBlNnAABDKAwALIAMgAy0AhBM6AKAWQYSdwABBKyADQaAWakGE2MAAQYTZwAAQygMACyADIAMtAIQTOgCgFkGEncAAQSsgA0GgFmpBhNjAAEH02MAAEMoDAAsgAyADLQCEEzoAoBZBhJ3AAEErIANBoBZqQYTYwABB5NjAABDKAwALIAMgAy0AhBM6AKAWQYSdwABBKyADQaAWakGE2MAAQdTYwAAQygMACyADIAMtAIQTOgCgFkGEncAAQSsgA0GgFmpBhNjAAEHE2MAAEMoDAAsgAyADLQCEEzoAoBZBhJ3AAEErIANBoBZqQYTYwABBtNjAABDKAwALIAMgAy0AhBM6AKAWQYSdwABBKyADQaAWakGE2MAAQaTYwAAQygMACyADIAMtAKQWOgCAE0GEncAAQSsgA0GAE2pBhNjAAEGU2MAAEMoDAAsgA0GIE2ogBCgCADYCACADIAMpA6ALNwOAE0GEncAAQSsgA0GAE2pB2KvAAEGwsMAAEMoDAAsCQCADKAK0AiIARQ0AIAAgAEEMbEETakF4cSIBakEJaiIARQ0AIAMoArACIAFrIAAQ3wQLIAMoArAFIgBBgICAgHhGIABFcg0AIAMoArQFIABBAnQQ3wQLIANB0BZqJAAPC0EIQTAQ/wQACyADIAMpA7ALNwPIESADIAMpA6gLNwPAEUGUpMQAQSsgA0HAEWpBkKfEAEGgq8QAEMoDAAuOVwJFfwV+IwBBwKQFayICJAAgAiABNgKAkQUgAiABQcABaiIVNgKEkQUgAkGAmgVqIhYgAkGAkQVqIhcQvQMgAkG4lwVqIiAgAkG4mgVqIgUpAwAiRzcDACACQbCXBWoiISACQbCaBWoiCSkDACJINwMAIAJBqJcFaiIiIAJBqJoFaiIKKQMAIkk3AwAgAkGglwVqIiMgAkGgmgVqIg8pAwAiSjcDACACQZiXBWoiGCACQZiaBWoiECkDACJLNwMAIAJBiJQFaiIDIAJBiJoFaiIRKQMANwMAIAJBkJQFaiIEIAJBkJoFaiISKQMANwMAIAJBmJQFaiINIEs3AwAgAkGglAVqIhMgSjcDACACQaiUBWoiCyBJNwMAIAJBsJQFaiIUIEg3AwAgAkG4lAVqIg4gRzcDACACIAIpA4CaBSJHNwOAlwUgAiBHNwOAlAUgAkG4nQVqIhkgDikDADcDACACQbCdBWoiGiAUKQMANwMAIAJBqJ0FaiIbIAspAwA3AwAgAkGgnQVqIhwgEykDADcDACACQZidBWoiHSANKQMANwMAIAJBkJ0FaiIeIAQpAwA3AwAgAkGInQVqIh8gAykDADcDACACIAIpA4CUBTcDgJ0FIAJBuKMFaiAZKQMANwMAIAJBsKMFaiAaKQMANwMAIAJBqKMFaiAbKQMANwMAIAJBoKMFaiAcKQMANwMAIAJBmKMFaiAdKQMANwMAIAJBkKMFaiAeKQMANwMAIAJBiKMFaiAfKQMANwMAIAIgAikDgJ0FNwOAowUgFiAXEL0DICAgBSkDACJHNwMAICEgCSkDACJINwMAICIgCikDACJJNwMAICMgDykDACJKNwMAIBggECkDACJLNwMAIAMgESkDADcDACAEIBIpAwA3AwAgDSBLNwMAIBMgSjcDACALIEk3AwAgFCBINwMAIA4gRzcDACACIAIpA4CaBSJHNwOAlwUgAiBHNwOAlAUgGSAOKQMANwMAIBogFCkDADcDACAbIAspAwA3AwAgHCATKQMANwMAIB0gDSkDADcDACAeIAQpAwA3AwAgHyADKQMANwMAIAIgAikDgJQFNwOAnQUgAkH4owVqIBkpAwA3AwAgAkHwowVqIBopAwA3AwAgAkHoowVqIBspAwA3AwAgAkHgowVqIBwpAwA3AwAgAkHYowVqIB0pAwA3AwAgAkHQowVqIB4pAwA3AwAgAkHIowVqIB8pAwA3AwAgAiACKQOAnQU3A8CjBSAWIBcQvQMgICAFKQMAIkc3AwAgISAJKQMAIkg3AwAgIiAKKQMAIkk3AwAgIyAPKQMAIko3AwAgGCAQKQMAIks3AwAgAyARKQMANwMAIAQgEikDADcDACANIEs3AwAgEyBKNwMAIAsgSTcDACAUIEg3AwAgDiBHNwMAIAIgAikDgJoFIkc3A4CXBSACIEc3A4CUBSAZIA4pAwA3AwAgGiAUKQMANwMAIBsgCykDADcDACAcIBMpAwA3AwAgHSANKQMANwMAIB4gBCkDADcDACAfIAMpAwA3AwAgAiACKQOAlAU3A4CdBSACQbikBWogGSkDADcDACACQbCkBWogGikDADcDACACQaikBWogGykDADcDACACQaCkBWogHCkDADcDACACQZikBWogHSkDADcDACACQZCkBWogHikDADcDACACQYikBWogHykDADcDACACIAIpA4CdBTcDgKQFQQBFBEAgAkGAoAVqIAJBgKMFakHAAfwKAAALIAIgAUGAA2o2AoSOBSACIBU2AoCOBSACQYCXBWoiJiACQYCOBWoiBxC9AyAOICApAwAiRzcDACAUICEpAwAiSDcDACALICIpAwAiSTcDACATICMpAwAiSjcDACANIBgpAwAiSzcDACACQYiRBWoiASACQYiXBWoiJykDADcDACACQZCRBWoiAyACQZCXBWoiKCkDADcDACACQZiRBWoiBCBLNwMAIAJBoJEFaiIVIEo3AwAgAkGokQVqIhYgSTcDACACQbCRBWoiFyBINwMAIAJBuJEFaiIkIEc3AwAgAiACKQOAlwUiRzcDgJQFIAIgRzcDgJEFIAUgJCkDADcDACAJIBcpAwA3AwAgCiAWKQMANwMAIA8gFSkDADcDACAQIAQpAwA3AwAgEiADKQMANwMAIBEgASkDADcDACACIAIpA4CRBTcDgJoFIBkgBSkDADcDACAaIAkpAwA3AwAgGyAKKQMANwMAIBwgDykDADcDACAdIBApAwA3AwAgHiASKQMANwMAIB8gESkDADcDACACIAIpA4CaBTcDgJ0FICYgBxC9AyAOICApAwAiRzcDACAUICEpAwAiSDcDACALICIpAwAiSTcDACATICMpAwAiSjcDACANIBgpAwAiSzcDACABICcpAwA3AwAgAyAoKQMANwMAIAQgSzcDACAVIEo3AwAgFiBJNwMAIBcgSDcDACAkIEc3AwAgAiACKQOAlwUiRzcDgJQFIAIgRzcDgJEFIAUgJCkDADcDACAJIBcpAwA3AwAgCiAWKQMANwMAIA8gFSkDADcDACAQIAQpAwA3AwAgEiADKQMANwMAIBEgASkDADcDACACIAIpA4CRBTcDgJoFIAJB+J0FaiAFKQMANwMAIAJB8J0FaiAJKQMANwMAIAJB6J0FaiAKKQMANwMAIAJB4J0FaiAPKQMANwMAIAJB2J0FaiAQKQMANwMAIAJB0J0FaiASKQMANwMAIAJByJ0FaiARKQMANwMAIAIgAikDgJoFNwPAnQUgJiAHEL0DIA4gICkDACJHNwMAIBQgISkDACJINwMAIAsgIikDACJJNwMAIBMgIykDACJKNwMAIA0gGCkDACJLNwMAIAEgJykDADcDACADICgpAwA3AwAgBCBLNwMAIBUgSjcDACAWIEk3AwAgFyBINwMAICQgRzcDACACIAIpA4CXBSJHNwOAlAUgAiBHNwOAkQUgBSAkKQMANwMAIAkgFykDADcDACAKIBYpAwA3AwAgDyAVKQMANwMAIBAgBCkDADcDACASIAMpAwA3AwAgESABKQMANwMAIAIgAikDgJEFNwOAmgUgAkG4ngVqIAUpAwA3AwAgAkGwngVqIAkpAwA3AwAgAkGongVqIAopAwA3AwAgAkGgngVqIA8pAwA3AwAgAkGYngVqIBApAwA3AwAgAkGQngVqIBIpAwA3AwAgAkGIngVqIBEpAwA3AwAgAiACKQOAmgU3A4CeBSAlRQRAIAJBgKMFaiACQYCdBWpBwAH8CgAACyAlRQRAIAJBwKEFaiACQYCjBWpBwAH8CgAACyACIAJBgKAFakGAA/wKAAAgAkGAA2oiASACQQEQdCACQYAGaiIqIAIgARD2ASACQYAJaiJEIAEgKhD2ASACQYAMaiI7IAEgRBD2ASACQYAPaiI8IAEgOxD2ASACQYASaiI9IAEgPBD2ASACQYAVaiISIAEgPRD2ASACQYAYaiI+IAEgEhD2ASACQYAbaiIlIAEgPhD2ASACQYAeaiIdIAEgJRD2ASACQYAhaiINIAEgHRD2ASACQYAkaiIeIAEgDRD2ASACQYAnaiIwIAEgHhD2ASACQYAqaiIOIAEgMBD2ASACQYAtaiIxIAEgDhD2ASACQYAwaiIfIAEgMRD2ASACQYAzaiIyIAEgHxD2ASACQYA2aiIrIAEgMhD2ASACQYA5aiIzIAEgKxD2ASACQYA8aiITIAEgMxD2ASACQYA/aiIsIAEgExD2ASACQYDCAGoiDCABICwQ9gEgAkGAxQBqIi0gASAMEPYBIAJBgMgAaiIgIAEgLRD2ASACQYDLAGoiFSABICAQ9gEgAkGAzgBqIhkgASAVEPYBIAJBgNEAaiILIAEgGRD2ASACQYDUAGoiCiABIAsQ9gEgAkGA1wBqIj8gASAKEPYBIAJBgNoAaiIhIAEgPxD2ASACQYDdAGoiNCABICEQ9gEgAkGA4ABqIkYgASA0EPYBIAJBgOMAaiImIAEgRhD2ASACQYDmAGoiNSABICYQ9gEgAkGA6QBqIg8gASA1EPYBIAJBgOwAaiIHIAEgDxD2ASACQYDvAGoiFCABIAcQ9gEgAkGA8gBqIgkgASAUEPYBIAJBgPUAaiIiIAEgCRD2ASACQYD4AGoiLiABICIQ9gEgAkGA+wBqIicgASAuEPYBIAJBgP4AaiIaIAEgJxD2ASACQYCBAWoiCCABIBoQ9gEgAkGAhAFqIiMgASAIEPYBIAJBgIcBaiIYIAEgIxD2ASACQYCKAWoiNiABIBgQ9gEgAkGAjQFqIkAgASA2EPYBIAJBgJABaiI3IAEgQBD2ASACQYCTAWoiQSABIDcQ9gEgAkGAlgFqIhYgASBBEPYBIAJBgJkBaiJCIAEgFhD2ASACQYCcAWoiGyABIEIQ9gEgAkGAnwFqIi8gASAbEPYBIAJBgKIBaiIoIAEgLxD2ASACQYClAWoiOCABICgQ9gEgAkGAqAFqIhAgASA4EPYBIAJBgKsBaiIpIAEgEBD2ASACQYCuAWoiHCABICkQ9gEgAkGAsQFqIhcgASAcEPYBIAJBgLQBaiJDIAEgFxD2ASACQYC3AWoiOSABIEMQ9gEgAkGAugFqIiQgASA5EPYBIAJBgL0BaiIRIAEgJBD2ASACQYDAAWoiRSABIBEQ9gEgAkGAwwFqIgEgRUEBEHQgAkGAxgFqIjogAiABEPYBIAJBgJQFaiIBIBEgOhD2ASACQYCXBWoiAyABQQQQdCACQYCaBWoiBCADIB4Q9gEgAkGAnQVqIgUgBEEIEHQgAkGAyQFqIgYgBSAyEPYBIAEgBkEHEHQgAyABID8Q9gEgBCADQQkQdCAFIAQgCRD2ASACQYDMAWoiBiAFQQYQdCABIBMgBhD2ASADIAFBCRB0IAQgAyAUEPYBIAUgBEEIEHQgAkGAzwFqIgYgBSAsEPYBIAEgBkEIEHQgAyABIBcQ9gEgBCADQQcQdCAFIAQgLhD2ASACQYDSAWoiBiAFQQgQdCABIAkgBhD2ASADIAFBBhB0IAQgAyAsEPYBIAUgBEEJEHQgAkGA1QFqIgYgBSAYEPYBIAEgBkEGEHQgAyABIDAQ9gEgBCADQQQQdCAFIAQgAhD2ASACQYDYAWoiBiAFQQwQdCABIAogBhD2ASADIAFBBhB0IAQgAyAdEPYBIAUgBEEIEHQgAkGA2wFqIgYgBSANEPYBIAEgBkEJEHQgAyABICkQ9gEgBCADQQkQdCAFIAQgNxD2ASACQYDeAWoiBiAFQQcQdCABIBIgBhD2ASADIAFBCRB0IAQgAyALEPYBIAUgBEEIEHQgAkGA4QFqIgYgBSAPEPYBIAEgBkEGEHQgAyABIC0Q9gEgBCADQQsQdCAFIAQgFRD2ASACQYDkAWoiBiAFQQYQdCABIB8gBhD2ASADIAFBERB0IAQgAyAjEPYBIAUgBEEGEHQgAkGA5wFqIgYgBSAZEPYBIAEgBkEGEHQgAyABIA4Q9gEgBCADQQwQdCAFIAQgOhD2ASACQYDqAWoiBiAFQQoQdCABIA0gBhD2ASADIAFBBxB0IAQgAyANEPYBIAUgBEEJEHQgAkGA7QFqIgYgBSAcEPYBIAEgBkEKEHQgAyABIA8Q9gEgBCADQQgQdCAFIAQgMhD2ASACQYDwAWoiBiAFQQgQdCABIBsgBhD2ASADIAFBBhB0IAQgAyAMEPYBIAUgBEEGEHQgAkGA8wFqIgYgBSAdEPYBIAEgBkEIEHQgAyABICEQ9gEgBCADQQkQdCAFIAQgHxD2ASACQYD2AWoiBiAFQQkQdCABIDogBhD2ASADIAFBARB0IAQgAyACEPYBIAUgBEEGEHQgAkGA+QFqIgYgBSA7EPYBIAEgBkELEHQgAyABIAkQ9gEgBCADQQYQdCAFIAQgFRD2ASACQYD8AWoiBiAFQQoQdCABIBsgBhD2ASADIAFBBxB0IAQgAyAiEPYBIAUgBEEIEHQgAkGA/wFqIgYgBSAbEPYBIAEgBkEGEHQgAyABIA4Q9gEgBCADQQkQdCAFIAQgChD2ASACQYCCAmoiBiAFQQkQdCABICQgBhD2ASADIAFBBBB0IAQgAyASEPYBIAUgBEEKEHQgAkGAhQJqIgYgBSAQEPYBIAEgBkEFEHQgAyABIA4Q9gEgBCADQQ0QdCAFIAQgIBD2ASACQYCIAmoiBiAFQQoQdCABIBwgBhD2ASADIAFBChB0IAQgAyAPEPYBIAUgBEEHEHQgAkGAiwJqIgYgBSA1EPYBIAEgBkEHEHQgAyABIAgQ9gEgBCADQQYQdCAFIAQgHxD2ASACQYCOAmoiBiAFQQYQdCABIDwgBhD2ASADIAFBChB0IAQgAyAzEPYBIAUgBEECEHQgAkGAkQJqIgYgBSACEPYBIAEgBkEJEHQgAyABIDoQ9gEgBCADQQkQdCAFIAQgQxD2ASACQYCUAmoiBiAFQQsQdCABIBYgBhD2ASADIAFBBhB0IAQgAyAZEPYBIAUgBEEIEHQgAkGAlwJqIgYgBSAcEPYBIAEgBkEHEHQgAyABIA8Q9gEgBCADQQcQdCAFIAQgKRD2ASACQYCaAmoiBiAFQQcQdCABIC4gBhD2ASADIAFBCRB0IAQgAyAPEPYBIAUgBEEEEHQgAkGAnQJqIgYgBSAqEPYBIAEgBkEMEHQgAyABICIQ9gEgBCADQQMQdCAFIAQgRBD2ASACQYCgAmoiBiAFQQoQdCABIBIgBhD2ASADIAFBChB0IAQgAyAJEPYBIAUgBEEGEHQgAkGAowJqIgYgBSAVEPYBIAEgBkEIEHQgAyABIAoQ9gEgBCADQQgQdCAFIAQgGRD2ASACQYCmAmoiBiAFQQgQdCABIAkgBhD2ASADIAFBARB0IAQgAyACEPYBIAUgBEEOEHQgAkGAqQJqIgYgBSAoEPYBIAEgBkEIEHQgAyABIAcQ9gEgBCADQQUQdCAFIAQgDRD2ASACQYCsAmoiBiAFQQoQdCABIA8gBhD2ASADIAFBBhB0IAQgAyAxEPYBIAUgBEEKEHQgAkGArwJqIgYgBSATEPYBIAEgBkEFEHQgAyABIBIQ9gEgBCADQQoQdCAFIAQgKxD2ASACQYCyAmoiBiAFQQUQdCABID0gBhD2ASADIAFBCRB0IAQgAyAKEPYBIAUgBEEIEHQgAkGAtQJqIgYgBSAaEPYBIAEgBkEHEHQgAyABICYQ9gEgBCADQQcQdCAFIAQgCxD2ASACQYC4AmoiBiAFQQgQdCABIDggBhD2ASADIAFBCxB0IAQgAyAREPYBIAUgBEELEHQgAkGAuwJqIgYgBSAIEPYBIAEgBkEHEHQgAyABIC4Q9gEgBCADQQkQdCAFIAQgBxD2ASACQYC+AmoiBiAFQQoQdCABICQgBhD2ASADIAFBCBB0IAQgAyAbEPYBIAUgBEEHEHQgAkGAwQJqIgYgBSA2EPYBIAEgBkEIEHQgAyABIDcQ9gEgBCADQQcQdCAFIAQgLBD2ASACQYDEAmoiBiAFQQgQdCABIBUgBhD2ASADIAFBBRB0IAQgAyASEPYBIAUgBEEIEHQgAkGAxwJqIgYgBSAdEPYBIAEgBkEJEHQgAyABICIQ9gEgBCADQQYQdCAFIAQgCxD2ASACQYDKAmoiBiAFQQgQdCABIBAgBhD2ASADIAFBCBB0IAQgAyAXEPYBIAUgBEEHEHQgAkGAzQJqIgYgBSAsEPYBIAEgBkEKEHQgAyABICIQ9gEgBCADQQcQdCAFIAQgJxD2ASACQYDQAmoiBiAFQQcQdCABIBEgBhD2ASADIAFBBRB0IAQgAyANEPYBIAUgBEEJEHQgAkGA0wJqIgYgBSATEPYBIAEgBkEHEHQgAyABIB8Q9gEgBCADQQgQdCAFIAQgChD2ASACQYDWAmoiBiAFQQoQdCABICAgBhD2ASADIAFBCBB0IAQgAyAHEPYBIAUgBEEIEHQgAkGA2QJqIgYgBSAREPYBIAEgBkEFEHQgAyABICUQ9gEgBCADQQwQdCAFIAQgCxD2ASACQYDcAmoiBiAFQQYQdCABIA4gBhD2ASADIAFBChB0IAQgAyAXEPYBIAUgBEEHEHQgAkGA3wJqIgYgBSAjEPYBIAEgBkEHEHQgAyABIDQQ9gEgBCADQQwQdCAFIAQgKBD2ASACQYDiAmoiBiAFQQcQdCABICAgBhD2ASADIAFBCBB0IAQgAyAUEPYBIAUgBEEIEHQgAkGA5QJqIgYgBSAJEPYBIAEgBkEMEHQgAyABIEEQ9gEgBCADQQoQdCAFIAQgKxD2ASACQYDoAmoiBiAFQQcQdCABIBMgBhD2ASADIAFBChB0IAQgAyA2EPYBIAUgBEEHEHQgAkGA6wJqIgYgBSAUEPYBIAEgBkEHEHQgAyABIBAQ9gEgBCADQQcQdCAFIAQgKBD2ASACQYDuAmoiBiAFQQYQdCABICUgBhD2ASADIAFBCBB0IAQgAyAhEPYBIAUgBEEJEHQgAkGA8QJqIgYgBSAnEPYBIAEgBkEHEHQgAyABIBYQ9gEgBCADQQgQdCAFIAQgIhD2ASACQYD0AmoiBiAFQQUQdCABIB4gBhD2ASADIAFBDRB0IAQgAyA5EPYBIAUgBEEHEHQgAkGA9wJqIgYgBSAYEPYBIAEgBkEHEHQgAyABIAgQ9gEgBCADQQcQdCAFIAQgLxD2ASACQYD6AmoiCCAFQQgQdCABIBkgCBD2ASADIAFBBhB0IAQgAyA9EPYBIAUgBEEKEHQgAkGA/QJqIgggBSAJEPYBIAEgCEEIEHQgAyABIBEQ9gEgBCADQQQQdCAFIAQgRBD2ASACQYCAA2oiCCAFQQ0QdCABIEIgCBD2ASADIAFBBxB0IAQgAyAPEPYBIAUgBEEJEHQgAkGAgwNqIgggBSATEPYBIAEgCEEIEHQgAyABIDgQ9gEgBCADQQoQdCAFIAQgCRD2ASACQYCGA2oiCCAFQQgQdCABIDUgCBD2ASADIAFBCRB0IAQgAyALEPYBIAUgBEEGEHQgAkGAiQNqIgggBSAeEPYBIAEgCEEJEHQgAyABIAoQ9gEgBCADQQkQdCAFIAQgNBD2ASACQYCMA2oiCCAFQQoQdCABIAwgCBD2ASADIAFBAhB0IAQgAyACEPYBIAUgBEEOEHQgAkGAjwNqIgggBSAREPYBIAEgCEEHEHQgAyABIBIQ9gEgBCADQQoQdCAFIAQgIBD2ASACQYCSA2oiCCAFQQgQdCABICkgCBD2ASADIAFBDxB0IAQgAyBAEPYBIAUgBEEHEHQgAkGAlQNqIgggBSAvEPYBIAEgCEEGEHQgAyABIDAQ9gEgBCADQQkQdCAFIAQgDBD2ASACQYCYA2oiCCAFQQoQdCABIC4gCBD2ASADIAFBARB0IAQgAyACEPYBIAUgBEENEHQgAkGAmwNqIgggBSAYEPYBIAEgCEEEEHQgAyABID4Q9gEgBCADQQkQdCAFIAQgIRD2ASACQYCeA2oiCCAFQQkQdCABIDYgCBD2ASADIAFBBhB0IAQgAyAZEPYBIAUgBEEIEHQgAkGAoQNqIgggBSASEPYBIAEgCEEKEHQgAyABICgQ9gEgBCADQQcQdCAFIAQgJxD2ASACQYCkA2oiCCAFQQsQdCABIDkgCBD2ASADIAFBBhB0IAQgAyArEPYBIAUgBEEMEHQgAkGApwNqIgggBSBFEPYBIAEgCEEIEHQgAyABIAcQ9gEgBCADQQcQdCAFIAQgJxD2ASACQYCqA2oiCCAFQQYQdCABIAsgCBD2ASADIAFBCBB0IAQgAyAYEPYBIAUgBEEIEHQgAkGArQNqIgggBSAKEPYBIAEgCEEKEHQgAyABIBwQ9gEgBCADQQYQdCAFIAQgDBD2ASACQYCwA2oiDCAFQQYQdCABIB8gDBD2ASADIAFBCBB0IAQgAyAtEPYBIAUgBEELEHQgAkGAswNqIgwgBSA5EPYBIAEgDEEJEHQgAyABIB4Q9gEgBCADQQoQdCAFIAQgBxD2ASACQYC2A2oiDCAFQQgQdCABIBggDBD2ASADIAFBBRB0IAQgAyAOEPYBIAUgBEEJEHQgAkGAuQNqIgwgBSAmEPYBIAEgDEECEHQgAyABICoQ9gEgBCADQRAQdCAFIAQgFhD2ASACQYC8A2oiDCAFQQcQdCABIBQgDBD2ASADIAFBBxB0IAQgAyAbEPYBIAUgBEEGEHQgAkGAvwNqIgwgBSAKEPYBIAEgDEEIEHQgAyABICQQ9gEgBCADQQoQdCAFIAQgGxD2ASACQYDCA2oiDCAFQQcQdCABIA4gDBD2ASADIAFBBhB0IAQgAyA7EPYBIAUgBEEMEHQgAkGAxQNqIgwgBSAtEPYBIAEgDEEIEHQgAyABIBQQ9gEgBCADQQcQdCAFIAQgEBD2ASACQYDIA2oiDCAFQQYQdCABIBkgDBD2ASADIAFBChB0IAQgAyAzEPYBIAUgBEEJEHQgAkGAywNqIgwgBSAvEPYBIAEgDEEHEHQgAyABIBcQ9gEgBCADQQYQdCAFIAQgDRD2ASACQYDOA2oiDCAFQQoQdCABIEEgDBD2ASADIAFBBxB0IAQgAyAPEPYBIAUgBEEJEHQgAkGA0QNqIgwgBSALEPYBIAEgDEEFEHQgAyABIBIQ9gEgBCADQQsQdCAFIAQgGxD2ASACQYDUA2oiDCAFQQcQdCABIBogDBD2ASADIAFBBhB0IAQgAyAyEPYBIAUgBEEJEHQgAkGA1wNqIgwgBSAHEPYBIAEgDEEFEHQgAyABIA4Q9gEgBCADQQkQdCAFIAQgFhD2ASACQYDaA2oiByAFQQoQdCABIAkgBxD2ASADIAFBBxB0IAQgAyAcEPYBIAUgBEEHEHQgAkGA3QNqIgcgBSAgEPYBIAEgB0EGEHQgAyABIDEQ9gEgBCADQQkQdCAFIAQgIxD2ASACQYDgA2oiByAFQQQQdCABIAIgBxD2ASADIAFBEBB0IAQgAyAgEPYBIAUgBEEJEHQgAkGA4wNqIgcgBSArEPYBIAEgB0EHEHQgAyABIDEQ9gEgBCADQQgQdCAFIAQgRhD2ASACQYDmA2oiByAFQQgQdCABIEAgBxD2ASADIAFBBhB0IAQgAyAlEPYBIAUgBEEJEHQgAkGA6QNqIgcgBSAWEPYBIAEgB0EHEHQgAyABIBAQ9gEgBCADQQgQdCAFIAQgFBD2ASACQYDsA2oiByAFQQkQdCABIB0gBxD2ASADIAFBCRB0IAQgAyAkEPYBIAUgBEEHEHQgAkGA7wNqIgcgBSBDEPYBIAEgB0EHEHQgAyABIBcQ9gEgBCADQQcQdCAFIAQgEBD2ASACQYDyA2oiByAFQQkQdCABICUgBxD2ASADIAFBCBB0IAQgAyATEPYBIAUgBEEIEHQgAkGA9QNqIgcgBSAJEPYBIAEgB0EFEHQgAyABIA0Q9gEgBCADQQkQdCAFIAQgFxD2ASACQYD4A2oiByAFQQgQdCABIBogBxD2ASADIAFBBxB0IAQgAyAQEPYBIAUgBEEKEHQgAkGA+wNqIgcgBSAaEPYBIAEgB0ENEHQgAyABICMQ9gEgBCADQQkQdCAFIAQgJxD2ASACQYD+A2oiByAFQQcQdCABIBEgBxD2ASADIAFBBxB0IAQgAyAVEPYBIAUgBEEIEHQgAkGAgQRqIgcgBSAUEPYBIAEgB0EHEHQgAyABICIQ9gEgBCADQQEQdCAFIAQgAhD2ASACQYCEBGoiByAFQRAQdCABICEgBxD2ASADIAFBCBB0IAQgAyAaEPYBIAUgBEEIEHQgAkGAhwRqIgcgBSAkEPYBIAEgB0EIEHQgAyABIDcQ9gEgBCADQQgQdCAFIAQgPxD2ASACQYCKBGoiByAFQQkQdCABIDIgBxD2ASADIAFBCBB0IAQgAyBCEPYBIAUgBEEIEHQgAkGAjQRqIgcgBSAaEPYBIAEgB0EJEHQgAyABICMQ9gEgBCADQQkQdCAFIAQgPBD2ASACQYCQBGoiByAFQQsQdCABIB4gBxD2ASADIAFBCRB0IAQgAyBFEPYBIAUgBEEIEHQgAkGAkwRqIgcgBSAjEPYBIAEgB0EGEHQgAyABIBUQ9gEgBCADQQgQdCAFIAQgJxD2ASACQYCWBGoiByAFQQcQdCABIEIgBxD2ASADIAFBBxB0IAQgAyAYEPYBIAUgBEEMEHQgAkGAmQRqIgcgBSA1EPYBIAEgB0EGEHQgAyABIAoQ9gEgBCADQQsQdCAFIAQgQxD2ASACQYCcBGoiByAFQQkQdCABIAogBxD2ASADIAFBBhB0IAQgAyA+EPYBIAUgBEEMEHQgAkGAnwRqIgcgBSA1EPYBIAEgB0EHEHQgAyABIDgQ9gEgBCADQQUQdCAFIAQgHhD2ASACQYCiBGoiByAFQQkQdCABICwgBxD2ASADIAFBCBB0IAQgAyApEPYBIAUgBEEBEHQgAkGApQRqIgcgBSACEPYBIAEgB0EOEHQgAyABIEEQ9gEgBCADQQYQdCAFIAQgNBD2ASACQYCoBGoiByAFQQcQdCABIAsgBxD2ASADIAFBCxB0IAQgAyApEPYBIAUgBEEGEHQgAkGAqwRqIgcgBSAhEPYBIAEgB0EJEHQgAyABIBwQ9gEgBCADQQwQdCAFIAQgDxD2ASACQYCuBGoiByAFQQcQdCABIC0gBxD2ASADIAFBBhB0IAQgAyANEPYBIAUgBEEJEHQgAkGAsQRqIgcgBSAUEPYBIAEgB0EEEHQgAyABIDwQ9gEgBCADQQoQdCAFIAQgFhD2ASACQYC0BGoiByAFQQcQdCABIBggBxD2ASADIAFBBRB0IAQgAyAfEPYBIAUgBEEKEHQgAkGAtwRqIhggBSAoEPYBIAEgGEEGEHQgAyABIA4Q9gEgBCADQQkQdCAFIAQgFRD2ASACQYC6BGoiDiAFQQcQdCABIB8gDhD2ASADIAFBCRB0IAQgAyAQEPYBIAUgBEEBEHQgAkGAvQRqIg4gBSACEPYBIAEgDkEMEHQgAyABICEQ9gEgBCADQQgQdCAFIAQgCxD2ASACQYDABGoiCyAFQQgQdCABIA8gCxD2ASADIAFBBxB0IAQgAyAxEPYBIAUgBEEJEHQgAkGAwwRqIgsgBSAREPYBIAEgC0EJEHQgAyABIAkQ9gEgBCADQQYQdCAFIAQgHRD2ASACQYDGBGoiCyAFQQkQdCABICkgCxD2ASADIAFBBhB0IAQgAyA0EPYBIAUgBEEHEHQgAkGAyQRqIgsgBSAeEPYBIAEgC0EJEHQgAyABICEQ9gEgBCADQQgQdCAFIAQgExD2ASACQYDMBGoiCyAFQQgQdCABICIgCxD2ASADIAFBBhB0IAQgAyAZEPYBIAUgBEEIEHQgAkGAzwRqIgsgBSAuEPYBIAEgC0EIEHQgAyABIBQQ9gEgBCADQQYQdCAFIAQgExD2ASACQYDSBGoiCyAFQQgQdCABIBwgCxD2ASADIAFBBRB0IAQgAyAdEPYBIAUgBEEHEHQgAkGA1QRqIgsgBSANEPYBIAEgC0EJEHQgAyABIDkQ9gEgBCADQQcQdCAFIAQgLxD2ASACQYDYBGoiDSAFQQcQdCABICQgDRD2ASADIAFBCBB0IAQgAyAtEPYBIAUgBEEJEHQgAkGA2wRqIg0gBSAmEPYBIAEgDUEIEHQgAyABID8Q9gEgBCADQQgQdCAFIAQgQBD2ASACQYDeBGoiDSAFQQcQdCABICQgDRD2ASADIAFBBRB0IAQgAyAlEPYBIAUgBEEIEHQgAkGA4QRqIg0gBSAKEPYBIAEgDUEIEHQgAyABIA8Q9gEgBCADQQYQdCAFIAQgIBD2ASACQYDkBGoiCiAFQQgQdCABICggChD2ASADIAFBAhB0IAQgAyAqEPYBIAUgBEENEHQgAkGA5wRqIgogBSAcEPYBIAEgCkEHEHQgAyABICYQ9gEgBCADQQUQdCAFIAQgHRD2ASACQYDqBGoiCiAFQQkQdCABIBEgChD2ASADIAFBBxB0IAQgAyAaEPYBIAUgBEEGEHQgAkGA7QRqIgogBSAZEPYBIAEgCkEIEHQgAyABIBoQ9gEgBCADQQUQdCAFIAQgPRD2ASACQYDwBGoiCiAFQQoQdCABIBcgChD2ASADIAFBChB0IAQgAyAQEPYBIAUgBEEGEHQgAkGA8wRqIgogBSAVEPYBIAEgCkEMEHQgAyABICsQ9gEgBCADQQkQdCAFIAQgNhD2ASACQYD2BGoiCiAFQQgQdCABIAkgChD2ASADIAFBBhB0IAQgAyATEPYBIAUgBEEIEHQgAkGA+QRqIgkgBSAWEPYBIAEgCUEHEHQgAyABIDcQ9gEgBCADQQcQdCAFIAQgOBD2ASACQYD8BGoiCSAFQQkQdCABICUgCRD2ASADIAFBChB0IAQgAyAvEPYBIAUgBEEEEHQgAkGA/wRqIgkgBSA+EPYBIAEgCUEMEHQgAyABIDMQ9gEgBCADQQgQdCAFIAQgJhD2ASACQYCCBWoiCSAFQQkQdCABIBsgCRD2ASADIAFBCRB0IAQgAyAjEPYBIAUgBEEHEHQgAkGAhQVqIgkgBSAmEPYBIAEgCUECEHQgAyABICoQ9gEgBCADQQsQdCAFIAQgOhD2ASACQYCIBWoiCSAFQQkQdCABIBEgCRD2ASADIAFBBRB0IAQgAyASEPYBIAUgBEEKEHQgAkGAiwVqIgkgBSAQEPYBIAEgCUEGEHQgAyABIDAQ9gEgBCADQQgQdCAFIAQgMBD2ASACQYCOBWoiCSAFQQcQdCABIDsgCRD2ASADIAFBCxB0IAQgAyAzEPYBIAUgBEEHEHQgAkGAkQVqIgEgBSAqEPYBIAAgAUEFEHQgAkHApAVqJAALolYCRn8FfiMAQcChBWsiAiQAIAIgATYCgI4FIAIgAUHAAWoiCTYChI4FIAJBgJcFaiIWIAJBgI4FaiIXEL0DIAJBuJQFaiIfIAJBuJcFaiIFKQMAIkg3AwAgAkGwlAVqIiAgAkGwlwVqIgcpAwAiSTcDACACQaiUBWoiISACQaiXBWoiDCkDACJKNwMAIAJBoJQFaiIiIAJBoJcFaiINKQMAIks3AwAgAkGYlAVqIiMgAkGYlwVqIg4pAwAiTDcDACACQYiRBWoiBCACQYiXBWoiDykDADcDACACQZCRBWoiAyACQZCXBWoiECkDADcDACACQZiRBWoiESBMNwMAIAJBoJEFaiISIEs3AwAgAkGokQVqIhMgSjcDACACQbCRBWoiFCBJNwMAIAJBuJEFaiIVIEg3AwAgAiACKQOAlwUiSDcDgJQFIAIgSDcDgJEFIAJBuJoFaiIYIBUpAwA3AwAgAkGwmgVqIhkgFCkDADcDACACQaiaBWoiGiATKQMANwMAIAJBoJoFaiIbIBIpAwA3AwAgAkGYmgVqIhwgESkDADcDACACQZCaBWoiHSADKQMANwMAIAJBiJoFaiIeIAQpAwA3AwAgAiACKQOAkQU3A4CaBSACQbigBWogGCkDADcDACACQbCgBWogGSkDADcDACACQaigBWogGikDADcDACACQaCgBWogGykDADcDACACQZigBWogHCkDADcDACACQZCgBWogHSkDADcDACACQYigBWogHikDADcDACACIAIpA4CaBTcDgKAFIBYgFxC9AyAfIAUpAwAiSDcDACAgIAcpAwAiSTcDACAhIAwpAwAiSjcDACAiIA0pAwAiSzcDACAjIA4pAwAiTDcDACAEIA8pAwA3AwAgAyAQKQMANwMAIBEgTDcDACASIEs3AwAgEyBKNwMAIBQgSTcDACAVIEg3AwAgAiACKQOAlwUiSDcDgJQFIAIgSDcDgJEFIBggFSkDADcDACAZIBQpAwA3AwAgGiATKQMANwMAIBsgEikDADcDACAcIBEpAwA3AwAgHSADKQMANwMAIB4gBCkDADcDACACIAIpA4CRBTcDgJoFIAJB+KAFaiAYKQMANwMAIAJB8KAFaiAZKQMANwMAIAJB6KAFaiAaKQMANwMAIAJB4KAFaiAbKQMANwMAIAJB2KAFaiAcKQMANwMAIAJB0KAFaiAdKQMANwMAIAJByKAFaiAeKQMANwMAIAIgAikDgJoFNwPAoAUgFiAXEL0DIB8gBSkDACJINwMAICAgBykDACJJNwMAICEgDCkDACJKNwMAICIgDSkDACJLNwMAICMgDikDACJMNwMAIAQgDykDADcDACADIBApAwA3AwAgESBMNwMAIBIgSzcDACATIEo3AwAgFCBJNwMAIBUgSDcDACACIAIpA4CXBSJINwOAlAUgAiBINwOAkQUgGCAVKQMANwMAIBkgFCkDADcDACAaIBMpAwA3AwAgGyASKQMANwMAIBwgESkDADcDACAdIAMpAwA3AwAgHiAEKQMANwMAIAIgAikDgJEFNwOAmgUgAkG4oQVqIBgpAwA3AwAgAkGwoQVqIBkpAwA3AwAgAkGooQVqIBopAwA3AwAgAkGgoQVqIBspAwA3AwAgAkGYoQVqIBwpAwA3AwAgAkGQoQVqIB0pAwA3AwAgAkGIoQVqIB4pAwA3AwAgAiACKQOAmgU3A4ChBUEARQRAIAJBgJ0FaiACQYCgBWpBwAH8CgAACyACIAFBgANqNgKEiwUgAiAJNgKAiwUgAkGAlAVqIiYgAkGAiwVqIggQvQMgFSAfKQMAIkg3AwAgFCAgKQMAIkk3AwAgEyAhKQMAIko3AwAgEiAiKQMAIks3AwAgESAjKQMAIkw3AwAgAkGIjgVqIgEgAkGIlAVqIicpAwA3AwAgAkGQjgVqIgQgAkGQlAVqIigpAwA3AwAgAkGYjgVqIgMgTDcDACACQaCOBWoiCSBLNwMAIAJBqI4FaiIWIEo3AwAgAkGwjgVqIhcgSTcDACACQbiOBWoiJCBINwMAIAIgAikDgJQFIkg3A4CRBSACIEg3A4COBSAFICQpAwA3AwAgByAXKQMANwMAIAwgFikDADcDACANIAkpAwA3AwAgDiADKQMANwMAIBAgBCkDADcDACAPIAEpAwA3AwAgAiACKQOAjgU3A4CXBSAYIAUpAwA3AwAgGSAHKQMANwMAIBogDCkDADcDACAbIA0pAwA3AwAgHCAOKQMANwMAIB0gECkDADcDACAeIA8pAwA3AwAgAiACKQOAlwU3A4CaBSAmIAgQvQMgFSAfKQMAIkg3AwAgFCAgKQMAIkk3AwAgEyAhKQMAIko3AwAgEiAiKQMAIks3AwAgESAjKQMAIkw3AwAgASAnKQMANwMAIAQgKCkDADcDACADIEw3AwAgCSBLNwMAIBYgSjcDACAXIEk3AwAgJCBINwMAIAIgAikDgJQFIkg3A4CRBSACIEg3A4COBSAFICQpAwA3AwAgByAXKQMANwMAIAwgFikDADcDACANIAkpAwA3AwAgDiADKQMANwMAIBAgBCkDADcDACAPIAEpAwA3AwAgAiACKQOAjgU3A4CXBSACQfiaBWogBSkDADcDACACQfCaBWogBykDADcDACACQeiaBWogDCkDADcDACACQeCaBWogDSkDADcDACACQdiaBWogDikDADcDACACQdCaBWogECkDADcDACACQciaBWogDykDADcDACACIAIpA4CXBTcDwJoFICYgCBC9AyAVIB8pAwAiSDcDACAUICApAwAiSTcDACATICEpAwAiSjcDACASICIpAwAiSzcDACARICMpAwAiTDcDACABICcpAwA3AwAgBCAoKQMANwMAIAMgTDcDACAJIEs3AwAgFiBKNwMAIBcgSTcDACAkIEg3AwAgAiACKQOAlAUiSDcDgJEFIAIgSDcDgI4FIAUgJCkDADcDACAHIBcpAwA3AwAgDCAWKQMANwMAIA0gCSkDADcDACAOIAMpAwA3AwAgECAEKQMANwMAIA8gASkDADcDACACIAIpA4COBTcDgJcFIAJBuJsFaiAFKQMANwMAIAJBsJsFaiAHKQMANwMAIAJBqJsFaiAMKQMANwMAIAJBoJsFaiANKQMANwMAIAJBmJsFaiAOKQMANwMAIAJBkJsFaiAQKQMANwMAIAJBiJsFaiAPKQMANwMAIAIgAikDgJcFNwOAmwUgJUUEQCACQYCgBWogAkGAmgVqQcAB/AoAAAsgJUUEQCACQcCeBWogAkGAoAVqQcAB/AoAAAsgAiACQYCdBWpBgAP8CgAAIAJBgANqIgEgAkEBEHQgAkGABmoiFSACIAEQ9gEgAkGACWoiCSABIBUQ9gEgAkGADGoiHCABIAkQ9gEgAkGAD2oiGCABIBwQ9gEgAkGAEmoiGSABIBgQ9gEgAkGAFWoiLSABIBkQ9gEgAkGAGGoiPCABIC0Q9gEgAkGAG2oiCCABIDwQ9gEgAkGAHmoiDiABIAgQ9gEgAkGAIWoiJyABIA4Q9gEgAkGAJGoiHSABICcQ9gEgAkGAJ2oiPyABIB0Q9gEgAkGAKmoiLiABID8Q9gEgAkGALWoiDyABIC4Q9gEgAkGAMGoiLyABIA8Q9gEgAkGAM2oiQCABIC8Q9gEgAkGANmoiHiABIEAQ9gEgAkGAOWoiHyABIB4Q9gEgAkGAPGoiMCABIB8Q9gEgAkGAP2oiECABIDAQ9gEgAkGAwgBqIj0gASAQEPYBIAJBgMUAaiILIAEgPRD2ASACQYDIAGoiNiABIAsQ9gEgAkGAywBqIiAgASA2EPYBIAJBgM4AaiJBIAEgIBD2ASACQYDRAGoiMSABIEEQ9gEgAkGA1ABqIhogASAxEPYBIAJBgNcAaiIhIAEgGhD2ASACQYDaAGoiByABICEQ9gEgAkGA3QBqIjIgASAHEPYBIAJBgOAAaiJCIAEgMhD2ASACQYDjAGoiMyABIEIQ9gEgAkGA5gBqIhsgASAzEPYBIAJBgOkAaiI3IAEgGxD2ASACQYDsAGoiESABIDcQ9gEgAkGA7wBqIgogASAREPYBIAJBgPIAaiI+IAEgChD2ASACQYD1AGoiIiABID4Q9gEgAkGA+ABqIiMgASAiEPYBIAJBgPsAaiI0IAEgIxD2ASACQYD+AGoiFiABIDQQ9gEgAkGAgQFqIhcgASAWEPYBIAJBgIQBaiINIAEgFxD2ASACQYCHAWoiEiABIA0Q9gEgAkGAigFqIiQgASASEPYBIAJBgI0BaiIoIAEgJBD2ASACQYCQAWoiQyABICgQ9gEgAkGAkwFqIikgASBDEPYBIAJBgJYBaiITIAEgKRD2ASACQYCZAWoiJSABIBMQ9gEgAkGAnAFqIiogASAlEPYBIAJBgJ8BaiImIAEgKhD2ASACQYCiAWoiRCABICYQ9gEgAkGApQFqIisgASBEEPYBIAJBgKgBaiIsIAEgKxD2ASACQYCrAWoiFCABICwQ9gEgAkGArgFqIjggASAUEPYBIAJBgLEBaiI5IAEgOBD2ASACQYC0AWoiOiABIDkQ9gEgAkGAtwFqIgwgASA6EPYBIAJBgLoBaiI7IAEgDBD2ASACQYC9AWoiNSABIDsQ9gEgAkGAwAFqIkUgASA1EPYBIAJBgMMBaiIBIBMgRRD2ASACQYDGAWoiRiAPIAEQ9gEgAkGAyQFqIgMgAUEBEHQgAkGAzAFqIkcgByADEPYBIAJBgJEFaiIEIANBChB0IAJBgJQFaiIDIAQgFxD2ASACQYCXBWoiBSADQQcQdCACQYCaBWoiASAFICkQ9gEgAkGAzwFqIgYgAUEHEHQgBCAbIAYQ9gEgAyAEQQgQdCAFIAMgBxD2ASABIAVBDRB0IAJBgNIBaiIGIAEgPRD2ASAEIAZBCBB0IAMgBCAsEPYBIAUgA0EIEHQgASAFIBoQ9gEgAkGA1QFqIgYgAUEKEHQgBCANIAYQ9gEgAyAEQQsQdCAFIAMgOhD2ASABIAVBBRB0IAJBgNgBaiIGIAEgGRD2ASAEIAZBBhB0IAMgBCAJEPYBIAUgA0EKEHQgASAFICEQ9gEgAkGA2wFqIgYgAUEIEHQgBCAfIAYQ9gEgAyAEQQUQdCAFIAMgFRD2ASABIAVBDRB0IAJBgN4BaiIGIAEgExD2ASAEIAZBChB0IAMgBCAcEPYBIAUgA0ELEHQgASAFICQQ9gEgAkGA4QFqIgYgAUEIEHQgBCApIAYQ9gEgAyAEQQQQdCAFIAMgPBD2ASABIAVBCxB0IAJBgOQBaiIGIAEgMRD2ASAEIAZBBhB0IAMgBCAdEPYBIAUgA0EJEHQgASAFIBcQ9gEgAkGA5wFqIgYgAUEJEHQgBCAOIAYQ9gEgAyAEQQkQdCAFIAMgQBD2ASABIAVBCRB0IAJBgOoBaiIGIAEgHhD2ASAEIAZBCRB0IAMgBCApEPYBIAUgA0EIEHQgASAFIAsQ9gEgAkGA7QFqIgYgAUEHEHQgBCAZIAYQ9gEgAyAEQQ0QdCAFIAMgExD2ASABIAVBCRB0IAJBgPABaiIGIAEgMBD2ASAEIAZBCRB0IAMgBCAmEPYBIAUgA0EFEHQgASAFIAgQ9gEgAkGA8wFqIgYgAUEJEHQgBCAfIAYQ9gEgAyAEQQkQdCAFIAMgNBD2ASABIAVBBhB0IAJBgPYBaiIGIAEgHhD2ASAEIAZBCRB0IAMgBCApEPYBIAUgA0EJEHQgASAFID4Q9gEgAkGA+QFqIgYgAUEEEHQgBCAtIAYQ9gEgAyAEQQcQdCAFIAMgLRD2ASABIAVBCRB0IAJBgPwBaiIGIAEgEBD2ASAEIAZBCBB0IAMgBCAmEPYBIAUgA0EFEHQgASAFIA4Q9gEgAkGA/wFqIgYgAUEJEHQgBCA1IAYQ9gEgAyAEQQkQdCAFIAMgNRD2ASABIAVBCBB0IAJBgIICaiIGIAEgORD2ASAEIAZBBxB0IAMgBCAHEPYBIAUgA0EKEHQgASAFIB4Q9gEgAkGAhQJqIgYgAUEHEHQgBCAhIAYQ9gEgAyAEQQUQdCAFIAMgLRD2ASABIAVBCRB0IAJBgIgCaiIGIAEgHBD2ASAEIAZBCxB0IAMgBCBGEPYBIAUgA0EIEHQgASAFIAwQ9gEgAkGAiwJqIgYgAUEIEHQgBCANIAYQ9gEgAyAEQQUQdCAFIAMgDxD2ASABIAVBBxB0IAJBgI4CaiIGIAEgGBD2ASAEIAZBChB0IAMgBCASEPYBIAUgA0EHEHQgASAFIAwQ9gEgAkGAkQJqIgYgAUEHEHQgBCA/IAYQ9gEgAyAEQQkQdCAFIAMgCxD2ASABIAVBCxB0IAJBgJQCaiIGIAEgMhD2ASAEIAZBBhB0IAMgBCAOEPYBIAUgA0EGEHQgASAFIAkQ9gEgAkGAlwJqIgYgAUEKEHQgBCAdIAYQ9gEgAyAEQQsQdCAFIAMgKxD2ASABIAVBCBB0IAJBgJoCaiIGIAEgDBD2ASAEIAZBCRB0IAMgBCAzEPYBIAUgA0EHEHQgASAFICsQ9gEgAkGAnQJqIgYgAUEHEHQgBCAqIAYQ9gEgAyAEQQcQdCAFIAMgCBD2ASABIAVBChB0IAJBgKACaiIGIAEgExD2ASAEIAZBBhB0IAMgBCAwEPYBIAUgA0EIEHQgASAFICsQ9gEgAkGAowJqIgYgAUEFEHQgBCAPIAYQ9gEgAyAEQQgQdCAFIAMgJxD2ASABIAVBDhB0IAJBgKYCaiIGIAEgDBD2ASAEIAZBBxB0IAMgBCA+EPYBIAUgA0EIEHQgASAFIBsQ9gEgAkGAqQJqIgYgAUEIEHQgBCAoIAYQ9gEgAyAEQQkQdCAFIAMgGhD2ASABIAVBBhB0IAJBgKwCaiIGIAEgCBD2ASAEIAZBBhB0IAMgBCA8EPYBIAUgA0EKEHQgASAFIBcQ9gEgAkGArwJqIgYgAUEHEHQgBCASIAYQ9gEgAyAEQQgQdCAFIAMgQxD2ASABIAVBBhB0IAJBgLICaiIGIAEgGBD2ASAEIAZBBRB0IAMgBCAVEPYBIAUgA0ELEHQgASAFIBoQ9gEgAkGAtQJqIgYgAUEHEHQgBCAfIAYQ9gEgAyAEQQUQdCAFIAMgGRD2ASABIAVBBxB0IAJBgLgCaiIGIAEgGRD2ASAEIAZBChB0IAMgBCAkEPYBIAUgA0EGEHQgASAFICcQ9gEgAkGAuwJqIgYgAUEIEHQgBCAhIAYQ9gEgAyAEQQgQdCAFIAMgChD2ASABIAVBDBB0IAJBgL4CaiIGIAEgOhD2ASAEIAZBChB0IAMgBCA2EPYBIAUgA0EIEHQgASAFIAgQ9gEgAkGAwQJqIgYgAUEJEHQgBCAWIAYQ9gEgAyAEQQcQdCAFIAMgOxD2ASABIAVBCRB0IAJBgMQCaiIGIAEgNBD2ASAEIAZBBhB0IAMgBCAOEPYBIAUgA0EJEHQgASAFIA0Q9gEgAkGAxwJqIgYgAUEDEHQgBCAcIAYQ9gEgAyAEQQoQdCAFIAMgIBD2ASABIAVBBhB0IAJBgMoCaiIGIAEgDxD2ASAEIAZBCxB0IAMgBCBHEPYBIAUgA0EIEHQgASAFICQQ9gEgAkGAzQJqIgYgAUEHEHQgBCA0IAYQ9gEgAyAEQQcQdCAFIAMgLBD2ASABIAVBChB0IAJBgNACaiIGIAEgBxD2ASAEIAZBCRB0IAMgBCAMEPYBIAUgA0EGEHQgASAFIBAQ9gEgAkGA0wJqIgYgAUELEHQgBCA2IAYQ9gEgAyAEQQkQdCAFIAMgEhD2ASABIAVBBxB0IAJBgNYCaiIGIAEgMxD2ASAEIAZBCRB0IAMgBCAbEPYBIAUgA0EHEHQgASAFIDIQ9gEgAkGA2QJqIgYgAUEHEHQgBCAhIAYQ9gEgAyAEQQQQdCAFIAMgFRD2ASABIAVBDBB0IAJBgNwCaiIGIAEgJRD2ASAEIAZBBBB0IAMgBCAYEPYBIAUgA0ELEHQgASAFIEEQ9gEgAkGA3wJqIgYgAUEIEHQgBCAlIAYQ9gEgAyAEQQQQdCAFIAMgLRD2ASABIAVBCxB0IAJBgOICaiIGIAEgRBD2ASAEIAZBBxB0IAMgBCAXEPYBIAUgA0EIEHQgASAFIC8Q9gEgAkGA5QJqIgYgAUEJEHQgBCAlIAYQ9gEgAyAEQQUQdCAFIAMgGRD2ASABIAVBCRB0IAJBgOgCaiIGIAEgBxD2ASAEIAZBCBB0IAMgBCANEPYBIAUgA0EHEHQgASAFIB8Q9gEgAkGA6wJqIgYgAUEHEHQgBCAgIAYQ9gEgAyAEQQgQdCAFIAMgOBD2ASABIAVBCRB0IAJBgO4CaiIGIAEgOxD2ASAEIAZBCRB0IAMgBCAWEPYBIAUgA0EFEHQgASAFIA4Q9gEgAkGA8QJqIgYgAUEJEHQgBCAMIAYQ9gEgAyAEQQYQdCAFIAMgCBD2ASABIAVBChB0IAJBgPQCaiIGIAEgDBD2ASAEIAZBBxB0IAMgBCAiEPYBIAUgA0EHEHQgASAFIBQQ9gEgAkGA9wJqIgYgAUEFEHQgBCAuIAYQ9gEgAyAEQQkQdCAFIAMgChD2ASABIAVBDRB0IAJBgPoCaiIKIAEgKhD2ASAEIApBCBB0IAMgBCA4EPYBIAUgA0EGEHQgASAFID0Q9gEgAkGA/QJqIgogAUEJEHQgBCAwIAoQ9gEgAyAEQQcQdCAFIAMgEBD2ASABIAVBBhB0IAJBgIADaiIKIAEgDxD2ASAEIApBCBB0IAMgBCAhEPYBIAUgA0EOEHQgASAFICYQ9gEgAkGAgwNqIgogAUELEHQgBCATIAoQ9gEgAyAEQQgQdCAFIAMgGhD2ASABIAVBCRB0IAJBgIYDaiIKIAEgIxD2ASAEIApBBBB0IAMgBCAVEPYBIAUgA0EMEHQgASAFIBYQ9gEgAkGAiQNqIgogAUECEHQgBCAVIAoQ9gEgAyAEQQwQdCAFIAMgORD2ASABIAVBBhB0IAJBgIwDaiIKIAEgGhD2ASAEIApBChB0IAMgBCAXEPYBIAUgA0EHEHQgASAFICgQ9gEgAkGAjwNqIgogAUEGEHQgBCAHIAoQ9gEgAyAEQQgQdCAFIAMgKhD2ASABIAVBBBB0IAJBgJIDaiIKIAEgHBD2ASAEIApBDBB0IAMgBCAcEPYBIAUgA0EKEHQgASAFIA8Q9gEgAkGAlQNqIgogAUELEHQgBCAjIAoQ9gEgAyAEQQgQdCAFIAMgFhD2ASABIAVBBRB0IAJBgJgDaiIKIAEgJxD2ASAEIApBChB0IAMgBCAjEPYBIAUgA0ELEHQgASAFIA0Q9gEgAkGAmwNqIgogAUEDEHQgBCAJIAoQ9gEgAyAEQQsQdCAFIAMgEhD2ASABIAVBCBB0IAJBgJ4DaiIKIAEgCxD2ASAEIApBCBB0IAMgBCAjEPYBIAUgA0EHEHQgASAFICMQ9gEgAkGAoQNqIgsgAUEFEHQgBCAZIAsQ9gEgAyAEQQoQdCAFIAMgDBD2ASABIAVBBxB0IAJBgKQDaiILIAEgNxD2ASAEIAtBBxB0IAMgBCAiEPYBIAUgA0EJEHQgASAFIAcQ9gEgAkGApwNqIgsgAUEJEHQgBCARIAsQ9gEgAyAEQQcQdCAFIAMgERD2ASABIAVBBxB0IAJBgKoDaiILIAEgEhD2ASAEIAtBBhB0IAMgBCAQEPYBIAUgA0EIEHQgASAFICsQ9gEgAkGArQNqIgsgAUEGEHQgBCAfIAsQ9gEgAyAEQQkQdCAFIAMgERD2ASABIAVBBhB0IAJBgLADaiILIAEgMRD2ASAEIAtBCRB0IAMgBCAqEPYBIAUgA0EHEHQgASAFICAQ9gEgAkGAswNqIgsgAUEKEHQgBCAsIAsQ9gEgAyAEQQcQdCAFIAMgJhD2ASABIAVBBhB0IAJBgLYDaiILIAEgHhD2ASAEIAtBBhB0IAMgBCAOEPYBIAUgA0EKEHQgASAFIBEQ9gEgAkGAuQNqIgsgAUEIEHQgBCAUIAsQ9gEgAyAEQQwQdCAFIAMgHhD2ASABIAVBBxB0IAJBgLwDaiILIAEgCRD2ASAEIAtBFBB0IAMgBCAHEPYBIAUgA0ELEHQgASAFIAgQ9gEgAkGAvwNqIgggAUEJEHQgBCASIAgQ9gEgAyAEQQYQdCAFIAMgIBD2ASABIAVBChB0IAJBgMIDaiIIIAEgMRD2ASAEIAhBCBB0IAMgBCAaEPYBIAUgA0EEEHQgASAFIBwQ9gEgAkGAxQNqIgggAUELEHQgBCAiIAgQ9gEgAyAEQQcQdCAFIAMgGxD2ASABIAVBBhB0IAJBgMgDaiIIIAEgNhD2ASAEIAhBCBB0IAMgBCAzEPYBIAUgA0EHEHQgASAFIBQQ9gEgAkGAywNqIgggAUEHEHQgBCAMIAgQ9gEgAyAEQQcQdCAFIAMgIhD2ASABIAVBBxB0IAJBgM4DaiIIIAEgEBD2ASAEIAhBChB0IAMgBCANEPYBIAUgA0EGEHQgASAFIAcQ9gEgAkGA0QNqIgggAUEGEHQgBCAvIAgQ9gEgAyAEQQgQdCAFIAMgIBD2ASABIAVBBxB0IAJBgNQDaiIIIAEgIBD2ASAEIAhBCBB0IAMgBCANEPYBIAUgA0ECEHQgASAFIAIQ9gEgAkGA1wNqIgggAUELEHQgBCAdIAgQ9gEgAyAEQQkQdCAFIAMgGxD2ASABIAVBBxB0IAJBgNoDaiIIIAEgEhD2ASAEIAhBBxB0IAMgBCAkEPYBIAUgA0EFEHQgASAFIA8Q9gEgAkGA3QNqIgggAUEJEHQgBCAQIAgQ9gEgAyAEQQgQdCAFIAMgOBD2ASABIAVBBxB0IAJBgOADaiIIIAEgExD2ASAEIAhBCRB0IAMgBCA6EPYBIAUgA0EIEHQgASAFIBYQ9gEgAkGA4wNqIgggAUEKEHQgBCAUIAgQ9gEgAyAEQQcQdCAFIAMgFBD2ASABIAVBARB0IAJBgOYDaiIIIAEgAhD2ASAEIAhBDhB0IAMgBCAyEPYBIAUgA0EJEHQgASAFIBQQ9gEgAkGA6QNqIgggAUEHEHQgBCA+IAgQ9gEgAyAEQQcQdCAFIAMgIRD2ASABIAVBBxB0IAJBgOwDaiIIIAEgLxD2ASAEIAhBChB0IAMgBCAqEPYBIAUgA0EHEHQgASAFICwQ9gEgAkGA7wNqIgggAUEHEHQgBCAkIAgQ9gEgAyAEQQoQdCAFIAMgRxD2ASABIAVBCBB0IAJBgPIDaiIIIAEgJRD2ASAEIAhBBxB0IAMgBCA4EPYBIAUgA0EGEHQgASAFIEAQ9gEgAkGA9QNqIgggAUEKEHQgBCA9IAgQ9gEgAyAEQQ0QdCAFIAMgNxD2ASABIAVBBhB0IAJBgPgDaiIIIAEgGRD2ASAEIAhBChB0IAMgBCAaEPYBIAUgA0EHEHQgASAFIDAQ9gEgAkGA+wNqIgggAUEIEHQgBCAlIAgQ9gEgAyAEQQcQdCAFIAMgJRD2ASABIAVBChB0IAJBgP4DaiIIIAEgQxD2ASAEIAhBDBB0IAMgBCAbEPYBIAUgA0EHEHQgASAFIBQQ9gEgAkGAgQRqIgggAUEHEHQgBCAoIAgQ9gEgAyAEQQgQdCAFIAMgJBD2ASABIAVBCBB0IAJBgIQEaiIIIAEgLBD2ASAEIAhBBRB0IAMgBCAPEPYBIAUgA0EJEHQgASAFIA4Q9gEgAkGAhwRqIgggAUEJEHQgBCAMIAgQ9gEgAyAEQQUQdCAFIAMgJxD2ASABIAVBBxB0IAJBgIoEaiIIIAEgHRD2ASAEIAhBCxB0IAMgBCAfEPYBIAUgA0EKEHQgASAFIAkQ9gEgAkGAjQRqIgggAUEKEHQgBCBBIAgQ9gEgAyAEQQgQdCAFIAMgEBD2ASABIAVBDhB0IAJBgJAEaiIIIAEgKhD2ASAEIAhBCRB0IAMgBCAbEPYBIAUgA0EEEHQgASAFIBgQ9gEgAkGAkwRqIgggAUEJEHQgBCAxIAgQ9gEgAyAEQQgQdCAFIAMgFhD2ASABIAVBBxB0IAJBgJYEaiIIIAEgExD2ASAEIAhBBRB0IAMgBCAYEPYBIAUgA0EGEHQgASAFIAkQ9gEgAkGAmQRqIgggAUEMEHQgBCAuIAgQ9gEgAyAEQQ0QdCAFIAMgCRD2ASABIAVBDBB0IAJBgJwEaiIIIAEgKxD2ASAEIAhBBBB0IAMgBCAJEPYBIAUgA0EOEHQgASAFIDMQ9gEgAkGAnwRqIgkgAUEHEHQgBCAHIAkQ9gEgAyAEQQYQdCAFIAMgDhD2ASABIAVBCBB0IAJBgKIEaiIJIAEgLhD2ASAEIAlBCBB0IAMgBCAdEPYBIAUgA0EJEHQgASAFIDQQ9gEgAkGApQRqIgkgAUEHEHQgBCAhIAkQ9gEgAyAEQQgQdCAFIAMgFxD2ASABIAVBBxB0IAJBgKgEaiIJIAEgERD2ASAEIAlBBBB0IAMgBCAZEPYBIAUgA0EKEHQgASAFIDcQ9gEgAkGAqwRqIgkgAUEIEHQgBCAoIAkQ9gEgAyAEQQYQdCAFIAMgIBD2ASABIAVBBhB0IAJBgK4EaiIJIAEgLhD2ASAEIAlBCRB0IAMgBCAREPYBIAUgA0EJEHQgASAFICkQ9gEgAkGAsQRqIgkgAUEGEHQgBCBCIAkQ9gEgAyAEQQkQdCAFIAMgRBD2ASABIAVBDRB0IAJBgLQEaiIJIAEgBxD2ASAEIAlBCBB0IAMgBCA1EPYBIAUgA0EGEHQgASAFIA8Q9gEgAkGAtwRqIgcgAUEMEHQgBCA5IAcQ9gEgAyAEQQIQdCAFIAMgFRD2ASABIAVBDBB0IAJBgLoEaiIHIAEgJhD2ASAEIAdBCBB0IAMgBCAxEPYBIAUgA0EIEHQgASAFICIQ9gEgAkGAvQRqIgcgAUEHEHQgBCA5IAcQ9gEgAyAEQQgQdCAFIAMgEhD2ASABIAVBBRB0IAJBgMAEaiIHIAEgHRD2ASAEIAdBCBB0IAMgBCAVEPYBIAUgA0ENEHQgASAFICgQ9gEgAkGAwwRqIgcgAUEJEHQgBCAoIAcQ9gEgAyAEQQoQdCAFIAMgRRD2ASABIAVBCRB0IAJBgMYEaiIHIAEgDRD2ASAEIAdBCBB0IAMgBCAUEPYBIAUgA0EEEHQgASAFIBgQ9gEgAkGAyQRqIgcgAUEKEHQgBCAmIAcQ9gEgAyAEQQYQdCAFIAMgPxD2ASABIAVBBxB0IAJBgMwEaiIHIAEgGBD2ASAEIAdBCRB0IAMgBCAeEPYBIAUgA0EHEHQgASAFIBAQ9gEgAkGAzwRqIgcgAUEKEHQgBCAvIAcQ9gEgAyAEQQkQdCAFIAMgDRD2ASABIAVBBxB0IAJBgNIEaiIHIAEgNxD2ASAEIAdBBxB0IAMgBCAeEPYBIAUgA0ELEHQgASAFIDUQ9gEgAkGA1QRqIgcgAUEHEHQgBCAzIAcQ9gEgAyAEQQcQdCAFIAMgOxD2ASABIAVBCRB0IAJBgNgEaiIHIAEgDRD2ASAEIAdBDhB0IAMgBCAiEPYBIAUgA0EIEHQgASAFICIQ9gEgAkGA2wRqIgcgAUEFEHQgBCA8IAcQ9gEgAyAEQQgQdCAFIAMgLhD2ASABIAVBChB0IAJBgN4EaiIHIAEgNRD2ASAEIAdBBxB0IAMgBCAwEPYBIAUgA0EJEHQgASAFICwQ9gEgAkGA4QRqIgcgAUEHEHQgBCAQIAcQ9gEgAyAEQQkQdCAFIAMgFxD2ASABIAVBCBB0IAJBgOQEaiIHIAEgOhD2ASAEIAdBBxB0IAMgBCAREPYBIAUgA0EGEHQgASAFIB8Q9gEgAkGA5wRqIgcgAUEHEHQgBCAyIAcQ9gEgAyAEQQUQdCAFIAMgGBD2ASABIAVBDBB0IAJBgOoEaiIHIAEgDBD2ASAEIAdBBRB0IAMgBCAnEPYBIAUgA0EJEHQgASAFIBEQ9gEgAkGA7QRqIgcgAUEHEHQgBCAWIAcQ9gEgAyAEQQcQdCAFIAMgIxD2ASABIAVBCBB0IAJBgPAEaiIHIAEgExD2ASAEIAdBBxB0IAMgBCArEPYBIAUgA0EGEHQgASAFIB0Q9gEgAkGA8wRqIgcgAUEIEHQgBCAaIAcQ9gEgAyAEQQcQdCAFIAMgQhD2ASABIAVBCBB0IAJBgPYEaiIHIAEgEhD2ASAEIAdBBxB0IAMgBCAkEPYBIAUgA0EIEHQgASAFIDYQ9gEgAkGA+QRqIgcgAUEIEHQgBCA0IAcQ9gEgAyAEQQQQdCAFIAMgLRD2ASABIAVBChB0IAJBgPwEaiIHIAEgIxD2ASAEIAdBBxB0IAMgBCATEPYBIAUgA0EIEHQgASAFIBsQ9gEgAkGA/wRqIgcgAUELEHQgBCA7IAcQ9gEgAyAEQQMQdCAFIAMgFRD2ASABIAVBCRB0IAJBgIIFaiIHIAEgRhD2ASAEIAdBDBB0IAMgBCAREPYBIAUgA0EHEHQgASAFIC8Q9gEgAkGAhQVqIgcgAUEGEHQgBCAcIAcQ9gEgAyAEQQsQdCAFIAMgFBD2ASABIAVBCxB0IAJBgIgFaiIHIAEgJxD2ASAEIAdBDBB0IAMgBCAmEPYBIAUgA0EFEHQgASAFIA4Q9gEgAkGAiwVqIgcgAUEJEHQgBCAyIAcQ9gEgAyAEQQsQdCAFIAMgKRD2ASABIAVBBxB0IAJBgI4FaiIEIAEgJRD2ASABIARBARB0IAAgASACEPYBIAJBwKEFaiQAC4OPAQILfyN+IwBBgBhrIgUkACAFQaAQahAmIAUtALgWIQ8gBSgCrBYiBgRAIAUoArAWIAZBAnQQ3wQLAkAgBSgCpBAiBkUNACAGIAZBDGxBE2pBeHEiB2pBCWoiBkUNACAFKAKgECAHayAGEN8ECyAFKAKgEyIGQYCAgIB4RiAGRXJFBEAgBSgCpBMgBkECdBDfBAsgBUHIEGoiCCABQShqKQMANwMAIAVBwBBqIgkgAUEgaikDADcDACAFQbgQaiIKIAFBGGopAwA3AwAgBUGwEGoiCyABQRBqKQMANwMAIAVBqBBqIgwgAUEIaikDADcDACAFQdgQaiABQThqKQMANwMAIAVB4BBqIAFBQGspAwA3AwAgBUHoEGogAUHIAGopAwA3AwAgBUHwEGogAUHQAGopAwA3AwAgBUH4EGogAUHYAGopAwA3AwAgBSABKQMANwOgECAFIAEpAzA3A9AQIAVBoBdqIgcgBUGgEGoiAUHgAPwKAAAgASAHEPcDIAUoAqQQIQEgBSgCoBAhBgJAAkACQAJAAkACQAJAAn8CQAJAIAUoAqgQIgdBAkYEQCAMIgcgAUE4aikDADcDACALIAFBQGspAwA3AwAgCiABQcgAaikDADcDACAJIAFB0ABqKQMANwMAIAggAUHYAGopAwA3AwAgBSABKQMwNwOgECABKQMoISQgASkDICEjIAEpAxghFiABKQMQISEgASkDCCEaIAEoAgQhDSABKAIAIQ4gBgRAIAEgBkEwbBDfBAsgBUHoFmogCCkDADcDACAFQeAWaiAJKQMANwMAIAVB2BZqIAopAwA3AwAgBUHQFmogCykDADcDACAFQcgWaiAHKQMANwMAIAUgBSkDoBA3A8AWIAggAkEoaikDADcDACAJIAJBIGopAwA3AwAgCiACQRhqKQMANwMAIAsgAkEQaikDADcDACAHIAJBCGopAwA3AwAgBUHYEGogAkE4aikDADcDACAFQeAQaiACQUBrKQMANwMAIAVB6BBqIAJByABqKQMANwMAIAVB8BBqIAJB0ABqKQMANwMAIAVB+BBqIAJB2ABqKQMANwMAIAUgAikDADcDoBAgBSACKQMwNwPQECAFQaAXaiICIAVBoBBqIgFB4AD8CgAAIAEgAhD3AyAFKAKkECEBIAUoAqAQIQIgBSgCqBAiBkECRw0BIAVBqBBqIgsgAUE4aikDADcDACAFQbAQaiIKIAFBQGspAwA3AwAgBUG4EGoiCSABQcgAaikDADcDACAFQcAQaiIIIAFB0ABqKQMANwMAIAVByBBqIgwgAUHYAGopAwA3AwAgBSABKQMwNwOgECABKQMoISkgASkDICEnIAEpAxghICABKQMQIR0gASkDCCEoIAEoAgQhBiABKAIAIQcgAgRAIAEgAkEwbBDfBAsgBUGYF2ogDCkDADcDACAFQZAXaiAIKQMANwMAIAVBiBdqIAkpAwA3AwAgBUGAF2ogCikDADcDACAFQfgWaiALKQMANwMAIAUgBSkDoBA3A/AWAkACQAJAIA8OAgECAAtB1LrCAEEPQeS6wgAQ/gMAC0HRzsUALQAAGkHABEEIENYEIgFFDQpCuKr1gICAgKwQISogBUK4qvWAgICArBA3A8gQQpiAgNmwjoDw9AAhJSAFQpiAgNmwjoDw9AA3A8AQQpXHrZmzleabh38hHiAFQpXHrZmzleabh383A7gQQrSchtLEyYL/9gAhFSAFQrSchtLEyYL/9gA3A7AQQvWr8u+Nq5a/LiEbIAVC9avy742rlr8uNwOoEEL29aLgw+/10A8hFyAFQvb1ouDD7/XQDzcDoBAgBUGgEGpB2LPCAEEwEPEDBEBCpNfc69/Nzq8KIRdC4a28qtbL084cIRtCjqWWnNy+zvxfIR5C5//Psbrx/+WpfyElQvOqif///7/TqX8hKkKKiY7KiqfQvG0hFQtBKCECA0AgBUGACWogBUHAFmogAmopAwAiFEIAICpCABDJAyAFQZAJaiAUQgAgJUIAEMkDIAVBoAlqIBRCACAeQgAQyQMgBUGwCWogFEIAIBVCABDJAyAFQcAJaiAUQgAgG0IAEMkDIAVB0AlqIBRCACAXQgAQyQMgBUHwCGogBSkDgAkiGCAcfCIZQgBCAEL9//P/z///+Yl/EMkDIAVB4AhqIAUpA/gIIhRCAEKr1f7///+//7l/QgAQyQMgBUHQCGogFEIAQv//z4rr///VHkIAEMkDIAVBwAhqIBRCAEKk7MO1j9S0mOcAQgAQyQMgBUGwCGogFEIAQr+llJzP8NK75ABCABDJAyAFQaAIaiAUQgBC19mumuT26Y3LAEIAEMkDIAVBkAhqIBRCAEKazf/Lo73EgBpCABDJAyAFKQOYCCAFKQPQCSImIBJ8IhIgBSkDyAkgBSkDwAkiFCATfCITIBRUrXwgEyATIAUpA7gJIAUpA7AJIhQgEXwiESAUVK18IBEgESAFKQOoCSAFKQOgCSIUIBB8IhAgFFStfCAQIBAgBSkDmAkgBSkDkAkiIiAffCIUICJUrXwgFCAFKQOICSAYIBlWrXx8IiIgFFStfHwiEFatfHwiEVatfHwiE1atfHwiFCAFKQOQCHwiGCAUVK18IBggBSkDqAggEyATIAUpA6AIfCITVq18IBMgBSkDuAggESARIAUpA7AIfCIRVq18IBEgBSkDyAggECAQIAUpA8AIfCIQVq18IBAgBSkD2AggBSkD0AgiHyAifCIiIB9UrXwgIiAFKQPoCCAZIAUpA+AIIhl8IBlUrXx8IhwgIlStfHwiHyAQVK18fCIQIBFUrXx8IhEgE1StfHwiEyAYVK18IBIgFFatIAUpA9gJIBIgJlStfHx8IRIgAkEIayICQXhHDQALIBJCms3/y6O9xIAaVg0HIBJCms3/y6O9xIAaUQ0GIB8hFyAQIRQgESEZIBMhGAwIC0HRzsUALQAAGkHABEEIENYEIgFFDQQgBSkD8BYiMSEcIAetIAatQiCGhCIQIRICfgJAIBAgMVINACAoIhIgBSkD+BYiHFINACAdIhIgBSkDgBciHFINACAgIhIgBSkDiBciHFINACAnIhIgBSkDkBciHFINACAoISwgICEmIBIhLSApIhIhFyAdIAUpA5gXIhwgElENARoLIAUpA5gXIRcgEiAcVA0DIAUpA/gWISwgBSkDiBchJiAFKQOQFyEtIAUpA4AXCyEiICcgLX0iESAXIClWrSISfSElICAgJn0iEyARIBJUICcgLVRyrSIRfSEeIB0gIn0iEiAgICZUIBEgE1ZyrSIRfSEVICggLH0iEyAdICJUIBEgElZyrSIRfSEbIBAgMX0hGCApIBd9IRkgKCAsVCARIBNWcgwDCyAFIAc2AqgQIAUgATYCpBAgBSAGNgKgEAwJCyAFIAY2AqgQIAUgATYCpBAgBSACNgKgEAwIC0Kk7MO1j9S0mOcAIAUpA4gXIiYgIH0iESAFKQOQFyItICdUIC0gJ30iEiAXIClUrSITVHKtIhR9IhV9IhkgEiATfSISQv//z4rr///VHlZC///Piuv//9UeIBJ9IhIgFyApfSITQqvV/v///7//uX9WrSIYVHKtIht9IR5Cv6WUnM/w0rvkACAFKQOAFyIiIB19Ih8gESAUVCAgICZWcq0iEX0iFH0iICAZIBtUIBVCpOzDtY/UtJjnAFZyrSIZfSEVQtfZrprk9umNywAgBSkD+BYiLCAofSIrIB0gIlYgESAfVnKtIhF9Ih19Ih8gGSAgViAUQr+llJzP8NK75ABWcq0iFH0hGyASIBh9ISUgKCAsViARICtWcq0gECAxfXxCms3/y6O9xIAafCEYQqvV/v///7//uX8gE30hGSAUIB9WIB1C19mumuT26Y3LAFZyCyECIBggAq19IStBKCECQgAhFEIAIRBCACERQgAhE0IAIR8DQCAFQcAPaiACIANqKQMAIhJCACAZQgAQyQMgBUHQD2ogEkIAICVCABDJAyAFQeAPaiASQgAgHkIAEMkDIAVB8A9qIBJCACAVQgAQyQMgBUGAEGogEkIAIBtCABDJAyAFQZAQaiASQgAgK0IAEMkDIAVBsA9qIAUpA8APIiAgKnwiGEIAQgBC/f/z/8////mJfxDJAyAFQaAPaiAFKQO4DyISQgBCq9X+////v/+5f0IAEMkDIAVBkA9qIBJCAEL//8+K6///1R5CABDJAyAFQYAPaiASQgBCpOzDtY/UtJjnAEIAEMkDIAVB8A5qIBJCAEK/pZScz/DSu+QAQgAQyQMgBUHgDmogEkIAQtfZrprk9umNywBCABDJAyAFQdAOaiASQgBCms3/y6O9xIAaQgAQyQMgBSkD2A4gHyAFKQOQECIffCISIAUpA4gQIAUpA4AQIh0gE3wiEyAdVK18IBMgEyAFKQP4DyAFKQPwDyIdIBF8IhEgHVStfCARIBEgBSkD6A8gBSkD4A8iHSAQfCIQIB1UrXwgECAQIAUpA9gPIAUpA9APIh0gFHwiFCAdVK18IBQgFCAFKQPIDyAYICBUrXx8IhRWrXx8IhBWrXx8IhFWrXx8IhNWrXx8IiAgBSkD0A58Ih0gIFStfCAdIAUpA+gOIBMgEyAFKQPgDnwiE1atfCATIAUpA/gOIBEgESAFKQPwDnwiEVatfCARIAUpA4gPIBAgECAFKQOAD3wiEFatfCAQIAUpA5gPIAUpA5APIiggFHwiFCAoVK18IBQgBSkDqA8gGCAFKQOgDyIYfCAYVK18fCIqIBRUrXx8IhQgEFStfHwiECARVK18fCIRIBNUrXx8IhMgHVStfCASICBWrSAFKQOYECASIB9UrXx8fCEfIAJBCGsiAkF4Rw0ACwJAAkAgH0Kazf/Lo73EgBpWDQAgH0Kazf/Lo73EgBpSBEAgFCEoIBAhMCARISAgEyEdDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAUISggECEwIBEhICATIR0MAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhHSARQr+llJzP8NK75ABSBEAgFCEoIBAhMCARISAMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhICAQQqTsw7WP1LSY5wBSBEAgFCEoIBAhMAwBCyAUQv//z4rr///VHlYNAUKk7MO1j9S0mOcAITAgFEL//8+K6///1R5SBEAgFCEoDAELQv//z4rr///VHiEoICpCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIR8MAQsgFEL//8+K6///1R59IhIgKkKr1f7///+//7l/VK0iFX0hKCAQQqTsw7WP1LSY5wB9IhkgFEL//8+K6///1R5UIBIgFVRyrSISfSEwIBFCv6WUnM/w0rvkAH0iFCAQQqTsw7WP1LSY5wBUIBIgGVZyrSIQfSEgIBNC19mumuT26Y3LAH0iEiARQr+llJzP8NK75ABUIBAgFFZyrSIQfSEdIB8gE0LX2a6a5PbpjcsAVCAQIBJWcq19QprN/8ujvcSAGn0hHyAqQtWqgYCAgMCAxgB8ISoLIAUpA8AWIjIhHCAOrSANrUIghoQiECESAn4CQAJ+AkAgECAyUg0AIBoiEiAFKQPIFiIcUg0AICEiEiAFKQPQFiIcUg0AIBYiEiAFKQPYFiIcUg0AICMiEiAFKQPgFiIcUg0AIBohLiAhIS8gEiEnICQiEiEZIBYgBSkD6BYiHCASUQ0BGgsgBSkD6BYhGSASIBxUDQEgBSkDyBYhLiAFKQPQFiEvIAUpA+AWIScgBSkD2BYLISkgIyAnfSIRIBkgJFatIhJ9IRUgFiApfSITIBEgElQgIyAnVHKtIhF9IRsgISAvfSISIBYgKVQgESATVnKtIhF9ISsgGiAufSITICEgL1QgESASVnKtIhF9ISMgGiAuVCARIBNWciECIBAgMn0hGCAkIBl9DAELQqTsw7WP1LSY5wAgBSkD2BYiKSAWfSIRIAUpA+AWIicgI1QgJyAjfSISIBkgJFStIhNUcq0iFH0iFX0iGCASIBN9IhJC///Piuv//9UeVkL//8+K6///1R4gEn0iEiAZICR9IhNCq9X+////v/+5f1atIiRUcq0iI30hG0K/pZScz/DSu+QAIAUpA9AWIi8gIX0iHiARIBRUIBYgKVZyrSIRfSIUfSIWIBggI1QgFUKk7MO1j9S0mOcAVnKtIhV9IStC19mumuT26Y3LACAFKQPIFiIuIBp9IhggISAvViARIB5Wcq0iEX0iIX0iHiAVIBZWIBRCv6WUnM/w0rvkAFZyrSIUfSEjIBQgHlYgIULX2a6a5PbpjcsAVnIhAiASICR9IRUgGiAuViARIBhWcq0gECAyfXxCms3/y6O9xIAafCEYQqvV/v///7//uX8gE30LISEgGCACrX0hJEEoIQJCACElQgAhFkIAIRBCACERQgAhE0IAIRQDQCAFQfANaiACIARqKQMAIhJCACAhQgAQyQMgBUGADmogEkIAIBVCABDJAyAFQZAOaiASQgAgG0IAEMkDIAVBoA5qIBJCACArQgAQyQMgBUGwDmogEkIAICNCABDJAyAFQcAOaiASQgAgJEIAEMkDIAVB4A1qIAUpA/ANIhggJXwiGkIAQgBC/f/z/8////mJfxDJAyAFQdANaiAFKQPoDSISQgBCq9X+////v/+5f0IAEMkDIAVBwA1qIBJCAEL//8+K6///1R5CABDJAyAFQbANaiASQgBCpOzDtY/UtJjnAEIAEMkDIAVBoA1qIBJCAEK/pZScz/DSu+QAQgAQyQMgBUGQDWogEkIAQtfZrprk9umNywBCABDJAyAFQYANaiASQgBCms3/y6O9xIAaQgAQyQMgBSkDiA0gBSkDwA4iHiAUfCISIAUpA7gOIAUpA7AOIhQgE3wiEyAUVK18IBMgEyAFKQOoDiAFKQOgDiIUIBF8IhEgFFStfCARIBEgBSkDmA4gBSkDkA4iFCAQfCIQIBRUrXwgECAQIAUpA4gOIBYgBSkDgA4iFnwiFCAWVK18IBQgBSkD+A0gGCAaVq18fCIWIBRUrXx8IhBWrXx8IhFWrXx8IhNWrXx8IhQgBSkDgA18IhggFFStfCAYIAUpA5gNIBMgEyAFKQOQDXwiE1atfCATIAUpA6gNIBEgESAFKQOgDXwiEVatfCARIAUpA7gNIBAgECAFKQOwDXwiEFatfCAQIAUpA8gNIAUpA8ANIhwgFnwiFiAcVK18IBYgBSkD2A0gGiAFKQPQDSIafCAaVK18fCIlIBZUrXx8IhYgEFStfHwiECARVK18fCIRIBNUrXx8IhMgGFStfCASIBRWrSAFKQPIDiASIB5UrXx8fCEUIAJBCGsiAkF4Rw0ACwJAAkAgFEKazf/Lo73EgBpWDQAgFEKazf/Lo73EgBpSBEAgFiEhIBAhGiARISMgEyErDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAWISEgECEaIBEhIyATISsMAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhKyARQr+llJzP8NK75ABSBEAgFiEhIBAhGiARISMMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhIyAQQqTsw7WP1LSY5wBSBEAgFiEhIBAhGgwBCyAWQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRogFkL//8+K6///1R5SBEAgFiEhDAELQv//z4rr///VHiEhICVCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRQMAQsgFkL//8+K6///1R59IhIgJUKr1f7///+//7l/VK0iFX0hISAQQqTsw7WP1LSY5wB9IhsgFkL//8+K6///1R5UIBIgFVRyrSISfSEaIBFCv6WUnM/w0rvkAH0iFSAQQqTsw7WP1LSY5wBUIBIgG1ZyrSIQfSEjIBNC19mumuT26Y3LAH0iEiARQr+llJzP8NK75ABUIBAgFVZyrSIQfSErIBQgE0LX2a6a5PbpjcsAVCAQIBJWcq19QprN/8ujvcSAGn0hFCAlQtWqgYCAgMCAxgB8ISULQSghAkIAIR5CACEVQgAhEEIAIRFCACETQgAhFgNAIAVBoAxqIAIgA2opAwAiEkIAIBdCABDJAyAFQbAMaiASQgAgLUIAEMkDIAVBwAxqIBJCACAmQgAQyQMgBUHQDGogEkIAICJCABDJAyAFQeAMaiASQgAgLEIAEMkDIAVB8AxqIBJCACAxQgAQyQMgBUGQDGogBSkDoAwiGCAefCIbQgBCAEL9//P/z///+Yl/EMkDIAVBgAxqIAUpA5gMIhJCAEKr1f7///+//7l/QgAQyQMgBUHwC2ogEkIAQv//z4rr///VHkIAEMkDIAVB4AtqIBJCAEKk7MO1j9S0mOcAQgAQyQMgBUHQC2ogEkIAQr+llJzP8NK75ABCABDJAyAFQcALaiASQgBC19mumuT26Y3LAEIAEMkDIAVBsAtqIBJCAEKazf/Lo73EgBpCABDJAyAFKQO4CyAFKQPwDCIkIBZ8IhIgBSkD6AwgBSkD4AwiFiATfCITIBZUrXwgEyATIAUpA9gMIAUpA9AMIhYgEXwiESAWVK18IBEgESAFKQPIDCAFKQPADCIWIBB8IhAgFlStfCAQIBAgBSkDuAwgBSkDsAwiFiAVfCIVIBZUrXwgFSAVIAUpA6gMIBggG1atfHwiFVatfHwiEFatfHwiEVatfHwiE1atfHwiFiAFKQOwC3wiGCAWVK18IBggBSkDyAsgEyATIAUpA8ALfCITVq18IBMgBSkD2AsgESARIAUpA9ALfCIRVq18IBEgBSkD6AsgECAQIAUpA+ALfCIQVq18IBAgBSkD+AsgBSkD8AsiHiAVfCIVIB5UrXwgFSAFKQOIDCAbIAUpA4AMIht8IBtUrXx8Ih4gFVStfHwiFSAQVK18fCIQIBFUrXx8IhEgE1StfHwiEyAYVK18IBIgFlatIAUpA/gMIBIgJFStfHx8IRYgAkEIayICQXhHDQALAkACQCAWQprN/8ujvcSAGlYNACAWQprN/8ujvcSAGlIEQCAVISIgECEmIBEhLCATISQMAgsgE0LX2a6a5PbpjcsAVg0AAkAgE0LX2a6a5PbpjcsAUgRAIBUhIiAQISYgESEsIBMhJAwBCyARQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEkIBFCv6WUnM/w0rvkAFIEQCAVISIgECEmIBEhLAwBCyAQQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEsIBBCpOzDtY/UtJjnAFIEQCAVISIgECEmDAELIBVC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhJiAVQv//z4rr///VHlIEQCAVISIMAQtC///Piuv//9UeISIgHkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohFgwBCyAVQv//z4rr///VHn0iEiAeQqvV/v///7//uX9UrSIXfSEiIBBCpOzDtY/UtJjnAH0iGyAVQv//z4rr///VHlQgEiAXVHKtIhJ9ISYgEUK/pZScz/DSu+QAfSIVIBBCpOzDtY/UtJjnAFQgEiAbVnKtIhB9ISwgE0LX2a6a5PbpjcsAfSISIBFCv6WUnM/w0rvkAFQgECAVVnKtIhB9ISQgFiATQtfZrprk9umNywBUIBAgElZyrX1Cms3/y6O9xIAafSEWIB5C1aqBgICAwIDGAHwhHgtBKCEDQgAhHEIAIRVCACEQQgAhEUIAIRNCACESA0AgBUHQCmogAyAEaikDACIXQgAgGUIAEMkDIAVB4ApqIBdCACAnQgAQyQMgBUHwCmogF0IAIClCABDJAyAFQYALaiAXQgAgL0IAEMkDIAVBkAtqIBdCACAuQgAQyQMgBUGgC2ogF0IAIDJCABDJAyAFQcAKaiAFKQPQCiIYIBx8IhtCAEIAQv3/8//P///5iX8QyQMgBUGwCmogBSkDyAoiF0IAQqvV/v///7//uX9CABDJAyAFQaAKaiAXQgBC///Piuv//9UeQgAQyQMgBUGQCmogF0IAQqTsw7WP1LSY5wBCABDJAyAFQYAKaiAXQgBCv6WUnM/w0rvkAEIAEMkDIAVB8AlqIBdCAELX2a6a5PbpjcsAQgAQyQMgBUHgCWogF0IAQprN/8ujvcSAGkIAEMkDIAUpA+gJIAUpA6ALIi0gEnwiEiAFKQOYCyAFKQOQCyIXIBN8IhMgF1StfCATIBMgBSkDiAsgBSkDgAsiFyARfCIRIBdUrXwgESARIAUpA/gKIAUpA/AKIhcgEHwiECAXVK18IBAgECAFKQPoCiAFKQPgCiIXIBV8IhUgF1StfCAVIBUgBSkD2AogGCAbVq18fCIVVq18fCIQVq18fCIRVq18fCITVq18fCIXIAUpA+AJfCIYIBdUrXwgGCAFKQP4CSATIBMgBSkD8Al8IhNWrXwgEyAFKQOICiARIBEgBSkDgAp8IhFWrXwgESAFKQOYCiAQIBAgBSkDkAp8IhBWrXwgECAFKQOoCiAFKQOgCiIcIBV8IhUgHFStfCAVIAUpA7gKIBsgBSkDsAoiG3wgG1StfHwiHCAVVK18fCIVIBBUrXx8IhAgEVStfHwiESATVK18fCITIBhUrXwgEiAXVq0gBSkDqAsgEiAtVK18fHwhEiADQQhrIgNBeEcNAAsCQAJAIBJCms3/y6O9xIAaVg0AIBJCms3/y6O9xIAaUgRAIBAhGyARIRkgEyEYIBUhFwwCCyATQtfZrprk9umNywBWDQACQAJAIBNC19mumuT26Y3LAFIEQCAQIRsgESEZIBMhGAwBCyARQr+llJzP8NK75ABWDQJC19mumuT26Y3LACEYIBFCv6WUnM/w0rvkAFIEQCAQIRsgESEZDAELIBBCpOzDtY/UtJjnAFYNAkK/pZScz/DSu+QAIRkgEEKk7MO1j9S0mOcAUgRAIBAhGwwBCyAVQv//z4rr///VHlYNAkKk7MO1j9S0mOcAIRsgFUL//8+K6///1R5RDQELQprN/8ujvcSAGiESIBUhFwwCC0L//8+K6///1R4hFyAcQqrV/v///7//uX9WDQBCms3/y6O9xIAaIRIMAQsgFUL//8+K6///1R59IhkgHEKr1f7///+//7l/VK0iG30hFyAQQqTsw7WP1LSY5wB9IhggFUL//8+K6///1R5UIBkgG1RyrSIVfSEbIBFCv6WUnM/w0rvkAH0iKSAQQqTsw7WP1LSY5wBUIBUgGFZyrSIQfSEZIBNC19mumuT26Y3LAH0iFSARQr+llJzP8NK75ABUIBAgKVZyrSIQfSEYIBIgE0LX2a6a5PbpjcsAVCAQIBVWcq19QprN/8ujvcSAGn0hEiAcQtWqgYCAgMCAxgB8IRwLIAFCADcDkAQgAUIANwMwIAEgKjcDKCABICg3AyAgASAwNwMYIAEgIDcDECABIB03AwggASAfNwMAIAFBuARqQgA3AwAgAUGwBGpCADcDACABQagEakIANwMAIAFBoARqQgA3AwAgAUGYBGpCADcDACABQThqQgA3AwAgAUFAa0IANwMAIAFByABqQgA3AwAgAUHQAGpCADcDACABQdgAakIANwMAIAFC/f+LgICAwIT2ADcDuAEgAUKCgLCgvIGA+ms3A7ABIAFCurGdnvWKpqTfADcDqAEgAULFrsmCt4qW5/cANwOgASABQu3Y25L60saD3AA3A5gBIAFCk8mD1L/Yl/sVNwOQASABICU3A4gBIAEgITcDgAEgASAaNwN4IAEgIzcDcCABICs3A2ggASAUNwNgQQAiAkUEQCABQcABakEAQeAA/AsACyABQgA3A9ACIAEgHjcDyAIgASAiNwPAAiABICY3A7gCIAEgLDcDsAIgASAkNwOoAiABIBY3A6ACIAFB2AJqQgA3AwAgAUHgAmpCADcDACABQegCakIANwMAIAFB8AJqQgA3AwAgAUH4AmpCADcDACABIBw3A6gDIAEgFzcDoAMgASAbNwOYAyABIBk3A5ADIAEgGDcDiAMgASASNwOAAyACDQQgAUGwA2pBAEHgAPwLAAwEC0EIQcAEEP8EAAsgE0LX2a6a5PbpjcsAVg0AAkAgE0LX2a6a5PbpjcsAUgRAIB8hFyAQIRQgESEZIBMhGAwBCyARQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEYIBFCv6WUnM/w0rvkAFIEQCAfIRcgECEUIBEhGQwBCyAQQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEZIBBCpOzDtY/UtJjnAFIEQCAfIRcgECEUDAELIB9C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCAfQv//z4rr///VHlIEQCAfIRcMAQtC///Piuv//9UeIRcgHEKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyAfQv//z4rr///VHn0iFCAcQqvV/v///7//uX9UrSIVfSEXIBBCpOzDtY/UtJjnAH0iGSAfQv//z4rr///VHlQgFCAVVHKtIhV9IRQgEUK/pZScz/DSu+QAfSIbIBBCpOzDtY/UtJjnAFQgFSAZVnKtIhB9IRkgE0LX2a6a5PbpjcsAfSIVIBFCv6WUnM/w0rvkAFQgECAbVnKtIhB9IRggEiATQtfZrprk9umNywBUIBAgFVZyrX1Cms3/y6O9xIAafSESIBxC1aqBgICAwIDGAHwhHAtCms3/y6O9xIAaIRAgGCAafCIVIBpUIBUgGSAhfCIZICFUIBkgFCAWfCITIBZUIBMgEyAXICN8IhEgI1QgESARIBwgJHwiHiAkVK18IhFWcq18IhNWcq18IhQgGVRyrXwiFiAVVHKtIA6tIA2tQiCGhCASfHwiJSESAkACQAJAICVCms3/y6O9xIAaUg0AQtfZrprk9umNywAhECAWIhJC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIRAgFCISQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEQIBMiEkKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEQIBEiEkL//8+K6///1R5SDQBCq9X+////v/+5fyEQIB4iEkKr1f7///+//7l/UQ0BCyAQIBJYDQAgESEVIBMhGyAUIRcgFiEZDAELIBFC///Piuv//9UefSIQIB5Cq9X+////v/+5f1StIhJ9IRUgE0Kk7MO1j9S0mOcAfSIXIBFC///Piuv//9UeVCAQIBJUcq0iEH0hGyAUQr+llJzP8NK75AB9IhEgE0Kk7MO1j9S0mOcAVCAQIBdWcq0iEH0hFyAWQtfZrprk9umNywB9IhIgFEK/pZScz/DSu+QAVCAQIBFWcq0iEH0hGSAlIBZC19mumuT26Y3LAFQgECASVnKtfUKazf/Lo73EgBp9ISUgHkLVqoGAgIDAgMYAfCEeC0EoIQJCACEqQgAhFEIAIRBCACERQgAhE0IAIR8DQCAFQbAHaiACIARqKQMAIhJCACAeQgAQyQMgBUHAB2ogEkIAIBVCABDJAyAFQdAHaiASQgAgG0IAEMkDIAVB4AdqIBJCACAXQgAQyQMgBUHwB2ogEkIAIBlCABDJAyAFQYAIaiASQgAgJUIAEMkDIAVBoAdqIAUpA7AHIiEgKnwiFkIAQgBC/f/z/8////mJfxDJAyAFQZAHaiAFKQOoByISQgBCq9X+////v/+5f0IAEMkDIAVBgAdqIBJCAEL//8+K6///1R5CABDJAyAFQfAGaiASQgBCpOzDtY/UtJjnAEIAEMkDIAVB4AZqIBJCAEK/pZScz/DSu+QAQgAQyQMgBUHQBmogEkIAQtfZrprk9umNywBCABDJAyAFQcAGaiASQgBCms3/y6O9xIAaQgAQyQMgBSkDyAYgBSkDgAgiGCAffCISIAUpA/gHIAUpA/AHIhogE3wiEyAaVK18IBMgEyAFKQPoByAFKQPgByIaIBF8IhEgGlStfCARIBEgBSkD2AcgBSkD0AciGiAQfCIQIBpUrXwgECAQIAUpA8gHIAUpA8AHIhogFHwiFCAaVK18IBQgFCAFKQO4ByAWICFUrXx8IhRWrXx8IhBWrXx8IhFWrXx8IhNWrXx8IiEgBSkDwAZ8IhogIVStfCAaIAUpA9gGIBMgEyAFKQPQBnwiE1atfCATIAUpA+gGIBEgESAFKQPgBnwiEVatfCARIAUpA/gGIBAgECAFKQPwBnwiEFatfCAQIAUpA4gHIAUpA4AHIiMgFHwiFCAjVK18IBQgBSkDmAcgFiAFKQOQByIWfCAWVK18fCIqIBRUrXx8IhQgEFStfHwiECARVK18fCIRIBNUrXx8IhMgGlStfCASICFWrSAFKQOICCASIBhUrXx8fCEfIAJBCGsiAkF4Rw0ACwJAAkAgH0Kazf/Lo73EgBpWDQAgH0Kazf/Lo73EgBpSBEAgFCEjIBAhISARISsgEyEtDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAUISMgECEhIBEhKyATIS0MAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhLSARQr+llJzP8NK75ABSBEAgFCEjIBAhISARISsMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhKyAQQqTsw7WP1LSY5wBSBEAgFCEjIBAhIQwBCyAUQv//z4rr///VHlYNAUKk7MO1j9S0mOcAISEgFEL//8+K6///1R5SBEAgFCEjDAELQv//z4rr///VHiEjICpCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIR8MAQsgFEL//8+K6///1R59IhIgKkKr1f7///+//7l/VK0iFX0hIyAQQqTsw7WP1LSY5wB9IhcgFEL//8+K6///1R5UIBIgFVRyrSISfSEhIBFCv6WUnM/w0rvkAH0iFCAQQqTsw7WP1LSY5wBUIBIgF1ZyrSIQfSErIBNC19mumuT26Y3LAH0iEiARQr+llJzP8NK75ABUIBAgFFZyrSIQfSEtIB8gE0LX2a6a5PbpjcsAVCAQIBJWcq19QprN/8ujvcSAGn0hHyAqQtWqgYCAgMCAxgB8ISoLQriq9YCAgICsECEeIAVCuKr1gICAgKwQNwPIEEKYgIDZsI6A8PQAIRUgBUKYgIDZsI6A8PQANwPAEEKVx62Zs5Xmm4d/IRsgBUKVx62Zs5Xmm4d/NwO4EEK0nIbSxMmC//YAIRcgBUK0nIbSxMmC//YANwOwEEL1q/LvjauWvy4hGSAFQvWr8u+Nq5a/LjcDqBBC9vWi4MPv9dAPISQgBUL29aLgw+/10A83A6AQIAVBoBBqQdizwgBBMBDxAwRAQqTX3Ovfzc6vCiEkQuGtvKrWy9POHCEZQoqJjsqKp9C8bSEXQo6llpzcvs78XyEbQvOqif///7/TqX8hHkLn/8+xuvH/5al/IRULQSghAkIAIRxCACEUQgAhEEIAIRFCACETQgAhEgNAIAVB4AVqIAVB8BZqIAJqKQMAIhZCACAeQgAQyQMgBUHwBWogFkIAIBVCABDJAyAFQYAGaiAWQgAgG0IAEMkDIAVBkAZqIBZCACAXQgAQyQMgBUGgBmogFkIAIBlCABDJAyAFQbAGaiAWQgAgJEIAEMkDIAVB0AVqIAUpA+AFIhggHHwiGkIAQgBC/f/z/8////mJfxDJAyAFQcAFaiAFKQPYBSIWQgBCq9X+////v/+5f0IAEMkDIAVBsAVqIBZCAEL//8+K6///1R5CABDJAyAFQaAFaiAWQgBCpOzDtY/UtJjnAEIAEMkDIAVBkAVqIBZCAEK/pZScz/DSu+QAQgAQyQMgBUGABWogFkIAQtfZrprk9umNywBCABDJAyAFQfAEaiAWQgBCms3/y6O9xIAaQgAQyQMgBSkD+AQgBSkDsAYiIiASfCISIAUpA6gGIAUpA6AGIhYgE3wiEyAWVK18IBMgEyAFKQOYBiAFKQOQBiIWIBF8IhEgFlStfCARIBEgBSkDiAYgBSkDgAYiFiAQfCIQIBZUrXwgECAQIAUpA/gFIAUpA/AFIhYgFHwiFCAWVK18IBQgFCAFKQPoBSAYIBpWrXx8IhRWrXx8IhBWrXx8IhFWrXx8IhNWrXx8IhYgBSkD8AR8IhggFlStfCAYIAUpA4gFIBMgEyAFKQOABXwiE1atfCATIAUpA5gFIBEgESAFKQOQBXwiEVatfCARIAUpA6gFIBAgECAFKQOgBXwiEFatfCAQIAUpA7gFIAUpA7AFIiYgFHwiFCAmVK18IBQgBSkDyAUgGiAFKQPABSIafCAaVK18fCIcIBRUrXx8IhQgEFStfHwiECARVK18fCIRIBNUrXx8IhMgGFStfCASIBZWrSAFKQO4BiASICJUrXx8fCESIAJBCGsiAkF4Rw0ACwJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgFCEXIBAhFiARIRkgEyEYDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAUIRcgECEWIBEhGSATIRgMAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGCARQr+llJzP8NK75ABSBEAgFCEXIBAhFiARIRkMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhGSAQQqTsw7WP1LSY5wBSBEAgFCEXIBAhFgwBCyAUQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRYgFEL//8+K6///1R5SBEAgFCEXDAELQv//z4rr///VHiEXIBxCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgFEL//8+K6///1R59IhUgHEKr1f7///+//7l/VK0iFn0hFyAQQqTsw7WP1LSY5wB9IhkgFEL//8+K6///1R5UIBUgFlRyrSIUfSEWIBFCv6WUnM/w0rvkAH0iFSAQQqTsw7WP1LSY5wBUIBQgGVZyrSIQfSEZIBNC19mumuT26Y3LAH0iFCARQr+llJzP8NK75ABUIBAgFVZyrSIQfSEYIBIgE0LX2a6a5PbpjcsAVCAQIBRWcq19QprN/8ujvcSAGn0hEiAcQtWqgYCAgMCAxgB8IRwLQprN/8ujvcSAGiEQIBggKHwiFSAoVCAVIBkgHXwiFCAdVCAUIBQgFiAgfCITICBUIBMgEyAXICd8IhEgJ1QgESARIBwgKXwiGyApVK18IhFWcq18IhNWcq18IhRWcq18IhYgFVRyrSAHrSAGrUIghoQgEnx8IhUhEgJAAkACQCAVQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIRAgFiISQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEQIBQiEkK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhECATIhJCpOzDtY/UtJjnAFINAEL//8+K6///1R4hECARIhJC///Piuv//9UeUg0AQqvV/v///7//uX8hECAbIhJCq9X+////v/+5f1ENAQsgECASWA0AIBEhFyATIRkgFCEkIBYhEgwBCyARQv//z4rr///VHn0iECAbQqvV/v///7//uX9UrSISfSEXIBNCpOzDtY/UtJjnAH0iGiARQv//z4rr///VHlQgECASVHKtIhB9IRkgFEK/pZScz/DSu+QAfSIRIBNCpOzDtY/UtJjnAFQgECAaVnKtIhB9ISQgFkLX2a6a5PbpjcsAfSITIBRCv6WUnM/w0rvkAFQgECARVnKtIhB9IRIgFSAWQtfZrprk9umNywBUIBAgE1ZyrX1Cms3/y6O9xIAafSEVIBtC1aqBgICAwIDGAHwhGwtBKCECQgAhJUIAIRZCACEQQgAhEUIAIRNCACEUA0AgBUGQBGogAiADaikDACIaQgAgG0IAEMkDIAVBoARqIBpCACAXQgAQyQMgBUGwBGogGkIAIBlCABDJAyAFQcAEaiAaQgAgJEIAEMkDIAVB0ARqIBpCACASQgAQyQMgBUHgBGogGkIAIBVCABDJAyAFQYAEaiAFKQOQBCIgICV8IhhCAEIAQv3/8//P///5iX8QyQMgBUHwA2ogBSkDiAQiGkIAQqvV/v///7//uX9CABDJAyAFQeADaiAaQgBC///Piuv//9UeQgAQyQMgBUHQA2ogGkIAQqTsw7WP1LSY5wBCABDJAyAFQcADaiAaQgBCv6WUnM/w0rvkAEIAEMkDIAVBsANqIBpCAELX2a6a5PbpjcsAQgAQyQMgBUGgA2ogGkIAQprN/8ujvcSAGkIAEMkDIAUpA6gDIAUpA+AEIh0gFHwiFCAFKQPYBCAFKQPQBCIaIBN8IhMgGlStfCATIBMgBSkDyAQgBSkDwAQiGiARfCIRIBpUrXwgESARIAUpA7gEIAUpA7AEIhogEHwiECAaVK18IBAgECAFKQOoBCAFKQOgBCIaIBZ8IhYgGlStfCAWIBYgBSkDmAQgGCAgVK18fCIWVq18fCIQVq18fCIRVq18fCITVq18fCIaIAUpA6ADfCIgIBpUrXwgICAFKQO4AyATIBMgBSkDsAN8IhNWrXwgEyAFKQPIAyARIBEgBSkDwAN8IhFWrXwgESAFKQPYAyAQIBAgBSkD0AN8IhBWrXwgECAFKQPoAyAFKQPgAyIiIBZ8IhYgIlStfCAWIAUpA/gDIBggBSkD8AMiGHwgGFStfHwiJSAWVK18fCIWIBBUrXx8IhAgEVStfHwiESATVK18fCITICBUrXwgFCAaVq0gBSkD6AQgFCAdVK18fHwhFCACQQhrIgJBeEcNAAsCQAJAIBRCms3/y6O9xIAaVg0AIBRCms3/y6O9xIAaUgRAIBYhGiAQISIgESEpIBMhLgwCCyATQtfZrprk9umNywBWDQACQCATQtfZrprk9umNywBSBEAgFiEaIBAhIiARISkgEyEuDAELIBFCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIS4gEUK/pZScz/DSu+QAUgRAIBYhGiAQISIgESEpDAELIBBCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAISkgEEKk7MO1j9S0mOcAUgRAIBYhGiAQISIMAQsgFkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEiIBZC///Piuv//9UeUgRAIBYhGgwBC0L//8+K6///1R4hGiAlQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEUDAELIBZC///Piuv//9UefSISICVCq9X+////v/+5f1StIhV9IRogEEKk7MO1j9S0mOcAfSIXIBZC///Piuv//9UeVCASIBVUcq0iEn0hIiARQr+llJzP8NK75AB9IhUgEEKk7MO1j9S0mOcAVCASIBdWcq0iEH0hKSATQtfZrprk9umNywB9IhIgEUK/pZScz/DSu+QAVCAQIBVWcq0iEH0hLiAUIBNC19mumuT26Y3LAFQgECASVnKtfUKazf/Lo73EgBp9IRQgJULVqoGAgIDAgMYAfCElC0EoIQIgBSkDwBYhGyAFKQPIFiEYIAUpA9AWISAgBSkD2BYhHSAFKQPgFiEmIAUpA+gWIShCACEeQgAhFUIAIRBCACERQgAhE0IAIRYDQCAFQcACaiACIARqKQMAIhJCACAoQgAQyQMgBUHQAmogEkIAICZCABDJAyAFQeACaiASQgAgHUIAEMkDIAVB8AJqIBJCACAgQgAQyQMgBUGAA2ogEkIAIBhCABDJAyAFQZADaiASQgAgG0IAEMkDIAVBsAJqIAUpA8ACIhkgHnwiF0IAQgBC/f/z/8////mJfxDJAyAFQaACaiAFKQO4AiISQgBCq9X+////v/+5f0IAEMkDIAVBkAJqIBJCAEL//8+K6///1R5CABDJAyAFQYACaiASQgBCpOzDtY/UtJjnAEIAEMkDIAVB8AFqIBJCAEK/pZScz/DSu+QAQgAQyQMgBUHgAWogEkIAQtfZrprk9umNywBCABDJAyAFQdABaiASQgBCms3/y6O9xIAaQgAQyQMgBSkD2AEgBSkDkAMiLCAWfCISIAUpA4gDIAUpA4ADIhYgE3wiEyAWVK18IBMgEyAFKQP4AiAFKQPwAiIWIBF8IhEgFlStfCARIBEgBSkD6AIgBSkD4AIiFiAQfCIQIBZUrXwgECAQIAUpA9gCIAUpA9ACIhYgFXwiFSAWVK18IBUgFSAFKQPIAiAXIBlUrXx8IhVWrXx8IhBWrXx8IhFWrXx8IhNWrXx8IhYgBSkD0AF8IhkgFlStfCAZIAUpA+gBIBMgEyAFKQPgAXwiE1atfCATIAUpA/gBIBEgESAFKQPwAXwiEVatfCARIAUpA4gCIBAgECAFKQOAAnwiEFatfCAQIAUpA5gCIAUpA5ACIicgFXwiFSAnVK18IBUgBSkDqAIgFyAFKQOgAiIXfCAXVK18fCIeIBVUrXx8IhUgEFStfHwiECARVK18fCIRIBNUrXx8IhMgGVStfCASIBZWrSAFKQOYAyASICxUrXx8fCEWIAJBCGsiAkF4Rw0ACwJAAkAgFkKazf/Lo73EgBpWDQAgFkKazf/Lo73EgBpSBEAgFSEdIBAhICARIScgEyEvDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAVIR0gECEgIBEhJyATIS8MAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhLyARQr+llJzP8NK75ABSBEAgFSEdIBAhICARIScMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhJyAQQqTsw7WP1LSY5wBSBEAgFSEdIBAhIAwBCyAVQv//z4rr///VHlYNAUKk7MO1j9S0mOcAISAgFUL//8+K6///1R5SBEAgFSEdDAELQv//z4rr///VHiEdIB5CqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRYMAQsgFUL//8+K6///1R59IhIgHkKr1f7///+//7l/VK0iF30hHSAQQqTsw7WP1LSY5wB9IhkgFUL//8+K6///1R5UIBIgF1RyrSISfSEgIBFCv6WUnM/w0rvkAH0iFSAQQqTsw7WP1LSY5wBUIBIgGVZyrSIQfSEnIBNC19mumuT26Y3LAH0iEiARQr+llJzP8NK75ABUIBAgFVZyrSIQfSEvIBYgE0LX2a6a5PbpjcsAVCAQIBJWcq19QprN/8ujvcSAGn0hFiAeQtWqgYCAgMCAxgB8IR4LQSghBCAFKQPwFiEYIAUpA/gWISYgBSkDgBchKCAFKQOIFyEsIAUpA5AXITAgBSkDmBchJEIAIRxCACEVQgAhEEIAIRFCACETQgAhEgNAIAVB8ABqIAMgBGopAwAiF0IAICRCABDJAyAFQYABaiAXQgAgMEIAEMkDIAVBkAFqIBdCACAsQgAQyQMgBUGgAWogF0IAIChCABDJAyAFQbABaiAXQgAgJkIAEMkDIAVBwAFqIBdCACAYQgAQyQMgBUHgAGogBSkDcCIbIBx8IhlCAEIAQv3/8//P///5iX8QyQMgBUHQAGogBSkDaCIXQgBCq9X+////v/+5f0IAEMkDIAVBQGsgF0IAQv//z4rr///VHkIAEMkDIAVBMGogF0IAQqTsw7WP1LSY5wBCABDJAyAFQSBqIBdCAEK/pZScz/DSu+QAQgAQyQMgBUEQaiAXQgBC19mumuT26Y3LAEIAEMkDIAUgF0IAQprN/8ujvcSAGkIAEMkDIAUpAwggBSkDwAEiMSASfCISIAUpA7gBIAUpA7ABIhcgE3wiEyAXVK18IBMgEyAFKQOoASAFKQOgASIXIBF8IhEgF1StfCARIBEgBSkDmAEgBSkDkAEiFyAQfCIQIBdUrXwgECAQIAUpA4gBIAUpA4ABIhcgFXwiFSAXVK18IBUgFSAFKQN4IBkgG1StfHwiFVatfHwiEFatfHwiEVatfHwiE1atfHwiFyAFKQMAfCIbIBdUrXwgGyAFKQMYIBMgEyAFKQMQfCITVq18IBMgBSkDKCARIBEgBSkDIHwiEVatfCARIAUpAzggECAQIAUpAzB8IhBWrXwgECAFKQNIIAUpA0AiHCAVfCIVIBxUrXwgFSAFKQNYIBkgBSkDUCIZfCAZVK18fCIcIBVUrXx8IhUgEFStfHwiECARVK18fCIRIBNUrXx8IhMgG1StfCASIBdWrSAFKQPIASASIDFUrXx8fCESIARBCGsiBEF4Rw0ACwJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgFSEXIBAhGyARIRkgEyEYDAILIBNC19mumuT26Y3LAFYNAAJAIBNC19mumuT26Y3LAFIEQCAVIRcgECEbIBEhGSATIRgMAQsgEUK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGCARQr+llJzP8NK75ABSBEAgFSEXIBAhGyARIRkMAQsgEEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhGSAQQqTsw7WP1LSY5wBSBEAgFSEXIBAhGwwBCyAVQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRsgFUL//8+K6///1R5SBEAgFSEXDAELQv//z4rr///VHiEXIBxCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgFUL//8+K6///1R59IhkgHEKr1f7///+//7l/VK0iG30hFyAQQqTsw7WP1LSY5wB9IhggFUL//8+K6///1R5UIBkgG1RyrSIVfSEbIBFCv6WUnM/w0rvkAH0iJiAQQqTsw7WP1LSY5wBUIBUgGFZyrSIQfSEZIBNC19mumuT26Y3LAH0iFSARQr+llJzP8NK75ABUIBAgJlZyrSIQfSEYIBIgE0LX2a6a5PbpjcsAVCAQIBVWcq19QprN/8ujvcSAGn0hEiAcQtWqgYCAgMCAxgB8IRwLIAFCADcDkAQgASAqNwNYIAEgIzcDUCABICE3A0ggASArNwNAIAEgLTcDOCABIB83AzAgAUL9/4uAgIDAhPYANwMoIAFCgoCwoLyBgPprNwMgIAFCurGdnvWKpqTfADcDGCABQsWuyYK3ipbn9wA3AxAgAULt2NuS+tLGg9wANwMIIAFCk8mD1L/Yl/sVNwMAIAFBuARqQgA3AwAgAUGwBGpCADcDACABQagEakIANwMAIAFBoARqQgA3AwAgAUGYBGpCADcDACABQYgBakIANwMAIAFBgAFqQgA3AwAgAUH4AGpCADcDACABQfAAakIANwMAIAFB6ABqQgA3AwAgAUIANwNgIAEgJTcDuAEgASAaNwOwASABICI3A6gBIAEgKTcDoAEgASAuNwOYASABIBQ3A5ABIAFBwAFqQQBBkAH8CwAgAUIANwOAAyABIB43A/gCIAEgHTcD8AIgASAgNwPoAiABICc3A+ACIAEgLzcD2AIgASAWNwPQAiABQYgDakIANwMAIAFBkANqQgA3AwAgAUGYA2pCADcDACABQaADakIANwMAIAFBqANqQgA3AwAgAUIANwPgAyABIBw3A9gDIAEgFzcD0AMgASAbNwPIAyABIBk3A8ADIAEgGDcDuAMgASASNwOwAyABQegDakIANwMAIAFB8ANqQgA3AwAgAUH4A2pCADcDACABQYAEakIANwMAIAFBiARqQgA3AwALQQwhBAJAAn8gAUGQBGpB+MPCAEEwEPEDBEBBCyEDQQwMAQsgAUHgA2pB+MPCAEEwEPEDBEBBCiEDQQsMAQsgAUGwA2pB+MPCAEEwEPEDBEBBCSEDQQoMAQsgAUGAA2pB+MPCAEEwEPEDBEBBCCEDQQkMAQsgAUHQAmpB+MPCAEEwEPEDBEBBByEDQQgMAQsgAUGgAmpB+MPCAEEwEPEDBEBBBiEDQQcMAQsgAUHwAWpB+MPCAEEwEPEDBEBBBSEDQQYMAQsgAUHAAWpB+MPCAEEwEPEDBEBBBCEDQQUMAQsgAUGQAWpB+MPCAEEwEPEDBEBBAyEDQQQMAQsgAUHgAGpB+MPCAEEwEPEDBEBBAiEDQQMMAQsgAUEwakH4w8IAQTAQ8QMEQEEBIQNBAgwBCyABQfjDwgBBMBDxAwRAQQAhA0EBDAELQdHOxQAtAAAaQTBBCBDWBCIERQ0BIARCADcDACAEQShqQgA3AwAgBEEgakIANwMAIARBGGpCADcDACAEQRBqQgA3AwAgBEEIakIANwMAIAFBwAQQ3wRBfyEDIAQhAUEBIQRBAQshAiAAIAM2AgwgACACNgIIIAAgATYCBCAAIAQ2AgAgBUGAGGokAA8LQQhBMBD/BAALQQhBwAQQ/wQAC0GAi8AAQSsgBUGgEGpBrIvAAEGkjcAAEMoDAAutjwECCX8sfiMAQfAgayIBJAAgAUHQIGpBqIPCAEHAABC3AiABQYAeaiABKQPoICIKQgBCifWrnLWLv5ZzQgAQyQMgAUHAHmogASkD4CAiC0IAQon1q5y1i7+Wc0IAEMkDIAFBgB9qIAEpA9ggIg1CAEKJ9auctYu/lnNCABDJAyABQcAfaiABKQPQICIOQgBCifWrnLWLv5ZzQgAQyQMgAUHwHWogASkDgB4iIEKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHgHWogDEIAQo2Vx8OW0trAl39CABDJAyABQZAdaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFBwBxqIAxCAEKpwMaJrs6TsjBCABDJAyABQZAeaiAKQgBC+4OUop2ixvO1f0IAEMkDIAFB0B5qIAtCAEL7g5SinaLG87V/QgAQyQMgAUGQH2ogDUIAQvuDlKKdosbztX9CABDJAyABQdAfaiAOQgBC+4OUop2ixvO1f0IAEMkDIAFB0B1qIAEpA+AdIhAgASkDiB4iEyABKQPAHnwiEnwiDyABKQP4HSAgIAEpA/AdIgx8IAxUrXx8IiAgASkDkB58IhhCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFBwB1qIAxCAEKNlcfDltLawJd/QgAQyQMgAUGwHWogDEIAQt2whYzotpGouH9CABDJAyABQaAdaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGgHmogCkIAQvb/hdLw38fVxwBCABDJAyABQeAeaiALQgBC9v+F0vDfx9XHAEIAEMkDIAFBoB9qIA1CAEL2/4XS8N/H1ccAQgAQyQMgAUHgH2ogDkIAQvb/hdLw38fVxwBCABDJAyABQYAdaiABKQOYHiAYICBUrXwiKiABKQPQHnwiFSABKQPIHiASIBNUrXwiISABKQOAH3wiEyABKQOQHXwiEiAPICBWrSABKQPoHSAPIBBUrXx8fCIffCIPIAEpA8AdfCIgIAEpA9gdIAEpA9AdIgwgGHwgDFStfHwiGCABKQOgHnwiEEKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHwHGogDEIAQo2Vx8OW0trAl39CABDJAyABQeAcaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFB0BxqIAxCAEKpwMaJrs6TsjBCABDJAyABQbAeaiAKQgBCn+rg1Zzup+wGQgAQyQMgAUHwHmogC0IAQp/q4NWc7qfsBkIAEMkDIAFBsB9qIA1CAEKf6uDVnO6n7AZCABDJAyABQfAfaiAOQgBCn+rg1Zzup+wGQgAQyQMgAUGwHGogASkDqB4gECAYVK18IhkgASkD4B58IgsgASkDiB8gEyAhVK18IiEgASkDwB98Ig0gASkDwBx8Ig4gEiAfVq0gASkDmB0gEiATVK18fHwiDCABKQOQH3wiEyAPIBVUrSABKQPYHiAVICpUrXx8fCIVIAEpA7AdfCISIBggIFStIAEpA8gdIA8gIFatfHx8Iip8Ig8gASkD8Bx8IiAgASkDiB0gASkDgB0iCiAQfCAKVK18fCIYIAEpA7AefCIQQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyABQaAcaiAKQgBCjZXHw5bS2sCXf0IAEMkDIAFBkBxqIApCAELdsIWM6LaRqLh/QgAQyQMgAUGAHGogCkIAQqnAxomuzpOyMEIAEMkDAkACQAJAIAEpA4gcIAEpA+gfIAEpA+AfIAwgDlStIAEpA8gcIA0gDlatfHwiDiABKQPIHyANICFUrXx8IgogDlSthCIOIAEpA9gfIAogCiABKQPQH3wiClatfCAKIAogEyAVVq0gASkDmB8gDCATVq18fHwiClatfHwiDSAOVK18IA0gDSABKQOoHSAKIAogASkDoB18IgpWrXwgCiAKIBIgKlatIAEpA7gdIBIgFVStfHx8IgpWrXx8Ig1WrXwgDSABKQOoHyAKIAogASkDoB98IgpWrXwgCiAKIAsgD1atIAEpA+geIAsgGVStfHx8IgpWrXx8IgsgDVStfCIVIAEpA/AffCINIAEpA9gcIAsgCyABKQPQHHwiC1atfCALIAEpA+gcIAogCiABKQPgHHwiClatfCAKIBggIFStIAEpA/gcIA8gIFatfHx8IgwgClStfHwiCiALVK18fCIOIAEpA7gfIAogCiABKQOwH3wiClatfCAKIAogASkD+B4gASkDuB4gECAYVK18Ig8gASkD8B58IgsgD1StfCALIAsgDHwiC1atfHwiClatfHwiDCABKQOAHHwiDyAMVK18IA8gASkDmBwgCiAKIAEpA5AcfCIKVq18IAogCiABKQOoHCALIAsgASkDoBx8IgtWrXwgCyABKQO4HCABKQOwHCIgIBB8ICBUrXx8Ii4gC1StfHwiClatfHwiCyAPVK18IAwgDlStIA0gDlatIAEpA/gfIA0gFVStfHx8fCIrQqnAxomuzpOyMFYNAAJAICtCqcDGia7Ok7IwUQRAIAtC3bCFjOi2kai4f1YNAiALQt2whYzotpGouH9RDQFCqcDGia7Ok7IwISsLIAshKiAKISAMAwsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hKiAKQo2Vx8OW0trAl39SIC5Cx/rzw+2Co5A8VHINAQsgCkLz6ri86a2lv+gAfCINIC5Cx/rzw+2Co5A8VK0iDn0hICALQqPP+vOXye7XxwB8IgwgCkKNlcfDltLawJd/VCANIA5Ucq0iCn0hKiArIAtC3bCFjOi2kai4f1QgCiAMVnKtfUKpwMaJrs6TsjB9ISsgLkLH+vPD7YKjkDx9IS4MAQtCqcDGia7Ok7IwISsgCiEgCyABQdAgakHog8IAQcAAELcCIAFBgBpqIAEpA+ggIgpCAEKJ9auctYu/lnNCABDJAyABQcAaaiABKQPgICILQgBCifWrnLWLv5ZzQgAQyQMgAUGAG2ogASkD2CAiDUIAQon1q5y1i7+Wc0IAEMkDIAFBwBtqIAEpA9AgIg5CAEKJ9auctYu/lnNCABDJAyABQfAZaiABKQOAGiIYQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQeAZaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFBkBlqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUHAGGogDEIAQqnAxomuzpOyMEIAEMkDIAFBkBpqIApCAEL7g5SinaLG87V/QgAQyQMgAUHQGmogC0IAQvuDlKKdosbztX9CABDJAyABQZAbaiANQgBC+4OUop2ixvO1f0IAEMkDIAFB0BtqIA5CAEL7g5SinaLG87V/QgAQyQMgAUHQGWogASkD4BkiISABKQOIGiISIAEpA8AafCIQfCIPIAEpA/gZIBggASkD8BkiDHwgDFStfHwiGCABKQOQGnwiFUKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHAGWogDEIAQo2Vx8OW0trAl39CABDJAyABQbAZaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFBoBlqIAxCAEKpwMaJrs6TsjBCABDJAyABQaAaaiAKQgBC9v+F0vDfx9XHAEIAEMkDIAFB4BpqIAtCAEL2/4XS8N/H1ccAQgAQyQMgAUGgG2ogDUIAQvb/hdLw38fVxwBCABDJAyABQeAbaiAOQgBC9v+F0vDfx9XHAEIAEMkDIAFBgBlqIAEpA5gaIBUgGFStfCIfIAEpA9AafCITIAEpA8gaIBAgElStfCIZIAEpA4AbfCISIAEpA5AZfCIQIA8gGFatIAEpA+gZIA8gIVStfHx8Ihp8Ig8gASkDwBl8IhggASkD2BkgASkD0BkiDCAVfCAMVK18fCIVIAEpA6AafCIhQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQfAYaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFB4BhqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUHQGGogDEIAQqnAxomuzpOyMEIAEMkDIAFBsBpqIApCAEKf6uDVnO6n7AZCABDJAyABQfAaaiALQgBCn+rg1Zzup+wGQgAQyQMgAUGwG2ogDUIAQp/q4NWc7qfsBkIAEMkDIAFB8BtqIA5CAEKf6uDVnO6n7AZCABDJAyABQbAYaiABKQOoGiAVICFWrXwiFCABKQPgGnwiCyABKQOIGyASIBlUrXwiGSABKQPAG3wiDSABKQPAGHwiDiAQIBpWrSABKQOYGSAQIBJUrXx8fCIMIAEpA5AbfCISIA8gE1StIAEpA9gaIBMgH1StfHx8IhMgASkDsBl8IhAgFSAYVK0gASkDyBkgDyAYVq18fHwiH3wiDyABKQPwGHwiGCABKQOIGSABKQOAGSIKICF8IApUrXx8IhUgASkDsBp8IiFCiceZpK7wgemHf34iCkIAQsf688PtgqOQPEIAEMkDIAFBoBhqIApCAEKNlcfDltLawJd/QgAQyQMgAUGQGGogCkIAQt2whYzotpGouH9CABDJAyABQYAYaiAKQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgASkDiBggASkD6BsgASkD4BsgDCAOVK0gASkDyBggDSAOVq18fCIOIAEpA8gbIA0gGVStfHwiCiAOVK2EIg4gASkD2BsgCiAKIAEpA9AbfCIKVq18IAogCiASIBNWrSABKQOYGyAMIBJWrXx8fCIKVq18fCINIA5UrXwgDSANIAEpA6gZIAogCiABKQOgGXwiClatfCAKIAogECAfVq0gASkDuBkgECATVK18fHwiClatfHwiDVatfCANIAEpA6gbIAogCiABKQOgG3wiClatfCAKIAogCyAPVq0gASkD6BogCyAUVK18fHwiClatfHwiCyANVK18IhMgASkD8Bt8Ig0gASkD2BggCyALIAEpA9AYfCILVq18IAsgASkD6BggCiAKIAEpA+AYfCIKVq18IAogFSAYVK0gASkD+BggDyAYVq18fHwiDCAKVK18fCIKIAtUrXx8Ig4gASkDuBsgCiAKIAEpA7AbfCIKVq18IAogCiABKQP4GiABKQO4GiAVICFWrXwiDyABKQPwGnwiCyAPVK18IAsgCyAMfCILVq18fCIKVq18fCIMIAEpA4AYfCIPIAxUrXwgDyABKQOYGCAKIAogASkDkBh8IgpWrXwgCiAKIAEpA6gYIAsgCyABKQOgGHwiC1atfCALIAEpA7gYIAEpA7AYIhggIXwgGFStfHwiLyALVK18fCIKVq18fCILIA9UrXwgDCAOVK0gDSAOVq0gASkD+BsgDSATVK18fHx8IixCqcDGia7Ok7IwVg0AAkAgLEKpwMaJrs6TsjBRBEAgC0LdsIWM6LaRqLh/Vg0CIAtC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhLAsgCyEhIAohGAwDCyAKQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEhIApCjZXHw5bS2sCXf1IgL0LH+vPD7YKjkDxUcg0BCyAKQvPquLzpraW/6AB8Ig0gL0LH+vPD7YKjkDxUrSIOfSEYIAtCo8/685fJ7tfHAHwiDCAKQo2Vx8OW0trAl39UIA0gDlRyrSIKfSEhICwgC0LdsIWM6LaRqLh/VCAKIAxWcq19QqnAxomuzpOyMH0hLCAvQsf688PtgqOQPH0hLwwBC0KpwMaJrs6TsjAhLCAKIRgLIAFB0CBqQaiEwgBBARC3AiABQYAWaiABKQPoICIKQgBCifWrnLWLv5ZzQgAQyQMgAUHAFmogASkD4CAiC0IAQon1q5y1i7+Wc0IAEMkDIAFBgBdqIAEpA9ggIg1CAEKJ9auctYu/lnNCABDJAyABQcAXaiABKQPQICIOQgBCifWrnLWLv5ZzQgAQyQMgAUHwFWogASkDgBYiFUKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHgFWogDEIAQo2Vx8OW0trAl39CABDJAyABQZAVaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFBwBRqIAxCAEKpwMaJrs6TsjBCABDJAyABQZAWaiAKQgBC+4OUop2ixvO1f0IAEMkDIAFB0BZqIAtCAEL7g5SinaLG87V/QgAQyQMgAUGQF2ogDUIAQvuDlKKdosbztX9CABDJAyABQdAXaiAOQgBC+4OUop2ixvO1f0IAEMkDIAFB0BVqIAEpA+AVIhkgASkDiBYiECABKQPAFnwiH3wiDyABKQP4FSAVIAEpA/AVIgx8IAxUrXx8IhUgASkDkBZ8IhNCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFBwBVqIAxCAEKNlcfDltLawJd/QgAQyQMgAUGwFWogDEIAQt2whYzotpGouH9CABDJAyABQaAVaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGgFmogCkIAQvb/hdLw38fVxwBCABDJAyABQeAWaiALQgBC9v+F0vDfx9XHAEIAEMkDIAFBoBdqIA1CAEL2/4XS8N/H1ccAQgAQyQMgAUHgF2ogDkIAQvb/hdLw38fVxwBCABDJAyABQYAVaiABKQOYFiATIBVUrXwiGiABKQPQFnwiEiABKQPIFiAQIB9WrXwiFCABKQOAF3wiECABKQOQFXwiHyAPIBVWrSABKQPoFSAPIBlUrXx8fCInfCIPIAEpA8AVfCIVIAEpA9gVIAEpA9AVIgwgE3wgDFStfHwiEyABKQOgFnwiGUKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHwFGogDEIAQo2Vx8OW0trAl39CABDJAyABQeAUaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFB0BRqIAxCAEKpwMaJrs6TsjBCABDJAyABQbAWaiAKQgBCn+rg1Zzup+wGQgAQyQMgAUHwFmogC0IAQp/q4NWc7qfsBkIAEMkDIAFBsBdqIA1CAEKf6uDVnO6n7AZCABDJAyABQfAXaiAOQgBCn+rg1Zzup+wGQgAQyQMgAUGwFGogASkDqBYgEyAZVq18IiQgASkD4BZ8IgsgASkDiBcgECAUVK18IhQgASkDwBd8Ig0gASkDwBR8Ig4gHyAnVq0gASkDmBUgECAfVq18fHwiDCABKQOQF3wiECAPIBJUrSABKQPYFiASIBpUrXx8fCISIAEpA7AVfCIfIBMgFVStIAEpA8gVIA8gFVatfHx8Ihp8Ig8gASkD8BR8IhUgASkDiBUgASkDgBUiCiAZfCAKVK18fCITIAEpA7AWfCIZQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyABQaAUaiAKQgBCjZXHw5bS2sCXf0IAEMkDIAFBkBRqIApCAELdsIWM6LaRqLh/QgAQyQMgAUGAFGogCkIAQqnAxomuzpOyMEIAEMkDAkACQAJAIAEpA4gUIAEpA+gXIAEpA+AXIAwgDlStIAEpA8gUIA0gDlatfHwiDiABKQPIFyANIBRUrXx8IgogDlSthCIOIAEpA9gXIAogCiABKQPQF3wiClatfCAKIAogECASVq0gASkDmBcgDCAQVq18fHwiClatfHwiDSAOVK18IA0gDSABKQOoFSAKIAogASkDoBV8IgpWrXwgCiAKIBogH1StIAEpA7gVIBIgH1atfHx8IgpWrXx8Ig1WrXwgDSABKQOoFyAKIAogASkDoBd8IgpWrXwgCiAKIAsgD1atIAEpA+gWIAsgJFStfHx8IgpWrXx8IgsgDVStfCISIAEpA/AXfCINIAEpA9gUIAsgCyABKQPQFHwiC1atfCALIAEpA+gUIAogCiABKQPgFHwiClatfCAKIBMgFVStIAEpA/gUIA8gFVatfHx8IgwgClStfHwiCiALVK18fCIOIAEpA7gXIAogCiABKQOwF3wiClatfCAKIAogASkD+BYgASkDuBYgEyAZVq18Ig8gASkD8BZ8IgsgD1StfCALIAsgDHwiC1atfHwiClatfHwiDCABKQOAFHwiDyAMVK18IA8gASkDmBQgCiAKIAEpA5AUfCIKVq18IAogCiABKQOoFCALIAsgASkDoBR8IgtWrXwgCyABKQO4FCABKQOwFCIVIBl8IBVUrXx8IjAgC1StfHwiClatfHwiCyAPVK18IAwgDlStIA0gDlatIAEpA/gXIA0gElStfHx8fCInQqnAxomuzpOyMFYNAAJAICdCqcDGia7Ok7IwUQRAIAtC3bCFjOi2kai4f1YNAiALQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIScLIAshHyAKIRUMAwsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hHyAKQo2Vx8OW0trAl39SIDBCx/rzw+2Co5A8VHINAQsgCkLz6ri86a2lv+gAfCINIDBCx/rzw+2Co5A8VK0iDn0hFSALQqPP+vOXye7XxwB8IgwgCkKNlcfDltLawJd/VCANIA5Ucq0iCn0hHyAnIAtC3bCFjOi2kai4f1QgCiAMVnKtfUKpwMaJrs6TsjB9IScgMELH+vPD7YKjkDx9ITAMAQtCqcDGia7Ok7IwIScgCiEVCyABQdAgakGphMIAQQEQtwIgAUGAEmogASkD6CAiCkIAQon1q5y1i7+Wc0IAEMkDIAFBwBJqIAEpA+AgIgtCAEKJ9auctYu/lnNCABDJAyABQYATaiABKQPYICINQgBCifWrnLWLv5ZzQgAQyQMgAUHAE2ogASkD0CAiDkIAQon1q5y1i7+Wc0IAEMkDIAFB8BFqIAEpA4ASIhNCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFB4BFqIAxCAEKNlcfDltLawJd/QgAQyQMgAUGQEWogDEIAQt2whYzotpGouH9CABDJAyABQcAQaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGQEmogCkIAQvuDlKKdosbztX9CABDJAyABQdASaiALQgBC+4OUop2ixvO1f0IAEMkDIAFBkBNqIA1CAEL7g5SinaLG87V/QgAQyQMgAUHQE2ogDkIAQvuDlKKdosbztX9CABDJAyABQdARaiABKQPgESIUIAEpA4gSIhkgASkDwBJ8Ihp8Ig8gASkD+BEgEyABKQPwESIMfCAMVK18fCITIAEpA5ASfCISQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQcARaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFBsBFqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUGgEWogDEIAQqnAxomuzpOyMEIAEMkDIAFBoBJqIApCAEL2/4XS8N/H1ccAQgAQyQMgAUHgEmogC0IAQvb/hdLw38fVxwBCABDJAyABQaATaiANQgBC9v+F0vDfx9XHAEIAEMkDIAFB4BNqIA5CAEL2/4XS8N/H1ccAQgAQyQMgAUGAEWogASkDmBIgEiATVK18IiQgASkD0BJ8IhAgASkDyBIgGSAaVq18Ih4gASkDgBN8IhkgASkDkBF8IhogDyATVq0gASkD6BEgDyAUVK18fHwiG3wiDyABKQPAEXwiEyABKQPYESABKQPQESIMIBJ8IAxUrXx8IhIgASkDoBJ8IhRCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFB8BBqIAxCAEKNlcfDltLawJd/QgAQyQMgAUHgEGogDEIAQt2whYzotpGouH9CABDJAyABQdAQaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGwEmogCkIAQp/q4NWc7qfsBkIAEMkDIAFB8BJqIAtCAEKf6uDVnO6n7AZCABDJAyABQbATaiANQgBCn+rg1Zzup+wGQgAQyQMgAUHwE2ogDkIAQp/q4NWc7qfsBkIAEMkDIAFBsBBqIAEpA6gSIBIgFFatfCIWIAEpA+ASfCILIAEpA4gTIBkgHlStfCIeIAEpA8ATfCINIAEpA8AQfCIOIBogG1atIAEpA5gRIBkgGlatfHx8IgwgASkDkBN8IhkgDyAQVK0gASkD2BIgECAkVK18fHwiECABKQOwEXwiGiASIBNUrSABKQPIESAPIBNWrXx8fCIkfCIPIAEpA/AQfCITIAEpA4gRIAEpA4ARIgogFHwgClStfHwiEiABKQOwEnwiFEKJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgAUGgEGogCkIAQo2Vx8OW0trAl39CABDJAyABQZAQaiAKQgBC3bCFjOi2kai4f0IAEMkDIAFBgBBqIApCAEKpwMaJrs6TsjBCABDJAwJAAkACQCABKQOIECABKQPoEyABKQPgEyAMIA5UrSABKQPIECANIA5WrXx8Ig4gASkDyBMgDSAeVK18fCIKIA5UrYQiDiABKQPYEyAKIAogASkD0BN8IgpWrXwgCiAKIBAgGVStIAEpA5gTIAwgGVatfHx8IgpWrXx8Ig0gDlStfCANIA0gASkDqBEgCiAKIAEpA6ARfCIKVq18IAogCiAaICRWrSABKQO4ESAQIBpWrXx8fCIKVq18fCINVq18IA0gASkDqBMgCiAKIAEpA6ATfCIKVq18IAogCiALIA9WrSABKQPoEiALIBZUrXx8fCIKVq18fCILIA1UrXwiECABKQPwE3wiDSABKQPYECALIAsgASkD0BB8IgtWrXwgCyABKQPoECAKIAogASkD4BB8IgpWrXwgCiASIBNUrSABKQP4ECAPIBNWrXx8fCIMIApUrXx8IgogC1StfHwiDiABKQO4EyAKIAogASkDsBN8IgpWrXwgCiAKIAEpA/gSIAEpA7gSIBIgFFatfCIPIAEpA/ASfCILIA9UrXwgCyALIAx8IgtWrXx8IgpWrXx8IgwgASkDgBB8Ig8gDFStfCAPIAEpA5gQIAogCiABKQOQEHwiClatfCAKIAogASkDqBAgCyALIAEpA6AQfCILVq18IAsgASkDuBAgASkDsBAiEyAUfCATVK18fCIxIAtUrXx8IgpWrXx8IgsgD1StfCAMIA5UrSANIA5WrSABKQP4EyANIBBUrXx8fHwiJEKpwMaJrs6TsjBWDQACQCAkQqnAxomuzpOyMFEEQCALQt2whYzotpGouH9WDQIgC0LdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCEkCyALIRkgCiETDAMLIApCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IRkgCkKNlcfDltLawJd/UiAxQsf688PtgqOQPFRyDQELIApC8+q4vOmtpb/oAHwiDSAxQsf688PtgqOQPFStIg59IRMgC0Kjz/rzl8nu18cAfCIMIApCjZXHw5bS2sCXf1QgDSAOVHKtIgp9IRkgJCALQt2whYzotpGouH9UIAogDFZyrX1CqcDGia7Ok7IwfSEkIDFCx/rzw+2Co5A8fSExDAELQqnAxomuzpOyMCEkIAohEwsgAUHQIGpBqoTCAEHAABC3AiABQYAOaiABKQPoICIKQgBCifWrnLWLv5ZzQgAQyQMgAUHADmogASkD4CAiC0IAQon1q5y1i7+Wc0IAEMkDIAFBgA9qIAEpA9ggIg1CAEKJ9auctYu/lnNCABDJAyABQcAPaiABKQPQICIOQgBCifWrnLWLv5ZzQgAQyQMgAUHwDWogASkDgA4iEkKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHgDWogDEIAQo2Vx8OW0trAl39CABDJAyABQZANaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFBwAxqIAxCAEKpwMaJrs6TsjBCABDJAyABQZAOaiAKQgBC+4OUop2ixvO1f0IAEMkDIAFB0A5qIAtCAEL7g5SinaLG87V/QgAQyQMgAUGQD2ogDUIAQvuDlKKdosbztX9CABDJAyABQdAPaiAOQgBC+4OUop2ixvO1f0IAEMkDIAFB0A1qIAEpA+ANIhsgASkDiA4iFCABKQPADnwiHnwiDyABKQP4DSASIAEpA/ANIgx8IAxUrXx8IhIgASkDkA58IhBCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFBwA1qIAxCAEKNlcfDltLawJd/QgAQyQMgAUGwDWogDEIAQt2whYzotpGouH9CABDJAyABQaANaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGgDmogCkIAQvb/hdLw38fVxwBCABDJAyABQeAOaiALQgBC9v+F0vDfx9XHAEIAEMkDIAFBoA9qIA1CAEL2/4XS8N/H1ccAQgAQyQMgAUHgD2ogDkIAQvb/hdLw38fVxwBCABDJAyABQYANaiABKQOYDiAQIBJUrXwiFiABKQPQDnwiGiABKQPIDiAUIB5WrXwiESABKQOAD3wiFCABKQOQDXwiHiAPIBJWrSABKQPoDSAPIBtUrXx8fCItfCIPIAEpA8ANfCISIAEpA9gNIAEpA9ANIgwgEHwgDFStfHwiECABKQOgDnwiG0KJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHwDGogDEIAQo2Vx8OW0trAl39CABDJAyABQeAMaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFB0AxqIAxCAEKpwMaJrs6TsjBCABDJAyABQbAOaiAKQgBCn+rg1Zzup+wGQgAQyQMgAUHwDmogC0IAQp/q4NWc7qfsBkIAEMkDIAFBsA9qIA1CAEKf6uDVnO6n7AZCABDJAyABQfAPaiAOQgBCn+rg1Zzup+wGQgAQyQMgAUGwDGogASkDqA4gECAbVq18IiIgASkD4A58IgsgASkDiA8gESAUVq18IhEgASkDwA98Ig0gASkDwAx8Ig4gHiAtVq0gASkDmA0gFCAeVq18fHwiDCABKQOQD3wiFCAPIBpUrSABKQPYDiAWIBpWrXx8fCIaIAEpA7ANfCIeIBAgElStIAEpA8gNIA8gElatfHx8IhZ8Ig8gASkD8Ax8IhIgASkDiA0gASkDgA0iCiAbfCAKVK18fCIQIAEpA7AOfCIbQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyABQaAMaiAKQgBCjZXHw5bS2sCXf0IAEMkDIAFBkAxqIApCAELdsIWM6LaRqLh/QgAQyQMgAUGADGogCkIAQqnAxomuzpOyMEIAEMkDAkACQAJAIAEpA4gMIAEpA+gPIAEpA+APIAwgDlStIAEpA8gMIA0gDlatfHwiDiABKQPIDyANIBFUrXx8IgogDlSthCIOIAEpA9gPIAogCiABKQPQD3wiClatfCAKIAogFCAaVq0gASkDmA8gDCAUVq18fHwiClatfHwiDSAOVK18IA0gDSABKQOoDSAKIAogASkDoA18IgpWrXwgCiAKIBYgHlStIAEpA7gNIBogHlatfHx8IgpWrXx8Ig1WrXwgDSABKQOoDyAKIAogASkDoA98IgpWrXwgCiAKIAsgD1atIAEpA+gOIAsgIlStfHx8IgpWrXx8IgsgDVStfCIaIAEpA/APfCINIAEpA9gMIAsgCyABKQPQDHwiC1atfCALIAEpA+gMIAogCiABKQPgDHwiClatfCAKIBAgElStIAEpA/gMIA8gElatfHx8IgwgClStfHwiCiALVK18fCIOIAEpA7gPIAogCiABKQOwD3wiClatfCAKIAogASkD+A4gASkDuA4gECAbVq18Ig8gASkD8A58IgsgD1StfCALIAsgDHwiC1atfHwiClatfHwiDCABKQOADHwiDyAMVK18IA8gASkDmAwgCiAKIAEpA5AMfCIKVq18IAogCiABKQOoDCALIAsgASkDoAx8IgtWrXwgCyABKQO4DCABKQOwDCISIBt8IBJUrXx8Ii0gC1StfHwiClatfHwiCyAPVK18IAwgDlStIA0gDlatIAEpA/gPIA0gGlStfHx8fCIeQqnAxomuzpOyMFYNAAJAIB5CqcDGia7Ok7IwUQRAIAtC3bCFjOi2kai4f1YNAiALQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIR4LIAshGiAKIRIMAwsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hGiAKQo2Vx8OW0trAl39SIC1Cx/rzw+2Co5A8VHINAQsgCkLz6ri86a2lv+gAfCINIC1Cx/rzw+2Co5A8VK0iDn0hEiALQqPP+vOXye7XxwB8IgwgCkKNlcfDltLawJd/VCANIA5Ucq0iCn0hGiAeIAtC3bCFjOi2kai4f1QgCiAMVnKtfUKpwMaJrs6TsjB9IR4gLULH+vPD7YKjkDx9IS0MAQtCqcDGia7Ok7IwIR4gCiESCyABQdAgakHqhMIAQcAAELcCIAFBgApqIAEpA+ggIgpCAEKJ9auctYu/lnNCABDJAyABQcAKaiABKQPgICILQgBCifWrnLWLv5ZzQgAQyQMgAUGAC2ogASkD2CAiDUIAQon1q5y1i7+Wc0IAEMkDIAFBwAtqIAEpA9AgIg5CAEKJ9auctYu/lnNCABDJAyABQfAJaiABKQOACiIQQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQeAJaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFBkAlqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUHACGogDEIAQqnAxomuzpOyMEIAEMkDIAFBkApqIApCAEL7g5SinaLG87V/QgAQyQMgAUHQCmogC0IAQvuDlKKdosbztX9CABDJAyABQZALaiANQgBC+4OUop2ixvO1f0IAEMkDIAFB0AtqIA5CAEL7g5SinaLG87V/QgAQyQMgAUHQCWogASkD4AkiIiABKQOICiIWIAEpA8AKfCIRfCIPIAEpA/gJIBAgASkD8AkiDHwgDFStfHwiECABKQOQCnwiFEKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgAUHACWogDEIAQo2Vx8OW0trAl39CABDJAyABQbAJaiAMQgBC3bCFjOi2kai4f0IAEMkDIAFBoAlqIAxCAEKpwMaJrs6TsjBCABDJAyABQaAKaiAKQgBC9v+F0vDfx9XHAEIAEMkDIAFB4ApqIAtCAEL2/4XS8N/H1ccAQgAQyQMgAUGgC2ogDUIAQvb/hdLw38fVxwBCABDJAyABQeALaiAOQgBC9v+F0vDfx9XHAEIAEMkDIAFBgAlqIAEpA5gKIBAgFFatfCIjIAEpA9AKfCIbIAEpA8gKIBEgFlStfCIXIAEpA4ALfCIWIAEpA5AJfCIRIA8gEFatIAEpA+gJIA8gIlStfHx8Ihx8Ig8gASkDwAl8IhAgASkD2AkgASkD0AkiDCAUfCAMVK18fCIUIAEpA6AKfCIiQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQfAIaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFB4AhqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUHQCGogDEIAQqnAxomuzpOyMEIAEMkDIAFBsApqIApCAEKf6uDVnO6n7AZCABDJAyABQfAKaiALQgBCn+rg1Zzup+wGQgAQyQMgAUGwC2ogDUIAQp/q4NWc7qfsBkIAEMkDIAFB8AtqIA5CAEKf6uDVnO6n7AZCABDJAyABQbAIaiABKQOoCiAUICJWrXwiHSABKQPgCnwiCyABKQOICyAWIBdUrXwiFyABKQPAC3wiDSABKQPACHwiDiARIBxWrSABKQOYCSARIBZUrXx8fCIMIAEpA5ALfCIWIA8gG1StIAEpA9gKIBsgI1StfHx8IhsgASkDsAl8IhEgECAUVq0gASkDyAkgDyAQVq18fHwiI3wiDyABKQPwCHwiECABKQOICSABKQOACSIKICJ8IApUrXx8IhQgASkDsAp8IiJCiceZpK7wgemHf34iCkIAQsf688PtgqOQPEIAEMkDIAFBoAhqIApCAEKNlcfDltLawJd/QgAQyQMgAUGQCGogCkIAQt2whYzotpGouH9CABDJAyABQYAIaiAKQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgASkDiAggASkD6AsgASkD4AsgDCAOVK0gASkDyAggDSAOVq18fCIOIAEpA8gLIA0gF1StfHwiCiAOVK2EIg4gASkD2AsgCiAKIAEpA9ALfCIKVq18IAogCiAWIBtWrSABKQOYCyAMIBZWrXx8fCIKVq18fCINIA5UrXwgDSANIAEpA6gJIAogCiABKQOgCXwiClatfCAKIAogESAjVq0gASkDuAkgESAbVK18fHwiClatfHwiDVatfCANIAEpA6gLIAogCiABKQOgC3wiClatfCAKIAogCyAPVq0gASkD6AogCyAdVK18fHwiClatfHwiCyANVK18IhsgASkD8At8Ig0gASkD2AggCyALIAEpA9AIfCILVq18IAsgASkD6AggCiAKIAEpA+AIfCIKVq18IAogECAUVq0gASkD+AggDyAQVq18fHwiDCAKVK18fCIKIAtUrXx8Ig4gASkDuAsgCiAKIAEpA7ALfCIKVq18IAogCiABKQP4CiABKQO4CiAUICJWrXwiDyABKQPwCnwiCyAPVK18IAsgCyAMfCILVq18fCIKVq18fCIMIAEpA4AIfCIPIAxUrXwgDyABKQOYCCAKIAogASkDkAh8IgpWrXwgCiAKIAEpA6gIIAsgCyABKQOgCHwiC1atfCALIAEpA7gIIAEpA7AIIhAgInwgEFStfHwiIiALVK18fCIKVq18fCILIA9UrXwgDCAOVK0gDSAOVq0gASkD+AsgDSAbVK18fHx8IhtCqcDGia7Ok7IwVg0AAkAgG0KpwMaJrs6TsjBRBEAgC0LdsIWM6LaRqLh/Vg0CIAtC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhGwsgCyEUIAohEAwDCyAKQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEUIApCjZXHw5bS2sCXf1IgIkLH+vPD7YKjkDxUcg0BCyAKQvPquLzpraW/6AB8Ig0gIkLH+vPD7YKjkDxUrSIOfSEQIAtCo8/685fJ7tfHAHwiDCAKQo2Vx8OW0trAl39UIA0gDlRyrSIKfSEUIBsgC0LdsIWM6LaRqLh/VCAKIAxWcq19QqnAxomuzpOyMH0hGyAiQsf688PtgqOQPH0hIgwBC0KpwMaJrs6TsjAhGyAKIRALIAFB0CBqQaqFwgBBwAAQtwIgAUGABmogASkD6CAiCkIAQon1q5y1i7+Wc0IAEMkDIAFBwAZqIAEpA+AgIgtCAEKJ9auctYu/lnNCABDJAyABQYAHaiABKQPYICINQgBCifWrnLWLv5ZzQgAQyQMgAUHAB2ogASkD0CAiDkIAQon1q5y1i7+Wc0IAEMkDIAFB8AVqIAEpA4AGIhZCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFB4AVqIAxCAEKNlcfDltLawJd/QgAQyQMgAUGQBWogDEIAQt2whYzotpGouH9CABDJAyABQcAEaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGQBmogCkIAQvuDlKKdosbztX9CABDJAyABQdAGaiALQgBC+4OUop2ixvO1f0IAEMkDIAFBkAdqIA1CAEL7g5SinaLG87V/QgAQyQMgAUHQB2ogDkIAQvuDlKKdosbztX9CABDJAyABQdAFaiABKQPgBSIdIAEpA4gGIhcgASkDwAZ8Ihx8Ig8gASkD+AUgFiABKQPwBSIMfCAMVK18fCIWIAEpA5AGfCIRQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyABQcAFaiAMQgBCjZXHw5bS2sCXf0IAEMkDIAFBsAVqIAxCAELdsIWM6LaRqLh/QgAQyQMgAUGgBWogDEIAQqnAxomuzpOyMEIAEMkDIAFBoAZqIApCAEL2/4XS8N/H1ccAQgAQyQMgAUHgBmogC0IAQvb/hdLw38fVxwBCABDJAyABQaAHaiANQgBC9v+F0vDfx9XHAEIAEMkDIAFB4AdqIA5CAEL2/4XS8N/H1ccAQgAQyQMgAUGABWogASkDmAYgESAWVK18IiUgASkD0AZ8IiMgASkDyAYgFyAcVq18IiYgASkDgAd8IhcgASkDkAV8IhwgDyAWVq0gASkD6AUgDyAdVK18fHwiKHwiDyABKQPABXwiFiABKQPYBSABKQPQBSIMIBF8IAxUrXx8IhEgASkDoAZ8Ih1CiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIAFB8ARqIAxCAEKNlcfDltLawJd/QgAQyQMgAUHgBGogDEIAQt2whYzotpGouH9CABDJAyABQdAEaiAMQgBCqcDGia7Ok7IwQgAQyQMgAUGwBmogCkIAQp/q4NWc7qfsBkIAEMkDIAFB8AZqIAtCAEKf6uDVnO6n7AZCABDJAyABQbAHaiANQgBCn+rg1Zzup+wGQgAQyQMgAUHwB2ogDkIAQp/q4NWc7qfsBkIAEMkDIAFBsARqIAEpA6gGIBEgHVatfCIpIAEpA+AGfCILIAEpA4gHIBcgJlStfCImIAEpA8AHfCINIAEpA8AEfCIOIBwgKFatIAEpA5gFIBcgHFatfHx8IgwgASkDkAd8IhcgDyAjVK0gASkD2AYgIyAlVK18fHwiIyABKQOwBXwiHCARIBZUrSABKQPIBSAPIBZWrXx8fCIlfCIPIAEpA/AEfCIWIAEpA4gFIAEpA4AFIgogHXwgClStfHwiESABKQOwBnwiHUKJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgAUGgBGogCkIAQo2Vx8OW0trAl39CABDJAyABQZAEaiAKQgBC3bCFjOi2kai4f0IAEMkDIAFBgARqIApCAEKpwMaJrs6TsjBCABDJAwJAAkACQAJAIAEpA4gEIAEpA+gHIAEpA+AHIAwgDlStIAEpA8gEIA0gDlatfHwiDiABKQPIByANICZUrXx8IgogDlSthCIOIAEpA9gHIAogCiABKQPQB3wiClatfCAKIAogFyAjVq0gASkDmAcgDCAXVq18fHwiClatfHwiDSAOVK18IA0gDSABKQOoBSAKIAogASkDoAV8IgpWrXwgCiAKIBwgJVatIAEpA7gFIBwgI1StfHx8IgpWrXx8Ig1WrXwgDSABKQOoByAKIAogASkDoAd8IgpWrXwgCiAKIAsgD1atIAEpA+gGIAsgKVStfHx8IgpWrXx8IgsgDVStfCIXIAEpA/AHfCIOIAEpA9gEIAsgCyABKQPQBHwiC1atfCALIAEpA+gEIAogCiABKQPgBHwiClatfCAKIBEgFlStIAEpA/gEIA8gFlatfHx8IgwgClStfHwiCiALVK18fCILIAEpA7gHIAogCiABKQOwB3wiClatfCAKIAogASkD+AYgASkDuAYgESAdVq18Ig8gASkD8AZ8Ig0gD1StfCANIAwgDXwiDVatfHwiClatfHwiDCABKQOABHwiDyAMVK18IA8gASkDmAQgCiAKIAEpA5AEfCIKVq18IAogCiABKQOoBCANIA0gASkDoAR8Ig1WrXwgDSABKQO4BCABKQOwBCIWIB18IBZUrXx8IiMgDVStfHwiClatfHwiDSAPVK18IAsgDFatIAsgDlStIAEpA/gHIA4gF1StfHx8fCIWQqnAxomuzpOyMFYNACAWQqnAxomuzpOyMFINASANQt2whYzotpGouH9WDQAgDULdsIWM6LaRqLh/UgRAIAohCyANIQxCqcDGia7Ok7IwIRYMBAsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hDCAKQo2Vx8OW0trAl39SICNCx/rzw+2Co5A8VHINAgsgCkLz6ri86a2lv+gAfCIOICNCx/rzw+2Co5A8VK0iDH0hCyANQqPP+vOXye7XxwB8Ig8gCkKNlcfDltLawJd/VCAMIA5Wcq0iCn0hDCAWIA1C3bCFjOi2kai4f1QgCiAPVnKtfUKpwMaJrs6TsjB9IRYgI0LH+vPD7YKjkDx9ISMMAgsgCiELIA0hDAwBCyAKIQtCqcDGia7Ok7IwIRYLIAFB0CBqQeqFwgBBwAAQtwIgAUGAAmogASkD6CAiCkIAQon1q5y1i7+Wc0IAEMkDIAFBwAJqIAEpA+AgIg1CAEKJ9auctYu/lnNCABDJAyABQYADaiABKQPYICIOQgBCifWrnLWLv5ZzQgAQyQMgAUHAA2ogASkD0CAiD0IAQon1q5y1i7+Wc0IAEMkDIAFB8AFqIAEpA4ACIhxCiceZpK7wgemHf34iEUIAQsf688PtgqOQPEIAEMkDIAFB4AFqIBFCAEKNlcfDltLawJd/QgAQyQMgAUGQAWogEUIAQt2whYzotpGouH9CABDJAyABQUBrIBFCAEKpwMaJrs6TsjBCABDJAyABQZACaiAKQgBC+4OUop2ixvO1f0IAEMkDIAFB0AJqIA1CAEL7g5SinaLG87V/QgAQyQMgAUGQA2ogDkIAQvuDlKKdosbztX9CABDJAyABQdADaiAPQgBC+4OUop2ixvO1f0IAEMkDIAFB0AFqIAEpA+ABIikgASkDiAIiJiABKQPAAnwiKHwiFyABKQP4ASAcIAEpA/ABIhF8IBFUrXx8IhwgASkDkAJ8Ih1CiceZpK7wgemHf34iEUIAQsf688PtgqOQPEIAEMkDIAFBwAFqIBFCAEKNlcfDltLawJd/QgAQyQMgAUGwAWogEUIAQt2whYzotpGouH9CABDJAyABQaABaiARQgBCqcDGia7Ok7IwQgAQyQMgAUGgAmogCkIAQvb/hdLw38fVxwBCABDJAyABQeACaiANQgBC9v+F0vDfx9XHAEIAEMkDIAFBoANqIA5CAEL2/4XS8N/H1ccAQgAQyQMgAUHgA2ogD0IAQvb/hdLw38fVxwBCABDJAyABQYABaiABKQOYAiAcIB1WrXwiMiABKQPQAnwiJSABKQPIAiAmIChWrXwiMyABKQOAA3wiJiABKQOQAXwiKCAXIBxWrSABKQPoASAXIClUrXx8fCI0fCIXIAEpA8ABfCIcIAEpA9gBIAEpA9ABIhEgHXwgEVStfHwiHSABKQOgAnwiKUKJx5mkrvCB6Yd/fiIRQgBCx/rzw+2Co5A8QgAQyQMgAUHwAGogEUIAQo2Vx8OW0trAl39CABDJAyABQeAAaiARQgBC3bCFjOi2kai4f0IAEMkDIAFB0ABqIBFCAEKpwMaJrs6TsjBCABDJAyABQbACaiAKQgBCn+rg1Zzup+wGQgAQyQMgAUHwAmogDUIAQp/q4NWc7qfsBkIAEMkDIAFBsANqIA5CAEKf6uDVnO6n7AZCABDJAyABQfADaiAPQgBCn+rg1Zzup+wGQgAQyQMgAUEwaiABKQOoAiAdIClWrXwiNSABKQPgAnwiDSABKQOIAyAmIDNUrXwiMyABKQPAA3wiDiABKQNAfCIPICggNFatIAEpA5gBICYgKFatfHx8IhEgASkDkAN8IiYgFyAlVK0gASkD2AIgJSAyVK18fHwiJSABKQOwAXwiKCAcIB1WrSABKQPIASAXIBxWrXx8fCIyfCIXIAEpA3B8IhwgASkDiAEgASkDgAEiCiApfCAKVK18fCIdIAEpA7ACfCIpQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyABQSBqIApCAEKNlcfDltLawJd/QgAQyQMgAUEQaiAKQgBC3bCFjOi2kai4f0IAEMkDIAEgCkIAQqnAxomuzpOyMEIAEMkDAkACQAJAAkAgASkDCCABKQPoAyABKQPgAyAPIBFWrSABKQNIIA4gD1atfHwiDyABKQPIAyAOIDNUrXx8IgogD1SthCIPIAEpA9gDIAogCiABKQPQA3wiClatfCAKIAogJSAmVK0gASkDmAMgESAmVq18fHwiClatfHwiDiAPVK18IA4gDiABKQOoASAKIAogASkDoAF8IgpWrXwgCiAKICggMlatIAEpA7gBICUgKFatfHx8IgpWrXx8Ig5WrXwgDiABKQOoAyAKIAogASkDoAN8IgpWrXwgCiAKIA0gF1atIAEpA+gCIA0gNVStfHx8IgpWrXx8Ig0gDlStfCIlIAEpA/ADfCIPIAEpA1ggDSANIAEpA1B8Ig1WrXwgDSABKQNoIAogCiABKQNgfCIKVq18IAogHCAdVq0gASkDeCAXIBxWrXx8fCIRIApUrXx8IgogDVStfHwiDSABKQO4AyAKIAogASkDsAN8IgpWrXwgCiAKIAEpA/gCIAEpA7gCIB0gKVatfCIXIAEpA/ACfCIOIBdUrXwgDiAOIBF8Ig5WrXx8IgpWrXx8IhEgASkDAHwiHCARVK18IBwgASkDGCAKIAogASkDEHwiClatfCAKIAogASkDKCAOIA4gASkDIHwiDlatfCAOIAEpAzggASkDMCIXICl8IBdUrXx8IhcgDlStfHwiClatfHwiDiAcVK18IA0gEVatIA0gD1StIAEpA/gDIA8gJVStfHx8fCIRQqnAxomuzpOyMFYNACARQqnAxomuzpOyMFINASAOQt2whYzotpGouH9WDQAgDkLdsIWM6LaRqLh/UgRAIAohDSAOIQ9CqcDGia7Ok7IwIREMBAsgCkKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hDyAKQo2Vx8OW0trAl39SIBdCx/rzw+2Co5A8VHINAgsgCkLz6ri86a2lv+gAfCIPIBdCx/rzw+2Co5A8VK0iHH0hDSAOQqPP+vOXye7XxwB8Ih0gCkKNlcfDltLawJd/VCAPIBxUcq0iCn0hDyARIA5C3bCFjOi2kai4f1QgCiAdVnKtfUKpwMaJrs6TsjB9IREgF0LH+vPD7YKjkDx9IRcMAgsgCiENIA4hDwwBCyAKIQ1CqcDGia7Ok7IwIRELIAFB0CBqIgVBqobCAEHAAEEQEPEBAkACQCABKALQIEGAgICAeEcEQCABQZAgaiIGIAFB2CBqIgMoAgA2AgAgASABKQLQIDcDiCAgAUENNgLMICABQfGGwgA2AsggIAFCh4CAgMABNwLAICABQeqGwgA2ArwgIAFBBjYCuCAQxwQiAkUNASACIAIpAwAiCkIBfDcDACACKQMIIQ4gA0GIscIAKQMANwMAIAFB6CBqIgIgDjcDACABQeAgaiIEIAo3AwAgAUGAscIAKQMANwPQICAFIAFBuCBqEIIBIAFBsCBqIgcgAikDADcDACABQaggaiIIIAQpAwA3AwAgAUGgIGoiCSADKQMANwMAIAEgASkD0CA3A5ggIAVBwIfCAEEwQRAQ8QEgAS0A1CAhAiABKALQICIEQYCAgIB4Rg0CIAAgAS8A1SA7AJUCIABBlwJqIAFB1yBqLQAAOgAAIAEoAtggIQMgAEIANwMAIABBADoAuAQgAEEIakIANwMAIABBEGpCADcDACAAQRhqQgA3AwAgACAXNwOgBCAAIA03A5gEIAAgDzcDkAQgACARNwOIBCAAICM3A4AEIAAgCzcD+AMgACAMNwPwAyAAIBY3A+gDIABCATcD4AMgACAiNwPYAyAAIBA3A9ADIAAgFDcDyAMgACAbNwPAAyAAIC03A7gDIAAgEjcDsAMgACAaNwOoAyAAIB43A6ADIABCATcDmAMgACAxNwO4ASAAIBM3A7ABIAAgGTcDqAEgACAkNwOgASAAIDA3A5gBIAAgFTcDkAEgACAfNwOIASAAICc3A4ABIAAgLzcDeCAAIBg3A3AgACAhNwNoIAAgLDcDYCAAIC43A1ggACAgNwNQIAAgKjcDSCAAICs3A0AgAELX0bSFldXyi/oANwM4IABCucPUiq6vsLUfNwMwIABChKWvy+bJ+qUzNwMoIABCjrve8Mzo2Y8qNwMgIABBATYCqAQgAELxk6TTxNbk9MQANwOAAiAAQgA3A4gCIABCjrve8Mzo2Y8qNwPAASAAQoSlr8vmyfqlMzcDyAEgAEK5w9SKrq+wtR83A9ABIABC19G0hZXV8ov6ADcD2AEgAEG0BGogBigCADYCACAAIAEpA4ggNwKsBCAAIAEpA5ggNwPgASAAQegBaiAJKQMANwMAIABB8AFqIAgpAwA3AwAgAEH4AWogBykDADcDACAAQcIANgKsAiAAQf6GwgA2AqgCIABCCTcDoAIgAEECQQEgAxs6AJwCIAAgAjoAlAIgAEIANwOwAiAAIAM2ApgCIAAgBDYCkAIgAUHwIGokAA8LIAEgAS0A1CA6AJggQYz3wQBBKyABQZggakHk+8EAQYCIwgAQygMACxDwAwALIAEgAjoA0CBBjPfBAEErIAFB0CBqQeT7wQBB8IfCABDKAwALp4cBAgp/G34jAEHwHGsiAyQAIAMgAjYC3BQgA0EMNgLYFAJAAkAgAkEMRgRAIANB4BRqECYgA0HwE2ogAykD8BciDUIAQsau0OHB5sfvdEIAEMkDIANB4BNqIAMpA/ATQn6DIhRCAEIAQv3/8//P///5iX8QyQMgA0HQE2ogAykD6BMiDkIAQqvV/v///7//uX9CABDJAyADQcATaiAOQgBC///Piuv//9UeQgAQyQMgA0HAEmogDkIAQqTsw7WP1LSY5wBCABDJAyADQcARaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBwBBqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HAD2ogDkIAQprN/8ujvcSAGkIAEMkDIANBgBRqIA1CAELxicTO4NS5uwpCABDJAyADQbATaiADKQOAFCIQIAMpA8ATIhMgAykD+BN8Ig8gAykD2BMgAykD0BMiDiAUfCAOVK18fCIRfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBNqIAMpA7gTIg5CAEKr1f7///+//7l/QgAQyQMgA0GQE2ogDkIAQv//z4rr///VHkIAEMkDIANBgBNqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEmogDkIAQr+llJzP8NK75ABCABDJAyADQeASaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BJqIA5CAEKazf/Lo73EgBpCABDJAyADQZAUaiANQgBC1e3W5MTt0fKNf0IAEMkDIANBsBJqIAMpA5AUIhUgAykDkBMiFyADKQOIFCAQIBRWrXwiECADKQPAEiIYIA8gEVatIAMpA8gTIA8gE1StfHx8IhN8IhF8Ig8gAykDqBMgAykDoBMiDiAUfCAOVK18fCIZfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBJqIAMpA7gSIg5CAEKr1f7///+//7l/QgAQyQMgA0GQEmogDkIAQv//z4rr///VHkIAEMkDIANBgBJqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEWogDkIAQr+llJzP8NK75ABCABDJAyADQeARaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BFqIA5CAEKazf/Lo73EgBpCABDJAyADQaAUaiANQgBCwIf2nJmV4vXnAEIAEMkDIANBsBFqIAMpA6AUIhsgAykDkBIiEiADKQOYFCAUIBVUrXwiFSAQIBFWrSIRIAMpA8ARIhYgAykDyBIgEyAYVK18fCIYfCIQIAMpA4ATfCITIA8gGVatIAMpA5gTIA8gF1StfHx8Ihd8Ihl8Ig8gAykDqBIgAykDoBIiDiAUfCAOVK18fCIcfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBFqIAMpA7gRIg5CAEKr1f7///+//7l/QgAQyQMgA0GQEWogDkIAQv//z4rr///VHkIAEMkDIANBgBFqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEGogDkIAQr+llJzP8NK75ABCABDJAyADQeAQaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BBqIA5CAEKazf/Lo73EgBpCABDJAyADQbAUaiANQgBCrarmqNvQz7yaf0IAEMkDIANBsBBqIAMpA7AUIh0gAykDkBEiGiADKQOoFCAUIBtUrXwiGyAVIBlWrSIZIBAgEVStIh4gAykDwBAiHyADKQPIESAWIBhWrXx8Ihh8IhEgAykD8BJ8IhUgEyAXVq0gAykDiBMgECATVq18fHwiFnwiECADKQOAEnwiEyAPIBxWrSADKQOYEiAPIBJUrXx8fCISfCIXfCIPIAMpA6gRIAMpA6ARIg4gFHwgDlStfHwiHHwiFEIAQgBC/f/z/8////mJfxDJAyADQaAQaiADKQO4ECIOQgBCq9X+////v/+5f0IAEMkDIANBkBBqIA5CAEL//8+K6///1R5CABDJAyADQYAQaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANB8A9qIA5CAEK/pZScz/DSu+QAQgAQyQMgA0HgD2ogDkIAQtfZrprk9umNywBCABDJAyADQdAPaiAOQgBCms3/y6O9xIAaQgAQyQMgA0HAFGogDUIAQqrHq5bZ/KPMEUIAEMkDIANBsA9qIAMpA8AUIiAgAykDkBAiISADKQO4FCAUIB1UrXwiHSAXIBtUrSIbIBAgGVStIhkgESAeVK0iHiADKQPADyIiIAMpA8gQIBggH1StfHwiGHwiDiADKQPgEnwiFyAVIBZWrSADKQP4EiARIBVWrXx8fCIWfCIRIAMpA/ARfCIVIBIgE1StIAMpA4gSIBAgE1atfHx8IhJ8IhAgAykDgBF8IhMgDyAcVq0gAykDmBEgDyAaVK18fHwiHHwiGnwiDyADKQOoECADKQOgECINIBR8IA1UrXx8Ih98IhRCAEIAQv3/8//P///5iX8QyQMgA0GgD2ogAykDuA8iDUIAQqvV/v///7//uX9CABDJAyADQZAPaiANQgBC///Piuv//9UeQgAQyQMgA0GAD2ogDUIAQqTsw7WP1LSY5wBCABDJAyADQfAOaiANQgBCv6WUnM/w0rvkAEIAEMkDIANB4A5qIA1CAELX2a6a5PbpjcsAQgAQyQMgA0HQDmogDUIAQprN/8ujvcSAGkIAEMkDIAMpA9gOIAMpA9AOIiMgAykD2A8gAykD0A8iJCADKQPYECADKQPQECIlIAMpA9gRIAMpA9ARIiYgAykD2BIgAykD0BIiJyAOIB5UrSADKQPIDyAYICJUrXx8fCINICdUrXwgDSANIBYgF1StIAMpA+gSIA4gF1atfHx8Ig5WrXwgDiARIBlUrSIOfCINIA5UrXx8Ig4gJlStfCAOIA4gAykD6BEgDSANIAMpA+ARfCIXVq18IBcgFyASIBVUrSADKQP4ESARIBVWrXx8fCINVq18fCIRVq18IBEgECAbVK0iDiANfCINIA5UrSIVfCIOIBVUrXx8IhEgJVStfCARIAMpA+gQIA4gDiADKQPgEHwiFVatfCAVIBUgAykD+BAgDSANIAMpA/AQfCIOVq18IA4gDiATIBxWrSADKQOIESAQIBNWrXx8fCINVq18fCIOVq18fCIQIBFUrXwgECAOIBogHVStIhMgDXwiDSATVK0iE3wiDiATVK0iE3wiECATVK18fCITICRUrXwgEyADKQPoDyAQIBAgAykD4A98IhFWrXwgESADKQP4DyAOIA4gAykD8A98IhBWrXwgECAQIAMpA4gQIA0gDSADKQOAEHwiDlatfCAOIA4gDyAfVq0gAykDmBAgDyAhVK18fHwiDVatfHwiDlatfHwiDyARVK18fCIQIBNUrXwgECAPIA4gDSADKQPIFCAUICBUrXwiE3wiESATVK0iE3wiDSATVK0iE3wiDiATVK0iE3wiDyATVK18fCIQICNUrXwgECADKQPoDiAPIA8gAykD4A58IhNWrXwgEyADKQP4DiAOIA4gAykD8A58Ig9WrXwgDyADKQOIDyANIA0gAykDgA98Ig5WrXwgDiADKQOYDyARIAMpA5APIhF8Ig0gEVStfCANIAMpA6gPIBQgAykDoA8iEXwgEVStfHwiHCANVK18fCIXIA5UrXx8IhggD1StfHwiGSATVK18fCIbIBBUrXwiHUKazf/Lo73EgBpSDQICQCAbQtfZrprk9umNywBWDQBCms3/y6O9xIAaIR0gG0LX2a6a5PbpjcsAUg0DIBlCv6WUnM/w0rvkAFYNACAZQr+llJzP8NK75ABSBEBC19mumuT26Y3LACEbDAQLIBhCpOzDtY/UtJjnAFYNACAYQqTsw7WP1LSY5wBSDQIgF0L//8+K6///1R5WDQAgF0L//8+K6///1R5SBEBCpOzDtY/UtJjnACEYDAMLIBxCq9X+////v/+5f1oNAEL//8+K6///1R4hF0Kk7MO1j9S0mOcAIRgMAgtCf0IAIBtC19mumuT26Y3LAH0iDSAZQr+llJzP8NK75ABUIBlCv6WUnM/w0rvkAH0iDiAYQqTsw7WP1LSY5wBUIBhCpOzDtY/UtJjnAH0iDyAXQv//z4rr///VHlQgF0L//8+K6///1R59IhQgHEKr1f7///+//7l/VK0iEFRyrSITVHKtIhFUcq0iFVQbIR0gFCAQfSEXIA8gE30hGCAOIBF9IRkgDSAVfSEbIBxC1aqBgICAwIDGAHwhHAwCCyADQQA2AuAUIANB3BRqIANB2BRqIANB4BRqQaCJwAAQlwQAC0K/pZScz/DSu+QAIRlC19mumuT26Y3LACEbCyADKALsGiIEBEAgAygC8BogBEECdBDfBAsCQCADKALkFCIERQ0AIAQgBEEMbEETakF4cSIFakEJaiIERQ0AIAMoAuAUIAVrIAQQ3wQLIAMoAuAXIgRBgICAgHhGIARFckUEQCADKALkFyAEQQJ0EN8ECwJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgAkECaw4LAQAAAAIAAAAAAAMACyADQQA2AvAUIANBATYC5BQgA0GIicAANgLgFCADQgQ3AugUIANB4BRqQcCKwAAQqAQAC0HRzsUALQAAGkHgAEEIENYEIgRFDQIgBCABKQMANwMAIAQgASkDMDcDMCAEQShqIAFBKGopAwA3AwAgBEEgaiABQSBqKQMANwMAIARBGGogAUEYaikDADcDACAEQRBqIAFBEGopAwA3AwAgBEEIaiABQQhqKQMANwMAIARBOGogAUE4aikDADcDACAEQUBrIAFBQGspAwA3AwAgBEHIAGogAUHIAGopAwA3AwAgBEHQAGogAUHQAGopAwA3AwAgBEHYAGogAUHYAGopAwA3AwAMCwtB0c7FAC0AABpBoAJBCBDWBCIERQ0JIAFBkAFqIQdBuAEhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANBkARqIAEgBWopAwAiD0IAIBxCABDJAyADQaAEaiAPQgAgF0IAEMkDIANBsARqIA9CACAYQgAQyQMgA0HABGogD0IAIBlCABDJAyADQdAEaiAPQgAgG0IAEMkDIANB4ARqIA9CACAdQgAQyQMgA0GABGogAykDkAQiFSAWfCIUQgBCAEL9//P/z///+Yl/EMkDIANB8ANqIAMpA4gEIg9CAEKr1f7///+//7l/QgAQyQMgA0HgA2ogD0IAQv//z4rr///VHkIAEMkDIANB0ANqIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0HAA2ogD0IAQr+llJzP8NK75ABCABDJAyADQbADaiAPQgBC19mumuT26Y3LAEIAEMkDIANBoANqIA9CAEKazf/Lo73EgBpCABDJAyADKQOoAyASIAMpA+AEIhp8Ig8gAykD2AQgESADKQPQBCISfCITIBJUrXwgEyADKQPIBCADKQPABCIRIBB8IhAgEVStfCAQIAMpA7gEIAMpA7AEIhEgDnwiDiARVK18IA4gAykDqAQgAykDoAQiESANfCINIBFUrXwgDSADKQOYBCAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQOgA3wiFSATVK18IBUgFSADKQO4AyAQIBAgAykDsAN8IhFWrXwgESARIAMpA8gDIA4gDiADKQPAA3wiEFatfCAQIBAgAykD2AMgDSANIAMpA9ADfCIOVq18IA4gDiADKQPoAyASIAMpA+ADIhJ8Ig0gElStfCANIAMpA/gDIBQgAykD8AMiEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA+gEIA8gGlStfHx8IRIgBUEIayIFQYgBRw0ACyASQprN/8ujvcSAGlYNByASQprN/8ujvcSAGlENBiANIQ8gDiEUIBAhEyARIRUMCAtB0c7FAC0AABpBwARBCBDWBCIERQ0EIAFBoAJqIQdByAIhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANB8A1qIAEgBWopAwAiD0IAIBxCABDJAyADQYAOaiAPQgAgF0IAEMkDIANBkA5qIA9CACAYQgAQyQMgA0GgDmogD0IAIBlCABDJAyADQbAOaiAPQgAgG0IAEMkDIANBwA5qIA9CACAdQgAQyQMgA0HgDWogAykD8A0iFSAWfCIUQgBCAEL9//P/z///+Yl/EMkDIANB0A1qIAMpA+gNIg9CAEKr1f7///+//7l/QgAQyQMgA0HADWogD0IAQv//z4rr///VHkIAEMkDIANBsA1qIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0GgDWogD0IAQr+llJzP8NK75ABCABDJAyADQZANaiAPQgBC19mumuT26Y3LAEIAEMkDIANBgA1qIA9CAEKazf/Lo73EgBpCABDJAyADKQOIDSASIAMpA8AOIhp8Ig8gAykDuA4gESADKQOwDiISfCITIBJUrXwgEyADKQOoDiADKQOgDiIRIBB8IhAgEVStfCAQIAMpA5gOIAMpA5AOIhEgDnwiDiARVK18IA4gAykDiA4gAykDgA4iESANfCINIBFUrXwgDSADKQP4DSAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQOADXwiFSATVK18IBUgFSADKQOYDSAQIBAgAykDkA18IhFWrXwgESARIAMpA6gNIA4gDiADKQOgDXwiEFatfCAQIBAgAykDuA0gDSANIAMpA7ANfCIOVq18IA4gDiADKQPIDSASIAMpA8ANIhJ8Ig0gElStfCANIAMpA9gNIBQgAykD0A0iEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA8gOIA8gGlStfHx8IRIgBUEIayIFQZgCRw0ACyASQprN/8ujvcSAGlYNAiASQprN/8ujvcSAGlENASANIQ8gDiEUIBAhEyARIRUMAwtBCEHgAEG4hcAAEMgEAAsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0GAG2ogASADQeAUahC9AiABQagDaiEGIAFBgANqIQhBACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0GgDGogBSAGaikDACIPQgAgHEIAEMkDIANBsAxqIA9CACAXQgAQyQMgA0HADGogD0IAIBhCABDJAyADQdAMaiAPQgAgGUIAEMkDIANB4AxqIA9CACAbQgAQyQMgA0HwDGogD0IAIB1CABDJAyADQZAMaiADKQOgDCIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0GADGogAykDmAwiD0IAQqvV/v///7//uX9CABDJAyADQfALaiAPQgBC///Piuv//9UeQgAQyQMgA0HgC2ogD0IAQqTsw7WP1LSY5wBCABDJAyADQdALaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANBwAtqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0GwC2ogD0IAQprN/8ujvcSAGkIAEMkDIAMpA7gLIBIgAykD8AwiGnwiDyADKQPoDCARIAMpA+AMIhJ8IhMgElStfCATIAMpA9gMIAMpA9AMIhEgEHwiECARVK18IBAgAykDyAwgAykDwAwiESAOfCIOIBFUrXwgDiADKQO4DCADKQOwDCIRIA18Ig0gEVStfCANIAMpA6gMIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA7ALfCIVIBNUrXwgFSAVIAMpA8gLIBAgECADKQPAC3wiEVatfCARIBEgAykD2AsgDiAOIAMpA9ALfCIQVq18IBAgECADKQPoCyANIA0gAykD4At8Ig5WrXwgDiAOIAMpA/gLIBIgAykD8AsiEnwiDSASVK18IA0gAykDiAwgFCADKQOADCISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykD+AwgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUHgAGohBQJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgDSEPIA4hFCAQIRMgESEVDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCANIQ8gDiEUIBAhEyARIRUMAQsgEEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhFSAQQr+llJzP8NK75ABSBEAgDSEPIA4hFCAQIRMMAQsgDkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhEyAOQqTsw7WP1LSY5wBSBEAgDSEPIA4hFAwBCyANQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRQgDUL//8+K6///1R5SBEAgDSEPDAELQv//z4rr///VHiEPIBZCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgDUL//8+K6///1R59IhQgFkKr1f7///+//7l/VK0iE30hDyAOQqTsw7WP1LSY5wB9IhUgDUL//8+K6///1R5UIBMgFFZyrSINfSEUIBBCv6WUnM/w0rvkAH0iGiAOQqTsw7WP1LSY5wBUIA0gFVZyrSINfSETIBFC19mumuT26Y3LAH0iDiAQQr+llJzP8NK75ABUIA0gGlZyrSINfSEVIBIgEULX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hEiAWQtWqgYCAgMCAxgB8IRYLIAMgFjcDiBUgAyAPNwOAFSADIBQ3A/gUIAMgEzcD8BQgAyAVNwPoFCADIBI3A+AUIANBsBtqIAUgA0HgFGoQvQIgAUGIBGohCSABQeADaiEGQQAhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANB0ApqIAUgCWopAwAiD0IAIBxCABDJAyADQeAKaiAPQgAgF0IAEMkDIANB8ApqIA9CACAYQgAQyQMgA0GAC2ogD0IAIBlCABDJAyADQZALaiAPQgAgG0IAEMkDIANBoAtqIA9CACAdQgAQyQMgA0HACmogAykD0AoiFSAWfCIUQgBCAEL9//P/z///+Yl/EMkDIANBsApqIAMpA8gKIg9CAEKr1f7///+//7l/QgAQyQMgA0GgCmogD0IAQv//z4rr///VHkIAEMkDIANBkApqIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0GACmogD0IAQr+llJzP8NK75ABCABDJAyADQfAJaiAPQgBC19mumuT26Y3LAEIAEMkDIANB4AlqIA9CAEKazf/Lo73EgBpCABDJAyADKQPoCSASIAMpA6ALIhp8Ig8gAykDmAsgESADKQOQCyISfCITIBJUrXwgEyADKQOICyADKQOACyIRIBB8IhAgEVStfCAQIAMpA/gKIAMpA/AKIhEgDnwiDiARVK18IA4gAykD6AogAykD4AoiESANfCINIBFUrXwgDSADKQPYCiAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQPgCXwiFSATVK18IBUgFSADKQP4CSAQIBAgAykD8Al8IhFWrXwgESARIAMpA4gKIA4gDiADKQOACnwiEFatfCAQIBAgAykDmAogDSANIAMpA5AKfCIOVq18IA4gDiADKQOoCiASIAMpA6AKIhJ8Ig0gElStfCANIAMpA7gKIBQgAykDsAoiEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA6gLIA8gGlStfHx8IRIgBUEIayIFQVBHDQALIAFBwAFqIQUCQAJAIBJCms3/y6O9xIAaVg0AIBJCms3/y6O9xIAaUgRAIA0hDyAOIRQgECETIBEhFQwCCyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgDSEPIA4hFCAQIRMgESEVDAELIBBCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRUgEEK/pZScz/DSu+QAUgRAIA0hDyAOIRQgECETDAELIA5CpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRMgDkKk7MO1j9S0mOcAUgRAIA0hDyAOIRQMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA1C///Piuv//9UeUgRAIA0hDwwBC0L//8+K6///1R4hDyAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiESDAELIA1C///Piuv//9UefSIUIBZCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIVIA1C///Piuv//9UeVCATIBRWcq0iDX0hFCAQQr+llJzP8NK75AB9IhogDkKk7MO1j9S0mOcAVCANIBVWcq0iDX0hEyARQtfZrprk9umNywB9Ig4gEEK/pZScz/DSu+QAVCANIBpWcq0iDX0hFSASIBFC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IRIgFkLVqoGAgIDAgMYAfCEWCyADIBY3A4gVIAMgDzcDgBUgAyAUNwP4FCADIBM3A/AUIAMgFTcD6BQgAyASNwPgFCADQeAbaiAFIANB4BRqEL0CIAFB+AJqIQogAUHQAmohCUEAIQVCACESQgAhEUIAIRBCACEOQgAhDUIAIRYDQCADQYAJaiAFIApqKQMAIg9CACAcQgAQyQMgA0GQCWogD0IAIBdCABDJAyADQaAJaiAPQgAgGEIAEMkDIANBsAlqIA9CACAZQgAQyQMgA0HACWogD0IAIBtCABDJAyADQdAJaiAPQgAgHUIAEMkDIANB8AhqIAMpA4AJIhUgFnwiFEIAQgBC/f/z/8////mJfxDJAyADQeAIaiADKQP4CCIPQgBCq9X+////v/+5f0IAEMkDIANB0AhqIA9CAEL//8+K6///1R5CABDJAyADQcAIaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANBsAhqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0GgCGogD0IAQtfZrprk9umNywBCABDJAyADQZAIaiAPQgBCms3/y6O9xIAaQgAQyQMgAykDmAggEiADKQPQCSIafCIPIAMpA8gJIBEgAykDwAkiEnwiEyASVK18IBMgAykDuAkgAykDsAkiESAQfCIQIBFUrXwgECADKQOoCSADKQOgCSIRIA58Ig4gEVStfCAOIAMpA5gJIAMpA5AJIhEgDXwiDSARVK18IA0gAykDiAkgFCAVVK18fCISIA1UrXx8Ig0gDlStfHwiDiAQVK18fCIQIBNUrXx8IhMgAykDkAh8IhUgE1StfCAVIBUgAykDqAggECAQIAMpA6AIfCIRVq18IBEgESADKQO4CCAOIA4gAykDsAh8IhBWrXwgECAQIAMpA8gIIA0gDSADKQPACHwiDlatfCAOIA4gAykD2AggEiADKQPQCCISfCINIBJUrXwgDSADKQPoCCAUIAMpA+AIIhJ8IBJUrXx8IhYgDVStfHwiDVatfHwiDlatfHwiEFatfHwiEVatfCAPIBNWrSADKQPYCSAPIBpUrXx8fCESIAVBCGsiBUFQRw0ACyABQTBqIQUCQAJAIBJCms3/y6O9xIAaVg0AIBJCms3/y6O9xIAaUgRAIA0hDyAOIRQgECETIBEhFQwCCyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgDSEPIA4hFCAQIRMgESEVDAELIBBCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRUgEEK/pZScz/DSu+QAUgRAIA0hDyAOIRQgECETDAELIA5CpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRMgDkKk7MO1j9S0mOcAUgRAIA0hDyAOIRQMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA1C///Piuv//9UeUgRAIA0hDwwBC0L//8+K6///1R4hDyAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiESDAELIA1C///Piuv//9UefSIUIBZCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIVIA1C///Piuv//9UeVCATIBRWcq0iDX0hFCAQQr+llJzP8NK75AB9IhogDkKk7MO1j9S0mOcAVCANIBVWcq0iDX0hEyARQtfZrprk9umNywB9Ig4gEEK/pZScz/DSu+QAVCANIBpWcq0iDX0hFSASIBFC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IRIgFkLVqoGAgIDAgMYAfCEWCyADIBY3A4gVIAMgDzcDgBUgAyAUNwP4FCADIBM3A/AUIAMgFTcD6BQgAyASNwPgFCADQZAcaiAFIANB4BRqEL0CIAFB2ANqIQsgAUGwA2ohCkEAIQVCACESQgAhEUIAIRBCACEOQgAhDUIAIRYDQCADQbAHaiAFIAtqKQMAIg9CACAcQgAQyQMgA0HAB2ogD0IAIBdCABDJAyADQdAHaiAPQgAgGEIAEMkDIANB4AdqIA9CACAZQgAQyQMgA0HwB2ogD0IAIBtCABDJAyADQYAIaiAPQgAgHUIAEMkDIANBoAdqIAMpA7AHIhUgFnwiFEIAQgBC/f/z/8////mJfxDJAyADQZAHaiADKQOoByIPQgBCq9X+////v/+5f0IAEMkDIANBgAdqIA9CAEL//8+K6///1R5CABDJAyADQfAGaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANB4AZqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0HQBmogD0IAQtfZrprk9umNywBCABDJAyADQcAGaiAPQgBCms3/y6O9xIAaQgAQyQMgAykDyAYgEiADKQOACCIafCIPIAMpA/gHIBEgAykD8AciEnwiEyASVK18IBMgAykD6AcgAykD4AciESAQfCIQIBFUrXwgECADKQPYByADKQPQByIRIA58Ig4gEVStfCAOIAMpA8gHIAMpA8AHIhEgDXwiDSARVK18IA0gAykDuAcgFCAVVK18fCISIA1UrXx8Ig0gDlStfHwiDiAQVK18fCIQIBNUrXx8IhMgAykDwAZ8IhUgE1StfCAVIBUgAykD2AYgECAQIAMpA9AGfCIRVq18IBEgESADKQPoBiAOIA4gAykD4AZ8IhBWrXwgECAQIAMpA/gGIA0gDSADKQPwBnwiDlatfCAOIA4gAykDiAcgEiADKQOAByISfCINIBJUrXwgDSADKQOYByAUIAMpA5AHIhJ8IBJUrXx8IhYgDVStfHwiDVatfHwiDlatfHwiEFatfHwiEVatfCAPIBNWrSADKQOICCAPIBpUrXx8fCESIAVBCGsiBUFQRw0ACyABQZABaiEFAkACQCASQprN/8ujvcSAGlYNACASQprN/8ujvcSAGlIEQCANIQ8gDiEUIBAhEyARIRUMAgsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0HAHGogBSADQeAUahC9AiABQbgEaiEMIAFBkARqIQtBACEFQgAhFkIAIQ1CACEOQgAhEEIAIRFCACESA0AgA0HgBWogBSAMaikDACIPQgAgHEIAEMkDIANB8AVqIA9CACAXQgAQyQMgA0GABmogD0IAIBhCABDJAyADQZAGaiAPQgAgGUIAEMkDIANBoAZqIA9CACAbQgAQyQMgA0GwBmogD0IAIB1CABDJAyADQdAFaiADKQPgBSIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0HABWogAykD2AUiD0IAQqvV/v///7//uX9CABDJAyADQbAFaiAPQgBC///Piuv//9UeQgAQyQMgA0GgBWogD0IAQqTsw7WP1LSY5wBCABDJAyADQZAFaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANBgAVqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HwBGogD0IAQprN/8ujvcSAGkIAEMkDIAMpA/gEIBIgAykDsAYiGnwiDyADKQOoBiARIAMpA6AGIhJ8IhMgElStfCATIAMpA5gGIAMpA5AGIhEgEHwiECARVK18IBAgAykDiAYgAykDgAYiESAOfCIOIBFUrXwgDiADKQP4BSADKQPwBSIRIA18Ig0gEVStfCANIAMpA+gFIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA/AEfCIVIBNUrXwgFSAVIAMpA4gFIBAgECADKQOABXwiEVatfCARIBEgAykDmAUgDiAOIAMpA5AFfCIQVq18IBAgECADKQOoBSANIA0gAykDoAV8Ig5WrXwgDiAOIAMpA7gFIBIgAykDsAUiEnwiDSASVK18IA0gAykDyAUgFCADKQPABSISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykDuAYgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUHwAWohAQJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgDSEXIA4hGCAQIRkgESEbDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCANIRcgDiEYIBAhGSARIRsMAQsgEEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGyAQQr+llJzP8NK75ABSBEAgDSEXIA4hGCAQIRkMAQsgDkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhGSAOQqTsw7WP1LSY5wBSBEAgDSEXIA4hGAwBCyANQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRggDUL//8+K6///1R5SBEAgDSEXDAELQv//z4rr///VHiEXIBZCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgDUL//8+K6///1R59Ig8gFkKr1f7///+//7l/VK0iFH0hFyAOQqTsw7WP1LSY5wB9IhMgDUL//8+K6///1R5UIA8gFFRyrSINfSEYIBBCv6WUnM/w0rvkAH0iDyAOQqTsw7WP1LSY5wBUIA0gE1ZyrSINfSEZIBFC19mumuT26Y3LAH0iDiAQQr+llJzP8NK75ABUIA0gD1ZyrSINfSEbIBIgEULX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hEiAWQtWqgYCAgMCAxgB8IRYLIAMgFjcDiBUgAyAXNwOAFSADIBg3A/gUIAMgGTcD8BQgAyAbNwPoFCADIBI3A+AUIARB4ANqIAEgA0HgFGoQvQIgBCADKQOAGzcDACAEQQhqIANBiBtqKQMANwMAIARBEGogA0GQG2opAwA3AwAgBEEYaiADQZgbaikDADcDACAEQSBqIANBoBtqKQMANwMAIARBKGogA0GoG2opAwA3AwAgBEG4BGogC0EoaikDADcDACAEQbAEaiALQSBqKQMANwMAIARBqARqIAtBGGopAwA3AwAgBEGgBGogC0EQaikDADcDACAEQZgEaiALQQhqKQMANwMAIAQgCykDADcDkAQgBEHYAGogB0EoaikDADcDACAEQdAAaiAHQSBqKQMANwMAIARByABqIAdBGGopAwA3AwAgBEFAayAHQRBqKQMANwMAIARBOGogB0EIaikDADcDACAEIAcpAwA3AzAgBEGIAWogA0HYG2opAwA3AwAgBEGAAWogA0HQG2opAwA3AwAgBEH4AGogA0HIG2opAwA3AwAgBEHwAGogA0HAG2opAwA3AwAgBEHoAGogA0G4G2opAwA3AwAgBCADKQOwGzcDYCAEQbgBaiAIQShqKQMANwMAIARBsAFqIAhBIGopAwA3AwAgBEGoAWogCEEYaikDADcDACAEQaABaiAIQRBqKQMANwMAIARBmAFqIAhBCGopAwA3AwAgBCAIKQMANwOQASAEQegBaiADQYgcaikDADcDACAEQeABaiADQYAcaikDADcDACAEQdgBaiADQfgbaikDADcDACAEQdABaiADQfAbaikDADcDACAEQcgBaiADQegbaikDADcDACAEIAMpA+AbNwPAASAEQZgCaiAGQShqKQMANwMAIARBkAJqIAZBIGopAwA3AwAgBEGIAmogBkEYaikDADcDACAEQYACaiAGQRBqKQMANwMAIARB+AFqIAZBCGopAwA3AwAgBCAGKQMANwPwASAEQcgCaiADQbgcaikDADcDACAEQcACaiADQbAcaikDADcDACAEQbgCaiADQagcaikDADcDACAEQbACaiADQaAcaikDADcDACAEQagCaiADQZgcaikDADcDACAEIAMpA5AcNwOgAiAEQfgCaiAJQShqKQMANwMAIARB8AJqIAlBIGopAwA3AwAgBEHoAmogCUEYaikDADcDACAEQeACaiAJQRBqKQMANwMAIARB2AJqIAlBCGopAwA3AwAgBCAJKQMANwPQAiAEQagDaiADQegcaikDADcDACAEQaADaiADQeAcaikDADcDACAEQZgDaiADQdgcaikDADcDACAEQZADaiADQdAcaikDADcDACAEQYgDaiADQcgcaikDADcDACAEIAMpA8AcNwOAAyAEQdgDaiAKQShqKQMANwMAIARB0ANqIApBIGopAwA3AwAgBEHIA2ogCkEYaikDADcDACAEQcADaiAKQRBqKQMANwMAIARBuANqIApBCGopAwA3AwAgBCAKKQMANwOwAwwFC0EIQcAEEP8EAAsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0GQHGogASADQeAUahC9AiABQegBaiEGIAFBwAFqIQhBACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0HAAmogBSAGaikDACIPQgAgHEIAEMkDIANB0AJqIA9CACAXQgAQyQMgA0HgAmogD0IAIBhCABDJAyADQfACaiAPQgAgGUIAEMkDIANBgANqIA9CACAbQgAQyQMgA0GQA2ogD0IAIB1CABDJAyADQbACaiADKQPAAiIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0GgAmogAykDuAIiD0IAQqvV/v///7//uX9CABDJAyADQZACaiAPQgBC///Piuv//9UeQgAQyQMgA0GAAmogD0IAQqTsw7WP1LSY5wBCABDJAyADQfABaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB4AFqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HQAWogD0IAQprN/8ujvcSAGkIAEMkDIAMpA9gBIBIgAykDkAMiGnwiDyADKQOIAyARIAMpA4ADIhJ8IhMgElStfCATIAMpA/gCIAMpA/ACIhEgEHwiECARVK18IBAgAykD6AIgAykD4AIiESAOfCIOIBFUrXwgDiADKQPYAiADKQPQAiIRIA18Ig0gEVStfCANIAMpA8gCIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA9ABfCIVIBNUrXwgFSAVIAMpA+gBIBAgECADKQPgAXwiEVatfCARIBEgAykD+AEgDiAOIAMpA/ABfCIQVq18IBAgECADKQOIAiANIA0gAykDgAJ8Ig5WrXwgDiAOIAMpA5gCIBIgAykDkAIiEnwiDSASVK18IA0gAykDqAIgFCADKQOgAiISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykDmAMgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUEwaiEFAkACQCASQprN/8ujvcSAGlYNACASQprN/8ujvcSAGlIEQCANIQ8gDiEUIBAhEyARIRUMAgsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0HAHGogBSADQeAUahC9AiABQZgCaiEJIAFB8AFqIQZBACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0HwAGogBSAJaikDACIPQgAgHEIAEMkDIANBgAFqIA9CACAXQgAQyQMgA0GQAWogD0IAIBhCABDJAyADQaABaiAPQgAgGUIAEMkDIANBsAFqIA9CACAbQgAQyQMgA0HAAWogD0IAIB1CABDJAyADQeAAaiADKQNwIhUgFnwiFEIAQgBC/f/z/8////mJfxDJAyADQdAAaiADKQNoIg9CAEKr1f7///+//7l/QgAQyQMgA0FAayAPQgBC///Piuv//9UeQgAQyQMgA0EwaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANBIGogD0IAQr+llJzP8NK75ABCABDJAyADQRBqIA9CAELX2a6a5PbpjcsAQgAQyQMgAyAPQgBCms3/y6O9xIAaQgAQyQMgAykDCCASIAMpA8ABIhp8Ig8gAykDuAEgESADKQOwASISfCITIBJUrXwgEyADKQOoASADKQOgASIRIBB8IhAgEVStfCAQIAMpA5gBIAMpA5ABIhEgDnwiDiARVK18IA4gAykDiAEgAykDgAEiESANfCINIBFUrXwgDSADKQN4IBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpAwB8IhUgE1StfCAVIBUgAykDGCAQIBAgAykDEHwiEVatfCARIBEgAykDKCAOIA4gAykDIHwiEFatfCAQIBAgAykDOCANIA0gAykDMHwiDlatfCAOIA4gAykDSCASIAMpA0AiEnwiDSASVK18IA0gAykDWCAUIAMpA1AiEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA8gBIA8gGlStfHx8IRIgBUEIayIFQVBHDQALIAFB4ABqIQECQAJAIBJCms3/y6O9xIAaVg0AIBJCms3/y6O9xIAaUgRAIA0hFyAOIRggECEZIBEhGwwCCyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgDSEXIA4hGCAQIRkgESEbDAELIBBCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRsgEEK/pZScz/DSu+QAUgRAIA0hFyAOIRggECEZDAELIA5CpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRkgDkKk7MO1j9S0mOcAUgRAIA0hFyAOIRgMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEYIA1C///Piuv//9UeUgRAIA0hFwwBC0L//8+K6///1R4hFyAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiESDAELIA1C///Piuv//9UefSIPIBZCq9X+////v/+5f1StIhR9IRcgDkKk7MO1j9S0mOcAfSITIA1C///Piuv//9UeVCAPIBRUcq0iDX0hGCAQQr+llJzP8NK75AB9Ig8gDkKk7MO1j9S0mOcAVCANIBNWcq0iDX0hGSARQtfZrprk9umNywB9Ig4gEEK/pZScz/DSu+QAVCANIA9Wcq0iDX0hGyASIBFC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IRIgFkLVqoGAgIDAgMYAfCEWCyADIBY3A4gVIAMgFzcDgBUgAyAYNwP4FCADIBk3A/AUIAMgGzcD6BQgAyASNwPgFCAEQcABaiABIANB4BRqEL0CIAQgAykDkBw3AwAgBEEIaiADQZgcaikDADcDACAEQRBqIANBoBxqKQMANwMAIARBGGogA0GoHGopAwA3AwAgBEEgaiADQbAcaikDADcDACAEQShqIANBuBxqKQMANwMAIARBmAJqIAZBKGopAwA3AwAgBEGQAmogBkEgaikDADcDACAEQYgCaiAGQRhqKQMANwMAIARBgAJqIAZBEGopAwA3AwAgBEH4AWogBkEIaikDADcDACAEIAYpAwA3A/ABIARB2ABqIAdBKGopAwA3AwAgBEHQAGogB0EgaikDADcDACAEQcgAaiAHQRhqKQMANwMAIARBQGsgB0EQaikDADcDACAEQThqIAdBCGopAwA3AwAgBCAHKQMANwMwIARBiAFqIANB6BxqKQMANwMAIARBgAFqIANB4BxqKQMANwMAIARB+ABqIANB2BxqKQMANwMAIARB8ABqIANB0BxqKQMANwMAIARB6ABqIANByBxqKQMANwMAIAQgAykDwBw3A2AgBEG4AWogCEEoaikDADcDACAEQbABaiAIQSBqKQMANwMAIARBqAFqIAhBGGopAwA3AwAgBEGgAWogCEEQaikDADcDACAEQZgBaiAIQQhqKQMANwMAIAQgCCkDADcDkAEMAQtBCEGgAhD/BAALIAAgAjYCCCAAIAQ2AgQgACACNgIAIANB8BxqJAALpocBAgp/G34jAEHwHGsiAyQAIAMgAjYC3BQgA0EMNgLYFAJAAkAgAkEMRgRAIANB4BRqECYgA0HwE2ogAykD8BciDUIAQsau0OHB5sfvdEIAEMkDIANB4BNqIAMpA/ATQn6DIhRCAEIAQv3/8//P///5iX8QyQMgA0HQE2ogAykD6BMiDkIAQqvV/v///7//uX9CABDJAyADQcATaiAOQgBC///Piuv//9UeQgAQyQMgA0HAEmogDkIAQqTsw7WP1LSY5wBCABDJAyADQcARaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBwBBqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HAD2ogDkIAQprN/8ujvcSAGkIAEMkDIANBgBRqIA1CAELxicTO4NS5uwpCABDJAyADQbATaiADKQOAFCIQIAMpA8ATIhMgAykD+BN8Ig8gAykD2BMgAykD0BMiDiAUfCAOVK18fCIRfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBNqIAMpA7gTIg5CAEKr1f7///+//7l/QgAQyQMgA0GQE2ogDkIAQv//z4rr///VHkIAEMkDIANBgBNqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEmogDkIAQr+llJzP8NK75ABCABDJAyADQeASaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BJqIA5CAEKazf/Lo73EgBpCABDJAyADQZAUaiANQgBC1e3W5MTt0fKNf0IAEMkDIANBsBJqIAMpA5AUIhUgAykDkBMiFyADKQOIFCAQIBRWrXwiECADKQPAEiIYIA8gEVatIAMpA8gTIA8gE1StfHx8IhN8IhF8Ig8gAykDqBMgAykDoBMiDiAUfCAOVK18fCIZfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBJqIAMpA7gSIg5CAEKr1f7///+//7l/QgAQyQMgA0GQEmogDkIAQv//z4rr///VHkIAEMkDIANBgBJqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEWogDkIAQr+llJzP8NK75ABCABDJAyADQeARaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BFqIA5CAEKazf/Lo73EgBpCABDJAyADQaAUaiANQgBCwIf2nJmV4vXnAEIAEMkDIANBsBFqIAMpA6AUIhsgAykDkBIiEiADKQOYFCAUIBVUrXwiFSAQIBFWrSIRIAMpA8ARIhYgAykDyBIgEyAYVK18fCIYfCIQIAMpA4ATfCITIA8gGVatIAMpA5gTIA8gF1StfHx8Ihd8Ihl8Ig8gAykDqBIgAykDoBIiDiAUfCAOVK18fCIcfCIUQgBCAEL9//P/z///+Yl/EMkDIANBoBFqIAMpA7gRIg5CAEKr1f7///+//7l/QgAQyQMgA0GQEWogDkIAQv//z4rr///VHkIAEMkDIANBgBFqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HwEGogDkIAQr+llJzP8NK75ABCABDJAyADQeAQaiAOQgBC19mumuT26Y3LAEIAEMkDIANB0BBqIA5CAEKazf/Lo73EgBpCABDJAyADQbAUaiANQgBCrarmqNvQz7yaf0IAEMkDIANBsBBqIAMpA7AUIh0gAykDkBEiGiADKQOoFCAUIBtUrXwiGyAVIBlWrSIZIBAgEVStIh4gAykDwBAiHyADKQPIESAWIBhWrXx8Ihh8IhEgAykD8BJ8IhUgEyAXVq0gAykDiBMgECATVq18fHwiFnwiECADKQOAEnwiEyAPIBxWrSADKQOYEiAPIBJUrXx8fCISfCIXfCIPIAMpA6gRIAMpA6ARIg4gFHwgDlStfHwiHHwiFEIAQgBC/f/z/8////mJfxDJAyADQaAQaiADKQO4ECIOQgBCq9X+////v/+5f0IAEMkDIANBkBBqIA5CAEL//8+K6///1R5CABDJAyADQYAQaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANB8A9qIA5CAEK/pZScz/DSu+QAQgAQyQMgA0HgD2ogDkIAQtfZrprk9umNywBCABDJAyADQdAPaiAOQgBCms3/y6O9xIAaQgAQyQMgA0HAFGogDUIAQqrHq5bZ/KPMEUIAEMkDIANBsA9qIAMpA8AUIiAgAykDkBAiISADKQO4FCAUIB1UrXwiHSAXIBtUrSIbIBAgGVStIhkgESAeVK0iHiADKQPADyIiIAMpA8gQIBggH1StfHwiGHwiDiADKQPgEnwiFyAVIBZWrSADKQP4EiARIBVWrXx8fCIWfCIRIAMpA/ARfCIVIBIgE1StIAMpA4gSIBAgE1atfHx8IhJ8IhAgAykDgBF8IhMgDyAcVq0gAykDmBEgDyAaVK18fHwiHHwiGnwiDyADKQOoECADKQOgECINIBR8IA1UrXx8Ih98IhRCAEIAQv3/8//P///5iX8QyQMgA0GgD2ogAykDuA8iDUIAQqvV/v///7//uX9CABDJAyADQZAPaiANQgBC///Piuv//9UeQgAQyQMgA0GAD2ogDUIAQqTsw7WP1LSY5wBCABDJAyADQfAOaiANQgBCv6WUnM/w0rvkAEIAEMkDIANB4A5qIA1CAELX2a6a5PbpjcsAQgAQyQMgA0HQDmogDUIAQprN/8ujvcSAGkIAEMkDIAMpA9gOIAMpA9AOIiMgAykD2A8gAykD0A8iJCADKQPYECADKQPQECIlIAMpA9gRIAMpA9ARIiYgAykD2BIgAykD0BIiJyAOIB5UrSADKQPIDyAYICJUrXx8fCINICdUrXwgDSANIBYgF1StIAMpA+gSIA4gF1atfHx8Ig5WrXwgDiARIBlUrSIOfCINIA5UrXx8Ig4gJlStfCAOIA4gAykD6BEgDSANIAMpA+ARfCIXVq18IBcgFyASIBVUrSADKQP4ESARIBVWrXx8fCINVq18fCIRVq18IBEgECAbVK0iDiANfCINIA5UrSIVfCIOIBVUrXx8IhEgJVStfCARIAMpA+gQIA4gDiADKQPgEHwiFVatfCAVIBUgAykD+BAgDSANIAMpA/AQfCIOVq18IA4gDiATIBxWrSADKQOIESAQIBNWrXx8fCINVq18fCIOVq18fCIQIBFUrXwgECAOIBogHVStIhMgDXwiDSATVK0iE3wiDiATVK0iE3wiECATVK18fCITICRUrXwgEyADKQPoDyAQIBAgAykD4A98IhFWrXwgESADKQP4DyAOIA4gAykD8A98IhBWrXwgECAQIAMpA4gQIA0gDSADKQOAEHwiDlatfCAOIA4gDyAfVq0gAykDmBAgDyAhVK18fHwiDVatfHwiDlatfHwiDyARVK18fCIQIBNUrXwgECAPIA4gDSADKQPIFCAUICBUrXwiE3wiESATVK0iE3wiDSATVK0iE3wiDiATVK0iE3wiDyATVK18fCIQICNUrXwgECADKQPoDiAPIA8gAykD4A58IhNWrXwgEyADKQP4DiAOIA4gAykD8A58Ig9WrXwgDyADKQOIDyANIA0gAykDgA98Ig5WrXwgDiADKQOYDyARIAMpA5APIhF8Ig0gEVStfCANIAMpA6gPIBQgAykDoA8iEXwgEVStfHwiHCANVK18fCIXIA5UrXx8IhggD1StfHwiGSATVK18fCIbIBBUrXwiHUKazf/Lo73EgBpSDQICQCAbQtfZrprk9umNywBWDQBCms3/y6O9xIAaIR0gG0LX2a6a5PbpjcsAUg0DIBlCv6WUnM/w0rvkAFYNACAZQr+llJzP8NK75ABSBEBC19mumuT26Y3LACEbDAQLIBhCpOzDtY/UtJjnAFYNACAYQqTsw7WP1LSY5wBSDQIgF0L//8+K6///1R5WDQAgF0L//8+K6///1R5SBEBCpOzDtY/UtJjnACEYDAMLIBxCq9X+////v/+5f1oNAEL//8+K6///1R4hF0Kk7MO1j9S0mOcAIRgMAgtCf0IAIBtC19mumuT26Y3LAH0iDSAZQr+llJzP8NK75ABUIBlCv6WUnM/w0rvkAH0iDiAYQqTsw7WP1LSY5wBUIBhCpOzDtY/UtJjnAH0iDyAXQv//z4rr///VHlQgF0L//8+K6///1R59IhQgHEKr1f7///+//7l/VK0iEFRyrSITVHKtIhFUcq0iFVQbIR0gFCAQfSEXIA8gE30hGCAOIBF9IRkgDSAVfSEbIBxC1aqBgICAwIDGAHwhHAwCCyADQQA2AuAUIANB3BRqIANB2BRqIANB4BRqQbyGwAAQlwQAC0K/pZScz/DSu+QAIRlC19mumuT26Y3LACEbCyADKALsGiIEBEAgAygC8BogBEECdBDfBAsCQCADKALkFCIERQ0AIAQgBEEMbEETakF4cSIFakEJaiIERQ0AIAMoAuAUIAVrIAQQ3wQLIAMoAuAXIgRBgICAgHhGIARFckUEQCADKALkFyAEQQJ0EN8ECwJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgAkECaw4LAQAAAAIAAAAAAAMACyADQQA2AvAUIANBATYC5BQgA0GIicAANgLgFCADQgQ3AugUIANB4BRqQZCJwAAQqAQAC0HRzsUALQAAGkHgAEEIENYEIgRFDQIgBCABKQMANwMAIAQgASkDMDcDMCAEQShqIAFBKGopAwA3AwAgBEEgaiABQSBqKQMANwMAIARBGGogAUEYaikDADcDACAEQRBqIAFBEGopAwA3AwAgBEEIaiABQQhqKQMANwMAIARBOGogAUE4aikDADcDACAEQUBrIAFBQGspAwA3AwAgBEHIAGogAUHIAGopAwA3AwAgBEHQAGogAUHQAGopAwA3AwAgBEHYAGogAUHYAGopAwA3AwAMCwtB0c7FAC0AABpBoAJBCBDWBCIERQ0JIAFBMGohB0HYACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0GQBGogASAFaikDACIPQgAgHEIAEMkDIANBoARqIA9CACAXQgAQyQMgA0GwBGogD0IAIBhCABDJAyADQcAEaiAPQgAgGUIAEMkDIANB0ARqIA9CACAbQgAQyQMgA0HgBGogD0IAIB1CABDJAyADQYAEaiADKQOQBCIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0HwA2ogAykDiAQiD0IAQqvV/v///7//uX9CABDJAyADQeADaiAPQgBC///Piuv//9UeQgAQyQMgA0HQA2ogD0IAQqTsw7WP1LSY5wBCABDJAyADQcADaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANBsANqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0GgA2ogD0IAQprN/8ujvcSAGkIAEMkDIAMpA6gDIBIgAykD4AQiGnwiDyADKQPYBCARIAMpA9AEIhJ8IhMgElStfCATIAMpA8gEIAMpA8AEIhEgEHwiECARVK18IBAgAykDuAQgAykDsAQiESAOfCIOIBFUrXwgDiADKQOoBCADKQOgBCIRIA18Ig0gEVStfCANIAMpA5gEIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA6ADfCIVIBNUrXwgFSAVIAMpA7gDIBAgECADKQOwA3wiEVatfCARIBEgAykDyAMgDiAOIAMpA8ADfCIQVq18IBAgECADKQPYAyANIA0gAykD0AN8Ig5WrXwgDiAOIAMpA+gDIBIgAykD4AMiEnwiDSASVK18IA0gAykD+AMgFCADKQPwAyISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykD6AQgDyAaVK18fHwhEiAFQQhrIgVBKEcNAAsgEkKazf/Lo73EgBpWDQcgEkKazf/Lo73EgBpRDQYgDSEPIA4hFCAQIRMgESEVDAgLQdHOxQAtAAAaQcAEQQgQ1gQiBEUNBCABQTBqIQdB2AAhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANB8A1qIAEgBWopAwAiD0IAIBxCABDJAyADQYAOaiAPQgAgF0IAEMkDIANBkA5qIA9CACAYQgAQyQMgA0GgDmogD0IAIBlCABDJAyADQbAOaiAPQgAgG0IAEMkDIANBwA5qIA9CACAdQgAQyQMgA0HgDWogAykD8A0iFSAWfCIUQgBCAEL9//P/z///+Yl/EMkDIANB0A1qIAMpA+gNIg9CAEKr1f7///+//7l/QgAQyQMgA0HADWogD0IAQv//z4rr///VHkIAEMkDIANBsA1qIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0GgDWogD0IAQr+llJzP8NK75ABCABDJAyADQZANaiAPQgBC19mumuT26Y3LAEIAEMkDIANBgA1qIA9CAEKazf/Lo73EgBpCABDJAyADKQOIDSASIAMpA8AOIhp8Ig8gAykDuA4gESADKQOwDiISfCITIBJUrXwgEyADKQOoDiADKQOgDiIRIBB8IhAgEVStfCAQIAMpA5gOIAMpA5AOIhEgDnwiDiARVK18IA4gAykDiA4gAykDgA4iESANfCINIBFUrXwgDSADKQP4DSAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQOADXwiFSATVK18IBUgFSADKQOYDSAQIBAgAykDkA18IhFWrXwgESARIAMpA6gNIA4gDiADKQOgDXwiEFatfCAQIBAgAykDuA0gDSANIAMpA7ANfCIOVq18IA4gDiADKQPIDSASIAMpA8ANIhJ8Ig0gElStfCANIAMpA9gNIBQgAykD0A0iEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA8gOIA8gGlStfHx8IRIgBUEIayIFQShHDQALIBJCms3/y6O9xIAaVg0CIBJCms3/y6O9xIAaUQ0BIA0hDyAOIRQgECETIBEhFQwDC0EIQeAAQbiFwAAQyAQACyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgDSEPIA4hFCAQIRMgESEVDAELIBBCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRUgEEK/pZScz/DSu+QAUgRAIA0hDyAOIRQgECETDAELIA5CpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRMgDkKk7MO1j9S0mOcAUgRAIA0hDyAOIRQMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA1C///Piuv//9UeUgRAIA0hDwwBC0L//8+K6///1R4hDyAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiESDAELIA1C///Piuv//9UefSIUIBZCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIVIA1C///Piuv//9UeVCATIBRWcq0iDX0hFCAQQr+llJzP8NK75AB9IhogDkKk7MO1j9S0mOcAVCANIBVWcq0iDX0hEyARQtfZrprk9umNywB9Ig4gEEK/pZScz/DSu+QAVCANIBpWcq0iDX0hFSASIBFC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IRIgFkLVqoGAgIDAgMYAfCEWCyADIBY3A4gVIAMgDzcDgBUgAyAUNwP4FCADIBM3A/AUIAMgFTcD6BQgAyASNwPgFCADQYAbaiABIANB4BRqEIMCIAFB+AJqIQYgAUHQAmohCEEAIQVCACESQgAhEUIAIRBCACEOQgAhDUIAIRYDQCADQaAMaiAFIAZqKQMAIg9CACAcQgAQyQMgA0GwDGogD0IAIBdCABDJAyADQcAMaiAPQgAgGEIAEMkDIANB0AxqIA9CACAZQgAQyQMgA0HgDGogD0IAIBtCABDJAyADQfAMaiAPQgAgHUIAEMkDIANBkAxqIAMpA6AMIhUgFnwiFEIAQgBC/f/z/8////mJfxDJAyADQYAMaiADKQOYDCIPQgBCq9X+////v/+5f0IAEMkDIANB8AtqIA9CAEL//8+K6///1R5CABDJAyADQeALaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANB0AtqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0HAC2ogD0IAQtfZrprk9umNywBCABDJAyADQbALaiAPQgBCms3/y6O9xIAaQgAQyQMgAykDuAsgEiADKQPwDCIafCIPIAMpA+gMIBEgAykD4AwiEnwiEyASVK18IBMgAykD2AwgAykD0AwiESAQfCIQIBFUrXwgECADKQPIDCADKQPADCIRIA58Ig4gEVStfCAOIAMpA7gMIAMpA7AMIhEgDXwiDSARVK18IA0gAykDqAwgFCAVVK18fCISIA1UrXx8Ig0gDlStfHwiDiAQVK18fCIQIBNUrXx8IhMgAykDsAt8IhUgE1StfCAVIBUgAykDyAsgECAQIAMpA8ALfCIRVq18IBEgESADKQPYCyAOIA4gAykD0At8IhBWrXwgECAQIAMpA+gLIA0gDSADKQPgC3wiDlatfCAOIA4gAykD+AsgEiADKQPwCyISfCINIBJUrXwgDSADKQOIDCAUIAMpA4AMIhJ8IBJUrXx8IhYgDVStfHwiDVatfHwiDlatfHwiEFatfHwiEVatfCAPIBNWrSADKQP4DCAPIBpUrXx8fCESIAVBCGsiBUFQRw0ACyABQaACaiEFAkACQCASQprN/8ujvcSAGlYNACASQprN/8ujvcSAGlIEQCANIQ8gDiEUIBAhEyARIRUMAgsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0GwG2ogBSADQeAUahCDAiABQbgBaiEJIAFBkAFqIQZBACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0HQCmogBSAJaikDACIPQgAgHEIAEMkDIANB4ApqIA9CACAXQgAQyQMgA0HwCmogD0IAIBhCABDJAyADQYALaiAPQgAgGUIAEMkDIANBkAtqIA9CACAbQgAQyQMgA0GgC2ogD0IAIB1CABDJAyADQcAKaiADKQPQCiIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0GwCmogAykDyAoiD0IAQqvV/v///7//uX9CABDJAyADQaAKaiAPQgBC///Piuv//9UeQgAQyQMgA0GQCmogD0IAQqTsw7WP1LSY5wBCABDJAyADQYAKaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB8AlqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HgCWogD0IAQprN/8ujvcSAGkIAEMkDIAMpA+gJIBIgAykDoAsiGnwiDyADKQOYCyARIAMpA5ALIhJ8IhMgElStfCATIAMpA4gLIAMpA4ALIhEgEHwiECARVK18IBAgAykD+AogAykD8AoiESAOfCIOIBFUrXwgDiADKQPoCiADKQPgCiIRIA18Ig0gEVStfCANIAMpA9gKIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA+AJfCIVIBNUrXwgFSAVIAMpA/gJIBAgECADKQPwCXwiEVatfCARIBEgAykDiAogDiAOIAMpA4AKfCIQVq18IBAgECADKQOYCiANIA0gAykDkAp8Ig5WrXwgDiAOIAMpA6gKIBIgAykDoAoiEnwiDSASVK18IA0gAykDuAogFCADKQOwCiISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykDqAsgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUHgAGohBQJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgDSEPIA4hFCAQIRMgESEVDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCANIQ8gDiEUIBAhEyARIRUMAQsgEEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhFSAQQr+llJzP8NK75ABSBEAgDSEPIA4hFCAQIRMMAQsgDkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhEyAOQqTsw7WP1LSY5wBSBEAgDSEPIA4hFAwBCyANQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRQgDUL//8+K6///1R5SBEAgDSEPDAELQv//z4rr///VHiEPIBZCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgDUL//8+K6///1R59IhQgFkKr1f7///+//7l/VK0iE30hDyAOQqTsw7WP1LSY5wB9IhUgDUL//8+K6///1R5UIBMgFFZyrSINfSEUIBBCv6WUnM/w0rvkAH0iGiAOQqTsw7WP1LSY5wBUIA0gFVZyrSINfSETIBFC19mumuT26Y3LAH0iDiAQQr+llJzP8NK75ABUIA0gGlZyrSINfSEVIBIgEULX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hEiAWQtWqgYCAgMCAxgB8IRYLIAMgFjcDiBUgAyAPNwOAFSADIBQ3A/gUIAMgEzcD8BQgAyAVNwPoFCADIBI3A+AUIANB4BtqIAUgA0HgFGoQgwIgAUHYA2ohCiABQbADaiEJQQAhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANBgAlqIAUgCmopAwAiD0IAIBxCABDJAyADQZAJaiAPQgAgF0IAEMkDIANBoAlqIA9CACAYQgAQyQMgA0GwCWogD0IAIBlCABDJAyADQcAJaiAPQgAgG0IAEMkDIANB0AlqIA9CACAdQgAQyQMgA0HwCGogAykDgAkiFSAWfCIUQgBCAEL9//P/z///+Yl/EMkDIANB4AhqIAMpA/gIIg9CAEKr1f7///+//7l/QgAQyQMgA0HQCGogD0IAQv//z4rr///VHkIAEMkDIANBwAhqIA9CAEKk7MO1j9S0mOcAQgAQyQMgA0GwCGogD0IAQr+llJzP8NK75ABCABDJAyADQaAIaiAPQgBC19mumuT26Y3LAEIAEMkDIANBkAhqIA9CAEKazf/Lo73EgBpCABDJAyADKQOYCCASIAMpA9AJIhp8Ig8gAykDyAkgESADKQPACSISfCITIBJUrXwgEyADKQO4CSADKQOwCSIRIBB8IhAgEVStfCAQIAMpA6gJIAMpA6AJIhEgDnwiDiARVK18IA4gAykDmAkgAykDkAkiESANfCINIBFUrXwgDSADKQOICSAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQOQCHwiFSATVK18IBUgFSADKQOoCCAQIBAgAykDoAh8IhFWrXwgESARIAMpA7gIIA4gDiADKQOwCHwiEFatfCAQIBAgAykDyAggDSANIAMpA8AIfCIOVq18IA4gDiADKQPYCCASIAMpA9AIIhJ8Ig0gElStfCANIAMpA+gIIBQgAykD4AgiEnwgElStfHwiFiANVK18fCINVq18fCIOVq18fCIQVq18fCIRVq18IA8gE1atIAMpA9gJIA8gGlStfHx8IRIgBUEIayIFQVBHDQALIAFBgANqIQUCQAJAIBJCms3/y6O9xIAaVg0AIBJCms3/y6O9xIAaUgRAIA0hDyAOIRQgECETIBEhFQwCCyARQtfZrprk9umNywBWDQACQCARQtfZrprk9umNywBSBEAgDSEPIA4hFCAQIRMgESEVDAELIBBCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRUgEEK/pZScz/DSu+QAUgRAIA0hDyAOIRQgECETDAELIA5CpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIRMgDkKk7MO1j9S0mOcAUgRAIA0hDyAOIRQMAQsgDUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEUIA1C///Piuv//9UeUgRAIA0hDwwBC0L//8+K6///1R4hDyAWQqrV/v///7//uX9WDQELQprN/8ujvcSAGiESDAELIA1C///Piuv//9UefSIUIBZCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIVIA1C///Piuv//9UeVCATIBRWcq0iDX0hFCAQQr+llJzP8NK75AB9IhogDkKk7MO1j9S0mOcAVCANIBVWcq0iDX0hEyARQtfZrprk9umNywB9Ig4gEEK/pZScz/DSu+QAVCANIBpWcq0iDX0hFSASIBFC19mumuT26Y3LAFQgDSAOVnKtfUKazf/Lo73EgBp9IRIgFkLVqoGAgIDAgMYAfCEWCyADIBY3A4gVIAMgDzcDgBUgAyAUNwP4FCADIBM3A/AUIAMgFTcD6BQgAyASNwPgFCADQZAcaiAFIANB4BRqEIMCIAFBmAJqIQsgAUHwAWohCkEAIQVCACESQgAhEUIAIRBCACEOQgAhDUIAIRYDQCADQbAHaiAFIAtqKQMAIg9CACAcQgAQyQMgA0HAB2ogD0IAIBdCABDJAyADQdAHaiAPQgAgGEIAEMkDIANB4AdqIA9CACAZQgAQyQMgA0HwB2ogD0IAIBtCABDJAyADQYAIaiAPQgAgHUIAEMkDIANBoAdqIAMpA7AHIhUgFnwiFEIAQgBC/f/z/8////mJfxDJAyADQZAHaiADKQOoByIPQgBCq9X+////v/+5f0IAEMkDIANBgAdqIA9CAEL//8+K6///1R5CABDJAyADQfAGaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANB4AZqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0HQBmogD0IAQtfZrprk9umNywBCABDJAyADQcAGaiAPQgBCms3/y6O9xIAaQgAQyQMgAykDyAYgEiADKQOACCIafCIPIAMpA/gHIBEgAykD8AciEnwiEyASVK18IBMgAykD6AcgAykD4AciESAQfCIQIBFUrXwgECADKQPYByADKQPQByIRIA58Ig4gEVStfCAOIAMpA8gHIAMpA8AHIhEgDXwiDSARVK18IA0gAykDuAcgFCAVVK18fCISIA1UrXx8Ig0gDlStfHwiDiAQVK18fCIQIBNUrXx8IhMgAykDwAZ8IhUgE1StfCAVIBUgAykD2AYgECAQIAMpA9AGfCIRVq18IBEgESADKQPoBiAOIA4gAykD4AZ8IhBWrXwgECAQIAMpA/gGIA0gDSADKQPwBnwiDlatfCAOIA4gAykDiAcgEiADKQOAByISfCINIBJUrXwgDSADKQOYByAUIAMpA5AHIhJ8IBJUrXx8IhYgDVStfHwiDVatfHwiDlatfHwiEFatfHwiEVatfCAPIBNWrSADKQOICCAPIBpUrXx8fCESIAVBCGsiBUFQRw0ACyABQcABaiEFAkACQCASQprN/8ujvcSAGlYNACASQprN/8ujvcSAGlIEQCANIQ8gDiEUIBAhEyARIRUMAgsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0HAHGogBSADQeAUahCDAiABQbgEaiEMIAFBkARqIQtBACEFQgAhFkIAIQ1CACEOQgAhEEIAIRFCACESA0AgA0HgBWogBSAMaikDACIPQgAgHEIAEMkDIANB8AVqIA9CACAXQgAQyQMgA0GABmogD0IAIBhCABDJAyADQZAGaiAPQgAgGUIAEMkDIANBoAZqIA9CACAbQgAQyQMgA0GwBmogD0IAIB1CABDJAyADQdAFaiADKQPgBSIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0HABWogAykD2AUiD0IAQqvV/v///7//uX9CABDJAyADQbAFaiAPQgBC///Piuv//9UeQgAQyQMgA0GgBWogD0IAQqTsw7WP1LSY5wBCABDJAyADQZAFaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANBgAVqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HwBGogD0IAQprN/8ujvcSAGkIAEMkDIAMpA/gEIBIgAykDsAYiGnwiDyADKQOoBiARIAMpA6AGIhJ8IhMgElStfCATIAMpA5gGIAMpA5AGIhEgEHwiECARVK18IBAgAykDiAYgAykDgAYiESAOfCIOIBFUrXwgDiADKQP4BSADKQPwBSIRIA18Ig0gEVStfCANIAMpA+gFIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA/AEfCIVIBNUrXwgFSAVIAMpA4gFIBAgECADKQOABXwiEVatfCARIBEgAykDmAUgDiAOIAMpA5AFfCIQVq18IBAgECADKQOoBSANIA0gAykDoAV8Ig5WrXwgDiAOIAMpA7gFIBIgAykDsAUiEnwiDSASVK18IA0gAykDyAUgFCADKQPABSISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykDuAYgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUHgA2ohAQJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgDSEXIA4hGCAQIRkgESEbDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCANIRcgDiEYIBAhGSARIRsMAQsgEEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGyAQQr+llJzP8NK75ABSBEAgDSEXIA4hGCAQIRkMAQsgDkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhGSAOQqTsw7WP1LSY5wBSBEAgDSEXIA4hGAwBCyANQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRggDUL//8+K6///1R5SBEAgDSEXDAELQv//z4rr///VHiEXIBZCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgDUL//8+K6///1R59Ig8gFkKr1f7///+//7l/VK0iFH0hFyAOQqTsw7WP1LSY5wB9IhMgDUL//8+K6///1R5UIA8gFFRyrSINfSEYIBBCv6WUnM/w0rvkAH0iDyAOQqTsw7WP1LSY5wBUIA0gE1ZyrSINfSEZIBFC19mumuT26Y3LAH0iDiAQQr+llJzP8NK75ABUIA0gD1ZyrSINfSEbIBIgEULX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hEiAWQtWqgYCAgMCAxgB8IRYLIAMgFjcDiBUgAyAXNwOAFSADIBg3A/gUIAMgGTcD8BQgAyAbNwPoFCADIBI3A+AUIARB8AFqIAEgA0HgFGoQgwIgBEHIAmogB0EoaikDADcDACAEQcACaiAHQSBqKQMANwMAIARBuAJqIAdBGGopAwA3AwAgBEGwAmogB0EQaikDADcDACAEQagCaiAHQQhqKQMANwMAIAQgBykDADcDoAIgBCAIKQMANwPQAiAEQdgCaiAIQQhqKQMANwMAIARB4AJqIAhBEGopAwA3AwAgBEHoAmogCEEYaikDADcDACAEQfACaiAIQSBqKQMANwMAIARB+AJqIAhBKGopAwA3AwAgBEGoA2ogBkEoaikDADcDACAEQaADaiAGQSBqKQMANwMAIARBmANqIAZBGGopAwA3AwAgBEGQA2ogBkEQaikDADcDACAEQYgDaiAGQQhqKQMANwMAIAQgBikDADcDgAMgBEHYA2ogCUEoaikDADcDACAEQdADaiAJQSBqKQMANwMAIARByANqIAlBGGopAwA3AwAgBEHAA2ogCUEQaikDADcDACAEQbgDaiAJQQhqKQMANwMAIAQgCSkDADcDsAMgBEGIBGogCkEoaikDADcDACAEQYAEaiAKQSBqKQMANwMAIARB+ANqIApBGGopAwA3AwAgBEHwA2ogCkEQaikDADcDACAEQegDaiAKQQhqKQMANwMAIAQgCikDADcD4AMgBEG4BGogC0EoaikDADcDACAEQbAEaiALQSBqKQMANwMAIARBqARqIAtBGGopAwA3AwAgBEGgBGogC0EQaikDADcDACAEQZgEaiALQQhqKQMANwMAIAQgCykDADcDkAQgBEEoaiADQagbaikDADcDACAEQSBqIANBoBtqKQMANwMAIARBGGogA0GYG2opAwA3AwAgBEEQaiADQZAbaikDADcDACAEQQhqIANBiBtqKQMANwMAIAQgAykDgBs3AwAgBEHYAGogA0HYG2opAwA3AwAgBEHQAGogA0HQG2opAwA3AwAgBEHIAGogA0HIG2opAwA3AwAgBEFAayADQcAbaikDADcDACAEQThqIANBuBtqKQMANwMAIAQgAykDsBs3AzAgBEGIAWogA0GIHGopAwA3AwAgBEGAAWogA0GAHGopAwA3AwAgBEH4AGogA0H4G2opAwA3AwAgBEHwAGogA0HwG2opAwA3AwAgBEHoAGogA0HoG2opAwA3AwAgBCADKQPgGzcDYCAEQbgBaiADQbgcaikDADcDACAEQbABaiADQbAcaikDADcDACAEQagBaiADQagcaikDADcDACAEQaABaiADQaAcaikDADcDACAEQZgBaiADQZgcaikDADcDACAEIAMpA5AcNwOQASAEQegBaiADQegcaikDADcDACAEQeABaiADQeAcaikDADcDACAEQdgBaiADQdgcaikDADcDACAEQdABaiADQdAcaikDADcDACAEQcgBaiADQcgcaikDADcDACAEIAMpA8AcNwPAAQwFC0EIQcAEEP8EAAsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hDyAOIRQgECETIBEhFQwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEVIBBCv6WUnM/w0rvkAFIEQCANIQ8gDiEUIBAhEwwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACETIA5CpOzDtY/UtJjnAFIEQCANIQ8gDiEUDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhFCANQv//z4rr///VHlIEQCANIQ8MAQtC///Piuv//9UeIQ8gFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iFCAWQqvV/v///7//uX9UrSITfSEPIA5CpOzDtY/UtJjnAH0iFSANQv//z4rr///VHlQgEyAUVnKtIg19IRQgEEK/pZScz/DSu+QAfSIaIA5CpOzDtY/UtJjnAFQgDSAVVnKtIg19IRMgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAaVnKtIg19IRUgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIA83A4AVIAMgFDcD+BQgAyATNwPwFCADIBU3A+gUIAMgEjcD4BQgA0GQHGogASADQeAUahCDAiABQbgBaiEGIAFBkAFqIQhBACEFQgAhEkIAIRFCACEQQgAhDkIAIQ1CACEWA0AgA0HAAmogBSAGaikDACIPQgAgHEIAEMkDIANB0AJqIA9CACAXQgAQyQMgA0HgAmogD0IAIBhCABDJAyADQfACaiAPQgAgGUIAEMkDIANBgANqIA9CACAbQgAQyQMgA0GQA2ogD0IAIB1CABDJAyADQbACaiADKQPAAiIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0GgAmogAykDuAIiD0IAQqvV/v///7//uX9CABDJAyADQZACaiAPQgBC///Piuv//9UeQgAQyQMgA0GAAmogD0IAQqTsw7WP1LSY5wBCABDJAyADQfABaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB4AFqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HQAWogD0IAQprN/8ujvcSAGkIAEMkDIAMpA9gBIBIgAykDkAMiGnwiDyADKQOIAyARIAMpA4ADIhJ8IhMgElStfCATIAMpA/gCIAMpA/ACIhEgEHwiECARVK18IBAgAykD6AIgAykD4AIiESAOfCIOIBFUrXwgDiADKQPYAiADKQPQAiIRIA18Ig0gEVStfCANIAMpA8gCIBQgFVStfHwiEiANVK18fCINIA5UrXx8Ig4gEFStfHwiECATVK18fCITIAMpA9ABfCIVIBNUrXwgFSAVIAMpA+gBIBAgECADKQPgAXwiEVatfCARIBEgAykD+AEgDiAOIAMpA/ABfCIQVq18IBAgECADKQOIAiANIA0gAykDgAJ8Ig5WrXwgDiAOIAMpA5gCIBIgAykDkAIiEnwiDSASVK18IA0gAykDqAIgFCADKQOgAiISfCASVK18fCIWIA1UrXx8Ig1WrXx8Ig5WrXx8IhBWrXx8IhFWrXwgDyATVq0gAykDmAMgDyAaVK18fHwhEiAFQQhrIgVBUEcNAAsgAUHgAGohBQJAAkAgEkKazf/Lo73EgBpWDQAgEkKazf/Lo73EgBpSBEAgDSEPIA4hFCAQIRMgESEVDAILIBFC19mumuT26Y3LAFYNAAJAIBFC19mumuT26Y3LAFIEQCANIQ8gDiEUIBAhEyARIRUMAQsgEEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhFSAQQr+llJzP8NK75ABSBEAgDSEPIA4hFCAQIRMMAQsgDkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhEyAOQqTsw7WP1LSY5wBSBEAgDSEPIA4hFAwBCyANQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRQgDUL//8+K6///1R5SBEAgDSEPDAELQv//z4rr///VHiEPIBZCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRIMAQsgDUL//8+K6///1R59IhQgFkKr1f7///+//7l/VK0iE30hDyAOQqTsw7WP1LSY5wB9IhUgDUL//8+K6///1R5UIBMgFFZyrSINfSEUIBBCv6WUnM/w0rvkAH0iGiAOQqTsw7WP1LSY5wBUIA0gFVZyrSINfSETIBFC19mumuT26Y3LAH0iDiAQQr+llJzP8NK75ABUIA0gGlZyrSINfSEVIBIgEULX2a6a5PbpjcsAVCANIA5Wcq19QprN/8ujvcSAGn0hEiAWQtWqgYCAgMCAxgB8IRYLIAMgFjcDiBUgAyAPNwOAFSADIBQ3A/gUIAMgEzcD8BQgAyAVNwPoFCADIBI3A+AUIANBwBxqIAUgA0HgFGoQgwIgAUGYAmohCSABQfABaiEGQQAhBUIAIRJCACERQgAhEEIAIQ5CACENQgAhFgNAIANB8ABqIAUgCWopAwAiD0IAIBxCABDJAyADQYABaiAPQgAgF0IAEMkDIANBkAFqIA9CACAYQgAQyQMgA0GgAWogD0IAIBlCABDJAyADQbABaiAPQgAgG0IAEMkDIANBwAFqIA9CACAdQgAQyQMgA0HgAGogAykDcCIVIBZ8IhRCAEIAQv3/8//P///5iX8QyQMgA0HQAGogAykDaCIPQgBCq9X+////v/+5f0IAEMkDIANBQGsgD0IAQv//z4rr///VHkIAEMkDIANBMGogD0IAQqTsw7WP1LSY5wBCABDJAyADQSBqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0EQaiAPQgBC19mumuT26Y3LAEIAEMkDIAMgD0IAQprN/8ujvcSAGkIAEMkDIAMpAwggEiADKQPAASIafCIPIAMpA7gBIBEgAykDsAEiEnwiEyASVK18IBMgAykDqAEgAykDoAEiESAQfCIQIBFUrXwgECADKQOYASADKQOQASIRIA58Ig4gEVStfCAOIAMpA4gBIAMpA4ABIhEgDXwiDSARVK18IA0gAykDeCAUIBVUrXx8IhIgDVStfHwiDSAOVK18fCIOIBBUrXx8IhAgE1StfHwiEyADKQMAfCIVIBNUrXwgFSAVIAMpAxggECAQIAMpAxB8IhFWrXwgESARIAMpAyggDiAOIAMpAyB8IhBWrXwgECAQIAMpAzggDSANIAMpAzB8Ig5WrXwgDiAOIAMpA0ggEiADKQNAIhJ8Ig0gElStfCANIAMpA1ggFCADKQNQIhJ8IBJUrXx8IhYgDVStfHwiDVatfHwiDlatfHwiEFatfHwiEVatfCAPIBNWrSADKQPIASAPIBpUrXx8fCESIAVBCGsiBUFQRw0ACyABQcABaiEBAkACQCASQprN/8ujvcSAGlYNACASQprN/8ujvcSAGlIEQCANIRcgDiEYIBAhGSARIRsMAgsgEULX2a6a5PbpjcsAVg0AAkAgEULX2a6a5PbpjcsAUgRAIA0hFyAOIRggECEZIBEhGwwBCyAQQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEbIBBCv6WUnM/w0rvkAFIEQCANIRcgDiEYIBAhGQwBCyAOQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEZIA5CpOzDtY/UtJjnAFIEQCANIRcgDiEYDAELIA1C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhGCANQv//z4rr///VHlIEQCANIRcMAQtC///Piuv//9UeIRcgFkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEgwBCyANQv//z4rr///VHn0iDyAWQqvV/v///7//uX9UrSIUfSEXIA5CpOzDtY/UtJjnAH0iEyANQv//z4rr///VHlQgDyAUVHKtIg19IRggEEK/pZScz/DSu+QAfSIPIA5CpOzDtY/UtJjnAFQgDSATVnKtIg19IRkgEULX2a6a5PbpjcsAfSIOIBBCv6WUnM/w0rvkAFQgDSAPVnKtIg19IRsgEiARQtfZrprk9umNywBUIA0gDlZyrX1Cms3/y6O9xIAafSESIBZC1aqBgICAwIDGAHwhFgsgAyAWNwOIFSADIBc3A4AVIAMgGDcD+BQgAyAZNwPwFCADIBs3A+gUIAMgEjcD4BQgBEHgAGogASADQeAUahCDAiAEQbgBaiAHQShqKQMANwMAIARBsAFqIAdBIGopAwA3AwAgBEGoAWogB0EYaikDADcDACAEQaABaiAHQRBqKQMANwMAIARBmAFqIAdBCGopAwA3AwAgBCAHKQMANwOQASAEIAgpAwA3A8ABIARByAFqIAhBCGopAwA3AwAgBEHQAWogCEEQaikDADcDACAEQdgBaiAIQRhqKQMANwMAIARB4AFqIAhBIGopAwA3AwAgBEHoAWogCEEoaikDADcDACAEQZgCaiAGQShqKQMANwMAIARBkAJqIAZBIGopAwA3AwAgBEGIAmogBkEYaikDADcDACAEQYACaiAGQRBqKQMANwMAIARB+AFqIAZBCGopAwA3AwAgBCAGKQMANwPwASAEQShqIANBuBxqKQMANwMAIARBIGogA0GwHGopAwA3AwAgBEEYaiADQagcaikDADcDACAEQRBqIANBoBxqKQMANwMAIARBCGogA0GYHGopAwA3AwAgBCADKQOQHDcDACAEQdgAaiADQegcaikDADcDACAEQdAAaiADQeAcaikDADcDACAEQcgAaiADQdgcaikDADcDACAEQUBrIANB0BxqKQMANwMAIARBOGogA0HIHGopAwA3AwAgBCADKQPAHDcDMAwBC0EIQaACEP8EAAsgACACNgIIIAAgBDYCBCAAIAI2AgAgA0HwHGokAAvnagIRfxV+IwBBgBFrIgQkACAEQQA2AowPIARCgICAgIABNwKEDyACrUIwfiIVpyEJAkACQAJAAkAgFUIgiKcgCUH4////B0tyDQACQCAJRQRAQQghBwwBC0HRzsUALQAAGkEIIQUgCUEIENYEIgdFDQEgAkUNAEEAIQUgAiEGA0AgBSAJRg0BIAUgB2oiDSABIAVqIgspAwA3AwAgDUEoaiALQShqKQMANwMAIA1BIGogC0EgaikDADcDACANQRhqIAtBGGopAwA3AwAgDUEQaiALQRBqKQMANwMAIA1BCGogC0EIaikDADcDACAFQTBqIQUgBkEBayIGDQALCyAEIAI2AowPIAQgBzYCiA8gBCACNgKEDyADRQRAIAQoAoQPIQMgAgRAIAJBMGwhBiAHIQEDQCAEQcAPaiABQShqKQMAIhU3AwAgBEG4D2ogAUEgaikDACIXNwMAIARBsA9qIAFBGGopAwAiFjcDACAEQagPaiABQRBqKQMAIho3AwAgBEGgD2ogAUEIaikDACIbNwMAIAQgASkDACIYNwOYDyAEQZgQaiAVNwMAIARBkBBqIBc3AwAgBEGIEGogFjcDACAEQYAQaiAaNwMAIARB+A9qIBs3AwAgBCAYNwPwDyAEQaAQaiICIARB8A9qEN8BIAAgAhBdIAFBMGohASAGQTBrIgYNAAsLIANFDQQMAwsgAkEESQ0BIAJBAnYhEyAAQSBqIQ8gBEHgEGohECAEQcAQaiERQQAhAQJAAkACQAJAAkACQANAIAFBAWoiDUECdCIDIAQoAowPIgZLDQZB0c7FAC0AABogBCgCiA9BgANBCBDWBCIGRQ0FIARBADYC0A8gBCAGNgLMDyAEQQQ2AsgPQTAhCyABQcABbGoiFCEBA0AgBEHUD2ogARCfASAEKALYDyESAkAgBCgC3A8iA0UEQCAEQegPakH0lMEAKAIANgIAIARB7JTBACkCADcD4A8MAQtBACEBAkAgA0EATgRAQdHOxQAtAAAaQQEhASADQQEQ1gQiCQ0BIAMhCQsgASAJQaCYwQAQyAQACyADBEAgCSASIAP8CgAAC0EBIQYCQCADQQFGDQAgAyAJaiEHQQAhASADQQF2IgVBAUcEQCADQQFrIQYgBUH+////A3EhCANAIAYgCWoiBS0AACEMIAUgASAJaiIFLQAAOgAAIAUgDDoAACAHIAFBfnNqIgwtAAAhCiAMIAVBAWoiBS0AADoAACAFIAo6AAAgBkECayEGIAggAUECaiIBRw0ACwsgAyIGQQJxRQ0AIAEgCWoiBS0AACEIIAUgByABQX9zaiIBLQAAOgAAIAEgCDoAAAsgBEHgD2ogCSAGQQgQzwIgCSADEN8ECyAEQfAPaiAEQeAPahDLASAEKQP4DyEZIAQpA/APIRYgBEEANgKgDyAEQoCAgIAQNwKYDwJAIBYgGYRQRQRAQQAhBkEBIQMDQCADIQUgBiIBIAQoApgPRgRAIARBmA9qQcTawgAQtgMLIAQoApwPIAFqIBY8AAAgBCABQQFqIgY2AqAPIBlCOIYgFkKAAlQhByAZUCEIIAVBAWohAyAZQgiIIRkgFkIIiIQhFiAHIAhxRQ0AC0EBIQMgBCgCnA8hByABBEAgBiAHaiEIQQAhAyAGQQF2QQFHBEAgBUEBdkH+////B3EhDANAIAEgB2oiBS0AACEKIAUgAyAHaiIFLQAAOgAAIAUgCjoAACAIIANBfnNqIgotAAAhDiAKIAVBAWoiBS0AADoAACAFIA46AAAgAUECayEBIAwgA0ECaiIDRw0ACwsgBkECcQRAIAMgB2oiAS0AACEGIAEgCCADQX9zaiIBLQAAOgAAIAEgBjoAAAsgBCgCnA8hByAEKAKgDyEDCyAEKAKYDyEBIARBoBBqIAcgAxCGASABRQ0BIAcgARDfBAwBCyAEQaAQakEBQQAQhgELIAQpA4gQIRkgBCkDgBAhFiAEQQA2AqAPIARCgICAgBA3ApgPAkAgFiAZhFBFBEBBACEGQQEhAwNAIAMhBSAGIgEgBCgCmA9GBEAgBEGYD2pBxNrCABC2AwsgBCgCnA8gAWogFjwAACAEIAFBAWoiBjYCoA8gGUI4hiAWQoACVCEHIBlQIQggBUEBaiEDIBlCCIghGSAWQgiIhCEWIAcgCHFFDQALQQEhAyAEKAKcDyEHIAEEQCAGIAdqIQhBACEDIAZBAXZBAUcEQCAFQQF2Qf7///8HcSEMA0AgASAHaiIFLQAAIQogBSADIAdqIgUtAAA6AAAgBSAKOgAAIAggA0F+c2oiCi0AACEOIAogBUEBaiIFLQAAOgAAIAUgDjoAACABQQJrIQEgDCADQQJqIgNHDQALCyAGQQJxBEAgAyAHaiIBLQAAIQYgASAIIANBf3NqIgEtAAA6AAAgASAGOgAACyAEKAKcDyEHIAQoAqAPIQMLIAQoApgPIQEgESAHIAMQhgEgAUUNASAHIAEQ3wQMAQsgEUEBQQAQhgELIAQpA5gQIRkgBCkDkBAhFiAEQQA2AqAPIARCgICAgBA3ApgPAkAgFiAZhFBFBEBBACEGQQEhAwNAIAMhBSAGIgEgBCgCmA9GBEAgBEGYD2pBxNrCABC2AwsgBCgCnA8gAWogFjwAACAEIAFBAWoiBjYCoA8gGUI4hiAWQoACVCEHIBlQIQggBUEBaiEDIBlCCIghGSAWQgiIhCEWIAcgCHFFDQALQQEhAyAEKAKcDyEHIAEEQCAGIAdqIQhBACEDIAZBAXZBAUcEQCAFQQF2Qf7///8HcSEMA0AgASAHaiIFLQAAIQogBSADIAdqIgUtAAA6AAAgBSAKOgAAIAggA0F+c2oiCi0AACEOIAogBUEBaiIFLQAAOgAAIAUgDjoAACABQQJrIQEgDCADQQJqIgNHDQALCyAGQQJxBEAgAyAHaiIBLQAAIQYgASAIIANBf3NqIgEtAAA6AAAgASAGOgAACyAEKAKcDyEHIAQoAqAPIQMLIAQoApgPIQEgECAHIAMQhgEgAUUNASAHIAEQ3wQMAQsgEEEBQQAQhgELIAQoAtAPIgEgBCgCyA9GBEAgBEHID2oQngMLIAQoAswPIAFB4ABsaiAEQaAQakHgAPwKAAAgBCABQQFqNgLQDyAEKALgDyIBBEAgBCgC5A8gAUECdBDfBAsgBCgC1A8iAQRAIBIgARDfBAsgCyAUaiEBQQBBMCALQcABRiIDGyALaiELIANFDQALIAQoAtAPIgMEQCAEQYANaiAEKALMDyIBKQM4IhVCAEKAgICAgIARQgAQyQMgBEGQDWogFUIAQoCAgICAfEIAEMkDIARBoA1qIBVCAEJ/QgAQyQMgBEGwDWogFUIAQv///////6ACQgAQyQMgBEHQDGpCACAEKQOADSIXfUIAQpGAgICAgICACEIAEMkDIARBwA1qIAEpAzAiFUIAQoCAgICAgBFCABDJAyAEQdANaiAVQgBCgICAgIB8QgAQyQMgBEHgDWogFUIAQn9CABDJAyAEQfANaiAVQgBC////////oAJCABDJAyAEQeAMakIAIBdCgICAgICAf4MiFSAXfSAVVK0iGiAEKQOIDSIbIAQpA5ANfCIYfCIXIAQpA8ANfCIWfUIAQpGAgICAgICACEIAEMkDIARBgA5qIAEpAygiFUIAQoCAgICAgBFCABDJAyAEQZAOaiAVQgBCgICAgIB8QgAQyQMgBEGgDmogFUIAQn9CABDJAyAEQbAOaiAVQgBC////////oAJCABDJAyAEQfAMakIAIBZCAFKtIiQgFyAaVK0iHCAEKQOYDSAYIBtUrXwiGCAEKQOgDXwiGXwiGiAEKQPQDXwiGyAEKQPIDSAWIBdUrXx8Ih58IhcgBCkDgA58IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEHADmogASkDICIVQgBCgICAgICAEUIAEMkDIARB0A5qIBVCAEKAgICAgHxCABDJAyAEQeAOaiAVQgBCf0IAEMkDIARB8A5qIBVCAEL///////+gAkIAEMkDIARBwAxqQgAgBCkDiA4gFiAXVK18Ih0gBCkDkA58IhUgBCkDqA0gGCAZVq18Ih8gBCkDsA18IhggBCkD0Ax8IhkgGiAcVK18IhwgBCkD4A18IiAgGyAeVq0gBCkD2A0gGiAbVq18fHwiGiAXICRUrXwiI3wiFyAWQgBSrXwiFiAEKQPADnwiG31CAEKRgICAgICAgAhCABDJAyABKQMYISQgASkDECEeIAEpAwghIiABKQMAISYCQAJAIAQpA8gMIAQpA9gOIAQpA8gOIBYgG1atfCIlIAQpA9AOfCIhICVUrXwgISAVIBdWrSAEKQOYDiAVIB1UrXx8IiUgBCkDoA58IhUgGiAjVq0iIyAEKQPgDHwiHSAEKQO4DSAYIB9UrXwiJyAEKQPwDXwiHyAZIBxWrSAEKQPYDCAYIBlWrXx8fCIYIBogIFStIAQpA+gNIBwgIFatfHx8Ihx8IiB8IhogFiAXVK18Ihl8IhcgIVStfCIhIAQpA+AOfCIWIBkgGlStIiggBCkD8Ax8IhkgGCAcVq0gGCAfVK0gBCkD+A0gHyAnVK18fHwiHyAEKQOwDnwiGCAdICBWrSAEKQPoDCAdICNUrXx8fCIcIBUgGlatIAQpA6gOIBUgJVStfHx8IiB8Ih18IhogFyAbQgBSrXwiFSAXVK18IhsgGlStIiMgBCkDwAx8IhcgI1StfCAXIBwgIFatIBggHFatIAQpA7gOIBggH1StfHx8IiAgBCkD8A58IhwgGSAdVq0gBCkD+AwgGSAoVK18fHwiGSAWIBpWrSAEKQPoDiAWICFUrXx8fCIWfCIYIBdUrXwgFiAZVK0gGSAcVK0gBCkD+A4gHCAgVK18fHx8IhlCkYCAgICAgIAIVg0AIBlCkYCAgICAgIAIUQRAIBUgG4QgGIRQRQ0BQgAhFkKRgICAgICAgAghGUIAIRpCACEXDAILIBghFiAbIRogFSEXDAELIBVCAX0hFyAbIBVQrSIVfSEaIBggFSAbVq0iFX0hFiAZIBUgGFatfUKRgICAgICAgAh9IRkLQpGAgICAgICACCEVIBYgInwiFiAiVCAWIBogHnwiGCAeVCAYIBggFyAkfCIaICRUrXwiG1ZyrXwiGCAWVHKtIBkgJnx8IhkhFwJAAkAgGUKRgICAgICAgAhRBEAgGCAbhEIAUg0BQgEhFSAaIhdCAVENAQsgFSAXWA0AIBghFSAbIRcgGiEWDAELIBpCAX0hFiAbIBpQrSIVfSEXIBggFSAbVq0iGn0hFULu/////////3dC7/////////93IBggGlQbIBl8IRkLQpGAgICAgICACCEaIBUgFSAAKQMofCIcViAcIBwgFyAXIAApAzB8IhVWIBUgFiAWIAApAzh8IhtWrXwiFiAVVHKtfCIYVnKtIAApAyAgGXx8IhkhFSAAAn4CQCAZQpGAgICAgICACFEEQCAWIBiEQgBSDQFCASEaIBsiFUIBUQ0BCyAVIBpaDQAgGCEVIBYhFyAbDAELIBYgG1CtIhV9IRcgGCAVIBZWrSIWfSEVQu7/////////d0Lv/////////3cgFiAYVhsgGXwhGSAbQgF9CzcDOCAAIBc3AzAgACAVNwMoIAAgGTcDICADQQFGDQIgASkDWCEcIAEpA1AhICABKQNIISQgASkDQCEjIARBwApqIAEpA3giFUIAQoCAgICAgBFCABDJAyAEQdAKaiAVQgBCgICAgIB8QgAQyQMgBEHgCmogFUIAQn9CABDJAyAEQfAKaiAVQgBC////////oAJCABDJAyAEQZAKakIAIAQpA8AKIhd9QgBCkYCAgICAgIAIQgAQyQMgBEGAC2ogASkDcCIVQgBCgICAgICAEUIAEMkDIARBkAtqIBVCAEKAgICAgHxCABDJAyAEQaALaiAVQgBCf0IAEMkDIARBsAtqIBVCAEL///////+gAkIAEMkDIARBoApqQgAgF0KAgICAgIB/gyIVIBd9IBVUrSIaIAQpA8gKIhsgBCkD0Ap8Ihh8IhcgBCkDgAt8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEHAC2ogASkDaCIVQgBCgICAgICAEUIAEMkDIARB0AtqIBVCAEKAgICAgHxCABDJAyAEQeALaiAVQgBCf0IAEMkDIARB8AtqIBVCAEL///////+gAkIAEMkDIARBsApqQgAgFkIAUq0iISAXIBpUrSIeIAQpA9gKIBggG1StfCIYIAQpA+AKfCIZfCIaIAQpA5ALfCIbIAQpA4gLIBYgF1StfHwiHXwiFyAEKQPAC3wiFn1CAEKRgICAgICAgAhCABDJAyAEQYAMaiABKQNgIhVCAEKAgICAgIARQgAQyQMgBEGQDGogFUIAQoCAgICAfEIAEMkDIARBoAxqIBVCAEJ/QgAQyQMgBEGwDGogFUIAQv///////6ACQgAQyQMgBEGACmpCACAEKQPICyAWIBdUrXwiHyAEKQPQC3wiFSAEKQPoCiAYIBlWrXwiJiAEKQPwCnwiGCAEKQOQCnwiGSAaIB5UrXwiHiAEKQOgC3wiIiAbIB1WrSAEKQOYCyAaIBtWrXx8fCIaIBcgIVStfCIdfCIXIBZCAFKtfCIWIAQpA4AMfCIbfUIAQpGAgICAgICACEIAEMkDAkACQCAEKQOICiAEKQOYDCAEKQOIDCAWIBtWrXwiJSAEKQOQDHwiISAlVK18ICEgFSAXVq0gBCkD2AsgFSAfVK18fCIlIAQpA+ALfCIVIBogHVatIicgBCkDoAp8Ih0gBCkD+AogGCAmVK18IiYgBCkDsAt8Ih8gGSAeVq0gBCkDmAogGCAZVq18fHwiGCAaICJUrSAEKQOoCyAeICJWrXx8fCIifCIofCIaIBYgF1StfCIXfCIWICFUrXwiISAEKQOgDHwiGSAXIBpUrSIpIAQpA7AKfCIeIBggIlatIBggH1StIAQpA7gLIB8gJlStfHx8Ih8gBCkD8At8IhggHSAoVq0gBCkDqAogHSAnVK18fHwiIiAVIBpWrSAEKQPoCyAVICVUrXx8fCIafCIdfCIVIBYgFiAbQgBSrXwiF1atfCIbIBVUrSImIAQpA4AKfCIWICZUrXwgFiAaICJUrSAYICJWrSAEKQP4CyAYIB9UrXx8fCIiIAQpA7AMfCIaIB0gHlStIAQpA7gKIB4gKVStfHx8Ih4gFSAZVK0gBCkDqAwgGSAhVK18fHwiFXwiGCAWVK18IBUgHlStIBogHlatIAQpA7gMIBogIlStfHx8fCIZQpGAgICAgICACFYNACAZQpGAgICAgICACFEEQCAXIBuEIBiEUEUNAUIAIRVCkYCAgICAgIAIIRlCACEWQgAhGgwCCyAYIRUgGyEWIBchGgwBCyAXQgF9IRogGyAXUK0iFX0hFiAYIBUgG1atIhd9IRUgGSAXIBhWrX1CkYCAgICAgIAIfSEZC0KRgICAgICAgAghFyAVICR8IhUgJFQgFSAWICB8IhYgIFQgFiAaIBx8IhogHFStfCIbIBZUcq18IhggFVRyrSAZICN8fCIZIRUCQAJAIBlCkYCAgICAgIAIUQRAIBggG4RCAFINAUIBIRcgGiIVQgFRDQELIBUgF1oNACAYIRUgGyEXIBohFgwBCyAaQgF9IRYgGyAaUK0iFX0hFyAYIBUgG1atIhp9IRVC7v////////93Qu//////////dyAYIBpUGyAZfCEZC0KRgICAgICAgAghGiAVIBUgACkDSHwiHFYgHCAcIBcgFyAAKQNQfCIVViAVIBYgFiAAKQNYfCIbVq18IhYgFVRyrXwiGFZyrSAAKQNAIBl8fCIZIRUgAAJ+AkAgGUKRgICAgICAgAhRBEAgFiAYhEIAUg0BQgEhGiAbIhVCAVENAQsgFSAaWg0AIBghFSAWIRcgGwwBCyAWIBtQrSIVfSEXIBggFSAWVq0iFn0hFULu/////////3dC7/////////93IBYgGFYbIBl8IRkgG0IBfQs3A1ggACAXNwNQIAAgFTcDSCAAIBk3A0AgDxBGIAQoAtAPIgNBAU0NAyAEQYAIaiAEKALMDyIBKQO4ASIVQgBCgICAgICAEUIAEMkDIARBkAhqIBVCAEKAgICAgHxCABDJAyAEQaAIaiAVQgBCf0IAEMkDIARBsAhqIBVCAEL///////+gAkIAEMkDIARB0AdqQgAgBCkDgAgiF31CAEKRgICAgICAgAhCABDJAyAEQcAIaiABKQOwASIVQgBCgICAgICAEUIAEMkDIARB0AhqIBVCAEKAgICAgHxCABDJAyAEQeAIaiAVQgBCf0IAEMkDIARB8AhqIBVCAEL///////+gAkIAEMkDIARB4AdqQgAgF0KAgICAgIB/gyIVIBd9IBVUrSIaIAQpA4gIIhsgBCkDkAh8Ihh8IhcgBCkDwAh8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEGACWogASkDqAEiFUIAQoCAgICAgBFCABDJAyAEQZAJaiAVQgBCgICAgIB8QgAQyQMgBEGgCWogFUIAQn9CABDJAyAEQbAJaiAVQgBC////////oAJCABDJAyAEQfAHakIAIBZCAFKtIiQgFyAaVK0iHCAEKQOYCCAYIBtUrXwiGCAEKQOgCHwiGXwiGiAEKQPQCHwiGyAEKQPICCAWIBdUrXx8Ih58IhcgBCkDgAl8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEHACWogASkDoAEiFUIAQoCAgICAgBFCABDJAyAEQdAJaiAVQgBCgICAgIB8QgAQyQMgBEHgCWogFUIAQn9CABDJAyAEQfAJaiAVQgBC////////oAJCABDJAyAEQcAHakIAIAQpA4gJIBYgF1StfCIdIAQpA5AJfCIVIAQpA6gIIBggGVatfCIfIAQpA7AIfCIYIAQpA9AHfCIZIBogHFStfCIcIAQpA+AIfCIgIBsgHlatIAQpA9gIIBogG1atfHx8IhogFyAkVK18IiN8IhcgFkIAUq18IhYgBCkDwAl8Iht9QgBCkYCAgICAgIAIQgAQyQMgASkDmAEhJCABKQOQASEeIAEpA4gBISIgASkDgAEhJgJAAkAgBCkDyAcgBCkD2AkgBCkDyAkgFiAbVq18IiUgBCkD0Al8IiEgJVStfCAhIBUgF1atIAQpA5gJIBUgHVStfHwiJSAEKQOgCXwiFSAaICNWrSIjIAQpA+AHfCIdIAQpA7gIIBggH1StfCInIAQpA/AIfCIfIBkgHFatIAQpA9gHIBggGVatfHx8IhggGiAgVK0gBCkD6AggHCAgVq18fHwiHHwiIHwiGiAWIBdUrXwiGXwiFyAhVK18IiEgBCkD4Al8IhYgGSAaVK0iKCAEKQPwB3wiGSAYIBxWrSAYIB9UrSAEKQP4CCAfICdUrXx8fCIfIAQpA7AJfCIYIB0gIFatIAQpA+gHIB0gI1StfHx8IhwgFSAaVq0gBCkDqAkgFSAlVK18fHwiIHwiHXwiGiAXIBtCAFKtfCIVIBdUrXwiGyAaVK0iIyAEKQPAB3wiFyAjVK18IBcgHCAgVq0gGCAcVq0gBCkDuAkgGCAfVK18fHwiICAEKQPwCXwiHCAZIB1WrSAEKQP4ByAZIChUrXx8fCIZIBYgGlatIAQpA+gJIBYgIVStfHx8IhZ8IhggF1StfCAWIBlUrSAZIBxUrSAEKQP4CSAcICBUrXx8fHwiGUKRgICAgICAgAhWDQAgGUKRgICAgICAgAhRBEAgFSAbhCAYhFBFDQFCACEWQpGAgICAgICACCEZQgAhGkIAIRcMAgsgGCEWIBshGiAVIRcMAQsgFUIBfSEXIBsgFVCtIhV9IRogGCAVIBtWrSIVfSEWIBkgFSAYVq19QpGAgICAgICACH0hGQtCkYCAgICAgIAIIRUgFiAifCIWICJUIBYgGiAefCIYIB5UIBggGCAXICR8IhogJFStfCIbVnKtfCIYIBZUcq0gGSAmfHwiGSEXAkACQCAZQpGAgICAgICACFEEQCAYIBuEQgBSDQFCASEVIBoiF0IBUQ0BCyAVIBdYDQAgGCEVIBshFyAaIRYMAQsgGkIBfSEWIBsgGlCtIhV9IRcgGCAVIBtWrSIafSEVQu7/////////d0Lv/////////3cgGCAaVBsgGXwhGQtCkYCAgICAgIAIIRogFSAVIAApAyh8IhxWIBwgHCAXIBcgACkDMHwiFVYgFSAWIBYgACkDOHwiG1atfCIWIBVUcq18IhhWcq0gACkDICAZfHwiGSEVIAACfgJAIBlCkYCAgICAgIAIUQRAIBYgGIRCAFINAUIBIRogGyIVQgFRDQELIBUgGloNACAYIRUgFiEXIBsMAQsgFiAbUK0iFX0hFyAYIBUgFlatIhZ9IRVC7v////////93Qu//////////dyAWIBhWGyAZfCEZIBtCAX0LNwM4IAAgFzcDMCAAIBU3AyggACAZNwMgIANBAkYNBCAEQcAFaiABKQP4ASIVQgBCgICAgICAEUIAEMkDIARB0AVqIBVCAEKAgICAgHxCABDJAyAEQeAFaiAVQgBCf0IAEMkDIARB8AVqIBVCAEL///////+gAkIAEMkDIARBkAVqQgAgBCkDwAUiF31CAEKRgICAgICAgAhCABDJAyAEQYAGaiABKQPwASIVQgBCgICAgICAEUIAEMkDIARBkAZqIBVCAEKAgICAgHxCABDJAyAEQaAGaiAVQgBCf0IAEMkDIARBsAZqIBVCAEL///////+gAkIAEMkDIARBoAVqQgAgF0KAgICAgIB/gyIVIBd9IBVUrSIaIAQpA8gFIhsgBCkD0AV8Ihh8IhcgBCkDgAZ8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEHABmogASkD6AEiFUIAQoCAgICAgBFCABDJAyAEQdAGaiAVQgBCgICAgIB8QgAQyQMgBEHgBmogFUIAQn9CABDJAyAEQfAGaiAVQgBC////////oAJCABDJAyAEQbAFakIAIBZCAFKtIiQgFyAaVK0iHCAEKQPYBSAYIBtUrXwiGCAEKQPgBXwiGXwiGiAEKQOQBnwiGyAEKQOIBiAWIBdUrXx8Ih58IhcgBCkDwAZ8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEGAB2ogASkD4AEiFUIAQoCAgICAgBFCABDJAyAEQZAHaiAVQgBCgICAgIB8QgAQyQMgBEGgB2ogFUIAQn9CABDJAyAEQbAHaiAVQgBC////////oAJCABDJAyAEQYAFakIAIAQpA8gGIBYgF1StfCIdIAQpA9AGfCIVIAQpA+gFIBggGVatfCIfIAQpA/AFfCIYIAQpA5AFfCIZIBogHFStfCIcIAQpA6AGfCIgIBsgHlatIAQpA5gGIBogG1atfHx8IhogFyAkVK18IiN8IhcgFkIAUq18IhYgBCkDgAd8Iht9QgBCkYCAgICAgIAIQgAQyQMgASkD2AEhJCABKQPQASEeIAEpA8gBISIgASkDwAEhJgJAAkAgBCkDiAUgBCkDmAcgBCkDiAcgFiAbVq18IiUgBCkDkAd8IiEgJVStfCAhIBUgF1atIAQpA9gGIBUgHVStfHwiJSAEKQPgBnwiFSAaICNWrSIjIAQpA6AFfCIdIAQpA/gFIBggH1StfCInIAQpA7AGfCIfIBkgHFatIAQpA5gFIBggGVatfHx8IhggGiAgVK0gBCkDqAYgHCAgVq18fHwiHHwiIHwiGiAWIBdUrXwiGXwiFyAhVK18IiEgBCkDoAd8IhYgGSAaVK0iKCAEKQOwBXwiGSAYIBxWrSAYIB9UrSAEKQO4BiAfICdUrXx8fCIfIAQpA/AGfCIYIB0gIFatIAQpA6gFIB0gI1StfHx8IhwgFSAaVq0gBCkD6AYgFSAlVK18fHwiIHwiHXwiGiAXIBtCAFKtfCIVIBdUrXwiGyAaVK0iIyAEKQOABXwiFyAjVK18IBcgHCAgVq0gGCAcVq0gBCkD+AYgGCAfVK18fHwiICAEKQOwB3wiHCAZIB1WrSAEKQO4BSAZIChUrXx8fCIZIBYgGlatIAQpA6gHIBYgIVStfHx8IhZ8IhggF1StfCAWIBlUrSAZIBxUrSAEKQO4ByAcICBUrXx8fHwiGUKRgICAgICAgAhWDQAgGUKRgICAgICAgAhRBEAgFSAbhCAYhFBFDQFCACEWQpGAgICAgICACCEZQgAhGkIAIRcMAgsgGCEWIBshGiAVIRcMAQsgFUIBfSEXIBsgFVCtIhV9IRogGCAVIBtWrSIVfSEWIBkgFSAYVq19QpGAgICAgICACH0hGQtCkYCAgICAgIAIIRUgFiAifCIWICJUIBYgGiAefCIYIB5UIBggGCAXICR8IhogJFStfCIbVnKtfCIYIBZUcq0gGSAmfHwiGSEXAkACQCAZQpGAgICAgICACFEEQCAYIBuEQgBSDQFCASEVIBoiF0IBUQ0BCyAVIBdYDQAgGCEVIBshFyAaIRYMAQsgGkIBfSEWIBsgGlCtIhV9IRcgGCAVIBtWrSIafSEVQu7/////////d0Lv/////////3cgGCAaVBsgGXwhGQtCkYCAgICAgIAIIRogFSAVIAApA0h8IhxWIBwgHCAXIBcgACkDUHwiFVYgFSAWIBYgACkDWHwiG1atfCIWIBVUcq18IhhWcq0gACkDQCAZfHwiGSEVIAACfgJAIBlCkYCAgICAgIAIUQRAIBYgGIRCAFINAUIBIRogGyIVQgFRDQELIBUgGloNACAYIRUgFiEXIBsMAQsgFiAbUK0iFX0hFyAYIBUgFlatIhZ9IRVC7v////////93Qu//////////dyAWIBhWGyAZfCEZIBtCAX0LNwNYIAAgFzcDUCAAIBU3A0ggACAZNwNAIA8QRiAEKALQDyIBQQNJDQUgAAJ+AkAgAUEDRwRAIAQoAswPIgEpA5gCIRwgASkDkAIhICABKQOIAiEkIAEpA4ACISMgBEGAA2ogASkDuAIiFUIAQoCAgICAgBFCABDJAyAEQZADaiAVQgBCgICAgIB8QgAQyQMgBEGgA2ogFUIAQn9CABDJAyAEQbADaiAVQgBC////////oAJCABDJAyAEQdACakIAIAQpA4ADIhd9QgBCkYCAgICAgIAIQgAQyQMgBEHAA2ogASkDsAIiFUIAQoCAgICAgBFCABDJAyAEQdADaiAVQgBCgICAgIB8QgAQyQMgBEHgA2ogFUIAQn9CABDJAyAEQfADaiAVQgBC////////oAJCABDJAyAEQeACakIAIBdCgICAgICAf4MiFSAXfSAVVK0iGiAEKQOIAyIbIAQpA5ADfCIYfCIXIAQpA8ADfCIWfUIAQpGAgICAgICACEIAEMkDIARBgARqIAEpA6gCIhVCAEKAgICAgIARQgAQyQMgBEGQBGogFUIAQoCAgICAfEIAEMkDIARBoARqIBVCAEJ/QgAQyQMgBEGwBGogFUIAQv///////6ACQgAQyQMgBEHwAmpCACAWQgBSrSIhIBcgGlStIh4gBCkDmAMgGCAbVK18IhggBCkDoAN8Ihl8IhogBCkD0AN8IhsgBCkDyAMgFiAXVK18fCIdfCIXIAQpA4AEfCIWfUIAQpGAgICAgICACEIAEMkDIARBwARqIAEpA6ACIhVCAEKAgICAgIARQgAQyQMgBEHQBGogFUIAQoCAgICAfEIAEMkDIARB4ARqIBVCAEJ/QgAQyQMgBEHwBGogFUIAQv///////6ACQgAQyQMgBEHAAmpCACAEKQOIBCAWIBdUrXwiHyAEKQOQBHwiFSAEKQOoAyAYIBlWrXwiJiAEKQOwA3wiGCAEKQPQAnwiGSAaIB5UrXwiHiAEKQPgA3wiIiAbIB1WrSAEKQPYAyAaIBtWrXx8fCIaIBcgIVStfCIdfCIXIBZCAFKtfCIWIAQpA8AEfCIbfUIAQpGAgICAgICACEIAEMkDAkACQCAEKQPIAiAEKQPYBCAEKQPIBCAWIBtWrXwiJSAEKQPQBHwiISAlVK18ICEgFSAXVq0gBCkDmAQgFSAfVK18fCIlIAQpA6AEfCIVIBogHVatIicgBCkD4AJ8Ih0gBCkDuAMgGCAmVK18IiYgBCkD8AN8Ih8gGSAeVq0gBCkD2AIgGCAZVq18fHwiGCAaICJUrSAEKQPoAyAeICJWrXx8fCIifCIofCIaIBYgF1StfCIXfCIWICFUrXwiISAEKQPgBHwiGSAXIBpUrSIpIAQpA/ACfCIeIBggIlatIBggH1StIAQpA/gDIB8gJlStfHx8Ih8gBCkDsAR8IhggHSAoVq0gBCkD6AIgHSAnVK18fHwiIiAVIBpWrSAEKQOoBCAVICVUrXx8fCIafCIdfCIVIBYgFiAbQgBSrXwiF1atfCIbIBVUrSImIAQpA8ACfCIWICZUrXwgFiAaICJUrSAYICJWrSAEKQO4BCAYIB9UrXx8fCIiIAQpA/AEfCIaIB0gHlStIAQpA/gCIB4gKVStfHx8Ih4gFSAZVK0gBCkD6AQgGSAhVK18fHwiFXwiGCAWVK18IBUgHlStIBogHlatIAQpA/gEIBogIlStfHx8fCIZQpGAgICAgICACFYNACAZQpGAgICAgICACFEEQCAXIBuEIBiEUEUNAUIAIRVCkYCAgICAgIAIIRlCACEWQgAhGgwCCyAYIRUgGyEWIBchGgwBCyAXQgF9IRogGyAXUK0iFX0hFiAYIBUgG1atIhd9IRUgGSAXIBhWrX1CkYCAgICAgIAIfSEZC0KRgICAgICAgAghFyAVICR8IhUgJFQgFSAWICB8IhYgIFQgFiAaIBx8IhogHFStfCIbIBZUcq18IhggFVRyrSAZICN8fCIZIRUCQAJAIBlCkYCAgICAgIAIUQRAIBggG4RCAFINAUIBIRcgGiIVQgFRDQELIBUgF1oNACAYIRUgGyEXIBohFgwBCyAaQgF9IRYgGyAaUK0iFX0hFyAYIBUgG1atIhp9IRVC7v////////93Qu//////////dyAYIBpUGyAZfCEZC0KRgICAgICAgAghGiAVIBUgACkDKHwiHFYgHCAcIBcgFyAAKQMwfCIVViAVIBYgFiAAKQM4fCIbVq18IhYgFVRyrXwiGFZyrSAAKQMgIBl8fCIZIRUgGUKRgICAgICAgAhRBEAgFiAYhEIAUg0CQgEhGiAbIhVCAVENAgsgFSAaWg0BIBghFSAWIRcgGwwCC0EDQQNB8MvBABDZAwALIBYgG1CtIhV9IRcgGCAVIBZWrSIWfSEVQu7/////////d0Lv/////////3cgFiAYVhsgGXwhGSAbQgF9CzcDOCAAIBc3AzAgACAVNwMoIAAgGTcDICAEQUBrIAEpA/gCIhVCAEKAgICAgIARQgAQyQMgBEHQAGogFUIAQoCAgICAfEIAEMkDIARB4ABqIBVCAEJ/QgAQyQMgBEHwAGogFUIAQv///////6ACQgAQyQMgBEEQakIAIAQpA0AiF31CAEKRgICAgICAgAhCABDJAyAEQYABaiABKQPwAiIVQgBCgICAgICAEUIAEMkDIARBkAFqIBVCAEKAgICAgHxCABDJAyAEQaABaiAVQgBCf0IAEMkDIARBsAFqIBVCAEL///////+gAkIAEMkDIARBIGpCACAXQoCAgICAgH+DIhUgF30gFVStIhogBCkDSCIbIAQpA1B8Ihh8IhcgBCkDgAF8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEHAAWogASkD6AIiFUIAQoCAgICAgBFCABDJAyAEQdABaiAVQgBCgICAgIB8QgAQyQMgBEHgAWogFUIAQn9CABDJAyAEQfABaiAVQgBC////////oAJCABDJAyAEQTBqQgAgFkIAUq0iJCAXIBpUrSIcIAQpA1ggGCAbVK18IhggBCkDYHwiGXwiGiAEKQOQAXwiGyAEKQOIASAWIBdUrXx8Ih58IhcgBCkDwAF8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEGAAmogASkD4AIiFUIAQoCAgICAgBFCABDJAyAEQZACaiAVQgBCgICAgIB8QgAQyQMgBEGgAmogFUIAQn9CABDJAyAEQbACaiAVQgBC////////oAJCABDJAyAEQgAgBCkDyAEgFiAXVK18Ih0gBCkD0AF8IhUgBCkDaCAYIBlWrXwiHyAEKQNwfCIYIAQpAxB8IhkgGiAcVK18IhwgBCkDoAF8IiAgGyAeVq0gBCkDmAEgGiAbVq18fHwiGiAXICRUrXwiI3wiFyAWQgBSrXwiFiAEKQOAAnwiG31CAEKRgICAgICAgAhCABDJAyABKQPYAiEkIAEpA9ACIR4gASkDyAIhIiABKQPAAiEmAkACQCAEKQMIIAQpA5gCIAQpA4gCIBYgG1atfCIlIAQpA5ACfCIhICVUrXwgISAVIBdWrSAEKQPYASAVIB1UrXx8IiUgBCkD4AF8IhUgGiAjVq0iIyAEKQMgfCIdIAQpA3ggGCAfVK18IicgBCkDsAF8Ih8gGSAcVq0gBCkDGCAYIBlWrXx8fCIYIBogIFStIAQpA6gBIBwgIFatfHx8Ihx8IiB8IhogFiAXVK18Ihl8IhcgIVStfCIhIAQpA6ACfCIWIBkgGlStIiggBCkDMHwiGSAYIBxWrSAYIB9UrSAEKQO4ASAfICdUrXx8fCIfIAQpA/ABfCIYIB0gIFatIAQpAyggHSAjVK18fHwiHCAVIBpWrSAEKQPoASAVICVUrXx8fCIgfCIdfCIaIBcgG0IAUq18IhUgF1StfCIbIBpUrSIjIAQpAwB8IhcgI1StfCAXIBwgIFatIBggHFatIAQpA/gBIBggH1StfHx8IiAgBCkDsAJ8IhwgGSAdVq0gBCkDOCAZIChUrXx8fCIZIBYgGlatIAQpA6gCIBYgIVStfHx8IhZ8IhggF1StfCAWIBlUrSAZIBxUrSAEKQO4AiAcICBUrXx8fHwiGUKRgICAgICAgAhWDQAgGUKRgICAgICAgAhRBEAgFSAbhCAYhFBFDQFCACEWQpGAgICAgICACCEZQgAhGkIAIRcMAgsgGCEWIBshGiAVIRcMAQsgFUIBfSEXIBsgFVCtIhV9IRogGCAVIBtWrSIVfSEWIBkgFSAYVq19QpGAgICAgICACH0hGQtCkYCAgICAgIAIIRUgFiAifCIWICJUIBYgGiAefCIYIB5UIBggGCAXICR8IhogJFStfCIbVnKtfCIYIBZUcq0gGSAmfHwiGSEXAkACQCAZQpGAgICAgICACFEEQCAYIBuEQgBSDQFCASEVIBoiF0IBUQ0BCyAVIBdYDQAgGCEVIBshFyAaIRYMAQsgGkIBfSEWIBsgGlCtIhV9IRcgGCAVIBtWrSIafSEVQu7/////////d0Lv/////////3cgGCAaVBsgGXwhGQtCkYCAgICAgIAIIRogFSAVIAApA0h8IhxWIBwgHCAXIBcgACkDUHwiFVYgFSAWIBYgACkDWHwiG1atfCIWIBVUcq18IhhWcq0gACkDQCAZfHwiGSEVIAACfgJAIBlCkYCAgICAgIAIUQRAIBYgGIRCAFINAUIBIRogGyIVQgFRDQELIBUgGloNACAYIRUgFiEXIBsMAQsgFiAbUK0iFX0hFyAYIBUgFlatIhZ9IRVC7v////////93Qu//////////dyAWIBhWGyAZfCEZIBtCAX0LNwNYIAAgFzcDUCAAIBU3A0ggACAZNwNAIA8QRiAEKALIDyIBBEAgBCgCzA8gAUHgAGwQ3wQLIA0iASATRw0BDAkLC0EAQQBBoMvBABDZAwALQQFBAUGwy8EAENkDAAtBASADQcDLwQAQ2QMAC0ECQQJB0MvBABDZAwALQQIgAUHgy8EAENkDAAtBCEGAA0GQy8EAEMgEAAsgAyAGQYDLwQAQ5QQACyAFIAlBkJjBABDIBAALAkAgAkEDcSIDBEAgAkH8//8fcSEBIAJBAnZB////B3FBwAFsIQYDQCABIAQoAowPIgJPDQIgBEGgEGoiAiAEKAKIDyAGahDfASAAIAIQXSAGQTBqIQYgAUEBaiEBIANBAWsiAw0ACwsgBCgChA8iA0UNAiAEKAKIDyEHDAELIAEgAkHwysEAENkDAAsgByADQTBsEN8ECyAEQYARaiQAC4NqAhF/FX4jAEHwEGsiBCQAIARBADYCjA8gBEKAgICAgAE3AoQPAkACQAJAAkAgAkH///8/SyACQQV0IglB+P///wdLcg0AAkAgCUUEQEEIIQYMAQtB0c7FAC0AABpBCCEHIAlBCBDWBCIGRQ0BIAJFDQBBACEHIAIhBQNAIAcgCUYNASAGIAdqIg0gASAHaiILKQMANwMAIA1BGGogC0EYaikDADcDACANQRBqIAtBEGopAwA3AwAgDUEIaiALQQhqKQMANwMAIAdBIGohByAFQQFrIgUNAAsLIAQgAjYCjA8gBCAGNgKIDyAEIAI2AoQPIANFBEAgBCgChA8hBSACBEAgAkEFdCEHIAYhAQNAIARBsA9qIAFBGGopAwAiFTcDACAEQagPaiABQRBqKQMAIhc3AwAgBEGgD2ogAUEIaikDACIWNwMAIAQgASkDACIaNwOYDyAEQfgPaiAVNwMAIARB8A9qIBc3AwAgBEHoD2ogFjcDACAEIBo3A+APIARBkBBqIgIgBEHgD2oQ3gEgACACEF0gAUEgaiEBIAdBIGsiBw0ACwsgBUUNBAwDCyACQQRJDQEgAkECdiETIABBIGohDyAEQdAQaiEQIARBsBBqIRFBACEBAkACQAJAAkACQAJAA0AgAUEBaiINQQJ0IgMgBCgCjA8iBUsNBkHRzsUALQAAGiAEKAKID0GAA0EIENYEIgVFDQUgBEEANgLADyAEIAU2ArwPIARBBDYCuA9BICELIAFBB3RqIhQhAQNAIARBxA9qIAEQvgEgBCgCyA8hEgJAIAQoAswPIgNFBEAgBEHYD2pB9JTBACgCADYCACAEQeyUwQApAgA3A9APDAELQQAhAQJAIANBAE4EQEHRzsUALQAAGkEBIQEgA0EBENYEIgkNASADIQkLIAEgCUGgmMEAEMgEAAsgAwRAIAkgEiAD/AoAAAtBASEHAkAgA0EBRg0AIAMgCWohBUEAIQEgA0EBdiIGQQFHBEAgA0EBayEHIAZB/v///wNxIQgDQCAHIAlqIgYtAAAhDCAGIAEgCWoiBi0AADoAACAGIAw6AAAgBSABQX5zaiIMLQAAIQogDCAGQQFqIgYtAAA6AAAgBiAKOgAAIAdBAmshByAIIAFBAmoiAUcNAAsLIAMiB0ECcUUNACABIAlqIgYtAAAhCCAGIAUgAUF/c2oiAS0AADoAACABIAg6AAALIARB0A9qIAkgB0EIEM8CIAkgAxDfBAsgBEHgD2ogBEHQD2oQywEgBCkD6A8hGCAEKQPgDyEWIARBADYCoA8gBEKAgICAEDcCmA8CQCAWIBiEUEUEQEEAIQdBASEFA0AgBSEDIAciASAEKAKYD0YEQCAEQZgPakHE2sIAELYDCyAEKAKcDyABaiAWPAAAIAQgAUEBaiIHNgKgDyAYQjiGIBZCgAJUIQYgGFAhCCADQQFqIQUgGEIIiCEYIBZCCIiEIRYgBiAIcUUNAAtBASEFIAQoApwPIQYgAQRAIAYgB2ohCEEAIQUgB0EBdkEBRwRAIANBAXZB/v///wdxIQwDQCABIAZqIgMtAAAhCiADIAUgBmoiAy0AADoAACADIAo6AAAgCCAFQX5zaiIKLQAAIQ4gCiADQQFqIgMtAAA6AAAgAyAOOgAAIAFBAmshASAMIAVBAmoiBUcNAAsLIAdBAnEEQCAFIAZqIgEtAAAhAyABIAggBUF/c2oiAS0AADoAACABIAM6AAALIAQoApwPIQYgBCgCoA8hBQsgBCgCmA8hASAEQZAQaiAGIAUQhgEgAUUNASAGIAEQ3wQMAQsgBEGQEGpBAUEAEIYBCyAEKQP4DyEYIAQpA/APIRYgBEEANgKgDyAEQoCAgIAQNwKYDwJAIBYgGIRQRQRAQQAhB0EBIQUDQCAFIQMgByIBIAQoApgPRgRAIARBmA9qQcTawgAQtgMLIAQoApwPIAFqIBY8AAAgBCABQQFqIgc2AqAPIBhCOIYgFkKAAlQhBiAYUCEIIANBAWohBSAYQgiIIRggFkIIiIQhFiAGIAhxRQ0AC0EBIQUgBCgCnA8hBiABBEAgBiAHaiEIQQAhBSAHQQF2QQFHBEAgA0EBdkH+////B3EhDANAIAEgBmoiAy0AACEKIAMgBSAGaiIDLQAAOgAAIAMgCjoAACAIIAVBfnNqIgotAAAhDiAKIANBAWoiAy0AADoAACADIA46AAAgAUECayEBIAwgBUECaiIFRw0ACwsgB0ECcQRAIAUgBmoiAS0AACEDIAEgCCAFQX9zaiIBLQAAOgAAIAEgAzoAAAsgBCgCnA8hBiAEKAKgDyEFCyAEKAKYDyEBIBEgBiAFEIYBIAFFDQEgBiABEN8EDAELIBFBAUEAEIYBCyAEKQOIECEYIAQpA4AQIRYgBEEANgKgDyAEQoCAgIAQNwKYDwJAIBYgGIRQRQRAQQAhB0EBIQUDQCAFIQMgByIBIAQoApgPRgRAIARBmA9qQcTawgAQtgMLIAQoApwPIAFqIBY8AAAgBCABQQFqIgc2AqAPIBhCOIYgFkKAAlQhBiAYUCEIIANBAWohBSAYQgiIIRggFkIIiIQhFiAGIAhxRQ0AC0EBIQUgBCgCnA8hBiABBEAgBiAHaiEIQQAhBSAHQQF2QQFHBEAgA0EBdkH+////B3EhDANAIAEgBmoiAy0AACEKIAMgBSAGaiIDLQAAOgAAIAMgCjoAACAIIAVBfnNqIgotAAAhDiAKIANBAWoiAy0AADoAACADIA46AAAgAUECayEBIAwgBUECaiIFRw0ACwsgB0ECcQRAIAUgBmoiAS0AACEDIAEgCCAFQX9zaiIBLQAAOgAAIAEgAzoAAAsgBCgCnA8hBiAEKAKgDyEFCyAEKAKYDyEBIBAgBiAFEIYBIAFFDQEgBiABEN8EDAELIBBBAUEAEIYBCyAEKALADyIBIAQoArgPRgRAIARBuA9qEJ4DCyAEKAK8DyABQeAAbGogBEGQEGpB4AD8CgAAIAQgAUEBajYCwA8gBCgC0A8iAQRAIAQoAtQPIAFBAnQQ3wQLIAQoAsQPIgEEQCASIAEQ3wQLIAsgFGohASALQYABRiALQYABR0EFdCALaiELRQ0ACyAEKALADyIDBEAgBEGADWogBCgCvA8iASkDOCIVQgBCgICAgICAEUIAEMkDIARBkA1qIBVCAEKAgICAgHxCABDJAyAEQaANaiAVQgBCf0IAEMkDIARBsA1qIBVCAEL///////+gAkIAEMkDIARB0AxqQgAgBCkDgA0iF31CAEKRgICAgICAgAhCABDJAyAEQcANaiABKQMwIhVCAEKAgICAgIARQgAQyQMgBEHQDWogFUIAQoCAgICAfEIAEMkDIARB4A1qIBVCAEJ/QgAQyQMgBEHwDWogFUIAQv///////6ACQgAQyQMgBEHgDGpCACAXQoCAgICAgH+DIhUgF30gFVStIhogBCkDiA0iGyAEKQOQDXwiGXwiFyAEKQPADXwiFn1CAEKRgICAgICAgAhCABDJAyAEQYAOaiABKQMoIhVCAEKAgICAgIARQgAQyQMgBEGQDmogFUIAQoCAgICAfEIAEMkDIARBoA5qIBVCAEJ/QgAQyQMgBEGwDmogFUIAQv///////6ACQgAQyQMgBEHwDGpCACAWQgBSrSIkIBcgGlStIhwgBCkDmA0gGSAbVK18IhkgBCkDoA18Ihh8IhogBCkD0A18IhsgBCkDyA0gFiAXVK18fCIefCIXIAQpA4AOfCIWfUIAQpGAgICAgICACEIAEMkDIARBwA5qIAEpAyAiFUIAQoCAgICAgBFCABDJAyAEQdAOaiAVQgBCgICAgIB8QgAQyQMgBEHgDmogFUIAQn9CABDJAyAEQfAOaiAVQgBC////////oAJCABDJAyAEQcAMakIAIAQpA4gOIBYgF1StfCIdIAQpA5AOfCIVIAQpA6gNIBggGVStfCIfIAQpA7ANfCIZIAQpA9AMfCIYIBogHFStfCIcIAQpA+ANfCIgIBsgHlatIAQpA9gNIBogG1atfHx8IhogFyAkVK18IiN8IhcgFkIAUq18IhYgBCkDwA58Iht9QgBCkYCAgICAgIAIQgAQyQMgASkDGCEkIAEpAxAhHiABKQMIISIgASkDACEmAkACQCAEKQPIDCAEKQPYDiAEKQPIDiAWIBtWrXwiJSAEKQPQDnwiISAlVK18ICEgFSAXVq0gBCkDmA4gFSAdVK18fCIlIAQpA6AOfCIVIBogI1atIiMgBCkD4Ax8Ih0gBCkDuA0gGSAfVK18IicgBCkD8A18Ih8gGCAcVq0gBCkD2AwgGCAZVK18fHwiGSAaICBUrSAEKQPoDSAcICBWrXx8fCIcfCIgfCIaIBYgF1StfCIYfCIXICFUrXwiISAEKQPgDnwiFiAYIBpUrSIoIAQpA/AMfCIYIBkgHFatIBkgH1StIAQpA/gNIB8gJ1StfHx8Ih8gBCkDsA58IhkgHSAgVq0gBCkD6AwgHSAjVK18fHwiHCAVIBpWrSAEKQOoDiAVICVUrXx8fCIgfCIdfCIaIBcgG0IAUq18IhUgF1StfCIbIBpUrSIjIAQpA8AMfCIXICNUrXwgFyAcICBWrSAZIBxWrSAEKQO4DiAZIB9UrXx8fCIgIAQpA/AOfCIcIBggHVatIAQpA/gMIBggKFStfHx8IhggFiAaVq0gBCkD6A4gFiAhVK18fHwiFnwiGSAXVK18IBYgGFStIBggHFStIAQpA/gOIBwgIFStfHx8fCIYQpGAgICAgICACFYNACAYQpGAgICAgICACFEEQCAVIBuEIBmEUEUNAUIAIRZCkYCAgICAgIAIIRhCACEaQgAhFwwCCyAZIRYgGyEaIBUhFwwBCyAVQgF9IRcgGyAVUK0iFX0hGiAZIBUgG1atIhV9IRYgGCAVIBlWrX1CkYCAgICAgIAIfSEYC0KRgICAgICAgAghFSAWICJ8IhYgIlQgFiAaIB58IhkgHlQgGSAZIBcgJHwiGiAkVK18IhtWcq18IhkgFlRyrSAYICZ8fCIYIRcCQAJAIBhCkYCAgICAgIAIUQRAIBkgG4RCAFINAUIBIRUgGiIXQgFRDQELIBUgF1gNACAZIRUgGyEXIBohFgwBCyAaQgF9IRYgGyAaUK0iFX0hFyAZIBUgG1atIhp9IRVC7v////////93Qu//////////dyAZIBpUGyAYfCEYC0KRgICAgICAgAghGiAVIBUgACkDKHwiHFYgHCAcIBcgFyAAKQMwfCIVViAVIBYgFiAAKQM4fCIbVq18IhYgFVRyrXwiGVZyrSAAKQMgIBh8fCIYIRUgAAJ+AkAgGEKRgICAgICAgAhRBEAgFiAZhEIAUg0BQgEhGiAbIhVCAVENAQsgFSAaWg0AIBkhFSAWIRcgGwwBCyAWIBtQrSIVfSEXIBkgFSAWVq0iFn0hFULu/////////3dC7/////////93IBYgGVYbIBh8IRggG0IBfQs3AzggACAXNwMwIAAgFTcDKCAAIBg3AyAgA0EBRg0CIAEpA1ghHCABKQNQISAgASkDSCEkIAEpA0AhIyAEQcAKaiABKQN4IhVCAEKAgICAgIARQgAQyQMgBEHQCmogFUIAQoCAgICAfEIAEMkDIARB4ApqIBVCAEJ/QgAQyQMgBEHwCmogFUIAQv///////6ACQgAQyQMgBEGQCmpCACAEKQPACiIXfUIAQpGAgICAgICACEIAEMkDIARBgAtqIAEpA3AiFUIAQoCAgICAgBFCABDJAyAEQZALaiAVQgBCgICAgIB8QgAQyQMgBEGgC2ogFUIAQn9CABDJAyAEQbALaiAVQgBC////////oAJCABDJAyAEQaAKakIAIBdCgICAgICAf4MiFSAXfSAVVK0iGiAEKQPICiIbIAQpA9AKfCIZfCIXIAQpA4ALfCIWfUIAQpGAgICAgICACEIAEMkDIARBwAtqIAEpA2giFUIAQoCAgICAgBFCABDJAyAEQdALaiAVQgBCgICAgIB8QgAQyQMgBEHgC2ogFUIAQn9CABDJAyAEQfALaiAVQgBC////////oAJCABDJAyAEQbAKakIAIBZCAFKtIiEgFyAaVK0iHiAEKQPYCiAZIBtUrXwiGSAEKQPgCnwiGHwiGiAEKQOQC3wiGyAEKQOICyAWIBdUrXx8Ih18IhcgBCkDwAt8IhZ9QgBCkYCAgICAgIAIQgAQyQMgBEGADGogASkDYCIVQgBCgICAgICAEUIAEMkDIARBkAxqIBVCAEKAgICAgHxCABDJAyAEQaAMaiAVQgBCf0IAEMkDIARBsAxqIBVCAEL///////+gAkIAEMkDIARBgApqQgAgBCkDyAsgFiAXVK18Ih8gBCkD0At8IhUgBCkD6AogGCAZVK18IiYgBCkD8Ap8IhkgBCkDkAp8IhggGiAeVK18Ih4gBCkDoAt8IiIgGyAdVq0gBCkDmAsgGiAbVq18fHwiGiAXICFUrXwiHXwiFyAWQgBSrXwiFiAEKQOADHwiG31CAEKRgICAgICAgAhCABDJAwJAAkAgBCkDiAogBCkDmAwgBCkDiAwgFiAbVq18IiUgBCkDkAx8IiEgJVStfCAhIBUgF1atIAQpA9gLIBUgH1StfHwiJSAEKQPgC3wiFSAaIB1WrSInIAQpA6AKfCIdIAQpA/gKIBkgJlStfCImIAQpA7ALfCIfIBggHlatIAQpA5gKIBggGVStfHx8IhkgGiAiVK0gBCkDqAsgHiAiVq18fHwiInwiKHwiGiAWIBdUrXwiF3wiFiAhVK18IiEgBCkDoAx8IhggFyAaVK0iKSAEKQOwCnwiHiAZICJWrSAZIB9UrSAEKQO4CyAfICZUrXx8fCIfIAQpA/ALfCIZIB0gKFatIAQpA6gKIB0gJ1StfHx8IiIgFSAaVq0gBCkD6AsgFSAlVK18fHwiGnwiHXwiFSAWIBYgG0IAUq18IhdWrXwiGyAVVK0iJiAEKQOACnwiFiAmVK18IBYgGiAiVK0gGSAiVq0gBCkD+AsgGSAfVK18fHwiIiAEKQOwDHwiGiAdIB5UrSAEKQO4CiAeIClUrXx8fCIeIBUgGFStIAQpA6gMIBggIVStfHx8IhV8IhkgFlStfCAVIB5UrSAaIB5WrSAEKQO4DCAaICJUrXx8fHwiGEKRgICAgICAgAhWDQAgGEKRgICAgICAgAhRBEAgFyAbhCAZhFBFDQFCACEVQpGAgICAgICACCEYQgAhFkIAIRoMAgsgGSEVIBshFiAXIRoMAQsgF0IBfSEaIBsgF1CtIhV9IRYgGSAVIBtWrSIXfSEVIBggFyAZVq19QpGAgICAgICACH0hGAtCkYCAgICAgIAIIRcgFSAkfCIVICRUIBUgFiAgfCIWICBUIBYgGiAcfCIaIBxUrXwiGyAWVHKtfCIZIBVUcq0gGCAjfHwiGCEVAkACQCAYQpGAgICAgICACFEEQCAZIBuEQgBSDQFCASEXIBoiFUIBUQ0BCyAVIBdaDQAgGSEVIBshFyAaIRYMAQsgGkIBfSEWIBsgGlCtIhV9IRcgGSAVIBtWrSIafSEVQu7/////////d0Lv/////////3cgGSAaVBsgGHwhGAtCkYCAgICAgIAIIRogFSAVIAApA0h8IhxWIBwgHCAXIBcgACkDUHwiFVYgFSAWIBYgACkDWHwiG1atfCIWIBVUcq18IhlWcq0gACkDQCAYfHwiGCEVIAACfgJAIBhCkYCAgICAgIAIUQRAIBYgGYRCAFINAUIBIRogGyIVQgFRDQELIBUgGloNACAZIRUgFiEXIBsMAQsgFiAbUK0iFX0hFyAZIBUgFlatIhZ9IRVC7v////////93Qu//////////dyAWIBlWGyAYfCEYIBtCAX0LNwNYIAAgFzcDUCAAIBU3A0ggACAYNwNAIA8QRiAEKALADyIDQQFNDQMgBEGACGogBCgCvA8iASkDuAEiFUIAQoCAgICAgBFCABDJAyAEQZAIaiAVQgBCgICAgIB8QgAQyQMgBEGgCGogFUIAQn9CABDJAyAEQbAIaiAVQgBC////////oAJCABDJAyAEQdAHakIAIAQpA4AIIhd9QgBCkYCAgICAgIAIQgAQyQMgBEHACGogASkDsAEiFUIAQoCAgICAgBFCABDJAyAEQdAIaiAVQgBCgICAgIB8QgAQyQMgBEHgCGogFUIAQn9CABDJAyAEQfAIaiAVQgBC////////oAJCABDJAyAEQeAHakIAIBdCgICAgICAf4MiFSAXfSAVVK0iGiAEKQOICCIbIAQpA5AIfCIZfCIXIAQpA8AIfCIWfUIAQpGAgICAgICACEIAEMkDIARBgAlqIAEpA6gBIhVCAEKAgICAgIARQgAQyQMgBEGQCWogFUIAQoCAgICAfEIAEMkDIARBoAlqIBVCAEJ/QgAQyQMgBEGwCWogFUIAQv///////6ACQgAQyQMgBEHwB2pCACAWQgBSrSIkIBcgGlStIhwgBCkDmAggGSAbVK18IhkgBCkDoAh8Ihh8IhogBCkD0Ah8IhsgBCkDyAggFiAXVK18fCIefCIXIAQpA4AJfCIWfUIAQpGAgICAgICACEIAEMkDIARBwAlqIAEpA6ABIhVCAEKAgICAgIARQgAQyQMgBEHQCWogFUIAQoCAgICAfEIAEMkDIARB4AlqIBVCAEJ/QgAQyQMgBEHwCWogFUIAQv///////6ACQgAQyQMgBEHAB2pCACAEKQOICSAWIBdUrXwiHSAEKQOQCXwiFSAEKQOoCCAYIBlUrXwiHyAEKQOwCHwiGSAEKQPQB3wiGCAaIBxUrXwiHCAEKQPgCHwiICAbIB5WrSAEKQPYCCAaIBtWrXx8fCIaIBcgJFStfCIjfCIXIBZCAFKtfCIWIAQpA8AJfCIbfUIAQpGAgICAgICACEIAEMkDIAEpA5gBISQgASkDkAEhHiABKQOIASEiIAEpA4ABISYCQAJAIAQpA8gHIAQpA9gJIAQpA8gJIBYgG1atfCIlIAQpA9AJfCIhICVUrXwgISAVIBdWrSAEKQOYCSAVIB1UrXx8IiUgBCkDoAl8IhUgGiAjVq0iIyAEKQPgB3wiHSAEKQO4CCAZIB9UrXwiJyAEKQPwCHwiHyAYIBxWrSAEKQPYByAYIBlUrXx8fCIZIBogIFStIAQpA+gIIBwgIFatfHx8Ihx8IiB8IhogFiAXVK18Ihh8IhcgIVStfCIhIAQpA+AJfCIWIBggGlStIiggBCkD8Ad8IhggGSAcVq0gGSAfVK0gBCkD+AggHyAnVK18fHwiHyAEKQOwCXwiGSAdICBWrSAEKQPoByAdICNUrXx8fCIcIBUgGlatIAQpA6gJIBUgJVStfHx8IiB8Ih18IhogFyAbQgBSrXwiFSAXVK18IhsgGlStIiMgBCkDwAd8IhcgI1StfCAXIBwgIFatIBkgHFatIAQpA7gJIBkgH1StfHx8IiAgBCkD8Al8IhwgGCAdVq0gBCkD+AcgGCAoVK18fHwiGCAWIBpWrSAEKQPoCSAWICFUrXx8fCIWfCIZIBdUrXwgFiAYVK0gGCAcVK0gBCkD+AkgHCAgVK18fHx8IhhCkYCAgICAgIAIVg0AIBhCkYCAgICAgIAIUQRAIBUgG4QgGYRQRQ0BQgAhFkKRgICAgICAgAghGEIAIRpCACEXDAILIBkhFiAbIRogFSEXDAELIBVCAX0hFyAbIBVQrSIVfSEaIBkgFSAbVq0iFX0hFiAYIBUgGVatfUKRgICAgICAgAh9IRgLQpGAgICAgICACCEVIBYgInwiFiAiVCAWIBogHnwiGSAeVCAZIBkgFyAkfCIaICRUrXwiG1ZyrXwiGSAWVHKtIBggJnx8IhghFwJAAkAgGEKRgICAgICAgAhRBEAgGSAbhEIAUg0BQgEhFSAaIhdCAVENAQsgFSAXWA0AIBkhFSAbIRcgGiEWDAELIBpCAX0hFiAbIBpQrSIVfSEXIBkgFSAbVq0iGn0hFULu/////////3dC7/////////93IBkgGlQbIBh8IRgLQpGAgICAgICACCEaIBUgFSAAKQMofCIcViAcIBwgFyAXIAApAzB8IhVWIBUgFiAWIAApAzh8IhtWrXwiFiAVVHKtfCIZVnKtIAApAyAgGHx8IhghFSAAAn4CQCAYQpGAgICAgICACFEEQCAWIBmEQgBSDQFCASEaIBsiFUIBUQ0BCyAVIBpaDQAgGSEVIBYhFyAbDAELIBYgG1CtIhV9IRcgGSAVIBZWrSIWfSEVQu7/////////d0Lv/////////3cgFiAZVhsgGHwhGCAbQgF9CzcDOCAAIBc3AzAgACAVNwMoIAAgGDcDICADQQJGDQQgBEHABWogASkD+AEiFUIAQoCAgICAgBFCABDJAyAEQdAFaiAVQgBCgICAgIB8QgAQyQMgBEHgBWogFUIAQn9CABDJAyAEQfAFaiAVQgBC////////oAJCABDJAyAEQZAFakIAIAQpA8AFIhd9QgBCkYCAgICAgIAIQgAQyQMgBEGABmogASkD8AEiFUIAQoCAgICAgBFCABDJAyAEQZAGaiAVQgBCgICAgIB8QgAQyQMgBEGgBmogFUIAQn9CABDJAyAEQbAGaiAVQgBC////////oAJCABDJAyAEQaAFakIAIBdCgICAgICAf4MiFSAXfSAVVK0iGiAEKQPIBSIbIAQpA9AFfCIZfCIXIAQpA4AGfCIWfUIAQpGAgICAgICACEIAEMkDIARBwAZqIAEpA+gBIhVCAEKAgICAgIARQgAQyQMgBEHQBmogFUIAQoCAgICAfEIAEMkDIARB4AZqIBVCAEJ/QgAQyQMgBEHwBmogFUIAQv///////6ACQgAQyQMgBEGwBWpCACAWQgBSrSIkIBcgGlStIhwgBCkD2AUgGSAbVK18IhkgBCkD4AV8Ihh8IhogBCkDkAZ8IhsgBCkDiAYgFiAXVK18fCIefCIXIAQpA8AGfCIWfUIAQpGAgICAgICACEIAEMkDIARBgAdqIAEpA+ABIhVCAEKAgICAgIARQgAQyQMgBEGQB2ogFUIAQoCAgICAfEIAEMkDIARBoAdqIBVCAEJ/QgAQyQMgBEGwB2ogFUIAQv///////6ACQgAQyQMgBEGABWpCACAEKQPIBiAWIBdUrXwiHSAEKQPQBnwiFSAEKQPoBSAYIBlUrXwiHyAEKQPwBXwiGSAEKQOQBXwiGCAaIBxUrXwiHCAEKQOgBnwiICAbIB5WrSAEKQOYBiAaIBtWrXx8fCIaIBcgJFStfCIjfCIXIBZCAFKtfCIWIAQpA4AHfCIbfUIAQpGAgICAgICACEIAEMkDIAEpA9gBISQgASkD0AEhHiABKQPIASEiIAEpA8ABISYCQAJAIAQpA4gFIAQpA5gHIAQpA4gHIBYgG1atfCIlIAQpA5AHfCIhICVUrXwgISAVIBdWrSAEKQPYBiAVIB1UrXx8IiUgBCkD4AZ8IhUgGiAjVq0iIyAEKQOgBXwiHSAEKQP4BSAZIB9UrXwiJyAEKQOwBnwiHyAYIBxWrSAEKQOYBSAYIBlUrXx8fCIZIBogIFStIAQpA6gGIBwgIFatfHx8Ihx8IiB8IhogFiAXVK18Ihh8IhcgIVStfCIhIAQpA6AHfCIWIBggGlStIiggBCkDsAV8IhggGSAcVq0gGSAfVK0gBCkDuAYgHyAnVK18fHwiHyAEKQPwBnwiGSAdICBWrSAEKQOoBSAdICNUrXx8fCIcIBUgGlatIAQpA+gGIBUgJVStfHx8IiB8Ih18IhogFyAbQgBSrXwiFSAXVK18IhsgGlStIiMgBCkDgAV8IhcgI1StfCAXIBwgIFatIBkgHFatIAQpA/gGIBkgH1StfHx8IiAgBCkDsAd8IhwgGCAdVq0gBCkDuAUgGCAoVK18fHwiGCAWIBpWrSAEKQOoByAWICFUrXx8fCIWfCIZIBdUrXwgFiAYVK0gGCAcVK0gBCkDuAcgHCAgVK18fHx8IhhCkYCAgICAgIAIVg0AIBhCkYCAgICAgIAIUQRAIBUgG4QgGYRQRQ0BQgAhFkKRgICAgICAgAghGEIAIRpCACEXDAILIBkhFiAbIRogFSEXDAELIBVCAX0hFyAbIBVQrSIVfSEaIBkgFSAbVq0iFX0hFiAYIBUgGVatfUKRgICAgICAgAh9IRgLQpGAgICAgICACCEVIBYgInwiFiAiVCAWIBogHnwiGSAeVCAZIBkgFyAkfCIaICRUrXwiG1ZyrXwiGSAWVHKtIBggJnx8IhghFwJAAkAgGEKRgICAgICAgAhRBEAgGSAbhEIAUg0BQgEhFSAaIhdCAVENAQsgFSAXWA0AIBkhFSAbIRcgGiEWDAELIBpCAX0hFiAbIBpQrSIVfSEXIBkgFSAbVq0iGn0hFULu/////////3dC7/////////93IBkgGlQbIBh8IRgLQpGAgICAgICACCEaIBUgFSAAKQNIfCIcViAcIBwgFyAXIAApA1B8IhVWIBUgFiAWIAApA1h8IhtWrXwiFiAVVHKtfCIZVnKtIAApA0AgGHx8IhghFSAAAn4CQCAYQpGAgICAgICACFEEQCAWIBmEQgBSDQFCASEaIBsiFUIBUQ0BCyAVIBpaDQAgGSEVIBYhFyAbDAELIBYgG1CtIhV9IRcgGSAVIBZWrSIWfSEVQu7/////////d0Lv/////////3cgFiAZVhsgGHwhGCAbQgF9CzcDWCAAIBc3A1AgACAVNwNIIAAgGDcDQCAPEEYgBCgCwA8iAUEDSQ0FIAACfgJAIAFBA0cEQCAEKAK8DyIBKQOYAiEcIAEpA5ACISAgASkDiAIhJCABKQOAAiEjIARBgANqIAEpA7gCIhVCAEKAgICAgIARQgAQyQMgBEGQA2ogFUIAQoCAgICAfEIAEMkDIARBoANqIBVCAEJ/QgAQyQMgBEGwA2ogFUIAQv///////6ACQgAQyQMgBEHQAmpCACAEKQOAAyIXfUIAQpGAgICAgICACEIAEMkDIARBwANqIAEpA7ACIhVCAEKAgICAgIARQgAQyQMgBEHQA2ogFUIAQoCAgICAfEIAEMkDIARB4ANqIBVCAEJ/QgAQyQMgBEHwA2ogFUIAQv///////6ACQgAQyQMgBEHgAmpCACAXQoCAgICAgH+DIhUgF30gFVStIhogBCkDiAMiGyAEKQOQA3wiGXwiFyAEKQPAA3wiFn1CAEKRgICAgICAgAhCABDJAyAEQYAEaiABKQOoAiIVQgBCgICAgICAEUIAEMkDIARBkARqIBVCAEKAgICAgHxCABDJAyAEQaAEaiAVQgBCf0IAEMkDIARBsARqIBVCAEL///////+gAkIAEMkDIARB8AJqQgAgFkIAUq0iISAXIBpUrSIeIAQpA5gDIBkgG1StfCIZIAQpA6ADfCIYfCIaIAQpA9ADfCIbIAQpA8gDIBYgF1StfHwiHXwiFyAEKQOABHwiFn1CAEKRgICAgICAgAhCABDJAyAEQcAEaiABKQOgAiIVQgBCgICAgICAEUIAEMkDIARB0ARqIBVCAEKAgICAgHxCABDJAyAEQeAEaiAVQgBCf0IAEMkDIARB8ARqIBVCAEL///////+gAkIAEMkDIARBwAJqQgAgBCkDiAQgFiAXVK18Ih8gBCkDkAR8IhUgBCkDqAMgGCAZVK18IiYgBCkDsAN8IhkgBCkD0AJ8IhggGiAeVK18Ih4gBCkD4AN8IiIgGyAdVq0gBCkD2AMgGiAbVq18fHwiGiAXICFUrXwiHXwiFyAWQgBSrXwiFiAEKQPABHwiG31CAEKRgICAgICAgAhCABDJAwJAAkAgBCkDyAIgBCkD2AQgBCkDyAQgFiAbVq18IiUgBCkD0AR8IiEgJVStfCAhIBUgF1atIAQpA5gEIBUgH1StfHwiJSAEKQOgBHwiFSAaIB1WrSInIAQpA+ACfCIdIAQpA7gDIBkgJlStfCImIAQpA/ADfCIfIBggHlatIAQpA9gCIBggGVStfHx8IhkgGiAiVK0gBCkD6AMgHiAiVq18fHwiInwiKHwiGiAWIBdUrXwiF3wiFiAhVK18IiEgBCkD4AR8IhggFyAaVK0iKSAEKQPwAnwiHiAZICJWrSAZIB9UrSAEKQP4AyAfICZUrXx8fCIfIAQpA7AEfCIZIB0gKFatIAQpA+gCIB0gJ1StfHx8IiIgFSAaVq0gBCkDqAQgFSAlVK18fHwiGnwiHXwiFSAWIBYgG0IAUq18IhdWrXwiGyAVVK0iJiAEKQPAAnwiFiAmVK18IBYgGiAiVK0gGSAiVq0gBCkDuAQgGSAfVK18fHwiIiAEKQPwBHwiGiAdIB5UrSAEKQP4AiAeIClUrXx8fCIeIBUgGFStIAQpA+gEIBggIVStfHx8IhV8IhkgFlStfCAVIB5UrSAaIB5WrSAEKQP4BCAaICJUrXx8fHwiGEKRgICAgICAgAhWDQAgGEKRgICAgICAgAhRBEAgFyAbhCAZhFBFDQFCACEVQpGAgICAgICACCEYQgAhFkIAIRoMAgsgGSEVIBshFiAXIRoMAQsgF0IBfSEaIBsgF1CtIhV9IRYgGSAVIBtWrSIXfSEVIBggFyAZVq19QpGAgICAgICACH0hGAtCkYCAgICAgIAIIRcgFSAkfCIVICRUIBUgFiAgfCIWICBUIBYgGiAcfCIaIBxUrXwiGyAWVHKtfCIZIBVUcq0gGCAjfHwiGCEVAkACQCAYQpGAgICAgICACFEEQCAZIBuEQgBSDQFCASEXIBoiFUIBUQ0BCyAVIBdaDQAgGSEVIBshFyAaIRYMAQsgGkIBfSEWIBsgGlCtIhV9IRcgGSAVIBtWrSIafSEVQu7/////////d0Lv/////////3cgGSAaVBsgGHwhGAtCkYCAgICAgIAIIRogFSAVIAApAyh8IhxWIBwgHCAXIBcgACkDMHwiFVYgFSAWIBYgACkDOHwiG1atfCIWIBVUcq18IhlWcq0gACkDICAYfHwiGCEVIBhCkYCAgICAgIAIUQRAIBYgGYRCAFINAkIBIRogGyIVQgFRDQILIBUgGloNASAZIRUgFiEXIBsMAgtBA0EDQfDLwQAQ2QMACyAWIBtQrSIVfSEXIBkgFSAWVq0iFn0hFULu/////////3dC7/////////93IBYgGVYbIBh8IRggG0IBfQs3AzggACAXNwMwIAAgFTcDKCAAIBg3AyAgBEFAayABKQP4AiIVQgBCgICAgICAEUIAEMkDIARB0ABqIBVCAEKAgICAgHxCABDJAyAEQeAAaiAVQgBCf0IAEMkDIARB8ABqIBVCAEL///////+gAkIAEMkDIARBEGpCACAEKQNAIhd9QgBCkYCAgICAgIAIQgAQyQMgBEGAAWogASkD8AIiFUIAQoCAgICAgBFCABDJAyAEQZABaiAVQgBCgICAgIB8QgAQyQMgBEGgAWogFUIAQn9CABDJAyAEQbABaiAVQgBC////////oAJCABDJAyAEQSBqQgAgF0KAgICAgIB/gyIVIBd9IBVUrSIaIAQpA0giGyAEKQNQfCIZfCIXIAQpA4ABfCIWfUIAQpGAgICAgICACEIAEMkDIARBwAFqIAEpA+gCIhVCAEKAgICAgIARQgAQyQMgBEHQAWogFUIAQoCAgICAfEIAEMkDIARB4AFqIBVCAEJ/QgAQyQMgBEHwAWogFUIAQv///////6ACQgAQyQMgBEEwakIAIBZCAFKtIiQgFyAaVK0iHCAEKQNYIBkgG1StfCIZIAQpA2B8Ihh8IhogBCkDkAF8IhsgBCkDiAEgFiAXVK18fCIefCIXIAQpA8ABfCIWfUIAQpGAgICAgICACEIAEMkDIARBgAJqIAEpA+ACIhVCAEKAgICAgIARQgAQyQMgBEGQAmogFUIAQoCAgICAfEIAEMkDIARBoAJqIBVCAEJ/QgAQyQMgBEGwAmogFUIAQv///////6ACQgAQyQMgBEIAIAQpA8gBIBYgF1StfCIdIAQpA9ABfCIVIAQpA2ggGCAZVK18Ih8gBCkDcHwiGSAEKQMQfCIYIBogHFStfCIcIAQpA6ABfCIgIBsgHlatIAQpA5gBIBogG1atfHx8IhogFyAkVK18IiN8IhcgFkIAUq18IhYgBCkDgAJ8Iht9QgBCkYCAgICAgIAIQgAQyQMgASkD2AIhJCABKQPQAiEeIAEpA8gCISIgASkDwAIhJgJAAkAgBCkDCCAEKQOYAiAEKQOIAiAWIBtWrXwiJSAEKQOQAnwiISAlVK18ICEgFSAXVq0gBCkD2AEgFSAdVK18fCIlIAQpA+ABfCIVIBogI1atIiMgBCkDIHwiHSAEKQN4IBkgH1StfCInIAQpA7ABfCIfIBggHFatIAQpAxggGCAZVK18fHwiGSAaICBUrSAEKQOoASAcICBWrXx8fCIcfCIgfCIaIBYgF1StfCIYfCIXICFUrXwiISAEKQOgAnwiFiAYIBpUrSIoIAQpAzB8IhggGSAcVq0gGSAfVK0gBCkDuAEgHyAnVK18fHwiHyAEKQPwAXwiGSAdICBWrSAEKQMoIB0gI1StfHx8IhwgFSAaVq0gBCkD6AEgFSAlVK18fHwiIHwiHXwiGiAXIBtCAFKtfCIVIBdUrXwiGyAaVK0iIyAEKQMAfCIXICNUrXwgFyAcICBWrSAZIBxWrSAEKQP4ASAZIB9UrXx8fCIgIAQpA7ACfCIcIBggHVatIAQpAzggGCAoVK18fHwiGCAWIBpWrSAEKQOoAiAWICFUrXx8fCIWfCIZIBdUrXwgFiAYVK0gGCAcVK0gBCkDuAIgHCAgVK18fHx8IhhCkYCAgICAgIAIVg0AIBhCkYCAgICAgIAIUQRAIBUgG4QgGYRQRQ0BQgAhFkKRgICAgICAgAghGEIAIRpCACEXDAILIBkhFiAbIRogFSEXDAELIBVCAX0hFyAbIBVQrSIVfSEaIBkgFSAbVq0iFX0hFiAYIBUgGVatfUKRgICAgICAgAh9IRgLQpGAgICAgICACCEVIBYgInwiFiAiVCAWIBogHnwiGSAeVCAZIBkgFyAkfCIaICRUrXwiG1ZyrXwiGSAWVHKtIBggJnx8IhghFwJAAkAgGEKRgICAgICAgAhRBEAgGSAbhEIAUg0BQgEhFSAaIhdCAVENAQsgFSAXWA0AIBkhFSAbIRcgGiEWDAELIBpCAX0hFiAbIBpQrSIVfSEXIBkgFSAbVq0iGn0hFULu/////////3dC7/////////93IBkgGlQbIBh8IRgLQpGAgICAgICACCEaIBUgFSAAKQNIfCIcViAcIBwgFyAXIAApA1B8IhVWIBUgFiAWIAApA1h8IhtWrXwiFiAVVHKtfCIZVnKtIAApA0AgGHx8IhghFSAAAn4CQCAYQpGAgICAgICACFEEQCAWIBmEQgBSDQFCASEaIBsiFUIBUQ0BCyAVIBpaDQAgGSEVIBYhFyAbDAELIBYgG1CtIhV9IRcgGSAVIBZWrSIWfSEVQu7/////////d0Lv/////////3cgFiAZVhsgGHwhGCAbQgF9CzcDWCAAIBc3A1AgACAVNwNIIAAgGDcDQCAPEEYgBCgCuA8iAQRAIAQoArwPIAFB4ABsEN8ECyANIgEgE0cNAQwJCwtBAEEAQaDLwQAQ2QMAC0EBQQFBsMvBABDZAwALQQEgA0HAy8EAENkDAAtBAkECQdDLwQAQ2QMAC0ECIAFB4MvBABDZAwALQQhBgANBkMvBABDIBAALIAMgBUGAy8EAEOUEAAsgByAJQZCYwQAQyAQACwJAIAJBA3EiBQRAIAJB/P//H3EhASACQQV0QYD///8HcSEHA0AgASAEKAKMDyICTw0CIARBkBBqIgIgBCgCiA8gB2oQ3gEgACACEF0gB0EgaiEHIAFBAWohASAFQQFrIgUNAAsLIAQoAoQPIgVFDQIgBCgCiA8hBgwBCyABIAJB8MrBABDZAwALIAYgBUEFdBDfBAsgBEHwEGokAAvTfgIFf05+IwBB8BJrIgEkACABQcASakGQiMIAQQEQpgJBKCECIAEpA8ASIREgASkDyBIhGiABKQPQEiESIAEpA9gSIQ0gASkD4BIhDiABKQPoEiEPA0AgAUGQEWogAkGo1MEAaikDACIHQgAgD0IAEMkDIAFBoBFqIAdCACAOQgAQyQMgAUGwEWogB0IAIA1CABDJAyABQcARaiAHQgAgEkIAEMkDIAFB0BFqIAdCACAaQgAQyQMgAUHgEWogB0IAIBFCABDJAyABQYARaiABKQOQESIKICZ8Ih5CAEIAQv3/8//P///5iX8QyQMgAUHwEGogASkDiBEiB0IAQqvV/v///7//uX9CABDJAyABQeAQaiAHQgBC///Piuv//9UeQgAQyQMgAUHQEGogB0IAQqTsw7WP1LSY5wBCABDJAyABQcAQaiAHQgBCv6WUnM/w0rvkAEIAEMkDIAFBsBBqIAdCAELX2a6a5PbpjcsAQgAQyQMgAUGgEGogB0IAQprN/8ujvcSAGkIAEMkDIAEpA6gQIAEpA+ARIgcgIXwiGyABKQPYESAJIAEpA9ARIgl8IgwgCVStfCAMIAEpA8gRIAggASkDwBEiCHwiCyAIVK18IAsgASkDuBEgBiABKQOwESIGfCIJIAZUrXwgCSABKQOoESABKQOgESIGIB18IgggBlStfCAIIAEpA5gRIAogHlatfHwiBiAIVK18fCITIAlUrXx8IgkgC1StfHwiCCAMVK18fCIQIAEpA6AQfCIMIBBUrXwgDCABKQO4ECAIIAEpA7AQfCILIAhUrXwgCyABKQPIECAJIAEpA8AQfCIKIAlUrXwgCiABKQPYECATIAEpA9AQfCIJIBNUrXwgCSABKQPoECAGIAEpA+AQIgZ8IgggBlStfCAIIAEpA/gQIAEpA/AQIgYgHnwgBlStfHwiJiAIVK18fCIdIAlUrXx8IgYgClStfHwiCCALVK18fCIJIAxUrXwiCyAQIBtUrSABKQPoESAHIBtWrXx8IgogFHwiB3wiISALVK0gByAKVK18IRQgAkEIayICQXhHDQALAkACQAJAAkACQCAUQgBSICFCms3/y6O9xIAaVnINAAJAICFCms3/y6O9xIAaUQRAIAlC19mumuT26Y3LAFYNAiAJQtfZrprk9umNywBRDQFCms3/y6O9xIAaISELIAkhNAwDCyAIQr+llJzP8NK75ABWDQBC19mumuT26Y3LACE0IAhCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohIQwDCyAGQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACE1IAZCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohIQwECyAdQv//z4rr///VHlYNAEKk7MO1j9S0mOcAITYgHUL//8+K6///1R5SICZCqtX+////v/+5f1hyDQELIB1C///Piuv//9UefSIKICZCq9X+////v/+5f1StIgd9ITcgBkKk7MO1j9S0mOcAfSILIB1C///Piuv//9UeVCAHIApWcq0iB30hNiAIQr+llJzP8NK75AB9IgogBkKk7MO1j9S0mOcAVCAHIAtWcq0iBn0hNSAJQtfZrprk9umNywB9IgcgCEK/pZScz/DSu+QAVCAGIApWcq0iBn0hNCAhIAlC19mumuT26Y3LAFQgBiAHVnKtfUKazf/Lo73EgBp9ISEgJkLVqoGAgIDAgMYAfCEmDAMLQprN/8ujvcSAGiEhIB0hNwwCCyAIITULIAYhNiAdITcLIAFBwBJqQZCIwgBBARCmAkEoIQIgASkDwBIhESABKQPIEiEaIAEpA9ASIRIgASkD2BIhDSABKQPgEiEOIAEpA+gSIQ9CACEUQgAhBkIAIQhCACEJQgAhHQNAIAFBwA9qIAJBqNTBAGopAwAiB0IAIA9CABDJAyABQdAPaiAHQgAgDkIAEMkDIAFB4A9qIAdCACANQgAQyQMgAUHwD2ogB0IAIBJCABDJAyABQYAQaiAHQgAgGkIAEMkDIAFBkBBqIAdCACARQgAQyQMgAUGwD2ogASkDwA8iCiAnfCIeQgBCAEL9//P/z///+Yl/EMkDIAFBoA9qIAEpA7gPIgdCAEKr1f7///+//7l/QgAQyQMgAUGQD2ogB0IAQv//z4rr///VHkIAEMkDIAFBgA9qIAdCAEKk7MO1j9S0mOcAQgAQyQMgAUHwDmogB0IAQr+llJzP8NK75ABCABDJAyABQeAOaiAHQgBC19mumuT26Y3LAEIAEMkDIAFB0A5qIAdCAEKazf/Lo73EgBpCABDJAyABKQPYDiABKQOQECIHIB18IhsgASkDiBAgCSABKQOAECIJfCIMIAlUrXwgDCABKQP4DyAIIAEpA/APIgh8IgsgCFStfCALIAEpA+gPIAYgASkD4A8iBnwiCSAGVK18IAkgASkD2A8gASkD0A8iBiAUfCIIIAZUrXwgCCABKQPIDyAKIB5WrXx8IgYgCFStfHwiEyAJVK18fCIJIAtUrXx8IgggDFStfHwiECABKQPQDnwiDCAQVK18IAwgASkD6A4gCCABKQPgDnwiCyAIVK18IAsgASkD+A4gCSABKQPwDnwiCiAJVK18IAogASkDiA8gEyABKQOAD3wiCSATVK18IAkgASkDmA8gBiABKQOQDyIGfCIIIAZUrXwgCCABKQOoDyABKQOgDyIGIB58IAZUrXx8IicgCFStfHwiFCAJVK18fCIGIApUrXx8IgggC1StfHwiCSAMVK18IgsgECAbVK0gASkDmBAgByAbVq18fCIKIBV8Igd8Ih0gC1StIAcgClStfCEVIAJBCGsiAkF4Rw0ACwJAAkACQAJAAkAgFUIAUiAdQprN/8ujvcSAGlZyDQACQCAdQprN/8ujvcSAGlEEQCAJQtfZrprk9umNywBWDQIgCULX2a6a5PbpjcsAUQ0BQprN/8ujvcSAGiEdCyAJITgMAwsgCEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhOCAIQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIR0MAwsgBkKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhOSAGQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIR0MBAsgFEL//8+K6///1R5WDQBCpOzDtY/UtJjnACE6IBRC///Piuv//9UeUiAnQqrV/v///7//uX9Ycg0BCyAUQv//z4rr///VHn0iCiAnQqvV/v///7//uX9UrSIHfSE7IAZCpOzDtY/UtJjnAH0iCyAUQv//z4rr///VHlQgByAKVnKtIgd9ITogCEK/pZScz/DSu+QAfSIKIAZCpOzDtY/UtJjnAFQgByALVnKtIgZ9ITkgCULX2a6a5PbpjcsAfSIHIAhCv6WUnM/w0rvkAFQgBiAKVnKtIgZ9ITggHSAJQtfZrprk9umNywBUIAYgB1ZyrX1Cms3/y6O9xIAafSEdICdC1aqBgICAwIDGAHwhJwwDC0Kazf/Lo73EgBohHSAUITsMAgsgCCE5CyAGITogFCE7CyABQcASakGRiMIAQeAAEKYCQSghAiABKQPAEiERIAEpA8gSIRogASkD0BIhEiABKQPYEiENIAEpA+ASIQ4gASkD6BIhD0IAIRVCACEGQgAhCEIAIQlCACEUA0AgAUHwDWogAkGo1MEAaikDACIHQgAgD0IAEMkDIAFBgA5qIAdCACAOQgAQyQMgAUGQDmogB0IAIA1CABDJAyABQaAOaiAHQgAgEkIAEMkDIAFBsA5qIAdCACAaQgAQyQMgAUHADmogB0IAIBFCABDJAyABQeANaiABKQPwDSIKICh8Ih5CAEIAQv3/8//P///5iX8QyQMgAUHQDWogASkD6A0iB0IAQqvV/v///7//uX9CABDJAyABQcANaiAHQgBC///Piuv//9UeQgAQyQMgAUGwDWogB0IAQqTsw7WP1LSY5wBCABDJAyABQaANaiAHQgBCv6WUnM/w0rvkAEIAEMkDIAFBkA1qIAdCAELX2a6a5PbpjcsAQgAQyQMgAUGADWogB0IAQprN/8ujvcSAGkIAEMkDIAEpA4gNIAEpA8AOIgcgFHwiGyABKQO4DiAJIAEpA7AOIgl8IgwgCVStfCAMIAEpA6gOIAggASkDoA4iCHwiCyAIVK18IAsgASkDmA4gBiABKQOQDiIGfCIJIAZUrXwgCSABKQOIDiABKQOADiIGIBV8IgggBlStfCAIIAEpA/gNIAogHlatfHwiBiAIVK18fCITIAlUrXx8IgkgC1StfHwiCCAMVK18fCIQIAEpA4ANfCIMIBBUrXwgDCABKQOYDSAIIAEpA5ANfCILIAhUrXwgCyABKQOoDSAJIAEpA6ANfCIKIAlUrXwgCiABKQO4DSATIAEpA7ANfCIJIBNUrXwgCSABKQPIDSAGIAEpA8ANIgZ8IgggBlStfCAIIAEpA9gNIAEpA9ANIgYgHnwgBlStfHwiKCAIVK18fCIVIAlUrXx8IgYgClStfHwiCCALVK18fCIJIAxUrXwiCyAQIBtUrSABKQPIDiAHIBtWrXx8IgogFnwiB3wiFCALVK0gByAKVK18IRYgAkEIayICQXhHDQALAkACQAJAAkACQCAWQgBSIBRCms3/y6O9xIAaVnINAAJAIBRCms3/y6O9xIAaUQRAIAlC19mumuT26Y3LAFYNAiAJQtfZrprk9umNywBRDQFCms3/y6O9xIAaIRQLIAkhPAwDCyAIQr+llJzP8NK75ABWDQBC19mumuT26Y3LACE8IAhCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohFAwDCyAGQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACE9IAZCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohFAwECyAVQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIT4gFUL//8+K6///1R5SIChCqtX+////v/+5f1hyDQELIBVC///Piuv//9UefSIKIChCq9X+////v/+5f1StIgd9IT8gBkKk7MO1j9S0mOcAfSILIBVC///Piuv//9UeVCAHIApWcq0iB30hPiAIQr+llJzP8NK75AB9IgogBkKk7MO1j9S0mOcAVCAHIAtWcq0iBn0hPSAJQtfZrprk9umNywB9IgcgCEK/pZScz/DSu+QAVCAGIApWcq0iBn0hPCAUIAlC19mumuT26Y3LAFQgBiAHVnKtfUKazf/Lo73EgBp9IRQgKELVqoGAgIDAgMYAfCEoDAMLQprN/8ujvcSAGiEUIBUhPwwCCyAIIT0LIAYhPiAVIT8LIAFBwBJqQfGIwgBB4AAQpgJBKCECIAEpA8ASIREgASkDyBIhGiABKQPQEiESIAEpA9gSIQ0gASkD4BIhDiABKQPoEiEPQgAhFkIAIQZCACEIQgAhCUIAIRUDQCABQaAMaiACQajUwQBqKQMAIgdCACAPQgAQyQMgAUGwDGogB0IAIA5CABDJAyABQcAMaiAHQgAgDUIAEMkDIAFB0AxqIAdCACASQgAQyQMgAUHgDGogB0IAIBpCABDJAyABQfAMaiAHQgAgEUIAEMkDIAFBkAxqIAEpA6AMIgogKXwiHkIAQgBC/f/z/8////mJfxDJAyABQYAMaiABKQOYDCIHQgBCq9X+////v/+5f0IAEMkDIAFB8AtqIAdCAEL//8+K6///1R5CABDJAyABQeALaiAHQgBCpOzDtY/UtJjnAEIAEMkDIAFB0AtqIAdCAEK/pZScz/DSu+QAQgAQyQMgAUHAC2ogB0IAQtfZrprk9umNywBCABDJAyABQbALaiAHQgBCms3/y6O9xIAaQgAQyQMgASkDuAsgASkD8AwiByAVfCIbIAEpA+gMIAkgASkD4AwiCXwiDCAJVK18IAwgASkD2AwgCCABKQPQDCIIfCILIAhUrXwgCyABKQPIDCAGIAEpA8AMIgZ8IgkgBlStfCAJIAEpA7gMIAEpA7AMIgYgFnwiCCAGVK18IAggASkDqAwgCiAeVq18fCIGIAhUrXx8IhMgCVStfHwiCSALVK18fCIIIAxUrXx8IhAgASkDsAt8IgwgEFStfCAMIAEpA8gLIAggASkDwAt8IgsgCFStfCALIAEpA9gLIAkgASkD0At8IgogCVStfCAKIAEpA+gLIBMgASkD4At8IgkgE1StfCAJIAEpA/gLIAYgASkD8AsiBnwiCCAGVK18IAggASkDiAwgASkDgAwiBiAefCAGVK18fCIpIAhUrXx8IhYgCVStfHwiBiAKVK18fCIIIAtUrXx8IgkgDFStfCILIBAgG1StIAEpA/gMIAcgG1atfHwiCiAXfCIHfCIVIAtUrSAHIApUrXwhFyACQQhrIgJBeEcNAAsCQAJAAkACQAJAIBdCAFIgFUKazf/Lo73EgBpWcg0AAkAgFUKazf/Lo73EgBpRBEAgCULX2a6a5PbpjcsAVg0CIAlC19mumuT26Y3LAFENAUKazf/Lo73EgBohFQsgCSFADAMLIAhCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAIUAgCEK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEVDAMLIAZCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIUEgBkKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEVDAQLIBZC///Piuv//9UeVg0AQqTsw7WP1LSY5wAhQiAWQv//z4rr///VHlIgKUKq1f7///+//7l/WHINAQsgFkL//8+K6///1R59IgogKUKr1f7///+//7l/VK0iB30hQyAGQqTsw7WP1LSY5wB9IgsgFkL//8+K6///1R5UIAcgClZyrSIHfSFCIAhCv6WUnM/w0rvkAH0iCiAGQqTsw7WP1LSY5wBUIAcgC1ZyrSIGfSFBIAlC19mumuT26Y3LAH0iByAIQr+llJzP8NK75ABUIAYgClZyrSIGfSFAIBUgCULX2a6a5PbpjcsAVCAGIAdWcq19QprN/8ujvcSAGn0hFSApQtWqgYCAgMCAxgB8ISkMAwtCms3/y6O9xIAaIRUgFiFDDAILIAghQQsgBiFCIBYhQwsgAUHAEmpB0YnCAEHfABCmAkEoIQIgASkDwBIhESABKQPIEiEaIAEpA9ASIRIgASkD2BIhDSABKQPgEiEOIAEpA+gSIQ9CACEXQgAhBkIAIQhCACEJQgAhFgNAIAFB0ApqIAJBqNTBAGopAwAiB0IAIA9CABDJAyABQeAKaiAHQgAgDkIAEMkDIAFB8ApqIAdCACANQgAQyQMgAUGAC2ogB0IAIBJCABDJAyABQZALaiAHQgAgGkIAEMkDIAFBoAtqIAdCACARQgAQyQMgAUHACmogASkD0AoiCiAqfCIeQgBCAEL9//P/z///+Yl/EMkDIAFBsApqIAEpA8gKIgdCAEKr1f7///+//7l/QgAQyQMgAUGgCmogB0IAQv//z4rr///VHkIAEMkDIAFBkApqIAdCAEKk7MO1j9S0mOcAQgAQyQMgAUGACmogB0IAQr+llJzP8NK75ABCABDJAyABQfAJaiAHQgBC19mumuT26Y3LAEIAEMkDIAFB4AlqIAdCAEKazf/Lo73EgBpCABDJAyABKQPoCSABKQOgCyIHIBZ8IhsgASkDmAsgCSABKQOQCyIJfCIMIAlUrXwgDCABKQOICyAIIAEpA4ALIgh8IgsgCFStfCALIAEpA/gKIAYgASkD8AoiBnwiCSAGVK18IAkgASkD6AogASkD4AoiBiAXfCIIIAZUrXwgCCABKQPYCiAKIB5WrXx8IgYgCFStfHwiEyAJVK18fCIJIAtUrXx8IgggDFStfHwiECABKQPgCXwiDCAQVK18IAwgASkD+AkgCCABKQPwCXwiCyAIVK18IAsgASkDiAogCSABKQOACnwiCiAJVK18IAogASkDmAogEyABKQOQCnwiCSATVK18IAkgASkDqAogBiABKQOgCiIGfCIIIAZUrXwgCCABKQO4CiABKQOwCiIGIB58IAZUrXx8IiogCFStfHwiFyAJVK18fCIGIApUrXx8IgggC1StfHwiCSAMVK18IgsgECAbVK0gASkDqAsgByAbVq18fCIKIBh8Igd8IhYgC1StIAcgClStfCEYIAJBCGsiAkF4Rw0ACwJAAkACQAJAAkAgGEIAUiAWQprN/8ujvcSAGlZyDQACQCAWQprN/8ujvcSAGlEEQCAJQtfZrprk9umNywBWDQIgCULX2a6a5PbpjcsAUQ0BQprN/8ujvcSAGiEWCyAJIUQMAwsgCEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhRCAIQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIRYMAwsgBkKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhRSAGQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIRYMBAsgF0L//8+K6///1R5WDQBCpOzDtY/UtJjnACFGIBdC///Piuv//9UeUiAqQqrV/v///7//uX9Ycg0BCyAXQv//z4rr///VHn0iCiAqQqvV/v///7//uX9UrSIHfSFHIAZCpOzDtY/UtJjnAH0iCyAXQv//z4rr///VHlQgByAKVnKtIgd9IUYgCEK/pZScz/DSu+QAfSIKIAZCpOzDtY/UtJjnAFQgByALVnKtIgZ9IUUgCULX2a6a5PbpjcsAfSIHIAhCv6WUnM/w0rvkAFQgBiAKVnKtIgZ9IUQgFiAJQtfZrprk9umNywBUIAYgB1ZyrX1Cms3/y6O9xIAafSEWICpC1aqBgICAwIDGAHwhKgwDC0Kazf/Lo73EgBohFiAXIUcMAgsgCCFFCyAGIUYgFyFHCyABQcASakGwisIAQeAAEKYCQSghAiABKQPAEiERIAEpA8gSIRogASkD0BIhEiABKQPYEiENIAEpA+ASIQ4gASkD6BIhD0IAIRhCACEGQgAhCEIAIQlCACEXA0AgAUGACWogAkGo1MEAaikDACIHQgAgD0IAEMkDIAFBkAlqIAdCACAOQgAQyQMgAUGgCWogB0IAIA1CABDJAyABQbAJaiAHQgAgEkIAEMkDIAFBwAlqIAdCACAaQgAQyQMgAUHQCWogB0IAIBFCABDJAyABQfAIaiABKQOACSIKICt8Ih5CAEIAQv3/8//P///5iX8QyQMgAUHgCGogASkD+AgiB0IAQqvV/v///7//uX9CABDJAyABQdAIaiAHQgBC///Piuv//9UeQgAQyQMgAUHACGogB0IAQqTsw7WP1LSY5wBCABDJAyABQbAIaiAHQgBCv6WUnM/w0rvkAEIAEMkDIAFBoAhqIAdCAELX2a6a5PbpjcsAQgAQyQMgAUGQCGogB0IAQprN/8ujvcSAGkIAEMkDIAEpA5gIIAEpA9AJIgcgF3wiGyABKQPICSAJIAEpA8AJIgl8IgwgCVStfCAMIAEpA7gJIAggASkDsAkiCHwiCyAIVK18IAsgASkDqAkgBiABKQOgCSIGfCIJIAZUrXwgCSABKQOYCSABKQOQCSIGIBh8IgggBlStfCAIIAEpA4gJIAogHlatfHwiBiAIVK18fCITIAlUrXx8IgkgC1StfHwiCCAMVK18fCIQIAEpA5AIfCIMIBBUrXwgDCABKQOoCCAIIAEpA6AIfCILIAhUrXwgCyABKQO4CCAJIAEpA7AIfCIKIAlUrXwgCiABKQPICCATIAEpA8AIfCIJIBNUrXwgCSABKQPYCCAGIAEpA9AIIgZ8IgggBlStfCAIIAEpA+gIIAEpA+AIIgYgHnwgBlStfHwiKyAIVK18fCIYIAlUrXx8IgYgClStfHwiCCALVK18fCIJIAxUrXwiCyAQIBtUrSABKQPYCSAHIBtWrXx8IgogGXwiB3wiFyALVK0gByAKVK18IRkgAkEIayICQXhHDQALAkACQAJAAkACQCAZQgBSIBdCms3/y6O9xIAaVnINAAJAIBdCms3/y6O9xIAaUQRAIAlC19mumuT26Y3LAFYNAiAJQtfZrprk9umNywBRDQFCms3/y6O9xIAaIRcLIAkhSAwDCyAIQr+llJzP8NK75ABWDQBC19mumuT26Y3LACFIIAhCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohFwwDCyAGQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACFJIAZCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohFwwECyAYQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIUogGEL//8+K6///1R5SICtCqtX+////v/+5f1hyDQELIBhC///Piuv//9UefSIKICtCq9X+////v/+5f1StIgd9IR4gBkKk7MO1j9S0mOcAfSILIBhC///Piuv//9UeVCAHIApWcq0iB30hSiAIQr+llJzP8NK75AB9IgogBkKk7MO1j9S0mOcAVCAHIAtWcq0iBn0hSSAJQtfZrprk9umNywB9IgcgCEK/pZScz/DSu+QAVCAGIApWcq0iBn0hSCAXIAlC19mumuT26Y3LAFQgBiAHVnKtfUKazf/Lo73EgBp9IRcgK0LVqoGAgIDAgMYAfCErDAMLQprN/8ujvcSAGiEXIBghHgwCCyAIIUkLIAYhSiAYIR4LIAFBwBJqQZCLwgBB3wAQpgJBKCECIAEpA8ASIREgASkDyBIhGiABKQPQEiESIAEpA9gSIQ0gASkD4BIhDiABKQPoEiEPQgAhGUIAIQZCACEIQgAhCUIAIRgDQCABQbAHaiACQajUwQBqKQMAIgdCACAPQgAQyQMgAUHAB2ogB0IAIA5CABDJAyABQdAHaiAHQgAgDUIAEMkDIAFB4AdqIAdCACASQgAQyQMgAUHwB2ogB0IAIBpCABDJAyABQYAIaiAHQgAgEUIAEMkDIAFBoAdqIAEpA7AHIgogLHwiH0IAQgBC/f/z/8////mJfxDJAyABQZAHaiABKQOoByIHQgBCq9X+////v/+5f0IAEMkDIAFBgAdqIAdCAEL//8+K6///1R5CABDJAyABQfAGaiAHQgBCpOzDtY/UtJjnAEIAEMkDIAFB4AZqIAdCAEK/pZScz/DSu+QAQgAQyQMgAUHQBmogB0IAQtfZrprk9umNywBCABDJAyABQcAGaiAHQgBCms3/y6O9xIAaQgAQyQMgASkDyAYgASkDgAgiByAYfCIbIAEpA/gHIAkgASkD8AciCXwiDCAJVK18IAwgASkD6AcgCCABKQPgByIIfCILIAhUrXwgCyABKQPYByAGIAEpA9AHIgZ8IgkgBlStfCAJIAEpA8gHIAEpA8AHIgYgGXwiCCAGVK18IAggASkDuAcgCiAfVq18fCIGIAhUrXx8IhMgCVStfHwiCSALVK18fCIIIAxUrXx8IhAgASkDwAZ8IgwgEFStfCAMIAEpA9gGIAggASkD0AZ8IgsgCFStfCALIAEpA+gGIAkgASkD4AZ8IgogCVStfCAKIAEpA/gGIBMgASkD8AZ8IgkgE1StfCAJIAEpA4gHIAYgASkDgAciBnwiCCAGVK18IAggASkDmAcgASkDkAciBiAffCAGVK18fCIsIAhUrXx8IhkgCVStfHwiBiAKVK18fCIIIAtUrXx8IgkgDFStfCILIBAgG1StIAEpA4gIIAcgG1atfHwiCiAcfCIHfCIYIAtUrSAHIApUrXwhHCACQQhrIgJBeEcNAAsCQAJAAkACQAJAIBxCAFIgGEKazf/Lo73EgBpWcg0AAkAgGEKazf/Lo73EgBpRBEAgCULX2a6a5PbpjcsAVg0CIAlC19mumuT26Y3LAFENAUKazf/Lo73EgBohGAsgCSFLDAMLIAhCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAIUsgCEK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEYDAMLIAZCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIUwgBkKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEYDAQLIBlC///Piuv//9UeVg0AQqTsw7WP1LSY5wAhTSAZQv//z4rr///VHlIgLEKq1f7///+//7l/WHINAQsgGUL//8+K6///1R59IgogLEKr1f7///+//7l/VK0iB30hGyAGQqTsw7WP1LSY5wB9IgsgGUL//8+K6///1R5UIAcgClZyrSIHfSFNIAhCv6WUnM/w0rvkAH0iCiAGQqTsw7WP1LSY5wBUIAcgC1ZyrSIGfSFMIAlC19mumuT26Y3LAH0iByAIQr+llJzP8NK75ABUIAYgClZyrSIGfSFLIBggCULX2a6a5PbpjcsAVCAGIAdWcq19QprN/8ujvcSAGn0hGCAsQtWqgYCAgMCAxgB8ISwMAwtCms3/y6O9xIAaIRggGSEbDAILIAghTAsgBiFNIBkhGwsgAUHAEmpB74vCAEHfABCmAkEoIQIgASkDwBIhDCABKQPIEiERIAEpA9ASIRogASkD2BIhEiABKQPgEiENIAEpA+gSIQ9CACEcQgAhBkIAIQhCACEJQgAhGUIAIQ4DQCABQeAFaiACQajUwQBqKQMAIgdCACAPQgAQyQMgAUHwBWogB0IAIA1CABDJAyABQYAGaiAHQgAgEkIAEMkDIAFBkAZqIAdCACAaQgAQyQMgAUGgBmogB0IAIBFCABDJAyABQbAGaiAHQgAgDEIAEMkDIAFB0AVqIAEpA+AFIgogLXwiJEIAQgBC/f/z/8////mJfxDJAyABQcAFaiABKQPYBSIHQgBCq9X+////v/+5f0IAEMkDIAFBsAVqIAdCAEL//8+K6///1R5CABDJAyABQaAFaiAHQgBCpOzDtY/UtJjnAEIAEMkDIAFBkAVqIAdCAEK/pZScz/DSu+QAQgAQyQMgAUGABWogB0IAQtfZrprk9umNywBCABDJAyABQfAEaiAHQgBCms3/y6O9xIAaQgAQyQMgASkD+AQgASkDsAYiByAZfCIiIAEpA6gGIAkgASkDoAYiCXwiECAJVK18IBAgASkDmAYgCCABKQOQBiIIfCILIAhUrXwgCyABKQOIBiAGIAEpA4AGIgZ8IgkgBlStfCAJIAEpA/gFIAEpA/AFIgYgHHwiCCAGVK18IAggASkD6AUgCiAkVq18fCIGIAhUrXx8Ih8gCVStfHwiCSALVK18fCIIIBBUrXx8IhMgASkD8AR8IhAgE1StfCAQIAEpA4gFIAggASkDgAV8IgsgCFStfCALIAEpA5gFIAkgASkDkAV8IgogCVStfCAKIAEpA6gFIB8gASkDoAV8IgkgH1StfCAJIAEpA7gFIAYgASkDsAUiBnwiCCAGVK18IAggASkDyAUgASkDwAUiBiAkfCAGVK18fCItIAhUrXx8IhwgCVStfHwiBiAKVK18fCIIIAtUrXx8IgkgEFStfCILIBMgIlStIAEpA7gGIAcgIlatfHwiCiAOfCIHfCIZIAtUrSAHIApUrXwhDiACQQhrIgJBeEcNAAsCQAJAAkACQAJAIA5CAFIgGUKazf/Lo73EgBpWcg0AAkAgGUKazf/Lo73EgBpRBEAgCULX2a6a5PbpjcsAVg0CIAlC19mumuT26Y3LAFENAUKazf/Lo73EgBohGQsgCSFODAMLIAhCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAIU4gCEK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEZDAMLIAZCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIU8gBkKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEZDAQLIBxC///Piuv//9UeVg0AQqTsw7WP1LSY5wAhUCAcQv//z4rr///VHlIgLUKq1f7///+//7l/WHINAQsgHEL//8+K6///1R59IgogLUKr1f7///+//7l/VK0iB30hEyAGQqTsw7WP1LSY5wB9IgsgHEL//8+K6///1R5UIAcgClZyrSIHfSFQIAhCv6WUnM/w0rvkAH0iCiAGQqTsw7WP1LSY5wBUIAcgC1ZyrSIGfSFPIAlC19mumuT26Y3LAH0iByAIQr+llJzP8NK75ABUIAYgClZyrSIGfSFOIBkgCULX2a6a5PbpjcsAVCAGIAdWcq19QprN/8ujvcSAGn0hGSAtQtWqgYCAgMCAxgB8IS0MAwtCms3/y6O9xIAaIRkgHCETDAILIAghTwsgBiFQIBwhEwsgAUHAEmoiAkHOjMIAQcAAQRAQ8QECQAJAAkACQAJAIAEoAsASQYCAgIB4RwRAIAFBgBJqIAFByBJqIgQoAgA2AgAgASABKQLAEjcD+BEgAUENNgK8EiABQZWNwgA2ArgSIAFCh4CAgMABNwKwEiABQY6NwgA2AqwSIAFBBjYCqBIQxwQiA0UNASADIAMpAwAiCEIBfDcDACADKQMIIQYgBEGIscIAKQMANwMAIAFB2BJqIgUgBjcDACABQdASaiIDIAg3AwAgAUGAscIAKQMANwPAEiACIAFBqBJqEIIBIAFBoBJqIAUpAwA3AwAgAUGYEmogAykDADcDACABQZASaiAEKQMANwMAIAEgASkDwBI3A4gSIAJB4o3CAEEgQRAQ8QEgAS0AxBIhBCABKALAEiIDQYCAgIB4Rg0CIAFBqhJqIAFBxxJqLQAAOgAAIAEgAS8AxRI7AagSIAEoAsgSIQUgAkGCjsIAQd4AEKYCQSghAiABKQPAEiEMIAEpA8gSIREgASkD0BIhGiABKQPYEiESIAEpA+ASIQ0gASkD6BIhD0IAIRxCACEJQgAhCEIAIQZCACEOA0AgAUGQBGogAkGo1MEAaikDACIHQgAgD0IAEMkDIAFBoARqIAdCACANQgAQyQMgAUGwBGogB0IAIBJCABDJAyABQcAEaiAHQgAgGkIAEMkDIAFB0ARqIAdCACARQgAQyQMgAUHgBGogB0IAIAxCABDJAyABQYAEaiABKQOQBCIKIC58IiRCAEIAQv3/8//P///5iX8QyQMgAUHwA2ogASkDiAQiB0IAQqvV/v///7//uX9CABDJAyABQeADaiAHQgBC///Piuv//9UeQgAQyQMgAUHQA2ogB0IAQqTsw7WP1LSY5wBCABDJAyABQcADaiAHQgBCv6WUnM/w0rvkAEIAEMkDIAFBsANqIAdCAELX2a6a5PbpjcsAQgAQyQMgAUGgA2ogB0IAQprN/8ujvcSAGkIAEMkDIAEpA6gDIAEpA+AEIgcgHHwiIiABKQPYBCAJIAEpA9AEIgl8IhAgCVStfCAQIAEpA8gEIAggASkDwAQiCHwiCyAIVK18IAsgASkDuAQgBiABKQOwBCIGfCIJIAZUrXwgCSABKQOoBCABKQOgBCIGIA58IgggBlStfCAIIAEpA5gEIAogJFatfHwiBiAIVK18fCIOIAlUrXx8IgkgC1StfHwiCCAQVK18fCIfIAEpA6ADfCIQIB9UrXwgECABKQO4AyAIIAEpA7ADfCILIAhUrXwgCyABKQPIAyAJIAEpA8ADfCIKIAlUrXwgCiABKQPYAyAOIAEpA9ADfCIJIA5UrXwgCSABKQPoAyAGIAEpA+ADIgZ8IgggBlStfCAIIAEpA/gDIAEpA/ADIgYgJHwgBlStfHwiLiAIVK18fCIOIAlUrXx8IgYgClStfHwiCCALVK18fCIJIBBUrXwiCyAfICJUrSABKQPoBCAHICJWrXx8IgogI3wiB3wiHCALVK0gByAKVK18ISMgAkEIayICQXhHDQALAkAgI0IAUiAcQprN/8ujvcSAGlZyDQAgHEKazf/Lo73EgBpSDQQgCULX2a6a5PbpjcsAVg0AIAlC19mumuT26Y3LAFIEQCAOIQsgBiEaIAghECAJISRCms3/y6O9xIAaIRwMBwsgCEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhJCAIQr+llJzP8NK75ABSBEAgDiELIAYhGiAIIRBCms3/y6O9xIAaIRwMBwsgBkKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhECAGQqTsw7WP1LSY5wBSBEAgDiELIAYhGkKazf/Lo73EgBohHAwHCyAOQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIRogDkL//8+K6///1R5SIC5CqtX+////v/+5f1hyDQULIA5C///Piuv//9UefSIKIC5Cq9X+////v/+5f1StIgd9IQsgBkKk7MO1j9S0mOcAfSIPIA5C///Piuv//9UeVCAHIApWcq0iB30hGiAIQr+llJzP8NK75AB9IgogBkKk7MO1j9S0mOcAVCAHIA9Wcq0iBn0hECAJQtfZrprk9umNywB9IgcgCEK/pZScz/DSu+QAVCAGIApWcq0iBn0hJCAcIAlC19mumuT26Y3LAFQgBiAHVnKtfUKazf/Lo73EgBp9IRwgLkLVqoGAgIDAgMYAfCEuDAULIAEgAS0AxBI6AIgSQYz3wQBBKyABQYgSakHk+8EAQdSPwgAQygMACxDwAwALIAEgBDoAwBJBjPfBAEErIAFBwBJqQeT7wQBBxI/CABDKAwALIA4hCyAGIRogCCEQIAkhJAwBCyAOIQtCms3/y6O9xIAaIRwLIAFBwBJqQeCOwgBB4AAQpgJBKCECIAEpA8ASIVEgASkDyBIhIiABKQPQEiEfIAEpA9gSIQwgASkD4BIhESABKQPoEiESQgAhDkIAIQlCACEIQgAhBkIAIQdCACEjQgAhDwNAIAFBwAJqIAJBqNTBAGopAwAiCkIAIBJCABDJAyABQdACaiAKQgAgEUIAEMkDIAFB4AJqIApCACAMQgAQyQMgAUHwAmogCkIAIB9CABDJAyABQYADaiAKQgAgIkIAEMkDIAFBkANqIApCACBRQgAQyQMgAUGwAmogASkDwAIiDSAjfCIxQgBCAEL9//P/z///+Yl/EMkDIAFBoAJqIAEpA7gCIgpCAEKr1f7///+//7l/QgAQyQMgAUGQAmogCkIAQv//z4rr///VHkIAEMkDIAFBgAJqIApCAEKk7MO1j9S0mOcAQgAQyQMgAUHwAWogCkIAQr+llJzP8NK75ABCABDJAyABQeABaiAKQgBC19mumuT26Y3LAEIAEMkDIAFB0AFqIApCAEKazf/Lo73EgBpCABDJAyABKQPYASABKQOQAyIKIA58IjIgASkDiAMgCSABKQOAAyIJfCIvIAlUrXwgLyABKQP4AiAIIAEpA/ACIgh8Ig4gCFStfCAOIAEpA+gCIAYgASkD4AIiBnwiCSAGVK18IAkgASkD2AIgASkD0AIiBiAHfCIIIAZUrXwgCCABKQPIAiANIDFWrXx8IgYgCFStfHwiByAJVK18fCIJIA5UrXx8IgggL1StfHwiMyABKQPQAXwiLyAzVK18IC8gASkD6AEgCCABKQPgAXwiDSAIVK18IA0gASkD+AEgCSABKQPwAXwiDiAJVK18IA4gASkDiAIgByABKQOAAnwiCSAHVK18IAkgASkDmAIgBiABKQOQAiIGfCIIIAZUrXwgCCABKQOoAiABKQOgAiIGIDF8IAZUrXx8IiMgCFStfHwiByAJVK18fCIGIA5UrXx8IgggDVStfHwiCSAvVK18Ig0gDyAyIDNWrSABKQOYAyAKIDJWrXx8Ig98Igp8Ig4gDVStIAogD1StfCEPIAJBCGsiAkF4Rw0ACwJAAkACQAJAIA9CAFIgDkKazf/Lo73EgBpWcg0AIA5Cms3/y6O9xIAaUg0BIAlC19mumuT26Y3LAFYNACAJQtfZrprk9umNywBSBEAgByEKIAYhEiAIIQwgCSEiQprN/8ujvcSAGiEODAQLIAhCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAISIgCEK/pZScz/DSu+QAUgRAIAchCiAGIRIgCCEMQprN/8ujvcSAGiEODAQLIAZCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIQwgBkKk7MO1j9S0mOcAUgRAIAchCiAGIRJCms3/y6O9xIAaIQ4MBAsgB0L//8+K6///1R5WDQBCpOzDtY/UtJjnACESIAdC///Piuv//9UeUiAjQqrV/v///7//uX9Ycg0CCyAHQv//z4rr///VHn0iEiAjQqvV/v///7//uX9UrSIPfSEKIAZCpOzDtY/UtJjnAH0iDSAHQv//z4rr///VHlQgDyASVnKtIgd9IRIgCEK/pZScz/DSu+QAfSIPIAZCpOzDtY/UtJjnAFQgByANVnKtIgZ9IQwgCULX2a6a5PbpjcsAfSIHIAhCv6WUnM/w0rvkAFQgBiAPVnKtIgZ9ISIgDiAJQtfZrprk9umNywBUIAYgB1ZyrX1Cms3/y6O9xIAafSEOICNC1aqBgICAwIDGAHwhIwwCCyAHIQogBiESIAghDCAJISIMAQsgByEKQprN/8ujvcSAGiEOCyABQcASakHAj8IAQQEQpgJBKCECIAEpA8ASITEgASkDyBIhMiABKQPQEiEzIAEpA9gSIS8gASkD4BIhUSABKQPoEiEfQgAhCUIAIQhCACEGQgAhB0IAIQ8DQCABQfAAaiACQajUwQBqKQMAIg1CACAfQgAQyQMgAUGAAWogDUIAIFFCABDJAyABQZABaiANQgAgL0IAEMkDIAFBoAFqIA1CACAzQgAQyQMgAUGwAWogDUIAIDJCABDJAyABQcABaiANQgAgMUIAEMkDIAFB4ABqIAEpA3AiESAlfCIlQgBCAEL9//P/z///+Yl/EMkDIAFB0ABqIAEpA2giDUIAQqvV/v///7//uX9CABDJAyABQUBrIA1CAEL//8+K6///1R5CABDJAyABQTBqIA1CAEKk7MO1j9S0mOcAQgAQyQMgAUEgaiANQgBCv6WUnM/w0rvkAEIAEMkDIAFBEGogDUIAQtfZrprk9umNywBCABDJAyABIA1CAEKazf/Lo73EgBpCABDJAyABKQMIIAEpA8ABIg0gIHwiUiABKQO4ASAJIAEpA7ABIgl8IjAgCVStfCAwIAEpA6gBIAggASkDoAEiCHwiICAIVK18ICAgASkDmAEgBiABKQOQASIGfCIJIAZUrXwgCSABKQOIASABKQOAASIGIAd8IgggBlStfCAIIAEpA3ggESAlVq18fCIGIAhUrXx8IgcgCVStfHwiCSAgVK18fCIIIDBUrXx8IlMgASkDAHwiMCBTVK18IDAgASkDGCAIIAEpAxB8IiAgCFStfCAgIAEpAyggCSABKQMgfCIRIAlUrXwgESABKQM4IAcgASkDMHwiCSAHVK18IAkgASkDSCAGIAEpA0AiBnwiCCAGVK18IAggASkDWCABKQNQIgYgJXwgBlStfHwiJSAIVK18fCIHIAlUrXx8IgYgEVStfHwiCCAgVK18fCIJIDBUrXwiESBSIFNWrSABKQPIASANIFJWrXx8Ig0gD3wiD3wiICARVK0gDSAPVq18IQ8gAkEIayICQXhHDQALAkACQAJAAkAgD0IAUiAgQprN/8ujvcSAGlZyDQAgIEKazf/Lo73EgBpSDQEgCULX2a6a5PbpjcsAVg0AIAlC19mumuT26Y3LAFIEQCAHIQ8gBiENIAghESAJIR9Cms3/y6O9xIAaISAMBAsgCEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhHyAIQr+llJzP8NK75ABSBEAgByEPIAYhDSAIIRFCms3/y6O9xIAaISAMBAsgBkKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhESAGQqTsw7WP1LSY5wBSBEAgByEPIAYhDUKazf/Lo73EgBohIAwECyAHQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIQ0gB0L//8+K6///1R5SICVCqtX+////v/+5f1hyDQILIAdC///Piuv//9UefSIfICVCq9X+////v/+5f1StIg19IQ8gBkKk7MO1j9S0mOcAfSIRIAdC///Piuv//9UeVCANIB9Wcq0iB30hDSAIQr+llJzP8NK75AB9Ih8gBkKk7MO1j9S0mOcAVCAHIBFWcq0iBn0hESAJQtfZrprk9umNywB9IgcgCEK/pZScz/DSu+QAVCAGIB9Wcq0iBn0hHyAgIAlC19mumuT26Y3LAFQgBiAHVnKtfUKazf/Lo73EgBp9ISAgJULVqoGAgIDAgMYAfCElDAILIAchDyAGIQ0gCCERIAkhHwwBCyAHIQ9Cms3/y6O9xIAaISALIABCADcDICAAQQE6AJgGIAAgLTcDgAYgACATNwP4BSAAIFA3A/AFIAAgTzcD6AUgACBONwPgBSAAIBk3A9gFIAAgLDcD0AUgACAbNwPIBSAAIE03A8AFIAAgTDcDuAUgACBLNwOwBSAAIBg3A6gFIABCATcDoAUgACArNwOYBSAAIB43A5AFIAAgSjcDiAUgACBJNwOABSAAIEg3A/gEIAAgFzcD8AQgACAqNwPoBCAAIEc3A+AEIAAgRjcD2AQgACBFNwPQBCAAIEQ3A8gEIAAgFjcDwAQgAEIBNwO4BCAAICk3A7gCIAAgQzcDsAIgACBCNwOoAiAAIEE3A6ACIAAgQDcDmAIgACAVNwOQAiAAICg3A4gCIAAgPzcDgAIgACA+NwP4ASAAID03A/ABIAAgPDcD6AEgACAUNwPgASAAICc3A9gBIAAgOzcD0AEgACA6NwPIASAAIDk3A8ABIAAgODcDuAEgACAdNwOwASAAICY3A6gBIAAgNzcDoAEgACA2NwOYASAAIDU3A5ABIAAgNDcDiAEgACAhNwOAASAAQvP/s4CAgMCTqn83A3ggAEKKgNDhr4aA5tMANwNwIABC/4Cq2Kav+sfHADcDaCAAQtfJ6LXu19/psX83A2AgAEKv1uL7u+fc5I5/NwNYIABC/ryP7JOqkesJNwNQIABBKGpCADcDACAAQTBqQgA3AwAgAEE4akIANwMAIABBQGtCADcDACAAQcgAakIANwMAIABBATYCiAYgAEKFwYvk946+8A03A9ACIABCmde1g6aLgO/9ADcD2AIgAELRwLPPhr6cvp5/NwPgAiAAQui70O/A+Ii8zwA3A+gCIABCh4Dwy96EgMKGfzcD8AIgAEKh1aaAgIDAjm43A/gCIABCgID8////v/8tNwPAAiAAQn83A8gCIABBlAZqIAFBgBJqKAIANgIAIAAgASkD+BE3AowGIAAgASkDiBI3AwAgAEEIaiABQZASaikDADcDACAAQRBqIAFBmBJqKQMANwMAIABBGGogAUGgEmopAwA3AwAgAEHAADYCnAMgAEGijcIANgKYAyAAQgE3A5ADIAAgBDoAhAMgACADNgKAAyAAQQJBASAFGzoAjAMgACAlNwOwBCAAIA83A6gEIAAgDTcDoAQgACARNwOYBCAAIB83A5AEIAAgIDcDiAQgACAjNwOABCAAIAo3A/gDIAAgEjcD8AMgACAMNwPoAyAAICI3A+ADIAAgDjcD2AMgACAuNwPQAyAAIAs3A8gDIAAgGjcDwAMgACAQNwO4AyAAICQ3A7ADIAAgHDcDqAMgAEIBNwOgAyAAIAU2AogDIAAgAS8BqBI7AIUDIABBhwNqIAFBqhJqLQAAOgAAIAFB8BJqJAALqmkCCn8dfiMAQfAYayIDJAACQAJAAkACfwJAAkACQAJAIAEtAGAiCiACLQBgRgRAIAFBiNLBAEEwEPEDRQRAIAFBMGpBiNLBAEEwEPEDRQ0CCyACQYjSwQBBMBDxA0UEQCACQTBqQYjSwQBBMBDxA0UNAwsCQCABIAJBMBDxA0UEQCABQTBqIgsgAkEwakEwEPEDRQ0BIABBAEHgAPwLAAwKCyABKQMwIg8hFyACKQMwIhUhFAJ+AkAgDyAVUg0AIAEpAzgiGCACKQM4IhRSBEAgGCEXDAELIAEpA0AiEyACKQNAIhRSBEAgEyEXDAELIAEpA0giGiACKQNIIhRSBEAgGiEXDAELIAEpA1AiGSACKQNQIhRSBEAgGSEXDAELIBghEiATIQ4gGSENIAEpA1giFyERIBogFyACKQNYIhRRDQEaCyAUIBdUDQUgASkDOCEYIAIpAzghEiABKQNAIRMgAikDQCEOIAEpA0ghGiABKQNQIRkgAikDUCENIAEpA1ghFyACKQNYIREgAikDSAshECANIBl9IhsgESAXVK0iFn0hFCAQIBp9IhwgDSAZVCAWIBtWcq0iDX0hGSAOIBN9IhsgECAaVCANIBxWcq0iEH0hGiASIBh9Ig0gDiATVCAQIBtWcq0iEH0hEyANIBBUIBIgGFRyIQQgFSAPfSEbIBEgF30hFwwHCyADQbAQahAmAkAgA0H4FmogCgR/IAMoAtATQQFxRQ0BIANB2BNqBSADQdAQagsiBEEoaikDADcDACADQfAWaiAEQSBqKQMANwMAIANB6BZqIARBGGopAwA3AwAgA0HgFmogBEEQaikDADcDACADQdgWaiAEQQhqKQMANwMAIAMgBCkDADcD0BYgA0Kh1aaAgIDAjm43A+gYIANCh4Dwy96EgMKGfzcD4BggA0Lou9DvwPiIvM8ANwPYGCADQtHAs8+Gvpy+nn83A9AYIANCmde1g6aLgO/9ADcDyBggA0KFwYvk946+8A03A8AYIANB8A5qIAEpAyAiGkIAIAEpAygiF0IAEMkDIANB0A5qIAEpAxgiGUIAIBdCABDJAyADQaAOaiABKQMQIhhCACAXQgAQyQMgA0HgDWogASkDCCIbQgAgF0IAEMkDIANBkA1qIAEpAwAiHEIAIBdCABDJAyADQcAOaiAZQgAgGkIAEMkDIANBkA5qIBhCACAaQgAQyQMgA0HQDWogG0IAIBpCABDJAyADQYANaiAcQgAgGkIAEMkDIANBgA5qIBhCACAZQgAQyQMgA0HADWogG0IAIBlCABDJAyADQfAMaiAcQgAgGUIAEMkDIANBsA1qIBtCACAYQgAQyQMgA0HgDGogHEIAIBhCABDJAyADQdAMaiAcQgAgG0IAEMkDIANB4A9qIBdCACAXQgAQyQMgA0HgDmogGkIAIBpCABDJAyADQbAOaiAZQgAgGUIAEMkDIANB8A1qIBhCACAYQgAQyQMgA0GgDWogG0IAIBtCABDJAyADQcAMaiAcQgAgHEIAEMkDIANB0A9qIAMpA+APIiNC/f/z/8////mJf34iEEIAQqvV/v///7//uX9CABDJAyADQcAPaiAQQgBC///Piuv//9UeQgAQyQMgA0GwD2ogEEIAQqTsw7WP1LSY5wBCABDJAyADQaAPaiAQQgBCv6WUnM/w0rvkAEIAEMkDIANBkA9qIBBCAELX2a6a5PbpjcsAQgAQyQMgA0GAD2ogEEIAQprN/8ujvcSAGkIAEMkDIAMpA9gMIAMpA+gMIAMpA7gNIAMpA8gNIAMpA4gOIAMpA5gOIAMpA8gOIAMpA9gOIAMpA/gOIhMgAykD0A58IhAgE1StfCISIAMpA6AOfCITIAMpA8AOfCIOIBNUrXwiDSADKQOoDiASIBNWrXwiEiADKQPgDXwiEXwiEyANVK18IBMgEyADKQOQDnwiE1atfCIPIAMpA+gNIBEgElStfCIVIAMpA5ANfCIUfCISIAMpA9ANfCINIAMpA4AOfCIRIA1UrXwiFiANIBJUrSADKQPYDSAPIBJWrXx8Ig8gAykDmA0gFCAVVK18fCISIAMpA4ANfCIVfCINIBZUrXwgDSANIAMpA8ANfCINVq18IhQgEiAVVq0gAykDiA0gDyASVq18fHwiEiADKQPwDHwiDyADKQOwDXwiFSAPVK18IhYgDyASVK0gAykD+AwgEiAUVK18fHwiEiAWVK18IBIgEiADKQPgDHwiElatfCIUIAMpA9AMfCIPIBRUrXwiFEI/iCADKQPIDCADKQPADCIWIBRCAYYgD0I/iIR8IhQgFlStfCAUIAMpA6gNIAMpA6ANIh0gEkIBhiAVQj+IhHwiFiAdVK18IBYgAykD+A0gAykD8A0iHiANQgGGIBFCP4iEfCIdIB5UrXwgHSADKQO4DiADKQOwDiIgIBNCAYYgDkI/iIR8Ih4gIFStfCAeIB4gAykD6A4gAykD4A4iISAQQgGGIAMpA/AOIiRCP4iEfCIgICFUrXwgICAgIAMpA+gPIiEgJEIBhnwiJCAhVK18IiBWrXwiISAOQgGGIBBCP4iEfCIfICFUrXwiHlatfCIQIBFCAYYgE0I/iIR8IiEgEFStfCIRIB1UrXwiECAVQgGGIA1CP4iEfCINIBBUrXwiDiAWVK18IhAgD0IBhiASQj+IhHwiEiAQVK18IhAgFFStfHwhEyADKQOIDyADKQOYDyADKQOoDyADKQO4DyADKQPIDyADKQPYDyADKQPQDyIPICNCfYN8IA9UrXwiFSADKQPAD3wiDyAVVK18IA8gJHwiFSAPVK18IhQgAykDsA98Ig8gFFStfCAPICB8IhQgD1StfCIWIAMpA6APfCIPIBZUrXwgDyAffCIWIA9UrXwiHSADKQOQD3wiDyAdVK18IA8gHnwiHSAPVK18Ih4gAykDgA98Ig8gHlStfCAPICF8Ih4gD1StfCIPUA0FIA8gEXwiESAPVCIERQ0FIAStIg8gDXwiDSAPWg0FIA0gD1StIg8gDnwiDiAPWg0FIA4gD1StIg8gEnwiEiAPWg0FIA8gElatIg8gEHwiECAPWg0FIA8gEFatIg8gE3wiEyAPVAwGC0Hs9sEAEOgEAAtBgPbBAEEzQdz2wQAQ/gMACyAAIAIpAzA3AzAgACACKQMANwMAIABB2ABqIAJB2ABqKQMANwMAIABB0ABqIAJB0ABqKQMANwMAIABByABqIAJByABqKQMANwMAIABBQGsgAkFAaykDADcDACAAQThqIAJBOGopAwA3AwAgAEEIaiACQQhqKQMANwMAIABBEGogAkEQaikDADcDACAAQRhqIAJBGGopAwA3AwAgAEEgaiACQSBqKQMANwMAIABBKGogAkEoaikDADcDAAwGCyAAIAEpAzA3AzAgACABKQMANwMAIABB2ABqIAFB2ABqKQMANwMAIABB0ABqIAFB0ABqKQMANwMAIABByABqIAFByABqKQMANwMAIABBQGsgAUFAaykDADcDACAAQThqIAFBOGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwAgAEEgaiABQSBqKQMANwMAIABBKGogAUEoaikDADcDAAwFC0Kk7MO1j9S0mOcAIAEpA0giECACKQNIIhN9Ig4gASkDUCIXIAIpA1AiElQgFyASfSIXIAEpA1giEiACKQNYIhlUrSINVHKtIhh9Ihp9IhEgFyANfSIXQv//z4rr///VHlZC///Piuv//9UeIBd9IhcgEiAZfSISQqvV/v///7//uX9WrSINVHKtIhR9IRlCv6WUnM/w0rvkACABKQNAIhsgAikDQCIWfSIcIBAgE1QgDiAYVHKtIhB9IhN9Ig4gESAUVCAaQqTsw7WP1LSY5wBWcq0iGH0hGkLX2a6a5PbpjcsAIAEpAzgiESACKQM4Ih19Ih4gFiAbViAQIBxWcq0iEH0iFH0iGyAOIBhUIBNCv6WUnM/w0rvkAFZyrSIOfSETIA4gG1YgFELX2a6a5PbpjcsAVnIhBCAXIA19IRQgESAdVCAQIB5Wcq0gFSAPfXxCms3/y6O9xIAafCEbQqvV/v///7//uX8gEn0hFwwCC0EACyEEIANBsAxqIBVC/f/z/8////mJf34iD0IAQqvV/v///7//uX9CABDJAyADQaAMaiAPQgBC///Piuv//9UeQgAQyQMgA0GQDGogD0IAQqTsw7WP1LSY5wBCABDJAyADQYAMaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB8AtqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HgC2ogD0IAQprN/8ujvcSAGkIAEMkDAkAgAykD6AsgAykD+AsgAykDiAwgAykDmAwgAykDqAwgAykDuAwgAykDsAwiDyAVfCAPVK18IhUgAykDoAx8Ig8gFVStfCAPIA8gFHwiD1atfCIUIAMpA5AMfCIVIBRUrXwgFSAWfCIUIBVUrXwiFiADKQOADHwiFSAWVK18IBUgHXwiFiAVVK18Ih0gAykD8At8IhUgHVStfCAVIB58Ih0gFVStfCIeIAMpA+ALfCIVIB5UrXwgFSARIBV8IhVWrXwiEVANACANIBF8Ig0gEVoNACANIBFUrSIRIA58Ig4gEVoNACAOIBFUrSIRIBJ8IhIgEVoNACARIBJWrSIRIBB8IhAgEVoNACAQIBFUrSIRIBN8IhMgEVQhBwsgA0HQC2ogD0L9//P/z///+Yl/fiIRQgBCq9X+////v/+5f0IAEMkDIANBwAtqIBFCAEL//8+K6///1R5CABDJAyADQbALaiARQgBCpOzDtY/UtJjnAEIAEMkDIANBoAtqIBFCAEK/pZScz/DSu+QAQgAQyQMgA0GQC2ogEUIAQtfZrprk9umNywBCABDJAyADQYALaiARQgBCms3/y6O9xIAaQgAQyQMCf0EAIAMpA4gLIAMpA5gLIAMpA6gLIAMpA7gLIAMpA8gLIAMpA9gLIAMpA9ALIhEgD3wgEVStfCIPIAMpA8ALfCIRIA9UrXwgESARIBR8IhFWrXwiFCADKQOwC3wiDyAUVK18IA8gFnwiFCAPVK18IhYgAykDoAt8Ig8gFlStfCAPIB18IhYgD1StfCIdIAMpA5ALfCIPIB1UrXwgDyAVfCIVIA9UrXwiHSADKQOAC3wiDyAdVK18IA8gDSAPfCIPVq18Ig1QDQAaQQAgDSANIA58Ig5YDQAaQQAgDSAOVq0iDSASfCISIA1aDQAaQQAgDSASVq0iDSAQfCIQIA1aDQAaIA0gEFatIg0gE3wiEyANVAshBSADQfAKaiARQv3/8//P///5iX9+Ig1CAEKr1f7///+//7l/QgAQyQMgA0HgCmogDUIAQv//z4rr///VHkIAEMkDIANB0ApqIA1CAEKk7MO1j9S0mOcAQgAQyQMgA0HACmogDUIAQr+llJzP8NK75ABCABDJAyADQbAKaiANQgBC19mumuT26Y3LAEIAEMkDIANBoApqIA1CAEKazf/Lo73EgBpCABDJAwJAIAMpA6gKIAMpA7gKIAMpA8gKIAMpA9gKIAMpA+gKIAMpA/gKIAMpA/AKIg0gEXwgDVStfCIRIAMpA+AKfCINIBFUrXwgDSANIBR8Ig1WrXwiFCADKQPQCnwiESAUVK18IBEgFnwiFCARVK18IhYgAykDwAp8IhEgFlStfCARIBV8IhUgEVStfCIWIAMpA7AKfCIRIBZUrXwgDyARfCIPIBFUrXwiFiADKQOgCnwiESAWVK18IBEgDiARfCIRVq18Ig5QDQAgDiASfCISIA5aDQAgDiASVq0iDiAQfCIQIA5aDQAgDiAQVq0iDiATfCITIA5UIQgLIANBkApqIA1C/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQYAKaiAOQgBC///Piuv//9UeQgAQyQMgA0HwCWogDkIAQqTsw7WP1LSY5wBCABDJAyADQeAJaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB0AlqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HACWogDkIAQprN/8ujvcSAGkIAEMkDIAMpA8gJIAMpA9gJIAMpA+gJIAMpA/gJIAMpA4gKIAMpA5gKIAMpA5AKIg4gDXwgDlStfCINIAMpA4AKfCIOIA1UrXwgDiAUfCINIA5UrXwiFCADKQPwCXwiDiAUVK18IA4gFXwiFSAOVK18IhQgAykD4Al8Ig4gFFStfCAOIA98Ig8gDlStfCIUIAMpA9AJfCIOIBRUrXwgDiARfCIRIA5UrXwiFCADKQPACXwiDiAUVK18IA4gEnwiFCAOVK18Ig5QRQRAIA4gEHwiECAOVCIGrSIOIBN8IhIgEyAGGyETIAYgDiASVnEhBgsgA0GwCWogDUL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIANBoAlqIA5CAEL//8+K6///1R5CABDJAyADQZAJaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANBgAlqIA5CAEK/pZScz/DSu+QAQgAQyQMgA0HwCGogDkIAQtfZrprk9umNywBCABDJAyADQeAIaiAOQgBCms3/y6O9xIAaQgAQyQMgAykD6AggAykD+AggAykDiAkgAykDmAkgAykDqAkgAykDuAkgAykDsAkiDiANfCAOVK18IhIgAykDoAl8Ig4gElStfCAOIBV8IhIgDlStfCINIAMpA5AJfCIOIA1UrXwgDiAPfCINIA5UrXwiDyADKQOACXwiDiAPVK18IA4gEXwiESAOVK18Ig8gAykD8Ah8Ig4gD1StfCAOIBR8Ig8gDlStfCIVIAMpA+AIfCIOIBVUrXwgDiAQfCIQIA5UrXwiDiATfCIVIBMgDkIAUiIJGyEUAkACQAJAIA4gFVYiDK0gDiAJG1BFBEAgECETDAELIAYgBCAHciAFciAIcnIEQCAQIRMMAQsgCSAMcQRAIBAhEwwBCyAUQprN/8ujvcSAGlYEQCAQIRMMAQsgFEKazf/Lo73EgBpSDQEgEELX2a6a5PbpjcsAVgRAIBAhEwwBCyAQQtfZrprk9umNywBSDQFC19mumuT26Y3LACETIA9Cv6WUnM/w0rvkAFYNACAPQr+llJzP8NK75ABSDQEgEUKk7MO1j9S0mOcAVg0AIBFCpOzDtY/UtJjnAFINASANQv//z4rr///VHlYNACANQv//z4rr///VHlIgEkKq1f7///+//7l/WHINAQsgDUL//8+K6///1R59IhAgEkKr1f7///+//7l/VK0iFX0hDiARQqTsw7WP1LSY5wB9IhYgDUL//8+K6///1R5UIBAgFVRyrSIQfSENIA9Cv6WUnM/w0rvkAH0iFSARQqTsw7WP1LSY5wBUIBAgFlZyrSIQfSERIBNC19mumuT26Y3LAH0iFiAPQr+llJzP8NK75ABUIBAgFVZyrSIPfSEQIBQgE0LX2a6a5PbpjcsAVCAPIBZWcq19QprN/8ujvcSAGn0hFCASQtWqgYCAgMCAxgB8IRIMAQsgDSEOIBEhDSAPIRELIAMgEjcDiBggAyAONwOAGCADIA03A/gXIAMgETcD8BcgAyAQNwPoFyADIBQ3A+AXIANBsBdqIgUgA0HAGGoiBiADQeAXahCyASADQegYaiADQfgWaikDADcDACADQeAYaiADQfAWaikDADcDACADQdgYaiADQegWaikDADcDACADQdAYaiADQeAWaikDADcDACADQcgYaiADQdgWaikDADcDACADIAMpA9AWNwPAGCADQYAXaiIEIAUgBhC9AiADQs+qmYCAgMCJMjcD6BggA0KFgJC2jYOAnrl/NwPgGCADQtH29obbwZew1wA3A9gYIANCy7f+6J6k2ZKLfzcD0BggA0KD2IiLkK+j+ewANwPIGCADQozFh9zb8+r1ETcDwBggA0GQGGoiBSAGIAsQsgEgA0H4D2ogBCAFEEwgAygCvBYiBARAIAMoAsAWIARBAnQQ3wQLAkAgAygCtBAiBEUNACAEIARBDGxBE2pBeHEiB2pBCWoiBEUNACADKAKwECAHayAEEN8ECyADKAKwEyIEQYCAgIB4RiAERXINASADKAK0EyAEQQJ0EN8EDAELIAMgFzcD6BggAyAUNwPgGCADIBk3A9gYIAMgGjcD0BggAyATNwPIGCADIBsgBK19NwPAGCABKQMAIhwhFyACKQMAIg8hEyADAn4CQAJ+AkAgDyAcUg0AIAEpAwgiGyACKQMIIhNSBEAgGyEXDAELIAEpAxAiGCACKQMQIhNSBEAgGCEXDAELIAEpAxgiGSACKQMYIhNSBEAgGSEXDAELIAEpAyAiGiACKQMgIhNSBEAgGiEXDAELIBshDSAZIQ4gGiESIAEpAygiFyERIBggFyACKQMoIhNRDQEaCyATIBdUDQEgASkDCCEbIAIpAwghDSABKQMQIRggASkDGCEZIAIpAxghDiABKQMgIRogAikDICESIAEpAyghFyACKQMoIREgAikDEAshECASIBp9IhUgESAXVK0iFH0hEyAOIBl9IhYgEiAaVCAUIBVWcq0iFX0hEiAQIBh9IhQgDiAZVCAVIBZWcq0iFX0hDiANIBt9IhYgFCAVVCAQIBhUcq0iFX0hECANIBtUIBUgFlZyIQQgDyAcfSEUIBEgF30MAQtCpOzDtY/UtJjnACABKQMYIhkgAikDGCIQfSITIAEpAyAiGiACKQMgIg5UIBogDn0iDiABKQMoIhcgAikDKCISVK0iDVRyrSIRfSIVfSIUIA4gDX0iDkL//8+K6///1R5WQv//z4rr///VHiAOfSINIBcgEn0iFkKr1f7///+//7l/Vq0iHVRyrSIOfSESQr+llJzP8NK75AAgASkDECIYIAIpAxAiHn0iICAQIBlWIBEgE1ZyrSIQfSITfSIRIA4gFFYgFUKk7MO1j9S0mOcAVnKtIhV9IQ5C19mumuT26Y3LACABKQMIIhsgAikDCCIUfSIjIBggHlQgECAgVnKtIh59IiB9IiEgESAVVCATQr+llJzP8NK75ABWcq0iE30hECATICFWICBC19mumuT26Y3LAFZyIQQgDSAdfSETIBQgG1YgHiAjVnKtIA8gHH18QprN/8ujvcSAGnwhFEKr1f7///+//7l/IBZ9CzcD2BAgAyATNwPQECADIBI3A8gQIAMgDjcDwBAgAyAQNwO4ECADIBQgBK19NwOwECADQfgPaiADQcAYaiADQbAQahBMCyADKAL4DwRAIAMgAykDiBA3A7gQIAMgAykDgBA3A7AQQYz3wQBBKyADQbAQakH89sEAQbj3wQAQygMACyADQeAGaiADKQOgECIdQgAgAykDqBAiHkIAEMkDIANB0AZqIAMpA5gQIiBCACAeQgAQyQMgA0HABmogAykDkBAiI0IAIB5CABDJAyADQbAGaiADKQOIECIhQgAgHkIAEMkDIANBoAZqIAMpA4AQIiRCACAeQgAQyQMgA0GwB2ogIEIAIB1CABDJAyADQaAHaiAjQgAgHUIAEMkDIANBkAdqICFCACAdQgAQyQMgA0GAB2ogJEIAIB1CABDJAyADQfAHaiAjQgAgIEIAEMkDIANB4AdqICFCACAgQgAQyQMgA0HQB2ogJEIAICBCABDJAyADQaAIaiAhQgAgI0IAEMkDIANBkAhqICRCACAjQgAQyQMgA0HACGogJEIAICFCABDJAyADQZAGaiAeQgAgHkIAEMkDIANB8AZqIB1CACAdQgAQyQMgA0HAB2ogIEIAICBCABDJAyADQYAIaiAjQgAgI0IAEMkDIANBsAhqICFCACAhQgAQyQMgA0HQCGogJEIAICRCABDJAyADQYAGaiADKQOQBiIoQv3/8//P///5iX9+IhBCAEKr1f7///+//7l/QgAQyQMgA0HwBWogEEIAQv//z4rr///VHkIAEMkDIANB4AVqIBBCAEKk7MO1j9S0mOcAQgAQyQMgA0HQBWogEEIAQr+llJzP8NK75ABCABDJAyADQcAFaiAQQgBC19mumuT26Y3LAEIAEMkDIANBsAVqIBBCAEKazf/Lo73EgBpCABDJAyADKQPICCADKQOYCCADKQOoCCADKQPoByADKQP4ByADKQOoByADKQO4ByADKQPYBiADKQPoBiITIAMpA9AGfCIQIBNUrXwiEiADKQPABnwiEyADKQOwB3wiDiATVK18Ig0gAykDyAYgEiATVq18IhIgAykDsAZ8IhF8IhMgDVStfCATIBMgAykDoAd8IhNWrXwiDyADKQO4BiARIBJUrXwiFSADKQOgBnwiFHwiEiADKQOQB3wiDSADKQPwB3wiESANVK18IhYgDSASVK0gAykDmAcgDyASVq18fCIPIAMpA6gGIBQgFVStfHwiEiADKQOAB3wiFXwiDSAWVK18IA0gDSADKQPgB3wiDVatfCIUIBIgFVatIAMpA4gHIA8gElatfHx8IhIgAykD0Ad8Ig8gAykDoAh8IhUgD1StfCIWIA8gElStIAMpA9gHIBIgFFStfHx8IhIgFlStfCASIBIgAykDkAh8IhJWrXwiDyADKQPACHwiFCAPVK18Ig9CP4ggAykD2AggAykD0AgiHyAPQgGGIBRCP4iEfCIWIB9UrXwgFiADKQO4CCADKQOwCCIPIBJCAYYgFUI/iIR8Ih8gD1StfCAfIAMpA4gIIAMpA4AIIiIgDUIBhiARQj+IhHwiDyAiVK18IA8gDyADKQPIByADKQPAByImIBNCAYYgDkI/iIR8IiIgJlStfCAiICIgAykD+AYgAykD8AYiJSAQQgGGIAMpA+AGIidCP4iEfCImICVUrXwgJiAmIAMpA5gGIiUgJ0IBhnwiJyAlVK18IiZWrXwiJSAOQgGGIBBCP4iEfCIpICVUrXwiIlatfCIQIBFCAYYgE0I/iIR8IiUgEFStfCIPVq18IhAgFUIBhiANQj+IhHwiESAQVK18Ig4gH1StfCIQIBRCAYYgEkI/iIR8IhMgEFStfCIQIBZUrXx8IRJBACEIAn8CQCADKQO4BSADKQPIBSADKQPYBSADKQPoBSADKQP4BSADKQOIBiAoIAMpA4AGIg18IA1UrXwiFSADKQPwBXwiDSAVVK18IA0gJ3wiFSANVK18IhQgAykD4AV8Ig0gFFStfCANICZ8IhQgDVStfCIWIAMpA9AFfCINIBZUrXwgDSApfCIWIA1UrXwiHyADKQPABXwiDSAfVK18IA0gInwiHyANVK18IiIgAykDsAV8Ig0gIlStfCANICV8IiIgDVStfCINUA0AIA0gD3wiDyANVCIERQ0AIAStIg0gEXwiESANWg0AIA0gEVatIg0gDnwiDiANWg0AIA0gDlatIg0gE3wiEyANWg0AIA0gE1atIg0gEHwiECANWg0AIA0gEFatIg0gEnwiEiANVAwBC0EACyEHIANBoAVqIBVC/f/z/8////mJf34iDUIAQqvV/v///7//uX9CABDJAyADQZAFaiANQgBC///Piuv//9UeQgAQyQMgA0GABWogDUIAQqTsw7WP1LSY5wBCABDJAyADQfAEaiANQgBCv6WUnM/w0rvkAEIAEMkDIANB4ARqIA1CAELX2a6a5PbpjcsAQgAQyQMgA0HQBGogDUIAQprN/8ujvcSAGkIAEMkDAkAgAykD2AQgAykD6AQgAykD+AQgAykDiAUgAykDmAUgAykDqAUgAykDoAUiDSAVfCANVK18IhUgAykDkAV8Ig0gFVStfCANIBR8IhUgDVStfCIUIAMpA4AFfCINIBRUrXwgDSAWfCIUIA1UrXwiFiADKQPwBHwiDSAWVK18IA0gH3wiFiANVK18Ih8gAykD4AR8Ig0gH1StfCANICJ8Ih8gDVStfCIiIAMpA9AEfCINICJUrXwgDSAPfCIiIA1UrXwiDVANACANIBF8IhEgDVoNACANIBFWrSINIA58Ig4gDVoNACANIA5WrSINIBN8IhMgDVoNACANIBNWrSINIBB8IhAgDVoNACANIBBWrSINIBJ8IhIgDVQhCAsgA0HABGogFUL9//P/z///+Yl/fiINQgBCq9X+////v/+5f0IAEMkDIANBsARqIA1CAEL//8+K6///1R5CABDJAyADQaAEaiANQgBCpOzDtY/UtJjnAEIAEMkDIANBkARqIA1CAEK/pZScz/DSu+QAQgAQyQMgA0GABGogDUIAQtfZrprk9umNywBCABDJAyADQfADaiANQgBCms3/y6O9xIAaQgAQyQNBACEGAn9BACADKQP4AyADKQOIBCADKQOYBCADKQOoBCADKQO4BCADKQPIBCADKQPABCINIBV8IA1UrXwiDyADKQOwBHwiDSAPVK18IA0gFHwiDyANVK18IhUgAykDoAR8Ig0gFVStfCANIBZ8IhUgDVStfCIUIAMpA5AEfCINIBRUrXwgDSAffCIUIA1UrXwiFiADKQOABHwiDSAWVK18IA0gInwiFiANVK18Ih8gAykD8AN8Ig0gH1StfCANIBF8Ih8gDVStfCINUA0AGkEAIA0gDSAOfCIOWA0AGkEAIA0gDlatIg0gE3wiEyANWg0AGkEAIA0gE1atIg0gEHwiECANWg0AGiANIBBWrSINIBJ8IhIgDVQLIQQgA0HgA2ogD0L9//P/z///+Yl/fiINQgBCq9X+////v/+5f0IAEMkDIANB0ANqIA1CAEL//8+K6///1R5CABDJAyADQcADaiANQgBCpOzDtY/UtJjnAEIAEMkDIANBsANqIA1CAEK/pZScz/DSu+QAQgAQyQMgA0GgA2ogDUIAQtfZrprk9umNywBCABDJAyADQZADaiANQgBCms3/y6O9xIAaQgAQyQMCQCADKQOYAyADKQOoAyADKQO4AyADKQPIAyADKQPYAyADKQPoAyADKQPgAyINIA98IA1UrXwiESADKQPQA3wiDSARVK18IA0gDSAVfCINVq18Ig8gAykDwAN8IhEgD1StfCARIBR8Ig8gEVStfCIVIAMpA7ADfCIRIBVUrXwgESAWfCIVIBFUrXwiFCADKQOgA3wiESAUVK18IBEgH3wiFCARVK18IhYgAykDkAN8IhEgFlStfCARIA4gEXwiEVatfCIOUA0AIA4gE3wiEyAOWg0AIA4gE1atIg4gEHwiECAOWg0AIA4gEFatIg4gEnwiEiAOVCEGCyADQYADaiANQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgA0HwAmogDkIAQv//z4rr///VHkIAEMkDIANB4AJqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0HQAmogDkIAQr+llJzP8NK75ABCABDJAyADQcACaiAOQgBC19mumuT26Y3LAEIAEMkDIANBsAJqIA5CAEKazf/Lo73EgBpCABDJA0EAIQUgAykDuAIgAykDyAIgAykD2AIgAykD6AIgAykD+AIgAykDiAMgAykDgAMiDiANfCAOVK18Ig0gAykD8AJ8Ig4gDVStfCAOIA4gD3wiDlatfCIPIAMpA+ACfCINIA9UrXwgDSAVfCIPIA1UrXwiFSADKQPQAnwiDSAVVK18IA0gFHwiFSANVK18IhQgAykDwAJ8Ig0gFFStfCANIBF8IhEgDVStfCIUIAMpA7ACfCINIBRUrXwgDSANIBN8Ig1WrXwiE1BFBEAgECATfCIQIBNUIgWtIhMgEnwiFCASIAUbIRIgBSATIBRWcSEFCyADQaACaiAOQv3/8//P///5iX9+IhNCAEKr1f7///+//7l/QgAQyQMgA0GQAmogE0IAQv//z4rr///VHkIAEMkDIANBgAJqIBNCAEKk7MO1j9S0mOcAQgAQyQMgA0HwAWogE0IAQr+llJzP8NK75ABCABDJAyADQeABaiATQgBC19mumuT26Y3LAEIAEMkDIANB0AFqIBNCAEKazf/Lo73EgBpCABDJAyADKQPYASADKQPoASADKQP4ASADKQOIAiADKQOYAiADKQOoAiADKQOgAiITIA58IBNUrXwiDiADKQOQAnwiEyAOVK18IBMgDyATfCITVq18Ig8gAykDgAJ8Ig4gD1StfCAOIBV8Ig8gDlStfCIVIAMpA/ABfCIOIBVUrXwgDiARfCIVIA5UrXwiESADKQPgAXwiDiARVK18IA0gDnwiDSAOVK18IhEgAykD0AF8Ig4gEVStfCAOIBB8IhYgDlStfCIQIBJ8Ig4gEiAQQgBSIgkbIRQCQAJAAkAgByAIciAEciAGciAFciAOIBBUIgStIBAgCRtCAFJyIAQgCXEgFEKazf/Lo73EgBpWcnINACAUQprN/8ujvcSAGlIEQCAPIREgFSEQIA0hDiAWIRIMAwsgFkLX2a6a5PbpjcsAVg0AIBZC19mumuT26Y3LAFIEQCAPIREgFSEQIA0hDiAWIRJCms3/y6O9xIAaIRQMAwsgDUK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhEiANQr+llJzP8NK75ABSBEAgDyERIBUhECANIQ5Cms3/y6O9xIAaIRQMAwsgFUKk7MO1j9S0mOcAVgRAQr+llJzP8NK75AAhDQwBC0K/pZScz/DSu+QAIQ4gFUKk7MO1j9S0mOcAUgRAIA8hESAVIRBCms3/y6O9xIAaIRQMAwsgD0L//8+K6///1R5WBEBCv6WUnM/w0rvkACENDAELQr+llJzP8NK75AAhDSAPQv//z4rr///VHlIgE0Kq1f7///+//7l/WHINAQsgD0L//8+K6///1R59IhAgE0Kr1f7///+//7l/VK0iDn0hESAVQqTsw7WP1LSY5wB9IhIgD0L//8+K6///1R5UIA4gEFZyrSIOfSEQIA1Cv6WUnM/w0rvkAH0iDyAVQqTsw7WP1LSY5wBUIA4gElZyrSISfSEOIBZC19mumuT26Y3LAH0iFSANQr+llJzP8NK75ABUIA8gElRyrSINfSESIBQgFkLX2a6a5PbpjcsAVCANIBVWcq19QprN/8ujvcSAGn0hFCATQtWqgYCAgMCAxgB8IRMMAQsgDyERIBUhEEKazf/Lo73EgBohFAsgAwJ+AkACQCAcIg8gFCINUg0AIBsiDyASIg1SDQAgGCIPIA4iDVINACAZIg8gECINUg0AIBoiDyARIg1SDQAgFyIPIBMiDVENAQsgDSAPWg0AQqTsw7WP1LSY5wAgGSAQfSINIBEgGlYgGiARfSIaIBMgF1atIhFUcq0iD30iFX0iFiAaIBF9IhpC///Piuv//9UeVkL//8+K6///1R4gGn0iESAXIBN9IhNCq9X+////v/+5f1atIhdUcq0iH30hGkK/pZScz/DSu+QAIBggDn0iIiANIA9UIBAgGVZyrSIQfSINfSIPIBYgH1QgFUKk7MO1j9S0mOcAVnKtIhV9IRlC19mumuT26Y3LACAbIBJ9IhYgDiAYViAQICJWcq0iEH0iDn0iHyAPIBVUIA1Cv6WUnM/w0rvkAFZyrSINfSEYIA0gH1YgDkLX2a6a5PbpjcsAVnIhBCARIBd9IQ8gEiAbViAQIBZWcq0gFCAcfXxCms3/y6O9xIAafCEbQqvV/v///7//uX8gE30MAQsgESAafSINIBMgF1StIhV9IQ8gECAZfSIWIA0gFVQgESAaVHKtIg19IRogDiAYfSIRIBAgGVQgDSAWVnKtIhB9IRkgEiAbfSINIA4gGFQgECARVnKtIhB9IRggDSAQVCASIBtUciEEIBQgHH0hGyATIBd9CzcD2BAgAyAPNwPQECADIBo3A8gQIAMgGTcDwBAgAyAYNwO4ECADIBsgBK19NwOwECADQcAYaiIGIANBsBBqIgUgAhCDAkEoIQIgA0HYEGogAUEoaikDADcDACADQdAQaiABQSBqKQMANwMAIANByBBqIAFBGGopAwA3AwAgA0HAEGogAUEQaikDADcDACADQbgQaiABQQhqKQMANwMAIAMgASkDADcDsBAgA0H4D2ogBSAGEIMCQgAhHEIAIRRCACEYQgAhGUIAIRJCACEbA0AgA0HwAGogA0H4D2ogAmopAwAiEEIAIB5CABDJAyADQYABaiAQQgAgHUIAEMkDIANBkAFqIBBCACAgQgAQyQMgA0GgAWogEEIAICNCABDJAyADQbABaiAQQgAgIUIAEMkDIANBwAFqIBBCACAkQgAQyQMgA0HgAGogAykDcCINIBt8IhNCAEIAQv3/8//P///5iX8QyQMgA0HQAGogAykDaCIQQgBCq9X+////v/+5f0IAEMkDIANBQGsgEEIAQv//z4rr///VHkIAEMkDIANBMGogEEIAQqTsw7WP1LSY5wBCABDJAyADQSBqIBBCAEK/pZScz/DSu+QAQgAQyQMgA0EQaiAQQgBC19mumuT26Y3LAEIAEMkDIAMgEEIAQprN/8ujvcSAGkIAEMkDIAMpAwggAykDwAEiESAcfCIQIAMpA7gBIAMpA7ABIhcgFHwiDiAXVK18IA4gDiADKQOoASAYIAMpA6ABIhh8IhcgGFStfCAXIBcgAykDmAEgAykDkAEiGCAZfCIZIBhUrXwgGSADKQOIASADKQOAASIYIBJ8IhIgGFStfCASIAMpA3ggDSATVq18fCIYIBJUrXx8IhIgGVStfHwiF1atfHwiDlatfHwiDSADKQMAfCIaIA1UrXwgGiADKQMYIA4gDiADKQMQfCIOVq18IA4gAykDKCAXIBcgAykDIHwiF1atfCAXIAMpAzggEiASIAMpAzB8IhJWrXwgEiASIAMpA0ggGCADKQNAIhh8IhkgGFStfCAZIAMpA1ggEyADKQNQIhN8IBNUrXx8IhsgGVStfHwiElatfHwiGSAXVK18fCIYIA5UrXx8IhQgGlStfCANIBBUrSADKQPIASAQIBFUrXx8fCEcIAJBCGsiAkF4Rw0ACwJAAkAgHEKazf/Lo73EgBpWDQAgHEKazf/Lo73EgBpSBEAgEiEOIBkhEyAYIRogFCEXDAILIBRC19mumuT26Y3LAFYNACAUQtfZrprk9umNywBSBEAgEiEOIBkhEyAYIRogFCEXQprN/8ujvcSAGiEcDAILIBhCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAIRcgGEK/pZScz/DSu+QAUgRAIBIhDiAZIRMgGCEaQprN/8ujvcSAGiEcDAILIBlCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIRogGUKk7MO1j9S0mOcAUgRAIBIhDiAZIRNCms3/y6O9xIAaIRwMAgsgEkL//8+K6///1R5WDQBCpOzDtY/UtJjnACETIBJC///Piuv//9UeUSAbQqrV/v///7//uX9WcQ0AIBIhDkKazf/Lo73EgBohHAwBCyASQv//z4rr///VHn0iECAbQqvV/v///7//uX9UrSITfSEOIBlCpOzDtY/UtJjnAH0iFyASQv//z4rr///VHlQgECATVHKtIhB9IRMgGEK/pZScz/DSu+QAfSISIBlCpOzDtY/UtJjnAFQgECAXVnKtIhB9IRogFELX2a6a5PbpjcsAfSIZIBhCv6WUnM/w0rvkAFQgECASVnKtIhB9IRcgHCAUQtfZrprk9umNywBUIBAgGVZyrX1Cms3/y6O9xIAafSEcIBtC1aqBgICAwIDGAHwhGwsgAyAbNwPYECADIA43A9AQIAMgEzcDyBAgAyAaNwPAECADIBc3A7gQIAMgHDcDsBAgAEEwaiADQbAQaiABQTBqEIMCIABBKGogA0HoGGopAwA3AwAgAEEgaiADQeAYaikDADcDACAAQRhqIANB2BhqKQMANwMAIABBEGogA0HQGGopAwA3AwAgAEEIaiADQcgYaikDADcDACAAIAMpA8AYNwMACyAAIAo6AGAgA0HwGGokAAuVWwIlfwJ+IwBB8CRrIgUkACAFQQw2AgQgBSACNgLgGwJAAkACQAJAAkACQAJAAkACQCACQQxGBEAgBSAENgLgGyACIARHDQECQAJAAkACQAJAAkACQCACQQJrDgsBAAAAAgAAAAAAAwALIAVBADYCuCAgBUEBNgKsICAFQYiJwAA2AqggIAVCBDcCsCAgBUGoIGpBnIzAABCoBAALQdHOxQAtAAAaQeAAQQgQ1gQiAg0CDAwLQdHOxQAtAAAaQaACQQgQ1gQiAg0CDAwLQdHOxQAtAAAaQcAEQQgQ1gQiAg0CDAwLIAIgASkDADcDACACIAEpAzA3AzAgAkEoaiABQShqKQMANwMAIAJBIGogAUEgaikDADcDACACQRhqIAFBGGopAwA3AwAgAkEQaiABQRBqKQMANwMAIAJBCGoiBCABQQhqKQMANwMAIAJBOGogAUE4aikDADcDACACQUBrIAFBQGspAwA3AwAgAkHIAGogAUHIAGopAwA3AwAgAkHQAGogAUHQAGopAwA3AwAgAkHYAGogAUHYAGopAwA3AwAgAikDACEqIAVBEGogBEHYAPwKAAAgAkHgABDfBEHRzsUALQAAGiAFICo3AwhB4ABBCBDWBCIBRQ0JIAEgAykDADcDACABIAMpAzA3AzAgAUEoaiADQShqKQMANwMAIAFBIGogA0EgaikDADcDACABQRhqIANBGGopAwA3AwAgAUEQaiADQRBqKQMANwMAIAFBCGoiAiADQQhqKQMANwMAIAFBOGogA0E4aikDADcDACABQUBrIANBQGspAwA3AwAgAUHIAGogA0HIAGopAwA3AwAgAUHQAGogA0HQAGopAwA3AwAgAUHYAGogA0HYAGopAwA3AwAgASkDACEqIAVB8ABqIAJB2AD8CgAAIAFB4AAQ3wQgBSAqNwNoIAVBqCBqIgEgBUEIaiAFQegAahDBAyAFKQO4ICEqIAUpA7AgISsgBSgCqCBBAUYNBCAFQdgBaiAFQcAgakHQAPwKAAAgBSAqNwPQASAFICs3A8gBIAEgBUHIAWoQ9wMgBSgCrCAhASAFKAKoICECIAUoArAgIgNBAkcNBSABKAIEIQMgASgCACEEIAVBiAlqIAFBCGpB2AD8CgAAIAIEQCABIAJBMGwQ3wQLQdHOxQAtAAAaQeAAQQgQ1gQiAUUNCSABIAM2AgQgASAENgIAIAEgBSkDiAk3AwggASAFKQOwCTcDMCABQRBqIAVBkAlqKQMANwMAIAFBGGogBUGYCWopAwA3AwAgAUEgaiAFQaAJaikDADcDACABQShqIAVBqAlqKQMANwMAIAFBOGogBUG4CWopAwA3AwAgAUFAayAFQcAJaikDADcDACABQcgAaiAFQcgJaikDADcDACABQdAAaiAFQdAJaikDADcDACABQdgAaiAFQdgJaikDADcDACAAQQI2AgggACABNgIEIABBAjYCAAwICyACIAEpAwA3AwAgAiABKQMwNwMwIAJBKGogAUEoaikDADcDACACQSBqIAFBIGopAwA3AwAgAkEYaiABQRhqKQMANwMAIAJBEGogAUEQaikDADcDACACQQhqIgQgAUEIaikDADcDACACQThqIAFBOGopAwA3AwAgAkFAayABQUBrKQMANwMAIAJByABqIAFByABqKQMANwMAIAJB0ABqIAFB0ABqKQMANwMAIAJB2ABqIAFB2ABqKQMANwMAIAJBiAFqIAFBiAFqKQMANwMAIAJBgAFqIAFBgAFqKQMANwMAIAJB+ABqIAFB+ABqKQMANwMAIAJB8ABqIAFB8ABqKQMANwMAIAJB6ABqIAFB6ABqKQMANwMAIAIgASkDYDcDYCACIAEpA5ABNwOQASACQZgBaiABQZgBaikDADcDACACQaABaiABQaABaikDADcDACACQagBaiABQagBaikDADcDACACQbABaiABQbABaikDADcDACACQbgBaiABQbgBaikDADcDACACQegBaiABQegBaikDADcDACACQeABaiABQeABaikDADcDACACQdgBaiABQdgBaikDADcDACACQdABaiABQdABaikDADcDACACQcgBaiABQcgBaikDADcDACACIAEpA8ABNwPAASACQZgCaiABQZgCaikDADcDACACQZACaiABQZACaikDADcDACACQYgCaiABQYgCaikDADcDACACQYACaiABQYACaikDADcDACACQfgBaiABQfgBaikDADcDACACIAEpA/ABNwPwASACKQMAISogBUGoIGoiCSAEQZgC/AoAACACQaACEN8EIAVBmApqIAVB2CBqKQMANwMAIAVBoApqIAVB4CBqKQMANwMAIAVBqApqIAVB6CBqKQMANwMAIAVBsApqIAVB8CBqKQMANwMAIAVBuApqIAVB+CBqKQMANwMAIAVBkB5qIgsgBUGIIWopAwA3AwAgBUGYHmoiBiAFQZAhaikDADcDACAFQaAeaiIMIAVBmCFqKQMANwMAIAVBqB5qIg0gBUGgIWopAwA3AwAgBUGwHmoiDiAFQaghaikDADcDACAFIAUpA9AgNwOQCiAFIAUpA4AhNwOIHiAFQeAeaiIPIAVB2CFqKQMANwMAIAVB2B5qIhAgBUHQIWopAwA3AwAgBUHQHmoiESAFQcghaikDADcDACAFQcgeaiISIAVBwCFqKQMANwMAIAVBwB5qIhMgBUG4IWopAwA3AwAgBUHoG2oiByAFQeghaikDADcDACAFQfAbaiIUIAVB8CFqKQMANwMAIAVB+BtqIgggBUH4IWopAwA3AwAgBUGAHGoiFSAFQYAiaikDADcDACAFQYgcaiIWIAVBiCJqKQMANwMAIAUgBSkDsCE3A7geIAUgBSkD4CE3A+AbIAVBuBxqIhcgBUG4ImopAwA3AwAgBUGwHGoiGCAFQbAiaikDADcDACAFQagcaiIZIAVBqCJqKQMANwMAIAVBoBxqIhogBUGgImopAwA3AwAgBUGYHGoiGyAFQZgiaikDADcDACAFQYgKaiAFQcggaikDADcDACAFQYAKaiAFQcAgaiIEKQMANwMAIAVB+AlqIAVBuCBqKQMANwMAIAVB8AlqIAVBsCBqKQMANwMAIAUgBSkDkCI3A5AcIAUgBSkDqCA3A+gJIAUgKjcD4AkgBUHACmogBUGIHmoiCkHgAPwKAAAgBUGgC2ogBUHgG2oiHEHgAPwKAABB0c7FAC0AABpBoAJBCBDWBCIBRQ0JIAEgAykDADcDACABIAMpAzA3AzAgAUEoaiADQShqKQMANwMAIAFBIGogA0EgaikDADcDACABQRhqIANBGGopAwA3AwAgAUEQaiADQRBqKQMANwMAIAFBCGoiAiADQQhqKQMANwMAIAFBOGogA0E4aikDADcDACABQUBrIANBQGspAwA3AwAgAUHIAGogA0HIAGopAwA3AwAgAUHQAGogA0HQAGopAwA3AwAgAUHYAGogA0HYAGopAwA3AwAgAUGIAWogA0GIAWopAwA3AwAgAUGAAWogA0GAAWopAwA3AwAgAUH4AGogA0H4AGopAwA3AwAgAUHwAGogA0HwAGopAwA3AwAgAUHoAGogA0HoAGopAwA3AwAgASADKQNgNwNgIAEgAykDkAE3A5ABIAFBmAFqIANBmAFqKQMANwMAIAFBoAFqIANBoAFqKQMANwMAIAFBqAFqIANBqAFqKQMANwMAIAFBsAFqIANBsAFqKQMANwMAIAFBuAFqIANBuAFqKQMANwMAIAFB6AFqIANB6AFqKQMANwMAIAFB4AFqIANB4AFqKQMANwMAIAFB2AFqIANB2AFqKQMANwMAIAFB0AFqIANB0AFqKQMANwMAIAFByAFqIANByAFqKQMANwMAIAEgAykDwAE3A8ABIAFBmAJqIANBmAJqKQMANwMAIAFBkAJqIANBkAJqKQMANwMAIAFBiAJqIANBiAJqKQMANwMAIAFBgAJqIANBgAJqKQMANwMAIAFB+AFqIANB+AFqKQMANwMAIAEgAykD8AE3A/ABIAEpAwAhKiAJIAJBmAL8CgAAIAFBoAIQ3wQgBUG4DGogBUHYIGopAwA3AwAgBUHADGogBUHgIGopAwA3AwAgBUHIDGogBUHoIGopAwA3AwAgBUHQDGogBUHwIGopAwA3AwAgBUHYDGogBUH4IGopAwA3AwAgCyAFQYghaikDADcDACAGIAVBkCFqKQMANwMAIAwgBUGYIWopAwA3AwAgDSAFQaAhaikDADcDACAOIAVBqCFqKQMANwMAIAUgBSkD0CA3A7AMIAUgBSkDgCE3A4geIA8gBUHYIWopAwA3AwAgECAFQdAhaikDADcDACARIAVByCFqKQMANwMAIBIgBUHAIWopAwA3AwAgEyAFQbghaikDADcDACAHIAVB6CFqKQMANwMAIBQgBUHwIWopAwA3AwAgCCAFQfghaikDADcDACAVIAVBgCJqKQMANwMAIBYgBUGIImopAwA3AwAgBSAFKQOwITcDuB4gBSAFKQPgITcD4BsgFyAFQbgiaikDADcDACAYIAVBsCJqKQMANwMAIBkgBUGoImopAwA3AwAgGiAFQaAiaikDADcDACAbIAVBmCJqKQMANwMAIAVBqAxqIAVByCBqKQMANwMAIAVBoAxqIAVBwCBqKQMANwMAIAVBmAxqIAVBuCBqKQMANwMAIAVBkAxqIAVBsCBqKQMANwMAIAUgBSkDkCI3A5AcIAUgBSkDqCA3A4gMIAUgKjcDgAwgBUHgDGogCkHgAPwKAAAgBUHADWogHEHgAPwKAAAgCSIBIAVBgAxqEGYgBSgCqCBBAUYNBSAFKQOwICEqIAUpA7ggISsgBiAEIgJBkAL8CgAAIAUgKzcDkB4gBSAqNwOIHiAHIAVB4AlqIAoQuQIgBSkD6BshKiAFKQPwGyErIAVBuAJqIAhBkAL8CgAAIAUgKzcDsAIgBSAqNwOoAiABIAVBqAJqEKQBQdHOxQAtAAAaQaACQQgQ1gQiAUUNCSABIAUpA6ggNwMAIAEgBSkD2CA3AzAgAUEoaiAFQdAgaikDADcDACABQSBqIAVByCBqKQMANwMAIAFBGGogAikDADcDACABQRBqIAVBuCBqKQMANwMAIAFBCGogBUGwIGopAwA3AwAgAUE4aiAFQeAgaikDADcDACABQUBrIAVB6CBqKQMANwMAIAFByABqIAVB8CBqKQMANwMAIAFB0ABqIAVB+CBqKQMANwMAIAFB2ABqIAVBgCFqKQMANwMAIAFBiAFqIAVBsCFqKQMANwMAIAFBgAFqIAVBqCFqKQMANwMAIAFB+ABqIAVBoCFqKQMANwMAIAFB8ABqIAVBmCFqKQMANwMAIAFB6ABqIAVBkCFqKQMANwMAIAEgBSkDiCE3A2AgAUG4AWogBUHgIWopAwA3AwAgAUGwAWogBUHYIWopAwA3AwAgAUGoAWogBUHQIWopAwA3AwAgAUGgAWogBUHIIWopAwA3AwAgAUGYAWogBUHAIWopAwA3AwAgASAFKQO4ITcDkAEgAUHoAWogBUGQImopAwA3AwAgAUHgAWogBUGIImopAwA3AwAgAUHYAWogBUGAImopAwA3AwAgAUHQAWogBUH4IWopAwA3AwAgAUHIAWogBUHwIWopAwA3AwAgASAFKQPoITcDwAEgAUGYAmogBUHAImopAwA3AwAgAUGQAmogBUG4ImopAwA3AwAgAUGIAmogBUGwImopAwA3AwAgAUGAAmogBUGoImopAwA3AwAgAUH4AWogBUGgImopAwA3AwAgASAFKQOYIjcD8AEgAEEGNgIIIAAgATYCBCAAQQY2AgAMBwsgAiABKQMANwMAIAIgASkDMDcDMCACQShqIAFBKGopAwA3AwAgAkEgaiABQSBqKQMANwMAIAJBGGogAUEYaikDADcDACACQRBqIAFBEGopAwA3AwAgAkEIaiIEIAFBCGopAwA3AwAgAkE4aiABQThqKQMANwMAIAJBQGsgAUFAaykDADcDACACQcgAaiABQcgAaikDADcDACACQdAAaiABQdAAaikDADcDACACQdgAaiABQdgAaikDADcDACACQYgBaiABQYgBaikDADcDACACQYABaiABQYABaikDADcDACACQfgAaiABQfgAaikDADcDACACQfAAaiABQfAAaikDADcDACACQegAaiABQegAaikDADcDACACIAEpA2A3A2AgAiABKQOQATcDkAEgAkGYAWogAUGYAWopAwA3AwAgAkGgAWogAUGgAWopAwA3AwAgAkGoAWogAUGoAWopAwA3AwAgAkGwAWogAUGwAWopAwA3AwAgAkG4AWogAUG4AWopAwA3AwAgAkHoAWogAUHoAWopAwA3AwAgAkHgAWogAUHgAWopAwA3AwAgAkHYAWogAUHYAWopAwA3AwAgAkHQAWogAUHQAWopAwA3AwAgAkHIAWogAUHIAWopAwA3AwAgAiABKQPAATcDwAEgAkGYAmogAUGYAmopAwA3AwAgAkGQAmogAUGQAmopAwA3AwAgAkGIAmogAUGIAmopAwA3AwAgAkGAAmogAUGAAmopAwA3AwAgAkH4AWogAUH4AWopAwA3AwAgAiABKQPwATcD8AEgAkHIAmogAUHIAmopAwA3AwAgAkHAAmogAUHAAmopAwA3AwAgAkG4AmogAUG4AmopAwA3AwAgAkGwAmogAUGwAmopAwA3AwAgAkGoAmogAUGoAmopAwA3AwAgAiABKQOgAjcDoAIgAkH4AmogAUH4AmopAwA3AwAgAkHwAmogAUHwAmopAwA3AwAgAkHoAmogAUHoAmopAwA3AwAgAkHgAmogAUHgAmopAwA3AwAgAkHYAmogAUHYAmopAwA3AwAgAiABKQPQAjcD0AIgAkGoA2ogAUGoA2opAwA3AwAgAkGgA2ogAUGgA2opAwA3AwAgAkGYA2ogAUGYA2opAwA3AwAgAkGQA2ogAUGQA2opAwA3AwAgAkGIA2ogAUGIA2opAwA3AwAgAiABKQOAAzcDgAMgAkHYA2ogAUHYA2opAwA3AwAgAkHQA2ogAUHQA2opAwA3AwAgAkHIA2ogAUHIA2opAwA3AwAgAkHAA2ogAUHAA2opAwA3AwAgAkG4A2ogAUG4A2opAwA3AwAgAiABKQOwAzcDsAMgAkGIBGogAUGIBGopAwA3AwAgAkGABGogAUGABGopAwA3AwAgAkH4A2ogAUH4A2opAwA3AwAgAkHwA2ogAUHwA2opAwA3AwAgAkHoA2ogAUHoA2opAwA3AwAgAiABKQPgAzcD4AMgAkG4BGogAUG4BGopAwA3AwAgAkGwBGogAUGwBGopAwA3AwAgAkGoBGogAUGoBGopAwA3AwAgAkGgBGogAUGgBGopAwA3AwAgAkGYBGogAUGYBGopAwA3AwAgAiABKQOQBDcDkAQgAikDACEqIAVBqCBqIgkgBEG4BPwKAAAgAkHABBDfBCAFQdgOaiAFQdggaikDADcDACAFQeAOaiAFQeAgaikDADcDACAFQegOaiAFQeggaikDADcDACAFQfAOaiAFQfAgaikDADcDACAFQfgOaiAFQfggaikDADcDACAFQegSaiAFQYghaikDADcDACAFQfASaiAFQZAhaikDADcDACAFQfgSaiAFQZghaikDADcDACAFQYATaiAFQaAhaikDADcDACAFQYgTaiAFQaghaikDADcDACAFIAUpA9AgNwPQDiAFIAUpA4AhNwPgEiAFQbgTaiAFQdghaikDADcDACAFQbATaiAFQdAhaikDADcDACAFQagTaiAFQcghaikDADcDACAFQaATaiAFQcAhaikDADcDACAFQZgTaiAFQbghaikDADcDACAFQcgTaiAFQeghaikDADcDACAFQdATaiAFQfAhaikDADcDACAFQdgTaiAFQfghaikDADcDACAFQeATaiAFQYAiaikDADcDACAFQegTaiAFQYgiaikDADcDACAFIAUpA7AhNwOQEyAFIAUpA+AhNwPAEyAFQZgUaiAFQbgiaikDADcDACAFQZAUaiAFQbAiaikDADcDACAFQYgUaiAFQagiaikDADcDACAFQYAUaiAFQaAiaikDADcDACAFQfgTaiAFQZgiaikDADcDACAFQcgOaiAFQcggaikDADcDACAFQcAOaiAFQcAgaikDADcDACAFQbgOaiAFQbggaikDADcDACAFQbAOaiAFQbAgaikDADcDACAFIAUpA5AiNwPwEyAFIAUpA6ggNwOoDiAFQfgaaiIGIAVBmCNqKQMANwMAIAVB8BpqIgcgBUGQI2opAwA3AwAgBUHoGmoiCCAFQYgjaikDADcDACAFQeAaaiIKIAVBgCNqKQMANwMAIAVB2BpqIgsgBUH4ImopAwA3AwAgBSAFKQPwIjcD0BogBUGIG2oiDCAFQagjaikDADcDACAFQZAbaiINIAVBsCNqKQMANwMAIAVBmBtqIg4gBUG4I2opAwA3AwAgBUGgG2oiDyAFQcAjaikDADcDACAFQagbaiIQIAVByCNqKQMANwMAIAUgBSkDoCM3A4AbIAVB2BtqIhEgBUH4I2opAwA3AwAgBUHQG2oiEiAFQfAjaikDADcDACAFQcgbaiITIAVB6CNqKQMANwMAIAVBwBtqIhQgBUHgI2opAwA3AwAgBUG4G2oiFSAFQdgjaikDADcDACAFIAUpA9AjNwOwGyAFQbAeaiIWIAVBqCRqKQMANwMAIAVBqB5qIhcgBUGgJGopAwA3AwAgBUGgHmoiGCAFQZgkaikDADcDACAFQZgeaiIZIAVBkCRqKQMANwMAIAVBkB5qIhogBUGIJGopAwA3AwAgBSAFKQOAJDcDiB4gBUHgHmoiGyAFQdgkaikDADcDACAFQdgeaiIcIAVB0CRqKQMANwMAIAVB0B5qIh0gBUHIJGopAwA3AwAgBUHIHmoiHiAFQcAkaikDADcDACAFQcAeaiIfIAVBuCRqKQMANwMAIAUgBSkDsCQ3A7geIAVByBpqIiAgBUHoImopAwA3AwAgBUHAGmoiISAFQeAiaikDADcDACAFQbgaaiIiIAVB2CJqKQMANwMAIAVBsBpqIiMgBUHQImopAwA3AwAgBUGoGmoiJCAFQcgiaikDADcDACAFIAUpA8AiNwOgGiAFQeAbaiICIAVBoBpqIiVB4AD8CgAAIAVBwBxqIiYgBUGAG2oiJ0HgAPwKAAAgBUGgHWoiKCAFQYgeaiIpQeAA/AoAACAFICo3A6AOIAVBgA9qIAVB4BJqQeAA/AoAACAFQeAPaiAFQcATakHgAPwKAAAgBUHAEGogAkGgAvwKAABB0c7FAC0AABpBwARBCBDWBCIBRQ0JIAEgAykDADcDACABIAMpAzA3AzAgAUEoaiADQShqKQMANwMAIAFBIGogA0EgaikDADcDACABQRhqIANBGGopAwA3AwAgAUEQaiADQRBqKQMANwMAIAFBCGoiBCADQQhqKQMANwMAIAFBOGogA0E4aikDADcDACABQUBrIANBQGspAwA3AwAgAUHIAGogA0HIAGopAwA3AwAgAUHQAGogA0HQAGopAwA3AwAgAUHYAGogA0HYAGopAwA3AwAgAUGIAWogA0GIAWopAwA3AwAgAUGAAWogA0GAAWopAwA3AwAgAUH4AGogA0H4AGopAwA3AwAgAUHwAGogA0HwAGopAwA3AwAgAUHoAGogA0HoAGopAwA3AwAgASADKQNgNwNgIAEgAykDkAE3A5ABIAFBmAFqIANBmAFqKQMANwMAIAFBoAFqIANBoAFqKQMANwMAIAFBqAFqIANBqAFqKQMANwMAIAFBsAFqIANBsAFqKQMANwMAIAFBuAFqIANBuAFqKQMANwMAIAFB6AFqIANB6AFqKQMANwMAIAFB4AFqIANB4AFqKQMANwMAIAFB2AFqIANB2AFqKQMANwMAIAFB0AFqIANB0AFqKQMANwMAIAFByAFqIANByAFqKQMANwMAIAEgAykDwAE3A8ABIAFBmAJqIANBmAJqKQMANwMAIAFBkAJqIANBkAJqKQMANwMAIAFBiAJqIANBiAJqKQMANwMAIAFBgAJqIANBgAJqKQMANwMAIAFB+AFqIANB+AFqKQMANwMAIAEgAykD8AE3A/ABIAFByAJqIANByAJqKQMANwMAIAFBwAJqIANBwAJqKQMANwMAIAFBuAJqIANBuAJqKQMANwMAIAFBsAJqIANBsAJqKQMANwMAIAFBqAJqIANBqAJqKQMANwMAIAEgAykDoAI3A6ACIAFB+AJqIANB+AJqKQMANwMAIAFB8AJqIANB8AJqKQMANwMAIAFB6AJqIANB6AJqKQMANwMAIAFB4AJqIANB4AJqKQMANwMAIAFB2AJqIANB2AJqKQMANwMAIAEgAykD0AI3A9ACIAFBqANqIANBqANqKQMANwMAIAFBoANqIANBoANqKQMANwMAIAFBmANqIANBmANqKQMANwMAIAFBkANqIANBkANqKQMANwMAIAFBiANqIANBiANqKQMANwMAIAEgAykDgAM3A4ADIAFB2ANqIANB2ANqKQMANwMAIAFB0ANqIANB0ANqKQMANwMAIAFByANqIANByANqKQMANwMAIAFBwANqIANBwANqKQMANwMAIAFBuANqIANBuANqKQMANwMAIAEgAykDsAM3A7ADIAFBiARqIANBiARqKQMANwMAIAFBgARqIANBgARqKQMANwMAIAFB+ANqIANB+ANqKQMANwMAIAFB8ANqIANB8ANqKQMANwMAIAFB6ANqIANB6ANqKQMANwMAIAEgAykD4AM3A+ADIAFBuARqIANBuARqKQMANwMAIAFBsARqIANBsARqKQMANwMAIAFBqARqIANBqARqKQMANwMAIAFBoARqIANBoARqKQMANwMAIAFBmARqIANBmARqKQMANwMAIAEgAykDkAQ3A5AEIAEpAwAhKiAJIARBuAT8CgAAIAFBwAQQ3wQgBUHYFGogBUHYIGopAwA3AwAgBUHgFGogBUHgIGopAwA3AwAgBUHoFGogBUHoIGopAwA3AwAgBUHwFGogBUHwIGopAwA3AwAgBUH4FGogBUH4IGopAwA3AwAgBUHoGGogBUGIIWopAwA3AwAgBUHwGGogBUGQIWopAwA3AwAgBUH4GGogBUGYIWopAwA3AwAgBUGAGWogBUGgIWopAwA3AwAgBUGIGWogBUGoIWopAwA3AwAgBSAFKQPQIDcD0BQgBSAFKQOAITcD4BggBUG4GWogBUHYIWopAwA3AwAgBUGwGWogBUHQIWopAwA3AwAgBUGoGWogBUHIIWopAwA3AwAgBUGgGWogBUHAIWopAwA3AwAgBUGYGWogBUG4IWopAwA3AwAgBUHIGWogBUHoIWopAwA3AwAgBUHQGWogBUHwIWopAwA3AwAgBUHYGWogBUH4IWopAwA3AwAgBUHgGWogBUGAImopAwA3AwAgBUHoGWogBUGIImopAwA3AwAgBSAFKQOwITcDkBkgBSAFKQPgITcDwBkgBUGYGmogBUG4ImopAwA3AwAgBUGQGmogBUGwImopAwA3AwAgBUGIGmogBUGoImopAwA3AwAgBUGAGmogBUGgImopAwA3AwAgBUH4GWogBUGYImopAwA3AwAgBUHIFGogBUHIIGopAwA3AwAgBUHAFGogBUHAIGopAwA3AwAgBUG4FGogBUG4IGopAwA3AwAgBUGwFGogBUGwIGopAwA3AwAgBSAFKQOQIjcD8BkgBSAFKQOoIDcDqBQgBiAFQZgjaikDADcDACAHIAVBkCNqKQMANwMAIAggBUGII2opAwA3AwAgCiAFQYAjaikDADcDACALIAVB+CJqKQMANwMAIAUgBSkD8CI3A9AaIAwgBUGoI2opAwA3AwAgDSAFQbAjaikDADcDACAOIAVBuCNqKQMANwMAIA8gBUHAI2opAwA3AwAgECAFQcgjaikDADcDACAFIAUpA6AjNwOAGyARIAVB+CNqKQMANwMAIBIgBUHwI2opAwA3AwAgEyAFQegjaikDADcDACAUIAVB4CNqKQMANwMAIBUgBUHYI2opAwA3AwAgBSAFKQPQIzcDsBsgFiAFQagkaikDADcDACAXIAVBoCRqKQMANwMAIBggBUGYJGopAwA3AwAgGSAFQZAkaikDADcDACAaIAVBiCRqKQMANwMAIAUgBSkDgCQ3A4geIBsgBUHYJGopAwA3AwAgHCAFQdAkaikDADcDACAdIAVByCRqKQMANwMAIB4gBUHAJGopAwA3AwAgHyAFQbgkaikDADcDACAFIAUpA7AkNwO4HiAgIAVB6CJqKQMANwMAICEgBUHgImopAwA3AwAgIiAFQdgiaikDADcDACAjIAVB0CJqKQMANwMAICQgBUHIImopAwA3AwAgBSAFKQPAIjcDoBogAiAlQeAA/AoAACAmICdB4AD8CgAAICggKUHgAPwKAAAgBSAqNwOgFCAFQYAVaiAFQeAYakHgAPwKAAAgBUHgFWogBUHAGWpB4AD8CgAAIAVBwBZqIAJBoAL8CgAAIAVBoA5qIQcjAEGAEmsiASQAIAFBwA1qIgMgBUGgFGoiAhBxIAFBqAlqQfCDwAApAwA3AwAgAUGgCWpB6IPAACkDADcDACABQZgJakHgg8AAKQMANwMAIAFBkAlqQdiDwAApAwA3AwAgAUGICWpB0IPAACkDADcDACABQbgJakIANwMAIAFBwAlqQgA3AwAgAUHICWpCADcDACABQdAJakIANwMAIAFB2AlqQgA3AwAgAUHIg8AAKQMANwOACSABQgA3A7AJIAFB4A9qIgZBAEHgAPwLACABQcAQaiABQYAJaiIEQeAA/AoAACABQaARakEAQeAA/AsAIAQgAkGgAmoiCBBxIAEgBiAEELkCIAFB4AZqIgYgAyABEI0BIAFBwAdqIAFBoA5qIAFB4ABqEI0BIAFBoAhqIAFBgA9qIAFBwAFqEI0BIAQgBhBmIAkiAwJ+IAEoAoAJQQFGBEAgA0IANwMIQgEMAQsgASkDiAkhKiABKQOQCSErIAFB0ARqIAFBmAlqQZAC/AoAACABICs3A8gEIAEgKjcDwAQgAUGACWogAiABQcAEaiIEELkCIAFBwA1qIgYgCBC0AiABQaAOaiACQYADahC0AiABQYAPaiACQeADahC0AiABIARBoAL8CgAAIAFBoAtqIAYgARC5AiABKQOACSEqIAEpA4gJISsgAUEQaiABQZAJakGwBPwKAAAgASArNwMIIAEgKjcDACADQQhqIAcgARCbAkIACzcDACABQYASaiQAIAUpA7ggISogBSkDsCAhKyAFKAKoIEEBRg0FIAVB2ARqIAVBwCBqIgJBsAT8CgAAIAUgKjcD0AQgBSArNwPIBCADIAVByARqEKABQdHOxQAtAAAaQcAEQQgQ1gQiAUUNCSABIAUpA6ggNwMAIAEgBSkD2CA3AzAgAUEoaiAFQdAgaikDADcDACABQSBqIAVByCBqKQMANwMAIAFBGGogAikDADcDACABQRBqIAVBuCBqKQMANwMAIAFBCGogBUGwIGopAwA3AwAgAUE4aiAFQeAgaikDADcDACABQUBrIAVB6CBqKQMANwMAIAFByABqIAVB8CBqKQMANwMAIAFB0ABqIAVB+CBqKQMANwMAIAFB2ABqIAVBgCFqKQMANwMAIAFBiAFqIAVBsCFqKQMANwMAIAFBgAFqIAVBqCFqKQMANwMAIAFB+ABqIAVBoCFqKQMANwMAIAFB8ABqIAVBmCFqKQMANwMAIAFB6ABqIAVBkCFqKQMANwMAIAEgBSkDiCE3A2AgAUG4AWogBUHgIWopAwA3AwAgAUGwAWogBUHYIWopAwA3AwAgAUGoAWogBUHQIWopAwA3AwAgAUGgAWogBUHIIWopAwA3AwAgAUGYAWogBUHAIWopAwA3AwAgASAFKQO4ITcDkAEgAUHoAWogBUGQImopAwA3AwAgAUHgAWogBUGIImopAwA3AwAgAUHYAWogBUGAImopAwA3AwAgAUHQAWogBUH4IWopAwA3AwAgAUHIAWogBUHwIWopAwA3AwAgASAFKQPoITcDwAEgAUGYAmogBUHAImopAwA3AwAgAUGQAmogBUG4ImopAwA3AwAgAUGIAmogBUGwImopAwA3AwAgAUGAAmogBUGoImopAwA3AwAgAUH4AWogBUGgImopAwA3AwAgASAFKQOYIjcD8AEgAUHIAmogBUHwImopAwA3AwAgAUHAAmogBUHoImopAwA3AwAgAUG4AmogBUHgImopAwA3AwAgAUGwAmogBUHYImopAwA3AwAgAUGoAmogBUHQImopAwA3AwAgASAFKQPIIjcDoAIgAUH4AmogBUGgI2opAwA3AwAgAUHwAmogBUGYI2opAwA3AwAgAUHoAmogBUGQI2opAwA3AwAgAUHgAmogBUGII2opAwA3AwAgAUHYAmogBUGAI2opAwA3AwAgASAFKQP4IjcD0AIgAUGoA2ogBUHQI2opAwA3AwAgAUGgA2ogBUHII2opAwA3AwAgAUGYA2ogBUHAI2opAwA3AwAgAUGQA2ogBUG4I2opAwA3AwAgAUGIA2ogBUGwI2opAwA3AwAgASAFKQOoIzcDgAMgAUHYA2ogBUGAJGopAwA3AwAgAUHQA2ogBUH4I2opAwA3AwAgAUHIA2ogBUHwI2opAwA3AwAgAUHAA2ogBUHoI2opAwA3AwAgAUG4A2ogBUHgI2opAwA3AwAgASAFKQPYIzcDsAMgAUGIBGogBUGwJGopAwA3AwAgAUGABGogBUGoJGopAwA3AwAgAUH4A2ogBUGgJGopAwA3AwAgAUHwA2ogBUGYJGopAwA3AwAgAUHoA2ogBUGQJGopAwA3AwAgASAFKQOIJDcD4AMgAUG4BGogBUHgJGopAwA3AwAgAUGwBGogBUHYJGopAwA3AwAgAUGoBGogBUHQJGopAwA3AwAgAUGgBGogBUHIJGopAwA3AwAgAUGYBGogBUHAJGopAwA3AwAgASAFKQO4JDcDkAQgAEEMNgIIIAAgATYCBCAAQQw2AgAMBgsgBUEANgKoICAFQeAbaiAFQQRqIAVBqCBqQbyLwAAQlwQACyAFQQA2AqggIAVB4BtqIAVBBGogBUGoIGpBzIvAABCXBAALIAUgKjcDsCAgBSArNwOoIEGAi8AAQSsgBUGoIGpB3IvAAEHsi8AAEMoDAAsgBSADNgKwICAFIAE2AqwgIAUgAjYCqCBBgIvAAEErIAVBqCBqQayLwABBpI3AABDKAwALIAVCADcDqCBBgIvAAEErIAVBqCBqQdyLwABB/IvAABDKAwALIAUgKjcDsCAgBSArNwOoIEGAi8AAQSsgBUGoIGpB3IvAAEGMjMAAEMoDAAsgBUHwJGokAA8LQQhB4ABBuIXAABDIBAALQQhBoAJBuIXAABDIBAALQQhBwARBuIXAABDIBAAL5F4CGn8CfiMAQcADayIGJAACQAJAAkACQANAAkAgA0UEQEEAIQsMAQsgAigCAARAIAMhCwwBCyADQQJ0QQRrIQdBACEIA0AgB0UNBSAAQQRqIQAgB0EEayEHIAhBAWohCCACQQRqIgIoAgBFDQALIAEgCEEBa0sEQCABIAhrIQEgAyAIayELDAELIAggAUH4xsQAEOQEAAsCQCAFRQRAQQAhBQwBCyAEKAIADQBBACEIIAVBAnRBBGsiB0UNBANAAkAgAEEEaiEAIAdBBGshByAIQQFqIQggBEEEaiIEKAIADQAgBw0BDAYLCyABIAhBAWtLBEAgASAIayEBIAUgCGshBQwBCyAIIAFBiMfEABDkBAALIAsgBSAFIAtJGyEOIAQgAiAFIAtLIgMbIRIgAiAEIAMbIQICQCALIAUgAxsiA0EhTwRAIANBAXQgDk0NASADQYECTw0EIA4gA0EBdiIQTw0DIAZBADYCuAMgBkEBNgKsAyAGQZTExAA2AqgDIAZCBDcCsAMgBkGoA2pB6MfEABCoBAALIANFDQQgAiADQQJ0aiEPIA5BfnEhECAOQQFxIREgAUECdCEDIAJBBGohCCAFIAsgBSALSxtBAnRBBGohDEEAIQcgACEFQQEhCQJAAkACQANAIAEgB08EQCAIIQogCSENAkAgAigCACICRQ0AIAEgB2siCCAOSQ0DIAAgB0ECdGohCSAOBH8gAq0hIUEAIQRCACEgIA5BAUcEQCASIQcgBSECA0AgAiAgIAI1AgB8IAc1AgAgIX58IiA+AgAgAkEEaiILIAs1AgAgIEIgiHwgB0EEajUCACAhfnwiID4CACAgQiCIISAgB0EIaiEHIAJBCGohAiAQIARBAmoiBEcNAAsLIBEEfiAJIARBAnQiAmoiBCAgIAQ1AgB8IAIgEmo1AgAgIX58IiA+AgAgIEIgiAUgIAunBUEACyECIAggDkYNBCAJIA5BAnRqIgQgAiAEKAIAIgRqIgI2AgAgAiAETw0AIAwhAiAIIA5rQf////8DcUEBRg0FA0AgAiAFaiIEIAQoAgBBAWoiBDYCACAEDQEgAkEEaiICIANHDQALDAULIANBBGshAyAFQQRqIQUgDSAKIA9HIgRqIQkgCiAEQQJ0aiEIIAohAiANIQcgBA0BDAkLCyAHIAFByMjEABDkBAALIAZBADYCuAMgBkEBNgKsAyAGQZTExAA2AqgDIAZCBDcCsAMgBkGoA2pBpMbEABCoBAALIAZBADYCuAMgBkEBNgKsAyAGQZTExAA2AqgDIAZCBDcCsAMgBkGoA2pBhMXEABCoBAALIAZBATYC+AIgBkIANwK0AyAGQoGAgIDAADcCrAMgBkHgxsQANgKoAyMAQRBrIgAkACAAQbTGxAA2AgwgACAGQfgCajYCCCAAQQhqQfiGxQAgAEEMakH4hsUAIAZBqANqQejGxAAQ5gIACyAAIAEgAiADIBIgDkEBdiIEECkgASAETwRAIAEgBGshASAOIARrIQUgACAEQQJ0IgRqIQAgBCASaiEEDAELCyAEIAFBuMjEABDkBAALIA4gEGsiGSADIBBrIhpqIhtBAWoiDUECdCEHQQAhBAJAAkAgDUH/////A0sgB0H8////B0tyDQACfyAHRQRAQQQhD0EADAELQdHOxQAtAAAaQQQhBCAHQQQQ1wQiD0UNASANCyEJIAYgDTYCgAMgBiAPNgL8AiAGIAk2AvgCIA8gDSACIBBBAnQiBGoiHCAaIAQgEmoiHSAZECkgDUUNASAPIA0iCkECdGpBBGsoAgANASAFIAsgBSALSRsgBSALIAUgC0sbaiIHIBBBAXRrQQJqIQQgB0ECdCAQQQN0ayEHAkADQCAHQXxGBEBBACEEDAILIARBAWshBCAHIA9qIQggB0EEayEHIAgoAgBFDQALIAQgDUsNAgsgBiAENgKAAyAEIQoMAQsgBCAHQfjHxAAQyAQACwJAAkACQAJAAkAgCUUgCiAJQQJ2T3JFBEAgCUECdCEEAkAgCkUEQCAPIAQQ3wRBBCEPDAELIA8gBEEEIApBAnQiBBDOBCIPRQ0CCyAGIAo2AvgCIAYgDzYC/AILIAEgEEkNASAKIAEgEGsiFEsNByAAIBBBAnRqIQwCQCAKRQ0AIApBAXECQCAKQQFGBEBBACEJDAELIApB/v///wFxIRVBACEJIA8hBCAMIQcDQCAHIAcoAgAiFiAEKAIAaiIIIAlqIhc2AgAgB0EEaiIJIAkoAgAiGCAEQQRqKAIAaiIJIAggFkkgCCAXS3JqIgg2AgAgCSAYSSAIIAlJciIIIQkgBEEIaiEEIAdBCGohByAVIBFBAmoiEUcNAAsLBEAgDCARQQJ0IgRqIgcgBygCACIHIAQgD2ooAgBqIgQgCWoiCDYCACAEIAdJIAQgCEtyIQgLIAhBAXFFIAogFEZyDQAgDCAKQQJ0IgRqIQcgAUECdCAEayAQQQJ0a0EEayEEA0AgByAHKAIAQQFqIgg2AgAgCA0BIAdBBGohByAEIQggBEEEayEEIAgNAAsLIAEgA0H+A3EiBEkNAiAGKAKAAyITIAEgBGsiFUsNBwJAIBNFDQAgACAEQQJ0aiEKIAYoAvwCIQ8gE0EBcQJAIBNBAUYEQEEAIQlBACERDAELIBNBfnEhF0EAIQkgDyEEIAohB0EAIREDQCAHIAcoAgAiGCAEKAIAaiIIIAlqIh42AgAgB0EEaiIJIAkoAgAiHyAEQQRqKAIAaiIJIAggGEkgCCAeS3JqIgg2AgAgCSAfSSAIIAlJciIIIQkgBEEIaiEEIAdBCGohByAXIBFBAmoiEUcNAAsLBEAgCiARQQJ0IgRqIgcgBygCACIHIAQgD2ooAgBqIgQgCWoiCDYCACAEIAdJIAQgCEtyIQgLIAhBAXFFIBMgFUZyDQAgCiATQQJ0IgRqIQcgAUECdCAEayAQQf8BcUEDdGtBBGshBANAIAcgBygCAEEBaiIINgIAIAgNASAHQQRqIQcgBCEIIARBBGshBCAIDQALC0EAIQcgBkEANgKAAyANRQRAQQAhCSAGKAL8AiIEQQAgAiAQIBIgEBApDAULIAYoAvgCIA1JBEAgBkH4AmpBACANEIkDIAYoAoADIQcLIAYoAvwCIgQgB0ECdGohCCANQQFHBEAgBSALaiADQf4DcWtBAnQiBQRAIAhBACAF/AsACyAEIAMgB2ogDmpBAnQgEEEDdGtqIQggByAbaiEHC0EAIQkgCEEANgIAIAYgB0EBaiIDNgKAAyAEIAMgAiAQIBIgEBApIANFDQQgBCADQQJ0akEEaygCAA0DIAdBAnQhByADQf////8DcSEIA0AgB0F8RgRAIAZBADYCgAMMBgsgCEEBayEIIAQgB2ogB0EEayEHKAIARQ0ACyAIQQFqIgkgA0sNAyAGIAk2AoADDAQLQQQgBEG0ycQAEMgEAAsgECABQajIxAAQ5AQACyAEIAFBmMjEABDkBAALIAMhCQsCQAJAAkACQCAGKAL4AiIDQQJ2IAlNBEAgBCEKDAELIANFBEAgBCEKDAELIANBAnQhAwJAIAlFBEBBBCEKIAQgAxDfBAwBCyAEIANBBCAJQQJ0IggQzgQiCkUNAgsgBiAJNgL4AiAGIAo2AvwCCyABIAlJDQUCQCAJRQ0AIAlBAXECQCAJQQFGBEBBACEFQQAhAwwBCyAJQf7///8BcSEPQQAhBSAKIQQgACEHQQAhAwNAIAcgBSAHKAIAIg4gBCgCAGoiCGoiETYCACAHQQRqIgUgBSgCACITIARBBGooAgBqIgUgCCAOSSAIIBFLcmoiCDYCACAFIBNJIAUgCEtyIgghBSAEQQhqIQQgB0EIaiEHIA8gA0ECaiIDRw0ACwsEfyAAIANBAnQiA2oiBCAEKAIAIgQgAyAKaigCAGoiAyAFaiIFNgIAIAMgBEkgAyAFS3IFIAgLQQFxRSABIAlGcg0AIAAgCUECdCIDaiEAIAFBAnQgA2tBBGshBwNAIAAgACgCAEEBaiIENgIAIAQNASAAQQRqIQAgByIEQQRrIQcgBA0ACwsgBigCgAMiCiAUSw0FAkAgCkUNACAGKAL8AiEDIApBAXECQCAKQQFGBEBBACEIQQAhBQwBCyAKQX5xIQtBACEIIAMhByAMIQBBACEFA0AgACAAKAIAIg8gBygCAGoiBCAIaiIONgIAIABBBGoiCCAIKAIAIhEgB0EEaigCAGoiCCAEIA9JIAQgDktyaiIENgIAIAggEUkgBCAISXIiBCEIIAdBCGohByAAQQhqIQAgCyAFQQJqIgVHDQALCwR/IAwgBUECdCIAaiIEIAQoAgAiBCAAIANqKAIAaiIAIAhqIgM2AgAgACAESSAAIANLcgUgBAtBAXFFIAogFEZyDQAgDCAKQQJ0IgNqIQAgAUECdCADayAQQQJ0a0EEayEHA0AgACAAKAIAQQFqIgE2AgAgAQ0BIABBBGohACAHIAdBBGshBw0ACwsgBkGoA2oiASAcIBogAiAQEHggBigCtAMhBSAGKAKwAyEEIAYoAqwDIQggBi0AqAMhACABIB0gGSASIBAQeCAGKAKwAyEKIAYoAqwDIQkgAEEBRg0CIAYoArQDIQsCQAJAAkAgBi0AqANBAWsOAgUAAQsgAEUNAQwDCyAARQ0CCyAMIBQgBCAFIAogCxApDAILQQQgCEG0ycQAEMgEAAtBACEHIAZBADYCgAMgBkH4AmoiAiACKAIIIgAgDUkEfyAAIQEgDSAAayIDIAIoAgAgAGtLBEAgAiAAIAMQiQMgAigCCCEBCyACKAIEIAFBAnRqIQIgA0ECTwRAIA0gAEF/c2oiDUEHcSEAIANBAmtBB08EQCANQXhxIQ0DQCACQQA2AgAgAkEcakEANgIAIAJBGGpBADYCACACQRRqQQA2AgAgAkEQakEANgIAIAJBDGpBADYCACACQQhqQQA2AgAgAkEEakEANgIAIAJBIGohAiANQQhrIg0NAAsLIAAEQANAIAJBADYCACACQQRqIQIgAEEBayIADQALCyABIANqQQFrIQELIAJBADYCACABQQFqBSANCzYCCCAGKAL8AiAGKAKAAyAEIAUgCiALECkCQCAGKAKAAyIARQ0AIAYoAvwCIgEgAEECdCIHakEEaygCAARAIAAhBwwBCyABQQRrIQEgAEH/////A3EhBQJAA0AgB0UEQEEAIQUMAgsgBUEBayEFIAEgB2ogB0EEayEHKAIARQ0ACyAAIgcgBUEBaiIFSQ0BCyAGIAU2AoADIAUhBwsCQCAGKAL4AkECdiAHSwRAIAYgBkH4AmogBxDTAyAGKAIAIgBBgYCAgHhHDQEgBigCgAMhBwsgDCAUIAYoAvwCIAcQwAIMAQsgACAGKAIEQbTJxAAQyAQACyAJBEAgCiAJQQJ0EN8ECyAIBEAgBCAIQQJ0EN8ECyAGKAL4AiIARQ0BIAYoAvwCIABBAnQQ3wQMAQsgBkHYAGoiByACIA5BA24iDUEBaiIKIAMgAyAKSxsiBBDWAgJAAkAgCiADIARrIgUgBSAKSxsiCCAEaiIFIANNBEAgBkHoAGoiCSACIARBAnRqIAgQ1gIgBkH4AGoiBCACIAVBAnRqIAMgBWsQ1gICQCAOBEAgBkGIAWoiAyASIAoQ1gIgDiAKIA4gCmsiAiACIApLGyIFIApqIgJJDQEgBkGYAWoiCCASIApBAnRqIAUQ1gIgBkGoAWoiBSASIAJBAnRqIA4gAmsQ1gIgBkG4AWoiAiAHIAQQmwEgBkHIAWoiBCADIAUQmwEgBkHYAWogAiAJEJMBIAZB6AFqIAQgCBCTAUEBIQdBASECIAYtAGQiA0EBRg0EAkACQAJAIAYtAJQBIgJBAWsOAgcBAAsgAw0BDAULIAMNBAtBACEHQQAhAgwECyAKQQBBqMfEABDlBAALIAIgDkG4x8QAEOUEAAsgBSADQZjHxAAQ5QQAC0ECIQJBACEHCwJAAkAgBigCYCIDBEAgBigCkAEiBA0BCyAGQbADakHwyMQAKAIANgIAIAZB6MjEACkCADcDqAMMAQsgBigCjAEhBSAEQQFGBEAgBSgCACEDIAZBqANqIAZB2ABqEMADIAZBgANqIgQgBkGwA2oiBSgCADYCACAGIAYpAqgDNwP4AiAGQfgCaiADELMCIAUgBCgCADYCACAGIAYpA/gCNwOoAwwBCyAGKAJcIQggA0EBRgRAIAgoAgAhAyAGQagDaiAGQYgBahDAAyAGQYADaiIEIAZBsANqIgUoAgA2AgAgBiAGKQKoAzcD+AIgBkH4AmogAxCzAiAFIAQoAgA2AgAgBiAGKQP4AjcDqAMMAQsgBkGoA2ogCCADIAUgBBDtAgsCQAJAAkACQCAHRQRAIAJBASAGKAKwAxshAgwBCyAGQQA2ArADIAYoAqgDQQRJDQAgBkHQAGogBkGoA2pBABDTAyAGKAJQIgNBgYCAgHhHDQELIAZBgAJqIAZBsANqKAIANgIAIAYgBikDqAM3A/gBIAYgAjoAhAJBASEHQQEhAiAGLQCEASIDQQFGDQICQAJAAkAgBi0AtAEiAkEBaw4CBQEACyADDQEMAwsgAw0CC0EAIQdBACECDAILIAMgBigCVEG0ycQAEMgEAAtBAiECQQAhBwsCQAJAIAYoAoABIgMEQCAGKAKwASIEDQELIAZBsANqQfDIxAAoAgA2AgAgBkHoyMQAKQIANwOoAwwBCyAGKAKsASEFIARBAUYEQCAFKAIAIQMgBkGoA2ogBkH4AGoQwAMgBkGAA2oiBCAGQbADaiIFKAIANgIAIAYgBikCqAM3A/gCIAZB+AJqIAMQswIgBSAEKAIANgIAIAYgBikD+AI3A6gDDAELIAYoAnwhCCADQQFGBEAgCCgCACEDIAZBqANqIAZBqAFqEMADIAZBgANqIgQgBkGwA2oiBSgCADYCACAGIAYpAqgDNwP4AiAGQfgCaiADELMCIAUgBCgCADYCACAGIAYpA/gCNwOoAwwBCyAGQagDaiAIIAMgBSAEEO0CCwJAAkACQAJAAkAgB0UEQCACQQEgBigCsAMbIQIMAQsgBkEANgKwAyAGKAKoA0EESQ0AIAZByABqIAZBqANqQQAQ0wMgBigCSCIDQYGAgIB4Rw0BCyAGQZACaiAGQbADaiIDKAIANgIAIAYgBikDqAM3A4gCIAYgAjoAlAIgBkGAA2oiAiAGQcABaikCADcDACAGIAYpArgBNwP4AiADIAZB8ABqKQIANwMAIAYgBikCaDcDqAMgBkHYAmogBkH4AmoiBCAGQagDaiIFEMABIAIgBkHQAWopAgA3AwAgBiAGKQLIATcD+AIgAyAGQaABaikCADcDACAGIAYpApgBNwOoAyAGQegCaiAEIAUQwAEgBiAGKALoAjYCyAIgBiAGKALsAjYCnAMgBiAGKALYAjYCkAMgBiAGKALcAjYCjAMgBigC8AIhAiAGKALgAiEDAkACQCAGLQDkAiIEQQFGDQACfwJAAkACQCAGLQD0AkEBaw4CBAEACyAEDQFBAgwCCyAERQ0AQQIMAQtBAAsgBkH4AmogBkHYAmogBkHoAmoQgANBASAGKAKAAxshAgwBCyAGKAKcAyEEAkACQCADQQAgAhtFBEAgBkKAgICAwAA3A/gCDAELIAJBAUYEQCAEKAIAIQIgBkGwA2ogBkHgAmooAgA2AgAgBiAGKQLYAjcDqAMgBkGoA2ogAhCzAiAGIAYpA6gDNwP4AiAGQcgCaiECIAZBnANqIQcMAgsgBigCjAMhBSADQQFGBEAgBSgCACECIAZBsANqIAZB8AJqKAIANgIAIAYgBikC6AI3A6gDIAZBqANqIAIQswIgBiAGKQOoAzcD+AIgBkGQA2ohAiAGQYwDaiEHDAILIAZB+AJqIAUgAyAEIAIQ7QILIAZBkANqIQIgBkGMA2ohByAGKALIAiIDRQ0AIAQgA0ECdBDfBAsgAigCACICBEAgBygCACACQQJ0EN8ECyAGQQA2AoADQQEhAiAGKAL4AkEESQ0AIAZBQGsgBkH4AmpBABDTAyAGKAJAIgNBgYCAgHhHDQILIAZBoAJqIAZBgANqKAIANgIAIAYgBikD+AI3A5gCIAYgAjoApAJBASEHQQEhAiAGLQDkASIDQQFGDQMCQAJAAkAgBi0A9AEiAkEBaw4CBgEACyADDQEMBAsgAw0DC0EAIQdBACECDAMLIAMgBigCTEG0ycQAEMgEAAsgAyAGKAJEQbTJxAAQyAQAC0ECIQJBACEHCwJAAkAgBigC4AEiAwRAIAYoAvABIgQNAQsgBkGwA2pB8MjEACgCADYCACAGQejIxAApAgA3A6gDDAELIAYoAuwBIQUgBEEBRgRAIAUoAgAhAyAGQagDaiAGQdgBahDAAyAGQYADaiIEIAZBsANqIgUoAgA2AgAgBiAGKQKoAzcD+AIgBkH4AmogAxCzAiAFIAQoAgA2AgAgBiAGKQP4AjcDqAMMAQsgBigC3AEhCCADQQFGBEAgCCgCACEDIAZBqANqIAZB6AFqEMADIAZBgANqIgQgBkGwA2oiBSgCADYCACAGIAYpAqgDNwP4AiAGQfgCaiADELMCIAUgBCgCADYCACAGIAYpA/gCNwOoAwwBCyAGQagDaiAIIAMgBSAEEO0CCwJAAn8CQAJAAkAgB0UEQCACQQEgBigCsAMbIQIMAQsgBkEANgKwAyAGKAKoA0EESQ0AIAZBOGogBkGoA2pBABDTAyAGKAI4IgNBgYCAgHhHDQELIAZBsAJqIAZBsANqIgMoAgA2AgAgBiAGKQOoAzcDqAIgBiACOgC0AiADIAZBgAFqKQIANwMAIAYgBikCeDcDqAMgBkH4AmogBkHYAWogBkGoA2oQwAEgBi0AhAMhAyAGKAL8AiECIAYoAoADIQQCfwJAIAYoAvgCIgdBgICAgHhHBEAgBA0BQQAMAgsgAigCCEUNAwsgBiAENgKwAyAGIAI2AqwDIAYgBzYCqAMgBkHoAmogBkGoA2pBAEEBEM8BIAYoAuwCIQIgBigC6AIhByAGKALwAgshBEEBIQggA0EBRwRAIANBASAEGyEIDAQLQQAhBCAHQQRJDQMgAiAHQQJ0EN8EQQQMAgsgAyAGKAI8QbTJxAAQyAQAC0EBIQhBACEEQQQLIQJBACEHCyAGIAg6APQCIAYgBDYC8AIgBiACNgLsAiAGIAc2AugCIAZBsANqIgIgBkHgAGopAgA3AwAgBiAGKQJYNwOoAyAGQdgCaiAGQegCaiAGQagDaiIDEJcBIAIgBkGwAWopAgA3AwAgBiAGKQKoATcDqAMgBkH4AmogBkHoAWogAxDAASAGLQCEAyEDIAYoAvwCIQIgBigCgAMhBAJAAn8CQAJ/AkAgBigC+AIiB0GAgICAeEcEQCAEDQFBAAwCCyACKAIIRQ0CCyAGIAQ2ArADIAYgAjYCrAMgBiAHNgKoAyAGQegCaiAGQagDakEAQQEQzwEgBigC7AIhAiAGKALoAiEHIAYoAvACCyEEQQEhCCADQQFHBEAgA0EBIAQbIQgMAwtBACEEIAdBBEkNAiACIAdBAnQQ3wRBBAwBC0EBIQhBACEEQQQLIQJBACEHCyAGIAg6APQCIAYgBDYC8AIgBiACNgLsAiAGIAc2AugCIAZBsANqIAZBkAFqKQIANwMAIAYgBikCiAE3A6gDIAZB+AJqIAZB6AJqIAZBqANqEJcBIAYgBigC+AI2AsgCIAYgBigC/AI2ApwDIAYgBigC2AI2ApADIAYgBigC3AI2AowDIAYoAoADIQIgBigC4AIhAwJAAkACQAJAIAYtAOQCIgRBAUYNAAJ/AkACQAJAIAYtAIQDQQFrDgIEAQALIAQNAUECDAILIARFDQBBAgwBC0EACyAGQegCaiAGQdgCaiAGQfgCahCAA0EBIAYoAvACGyECDAELIAYoApwDIQQCQAJAIANBACACG0UEQCAGQoCAgIDAADcD6AIMAQsgAkEBRgRAIAQoAgAhAiAGQbADaiAGQeACaigCADYCACAGIAYpAtgCNwOoAyAGQagDaiACELMCIAYgBikDqAM3A+gCIAZByAJqIQIgBkGcA2ohBwwCCyAGKAKMAyEFIANBAUYEQCAFKAIAIQIgBkGwA2ogBkGAA2ooAgA2AgAgBiAGKQL4AjcDqAMgBkGoA2ogAhCzAiAGIAYpA6gDNwPoAiAGQZADaiECIAZBjANqIQcMAgsgBkHoAmogBSADIAQgAhDtAgsgBkGQA2ohAiAGQYwDaiEHIAYoAsgCIgNFDQAgBCADQQJ0EN8ECyACKAIAIgIEQCAHKAIAIAJBAnQQ3wQLIAZBADYC8AJBASECIAYoAugCQQRJDQAgBkEwaiAGQegCakEAENMDIAYoAjAiA0GBgICAeEcNAQsgBkHAAmogBkHwAmooAgA2AgAgBiAGKQPoAjcDuAIgBiACOgDEAiAGQagDaiAGQbgCaiAGQZgCahCxASAGLQC0AyEIIAYoAqwDIQQgBigCsAMiA0UEQEEAIQMgBigCqAMhBQwCCyAEQQRrIQUgBCADQQJ0IgJqQQAhBwNAIAIgBWoiDCAMKAIAIgxBEHYiCyALIAdBEHRyQQNuIgdBA2xrQRB0IAxB//8DcXIiDEEDbiILIAdBEHRyNgIAIAwgC0EDbGshByACQQRrIgINAAsgBigCqAMhBUEEaygCAA0BIANBAnQhAiAEQQRrIQkgA0H/////A3EhBwNAIAJFBEBBACEDDAMLIAdBAWshByACIAlqIAJBBGshAigCAEUNAAsgB0EBaiICIAMgAiADSRshAwwBCyADIAYoAjRBtMnEABDIBAALAkACQAJAAkACQAJAAkAgBUECdiADTQRAIAUhAiAEIQcMAQtBACECIAVFBEAgBCEHDAELIAVBAnQhBSADRQRAQQQhByAEIAUQ3wQMAQsgBCAFQQQgAyICQQJ0IgQQzgQiB0UNAQsgBiADNgKAAyAGIAc2AvwCIAYgAjYC+AJBASEHAkAgCEEBRwRAIAhBASADGyEHDAELIAZBADYCgAMgAkEESQ0AIAZBKGogBkH4AmpBABDTAyAGKAIoIgJBgYCAgHhHDQILIAZB0AJqIgIgBkGAA2ooAgA2AgAgBiAGKQL4AjcDyAIgBiAHOgDUAiAGQbADaiIDIAZBoAJqKQMANwMAIAYgBikDmAI3A6gDIAZB+AJqIgQgBkGoA2oiBSAGQagCahCxASAGQdgCaiAEEKoCIAMgBkGwAmopAwA3AwAgBiAGKQOoAjcDqAMgBkHoAmogBSAGQfgBahCxASAGLQD0AiEFIAYoAswCIQcgBigCyAIhCCAGLQDUAiIEQQFHDQMgBigC8AIiCUECdCEDQQAhAiAJQf////8DSyADQfz///8HS3INAiAGKALsAiEMAn8gA0UEQEEEIQRBAAwBC0HRzsUALQAAGkEEIQIgA0EEENYEIgRFDQMgCQshAiADBEAgBCAMIAP8CgAACyAGIAU6ALQDIAYgCTYCsAMgBiAENgKsAyAGIAI2AqgDDAQLQQQgBEG0ycQAEMgEAAsgAiAGKAIsQbTJxAAQyAQACyACIANBpIPFABDIBAALIAIoAgAhAwJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIAVBAWsOAgECAAsgBEUNAgwDCyAGQdUCaiECIAZBsANqIAZB0AJqKAIANgIAIAYgBikDyAI3A6gDIAZBtQNqIQMgBARAIAMgAi8AADsAACADQQJqIAJBAmotAAA6AAAgBkEAOgC0AwwNCyADIAIvAAA7AAAgBkECOgC0AyADQQJqIAJBAmotAAA6AAAMDAsgBEUNAQsCfyADIAYoAvACIgJGBEAgBigC7AJBBGshDCAHQQRrIQsgA0ECdCECAkADQCACRQ0BIAIgC2ohCSACIAxqIAJBBGshAigCACIEIAkoAgAiCUYNAAsgBCAJSyAEIAlJawwCC0F/QQAgAhsMAQsgAiADSyACIANJawtB/wFxDgICBgELIAZBsANqIgIgBkHQAmooAgA2AgAgBiAGKQPIAjcDqAMgBkH4AmogBkGoA2ogBkHoAmoQygEgBigCgANFBEAgAiAGQYADaigCADYCACAGQQE6ALQDIAYgBikC+AI3A6gDDAoLIAIgBkGAA2ooAgA2AgAgBiAFOgC0AyAGIAYpAvgCNwOoAwwJC0ECIQIgBUEBaw4CAwECCyAGQbADakGAxMQAKQIANwMAIAZB+MPEACkCADcDqAMMBgtBACECCyAGIAM2ArADIAYgBzYCrAMgBiAINgKoAyAGQfgCaiAGQagDaiAGQegCahCHAiACQQEgBigCgAMbIQIMAwsgBiADNgKwAyAGIAc2AqwDIAYgCDYCqAMgBkH4AmoiAiAGQagDaiAGQegCahCHAkEAIQQgBkEANgKAAyACEOUDIAYoAoADIgNFDQEgBigC/AIiBCADQQJ0IgJqQQRrKAIABEAgAyEEDAILIARBBGshBCADQf////8DcSEHAkADQCACRQRAQQAhAgwCCyAHQQFrIQcgAiAEaiACQQRrIQIoAgBFDQALIAMiBCAHQQFqIgJJDQILIAYgAjYCgAMgAiEEDAELIAYgAzYCsAMgBiAHNgKsAyAGIAg2AqgDIAZB+AJqIAZB6AJqIAZBqANqEJ4BAkAgBUEBRwRAIAVBASAGKAKAAxshAgwBC0EAIQQgBkEANgKAAyAGQfgCahDlAwJAIAYoAoADIgNFDQAgBigC/AIiBCADQQJ0IgJqQQRrKAIABEAgAyEEDAELIARBBGshBCADQf////8DcSEHAkADQCACRQRAQQAhAgwCCyAHQQFrIQcgAiAEaiACQQRrIQIoAgBFDQALIAMiBCAHQQFqIgJJDQELIAYgAjYCgAMgAiEEC0EBIQIgBCAGKAL4AkECdk8NACAGQSBqIAZB+AJqIAQQ0wMgBigCICIDQYGAgIB4Rg0AIAMgBigCJEG0ycQAEMgEAAsgBkGwA2ogBkGAA2ooAgA2AgAgBiAGKQL4AjcDqAMgBiACOgC0AwwDC0EBIQIgBCAGKAL4AkECdk8NACAGQRhqIAZB+AJqIAQQ0wMgBigCGCIDQYGAgIB4Rg0AIAMgBigCHEG0ycQAEMgEAAsgBkGwA2ogBkGAA2ooAgA2AgAgBiAGKQL4AjcDqAMgBiACOgC0AwwBCyAIRQ0AIAcgCEECdBDfBAsgBkH4AmogBkGoA2oQqgIgBi0AlAIhAgJAIAYoApACRQRAIAZBnANqIAZBiAJqEMADDAELIAZBgICAgHg2AqgDIAYgBkGIAmo2AqwDIAZBnANqIAZBqANqQQBBARDPAQtBASEHAkACQAJAAkACQCACQQFHBEAgAkEBIAYoAqQDGyEHDAELIAZBADYCpAMgBigCnANBBEkNACAGQRBqIAZBnANqQQAQ0wMgBigCECICQYGAgIB4Rw0BCyAGQbADaiAGQaQDaigCADYCACAGIAYpApwDNwOoAyAGIAc6ALQDIAZByAJqIAZB+AJqIgIgBkGoA2oQwAEgAiAGQdgCaiAGQYgCahCTASAGQfACaiICKAIAIQMgBkH3AmotAAAhBCAGLQD0AiEHIAYvAPUCIQggAkGAxMQAKQIANwMAIAZBjgNqIgIgBDoAACAGKALoAiEEIAYoAuwCIQUgBkH4w8QAKQIANwPoAiAGIAg7AYwDIAYtAIQDIghBAUYEQCAGQbcDaiACLQAAOgAAIAYgBzoAtAMgBiADNgKwAyAGIAU2AqwDIAYgBDYCqAMgBiAGLwGMAzsAtQMMBAsCQAJAAkACQCAHQQFrDgIBAAILIAgNAgwECyAGQagDaiAGQfgCahDAAyAGIAg6ALQDDAQLIAgNAgsgBiADNgKwAyAGIAU2AqwDIAYgBDYCqAMgBkGcA2ogBkGoA2ogBkH4AmoQygEgBigCpANFBEAgBkGwA2ogBkGkA2ooAgA2AgAgBkEBOgC0AyAGIAYpApwDNwOoAwwECyAGQbADaiAGQaQDaigCADYCACAGIAc6ALQDIAYgBikCnAM3A6gDDAMLIAIgBigCFEG0ycQAEMgEAAsCQAJAAkACfyAGKAKAAyICIANGBEAgBUEEayELIAYoAvwCQQRrIQ8gA0ECdCECAkADQCACRQ0BIAIgD2ohDCACIAtqIAJBBGshAigCACIJIAwoAgAiDEYNAAsgCSAMSyAJIAxJawwCC0F/QQAgAhsMAQsgAiADSSACIANLawtB/wFxDgIAAgELIAZBsANqQYDExAApAgA3AwAgBkH4w8QAKQIANwOoAwwCCyAGIAM2AqQDIAYgBTYCoAMgBiAENgKcAyAGQZADaiAGQfgCaiAGQZwDahCeASAGQbADaiAGQZgDaigCACICNgIAIAYgBikCkAM3A6gDIAYgCEEBIAIbOgC0AwwCCyAGIAM2ArADIAYgBTYCrAMgBiAENgKoAyAGQZwDaiAGQagDaiAGQfgCahCHAgJAIAdBAUcEQCAHQQEgBigCpAMbIQIMAQtBACEEIAZBADYCpAMgBkGcA2oQ5QMCQCAGKAKkAyIDRQ0AIAYoAqADIgQgA0ECdCICakEEaygCAARAIAMhBAwBCyAEQQRrIQQgA0H/////A3EhBwJAA0AgAkUEQEEAIQIMAgsgB0EBayEHIAIgBGogAkEEayECKAIARQ0ACyADIgQgB0EBaiICSQ0BCyAGIAI2AqQDIAIhBAtBASECIAQgBigCnANBAnZPDQAgBkEIaiAGQZwDaiAEENMDIAYoAggiA0GBgICAeEYNACADIAYoAgxBtMnEABDIBAALIAZBsANqIAZBpANqKAIANgIAIAYgBikCnAM3A6gDIAYgAjoAtAMMAQsgBEUNACAFIARBAnQQ3wQLIAYoAugCIgIEQCAGKALsAiACQQJ0EN8ECyAGQfACaiAGQbADaikDADcDACAGIAYpA6gDNwPoAiAGKAL4AiICBEAgBigC/AIgAkECdBDfBAsgBkHgAmoiAikDACEgIAJBgMTEACkCADcDACAGQYADaiAgNwMAIAYpA9gCISAgBkH4w8QAKQIANwPYAiAGICA3A/gCIAZBqANqIAZB+AJqIAZByAJqELEBIAYoAtgCIgIEQCAGKALcAiACQQJ0EN8ECyAGQeACaiAGQbADaikCADcDACAGIAYpAqgDNwPYAgJAAkACQAJAAkACQAJAAkACQCAGLQCUAkEBaw4CAgEACyABIApBAnQiAkkNBSAAIAJBAnRqIAEgAmsgBigCjAIgBigCkAIQwAIMAQsgASAKQQJ0IgJJDQEgACACQQJ0aiABIAJrIAYoAowCIAYoApACEM4CCwJAAkACQCAGLQDUAkEBaw4CAgEACyABIApBA2wiAkkNBSAAIAJBAnRqIAEgAmsgBigCzAIgBigC0AIQwAIMAQsgASAKQQNsIgJJDQEgACACQQJ0aiABIAJrIAYoAswCIAYoAtACEM4CCwJAAkACQCAGLQD0AkEBaw4CAgABCyABIApBAXQiAkkNAiAAIAJBAnRqIAEgAmsgBigC7AIgBigC8AIQzgIMAQsgASAKQQF0IgJJDQQgACACQQJ0aiABIAJrIAYoAuwCIAYoAvACEMACCwJAIAYtAOQCQQFrDgIGAAMLIAEgDUsNASAKIQILIAIgAUHYx8QAEOQEAAsgACAKQQJ0aiABIAprIAYoAtwCIAYoAuACEM4CDAMLIAEgDUsNASAKIQILIAIgAUHIx8QAEOQEAAsgACAKQQJ0aiABIAprIAYoAtwCIAYoAuACEMACCwJAAkACQCAGLQCEAkEBaw4CAgABCyAAIAEgBigC/AEgBigCgAIQzgIMAQsgACABIAYoAvwBIAYoAoACEMACCyAGKALoAiIABEAgBigC7AIgAEECdBDfBAsgBigC2AIiAARAIAYoAtwCIABBAnQQ3wQLIAYoAsgCIgAEQCAGKALMAiAAQQJ0EN8ECyAGKAKIAiIABEAgBigCjAIgAEECdBDfBAsgBigC+AEiAEUNACAGKAL8ASAAQQJ0EN8ECyAGQcADaiQADwsgBkEANgK4AyAGQQE2AqwDIAZBlIfFADYCqAMgBkIENwKwAyAGQagDakGEiMUAEKgEAAvWYQIOfyN+IwBBoBBrIgIkAAJAAkACQAJAAkACQCABEPECQf8BcUEBaw4CAAECCyAAQQhqQQBB4AD8CwAgAEIBNwMADAQLIAJB8A1qQgA3AwAgAkHoDWpCADcDACACQeANakIANwMAIAJB2A1qQgA3AwAgAkIANwPQDSACQgE3A/gNAkBB+NPBAEGI0sEAQTAQ8QMiDwRAIAJCrtXy//////rDADcDmBAgAkL9/5/qrv7/2zI3A5AQIAJC6bqml5rJjvQHNwOIECACQvr2ypmY5rzUbDcDgBAgAkLpgNOH6qOjim83A/gPIAJChoT89+PkrIUENwPwDwwBCyACQZgQakGg1MEAKQMANwMAIAJBkBBqQZjUwQApAwA3AwAgAkGIEGpBkNTBACkDADcDACACQYAQakGI1MEAKQMANwMAIAJB+A9qQYDUwQApAwA3AwAgAkH408EAKQMANwPwDwsgAkGADmogAkHwD2oiBRCmASACKQOADiEcIAIpA6AOISEgAikDmA4hFyACKQOQDiEbIAIpA4gOIRkgAikDqA4hHSACQZAQaiIEQgA3AwAgAkGIEGoiA0IANwMAIAJBgBBqIgdCADcDACACQfgPaiIIQgA3AwAgAkIANwPwDyACIB1CAYM3A5gQIAUgAkHQDWpBMBDxAw0BQQAhBQwCCyAAQgA3AwAMAgtBACEFIBchESAbIRIgGSEVA0AgBEIANwMAIANCADcDACAHQgA3AwAgCEIANwMAIAJCADcD8A8gAiAhQj+GIB1CAYiEIh1CAYM3A5gQIBxCP4YgEUI/hiAhQgGIhCEhIBxCAYghHCAFQQFqIQUgEkI/hiARQgGIhCIXIREgFUI/hiASQgGIhCIbIRIgFUIBiIQiGSEVIAJB8A9qIAJB0A1qQTAQ8QMNAAsLIAIgITcDoA4gAiAdNwOoDiACIBc3A5gOIAIgGzcDkA4gAiAZNwOIDiACIBw3A4AOQs+qmYCAgMCJMiESIAJCz6qZgICAwIkyNwPoD0KFgJC2jYOAnrl/IRUgAkKFgJC2jYOAnrl/NwPgD0LR9vaG28GXsNcAIRMgAkLR9vaG28GXsNcANwPYD0LLt/7onqTZkot/IRQgAkLLt/7onqTZkot/NwPQD0KD2IiLkK+j+ewAIRAgAkKD2IiLkK+j+ewANwPID0KMxYfc2/Pq9REhESACQozFh9zb8+r1ETcDwA8gAkHAD2oQ8QJB/wFxBEADQEKazf/Lo73EgBohICARIBAgEELt2NuS+tLGg9wAfCIQViAQIBQgFELFrsmCt4qW5/cAfCIUViAUIBMgE0K6sZ2e9YqmpN8AfCITViATIBUgFUL+/8/fw/7/hRR9IhVWIBUgEiASQv3/i4CAgMCE9gB8IhJWrXwiFiAVVHKtfCIYIBNUcq18IhogFFRyrXwiIiAQVHKtfEKTyYPUv9iX+xV8IhEhFQJAAkACQCARQprN/8ujvcSAGlINAELX2a6a5PbpjcsAISAgIiIVQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEgIBoiFUK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhICAYIhVCpOzDtY/UtJjnAFINAEL//8+K6///1R4hICAWIhVC///Piuv//9UeUg0AQqvV/v///7//uX8hICASIhVCq9X+////v/+5f1ENAQsgFSAgWg0AICIhECAaIRQgGCETIBYhFQwBCyAWQv//z4rr///VHn0iECASQqvV/v///7//uX9UrSITfSEVIBhCpOzDtY/UtJjnAH0iFCAWQv//z4rr///VHlQgECATVHKtIhB9IRMgGkK/pZScz/DSu+QAfSIWIBhCpOzDtY/UtJjnAFQgECAUVnKtIhB9IRQgIkLX2a6a5PbpjcsAfSIYIBpCv6WUnM/w0rvkAFQgECAWVnKtIhZ9IRAgESAiQtfZrprk9umNywBUIBYgGFZyrX1Cms3/y6O9xIAafSERIBJC1aqBgICAwIDGAHwhEgsgAiASNwPoDyACIBU3A+APIAIgEzcD2A8gAiAUNwPQDyACIBA3A8gPIAIgETcDwA8gAkHAD2oQ8QJB/wFxDQALCyACQZgQaiIHIAJBqA5qIgQpAwA3AwAgAkGQEGoiCCACQaAOaiIDKQMANwMAIAJBiBBqIgwgAkGYDmoiCSkDADcDACACQYAQaiINIAJBkA5qIgspAwA3AwAgAkH4D2oiDiACQYgOaiIKKQMANwMAIAIgAikDgA43A/APIAJBsA5qIAJBwA9qIAJB8A9qIgYQLCACICEgHUIBfCIQUK18IhJCP4YgEEIBiIQ3A5gQIAIgFyASICFUrXwiEEI/hiASQgGIhDcDkBAgAiAbIBAgF1StfCISQj+GIBBCAYiENwOIECACIBkgEiAbVK18IhBCP4YgEkIBiIQ3A4AQIAIgHCAQIBlUrXwiEkIBiDcD8A8gAiASQj+GIBBCAYiENwP4DyACQeAOaiABIAYQLCAHIAQpAwA3AwAgCCADKQMANwMAIAwgCSkDADcDACANIAspAwA3AwAgDiAKKQMANwMAIAIgAikDgA43A/APIAJBkA9qIgQgASAGECwgAikD4A4hJyACKQPoDiElIAIpA/AOISQgAikD+A4hICACKQOADyEiIAIpA4gPISEgBEH408EAQTAQ8QMEQCACKQPYDiEZIAIpA9AOIRYgAikDyA4hGCACKQPADiEaIAIpA7gOIRwgAikDsA4hHyACKQO4DyEvIAIpA7APIS0gAikDqA8hKCACKQOgDyEqIAIpA5gPISsgAikDkA8hLANAIAJB6A9qIAJBuA9qKQMANwMAIAJB4A9qIAJBsA9qKQMANwMAIAJB2A9qIAJBqA9qKQMANwMAIAJB0A9qIAJBoA9qKQMANwMAIAJByA9qIAJBmA9qKQMANwMAIAIgAikDkA83A8APAkAgDwRAIAJCrtXy//////rDADcDmBAgAkL9/5/qrv7/2zI3A5AQIAJC6bqml5rJjvQHNwOIECACQvr2ypmY5rzUbDcDgBAgAkLpgNOH6qOjim83A/gPIAJChoT89+PkrIUENwPwDwwBCyAHQaDUwQApAwA3AwAgCEGY1MEAKQMANwMAIAxBkNTBACkDADcDACANQYjUwQApAwA3AwAgDkGA1MEAKQMANwMAIAJB+NPBACkDADcD8A8LIAVBAmshAQJAIAJBwA9qIAJB8A9qQTAQ8QNFBEBBACEFIAEhBAwBC0EAIQUgAikD6A8hFyACKQPgDyEbIAIpA9gPIR0gAikD0A8hHiACKQPIDyEjIAIpA8APISYgASEEA0BCACEVQSghA0IAIRNCACEUQgAhEEIAIRFCACESA0AgAkHwDGogAkHAD2ogA2opAwAiKUIAIBdCABDJAyACQYANaiApQgAgG0IAEMkDIAJBkA1qIClCACAdQgAQyQMgAkGgDWogKUIAIB5CABDJAyACQbANaiApQgAgI0IAEMkDIAJBwA1qIClCACAmQgAQyQMgAkHgDGogAikD8AwiLiASfCIpQgBCAEL9//P/z///+Yl/EMkDIAJB0AxqIAIpA+gMIhJCAEKr1f7///+//7l/QgAQyQMgAkHADGogEkIAQv//z4rr///VHkIAEMkDIAJBsAxqIBJCAEKk7MO1j9S0mOcAQgAQyQMgAkGgDGogEkIAQr+llJzP8NK75ABCABDJAyACQZAMaiASQgBC19mumuT26Y3LAEIAEMkDIAJBgAxqIBJCAEKazf/Lo73EgBpCABDJAyACKQOIDCACKQPADSIxIBV8IhUgAikDuA0gEyACKQOwDSITfCISIBNUrXwgEiASIAIpA6gNIBQgAikDoA0iFHwiEyAUVK18IBMgAikDmA0gAikDkA0iFCAQfCIQIBRUrXwgECAQIAIpA4gNIAIpA4ANIhQgEXwiESAUVK18IBEgAikD+AwgKSAuVK18fCIyIBFUrXx8IhBWrXx8IhEgE1StfHwiElatfHwiLiACKQOADHwiEyAuVK18IBMgEyACKQOYDCASIAIpA5AMfCIUIBJUrXwgFCAUIAIpA6gMIBEgAikDoAx8IjAgEVStfCAwIAIpA7gMIBAgECACKQOwDHwiEFatfCAQIAIpA8gMIAIpA8AMIhEgMnwiEiARVK18IBIgEiACKQPYDCACKQPQDCIRICl8IBFUrXx8IhJWrXx8IhEgEFStfHwiECAwVK18fCIUVq18fCITVq18IBUgLlatIAIpA8gNIBUgMVStfHx8IRUgA0EIayIDQXhHDQALIAVBAWohBSACAn4CQCAVQprN/8ujvcSAGlYNACAVQprN/8ujvcSAGlIEQCARIRsgECEdIBQhHiATISMgFSEmIBIMAgsgE0LX2a6a5PbpjcsAVg0AQprN/8ujvcSAGiEmIBNC19mumuT26Y3LAFIEQCARIRsgECEdIBQhHiATISMgEgwCCyAUQr+llJzP8NK75ABWDQBC19mumuT26Y3LACEjIBRCv6WUnM/w0rvkAFIEQCARIRsgECEdIBQhHiASDAILIBBCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIR4gEEKk7MO1j9S0mOcAUgRAIBEhGyAQIR0gEgwCCyARQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIR0gEUL//8+K6///1R5RIBJCqtX+////v/+5f1ZxDQAgESEbIBIMAQsgEUL//8+K6///1R59IhcgEkKr1f7///+//7l/VK0iHX0hGyAQQqTsw7WP1LSY5wB9Ih4gEUL//8+K6///1R5UIBcgHVRyrSIRfSEdIBRCv6WUnM/w0rvkAH0iFyAQQqTsw7WP1LSY5wBUIBEgHlZyrSIQfSEeIBNC19mumuT26Y3LAH0iESAUQr+llJzP8NK75ABUIBAgF1ZyrSIQfSEjIBUgE0LX2a6a5PbpjcsAVCAQIBFWcq19QprN/8ujvcSAGn0hJiASQtWqgYCAgMCAxgB8CyIXNwPoDyACIBs3A+APIAIgHTcD2A8gAiAeNwPQDyACICM3A8gPIAIgJjcDwA8gBEEBayEEIAJBwA9qIAJB8A9qQTAQ8QMNAAsLIAEgBUcEQEEBIAQgBEEBTRshCQNAIAJBgAtqIBZCACAZQgAQyQMgAkHgCmogGEIAIBlCABDJAyACQbAKaiAaQgAgGUIAEMkDIAJB8AlqIBxCACAZQgAQyQMgAkGgCWogH0IAIBlCABDJAyACQdAKaiAYQgAgFkIAEMkDIAJBoApqIBpCACAWQgAQyQMgAkHgCWogHEIAIBZCABDJAyACQZAJaiAfQgAgFkIAEMkDIAJBkApqIBpCACAYQgAQyQMgAkHQCWogHEIAIBhCABDJAyACQYAJaiAfQgAgGEIAEMkDIAJBwAlqIBxCACAaQgAQyQMgAkHwCGogH0IAIBpCABDJAyACQeAIaiAfQgAgHEIAEMkDIAJB8AtqIBlCACAZQgAQyQMgAkHwCmogFkIAIBZCABDJAyACQcAKaiAYQgAgGEIAEMkDIAJBgApqIBpCACAaQgAQyQMgAkGwCWogHEIAIBxCABDJAyACQdAIaiAfQgAgH0IAEMkDIAJB4AtqIAIpA/ALIh1C/f/z/8////mJf34iEkIAQqvV/v///7//uX9CABDJAyACQdALaiASQgBC///Piuv//9UeQgAQyQMgAkHAC2ogEkIAQqTsw7WP1LSY5wBCABDJAyACQbALaiASQgBCv6WUnM/w0rvkAEIAEMkDIAJBoAtqIBJCAELX2a6a5PbpjcsAQgAQyQMgAkGQC2ogEkIAQprN/8ujvcSAGkIAEMkDIAIpA+gIIAIpA/gIIAIpA8gJIAIpA9gJIAIpA5gKIAIpA6gKIAIpA9gKIAIpA+gKIAIpA4gLIhAgAikD4Ap8IhIgEFStfCIVIAIpA7AKfCIQIAIpA9AKfCIRIBBUrXwiEyACKQO4CiAQIBVUrXwiFSACKQPwCXwiFHwiECATVK18IBAgECACKQOgCnwiEFatfCIWIAIpA/gJIBQgFVStfCIYIAIpA6AJfCIZfCIVIAIpA+AJfCITIAIpA5AKfCIUIBNUrXwiGiATIBVUrSACKQPoCSAVIBZUrXx8IhYgAikDqAkgGCAZVq18fCIVIAIpA5AJfCIYfCITIBpUrXwgEyATIAIpA9AJfCITVq18IhkgFSAYVq0gAikDmAkgFSAWVK18fHwiFSACKQOACXwiFiACKQPACXwiGCAWVK18IhogFSAWVq0gAikDiAkgFSAZVK18fHwiFSAaVK18IBUgFSACKQPwCHwiFVatfCIZIAIpA+AIfCIWIBlUrXwiGUI/iCACKQPYCCACKQPQCCIaIBlCAYYgFkI/iIR8IhkgGlStfCAZIAIpA7gJIAIpA7AJIhcgFUIBhiAYQj+IhHwiGiAXVK18IBogAikDiAogAikDgAoiGyATQgGGIBRCP4iEfCIXIBtUrXwgFyACKQPICiACKQPACiIcIBBCAYYgEUI/iIR8IhsgHFStfCAbIBsgAikD+AogAikD8AoiHiASQgGGIAIpA4ALIh9CP4iEfCIcIB5UrXwgHCAcIAIpA/gLIh4gH0IBhnwiHyAeVK18IhxWrXwiHiARQgGGIBJCP4iEfCIjIB5UrXwiG1atfCISIBRCAYYgEEI/iIR8Ih4gElStfCImIBdUrXwiEiAYQgGGIBNCP4iEfCIQIBJUrXwiEyAaVK18IhIgFkIBhiAVQj+IhHwiFSASVK18IhQgGVStfHwhEkEAIQECfwJAIAIpA5gLIAIpA6gLIAIpA7gLIAIpA8gLIAIpA9gLIAIpA+gLIAIpA+ALIhEgHUJ9g3wgEVStfCIWIAIpA9ALfCIRIBZUrXwgESAffCIWIBFUrXwiGCACKQPAC3wiESAYVK18IBEgHHwiGCARVK18IhkgAikDsAt8IhEgGVStfCARICN8IhkgEVStfCIaIAIpA6ALfCIRIBpUrXwgESAbfCIaIBFUrXwiFyACKQOQC3wiESAXVK18IBEgHnwiFyARVK18IhFQDQAgESAmfCImIBFUIgRFDQAgBK0iESAQfCIQIBFaDQAgECARVK0iESATfCITIBFaDQAgESATVq0iESAVfCIVIBFaDQAgESAVVq0iESAUfCIUIBFaDQAgESAUVq0iESASfCISIBFUDAELQQALIQsgAkHACGogFkL9//P/z///+Yl/fiIRQgBCq9X+////v/+5f0IAEMkDIAJBsAhqIBFCAEL//8+K6///1R5CABDJAyACQaAIaiARQgBCpOzDtY/UtJjnAEIAEMkDIAJBkAhqIBFCAEK/pZScz/DSu+QAQgAQyQMgAkGACGogEUIAQtfZrprk9umNywBCABDJAyACQfAHaiARQgBCms3/y6O9xIAaQgAQyQMCQCACKQP4ByACKQOICCACKQOYCCACKQOoCCACKQO4CCACKQPICCACKQPACCIRIBZ8IBFUrXwiFiACKQOwCHwiESAWVK18IBEgGHwiFiARVK18IhggAikDoAh8IhEgGFStfCARIBl8IhggEVStfCIZIAIpA5AIfCIRIBlUrXwgESAafCIZIBFUrXwiGiACKQOACHwiESAaVK18IBEgF3wiGiARVK18IhcgAikD8Ad8IhEgF1StfCARICZ8IhcgEVStfCIRUA0AIBAgEXwiECARWg0AIBAgEVStIhEgE3wiEyARWg0AIBEgE1atIhEgFXwiFSARWg0AIBEgFVatIhEgFHwiFCARWg0AIBEgFFatIhEgEnwiEiARVCEBCyACQeAHaiAWQv3/8//P///5iX9+IhFCAEKr1f7///+//7l/QgAQyQMgAkHQB2ogEUIAQv//z4rr///VHkIAEMkDIAJBwAdqIBFCAEKk7MO1j9S0mOcAQgAQyQMgAkGwB2ogEUIAQr+llJzP8NK75ABCABDJAyACQaAHaiARQgBC19mumuT26Y3LAEIAEMkDIAJBkAdqIBFCAEKazf/Lo73EgBpCABDJA0EAIQoCf0EAIAIpA5gHIAIpA6gHIAIpA7gHIAIpA8gHIAIpA9gHIAIpA+gHIAIpA+AHIhEgFnwgEVStfCIWIAIpA9AHfCIRIBZUrXwgESARIBh8IhFWrXwiGCACKQPAB3wiFiAYVK18IBYgGXwiGCAWVK18IhkgAikDsAd8IhYgGVStfCAWIBp8IhkgFlStfCIaIAIpA6AHfCIWIBpUrXwgFiAXfCIaIBZUrXwiFyACKQOQB3wiFiAXVK18IBYgECAWfCIWVq18IhBQDQAaQQAgECAQIBN8IhNYDQAaQQAgECATVq0iECAVfCIVIBBaDQAaQQAgECAVVq0iECAUfCIUIBBaDQAaIBAgFFatIhAgEnwiEiAQVAshAyACQYAHaiARQv3/8//P///5iX9+IhBCAEKr1f7///+//7l/QgAQyQMgAkHwBmogEEIAQv//z4rr///VHkIAEMkDIAJB4AZqIBBCAEKk7MO1j9S0mOcAQgAQyQMgAkHQBmogEEIAQr+llJzP8NK75ABCABDJAyACQcAGaiAQQgBC19mumuT26Y3LAEIAEMkDIAJBsAZqIBBCAEKazf/Lo73EgBpCABDJAwJAIAIpA7gGIAIpA8gGIAIpA9gGIAIpA+gGIAIpA/gGIAIpA4gHIAIpA4AHIhAgEXwgEFStfCIRIAIpA/AGfCIQIBFUrXwgECAYfCIRIBBUrXwiGCACKQPgBnwiECAYVK18IBAgGXwiGCAQVK18IhkgAikD0AZ8IhAgGVStfCAQIBp8IhkgEFStfCIaIAIpA8AGfCIQIBpUrXwgECAWfCIWIBBUrXwiGiACKQOwBnwiECAaVK18IBAgE3wiEyAQVK18IhBQDQAgECAVfCIVIBBaDQAgECAVVq0iECAUfCIUIBBaDQAgECAUVq0iECASfCISIBBUIQoLIAJBoAZqIBFC/f/z/8////mJf34iEEIAQqvV/v///7//uX9CABDJAyACQZAGaiAQQgBC///Piuv//9UeQgAQyQMgAkGABmogEEIAQqTsw7WP1LSY5wBCABDJAyACQfAFaiAQQgBCv6WUnM/w0rvkAEIAEMkDIAJB4AVqIBBCAELX2a6a5PbpjcsAQgAQyQMgAkHQBWogEEIAQprN/8ujvcSAGkIAEMkDQQAhBCACKQPYBSACKQPoBSACKQP4BSACKQOIBiACKQOYBiACKQOoBiACKQOgBiIQIBF8IBBUrXwiESACKQOQBnwiECARVK18IBAgGHwiESAQVK18IhggAikDgAZ8IhAgGFStfCAQIBl8IhggEFStfCIZIAIpA/AFfCIQIBlUrXwgECAWfCIWIBBUrXwiGSACKQPgBXwiECAZVK18IBAgE3wiEyAQVK18IhkgAikD0AV8IhAgGVStfCAQIBV8IhogEFStfCIQUEUEQCAQIBR8IhQgEFQiBK0iECASfCIVIBIgBBshEiAEIBAgFVZxIQQLIAJBwAVqIBFC/f/z/8////mJf34iEEIAQqvV/v///7//uX9CABDJAyACQbAFaiAQQgBC///Piuv//9UeQgAQyQMgAkGgBWogEEIAQqTsw7WP1LSY5wBCABDJAyACQZAFaiAQQgBCv6WUnM/w0rvkAEIAEMkDIAJBgAVqIBBCAELX2a6a5PbpjcsAQgAQyQMgAkHwBGogEEIAQprN/8ujvcSAGkIAEMkDIAIpA/gEIAIpA4gFIAIpA5gFIAIpA6gFIAIpA7gFIAIpA8gFIAIpA8AFIhAgEXwgEFStfCIRIAIpA7AFfCIQIBFUrXwgECAYfCIZIBBUrXwiESACKQOgBXwiECARVK18IBAgECAWfCIQVq18IhUgAikDkAV8IhEgFVStfCARIBEgE3wiEVatfCITIAIpA4AFfCIVIBNUrXwgFSAafCITIBVUrXwiFiACKQPwBHwiFSAWVK18IBUgFCAVfCIVVq18IhQgEnwiFiASIBRCAFIiBhshEgJAAkAgASALciADciAKciAEciAUIBZWIgGtIBQgBhtCAFJyIAEgBnEgEkKazf/Lo73EgBpWcnINACASQprN/8ujvcSAGlIEQCAQIRYgESEYIBMhGiAVIRwgEiEfDAILIBVC19mumuT26Y3LAFYNAEKazf/Lo73EgBohHyAVQtfZrprk9umNywBSBEAgECEWIBEhGCATIRogFSEcDAILIBNCv6WUnM/w0rvkAFYEQELX2a6a5PbpjcsAIRUMAQsgE0K/pZScz/DSu+QAUgRAQtfZrprk9umNywAhHCAQIRYgESEYIBMhGgwCCwJAIBFCpOzDtY/UtJjnAFYNACARQqTsw7WP1LSY5wBSBEBC19mumuT26Y3LACEcQr+llJzP8NK75AAhGiAQIRYgESEYDAMLIBBC///Piuv//9UeVg0AQtfZrprk9umNywAhFUK/pZScz/DSu+QAIRMgEEL//8+K6///1R5RIBlCqtX+////v/+5f1ZxDQEgECEWIBEhGEK/pZScz/DSu+QAIRpC19mumuT26Y3LACEcDAILQtfZrprk9umNywAhFUK/pZScz/DSu+QAIRMLIBBC///Piuv//9UefSIUIBlCq9X+////v/+5f1StIhh9IRYgEUKk7MO1j9S0mOcAfSIaIBBC///Piuv//9UeVCAUIBhUcq0iEH0hGCATQr+llJzP8NK75AB9IhQgEUKk7MO1j9S0mOcAVCAQIBpWcq0iEH0hGiAVQtfZrprk9umNywB9IhEgE0K/pZScz/DSu+QAVCAQIBRWcq0iEH0hHCASIBVC19mumuT26Y3LAFQgECARVnKtfUKazf/Lo73EgBp9IR8gGULVqoGAgIDAgMYAfCEZCyAJQQFrIgkNAAsLIAVBAWohBSACIBk3A5gQIAIgFjcDkBAgAiAYNwOIECACIBo3A4AQIAIgHDcD+A8gAiAfNwPwD0IAIRVBKCEDQgAhE0IAIRRCACEQQgAhEUIAIRIDQCACQZAEaiACQfAPaiADaikDACIXQgAgGUIAEMkDIAJBoARqIBdCACAWQgAQyQMgAkGwBGogF0IAIBhCABDJAyACQcAEaiAXQgAgGkIAEMkDIAJB0ARqIBdCACAcQgAQyQMgAkHgBGogF0IAIB9CABDJAyACQYAEaiACKQOQBCIbIBJ8IhdCAEIAQv3/8//P///5iX8QyQMgAkHwA2ogAikDiAQiEkIAQqvV/v///7//uX9CABDJAyACQeADaiASQgBC///Piuv//9UeQgAQyQMgAkHQA2ogEkIAQqTsw7WP1LSY5wBCABDJAyACQcADaiASQgBCv6WUnM/w0rvkAEIAEMkDIAJBsANqIBJCAELX2a6a5PbpjcsAQgAQyQMgAkGgA2ogEkIAQprN/8ujvcSAGkIAEMkDIAIpA6gDIAIpA+AEIh4gFXwiFSACKQPYBCATIAIpA9AEIhN8IhIgE1StfCASIBIgAikDyAQgFCACKQPABCIUfCITIBRUrXwgEyACKQO4BCACKQOwBCIUIBB8IhAgFFStfCAQIBAgAikDqAQgAikDoAQiFCARfCIRIBRUrXwgESACKQOYBCAXIBtUrXx8IiMgEVStfHwiEFatfHwiESATVK18fCISVq18fCIbIAIpA6ADfCITIBtUrXwgEyATIAIpA7gDIBIgAikDsAN8IhQgElStfCAUIBQgAikDyAMgESACKQPAA3wiHSARVK18IB0gAikD2AMgECAQIAIpA9ADfCIQVq18IBAgAikD6AMgAikD4AMiESAjfCISIBFUrXwgEiASIAIpA/gDIAIpA/ADIhEgF3wgEVStfHwiElatfHwiESAQVK18fCIQIB1UrXx8IhRWrXx8IhNWrXwgFSAbVq0gAikD6AQgFSAeVK18fHwhFSADQQhrIgNBeEcNAAsgAgJ+AkACQCAVQprN/8ujvcSAGlYNACAVQprN/8ujvcSAGlIEQCARIRYgECEYIBQhGiATIRwgFSEfIBIMAwsgE0LX2a6a5PbpjcsAVg0AQprN/8ujvcSAGiEfIBNC19mumuT26Y3LAFIEQCARIRYgECEYIBQhGiATIRwgEgwDCyAUQr+llJzP8NK75ABWDQBC19mumuT26Y3LACEcIBRCv6WUnM/w0rvkAFIEQCARIRYgECEYIBQhGiASDAMLIBBCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIRogEEKk7MO1j9S0mOcAUgRAIBEhFiAQIRggEgwDCyARQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIRggEUL//8+K6///1R5SIBJCqtX+////v/+5f1hyDQELIBFC///Piuv//9UefSIYIBJCq9X+////v/+5f1StIhl9IRYgEEKk7MO1j9S0mOcAfSIaIBFC///Piuv//9UeVCAYIBlUcq0iEX0hGCAUQr+llJzP8NK75AB9IhkgEEKk7MO1j9S0mOcAVCARIBpWcq0iEH0hGiATQtfZrprk9umNywB9IhEgFEK/pZScz/DSu+QAVCAQIBlWcq0iEH0hHCAVIBNC19mumuT26Y3LAFQgECARVnKtfUKazf/Lo73EgBp9IR8gEkLVqoGAgIDAgMYAfAwBCyARIRYgEgsiGTcD2A4gAiAWNwPQDiACIBg3A8gOIAIgGjcDwA4gAiAcNwO4DiACIB83A7AOQgAhFUEoIQNCACETQgAhFEIAIRBCACERQgAhEgNAIAJBwAJqIAJB8A9qIANqKQMAIhdCACAhQgAQyQMgAkHQAmogF0IAICJCABDJAyACQeACaiAXQgAgIEIAEMkDIAJB8AJqIBdCACAkQgAQyQMgAkGAA2ogF0IAICVCABDJAyACQZADaiAXQgAgJ0IAEMkDIAJBsAJqIAIpA8ACIhsgEnwiF0IAQgBC/f/z/8////mJfxDJAyACQaACaiACKQO4AiISQgBCq9X+////v/+5f0IAEMkDIAJBkAJqIBJCAEL//8+K6///1R5CABDJAyACQYACaiASQgBCpOzDtY/UtJjnAEIAEMkDIAJB8AFqIBJCAEK/pZScz/DSu+QAQgAQyQMgAkHgAWogEkIAQtfZrprk9umNywBCABDJAyACQdABaiASQgBCms3/y6O9xIAaQgAQyQMgAikD2AEgAikDkAMiHiAVfCIVIAIpA4gDIBMgAikDgAMiE3wiEiATVK18IBIgEiACKQP4AiAUIAIpA/ACIhR8IhMgFFStfCATIAIpA+gCIAIpA+ACIhQgEHwiECAUVK18IBAgECACKQPYAiACKQPQAiIUIBF8IhEgFFStfCARIAIpA8gCIBcgG1StfHwiIyARVK18fCIQVq18fCIRIBNUrXx8IhJWrXx8IhsgAikD0AF8IhMgG1StfCATIBMgAikD6AEgEiACKQPgAXwiFCASVK18IBQgFCACKQP4ASARIAIpA/ABfCIdIBFUrXwgHSACKQOIAiAQIBAgAikDgAJ8IhBWrXwgECACKQOYAiACKQOQAiIRICN8IhIgEVStfCASIBIgAikDqAIgAikDoAIiESAXfCARVK18fCISVq18fCIRIBBUrXx8IhAgHVStfHwiFFatfHwiE1atfCAVIBtWrSACKQOYAyAVIB5UrXx8fCEVIANBCGsiA0F4Rw0ACwJ+AkAgFUKazf/Lo73EgBpWDQAgFUKazf/Lo73EgBpSBEAgESEiIBAhICAUISQgEyElIBUhJyASDAILIBNC19mumuT26Y3LAFYNAEKazf/Lo73EgBohJyATQtfZrprk9umNywBSBEAgESEiIBAhICAUISQgEyElIBIMAgsgFEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhJSAUQr+llJzP8NK75ABSBEAgESEiIBAhICAUISQgEgwCCyAQQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACEkIBBCpOzDtY/UtJjnAFIEQCARISIgECEgIBIMAgsgEUL//8+K6///1R5WDQBCpOzDtY/UtJjnACEgIBFC///Piuv//9UeUSASQqrV/v///7//uX9WcQ0AIBEhIiASDAELIBFC///Piuv//9UefSIXIBJCq9X+////v/+5f1StIht9ISIgEEKk7MO1j9S0mOcAfSIhIBFC///Piuv//9UeVCAXIBtUcq0iEX0hICAUQr+llJzP8NK75AB9IhcgEEKk7MO1j9S0mOcAVCARICFWcq0iEH0hJCATQtfZrprk9umNywB9IhEgFEK/pZScz/DSu+QAVCAQIBdWcq0iEH0hJSAVIBNC19mumuT26Y3LAFQgECARVnKtfUKazf/Lo73EgBp9IScgEkLVqoGAgIDAgMYAfAshIUIAIRFBKCEDQgAhEkIAIRBCACEUQgAhE0IAIRUDQCACQfAAaiACQbAOaiADaikDACIXQgAgL0IAEMkDIAJBgAFqIBdCACAtQgAQyQMgAkGQAWogF0IAIChCABDJAyACQaABaiAXQgAgKkIAEMkDIAJBsAFqIBdCACArQgAQyQMgAkHAAWogF0IAICxCABDJAyACQeAAaiACKQNwIhsgEnwiF0IAQgBC/f/z/8////mJfxDJAyACQdAAaiACKQNoIhJCAEKr1f7///+//7l/QgAQyQMgAkFAayASQgBC///Piuv//9UeQgAQyQMgAkEwaiASQgBCpOzDtY/UtJjnAEIAEMkDIAJBIGogEkIAQr+llJzP8NK75ABCABDJAyACQRBqIBJCAELX2a6a5PbpjcsAQgAQyQMgAiASQgBCms3/y6O9xIAaQgAQyQMgAikDCCACKQPAASIeIBV8IhUgAikDuAEgEyACKQOwASITfCISIBNUrXwgEiASIAIpA6gBIBQgAikDoAEiFHwiEyAUVK18IBMgAikDmAEgAikDkAEiFCAQfCIQIBRUrXwgECAQIAIpA4gBIAIpA4ABIhQgEXwiESAUVK18IBEgAikDeCAXIBtUrXx8IiMgEVStfHwiEFatfHwiESATVK18fCISVq18fCIbIAIpAwB8IhMgG1StfCATIBMgAikDGCASIAIpAxB8IhQgElStfCAUIBQgAikDKCARIAIpAyB8Ih0gEVStfCAdIAIpAzggECAQIAIpAzB8IhBWrXwgECACKQNIIAIpA0AiESAjfCISIBFUrXwgEiASIAIpA1ggAikDUCIRIBd8IBFUrXx8IhJWrXx8IhEgEFStfHwiECAdVK18fCIUVq18fCITVq18IBUgG1atIAIpA8gBIBUgHlStfHx8IRUgA0EIayIDQXhHDQALIAICfgJAIBVCms3/y6O9xIAaVg0AAkAgFUKazf/Lo73EgBpSBEAgFSEsIBMhKyAUISogECEoDAELIBNC19mumuT26Y3LAFYNAUKazf/Lo73EgBohLCATQtfZrprk9umNywBSBEAgEyErIBQhKiAQISgMAQsgFEK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhKyAUQr+llJzP8NK75ABSBEAgFCEqIBAhKAwBCyAQQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEqIBBCpOzDtY/UtJjnAFIEQCAQISgMAQsgEUL//8+K6///1R5WDQFCpOzDtY/UtJjnACEoIBFC///Piuv//9UeUg0AIBJCqtX+////v/+5f1YNAQsgESEtIBIMAQsgEUL//8+K6///1R59IhcgEkKr1f7///+//7l/VK0iG30hLSAQQqTsw7WP1LSY5wB9Ih0gEUL//8+K6///1R5UIBcgG1RyrSIRfSEoIBRCv6WUnM/w0rvkAH0iFyAQQqTsw7WP1LSY5wBUIBEgHVZyrSIQfSEqIBNC19mumuT26Y3LAH0iESAUQr+llJzP8NK75ABUIBAgF1ZyrSIQfSErIBUgE0LX2a6a5PbpjcsAVCAQIBFWcq19QprN/8ujvcSAGn0hLCASQtWqgYCAgMCAxgB8CyIvNwO4DyACIC03A7APIAIgKDcDqA8gAiAqNwOgDyACICs3A5gPIAIgLDcDkA8gAkGQD2pB+NPBAEEwEPEDDQALCyACICI3A4APIAIgITcDiA8gAiAgNwP4DiACICQ3A/AOIAIgJTcD6A4gAiAnNwPgDgJAIAJB4A5qQYjSwQBBMBDxA0UEQCAlIREgJCESICAhFSAiIRMMAQtC///Piuv//9UeICJ9IhIgIUKr1f7///+//7l/Vq0iEH0hE0Kk7MO1j9S0mOcAICB9IhEgECASViAiQv//z4rr///VHlZyrSISfSEVQr+llJzP8NK75AAgJH0iECARIBJUICBCpOzDtY/UtJjnAFZyrSIRfSESQtfZrprk9umNywAgJX0iFCAQIBFUICRCv6WUnM/w0rvkAFZyrSIQfSERQprN/8ujvcSAGiAQIBRWICVC19mumuT26Y3LAFZyrSAnfH0hJ0Kr1f7///+//7l/ICF9ISELIAAgAikD4A43AwggACAhNwNgIAAgEzcDWCAAIBU3A1AgACASNwNIIAAgETcDQCAAICc3AzggAEEwaiACQYgPaikDADcDACAAQShqIAJBgA9qKQMANwMAIABBIGogAkH4DmopAwA3AwAgAEEYaiACQfAOaikDADcDACAAQRBqIAJB6A5qKQMANwMAIABCATcDAAsgAkGgEGokAAvTSQI3fwd+IwBB0BtrIgUkACAFQQw2AgQgBSACNgLAEgJAAkACQAJAAkACQAJAAkACQCACQQxGBEAgBSAENgLAEiACIARHDQECQAJAAkACQAJAAkACQCACQQJrDgsBAAAAAgAAAAAAAwALIAVBADYC2BggBUEBNgLMGCAFQYiJwAA2AsgYIAVCBDcC0BggBUHIGGpBnIzAABCoBAALQdHOxQAtAAAaQcAAQQgQ1gQiAg0CDAwLQdHOxQAtAAAaQcABQQgQ1gQiAg0CDAwLQdHOxQAtAAAaQYADQQgQ1gQiAg0CDAwLIAIgASkDACI8NwMAIAIgASkDICI9NwMgIAVBKGogPTcDACACQRhqIAFBGGopAwAiPTcDACACQRBqIAFBEGopAwAiPjcDACACQQhqIAFBCGopAwAiPzcDACACQShqIAFBKGopAwAiQDcDACACQTBqIAFBMGopAwAiQTcDACACQThqIAFBOGopAwAiQjcDACAFQRhqID43AwAgBUEgaiA9NwMAIAVBMGogQDcDACAFQThqIEE3AwAgBUFAayBCNwMAIAUgPzcDECACQcAAEN8EQdHOxQAtAAAaIAUgPDcDCEHAAEEIENYEIgFFDQkgASADKQMAIjw3AwAgASADKQMgIj03AyAgBUHoAGogPTcDACABQRhqIANBGGopAwAiPTcDACABQRBqIANBEGopAwAiPjcDACABQQhqIANBCGopAwAiPzcDACABQShqIANBKGopAwAiQDcDACABQTBqIANBMGopAwAiQTcDACABQThqIANBOGopAwAiQjcDACAFQdgAaiA+NwMAIAVB4ABqID03AwAgBUHwAGogQDcDACAFQfgAaiBBNwMAIAVBgAFqIEI3AwAgBSA/NwNQIAFBwAAQ3wQgBSA8NwNIIAVByBhqIgEgBUEIaiAFQcgAahCRAyAFKQPYGCE8IAUpA9AYIT0gBSgCyBhBAUYNBCAFQcABaiAFQYgZaikDADcDACAFQbgBaiAFQYAZaikDADcDACAFQbABaiAFQfgYaikDADcDACAFQagBaiAFQfAYaikDADcDACAFQaABaiAFQegYaikDADcDACAFIAUpA+AYNwOYASAFIDw3A5ABIAUgPTcDiAEgASAFQYgBahCvAyAFKALMGCEBIAUoAsgYIQIgBSgC0BgiA0ECRw0FIAVBkAZqIAFBEGopAwA3AwAgBUGYBmogAUEYaikDADcDACAFQaAGaiABQSBqKQMANwMAIAVBqAZqIAFBKGopAwA3AwAgBUGwBmogAUEwaikDADcDACAFQbgGaiABQThqKQMANwMAIAUgASkDCDcDiAYgASgCBCEDIAEoAgAhBCACBEAgASACQQV0EN8EC0HRzsUALQAAGkHAAEEIENYEIgFFDQkgASADNgIEIAEgBDYCACABIAUpA4gGNwMIIAEgBSkDoAY3AyAgAEECNgIIIAAgATYCBCAAQQI2AgAgAUEQaiAFQZAGaikDADcDACABQRhqIAVBmAZqKQMANwMAIAFBKGogBUGoBmopAwA3AwAgAUEwaiAFQbAGaikDADcDACABQThqIAVBuAZqKQMANwMADAgLIAIgASkDADcDACACIAEpAyA3AyAgAiABKQNANwNAIAJBGGogAUEYaikDADcDACACQRBqIAFBEGopAwA3AwAgAkEIaiIEIAFBCGopAwA3AwAgAkEoaiABQShqKQMANwMAIAJBMGogAUEwaikDADcDACACQThqIAFBOGopAwA3AwAgAkHIAGogAUHIAGopAwA3AwAgAkHQAGogAUHQAGopAwA3AwAgAkHYAGogAUHYAGopAwA3AwAgAkH4AGogAUH4AGopAwA3AwAgAkHwAGogAUHwAGopAwA3AwAgAkHoAGogAUHoAGopAwA3AwAgAiABKQNgNwNgIAIgASkDgAE3A4ABIAJBiAFqIAFBiAFqKQMANwMAIAJBkAFqIAFBkAFqKQMANwMAIAJBmAFqIAFBmAFqKQMANwMAIAIgASkDoAE3A6ABIAJBqAFqIAFBqAFqKQMANwMAIAJBsAFqIAFBsAFqKQMANwMAIAJBuAFqIAFBuAFqKQMANwMAIAIpAwAhPCAFQcgYaiIRIARBuAH8CgAAIAJBwAEQ3wQgBUHoBmogBUHoGGopAwA3AwAgBUHwBmogBUHwGGopAwA3AwAgBUH4BmogBUH4GGopAwA3AwAgBUHQFWoiEiICIAVBiBlqKQMANwMAIAVB2BVqIgEgBUGQGWopAwA3AwAgBUHgFWoiBCAFQZgZaikDADcDACAFQegVaiIHIAUpA6AZNwMAIAVB8BVqIgggBUGoGWopAwA3AwAgBUH4FWoiCSAFQbAZaikDADcDACAFQYAWaiIKIAVBuBlqKQMANwMAIAUgBSkD4Bg3A+AGIAUgBSkDgBk3A8gVIAVB2BJqIgsgBUHYGWopAwA3AwAgBUHQEmoiDCAFQdAZaikDADcDACAFQcgSaiINIAVByBlqKQMANwMAIAVB4BJqIg4gBSkD4Bk3AwAgBUHoEmoiBiAFQegZaikDADcDACAFQfASaiIPIAVB8BlqKQMANwMAIAVB+BJqIhAgBUH4GWopAwA3AwAgBUHQBmogBUHQGGopAwA3AwAgBUHYBmogBUHYGGopAwA3AwAgBSAFKQPAGTcDwBIgBSAFKQPIGDcDyAYgBUG4B2ogCikDADcDACAFQbAHaiAJKQMANwMAIAVBqAdqIAgpAwA3AwAgBUGgB2ogBykDADcDACAFQZgHaiAEKQMANwMAIAVBkAdqIAEpAwA3AwAgBUGIB2ogAikDADcDACAFQfgHaiAQKQMANwMAIAVB8AdqIA8pAwA3AwAgBUHoB2ogBikDADcDACAFQeAHaiAOKQMANwMAIAVB2AdqIAspAwA3AwAgBUHQB2ogDCkDADcDACAFQcgHaiANKQMANwMAIAUgPDcDwAYgBSAFKQPIFTcDgAcgBSAFKQPAEjcDwAdB0c7FAC0AABpBwAFBCBDWBCICRQ0JIAIgAykDADcDACACIAMpAyA3AyAgAiADKQNANwNAIAJBGGogA0EYaikDADcDACACQRBqIANBEGopAwA3AwAgAkEIaiITIANBCGopAwA3AwAgAkEoaiADQShqKQMANwMAIAJBMGogA0EwaikDADcDACACQThqIANBOGopAwA3AwAgAkHIAGogA0HIAGopAwA3AwAgAkHQAGogA0HQAGopAwA3AwAgAkHYAGogA0HYAGopAwA3AwAgAkH4AGogA0H4AGopAwA3AwAgAkHwAGogA0HwAGopAwA3AwAgAkHoAGogA0HoAGopAwA3AwAgAiADKQNgNwNgIAIgAykDgAE3A4ABIAJBiAFqIANBiAFqKQMANwMAIAJBkAFqIANBkAFqKQMANwMAIAJBmAFqIANBmAFqKQMANwMAIAIgAykDoAE3A6ABIAJBqAFqIANBqAFqKQMANwMAIAJBsAFqIANBsAFqKQMANwMAIAJBuAFqIANBuAFqKQMANwMAIAIpAwAhPCARIBNBuAH8CgAAIAJBwAEQ3wQgBUGoCGogBUHoGGopAwA3AwAgBUGwCGogBUHwGGopAwA3AwAgBUG4CGogBUH4GGopAwA3AwAgEiAFQYgZaikDADcDACABIAVBkBlqKQMANwMAIAQgBUGYGWopAwA3AwAgByAFKQOgGTcDACAIIAVBqBlqKQMANwMAIAkgBUGwGWopAwA3AwAgCiAFQbgZaikDADcDACAFIAUpA+AYNwOgCCAFIAUpA4AZNwPIFSALIAVB2BlqKQMANwMAIAwgBUHQGWopAwA3AwAgDSAFQcgZaikDADcDACAOIAUpA+AZNwMAIAYgBUHoGWopAwA3AwAgDyAFQfAZaikDADcDACAQIAVB+BlqKQMANwMAIAVBkAhqIAVB0BhqKQMANwMAIAVBmAhqIAVB2BhqKQMANwMAIAUgBSkDwBk3A8ASIAUgBSkDyBg3A4gIIAVB+AhqIAopAwA3AwAgBUHwCGogCSkDADcDACAFQegIaiAIKQMANwMAIAVB4AhqIAcpAwA3AwAgBUHYCGogBCkDADcDACAFQdAIaiABKQMANwMAIAVByAhqIBIpAwA3AwAgBUG4CWogECkDADcDACAFQbAJaiAPKQMANwMAIAVBqAlqIAYpAwA3AwAgBUGgCWogDikDADcDACAFQZgJaiALKQMANwMAIAVBkAlqIAwpAwA3AwAgBUGICWogDSkDADcDACAFIDw3A4AIIAUgBSkDyBU3A8AIIAUgBSkDwBI3A4AJIBEgBUGACGoQYyAFKALIGEEBRg0FIAUpA9AYITwgBSkD2BghPSABIAVB4BhqQbAB/AoAACAFID03A9AVIAUgPDcDyBUgBUHIEmogBUHABmogBUHIFWoQ6wEgBSkDyBIhPCAFKQPQEiE9IAVB2AFqIAVB2BJqQbAB/AoAACAFID03A9ABIAUgPDcDyAEgBUHIGGogBUHIAWoQhQFB0c7FAC0AABpBwAFBCBDWBCIBRQ0JIAEgBSkDyBg3AwAgASAFKQPoGDcDICABIAUpA4gZNwNAIAFBGGogBUHgGGopAwA3AwAgAUEQaiAFQdgYaikDADcDACABQQhqIAVB0BhqKQMANwMAIAFBKGogBUHwGGopAwA3AwAgAUEwaiAFQfgYaikDADcDACABQThqIAVBgBlqKQMANwMAIAFByABqIAVBkBlqKQMANwMAIAFB0ABqIAVBmBlqKQMANwMAIAFB2ABqIAVBoBlqKQMANwMAIAFB+ABqIAVBwBlqKQMANwMAIAFB8ABqIAVBuBlqKQMANwMAIAFB6ABqIAVBsBlqKQMANwMAIAEgBSkDqBk3A2AgAUGYAWogBUHgGWopAwA3AwAgAUGQAWogBUHYGWopAwA3AwAgAUGIAWogBUHQGWopAwA3AwAgASAFKQPIGTcDgAEgAUG4AWogBUGAGmopAwA3AwAgAUGwAWogBUH4GWopAwA3AwAgAUGoAWogBUHwGWopAwA3AwAgASAFKQPoGTcDoAEgAEEGNgIIIAAgATYCBCAAQQY2AgAMBwsgAiABKQMANwMAIAIgASkDIDcDICACIAEpA0A3A0AgAkEYaiABQRhqKQMANwMAIAJBEGogAUEQaikDADcDACACQQhqIgQgAUEIaikDADcDACACQShqIAFBKGopAwA3AwAgAkEwaiABQTBqKQMANwMAIAJBOGogAUE4aikDADcDACACQcgAaiABQcgAaikDADcDACACQdAAaiABQdAAaikDADcDACACQdgAaiABQdgAaikDADcDACACQfgAaiABQfgAaikDADcDACACQfAAaiABQfAAaikDADcDACACQegAaiABQegAaikDADcDACACIAEpA2A3A2AgAiABKQOAATcDgAEgAkGIAWogAUGIAWopAwA3AwAgAkGQAWogAUGQAWopAwA3AwAgAkGYAWogAUGYAWopAwA3AwAgAiABKQOgATcDoAEgAkGoAWogAUGoAWopAwA3AwAgAkGwAWogAUGwAWopAwA3AwAgAkG4AWogAUG4AWopAwA3AwAgAkHYAWogAUHYAWopAwA3AwAgAkHQAWogAUHQAWopAwA3AwAgAkHIAWogAUHIAWopAwA3AwAgAiABKQPAATcDwAEgAkH4AWogAUH4AWopAwA3AwAgAkHwAWogAUHwAWopAwA3AwAgAkHoAWogAUHoAWopAwA3AwAgAiABKQPgATcD4AEgAkGYAmogAUGYAmopAwA3AwAgAkGQAmogAUGQAmopAwA3AwAgAkGIAmogAUGIAmopAwA3AwAgAiABKQOAAjcDgAIgAkG4AmogAUG4AmopAwA3AwAgAkGwAmogAUGwAmopAwA3AwAgAkGoAmogAUGoAmopAwA3AwAgAiABKQOgAjcDoAIgAkHYAmogAUHYAmopAwA3AwAgAkHQAmogAUHQAmopAwA3AwAgAkHIAmogAUHIAmopAwA3AwAgAiABKQPAAjcDwAIgAkH4AmogAUH4AmopAwA3AwAgAkHwAmogAUHwAmopAwA3AwAgAkHoAmogAUHoAmopAwA3AwAgAiABKQPgAjcD4AIgAikDACE8IAVByBhqIiYgBEH4AvwKAAAgAkGAAxDfBCAFQegJaiAFQegYaikDADcDACAFQfAJaiAFQfAYaikDADcDACAFQfgJaiAFQfgYaikDADcDACAFQcgMaiIBIAVBiBlqKQMANwMAIAVB0AxqIhUgBUGQGWopAwA3AwAgBUHYDGoiFCAFQZgZaikDADcDACAFQeAMaiIWIAUpA6AZNwMAIAVB6AxqIhcgBUGoGWopAwA3AwAgBUHwDGoiGCAFQbAZaikDADcDACAFQfgMaiIZIAVBuBlqKQMANwMAIAUgBSkD4Bg3A+AJIAUgBSkDgBk3A8AMIAVBmA1qIhogBUHYGWopAwA3AwAgBUGQDWoiGyAFQdAZaikDADcDACAFQYgNaiIcIAVByBlqKQMANwMAIAVBoA1qIh0gBSkD4Bk3AwAgBUGoDWoiHiAFQegZaikDADcDACAFQbANaiIfIAVB8BlqKQMANwMAIAVBuA1qIiAgBUH4GWopAwA3AwAgBUHQCWogBUHQGGopAwA3AwAgBUHYCWogBUHYGGopAwA3AwAgBSAFKQPAGTcDgA0gBSAFKQPIGDcDyAkgBUGIEmoiAiAFQcgaaikDADcDACAFQZASaiIEIAVB0BpqKQMANwMAIAVBmBJqIgcgBUHYGmopAwA3AwAgBUH4EWoiESAFQbgaaikDADcDACAFQfARaiISIAVBsBpqKQMANwMAIAVB6BFqIgggBUGoGmopAwA3AwAgBUHgEWoiCSAFKQOgGjcDACAFIAUpA8AaNwOAEiAFQaASaiIKIAUpA+AaNwMAIAVBqBJqIgsgBUHoGmopAwA3AwAgBUGwEmoiDCAFQfAaaikDADcDACAFQbgSaiINIAVB+BpqKQMANwMAIAVB4BVqIg4gBUGYG2opAwA3AwAgBUHYFWoiBiAFQZAbaikDADcDACAFQdAVaiIPIAVBiBtqKQMANwMAIAUgBSkDgBs3A8gVIAVBgBZqIhAgBUG4G2opAwA3AwAgBUH4FWoiEyAFQbAbaikDADcDACAFQfAVaiIhIAVBqBtqKQMANwMAIAVB6BVqIiIgBSkDoBs3AwAgBUHYEWoiIyAFQZgaaikDADcDACAFQdARaiIkIAVBkBpqKQMANwMAIAVByBFqIiUgBUGIGmopAwA3AwAgBSAFKQOAGjcDwBEgBUH4EmoiJyARKQMANwMAIAVB8BJqIiggEikDADcDACAFQegSaiIpIAgpAwA3AwAgBUHgEmoiKiAJKQMANwMAIAVB2BJqIisgIykDADcDACAFQdASaiIsICQpAwA3AwAgBUHIEmoiLSAlKQMANwMAIAUgBSkDwBE3A8ASIAVBuBNqIi4gDSkDADcDACAFQbATaiIvIAwpAwA3AwAgBUGoE2oiMCALKQMANwMAIAVBoBNqIjEgCikDADcDACAFQZgTaiIyIAcpAwA3AwAgBUGQE2oiMyAEKQMANwMAIAVBiBNqIjQgAikDADcDACAFIAUpA4ASNwOAEyAFQfgTaiI1IBApAwA3AwAgBUHwE2oiNiATKQMANwMAIAVB6BNqIjcgISkDADcDACAFQeATaiI4ICIpAwA3AwAgBUHYE2oiOSAOKQMANwMAIAVB0BNqIjogBikDADcDACAFQcgTaiI7IA8pAwA3AwAgBSAFKQPIFTcDwBMgBSA8NwPACSAFQbgKaiAZKQMANwMAIAVBsApqIBgpAwA3AwAgBUGoCmogFykDADcDACAFQaAKaiAWKQMANwMAIAVBmApqIBQpAwA3AwAgBUGQCmogFSkDADcDACAFQYgKaiABKQMANwMAIAUgBSkDwAw3A4AKIAVB+ApqICApAwA3AwAgBUHwCmogHykDADcDACAFQegKaiAeKQMANwMAIAVB4ApqIB0pAwA3AwAgBUHYCmogGikDADcDACAFQdAKaiAbKQMANwMAIAVByApqIBwpAwA3AwAgBSAFKQOADTcDwAogBUGAC2ogBUHAEmoiFUHAAfwKAABB0c7FAC0AABpBgANBCBDWBCIBRQ0JIAEgAykDADcDACABIAMpAyA3AyAgASADKQNANwNAIAFBGGogA0EYaikDADcDACABQRBqIANBEGopAwA3AwAgAUEIaiIUIANBCGopAwA3AwAgAUEoaiADQShqKQMANwMAIAFBMGogA0EwaikDADcDACABQThqIANBOGopAwA3AwAgAUHIAGogA0HIAGopAwA3AwAgAUHQAGogA0HQAGopAwA3AwAgAUHYAGogA0HYAGopAwA3AwAgAUH4AGogA0H4AGopAwA3AwAgAUHwAGogA0HwAGopAwA3AwAgAUHoAGogA0HoAGopAwA3AwAgASADKQNgNwNgIAEgAykDgAE3A4ABIAFBiAFqIANBiAFqKQMANwMAIAFBkAFqIANBkAFqKQMANwMAIAFBmAFqIANBmAFqKQMANwMAIAEgAykDoAE3A6ABIAFBqAFqIANBqAFqKQMANwMAIAFBsAFqIANBsAFqKQMANwMAIAFBuAFqIANBuAFqKQMANwMAIAFB2AFqIANB2AFqKQMANwMAIAFB0AFqIANB0AFqKQMANwMAIAFByAFqIANByAFqKQMANwMAIAEgAykDwAE3A8ABIAFB+AFqIANB+AFqKQMANwMAIAFB8AFqIANB8AFqKQMANwMAIAFB6AFqIANB6AFqKQMANwMAIAEgAykD4AE3A+ABIAFBmAJqIANBmAJqKQMANwMAIAFBkAJqIANBkAJqKQMANwMAIAFBiAJqIANBiAJqKQMANwMAIAEgAykDgAI3A4ACIAFBuAJqIANBuAJqKQMANwMAIAFBsAJqIANBsAJqKQMANwMAIAFBqAJqIANBqAJqKQMANwMAIAEgAykDoAI3A6ACIAFB2AJqIANB2AJqKQMANwMAIAFB0AJqIANB0AJqKQMANwMAIAFByAJqIANByAJqKQMANwMAIAEgAykDwAI3A8ACIAFB+AJqIANB+AJqKQMANwMAIAFB8AJqIANB8AJqKQMANwMAIAFB6AJqIANB6AJqKQMANwMAIAEgAykD4AI3A+ACIAEpAwAhPCAmIBRB+AL8CgAAIAFBgAMQ3wQgBUHoDWogBUHoGGopAwA3AwAgBUHwDWogBUHwGGopAwA3AwAgBUH4DWogBUH4GGopAwA3AwAgBUHIEGoiASAFQYgZaikDADcDACAFQdAQaiIDIAVBkBlqKQMANwMAIAVB2BBqIhQgBUGYGWopAwA3AwAgBUHgEGoiFiAFKQOgGTcDACAFQegQaiIXIAVBqBlqKQMANwMAIAVB8BBqIhggBUGwGWopAwA3AwAgBUH4EGoiGSAFQbgZaikDADcDACAFIAUpA+AYNwPgDSAFIAUpA4AZNwPAECAFQZgRaiIaIAVB2BlqKQMANwMAIAVBkBFqIhsgBUHQGWopAwA3AwAgBUGIEWoiHCAFQcgZaikDADcDACAFQaARaiIdIAUpA+AZNwMAIAVBqBFqIh4gBUHoGWopAwA3AwAgBUGwEWoiHyAFQfAZaikDADcDACAFQbgRaiIgIAVB+BlqKQMANwMAIAVB0A1qIAVB0BhqKQMANwMAIAVB2A1qIAVB2BhqKQMANwMAIAUgBSkDwBk3A4ARIAUgBSkDyBg3A8gNIAIgBUHIGmopAwA3AwAgBCAFQdAaaikDADcDACAHIAVB2BpqKQMANwMAIBEgBUG4GmopAwA3AwAgEiAFQbAaaikDADcDACAIIAVBqBpqKQMANwMAIAkgBSkDoBo3AwAgBSAFKQPAGjcDgBIgCiAFKQPgGjcDACALIAVB6BpqKQMANwMAIAwgBUHwGmopAwA3AwAgDSAFQfgaaikDADcDACAOIAVBmBtqKQMANwMAIAYgBUGQG2opAwA3AwAgDyAFQYgbaikDADcDACAFIAUpA4AbNwPIFSAQIAVBuBtqKQMANwMAIBMgBUGwG2opAwA3AwAgISAFQagbaikDADcDACAiIAUpA6AbNwMAICMgBUGYGmopAwA3AwAgJCAFQZAaaikDADcDACAlIAVBiBpqKQMANwMAIAUgBSkDgBo3A8ARICcgESkDADcDACAoIBIpAwA3AwAgKSAIKQMANwMAICogCSkDADcDACArICMpAwA3AwAgLCAkKQMANwMAIC0gJSkDADcDACAFIAUpA8ARNwPAEiAuIA0pAwA3AwAgLyAMKQMANwMAIDAgCykDADcDACAxIAopAwA3AwAgMiAHKQMANwMAIDMgBCkDADcDACA0IAIpAwA3AwAgBSAFKQOAEjcDgBMgNSAQKQMANwMAIDYgEykDADcDACA3ICEpAwA3AwAgOCAiKQMANwMAIDkgDikDADcDACA6IAYpAwA3AwAgOyAPKQMANwMAIAUgBSkDyBU3A8ATIAUgPDcDwA0gBUG4DmogGSkDADcDACAFQbAOaiAYKQMANwMAIAVBqA5qIBcpAwA3AwAgBUGgDmogFikDADcDACAFQZgOaiAUKQMANwMAIAVBkA5qIAMpAwA3AwAgBUGIDmogASkDADcDACAFIAUpA8AQNwOADiAFQfgOaiAgKQMANwMAIAVB8A5qIB8pAwA3AwAgBUHoDmogHikDADcDACAFQeAOaiAdKQMANwMAIAVB2A5qIBopAwA3AwAgBUHQDmogGykDADcDACAFQcgOaiAcKQMANwMAIAUgBSkDgBE3A8AOIAVBgA9qIBVBwAH8CgAAICYgBUHADWoQ+QEgBSgCyBhBAUYNBSAFKQPQGCE8IAUpA9gYIT0gBiAFQeAYakHwAvwKAAAgBSA9NwPQFSAFIDw3A8gVIAVByBJqIAVBwAlqIAVByBVqEPYBIAUpA8gSITwgBSkD0BIhPSAFQZgDaiAFQdgSakHwAvwKAAAgBSA9NwOQAyAFIDw3A4gDIAVByBhqIAVBiANqEOgBQdHOxQAtAAAaQYADQQgQ1gQiAUUNCSABIAUpA8gYNwMAIAEgBSkD6Bg3AyAgASAFKQOIGTcDQCABQRhqIAVB4BhqKQMANwMAIAFBEGogBUHYGGopAwA3AwAgAUEIaiAFQdAYaikDADcDACABQShqIAVB8BhqKQMANwMAIAFBMGogBUH4GGopAwA3AwAgAUE4aiAFQYAZaikDADcDACABQcgAaiAFQZAZaikDADcDACABQdAAaiAFQZgZaikDADcDACABQdgAaiAFQaAZaikDADcDACABQfgAaiAFQcAZaikDADcDACABQfAAaiAFQbgZaikDADcDACABQegAaiAFQbAZaikDADcDACABIAUpA6gZNwNgIAFBmAFqIAVB4BlqKQMANwMAIAFBkAFqIAVB2BlqKQMANwMAIAFBiAFqIAVB0BlqKQMANwMAIAEgBSkDyBk3A4ABIAFBuAFqIAVBgBpqKQMANwMAIAFBsAFqIAVB+BlqKQMANwMAIAFBqAFqIAVB8BlqKQMANwMAIAEgBSkD6Bk3A6ABIAFB2AFqIAVBoBpqKQMANwMAIAFB0AFqIAVBmBpqKQMANwMAIAFByAFqIAVBkBpqKQMANwMAIAEgBSkDiBo3A8ABIAFB+AFqIAVBwBpqKQMANwMAIAFB8AFqIAVBuBpqKQMANwMAIAFB6AFqIAVBsBpqKQMANwMAIAEgBSkDqBo3A+ABIAFBmAJqIAVB4BpqKQMANwMAIAFBkAJqIAVB2BpqKQMANwMAIAFBiAJqIAVB0BpqKQMANwMAIAEgBSkDyBo3A4ACIAFBuAJqIAVBgBtqKQMANwMAIAFBsAJqIAVB+BpqKQMANwMAIAFBqAJqIAVB8BpqKQMANwMAIAEgBSkD6Bo3A6ACIAFB2AJqIAVBoBtqKQMANwMAIAFB0AJqIAVBmBtqKQMANwMAIAFByAJqIAVBkBtqKQMANwMAIAEgBSkDiBs3A8ACIAFB+AJqIAVBwBtqKQMANwMAIAFB8AJqIAVBuBtqKQMANwMAIAFB6AJqIAVBsBtqKQMANwMAIAEgBSkDqBs3A+ACIABBDDYCCCAAIAE2AgQgAEEMNgIADAYLIAVBADYCyBggBUHAEmogBUEEaiAFQcgYakG8i8AAEJcEAAsgBUEANgLIGCAFQcASaiAFQQRqIAVByBhqQcyLwAAQlwQACyAFIDw3A9AYIAUgPTcDyBhBgIvAAEErIAVByBhqQdyLwABB7IvAABDKAwALIAUgAzYC0BggBSABNgLMGCAFIAI2AsgYQYCLwABBKyAFQcgYakHwisAAQaSNwAAQygMACyAFQgA3A8gYQYCLwABBKyAFQcgYakHci8AAQfyLwAAQygMACyAFQgA3A8gYQYCLwABBKyAFQcgYakHci8AAQYyMwAAQygMACyAFQdAbaiQADwtBCEHAAEG4hcAAEMgEAAtBCEHAAUG4hcAAEMgEAAtBCEGAA0G4hcAAEMgEAAvKVQILfx5+IwBBsBFrIgMkACADQZgQakIANwMAIANBkBBqQgA3AwAgA0GIEGpCADcDACADQYAQakIANwMAIANB+A9qQgA3AwAgA0IANwPwDyADQcAQakIANwMAIANBuBBqQgA3AwAgA0GwEGpCADcDACADQagQakIANwMAIANCADcDoBAgA0IBNwPIEAJAAkAgAiADQfAPaiIEQTAQ8QMEQCACIANBoBBqQTAQ8QNFDQEgAikDCCEaIAIpAxAhGCACKQMYIRwgAikDICESIAIpAwAhFiABKQMoIR0gASkDICEVIAEpAxghDiABKQMQIRcgASkDCCEZIAEpAwAhHiACKQMoISMgA0GgEWoiCEIANwMAIANBmBFqIglCADcDACADQZARaiIKQgA3AwAgA0GIEWoiC0IANwMAIANCADcDgBEgAyAjQgGDNwOoESADQYARaiAEQTAQ8QNFBEADQCAWIRsgA0HwDmogFUIAIB1CABDJAyADQdAOaiAOQgAgHUIAEMkDIANBoA5qIBdCACAdQgAQyQMgA0HgDWogGUIAIB1CABDJAyADQZANaiAeQgAgHUIAEMkDIANBwA5qIA5CACAVQgAQyQMgA0GQDmogF0IAIBVCABDJAyADQdANaiAZQgAgFUIAEMkDIANBgA1qIB5CACAVQgAQyQMgA0GADmogF0IAIA5CABDJAyADQcANaiAZQgAgDkIAEMkDIANB8AxqIB5CACAOQgAQyQMgA0GwDWogGUIAIBdCABDJAyADQeAMaiAeQgAgF0IAEMkDIANB0AxqIB5CACAZQgAQyQMgA0HgD2ogHUIAIB1CABDJAyADQeAOaiAVQgAgFUIAEMkDIANBsA5qIA5CACAOQgAQyQMgA0HwDWogF0IAIBdCABDJAyADQaANaiAZQgAgGUIAEMkDIANBwAxqIB5CACAeQgAQyQMgA0HQD2ogAykD4A8iIUL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIANBwA9qIA5CAEL//8+K6///1R5CABDJAyADQbAPaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANBoA9qIA5CAEK/pZScz/DSu+QAQgAQyQMgA0GQD2ogDkIAQtfZrprk9umNywBCABDJAyADQYAPaiAOQgBCms3/y6O9xIAaQgAQyQMgAykD2AwgAykD6AwgAykDuA0gAykDyA0gAykDiA4gAykDmA4gAykDyA4gAykD2A4gAykD+A4iFSADKQPQDnwiDiAVVK18IhAgAykDoA58IhUgAykDwA58IhcgFVStfCIPIAMpA6gOIBAgFVatfCIQIAMpA+ANfCIUfCIVIA9UrXwgFSAVIAMpA5AOfCIVVq18IhEgAykD6A0gECAUVq18IhkgAykDkA18IhN8IhAgAykD0A18Ig8gAykDgA58IhQgD1StfCIWIA8gEFStIAMpA9gNIBAgEVStfHwiESADKQOYDSATIBlUrXx8IhAgAykDgA18Ihl8Ig8gFlStfCAPIA8gAykDwA18Ig9WrXwiEyAQIBlWrSADKQOIDSAQIBFUrXx8fCIQIAMpA/AMfCIRIAMpA7ANfCIZIBFUrXwiFiAQIBFWrSADKQP4DCAQIBNUrXx8fCIQIBZUrXwgECADKQPgDHwiEyAQVK18IhAgAykD0Ax8IhYgEFStfCIQQj+IIAMpA8gMIAMpA8AMIhEgEEIBhiAWQj+IhHwiHiARVK18IB4gAykDqA0gAykDoA0iESATQgGGIBlCP4iEfCIQIBFUrXwgECAQIAMpA/gNIAMpA/ANIh0gD0IBhiAUQj+IhHwiESAdVK18IBEgAykDuA4gAykDsA4iICAVQgGGIBdCP4iEfCIdICBUrXwgHSAdIAMpA+gOIAMpA+AOIh8gDkIBhiADKQPwDiIkQj+IhHwiICAfVK18ICAgICADKQPoDyIfICRCAYZ8IiQgH1StfCIgVq18Ih8gF0IBhiAOQj+IhHwiJiAfVK18Ih1WrXwiDiAUQgGGIBVCP4iEfCIfIA5UrXwiFSARVK18Ig4gGUIBhiAPQj+IhHwiESAOVK18IhBWrXwiDiAWQgGGIBNCP4iEfCIUIA5UrXwiEyAeVK18fCEWQQAhBQJ/AkAgAykDiA8gAykDmA8gAykDqA8gAykDuA8gAykDyA8gAykD2A8gAykD0A8iDiAhQn2DfCAOVK18IhcgAykDwA98Ig4gF1StfCAOICR8IhcgDlStfCIPIAMpA7APfCIOIA9UrXwgDiAgfCIPIA5UrXwiGSADKQOgD3wiDiAZVK18IA4gJnwiGSAOVK18Ih4gAykDkA98Ig4gHlStfCAOIB18Ih4gDlStfCIdIAMpA4APfCIOIB1UrXwgDiAffCIdIA5UrXwiDlANACAOIBV8IhUgDlQiAUUNACABrSIOIBF8IhEgDloNACAOIBFWrSIOIBB8IhAgDloNACAOIBBWrSIOIBR8IhQgDloNACAOIBRWrSIOIBN8IhMgDloNACAOIBNWrSIOIBZ8IhYgDlQMAQtBAAshDCADQbAMaiAXQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgA0GgDGogDkIAQv//z4rr///VHkIAEMkDIANBkAxqIA5CAEKk7MO1j9S0mOcAQgAQyQMgA0GADGogDkIAQr+llJzP8NK75ABCABDJAyADQfALaiAOQgBC19mumuT26Y3LAEIAEMkDIANB4AtqIA5CAEKazf/Lo73EgBpCABDJAwJAIAMpA+gLIAMpA/gLIAMpA4gMIAMpA5gMIAMpA6gMIAMpA7gMIAMpA7AMIg4gF3wgDlStfCIXIAMpA6AMfCIOIBdUrXwgDiAPfCIXIA5UrXwiDyADKQOQDHwiDiAPVK18IA4gGXwiDyAOVK18IhkgAykDgAx8Ig4gGVStfCAOIB58IhkgDlStfCIeIAMpA/ALfCIOIB5UrXwgDiAdfCIeIA5UrXwiHSADKQPgC3wiDiAdVK18IA4gFXwiHSAOVK18Ig5QDQAgDiARfCIRIA5aDQAgDiARVq0iDiAQfCIQIA5aDQAgDiAQVq0iDiAUfCIUIA5aDQAgDiAUVq0iDiATfCITIA5aDQAgDiATVq0iDiAWfCIWIA5UIQULIANB0AtqIBdC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQcALaiAOQgBC///Piuv//9UeQgAQyQMgA0GwC2ogDkIAQqTsw7WP1LSY5wBCABDJAyADQaALaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBkAtqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0GAC2ogDkIAQprN/8ujvcSAGkIAEMkDQQAhBgJ/QQAgAykDiAsgAykDmAsgAykDqAsgAykDuAsgAykDyAsgAykD2AsgAykD0AsiDiAXfCAOVK18IhUgAykDwAt8Ig4gFVStfCAOIA98IhUgDlStfCIXIAMpA7ALfCIOIBdUrXwgDiAZfCIXIA5UrXwiDyADKQOgC3wiDiAPVK18IA4gHnwiDyAOVK18IhkgAykDkAt8Ig4gGVStfCAOIB18IhkgDlStfCIeIAMpA4ALfCIOIB5UrXwgDiARfCIRIA5UrXwiDlANABpBACAOIA4gEHwiEFgNABpBACAOIBBWrSIOIBR8IhQgDloNABpBACAOIBRWrSIOIBN8IhMgDloNABogDiATVq0iDiAWfCIWIA5UCyEBIANB8ApqIBVC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQeAKaiAOQgBC///Piuv//9UeQgAQyQMgA0HQCmogDkIAQqTsw7WP1LSY5wBCABDJAyADQcAKaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANBsApqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0GgCmogDkIAQprN/8ujvcSAGkIAEMkDAkAgAykDqAogAykDuAogAykDyAogAykD2AogAykD6AogAykD+AogAykD8AoiDiAVfCAOVK18IhUgAykD4Ap8Ig4gFVStfCAOIBd8IhUgDlStfCIXIAMpA9AKfCIOIBdUrXwgDiAPfCIXIA5UrXwiDyADKQPACnwiDiAPVK18IA4gGXwiDyAOVK18IhkgAykDsAp8Ig4gGVStfCAOIBF8IhEgDlStfCIZIAMpA6AKfCIOIBlUrXwgDiAQfCIQIA5UrXwiDlANACAOIBR8IhQgDloNACAOIBRWrSIOIBN8IhMgDloNACAOIBNWrSIOIBZ8IhYgDlQhBgsgA0GQCmogFUL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIANBgApqIA5CAEL//8+K6///1R5CABDJAyADQfAJaiAOQgBCpOzDtY/UtJjnAEIAEMkDIANB4AlqIA5CAEK/pZScz/DSu+QAQgAQyQMgA0HQCWogDkIAQtfZrprk9umNywBCABDJAyADQcAJaiAOQgBCms3/y6O9xIAaQgAQyQNBACEEIAMpA8gJIAMpA9gJIAMpA+gJIAMpA/gJIAMpA4gKIAMpA5gKIAMpA5AKIg4gFXwgDlStfCIVIAMpA4AKfCIOIBVUrXwgDiAXfCIVIA5UrXwiFyADKQPwCXwiDiAXVK18IA4gD3wiFyAOVK18Ig8gAykD4Al8Ig4gD1StfCAOIBF8Ig8gDlStfCIRIAMpA9AJfCIOIBFUrXwgDiAQfCIQIA5UrXwiESADKQPACXwiDiARVK18IA4gFHwiFCAOVK18Ig5QRQRAIA4gE3wiEyAOVCIErSIOIBZ8IhEgFiAEGyEWIAQgDiARVnEhBAsgEiERIANBsAlqIBVC/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyADQaAJaiAOQgBC///Piuv//9UeQgAQyQMgA0GQCWogDkIAQqTsw7WP1LSY5wBCABDJAyADQYAJaiAOQgBCv6WUnM/w0rvkAEIAEMkDIANB8AhqIA5CAELX2a6a5PbpjcsAQgAQyQMgA0HgCGogDkIAQprN/8ujvcSAGkIAEMkDIAMpA+gIIAMpA/gIIAMpA4gJIAMpA5gJIAMpA6gJIAMpA7gJIAMpA7AJIg4gFXwgDlStfCISIAMpA6AJfCIOIBJUrXwgDiAXfCIdIA5UrXwiEiADKQOQCXwiDiASVK18IA4gDiAPfCIOVq18IhUgAykDgAl8IhIgFVStfCASIBAgEnwiElatfCIXIAMpA/AIfCIVIBdUrXwgFCAVfCIQIBVUrXwiFyADKQPgCHwiFSAXVK18IBMgFXwiFCAVVK18IhUgFnwiFyAWIBVCAFIiBxshDwJAAkAgBSAMciABciAGciAEciAVIBdWIgGtIBUgBxtCAFJyIAEgB3EgD0Kazf/Lo73EgBpWcnINACAPQprN/8ujvcSAGlIEQCAOIRUgEiEOIBAhFyAUIRkgDyEeDAILIBRC19mumuT26Y3LAFYNAEKazf/Lo73EgBohHiAUQtfZrprk9umNywBSBEAgDiEVIBIhDiAQIRcgFCEZDAILIBBCv6WUnM/w0rvkAFYEQELX2a6a5PbpjcsAIRQMAQsgEEK/pZScz/DSu+QAUgRAQtfZrprk9umNywAhGSAOIRUgEiEOIBAhFwwCCwJAIBJCpOzDtY/UtJjnAFYNACASQqTsw7WP1LSY5wBSBEBC19mumuT26Y3LACEZQr+llJzP8NK75AAhFyAOIRUgEiEODAMLIA5C///Piuv//9UeVg0AQtfZrprk9umNywAhFEK/pZScz/DSu+QAIRAgDkL//8+K6///1R5RIB1CqtX+////v/+5f1ZxDQEgDiEVIBIhDkK/pZScz/DSu+QAIRdC19mumuT26Y3LACEZDAILQtfZrprk9umNywAhFEK/pZScz/DSu+QAIRALIA5C///Piuv//9UefSIXIB1Cq9X+////v/+5f1StIhl9IRUgEkKk7MO1j9S0mOcAfSITIA5C///Piuv//9UeVCAXIBlUcq0iF30hDiAQQr+llJzP8NK75AB9IhkgEkKk7MO1j9S0mOcAVCATIBdUcq0iEn0hFyAUQtfZrprk9umNywB9IhMgEEK/pZScz/DSu+QAVCASIBlWcq0iEn0hGSAPIBRC19mumuT26Y3LAFQgEiATVnKtfUKazf/Lo73EgBp9IR4gHULVqoGAgIDAgMYAfCEdCyACIBtCAYgiFjcDACACIBxCP4YgEUIBiIQiEjcDICACIBFCP4YgI0IBiIQiIzcDKCACIBhCP4YgHEIBiIQiHDcDGCACIBpCP4YgGEIBiIQiGDcDECACIBtCP4YgGkIBiIQiGjcDCCAIQgA3AwAgCUIANwMAIApCADcDACALQgA3AwAgA0IANwOAESADICNCAYM3A6gRIANBgBFqIANB8A9qQTAQ8QNFDQALCwJAIAIgA0HwD2pBMBDxA0UNACACIBZCAYgiFDcDACACIBJCP4YgI0IBiIQiJDcDKCACIBxCP4YgEkIBiIQiEjcDICACIBhCP4YgHEIBiIQiJjcDGCACIBpCP4YgGEIBiIQiKDcDECACIBZCP4YgGkIBiIQiKTcDCCADIB03A/gQIAMgFTcD8BAgAyAONwPoECADIBc3A+AQIAMgGTcD2BAgAyAeNwPQECACIANB8A9qQTAQ8QNFDQAgAykD0BAhISADKQPYECEPIAMpA+AQIRsgAykD6BAhGiADKQPwECEcIAMpA/gQIR8gA0GgEWohCCADQZgRaiEJIANBkBFqIQogA0GIEWohCwNAIBQhIyADQeAHaiAcQgAgH0IAEMkDIANBwAdqIBpCACAfQgAQyQMgA0GQB2ogG0IAIB9CABDJAyADQdAGaiAPQgAgH0IAEMkDIANBgAZqICFCACAfQgAQyQMgA0GwB2ogGkIAIBxCABDJAyADQYAHaiAbQgAgHEIAEMkDIANBwAZqIA9CACAcQgAQyQMgA0HwBWogIUIAIBxCABDJAyADQfAGaiAbQgAgGkIAEMkDIANBsAZqIA9CACAaQgAQyQMgA0HgBWogIUIAIBpCABDJAyADQaAGaiAPQgAgG0IAEMkDIANB0AVqICFCACAbQgAQyQMgA0HABWogIUIAIA9CABDJAyADQdAIaiAfQgAgH0IAEMkDIANB0AdqIBxCACAcQgAQyQMgA0GgB2ogGkIAIBpCABDJAyADQeAGaiAbQgAgG0IAEMkDIANBkAZqIA9CACAPQgAQyQMgA0GwBWogIUIAICFCABDJAyADQcAIaiADKQPQCCIlQv3/8//P///5iX9+IhBCAEKr1f7///+//7l/QgAQyQMgA0GwCGogEEIAQv//z4rr///VHkIAEMkDIANBoAhqIBBCAEKk7MO1j9S0mOcAQgAQyQMgA0GQCGogEEIAQr+llJzP8NK75ABCABDJAyADQYAIaiAQQgBC19mumuT26Y3LAEIAEMkDIANB8AdqIBBCAEKazf/Lo73EgBpCABDJAyADKQPIBSADKQPYBSADKQOoBiADKQO4BiADKQP4BiADKQOIByADKQO4ByADKQPIByADKQPoByIPIAMpA8AHfCIQIA9UrXwiESADKQOQB3wiDyADKQOwB3wiFCAPVK18IhMgAykDmAcgDyARVK18IhEgAykD0AZ8IhZ8Ig8gE1StfCAPIA8gAykDgAd8Ig9WrXwiGCADKQPYBiARIBZWrXwiGyADKQOABnwiGnwiESADKQPABnwiEyADKQPwBnwiFiATVK18IhwgESATVq0gAykDyAYgESAYVK18fCIYIAMpA4gGIBogG1StfHwiESADKQPwBXwiG3wiEyAcVK18IBMgEyADKQOwBnwiE1atfCIaIBEgG1atIAMpA/gFIBEgGFStfHx8IhEgAykD4AV8IhggAykDoAZ8IhsgGFStfCIcIBEgGFatIAMpA+gFIBEgGlStfHx8IhEgHFStfCARIAMpA9AFfCIYIBFUrXwiESADKQPABXwiGiARVK18IhFCP4ggAykDuAUgAykDsAUiICARQgGGIBpCP4iEfCIcICBUrXwgHCADKQOYBiADKQOQBiIRIBhCAYYgG0I/iIR8IiAgEVStfCAgIAMpA+gGIAMpA+AGIiEgE0IBhiAWQj+IhHwiESAhVK18IBEgAykDqAcgAykDoAciHyAPQgGGIBRCP4iEfCIhIB9UrXwgISADKQPYByADKQPQByIiIBBCAYYgAykD4AciJ0I/iIR8Ih8gIlStfCAfIB8gAykD2AgiIiAnQgGGfCInICJUrXwiH1atfCIiIBRCAYYgEEI/iIR8IiogIlStfCIiICFUrXwiECAWQgGGIA9CP4iEfCIrIBBUrXwiISARVK18IhAgG0IBhiATQj+IhHwiESAQVK18IhAgIFStfCIPIBpCAYYgGEI/iIR8IhQgD1StfCITIBxUrXx8IRZBACEFAn8CQCADKQP4ByADKQOICCADKQOYCCADKQOoCCADKQO4CCADKQPICCADKQPACCIPICVCfYN8IA9UrXwiGCADKQOwCHwiDyAYVK18IA8gJ3wiGCAPVK18IhsgAykDoAh8Ig8gG1StfCAPIB98IhsgD1StfCIaIAMpA5AIfCIPIBpUrXwgDyAqfCIaIA9UrXwiHCADKQOACHwiDyAcVK18IA8gInwiHCAPVK18IiAgAykD8Ad8Ig8gIFStfCAPICt8IiAgD1StfCIPUA0AIA8gIXwiISAPVCIBRQ0AIAGtIg8gEXwiESAPWg0AIA8gEVatIg8gEHwiECAPWg0AIA8gEFatIg8gFHwiFCAPWg0AIA8gFFatIg8gE3wiEyAPWg0AIA8gE1atIg8gFnwiFiAPVAwBC0EACyEMIANBoAVqIBhC/f/z/8////mJf34iD0IAQqvV/v///7//uX9CABDJAyADQZAFaiAPQgBC///Piuv//9UeQgAQyQMgA0GABWogD0IAQqTsw7WP1LSY5wBCABDJAyADQfAEaiAPQgBCv6WUnM/w0rvkAEIAEMkDIANB4ARqIA9CAELX2a6a5PbpjcsAQgAQyQMgA0HQBGogD0IAQprN/8ujvcSAGkIAEMkDAkAgAykD2AQgAykD6AQgAykD+AQgAykDiAUgAykDmAUgAykDqAUgAykDoAUiDyAYfCAPVK18IhggAykDkAV8Ig8gGFStfCAPIBt8IhggD1StfCIbIAMpA4AFfCIPIBtUrXwgDyAafCIbIA9UrXwiGiADKQPwBHwiDyAaVK18IA8gHHwiGiAPVK18IhwgAykD4AR8Ig8gHFStfCAPICB8IhwgD1StfCIgIAMpA9AEfCIPICBUrXwgDyAhfCIgIA9UrXwiD1ANACAPIBF8IhEgD1oNACAPIBFWrSIPIBB8IhAgD1oNACAPIBBWrSIPIBR8IhQgD1oNACAPIBRWrSIPIBN8IhMgD1oNACAPIBNWrSIPIBZ8IhYgD1QhBQsgA0HABGogGEL9//P/z///+Yl/fiIPQgBCq9X+////v/+5f0IAEMkDIANBsARqIA9CAEL//8+K6///1R5CABDJAyADQaAEaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANBkARqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0GABGogD0IAQtfZrprk9umNywBCABDJAyADQfADaiAPQgBCms3/y6O9xIAaQgAQyQNBACEGAn9BACADKQP4AyADKQOIBCADKQOYBCADKQOoBCADKQO4BCADKQPIBCADKQPABCIPIBh8IA9UrXwiGCADKQOwBHwiDyAYVK18IA8gG3wiGCAPVK18IhsgAykDoAR8Ig8gG1StfCAPIBp8IhsgD1StfCIaIAMpA5AEfCIPIBpUrXwgDyAcfCIaIA9UrXwiHCADKQOABHwiDyAcVK18IA8gIHwiHCAPVK18IiAgAykD8AN8Ig8gIFStfCAPIBF8IiAgD1StfCIPUA0AGkEAIA8gDyAQfCIQWA0AGkEAIA8gEFatIg8gFHwiFCAPWg0AGkEAIA8gFFatIg8gE3wiEyAPWg0AGiAPIBNWrSIPIBZ8IhYgD1QLIQEgA0HgA2ogGEL9//P/z///+Yl/fiIPQgBCq9X+////v/+5f0IAEMkDIANB0ANqIA9CAEL//8+K6///1R5CABDJAyADQcADaiAPQgBCpOzDtY/UtJjnAEIAEMkDIANBsANqIA9CAEK/pZScz/DSu+QAQgAQyQMgA0GgA2ogD0IAQtfZrprk9umNywBCABDJAyADQZADaiAPQgBCms3/y6O9xIAaQgAQyQMCQCADKQOYAyADKQOoAyADKQO4AyADKQPIAyADKQPYAyADKQPoAyADKQPgAyIPIBh8IA9UrXwiESADKQPQA3wiDyARVK18IA8gDyAbfCIPVq18IhggAykDwAN8IhEgGFStfCARIBp8IhggEVStfCIbIAMpA7ADfCIRIBtUrXwgESAcfCIbIBFUrXwiGiADKQOgA3wiESAaVK18IBEgIHwiGiARVK18IhwgAykDkAN8IhEgHFStfCARIBAgEXwiEVatfCIQUA0AIBAgFHwiFCAQWg0AIBAgFFatIhAgE3wiEyAQWg0AIBAgE1atIhAgFnwiFiAQVCEGCyADQYADaiAPQv3/8//P///5iX9+IhBCAEKr1f7///+//7l/QgAQyQMgA0HwAmogEEIAQv//z4rr///VHkIAEMkDIANB4AJqIBBCAEKk7MO1j9S0mOcAQgAQyQMgA0HQAmogEEIAQr+llJzP8NK75ABCABDJAyADQcACaiAQQgBC19mumuT26Y3LAEIAEMkDIANBsAJqIBBCAEKazf/Lo73EgBpCABDJA0EAIQQgAykDuAIgAykDyAIgAykD2AIgAykD6AIgAykD+AIgAykDiAMgAykDgAMiECAPfCAQVK18Ig8gAykD8AJ8IhAgD1StfCAQIBAgGHwiEFatfCIYIAMpA+ACfCIPIBhUrXwgDyAbfCIYIA9UrXwiGyADKQPQAnwiDyAbVK18IA8gGnwiGyAPVK18IhogAykDwAJ8Ig8gGlStfCAPIBF8IhEgD1StfCIaIAMpA7ACfCIPIBpUrXwgDyAUfCIaIA9UrXwiD1BFBEAgDyATfCITIA9UIgStIg8gFnwiFCAWIAQbIRYgBCAPIBRWcSEECyASISAgA0GgAmogEEL9//P/z///+Yl/fiISQgBCq9X+////v/+5f0IAEMkDIANBkAJqIBJCAEL//8+K6///1R5CABDJAyADQYACaiASQgBCpOzDtY/UtJjnAEIAEMkDIANB8AFqIBJCAEK/pZScz/DSu+QAQgAQyQMgA0HgAWogEkIAQtfZrprk9umNywBCABDJAyADQdABaiASQgBCms3/y6O9xIAaQgAQyQMgAykD2AEgAykD6AEgAykD+AEgAykDiAIgAykDmAIgAykDqAIgAykDoAIiEiAQfCASVK18IhAgAykDkAJ8IhIgEFStfCASIBh8Ih8gElStfCIQIAMpA4ACfCISIBBUrXwgEiAbfCIQIBJUrXwiDyADKQPwAXwiEiAPVK18IBEgEnwiFCASVK18Ig8gAykD4AF8IhIgD1StfCASIBp8IhEgElStfCIPIAMpA9ABfCISIA9UrXwgEiATfCIPIBJUrXwiEiAWfCITIBYgEkIAUiIHGyEhAkACQAJAIBIgE1YiDa0gEiAHG1BFBEAgDyESDAELIAQgBSAMciABciAGcnIEQCAPIRIMAQsgByANcQRAIA8hEgwBCyAhQprN/8ujvcSAGlYEQCAPIRIMAQsgIUKazf/Lo73EgBpSDQEgD0LX2a6a5PbpjcsAVgRAIA8hEgwBCyAPQtfZrprk9umNywBSDQFC19mumuT26Y3LACESIBFCv6WUnM/w0rvkAFYNACARQr+llJzP8NK75ABSDQEgFEKk7MO1j9S0mOcAVg0AIBRCpOzDtY/UtJjnAFINASAQQv//z4rr///VHlYNACAQQv//z4rr///VHlIgH0Kq1f7///+//7l/WHINAQsgEEL//8+K6///1R59Ig8gH0Kr1f7///+//7l/VK0iE30hHCAUQqTsw7WP1LSY5wB9IhYgEEL//8+K6///1R5UIA8gE1RyrSIQfSEaIBFCv6WUnM/w0rvkAH0iDyAUQqTsw7WP1LSY5wBUIBAgFlZyrSIQfSEbIBJC19mumuT26Y3LAH0iFCARQr+llJzP8NK75ABUIA8gEFRyrSIQfSEPICEgEkLX2a6a5PbpjcsAVCAQIBRWcq19QprN/8ujvcSAGn0hISAfQtWqgYCAgMCAxgB8IR8MAQsgECEcIBQhGiARIRsLIAMgHzcD+BAgAyAcNwPwECADIBo3A+gQIAMgGzcD4BAgAyAPNwPYECADICE3A9AQIAhCADcDACAJQgA3AwAgCkIANwMAIAtCADcDACADQgA3A4ARIAMgJEIBgzcDqBECQCADQYARaiADQaAQakEwEPEDDQBCACEUQSghAUIAIRBCACETQgAhEUIAIRhCACEWA0AgA0HwAGogA0HQEGogAWopAwAiEkIAIB1CABDJAyADQYABaiASQgAgFUIAEMkDIANBkAFqIBJCACAOQgAQyQMgA0GgAWogEkIAIBdCABDJAyADQbABaiASQgAgGUIAEMkDIANBwAFqIBJCACAeQgAQyQMgA0HgAGogAykDcCIlIBZ8IhZCAEIAQv3/8//P///5iX8QyQMgA0HQAGogAykDaCISQgBCq9X+////v/+5f0IAEMkDIANBQGsgEkIAQv//z4rr///VHkIAEMkDIANBMGogEkIAQqTsw7WP1LSY5wBCABDJAyADQSBqIBJCAEK/pZScz/DSu+QAQgAQyQMgA0EQaiASQgBC19mumuT26Y3LAEIAEMkDIAMgEkIAQprN/8ujvcSAGkIAEMkDIAMpAwggAykDwAEiJyAUfCISIAMpA7gBIAMpA7ABIhQgEHwiECAUVK18IBAgECADKQOoASATIAMpA6ABIhN8IhQgE1StfCAUIBQgAykDmAEgAykDkAEiEyARfCIRIBNUrXwgESARIAMpA4gBIBggAykDgAEiGHwiEyAYVK18IBMgEyADKQN4IBYgJVStfHwiE1atfHwiEVatfHwiFFatfHwiEFatfHwiJSADKQMAfCIiICVUrXwgIiADKQMYIBAgECADKQMQfCIQVq18IBAgAykDKCAUIBQgAykDIHwiFFatfCAUIAMpAzggESARIAMpAzB8IhFWrXwgESADKQNIIAMpA0AiGCATfCITIBhUrXwgEyADKQNYIBYgAykDUCIWfCAWVK18fCIWIBNUrXx8IhggEVStfHwiESAUVK18fCITIBBUrXx8IhAgIlStfCASICVWrSADKQPIASASICdUrXx8fCEUIAFBCGsiAUF4Rw0ACwJAIBRCms3/y6O9xIAaVg0AAkAgFEKazf/Lo73EgBpSBEAgFCEeIBAhGSATIRcgESEODAELIBBC19mumuT26Y3LAFYNAUKazf/Lo73EgBohHiAQQtfZrprk9umNywBSBEAgECEZIBMhFyARIQ4MAQsgE0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGSATQr+llJzP8NK75ABSBEAgEyEXIBEhDgwBCyARQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEXIBFCpOzDtY/UtJjnAFIEQCARIQ4MAQsgGEL//8+K6///1R5WDQFCpOzDtY/UtJjnACEOIBhC///Piuv//9UeUg0AIBZCqtX+////v/+5f1YNAQsgGCEVIBYhHQwBCyAYQv//z4rr///VHn0iDiAWQqvV/v///7//uX9UrSISfSEVIBFCpOzDtY/UtJjnAH0iFyAYQv//z4rr///VHlQgDiASVHKtIhJ9IQ4gE0K/pZScz/DSu+QAfSIZIBFCpOzDtY/UtJjnAFQgEiAXVnKtIhJ9IRcgEELX2a6a5PbpjcsAfSIRIBNCv6WUnM/w0rvkAFQgEiAZVnKtIhJ9IRkgFCAQQtfZrprk9umNywBUIBEgElRyrX1Cms3/y6O9xIAafSEeIBZC1aqBgICAwIDGAHwhHQsgAiAjQgGIIhQ3AwAgAiAmQj+GICBCAYiEIhI3AyAgAiAgQj+GICRCAYiEIiQ3AyggAiAoQj+GICZCAYiEIiY3AxggAiApQj+GIChCAYiEIig3AxAgAiAjQj+GIClCAYiEIik3AwggAiADQfAPakEwEPEDDQALCyAAIB03AyggACAVNwMgIAAgDjcDGCAAIBc3AxAgACAZNwMIIAAgHjcDAAwCCyAAQShqQaDUwQApAwA3AwAgAEEgakGY1MEAKQMANwMAIABBGGpBkNTBACkDADcDACAAQRBqQYjUwQApAwA3AwAgAEEIakGA1MEAKQMANwMAIABB+NPBACkDADcDAAwBCyAAIAEpAwA3AwAgAEEoaiABQShqKQMANwMAIABBIGogAUEgaikDADcDACAAQRhqIAFBGGopAwA3AwAgAEEQaiABQRBqKQMANwMAIABBCGogAUEIaikDADcDAAsgA0GwEWokAAv+PgEhfyAAKAIcISEgACgCGCEfIAAoAhQhHiAAKAIQIRwgACgCDCEiIAAoAgghICAAKAIEIR0gACgCACEDIAIEQCABIAJBBnRqISMDQCADIAEoAAAiAkEYdCACQYD+A3FBCHRyIAJBCHZBgP4DcSACQRh2cnIiESAhIBxBGncgHEEVd3MgHEEHd3NqIB4gH3MgHHEgH3NqakGY36iUBGoiBCAdICBzIANxIB0gIHFzIANBHncgA0ETd3MgA0EKd3NqaiICQR53IAJBE3dzIAJBCndzIAIgAyAdc3EgAyAdcXNqIB8gAUEEaigAACIFQRh0IAVBgP4DcUEIdHIgBUEIdkGA/gNxIAVBGHZyciISaiAEICJqIgkgHCAec3EgHnNqIAlBGncgCUEVd3MgCUEHd3NqQZGJ3YkHaiIGaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIB4gAUEIaigAACIEQRh0IARBgP4DcUEIdHIgBEEIdkGA/gNxIARBGHZyciITaiAGICBqIgogCSAcc3EgHHNqIApBGncgCkEVd3MgCkEHd3NqQbGI/NEEayIHaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIBwgAUEMaigAACIGQRh0IAZBgP4DcUEIdHIgBkEIdkGA/gNxIAZBGHZyciIUaiAHIB1qIgcgCSAKc3EgCXNqIAdBGncgB0EVd3MgB0EHd3NqQdvIqLIBayIOaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIAkgAUEQaigAACIIQRh0IAhBgP4DcUEIdHIgCEEIdkGA/gNxIAhBGHZyciIVaiADIA5qIgkgByAKc3EgCnNqIAlBGncgCUEVd3MgCUEHd3NqQduE28oDaiIIaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIAogAUEUaigAACIKQRh0IApBgP4DcUEIdHIgCkEIdkGA/gNxIApBGHZyciIWaiACIAhqIgogByAJc3EgB3NqIApBGncgCkEVd3MgCkEHd3NqQfGjxM8FaiIIaiICQR53IAJBE3dzIAJBCndzIAIgAyAGc3EgAyAGcXNqIAcgAUEYaigAACIHQRh0IAdBgP4DcUEIdHIgB0EIdkGA/gNxIAdBGHZyciIXaiAFIAhqIgcgCSAKc3EgCXNqIAdBGncgB0EVd3MgB0EHd3NqQdz6ge4GayIIaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIAkgAUEcaigAACIJQRh0IAlBgP4DcUEIdHIgCUEIdkGA/gNxIAlBGHZyciIZaiAEIAhqIgkgByAKc3EgCnNqIAlBGncgCUEVd3MgCUEHd3NqQavCjqcFayIIaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIAogAUEgaigAACIKQRh0IApBgP4DcUEIdHIgCkEIdkGA/gNxIApBGHZyciIaaiAGIAhqIgogByAJc3EgB3NqIApBGncgCkEVd3MgCkEHd3NqQeiq4b8CayIIaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIAcgAUEkaigAACIHQRh0IAdBgP4DcUEIdHIgB0EIdkGA/gNxIAdBGHZyciIYaiADIAhqIgcgCSAKc3EgCXNqIAdBGncgB0EVd3MgB0EHd3NqQYG2jZQBaiIIaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIAkgAUEoaigAACIJQRh0IAlBgP4DcUEIdHIgCUEIdkGA/gNxIAlBGHZyciILaiACIAhqIgkgByAKc3EgCnNqIAlBGncgCUEVd3MgCUEHd3NqQb6LxqECaiIIaiICQR53IAJBE3dzIAJBCndzIAIgAyAGc3EgAyAGcXNqIAogAUEsaigAACIKQRh0IApBgP4DcUEIdHIgCkEIdkGA/gNxIApBGHZyciIMaiAFIAhqIgogByAJc3EgB3NqIApBGncgCkEVd3MgCkEHd3NqQcP7sagFaiIIaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIAcgAUEwaigAACIHQRh0IAdBgP4DcUEIdHIgB0EIdkGA/gNxIAdBGHZyciINaiAEIAhqIgcgCSAKc3EgCXNqIAdBGncgB0EVd3MgB0EHd3NqQfS6+ZUHaiIIaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIAkgAUE0aigAACIJQRh0IAlBgP4DcUEIdHIgCUEIdkGA/gNxIAlBGHZyciIPaiAGIAhqIgggByAKc3EgCnNqIAhBGncgCEEVd3MgCEEHd3NqQYKchfkHayIOaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIAFBOGooAAAiCUEYdCAJQYD+A3FBCHRyIAlBCHZBgP4DcSAJQRh2cnIiCSAKaiADIA5qIg4gByAIc3EgB3NqIA5BGncgDkEVd3MgDkEHd3NqQdnyj6EGayIQaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIAFBPGooAAAiCkEYdCAKQYD+A3FBCHRyIApBCHZBgP4DcSAKQRh2cnIiCiAHaiACIBBqIhAgCCAOc3EgCHNqIBBBGncgEEEVd3MgEEEHd3NqQYydkPMDayIbaiICQR53IAJBE3dzIAJBCndzIAIgAyAGc3EgAyAGcXNqIBJBGXcgEkEOd3MgEkEDdnMgEWogGGogCUEPdyAJQQ13cyAJQQp2c2oiByAIaiAFIBtqIhEgDiAQc3EgDnNqIBFBGncgEUEVd3MgEUEHd3NqQb+sktsBayIbaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIBNBGXcgE0EOd3MgE0EDdnMgEmogC2ogCkEPdyAKQQ13cyAKQQp2c2oiCCAOaiAEIBtqIhIgECARc3EgEHNqIBJBGncgEkEVd3MgEkEHd3NqQfrwhoIBayIbaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIBRBGXcgFEEOd3MgFEEDdnMgE2ogDGogB0EPdyAHQQ13cyAHQQp2c2oiDiAQaiAGIBtqIhMgESASc3EgEXNqIBNBGncgE0EVd3MgE0EHd3NqQca7hv4AaiIbaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIBVBGXcgFUEOd3MgFUEDdnMgFGogDWogCEEPdyAIQQ13cyAIQQp2c2oiECARaiADIBtqIhQgEiATc3EgEnNqIBRBGncgFEEVd3MgFEEHd3NqQczDsqACaiIbaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIBZBGXcgFkEOd3MgFkEDdnMgFWogD2ogDkEPdyAOQQ13cyAOQQp2c2oiESASaiACIBtqIhUgEyAUc3EgE3NqIBVBGncgFUEVd3MgFUEHd3NqQe/YpO8CaiIbaiICQR53IAJBE3dzIAJBCndzIAIgAyAGc3EgAyAGcXNqIBdBGXcgF0EOd3MgF0EDdnMgFmogCWogEEEPdyAQQQ13cyAQQQp2c2oiEiATaiAFIBtqIhYgFCAVc3EgFHNqIBZBGncgFkEVd3MgFkEHd3NqQaqJ0tMEaiIbaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIBlBGXcgGUEOd3MgGUEDdnMgF2ogCmogEUEPdyARQQ13cyARQQp2c2oiEyAUaiAEIBtqIhcgFSAWc3EgFXNqIBdBGncgF0EVd3MgF0EHd3NqQdzTwuUFaiIbaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIBpBGXcgGkEOd3MgGkEDdnMgGWogB2ogEkEPdyASQQ13cyASQQp2c2oiFCAVaiAGIBtqIhkgFiAXc3EgFnNqIBlBGncgGUEVd3MgGUEHd3NqQdqR5rcHaiIbaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIBhBGXcgGEEOd3MgGEEDdnMgGmogCGogE0EPdyATQQ13cyATQQp2c2oiFSAWaiADIBtqIhogFyAZc3EgF3NqIBpBGncgGkEVd3MgGkEHd3NqQa7dhr4GayIbaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIAtBGXcgC0EOd3MgC0EDdnMgGGogDmogFEEPdyAUQQ13cyAUQQp2c2oiFiAXaiACIBtqIhggGSAac3EgGXNqIBhBGncgGEEVd3MgGEEHd3NqQZPzuL4FayIbaiICQR53IAJBE3dzIAJBCndzIAIgAyAGc3EgAyAGcXNqIAxBGXcgDEEOd3MgDEEDdnMgC2ogEGogFUEPdyAVQQ13cyAVQQp2c2oiFyAZaiAFIBtqIgsgGCAac3EgGnNqIAtBGncgC0EVd3MgC0EHd3NqQbiw8/8EayIbaiIFQR53IAVBE3dzIAVBCndzIAUgAiADc3EgAiADcXNqIA1BGXcgDUEOd3MgDUEDdnMgDGogEWogFkEPdyAWQQ13cyAWQQp2c2oiGSAaaiAEIBtqIgwgCyAYc3EgGHNqIAxBGncgDEEVd3MgDEEHd3NqQbmAmoUEayIbaiIEQR53IARBE3dzIARBCndzIAQgAiAFc3EgAiAFcXNqIA9BGXcgD0EOd3MgD0EDdnMgDWogEmogF0EPdyAXQQ13cyAXQQp2c2oiGiAYaiAGIBtqIg0gCyAMc3EgC3NqIA1BGncgDUEVd3MgDUEHd3NqQY3o/8gDayIbaiIGQR53IAZBE3dzIAZBCndzIAYgBCAFc3EgBCAFcXNqIAlBGXcgCUEOd3MgCUEDdnMgD2ogE2ogGUEPdyAZQQ13cyAZQQp2c2oiGCALaiADIBtqIgsgDCANc3EgDHNqIAtBGncgC0EVd3MgC0EHd3NqQbnd4dICayIPaiIDQR53IANBE3dzIANBCndzIAMgBCAGc3EgBCAGcXNqIApBGXcgCkEOd3MgCkEDdnMgCWogFGogGkEPdyAaQQ13cyAaQQp2c2oiCSAMaiACIA9qIgwgCyANc3EgDXNqIAxBGncgDEEVd3MgDEEHd3NqQdHGqTZqIg9qIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogB0EZdyAHQQ53cyAHQQN2cyAKaiAVaiAYQQ93IBhBDXdzIBhBCnZzaiIKIA1qIAUgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pB59KkoQFqIg9qIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogCEEZdyAIQQ53cyAIQQN2cyAHaiAWaiAJQQ93IAlBDXdzIAlBCnZzaiIHIAtqIAQgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pBhZXcvQJqIg9qIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogDkEZdyAOQQ53cyAOQQN2cyAIaiAXaiAKQQ93IApBDXdzIApBCnZzaiIIIAxqIAYgD2oiDCALIA1zcSANc2ogDEEadyAMQRV3cyAMQQd3c2pBuMLs8AJqIg9qIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogEEEZdyAQQQ53cyAQQQN2cyAOaiAZaiAHQQ93IAdBDXdzIAdBCnZzaiIOIA1qIAMgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pB/Nux6QRqIg9qIgNBHncgA0ETd3MgA0EKd3MgAyAEIAZzcSAEIAZxc2ogEUEZdyARQQ53cyARQQN2cyAQaiAaaiAIQQ93IAhBDXdzIAhBCnZzaiIQIAtqIAIgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pBk5rgmQVqIg9qIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogEkEZdyASQQ53cyASQQN2cyARaiAYaiAOQQ93IA5BDXdzIA5BCnZzaiIRIAxqIAUgD2oiDCALIA1zcSANc2ogDEEadyAMQRV3cyAMQQd3c2pB1OapqAZqIg9qIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogE0EZdyATQQ53cyATQQN2cyASaiAJaiAQQQ93IBBBDXdzIBBBCnZzaiISIA1qIAQgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pBu5WoswdqIg9qIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogFEEZdyAUQQ53cyAUQQN2cyATaiAKaiARQQ93IBFBDXdzIBFBCnZzaiITIAtqIAYgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pB0u308QdrIg9qIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogFUEZdyAVQQ53cyAVQQN2cyAUaiAHaiASQQ93IBJBDXdzIBJBCnZzaiIUIAxqIAMgD2oiDCALIA1zcSANc2ogDEEadyAMQRV3cyAMQQd3c2pB+6a37AZrIg9qIgNBHncgA0ETd3MgA0EKd3MgAyAEIAZzcSAEIAZxc2ogFkEZdyAWQQ53cyAWQQN2cyAVaiAIaiATQQ93IBNBDXdzIBNBCnZzaiIVIA1qIAIgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pB366A6gVrIg9qIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogF0EZdyAXQQ53cyAXQQN2cyAWaiAOaiAUQQ93IBRBDXdzIBRBCnZzaiIWIAtqIAUgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pBtbOWvwVrIg9qIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogGUEZdyAZQQ53cyAZQQN2cyAXaiAQaiAVQQ93IBVBDXdzIBVBCnZzaiIXIAxqIAQgD2oiDCALIA1zcSANc2ogDEEadyAMQRV3cyAMQQd3c2pBkOnR7QNrIg9qIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogGkEZdyAaQQ53cyAaQQN2cyAZaiARaiAWQQ93IBZBDXdzIBZBCnZzaiIZIA1qIAYgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pB3dzOxANrIg9qIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogGEEZdyAYQQ53cyAYQQN2cyAaaiASaiAXQQ93IBdBDXdzIBdBCnZzaiIaIAtqIAMgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pB56+08wJrIg9qIgNBHncgA0ETd3MgA0EKd3MgAyAEIAZzcSAEIAZxc2ogCUEZdyAJQQ53cyAJQQN2cyAYaiATaiAZQQ93IBlBDXdzIBlBCnZzaiIYIAxqIAIgD2oiDCALIA1zcSANc2ogDEEadyAMQRV3cyAMQQd3c2pB3PObywJrIg9qIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogCkEZdyAKQQ53cyAKQQN2cyAJaiAUaiAaQQ93IBpBDXdzIBpBCnZzaiIJIA1qIAUgD2oiDSALIAxzcSALc2ogDUEadyANQRV3cyANQQd3c2pB+5TH3wBrIg9qIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogB0EZdyAHQQ53cyAHQQN2cyAKaiAVaiAYQQ93IBhBDXdzIBhBCnZzaiIKIAtqIAQgD2oiCyAMIA1zcSAMc2ogC0EadyALQRV3cyALQQd3c2pB8MCqgwFqIg9qIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogDCAIQRl3IAhBDndzIAhBA3ZzIAdqIBZqIAlBD3cgCUENd3MgCUEKdnNqIgxqIAYgD2oiByALIA1zcSANc2ogB0EadyAHQRV3cyAHQQd3c2pBloKTzQFqIg9qIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogDSAOQRl3IA5BDndzIA5BA3ZzIAhqIBdqIApBD3cgCkENd3MgCkEKdnNqIg1qIAMgD2oiCCAHIAtzcSALc2ogCEEadyAIQRV3cyAIQQd3c2pBiNjd8QFqIg9qIgNBHncgA0ETd3MgA0EKd3MgAyAEIAZzcSAEIAZxc2ogCyAQQRl3IBBBDndzIBBBA3ZzIA5qIBlqIAxBD3cgDEENd3MgDEEKdnNqIgtqIAIgD2oiDiAHIAhzcSAHc2ogDkEadyAOQRV3cyAOQQd3c2pBzO6hugJqIhtqIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogEUEZdyARQQ53cyARQQN2cyAQaiAaaiANQQ93IA1BDXdzIA1BCnZzaiIPIAdqIAUgG2oiByAIIA5zcSAIc2ogB0EadyAHQRV3cyAHQQd3c2pBtfnCpQNqIhBqIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogEkEZdyASQQ53cyASQQN2cyARaiAYaiALQQ93IAtBDXdzIAtBCnZzaiIRIAhqIAQgEGoiCCAHIA5zcSAOc2ogCEEadyAIQRV3cyAIQQd3c2pBs5nwyANqIhBqIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogE0EZdyATQQ53cyATQQN2cyASaiAJaiAPQQ93IA9BDXdzIA9BCnZzaiISIA5qIAYgEGoiDiAHIAhzcSAHc2ogDkEadyAOQRV3cyAOQQd3c2pBytTi9gRqIhBqIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogFEEZdyAUQQ53cyAUQQN2cyATaiAKaiARQQ93IBFBDXdzIBFBCnZzaiITIAdqIAMgEGoiByAIIA5zcSAIc2ogB0EadyAHQRV3cyAHQQd3c2pBz5Tz3AVqIhBqIgNBHncgA0ETd3MgA0EKd3MgAyAEIAZzcSAEIAZxc2ogFUEZdyAVQQ53cyAVQQN2cyAUaiAMaiASQQ93IBJBDXdzIBJBCnZzaiIUIAhqIAIgEGoiCCAHIA5zcSAOc2ogCEEadyAIQRV3cyAIQQd3c2pB89+5wQZqIhBqIgJBHncgAkETd3MgAkEKd3MgAiADIAZzcSADIAZxc2ogFkEZdyAWQQ53cyAWQQN2cyAVaiANaiATQQ93IBNBDXdzIBNBCnZzaiIVIA5qIAUgEGoiDiAHIAhzcSAHc2ogDkEadyAOQRV3cyAOQQd3c2pB7oW+pAdqIhBqIgVBHncgBUETd3MgBUEKd3MgBSACIANzcSACIANxc2ogByAXQRl3IBdBDndzIBdBA3ZzIBZqIAtqIBRBD3cgFEENd3MgFEEKdnNqIgdqIAQgEGoiECAIIA5zcSAIc2ogEEEadyAQQRV3cyAQQQd3c2pB78aVxQdqIgtqIgRBHncgBEETd3MgBEEKd3MgBCACIAVzcSACIAVxc2ogGUEZdyAZQQ53cyAZQQN2cyAXaiAPaiAVQQ93IBVBDXdzIBVBCnZzaiIWIAhqIAYgC2oiCCAOIBBzcSAOc2ogCEEadyAIQRV3cyAIQQd3c2pB7I/e2QdrIhdqIgZBHncgBkETd3MgBkEKd3MgBiAEIAVzcSAEIAVxc2ogGkEZdyAaQQ53cyAaQQN2cyAZaiARaiAHQQ93IAdBDXdzIAdBCnZzaiIRIA5qIAMgF2oiAyAIIBBzcSAQc2ogA0EadyADQRV3cyADQQd3c2pB+PvjmQdrIg5qIgdBHncgB0ETd3MgB0EKd3MgByAEIAZzcSAEIAZxc2ogECAYQRl3IBhBDndzIBhBA3ZzIBpqIBJqIBZBD3cgFkENd3MgFkEKdnNqIhBqIAIgDmoiDiADIAhzcSAIc2ogDkEadyAOQRV3cyAOQQd3c2pBhoCE+gZrIhJqIgJBHncgAkETd3MgAkEKd3MgAiAGIAdzcSAGIAdxc2ogCUEZdyAJQQ53cyAJQQN2cyAYaiATaiARQQ93IBFBDXdzIBFBCnZzaiIRIAhqIAUgEmoiBSADIA5zcSADc2ogBUEadyAFQRV3cyAFQQd3c2pBlaa+3QVrIhJqIghBHncgCEETd3MgCEEKd3MgCCACIAdzcSACIAdxc2ogCSAKQRl3IApBDndzIApBA3ZzaiAUaiAQQQ93IBBBDXdzIBBBCnZzaiADaiAEIBJqIgQgBSAOc3EgDnNqIARBGncgBEEVd3MgBEEHd3NqQYm4mYgEayIDaiIJIAIgCHNxIAIgCHFzaiAJQR53IAlBE3dzIAlBCndzaiAKIAxBGXcgDEEOd3MgDEEDdnNqIBVqIBFBD3cgEUENd3MgEUEKdnNqIA5qIAMgBmoiBiAEIAVzcSAFc2ogBkEadyAGQRV3cyAGQQd3c2pBjo66zANrIgpqIQMgCSAdaiEdIAcgHGogCmohHCAIICBqISAgBiAeaiEeIAIgImohIiAEIB9qIR8gBSAhaiEhIAFBQGsiASAjRw0ACwsgACAhNgIcIAAgHzYCGCAAIB42AhQgACAcNgIQIAAgIjYCDCAAICA2AgggACAdNgIEIAAgAzYCAAuBVAIFfx9+IwBBwBBrIgIkACACQeAOaiABKQMQIh9CACABKQMYIiBCABDJAyACQcAOaiABKQMIIiFCACAgQgAQyQMgAkGQDmogASkDACIiQgAgIEIAEMkDIAJBsA5qICFCACAfQgAQyQMgAkGADmogIkIAIB9CABDJAyACQfANaiAiQgAgIUIAEMkDIAJBsA9qICBCACAgQgAQyQMgAkHQDmogH0IAIB9CABDJAyACQaAOaiAhQgAgIUIAEMkDIAJB4A1qICJCACAiQgAQyQMgAkGgD2ogAikDsA8iDEKJx5mkrvCB6Yd/fiIHQgBCx/rzw+2Co5A8QgAQyQMgAkGQD2ogB0IAQo2Vx8OW0trAl39CABDJAyACQYAPaiAHQgBC3bCFjOi2kai4f0IAEMkDIAJB8A5qIAdCAEKpwMaJrs6TsjBCABDJAyACKQP4DSACKQOIDiACKQOYDiACKQPIDiACKQPoDiIHIAIpA8AOfCIPIAdUrXwiByACKQOQDnwiCiAHVK18IgcgAikDgA58IgkgB1StfCAJIAIpA7gOIAogAikDsA58IhMgClStfHwiDSAJVK18IgcgAikD8A18IhEgB1StfCIJQj+IIAIpA+gNIAIpA+ANIgcgCUIBhiARQj+IhHwiECAHVK18IBAgAikDqA4gAikD2A4gAikD0A4iByAPQgGGIAIpA+AOIglCP4iEfCIKIAdUrXwgCiACKQO4DyIHIAlCAYZ8IgsgB1StfCIIIApUrXwiByATQgGGIA9CP4iEfCIJIAdUrSIHIAIpA6AOfCIKIAdUrXwgCiAKIA1CAYYgE0I/iIR8IgpWrXwiByARQgGGIA1CP4iEfCINIAdUrXwiDyAQVK18fCEOAn8CQCACKQP4DiACKQOIDyACKQOYDyACKQOoDyACKQOgDyIHIAxCfYN8IAdUrXwiByACKQOQD3wiDCAHVK18IAwgCyAMfCIMVq18IgcgAikDgA98IgsgB1StfCAIIAt8IgggC1StfCIHIAIpA/AOfCILIAdUrXwgCSALfCIJIAtUrXwiB1ANACAHIAp8IgogB1QiA0UNACADrSIHIA18Ig0gB1oNACAHIA1WrSIHIA98Ig8gB1oNACAHIA9WrSIHIA58Ig4gB1QMAQtBAAshBiACQdANaiAMQonHmaSu8IHph39+IgdCAELH+vPD7YKjkDxCABDJAyACQcANaiAHQgBCjZXHw5bS2sCXf0IAEMkDIAJBsA1qIAdCAELdsIWM6LaRqLh/QgAQyQMgAkGgDWogB0IAQqnAxomuzpOyMEIAEMkDAkAgAikDqA0gAikDuA0gAikDyA0gAikD2A0gAikD0A0iByAMfCAHVK18IgcgAikDwA18IgsgB1StfCALIAggC3wiC1atfCIHIAIpA7ANfCIIIAdUrXwgCCAIIAl8IghWrXwiByACKQOgDXwiCSAHVK18IAkgCSAKfCIJVq18IgdQDQAgByANfCINIAdaDQAgByANVq0iByAPfCIPIAdaDQAgByAPVq0iByAOfCIOIAdUIQQLIAJBkA1qIAtCiceZpK7wgemHf34iB0IAQsf688PtgqOQPEIAEMkDIAJBgA1qIAdCAEKNlcfDltLawJd/QgAQyQMgAkHwDGogB0IAQt2whYzotpGouH9CABDJAyACQeAMaiAHQgBCqcDGia7Ok7IwQgAQyQNBACEDIAIpA+gMIAIpA/gMIAIpA4gNIAIpA5gNIAIpA5ANIgcgC3wgB1StfCIHIAIpA4ANfCIKIAdUrXwgCCAKfCILIApUrXwiByACKQPwDHwiCiAHVK18IAkgCnwiCCAKVK18IgcgAikD4Ax8IgkgB1StfCAJIA18IgogCVStfCIHUEUEQCAHIA98Ig8gB1QiA60iCSAOfCIHIA4gAxshDiADIAcgCVRxIQMLIAJB0AxqIAtCiceZpK7wgemHf34iB0IAQsf688PtgqOQPEIAEMkDIAJBwAxqIAdCAEKNlcfDltLawJd/QgAQyQMgAkGwDGogB0IAQt2whYzotpGouH9CABDJAyACQaAMaiAHQgBCqcDGia7Ok7IwQgAQyQMgAikDqAwgAikDuAwgAikDyAwgAikD2AwgAikD0AwiByALfCAHVK18IgcgAikDwAx8IgkgB1StfCAIIAl8IhIgCVStfCIHIAIpA7AMfCIJIAdUrXwgCSAJIAp8IglWrXwiByACKQOgDHwiCiAHVK18IAogD3wiByAKVK18IgggDnwiCiAOIAhCAFIiBRshDwJAAkACQAJAIAQgBnIgA3IgCCAKViIDrSAIIAUbQgBSciADIAVxIA9CqcDGia7Ok7IwVnJyDQAgD0KpwMaJrs6TsjBSDQEgB0LdsIWM6LaRqLh/Vg0AIAdC3bCFjOi2kai4f1IEQCAJIRAgByEJQqnAxomuzpOyMCEPDAQLQt2whYzotpGouH8hByAJQo2Vx8OW0trAl39WDQAgCUKNlcfDltLawJd/UiASQsb688PtgqOQPFhyDQILIAlC8+q4vOmtpb/oAHwiCyASQsf688PtgqOQPFStIgp9IRAgB0Kjz/rzl8nu18cAfCIIIAlCjZXHw5bS2sCXf1QgCiALVnKtIgp9IQkgDyAHQt2whYzotpGouH9UIAggClRyrX1CqcDGia7Ok7IwfSEPIBJCx/rzw+2Co5A8fSESDAILIAkhECAHIQkMAQsgCSEQQt2whYzotpGouH8hCUKpwMaJrs6TsjAhDwsgAkGgC2ogASkDMCIbQgAgASkDOCIcQgAQyQMgAkHwCmogASkDKCIdQgAgHEIAEMkDIAJBgAxqIAEpAyAiHkIAIBxCABDJAyACQeAKaiAdQgAgG0IAEMkDIAJBkAtqIB5CACAbQgAQyQMgAkHQCmogHkIAIB1CABDJAyACQfALaiAcQgAgHEIAEMkDIAJBgAtqIBtCACAbQgAQyQMgAkHACmogHUIAIB1CABDJAyACQZAMaiAeQgAgHkIAEMkDIAJB4AtqIAIpA/ALIhNCiceZpK7wgemHf34iB0IAQsf688PtgqOQPEIAEMkDIAJB0AtqIAdCAEKNlcfDltLawJd/QgAQyQMgAkHAC2ogB0IAQt2whYzotpGouH9CABDJAyACQbALaiAHQgBCqcDGia7Ok7IwQgAQyQMgAikD2AogAikDmAsgAikDiAwgAikD+AogAikDqAsiByACKQPwCnwiDCAHVK18IgcgAikDgAx8IgggB1StfCIHIAIpA5ALfCIKIAdUrXwgCiACKQPoCiAIIAIpA+AKfCIVIAhUrXx8IhQgClStfCIHIAIpA9AKfCIWIAdUrXwiCkI/iCACKQOYDCACKQOQDCIHIApCAYYgFkI/iIR8IgsgB1StfCALIAIpA8gKIAIpA4gLIAIpA4ALIgcgDEIBhiACKQOgCyIKQj+IhHwiCCAHVK18IAggAikD+AsiByAKQgGGfCINIAdUrXwiESAIVK18IgcgFUIBhiAMQj+IhHwiDCAHVK0iByACKQPACnwiCiAHVK18IAogFEIBhiAVQj+IhHwiCCAKVK18IgcgFkIBhiAUQj+IhHwiCiAHVK18IgcgC1StfHwhDkEAIQQCfwJAIAIpA7gLIAIpA8gLIAIpA9gLIAIpA+gLIAIpA+ALIgsgE0J9g3wgC1StfCILIAIpA9ALfCITIAtUrXwgEyANIBN8IhNWrXwiCyACKQPAC3wiDSALVK18IA0gEXwiESANVK18IgsgAikDsAt8Ig0gC1StfCAMIA18IgwgDVStfCILUA0AIAggC3wiCCALVCIDRQ0AIAOtIgsgCnwiCiALWg0AIAogC1StIgsgB3wiByALWg0AIAcgC1StIgsgDnwiDiALVAwBC0EACyEGIAJBsApqIBNCiceZpK7wgemHf34iC0IAQsf688PtgqOQPEIAEMkDIAJBoApqIAtCAEKNlcfDltLawJd/QgAQyQMgAkGQCmogC0IAQt2whYzotpGouH9CABDJAyACQYAKaiALQgBCqcDGia7Ok7IwQgAQyQMCQCACKQOICiACKQOYCiACKQOoCiACKQO4CiACKQOwCiILIBN8IAtUrXwiCyACKQOgCnwiDSALVK18IA0gDSARfCINVq18IgsgAikDkAp8IhEgC1StfCAMIBF8IgwgEVStfCILIAIpA4AKfCIRIAtUrXwgCCARfCILIBFUrXwiCFANACAIIAp8IgogCFoNACAIIApWrSIIIAd8IgcgCFoNACAHIAhUrSIIIA58Ig4gCFQhBAsgAkHwCWogDUKJx5mkrvCB6Yd/fiIIQgBCx/rzw+2Co5A8QgAQyQMgAkHgCWogCEIAQo2Vx8OW0trAl39CABDJAyACQdAJaiAIQgBC3bCFjOi2kai4f0IAEMkDIAJBwAlqIAhCAEKpwMaJrs6TsjBCABDJA0EAIQMgAikDyAkgAikD2AkgAikD6AkgAikD+AkgAikD8AkiCCANfCAIVK18IgggAikD4Al8IhEgCFStfCARIAwgEXwiEVatfCIIIAIpA9AJfCIMIAhUrXwgDCALIAx8IgxWrXwiCCACKQPACXwiCyAIVK18IAsgCiALfCILVq18IgpQRQRAIAcgCnwiByAKVCIDrSIIIA58IgogDiADGyEOIAMgCCAKVnEhAwsgAkGwCWogEUKJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgAkGgCWogCkIAQo2Vx8OW0trAl39CABDJAyACQZAJaiAKQgBC3bCFjOi2kai4f0IAEMkDIAJBgAlqIApCAEKpwMaJrs6TsjBCABDJAyACKQOICSACKQOYCSACKQOoCSACKQO4CSACKQOwCSIKIBF8IApUrXwiCiACKQOgCXwiCCAKVK18IAggDHwiDSAIVK18IgogAikDkAl8IgggClStfCAIIAggC3wiCFatfCIKIAIpA4AJfCILIApUrXwgByALfCIKIAtUrXwiCyAOfCIHIA4gC0IAUiIFGyEOAkACQAJAIAQgBnIgA3IgByALVCIDrSALIAUbQgBSciADIAVxIA5CqcDGia7Ok7IwVnJyDQAgDkKpwMaJrs6TsjBSBEAgCCEWIAohBwwDCyAKQt2whYzotpGouH9WDQAgCkLdsIWM6LaRqLh/UgRAIAghFiAKIQdCqcDGia7Ok7IwIQ4MAwtC3bCFjOi2kai4fyEKIAhCjZXHw5bS2sCXf1YNACAIQo2Vx8OW0trAl39SIA1Cxvrzw+2Co5A8WHINAQsgCELz6ri86a2lv+gAfCIMIA1Cx/rzw+2Co5A8VK0iB30hFiAKQqPP+vOXye7XxwB8IgsgCEKNlcfDltLawJd/VCAHIAxWcq0iCH0hByAOIApC3bCFjOi2kai4f1QgCCALVnKtfUKpwMaJrs6TsjB9IQ4gDULH+vPD7YKjkDx9IQ0MAQsgCCEWQt2whYzotpGouH8hB0KpwMaJrs6TsjAhDgtCqcDGia7Ok7IwIQogDiAPfCAJIAcgCXwiCVYgCSAJIBAgFnwiByAQVCAHIA0gEnwiDiASVK18IgggB1RyrXwiCVZyrXwiEiEHAkACQAJAIBJCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hCiAJIgdC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQogCCIHQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQogDiIHQsf688PtgqOQPFENAQsgByAKWg0AIAkhByAIIQoMAQsgCELz6ri86a2lv+gAfCIMIA5Cx/rzw+2Co5A8VK0iB30hCiAJQqPP+vOXye7XxwB8IgsgCEKNlcfDltLawJd/VCAHIAxWcq0iCH0hByASIAlC3bCFjOi2kai4f1QgCCALVnKtfUKpwMaJrs6TsjB9IRIgDkLH+vPD7YKjkDx9IQ4LIAIgDjcD2A8gAiAKNwPQDyACIAc3A8gPIAIgEjcDwA8CQAJAAkAgAkHAD2pByKXFAEEgEPEDBEBCACEOIAJB8A9qQgA3AwAgAkHoD2pCADcDACACQgA3A+APIAJCATcD+A8gAkGYEGogAkHYD2opAwA3AwAgAkGQEGogAkHQD2opAwA3AwAgAkGIEGogAkHID2opAwA3AwAgAiACKQPADzcDgBAgAkG4EGpBwKXFACkDADcDACACQbAQakG4pcUAKQMANwMAIAJBqBBqQbClxQApAwA3AwAgAkGopcUAKQMANwOgEAJAIAJBgBBqIAJB4A9qQSAQ8QNFBEBCn+rg1Zzup+wGIRJCifWrnLWLv5ZzIQ9C+4OUop2ixvO1fyEVQvb/hdLw38fVxwAhFAwBC0KJ9auctYu/lnMhD0L7g5SinaLG87V/IRVC9v+F0vDfx9XHACEUQp/q4NWc7qfsBiESIAIpA5gQIQcgAikDgBAhECACKQOIECEJIAIpA5AQIRhCACETQgAhEUIAIQ1Cx/rzw+2Co5A8IQpCqcDGia7Ok7IwIRZC3bCFjOi2kai4fyEIQo2Vx8OW0trAl38hFwNAIAJBoBBqIAJB4A9qQSAQ8QNFBEAgEyEUIBEhFSANIQ8gDiESDAILIAenQQFxRQRAA0AgGEI/hiAHQgGIhCEHAkAgD0IBg1AEQCAPIQsgFSEPIBQhDAwBCyASIBQgFEKjz/rzl8nu18cAfSIUViAUIBVC8+q4vOmtpb/oAH0iDCAVVCAMIA9Cx/rzw+2Co5A8fCILIA9UrXwiDyAMVHKtfCIMIBRUcq18QqnAxomuzpOyMHwhEgsgEEI/hiAJQj+GIBhCAYiEIRggEEIBiCEQIBJCP4YgDEIBiIQhFCAMQj+GIA9CAYiEIRUgD0I/hiALQgGIhCEPIBJCAYghEiAJQgGIhCEJIAdCAYNQDQALIAIgGDcDkBAgAiAHNwOYECACIAk3A4gQIAIgEDcDgBALIAqnQQFxRQRAA0AgF0I/hiAKQgGIhCEKAkAgDUIBg1AEQCANIQsgESENIBMhDAwBCyAOIBMgE0Kjz/rzl8nu18cAfSITViATIBFC8+q4vOmtpb/oAH0iDCARVCAMIA1Cx/rzw+2Co5A8fCILIA1UrXwiDSAMVHKtfCIMIBNUcq18QqnAxomuzpOyMHwhDgsgFkI/hiAIQj+GIBdCAYiEIRcgFkIBiCEWIA5CP4YgDEIBiIQhEyAMQj+GIA1CAYiEIREgDUI/hiALQgGIhCENIA5CAYghDiAIQgGIhCEIIApCAYNQDQALIAIgFzcDsBAgAiAKNwO4ECACIAg3A6gQIAIgFjcDoBALAkACQAJAAkACQCAQIgsgFiIMUg0AIAghDCAJIQsgCCAJUg0AIBgiCyAXIgxSDQAgCiEMIAchCyAHIApRDQELIAsgDFoNACACIAogB30iGTcDuBAgAiAXIBh9IgsgByAKVq0iCn0iDDcDsBAgAiAIIAl9IhogFyAYVCAKIAtWcq0iCn0iCzcDqBAgAiAWIBB9IAggCVQgCiAaVnKtfSIWNwOgEAJAAkAgEiIIIA4iClINACAUIgggEyIKUg0AIBUiCCARIgpSDQAgDyIIIA0iClENAQsgCCAKVg0CCyAOIBJ9IBMgFH0iJCARIBV9IiUgDSAPVK0iI1QgESAVVHKtIhpUIBMgFFRyrX0hDiANIA99IQ0gDCEXIAshCCAZIQogJSAjfSERICQgGn0hEwwDCyACIAcgCn0iGTcDmBAgAiAYIBd9IgsgByAKVK0iB30iDDcDkBAgAiAJIAh9IhogFyAYViAHIAtWcq0iB30iCzcDiBAgAiAQIBZ9IAggCVYgByAaVnKtfSIQNwOAEAJAAkAgEiIHIA4iCVINACAUIgcgEyIJUg0AIBUiByARIglSDQAgDyIHIA0iCVENAQsgByAJVA0CCyASIA59IBMgFFYgFCATfSIjIBEgFVYgFSARfSIaIA0gD1atIhVUcq0iFFRyrX0hEiAPIA19IQ8gDCEYIAshCSAZIQcgGiAVfSEVICMgFH0hFAwCCyAOQt2whYzotpGouH8gFH0iF0KNlcfDltLawJd/IBV9Ig4gD0LH+vPD7YKjkDxWrSIIVCAVQo2Vx8OW0trAl39Wcq0iClQgFELdsIWM6LaRqLh/VnKtIBJ8fSAXIAp9IgogE3wiEyAKVCATIBMgDiAIfSIKIBF8IgggClQgCELH+vPD7YKjkDwgD30iCiANfCINIApUrXwiESAIVHKtfCITVnKtfEKpwMaJrs6TsjB8IQ4gDCEXIAshCCAZIQoMAQsgEiAOfULdsIWM6LaRqLh/IBN9IhJCjZXHw5bS2sCXfyARfSIYIA1Cx/rzw+2Co5A8Vq0iCVQgEUKNlcfDltLawJd/VnKtIgdUIBNC3bCFjOi2kai4f1ZyrX0gEiAHfSIHIBR8IhQgB1QgFCAUIBggCX0iByAVfCIJIAdUIAlCx/rzw+2Co5A8IA19IgcgD3wiDyAHVK18IhUgCVRyrXwiFFZyrXxCqcDGia7Ok7IwfCESIAwhGCALIQkgGSEHCyACQYAQaiACQeAPakEgEPEDDQALCyABQSBqIQEgAkHwCGogD0IAICBCABDJAyACQZAIaiAPQgAgH0IAEMkDIAJBgAhqIA9CACAhQgAQyQMgAkHwB2ogD0IAICJCABDJAyACQeAIaiACKQPwCCILQgBCAEKJx5mkrvCB6Yd/EMkDIAJB0AhqIAIpA+gIIgdCAELH+vPD7YKjkDxCABDJAyACQcAIaiAHQgBCjZXHw5bS2sCXf0IAEMkDIAJBsAhqIAdCAELdsIWM6LaRqLh/QgAQyQMgAkGgCGogB0IAQqnAxomuzpOyMEIAEMkDIAJB4AdqIBVCACAgQgAQyQMgAkGAB2ogFUIAIB9CABDJAyACQfAGaiAVQgAgIUIAEMkDIAJB4AZqIBVCACAiQgAQyQMgAkHQB2ogAikDwAgiCCACKQP4CCIKIAIpA5AIfCIJfCIQIAIpA9gIIAsgAikD0AgiB3wgB1StfHwiDCACKQPgB3wiB0IAQgBCiceZpK7wgemHfxDJAyACQcAHaiACKQPYByILQgBCx/rzw+2Co5A8QgAQyQMgAkGwB2ogC0IAQo2Vx8OW0trAl39CABDJAyACQaAHaiALQgBC3bCFjOi2kai4f0IAEMkDIAJBkAdqIAtCAEKpwMaJrs6TsjBCABDJAyACQdAGaiAUQgAgIEIAEMkDIAJB8AVqIBRCACAfQgAQyQMgAkHgBWogFEIAICFCABDJAyACQdAFaiAUQgAgIkIAEMkDIAJBwAZqIAIpA+gHIAcgDFStfCILIAIpA4AHfCIOIAIpA5gIIAkgClStfCIKIAIpA4AIfCIWIAIpA7AIfCITIAwgEFStIAIpA8gIIAggEFatfHx8Igl8Ig0gAikDsAd8IhEgAikDyAcgByACKQPAByIHfCAHVK18fCIQIAIpA9AGfCIHQgBCAEKJx5mkrvCB6Yd/EMkDIAJBsAZqIAIpA8gGIghCAELH+vPD7YKjkDxCABDJAyACQaAGaiAIQgBCjZXHw5bS2sCXf0IAEMkDIAJBkAZqIAhCAELdsIWM6LaRqLh/QgAQyQMgAkGABmogCEIAQqnAxomuzpOyMEIAEMkDIAJBwAVqIBJCACAgQgAQyQMgAkHgBGogEkIAIB9CABDJAyACQdAEaiASQgAgIUIAEMkDIAJBwARqIBJCACAiQgAQyQMgAkGwBWogAikD2AYgByAQVK18IgggAikD8AV8IhogAikDiAggCiAWVq18IgogAikD8Ad8IhkgAikDoAh8IgwgCSATVK0gAikDuAggEyAWVK18fHwiGCACKQPwBnwiFyANIA5UrSACKQOIByALIA5WrXx8fCIOIAIpA6AHfCIWIBAgEVStIAIpA7gHIA0gEVatfHx8Igl8IhMgAikDoAZ8IhAgAikDuAYgByACKQOwBiIHfCAHVK18fCINIAIpA8AFfCIRQgBCAEKJx5mkrvCB6Yd/EMkDIAJBoAVqIAIpA7gFIgdCAELH+vPD7YKjkDxCABDJAyACQZAFaiAHQgBCjZXHw5bS2sCXf0IAEMkDIAJBgAVqIAdCAELdsIWM6LaRqLh/QgAQyQMgAkHwBGogB0IAQqnAxomuzpOyMEIAEMkDAkAgAikD+AQgAikDiAYgAikDmAcgDCAYVq0gAikDqAggDCAZVK18fCACKQP4ByAKIBlWrXx8IgcgAikD4AZ8IgwgDiAXVK0gAikD+AYgFyAYVK18fHwiCyACKQOQB3wiCiALVK18IAogCSAWVK0gAikDqAcgDiAWVq18fHwiCSAKVK18IAsgDFStIAIpA+gGIAcgDFatfHx8IgcgAikD0AV8IgwgAikD6AUgCSAJIAIpA+AFfCIJVq18IAkgCSATIBpUrSACKQP4BSAIIBpWrXx8fCIJVq18fCILIAIpA4AGfCIKIAtUrXwgCiACKQOYBiAJIAkgAikDkAZ8IglWrXwgCSAJIA0gEFStIAIpA6gGIBAgE1StfHx8IglWrXx8IgggClStfCALIAxUrSACKQPYBSAHIAxWrXx8fCIKIAIpA8AEfCIQIAIpA9gEIAggAikD0AR8IgsgCFStfCALIAIpA+gEIAIpA8gFIA0gEVatfCIHIAIpA+AEfCIIIAdUrXwgCCAJfCIJIAhUrXx8IgcgC1StfHwiDCACKQPwBHwiCyAMVK18IAsgAikDiAUgByACKQOABXwiCCAHVK18IAggAikDmAUgCSAJIAIpA5AFfCIJVq18IAkgAikDqAUgAikDoAUiByARfCAHVK18fCIHIAlUrXx8IgkgCFStfHwiCCALVK18IAwgEFStIAIpA8gEIAogEFatfHx8IgpCqcDGia7Ok7IwVg0AIApCqcDGia7Ok7IwUg0CIAhC3bCFjOi2kai4f1YNACAIQt2whYzotpGouH9SBEBCqcDGia7Ok7IwIQoMAwsgCUKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hEyAJQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIQogCSERDAQLQo2Vx8OW0trAl38hESAHQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhCgwDCyAJQvPquLzpraW/6AB8IhAgB0LH+vPD7YKjkDxUrSIMfSERIAhCo8/685fJ7tfHAHwiCyAJQo2Vx8OW0trAl39UIAwgEFZyrSIJfSETIAogCELdsIWM6LaRqLh/VCAJIAtWcq19QqnAxomuzpOyMH0hCiAHQsf688PtgqOQPH0hBwwCCyAAQgE3AwAgAEICNwMIDAILIAghEyAJIRELAn4gAUHIpcUAQSAQ8QNFBEBCACEOQgAMAQtCqcDGia7Ok7IwQt2whYzotpGouH8gHX0iDEKNlcfDltLawJd/IBt9IgsgHELH+vPD7YKjkDxWrSIIVCAbQo2Vx8OW0trAl39Wcq0iCVQgHULdsIWM6LaRqLh/VnKtIB58fSEeQsf688PtgqOQPCAcfSEcQgAhDiAMIAl9IR0gCyAIfSEbQgALIQ0gAkGwBGogHEIAIA9CABDJAyACQaADaiAbQgAgD0IAEMkDIAJBkAJqIB0gDSAPQgAQyQMgAkGAAWogHiAOIA9CABDJAyACQaAEaiACKQOwBCIQQgBCAEKJx5mkrvCB6Yd/EMkDIAJBkARqIAIpA6gEIglCAELH+vPD7YKjkDxCABDJAyACQYAEaiAJQgBCjZXHw5bS2sCXf0IAEMkDIAJB8ANqIAlCAELdsIWM6LaRqLh/QgAQyQMgAkHgA2ogCUIAQqnAxomuzpOyMEIAEMkDIAJB0ANqIBxCACAVQgAQyQMgAkHAAmogG0IAIBVCABDJAyACQbABaiAdIA0gFUIAEMkDIAJBIGogHiAOIBVCABDJAyACQZADaiACKQOABCIMIAIpA7gEIgsgAikDoAN8Igh8IhYgAikDmAQgECACKQOQBCIJfCAJVK18fCIPIAIpA9ADfCIJQgBCAEKJx5mkrvCB6Yd/EMkDIAJBgANqIAIpA5gDIhBCAELH+vPD7YKjkDxCABDJAyACQfACaiAQQgBCjZXHw5bS2sCXf0IAEMkDIAJB4AJqIBBCAELdsIWM6LaRqLh/QgAQyQMgAkHQAmogEEIAQqnAxomuzpOyMEIAEMkDIAJBwANqIBxCACAUQgAQyQMgAkGwAmogG0IAIBRCABDJAyACQaABaiAdIA0gFEIAEMkDIAJBEGogHiAOIBRCABDJAyACQYACaiACKQPYAyAJIA9UrXwiECACKQPAAnwiIyACKQOoAyAIIAtUrXwiCyACKQOQAnwiFyACKQPwA3wiFSAPIBZUrSACKQOIBCAMIBZWrXx8fCIIfCIUIAIpA/ACfCIWIAIpA4gDIAkgAikDgAMiCXwgCVStfHwiDyACKQPAA3wiCUIAQgBCiceZpK7wgemHfxDJAyACQfABaiACKQOIAiIMQgBCx/rzw+2Co5A8QgAQyQMgAkHgAWogDEIAQo2Vx8OW0trAl39CABDJAyACQdABaiAMQgBC3bCFjOi2kai4f0IAEMkDIAJBwAFqIAxCAEKpwMaJrs6TsjBCABDJAyACQbADaiAcQgAgEkIAEMkDIAJBoAJqIBtCACASQgAQyQMgAkGQAWogHSANIBJCABDJAyACIB4gDiASQgAQyQMgAkHwAGogAikDyAMgCSAPVK18IgwgAikDsAJ8IhogAikDmAIgCyAXVq18IgsgAikDgAF8IhkgAikD4AN8Ig0gCCAVVK0gAikD+AMgFSAXVK18fHwiEiACKQOwAXwiGCAUICNUrSACKQPIAiAQICNWrXx8fCIXIAIpA+ACfCIOIA8gFlStIAIpA/gCIBQgFlatfHx8Igh8IhUgAikD4AF8Ig8gAikD+AEgCSACKQPwASIJfCAJVK18fCIUIAIpA7ADfCIWQgBCAEKJx5mkrvCB6Yd/EMkDIAJB4ABqIAIpA3giCUIAQsf688PtgqOQPEIAEMkDIAJB0ABqIAlCAEKNlcfDltLawJd/QgAQyQMgAkFAayAJQgBC3bCFjOi2kai4f0IAEMkDIAJBMGogCUIAQqnAxomuzpOyMEIAEMkDAkACQCACKQM4IAIpA8gBIAIpA9gCIA0gElatIAIpA+gDIA0gGVStfHwgAikDiAEgCyAZVq18fCIJIAIpAyB8Ig0gFyAYVK0gAikDuAEgEiAYVq18fHwiECACKQPQAnwiCyAQVK18IAsgCCAOVK0gAikD6AIgDiAXVK18fHwiCCALVK18IA0gEFatIAIpAyggCSANVq18fHwiCSACKQMQfCINIAIpA6gBIAggCCACKQOgAXwiCFatfCAIIAggFSAaVK0gAikDuAIgDCAaVq18fHwiCFatfHwiECACKQPAAXwiCyAQVK18IAsgAikD2AEgCCAIIAIpA9ABfCIIVq18IAggCCAPIBRWrSACKQPoASAPIBVUrXx8fCIIVq18fCIMIAtUrXwgDSAQVq0gAikDGCAJIA1WrXx8fCILIAIpAwB8Ig8gAikDmAEgDCACKQOQAXwiECAMVK18IBAgAikDqAIgAikDuAMgFCAWVq18IgkgAikDoAJ8IgwgCVStfCAIIAx8IgggDFStfHwiCSAQVK18fCINIAIpAzB8IhAgDVStfCAQIAIpA0ggCSACKQNAfCIMIAlUrXwgDCACKQNYIAggCCACKQNQfCIIVq18IAggAikDaCACKQNgIgkgFnwgCVStfHwiEiAIVK18fCIJIAxUrXx8IgggEFStfCANIA9UrSACKQMIIAsgD1atfHx8Ig5CqcDGia7Ok7IwVg0AAkAgDkKpwMaJrs6TsjBRBEAgCELdsIWM6LaRqLh/Vg0CIAhC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhDgsgCCENIAkhEAwCCyAJQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyENIAlCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhDiAJIRAMAgtCjZXHw5bS2sCXfyEQIBJCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEODAELIAlC8+q4vOmtpb/oAHwiDSASQsf688PtgqOQPFStIgx9IRAgCEKjz/rzl8nu18cAfCILIAlCjZXHw5bS2sCXf1QgDCANVnKtIgl9IQ0gDiAIQt2whYzotpGouH9UIAkgC1ZyrX1CqcDGia7Ok7IwfSEOIBJCx/rzw+2Co5A8fSESCyAAIBI3A0AgACAQNwM4IAAgDTcDMCAAIA43AyggACAHNwMgIAAgETcDGCAAIBM3AxAgACAKNwMIIABCADcDAAsgAkHAEGokAAvaTQIGfxh+QgIhDCMAQZAQayICJAAgASkDKCEaIAEpAyAhCCABKQMYIQ4gASkDECERIAEpAwghEiABKQMAIRgDQCAMIRAgAkHgDmogCEIAIBpCABDJAyACQcAOaiAOQgAgGkIAEMkDIAJBkA5qIBFCACAaQgAQyQMgAkHQDWogEkIAIBpCABDJAyACQYANaiAYQgAgGkIAEMkDIAJBsA5qIA5CACAIQgAQyQMgAkGADmogEUIAIAhCABDJAyACQcANaiASQgAgCEIAEMkDIAJB8AxqIBhCACAIQgAQyQMgAkHwDWogEUIAIA5CABDJAyACQbANaiASQgAgDkIAEMkDIAJB4AxqIBhCACAOQgAQyQMgAkGgDWogEkIAIBFCABDJAyACQdAMaiAYQgAgEUIAEMkDIAJBwAxqIBhCACASQgAQyQMgAkHQD2ogGkIAIBpCABDJAyACQdAOaiAIQgAgCEIAEMkDIAJBoA5qIA5CACAOQgAQyQMgAkHgDWogEUIAIBFCABDJAyACQZANaiASQgAgEkIAEMkDIAJBsAxqIBhCACAYQgAQyQMgAkHAD2ogAikD0A8iGEL9//P/z///+Yl/fiIIQgBCq9X+////v/+5f0IAEMkDIAJBsA9qIAhCAEL//8+K6///1R5CABDJAyACQaAPaiAIQgBCpOzDtY/UtJjnAEIAEMkDIAJBkA9qIAhCAEK/pZScz/DSu+QAQgAQyQMgAkGAD2ogCEIAQtfZrprk9umNywBCABDJAyACQfAOaiAIQgBCms3/y6O9xIAaQgAQyQMgAikDyAwgAikD2AwgAikDqA0gAikDuA0gAikD+A0gAikDiA4gAikDuA4gAikDyA4gAikD6A4iCCACKQPADnwiGiAIVK18IgggAikDkA58Ig4gAikDsA58IhQgDlStfCIRIAIpA5gOIAggDlatfCIOIAIpA9ANfCIIfCIJIBFUrXwgCSACKQOADnwiEyAJVK18IhEgAikD2A0gCCAOVK18IgkgAikDgA18Igh8IgsgAikDwA18IhIgAikD8A18IgogElStfCIOIAsgElatIAIpA8gNIAsgEVStfHwiESACKQOIDSAIIAlUrXx8IhIgAikD8Ax8Igh8IgkgDlStfCAJIAIpA7ANfCIPIAlUrXwiDiAIIBJUrSACKQP4DCARIBJWrXx8fCIJIAIpA+AMfCIRIAIpA6ANfCINIBFUrXwiCCAJIBFWrSACKQPoDCAJIA5UrXx8fCIOIAhUrXwgDiACKQPQDHwiFyAOVK18IgggAikDwAx8IhYgCFStfCILQj+IIAIpA7gMIAIpA5gNIAIpA+gNIAIpA6gOIAIpA9gOIAIpA9gPIgggAikD4A4iDkIBhnwiDCAIVK0iCCAaQgGGIA5CP4iEfCIOIAhUrXwgDiACKQPQDnwiEiAOVK18IgggFEIBhiAaQj+IhHwiCSAIVK0iCCATQgGGIBRCP4iEfCIOIAhUrXwgDiACKQOgDnwiESAOVK18IgggCkIBhiATQj+IhHwiDiAIVK0iCCAPQgGGIApCP4iEfCIKIAhUrXwgCiACKQPgDXwiFCAKVK18IgggDUIBhiAPQj+IhHwiCiAIVK0iCCAXQgGGIA1CP4iEfCINIAhUrXwgDSACKQOQDXwiDyANVK18IgggFkIBhiAXQj+IhHwiDSAIVK0iCCALQgGGIBZCP4iEfCIWIAhUrXwgFiAWIAIpA7AMfCILVq18fCEVQQAhAwJ/AkAgAikD+A4gAikDiA8gAikDmA8gAikDqA8gAikDuA8gAikDyA8gAikDwA8iCCAYQn2DfCAIVK18IgggAikDsA98IhYgCFStfCAWIAwgFnwiGFatfCIIIAIpA6APfCIMIAhUrXwgDCASfCISIAxUrXwiCCACKQOQD3wiDCAIVK18IAkgDHwiCSAMVK18IgggAikDgA98IgwgCFStfCAMIBF8IhEgDFStfCIIIAIpA/AOfCIMIAhUrXwgDCAOfCIOIAxUrXwiCFANACAIIBR8IhQgCFQiAUUNACABrSIIIAp8IgogCFoNACAIIApWrSIIIA98Ig8gCFoNACAIIA9WrSIIIA18Ig0gCFoNACAIIA1WrSIIIAt8IgsgCFoNACAIIAtWrSIIIBV8IhUgCFQMAQtBAAshBiACQaAMaiAYQv3/8//P///5iX9+IghCAEKr1f7///+//7l/QgAQyQMgAkGQDGogCEIAQv//z4rr///VHkIAEMkDIAJBgAxqIAhCAEKk7MO1j9S0mOcAQgAQyQMgAkHwC2ogCEIAQr+llJzP8NK75ABCABDJAyACQeALaiAIQgBC19mumuT26Y3LAEIAEMkDIAJB0AtqIAhCAEKazf/Lo73EgBpCABDJAwJAIAIpA9gLIAIpA+gLIAIpA/gLIAIpA4gMIAIpA5gMIAIpA6gMIAIpA6AMIgggGHwgCFStfCIIIAIpA5AMfCIMIAhUrXwgDCAMIBJ8IhhWrXwiCCACKQOADHwiDCAIVK18IAwgCSAMfCISVq18IgggAikD8At8IgwgCFStfCAMIAwgEXwiCVatfCIIIAIpA+ALfCIMIAhUrXwgDCAMIA58IhFWrXwiCCACKQPQC3wiDCAIVK18IAwgDCAUfCIOVq18IghQDQAgCCAKfCIKIAhaDQAgCCAKVq0iCCAPfCIPIAhaDQAgCCAPVq0iCCANfCINIAhaDQAgCCANVq0iCCALfCILIAhaDQAgCCALVq0iCCAVfCIVIAhUIQMLIAJBwAtqIBhC/f/z/8////mJf34iCEIAQqvV/v///7//uX9CABDJAyACQbALaiAIQgBC///Piuv//9UeQgAQyQMgAkGgC2ogCEIAQqTsw7WP1LSY5wBCABDJAyACQZALaiAIQgBCv6WUnM/w0rvkAEIAEMkDIAJBgAtqIAhCAELX2a6a5PbpjcsAQgAQyQMgAkHwCmogCEIAQprN/8ujvcSAGkIAEMkDQQAhBAJ/QQAgAikD+AogAikDiAsgAikDmAsgAikDqAsgAikDuAsgAikDyAsgAikDwAsiCCAYfCAIVK18IgggAikDsAt8IgwgCFStfCAMIAwgEnwiGFatfCIIIAIpA6ALfCIMIAhUrXwgDCAJIAx8IhJWrXwiCCACKQOQC3wiDCAIVK18IAwgDCARfCIJVq18IgggAikDgAt8IgwgCFStfCAMIAwgDnwiEVatfCIIIAIpA/AKfCIMIAhUrXwgDCAKIAx8Ig5WrXwiCFANABpBACAIIAggD3wiD1gNABpBACAIIA9WrSIIIA18Ig0gCFoNABpBACAIIA1WrSIIIAt8IgsgCFoNABogCCALVq0iCCAVfCIVIAhUCyEHIAJB4ApqIBhC/f/z/8////mJf34iCEIAQqvV/v///7//uX9CABDJAyACQdAKaiAIQgBC///Piuv//9UeQgAQyQMgAkHACmogCEIAQqTsw7WP1LSY5wBCABDJAyACQbAKaiAIQgBCv6WUnM/w0rvkAEIAEMkDIAJBoApqIAhCAELX2a6a5PbpjcsAQgAQyQMgAkGQCmogCEIAQprN/8ujvcSAGkIAEMkDAkAgAikDmAogAikDqAogAikDuAogAikDyAogAikD2AogAikD6AogAikD4AoiCCAYfCAIVK18IgggAikD0Ap8IgogCFStfCAKIAogEnwiDFatfCIIIAIpA8AKfCIKIAhUrXwgCiAJIAp8IhJWrXwiCCACKQOwCnwiCiAIVK18IAogCiARfCIJVq18IgggAikDoAp8IgogCFStfCAKIAogDnwiEVatfCIIIAIpA5AKfCIKIAhUrXwgCiAKIA98Ig5WrXwiCFANACAIIA18Ig0gCFoNACAIIA1WrSIIIAt8IgsgCFoNACAIIAtWrSIIIBV8IhUgCFQhBAsgAkGACmogDEL9//P/z///+Yl/fiIIQgBCq9X+////v/+5f0IAEMkDIAJB8AlqIAhCAEL//8+K6///1R5CABDJAyACQeAJaiAIQgBCpOzDtY/UtJjnAEIAEMkDIAJB0AlqIAhCAEK/pZScz/DSu+QAQgAQyQMgAkHACWogCEIAQtfZrprk9umNywBCABDJAyACQbAJaiAIQgBCms3/y6O9xIAaQgAQyQNBACEBIAIpA7gJIAIpA8gJIAIpA9gJIAIpA+gJIAIpA/gJIAIpA4gKIAIpA4AKIgggDHwgCFStfCIIIAIpA/AJfCIKIAhUrXwgCiASfCIMIApUrXwiCCACKQPgCXwiEiAIVK18IAkgEnwiCiASVK18IgggAikD0Al8IgkgCFStfCAJIBF8IhIgCVStfCIIIAIpA8AJfCIRIAhUrXwgDiARfCIJIBFUrXwiCCACKQOwCXwiDiAIVK18IA0gDnwiESAOVK18IghQRQRAIAggC3wiCyAIVCIBrSIOIBV8IgggFSABGyEVIAEgCCAOVHEhAQsgAkGgCWogDEL9//P/z///+Yl/fiIIQgBCq9X+////v/+5f0IAEMkDIAJBkAlqIAhCAEL//8+K6///1R5CABDJAyACQYAJaiAIQgBCpOzDtY/UtJjnAEIAEMkDIAJB8AhqIAhCAEK/pZScz/DSu+QAQgAQyQMgAkHgCGogCEIAQtfZrprk9umNywBCABDJAyACQdAIaiAIQgBCms3/y6O9xIAaQgAQyQMgAikD2AggAikD6AggAikD+AggAikDiAkgAikDmAkgAikDqAkgAikDoAkiCCAMfCAIVK18IgggAikDkAl8Ig4gCFStfCAKIA58IhogDlStfCIIIAIpA4AJfCIOIAhUrXwgDiAOIBJ8Ig5WrXwiCCACKQPwCHwiEiAIVK18IAkgEnwiCSASVK18IgggAikD4Ah8IhIgCFStfCASIBEgEnwiClatfCIIIAIpA9AIfCIRIAhUrXwgCyARfCINIBFUrXwiESAVfCIIIBUgEUIAUiIFGyELAkACQAJAIAMgBnIgB3IgBHIgAXIgCCARVCIBrSARIAUbQgBSciABIAVxIAtCms3/y6O9xIAaVnJyDQAgC0Kazf/Lo73EgBpSBEAgDiEIIAkhDiAKIREgDSESIAshGAwDCyANQtfZrprk9umNywBWDQBCms3/y6O9xIAaIRggDULX2a6a5PbpjcsAUgRAIA4hCCAJIQ4gCiERIA0hEgwDCyAKQr+llJzP8NK75ABWBEBC19mumuT26Y3LACENDAELIApCv6WUnM/w0rvkAFIEQELX2a6a5PbpjcsAIRIgDiEIIAkhDiAKIREMAwsgCUKk7MO1j9S0mOcAVgRAQtfZrprk9umNywAhDQwBC0K/pZScz/DSu+QAIREgCUKk7MO1j9S0mOcAUgRAQtfZrprk9umNywAhEiAOIQggCSEODAMLIA5C///Piuv//9UeVgRAQtfZrprk9umNywAhDQwBC0LX2a6a5PbpjcsAIQ0gDkL//8+K6///1R5SIBpCqtX+////v/+5f1hyDQELIA5C///Piuv//9UefSISIBpCq9X+////v/+5f1StIhF9IQggCUKk7MO1j9S0mOcAfSIMIA5C///Piuv//9UeVCARIBJWcq0iEX0hDiAKQr+llJzP8NK75AB9IhIgCUKk7MO1j9S0mOcAVCAMIBFUcq0iCX0hESANQtfZrprk9umNywB9IgwgCkK/pZScz/DSu+QAVCAJIBJWcq0iCX0hEiALIA1C19mumuT26Y3LAFQgCSAMVnKtfUKazf/Lo73EgBp9IRggGkLVqoGAgIDAgMYAfCEaDAELIA4hCCAJIQ5C19mumuT26Y3LACESCyAQQgGIIQwgEEICg1ANAAsgAiAaNwOIECACIAg3A4AQIAIgDjcD+A8gAiARNwPwDyACIBI3A+gPIAIgGDcD4A8CQCAQQgJRBEAMAQsgAikD4A8hHCACKQPoDyETIAIpA/APIRQgAikD+A8hFyACKQOAECEWIAIpA4gQIRsDQCACQdAHaiAWQgAgG0IAEMkDIAJBsAdqIBdCACAbQgAQyQMgAkGAB2ogFEIAIBtCABDJAyACQcAGaiATQgAgG0IAEMkDIAJB8AVqIBxCACAbQgAQyQMgAkGgB2ogF0IAIBZCABDJAyACQfAGaiAUQgAgFkIAEMkDIAJBsAZqIBNCACAWQgAQyQMgAkHgBWogHEIAIBZCABDJAyACQeAGaiAUQgAgF0IAEMkDIAJBoAZqIBNCACAXQgAQyQMgAkHQBWogHEIAIBdCABDJAyACQZAGaiATQgAgFEIAEMkDIAJBwAVqIBxCACAUQgAQyQMgAkGwBWogHEIAIBNCABDJAyACQcAIaiAbQgAgG0IAEMkDIAJBwAdqIBZCACAWQgAQyQMgAkGQB2ogF0IAIBdCABDJAyACQdAGaiAUQgAgFEIAEMkDIAJBgAZqIBNCACATQgAQyQMgAkGgBWogHEIAIBxCABDJAyACQbAIaiACKQPACCIdQv3/8//P///5iX9+IglCAEKr1f7///+//7l/QgAQyQMgAkGgCGogCUIAQv//z4rr///VHkIAEMkDIAJBkAhqIAlCAEKk7MO1j9S0mOcAQgAQyQMgAkGACGogCUIAQr+llJzP8NK75ABCABDJAyACQfAHaiAJQgBC19mumuT26Y3LAEIAEMkDIAJB4AdqIAlCAEKazf/Lo73EgBpCABDJAyACKQO4BSACKQPIBSACKQOYBiACKQOoBiACKQPoBiACKQP4BiACKQOoByACKQO4ByACKQPYByIJIAIpA7AHfCITIAlUrXwiCSACKQOAB3wiCiACKQOgB3wiFyAKVK18IgsgAikDiAcgCSAKVq18IgogAikDwAZ8Igl8Ig0gC1StfCANIAIpA/AGfCIWIA1UrXwiCyACKQPIBiAJIApUrXwiDSACKQPwBXwiCXwiECACKQOwBnwiDyACKQPgBnwiGyAPVK18IgogDyAQVK0gAikDuAYgCyAQVq18fCILIAIpA/gFIAkgDVStfHwiDyACKQPgBXwiCXwiDSAKVK18IA0gAikDoAZ8Ih8gDVStfCIKIAkgD1StIAIpA+gFIAsgD1atfHx8Ig8gAikD0AV8IgsgAikDkAZ8Ig0gC1StfCIJIAsgD1StIAIpA9gFIAogD1atfHx8IgogCVStfCAKIAIpA8AFfCIeIApUrXwiCSACKQOwBXwiFSAJVK18IhBCP4ggAikDqAUgAikDiAYgAikD2AYgAikDmAcgAikDyAcgAikDyAgiCSACKQPQByIKQgGGfCIZIAlUrSIJIBNCAYYgCkI/iIR8IgogCVStfCAKIAIpA8AHfCIUIApUrXwiCSAXQgGGIBNCP4iEfCITIAlUrSIJIBZCAYYgF0I/iIR8IgogCVStfCAKIAIpA5AHfCIXIApUrXwiCSAbQgGGIBZCP4iEfCIWIAlUrSIJIB9CAYYgG0I/iIR8IgogCVStfCAKIAIpA9AGfCIJIApUrXwiCyANQgGGIB9CP4iEfCIKIAtUrSILIB5CAYYgDUI/iIR8Ig0gC1StfCANIAIpA4AGfCIPIA1UrXwiCyAVQgGGIB5CP4iEfCINIAtUrSILIBBCAYYgFUI/iIR8IhAgC1StfCAQIAIpA6AFfCILIBBUrXx8IRVBACEDAn8CQCACKQPoByACKQP4ByACKQOICCACKQOYCCACKQOoCCACKQO4CCACKQOwCCIQIB1CfYN8IBBUrXwiECACKQOgCHwiHiAQVK18IB4gGSAefCIdVq18IhAgAikDkAh8IhkgEFStfCAUIBl8IhQgGVStfCIQIAIpA4AIfCIZIBBUrXwgEyAZfCITIBlUrXwiECACKQPwB3wiGSAQVK18IBcgGXwiFyAZVK18IhAgAikD4Ad8IhkgEFStfCAWIBl8IhYgGVStfCIQUA0AIAkgEHwiCSAQVCIBRQ0AIAGtIhAgCnwiCiAQWg0AIAogEFStIhAgD3wiDyAQWg0AIA8gEFStIhAgDXwiDSAQWg0AIA0gEFStIhAgC3wiCyAQWg0AIAsgEFStIhAgFXwiFSAQVAwBC0EACyEGIAJBkAVqIB1C/f/z/8////mJf34iEEIAQqvV/v///7//uX9CABDJAyACQYAFaiAQQgBC///Piuv//9UeQgAQyQMgAkHwBGogEEIAQqTsw7WP1LSY5wBCABDJAyACQeAEaiAQQgBCv6WUnM/w0rvkAEIAEMkDIAJB0ARqIBBCAELX2a6a5PbpjcsAQgAQyQMgAkHABGogEEIAQprN/8ujvcSAGkIAEMkDAkAgAikDyAQgAikD2AQgAikD6AQgAikD+AQgAikDiAUgAikDmAUgAikDkAUiECAdfCAQVK18IhAgAikDgAV8Ih0gEFStfCAdIBQgHXwiGVatfCIQIAIpA/AEfCIUIBBUrXwgEyAUfCITIBRUrXwiECACKQPgBHwiFCAQVK18IBQgF3wiFyAUVK18IhAgAikD0AR8IhQgEFStfCAUIBZ8IhYgFFStfCIQIAIpA8AEfCIUIBBUrXwgCSAUfCIQIBRUrXwiCVANACAJIAp8IgogCVoNACAJIApWrSIJIA98Ig8gCVoNACAJIA9WrSIJIA18Ig0gCVoNACAJIA1WrSIJIAt8IgsgCVoNACAJIAtWrSIJIBV8IhUgCVQhAwsgAkGwBGogGUL9//P/z///+Yl/fiIJQgBCq9X+////v/+5f0IAEMkDIAJBoARqIAlCAEL//8+K6///1R5CABDJAyACQZAEaiAJQgBCpOzDtY/UtJjnAEIAEMkDIAJBgARqIAlCAEK/pZScz/DSu+QAQgAQyQMgAkHwA2ogCUIAQtfZrprk9umNywBCABDJAyACQeADaiAJQgBCms3/y6O9xIAaQgAQyQNBACEEAn9BACACKQPoAyACKQP4AyACKQOIBCACKQOYBCACKQOoBCACKQO4BCACKQOwBCIJIBl8IAlUrXwiCSACKQOgBHwiGSAJVK18IBkgEyAZfCIUVq18IgkgAikDkAR8IhMgCVStfCATIBd8IhcgE1StfCIJIAIpA4AEfCITIAlUrXwgEyAWfCIWIBNUrXwiCSACKQPwA3wiEyAJVK18IBAgE3wiECATVK18IgkgAikD4AN8IhMgCVStfCAKIBN8IgogE1StfCIJUA0AGkEAIAkgCSAPfCIPWA0AGkEAIAkgD1atIgkgDXwiDSAJWg0AGkEAIAkgDVatIgkgC3wiCyAJWg0AGiAJIAtWrSIJIBV8IhUgCVQLIQcgAkHQA2ogFEL9//P/z///+Yl/fiIJQgBCq9X+////v/+5f0IAEMkDIAJBwANqIAlCAEL//8+K6///1R5CABDJAyACQbADaiAJQgBCpOzDtY/UtJjnAEIAEMkDIAJBoANqIAlCAEK/pZScz/DSu+QAQgAQyQMgAkGQA2ogCUIAQtfZrprk9umNywBCABDJAyACQYADaiAJQgBCms3/y6O9xIAaQgAQyQMCQCACKQOIAyACKQOYAyACKQOoAyACKQO4AyACKQPIAyACKQPYAyACKQPQAyIJIBR8IAlUrXwiCSACKQPAA3wiEyAJVK18IBMgEyAXfCIUVq18IgkgAikDsAN8IhMgCVStfCATIBMgFnwiF1atfCIJIAIpA6ADfCITIAlUrXwgEyAQIBN8IhZWrXwiCSACKQOQA3wiEyAJVK18IBMgCiATfCIQVq18IgkgAikDgAN8IhMgCVStfCATIA8gE3wiClatfCIJUA0AIAkgDXwiDSAJWg0AIAkgDVatIgkgC3wiCyAJWg0AIAkgC1atIgkgFXwiFSAJVCEECyACQfACaiAUQv3/8//P///5iX9+IglCAEKr1f7///+//7l/QgAQyQMgAkHgAmogCUIAQv//z4rr///VHkIAEMkDIAJB0AJqIAlCAEKk7MO1j9S0mOcAQgAQyQMgAkHAAmogCUIAQr+llJzP8NK75ABCABDJAyACQbACaiAJQgBC19mumuT26Y3LAEIAEMkDIAJBoAJqIAlCAEKazf/Lo73EgBpCABDJA0EAIQEgAikDqAIgAikDuAIgAikDyAIgAikD2AIgAikD6AIgAikD+AIgAikD8AIiCSAUfCAJVK18IgkgAikD4AJ8Ig8gCVStfCAPIBd8IhQgD1StfCIJIAIpA9ACfCIPIAlUrXwgDyAWfCITIA9UrXwiCSACKQPAAnwiDyAJVK18IA8gEHwiFyAPVK18IgkgAikDsAJ8Ig8gCVStfCAKIA98IhYgD1StfCIJIAIpA6ACfCIKIAlUrXwgCiANfCIPIApUrXwiCVBFBEAgCSALfCILIAlUIgGtIgogFXwiCSAVIAEbIRUgASAJIApUcSEBCyAMIRAgAkGQAmogFEL9//P/z///+Yl/fiIJQgBCq9X+////v/+5f0IAEMkDIAJBgAJqIAlCAEL//8+K6///1R5CABDJAyACQfABaiAJQgBCpOzDtY/UtJjnAEIAEMkDIAJB4AFqIAlCAEK/pZScz/DSu+QAQgAQyQMgAkHQAWogCUIAQtfZrprk9umNywBCABDJAyACQcABaiAJQgBCms3/y6O9xIAaQgAQyQMgAikDyAEgAikD2AEgAikD6AEgAikD+AEgAikDiAIgAikDmAIgAikDkAIiCSAUfCAJVK18IgkgAikDgAJ8IgogCVStfCAKIBN8IhsgClStfCIJIAIpA/ABfCIKIAlUrXwgCiAXfCIMIApUrXwiCSACKQPgAXwiCiAJVK18IAogFnwiDSAKVK18IgkgAikD0AF8IhYgCVStfCAWIA8gFnwiClatfCIJIAIpA8ABfCIPIAlUrXwgCyAPfCIJIA9UrXwiDyAVfCILIBUgD0IAUiIFGyEcAkACQCADIAZyIAdyIARyIAFyIAsgD1QiAa0gDyAFG0IAUnIgASAFcSAcQprN/8ujvcSAGlZycg0AAkAgHEKazf/Lo73EgBpSDQAgCULX2a6a5PbpjcsAVg0BIAlC19mumuT26Y3LAFINACAKQr+llJzP8NK75ABWDQEgCkK/pZScz/DSu+QAUg0AIA1CpOzDtY/UtJjnAFYNASANQqTsw7WP1LSY5wBSDQAgDEL//8+K6///1R5WDQEgDEL//8+K6///1R5SDQAgG0Kq1f7///+//7l/Vg0BCyAMIRYgDSEXIAohFCAJIRMMAQsgDEL//8+K6///1R59IhcgG0Kr1f7///+//7l/VK0iC30hFiANQqTsw7WP1LSY5wB9Ig8gDEL//8+K6///1R5UIAsgF1ZyrSILfSEXIApCv6WUnM/w0rvkAH0iDCANQqTsw7WP1LSY5wBUIAsgD1ZyrSINfSEUIAlC19mumuT26Y3LAH0iCyAKQr+llJzP8NK75ABUIAwgDVRyrSIKfSETIBwgCULX2a6a5PbpjcsAVCAKIAtWcq19QprN/8ujvcSAGn0hHCAbQtWqgYCAgMCAxgB8IRsLIAIgGzcDiBAgAiAWNwOAECACIBc3A/gPIAIgFDcD8A8gAiATNwPoDyACIBw3A+APAkAgEEICg1ANAEIAIQ1BKCEBQgAhD0IAIQtCACEKQgAhCUIAIRUDQCACQeAAaiACQeAPaiABaikDACIMQgAgGkIAEMkDIAJB8ABqIAxCACAIQgAQyQMgAkGAAWogDEIAIA5CABDJAyACQZABaiAMQgAgEUIAEMkDIAJBoAFqIAxCACASQgAQyQMgAkGwAWogDEIAIBhCABDJAyACQdAAaiAVIAIpA2AiGXwiH0L9//P/z///+Yl/fiIMQgBCq9X+////v/+5f0IAEMkDIAJBQGsgDEIAQv//z4rr///VHkIAEMkDIAJBMGogDEIAQqTsw7WP1LSY5wBCABDJAyACQSBqIAxCAEK/pZScz/DSu+QAQgAQyQMgAkEQaiAMQgBC19mumuT26Y3LAEIAEMkDIAIgDEIAQprN/8ujvcSAGkIAEMkDIAIpAwggDSACKQOwASIMfCIeIAIpA6gBIAIpA6ABIg0gD3wiDyANVK18IA8gAikDmAEgCyACKQOQASILfCINIAtUrXwgDSACKQOIASAKIAIpA4ABIgp8IgsgClStfCALIAIpA3ggCSACKQNwIgl8IgogCVStfCAKIAogAikDaCAZIB9WrXx8IgpWrXx8IhUgC1StfHwiCyANVK18fCIJIA9UrXx8Ih0gAikDAHwiGSAdVK18IBkgAikDGCAJIAIpAxB8Ig8gCVStfCAPIAIpAyggCyACKQMgfCINIAtUrXwgDSACKQM4IBUgAikDMHwiCyAVVK18IAsgAikDSCAKIAIpA0AiCXwiCiAJVK18IAogAikDWCACKQNQIgkgH3wgCVStfHwiFSAKVK18fCIJIAtUrXx8IgogDVStfHwiCyAPVK18fCIPIBlUrXwgHSAeVK0gAikDuAEgDCAeVq18fHwhDSABQQhrIgFBeEcNAAsCQCANQprN/8ujvcSAGlYNAAJAIA1Cms3/y6O9xIAaUgRAIA0hGCAPIRIgCyERIAohDiAJIQgMAQsgD0LX2a6a5PbpjcsAVg0BQprN/8ujvcSAGiEYIA9C19mumuT26Y3LAFIEQCAPIRIgCyERIAohDiAJIQgMAQsgC0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhEiALQr+llJzP8NK75ABSBEAgCyERIAohDiAJIQgMAQsgCkKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhESAKQqTsw7WP1LSY5wBSBEAgCiEOIAkhCAwBCyAJQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIQ4gCUL//8+K6///1R5SBEAgCSEIDAELQv//z4rr///VHiEIIBVCqtX+////v/+5f1YNAQsgFSEaDAELIAlC///Piuv//9UefSIRIBVCq9X+////v/+5f1StIg59IQggCkKk7MO1j9S0mOcAfSIMIAlC///Piuv//9UeVCAOIBFWcq0iEX0hDiALQr+llJzP8NK75AB9IhIgCkKk7MO1j9S0mOcAVCAMIBFUcq0iCX0hESAPQtfZrprk9umNywB9IgogC0K/pZScz/DSu+QAVCAJIBJWcq0iCX0hEiANIA9C19mumuT26Y3LAFQgCSAKVnKtfUKazf/Lo73EgBp9IRggFULVqoGAgIDAgMYAfCEaCyAQQgGIIQwgEEIEWg0ACwsgACAaNwMoIAAgCDcDICAAIA43AxggACARNwMQIAAgEjcDCCAAIBg3AwAgAkGQEGokAAuodwIMfyR+IwBBkA5rIgIkACACQfANakGMocQAKAIANgIAIAJBhKHEACkCADcD6A0gAkHoDWpB6KLEABClAyACKALsDUEBNgIAIAIoAuwNIQQCQAJAIAIoAugNIgVBgICAgHhHDQAgBCgCCA0AIAJBADYCyAwgAkKAgICAwAA3AsAMDAELIAJBATYC8A0gAiAENgLsDSACIAU2AugNIAJBwAxqIAJB6A1qQQdBHxDPAQsgASgCCCIGQQJ0IQkCfwJAAkACQAJAAkAgBkH/////A0sgCUH8////B0tyDQAgASgCBCEEAn8gCUUEQEEEIQdBAAwBC0HRzsUALQAAGkEEIQggCUEEENYEIgdFDQEgBgshBSAJBEAgByAEIAn8CgAACyACIAY2AqANIAIgBzYCnA0gAiAFNgKYDSACKALIDCIGQQJ0IQlBACEIIAZB/////wNLIAlB/P///wdLcg0BIAIoAsQMIQQCfyAJRQRAQQQhB0EADAELQdHOxQAtAAAaQQQhCCAJQQQQ1gQiB0UNAiAGCyEFIAkEQCAHIAQgCfwKAAALIAIgBjYCwA0gAiAHNgK8DSACIAU2ArgNIAJB6A1qIAJBmA1qIAJBuA1qEJwBIAIoAvANIQsgAigC7A0hDCACKALoDSENIAIoAvQNIgUEQCACKAL4DSAFQQJ0EN8ECyACQcwMaiIFIAEgAkHADGoQ8AEgAkHYDGogBRD1AiACKQPwDCESIAIpA+gMIREgAikD4AwhDyACKQPYDCEOIAJB6A1qIgFB763EABCwASACLQDoDUEBRg0CIAIpA4gOISQgAikDgA4hISACKQP4DSEfIAIpA/ANIR0gAUGvrsQAELABIAItAOgNQQFGDQMgAkHwC2ogEkIAIBFCABDJAyACQdALaiASQgAgD0IAEMkDIAJBoAtqIBJCACAOQgAQyQMgAkHAC2ogEUIAIA9CABDJAyACQZALaiARQgAgDkIAEMkDIAJBgAtqIA9CACAOQgAQyQMgAkGwDGogEkIAIBJCABDJAyACQeALaiARQgAgEUIAEMkDIAJBsAtqIA9CACAPQgAQyQMgAkHwCmogDkIAIA5CABDJAyACQaAMaiACKQOwDCIRQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkGQDGogDkIAQn9CABDJAyACQYAMaiAOQgBC////////////AEIAEMkDIAIpA4gLIAIpA5gLIAIpA6gLIAIpA9gLIAIpA/gLIg4gAikD0At8IhMgDlStfCIOIAIpA6ALfCISIA5UrXwiDiACKQOQC3wiDyAOVK18IA8gDyACKQPICyASIBIgAikDwAt8IhhWrXx8IhVWrXwiDiACKQOAC3wiFCAOVK18Ig9CP4ggAikD+AogAikD8AoiDiAPQgGGIBRCP4iEfCIQIA5UrXwgECACKQO4CyACKQPoCyACKQPgCyIOIBNCAYYgAikD8AsiD0I/iIR8IhIgDlStfCASIBIgAikDuAwiDiAPQgGGfCIXIA5UrXwiFlatfCIOIBhCAYYgE0I/iIR8IhMgDlStIg4gAikDsAt8Ig8gDlStfCAPIA8gFUIBhiAYQj+IhHwiD1atfCIOIBRCAYYgFUI/iIR8IhwgDlStfCISIBBUrXx8IRRBACEIIAIpA4gMIAIpA5gMIhAgECACKQOoDCACKQOgDCIOIBFCfYN8IA5UrXwiDiACKQOQDCIRfCIVIA5UrXwgFSAVIBd8IhdWrXwiDiARfCIRIA5UrXwgESAWfCIWIBFUrXwiDiACKQOADHwiESAOVK18IBEgE3wiEyARVK18Ig5QDQQgDiAPfCIPIA5UIgFFDQQgAa0iDiAcfCIcIA5aDQQgDiAcVq0iDiASfCISIA5aDQQgDiASVq0iDiAUfCIUIA5UDAULIAggCUH4gcAAEMgEAAsgCCAJQfiBwAAQyAQACyACIAItAOkNOgDoDUGUpMQAQSsgAkHoDWpBsK/EAEHwr8QAEMoDAAsgAiACLQDpDToA6A1BlKTEAEErIAJB6A1qQbCvxABB4K/EABDKAwALQQALIQUgAikDiA4hJyACKQOADiEoIAIpA/gNISkgAikD8A0hKiACQeAKaiAXQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkHQCmogDkIAQn9CABDJAyACQcAKaiAOQgBC////////////AEIAEMkDAkAgAikDyAogAikD2AoiECAQIAIpA+gKIBcgAikD4AoiDnwgDlStfCIOIAIpA9AKIhF8IhcgDlStfCAWIBd8IhYgF1StfCIOIBF8IhEgDlStfCARIBN8IhMgEVStfCIOIAIpA8AKfCIRIA5UrXwgDyARfCIQIBFUrXwiDlANACAOIBx8IhwgDloNACAOIBxWrSIOIBJ8IhIgDloNACAOIBJWrSIOIBR8IhQgDlQhCAsgAkGwCmogFkKblK/D8rWo3oZ/fiIOQgBCbUIAEMkDIAJBoApqIA5CAEJ/QgAQyQMgAkGQCmogDkIAQv///////////wBCABDJA0EAIQEgAikDmAogAikDqAoiESARIAIpA7gKIAIpA7AKIg4gFnwgDlStfCIOIAIpA6AKIg98IhcgDlStfCAXIBMgF3wiFlatfCIOIA98Ig8gDlStfCAPIBB8IhMgD1StfCIOIAIpA5AKfCIPIA5UrXwgDyAcfCIQIA9UrXwiDlBFBEAgDiASfCISIA5UIgGtIg8gFHwiDiAUIAEbIRQgASAOIA9UcSEBCyACQYAKaiAWQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkHwCWogDkIAQn9CABDJAyACQeAJaiAOQgBC////////////AEIAEMkDIAIpA+gJIAIpA/gJIhEgESACKQOICiAWIAIpA4AKIg58IA5UrXwiDiACKQPwCSIPfCIWIA5UrXwgEyAWfCIcIBZUrXwiDiAPfCIPIA5UrXwgDyAQfCITIA9UrXwiDiACKQPgCXwiDyAOVK18IA8gEnwiECAPVK18Ig8gFHwiDiAUIA9CAFIiBBshFCACAn4CQAJAAkACQCAFIAhyIAFyIA4gD1QiAa0gDyAEG0IAUnIgASAEcSAUQgBTcnJFBEAgFEL///////////8AUiAQQn9SciATQn9Scg0CIBxCbFgNAUL///////////8AIRRCfyETQn8hEAsgE0IBfCISIBxCbVStIg59IQ8gEEIBfCIRIBNCf1IgDiASVnKtIg59IRIgFCAQQn9SIA4gEVZyrX1C////////////AH0hFCAcQhN8IRwMAgtCfyESQv///////////wAhFEJ/IQ8MAgsgEyEPIBAhEgsgFEIAUg0AIBJQRQRAQgAhFAwBC0IAIRQgD1BFBEBCACESDAELIBxCJlEEQEIAIRJCACEPQiYhHAwBCyAcQiVWBEBCACESQgAhDwwBC0L///////////8AIRNCfyEWQgAhEkIAIQ9CfyEOIBxCOX0MAQsgDyAcQiZUrSIRfSEOIBIgDyARVK0iEX0hFiAUIBEgElatfSETIBxCJn0LNwOwDSACIA43A6gNIAIgFjcDoA0gAiATNwOYDSACQdAJaiAcQgAgJEIAEMkDIAJBkAlqIBxCACAhQgAQyQMgAkGACWogHEIAIB9CABDJAyACQfAIaiAcQgAgHUIAEMkDIAJBwAlqIAIpA9AJIhBCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyACQbAJaiAOQgBCf0IAEMkDIAJBoAlqIA5CAEL///////////8AQgAQyQMgAkHgCGogD0IAICRCABDJAyACQaAIaiAPQgAgIUIAEMkDIAJBkAhqIA9CACAfQgAQyQMgAkGACGogD0IAIB1CABDJAyACQdAIaiACKQOwCSIaIAIpA9gJIhEgAikDkAl8Ig98IhggAikDyAkgECACKQPACSIOfCAOVK18fCIVIAIpA+AIfCITQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkHACGogDkIAQn9CABDJAyACQbAIaiAOQgBC////////////AEIAEMkDIAJB8AdqIBJCACAkQgAQyQMgAkGwB2ogEkIAICFCABDJAyACQaAHaiASQgAgH0IAEMkDIAJBkAdqIBJCACAdQgAQyQMgAkHgB2ogAikD6AggEyAVVK18IhYgAikDoAh8IhwgGiACKQOYCSAPIBFUrXwiECACKQOACXwiHnwiFyAVIBhUrSACKQO4CSISIBggGlStfHx8IhF8IhkgAikDwAgiD3wiGiACKQPYCCACKQPQCCIOIBN8IA5UrXx8IhggAikD8Ad8IhtCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyACQdAHaiAOQgBCf0IAEMkDIAJBwAdqIA5CAEL///////////8AQgAQyQMgAkGAB2ogFEIAICRCABDJAyACQcAGaiAUQgAgIUIAEMkDIAJBsAZqIBRCACAfQgAQyQMgAkGgBmogFEIAIB1CABDJAyACQfAGaiACKQP4ByAYIBtWrXwiEyACKQOwB3wiHyAPIAIpA4gJIBAgHlatfCIQIAIpA/AIfCIVIAIpA6AJfCIUIBEgF1StIBIgFyAeVK18fHwiHSACKQOQCHwiFyAZIBxUrSACKQOoCCAWIBxWrXx8fCIefCIWIBggGlStIAIpA8gIIhIgGSAaVq18fHwiEXwiGiACKQPQByIPfCIYIAIpA+gHIAIpA+AHIg4gG3wgDlStfHwiGSACKQOAB3wiG0KblK/D8rWo3oZ/fiIOQgBCbUIAEMkDIAJB4AZqIA5CAEJ/QgAQyQMgAkHQBmogDkIAQv///////////wBCABDJAwJAAkAgAikD2AYgAikDyAcgAikDuAggFCAdVq0gAikDqAkgFCAVVK18fCIOIAIpA/gIIBAgFVatfHwiFSACKQOACHwiFCAXIB5WrSACKQOYCCAXIB1UrXx8fCIXIAIpA7AIfCIQIBdUrXwgECARIBZUrSASIBYgHlStfHx8IhYgEFStfCIQIBQgF1atIAIpA4gIIBQgFVStfHwiEiAOIBVWrXwiEXwiFSACKQOQB3wiFCACKQOoByAWIBYgAikDoAd8Ig5WrXwgDiAOIBogH1StIAIpA7gHIBMgH1atfHx8IhdWrXx8IhYgAikDwAd8IhMgFlStfCATIAIpA9gHIg4gFyAPIBd8Ig9WrXwgDyAPIBggGVatIA4gGCAaVK18fHwiD1atfHwiDiATVK18IhcgFCAWVq0gAikDmAcgFCAVVK18fCIWIBAgFVatIBEgElStfHwiE3wiGiACKQOgBnwiGCACKQO4BiAOIA4gAikDsAZ8IhJWrXwgEiASIAIpA8gGIAIpA4gHIBkgG1atfCIOIAIpA8AGfCIRIA5UrXwgESAPIBF8IhVWrXx8IhFWrXx8IhQgAikD0AZ8IhAgFFStfCAQIBAgAikD6AYiDyARIBEgAikD4AYiDnwiElatfCASIA8gFSAOIBV8IhFWrXwgESACKQP4BiAbIAIpA/AGIg58IA5UrXx8IhwgEVStfHwiESASVK18fCISVq18IhAgFCAYVK0gAikDqAYgGCAaVK18fCIPIBcgGlatIBMgFlStfHwiDnwiFCAQVCAOIA9UciAUQgBTcg0AAkAgFEL///////////8AUQRAQn8hDyASQn9RDQFC////////////ACEUCyASIQ8gESEODAILIBFCf1IEQEL///////////8AIRQgESEODAILIBxCbVoNAEL///////////8AIRRCfyEODAELIBFCAXwiEyAcQm1UrSIPfSEOIBJCAXwiECARQn9SIA8gE1ZyrSIRfSEPIBQgEkJ/UiAQIBFUcq19Qv///////////wB9IRQgHEITfCEcCwJAAkACQCAUIA8gDiAcQiZ8IhIgHFStfCIQIA5UrXwiEyAPVK18Ig8gFFQNAEL///////////8AIRQgDyIOQv///////////wBRBEBCfyEUQv///////////wAhDiATQn9SDQIgEEJ/UgRAIBAhEQwEC0JtIRQgEiIOQm1RDQELIA4gFFoNACAPIQ4MAQsgEEIBfCIXIBJCbVStIg59IREgE0IBfCIWIBBCf1IgDiAXVnKtIg59IRQgDyATQn9SIA4gFlZyrX1C////////////AH0hDiASQhN8IRIMAQsgEyEUIBAhEQsgAiASNwPQDSACIBE3A8gNIAIgFDcDwA0gAiAONwO4DSACQegNaiIFIAJBmA1qIgEgAkG4DWoQXAJ/AkACQCACKALoDUEBRwRAIAJBkA1qIAJBiA5qIgkpAwA3AwAgAkGIDWogAkGADmoiBikDADcDACACQYANaiACQfgNaiIEKQMANwMAIAIgAikD8A03A/gMIAVB767EAEE/ELECIAItAOgNQQFGDQEgAkGwDWogCSkDADcDACACQagNaiAGKQMANwMAIAJBoA1qIAQpAwA3AwAgAiACKQPwDTcDmA0gAkH4DGohBiMAQeAJayIDJAAgA0GYCWpCADcDACADQZAJakIANwMAIANBiAlqQgA3AwAgA0IANwOACSADQbAJakIANwMAIANBqAlqQgA3AwAgA0IANwOgCSADQgE3A7gJAkACQCABIANBgAlqIgRBIBDxAwRAIAEgA0GgCWpBIBDxA0UNASABKQMIIRYgASkDECEQIAEpAwAhDiAGKQMYIRsgBikDECERIAYpAwghEiAGKQMAIRQgASkDGCEXIANB0AlqIglCADcDACADQcgJaiIGQgA3AwAgA0IANwPACSADIBdCAYM3A9gJIANBwAlqIARBIBDxA0UEQANAIBAhFSADQbAIaiARQgAgG0IAEMkDIANBkAhqIBJCACAbQgAQyQMgA0HgB2ogFEIAIBtCABDJAyADQYAIaiASQgAgEUIAEMkDIANB0AdqIBRCACARQgAQyQMgA0HAB2ogFEIAIBJCABDJAyADQfAIaiAbQgAgG0IAEMkDIANBoAhqIBFCACARQgAQyQMgA0HwB2ogEkIAIBJCABDJAyADQbAHaiAUQgAgFEIAEMkDIANB4AhqIAMpA/AIIh5Cm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQdAIaiAPQgBCf0IAEMkDIANBwAhqIA9CAEL///////////8AQgAQyQMgAykDyAcgAykD2AcgAykD6AcgAykDmAggAykDuAgiDyADKQOQCHwiGCAPVK18Ig8gAykD4Ad8IhIgD1StfCIPIAMpA9AHfCIRIA9UrXwgESADKQOICCASIAMpA4AIfCIbIBJUrXx8IhQgEVStfCIPIAMpA8AHfCITIA9UrXwiEUI/iCADKQO4ByADKQOwByIPIBFCAYYgE0I/iIR8IhAgD1StfCAQIBAgAykD+AcgAykDqAggAykDoAgiDyAYQgGGIAMpA7AIIhFCP4iEfCISIA9UrXwgEiADKQP4CCIPIBFCAYZ8IhkgD1StfCIaIBJUrXwiDyAbQgGGIBhCP4iEfCIYIA9UrSIPIAMpA/AHfCIRIA9UrXwgESARIBRCAYYgG0I/iIR8IhJWrXwiDyATQgGGIBRCP4iEfCIbIA9UrXwiEFatfHwhFEEAIQoCfwJAIAMpA8gIIAMpA9gIIhMgEyADKQPoCCADKQPgCCIPIB5CfYN8IA9UrXwiDyADKQPQCCIRfCIeIA9UrXwgGSAefCIZIB5UrXwiDyARfCIRIA9UrXwgESAafCIaIBFUrXwiDyADKQPACHwiESAPVK18IBEgGHwiGCARVK18Ig9QDQAgDyASfCISIA9UIgRFDQAgBK0iDyAbfCIbIA9aDQAgDyAbVq0iDyAQfCIQIA9aDQAgDyAQVq0iDyAUfCIUIA9UDAELQQALIQQgA0GgB2ogGUKblK/D8rWo3oZ/fiIPQgBCbUIAEMkDIANBkAdqIA9CAEJ/QgAQyQMgA0GAB2ogD0IAQv///////////wBCABDJAwJAIAMpA4gHIAMpA5gHIhMgEyADKQOoByADKQOgByIPIBl8IA9UrXwiDyADKQOQByIRfCIZIA9UrXwgGSAafCIaIBlUrXwiDyARfCIRIA9UrXwgESAYfCIYIBFUrXwiDyADKQOAB3wiESAPVK18IBEgEnwiEyARVK18Ig9QDQAgDyAbfCIbIA9aDQAgDyAbVq0iDyAQfCIQIA9aDQAgDyAQVq0iDyAUfCIUIA9UIQoLIANB8AZqIBpCm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQeAGaiAPQgBCf0IAEMkDIANB0AZqIA9CAEL///////////8AQgAQyQNBACEHIAMpA9gGIAMpA+gGIhIgEiADKQP4BiADKQPwBiIPIBp8IA9UrXwiDyADKQPgBiIRfCIaIA9UrXwgGiAYIBp8IhpWrXwiDyARfCIRIA9UrXwgESATfCIYIBFUrXwiDyADKQPQBnwiESAPVK18IBEgG3wiEiARVK18Ig9QRQRAIA8gEHwiECAPVCIIrSIRIBR8Ig8gFCAIGyEUIAggDyARVHEhBwsgDiETIANBwAZqIBpCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyADQbAGaiAOQgBCf0IAEMkDIANBoAZqIA5CAEL///////////8AQgAQyQMgAykDqAYgAykDuAYiESARIAMpA8gGIAMpA8AGIg4gGnwgDlStfCIOIAMpA7AGIg98IhogDlStfCAYIBp8IhsgGlStfCIOIA98Ig8gDlStfCAPIBJ8IhEgD1StfCIOIAMpA6AGfCIPIA5UrXwgDyAQfCISIA9UrXwiDyAUfCIOIBQgD0IAUiIIGyEUAkACQCAEIApyIAdyIA4gD1QiBK0gDyAIG0IAUnIgBCAIcSAUQgBTcnJFBEBC////////////ACEPIBRC////////////AFIgEkJ/UnIgEUJ/UnINAkJ/IRBCfyEOIBtCbVQNAgwBCyAUIQ8gEiEQIBEhDgsgDkIBfCIYIBtCbVStIhJ9IREgEEIBfCIUIA5Cf1IgEiAYVnKtIg59IRIgDyAQQn9SIA4gFFZyrX1C////////////AH0hFCAbQhN8IRsLIAEgE0IBiCIONwMAIAEgFkI/hiAVQgGIhCIQNwMQIAEgFUI/hiAXQgGIhCIXNwMYIAEgE0I/hiAWQgGIhCIWNwMIIAlCADcDACAGQgA3AwAgA0IANwPACSADIBdCAYM3A9gJIANBwAlqIANBgAlqQSAQ8QNFDQALCwJAIAEgA0GACWpBIBDxA0UNACABIA5CAYgiEzcDACABIBZCP4YgEEIBiIQiDzcDECABIBBCP4YgF0IBiIQiLDcDGCABIA5CP4YgFkIBiIQiKzcDCCABIANBgAlqQSAQ8QNFDQAgAykDuAkhMSADKQOwCSEkIAMpA6gJISEgAykDoAkhHCAUIRcgEiEWIBEhDiAbIRADQCADQdAFaiAOQgAgEEIAEMkDIANBsAVqIBZCACAQQgAQyQMgA0GABWogF0IAIBBCABDJAyADQaAFaiAWQgAgDkIAEMkDIANB8ARqIBdCACAOQgAQyQMgA0HgBGogF0IAIBZCABDJAyADQZAGaiAQQgAgEEIAEMkDIANBwAVqIA5CACAOQgAQyQMgA0GQBWogFkIAIBZCABDJAyADQdAEaiAXQgAgF0IAEMkDIANBgAZqIAMpA5AGIhhCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyADQfAFaiAOQgBCf0IAEMkDIANB4AVqIA5CAEL///////////8AQgAQyQMgAykD6AQgAykD+AQgAykDiAUgAykDuAUgAykD2AUiDiADKQOwBXwiGSAOVK18Ig4gAykDgAV8IhYgDlStfCIOIAMpA/AEfCIQIA5UrXwgECADKQOoBSAWIAMpA6AFfCIfIBZUrXx8IhogEFStfCIOIAMpA+AEfCIVIA5UrXwiEEI/iCADKQPYBCADKQPQBCIOIBBCAYYgFUI/iIR8IhcgDlStfCAXIAMpA5gFIAMpA8gFIAMpA8AFIg4gGUIBhiADKQPQBSIQQj+IhHwiFiAOVK18IBYgAykDmAYiDiAQQgGGfCIdIA5UrXwiHiAWVK18Ig4gH0IBhiAZQj+IhHwiGSAOVK0iDiADKQOQBXwiECAOVK18IBAgECAaQgGGIB9CP4iEfCIOVq18IhYgFUIBhiAaQj+IhHwiECAWVK18IhYgF1StfHwhF0EAIQoCfwJAIAMpA+gFIAMpA/gFIhogGiADKQOIBiADKQOABiIVIBhCfYN8IBVUrXwiFSADKQPwBSIYfCIfIBVUrXwgHSAffCIdIB9UrXwiFSAYfCIYIBVUrXwgGCAefCIeIBhUrXwiFSADKQPgBXwiGCAVVK18IBggGXwiGSAYVK18IhVQDQAgDiAVfCIOIBVUIgRFDQAgBK0iFSAQfCIQIBVaDQAgECAVVK0iFSAWfCIWIBVaDQAgFSAWVq0iFSAXfCIXIBVUDAELQQALIQQgA0HABGogHUKblK/D8rWo3oZ/fiIVQgBCbUIAEMkDIANBsARqIBVCAEJ/QgAQyQMgA0GgBGogFUIAQv///////////wBCABDJAwJAIAMpA6gEIAMpA7gEIhogGiADKQPIBCADKQPABCIVIB18IBVUrXwiFSADKQOwBCIYfCIdIBVUrXwgHSAefCIeIB1UrXwiFSAYfCIYIBVUrXwgGCAZfCIZIBhUrXwiFSADKQOgBHwiGCAVVK18IA4gGHwiGiAYVK18Ig5QDQAgDiAQfCIQIA5aDQAgDiAQVq0iDiAWfCIWIA5aDQAgDiAWVq0iDiAXfCIXIA5UIQoLIANBkARqIB5Cm5Svw/K1qN6Gf34iDkIAQm1CABDJAyADQYAEaiAOQgBCf0IAEMkDIANB8ANqIA5CAEL///////////8AQgAQyQNBACEHIAMpA/gDIAMpA4gEIhggGCADKQOYBCADKQOQBCIOIB58IA5UrXwiDiADKQOABCIVfCIdIA5UrXwgHSAZIB18Ih5WrXwiDiAVfCIVIA5UrXwgFSAafCIZIBVUrXwiDiADKQPwA3wiGCAOVK18IBggECAYfCIVVq18Ig5QRQRAIA4gFnwiFiAOVCIGrSIQIBd8Ig4gFyAGGyEXIAYgDiAQVHEhBwsgDyEaIBMhGCADQeADaiAeQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgA0HQA2ogDkIAQn9CABDJAyADQcADaiAOQgBC////////////AEIAEMkDIAMpA8gDIAMpA9gDIhAgECADKQPoAyADKQPgAyIOIB58IA5UrXwiDiADKQPQAyIPfCITIA5UrXwgEyAZfCIQIBNUrXwiDiAPfCIPIA5UrXwgDyAVfCIOIA9UrXwiDyADKQPAA3wiEyAPVK18IBMgFnwiFiATVK18IhMgF3wiDyAXIBNCAFIiBhshFwJAAkAgBCAKciAHciAPIBNUIgStIBMgBhtCAFJyIAQgBnEgF0IAU3JyRQRAQv///////////wAhFSAXQv///////////wBSIBZCf1JyIA5Cf1JyDQJCfyETQn8hDyAQQm1UDQIMAQsgFyEVIBYhEyAOIQ8LIA9CAXwiGSAQQm1UrSIWfSEOIBNCAXwiFyAPQn9SIBYgGVZyrSIPfSEWIBUgE0J/UiAPIBdWcq19Qv///////////wB9IRcgEEITfCEQCyADICwgMYM3A9gJIAMgGiAkgzcD0AkgAyAhICuDNwPICSADIBggHIM3A8AJAkAgA0HACWogA0GgCWpBIBDxAw0AIANBsANqIBBCACAbQgAQyQMgA0HwAmogEEIAIBFCABDJAyADQeACaiAQQgAgEkIAEMkDIANB0AJqIBBCACAUQgAQyQMgA0GgA2ogAykDsAMiGUKblK/D8rWo3oZ/fiIPQgBCbUIAEMkDIANBkANqIA9CAEJ/QgAQyQMgA0GAA2ogD0IAQv///////////wBCABDJAyADQcACaiAOQgAgG0IAEMkDIANBgAJqIA5CACARQgAQyQMgA0HwAWogDkIAIBJCABDJAyADQeABaiAOQgAgFEIAEMkDIANBsAJqIAMpA5ADIiIgAykDuAMiFSADKQPwAnwiE3wiIyADKQOoAyAZIAMpA6ADIg98IA9UrXx8IhkgAykDwAJ8IiBCm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQaACaiAPQgBCf0IAEMkDIANBkAJqIA9CAEL///////////8AQgAQyQMgA0HQAWogFkIAIBtCABDJAyADQZABaiAWQgAgEUIAEMkDIANBgAFqIBZCACASQgAQyQMgA0HwAGogFkIAIBRCABDJAyADQcABaiADKQPIAiAZICBWrXwiHyADKQOAAnwiLSAiIAMpA/gCIBMgFVStfCIdIAMpA+ACfCIufCIlIBkgI1StIAMpA5gDIh4gIiAjVq18fHwiGXwiJiADKQOgAiITfCIiIAMpA7gCIAMpA7ACIg8gIHwgD1StfHwiICADKQPQAXwiI0KblK/D8rWo3oZ/fiIPQgBCbUIAEMkDIANBsAFqIA9CAEJ/QgAQyQMgA0GgAWogD0IAQv///////////wBCABDJAyADQeAAaiAXQgAgG0IAEMkDIANBIGogF0IAIBFCABDJAyADQRBqIBdCACASQgAQyQMgAyAXQgAgFEIAEMkDIANB0ABqIAMpA9gBICAgI1atfCIVIAMpA5ABfCIvIBMgAykD6AIgHSAuVq18IhQgAykD0AJ8IjAgAykDgAN8Ih0gGSAlVK0gHiAlIC5UrXx8fCIlIAMpA/ABfCIZICYgLVStIAMpA4gCIB8gLVatfHx8Ih98IhsgICAiVK0gAykDqAIiEyAiICZUrXx8fCISfCImIAMpA7ABIhF8IiAgAykDyAEgAykDwAEiDyAjfCAPVK18fCIiIAMpA2B8IiNCm5Svw/K1qN6Gf34iD0IAQm1CABDJAyADQUBrIA9CAEJ/QgAQyQMgA0EwaiAPQgBC////////////AEIAEMkDAkAgAykDOCADKQOoASADKQOYAiAdICVWrSADKQOIAyAdIDBUrXx8Ig8gAykD2AIgFCAwVq18fCIdIAMpA+ABfCIeIBkgH1atIAMpA/gBIBkgJVStfHx8IhkgAykDkAJ8IhQgGVStfCAUIBIgG1StIBMgGyAfVK18fHwiGyAUVK18IhQgGSAeVK0gAykD6AEgHSAeVq18fCITIA8gHVatfCISfCIfIAMpA3B8Ih0gAykDiAEgGyADKQOAAXwiDyAbVK18IA8gJiAvVK0gAykDmAEgFSAvVq18fHwiFSAPVK18fCIZIAMpA6ABfCIbIBlUrXwgGyADKQO4ASIPIBUgESAVfCIVVq18IBUgFSAgICJWrSAPICAgJlStfHx8IhFWrXx8Ig8gG1StfCIeIBkgHVStIAMpA3ggHSAfVK18fCIZIBQgH1atIBIgE1StfHwiFHwiICADKQMAfCIfIAMpAxggDyADKQMQfCITIA9UrXwgEyADKQMoIAMpA2ggIiAjVq18Ig8gAykDIHwiEiAPVK18IBEgEnwiGyASVK18fCISIBNUrXx8Ih0gAykDMHwiFSAdVK18IBUgAykDSCIRIBIgAykDQCIPfCITIBJUrXwgEyARIA8gG3wiEiAbVK18IBIgAykDWCADKQNQIg8gI3wgD1StfHwiGyASVK18fCISIBNUrXx8Ig8gFVStfCIVIB0gH1StIAMpAwggHyAgVK18fCITIB4gIFatIBQgGVStfHwiEXwiFCAVVCARIBNUciAUQgBTckUEQCAPIBKDQn9SIBtCbVRyIBRC////////////AFJyDQELIBJCAXwiGSAbQm1UrSITfSERIA9CAXwiFSASQn9SIBMgGVZyrSITfSESIBQgD0J/UiATIBVWcq19Qv///////////wB9IRQgG0ITfCEbDAELIBIhESAPIRILIAEgGEIBiCITNwMAIAEgK0I/hiAaQgGIhCIPNwMQIAEgGkI/hiAsQgGIhCIsNwMYIAEgGEI/hiArQgGIhCIrNwMIIAEgA0GACWpBIBDxAw0ACwsgBSAbNwMYIAUgETcDECAFIBI3AwggBSAUNwMADAILIAVBGGpBsNPBACkDADcDACAFQRBqQajTwQApAwA3AwAgBUEIakGg08EAKQMANwMAIAVBmNPBACkDADcDAAwBCyAFIAYpAwA3AwAgBUEYaiAGQRhqKQMANwMAIAVBEGogBkEQaikDADcDACAFQQhqIAZBCGopAwA3AwALIANB4AlqJAAgAkGwBWogAikDgA4iHEIAIAIpA/gNIg9CABDJAyACQaAFaiAcQgAgAikD8A0iEkIAEMkDIAJBkAVqIBxCACACKQPoDSIUQgAQyQMgAkHgBWogD0IAIBJCABDJAyACQdAFaiAPQgAgFEIAEMkDIAJBgAZqIBJCACAUQgAQyQMgAkGABWogHEIAIBxCABDJAyACQcAFaiAPQgAgD0IAEMkDIAJB8AVqIBJCACASQgAQyQMgAkGQBmogFEIAIBRCABDJAyACQfAEaiACKQOABSITQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkHgBGogDkIAQn9CABDJAyACQdAEaiAOQgBC////////////AEIAEMkDIAIpA4gGIAIpA9gFIAIpA5gFIAIpA6gFIAIpA7gFIg4gAikDoAV8IhUgDlStfCIOIAIpA5AFfCIQIA5UrXwiDiACKQPQBXwiESAOVK18IBEgESACKQPoBSAQIBAgAikD4AV8IhdWrXx8IhlWrXwiDiACKQOABnwiGyAOVK18IhFCP4ggAikDmAYgAikDkAYiDiARQgGGIBtCP4iEfCIWIA5UrXwgFiACKQP4BSACKQPIBSACKQPABSIOIBVCAYYgAikDsAUiEUI/iIR8IhAgDlStfCAQIAIpA4gFIg4gEUIBhnwiGiAOVK18IhggEFStfCIOIBdCAYYgFUI/iIR8IhUgDlStIg4gAikD8AV8IhEgDlStfCARIBlCAYYgF0I/iIR8IhcgEVStfCIOIBtCAYYgGUI/iIR8IhkgDlStfCIRIBZUrXx8IQ5BACEIIAIpA9gEIAIpA+gEIhYgFiACKQP4BCATIAIpA/AEIhB8IBBUrXwiECACKQPgBCITfCIbIBBUrXwgGyAaIBt8IhpWrXwiECATfCITIBBUrXwgEyAYfCIYIBNUrXwiECACKQPQBHwiEyAQVK18IBMgFXwiFSATVK18IhBQDQIgECAXfCIXIBBUIgFFDQIgAa0iECAZfCIZIBBaDQIgECAZVq0iECARfCIRIBBaDQIgECARVq0iECAOfCIOIBBUDAMLIAIgAikD+A03A8ANIAIgAikD8A03A7gNQZSkxABBKyACQbgNakGQp8QAQdCvxAAQygMACyACIAItAOkNOgC4DUGUpMQAQSsgAkG4DWpBsK/EAEHAr8QAEMoDAAtBAAshBSACQcAEaiAaQpuUr8Pytajehn9+IhBCAEJtQgAQyQMgAkGwBGogEEIAQn9CABDJAyACQaAEaiAQQgBC////////////AEIAEMkDAkAgAikDqAQgAikDuAQiFiAWIAIpA8gEIBogAikDwAQiEHwgEFStfCIQIAIpA7AEIhN8IhogEFStfCAYIBp8IhggGlStfCIQIBN8IhMgEFStfCATIBV8IhUgE1StfCIQIAIpA6AEfCITIBBUrXwgEyAXfCIXIBNUrXwiEFANACAQIBl8IhkgEFoNACAQIBlWrSIQIBF8IhEgEFoNACAQIBFWrSIQIA58Ig4gEFQhCAsgAkGQBGogGEKblK/D8rWo3oZ/fiIQQgBCbUIAEMkDIAJBgARqIBBCAEJ/QgAQyQMgAkHwA2ogEEIAQv///////////wBCABDJA0EAIQEgAikD+AMgAikDiAQiFiAWIAIpA5gEIAIpA5AEIhAgGHwgEFStfCIQIAIpA4AEIhN8IhogEFStfCAaIBUgGnwiGFatfCIQIBN8IhMgEFStfCATIBd8IhUgE1StfCIQIAIpA/ADfCITIBBUrXwgEyAZfCIXIBNUrXwiEFBFBEAgECARfCIRIBBUIgGtIhMgDnwiECAOIAEbIQ4gASAQIBNUcSEBCyACQeADaiAYQpuUr8Pytajehn9+IhBCAEJtQgAQyQMgAkHQA2ogEEIAQn9CABDJAyACQcADaiAQQgBC////////////AEIAEMkDIAIpA8gDIAIpA9gDIhYgFiACKQPoAyAYIAIpA+ADIhB8IBBUrXwiECACKQPQAyITfCIYIBBUrXwgFSAYfCIZIBhUrXwiECATfCITIBBUrXwgEyATIBd8IhBWrXwiEyACKQPAA3wiFiATVK18IBEgFnwiFyAWVK18IhMgDnwiESAOIBNCAFIiBBshDgJAAkAgBSAIciABciARIBNUIgGtIBMgBBtCAFJyIAEgBHEgDkIAU3JyRQRAQv///////////wAhFiAOQv///////////wBSIBdCf1JyIBBCf1JyDQJCfyERQn8hEyAZQm1UDQIMAQsgDiEWIBchESAQIRMLIBNCAXwiFyAZQm1UrSIOfSEQIBFCAXwiFSATQn9SIA4gF1ZyrSIOfSEXIBYgEUJ/UiAOIBVWcq19Qv///////////wB9IQ4gGUITfCEZCyACIBk3A4AOIAIgEDcD+A0gAiAXNwPwDSACIA43A+gNAkAgAkHoDWogAkH4DGpBIBDxA0UNACACQbADaiAcQgAgJ0IAEMkDIAJB8AJqIA9CACAnQgAQyQMgAkHgAmogEkIAICdCABDJAyACQdACaiAUQgAgJ0IAEMkDIAJBoANqIAIpA7ADIhNCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyACQZADaiAOQgBCf0IAEMkDIAJBgANqIA5CAEL///////////8AQgAQyQMgAkHAAmogHEIAIChCABDJAyACQYACaiAPQgAgKEIAEMkDIAJB8AFqIBJCACAoQgAQyQMgAkHgAWogFEIAIChCABDJAyACQbACaiACKQOQAyIaIAIpA7gDIhAgAikD8AJ8IhF8IhggAikDqAMgEyACKQOgAyIOfCAOVK18fCIWIAIpA8ACfCITQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkGgAmogDkIAQn9CABDJAyACQZACaiAOQgBC////////////AEIAEMkDIAJB0AFqIBxCACApQgAQyQMgAkGQAWogD0IAIClCABDJAyACQYABaiASQgAgKUIAEMkDIAJB8ABqIBRCACApQgAQyQMgAkHAAWogAikDyAIgEyAWVK18IhUgAikDgAJ8IiEgGiACKQP4AiAQIBFWrXwiECACKQPgAnwiHXwiHiAWIBhUrSACKQOYAyIXIBggGlStfHx8IhZ8IhkgAikDoAIiEXwiGiACKQO4AiACKQOwAiIOIBN8IA5UrXx8IhggAikD0AF8IhtCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyACQbABaiAOQgBCf0IAEMkDIAJBoAFqIA5CAEL///////////8AQgAQyQMgAkHgAGogHEIAICpCABDJAyACQSBqIA9CACAqQgAQyQMgAkEQaiASQgAgKkIAEMkDIAIgFEIAICpCABDJAyACQdAAaiACKQPYASAYIBtWrXwiEyACKQOQAXwiHCARIAIpA+gCIBAgHVatfCIQIAIpA9ACfCIfIAIpA4ADfCIUIBYgHlStIBcgHSAeVq18fHwiHSACKQPwAXwiFyAZICFUrSACKQOIAiAVICFWrXx8fCIefCIWIBggGlStIAIpA6gCIhIgGSAaVq18fHwiEXwiGiACKQOwASIPfCIYIAIpA8gBIAIpA8ABIg4gG3wgDlStfHwiGSACKQNgfCIbQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkFAayAOQgBCf0IAEMkDIAJBMGogDkIAQv///////////wBCABDJAwJAAkAgAikDOCACKQOoASACKQOYAiAUIB1WrSACKQOIAyAUIB9UrXx8Ig4gAikD2AIgECAfVq18fCIVIAIpA+ABfCIUIBcgHlatIAIpA/gBIBcgHVStfHx8IhcgAikDkAJ8IhAgF1StfCAQIBEgFlStIBIgFiAeVK18fHwiFiAQVK18IhAgFCAXVq0gAikD6AEgFCAVVK18fCISIA4gFVatfCIRfCIVIAIpA3B8IhQgAikDiAEgFiAWIAIpA4ABfCIOVq18IA4gGiAcVK0gAikDmAEgEyAcVq18fHwiFyAOVK18fCIWIAIpA6ABfCITIBZUrXwgEyACKQO4ASIOIBcgDyAXfCIPVq18IA8gDyAYIBlWrSAOIBggGlStfHx8Ig9WrXx8Ig4gE1StfCIXIBQgFlatIAIpA3ggFCAVVK18fCIWIBAgFVatIBEgElStfHwiE3wiGiACKQMAfCIYIAIpAxggDiAOIAIpAxB8IhJWrXwgEiASIAIpAyggAikDaCAZIBtWrXwiDiACKQMgfCIRIA5UrXwgESAPIBF8IhVWrXx8IhFWrXx8IhQgAikDMHwiECAUVK18IBAgAikDSCIPIBEgESACKQNAIg58IhJWrXwgEiASIA8gFSAOIBV8IhFWrXwgESACKQNYIBsgAikDUCIOfCAOVK18fCIcIBFUrXx8Ig5WrXx8IhEgEFStfCIQIBQgGFStIAIpAwggGCAaVK18fCISIBcgGlatIBMgFlStfHwiD3wiFCAQVCAPIBJUciAUQgBTcg0AIBRC////////////AFINAUJ/IRIgEUJ/UgRAQv///////////wAhFAwCCyAOQn9SBEBC////////////ACEUIA4hDwwDCyAcQm1aDQBC////////////ACEUQn8hDwwCCyAOQgF8IhMgHEJtVK0iEn0hDyARQgF8IhAgDkJ/UiASIBNWcq0iDn0hEiAUIBFCf1IgDiAQVnKtfUL///////////8AfSEUIBxCE3whHAwBCyARIRIgDiEPCyACIBw3A9ANIAIgDzcDyA0gAiASNwPADSACIBQ3A7gNIAJB3A1qIAJBuA1qENkCAn8gAigC5A0EQCACKALgDSgCACEBQQAhByACQfANakGMocQAKAIANgIAIAJBhKHEACkCADcD6A1BBCEIQQEgAUEBcUUNARogAkHoDWpB6KLEABClAyACKALsDUEBNgIAIAIoAuwNIQggAigC6A0hB0EADAELQQAhB0EEIQhBAQshBSACKALcDSIBBEAgAigC4A0gAUECdBDfBAsgBwRAIAggB0ECdBDfBAsCfiAFRQRAIAJBgA5qIAJB0A1qKQMANwMAIAJB+A1qIAJByA1qKQMANwMAIAJB8A1qIAJBwA1qKQMANwMAIAIgAikDuA03A+gNIAJB6A1qQZCmxABBIBDxAwRAIAIpA/gNQn+FIhIgAikDgA4iEUJtVq0iDn0hHCACKQPwDUJ/hSIPIA4gElatIg59IRJCbSARfSEUQn9CACAOIA9WGyACKQPoDX1C////////////AHwMAgsgAikDgA4hFCACKQP4DSEcIAIpA/ANIRIgAikD6A0MAQsgAikD0A0hFCACKQPIDSEcIAIpA8ANIRIgAikDuA0LIQ8gAiAUNwOADiACIBw3A/gNIAIgEjcD8A0gAiAPNwPoDSACQZgNaiACQegNahDZAgJ/IAIoAqANBEAgAigCnA0oAgAhAUEAIQQgAkHADWpBjKHEACgCADYCACACQYShxAApAgA3A7gNQQAhB0EEIAFBAXFFDQEaIAJBuA1qQeiixAAQpQMgAigCvA1BATYCACACKAK4DSEHQQEhBCACKAK8DQwBC0EAIQRBACEHQQQLIQUgAigCmA0iAQRAIAIoApwNIAFBAnQQ3wQLQQAhASAEIAtGBEAgBSAMIAtBAnQQ8QNFIQELIAcEQCAFIAdBAnQQ3wQLAkAgAQ0AIAIgFDcDgA4gAiAcNwP4DSACIBI3A/ANIAIgDzcD6A0gAkHoDWpBkKbEAEEgEPEDRQ0AIBxCf4UiECAUQm1WrSIOfSEcIBJCf4UiESAOIBBWrSIOfSESQn9CACAOIBFWGyAPfUL///////////8AfCEPQm0gFH0hFAsgACAUNwMYIAAgHDcDECAAIBI3AwggACAPNwMAIAAgAikD2Aw3AyAgAEEoaiACQeAMaikDADcDACAAQTBqIAJB6AxqKQMANwMAIABBOGogAkHwDGopAwA3AwAgAigCzAwiAARAIAIoAtAMIABBAnQQ3wQLIA0EQCAMIA1BAnQQ3wQLIAJBkA5qJAALnUwCDX8QfiMAQfAXayIEJAAgBEHQDmogAUEoaikDADcDACAEQcgOaiABQSBqKQMANwMAIARBwA5qIAFBGGopAwA3AwAgBEG4DmogAUEQaikDADcDACAEQbAOaiABQQhqKQMANwMAIARB4A5qIAJBCGopAwA3AwAgBEHoDmogAkEQaikDADcDACAEQfAOaiACQRhqKQMANwMAIARB+A5qIAJBIGopAwA3AwAgBEGAD2ogAkEoaikDADcDACAEIAEpAwA3A6gOIAQgAikDADcD2A4gBCADOgCIDyAEQdgOaiEMAkACQAJAAkAgBEGoDmpBiNLBAEEwEPEDRQRAIAxBiNLBAEEwEPEDRQ0BCyAEQaAPahAmAn8CQAJAAn8gA0UEQCAEQcAPaiEDIARB8A9qDAELIAQoAsASQQFxRQ0BIARByBJqIQMgBEH4EmoLIQIgBEGwF2ogA0EoaikDADcDACAEQagXaiADQSBqKQMANwMAIARBoBdqIANBGGopAwA3AwAgBEGYF2ogA0EQaikDADcDACAEQZAXaiADQQhqKQMANwMAIARBwBdqIAJBCGopAwA3AwAgBEHIF2ogAkEQaikDADcDACAEQdAXaiACQRhqKQMANwMAIARB2BdqIAJBIGopAwA3AwAgBEHgF2ogAkEoaikDADcDACAEIAMpAwA3A4gXIAQgAikDADcDuBcgBEHQC2ogBCkD+A4iFUIAIAQpA4APIhdCABDJAyAEQeALaiAEKQPwDiISQgAgF0IAEMkDIARB8AtqIAQpA+gOIhRCACAXQgAQyQMgBEGADGogBCkD4A4iE0IAIBdCABDJAyAEQZAMaiAEKQPYDiIRQgAgF0IAEMkDIARBsAxqIBJCACAVQgAQyQMgBEHADGogFEIAIBVCABDJAyAEQdAMaiATQgAgFUIAEMkDIARB4AxqIBFCACAVQgAQyQMgBEGADWogFEIAIBJCABDJAyAEQZANaiATQgAgEkIAEMkDIARBoA1qIBFCACASQgAQyQMgBEHADWogE0IAIBRCABDJAyAEQdANaiARQgAgFEIAEMkDIARB8A1qIBFCACATQgAQyQMgBEGgDGogF0IAIBdCABDJAyAEQfAMaiAVQgAgFUIAEMkDIARBsA1qIBJCACASQgAQyQMgBEHgDWogFEIAIBRCABDJAyAEQYAOaiATQgAgE0IAEMkDIARBkA5qIBFCACARQgAQyQMgBEHAC2ogBCkDoAwiG0L9//P/z///+Yl/fiIVQgBCq9X+////v/+5f0IAEMkDIARBsAtqIBVCAEL//8+K6///1R5CABDJAyAEQaALaiAVQgBCpOzDtY/UtJjnAEIAEMkDIARBkAtqIBVCAEK/pZScz/DSu+QAQgAQyQMgBEGAC2ogFUIAQtfZrprk9umNywBCABDJAyAEQfAKaiAVQgBCms3/y6O9xIAaQgAQyQMgBCkD+A0gBCkD2A0gBCkDqA0gBCkD6AwgBCkDmAwgBCkDiAwgBCkD+AsgBCkD6AsgBCkD2AsiFyAEKQPgC3wiFSAXVK18IhIgBCkD8At8IhcgElStfCIUIAQpA4AMfCISIBRUrXwiEyAEKQOQDHwiFCATVK18IhEgBCkD4Ax8IhMgEVStfCATIAQpA9gMIBQgFCAEKQPQDHwiFFatfCAUIBQgBCkDyAwgEiASIAQpA8AMfCISVq18IBIgEiAEKQO4DCAXIBcgBCkDsAx8IhdWrXx8IhJWrXx8IhRWrXx8IhkgE1StfCIRIAQpA6ANfCITIBFUrXwgEyATIAQpA5gNIAQpA4gNIBQgFCAEKQOADXwiFFatfCIWIAQpA5ANfCIRIBZUrXwgESARIBl8IhFWrXx8IhNWrXwiFiAEKQPQDXwiGSAWVK18IBkgGSAEKQPIDSATIAQpA8ANfCIWIBNUrXx8IhlWrXwiEyAEKQPwDXwiGCATVK18IhNCP4ggBCkDmA4gBCkDkA4iHCATQgGGIBhCP4iEfCIaIBxUrXwgGiAEKQOIDiAEKQPoDSAEKQO4DSAEKQP4DCAEKQPwDCIcIBVCAYYgBCkD0AsiHUI/iIR8IhMgHFStfCATIAQpA6gMIhwgHUIBhnwiHSAcVK18IhwgE1StfCITIBdCAYYgFUI/iIR8Ih4gE1StIhMgBCkDsA18IhUgE1StfCAVIBJCAYYgF0I/iIR8Ih8gFVStfCIVIBRCAYYgEkI/iIR8IiAgFVStIhcgBCkD4A18IhUgF1StfCAVIBFCAYYgFEI/iIR8IhMgFVStfCIVIBZCAYYgEUI/iIR8IhQgFVStIhcgBCkDgA58IhUgF1StfCAVIBlCAYYgFkI/iIR8IhIgFVStfCIVIBhCAYYgGUI/iIR8IhkgFVStfCIVIBpUrXx8IRcgBCkD+AogBCkDiAsgBCkDmAsgBCkDqAsgBCkDuAsgBCkDyAsgBCkDwAsiESAbQn2DfCARVK18IhYgBCkDsAt8IhEgFlStfCARIB18IhYgEVStfCIYIAQpA6ALfCIRIBhUrXwgESAcfCIYIBFUrXwiGiAEKQOQC3wiESAaVK18IBEgHnwiGiARVK18IhsgBCkDgAt8IhEgG1StfCARIB98IhsgEVStfCIcIAQpA/AKfCIRIBxUrXwgESAgfCIcIBFUrXwiEVANASARIBN8IhMgEVQiAkUNASACrSIRIBR8IhQgEVoNASARIBRWrSIRIBJ8IhIgEVoNASARIBJWrSIRIBl8IhkgEVoNASARIBlWrSIRIBV8IhUgEVoNASARIBVWrSIRIBd8IhcgEVQMAgtB3PjBABDoBAALQQALIQggBEHgCmogFkL9//P/z///+Yl/fiIRQgBCq9X+////v/+5f0IAEMkDIARB0ApqIBFCAEL//8+K6///1R5CABDJAyAEQcAKaiARQgBCpOzDtY/UtJjnAEIAEMkDIARBsApqIBFCAEK/pZScz/DSu+QAQgAQyQMgBEGgCmogEUIAQtfZrprk9umNywBCABDJAyAEQZAKaiARQgBCms3/y6O9xIAaQgAQyQMCQCAEKQOYCiAEKQOoCiAEKQO4CiAEKQPICiAEKQPYCiAEKQPoCiAEKQPgCiIRIBZ8IBFUrXwiFiAEKQPQCnwiESAWVK18IBEgESAYfCIRVq18IhggBCkDwAp8IhYgGFStfCAWIBp8IhggFlStfCIaIAQpA7AKfCIWIBpUrXwgFiAbfCIaIBZUrXwiGyAEKQOgCnwiFiAbVK18IBYgHHwiGyAWVK18IhwgBCkDkAp8IhYgHFStfCAWIBMgFnwiFlatfCITUA0AIBMgFHwiFCATWg0AIBMgFFatIhMgEnwiEiATWg0AIBIgE1StIhMgGXwiGSATWg0AIBMgGVatIhMgFXwiFSATWg0AIBMgFVatIhMgF3wiFyATVCEFCyAEQYAKaiARQv3/8//P///5iX9+IhNCAEKr1f7///+//7l/QgAQyQMgBEHwCWogE0IAQv//z4rr///VHkIAEMkDIARB4AlqIBNCAEKk7MO1j9S0mOcAQgAQyQMgBEHQCWogE0IAQr+llJzP8NK75ABCABDJAyAEQcAJaiATQgBC19mumuT26Y3LAEIAEMkDIARBsAlqIBNCAEKazf/Lo73EgBpCABDJAwJ/QQAgBCkDuAkgBCkDyAkgBCkD2AkgBCkD6AkgBCkD+AkgBCkDiAogBCkDgAoiEyARfCATVK18IhEgBCkD8Al8IhMgEVStfCATIBMgGHwiE1atfCIYIAQpA+AJfCIRIBhUrXwgESAafCIYIBFUrXwiGiAEKQPQCXwiESAaVK18IBEgG3wiGiARVK18IhsgBCkDwAl8IhEgG1StfCARIBZ8IhYgEVStfCIbIAQpA7AJfCIRIBtUrXwgESARIBR8IhFWrXwiFFANABpBACAUIBIgFHwiElgNABpBACASIBRUrSIUIBl8IhkgFFoNABpBACAUIBlWrSIUIBV8IhUgFFoNABogFCAVVq0iFCAXfCIXIBRUCyECIARBoAlqIBNC/f/z/8////mJf34iFEIAQqvV/v///7//uX9CABDJAyAEQZAJaiAUQgBC///Piuv//9UeQgAQyQMgBEGACWogFEIAQqTsw7WP1LSY5wBCABDJAyAEQfAIaiAUQgBCv6WUnM/w0rvkAEIAEMkDIARB4AhqIBRCAELX2a6a5PbpjcsAQgAQyQMgBEHQCGogFEIAQprN/8ujvcSAGkIAEMkDAkAgBCkD2AggBCkD6AggBCkD+AggBCkDiAkgBCkDmAkgBCkDqAkgBCkDoAkiFCATfCAUVK18IhMgBCkDkAl8IhQgE1StfCAUIBQgGHwiFFatfCIYIAQpA4AJfCITIBhUrXwgEyAafCIYIBNUrXwiGiAEKQPwCHwiEyAaVK18IBMgFnwiFiATVK18IhogBCkD4Ah8IhMgGlStfCARIBN8IhEgE1StfCIaIAQpA9AIfCITIBpUrXwgEyASIBN8IhNWrXwiElANACASIBl8IhkgEloNACASIBlWrSISIBV8IhUgEloNACASIBVWrSISIBd8IhcgElQhBgsgBEHACGogFEL9//P/z///+Yl/fiISQgBCq9X+////v/+5f0IAEMkDIARBsAhqIBJCAEL//8+K6///1R5CABDJAyAEQaAIaiASQgBCpOzDtY/UtJjnAEIAEMkDIARBkAhqIBJCAEK/pZScz/DSu+QAQgAQyQMgBEGACGogEkIAQtfZrprk9umNywBCABDJAyAEQfAHaiASQgBCms3/y6O9xIAaQgAQyQNBACEDIAQpA/gHIAQpA4gIIAQpA5gIIAQpA6gIIAQpA7gIIAQpA8gIIAQpA8AIIhIgFHwgElStfCIUIAQpA7AIfCISIBRUrXwgEiAYfCIUIBJUrXwiGCAEKQOgCHwiEiAYVK18IBIgFnwiFiASVK18IhggBCkDkAh8IhIgGFStfCARIBJ8IhEgElStfCIYIAQpA4AIfCISIBhUrXwgEiATfCITIBJUrXwiGCAEKQPwB3wiEiAYVK18IBIgGXwiGCASVK18IhJQRQRAIBIgFXwiFSASVCIDrSISIBd8IhkgFyADGyEXIAMgEiAZVnEhAwsgBEHgB2ogFEL9//P/z///+Yl/fiISQgBCq9X+////v/+5f0IAEMkDIARB0AdqIBJCAEL//8+K6///1R5CABDJAyAEQcAHaiASQgBCpOzDtY/UtJjnAEIAEMkDIARBsAdqIBJCAEK/pZScz/DSu+QAQgAQyQMgBEGgB2ogEkIAQtfZrprk9umNywBCABDJAyAEQZAHaiASQgBCms3/y6O9xIAaQgAQyQMgBCkDmAcgBCkDqAcgBCkDuAcgBCkDyAcgBCkD2AcgBCkD6AcgBCkD4AciEiAUfCASVK18IhQgBCkD0Ad8IhIgFFStfCASIBZ8IhkgElStfCIUIAQpA8AHfCISIBRUrXwgESASfCIUIBJUrXwiESAEKQOwB3wiEiARVK18IBIgE3wiEyASVK18IhEgBCkDoAd8IhIgEVStfCASIBh8IhEgElStfCIWIAQpA5AHfCISIBZUrXwgEiAVfCIVIBJUrXwiEiAXfCIYIBcgEkIAUiIHGyEWAkACQAJAIBIgGFYiCa0gEiAHG1BFBEAgFSEXDAELIAUgCHIgAnIgBnIgA3IEQCAVIRcMAQsgByAJcQRAIBUhFwwBCyAWQprN/8ujvcSAGlYEQCAVIRcMAQsgFkKazf/Lo73EgBpSDQEgFULX2a6a5PbpjcsAVgRAIBUhFwwBCyAVQtfZrprk9umNywBSDQFC19mumuT26Y3LACEXIBFCv6WUnM/w0rvkAFYNACARQr+llJzP8NK75ABSDQEgE0Kk7MO1j9S0mOcAVg0AIBNCpOzDtY/UtJjnAFINASAUQv//z4rr///VHlYNACAUQv//z4rr///VHlIgGUKq1f7///+//7l/WHINAQsgFEL//8+K6///1R59IhUgGUKr1f7///+//7l/VK0iGH0hEiATQqTsw7WP1LSY5wB9IhogFEL//8+K6///1R5UIBUgGFRyrSIVfSEUIBFCv6WUnM/w0rvkAH0iGCATQqTsw7WP1LSY5wBUIBUgGlZyrSIVfSETIBdC19mumuT26Y3LAH0iGiARQr+llJzP8NK75ABUIBUgGFZyrSIRfSEVIBYgF0LX2a6a5PbpjcsAVCARIBpWcq19QprN/8ujvcSAGn0hFiAZQtWqgYCAgMCAxgB8IRkMAQsgFCESIBMhFCARIRMLIAQgGTcD8BUgBCASNwPoFSAEIBQ3A+AVIAQgEzcD2BUgBCAVNwPQFSAEIBY3A8gVIARBkAVqIAQpA8gOIhVCACAEKQPQDiIXQgAQyQMgBEGABWogBCkDwA4iEkIAIBdCABDJAyAEQfAEaiAEKQO4DiIUQgAgF0IAEMkDIARB4ARqIAQpA7AOIhNCACAXQgAQyQMgBEHQBGogBCkDqA4iEUIAIBdCABDJAyAEQeAFaiASQgAgFUIAEMkDIARB0AVqIBRCACAVQgAQyQMgBEHABWogE0IAIBVCABDJAyAEQbAFaiARQgAgFUIAEMkDIARBoAZqIBRCACASQgAQyQMgBEGQBmogE0IAIBJCABDJAyAEQYAGaiARQgAgEkIAEMkDIARB0AZqIBNCACAUQgAQyQMgBEHABmogEUIAIBRCABDJAyAEQfAGaiARQgAgE0IAEMkDIARBwARqIBdCACAXQgAQyQMgBEGgBWogFUIAIBVCABDJAyAEQfAFaiASQgAgEkIAEMkDIARBsAZqIBRCACAUQgAQyQMgBEHgBmogE0IAIBNCABDJAyAEQYAHaiARQgAgEUIAEMkDIARBsARqIAQpA8AEIhtC/f/z/8////mJf34iFUIAQqvV/v///7//uX9CABDJAyAEQaAEaiAVQgBC///Piuv//9UeQgAQyQMgBEGQBGogFUIAQqTsw7WP1LSY5wBCABDJAyAEQYAEaiAVQgBCv6WUnM/w0rvkAEIAEMkDIARB8ANqIBVCAELX2a6a5PbpjcsAQgAQyQMgBEHgA2ogFUIAQprN/8ujvcSAGkIAEMkDIAQpA/gGIAQpA8gGIAQpA4gGIAQpA7gFIAQpA9gEIAQpA+gEIAQpA/gEIAQpA4gFIAQpA5gFIhcgBCkDgAV8IhUgF1StfCISIAQpA/AEfCIXIBJUrXwiFCAEKQPgBHwiEiAUVK18IhMgBCkD0AR8IhQgE1StfCIRIAQpA7AFfCITIBFUrXwgEyAEKQPIBSAUIBQgBCkDwAV8IhRWrXwgFCAUIAQpA9gFIBIgEiAEKQPQBXwiElatfCASIBIgBCkD6AUgFyAXIAQpA+AFfCIXVq18fCISVq18fCIUVq18fCIZIBNUrXwiESAEKQOABnwiEyARVK18IBMgEyAEKQOYBiAEKQOoBiAUIBQgBCkDoAZ8IhRWrXwiFiAEKQOQBnwiESAWVK18IBEgESAZfCIRVq18fCITVq18IhYgBCkDwAZ8IhkgFlStfCAZIBkgBCkD2AYgEyAEKQPQBnwiFiATVK18fCIZVq18IhMgBCkD8AZ8IhggE1StfCITQj+IIAQpA4gHIAQpA4AHIhwgE0IBhiAYQj+IhHwiGiAcVK18IBogBCkD6AYgBCkDuAYgBCkD+AUgBCkDqAUgBCkDoAUiHCAVQgGGIAQpA5AFIh1CP4iEfCITIBxUrXwgEyAEKQPIBCIcIB1CAYZ8Ih0gHFStfCIcIBNUrXwiEyAXQgGGIBVCP4iEfCIeIBNUrSITIAQpA/AFfCIVIBNUrXwgFSASQgGGIBdCP4iEfCIfIBVUrXwiFSAUQgGGIBJCP4iEfCIgIBVUrSIXIAQpA7AGfCIVIBdUrXwgFSARQgGGIBRCP4iEfCITIBVUrXwiFSAWQgGGIBFCP4iEfCIUIBVUrSIXIAQpA+AGfCIVIBdUrXwgFSAZQgGGIBZCP4iEfCISIBVUrXwiFSAYQgGGIBlCP4iEfCIZIBVUrXwiFSAaVK18fCEXQQAhBQJ/AkAgBCkD6AMgBCkD+AMgBCkDiAQgBCkDmAQgBCkDqAQgBCkDuAQgBCkDsAQiESAbQn2DfCARVK18IhYgBCkDoAR8IhEgFlStfCARIB18IhYgEVStfCIYIAQpA5AEfCIRIBhUrXwgESAcfCIYIBFUrXwiGiAEKQOABHwiESAaVK18IBEgHnwiGiARVK18IhsgBCkD8AN8IhEgG1StfCARIB98IhsgEVStfCIcIAQpA+ADfCIRIBxUrXwgESAgfCIcIBFUrXwiEVANACARIBN8IhMgEVQiAkUNACACrSIRIBR8IhQgEVoNACARIBRWrSIRIBJ8IhIgEVoNACARIBJWrSIRIBl8IhkgEVoNACARIBlWrSIRIBV8IhUgEVoNACARIBVWrSIRIBd8IhcgEVQMAQtBAAshCCAEQdADaiAWQv3/8//P///5iX9+IhFCAEKr1f7///+//7l/QgAQyQMgBEHAA2ogEUIAQv//z4rr///VHkIAEMkDIARBsANqIBFCAEKk7MO1j9S0mOcAQgAQyQMgBEGgA2ogEUIAQr+llJzP8NK75ABCABDJAyAEQZADaiARQgBC19mumuT26Y3LAEIAEMkDIARBgANqIBFCAEKazf/Lo73EgBpCABDJAwJAIAQpA4gDIAQpA5gDIAQpA6gDIAQpA7gDIAQpA8gDIAQpA9gDIAQpA9ADIhEgFnwgEVStfCIWIAQpA8ADfCIRIBZUrXwgESARIBh8IhFWrXwiGCAEKQOwA3wiFiAYVK18IBYgGnwiGCAWVK18IhogBCkDoAN8IhYgGlStfCAWIBt8IhogFlStfCIbIAQpA5ADfCIWIBtUrXwgFiAcfCIbIBZUrXwiHCAEKQOAA3wiFiAcVK18IBYgEyAWfCIWVq18IhNQDQAgEyAUfCIUIBNaDQAgEyAUVq0iEyASfCISIBNaDQAgEiATVK0iEyAZfCIZIBNaDQAgEyAZVq0iEyAVfCIVIBNaDQAgEyAVVq0iEyAXfCIXIBNUIQULIARB8AJqIBFC/f/z/8////mJf34iE0IAQqvV/v///7//uX9CABDJAyAEQeACaiATQgBC///Piuv//9UeQgAQyQMgBEHQAmogE0IAQqTsw7WP1LSY5wBCABDJAyAEQcACaiATQgBCv6WUnM/w0rvkAEIAEMkDIARBsAJqIBNCAELX2a6a5PbpjcsAQgAQyQMgBEGgAmogE0IAQprN/8ujvcSAGkIAEMkDQQAhBgJ/QQAgBCkDqAIgBCkDuAIgBCkDyAIgBCkD2AIgBCkD6AIgBCkD+AIgBCkD8AIiEyARfCATVK18IhEgBCkD4AJ8IhMgEVStfCATIBMgGHwiE1atfCIYIAQpA9ACfCIRIBhUrXwgESAafCIYIBFUrXwiGiAEKQPAAnwiESAaVK18IBEgG3wiGiARVK18IhsgBCkDsAJ8IhEgG1StfCARIBZ8IhYgEVStfCIbIAQpA6ACfCIRIBtUrXwgESARIBR8IhFWrXwiFFANABpBACAUIBIgFHwiElgNABpBACASIBRUrSIUIBl8IhkgFFoNABpBACAUIBlWrSIUIBV8IhUgFFoNABogFCAVVq0iFCAXfCIXIBRUCyECIARBkAJqIBNC/f/z/8////mJf34iFEIAQqvV/v///7//uX9CABDJAyAEQYACaiAUQgBC///Piuv//9UeQgAQyQMgBEHwAWogFEIAQqTsw7WP1LSY5wBCABDJAyAEQeABaiAUQgBCv6WUnM/w0rvkAEIAEMkDIARB0AFqIBRCAELX2a6a5PbpjcsAQgAQyQMgBEHAAWogFEIAQprN/8ujvcSAGkIAEMkDAkAgBCkDyAEgBCkD2AEgBCkD6AEgBCkD+AEgBCkDiAIgBCkDmAIgBCkDkAIiFCATfCAUVK18IhMgBCkDgAJ8IhQgE1StfCAUIBQgGHwiFFatfCIYIAQpA/ABfCITIBhUrXwgEyAafCIYIBNUrXwiGiAEKQPgAXwiEyAaVK18IBMgFnwiFiATVK18IhogBCkD0AF8IhMgGlStfCARIBN8IhEgE1StfCIaIAQpA8ABfCITIBpUrXwgEyASIBN8IhNWrXwiElANACASIBl8IhkgEloNACASIBlWrSISIBV8IhUgEloNACASIBVWrSISIBd8IhcgElQhBgsgBEGwAWogFEL9//P/z///+Yl/fiISQgBCq9X+////v/+5f0IAEMkDIARBoAFqIBJCAEL//8+K6///1R5CABDJAyAEQZABaiASQgBCpOzDtY/UtJjnAEIAEMkDIARBgAFqIBJCAEK/pZScz/DSu+QAQgAQyQMgBEHwAGogEkIAQtfZrprk9umNywBCABDJAyAEQeAAaiASQgBCms3/y6O9xIAaQgAQyQNBACEDIAQpA2ggBCkDeCAEKQOIASAEKQOYASAEKQOoASAEKQO4ASAEKQOwASISIBR8IBJUrXwiFCAEKQOgAXwiEiAUVK18IBIgGHwiFCASVK18IhggBCkDkAF8IhIgGFStfCASIBZ8IhYgElStfCIYIAQpA4ABfCISIBhUrXwgESASfCIRIBJUrXwiGCAEKQNwfCISIBhUrXwgEiATfCITIBJUrXwiGCAEKQNgfCISIBhUrXwgEiAZfCIYIBJUrXwiElBFBEAgEiAVfCIVIBJUIgOtIhIgF3wiGSAXIAMbIRcgAyASIBlWcSEDCyAEQdAAaiAUQv3/8//P///5iX9+IhJCAEKr1f7///+//7l/QgAQyQMgBEFAayASQgBC///Piuv//9UeQgAQyQMgBEEwaiASQgBCpOzDtY/UtJjnAEIAEMkDIARBIGogEkIAQr+llJzP8NK75ABCABDJAyAEQRBqIBJCAELX2a6a5PbpjcsAQgAQyQMgBCASQgBCms3/y6O9xIAaQgAQyQMgBCkDCCAEKQMYIAQpAyggBCkDOCAEKQNIIAQpA1ggBCkDUCISIBR8IBJUrXwiFCAEKQNAfCISIBRUrXwgEiAWfCIZIBJUrXwiFCAEKQMwfCISIBRUrXwgESASfCIUIBJUrXwiESAEKQMgfCISIBFUrXwgEiATfCITIBJUrXwiESAEKQMQfCISIBFUrXwgEiAYfCIRIBJUrXwiFiAEKQMAfCISIBZUrXwgEiAVfCIVIBJUrXwiEiAXfCIYIBcgEkIAUiIHGyEWAkACQAJAIBIgGFYiCa0gEiAHG1BFBEAgFSEXDAELIAUgCHIgAnIgBnIgA3IEQCAVIRcMAQsgByAJcQRAIBUhFwwBCyAWQprN/8ujvcSAGlYEQCAVIRcMAQsgFkKazf/Lo73EgBpSDQEgFULX2a6a5PbpjcsAVgRAIBUhFwwBCyAVQtfZrprk9umNywBSDQFC19mumuT26Y3LACEXIBFCv6WUnM/w0rvkAFYNACARQr+llJzP8NK75ABSDQEgE0Kk7MO1j9S0mOcAVg0AIBNCpOzDtY/UtJjnAFINASAUQv//z4rr///VHlYNACAUQv//z4rr///VHlIgGUKq1f7///+//7l/WHINAQsgFEL//8+K6///1R59IhUgGUKr1f7///+//7l/VK0iGH0hEiATQqTsw7WP1LSY5wB9IhogFEL//8+K6///1R5UIBUgGFRyrSIVfSEUIBFCv6WUnM/w0rvkAH0iGCATQqTsw7WP1LSY5wBUIBUgGlZyrSIVfSETIBdC19mumuT26Y3LAH0iGiARQr+llJzP8NK75ABUIBUgGFZyrSIRfSEVIBYgF0LX2a6a5PbpjcsAVCARIBpWcq19QprN/8ujvcSAGn0hFiAZQtWqgYCAgMCAxgB8IRkMAQsgFCESIBMhFCARIRMLIAQgGTcD0BYgBCASNwPIFiAEIBQ3A8AWIAQgEzcDuBYgBCAVNwOwFiAEIBY3A6gWIARBgBdqIgIgAUEoaiIDKQMANwMAIARB+BZqIgUgAUEgaiIIKQMANwMAIARB8BZqIgYgAUEYaiIHKQMANwMAIARB6BZqIgkgAUEQaiINKQMANwMAIARB4BZqIg4gAUEIaiIPKQMANwMAIAQgASkDADcD2BYgBEH4FWoiECAEQagWaiIKIARB2BZqIgsQsgEgAiADKQMANwMAIAUgCCkDADcDACAGIAcpAwA3AwAgCSANKQMANwMAIA4gDykDADcDACAEIAEpAwA3A9gWIAogBEGIF2ogCxCyASALIBAgChC9AiAKIAsgBEG4F2oQvQIgBEHIFWogCkEwEPEDIAQoAqwVIgEEQCAEKAKwFSABQQJ0EN8ECwJAIAQoAqQPIgFFDQAgASABQQxsQRNqQXhxIgNqQQlqIgFFDQAgBCgCoA8gA2sgARDfBAsgBCgCoBIiAUGAgICAeEYgAUVyRQRAIAQoAqQSIAFBAnQQ3wQLDQELIAAgBEGoDmpB6AD8CgAADAELIARBuBdqIgIgBEGoDmoQpgEgBEEANgKQFyAEQoCAgIAQNwKIFyAEQbDXwQA2AqQPIARCoICAgA43AqgPIAQgBEGIF2oiATYCoA8gAiAEQaAPaiICEMUCDQEgBEGYD2ogBEGQF2ooAgA2AgAgBCAEKQKIFzcDkA8gAiAMEKYBIARBADYCgBYgBEKAgICAEDcC+BUgBEGw18EANgLcFiAEQqCAgIAONwLgFiAEIARB+BVqNgLYFiACIARB2BZqEMUCDQEgBEHQFWogBEGAFmooAgA2AgAgBCAEKQL4FTcDyBUgBEEDNgKMFyAEQej1wQA2AogXIARCAjcClBcgBEKAgICAwAciFSAEQcgVaq2ENwOwFiAEIBUgBEGQD2qthDcDqBYgBCAEQagWajYCkBcgACABENICIAQoAsgVIgEEQCAEKALMFSABEN8ECyAEKAKQDyIBBEAgBCgClA8gARDfBAsgAEECOgBgCyAEQfAXaiQADwtB2NfBAEE3IARB7xdqQcjXwQBB3NjBABDKAwAL4/EEAkx/EX4jAEHgCWsiDCQAAkACQAJAAkACQAJAAkACQAJAIAJBAUsEQCACIANJDQEgDEHAA2oQJiAMLQDYCSFDIAwoAswJIgcEQCAMKALQCSAHQQJ0EN8ECwJAIAwoAsQDIgdFDQAgByAHQQxsQRNqQXhxIgVqQQlqIgdFDQAgDCgCwAMgBWsgBxDfBAsgDCgCwAYiB0GAgICAeEYgB0VyRQRAIAwoAsQGIAdBAnQQ3wQLAkAgBC0AoAJBAkcEQCAMQcADaiAEQcABakEBIARBARBBIAxBEGogDEHIA2opAgA3AwAgDCAMKQLAAzcDCAwBCyAMQYCAgIB4NgIICyAMQQA2AkAgDEKAgICAgAE3AjggDEEANgIwIAxCgICAgIABNwIoIAJBqAJsIQ0gDEGIAmohECAMQfADaiEFIAxB+ABqIQoDQCAMQfAAaiABIDdqIgRB6AFqKQMANwMAIAxB6ABqIARB4AFqKQMANwMAIAxB4ABqIARB2AFqKQMANwMAIAxB2ABqIARB0AFqKQMANwMAIAxB0ABqIARByAFqKQMANwMAIAogBEHwAWopAwA3AwAgCkEIaiAEQfgBaikDADcDACAKQRBqIARBgAJqKQMANwMAIApBGGogBEGIAmopAwA3AwAgCkEgaiAEQZACaikDADcDACAKQShqIARBmAJqKQMANwMAIAwgBEHAAWopAwA3A0ggBEGgAmotAAAhLyAMKAJAIhEgDCgCOEYEQCMAQSBrIgckAEEEIAxBOGoiCCgCACI0QQF0IgkgCUEETRsiD61C6AB+IldCIIhQRQRAQQBBAEGIjsEAEMgEAAsCQCBXpyIOQfj///8HTQRAIAcgNAR/IAcgNEHoAGw2AhwgByAIKAIENgIUQQgFQQALNgIYIAdBCGpBCCAOIAdBFGoQuAMgBygCCEEBRw0BIAcoAgwhCyAHKAIQIQkLIAsgCUGIjsEAEMgEAAsgBygCDCEJIAggDzYCACAIIAk2AgQgB0EgaiQACyAMKAI8IBFB6ABsaiIHIAxByABqQeAA/AoAACAHIC86AGAgDCARQQFqNgJAIAxB6ANqIgcgBEEoaikDADcDACAMQeADaiIJIARBIGopAwA3AwAgDEHYA2oiCCAEQRhqKQMANwMAIAxB0ANqIhEgBEEQaikDADcDACAMQcgDaiI0IARBCGopAwA3AwAgBSAEQTBqKQMANwMAIAVBCGoiLyAEQThqKQMANwMAIAVBEGoiDyAEQUBrKQMANwMAIAVBGGoiDiAEQcgAaikDADcDACAFQSBqIhMgBEHQAGopAwA3AwAgBUEoaiI9IARB2ABqKQMANwMAIAwgBCkDADcDwAMgDEGoAWogDEHAA2oiEkHgAPwKAAAgByAEQYgBaikDADcDACAJIARBgAFqKQMANwMAIAggBEH4AGopAwA3AwAgESAEQfAAaikDADcDACA0IARB6ABqKQMANwMAIAUgBEGQAWopAwA3AwAgLyAEQZgBaikDADcDACAPIARBoAFqKQMANwMAIA4gBEGoAWopAwA3AwAgEyAEQbABaikDADcDACA9IARBuAFqKQMANwMAIAwgBEHgAGopAwA3A8ADIBAgEkHgAPwKAAAgDCgCMCIEIAwoAihGBEAgDEEoakGYjsEAEJ0DCyAMKAIsIj0gBEHAAWxqIAxBqAFqQcAB/AoAACAMIARBAWoiBDYCMCANIDdBqAJqIjdHDQALIAxBwANqITwgDCgCPCEHIAwoAkAhPiAMQQhqIUIjAEHQIWsiBiQAIAYgPjYCECAGIAQ2AgwCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgBCA+RgRAIAZB8BpqIgQgByA+EFIgBigChBshOiAGKAKAGyE3IAYoAvwaIUogBigC+BohOyAGKAL0GiE0IAYoAvAaIUsgBkEQahAmIAZBADYCwAYgBkKAgICAwAA3ArgGIAZBADYCzAYgBkKAgICAwAA3AsQGID5BAU0NASAGQYALaiIFIAcgPiA9ID4QQSAEIAUQxgEgBkHAIWogBigC9BoiBCAGKAL4GhAiIAYoAvAaIgcEQCAEIAdBMGwQ3wQLAn8gQigCACJMQYCAgIB4RwRAIAZB8BpqIEIQxgEgBkHQBmogBigC9BoiBCAGKAL4GhAiIAYoAvAaIgcEQCAEIAdBMGwQ3wQLIAYoAsQhIQcgBigC1AYhBSAGKALYBiEEIAYoAsghIQkgBkEMNgK0ISAGIAk2ApAUIAlBDEcNBCAGIAQ2ApAUIARBDEcNBUHRzsUALQAAGkHABEEIENYEIgRFDQkgBCAHKQMANwMAIARBKGogB0EoaikDADcDACAEQSBqIAdBIGopAwA3AwAgBEEYaiAHQRhqKQMANwMAIARBEGogB0EQaikDADcDACAEQQhqIgkgB0EIaikDADcDACAEIAcpAzA3AzAgBEE4aiAHQThqKQMANwMAIARBQGsgB0FAaykDADcDACAEQcgAaiAHQcgAaikDADcDACAEQdAAaiAHQdAAaikDADcDACAEQdgAaiAHQdgAaikDADcDACAEQYgBaiAHQYgBaikDADcDACAEQYABaiAHQYABaikDADcDACAEQfgAaiAHQfgAaikDADcDACAEQfAAaiAHQfAAaikDADcDACAEQegAaiAHQegAaikDADcDACAEIAcpA2A3A2AgBCAHKQOQATcDkAEgBEGYAWogB0GYAWopAwA3AwAgBEGgAWogB0GgAWopAwA3AwAgBEGoAWogB0GoAWopAwA3AwAgBEGwAWogB0GwAWopAwA3AwAgBEG4AWogB0G4AWopAwA3AwAgBCAHKQPAATcDwAEgBEHIAWogB0HIAWopAwA3AwAgBEHQAWogB0HQAWopAwA3AwAgBEHYAWogB0HYAWopAwA3AwAgBEHoAWogB0HoAWopAwA3AwAgBEHgAWogB0HgAWopAwA3AwAgBCAHKQPwATcD8AEgBEH4AWogB0H4AWopAwA3AwAgBEGAAmogB0GAAmopAwA3AwAgBEGIAmogB0GIAmopAwA3AwAgBEGQAmogB0GQAmopAwA3AwAgBEGYAmogB0GYAmopAwA3AwAgBCAHKQOgAjcDoAIgBEGoAmogB0GoAmopAwA3AwAgBEGwAmogB0GwAmopAwA3AwAgBEG4AmogB0G4AmopAwA3AwAgBEHAAmogB0HAAmopAwA3AwAgBEHIAmogB0HIAmopAwA3AwAgBEH4AmogB0H4AmopAwA3AwAgBEHwAmogB0HwAmopAwA3AwAgBEHoAmogB0HoAmopAwA3AwAgBEHgAmogB0HgAmopAwA3AwAgBEHYAmogB0HYAmopAwA3AwAgBCAHKQPQAjcD0AIgBCAHKQOAAzcDgAMgBEGIA2ogB0GIA2opAwA3AwAgBEGQA2ogB0GQA2opAwA3AwAgBEGYA2ogB0GYA2opAwA3AwAgBEGgA2ogB0GgA2opAwA3AwAgBEGoA2ogB0GoA2opAwA3AwAgBEHYA2ogB0HYA2opAwA3AwAgBEHQA2ogB0HQA2opAwA3AwAgBEHIA2ogB0HIA2opAwA3AwAgBEHAA2ogB0HAA2opAwA3AwAgBEG4A2ogB0G4A2opAwA3AwAgBCAHKQOwAzcDsAMgBCAHKQPgAzcD4AMgBEHoA2ogB0HoA2opAwA3AwAgBEHwA2ogB0HwA2opAwA3AwAgBEH4A2ogB0H4A2opAwA3AwAgBEGABGogB0GABGopAwA3AwAgBEGIBGogB0GIBGopAwA3AwAgBEG4BGogB0G4BGopAwA3AwAgBEGwBGogB0GwBGopAwA3AwAgBEGoBGogB0GoBGopAwA3AwAgBEGgBGogB0GgBGopAwA3AwAgBCAHKQOQBDcDkAQgBEGYBGogB0GYBGopAwA3AwAgBCkDACFXIAZB8BpqIhUgCUG4BPwKAAAgBEHABBDfBCAGQcgUaiAGQaAbaikDADcDACAGQdAUaiAGQagbaiIXKQMANwMAIAZB2BRqIAZBsBtqIj8pAwA3AwAgBkHgFGogBkG4G2oiHikDADcDACAGQegUaiAGQcAbaiJFKQMANwMAIAZBmAtqIgogBkHQG2oiRykDADcDACAGQaALaiIIIAZB2BtqKQMANwMAIAZBqAtqIgsgBkHgG2opAwA3AwAgBkGwC2oiESAGQegbaikDADcDACAGQbgLaiINIAZB8BtqKQMANwMAIAYgBikDmBs3A8AUIAYgBikDyBs3A5ALIAZB6AtqIioiByAGQaAcaikDADcDACAGQeALaiIrIhsgBkGYHGopAwA3AwAgBkHYC2oiKCAGQZAcaikDADcDACAGQdALaiI1IAZBiBxqKQMANwMAIAZByAtqIjYgBkGAHGopAwA3AwAgBkHYD2oiOCAGQbAcaiIfKQMANwMAIAZB4A9qIhogBkG4HGopAwA3AwAgBkHoD2oiGSAGQcAcaikDADcDACAGQfAPaiIwIAZByBxqKQMANwMAIAZB+A9qIi0gBkHQHGopAwA3AwAgBiAGKQP4GzcDwAsgBiAGKQOoHDcD0A8gBkGoEGoiMSAGQYAdaikDADcDACAGQaAQaiIyIAZB+BxqKQMANwMAIAZBmBBqIjMgBkHwHGopAwA3AwAgBkGQEGoiISAGQegcaikDADcDACAGQYgQaiIiIAZB4BxqKQMANwMAIAZBuBRqIAZBkBtqIiMpAwA3AwAgBkGwFGogBkGIG2oiJCkDADcDACAGQagUaiAGQYAbaiIlKQMANwMAIAZBoBRqIAZB+BpqKQMANwMAIAYgBikD2Bw3A4AQIAYgBikD8Bo3A5gUIAZB8BRqIAZBkAtqIgRB4AD8CgAAIAZB0BVqIAZB0A9qIglB4AD8CgAAIAZBmBpqIhAgBkHwHWopAwA3AwAgBkGgGmoiLyAGQfgdaikDADcDACAGQagaaiIPIAZBgB5qKQMANwMAIAZBsBpqIg4gBkGIHmopAwA3AwAgBkG4GmoiEyAGQZAeaikDADcDACAGQYgaaiImIAZB4B1qKQMANwMAIAZBgBpqIicgBkHYHWopAwA3AwAgBkH4GWoiKSAGQdAdaikDADcDACAGQfAZaiIsIAZByB1qKQMANwMAIAZB6BlqIi4gBkHAHWopAwA3AwAgBiAGKQPoHTcDkBogBiAGKQO4HTcD4BkgBkHoGmoiEiAGQcAeaikDADcDACAGQeAaaiIUIAZBuB5qKQMANwMAIAZB2BpqIhYgBkGwHmopAwA3AwAgBkHQGmoiHCAGQageaikDADcDACAGQcgaaiIdIAZBoB5qKQMANwMAIAogBkHQHmopAwA3AwAgCCAGQdgeaikDADcDACALIAZB4B5qKQMANwMAIBEgBkHoHmopAwA3AwAgDSAGQfAeaikDADcDACAGIAYpA5geNwPAGiAGIAYpA8geNwOQCyAHIAZBoB9qKQMANwMAIBsgBkGYH2opAwA3AwAgKCAGQZAfaikDADcDACA1IAZBiB9qKQMANwMAIDYgBkGAH2opAwA3AwAgBkHYGWoiOSAGQbAdaikDADcDACAGQdAZaiJAIAZBqB1qKQMANwMAIAZByBlqIkEgBkGgHWopAwA3AwAgBkHAGWoiRCAGQZgdaikDADcDACAGQbgZaiJGIAZBkB1qIkgpAwA3AwAgBiAGKQP4HjcDwAsgBiAGKQOIHTcDsBkgCSAGQbAZaiJNQeAA/AoAACAGQbAQaiJOIAZBkBpqIhtB4AD8CgAAIAZBkBFqIk8gBEHgAPwKAAAgBiBXNwOQFCAGQbAWaiAJQaAC/AoAAEHRzsUALQAAGkHABEEIENYEIgdFDQkgByAFKQMANwMAIAdBKGogBUEoaikDADcDACAHQSBqIAVBIGopAwA3AwAgB0EYaiAFQRhqKQMANwMAIAdBEGogBUEQaikDADcDACAHQQhqIlAgBUEIaikDADcDACAHIAUpAzA3AzAgB0E4aiAFQThqKQMANwMAIAdBQGsgBUFAaykDADcDACAHQcgAaiAFQcgAaikDADcDACAHQdAAaiAFQdAAaikDADcDACAHQdgAaiAFQdgAaikDADcDACAHQYgBaiAFQYgBaikDADcDACAHQYABaiAFQYABaikDADcDACAHQfgAaiAFQfgAaikDADcDACAHQfAAaiAFQfAAaikDADcDACAHQegAaiAFQegAaikDADcDACAHIAUpA2A3A2AgByAFKQOQATcDkAEgB0GYAWogBUGYAWopAwA3AwAgB0GgAWogBUGgAWopAwA3AwAgB0GoAWogBUGoAWopAwA3AwAgB0GwAWogBUGwAWopAwA3AwAgB0G4AWogBUG4AWopAwA3AwAgByAFKQPAATcDwAEgB0HIAWogBUHIAWopAwA3AwAgB0HQAWogBUHQAWopAwA3AwAgB0HYAWogBUHYAWopAwA3AwAgB0HoAWogBUHoAWopAwA3AwAgB0HgAWogBUHgAWopAwA3AwAgByAFKQPwATcD8AEgB0H4AWogBUH4AWopAwA3AwAgB0GAAmogBUGAAmopAwA3AwAgB0GIAmogBUGIAmopAwA3AwAgB0GQAmogBUGQAmopAwA3AwAgB0GYAmogBUGYAmopAwA3AwAgByAFKQOgAjcDoAIgB0GoAmogBUGoAmopAwA3AwAgB0GwAmogBUGwAmopAwA3AwAgB0G4AmogBUG4AmopAwA3AwAgB0HAAmogBUHAAmopAwA3AwAgB0HIAmogBUHIAmopAwA3AwAgB0H4AmogBUH4AmopAwA3AwAgB0HwAmogBUHwAmopAwA3AwAgB0HoAmogBUHoAmopAwA3AwAgB0HgAmogBUHgAmopAwA3AwAgB0HYAmogBUHYAmopAwA3AwAgByAFKQPQAjcD0AIgByAFKQOAAzcDgAMgB0GIA2ogBUGIA2opAwA3AwAgB0GQA2ogBUGQA2opAwA3AwAgB0GYA2ogBUGYA2opAwA3AwAgB0GgA2ogBUGgA2opAwA3AwAgB0GoA2ogBUGoA2opAwA3AwAgB0HYA2ogBUHYA2opAwA3AwAgB0HQA2ogBUHQA2opAwA3AwAgB0HIA2ogBUHIA2opAwA3AwAgB0HAA2ogBUHAA2opAwA3AwAgB0G4A2ogBUG4A2opAwA3AwAgByAFKQOwAzcDsAMgByAFKQPgAzcD4AMgB0HoA2ogBUHoA2opAwA3AwAgB0HwA2ogBUHwA2opAwA3AwAgB0H4A2ogBUH4A2opAwA3AwAgB0GABGogBUGABGopAwA3AwAgB0GIBGogBUGIBGopAwA3AwAgB0G4BGogBUG4BGopAwA3AwAgB0GwBGogBUGwBGopAwA3AwAgB0GoBGogBUGoBGopAwA3AwAgB0GgBGogBUGgBGopAwA3AwAgByAFKQOQBDcDkAQgB0GYBGogBUGYBGopAwA3AwAgBykDACFXIAkgUEG4BPwKAAAgB0HABBDfBCAXIAZBgBBqKQMANwMAID8gIikDADcDACAeICEpAwA3AwAgRSAzKQMANwMAIAZByBtqIDIpAwA3AwAgECBOKQMANwMAIC8gBkG4EGopAwA3AwAgDyAGQcAQaikDADcDACAOIAZByBBqKQMANwMAIBMgBkHQEGopAwA3AwAgBiAGKQP4DzcDoBsgBiAGKQOoEDcDkBogEiAGQYARaikDADcDACAUIAZB+BBqKQMANwMAIBYgBkHwEGopAwA3AwAgHCAGQegQaikDADcDACAdIAZB4BBqKQMANwMAIAogTykDADcDACAIIAZBmBFqKQMANwMAIAsgBkGgEWopAwA3AwAgESAGQagRaikDADcDACANIAZBsBFqKQMANwMAIAYgBikD2BA3A8AaIAYgBikDiBE3A5ALICogBkHgEWopAwA3AwAgKyAGQdgRaikDADcDACAoIAZB0BFqKQMANwMAIDUgBkHIEWopAwA3AwAgNiAGQcARaikDADcDACAGQZgbaiAwKQMANwMAICMgGSkDADcDACAkIBopAwA3AwAgJSA4KQMANwMAIAYgBikDuBE3A8ALIAYgBikD0A83A/gaIEcgG0HgAPwKAAAgHyAEQeAA/AoAACBGIAZB0BJqKQMANwMAIEQgBkHYEmopAwA3AwAgQSAGQeASaikDADcDACBAIAZB6BJqKQMANwMAIDkgBkHwEmopAwA3AwAgBkGoGWogBkHAEmopAwA3AwAgBkGgGWogBkG4EmopAwA3AwAgBkGYGWogBkGwEmopAwA3AwAgBkGQGWogBkGoEmopAwA3AwAgBkGIGWogBkGgEmopAwA3AwAgBiAGKQPIEjcDsBkgBiAGKQOYEjcDgBkgJiAGQaATaikDADcDACAnIAZBmBNqKQMANwMAICkgBkGQE2opAwA3AwAgLCAGQYgTaikDADcDACAuIAZBgBNqKQMANwMAIBAgBkGwE2opAwA3AwAgLyAGQbgTaikDADcDACAPIAZBwBNqKQMANwMAIA4gBkHIE2opAwA3AwAgEyAGQdATaikDADcDACAGIAYpA/gSNwPgGSAGIAYpA6gTNwOQGiASIAZBgBRqKQMANwMAIBQgBkH4E2opAwA3AwAgFiAGQfATaikDADcDACAcIAZB6BNqKQMANwMAIB0gBkHgE2opAwA3AwAgBkH4GGogBkGQEmopAwA3AwAgBkHwGGogBkGIEmopAwA3AwAgBkHoGGogBkGAEmopAwA3AwAgBkHgGGogBkH4EWopAwA3AwAgBkHYGGogBkHwEWopAwA3AwAgBiAGKQPYEzcDwBogBiAGKQPoETcD0BggBCAGQdAYakHgAPwKAAAgBkHwC2ogTUHgAPwKAAAgBkHQDGogG0HgAPwKAAAgBiBXNwPwGiBIIARBoAL8CgAAIAQgBkGQFGogFRCbAiAJIAQQoAFB0c7FAC0AABpBwARBCBDWBCIERQ0JIAQgBikD0A83AwAgBCAGKQOAEDcDMCAEQShqIC0pAwA3AwAgBEEgaiAwKQMANwMAIARBGGogGSkDADcDACAEQRBqIBopAwA3AwAgBEEIaiA4KQMANwMAIARBOGogIikDADcDACAEQUBrICEpAwA3AwAgBEHIAGogMykDADcDACAEQdAAaiAyKQMANwMAIARB2ABqIDEpAwA3AwAgBEGIAWogBkHYEGopAwA3AwAgBEGAAWogBkHQEGopAwA3AwAgBEH4AGogBkHIEGopAwA3AwAgBEHwAGogBkHAEGopAwA3AwAgBEHoAGogBkG4EGopAwA3AwAgBCAGKQOwEDcDYCAEIAYpA+AQNwOQASAEQZgBaiAGQegQaikDADcDACAEQaABaiAGQfAQaikDADcDACAEQagBaiAGQfgQaikDADcDACAEQbABaiAGQYARaikDADcDACAEQbgBaiAGQYgRaikDADcDACAEQegBaiAGQbgRaikDADcDACAEQeABaiAGQbARaikDADcDACAEQdgBaiAGQagRaikDADcDACAEQdABaiAGQaARaikDADcDACAEQcgBaiAGQZgRaikDADcDACAEIAYpA5ARNwPAASAEQZgCaiAGQegRaikDADcDACAEQZACaiAGQeARaikDADcDACAEQYgCaiAGQdgRaikDADcDACAEQYACaiAGQdARaikDADcDACAEQfgBaiAGQcgRaikDADcDACAEIAYpA8ARNwPwASAEQcgCaiAGQZgSaikDADcDACAEQcACaiAGQZASaikDADcDACAEQbgCaiAGQYgSaikDADcDACAEQbACaiAGQYASaikDADcDACAEQagCaiAGQfgRaikDADcDACAEIAYpA/ARNwOgAiAEQfgCaiAGQcgSaikDADcDACAEQfACaiAGQcASaikDADcDACAEQegCaiAGQbgSaikDADcDACAEQeACaiAGQbASaikDADcDACAEQdgCaiAGQagSaikDADcDACAEIAYpA6ASNwPQAiAEQagDaiAGQfgSaikDADcDACAEQaADaiAGQfASaikDADcDACAEQZgDaiAGQegSaikDADcDACAEQZADaiAGQeASaikDADcDACAEQYgDaiAGQdgSaikDADcDACAEIAYpA9ASNwOAAyAEQdgDaiAGQagTaikDADcDACAEQdADaiAGQaATaikDADcDACAEQcgDaiAGQZgTaikDADcDACAEQcADaiAGQZATaikDADcDACAEQbgDaiAGQYgTaikDADcDACAEIAYpA4ATNwOwAyAEQYgEaiAGQdgTaikDADcDACAEQYAEaiAGQdATaikDADcDACAEQfgDaiAGQcgTaikDADcDACAEQfADaiAGQcATaikDADcDACAEQegDaiAGQbgTaikDADcDACAEIAYpA7ATNwPgAyAEQbgEaiAGQYgUaikDADcDACAEQbAEaiAGQYAUaikDADcDACAEQagEaiAGQfgTaikDADcDACAEQaAEaiAGQfATaikDADcDACAEQZgEaiAGQegTaikDADcDACAEIAYpA+ATNwOQBCAGKALAISIHBEAgBigCxCEgB0EwbBDfBAtBDCEJIAZBDDYCyCEgBiAENgLEISAGQQw2AsAhIAYoAtAGIgcEQCAGKALUBiAHQTBsEN8EC0GQAQwBCyAGKALEISEEIAYoAsghIglFDQUgCUEMbAshB0HRzsUALQAAGiAHQQQQ1gQiBUUNBSAEIQcgBSEKIAkhCANAIAZB8BpqIAcQ2AIgCkEIaiAGQfgaaigCADYCACAKIAYpAvAaNwIAIApBDGohCiAHQTBqIQcgCEEBayIIDQALDAYLIAZBADYC8BogBkEQaiAGQQxqIAZB8BpqQbCXwAAQlwQAC0GAkMAAQR5BoJDAABD+AwALIAZBADYC8BogBkGQFGogBkG0IWogBkHwGmpB0IrAABCXBAALIAZBADYC8BogBkGQFGogBkG0IWogBkHwGmpB4IrAABCXBAALQQAhCUEEIQUMAQtBBCAHQZSNwAAQyAQACyAGQfAaahAmIAYtAIghIQ0gBigC/CAiBwRAIAYoAoAhIAdBAnQQ3wQLAkAgBigC9BoiB0UNACAHIAdBDGxBE2pBeHEiCmpBCWoiB0UNACAGKALwGiAKayAHEN8ECyAGKALwHSIHQYCAgIB4RiAHRXJFBEAgBigC9B0gB0ECdBDfBAsCQCAJQQxHBEAgBSEHIAkhCAwBCyAFKAIMIQkgBSgCCCEHIAUoAgQhCCAFKAIAIREgBkHwGmoiCyIKIAVBEGpBgAH8CgAAIAVBkAEQ3wQgEUGAgICAeEYNACAGIAk2ApwUIAYgBzYCmBQgBiAINgKUFCAGIBE2ApAUIAZBoBRqIApBgAH8CgAAIAogDSAGQZAUaiIQEG8gBkHQD2oiLyAKQZAB/AoAACAQIAZBgBxqQZAB/AoAAEHRzsUALQAAGgJAAkACQEHABEEIENYEIgcEQCALIC8Q9gIgB0EoaiAGQZgbaiIFKQMANwMAIAdBIGogBkGQG2oiCSkDADcDACAHQRhqIAZBiBtqIggpAwA3AwAgB0EQaiAGQYAbaiIRKQMANwMAIAdBCGogBkH4GmoiDSkDADcDACAHIAYpA/AaNwMAIAsgBkHcD2oQ9gIgB0HYAGogBSkDADcDACAHQdAAaiAJKQMANwMAIAdByABqIAgpAwA3AwAgB0FAayARKQMANwMAIAdBOGogDSkDADcDACAHIAYpA/AaNwMwIAsgBkHoD2oQ9gIgB0GIAWogBSkDADcDACAHQYABaiAJKQMANwMAIAdB+ABqIAgpAwA3AwAgB0HwAGogESkDADcDACAHQegAaiANKQMANwMAIAcgBikD8Bo3A2AgCyAGQfQPahD2AiAHQbgBaiAFKQMANwMAIAdBsAFqIAkpAwA3AwAgB0GoAWogCCkDADcDACAHQaABaiARKQMANwMAIAdBmAFqIA0pAwA3AwAgByAGKQPwGjcDkAEgCyAGQYAQahD2AiAHQegBaiAFKQMANwMAIAdB4AFqIAkpAwA3AwAgB0HYAWogCCkDADcDACAHQdABaiARKQMANwMAIAdByAFqIA0pAwA3AwAgByAGKQPwGjcDwAEgCyAGQYwQahD2AiAHQZgCaiAFKQMANwMAIAdBkAJqIAkpAwA3AwAgB0GIAmogCCkDADcDACAHQYACaiARKQMANwMAIAdB+AFqIA0pAwA3AwAgByAGKQPwGjcD8AEgCyAGQZgQahD2AiAHQcgCaiAFKQMANwMAIAdBwAJqIAkpAwA3AwAgB0G4AmogCCkDADcDACAHQbACaiARKQMANwMAIAdBqAJqIA0pAwA3AwAgByAGKQPwGjcDoAIgCyAGQaQQahD2AiAHQfgCaiAFKQMANwMAIAdB8AJqIAkpAwA3AwAgB0HoAmogCCkDADcDACAHQeACaiARKQMANwMAIAdB2AJqIA0pAwA3AwAgByAGKQPwGjcD0AIgCyAGQbAQahD2AiAHQagDaiAFKQMANwMAIAdBoANqIAkpAwA3AwAgB0GYA2ogCCkDADcDACAHQZADaiARKQMANwMAIAdBiANqIA0pAwA3AwAgByAGKQPwGjcDgAMgCyAGQbwQahD2AiAHQdgDaiAFKQMANwMAIAdB0ANqIAkpAwA3AwAgB0HIA2ogCCkDADcDACAHQcADaiARKQMANwMAIAdBuANqIA0pAwA3AwAgByAGKQPwGjcDsAMgCyAGQcgQahD2AiAHQYgEaiAFKQMANwMAIAdBgARqIAkpAwA3AwAgB0H4A2ogCCkDADcDACAHQfADaiARKQMANwMAIAdB6ANqIA0pAwA3AwAgByAGKQPwGjcD4AMgCyAGQdQQahD2AiAHQbgEaiAFKQMANwMAIAdBsARqIAkpAwA3AwAgB0GoBGogCCkDADcDACAHQaAEaiARKQMANwMAIAdBmARqIA0pAwA3AwAgByAGKQPwGjcDkARB0c7FAC0AABpBwARBCBDWBCIKRQ0BIAsgEBD2AiAKQShqIAUpAwA3AwAgCkEgaiAJKQMANwMAIApBGGogCCkDADcDACAKQRBqIBEpAwA3AwAgCkEIaiANKQMANwMAIAogBikD8Bo3AwAgCyAGQZwUahD2AiAKQdgAaiAFKQMANwMAIApB0ABqIAkpAwA3AwAgCkHIAGogCCkDADcDACAKQUBrIBEpAwA3AwAgCkE4aiANKQMANwMAIAogBikD8Bo3AzAgCyAGQagUahD2AiAKQYgBaiAFKQMANwMAIApBgAFqIAkpAwA3AwAgCkH4AGogCCkDADcDACAKQfAAaiARKQMANwMAIApB6ABqIA0pAwA3AwAgCiAGKQPwGjcDYCALIAZBtBRqEPYCIApBuAFqIAUpAwA3AwAgCkGwAWogCSkDADcDACAKQagBaiAIKQMANwMAIApBoAFqIBEpAwA3AwAgCkGYAWogDSkDADcDACAKIAYpA/AaNwOQASALIAZBwBRqEPYCIApB6AFqIAUpAwA3AwAgCkHgAWogCSkDADcDACAKQdgBaiAIKQMANwMAIApB0AFqIBEpAwA3AwAgCkHIAWogDSkDADcDACAKIAYpA/AaNwPAASALIAZBzBRqEPYCIApBmAJqIAUpAwA3AwAgCkGQAmogCSkDADcDACAKQYgCaiAIKQMANwMAIApBgAJqIBEpAwA3AwAgCkH4AWogDSkDADcDACAKIAYpA/AaNwPwASALIAZB2BRqEPYCIApByAJqIAUpAwA3AwAgCkHAAmogCSkDADcDACAKQbgCaiAIKQMANwMAIApBsAJqIBEpAwA3AwAgCkGoAmogDSkDADcDACAKIAYpA/AaNwOgAiALIAZB5BRqEPYCIApB+AJqIAUpAwA3AwAgCkHwAmogCSkDADcDACAKQegCaiAIKQMANwMAIApB4AJqIBEpAwA3AwAgCkHYAmogDSkDADcDACAKIAYpA/AaNwPQAiALIAZB8BRqEPYCIApBqANqIAUpAwA3AwAgCkGgA2ogCSkDADcDACAKQZgDaiAIKQMANwMAIApBkANqIBEpAwA3AwAgCkGIA2ogDSkDADcDACAKIAYpA/AaNwOAAyALIAZB/BRqEPYCIApB2ANqIAUpAwA3AwAgCkHQA2ogCSkDADcDACAKQcgDaiAIKQMANwMAIApBwANqIBEpAwA3AwAgCkG4A2ogDSkDADcDACAKIAYpA/AaNwOwAyALIAZBiBVqEPYCIApBiARqIAUpAwA3AwAgCkGABGogCSkDADcDACAKQfgDaiAIKQMANwMAIApB8ANqIBEpAwA3AwAgCkHoA2ogDSkDADcDACAKIAYpA/AaNwPgAyALIAZBlBVqEPYCIApBuARqIAUpAwA3AwAgCkGwBGogCSkDADcDACAKQagEaiAIKQMANwMAIApBoARqIBEpAwA3AwAgCkGYBGogDSkDADcDACAKIAYpA/AaNwOQBCAQEPwCIC8Q/AIgCxAmIAYtAIghIQkgBigC/CAiBQRAIAYoAoAhIAVBAnQQ3wQLAkAgBigC9BoiBUUNACAFIAVBDGxBE2pBeHEiCGpBCWoiBUUNACAGKALwGiAIayAFEN8ECyAGKALwHSIFQYCAgIB4RiAFRXJFBEAgBigC9B0gBUECdBDfBAsCfwJAAkACQCAJDgICAQALQYyPwABBD0HQkMAAEP4DAAtB0c7FAC0AABpBwARBCBDWBCIFBEAgBUEwakEAQZAE/AsAIAVC/f+LgICAwIT2ADcDKCAFQoKAsKC8gYD6azcDICAFQrqxnZ71iqak3wA3AxggBULFrsmCt4qW5/cANwMQIAVC7djbkvrSxoPcADcDCCAFQpPJg9S/2Jf7FTcDACAGQZAaaiAFQQwgB0EMECggBUHABBDfBEEBIRggBigClBohFSAGKAKYGgwCC0EIQcAEQayMwAAQyAQACyAGQQw2ApgaIAYgBzYClBogBkEMNgKQGiAHIRVBDAshBSAGQYQLaiEqIAZB1BhqIRwgBkGIC2ohKyAGQdgYaiEdIAZBjAtqISggBkHcGGohGyAGQfAaaiAVIAUQIyAGKAL4GiIJQTBsIQggBigC9BohCyAJIQUCQANAIAhFDQEgBUEBayEFIAhBMGsiCCALakH4w8IAQTAQ8QNFDQALIAVBAWoiCCAJSw0EDAMLQdHOxQAtAAAaQTBBCBDWBCIFRQ0UIAVCADcDACAFQShqQgA3AwAgBUEgakIANwMAIAVBGGpCADcDACAFQRBqQgA3AwAgBUEIakIANwMAIAYoAvAaIgkEQCALIAlBMGwQ3wQLIAYgBTYC9BpBASEIIAZBATYC8BpBfyEFDAILQQhBwARBlI3AABDIBAALQQhBwARBlI3AABDIBAALIAYgCDYC+BoLIAZBmAtqIAZB+BpqIgsoAgA2AgAgBiAGKQLwGjcDkAsgBkHQD2ogCkEMECNB0c7FAC0AABoCQAJAQQxBARDWBCI4BEAgOEGBgAQ2AAggOEKBgISAkIDAADcAACAGKALUDyE1IAYoAtgPIglBAU0NAiAGQZgbaiIRQgA3AwAgBkGQG2oiDUIANwMAIAZBiBtqIhBCADcDACAGQYAbaiIvQgA3AwAgC0IANwMAIAZCADcD8BoCQCA1QTBqIgggBkHwGmoiD0EwEPEDDQAgCUECRiIODQMgOC0AAkUEQCARQgA3AwAgDUIANwMAIBBCADcDACAvQgA3AwAgC0IANwMAIAZCADcD8BogNUHgAGoiCCAPQTAQ8QMNAQtBAkEDIA4bIgsgCU8NAyALIDhqLQAARQRAIAZBmBtqQgA3AwAgBkGQG2pCADcDACAGQYgbakIANwMAIAZBgBtqQgA3AwAgBkH4GmpCADcDACAGQgA3A/AaIDUgC0EwbGoiCCAGQfAaakEwEPEDDQELIAsgCSALS2oiCyAJTw0DIAsgOGotAABFBEAgBkGYG2pCADcDACAGQZAbakIANwMAIAZBiBtqQgA3AwAgBkGAG2pCADcDACAGQfgaakIANwMAIAZCADcD8BogNSALQTBsaiIIIAZB8BpqQTAQ8QMNAQsgCyAJIAtLaiILIAlPDQMgCyA4ai0AAEUEQCAGQZgbakIANwMAIAZBkBtqQgA3AwAgBkGIG2pCADcDACAGQYAbakIANwMAIAZB+BpqQgA3AwAgBkIANwPwGiA1IAtBMGxqIgggBkHwGmpBMBDxAw0BCyALIAkgC0tqIgsgCU8NAyALIDhqLQAARQRAIAZBmBtqQgA3AwAgBkGQG2pCADcDACAGQYgbakIANwMAIAZBgBtqQgA3AwAgBkH4GmpCADcDACAGQgA3A/AaIDUgC0EwbGoiCCAGQfAaakEwEPEDDQELIAsgCSALS2oiCyAJTw0DIAsgOGotAABFBEAgBkGYG2pCADcDACAGQZAbakIANwMAIAZBiBtqQgA3AwAgBkGAG2pCADcDACAGQfgaakIANwMAIAZCADcD8BogNSALQTBsaiIIIAZB8BpqQTAQ8QMNAQsgCyAJIAtLaiILIAlPDQMgCyA4ai0AAEUEQCAGQZgbakIANwMAIAZBkBtqQgA3AwAgBkGIG2pCADcDACAGQYAbakIANwMAIAZB+BpqQgA3AwAgBkIANwPwGiA1IAtBMGxqIgggBkHwGmpBMBDxAw0BCyALIAkgC0tqIgsgCU8NAyALIDhqLQAARQRAIAZBmBtqQgA3AwAgBkGQG2pCADcDACAGQYgbakIANwMAIAZBgBtqQgA3AwAgBkH4GmpCADcDACAGQgA3A/AaIDUgC0EwbGoiCCAGQfAaakEwEPEDDQELIAsgCSALS2oiCyAJTw0DIAsgOGotAABFBEAgBkGYG2pCADcDACAGQZAbakIANwMAIAZBiBtqQgA3AwAgBkGAG2pCADcDACAGQfgaakIANwMAIAZCADcD8BogNSALQTBsaiIIIAZB8BpqQTAQ8QMNAQsgCyAJIAtLaiILIAlPDQMgCyA4ai0AAEUEQCAGQZgbakIANwMAIAZBkBtqQgA3AwAgBkGIG2pCADcDACAGQYAbakIANwMAIAZB+BpqQgA3AwAgBkIANwPwGiA1IAtBMGxqIgggBkHwGmpBMBDxAw0BCyALIAkgC0tqIgggCU8NAyAIQQtLDQIgCCA4ai0AAA0DIAZBmBtqQgA3AwAgBkGQG2pCADcDACAGQYgbakIANwMAIAZBgBtqQgA3AwAgBkH4GmpCADcDACAGQgA3A/AaIDUgCEEwbGoiCCAGQfAaakEwEPEDRQ0DCyAGQQA2ApAUIwBBEGsiACQAIAAgBkHwGmo2AgwgACAINgIIIABBCGpBqJbBACAAQQxqQaiWwQAgBkGQFGpBwJDAABDmAgALQQFBDBD/BAALQQxBDEGwkMAAENkDAAsgBkH4GmogBkGYC2ooAgA2AgAgBiAGKQOQCzcD8BogBigC0A8hSCAGKAKQGiIIBEAgFSAIQTBsEN8ECyAKQcAEEN8EIBgEQCAHQcAEEN8ECyAGKALAISIHBEAgBCAHQTBsEN8ECyAGKAKACyIEBEAgBigChAsgBEEwbBDfBAtBCCEEIAZB2AZqIAZB+BpqKAIANgIAIAYgBikD8Bo3A9AGIAYgBTYC3AYgCUEwbCELAkACQAJAAkACQCAJRQ0AQQAhCEHRzsUALQAAGiALQQgQ1gQiBEUNASAJIQUDQCAIIAtGDQEgBCAIaiIHIAggNWoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAFQQFrIgUNAAsLIAshCiAJIQcCfwJAA0AgCkUNASAHQQFrIQcgCkEwayIKIARqQfjDwgBBMBDxA0UNAAsgB0EBaiIFIAkgBSAJSRshCCAJDAELQdHOxQAtAAAaQTBBCBDWBCIFRQ0VIAVCADcDACAFQShqQgA3AwAgBUEgakIANwMAIAVBGGpCADcDACAFQRBqQgA3AwAgBUEIakIANwMAQX8hB0EBIQggCQRAIAQgCxDfBAsgBSEEQQELIQUgBiAHNgLsBiAGIAg2AugGIAYgBDYC5AYgBiAFNgLgBiAGIAk2ApAUIAZBDDYC0A8gCUEMRw0BQQAhCiAGQQA2AvgaIAZCgICAgIABNwLwGkEIIQcgOC0AAA0CDAMLQQggC0HogcAAEMgEAAsgBkEANgLwGiAGQdAPaiAGQZAUaiAGQfAaakHUt8IAEJcEAAsgBkHwGmpB5LfCABCcAyAGKAL0GiIHIDUpAwA3AwAgB0EIaiA1QQhqKQMANwMAIAdBEGogNUEQaikDADcDACAHQRhqIDVBGGopAwA3AwAgB0EgaiA1QSBqKQMANwMAIAdBKGogNUEoaikDADcDAEEBIQogBkEBNgL4GgsgOC0AAUEBRgRAIAYoAvAaIApGBEAgBkHwGmpB5LfCABCcAyAGKAL0GiEHCyAHIApBMGxqIgQgNUEwaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQACQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QeAAaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQADQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QZABaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAEQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QcABaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAFQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QfABaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAGQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QaACaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAHQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QdACaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAIQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QYADaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAJQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QbADaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQAKQQFGBEAgBigC8BogCkYEQCAGQfAaakHkt8IAEJwDIAYoAvQaIQcLIAcgCkEwbGoiBCA1QeADaiIFKQMANwMAIARBKGogBUEoaikDADcDACAEQSBqIAVBIGopAwA3AwAgBEEYaiAFQRhqKQMANwMAIARBEGogBUEQaikDADcDACAEQQhqIAVBCGopAwA3AwAgBiAKQQFqIgo2AvgaCyA4LQALQQFGBEAgBigC8BogCkYEfyAGQfAaakHkt8IAEJwDIAYoAvQaBSAHCyAKQTBsaiIEIDVBkARqIgcpAwA3AwAgBEEoaiAHQShqKQMANwMAIARBIGogB0EgaikDADcDACAEQRhqIAdBGGopAwA3AwAgBEEQaiAHQRBqKQMANwMAIARBCGogB0EIaikDADcDACAGIApBAWo2AvgaCyAGQfgGaiAGQfgaaigCADYCACAGIAYpAvAaNwPwBiAGQfAaahAmIAYtAIghIUYgBigC/CAiBARAIAYoAoAhIARBAnQQ3wQLAkAgBigC9BoiBEUNACAEIARBDGxBE2pBeHEiB2pBCWoiBEUNACAGKALwGiAHayAEEN8ECyAGKALwHSIEQYCAgIB4RiAERXJFBEAgBigC9B0gBEECdBDfBAsCfwJAAkACQAJAAkACQAJAAkAgRg4CAQIAC0GMj8AAQQ9BlJrAABD+AwALIAYoAtgGIkWtIldCMH4iUachB0EAIQogUUIgiKcgB0H4////B0tyDRoCQCAHRQRAQQghDQwBCyAGKALUBiELQdHOxQAtAAAaQQghCiAHQQgQ1gQiDUUNGyBFRQ0AQQAhCCBFIQQDQCAHIAhGDQEgCCANaiIFIAggC2oiCSkDADcDACAFQShqIAlBKGopAwA3AwAgBUEgaiAJQSBqKQMANwMAIAVBGGogCUEYaikDADcDACAFQRBqIAlBEGopAwA3AwAgBUEIaiAJQQhqKQMANwMAIAhBMGohCCAEQQFrIgQNAAsLIAYoAtwGIUkgBkHwGmohDiAGQdAGaiERIAZBuAZqIS8gBkHEBmohEEEAIQdBACEEIwBB4ABrIgokAEHRzsUALQAAGgJAAkACQAJAAkBBMEEIENYEIgUEQCAFQShqQaDFwgApAwA3AwAgBUEgakGYxcIAKQMANwMAIAVBGGpBkMXCACkDADcDACAFQRBqQYjFwgApAwA3AwAgBUEIakGAxcIAKQMANwMAIAVB+MTCACkDADcDACAKQgE3AgggCiAFNgIEIApBATYCACARKAIIIgmtQjB+IlGnIQggUUIgiKcgCEH4////B0tyDR4gESgCBCEVAkAgCEUEQEEIIQ8MAQtB0c7FAC0AABpBCCEHIAhBCBDWBCIPRQ0fIAlFDQAgCSEHA0AgBCAIRg0BIAQgD2oiBSAEIBVqIgspAwA3AwAgBUEoaiALQShqKQMANwMAIAVBIGogC0EgaikDADcDACAFQRhqIAtBGGopAwA3AwAgBUEQaiALQRBqKQMANwMAIAVBCGogC0EIaikDADcDACAEQTBqIQQgB0EBayIHDQALCyAKIAk2AiggCiAPNgIkIAogCTYCICAKIBEoAgwiFzYCLCMAQTBrIgckACAHQSRqIAoQxgEgByAHKAIoIgQgBygCLBAiIAcoAiQiBQRAIAQgBUEwbBDfBAsgB0EkaiAKQSBqIhEQxgEgB0EMaiAHKAIoIgQgBygCLBAiIAcoAiQiBQRAIAQgBUEwbBDfBAsgCkEQaiELIAdBGGogBygCBCITIAcoAgggBygCECISIAcoAhQQKCAHQSRqIAcoAhwiFCAHKAIgECMgBygCLCIEQTBsIRYgBygCKCEPIAQhBQJAAkACQANAIBZFDQEgBUEBayEFIBZBMGsiFiAPakH4w8IAQTAQ8QNFDQALIAVBAWoiFiAESw0CDAELQdHOxQAtAAAaQTBBCBDWBCIEBEAgBEIANwMAIARBKGpCADcDACAEQSBqQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgBygCJCIFBEAgDyAFQTBsEN8ECyAHIAQ2AihBASEWIAdBATYCJEF/IQUMAQsMHwsgByAWNgIsCyALIAcpAiQ3AgAgCyAFNgIMIAtBCGogB0EsaigCADYCACAHKAIYIgQEQCAUIARBMGwQ3wQLIAcoAgwiBARAIBIgBEEwbBDfBAsgBygCACIEBEAgEyAEQTBsEN8ECyARKAIAIgQEQCARKAIEIARBMGwQ3wQLIAooAgAiBARAIAooAgQgBEEwbBDfBAsgB0EwaiQAQQAhC0HRzsUALQAAGkEgQQQQ1gQiEUUNASAKKAIYIgWtQjB+IlGnIQ8gUUIgiKcgD0H4////B0tyDQJBCCESQQghFAJAIA9FDQAgCigCFCEWQdHOxQAtAAAaQQghCyAPQQgQ1gQiFEUNAyAFRQ0AQQAhBCAFIQcDQCAEIA9GDQEgBCAUaiILIAQgFmoiEykDADcDACALQShqIBNBKGopAwA3AwAgC0EgaiATQSBqKQMANwMAIAtBGGogE0EYaikDADcDACALQRBqIBNBEGopAwA3AwAgC0EIaiATQQhqKQMANwMAIARBMGohBCAHQQFrIgcNAAsLIBEgBTYCCCARIBQ2AgQgESAFNgIAIAooAhwhDwJAIAhFDQBB0c7FAC0AABogCEEIENYEIhJFDQQgCUUNAEEAIQQgCSEHA0AgBCAIRg0BIAQgEmoiBSAEIBVqIgspAwA3AwAgBUEoaiALQShqKQMANwMAIAVBIGogC0EgaikDADcDACAFQRhqIAtBGGopAwA3AwAgBUEQaiALQRBqKQMANwMAIAVBCGogC0EIaikDADcDACAEQTBqIQQgB0EBayIHDQALCyARIAk2AhggESASNgIUIBEgCTYCECARIBc2AhwgESAPNgIMIApBAjYCWCAKIBE2AlQgCkECNgJQIApBIGogCkHQAGoQ4AEgCigCOCIFQTBsIQsgCigCICEIIAooAiQhESAKKQIoIVEgCigCMCEJIAooAjQhBCAFIQcCQAJAA0AgC0UNASAHQQFrIQcgC0EwayILIARqQfjDwgBBMBDxA0UNAAsgB0EBaiILIAUgBSALSxshCwwBC0HRzsUALQAAGkEwQQgQ1gQiBUUNHiAFQgA3AwAgBUEoakIANwMAIAVBIGpCADcDACAFQRhqQgA3AwAgBUEQakIANwMAIAVBCGpCADcDAEF/IQdBASELIAkEQCAEIAlBMGwQ3wQLQQEhCSAFIQQLIAogBzYCTCAKIAs2AkggCiAENgJEIAogCTYCQEHRzsUALQAAGkEwQQgQ1gQiBUUNHSAFQShqQaDFwgApAwA3AwAgBUEgakGYxcIAKQMANwMAIAVBGGpBkMXCACkDADcDACAFQRBqQYjFwgApAwA3AwAgBUEIakGAxcIAKQMANwMAIAVB+MTCACkDADcDACAKQgE3AlggCiAFNgJUIApBATYCUCAHDQQgC0UNHyAEIAVBMBDxAw0EIAVBMBDfBCAvBEAgLygCCCIHIC8oAgBGBEAgL0GkuMIAEKMDCyAvKAIEIAdBBHRqIgUgUTcCCCAFIBE2AgQgBSAINgIAIC8gB0EBajYCCAsCQAJAIBAEQCAQKAIIIgQgECgCAEYNASAKQcgAaikCACFRIBAoAgQgBEEEdGoiByAKKQJANwIAIAdBCGogUTcCACAOIAopAhA3AgAgDkEIaiAKQRhqKQIANwIAIBAgBEEBajYCCAwCCyAOIAopAhA3AgAgDkEIaiAKQRhqKQIANwIAIAlFDQEgBCAJQTBsEN8EDAELIBBBtLjCABCjAyAQKAIEIARBBHRqIgcgCikCQDcCACAHQQhqIApByABqKQIANwIAIA4gCikCEDcCACAOQQhqIApBGGopAgA3AgAgECAEQQFqNgIICyAvIAhFckUEQCARIAhBMGwQ3wQLIApB4ABqJAAMBQsMHAtBBEEgEP8EAAsgCyAPQeiBwAAQyAQAC0EIIAhB6IHAABDIBAALIApBADYCICAKQUBrIApB0ABqIApBIGpBlLjCABCVBAALIAYoAtgGIgetQjB+IlGnIQVBACEKIFFCIIinIAVB+P///wdLcg0JIAYoAvwaIUQgBigC+BohCyAGKAL0GiE/IAYoAvAaIUcCQCAFRQRAQQghCQwBCyAGKALUBiEQQdHOxQAtAAAaQQghCiAFQQgQ1gQiCUUNCiAHRQ0AQQAhCCAHIQQDQCAFIAhGDQEgCCAJaiIKIAggEGoiESkDADcDACAKQShqIBFBKGopAwA3AwAgCkEgaiARQSBqKQMANwMAIApBGGogEUEYaikDADcDACAKQRBqIBFBEGopAwA3AwAgCkEIaiARQQhqKQMANwMAIAhBMGohCCAEQQFrIgQNAAsLIAYgBigC3AY2AowLIAYgBzYCiAsgBiAJNgKECyAGIAc2AoALIAutQjB+IlGnIQkgUUIgiKciESAJQfj///8HS3INBQJAIAlFBEBBCCEFDAELQdHOxQAtAAAaQQggCUEIENYEIgVFDQcaIAtFDQBBACEIIAshBANAIAggCUYNASAFIAhqIgcgCCA/aiIKKQMANwMAIAdBKGogCkEoaikDADcDACAHQSBqIApBIGopAwA3AwAgB0EYaiAKQRhqKQMANwMAIAdBEGogCkEQaikDADcDACAHQQhqIApBCGopAwA3AwAgCEEwaiEIIARBAWsiBA0ACwsgDa0gV0IghoQhVyARQQBHIQogBiBENgLcGCAGIAs2AtgYIAYgBTYC1BggBiALNgLQGCALIS8MBAsgBigC2AYiL61CMH4iV6chCUEAIQcgV0IgiKcgCUH4////B0tyDQAgCUUEQCAGQYCAgIB4NgKACyAGKALcBiFEQQghP0EIIQUMAwsgBigC1AYhCkHRzsUALQAAGkEIIQcgCUEIENYEIj9FDQAgL0UNASA/IQcgCSEIIC8hBANAIAgEQCAHIAopAwA3AwAgB0EoaiAKQShqKQMANwMAIAdBIGogCkEgaikDADcDACAHQRhqIApBGGopAwA3AwAgB0EQaiAKQRBqKQMANwMAIAdBCGogCkEIaikDADcDACAHQTBqIQcgCEEwayEIIApBMGohCiAEQQFrIgQNAQsLDAELIAcgCUHogcAAEMgEAAsgBkGAgICAeDYCgAsgBigC3AYhREHRzsUALQAAGiAJQQgQ1gQiBUUNByAvRQ0AIC9BMGwhCkEAIQggLyEEA0AgCCAKRg0BIAUgCGoiByAIID9qIgkpAwA3AwAgB0EoaiAJQShqKQMANwMAIAdBIGogCUEgaikDADcDACAHQRhqIAlBGGopAwA3AwAgB0EQaiAJQRBqKQMANwMAIAdBCGogCUEIaikDADcDACAIQTBqIQggBEEBayIEDQALCyAGIEQ2AvwaIAYgLzYC+BogBiAFNgL0GiAGIC82AvAaIAZBkBRqIAZB8BpqEGkgBkHYGGogBkGYFGopAgAiUTcDACAGIAYpApAUNwPQGCBRQv////8Pg0IwfiJXQiCIp0EARyEKIFenIQkgUachC0GAgICAeCFFIAYoAtQYIQUgLyFHC0EAIQcCQAJAAkACQAJAIApBAXEgCUH4////B0tyDQACQCAJRQRAQQghFwwBC0HRzsUALQAAGkEIIQcgCUEIENYEIhdFDQEgC0UNACALQTBsIRFBACEIIAshBANAIAggEUYNASAIIBdqIgcgBSAIaiIKKQMANwMAIAdBKGogCkEoaikDADcDACAHQSBqIApBIGopAwA3AwAgB0EYaiAKQRhqKQMANwMAIAdBEGogCkEQaikDADcDACAHQQhqIApBCGopAwA3AwAgCEEwaiEIIARBAWsiBA0ACwsgBiAGKALcGCIQNgKMByAGIAs2AogHIAYgFzYChAcgBiALNgKAByAGQQA2ApwHIAZCgICAgIABNwKUByAGKAKoAyEZIAYoAqwDIh9BB00EQCAfRQRAQX4hCgwGCyAZLQAAQf8BRg0CIB9BAUYNAyAZLQABQf8BRg0CIB9BAkYNAyAZLQACQf8BRg0CIB9BA0YNAyAZLQADQf8BRg0CIB9BBEYNAyAZLQAEQf8BRg0CIB9BBUYNAyAZLQAFQf8BRg0CIB9BBkYNAyAZLQAGQf8BRw0DDAILIAYgGSAfEIQDIAYoAgBBAUYNASAfQQJrIQoMAwsgByAJQeiBwAAQyAQACyA+QcABbCEIID0hCgNAIAZBoAdqIAoQyAEgBigCnAciBCAGKAKUB0YEQCAGQZQHakHAl8AAEJ0DCyAGKAKYByAEQcABbGogBkGgB2pBwAH8CgAAIAYgBEEBajYCnAcgCkHAAWohCiAIQcABayIIDQALCyAfQQJrIQogH0EBTQ0BCwJAAkACQAJAAkACQCAKIBlqLQAADgIBAAILQdHOxQAtAAAaQTBBBBDWBCIHRQ0MAkAgCUUEQCAHIAs2AghBCCENIAdBCDYCBCAHIAs2AgAMAQtB0c7FAC0AABogCUEIENYEIhFFDQwCQCALRQ0AIAtBMGwhDUEAIQggCyEFA0AgCCANRg0BIAggEWoiBCAIIBdqIgopAwA3AwAgBEEoaiAKQShqKQMANwMAIARBIGogCkEgaikDADcDACAEQRhqIApBGGopAwA3AwAgBEEQaiAKQRBqKQMANwMAIARBCGogCkEIaikDADcDACAIQTBqIQggBUEBayIFDQALCyAHIAs2AgggByARNgIEIAcgCzYCAEHRzsUALQAAGiAJQQgQ1gQiDUUNDCALRQ0AIAtBMGwhCkEAIQggCyEFA0AgCCAKRg0BIAggDWoiBCAIIBdqIgkpAwA3AwAgBEEoaiAJQShqKQMANwMAIARBIGogCUEgaikDADcDACAEQRhqIAlBGGopAwA3AwAgBEEQaiAJQRBqKQMANwMAIARBCGogCUEIaikDADcDACAIQTBqIQggBUEBayIFDQALCyAHIAs2AhggByANNgIUIAcgCzYCECAGKALYGCIErUIwfiJRpyEJQQAhCiBRQiCIpyAJQfj///8HS3INDUEIIQ0CQCAJRQ0AIAYoAtQYIQ9B0c7FAC0AABpBCCEKIAlBCBDWBCINRQ0OIARFDQBBACEIIAQhBQNAIAggCUYNASAIIA1qIgogCCAPaiIRKQMANwMAIApBKGogEUEoaikDADcDACAKQSBqIBFBIGopAwA3AwAgCkEYaiARQRhqKQMANwMAIApBEGogEUEQaikDADcDACAKQQhqIBFBCGopAwA3AwAgCEEwaiEIIAVBAWsiBQ0ACwsgByAENgIoIAcgDTYCJCAHIAQ2AiAgByAGKALcGDYCLCAHIBA2AhwgByAQNgIMIAZBAzYCvCEgBiAHNgK4ISAGQQM2ArQhQQAhCiAGQQA2AsghIAZCgICAgIABNwLAISAGQcAcaiEJIAZBgBtqIRAgPSEIIDchBCA0IQUDQCAKIDtGDQMgCiA6Rg0EIAZB8BpqIAggBSAEEMcBIAZBkBRqIBBBwAH8CgAAIAZBmAtqIhEgBkH4GmopAwA3AwAgBkHYD2oiDyAJQQhqKQIANwMAIAYgBikD8Bo3A5ALIAYgCSkCADcD0A8gBigCvCEiByAGKAK0ISINRgRAIAZBtCFqQeCSwAAQowMgBigCtCEhDQsgBigCuCEiDiAHQQR0aiITIAYpA5ALNwIAIBNBCGogESkDADcCACAGIAdBAWoiETYCvCEgDSARRgR/IAZBtCFqQfCSwAAQowMgBigCuCEFIA4LIBFBBHRqIhEgBikD0A83AgAgEUEIaiAPKQMANwIAIAYgB0ECajYCvCEgBigCyCEiByAGKALAIUYEQCAGQcAhakGAk8AAEJ0DCyAGKALEISAHQcABbGogBkGQFGpBwAH8CgAAIAYgB0EBajYCyCEgCEHAAWohCCAEQTBqIQQgBUEwaiEFID4gCkEBaiIKRw0ACyAGQbgZaiAGQbwhaigCADYCACAGIAYpArQhNwOwGSAGQYCAgIB4NgKQGiAGQfAaaiAGQbAZaiAGQZAaaiAGQbgGaiAGQcQGahCrASAGQYgbaiIEIAZByCFqKAIANgIAIAZB6AhqIAZB+BpqKQIANwMAIAYgBikCwCEiUTcCgBsgBiAGKQLwGjcD4AggBiBRpyIKNgL8CCAGIAYoAoQbIhE2AvgIIAYgBCgCACI2NgL0CCAGQfwIaiEIIAZB9AhqIQQgBkH4CGohBSAGQeAIaiEHDAQLIAZB8BpqIAZBgAdqID0gPiA0IDsgNyA6IAZBuAZqIAZBxAZqENABIAZBiAlqIAZB+BpqKQIANwMAIAYgBikC8Bo3A4AJIAYgBigCgBsiCjYCnAkgBiAGKAKEGyIRNgKYCSAGIAYoAogbIjY2ApQJIAZBnAlqIQggBkGUCWohBCAGQZgJaiEFIAZBgAlqIQcMAwtBjI/AAEEPQYSawAAQ/gMACyA7IDtBwJLAABDZAwALIDogOkHQksAAENkDAAsgCwRAIBcgC0EwbBDfBCAEKAIAITYgBSgCACERIAgoAgAhCgsgBkGIB2oiMSAHQQhqKQIANwMAIAYgBykCADcDgAcCQCAfQQNrIhBBAEgNACA6QQFqISEgO0EBaiEiIAZB2A9qISMgBkGgC2ohMCAGQbAcaiEyIAZBwBxqITMgBkGAG2ohJCAGQeAPaiElA0AgCiETIAYgEDYCoAkCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAn8CQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgECAfSQRAIBAgGWoiBC0AACIHDgIBAwILIBAgH0HQmMAAENkDAAsgEEUEQCAGQfAaaiAGQYAHaiARIDYgNCA7IDcgOiAGQbgGaiAGQcQGahDQASAGQeAJaiIHIAZB+BpqKQIANwMAIAYgBikC8Bo3A9gJIAYoAoAbIQogBigChBsgBigCiBshNiAGKAKAByIFBEAgBigChAcgBUEwbBDfBAsgBkGIB2ogBykDADcDACAGIAYpA9gJNwOAByATBEAgESATQcABbBDfBAshEQwfCyAQQQFrIhIgH08NAyAGIBIgGWotAAAiFToApwkgFUUEQEHRzsUALQAAGkHAAEEEENYEIgdFDSogBigCiAciBK1CMH4iUachCUEAIQogUUIgiKcgCUH4////B0tyDSggBigChAchEAJAIAlFBEAgByAENgIIQQghFSAHQQg2AgQgByAENgIAIAcgBDYCKCAHQQg2AiQgByAENgIgIAcgBDYCGCAHQQg2AhQgByAENgIQIAYoAowHIRgMAQtB0c7FAC0AABpBCCEKIAlBCBDWBCILRQ0pAkAgBEUNAEEAIQggBCENA0AgCCAJRg0BIAggC2oiBSAIIBBqIgopAwA3AwAgBUEoaiAKQShqKQMANwMAIAVBIGogCkEgaikDADcDACAFQRhqIApBGGopAwA3AwAgBUEQaiAKQRBqKQMANwMAIAVBCGogCkEIaikDADcDACAIQTBqIQggDUEBayINDQALCyAHIAQ2AgggByALNgIEIAcgBDYCACAGKAKMByEYQdHOxQAtAAAaIAlBCBDWBCILRQ0nAkAgBEUNAEEAIQggBCENA0AgCCAJRg0BIAggC2oiBSAIIBBqIgopAwA3AwAgBUEoaiAKQShqKQMANwMAIAVBIGogCkEgaikDADcDACAFQRhqIApBGGopAwA3AwAgBUEQaiAKQRBqKQMANwMAIAVBCGogCkEIaikDADcDACAIQTBqIQggDUEBayINDQALCyAHIAQ2AhggByALNgIUIAcgBDYCEEHRzsUALQAAGiAJQQgQ1gQiC0UNJwJAIARFDQBBACEIIAQhDQNAIAggCUYNASAIIAtqIgUgCCAQaiIKKQMANwMAIAVBKGogCkEoaikDADcDACAFQSBqIApBIGopAwA3AwAgBUEYaiAKQRhqKQMANwMAIAVBEGogCkEQaikDADcDACAFQQhqIApBCGopAwA3AwAgCEEwaiEIIA1BAWsiDQ0ACwsgByAENgIoIAcgCzYCJCAHIAQ2AiBB0c7FAC0AABogCUEIENYEIhVFDScgBEUNAEEAIQggBCENA0AgCCAJRg0BIAggFWoiBSAIIBBqIgopAwA3AwAgBUEoaiAKQShqKQMANwMAIAVBIGogCkEgaikDADcDACAFQRhqIApBGGopAwA3AwAgBUEQaiAKQRBqKQMANwMAIAVBCGogCkEIaikDADcDACAIQTBqIQggDUEBayINDQALCyAHIAQ2AjggByAVNgI0IAcgBDYCMCAHIBg2AjwgByAYNgIsIAcgGDYCHCAHIBg2AgwgBkEENgKwISAGIAc2AqwhIAZBBDYCqCEgBkEANgK8ISAGQoCAgICAATcCtCEgNgRAQQAhCkEBIQcDQAJAAkAgIiAHIgVHBEAgBSAhRg0KIAZB8BpqIgQgESAKQcABbGogNCAKQTBsIgdqIAcgN2oQxgIgBkHQD2ogBEHAAfwKAAAgBigCuBwiB61CMH4iUachC0EAIQogUUIgiKcgC0H4////B0tyDTAgBigCvBwhDyAGKAK0HCEOIAYoArAcIRQgCw0BQQghDQwCCyA7IDtB8JHAABDZAwALQdHOxQAtAAAaQQghCiALQQgQ1gQiDUUNLiAHRQ0AQQAhCCAHIQQDQCAIIAtGDQEgCCANaiIJIAggDmoiCikDADcDACAJQShqIApBKGopAwA3AwAgCUEgaiAKQSBqKQMANwMAIAlBGGogCkEYaikDADcDACAJQRBqIApBEGopAwA3AwAgCUEIaiAKQQhqKQMANwMAIAhBMGohCCAEQQFrIgQNAAsLIAYoArAhIgQgBigCqCFGBEAgBkGoIWpBkJLAABCjAwsgBigCrCEgBEEEdGoiCSAPNgIMIAkgBzYCCCAJIA02AgQgCSAHNgIAIAYgBEEBaiIJNgKwISAGKAKoISAJRgRAIAZBqCFqQaCSwAAQowMLIAYoAqwhIAlBBHRqIgkgDzYCDCAJIAc2AgggCSAONgIEIAkgFDYCACAGIARBAmo2ArAhIAYoArwhIgQgBigCtCFGBEAgBkG0IWpBsJLAABCdAwsgBigCuCEgBEHAAWxqIAZB0A9qQcAB/AoAACAGIARBAWo2ArwhIAVBAWohByAFIgogNkcNAAsMGAsgBkEANgLIISAGQoCAgICAATcCwCEMGAsCQAJAIBVB/wFHIBVBAUdxDQAgBkHwGmoQJiAGLQCIISAGKAL8ICIEBEAgBigCgCEgBEECdBDfBAsCQCAGKAL0GiIERQ0AIAQgBEEMbEETakF4cSIFakEJaiIERQ0AIAYoAvAaIAVrIAQQ3wQLIAYoAvAdIQRFDQEgBEUgBEGAgICAeEZyDQAgBigC9B0gBEECdBDfBAsgBkHwGmogBkGAB2ogESA2IDQgOyA3IDogBkG4BmogBkHEBmoQ0AEgBkHQCWoiByAGQfgaaikCADcDACAGIAYpAvAaNwPICSAGKAKAGyEKIAYoAoQbIAYoAogbITYgBigCgAciBQRAIAYoAoQHIAVBMGwQ3wQLIDEgBykDADcDACAGIAYpA8gJNwOAByATIRYgESEPIREgECESIBMNGQwdCyAERSAEQYCAgIB4RnJFBEAgBigC9B0gBEECdBDfBAsgNkHAAWwhBAJAIDZFBEBBCCEHDAELQdHOxQAtAAAaIARBCBDWBCIHRQ0GCyAGQQA2AtgPIAYgBzYC1A8gBiA2NgLQDyAGID42AoQbIAYgPTYCgBsgBkEANgL4GiAGIAQgEWo2AvQaIAYgETYC8BogBiAGQZQHajYCiBsgBiAGQacJajYC/BogBiAHNgKYFCAGQQA2ApQUIAYgIzYCkBQjAEHABGsiDSQAIAZBkBRqIgcoAgQhFCAHKAIAIS0CQAJAIAZB8BpqIgQoAgAiBSAEKAIEIglHBEAgBCgCGCEYIAQoAhQhHiAEKAIQISYgBCgCDCEnIAQoAggiDkHAAWwhFiAHKAIIIBRBwAFsaiEXIAkgBWtBwAFuIRogDUHgAGohKSANQdACaiEEIA1B8AFqIQUgDUGQBGohCSANQbADaiEIA0ACfyAnLQAAQQFGBEAgDiAeSQRAIA1BoAJqIRAgDUHAAWohDyAFIQcgBCEKICYMAgsgDiAeQdT7wAAQ2QMACyAOIBgoAggiB08NAyANQeADaiEQIA1BgANqIQ8gCCEHIAkhCiAYKAIECyELIA8gCyAWaiILKQMANwMAIA9BKGogC0EoaikDADcDACAPQSBqIAtBIGopAwA3AwAgD0EYaiALQRhqKQMANwMAIA9BEGogC0EQaikDADcDACAPQQhqIAtBCGopAwA3AwAgByALQTBqKQMANwMAIAdBCGogC0E4aikDADcDACAHQRBqIAtBQGspAwA3AwAgB0EYaiALQcgAaikDADcDACAHQSBqIAtB0ABqKQMANwMAIAdBKGogC0HYAGopAwA3AwAgEEEoaiALQYgBaikDADcDACAQQSBqIAtBgAFqKQMANwMAIBBBGGogC0H4AGopAwA3AwAgEEEQaiALQfAAaikDADcDACAQQQhqIAtB6ABqKQMANwMAIBAgC0HgAGopAwA3AwAgCiALQZABaikDADcDACAKQQhqIAtBmAFqKQMANwMAIApBEGogC0GgAWopAwA3AwAgCkEYaiALQagBaikDADcDACAKQSBqIAtBsAFqKQMANwMAIApBKGogC0G4AWopAwA3AwAgDSAPQeAA/AoAACApIBBB4AD8CgAAIBcgDUHAAfwKAAAgFkHAAWohFiAXQcABaiEXIA5BAWohDiAUQQFqIRQgGkEBayIaDQALCyAtIBQ2AgAgDUHABGokAAwBCyAOIAdB5PvAABDZAwALIAYoAtAPIRYgBigC1A8hDyAGKALYDyEtIBshDiAdIRQgHCEQIBVBAUcEQCAoIQ4gKyEUICohECAGKAKAC0GAgICAeEYNBwtB0c7FAC0AABpBwABBBBDWBCINRQ0pIAYoAogHIgStQjB+IlGnIQVBACEKIFFCIIinIAVB+P///wdLcg0kIAYoAoQHIR4CQCAFRQRAQQghGCAGKAKMByEXQQghC0EIIRVBCCEaDAELQdHOxQAtAAAaQQghCiAFQQgQ1gQiC0UNJQJAIAQEQCALIQogBSEIIB4hByAEIQkDQCAIBEAgCiAHKQMANwMAIApBKGogB0EoaikDADcDACAKQSBqIAdBIGopAwA3AwAgCkEYaiAHQRhqKQMANwMAIApBEGogB0EQaikDADcDACAKQQhqIAdBCGopAwA3AwAgCkEwaiEKIAhBMGshCCAHQTBqIQcgCUEBayIJDQELC0HRzsUALQAAGiAGKAKMByEXIAVBCBDWBCIVRQ0rQQAhCCAEIQkDQCAFIAhGDQIgCCAVaiIHIAggHmoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAAsMAQtB0c7FAC0AABogBigCjAchFyAFQQgQ1gQiFUUNKgtB0c7FAC0AABogBUEIENYEIhhFDSkgBARAQQAhCCAEIQkDQCAFIAhHBEAgCCAYaiIHIAggHmoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAQsLQdHOxQAtAAAaIAVBCBDWBCIaRQ0qQQAhCCAEIQkDQCAFIAhGDQIgCCAaaiIHIAggHmoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAAsMAQtB0c7FAC0AABogBUEIENYEIhpFDSkLIA0gFzYCPCANIAQ2AjggDSAaNgI0IA0gBDYCMCANIBc2AiwgDSAENgIoIA0gGDYCJCANIAQ2AiAgDSAXNgIcIA0gBDYCGCANIBU2AhQgDSAENgIQIA0gFzYCDCANIAQ2AgggDSALNgIEIA0gBDYCACAGQQQ2AqQhIAYgDTYCoCEgBkEENgKcISAGQQA2ArAhIAZCgICAgIABNwKoISA2RQ0PQQAhCkEBIQcDQAJAAkAgIiAHIglHBEAgByAhRg0LIAZB8BpqIgQgESAKQcABbGogNCAKQTBsIgdqIAcgN2oQxgIgBkHQD2ogBEHAAfwKAAAgBigCuBwiB61CMH4iUachBUEAIQogUUIgiKcgBUH4////B0tyDSggBigCvBwhFSAGKAK0HCEXIAYoArAcIRggBQ0BQQghDQwCCyA7IDtB8JTAABDZAwALQdHOxQAtAAAaQQghCiAFQQgQ1gQiDUUNJiAHRQ0AQQAhCCAHIQQDQCAFIAhGDQEgCCANaiIKIAggF2oiCykDADcDACAKQShqIAtBKGopAwA3AwAgCkEgaiALQSBqKQMANwMAIApBGGogC0EYaikDADcDACAKQRBqIAtBEGopAwA3AwAgCkEIaiALQQhqKQMANwMAIAhBMGohCCAEQQFrIgQNAAsLIAYoAqQhIgQgBigCnCFGBEAgBkGcIWpBkJXAABCjAwsgBigCoCEgBEEEdGoiBSAVNgIMIAUgBzYCCCAFIA02AgQgBSAHNgIAIAYgBEEBaiIFNgKkISAGKAKcISAFRgRAIAZBnCFqQaCVwAAQowMLIAYoAqAhIAVBBHRqIgUgFTYCDCAFIAc2AgggBSAXNgIEIAUgGDYCACAGIARBAmo2AqQhIAYoArAhIgQgBigCqCFGBEAgBkGoIWpBsJXAABCdAwsgBigCrCEgBEHAAWxqIAZB0A9qQcAB/AoAACAGIARBAWo2ArAhIAlBAWohByAJIgogNkcNAAsMEAsgB0H/AUcNAQsgNkHAAWwhBAJAIDZFBEBBCCEKDAELQdHOxQAtAAAaIARBCBDWBCIKRQ0HCyAGQQA2AtgPIAYgCjYC1A8gBiA2NgLQDyAGID42AowbIAYgPTYCiBsgBiAZNgL8GiAGQQA2AvgaIAYgBCARajYC9BogBiARNgLwGiAGIAZBlAdqNgKQGyAGIAZBoAlqNgKEGyAGIB82AoAbIAYgCjYCmBQgBkEANgKUFCAGICM2ApAUIwBBwARrIg0kACAGQZAUaiIHKAIEIRQgBygCACEtAkACQAJAIAZB8BpqIgQoAgAiBSAEKAIEIglHBEAgBCgCICEXIAQoAhwhGCAEKAIYISYgBCgCFCEnIAQoAhAhHiAEKAIMISkgBCgCCCISQcABbCEWIAcoAgggFEHAAWxqIRUgCSAFa0HAAW4hGiANQeAAaiEsIA1B0AJqIQQgDUHwAWohBSANQZAEaiEJIA1BsANqIQgDQCAnKAIAIgcgHk8NAgJ/IAcgKWotAABBAUYEQCASIBhJBEAgDUGgAmohDyANQcABaiEOIAUhByAEIQogJgwCCyASIBhBhPzAABDZAwALIBIgFygCCCIHTw0EIA1B4ANqIQ8gDUGAA2ohDiAIIQcgCSEKIBcoAgQLIQsgDiALIBZqIgspAwA3AwAgDkEoaiALQShqKQMANwMAIA5BIGogC0EgaikDADcDACAOQRhqIAtBGGopAwA3AwAgDkEQaiALQRBqKQMANwMAIA5BCGogC0EIaikDADcDACAHIAtBMGopAwA3AwAgB0EIaiALQThqKQMANwMAIAdBEGogC0FAaykDADcDACAHQRhqIAtByABqKQMANwMAIAdBIGogC0HQAGopAwA3AwAgB0EoaiALQdgAaikDADcDACAPQShqIAtBiAFqKQMANwMAIA9BIGogC0GAAWopAwA3AwAgD0EYaiALQfgAaikDADcDACAPQRBqIAtB8ABqKQMANwMAIA9BCGogC0HoAGopAwA3AwAgDyALQeAAaikDADcDACAKIAtBkAFqKQMANwMAIApBCGogC0GYAWopAwA3AwAgCkEQaiALQaABaikDADcDACAKQRhqIAtBqAFqKQMANwMAIApBIGogC0GwAWopAwA3AwAgCkEoaiALQbgBaikDADcDACANIA5B4AD8CgAAICwgD0HgAPwKAAAgFSANQcAB/AoAACAWQcABaiEWIBVBwAFqIRUgEkEBaiESIBRBAWohFCAaQQFrIhoNAAsLIC0gFDYCACANQcAEaiQADAILIAcgHkH0+8AAENkDAAsgEiAHQZT8wAAQ2QMACyAGKAKgCSIKIB9PDQcgBigC0A8hFiAGKALUDyEPIAYoAtgPIS0gGyEXIB0hGCAcIQsgCiAZai0AAEEBRiImRQRAIAYoAoALQYCAgIB4Rg0KIAYoAogLIiCtQjB+IlGnIQdBACEKIFFCIIinIAdB+P///wdLcg00AkAgB0UEQEEIIQkMAQsgBigChAshC0HRzsUALQAAGkEIIQogB0EIENYEIglFDTUgIEUNAEEAIQggICEEA0AgByAIRwRAIAggCWoiBSAIIAtqIgopAwA3AwAgBUEoaiAKQShqKQMANwMAIAVBIGogCkEgaikDADcDACAFQRhqIApBGGopAwA3AwAgBUEQaiAKQRBqKQMANwMAIAVBCGogCkEIaikDADcDACAIQTBqIQggBEEBayIEDQELCyAgQYCAgIB4Rg0LCyAGKAKMCyEEIAYgIDYC7AkgBiAJNgKcISAGIAQ2AugJIAZBnCFqIQsgBkHsCWohGCAGQegJaiEXIAYoAqAJIQoLIApFDQsgCkEBayIEIB9PDQgCQCAEIBlqLQAADQAgBkHwGmoQJiAGLQCIISAGKAL8ICIEBEAgBigCgCEgBEECdBDfBAsCQCAGKAL0GiIERQ0AIAQgBEEMbEETakF4cSIFakEJaiIERQ0AIAYoAvAaIAVrIAQQ3wQLIAYoAvAdIQQEQCAERSAEQYCAgIB4RnJFBEAgBigC9B0gBEECdBDfBAsgBigCoAkNAQwNCyAERSAEQYCAgIB4RnJFBEAgBigC9B0gBEECdBDfBAtB0c7FAC0AABpBwABBBBDWBCINRQ0oIAYoAogHIgStQjB+IlGnIQVBACEKIFFCIIinIAVB+P///wdLcg0jIAYoAoQHIR4gBUUEQEEIIRogBigCjAchFEEIIQ5BCCEVQQghEgwMC0HRzsUALQAAGkEIIQogBUEIENYEIg5FDSMCQCAEBEAgDiEKIAUhCCAeIQcgBCEJA0AgCARAIAogBykDADcDACAKQShqIAdBKGopAwA3AwAgCkEgaiAHQSBqKQMANwMAIApBGGogB0EYaikDADcDACAKQRBqIAdBEGopAwA3AwAgCkEIaiAHQQhqKQMANwMAIApBMGohCiAIQTBrIQggB0EwaiEHIAlBAWsiCQ0BCwtB0c7FAC0AABogBigCjAchFCAFQQgQ1gQiFUUNKUEAIQggBCEJA0AgBSAIRg0CIAggFWoiByAIIB5qIgopAwA3AwAgB0EoaiAKQShqKQMANwMAIAdBIGogCkEgaikDADcDACAHQRhqIApBGGopAwA3AwAgB0EQaiAKQRBqKQMANwMAIAdBCGogCkEIaikDADcDACAIQTBqIQggCUEBayIJDQALDAELQdHOxQAtAAAaIAYoAowHIRQgBUEIENYEIhVFDSgLQdHOxQAtAAAaIAVBCBDWBCIaRQ0nAkAgBARAQQAhCCAEIQkDQCAFIAhHBEAgCCAaaiIHIAggHmoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAQsLQdHOxQAtAAAaIAVBCBDWBCISRQ0BQQAhCCAEIQkDQCAFIAhGDQ4gCCASaiIHIAggHmoiCikDADcDACAHQShqIApBKGopAwA3AwAgB0EgaiAKQSBqKQMANwMAIAdBGGogCkEYaikDADcDACAHQRBqIApBEGopAwA3AwAgB0EIaiAKQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAAsMDQtB0c7FAC0AABogBUEIENYEIhINDAsMJwsgBkHwGmoiBBAmAkAgBi0AiCFBAUcEQCAEKAKMBiIABEAgBCgCkAYgAEECdBDfBAsCQCAEKAIEIgBFDQAgACAAQQxsQRNqQXhxIgFqQQlqIgBFDQAgBCgCACABayAAEN8ECyAEKAKAAyIAQYCAgIB4RiAARXJFBEAgBCgChAMgAEECdBDfBAsgBigCoAkiACAfTw0BIAZBAjYC9BogBkHUmcAANgLwGiAGQgE3AvwaIAYgACAZaq1CgICAgBCENwOQFCAGIAZBkBRqNgL4GiAEQeSZwAAQqAQACyAGKAL8ICIEBEAgBigCgCEgBEECdBDfBAsCQCAGKAL0GiIERQ0AIAQgBEEMbEETakF4cSIHakEJaiIERQ0AIAYoAvAaIAdrIAQQ3wQLIAYoAvAdIgRBgICAgHhGIARFcg0MIAYoAvQdIARBAnQQ3wQMDAsgACAfQbCZwAAQ2QMACyAGQQI2AvQaIAZB1JnAADYC8BogBkIBNwL8GiAGIAStQoCAgIAQhDcDkBQgBiAGQZAUajYC+BogBkHwGmpB9JnAABCoBAALIBIgH0HgmMAAENkDAAsgOiA6QYCSwAAQ2QMAC0EIIARBlI3AABDIBAALQfCYwAAQ6AQACyA6IDpBgJXAABDZAwALQQggBEGUjcAAEMgEAAsgCiAfQYCZwAAQ2QMACyAEIB9BoJnAABDZAwALQZCZwAAQ6AQACyANIBQ2AjwgDSAENgI4IA0gEjYCNCANIAQ2AjAgDSAUNgIsIA0gBDYCKCANIBo2AiQgDSAENgIgIA0gFDYCHCANIAQ2AhggDSAVNgIUIA0gBDYCECANIBQ2AgwgDSAENgIIIA0gDjYCBCANIAQ2AgAgBkEENgKwISAGIA02AqwhIAZBBDYCqCEgGCgCACIHrUIwfiJRpyEFQQAhCiBRQiCIpyAFQfj///8HS3INFwJAIAVFBEBBCCEJDAELIAsoAgAhDkHRzsUALQAAGkEIIQogBUEIENYEIglFDRggB0UNAEEAIQggByEEA0AgBSAIRg0BIAggCWoiCiAIIA5qIg0pAwA3AwAgCkEoaiANQShqKQMANwMAIApBIGogDUEgaikDADcDACAKQRhqIA1BGGopAwA3AwAgCkEQaiANQRBqKQMANwMAIApBCGogDUEIaikDADcDACAIQTBqIQggBEEBayIEDQALCyAXKAIAIQ0gBigCsCEiBSAGKAKoIUYEQCAGQaghakHAlcAAEKMDCyAGKAKsISAFQQR0aiIEIA02AgwgBCAHNgIIIAQgCTYCBCAEIAc2AgAgBiAFQQFqNgKwISAYKAIAIgetQjB+IlGnIQVBACEKIFFCIIinIAVB+P///wdLcg0XAkAgBUUEQEEIIQkMAQsgCygCACEOQdHOxQAtAAAaQQghCiAFQQgQ1gQiCUUNGCAHRQ0AQQAhCCAHIQQDQCAFIAhGDQEgCCAJaiIKIAggDmoiCykDADcDACAKQShqIAtBKGopAwA3AwAgCkEgaiALQSBqKQMANwMAIApBGGogC0EYaikDADcDACAKQRBqIAtBEGopAwA3AwAgCkEIaiALQQhqKQMANwMAIAhBMGohCCAEQQFrIgQNAAsLIAYoArAhIgUgBigCqCFGBEAgBkGoIWpB0JXAABCjAwsgBigCrCEgBUEEdGoiBCANNgIMIAQgBzYCCCAEIAk2AgQgBCAHNgIAIAYgBUEBajYCsCEgBkEANgK8ISAGQoCAgICAATcCtCECQCA2RQRAIAZBADYCyCEgBkKAgICAgAE3AsAhDAELQQEhByAtQQFqIRhBACEKAkACQANAAkACQAJAIBggByIFRwRAIAUgIkYNASAFICFGDQUgBkHwGmogESAKQcABbCIEaiAEIA9qIDQgCkEwbCIEaiAEIDdqEKkBIAZB0A9qICRBwAH8CgAAIAYoAvgaIgmtQjB+IlGnIQtBACEKIFFCIIinIAtB+P///wdLcg0lIAYoAswcIRIgBigCyBwhByAGKALEHCEUIAYoAsAcIRogBigC/BohFSAGKAL0GiEXIAYoAvAaIScgCw0CQQghDQwDCyAtIC1BsJbAABDZAwALIDsgO0HAlsAAENkDAAtB0c7FAC0AABpBCCEKIAtBCBDWBCINRQ0iIAlFDQBBACEIIAkhBANAIAggC0YNASAIIA1qIgogCCAXaiIOKQMANwMAIApBKGogDkEoaikDADcDACAKQSBqIA5BIGopAwA3AwAgCkEYaiAOQRhqKQMANwMAIApBEGogDkEQaikDADcDACAKQQhqIA5BCGopAwA3AwAgCEEwaiEIIARBAWsiBA0ACwsgBigCsCEiBCAGKAKoIUYEQCAGQaghakHglsAAEKMDCyAGKAKsISAEQQR0aiIKIBU2AgwgCiAJNgIIIAogDTYCBCAKIAk2AgAgBiAEQQFqIgo2ArAhIAYoAqghIApGBEAgBkGoIWpB8JbAABCjAwsgBigCrCEgCkEEdGoiCiAVNgIMIAogCTYCCCAKIBc2AgQgCiAnNgIAIAYgBEECajYCsCEgB61CMH4iUachC0EAIQogUUIgiKcgC0H4////B0tyDSECQCALRQRAQQghCQwBC0HRzsUALQAAGkEIIQogC0EIENYEIglFDSIgB0UNAEEAIQggByEEA0AgCCALRg0BIAggCWoiCiAIIBRqIg0pAwA3AwAgCkEoaiANQShqKQMANwMAIApBIGogDUEgaikDADcDACAKQRhqIA1BGGopAwA3AwAgCkEQaiANQRBqKQMANwMAIApBCGogDUEIaikDADcDACAIQTBqIQggBEEBayIEDQALCyAGKAKwISIEIAYoAqghRgRAIAZBqCFqQYCXwAAQowMLIAYoAqwhIARBBHRqIgogEjYCDCAKIAc2AgggCiAJNgIEIAogBzYCACAGIARBAWoiCTYCsCEgBigCqCEgCUYEQCAGQaghakGQl8AAEKMDCyAGKAKsISAJQQR0aiIJIBI2AgwgCSAHNgIIIAkgFDYCBCAJIBo2AgAgBiAEQQJqNgKwISAGKAK8ISIEIAYoArQhRgRAIAZBtCFqQaCXwAAQnQMLIAYoArghIARBwAFsaiAGQdAPakHAAfwKAAAgBiAEQQFqNgK8ISAFQQFqIQcgBSIKIDZHDQALDAELIDogOkHQlsAAENkDAAtBACEHIAZBADYCyCEgBkKAgICAgAE3AsAhIDchCCA0IQRBACEKAkACQANAIAYoArwhIgUgCksEQCAKIDtGDQIgCiA6Rg0DIAZB8BpqIgUgBigCuCEgB2ogBCAIEMYCIAZBkBRqIAVBwAH8CgAAIAZBmBpqIgkgMkEIaikCADcDACAGIDIpAgA3A5AaIAYoArAhIgUgBigCqCFGBEAgBkGoIWpBkJbAABCjAwsgBigCrCEgBUEEdGoiCyAGKQOQGjcCACALQQhqIAkpAwA3AgAgBiAFQQFqNgKwISAGKALIISIFIAYoAsAhRgRAIAZBwCFqQaCWwAAQnQMLIAYoAsQhIAVBwAFsaiAGQZAUakHAAfwKAAAgBiAFQQFqNgLIISAIQTBqIQggBEEwaiEEIAdBwAFqIQcgCkEBaiIKIDZHDQEMBAsLIAogBUHglcAAENkDAAsgOyA7QfCVwAAQ2QMACyA6IDpBgJbAABDZAwALIAZBuBlqIAZBsCFqKAIANgIAIAYgBikCqCE3A7AZIAZBgICAgHg2AvAaIAZBkAtqIAZBsBlqIAZB8BpqIAZBuAZqIAZBxAZqEKsBIDBBCGogBkHIIWooAgA2AgAgMCAGKQLAITcCACAGKAK0ISIEBEAgBigCuCEgBEHAAWwQ3wQLIAZB+AlqIgQgBkGYC2opAgA3AwAgBiAGKQKQCzcD8AkgBigCoAshCiAGKAKkCyAGKAKoCyE2IAYoAoAHIgUEQCAeIAVBMGwQ3wQLIDEgBCkDADcDACAGIAYpA/AJNwOAByATBEAgESATQcABbBDfBAsgEEEBayESDAELQdHOxQAtAAAaAkBBMEEEENYEIgUEQCAGKAKIByIErUIwfiJRpyEHQQAhCiBRQiCIpyAHQfj///8HS3INKSAGKAKEByESIAdFBEAgBSAENgIIQQghDSAFQQg2AgQgBSAENgIAIAYoAowHIRoMAgtB0c7FAC0AABpBCCEKIAdBCBDWBCIORQ0pAkAgBARAQQAhCCAEIQkDQCAHIAhHBEAgCCAOaiIKIAggEmoiDSkDADcDACAKQShqIA1BKGopAwA3AwAgCkEgaiANQSBqKQMANwMAIApBGGogDUEYaikDADcDACAKQRBqIA1BEGopAwA3AwAgCkEIaiANQQhqKQMANwMAIAhBMGohCCAJQQFrIgkNAQsLIAUgBDYCCCAFIA42AgQgBSAENgIAQdHOxQAtAAAaIAYoAowHIRogB0EIENYEIg1FDQFBACEIIAQhCQNAIAcgCEYNBCAIIA1qIgogCCASaiIOKQMANwMAIApBKGogDkEoaikDADcDACAKQSBqIA5BIGopAwA3AwAgCkEYaiAOQRhqKQMANwMAIApBEGogDkEQaikDADcDACAKQQhqIA5BCGopAwA3AwAgCEEwaiEIIAlBAWsiCQ0ACwwDCyAFQQA2AgggBSAONgIEIAVBADYCAEHRzsUALQAAGiAGKAKMByEaIAdBCBDWBCINDQILQQggB0HogcAAEMgEAAsMGQsgBSAENgIYIAUgDTYCFCAFIAQ2AhAgGCgCACIHrUIwfiJRpyEJQQAhCiBRQiCIpyAJQfj///8HS3INGQJAIAlFBEBBCCENDAELIAsoAgAhDkHRzsUALQAAGkEIIQogCUEIENYEIg1FDRogB0UNAEEAIQggByEEA0AgCCAJRg0BIAggDWoiCiAIIA5qIgspAwA3AwAgCkEoaiALQShqKQMANwMAIApBIGogC0EgaikDADcDACAKQRhqIAtBGGopAwA3AwAgCkEQaiALQRBqKQMANwMAIApBCGogC0EIaikDADcDACAIQTBqIQggBEEBayIEDQALCyAFIAc2AiggBSANNgIkIAUgBzYCICAFIBo2AhwgBSAaNgIMIAUgFygCADYCLCAGQQM2ArwhIAYgBTYCuCEgBkEDNgK0ISAGQQA2AsghIAZCgICAgIABNwLAIQJAAkACQAJAIDYEQEEAIQogESEIIA8hBCA3IQUgNCEJA0AgCiAtRg0CIAogO0YNAyAKIDpGDQQgBkHwGmogCCAEIAkgBRCpASAGQZAUaiAkQcAB/AoAACAGQZgaaiILIAZB+BpqKQMANwMAIAZBmAtqIg0gM0EIaikCADcDACAGIAYpA/AaNwOQGiAGIDMpAgA3A5ALIAYoArwhIgcgBigCtCEiFUYEQCAGQbQhakHAk8AAEKMDIAYoArQhIRULIAYoArghIg4gB0EEdGoiFCAGKQOQGjcCACAUQQhqIAspAwA3AgAgBiAHQQFqIgs2ArwhIAsgFUYEfyAGQbQhakHQk8AAEKMDIAYoArghBSAOCyALQQR0aiILIAYpA5ALNwIAIAtBCGogDSkDADcCACAGIAdBAmo2ArwhIAYoAsghIgcgBigCwCFGBEAgBkHAIWpB4JPAABCdAwsgBigCxCEgB0HAAWxqIAZBkBRqQcAB/AoAACAGIAdBAWo2AsghIAhBwAFqIQggBEHAAWohBCAFQTBqIQUgCUEwaiEJIDYgCkEBaiIKRw0ACwsgBkG4GWogBkG8IWooAgA2AgAgBiAGKQK0ITcDsBkgBkGAgICAeDYC8BogBkHQD2ogBkGwGWogBkHwGmogBkG4BmogBkHEBmoQqwEgJUEIaiAGQcghaigCADYCACAlIAYpAsAhNwIAIAZBiApqIgQgIykCADcDACAGIAYpAtAPNwOACiAGKALgDyEKIAYoAuQPIQcgBigC6A8hNiAGKAKAByIFBEAgEiAFQTBsEN8ECyAxIAQpAwA3AwAgBiAGKQOACjcDgAcgE0UNAyARIBNBwAFsEN8EDAMLIC0gLUGQk8AAENkDAAsgOyA7QaCTwAAQ2QMACyA6IDpBsJPAABDZAwALIBAhEiAHCyERICYgIEVyRQRAIAYoApwhICBBMGwQ3wQgFkUNDgwKCyAWRQ0NDAkLIAZBADYCvCEgBkKAgICAgAE3ArQhDAELQQAhByAGQQA2ArwhIAZCgICAgIABNwK0ISA3IQQgNCEFQQAhCgNAIAogBigCsCEiCU8NAiAKIC1GDQMgCiA7Rg0EIAogOkYNBSAGQfAaaiAGKAKsISAHaiAHIA9qIAUgBBCpASAGQZAUaiAkQcAB/AoAACAGQbgZaiIIIAZB+BpqKQMANwMAIAZBmBpqIgsgM0EIaikCADcDACAGIAYpA/AaNwOwGSAGIDMpAgA3A5AaIAYoAqQhIgkgBigCnCEiDUYEQCAGQZwhakHAlMAAEKMDIAYoApwhIQ0LIAYoAqAhIhUgCUEEdGoiFyAGKQOwGTcCACAXQQhqIAgpAwA3AgAgBiAJQQFqIgg2AqQhIAggDUYEfyAGQZwhakHQlMAAEKMDIAYoAqAhBSAVCyAIQQR0aiIIIAYpA5AaNwIAIAhBCGogCykDADcCACAGIAlBAmo2AqQhIAYoArwhIgkgBigCtCFGBEAgBkG0IWpB4JTAABCdAwsgBigCuCEgCUHAAWxqIAZBkBRqQcAB/AoAACAGIAlBAWo2ArwhIARBMGohBCAFQTBqIQUgB0HAAWohByA2IApBAWoiCkcNAAsLIBQoAgAiB61CMH4iUachBUEAIQogUUIgiKcgBUH4////B0tyDRICQCAFRQRAQQghCQwBCyAQKAIAIQ1B0c7FAC0AABpBCCEKIAVBCBDWBCIJRQ0TIAdFDQBBACEIIAchBANAIAUgCEYNASAIIAlqIgogCCANaiILKQMANwMAIApBKGogC0EoaikDADcDACAKQSBqIAtBIGopAwA3AwAgCkEYaiALQRhqKQMANwMAIApBEGogC0EQaikDADcDACAKQQhqIAtBCGopAwA3AwAgCEEwaiEIIARBAWsiBA0ACwsgDigCACEKIAYoAqQhIgUgBigCnCFGBEAgBkGcIWpB8JPAABCjAwsgBigCoCEgBUEEdGoiBCAKNgIMIAQgBzYCCCAEIAk2AgQgBCAHNgIAIAZBpCFqIAVBAWoiBDYCACAGQcghaiAENgIAIAYgBikCnCE3A8AhIAZBgICAgHg2AvAaIAZBkAtqIAZBwCFqIAZB8BpqIAZBuAZqIAZBxAZqEKsBIDBBCGogBkG8IWooAgA2AgAgMCAGKQK0ITcCACAGKAKoISIEBEAgBigCrCEgBEHAAWwQ3wQLIAZBwAlqIgcgBkGYC2opAgA3AwAgBiAGKQKQCzcDuAkgBigCoAshCiAGKAKkCyAGKAKoCyE2IAYoAoAHIgUEQCAeIAVBMGwQ3wQLIDEgBykDADcDACAGIAYpA7gJNwOAByATBEAgESATQcABbBDfBAshESAWRQ0KDAYLIAogCUGAlMAAENkDAAsgLSAtQZCUwAAQ2QMACyA7IDtBoJTAABDZAwALIDogOkGwlMAAENkDAAtBACEHIAZBADYCyCEgBkKAgICAgAE3AsAhIDchCCA0IQRBACEKA0AgCiAGKAK8ISIFTw0DIAogO0YNBCAKIDpGDQUgBkHwGmoiBSAGKAK4ISAHaiAEIAgQxgIgBkGQFGogBUHAAfwKAAAgBkGYGmoiCSAyQQhqKQIANwMAIAYgMikCADcDkBogBigCsCEiBSAGKAKoIUYEQCAGQaghakHQkcAAEKMDCyAGKAKsISAFQQR0aiILIAYpA5AaNwIAIAtBCGogCSkDADcCACAGIAVBAWo2ArAhIAYoAsghIgUgBigCwCFGBEAgBkHAIWpB4JHAABCdAwsgBigCxCEgBUHAAWxqIAZBkBRqQcAB/AoAACAGIAVBAWo2AsghIAhBMGohCCAEQTBqIQQgB0HAAWohByA2IApBAWoiCkcNAAsLIAZBuBlqIAZBsCFqKAIANgIAIAYgBikCqCE3A7AZIAZBgICAgHg2AvAaIAZBkAtqIAZBsBlqIAZB8BpqIAZBuAZqIAZBxAZqEKsBIDBBCGogBkHIIWooAgA2AgAgMCAGKQLAITcCACAGKAK0ISIEBEAgBigCuCEgBEHAAWwQ3wQLIAZBsAlqIgcgBkGYC2opAgA3AwAgBiAGKQKQCzcDqAkgBigCoAshCiAGKAKkCyAGKAKoCyE2IAYoAoAHIgUEQCAQIAVBMGwQ3wQLIDEgBykDADcDACAGIAYpA6gJNwOAByATIRYgESEPIREgE0UNBAsgDyAWQcABbBDfBAwDCyAKIAVBoJHAABDZAwALIDsgO0GwkcAAENkDAAsgOiA6QcCRwAAQ2QMACyASQQFrIRAgEkEASg0ACwtB0c7FAC0AABpBDEEBENYEIgRFBEBBAUEMEP8EAAsgBEIANwABIARBAToAACAEQQhqQQA2AAAgBkEMNgKcCiAGIAQ2ApgKIAZBDDYClAogBkHwGmohQSMAQeABayIFJAACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgRg4CAQIAC0GYycEAQQ9BqMnBABD+AwALQdHOxQAtAAAaQZABQQQQ1gQiH0UNU0HRzsUALQAAGkHwAEEIENYEIhpFDVEgBUGoAWoiFEHYn8EAQQEQgwEgBS0AqAFBAUYNASAFQZ4BaiIWIg0gBUHYAWoiCykDACJRNwEAIAVBlgFqIhwiECAFQdABaiIEKQMAIlI3AQAgBUHIAGoiHSIPIAVBuAFqIgcpAwAiVTcBACAFQdAAaiIbIg4gBUHAAWoiCSkDACJTNwEAIAVB2ABqIhUiEyAFQcgBaiIIKQMAIlY3AQAgBUHgAGoiFyBSNwEAIAVB6ABqIhggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIAVBsAFqIhIgVTcDACAFIFQ3A6gBIAVBMGoiMCAEKQMANwIAIAVBKGoiLSAIKQMANwIAIAVBIGoiMSAJKQMANwIAIAVBGGoiMiAHKQMANwIAIAVBEGoiMyASKQMANwIAIAUgBSkDqAE3AgggFEHZn8EAQQIQgwEgBS0AqAFBAUYNAiANIAspAwAiUTcBACAQIAQpAwAiUjcBACAPIAcpAwAiVTcBACAOIAkpAwAiUzcBACATIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAFQZgBaiINIFE3AwAgBUGQAWoiEyBSNwMAIAVBiAFqIhAgVjcDACAFQYABaiIPIFM3AwAgBUH4AGoiDiBVNwMAIAUgVDcDcCAFQdQBaiIgIA0pAwA3AgAgBUHMAWoiHiATKQMANwIAIAVBxAFqIiogECkDADcCACAFQbwBaiIrIA8pAwA3AgAgBUG0AWoiKCAOKQMANwIAIAUgBSkDcDcCrAEgGkEANgIAIBpBBjYCOCAaIAUpAgQ3AgQgGkEMaiAFQQxqKQIANwIAIBpBFGogBUEUaikCADcCACAaQRxqIAVBHGopAgA3AgAgGkEkaiAFQSRqKQIANwIAIBpBLGogBUEsaikCADcCACAaQTRqIAVBNGooAgA2AgAgGiAFKQKoATcCPCAaQcQAaiASKQIANwIAIBpBzABqIAcpAgA3AgAgGkHUAGogCSkCADcCACAaQdwAaiAIKQIANwIAIBpB5ABqIAQpAgA3AgAgGkHsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIhlFDVEgFEHbn8EAQcAAEIMBIAUtAKgBQQFGDQMgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQZugwQBBwAAQgwEgBS0AqAFBAUYNBCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgGUEBNgIAIBlBBzYCOCAZIAUpAgQ3AgQgGUEMaiAFQQxqKQIANwIAIBlBFGogBUEUaikCADcCACAZQRxqIAVBHGopAgA3AgAgGUEkaiAFQSRqKQIANwIAIBlBLGogBUEsaikCADcCACAZQTRqIAVBNGooAgA2AgAgGSAFKQKoATcCPCAZQcQAaiASKQIANwIAIBlBzABqIAcpAgA3AgAgGUHUAGogCSkCADcCACAZQdwAaiAIKQIANwIAIBlB5ABqIAQpAgA3AgAgGUHsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIiFFDVEgFEHboMEAQcAAEIMBIAUtAKgBQQFGDQUgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQZuhwQBBPxCDASAFLQCoAUEBRg0GIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAhQQI2AgAgIUEINgI4ICEgBSkCBDcCBCAhQQxqIAVBDGopAgA3AgAgIUEUaiAFQRRqKQIANwIAICFBHGogBUEcaikCADcCACAhQSRqIAVBJGopAgA3AgAgIUEsaiAFQSxqKQIANwIAICFBNGogBUE0aigCADYCACAhIAUpAqgBNwI8ICFBxABqIBIpAgA3AgAgIUHMAGogBykCADcCACAhQdQAaiAJKQIANwIAICFB3ABqIAgpAgA3AgAgIUHkAGogBCkCADcCACAhQewAaiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiIkUNUSAUQdqhwQBBwAAQgwEgBS0AqAFBAUYNByAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRBmqLBAEHAABCDASAFLQCoAUEBRg0IIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAiQQM2AgAgIkEJNgI4ICIgBSkCBDcCBCAiQQxqIAVBDGopAgA3AgAgIkEUaiAFQRRqKQIANwIAICJBHGogBUEcaikCADcCACAiQSRqIAVBJGopAgA3AgAgIkEsaiAFQSxqKQIANwIAICJBNGogBUE0aigCADYCACAiIAUpAqgBNwI8ICJBxABqIBIpAgA3AgAgIkHMAGogBykCADcCACAiQdQAaiAJKQIANwIAICJB3ABqIAgpAgA3AgAgIkHkAGogBCkCADcCACAiQewAaiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiI0UNUSAUQdqiwQBBwAAQgwEgBS0AqAFBAUYNCSAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRBmqPBAEE/EIMBIAUtAKgBQQFGDQogFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICNBBDYCACAjQQo2AjggIyAFKQIENwIEICNBDGogBUEMaikCADcCACAjQRRqIAVBFGopAgA3AgAgI0EcaiAFQRxqKQIANwIAICNBJGogBUEkaikCADcCACAjQSxqIAVBLGopAgA3AgAgI0E0aiAFQTRqKAIANgIAICMgBSkCqAE3AjwgI0HEAGogEikCADcCACAjQcwAaiAHKQIANwIAICNB1ABqIAkpAgA3AgAgI0HcAGogCCkCADcCACAjQeQAaiAEKQIANwIAICNB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIkRQ1RIBRB2aPBAEHAABCDASAFLQCoAUEBRg0LIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAIIFI3AwAgCSBWNwMAIAcgUzcDACASIFU3AwAgBSBUNwOoASAwIAQpAwA3AgAgLSAIKQMANwIAIDEgCSkDADcCACAyIAcpAwA3AgAgMyASKQMANwIAIAUgBSkDqAE3AgggFEGZpMEAQcAAEIMBIAUtAKgBQQFGDQwgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICRBBTYCACAkQQs2AjggJCAFKQIENwIEICRBDGogBUEMaikCADcCACAkQRRqIAVBFGopAgA3AgAgJEEcaiAFQRxqKQIANwIAICRBJGogBUEkaikCADcCACAkQSxqIAVBLGopAgA3AgAgJEE0aiAFQTRqKAIANgIAICQgBSkCqAE3AjwgJEHEAGogEikCADcCACAkQcwAaiAHKQIANwIAICRB1ABqIAkpAgA3AgAgJEHcAGogCCkCADcCACAkQeQAaiAEKQIANwIAICRB7ABqIAsoAgA2AgBB0c7FAC0AABpBOEEIENYEIi5FDVIgFEHZpMEAQcAAEIMBIAUtAKgBQQFGDQ0gFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBIC5BBjYCACAuIAUpAqgBNwIEIC5BDGogEikCADcCACAuQRRqIAcpAgA3AgAgLkEcaiAJKQIANwIAIC5BJGogCCkCADcCACAuQSxqIAQpAgA3AgAgLkE0aiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiJUUNUSAUQZmlwQBBwAAQgwEgBS0AqAFBAUYNDiAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB2aXBAEHAABCDASAFLQCoAUEBRg0PIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAlQQE2AgAgJUEHNgI4ICUgBSkCBDcCBCAlQQxqIAVBDGopAgA3AgAgJUEUaiAFQRRqKQIANwIAICVBHGogBUEcaikCADcCACAlQSRqIAVBJGopAgA3AgAgJUEsaiAFQSxqKQIANwIAICVBNGogBUE0aigCADYCACAlIAUpAqgBNwI8ICVBxABqIBIpAgA3AgAgJUHMAGogBykCADcCACAlQdQAaiAJKQIANwIAICVB3ABqIAgpAgA3AgAgJUHkAGogBCkCADcCACAlQewAaiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiJkUNUSAUQZmmwQBBwAAQgwEgBS0AqAFBAUYNECAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB2abBAEE/EIMBIAUtAKgBQQFGDREgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICZBAjYCACAmQQg2AjggJiAFKQIENwIEICZBDGogBUEMaikCADcCACAmQRRqIAVBFGopAgA3AgAgJkEcaiAFQRxqKQIANwIAICZBJGogBUEkaikCADcCACAmQSxqIAVBLGopAgA3AgAgJkE0aiAFQTRqKAIANgIAICYgBSkCqAE3AjwgJkHEAGogEikCADcCACAmQcwAaiAHKQIANwIAICZB1ABqIAkpAgA3AgAgJkHcAGogCCkCADcCACAmQeQAaiAEKQIANwIAICZB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCInRQ1RIBRBmKfBAEE/EIMBIAUtAKgBQQFGDRIgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQdenwQBBPxCDASAFLQCoAUEBRg0TIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAnQQM2AgAgJ0EJNgI4ICcgBSkCBDcCBCAnQQxqIAVBDGopAgA3AgAgJ0EUaiAFQRRqKQIANwIAICdBHGogBUEcaikCADcCACAnQSRqIAVBJGopAgA3AgAgJ0EsaiAFQSxqKQIANwIAICdBNGogBUE0aigCADYCACAnIAUpAqgBNwI8ICdBxABqIBIpAgA3AgAgJ0HMAGogBykCADcCACAnQdQAaiAJKQIANwIAICdB3ABqIAgpAgA3AgAgJ0HkAGogBCkCADcCACAnQewAaiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiKUUNUSAUQZaowQBBwAAQgwEgBS0AqAFBAUYNFCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB1qjBAEE/EIMBIAUtAKgBQQFGDRUgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBIClBBDYCACApQQo2AjggKSAFKQIENwIEIClBDGogBUEMaikCADcCACApQRRqIAVBFGopAgA3AgAgKUEcaiAFQRxqKQIANwIAIClBJGogBUEkaikCADcCACApQSxqIAVBLGopAgA3AgAgKUE0aiAFQTRqKAIANgIAICkgBSkCqAE3AjwgKUHEAGogEikCADcCACApQcwAaiAHKQIANwIAIClB1ABqIAkpAgA3AgAgKUHcAGogCCkCADcCACApQeQAaiAEKQIANwIAIClB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIsRQ1RIBRBlanBAEHAABCDASAFLQCoAUEBRg0WIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAIIFI3AwAgCSBWNwMAIAcgUzcDACASIFU3AwAgBSBUNwOoASAwIAQpAwA3AgAgLSAIKQMANwIAIDEgCSkDADcCACAyIAcpAwA3AgAgMyASKQMANwIAIAUgBSkDqAE3AgggFEHVqcEAQcAAEIMBIAUtAKgBQQFGDRcgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICxBBTYCACAsQQs2AjggLCAFKQIENwIEICxBDGogBUEMaikCADcCACAsQRRqIAVBFGopAgA3AgAgLEEcaiAFQRxqKQIANwIAICxBJGogBUEkaikCADcCACAsQSxqIAVBLGopAgA3AgAgLEE0aiAFQTRqKAIANgIAICwgBSkCqAE3AjwgLEHEAGogEikCADcCACAsQcwAaiAHKQIANwIAICxB1ABqIAkpAgA3AgAgLEHcAGogCCkCADcCACAsQeQAaiAEKQIANwIAICxB7ABqIAsoAgA2AgAgH0ECNgKMASAfICw2AogBIB9CgoCAgCA3AoABIB8gKTYCfCAfQoKAgIAgNwJ0IB8gJzYCcCAfQoKAgIAgNwJoIB8gJjYCZCAfQoKAgIAgNwJcIB8gJTYCWCAfQoGAgIAgNwJQIB8gLjYCTCAfQoKAgIAQNwJEIB8gJDYCQCAfQoKAgIAgNwI4IB8gIzYCNCAfQoKAgIAgNwIsIB8gIjYCKCAfQoKAgIAgNwIgIB8gITYCHCAfQoKAgIAgNwIUIB8gGTYCECAfQoKAgIAgNwIIIB8gGjYCBCAfQQI2AgBB0c7FAC0AABpBkAFBBBDWBCIaRQ1TQdHOxQAtAAAaQThBCBDWBCIZRQ1SIBRB2J/BAEEBEIMBIAUtAKgBQQFGDRggFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBIBlBADYCACAZIAUpAqgBNwIEIBlBDGogEikCADcCACAZQRRqIAcpAgA3AgAgGUEcaiAJKQIANwIAIBlBJGogCCkCADcCACAZQSxqIAQpAgA3AgAgGUE0aiALKAIANgIAQdHOxQAtAAAaQThBCBDWBCIhRQ1SIBRBlarBAEHAABCDASAFLQCoAUEBRg0ZIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAhQQE2AgAgISAFKQKoATcCBCAhQQxqIBIpAgA3AgAgIUEUaiAHKQIANwIAICFBHGogCSkCADcCACAhQSRqIAgpAgA3AgAgIUEsaiAEKQIANwIAICFBNGogCygCADYCAEHRzsUALQAAGkE4QQgQ1gQiIkUNUiAUQdWqwQBBwAAQgwEgBS0AqAFBAUYNGiAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgIkECNgIAICIgBSkCqAE3AgQgIkEMaiASKQIANwIAICJBFGogBykCADcCACAiQRxqIAkpAgA3AgAgIkEkaiAIKQIANwIAICJBLGogBCkCADcCACAiQTRqIAsoAgA2AgBB0c7FAC0AABpBOEEIENYEIiNFDVIgFEHZpMEAQcAAEIMBIAUtAKgBQQFGDRsgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICNBAzYCACAjIAUpAqgBNwIEICNBDGogBUGwAWopAgA3AgAgI0EUaiAHKQIANwIAICNBHGogCSkCADcCACAjQSRqIAgpAgA3AgAgI0EsaiAEKQIANwIAICNBNGogCygCADYCAEHRzsUALQAAGkE4QQgQ1gQiJEUNUiAUQZWrwQBBMBCDASAFLQCoAUEBRg0cIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAkQQQ2AgAgJCAFKQKoATcCBCAkQQxqIAVBsAFqKQIANwIAICRBFGogBykCADcCACAkQRxqIAkpAgA3AgAgJEEkaiAIKQIANwIAICRBLGogBCkCADcCACAkQTRqIAsoAgA2AgBB0c7FAC0AABpBOEEIENYEIiVFDVIgFEHFq8EAQTAQgwEgBS0AqAFBAUYNHSAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgJUEFNgIAICUgBSkCqAE3AgQgJUEMaiAFQbABaikCADcCACAlQRRqIAcpAgA3AgAgJUEcaiAJKQIANwIAICVBJGogCCkCADcCACAlQSxqIAQpAgA3AgAgJUE0aiALKAIANgIAQdHOxQAtAAAaQThBCBDWBCImRQ1SIBRB2J/BAEEBEIMBIAUtAKgBQQFGDR4gFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICZBBjYCACAmIAUpAqgBNwIEICZBDGogBUGwAWopAgA3AgAgJkEUaiAHKQIANwIAICZBHGogCSkCADcCACAmQSRqIAgpAgA3AgAgJkEsaiAEKQIANwIAICZBNGogCygCADYCAEHRzsUALQAAGkE4QQgQ1gQiJ0UNUiAUQZWqwQBBwAAQgwEgBS0AqAFBAUYNHyAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgJ0EHNgIAICcgBSkCqAE3AgQgJ0EMaiAFQbABaikCADcCACAnQRRqIAcpAgA3AgAgJ0EcaiAJKQIANwIAICdBJGogCCkCADcCACAnQSxqIAQpAgA3AgAgJ0E0aiALKAIANgIAQdHOxQAtAAAaQThBCBDWBCIpRQ1SIBRB1arBAEHAABCDASAFLQCoAUEBRg0gIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASApQQg2AgAgKSAFKQKoATcCBCApQQxqIAVBsAFqKQIANwIAIClBFGogBykCADcCACApQRxqIAkpAgA3AgAgKUEkaiAIKQIANwIAIClBLGogBCkCADcCACApQTRqIAsoAgA2AgBB0c7FAC0AABpBOEEIENYEIixFDVIgFEHZpMEAQcAAEIMBIAUtAKgBQQFGDSEgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICxBCTYCACAsIAUpAqgBNwIEICxBDGogBUGwAWopAgA3AgAgLEEUaiAHKQIANwIAICxBHGogCSkCADcCACAsQSRqIAgpAgA3AgAgLEEsaiAEKQIANwIAICxBNGogCygCADYCAEHRzsUALQAAGkE4QQgQ1gQiLkUNUiAUQZWrwQBBMBCDASAFLQCoAUEBRg0iIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAuQQo2AgAgLiAFKQKoATcCBCAuQQxqIAVBsAFqKQIANwIAIC5BFGogBykCADcCACAuQRxqIAkpAgA3AgAgLkEkaiAIKQIANwIAIC5BLGogBCkCADcCACAuQTRqIAsoAgA2AgBB0c7FAC0AABpBOEEIENYEIjlFDVIgFEHFq8EAQTAQgwEgBS0AqAFBAUYNIyAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgOUELNgIAIDkgBSkCqAE3AgQgOUEMaiAFQbABaikCADcCACA5QRRqIAcpAgA3AgAgOUEcaiAJKQIANwIAIDlBJGogCCkCADcCACA5QSxqIAQpAgA3AgAgOUE0aiALKAIANgIAIBpBATYCjAEgGiA5NgKIASAaQoGAgIAQNwKAASAaIC42AnwgGkKBgICAEDcCdCAaICw2AnAgGkKBgICAEDcCaCAaICk2AmQgGkKBgICAEDcCXCAaICc2AlggGkKBgICAEDcCUCAaICY2AkwgGkKBgICAEDcCRCAaICU2AkAgGkKBgICAEDcCOCAaICQ2AjQgGkKBgICAEDcCLCAaICM2AiggGkKBgICAEDcCICAaICI2AhwgGkKBgICAEDcCFCAaICE2AhAgGkKBgICAEDcCCCAaIBk2AgQgGkEBNgIAQdHOxQAtAAAaQZABQQQQ1gQiGUUNU0HRzsUALQAAGkHwAEEIENYEIiFFDVEgFEHYn8EAQQEQgwEgBS0AqAFBAUYNJCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB2Z/BAEECEIMBIAUtAKgBQQFGDSUgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICFBADYCACAhQQY2AjggISAFKQIENwIEICFBDGogBUEMaikCADcCACAhQRRqIAVBFGopAgA3AgAgIUEcaiAFQRxqKQIANwIAICFBJGogBUEkaikCADcCACAhQSxqIAVBLGopAgA3AgAgIUE0aiAFQTRqKAIANgIAICEgBSkCqAE3AjwgIUHEAGogEikCADcCACAhQcwAaiAHKQIANwIAICFB1ABqIAkpAgA3AgAgIUHcAGogCCkCADcCACAhQeQAaiAEKQIANwIAICFB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIiRQ1RIBRB9avBAEHAABCDASAFLQCoAUEBRg0mIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAIIFI3AwAgCSBWNwMAIAcgUzcDACASIFU3AwAgBSBUNwOoASAwIAQpAwA3AgAgLSAIKQMANwIAIDEgCSkDADcCACAyIAcpAwA3AgAgMyASKQMANwIAIAUgBSkDqAE3AgggFEG1rMEAQcAAEIMBIAUtAKgBQQFGDScgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICJBATYCACAiQQc2AjggIiAFKQIENwIEICJBDGogBUEMaikCADcCACAiQRRqIAVBFGopAgA3AgAgIkEcaiAFQRxqKQIANwIAICJBJGogBUEkaikCADcCACAiQSxqIAVBLGopAgA3AgAgIkE0aiAFQTRqKAIANgIAICIgBSkCqAE3AjwgIkHEAGogEikCADcCACAiQcwAaiAHKQIANwIAICJB1ABqIAkpAgA3AgAgIkHcAGogCCkCADcCACAiQeQAaiAEKQIANwIAICJB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIjRQ1RIBRB9azBAEE/EIMBIAUtAKgBQQFGDSggFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQbStwQBBwAAQgwEgBS0AqAFBAUYNKSAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgI0ECNgIAICNBCDYCOCAjIAUpAgQ3AgQgI0EMaiAFQQxqKQIANwIAICNBFGogBUEUaikCADcCACAjQRxqIAVBHGopAgA3AgAgI0EkaiAFQSRqKQIANwIAICNBLGogBUEsaikCADcCACAjQTRqIAVBNGooAgA2AgAgIyAFKQKoATcCPCAjQcQAaiASKQIANwIAICNBzABqIAcpAgA3AgAgI0HUAGogCSkCADcCACAjQdwAaiAIKQIANwIAICNB5ABqIAQpAgA3AgAgI0HsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIiRFDVEgFEHXp8EAQT8QgwEgBS0AqAFBAUYNKiAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB9K3BAEHAABCDASAFLQCoAUEBRg0rIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIA0gUTcDACATIFI3AwAgECBWNwMAIA8gUzcDACAOIFU3AwAgBSBUNwNwICAgDSkDADcCACAeIBMpAwA3AgAgKiAQKQMANwIAICsgDykDADcCACAoIA4pAwA3AgAgBSAFKQNwNwKsASAkQQM2AgAgJEEJNgI4ICQgBSkCBDcCBCAkQQxqIAVBDGopAgA3AgAgJEEUaiAFQRRqKQIANwIAICRBHGogBUEcaikCADcCACAkQSRqIAVBJGopAgA3AgAgJEEsaiAFQSxqKQIANwIAICRBNGogBUE0aigCADYCACAkIAUpAqgBNwI8ICRBxABqIBIpAgA3AgAgJEHMAGogBykCADcCACAkQdQAaiAJKQIANwIAICRB3ABqIAgpAgA3AgAgJEHkAGogBCkCADcCACAkQewAaiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiJUUNUSAUQbSuwQBBwAAQgwEgBS0AqAFBAUYNLCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgCCBSNwMAIAkgVjcDACAHIFM3AwAgEiBVNwMAIAUgVDcDqAEgMCAEKQMANwIAIC0gCCkDADcCACAxIAkpAwA3AgAgMiAHKQMANwIAIDMgEikDADcCACAFIAUpA6gBNwIIIBRB9K7BAEE/EIMBIAUtAKgBQQFGDS0gFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICVBBDYCACAlQQo2AjggJSAFKQIENwIEICVBDGogBUEMaikCADcCACAlQRRqIAVBFGopAgA3AgAgJUEcaiAFQRxqKQIANwIAICVBJGogBUEkaikCADcCACAlQSxqIAVBLGopAgA3AgAgJUE0aiAFQTRqKAIANgIAICUgBSkCqAE3AjwgJUHEAGogEikCADcCACAlQcwAaiAHKQIANwIAICVB1ABqIAkpAgA3AgAgJUHcAGogCCkCADcCACAlQeQAaiAEKQIANwIAICVB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCImRQ1RIBRBs6/BAEE/EIMBIAUtAKgBQQFGDS4gFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQfKvwQBBwAAQgwEgBS0AqAFBAUYNLyAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgJkEFNgIAICZBCzYCOCAmIAUpAgQ3AgQgJkEMaiAFQQxqKQIANwIAICZBFGogBUEUaikCADcCACAmQRxqIAVBHGopAgA3AgAgJkEkaiAFQSRqKQIANwIAICZBLGogBUEsaikCADcCACAmQTRqIAVBNGooAgA2AgAgJiAFKQKoATcCPCAmQcQAaiASKQIANwIAICZBzABqIAcpAgA3AgAgJkHUAGogCSkCADcCACAmQdwAaiAIKQIANwIAICZB5ABqIAQpAgA3AgAgJkHsAGogCygCADYCAEHRzsUALQAAGkE4QQgQ1gQiQEUNUiAUQdmkwQBBwAAQgwEgBS0AqAFBAUYNMCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgQEEGNgIAIEAgBSkCqAE3AgQgQEEMaiAFQbABaikCADcCACBAQRRqIAcpAgA3AgAgQEEcaiAJKQIANwIAIEBBJGogCCkCADcCACBAQSxqIAQpAgA3AgAgQEE0aiALKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiJ0UNUSAUQbKwwQBBPhCDASAFLQCoAUEBRg0xIBYgCykDACJRNwEAIBwgBCkDACJSNwEAIB0gBykDACJVNwEAIBsgCSkDACJTNwEAIBUgCCkDACJWNwEAIBcgUjcBACAYIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAIIFI3AwAgCSBWNwMAIAcgUzcDACASIFU3AwAgBSBUNwOoASAwIAQpAwA3AgAgLSAIKQMANwIAIDEgCSkDADcCACAyIAcpAwA3AgAgMyASKQMANwIAIAUgBSkDqAE3AgggFEHwsMEAQcAAEIMBIAUtAKgBQQFGDTIgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgDSBRNwMAIBMgUjcDACAQIFY3AwAgDyBTNwMAIA4gVTcDACAFIFQ3A3AgICANKQMANwIAIB4gEykDADcCACAqIBApAwA3AgAgKyAPKQMANwIAICggDikDADcCACAFIAUpA3A3AqwBICdBATYCACAnQQc2AjggJyAFKQIENwIEICdBDGogBUEMaikCADcCACAnQRRqIAVBFGopAgA3AgAgJ0EcaiAFQRxqKQIANwIAICdBJGogBUEkaikCADcCACAnQSxqIAVBLGopAgA3AgAgJ0E0aiAFQTRqKAIANgIAICcgBSkCqAE3AjwgJ0HEAGogEikCADcCACAnQcwAaiAHKQIANwIAICdB1ABqIAkpAgA3AgAgJ0HcAGogCCkCADcCACAnQeQAaiAEKQIANwIAICdB7ABqIAsoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIpRQ1RIBRBsLHBAEE/EIMBIAUtAKgBQQFGDTMgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQe+xwQBBwAAQgwEgBS0AqAFBAUYNNCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgKUECNgIAIClBCDYCOCApIAUpAgQ3AgQgKUEMaiAFQQxqKQIANwIAIClBFGogBUEUaikCADcCACApQRxqIAVBHGopAgA3AgAgKUEkaiAFQSRqKQIANwIAIClBLGogBUEsaikCADcCACApQTRqIAVBNGooAgA2AgAgKSAFKQKoATcCPCApQcQAaiASKQIANwIAIClBzABqIAcpAgA3AgAgKUHUAGogCSkCADcCACApQdwAaiAIKQIANwIAIClB5ABqIAQpAgA3AgAgKUHsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIixFDVEgFEGvssEAQcAAEIMBIAUtAKgBQQFGDTUgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQdqhwQBBwAAQgwEgBS0AqAFBAUYNNiAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgLEEDNgIAICxBCTYCOCAsIAUpAgQ3AgQgLEEMaiAFQQxqKQIANwIAICxBFGogBUEUaikCADcCACAsQRxqIAVBHGopAgA3AgAgLEEkaiAFQSRqKQIANwIAICxBLGogBUEsaikCADcCACAsQTRqIAVBNGooAgA2AgAgLCAFKQKoATcCPCAsQcQAaiASKQIANwIAICxBzABqIAcpAgA3AgAgLEHUAGogCSkCADcCACAsQdwAaiAIKQIANwIAICxB5ABqIAQpAgA3AgAgLEHsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIi5FDVEgFEHvssEAQcAAEIMBIAUtAKgBQQFGDTcgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQa+zwQBBwAAQgwEgBS0AqAFBAUYNOCAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgLkEENgIAIC5BCjYCOCAuIAUpAgQ3AgQgLkEMaiAFQQxqKQIANwIAIC5BFGogBUEUaikCADcCACAuQRxqIAVBHGopAgA3AgAgLkEkaiAFQSRqKQIANwIAIC5BLGogBUEsaikCADcCACAuQTRqIAVBNGooAgA2AgAgLiAFKQKoATcCPCAuQcQAaiASKQIANwIAIC5BzABqIAcpAgA3AgAgLkHUAGogCSkCADcCACAuQdwAaiAIKQIANwIAIC5B5ABqIAQpAgA3AgAgLkHsAGogCygCADYCAEHRzsUALQAAGkHwAEEIENYEIjlFDVEgFEHvs8EAQcAAEIMBIAUtAKgBQQFGDTkgFiALKQMAIlE3AQAgHCAEKQMAIlI3AQAgHSAHKQMAIlU3AQAgGyAJKQMAIlM3AQAgFSAIKQMAIlY3AQAgFyBSNwEAIBggUTcBACAFIAUpA7ABIlQ3AUAgBCBRNwMAIAggUjcDACAJIFY3AwAgByBTNwMAIBIgVTcDACAFIFQ3A6gBIDAgBCkDADcCACAtIAgpAwA3AgAgMSAJKQMANwIAIDIgBykDADcCACAzIBIpAwA3AgAgBSAFKQOoATcCCCAUQa+0wQBBwAAQgwEgBS0AqAFBAUYNOiAWIAspAwAiUTcBACAcIAQpAwAiUjcBACAdIAcpAwAiVTcBACAbIAkpAwAiUzcBACAVIAgpAwAiVjcBACAXIFI3AQAgGCBRNwEAIAUgBSkDsAEiVDcBQCANIFE3AwAgEyBSNwMAIBAgVjcDACAPIFM3AwAgDiBVNwMAIAUgVDcDcCAgIA0pAwA3AgAgHiATKQMANwIAICogECkDADcCACArIA8pAwA3AgAgKCAOKQMANwIAIAUgBSkDcDcCrAEgOUEFNgIAIDlBCzYCOCA5IAUpAgQ3AgQgOUEMaiAFQQxqKQIANwIAIDlBFGogBUEUaikCADcCACA5QRxqIAVBHGopAgA3AgAgOUEkaiAFQSRqKQIANwIAIDlBLGogBUEsaikCADcCACA5QTRqIAVBNGooAgA2AgAgOSAFKQKoATcCPCA5QcQAaiASKQIANwIAIDlBzABqIAcpAgA3AgAgOUHUAGogCSkCADcCACA5QdwAaiAIKQIANwIAIDlB5ABqIAQpAgA3AgAgOUHsAGogCygCADYCACAZQQI2AowBIBkgOTYCiAEgGUKCgICAIDcCgAEgGSAuNgJ8IBlCgoCAgCA3AnQgGSAsNgJwIBlCgoCAgCA3AmggGSApNgJkIBlCgoCAgCA3AlwgGSAnNgJYIBlCgYCAgCA3AlAgGSBANgJMIBlCgoCAgBA3AkQgGSAmNgJAIBlCgoCAgCA3AjggGSAlNgI0IBlCgoCAgCA3AiwgGSAkNgIoIBlCgoCAgCA3AiAgGSAjNgIcIBlCgoCAgCA3AhQgGSAiNgIQIBlCgoCAgCA3AgggGSAhNgIEIBlBAjYCACAFQQw2AtQBIAUgGTYC0AEgBUEMNgLMASAFQoyAgIAwNwLEASAFIBo2AsABIAVBDDYCvAEgBUKMgICAIDcCtAEgBSAfNgKwASAFQoGAgIDAATcCqAEQxwQiBEUNOyAEIAQpAwAiUUIBfDcDACAEKQMIIVIgDkGIscIAKQMANwMAIBAgUjcDACAPIFE3AwAgBUGAscIAKQMANwNwIwBBMGsiCSQAQQJBAyAFQfAAaiIIKAIMGyIEIAgoAghLBEAgCUEIaiAIIAQgCEEQahClAQsgCUEYaiISIBRBCGopAgA3AwAgCSAUKQIAIlE3AxAgCUEkaiAIIFGnIAlBEGpBBHIiCxDpAQJAIAkoAiQiE0GAgICAeEYNACAJKAIoIQQgCSgCLCINBEAgBCEHA0AgBygCACIWBEAgB0EEaigCACAWQThsEN8ECyAHQQxqIQcgDUEBayINDQALCyATRQ0AIAQgE0EMbBDfBAsgEiAUQRhqKQIANwMAIAkgFCkCECJRNwMQIAlBJGogCCBRpyALEOkBAkAgCSgCJCITQYCAgIB4Rg0AIAkoAighBCAJKAIsIg0EQCAEIQcDQCAHKAIAIhIEQCAHQQRqKAIAIBJBOGwQ3wQLIAdBDGohByANQQFrIg0NAAsLIBNFDQAgBCATQQxsEN8ECyAJQRhqIBRBKGopAgA3AwAgCSAUKQIgIlE3AxAgCUEkaiAIIFGnIAsQ6QECQCAJKAIkIghBgICAgHhGDQAgCSgCKCEEIAkoAiwiDQRAIAQhBwNAIAcoAgAiCwRAIAdBBGooAgAgC0E4bBDfBAsgB0EMaiEHIA1BAWsiDQ0ACwsgCEUNACAEIAhBDGwQ3wQLIAlBMGokACBBQRhqIBApAwA3AwAgQUEQaiAPKQMANwMAIEFBCGogDikDADcDACBBIAUpA3A3AwAMUAtB0c7FAC0AABpBkAFBBBDWBCINRQ1SQdHOxQAtAAAaQfAAQQgQ1gQiHEUNUCAFQagBaiIPQdifwQBBARCDASAFLQCoAUEBRg07IAVBngFqIh0iDiAFQdgBaiIJKQMAIlE3AQAgBUGWAWoiGyITIAVB0AFqIgQpAwAiUjcBACAFQcgAaiIVIhIgBUG4AWoiCCkDACJVNwEAIAVB0ABqIhciFCAFQcABaiILKQMAIlM3AQAgBUHYAGoiGCIWIAVByAFqIgcpAwAiVjcBACAFQeAAaiIgIFI3AQAgBUHoAGoiHiBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgByBSNwMAIAsgVjcDACAIIFM3AwAgBUGwAWoiECBVNwMAIAUgVDcDqAEgBUEwaiImIAQpAwA3AgAgBUEoaiInIAcpAwA3AgAgBUEgaiIpIAspAwA3AgAgBUEYaiIsIAgpAwA3AgAgBUEQaiIuIBApAwA3AgAgBSAFKQOoATcCCCAPQcy8wQBBARCDASAFLQCoAUEBRg08IA4gCSkDACJRNwEAIBMgBCkDACJSNwEAIBIgCCkDACJVNwEAIBQgCykDACJTNwEAIBYgBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIAVBmAFqIg4gUTcDACAFQZABaiITIFI3AwAgBUGIAWoiEiBWNwMAIAVBgAFqIhQgUzcDACAFQfgAaiIWIFU3AwAgBSBUNwNwIAVB1AFqIjAgDikDADcCACAFQcwBaiItIBMpAwA3AgAgBUHEAWoiMSASKQMANwIAIAVBvAFqIjIgFCkDADcCACAFQbQBaiIzIBYpAwA3AgAgBSAFKQNwNwKsASAcQQA2AgAgHEEGNgI4IBwgBSkCBDcCBCAcQQxqIAVBDGopAgA3AgAgHEEUaiAFQRRqKQIANwIAIBxBHGogBUEcaikCADcCACAcQSRqIAVBJGopAgA3AgAgHEEsaiAFQSxqKQIANwIAIBxBNGogBUE0aigCADYCACAcIAUpAqgBNwI8IBxBxABqIBApAgA3AgAgHEHMAGogCCkCADcCACAcQdQAaiALKQIANwIAIBxB3ABqIAcpAgA3AgAgHEHkAGogBCkCADcCACAcQewAaiAJKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiKkUNUCAPQc28wQBB4AAQgwEgBS0AqAFBAUYNPSAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgByBSNwMAIAsgVjcDACAIIFM3AwAgECBVNwMAIAUgVDcDqAEgJiAEKQMANwIAICcgBykDADcCACApIAspAwA3AgAgLCAIKQMANwIAIC4gECkDADcCACAFIAUpA6gBNwIIIA9BzbzBAEHgABCDASAFLQCoAUEBRg0+IB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAqQQE2AgAgKkEHNgI4ICogBSkCBDcCBCAqQQxqIAVBDGopAgA3AgAgKkEUaiAFQRRqKQIANwIAICpBHGogBUEcaikCADcCACAqQSRqIAVBJGopAgA3AgAgKkEsaiAFQSxqKQIANwIAICpBNGogBUE0aigCADYCACAqIAUpAqgBNwI8ICpBxABqIBApAgA3AgAgKkHMAGogCCkCADcCACAqQdQAaiALKQIANwIAICpB3ABqIAcpAgA3AgAgKkHkAGogBCkCADcCACAqQewAaiAJKAIANgIAQdHOxQAtAAAaQThBCBDWBCIhRQ1RIA9Brb3BAEHQABCDASAFLQCoAUEBRg0/IB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAhQQI2AgAgISAFKQKoATcCBCAhQQxqIBApAgA3AgAgIUEUaiAIKQIANwIAICFBHGogCykCADcCACAhQSRqIAcpAgA3AgAgIUEsaiAEKQIANwIAICFBNGogCSgCADYCAEHRzsUALQAAGkE4QQgQ1gQiIkUNUSAPQf29wQBB3wAQgwEgBS0AqAFBAUYNQCAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAOIFE3AwAgEyBSNwMAIBIgVjcDACAUIFM3AwAgFiBVNwMAIAUgVDcDcCAwIA4pAwA3AgAgLSATKQMANwIAIDEgEikDADcCACAyIBQpAwA3AgAgMyAWKQMANwIAIAUgBSkDcDcCrAEgIkEJNgIAICIgBSkCqAE3AgQgIkEMaiAQKQIANwIAICJBFGogCCkCADcCACAiQRxqIAspAgA3AgAgIkEkaiAHKQIANwIAICJBLGogBCkCADcCACAiQTRqIAkoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIrRQ1QIA9B3L7BAEHgABCDASAFLQCoAUEBRg1BIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAHIFI3AwAgCyBWNwMAIAggUzcDACAQIFU3AwAgBSBUNwOoASAmIAQpAwA3AgAgJyAHKQMANwIAICkgCykDADcCACAsIAgpAwA3AgAgLiAQKQMANwIAIAUgBSkDqAE3AgggD0G8v8EAQeAAEIMBIAUtAKgBQQFGDUIgHSAJKQMAIlE3AQAgGyAEKQMAIlI3AQAgFSAIKQMAIlU3AQAgFyALKQMAIlM3AQAgGCAHKQMAIlY3AQAgICBSNwEAIB4gUTcBACAFIAUpA7ABIlQ3AUAgDiBRNwMAIBMgUjcDACASIFY3AwAgFCBTNwMAIBYgVTcDACAFIFQ3A3AgMCAOKQMANwIAIC0gEykDADcCACAxIBIpAwA3AgAgMiAUKQMANwIAIDMgFikDADcCACAFIAUpA3A3AqwBICtBBDYCACArQQo2AjggKyAFKQIENwIEICtBDGogBUEMaikCADcCACArQRRqIAVBFGopAgA3AgAgK0EcaiAFQRxqKQIANwIAICtBJGogBUEkaikCADcCACArQSxqIAVBLGopAgA3AgAgK0E0aiAFQTRqKAIANgIAICsgBSkCqAE3AjwgK0HEAGogECkCADcCACArQcwAaiAIKQIANwIAICtB1ABqIAspAgA3AgAgK0HcAGogBykCADcCACArQeQAaiAEKQIANwIAICtB7ABqIAkoAgA2AgBB0c7FAC0AABpB8ABBCBDWBCIoRQ1QIA9BnMDBAEHfABCDASAFLQCoAUEBRg1DIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIAQgUTcDACAHIFI3AwAgCyBWNwMAIAggUzcDACAQIFU3AwAgBSBUNwOoASAmIAQpAwA3AgAgJyAHKQMANwIAICkgCykDADcCACAsIAgpAwA3AgAgLiAQKQMANwIAIAUgBSkDqAE3AgggD0GcwMEAQd8AEIMBIAUtAKgBQQFGDUQgHSAJKQMAIlE3AQAgGyAEKQMAIlI3AQAgFSAIKQMAIlU3AQAgFyALKQMAIlM3AQAgGCAHKQMAIlY3AQAgICBSNwEAIB4gUTcBACAFIAUpA7ABIlQ3AUAgDiBRNwMAIBMgUjcDACASIFY3AwAgFCBTNwMAIBYgVTcDACAFIFQ3A3AgMCAOKQMANwIAIC0gEykDADcCACAxIBIpAwA3AgAgMiAUKQMANwIAIDMgFikDADcCACAFIAUpA3A3AqwBIChBBTYCACAoQQs2AjggKCAFKQIENwIEIChBDGogBUEMaikCADcCACAoQRRqIAVBFGopAgA3AgAgKEEcaiAFQRxqKQIANwIAIChBJGogBUEkaikCADcCACAoQSxqIAVBLGopAgA3AgAgKEE0aiAFQTRqKAIANgIAICggBSkCqAE3AjwgKEHEAGogECkCADcCACAoQcwAaiAIKQIANwIAIChB1ABqIAspAgA3AgAgKEHcAGogBykCADcCACAoQeQAaiAEKQIANwIAIChB7ABqIAkoAgA2AgBB0c7FAC0AABpBOEEIENYEIiNFDVEgD0H7wMEAQeAAEIMBIAUtAKgBQQFGDUUgHSAJKQMAIlE3AQAgGyAEKQMAIlI3AQAgFSAIKQMAIlU3AQAgFyALKQMAIlM3AQAgGCAHKQMAIlY3AQAgICBSNwEAIB4gUTcBACAFIAUpA7ABIlQ3AUAgDiBRNwMAIBMgUjcDACASIFY3AwAgFCBTNwMAIBYgVTcDACAFIFQ3A3AgMCAOKQMANwIAIC0gEykDADcCACAxIBIpAwA3AgAgMiAUKQMANwIAIDMgFikDADcCACAFIAUpA3A3AqwBICNBBjYCACAjIAUpAqgBNwIEICNBDGogECkCADcCACAjQRRqIAgpAgA3AgAgI0EcaiALKQIANwIAICNBJGogBykCADcCACAjQSxqIAQpAgA3AgAgI0E0aiAJKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiH0UNUCAPQdvBwQBB3gAQgwEgBS0AqAFBAUYNRiAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgByBSNwMAIAsgVjcDACAIIFM3AwAgECBVNwMAIAUgVDcDqAEgJiAEKQMANwIAICcgBykDADcCACApIAspAwA3AgAgLCAIKQMANwIAIC4gECkDADcCACAFIAUpA6gBNwIIIA9BucLBAEHfABCDASAFLQCoAUEBRg1HIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAfQQE2AgAgH0EHNgI4IB8gBSkCBDcCBCAfQQxqIAVBDGopAgA3AgAgH0EUaiAFQRRqKQIANwIAIB9BHGogBUEcaikCADcCACAfQSRqIAVBJGopAgA3AgAgH0EsaiAFQSxqKQIANwIAIB9BNGogBUE0aigCADYCACAfIAUpAqgBNwI8IB9BxABqIBApAgA3AgAgH0HMAGogCCkCADcCACAfQdQAaiALKQIANwIAIB9B3ABqIAcpAgA3AgAgH0HkAGogBCkCADcCACAfQewAaiAJKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiGkUNUCAPQZjDwQBB4AAQgwEgBS0AqAFBAUYNSCAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgByBSNwMAIAsgVjcDACAIIFM3AwAgECBVNwMAIAUgVDcDqAEgJiAEKQMANwIAICcgBykDADcCACApIAspAwA3AgAgLCAIKQMANwIAIC4gECkDADcCACAFIAUpA6gBNwIIIA9BmMPBAEHgABCDASAFLQCoAUEBRg1JIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAaQQI2AgAgGkEINgI4IBogBSkCBDcCBCAaQQxqIAVBDGopAgA3AgAgGkEUaiAFQRRqKQIANwIAIBpBHGogBUEcaikCADcCACAaQSRqIAVBJGopAgA3AgAgGkEsaiAFQSxqKQIANwIAIBpBNGogBUE0aigCADYCACAaIAUpAqgBNwI8IBpBxABqIBApAgA3AgAgGkHMAGogCCkCADcCACAaQdQAaiALKQIANwIAIBpB3ABqIAcpAgA3AgAgGkHkAGogBCkCADcCACAaQewAaiAJKAIANgIAQdHOxQAtAAAaQThBCBDWBCIkRQ1RIA9B+MPBAEHfABCDASAFLQCoAUEBRg1KIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAkQQM2AgAgJCAFKQKoATcCBCAkQQxqIBApAgA3AgAgJEEUaiAIKQIANwIAICRBHGogCykCADcCACAkQSRqIAcpAgA3AgAgJEEsaiAEKQIANwIAICRBNGogCSgCADYCAEHRzsUALQAAGkE4QQgQ1gQiJUUNUSAPQdfEwQBB0AAQgwEgBS0AqAFBAUYNSyAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAOIFE3AwAgEyBSNwMAIBIgVjcDACAUIFM3AwAgFiBVNwMAIAUgVDcDcCAwIA4pAwA3AgAgLSATKQMANwIAIDEgEikDADcCACAyIBQpAwA3AgAgMyAWKQMANwIAIAUgBSkDcDcCrAEgJUEKNgIAICUgBSkCqAE3AgQgJUEMaiAFQbABaikCADcCACAlQRRqIAgpAgA3AgAgJUEcaiALKQIANwIAICVBJGogBykCADcCACAlQSxqIAQpAgA3AgAgJUE0aiAJKAIANgIAQdHOxQAtAAAaQfAAQQgQ1gQiGUUNUCAPQafFwQBB4AAQgwEgBS0AqAFBAUYNTCAdIAkpAwAiUTcBACAbIAQpAwAiUjcBACAVIAgpAwAiVTcBACAXIAspAwAiUzcBACAYIAcpAwAiVjcBACAgIFI3AQAgHiBRNwEAIAUgBSkDsAEiVDcBQCAEIFE3AwAgByBSNwMAIAsgVjcDACAIIFM3AwAgECBVNwMAIAUgVDcDqAEgJiAEKQMANwIAICcgBykDADcCACApIAspAwA3AgAgLCAIKQMANwIAIC4gECkDADcCACAFIAUpA6gBNwIIIA9Bh8bBAEHfABCDASAFLQCoAUEBRg1NIB0gCSkDACJRNwEAIBsgBCkDACJSNwEAIBUgCCkDACJVNwEAIBcgCykDACJTNwEAIBggBykDACJWNwEAICAgUjcBACAeIFE3AQAgBSAFKQOwASJUNwFAIA4gUTcDACATIFI3AwAgEiBWNwMAIBQgUzcDACAWIFU3AwAgBSBUNwNwIDAgDikDADcCACAtIBMpAwA3AgAgMSASKQMANwIAIDIgFCkDADcCACAzIBYpAwA3AgAgBSAFKQNwNwKsASAZQQU2AgAgGUELNgI4IBkgBSkCBDcCBCAZQQxqIAVBDGopAgA3AgAgGUEUaiAFQRRqKQIANwIAIBlBHGogBUEcaikCADcCACAZQSRqIAVBJGopAgA3AgAgGUEsaiAFQSxqKQIANwIAIBlBNGogBUE0aigCADYCACAZIAUpAqgBNwI8IBlBxABqIBApAgA3AgAgGUHMAGogCCkCADcCACAZQdQAaiALKQIANwIAIBlB3ABqIAcpAgA3AgAgGUHkAGogBCkCADcCACAZQewAaiAJKAIANgIAIA1BAjYCjAEgDSAZNgKIASANQoGAgIAgNwKAASANICU2AnwgDUKBgICAEDcCdCANICQ2AnAgDUKCgICAEDcCaCANIBo2AmQgDUKCgICAIDcCXCANIB82AlggDUKBgICAIDcCUCANICM2AkwgDUKCgICAEDcCRCANICg2AkAgDUKCgICAIDcCOCANICs2AjQgDUKBgICAIDcCLCANICI2AiggDUKBgICAEDcCICANICE2AhwgDUKCgICAEDcCFCANICo2AhAgDUKCgICAIDcCCCANIBw2AgQgDUECNgIAIAVBDDYCfCAFIA02AnggBUKBgICAwAE3AnAQxwQiBEUNTiAEIAQpAwAiUUIBfDcDACAEKQMIIVIgEEGIscIAKQMANwMAIAsgUjcDACAIIFE3AwAgBUGAscIAKQMANwOoASMAQTBrIg0kACAPKAIIRQRAIA0gD0EBIA9BEGoQpQELIA1BEGogBUHwAGoiBEEIaikCADcDACANQQE2AhwgDSAEKQIAIlE3AwggDUEkaiAPIFGnIA1BCGpBBHIQ6QECQCANKAIkIg9BgICAgHhGDQAgDSgCKCEHIA0oAiwiCQRAIAchBANAIAQoAgAiDgRAIARBBGooAgAgDkE4bBDfBAsgBEEMaiEEIAlBAWsiCQ0ACwsgD0UNACAHIA9BDGwQ3wQLIA1BMGokACBBQRhqIAspAwA3AwAgQUEQaiAIKQMANwMAIEFBCGogECkDADcDACBBIAUpA6gBNwMADE8LIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQby8wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGsvMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBnLzBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQYy8wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEH8u8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB7LvBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQdy7wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHMu8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBvLvBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQay7wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGcu8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBjLvBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQfy6wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHsusEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB3LrBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQcy6wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEG8usEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBrLrBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQZy6wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGMusEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB/LnBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQey5wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHcucEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBzLnBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQby5wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGsucEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBnLnBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQYy5wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEH8uMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB7LjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQdy4wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHMuMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBvLjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQay4wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGcuMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBjLjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQfy3wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHst8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB3LfBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQcy3wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEG8t8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBrLfBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQZy3wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGMt8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB/LbBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQey2wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHctsEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBzLbBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQby2wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGstsEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBnLbBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQYy2wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEH8tcEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB7LXBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQdy1wQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHMtcEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBvLXBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQay1wQAQygMACxDwAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQYjJwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEH4yMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB6MjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQdjIwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHIyMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBuMjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQajIwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGYyMEAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBiMjBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQfjHwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEHox8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB2MfBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQcjHwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEG4x8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBBqMfBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQZjHwQAQygMACyAFIAUtAKkBOgCoAUGAtcEAQSsgBUGoAWpB8LTBAEGIx8EAEMoDAAsgBSAFLQCpAToAqAFBgLXBAEErIAVBqAFqQfC0wQBB+MbBABDKAwALIAUgBS0AqQE6AKgBQYC1wQBBKyAFQagBakHwtMEAQejGwQAQygMACxDwAwALIAVB4AFqJAAMAwtBCEHwABD/BAALQQhBOBD/BAALQQRBkAEQ/wQACwJAAkACQAJAAkACQAJAAkAgRg4CAQIAC0GMj8AAQQ9BwJjAABD+AwALIAZBkAtqIgQgESA2ID0gPiA0IDsgNyA6EEggBigCmAsiByAGKAKQC0YEQCAEQeCXwAAQowMLIAYoApQLIQQCQCAHRQ0AIAdBBHQiBUUNACAEQRBqIAQgBfwKAAALIAQgBikDgAc3AgAgBkGYC2ogB0EBaiIHNgIAIARBCGogBkGIB2opAwA3AgAgBkHYD2ogBzYCACAGIAYpApALNwPQDyAGQYCAgIB4NgKQFCAGQYAHaiAGQdAPaiAGQZAUaiAGQbgGaiAGQcQGahCrASAGQaAKaiAGQfAaaiIEIAZB0BhqIgdBARBrIAYoAoALQYCAgIB4Rg0BIAZBsApqIAQgBkGAC2pBAhBrIAZBwApqIAQgB0EDEGtB0c7FAC0AABpB0ABBBBDWBCIERQ0CIAQgBikDgAc3AgAgBCAGKQLgBjcCECAEIAYpAqAKNwIgIAQgBikCsAo3AjAgBCAGKQLACjcCQCAEQQhqIAZBiAdqKQMANwIAIARBGGogBkHoBmopAgA3AgAgBEEoaiAGQagKaikCADcCACAEQThqIAZBuApqKQIANwIAIARByABqIAZByApqKQIANwIAIAZBBTYC2A8gBiAENgLUDyAGQQU2AtAPIExBgICAgHhHBEAgQigCCCIJrUIwfiJRpyEIQQAhByBRQiCIpyAIQfj///8HS3INGwJAIAhFBEBBCCENDAELIEIoAgQhEEHRzsUALQAAGkEIIQcgCEEIENYEIg1FDRwgCUUNAEEAIQQgCSEFA0AgBCAIRwRAIAQgDWoiByAEIBBqIgspAwA3AwAgB0EoaiALQShqKQMANwMAIAdBIGogC0EgaikDADcDACAHQRhqIAtBGGopAwA3AwAgB0EQaiALQRBqKQMANwMAIAdBCGogC0EIaikDADcDACAEQTBqIQQgBUEBayIFDQELCyAJQYCAgIB4Rg0FCyBCKAIMIQcgBkHQD2pBkJjAABCjAyAGKALUDyIEIAc2AlwgBCAJNgJYIAQgDTYCVCAEIAk2AlAgBkEGNgLYDwsMBQsgBkHQCmoiBCAGQfAaaiAGQdAYakEBEGsgBkGYFGogBkGIB2opAwA3AwAgBiAGKQOABzcDkBQgBkGAB2ogBkGQFGoQaSAGQeAKaiAGQeAGahBpIAZB8ApqIAQQaUHRzsUALQAAGkEwQQQQ1gQiBEUNDCAEIAYpA4AHNwIAIAQgBikC4Ao3AhAgBCAGKQLwCjcCICAEQQhqIAZBiAdqKQMANwIAIARBGGogBkHoCmopAgA3AgAgBEEoaiAGQfgKaikCADcCACAGQQM2AtgPIAYgBDYC1A8gBkEDNgLQDyBMQYCAgIB4RwRAIEIoAggiCa1CMH4iUachCEEAIQcgUUIgiKcgCEH4////B0tyDRoCQCAIRQRAQQghDQwBCyBCKAIEIRBB0c7FAC0AABpBCCEHIAhBCBDWBCINRQ0bIAlFDQBBACEEIAkhBQNAIAQgCEcEQCAEIA1qIgcgBCAQaiILKQMANwMAIAdBKGogC0EoaikDADcDACAHQSBqIAtBIGopAwA3AwAgB0EYaiALQRhqKQMANwMAIAdBEGogC0EQaikDADcDACAHQQhqIAtBCGopAwA3AwAgBEEwaiEEIAVBAWsiBQ0BCwsgCUGAgICAeEYNBQsgQigCDCEHIAZB0A9qQbCYwAAQowMgBigC1A8iBCAHNgI8IAQgCTYCOCAEIA02AjQgBCAJNgIwIAZBBDYC2A8LDAQLQfCXwAAQ6AQAC0EEQdAAEP8EAAtBgJjAABDoBAALQaCYwAAQ6AQACyAGQZgUaiAGQdgPaigCADYCACAGIAYpAtAPNwOQFCAGQYAHaiAGQZAUaiAGQZQKaiAGQbgGaiAGQcQGahCrASA8IAYpA4AHNwIAIDwgRDYCHCA8IC82AhggPCA/NgIUIDwgRzYCECA8IAYpArgGNwIsIDwgBikCxAY3AkggPCBJNgJEIDwgVzcCPCA8IEU2AjggPEEIaiAGQYgHaikDADcCACA8QTRqIAZBwAZqKAIANgIAIDxB0ABqIAZBzAZqKAIANgIAIDxBKGogBkH4BmooAgA2AgAgPCAGKQPwBjcCIAJAIAZB8BpqIggoAgQiDUUNACAIKAIMIgQEQCAIKAIAIglBCGohCyAJKQMAQn+FQoCBgoSIkKDAgH+DIVcDQCBXUARAA0AgCUGAAWshCSALKQMAIAtBCGohC0KAgYKEiJCgwIB/gyJXQoCBgoSIkKDAgH9RDQALIFdCgIGChIiQoMCAf4UhVwsgCSBXeqdBAXRB8AFxayIHQQxrIAdBCGshECAHQQRrKAIAIgUEQCAQKAIAIQcDQCAHKAIAIg8EQCAHQQRqKAIAIA9BOGwQ3wQLIAdBDGohByAFQQFrIgUNAAsLKAIAIgcEQCAQKAIAIAdBDGwQ3wQLIFdCAX0gV4MhVyAEQQFrIgQNAAsLIA1BEWxBGWoiBEUNACAIKAIAIA1BBHRrQRBrIAQQ3wQLIAYoApQHIgQEQCAGKAKYByAEQcABbBDfBAsgCgRAIBEgCkHAAWwQ3wQLIAYoAtAYIgQEQCAGKALUGCAEQTBsEN8ECyAGKAKACyIEQYCAgIB4RiAERXJFBEAgBigChAsgBEEwbBDfBAsgOEEMEN8EIEgEQCA1IEhBMGwQ3wQLIAYoAtAGIgQEQCAGKALUBiAEQTBsEN8ECyAGKAKcBiIEBEAgBigCoAYgBEECdBDfBAsCQCAGKAIUIgRFDQAgBCAEQQxsQRNqQXhxIgdqQQlqIgRFDQAgBigCECAHayAEEN8ECyAGKAKQAyIEQYCAgIB4RiAERXJFBEAgBigClAMgBEECdBDfBAsgSgRAIDcgSkEwbBDfBAsgSwRAIDQgS0EwbBDfBAsgBkHQIWokAAwMCyAKIB9B0JfAABDZAwALQQALIAlB6IHAABDIBAALIAYgCTYCmBQgBiAHNgKUFCAGIAg2ApAUQYCLwABBKyAGQZAUakHgj8AAQfCPwAAQygMAC0EIQcAEQbiFwAAQyAQACyAKIAVB6IHAABDIBAALQQggCUHogcAAEMgEAAtBBEEwEP8EAAsgCiAJQeiBwAAQyAQAC0EIIAVB6IHAABDIBAALQQRBwAAQ/wQACyAKIAtB6IHAABDIBAALIAxBuANqIAxBgARqKQIANwMAIAxBgANqIAxB2ANqKQIANwMAIAwgDCkC+AM3A7ADIAwgDCkC0AM3A/gCIAwoAswDIRcgDCgCxAMhHCAMKALAAyEdIAwoAuADIRQgDCgC5AMhFiAMKALoAyEbIAwoAuwDIRUgDCgC8AMhECAMKAL0AyETIAwoAogEIT0gDCgCjAQhBSAMKAKQBCE3IAwoAsgDIRggPBAmIAwtANgJIQcgDCgCzAkiBARAIAwoAtAJIARBAnQQ3wQLAkAgDCgCxAMiBEUNACAEIARBDGxBE2pBeHEiCWpBCWoiBEUNACAMKALAAyAJayAEEN8ECyAMKALABiIEQYCAgIB4RiAERXJFBEAgDCgCxAYgBEECdBDfBAsCQAJAAkAgBw4CAQIAC0G4jsEAQQ9ByI7BABD+AwALIDcEQCA3QQFrIghBBHQhBEEAIQcgCEH/////AEsgBEH8////B0tyDQRBBCEKAkAgBEUNAEHRzsUALQAAGkEEIQcgBEEEENYEIgpFDQUgCEUNACAFIDdBBHRqISAgBSEJIAghNEEAIQcDQCAJIi9BEGoiCSAgRg0BIC8oAhgiDa1CMH4iV6chEkEAIQQgV0IgiKcgEkH4////B0tyDQcgByEPAkAgEkUEQEEIIQ4MAQsgLygCFCE/QdHOxQAtAAAaQQghBCASQQgQ1gQiDkUNCCANRQ0AQQAhESANIQsDQCARIBJGDQEgDiARaiIEIBEgP2oiBykDADcDACAEQShqIAdBKGopAwA3AwAgBEEgaiAHQSBqKQMANwMAIARBGGogB0EYaikDADcDACAEQRBqIAdBEGopAwA3AwAgBEEIaiAHQQhqKQMANwMAIBFBMGohESALQQFrIgsNAAsLIA9BAWohByAKIA9BBHRqIgQgLygCHDYCDCAEIA02AgggBCAONgIEIAQgDTYCACA0QQFrIjQNAAsLIAxBqANqIAxBuANqKQMANwMAIAxByANqIAxBgANqKQMANwMAIAwgDCkDsAM3A6ADIAwgDCkD+AI3A8ADIAUhBANAIAQoAgAiBwRAIARBBGooAgAgB0EwbBDfBAsgBEEQaiEEIDdBAWsiNw0ACyA9RQ0GIAUgPUEEdBDfBAwGC0EBQQBBqI7BABDkBAALIAxBqANqIAxBuANqKQMANwMAIAxByANqIAxBgANqKQMANwMAIAwgDCkDsAM3A6ADIAwgDCkD+AI3A8ADDAULQZSQwQBBHkG0kMEAEP4DAAtBxJDBAEEnQeyQwQAQ/gMACyAHIARBnIPBABDIBAALIAQgEkHogcAAEMgEAAsgCiEFIAgiNyE9CyAMKAIoIgQEQCAMKAIsIARBwAFsEN8ECyAMKAI4IgQEQCAMKAI8IARB6ABsEN8ECyAMQSBqIAxBqANqIgQpAwA3AwAgDEEwaiAMQcgDaikDADcDACAMIAwpA6ADNwMYIAwgDCkDwAM3AyggDCgCCCEvIAQgDEEUaigCADYCACAMIAwpAgw3A6ADIAwgQzoA7wIgDCADNgLoAkEFIQRB2I7BACEHAkACQAJAIEMOAgIBAAtBuI7BAEEPQcSPwQAQ/gMAC0EJIQRB3Y7BACEHCyAMIAQ2AvQCIAwgBzYC8AIgDEEENgKsASAMQfSOwQA2AqgBIAxCAzcCtAEgDCAMQegCaq1CgICAgOABhDcD0AMgDCAMQcgAaq1CgICAgOABhDcDyAMgDCAMQfACaq1CgICAgKAChDcDwAMgDCACNgJIIAwgDEHAA2o2ArABIAxBsANqIAxBqAFqENICQQAhB0HRzsUALQAAGkEBIRFBAiENAkACQEECQQEQ1gQiDgRAIA5BsPABOwAAIAxBAjYCgAMgDCAONgL8AiAMQQI2AvgCIAwoArQDIQoCfyAMKAK4AyI0RQRAQQAhC0ECDAELIAxBnANqrUKAgICA8ASEIVdBACELIAohBANAIAwgBDYCVCAMIAc2AlAgDCARNgJMIAwgCzYCSCAMIAQ2ApwDIAwgVzcDOCAMQQE2ArwBIAxBATYCrAEgDEGgi8EANgKoASAMQQE2ArQBIAxCgICAgICEgIBpNwLQAyAMQoCACDcCyAMgDEECOwHAAyAMIAxBwANqNgK4ASAMIAxBOGo2ArABIAxByABqQdD/wAAgDEGoAWoQqwINAyAEQQFqIQQgDCgCSCELIAwoAkwhESAMKAJQIQcgNEEBayI0DQALIAdFBEBBACEHQQIMAQsgDEH4AmpBAiAHQQFBARCIAyAMKAL4AiENIAwoAvwCIQ4gDCgCgAMLIQQgBwRAIAQgDmogESAH/AoAAAsgCwRAIBEgCxDfBAsCQCAMIAQgB2oiBAR/IAxBwANqIA4gBBCVASAMLQDAA0EBRw0BIAwtAMEDBUEDCzoAwANB1P7AAEErIAxBwANqQaSPwQBBtI/BABDKAwALIAxB1gBqIAxB0ANqIggpAwAiVzcBACAMQd4AaiAMQdgDaiILKQMAIlE3AQAgDEGAA2oiBCBXNwMAIAxBkANqIgcgDEHgA2oiESkDADcDACAMQYgDaiIJIFE3AwAgDCAMKQPIAzcD+AIgDEH4A2pCADcDACAMQfADakIANwMAIAxB6ANqQgA3AwAgEUIANwMAIAtCADcDACAIQgA3AwAgDEHIA2pCADcDACAMQgA3A8ADIAxBiARqIAQpAwA3AwAgDEGQBGogCSkDADcDACAMQZgEaiAHKQMANwMAIAwgDCkD+AI3A4AEIAxBwANqIggQRiAMQcgBaiAIQeAA/AoAACAMQcABaiAHKQMANwMAIAxBuAFqIAkpAwA3AwAgDEGwAWogBCkDADcDACAMIAwpA/gCNwOoASACQagCbCEEA0AjAEGQA2siCCQAIAhBADYCDCAIQoCAgICAATcCBCAIQQRqIglBjMbCABCcAyAIKAIEIAgoAggiByABKQPAATcDACAHQQhqIAFByAFqKQMANwMAIAdBEGogAUHQAWopAwA3AwAgB0EYaiABQdgBaikDADcDACAHQSBqIAFB4AFqKQMANwMAIAdBKGogAUHoAWopAwA3AwAgCEEBNgIMQQFGBEAgCUGcxsIAEJwDIAgoAgghBwsgByABQfABaiIJKQMANwMwIAdB2ABqIAlBKGopAwA3AwAgB0HQAGogCUEgaikDADcDACAHQcgAaiAJQRhqKQMANwMAIAdBQGsgCUEQaikDADcDACAHQThqIAlBCGopAwA3AwAgCEECNgIMIAhB0AFqIQkjAEHwAmsiByQAIAdB4ABqIAFBCGopAwA3AwAgB0HoAGogAUEQaikDADcDACAHQfAAaiABQRhqKQMANwMAIAdB+ABqIAFBIGopAwA3AwAgB0GAAWogAUEoaikDADcDACAHQZABaiABQThqKQMANwMAIAdBmAFqIAFBQGspAwA3AwAgB0GgAWogAUHIAGopAwA3AwAgB0GoAWogAUHQAGopAwA3AwAgB0GwAWogAUHYAGopAwA3AwAgByABKQMANwNYIAcgASkDMDcDiAEgB0GYAmoiNCAHQdgAahD3AyAHKAKcAiELIAcoApgCIRECQAJAAkAgBygCoAIiD0ECRgRAIAsoAgQhDyALKAIAIRIgNCALQQhqQdgA/AoAACARBEAgCyARQTBsEN8ECyAHQdAAaiAHQbgCaikDADcDACAHQcgAaiAHQbACaikDADcDACAHQUBrIAdBqAJqKQMANwMAIAdBOGogB0GgAmopAwA3AwAgB0EIaiAHQcgCaikDADcDACAHQRBqIAdB0AJqKQMANwMAIAdBGGogB0HYAmopAwA3AwAgB0EgaiAHQeACaikDADcDACAHQShqIAdB6AJqKQMANwMAIAcgBykDmAI3AzAgByAHKQPAAjcDACAHQcABaiABQeAAaiILQQhqKQMANwMAIAdByAFqIAtBEGopAwA3AwAgB0HQAWogC0EYaikDADcDACAHQdgBaiALQSBqKQMANwMAIAdB4AFqIAtBKGopAwA3AwAgB0HwAWogAUGYAWopAwA3AwAgB0H4AWogAUGgAWopAwA3AwAgB0GAAmogAUGoAWopAwA3AwAgB0GIAmogAUGwAWopAwA3AwAgB0GQAmogAUG4AWopAwA3AwAgByALKQMANwO4ASAHIAEpA5ABNwPoASAHQZgCaiI0IAdBuAFqEPcDIAcoApwCIQsgBygCmAIhESAHKAKgAiIgQQJHDQEgCygCBCEgIAsoAgAhPyA0IAtBCGpB2AD8CgAAIBEEQCALIBFBMGwQ3wQLIAkgIDYCZCAJID82AmAgCSAHKQOYAjcDaCAJIAcpA8ACNwOQASAJQfAAaiAHQaACaikDADcDACAJQfgAaiAHQagCaikDADcDACAJQYABaiAHQbACaikDADcDACAJQYgBaiAHQbgCaikDADcDACAJQZgBaiAHQcgCaikDADcDACAJQaABaiAHQdACaikDADcDACAJQagBaiAHQdgCaikDADcDACAJQbABaiAHQeACaikDADcDACAJQbgBaiAHQegCaikDADcDACAJIA82AgQgCSASNgIAIAkgBykDMDcDCCAJQRBqIAdBOGopAwA3AwAgCUEYaiAHQUBrKQMANwMAIAlBIGogB0HIAGopAwA3AwAgCUEoaiAHQdAAaikDADcDACAJIAcpAwA3AzAgCUE4aiAHQQhqKQMANwMAIAlBQGsgB0EQaikDADcDACAJQcgAaiAHQRhqKQMANwMAIAlB0ABqIAdBIGopAwA3AwAgCUHYAGogB0EoaikDADcDACAHQfACaiQADAMLIAcgDzYCoAIMAQsgByAgNgKgAgsgByALNgKcAiAHIBE2ApgCQYCLwABBKyAHQZgCakGsi8AAQaSNwAAQygMACyAIQRBqIAlB4AD8CgAAIAhB8ABqIAhBsAJqQeAA/AoAACAIKAIMIgsgCCgCBCIJRgRAIAhBBGpBrMbCABCcAyAIKAIEIQkLIAgoAggiByALQTBsaiIRIAgpAxA3AwAgEUEIaiAIQRhqKQMANwMAIBFBEGogCEEgaikDADcDACARQRhqIAhBKGopAwA3AwAgEUEgaiAIQTBqKQMANwMAIBFBKGogCEE4aikDADcDACAIIAtBAWoiETYCDCAJIBFGBEAgCEEEakG8xsIAEJwDIAgoAgQhCSAIKAIIIQcLIAcgEUEwbGoiESAIQUBrIjQpAwA3AwAgEUEoaiA0QShqKQMANwMAIBFBIGogNEEgaikDADcDACARQRhqIDRBGGopAwA3AwAgEUEQaiA0QRBqKQMANwMAIBFBCGogNEEIaikDADcDACAIIAtBAmoiETYCDCAJIBFGBEAgCEEEakHMxsIAEJwDIAgoAgQhCSAIKAIIIQcLIAhB+ABqKQMAIVcgCEGAAWopAwAhUSAIQYgBaikDACFSIAhBkAFqKQMAIVUgCEGYAWopAwAhUyAHIBFBMGxqIhEgCCkDcDcDACARQShqIFM3AwAgEUEgaiBVNwMAIBFBGGogUjcDACARQRBqIFE3AwAgEUEIaiBXNwMAIAggC0EDaiIRNgIMIAkgEUYEQCAIQQRqQdzGwgAQnAMgCCgCCCEHCyAIQbABaikDACFXIAhBuAFqKQMAIVEgCEHAAWopAwAhUiAIQcgBaikDACFVIAhBqAFqKQMAIVMgByARQTBsaiIHIAgpA6ABNwMAIAdBCGogUzcDACAHQShqIFU3AwAgB0EgaiBSNwMAIAdBGGogUTcDACAHQRBqIFc3AwAgDEHAA2oiByAIKQIENwIAIAdBCGogC0EEajYCACAIQZADaiQAIAxBqAFqIAwoAsQDIgcgDCgCyANBABAkIAwoAsADIgkEQCAHIAlBMGwQ3wQLIAFBqAJqIQEgBEGoAmsiBA0ACyAMKAIYQYCAgIB4Rg0CIAwtAO8CBEAgDEEANgLAAyAMQe8CaiAMQcADahCTBAALIAxBwANqIAxBGGoQxgEgDEGoAWogDCgCxAMiASAMKALIAyBDQQFHECQgDCgCwAMiBEUNAiABIARBMGwQ3wQMAgtBAUECQayDwQAQyAQAC0HU/sAAQSsgDEGoAWpB6P/AAEHUj8EAEMoDAAsgDEHAA2ogDEEoahDGASAMQagBaiAMKALEAyIBIAwoAsgDIENBAUciBBAkIAwoAsADIgcEQCABIAdBMGwQ3wQLIAxBqAFqIBYgGyAEECQgNwRAIDdBBHQhByBDQQFHIQEgBSEEA0AgDEHAA2ogBBDGASAMQagBaiAMKALEAyIJIAwoAsgDIAEQJCAMKALAAyIIBEAgCSAIQTBsEN8ECyAEQRBqIQQgB0EQayIHDQALCwJAIC9BgICAgHhGDQAgDEHMA2ogDEGoA2ooAgA2AgAgDCAvNgLAAyAMIAwpA6ADNwLEAyAMQcgAaiAMQcADahDGASAMQagBaiAMKAJMIgEgDCgCUCBDQQFHECQgDCgCSCIEBEAgASAEQTBsEN8ECyAMKALAAyIBRQ0AIAwoAsQDIAFBMGwQ3wQLIAxByABqIgEgDEHoAWoQ0QIgDEHAA2ogAUEgEI4BIA0EQCAOIA0Q3wQLIAwoArADIgEEQCAKIAEQ3wQLIAxB0AFqIAxB6ANqKQMANwMAIAxByAFqIAxB4ANqKQMANwMAIAxBwAFqIAxB2ANqKQMANwMAIAxBuAFqIAxB0ANqKQMANwMAIAxBsAFqIAxByANqKQMANwMAIAwgDCkDwAM3A6gBIAxBwANqECYgDC0A2AkhCSAMKALMCSIBBEAgDCgC0AkgAUECdBDfBAsCQCAMKALEAyIBRQ0AIAEgAUEMbEETakF4cSIEakEJaiIBRQ0AIAwoAsADIARrIAEQ3wQLIAwoAsAGIgFBgICAgHhGIAFFckUEQCAMKALEBiABQQJ0EN8EC0EBIQcCQAJAAkAgCQ4CAgEAC0G4jsEAQQ9BhJDBABD+AwALQQAhBwtB0c7FAC0AABoCQAJAAkACQAJAAkBBMEEIENYEIgEEQCABQgA3AwAgAUEoakIANwMAIAFBIGpCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACAMQoGAgIBwNwKoAyAMIAE2AqQDIAxBATYCoAMgDEHoA2pByP/AACkDADcDACAMQeADakHA/8AAKQMANwMAIAxB2ANqQbj/wAApAwA3AwAgDEHQA2pBsP/AACkDADcDACAMQcgDakGo/8AAKQMANwMAIAxBoP/AACkDADcDwAMgByA3aiILBEAgC0EBayIBIBNPDQIgC0EEdCAQakEQayERA0AgDEG4A2ogDEGoA2opAgA3AwAgDCAMKQKgAzcDsANB0c7FAC0AABpBMEEIENYEIgRFDQggBCAMKQPAAzcDACAEQShqIAxB6ANqKQMANwMAIARBIGogDEHgA2opAwA3AwAgBEEYaiAMQdgDaikDADcDACAEQRBqIAxB0ANqKQMANwMAIARBCGogDEHIA2opAwA3AwBBACEBAkAgBEH4w8IAQTAQ8QMEQCAEIQcMAQtB0c7FAC0AABpBMEEIENYEIgdFDQkgB0IANwMAIAdBKGpCADcDACAHQSBqQgA3AwAgB0EYakIANwMAIAdBEGpCADcDACAHQQhqQgA3AwAgBEEwEN8EQX8hAQsgDCABNgJUIAxBATYCUCAMIAc2AkwgDEEBNgJIIAxB+AJqIgEgESAMQcgAahBuIAxBoANqIAxBsANqIAEQ2QEgDCgCSCIBBEAgDCgCTCABQTBsEN8ECyARQRBrIREgDEHAA2ohBEIAIVdCACFSQgAhVEIAIVNCACFYQgAhWiMAQdABayIBJAAgDEGoAWoiBykDACFbIAcpAwghXCAHKQMQIV0gBykDGCFeIAcpAyAhXyAHKQMoIWBBKCEHA0AgAUHwAGogBCAHaikDACJRQgAgYEIAEMkDIAFBgAFqIFFCACBfQgAQyQMgAUGQAWogUUIAIF5CABDJAyABQaABaiBRQgAgXUIAEMkDIAFBsAFqIFFCACBcQgAQyQMgAUHAAWogUUIAIFtCABDJAyABQeAAaiABKQNwIlkgWnwiVUIAQgBC/f/z/8////mJfxDJAyABQdAAaiABKQNoIlFCAEKr1f7///+//7l/QgAQyQMgAUFAayBRQgBC///Piuv//9UeQgAQyQMgAUEwaiBRQgBCpOzDtY/UtJjnAEIAEMkDIAFBIGogUUIAQr+llJzP8NK75ABCABDJAyABQRBqIFFCAELX2a6a5PbpjcsAQgAQyQMgASBRQgBCms3/y6O9xIAaQgAQyQMgASkDCCBYIAEpA8ABImF8IlEgASkDuAEgVCABKQOwASJYfCJWIFhUrXwgViABKQOoASABKQOgASJUIFN8IlMgVFStfCBTIAEpA5gBIAEpA5ABIlQgUnwiUiBUVK18IFIgASkDiAEgASkDgAEiVCBXfCJXIFRUrXwgVyBXIAEpA3ggVSBZVK18fCJYVq18fCJXIFJUrXx8IlIgU1StfHwiUyBWVK18fCJWIAEpAwB8IlkgVlStfCBZIFkgASkDGCBTIFMgASkDEHwiVFatfCBUIFQgASkDKCBSIFIgASkDIHwiU1atfCBTIFMgASkDOCBXIFcgASkDMHwiUlatfCBSIFIgASkDSCBYIAEpA0AiWnwiVyBaVK18IFcgASkDWCBVIAEpA1AiWHwgWFStfHwiWiBXVK18fCJXVq18fCJSVq18fCJTVq18fCJUVq18IFEgVlatIAEpA8gBIFEgYVStfHx8IVggB0EIayIHQXhHDQALAkACQCBYQprN/8ujvcSAGlYNACBYQprN/8ujvcSAGlIEQCBXIVEgUiFVIFMhViBUIVkMAgsgVELX2a6a5PbpjcsAVg0AAkAgVELX2a6a5PbpjcsAUgRAIFchUSBSIVUgUyFWIFQhWQwBCyBTQr+llJzP8NK75ABWDQFC19mumuT26Y3LACFZIFNCv6WUnM/w0rvkAFIEQCBXIVEgUiFVIFMhVgwBCyBSQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACFWIFJCpOzDtY/UtJjnAFIEQCBXIVEgUiFVDAELIFdC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhVSBXQv//z4rr///VHlIEQCBXIVEMAQtC///Piuv//9UeIVEgWkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohWAwBCyBXQv//z4rr///VHn0iVSBaQqvV/v///7//uX9UrSJWfSFRIFJCpOzDtY/UtJjnAH0iWSBXQv//z4rr///VHlQgVSBWVHKtIld9IVUgU0K/pZScz/DSu+QAfSJbIFJCpOzDtY/UtJjnAFQgVyBZVnKtIld9IVYgVELX2a6a5PbpjcsAfSJSIFNCv6WUnM/w0rvkAFQgVyBbVnKtIld9IVkgWCBUQtfZrprk9umNywBUIFIgV1RyrX1Cms3/y6O9xIAafSFYIFpC1aqBgICAwIDGAHwhWgsgBCBaNwMoIAQgUTcDICAEIFU3AxggBCBWNwMQIAQgWTcDCCAEIFg3AwAgAUHQAWokACALQQFrIgsNAAsLQTYhBEEtIQcCQAJAAkAgCQ4CAgEAC0GMj8AAQQ9B0I/AABD+AwALQSAhBEEYIQcLIAxB0ABqIAxBqANqKAIAIgs2AgAgDCAMKQKgAzcDSAJAIAIgB2wgBGpBAWoiBCALSwRAIAtBMGwhBwNAIAwoAkggC0YEQCAMQcgAakHkj8EAEJwDCyAMKAJMIjQgB2oiAUIANwMAIAFBCGpCADcDACABQRBqQgA3AwAgAUEYakIANwMAIAFBIGpCADcDACABQShqQgA3AwAgDCALQQFqIgs2AlAgB0EwaiEHIAQgC0sNAAsMAQsgDCgCTCE0CyAMKAJIIQ8gDCADNgKgAyAMIAI2AjggDEHAA2oQJkEFIQRB2I7BACEHAkACQAJAIAwtANgJDgICAQALQcCRwQBBKEHokcEAEP4DAAtBCSEEQd2OwQAhBwsgDCAENgK0AyAMIAc2ArADIAwoAswJIgEEQCAMKALQCSABQQJ0EN8ECwJAIAwoAsQDIgFFDQAgASABQQxsQRNqQXhxIgJqQQlqIgFFDQAgDCgCwAMgAmsgARDfBAsgDCgCwAYiAUGAgICAeEYgAUVyRQRAIAwoAsQGIAFBAnQQ3wQLIAxBBDYCTCAMQaCRwQA2AkggDEIDNwJUIAwgDEGgA2qtQoCAgIDgAYQ3A9ADIAwgDEE4aq1CgICAgOABhDcDyAMgDCAMQbADaq1CgICAgKAChDcDwAMgDCAMQcADaiIBNgJQIAxB+AJqIgIgDEHIAGoQ0gIgASACEPMBIAEgDEGoAWpBASBDQQFHIgIQJCABIDQgCyACECQgDEHgAGogDEH4A2opAwA3AwAgDEHYAGogDEHwA2opAwA3AwAgDEHQAGogDEHoA2opAwA3AwAgDCAMKQPgAzcDSCA3QQFrIQMCQCA3BEBB0c7FAC0AABpBMEEIENYEIgFFDQggAUEoakGgxcIAKQMANwMAIAFBIGpBmMXCACkDADcDACABQRhqQZDFwgApAwA3AwAgAUEQakGIxcIAKQMANwMAIAFBCGpBgMXCACkDADcDACABQfjEwgApAwA3AwAgDEIBNwKAAyAMIAE2AvwCIAxBATYC+AICQCAFIANBBHRqIhIoAgxFBEAgEigCCEUNASASKAIEIAFBMBDxA0UNAwsgDEEANgLAAyASIAxB+AJqIAxBwANqQYyRwQAQlQQACwwLCyADQQBB/JDBABDZAwALIAFBMBDfBEEAIQcgA0H/////AEsgA0EEdCIEQfz///8HS3INAkEBIQFBACEOAkAgBEUEQEEEIQIMAQtB0c7FAC0AABpBBCEHIARBBBDWBCICRQ0DIANFDQAgBSEHIAMhCkEAIREDQCASIAciCEcEQCAHKAIIIgmtQjB+IlenIQdBACEEIFdCIIinIAdB+P///wdLcg0GIBEhDQJAIAdFBEBBCCEODAELIAgoAgQhIEHRzsUALQAAGkEIIQQgB0EIENYEIg5FDQcgCUUNAEEAIREgCSEBA0AgByARRg0BIA4gEWoiBCARICBqIi8pAwA3AwAgBEEoaiAvQShqKQMANwMAIARBIGogL0EgaikDADcDACAEQRhqIC9BGGopAwA3AwAgBEEQaiAvQRBqKQMANwMAIARBCGogL0EIaikDADcDACARQTBqIREgAUEBayIBDQALCyAIQRBqIQcgDUEBaiERIAIgDUEEdGoiASAIKAIMNgIMIAEgCTYCCCABIA42AgQgASAJNgIAIApBAWsiCg0BCwsgA0EEdCEOQQAhAQsgDEGAA2ogDEEwaikDADcDACAMQcwDaiAMQdAAaikDADcCACAMQdQDaiAMQdgAaikDADcCACAMQdwDaiAMQeAAaikDADcCACAMIAwpAyg3A/gCIAwgDCkDSDcCxAMgDCkDICFXIAwoAhwhCSAMKAIYIQcgBSEEA0AgBCgCACIKBEAgBEEEaigCACAKQTBsEN8ECyAEQRBqIQQgN0EBayI3DQALID0EQCAFID1BBHQQ3wQLIBMEQCAQIQQDQCAEKAIAIgUEQCAEQQRqKAIAIAVBMGwQ3wQLIARBEGohBCATQQFrIhMNAAsLIBUEQCAQIBVBBHQQ3wQLIAxB0ABqIAxBgANqKQMANwMAIAwgDCkD+AI3A0ggDEHAAWogDEHEA2oiBEEYaikCADcDACAMQbgBaiAEQRBqKQIANwMAIAxBsAFqIARBCGopAgA3AwAgDCAEKQIANwOoAUHRzsUALQAAGkEwQQgQ1gQiBEUNBiAEQShqQaDFwgApAwA3AwAgBEEgakGYxcIAKQMANwMAIARBGGpBkMXCACkDADcDACAEQRBqQYjFwgApAwA3AwAgBEEIakGAxcIAKQMANwMAIARB+MTCACkDADcDAAJAAkAgFw0AIBhFDQsgHCAEQTAQ8QMNACAEQTAQ3wQgDEEANgK4AyAMQoCAgIDAADcCsAMCQCAHQYCAgIB4Rg0AIAwgVzcCyAMgDCAJNgLEAyAMIAc2AsADIAxB+AJqIAxBwANqEMYBIAxBsANqIAwoAvwCIgQgDCgCgANBABCjASAMKAL4AiIHBEAgBCAHQTBsEN8ECyAMKALAAyIERQ0AIAwoAsQDIARBMGwQ3wQLIAxBwANqIAxByABqEMYBIAxBsANqIAwoAsQDIgQgDCgCyANBABCjASAMKALAAyIHBEAgBCAHQTBsEN8ECyAMQbADaiAWIBtBABCjASAMQcgDaiIEQaz8wAAoAgA2AgAgDEGk/MAAKQIANwPAAyADBEAgDEHAA2pBmP3AABClAyAMKALEAyADNgIAIAxBATYCyAMLIAxBgANqIAQoAgA2AgAgDCAMKQPAAzcD+AIgDCgCuAMiBCAMKAKwA0YEQCAMQbADakG0ksEAEJ8DCyAMKAK0AyAEQQxsaiIHIAwpA/gCNwIAIAdBCGogDEGAA2ooAgA2AgAgDCAEQQFqNgK4AyACIANBBHRqIQUgAiEEIAMEQCAMQcQDaiIJQQhqIQogBCEHA0AgByIDKAIAIgRBgICAgHhHBEAgDCAENgLAAyAJIAdBBGopAgA3AgAgCiAHQQxqKAIANgIAIAxB+AJqIAxBwANqEMYBIAxBsANqIAwoAvwCIgQgDCgCgANBABCjASAMKAL4AiIHBEAgBCAHQTBsEN8ECyAMKALAAyIEBEAgDCgCxAMgBEEwbBDfBAsgA0EQaiIHIAVHDQELCyADQRBqIQQLIAQgBUcEQCAFIARrQQR2IQcDQCAEKAIAIgMEQCAEQQRqKAIAIANBMGwQ3wQLIARBEGohBCAHQQFrIgcNAAsLIAFFBEAgAiAOEN8ECyAMQbADaiIHIDQgC0EBEKMBIAxBwANqIAxBqAFqENECQdHOxQAtAAAaQSBBARDWBCIBRQ0HIAFBGGoiAiAMQdgDaikAADcAACABIAwpAMADIlc3AAAgAUEQaiIDIAxB0ANqKQAANwAAIAFBCGoiBCAMQcgDaikAADcAACABIAFBH2oiBS0AADoAACAFIFc8AAAgAS0AASEFIAEgAUEeaiIJLQAAOgABIAkgBToAACABQR1qIgUtAAAhCSAFIAEtAAI6AAAgASAJOgACIAFBHGoiBS0AACEJIAUgAS0AAzoAACABIAk6AAMgAUEbaiIFLQAAIQkgBSABLQAEOgAAIAEgCToABCABQRpqIgUtAAAhCSAFIAEtAAU6AAAgASAJOgAFIAFBGWoiBS0AACEJIAUgAS0ABjoAACABIAk6AAYgAi0AACEFIAIgAS0ABzoAACABIAU6AAcgAUEXaiICLQAAIQUgAiAELQAAOgAAIAQgBToAACABQRZqIgItAAAhBCACIAEtAAk6AAAgASAEOgAJIAFBFWoiAi0AACEEIAIgAS0ACjoAACABIAQ6AAogAUEUaiICLQAAIQQgAiABLQALOgAAIAEgBDoACyABQRNqIgItAAAhBCACIAEtAAw6AAAgASAEOgAMIAFBEmoiAi0AACEEIAIgAS0ADToAACABIAQ6AA0gAUERaiICLQAAIQQgAiABLQAOOgAAIAEgBDoADiADLQAAIQIgAyABLQAPOgAAIAEgAjoADyAMQfgCaiABQSBBCBDPAiABQSAQ3wQgDCgCuAMiASAMKAKwA0YEQCAHQbSSwQAQnwMLIAwoArQDIAFBDGxqIgIgDCkC+AI3AgAgAkEIaiAMQYADaigCADYCACAMQbgDaiABQQFqIgE2AgAgAEEMaiABNgIAIAAgDCkCsAM3AgQgAEEANgIAIA8EQCA0IA9BMGwQ3wQLIBQEQCAWIBRBMGwQ3wQLIAwoAkgiAEUNASAMKAJMIABBMGwQ3wQMAQsgBEEwEN8EQdHOxQAtAAAaQRlBARDWBCIERQ0FIABBGTYCDCAAIAQ2AgggAEKBgICAkAM3AgAgBEEYakGwksEALQAAOgAAIARBEGpBqJLBACkAADcAACAEQQhqQaCSwQApAAA3AAAgBEGYksEAKQAANwAAIA8EQCA0IA9BMGwQ3wQLIAMEQCACIQQDQCAEKAIAIgAEQCAEQQRqKAIAIABBMGwQ3wQLIARBEGohBCADQQFrIgMNAAsLIAFFBEAgAiAOEN8ECyAUBEAgFiAUQTBsEN8ECyAMKAJIIgAEQCAMKAJMIABBMGwQ3wQLIAdBgICAgHhyQYCAgIB4Rg0AIAkgB0EwbBDfBAsgHQRAIBwgHUEwbBDfBAsgDEHgCWokAA8LDAULIAEgE0H0j8EAENkDAAsgByAEQZyDwQAQyAQACyAEIAdB6IHAABDIBAALQQFBGUGsg8EAEMgEAAtBAUEgQayDwQAQyAQACwtBCEEwEP8EAAsgByAIQeiBwAAQyAQAC0EAQQBB5MrCABDZAwALIAogB0HogcAAEMgEAAuTPgIHfxJ+IwBBkA9rIgMkAAJAAkACQAJ+AkACQAJAAkAgAS0AQCIHIAItAEBGBEAgAUHo0cEAQSAQ8QNFBEAgAUEgakHo0cEAQSAQ8QNFDQILIAJB6NHBAEEgEPEDRQRAIAJBIGpB6NHBAEEgEPEDRQ0DCwJAIAEgAkEgEPEDRQRAIAFBIGoiCSACQSBqQSAQ8QNFDQEgAEIANwMAIAAgBzoAQCAAQThqQgA3AwAgAEEwakIANwMAIABBKGpCADcDACAAQSBqQgA3AwAgAEEYakIANwMAIABBEGpCADcDACAAQQhqQgA3AwAMCgsgASkDICIOIQogAikDICIUIQsCfgJAIA4gFFINACABKQMoIhEgAikDKCILUgRAIBEhCgwBCyABKQMwIhMgAikDMCILUgRAIBMhCgwBCyARIQ0gASkDOCIKIRIgEyAKIAIpAzgiC1ENARoLIAogC1YNBSABKQMoIREgAikDKCENIAEpAzAhEyABKQM4IQogAikDOCESIAIpAzALIgwgE30iECAKIBJWrSIPfSELIA0gEX0iFSAMIBNUIA8gEFZyrSIMfSETIA0gEVQgDCAVVnIhBCAUIA59IQ8gEiAKfSEKDAcLIANBsAlqEEkgB0UEQCADQcgJaiEEIAMpA7gJIRUgAykDsAkhGCADKQPACQwGCyADKALgC0EBcQ0EQez2wQAQ6AQAC0GA9sEAQTNB3PbBABD+AwALIAAgBzoAQCAAIAIpAyA3AyAgACACKQMANwMAIABBOGogAkE4aikDADcDACAAQTBqIAJBMGopAwA3AwAgAEEoaiACQShqKQMANwMAIABBCGogAkEIaikDADcDACAAQRBqIAJBEGopAwA3AwAgAEEYaiACQRhqKQMANwMADAYLIAAgBzoAQCAAIAEpAyA3AyAgACABKQMANwMAIABBOGogAUE4aikDADcDACAAQTBqIAFBMGopAwA3AwAgAEEoaiABQShqKQMANwMAIABBCGogAUEIaikDADcDACAAQRBqIAFBEGopAwA3AwAgAEEYaiABQRhqKQMANwMADAULIAEpAzAiCiACKQMwIhFUIAogEX0iCiABKQM4IhEgAikDOCIMVK0iC1RyrSINIAEpAygiEiACKQMoIhB9Ig9Cf4V8IhUgCkJ/hSALfCIKIBEgDH0iEUJtVq0iDFStIgt9IRMgCyAVViEEIAogDH0hCyAQIBJWIA0gD1ZyrSAUIA59fEL///////////8AfCEPQm0gEX0hCgwCCyADQYAMaiEEIAMpA/ALIRUgAykD6AshGCADKQP4CwshEiAEKQMAIRkgA0HADmpCADcDACADQbgOakIANwMAIANCADcDsA4gA0LyADcDyA4gA0GwCGogASkDECIUQgAgASkDGCIRQgAQyQMgA0GQCGogASkDCCITQgAgEUIAEMkDIANBsAdqIAEpAwAiCkIAIBFCABDJAyADQYAIaiATQgAgFEIAEMkDIANBwAdqIApCACAUQgAQyQMgA0HQB2ogCkIAIBNCABDJAyADQfAIaiARQgAgEUIAEMkDIANBoAhqIBRCACAUQgAQyQMgA0HwB2ogE0IAIBNCABDJAyADQeAHaiAKQgAgCkIAEMkDIANB4AhqIAMpA/AIIhdCm5Svw/K1qN6Gf34iCkIAQm1CABDJAyADQdAIaiAKQgBCf0IAEMkDIANBwAhqIApCAEL///////////8AQgAQyQMgAykD2AcgAykDyAcgAykDuAcgAykDmAggAykDuAgiDCADKQOQCHwiCiAMVK18IgsgAykDsAd8IgwgC1StfCINIAMpA8AHfCILIA1UrXwgCyADKQOICCAMIAwgAykDgAh8IgxWrXx8Ig0gC1StfCILIAMpA9AHfCIOIAtUrXwiC0I/iCADKQPoByADKQPgByIPIAtCAYYgDkI/iIR8IhAgD1StfCAQIAMpA/gHIAMpA6gIIAMpA6AIIg8gCkIBhiADKQOwCCIWQj+IhHwiCyAPVK18IAsgAykD+AgiDyAWQgGGfCIWIA9UrXwiGiALVK18IgsgDEIBhiAKQj+IhHwiGyALVK0iCyADKQPwB3wiCiALVK18IAogDUIBhiAMQj+IhHwiCyAKVK18IgogDkIBhiANQj+IhHwiDyAKVK18Ig4gEFStfHwhCgJ/AkAgAykDyAggAykD2AgiDSANIAMpA+gIIAMpA+AIIgwgF0J9g3wgDFStfCIQIAMpA9AIIhd8IgwgEFStfCAMIAwgFnwiDFatfCIQIBd8Ig0gEFStfCANIBp8IhAgDVStfCIXIAMpA8AIfCINIBdUrXwgDSAbfCIXIA1UrXwiDVANACALIA18IgsgDVQiBEUNACAErSINIA98Ig8gDVoNACANIA9WrSINIA58Ig4gDVoNACANIA5WrSINIAp8IgogDVQMAQtBAAshBCADQaAHaiAMQpuUr8Pytajehn9+Ig1CAEJtQgAQyQMgA0GQB2ogDUIAQn9CABDJAyADQYAHaiANQgBC////////////AEIAEMkDAkAgAykDiAcgAykDmAciDSANIAMpA6gHIAwgAykDoAciDHwgDFStfCIWIAMpA5AHIhp8IgwgFlStfCAMIBB8Ig0gDFStfCIQIBp8IgwgEFStfCAMIBd8IhAgDFStfCIXIAMpA4AHfCIMIBdUrXwgCyAMfCIXIAxUrXwiDFANACAMIA98Ig8gDFoNACAMIA9WrSIMIA58Ig4gDFoNACAMIA5WrSIMIAp8IgogDFQhBgsgA0HwBmogDUKblK/D8rWo3oZ/fiIMQgBCbUIAEMkDIANB4AZqIAxCAEJ/QgAQyQMgA0HQBmogDEIAQv///////////wBCABDJAyADKQPYBiADKQPoBiILIAsgAykD+AYgAykD8AYiDCANfCAMVK18Ig0gAykD4AYiFnwiDCANVK18IAwgDCAQfCIMVq18Ig0gFnwiCyANVK18IAsgF3wiDSALVK18IhAgAykD0AZ8IgsgEFStfCALIA98IhAgC1StfCILUEUEQCALIA58Ig4gC1QiBa0iCyAKfCIPIAogBRshCiAFIAsgD1ZxIQULIANBwAZqIAxCm5Svw/K1qN6Gf34iC0IAQm1CABDJAyADQbAGaiALQgBCf0IAEMkDIANBoAZqIAtCAEL///////////8AQgAQyQMgAykDqAYgAykDuAYiCyALIAMpA8gGIAwgAykDwAYiDHwgDFStfCIPIAMpA7AGIhd8IgwgD1StfCAMIA18Ig8gDFStfCILIBd8IgwgC1StfCAMIBB8Ig0gDFStfCILIAMpA6AGfCIMIAtUrXwgDCAOfCILIAxUrXwiDCAKfCIOIAogDEIAUiIIGyEKAkACQCAEIAZyIAVyIAwgDlYiBK0gDCAIG0IAUnIgBCAIcSAKQgBTcnJFBEBC////////////ACEQIApC////////////AFIgC0J/UnIgDUJ/UnINAkJ/IQ5CfyEMIA9CbVQNAgwBCyAKIRAgCyEOIA0hDAsgDEIBfCIKIA9CbVStIgt9IQ0gDkIBfCIXIAxCf1IgCiALVHKtIgp9IQsgECAOQn9SIAogF1ZyrX1C////////////AH0hCiAPQhN8IQ8LIAMgDzcDiA8gAyANNwOADyADIAs3A/gOIAMgCjcD8A4gA0GQDmogA0GwDmogA0HwDmoQfCADKQOQDiIPIBh8IgwgAykDmA4iCiAVfCILIApUIAsgAykDoA4iCiASfCINIApUIA0gDSADKQOoDiIOIBl8IgogDlStfCINVnKtfCIQIAtUcq18IQ4CQAJAAkAgDCAPVCAMIA5Wcg0AQv///////////wAhCyAOIgxC////////////AFEEQEJ/IQtC////////////ACEMIBBCf1INAiANQn9SBEAgDSESDAQLQm0hCyAKIQwgCkJtUQ0BCyALIAxYDQAgDiEMDAELIA1CAXwiDCAKQm1UrSILfSESIBBCAXwiDyANQn9SIAsgDFZyrSIMfSELIA4gEEJ/UiAMIA9Wcq19Qv///////////wB9IQwgCkITfCEKDAELIBAhCyANIRILIAMgCjcDiA4gAyASNwOADiADIAs3A/gNIAMgDDcD8A0gA0GAD2pCADcDACADQfgOakIANwMAIANCADcD8A4gA0LMADcDiA8gA0HQDmoiBCADQfAOaiAJEHwgA0GICWogA0HwDWogBBBcIAMoAtwNIgQEQCADKALgDSAEQQJ0EN8ECwJAIAMoApQLIgRFDQAgBCAEQQxsQRNqQXhxIgZqQQlqIgRFDQAgAygCkAsgBmsgBBDfBAsgAygCwAsiBEGAgICAeEYgBEVyDQEgAygCxAsgBEECdBDfBAwBCyADIAo3A4gPIAMgCzcDgA8gAyATNwP4DiADIA8gBK19NwPwDiABKQMAIgohESACKQMAIhIhDiADAn4CQAJ+AkAgCiASUg0AIAEpAwgiEyACKQMIIg5SBEAgEyERDAELIAEpAxAiFCACKQMQIg5SBEAgFCERDAELIBMhDSABKQMYIhEhDCAUIBEgAikDGCIOUQ0BGgsgDiARVA0BIAEpAwghEyACKQMIIQ0gASkDECEUIAEpAxghESACKQMYIQwgAikDEAsiCyAUfSIQIAwgEVStIg99IQ4gDSATfSIVIAsgFFQgDyAQVnKtIhB9IQsgDSATVCAQIBVWciEEIBIgCn0hCiAMIBF9DAELIAEpAxAiFCACKQMQIhFUIBQgEX0iDCABKQMYIhEgAikDGCILVK0iDVRyrSIQIAEpAwgiEyACKQMIIg99IhVCf4V8Ig4gDEJ/hSANfCIMIBEgC30iDUJtVq0iGFStIhl9IQsgDiAZVCEEIAwgGH0hDiAPIBNWIBAgFVZyrSASIAp9fEL///////////8AfCEKQm0gDX0LNwPICSADIA43A8AJIAMgCzcDuAkgAyAKIAStfTcDsAkgA0GICWogA0HwDmogA0GwCWoQXAsgAygCiAkEQCADIAMpA5gJNwO4CSADIAMpA5AJNwOwCUGM98EAQSsgA0GwCWpB/PbBAEG498EAEMoDAAsgA0GwBWogAykDqAkiFUIAIAMpA6AJIhhCABDJAyADQaAFaiAVQgAgAykDmAkiGUIAEMkDIANBkAVqIBVCACADKQOQCSIXQgAQyQMgA0HgBWogGEIAIBlCABDJAyADQdAFaiAYQgAgF0IAEMkDIANBgAZqIBlCACAXQgAQyQMgA0GABWogFUIAIBVCABDJAyADQcAFaiAYQgAgGEIAEMkDIANB8AVqIBlCACAZQgAQyQMgA0GQBmogF0IAIBdCABDJAyADQfAEaiADKQOABSIPQpuUr8Pytajehn9+IgpCAEJtQgAQyQMgA0HgBGogCkIAQn9CABDJAyADQdAEaiAKQgBC////////////AEIAEMkDIAMpA4gGIAMpA9gFIAMpA5gFIAMpA6gFIAMpA7gFIgwgAykDoAV8IgogDFStfCILIAMpA5AFfCIMIAtUrXwiDSADKQPQBXwiCyANVK18IAsgCyADKQPoBSAMIAwgAykD4AV8IgxWrXx8IgtWrXwiDiADKQOABnwiDSAOVK18Ig5CP4ggAykDmAYgAykDkAYiEiAOQgGGIA1CP4iEfCIOIBJUrXwgDiADKQP4BSADKQPIBSADKQPABSIQIApCAYYgAykDsAUiFkI/iIR8IhIgEFStfCASIAMpA4gFIhAgFkIBhnwiFiAQVK18IhogElStfCISIAxCAYYgCkI/iIR8IhsgElStIhIgAykD8AV8IgogElStfCAKIAtCAYYgDEI/iIR8IhAgClStfCIKIA1CAYYgC0I/iIR8IhIgClStfCIMIA5UrXx8IQ1BACEFAn8CQCADKQPYBCADKQPoBCILIAsgAykD+AQgDyADKQPwBCIKfCAKVK18Ig4gAykD4AQiD3wiCiAOVK18IAogCiAWfCIKVq18Ig4gD3wiCyAOVK18IAsgGnwiDiALVK18Ig8gAykD0AR8IgsgD1StfCALIBt8Ig8gC1StfCILUA0AIAsgEHwiECALVCIERQ0AIAStIgsgEnwiEiALWg0AIAsgElatIgsgDHwiDCALWg0AIAsgDFatIgsgDXwiDSALVAwBC0EACyEGIANBwARqIApCm5Svw/K1qN6Gf34iC0IAQm1CABDJAyADQbAEaiALQgBCf0IAEMkDIANBoARqIAtCAEL///////////8AQgAQyQMCQCADKQOoBCADKQO4BCILIAsgAykDyAQgCiADKQPABCIKfCAKVK18IhYgAykDsAQiGnwiCiAWVK18IAogDnwiCyAKVK18Ig4gGnwiCiAOVK18IAogD3wiDiAKVK18Ig8gAykDoAR8IgogD1StfCAKIBB8IhAgClStfCIKUA0AIAogEnwiEiAKWg0AIAogElatIgogDHwiDCAKWg0AIAogDFatIgogDXwiDSAKVCEFCyADQZAEaiALQpuUr8Pytajehn9+IgpCAEJtQgAQyQMgA0GABGogCkIAQn9CABDJAyADQfADaiAKQgBC////////////AEIAEMkDQQAhBCADKQP4AyADKQOIBCIPIA8gAykDmAQgAykDkAQiCiALfCAKVK18IgsgAykDgAQiFnwiCiALVK18IAogCiAOfCIKVq18Ig4gFnwiCyAOVK18IAsgEHwiDiALVK18IhAgAykD8AN8IgsgEFStfCALIBJ8IhAgC1StfCILUEUEQCALIAx8IgwgC1QiBK0iCyANfCISIA0gBBshDSAEIAsgElZxIQQLIANB4ANqIApCm5Svw/K1qN6Gf34iC0IAQm1CABDJAyADQdADaiALQgBCf0IAEMkDIANBwANqIAtCAEL///////////8AQgAQyQMgAykDyAMgAykD2AMiCyALIAMpA+gDIAogAykD4AMiCnwgClStfCISIAMpA9ADIg98IgogElStfCAKIA58IhIgClStfCILIA98IgogC1StfCAKIAogEHwiClatfCIOIAMpA8ADfCILIA5UrXwgCyAMfCIQIAtUrXwiDCANfCILIA0gDEIAUiIIGyENAkACQCAFIAZyIARyIAsgDFQiBK0gDCAIG0IAUnIgBCAIcSANQgBTcnJFBEBC////////////ACELIA1C////////////AFIgEEJ/UnIgCkJ/UnINAkJ/IQxCfyEOIBJCbVQNAgwBCyANIQsgECEMIAohDgsgDkIBfCINIBJCbVStIhB9IQogDEIBfCIPIA5Cf1IgDSAQVHKtIg19IRAgCyAMQn9SIA0gD1ZyrX1C////////////AH0hDSASQhN8IRILIAEpAwAiDyEOIAMCfgJAAkAgDyANIgtSDQAgEyIOIBAiC1INACAKIQsgCiAUIg5SDQAgESIOIBIiC1ENAQsgCyAOWg0AIAogFFYgFCAKfSIKIBEgElStIgxUcq0iCyATIBB9IhZCf4V8Ig4gCkJ/hSAMfCIKIBEgEn0iEUJtVq0iDFStIhJ9IRQgDiASVCEEIAogDH0hDiAQIBNWIAsgFlZyrSANIA99fEL///////////8AfCETQm0gEX0MAQsgCiAUfSIMIBEgElatIgt9IQ4gECATfSIWIAogFFQgCyAMVnKtIgp9IRQgECATVCAKIBZWciEEIA0gD30hEyASIBF9CzcDyAkgAyAONwPACSADIBQ3A7gJIAMgEyAErX03A7AJIANBiAlqIANBsAlqIAIQyAIgASkDGCENIAEpAxAhEyABKQMIIQwgAykDiAkiEiERIANB8AJqAn4CQAJ+AkAgEiAPIgpSDQAgDCIKIAMpA5AJIhFSDQAgEyIKIAMpA5gJIhFSDQAgCiELIAwgDSIKIhQgAykDoAkiEVENARoLIAMpA6AJIRQgCiARVA0BIAMpA5gJIQsgAykDkAkLIQ4gEyALfSIKIA0gFFStIhB9IREgDCAOfSIWIAogEFQgCyATVnKtIgp9IRMgDCAOVCAKIBZWciECIA8gEn0hDiANIBR9DAELIAMpA5gJIgogE1QgCiATfSIKIA0gFFatIhFUcq0iCyADKQOQCSIOIAx9IhBCf4V8IhYgCkJ/hSARfCIKIBQgDX0iDUJtVq0iEVStIhR9IRMgFCAWViECIAogEX0hESAMIA5WIAsgEFZyrSAPIBJ9fEL///////////8AfCEOQm0gDX0LIg1CACAVQgAQyQMgA0GwAmogDUIAIBhCABDJAyADQaACaiANQgAgGUIAEMkDIANBkAJqIA1CACAXQgAQyQMgA0HgAmogAykD8AIiDEKblK/D8rWo3oZ/fiIKQgBCbUIAEMkDIANB0AJqIApCAEJ/QgAQyQMgA0HAAmogCkIAQv///////////wBCABDJAyADQYACaiARQgAgFUIAEMkDIANBwAFqIBFCACAYQgAQyQMgA0GwAWogEUIAIBlCABDJAyADQaABaiARQgAgF0IAEMkDIANB8AFqIAMpA9ACIgogAykD+AIiFCADKQOwAnwiEnwiESADKQPoAiAMIAMpA+ACIgt8IAtUrXx8IgwgAykDgAJ8IgtCm5Svw/K1qN6Gf34iDUIAQm1CABDJAyADQeABaiANQgBCf0IAEMkDIANB0AFqIA1CAEL///////////8AQgAQyQMgA0GQAWogE0IAIBVCABDJAyADQdAAaiATQgAgGEIAEMkDIANBEGogE0IAIBlCABDJAyADIBNCACAXQgAQyQMgA0GAAWogAykDiAIgCyAMVK18Ig8gAykDwAF8Ig0gCiADKQO4AiASIBRUrXwiECADKQOgAnwiE3wiFCAMIBFUrSADKQPYAiIWIAogEVatfHx8Ihp8IhEgAykD4AEiG3wiDCADKQP4ASADKQPwASIKIAt8IApUrXx8IgsgAykDkAF8IhJCm5Svw/K1qN6Gf34iCkIAQm1CABDJAyADQfAAaiAKQgBCf0IAEMkDIANB4ABqIApCAEL///////////8AQgAQyQMgA0GwA2ogDiACrX0iCkIAIBVCABDJAyADQaADaiAKQgAgGEIAEMkDIANBkANqIApCACAZQgAQyQMgA0GAA2ogCkIAIBdCABDJAyADQUBrIAMpA5gBIAsgElatfCIYIAMpA1B8IgogGyADKQOoAiAQIBNWrXwiGSADKQOQAnwiDiADKQPAAnwiECAUIBpWrSAWIBMgFFatfHx8IhMgAykDsAF8IhQgDSARVq0gAykDyAEgDSAPVK18fHwiDXwiDyALIAxUrSADKQPoASIXIAwgEVStfHx8IhZ8IhEgAykDcCIafCIMIAMpA4gBIAMpA4ABIgsgEnwgC1StfHwiCyADKQOwA3wiEkKblK/D8rWo3oZ/fiIVQgBCbUIAEMkDIANBMGogFUIAQn9CABDJAyADQSBqIBVCAEL///////////8AQgAQyQMCQAJAIAMpAyggAykDaCADKQPYASAQIBNWrSADKQPIAiAOIBBWrXx8IhUgAykDmAIgDiAZVK18fCIOIAMpA6ABfCIQIA0gFFStIAMpA7gBIBMgFFatfHx8IhMgAykD0AF8IhQgE1StfCAUIA8gFlatIBcgDSAPVq18fHwiDSAUVK18Ig8gECATVq0gAykDqAEgDiAQVq18fCIQIA4gFVStfCIVfCITIAMpAwB8Ig4gAykDGCANIA0gAykDEHwiDVatfCANIAogEVatIAMpA1ggCiAYVK18fHwiCiANVK18fCINIAMpA2B8IhQgDVStfCAUIAMpA3giGCAKIAogGnwiClatfCAKIAsgDFStIBggDCARVK18fHwiGCAKVK18fCIKIBRUrXwiFCANIA5UrSADKQMIIA4gE1StfHwiGSAPIBNWrSAQIBVWrXx8IhB8IhEgAykDgAN8Ig0gAykDmAMgCiAKIAMpA5ADfCIKVq18IAogCiADKQOoAyADKQO4AyALIBJWrXwiCyADKQOgA3wiDCALVK18IAwgDCAYfCIMVq18fCIKVq18fCITIAMpAyB8IgsgE1StfCALIAsgAykDOCIPIAogAykDMCIVfCIOIApUrXwgDiAPIAwgFXwiCiAMVK18IAogCiADKQNIIAMpA0AiDCASfCAMVK18fCIKVq18fCIMIA5UrXx8IgtWrXwiDiANIBNWrSADKQOIAyANIBFUrXx8Ig0gESAUVK0gECAZVK18fCIRfCIPIA5UIA0gEVZyIA9CAFNyRQRAIAsgDINCf1IgCkJtVHIgD0L///////////8AUnINAQsgDEIBfCINIApCbVStIhN9IREgC0IBfCIUIAxCf1IgDSATVHKtIgx9IQ4gDyALQn9SIAwgFFZyrX1C////////////AH0hDyAKQhN8IQoMAQsgDCERIAshDgsgAyAKNwPICSADIBE3A8AJIAMgDjcDuAkgAyAPNwOwCSAAQSBqIANBsAlqIAFBIGoQyAIgAEEYaiADQaAJaikDADcDACAAQRBqIANBmAlqKQMANwMAIABBCGogA0GQCWopAwA3AwAgACADKQOICTcDACAAIAc6AEALIANBkA9qJAAL30sCBX8XfiMAQZARayICJAAgAkHID2oiBEHc4MAAEK4CAkACQAJAAkAgASAEQSAQ8QMEQCAEQZzhwAAQrgIgASACQcgPakEgEPEDRQ0BIAJBATYCzA8gAkH048AANgLIDyACQgE3AtQPIAIgAa1CgICAgPABhDcDiA4gAiACQYgOajYC0A8gAEEIaiAEENICIABCAjcDAAwECyACQcgPakHg58AAQd8AEKYCQSghAyACKQPIDyEQIAIpA9APIRIgAikD2A8hFCACKQPgDyEVIAIpA+gPIRYgAikD8A8hFwNAIAJBwAJqIANBqJ/AAGopAwAiB0IAIBdCABDJAyACQdACaiAHQgAgFkIAEMkDIAJB4AJqIAdCACAVQgAQyQMgAkHwAmogB0IAIBRCABDJAyACQYADaiAHQgAgEkIAEMkDIAJBkANqIAdCACAQQgAQyQMgAkGwAmogAikDwAIiEyAPfCIJQgBCAEL9//P/z///+Yl/EMkDIAJBoAJqIAIpA7gCIgdCAEKr1f7///+//7l/QgAQyQMgAkGQAmogB0IAQv//z4rr///VHkIAEMkDIAJBgAJqIAdCAEKk7MO1j9S0mOcAQgAQyQMgAkHwAWogB0IAQr+llJzP8NK75ABCABDJAyACQeABaiAHQgBC19mumuT26Y3LAEIAEMkDIAJB0AFqIAdCAEKazf/Lo73EgBpCABDJAyACKQPYASAOIAIpA5ADIg58IgcgAikDiAMgAikDgAMiDCALfCILIAxUrXwgCyALIAIpA/gCIAIpA/ACIgwgCnwiCiAMVK18IAogCiACKQPoAiACKQPgAiIMIAh8IgggDFStfCAIIAggAikD2AIgDSACKQPQAiINfCIMIA1UrXwgDCACKQPIAiAJIBNUrXx8Ig0gDFStfHwiCFatfHwiClatfHwiC1atfHwiDCACKQPQAXwiEyAMVK18IBMgAikD6AEgCyALIAIpA+ABfCILVq18IAsgAikD+AEgCiAKIAIpA/ABfCIKVq18IAogAikDiAIgCCAIIAIpA4ACfCIIVq18IAggAikDmAIgAikDkAIiDyANfCINIA9UrXwgDSACKQOoAiAJIAIpA6ACIgl8IAlUrXx8Ig8gDVStfHwiDSAIVK18fCIIIApUrXx8IgogC1StfHwiCyATVK18IgkgByAMVq0gAikDmAMgByAOVK18fCIHIBF8Igx8Ig4gCVStIAcgDFatfCERIANBCGsiA0F4Rw0ACwwBCyACQcgPakH848AAQd8AEKYCQSghAyACKQPIDyESIAIpA9APIRQgAikD2A8hFSACKQPgDyEWIAIpA+gPIQ4gAikD8A8hDwNAIAJBgAlqIANBqJ/AAGopAwAiB0IAIA9CABDJAyACQZAJaiAHQgAgDkIAEMkDIAJBoAlqIAdCACAWQgAQyQMgAkGwCWogB0IAIBVCABDJAyACQcAJaiAHQgAgFEIAEMkDIAJB0AlqIAdCACASQgAQyQMgAkHwCGogAikDgAkiEyARfCIMQgBCAEL9//P/z///+Yl/EMkDIAJB4AhqIAIpA/gIIgdCAEKr1f7///+//7l/QgAQyQMgAkHQCGogB0IAQv//z4rr///VHkIAEMkDIAJBwAhqIAdCAEKk7MO1j9S0mOcAQgAQyQMgAkGwCGogB0IAQr+llJzP8NK75ABCABDJAyACQaAIaiAHQgBC19mumuT26Y3LAEIAEMkDIAJBkAhqIAdCAEKazf/Lo73EgBpCABDJAyACKQOYCCACKQPQCSIXIA18IgcgAikDyAkgAikDwAkiDSALfCILIA1UrXwgCyACKQO4CSACKQOwCSINIAp8IgogDVStfCAKIAogAikDqAkgAikDoAkiDSAIfCIIIA1UrXwgCCAIIAIpA5gJIAIpA5AJIg0gCXwiCSANVK18IAkgAikDiAkgDCATVK18fCIRIAlUrXx8IghWrXx8IgpWrXx8IgkgC1StfHwiDSACKQOQCHwiCyANVK18IAsgCyACKQOoCCAJIAIpA6AIfCITIAlUrXwgEyACKQO4CCAKIAogAikDsAh8IgpWrXwgCiACKQPICCAIIAggAikDwAh8IghWrXwgCCACKQPYCCARIAIpA9AIIhF8IgkgEVStfCAJIAIpA+gIIAwgAikD4AgiDHwgDFStfHwiESAJVK18fCIJIAhUrXx8IgggClStfHwiCiATVK18fCILVq18IgwgByANVq0gAikD2AkgByAXVK18fCIHIBB8IhN8Ig0gDFStIAcgE1atfCEQIANBCGsiA0F4Rw0ACwJAAkAgEEIAUiANQprN/8ujvcSAGlZyDQAgDUKazf/Lo73EgBpSBEAgCCETIAohFCALIRYgCSEVDAILIAtC19mumuT26Y3LAFYNAAJAAkAgC0LX2a6a5PbpjcsAUgRAIAghEyAKIRQgCyEWDAELIApCv6WUnM/w0rvkAFYNAkLX2a6a5PbpjcsAIRYgCkK/pZScz/DSu+QAUgRAIAghEyAKIRQMAQsgCEKk7MO1j9S0mOcAVg0CQr+llJzP8NK75AAhFCAIQqTsw7WP1LSY5wBSBEAgCCETDAELIAlC///Piuv//9UeVg0CQqTsw7WP1LSY5wAhEyAJQv//z4rr///VHlENAQtCms3/y6O9xIAaIQ0gCSEVDAILQv//z4rr///VHiEVIBFCq9X+////v/+5f1oNAEKazf/Lo73EgBohDQwBCyAJQv//z4rr///VHn0iByARQqvV/v///7//uX9UrSIMfSEVIAhCpOzDtY/UtJjnAH0iECAJQv//z4rr///VHlQgByAMVHKtIgd9IRMgCkK/pZScz/DSu+QAfSIJIAhCpOzDtY/UtJjnAFQgByAQVnKtIgh9IRQgC0LX2a6a5PbpjcsAfSIHIApCv6WUnM/w0rvkAFQgCCAJVnKtIgh9IRYgDSALQtfZrprk9umNywBUIAcgCFRyrX1Cms3/y6O9xIAafSENIBFC1aqBgICAwIDGAHwhEQsgAkHID2pB2+TAAEHfABCmAkEoIQMgAikDyA8hFyACKQPQDyEYIAIpA9gPIRkgAikD4A8hGiACKQPoDyEbIAIpA/APIRxCACEOQgAhC0IAIQpCACEIQgAhCUIAIQ9CACEQA0AgAkGwB2ogA0Gon8AAaikDACIHQgAgHEIAEMkDIAJBwAdqIAdCACAbQgAQyQMgAkHQB2ogB0IAIBpCABDJAyACQeAHaiAHQgAgGUIAEMkDIAJB8AdqIAdCACAYQgAQyQMgAkGACGogB0IAIBdCABDJAyACQaAHaiACKQOwByISIA98IgxCAEIAQv3/8//P///5iX8QyQMgAkGQB2ogAikDqAciB0IAQqvV/v///7//uX9CABDJAyACQYAHaiAHQgBC///Piuv//9UeQgAQyQMgAkHwBmogB0IAQqTsw7WP1LSY5wBCABDJAyACQeAGaiAHQgBCv6WUnM/w0rvkAEIAEMkDIAJB0AZqIAdCAELX2a6a5PbpjcsAQgAQyQMgAkHABmogB0IAQprN/8ujvcSAGkIAEMkDIAIpA8gGIAIpA4AIIh0gDnwiByACKQP4ByACKQPwByIOIAt8IgsgDlStfCALIAIpA+gHIAIpA+AHIg4gCnwiCiAOVK18IAogCiACKQPYByACKQPQByIOIAh8IgggDlStfCAIIAggAikDyAcgAikDwAciDiAJfCIJIA5UrXwgCSACKQO4ByAMIBJUrXx8Ig8gCVStfHwiCFatfHwiClatfHwiCSALVK18fCISIAIpA8AGfCILIBJUrXwgCyALIAIpA9gGIAkgAikD0AZ8Ig4gCVStfCAOIAIpA+gGIAogCiACKQPgBnwiClatfCAKIAIpA/gGIAggCCACKQPwBnwiCFatfCAIIAIpA4gHIA8gAikDgAciD3wiCSAPVK18IAkgAikDmAcgDCACKQOQByIMfCAMVK18fCIPIAlUrXx8IgkgCFStfHwiCCAKVK18fCIKIA5UrXx8IgtWrXwiDCAHIBJWrSACKQOICCAHIB1UrXx8IgcgEHwiEHwiDiAMVK0gByAQVq18IRAgA0EIayIDQXhHDQALAkACQCAQQgBSIA5Cms3/y6O9xIAaVnINAAJAIA5Cms3/y6O9xIAaUQRAIAtC19mumuT26Y3LAFYNAiALQtfZrprk9umNywBSBEAgCSEHIAghECAKIQwgCyESQprN/8ujvcSAGiEODAQLIApCv6WUnM/w0rvkAFYNAkLX2a6a5PbpjcsAIRIgCkK/pZScz/DSu+QAUgRAIAkhByAIIRAgCiEMQprN/8ujvcSAGiEODAQLIAhCpOzDtY/UtJjnAFYNAkK/pZScz/DSu+QAIQwgCEKk7MO1j9S0mOcAUgRAIAkhByAIIRBCms3/y6O9xIAaIQ4MBAsgCUL//8+K6///1R5WDQJCpOzDtY/UtJjnACEQIAlC///Piuv//9UeUQ0BIAkhB0Kazf/Lo73EgBohDgwDCyAJIQcgCCEQIAohDCALIRIMAgtC///Piuv//9UeIQcgD0Kr1f7///+//7l/Wg0AQprN/8ujvcSAGiEODAELIAlC///Piuv//9UefSIMIA9Cq9X+////v/+5f1StIhB9IQcgCEKk7MO1j9S0mOcAfSISIAlC///Piuv//9UeVCAMIBBUcq0iCX0hECAKQr+llJzP8NK75AB9IhcgCEKk7MO1j9S0mOcAVCAJIBJWcq0iCH0hDCALQtfZrprk9umNywB9IgkgCkK/pZScz/DSu+QAVCAIIBdWcq0iCH0hEiAOIAtC19mumuT26Y3LAFQgCCAJVnKtfUKazf/Lo73EgBp9IQ4gD0LVqoGAgIDAgMYAfCEPCyACIA83A6ANIAIgBzcDmA0gAiAQNwOQDSACIAw3A4gNIAIgEjcDgA0gAiAONwP4DCACIBE3A/AMIAIgFTcD6AwgAiATNwPgDCACIBQ3A9gMIAIgFjcD0AwgAiANNwPIDCACQcgPakG65cAAQd8AEKYCQSghAyACKQPIDyESIAIpA9APIRQgAikD2A8hFSACKQPgDyEWIAIpA+gPIQ4gAikD8A8hD0IAIQ1CACELQgAhCkIAIQhCACEJQgAhEUIAIRADQCACQeAFaiADQaifwABqKQMAIgdCACAPQgAQyQMgAkHwBWogB0IAIA5CABDJAyACQYAGaiAHQgAgFkIAEMkDIAJBkAZqIAdCACAVQgAQyQMgAkGgBmogB0IAIBRCABDJAyACQbAGaiAHQgAgEkIAEMkDIAJB0AVqIAIpA+AFIhMgEXwiDEIAQgBC/f/z/8////mJfxDJAyACQcAFaiACKQPYBSIHQgBCq9X+////v/+5f0IAEMkDIAJBsAVqIAdCAEL//8+K6///1R5CABDJAyACQaAFaiAHQgBCpOzDtY/UtJjnAEIAEMkDIAJBkAVqIAdCAEK/pZScz/DSu+QAQgAQyQMgAkGABWogB0IAQtfZrprk9umNywBCABDJAyACQfAEaiAHQgBCms3/y6O9xIAaQgAQyQMgAikD+AQgAikDsAYiFyANfCIHIAIpA6gGIAIpA6AGIg0gC3wiCyANVK18IAsgAikDmAYgAikDkAYiDSAKfCIKIA1UrXwgCiAKIAIpA4gGIAIpA4AGIg0gCHwiCCANVK18IAggCCACKQP4BSACKQPwBSINIAl8IgkgDVStfCAJIAIpA+gFIAwgE1StfHwiESAJVK18fCIIVq18fCIKVq18fCIJIAtUrXx8Ig0gAikD8AR8IgsgDVStfCALIAsgAikDiAUgCSACKQOABXwiEyAJVK18IBMgAikDmAUgCiAKIAIpA5AFfCIKVq18IAogAikDqAUgCCAIIAIpA6AFfCIIVq18IAggAikDuAUgESACKQOwBSIRfCIJIBFUrXwgCSACKQPIBSAMIAIpA8AFIgx8IAxUrXx8IhEgCVStfHwiCSAIVK18fCIIIApUrXx8IgogE1StfHwiC1atfCIMIAcgDVatIAIpA7gGIAcgF1StfHwiByAQfCITfCINIAxUrSAHIBNWrXwhECADQQhrIgNBeEcNAAsCQAJAIBBCAFIgDUKazf/Lo73EgBpWcg0AAkAgDUKazf/Lo73EgBpRBEAgC0LX2a6a5PbpjcsAVg0CIAtC19mumuT26Y3LAFIEQCAJIRMgCCEVIAohFCALIRZCms3/y6O9xIAaIQ0MBAsgCkK/pZScz/DSu+QAVg0CQtfZrprk9umNywAhFiAKQr+llJzP8NK75ABSBEAgCSETIAghFSAKIRRCms3/y6O9xIAaIQ0MBAsgCEKk7MO1j9S0mOcAVg0CQr+llJzP8NK75AAhFCAIQqTsw7WP1LSY5wBSBEAgCSETIAghFUKazf/Lo73EgBohDQwECyAJQv//z4rr///VHlYNAkKk7MO1j9S0mOcAIRUgCUL//8+K6///1R5RDQEgCSETQprN/8ujvcSAGiENDAMLIAkhEyAIIRUgCiEUIAshFgwCC0L//8+K6///1R4hEyARQqvV/v///7//uX9aDQBCms3/y6O9xIAaIQ0MAQsgCUL//8+K6///1R59IgcgEUKr1f7///+//7l/VK0iDH0hEyAIQqTsw7WP1LSY5wB9IhAgCUL//8+K6///1R5UIAcgDFRyrSIHfSEVIApCv6WUnM/w0rvkAH0iCSAIQqTsw7WP1LSY5wBUIAcgEFZyrSIIfSEUIAtC19mumuT26Y3LAH0iByAKQr+llJzP8NK75ABUIAggCVZyrSIIfSEWIA0gC0LX2a6a5PbpjcsAVCAHIAhUcq19QprN/8ujvcSAGn0hDSARQtWqgYCAgMCAxgB8IRELIAJByA9qQZnmwABB3wAQpgJBKCEDIAIpA8gPIRcgAikD0A8hGCACKQPYDyEZIAIpA+APIRogAikD6A8hGyACKQPwDyEcQgAhDkIAIQtCACEKQgAhCEIAIQlCACEPQgAhEANAIAJBkARqIANBqJ/AAGopAwAiB0IAIBxCABDJAyACQaAEaiAHQgAgG0IAEMkDIAJBsARqIAdCACAaQgAQyQMgAkHABGogB0IAIBlCABDJAyACQdAEaiAHQgAgGEIAEMkDIAJB4ARqIAdCACAXQgAQyQMgAkGABGogAikDkAQiEiAPfCIMQgBCAEL9//P/z///+Yl/EMkDIAJB8ANqIAIpA4gEIgdCAEKr1f7///+//7l/QgAQyQMgAkHgA2ogB0IAQv//z4rr///VHkIAEMkDIAJB0ANqIAdCAEKk7MO1j9S0mOcAQgAQyQMgAkHAA2ogB0IAQr+llJzP8NK75ABCABDJAyACQbADaiAHQgBC19mumuT26Y3LAEIAEMkDIAJBoANqIAdCAEKazf/Lo73EgBpCABDJAyACKQOoAyACKQPgBCIdIA58IgcgAikD2AQgAikD0AQiDiALfCILIA5UrXwgCyACKQPIBCACKQPABCIOIAp8IgogDlStfCAKIAogAikDuAQgAikDsAQiDiAIfCIIIA5UrXwgCCAIIAIpA6gEIAIpA6AEIg4gCXwiCSAOVK18IAkgAikDmAQgDCASVK18fCIPIAlUrXx8IghWrXx8IgpWrXx8IgkgC1StfHwiEiACKQOgA3wiCyASVK18IAsgCyACKQO4AyAJIAIpA7ADfCIOIAlUrXwgDiACKQPIAyAKIAogAikDwAN8IgpWrXwgCiACKQPYAyAIIAggAikD0AN8IghWrXwgCCACKQPoAyAPIAIpA+ADIg98IgkgD1StfCAJIAIpA/gDIAwgAikD8AMiDHwgDFStfHwiDyAJVK18fCIJIAhUrXx8IgggClStfHwiCiAOVK18fCILVq18IgwgByASVq0gAikD6AQgByAdVK18fCIHIBB8IhB8Ig4gDFStIAcgEFatfCEQIANBCGsiA0F4Rw0ACwJAAkAgEEIAUiAOQprN/8ujvcSAGlZyDQACQCAOQprN/8ujvcSAGlEEQCALQtfZrprk9umNywBWDQIgC0LX2a6a5PbpjcsAUgRAIAkhByAIIRAgCiEMIAshEkKazf/Lo73EgBohDgwECyAKQr+llJzP8NK75ABWDQJC19mumuT26Y3LACESIApCv6WUnM/w0rvkAFIEQCAJIQcgCCEQIAohDEKazf/Lo73EgBohDgwECyAIQqTsw7WP1LSY5wBWDQJCv6WUnM/w0rvkACEMIAhCpOzDtY/UtJjnAFIEQCAJIQcgCCEQQprN/8ujvcSAGiEODAQLIAlC///Piuv//9UeVg0CQqTsw7WP1LSY5wAhECAJQv//z4rr///VHlENASAJIQdCms3/y6O9xIAaIQ4MAwsgCSEHIAghECAKIQwgCyESDAILQv//z4rr///VHiEHIA9Cq9X+////v/+5f1oNAEKazf/Lo73EgBohDgwBCyAJQv//z4rr///VHn0iDCAPQqvV/v///7//uX9UrSIQfSEHIAhCpOzDtY/UtJjnAH0iEiAJQv//z4rr///VHlQgDCAQVHKtIgl9IRAgCkK/pZScz/DSu+QAfSIXIAhCpOzDtY/UtJjnAFQgCSASVnKtIgh9IQwgC0LX2a6a5PbpjcsAfSIJIApCv6WUnM/w0rvkAFQgCCAXVnKtIgh9IRIgDiALQtfZrprk9umNywBUIAggCVZyrX1Cms3/y6O9xIAafSEOIA9C1aqBgICAwIDGAHwhDwsgAiAPNwOADiACIAc3A/gNIAIgEDcD8A0gAiAMNwPoDSACIBI3A+ANIAIgDjcD2A0gAiARNwPQDSACIBM3A8gNIAIgFTcDwA0gAiAUNwO4DSACIBY3A7ANIAIgDTcDqA0gAkHID2oiBiACQcgMaiACQagNahBsAkAgAigCyA9FBEAgAkGIDmoiBSACQdAPaiIEQcAB/AoAACAGQfjmwAAQrgJB0c7FAC0AABpBGEEBENYEIgNFDQEgA0EQakHI58AAKQAANwAAIANBCGpBwOfAACkAADcAACADQbjnwAApAAA3AAAgAkGAC2ogBUHoAPwKAAAgAkGoCmogAkHwDmpB2AD8CgAAQRghBiACQaAKaiABQRhqKQAANwMAIAJBmApqIAFBEGopAAA3AwAgAkGQCmogAUEIaikAADcDACACQfAJaiAEKQAANwMAIAJB+AlqIAJB2A9qKQAANwMAIAJBgApqIAJB4A9qKQAANwMAIAIgASkAADcDiAogAiACKQDIDzcD6AlBAyEBQafCmKcGIQVBASEEQgEhEgwDCyACQZAOaiACQdQPaigCADYCACACIAIpAswPNwOIDkGEncAAQSsgAkGIDmpB2KvAAEHQ58AAEMoDAAtBAUEYQYSkwAAQyAQACwJAAkAgEUIAUiAOQprN/8ujvcSAGlZyDQAgDkKazf/Lo73EgBpSBEAgDSEHIAghESAKIQwgCyESDAILIAtC19mumuT26Y3LAFYNACALQtfZrprk9umNywBSBEAgDSEHIAghESAKIQwgCyESQprN/8ujvcSAGiEODAILIApCv6WUnM/w0rvkAFYNAELX2a6a5PbpjcsAIRIgCkK/pZScz/DSu+QAUgRAIA0hByAIIREgCiEMQprN/8ujvcSAGiEODAILIAhCpOzDtY/UtJjnAFYNAEK/pZScz/DSu+QAIQwgCEKk7MO1j9S0mOcAUgRAIA0hByAIIRFCms3/y6O9xIAaIQ4MAgsgDUL//8+K6///1R5WDQBCpOzDtY/UtJjnACERIA1C///Piuv//9UeUgRAIA0hB0Kazf/Lo73EgBohDgwCC0L//8+K6///1R4hByAPQqvV/v///7//uX9aDQBCms3/y6O9xIAaIQ4MAQsgDUL//8+K6///1R59IgkgD0Kr1f7///+//7l/VK0iDH0hByAIQqTsw7WP1LSY5wB9IhMgDUL//8+K6///1R5UIAkgDFRyrSIJfSERIApCv6WUnM/w0rvkAH0iDSAIQqTsw7WP1LSY5wBUIAkgE1ZyrSIIfSEMIAtC19mumuT26Y3LAH0iCSAKQr+llJzP8NK75ABUIAggDVZyrSIIfSESIA4gC0LX2a6a5PbpjcsAVCAIIAlWcq19QprN/8ujvcSAGn0hDiAPQtWqgYCAgMCAxgB8IQ8LIAIgDzcDkAwgAiAHNwOIDCACIBE3A4AMIAIgDDcD+AsgAiASNwPwCyACIA43A+gLIAJByA9qQb/owABB3wAQpgJBKCEDIAIpA8gPIRAgAikD0A8hEiACKQPYDyEUIAIpA+APIRUgAikD6A8hFiACKQPwDyEXQgAhDkIAIQtCACEKQgAhCEIAIQ1CACEPQgAhEQNAIAJB8ABqIANBqJ/AAGopAwAiB0IAIBdCABDJAyACQYABaiAHQgAgFkIAEMkDIAJBkAFqIAdCACAVQgAQyQMgAkGgAWogB0IAIBRCABDJAyACQbABaiAHQgAgEkIAEMkDIAJBwAFqIAdCACAQQgAQyQMgAkHgAGogAikDcCITIA98IglCAEIAQv3/8//P///5iX8QyQMgAkHQAGogAikDaCIHQgBCq9X+////v/+5f0IAEMkDIAJBQGsgB0IAQv//z4rr///VHkIAEMkDIAJBMGogB0IAQqTsw7WP1LSY5wBCABDJAyACQSBqIAdCAEK/pZScz/DSu+QAQgAQyQMgAkEQaiAHQgBC19mumuT26Y3LAEIAEMkDIAIgB0IAQprN/8ujvcSAGkIAEMkDIAIpAwggDiACKQPAASIOfCIHIAIpA7gBIAIpA7ABIgwgC3wiCyAMVK18IAsgCyACKQOoASACKQOgASIMIAp8IgogDFStfCAKIAogAikDmAEgAikDkAEiDCAIfCIIIAxUrXwgCCAIIAIpA4gBIA0gAikDgAEiDXwiDCANVK18IAwgAikDeCAJIBNUrXx8Ig0gDFStfHwiCFatfHwiClatfHwiC1atfHwiDCACKQMAfCITIAxUrXwgEyACKQMYIAsgCyACKQMQfCILVq18IAsgAikDKCAKIAogAikDIHwiClatfCAKIAIpAzggCCAIIAIpAzB8IghWrXwgCCACKQNIIAIpA0AiDyANfCINIA9UrXwgDSACKQNYIAkgAikDUCIJfCAJVK18fCIPIA1UrXx8Ig0gCFStfHwiCCAKVK18fCIKIAtUrXx8IgsgE1StfCIJIAcgDFatIAIpA8gBIAcgDlStfHwiByARfCIMfCIOIAlUrSAHIAxWrXwhESADQQhrIgNBeEcNAAsCQAJAIBFCAFIgDkKazf/Lo73EgBpWcg0AAkAgDkKazf/Lo73EgBpRBEAgC0LX2a6a5PbpjcsAVg0CIAtC19mumuT26Y3LAFIEQCANIQcgCCERIAohDCALIRJCms3/y6O9xIAaIQ4MBAsgCkK/pZScz/DSu+QAVg0CQtfZrprk9umNywAhEiAKQr+llJzP8NK75ABSBEAgDSEHIAghESAKIQxCms3/y6O9xIAaIQ4MBAsgCEKk7MO1j9S0mOcAVg0CQr+llJzP8NK75AAhDCAIQqTsw7WP1LSY5wBSBEAgDSEHIAghEUKazf/Lo73EgBohDgwECyANQv//z4rr///VHlYNAkKk7MO1j9S0mOcAIREgDUL//8+K6///1R5RDQEgDSEHQprN/8ujvcSAGiEODAMLIA0hByAIIREgCiEMIAshEgwCC0L//8+K6///1R4hByAPQqvV/v///7//uX9aDQBCms3/y6O9xIAaIQ4MAQsgDUL//8+K6///1R59IgkgD0Kr1f7///+//7l/VK0iDH0hByAIQqTsw7WP1LSY5wB9IhMgDUL//8+K6///1R5UIAkgDFRyrSIJfSERIApCv6WUnM/w0rvkAH0iDSAIQqTsw7WP1LSY5wBUIAkgE1ZyrSIIfSEMIAtC19mumuT26Y3LAH0iCSAKQr+llJzP8NK75ABUIAggDVZyrSIIfSESIA4gC0LX2a6a5PbpjcsAVCAIIAlWcq19QprN/8ujvcSAGn0hDiAPQtWqgYCAgMCAxgB8IQ8LIAIgDzcDwAwgAiAHNwO4DCACIBE3A7AMIAIgDDcDqAwgAiASNwOgDCACIA43A5gMIAJByA9qIAJB6AtqIAJBmAxqQQAQMSACLQCoEEECRgRAIAJBkA5qIAJB0A9qKAIANgIAIAIgAikDyA83A4gOQYSdwABBKyACQYgOakHYq8AAQfTpwAAQygMACyACQYgOaiIFIAJByA9qIgRB6AD8CgAAIARBnunAABCuAkEAIQRB0c7FAC0AABpBFEEBENYEIgMEQCADQRBqQe7pwAAoAAA2AAAgA0EIakHm6cAAKQAANwAAIANB3unAACkAADcAACACQYALaiAFQegA/AoAACACQaAKaiABQRhqKQAANwMAIAJBmApqIAFBEGopAAA3AwAgAkGQCmogAUEIaikAADcDACACQfAJaiACQdAPaikAADcDACACQfgJaiACQdgPaikAADcDACACQYAKaiACQeAPaikAADcDACACIAEpAAA3A4gKIAIgAikAyA83A+gJQR4hAUGKseH4BSEFQgAhEkEUIQYMAQtBAUEUQYSkwAAQyAQACyAAIBI3AwAgAEEIaiACQYALakHoAPwKAAAgAEHwAGogAkGoCmpB2AD8CgAAIAAgBDoAnAIgACAFNgKYAiAAIAE2ApQCIAAgBjYCkAIgACADNgKMAiAAIAY2AogCIABB4AFqIAJBoApqKQMANwMAIABB2AFqIAJBmApqKQMANwMAIABB0AFqIAJBkApqKQMANwMAIAAgAikDiAo3A8gBIAAgAikD6Ak3A+gBIABB8AFqIAJB8AlqKQMANwMAIABB+AFqIAJB+AlqKQMANwMAIABBgAJqIAJBgApqKQMANwMACyACQZARaiQAC5RGAgd/EX4jAEHQEGsiAyQAAkACQAJAAn8CQAJAAkACQCABLQBAIgcgAi0AQEYEQCABQejRwQBBIBDxA0UEQCABQSBqQejRwQBBIBDxA0UNAgsgAkHo0cEAQSAQ8QNFBEAgAkEgakHo0cEAQSAQ8QNFDQMLAkAgASACQSAQ8QNFBEAgAUEgaiIJIAJBIGpBIBDxA0UNASAAQgA3AwAgACAHOgBAIABBOGpCADcDACAAQTBqQgA3AwAgAEEoakIANwMAIABBIGpCADcDACAAQRhqQgA3AwAgAEEQakIANwMAIABBCGpCADcDAAwKCyABKQMgIg8hDSACKQMgIg4hDAJ+AkAgDiAPUg0AIAEpAygiECACKQMoIgxSBEAgECENDAELIAEpAzAiCiACKQMwIgxSBEAgCiENDAELIBAhEiABKQM4Ig0hCyAKIA0gAikDOCIMUQ0BGgsgDCANVA0FIAEpAyghECACKQMoIRIgASkDMCEKIAEpAzghDSACKQM4IQsgAikDMAsiESAKfSIVIAsgDVStIhZ9IQwgEiAQfSIXIBUgFlQgCiARVnKtIhF9IQogESAXViAQIBJWciEEIA4gD30hDiALIA19IQ0MBwsgA0HwCmoQOiAHRQRAIAMpA4ALIRUgAykD+AohFiADKQPwCiEXIANBiAtqDAYLIAMoAqANQQFxDQRB7PbBABDoBAALQYD2wQBBM0Hc9sEAEP4DAAsgACAHOgBAIAAgAikDIDcDICAAIAIpAwA3AwAgAEE4aiACQThqKQMANwMAIABBMGogAkEwaikDADcDACAAQShqIAJBKGopAwA3AwAgAEEIaiACQQhqKQMANwMAIABBEGogAkEQaikDADcDACAAQRhqIAJBGGopAwA3AwAMBgsgACAHOgBAIAAgASkDIDcDICAAIAEpAwA3AwAgAEE4aiABQThqKQMANwMAIABBMGogAUEwaikDADcDACAAQShqIAFBKGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwAMBQtC3bCFjOi2kai4fyABKQMoIhAgAikDKCILfSIRIAEpAzAiCiACKQMwIgxUIAogDH0iCiABKQM4IgwgAikDOCISVK0iDVRyrSIVfSIWfSIXIAogDX0iCkKR4eXNh4n6mShWQpHh5c2HifqZKCAKfSINIAwgEn0iEkKBgICAv7L98MMAVq0iDFRyrSIYfSEKIBcgGFQgFkLdsIWM6LaRqLh/VnIhBCANIAx9IQwgESAVVCALIBBWcq0gDiAPfXxCqcDGia7Ok7IwfCEOQoGAgIC/sv3wwwAgEn0hDQwCCyADKQO4DSEVIAMpA7ANIRYgAykDqA0hFyADQcANagspAwAhGCADQvH////OiqfhBTcDiBAgA0L9zonxjfjY+qR/NwOAECADQoqlr8vmyfqlMzcD+A8gA0KOu97wzOjZjyo3A/APIANB4AlqIAEpAxAiEUIAIAEpAxgiEEIAEMkDIANBwAlqIAEpAwgiEkIAIBBCABDJAyADQeAIaiABKQMAIgpCACAQQgAQyQMgA0GwCWogEkIAIBFCABDJAyADQfAIaiAKQgAgEUIAEMkDIANBgAlqIApCACASQgAQyQMgA0GwCmogEEIAIBBCABDJAyADQdAJaiARQgAgEUIAEMkDIANBoAlqIBJCACASQgAQyQMgA0GQCWogCkIAIApCABDJAyADQaAKaiADKQOwCiITQv////++sv3wQn4iCkIAQoGAgIC/sv3wwwBCABDJAyADQZAKaiAKQgBCkeHlzYeJ+pkoQgAQyQMgA0GACmogCkIAQt2whYzotpGouH9CABDJAyADQfAJaiAKQgBCqcDGia7Ok7IwQgAQyQMgAykDiAkgAykD+AggAykD6AggAykDyAkgAykD6AkiCyADKQPACXwiCiALVK18IgwgAykD4Ah8IgsgDFStfCINIAMpA/AIfCIMIA1UrXwgDCAMIAMpA7gJIAsgCyADKQOwCXwiC1atfHwiDFatfCIPIAMpA4AJfCINIA9UrXwiD0I/iCADKQOYCSADKQOQCSIOIA9CAYYgDUI/iIR8Ig8gDlStfCAPIA8gAykDqAkgAykD2AkgAykD0AkiFCAKQgGGIAMpA+AJIhlCP4iEfCIOIBRUrXwgDiADKQO4CiIUIBlCAYZ8IhkgFFStfCIUIA5UrXwiDiALQgGGIApCP4iEfCIaIA5UrSIOIAMpA6AJfCIKIA5UrXwgCiAMQgGGIAtCP4iEfCILIApUrXwiCiANQgGGIAxCP4iEfCIMIApUrXwiD1atfHwhDQJ/AkAgAykD+AkgAykDiAogAykDmAogAykDqAogAykDoAoiCiATQn2DfCAKVK18Ig4gAykDkAp8IgogDlStfCAKIBl8Ig4gClStfCITIAMpA4AKfCIKIBNUrXwgCiAUfCITIApUrXwiFCADKQPwCXwiCiAUVK18IAogGnwiFCAKVK18IgpQDQAgCiALfCILIApUIgRFDQAgBK0iCiAMfCIMIApaDQAgCiAMVq0iCiAPfCIPIApaDQAgCiAPVq0iCiANfCINIApUDAELQQALIQQgA0HQCGogDkL/////vrL98EJ+IgpCAEKBgICAv7L98MMAQgAQyQMgA0HACGogCkIAQpHh5c2HifqZKEIAEMkDIANBsAhqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgCGogCkIAQqnAxomuzpOyMEIAEMkDAkAgAykDqAggAykDuAggAykDyAggAykD2AggAykD0AgiCiAOfCAKVK18Ig4gAykDwAh8IgogDlStfCAKIBN8Ig4gClStfCITIAMpA7AIfCIKIBNUrXwgCiAUfCITIApUrXwiFCADKQOgCHwiCiAUVK18IAogC3wiFCAKVK18IgpQDQAgCiAMfCIMIApaDQAgCiAMVq0iCiAPfCIPIApaDQAgCiAPVq0iCiANfCINIApUIQYLIANBkAhqIA5C/////76y/fBCfiIKQgBCgYCAgL+y/fDDAEIAEMkDIANBgAhqIApCAEKR4eXNh4n6mShCABDJAyADQfAHaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4AdqIApCAEKpwMaJrs6TsjBCABDJAyADKQPoByADKQP4ByADKQOICCADKQOYCCADKQOQCCIKIA58IApUrXwiCyADKQOACHwiCiALVK18IAogE3wiCyAKVK18Ig4gAykD8Ad8IgogDlStfCAKIBR8Ig4gClStfCITIAMpA+AHfCIKIBNUrXwgCiAMfCIMIApUrXwiClBFBEAgCiAPfCIPIApUIgWtIgogDXwiEyANIAUbIQ0gBSAKIBNWcSEFCyADQdAHaiALQv////++sv3wQn4iCkIAQoGAgIC/sv3wwwBCABDJAyADQcAHaiAKQgBCkeHlzYeJ+pkoQgAQyQMgA0GwB2ogCkIAQt2whYzotpGouH9CABDJAyADQaAHaiAKQgBCqcDGia7Ok7IwQgAQyQMgAykDqAcgAykDuAcgAykDyAcgAykD2AcgAykD0AciCiALfCAKVK18IgsgAykDwAd8IgogC1StfCAKIA58Ig4gClStfCILIAMpA7AHfCIKIAtUrXwgCiAMfCILIApUrXwiDCADKQOgB3wiCiAMVK18IAogD3wiDCAKVK18IgogDXwiDyANIApCAFIiCBshDQJAAkACQCAEIAZyIAVyIAogD1YiBK0gCiAIG0IAUnIgBCAIcSANQqnAxomuzpOyMFZycg0AIA1CqcDGia7Ok7IwUgRAIAshCgwDCyAMQt2whYzotpGouH9WDQAgDELdsIWM6LaRqLh/UgRAIAshCgwDC0LdsIWM6LaRqLh/IQ8gC0KR4eXNh4n6mShWDQEgC0KR4eXNh4n6mShSBEAgCyEKDAMLIA5CgICAgL+y/fDDAFYNASALIQoMAgsgDCEPCyALQpHh5c2HifqZKH0iDCAOQoGAgIC/sv3wwwBUrSITfSEKIA9Co8/685fJ7tfHAHwiFCALQpHh5c2HifqZKFQgDCATVHKtIgt9IQwgDSAPQt2whYzotpGouH9UIAsgFFZyrX1CqcDGia7Ok7IwfSENIA5CgYCAgL+y/fDDAH0hDgsgAyAONwPIECADIAo3A8AQIAMgDDcDuBAgAyANNwOwECADQdAPaiADQfAPaiADQbAQahB9QqnAxomuzpOyMCEKIAMpA9gPIgwgFnwiCyAMVCALIAMpA+APIg0gFXwiDCANVCAMIAwgAykD6A8iDSAYfCIOIA1UrXwiDFZyrXwiDyALVHKtIAMpA9APIBd8fCINIQsCQAJAAkAgDUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEKIA8iC0LdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCEKIAwiC0KR4eXNh4n6mShSDQBCgYCAgL+y/fDDACEKIA4iC0KBgICAv7L98MMAUQ0BCyAKIAtYDQAgDyEKIAwhCwwBCyAMQpHh5c2HifqZKH0iCiAOQoGAgIC/sv3wwwBUrSIVfSELIA9Co8/685fJ7tfHAHwiFiAMQpHh5c2HifqZKFQgCiAVVHKtIgx9IQogDSAPQt2whYzotpGouH9UIAwgFlZyrX1CqcDGia7Ok7IwfSENIA5CgYCAgL+y/fDDAH0hDgsgAyAONwPIDyADIAs3A8APIAMgCjcDuA8gAyANNwOwDyADQvb///+Jh5qW2QA3A8gQIANC07SG9rOlu/ztADcDwBAgA0LcmMqH79vR7kw3A7gQIANC3vy+oLPwu4ocNwOwECADQZAQaiIFIANBsBBqIAkQfSADQcgKaiADQbAPaiAFEFogAygCnA8iBARAIAMoAqAPIARBAnQQ3wQLAkAgAygC1AwiBEUNACAEIARBDGxBE2pBeHEiBmpBCWoiBEUNACADKALQDCAGayAEEN8ECyADKAKADSIEQYCAgIB4RiAERXINASADKAKEDSAEQQJ0EN8EDAELIAMgDTcDyBAgAyAMNwPAECADIAo3A7gQIAMgDiAErX03A7AQIAEpAwAiDSEQIAIpAwAiDiEPIAMCfgJAAn4CQCANIA5SDQAgASkDCCISIAIpAwgiD1IEQCASIRAMAQsgASkDECIRIAIpAxAiD1IEQCARIRAMAQsgESEMIAEpAxgiECELIBIgECACKQMYIg9RDQEaCyAPIBBUDQEgASkDCCESIAEpAxAhESACKQMQIQwgASkDGCEQIAIpAxghCyACKQMICyEKIAwgEX0iFSALIBBUrSIWfSEPIAogEn0iFyAMIBFUIBUgFlRyrSIVfSEMIAogElQgFSAXVnIhBCAOIA19IQ0gCyAQfQwBC0LdsIWM6LaRqLh/IAEpAwgiEiACKQMIIgp9IgsgASkDECIRIAIpAxAiEFQgESAQfSIMIAEpAxgiECACKQMYIg9UrSIVVHKtIhZ9Ihd9IhggDCAVfSIMQpHh5c2HifqZKFZCkeHlzYeJ+pkoIAx9IhUgECAPfSITQoGAgIC/sv3wwwBWrSIPVHKtIhR9IQwgFCAYViAXQt2whYzotpGouH9WciEEIBUgD30hDyALIBZUIAogElZyrSAOIA19fEKpwMaJrs6TsjB8IQ1CgYCAgL+y/fDDACATfQs3A4gLIAMgDzcDgAsgAyAMNwP4CiADIA0gBK19NwPwCiADQcgKaiADQbAQaiADQfAKahBaCyADKALICgRAIAMgAykD2Ao3A/gKIAMgAykD0Ao3A/AKQYz3wQBBKyADQfAKakH89sEAQbj3wQAQygMACyADQbAGaiADKQPoCiIVQgAgAykD4AoiFkIAEMkDIANBoAZqIBVCACADKQPYCiIXQgAQyQMgA0GQBmogFUIAIAMpA9AKIhhCABDJAyADQeAGaiAWQgAgF0IAEMkDIANB0AZqIBZCACAYQgAQyQMgA0GAB2ogF0IAIBhCABDJAyADQYAGaiAVQgAgFUIAEMkDIANBwAZqIBZCACAWQgAQyQMgA0HwBmogF0IAIBdCABDJAyADQZAHaiAYQgAgGEIAEMkDIANB8AVqIAMpA4AGIhNC/////76y/fBCfiIKQgBCgYCAgL+y/fDDAEIAEMkDIANB4AVqIApCAEKR4eXNh4n6mShCABDJAyADQdAFaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBwAVqIApCAEKpwMaJrs6TsjBCABDJAyADKQOIByADKQPYBiADKQOYBiADKQOoBiADKQO4BiILIAMpA6AGfCIKIAtUrXwiDCADKQOQBnwiCyAMVK18Ig0gAykD0AZ8IgwgDVStfCAMIAwgAykD6AYgCyALIAMpA+AGfCILVq18fCIMVq18Ig8gAykDgAd8Ig0gD1StfCIPQj+IIAMpA5gHIAMpA5AHIg4gD0IBhiANQj+IhHwiDyAOVK18IA8gDyADKQP4BiADKQPIBiADKQPABiIUIApCAYYgAykDsAYiGUI/iIR8Ig4gFFStfCAOIAMpA4gGIhQgGUIBhnwiGSAUVK18IhQgDlStfCIOIAtCAYYgCkI/iIR8IhogDlStIg4gAykD8AZ8IgogDlStfCAKIAxCAYYgC0I/iIR8Ig4gClStfCIKIA1CAYYgDEI/iIR8IgwgClStfCIPVq18fCEKQQAhBQJ/AkAgAykDyAUgAykD2AUgAykD6AUgAykD+AUgEyADKQPwBSILfCALVK18Ig0gAykD4AV8IgsgDVStfCALIBl8Ig0gC1StfCITIAMpA9AFfCILIBNUrXwgCyAUfCITIAtUrXwiFCADKQPABXwiCyAUVK18IAsgGnwiFCALVK18IgtQDQAgCyAOfCIOIAtUIgRFDQAgBK0iCyAMfCIMIAtaDQAgCyAMVq0iCyAPfCIPIAtaDQAgCyAPVq0iCyAKfCIKIAtUDAELQQALIQYgA0GwBWogDUL/////vrL98EJ+IgtCAEKBgICAv7L98MMAQgAQyQMgA0GgBWogC0IAQpHh5c2HifqZKEIAEMkDIANBkAVqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0GABWogC0IAQqnAxomuzpOyMEIAEMkDAkAgAykDiAUgAykDmAUgAykDqAUgAykDuAUgAykDsAUiCyANfCALVK18Ig0gAykDoAV8IgsgDVStfCALIBN8Ig0gC1StfCITIAMpA5AFfCILIBNUrXwgCyAUfCITIAtUrXwiFCADKQOABXwiCyAUVK18IAsgDnwiDiALVK18IgtQDQAgCyAMfCIMIAtaDQAgCyAMVq0iCyAPfCIPIAtaDQAgCyAPVq0iCyAKfCIKIAtUIQULIANB8ARqIA1C/////76y/fBCfiILQgBCgYCAgL+y/fDDAEIAEMkDIANB4ARqIAtCAEKR4eXNh4n6mShCABDJAyADQdAEaiALQgBC3bCFjOi2kai4f0IAEMkDIANBwARqIAtCAEKpwMaJrs6TsjBCABDJA0EAIQQgAykDyAQgAykD2AQgAykD6AQgAykD+AQgAykD8AQiCyANfCALVK18Ig0gAykD4AR8IgsgDVStfCALIBN8Ig0gC1StfCITIAMpA9AEfCILIBNUrXwgCyAOfCIOIAtUrXwiEyADKQPABHwiCyATVK18IAsgDHwiEyALVK18IgtQRQRAIAsgD3wiDyALVCIErSILIAp8IgwgCiAEGyEKIAQgCyAMVnEhBAsgA0GwBGogDUL/////vrL98EJ+IgtCAEKBgICAv7L98MMAQgAQyQMgA0GgBGogC0IAQpHh5c2HifqZKEIAEMkDIANBkARqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0GABGogC0IAQqnAxomuzpOyMEIAEMkDIAMpA4gEIAMpA5gEIAMpA6gEIAMpA7gEIAMpA7AEIgsgDXwgC1StfCIMIAMpA6AEfCILIAxUrXwgCyALIA58IgtWrXwiDSADKQOQBHwiDCANVK18IAwgE3wiDSAMVK18Ig4gAykDgAR8IgwgDlStfCAMIA98Ig4gDFStfCIMIAp8Ig8gCiAMQgBSIggbIQoCQAJAAkACQCAFIAZyIARyIAwgD1YiBK0gDCAIG0IAUnIgBCAIcSAKQqnAxomuzpOyMFZycg0AIApCqcDGia7Ok7IwUg0BIA5C3bCFjOi2kai4f1YNACAOQt2whYzotpGouH9SBEAgDSEMIA4hD0KpwMaJrs6TsjAhCgwEC0LdsIWM6LaRqLh/IQ4gDUKR4eXNh4n6mShWDQAgDUKR4eXNh4n6mShSIAtCgICAgL+y/fDDAFhyDQILIA1CkeHlzYeJ+pkofSIPIAtCgYCAgL+y/fDDAFStIhN9IQwgDkKjz/rzl8nu18cAfCIUIA1CkeHlzYeJ+pkoVCAPIBNUcq0iDX0hDyAKIA5C3bCFjOi2kai4f1QgDSAUVnKtfUKpwMaJrs6TsjB9IQogC0KBgICAv7L98MMAfSELDAILIA0hDCAOIQ8MAQsgDSEMQt2whYzotpGouH8hD0KpwMaJrs6TsjAhCgsgASkDACITIQ4gCiENAn4CQAJAIAogE1INACASIg4gDyINUg0AIAwhDSAMIBEiDlINACALIQ0gCyAQIg5RDQELIA0gDloNAELdsIWM6LaRqLh/IBIgD30iDSAMIBFWIBEgDH0iDCALIBBWrSIRVHKtIhR9Ig59IhkgDCARfSIMQpHh5c2HifqZKFZCkeHlzYeJ+pkoIAx9IgwgECALfSIQQoGAgIC/sv3wwwBWrSILVHKtIhp9IREgGSAaVCAOQt2whYzotpGouH9WciEEIAwgC30hDkKBgICAv7L98MMAIBB9IRAgDSAUVCAPIBJWcq0gCiATfXxCqcDGia7Ok7IwfAwBCyAMIBF9Ig0gCyAQVK0iFH0hDiAPIBJ9IhkgDSAUVCAMIBFUcq0iDH0hESAPIBJUIAwgGVZyIQQgCyAQfSEQIAogE30LIQogAyAQNwOICyADIA43A4ALIAMgETcD+AogAyAKIAStfTcD8AogA0GwEGoiBCADQfAKaiIFIAIQwQIgA0GIC2ogAUEYaikDADcDACADQYALaiABQRBqKQMANwMAIANB+ApqIAFBCGopAwA3AwAgAyABKQMANwPwCiADQcgKaiAFIAQQwQIgA0GwAmogAykD4AoiCkIAIBVCABDJAyADQaACaiAKQgAgFkIAEMkDIANBkAJqIApCACAXQgAQyQMgA0GAAmogCkIAIBhCABDJAyADQfABaiADKQOwAiILQv////++sv3wQn4iCkIAQoGAgIC/sv3wwwBCABDJAyADQeABaiAKQgBCkeHlzYeJ+pkoQgAQyQMgA0HQAWogCkIAQt2whYzotpGouH9CABDJAyADQcABaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwAmogAykD2AoiCkIAIBVCABDJAyADQeACaiAKQgAgFkIAEMkDIANB0AJqIApCACAXQgAQyQMgA0HAAmogCkIAIBhCABDJAyADQbABaiADKQPgASIPIAMpA7gCIhIgAykDoAJ8Ig18IhAgAykD+AEgCyADKQPwASIKfCAKVK18fCILIAMpA/ACfCIMQv////++sv3wQn4iCkIAQoGAgIC/sv3wwwBCABDJAyADQaABaiAKQgBCkeHlzYeJ+pkoQgAQyQMgA0GQAWogCkIAQt2whYzotpGouH9CABDJAyADQYABaiAKQgBCqcDGia7Ok7IwQgAQyQMgA0GwA2ogAykD0AoiCkIAIBVCABDJAyADQaADaiAKQgAgFkIAEMkDIANBkANqIApCACAXQgAQyQMgA0GAA2ogCkIAIBhCABDJAyADQfAAaiADKQP4AiALIAxWrXwiEyADKQPgAnwiESADKQOoAiANIBJUrXwiFCADKQOQAnwiEiADKQPQAXwiDSALIBBUrSADKQPoASAPIBBWrXx8fCIZfCIQIAMpA6ABfCILIAMpA7gBIAMpA7ABIgogDHwgClStfHwiDCADKQOwA3wiD0L/////vrL98EJ+IgpCAEKBgICAv7L98MMAQgAQyQMgA0HgAGogCkIAQpHh5c2HifqZKEIAEMkDIANB0ABqIApCAELdsIWM6LaRqLh/QgAQyQMgA0FAayAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwA2ogAykDyAoiCkIAIBVCABDJAyADQeADaiAKQgAgFkIAEMkDIANB0ANqIApCACAXQgAQyQMgA0HAA2ogCkIAIBhCABDJAyADQTBqIAMpA7gDIAwgD1atfCIYIAMpA6ADfCIOIAMpA5gCIBIgFFStfCIUIAMpA4ACfCIVIAMpA8ABfCIWIA0gGVatIAMpA9gBIA0gElStfHx8IhIgAykD0AJ8Ig0gECARVK0gAykD6AIgESATVK18fHwiESADKQOQAXwiFyALIAxWrSADKQOoASALIBBUrXx8fCITfCIQIAMpA2B8IgsgAykDeCADKQNwIgogD3wgClStfHwiDCADKQPwA3wiD0L/////vrL98EJ+IgpCAEKBgICAv7L98MMAQgAQyQMgA0EgaiAKQgBCkeHlzYeJ+pkoQgAQyQMgA0EQaiAKQgBC3bCFjOi2kai4f0IAEMkDIAMgCkIAQqnAxomuzpOyMEIAEMkDAkACQAJAAkAgAykDCCADKQNIIAMpA4gBIBIgFlStIAMpA8gBIBUgFlatfHwgAykDiAIgFCAVVq18fCIVIAMpA8ACfCIKIA0gEVatIAMpA9gCIA0gElStfHx8IhIgAykDgAF8Ig0gElStfCANIBMgF1StIAMpA5gBIBEgF1atfHx8IhEgDVStfCAKIBJWrSADKQPIAiAKIBVUrXx8fCIVIAMpA4ADfCIKIAMpA5gDIBEgESADKQOQA3wiEVatfCARIBEgDiAQVq0gAykDqAMgDiAYVK18fHwiEVatfHwiEiADKQNAfCINIBJUrXwgDSADKQNYIBEgESADKQNQfCIRVq18IBEgCyAMVq0gAykDaCALIBBUrXx8fCILIBFUrXx8IhAgDVStfCAKIBJWrSADKQOIAyAKIBVUrXx8fCISIAMpA8ADfCIRIAMpA9gDIBAgAykD0AN8IgogEFStfCAKIAogAykD6AMgAykD+AMgDCAPVq18IgwgAykD4AN8IhAgDFStfCAQIAsgEHwiEFatfHwiClatfHwiDCADKQMAfCILIAxUrXwgCyALIAMpAxggCiAKIAMpAxB8IgpWrXwgCiAKIAMpAyggECAQIAMpAyB8IhBWrXwgECADKQM4IAMpAzAiDSAPfCANVK18fCINIBBUrXx8IgpWrXx8IgtWrXwgDCARVK0gAykDyAMgESASVK18fHwiDkKpwMaJrs6TsjBWDQAgDkKpwMaJrs6TsjBSDQEgC0LdsIWM6LaRqLh/Vg0AIAtC3bCFjOi2kai4f1IEQCAKIRAgCyEMQqnAxomuzpOyMCEODAQLIApCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8hDCAKQpHh5c2HifqZKFIgDUKBgICAv7L98MMAVHINAgsgCkKR4eXNh4n6mSh9IgwgDUKBgICAv7L98MMAVK0iEX0hECALQqPP+vOXye7XxwB8IhIgCkKR4eXNh4n6mShUIAwgEVRyrSIKfSEMIA4gC0LdsIWM6LaRqLh/VCAKIBJWcq19QqnAxomuzpOyMH0hDiANQoGAgIC/sv3wwwB9IQ0MAgsgCiEQIAshDAwBCyAKIRBCqcDGia7Ok7IwIQ4LIAMgDTcDiAsgAyAQNwOACyADIAw3A/gKIAMgDjcD8AogAEEgaiADQfAKaiABQSBqEMECIABBGGogA0HIEGopAwA3AwAgAEEQaiADQcAQaikDADcDACAAQQhqIANBuBBqKQMANwMAIAAgAykDsBA3AwAgACAHOgBACyADQdAQaiQAC6JGAgd/EX4jAEHQEGsiAyQAAkACQAJAAn8CQAJAAkACQCABLQBAIgcgAi0AQEYEQCABQejRwQBBIBDxA0UEQCABQSBqQejRwQBBIBDxA0UNAgsgAkHo0cEAQSAQ8QNFBEAgAkEgakHo0cEAQSAQ8QNFDQMLAkAgASACQSAQ8QNFBEAgAUEgaiIJIAJBIGpBIBDxA0UNASAAQgA3AwAgACAHOgBAIABBOGpCADcDACAAQTBqQgA3AwAgAEEoakIANwMAIABBIGpCADcDACAAQRhqQgA3AwAgAEEQakIANwMAIABBCGpCADcDAAwKCyABKQMgIg8hDSACKQMgIg4hDAJ+AkAgDiAPUg0AIAEpAygiECACKQMoIgxSBEAgECENDAELIAEpAzAiCiACKQMwIgxSBEAgCiENDAELIBAhEiABKQM4Ig0hCyAKIA0gAikDOCIMUQ0BGgsgDCANVA0FIAEpAyghECACKQMoIRIgASkDMCEKIAEpAzghDSACKQM4IQsgAikDMAsiESAKfSIVIAsgDVStIhZ9IQwgEiAQfSIXIBUgFlQgCiARVnKtIhF9IQogESAXViAQIBJWciEEIA4gD30hDiALIA19IQ0MBwsgA0HwCmoQISAHRQRAIAMpA4ALIRUgAykD+AohFiADKQPwCiEXIANBiAtqDAYLIAMoAqANQQFxDQRB7PbBABDoBAALQYD2wQBBM0Hc9sEAEP4DAAsgACAHOgBAIAAgAikDIDcDICAAIAIpAwA3AwAgAEE4aiACQThqKQMANwMAIABBMGogAkEwaikDADcDACAAQShqIAJBKGopAwA3AwAgAEEIaiACQQhqKQMANwMAIABBEGogAkEQaikDADcDACAAQRhqIAJBGGopAwA3AwAMBgsgACAHOgBAIAAgASkDIDcDICAAIAEpAwA3AwAgAEE4aiABQThqKQMANwMAIABBMGogAUEwaikDADcDACAAQShqIAFBKGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwAMBQtC3bCFjOi2kai4fyABKQMoIhAgAikDKCILfSIRIAEpAzAiCiACKQMwIgxUIAogDH0iCiABKQM4IgwgAikDOCISVK0iDVRyrSIVfSIWfSIXIAogDX0iCkKNlcfDltLawJd/VkKNlcfDltLawJd/IAp9Ig0gDCASfSISQsf688PtgqOQPFatIgxUcq0iGH0hCiAXIBhUIBZC3bCFjOi2kai4f1ZyIQQgDSAMfSEMIBEgFVQgCyAQVnKtIA4gD318QqnAxomuzpOyMHwhDkLH+vPD7YKjkDwgEn0hDQwCCyADKQO4DSEVIAMpA7ANIRYgAykDqA0hFyADQcANagspAwAhGCADQtfRtIWV1fKL+gA3A4gQIANCucPUiq6vsLUfNwOAECADQoSlr8vmyfqlMzcD+A8gA0KOu97wzOjZjyo3A/APIANB4AlqIAEpAxAiEUIAIAEpAxgiEEIAEMkDIANBwAlqIAEpAwgiEkIAIBBCABDJAyADQeAIaiABKQMAIgpCACAQQgAQyQMgA0GwCWogEkIAIBFCABDJAyADQfAIaiAKQgAgEUIAEMkDIANBgAlqIApCACASQgAQyQMgA0GwCmogEEIAIBBCABDJAyADQdAJaiARQgAgEUIAEMkDIANBoAlqIBJCACASQgAQyQMgA0GQCWogCkIAIApCABDJAyADQaAKaiADKQOwCiITQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyADQZAKaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBgApqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HwCWogCkIAQqnAxomuzpOyMEIAEMkDIAMpA4gJIAMpA/gIIAMpA+gIIAMpA8gJIAMpA+gJIgsgAykDwAl8IgogC1StfCIMIAMpA+AIfCILIAxUrXwiDSADKQPwCHwiDCANVK18IAwgDCADKQO4CSALIAsgAykDsAl8IgtWrXx8IgxWrXwiDyADKQOACXwiDSAPVK18Ig9CP4ggAykDmAkgAykDkAkiDiAPQgGGIA1CP4iEfCIPIA5UrXwgDyAPIAMpA6gJIAMpA9gJIAMpA9AJIhQgCkIBhiADKQPgCSIZQj+IhHwiDiAUVK18IA4gAykDuAoiFCAZQgGGfCIZIBRUrXwiFCAOVK18Ig4gC0IBhiAKQj+IhHwiGiAOVK0iDiADKQOgCXwiCiAOVK18IAogDEIBhiALQj+IhHwiCyAKVK18IgogDUIBhiAMQj+IhHwiDCAKVK18Ig9WrXx8IQ0CfwJAIAMpA/gJIAMpA4gKIAMpA5gKIAMpA6gKIAMpA6AKIgogE0J9g3wgClStfCIOIAMpA5AKfCIKIA5UrXwgCiAZfCIOIApUrXwiEyADKQOACnwiCiATVK18IAogFHwiEyAKVK18IhQgAykD8Al8IgogFFStfCAKIBp8IhQgClStfCIKUA0AIAogC3wiCyAKVCIERQ0AIAStIgogDHwiDCAKWg0AIAogDFatIgogD3wiDyAKWg0AIAogD1atIgogDXwiDSAKVAwBC0EACyEEIANB0AhqIA5CiceZpK7wgemHf34iCkIAQsf688PtgqOQPEIAEMkDIANBwAhqIApCAEKNlcfDltLawJd/QgAQyQMgA0GwCGogCkIAQt2whYzotpGouH9CABDJAyADQaAIaiAKQgBCqcDGia7Ok7IwQgAQyQMCQCADKQOoCCADKQO4CCADKQPICCADKQPYCCADKQPQCCIKIA58IApUrXwiDiADKQPACHwiCiAOVK18IAogE3wiDiAKVK18IhMgAykDsAh8IgogE1StfCAKIBR8IhMgClStfCIUIAMpA6AIfCIKIBRUrXwgCiALfCIUIApUrXwiClANACAKIAx8IgwgCloNACAKIAxWrSIKIA98Ig8gCloNACAKIA9WrSIKIA18Ig0gClQhBgsgA0GQCGogDkKJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgA0GACGogCkIAQo2Vx8OW0trAl39CABDJAyADQfAHaiAKQgBC3bCFjOi2kai4f0IAEMkDIANB4AdqIApCAEKpwMaJrs6TsjBCABDJAyADKQPoByADKQP4ByADKQOICCADKQOYCCADKQOQCCIKIA58IApUrXwiCyADKQOACHwiCiALVK18IAogE3wiCyAKVK18Ig4gAykD8Ad8IgogDlStfCAKIBR8Ig4gClStfCITIAMpA+AHfCIKIBNUrXwgCiAMfCIMIApUrXwiClBFBEAgCiAPfCIPIApUIgWtIgogDXwiEyANIAUbIQ0gBSAKIBNWcSEFCyADQdAHaiALQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyADQcAHaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBsAdqIApCAELdsIWM6LaRqLh/QgAQyQMgA0GgB2ogCkIAQqnAxomuzpOyMEIAEMkDIAMpA6gHIAMpA7gHIAMpA8gHIAMpA9gHIAMpA9AHIgogC3wgClStfCILIAMpA8AHfCIKIAtUrXwgCiAOfCIOIApUrXwiCyADKQOwB3wiCiALVK18IAogDHwiCyAKVK18IgwgAykDoAd8IgogDFStfCAKIA98IgwgClStfCIKIA18Ig8gDSAKQgBSIggbIQ0CQAJAAkAgBCAGciAFciAKIA9WIgStIAogCBtCAFJyIAQgCHEgDUKpwMaJrs6TsjBWcnINACANQqnAxomuzpOyMFIEQCALIQoMAwsgDELdsIWM6LaRqLh/Vg0AIAxC3bCFjOi2kai4f1IEQCALIQoMAwtC3bCFjOi2kai4fyEPIAtCjZXHw5bS2sCXf1YNASALQo2Vx8OW0trAl39SBEAgCyEKDAMLIA5Cxvrzw+2Co5A8Vg0BIAshCgwCCyAMIQ8LIAtC8+q4vOmtpb/oAHwiDCAOQsf688PtgqOQPFStIhN9IQogD0Kjz/rzl8nu18cAfCIUIAtCjZXHw5bS2sCXf1QgDCATVHKtIgt9IQwgDSAPQt2whYzotpGouH9UIAsgFFZyrX1CqcDGia7Ok7IwfSENIA5Cx/rzw+2Co5A8fSEOCyADIA43A8gQIAMgCjcDwBAgAyAMNwO4ECADIA03A7AQIANB0A9qIANB8A9qIANBsBBqEH5CqcDGia7Ok7IwIQogAykD2A8iDCAWfCILIAxUIAsgAykD4A8iDSAVfCIMIA1UIAwgDCADKQPoDyINIBh8Ig4gDVStfCIMVnKtfCIPIAtUcq0gAykD0A8gF3x8Ig0hCwJAAkACQCANQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IQogDyILQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEKIAwiC0KNlcfDltLawJd/Ug0AQsf688PtgqOQPCEKIA4iC0LH+vPD7YKjkDxRDQELIAogC1gNACAPIQogDCELDAELIAxC8+q4vOmtpb/oAHwiCiAOQsf688PtgqOQPFStIhV9IQsgD0Kjz/rzl8nu18cAfCIWIAxCjZXHw5bS2sCXf1QgCiAVVHKtIgx9IQogDSAPQt2whYzotpGouH9UIAwgFlZyrX1CqcDGia7Ok7IwfSENIA5Cx/rzw+2Co5A8fSEOCyADIA43A8gPIAMgCzcDwA8gAyAKNwO4DyADIA03A7APIANCurb42Ljjod2mfzcDyBAgA0L7rLjcnsr1+BQ3A8AQIANC2JjKh+/b0e5MNwO4ECADQt78vqCz8LuKHDcDsBAgA0GQEGoiBSADQbAQaiAJEH4gA0HICmogA0GwD2ogBRBbIAMoApwPIgQEQCADKAKgDyAEQQJ0EN8ECwJAIAMoAtQMIgRFDQAgBCAEQQxsQRNqQXhxIgZqQQlqIgRFDQAgAygC0AwgBmsgBBDfBAsgAygCgA0iBEGAgICAeEYgBEVyDQEgAygChA0gBEECdBDfBAwBCyADIA03A8gQIAMgDDcDwBAgAyAKNwO4ECADIA4gBK19NwOwECABKQMAIg0hECACKQMAIg4hDyADAn4CQAJ+AkAgDSAOUg0AIAEpAwgiEiACKQMIIg9SBEAgEiEQDAELIAEpAxAiESACKQMQIg9SBEAgESEQDAELIBEhDCABKQMYIhAhCyASIBAgAikDGCIPUQ0BGgsgDyAQVA0BIAEpAwghEiABKQMQIREgAikDECEMIAEpAxghECACKQMYIQsgAikDCAshCiAMIBF9IhUgCyAQVK0iFn0hDyAKIBJ9IhcgDCARVCAVIBZUcq0iFX0hDCAKIBJUIBUgF1ZyIQQgDiANfSENIAsgEH0MAQtC3bCFjOi2kai4fyABKQMIIhIgAikDCCIKfSILIAEpAxAiESACKQMQIhBUIBEgEH0iDCABKQMYIhAgAikDGCIPVK0iFVRyrSIWfSIXfSIYIAwgFX0iDEKNlcfDltLawJd/VkKNlcfDltLawJd/IAx9IhUgECAPfSITQsf688PtgqOQPFatIg9Ucq0iFH0hDCAUIBhWIBdC3bCFjOi2kai4f1ZyIQQgFSAPfSEPIAsgFlQgCiASVnKtIA4gDX18QqnAxomuzpOyMHwhDULH+vPD7YKjkDwgE30LNwOICyADIA83A4ALIAMgDDcD+AogAyANIAStfTcD8AogA0HICmogA0GwEGogA0HwCmoQWwsgAygCyAoEQCADIAMpA9gKNwP4CiADIAMpA9AKNwPwCkGM98EAQSsgA0HwCmpB/PbBAEG498EAEMoDAAsgA0GwBmogAykD6AoiFUIAIAMpA+AKIhZCABDJAyADQaAGaiAVQgAgAykD2AoiF0IAEMkDIANBkAZqIBVCACADKQPQCiIYQgAQyQMgA0HgBmogFkIAIBdCABDJAyADQdAGaiAWQgAgGEIAEMkDIANBgAdqIBdCACAYQgAQyQMgA0GABmogFUIAIBVCABDJAyADQcAGaiAWQgAgFkIAEMkDIANB8AZqIBdCACAXQgAQyQMgA0GQB2ogGEIAIBhCABDJAyADQfAFaiADKQOABiITQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyADQeAFaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0AVqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HABWogCkIAQqnAxomuzpOyMEIAEMkDIAMpA4gHIAMpA9gGIAMpA5gGIAMpA6gGIAMpA7gGIgsgAykDoAZ8IgogC1StfCIMIAMpA5AGfCILIAxUrXwiDSADKQPQBnwiDCANVK18IAwgDCADKQPoBiALIAsgAykD4AZ8IgtWrXx8IgxWrXwiDyADKQOAB3wiDSAPVK18Ig9CP4ggAykDmAcgAykDkAciDiAPQgGGIA1CP4iEfCIPIA5UrXwgDyAPIAMpA/gGIAMpA8gGIAMpA8AGIhQgCkIBhiADKQOwBiIZQj+IhHwiDiAUVK18IA4gAykDiAYiFCAZQgGGfCIZIBRUrXwiFCAOVK18Ig4gC0IBhiAKQj+IhHwiGiAOVK0iDiADKQPwBnwiCiAOVK18IAogDEIBhiALQj+IhHwiDiAKVK18IgogDUIBhiAMQj+IhHwiDCAKVK18Ig9WrXx8IQpBACEFAn8CQCADKQPIBSADKQPYBSADKQPoBSADKQP4BSATIAMpA/AFIgt8IAtUrXwiDSADKQPgBXwiCyANVK18IAsgGXwiDSALVK18IhMgAykD0AV8IgsgE1StfCALIBR8IhMgC1StfCIUIAMpA8AFfCILIBRUrXwgCyAafCIUIAtUrXwiC1ANACALIA58Ig4gC1QiBEUNACAErSILIAx8IgwgC1oNACALIAxWrSILIA98Ig8gC1oNACALIA9WrSILIAp8IgogC1QMAQtBAAshBiADQbAFaiANQonHmaSu8IHph39+IgtCAELH+vPD7YKjkDxCABDJAyADQaAFaiALQgBCjZXHw5bS2sCXf0IAEMkDIANBkAVqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0GABWogC0IAQqnAxomuzpOyMEIAEMkDAkAgAykDiAUgAykDmAUgAykDqAUgAykDuAUgAykDsAUiCyANfCALVK18Ig0gAykDoAV8IgsgDVStfCALIBN8Ig0gC1StfCITIAMpA5AFfCILIBNUrXwgCyAUfCITIAtUrXwiFCADKQOABXwiCyAUVK18IAsgDnwiDiALVK18IgtQDQAgCyAMfCIMIAtaDQAgCyAMVq0iCyAPfCIPIAtaDQAgCyAPVq0iCyAKfCIKIAtUIQULIANB8ARqIA1CiceZpK7wgemHf34iC0IAQsf688PtgqOQPEIAEMkDIANB4ARqIAtCAEKNlcfDltLawJd/QgAQyQMgA0HQBGogC0IAQt2whYzotpGouH9CABDJAyADQcAEaiALQgBCqcDGia7Ok7IwQgAQyQNBACEEIAMpA8gEIAMpA9gEIAMpA+gEIAMpA/gEIAMpA/AEIgsgDXwgC1StfCINIAMpA+AEfCILIA1UrXwgCyATfCINIAtUrXwiEyADKQPQBHwiCyATVK18IAsgDnwiDiALVK18IhMgAykDwAR8IgsgE1StfCALIAx8IhMgC1StfCILUEUEQCALIA98Ig8gC1QiBK0iCyAKfCIMIAogBBshCiAEIAsgDFZxIQQLIANBsARqIA1CiceZpK7wgemHf34iC0IAQsf688PtgqOQPEIAEMkDIANBoARqIAtCAEKNlcfDltLawJd/QgAQyQMgA0GQBGogC0IAQt2whYzotpGouH9CABDJAyADQYAEaiALQgBCqcDGia7Ok7IwQgAQyQMgAykDiAQgAykDmAQgAykDqAQgAykDuAQgAykDsAQiCyANfCALVK18IgwgAykDoAR8IgsgDFStfCALIAsgDnwiC1atfCINIAMpA5AEfCIMIA1UrXwgDCATfCINIAxUrXwiDiADKQOABHwiDCAOVK18IAwgD3wiDiAMVK18IgwgCnwiDyAKIAxCAFIiCBshCgJAAkACQAJAIAUgBnIgBHIgDCAPViIErSAMIAgbQgBSciAEIAhxIApCqcDGia7Ok7IwVnJyDQAgCkKpwMaJrs6TsjBSDQEgDkLdsIWM6LaRqLh/Vg0AIA5C3bCFjOi2kai4f1IEQCANIQwgDiEPQqnAxomuzpOyMCEKDAQLQt2whYzotpGouH8hDiANQo2Vx8OW0trAl39WDQAgDUKNlcfDltLawJd/UiALQsb688PtgqOQPFhyDQILIA1C8+q4vOmtpb/oAHwiDyALQsf688PtgqOQPFStIhN9IQwgDkKjz/rzl8nu18cAfCIUIA1CjZXHw5bS2sCXf1QgDyATVHKtIg19IQ8gCiAOQt2whYzotpGouH9UIA0gFFZyrX1CqcDGia7Ok7IwfSEKIAtCx/rzw+2Co5A8fSELDAILIA0hDCAOIQ8MAQsgDSEMQt2whYzotpGouH8hD0KpwMaJrs6TsjAhCgsgASkDACITIQ4gCiENAn4CQAJAIAogE1INACASIg4gDyINUg0AIAwhDSAMIBEiDlINACALIQ0gCyAQIg5RDQELIA0gDloNAELdsIWM6LaRqLh/IBIgD30iDSAMIBFWIBEgDH0iDCALIBBWrSIRVHKtIhR9Ig59IhkgDCARfSIMQo2Vx8OW0trAl39WQo2Vx8OW0trAl38gDH0iDCAQIAt9IhBCx/rzw+2Co5A8Vq0iC1RyrSIafSERIBkgGlQgDkLdsIWM6LaRqLh/VnIhBCAMIAt9IQ5Cx/rzw+2Co5A8IBB9IRAgDSAUVCAPIBJWcq0gCiATfXxCqcDGia7Ok7IwfAwBCyAMIBF9Ig0gCyAQVK0iFH0hDiAPIBJ9IhkgDSAUVCAMIBFUcq0iDH0hESAPIBJUIAwgGVZyIQQgCyAQfSEQIAogE30LIQogAyAQNwOICyADIA43A4ALIAMgETcD+AogAyAKIAStfTcD8AogA0GwEGoiBCADQfAKaiIFIAIQwgIgA0GIC2ogAUEYaikDADcDACADQYALaiABQRBqKQMANwMAIANB+ApqIAFBCGopAwA3AwAgAyABKQMANwPwCiADQcgKaiAFIAQQwgIgA0GwAmogAykD4AoiCkIAIBVCABDJAyADQaACaiAKQgAgFkIAEMkDIANBkAJqIApCACAXQgAQyQMgA0GAAmogCkIAIBhCABDJAyADQfABaiADKQOwAiILQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyADQeABaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0AFqIApCAELdsIWM6LaRqLh/QgAQyQMgA0HAAWogCkIAQqnAxomuzpOyMEIAEMkDIANB8AJqIAMpA9gKIgpCACAVQgAQyQMgA0HgAmogCkIAIBZCABDJAyADQdACaiAKQgAgF0IAEMkDIANBwAJqIApCACAYQgAQyQMgA0GwAWogAykD4AEiDyADKQO4AiISIAMpA6ACfCINfCIQIAMpA/gBIAsgAykD8AEiCnwgClStfHwiCyADKQPwAnwiDEKJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgA0GgAWogCkIAQo2Vx8OW0trAl39CABDJAyADQZABaiAKQgBC3bCFjOi2kai4f0IAEMkDIANBgAFqIApCAEKpwMaJrs6TsjBCABDJAyADQbADaiADKQPQCiIKQgAgFUIAEMkDIANBoANqIApCACAWQgAQyQMgA0GQA2ogCkIAIBdCABDJAyADQYADaiAKQgAgGEIAEMkDIANB8ABqIAMpA/gCIAsgDFatfCITIAMpA+ACfCIRIAMpA6gCIA0gElStfCIUIAMpA5ACfCISIAMpA9ABfCINIAsgEFStIAMpA+gBIA8gEFatfHx8Ihl8IhAgAykDoAF8IgsgAykDuAEgAykDsAEiCiAMfCAKVK18fCIMIAMpA7ADfCIPQonHmaSu8IHph39+IgpCAELH+vPD7YKjkDxCABDJAyADQeAAaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANB0ABqIApCAELdsIWM6LaRqLh/QgAQyQMgA0FAayAKQgBCqcDGia7Ok7IwQgAQyQMgA0HwA2ogAykDyAoiCkIAIBVCABDJAyADQeADaiAKQgAgFkIAEMkDIANB0ANqIApCACAXQgAQyQMgA0HAA2ogCkIAIBhCABDJAyADQTBqIAMpA7gDIAwgD1atfCIYIAMpA6ADfCIOIAMpA5gCIBIgFFStfCIUIAMpA4ACfCIVIAMpA8ABfCIWIA0gGVatIAMpA9gBIA0gElStfHx8IhIgAykD0AJ8Ig0gECARVK0gAykD6AIgESATVK18fHwiESADKQOQAXwiFyALIAxWrSADKQOoASALIBBUrXx8fCITfCIQIAMpA2B8IgsgAykDeCADKQNwIgogD3wgClStfHwiDCADKQPwA3wiD0KJx5mkrvCB6Yd/fiIKQgBCx/rzw+2Co5A8QgAQyQMgA0EgaiAKQgBCjZXHw5bS2sCXf0IAEMkDIANBEGogCkIAQt2whYzotpGouH9CABDJAyADIApCAEKpwMaJrs6TsjBCABDJAwJAAkACQAJAIAMpAwggAykDSCADKQOIASASIBZUrSADKQPIASAVIBZWrXx8IAMpA4gCIBQgFVatfHwiFSADKQPAAnwiCiANIBFWrSADKQPYAiANIBJUrXx8fCISIAMpA4ABfCINIBJUrXwgDSATIBdUrSADKQOYASARIBdWrXx8fCIRIA1UrXwgCiASVq0gAykDyAIgCiAVVK18fHwiFSADKQOAA3wiCiADKQOYAyARIBEgAykDkAN8IhFWrXwgESARIA4gEFatIAMpA6gDIA4gGFStfHx8IhFWrXx8IhIgAykDQHwiDSASVK18IA0gAykDWCARIBEgAykDUHwiEVatfCARIAsgDFatIAMpA2ggCyAQVK18fHwiCyARVK18fCIQIA1UrXwgCiASVq0gAykDiAMgCiAVVK18fHwiEiADKQPAA3wiESADKQPYAyAQIAMpA9ADfCIKIBBUrXwgCiAKIAMpA+gDIAMpA/gDIAwgD1atfCIMIAMpA+ADfCIQIAxUrXwgECALIBB8IhBWrXx8IgpWrXx8IgwgAykDAHwiCyAMVK18IAsgCyADKQMYIAogCiADKQMQfCIKVq18IAogCiADKQMoIBAgECADKQMgfCIQVq18IBAgAykDOCADKQMwIg0gD3wgDVStfHwiDSAQVK18fCIKVq18fCILVq18IAwgEVStIAMpA8gDIBEgElStfHx8Ig5CqcDGia7Ok7IwVg0AIA5CqcDGia7Ok7IwUg0BIAtC3bCFjOi2kai4f1YNACALQt2whYzotpGouH9SBEAgCiEQIAshDEKpwMaJrs6TsjAhDgwECyAKQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEMIApCjZXHw5bS2sCXf1IgDULH+vPD7YKjkDxUcg0CCyAKQvPquLzpraW/6AB8IgwgDULH+vPD7YKjkDxUrSIRfSEQIAtCo8/685fJ7tfHAHwiEiAKQo2Vx8OW0trAl39UIAwgEVRyrSIKfSEMIA4gC0LdsIWM6LaRqLh/VCAKIBJWcq19QqnAxomuzpOyMH0hDiANQsf688PtgqOQPH0hDQwCCyAKIRAgCyEMDAELIAohEEKpwMaJrs6TsjAhDgsgAyANNwOICyADIBA3A4ALIAMgDDcD+AogAyAONwPwCiAAQSBqIANB8ApqIAFBIGoQwgIgAEEYaiADQcgQaikDADcDACAAQRBqIANBwBBqKQMANwMAIABBCGogA0G4EGopAwA3AwAgACADKQOwEDcDACAAIAc6AEALIANB0BBqJAALgPYDAkx/EH4jAEGgB2siCSQAAkACQAJAAkACQAJAAkAgAkEBSwRAIAIgA0kNASAJQeACahAhIAktAJgHIUogCSgCjAciCARAIAkoApAHIAhBAnQQ3wQLAkAgCSgCxAQiCEUNACAIIAhBDGxBE2pBeHEiB2pBCWoiCEUNACAJKALABCAHayAIEN8ECyAJKALwBCIIQYCAgIB4RiAIRXJFBEAgCSgC9AQgCEECdBDfBAsCQCAELQDAAUECRwRAIAlB4AJqIARBgAFqQQEgBEEBEEIgCUEQaiAJQegCaikCADcDACAJIAkpAuACNwMIDAELIAlBgICAgHg2AggLIAlBADYCQCAJQoCAgICAATcCOCAJQQA2AjAgCUKAgICAgAE3AiggAkHIAWwhFSAJQfgBaiE5IAlBgANqIScgCUHoAGohDgNAIAlB4ABqIgogASAMaiIiQZgBaikDADcDACAJQdgAaiIHICJBkAFqKQMANwMAIAlB0ABqIgggIkGIAWopAwA3AwAgDiAiQaABaikDADcDACAOQQhqICJBqAFqKQMANwMAIA5BEGogIkGwAWopAwA3AwAgDkEYaiAiQbgBaikDADcDACAJICJBgAFqKQMANwNIICJBwAFqLQAAIQQgCSgCQCILIAkoAjhGBEAgCUE4akGIjsEAEJoDCyAJKAI8IAtByABsaiINIAkpA0g3AwAgDSAEOgBAIA1BCGogCCkDADcDACANQRBqIAcpAwA3AwAgDUEYaiAKKQMANwMAIA1BIGogDikDADcDACANQShqIAlB8ABqKQMANwMAIA1BMGogCUH4AGopAwA3AwAgDUE4aiAJQYABaikDADcDACAJIAtBAWo2AkAgJyAiQSBqKQMANwMAICdBCGoiDSAiQShqKQMANwMAICdBEGoiCyAiQTBqKQMANwMAICdBGGoiCiAiQThqKQMANwMAIAlBwAFqICJBCGopAwA3AwAgCUHIAWogIkEQaikDADcDACAJQdABaiAiQRhqKQMANwMAIAlB2AFqICcpAwA3AwAgCUHgAWogCUGIA2oiBykDADcDACAJQegBaiAJQZADaiIIKQMANwMAIAlB8AFqIAlBmANqIgQpAwA3AwAgCSAiKQMANwO4ASAnICJB4ABqKQMANwMAIA0gIkHoAGopAwA3AwAgCyAiQfAAaikDADcDACAKICJB+ABqKQMANwMAIDkgIkFAaykDADcDACA5QQhqICJByABqKQMANwMAIDlBEGogIkHQAGopAwA3AwAgOUEYaiAiQdgAaikDADcDACA5QSBqICcpAwA3AwAgOUEoaiAHKQMANwMAIDlBMGogCCkDADcDACA5QThqIAQpAwA3AwAgCSgCMCIEIAkoAihGBEAgCUEoakGYjsEAEKQDCyAJKAIsIjMgBEEHdGogCUG4AWpBgAH8CgAAIAkgBEEBaiIENgIwIBUgDEHIAWoiDEcNAAsgCUHgAmohPiAJKAI8IQcgCSgCQCE/IAlBCGohRSMAQbAYayIFJAAgBSA/NgIQIAUgBDYCDAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIAQgP0YEQCAFQbATaiIIIAcgPxBwIAUoAsQTITogBSgCwBMhOSAFKAK8EyFOIAUoArgTITsgBSgCtBMhJyAFKAKwEyFPIAVBEGoQISAFQQA2AuAEIAVCgICAgMAANwLYBCAFQQA2AuwEIAVCgICAgMAANwLkBCA/QQFNDQEgBUHgCGoiBCAHID8gMyA/EEIgCCAEEPcBIAVBoBhqIAUoArQTIgggBSgCuBMQGCAFKAKwEyIEBEAgCCAEQQV0EN8ECwJ/IEUoAgAiUEGAgICAeEcEQCAFQbATaiBFEPcBIAVB8ARqIAUoArQTIgggBSgCuBMQGCAFKAKwEyIEBEAgCCAEQQV0EN8ECyAFKAKkGCEHIAUoAvQEIS8gBSgC+AQhCCAFKAKoGCEEIAVBDDYClBggBSAENgLwDiAEQQxHDQQgBSAINgLwDiAIQQxHDQVB0c7FAC0AABpBgANBCBDWBCIIRQ0JIAggBykDADcDACAIQRhqIAdBGGopAwA3AwAgCEEQaiAHQRBqKQMANwMAIAhBCGoiBCAHQQhqKQMANwMAIAhBOGogB0E4aikDADcDACAIQTBqIAdBMGopAwA3AwAgCEEoaiAHQShqKQMANwMAIAggBykDIDcDICAIIAcpA0A3A0AgCEHIAGogB0HIAGopAwA3AwAgCEHQAGogB0HQAGopAwA3AwAgCEHYAGogB0HYAGopAwA3AwAgCCAHKQNgNwNgIAhB6ABqIAdB6ABqKQMANwMAIAhB8ABqIAdB8ABqKQMANwMAIAhB+ABqIAdB+ABqKQMANwMAIAggBykDgAE3A4ABIAhBiAFqIAdBiAFqKQMANwMAIAhBkAFqIAdBkAFqKQMANwMAIAhBmAFqIAdBmAFqKQMANwMAIAggBykDoAE3A6ABIAhBqAFqIAdBqAFqKQMANwMAIAhBsAFqIAdBsAFqKQMANwMAIAhBuAFqIAdBuAFqKQMANwMAIAggBykDwAE3A8ABIAhByAFqIAdByAFqKQMANwMAIAhB2AFqIAdB2AFqKQMANwMAIAhB0AFqIAdB0AFqKQMANwMAIAggBykD4AE3A+ABIAhB6AFqIAdB6AFqKQMANwMAIAhB8AFqIAdB8AFqKQMANwMAIAhB+AFqIAdB+AFqKQMANwMAIAggBykDgAI3A4ACIAhBiAJqIAdBiAJqKQMANwMAIAhBkAJqIAdBkAJqKQMANwMAIAhBmAJqIAdBmAJqKQMANwMAIAggBykDoAI3A6ACIAhBqAJqIAdBqAJqKQMANwMAIAhBsAJqIAdBsAJqKQMANwMAIAhBuAJqIAdBuAJqKQMANwMAIAhB2AJqIAdB2AJqKQMANwMAIAhB0AJqIAdB0AJqKQMANwMAIAhByAJqIAdByAJqKQMANwMAIAggBykDwAI3A8ACIAggBykD4AI3A+ACIAhB6AJqIAdB6AJqKQMANwMAIAhB+AJqIAdB+AJqKQMANwMAIAhB8AJqIAdB8AJqKQMANwMAIAgpAwAhUSAFQbATaiIeIARB+AL8CgAAIAhBgAMQ3wQgBUGYD2ogBUHQE2opAwA3AwAgBUGgD2ogBUHYE2oiLSkDADcDACAFQagPaiAFQeATaiIoKQMANwMAIAVB+AhqIksgBUHwE2opAwA3AwAgBUGACWoiNCAFQfgTaiIxKQMANwMAIAVBiAlqIjUgBUGAFGoiMikDADcDACAFIAUpA8gTNwOQDyAFIAUpA+gTNwPwCCAFQZAJaiI3IAUpA4gUNwMAIAVBmAlqIjggBUGQFGoiDykDADcDACAFQaAJaiI8IAVBmBRqIh8pAwA3AwAgBUGoCWoiPSAFQaAUaiIWKQMANwMAIAVBiAxqIioiCCAFQcAUaiIgKQMANwMAIAVBgAxqIkYgBUG4FGoiJCkDADcDACAFQfgLaiJHIAVBsBRqKQMANwMAIAUgBSkDqBQ3A/ALIAVBqAxqIisiBCAFQeAUaiINKQMANwMAIAVBoAxqIkggBUHYFGoiDCkDADcDACAFQZgMaiJJIAVB0BRqIgspAwA3AwAgBUGQDGoiBiAFKQPIFDcDACAFQYgPaiAFQcATaiIKKQMANwMAIAVBgA9qIAVBuBNqKQMANwMAIAUgBSkDsBM3A/gOIAVB6A9qID0pAwA3AwAgBUHgD2ogPCkDADcDACAFQdgPaiA4KQMANwMAIAVB0A9qIDcpAwA3AwAgBUHID2ogNSkDADcDACAFQcAPaiA0KQMANwMAIAVBuA9qIEspAwA3AwAgBSAFKQPwCDcDsA8gBUGoEGogBCkDADcDACAFQaAQaiBIKQMANwMAIAVBmBBqIEkpAwA3AwAgBUGQEGogBikDADcDACAFQYgQaiAIKQMANwMAIAVBgBBqIEYpAwA3AwAgBUH4D2ogRykDADcDACAFIAUpA/ALNwPwDyAFQegSaiIdIAVBoBVqKQMANwMAIAVB4BJqIkwgBUGYFWopAwA3AwAgBUHYEmoiLCAFQZAVaikDADcDACAFQdASaiIhIAUpA4gVNwMAIAVB+BJqIjAgBUGwFWopAwA3AwAgBUGAE2oiNiAFQbgVaikDADcDACAFQYgTaiJAIAVBwBVqKQMANwMAIAUgBSkDqBU3A/ASIAVBkBNqIkEgBSkDyBU3AwAgBUGYE2oiQiAFQdAVaikDADcDACAFQaATaiJDIAVB2BVqKQMANwMAIAVBqBNqIkQgBUHgFWopAwA3AwAgNSAFQYAWaikDADcDACA0IAVB+BVqKQMANwMAIEsgBUHwFWopAwA3AwAgBSAFKQPoFTcD8AggPSAFQaAWaikDADcDACA8IAVBmBZqKQMANwMAIDggBUGQFmopAwA3AwAgNyAFKQOIFjcDACAFQcgSaiITIAVBgBVqKQMANwMAIAVBwBJqIhcgBUH4FGopAwA3AwAgBUG4EmoiFCAFQfAUaiIRKQMANwMAIAUgBSkD6BQ3A7ASIAQgHSkDADcDACBIIEwpAwA3AwAgSSAsKQMANwMAIAYgISkDADcDACAIIBMpAwA3AwAgRiAXKQMANwMAIEcgFCkDADcDACAFIAUpA7ASNwPwCyAFQegMaiIQIEQpAwA3AwAgBUHgDGoiJSBDKQMANwMAIAVB2AxqIikgQikDADcDACAFQdAMaiIHIEEpAwA3AwAgBUHIDGoiIiBAKQMANwMAIAVBwAxqIiMgNikDADcDACAFQbgMaiIbIDApAwA3AwAgBSAFKQPwEjcDsAwgBUGoDWoiDiA9KQMANwMAIAVBoA1qIhwgPCkDADcDACAFQZgNaiIZIDgpAwA3AwAgBUGQDWoiCCA3KQMANwMAIAVBiA1qIhUgNSkDADcDACAFQYANaiImIDQpAwA3AwAgBUH4DGoiGCBLKQMANwMAIAUgBSkD8Ag3A/AMIAUgUTcD8A4gBUGwEGogBUHwC2oiGkHAAfwKAABB0c7FAC0AABpBgANBCBDWBCIuRQ0JIC4gLykDADcDACAuQRhqIC9BGGopAwA3AwAgLkEQaiAvQRBqKQMANwMAIC5BCGoiBCAvQQhqKQMANwMAIC5BOGogL0E4aikDADcDACAuQTBqIC9BMGopAwA3AwAgLkEoaiAvQShqKQMANwMAIC4gLykDIDcDICAuIC8pA0A3A0AgLkHIAGogL0HIAGopAwA3AwAgLkHQAGogL0HQAGopAwA3AwAgLkHYAGogL0HYAGopAwA3AwAgLiAvKQNgNwNgIC5B6ABqIC9B6ABqKQMANwMAIC5B8ABqIC9B8ABqKQMANwMAIC5B+ABqIC9B+ABqKQMANwMAIC4gLykDgAE3A4ABIC5BiAFqIC9BiAFqKQMANwMAIC5BkAFqIC9BkAFqKQMANwMAIC5BmAFqIC9BmAFqKQMANwMAIC4gLykDoAE3A6ABIC5BqAFqIC9BqAFqKQMANwMAIC5BsAFqIC9BsAFqKQMANwMAIC5BuAFqIC9BuAFqKQMANwMAIC4gLykDwAE3A8ABIC5ByAFqIC9ByAFqKQMANwMAIC5B2AFqIC9B2AFqKQMANwMAIC5B0AFqIC9B0AFqKQMANwMAIC4gLykD4AE3A+ABIC5B6AFqIC9B6AFqKQMANwMAIC5B8AFqIC9B8AFqKQMANwMAIC5B+AFqIC9B+AFqKQMANwMAIC4gLykDgAI3A4ACIC5BiAJqIC9BiAJqKQMANwMAIC5BkAJqIC9BkAJqKQMANwMAIC5BmAJqIC9BmAJqKQMANwMAIC4gLykDoAI3A6ACIC5BqAJqIC9BqAJqKQMANwMAIC5BsAJqIC9BsAJqKQMANwMAIC5BuAJqIC9BuAJqKQMANwMAIC5B2AJqIC9B2AJqKQMANwMAIC5B0AJqIC9B0AJqKQMANwMAIC5ByAJqIC9ByAJqKQMANwMAIC4gLykDwAI3A8ACIC4gLykD4AI3A+ACIC5B6AJqIC9B6AJqKQMANwMAIC5B+AJqIC9B+AJqKQMANwMAIC5B8AJqIC9B8AJqKQMANwMAIC4pAwAhUSAaIARB+AL8CgAAIC5BgAMQ3wQgLSAGKQMANwMAICggSSkDADcDACAFQegTaiBIKQMANwMAIDAgBUGwDGopAwA3AwAgNiAbKQMANwMAIEAgIykDADcDACAFIAUpA4gMNwPQEyAFIAUpA6gMNwPwEiBBIAUpA8gMNwMAIEIgBykDADcDACBDICkpAwA3AwAgRCAlKQMANwMAIDUgJikDADcDACA0IBgpAwA3AwAgSyAFQfAMaikDADcDACAFIAUpA+gMNwPwCCA9IBwpAwA3AwAgPCAZKQMANwMAIDggCCkDADcDACA3IAUpA4gNNwMAIAVByBNqIEYpAwA3AwAgCiBHKQMANwMAIAUgBSkD8As3A7gTIAVBqBRqIEQpAwA3AwAgFiBDKQMANwMAIB8gQikDADcDACAPIEEpAwA3AwAgBUGIFGogQCkDADcDACAyIDYpAwA3AwAgMSAwKQMANwMAIAUgBSkD8BI3A/ATIAVB6BRqID0pAwA3AwAgDSA8KQMANwMAIAwgOCkDADcDACALIDcpAwA3AwAgBUHIFGogNSkDADcDACAgIDQpAwA3AwAgJCBLKQMANwMAIAUgBSkD8Ag3A7AUIAVBqBJqIg0gBUHgDWopAwA3AwAgBUGgEmoiDCAFQdgNaikDADcDACAFQZgSaiILIAVB0A1qKQMANwMAIAVBkBJqIgogBSkDyA03AwAgFCAFQfANaikDADcDACAXIAVB+A1qKQMANwMAIBMgBUGADmopAwA3AwAgBSAFKQPoDTcDsBIgISAFKQOIDjcDACAsIAVBkA5qKQMANwMAIEwgBUGYDmopAwA3AwAgHSAFQaAOaikDADcDACBAIAVBwA5qKQMANwMAIDYgBUG4DmopAwA3AwAgMCAFQbAOaikDADcDACAFIAUpA6gONwPwEiBEIAVB4A5qKQMANwMAIEMgBUHYDmopAwA3AwAgQiAFQdAOaikDADcDACBBIAUpA8gONwMAIAVBiBJqIgcgBUHADWopAwA3AwAgBUGAEmoiCCAFQbgNaikDADcDACAFQfgRaiIEIAVBsA1qKQMANwMAIAUgBSkDqA03A/ARID0gDSkDADcDACA8IAwpAwA3AwAgOCALKQMANwMAIDcgCikDADcDACA1IAcpAwA3AwAgNCAIKQMANwMAIEsgBCkDADcDACAFIAUpA/ARNwPwCCAFQegJaiAdKQMANwMAIAVB4AlqIEwpAwA3AwAgBUHYCWogLCkDADcDACAFQdAJaiAhKQMANwMAIAVByAlqIBMpAwA3AwAgBUHACWogFykDADcDACAFQbgJaiAUKQMANwMAIAUgBSkDsBI3A7AJIAVBqApqIEQpAwA3AwAgBUGgCmogQykDADcDACAFQZgKaiBCKQMANwMAIAVBkApqIEEpAwA3AwAgBUGICmogQCkDADcDACAFQYAKaiA2KQMANwMAIAVB+AlqIDApAwA3AwAgBSAFKQPwEjcD8AkgBSBRNwOwEyARIAVB8AhqIgRBwAH8CgAAIAQgBUHwDmogHhD2ASAaIAQQ6AFB0c7FAC0AABpBgANBCBDWBCIMRQ0JIAwgBSkD8As3AwAgDCAFKQOQDDcDICAMIAUpA7AMNwNAIAxBGGogKikDADcDACAMQRBqIEYpAwA3AwAgDEEIaiBHKQMANwMAIAxBKGogSSkDADcDACAMQTBqIEgpAwA3AwAgDEE4aiArKQMANwMAIAxByABqIBspAwA3AwAgDEHQAGogIykDADcDACAMQdgAaiAiKQMANwMAIAxB+ABqIBApAwA3AwAgDEHwAGogJSkDADcDACAMQegAaiApKQMANwMAIAwgBSkD0Aw3A2AgDCAFKQPwDDcDgAEgDEGIAWogGCkDADcDACAMQZABaiAmKQMANwMAIAxBmAFqIBUpAwA3AwAgDCAFKQOQDTcDoAEgDEGoAWogGSkDADcDACAMQbABaiAcKQMANwMAIAxBuAFqIA4pAwA3AwAgDEHYAWogBUHIDWopAwA3AwAgDEHQAWogBUHADWopAwA3AwAgDEHIAWogBUG4DWopAwA3AwAgDCAFKQOwDTcDwAEgDEH4AWogBUHoDWopAwA3AwAgDEHwAWogBUHgDWopAwA3AwAgDEHoAWogBUHYDWopAwA3AwAgDCAFKQPQDTcD4AEgDEGYAmogBUGIDmopAwA3AwAgDEGQAmogBUGADmopAwA3AwAgDEGIAmogBUH4DWopAwA3AwAgDCAFKQPwDTcDgAIgDEG4AmogBUGoDmopAwA3AwAgDEGwAmogBUGgDmopAwA3AwAgDEGoAmogBUGYDmopAwA3AwAgDCAFKQOQDjcDoAIgDEHYAmogBUHIDmopAwA3AwAgDEHQAmogBUHADmopAwA3AwAgDEHIAmogBUG4DmopAwA3AwAgDCAFKQOwDjcDwAIgDEH4AmogBUHoDmopAwA3AwAgDEHwAmogBUHgDmopAwA3AwAgDEHoAmogBUHYDmopAwA3AwAgDCAFKQPQDjcD4AIgBSgCoBgiBARAIAUoAqQYIARBBXQQ3wQLQQwhDiAFQQw2AqgYIAUgDDYCpBggBUEMNgKgGCAFKALwBCIEBEAgBSgC9AQgBEEFdBDfBAtBkAEMAQsgBSgCpBghDCAFKAKoGCIORQ0FIA5BDGwLIQhB0c7FAC0AABogCEEEENYEIgRFDQUgDCEIIAQhByAOIQsDQCAFQbATaiAIENoCIAdBCGogBUG4E2ooAgA2AgAgByAFKQKwEzcCACAHQQxqIQcgCEEgaiEIIAtBAWsiCw0ACwwGCyAFQQA2ArATIAVBEGogBUEMaiAFQbATakGwl8AAEJcEAAtBgJDAAEEeQaCQwAAQ/gMACyAFQQA2ArATIAVB8A5qIAVBlBhqIAVBsBNqQdCKwAAQlwQACyAFQQA2ArATIAVB8A5qIAVBlBhqIAVBsBNqQeCKwAAQlwQAC0EAIQ5BBCEEDAELQQQgCEGUjcAAEMgEAAsgBUGwE2oQISAFLQDoFyEKIAUoAtwXIggEQCAFKALgFyAIQQJ0EN8ECwJAIAUoApQVIghFDQAgCCAIQQxsQRNqQXhxIgdqQQlqIghFDQAgBSgCkBUgB2sgCBDfBAsgBSgCwBUiCEGAgICAeEYgCEVyRQRAIAUoAsQVIAhBAnQQ3wQLAkAgDkEMRwRAIAQhCCAOIQsMAQsgBCgCDCEOIAQoAgghCCAEKAIEIQsgBCgCACENIAVBsBNqIgcgBEEQakGAAfwKAAAgBEGQARDfBCANQYCAgIB4Rg0AIAUgDjYC/A4gBSAINgL4DiAFIAs2AvQOIAUgDTYC8A4gBUGAD2ogB0GAAfwKAAAgByAKIAVB8A5qIggQbyAFQfALaiIEIAdBkAH8CgAAIAggBUHAFGpBkAH8CgAAQdHOxQAtAAAaAkACQAJAQYADQQgQ1gQiEQRAIAcgBBD3AiARQRhqIAVByBNqIg0pAwA3AwAgEUEQaiAFQcATaiILKQMANwMAIBFBCGogBUG4E2oiCikDADcDACARIAUpA7ATNwMAIAcgBUH8C2oQ9wIgEUE4aiANKQMANwMAIBFBMGogCykDADcDACARQShqIAopAwA3AwAgESAFKQOwEzcDICAHIAVBiAxqEPcCIBFB2ABqIA0pAwA3AwAgEUHQAGogCykDADcDACARQcgAaiAKKQMANwMAIBEgBSkDsBM3A0AgByAFQZQMahD3AiARQfgAaiANKQMANwMAIBFB8ABqIAspAwA3AwAgEUHoAGogCikDADcDACARIAUpA7ATNwNgIAcgBUGgDGoQ9wIgEUGYAWogDSkDADcDACARQZABaiALKQMANwMAIBFBiAFqIAopAwA3AwAgESAFKQOwEzcDgAEgByAFQawMahD3AiARQbgBaiANKQMANwMAIBFBsAFqIAspAwA3AwAgEUGoAWogCikDADcDACARIAUpA7ATNwOgASAHIAVBuAxqEPcCIBFB2AFqIA0pAwA3AwAgEUHQAWogCykDADcDACARQcgBaiAKKQMANwMAIBEgBSkDsBM3A8ABIAcgBUHEDGoQ9wIgEUH4AWogDSkDADcDACARQfABaiALKQMANwMAIBFB6AFqIAopAwA3AwAgESAFKQOwEzcD4AEgByAFQdAMahD3AiARQZgCaiANKQMANwMAIBFBkAJqIAspAwA3AwAgEUGIAmogCikDADcDACARIAUpA7ATNwOAAiAHIAVB3AxqEPcCIBFBuAJqIA0pAwA3AwAgEUGwAmogCykDADcDACARQagCaiAKKQMANwMAIBEgBSkDsBM3A6ACIAcgBUHoDGoQ9wIgEUHYAmogDSkDADcDACARQdACaiALKQMANwMAIBFByAJqIAopAwA3AwAgESAFKQOwEzcDwAIgByAFQfQMahD3AiARQfgCaiANKQMANwMAIBFB8AJqIAspAwA3AwAgEUHoAmogCikDADcDACARIAUpA7ATNwPgAkHRzsUALQAAGkGAA0EIENYEIhBFDQEgByAIEPcCIBBBGGogDSkDADcDACAQQRBqIAspAwA3AwAgEEEIaiAKKQMANwMAIBAgBSkDsBM3AwAgByAFQfwOahD3AiAQQThqIA0pAwA3AwAgEEEwaiALKQMANwMAIBBBKGogCikDADcDACAQIAUpA7ATNwMgIAcgBUGID2oQ9wIgEEHYAGogDSkDADcDACAQQdAAaiALKQMANwMAIBBByABqIAopAwA3AwAgECAFKQOwEzcDQCAHIAVBlA9qEPcCIBBB+ABqIA0pAwA3AwAgEEHwAGogCykDADcDACAQQegAaiAKKQMANwMAIBAgBSkDsBM3A2AgByAFQaAPahD3AiAQQZgBaiANKQMANwMAIBBBkAFqIAspAwA3AwAgEEGIAWogCikDADcDACAQIAUpA7ATNwOAASAHIAVBrA9qEPcCIBBBuAFqIA0pAwA3AwAgEEGwAWogCykDADcDACAQQagBaiAKKQMANwMAIBAgBSkDsBM3A6ABIAcgBUG4D2oQ9wIgEEHYAWogDSkDADcDACAQQdABaiALKQMANwMAIBBByAFqIAopAwA3AwAgECAFKQOwEzcDwAEgByAFQcQPahD3AiAQQfgBaiANKQMANwMAIBBB8AFqIAspAwA3AwAgEEHoAWogCikDADcDACAQIAUpA7ATNwPgASAHIAVB0A9qEPcCIBBBmAJqIA0pAwA3AwAgEEGQAmogCykDADcDACAQQYgCaiAKKQMANwMAIBAgBSkDsBM3A4ACIAcgBUHcD2oQ9wIgEEG4AmogDSkDADcDACAQQbACaiALKQMANwMAIBBBqAJqIAopAwA3AwAgECAFKQOwEzcDoAIgByAFQegPahD3AiAQQdgCaiANKQMANwMAIBBB0AJqIAspAwA3AwAgEEHIAmogCikDADcDACAQIAUpA7ATNwPAAiAHIAVB9A9qEPcCIBBB+AJqIA0pAwA3AwAgEEHwAmogCykDADcDACAQQegCaiAKKQMANwMAIBAgBSkDsBM3A+ACIAgQ/AIgBBD8AiAHECEgBS0A6BchByAFKALcFyIEBEAgBSgC4BcgBEECdBDfBAsCQCAFKAKUFSIERQ0AIAQgBEEMbEETakF4cSIIakEJaiIERQ0AIAUoApAVIAhrIAQQ3wQLIAUoAsAVIgRBgICAgHhGIARFckUEQCAFKALEFSAEQQJ0EN8ECyAFQeQIaiEoIAVB9BFqISAgBUHoCGohMSAFQfgRaiEkIAVB7AhqITIgBUH8EWohKyAFQbATagJ/AkACQAJAIAcOAgIBAAtBjI/AAEEPQdCQwAAQ/gMAC0HRzsUALQAAGkGAA0EIENYEIgQEQCAEQSBqQQBB4AL8CwAgBEKdm7ys3PHQrlM3AxggBEK9lpyuj+W6vAo3AxAgBEKsjOXD9+2ot+YANwMIIARCr76f0Jn4nYUONwMAIAVB8BJqIARBDCARQQwQKyAEQYADEN8EQQEhGSAFKAL4EiELIAUoAvQSDAILQQhBgANBrIzAABDIBAALQQwhCyAFQQw2AvgSIAUgETYC9BIgBUEMNgLwEkEAIRkgEQsiDiALEBogBSgCuBMiCEEFdCELIAUoArQTIQcgCCEEAkADQCALRQ0BIARBAWshBCALQSBrIgsgB2pB2MPCAEEgEPEDRQ0ACyAEQQFqIgsgCEsNBAwDC0HRzsUALQAAGkEgQQgQ1gQiCEUNFSAIQgA3AwAgCEEYakIANwMAIAhBEGpCADcDACAIQQhqQgA3AwAgBSgCsBMiBARAIAcgBEEFdBDfBAsgBSAINgK0E0EBIQsgBUEBNgKwE0F/IQQMAgtBCEGAA0GUjcAAEMgEAAtBCEGAA0GUjcAAEMgEAAsgBSALNgK4EwsgBUH4CGogBUG4E2oiIigCADYCACAFIAUpArATNwPwCCAFQfALaiAQQQwQGkHRzsUALQAAGgJAAkBBDEEBENYEIjcEQCA3QYGABDYACCA3QoGAhICQgMAANwAAIAUoAvQLITQgBSgC+AsiDUEBTQ0CIAVByBNqIhVCADcDACAFQcATaiIKQgA3AwAgIkIANwMAIAVCADcDsBMCQCA0QSBqIgsgBUGwE2oiB0EgEPEDDQAgDUECRiIIDQMgNy0AAkUEQCAVQgA3AwAgCkIANwMAICJCADcDACAFQgA3A7ATIDRBQGsiCyAHQSAQ8QMNAQtBAkEDIAgbIgggDU8NAyAIIDdqLQAARQRAIAVByBNqQgA3AwAgBUHAE2pCADcDACAFQbgTakIANwMAIAVCADcDsBMgNCAIQQV0aiILIAVBsBNqQSAQ8QMNAQsgCCAIIA1JaiIIIA1PDQMgCCA3ai0AAEUEQCAFQcgTakIANwMAIAVBwBNqQgA3AwAgBUG4E2pCADcDACAFQgA3A7ATIDQgCEEFdGoiCyAFQbATakEgEPEDDQELIAggCCANSWoiCCANTw0DIAggN2otAABFBEAgBUHIE2pCADcDACAFQcATakIANwMAIAVBuBNqQgA3AwAgBUIANwOwEyA0IAhBBXRqIgsgBUGwE2pBIBDxAw0BCyAIIAggDUlqIgggDU8NAyAIIDdqLQAARQRAIAVByBNqQgA3AwAgBUHAE2pCADcDACAFQbgTakIANwMAIAVCADcDsBMgNCAIQQV0aiILIAVBsBNqQSAQ8QMNAQsgCCAIIA1JaiIIIA1PDQMgCCA3ai0AAEUEQCAFQcgTakIANwMAIAVBwBNqQgA3AwAgBUG4E2pCADcDACAFQgA3A7ATIDQgCEEFdGoiCyAFQbATakEgEPEDDQELIAggCCANSWoiCCANTw0DIAggN2otAABFBEAgBUHIE2pCADcDACAFQcATakIANwMAIAVBuBNqQgA3AwAgBUIANwOwEyA0IAhBBXRqIgsgBUGwE2pBIBDxAw0BCyAIIAggDUlqIgggDU8NAyAIIDdqLQAARQRAIAVByBNqQgA3AwAgBUHAE2pCADcDACAFQbgTakIANwMAIAVCADcDsBMgNCAIQQV0aiILIAVBsBNqQSAQ8QMNAQsgCCAIIA1JaiIIIA1PDQMgCCA3ai0AAEUEQCAFQcgTakIANwMAIAVBwBNqQgA3AwAgBUG4E2pCADcDACAFQgA3A7ATIDQgCEEFdGoiCyAFQbATakEgEPEDDQELIAggCCANSWoiCCANTw0DIAggN2otAABFBEAgBUHIE2pCADcDACAFQcATakIANwMAIAVBuBNqQgA3AwAgBUIANwOwEyA0IAhBBXRqIgsgBUGwE2pBIBDxAw0BCyAIIAggDUlqIgggDU8NAyAIQQtLDQIgCCA3ai0AAA0DIAVByBNqQgA3AwAgBUHAE2pCADcDACAFQbgTakIANwMAIAVCADcDsBMgNCAIQQV0aiILIAVBsBNqQSAQ8QNFDQMLIAVBADYC8A4jAEEQayIAJAAgACAFQbATajYCDCAAIAs2AgggAEEIakHolsEAIABBDGpB6JbBACAFQfAOakHAkMAAEOYCAAtBAUEMEP8EAAtBDEEMQbCQwAAQ2QMACyAFQbgTaiAFQfgIaigCADYCACAFIAUpA/AINwOwEyAFKALwCyFMIAUoAvASIggEQCAOIAhBBXQQ3wQLIBBBgAMQ3wQgGQRAIBFBgAMQ3wQLIAUoAqAYIggEQCAMIAhBBXQQ3wQLIAUoAuAIIggEQCAFKALkCCAIQQV0EN8EC0EIIQwgBUH4BGogBUG4E2ooAgA2AgAgBSAFKQOwEzcD8AQgBSAENgL8BCANQQV0IQoCQAJAAkACQAJAIA1FDQBBACEHQdHOxQAtAAAaIApBCBDWBCIMRQ0BA0AgByAKRg0BIAcgDGoiCCAHIDRqIgQpAwA3AwAgCEEYaiAEQRhqKQMANwMAIAhBEGogBEEQaikDADcDACAIQQhqIARBCGopAwA3AwAgCiAHQSBqIgdHDQALCyAKIQcgDSEIAn8CQANAIAdFDQEgCEEBayEIIAdBIGsiByAMakHYw8IAQSAQ8QNFDQALIAhBAWoiBCANIAQgDUkbIQsgDQwBC0HRzsUALQAAGkEgQQgQ1gQiBEUNFiAEQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwBBfyEIQQEhCyANBEAgDCAKEN8ECyAEIQxBAQshBCAFIAg2AowFIAUgCzYCiAUgBSAMNgKEBSAFIAQ2AoAFIAUgDTYC8A4gBUEMNgLwCyANQQxHDQFBACEHIAVBADYCuBMgBUKAgICAgAE3ArATQQghCCA3LQAADQIMAwtBCCAKQeiBwAAQyAQACyAFQQA2ArATIAVB8AtqIAVB8A5qIAVBsBNqQdS3wgAQlwQACyAFQbATakHkt8IAEKIDIAUoArQTIgggNCkDADcDACAIQQhqIDRBCGopAwA3AwAgCEEQaiA0QRBqKQMANwMAIAhBGGogNEEYaikDADcDAEEBIQcgBUEBNgK4EwsgNy0AAUEBRgRAIAUoArATIAdGBEAgBUGwE2pB5LfCABCiAyAFKAK0EyEICyAIIAdBBXRqIgogNEEgaiIEKQMANwMAIApBGGogBEEYaikDADcDACAKQRBqIARBEGopAwA3AwAgCkEIaiAEQQhqKQMANwMAIAUgB0EBaiIHNgK4EwsgNy0AAkEBRgRAIAUoArATIAdGBEAgBUGwE2pB5LfCABCiAyAFKAK0EyEICyAIIAdBBXRqIgogNEFAayIEKQMANwMAIApBGGogBEEYaikDADcDACAKQRBqIARBEGopAwA3AwAgCkEIaiAEQQhqKQMANwMAIAUgB0EBaiIHNgK4EwsgNy0AA0EBRgRAIAUoArATIAdGBEAgBUGwE2pB5LfCABCiAyAFKAK0EyEICyAIIAdBBXRqIgogNEHgAGoiBCkDADcDACAKQRhqIARBGGopAwA3AwAgCkEQaiAEQRBqKQMANwMAIApBCGogBEEIaikDADcDACAFIAdBAWoiBzYCuBMLIDctAARBAUYEQCAFKAKwEyAHRgRAIAVBsBNqQeS3wgAQogMgBSgCtBMhCAsgCCAHQQV0aiIKIDRBgAFqIgQpAwA3AwAgCkEYaiAEQRhqKQMANwMAIApBEGogBEEQaikDADcDACAKQQhqIARBCGopAwA3AwAgBSAHQQFqIgc2ArgTCyA3LQAFQQFGBEAgBSgCsBMgB0YEQCAFQbATakHkt8IAEKIDIAUoArQTIQgLIAggB0EFdGoiCiA0QaABaiIEKQMANwMAIApBGGogBEEYaikDADcDACAKQRBqIARBEGopAwA3AwAgCkEIaiAEQQhqKQMANwMAIAUgB0EBaiIHNgK4EwsgNy0ABkEBRgRAIAUoArATIAdGBEAgBUGwE2pB5LfCABCiAyAFKAK0EyEICyAIIAdBBXRqIgogNEHAAWoiBCkDADcDACAKQRhqIARBGGopAwA3AwAgCkEQaiAEQRBqKQMANwMAIApBCGogBEEIaikDADcDACAFIAdBAWoiBzYCuBMLIDctAAdBAUYEQCAFKAKwEyAHRgRAIAVBsBNqQeS3wgAQogMgBSgCtBMhCAsgCCAHQQV0aiIKIDRB4AFqIgQpAwA3AwAgCkEYaiAEQRhqKQMANwMAIApBEGogBEEQaikDADcDACAKQQhqIARBCGopAwA3AwAgBSAHQQFqIgc2ArgTCyA3LQAIQQFGBEAgBSgCsBMgB0YEQCAFQbATakHkt8IAEKIDIAUoArQTIQgLIAggB0EFdGoiCiA0QYACaiIEKQMANwMAIApBGGogBEEYaikDADcDACAKQRBqIARBEGopAwA3AwAgCkEIaiAEQQhqKQMANwMAIAUgB0EBaiIHNgK4EwsgNy0ACUEBRgRAIAUoArATIAdGBEAgBUGwE2pB5LfCABCiAyAFKAK0EyEICyAIIAdBBXRqIgogNEGgAmoiBCkDADcDACAKQRhqIARBGGopAwA3AwAgCkEQaiAEQRBqKQMANwMAIApBCGogBEEIaikDADcDACAFIAdBAWoiBzYCuBMLIDctAApBAUYEQCAFKAKwEyAHRgRAIAVBsBNqQeS3wgAQogMgBSgCtBMhCAsgCCAHQQV0aiIKIDRBwAJqIgQpAwA3AwAgCkEYaiAEQRhqKQMANwMAIApBEGogBEEQaikDADcDACAKQQhqIARBCGopAwA3AwAgBSAHQQFqIgc2ArgTCyA3LQALQQFGBEAgBSgCsBMgB0YEfyAFQbATakHkt8IAEKIDIAUoArQTBSAICyAHQQV0aiIIIDRB4AJqIgQpAwA3AwAgCEEYaiAEQRhqKQMANwMAIAhBEGogBEEQaikDADcDACAIQQhqIARBCGopAwA3AwAgBSAHQQFqNgK4EwsgBUGYBWogBUG4E2ooAgA2AgAgBSAFKQKwEzcDkAUgBUGwE2oQISAFLQDoFyFGIAUoAtwXIgQEQCAFKALgFyAEQQJ0EN8ECwJAIAUoApQVIgRFDQAgBCAEQQxsQRNqQXhxIghqQQlqIgRFDQAgBSgCkBUgCGsgBBDfBAsgBSgCwBUiBEGAgICAeEYgBEVyRQRAIAUoAsQVIARBAnQQ3wQLAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgRg4CAQIAC0GMj8AAQQ9BlJrAABD+AwALIAUoAvgEIhhBBXQhCEEAIQcgGEH///8/SyAIQfj///8HS3INDQJAIAhFBEBBCCEKDAELIAUoAvQEIQtB0c7FAC0AABpBCCEHIAhBCBDWBCIKRQ0OIBhFDQBBACEHIBghBANAIAcgCEYNASAHIApqIg0gByALaiIMKQMANwMAIA1BGGogDEEYaikDADcDACANQRBqIAxBEGopAwA3AwAgDUEIaiAMQQhqKQMANwMAIAdBIGohByAEQQFrIgQNAAsLIAUoAvwEIU0gBUGwE2ohFiAFQfAEaiEVIAVB2ARqIR8gBUHkBGohD0EAIQ1BACEIIwBB4ABrIhokAEHRzsUALQAAGgJAAkACQAJAAkACQEEgQQgQ1gQiBARAIARBGGpB8MTCACkDADcDACAEQRBqQejEwgApAwA3AwAgBEEIakHgxMIAKQMANwMAIARB2MTCACkDADcDACAaQgE3AgggGiAENgIEIBpBATYCACAVKAIIIgRBBXQhHiAEQf///z9LIB5B+P///wdLcg0BIBUoAgQhEQJAIB5FBEBBCCEMDAELQdHOxQAtAAAaQQghCCAeQQgQ1gQiDEUNAiAERQ0AIAQhCANAIA0gHkYNASAMIA1qIgsgDSARaiIHKQMANwMAIAtBGGogB0EYaikDADcDACALQRBqIAdBEGopAwA3AwAgC0EIaiAHQQhqKQMANwMAIA1BIGohDSAIQQFrIggNAAsLIBogBDYCKCAaIAw2AiQgGiAENgIgIBogFSgCDCIONgIsIwBBMGsiLSQAIC1BJGogGhD3ASAtIC0oAigiByAtKAIsEBggLSgCJCIIBEAgByAIQQV0EN8ECyAtQSRqIBpBIGoiEBD3ASAtQQxqIC0oAigiByAtKAIsEBggLSgCJCIIBEAgByAIQQV0EN8ECyAaQRBqISogLUEYaiAtKAIEIhUgLSgCCCAtKAIQIgwgLSgCFBArIC1BJGogLSgCHCILIC0oAiAQGiAtKAIsIgdBBXQhDSAtKAIoISIgByEIAkACQAJAA0AgDUUNASAIQQFrIQggDUEgayINICJqQdjDwgBBIBDxA0UNAAsgCEEBaiINIAdLDQIMAQtB0c7FAC0AABpBIEEIENYEIgcEQCAHQgA3AwAgB0EYakIANwMAIAdBEGpCADcDACAHQQhqQgA3AwAgLSgCJCIIBEAgIiAIQQV0EN8ECyAtIAc2AihBASENIC1BATYCJEF/IQgMAQsMJQsgLSANNgIsCyAqIC0pAiQ3AgAgKiAINgIMICpBCGogLUEsaigCADYCACAtKAIYIggEQCALIAhBBXQQ3wQLIC0oAgwiCARAIAwgCEEFdBDfBAsgLSgCACIIBEAgFSAIQQV0EN8ECyAQKAIAIggEQCAQKAIEIAhBBXQQ3wQLIBooAgAiCARAIBooAgQgCEEFdBDfBAsgLUEwaiQAQQAhDUHRzsUALQAAGkEgQQQQ1gQiLUUNAiAaKAIYIgdBBXQhKiAHQf///z9LICpB+P///wdLcg0DQQghEEEIISICQCAqRQ0AIBooAhQhC0HRzsUALQAAGkEIIQ0gKkEIENYEIiJFDQQgB0UNAEEAIQ0gByEIA0AgDSAqRg0BIA0gImoiFSALIA1qIgwpAwA3AwAgFUEYaiAMQRhqKQMANwMAIBVBEGogDEEQaikDADcDACAVQQhqIAxBCGopAwA3AwAgDUEgaiENIAhBAWsiCA0ACwsgLSAHNgIIIC0gIjYCBCAtIAc2AgAgGigCHCEHAkAgHkUNAEHRzsUALQAAGiAeQQgQ1gQiEEUNBSAERQ0AQQAhDSAEIQgDQCANIB5GDQEgDSAQaiIMIA0gEWoiCykDADcDACAMQRhqIAtBGGopAwA3AwAgDEEQaiALQRBqKQMANwMAIAxBCGogC0EIaikDADcDACANQSBqIQ0gCEEBayIIDQALCyAtIAQ2AhggLSAQNgIUIC0gBDYCECAtIA42AhwgLSAHNgIMIBpBAjYCWCAaIC02AlQgGkECNgJQIBpBIGogGkHQAGoQ5gEgGigCOCIHQQV0IQ0gGigCICEVIBooAiQhDCAaKQIoIVEgGigCMCEOIBooAjQhBCAHIQgCQAJAA0AgDUUNASAIQQFrIQggDUEgayINIARqQdjDwgBBIBDxA0UNAAsgCEEBaiILIAcgByALSxshDQwBC0HRzsUALQAAGkEgQQgQ1gQiB0UNJCAHQgA3AwAgB0EYakIANwMAIAdBEGpCADcDACAHQQhqQgA3AwBBfyEIQQEhDSAOBEAgBCAOQQV0EN8EC0EBIQ4gByEECyAaIAg2AkwgGiANNgJIIBogBDYCRCAaIA42AkBB0c7FAC0AABpBIEEIENYEIgdFDSMgB0EYakHwxMIAKQMANwMAIAdBEGpB6MTCACkDADcDACAHQQhqQeDEwgApAwA3AwAgB0HYxMIAKQMANwMAIBpCATcCWCAaIAc2AlQgGkEBNgJQIAgNBSANRQ0kIAQgB0EgEPEDDQUgB0EgEN8EIB8EQCAfKAIIIgcgHygCAEYEQCAfQaS4wgAQowMLIB8oAgQgB0EEdGoiCCBRNwIIIAggDDYCBCAIIBU2AgAgHyAHQQFqNgIICwJAAkAgDwRAIA8oAggiCCAPKAIARg0BIBpByABqKQIAIVEgDygCBCAIQQR0aiIEIBopAkA3AgAgBEEIaiBRNwIAIBYgGikCEDcCACAWQQhqIBpBGGopAgA3AgAgDyAIQQFqNgIIDAILIBYgGikCEDcCACAWQQhqIBpBGGopAgA3AgAgDkUNASAEIA5BBXQQ3wQMAQsgD0G0uMIAEKMDIA8oAgQgCEEEdGoiBCAaKQJANwIAIARBCGogGkHIAGopAgA3AgAgFiAaKQIQNwIAIBZBCGogGkEYaikCADcCACAPIAhBAWo2AggLIB8gFUVyRQRAIAwgFUEFdBDfBAsgGkHgAGokAAwGCwwiCyAIIB5B6IHAABDIBAALQQRBIBD/BAALIA0gKkHogcAAEMgEAAtBCCAeQeiBwAAQyAQACyAaQQA2AiAgGkFAayAaQdAAaiAaQSBqQZS4wgAQlAQACyAFKAL4BCIIQQV0ISJBACEHIAhB////P0sgIkH4////B0tyDQEgBSgCvBMhQSAFKAK4EyENIAUoArQTIRogBSgCsBMhLQJAICJFBEBBCCEODAELIAUoAvQEIQtB0c7FAC0AABpBCCEHICJBCBDWBCIORQ0CIAhFDQBBACEHIAghBANAIAcgIkYNASAHIA5qIhUgByALaiIMKQMANwMAIBVBGGogDEEYaikDADcDACAVQRBqIAxBEGopAwA3AwAgFUEIaiAMQQhqKQMANwMAIAdBIGohByAEQQFrIgQNAAsLIAUgBSgC/AQ2AuwIIAUgCDYC6AggBSAONgLkCCAFIAg2AuAIQQAhByANQf///z9LIA1BBXQiCEH4////B0tyDQ0CQCAIRQRAQQghDAwBC0HRzsUALQAAGkEIIQcgCEEIENYEIgxFDQ4gDUUNAEEAIQcgDSEEA0AgByAIRg0BIAcgDGoiFSAHIBpqIgspAwA3AwAgFUEYaiALQRhqKQMANwMAIBVBEGogC0EQaikDADcDACAVQQhqIAtBCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgCq0gGK1CIIaEIVQgBSBBNgL8ESAFIA02AvgRIAUgDDYC9BEgBSANNgLwESANISIMBQsgBSgC+AQiIkEFdCEKQQAhCCAiQf///z9LIApB+P///wdLcg0BIApFBEAgBUGAgICAeDYC4AggBSgC/AQhQUEIIRpBCCEMDAQLIAUoAvQEIQdB0c7FAC0AABpBCCEIIApBCBDWBCIaRQ0BICJFDQIgGiEIIAohCyAiIQQDQCALBEAgCCAHKQMANwMAIAhBGGogB0EYaikDADcDACAIQRBqIAdBEGopAwA3AwAgCEEIaiAHQQhqKQMANwMAIAhBIGohCCALQSBrIQsgB0EgaiEHIARBAWsiBA0BCwsMAgsgByAiQeiBwAAQyAQACyAIIApB6IHAABDIBAALIAVBgICAgHg2AuAIIAUoAvwEIUFB0c7FAC0AABogCkEIENYEIgxFDQIgIkUNACAiQQV0IQhBACEHICIhBANAIAcgCEYNASAHIAxqIgsgByAaaiIKKQMANwMAIAtBGGogCkEYaikDADcDACALQRBqIApBEGopAwA3AwAgC0EIaiAKQQhqKQMANwMAIAdBIGohByAEQQFrIgQNAAsLIAUgQTYCvBMgBSAiNgK4EyAFIAw2ArQTIAUgIjYCsBMgBUHwDmogBUGwE2oQdiAFQfgRaiAFQfgOaikCACJUNwMAIAUgBSkC8A43A/ARIFSnIQ1BgICAgHghGCAFKAL0ESEMICIhLQtBACEHIA1B////P0sgDUEFdCIPQfj///8HS3INDAJAIA9FBEBBCCEfDAELQdHOxQAtAAAaQQghByAPQQgQ1gQiH0UNDSANRQ0AQQAhByANIQQDQCAHIA9GDQEgByAfaiIKIAcgDGoiCCkDADcDACAKQRhqIAhBGGopAwA3AwAgCkEQaiAIQRBqKQMANwMAIApBCGogCEEIaikDADcDACAHQSBqIQcgBEEBayIEDQALCyAFIAUoAvwRIhU2AqwFIAUgDTYCqAUgBSAfNgKkBSAFIA02AqAFIAVBADYCvAUgBUKAgICAgAE3ArQFIAUoArgCIT0gBSgCvAIiOEEHTQRAIDhFBEBBfiEHDAYLID0tAABB/wFGDQIgOEEBRg0DID0tAAFB/wFGDQIgOEECRg0DID0tAAJB/wFGDQIgOEEDRg0DID0tAANB/wFGDQIgOEEERg0DID0tAARB/wFGDQIgOEEFRg0DID0tAAVB/wFGDQIgOEEGRg0DID0tAAZB/wFHDQMMAgsgBSA9IDgQhAMgBSgCAEEBRg0BIDhBAmshBwwDC0EIIApB6IHAABDIBAALID9BB3QhCyAzIQcDQCAFQcAFaiAHEK8BIAUoArwFIgQgBSgCtAVGBEAgBUG0BWpBwJfAABCkAwsgBSgCuAUgBEEHdGogBUHABWpBgAH8CgAAIAUgBEEBajYCvAUgB0GAAWohByALQYABayILDQALCyA4QQJrIQcgOEEBTQ0BCwJAAkACQAJAAkACQCAHID1qLQAADgIBAAILQdHOxQAtAAAaQTBBBBDWBCIRRQ0JAkAgD0UEQCARIA02AghBCCEOIBFBCDYCBCARIA02AgAMAQtB0c7FAC0AABogD0EIENYEIgRFDQ8CQCANRQ0AQQAhByANIQwDQCAHIA9GDQEgBCAHaiIKIAcgH2oiCCkDADcDACAKQRhqIAhBGGopAwA3AwAgCkEQaiAIQRBqKQMANwMAIApBCGogCEEIaikDADcDACAHQSBqIQcgDEEBayIMDQALCyARIA02AgggESAENgIEIBEgDTYCAEHRzsUALQAAGiAPQQgQ1gQiDkUNDyANRQ0AQQAhByANIQwDQCAHIA9GDQEgByAOaiIIIAcgH2oiBCkDADcDACAIQRhqIARBGGopAwA3AwAgCEEQaiAEQRBqKQMANwMAIAhBCGogBEEIaikDADcDACAHQSBqIQcgDEEBayIMDQALCyARIA02AhggESAONgIUIBEgDTYCECAFKAL4ESIEQQV0IQtBACEHIARB////P0sgC0H4////B0tyDQ9BCCEKAkAgC0UNACAFKAL0ESEIQdHOxQAtAAAaQQghByALQQgQ1gQiCkUNECAERQ0AQQAhByAEIQwDQCAHIAtGDQEgByAKaiIQIAcgCGoiDikDADcDACAQQRhqIA5BGGopAwA3AwAgEEEQaiAOQRBqKQMANwMAIBBBCGogDkEIaikDADcDACAHQSBqIQcgDEEBayIMDQALCyARIAQ2AiggESAKNgIkIBEgBDYCICARIAUoAvwRNgIsIBEgFTYCHCARIBU2AgwgBUEDNgKcGCAFIBE2ApgYIAVBAzYClBhBACEHIAVBADYCqBggBUKAgICAgAE3AqAYIAVBwBRqISogBUHAE2ohESAzIQsgOSEEICchDANAIAcgO0YNAyAHIDpGDQQgBUGwE2ogCyAMIAQQvAEgBUHwDmogEUGAAfwKAAAgBUH4CGoiECAFQbgTaikDADcDACAFQfgLaiIOICpBCGopAgA3AwAgBSAFKQOwEzcD8AggBSAqKQIANwPwCyAFKAKcGCIWIAUoApQYIgpGBEAgBUGUGGpB4JLAABCjAyAFKAKUGCEKCyAFKAKYGCIVIBZBBHRqIgggBSkD8Ag3AgAgCEEIaiAQKQMANwIAIAUgFkEBaiIINgKcGCAIIApGBH8gBUGUGGpB8JLAABCjAyAFKAKYGAUgFQsgCEEEdGoiCCAFKQPwCzcCACAIQQhqIA4pAwA3AgAgBSAWQQJqNgKcGCAFKAKoGCIIIAUoAqAYRgRAIAVBoBhqQYCTwAAQpAMLIAUoAqQYIAhBB3RqIAVB8A5qQYAB/AoAACAFIAhBAWo2AqgYIAtBgAFqIQsgBEEgaiEEIAxBIGohDCA/IAdBAWoiB0cNAAsgBUG4EmogBUGcGGooAgA2AgAgBSAFKQKUGDcDsBIgBUGAgICAeDYC8BIgBUGwE2ogBUGwEmogBUHwEmogBUHYBGogBUHkBGoQwQEgBUHIE2oiBCAFQagYaigCADYCACAFQcgGaiAFQbgTaikCADcDACAFIAUpAqAYIlE3AsATIAUgBSkCsBM3A8AGIAUgUaciBzYC3AYgBSAFKALEEyIVNgLYBiAFIAQoAgAiNTYC1AYgBUHcBmohCyAFQdQGaiEEIAVB2AZqIQwgBUHABmohCAwECyAFQbATaiAFQaAFaiAzID8gJyA7IDkgOiAFQdgEaiAFQeQEahDaASAFQegGaiAFQbgTaikCADcDACAFIAUpArATNwPgBiAFIAUoAsATIgc2AvwGIAUgBSgCxBMiFTYC+AYgBSAFKALIEyI1NgL0BiAFQfwGaiELIAVB9AZqIQQgBUH4BmohDCAFQeAGaiEIDAMLQYyPwABBD0GEmsAAEP4DAAsgOyA7QcCSwAAQ2QMACyA6IDpB0JLAABDZAwALIA0EQCAfIA8Q3wQgBCgCACE1IAwoAgAhFSALKAIAIQcLIAVBqAVqIkIgCEEIaikCADcDACAFIAgpAgA3A6AFAkAgOEEDayINQQBIDQAgOkEBaiFHIDtBAWohSCAFQfgLaiFJIAVBgAlqIUAgBUGwFGohQyAFQcAUaiFEIAVBwBNqIQYgBUGADGohLANAIAchESAFIA02AoAHAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJ/AkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQCANIDhJBEAgDSA9aiIILQAAIgQOAgEDAgsgDSA4QdCYwAAQ2QMACyANRQRAIAVBsBNqIAVBoAVqIBUgNSAnIDsgOSA6IAVB2ARqIAVB5ARqENoBIAVBwAdqIgogBUG4E2opAgA3AwAgBSAFKQKwEzcDuAcgBSgCwBMhByAFKALEEyAFKALIEyE1IAUoAqAFIggEQCAFKAKkBSAIQQV0EN8ECyAFQagFaiAKKQMANwMAIAUgBSkDuAc3A6AFIBEEQCAVIBFBB3QQ3wQLIRUMIQsgDUEBayIWIDhPDQMgBSAWID1qLQAAIhc6AIcHIBdFBEBB0c7FAC0AABpBwABBBBDWBCIORQ0nIAUoAqgFIgRBBXQhDUEAIQcgBEH///8/SyANQfj///8HS3INBSAFKAKkBSEPAkAgDUUEQCAOIAQ2AghBCCEwIA5BCDYCBCAOIAQ2AgAgDiAENgIoIA5BCDYCJCAOIAQ2AiAgDiAENgIYIA5BCDYCFCAOIAQ2AhAgBSgCrAUhGQwBC0HRzsUALQAAGkEIIQcgDUEIENYEIghFDQYCQCAERQ0AQQAhByAEIQoDQCAHIA1GDQEgByAIaiIMIAcgD2oiCykDADcDACAMQRhqIAtBGGopAwA3AwAgDEEQaiALQRBqKQMANwMAIAxBCGogC0EIaikDADcDACAHQSBqIQcgCkEBayIKDQALCyAOIAQ2AgggDiAINgIEIA4gBDYCACAFKAKsBSEZQdHOxQAtAAAaIA1BCBDWBCIIRQ0pAkAgBEUNAEEAIQcgBCEKA0AgByANRg0BIAcgCGoiDCAHIA9qIgspAwA3AwAgDEEYaiALQRhqKQMANwMAIAxBEGogC0EQaikDADcDACAMQQhqIAtBCGopAwA3AwAgB0EgaiEHIApBAWsiCg0ACwsgDiAENgIYIA4gCDYCFCAOIAQ2AhBB0c7FAC0AABogDUEIENYEIghFDSkCQCAERQ0AQQAhByAEIQoDQCAHIA1GDQEgByAIaiIMIAcgD2oiCykDADcDACAMQRhqIAtBGGopAwA3AwAgDEEQaiALQRBqKQMANwMAIAxBCGogC0EIaikDADcDACAHQSBqIQcgCkEBayIKDQALCyAOIAQ2AiggDiAINgIkIA4gBDYCIEHRzsUALQAAGiANQQgQ1gQiMEUNKSAERQ0AQQAhByAEIQoDQCAHIA1GDQEgByAwaiILIAcgD2oiCCkDADcDACALQRhqIAhBGGopAwA3AwAgC0EQaiAIQRBqKQMANwMAIAtBCGogCEEIaikDADcDACAHQSBqIQcgCkEBayIKDQALCyAOIAQ2AjggDiAwNgI0IA4gBDYCMCAOIBk2AjwgDiAZNgIsIA4gGTYCHCAOIBk2AgwgBUEENgKQGCAFIA42AowYIAVBBDYCiBggBUEANgKcGCAFQoCAgICAATcClBggNQRAQQAhB0EBIQgDQAJAAkAgSCAIIgxHBEAgCCBHRg0LIAVBsBNqIgggFSAHQQd0aiAnIAdBBXQiBGogBCA5ahC1AiAFQfALaiAIQYAB/AoAACAFKAK4FCIIQQV0IQtBACEHIAhB////P0sgC0H4////B0tyDTEgBSgCvBQhECAFKAK0FCEOIAUoArAUIQ0gCw0BQQghCgwCCyA7IDtB8JHAABDZAwALQdHOxQAtAAAaQQghByALQQgQ1gQiCkUNLyAIRQ0AQQAhByAIIQQDQCAHIAtGDQEgByAKaiIfIAcgDmoiKikDADcDACAfQRhqICpBGGopAwA3AwAgH0EQaiAqQRBqKQMANwMAIB9BCGogKkEIaikDADcDACAHQSBqIQcgBEEBayIEDQALCyAFKAKQGCIHIAUoAogYRgRAIAVBiBhqQZCSwAAQowMLIAUoAowYIAdBBHRqIgQgEDYCDCAEIAg2AgggBCAKNgIEIAQgCDYCACAFIAdBAWoiBDYCkBggBSgCiBggBEYEQCAFQYgYakGgksAAEKMDCyAFKAKMGCAEQQR0aiIEIBA2AgwgBCAINgIIIAQgDjYCBCAEIA02AgAgBSAHQQJqNgKQGCAFKAKcGCIEIAUoApQYRgRAIAVBlBhqQbCSwAAQpAMLIAUoApgYIARBB3RqIAVB8AtqQYAB/AoAACAFIARBAWo2ApwYIAxBAWohCCAMIgcgNUcNAAsMGgsgBUEANgKoGCAFQoCAgICAATcCoBgMGgsCQAJAIBdB/wFHIBdBAUdxDQAgBUGwE2oQISAFLQDoFyAFKALcFyIEBEAgBSgC4BcgBEECdBDfBAsCQCAFKAKUFSIERQ0AIAQgBEEMbEETakF4cSIIakEJaiIERQ0AIAUoApAVIAhrIAQQ3wQLIAUoAsAVIQRFDQEgBEUgBEGAgICAeEZyDQAgBSgCxBUgBEECdBDfBAsgBUGwE2ogBUGgBWogFSA1ICcgOyA5IDogBUHYBGogBUHkBGoQ2gEgBUGwB2oiCiAFQbgTaikCADcDACAFIAUpArATNwOoByAFKALAEyEHIAUoAsQTIAUoAsgTITUgBSgCoAUiCARAIAUoAqQFIAhBBXQQ3wQLIEIgCikDADcDACAFIAUpA6gHNwOgBSARISogFSEQIRUgDSEWIBENGwwfCyAERSAEQYCAgIB4RnJFBEAgBSgCxBUgBEECdBDfBAsgNUEHdCEEAkAgNUUEQEEIIQgMAQtB0c7FAC0AABogBEEIENYEIghFDQcLIAVBADYC+AsgBSAINgL0CyAFIDU2AvALIAUgPzYCxBMgBSAzNgLAEyAFQQA2ArgTIAUgBCAVajYCtBMgBSAVNgKwEyAFIAVBtAVqNgLIEyAFIAVBhwdqNgK8EyAFIAg2AvgOIAVBADYC9A4gBSBJNgLwDiMAQYADayI2JAAgBUHwDmoiBygCBCEqIAcoAgAhKQJAAkAgBUGwE2oiCigCACIIIAooAgQiBEcEQCAKKAIYIRQgCigCFCElIAooAhAhIyAKKAIMIRsgCigCCCIfQQd0ITAgBygCCCAqQQd0aiEdIAQgCGtBB3YhGSA2QUBrIRMgNkHgAWohDCA2QaABaiELIDZB4AJqIQogNkGgAmohBANAAn8gGy0AAEEBRgRAIB8gJUkEQCA2QcABaiEOIDZBgAFqIQ8gCyEHIAwhCCAjDAILIB8gJUHU+8AAENkDAAsgHyAUKAIIIghPDQMgNkHAAmohDiA2QYACaiEPIAQhByAKIQggFCgCBAshDSAPIA0gMGoiISkDADcDACAPQRhqIhwgIUEYaikDADcDACAPQRBqIiYgIUEQaikDADcDACAPQQhqIh4gIUEIaikDADcDACAHICFBIGopAwA3AwAgB0EIaiAhQShqKQMANwMAIAdBEGogIUEwaikDADcDACAHQRhqICFBOGopAwA3AwAgDiAhQUBrKQMANwMAIA5BCGoiECAhQcgAaikDADcDACAOQRBqIg0gIUHQAGopAwA3AwAgDkEYaiIHICFB2ABqKQMANwMAIAhBGGogIUH4AGopAwA3AwAgCEEQaiAhQfAAaikDADcDACAIQQhqICFB6ABqKQMANwMAIAggIUHgAGopAwA3AwAgNkEIaiAeKQMANwMAIDZBEGogJikDADcDACA2QRhqIBwpAwA3AwAgNkEgaiAPQSBqKQMANwMAIDZBKGogD0EoaikDADcDACA2QTBqIA9BMGopAwA3AwAgNkE4aiAPQThqKQMANwMAIDYgDykDADcDACATQThqIA5BOGopAwA3AwAgE0EwaiAOQTBqKQMANwMAIBNBKGogDkEoaikDADcDACATQSBqIA5BIGopAwA3AwAgE0EYaiAHKQMANwMAIBNBEGogDSkDADcDACATQQhqIBApAwA3AwAgEyAOKQMANwMAIB0gNkGAAfwKAAAgMEGAAWohMCAdQYABaiEdIB9BAWohHyAqQQFqISogGUEBayIZDQALCyApICo2AgAgNkGAA2okAAwBCyAfIAhB5PvAABDZAwALIAUoAvALISogBSgC9AshECAFKAL4CyEbICshCyAkIQ4gICENIBdBAUcEQCAyIQsgMSEOICghDSAFKALgCEGAgICAeEYNCAtB0c7FAC0AABpBwABBBBDWBCIcRQ0mIAUoAqgFIgxBBXQhD0EAIQcgDEH///8/SyAPQfj///8HS3INKSAFKAKkBSEeAkAgD0UEQEEIIRkgBSgCrAUhJkEIIR9BCCEwQQghHQwBC0HRzsUALQAAGkEIIQcgD0EIENYEIh9FDSoCQCAMBEAgHyEHIA8hBCAeIQggDCEKA0AgBARAIAcgCCkDADcDACAHQRhqIAhBGGopAwA3AwAgB0EQaiAIQRBqKQMANwMAIAdBCGogCEEIaikDADcDACAHQSBqIQcgBEEgayEEIAhBIGohCCAKQQFrIgoNAQsLQdHOxQAtAAAaIAUoAqwFISYgD0EIENYEIjBFDS1BACEHIAwhCgNAIAcgD0YNAiAHIDBqIgggByAeaiIEKQMANwMAIAhBGGogBEEYaikDADcDACAIQRBqIARBEGopAwA3AwAgCEEIaiAEQQhqKQMANwMAIAdBIGohByAKQQFrIgoNAAsMAQtB0c7FAC0AABogBSgCrAUhJiAPQQgQ1gQiMEUNLAtB0c7FAC0AABogD0EIENYEIhlFDSsgDARAQQAhByAMIQoDQCAHIA9HBEAgByAZaiIIIAcgHmoiBCkDADcDACAIQRhqIARBGGopAwA3AwAgCEEQaiAEQRBqKQMANwMAIAhBCGogBEEIaikDADcDACAHQSBqIQcgCkEBayIKDQELC0HRzsUALQAAGiAPQQgQ1gQiHUUNLEEAIQcgDCEKA0AgByAPRg0CIAcgHWoiCCAHIB5qIgQpAwA3AwAgCEEYaiAEQRhqKQMANwMAIAhBEGogBEEQaikDADcDACAIQQhqIARBCGopAwA3AwAgB0EgaiEHIApBAWsiCg0ACwwBC0HRzsUALQAAGiAPQQgQ1gQiHUUNKwsgHCAmNgI8IBwgDDYCOCAcIB02AjQgHCAMNgIwIBwgJjYCLCAcIAw2AiggHCAZNgIkIBwgDDYCICAcICY2AhwgHCAMNgIYIBwgMDYCFCAcIAw2AhAgHCAmNgIMIBwgDDYCCCAcIB82AgQgHCAMNgIAIAVBBDYChBggBSAcNgKAGCAFQQQ2AvwXIAVBADYCkBggBUKAgICAgAE3AogYIDVFDRFBACEHQQEhCANAAkACQCBIIAgiDEcEQCAIIEdGDQ0gBUGwE2oiCCAVIAdBB3RqICcgB0EFdCIEaiAEIDlqELUCIAVB8AtqIAhBgAH8CgAAIAUoArgUIghBBXQhI0EAIQcgCEH///8/SyAjQfj///8HS3INDCAFKAK8FCEmIAUoArQUIQ8gBSgCsBQhHyAjDQFBCCEKDAILIDsgO0HwlMAAENkDAAtB0c7FAC0AABpBCCEHICNBCBDWBCIKRQ0KIAhFDQBBACEHIAghBANAIAcgI0YNASAHIApqIhwgByAPaiIZKQMANwMAIBxBGGogGUEYaikDADcDACAcQRBqIBlBEGopAwA3AwAgHEEIaiAZQQhqKQMANwMAIAdBIGohByAEQQFrIgQNAAsLIAUoAoQYIgcgBSgC/BdGBEAgBUH8F2pBkJXAABCjAwsgBSgCgBggB0EEdGoiBCAmNgIMIAQgCDYCCCAEIAo2AgQgBCAINgIAIAUgB0EBaiIENgKEGCAFKAL8FyAERgRAIAVB/BdqQaCVwAAQowMLIAUoAoAYIARBBHRqIgQgJjYCDCAEIAg2AgggBCAPNgIEIAQgHzYCACAFIAdBAmo2AoQYIAUoApAYIgQgBSgCiBhGBEAgBUGIGGpBsJXAABCkAwsgBSgCjBggBEEHdGogBUHwC2pBgAH8CgAAIAUgBEEBajYCkBggDEEBaiEIIAwiByA1Rw0ACwwSCyAEQf8BRw0BCyA1QQd0IQQCQCA1RQRAQQghBwwBC0HRzsUALQAAGiAEQQgQ1gQiB0UNCQsgBUEANgL4CyAFIAc2AvQLIAUgNTYC8AsgBSA/NgLMEyAFIDM2AsgTIAUgPTYCvBMgBUEANgK4EyAFIAQgFWo2ArQTIAUgFTYCsBMgBSAFQbQFajYC0BMgBSAFQYAHajYCxBMgBSA4NgLAEyAFIAc2AvgOIAVBADYC9A4gBSBJNgLwDiMAQYADayI8JAAgBUHwDmoiBygCBCEfIAcoAgAhJQJAAkACQCAFQbATaiIKKAIAIgggCigCBCIERwRAIAooAiAhISAKKAIcIRMgCigCGCEpIAooAhQhIyAKKAIQIRcgCigCDCEbIAooAggiJkEHdCEdIAcoAgggH0EHdGohKiAEIAhrQQd2IRQgPEFAayE2IDxB4AFqIQwgPEGgAWohCyA8QeACaiEKIDxBoAJqIQQDQCAjKAIAIgggF08NAgJ/IAggG2otAABBAUYEQCATICZLBEAgPEHAAWohFiA8QYABaiEOIAshByAMIQggKQwCCyAmIBNBhPzAABDZAwALICYgISgCCCIITw0EIDxBwAJqIRYgPEGAAmohDiAEIQcgCiEIICEoAgQLIRAgDiAQIB1qIjApAwA3AwAgDkEYaiIcIDBBGGopAwA3AwAgDkEQaiIZIDBBEGopAwA3AwAgDkEIaiIeIDBBCGopAwA3AwAgByAwQSBqKQMANwMAIAdBCGogMEEoaikDADcDACAHQRBqIDBBMGopAwA3AwAgB0EYaiAwQThqKQMANwMAIBYgMEFAaykDADcDACAWQQhqIg8gMEHIAGopAwA3AwAgFkEQaiIQIDBB0ABqKQMANwMAIBZBGGoiByAwQdgAaikDADcDACAIQRhqIDBB+ABqKQMANwMAIAhBEGogMEHwAGopAwA3AwAgCEEIaiAwQegAaikDADcDACAIIDBB4ABqKQMANwMAIDxBCGogHikDADcDACA8QRBqIBkpAwA3AwAgPEEYaiAcKQMANwMAIDxBIGogDkEgaikDADcDACA8QShqIA5BKGopAwA3AwAgPEEwaiAOQTBqKQMANwMAIDxBOGogDkE4aikDADcDACA8IA4pAwA3AwAgNkE4aiAWQThqKQMANwMAIDZBMGogFkEwaikDADcDACA2QShqIBZBKGopAwA3AwAgNkEgaiAWQSBqKQMANwMAIDZBGGogBykDADcDACA2QRBqIBApAwA3AwAgNkEIaiAPKQMANwMAIDYgFikDADcDACAqIDxBgAH8CgAAIB1BgAFqIR0gKkGAAWohKiAmQQFqISYgH0EBaiEfIBRBAWsiFA0ACwsgJSAfNgIAIDxBgANqJAAMAgsgCCAXQfT7wAAQ2QMACyAmIAhBlPzAABDZAwALIAUoAoAHIgcgOE8NCSAFKALwCyEqIAUoAvQLIRAgBSgC+AshFCArISYgJCEZICAhHyAHID1qLQAAQQFGIhxFBEAgBSgC4AhBgICAgHhGDQwgBSgC6AgiEkEFdCEIQQAhByASQf///z9LIAhB+P///wdLcg0jAkAgCEUEQEEIIQ4MAQsgBSgC5AghCkHRzsUALQAAGkEIIQcgCEEIENYEIg5FDSQgEkUNAEEAIQcgEiEEA0AgByAIRg0BIAcgDmoiDCAHIApqIgspAwA3AwAgDEEYaiALQRhqKQMANwMAIAxBEGogC0EQaikDADcDACAMQQhqIAtBCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgBSAONgL8FyAFIBI2AswHIAUgBSgC7Ag2AsgHIAVB/BdqIR8gBUHMB2ohGSAFQcgHaiEmIAUoAoAHIQcLIAdFDQ0gB0EBayIEIDhPDQoCQCAEID1qLQAADQAgBUGwE2oQISAFLQDoFyAFKALcFyIEBEAgBSgC4BcgBEECdBDfBAsCQCAFKAKUFSIERQ0AIAQgBEEMbEETakF4cSIIakEJaiIERQ0AIAUoApAVIAhrIAQQ3wQLIAUoAsAVIQQEQCAERSAEQYCAgIB4RnJFBEAgBSgCxBUgBEECdBDfBAsgBSgCgAcNAQwPCyAERSAEQYCAgIB4RnJFBEAgBSgCxBUgBEECdBDfBAtB0c7FAC0AABpBwABBBBDWBCIbRQ0lIAUoAqgFIgxBBXQhD0EAIQcgDEH///8/SyAPQfj///8HS3INKCAFKAKkBSEeIA9FBEBBCCEdIAUoAqwFIQ5BCCELQQghMEEIIRYMDgtB0c7FAC0AABpBCCEHIA9BCBDWBCILRQ0oAkAgDARAIAshByAPIQQgHiEIIAwhCgNAIAQEQCAHIAgpAwA3AwAgB0EYaiAIQRhqKQMANwMAIAdBEGogCEEQaikDADcDACAHQQhqIAhBCGopAwA3AwAgB0EgaiEHIARBIGshBCAIQSBqIQggCkEBayIKDQELC0HRzsUALQAAGiAFKAKsBSEOIA9BCBDWBCIwRQ0rQQAhByAMIQoDQCAHIA9GDQIgByAwaiIIIAcgHmoiBCkDADcDACAIQRhqIARBGGopAwA3AwAgCEEQaiAEQRBqKQMANwMAIAhBCGogBEEIaikDADcDACAHQSBqIQcgCkEBayIKDQALDAELQdHOxQAtAAAaIAUoAqwFIQ4gD0EIENYEIjBFDSoLQdHOxQAtAAAaIA9BCBDWBCIdRQ0pAkAgDARAQQAhByAMIQoDQCAHIA9HBEAgByAdaiIIIAcgHmoiBCkDADcDACAIQRhqIARBGGopAwA3AwAgCEEQaiAEQRBqKQMANwMAIAhBCGogBEEIaikDADcDACAHQSBqIQcgCkEBayIKDQELC0HRzsUALQAAGiAPQQgQ1gQiFkUNAUEAIQcgDCEKA0AgByAPRg0QIAcgFmoiCCAHIB5qIgQpAwA3AwAgCEEYaiAEQRhqKQMANwMAIAhBEGogBEEQaikDADcDACAIQQhqIARBCGopAwA3AwAgB0EgaiEHIApBAWsiCg0ACwwPC0HRzsUALQAAGiAPQQgQ1gQiFg0OCwwpCyAFQbATaiIEECECQCAFLQDoF0EBRwRAIAQoAqwEIgAEQCAEKAKwBCAAQQJ0EN8ECwJAIAQoAuQBIgBFDQAgACAAQQxsQRNqQXhxIgFqQQlqIgBFDQAgBCgC4AEgAWsgABDfBAsgBCgCkAIiAEGAgICAeEYgAEVyRQRAIAQoApQCIABBAnQQ3wQLIAUoAoAHIgAgOE8NASAFQQI2ArQTIAVB1JnAADYCsBMgBUIBNwK8EyAFIAAgPWqtQoCAgIAQhDcD8A4gBSAFQfAOajYCuBMgBEHkmcAAEKgEAAsgBSgC3BciBARAIAUoAuAXIARBAnQQ3wQLAkAgBSgClBUiBEUNACAEIARBDGxBE2pBeHEiCGpBCWoiBEUNACAFKAKQFSAIayAEEN8ECyAFKALAFSIEQYCAgIB4RiAERXINDiAFKALEFSAEQQJ0EN8EDA4LIAAgOEGwmcAAENkDAAsgBUECNgK0EyAFQdSZwAA2ArATIAVCATcCvBMgBSAIrUKAgICAEIQ3A/AOIAUgBUHwDmo2ArgTIAVBsBNqQfSZwAAQqAQACyAWIDhB4JjAABDZAwALIAcgDUHogcAAEMgEAAsgOiA6QYCSwAAQ2QMAC0EIIARBlI3AABDIBAALQfCYwAAQ6AQACyAHICNB6IHAABDIBAALIDogOkGAlcAAENkDAAtBCCAEQZSNwAAQyAQACyAHIDhBgJnAABDZAwALIAQgOEGgmcAAENkDAAtBkJnAABDoBAALIBsgDjYCPCAbIAw2AjggGyAWNgI0IBsgDDYCMCAbIA42AiwgGyAMNgIoIBsgHTYCJCAbIAw2AiAgGyAONgIcIBsgDDYCGCAbIDA2AhQgGyAMNgIQIBsgDjYCDCAbIAw2AgggGyALNgIEIBsgDDYCACAFQQQ2ApAYIAUgGzYCjBggBUEENgKIGCAZKAIAIghBBXQhCkEAIQcgCEH///8/SyAKQfj///8HS3INGQJAIApFBEBBCCEODAELIB8oAgAhC0HRzsUALQAAGkEIIQcgCkEIENYEIg5FDRogCEUNAEEAIQcgCCEEA0AgByAKRg0BIAcgDmoiFiAHIAtqIgwpAwA3AwAgFkEYaiAMQRhqKQMANwMAIBZBEGogDEEQaikDADcDACAWQQhqIAxBCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgJigCACEMIAUoApAYIgQgBSgCiBhGBEAgBUGIGGpBwJXAABCjAwsgBSgCjBggBEEEdGoiByAMNgIMIAcgCDYCCCAHIA42AgQgByAINgIAIAUgBEEBajYCkBggGSgCACIIQQV0IQpBACEHIAhB////P0sgCkH4////B0tyDRkCQCAKRQRAQQghDgwBCyAfKAIAIQtB0c7FAC0AABpBCCEHIApBCBDWBCIORQ0aIAhFDQBBACEHIAghBANAIAcgCkYNASAHIA5qIh8gByALaiIWKQMANwMAIB9BGGogFkEYaikDADcDACAfQRBqIBZBEGopAwA3AwAgH0EIaiAWQQhqKQMANwMAIAdBIGohByAEQQFrIgQNAAsLIAUoApAYIgQgBSgCiBhGBEAgBUGIGGpB0JXAABCjAwsgBSgCjBggBEEEdGoiByAMNgIMIAcgCDYCCCAHIA42AgQgByAINgIAIAUgBEEBajYCkBggBUEANgKcGCAFQoCAgICAATcClBgCQCA1RQRAIAVBADYCqBggBUKAgICAgAE3AqAYDAELQQEhCCAUQQFqIR9BACEHAkACQAJAA0ACQAJAAkAgHyAIIgtHBEAgCCBIRg0BIAggR0YNBiAFQbATaiAVIAdBB3QiBGogBCAQaiAnIAdBBXQiBGogBCA5ahCZASAFQfALaiAGQYAB/AoAACAFKAK4EyIIQQV0ISVBACEHIAhB////P0sgJUH4////B0tyDQUgBSgCzBQhGyAFKALIFCEMIAUoAsQUIRkgBSgCwBQhFiAFKAK8EyEmIAUoArQTIQ8gBSgCsBMhDiAlDQJBCCEKDAMLIBQgFEGwlsAAENkDAAsgOyA7QcCWwAAQ2QMAC0HRzsUALQAAGkEIIQcgJUEIENYEIgpFDQIgCEUNAEEAIQcgCCEEA0AgByAlRg0BIAcgCmoiKSAHIA9qIiMpAwA3AwAgKUEYaiAjQRhqKQMANwMAIClBEGogI0EQaikDADcDACApQQhqICNBCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgBSgCkBgiByAFKAKIGEYEQCAFQYgYakHglsAAEKMDCyAFKAKMGCAHQQR0aiIEICY2AgwgBCAINgIIIAQgCjYCBCAEIAg2AgAgBSAHQQFqIgQ2ApAYIAUoAogYIARGBEAgBUGIGGpB8JbAABCjAwsgBSgCjBggBEEEdGoiBCAmNgIMIAQgCDYCCCAEIA82AgQgBCAONgIAIAUgB0ECajYCkBhBACEHIAxB////P0sgDEEFdCIKQfj///8HS3INHgJAIApFBEBBCCEODAELQdHOxQAtAAAaQQghByAKQQgQ1gQiDkUNHyAMRQ0AQQAhByAMIQQDQCAHIApGDQEgByAOaiIPIAcgGWoiCCkDADcDACAPQRhqIAhBGGopAwA3AwAgD0EQaiAIQRBqKQMANwMAIA9BCGogCEEIaikDADcDACAHQSBqIQcgBEEBayIEDQALCyAFKAKQGCIIIAUoAogYRgRAIAVBiBhqQYCXwAAQowMLIAUoAowYIAhBBHRqIgQgGzYCDCAEIAw2AgggBCAONgIEIAQgDDYCACAFIAhBAWoiBDYCkBggBSgCiBggBEYEQCAFQYgYakGQl8AAEKMDCyAFKAKMGCAEQQR0aiIEIBs2AgwgBCAMNgIIIAQgGTYCBCAEIBY2AgAgBSAIQQJqNgKQGCAFKAKcGCIEIAUoApQYRgRAIAVBlBhqQaCXwAAQpAMLIAUoApgYIARBB3RqIAVB8AtqQYAB/AoAACAFIARBAWo2ApwYIAtBAWohCCALIgcgNUcNAAsMAgsgByAlQeiBwAAQyAQACyA6IDpB0JbAABDZAwALQQAhCCAFQQA2AqgYIAVCgICAgIABNwKgGCA5IQsgJyEEQQAhBwJAAkADQCAFKAKcGCIKIAdLBEAgByA7Rg0CIAcgOkYNAyAFQbATaiIKIAUoApgYIAhqIAQgCxC1AiAFQfAOaiAKQYAB/AoAACAFQfgSaiIMIENBCGopAgA3AwAgBSBDKQIANwPwEiAFKAKQGCIOIAUoAogYRgRAIAVBiBhqQZCWwAAQowMLIAUoAowYIA5BBHRqIgogBSkD8BI3AgAgCkEIaiAMKQMANwIAIAUgDkEBajYCkBggBSgCqBgiCiAFKAKgGEYEQCAFQaAYakGglsAAEKQDCyAFKAKkGCAKQQd0aiAFQfAOakGAAfwKAAAgBSAKQQFqNgKoGCALQSBqIQsgBEEgaiEEIAhBgAFqIQggB0EBaiIHIDVHDQEMBAsLIAcgCkHglcAAENkDAAsgOyA7QfCVwAAQ2QMACyA6IDpBgJbAABDZAwALIAVBuBJqIAVBkBhqKAIANgIAIAUgBSkCiBg3A7ASIAVBgICAgHg2ArATIAVB8AhqIAVBsBJqIAVBsBNqIAVB2ARqIAVB5ARqEMEBIEBBCGogBUGoGGooAgA2AgAgQCAFKQKgGDcCACAFKAKUGCIEBEAgBSgCmBggBEEHdBDfBAsgBUHYB2oiCiAFQfgIaikCADcDACAFIAUpAvAINwPQByAFKAKACSEHIAUoAoQJIAUoAogJITUgBSgCoAUiBARAIB4gBEEFdBDfBAsgQiAKKQMANwMAIAUgBSkD0Ac3A6AFIBEEQCAVIBFBB3QQ3wQLIA1BAWshFgwBC0HRzsUALQAAGgJAAkBBMEEEENYEIg8EQCAFKAKoBSIEQQV0IQxBACEHIARB////P0sgDEH4////B0tyDQEgBSgCpAUhHiAMRQRAIA8gBDYCCEEIIQogD0EINgIEIA8gBDYCACAFKAKsBSEdDAMLQdHOxQAtAAAaQQghByAMQQgQ1gQiC0UNAQJAIAQEQEEAIQcgBCEOA0AgByAMRwRAIAcgC2oiCiAHIB5qIggpAwA3AwAgCkEYaiAIQRhqKQMANwMAIApBEGogCEEQaikDADcDACAKQQhqIAhBCGopAwA3AwAgB0EgaiEHIA5BAWsiDg0BCwsgDyAENgIIIA8gCzYCBCAPIAQ2AgBB0c7FAC0AABogBSgCrAUhHSAMQQgQ1gQiCkUNAUEAIQcgBCEOA0AgByAMRg0FIAcgCmoiCyAHIB5qIggpAwA3AwAgC0EYaiAIQRhqKQMANwMAIAtBEGogCEEQaikDADcDACALQQhqIAhBCGopAwA3AwAgB0EgaiEHIA5BAWsiDg0ACwwECyAPQQA2AgggDyALNgIEIA9BADYCAEHRzsUALQAAGiAFKAKsBSEdIAxBCBDWBCIKDQMLQQggDEHogcAAEMgEAAsMFwsgByAMQeiBwAAQyAQACyAPIAQ2AhggDyAKNgIUIA8gBDYCECAZKAIAIghBBXQhC0EAIQcgCEH///8/SyALQfj///8HS3INGwJAIAtFBEBBCCEKDAELIB8oAgAhDEHRzsUALQAAGkEIIQcgC0EIENYEIgpFDRwgCEUNAEEAIQcgCCEEA0AgByALRg0BIAcgCmoiFiAHIAxqIg4pAwA3AwAgFkEYaiAOQRhqKQMANwMAIBZBEGogDkEQaikDADcDACAWQQhqIA5BCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgDyAINgIoIA8gCjYCJCAPIAg2AiAgDyAdNgIcIA8gHTYCDCAPICYoAgA2AiwgBUEDNgKcGCAFIA82ApgYIAVBAzYClBggBUEANgKoGCAFQoCAgICAATcCoBgCQAJAAkACQCA1BEBBACEHIBUhCyAQIQQgOSEMICchDgNAIAcgFEYNAiAHIDtGDQMgByA6Rg0EIAVBsBNqIAsgBCAOIAwQmQEgBUHwDmogBkGAAfwKAAAgBUH4EmoiHyAFQbgTaikDADcDACAFQfgIaiIWIERBCGopAgA3AwAgBSAFKQOwEzcD8BIgBSBEKQIANwPwCCAFKAKcGCIPIAUoApQYIjBGBEAgBUGUGGpBwJPAABCjAyAFKAKUGCEwCyAFKAKYGCIKIA9BBHRqIgggBSkD8BI3AgAgCEEIaiAfKQMANwIAIAUgD0EBaiIINgKcGCAIIDBGBH8gBUGUGGpB0JPAABCjAyAFKAKYGAUgCgsgCEEEdGoiCCAFKQPwCDcCACAIQQhqIBYpAwA3AgAgBSAPQQJqNgKcGCAFKAKoGCIIIAUoAqAYRgRAIAVBoBhqQeCTwAAQpAMLIAUoAqQYIAhBB3RqIAVB8A5qQYAB/AoAACAFIAhBAWo2AqgYIAtBgAFqIQsgBEGAAWohBCAMQSBqIQwgDkEgaiEOIDUgB0EBaiIHRw0ACwsgBUG4EmogBUGcGGooAgA2AgAgBSAFKQKUGDcDsBIgBUGAgICAeDYCsBMgBUHwC2ogBUGwEmogBUGwE2ogBUHYBGogBUHkBGoQwQEgLEEIaiAFQagYaigCADYCACAsIAUpAqAYNwIAIAVB6AdqIgogSSkCADcDACAFIAUpAvALNwPgByAFKAKADCEHIAUoAoQMIQggBSgCiAwhNSAFKAKgBSIEBEAgHiAEQQV0EN8ECyBCIAopAwA3AwAgBSAFKQPgBzcDoAUgEUUNAyAVIBFBB3QQ3wQMAwsgFCAUQZCTwAAQ2QMACyA7IDtBoJPAABDZAwALIDogOkGwk8AAENkDAAsgDSEWIAgLIRUgHCASRXJFBEAgBSgC/BcgEkEFdBDfBCAqRQ0ODAoLICpFDQ0MCQsgBUEANgKcGCAFQoCAgICAATcClBgMAQtBACEIIAVBADYCnBggBUKAgICAgAE3ApQYIDkhBCAnIQxBACEHA0AgByAFKAKQGCIKTw0CIAcgG0YNAyAHIDtGDQQgByA6Rg0FIAVBsBNqIAUoAowYIAhqIAggEGogDCAEEJkBIAVB8A5qIAZBgAH8CgAAIAVBuBJqIhkgBUG4E2opAwA3AwAgBUH4EmoiJiBEQQhqKQIANwMAIAUgBSkDsBM3A7ASIAUgRCkCADcD8BIgBSgChBgiHCAFKAL8FyIKRgRAIAVB/BdqQcCUwAAQowMgBSgC/BchCgsgBSgCgBgiDyAcQQR0aiIfIAUpA7ASNwIAIB9BCGogGSkDADcCACAFIBxBAWoiHzYChBggCiAfRgR/IAVB/BdqQdCUwAAQowMgBSgCgBgFIA8LIB9BBHRqIgogBSkD8BI3AgAgCkEIaiAmKQMANwIAIAUgHEECajYChBggBSgCnBgiCiAFKAKUGEYEQCAFQZQYakHglMAAEKQDCyAFKAKYGCAKQQd0aiAFQfAOakGAAfwKAAAgBSAKQQFqNgKcGCAEQSBqIQQgDEEgaiEMIAhBgAFqIQggNSAHQQFqIgdHDQALCyAOKAIAIghBBXQhCkEAIQcgCEH///8/SyAKQfj///8HS3INFAJAIApFBEBBCCEODAELIA0oAgAhDEHRzsUALQAAGkEIIQcgCkEIENYEIg5FDRUgCEUNAEEAIQcgCCEEA0AgByAKRg0BIAcgDmoiHyAHIAxqIg0pAwA3AwAgH0EYaiANQRhqKQMANwMAIB9BEGogDUEQaikDADcDACAfQQhqIA1BCGopAwA3AwAgB0EgaiEHIARBAWsiBA0ACwsgCygCACEEIAUoAoQYIgcgBSgC/BdGBEAgBUH8F2pB8JPAABCjAwsgBSgCgBggB0EEdGoiCiAENgIMIAogCDYCCCAKIA42AgQgCiAINgIAIAVBhBhqIAdBAWoiBDYCACAFQagYaiAENgIAIAUgBSkC/Bc3A6AYIAVBgICAgHg2ArATIAVB8AhqIAVBoBhqIAVBsBNqIAVB2ARqIAVB5ARqEMEBIEBBCGogBUGcGGooAgA2AgAgQCAFKQKUGDcCACAFKAKIGCIEBEAgBSgCjBggBEEHdBDfBAsgBUGgB2oiCiAFQfgIaikCADcDACAFIAUpAvAINwOYByAFKAKACSEHIAUoAoQJIAUoAogJITUgBSgCoAUiCARAIB4gCEEFdBDfBAsgQiAKKQMANwMAIAUgBSkDmAc3A6AFIBEEQCAVIBFBB3QQ3wQLIRUgKkUNCgwGCyAHIApBgJTAABDZAwALIBsgG0GQlMAAENkDAAsgOyA7QaCUwAAQ2QMACyA6IDpBsJTAABDZAwALQQAhCCAFQQA2AqgYIAVCgICAgIABNwKgGCA5IQsgJyEEQQAhBwNAIAcgBSgCnBgiCk8NAyAHIDtGDQQgByA6Rg0FIAVBsBNqIgogBSgCmBggCGogBCALELUCIAVB8A5qIApBgAH8CgAAIAVB+BJqIgwgQ0EIaikCADcDACAFIEMpAgA3A/ASIAUoApAYIg0gBSgCiBhGBEAgBUGIGGpB0JHAABCjAwsgBSgCjBggDUEEdGoiCiAFKQPwEjcCACAKQQhqIAwpAwA3AgAgBSANQQFqNgKQGCAFKAKoGCIKIAUoAqAYRgRAIAVBoBhqQeCRwAAQpAMLIAUoAqQYIApBB3RqIAVB8A5qQYAB/AoAACAFIApBAWo2AqgYIAtBIGohCyAEQSBqIQQgCEGAAWohCCA1IAdBAWoiB0cNAAsLIAVBuBJqIAVBkBhqKAIANgIAIAUgBSkCiBg3A7ASIAVBgICAgHg2ArATIAVB8AhqIAVBsBJqIAVBsBNqIAVB2ARqIAVB5ARqEMEBIEBBCGogBUGoGGooAgA2AgAgQCAFKQKgGDcCACAFKAKUGCIEBEAgBSgCmBggBEEHdBDfBAsgBUGQB2oiCiAFQfgIaikCADcDACAFIAUpAvAINwOIByAFKAKACSEHIAUoAoQJIAUoAogJITUgBSgCoAUiCARAIA8gCEEFdBDfBAsgQiAKKQMANwMAIAUgBSkDiAc3A6AFIBEhKiAVIRAhFSARRQ0ECyAQICpBB3QQ3wQMAwsgByAKQaCRwAAQ2QMACyA7IDtBsJHAABDZAwALIDogOkHAkcAAENkDAAsgFkEBayENIBZBAEoNAAsLQdHOxQAtAAAaQQxBARDWBCIERQRAQQFBDBD/BAALIARCADcAASAEQQE6AAAgBEEIakEANgAAIAVBDDYC/AcgBSAENgL4ByAFQQw2AvQHIAVBsBNqIR8jAEHAGGsiBiQAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIEYOAgECAAtBmMnBAEEPQajJwQAQ/gMAC0HRzsUALQAAGkGQAUEEENYEIhtFDVNB0c7FAC0AABpB0ABBCBDWBCIgRQ1RIAZB2J/BAEEBEHkgBi0AAEEBRg0BIAZBsBdqIjAiHSAGQRBqIhkiLCkDACJTNwMAIAZBwBdqIiEgBkEgaiITKQMAIlI3AwAgBkG4F2oiFyAGQRhqIhQpAwAiUTcDACAGQfQWaiImIFI3AgAgBkHsFmoiEiBRNwIAIAZB5BZqIh4gUzcCACAGIAYpAwg3AtwWIAZB2Z/BAEECEHkgBi0AAEEBRg0CIAZB2BdqIiggLCkDACJTNwMAIAZB6BdqIjEgEykDACJSNwMAIAZB4BdqIjIgFCkDACJRNwMAIAZBxBdqIiUgUjcCACAGQbwXaiIpIFE3AgAgBkG0F2oiIyBTNwIAIAYgBikDCDcCrBcgIEEANgIAICBBBjYCKCAgIAYpAtgWNwIEICBBDGogBkHgFmoiBCIqKQIANwIAICBBFGogBkHoFmoiCCIPKQIANwIAICBBHGogBkHwFmoiDCIWKQIANwIAICBBJGogBkH4FmooAgA2AgAgICAGKQKoFzcCLCAgQTRqIB0pAgA3AgAgIEE8aiAXKQIANwIAICBBxABqICEpAgA3AgAgIEHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIkRQ1RIAZB25/BAEHAABB5IAYtAABBAUYNAyAdICwpAwAiUzcDACAhIBMpAwAiUjcDACAXIBQpAwAiUTcDACAmIFI3AgAgEiBRNwIAIB4gUzcCACAGIAYpAwg3AtwWIAZBm6DBAEHAABB5IAYtAABBAUYNBCAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXICRBATYCACAkQQc2AiggJCAGKQLYFjcCBCAkQQxqICopAgA3AgAgJEEUaiAPKQIANwIAICRBHGogFikCADcCACAkQSRqIAZB+BZqKAIANgIAICQgBikCqBc3AiwgJEE0aiAdKQIANwIAICRBPGogFykCADcCACAkQcQAaiAhKQIANwIAICRBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiK0UNUSAGQdugwQBBwAAQeSAGLQAAQQFGDQUgHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQZuhwQBBPxB5IAYtAABBAUYNBiAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXICtBAjYCACArQQg2AiggKyAGKQLYFjcCBCArQQxqIAQpAgA3AgAgK0EUaiAPKQIANwIAICtBHGogFikCADcCACArQSRqIAZB+BZqKAIANgIAICsgBikCqBc3AiwgK0E0aiAdKQIANwIAICtBPGogFykCADcCACArQcQAaiAhKQIANwIAICtBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiEUUNUSAGQdqhwQBBwAAQeSAGLQAAQQFGDQcgHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQZqiwQBBwAAQeSAGLQAAQQFGDQggKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyARQQM2AgAgEUEJNgIoIBEgBikC2BY3AgQgEUEMaiAEKQIANwIAIBFBFGogCCkCADcCACARQRxqIAwpAgA3AgAgEUEkaiAGQfgWaigCADYCACARIAYpAqgXNwIsIBFBNGogHSkCADcCACARQTxqIBcpAgA3AgAgEUHEAGogISkCADcCACARQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIhBFDVEgBkHaosEAQcAAEHkgBi0AAEEBRg0JIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkGao8EAQT8QeSAGLQAAQQFGDQogKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAQQQQ2AgAgEEEKNgIoIBAgBikC2BY3AgQgEEEMaiAGQeAWaikCADcCACAQQRRqIAZB6BZqKQIANwIAIBBBHGogBkHwFmopAgA3AgAgEEEkaiAGQfgWaigCADYCACAQIAYpAqgXNwIsIBBBNGogHSkCADcCACAQQTxqIBcpAgA3AgAgEEHEAGogISkCADcCACAQQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIg5FDVEgBkHZo8EAQcAAEHkgBi0AAEEBRg0LIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkGZpMEAQcAAEHkgBi0AAEEBRg0MICggLCkDACJTNwMAIDEgEykDACJSNwMAIDIgFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgDkEFNgIAIA5BCzYCKCAOIAYpAtgWNwIEIA5BDGogBkHgFmopAgA3AgAgDkEUaiAGQegWaikCADcCACAOQRxqIAZB8BZqKQIANwIAIA5BJGogBkH4FmooAgA2AgAgDiAGKQKoFzcCLCAOQTRqIB0pAgA3AgAgDkE8aiAXKQIANwIAIA5BxABqICEpAgA3AgAgDkHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIgRFDVIgBkHZpMEAQcAAEHkgBi0AAEEBRg0NICogLCkDACJTNwMAIBYgEykDACJSNwMAIA8gFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgBEEGNgIAIAQgBikCqBc3AgQgBEEMaiAdKQIANwIAIARBFGogFykCADcCACAEQRxqICEpAgA3AgAgBEEkaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIg1FDVEgBkGZpcEAQcAAEHkgBi0AAEEBRg0OIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkHZpcEAQcAAEHkgBi0AAEEBRg0PICggLCkDACJTNwMAIDEgEykDACJSNwMAIDIgFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgDUEBNgIAIA1BBzYCKCANIAYpAtgWNwIEIA1BDGogBkHgFmopAgA3AgAgDUEUaiAGQegWaikCADcCACANQRxqIAZB8BZqKQIANwIAIA1BJGogBkH4FmooAgA2AgAgDSAGKQKoFzcCLCANQTRqIB0pAgA3AgAgDUE8aiAXKQIANwIAIA1BxABqICEpAgA3AgAgDUHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIMRQ1RIAZBmabBAEHAABB5IAYtAABBAUYNECAdICwpAwAiUzcDACAhIBMpAwAiUjcDACAXIBQpAwAiUTcDACAmIFI3AgAgEiBRNwIAIB4gUzcCACAGIAYpAwg3AtwWIAZB2abBAEE/EHkgBi0AAEEBRg0RICggLCkDACJTNwMAIDEgEykDACJSNwMAIDIgFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgDEECNgIAIAxBCDYCKCAMIAYpAtgWNwIEIAxBDGogBkHgFmopAgA3AgAgDEEUaiAGQegWaikCADcCACAMQRxqIAZB8BZqKQIANwIAIAxBJGogBkH4FmooAgA2AgAgDCAGKQKoFzcCLCAMQTRqIB0pAgA3AgAgDEE8aiAXKQIANwIAIAxBxABqICEpAgA3AgAgDEHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCILRQ1RIAZBmKfBAEE/EHkgBi0AAEEBRg0SIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkHXp8EAQT8QeSAGLQAAQQFGDRMgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyALQQM2AgAgC0EJNgIoIAsgBikC2BY3AgQgC0EMaiAGQeAWaikCADcCACALQRRqIAZB6BZqKQIANwIAIAtBHGogBkHwFmopAgA3AgAgC0EkaiAGQfgWaigCADYCACALIAYpAqgXNwIsIAtBNGogHSkCADcCACALQTxqIBcpAgA3AgAgC0HEAGogISkCADcCACALQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIgpFDVEgBkGWqMEAQcAAEHkgBi0AAEEBRg0UIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkHWqMEAQT8QeSAGLQAAQQFGDRUgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAKQQQ2AgAgCkEKNgIoIAogBikC2BY3AgQgCkEMaiAGQeAWaikCADcCACAKQRRqIAZB6BZqKQIANwIAIApBHGogBkHwFmopAgA3AgAgCkEkaiAGQfgWaigCADYCACAKIAYpAqgXNwIsIApBNGogHSkCADcCACAKQTxqIBcpAgA3AgAgCkHEAGogISkCADcCACAKQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIghFDVEgBkGVqcEAQcAAEHkgBi0AAEEBRg0WIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkHVqcEAQcAAEHkgBi0AAEEBRg0XICggLCkDACJTNwMAIDEgEykDACJSNwMAIDIgFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgCEEFNgIAIAhBCzYCKCAIIAYpAtgWNwIEIAhBDGogBkHgFmopAgA3AgAgCEEUaiAGQegWaikCADcCACAIQRxqIAZB8BZqKQIANwIAIAhBJGogBkH4FmooAgA2AgAgCCAGKQKoFzcCLCAIQTRqIB0pAgA3AgAgCEE8aiAXKQIANwIAIAhBxABqICEpAgA3AgAgCEHMAGogBkHIF2ooAgA2AgAgG0ECNgKMASAbIAg2AogBIBtCgoCAgCA3AoABIBsgCjYCfCAbQoKAgIAgNwJ0IBsgCzYCcCAbQoKAgIAgNwJoIBsgDDYCZCAbQoKAgIAgNwJcIBsgDTYCWCAbQoGAgIAgNwJQIBsgBDYCTCAbQoKAgIAQNwJEIBsgDjYCQCAbQoKAgIAgNwI4IBsgEDYCNCAbQoKAgIAgNwIsIBsgETYCKCAbQoKAgIAgNwIgIBsgKzYCHCAbQoKAgIAgNwIUIBsgJDYCECAbQoKAgIAgNwIIIBsgIDYCBCAbQQI2AgBB0c7FAC0AABpBkAFBBBDWBCIcRQ1TQdHOxQAtAAAaQShBCBDWBCIgRQ1SIAZB2J/BAEEBEHkgBi0AAEEBRg0YICogLCkDACJTNwMAIBYgEykDACJSNwMAIA8gFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgIEEANgIAICAgBikCqBc3AgQgIEEMaiAdKQIANwIAICBBFGogFykCADcCACAgQRxqICEpAgA3AgAgIEEkaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiJEUNUiAGQZWqwQBBwAAQeSAGLQAAQQFGDRkgKiAsKQMAIlM3AwAgFiATKQMAIlI3AwAgDyAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAkQQE2AgAgJCAGKQKoFzcCBCAkQQxqIB0pAgA3AgAgJEEUaiAXKQIANwIAICRBHGogISkCADcCACAkQSRqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCIrRQ1SIAZB1arBAEHAABB5IAYtAABBAUYNGiAqIBkpAwAiUzcDACAWIBMpAwAiUjcDACAPIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXICtBAjYCACArIAYpAqgXNwIEICtBDGogMCkCADcCACArQRRqIBcpAgA3AgAgK0EcaiAhKQIANwIAICtBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIhFFDVIgBkHZpMEAQcAAEHkgBi0AAEEBRg0bICogBkEQaikDACJTNwMAIBYgBkEgaikDACJSNwMAIA8gBkEYaikDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgEUEDNgIAIBEgBikCqBc3AgQgEUEMaiAGQbAXaikCADcCACARQRRqIAZBuBdqKQIANwIAIBFBHGogBkHAF2opAgA3AgAgEUEkaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiEEUNUiAGQZWrwQBBMBB5IAYtAABBAUYNHCAqIAZBEGopAwAiUzcDACAWIAZBIGopAwAiUjcDACAPIAZBGGopAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIBBBBDYCACAQIAYpAqgXNwIEIBBBDGogBkGwF2opAgA3AgAgEEEUaiAGQbgXaikCADcCACAQQRxqIAZBwBdqKQIANwIAIBBBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIg5FDVIgBkHFq8EAQTAQeSAGLQAAQQFGDR0gKiAGQRBqKQMAIlM3AwAgFiAGQSBqKQMAIlI3AwAgDyAGQRhqKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAOQQU2AgAgDiAGKQKoFzcCBCAOQQxqIAZBsBdqKQIANwIAIA5BFGogBkG4F2opAgA3AgAgDkEcaiAGQcAXaikCADcCACAOQSRqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCINRQ1SIAZB2J/BAEEBEHkgBi0AAEEBRg0eICogBkEQaikDACJTNwMAIBYgBkEgaikDACJSNwMAIA8gBkEYaikDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgDUEGNgIAIA0gBikCqBc3AgQgDUEMaiAGQbAXaikCADcCACANQRRqIAZBuBdqKQIANwIAIA1BHGogBkHAF2opAgA3AgAgDUEkaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiDEUNUiAGQZWqwQBBwAAQeSAGLQAAQQFGDR8gKiAGQRBqKQMAIlM3AwAgFiAGQSBqKQMAIlI3AwAgDyAGQRhqKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAMQQc2AgAgDCAGKQKoFzcCBCAMQQxqIAZBsBdqKQIANwIAIAxBFGogBkG4F2opAgA3AgAgDEEcaiAGQcAXaikCADcCACAMQSRqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCILRQ1SIAZB1arBAEHAABB5IAYtAABBAUYNICAqIAZBEGopAwAiUzcDACAWIAZBIGopAwAiUjcDACAPIAZBGGopAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIAtBCDYCACALIAYpAqgXNwIEIAtBDGogBkGwF2opAgA3AgAgC0EUaiAGQbgXaikCADcCACALQRxqIAZBwBdqKQIANwIAIAtBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIgpFDVIgBkHZpMEAQcAAEHkgBi0AAEEBRg0hICogBkEQaikDACJTNwMAIBYgBkEgaikDACJSNwMAIA8gBkEYaikDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgCkEJNgIAIAogBikCqBc3AgQgCkEMaiAGQbAXaikCADcCACAKQRRqIAZBuBdqKQIANwIAIApBHGogBkHAF2opAgA3AgAgCkEkaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiCEUNUiAGQZWrwQBBMBB5IAYtAABBAUYNIiAqIAZBEGopAwAiUzcDACAWIAZBIGopAwAiUjcDACAPIAZBGGopAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIAhBCjYCACAIIAYpAqgXNwIEIAhBDGogBkGwF2opAgA3AgAgCEEUaiAGQbgXaikCADcCACAIQRxqIAZBwBdqKQIANwIAIAhBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIgRFDVIgBkHFq8EAQTAQeSAGLQAAQQFGDSMgKiAGQRBqKQMAIlM3AwAgFiAGQSBqKQMAIlI3AwAgDyAGQRhqKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAEQQs2AgAgBCAGKQKoFzcCBCAEQQxqIAZBsBdqKQIANwIAIARBFGogBkG4F2opAgA3AgAgBEEcaiAGQcAXaikCADcCACAEQSRqIAZByBdqKAIANgIAIBxBATYCjAEgHCAENgKIASAcQoGAgIAQNwKAASAcIAg2AnwgHEKBgICAEDcCdCAcIAo2AnAgHEKBgICAEDcCaCAcIAs2AmQgHEKBgICAEDcCXCAcIAw2AlggHEKBgICAEDcCUCAcIA02AkwgHEKBgICAEDcCRCAcIA42AkAgHEKBgICAEDcCOCAcIBA2AjQgHEKBgICAEDcCLCAcIBE2AiggHEKBgICAEDcCICAcICs2AhwgHEKBgICAEDcCFCAcICQ2AhAgHEKBgICAEDcCCCAcICA2AgQgHEEBNgIAQdHOxQAtAAAaQZABQQQQ1gQiGUUNU0HRzsUALQAAGkHQAEEIENYEIiBFDVEgBkHYn8EAQQEQeSAGLQAAQQFGDSQgHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQdmfwQBBAhB5IAYtAABBAUYNJSAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXICBBADYCACAgQQY2AiggICAGKQLYFjcCBCAgQQxqIAZB4BZqKQIANwIAICBBFGogBkHoFmopAgA3AgAgIEEcaiAGQfAWaikCADcCACAgQSRqIAZB+BZqKAIANgIAICAgBikCqBc3AiwgIEE0aiAdKQIANwIAICBBPGogFykCADcCACAgQcQAaiAhKQIANwIAICBBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiJEUNUSAGQfWrwQBBwAAQeSAGLQAAQQFGDSYgHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQbWswQBBwAAQeSAGLQAAQQFGDScgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAkQQE2AgAgJEEHNgIoICQgBikC2BY3AgQgJEEMaiAGQeAWaikCADcCACAkQRRqIAZB6BZqKQIANwIAICRBHGogBkHwFmopAgA3AgAgJEEkaiAGQfgWaigCADYCACAkIAYpAqgXNwIsICRBNGogHSkCADcCACAkQTxqIBcpAgA3AgAgJEHEAGogISkCADcCACAkQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIitFDVEgBkH1rMEAQT8QeSAGLQAAQQFGDSggHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQbStwQBBwAAQeSAGLQAAQQFGDSkgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyArQQI2AgAgK0EINgIoICsgBikC2BY3AgQgK0EMaiAGQeAWaikCADcCACArQRRqIAZB6BZqKQIANwIAICtBHGogBkHwFmopAgA3AgAgK0EkaiAGQfgWaigCADYCACArIAYpAqgXNwIsICtBNGogHSkCADcCACArQTxqIBcpAgA3AgAgK0HEAGogISkCADcCACArQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIhFFDVEgBkHXp8EAQT8QeSAGLQAAQQFGDSogHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQfStwQBBwAAQeSAGLQAAQQFGDSsgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyARQQM2AgAgEUEJNgIoIBEgBikC2BY3AgQgEUEMaiAGQeAWaikCADcCACARQRRqIAZB6BZqKQIANwIAIBFBHGogBkHwFmopAgA3AgAgEUEkaiAGQfgWaigCADYCACARIAYpAqgXNwIsIBFBNGogHSkCADcCACARQTxqIBcpAgA3AgAgEUHEAGogISkCADcCACARQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIhBFDVEgBkG0rsEAQcAAEHkgBi0AAEEBRg0sIB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkH0rsEAQT8QeSAGLQAAQQFGDS0gKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAQQQQ2AgAgEEEKNgIoIBAgBikC2BY3AgQgEEEMaiAGQeAWaikCADcCACAQQRRqIAZB6BZqKQIANwIAIBBBHGogBkHwFmopAgA3AgAgEEEkaiAGQfgWaigCADYCACAQIAYpAqgXNwIsIBBBNGogHSkCADcCACAQQTxqIBcpAgA3AgAgEEHEAGogISkCADcCACAQQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIg5FDVEgBkGzr8EAQT8QeSAGLQAAQQFGDS4gHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQfKvwQBBwAAQeSAGLQAAQQFGDS8gKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAOQQU2AgAgDkELNgIoIA4gBikC2BY3AgQgDkEMaiAGQeAWaikCADcCACAOQRRqIAZB6BZqKQIANwIAIA5BHGogBkHwFmopAgA3AgAgDkEkaiAGQfgWaigCADYCACAOIAYpAqgXNwIsIA5BNGogHSkCADcCACAOQTxqIBcpAgA3AgAgDkHEAGogISkCADcCACAOQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiBEUNUiAGQdmkwQBBwAAQeSAGLQAAQQFGDTAgKiAGQRBqKQMAIlM3AwAgFiAGQSBqKQMAIlI3AwAgDyAGQRhqKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyAEQQY2AgAgBCAGKQKoFzcCBCAEQQxqIAZBsBdqKQIANwIAIARBFGogBkG4F2opAgA3AgAgBEEcaiAGQcAXaikCADcCACAEQSRqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiDUUNUSAGQbKwwQBBPhB5IAYtAABBAUYNMSAdICwpAwAiUzcDACAhIBMpAwAiUjcDACAXIBQpAwAiUTcDACAmIFI3AgAgEiBRNwIAIB4gUzcCACAGIAYpAwg3AtwWIAZB8LDBAEHAABB5IAYtAABBAUYNMiAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIA1BATYCACANQQc2AiggDSAGKQLYFjcCBCANQQxqIAZB4BZqKQIANwIAIA1BFGogBkHoFmopAgA3AgAgDUEcaiAGQfAWaikCADcCACANQSRqIAZB+BZqKAIANgIAIA0gBikCqBc3AiwgDUE0aiAdKQIANwIAIA1BPGogFykCADcCACANQcQAaiAhKQIANwIAIA1BzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiDEUNUSAGQbCxwQBBPxB5IAYtAABBAUYNMyAdICwpAwAiUzcDACAhIBMpAwAiUjcDACAXIBQpAwAiUTcDACAmIFI3AgAgEiBRNwIAIB4gUzcCACAGIAYpAwg3AtwWIAZB77HBAEHAABB5IAYtAABBAUYNNCAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIAxBAjYCACAMQQg2AiggDCAGKQLYFjcCBCAMQQxqIAZB4BZqKQIANwIAIAxBFGogBkHoFmopAgA3AgAgDEEcaiAGQfAWaikCADcCACAMQSRqIAZB+BZqKAIANgIAIAwgBikCqBc3AiwgDEE0aiAdKQIANwIAIAxBPGogFykCADcCACAMQcQAaiAhKQIANwIAIAxBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiC0UNUSAGQa+ywQBBwAAQeSAGLQAAQQFGDTUgHSAsKQMAIlM3AwAgISATKQMAIlI3AwAgFyAUKQMAIlE3AwAgJiBSNwIAIBIgUTcCACAeIFM3AgAgBiAGKQMINwLcFiAGQdqhwQBBwAAQeSAGLQAAQQFGDTYgKCAsKQMAIlM3AwAgMSATKQMAIlI3AwAgMiAUKQMAIlE3AwAgJSBSNwIAICkgUTcCACAjIFM3AgAgBiAGKQMINwKsFyALQQM2AgAgC0EJNgIoIAsgBikC2BY3AgQgC0EMaiAGQeAWaikCADcCACALQRRqIAZB6BZqKQIANwIAIAtBHGogBkHwFmopAgA3AgAgC0EkaiAGQfgWaigCADYCACALIAYpAqgXNwIsIAtBNGogHSkCADcCACALQTxqIBcpAgA3AgAgC0HEAGogISkCADcCACALQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIgpFDVEgBkHvssEAQcAAEHkgBi0AAEEBRg03IB0gLCkDACJTNwMAICEgEykDACJSNwMAIBcgFCkDACJRNwMAICYgUjcCACASIFE3AgAgHiBTNwIAIAYgBikDCDcC3BYgBkGvs8EAQcAAEHkgBi0AAEEBRg04ICggLCkDACJTNwMAIDEgEykDACJSNwMAIDIgFCkDACJRNwMAICUgUjcCACApIFE3AgAgIyBTNwIAIAYgBikDCDcCrBcgCkEENgIAIApBCjYCKCAKIAYpAtgWNwIEIApBDGogBkHgFmopAgA3AgAgCkEUaiAGQegWaikCADcCACAKQRxqIAZB8BZqKQIANwIAIApBJGogBkH4FmooAgA2AgAgCiAGKQKoFzcCLCAKQTRqIB0pAgA3AgAgCkE8aiAXKQIANwIAIApBxABqICEpAgA3AgAgCkHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIIRQ1RIAZB77PBAEHAABB5IAYtAABBAUYNOSAdICwpAwAiUzcDACAhIBMpAwAiUjcDACAXIBQpAwAiUTcDACAmIFI3AgAgEiBRNwIAIB4gUzcCACAGIAYpAwg3AtwWIAZBr7TBAEHAABB5IAYtAABBAUYNOiAoICwpAwAiUzcDACAxIBMpAwAiUjcDACAyIBQpAwAiUTcDACAlIFI3AgAgKSBRNwIAICMgUzcCACAGIAYpAwg3AqwXIAhBBTYCACAIQQs2AiggCCAGKQLYFjcCBCAIQQxqIAZB4BZqKQIANwIAIAhBFGogBkHoFmopAgA3AgAgCEEcaiAGQfAWaikCADcCACAIQSRqIAZB+BZqKAIANgIAIAggBikCqBc3AiwgCEE0aiAdKQIANwIAIAhBPGogFykCADcCACAIQcQAaiAhKQIANwIAIAhBzABqIAZByBdqKAIANgIAIBlBAjYCjAEgGSAINgKIASAZQoKAgIAgNwKAASAZIAo2AnwgGUKCgICAIDcCdCAZIAs2AnAgGUKCgICAIDcCaCAZIAw2AmQgGUKCgICAIDcCXCAZIA02AlggGUKBgICAIDcCUCAZIAQ2AkwgGUKCgICAEDcCRCAZIA42AkAgGUKCgICAIDcCOCAZIBA2AjQgGUKCgICAIDcCLCAZIBE2AiggGUKCgICAIDcCICAZICs2AhwgGUKCgICAIDcCFCAZICQ2AhAgGUKCgICAIDcCCCAZICA2AgQgGUECNgIAIAZBDDYCLCAGIBk2AiggBkEMNgIkIAZCjICAgDA3AhwgBiAcNgIYIAZBDDYCFCAGQoyAgIAgNwIMIAYgGzYCCCAGQoGAgIDAATcCABDHBCIERQ07IAQgBCkDACJSQgF8NwMAIAQpAwghUSAGQaAYaiIQQYixwgApAwA3AwAgBkGwGGoiDiBRNwMAIAZBqBhqIg0gUjcDACAGQYCxwgApAwA3A5gYIwBBMGsiICQAQQJBAyAGQZgYaiIkKAIMGyIEICQoAghLBEAgIEEIaiAkIAQgJEEQahClAQsgIEEYaiIMIAZBCGopAgA3AwAgICAGKQIAIlE3AxAgIEEkaiAkIFGnICBBEGpBBHIiKxDpAQJAICAoAiQiEUGAgICAeEYNACAgKAIoIQQgICgCLCILBEAgBCEIA0AgCCgCACIKBEAgCEEEaigCACAKQShsEN8ECyAIQQxqIQggC0EBayILDQALCyARRQ0AIAQgEUEMbBDfBAsgDCAGQRhqKQIANwMAICAgBikCECJRNwMQICBBJGogJCBRpyArEOkBAkAgICgCJCIMQYCAgIB4Rg0AICAoAighBCAgKAIsIgsEQCAEIQgDQCAIKAIAIgoEQCAIQQRqKAIAIApBKGwQ3wQLIAhBDGohCCALQQFrIgsNAAsLIAxFDQAgBCAMQQxsEN8ECyAgQRhqIAZBKGopAgA3AwAgICAGKQIgIlE3AxAgIEEkaiAkIFGnICsQ6QECQCAgKAIkIgxBgICAgHhGDQAgICgCKCEEICAoAiwiCwRAIAQhCANAIAgoAgAiCgRAIAhBBGooAgAgCkEobBDfBAsgCEEMaiEIIAtBAWsiCw0ACwsgDEUNACAEIAxBDGwQ3wQLICBBMGokACAfQRhqIA4pAwA3AwAgH0EQaiANKQMANwMAIB9BCGogECkDADcDACAfIAYpA5gYNwMADFALQdHOxQAtAAAaQZABQQQQ1gQiE0UNUkHRzsUALQAAGkHQAEEIENYEIhxFDVAgBkHYn8EAQQEQeSAGLQAAQQFGDTsgBkGwF2oiKyIlIAZBEGoiMCIXKQMAIlM3AwAgBkHAF2oiHSIpIAZBIGoiISIjKQMAIlI3AwAgBkG4F2oiGyAGQRhqIhQpAwAiUTcDACAGQfQWaiIRIFI3AgAgBkHsFmoiECBRNwIAIAZB5BZqIg4gUzcCACAGIAYpAwg3AtwWIAZBzLzBAEEBEHkgBi0AAEEBRg08IAZB2BdqIg0gFykDACJTNwMAIAZB6BdqIgwgIykDACJSNwMAIAZB4BdqIgsgFCkDACJRNwMAIAZBxBdqIjEgUjcCACAGQbwXaiIyIFE3AgAgBkG0F2oiDyBTNwIAIAYgBikDCDcCrBcgHEEANgIAIBxBBjYCKCAcIAYpAtgWNwIEIBxBDGogBkHgFmoiCikCADcCACAcQRRqIAZB6BZqIggpAgA3AgAgHEEcaiAGQfAWaiIEKQIANwIAIBxBJGogBkH4FmooAgA2AgAgHCAGKQKoFzcCLCAcQTRqICUpAgA3AgAgHEE8aiAbKQIANwIAIBxBxABqICkpAgA3AgAgHEHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIZRQ1QIAZBzbzBAEHgABB5IAYtAABBAUYNPSAlIBcpAwAiUzcDACApICMpAwAiUjcDACAbIBQpAwAiUTcDACARIFI3AgAgECBRNwIAIA4gUzcCACAGIAYpAwg3AtwWIAZBzbzBAEHgABB5IAYtAABBAUYNPiANIBcpAwAiUzcDACAMICMpAwAiUjcDACALIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXIBlBATYCACAZQQc2AiggGSAGKQLYFjcCBCAZQQxqIAopAgA3AgAgGUEUaiAIKQIANwIAIBlBHGogBCkCADcCACAZQSRqIAZB+BZqKAIANgIAIBkgBikCqBc3AiwgGUE0aiAlKQIANwIAIBlBPGogGykCADcCACAZQcQAaiApKQIANwIAIBlBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCIWRQ1RIAZBrb3BAEHQABB5IAYtAABBAUYNPyAKIBcpAwAiUzcDACAEICMpAwAiUjcDACAIIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXIBZBAjYCACAWIAYpAqgXNwIEIBZBDGogJSkCADcCACAWQRRqIBspAgA3AgAgFkEcaiApKQIANwIAIBZBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpBKEEIENYEIipFDVEgBkH9vcEAQd8AEHkgBi0AAEEBRg1AIAogFykDACJTNwMAIAQgIykDACJSNwMAIAggFCkDACJRNwMAIDEgUjcCACAyIFE3AgAgDyBTNwIAIAYgBikDCDcCrBcgKkEJNgIAICogBikCqBc3AgQgKkEMaiAlKQIANwIAICpBFGogGykCADcCACAqQRxqICkpAgA3AgAgKkEkaiAGQcgXaigCADYCAEHRzsUALQAAGkHQAEEIENYEIiZFDVAgBkHcvsEAQeAAEHkgBi0AAEEBRg1BICUgFykDACJTNwMAICkgIykDACJSNwMAIBsgFCkDACJRNwMAIBEgUjcCACAQIFE3AgAgDiBTNwIAIAYgBikDCDcC3BYgBkG8v8EAQeAAEHkgBi0AAEEBRg1CIA0gFykDACJTNwMAIAwgIykDACJSNwMAIAsgFCkDACJRNwMAIDEgUjcCACAyIFE3AgAgDyBTNwIAIAYgBikDCDcCrBcgJkEENgIAICZBCjYCKCAmIAYpAtgWNwIEICZBDGogCikCADcCACAmQRRqIAgpAgA3AgAgJkEcaiAEKQIANwIAICZBJGogBkH4FmooAgA2AgAgJiAGKQKoFzcCLCAmQTRqICUpAgA3AgAgJkE8aiAbKQIANwIAICZBxABqICkpAgA3AgAgJkHMAGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCISRQ1QIAZBnMDBAEHfABB5IAYtAABBAUYNQyAlIBcpAwAiUzcDACApICMpAwAiUjcDACAbIBQpAwAiUTcDACARIFI3AgAgECBRNwIAIA4gUzcCACAGIAYpAwg3AtwWIAZBnMDBAEHfABB5IAYtAABBAUYNRCANIBcpAwAiUzcDACAMICMpAwAiUjcDACALIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXIBJBBTYCACASQQs2AiggEiAGKQLYFjcCBCASQQxqIAopAgA3AgAgEkEUaiAIKQIANwIAIBJBHGogBCkCADcCACASQSRqIAZB+BZqKAIANgIAIBIgBikCqBc3AiwgEkE0aiAlKQIANwIAIBJBPGogGykCADcCACASQcQAaiApKQIANwIAIBJBzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCIgRQ1RIAZB+8DBAEHgABB5IAYtAABBAUYNRSAKIBcpAwAiUzcDACAEICMpAwAiUjcDACAIIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXICBBBjYCACAgIAYpAqgXNwIEICBBDGogJSkCADcCACAgQRRqIBspAgA3AgAgIEEcaiApKQIANwIAICBBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIeRQ1QIAZB28HBAEHeABB5IAYtAABBAUYNRiAlIBcpAwAiUzcDACApICMpAwAiUjcDACAbIBQpAwAiUTcDACARIFI3AgAgECBRNwIAIA4gUzcCACAGIAYpAwg3AtwWIAZBucLBAEHfABB5IAYtAABBAUYNRyANIBcpAwAiUzcDACAMICMpAwAiUjcDACALIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXIB5BATYCACAeQQc2AiggHiAGKQLYFjcCBCAeQQxqIAZB4BZqKQIANwIAIB5BFGogBkHoFmopAgA3AgAgHkEcaiAGQfAWaikCADcCACAeQSRqIAZB+BZqKAIANgIAIB4gBikCqBc3AiwgHkE0aiAlKQIANwIAIB5BPGogGykCADcCACAeQcQAaiApKQIANwIAIB5BzABqIAZByBdqKAIANgIAQdHOxQAtAAAaQdAAQQgQ1gQiKEUNUCAGQZjDwQBB4AAQeSAGLQAAQQFGDUggJSAXKQMAIlM3AwAgKSAjKQMAIlI3AwAgGyAUKQMAIlE3AwAgESBSNwIAIBAgUTcCACAOIFM3AgAgBiAGKQMINwLcFiAGQZjDwQBB4AAQeSAGLQAAQQFGDUkgDSAXKQMAIlM3AwAgDCAjKQMAIlI3AwAgCyAUKQMAIlE3AwAgMSBSNwIAIDIgUTcCACAPIFM3AgAgBiAGKQMINwKsFyAoQQI2AgAgKEEINgIoICggBikC2BY3AgQgKEEMaiAGQeAWaikCADcCACAoQRRqIAZB6BZqKQIANwIAIChBHGogBkHwFmopAgA3AgAgKEEkaiAGQfgWaigCADYCACAoIAYpAqgXNwIsIChBNGogJSkCADcCACAoQTxqIBspAgA3AgAgKEHEAGogKSkCADcCACAoQcwAaiAGQcgXaigCADYCAEHRzsUALQAAGkEoQQgQ1gQiJEUNUSAGQfjDwQBB3wAQeSAGLQAAQQFGDUogCiAwKQMAIlM3AwAgBCAhKQMAIlI3AwAgCCAUKQMAIlE3AwAgMSBSNwIAIDIgUTcCACAPIFM3AgAgBiAGKQMINwKsFyAkQQM2AgAgJCAGKQKoFzcCBCAkQQxqICspAgA3AgAgJEEUaiAbKQIANwIAICRBHGogHSkCADcCACAkQSRqIAZByBdqKAIANgIAQdHOxQAtAAAaQShBCBDWBCIrRQ1RIAZB18TBAEHQABB5IAYtAABBAUYNSyAKIAZBEGopAwAiUzcDACAEIAZBIGopAwAiUjcDACAIIAZBGGopAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXICtBCjYCACArIAYpAqgXNwIEICtBDGogBkGwF2opAgA3AgAgK0EUaiAGQbgXaikCADcCACArQRxqIAZBwBdqKQIANwIAICtBJGogBkHIF2ooAgA2AgBB0c7FAC0AABpB0ABBCBDWBCIERQ1QIAZBp8XBAEHgABB5IAYtAABBAUYNTCAlIBcpAwAiUzcDACApICMpAwAiUjcDACAbIBQpAwAiUTcDACARIFI3AgAgECBRNwIAIA4gUzcCACAGIAYpAwg3AtwWIAZBh8bBAEHfABB5IAYtAABBAUYNTSANIBcpAwAiUzcDACAMICMpAwAiUjcDACALIBQpAwAiUTcDACAxIFI3AgAgMiBRNwIAIA8gUzcCACAGIAYpAwg3AqwXIARBBTYCACAEQQs2AiggBCAGKQLYFjcCBCAEQQxqIAZB4BZqKQIANwIAIARBFGogBkHoFmopAgA3AgAgBEEcaiAGQfAWaikCADcCACAEQSRqIAZB+BZqKAIANgIAIAQgBikCqBc3AiwgBEE0aiAlKQIANwIAIARBPGogGykCADcCACAEQcQAaiApKQIANwIAIARBzABqIAZByBdqKAIANgIAIBNBAjYCjAEgEyAENgKIASATQoGAgIAgNwKAASATICs2AnwgE0KBgICAEDcCdCATICQ2AnAgE0KCgICAEDcCaCATICg2AmQgE0KCgICAIDcCXCATIB42AlggE0KBgICAIDcCUCATICA2AkwgE0KCgICAEDcCRCATIBI2AkAgE0KCgICAIDcCOCATICY2AjQgE0KBgICAIDcCLCATICo2AiggE0KBgICAEDcCICATIBY2AhwgE0KCgICAEDcCFCATIBk2AhAgE0KCgICAIDcCCCATIBw2AgQgE0ECNgIAIAZBDDYCpBggBiATNgKgGCAGQoGAgIDAATcCmBgQxwQiBEUNTiAEIAQpAwAiUkIBfDcDACAEKQMIIVEgBkEIaiILQYixwgApAwA3AwAgFCBRNwMAIBcgUjcDACAGQYCxwgApAwA3AwAjAEEwayIOJAAgBigCCEUEQCAOIAZBASAXEKUBCyAOQRBqIAZBmBhqIgRBCGopAgA3AwAgDkEBNgIcIA4gBCkCACJRNwMIIA5BJGogBiBRpyAOQQhqQQRyEOkBAkAgDigCJCINQYCAgIB4Rg0AIA4oAighBCAOKAIsIgwEQCAEIQgDQCAIKAIAIgoEQCAIQQRqKAIAIApBKGwQ3wQLIAhBDGohCCAMQQFrIgwNAAsLIA1FDQAgBCANQQxsEN8ECyAOQTBqJAAgH0EYaiAUKQMANwMAIB9BEGogFykDADcDACAfQQhqIAspAwA3AwAgHyAGKQMANwMADE8LIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQby8wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGsvMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBnLzBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQYy8wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEH8u8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB7LvBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQdy7wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHMu8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBvLvBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQay7wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGcu8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBjLvBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQfy6wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHsusEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB3LrBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQcy6wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEG8usEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBrLrBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQZy6wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGMusEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB/LnBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQey5wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHcucEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBzLnBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQby5wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGsucEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBnLnBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQYy5wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEH8uMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB7LjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQdy4wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHMuMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBvLjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQay4wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGcuMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBjLjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQfy3wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHst8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB3LfBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQcy3wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEG8t8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBrLfBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQZy3wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGMt8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB/LbBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQey2wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHctsEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBzLbBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQby2wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGstsEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBnLbBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQYy2wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEH8tcEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB7LXBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQdy1wQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHMtcEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBvLXBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQay1wQAQygMACxDwAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQYjJwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEH4yMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB6MjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQdjIwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHIyMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBuMjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQajIwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGYyMEAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBiMjBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQfjHwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEHox8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB2MfBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQcjHwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEG4x8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBBqMfBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQZjHwQAQygMACyAGIAYtAAE6AABBgLXBAEErIAZB8LTBAEGIx8EAEMoDAAsgBiAGLQABOgAAQYC1wQBBKyAGQfC0wQBB+MbBABDKAwALIAYgBi0AAToAAEGAtcEAQSsgBkHwtMEAQejGwQAQygMACxDwAwALIAZBwBhqJAAMAwtBCEHQABD/BAALQQhBKBD/BAALQQRBkAEQ/wQACwJAAkACQAJAAkACQAJAAkAgRg4CAQIAC0GMj8AAQQ9BwJjAABD+AwALIAVB8AhqIgQgFSA1IDMgPyAnIDsgOSA6EE4gBSgC+AgiCCAFKALwCEYEQCAEQeCXwAAQowMLIAUoAvQIIQoCQCAIRQ0AIAhBBHQiBEUNACAKQRBqIAogBPwKAAALIAogBSkDoAU3AgAgBUH4CGogCEEBaiIENgIAIApBCGogBUGoBWopAwA3AgAgBUH4C2ogBDYCACAFIAUpAvAINwPwCyAFQYCAgIB4NgLwDiAFQaAFaiAFQfALaiAFQfAOaiAFQdgEaiAFQeQEahDBASAFQYAIaiAFQbATaiIIIAVB8BFqIgRBARBkIAUoAuAIQYCAgIB4Rg0BIAVBkAhqIAggBUHgCGpBAhBkIAVBoAhqIAggBEEDEGRB0c7FAC0AABpB0ABBBBDWBCIERQ0CIAQgBSkDoAU3AgAgBCAFKQKABTcCECAEIAUpAoAINwIgIAQgBSkCkAg3AjAgBCAFKQKgCDcCQCAEQQhqIAVBqAVqKQMANwIAIARBGGogBUGIBWopAgA3AgAgBEEoaiAFQYgIaikCADcCACAEQThqIAVBmAhqKQIANwIAIARByABqIAVBqAhqKQIANwIAIAVBBTYC+AsgBSAENgL0CyAFQQU2AvALIFBBgICAgHhHBEAgRSgCCCIEQQV0ITNBACEIIARB////P0sgM0H4////B0tyDQQCQCAzRQRAQQghCgwBCyBFKAIEIQtB0c7FAC0AABpBCCEIIDNBCBDWBCIKRQ0FIARFDQBBACEIIAQhDANAIAggM0YNASAIIApqIg4gCCALaiINKQMANwMAIA5BGGogDUEYaikDADcDACAOQRBqIA1BEGopAwA3AwAgDkEIaiANQQhqKQMANwMAIAhBIGohCCAMQQFrIgwNAAsLIEUoAgwhCCAFQfALakGQmMAAEKMDIAUoAvQLIgsgCDYCXCALIAQ2AlggCyAKNgJUIAsgBDYCUCAFQQY2AvgLCwwFCyAFQbAIaiIEIAVBsBNqIAVB8BFqQQEQZCAFQfgOaiAFQagFaikDADcDACAFIAUpA6AFNwPwDiAFQaAFaiAFQfAOahB2IAVBwAhqIAVBgAVqEHYgBUHQCGogBBB2QdHOxQAtAAAaQTBBBBDWBCIERQ0JIAQgBSkDoAU3AgAgBCAFKQLACDcCECAEIAUpAtAINwIgIARBCGogBUGoBWopAwA3AgAgBEEYaiAFQcgIaikCADcCACAEQShqIAVB2AhqKQIANwIAIAVBAzYC+AsgBSAENgL0CyAFQQM2AvALIFBBgICAgHhHBEAgRSgCCCIEQQV0ITNBACEIIARB////P0sgM0H4////B0tyDQQCQCAzRQRAQQghCgwBCyBFKAIEIQtB0c7FAC0AABpBCCEIIDNBCBDWBCIKRQ0FIARFDQBBACEIIAQhDANAIAggM0YNASAIIApqIg4gCCALaiINKQMANwMAIA5BGGogDUEYaikDADcDACAOQRBqIA1BEGopAwA3AwAgDkEIaiANQQhqKQMANwMAIAhBIGohCCAMQQFrIgwNAAsLIEUoAgwhCCAFQfALakGwmMAAEKMDIAUoAvQLIgsgCDYCPCALIAQ2AjggCyAKNgI0IAsgBDYCMCAFQQQ2AvgLCwwEC0Hwl8AAEOgEAAtBBEHQABD/BAALIAggM0HogcAAEMgEAAsgCCAzQeiBwAAQyAQACyAFQfgOaiAFQfgLaigCADYCACAFIAUpAvALNwPwDiAFQaAFaiAFQfAOaiAFQfQHaiAFQdgEaiAFQeQEahDBASA+IAUpA6AFNwIAID4gQTYCHCA+ICI2AhggPiAaNgIUID4gLTYCECA+IAUpAtgENwIsID4gBSkC5AQ3AkggPiBNNgJEID4gVDcCPCA+IBg2AjggPkEIaiAFQagFaikDADcCACA+QTRqIAVB4ARqKAIANgIAID5B0ABqIAVB7ARqKAIANgIAID5BKGogBUGYBWooAgA2AgAgPiAFKQOQBTcCIAJAIAVBsBNqIhAoAgQiM0UNACAQKAIMIiIEQCAQKAIAIg5BCGohCiAOKQMAQn+FQoCBgoSIkKDAgH+DIVQDQCBUUARAA0AgDkGAAWshDiAKKQMAIApBCGohCkKAgYKEiJCgwIB/gyJRQoCBgoSIkKDAgH9RDQALIFFCgIGChIiQoMCAf4UhVAsgDiBUeqdBAXRB8AFxayIEQQxrIARBCGshDSAEQQRrKAIAIgsEQCANKAIAIQwDQCAMKAIAIgQEQCAMQQRqKAIAIARBKGwQ3wQLIAxBDGohDCALQQFrIgsNAAsLKAIAIgQEQCANKAIAIARBDGwQ3wQLIFRCAX0gVIMhVCAiQQFrIiINAAsLIDNBEWxBGWoiBEUNACAQKAIAIDNBBHRrQRBrIAQQ3wQLIAUoArQFIgQEQCAFKAK4BSAEQQd0EN8ECyAHBEAgFSAHQQd0EN8ECyAFKALwESIEBEAgBSgC9BEgBEEFdBDfBAsgBSgC4AgiBEGAgICAeEYgBEVyRQRAIAUoAuQIIARBBXQQ3wQLIDdBDBDfBCBMBEAgNCBMQQV0EN8ECyAFKALwBCIEBEAgBSgC9AQgBEEFdBDfBAsgBSgCvAQiBARAIAUoAsAEIARBAnQQ3wQLAkAgBSgC9AEiBEUNACAEIARBDGxBE2pBeHEiCGpBCWoiBEUNACAFKALwASAIayAEEN8ECyAFKAKgAiIEQYCAgIB4RiAERXJFBEAgBSgCpAIgBEECdBDfBAsgTgRAIDkgTkEFdBDfBAsgTwRAICcgT0EFdBDfBAsgBUGwGGokAAwLCyAHIDhB0JfAABDZAwALIAUgDjYC+A4gBSAINgL0DiAFIAs2AvAOQYCLwABBKyAFQfAOakHgj8AAQfCPwAAQygMAC0EIQYADQbiFwAAQyAQACyAHIAhB6IHAABDIBAALQQRBMBD/BAALQQRBwAAQ/wQAC0EIIA1B6IHAABDIBAALIAcgCkHogcAAEMgEAAsgByAPQeiBwAAQyAQAC0EIIA9B6IHAABDIBAALIAcgC0HogcAAEMgEAAsgCUHYAmogCUGgA2opAgA3AwAgCUGgAWogCUH4AmopAgA3AwAgCSAJKQKYAzcD0AIgCSAJKQLwAjcDmAEgCSgC7AIhKyAJKALkAiEfIAkoAuACIRYgCSgCgAMhMSAJKAKEAyEyIAkoAogDISogCSgCjAMhICAJKAKQAyE5IAkoApQDIR4gCSgCqAMhLSAJKAKsAyEIIAkoArADITMgCSgC6AIhESA+ECEgCS0AmAchCiAJKAKMByIEBEAgCSgCkAcgBEECdBDfBAsCQCAJKALEBCIERQ0AIAQgBEEMbEETakF4cSIHakEJaiIERQ0AIAkoAsAEIAdrIAQQ3wQLIAkoAvAEIgRBgICAgHhGIARFckUEQCAJKAL0BCAEQQJ0EN8ECwJAAkACQCAKDgIBAgALQbiOwQBBD0HIjsEAEP4DAAsgMwRAIDNBAWsiC0EEdCEEQQAhByALQf////8ASyAEQfz///8HS3INBEEEIQoCQCAERQ0AQdHOxQAtAAAaQQQhByAEQQQQ1gQiCkUNBSALRQ0AIAggM0EEdGohECAIIQwgCyEOQQAhBwNAIAwiJ0EQaiIMIBBGDQEgJygCGCIiQQV0IShBACEEICJB////P0sgKEH4////B0tyDQcgByEVAkAgKEUEQEEIIRoMAQsgJygCFCEHQdHOxQAtAAAaQQghBCAoQQgQ1gQiGkUNCCAiRQ0AQQAhBCAiIQ0DQCAEIChGDQEgBCAaaiIPIAQgB2oiJCkDADcDACAPQRhqICRBGGopAwA3AwAgD0EQaiAkQRBqKQMANwMAIA9BCGogJEEIaikDADcDACAEQSBqIQQgDUEBayINDQALCyAVQQFqIQcgCiAVQQR0aiIEICcoAhw2AgwgBCAiNgIIIAQgGjYCBCAEICI2AgAgDkEBayIODQALCyAJQcgCaiAJQdgCaikDADcDACAJQegCaiAJQaABaikDADcDACAJIAkpA9ACNwPAAiAJIAkpA5gBNwPgAiAIIQQDQCAEKAIAIgcEQCAEQQRqKAIAIAdBBXQQ3wQLIARBEGohBCAzQQFrIjMNAAsgLUUNBiAIIC1BBHQQ3wQMBgtBAUEAQaiOwQAQ5AQACyAJQcgCaiAJQdgCaikDADcDACAJQegCaiAJQaABaikDADcDACAJIAkpA9ACNwPAAiAJIAkpA5gBNwPgAgwFC0GUkMEAQR5BtJDBABD+AwALQcSQwQBBJ0HskMEAEP4DAAsgByAEQZyDwQAQyAQACyAEIChB6IHAABDIBAALIAohCCALIjMhLQsgCSgCKCIEBEAgCSgCLCAEQQd0EN8ECyAJKAI4IgQEQCAJKAI8IARByABsEN8ECyAJQSBqIAlByAJqIgQpAwA3AwAgCUEwaiAJQegCaikDADcDACAJIAkpA8ACNwMYIAkgCSkD4AI3AyggCSgCCCEkIAQgCUEUaigCADYCACAJIAkpAgw3A8ACIAkgSjoAjwEgCSADNgKIAUEFIQRB2I7BACEHAkACQAJAIEoOAgIBAAtBuI7BAEEPQcSPwQAQ/gMAC0EJIQRB3Y7BACEHCyAJIAQ2ApQBIAkgBzYCkAEgCUEENgK8ASAJQfSOwQA2ArgBIAlCAzcCxAEgCSAJQYgBaq1CgICAgOABhDcD8AIgCSAJQcgAaq1CgICAgOABhDcD6AIgCSAJQZABaq1CgICAgKAChDcD4AIgCSACNgJIIAkgCUHgAmo2AsABIAlB0AJqIAlBuAFqENICQQAhB0HRzsUALQAAGkEBISdBAiEOAkACQEECQQEQ1gQiGgRAIBpBsPABOwAAIAlBAjYCoAEgCSAaNgKcASAJQQI2ApgBIAkoAtQCIQoCfyAJKALYAiIMRQRAQQAhDUECDAELIAlBvAJqrUKAgICA8ASEIVFBACENIAohBANAIAkgBDYCVCAJIAc2AlAgCSAnNgJMIAkgDTYCSCAJIAQ2ArwCIAkgUTcDOCAJQQE2AswBIAlBATYCvAEgCUGgi8EANgK4ASAJQQE2AsQBIAlCgICAgICEgIBpNwLwAiAJQoCACDcC6AIgCUECOwHgAiAJIAlB4AJqNgLIASAJIAlBOGo2AsABIAlByABqQdD/wAAgCUG4AWoQqwINAyAEQQFqIQQgCSgCSCENIAkoAkwhJyAJKAJQIQcgDEEBayIMDQALIAdFBEBBACEHQQIMAQsgCUGYAWpBAiAHQQFBARCIAyAJKAKYASEOIAkoApwBIRogCSgCoAELIQQgBwRAIAQgGmogJyAH/AoAAAsgDQRAICcgDRDfBAsCQCAJIAQgB2oiBAR/IAlB4AJqIBogBBCVASAJLQDgAkEBRw0BIAktAOECBUEDCzoA4AJB1P7AAEErIAlB4AJqQaSPwQBBtI/BABDKAwALIAlB1gBqIAlB8AJqIgspAwAiUjcBACAJQd4AaiAJQfgCaiIHKQMAIlE3AQAgCUGgAWoiFSBSNwMAIAlBsAFqIg0gCUGAA2oiBCkDADcDACAJQagBaiIMIFE3AwAgCSAJKQPoAjcDmAEgCUGYA2pCADcDACAJQZADakIANwMAIAlBiANqQgA3AwAgBEIANwMAIAdCADcDACALQgA3AwAgCUHoAmpCADcDACAJQgA3A+ACIAlBqANqIBUpAwA3AwAgCUGwA2ogDCkDADcDACAJQbgDaiANKQMANwMAIAkgCSkDmAE3A6ADIAlB4AJqIgQQRiAJQdgBaiAEQeAA/AoAACAJQdABaiANKQMANwMAIAlByAFqIAwpAwA3AwAgCUHAAWogFSkDADcDACAJIAkpA5gBNwO4ASACQcgBbCEEA0AjAEGQAmsiEiQAIBJBADYCDCASQoCAgICAATcCBCASQQRqIgtBjMbCABCiAyASKAIEIBIoAggiDSABKQOAATcDACANQQhqIAFBiAFqKQMANwMAIA1BEGogAUGQAWopAwA3AwAgDUEYaiABQZgBaikDADcDACASQQE2AgxBAUYEQCALQZzGwgAQogMgEigCCCENCyANIAFBoAFqIgcpAwA3AyAgDUE4aiAHQRhqKQMANwMAIA1BMGogB0EQaikDADcDACANQShqIAdBCGopAwA3AwAgEkECNgIMIBJBkAFqISgjAEHwAWsiGCQAIBhBQGsgAUEIaikDADcDACAYQcgAaiABQRBqKQMANwMAIBhB0ABqIAFBGGopAwA3AwAgGEHgAGogAUEoaikDADcDACAYQegAaiABQTBqKQMANwMAIBhB8ABqIAFBOGopAwA3AwAgGCABKQMANwM4IBggASkDIDcDWCAYQbgBaiAYQThqEK8DIBgoArwBIScgGCgCuAEhDwJAIBgoAsABIgdBAkYEQAJAIBhBwAFqICdBEGopAwA3AwAgGEHIAWogJ0EYaikDADcDACAYQdABaiAnQSBqKQMANwMAIBhB2AFqIgcgJ0EoaikDADcDACAYQeABaiAnQTBqKQMANwMAIBhB6AFqICdBOGopAwA3AwAgGCAnKQMINwO4ASAnKAIEIRAgJygCACEiIA8EQCAnIA9BBXQQ3wQLIBhBMGogGEHIAWoiFSkDADcDACAYQShqIBhBwAFqIgwpAwA3AwAgGEEIaiAHKQMANwMAIBhBEGogGEHgAWoiDSkDADcDACAYQRhqIBhB6AFqIgspAwA3AwAgGCAYKQO4ATcDICAYIBgpA9ABNwMAIBhBgAFqIAFBQGsiB0EIaikDADcDACAYQYgBaiAHQRBqKQMANwMAIBhBkAFqIAdBGGopAwA3AwAgGCAHKQMANwN4IBhBsAFqIAFB+ABqKQMANwMAIBhBqAFqIAFB8ABqKQMANwMAIBhBoAFqIAFB6ABqKQMANwMAIBggASkDYDcDmAEgGEG4AWogGEH4AGoQrwMgGCgCvAEhJyAYKAK4ASEPIBgoAsABIgdBAkcNACAMICdBEGopAwA3AwAgFSAnQRhqKQMANwMAIBhB0AFqICdBIGopAwA3AwAgGEHYAWoiDCAnQShqKQMANwMAIA0gJ0EwaikDADcDACALICdBOGopAwA3AwAgGCAnKQMINwO4ASAnKAIEIQsgJygCACEHIA8EQCAnIA9BBXQQ3wQLICggCzYCRCAoIAc2AkAgKCAYKQO4ATcDSCAoIBgpA9ABNwNgIChB0ABqIBhBwAFqKQMANwMAIChB2ABqIBhByAFqKQMANwMAIChB6ABqIAwpAwA3AwAgKEHwAGogGEHgAWopAwA3AwAgKEH4AGogGEHoAWopAwA3AwAgKCAQNgIEICggIjYCACAoIBgpAyA3AwggKEEQaiAYQShqKQMANwMAIChBGGogGEEwaikDADcDACAoIBgpAwA3AyAgKEEoaiAYQQhqKQMANwMAIChBMGogGEEQaikDADcDACAoQThqIBhBGGopAwA3AwAgGEHwAWokAAwCCwsgGCAHNgLAASAYICc2ArwBIBggDzYCuAFBgIvAAEErIBhBuAFqQfCKwABBpI3AABDKAwALIBJByABqIBJByAFqKQMANwMAIBJBQGsgEkHAAWopAwA3AwAgEkE4aiASQbgBaikDADcDACASQTBqIgsgEkGwAWopAwA3AwAgEkEoaiASQagBaikDADcDACASQSBqIBJBoAFqKQMANwMAIBJBGGogEkGYAWopAwA3AwAgEiASKQOQATcDECASQYgBaiASQYgCaikDADcDACASQYABaiASQYACaikDADcDACASQfgAaiASQfgBaikDADcDACASQfAAaiASQfABaikDADcDACASQegAaiASQegBaikDADcDACASQeAAaiASQeABaikDADcDACASQdgAaiASQdgBaikDADcDACASIBIpA9ABNwNQIBIoAgwiFSASKAIEIgxGBEAgEkEEakGsxsIAEKIDIBIoAgQhDAsgEigCCCINIBVBBXRqIgcgEikDEDcDACAHQQhqIBJBGGopAwA3AwAgB0EQaiASQSBqKQMANwMAIAdBGGogEkEoaikDADcDACASIBVBAWoiBzYCDCAHIAxGBEAgEkEEakG8xsIAEKIDIBIoAgghDSASKAIEIQwLIA0gB0EFdGoiByALKQMANwMAIAdBGGogC0EYaikDADcDACAHQRBqIAtBEGopAwA3AwAgB0EIaiALQQhqKQMANwMAIBIgFUECaiIHNgIMIAcgDEYEQCASQQRqQczGwgAQogMgEigCCCENIBIoAgQhDAsgEkHYAGopAwAhUyASQeAAaikDACFSIBJB6ABqKQMAIVEgDSAHQQV0aiIHIBIpA1A3AwAgB0EYaiBRNwMAIAdBEGogUjcDACAHQQhqIFM3AwAgEiAVQQNqIgc2AgwgByAMRgRAIBJBBGpB3MbCABCiAyASKAIIIQ0LIBJBgAFqKQMAIVMgEkGIAWopAwAhUiASQfgAaikDACFRIA0gB0EFdGoiByASKQNwNwMAIAdBCGogUTcDACAHQRhqIFI3AwAgB0EQaiBTNwMAIAlB4AJqIgcgEikCBDcCACAHQQhqIBVBBGo2AgAgEkGQAmokACAJQbgBaiAJKALkAiILIAkoAugCQQAQJSAJKALgAiIHBEAgCyAHQQV0EN8ECyABQcgBaiEBIARByAFrIgQNAAsgCSgCGEGAgICAeEYNAiAJLQCPAQRAIAlBADYC4AIgCUGPAWogCUHgAmoQkwQACyAJQeACaiAJQRhqEPcBIAlBuAFqIAkoAuQCIgQgCSgC6AIgSkEBRxAlIAkoAuACIgFFDQIgBCABQQV0EN8EDAILQQFBAkGsg8EAEMgEAAtB1P7AAEErIAlBuAFqQej/wABB1I/BABDKAwALIAlB4AJqIAlBKGoQ9wEgCUG4AWogCSgC5AIiByAJKALoAiBKQQFHIgQQJSAJKALgAiIBBEAgByABQQV0EN8ECyAJQbgBaiAyICogBBAlIDMEQCAzQQR0IQcgSkEBRyEMIAghBANAIAlB4AJqIAQQ9wEgCUG4AWogCSgC5AIiCyAJKALoAiAMECUgCSgC4AIiAQRAIAsgAUEFdBDfBAsgBEEQaiEEIAdBEGsiBw0ACwsCQCAkQYCAgIB4Rg0AIAlB7AJqIAlByAJqKAIANgIAIAkgJDYC4AIgCSAJKQPAAjcC5AIgCUHIAGogCUHgAmoQ9wEgCUG4AWogCSgCTCIEIAkoAlAgSkEBRxAlIAkoAkgiAQRAIAQgAUEFdBDfBAsgCSgC4AIiAUUNACAJKALkAiABQQV0EN8ECyAJQcgAaiIBIAlB+AFqENECIAlB4AJqIAFBIBCKASAOBEAgGiAOEN8ECyAJKALQAiIBBEAgCiABEN8ECyAJQeAAaiAJQfgCaikDADcDACAJQdgAaiAJQfACaikDADcDACAJQdAAaiAJQegCaikDADcDACAJIAkpA+ACNwNIIAlB4AJqECEgCS0AmAchCiAJKAKMByIBBEAgCSgCkAcgAUECdBDfBAsCQCAJKALEBCIBRQ0AIAEgAUEMbEETakF4cSIEakEJaiIBRQ0AIAkoAsAEIARrIAEQ3wQLIAkoAvAEIgFBgICAgHhGIAFFckUEQCAJKAL0BCABQQJ0EN8EC0EBIQcCQAJAAkAgCg4CAgEAC0G4jsEAQQ9BhJDBABD+AwALQQAhBwtB0c7FAC0AABoCQAJAAkACQAJAAkBBIEEIENYEIgEEQCABQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgCUKBgICAcDcCyAIgCSABNgLEAiAJQQE2AsACIAlB+AJqQZj/wAApAwA3AwAgCUHwAmpBkP/AACkDADcDACAJQegCakGI/8AAKQMANwMAIAlBgP/AACkDADcD4AIgByAzaiIBBEAgAUEBayIEIB5PDQIgAUEEdCA5akEQayEnA0AgCUHYAmogCUHIAmopAgA3AwAgCSAJKQLAAjcD0AJB0c7FAC0AABpBIEEIENYEIgRFDQggBCAJKQPgAjcDACAEQRhqIAlB+AJqKQMANwMAIARBEGogCUHwAmopAwA3AwAgBEEIaiAJQegCaikDADcDAEEAIQ0CQCAEQdjDwgBBIBDxAwRAIAQhBwwBC0HRzsUALQAAGkEgQQgQ1gQiB0UNCSAHQgA3AwAgB0EYakIANwMAIAdBEGpCADcDACAHQQhqQgA3AwAgBEEgEN8EQX8hDQsgCSANNgLEASAJQQE2AsABIAkgBzYCvAEgCUEBNgK4ASAJQZgBaiIEICcgCUG4AWoQZyAJQcACaiAJQdACaiAEEOUBIAkoArgBIgQEQCAJKAK8ASAEQQV0EN8ECyAnQRBrIScjAEGABGsiCyQAIAtBgAJqIAlByABqIgQpAxgiWUIAIAlB4AJqIgcpAxgiUUIAEMkDIAtBkAJqIAQpAxAiWkIAIFFCABDJAyALQaACaiAEKQMIIltCACBRQgAQyQMgC0GwAmogBCkDACJcQgAgUUIAEMkDIAtB8AFqIAspA4ACIlVCiceZpK7wgemHf34iUUIAQsf688PtgqOQPEIAEMkDIAtB4AFqIFFCAEKNlcfDltLawJd/QgAQyQMgC0GQAWogUUIAQt2whYzotpGouH9CABDJAyALQUBrIFFCAEKpwMaJrs6TsjBCABDJAyALQcACaiAHKQMQIlFCACBZQgAQyQMgC0HwAmogUUIAIFpCABDJAyALQaADaiBRQgAgW0IAEMkDIAtB0ANqIFFCACBcQgAQyQMgC0HQAWogCykD4AEiVCALKQOIAiJTIAspA5ACfCJSfCJWIAspA/gBIFUgCykD8AEiUXwgUVStfHwiVyALKQPAAnwiUUKJx5mkrvCB6Yd/fiJVQgBCx/rzw+2Co5A8QgAQyQMgC0HAAWogVUIAQo2Vx8OW0trAl39CABDJAyALQbABaiBVQgBC3bCFjOi2kai4f0IAEMkDIAtBoAFqIFVCAEKpwMaJrs6TsjBCABDJAyALQdACaiAHKQMIIlVCACBZQgAQyQMgC0GAA2ogVUIAIFpCABDJAyALQbADaiBVQgAgW0IAEMkDIAtB4ANqIFVCACBcQgAQyQMgC0GAAWogCykDyAIgUSBXVK18IlUgCykD8AJ8Il0gCykDmAIgUiBTVK18IlMgCykDoAJ8Il4gCykDkAF8Il8gViBXVq0gCykD6AEgVCBWVq18fHwiUnwiYCALKQPAAXwiWCALKQPYASBRIAspA9ABIlF8IFFUrXx8IlYgCykD0AJ8IlFCiceZpK7wgemHf34iVEIAQsf688PtgqOQPEIAEMkDIAtB8ABqIFRCAEKNlcfDltLawJd/QgAQyQMgC0HgAGogVEIAQt2whYzotpGouH9CABDJAyALQdAAaiBUQgBCqcDGia7Ok7IwQgAQyQMgC0HgAmogBykDACJUQgAgWUIAEMkDIAtBkANqIFRCACBaQgAQyQMgC0HAA2ogVEIAIFtCABDJAyALQfADaiBUQgAgXEIAEMkDIAtBMGogCykD2AIgUSBWVK18IlQgCykDgAN8IlkgCykDqAIgUyBeVq18IlMgCykDsAJ8IlogCykDQHwiVyBSIF9UrSALKQOYASBeIF9WrXx8fCJbIAspA6ADfCJcIF0gYFatIAspA/gCIFUgXVatfHx8Il0gCykDsAF8Il4gViBYVK0gCykDyAEgWCBgVK18fHwiUnwiXyALKQNwfCJYIAspA4gBIFEgCykDgAEiUXwgUVStfHwiViALKQPgAnwiYEKJx5mkrvCB6Yd/fiJRQgBCx/rzw+2Co5A8QgAQyQMgC0EgaiBRQgBCjZXHw5bS2sCXf0IAEMkDIAtBEGogUUIAQt2whYzotpGouH9CABDJAyALIFFCAEKpwMaJrs6TsjBCABDJAwJAAkAgCykDCCALKQNYIAspA6gBIFcgW1atIAspA0ggVyBaVK18fCALKQO4AiBTIFpWrXx8IlEgCykD0AN8IlcgXCBdVq0gCykDqAMgWyBcVq18fHwiVSALKQOgAXwiUyBVVK18IFMgUyBSIF5UrSALKQO4ASBdIF5WrXx8fCJSVq18IFUgV1StIAspA9gDIFEgV1atfHx8IlEgCykD4AN8IlcgCykDuAMgUiBSIAspA7ADfCJSVq18IFIgUiBZIF9WrSALKQOIAyBUIFlWrXx8fCJSVq18fCJVIAspA1B8IlQgVVStfCBUIFQgCykDaCBSIFIgCykDYHwiU1atfCBTIFMgViBYVK0gCykDeCBYIF9UrXx8fCJSVq18fCJUVq18IFUgV1StIAspA+gDIFEgV1atfHx8IlMgCykD8AN8IlggCykDyAMgVCALKQPAA3wiVSBUVK18IFUgVSALKQOYAyALKQPoAiBWIGBWrXwiUSALKQOQA3wiVCBRVK18IFQgUiBUfCJWVq18fCJRVq18fCJXIAspAwB8IlUgV1StfCBVIFUgCykDGCBRIFEgCykDEHwiVFatfCBUIFQgCykDKCBWIFYgCykDIHwiUlatfCBSIAspAzggCykDMCJRIGB8IFFUrXx8IlYgUlStfHwiUlatfHwiVFatfCBXIFhUrSALKQP4AyBTIFhWrXx8fCJYQqnAxomuzpOyMFYNAAJAIFhCqcDGia7Ok7IwUQRAIFRC3bCFjOi2kai4f1YNAiBUQt2whYzotpGouH9SBEAgUiFRIFQhU0KpwMaJrs6TsjAhWAwECyBSQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyFTIFJCjZXHw5bS2sCXf1ENASBSIVFCqcDGia7Ok7IwIVgMAwsgUiFRIFQhUwwCC0KNlcfDltLawJd/IVEgVkLH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIVgMAQsgUkLz6ri86a2lv+gAfCJXIFZCx/rzw+2Co5A8VK0iU30hUSBUQqPP+vOXye7XxwB8IlUgUkKNlcfDltLawJd/VCBTIFdWcq0iUn0hUyBYIFRC3bCFjOi2kai4f1QgUiBVVnKtfUKpwMaJrs6TsjB9IVggVkLH+vPD7YKjkDx9IVYLIAcgVjcDGCAHIFE3AxAgByBTNwMIIAcgWDcDACALQYAEaiQAIAFBAWsiAQ0ACwtBNiEEQS0hBwJAAkACQCAKDgICAQALQYyPwABBD0HQj8AAEP4DAAtBICEEQRghBwsgCUHAAWogCUHIAmooAgAiATYCACAJIAkpAsACNwO4AQJAIAIgB2wgBGpBAWoiBCABSwRAIAFBBXQhBwNAIAkoArgBIAFGBEAgCUG4AWpB5I/BABCiAwsgCSgCvAEiDCAHaiIKQgA3AwAgCkEIakIANwMAIApBEGpCADcDACAKQRhqQgA3AwAgCSABQQFqIgE2AsABIAdBIGohByABIARJDQALDAELIAkoArwBIQwLIAkoArgBISQgCSADNgLAAiAJIAI2AjggCUHgAmoQIUEFIQRB2I7BACEHAkACQAJAIAktAJgHDgICAQALQcCRwQBBKEHokcEAEP4DAAtBCSEEQd2OwQAhBwsgCSAENgLUAiAJIAc2AtACIAkoAowHIgIEQCAJKAKQByACQQJ0EN8ECwJAIAkoAsQEIgJFDQAgAiACQQxsQRNqQXhxIgNqQQlqIgJFDQAgCSgCwAQgA2sgAhDfBAsgCSgC8AQiAkGAgICAeEYgAkVyRQRAIAkoAvQEIAJBAnQQ3wQLIAlBBDYCvAEgCUGgkcEANgK4ASAJQgM3AsQBIAkgCUHAAmqtQoCAgIDgAYQ3A/ACIAkgCUE4aq1CgICAgOABhDcD6AIgCSAJQdACaq1CgICAgKAChDcD4AIgCSAJQeACaiIDNgLAASAJQZgBaiICIAlBuAFqENICIAMgAhDzASADIAlByABqQQEgSkEBRyICECUgAyAMIAEgAhAlIAlB0AFqIAlBmANqKQMANwMAIAlByAFqIAlBkANqKQMANwMAIAlBwAFqIAlBiANqKQMANwMAIAkgCSkDgAM3A7gBIDNBAWshAgJAIDMEQEHRzsUALQAAGkEgQQgQ1gQiA0UNCCADQRhqQfDEwgApAwA3AwAgA0EQakHoxMIAKQMANwMAIANBCGpB4MTCACkDADcDACADQdjEwgApAwA3AwAgCUIBNwKgASAJIAM2ApwBIAlBATYCmAECQCAIIAJBBHRqIhAoAgxFBEAgECgCCEUNASAQKAIEIANBIBDxA0UNAwsgCUEANgLgAiAQIAlBmAFqIAlB4AJqQYyRwQAQlAQACwwKCyACQQBB/JDBABDZAwALIANBIBDfBEEAIQcgAkH/////AEsgAkEEdCIDQfz///8HS3INAkEBIQ1BACEaAkAgA0UEQEEEIQoMAQtB0c7FAC0AABpBBCEHIANBBBDWBCIKRQ0DIAJFDQAgCCEHIAIhDkEAIScDQCAQIAciC0cEQCAHKAIIIhVBBXQhD0EAIQQgFUH///8/SyAPQfj///8HS3INBiAnIQMCQCAPRQRAQQghGgwBCyALKAIEIQdB0c7FAC0AABpBCCEEIA9BCBDWBCIaRQ0HIBVFDQBBACEEIBUhDQNAIAQgD0YNASAEIBpqIiIgBCAHaiInKQMANwMAICJBGGogJ0EYaikDADcDACAiQRBqICdBEGopAwA3AwAgIkEIaiAnQQhqKQMANwMAIARBIGohBCANQQFrIg0NAAsLIAtBEGohByADQQFqIScgCiADQQR0aiIDIAsoAgw2AgwgAyAVNgIIIAMgGjYCBCADIBU2AgAgDkEBayIODQELCyACQQR0IRpBACENCyAJQaABaiAJQTBqKQMANwMAIAlB7AJqIAlBwAFqKQMANwIAIAlB9AJqIAlByAFqKQMANwIAIAlB/AJqIAlB0AFqKQMANwIAIAkgCSkDKDcDmAEgCSAJKQO4ATcC5AIgCSkDICFRIAkoAhwhByAJKAIYIQsgCCEEA0AgBCgCACIDBEAgBEEEaigCACADQQV0EN8ECyAEQRBqIQQgM0EBayIzDQALIC0EQCAIIC1BBHQQ3wQLIB4EQCA5IQQDQCAEKAIAIgMEQCAEQQRqKAIAIANBBXQQ3wQLIARBEGohBCAeQQFrIh4NAAsLICAEQCA5ICBBBHQQ3wQLIAlB0ABqIAlBoAFqKQMANwMAIAkgCSkDmAE3A0ggCUHQAWogCUHkAmoiA0EYaikCADcDACAJQcgBaiADQRBqKQIANwMAIAlBwAFqIANBCGopAgA3AwAgCSADKQIANwO4AUHRzsUALQAAGkEgQQgQ1gQiA0UNBiADQRhqQfDEwgApAwA3AwAgA0EQakHoxMIAKQMANwMAIANBCGpB4MTCACkDADcDACADQdjEwgApAwA3AwACQAJAICsNACARRQ0KIB8gA0EgEPEDDQAgA0EgEN8EIAlBADYC2AIgCUKAgICAwAA3AtACAkAgC0GAgICAeEYNACAJIFE3AugCIAkgBzYC5AIgCSALNgLgAiAJQZgBaiAJQeACahD3ASAJQdACaiAJKAKcASIEIAkoAqABQQAQ0QEgCSgCmAEiAwRAIAQgA0EFdBDfBAsgCSgC4AIiA0UNACAJKALkAiADQQV0EN8ECyAJQeACaiAJQcgAahD3ASAJQdACaiAJKALkAiIEIAkoAugCQQAQ0QEgCSgC4AIiAwRAIAQgA0EFdBDfBAsgCUHQAmogMiAqQQAQ0QEgCUHoAmoiA0Gs/MAAKAIANgIAIAlBpPzAACkCADcD4AIgAgRAIAlB4AJqQZj9wAAQpQMgCSgC5AIgAjYCACAJQQE2AugCCyAJQaABaiADKAIANgIAIAkgCSkD4AI3A5gBIAkoAtgCIgQgCSgC0AJGBEAgCUHQAmpBtJLBABCfAwsgCSgC1AIgBEEMbGoiAyAJKQOYATcCACADQQhqIAlBoAFqKAIANgIAIAkgBEEBajYC2AIgCiACQQR0aiEVIAohBCACBEAgCUHkAmoiC0EIaiEIIAQhBwNAIAciAigCACIDQYCAgIB4RwRAIAkgAzYC4AIgCyAHQQRqKQIANwIAIAggB0EMaigCADYCACAJQZgBaiAJQeACahD3ASAJQdACaiAJKAKcASIEIAkoAqABQQAQ0QEgCSgCmAEiAwRAIAQgA0EFdBDfBAsgCSgC4AIiAwRAIAkoAuQCIANBBXQQ3wQLIAJBEGoiByAVRw0BCwsgAkEQaiEECyAEIBVHBEAgFSAEa0EEdiEHA0AgBCgCACICBEAgBEEEaigCACACQQV0EN8ECyAEQRBqIQQgB0EBayIHDQALCyANRQRAIAogGhDfBAsgCUHQAmoiAyAMIAFBARDRASAJQeACaiAJQbgBahDRAkHRzsUALQAAGkEgQQEQ1gQiCkUNByAKQRhqIgcgCUH4AmopAAA3AAAgCiAJKQDgAiJRNwAAIApBEGoiCCAJQfACaikAADcAACAKQQhqIgQgCUHoAmopAAA3AAAgCiAKQR9qIgEtAAA6AAAgASBRPAAAIAotAAEhAiAKIApBHmoiAS0AADoAASABIAI6AAAgCkEdaiICLQAAIQEgAiAKLQACOgAAIAogAToAAiAKQRxqIgItAAAhASACIAotAAM6AAAgCiABOgADIApBG2oiAi0AACEBIAIgCi0ABDoAACAKIAE6AAQgCkEaaiICLQAAIQEgAiAKLQAFOgAAIAogAToABSAKQRlqIgItAAAhASACIAotAAY6AAAgCiABOgAGIActAAAhASAHIAotAAc6AAAgCiABOgAHIApBF2oiAi0AACEBIAIgBC0AADoAACAEIAE6AAAgCkEWaiICLQAAIQEgAiAKLQAJOgAAIAogAToACSAKQRVqIgItAAAhASACIAotAAo6AAAgCiABOgAKIApBFGoiAi0AACEBIAIgCi0ACzoAACAKIAE6AAsgCkETaiICLQAAIQEgAiAKLQAMOgAAIAogAToADCAKQRJqIgItAAAhASACIAotAA06AAAgCiABOgANIApBEWoiAi0AACEBIAIgCi0ADjoAACAKIAE6AA4gCC0AACEBIAggCi0ADzoAACAKIAE6AA8gCUGYAWogCkEgQQgQzwIgCkEgEN8EIAkoAtgCIgIgCSgC0AJGBEAgA0G0ksEAEJ8DCyAJKALUAiACQQxsaiIBIAkpApgBNwIAIAFBCGogCUGgAWooAgA2AgAgCUHYAmogAkEBaiIBNgIAIABBDGogATYCACAAIAkpAtACNwIEIABBADYCACAkBEAgDCAkQQV0EN8ECyAxBEAgMiAxQQV0EN8ECyAJKAJIIgBFDQEgCSgCTCAAQQV0EN8EDAELIANBIBDfBEHRzsUALQAAGkEZQQEQ1gQiAUUNBSAAQRk2AgwgACABNgIIIABCgYCAgJADNwIAIAFBGGpBsJLBAC0AADoAACABQRBqQaiSwQApAAA3AAAgAUEIakGgksEAKQAANwAAIAFBmJLBACkAADcAACAkBEAgDCAkQQV0EN8ECyACBEAgCiEEA0AgBCgCACIABEAgBEEEaigCACAAQQV0EN8ECyAEQRBqIQQgAkEBayICDQALCyANRQRAIAogGhDfBAsgMQRAIDIgMUEFdBDfBAsgCSgCSCIABEAgCSgCTCAAQQV0EN8ECyALQYCAgIB4ckGAgICAeEYNACAHIAtBBXQQ3wQLIBYEQCAfIBZBBXQQ3wQLIAlBoAdqJAAPCwwFCyAEIB5B9I/BABDZAwALIAcgA0Gcg8EAEMgEAAsgBCAPQeiBwAAQyAQAC0EBQRlBrIPBABDIBAALQQFBIEGsg8EAEMgEAAsLQQhBIBD/BAALQQBBAEHkysIAENkDAAusRgIBfyN+IwBBgBJrIgMkACADQfARaiABKQMYIgxCACACKQMYIg5CABDJAyADQZARaiABKQMQIhBCACAOQgAQyQMgA0GAEWogASkDCCIUQgAgDkIAEMkDIANB8BBqIAEpAwAiD0IAIA5CABDJAyADQeARaiADKQPwESISQgBCAEKJx5mkrvCB6Yd/EMkDIANB0BFqIAMpA+gRIgVCAELH+vPD7YKjkDxCABDJAyADQcARaiAFQgBCjZXHw5bS2sCXf0IAEMkDIANBsBFqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GgEWogBUIAQqnAxomuzpOyMEIAEMkDIANB4BBqIAIpAxAiFUIAIAxCABDJAyADQYAQaiAVQgAgEEIAEMkDIANB8A9qIBVCACAUQgAQyQMgA0HgD2ogFUIAIA9CABDJAyADQdAQaiADKQPAESIIIAMpA/gRIgkgAykDkBF8Igd8IgQgAykD2BEgEiADKQPQESIFfCAFVK18fCISIAMpA+AQfCINQgBCAEKJx5mkrvCB6Yd/EMkDIANBwBBqIAMpA9gQIgVCAELH+vPD7YKjkDxCABDJAyADQbAQaiAFQgBCjZXHw5bS2sCXf0IAEMkDIANBoBBqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GQEGogBUIAQqnAxomuzpOyMEIAEMkDIANB0A9qIAIpAwgiH0IAIAxCABDJAyADQfAOaiAfQgAgEEIAEMkDIANB4A5qIB9CACAUQgAQyQMgA0HQDmogH0IAIA9CABDJAyADQcAPaiADKQPoECANIBJUrXwiEyADKQOAEHwiCyADKQOYESAHIAlUrXwiCiADKQOAEXwiCSADKQOwEXwiByAEIBJWrSADKQPIESAEIAhUrXx8fCIYfCIEIAMpA7AQfCISIAMpA8gQIAMpA8AQIgUgDXwgBVStfHwiDSADKQPQD3wiCEIAQgBCiceZpK7wgemHfxDJAyADQbAPaiADKQPIDyIFQgBCx/rzw+2Co5A8QgAQyQMgA0GgD2ogBUIAQo2Vx8OW0trAl39CABDJAyADQZAPaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBgA9qIAVCAEKpwMaJrs6TsjBCABDJAyADQcAOaiACKQMAIhdCACAMQgAQyQMgA0HgDWogF0IAIBBCABDJAyADQdANaiAXQgAgFEIAEMkDIANBwA1qIBdCACAPQgAQyQMgA0GwDmogAykD2A8gCCANVK18IhwgAykD8A58IgYgAykDiBEgCSAKVK18Ih0gAykD8BB8IgogAykDoBF8IhkgByAYVq0gAykDuBEgByAJVK18fHwiCSADKQPwD3wiByAEIAtUrSADKQOIECALIBNUrXx8fCILIAMpA6AQfCITIA0gElStIAMpA7gQIAQgElatfHx8Ihh8IgQgAykDoA98IhIgAykDuA8gAykDsA8iBSAIfCAFVK18fCINIAMpA8AOfCIIQgBCAEKJx5mkrvCB6Yd/EMkDIANBoA5qIAMpA7gOIgVCAELH+vPD7YKjkDxCABDJAyADQZAOaiAFQgBCjZXHw5bS2sCXf0IAEMkDIANBgA5qIAVCAELdsIWM6LaRqLh/QgAQyQMgA0HwDWogBUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQP4DSADKQOIDyADKQOYECAJIBlUrSADKQOoESAKIBlWrXx8IAMpA/gQIAogHVStfHwiCiADKQPgD3wiBSAHIAtWrSADKQP4DyAHIAlUrXx8fCIJIAMpA5AQfCIHIAlUrXwgByATIBhWrSADKQOoECALIBNWrXx8fCILIAdUrXwgBSAJVq0gAykD6A8gBSAKVK18fHwiCiADKQPQDnwiBSADKQPoDiALIAsgAykD4A58IgtWrXwgCyALIAQgBlStIAMpA/gOIAYgHFStfHx8IgtWrXx8IgkgAykDgA98IgcgCVStfCAHIAMpA5gPIAsgCyADKQOQD3wiC1atfCALIAsgDSASVK0gAykDqA8gBCASVq18fHwiC1atfHwiBCAHVK18IAUgCVatIAMpA9gOIAUgClStfHx8IgkgAykDwA18IhIgAykD2A0gBCADKQPQDXwiBSAEVK18IAUgBSADKQPoDSADKQPIDiAIIA1UrXwiDSADKQPgDXwiBCANVK18IAQgBCALfCIEVq18fCIFVq18fCINIAMpA/ANfCILIA1UrXwgCyADKQOIDiAFIAUgAykDgA58IgVWrXwgBSAFIAMpA5gOIAQgBCADKQOQDnwiBFatfCAEIAMpA6gOIAMpA6AOIgcgCHwgB1StfHwiByAEVK18fCIFVq18fCIEIAtUrXwgDSASVK0gAykDyA0gCSASVq18fHwiCEKpwMaJrs6TsjBWDQACQCAIQqnAxomuzpOyMFEEQCAEQt2whYzotpGouH9WDQIgBELdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCEICyAEIQkgBSESDAILIAVCjZXHw5bS2sCXf1YNAELdsIWM6LaRqLh/IQkgBUKNlcfDltLawJd/UgRAQqnAxomuzpOyMCEIIAUhEgwCC0KNlcfDltLawJd/IRIgB0LH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIQgMAQsgBULz6ri86a2lv+gAfCINIAdCx/rzw+2Co5A8VK0iC30hEiAEQqPP+vOXye7XxwB8IgYgBUKNlcfDltLawJd/VCALIA1Wcq0iBX0hCSAIIARC3bCFjOi2kai4f1QgBSAGVnKtfUKpwMaJrs6TsjB9IQggB0LH+vPD7YKjkDx9IQcLIANB8AxqIAEpAzgiGUIAIAIpAzgiE0IAEMkDIANBkAxqIAEpAzAiGEIAIBNCABDJAyADQYAMaiABKQMoIhxCACATQgAQyQMgA0HwC2ogASkDICIdQgAgE0IAEMkDIANB4AxqIAMpA/AMIg1CAEIAQonHmaSu8IHph38QyQMgA0HQDGogAykD6AwiBUIAQsf688PtgqOQPEIAEMkDIANBwAxqIAVCAEKNlcfDltLawJd/QgAQyQMgA0GwDGogBUIAQt2whYzotpGouH9CABDJAyADQaAMaiAFQgBCqcDGia7Ok7IwQgAQyQMgA0HgC2ogAikDMCIWQgAgGUIAEMkDIANBgAtqIBZCACAYQgAQyQMgA0HwCmogFkIAIBxCABDJAyADQeAKaiAWQgAgHUIAEMkDIANB0AtqIAMpA8AMIh4gAykD+AwiCiADKQOQDHwiEXwiBCADKQPYDCANIAMpA9AMIgV8IAVUrXx8Ig0gAykD4At8IgtCAEIAQonHmaSu8IHph38QyQMgA0HAC2ogAykD2AsiBUIAQsf688PtgqOQPEIAEMkDIANBsAtqIAVCAEKNlcfDltLawJd/QgAQyQMgA0GgC2ogBUIAQt2whYzotpGouH9CABDJAyADQZALaiAFQgBCqcDGia7Ok7IwQgAQyQMgA0HQCmogAikDKCIaQgAgGUIAEMkDIANB8AlqIBpCACAYQgAQyQMgA0GQCWogGkIAIBxCABDJAyADQYAJaiAaQgAgHUIAEMkDIANBwApqIAMpA+gLIAsgDVStfCIhIAMpA4ALfCIGIAMpA5gMIAogEVatfCIgIAMpA4AMfCIKIAMpA7AMfCIRIAQgDVatIAMpA8gMIAQgHlStfHx8IiN8IgQgAykDsAt8Ig0gAykDyAsgAykDwAsiBSALfCAFVK18fCILIAMpA9AKfCIbQgBCAEKJx5mkrvCB6Yd/EMkDIANBsApqIAMpA8gKIgVCAELH+vPD7YKjkDxCABDJAyADQaAKaiAFQgBCjZXHw5bS2sCXf0IAEMkDIANBkApqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GACmogBUIAQqnAxomuzpOyMEIAEMkDIANBsA1qIAIpAyAiHkIAIBlCABDJAyADQaANaiAeQgAgGEIAEMkDIANBkA1qIB5CACAcQgAQyQMgA0GADWogHkIAIB1CABDJAyADQeAJaiADKQPYCiALIBtWrXwiJSADKQPwCXwiIiADKQOIDCAKICBUrXwiJiADKQPwC3wiICADKQOgDHwiJCARICNWrSADKQO4DCAKIBFWrXx8fCIKIAMpA/AKfCIRIAQgBlStIAMpA4gLIAYgIVStfHx8IgYgAykDoAt8IiEgCyANVK0gAykDuAsgBCANVq18fHwiI3wiBCADKQOgCnwiDSADKQO4CiADKQOwCiIFIBt8IAVUrXx8IgsgAykDsA18IhtCAEIAQonHmaSu8IHph38QyQMgA0HQCWogAykD6AkiBUIAQsf688PtgqOQPEIAEMkDIANBwAlqIAVCAEKNlcfDltLawJd/QgAQyQMgA0GwCWogBUIAQt2whYzotpGouH9CABDJAyADQaAJaiAFQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA6gJIAMpA4gKIAMpA5gLIAogJFStIAMpA6gMICAgJFatfHwgAykD+AsgICAmVK18fCIgIAMpA+AKfCIFIAYgEVStIAMpA/gKIAogEVatfHx8IgogAykDkAt8IhEgClStfCARICEgI1atIAMpA6gLIAYgIVatfHx8IgYgEVStfCAFIApWrSADKQPoCiAFICBUrXx8fCIgIAMpA4AJfCIFIAMpA5gJIAYgBiADKQOQCXwiBlatfCAGIAYgBCAiVK0gAykD+AkgIiAlVK18fHwiBlatfHwiCiADKQOACnwiESAKVK18IBEgAykDmAogBiAGIAMpA5AKfCIGVq18IAYgBiALIA1UrSADKQOoCiAEIA1WrXx8fCIGVq18fCIEIBFUrXwgBSAKVq0gAykDiAkgBSAgVK18fHwiESADKQOADXwiDSADKQOYDSAEIAMpA5ANfCIFIARUrXwgBSAFIAMpA6gNIAMpA7gNIAsgG1atfCILIAMpA6ANfCIEIAtUrXwgBCAEIAZ8IgRWrXx8IgVWrXx8IgsgAykDoAl8IgogC1StfCAKIAMpA7gJIAUgBSADKQOwCXwiBVatfCAFIAUgAykDyAkgBCAEIAMpA8AJfCIEVq18IAQgAykD2AkgAykD0AkiBiAbfCAGVK18fCIGIARUrXx8IgVWrXx8IgQgClStfCALIA1UrSADKQOIDSANIBFUrXx8fCIKQqnAxomuzpOyMFYNAAJAIApCqcDGia7Ok7IwUQRAIARC3bCFjOi2kai4f1YNAiAEQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIQoLIAQhCyAFIQ0MAgsgBUKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hCyAFQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIQogBSENDAILQo2Vx8OW0trAl38hDSAGQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhCgwBCyAFQvPquLzpraW/6AB8IgsgBkLH+vPD7YKjkDxUrSIRfSENIARCo8/685fJ7tfHAHwiGyAFQo2Vx8OW0trAl39UIAsgEVRyrSIFfSELIAogBELdsIWM6LaRqLh/VCAFIBtWcq19QqnAxomuzpOyMH0hCiAGQsf688PtgqOQPH0hBgsCfgJAAkAgCCIEIAoiBVINACAJIgQgCyIFUg0AIBIiBCANIgVSDQAgByIEIAYiBVENAQsgBCAFWg0AQt2whYzotpGouH8gCyAJfSIEIA0gEn0iBSAGIAdUrSIRVCANIBJUcq0iDX0iG30iIiAFIBF9IgVCjZXHw5bS2sCXf1ZCjZXHw5bS2sCXfyAFfSIFIAYgB30iB0LH+vPD7YKjkDxWrSIGVHKtIhF9IRIgESAiViAbQt2whYzotpGouH9WciECIAUgBn0hBSAEIA1UIAkgC1ZyrSAIIAp9fEKpwMaJrs6TsjB8IQtCx/rzw+2Co5A8IAd9DAELIBIgDX0iBCAGIAdWrSIRfSEFIAkgC30iGyAEIBFUIA0gElZyrSIEfSESIAkgC1QgBCAbVnIhAiAIIAp9IQsgByAGfQshDSADQbAHaiATQgAgDEIAEMkDIANB8AdqIBNCACAQQgAQyQMgA0GwCGogE0IAIBRCABDJAyADQfAIaiATQgAgD0IAEMkDIANBoAdqIAMpA7AHIgdCAEIAQonHmaSu8IHph38QyQMgA0GQB2ogAykDqAciBEIAQsf688PtgqOQPEIAEMkDIANBgAdqIARCAEKNlcfDltLawJd/QgAQyQMgA0HwBmogBEIAQt2whYzotpGouH9CABDJAyADQeAGaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0HQBmogFkIAIAxCABDJAyADQeAHaiAWQgAgEEIAEMkDIANBoAhqIBZCACAUQgAQyQMgA0HgCGogFkIAIA9CABDJAyADQcAGaiADKQOAByIWIAMpA7gHIgogAykD8Ad8IhN8IgkgAykDmAcgByADKQOQByIEfCAEVK18fCIHIAMpA9AGfCIIQgBCAEKJx5mkrvCB6Yd/EMkDIANBsAZqIAMpA8gGIgRCAELH+vPD7YKjkDxCABDJAyADQaAGaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANBkAZqIARCAELdsIWM6LaRqLh/QgAQyQMgA0GABmogBEIAQqnAxomuzpOyMEIAEMkDIANB8AVqIBpCACAMQgAQyQMgA0HQB2ogGkIAIBBCABDJAyADQZAIaiAaQgAgFEIAEMkDIANB0AhqIBpCACAPQgAQyQMgA0HgBWogAykD2AYgByAIVq18IhogAykD4Ad8IgYgAykD+AcgCiATVq18IhEgAykDsAh8IgogAykD8AZ8IhMgByAJVK0gAykDiAcgCSAWVK18fHwiG3wiCSADKQOgBnwiByADKQO4BiADKQOwBiIEIAh8IARUrXx8IgggAykD8AV8IhZCAEIAQonHmaSu8IHph38QyQMgA0HQBWogAykD6AUiBEIAQsf688PtgqOQPEIAEMkDIANBwAVqIARCAEKNlcfDltLawJd/QgAQyQMgA0GwBWogBEIAQt2whYzotpGouH9CABDJAyADQaAFaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0GQBWogHkIAIAxCABDJAyADQcAHaiAeQgAgEEIAEMkDIANBgAhqIB5CACAUQgAQyQMgA0HACGogHkIAIA9CABDJAyADQYAFaiADKQP4BSAIIBZWrXwiHiADKQPQB3wiDCADKQO4CCAKIBFUrXwiESADKQPwCHwiECADKQPgBnwiFCATIBtWrSADKQP4BiAKIBNWrXx8fCIKIAMpA6AIfCIPIAYgCVatIAMpA+gHIAYgGlStfHx8IgYgAykDkAZ8IhMgByAIVq0gAykDqAYgByAJVK18fHwiGnwiCSADKQPABXwiByADKQPYBSADKQPQBSIEIBZ8IARUrXx8IgggAykDkAV8IhZCAEIAQonHmaSu8IHph38QyQMgA0HwBGogAykDiAUiBEIAQsf688PtgqOQPEIAEMkDIANB4ARqIARCAEKNlcfDltLawJd/QgAQyQMgA0HQBGogBEIAQt2whYzotpGouH9CABDJAyADQcAEaiAEQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA8gEIAMpA6gFIAMpA4gGIAogFFStIAMpA+gGIBAgFFatfHwgAykD+AggECARVK18fCIUIAMpA+AIfCIEIAYgD1StIAMpA6gIIAogD1atfHx8IgogAykDgAZ8IhAgClStfCAQIBMgGlatIAMpA5gGIAYgE1atfHx8IgYgEFStfCAEIApWrSADKQPoCCAEIBRUrXx8fCIQIAMpA9AIfCIEIAMpA5gIIAYgBiADKQOQCHwiBlatfCAGIAYgCSAMVK0gAykD2AcgDCAeVK18fHwiBlatfHwiCiADKQOgBXwiDCAKVK18IAwgAykDuAUgBiAGIAMpA7AFfCIGVq18IAYgByAIVq0gAykDyAUgByAJVK18fHwiByAGVK18fCIJIAxUrXwgBCAKVq0gAykD2AggBCAQVK18fHwiCiADKQPACHwiBiADKQOICCAJIAMpA4AIfCIEIAlUrXwgBCAEIAMpA8gHIAMpA5gFIAggFlatfCIIIAMpA8AHfCIJIAhUrXwgCSAHIAl8IglWrXx8IgRWrXx8IgggAykDwAR8IgcgCFStfCAHIAcgAykD2AQgBCAEIAMpA9AEfCIEVq18IAQgBCADKQPoBCAJIAkgAykD4AR8IglWrXwgCSADKQP4BCADKQPwBCIMIBZ8IAxUrXx8IhAgCVStfHwiBFatfHwiB1atfCAGIAhWrSADKQPICCAGIApUrXx8fCIUQqnAxomuzpOyMFYNAAJAIBRCqcDGia7Ok7IwUQRAIAdC3bCFjOi2kai4f1YNAiAHQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRQLIAchCiAEIQkMAgsgBEKNlcfDltLawJd/Vg0AQt2whYzotpGouH8hCiAEQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRQgBCEJDAILQo2Vx8OW0trAl38hCSAQQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhFAwBCyAEQvPquLzpraW/6AB8IgggEELH+vPD7YKjkDxUrSIGfSEJIAdCo8/685fJ7tfHAHwiDCAEQo2Vx8OW0trAl39UIAYgCFZyrSIEfSEKIBQgB0LdsIWM6LaRqLh/VCAEIAxWcq19QqnAxomuzpOyMH0hFCAQQsf688PtgqOQPH0hEAsgA0HwAmogGUIAIA5CABDJAyADQZACaiAYQgAgDkIAEMkDIANBsAFqIBxCACAOQgAQyQMgA0HQAGogHUIAIA5CABDJAyADQeACaiADKQPwAiIIQgBCAEKJx5mkrvCB6Yd/EMkDIANB0AJqIAMpA+gCIgRCAELH+vPD7YKjkDxCABDJAyADQcACaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANBsAJqIARCAELdsIWM6LaRqLh/QgAQyQMgA0GgAmogBEIAQqnAxomuzpOyMEIAEMkDIANBsANqIBlCACAVQgAQyQMgA0GgA2ogGEIAIBVCABDJAyADQZADaiAcQgAgFUIAEMkDIANBgANqIB1CACAVQgAQyQMgA0GAAmogAykDwAIiFSADKQP4AiIOIAMpA5ACfCIPfCIHIAMpA9gCIAggAykD0AIiBHwgBFStfHwiCCADKQOwA3wiBkIAQgBCiceZpK7wgemHfxDJAyADQfABaiADKQOIAiIEQgBCx/rzw+2Co5A8QgAQyQMgA0HgAWogBEIAQo2Vx8OW0trAl39CABDJAyADQdABaiAEQgBC3bCFjOi2kai4f0IAEMkDIANBwAFqIARCAEKpwMaJrs6TsjBCABDJAyADQfADaiAZQgAgH0IAEMkDIANB4ANqIBhCACAfQgAQyQMgA0HQA2ogHEIAIB9CABDJAyADQcADaiAdQgAgH0IAEMkDIANBoAFqIAMpA7gDIAYgCFStfCITIAMpA6ADfCIMIAMpA5gCIA4gD1atfCIWIAMpA7ABfCIOIAMpA7ACfCIPIAcgCFatIAMpA8gCIAcgFVStfHx8Ihp8IgcgAykD4AF8IgggAykD+AEgAykD8AEiBCAGfCAEVK18fCIGIAMpA/ADfCIVQgBCAEKJx5mkrvCB6Yd/EMkDIANBkAFqIAMpA6gBIgRCAELH+vPD7YKjkDxCABDJAyADQYABaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANB8ABqIARCAELdsIWM6LaRqLh/QgAQyQMgA0HgAGogBEIAQqnAxomuzpOyMEIAEMkDIANBsARqIBlCACAXQgAQyQMgA0GgBGogGEIAIBdCABDJAyADQZAEaiAcQgAgF0IAEMkDIANBgARqIB1CACAXQgAQyQMgA0FAayADKQP4AyAGIBVWrXwiGCADKQPgA3wiHyADKQO4ASAOIBZUrXwiHCADKQNQfCIXIAMpA6ACfCIZIA8gGlatIAMpA7gCIA4gD1atfHx8Ig4gAykDkAN8Ig8gByAMVK0gAykDqAMgDCATVK18fHwiDCADKQPQAXwiEyAGIAhUrSADKQPoASAHIAhWrXx8fCIdfCIHIAMpA4ABfCIIIAMpA5gBIAMpA5ABIgQgFXwgBFStfHwiBiADKQOwBHwiFUIAQgBCiceZpK7wgemHfxDJAyADQTBqIAMpA0giBEIAQsf688PtgqOQPEIAEMkDIANBIGogBEIAQo2Vx8OW0trAl39CABDJAyADQRBqIARCAELdsIWM6LaRqLh/QgAQyQMgAyAEQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpAwggAykDaCADKQPIASAOIBlUrSADKQOoAiAXIBlWrXx8IAMpA1ggFyAcVK18fCIXIAMpA4ADfCIEIAwgD1StIAMpA5gDIA4gD1atfHx8Ig4gAykDwAF8Ig8gDlStfCAPIBMgHVatIAMpA9gBIAwgE1atfHx8IgwgD1StfCAEIA5WrSADKQOIAyAEIBdUrXx8fCIXIAMpA8ADfCIEIAMpA9gDIAwgDCADKQPQA3wiDFatfCAMIAwgByAfVK0gAykD6AMgGCAfVq18fHwiDFatfHwiDiADKQNgfCIPIA5UrXwgDyADKQN4IAwgDCADKQNwfCIMVq18IAwgBiAIVK0gAykDiAEgByAIVq18fHwiCCAMVK18fCIHIA9UrXwgBCAOVq0gAykDyAMgBCAXVK18fHwiDyADKQOABHwiDCADKQOYBCAHIAMpA5AEfCIEIAdUrXwgBCAEIAMpA6gEIAMpA7gEIAYgFVatfCIGIAMpA6AEfCIHIAZUrXwgByAHIAh8IgdWrXx8IgRWrXx8Ig4gAykDAHwiBiAOVK18IAYgBiADKQMYIAQgBCADKQMQfCIEVq18IAQgBCADKQMoIAcgByADKQMgfCIHVq18IAcgAykDOCADKQMwIgggFXwgCFStfHwiCCAHVK18fCIEVq18fCIGVq18IAwgDlatIAMpA4gEIAwgD1StfHx8Ig5CqcDGia7Ok7IwVg0AAkAgDkKpwMaJrs6TsjBRBEAgBkLdsIWM6LaRqLh/Vg0CIAZC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhDgsgBiEMIAQhBwwCCyAEQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEMIARCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhDiAEIQcMAgtCjZXHw5bS2sCXfyEHIAhCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEODAELIARC8+q4vOmtpb/oAHwiDCAIQsf688PtgqOQPFStIg99IQcgBkKjz/rzl8nu18cAfCIVIARCjZXHw5bS2sCXf1QgDCAPVHKtIgR9IQwgDiAGQt2whYzotpGouH9UIAQgFVZyrX1CqcDGia7Ok7IwfSEOIAhCx/rzw+2Co5A8fSEIC0KpwMaJrs6TsjAhBiAKIAx8IgQgClQgBCAJIAcgCXwiCVYgCSAJIAggEHwiCCAQVK18IglWcq18IgcgBFRyrSAOIBR8fCIQIQQCQAJAAkAgEEKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEGIAciBELdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hBiAJIgRCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhBiAIIgRCx/rzw+2Co5A8UQ0BCyAEIAZaDQAgByEEIAkhBgwBCyAJQvPquLzpraW/6AB8IgQgCELH+vPD7YKjkDxUrSIKfSEGIAdCo8/685fJ7tfHAHwiDCAJQo2Vx8OW0trAl39UIAQgClRyrSIJfSEEIBAgB0LdsIWM6LaRqLh/VCAJIAxWcq19QqnAxomuzpOyMH0hECAIQsf688PtgqOQPH0hCAsgACAINwM4IAAgBjcDMCAAIAQ3AyggACAQNwMgIAAgDTcDGCAAIAU3AxAgACASNwMIIAAgCyACrX03AwAgA0GAEmokAAuZOgIHfxV+IwBB0A1rIgMkAAJAAkACQAJ+AkACQAJAAkAgAS0AQCIHIAItAEBGBEAgAUHo0cEAQSAQ8QNFBEAgAUEgakHo0cEAQSAQ8QNFDQILIAJB6NHBAEEgEPEDRQRAIAJBIGpB6NHBAEEgEPEDRQ0DCwJAIAEgAkEgEPEDRQRAIAFBIGoiCSACQSBqQSAQ8QNFDQEgAEIANwMAIAAgBzoAQCAAQThqQgA3AwAgAEEwakIANwMAIABBKGpCADcDACAAQSBqQgA3AwAgAEEYakIANwMAIABBEGpCADcDACAAQQhqQgA3AwAMCgsgASkDICITIQsgAikDICIOIQwCfgJAIA4gE1INACABKQMoIg8gAikDKCIMUgRAIA8hCwwBCyABKQMwIhEgAikDMCIMUgRAIBEhCwwBCyARIQ0gASkDOCILIRIgDyALIAIpAzgiDFENARoLIAsgDFYNBSABKQMoIQ8gASkDMCERIAIpAzAhDSABKQM4IQsgAikDOCESIAIpAygLIQogDSARfSIQIAsgElatIhh9IQwgCiAPfSIZIBAgGFQgDSARVHKtIg19IREgCiAPVCANIBlWciEEIA4gE30hECASIAt9IQsMBwsgA0HwB2oQVSAHRQRAIANBiAhqIQQgAykD+AchGCADKQPwByEZIAMpA4AIDAYLIAMoAqAKQQFxDQRB7PbBABDoBAALQYD2wQBBM0Hc9sEAEP4DAAsgACAHOgBAIAAgAikDIDcDICAAIAIpAwA3AwAgAEE4aiACQThqKQMANwMAIABBMGogAkEwaikDADcDACAAQShqIAJBKGopAwA3AwAgAEEIaiACQQhqKQMANwMAIABBEGogAkEQaikDADcDACAAQRhqIAJBGGopAwA3AwAMBgsgACAHOgBAIAAgASkDIDcDICAAIAEpAwA3AwAgAEE4aiABQThqKQMANwMAIABBMGogAUEwaikDADcDACAAQShqIAFBKGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwAMBQsgASkDMCIKIAIpAzAiD1QgCiAPfSIKIAEpAzgiDyACKQM4IhFUrSILVHKtIg0gASkDKCISIAIpAygiEH0iGEJ/hXwiDCAKQn+FIAt8IgogDyARfSIPQq/4//9vVq0iC1StIhl9IREgDCAZVCEEIAogC30hDCAQIBJWIA0gGFZyrSAOIBNCf4V8fCEQQq/4//9vIA99IQsMAgsgA0HACmohBCADKQOwCiEYIAMpA6gKIRkgAykDuAoLIRIgBCkDACEWIANBgA1qQgA3AwAgA0H4DGpCADcDACADQgA3A/AMIANC85aAgDA3A4gNIANBgAdqIAEpAxAiE0IAIAEpAxgiD0IAEMkDIANB4AZqIAEpAwgiEUIAIA9CABDJAyADQYAGaiABKQMAIgpCACAPQgAQyQMgA0HQBmogEUIAIBNCABDJAyADQZAGaiAKQgAgE0IAEMkDIANBoAZqIApCACARQgAQyQMgA0GwB2ogD0IAIA9CABDJAyADQfAGaiATQgAgE0IAEMkDIANBwAZqIBFCACARQgAQyQMgA0GwBmogCkIAIApCABDJAyADQaAHaiADKQOwByIXQrHqlJHdo4KcWH4iCkIAQq/4//9vQgAQyQMgA0GQB2ogCkIAQn9CABDJAyADKQOoBiADKQOYBiADKQOIBiADKQPoBiADKQOIByILIAMpA+AGfCIKIAtUrXwiDSADKQOABnwiCyANVK18IgwgAykDkAZ8Ig0gDFStfCANIA0gAykD2AYgCyALIAMpA9AGfCILVq18fCINVq18IgwgAykDoAZ8Ig4gDFStfCIMQj+IIAMpA7gGIAMpA7AGIhAgDEIBhiAOQj+IhHwiFSAQVK18IBUgAykDyAYgAykD+AYgAykD8AYiECAKQgGGIAMpA4AHIhRCP4iEfCIMIBBUrXwgDCADKQO4ByIQIBRCAYZ8IhQgEFStfCIaIAxUrXwiDCALQgGGIApCP4iEfCIbIAxUrSIMIAMpA8AGfCIKIAxUrXwgCiANQgGGIAtCP4iEfCIMIApUrXwiCiAOQgGGIA1CP4iEfCIQIApUrXwiDiAVVK18fCELAn8CQCADKQOYByIKIAogCiADKQOoByADKQOgByINIBdCfYN8IA1UrXwiFyADKQOQByINfCIVIBdUrXwgFSAUIBV8IhVWrXwiFCANfCIXIBRUrXwgFyAXIBp8IhdWrXwiFCANfCIKIBRUrXwgCiAbfCIUIApUrXwiClANACAKIAx8IgwgClQiBEUNACAErSIKIBB8IhAgCloNACAKIBBWrSIKIA58Ig4gCloNACAKIA5WrSIKIAt8IgsgClQMAQtBAAshBCADQfAFaiAVQrHqlJHdo4KcWH4iCkIAQq/4//9vQgAQyQMgA0HgBWogCkIAQn9CABDJAwJAIAMpA+gFIgogCiAKIAMpA/gFIAMpA/AFIg0gFXwgDVStfCIaIAMpA+AFIg18IhUgGlStfCAVIBUgF3wiFVatfCIaIA18IhcgGlStfCAXIBQgF3wiF1atfCIUIA18IgogFFStfCAKIAx8IhQgClStfCIKUA0AIAogEHwiECAKWg0AIAogEFatIgogDnwiDiAKWg0AIAogDlatIgogC3wiCyAKVCEGCyADQdAFaiAVQrHqlJHdo4KcWH4iCkIAQq/4//9vQgAQyQMgA0HABWogCkIAQn9CABDJAyADKQPIBSIKIAogCiADKQPYBSADKQPQBSINIBV8IA1UrXwiFSADKQPABSINfCIMIBVUrXwgDCAMIBd8IgxWrXwiFyANfCIVIBdUrXwgFSAUIBV8IhVWrXwiFyANfCIKIBdUrXwgCiAQfCIXIApUrXwiClBFBEAgCiAOfCIOIApUIgWtIgogC3wiDSALIAUbIQsgBSAKIA1WcSEFCyADQbAFaiAMQrHqlJHdo4KcWH4iCkIAQq/4//9vQgAQyQMgA0GgBWogCkIAQn9CABDJAyADKQOoBSIKIAogCiADKQO4BSADKQOwBSINIAx8IA1UrXwiECADKQOgBSINfCIMIBBUrXwgDCAVfCIQIAxUrXwiFSANfCIMIBVUrXwgDCAXfCIKIAxUrXwiDCANfCINIAxUrXwgDSANIA58Ig1WrXwiDCALfCIOIAsgDEIAUiIIGyELAkACQCAEIAZyIAVyIAwgDlYiBK0gDCAIG0IAUnIgBCAIcXJFBEAgCkJ/UiAQQq/4//9vVHIgCyANg0J/UnINAQsgCkIBfCIMIBBCr/j//29UrSIVfSEOIA1CAXwiFyAKQn9SIAwgFVRyrSIMfSEKIAsgDUJ/UiAMIBdWcq19QgF8IQsgEELRh4CAEHwhEAwBCyAKIQ4gDSEKCyADIBA3A8gNIAMgDjcDwA0gAyAKNwO4DSADIAs3A7ANIANB0AxqIANB8AxqIANBsA1qEIABAkACQAJAIAMpA9AMIgwgGXwiDSADKQPYDCIKIBh8IgsgClQgCyADKQPgDCIOIBJ8IgogDlQgCiAKIAMpA+gMIg4gFnwiECAOVK18IgpWcq18Ig4gC1RyrXwiCyANVCAMIA1Wcg0AIAtCf1INASAOQn9SBEBCfyELDAILQn8hDCAKQn9SBEBCfyELIAohDQwDCyAQQq/4//9vWg0AQn8hC0J/IQ0MAgsgCkIBfCIMIBBCr/j//29UrSISfSENIA5CAXwiGCAKQn9SIAwgElRyrSIKfSEMIAsgDkJ/UiAKIBhWcq19QgF8IQsgEELRh4CAEHwhEAwBCyAOIQwgCiENCyADIBA3A8gMIAMgDTcDwAwgAyAMNwO4DCADIAs3A7AMIANBwA1qQgA3AwAgA0G4DWpCADcDACADQgA3A7ANIANCoo+AgCA3A8gNIANBkA1qIgUgA0GwDWogCRCAASADQcgHaiADQbAMaiAFEFggAygCnAwiBARAIAMoAqAMIARBAnQQ3wQLAkAgAygC1AkiBEUNACAEIARBDGxBE2pBeHEiBmpBCWoiBEUNACADKALQCSAGayAEEN8ECyADKAKACiIEQYCAgIB4RiAERXINASADKAKECiAEQQJ0EN8EDAELIAMgCzcDyA0gAyAMNwPADSADIBE3A7gNIAMgECAErX03A7ANIAEpAwAiCyEPIAIpAwAiEiEOIAMCfgJAAn4CQCALIBJSDQAgASkDCCIRIAIpAwgiDlIEQCARIQ8MAQsgASkDECITIAIpAxAiDlIEQCATIQ8MAQsgEyEMIAEpAxgiDyENIBEgDyACKQMYIg5RDQEaCyAOIA9UDQEgASkDCCERIAEpAxAhEyACKQMQIQwgASkDGCEPIAIpAxghDSACKQMICyEKIAwgE30iECANIA9UrSIYfSEOIAogEX0iGSAMIBNUIBAgGFRyrSIQfSEMIAogEVQgECAZVnIhBCASIAt9IQsgDSAPfQwBCyABKQMQIhMgAikDECIKVCATIAp9IgogASkDGCIPIAIpAxgiDVStIgxUcq0iECABKQMIIhEgAikDCCIYfSIZQn+FfCIOIApCf4UgDHwiCiAPIA19Ig1Cr/j//29WrSIVVK0iF30hDCAOIBdUIQQgCiAVfSEOIBEgGFQgECAZVnKtIBIgC0J/hXx8IQtCr/j//28gDX0LNwOICCADIA43A4AIIAMgDDcD+AcgAyALIAStfTcD8AcgA0HIB2ogA0GwDWogA0HwB2oQWAsgAygCyAcEQCADIAMpA9gHNwP4ByADIAMpA9AHNwPwB0GM98EAQSsgA0HwB2pB/PbBAEG498EAEMoDAAsgA0GwBGogAykD6AciGEIAIAMpA+AHIhlCABDJAyADQaAEaiAYQgAgAykD2AciFUIAEMkDIANBkARqIBhCACADKQPQByIXQgAQyQMgA0HgBGogGUIAIBVCABDJAyADQdAEaiAZQgAgF0IAEMkDIANBgAVqIBVCACAXQgAQyQMgA0GABGogGEIAIBhCABDJAyADQcAEaiAZQgAgGUIAEMkDIANB8ARqIBVCACAVQgAQyQMgA0GQBWogF0IAIBdCABDJAyADQfADaiADKQOABCIWQrHqlJHdo4KcWH4iCkIAQq/4//9vQgAQyQMgA0HgA2ogCkIAQn9CABDJAyADKQOIBSADKQPYBCADKQOYBCADKQOoBCADKQO4BCILIAMpA6AEfCIKIAtUrXwiDSADKQOQBHwiCyANVK18IgwgAykD0AR8Ig0gDFStfCANIA0gAykD6AQgCyALIAMpA+AEfCILVq18fCINVq18Ig4gAykDgAV8IgwgDlStfCIOQj+IIAMpA5gFIAMpA5AFIhIgDkIBhiAMQj+IhHwiECASVK18IBAgAykD+AQgAykDyAQgAykDwAQiEiAKQgGGIAMpA7AEIhRCP4iEfCIOIBJUrXwgDiADKQOIBCISIBRCAYZ8IhQgElStfCIaIA5UrXwiDiALQgGGIApCP4iEfCIbIA5UrSIOIAMpA/AEfCIKIA5UrXwgCiANQgGGIAtCP4iEfCIOIApUrXwiCiAMQgGGIA1CP4iEfCISIApUrXwiDSAQVK18fCEKQQAhBQJ/AkAgAykD6AMiCyALIAsgAykD+AMgFiADKQPwAyIMfCAMVK18IhYgAykD4AMiDHwiECAWVK18IBAgECAUfCIQVq18IhQgDHwiFiAUVK18IBYgFiAafCIWVq18IhQgDHwiCyAUVK18IAsgG3wiFCALVK18IgtQDQAgCyAOfCIOIAtUIgRFDQAgBK0iCyASfCISIAtaDQAgCyASVq0iCyANfCINIAtaDQAgCyANVq0iCyAKfCIKIAtUDAELQQALIQYgA0HQA2ogEEKx6pSR3aOCnFh+IgtCAEKv+P//b0IAEMkDIANBwANqIAtCAEJ/QgAQyQMCQCADKQPIAyILIAsgCyADKQPYAyADKQPQAyIMIBB8IAxUrXwiGiADKQPAAyIMfCIQIBpUrXwgECAQIBZ8IhBWrXwiGiAMfCIWIBpUrXwgFiAUIBZ8IhZWrXwiFCAMfCILIBRUrXwgCyAOfCIUIAtUrXwiC1ANACALIBJ8IhIgC1oNACALIBJWrSILIA18Ig0gC1oNACALIA1WrSILIAp8IgogC1QhBQsgA0GwA2ogEEKx6pSR3aOCnFh+IgtCAEKv+P//b0IAEMkDIANBoANqIAtCAEJ/QgAQyQNBACEEIAMpA6gDIgsgCyALIAMpA7gDIAMpA7ADIgwgEHwgDFStfCIQIAMpA6ADIgx8Ig4gEFStfCAOIA4gFnwiDlatfCIWIAx8IhAgFlStfCAQIBAgFHwiEFatfCIWIAx8IgsgFlStfCALIBJ8IhYgC1StfCILUEUEQCALIA18Ig0gC1QiBK0iCyAKfCIMIAogBBshCiAEIAsgDFZxIQQLIANBkANqIA5CseqUkd2jgpxYfiILQgBCr/j//29CABDJAyADQYADaiALQgBCf0IAEMkDIAMpA4gDIgsgCyALIAMpA5gDIAMpA5ADIgwgDnwgDFStfCISIAMpA4ADIgx8Ig4gElStfCAOIBB8IhIgDlStfCIQIAx8Ig4gEFStfCAOIBZ8IgsgDlStfCIOIAx8IgwgDlStfCAMIAwgDXwiDFatfCIOIAp8IhAgCiAOQgBSIggbIQ0CQAJAIAUgBnIgBHIgDiAQViIErSAOIAgbQgBSciAEIAhxckUEQCALQn9SIBJCr/j//29UciAMIA2DQn9Scg0BCyALQgF8Ig4gEkKv+P//b1StIhB9IQogDEIBfCIWIAtCf1IgDiAQVHKtIgt9IQ4gDSAMQn9SIAsgFlZyrX1CAXwhDSASQtGHgIAQfCESDAELIAshCiAMIQ4LIAEpAwAiECEMIAMCfgJAAkAgECANIgtSDQAgESIMIA4iC1INACAKIQsgCiATIgxSDQAgDyIMIBIiC1ENAQsgCyAMWg0AIAogE1YgEyAKfSIKIA8gElStIgtUcq0iFiARIA59IhRCf4V8IgwgCkJ/hSALfCIKIA8gEn0iD0Kv+P//b1atIgtUrSISfSETIAwgElQhBCAKIAt9IQwgFCAWVCAOIBFWcq0gDSAQQn+FfHwhEUKv+P//byAPfQwBCyAKIBN9IgsgDyASVq0iFn0hDCAOIBF9IhQgCyAWVCAKIBNUcq0iCn0hEyAOIBFUIAogFFZyIQQgDSAQfSERIBIgD30LNwOICCADIAw3A4AIIAMgEzcD+AcgAyARIAStfTcD8AcgA0HIB2ogA0HwB2ogAhDJAiABKQMYIQ4gASkDECERIAEpAwghDSADKQPIByISIQ8gA0GwAmoCfgJAAn4CQCASIBAiClINACANIgogAykD0AciD1INACARIgogAykD2AciD1INACAKIQsgDSAOIgoiEyADKQPgByIPUQ0BGgsgAykD4AchEyAKIA9UDQEgAykD2AchCyADKQPQBwshDCARIAt9IgogDiATVK0iFn0hDyANIAx9IhQgCiAWVCALIBFWcq0iCn0hESAKIBRWIAwgDVZyIQIgECASfSESIA4gE30MAQsgAykD2AciCiARVCAKIBF9IgogDiATVq0iD1RyrSILIAMpA9AHIgwgDX0iFkJ/hXwiFCAKQn+FIA98IgogEyAOfSITQq/4//9vVq0iD1StIg59IREgDiAUViECIAogD30hDyAMIA1UIAsgFlZyrSAQIBJCf4V8fCESQq/4//9vIBN9CyIKQgAgGEIAEMkDIANBgAJqIApCACAZQgAQyQMgA0HwAWogCkIAIBVCABDJAyADQeABaiAKQgAgF0IAEMkDIANBoAJqIAMpA7ACIgtCseqUkd2jgpxYfiIKQgBCr/j//29CABDJAyADQZACaiAKQgBCf0IAEMkDIANB0AFqIA9CACAYQgAQyQMgA0GgAWogD0IAIBlCABDJAyADQZABaiAPQgAgFUIAEMkDIANBgAFqIA9CACAXQgAQyQMgA0HAAWogAykDkAIiCiADKQO4AiIMIAMpA4ACfCITfCIPIAMpA6gCIAsgAykDoAIiDXwgDVStfHwiCyADKQPQAXwiDUKx6pSR3aOCnFh+Ig5CAEKv+P//b0IAEMkDIANBsAFqIA5CAEJ/QgAQyQMgA0HwAGogEUIAIBhCABDJAyADQUBrIBFCACAZQgAQyQMgA0EQaiARQgAgFUIAEMkDIAMgEUIAIBdCABDJAyADQeAAaiADKQPYASALIA1WrXwiGiADKQOgAXwiESAKIAMpA4gCIAwgE1atfCIbIAMpA/ABfCIMfCITIAsgD1StIAMpA5gCIgsgCiAPVq18fHwiHHwiDiADKQOwASIQfCIWIAMpA8gBIAMpA8ABIg8gDXwgD1StfHwiDSADKQNwfCIUQrHqlJHdo4KcWH4iD0IAQq/4//9vQgAQyQMgA0HQAGogD0IAQn9CABDJAyADQfACaiASIAKtfSIPQgAgGEIAEMkDIANB4AJqIA9CACAZQgAQyQMgA0HQAmogD0IAIBVCABDJAyADQcACaiAPQgAgF0IAEMkDIANBMGogAykDeCANIBRWrXwiHSADKQNAfCIPIBAgCiADKQP4ASAMIBtUrXwiGyADKQPgAXwiEnwiCiATIBxWrSALIAwgE1atfHx8IgwgAykDkAF8IhMgDiARVK0gAykDqAEgESAaVK18fHwiEXwiGCANIBZUrSADKQO4ASINIA4gFlatfHx8Ihx8Ig4gAykDUCIZfCIVIAMpA2ggAykDYCIXIBR8IBdUrXx8IhcgAykD8AJ8IhZCseqUkd2jgpxYfiIUQgBCr/j//29CABDJAyADQSBqIBRCAEJ/QgAQyQMCQCADKQMoIhQgAykDWCIaIBkgDSAQIAogDFatIAsgCiASVK18fCIeIAMpA+gBIBIgG1StfHwiCiADKQOAAXwiCyARIBNUrSADKQOYASAMIBNWrXx8fCIMfCITIAxUrXwgEyAYIBxWrSANIBEgGFatfHx8IhEgE1StfCITIAsgDFatIAMpA4gBIAogC1atfHwiDCAKIB5UrXwiEnwiCiADKQMAfCILIAMpAxggESARIAMpAxB8IhFWrXwgESAOIA9UrSADKQNIIA8gHVStfHx8Ig8gEVStfHwiEXwiDSARVK18IA0gGiAPIA8gGXwiD1atfCAPIBUgF1atIBogDiAVVq18fHwiDiAPVK18fCIPIA1UrXwiECALIBFWrSADKQMIIAogC1atfHwiGCAKIBNUrSAMIBJWrXx8IhJ8Ig0gAykDwAJ8IgwgAykD2AIgDyADKQPQAnwiCiAPVK18IAogCiADKQPoAiADKQP4AiAWIBdUrXwiESADKQPgAnwiDyARVK18IA8gDiAPfCIPVq18fCIKVq18fCITIAMpAyAiEXwiDiATVK18IA4gFCAKIAogEXwiClatfCAKIAogFCAPIA8gEXwiD1atfCAPIAMpAzggAykDMCIRIBZ8IBFUrXx8IgsgD1StfHwiClatfHwiESAOVK18Ig8gDCATVq0gAykDyAIgDCANVK18fCIMIA0gEFStIBIgGFStfHwiDXwiECAPVCAMIA1WckUgC0Kv+P//b1QiAiAKIBGDIBCDQn9ScnFFBEAgCkIBfCINIAKtIgx9IQ8gEUIBfCITIApCf1IgDCANVnKtIgp9IQ4gECARQn9SIAogE1ZyrX1CAXwhECALQtGHgIAQfCELDAELIAohDyARIQ4LIAMgCzcDiAggAyAPNwOACCADIA43A/gHIAMgEDcD8AcgAEEgaiADQfAHaiABQSBqEMkCIABBGGogA0HgB2opAwA3AwAgAEEQaiADQdgHaikDADcDACAAQQhqIANB0AdqKQMANwMAIAAgAykDyAc3AwAgACAHOgBACyADQdANaiQAC8lHAgJ/HH4jAEGwEGsiASQAIAFBiBBqQdyBwgBBARC3AiABQYAOaiABKQOgECIDQgBCp9uF8drIudwbQgAQyQMgAUHADmogASkDmBAiBEIAQqfbhfHayLncG0IAEMkDIAFBgA9qIAEpA5AQIgVCAEKn24Xx2si53BtCABDJAyABQcAPaiABKQOIECIGQgBCp9uF8drIudwbQgAQyQMgAUHwDWogASkDgA4iB0L/////vrL98EJ+Ig1CAEKBgICAv7L98MMAQgAQyQMgAUHgDWogDUIAQpHh5c2HifqZKEIAEMkDIAFBkA1qIA1CAELdsIWM6LaRqLh/QgAQyQMgAUHADGogDUIAQqnAxomuzpOyMEIAEMkDIAFBkA5qIANCAELjs/GantaO/9MAQgAQyQMgAUHQDmogBEIAQuOz8Zqe1o7/0wBCABDJAyABQZAPaiAFQgBC47Pxmp7Wjv/TAEIAEMkDIAFB0A9qIAZCAELjs/GantaO/9MAQgAQyQMgAUHQDWogASkD4A0iECABKQOIDiIKIAEpA8AOfCISfCIJIAEpA/gNIAcgASkD8A0iDXwgDVStfHwiByABKQOQDnwiFkL/////vrL98EJ+Ig1CAEKBgICAv7L98MMAQgAQyQMgAUHADWogDUIAQpHh5c2HifqZKEIAEMkDIAFBsA1qIA1CAELdsIWM6LaRqLh/QgAQyQMgAUGgDWogDUIAQqnAxomuzpOyMEIAEMkDIAFBoA5qIANCAEKFge6d1efgpIx/QgAQyQMgAUHgDmogBEIAQoWB7p3V5+CkjH9CABDJAyABQaAPaiAFQgBChYHundXn4KSMf0IAEMkDIAFB4A9qIAZCAEKFge6d1efgpIx/QgAQyQMgAUGADWogASkDmA4gByAWVq18IgwgASkD0A58Ig8gASkDyA4gCiASVq18IgggASkDgA98IgogASkDkA18IhIgByAJVK0gASkD6A0gCSAQVK18fHwiGnwiCSABKQPADXwiByABKQPYDSABKQPQDSINIBZ8IA1UrXx8IhYgASkDoA58IhBC/////76y/fBCfiINQgBCgYCAgL+y/fDDAEIAEMkDIAFB8AxqIA1CAEKR4eXNh4n6mShCABDJAyABQeAMaiANQgBC3bCFjOi2kai4f0IAEMkDIAFB0AxqIA1CAEKpwMaJrs6TsjBCABDJAyABQbAOaiADQgBCpYm5+peWtIsCQgAQyQMgAUHwDmogBEIAQqWJufqXlrSLAkIAEMkDIAFBsA9qIAVCAEKlibn6l5a0iwJCABDJAyABQfAPaiAGQgBCpYm5+peWtIsCQgAQyQMgAUGwDGogASkDqA4gECAWVK18IhMgASkD4A58IgQgASkDiA8gCCAKVq18IgggASkDwA98IgUgASkDwAx8IgYgEiAaVq0gASkDmA0gCiASVq18fHwiDSABKQOQD3wiCiAJIA9UrSABKQPYDiAMIA9WrXx8fCIPIAEpA7ANfCISIAcgFlatIAEpA8gNIAcgCVStfHx8Igx8IgkgASkD8Ax8IgcgASkDiA0gASkDgA0iAyAQfCADVK18fCIWIAEpA7AOfCIQQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyABQaAMaiADQgBCkeHlzYeJ+pkoQgAQyQMgAUGQDGogA0IAQt2whYzotpGouH9CABDJAyABQYAMaiADQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgASkDiAwgASkD6A8gASkD2A8gASkDyA8gBSAIVK18IgggASkD0A98IgMgCFStfCADIAMgBiANVq0gASkDyAwgBSAGVq18fHwiA1atfCADIAMgCiAPVq0gASkDmA8gCiANVK18fHwiA1atfCIGIAEpA+APfCIFIAZUrXwgBSAFIAEpA6gNIAMgAyABKQOgDXwiA1atfCADIAMgDCASVK0gASkDuA0gDyASVq18fHwiA1atfHwiBVatfCAFIAEpA6gPIAMgAyABKQOgD3wiA1atfCADIAMgBCAJVq0gASkD6A4gBCATVK18fHwiA1atfHwiBCAFVK18Ig8gASkD8A98IgUgASkD2AwgBCAEIAEpA9AMfCIEVq18IAQgASkD6AwgAyADIAEpA+AMfCIDVq18IAMgByAWVq0gASkD+AwgByAJVK18fHwiDSADVK18fCIDIARUrXx8IgYgASkDuA8gAyADIAEpA7APfCIDVq18IAMgAyABKQP4DiABKQO4DiAQIBZUrXwiCSABKQPwDnwiBCAJVK18IAQgBCANfCIEVq18fCIDVq18fCINIAEpA4AMfCIJIA1UrXwgCSABKQOYDCADIAMgASkDkAx8IgNWrXwgAyADIAEpA6gMIAQgBCABKQOgDHwiBFatfCAEIAEpA7gMIAEpA7AMIgcgEHwgB1StfHwiGiAEVK18fCIDVq18fCIEIAlUrXwgBiANVq0gBSAGVq0gASkD+A8gBSAPVK18fHx8IhJCqcDGia7Ok7IwVg0AAkAgEkKpwMaJrs6TsjBRBEAgBELdsIWM6LaRqLh/Vg0CIARC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhEgsgBCEWIAMhDQwDCyADQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IRYgA0KR4eXNh4n6mShSIBpCgYCAgL+y/fDDAFRyDQELIANCkeHlzYeJ+pkofSIFIBpCgYCAgL+y/fDDAFStIgZ9IQ0gBEKjz/rzl8nu18cAfCIJIANCkeHlzYeJ+pkoVCAFIAZUcq0iA30hFiASIARC3bCFjOi2kai4f1QgAyAJVnKtfUKpwMaJrs6TsjB9IRIgGkKBgICAv7L98MMAfSEaDAELQqnAxomuzpOyMCESIAMhDQsgAUGIEGpB3YHCAEHCABC3AiABQYAKaiABKQOgECIDQgBCp9uF8drIudwbQgAQyQMgAUHACmogASkDmBAiBEIAQqfbhfHayLncG0IAEMkDIAFBgAtqIAEpA5AQIgVCAEKn24Xx2si53BtCABDJAyABQcALaiABKQOIECIGQgBCp9uF8drIudwbQgAQyQMgAUHwCWogASkDgAoiD0L/////vrL98EJ+IglCAEKBgICAv7L98MMAQgAQyQMgAUHgCWogCUIAQpHh5c2HifqZKEIAEMkDIAFBkAlqIAlCAELdsIWM6LaRqLh/QgAQyQMgAUHACGogCUIAQqnAxomuzpOyMEIAEMkDIAFBkApqIANCAELjs/GantaO/9MAQgAQyQMgAUHQCmogBEIAQuOz8Zqe1o7/0wBCABDJAyABQZALaiAFQgBC47Pxmp7Wjv/TAEIAEMkDIAFB0AtqIAZCAELjs/GantaO/9MAQgAQyQMgAUHQCWogASkD4AkiEyABKQOICiIMIAEpA8AKfCIIfCIHIAEpA/gJIA8gASkD8AkiCXwgCVStfHwiDyABKQOQCnwiCkL/////vrL98EJ+IglCAEKBgICAv7L98MMAQgAQyQMgAUHACWogCUIAQpHh5c2HifqZKEIAEMkDIAFBsAlqIAlCAELdsIWM6LaRqLh/QgAQyQMgAUGgCWogCUIAQqnAxomuzpOyMEIAEMkDIAFBoApqIANCAEKFge6d1efgpIx/QgAQyQMgAUHgCmogBEIAQoWB7p3V5+CkjH9CABDJAyABQaALaiAFQgBChYHundXn4KSMf0IAEMkDIAFB4AtqIAZCAEKFge6d1efgpIx/QgAQyQMgAUGACWogASkDmAogCiAPVK18IhQgASkD0Ap8IhAgASkDyAogCCAMVK18IgsgASkDgAt8IgwgASkDkAl8IgggByAPVq0gASkD6AkgByATVK18fHwiDnwiByABKQPACXwiDyABKQPYCSABKQPQCSIJIAp8IAlUrXx8IgogASkDoAp8IhNC/////76y/fBCfiIJQgBCgYCAgL+y/fDDAEIAEMkDIAFB8AhqIAlCAEKR4eXNh4n6mShCABDJAyABQeAIaiAJQgBC3bCFjOi2kai4f0IAEMkDIAFB0AhqIAlCAEKpwMaJrs6TsjBCABDJAyABQbAKaiADQgBCpYm5+peWtIsCQgAQyQMgAUHwCmogBEIAQqWJufqXlrSLAkIAEMkDIAFBsAtqIAVCAEKlibn6l5a0iwJCABDJAyABQfALaiAGQgBCpYm5+peWtIsCQgAQyQMgAUGwCGogASkDqAogCiATVq18IhEgASkD4Ap8IgQgASkDiAsgCyAMVq18IgsgASkDwAt8IgUgASkDwAh8IgYgCCAOVq0gASkDmAkgCCAMVK18fHwiCSABKQOQC3wiDCAHIBBUrSABKQPYCiAQIBRUrXx8fCIQIAEpA7AJfCIIIAogD1StIAEpA8gJIAcgD1atfHx8IhR8IgcgASkD8Ah8Ig8gASkDiAkgASkDgAkiAyATfCADVK18fCIKIAEpA7AKfCITQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyABQaAIaiADQgBCkeHlzYeJ+pkoQgAQyQMgAUGQCGogA0IAQt2whYzotpGouH9CABDJAyABQYAIaiADQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgASkDiAggASkD6AsgASkD2AsgASkDyAsgBSALVK18IgsgASkD0At8IgMgC1StfCADIAMgBiAJVq0gASkDyAggBSAGVq18fHwiA1atfCADIAMgDCAQVq0gASkDmAsgCSAMVq18fHwiA1atfCIGIAEpA+ALfCIFIAZUrXwgBSAFIAEpA6gJIAMgAyABKQOgCXwiA1atfCADIAMgCCAUVq0gASkDuAkgCCAQVK18fHwiA1atfHwiBVatfCAFIAEpA6gLIAMgAyABKQOgC3wiA1atfCADIAMgBCAHVq0gASkD6AogBCARVK18fHwiA1atfHwiBCAFVK18IhAgASkD8At8IgUgASkD2AggBCAEIAEpA9AIfCIEVq18IAQgASkD6AggAyADIAEpA+AIfCIDVq18IAMgCiAPVK0gASkD+AggByAPVq18fHwiCSADVK18fCIDIARUrXx8IgYgASkDuAsgAyADIAEpA7ALfCIDVq18IAMgAyABKQP4CiABKQO4CiAKIBNWrXwiByABKQPwCnwiBCAHVK18IAQgBCAJfCIEVq18fCIDVq18fCIJIAEpA4AIfCIHIAlUrXwgByABKQOYCCADIAMgASkDkAh8IgNWrXwgAyADIAEpA6gIIAQgBCABKQOgCHwiBFatfCAEIAEpA7gIIAEpA7AIIg8gE3wgD1StfHwiEyAEVK18fCIDVq18fCIEIAdUrXwgBiAJVq0gBSAGVq0gASkD+AsgBSAQVK18fHx8IhBCqcDGia7Ok7IwVg0AAkAgEEKpwMaJrs6TsjBRBEAgBELdsIWM6LaRqLh/Vg0CIARC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhEAsgBCEPIAMhCQwDCyADQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IQ8gA0KR4eXNh4n6mShSIBNCgYCAgL+y/fDDAFRyDQELIANCkeHlzYeJ+pkofSIFIBNCgYCAgL+y/fDDAFStIgZ9IQkgBEKjz/rzl8nu18cAfCIHIANCkeHlzYeJ+pkoVCAFIAZUcq0iA30hDyAQIARC3bCFjOi2kai4f1QgAyAHVnKtfUKpwMaJrs6TsjB9IRAgE0KBgICAv7L98MMAfSETDAELQqnAxomuzpOyMCEQIAMhCQsgAUGIEGpBn4LCAEEDELcCIAFBgAZqIAEpA6AQIgNCAEKn24Xx2si53BtCABDJAyABQcAGaiABKQOYECIEQgBCp9uF8drIudwbQgAQyQMgAUGAB2ogASkDkBAiBUIAQqfbhfHayLncG0IAEMkDIAFBwAdqIAEpA4gQIgZCAEKn24Xx2si53BtCABDJAyABQfAFaiABKQOABiIMQv////++sv3wQn4iB0IAQoGAgIC/sv3wwwBCABDJAyABQeAFaiAHQgBCkeHlzYeJ+pkoQgAQyQMgAUGQBWogB0IAQt2whYzotpGouH9CABDJAyABQcAEaiAHQgBCqcDGia7Ok7IwQgAQyQMgAUGQBmogA0IAQuOz8Zqe1o7/0wBCABDJAyABQdAGaiAEQgBC47Pxmp7Wjv/TAEIAEMkDIAFBkAdqIAVCAELjs/GantaO/9MAQgAQyQMgAUHQB2ogBkIAQuOz8Zqe1o7/0wBCABDJAyABQdAFaiABKQPgBSIRIAEpA4gGIgsgASkDwAZ8Ig58IgogASkD+AUgDCABKQPwBSIHfCAHVK18fCIMIAEpA5AGfCIIQv////++sv3wQn4iB0IAQoGAgIC/sv3wwwBCABDJAyABQcAFaiAHQgBCkeHlzYeJ+pkoQgAQyQMgAUGwBWogB0IAQt2whYzotpGouH9CABDJAyABQaAFaiAHQgBCqcDGia7Ok7IwQgAQyQMgAUGgBmogA0IAQoWB7p3V5+CkjH9CABDJAyABQeAGaiAEQgBChYHundXn4KSMf0IAEMkDIAFBoAdqIAVCAEKFge6d1efgpIx/QgAQyQMgAUHgB2ogBkIAQoWB7p3V5+CkjH9CABDJAyABQYAFaiABKQOYBiAIIAxUrXwiFyABKQPQBnwiFCABKQPIBiALIA5WrXwiFSABKQOAB3wiCyABKQOQBXwiDiAKIAxWrSABKQPoBSAKIBFUrXx8fCIYfCIKIAEpA8AFfCIMIAEpA9gFIAEpA9AFIgcgCHwgB1StfHwiCCABKQOgBnwiEUL/////vrL98EJ+IgdCAEKBgICAv7L98MMAQgAQyQMgAUHwBGogB0IAQpHh5c2HifqZKEIAEMkDIAFB4ARqIAdCAELdsIWM6LaRqLh/QgAQyQMgAUHQBGogB0IAQqnAxomuzpOyMEIAEMkDIAFBsAZqIANCAEKlibn6l5a0iwJCABDJAyABQfAGaiAEQgBCpYm5+peWtIsCQgAQyQMgAUGwB2ogBUIAQqWJufqXlrSLAkIAEMkDIAFB8AdqIAZCAEKlibn6l5a0iwJCABDJAyABQbAEaiABKQOoBiAIIBFWrXwiGSABKQPgBnwiBCABKQOIByALIBVUrXwiFSABKQPAB3wiBSABKQPABHwiBiAOIBhWrSABKQOYBSALIA5WrXx8fCIHIAEpA5AHfCILIAogFFStIAEpA9gGIBQgF1StfHx8IhQgASkDsAV8Ig4gCCAMVK0gASkDyAUgCiAMVq18fHwiF3wiCiABKQPwBHwiDCABKQOIBSABKQOABSIDIBF8IANUrXx8IgggASkDsAZ8IhFC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAFBoARqIANCAEKR4eXNh4n6mShCABDJAyABQZAEaiADQgBC3bCFjOi2kai4f0IAEMkDIAFBgARqIANCAEKpwMaJrs6TsjBCABDJAwJAAkACQCABKQOIBCABKQPoByABKQPYByABKQPIByAFIBVUrXwiFSABKQPQB3wiAyAVVK18IAMgAyAGIAdWrSABKQPIBCAFIAZWrXx8fCIDVq18IAMgAyALIBRWrSABKQOYByAHIAtWrXx8fCIDVq18IgYgASkD4Ad8IgUgBlStfCAFIAUgASkDqAUgAyADIAEpA6AFfCIDVq18IAMgAyAOIBdWrSABKQO4BSAOIBRUrXx8fCIDVq18fCIFVq18IAUgASkDqAcgAyADIAEpA6AHfCIDVq18IAMgAyAEIApWrSABKQPoBiAEIBlUrXx8fCIDVq18fCIEIAVUrXwiCyABKQPwB3wiBSABKQPYBCAEIAQgASkD0AR8IgRWrXwgBCABKQPoBCADIAMgASkD4AR8IgNWrXwgAyAIIAxUrSABKQP4BCAKIAxWrXx8fCIHIANUrXx8IgMgBFStfHwiBiABKQO4ByADIAMgASkDsAd8IgNWrXwgAyADIAEpA/gGIAEpA7gGIAggEVatfCIKIAEpA/AGfCIEIApUrXwgBCAEIAd8IgRWrXx8IgNWrXx8IgcgASkDgAR8IgogB1StfCAKIAEpA5gEIAMgAyABKQOQBHwiA1atfCADIAMgASkDqAQgBCAEIAEpA6AEfCIEVq18IAQgASkDuAQgASkDsAQiDCARfCAMVK18fCIUIARUrXx8IgNWrXx8IgQgClStfCAGIAdWrSAFIAZWrSABKQP4ByAFIAtUrXx8fHwiDEKpwMaJrs6TsjBWDQACQCAMQqnAxomuzpOyMFEEQCAEQt2whYzotpGouH9WDQIgBELdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCEMCyAEIQogAyEHDAMLIANCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8hCiADQpHh5c2HifqZKFIgFEKBgICAv7L98MMAVHINAQsgA0KR4eXNh4n6mSh9IgUgFEKBgICAv7L98MMAVK0iBn0hByAEQqPP+vOXye7XxwB8IgggA0KR4eXNh4n6mShUIAUgBlRyrSIDfSEKIAwgBELdsIWM6LaRqLh/VCADIAhWcq19QqnAxomuzpOyMH0hDCAUQoGAgIC/sv3wwwB9IRQMAQtCqcDGia7Ok7IwIQwgAyEHCyABQYgQakGigsIAQTMQtwIgAUGAAmogASkDoBAiA0IAQqfbhfHayLncG0IAEMkDIAFBwAJqIAEpA5gQIgRCAEKn24Xx2si53BtCABDJAyABQYADaiABKQOQECIFQgBCp9uF8drIudwbQgAQyQMgAUHAA2ogASkDiBAiBkIAQqfbhfHayLncG0IAEMkDIAFB8AFqIAEpA4ACIg5C/////76y/fBCfiIIQgBCgYCAgL+y/fDDAEIAEMkDIAFB4AFqIAhCAEKR4eXNh4n6mShCABDJAyABQZABaiAIQgBC3bCFjOi2kai4f0IAEMkDIAFBQGsgCEIAQqnAxomuzpOyMEIAEMkDIAFBkAJqIANCAELjs/GantaO/9MAQgAQyQMgAUHQAmogBEIAQuOz8Zqe1o7/0wBCABDJAyABQZADaiAFQgBC47Pxmp7Wjv/TAEIAEMkDIAFB0ANqIAZCAELjs/GantaO/9MAQgAQyQMgAUHQAWogASkD4AEiGSABKQOIAiIVIAEpA8ACfCIYfCILIAEpA/gBIA4gASkD8AEiCHwgCFStfHwiDiABKQOQAnwiEUL/////vrL98EJ+IghCAEKBgICAv7L98MMAQgAQyQMgAUHAAWogCEIAQpHh5c2HifqZKEIAEMkDIAFBsAFqIAhCAELdsIWM6LaRqLh/QgAQyQMgAUGgAWogCEIAQqnAxomuzpOyMEIAEMkDIAFBoAJqIANCAEKFge6d1efgpIx/QgAQyQMgAUHgAmogBEIAQoWB7p3V5+CkjH9CABDJAyABQaADaiAFQgBChYHundXn4KSMf0IAEMkDIAFB4ANqIAZCAEKFge6d1efgpIx/QgAQyQMgAUGAAWogASkDmAIgDiARVq18IhwgASkD0AJ8IhcgASkDyAIgFSAYVq18IhsgASkDgAN8IhUgASkDkAF8IhggCyAOVq0gASkD6AEgCyAZVK18fHwiHXwiCyABKQPAAXwiDiABKQPYASABKQPQASIIIBF8IAhUrXx8IhEgASkDoAJ8IhlC/////76y/fBCfiIIQgBCgYCAgL+y/fDDAEIAEMkDIAFB8ABqIAhCAEKR4eXNh4n6mShCABDJAyABQeAAaiAIQgBC3bCFjOi2kai4f0IAEMkDIAFB0ABqIAhCAEKpwMaJrs6TsjBCABDJAyABQbACaiADQgBCpYm5+peWtIsCQgAQyQMgAUHwAmogBEIAQqWJufqXlrSLAkIAEMkDIAFBsANqIAVCAEKlibn6l5a0iwJCABDJAyABQfADaiAGQgBCpYm5+peWtIsCQgAQyQMgAUEwaiABKQOoAiARIBlWrXwiHiABKQPgAnwiBCABKQOIAyAVIBtUrXwiGyABKQPAA3wiBSABKQNAfCIGIBggHVatIAEpA5gBIBUgGFatfHx8IgggASkDkAN8IhUgCyAXVK0gASkD2AIgFyAcVK18fHwiFyABKQOwAXwiGCAOIBFWrSABKQPIASALIA5WrXx8fCIcfCILIAEpA3B8Ig4gASkDiAEgASkDgAEiAyAZfCADVK18fCIRIAEpA7ACfCIZQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyABQSBqIANCAEKR4eXNh4n6mShCABDJAyABQRBqIANCAELdsIWM6LaRqLh/QgAQyQMgASADQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkACQCABKQMIIAEpA+gDIAEpA9gDIAEpA8gDIAUgG1StfCIbIAEpA9ADfCIDIBtUrXwgAyADIAYgCFatIAEpA0ggBSAGVq18fHwiA1atfCADIAMgFSAXVq0gASkDmAMgCCAVVq18fHwiA1atfCIGIAEpA+ADfCIFIAZUrXwgBSAFIAEpA6gBIAMgAyABKQOgAXwiA1atfCADIAMgGCAcVq0gASkDuAEgFyAYVq18fHwiA1atfHwiBVatfCAFIAEpA6gDIAMgAyABKQOgA3wiA1atfCADIAMgBCALVq0gASkD6AIgBCAeVK18fHwiA1atfHwiBCAFVK18IhcgASkD8AN8IgYgASkDWCAEIAQgASkDUHwiBFatfCAEIAEpA2ggAyADIAEpA2B8IgNWrXwgAyAOIBFWrSABKQN4IAsgDlatfHx8IgggA1StfHwiAyAEVK18fCIEIAEpA7gDIAMgAyABKQOwA3wiA1atfCADIAMgASkD+AIgASkDuAIgESAZVq18IgsgASkD8AJ8IgUgC1StfCAFIAUgCHwiBVatfHwiA1atfHwiCCABKQMAfCIOIAhUrXwgDiABKQMYIAMgAyABKQMQfCIDVq18IAMgAyABKQMoIAUgBSABKQMgfCIFVq18IAUgASkDOCABKQMwIgsgGXwgC1StfHwiCyAFVK18fCIDVq18fCIFIA5UrXwgBCAIVq0gBCAGVK0gASkD+AMgBiAXVK18fHx8IghCqcDGia7Ok7IwVg0AIAhCqcDGia7Ok7IwUg0BIAVC3bCFjOi2kai4f1YNACAFQt2whYzotpGouH9SBEAgAyEEIAUhBkKpwMaJrs6TsjAhCAwECyADQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IQYgA0KR4eXNh4n6mShSIAtCgYCAgL+y/fDDAFRyDQILIANCkeHlzYeJ+pkofSIGIAtCgYCAgL+y/fDDAFStIg59IQQgBUKjz/rzl8nu18cAfCIRIANCkeHlzYeJ+pkoVCAGIA5Ucq0iA30hBiAIIAVC3bCFjOi2kai4f1QgAyARVnKtfUKpwMaJrs6TsjB9IQggC0KBgICAv7L98MMAfSELDAILIAMhBCAFIQYMAQsgAyEEQqnAxomuzpOyMCEICyABQYgQakHVgsIAQcAAQRAQ8QECQCABKAKIEEGAgICAeEcEQCAAIAEpAogQNwKsBCAAQbQEaiABQZAQaigCADYCABDHBCICRQ0BIABBBToAuAQgACATNwM4IAAgCTcDMCAAIA83AyggACAQNwMgIAAgGjcDGCAAIA03AxAgACAWNwMIIAAgEjcDACAAQYCxwgApAwA3A+ABIABB6AFqQYixwgApAwA3AwAgACACKQMINwP4ASAAIAIpAwAiAzcD8AEgAiADQgF8NwMAIABB+ABqQgA3AwAgAEHwAGpCADcDACAAQegAakIANwMAIABB4ABqQgA3AwAgAEHYAGpCADcDACAAQdAAakIANwMAIABByABqQgA3AwAgAEIANwNAIAAgDDcDgAEgACAKNwOIASAAIAc3A5ABIAAgFDcDmAEgACAINwOgASAAIAY3A6gBIAAgBDcDsAEgACALNwO4ASAAQgA3A5gDIABCADcD4AMgAEEBNgKoBCAAQgA3A4gCIABCADcDgAIgAELD99aH0oqC6BU3A8ABIABCiY30xu3uuuzHADcDyAEgAEK/oqqZupSa3Wo3A9ABIABC5v///5nfw4YbNwPYASAAQgE3A6gCIABCADcDsAIgAEIANwOgAiAAQYCAgIB4NgKQAiABQbAQaiQADwsgASABLQCMEDoArxBBjPfBAEErIAFBrxBqQeT7wQBBmIPCABDKAwALEPADAAu4NAIIfxR+IwBBkAxrIgMkAAJAAkACQAJ/AkACQAJAAkAgAS0AQCIHIAItAEBGBEAgAUHo0cEAQSAQ8QNFBEAgAUEgakHo0cEAQSAQ8QNFDQILIAJB6NHBAEEgEPEDRQRAIAJBIGpB6NHBAEEgEPEDRQ0DCwJAIAEgAkEgEPEDRQRAIAFBIGoiBSACQSBqQSAQ8QNFDQEgAEIANwMAIAAgBzoAQCAAQThqQgA3AwAgAEEwakIANwMAIABBKGpCADcDACAAQSBqQgA3AwAgAEEYakIANwMAIABBEGpCADcDACAAQQhqQgA3AwAMCgsgASkDICIYIQ0gAikDICIWIQ4CfgJAIBYgGFINACABKQMoIhAgAikDKCIOUgRAIBAhDQwBCyABKQMwIgsgAikDMCIOUgRAIAshDQwBCyAQIRMgASkDOCINIRUgCyANIAIpAzgiDlENARoLIA0gDlYNBSABKQMoIRAgAikDKCETIAEpAzAhCyABKQM4IQ0gAikDOCEVIAIpAzALIgwgC30iEiANIBVWrSIRfSEOIBMgEH0iDyARIBJWIAsgDFZyrSIMfSELIAwgD1YgECATVnIhBCAWIBh9IRcgFSANfSENDAcLIANBsAZqED4gB0UEQCADKQPABiEdIAMpA7gGIRsgAykDsAYhHCADQcgGagwGCyADKALgCEEBcQ0EQez2wQAQ6AQAC0GA9sEAQTNB3PbBABD+AwALIAAgBzoAQCAAIAIpAyA3AyAgACACKQMANwMAIABBOGogAkE4aikDADcDACAAQTBqIAJBMGopAwA3AwAgAEEoaiACQShqKQMANwMAIABBCGogAkEIaikDADcDACAAQRBqIAJBEGopAwA3AwAgAEEYaiACQRhqKQMANwMADAYLIAAgBzoAQCAAIAEpAyA3AyAgACABKQMANwMAIABBOGogAUE4aikDADcDACAAQTBqIAFBMGopAwA3AwAgAEEoaiABQShqKQMANwMAIABBCGogAUEIaikDADcDACAAQRBqIAFBEGopAwA3AwAgAEEYaiABQRhqKQMANwMADAULIAEpAzAiDCACKQMwIgtUIAwgC30iDCABKQM4IhEgAikDOCIPVK0iC1RyrSIUIAEpAygiFSACKQMoIhN9IhJ9Ig0gDCALfSIQQv////8PVq0iDH0hCyASIBRSIAwgDVZyIQRC/////w8gEH0hDiASIBRUIBMgFVZyrSAWIBh9fEL/////D30hFyAPIBFCf4V8IQ0MAgsgAykD+AghHSADKQPwCCEbIAMpA+gIIRwgA0GACWoLKQMAIRkgA0IDNwPICyADQoCAgIBQNwPACyADQn83A7gLIANC/P///y83A7ALIANB0AVqIAEpAxAiFUIAIAEpAxgiEEIAEMkDIANBsAVqIAEpAwgiE0IAIBBCABDJAyADQdAEaiABKQMAIgtCACAQQgAQyQMgA0GgBWogE0IAIBVCABDJAyADQeAEaiALQgAgFUIAEMkDIANB8ARqIAtCACATQgAQyQMgA0HwBWogEEIAIBBCABDJAyADQcAFaiAVQgAgFUIAEMkDIANBkAVqIBNCACATQgAQyQMgA0GABWogC0IAIAtCABDJAyADQeAFaiADKQPwBSIYQn2DIhZCAEKBgICAcEIAEMkDIAMpA/gEIAMpA+gEIAMpA9gEIAMpA7gFIAMpA9gFIgsgAykDsAV8IhEgC1StfCILIAMpA9AEfCINIAtUrXwiCyADKQPgBHwiDCALVK18IAwgAykDqAUgDSADKQOgBXwiHiANVK18fCIaIAxUrXwiCyADKQPwBHwiDiALVK18IgxCP4ggAykDiAUgAykDgAUiCyAMQgGGIA5CP4iEfCIPIAtUrXwgDyAPIAMpA5gFIAMpA8gFIAMpA8AFIgsgEUIBhiADKQPQBSIMQj+IhHwiDSALVK18IA0gAykD+AUiCyAMQgGGfCIUIAtUrXwiEiANVK18IgsgHkIBhiARQj+IhHwiESALVK0iCyADKQOQBXwiDCALVK18IAwgDCAaQgGGIB5CP4iEfCIMVq18IgsgDkIBhiAaQj+IhHwiDiALVK18Ig9WrXx8IQ0CfwJAIAMpA+gFIBZCIIYiCyAUfCIWIAtUrSAYQiCIfCILIBJ8IhIgC1StIgsgAykD4AV8IhQgC1StfCARIBR8IhEgFFStfCILUA0AIAsgDHwiDCALVCIERQ0AIAStIgsgDnwiDiALWg0AIAsgDlatIgsgD3wiDyALWg0AIAsgD1atIgsgDXwiDSALVAwBC0EACyEKIANBwARqIBZCAEKBgICAcEIAEMkDAkAgAykDyAQgFkIghiILIBJ8IhQgC1StIBZCIIh8IgsgEXwiESALVK0iCyADKQPABHwiEiALVK18IAwgEnwiDCASVK18IgtQDQAgCyAOfCIOIAtaDQAgCyAOVq0iCyAPfCIPIAtaDQAgCyAPVq0iCyANfCINIAtUIQgLIANBsARqIBRCAEKBgICAcEIAEMkDIAMpA7gEIBRCIIYiCyARfCISIAtUrSAUQiCIfCILIAx8IhEgC1StIgsgAykDsAR8IgwgC1StfCAMIA58Ig4gDFStfCILUEUEQCALIA98Ig8gC1QiBK0iDCANfCILIA0gBBshDSAEIAsgDFRxIQYLIANBoARqIBJCAEKBgICAcEIAEMkDIAMpA6gEIBJCIIYiCyARfCIXIAtUrSASQiCIfCIMIA58IgsgDFStIgwgAykDoAR8Ig4gDFStfCAOIA4gD3wiDlatfCIPIA18IgwgDSAPQgBSIgkbIQ0CQAJAAkAgCCAKciAGciAMIA9UIgStIA8gCRtCAFJyIAQgCXEgDUKBgICAcFZycg0AIA1CgYCAgHBSDQJCACEPIA5CAFINAEL/////DyEMIAtC/////w9WBEAgCyEMDAILIAtC/////w9SIBdCf1JyDQIMAQsgDiEPIAshDAsgDEL/////D30iESAXQn9SrSIOfSELIA8gDEL/////D1QgDiARVnKtIgx9IQ4gDSAMIA9WrX1C/////w98IQ0gF0IBfCEXCyADIBc3A4gMIAMgCzcDgAwgAyAONwP4CyADIA03A/ALIANBkAtqIANBsAtqIANB8AtqEJEBAkACQCADKQOQCyIMIBx8IhEgAykDmAsiCyAbfCIPIAtUIA8gDyADKQOgCyILIB18Ig0gC1QgDSADKQOoCyILIBl8IhcgC1StfCIOIA1Ucq18Ig9Wcq18Ig0gEVQgDCARVnINAEKBgICAcCELAkAgDSIMQoGAgIBwUg0AIA9CAFINAUL/////DyELIA4iDEL/////D1INACAXQn9RDQFCACEMQoGAgIBwIQ0MAgsgCyAMWA0AIA8hDCAOIQsMAQsgDkL/////D30iESAXQn9SrSIMfSELIA8gDkL/////D1QgDCARVnKtIg59IQwgDUL+////D0L/////DyAOIA9WG3whDSAXQgF8IRcLIAMgFzcDiAsgAyALNwOACyADIAw3A/gKIAMgDTcD8AogA0ICNwOIDCADQoCAgIBgNwOADCADQn83A/gLIANC/f///x83A/ALIANB0AtqIgQgA0HwC2ogBRCRASADQYgGaiADQfAKaiAEEF8gAygC3AoiBARAIAMoAuAKIARBAnQQ3wQLAkAgAygClAgiBEUNACAEIARBDGxBE2pBeHEiBWpBCWoiBEUNACADKAKQCCAFayAEEN8ECyADKALACCIEQYCAgIB4RiAERXINASADKALECCAEQQJ0EN8EDAELIAMgDTcDiAwgAyAONwOADCADIAs3A/gLIAMgFyAErX03A/ALIAEpAwAiGSEQIAIpAwAiGCEPAn4CQAJ+AkAgGCAZUg0AIAEpAwgiEyACKQMIIg9SBEAgEyEQDAELIAEpAxAiFSACKQMQIg9SBEAgFSEQDAELIBUhDiABKQMYIhAhDCATIBAgAikDGCIPUQ0BGgsgDyAQVA0BIAEpAwghEyABKQMQIRUgAikDECEOIAEpAxghECACKQMYIQwgAikDCAshCyAOIBV9IhIgDCAQVK0iDX0hDyALIBN9IhEgDiAVVCANIBJWcq0iDX0hDiALIBNUIA0gEVZyIQQgDCAQfSEXIBggGX0MAQsgASkDECIVIAIpAxAiC1QgFSALfSIMIAEpAxgiECACKQMYIhJUrSILVHKtIhYgASkDCCITIAIpAwgiEX0iFH0iDSAMIAt9IgxC/////w9WrSILfSEOIBQgFlIgCyANVnIhBEL/////DyAMfSEPIBIgEEJ/hXwhFyAUIBZUIBEgE1ZyrSAYIBl9fEL/////D30LIQ0gAyAXNwPIBiADIA83A8AGIAMgDjcDuAYgAyANIAStfTcDsAYgA0GIBmogA0HwC2ogA0GwBmoQXwsgAygCiAYEQCADIAMpA5gGNwO4BiADIAMpA5AGNwOwBkGM98EAQSsgA0GwBmpB/PbBAEG498EAEMoDAAsgA0GwA2ogAykDqAYiHUIAIAMpA6AGIhtCABDJAyADQaADaiAdQgAgAykDmAYiHEIAEMkDIANBkANqIB1CACADKQOQBiIaQgAQyQMgA0HgA2ogG0IAIBxCABDJAyADQdADaiAbQgAgGkIAEMkDIANBgARqIBxCACAaQgAQyQMgA0GAA2ogHUIAIB1CABDJAyADQcADaiAbQgAgG0IAEMkDIANB8ANqIBxCACAcQgAQyQMgA0GQBGogGkIAIBpCABDJAyADQfACaiADKQOAAyIYQgBCgYCAgHBCABDJAyADKQOIBCADKQPYAyADKQOYAyADKQOoAyADKQO4AyILIAMpA6ADfCIOIAtUrXwiCyADKQOQA3wiDSALVK18IgsgAykD0AN8IgwgC1StfCAMIAMpA+gDIA0gAykD4AN8IhYgDVStfHwiFCAMVK18IgsgAykDgAR8IhIgC1StfCIMQj+IIAMpA5gEIAMpA5AEIgsgDEIBhiASQj+IhHwiDyALVK18IA8gDyADKQP4AyADKQPIAyADKQPAAyILIA5CAYYgAykDsAMiDEI/iIR8Ig0gC1StfCANIA0gAykDiAMiCyAMQgGGfCIRIAtUrXwiDVatfCILIBZCAYYgDkI/iIR8Ig4gC1StIgsgAykD8AN8IgwgC1StfCAMIAwgFEIBhiAWQj+IhHwiDFatfCILIBJCAYYgFEI/iIR8IhIgC1StfCIPVq18fCELQQAhBgJ/AkAgAykD+AIgDSAYQiCGIg0gEXwiGSANVK0gGEIgiHwiDXwiESANVK0iDSADKQPwAnwiFCANVK18IA4gFHwiDiAUVK18Ig1QDQAgDCANfCIMIA1UIgRFDQAgBK0iDSASfCISIA1aDQAgDSASVq0iDSAPfCIPIA1aDQAgDSAPVq0iDSALfCILIA1UDAELQQALIQggA0HgAmogGUIAQoGAgIBwQgAQyQMCQCADKQPoAiAZQiCGIg0gEXwiFiANVK0gGUIgiHwiDSAOfCIOIA1UrSINIAMpA+ACfCIRIA1UrXwgDCARfCINIBFUrXwiDFANACAMIBJ8IhIgDFoNACAMIBJWrSIMIA98Ig8gDFoNACAMIA9WrSIMIAt8IgsgDFQhBgsgA0HQAmogFkIAQoGAgIBwQgAQyQNBACEEIAMpA9gCIBZCIIYiDCAOfCIUIAxUrSAWQiCIfCIMIA18IhEgDFStIgwgAykD0AJ8Ig0gDFStfCANIBJ8Ig4gDVStfCIMUEUEQCAMIA98Ig8gDFQiBK0iDSALfCIMIAsgBBshCyAEIAwgDVRxIQQLIANBwAJqIBRCAEKBgICAcEIAEMkDIAMpA8gCIBRCIIYiDCARfCISIAxUrSAUQiCIfCIMIA58Ig0gDFStIgwgAykDwAJ8Ig4gDFStfCAOIA4gD3wiDlatfCIPIAt8IgwgCyAPQgBSIgUbIQsCQAJAAkACQCAGIAhyIARyIAwgD1QiBK0gDyAFG0IAUnIgBCAFcSALQoGAgIBwVnJyDQAgC0KBgICAcFINASAOQgBSDQBCACEOIA1C/////w9WDQAgDUL/////D1IgEkJ/UnINAgsgDUL/////D30iESASQn9SrSIPfSEMIA4gDUL/////D1QgDyARVnKtIg19IQ8gCyANIA5WrX1C/////w98IQsgEkIBfCESDAILIA0hDCAOIQ8MAQsgDSEMQgAhD0KBgICAcCELCyABKQMAIhEhDiALIQ0CfgJAAkAgCyARUg0AIBMiDiAPIg1SDQAgDCENIAwgFSIOUg0AIBAiDiASIg1RDQELIA0gDloNACAMIBVWIBUgDH0iDSAQIBJUrSIMVHKtIhYgEyAPfSIUfSIOIA0gDH0iDUL/////D1atIgx9IRUgFCAWUiAMIA5WciEEQv////8PIA19IQ4gEiAQQn+FfCEQIBQgFlQgDyATVnKtIAsgEX18Qv////8PfQwBCyAMIBV9IhYgECASVq0iFH0hDiAPIBN9Ig0gDCAVVCAUIBZWcq0iDH0hFSAPIBNUIAwgDVZyIQQgEiAQfSEQIAsgEX0LIQsgAyAQNwPIBiADIA43A8AGIAMgFTcDuAYgAyALIAStfTcDsAYgA0GIBmogA0GwBmogAhDKAiABKQMYIRUgASkDECELIAEpAwghEyADKQOIBiIWIRAgA0HwAWoCfgJAAn4CQCAWIBEiDFINACATIgwgAykDkAYiEFINACALIgwgAykDmAYiEFINACALIQ0gEyAVIgwiEiADKQOgBiIQUQ0BGgsgAykDoAYhEiAMIBBUDQEgAykDmAYhDSADKQOQBgshDiALIA19IhQgEiAVVq0iDH0hECATIA59Ig8gCyANVCAMIBRWcq0iDH0hCyAMIA9WIA4gE1ZyIQIgESAWfSEPIBUgEn0MAQsgAykDmAYiDCALVCAMIAt9IgwgEiAVVK0iC1RyrSIUIAMpA5AGIg4gE30iD30iDSAMIAt9IhBC/////w9WrSIMfSELIA8gFFIgDCANVnIhAkL/////DyAQfSEQIA4gE1QgDyAUVHKtIBEgFn18Qv////8PfSEPIBUgEkJ/hXwLIhNCACAdQgAQyQMgA0HQAWogE0IAIBtCABDJAyADQcABaiATQgAgHEIAEMkDIANBsAFqIBNCACAaQgAQyQMgA0HgAWogAykD8AEiE0IAQoGAgIBwQgAQyQMgA0GgAWogEEIAIB1CABDJAyADQYABaiAQQgAgG0IAEMkDIANB8ABqIBBCACAcQgAQyQMgA0HgAGogEEIAIBpCABDJAyADQZABaiATQiCGIg4gAykD+AEiECADKQPQAXwiDHwiFSADKQOgAXwiFEIAQoGAgIBwQgAQyQMgA0HQAGogC0IAIB1CABDJAyADQTBqIAtCACAbQgAQyQMgA0EQaiALQgAgHEIAEMkDIAMgC0IAIBpCABDJAyADQUBrIBRCIIYiDSAOIBVWrSATQiCIfCITIAMpA9gBIAwgEFStfCIQIAMpA8ABfCIMfCIZIAMpA4ABfCIRIAMpA6gBIBQgFVStfHwiC3wiEiADKQNQfCIeQgBCgYCAgHBCABDJAyADQbACaiAPIAKtfSIOQgAgHUIAEMkDIANBoAJqIA5CACAbQgAQyQMgA0GQAmogDkIAIBxCABDJAyADQYACaiAOQgAgGkIAEMkDIANBIGogHkIghiIVIA0gElatIBRCIIh8Ig4gAykDyAEgDCAQVK18Ig0gAykDsAF8IhggAykD4AF8IhYgEyAZVq18IhogAykDcHwiFCALIBFUrSADKQOIASARIBlUrXx8fCIQfCIRIAMpAzB8IhMgAykDWCASIB5WrXx8Igx8IhkgAykDsAJ8IhtCAEKBgICAcEIAEMkDAkACQAJAAkAgAykDKCADKQOoAiADKQO4AiAZIBtWrXwiCyADKQOgAnwiEiALVK18IBIgDCATVK0gAykDOCARIBNWrXx8Ig8gAykDEHwiHCAOIBFWrSITIAMpA5ABfCIRIBYgGlatIAMpA+gBIBYgGFStfHwiDiADKQO4ASANIBhWrXx8IhggAykDYHwiFiAQIBRUrSADKQN4IBQgGlStfHx8Ig18IhB8IhQgFSAZVq0gHkIgiHx8Igx8IgsgElStfCISIAMpA5ACfCIeIAwgFFStIhUgAykDQHwiGiAQIBFUrSADKQOYASARIBNUrXx8IhEgDSAWVK0gAykDaCAWIBhUrXx8IhMgDiAYVq18Ig58IhkgAykDAHwiGCAUIBxUrSADKQMYIA8gHFatfHx8Ig18IhB8IhYgCyAbQiCGIgt8IhcgC1StIBtCIIh8fCIMIBZUrSILIAMpAyB8IhQgC1StfCAUIBAgGlStIAMpA0ggFSAaVq18fCIPIA0gGFStIAMpAwggGCAZVK18fCIVIBEgGVatIA4gE1StfHwiDXwiESADKQOAAnwiECAWIB5UrSADKQOYAiASIB5WrXx8fCILfCIOIBRUrXwiEyALIBBUrSADKQOIAiAQIBFUrXx8IhAgDyARVq0gDSAVVK18fCILfCINIBNUIAsgEFRyIA1CgYCAgHBWcg0AIA1CgYCAgHBSDQEgDEL/////D1YNAEIAIRAgDkIAUg0AIBdCf1IgDEL/////D1JyDQILIAxC/////w99IhMgF0J/Uq0iEH0hCyAOIAxC/////w9UIBAgE1ZyrSIMfSEQIA0gDCAOVq19Qv////8PfCENIBdCAXwhFwwCCyAMIQsgDiEQDAELIAwhC0KBgICAcCENCyADIBc3A8gGIAMgCzcDwAYgAyAQNwO4BiADIA03A7AGIABBIGogA0GwBmogAUEgahDKAiAAQRhqIANBoAZqKQMANwMAIABBEGogA0GYBmopAwA3AwAgAEEIaiADQZAGaikDADcDACAAIAMpA4gGNwMAIAAgBzoAQAsgA0GQDGokAAvzNAIhfwJ+IwBB4ANrIgMkACABKAIIIgtBAnQhBAJAAkACQAJAAkACQCALQf////8DSyAEQfz///8HS3INACABKAIEIQkgAS0ADCEfAn8gBEUEQEEEIRRBAAwBC0HRzsUALQAAGkEEIQUgBEEEENYEIhRFDQEgCwshFSAEBEAgFCAJIAT8CgAACyADQYgDakG4zMIAKAIANgIAIANBsMzCACkCADcDgAMgA0GAA2pBpM3CABClAyADKAKEA0EBNgIAIAIoAggiBUECdCEEAkAgBUH/////A0sgBEH8////B0tyDQAgAygChAMhFiADKAKAAyEXIAIoAgQhCSACLQAMIQ0CfyAERQRAQQQhEkEADAELQdHOxQAtAAAaQQQhCiAEQQQQ1gQiEkUNASAFCyEYIAQEQCASIAkgBPwKAAALIANBiANqQbjMwgAoAgA2AgAgA0GwzMIAKQIANwOAAyADQYADakGkzcIAEKUDIAMoAoQDQQE2AgAgAygChAMhGSADKAKAAyEaIAMgARCoA0ECIQdBASEMQQEhCEEEIRtBASEgQQAhCkEEIR1BAiEjQQEhAgJAAkACQAJAA0AgEyERIAghECAMIQYgByEPIAVB/////wNLIg4gBUECdCIBQfz///8HSyIhciEEAn8CQCANQf8BcUUEQCAEBEBBACEHDA8LIAEEQEHRzsUALQAAGkEEIQcgAUEEENYEIgxFDQ8gAQRAIAwgEiAB/AoAAAtBAiEHIAUhCSAFIgQgBA0DGkEBIQdBBCEMDAILQQQhDCABBEBBBCASIAH8CgAAC0EBIQcMAQsCQCAEBEBBACEHDAELAn8gAUUEQEEEIQxBAAwBC0HRzsUALQAAGkEEIQcgAUEEENYEIgxFDQEgBQshCSABBEAgDCASIAH8CgAACyANIQcgBQwCCwwNC0EAIQlBAAshBAJAIAdB/wFxIgggAy0ADCIHRgRAIAhBAkcNASADKAIIIgggBEYEQCAMQQRrIQggAygCBEEEayEiIARBAnQhBwJAA0AgB0UNASAHICJqIQQgByAIaiAHQQRrIQcoAgAiEyAEKAIAIgRGDQALIAQgE0sNDQwDCyAHDQwMAgsgBCAITw0BDAsLIAcgCEsNCgsgCQRAIAwgCUECdBDfBAtBACEHIA4gIXINCwJ/IAFFBEBBBCEMQQAMAQtB0c7FAC0AABpBBCEHIAFBBBDWBCIMRQ0MIAULIQggAQRAIAwgEiAB/AoAAAtBACEEIBFB/////wNLIBFBAnQiCUH8////B0tyDQECfyAJRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhBCAJQQQQ1gQiAUUNAiARCyEOIAkEQCABIBsgCfwKAAALQQAhCSAGQf////8DSyAGQQJ0IgdB/P///wdLcg0CAn8gB0UEQEEEIQRBAAwBC0HRzsUALQAAGkEEIQkgB0EEENYEIgRFDQMgBgshCSAHBEAgBCAZIAf8CgAACyADIA06AKwCIAMgBTYCqAIgAyAMNgKkAiADIAg2AqACIAMgEDoA3AIgAyARNgLYAiADIAE2AtQCIAMgDjYC0AIgAyAPOgD8AiADIAY2AvgCIAMgBDYC9AIgAyAJNgLwAkEAIQ0gC0H/////A0sgC0ECdCIHQfz///8HS3INAwJ/IAdFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCENIAdBBBDWBCIFRQ0EIAsLIQggBwRAIAUgFCAH/AoAAAsgAkECdCEHIAJB/////wFLBEBBACEMDAkLAkAgAkUEQEEEIQ0MAQtB0c7FAC0AABpBBCEMIAdBBBDWBCINRQ0JCyAHBEAgDSAWIAf8CgAACyAKQQJ0IQcgCkH/////AUsEQEEAIRMMCAsCQCAKRQRAQQQhDAwBC0HRzsUALQAAGkEEIRMgB0EEENYEIgxFDQgLIAcEQCAMIB0gB/wKAAALIAMgHzoAvAEgAyALNgK4ASADIAU2ArQBIAMgCDYCsAEgAyAjOgDcASADIAI2AtgBIAMgDTYC1AEgAyACNgLQASADICA6APwBIAMgCjYC+AEgAyAMNgL0ASADIAo2AvABIAMtAKwCQQFHBEAgA0GwAmoiBSADQbABaiICIANBoAJqIgcQ7wIgA0EQaiACIAcQgQMgA0GAA2oiAiADQdACaiAFEJcCIANBIGogA0HQAWogAhCdASACIANB8AJqIAUQlwIgA0EwaiADQfABaiACEJ0BIAMtAKwCIR8gAygCqAIhCyADKAKkAiADKAKgAiEiIBUEQCAUIBVBAnQQ3wQLIBcEQCAWIBdBAnQQ3wQLIB4EQCAdIB5BAnQQ3wQLIBgEQCASIBhBAnQQ3wQLIBwEQCAbIBxBAnQQ3wQLIBoEQCAZIBpBAnQQ3wQLIAMtADwhByADKAI4IQwgAygCNCEZIAMoAjAhGiADLQAsIQggAygCKCETIAMoAiQhGyADKAIgIRwgAy0AHCENIAMoAhghBSADKAIUIRIgAygCECEYIAMoArACIgIEQCADKAK0AiACQQJ0EN8ECyADKALwASICBEAgAygC9AEgAkECdBDfBAsgAygC0AEiAgRAIAMoAtQBIAJBAnQQ3wQLIAMoArABIgIEQCADKAK0ASACQQJ0EN8ECyAPISAgBiEKIAQhHSAJIR4gECEjIBEhAiABIRYgDiEXIRQgIiEVDAELC0HRzsUALQAAGkHAAEEBENYEIgJFDQMgAEHAADYCDCAAIAI2AgggAEHAADYCBCACQThqQeXfwgApAAA3AAAgAkEwakHd38IAKQAANwAAIAJBKGpB1d/CACkAADcAACACQSBqQc3fwgApAAA3AAAgAkEYakHF38IAKQAANwAAIAJBEGpBvd/CACkAADcAACACQQhqQbXfwgApAAA3AAAgAkGt38IAKQAANwAAIABBgICAgHg2AgAgAygC8AEiAARAIAMoAvQBIABBAnQQ3wQLIAMoAtABIgAEQCADKALUASAAQQJ0EN8ECyADKAKwASIABEAgAygCtAEgAEECdBDfBAsgCQRAIAQgCUECdBDfBAsgDgRAIAEgDkECdBDfBAsgAygCoAIiAEUNCSADKAKkAiAAQQJ0EN8EDAkLIAQgCUH4gcAAEMgEAAsgCSAHQfiBwAAQyAQACyANIAdB+IHAABDIBAALQQFBwABB1NjCABDIBAALIAogBEH4gcAAEMgEAAsgBSAEQfiBwAAQyAQACyATIAdB+IHAABDIBAALIAwgB0H4gcAAEMgEAAsgCQRAIAwgCUECdBDfBAtBACEBAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQCAFQf////8DSyAFQQJ0IgRB/P///wdLcg0AAn8gBEUEQEEEIQ5BAAwBC0HRzsUALQAAGkEEIQEgBEEEENYEIg5FDQEgBQshCCAEBEAgDiASIAT8CgAAC0EAIQEgEUH/////A0sgEUECdCIEQfz///8HS3INAQJAIARFBEBBBCEJQQAhEQwBC0HRzsUALQAAGkEEIQEgBEEEENYEIglFDQILIAQEQCAJIBsgBPwKAAALQQAhBCAGQf////8DSyAGQQJ0IhBB/P///wdLcg0CAn8gEEUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQQgEEEEENYEIgFFDQMgBgshBCAQBEAgASAZIBD8CgAACyADIAWtIA2tQv8Bg0IghoQ3AkggAyAONgJEIAMgCDYCQCADIAatIA+tQv8Bg0IghoQ3AlggAyABNgJUIAMgBDYCUEEAIQYgC0H/////A0sgC0ECdCIIQfz///8HS3INAwJ/IAhFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIAhBBBDWBCIFRQ0EIAsLIQ0gCARAIAUgFCAI/AoAAAtBACEGIAJB/////wNLIAJBAnQiCEH8////B0tyDQQCQCAIRQRAQQQhDkEAIQIMAQtB0c7FAC0AABpBBCEGIAhBBBDWBCIORQ0FCyAIBEAgDiAWIAj8CgAAC0EAIQggCkH/////A0sgCkECdCIQQfz///8HS3INBQJ/IBBFBEBBBCEGQQAMAQtB0c7FAC0AABpBBCEIIBBBBBDWBCIGRQ0GIAoLIQggEARAIAYgHSAQ/AoAAAsgAyALrSAfrUL/AYNCIIaENwJoIAMgBTYCZCADIA02AmAgAyAKrSAgrUL/AYNCIIaENwJ4IAMgBjYCdCADIAg2AnACfwJAIAMtAExBAUcEQCADQYABaiIBIANB4ABqIgYgA0FAayIFEO8CIANBkAFqIAYgBRCBAyADQYADaiIGIANB0ABqIAEQlwIgA0GgAWogA0HwAGogBhCdASADKAJIIgFBAnQhBEEAIQYgAUH/////A0sgBEH8////B0tyDQkgAygCRCELIAMtAEwhCAJ/IARFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIARBBBDWBCIFRQ0KIAELIQYgBARAIAUgCyAE/AoAAAsgA0HIAWogA0HYAGooAgA2AgAgA0HPAWogA0HfAGotAAA6AAAgA0ECIA9rOgDMASADIAg6ALwBIAMgATYCuAEgAyAFNgK0ASADIAY2ArABIAMgAykCUDcCwAEgAyADLwBdOwDNASADKAJoIgFBAnQhBEEAIQYgAUH/////A0sgBEH8////B0tyDQsgAygCZCELIAMtAGwhCCAEDQFBBCEFQQAMAgtB0c7FAC0AABpBywBBARDWBCIFRQ0JIAVB4t7CAEHLAPwKAAAgAEHLADYCDCAAIAU2AgggAEKAgICAuAk3AgAgAygCcCIABEAgAygCdCAAQQJ0EN8ECyACBEAgDiACQQJ0EN8ECyADKAJgIgAEQCADKAJkIABBAnQQ3wQLIARFDQ8gASAEQQJ0EN8EDA8LQdHOxQAtAAAaQQQhBiAEQQQQ1gQiBUUNCSABCyEGIAQEQCAFIAsgBPwKAAALIANB6AFqIANB+ABqKAIANgIAIANB7wFqIANB/wBqLQAAOgAAIAMgCDoA3AEgAyABNgLYASADIAU2AtQBIAMgBjYC0AEgAyADKQJwNwLgASADIAMvAH07AO0BIANBAiADLQB8azoA7AEgAygCmAEiAUECdCELQQAhBiABQf////8DSyALQfz///8HS3INCSADKAKUASEIIAMtAJwBIQoCfyALRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhBiALQQQQ1gQiBUUNCiABCyEEIAsEQCAFIAggC/wKAAALIANBwAFqIQsgA0GIAmogA0GoAWooAgA2AgAgA0GPAmogA0GvAWotAAA6AAAgAyAKOgD8ASADIAE2AvgBIAMgBTYC9AEgAyAENgLwASADIAMpAqABNwKAAiADIAMvAK0BOwCNAiADQQIgAy0ArAFrOgCMAiADQbACaiIBIANB0AFqIgYQ5QIgA0GAA2oiBSADQeABahDlAiADQZACaiABIAUQrgEgASADQfABahDlAiAFIANBgAJqEOUCIANBoAJqIAEgBRCuAQJAAkAgAy0AnAIiBSADLQCsAiIBRgRAQQAhBEEBIQ0gBiEBIAVBAWsOAg8CAQsgASAFSQ0NQQAhBEEBIQ0gA0HQAWohAQwOCyADKAKoAiIFIAMoApgCIgZGBEAgAygCpAJBBGshBiAFQQJ0IQcgAygClAJBBGshBQNAIAdFDQ8gBSAHaiEKIAYgB2ogB0EEayEHKAIAIg8gCigCACIKRg0ACyAKIA9JDQ0MDgsgBSAGSw0MDA0LIAMoApgCIgUgAygCqAIiBkcNCiADKAKUAkEEayEGIAVBAnQhByADKAKkAkEEayEFA0AgB0UNDSAFIAdqIQogBiAHaiAHQQRrIQcoAgAiDyAKKAIAIgpGDQALIAogD08NDAwLCyABIARB+IHAABDIBAALIAEgBEH4gcAAEMgEAAsgBCAQQfiBwAAQyAQACyAGIAhB+IHAABDIBAALIAYgCEH4gcAAEMgEAAsgCCAQQfiBwAAQyAQACyAGIARB+IHAABDIBAALQQFBywBB1NjCABDIBAALIAYgBEH4gcAAEMgEAAsgBiALQfiBwAAQyAQACyAFIAZNDQELQQEhBEEAIQ0gA0HwAWohAQsgA0HIAmogAUEYaikCADcDACADQcACaiIKIAFBEGopAgA3AwAgA0G4AmogAUEIaikCADcDACADIAEpAgA3A7ACIANB8AJqIgEgA0GwAWogChCXAiADQYADaiIGIAsgA0GwAmoQlwIgA0HQAmogASAGEJQBAkACQAJAAkACQAJAAkAgAy0A3AIiAUEBRwRAIANBiANqQbjMwgAoAgA2AgAgA0GwzMIAKQIANwOAAyAGQaTNwgAQpQMgAygChANBATYCACADKAKEAyEFIAMoAoADIQ8CQAJAIAFBAkcNACADKALUAiEGAkAgAygC2AIiAQ4CAQACC0EBIQEgBigCACAFKAIATw0BC0EBIQEgBSEGCyABrUIGhiAGIAFBAnRqQQRrKAIAZ0EBdK19QkB9IA8EQCAFIA9BAnQQ3wQLQoD/////AYMhJCADLQDMAiEBAkAgAygCyAJFBEAgA0EANgLcAyADQoCAgIDAADcC1AMMAQsgAyAKNgL0AiADQYCAgIB4NgLwAiADQdQDaiADQfACaiAkQgWIp0EAEM8BC0EBIQcCQCABQQFHBEAgAUEBIAMoAtwDGyEHDAELIANBADYC3AMgAygC1AMiAUEESQ0AIAMoAtgDIAFBAnQQ3wQgA0KAgICAwAA3AtQDCyADQYgDaiADQdwDaigCADYCACADIAMpAtQDNwOAAyADIAc6AIwDIANB8AJqIANBgANqIANB0AJqEHogAykC+AIhJSADKAL0AiEBIAMoAvACIgVBgICAgHhHDQEgACAlNwIIIAAgATYCBCAAQYCAgIB4NgIAIAMoAoADIgBFDQIgAygChAMgAEECdBDfBAwCC0HRzsUALQAAGkHCAEEBENYEIgFFDQQgAUGg3sIAQcIA/AoAACAAQcIANgIMIAAgATYCCCAAQoCAgICoCDcCAAwBCyADKAKAAyIGBEAgAygChAMgBkECdBDfBAsgAy0AzAEhBgJAIAMoAsgBRQRAIANBADYC3AMgA0KAgICAwAA3AtQDDAELIAMgCzYC9AIgA0GAgICAeDYC8AIgA0HUA2ogA0HwAmogJEIFiKdBABDPAQtBASEKAkAgBkEBRwRAIAZBASADKALcAxshCgwBCyADQQA2AtwDIAMoAtQDIgZBBEkNACADKALYAyAGQQJ0EN8EIANCgICAgMAANwLUAwsgA0GIA2ogA0HcA2ooAgA2AgAgAyADKQLUAzcDgAMgAyAKOgCMAyADQfACaiADQYADaiADQdACahB6IANB6AJqIgYgA0H8AmooAgA2AgAgAyADKQL0AjcD4AIgAygC8AIiC0GAgICAeEcNASAAIAMpA+ACNwIEIABBgICAgHg2AgAgAEEMaiAGKAIANgIAIAMoAoADIgAEQCADKAKEAyAAQQJ0EN8ECyAFRQ0AIAEgBUECdBDfBAsgAygC0AIiAARAIAMoAtQCIABBAnQQ3wQLIAMoArACIgAEQCADKAK0AiAAQQJ0EN8ECyADKALAAiIABEAgAygCxAIgAEECdBDfBAsgAygCoAIiAARAIAMoAqQCIABBAnQQ3wQLIAMoApACIgAEQCADKAKUAiAAQQJ0EN8ECyANDQEMBAsgACADKQPgAjcCZCAAQewAaiAGKAIANgIAIAMoAoADIgYEQCADKAKEAyAGQQJ0EN8ECyADQZgDaiADQcgBaikCADcDACADQZADaiADQcABaikCADcDACADQYgDaiADQbgBaikCADcDACADQagDaiADQbgCaikDADcDACADQbADaiADQcACaikDADcDACADQbgDaiADQcgCaikDADcDACADIAMpArABNwOAAyADIAMpA7ACNwOgAyADQcgDaiADQdgCaikCADcDACADIAMpAtACNwPAAyAAIANBgANqQdAA/AoAACAAIAs2AmAgACAlNwJYIAAgATYCVCAAIAU2AlAgAygCoAIiAARAIAMoAqQCIABBAnQQ3wQLIAMoApACIgAEQCADKAKUAiAAQQJ0EN8ECyANRQ0CIAMoAvABIgAEQCADKAL0ASAAQQJ0EN8ECyADKAKAAiIARQ0CIAMoAoQCIABBAnQQ3wQMAgsgAygC8AEiAARAIAMoAvQBIABBAnQQ3wQLIAMoAoACIgBFDQIgAygChAIgAEECdBDfBAwCC0EBQcIAQdTYwgAQyAQACwJAIARFDQAgAygC0AEiAARAIAMoAtQBIABBAnQQ3wQLIAMoAuABIgBFDQAgAygC5AEgAEECdBDfBAsgAygCkAEiAARAIAggAEECdBDfBAsgAygCgAEiAARAIAMoAoQBIABBAnQQ3wQLIAIEQCAOIAJBAnQQ3wQLIAMoAmAiAARAIAMoAmQgAEECdBDfBAsgEQRAIAkgEUECdBDfBAsgAygCQCIARQ0CIAMoAkQgAEECdBDfBAwCCwJAIARFDQAgAygC0AEiAARAIAMoAtQBIABBAnQQ3wQLIAMoAuABIgBFDQAgAygC5AEgAEECdBDfBAsgAygCsAEiAARAIAMoArQBIABBAnQQ3wQLIAMoAsABIgAEQCADKALEASAAQQJ0EN8ECyADKAKQASIABEAgCCAAQQJ0EN8ECyADKAKAASIABEAgAygChAEgAEECdBDfBAsgAgRAIA4gAkECdBDfBAsgAygCYCIARQ0AIAMoAmQgAEECdBDfBAsgEQRAIAkgEUECdBDfBAsgAygCQCIARQ0AIAMoAkQgAEECdBDfBAsgAygCACIABEAgAygCBCAAQQJ0EN8ECyAVBEAgFCAVQQJ0EN8ECyAXBEAgFiAXQQJ0EN8ECyAeBEAgHSAeQQJ0EN8ECyAYBEAgEiAYQQJ0EN8ECyAcBEAgGyAcQQJ0EN8ECyAaBEAgGSAaQQJ0EN8ECyADQeADaiQADwsgByABQfiBwAAQyAQAC7M4AgZ/F34jAEGQBmsiAiQAIAJBsAVqIAEQLyACQeAFaiABQTBqIgcQL0Kazf/Lo73EgBohCyACKQO4BSIIIAIpA+gFfCIKIAhUIAogAikDwAUiCCACKQPwBXwiDiAIVCAOIAIpA8gFIgggAikD+AV8Ig0gCFQgDSANIAIpA9AFIgkgAikDgAZ8IgggCVQgCCAIIAIpA9gFIg8gAikDiAZ8IgkgD1StfCIIVnKtfCINVnKtfCIMIA5Ucq18IhAgClRyrSACKQPgBSACKQOwBXx8Ig4hCgJAAkACQCAOQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIQsgECIKQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACELIAwiCkK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhCyANIgpCpOzDtY/UtJjnAFINAEL//8+K6///1R4hCyAIIgpC///Piuv//9UeUg0AQqvV/v///7//uX8hCyAJIgpCq9X+////v/+5f1ENAQsgCiALWg0AIBAhCiAMIQsgDSEPIAghEgwBCyAIQv//z4rr///VHn0iCiAJQqvV/v///7//uX9UrSILfSESIA1CpOzDtY/UtJjnAH0iEyAIQv//z4rr///VHlQgCiALVHKtIgh9IQ8gDEK/pZScz/DSu+QAfSIKIA1CpOzDtY/UtJjnAFQgCCATVnKtIgh9IQsgEELX2a6a5PbpjcsAfSINIAxCv6WUnM/w0rvkAFQgCCAKVnKtIgh9IQogDiAQQtfZrprk9umNywBUIAggDVZyrX1Cms3/y6O9xIAafSEOIAlC1aqBgICAwIDGAHwhCQsgAiAJNwP4AyACIBI3A/ADIAIgDzcD6AMgAiALNwPgAyACIAo3A9gDIAIgDjcD0AMCQAJAIAJB0ANqQYCgxQBBMBDxAwRAIAJBwARqQgA3AwAgAkG4BGpCADcDACACQbAEakIANwMAIAJBqARqQgA3AwAgAkIANwOgBCACQgE3A8gEQSghAyACQfgEaiACQfgDaikDADcDACACQfAEaiACQfADaikDADcDACACQegEaiACQegDaikDADcDACACQeAEaiACQeADaikDADcDACACQdgEaiACQdgDaikDADcDACACIAIpA9ADNwPQBCACQagFakHYoMUAKQMANwMAIAJBoAVqQdCgxQApAwA3AwAgAkGYBWpByKDFACkDADcDACACQZAFakHAoMUAKQMANwMAIAJBiAVqQbigxQApAwA3AwAgAkGwoMUAKQMANwOABSACQdgFakGIocUAKQMANwMAIAJB0AVqQYChxQApAwA3AwAgAkHIBWpB+KDFACkDADcDACACQcAFaiIFQfCgxQApAwA3AwAgAkG4BWpB6KDFACkDADcDACACQeCgxQApAwA3A7AFIAJBiAZqQgA3AwAgAkGABmpCADcDACACQfgFakIANwMAIAJB8AVqIgZCADcDACACQegFakIANwMAIAJCADcD4AUgAkHQBGogAkGgBGpBMBDxA0UEQEKqx6uW2fyjzBEhFUKtquao29DPvJp/IRAMAgsgAkGABWogAkGgBGpBMBDxA0UEQCAGIQVCACEQDAILQqvV/v///7//uX8hDgNAIAItAPgEQQFxRQRAA0AgAkHQBGoQvwIgAikD2AUiCEIBg1BFBEAgAikD0AUhCSACIAhC1aqBgICAwIDGAH0iDTcD2AUgAiAJQv//z4rr///VHnwiCiAIIA1WrXwiDTcD0AUgAiACKQPIBSILQqTsw7WP1LSY5wB8IgggCSAKViAKIA1Wcq18Igo3A8gFIAIgAikDwAUiDUK/pZScz/DSu+QAfCIJIAggC1QgCCAKVnKtfCIKNwPABSACIAIpA7gFIgtC19mumuT26Y3LAHwiCCAJIA1UIAkgClZyrXwiCTcDuAUgAiACKQOwBSAIIAtUIAggCVZyrXxCms3/y6O9xIAafDcDsAULIAJBsAVqEL8CIAItAPgEQQFxRQ0ACyACKQOoBSEOCyAOp0EBcUUEQANAIAJBgAVqEL8CIAIpA4gGIghCAYNQRQRAIAIpA4AGIQkgAiAIQtWqgYCAgMCAxgB9Ig03A4gGIAIgCUL//8+K6///1R58IgogCCANVq18Ig03A4AGIAIgAikD+AUiC0Kk7MO1j9S0mOcAfCIIIAkgClYgCiANVnKtfCIKNwP4BSACIAIpA/AFIg1Cv6WUnM/w0rvkAHwiCSAIIAtUIAggClZyrXwiCjcD8AUgAiACKQPoBSILQtfZrprk9umNywB8IgggCSANVCAJIApWcq18Igk3A+gFIAIgAikD4AUgCCALVCAIIAlWcq18QprN/8ujvcSAGnw3A+AFCyACQeAFahC/AiACKQOoBSIOQgGDUA0ACwsgAikD2AQhDAJAAkAgAgJ+AkACQAJAAn4gAikDgAUiFCACKQPQBCIWUgRAIAIpA5AFIRAgAikDiAUhCiAUIQkgFiETIAIpA+AEDAELIAIpA5AFIRAgAikD4AQhCCAMIAIpA4gFIgpSBEAgCiEJIAwhEyAIDAELIAggEFIEQCAMIQogECEJIAghEyAIDAELIAIpA5gFIgkgAikD6AQiE1IEQCAIIRAgDCEKIAgMAQsgAikDoAUiCyACKQPwBCITUgRAIAghECAMIQogCyEJIAgMAQsgDiACKQP4BCITUQ0BIAghECAMIQogDiEJIAgLIQ0gCSATViACKQPgBSETIAIpA7AFIRUgAikDoAUhCyACKQOYBSEJIAIpA/gEIREgAikD8AQhDyACKQPoBCESRQRAIBAhCAwCCyACIA4gEX0iFzcDqAUgAiALIA99IgggDiARVK0iDn03A6AFIAIgCSASfSIRIAsgD1QgCCAOVHKtIgh9NwOYBSACIBAgDX0iCyAJIBJUIAggEVZyrSIIfTcDkAUgAiAKIAx9IgkgCCALViANIBBWcq0iCH03A4gFIAIgFCAWfSAKIAxUIAggCVZyrX03A4AFIAIpA+gFIQwCQAJAIBMgFVIEQCACKQPABSEJIAIpA7gFIRAgAikD8AUhDSATIQ4gFSEIDAELIAIpA8AFIQkgAikD8AUhDSACKQO4BSIQIAxSBEAgDCEOIBAhCAwBCyAJIA1SBEAgDCEQIA0hDiAJIQgMAQsgAikD+AUiCiACKQPIBSIIUgRAIA0hCSAMIRAgCiEODAELIAIpA4AGIgsgAikD0AUiCFIEQCANIQkgDCEQIAshDgwBCyANIQkgDCEQIAIpA4gGIg4hESALIQ8gCiESIA4gAikD2AUiCFENAQsgCCAOViACKQPYBSEOIAIpA9AFIQsgAikDyAUhCiACKQOIBiERIAIpA4AGIQ8gAikD+AUhEg0DCyACIBEgDn03A4gGIAIgDyALfSIIIA4gEVatIg59NwOABiACIBIgCn0iESAIIA5UIAsgD1ZyrSIIfTcD+AUgAiANIAl9IgsgCCARViAKIBJWcq0iCH03A/AFIAIgDCAQfSIKIAggC1YgCSANVnKtIgh9Igk3A+gFIBMgFX0gDCAQVCAIIApWcq19DAMLIAIpA+AFIRMgAikDsAUhFSAMIQogDiERIAshDyAJIRIgCCENCyACIBEgDn03A/gEIAIgDyALfSIQIA4gEVatIhF9NwPwBCACIBIgCX0iFyAQIBFUIAsgD1ZyrSILfTcD6AQgAiANIAh9Ig8gCyAXViAJIBJWcq0iCX03A+AEIAIgDCAKfSILIAggDVYgCSAPVnKtIgh9NwPYBCACIBYgFH0gCCALViAKIAxWcq19NwPQBCACKQO4BSEKAkACQCATIBVSBEAgAikD8AUhCyACKQPoBSEJIAIpA8AFIQ8gFSEMIBMhFAwBCyACKQPwBSELIAIpA8AFIQ8gAikD6AUiCSAKUgRAIAohDCAJIRQMAQsgCyAPUgRAIAohCSAPIQwgCyEUDAELIAIpA8gFIg0gAikD+AUiFFIEQCAPIQsgCiEJIA0hDAwBCyACKQPQBSIRIAIpA4AGIhRSBEAgDyELIAohCSARIQwMAQsgDyELIAohCSACKQPYBSIMIRIgESEIIA0hECAMIAIpA4gGIhRRDQELIAwgFFQgAikDiAYhDCACKQOABiERIAIpA/gFIQ0gAikD2AUhEiACKQPQBSEIIAIpA8gFIRANAwsgAiASIAx9NwPYBSACIAggEX0iFCAMIBJWrSIMfTcD0AUgAiAQIA19IhIgCCARVCAMIBRWcq0iCH03A8gFIAIgDyALfSIMIAggElYgDSAQVnKtIgh9NwPABSACIAogCX0iDSAIIAxWIAsgD1ZyrSIIfSIQNwO4BSACIBUgE30gCCANViAJIApWcq19IhU3A7AFDAMLIAIgEUKr1f7///+//7l/IA59IhF8IhQ3A4gGIAIgD0L//8+K6///1R4gC30iDyAOQqvV/v///7//uX9WrSIOfSIWfCIIIBEgFFatfCIRNwOABiACIBJCpOzDtY/UtJjnACAKfSISIA4gD1YgC0L//8+K6///1R5Wcq0iDn0iD3wiCyAIIBZUIAggEVZyrXwiETcD+AUgAiANQr+llJzP8NK75AAgCX0iDSAOIBJWIApCpOzDtY/UtJjnAFZyrSIKfSIOfCIIIAsgD1QgCyARVnKtfCILNwPwBSACIAxC19mumuT26Y3LACAQfSIPIAogDVYgCUK/pZScz/DSu+QAVnKtIg19Igx8IgogCCAOVCAIIAtWcq18Igk3A+gFIAkgClQgCiAMVHKtIBMgFX0gDSAPViAQQtfZrprk9umNywBWcq19fEKazf/Lo73EgBp8CyITNwPgBSAXIQ4MAQsgAiASQqvV/v///7//uX8gDH0iEnwiFDcD2AUgAkL//8+K6///1R4gEX0iFiAMQqvV/v///7//uX9WrSIMfSIXIAh8IgggEiAUVq18IhI3A9AFIAIgEEKk7MO1j9S0mOcAIA19IhAgDCAWViARQv//z4rr///VHlZyrSIRfSIUfCIMIAggF1QgCCASVnKtfCISNwPIBSACIA9Cv6WUnM/w0rvkACALfSIPIBAgEVQgDUKk7MO1j9S0mOcAVnKtIg19IhB8IgggDCAUVCAMIBJWcq18Igw3A8AFIAJC19mumuT26Y3LACAJfSIRIA0gD1YgC0K/pZScz/DSu+QAVnKtIg19IgsgCnwiCiAIIBBUIAggDFZyrXwiEDcDuAUgAiAKIAtUIAogEFZyrSAVIBN9IA0gEVYgCULX2a6a5PbpjcsAVnKtfXxCms3/y6O9xIAafCIVNwOwBQsgAkHQBGogAkGgBGoiBEEwEPEDRQ0CIAJBgAVqIARBMBDxAw0ACyAGIQUgCSEQIBMhFQwBCyAAQgE3AwAgAEICNwMIDAELIAJBmARqIAVBGGopAwAiCDcDACACQZAEaiAFQRBqKQMAIgk3AwAgAkGIBGogBUEIaikDACIKNwMAIAJBuANqIAo3AwAgAkHAA2ogCTcDACACQcgDaiAINwMAIAIgBSkDACIINwOABCACIBA3A6gDIAIgFTcDoAMgAiAINwOwAyABKQMAIRMgASkDCCERIAEpAxAhFCABKQMYIRYgASkDICEXIAEpAyghGEIAIRJCACEIQgAhC0IAIQpCACEMQgAhDwNAIAJBwAJqIAJBoANqIANqKQMAIglCACAYQgAQyQMgAkHQAmogCUIAIBdCABDJAyACQeACaiAJQgAgFkIAEMkDIAJB8AJqIAlCACAUQgAQyQMgAkGAA2ogCUIAIBFCABDJAyACQZADaiAJQgAgE0IAEMkDIAJBsAJqIBIgAikDwAIiEnwiDUIAQgBC/f/z/8////mJfxDJAyACQaACaiACKQO4AiIJQgBCq9X+////v/+5f0IAEMkDIAJBkAJqIAlCAEL//8+K6///1R5CABDJAyACQYACaiAJQgBCpOzDtY/UtJjnAEIAEMkDIAJB8AFqIAlCAEK/pZScz/DSu+QAQgAQyQMgAkHgAWogCUIAQtfZrprk9umNywBCABDJAyACQdABaiAJQgBCms3/y6O9xIAaQgAQyQMgAikD2AEgAikDkAMiGSAPfCIJIAIpA4gDIAIpA4ADIg8gDHwiDiAPVK18IA4gAikD+AIgAikD8AIiDyAKfCIKIA9UrXwgCiAKIAIpA+gCIAIpA+ACIg8gC3wiCyAPVK18IAsgAikD2AIgAikD0AIiDyAIfCIIIA9UrXwgCCACKQPIAiANIBJUrXx8IhIgCFStfHwiCCALVK18fCIKVq18fCILIA5UrXx8Ig4gAikD0AF8Ig8gDlStfCAPIAIpA+gBIAsgAikD4AF8IgwgC1StfCAMIAIpA/gBIAogCiACKQPwAXwiClatfCAKIAIpA4gCIAggCCACKQOAAnwiCFatfCAIIAggAikDmAIgEiACKQOQAiISfCILIBJUrXwgCyACKQOoAiANIAIpA6ACIg18IA1UrXx8IhIgC1StfHwiCFatfHwiCyAKVK18fCIKIAxUrXx8IgwgD1StfCAJIA5WrSACKQOYAyAJIBlUrXx8fCEPIANBCGsiA0F4Rw0ACwJAAkAgD0Kazf/Lo73EgBpWDQACQAJAAkACQCAPQprN/8ujvcSAGlINACAMQtfZrprk9umNywBWDQQgDELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEPDAELIApCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRYgCkK/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEPDAILIAtCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRcgC0Kk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEPDAMLIAhC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhGCAIQv//z4rr///VHlENA0Kazf/Lo73EgBohDyAIIRQMBQsgDCEWCyAKIRcLIAshGCAIIRQMAgtC///Piuv//9UeIRQgEkKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEPDAELIAhC///Piuv//9UefSIJIBJCq9X+////v/+5f1StIg19IRQgC0Kk7MO1j9S0mOcAfSIOIAhC///Piuv//9UeVCAJIA1Ucq0iCH0hGCAKQr+llJzP8NK75AB9IgkgC0Kk7MO1j9S0mOcAVCAIIA5Wcq0iCH0hFyAMQtfZrprk9umNywB9Ig0gCkK/pZScz/DSu+QAVCAIIAlWcq0iCH0hFiAPIAxC19mumuT26Y3LAFQgCCANVnKtfUKazf/Lo73EgBp9IQ8gEkLVqoGAgIDAgMYAfCESCwJ+IAdBgKDFAEEwEPEDBEBC///Piuv//9UeIAEpA1AiCH0iCSABKQNYIgpCq9X+////v/+5f1atIg19IQ5CpOzDtY/UtJjnACABKQNIIgt9IgwgCSANVCAIQv//z4rr///VHlZyrSIIfSERQr+llJzP8NK75AAgASkDQCIJfSINIAggDFYgC0Kk7MO1j9S0mOcAVnKtIgh9IRlC19mumuT26Y3LACABKQM4Igt9IgwgCCANViAJQr+llJzP8NK75ABWcq0iCH0hGkKr1f7///+//7l/IAp9IRtCms3/y6O9xIAaIAEpAzAgCCAMViALQtfZrprk9umNywBWcq18fQwBCyABKQNYIRsgASkDUCEOIAEpA0ghESABKQNAIRkgASkDOCEaIAEpAzALIRwgAkH4BWogAkGIBGopAwA3AwAgAkGABmogAkGQBGopAwA3AwBBKCEDIAJBiAZqIAJBmARqKQMANwMAIAIgEDcD6AUgAiAVNwPgBSACIAIpA4AENwPwBUIAIQlCACEIQgAhC0IAIQpCACEMQgAhEwNAIAJB8ABqIAJB4AVqIANqKQMAIg1CACAbQgAQyQMgAkGAAWogDUIAIA5CABDJAyACQZABaiANQgAgEUIAEMkDIAJBoAFqIA1CACAZQgAQyQMgAkGwAWogDUIAIBpCABDJAyACQcABaiANQgAgHEIAEMkDIAJB4ABqIAIpA3AiFSAJfCINQgBCAEL9//P/z///+Yl/EMkDIAJB0ABqIAIpA2giCUIAQqvV/v///7//uX9CABDJAyACQUBrIAlCAEL//8+K6///1R5CABDJAyACQTBqIAlCAEKk7MO1j9S0mOcAQgAQyQMgAkEgaiAJQgBCv6WUnM/w0rvkAEIAEMkDIAJBEGogCUIAQtfZrprk9umNywBCABDJAyACIAlCAEKazf/Lo73EgBpCABDJAyACKQMIIAIpA8ABIh0gE3wiECACKQO4ASAMIAIpA7ABIgx8IgkgDFStfCAJIAkgAikDqAEgAikDoAEiDCAKfCIKIAxUrXwgCiAKIAIpA5gBIAIpA5ABIgwgC3wiCyAMVK18IAsgAikDiAEgAikDgAEiDCAIfCIIIAxUrXwgCCACKQN4IA0gFVStfHwiHiAIVK18fCIIIAtUrXx8IgpWrXx8IglWrXx8IhMgAikDAHwiDCATVK18IAwgDCACKQMYIAkgAikDEHwiFSAJVK18IBUgAikDKCAKIAogAikDIHwiClatfCAKIAIpAzggCCAIIAIpAzB8IghWrXwgCCAIIAIpA0ggAikDQCILIB58IgkgC1StfCAJIAkgAikDWCANIAIpA1AiDXwgDVStfHwiCVatfHwiCFatfHwiCyAKVK18fCIKIBVUrXx8IgxWrXwgECATVq0gAikDyAEgECAdVK18fHwhEyADQQhrIgNBeEcNAAsCQAJAIBNCms3/y6O9xIAaVg0AAkACQAJAAkAgE0Kazf/Lo73EgBpSDQAgDELX2a6a5PbpjcsAVg0EIAxC19mumuT26Y3LAFIEQEKazf/Lo73EgBohEwwBCyAKQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEOIApCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohEwwCCyALQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACENIAtCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohEwwDCyAIQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIRAgCEL//8+K6///1R5RDQNCms3/y6O9xIAaIRMgCCERDAULIAwhDgsgCiENCyALIRAgCCERDAILQv//z4rr///VHiERIAlCqtX+////v/+5f1YNAEKazf/Lo73EgBohEwwBCyAIQv//z4rr///VHn0iDSAJQqvV/v///7//uX9UrSIOfSERIAtCpOzDtY/UtJjnAH0iFSAIQv//z4rr///VHlQgDSAOVHKtIgh9IRAgCkK/pZScz/DSu+QAfSIOIAtCpOzDtY/UtJjnAFQgCCAVVnKtIgh9IQ0gDELX2a6a5PbpjcsAfSILIApCv6WUnM/w0rvkAFQgCCAOVnKtIgh9IQ4gEyAMQtfZrprk9umNywBUIAggC1ZyrX1Cms3/y6O9xIAafSETIAlC1aqBgICAwIDGAHwhCQsgACAJNwNgIAAgETcDWCAAIBA3A1AgACANNwNIIAAgDjcDQCAAIBM3AzggACASNwMwIAAgFDcDKCAAIBg3AyAgACAXNwMYIAAgFjcDECAAIA83AwggAEIANwMACyACQZAGaiQAC9cuAgJ/G34jAEGwCmsiASQAIAFBiApqQbj8wQBBwAAQtwIgAUGACGogASkDoAoiBkIAQgNCABDJAyABQcAIaiABKQOYCiIPQgBCA0IAEMkDIAFBgAlqIAEpA5AKIgpCAEIDQgAQyQMgAUHACWogASkDiAoiBUIAQgNCABDJAyABQdAHaiABKQOACCIEQgBCgYCAgHBCABDJAyABQZAIaiAGQgBC/////79/QgAQyQMgAUHQCGogD0IAQv////+/f0IAEMkDIAFBkAlqIApCAEL/////v39CABDJAyABQdAJaiAFQgBC/////79/QgAQyQMgAUHgB2ogBEIghiIOIAEpA4gIIgkgASkDwAh8Igd8IhIgASkDkAh8IgNCAEKBgICAcEIAEMkDIAFBoAhqIAZCAEJ+QgAQyQMgAUHgCGogD0IAQn5CABDJAyABQaAJaiAKQgBCfkIAEMkDIAFB4AlqIAVCAEJ+QgAQyQMgAUHwB2ogA0IghiITIA4gElatIARCIIh8IhEgASkDyAggByAJVK18IgcgASkDgAl8Igt8Ig4gASkD0Ah8IgkgASkDmAggAyASVK18fCIIfCISIAEpA6AIfCIEQgBCgYCAgHBCABDJAyABQbAIaiAGQgBC/f///88AQgAQyQMgAUHwCGogD0IAQv3////PAEIAEMkDIAFBsAlqIApCAEL9////zwBCABDJAyABQfAJaiAFQgBC/f///88AQgAQyQMgAUHAB2ogBEIghiIZIBIgE1StIANCIIh8IhMgASkDiAkgByALVq18IgsgASkDwAl8Ig8gASkD0Ad8IgogDiARVK18IgUgASkDkAl8IgMgCCAJVK0gASkD2AggCSAOVK18fHwiEXwiDiABKQPgCHwiCSABKQOoCCAEIBJUrXx8Igh8IhIgASkDsAh8IgZCAEKBgICAcEIAEMkDAkACQAJAAkAgASkD+AkgASkD6AkgASkD6AcgDiATVK0iEyABKQPgB3wiByATVK18IAcgASkDyAkgCyAPVq18IgsgASkD0Al8IhMgBSAKVK0gASkD2AcgCiAPVK18fHwiDyADIBFWrSABKQOYCSADIAVUrXx8fCIKfCIDIAdUrXwiByAKIA9UrSAPIBNUrSABKQPYCSALIBNWrXx8fHwiDyABKQPgCXwiCiAPVK18IAogASkDqAkgCCAJVK0gASkD6AggCSAOVK18fCIOIAEpA6AJfCIFIA5UrXwgBSADIAV8IgVWrXx8IgMgClStfCIOIAcgD1atfCIPIAEpA/gHIAUgEiAZVK0gBEIgiHx8IgQgBVStIgUgASkD8Ad8IgogBVStfCADIAp8IgkgClStfHwiCiABKQPwCXwiBSAKVK18IAUgBSABKQO4CSABKQP4CCABKQO4CCAGIBJUrXwiEiABKQPwCHwiAyASVK18IAMgBHwiBCADVK18IhIgASkDsAl8IgMgElStfCADIAMgCXwiA1atfHwiBVatfCISIA4gD1atIAogD1StfHwiDyASVK0gDyABKQPIByADIAZCIIYiCiAEfCIZIApUrSAGQiCIfHwiBiADVK0iAyABKQPAB3wiCiADVK18IAogBSAKfCIKVq18fCITIA9UrXxCAFIgE0KBgICAcFZyDQAgE0KBgICAcFINASAGQv////8PVg0AQgAhEiAKQgBSDQAgGUJ/UiAGQv////8PUnINAgsgBkL/////D30iBSAZQn9SrSIDfSEPIAogBkL/////D1QgAyAFVnKtIgZ9IRIgEyAGIApWrX1C/////w98IRMgGUIBfCEZDAILIAohEiAGIQ8MAQtCgYCAgHAhEyAGIQ8LIAFBiApqQfj8wQBBwAAQtwIgAUHABWogASkDoAoiBkIAQgNCABDJAyABQYAGaiABKQOYCiIKQgBCA0IAEMkDIAFBwAZqIAEpA5AKIgVCAEIDQgAQyQMgAUGAB2ogASkDiAoiA0IAQgNCABDJAyABQZAFaiABKQPABSIOQgBCgYCAgHBCABDJAyABQdAFaiAGQgBC/////79/QgAQyQMgAUGQBmogCkIAQv////+/f0IAEMkDIAFB0AZqIAVCAEL/////v39CABDJAyABQZAHaiADQgBC/////79/QgAQyQMgAUGgBWogDkIghiIHIAEpA8gFIhEgASkDgAZ8Igt8IgkgASkD0AV8IgRCAEKBgICAcEIAEMkDIAFB4AVqIAZCAEJ+QgAQyQMgAUGgBmogCkIAQn5CABDJAyABQeAGaiAFQgBCfkIAEMkDIAFBoAdqIANCAEJ+QgAQyQMgAUGwBWogBEIghiIIIAcgCVatIA5CIIh8IhggASkDiAYgCyARVK18IgsgASkDwAZ8IhB8IgcgASkDkAZ8IhEgASkD2AUgBCAJVK18fCIMfCIJIAEpA+AFfCIOQgBCgYCAgHBCABDJAyABQfAFaiAGQgBC/f///88AQgAQyQMgAUGwBmogCkIAQv3////PAEIAEMkDIAFB8AZqIAVCAEL9////zwBCABDJAyABQbAHaiADQgBC/f///88AQgAQyQMgAUGABWogDkIghiINIAggCVatIARCIIh8IgggASkDyAYgCyAQVq18IhAgASkDgAd8IgogASkDkAV8IgUgByAYVK18IgMgASkD0AZ8IgQgDCARVK0gASkDmAYgByARVq18fHwiGHwiByABKQOgBnwiESABKQPoBSAJIA5WrXx8Igx8IgkgASkD8AV8IgZCAEKBgICAcEIAEMkDAkACQAJAAkAgASkDuAcgASkDqAcgASkDqAUgByAIVK0iCCABKQOgBXwiCyAIVK18IAsgASkDiAcgCiAQVK18IhAgASkDkAd8IgggAyAFVK0gASkDmAUgBSAKVK18fHwiCiAEIBhWrSABKQPYBiADIARWrXx8fCIFfCIEIAtUrXwiCyAFIApUrSAIIApWrSABKQOYByAIIBBUrXx8fHwiCiABKQOgB3wiBSAKVK18IAUgASkD6AYgDCARVK0gASkDqAYgByARVq18fCIHIAEpA+AGfCIDIAdUrXwgAyADIAR8IgNWrXx8IgQgBVStfCIHIAogC1StfCIKIAEpA7gFIAMgCSANVK0gDkIgiHx8Ig4gA1StIgMgASkDsAV8IgUgA1StfCAEIAV8IhEgBVStfHwiBSABKQOwB3wiAyAFVK18IAMgAyABKQP4BiABKQO4BiABKQP4BSAGIAlUrXwiCSABKQOwBnwiBCAJVK18IAQgDnwiDiAEVK18IgkgASkD8AZ8IgQgCVStfCAEIAQgEXwiBFatfHwiA1atfCIJIAcgClatIAUgClStfHwiCiAJVK0gCiABKQOIBSAEIAZCIIYiBSAOfCIYIAVUrSAGQiCIfHwiBiAEVK0iBCABKQOABXwiBSAEVK18IAUgAyAFfCIFVq18fCIRIApUrXxCAFIgEUKBgICAcFZyDQAgEUKBgICAcFINASAGQv////8PVg0AQgAhDiAFQgBSDQAgGEJ/UiAGQv////8PUnINAgsgBkL/////D30iAyAYQn9SrSIEfSEKIAUgBkL/////D1QgAyAEVHKtIgZ9IQ4gESAFIAZUrX1C/////w98IREgGEIBfCEYDAILIAUhDiAGIQoMAQtCgYCAgHAhESAGIQoLIAFBiApqQbj9wQBBwAAQtwIgAUGAA2ogASkDoAoiBkIAQgNCABDJAyABQcADaiABKQOYCiIFQgBCA0IAEMkDIAFBgARqIAEpA5AKIgNCAEIDQgAQyQMgAUHABGogASkDiAoiBEIAQgNCABDJAyABQdACaiABKQOAAyIHQgBCgYCAgHBCABDJAyABQZADaiAGQgBC/////79/QgAQyQMgAUHQA2ogBUIAQv////+/f0IAEMkDIAFBkARqIANCAEL/////v39CABDJAyABQdAEaiAEQgBC/////79/QgAQyQMgAUHgAmogB0IghiIIIAEpA4gDIhAgASkDwAN8Igx8IgsgASkDkAN8IglCAEKBgICAcEIAEMkDIAFBoANqIAZCAEJ+QgAQyQMgAUHgA2ogBUIAQn5CABDJAyABQaAEaiADQgBCfkIAEMkDIAFB4ARqIARCAEJ+QgAQyQMgAUHwAmogCUIghiINIAggC1atIAdCIIh8IhQgASkDyAMgDCAQVK18IgwgASkDgAR8IhV8IgggASkD0AN8IhAgASkDmAMgCSALVK18fCIWfCILIAEpA6ADfCIHQgBCgYCAgHBCABDJAyABQbADaiAGQgBC/f///88AQgAQyQMgAUHwA2ogBUIAQv3////PAEIAEMkDIAFBsARqIANCAEL9////zwBCABDJAyABQfAEaiAEQgBC/f///88AQgAQyQMgAUHAAmogB0IghiIXIAsgDVStIAlCIIh8Ig0gASkDiAQgDCAVVq18IhUgASkDwAR8IgUgASkD0AJ8IgMgCCAUVK18IgQgASkDkAR8IgkgECAWVq0gASkD2AMgCCAQVq18fHwiFHwiCCABKQPgA3wiECABKQOoAyAHIAtUrXx8IhZ8IgsgASkDsAN8IgZCAEKBgICAcEIAEMkDAkACQAJAAkAgASkD+AQgASkD6AQgASkD6AIgCCANVK0iDSABKQPgAnwiDCANVK18IAwgASkDyAQgBSAVVK18IhUgASkD0AR8Ig0gAyAEVq0gASkD2AIgAyAFVK18fHwiBSAJIBRWrSABKQOYBCAEIAlWrXx8fCIDfCIJIAxUrXwiDCADIAVUrSAFIA1UrSABKQPYBCANIBVUrXx8fHwiBSABKQPgBHwiAyAFVK18IAMgASkDqAQgECAWVq0gASkD6AMgCCAQVq18fCIIIAEpA6AEfCIEIAhUrXwgBCAEIAl8IgRWrXx8IgkgA1StfCIIIAUgDFStfCIFIAEpA/gCIAQgCyAXVK0gB0IgiHx8IgcgBFStIgQgASkD8AJ8IgMgBFStfCADIAl8IhAgA1StfHwiAyABKQPwBHwiBCADVK18IAQgBCABKQO4BCABKQP4AyABKQO4AyAGIAtUrXwiCyABKQPwA3wiCSALVK18IAcgCXwiByAJVK18IgsgASkDsAR8IgkgC1StfCAJIAkgEHwiCVatfHwiBFatfCILIAUgCFStIAMgBVStfHwiBSALVK0gBSABKQPIAiAJIAZCIIYiAyAHfCIQIANUrSAGQiCIfHwiBiAJVK0iCSABKQPAAnwiAyAJVK18IAMgAyAEfCIDVq18fCILIAVUrXxCAFIgC0KBgICAcFZyDQAgC0KBgICAcFINASAGQv////8PVg0AQgAhCSADQgBSDQAgEEJ/UiAGQv////8PUnINAgsgBkL/////D30iBCAQQn9SrSIJfSEFIAMgBkL/////D1QgBCAJVHKtIgZ9IQkgCyADIAZUrX1C/////w98IQsgEEIBfCEQDAILIAMhCSAGIQUMAQtCgYCAgHAhCyAGIQULIAFBiApqQfj9wQBBwAAQtwIgAUFAayABKQOgCiIGQgBCA0IAEMkDIAFBgAFqIAEpA5gKIgNCAEIDQgAQyQMgAUHAAWogASkDkAoiBEIAQgNCABDJAyABQYACaiABKQOICiIHQgBCA0IAEMkDIAFBEGogASkDQCIMQgBCgYCAgHBCABDJAyABQdAAaiAGQgBC/////79/QgAQyQMgAUGQAWogA0IAQv////+/f0IAEMkDIAFB0AFqIARCAEL/////v39CABDJAyABQZACaiAHQgBC/////79/QgAQyQMgAUEgaiAMQiCGIhQgASkDSCIVIAEpA4ABfCIWfCINIAEpA1B8IghCAEKBgICAcEIAEMkDIAFB4ABqIAZCAEJ+QgAQyQMgAUGgAWogA0IAQn5CABDJAyABQeABaiAEQgBCfkIAEMkDIAFBoAJqIAdCAEJ+QgAQyQMgAUEwaiAIQiCGIhcgDSAUVK0gDEIgiHwiGyABKQOIASAVIBZWrXwiFiABKQPAAXwiGnwiFCABKQOQAXwiFSABKQNYIAggDVStfHwiHHwiDSABKQNgfCIMQgBCgYCAgHBCABDJAyABQfAAaiAGQgBC/f///88AQgAQyQMgAUGwAWogA0IAQv3////PAEIAEMkDIAFB8AFqIARCAEL9////zwBCABDJAyABQbACaiAHQgBC/f///88AQgAQyQMgASAMQiCGIh0gDSAXVK0gCEIgiHwiFyABKQPIASAWIBpWrXwiGiABKQOAAnwiAyABKQMQfCIEIBQgG1StfCIHIAEpA9ABfCIIIBUgHFatIAEpA5gBIBQgFVatfHx8Iht8IhQgASkDoAF8IhUgASkDaCAMIA1UrXx8Ihx8Ig0gASkDcHwiBkIAQoGAgIBwQgAQyQMCQAJAAkACQCABKQO4AiABKQOoAiABKQMoIBQgF1StIhcgASkDIHwiFiAXVK18IBYgASkDiAIgAyAaVK18IhogASkDkAJ8IhcgBCAHVq0gASkDGCADIARWrXx8fCIDIAggG1atIAEpA9gBIAcgCFatfHx8IgR8IgggFlStfCIWIAMgBFatIAMgF1StIAEpA5gCIBcgGlStfHx8fCIDIAEpA6ACfCIEIANUrXwgBCABKQPoASAVIBxWrSABKQOoASAUIBVWrXx8IhQgASkD4AF8IgcgFFStfCAHIAcgCHwiB1atfHwiCCAEVK18IhQgAyAWVK18IgMgASkDOCAHIA0gHVStIAxCIIh8fCIMIAdUrSIHIAEpAzB8IgQgB1StfCAEIAh8IhUgBFStfHwiBCABKQOwAnwiByAEVK18IAcgByABKQP4ASABKQO4ASABKQN4IAYgDVStfCINIAEpA7ABfCIIIA1UrXwgCCAMfCIMIAhUrXwiDSABKQPwAXwiCCANVK18IAggCCAVfCIIVq18fCIHVq18Ig0gAyAUVK0gAyAEVq18fCIDIA1UrSADIAEpAwggCCAGQiCGIgQgDHwiDCAEVK0gBkIgiHx8IgYgCFStIgggASkDAHwiBCAIVK18IAQgBCAHfCIEVq18fCIIIANUrXxCAFIgCEKBgICAcFZyDQAgCEKBgICAcFINASAGQv////8PVg0AQgAhByAEQgBSDQAgDEJ/UiAGQv////8PUnINAgsgBkL/////D30iByAMQn9SrSINfSEDIAQgBkL/////D1QgByANVHKtIgZ9IQcgCCAEIAZUrX1C/////w98IQggDEIBfCEMDAILIAYhAyAEIQcMAQsgBiEDQoGAgIBwIQgLIAFBiApqQbj+wQBBwABBEBDxAQJAIAEoAogKQYCAgIB4RwRAIAAgASkCiAo3AqwEIABBtARqIAFBkApqKAIANgIAEMcEIgJFDQEgAEEDOgC4BCAAIBg3AzggACAKNwMwIAAgDjcDKCAAIBE3AyAgACAZNwMYIAAgDzcDECAAIBI3AwggACATNwMAIABBgLHCACkDADcD4AEgAEHoAWpBiLHCACkDADcDACAAIAIpAwg3A/gBIAAgAikDACIGNwPwASACIAZCAXw3AwAgAEH4AGpCADcDACAAQfAAakIANwMAIABB6ABqQgA3AwAgAEHgAGpCADcDACAAQdgAakIANwMAIABB0ABqQgA3AwAgAEHIAGpCADcDACAAQgA3A0AgACALNwOAASAAIAk3A4gBIAAgBTcDkAEgACAQNwOYASAAIAg3A6ABIAAgBzcDqAEgACADNwOwASAAIAw3A7gBIABCADcDmAMgAEIANwPgAyAAQQE2AqgEIABCADcDiAIgAEIANwOAAiAAQvn////fADcDwAEgAEJ/NwPIASAAQoCAgICgfzcD0AEgAEIGNwPYASAAQgE3A6gCIABCADcDsAIgAEIANwOgAiAAQYCAgIB4NgKQAiABQbAKaiQADwsgASABLQCMCjoArwpBjPfBAEErIAFBrwpqQeT7wQBB+P7BABDKAwALEPADAAuMNAIefgJ/IwBBoAVrIiEkACABKQMAIRogASkDCCEIIAEpAxAhCyABKQMYIQwgASkDICEOIAEpAyghD0EoISIDQCAhQZAEaiACICJqKQMAIgVCACAPQgAQyQMgIUGgBGogBUIAIA5CABDJAyAhQbAEaiAFQgAgDEIAEMkDICFBwARqIAVCACALQgAQyQMgIUHQBGogBUIAIAhCABDJAyAhQeAEaiAFQgAgGkIAEMkDICFBgARqICEpA5AEIg0gFHwiBkIAQgBC/f/z/8////mJfxDJAyAhQfADaiAhKQOIBCIFQgBCq9X+////v/+5f0IAEMkDICFB4ANqIAVCAEL//8+K6///1R5CABDJAyAhQdADaiAFQgBCpOzDtY/UtJjnAEIAEMkDICFBwANqIAVCAEK/pZScz/DSu+QAQgAQyQMgIUGwA2ogBUIAQtfZrprk9umNywBCABDJAyAhQaADaiAFQgBCms3/y6O9xIAaQgAQyQMgISkDqAMgISkD4AQiECAYfCIFICEpA9gEICEpA9AEIgogBHwiBCAKVK18IAQgBCAhKQPIBCAhKQPABCIKIAN8IgMgClStfCADIAMgISkDuAQgISkDsAQiCiAHfCIHIApUrXwgByAHICEpA6gEICEpA6AEIgogCXwiCSAKVK18IAkgCSAhKQOYBCAGIA1UrXx8IglWrXx8IgdWrXx8IgNWrXx8IgRWrXx8Ig0gISkDoAN8IgogDVStfCAKICEpA7gDIAQgBCAhKQOwA3wiBFatfCAEICEpA8gDIAMgAyAhKQPAA3wiA1atfCADICEpA9gDIAcgByAhKQPQA3wiB1atfCAHICEpA+gDICEpA+ADIhUgCXwiCSAVVK18IAkgISkD+AMgBiAhKQPwAyIGfCAGVK18fCIUIAlUrXx8IgkgB1StfHwiByADVK18fCIDIARUrXx8IgQgClStfCAFIA1WrSAhKQPoBCAFIBBUrXx8fCEYICJBCGsiIkF4Rw0ACwJAAkAgGEKazf/Lo73EgBpWDQACQAJAAkACQCAYQprN/8ujvcSAGlINACAEQtfZrprk9umNywBWDQQgBELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEYDAELIANCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRAgA0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEYDAILIAdCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRUgB0Kk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEYDAMLIAlC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhESAJQv//z4rr///VHlENA0Kazf/Lo73EgBohGCAJIQ0MBQsgBCEQCyADIRULIAchESAJIQ0MAgtC///Piuv//9UeIQ0gFEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEYDAELIAlC///Piuv//9UefSIFIBRCq9X+////v/+5f1StIgZ9IQ0gB0Kk7MO1j9S0mOcAfSIKIAlC///Piuv//9UeVCAFIAZUcq0iBX0hESADQr+llJzP8NK75AB9IgYgB0Kk7MO1j9S0mOcAVCAFIApWcq0iBX0hFSAEQtfZrprk9umNywB9IgcgA0K/pZScz/DSu+QAVCAFIAZWcq0iA30hECAYIARC19mumuT26Y3LAFQgAyAHVnKtfUKazf/Lo73EgBp9IRggFELVqoGAgIDAgMYAfCEUCyABKQMwIR0gASkDOCESIAEpA0AhHCABKQNIIR8gASkDUCEeIAEpA1ghG0HYACEiQgAhBkIAIQdCACEDQgAhBEIAIQkDQCAhQcACaiACICJqKQMAIgVCACAbQgAQyQMgIUHQAmogBUIAIB5CABDJAyAhQeACaiAFQgAgH0IAEMkDICFB8AJqIAVCACAcQgAQyQMgIUGAA2ogBUIAIBJCABDJAyAhQZADaiAFQgAgHUIAEMkDICFBsAJqICEpA8ACIhMgGXwiCkIAQgBC/f/z/8////mJfxDJAyAhQaACaiAhKQO4AiIFQgBCq9X+////v/+5f0IAEMkDICFBkAJqIAVCAEL//8+K6///1R5CABDJAyAhQYACaiAFQgBCpOzDtY/UtJjnAEIAEMkDICFB8AFqIAVCAEK/pZScz/DSu+QAQgAQyQMgIUHgAWogBUIAQtfZrprk9umNywBCABDJAyAhQdABaiAFQgBCms3/y6O9xIAaQgAQyQMgISkD2AEgISkDkAMiFiAJfCIFICEpA4gDICEpA4ADIgkgBHwiBCAJVK18IAQgBCAhKQP4AiAhKQPwAiIJIAN8IgMgCVStfCADIAMgISkD6AIgISkD4AIiCSAHfCIHIAlUrXwgByAhKQPYAiAhKQPQAiIJIAZ8IgYgCVStfCAGICEpA8gCIAogE1StfHwiFyAGVK18fCIGIAdUrXx8IgNWrXx8IgRWrXx8IgkgISkD0AF8IhMgCVStfCATICEpA+gBIAQgBCAhKQPgAXwiBFatfCAEICEpA/gBIAMgAyAhKQPwAXwiA1atfCADICEpA4gCIAYgBiAhKQOAAnwiBlatfCAGIAYgISkDmAIgFyAhKQOQAiIXfCIHIBdUrXwgByAhKQOoAiAKICEpA6ACIgp8IApUrXx8IhkgB1StfHwiBlatfHwiByADVK18fCIDIARUrXx8IgQgE1StfCAFIAlWrSAhKQOYAyAFIBZUrXx8fCEJICJBCGsiIkEoRw0ACwJAAkAgCUKazf/Lo73EgBpWDQACQAJAAkACQCAJQprN/8ujvcSAGlINACAEQtfZrprk9umNywBWDQQgBELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEJDAELIANCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIRMgA0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEJDAILIAdCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIRYgB0Kk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEJDAMLIAZC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhFyAGQv//z4rr///VHlENA0Kazf/Lo73EgBohCSAGIQoMBQsgBCETCyADIRYLIAchFyAGIQoMAgtC///Piuv//9UeIQogGUKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEJDAELIAZC///Piuv//9UefSIFIBlCq9X+////v/+5f1StIhN9IQogB0Kk7MO1j9S0mOcAfSIWIAZC///Piuv//9UeVCAFIBNUcq0iBX0hFyADQr+llJzP8NK75AB9IgYgB0Kk7MO1j9S0mOcAVCAFIBZWcq0iBX0hFiAEQtfZrprk9umNywB9IgcgA0K/pZScz/DSu+QAVCAFIAZWcq0iA30hEyAJIARC19mumuT26Y3LAFQgAyAHVnKtfUKazf/Lo73EgBp9IQkgGULVqoGAgIDAgMYAfCEZC0Kazf/Lo73EgBohAyAIIBJ8IgUgCFQgBSALIBx8IgYgC1QgBiAGIAwgH3wiCCAMVCAIIAggDiAefCIEIA5UIAQgBCAPIBt8IhIgD1StfCIEVnKtfCIIVnKtfCIGVnKtfCIHIAVUcq0gGiAdfHwiHiEFAkACQAJAIB5Cms3/y6O9xIAaUg0AQtfZrprk9umNywAhAyAHIgVC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQMgBiIFQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEDIAgiBUKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEDIAQiBUL//8+K6///1R5SDQBCq9X+////v/+5fyEDIBIiBUKr1f7///+//7l/UQ0BCyADIAVYDQAgBCEaIAghHSAGIRwgByEfDAELIARC///Piuv//9UefSIDIBJCq9X+////v/+5f1StIgV9IRogCEKk7MO1j9S0mOcAfSILIARC///Piuv//9UeVCADIAVUcq0iA30hHSAGQr+llJzP8NK75AB9IgQgCEKk7MO1j9S0mOcAVCADIAtWcq0iA30hHCAHQtfZrprk9umNywB9IgUgBkK/pZScz/DSu+QAVCADIARWcq0iA30hHyAeIAdC19mumuT26Y3LAFQgAyAFVnKtfUKazf/Lo73EgBp9IR4gEkLVqoGAgIDAgMYAfCESC0Kazf/Lo73EgBohByACKQMIIgQgAikDOHwiAyAEVCADIAIpAxAiBCACKQNAfCIIIARUIAggCCACKQMYIgQgAikDSHwiBSAEVCAFIAUgAikDICIGIAIpA1B8IgQgBlQgBCAEIAIpAygiBiACKQNYfCIOIAZUrXwiBFZyrXwiBVZyrXwiCFZyrXwiDyADVHKtIAIpAzAgAikDAHx8IgwhAwJAAkACQCAMQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIQcgDyIDQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEHIAgiA0K/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhByAFIgNCpOzDtY/UtJjnAFINAEL//8+K6///1R4hByAEIgNC///Piuv//9UeUg0AQqvV/v///7//uX8hByAOIgNCq9X+////v/+5f1ENAQsgAyAHWg0AIA8hAyAIIQcgBSEGIAQhCwwBCyAEQv//z4rr///VHn0iAyAOQqvV/v///7//uX9UrSIGfSELIAVCpOzDtY/UtJjnAH0iByAEQv//z4rr///VHlQgAyAGVHKtIgN9IQYgCEK/pZScz/DSu+QAfSIEIAVCpOzDtY/UtJjnAFQgAyAHVnKtIgN9IQcgD0LX2a6a5PbpjcsAfSIFIAhCv6WUnM/w0rvkAFQgAyAEVnKtIgR9IQMgDCAPQtfZrprk9umNywBUIAQgBVZyrX1Cms3/y6O9xIAafSEMIA5C1aqBgICAwIDGAHwhDgsgISAONwOYBSAhIAs3A5AFICEgBjcDiAUgISAHNwOABSAhIAM3A/gEICEgDDcD8ARBKCEiQgAhDkIAIQZCACEHQgAhA0IAIQRCACEFA0AgIUHwAGogIUHwBGogImopAwAiCEIAIBJCABDJAyAhQYABaiAIQgAgGkIAEMkDICFBkAFqIAhCACAdQgAQyQMgIUGgAWogCEIAIBxCABDJAyAhQbABaiAIQgAgH0IAEMkDICFBwAFqIAhCACAeQgAQyQMgIUHgAGogISkDcCIMIA58IgtCAEIAQv3/8//P///5iX8QyQMgIUHQAGogISkDaCIIQgBCq9X+////v/+5f0IAEMkDICFBQGsgCEIAQv//z4rr///VHkIAEMkDICFBMGogCEIAQqTsw7WP1LSY5wBCABDJAyAhQSBqIAhCAEK/pZScz/DSu+QAQgAQyQMgIUEQaiAIQgBC19mumuT26Y3LAEIAEMkDICEgCEIAQprN/8ujvcSAGkIAEMkDICEpAwggISkDwAEiGyAFfCIFICEpA7gBICEpA7ABIgggBHwiBCAIVK18IAQgBCAhKQOoASAhKQOgASIIIAN8IgMgCFStfCADIAMgISkDmAEgByAhKQOQASIHfCIIIAdUrXwgCCAIICEpA4gBICEpA4ABIgcgBnwiBiAHVK18IAYgBiAhKQN4IAsgDFStfHwiBlatfHwiCFatfHwiA1atfHwiBFatfHwiDCAhKQMAfCIPIAxUrXwgDyAhKQMYIAQgBCAhKQMQfCIEVq18IAQgISkDKCADIAMgISkDIHwiA1atfCADICEpAzggCCAIICEpAzB8IghWrXwgCCAhKQNIICEpA0AiByAGfCIGIAdUrXwgBiAhKQNYICEpA1AiByALfCAHVK18fCIOIAZUrXx8IgYgCFStfHwiByADVK18fCIDIARUrXx8IgQgD1StfCAFIAxWrSAhKQPIASAFIBtUrXx8fCEFICJBCGsiIkF4Rw0ACwJAAkAgBUKazf/Lo73EgBpWDQACQAJAAkACQCAFQprN/8ujvcSAGlINACAEQtfZrprk9umNywBWDQQgBELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiEFDAELIANCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIQwgA0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiEFDAILIAdCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIQggB0Kk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiEFDAMLIAZC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhDyAGQv//z4rr///VHlENA0Kazf/Lo73EgBohBSAGIQsMBQsgBCEMCyADIQgLIAchDyAGIQsMAgtC///Piuv//9UeIQsgDkKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEFDAELIAZC///Piuv//9UefSIIIA5Cq9X+////v/+5f1StIgx9IQsgB0Kk7MO1j9S0mOcAfSISIAZC///Piuv//9UeVCAIIAxUcq0iCH0hDyADQr+llJzP8NK75AB9IgYgB0Kk7MO1j9S0mOcAVCAIIBJWcq0iB30hCCAEQtfZrprk9umNywB9IhIgA0K/pZScz/DSu+QAVCAGIAdUcq0iA30hDCAFIARC19mumuT26Y3LAFQgAyASVnKtfUKazf/Lo73EgBp9IQUgDkLVqoGAgIDAgMYAfCEOCwJ+AkACQCAJIgQgGCIDUg0AIBAiAyATIgRSDQAgFSIDIBYiBFINACARIgMgFyIEUg0AIA0iAyAKIgRSDQAgFCIDIBkiBFENAQsgAyAEWg0AQqTsw7WP1LSY5wAgFyARfSIDIAogDX0iBCAUIBlWrSIGVCAKIA1Ucq0iB30iEn0iGiAEIAZ9IgRC///Piuv//9UeVkL//8+K6///1R4gBH0iBCAZIBR9IgZCq9X+////v/+5f1atIh1Ucq0iHH0hH0K/pZScz/DSu+QAIBYgFX0iGyADIAdUIBEgF1ZyrSIDfSIHfSIgIBogHFQgEkKk7MO1j9S0mOcAVnKtIhJ9IR5C19mumuT26Y3LACATIBB9IhwgAyAbViAVIBZWcq0iA30iGn0iGyASICBWIAdCv6WUnM/w0rvkAFZyrSIHfSESIAcgG1YgGkLX2a6a5PbpjcsAVnIhIiAEIB19IRogAyAcViAQIBNWcq0gGCAJfXxCms3/y6O9xIAafCEdQqvV/v///7//uX8gBn0MAQsgDSAKfSIDIBQgGVStIgR9IRogESAXfSIGIAMgBFQgCiANVnKtIgN9IR8gFSAWfSIEIBEgF1QgAyAGVnKtIgN9IR4gECATfSIGIBUgFlQgAyAEVnKtIgN9IRIgECATVCADIAZWciEiIBggCX0hHSAUIBl9CyEcAn4CQAJAIBgiBCAFIgNSDQAgDCIDIBAiBFINACAIIgMgFSIEUg0AIA8iAyARIgRSDQAgDSIEIAsiA1INACAUIgQgDiIDUQ0BCyADIARaDQBCpOzDtY/UtJjnACARIA99IgMgDSALfSIEIA4gFFatIgZUIAsgDVZyrSINfSILfSIbIAQgBn0iBEL//8+K6///1R5WQv//z4rr///VHiAEfSIGIBQgDn0iDkKr1f7///+//7l/Vq0iFFRyrSIEfSEHQr+llJzP8NK75AAgFSAIfSIgIAMgDVQgDyARVnKtIg19IhF9Ig8gBCAbViALQqTsw7WP1LSY5wBWcq0iBH0hA0LX2a6a5PbpjcsAIBAgDH0iCyANICBWIAggFVZyrSIIfSINfSIVIAQgD1YgEUK/pZScz/DSu+QAVnKtIhF9IQQgESAVViANQtfZrprk9umNywBWciECIAYgFH0hBiAIIAtWIAwgEFZyrSAFIBh9fEKazf/Lo73EgBp8IQhCq9X+////v/+5fyAOfQwBCyALIA19IgMgDiAUVK0iBH0hBiAPIBF9IhsgAyAEVCALIA1Ucq0iA30hByAIIBV9IgQgDyARVCADIBtWcq0iDX0hAyAMIBB9IgsgCCAVVCAEIA1Ucq0iCH0hBCAMIBBUIAggC1ZyIQIgBSAYfSEIIA4gFH0LIQwgCCACrX0iDSEIIAACfgJAAkAgDSAJIgVSDQAgBCEIIBMiBSAEUg0AIAMhCCAWIgUgA1INACAHIQggFyIFIAdSDQAgBiEIIAoiBSAGUg0AIAwiCCAZIgVRDQELIAUgCFgNAEKk7MO1j9S0mOcAIBcgB30iCCAKIAZ9IgUgDCAZVq0iC1QgBiAKVnKtIgZ9Igp9IhAgBSALfSIFQv//z4rr///VHlZC///Piuv//9UeIAV9IgsgGSAMfSIMQqvV/v///7//uX9WrSIVVHKtIhF9IQVCv6WUnM/w0rvkACAWIAN9Ig4gBiAIViAHIBdWcq0iCH0iBn0iFyAQIBFUIApCpOzDtY/UtJjnAFZyrSIKfSEHQtfZrprk9umNywAgEyAEfSIQIAggDlYgAyAWVnKtIhF9Igh9IhYgCiAXViAGQr+llJzP8NK75ABWcq0iBn0hAyAGIBZWIAhC19mumuT26Y3LAFZyIQIgCyAVfSEIIBAgEVQgBCATVnKtIA0gCX18QprN/8ujvcSAGnwhDkKr1f7///+//7l/IAx9DAELIAYgCn0iBSAMIBlUrSILfSEIIAcgF30iECAGIApUIAUgC1RyrSIGfSEFIAMgFn0iCiAHIBdUIAYgEFZyrSIGfSEHIAQgE30iCyADIBZUIAYgClZyrSIGfSEDIAQgE1QgBiALVnIhAiANIAl9IQ4gDCAZfQs3A1ggACAINwNQIAAgBTcDSCAAIAc3A0AgACADNwM4IAAgHDcDKCAAIBo3AyAgACAfNwMYIAAgHjcDECAAIBI3AwggACAOIAKtfTcDMCAAIB0gIq19NwMAICFBoAVqJAAL4CoDDX8DfgF8IwBB4ABrIgMkAAJAAkACQAJAAkACQAJAAkACQAJAAkACQCABKAIIIgVFBEBB0c7FAC0AABpBAUEBENYEIgFFDQEgAEEBNgIIIAAgATYCBCAAQQE2AgAgAUEAOgAADAsLIAJpQQFHBEAgAkEKRw0CQQEhBiAFrUIFhiABKAIEIgggBUECdCIBakEEaygCAGetfbpEcaN5CU+TCkCjmyITRAAAAAAAAPC/ZA0DDAQLIAJnIgJBH0cEQEEgQR8gAmsiCkH/AXFwRQRAIAAgASAKELACDAwLAkBBfyAFrUIFhiABKAIEIgYgBUECdGoiCUEEaygCAGetfSIQIAqsIhKAIhEgECARIBJ+Uq18IhCnIgUgEEKAgICAEFobIgRBAEgNAEEAIQFBASECIAQEQEHRzsUALQAAGkEBIQcgBEEBENYEIgJFDQEgBSEIC0F/IAp0QX9zIQcgA0EANgJQIAMgAjYCTCADIAg2AkggBkEEaiEFQQAhAkEAIQQDQCAGIQggBSEGIAgoAgAgBHQgAnIhAiAEQSBqIQQDQCADKAJIIAFGBEAgA0HIAGpBlM/EABC2AwsgAygCTCABaiACIAdxOgAAIAMgAUEBaiIBNgJQIARB/wFxQSFJBH8gAiAKdgUgCCgCACAKIARrdgshAiAEIAprIgRB/wFxIApB/wFxTw0ACyAGIAYgCUciCEECdGohBSAIDQALIARB/wFxBEAgASADKAJIRgRAIANByABqQYTPxAAQtgMLIAMoAkwgAWogAjoAACADIAFBAWoiATYCUAsCQCABRQ0AIAMoAkwiBSABakEBRg0AA0AgASAFaiIIQQFrLQAADQEgAyABQQFrIgI2AlAgAUEBRg0BIAIhASAIQQJrDQALCyAAIAMpAkg3AgAgAEEIaiADQdAAaigCADYCAAwMCyAHIARB9M7EABDIBAALQaTRxAAQmwQAC0EBQQEQ/wQAC0EBIQYCQAJAAkAgBa1CBYYgASgCBCIHIAVBAnQiAWpBBGsoAgBnrX26IAK4EOcCo5siE0QAAAAAAADwv2RFIBNEAAAAAAAA8EFjRXINACATqyIEQQBIDQEgBEUEQEEAIQQMAQtB0c7FAC0AABpBASEIIARBARDWBCIGRQ0BCyADQQA2AhQgAyAGNgIQIAMgBDYCDEHRzsUALQAAGiABQQQQ1gQiCARAIAEEQCAIIAcgAfwKAAALIAMgBTYCICADIAg2AhwgAyAFNgIYIAJBgAJNBEAgAkEDdCIBQfjhxABqKAIAIQogAUH04cQAaigCACELIAVBP00NAyADQdAAaiIBQaDOxAAoAgA2AgAgA0GYzsQAKQIANwNIIAsEQCADQcgAakGU0cQAEKUDIAMoAkwgCzYCACADQQE2AlAgAygCICEFCyADQTBqIgYgASgCADYCACADIAMpA0g3AyggBRCzAyEIAkACQCAIIAYoAgAiAU0EQEEBIQwMAQtBASEMA0AgAygCLCEFAkACQAJAAkAgAQ4CAAECCyADQUBrQaDOxAAoAgA2AgAgA0GYzsQAKQIANwM4DAILIAUoAgAhBkHRzsUALQAAGkEEQQQQ1gQiAUUNBCADQdAAaiIHQQE2AgAgASAFKAIANgIAIAMgATYCTCADQQE2AkggA0HIAGogBhCzAiADQUBrIAcoAgA2AgAgAyADKQJINwM4DAELIANBOGogBSABIAUgARDtAgsgAygCKCIBBEAgAygCLCABQQJ0EN8ECyADQTBqIANBQGsoAgAiATYCACADIAMpAzg3AyggDEEBdCEMIAEgCEkNAAsLIAutIRIgC0GAgARJIQ0DQAJAAkAgASADKAIgIgVGBEAgAygCHEEEayEIIAFBAnQhASADKAIsQQRrIQYDQCABRQ0CIAEgBmohByABIAhqIAFBBGshASgCACIEIAcoAgAiB0YNAAsgBCAHTQ0BDAILIAEgBUkNAQsgAygCKCIBRQ0GIAMoAiwgAUECdBDfBCADKAIgIQUMBgsgA0HIAGogA0EYaiADQShqEKEBIANBQGsiASADQdAAaigCADYCACADIAMpAkg3AzggAygCVCEIIAMoAlghBiADKAJcIQkgAygCGCIFBEAgAygCHCAFQQJ0EN8ECyADQSBqIAEoAgA2AgAgAyADKQM4NwMYIAwEQAJAIAsEQEEBIQEMAQsMEQsDQCABIQUCQAJAAkACfwJAIA1FBEAgCUUNBCAJQf////8DaiEHIAlBAnQhASAJQf////8DcUEBRw0BQgAhESABIAZqDAILIAlFDQMgBkEEayEHIAlBAnQhBEEAIQEDQCAEIAdqIg4gDigCACIOQRB2Ig8gDyABQRB0ciALbiIBIAtsa0EQdCAOQf//A3FyIg4gC24iDyABQRB0cjYCACAOIAsgD2xrIQEgBEEEayIEDQALDAILIAEgBmpBCGshASAHQf////8DcUEBakH+////B3EhBEIAIRADQCABQQRqIg4gDjUCACAQQiCGhCIQIBKAIhE+AgAgASABNQIAIBAgESASfn1CIIaEIhAgEoAiET4CACAQIBEgEn59IRAgAUEIayEBIARBAmsiBA0ACyAQQiCGIREgAUEIagshASAHQQFxRQRAIAFBBGsiASARIAE1AgCEIhAgEoAiET4CACAQIBEgEn59IRALIBCnIQELIAlFBEBBACEJDAILIAYgCUECdCIEakEEaygCAA0BIAZBBGshDiAJQf////8DcSEHA0AgBEUEQEEAIQkMAwsgB0EBayEHIAQgDmogBEEEayEEKAIARQ0ACyAHQQFqIgcgCSAHIAlJGyEJDAELQQAhCUEAIQELAkAgCSAIQQJ2Tw0AIAhFBEBBACEIDAELIAhBAnQhCCAJRQRAIAYgCBDfBEEAIQhBBCEGDAELIAYgCEEEIAkiCEECdCIHEM4EIgYNAEEEIAdB/PHEABDIBAALAkAgCkUNACACBEAgAygCFCEEIAohBwNAIAEgASACbiIBIAJsayEOIAMoAgwgBEYEQCADQQxqQYTRxAAQtgMLIAMoAhAgBGogDjoAACADIARBAWoiBDYCFCAHQQFrIgcNAAsMAQtB9NDEABCbBAALIAUgBSAMSSIHaiEBIAcNAAsLIAgEQCAGIAhBAnQQ3wQLIAMoAjAhAQwACwALQQRBBEGkg8UAEMgEAAsgAkGBAkGU0MQAENkDAAtBBCABQaSDxQAQyAQACyAIIARBpM/EABDIBAALAkAgBUECTwRAIAtFDQEgC60hEiADKAIcIQwgAygCGCEIIAtB//8DSyEJA0AgBUECdCIEIQYCQCAJRQRAIAxBBGshB0EAIQEDQCAEIAdqIg0gDSgCACINQRB2Ig4gDiABQRB0ciALbiIBIAtsa0EQdCANQf//A3FyIg0gC24iDiABQRB0cjYCACANIAsgDmxrIQEgBEEEayIEDQALDAELIAVB/////wNqIQcCfyAFQQFGBEBCACERIAYgDGoMAQsgBiAMakEIayEBIAdB/////wNxQQFqQf7///8HcSEEQgAhEANAIAFBBGoiDSANNQIAIBBCIIaEIhAgEoAiET4CACABIAE1AgAgECARIBJ+fUIghoQiECASgCIRPgIAIBAgESASfn0hECABQQhrIQEgBEECayIEDQALIBBCIIYhESABQQhqCyEBIAdBAXFFBEAgAUEEayIBIBEgATUCAIQiECASgCIRPgIAIBAgESASfn0hEAsgEKchAQsCQCAGIAxqQQRrKAIADQAgDEEEayEHIAUhBANAIAZFBEBBACEFDAILIARBAWshBCAGIAdqIAZBBGshBigCAEUNAAsgBEEBaiIGIAUgBSAGSxshBQsCQCAFIAhBAnZPDQACQCAIBEAgCEECdCEGIAUNASAMIAYQ3wRBBCEMC0EAIQgMAQsgBSEIIAwgBkEEIAVBAnQiBhDOBCIMDQBBBCAGQfzxxAAQyAQACwJAIApFDQAgAgRAIAMoAhQhBCAKIQcDQCABIAEgAm4iASACbGshBiADKAIMIARGBEAgA0EMakHk0MQAELYDCyADKAIQIARqIAY6AAAgAyAEQQFqIgQ2AhQgB0EBayIHDQALDAELQdTQxAAQmwQACyADIAw2AhwgAyAINgIYIAMgBTYCICAFQQFLDQALCwJAIAUEQCADKAIcKAIAIgEEQCACRQ0CIAMoAhQhBANAIAEgASACbiIFIAJsayEIIAMoAgwgBEYEQCADQQxqQcTQxAAQtgMLIAMoAhAgBGogCDoAACADIARBAWoiBDYCFCABIAJJIAUhAUUNAAsLIAAgAykCDDcCACAAQQhqIANBFGooAgA2AgAgAygCGCIARQ0LIAMoAhwgAEECdBDfBAwLC0EAQQBBpNDEABDZAwALQbTQxAAQmwQACwwJCyATRAAAAAAAAPBBY0UNACATqyIEQQBIDQEgBEUEQEEAIQQMAQtB0c7FAC0AABpBASEHIARBARDWBCIGRQ0BCyADQQA2AhQgAyAGNgIQIAMgBDYCDEHRzsUALQAAGiABQQQQ1gQiAkUNASABBEAgAiAIIAH8CgAACyADIAU2AiAgAyACNgIcIAMgBTYCGCAFQT9NDQUgA0HQAGoiCkGgzsQAKAIAIgg2AgAgA0GYzsQAKQIAIhA3A0ggA0HIAGpBlNHEABClAyADKAJMQZDOADYCACADQTBqIgVBATYCACADIAMpA0g3AyggAygCIBCzAyIGIAUoAgAiAUsNAkEBIQwMAwsgByAEQaTPxAAQyAQAC0EEIAFBpIPFABDIBAALQQEhDANAIAMoAiwhAgJAAkACQAJAIAEOAgABAgsgA0FAayAINgIAIAMgEDcDOAwCCyACKAIAIQdB0c7FAC0AABpBBEEEENYEIgFFDQQgCkEBNgIAIAEgAigCADYCACADIAE2AkwgA0EBNgJIIANByABqIAcQswIgA0FAayAKKAIANgIAIAMgAykCSDcDOAwBCyADQThqIAIgASACIAEQ7QILIAMoAigiAQRAIAMoAiwgAUECdBDfBAsgBSADQUBrKAIAIgE2AgAgAyADKQM4NwMoIAxBAXQhDCABIAZJDQALCwNAAkACQCABIAMoAiAiBUYEQCADKAIcQQRrIQIgAUECdCEBIAMoAixBBGshCANAIAFFDQIgASAIaiEGIAEgAmogAUEEayEBKAIAIgcgBigCACIGRg0ACyAGIAdPDQEMAgsgASAFSQ0BCyADKAIoIgFFDQMgAygCLCABQQJ0EN8EIAMoAiAhBQwDCyADQcgAaiADQRhqIANBKGoQoQEgA0FAayIBIAooAgA2AgAgAyADKQJINwM4IAMoAlQhBSADKAJYIQcgAygCXCEGIAMoAhgiAgRAIAMoAhwgAkECdBDfBAsgA0EgaiABKAIANgIAIAMgAykDODcDGCAMBEBBASEJA0ACQCAGRQRAQQAhBkEAIQQMAQsgByAGQQJ0IghqQQAhBCAIIQEDQCABQQRrIgEgB2oiCyALKAIAIgtBEHYiDSANIARBEHRyQZDOAG4iBEGQzgBsa0EQdCALQf//A3FyIgtBkM4AbiINIARBEHRyNgIAIAsgDUGQzgBsayEEIAENAAtBBGsoAgANACAHQQRrIQIgBkH/////A3EhAQNAIAhFBEBBACEGDAILIAFBAWshASACIAhqIAhBBGshCCgCAEUNAAsgAUEBaiIBIAYgASAGSRshBgsCQCAGIAVBAnZPDQAgBUUEQEEAIQUMAQsgBUECdCEBIAZFBEAgByABEN8EQQAhBUEEIQcMAQsgByABQQQgBiIFQQJ0IgEQzgQiBw0AQQQgAUH88cQAEMgEAAsgBCAEQQpuIghBCmxrIQIgAygCFCIBIAMoAgxGBEAgA0EMakGE0cQAELYDCyADKAIQIAFqIAI6AAAgAyABQQFqIgI2AhQgAygCDCACRgRAIANBDGpBhNHEABC2AwsgAygCECACaiAIQQpwOgAAIAMgAUECaiICNgIUIAMoAgwgAkYEQCADQQxqQYTRxAAQtgMLIAMoAhAgAmogBEHkAG5BCnA6AAAgAyABQQNqIgI2AhQgAygCDCACRgRAIANBDGpBhNHEABC2AwsgAygCECACaiAEQegHbkEKcDoAACADIAFBBGo2AhQgCSAJIAxJIgFqIQkgAQ0ACwsgBQRAIAcgBUECdBDfBAsgAygCMCEBDAALAAtBBEEEQaSDxQAQyAQACyAFQQJPBEAgAygCHCEHIAMoAhghBgNAIAcgBUECdCIIaiECQQAhBCAIIQEDQCABQQRrIgEgB2oiCiAKKAIAIgpBEHYiCSAJIARBEHRyQZDOAG4iBEGQzgBsa0EQdCAKQf//A3FyIgpBkM4AbiIJIARBEHRyNgIAIAogCUGQzgBsayEEIAENAAsCQCACQQRrKAIADQAgB0EEayECIAUhAQNAIAhFBEBBACEFDAILIAFBAWshASACIAhqIAhBBGshCCgCAEUNAAsgAUEBaiIBIAUgASAFSRshBQsCQCAFIAZBAnZPDQAgBkUEQEEAIQYMAQsgBkECdCEBIAVFBEAgByABEN8EQQAhBkEEIQcMAQsgBSEGIAcgAUEEIAVBAnQiARDOBCIHDQBBBCABQfzxxAAQyAQACyAEIARBCm4iCEEKbGshAiADKAIUIgEgAygCDEYEQCADQQxqQeTQxAAQtgMLIAMoAhAgAWogAjoAACADIAFBAWoiAjYCFCADKAIMIAJGBEAgA0EMakHk0MQAELYDCyADKAIQIAJqIAhBCnA6AAAgAyABQQJqIgI2AhQgAygCDCACRgRAIANBDGpB5NDEABC2AwsgAygCECACaiAEQeQAbkEKcDoAACADIAFBA2oiAjYCFCADKAIMIAJGBEAgA0EMakHk0MQAELYDCyADKAIQIAJqIARB6AduQQpwOgAAIAMgBzYCHCADIAY2AhggAyABQQRqNgIUIAMgBTYCICAFQQFLDQALCyAFBEAgAygCHCgCACIBBEAgAygCFCEEA0AgASABQQpuIgJBCmxrIQUgAygCDCAERgRAIANBDGpBxNDEABC2AwsgAygCECAEaiAFOgAAIAMgBEEBaiIENgIUIAFBCkkgAiEBRQ0ACwsgACADKQIMNwIAIABBCGogA0EUaigCADYCACADKAIYIgBFDQEgAygCHCAAQQJ0EN8EDAELQQBBAEGk0MQAENkDAAsgA0HgAGokAA8LIANBADYCWCADQQE2AkwgA0H0ycQANgJIIANCBDcCUCADQcgAakHkysQAEKgEAAv1LQIkfwF+IwBB0BFrIgUkACAFIAI2AhAgBSAENgIMAkACQAJAAkACQAJAIAIgBEYEQCAFQaAJaiABIAIQUiAFKAK0CSEYIAUoArAJIRsgBSgCrAkhHyAFKAKoCSEZIAUoAqQJIRwgBSgCoAkhICAFQRBqECZB0c7FAC0AABpBwARBCBDWBCIHRQ0BIAdCADcDkAQgB0L9/4uAgIDAhPYANwMoIAdCgoCwoLyBgPprNwMgIAdCurGdnvWKpqTfADcDGCAHQsWuyYK3ipbn9wA3AxAgB0Lt2NuS+tLGg9wANwMIIAdCk8mD1L/Yl/sVNwMAIAdBuARqQgA3AwAgB0GwBGpCADcDACAHQagEakIANwMAIAdBoARqQgA3AwAgB0GYBGpCADcDACAHQTBqQQBB4AP8CwBBDCENAn8gB0GQBGpB+MPCAEEwEPEDBEBBCyEOQQwMAQsgB0HgA2pB+MPCAEEwEPEDBEBBCiEOQQsMAQsgB0GwA2pB+MPCAEEwEPEDBEBBCSEOQQoMAQsgB0GAA2pB+MPCAEEwEPEDBEBBCCEOQQkMAQsgB0HQAmpB+MPCAEEwEPEDBEBBByEOQQgMAQsgB0GgAmpB+MPCAEEwEPEDBEBBBiEOQQcMAQsgB0HwAWpB+MPCAEEwEPEDBEBBBSEOQQYMAQsgB0HAAWpB+MPCAEEwEPEDBEBBBCEOQQUMAQsgB0GQAWpB+MPCAEEwEPEDBEBBAyEOQQQMAQsgB0HgAGpB+MPCAEEwEPEDBEBBAiEOQQMMAQsgB0EwakH4w8IAQTAQ8QMEQEEBIQ5BAgwBCyAHQfjDwgBBMBDxAwRAQQEMAQtB0c7FAC0AABpBMEEIENYEIgFFDQMgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgB0HABBDfBEF/IQ4gASEHQQEhDUEBCyEJIAUgDjYCvAYgBSAJNgK4BiAFIAc2ArQGIAUgDTYCsAYgBUEANgLMBiAFQoCAgICAATcCxAYgBSgCqAMhFiAFKAKsAyITQQdNBEAgE0UEQEF+IRUMCAsgFi0AAEH/AUYNBCATQQFGDQUgFi0AAUH/AUYNBCATQQJGDQUgFi0AAkH/AUYNBCATQQNGDQUgFi0AA0H/AUYNBCATQQRGDQUgFi0ABEH/AUYNBCATQQVGDQUgFi0ABUH/AUYNBCATQQZGDQUgFi0ABkH/AUcNBQwECyAFIBYgExCEAyAFKAIAQQFGDQMgE0ECayEVDAULIAVBADYCoAkgBUEQaiAFQQxqIAVBoAlqQcTBwgAQlwQAC0EIQcAEEP8EAAtBCEEwEP8EAAsgAkUNACACQcABbCEIIAMhBANAIAVB0AZqIAQQyAEgBSgCzAYiASAFKALEBkYEQCAFQcQGakHUwcIAEJ0DCyAFKALIBiABQcABbGogBUHQBmpBwAH8CgAAIAUgAUEBajYCzAYgBEHAAWohBCAIQcABayIIDQALCyATQQJrIRUgE0EBTQ0BCwJAAkACQAJAAkACQAJAAkACQCAVIBZqLQAADgIBAAILQdHOxQAtAAAaQSBBBBDWBCIQRQ0CQdHOxQAtAAAaIAlBMGwiCkEIENYEIgFFDQNBACEIA0AgCCAKRwRAIAEgCGoiCyAHIAhqIgQpAwA3AwAgC0EoaiAEQShqKQMANwMAIAtBIGogBEEgaikDADcDACALQRhqIARBGGopAwA3AwAgC0EQaiAEQRBqKQMANwMAIAtBCGogBEEIaikDADcDACAKIAhBMGoiCEcNAQsLIBAgCTYCCCAQIAE2AgQgECAJNgIAQQAhCEHRzsUALQAAGiAKQQgQ1gQiBEUNBCAJQTBsIQEDQCABIAhHBEAgBCAIaiIKIAcgCGoiCykDADcDACAKQShqIAtBKGopAwA3AwAgCkEgaiALQSBqKQMANwMAIApBGGogC0EYaikDADcDACAKQRBqIAtBEGopAwA3AwAgCkEIaiALQQhqKQMANwMAIAEgCEEwaiIIRw0BCwsgECAJNgIYIBAgBDYCFCAQIAk2AhAgECAONgIcIBAgDjYCDCAFQQI2AtAPIAUgEDYCzA8gBUECNgLID0EAIQQgBUEANgLcDyAFQoCAgICAATcC1A8gAgRAIAVB8ApqIREgBUGwCWohDyADIQggGyEKIBwhDANAIAQgGUYNByAEIBhGDQggBUGgCWogCCAMIAoQxwFBAEUEQCAFQeAPaiAPQcAB/AoAAAsgBUG4EWoiCSAFQagJaikDADcDACAFQYgJaiIQIBFBCGopAgA3AwAgBSAFKQOgCTcDsBEgBSARKQIANwOACSAFKALQDyISIAUoAsgPIgFGBEAgBUHID2pB9LvCABCjAyAFKALIDyEBCyAFKALMDyIOIBJBBHRqIgsgBSkDsBE3AgAgC0EIaiAJKQMANwIAIAUgEkEBaiILNgLQDyABIAtGBH8gBUHID2pBhLzCABCjAyAFKALMDwUgDgsgC0EEdGoiASAFKQOACTcCACABQQhqIBApAwA3AgAgBSASQQJqNgLQDyAFKALcDyIBIAUoAtQPRgRAIAVB1A9qQZS8wgAQnQMLIB5FBEAgBSgC2A8gAUHAAWxqIAVB4A9qQcAB/AoAAAsgBSABQQFqNgLcDyAIQcABaiEIIApBMGohCiAMQTBqIQwgAiAEQQFqIgRHDQALCyAFQcgRaiAFQdAPaigCADYCACAFIAUpAsgPNwPAESAFQYCAgIB4NgKgESAFQaAJaiAFQcARaiAFQaARakEAQQAQqwEgBUG4CWoiASAFQdwPaigCADYCACAFQZgIaiAFQagJaikCADcDACAFIAUpAtQPIik3ArAJIAUgBSkCoAk3A5AIIAUgKT4CrAggBSAFKAK0CTYCqAggBSABKAIANgKkCCAFQawIaiEBIAVBpAhqIQggBUGoCGohCiAFQZAIaiEEDAcLIAVBoAlqIAVBsAZqIAMgAiAcIBkgGyAYENIBIAVBuAhqIAVBqAlqKQIANwMAIAUgBSkCoAk3A7AIIAUgBSgCsAk2AswIIAUgBSgCtAk2AsgIIAUgBSgCuAk2AsQIIAVBzAhqIQEgBUHECGohCCAFQcgIaiEKIAVBsAhqIQQMBgtB1LrCAEEPQdTCwgAQ/gMAC0EEQSAQ/wQAC0EIIApB6IHAABDIBAALQQggCkHogcAAEMgEAAsgGSAZQdS7wgAQ2QMACyAYIBhB5LvCABDZAwALIAcgDUEwbBDfBCAFQbgGaiIhIARBCGopAgA3AwAgBSAEKQIANwOwBiAIKAIAIR0gCigCACELIAEoAgAhECAVBEBBASACIAJBAU0bISUgBUGQCWohIiAFQfAKaiEjIAVBsAlqISYgBUGQEGohFCAFQYAKaiEkIBNBAkshJyACIQogE0EDayIoIQQDQCAEIR4CQAJAAkACQAJAAkACQCAnBEAgBCAWaiIXLQAAIgEOAgEDAgsgKCATQZTCwgAQ2QMACyAFQaAJaiAFQbAGaiALIB0gHCAZIBsgGBDSASAFQdgIaiIMIAVBqAlqKQIANwMAIAUgBSkCoAk3A9AIIAUoArAJIQQgBSgCtAkhASAFKAK4CSEdIAUoArAGIgkEQCAFKAK0BiAJQTBsEN8ECyAhIAwpAwA3AwAgBSAFKQPQCDcDsAYgEARAIAsgEEHAAWwQ3wQLDAULIAFB/wFHDQELQQAhCCAFQQA2AuwIIAVCgICAgIABNwLkCEEIIQcgCkUEQEEAIQoMAwtBACEKA0ACQCAXLQAAQQFHBEAgCCAFKALMBiIBTw0EIAVBiBBqIhogBSgCyAYgCmoiBkEoaikDADcDACAFQYAQaiIOIAZBIGopAwA3AwAgBUH4D2oiFSAGQRhqKQMANwMAIAVB8A9qIg0gBkEQaikDADcDACAFQegPaiISIAZBCGopAwA3AwAgFCAGQTBqKQMANwMAIBRBCGoiESAGQThqKQMANwMAIBRBEGoiDyAGQUBrKQMANwMAIBRBGGoiDCAGQcgAaikDADcDACAUQSBqIgkgBkHQAGopAwA3AwAgFEEoaiIEIAZB2ABqKQMANwMAIAUgBikDADcD4A9BACIBRQRAIAVBoAlqIAVB4A9qQeAA/AoAAAsgGiAGQYgBaikDADcDACAOIAZBgAFqKQMANwMAIBUgBkH4AGopAwA3AwAgDSAGQfAAaikDADcDACASIAZB6ABqKQMANwMAIBQgBkGQAWopAwA3AwAgESAGQZgBaikDADcDACAPIAZBoAFqKQMANwMAIAwgBkGoAWopAwA3AwAgCSAGQbABaikDADcDACAEIAZBuAFqKQMANwMAIAUgBkHgAGopAwA3A+APIAENASAkIAVB4A9qQeAA/AoAAAwBCyAFQYgQaiIaIAMgCmoiBkEoaikDADcDACAFQYAQaiIOIAZBIGopAwA3AwAgBUH4D2oiFSAGQRhqKQMANwMAIAVB8A9qIg0gBkEQaikDADcDACAFQegPaiISIAZBCGopAwA3AwAgFCAGQTBqKQMANwMAIBRBCGoiESAGQThqKQMANwMAIBRBEGoiDyAGQUBrKQMANwMAIBRBGGoiDCAGQcgAaikDADcDACAUQSBqIgkgBkHQAGopAwA3AwAgFEEoaiIEIAZB2ABqKQMANwMAIAUgBikDADcD4A9BACIBRQRAIAVBoAlqIAVB4A9qQeAA/AoAAAsgGiAGQYgBaikDADcDACAOIAZBgAFqKQMANwMAIBUgBkH4AGopAwA3AwAgDSAGQfAAaikDADcDACASIAZB6ABqKQMANwMAIBQgBkGQAWopAwA3AwAgESAGQZgBaikDADcDACAPIAZBoAFqKQMANwMAIAwgBkGoAWopAwA3AwAgCSAGQbABaikDADcDACAEIAZBuAFqKQMANwMAIAUgBkHgAGopAwA3A+APIAENACAkIAVB4A9qQeAA/AoAAAsgBSgC5AggCEYEQCAFQeQIakG0wsIAEJ0DIAUoAugIIQcLIAcgCmogBUGgCWpBwAH8CgAAIAUgCEEBaiIINgLsCCAKQcABaiEKIAggJUcNAAsgAiEKDAILQdS6wgBBD0HEwsIAEP4DAAsgCCABQaTCwgAQ2QMAC0HRzsUALQAAGgJAAkBBIEEEENYEIg0EQCAFKAK4BiIJrUIwfiIppyESQQAhBCApQiCIpyASQfj///8HS3INASAFKAK0BiEaIBJFBEAgDSAJNgIIQQghFyANQQg2AgQgDSAJNgIAIAUoArwGIQQMAwtB0c7FAC0AABpBCCEEIBJBCBDWBCIPRQ0BAkAgCQRAQQAhDCAJIQEDQCAMIBJHBEAgDCAPaiIRIAwgGmoiBCkDADcDACARQShqIARBKGopAwA3AwAgEUEgaiAEQSBqKQMANwMAIBFBGGogBEEYaikDADcDACARQRBqIARBEGopAwA3AwAgEUEIaiAEQQhqKQMANwMAIAxBMGohDCABQQFrIgENAQsLIA0gCTYCCCANIA82AgQgDSAJNgIAQdHOxQAtAAAaIAUoArwGIQQgEkEIENYEIhdFDQFBACEMIAkhAQNAIAwgEkYNBSAMIBdqIhEgDCAaaiIPKQMANwMAIBFBKGogD0EoaikDADcDACARQSBqIA9BIGopAwA3AwAgEUEYaiAPQRhqKQMANwMAIBFBEGogD0EQaikDADcDACARQQhqIA9BCGopAwA3AwAgDEEwaiEMIAFBAWsiAQ0ACwwECyANQQA2AgggDSAPNgIEIA1BADYCAEHRzsUALQAAGiAFKAK8BiEEIBJBCBDWBCIXDQMLQQggEkHogcAAEMgEAAtBBEEgEP8EAAsgBCASQeiBwAAQyAQACyANIAk2AhggDSAXNgIUIA0gCTYCECANIAQ2AhwgDSAENgIMIAVBAjYC0A8gBSANNgLMDyAFQQI2AsgPIAVBADYC3A8gBUKAgICAgAE3AtQPAkACQAJAIB0EQEEAIQQgCyEMIBshCSAcIQEDQCAEIAhGDQIgBCAZRg0DIAQgGEYNBCAFQaAJaiAMIAcgASAJEKkBQQAiDUUEQCAFQeAPaiAmQcAB/AoAAAsgBUGoEWoiEiAFQagJaikDADcDACAFQbgRaiIRICNBCGopAgA3AwAgBSAFKQOgCTcDoBEgBSAjKQIANwOwESAFKALQDyIOIAUoAsgPIhdGBEAgBUHID2pB1LzCABCjAyAFKALIDyEXCyAFKALMDyIVIA5BBHRqIg8gBSkDoBE3AgAgD0EIaiASKQMANwIAIAUgDkEBaiIPNgLQDyAPIBdGBH8gBUHID2pB5LzCABCjAyAFKALMDwUgFQsgD0EEdGoiDyAFKQOwETcCACAPQQhqIBEpAwA3AgAgBSAOQQJqNgLQDyAFKALcDyIPIAUoAtQPRgRAIAVB1A9qQfS8wgAQnQMLIA1FBEAgBSgC2A8gD0HAAWxqIAVB4A9qQcAB/AoAAAsgBSAPQQFqNgLcDyAMQcABaiEMIAdBwAFqIQcgCUEwaiEJIAFBMGohASAdIARBAWoiBEcNAAsLIAVByBFqIAVB0A9qKAIANgIAIAUgBSkCyA83A8ARIAVBgICAgHg2AqAJIAVBgAlqIAVBwBFqIAVBoAlqQQBBABCrASAiQQhqIAVB3A9qKAIANgIAICIgBSkC1A83AgAgBUH4CGoiDCAFQYgJaikCADcDACAFIAUpAoAJNwPwCCAFKAKQCSEEIAUoApQJIQEgBSgCmAkhHSAFKAKwBiIJBEAgGiAJQTBsEN8ECyAhIAwpAwA3AwAgBSAFKQPwCDcDsAYgEARAIAsgEEHAAWwQ3wQLIAUoAuQIIgsEQCAFKALoCCALQcABbBDfBAsMAwsgCCAIQaS8wgAQ2QMACyAZIBlBtLzCABDZAwALIBggGEHEvMIAENkDAAsgASELIAQhECAeQQFrIQQgHg0ACwsgBUGgCWoQJiAFLQC4DyEKIAUoAqwPIgEEQCAFKAKwDyABQQJ0EN8ECwJAIAUoAqQJIgFFDQAgASABQQxsQRNqQXhxIgRqQQlqIgFFDQAgBSgCoAkgBGsgARDfBAsgBSgCoAwiAUGAgICAeEYgAUVyRQRAIAUoAqQMIAFBAnQQ3wQLAkACQAJAAkAgCg4CAQIAC0HUusIAQQ9BhMLCABD+AwALIAVBgAlqIgEgCyAdIAMgAiAcIBkgGyAYEEggBSgCiAkiAiAFKAKACUYEQCABQfTBwgAQowMLIAUoAoQJIQMCQCACRQ0AIAJBBHQiAUUNACADQRBqIAMgAfwKAAALIAMgBSkDsAY3AgAgBUGICWogAkEBaiIBNgIAIANBCGogBUG4BmopAwA3AgAgBUHoD2ogATYCACAFIAUpAoAJNwPgDyAFQYCAgIB4NgKgCSAFQbAGaiAFQeAPaiAFQaAJakEAQQAQqwEMAQsgBUGoCWogBUG4BmopAwA3AwAgBSAFKQOwBjcDoAkgBUGwBmogBUGgCWoQaQsgACAFKQOwBjcCACAAQQhqIAVBuAZqKQMANwIAIAUoAsQGIgAEQCAFKALIBiAAQcABbBDfBAsgEARAIAsgEEHAAWwQ3wQLIAUoApwGIgAEQCAFKAKgBiAAQQJ0EN8ECwJAIAUoAhQiAEUNACAAIABBDGxBE2pBeHEiAWpBCWoiAEUNACAFKAIQIAFrIAAQ3wQLIAUoApADIgBBgICAgHhGIABFckUEQCAFKAKUAyAAQQJ0EN8ECyAfBEAgGyAfQTBsEN8ECyAgBEAgHCAgQTBsEN8ECyAFQdARaiQADwsgFSATQeTBwgAQ2QMAC7cqAiN/BH4jAEGQDWsiBSQAIAUgAjYCECAFIAQ2AgwCQAJAAkACQAJAAkAgAiAERgRAIAVBgAdqIAEgAhBwIAUoApQHIRUgBSgCkAchGiAFKAKMByEhIAUoAogHIRYgBSgChAchGyAFKAKAByEiIAVBEGoQIUHRzsUALQAAGkGAA0EIENYEIgZFDQEgBkIANwPgAiAGQp2bvKzc8dCuUzcDGCAGQr2WnK6P5bq8CjcDECAGQqyM5cP37ai35gA3AwggBkKvvp/QmfidhQ43AwAgBkH4AmpCADcDACAGQfACakIANwMAIAZB6AJqQgA3AwAgBkEgakEAQcAC/AsAQQwhHSAFAn8gBkHgAmpB2MPCAEEgEPEDBEBBDCEHQQsMAQsgBkHAAmpB2MPCAEEgEPEDBEBBCyEHQQoMAQsgBkGgAmpB2MPCAEEgEPEDBEBBCiEHQQkMAQsgBkGAAmpB2MPCAEEgEPEDBEBBCSEHQQgMAQsgBkHgAWpB2MPCAEEgEPEDBEBBCCEHQQcMAQsgBkHAAWpB2MPCAEEgEPEDBEBBByEHQQYMAQsgBkGgAWpB2MPCAEEgEPEDBEBBBiEHQQUMAQsgBkGAAWpB2MPCAEEgEPEDBEBBBSEHQQQMAQsgBkHgAGpB2MPCAEEgEPEDBEBBBCEHQQMMAQsgBkFAa0HYw8IAQSAQ8QMEQEEDIQdBAgwBCyAGQSBqQdjDwgBBIBDxAwRAQQIhB0EBDAELIAZB2MPCAEEgEPEDBEBBASEHQQAMAQtB0c7FAC0AABpBIEEIENYEIgFFDQMgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIAZBgAMQ3wRBASEHIAEhBkEBIR1BfwsiCzYC3AQgBSAHNgLYBCAFIAY2AtQEIAUgHTYC0AQgBUEANgLsBCAFQoCAgICAATcC5AQgBSgCuAIhFCAFKAK8AiIQQQdNBEAgEEUEQEF+IRkMCAsgFC0AAEH/AUYNBCAQQQFGDQUgFC0AAUH/AUYNBCAQQQJGDQUgFC0AAkH/AUYNBCAQQQNGDQUgFC0AA0H/AUYNBCAQQQRGDQUgFC0ABEH/AUYNBCAQQQVGDQUgFC0ABUH/AUYNBCAQQQZGDQUgFC0ABkH/AUcNBQwECyAFIBQgEBCEAyAFKAIAQQFGDQMgEEECayEZDAULIAVBADYCgAcgBUEQaiAFQQxqIAVBgAdqQcTBwgAQlwQAC0EIQYADEP8EAAtBCEEgEP8EAAsgAkUNACACQQd0IQogAyEEA0AgBUHwBGogBBCvASAFKALsBCIBIAUoAuQERgRAIAVB5ARqQdTBwgAQpAMLIAUoAugEIAFBB3RqIAVB8ARqQYAB/AoAACAFIAFBAWo2AuwEIARBgAFqIQQgCkGAAWsiCg0ACwsgEEECayEZIBBBAU0NAQsCQAJAAkACQAJAAkACQAJAAkAgFCAZai0AAA4CAQACC0HRzsUALQAAGkEgQQQQ1gQiCUUNAkHRzsUALQAAGiAHQQV0IhFBCBDWBCIBRQ0DQQAhBANAIAQgEUcEQCABIARqIg0gBCAGaiIKKQMANwMAIA1BGGogCkEYaikDADcDACANQRBqIApBEGopAwA3AwAgDUEIaiAKQQhqKQMANwMAIBEgBEEgaiIERw0BCwsgCSAHNgIIIAkgATYCBCAJIAc2AgBBACEEQdHOxQAtAAAaIBFBCBDWBCIKRQ0EIAdBBXQhAQNAIAEgBEcEQCAEIApqIhEgBCAGaiINKQMANwMAIBFBGGogDUEYaikDADcDACARQRBqIA1BEGopAwA3AwAgEUEIaiANQQhqKQMANwMAIAEgBEEgaiIERw0BCwsgCSAHNgIYIAkgCjYCFCAJIAc2AhAgCSALNgIcIAkgCzYCDCAFQQI2AtALIAUgCTYCzAsgBUECNgLIC0EAIQQgBUEANgLcCyAFQoCAgICAATcC1AsgAgRAIAVBkAhqIQggBUGQB2ohEiADIQogGiEOIBshFwNAIAQgFkYNByAEIBVGDQggBUGAB2ogCiAXIA4QvAFBAEUEQCAFQeALaiASQYAB/AoAAAsgBUH4DGoiESAFQYgHaikDADcDACAFQegGaiINIAhBCGopAgA3AwAgBSAFKQOABzcD8AwgBSAIKQIANwPgBiAFKALQCyIHIAUoAsgLIglGBEAgBUHIC2pB9LvCABCjAyAFKALICyEJCyAFKALMCyILIAdBBHRqIgEgBSkD8Aw3AgAgAUEIaiARKQMANwIAIAUgB0EBaiIBNgLQCyABIAlGBH8gBUHIC2pBhLzCABCjAyAFKALMCwUgCwsgAUEEdGoiASAFKQPgBjcCACABQQhqIA0pAwA3AgAgBSAHQQJqNgLQCyAFKALcCyIBIAUoAtQLRgRAIAVB1AtqQZS8wgAQpAMLIAxFBEAgBSgC2AsgAUEHdGogBUHgC2pBgAH8CgAACyAFIAFBAWo2AtwLIApBgAFqIQogDkEgaiEOIBdBIGohFyACIARBAWoiBEcNAAsLIAVBiA1qIAVB0AtqKAIANgIAIAUgBSkCyAs3A4ANIAVBgICAgHg2AuAMIAVBgAdqIAVBgA1qIAVB4AxqQQBBABDBASAFQZgHaiIBIAVB3AtqKAIANgIAIAVB+AVqIAVBiAdqKQIANwMAIAUgBSkC1AsiKDcCkAcgBSAFKQKABzcD8AUgBSAoPgKMBiAFIAUoApQHNgKIBiAFIAEoAgA2AoQGIAVBjAZqIQEgBUGEBmohCiAFQYgGaiEOIAVB8AVqIQQMBwsgBUGAB2ogBUHQBGogAyACIBsgFiAaIBUQ2wEgBUGYBmogBUGIB2opAgA3AwAgBSAFKQKABzcDkAYgBSAFKAKQBzYCrAYgBSAFKAKUBzYCqAYgBSAFKAKYBzYCpAYgBUGsBmohASAFQaQGaiEKIAVBqAZqIQ4gBUGQBmohBAwGC0HUusIAQQ9B1MLCABD+AwALQQRBIBD/BAALQQggEUHogcAAEMgEAAtBCCARQeiBwAAQyAQACyAWIBZB1LvCABDZAwALIBUgFUHku8IAENkDAAsgBiAdQQV0EN8EIAVB2ARqIiMgBEEIaikCADcDACAFIAQpAgA3A9AEIAooAgAhHCAOKAIAIQQgASgCACENIBkEQEEBIAIgAkEBTRshJiAFQfAGaiEkIAVBkAhqISUgBUGQB2ohHiAFQYAMaiETIAVBwAdqIQ8gEEECSyEZIAIhCiAQQQNrIh0hAQNAIAEhEQJAAkACQAJAAkACQAJAIBkEQCABIBRqIhItAAAiAQ4CAQMCCyAdIBBBlMLCABDZAwALIAVBgAdqIAVB0ARqIAQgHCAbIBYgGiAVENsBIAVBuAZqIgkgBUGIB2opAgA3AwAgBSAFKQKABzcDsAYgBSgCkAchCyAFKAKUByEBIAUoApgHIRwgBSgC0AQiBgRAIAUoAtQEIAZBBXQQ3wQLICMgCSkDADcDACAFIAUpA7AGNwPQBCANBEAgBCANQQd0EN8ECwwFCyABQf8BRw0BC0EAIQ4gBUEANgLMBiAFQoCAgICAATcCxAZBCCEXIApFBEBBACEKDAMLQQAhBwNAAkAgEi0AAEEBRwRAIA4gBSgC7AQiAU8NBCAFQfgLaiAFKALoBCAHaiIIQRhqKQMAIik3AwAgBUHwC2ogCEEQaikDACIqNwMAIAVB6AtqIAhBCGopAwAiKzcDACATIAhBIGopAwA3AwAgE0EYaiIMIAhBOGopAwA3AwAgE0EQaiIJIAhBMGopAwA3AwAgE0EIaiIGIAhBKGopAwA3AwAgBSAIKQMAIig3A+ALIAVBmAdqICk3AwAgHiAqNwMAIAVBiAdqICs3AwAgBUG4B2ogBUGYDGoiCikDADcDACAFQbAHaiAFQZAMaiILKQMANwMAIAVBqAdqIAVBiAxqIgEpAwA3AwAgBUGgB2ogEykDADcDACAFICg3A4AHDAELIBNBGGoiDCADIAdqIghBOGopAwA3AwAgE0EQaiIJIAhBMGopAwA3AwAgE0EIaiIGIAhBKGopAwA3AwAgEyAIQSBqKQMANwMAIAVBmAdqIAhBGGopAwA3AwAgHiAIQRBqKQMANwMAIAVBiAdqIAhBCGopAwA3AwAgBUG4B2ogBUGYDGoiCikDADcDACAFQbAHaiAFQZAMaiILKQMANwMAIAVBqAdqIAVBiAxqIgEpAwA3AwAgBUGgB2ogEykDADcDACAFIAgpAwA3A4AHCyATIAhB4ABqKQMANwMAIAYgCEHoAGopAwA3AwAgCSAIQfAAaikDADcDACAMIAhB+ABqKQMANwMAIA8gCEFAaykDADcDACAPQQhqIAhByABqKQMANwMAIA9BEGogCEHQAGopAwA3AwAgD0EYaiAIQdgAaikDADcDACAPQSBqIBMpAwA3AwAgD0EoaiABKQMANwMAIA9BMGogCykDADcDACAPQThqIAopAwA3AwAgBSgCxAYgDkYEQCAFQcQGakG0wsIAEKQDIAUoAsgGIRcLIAcgF2ogBUGAB2pBgAH8CgAAIAUgDkEBaiIONgLMBiAHQYABaiEHIA4gJkcNAAsgAiEKDAILQdS6wgBBD0HEwsIAEP4DAAsgDiABQaTCwgAQ2QMAC0HRzsUALQAAGgJAAkBBIEEEENYEIgcEQCAFKALYBCIGQQV0IQhBACEBIAZB////P0sgCEH4////B0tyDQEgBSgC1AQhHyAIRQRAIAcgBjYCCEEIIRggB0EINgIEIAcgBjYCACAFKALcBCESDAMLQdHOxQAtAAAaQQghASAIQQgQ1gQiEkUNAQJAIAYEQEEAIQEgBiELA0AgASAIRwRAIAEgEmoiDCABIB9qIgkpAwA3AwAgDEEYaiAJQRhqKQMANwMAIAxBEGogCUEQaikDADcDACAMQQhqIAlBCGopAwA3AwAgAUEgaiEBIAtBAWsiCw0BCwsgByAGNgIIIAcgEjYCBCAHIAY2AgBB0c7FAC0AABogBSgC3AQhEiAIQQgQ1gQiGEUNAUEAIQEgBiELA0AgASAIRg0FIAEgGGoiDCABIB9qIgkpAwA3AwAgDEEYaiAJQRhqKQMANwMAIAxBEGogCUEQaikDADcDACAMQQhqIAlBCGopAwA3AwAgAUEgaiEBIAtBAWsiCw0ACwwECyAHQQA2AgggByASNgIEIAdBADYCAEHRzsUALQAAGiAFKALcBCESIAhBCBDWBCIYDQMLQQggCEHogcAAEMgEAAtBBEEgEP8EAAsgASAIQeiBwAAQyAQACyAHIAY2AhggByAYNgIUIAcgBjYCECAHIBI2AhwgByASNgIMIAVBAjYC0AsgBSAHNgLMCyAFQQI2AsgLIAVBADYC3AsgBUKAgICAgAE3AtQLAkACQAJAIBwEQEEAIQEgBCEGIBohCSAbIQsDQCABIA5GDQIgASAWRg0DIAEgFUYNBCAFQYAHaiAGIBcgCyAJEJkBQQAiB0UEQCAFQeALaiAeQYAB/AoAAAsgBUHoDGoiCCAFQYgHaikDADcDACAFQfgMaiISICVBCGopAgA3AwAgBSAFKQOABzcD4AwgBSAlKQIANwPwDCAFKALQCyIgIAUoAsgLIhhGBEAgBUHIC2pB1LzCABCjAyAFKALICyEYCyAFKALMCyInICBBBHRqIgwgBSkD4Aw3AgAgDEEIaiAIKQMANwIAIAUgIEEBaiIMNgLQCyAMIBhGBH8gBUHIC2pB5LzCABCjAyAFKALMCwUgJwsgDEEEdGoiDCAFKQPwDDcCACAMQQhqIBIpAwA3AgAgBSAgQQJqNgLQCyAFKALcCyIMIAUoAtQLRgRAIAVB1AtqQfS8wgAQpAMLIAdFBEAgBSgC2AsgDEEHdGogBUHgC2pBgAH8CgAACyAFIAxBAWo2AtwLIAZBgAFqIQYgF0GAAWohFyAJQSBqIQkgC0EgaiELIBwgAUEBaiIBRw0ACwsgBUGIDWogBUHQC2ooAgA2AgAgBSAFKQLICzcDgA0gBUGAgICAeDYCgAcgBUHgBmogBUGADWogBUGAB2pBAEEAEMEBICRBCGogBUHcC2ooAgA2AgAgJCAFKQLUCzcCACAFQdgGaiIJIAVB6AZqKQIANwMAIAUgBSkC4AY3A9AGIAUoAvAGIQsgBSgC9AYhASAFKAL4BiEcIAUoAtAEIgYEQCAfIAZBBXQQ3wQLICMgCSkDADcDACAFIAUpA9AGNwPQBCANBEAgBCANQQd0EN8ECyAFKALEBiIEBEAgBSgCyAYgBEEHdBDfBAsMAwsgDiAOQaS8wgAQ2QMACyAWIBZBtLzCABDZAwALIBUgFUHEvMIAENkDAAsgASEEIAshDSARQQFrIQEgEQ0ACwsgBUGAB2oQISAFLQC4CyEKIAUoAqwLIgEEQCAFKAKwCyABQQJ0EN8ECwJAIAUoAuQIIgFFDQAgASABQQxsQRNqQXhxIgtqQQlqIgFFDQAgBSgC4AggC2sgARDfBAsgBSgCkAkiAUGAgICAeEYgAUVyRQRAIAUoApQJIAFBAnQQ3wQLAkACQAJAAkAgCg4CAQIAC0HUusIAQQ9BhMLCABD+AwALIAVB4AZqIgEgBCAcIAMgAiAbIBYgGiAVEE4gBSgC6AYiAiAFKALgBkYEQCABQfTBwgAQowMLIAUoAuQGIQMCQCACRQ0AIAJBBHQiAUUNACADQRBqIAMgAfwKAAALIAMgBSkD0AQ3AgAgBUHoBmogAkEBaiIBNgIAIANBCGogBUHYBGopAwA3AgAgBUHoC2ogATYCACAFIAUpAuAGNwPgCyAFQYCAgIB4NgKAByAFQdAEaiAFQeALaiAFQYAHakEAQQAQwQEMAQsgBUGIB2ogBUHYBGopAwA3AwAgBSAFKQPQBDcDgAcgBUHQBGogBUGAB2oQdgsgACAFKQPQBDcCACAAQQhqIAVB2ARqKQMANwIAIAUoAuQEIgAEQCAFKALoBCAAQQd0EN8ECyANBEAgBCANQQd0EN8ECyAFKAK8BCIABEAgBSgCwAQgAEECdBDfBAsCQCAFKAL0ASIARQ0AIAAgAEEMbEETakF4cSIBakEJaiIARQ0AIAUoAvABIAFrIAAQ3wQLIAUoAqACIgBBgICAgHhGIABFckUEQCAFKAKkAiAAQQJ0EN8ECyAhBEAgGiAhQQV0EN8ECyAiBEAgGyAiQQV0EN8ECyAFQZANaiQADwsgGSAQQeTBwgAQ2QMAC8ctAgl/Dn4jAEGgDWsiAyQAIANB4AZqIAFBGGopAwA3AwAgA0HYBmogAUEQaikDADcDACADQdAGaiABQQhqKQMANwMAIANB8AZqIAJBCGopAwA3AwAgA0H4BmogAkEQaikDADcDACADQYAHaiACQRhqKQMANwMAIANBADoAiAcgAyABKQMANwPIBiADIAIpAwA3A+gGIANB6AZqIQcCQAJAAkACQCADQcgGakHo0cEAQSAQ8QNFBEAgB0Ho0cEAQSAQ8QNFDQELIANBsAdqIgIQISADQdAHaiEEIANBkA1qIAJBGGopAwA3AwAgA0GIDWogAkEQaikDADcDACADQYANaiACQQhqKQMANwMAIAMgAikDADcD+AwgA0HQBWogAykD+AYiDEIAIAMpA4AHIg1CABDJAyADQcAFaiADKQPwBiIOQgAgDUIAEMkDIANBsAVqIAMpA+gGIg9CACANQgAQyQMgA0GABmogDkIAIAxCABDJAyADQfAFaiAPQgAgDEIAEMkDIANBoAZqIA9CACAOQgAQyQMgA0GgBWogDUIAIA1CABDJAyADQeAFaiAMQgAgDEIAEMkDIANBkAZqIA5CACAOQgAQyQMgA0GwBmogD0IAIA9CABDJAyADQZAFaiADKQOgBSISQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyADQYAFaiAMQgBCjZXHw5bS2sCXf0IAEMkDIANB8ARqIAxCAELdsIWM6LaRqLh/QgAQyQMgA0HgBGogDEIAQqnAxomuzpOyMEIAEMkDIAMpA6gGIAMpA/gFIAMpA7gFIAMpA8gFIAMpA9gFIg0gAykDwAV8IgwgDVStfCIOIAMpA7AFfCINIA5UrXwiDyADKQPwBXwiDiAPVK18IA4gDiADKQOIBiANIA0gAykDgAZ8Ig9WrXx8IhFWrXwiDSADKQOgBnwiDiANVK18Ig1CP4ggAykDuAYgAykDsAYiEyANQgGGIA5CP4iEfCIQIBNUrXwgECADKQOYBiADKQPoBSADKQPgBSITIAxCAYYgAykD0AUiFEI/iIR8Ig0gE1StfCANIAMpA6gFIhMgFEIBhnwiFCATVK18IhMgDVStfCINIA9CAYYgDEI/iIR8IhUgDVStIg0gAykDkAZ8IgwgDVStfCAMIBFCAYYgD0I/iIR8Ig0gDFStfCIMIA5CAYYgEUI/iIR8Ig4gDFStfCIPIBBUrXx8IRECfwJAIAMpA+gEIAMpA/gEIAMpA4gFIAMpA5gFIAMpA5AFIgwgEkJ9g3wgDFStfCIQIAMpA4AFfCIMIBBUrXwgDCAUfCIQIAxUrXwiEiADKQPwBHwiDCASVK18IAwgE3wiEiAMVK18IhMgAykD4AR8IgwgE1StfCAMIBV8IhMgDFStfCIMUA0AIAwgDXwiDSAMVCICRQ0AIAKtIgwgDnwiDiAMWg0AIAwgDlatIgwgD3wiDyAMWg0AIAwgD1atIgwgEXwiESAMVAwBC0EACyEGIAQpAwAhFCAEKQMIIRUgBCkDECEXIAQpAxghGCADQdAEaiAQQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyADQcAEaiAMQgBCjZXHw5bS2sCXf0IAEMkDIANBsARqIAxCAELdsIWM6LaRqLh/QgAQyQMgA0GgBGogDEIAQqnAxomuzpOyMEIAEMkDAkAgAykDqAQgAykDuAQgAykDyAQgAykD2AQgAykD0AQiDCAQfCAMVK18IhAgAykDwAR8IgwgEFStfCAMIBJ8IhAgDFStfCISIAMpA7AEfCIMIBJUrXwgDCATfCISIAxUrXwiEyADKQOgBHwiDCATVK18IAwgDXwiEyAMVK18IgxQDQAgDCAOfCIOIAxaDQAgDCAOVq0iDCAPfCIPIAxaDQAgDCAPVq0iDCARfCIRIAxUIQULIANBkARqIBBCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIANBgARqIAxCAEKNlcfDltLawJd/QgAQyQMgA0HwA2ogDEIAQt2whYzotpGouH9CABDJAyADQeADaiAMQgBCqcDGia7Ok7IwQgAQyQNBACECIAMpA+gDIAMpA/gDIAMpA4gEIAMpA5gEIAMpA5AEIgwgEHwgDFStfCINIAMpA4AEfCIMIA1UrXwgDCASfCINIAxUrXwiECADKQPwA3wiDCAQVK18IAwgE3wiECAMVK18IhIgAykD4AN8IgwgElStfCAMIA58Ig4gDFStfCIMUEUEQCAMIA98Ig8gDFQiAq0iDCARfCISIBEgAhshESACIAwgElZxIQILIANB0ANqIA1CiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIANBwANqIAxCAEKNlcfDltLawJd/QgAQyQMgA0GwA2ogDEIAQt2whYzotpGouH9CABDJAyADQaADaiAMQgBCqcDGia7Ok7IwQgAQyQMgAykDqAMgAykDuAMgAykDyAMgAykD2AMgAykD0AMiDCANfCAMVK18Ig0gAykDwAN8IgwgDVStfCAMIBB8IhAgDFStfCINIAMpA7ADfCIMIA1UrXwgDCAOfCINIAxUrXwiDiADKQOgA3wiDCAOVK18IAwgD3wiDiAMVK18IgwgEXwiDyARIAxCAFIiBBshEQJAAkACQCAFIAZyIAJyIAwgD1YiAq0gDCAEG0IAUnIgAiAEcSARQqnAxomuzpOyMFZycg0AIBFCqcDGia7Ok7IwUgRAIA0hDAwDCyAOQt2whYzotpGouH9WDQAgDkLdsIWM6LaRqLh/UgRAIA0hDAwDC0LdsIWM6LaRqLh/IQ8gDUKNlcfDltLawJd/Vg0BIA1CjZXHw5bS2sCXf1IEQCANIQwMAwsgEELG+vPD7YKjkDxWDQEgDSEMDAILIA4hDwsgDULz6ri86a2lv+gAfCIOIBBCx/rzw+2Co5A8VK0iEn0hDCAPQqPP+vOXye7XxwB8IhMgDUKNlcfDltLawJd/VCAOIBJUcq0iDX0hDiARIA9C3bCFjOi2kai4f1QgDSATVnKtfUKpwMaJrs6TsjB9IREgEELH+vPD7YKjkDx9IRALIAMgEDcDkAwgAyAMNwOIDCADIA43A4AMIAMgETcD+AsgA0GwAmogAykD2AYiDEIAIAMpA+AGIg1CABDJAyADQaACaiADKQPQBiIOQgAgDUIAEMkDIANBkAJqIAMpA8gGIg9CACANQgAQyQMgA0HgAmogDkIAIAxCABDJAyADQdACaiAPQgAgDEIAEMkDIANBgANqIA9CACAOQgAQyQMgA0GAAmogDUIAIA1CABDJAyADQcACaiAMQgAgDEIAEMkDIANB8AJqIA5CACAOQgAQyQMgA0GQA2ogD0IAIA9CABDJAyADQfABaiADKQOAAiISQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyADQeABaiAMQgBCjZXHw5bS2sCXf0IAEMkDIANB0AFqIAxCAELdsIWM6LaRqLh/QgAQyQMgA0HAAWogDEIAQqnAxomuzpOyMEIAEMkDIAMpA4gDIAMpA9gCIAMpA5gCIAMpA6gCIAMpA7gCIg0gAykDoAJ8IgwgDVStfCIOIAMpA5ACfCINIA5UrXwiDyADKQPQAnwiDiAPVK18IA4gDiADKQPoAiANIA0gAykD4AJ8Ig9WrXx8IhFWrXwiDSADKQOAA3wiDiANVK18Ig1CP4ggAykDmAMgAykDkAMiEyANQgGGIA5CP4iEfCIQIBNUrXwgECADKQP4AiADKQPIAiADKQPAAiITIAxCAYYgAykDsAIiFkI/iIR8Ig0gE1StfCANIAMpA4gCIhMgFkIBhnwiFiATVK18IhMgDVStfCINIA9CAYYgDEI/iIR8IhkgDVStIg0gAykD8AJ8IgwgDVStfCAMIBFCAYYgD0I/iIR8Ig0gDFStfCIMIA5CAYYgEUI/iIR8Ig4gDFStfCIPIBBUrXx8IRFBACEFAn8CQCADKQPIASADKQPYASADKQPoASADKQP4ASADKQPwASIMIBJCfYN8IAxUrXwiECADKQPgAXwiDCAQVK18IAwgFnwiECAMVK18IhIgAykD0AF8IgwgElStfCAMIBN8IhIgDFStfCITIAMpA8ABfCIMIBNUrXwgDCAZfCITIAxUrXwiDFANACAMIA18Ig0gDFQiAkUNACACrSIMIA58Ig4gDFoNACAMIA5WrSIMIA98Ig8gDFoNACAMIA9WrSIMIBF8IhEgDFQMAQtBAAshBiADQbABaiAQQonHmaSu8IHph39+IgxCAELH+vPD7YKjkDxCABDJAyADQaABaiAMQgBCjZXHw5bS2sCXf0IAEMkDIANBkAFqIAxCAELdsIWM6LaRqLh/QgAQyQMgA0GAAWogDEIAQqnAxomuzpOyMEIAEMkDAkAgAykDiAEgAykDmAEgAykDqAEgAykDuAEgAykDsAEiDCAQfCAMVK18IhAgAykDoAF8IgwgEFStfCAMIBJ8IhAgDFStfCISIAMpA5ABfCIMIBJUrXwgDCATfCISIAxUrXwiEyADKQOAAXwiDCATVK18IAwgDXwiEyAMVK18IgxQDQAgDCAOfCIOIAxaDQAgDCAOVq0iDCAPfCIPIAxaDQAgDCAPVq0iDCARfCIRIAxUIQULIANB8ABqIBBCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIANB4ABqIAxCAEKNlcfDltLawJd/QgAQyQMgA0HQAGogDEIAQt2whYzotpGouH9CABDJAyADQUBrIAxCAEKpwMaJrs6TsjBCABDJA0EAIQIgAykDSCADKQNYIAMpA2ggAykDeCADKQNwIgwgEHwgDFStfCINIAMpA2B8IgwgDVStfCAMIBJ8Ig0gDFStfCIQIAMpA1B8IgwgEFStfCAMIBN8IhAgDFStfCISIAMpA0B8IgwgElStfCAMIA58Ig4gDFStfCIMUEUEQCAMIA98Ig8gDFQiAq0iDCARfCISIBEgAhshESACIAwgElZxIQILIANBMGogDUKJx5mkrvCB6Yd/fiIMQgBCx/rzw+2Co5A8QgAQyQMgA0EgaiAMQgBCjZXHw5bS2sCXf0IAEMkDIANBEGogDEIAQt2whYzotpGouH9CABDJAyADIAxCAEKpwMaJrs6TsjBCABDJAyADKQMIIAMpAxggAykDKCADKQM4IAMpAzAiDCANfCAMVK18Ig0gAykDIHwiDCANVK18IAwgEHwiECAMVK18Ig0gAykDEHwiDCANVK18IAwgDnwiDSAMVK18Ig4gAykDAHwiDCAOVK18IAwgD3wiDiAMVK18IgwgEXwiDyARIAxCAFIiBBshEQJAAkACQCAFIAZyIAJyIAwgD1YiAq0gDCAEG0IAUnIgAiAEcSARQqnAxomuzpOyMFZycg0AIBFCqcDGia7Ok7IwUgRAIA0hDAwDCyAOQt2whYzotpGouH9WDQAgDkLdsIWM6LaRqLh/UgRAIA0hDAwDC0LdsIWM6LaRqLh/IQ8gDUKNlcfDltLawJd/Vg0BIA1CjZXHw5bS2sCXf1IEQCANIQwMAwsgEELG+vPD7YKjkDxWDQEgDSEMDAILIA4hDwsgDULz6ri86a2lv+gAfCIOIBBCx/rzw+2Co5A8VK0iEn0hDCAPQqPP+vOXye7XxwB8IhMgDUKNlcfDltLawJd/VCAOIBJUcq0iDX0hDiARIA9C3bCFjOi2kai4f1QgDSATVnKtfUKpwMaJrs6TsjB9IREgEELH+vPD7YKjkDx9IRALIAMgEDcD0AwgAyAMNwPIDCADIA43A8AMIAMgETcDuAwgA0HwDGoiAiABQRhqIgQpAwA3AwAgA0HoDGoiBSABQRBqIgYpAwA3AwAgA0HgDGoiCCABQQhqIgkpAwA3AwAgAyABKQMANwPYDCADQZgMaiADQbgMaiIKIANB2AxqIgsQfiACIAQpAwA3AwAgBSAGKQMANwMAIAggCSkDADcDACADIAEpAwA3A9gMIAogA0H4DGogCxB+QqnAxomuzpOyMCEMIAMpA6AMIg4gAykDwAx8Ig0gDlQgDSADKQOoDCIOIAMpA8gMfCIPIA5UIA8gDyADKQOwDCIOIAMpA9AMfCIRIA5UrXwiDlZyrXwiDyANVHKtIAMpA7gMIAMpA5gMfHwiECENAkACQAJAIBBCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hDCAPIg1C3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQwgDiINQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQwgESINQsf688PtgqOQPFENAQsgDCANWA0AIA8hDCAOIQ0MAQsgDkLz6ri86a2lv+gAfCIMIBFCx/rzw+2Co5A8VK0iEn0hDSAPQqPP+vOXye7XxwB8IhMgDkKNlcfDltLawJd/VCAMIBJUcq0iDn0hDCAQIA9C3bCFjOi2kai4f1QgDiATVnKtfUKpwMaJrs6TsjB9IRAgEULH+vPD7YKjkDx9IRELQqnAxomuzpOyMCESIBAgFHwgDCAMIBV8Ig9WIA8gDyANIA0gF3wiDFYgDCARIBh8IhAgEVStfCIOIAxUcq18Ig9Wcq18IhEhDAJAAkACQCARQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRIgDyIMQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyESIA4iDEKNlcfDltLawJd/Ug0AQsf688PtgqOQPCESIBAiDELH+vPD7YKjkDxRDQELIAwgEloNACAPIQwgDiENDAELIA5C8+q4vOmtpb/oAHwiDCAQQsf688PtgqOQPFStIhJ9IQ0gD0Kjz/rzl8nu18cAfCITIA5CjZXHw5bS2sCXf1QgDCASVHKtIg59IQwgESAPQt2whYzotpGouH9UIA4gE1ZyrX1CqcDGia7Ok7IwfSERIBBCx/rzw+2Co5A8fSEQCyADIBA3A/AMIAMgDTcD6AwgAyAMNwPgDCADIBE3A9gMIANB+AtqIANB2AxqQSAQ8QMgAygC3AsiAQRAIAMoAuALIAFBAnQQ3wQLAkAgAygClAkiAUUNACABIAFBDGxBE2pBeHEiBGpBCWoiAUUNACADKAKQCSAEayABEN8ECyADKALACSIBQYCAgIB4RiABRXJFBEAgAygCxAkgAUECdBDfBAsNAQsgACADQcgGakHIAPwKAAAMAQsgA0H4DGoiASADQcgGahDNASADQQA2AuAMIANCgICAgBA3AtgMIANBsNfBADYCtAcgA0KggICADjcCuAcgAyADQdgMaiICNgKwByABIANBsAdqIgEQ0wINASADQZgHaiADQeAMaigCADYCACADIAMpAtgMNwOQByABIAcQzQEgA0EANgKADCADQoCAgIAQNwL4CyADQbDXwQA2ArwMIANCoICAgA43AsAMIAMgA0H4C2o2ArgMIAEgA0G4DGoQ0wINASADQagHaiADQYAMaigCADYCACADIAMpAvgLNwOgByADQQM2AtwMIANB6PXBADYC2AwgA0ICNwLkDCADIANBoAdqrUKAgICAwAeENwOgDCADIANBkAdqrUKAgICAwAeENwOYDCADIANBmAxqNgLgDCAAIAIQ0gIgAygCoAciAQRAIAMoAqQHIAEQ3wQLIAMoApAHIgEEQCADKAKUByABEN8ECyAAQQI6AEALIANBoA1qJAAPC0HY18EAQTcgA0GfDWpByNfBAEHc2MEAEMoDAAvVJgIVfgp/IwBBoARrIhckACABQQV0IRxBgGUhAQNAAn8CQCAcIAEiGEEgaiIBagRAQpGAgICAgICACCEGIBggHGoiGUGo9MEAaikDACAAIBhqIhhBgBtqIhopAwB8IBhBiBtqIh0pAwAiAiAZQbD0wQBqKQMAfCILIAJUIAsgGEGQG2oiHikDACICIBlBuPTBAGopAwB8IgUgAlQgBSAFIBhBmBtqIh8pAwAiAyAZQcD0wQBqKQMAfCICIANUrXwiBFZyrXwiAyALVHKtfCIJIQoCQAJAIAlCkYCAgICAgIAIUQRAQgEhBiACQgFRDQEgAiEKIAMgBIRCAFINAQsgBiAKWA0AIAIhCiAEIQsgAyEMDAELIAJCAX0hCiAEIAJQrSICfSELIAMgAiAEVq0iAn0hDELu/////////3dC7/////////93IAIgA1YbIAl8IQkLIB0gDDcDACAaIAk3AwAgHiALNwMAIB8gCjcDACAXQbADaiALQgAgCkIAEMkDIBdBoANqIAxCACAKQgAQyQMgF0GQA2ogCUIAIApCABDJAyAXQeADaiAMQgAgC0IAEMkDIBdB0ANqIAlCACALQgAQyQMgF0GABGogCUIAIAxCABDJAyAXQYADaiAKQgAgCkIAEMkDIBdBwANqIAtCACALQgAQyQMgF0HwA2ogDEIAIAxCABDJAyAXQZAEaiAJQgAgCUIAEMkDIBdB8AJqQgAgFykDgAMiD31CAEKRgICAgICAgAhCABDJAyAXKQOIBCAXKQPYAyAXKQOYAyAXKQOoAyAXKQO4AyICIBcpA6ADfCIFIAJUrXwiAiAXKQOQA3wiBCACVK18IgIgFykD0AN8IgMgAlStfCADIAMgFykD6AMgBCAEIBcpA+ADfCINVq18fCIOVq18IgIgFykDgAR8IgcgAlStfCIDQj+IIBcpA5gEIBcpA5AEIgIgA0IBhiAHQj+IhHwiCSACVK18IAkgFykD+AMgFykDyAMgFykDwAMiAiAFQgGGIBcpA7ADIgNCP4iEfCIEIAJUrXwgBCAXKQOIAyICIANCAYZ8IgggAlStfCIGIARUrXwiAiANQgGGIAVCP4iEfCIFIAJUrSICIBcpA/ADfCIDIAJUrXwgAyADIA5CAYYgDUI/iIR8IgNWrXwiAiAHQgGGIA5CP4iEfCIEIAJUrXwiByAJVK18fCEJQQAhICAXKQP4AiAPQn2DIgIgD30gAlStIgIgCHwiDiACVK0iAiAGfCIGIAJUrSICIBcpA/ACfCIIIAJUrXwgBSAIfCIFIAhUrXwiAlANASACIAN8IgMgAlQiGEUNASAYrSICIAR8IgQgAloNASACIARWrSICIAd8IgcgAloNASACIAdWrSICIAl8IgkgAlQMAgtB6wBB6wBB7PTBABDZAwALQQALIRggF0HgAmpCACAOfUIAQpGAgICAgICACEIAEMkDAkAgFykD6AIgDkIAUq0iAiAGfCIIIAJUrSICIAV8IgUgAlStIgIgFykD4AJ8IgYgAlStfCADIAZ8IgMgBlStfCICUA0AIAIgBHwiBCACWg0AIAIgBFatIgIgB3wiByACWg0AIAIgB1atIgIgCXwiCSACVCEgCyAXQdACakIAIAh9QgBCkYCAgICAgIAIQgAQyQNBACEbIBcpA9gCIAhCAFKtIgIgBXwiBiACVK0iAiADfCIFIAJUrSICIBcpA9ACfCIDIAJUrXwgAyADIAR8IgRWrXwiAlBFBEAgAiAHfCIHIAJUIhmtIgMgCXwiAiAJIBkbIQkgGSACIANUcSEbCyAXQcACakIAIAZ9QgBCkYCAgICAgIAIQgAQyQMgFykDyAIgBkIAUq0iAiAFfCIFIAJUrSICIAR8IgMgAlStIgIgFykDwAJ8IgQgAlStfCAEIAd8IgIgBFStfCIGIAl8IgQgCSAGQgBSIhkbIQgCfgJAIBggIHIgG3IgBCAGVCIYrSAGIBkbQgBSciAYIBlxIAhCkYCAgICAgIAIVnJyDQAgCEKRgICAgICAgAhSBEAgBSEJIAMhByACIQQgCAwCC0IAIQkgAiADhEIAUg0AQgAhB0IAIQRCkYCAgICAgIAIIAVQDQEaCyAFQgF9IQkgAyAFUK0iBH0hByACIAMgBFStIgN9IQQgCCACIANUrX1CkYCAgICAgIAIfQshDSABQeAAayAXQbACaiAJQgAgCkIAEMkDIBdB8AFqIAdCACAKQgAQyQMgF0GwAWogBEIAIApCABDJAyAXQfAAaiANQgAgCkIAEMkDIBdBoAJqQgAgFykDsAIiAn1CAEKRgICAgICAgAhCABDJAyAXQZACaiAJQgAgC0IAEMkDIBdB0AFqIAdCACALQgAQyQMgF0GQAWogBEIAIAtCABDJAyAXQeAAaiANQgAgC0IAEMkDIBdB4AFqQgAgAkIAUq0iBSAXKQO4AiIDIBcpA/ABfCICfCIIIBcpA5ACfCIKfUIAQpGAgICAgICACEIAEMkDIBdBgAJqIAlCACAMQgAQyQMgF0HAAWogB0IAIAxCABDJAyAXQYABaiAEQgAgDEIAEMkDIBdB0ABqIA1CACAMQgAQyQMgF0GgAWpCACAKQgBSrSIMIAUgCFatIgYgFykD+AEgAiADVK18IgsgFykDsAF8IgN8IhAgFykD0AF8Ig4gFykDmAIgCCAKVq18fCICfCIIIBcpA4ACfCIKfUIAQpGAgICAgICACEIAEMkDIBdBEGogGikDACIFQgAgCUIAEMkDIBdBIGogBUIAIAdCABDJAyAXQTBqIAVCACAEQgAQyQMgF0FAayAFQgAgDUIAEMkDIBdCACAXKQOIAiAIIApWrXwiBSAXKQPAAXwiCSAXKQO4ASADIAtUrXwiBCAXKQNwfCIRIBcpA6ACfCISIAYgEFatfCIPIBcpA5ABfCINIAIgDlStIBcpA9gBIA4gEFStfHx8IgcgCCAMVK18IgN8Ig4gCkIAUq18IgogFykDEHwiE31CAEKRgICAgICAgAhCABDJAwJAAkAgFykDCCAXKQMoIBcpAxggCiATVq18IgIgFykDIHwiDCACVK18IAwgCSAOVq0gFykDyAEgBSAJVq18fCIJIBcpA4ABfCIQIAMgB1StIgsgFykD4AF8IgggDyASVK0gFykDqAIgESASVq18fCAXKQN4IAQgEVatfHwiBSAXKQNgfCIGIAcgDVStIBcpA5gBIA0gD1StfHx8IgR8IgN8IgcgCiAOVK18IgJ8Ig8gDFStfCIKIBcpAzB8Ig0gAiAHVK0iDCAXKQOgAXwiDiADIAhUrSAXKQPoASAIIAtUrXx8IAQgBlStIBcpA2ggBSAGVq18fHwiBiAXKQNQfCIIIAcgEFStIBcpA4gBIAkgEFatfHx8Igt8IgV8IgcgDyATQgBSrXwiBCAPVK18IgMgB1StIgIgFykDAHwiCSACVK18IAkgBSAOVK0gFykDqAEgDCAOVq18fCAIIAtWrSAXKQNYIAYgCFatfHx8IgsgFykDQHwiBiAHIA1UrSAXKQM4IAogDVatfHx8IgV8IgIgCVStfCAFIAZUrSAXKQNIIAYgC1StfHx8IgpCkYCAgICAgIAIVg0AIApCkYCAgICAgIAIUgRAIAQhCyADIQwgAiEHDAILIAMgBIQgAoRQRQ0AQpGAgICAgICACCEKQgAhC0IAIQxCACEHDAELIARCAX0hCyADIARQrSIEfSEMIAIgAyAEVK0iA30hByAKIAIgA1StfUKRgICAgICAgAh9IQoLIB0gBzcDACAaIAo3AwAgHiAMNwMAIB8gCzcDAEGAZUcNAAtCkYCAgICAgIAIIQMgACkDCCIUIAApAygiEnwiBSAUVCAFIAApAxAiDSAAKQMwIhN8IgIgDVQgAiACIAApAxgiCCAAKQM4Ig98IgQgCFStfCIMVnKtfCILIAVUcq0gACkDICIOIAApAwAiB3x8IgohBQJ+AkAgCkKRgICAgICAgAhRBEBCASEDIARCAVENASAEIQUgCyAMhEIAUg0BCyADIAVYDQAgCyEFIAwhAiAEDAELIAwgBFCtIgN9IQIgCyADIAxWrSIDfSEFQu7/////////d0Lv/////////3cgAyALVhsgCnwhCiAEQgF9CyEGIAACfkKRgICAgICAgAghDCAFIAUgACkDSCIVfCIFViAFIAIgAiAAKQNQIhZ8IgNWIAMgAyAGIAApA1giEXwiAiAGVK18IgRWcq18IgMgBVRyrSAAKQNAIhAgCnx8IgohCwJAAkAgCkKRgICAgICAgAhRBEBCASEMIAJCAVEgA0IAUnINASACIQsgBEIAUg0BCyALIAxaDQAgAyELIAQhDCACIQkMAQsgAkIBfSEJIAQgAlCtIgJ9IQwgAyACIARWrSICfSELQu7/////////d0Lv/////////3cgAiADVhsgCnwhCgtCkYCAgICAgIAIIQQgFCAUIBR8IgVWIAUgDSANfCIDIA1UIAMgAyAIIAh8IgIgCFStfCIIVnKtfCIGIAVUcq0gB0IBhoQiByEDAkACQCAHQpGAgICAgICACFEEQCACQgFRDQEgAiEDQgEhBCAGIAiEQgBSDQELIAMgBFoNACAGIQMgCCEEIAIhBQwBCyACQgF9IQUgCCACUK0iAn0hBCAGIAIgCFatIgJ9IQNC7v////////93Qu//////////dyACIAZWGyAHfCEHC0KRgICAgICAgAghBiADIAt8Ig0gC1QgDSANIAQgDHwiAyAMVCADIAUgCXwiAiAJVK18IgggA1RyrXwiA1ZyrSAHIAp8fCIHIQQCQAJAIAdCkYCAgICAgIAIUQRAIAMgCIRCAFINAUIBIQYgAiIEQgFRDQELIAQgBloNACADIQYgCCEEIAIhBQwBCyACQgF9IQUgCCACUK0iAn0hBCADIAIgCFatIgJ9IQZC7v////////93Qu//////////dyACIANWGyAHfCEHCyAAIAU3AxggACAENwMQIAAgBjcDCCAAIAc3AwBCkYCAgICAgIAIIQYgEiASfCIEIBJUIAQgEyATfCIDIBNUIAMgDyAPfCICIA9UrXwiCCADVHKtfCIDIARUcq0gDkIBhoQiByEEAkACQCAHQpGAgICAgICACFEEQCACQgFRDQEgAiEEQgEhBiADIAiEQgBSDQELIAQgBloNACADIQQgCCEGIAIhBQwBCyACQgF9IQUgCCACUK0iAn0hBiADIAIgCFatIgJ9IQRC7v////////93Qu//////////dyACIANWGyAHfCEHCyAAAn4CQAJAIAoiAiAHIgNSDQAgCyICIAQiA1INACAGIgMgDCICUg0AIAkiAiAFIgNRDQELIAIgA1oNACAGIAxUIAUgCVStIgMgBiAMfSICVnKtIg8gBCALfSINfSIOIAIgA1IgAyACfSIIIAUgCX0iBUIBVq0iA1RyrSICfSEGIA0gD1IgAiAOVnIhASAIIAN9IQMgBCALVCANIA9Ucq0gCiAHfXxCkYCAgICAgIAIfCEHQgEgBX0MAQsgDCAGfSIOIAUgCVatIgJ9IQMgCyAEfSIIIAIgDlYgBiAMVnKtIgJ9IQYgAiAIViAEIAtWciEBIAogB30hByAJIAV9CzcDOCAAIAM3AzAgACAGNwMoIAAgByABrX03AyBCkYCAgICAgIAIIQUgFSAVfCIDIBVUIAMgFiAWfCICIBZUIAIgAiARIBF8IgQgEVStfCIIVnKtfCIGIANUcq0gEEIBhoQiByECAkACQCAHQpGAgICAgICACFEEQCAEQgFRDQEgBCECQgEhBSAGIAiEQgBSDQELIAIgBVoNACAGIQUgCCECIAQhAwwBCyAEQgF9IQMgCCAEUK0iBH0hAiAGIAQgCFatIgR9IQVC7v////////93Qu//////////dyAEIAZWGyAHfCEHC0KRgICAgICAgAghBiAFIAUgFXwiBVYgBSACIBZ8IgQgAlQgBCADIBF8IgIgA1StfCIIIARUcq18IgMgBVRyrSAHIBB8fCIHIQQCQAJAIAdCkYCAgICAgIAIUQRAQgEhBiACQgFRIANCAFJyDQEgAiEEIAhCAFINAQsgBCAGWg0AIAMhBCAIIQYgAiEFDAELIAJCAX0hBSAIIAJQrSICfSEGIAMgAiAIVq0iAn0hBELu/////////3dC7/////////93IAIgA1YbIAd8IQcLAkACQCAKIgIgByIDUg0AIAsiAiAEIgNSDQAgBiIDIAwiAlINACAJIgIgBSIDUQ0BCyACIANaDQAgBiAMVCAFIAlUrSIDIAYgDH0iAlZyrSINIAQgC30iDn0iCCACIANSIAMgAn0iBiAFIAl9IgVCAVatIgNUcq0iAn0hDCANIA5SIAIgCFZyIQEgBiADfSEDIAQgC1QgDSAOVnKtIAogB318QpGAgICAgICACHwhCkIBIAV9DAELIAwgBn0iDiAFIAlWrSICfSEDIAsgBH0iCCACIA5WIAYgDFZyrSICfSEMIAIgCFYgBCALVnIhASAKIAd9IQogCSAFfQs3A1ggACADNwNQIAAgDDcDSCAAIAogAa19NwNAIBdBoARqJAAL0ycCCX8PfiMAQaAMayIDJAAgA0HgBWogAUEYaikDADcDACADQdgFaiABQRBqKQMANwMAIANB0AVqIAFBCGopAwA3AwAgA0HwBWogAkEIaikDADcDACADQfgFaiACQRBqKQMANwMAIANBgAZqIAJBGGopAwA3AwAgA0EAOgCIBiADIAEpAwA3A8gFIAMgAikDADcD6AUgA0HoBWohBwJAAkACQAJAIANByAVqQejRwQBBIBDxA0UEQCAHQejRwQBBIBDxA0UNAQsgA0GwBmoiAhBJIANB0AZqIQQgA0GQDGogAkEYaikDADcDACADQYgMaiACQRBqKQMANwMAIANBgAxqIAJBCGopAwA3AwAgAyACKQMANwP4CyADQdAEaiADKQP4BSINQgAgAykDgAYiDEIAEMkDIANBwARqIAMpA/AFIg5CACAMQgAQyQMgA0GwBGogAykD6AUiD0IAIAxCABDJAyADQYAFaiAOQgAgDUIAEMkDIANB8ARqIA9CACANQgAQyQMgA0GgBWogD0IAIA5CABDJAyADQaAEaiAMQgAgDEIAEMkDIANB4ARqIA1CACANQgAQyQMgA0GQBWogDkIAIA5CABDJAyADQbAFaiAPQgAgD0IAEMkDIANBkARqIAMpA6AEIhNCm5Svw/K1qN6Gf34iDUIAQm1CABDJAyADQYAEaiANQgBCf0IAEMkDIANB8ANqIA1CAEL///////////8AQgAQyQMgAykDqAUgAykD+AQgAykDuAQgAykDyAQgAykD2AQiDCADKQPABHwiDSAMVK18Ig4gAykDsAR8IgwgDlStfCIPIAMpA/AEfCIOIA9UrXwgDiAOIAMpA4gFIAwgDCADKQOABXwiD1atfHwiDFatfCIRIAMpA6AFfCIOIBFUrXwiEUI/iCADKQO4BSADKQOwBSIQIBFCAYYgDkI/iIR8IhEgEFStfCARIAMpA5gFIAMpA+gEIAMpA+AEIhIgDUIBhiADKQPQBCIVQj+IhHwiECASVK18IBAgAykDqAQiEiAVQgGGfCIVIBJUrXwiFyAQVK18IhAgD0IBhiANQj+IhHwiGCAQVK0iDSADKQOQBXwiECANVK18IBAgECAMQgGGIA9CP4iEfCINVq18Ig8gDkIBhiAMQj+IhHwiEiAPVK18IhAgEVStfHwhEQJ/AkAgAykD+AMgAykDiAQiDiAOIAMpA5gEIAMpA5AEIgwgE0J9g3wgDFStfCIPIAMpA4AEIhN8IgwgD1StfCAMIAwgFXwiDlatfCIPIBN8IgwgD1StfCAMIBd8Ig8gDFStfCITIAMpA/ADfCIMIBNUrXwgDCAYfCITIAxUrXwiDFANACAMIA18Ig0gDFQiAkUNACACrSIMIBJ8IhIgDFoNACAMIBJWrSIMIBB8IhAgDFoNACAMIBBWrSIMIBF8IhEgDFQMAQtBAAshBiAEKQMAIRUgBCkDCCEXIAQpAxAhGCAEKQMYIRkgA0HgA2ogDkKblK/D8rWo3oZ/fiIMQgBCbUIAEMkDIANB0ANqIAxCAEJ/QgAQyQMgA0HAA2ogDEIAQv///////////wBCABDJAwJAIAMpA8gDIAMpA9gDIhQgFCADKQPoAyAOIAMpA+ADIgx8IAxUrXwiDiADKQPQAyIWfCIMIA5UrXwgDCAMIA98Ig5WrXwiDyAWfCIMIA9UrXwgDCATfCIPIAxUrXwiEyADKQPAA3wiDCATVK18IAwgDCANfCITVq18Ig1QDQAgDSASfCISIA1aDQAgDSASVq0iDSAQfCIQIA1aDQAgDSAQVq0iDSARfCIRIA1UIQULIANBsANqIA5Cm5Svw/K1qN6Gf34iDUIAQm1CABDJAyADQaADaiANQgBCf0IAEMkDIANBkANqIA1CAEL///////////8AQgAQyQNBACECIAMpA5gDIAMpA6gDIgwgDCADKQO4AyADKQOwAyINIA58IA1UrXwiDiADKQOgAyIUfCINIA5UrXwgDSANIA98IgxWrXwiDiAUfCINIA5UrXwgDSATfCIOIA1UrXwiDyADKQOQA3wiDSAPVK18IA0gEnwiDyANVK18Ig1QRQRAIA0gEHwiECANVCICrSINIBF8IhIgESACGyERIAIgDSASVnEhAgsgA0GAA2ogDEKblK/D8rWo3oZ/fiINQgBCbUIAEMkDIANB8AJqIA1CAEJ/QgAQyQMgA0HgAmogDUIAQv///////////wBCABDJAyADKQPoAiADKQP4AiISIBIgAykDiAMgDCADKQOAAyINfCANVK18IgwgAykD8AIiE3wiDSAMVK18IA0gDnwiEiANVK18IgwgE3wiDSAMVK18IA0gD3wiDiANVK18Ig0gAykD4AJ8IgwgDVStfCAMIAwgEHwiDVatfCIMIBF8Ig8gESAMQgBSIgQbIRECQAJAIAUgBnIgAnIgDCAPViICrSAMIAQbQgBSciACIARxIBFCAFNyckUEQEL///////////8AIQ8gEUL///////////8AUiANQn9SciAOQn9Scg0CQn8hEEJ/IQwgEkJtVA0CDAELIBEhDyANIRAgDiEMCyAMQgF8Ig0gEkJtVK0iEX0hDiAQQgF8IhMgDEJ/UiANIBFUcq0iDH0hDSAPIBBCf1IgDCATVnKtfUL///////////8AfSERIBJCE3whEgsgAyASNwOQCyADIA43A4gLIAMgDTcDgAsgAyARNwP4CiADQfABaiADKQPYBSINQgAgAykD4AUiDEIAEMkDIANB4AFqIAMpA9AFIg5CACAMQgAQyQMgA0HQAWogAykDyAUiD0IAIAxCABDJAyADQaACaiAOQgAgDUIAEMkDIANBkAJqIA9CACANQgAQyQMgA0HAAmogD0IAIA5CABDJAyADQcABaiAMQgAgDEIAEMkDIANBgAJqIA1CACANQgAQyQMgA0GwAmogDkIAIA5CABDJAyADQdACaiAPQgAgD0IAEMkDIANBsAFqIAMpA8ABIhNCm5Svw/K1qN6Gf34iDUIAQm1CABDJAyADQaABaiANQgBCf0IAEMkDIANBkAFqIA1CAEL///////////8AQgAQyQMgAykDyAIgAykDmAIgAykD2AEgAykD6AEgAykD+AEiDCADKQPgAXwiDSAMVK18Ig4gAykD0AF8IgwgDlStfCIPIAMpA5ACfCIOIA9UrXwgDiAOIAMpA6gCIAwgDCADKQOgAnwiD1atfHwiDFatfCIRIAMpA8ACfCIOIBFUrXwiEUI/iCADKQPYAiADKQPQAiIQIBFCAYYgDkI/iIR8IhEgEFStfCARIAMpA7gCIAMpA4gCIAMpA4ACIhIgDUIBhiADKQPwASIUQj+IhHwiECASVK18IBAgAykDyAEiEiAUQgGGfCIUIBJUrXwiFiAQVK18IhAgD0IBhiANQj+IhHwiGiAQVK0iDSADKQOwAnwiECANVK18IBAgECAMQgGGIA9CP4iEfCINVq18Ig8gDkIBhiAMQj+IhHwiEiAPVK18IhAgEVStfHwhEUEAIQUCfwJAIAMpA5gBIAMpA6gBIg4gDiADKQO4ASADKQOwASIMIBNCfYN8IAxUrXwiDyADKQOgASITfCIMIA9UrXwgDCAMIBR8Ig5WrXwiDyATfCIMIA9UrXwgDCAWfCIPIAxUrXwiEyADKQOQAXwiDCATVK18IAwgGnwiEyAMVK18IgxQDQAgDCANfCINIAxUIgJFDQAgAq0iDCASfCISIAxaDQAgDCASVq0iDCAQfCIQIAxaDQAgDCAQVq0iDCARfCIRIAxUDAELQQALIQYgA0GAAWogDkKblK/D8rWo3oZ/fiIMQgBCbUIAEMkDIANB8ABqIAxCAEJ/QgAQyQMgA0HgAGogDEIAQv///////////wBCABDJAwJAIAMpA2ggAykDeCIUIBQgAykDiAEgDiADKQOAASIMfCAMVK18Ig4gAykDcCIWfCIMIA5UrXwgDCAMIA98Ig5WrXwiDyAWfCIMIA9UrXwgDCATfCIPIAxUrXwiEyADKQNgfCIMIBNUrXwgDCAMIA18IhNWrXwiDVANACANIBJ8IhIgDVoNACANIBJWrSINIBB8IhAgDVoNACANIBBWrSINIBF8IhEgDVQhBQsgA0HQAGogDkKblK/D8rWo3oZ/fiINQgBCbUIAEMkDIANBQGsgDUIAQn9CABDJAyADQTBqIA1CAEL///////////8AQgAQyQNBACECIAMpAzggAykDSCIMIAwgAykDWCADKQNQIg0gDnwgDVStfCIOIAMpA0AiFHwiDSAOVK18IA0gDSAPfCIMVq18Ig4gFHwiDSAOVK18IA0gE3wiDiANVK18Ig8gAykDMHwiDSAPVK18IA0gEnwiDyANVK18Ig1QRQRAIA0gEHwiECANVCICrSINIBF8IhIgESACGyERIAIgDSASVnEhAgsgA0EgaiAMQpuUr8Pytajehn9+Ig1CAEJtQgAQyQMgA0EQaiANQgBCf0IAEMkDIAMgDUIAQv///////////wBCABDJAyADKQMIIAMpAxgiEiASIAMpAyggDCADKQMgIg18IA1UrXwiDCADKQMQIhN8Ig0gDFStfCANIA58IhIgDVStfCIMIBN8Ig0gDFStfCANIA98Ig4gDVStfCINIAMpAwB8IgwgDVStfCAMIAwgEHwiDVatfCIMIBF8Ig8gESAMQgBSIgQbIRECQAJAIAUgBnIgAnIgDCAPViICrSAMIAQbQgBSciACIARxIBFCAFNyckUEQEL///////////8AIQ8gEUL///////////8AUiANQn9SciAOQn9Scg0CQn8hEEJ/IQwgEkJtVA0CDAELIBEhDyANIRAgDiEMCyAMQgF8Ig0gEkJtVK0iEX0hDiAQQgF8IhMgDEJ/UiANIBFUcq0iDH0hDSAPIBBCf1IgDCATVnKtfUL///////////8AfSERIBJCE3whEgsgAyASNwPQCyADIA43A8gLIAMgDTcDwAsgAyARNwO4CyADQfALaiICIAFBGGoiBCkDADcDACADQegLaiIFIAFBEGoiBikDADcDACADQeALaiIIIAFBCGoiCSkDADcDACADIAEpAwA3A9gLIANBmAtqIANBuAtqIgogA0HYC2oiCxB8IAIgBCkDADcDACAFIAYpAwA3AwAgCCAJKQMANwMAIAMgASkDADcD2AsgCiADQfgLaiALEHwgAykDmAsiECADKQO4C3wiDSADKQOgCyIMIAMpA8ALfCIOIAxUIA4gAykDqAsiDCADKQPIC3wiDyAMVCAPIA8gAykDsAsiDCADKQPQC3wiESAMVK18IgxWcq18IhIgDlRyrXwhDwJAAkACQCANIBBUIA0gD1ZyDQBC////////////ACEQIA8iDUL///////////8AUQRAQn8hEEL///////////8AIQ0gEkJ/Ug0CIAxCf1IEQCAMIQ4MBAtCbSEQIBEiDUJtUQ0BCyANIBBaDQAgDyENDAELIAxCAXwiDSARQm1UrSIQfSEOIBJCAXwiEyAMQn9SIA0gEFRyrSINfSEQIA8gEkJ/UiANIBNWcq19Qv///////////wB9IQ0gEUITfCERDAELIBIhECAMIQ4LIA0gFXwiDCAQIBd8Ig8gEFQgDyAOIA4gGHwiEFYgECAQIBEgGXwiEiARVK18Ig5Wcq18IhAgD1RyrXwhEQJAAkACQCAMIA1UIAwgEVZyDQBC////////////ACENIBEiDEL///////////8AUQRAQn8hDUL///////////8AIQwgEEJ/Ug0CIA5Cf1IEQCAOIQ8MBAtCbSENIBIiDEJtUQ0BCyAMIA1aDQAgESEMDAELIA5CAXwiDSASQm1UrSIMfSEPIBBCAXwiEyAOQn9SIAwgDVZyrSIMfSENIBEgEEJ/UiAMIBNWcq19Qv///////////wB9IQwgEkITfCESDAELIBAhDSAOIQ8LIAMgEjcD8AsgAyAPNwPoCyADIA03A+ALIAMgDDcD2AsgA0H4CmogA0HYC2pBIBDxAyADKALcCiIBBEAgAygC4AogAUECdBDfBAsCQCADKAKUCCIBRQ0AIAEgAUEMbEETakF4cSIEakEJaiIBRQ0AIAMoApAIIARrIAEQ3wQLIAMoAsAIIgFBgICAgHhGIAFFckUEQCADKALECCABQQJ0EN8ECw0BCyAAIANByAVqQcgA/AoAAAwBCyADQfgLaiIBIANByAVqENgBIANBADYC4AsgA0KAgICAEDcC2AsgA0Gw18EANgK0BiADQqCAgIAONwK4BiADIANB2AtqIgI2ArAGIAEgA0GwBmoiARDTAg0BIANBmAZqIANB4AtqKAIANgIAIAMgAykC2As3A5AGIAEgBxDYASADQQA2AoALIANCgICAgBA3AvgKIANBsNfBADYCvAsgA0KggICADjcCwAsgAyADQfgKajYCuAsgASADQbgLahDTAg0BIANBqAZqIANBgAtqKAIANgIAIAMgAykC+Ao3A6AGIANBAzYC3AsgA0Ho9cEANgLYCyADQgI3AuQLIAMgA0GgBmqtQoCAgIDAB4Q3A6ALIAMgA0GQBmqtQoCAgIDAB4Q3A5gLIAMgA0GYC2o2AuALIAAgAhDSAiADKAKgBiIBBEAgAygCpAYgARDfBAsgAygCkAYiAQRAIAMoApQGIAEQ3wQLIABBAjoAQAsgA0GgDGokAA8LQdjXwQBBNyADQZ8MakHI18EAQdzYwQAQygMAC4UmAhR+Bn8jAEGgBGsiFSQAIABBABBEIABBAxBEIABBBhBEIABBCRBEIAApA0AhCSAAKQNIIQsgACkDUCEHIAApA1ghDUGgayEXA0AgCyAXQZDxwQBqKQMAfCIKIAtUIAogByAHIBdBmPHBAGopAwB8IgJWIAIgDSAXQaDxwQBqKQMAfCIBIA1UrXwiAyACVHKtfCICIApUcq0gF0GI8cEAaikDACAJfHwiDSEKQpGAgICAgICACCEJAkACQCANQpGAgICAgICACFEEQEIBIQkgAUIBUQ0BIAEhCiACIAOEQgBSDQELIAkgClgNACABIQkgAyELIAIhCgwBCyABQgF9IQkgAyABUK0iAX0hCyACIAEgA1atIgF9IQogDULu/////////3dC7/////////93IAEgAlYbfCENCyAVQfADaiALQgAgCUIAEMkDIBVB0ANqIApCACAJQgAQyQMgFUGgA2ogDUIAIAlCABDJAyAVQcADaiAKQgAgC0IAEMkDIBVBkANqIA1CACALQgAQyQMgFUGAA2ogDUIAIApCABDJAyAVQZAEaiAJQgAgCUIAEMkDIBVB4ANqIAtCACALQgAQyQMgFUGwA2ogCkIAIApCABDJAyAVQfACaiANQgAgDUIAEMkDIBVBgARqQgAgFSkDkAQiD31CAEKRgICAgICAgAhCABDJAyAVKQOIAyAVKQOYAyAVKQOoAyAVKQPYAyAVKQP4AyIBIBUpA9ADfCIGIAFUrXwiASAVKQOgA3wiAyABVK18IgEgFSkDkAN8IgIgAVStfCACIBUpA8gDIAMgFSkDwAN8IgcgA1StfHwiBSACVK18IgEgFSkDgAN8IgwgAVStfCICQj+IIBUpA/gCIBUpA/ACIgEgAkIBhiAMQj+IhHwiCCABVK18IAggCCAVKQO4AyAVKQPoAyAVKQPgAyIBIAZCAYYgFSkD8AMiAkI/iIR8IgMgAVStfCADIAMgFSkDmAQiASACQgGGfCIEIAFUrXwiA1atfCIBIAdCAYYgBkI/iIR8IgIgAVStIgEgFSkDsAN8IgYgAVStfCAGIAYgBUIBhiAHQj+IhHwiB1atfCIBIAxCAYYgBUI/iIR8IgwgAVStfCIGVq18fCEFQQAhGgJ/QQAgFSkDiAQgD0J9gyIBIA99IAFUrSIBIAR8IgggAVStIgEgA3wiAyABVK0iASAVKQOABHwiBCABVK18IAIgBHwiAiAEVK18IgFQDQAaQQAgASABIAd8IgdYDQAaQQAgASAHVq0iASAMfCIMIAFaDQAaQQAgASAMVq0iASAGfCIGIAFaDQAaIAEgBlatIgEgBXwiBSABVAshGSAVQeACakIAIAh9QgBCkYCAgICAgIAIQgAQyQMCQCAVKQPoAiAIQgBSrSIBIAN8IgQgAVStIgEgAnwiAyABVK0iASAVKQPgAnwiAiABVK18IAIgAiAHfCICVq18IgFQDQAgASAMfCIMIAFaDQAgASAMVq0iASAGfCIGIAFaDQAgASAGVq0iASAFfCIFIAFUIRoLIBVB0AJqQgAgBH1CAEKRgICAgICAgAhCABDJA0EAIRYgFSkD2AIgBEIAUq0iASADfCIEIAFUrSIBIAJ8IgcgAVStIgEgFSkD0AJ8IgIgAVStfCACIAx8IgMgAlStfCIBUEUEQCABIAZ8IgYgAVQiGK0iAiAFfCIBIAUgGBshBSAYIAEgAlRxIRYLIBVBwAJqQgAgBH1CAEKRgICAgICAgAhCABDJAyAVKQPIAiADIARCAFKtIgEgB3wiAyABVK0iAXwiAiABVK0iASAVKQPAAnwiByABVK18IAYgB3wiASAHVK18IgYgBXwiByAFIAZCAFIiGBshBAJ+AkAgGSAaciAWciAGIAdWIhmtIAYgGBtCAFJyIBggGXEgBEKRgICAgICAgAhWcnINACAEQpGAgICAgICACFIEQCADIQUgAiEGIAEhDCAEDAILQgAhBSABIAKEQgBSDQBCACEGQgAhDEKRgICAgICAgAggA1ANARoLIANCAX0hBSACIANQrSIDfSEGIAEgAiADVK0iAn0hDCAEIAEgAlStfUKRgICAgICAgAh9CyEPIBVBsAJqIAVCACAJQgAQyQMgFUHgAWogBkIAIAlCABDJAyAVQZABaiAMQgAgCUIAEMkDIBVBQGsgD0IAIAlCABDJAyAVQaACakIAIBUpA7ACIgF9QgBCkYCAgICAgIAIQgAQyQMgFUGQAmogBUIAIAtCABDJAyAVQcABaiAGQgAgC0IAEMkDIBVB8ABqIAxCACALQgAQyQMgFUEgaiAPQgAgC0IAEMkDIBVB0AFqQgAgAUIAUq0iAyAVKQO4AiICIBUpA+ABfCIBfCIEIBUpA5ACfCIHfUIAQpGAgICAgICACEIAEMkDIBVBgAJqIAVCACAKQgAQyQMgFUGwAWogBkIAIApCABDJAyAVQeAAaiAMQgAgCkIAEMkDIBVBEGogD0IAIApCABDJAyAVQYABakIAIAdCAFKtIgkgAyAEVq0iCiAVKQPoASABIAJUrXwiAyAVKQOQAXwiAnwiDiAVKQPAAXwiCyAVKQOYAiAEIAdWrXx8IgF8IgggFSkDgAJ8IgR9QgBCkYCAgICAgIAIQgAQyQMgFUHwAWogBUIAIA1CABDJAyAVQaABaiAGQgAgDUIAEMkDIBVB0ABqIAxCACANQgAQyQMgFSAPQgAgDUIAEMkDIBVBMGpCACAVKQOIAiAEIAhUrXwiByAVKQOwAXwiDCAVKQOYASACIANUrXwiAyAVKQNAfCIQIBUpA6ACfCIGIAogDlatfCINIBUpA3B8Ig8gASALVK0gFSkDyAEgCyAOVK18fHwiCyAIIAlUrXwiAnwiBSAEQgBSrXwiBCAVKQPwAXwiEX1CAEKRgICAgICAgAhCABDJAwJAAkAgFSkDOCAVKQOoASAVKQP4ASAEIBFWrXwiASAVKQOgAXwiCSABVK18IAkgBSAMVK0gFSkDuAEgByAMVq18fCIMIBUpA2B8Ig4gAiALVK0iCiAVKQPQAXwiCCAGIA1WrSAVKQOoAiAGIBBUrXx8IBUpA0ggAyAQVq18fCIHIBUpAyB8IgYgCyAPVK0gFSkDeCANIA9WrXx8fCIDfCICfCILIAQgBVStfCIBfCINIAlUrXwiBCAVKQNQfCIPIAEgC1StIgkgFSkDgAF8IgUgAiAIVK0gFSkD2AEgCCAKVK18fCADIAZUrSAVKQMoIAYgB1StfHx8IgYgFSkDEHwiCCALIA5UrSAVKQNoIAwgDlatfHx8Igp8Igd8IgsgDSARQgBSrXwiAyANVK18IgIgC1StIgEgFSkDMHwiDCABVK18IAwgBSAHVq0gFSkDiAEgBSAJVK18fCAIIApWrSAVKQMYIAYgCFatfHx8IgogFSkDAHwiBiALIA9UrSAVKQNYIAQgD1atfHx8Igd8IgEgDFStfCAGIAdWrSAVKQMIIAYgClStfHx8Ig9CkYCAgICAgIAIVg0AIA9CkYCAgICAgIAIUgRAIAMhBiACIQwgASEHDAILIAIgA4QgAYRQRQ0AQpGAgICAgICACCEPQgAhBkIAIQxCACEHDAELIANCAX0hBiACIANQrSIDfSEMIAEgAiADVK0iAn0hByAPIAEgAlStfUKRgICAgICAgAh9IQ8LQpGAgICAgICACCEDIAApAwgiECAAKQMoIhN8IgIgEFQgAiAAKQMQIg4gACkDMCIUfCIBIA5UIAEgACkDGCIIIAApAzgiEnwiCiAIVK18IgQgAVRyrXwiCSACVHKtIAApAyAiESAAKQMAIgV8fCINIQICQAJAIA1CkYCAgICAgIAIUQRAQgEhAyAKQgFRDQEgCiECIAQgCYRCAFINAQsgAiADWg0AIAkhAyAEIQIgCiEBDAELIApCAX0hASAEIApQrSIDfSECIAkgAyAEVq0iCn0hAyANQu7/////////d0Lv/////////3cgCSAKVBt8IQ0LQpGAgICAgICACCELIAMgB3wiCiADVCAKIAIgAiAMfCIDViADIAMgASABIAZ8IgJWrXwiA1ZyrXwiASAKVHKtIA0gD3x8Ig0hCQJAAkAgDUKRgICAgICAgAhRBEBCASELIAJCAVEgAUIAUnINASACIQkgA0IAUg0BCyAJIAtaDQAgASEJIAMhCyACIQoMAQsgAkIBfSEKIAMgAlCtIgJ9IQsgASACIANWrSICfSEJIA1C7v////////93Qu//////////dyABIAJUG3whDQtCkYCAgICAgIAIIQEgECAQfCIEIBBUIAQgDiAOfCIDIA5UIAMgCCAIfCICIAhUrXwiDiADVHKtfCIIIARUcq0gBUIBhoQiBSEDAkACQCAFQpGAgICAgICACFEEQEIBIQEgAkIBUQ0BIAIhAyAIIA6EQgBSDQELIAEgA1gNACAIIQMgDiEBIAIhBAwBCyACQgF9IQQgDiACUK0iAn0hASAIIAIgDlatIgJ9IQMgBULu/////////3dC7/////////93IAIgCFYbfCEFC0KRgICAgICAgAghAiADIAl8IhAgCVQgECAQIAEgC3wiASALVCABIAQgCnwiAyAKVK18Ig4gAVRyrXwiCFZyrSAFIA18fCIFIQECQAJAIAVCkYCAgICAgIAIUQRAIAggDoRCAFINAUIBIQIgAyIBQgFRDQELIAEgAloNACAIIQIgDiEBIAMhBAwBCyADQgF9IQQgDiADUK0iAn0hASAIIAIgDlatIgN9IQIgBULu/////////3dC7/////////93IAMgCFYbfCEFCyAAIAQ3AxggACABNwMQIAAgAjcDCCAAIAU3AwBCkYCAgICAgIAIIQIgEyATfCIDIBNUIAMgAyAUIBR8IgEgFFQgASASIBJ8Ig4gElStfCIEIAFUcq18IgNWcq0gEUIBhoQiBSEBAn4CQCAFQpGAgICAgICACFEEQEIBIQIgDkIBUQ0BIA4hASADIASEQgBSDQELIAEgAloNACADIQEgBCEIIA4MAQsgBCAOUK0iAX0hCCADIAEgBFatIgJ9IQEgBULu/////////3dC7/////////93IAIgA1YbfCEFIA5CAX0LIQQgAAJ+AkACQCANIgIgBSIDUg0AIAEhAyABIAkiAlINACALIgIgCCIDUg0AIAoiAiAEIgNRDQELIAIgA1oNACAIIAtUIAQgClStIgMgCCALfSICVnKtIhIgASAJfSIQfSIRIAIgA1IgAyACfSIOIAQgCn0iCEIBVq0iBFRyrSICfSEDIBAgElIgAiARVnIhFiAOIAR9IQIgASAJVCAQIBJUcq0gDSAFfXxCkYCAgICAgIAIfCEFQgEgCH0MAQsgCyAIfSIRIAQgClatIgN9IQIgCSABfSIOIAMgEVYgCCALVnKtIgh9IQMgCCAOViABIAlWciEWIA0gBX0hBSAKIAR9CzcDOCAAIAI3AzAgACADNwMoIAAgBSAWrX03AyBCkYCAgICAgIAIIQggByAHfCIEIAdUIAQgBCAMIAx8IgIgDFQgAiAGIAZ8IgEgBlStfCIOIAJUcq18IgNWcq0gD0IBhoQiBSEEAkACQCAFQpGAgICAgICACFEEQEIBIQggAUIBUSADQgBScg0BIAEhBCAOQgBSDQELIAQgCFoNACADIQggDiEEIAEhAgwBCyABQgF9IQIgDiABUK0iAX0hBCADIAEgDlatIgF9IQggBULu/////////3dC7/////////93IAEgA1YbfCEFC0KRgICAgICAgAghAyAIIAcgCHwiDlYgDiAEIAx8IgcgBFQgByAHIAIgBnwiASACVK18IgdWcq18IgIgDlRyrSAFIA98fCIFIQYCQAJAIAVCkYCAgICAgIAIUQRAIAIgB4RCAFINAUIBIQMgASIGQgFRDQELIAMgBlgNACACIQYgByEMIAEhDwwBCyABQgF9IQ8gByABUK0iAX0hDCACIAEgB1atIgF9IQYgBULu/////////3dC7/////////93IAEgAlYbfCEFCwJ+AkACQCANIgEgBSIHUg0AIAkiASAGIgdSDQAgCyIBIAwiB1INACAKIgEgDyIHUQ0BCyABIAdaDQAgCyAMViAKIA9WrSICIAwgC30iAVZyrSIIIAYgCX0iDH0iBCABIAJSIAIgAX0iByAPIAp9IgNCAVatIgJUcq0iAX0hCyAIIAxSIAEgBFZyIRYgByACfSEHIAYgCVQgCCAMVnKtIA0gBX18QpGAgICAgICACHwhCUIBIAN9DAELIAsgDH0iAyAKIA9UrSIBfSEHIAkgBn0iAiALIAxUIAEgA1ZyrSIBfSELIAYgCVYgASACVnIhFiANIAV9IQkgCiAPfQshDSAJIBatfSEJIBdBIGoiFw0ACyAAIAc3A1AgACANNwNYIAAgCzcDSCAAIAk3A0AgAEHfABBEIABB4gAQRCAAQeUAEEQgAEHoABBEIBVBoARqJAAL/SwCAX8UfiMAQcAKayICJAAgAkGwCmogASkDGCILQgAgC0IAEMkDIAJB4AlqIAEpAxAiDUIAIAtCABDJAyACQYAJaiABKQMIIhFCACALQgAQyQMgAkGQCGogASkDACISQgAgC0IAEMkDIAJBoApqIAIpA7AKIgRC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJBkApqIANCAEKR4eXNh4n6mShCABDJAyACQYAKaiADQgBC3bCFjOi2kai4f0IAEMkDIAJB8AlqIANCAEKpwMaJrs6TsjBCABDJAyACQZAJaiANQgAgDUIAEMkDIAJBsAhqIBFCACANQgAQyQMgAkHAB2ogEkIAIA1CABDJAyACQdAJaiACKQOQCiIKIAIpA7gKIgggAikD4AkiA3wiCXwiBSACKQOoCiACKQOgCiIHIARCfYN8IAdUrXx8IgQgA3wiB0L/////vrL98EJ+IgNCAEKBgICAv7L98MMAQgAQyQMgAkHACWogA0IAQpHh5c2HifqZKEIAEMkDIAJBsAlqIANCAELdsIWM6LaRqLh/QgAQyQMgAkGgCWogA0IAQqnAxomuzpOyMEIAEMkDIAJBoAhqIBFCACARQgAQyQMgAkGwB2ogEkIAIBFCABDJAyACQfAIaiACKQPoCSIDIAQgB1atfCIQIAIpA5AJfCIGIAMgCCAJVq18IgwgAikDgAkiA3wiCCACKQOACnwiCSAEIAVUrSACKQOYCiAFIApUrXx8fCITfCIFIAIpA8AJfCIEIAIpA9gJIAcgAikD0AkiB3wgB1StfHwiByADfCIKQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyACQeAIaiADQgBCkeHlzYeJ+pkoQgAQyQMgAkHQCGogA0IAQt2whYzotpGouH9CABDJAyACQcAIaiADQgBCqcDGia7Ok7IwQgAQyQMgAkGgB2ogEkIAIBJCABDJAyACQYAIaiACKQOICSIDIAcgClatfCIVIAIpA7AIIg58Ig8gDiADIAggDFStfCIUIAIpA5AIIgN8IgwgAikD8Al8Ig4gCSATVq0gAikDiAogCCAJVq18fHwiCHwiCSAFIAZUrSACKQOYCSAGIBBUrXx8fCIGIAIpA7AJfCIQIAQgB1atIAIpA8gJIAQgBVStfHx8IhN8IgUgAikD4Ah8IgQgAikD+AggAikD8AgiByAKfCAHVK18fCIHIAN8IgpC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJB8AdqIANCAEKR4eXNh4n6mShCABDJAyACQeAHaiADQgBC3bCFjOi2kai4f0IAEMkDIAJB0AdqIANCAEKpwMaJrs6TsjBCABDJAwJAAkAgAikD2AcgAikDyAggAikDqAkgCCAOVK0gAikD+AkgDCAOVq18fCACKQOYCCIOIAwgFFStfHwiDCACKQPAByIUfCIDIAYgCVStIAIpA7gIIhYgCCAJVq18fHwiCCACKQOgCXwiCSAIVK18IAkgECATVq0gAikDuAkgBiAQVq18fHwiBiAJVK18IAMgCFatIAIpA8gHIhAgAyAMVK18fHwiDCACKQOwByITfCIDIAIpA6gIIAYgBiACKQOgCHwiBlatfCAGIAYgBSAPVK0gFiAPIBVUrXx8fCIGVq18fCIIIAIpA8AIfCIJIAhUrXwgCSACKQPYCCAGIAYgAikD0Ah8IgZWrXwgBiAGIAQgB1atIAIpA+gIIAQgBVStfHx8IgZWrXx8IgUgCVStfCADIAhWrSACKQO4ByIEIAMgDFStfHx8IgkgAikDoAd8IgMgBCAFIAUgE3wiBVatfCAFIAUgECAOIAcgClatfCIHIBR8IgQgB1StfCAEIAQgBnwiBFatfHwiBVatfHwiCCACKQPQB3wiBiAIVK18IAYgBiACKQPoByAFIAUgAikD4Ad8IgVWrXwgBSACKQP4ByAEIAQgAikD8Ad8IgRWrXwgBCACKQOICCACKQOACCIHIAp8IAdUrXx8IgcgBFStfHwiBCAFVK18fCIGVq18IAMgCFatIAIpA6gHIAMgCVStfHx8IghCqcDGia7Ok7IwVg0AAkAgCEKpwMaJrs6TsjBRBEAgBkLdsIWM6LaRqLh/Vg0CIAZC3bCFjOi2kai4f1IEQCAEIQMgBiEFQqnAxomuzpOyMCEIDAQLIARCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8hBSAEQpHh5c2HifqZKFENASAEIQNCqcDGia7Ok7IwIQgMAwsgBCEDIAYhBQwCC0KR4eXNh4n6mSghAyAHQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIQgMAQsgBEKR4eXNh4n6mSh9IgUgB0KBgICAv7L98MMAVK0iCX0hAyAGQqPP+vOXye7XxwB8IgogBEKR4eXNh4n6mShUIAUgCVRyrSIEfSEFIAggBkLdsIWM6LaRqLh/VCAEIApWcq19QqnAxomuzpOyMH0hCCAHQoGAgIC/sv3wwwB9IQcLIAJBkAdqIAdCACAHQgAQyQMgAkHABmogA0IAIAdCABDJAyACQeAFaiAFQgAgB0IAEMkDIAJB8ARqIAhCACAHQgAQyQMgAkGAB2ogAikDkAciB0L/////vrL98EJ+IgRCAEKBgICAv7L98MMAQgAQyQMgAkHwBmogBEIAQpHh5c2HifqZKEIAEMkDIAJB4AZqIARCAELdsIWM6LaRqLh/QgAQyQMgAkHQBmogBEIAQqnAxomuzpOyMEIAEMkDIAJB8AVqIANCACADQgAQyQMgAkGQBWogBUIAIANCABDJAyACQaAEaiAIQgAgA0IAEMkDIAJBsAZqIAIpA/AGIg8gAikDmAciCSACKQPABiIDfCIKfCIEIAIpA4gHIAIpA4AHIgYgB0J9g3wgBlStfHwiByADfCIGQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyACQaAGaiADQgBCkeHlzYeJ+pkoQgAQyQMgAkGQBmogA0IAQt2whYzotpGouH9CABDJAyACQYAGaiADQgBCqcDGia7Ok7IwQgAQyQMgAkGABWogBUIAIAVCABDJAyACQZAEaiAIQgAgBUIAEMkDIAJB0AVqIAIpA8gGIgMgBiAHVK18IhAgAikD8AV8IgUgAyAJIApWrXwiDCACKQPgBSIDfCIJIAIpA+AGfCIKIAQgB1atIAIpA/gGIAQgD1StfHx8IhN8IgQgAikDoAZ8IgcgAikDuAYgBiACKQOwBiIGfCAGVK18fCIGIAN8Ig9C/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJBwAVqIANCAEKR4eXNh4n6mShCABDJAyACQbAFaiADQgBC3bCFjOi2kai4f0IAEMkDIAJBoAVqIANCAEKpwMaJrs6TsjBCABDJAyACQYAEaiAIQgAgCEIAEMkDIAJB4ARqIAIpA+gFIgMgBiAPVq18IhUgAikDkAUiDnwiCCAOIAMgCSAMVK18IhQgAikD8AQiA3wiDCACKQPQBnwiDiAKIBNWrSACKQPoBiAJIApWrXx8fCIJfCIKIAQgBVStIAIpA/gFIAUgEFStfHx8IgUgAikDkAZ8IhAgBiAHVK0gAikDqAYgBCAHVq18fHwiE3wiBCACKQPABXwiByACKQPYBSACKQPQBSIGIA98IAZUrXx8IgYgA3wiD0L/////vrL98EJ+IgNCAEKBgICAv7L98MMAQgAQyQMgAkHQBGogA0IAQpHh5c2HifqZKEIAEMkDIAJBwARqIANCAELdsIWM6LaRqLh/QgAQyQMgAkGwBGogA0IAQqnAxomuzpOyMEIAEMkDAkACQCACKQO4BCACKQOoBSACKQOIBiAJIA5UrSACKQPYBiAMIA5WrXx8IAIpA/gEIg4gDCAUVK18fCIMIAIpA6AEIhR8IgMgBSAKVK0gAikDmAUiFiAJIApWrXx8fCIJIAIpA4AGfCIKIAlUrXwgCiAQIBNWrSACKQOYBiAFIBBWrXx8fCIFIApUrXwgAyAJVq0gAikDqAQiCiADIAxUrXx8fCIMIAIpA5AEIhB8IgMgAikDiAUgBSAFIAIpA4AFfCIFVq18IAUgBSAEIAhUrSAWIAggFVStfHx8IgVWrXx8IgggAikDoAV8IgkgCFStfCAJIAIpA7gFIAUgBSACKQOwBXwiBVatfCAFIAYgB1StIAIpA8gFIAQgB1atfHx8IgcgBVStfHwiBSAJVK18IAMgCFatIAIpA5gEIgQgAyAMVK18fHwiCSACKQOABHwiAyAEIAUgBSAQfCIFVq18IAUgBSAKIA4gBiAPVq18IgYgFHwiBCAGVK18IAQgBCAHfCIEVq18fCIFVq18fCIIIAIpA7AEfCIGIAhUrXwgBiAGIAIpA8gEIAUgBSACKQPABHwiBVatfCAFIAIpA9gEIAQgBCACKQPQBHwiBFatfCAEIAIpA+gEIAIpA+AEIgcgD3wgB1StfHwiByAEVK18fCIEIAVUrXx8IgZWrXwgAyAIVq0gAikDiAQgAyAJVK18fHwiCEKpwMaJrs6TsjBWDQACQCAIQqnAxomuzpOyMFEEQCAGQt2whYzotpGouH9WDQIgBkLdsIWM6LaRqLh/UgRAIAQhAyAGIQVCqcDGia7Ok7IwIQgMBAsgBEKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyEFIARCkeHlzYeJ+pkoUQ0BIAQhA0KpwMaJrs6TsjAhCAwDCyAEIQMgBiEFDAILQpHh5c2HifqZKCEDIAdCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhCAwBCyAEQpHh5c2HifqZKH0iBSAHQoGAgIC/sv3wwwBUrSIJfSEDIAZCo8/685fJ7tfHAHwiCiAEQpHh5c2HifqZKFQgBSAJVHKtIgR9IQUgCCAGQt2whYzotpGouH9UIAQgClZyrX1CqcDGia7Ok7IwfSEIIAdCgYCAgL+y/fDDAH0hBwsgAkHwA2ogB0IAIAtCABDJAyACQfACaiADQgAgC0IAEMkDIAJB8AFqIAVCACALQgAQyQMgAkHwAGogCEIAIAtCABDJAyACQeADaiACKQPwAyILQv////++sv3wQn4iBEIAQoGAgIC/sv3wwwBCABDJAyACQdADaiAEQgBCkeHlzYeJ+pkoQgAQyQMgAkHAA2ogBEIAQt2whYzotpGouH9CABDJAyACQbADaiAEQgBCqcDGia7Ok7IwQgAQyQMgAkGgA2ogB0IAIA1CABDJAyACQaACaiADQgAgDUIAEMkDIAJBoAFqIAVCACANQgAQyQMgAkEgaiAIQgAgDUIAEMkDIAJB4AJqIAIpA9ADIg8gAikD+AMiCSACKQPwAnwiCnwiBiACKQPoAyALIAIpA+ADIgR8IARUrXx8IgsgAikDoAN8Ig1C/////76y/fBCfiIEQgBCgYCAgL+y/fDDAEIAEMkDIAJB0AJqIARCAEKR4eXNh4n6mShCABDJAyACQcACaiAEQgBC3bCFjOi2kai4f0IAEMkDIAJBsAJqIARCAEKpwMaJrs6TsjBCABDJAyACQZADaiAHQgAgEUIAEMkDIAJBkAJqIANCACARQgAQyQMgAkGQAWogBUIAIBFCABDJAyACQRBqIAhCACARQgAQyQMgAkHgAWogAikDqAMgCyANVq18IgwgAikDoAJ8IhEgAikD+AIgCSAKVq18Ig4gAikD8AF8IgkgAikDwAN8IgogBiALVq0gAikD2AMgBiAPVK18fHwiEHwiBiACKQPQAnwiCyACKQPoAiACKQPgAiIEIA18IARUrXx8Ig0gAikDkAN8Ig9C/////76y/fBCfiIEQgBCgYCAgL+y/fDDAEIAEMkDIAJB0AFqIARCAEKR4eXNh4n6mShCABDJAyACQcABaiAEQgBC3bCFjOi2kai4f0IAEMkDIAJBsAFqIARCAEKpwMaJrs6TsjBCABDJAyACQYADaiAHQgAgEkIAEMkDIAJBgAJqIANCACASQgAQyQMgAkGAAWogBUIAIBJCABDJAyACIAhCACASQgAQyQMgAkHgAGogAikDmAMgDSAPVq18IhMgAikDkAJ8IgUgAikD+AEgCSAOVK18Ig4gAikDcHwiBCACKQOwA3wiByAKIBBWrSACKQPIAyAJIApWrXx8fCIIIAIpA6ABfCISIAYgEVStIAIpA6gCIAwgEVatfHx8IhEgAikDwAJ8IgkgCyANVq0gAikD2AIgBiALVq18fHwiDHwiBiACKQPQAXwiCyACKQPoASACKQPgASIDIA98IANUrXx8Ig0gAikDgAN8IgpC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJB0ABqIANCAEKR4eXNh4n6mShCABDJAyACQUBrIANCAELdsIWM6LaRqLh/QgAQyQMgAkEwaiADQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAIpAzggAikDuAEgAikDuAIgByAIVq0gAikDuAMgBCAHVq18fCACKQN4IAQgDlStfHwiDyACKQMgfCIDIBEgElStIAIpA6gBIAggElatfHx8IgQgAikDsAJ8IgcgBFStfCAHIAcgCSAMVq0gAikDyAIgCSARVK18fHwiB1atfCADIARWrSACKQMoIAMgD1StfHx8IgggAikDEHwiAyACKQOYASAHIAIpA5ABfCIEIAdUrXwgBCAFIAZWrSACKQOYAiAFIBNUrXx8fCIFIARUrXx8IgQgAikDsAF8IgcgBFStfCAHIAIpA8gBIAUgBSACKQPAAXwiBVatfCAFIAsgDVatIAIpA9gBIAYgC1atfHx8IgYgBVStfHwiBSAHVK18IAMgBFatIAIpAxggAyAIVK18fHwiCyACKQMAfCIHIAIpA4gBIAUgAikDgAF8IgMgBVStfCADIAMgAikDiAIgAikDiAMgCiANVK18IgQgAikDgAJ8IgUgBFStfCAFIAUgBnwiBVatfHwiA1atfHwiBiACKQMwfCIEIAZUrXwgBCAEIAIpA0ggAyADIAIpA0B8IgNWrXwgAyADIAIpA1ggBSAFIAIpA1B8IgVWrXwgBSACKQNoIAIpA2AiCCAKfCAIVK18fCIIIAVUrXx8IgNWrXx8IgRWrXwgBiAHVK0gAikDCCAHIAtUrXx8fCIGQqnAxomuzpOyMFYNAAJAIAZCqcDGia7Ok7IwUQRAIARC3bCFjOi2kai4f1YNAiAEQt2whYzotpGouH9SBEAgAyEFIAQhB0KpwMaJrs6TsjAhBgwECyADQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IQcgA0KR4eXNh4n6mShRDQEgAyEFQqnAxomuzpOyMCEGDAMLIAMhBSAEIQcMAgtCkeHlzYeJ+pkoIQUgCEKBgICAv7L98MMAWg0AQqnAxomuzpOyMCEGDAELIANCkeHlzYeJ+pkofSIHIAhCgYCAgL+y/fDDAFStIgt9IQUgBEKjz/rzl8nu18cAfCINIANCkeHlzYeJ+pkoVCAHIAtUcq0iA30hByAGIARC3bCFjOi2kai4f1QgAyANVnKtfUKpwMaJrs6TsjB9IQYgCEKBgICAv7L98MMAfSEICyAAIAg3AxggACAFNwMQIAAgBzcDCCAAIAY3AwAgAkHACmokAAuDJQI1fwl+IwBBwA5rIgkkACAJQZgFaiINQYS9wgBBwAAQgwECQAJAAkACQAJAAkACQAJAAkACQCAJLQCYBUEBRwRAIAlBxglqIhEgCUHIBWoiFikDACJBNwEAIAlBvglqIhcgCUHABWoiGSkDACI/NwEAIAlB9gZqIhggCUGoBWoiCiISKQMAIkI3AQAgCUH+BmoiECITIAlBsAVqIhUpAwAiQzcBACAJQYYHaiILIAlBuAVqIhopAwAiQDcBACAJQY4HaiIbID83AQAgCUGWB2oiHCBBNwEAIAkgCSkDoAUiPjcB7gYgCUGgDWoiISBBNwMAIAlBmA1qIgwgPzcDACAJQZANaiIUIEA3AwAgCUGIDWoiDyBDNwMAIAlBgA1qIg4gQjcDACAJID43A/gMIA1BxL3CAEHAABCDASAJLQCYBUEBRg0BIBEgFikDACJBNwEAIBcgGSkDACI/NwEAIBggEikDACJCNwEAIBMgFSkDACJDNwEAIAsgGikDACJANwEAIBsgPzcBACAcIEE3AQAgCSAJKQOgBSI+NwHuBiAJQTBqIEE3AwAgCUEoaiA/NwMAIAlBIGogQDcDACAJQRhqIEM3AwAgCUEQaiBCNwMAIAkgPjcDCCAJQeAAaiAhKQMANwMAIAlB2ABqIAwpAwA3AwAgCUHQAGogFCkDADcDACAJQcgAaiAPKQMANwMAIAlBQGsgDikDADcDACAJIAkpA/gMNwM4IA1BhL7CAEE/EIMBIAktAJgFQQFGDQIgESAWKQMAIkE3AQAgFyAZKQMAIj83AQAgGCAKKQMAIkI3AQAgECAVKQMAIkM3AQAgCyAaKQMAIkA3AQAgGyA/NwEAIBwgQTcBACAJIAkpA6AFIj43Ae4GICEgQTcDACAMID83AwAgFCBANwMAIA8gQzcDACAOIEI3AwAgCSA+NwP4DCANQcO+wgBBPxCDASAJLQCYBUEBRg0DIBEgFikDACJBNwEAIBcgGSkDACI/NwEAIBggEikDACJCNwEAIBMgFSkDACJDNwEAIAsgGikDACJANwEAIBsgPzcBACAcIEE3AQAgCSAJKQOgBSI+NwHuBiAJQZABaiBBNwMAIAlBiAFqID83AwAgCUGAAWogQDcDACAJQfgAaiBDNwMAIAlB8ABqIEI3AwAgCSA+NwNoIAlBwAFqICEpAwA3AwAgCUG4AWogDCkDADcDACAJQbABaiAUKQMANwMAIAlBqAFqIA8pAwA3AwAgCUGgAWogDikDADcDACAJIAkpA/gMNwOYASANQYK/wgBBwAAQgwEgCS0AmAVBAUYNBCARIBYpAwAiQTcBACAXIBkiEikDACI/NwEAIBggCiITKQMAIkI3AQAgECIMIBUpAwAiQzcBACALIhQgGiILKQMAIkA3AQAgGyIPID83AQAgHCIOIEE3AQAgCSAJKQOgBSI+NwHuBiAJQfABaiBBNwMAIAlB6AFqID83AwAgCUHgAWogQDcDACAJQdgBaiBDNwMAIAlB0AFqIEI3AwAgCSA+NwPIASANQcK/wgBBwAAQgwEgCS0AmAVBAUYNBSARIBYpAwAiQTcBACAXIBIpAwAiPzcBACAYIBMpAwAiQjcBACAMIBUpAwAiQzcBACAUIAspAwAiQDcBACAPID83AQAgDiBBNwEAIAkgCSkDoAUiPjcB7gYgEiBBNwMAIAsgPzcDACAVIEA3AwAgEyBDNwMAIAlBoAVqIEI3AwAgCSA+NwOYBQJ+IA1B2LPCAEEwEPEDBEBC///Piuv//9UeIAkpA7gFIj99IkIgCSkDwAUiQUKr1f7///+//7l/Vq0iPn0hREKk7MO1j9S0mOcAIAkpA7AFIkN9IkAgPiBCViA/Qv//z4rr///VHlZyrSI+fSFFQr+llJzP8NK75AAgCSkDqAUiP30iQiA+IEBWIENCpOzDtY/UtJjnAFZyrSI+fSFGQtfZrprk9umNywAgCSkDoAUiQ30iQCA+IEJWID9Cv6WUnM/w0rvkAFZyrSI+fSE/QprN/8ujvcSAGiAJKQOYBSA+IEBWIENC19mumuT26Y3LAFZyrXx9IUJCq9X+////v/+5fyBBfQwBCyAJKQO4BSFEIAkpA7AFIUUgCSkDqAUhRiAJKQOgBSE/IAkpA5gFIUIgCSkDwAULIUMgCUEANgKEAiAJQoCAgIDAADcC/AEgBARAIAlByAxqIR0gCUGoDGohMCAJQYAHaiExIAlB6AhqIR4gCUHICGohMiAJQZANaiE2IAlB+AlqIS4gCUHoC2ohHyAJQfgFaiEzIAlB2AZqIS8gCUGIC2ohICAJQcgHaiE0IAlByAVqIRADQCAQIAkpAwg3AwAgCUHABWoiIyAJQeAAaikDADcDACAJQbgFaiIkIAlB2ABqKQMANwMAIAlBsAVqIiUgCUHQAGopAwA3AwAgCUGoBWoiJiAJQcgAaikDADcDACAJQaAFaiInIAlBQGspAwA3AwAgEEEIaiIoIAlBEGopAwA3AwAgEEEQaiIpIAlBGGopAwA3AwAgEEEYaiIqIAlBIGopAwA3AwAgEEEgaiIrIAlBKGopAwA3AwAgEEEoaiIsIAlBMGopAwA3AwAgCSAJKQM4NwOYBUEAIg1FBEAgCUHoBmogCUGYBWpB4AD8CgAACyAjIAMgLWoiCkEoaiI3KQMANwMAICQgCkEgaiI4KQMANwMAICUgCkEYaiI5KQMANwMAICYgCkEQaiI6KQMANwMAICcgCkEIaiI7KQMANwMAIBAgCkEwaiI8KQMANwMAICggCkE4aiIRKQMANwMAICkgCkFAayIWKQMANwMAICogCkHIAGoiFykDADcDACArIApB0ABqIhkpAwA3AwAgLCAKQdgAaiIYKQMANwMAIAkgCikDADcDmAUgDUUEQCAJQZgJaiAJQZgFakHgAPwKAAALIAlBmAVqIgsgCUGYCWoQuAIgCUGIAmogCUHoBmoiDCALED8gIyAJQcABaikDADcDACAkIAlBuAFqKQMANwMAICUgCUGwAWopAwA3AwAgJiAJQagBaikDADcDACAnIAlBoAFqKQMANwMAIBAgCSkDaDcDACAoIAlB8ABqKQMANwMAICkgCUH4AGopAwA3AwAgKiAJQYABaikDADcDACArIAlBiAFqKQMANwMAICwgCUGQAWopAwA3AwAgCSAJKQOYATcDmAUgDUUEQCAMIAtB4AD8CgAACyAjIApBiAFqIhIpAwA3AwAgJCAKQYABaiITKQMANwMAICUgCkH4AGoiFSkDADcDACAmIApB8ABqIgspAwA3AwAgJyAKQegAaiIaKQMANwMAIBAgCkGQAWoiGykDADcDACAoIApBmAFqIhwpAwA3AwAgKSAKQaABaiIhKQMANwMAICogCkGoAWoiDCkDADcDACArIApBsAFqIhQpAwA3AwAgLCAKQbgBaiIPKQMANwMAIAkgCkHgAGoiDikDADcDmAUgDUUEQCAJQZgJaiAJQZgFakHgAPwKAAALIAlBmAVqIjUgCUGYCWoiPRC4AiAJQegCaiAJQegGaiA1ED8gCUGQB2ogCUHwAWopAwA3AwAgCUGIB2ogCUHoAWopAwA3AwAgMSAJQeABaikDADcDACAJQfgGaiAJQdgBaikDADcDACAJQfAGaiAJQdABaikDADcDACAJIAkpA8gBNwPoBiAjIDcpAwA3AwAgJCA4KQMANwMAICUgOSkDADcDACAmIDopAwA3AwAgJyA7KQMANwMAIBAgPCkDADcDACAoIBEpAwA3AwAgKSAWKQMANwMAICogFykDADcDACArIBkpAwA3AwAgLCAYKQMANwMAIAkgCikDADcDmAUgDUUEQCA9IDVB4AD8CgAACyAJQcgDaiAJQegGaiAJQZgJaiIREHcgCSBDNwOQByAJIEQ3A4gHIAkgRTcDgAcgCSBGNwP4BiAJID83A/AGIAkgQjcD6AYgIyASKQMANwMAICQgEykDADcDACAlIBUpAwA3AwAgJiALKQMANwMAICcgGikDADcDACAQIBspAwA3AwAgKCAcKQMANwMAICkgISkDADcDACAqIAwpAwA3AwAgKyAUKQMANwMAICwgDykDADcDACAJIA4pAwA3A5gFIA1FBEAgESAJQZgFakHgAPwKAAALIAlBqARqIAlB6AZqIgsgCUGYCWoQdyACICJGDQggDUUEQCALIAlBiAJqQeAA/AoAAAsgDUUEQCA0IAlB6AJqQeAA/AoAAAsgBiAiRg0JIAggIkYNCyAJQZgMaiILIAEgLWoiDEHgAGoiDyA0EI0BIAlB4A1qIg4gDCAJQegGahCNASAJQfgMaiALIA4QwQMgCSkDiA0hQCAJKQOADSE+IAkoAvgMQQFGDQpBACIURQRAIDIgNkHQAPwKAAALIAlBwAhqIg4gQDcDACAJID43A7gIIAlB4A1qIgsgCUG4CGoiEyATED8gCUH4DGoiEiAMIAlB6AZqENUBIAlBmAxqIhEgCyASEI0BIBIgDCAREI0BIAsgEyASED8gLiALIA8QjQEgDUUEQCAJQZgJaiARQeAA/AoAAAsgCUGAC2ogCUHgCGopAwA3AwAgCUH4CmogCUHYCGopAwA3AwAgCUHwCmogCUHQCGopAwA3AwAgCUHoCmogMikDADcDACAJQeAKaiAOKQMANwMAICAgHikDADcDACAgQQhqIB5BCGopAwA3AwAgIEEQaiAeQRBqKQMANwMAICBBGGogHkEYaikDADcDACAgQSBqIB5BIGopAwA3AwAgIEEoaiAeQShqKQMANwMAIAkgCSkDuAg3A9gKIAlB+AxqIgsgCUG4CGogDBA/IAlB4A1qIgwgCyAPEI0BIC8gCUHYCmogDCAFIAcQIEEAIg5FBEAgCUGYBWogCUGYCWpBwAH8CgAACyAORQRAIAlBmAlqIAlBmAVqQcAB/AoAAAsgCUGQBWoiDyAvQQhqKQIANwMAIAkgLykCADcDiAUgCSgChAIiDCAJKAL8AUYEQCAJQfwBakG0wMIAEKMDCyAJKAKAAiAMQQR0aiIOIAkpA4gFNwIAIA5BCGogDykDADcCACAJIAxBAWo2AoQCIA1FBEAgCUGYBWogCUHIA2pB4AD8CgAACyANRQRAIDMgCUGoBGpB4AD8CgAACyAJQeANaiILIC4gMxCNASAJQfgMaiIMIAlBmAlqIAlBmAVqEI0BIAlB6AZqIAsgDBDBAyAJKQP4BiFAIAkpA/AGIT4gCSgC6AZBAUYNDCAURQRAIDAgMUHQAPwKAAALIAlBoAxqIEA3AwAgCUHAC2ogQDcDACAJQcgLaiAwKQMANwMAIAlB0AtqIAlBsAxqKQMANwMAIAlB2AtqIAlBuAxqKQMANwMAIAlB4AtqIAlBwAxqKQMANwMAIB8gHSkDADcDACAfQQhqIB1BCGopAwA3AwAgH0EQaiAdQRBqKQMANwMAIB9BGGogHUEYaikDADcDACAfQSBqIB1BIGopAwA3AwAgH0EoaiAdQShqKQMANwMAIAkgPjcDmAwgCSA+NwO4CyAJQegGaiILIAlBmAxqIAlBmAlqED8gCUH4DGoiDCALIC4QjQEgCUGoCGogCUG4C2ogDCAFIAcQICAJKAKEAiIPIAkoAvwBRgRAIAlB/AFqQcTAwgAQowMLIAkoAoACIA9BBHRqIg4gCSkCqAg3AgAgDkEIaiAJQbAIaikCADcCACAJIA9BAWo2AoQCIC1BwAFqIS0gBUEwaiEFIAdBMGohByAEICJBAWoiIkcNAAsLIAAgCSkC/AE3AgAgAEEIaiAJQYQCaigCADYCACAJQcAOaiQADwsgCSAJLQCZBToAmAVBoLHCAEErIAlBmAVqQdTAwgBBtMHCABDKAwALIAkgCS0AmQU6AJgFQaCxwgBBKyAJQZgFakHUwMIAQaTBwgAQygMACyAJIAktAJkFOgCYBUGgscIAQSsgCUGYBWpB1MDCAEGUwcIAEMoDAAsgCSAJLQCZBToAmAVBoLHCAEErIAlBmAVqQdTAwgBBhMHCABDKAwALIAkgCS0AmQU6AJgFQaCxwgBBKyAJQZgFakHUwMIAQfTAwgAQygMACyAJIAktAJkFOgCYBUGgscIAQSsgCUGYBWpB1MDCAEHkwMIAEMoDAAsgAiACQYTAwgAQ2QMACyAGIAZBlMDCABDZAwALIAkgQDcDgA0gCSA+NwP4DEHU/sAAQSsgCUH4DGpBsIXBAEHQhcEAEMoDAAsgCCAIQaTAwgAQ2QMACyAJIEA3A/AGIAkgPjcD6AZB1P7AAEErIAlB6AZqQbCFwQBB0IXBABDKAwAL5CUCAn8YfiMAQbAIayIBJAAgAUGICGpBiP/BAEHCABC3AiABQcAHaiABKQOgCEIAQqQLQgAQyQMgAUHQB2ogASkDmAhCAEKkC0IAEMkDIAFB4AdqIAEpA5AIQgBCpAtCABDJAyABQfAHaiABKQOICEIAQqQLQgAQyQMgAUGwB2ogASkDwAciB0KblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFBoAdqIANCAEJ/QgAQyQMgAUGwBmogA0IAQv///////////wBCABDJAyABQZAHaiABKQOgByIGIAEpA8gHIgUgASkD0Ad8IgR8IgkgASkDuAcgASkDsAciAyAHQnyDfCADVK18fCIMQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAUGAB2ogA0IAQn9CABDJAyABQcAGaiADQgBC////////////AEIAEMkDIAFB8AZqIAEpA4AHIgsgBiABKQPYByAEIAVUrXwiByABKQPgB3wiD3wiECAJIAxWrSABKQOoByIFIAYgCVatfHx8IgR8IgkgASkDmAcgASkDkAciAyAMfCADVK18fCIMQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAUHgBmogA0IAQn9CABDJAyABQdAGaiADQgBC////////////AEIAEMkDIAFBoAZqIAEpA+AGIgogCyABKQPoByAHIA9WrXwiByABKQPwB3wiCCABKQOwBnwiBiAEIBBUrSAFIA8gEFatfHx8Ig98IhAgCSAMVq0gASkDiAciBSAJIAtUrXx8fCIEfCIJIAEpA/gGIAEpA/AGIgMgDHwgA1StfHwiDEKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFBkAZqIANCAEJ/QgAQyQMgAUGABmogA0IAQv///////////wBCABDJAwJAAkAgASkDiAYgASkD2AYgASkDyAYgASkDwAYiAyABKQP4ByAHIAhWrXx8IgcgA1StfCAHIAYgD1atIAEpA7gGIAYgCFStfHx8IgMgB1StfCADIAQgEFStIAUgDyAQVq18fHwiBCADVK18IgMgASkD0AZ8IgUgA1StfCAFIAUgASkD6AYiAyAEIAQgCnwiBFatfCAEIAQgCSAMVq0gAyAJIApUrXx8fCIEVq18fCIFVq18IgMgASkDgAZ8IgkgA1StfCAJIAEpA5gGIgMgBSAFIAEpA5AGIgd8IgVWrXwgBSADIAQgB3wiBCAHVK18IAQgASkDqAYgASkDoAYiAyAMfCADVK18fCISIARUrXx8IgQgBVStfHwiAyAJVK18IhZCAFkEQCAWQv///////////wBSIBJCbVRyIAMgBINCf1JyDQELIARCAXwiCSASQm1UrSIHfSEPIANCAXwiBSAEQn9SIAcgCVZyrSIEfSEQIBYgA0J/UiAEIAVWcq19Qv///////////wB9IRYgEkITfCESDAELIAMhECAEIQ8LIAFBiAhqQcr/wQBBwgAQtwIgAUHABWogASkDoAhCAEKkC0IAEMkDIAFB0AVqIAEpA5gIQgBCpAtCABDJAyABQeAFaiABKQOQCEIAQqQLQgAQyQMgAUHwBWogASkDiAhCAEKkC0IAEMkDIAFBsAVqIAEpA8AFIgdCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyABQaAFaiADQgBCf0IAEMkDIAFBsARqIANCAEL///////////8AQgAQyQMgAUGQBWogASkDoAUiCiABKQPIBSIFIAEpA9AFfCIEfCIJIAEpA7gFIAEpA7AFIgMgB0J8g3wgA1StfHwiDEKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFBgAVqIANCAEJ/QgAQyQMgAUHABGogA0IAQv///////////wBCABDJAyABQfAEaiABKQOABSIOIAogASkD2AUgBCAFVK18IgcgASkD4AV8Igh8IgYgCSAMVq0gASkDqAUiBSAJIApUrXx8fCIEfCIJIAEpA5gFIAEpA5AFIgMgDHwgA1StfHwiDEKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFB4ARqIANCAEJ/QgAQyQMgAUHQBGogA0IAQv///////////wBCABDJAyABQaAEaiABKQPgBCINIA4gASkD6AUgByAIVq18IgcgASkD8AV8IgsgASkDsAR8IgogBCAGVK0gBSAGIAhUrXx8fCIIfCIGIAkgDFatIAEpA4gFIgUgCSAOVK18fHwiBHwiCSABKQP4BCABKQPwBCIDIAx8IANUrXx8IgxCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyABQZAEaiADQgBCf0IAEMkDIAFBgARqIANCAEL///////////8AQgAQyQMCQAJAIAEpA4gEIAEpA9gEIAEpA8gEIAEpA8AEIgMgASkD+AUgByALVq18fCIHIANUrXwgByAIIApUrSABKQO4BCAKIAtUrXx8fCIDIAdUrXwgAyAEIAZUrSAFIAYgCFStfHx8IgQgA1StfCIDIAEpA9AEfCIFIANUrXwgBSAFIAEpA+gEIgMgBCAEIA18IgRWrXwgBCAEIAkgDFatIAMgCSANVK18fHwiBFatfHwiBVatfCIDIAEpA4AEfCIJIANUrXwgCSABKQOYBCIDIAUgBSABKQOQBCIHfCIFVq18IAUgAyAEIAd8IgQgB1StfCAEIAEpA6gEIAEpA6AEIgMgDHwgA1StfHwiEyAEVK18fCIEIAVUrXx8IgMgCVStfCIXQgBZBEAgF0L///////////8AUiATQm1UciADIASDQn9Scg0BCyAEQgF8IgkgE0JtVK0iB30hDCADQgF8IgUgBEJ/UiAHIAlWcq0iBH0hCSAXIANCf1IgBCAFVnKtfUL///////////8AfSEXIBNCE3whEwwBCyADIQkgBCEMCyABQYgIakGMgMIAQcAAELcCIAFBwANqIAEpA6AIQgBCpAtCABDJAyABQdADaiABKQOYCEIAQqQLQgAQyQMgAUHgA2ogASkDkAhCAEKkC0IAEMkDIAFB8ANqIAEpA4gIQgBCpAtCABDJAyABQbADaiABKQPAAyIHQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAUGgA2ogA0IAQn9CABDJAyABQbACaiADQgBC////////////AEIAEMkDIAFBkANqIAEpA6ADIg0gASkDyAMiBSABKQPQA3wiBHwiBiABKQO4AyABKQOwAyIDIAdCfIN8IANUrXx8IghCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyABQYADaiADQgBCf0IAEMkDIAFBwAJqIANCAEL///////////8AQgAQyQMgAUHwAmogASkDgAMiFCANIAEpA9gDIAQgBVStfCIHIAEpA+ADfCILfCIKIAYgCFatIAEpA6gDIgUgBiANVK18fHwiBHwiBiABKQOYAyABKQOQAyIDIAh8IANUrXx8IghCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyABQeACaiADQgBCf0IAEMkDIAFB0AJqIANCAEL///////////8AQgAQyQMgAUGgAmogASkD4AIiESAUIAEpA+gDIAcgC1atfCIHIAEpA/ADfCIOIAEpA7ACfCINIAQgClStIAUgCiALVK18fHwiC3wiCiAGIAhWrSABKQOIAyIFIAYgFFStfHx8IgR8IgYgASkD+AIgASkD8AIiAyAIfCADVK18fCIIQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAUGQAmogA0IAQn9CABDJAyABQYACaiADQgBC////////////AEIAEMkDAkACQCABKQOIAiABKQPYAiABKQPIAiABKQPAAiIDIAEpA/gDIAcgDlatfHwiByADVK18IAcgCyANVK0gASkDuAIgDSAOVK18fHwiAyAHVK18IAMgBCAKVK0gBSAKIAtUrXx8fCIEIANUrXwiAyABKQPQAnwiBSADVK18IAUgBSABKQPoAiIDIAQgBCARfCIEVq18IAQgBCAGIAhWrSADIAYgEVStfHx8IgRWrXx8IgVWrXwiAyABKQOAAnwiBiADVK18IAYgASkDmAIiAyAFIAUgASkDkAIiB3wiBVatfCAFIAMgBCAHfCIEIAdUrXwgBCABKQOoAiABKQOgAiIDIAh8IANUrXx8IhUgBFStfHwiBCAFVK18fCIDIAZUrXwiGEIAWQRAIBhC////////////AFIgFUJtVHIgAyAEg0J/UnINAQsgBEIBfCIIIBVCbVStIgV9IQcgA0IBfCIGIARCf1IgBSAIVnKtIgR9IQUgGCADQn9SIAQgBlZyrX1C////////////AH0hGCAVQhN8IRUMAQsgAyEFIAQhBwsgAUGICGpBzIDCAEHAABC3AiABQcABaiABKQOgCEIAQqQLQgAQyQMgAUHQAWogASkDmAhCAEKkC0IAEMkDIAFB4AFqIAEpA5AIQgBCpAtCABDJAyABQfABaiABKQOICEIAQqQLQgAQyQMgAUGwAWogASkDwAEiCEKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFBoAFqIANCAEJ/QgAQyQMgAUEwaiADQgBC////////////AEIAEMkDIAFBkAFqIAEpA6ABIhEgASkDyAEiBiABKQPQAXwiBHwiCiABKQO4ASABKQOwASIDIAhCfIN8IANUrXx8IgtCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyABQYABaiADQgBCf0IAEMkDIAFBQGsgA0IAQv///////////wBCABDJAyABQfAAaiABKQOAASIZIBEgASkD2AEgBCAGVK18IgggASkD4AF8Ig58Ig0gCiALVq0gASkDqAEiBiAKIBFUrXx8fCIEfCIKIAEpA5gBIAEpA5ABIgMgC3wgA1StfHwiC0KblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAFB4ABqIANCAEJ/QgAQyQMgAUHQAGogA0IAQv///////////wBCABDJAyABQSBqIAEpA2AiGiAZIAEpA+gBIAggDlatfCIIIAEpA/ABfCIUIAEpAzB8IhEgBCANVK0gBiANIA5UrXx8fCIOfCINIAogC1atIAEpA4gBIgYgCiAZVK18fHwiBHwiCiABKQN4IAEpA3AiAyALfCADVK18fCILQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAUEQaiADQgBCf0IAEMkDIAEgA0IAQv///////////wBCABDJAwJAAkAgASkDCCABKQNYIAEpA0ggASkDQCIDIAEpA/gBIAggFFatfHwiCCADVK18IAggDiARVK0gASkDOCARIBRUrXx8fCIDIAhUrXwgAyAEIA1UrSAGIA0gDlStfHx8IgQgA1StfCIDIAEpA1B8IgYgA1StfCAGIAYgASkDaCIDIAQgBCAafCIEVq18IAQgBCAKIAtWrSADIAogGlStfHx8IgRWrXx8IgZWrXwiAyABKQMAfCIKIANUrXwgCiABKQMYIgMgBiAGIAEpAxAiCHwiBlatfCAGIAMgBCAIfCIEIAhUrXwgBCABKQMoIAEpAyAiAyALfCADVK18fCIOIARUrXx8IgMgBlStfHwiBiAKVK18Ig1CAFkEQCANQv///////////wBSIA5CbVRyIAMgBoNCf1JyDQELIANCAXwiCyAOQm1UrSIIfSEEIAZCAXwiCiADQn9SIAggC1ZyrSIIfSEDIA0gBkJ/UiAIIApWcq19Qv///////////wB9IQ0gDkITfCEODAELIAMhBCAGIQMLIAFBiAhqQYyBwgBBwABBEBDxAQJAIAEoAogIQYCAgIB4RwRAIAAgASkCiAg3AqwEIABBtARqIAFBkAhqKAIANgIAEMcEIgJFDQEgAEEEOgC4BCAAIBM3AzggACAMNwMwIAAgCTcDKCAAIBc3AyAgACASNwMYIAAgDzcDECAAIBA3AwggACAWNwMAIABBgLHCACkDADcD4AEgAEHoAWpBiLHCACkDADcDACAAIAIpAwg3A/gBIAAgAikDACIJNwPwASACIAlCAXw3AwAgAEH4AGpCADcDACAAQfAAakIANwMAIABB6ABqQgA3AwAgAEHgAGpCADcDACAAQdgAakIANwMAIABB0ABqQgA3AwAgAEHIAGpCADcDACAAQgA3A0AgACAYNwOAASAAIAU3A4gBIAAgBzcDkAEgACAVNwOYASAAIA03A6ABIAAgAzcDqAEgACAENwOwASAAIA43A7gBIABCADcDmAMgAEIANwPgAyAAQQg2AqgEIABCADcDiAIgAEIANwOAAiAAQgA3A8ABIABByAFqQgA3AwAgAEHQAWpCADcDACAAQgE3A6gCIABC5AE3A9gBIABCADcDsAIgAEIANwOgAiAAQYCAgIB4NgKQAiABQbAIaiQADwsgASABLQCMCDoArwhBjPfBAEErIAFBrwhqQeT7wQBBzIHCABDKAwALEPADAAuBIgEEfyAAKAIEIQIgACgCCCIDBEAgAiEBA0AgASgCACIEBEAgAUEEaigCACAEQQJ0EN8ECyABQQxqIQEgA0EBayIDDQALCyAAKAIAIgEEQCACIAFBDGwQ3wQLIABBDGoQywIgACgCzAEiAQRAIAAoAtABIAFBAnQQ3wQLIAAoAtgBIgEEQCAAKALcASABQQJ0EN8ECyAAKALkASIBBEAgACgC6AEgAUECdBDfBAsgACgC8AEiAQRAIAAoAvQBIAFBAnQQ3wQLIAAoAvwBIgEEQCAAKAKAAiABQQJ0EN8ECyAAKAKIAiIBBEAgACgCjAIgAUECdBDfBAsgACgClAIiAQRAIAAoApgCIAFBAnQQ3wQLIAAoAqACIgEEQCAAKAKkAiABQQJ0EN8ECyAAKAKsAiIBBEAgACgCsAIgAUECdBDfBAsgACgCuAIiAQRAIAAoArwCIAFBAnQQ3wQLIAAoAsQCIgEEQCAAKALIAiABQQJ0EN8ECyAAKALQAiIBBEAgACgC1AIgAUECdBDfBAsgACgC3AIiAQRAIAAoAuACIAFBAnQQ3wQLIAAoAugCIgEEQCAAKALsAiABQQJ0EN8ECyAAKAL0AiIBBEAgACgC+AIgAUECdBDfBAsgACgCgAMiAQRAIAAoAoQDIAFBAnQQ3wQLIAAoAowDIgEEQCAAKAKQAyABQQJ0EN8ECyAAKAKYAyIBBEAgACgCnAMgAUECdBDfBAsgACgCpAMiAQRAIAAoAqgDIAFBAnQQ3wQLIAAoArADIgEEQCAAKAK0AyABQQJ0EN8ECyAAKAK8AyIBBEAgACgCwAMgAUECdBDfBAsgACgCyAMiAQRAIAAoAswDIAFBAnQQ3wQLIAAoAtQDIgEEQCAAKALYAyABQQJ0EN8EC0EAIQMDQCAAIANqIgFB4ANqKAIAIgIEQCABQeQDaigCACACQQJ0EN8ECyABQewDaigCACICBEAgAUHwA2ooAgAgAkECdBDfBAsgAUH4A2ooAgAiAgRAIAFB/ANqKAIAIAJBAnQQ3wQLIAFBhARqKAIAIgIEQCABQYgEaigCACACQQJ0EN8ECyABQZAEaigCACICBEAgAUGUBGooAgAgAkECdBDfBAsgAUGcBGooAgAiAgRAIAFBoARqKAIAIAJBAnQQ3wQLIAFBqARqKAIAIgIEQCABQawEaigCACACQQJ0EN8ECyABQbQEaigCACICBEAgAUG4BGooAgAgAkECdBDfBAsgAUHABGooAgAiAgRAIAFBxARqKAIAIAJBAnQQ3wQLIANB7ABqIgNB0BdHDQALIAAoArAbIgEEQCAAKAK0GyABQQJ0EN8ECyAAKAK8GyIBBEAgACgCwBsgAUECdBDfBAsgACgCyBsiAQRAIAAoAswbIAFBAnQQ3wQLIAAoAtQbIgEEQCAAKALYGyABQQJ0EN8ECyAAKALgGyIBBEAgACgC5BsgAUECdBDfBAsgACgC7BsiAQRAIAAoAvAbIAFBAnQQ3wQLIAAoAvgbIgEEQCAAKAL8GyABQQJ0EN8ECyAAKAKEHCIBBEAgACgCiBwgAUECdBDfBAsgACgCkBwiAQRAIAAoApQcIAFBAnQQ3wQLIAAoApwcIgEEQCAAKAKgHCABQQJ0EN8ECyAAKAKoHCIBBEAgACgCrBwgAUECdBDfBAsgACgCtBwiAQRAIAAoArgcIAFBAnQQ3wQLIAAoAsAcIgEEQCAAKALEHCABQQJ0EN8ECyAAKALMHCIBBEAgACgC0BwgAUECdBDfBAsgACgC2BwiAQRAIAAoAtwcIAFBAnQQ3wQLIAAoAuQcIgEEQCAAKALoHCABQQJ0EN8ECyAAKALwHCIBBEAgACgC9BwgAUECdBDfBAsgACgC/BwiAQRAIAAoAoAdIAFBAnQQ3wQLIAAoAogdIgEEQCAAKAKMHSABQQJ0EN8ECyAAKAKUHSIBBEAgACgCmB0gAUECdBDfBAsgACgCoB0iAQRAIAAoAqQdIAFBAnQQ3wQLIAAoAqwdIgEEQCAAKAKwHSABQQJ0EN8ECyAAKAK4HSIBBEAgACgCvB0gAUECdBDfBAsgACgCxB0iAQRAIAAoAsgdIAFBAnQQ3wQLIAAoAtAdIgEEQCAAKALUHSABQQJ0EN8ECyAAKALcHSIBBEAgACgC4B0gAUECdBDfBAsgACgC6B0iAQRAIAAoAuwdIAFBAnQQ3wQLIAAoAvQdIgEEQCAAKAL4HSABQQJ0EN8ECyAAKAKAHiIBBEAgACgChB4gAUECdBDfBAsgACgCjB4iAQRAIAAoApAeIAFBAnQQ3wQLIAAoApgeIgEEQCAAKAKcHiABQQJ0EN8ECyAAKAKkHiIBBEAgACgCqB4gAUECdBDfBAsgACgCsB4iAQRAIAAoArQeIAFBAnQQ3wQLIAAoArweIgEEQCAAKALAHiABQQJ0EN8ECyAAKALIHiIBBEAgACgCzB4gAUECdBDfBAsgACgC1B4iAQRAIAAoAtgeIAFBAnQQ3wQLIAAoAuAeIgEEQCAAKALkHiABQQJ0EN8ECyAAKALsHiIBBEAgACgC8B4gAUECdBDfBAsgACgC+B4iAQRAIAAoAvweIAFBAnQQ3wQLIAAoAoQfIgEEQCAAKAKIHyABQQJ0EN8ECyAAKAKQHyIBBEAgACgClB8gAUECdBDfBAsgACgCnB8iAQRAIAAoAqAfIAFBAnQQ3wQLIAAoAqgfIgEEQCAAKAKsHyABQQJ0EN8ECyAAKAK0HyIBBEAgACgCuB8gAUECdBDfBAsgACgCwB8iAQRAIAAoAsQfIAFBAnQQ3wQLIAAoAswfIgEEQCAAKALQHyABQQJ0EN8ECyAAKALYHyIBBEAgACgC3B8gAUECdBDfBAsgACgC5B8iAQRAIAAoAugfIAFBAnQQ3wQLIAAoAvAfIgEEQCAAKAL0HyABQQJ0EN8ECyAAKAL8HyIBBEAgACgCgCAgAUECdBDfBAsgACgCiCAiAQRAIAAoAowgIAFBAnQQ3wQLIAAoApQgIgEEQCAAKAKYICABQQJ0EN8ECyAAKAKgICIBBEAgACgCpCAgAUECdBDfBAsgACgCrCAiAQRAIAAoArAgIAFBAnQQ3wQLIAAoArggIgEEQCAAKAK8ICABQQJ0EN8ECyAAKALEICIBBEAgACgCyCAgAUECdBDfBAsgACgC0CAiAQRAIAAoAtQgIAFBAnQQ3wQLIAAoAtwgIgEEQCAAKALgICABQQJ0EN8ECyAAKALoICIBBEAgACgC7CAgAUECdBDfBAsgACgC9CAiAQRAIAAoAvggIAFBAnQQ3wQLIAAoAoAhIgEEQCAAKAKEISABQQJ0EN8ECyAAKAKMISIBBEAgACgCkCEgAUECdBDfBAsgACgCmCEiAQRAIAAoApwhIAFBAnQQ3wQLIAAoAqQhIgEEQCAAKAKoISABQQJ0EN8ECyAAKAKwISIBBEAgACgCtCEgAUECdBDfBAsgACgCvCEiAQRAIAAoAsAhIAFBAnQQ3wQLIAAoAsghIgEEQCAAKALMISABQQJ0EN8ECyAAKALUISIBBEAgACgC2CEgAUECdBDfBAsgACgC4CEiAQRAIAAoAuQhIAFBAnQQ3wQLIAAoAuwhIgEEQCAAKALwISABQQJ0EN8ECyAAKAL4ISIBBEAgACgC/CEgAUECdBDfBAsgACgChCIiAQRAIAAoAogiIAFBAnQQ3wQLIAAoApAiIgEEQCAAKAKUIiABQQJ0EN8ECyAAKAKcIiIBBEAgACgCoCIgAUECdBDfBAsgACgCqCIiAQRAIAAoAqwiIAFBAnQQ3wQLIAAoArQiIgEEQCAAKAK4IiABQQJ0EN8ECyAAKALAIiIBBEAgACgCxCIgAUECdBDfBAsgACgCzCIiAQRAIAAoAtAiIAFBAnQQ3wQLIAAoAtgiIgEEQCAAKALcIiABQQJ0EN8ECyAAKALkIiIBBEAgACgC6CIgAUECdBDfBAsgACgC8CIiAQRAIAAoAvQiIAFBAnQQ3wQLIAAoAvwiIgEEQCAAKAKAIyABQQJ0EN8ECyAAKAKIIyIBBEAgACgCjCMgAUECdBDfBAsgACgClCMiAQRAIAAoApgjIAFBAnQQ3wQLIAAoAqAjIgEEQCAAKAKkIyABQQJ0EN8ECyAAKAKsIyIBBEAgACgCsCMgAUECdBDfBAsgACgCuCMiAQRAIAAoArwjIAFBAnQQ3wQLIAAoAsQjIgEEQCAAKALIIyABQQJ0EN8ECyAAKALQIyIBBEAgACgC1CMgAUECdBDfBAsgACgC3CMiAQRAIAAoAuAjIAFBAnQQ3wQLIAAoAugjIgEEQCAAKALsIyABQQJ0EN8ECyAAKAL0IyIBBEAgACgC+CMgAUECdBDfBAsgACgCgCQiAQRAIAAoAoQkIAFBAnQQ3wQLIAAoAowkIgEEQCAAKAKQJCABQQJ0EN8ECyAAKAKYJCIBBEAgACgCnCQgAUECdBDfBAsgACgCpCQiAQRAIAAoAqgkIAFBAnQQ3wQLIAAoArAkIgEEQCAAKAK0JCABQQJ0EN8ECyAAKAK8JCIBBEAgACgCwCQgAUECdBDfBAsgACgCyCQiAQRAIAAoAswkIAFBAnQQ3wQLIAAoAtQkIgEEQCAAKALYJCABQQJ0EN8ECyAAKALgJCIBBEAgACgC5CQgAUECdBDfBAsgACgC7CQiAQRAIAAoAvAkIAFBAnQQ3wQLIAAoAvgkIgEEQCAAKAL8JCABQQJ0EN8ECyAAKAKEJSIBBEAgACgCiCUgAUECdBDfBAsgACgCkCUiAQRAIAAoApQlIAFBAnQQ3wQLIAAoApwlIgEEQCAAKAKgJSABQQJ0EN8ECyAAKAKoJSIBBEAgACgCrCUgAUECdBDfBAsgACgCtCUiAQRAIAAoArglIAFBAnQQ3wQLIAAoAsAlIgEEQCAAKALEJSABQQJ0EN8ECyAAKALMJSIBBEAgACgC0CUgAUECdBDfBAsgACgC2CUiAQRAIAAoAtwlIAFBAnQQ3wQLIAAoAuQlIgEEQCAAKALoJSABQQJ0EN8ECyAAKALwJSIBBEAgACgC9CUgAUECdBDfBAsgACgC/CUiAQRAIAAoAoAmIAFBAnQQ3wQLIAAoAogmIgEEQCAAKAKMJiABQQJ0EN8ECyAAKAKUJiIBBEAgACgCmCYgAUECdBDfBAsgACgCoCYiAQRAIAAoAqQmIAFBAnQQ3wQLIAAoAqwmIgEEQCAAKAKwJiABQQJ0EN8ECyAAKAK4JiIBBEAgACgCvCYgAUECdBDfBAsgACgCxCYiAQRAIAAoAsgmIAFBAnQQ3wQLIAAoAtAmIgEEQCAAKALUJiABQQJ0EN8ECyAAKALcJiIBBEAgACgC4CYgAUECdBDfBAsgACgC6CYiAQRAIAAoAuwmIAFBAnQQ3wQLIAAoAvQmIgEEQCAAKAL4JiABQQJ0EN8ECyAAKAKAJyIBBEAgACgChCcgAUECdBDfBAsgACgCjCciAQRAIAAoApAnIAFBAnQQ3wQLIAAoApgnIgEEQCAAKAKcJyABQQJ0EN8ECyAAKAKkJyIBBEAgACgCqCcgAUECdBDfBAsgACgCsCciAQRAIAAoArQnIAFBAnQQ3wQLIAAoArwnIgEEQCAAKALAJyABQQJ0EN8ECyAAKALIJyIBBEAgACgCzCcgAUECdBDfBAsgACgC1CciAQRAIAAoAtgnIAFBAnQQ3wQLIAAoAuAnIgEEQCAAKALkJyABQQJ0EN8ECyAAKALsJyIBBEAgACgC8CcgAUECdBDfBAsgACgC+CciAQRAIAAoAvwnIAFBAnQQ3wQLC9YoAgF/F34jAEGACWsiAiQAIAJB8AhqIAEpAxgiCUIAIAEpAzgiFUIAEMkDIAJBkAhqIAEpAxAiC0IAIBVCABDJAyACQYAIaiABKQMIIgxCACAVQgAQyQMgAkHwB2ogASkDACIPQgAgFUIAEMkDIAJB4AhqIAIpA/AIIgZCAEIAQonHmaSu8IHph38QyQMgAkHQCGogAikD6AgiA0IAQsf688PtgqOQPEIAEMkDIAJBwAhqIANCAEKNlcfDltLawJd/QgAQyQMgAkGwCGogA0IAQt2whYzotpGouH9CABDJAyACQaAIaiADQgBCqcDGia7Ok7IwQgAQyQMgAkHgB2ogASkDMCIXQgAgCUIAEMkDIAJBgAdqIBdCACALQgAQyQMgAkHwBmogF0IAIAxCABDJAyACQeAGaiAXQgAgD0IAEMkDIAJB0AdqIAIpA8AIIhAgAikD+AgiByACKQOQCHwiCHwiBCACKQPYCCAGIAIpA9AIIgN8IANUrXx8IgYgAikD4Ad8IgVCAEIAQonHmaSu8IHph38QyQMgAkHAB2ogAikD2AciA0IAQsf688PtgqOQPEIAEMkDIAJBsAdqIANCAEKNlcfDltLawJd/QgAQyQMgAkGgB2ogA0IAQt2whYzotpGouH9CABDJAyACQZAHaiADQgBCqcDGia7Ok7IwQgAQyQMgAkHQBmogASkDKCINQgAgCUIAEMkDIAJB8AVqIA1CACALQgAQyQMgAkHgBWogDUIAIAxCABDJAyACQdAFaiANQgAgD0IAEMkDIAJBwAZqIAIpA+gHIAUgBlStfCIRIAIpA4AHfCIKIAIpA5gIIAcgCFatfCIOIAIpA4AIfCIHIAIpA7AIfCIIIAQgBlatIAIpA8gIIAQgEFStfHx8IhJ8IgQgAikDsAd8IgYgAikDyAcgAikDwAciAyAFfCADVK18fCIFIAIpA9AGfCIWQgBCAEKJx5mkrvCB6Yd/EMkDIAJBsAZqIAIpA8gGIgNCAELH+vPD7YKjkDxCABDJAyACQaAGaiADQgBCjZXHw5bS2sCXf0IAEMkDIAJBkAZqIANCAELdsIWM6LaRqLh/QgAQyQMgAkGABmogA0IAQqnAxomuzpOyMEIAEMkDIAJBwAVqIAEpAyAiEEIAIAlCABDJAyACQeAEaiAQQgAgC0IAEMkDIAJB0ARqIBBCACAMQgAQyQMgAkHABGogEEIAIA9CABDJAyACQbAFaiACKQPYBiAFIBZWrXwiGCACKQPwBXwiEyACKQOICCAHIA5UrXwiGSACKQPwB3wiDiACKQOgCHwiFCAIIBJWrSACKQO4CCAHIAhWrXx8fCIHIAIpA/AGfCIIIAQgClStIAIpA4gHIAogEVStfHx8IgogAikDoAd8IhEgBSAGVK0gAikDuAcgBCAGVq18fHwiEnwiBCACKQOgBnwiBiACKQO4BiACKQOwBiIDIBZ8IANUrXx8IgUgAikDwAV8IhZCAEIAQonHmaSu8IHph38QyQMgAkGgBWogAikDuAUiA0IAQsf688PtgqOQPEIAEMkDIAJBkAVqIANCAEKNlcfDltLawJd/QgAQyQMgAkGABWogA0IAQt2whYzotpGouH9CABDJAyACQfAEaiADQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAIpA/gEIAIpA4gGIAIpA5gHIAcgFFStIAIpA6gIIA4gFFatfHwgAikD+AcgDiAZVK18fCIOIAIpA+AGfCIDIAggClatIAIpA/gGIAcgCFatfHx8IgcgAikDkAd8IgggB1StfCAIIBEgElatIAIpA6gHIAogEVatfHx8IgogCFStfCADIAdWrSACKQPoBiADIA5UrXx8fCIOIAIpA9AFfCIDIAIpA+gFIAogCiACKQPgBXwiClatfCAKIAogBCATVK0gAikD+AUgEyAYVK18fHwiClatfHwiByACKQOABnwiCCAHVK18IAggAikDmAYgCiAKIAIpA5AGfCIKVq18IAogCiAFIAZUrSACKQOoBiAEIAZWrXx8fCIKVq18fCIEIAhUrXwgAyAHVq0gAikD2AUgAyAOVK18fHwiByACKQPABHwiBiACKQPYBCAEIAIpA9AEfCIDIARUrXwgAyADIAIpA+gEIAIpA8gFIAUgFlatfCIFIAIpA+AEfCIEIAVUrXwgBCAEIAp8IgRWrXx8IgNWrXx8IgUgAikD8AR8IgogBVStfCAKIAIpA4gFIAMgAyACKQOABXwiA1atfCADIAMgAikDmAUgBCAEIAIpA5AFfCIEVq18IAQgAikDqAUgAikDoAUiCCAWfCAIVK18fCIRIARUrXx8IgNWrXx8IgQgClStfCAFIAZUrSACKQPIBCAGIAdUrXx8fCISQqnAxomuzpOyMFYNAAJAIBJCqcDGia7Ok7IwUQRAIARC3bCFjOi2kai4f1YNAiAEQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIRILIAQhFiADIQoMAgsgA0KNlcfDltLawJd/Vg0AQt2whYzotpGouH8hFiADQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIRIgAyEKDAILQo2Vx8OW0trAl38hCiARQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhEgwBCyADQvPquLzpraW/6AB8IgYgEULH+vPD7YKjkDxUrSIFfSEKIARCo8/685fJ7tfHAHwiByADQo2Vx8OW0trAl39UIAUgBlZyrSIDfSEWIBIgBELdsIWM6LaRqLh/VCADIAdWcq19QqnAxomuzpOyMH0hEiARQsf688PtgqOQPH0hEQtCqcDGia7Ok7IwIQQgDCANfCIGIAxUIAYgCyABKQMwIg58IgUgC1QgBSAFIAkgASkDOCIUfCIDIAlUrXwiBVZyrXwiByAGVHKtIA8gEHx8IgghBgJAAkACQCAIQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IQQgByIGQt2whYzotpGouH9SDQBCjZXHw5bS2sCXfyEEIAUiBkKNlcfDltLawJd/Ug0AQsf688PtgqOQPCEEIAMhBiADQsf688PtgqOQPFENAQsgBCAGWA0AIAUhBiAHIRMMAQsgBULz6ri86a2lv+gAfCIEIANCx/rzw+2Co5A8VK0iE30hBiAHQqPP+vOXye7XxwB8IhggBUKNlcfDltLawJd/VCAEIBNUcq0iBH0hEyAIIAdC3bCFjOi2kai4f1QgBCAYVnKtfUKpwMaJrs6TsjB9IQggA0LH+vPD7YKjkDx9IQMLAn4CQAJAIA8iBCAQIgVSDQAgDCIEIA0iBVINACALIgQgDiIFUg0AIAkiBCAUIgVRDQELIAQgBVoNAELdsIWM6LaRqLh/IA0gDH0iBCAXIAt9IgUgCSAVVq0iB1QgCyAXVnKtIg59IhR9IhcgBSAHfSIFQo2Vx8OW0trAl39WQo2Vx8OW0trAl38gBX0iBSAVIAl9IgdCx/rzw+2Co5A8Vq0iCVRyrSIVfSELIBUgF1YgFELdsIWM6LaRqLh/VnIhASAFIAl9IQVCx/rzw+2Co5A8IAd9IQkgBCAOVCAMIA1Wcq0gDyAQfXxCqcDGia7Ok7IwfAwBCyALIBd9IgQgCSAVVK0iB30hBSAMIA19Ig4gCyAXVCAEIAdUcq0iBH0hCyAMIA1UIAQgDlZyIQEgCSAVfSEJIA8gEH0LIQQgAkGwBGogCUIAIANCABDJAyACQcADaiAJQgAgBkIAEMkDIAJBoANqIAlCACATQgAQyQMgAkGAA2ogCUIAIAhCABDJAyACQaAEaiACKQOwBCIJQgBCAEKJx5mkrvCB6Yd/EMkDIAJBkARqIAIpA6gEIgdCAELH+vPD7YKjkDxCABDJAyACQYAEaiAHQgBCjZXHw5bS2sCXf0IAEMkDIAJB8ANqIAdCAELdsIWM6LaRqLh/QgAQyQMgAkHgA2ogB0IAQqnAxomuzpOyMEIAEMkDIAJB4AJqIAVCACADQgAQyQMgAkGAAmogBUIAIAZCABDJAyACQfABaiAFQgAgE0IAEMkDIAJB4AFqIAVCACAIQgAQyQMgAkHQAmogAikDgAQiECACKQO4BCINIAIpA8ADfCIPfCIHIAIpA5gEIAkgAikDkAQiBXwgBVStfHwiCSACKQPgAnwiDEIAQgBCiceZpK7wgemHfxDJAyACQcACaiACKQPYAiIFQgBCx/rzw+2Co5A8QgAQyQMgAkGwAmogBUIAQo2Vx8OW0trAl39CABDJAyACQaACaiAFQgBC3bCFjOi2kai4f0IAEMkDIAJBkAJqIAVCAEKpwMaJrs6TsjBCABDJAyACQdABaiALQgAgA0IAEMkDIAJB8ABqIAtCACAGQgAQyQMgAkEQaiALQgAgE0IAEMkDIAIgC0IAIAhCABDJAyACQcABaiACKQPoAiAJIAxWrXwiDiACKQOAAnwiCyACKQPIAyANIA9WrXwiFCACKQOgA3wiDSACKQPwA3wiDyAHIAlWrSACKQOIBCAHIBBUrXx8fCIVfCIHIAIpA7ACfCIJIAIpA8gCIAIpA8ACIgUgDHwgBVStfHwiDCACKQPQAXwiEEIAQgBCiceZpK7wgemHfxDJAyACQbABaiACKQPIASIFQgBCx/rzw+2Co5A8QgAQyQMgAkGgAWogBUIAQo2Vx8OW0trAl39CABDJAyACQZABaiAFQgBC3bCFjOi2kai4f0IAEMkDIAJBgAFqIAVCAEKpwMaJrs6TsjBCABDJAyACQdADaiAEIAGtfSIEQgAgA0IAEMkDIAJBsANqIARCACAGQgAQyQMgAkGQA2ogBEIAIBNCABDJAyACQfACaiAEQgAgCEIAEMkDIAJB4ABqIAIpA9gBIAwgEFatfCITIAIpA3B8IgQgAikDqAMgDSAUVK18IhQgAikDgAN8IgYgAikD4AN8IgUgDyAVVq0gAikD+AMgDSAPVq18fHwiCCACKQPwAXwiDSAHIAtUrSACKQOIAiALIA5UrXx8fCILIAIpA6ACfCIPIAkgDFatIAIpA7gCIAcgCVatfHx8Ig58IgcgAikDoAF8IgkgAikDuAEgAikDsAEiAyAQfCADVK18fCIMIAIpA9ADfCIQQgBCAEKJx5mkrvCB6Yd/EMkDIAJB0ABqIAIpA2giA0IAQsf688PtgqOQPEIAEMkDIAJBQGsgA0IAQo2Vx8OW0trAl39CABDJAyACQTBqIANCAELdsIWM6LaRqLh/QgAQyQMgAkEgaiADQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAIpAyggAikDiAEgAikDmAIgBSAIVq0gAikD6AMgBSAGVK18fCACKQOIAyAGIBRUrXx8IhQgAikD4AF8IgMgCyANVK0gAikD+AEgCCANVq18fHwiBiACKQOQAnwiBSAGVK18IAUgBSAOIA9UrSACKQOoAiALIA9WrXx8fCIFVq18IAMgBlatIAIpA+gBIAMgFFStfHx8IgggAikDAHwiAyACKQMYIAUgAikDEHwiBiAFVK18IAYgBCAHVq0gAikDeCAEIBNUrXx8fCIEIAZUrXx8IgYgAikDgAF8IgUgBlStfCAFIAIpA5gBIAQgBCACKQOQAXwiBFatfCAEIAkgDFatIAIpA6gBIAcgCVatfHx8IgcgBFStfHwiBCAFVK18IAMgBlatIAIpAwggAyAIVK18fHwiCCACKQPwAnwiBSACKQOYAyAEIAIpA5ADfCIDIARUrXwgAyADIAIpA7gDIAIpA9gDIAwgEFatfCIGIAIpA7ADfCIEIAZUrXwgBCAEIAd8IgRWrXx8IgNWrXx8IgcgAikDIHwiBiAHVK18IAYgBiACKQM4IAMgAyACKQMwfCIDVq18IAMgAyACKQNIIAQgBCACKQNAfCIEVq18IAQgAikDWCACKQNQIgkgEHwgCVStfHwiCyAEVK18fCIDVq18fCIGVq18IAUgB1atIAIpA/gCIAUgCFStfHx8IgxCqcDGia7Ok7IwVg0AAkAgDEKpwMaJrs6TsjBRBEAgBkLdsIWM6LaRqLh/Vg0CIAZC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhDAsgBiEHIAMhBAwCCyADQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEHIANCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhDCADIQQMAgtCjZXHw5bS2sCXfyEEIAtCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEMDAELIANC8+q4vOmtpb/oAHwiBSALQsf688PtgqOQPFStIgd9IQQgBkKjz/rzl8nu18cAfCIIIANCjZXHw5bS2sCXf1QgBSAHVHKtIgN9IQcgDCAGQt2whYzotpGouH9UIAMgCFZyrX1CqcDGia7Ok7IwfSEMIAtCx/rzw+2Co5A8fSELC0KpwMaJrs6TsjAhCCAWIBZ8IgMgFlQgAyAKIAp8IgYgClQgBiAGIBEgEXwiCiARVK18IgZWcq18IgUgA1RyrSASQgGGhCIJIQMCQAJAAkAgCUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEIIAUiA0LdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hCCAGIgNCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhCCAKIgNCx/rzw+2Co5A8UQ0BCyADIAhaDQAgBSEIIAYhAwwBCyAGQvPquLzpraW/6AB8IgggCkLH+vPD7YKjkDxUrSINfSEDIAVCo8/685fJ7tfHAHwiDyAGQo2Vx8OW0trAl39UIAggDVRyrSIGfSEIIAkgBULdsIWM6LaRqLh/VCAGIA9Wcq19QqnAxomuzpOyMH0hCSAKQsf688PtgqOQPH0hCgsgACAKNwM4IAAgAzcDMCAAIAg3AyggACAJNwMgIAAgCzcDGCAAIAQ3AxAgACAHNwMIIAAgDDcDACACQYAJaiQAC+QlAgR/EX4jAEGQBGsiAyQAAn4CQAJAAkAgAkGwpsQAQTAQ8QMEQCADQcACakIANwMAIANBuAJqQgA3AwAgA0GwAmpCADcDACADQagCakIANwMAIANCADcDoAIgA0IBNwPIAkEoIQUgA0H4AmogAkEoaikDADcDACADQfACaiACQSBqKQMANwMAIANB6AJqIAJBGGopAwA3AwAgA0HgAmogAkEQaikDADcDACADQdgCaiACQQhqKQMANwMAIAMgAikDADcD0AIgA0GoA2pB6KTEACkDADcDACADQaADakHgpMQAKQMANwMAIANBmANqQdikxAApAwA3AwAgA0GQA2pB0KTEACkDADcDACADQYgDakHIpMQAKQMANwMAIANBwKTEACkDADcDgAMgA0HYA2pBiKfEACkDADcDACADQdADakGAp8QAKQMANwMAIANByANqQfimxAApAwA3AwAgA0HAA2oiAkHwpsQAKQMANwMAIANBuANqQeimxAApAwA3AwAgA0HgpsQAKQMANwOwAyADQYgEakIANwMAIANBgARqQgA3AwAgA0H4A2pCADcDACADQfADaiIGQgA3AwAgA0HoA2pCADcDACADQgA3A+ADAkAgA0HQAmogA0GgAmpBMBDxA0UEQEKqx6uW2fyjzBEhE0Ktquao29DPvJp/IQcMAQsgA0GAA2ogA0GgAmpBMBDxA0UEQCAGIQIMAQtCq9X+////v/+5fyEOA0AgAy0A+AJBAXFFBEADQCADQdACahC/AiADKQPYAyIHQgGDUEUEQCADKQPQAyEIIAMgB0LVqoGAgIDAgMYAfSILNwPYAyADIAhC///Piuv//9UefCIJIAcgC1atfCILNwPQAyADIAMpA8gDIgpCpOzDtY/UtJjnAHwiByAIIAlWIAkgC1ZyrXwiCTcDyAMgAyADKQPAAyILQr+llJzP8NK75AB8IgggByAKVCAHIAlWcq18Igk3A8ADIAMgAykDuAMiCkLX2a6a5PbpjcsAfCIHIAggC1QgCCAJVnKtfCIINwO4AyADIAMpA7ADIAcgClQgByAIVnKtfEKazf/Lo73EgBp8NwOwAwsgA0GwA2oQvwIgAy0A+AJBAXFFDQALIAMpA6gDIQ4LIA6nQQFxRQRAA0AgA0GAA2oQvwIgAykDiAQiB0IBg1BFBEAgAykDgAQhCCADIAdC1aqBgICAwIDGAH0iCzcDiAQgAyAIQv//z4rr///VHnwiCSAHIAtWrXwiCzcDgAQgAyADKQP4AyIKQqTsw7WP1LSY5wB8IgcgCCAJViAJIAtWcq18Igk3A/gDIAMgAykD8AMiC0K/pZScz/DSu+QAfCIIIAcgClQgByAJVnKtfCIJNwPwAyADIAMpA+gDIgpC19mumuT26Y3LAHwiByAIIAtUIAggCVZyrXwiCDcD6AMgAyADKQPgAyAHIApUIAcgCFZyrXxCms3/y6O9xIAafDcD4AMLIANB4ANqEL8CIAMpA6gDIg5CAYNQDQALCyADKQPYAiEJAkACQCADAn4CQAJAAkACfiADKQOAAyIUIAMpA9ACIhVSBEAgAykDkAMhECADKQOIAyEMIBQhByAVIREgAykD4AIMAQsgAykDkAMhECADKQPgAiELIAkgAykDiAMiDFIEQCAMIQcgCSERIAsMAQsgCyAQUgRAIAkhDCAQIQcgCyERIAsMAQsgAykDmAMiByADKQPoAiIRUgRAIAshECAJIQwgCwwBCyADKQOgAyINIAMpA/ACIhFSBEAgCyEQIAkhDCANIQcgCwwBCyAOIAMpA/gCIhFRDQEgCyEQIAkhDCAOIQcgCwshCCAHIBFWIAMpA+ADIREgAykDsAMhEyADKQOgAyENIAMpA5gDIQcgAykD+AIhCiADKQPwAiEPIAMpA+gCIRJFBEAgECELDAILIAMgDiAKfSIWNwOoAyADIA0gD30iCyAKIA5WrSIKfTcDoAMgAyAHIBJ9Ig4gDSAPVCAKIAtWcq0iC303A5gDIAMgECAIfSIKIAcgElQgCyAOVnKtIgd9NwOQAyADIAwgCX0iCyAIIBBWIAcgClZyrSIHfTcDiAMgAyAUIBV9IAkgDFYgByALVnKtfTcDgAMgAykD6AMhDAJAAkAgESATUgRAIAMpA8ADIQkgAykDuAMhByADKQPwAyEKIBEhDiATIRAMAQsgAykDwAMhCSADKQPwAyEKIAMpA7gDIgcgDFIEQCAMIQ4gByEQDAELIAkgClIEQCAMIQcgCiEOIAkhEAwBCyADKQP4AyINIAMpA8gDIhBSBEAgCiEJIAwhByANIQ4MAQsgAykDgAQiCCADKQPQAyIQUgRAIAohCSAMIQcgCCEODAELIAohCSAMIQcgAykDiAQiDiEPIAghEiANIQsgDiADKQPYAyIQUQ0BCyAOIBBUIAMpA9gDIQ4gAykD0AMhCCADKQPIAyENIAMpA4gEIQ8gAykDgAQhEiADKQP4AyELDQMLIAMgDyAOfTcDiAQgAyASIAh9IhAgDiAPVq0iDn03A4AEIAMgCyANfSIPIA4gEFYgCCASVnKtIgh9NwP4AyADIAogCX0iDiALIA1UIAggD1ZyrSIIfTcD8AMgAyAMIAd9IgsgCCAOViAJIApWcq0iCH0iCTcD6AMgESATfSAIIAtWIAcgDFZyrX0MAwsgAykD4AMhESADKQOwAyETIAkhDCAOIQogDSEPIAchEiALIQgLIAMgCiAOfTcD+AIgAyAPIA19IhAgCiAOVK0iCn03A/ACIAMgEiAHfSIWIAogEFYgDSAPVnKtIgp9NwPoAiADIAggC30iDSAKIBZWIAcgElZyrSIHfTcD4AIgAyAJIAx9IgogCCALVCAHIA1Wcq0iB303A9gCIAMgFSAUfSAJIAxUIAcgClZyrX03A9ACIAMpA7gDIQwCQAJAIBEgE1IEQCADKQPwAyENIAMpA+gDIQkgAykDwAMhDyATIQcgESEUDAELIAMpA/ADIQ0gAykDwAMhDyADKQPoAyIJIAxSBEAgDCEHIAkhFAwBCyANIA9SBEAgDCEJIA8hByANIRQMAQsgAykDyAMiCCADKQP4AyIUUgRAIA8hDSAMIQkgCCEHDAELIAMpA9ADIgogAykDgAQiFFIEQCAPIQ0gDCEJIAohBwwBCyAPIQ0gDCEJIAMpA9gDIgchEiAKIQsgCCEQIAcgAykDiAQiFFENAQsgByAUVCADKQOIBCEHIAMpA4AEIQogAykD+AMhCCADKQPYAyESIAMpA9ADIQsgAykDyAMhEA0DCyADIBIgB303A9gDIAMgCyAKfSIUIAcgElatIgd9NwPQAyADIBAgCH0iEiAKIAtWIAcgFFZyrSIHfTcDyAMgAyAPIA19IgsgCCAQViAHIBJWcq0iB303A8ADIAMgDCAJfSIIIAcgC1YgDSAPVnKtIgt9Igc3A7gDIAMgEyARfSAIIAtUIAkgDFZyrX0iEzcDsAMMAwsgAyAPQqvV/v///7//uX8gDn0iD3wiEDcDiAQgAyASQv//z4rr///VHiAIfSIUIA5Cq9X+////v/+5f1atIhJ9IhV8Ig4gDyAQVq18Ig83A4AEIAMgC0Kk7MO1j9S0mOcAIA19IgsgEiAUViAIQv//z4rr///VHlZyrSIQfSIUfCIIIA4gFVQgDiAPVnKtfCIONwP4AyADIApCv6WUnM/w0rvkACAJfSIKIAsgEFQgDUKk7MO1j9S0mOcAVnKtIg19Ig98IgsgCCAUVCAIIA5Wcq18Ig43A/ADIAMgDELX2a6a5PbpjcsAIAd9IgwgCiANVCAJQr+llJzP8NK75ABWcq0iCn0iDXwiCCALIA9UIAsgDlZyrXwiCTcD6AMgCCANVCAIIAlWcq0gESATfSAKIAxWIAdC19mumuT26Y3LAFZyrX18QprN/8ujvcSAGnwLIhE3A+ADIBYhDgwBCyADQqvV/v///7//uX8gB30iFCASfCISNwPYAyADIAtC///Piuv//9UeIAp9IgsgB0Kr1f7///+//7l/Vq0iFX0iFnwiByASIBRUrXwiFDcD0AMgAyAQQqTsw7WP1LSY5wAgCH0iECALIBVUIApC///Piuv//9UeVnKtIgp9IhJ8IgsgByAWVCAHIBRWcq18IhQ3A8gDIAMgD0K/pZScz/DSu+QAIA19Ig8gCiAQViAIQqTsw7WP1LSY5wBWcq0iCH0iCnwiByALIBJUIAsgFFZyrXwiCzcDwAMgAyAMQtfZrprk9umNywAgCX0iDCAIIA9WIA1Cv6WUnM/w0rvkAFZyrSINfSIPfCIIIAcgClQgByALVnKtfCIHNwO4AyADIAcgCFQgCCAPVHKtIBMgEX0gDCANVCAJQtfZrprk9umNywBWcq19fEKazf/Lo73EgBp8IhM3A7ADCyADQdACaiADQaACaiIEQTAQ8QNFDQEgA0GAA2ogBEEwEPEDDQALIAYhAiAJIQcgESETCyADQZgCaiACQRhqKQMAIgg3AwAgA0GQAmogAkEQaikDACIJNwMAIANBiAJqIAJBCGopAwAiCzcDACADQegBaiALNwMAIANB8AFqIAk3AwAgA0H4AWogCDcDACADIAIpAwAiCDcDgAIgAyAHNwPYASADIBM3A9ABIAMgCDcD4AEgASkDACEQIAEpAwghFCABKQMQIRIgASkDGCEVIAEpAyAhFiABKQMoIRdCACEHQgAhCkIAIQxCACEJQgAhE0IAIREDQCADQfAAaiADQdABaiAFaikDACIIQgAgF0IAEMkDIANBgAFqIAhCACAWQgAQyQMgA0GQAWogCEIAIBVCABDJAyADQaABaiAIQgAgEkIAEMkDIANBsAFqIAhCACAUQgAQyQMgA0HAAWogCEIAIBBCABDJAyADQeAAaiADKQNwIg4gB3wiCEIAQgBC/f/z/8////mJfxDJAyADQdAAaiADKQNoIgdCAEKr1f7///+//7l/QgAQyQMgA0FAayAHQgBC///Piuv//9UeQgAQyQMgA0EwaiAHQgBCpOzDtY/UtJjnAEIAEMkDIANBIGogB0IAQr+llJzP8NK75ABCABDJAyADQRBqIAdCAELX2a6a5PbpjcsAQgAQyQMgAyAHQgBCms3/y6O9xIAaQgAQyQMgAykDCCARIAMpA8ABIhF8IgsgAykDuAEgAykDsAEiDSATfCIHIA1UrXwgByAHIAMpA6gBIAMpA6ABIg0gCXwiCSANVK18IAkgCSADKQOYASAMIAMpA5ABIgx8Ig0gDFStfCANIAMpA4gBIAMpA4ABIgwgCnwiCiAMVK18IAogAykDeCAIIA5UrXx8IgwgClStfHwiCiANVK18fCIJVq18fCIHVq18fCINIAMpAwB8Ig4gDVStfCAOIAMpAxggByADKQMQfCIPIAdUrXwgDyADKQMoIAkgCSADKQMgfCIJVq18IAkgAykDOCAKIAogAykDMHwiClatfCAKIAogAykDSCAMIAMpA0AiDHwiByAMVK18IAcgByADKQNYIAggAykDUCIIfCAIVK18fCIHVq18fCIKVq18fCIMIAlUrXx8IgkgD1StfHwiEyAOVK18IAsgDVatIAMpA8gBIAsgEVStfHx8IREgBUEIayIFQXhHDQALIBFCms3/y6O9xIAaVg0CIBFCms3/y6O9xIAaUQ0BIAkhDSAMIQ8gCiEIIBMhDgwDC0ICIQ5BCCEFQgEMAwsgE0LX2a6a5PbpjcsAVg0AAkAgE0LX2a6a5PbpjcsAUgRAIAkhDSAMIQ8gCiEIIBMhDgwBCyAJQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEOIAlCv6WUnM/w0rvkAFIEQCAJIQ0gDCEPIAohCAwBCyAMQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACENIAxCpOzDtY/UtJjnAFIEQCAMIQ8gCiEIDAELIApC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhDyAKQv//z4rr///VHlIEQCAKIQgMAQtC///Piuv//9UeIQggB0Kq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohEQwBCyAKQv//z4rr///VHn0iCyAHQqvV/v///7//uX9UrSINfSEIIAxCpOzDtY/UtJjnAH0iDiAKQv//z4rr///VHlQgCyANVHKtIgt9IQ8gCUK/pZScz/DSu+QAfSIKIAxCpOzDtY/UtJjnAFQgCyAOVnKtIgt9IQ0gE0LX2a6a5PbpjcsAfSIMIAlCv6WUnM/w0rvkAFQgCiALVHKtIgl9IQ4gESATQtfZrprk9umNywBUIAkgDFZyrX1Cms3/y6O9xIAafSERIAdC1aqBgICAwIDGAHwhBwsgACAHNwMwIAAgCDcDKCAAIA83AyAgACANNwMYIAAgETcDCEEQIQVCAAshByAAIAVqIA43AwAgACAHNwMAIANBkARqJAALySQCNX8FfiMAQZAOayICJAAgAiABNgKQDSACIAFBwAFqIhU2ApQNIAJBiANqIhEgAkGQDWoiEhC9AyACQUBrIgMgAkHAA2oiISkDACI3NwMAIAJBOGoiBCACQbgDaiIiKQMAIjg3AwAgAkEwaiIWIAJBsANqIiMpAwAiOTcDACACQShqIhcgAkGoA2oiJCkDACI6NwMAIAJBIGoiGSACQaADaiIlKQMAIjs3AwAgAkHYDWoiEyACQZADaiImKQMANwMAIAJB4A1qIhQgAkGYA2oiJykDADcDACACQegNaiIFIDs3AwAgAkHwDWoiBiA6NwMAIAJB+A1qIgcgOTcDACACQYAOaiIIIDg3AwAgAkGIDmoiCSA3NwMAIAIgAikDiAMiNzcDCCACIDc3A9ANIAJBwAZqIgogCSkDADcDACACQbgGaiILIAgpAwA3AwAgAkGwBmoiDCAHKQMANwMAIAJBqAZqIg0gBikDADcDACACQaAGaiIOIAUpAwA3AwAgAkGYBmoiDyAUKQMANwMAIAJBkAZqIhAgEykDADcDACACIAIpA9ANNwOIBiACQcAJaiAKKQMANwMAIAJBuAlqIAspAwA3AwAgAkGwCWogDCkDADcDACACQagJaiANKQMANwMAIAJBoAlqIA4pAwA3AwAgAkGYCWogDykDADcDACACQZAJaiAQKQMANwMAIAIgAikDiAY3A4gJIBEgEhC9AyADICEpAwAiNzcDACAEICIpAwAiODcDACAWICMpAwAiOTcDACAXICQpAwAiOjcDACAZICUpAwAiOzcDACATICYpAwA3AwAgFCAnKQMANwMAIAUgOzcDACAGIDo3AwAgByA5NwMAIAggODcDACAJIDc3AwAgAiACKQOIAyI3NwMIIAIgNzcD0A0gCiAJKQMANwMAIAsgCCkDADcDACAMIAcpAwA3AwAgDSAGKQMANwMAIA4gBSkDADcDACAPIBQpAwA3AwAgECATKQMANwMAIAIgAikD0A03A4gGIAJBgApqIAopAwA3AwAgAkH4CWogCykDADcDACACQfAJaiAMKQMANwMAIAJB6AlqIA0pAwA3AwAgAkHgCWogDikDADcDACACQdgJaiAPKQMANwMAIAJB0AlqIBApAwA3AwAgAiACKQOIBjcDyAkgESASEL0DIAMgISkDACI3NwMAIAQgIikDACI4NwMAIBYgIykDACI5NwMAIBcgJCkDACI6NwMAIBkgJSkDACI7NwMAIBMgJikDADcDACAUICcpAwA3AwAgBSA7NwMAIAYgOjcDACAHIDk3AwAgCCA4NwMAIAkgNzcDACACIAIpA4gDIjc3AwggAiA3NwPQDSAKIAkpAwA3AwAgCyAIKQMANwMAIAwgBykDADcDACANIAYpAwA3AwAgDiAFKQMANwMAIA8gFCkDADcDACAQIBMpAwA3AwAgAiACKQPQDTcDiAYgAkHACmogCikDADcDACACQbgKaiALKQMANwMAIAJBsApqIAwpAwA3AwAgAkGoCmogDSkDADcDACACQaAKaiAOKQMANwMAIAJBmApqIA8pAwA3AwAgAkGQCmogECkDADcDACACIAIpA4gGNwOICkEARQRAIAJBiAZqIAJBiAlqQcAB/AoAAAsgAiABQYADajYClAwgAiAVNgKQDCACQdANaiIbIAJBkAxqIigQvQMgAkHIDWoiASAJKQMAIjc3AwAgAkHADWoiFSAIKQMAIjg3AwAgAkG4DWoiESAHKQMAIjk3AwAgAkGwDWoiEiAGKQMAIjo3AwAgAkGoDWoiGCAFKQMAIjs3AwAgAkHYDGoiKSATKQMANwMAIAJB4AxqIiogFCkDADcDACACQegMaiIcIDs3AwAgAkHwDGoiHSA6NwMAIAJB+AxqIh4gOTcDACACQYANaiIfIDg3AwAgAkGIDWoiICA3NwMAIAIgAikD0A0iNzcDkA0gAiA3NwPQDCADICApAwA3AwAgBCAfKQMANwMAIBYgHikDADcDACAXIB0pAwA3AwAgGSAcKQMANwMAIAJBGGoiKyAqKQMANwMAIAJBEGoiGiApKQMANwMAIAIgAikD0Aw3AwggISADKQMANwMAICIgBCkDADcDACAjIBYpAwA3AwAgJCAXKQMANwMAICUgGSkDADcDACAnICspAwA3AwAgJiAaKQMANwMAIAIgAikDCDcDiAMgGyAoEL0DIAEgCSkDACI3NwMAIBUgCCkDACI4NwMAIBEgBykDACI5NwMAIBIgBikDACI6NwMAIBggBSkDACI7NwMAICkgEykDADcDACAqIBQpAwA3AwAgHCA7NwMAIB0gOjcDACAeIDk3AwAgHyA4NwMAICAgNzcDACACIAIpA9ANIjc3A5ANIAIgNzcD0AwgAyAgKQMANwMAIAQgHykDADcDACAWIB4pAwA3AwAgFyAdKQMANwMAIBkgHCkDADcDACArICopAwA3AwAgGiApKQMANwMAIAIgAikD0Aw3AwggAkGABGoiLSADKQMANwMAIAJB+ANqIi4gBCkDADcDACACQfADaiIvIBYpAwA3AwAgAkHoA2oiMCAXKQMANwMAIAJB4ANqIjEgGSkDADcDACACQdgDaiIyICspAwA3AwAgAkHQA2oiMyAaKQMANwMAIAIgAikDCDcDyAMgGyAoEL0DIAEgCSkDACI3NwMAIBUgCCkDACI4NwMAIBEgBykDACI5NwMAIBIgBikDACI6NwMAIBggBSkDACI7NwMAICkgEykDADcDACAqIBQpAwA3AwAgHCA7NwMAIB0gOjcDACAeIDk3AwAgHyA4NwMAICAgNzcDACACIAIpA9ANIjc3A5ANIAIgNzcD0AwgAyAgKQMANwMAIAQgHykDADcDACAWIB4pAwA3AwAgFyAdKQMANwMAIBkgHCkDADcDACArICopAwA3AwAgGiApKQMANwMAIAIgAikD0Aw3AwggAkHABGoiKSADKQMANwMAIAJBuARqIiogBCkDADcDACACQbAEaiI0IBYpAwA3AwAgAkGoBGoiNSAXKQMANwMAIAJBoARqIjYgGSkDADcDACACQZgEaiIZICspAwA3AwAgAkGQBGoiKyAaKQMANwMAIAIgAikDCDcDiAQgLEUEQCACQYgJaiACQYgDakHAAfwKAAALIAJByAdqIRcgLEUEQCAXIAJBiAlqQcAB/AoAAAtBACIWRQRAIAJBCGogAkGIBmpBgAP8CgAACyACIAJByAFqIho2AtQMIAIgAkEIajYC0AwgAkGIA2oiGyACQdAMaiIoEL0DIAkgISkDACI3NwMAIAggIikDACI4NwMAIAcgIykDACI5NwMAIAYgJCkDACI6NwMAIAUgJSkDACI7NwMAIAJBmA1qIgMgJikDADcDACACQaANaiIEICcpAwA3AwAgGCA7NwMAIBIgOjcDACARIDk3AwAgFSA4NwMAIAEgNzcDACACIAIpA4gDIjc3A9ANIAIgNzcDkA0gCiABKQMANwMAIAsgFSkDADcDACAMIBEpAwA3AwAgDSASKQMANwMAIA4gGCkDADcDACAPIAQpAwA3AwAgECADKQMANwMAIAIgAikDkA03A4gGIAJBgAtqIAopAwA3AwAgAkH4CmogCykDADcDACACQfAKaiAMKQMANwMAIAJB6ApqIA0pAwA3AwAgAkHgCmogDikDADcDACACQdgKaiAPKQMANwMAIAJB0ApqIBApAwA3AwAgAiACKQOIBjcDyAogGyAoEL0DIAkgISkDACI3NwMAIAggIikDACI4NwMAIAcgIykDACI5NwMAIAYgJCkDACI6NwMAIAUgJSkDACI7NwMAIAMgJikDADcDACAEICcpAwA3AwAgGCA7NwMAIBIgOjcDACARIDk3AwAgFSA4NwMAIAEgNzcDACACIAIpA4gDIjc3A9ANIAIgNzcDkA0gCiABKQMANwMAIAsgFSkDADcDACAMIBEpAwA3AwAgDSASKQMANwMAIA4gGCkDADcDACAPIAQpAwA3AwAgECADKQMANwMAIAIgAikDkA03A4gGIAJBwAtqIAopAwA3AwAgAkG4C2ogCykDADcDACACQbALaiAMKQMANwMAIAJBqAtqIA0pAwA3AwAgAkGgC2ogDikDADcDACACQZgLaiAPKQMANwMAIAJBkAtqIBApAwA3AwAgAiACKQOIBjcDiAsgGyAoEL0DIAkgISkDACI3NwMAIAggIikDACI4NwMAIAcgIykDACI5NwMAIAYgJCkDACI6NwMAIAUgJSkDACI7NwMAIAMgJikDADcDACAEICcpAwA3AwAgGCA7NwMAIBIgOjcDACARIDk3AwAgFSA4NwMAIAEgNzcDACACIAIpA4gDIjc3A9ANIAIgNzcDkA0gCiABKQMANwMAIAsgFSkDADcDACAMIBEpAwA3AwAgDSASKQMANwMAIA4gGCkDADcDACAPIAQpAwA3AwAgECADKQMANwMAIAIgAikDkA03A4gGIAJBgAxqIAopAwA3AwAgAkH4C2ogCykDADcDACACQfALaiAMKQMANwMAIAJB6AtqIA0pAwA3AwAgAkHgC2ogDikDADcDACACQdgLaiAPKQMANwMAIAJB0AtqIBApAwA3AwAgAiACKQOIBjcDyAsgLEUEQCACQYgGaiACQcgKakHAAfwKAAALIAIgAkGIA2oiKDYCjAwgAiAaNgKIDCACQZANaiIaIAJBiAxqIhsQvQMgICABKQMAIjc3AwAgHyAVKQMAIjg3AwAgHiARKQMAIjk3AwAgHSASKQMAIjo3AwAgHCAYKQMAIjs3AwAgAkGYDGoiCiADKQMANwMAIAJBoAxqIgsgBCkDADcDACACQagMaiIMIDs3AwAgAkGwDGoiDSA6NwMAIAJBuAxqIg4gOTcDACACQcAMaiIPIDg3AwAgAkHIDGoiECA3NwMAIAIgAikDkA0iNzcD0AwgAiA3NwOQDCAJIBApAwA3AwAgCCAPKQMANwMAIAcgDikDADcDACAGIA0pAwA3AwAgBSAMKQMANwMAIBQgCykDADcDACATIAopAwA3AwAgAiACKQOQDDcD0A0gISAJKQMANwMAICIgCCkDADcDACAjIAcpAwA3AwAgJCAGKQMANwMAICUgBSkDADcDACAnIBQpAwA3AwAgJiATKQMANwMAIAIgAikD0A03A4gDIBogGxC9AyAgIAEpAwAiNzcDACAfIBUpAwAiODcDACAeIBEpAwAiOTcDACAdIBIpAwAiOjcDACAcIBgpAwAiOzcDACAKIAMpAwA3AwAgCyAEKQMANwMAIAwgOzcDACANIDo3AwAgDiA5NwMAIA8gODcDACAQIDc3AwAgAiACKQOQDSI3NwPQDCACIDc3A5AMIAkgECkDADcDACAIIA8pAwA3AwAgByAOKQMANwMAIAYgDSkDADcDACAFIAwpAwA3AwAgFCALKQMANwMAIBMgCikDADcDACACIAIpA5AMNwPQDSAtIAkpAwA3AwAgLiAIKQMANwMAIC8gBykDADcDACAwIAYpAwA3AwAgMSAFKQMANwMAIDIgFCkDADcDACAzIBMpAwA3AwAgAiACKQPQDTcDyAMgGiAbEL0DICAgASkDACI3NwMAIB8gFSkDACI4NwMAIB4gESkDACI5NwMAIB0gEikDACI6NwMAIBwgGCkDACI7NwMAIAogAykDADcDACALIAQpAwA3AwAgDCA7NwMAIA0gOjcDACAOIDk3AwAgDyA4NwMAIBAgNzcDACACIAIpA5ANIjc3A9AMIAIgNzcDkAwgCSAQKQMANwMAIAggDykDADcDACAHIA4pAwA3AwAgBiANKQMANwMAIAUgDCkDADcDACAUIAspAwA3AwAgEyAKKQMANwMAIAIgAikDkAw3A9ANICkgCSkDADcDACAqIAgpAwA3AwAgNCAHKQMANwMAIDUgBikDADcDACA2IAUpAwA3AwAgGSAUKQMANwMAICsgEykDADcDACACIAIpA9ANNwOIBCAsRQRAIAJByApqIChBwAH8CgAACyAsRQRAIBcgAkHICmpBwAH8CgAACyAWRQRAIAJBiANqIAJBiAZqQYAD/AoAAAsgAkGIBmoiASACQYgDaiIDEKoBIBZFBEAgAyABQYAD/AoAAAsgAkGIBmoiASACQQhqIgMgAkGIA2oQ9gEgFkUEQCADIAFBgAP8CgAACyAWRQRAIAAgAkEIakGAA/wKAAALIAJBkA5qJAALxyACNn8HfiMAQfAJayIJJAAgCUHIA2oiDEGEvcIAQcAAEHkCQAJAAkACQAJAAkACQAJAAkACQCAJLQDIA0EBRwRAIAlB5gRqIgsgCUHYA2oiCikDACI/NwEAIAlB8AhqIg0iDiA/NwMAIAlBgAlqIhAiDyAJQegDaiIRKQMANwMAIAlB+AhqIhIgCUHgA2oiEykDADcDACAJIAkpA9ADNwPoCCAMQcS9wgBBwAAQeSAJLQDIA0EBRg0BIAsgCikDACI/NwEAIAlBEGogPzcDACAJQSBqIBEpAwA3AwAgCUEYaiATKQMANwMAIAlBQGsgDykDADcDACAJQThqIBIpAwA3AwAgCUEwaiAOKQMANwMAIAkgCSkD0AM3AwggCSAJKQPoCDcDKCAMQYS+wgBBPxB5IAktAMgDQQFGDQIgCyAKKQMAIj83AQAgDSA/NwMAIBAgESkDADcDACASIBMpAwA3AwAgCSAJKQPQAzcD6AggDEHDvsIAQT8QeSAJLQDIA0EBRg0DIAsgCikDACI/NwEAIAlB0ABqID83AwAgCUHgAGogESkDADcDACAJQdgAaiATKQMANwMAIAlBgAFqIA8pAwA3AwAgCUH4AGogEikDADcDACAJQfAAaiAOKQMANwMAIAkgCSkD0AM3A0ggCSAJKQPoCDcDaCAMQYK/wgBBwAAQeSAJLQDIA0EBRg0EIAsgCikDACI/NwEAIAlBkAFqID83AwAgCUGgAWogESIOKQMANwMAIAlBmAFqIBMiDykDADcDACAJIAkpA9ADNwOIASAMQcK/wgBBwAAQeSAJLQDIA0EBRg0FIAsgCikDACI/NwEAIA0gPzcDACAQIA4pAwA3AwAgEiAPKQMANwMAIAkgCSkD0AM3A+gIAn4gCUHoCGpBuLPCAEEgEPEDBEBCjZXHw5bS2sCXfyAJKQP4CCI/fSJAIAkpA4AJIkFCx/rzw+2Co5A8Vq0iQn0hRELdsIWM6LaRqLh/IAkpA/AIIkN9IkUgQCBCVCA/Qo2Vx8OW0trAl39Wcq0iP30hQkLH+vPD7YKjkDwgQX0hQUKpwMaJrs6TsjAgCSkD6AggPyBFViBDQt2whYzotpGouH9Wcq18fQwBCyAJKQOACSFBIAkpA/gIIUQgCSkD8AghQiAJKQPoCAshQyAJQQA2ArQBIAlCgICAgMAANwKsASAEBEAgCUHICGohHCAJQbgIaiESIAlB8ARqIQ4gCUGIBmohICAJQfgFaiETIAlBgAlqIRcgCUHoBmohKyAJQYgIaiEhIAlBiARqIQ8gCUHIBGohLCAJQcgHaiEiIAlBmAVqIREgCUHoA2ohCwNAIAsgCSkDCDcDACALQQhqIg0gCUEQaikDADcDACALQRBqIhAgCUEYaikDADcDACALQRhqIhQgCUEgaikDADcDACAJQeAEaiIVIAlBMGopAwA3AwAgCUHoBGoiFiAJQThqKQMANwMAIA4gCUFAaykDADcDACAJQfgEaiIYIAspAwA3AwAgCUGABWoiLSAJQfADaiIMKQMANwMAIAlBiAVqIi4gCUH4A2oiGSkDADcDACAJQZAFaiIvIAlBgARqIhopAwA3AwAgCSAJKQMoNwPYBCALIAMgH2oiCkEgaiIwKQMANwMAIA0gCkEoaiIxKQMANwMAIBAgCkEwaiIyKQMANwMAIBQgCkE4aiIzKQMANwMAIAlBsAZqIhsgCkEIaiI0KQMANwMAIAlBuAZqIiMgCkEQaiI1KQMANwMAIAlBwAZqIiQgCkEYaiI2KQMANwMAIAlByAZqIiUgCykDADcDACAJQdAGaiImIAwpAwA3AwAgCUHYBmoiJyAZKQMANwMAIAlB4AZqIiggGikDADcDACAJIAopAwA3A6gGIAlByANqIikgCUGoBmoiKhC+AiAJQbgBaiAJQdgEaiIeICkQOCALIAkpA0g3AwAgDSAJQdAAaikDADcDACAQIAlB2ABqKQMANwMAIBQgCUHgAGopAwA3AwAgFSAJQfAAaikDADcDACAWIAlB+ABqKQMANwMAIA4gCUGAAWopAwA3AwAgGCALKQMANwMAIC0gDCkDADcDACAuIBkpAwA3AwAgLyAaKQMANwMAIAkgCSkDaDcD2AQgCyAKQeAAaiI3KQMANwMAIA0gCkHoAGoiOCkDADcDACAQIApB8ABqIjkpAwA3AwAgFCAKQfgAaiI6KQMANwMAIBsgCkHIAGoiOykDADcDACAjIApB0ABqIjwpAwA3AwAgJCAKQdgAaiI9KQMANwMAICUgCykDADcDACAmIAwpAwA3AwAgJyAZKQMANwMAICggGikDADcDACAJIApBQGsiPikDADcDqAYgKSAqEL4CIAlB+AFqIB4gKRA4IA4gCUGgAWopAwA3AwAgFiAJQZgBaikDADcDACAVIAlBkAFqKQMANwMAIAkgCSkDiAE3A9gEIAsgMCkDADcDACANIDEpAwA3AwAgECAyKQMANwMAIBQgMykDADcDACAbIDQpAwA3AwAgIyA1KQMANwMAICQgNikDADcDACAlIAspAwA3AwAgJiAMKQMANwMAICcgGSkDADcDACAoIBopAwA3AwAgCSAKKQMANwOoBiAJQbgCaiAeICoQWSAJIEE3A/AEIAkgRDcD6AQgCSBCNwPgBCAJIEM3A9gEIAsgNykDADcDACANIDgpAwA3AwAgECA5KQMANwMAIBQgOikDADcDACAbIDspAwA3AwAgIyA8KQMANwMAICQgPSkDADcDACAlIAspAwA3AwAgJiAMKQMANwMAICcgGSkDADcDACAoIBopAwA3AwAgCSA+KQMANwOoBiAJQfgCaiAeICoQWSACIB1GDQggESAJKQP4ATcDACAvIAlB8AFqKQMANwMAIC4gCUHoAWopAwA3AwAgLSAJQeABaikDADcDACAYIAlB2AFqKQMANwMAIA4gCUHQAWopAwA3AwAgFiAJQcgBaikDADcDACAVIAlBwAFqKQMANwMAIBFBCGogCUGAAmopAwA3AwAgEUEQaiAJQYgCaikDADcDACARQRhqIAlBkAJqKQMANwMAIBFBIGogCUGYAmopAwA3AwAgEUEoaiAJQaACaikDADcDACARQTBqIAlBqAJqKQMANwMAIBFBOGogCUGwAmopAwA3AwAgCSAJKQO4ATcD2AQgBiAdRg0JIAggHUYNCyAJQagIaiIUIAEgH2oiCkFAayINIBEQ3AEgCUGwCWoiFSAKIB4Q3AEgCUHoCGoiFiAUIBUQkQMgCSkD+AghPyAJKQPwCCFAIAkoAugIQQFGDQogEyAXKQMANwMAIBNBKGogF0EoaikDADcDACATQSBqIBdBIGopAwA3AwAgE0EYaiAXQRhqKQMANwMAIBNBEGogF0EQaikDADcDACATQQhqIBdBCGopAwA3AwAgCUHwBWoiECA/NwMAIAkgQDcD6AUgFSAJQegFaiIYIBgQOCAWIAogHhCgAiAUIBUgFhDcASAWIAogFBDcASAVIBggFhA4ICsgFSANENwBIBsgCUGwCGoiFCkDADcDACAjIBIpAwA3AwAgJCAJQcAIaiIbKQMANwMAICUgHCkDADcDACAmIAlB0AhqKQMANwMAICcgCUHYCGopAwA3AwAgKCAJQeAIaikDADcDACAJQbAHaiAQKQMANwMAIAlBuAdqIBMpAwA3AwAgCUHAB2ogCUGABmopAwA3AwAgCSAJKQOoCDcDqAYgCSAJKQPoBTcDqAcgIkEYaiAgQRhqKQMANwMAICJBEGogIEEQaikDADcDACAiQQhqICBBCGopAwA3AwAgIiAgKQMANwMAIBYgGCAKEDggFSAWIA0Q3AEgLCAJQagHaiAVIAUgBxAZQQAiCkUEQCApICpBgAH8CgAACyAKRQRAIAlBqAZqIAlByANqQYAB/AoAAAsgCUHAA2oiDSAsQQhqKQIANwMAIAkgLCkCADcDuAMgCSgCtAEiCiAJKAKsAUYEQCAJQawBakG0wMIAEKMDCyAJKAKwASAKQQR0aiIQIAkpA7gDNwIAIBBBCGogDSkDADcCACAJIApBAWo2ArQBIBogCUHwAmopAwA3AwAgGSAJQegCaikDADcDACAMIAlB4AJqKQMANwMAIAsgCUHYAmopAwA3AwAgCUHgA2ogCUHQAmopAwA3AwAgCUHYA2ogCUHIAmopAwA3AwAgCUHQA2ogCUHAAmopAwA3AwAgCSAJKQO4AjcDyAMgDyAJKQP4AjcDACAPQQhqIAlBgANqKQMANwMAIA9BEGogCUGIA2opAwA3AwAgD0EYaiAJQZADaikDADcDACAPQSBqIAlBmANqKQMANwMAIA9BKGogCUGgA2opAwA3AwAgD0EwaiAJQagDaikDADcDACAPQThqIAlBsANqKQMANwMAIAlBsAlqIhAgKyAPENwBIAlB6AhqIgogCUGoBmoiDCAJQcgDahDcASAJQdgEaiINIBAgChCRAyAJKQPoBCE/IAkpA+AEIUAgCSgC2ARBAUYNDCASIA4pAwA3AwAgEkEIaiAOQQhqKQMANwMAIBJBKGogDkEoaikDADcDACASQSBqIA5BIGopAwA3AwAgEkEYaiAOQRhqKQMANwMAIBJBEGogDkEQaikDADcDACAUID83AwAgCUHwB2ogPzcDACAJQfgHaiASKQMANwMAIAlBgAhqIBspAwA3AwAgISAcKQMANwMAICFBCGogHEEIaikDADcDACAhQRBqIBxBEGopAwA3AwAgIUEYaiAcQRhqKQMANwMAIAkgQDcDqAggCSBANwPoByANIAlBqAhqIAwQOCAKIA0gKxDcASAJQdgFaiAJQegHaiAKIAUgBxAZIAkoArQBIgogCSgCrAFGBEAgCUGsAWpBxMDCABCjAwsgCSgCsAEgCkEEdGoiDCAJKQLYBTcCACAMQQhqIAlB4AVqKQIANwIAIAkgCkEBajYCtAEgH0GAAWohHyAFQSBqIQUgB0EgaiEHIAQgHUEBaiIdRw0ACwsgACAJKQKsATcCACAAQQhqIAlBtAFqKAIANgIAIAlB8AlqJAAPCyAJIAktAMkDOgDIA0GgscIAQSsgCUHIA2pB1MDCAEG0wcIAEMoDAAsgCSAJLQDJAzoAyANBoLHCAEErIAlByANqQdTAwgBBpMHCABDKAwALIAkgCS0AyQM6AMgDQaCxwgBBKyAJQcgDakHUwMIAQZTBwgAQygMACyAJIAktAMkDOgDIA0GgscIAQSsgCUHIA2pB1MDCAEGEwcIAEMoDAAsgCSAJLQDJAzoAyANBoLHCAEErIAlByANqQdTAwgBB9MDCABDKAwALIAkgCS0AyQM6AMgDQaCxwgBBKyAJQcgDakHUwMIAQeTAwgAQygMACyACIAJBhMDCABDZAwALIAYgBkGUwMIAENkDAAsgCSA/NwPwCCAJIEA3A+gIQdT+wABBKyAJQegIakGwhcEAQdCFwQAQygMACyAIIAhBpMDCABDZAwALIAkgPzcD4AQgCSBANwPYBEHU/sAAQSsgCUHYBGpBsIXBAEHQhcEAEMoDAAvbYAI0fwd+IwBB8AJrIgYkACAGQfAAaiABIAMQPCAGQZgCaiIDIAZB/ABqKAIANgIAIAYgBikCdDcDkAICQAJAAkACQAJAAkACQAJAIAYoAnAiCUGAgICAeEYEQCAAIAYpA5ACNwIEIABBgICAgHg2AgAgAEEMaiADKAIANgIADAELIAZBEGoiByAGQYABakHgAPwKAAAgBkEMaiAGQZgCaigCACILNgIAIAYgBikDkAIiODcCBCAGIAk2AgAgBigCCCIKQQJ0IQlBACEDAkACQAJAAkACQAJAAkAgCkH/////A0sgCUH8////B0tyDQACfyAJRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhAyAJQQQQ1gQiCEUNASAKCyEDIAkEQCAIIDinIAn8CgAACyAGIAo2AugBIAYgCDYC5AEgBiADNgLgASAGKAIYIgpBAnQhA0EAIQkgCkH/////A0sgA0H8////B0tyDQEgBigCFCEMIAYtABwhEwJ/IANFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIANBBBDWBCIIRQ0CIAoLIQkgAwRAIAggDCAD/AoAAAsgBiAKNgL4ASAGIAg2AvQBIAYgCTYC8AEgBiATOgD8ASAGIAs6AOwBAkACfwJAAkACQAJAAkACQAJAAkAgAS0ADCINQQFrDgIFAAELIAEoAggiC0UNBCABKAIEIQkgC0EBayIDQf7///8DcQ0FIANB/////wNxIhNBAWoiDEEDcSEKQgAhOCAJIQMgE0EDTwRAIAxB/P///wdxIQgDQCA4QoABfCE4IANBEGohAyAIQQRrIggNAAsLIAoEQCAKIQgDQCADNQIAIDiGIDl8ITkgOEIgfCE4IANBBGohAyAIQQFrIggNAAsLIDlCgICAgBBUDQRCACE4IAkhAyATQQNPBEAgDEH8////B3EhCANAIDhCgAF8ITggA0EQaiEDIAhBBGsiCA0ACwsgDEEDcQ0BDAILIAEoAgQhCSABKAIIIgsEQCALQQFrIgNB/v///wNxDQUgA0H/////A3EiCkEBaiIMQQNxIQhCACE4IAkhAyAKQQNPBEAgDEH8////B3EhCgNAIDhCgAF8ITggA0EQaiEDIApBBGsiCg0ACwsgCARAA0AgAzUCACA4hiA5fCE5IDhCIHwhOCADQQRqIQMgCEEBayIIDQALCyA5QgBTDQULQgAgOX0hOQwCC0IAITkDQCADNQIAIDiGIDl8ITkgOEIgfCE4IANBBGohAyAKQQFrIgoNAAsLIDlCAFMNAgsgOUKAgICACHxCgICAgBBaDQEgAigCCCIIQQJ0IQFBACEKIAhB/////wNLIAFB/P///wdLcg0IIAIoAgQhDCACLQAMIQMgAQ0CQQQhEkEADAMLIAIoAggiC0ECdCEIQQAhCSALQf////8DSyAIQfz///8HS3INBiACKAIEIQwgAi0ADCEDAn8gCEUEQEEEIQpBAAwBC0HRzsUALQAAGkEEIQkgCEEEENYEIgpFDQcgCwshCSAIBEAgCiAMIAj8CgAACyAGIAM6AHwgBiALNgJ4IAYgCjYCdCAGIAk2AnAgBkHgAmogBkHwAGogOacQnQIgASgCCCELIAEoAgQhCQwDCyAGQfAAaiACIAEQoQEgBigCdCETIAYoAnAhASAGKQJ8IjhCIIinIQogOKchCAJAIAItAAwiA0EBRwRAIANBASAGKAKEASISGyEMDAELIAFBBE8EQCATIAFBAnQQ3wRBBCETQQAhAQtBASEMIAhBBEkNACAKIAhBAnQQ3wRBACEIQQQhCgsgBiAMOgDsAiAGIBI2AugCIAYgCjYC5AIgBiAINgLgAiABRQ0CIBMgAUECdBDfBAwCC0HRzsUALQAAGkEEIQogAUEEENYEIhJFDQUgCAshCiABBEAgEiAMIAH8CgAACyAGIAM6AHwgBiAINgJ4IAYgEjYCdCAGIAo2AnAgBkHgAmogBkHwAGpBACA5pyIBayABIDlCAFMbEJ0CC0EAIQogC0H/////A0sgC0ECdCIBQfz///8HS3INBAJ/IAFFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEKIAFBBBDWBCIIRQ0FIAsLIQogAQRAIAggCSAB/AoAAAsgBiANOgB8IAYgCzYCeCAGIAg2AnQgBiAKNgJwIAZBkAJqIAZB8ABqQQEQ0wEgBi0A7AIiASAGLQCcAkcNBSABQQFHBEAgBigC6AIiASAGKAKYAkcNBiAGKALkAiAGKAKUAiABQQJ0EPEDDQYLIAYoApACIgEEQCAGKAKUAiABQQJ0EN8ECyAGKALgAiIBBEAgBigC5AIgAUECdBDfBAsgBkH4AGpBuMzCACgCADYCACAGQbDMwgApAgA3A3AgBkHwAGpBpM3CABClAyAGKAJ0QQE2AgAgBkGIAmpBATYCACAGIAYpA3A3A4ACQQIhAwwGCyADIAlB+IHAABDIBAALIAkgA0H4gcAAEMgEAAsgCSAIQfiBwAAQyAQACyAKIAFB+IHAABDIBAALIAogAUH4gcAAEMgEAAsgBigCkAIiAQRAIAYoApQCIAFBAnQQ3wQLIAYoAuACIgEEQCAGKALkAiABQQJ0EN8ECyACKAIIIglBAnQhAUEAIQggCUH/////A0sgAUH8////B0tyDQIgAigCBCEKAn8gAUUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQggAUEEENYEIgJFDQMgCQshCCABBEAgAiAKIAH8CgAACyAGIAk2AogCIAYgAjYChAIgBiAINgKAAgsgBiADOgCMAiAGQbACaiAGQYACaiIBIAZB0ABqEJcCIAZB8ABqIgIgASAGQeAAahCXAiAGQQIgBi0AfGs6AHwgBkHIAmogBkH4AGoiASkCADcDACAGIAYpAnA3A8ACQQAhCyABQbjMwgAoAgA2AgAgBkGwzMIAKQIANwNwIAJBpM3CABClAyAGKAJ0QQE2AgAgBiAGKAJ0Igo2ApACIAYoAkgiCUECdCEBIAlB/////wNLIAFB/P///wdLcg0CIAYoAnAhAiAGKAJEIQwgBi0ATCETAn8gAUUEQEEEIQhBAAwBC0HRzsUALQAAGkEEIQsgAUEEENYEIghFDQMgCQshAyABBEAgCCAMIAH8CgAACyAGIAg2AnBBASEBIAZB8ABqIRIgAyELAkAgE0ECRw0AAkACQCAJDgICAAELIAgoAgAgCigCAE8NAAwBCyAGQZACaiESIAIhCyAIIQogAyECIAkhAQsgCwRAIBIoAgAgC0ECdBDfBAsgAQR+IAGtQgaGIAogAUECdGpBBGsoAgBnQQF0rX1CQH1CgP////8BgwVCAAshOCACBEAgCiACQQJ0EN8ECyAGQbACaiIDIDgQvAIgBkHAAmoiCSA4ELwCIAZBkAJqIgIgAyAGEJcCIAZB8ABqIgEgCSAGQSBqEJcCIAZB0AJqIgggAiABEK4BIAIgAyAHEJcCIAEgCSAGQTBqEJcCIAZB4AJqIAIgARCuASABIAZBgAJqIAgQkgEgBi0AfCEIIAYoAnghAyAGKAJ0ISsgBigCcCEnIAYoAugCIQkgBigC5AIhLCAGKALgAiEoIAYtAOwCIQwgBigC0AIiAQRAIAYoAtQCIAFBAnQQ3wQLIAYoAsACIgEEQCAGKALEAiABQQJ0EN8ECyAGKAKwAiIBBEAgBigCtAIgAUECdBDfBAtBACELIANB/////wNLIANBAnQiAUH8////B0tyDQMCfyABRQRAQQQhCkEADAELQdHOxQAtAAAaQQQhCyABQQQQ1gQiCkUNBCADCyESIAEEQCAKICsgAfwKAAALQQAhASAJQf////8DSyAJQQJ0IgJB/P///wdLcg0EAn8gAkUEQEEEIQtBAAwBC0HRzsUALQAAGkEEIQEgAkEEENYEIgtFDQUgCQshASACBEAgCyAsIAL8CgAACyAGIAk2AqgCIAYgCzYCpAIgBiABNgKgAiAGIAw6AKwCIAZBAiAIazoAnAIgBiADNgKYAiAGIAo2ApQCIAYgEjYCkAIgBkHwAGohHiMAQZAEayIEJAAgBCAGQZACaiICNgIMIAQgBkHgAWoiATYCCCABKAIIIgNBAnQhEQJAAkAgA0H/////A0sgEUH8////B0tyDQAgASgCBCEJIAEtAAwhCAJ/IBFFBEBBBCEVQQAMAQtB0c7FAC0AABpBBCEUIBFBBBDWBCIVRQ0BIAMLIQogEQRAIBUgCSAR/AoAAAsgBCADNgIYIAQgFTYCFCAEIAo2AhAgASgCGCIDQQJ0IRFBACEUIANB/////wNLIBFB/P///wdLcg0AIAEoAhQhCSABLQAcIQoCfyARRQRAQQQhFUEADAELQdHOxQAtAAAaQQQhFCARQQQQ1gQiFUUNASADCyELIBEEQCAVIAkgEfwKAAALIAQgAzYCKCAEIBU2AiQgBCALNgIgIAQgCjoALCAEIAg6ABwgAigCCCIDQQJ0IRFBACEUIANB/////wNLIBFB/P///wdLcg0AIAIoAgQhCSACLQAMIQgCfyARRQRAQQQhFUEADAELQdHOxQAtAAAaQQQhFCARQQQQ1gQiFUUNASADCyEKIBEEQCAVIAkgEfwKAAALIAQgAzYCOCAEIBU2AjQgBCAKNgIwIAIoAhgiCUECdCEDQQAhFAJAAkACQAJAAkACQAJAAkAgCUH/////A0sgA0H8////B0tyDQAgAigCFCEKIAItABwhAgJ/IANFBEBBBCELQQAMAQtB0c7FAC0AABpBBCEUIANBBBDWBCILRQ0BIAkLIQwgAwRAIAsgCiAD/AoAAAsgBCAJNgJIIAQgCzYCRCAEIAw2AkAgBCACOgBMIAQgCDoAPEHRzsUALQAAGkEEQQQQ1gQiIEUNASAgQQE2AgBB0c7FAC0AABogBEHgAGpBqMzCACkCACI4NwMAIARB8ABqIDg3AwAgBEGgzMIAKQIAIjg3A1ggBCA4NwNoQQRBBBDWBCICRQ0CIAJBATYCACAEQZABakGozMIAKQIANwIAIARBAjoAhAEgBEEBNgKAASAEIAI2AnwgBEEBNgJ4IARBoMzCACkCADcCiAEgBEHAAWoiAiABEOUCIARBwAJqIgMgAUEQaiIJEOUCIARBgARqIgggAiADEJoBIARBgANqIgIgASAJEJcCIARBnAFqIAggAhCUASAEKALAAiIBBEAgBCgCxAIgAUECdBDfBAsgBCgCwAEiAQRAIAQoAsQBIAFBAnQQ3wQLIAQtAKgBRQ0EIARBQGshMSAEQegAaiEtIARBiAFqIS4gBEGsAWogBEGcAWoQqAMgBEGgnAE2ArwBIARB5QBqITIgBEHNAmohMyAEQaADaiEpIARBsAJqITQgBEHQAmohNSAEQZADaiEhIARBkAJqITYgBEHQAWohG0KAgICAECE8QQQhIkEAIRRCgICAgBAhOUEEISNCgICAgBAhOEEEISRBACERQQIhCEEBIQpBASEcQQAhFQNAIARBwAFqIgEgBEEwaiICEOUCIARBwAJqIgMgMRDlAiAEQYAEaiIJIAEgAxCaASAEQYADaiIBIAIgMRCXAiAEQfADaiAJIAEQlAEgBCgCwAIiAQRAIAQoAsQCIAFBAnQQ3wQLIAQoAsABIgEEQCAEKALEASABQQJ0EN8ECwJAAn8CQAJAIAQtAPwDIgEgBC0AuAEiAkYEQCABQQFrDgIEAgELIAEgAkogASACSGsMAgsgBCgCtAEiASAEKAL4AyICRgRAIAQoArABQQRrIQMgBCgC9ANBBGshCSABQQJ0IQwCQANAIAxFDQEgCSAMaiECIAMgDGogDEEEayEMKAIAIgEgAigCACICRg0ACyABIAJLIAEgAklrDAMLQX9BACAMGwwCCyABIAJLIAEgAklrDAELIAQoAvgDIgEgBCgCtAEiAkYEQCAEKAL0A0EEayEDIAQoArABQQRrIQkgAUECdCEMAkADQCAMRQ0BIAkgDGohAiADIAxqIAxBBGshDCgCACIBIAIoAgAiAkYNAAsgASACSyABIAJJawwCC0F/QQAgDBsMAQsgASACSyABIAJJawtBAE4NACAEKALwAyIBRQ0FIAQoAvQDIAFBAnQQ3wQMBQsgBCgC8AMiAQRAIAQoAvQDIAFBAnQQ3wQLAkAgFUGhnAFHBEAgBC0APEEBRgRAIAQtAExBAUYNBwsgBEGAA2ohFyAEQRBqISVBACEZQQAhA0IAITpCACE7QQAhCUEAIQtBACEMQQAhEkEAIRNCACE9QgAhPiMAQbADayIFJAACQAJAAkACQCAEQTBqIhgtAAxBAUYgGC0AHCINQQFGcUUEQCAFQcABaiIBIBgQ5QIgBUHgAWoiAiAYQRBqIhoQ5QIgBUGQAWoiByABIAIQmgEgBUGAAmoiASAYIBoQlwIgBSAHIAEQlAEgBSgC4AEiAQRAIAUoAuQBIAFBAnQQ3wQLIAUoAsABIgEEQCAFKALEASABQQJ0EN8ECyAFQeABaiAYIBoQkgEgGCgCGCICQQJ0IQFBACEHAn8gAkH/////A0sgAUH8////B0tyDQQgGCgCFCEPAn8gAUUEQEEEIQ5BAAwBC0HRzsUALQAAGkEEIQcgAUEEENYEIg5FDQUgAgshByABBEAgDiAPIAH8CgAACyAFQYgCaiAFQegBaikCADcDACAFIAI2ApgCIAUgDjYClAIgBSAHNgKQAiAFQQIgDWs6AJwCIAUgBSkC4AE3A4ACIAVBwAFqIgIgJSAFQYACaiIPEJcCIAVB4AFqIgEgJUEQaiIqIAVBkAJqIg0QlwIgBUEQaiACIAEQlAEgAiAlIA0QlwIgASAqIA8QlwIgBUGQAWoiDyACIAEQrgEgASAqIA0QlwIgBUEgaiICIA8gARCUASAFKAKAAiIBBEAgBSgChAIgAUECdBDfBAsgBwRAIA4gB0ECdBDfBAsgBUEwaiAFQRBqIAUQhAEgBUFAayACIAUQhAEgBSgCOCIQQQJ0IQECQAJAIBBB/////wNLIAFB/P///wdLcg0AIAUoAjQhDyAFLQA8IR0CfyABRQRAQQQhB0EADAELQdHOxQAtAAAaQQQhGSABQQQQ1gQiB0UNASAQCyEZIAEEQCAHIA8gAfwKAAALIAUoAkgiFkECdCEBQQAhAgJAIBZB/////wNLIAFB/P///wdLcg0AIAUoAkQhDSAFLQBMIR8CfyABRQRAQQQhDkEADAELQdHOxQAtAAAaQQQhAiABQQQQ1gQiDkUNASAWCyECIAEEQCAOIA0gAfwKAAALIAUgHzoAbCAFIBY2AmggBSAONgJkIAUgAjYCYCAFIB06AFwgBSAQNgJYIAUgBzYCVCAFIBk2AlAgBUHgAWoiAiAFQdAAaiIOIBgQlwIgBUGAAmoiASAFQeAAaiIHIBoQlwIgBUHwAGoiECACIAEQlAEgAiAOIBoQlwIgASAHIBgQlwIgBUHAAWoiDiACIAEQrgEgASAHIBoQlwIgBUGAAWoiAiAOIAEQlAEgBUGQAWogJSAQEJIBIAVBoAFqIh8gKiACEJIBIAVBkAJqIS8gBUHwAWohNyAFQdABaiEdAkACQANAIAVBwAFqIgEgBUGQAWoiAhDlAiAFQeABaiIHIB8Q5QIgBUGgA2oiDiABIAcQmgEgBUGAAmoiASACIB8QlwIgBUGQA2ogDiABEJQBIAUoAuABIgEEQCAFKALkASABQQJ0EN8ECyAFKALAASIBBEAgBSgCxAEgAUECdBDfBAsCQAJ/AkACQCAFLQCcAyIBIAUtAAwiAkYEQCABQQFrDgIEAgELIAEgAkogASACSGsMAgsgBSgCCCIBIAUoApgDIgJGBEAgBSgCBEEEayEOIAUoApQDQQRrIRAgAUECdCEHAkADQCAHRQ0BIAcgEGohAiAHIA5qIAdBBGshBygCACIBIAIoAgAiAkYNAAsgASACSyABIAJJawwDC0F/QQAgBxsMAgsgASACSyABIAJJawwBCyAFKAKYAyIBIAUoAggiAkYEQCAFKAKUA0EEayEOIAUoAgRBBGshECABQQJ0IQcCQANAIAdFDQEgByAQaiECIAcgDmogB0EEayEHKAIAIgEgAigCACICRg0ACyABIAJLIAEgAklrDAILQX9BACAHGwwBCyABIAJLIAEgAklrC0EATg0AIAUoApADIgEEQCAFKAKUAyABQQJ0EN8ECyAXIAUpAlA3AgAgF0EgaiAFKQKQATcCACAXQQhqIAVB2ABqKQIANwIAIBdBEGogBUHgAGopAgA3AgAgF0EYaiAFQegAaikCADcCACAXQShqIAVBmAFqKQIANwIAIBdBMGogBUGgAWopAgA3AgAgF0E4aiAFQagBaikCADcCACAFKAJwIgEEQCAFKAJ0IAFBAnQQ3wQLIAUoAoABIgEEQCAFKAKEASABQQJ0EN8ECyAFKAJAIgEEQCANIAFBAnQQ3wQLIAUoAjAiAQRAIA8gAUECdBDfBAsgBSgCECIBBEAgBSgCFCABQQJ0EN8ECyAFKAIgIgEEQCAFKAIkIAFBAnQQ3wQLIAUoAgAiAUUNCSAFKAIEIAFBAnQQ3wQMCQsgBSgCkAMiAQRAIAUoApQDIAFBAnQQ3wQLIAVBwAFqIgEgBUGQAWoiAhDlAiAFQeABaiIHIB8Q5QIgBUGgA2oiDSABIAcQmgEgBUGAAmoiASACIB8QlwIgBUGwAWogDSABEJQBIAUoAuABIgEEQCAFKALkASABQQJ0EN8ECyAFKALAASIBBEAgBSgCxAEgAUECdBDfBAtBgICAgHghAkGAgICAeCEBQQAhGQNAIAUoAjgiDkECdCEHIA5B/////wNLIAdB/P///wdLcg0GIBlBxNvCAGooAgAhDyAFKAI0IRAgBS0APCEWAn8gB0UEQEEEIQ1BAAwBC0HRzsUALQAAGkEEIAdBBBDWBCINRQ0IGiAOCyEwIAcEQCANIBAgB/wKAAALIAUgFjoAjAIgBSAONgKIAiAFIA02AoQCIAUgMDYCgAICQCAPQQBIBEAgBUGgA2ogBUGAAmpBACAPaxDTAQwBCyAFQaADaiAFQYACaiAPEL0BCyAFKAJIIg9BAnQhDkEAIQcCQAJAAkAgD0H/////A0sgDkH8////B0tyDQAgGUHI28IAaigCACEQIAUoAkQhFiAFLQBMITACfyAORQRAQQQhDUEADAELQdHOxQAtAAAaQQQhByAOQQQQ1gQiDUUNASAPCyEHIA4EQCANIBYgDvwKAAALIAUgMDoAjAIgBSAPNgKIAiAFIA02AoQCIAUgBzYCgAICQCAQQQBIBEAgBUHgAWogBUGAAmpBACAQaxDTAQwBCyAFQeABaiAFQYACaiAQEL0BCyAdIAUpAuABNwIAIAVByAFqIAVBqANqKQIANwMAIB1BCGogBUHoAWopAgA3AgAgBSAFKQKgAzcDwAEgBUGgA2oiDSAFQcABaiIOIBgQlwIgBUGAAmoiByAdIBoQlwIgBUHgAWoiDyANIAcQlAEgDSAOIBoQlwIgByAdIBgQlwIgBUGQA2oiDiANIAcQrgEgByAdIBoQlwIgNyAOIAcQlAEgByAlIA8QkgEgLyAqIDcQkgEgBUGAA2oiDyAHEOUCIA4gLxDlAiAFQfACaiIQIA8gDhCaASANIAcgLxCXAiAFQaACaiAQIA0QlAEgBSgCkAMiBwRAIAUoApQDIAdBAnQQ3wQLIAUoAoADIgcEQCAFKAKEAyAHQQJ0EN8ECwJAIAUtAKwCIgcgBS0AvAEiDUYEQAJAAkACQCAHQQFrDgIGAQALIAUoArgBIgcgBSgCqAIiDUYEQCAFKAK0AUEEayENIAUoAqQCQQRrIQ4gB0ECdCEHA0AgB0UNAyAHIA5qIQ8gByANaiAHQQRrIQcoAgAiECAPKAIAIg9GDQALIA8gEE0NBgwECyAHIA1PDQUMAwsgBSgCqAIiByAFKAK4ASINRgRAIAUoAqQCQQRrIQ0gBSgCtAFBBGshDiAHQQJ0IQcCQANAIAdFDQEgByAOaiEPIAcgDWogB0EEayEHKAIAIhAgDygCACIPRg0ACyAPIBBNDQYMBAsgB0UNBQwDCyAHIA1PDQQMAgsgBw0BDAMLIAcgDU8NAgsgBSkD2AEhOiAFKALUASAFKALQASENIAUpA8gBITsgBSgCxAEhDiAFKALAASEPAkAgAUGAgICAeEYNACABBEAgAyABQQJ0EN8ECyAJRQ0AIAsgCUECdBDfBAsgBSkCmAIhPSAFKAKUAiEQIAUoApACIRYgBSkCiAIhPiAFKAKEAiAFKAKAAiEDAkAgAkGAgICAeEYNACACBEAgEiACQQJ0EN8ECyAMRQ0AIBMgDEECdBDfBAsgBSgCsAEiAgRAIAUoArQBIAJBAnQQ3wQLIAVBuAFqIAVBqAJqKQIANwMAIAUgBSkCoAI3A7ABIAUoAuABIgIEQCAFKALkASACQQJ0EN8ECyAFKALwASICBEAgBSgC9AEgAkECdBDfBAshEiADIQIhCyANIQkgDiEDIA8hASAWIQwgECETDAILIAcgDkH4gcAAEMgEAAsgBSgCoAIiBwRAIAUoAqQCIAdBAnQQ3wQLIAUoAoACIgcEQCAFKAKEAiAHQQJ0EN8ECyAFKAKQAiIHBEAgBSgClAIgB0ECdBDfBAsgBSgC4AEiBwRAIAUoAuQBIAdBAnQQ3wQLIAUoAvABIgcEQCAFKAL0ASAHQQJ0EN8ECyAFKALAASIHBEAgBSgCxAEgB0ECdBDfBAsgBSgC0AEiB0UNACAFKALUASAHQQJ0EN8ECyAZQQhqIhlBMEcNAAsgAUGAgICAeEYNASAFKAJQIgcEQCAFKAJUIAdBAnQQ3wQLIAUoAmAiBwRAIAUoAmQgB0ECdBDfBAsgBSALNgJkIAUgCTYCYCAFIAM2AlQgBSABNgJQIAUgOjcCaCAFIDs3AlggAkGAgICAeEcEQCAFKAKQASIBBEAgBSgClAEgAUECdBDfBAsgBSgCoAEiAQRAIAUoAqQBIAFBAnQQ3wQLIAUgPTcCqAEgBSATNgKkASAFIAw2AqABIAUgPjcCmAEgBSASNgKUASAFIAI2ApABIDunIgJBAnQhAUEAIQcgAkH/////A0sgAUH8////B0tyDQsCfyABRQRAQQQhD0EADAELQdHOxQAtAAAaQQQhByABQQQQ1gQiD0UNDCACCyEHIAEEQCAPIAMgAfwKAAALIAUoAjAiAQRAIAUoAjQgAUECdBDfBAsgBSA7QiCIPAA8IAUgAjYCOCAFIA82AjQgBSAHNgIwIDqnIgJBAnQhAUEAIQcgAkH/////A0sgAUH8////B0tyDQMCfyABRQRAQQQhDUEADAELQdHOxQAtAAAaQQQhByABQQQQ1gQiDUUNBCACCyEHIAEEQCANIAsgAfwKAAALIAUoAkAiAQRAIAUoAkQgAUECdBDfBAsgBSA6QiCIPABMIAUgAjYCSCAFIA02AkQgBSAHNgJAIAUoArABIgFFDQEgBSgCtAEgAUECdBDfBAwBCwtByNzCABDoBAALQfTbwgBBG0G43MIAEOgDAAsMBwsMHAsgGSABQfiBwAAQyAQAC0EACyAHQfiBwAAQyAQAC0HRzsUALQAAGkEiQQEQ1gQiAUUNASAXQSI2AgwgFyABNgIIIBdCgICAgKgENwIAIAFBIGpB+NzCAC8AADsAACABQRhqQfDcwgApAAA3AAAgAUEQakHo3MIAKQAANwAAIAFBCGpB4NzCACkAADcAACABQdjcwgApAAA3AAALIAVBsANqJAAMAgtBAUEiQdTYwgAQyAQACyAHIAFB+IHAABDIBAALIAQoAoADQYCAgIB4Rw0BIAQoAoQDIgFFDQYgBCgCiAMgARDfBAwGCyAEQQM2AsQCIARB5N3CADYCwAIgBEIDNwLMAiAEIARBDGqtQoCAgIDAC4Q3A5ADIAQgBEEIaq1CgICAgMALhDcDiAMgBCAEQbwBaq1CgICAgNALhDcDgAMgBCAEQYADajYCyAIgHkEEaiAEQcACahDSAiAeQYCAgIB4NgIAIAQoAqwBIgFFDQcgBCgCsAEgAUECdBDfBAwHCyAEQdgBaiAEQZgDaikCADcDACAbICEpAgA3AwAgBEHIAWogBEGIA2opAgA3AwAgBEHoAWoiAyApQQhqKQIANwMAIARB8AFqIgkgKUEQaikCADcDACAEQfgBaiILIClBGGopAgA3AwAgBCAEKQKAAzcDwAEgBCApKQIANwPgASAEIAg6AMwCIAQgCjYCyAIgBCAgNgLEAiAEIBw2AsACIDMgBC8AVDsAACAzQQJqIARB1gBqIgwtAAA6AAAgBCA4NwLYAiAEICQ2AtQCIAQgETYC0AIgBEHwA2oiAiAEQcABaiIIIARB2ABqIgoQlwIgBEGABGoiASAbIC0QlwIgBEGAA2oiEiACIAEQlAEgAiAIIC0QlwIgASAbIAoQlwIgBEHgA2oiCCACIAEQrgEgASAbIC0QlwIgISAIIAEQlAEgBEGAAmogBEHAAmogEhCSASA2IDUgIRCSASAEKAKAAyIBBEAgBCgChAMgAUECdBDfBAsgBCgCkAMiAQRAIAQoApQDIAFBAnQQ3wQLIAQoAsACIgEEQCAEKALEAiABQQJ0EN8ECyAEKALQAiIBBEAgBCgC1AIgAUECdBDfBAsgBCA8NwLYAiAEICI2AtQCIAQgFDYC0AIgBCA5NwLIAiAEICM2AsQCIAQgJjYCwAIgBEHwA2oiAiAEQcABaiIIIARB+ABqIgoQlwIgBEGABGoiASAbIC4QlwIgBEGAA2oiEiACIAEQlAEgAiAIIC4QlwIgASAbIAoQlwIgBEHgA2oiCCACIAEQrgEgASAbIC4QlwIgISAIIAEQlAEgBEGgAmogBEHAAmogEhCSASA0IDUgIRCSASAEKAKAAyIBBEAgBCgChAMgAUECdBDfBAsgBCgCkAMiAQRAIAQoApQDIAFBAnQQ3wQLIAQoAsACIgEEQCAEKALEAiABQQJ0EN8ECyAEKALQAiIBBEAgBCgC1AIgAUECdBDfBAsgBEHoAmoiASAEQThqIgIpAgA3AwAgBEHwAmoiCCAEQUBrIgopAgA3AwAgBEH4AmoiEiAEQcgAaiITKQIANwMAIAQgBCkCMDcD4AIgBCgCECIHBEAgBCgCFCAHQQJ0EN8ECyAEKAIgIgcEQCAEKAIkIAdBAnQQ3wQLIARBKGogEikDADcDACAEQSBqIAgpAwA3AwAgBEEYaiABKQMANwMAIAIgAykDADcDACAKIAkpAwA3AwAgEyALKQMANwMAIAQgBCkD4AI3AxAgBCAEKQPgATcDMCAEQeAAaiIBKAIAIQogBCgCWCEcIAQoAlwhICAELQBkIQggDCAyQQJqLQAAOgAAIARB6ABqIgIoAgAhESAyLwAAIQMgBCgCbCEkIAIgNikCADcDACAEQfAAaiICKQMAITggAiAEQZgCaikCADcDACABIARBiAJqKQIANwMAIAQgAzsBVCAEIAQpAoACNwNYIARBgAFqIgEpAwAhOSAEQYgBaiICKAIAIRQgBEGQAWoiAykDACE8IAQoAnwhIyAEKAJ4ISYgBCgCjAEhIiADIARBuAJqKQIANwMAIAIgNCkCADcDACABIARBqAJqKQIANwMAIAQgBCkCoAI3A3ggBCgCwAEiAQRAIAQoAsQBIAFBAnQQ3wQLIAQoAtABIgEEQCAEKALUASABQQJ0EN8ECyAVQQFqIRUMAAsACyAUIANB+IHAABDIBAALQQRBBBD/BAALQQRBBBD/BAALIARBmANqIARByABqKQMANwMAIARBkANqIARBQGspAwA3AwAgBEGIA2ogBEE4aikDADcDACAEQagDaiAEQYABaikDADcDACAEQbADaiAEQYgBaikDADcDACAEQbgDaiAEQZABaikDADcDACAEQcgDaiAEQeAAaikDADcDACAEQdADaiAEQegAaikDADcDACAEQdgDaiAEQfAAaikDADcDACAEIAQpAzA3A4ADIAQgBCkDeDcDoAMgBCAEKQNYNwPAAyAeIARBgANqQeAA/AoAACAEKAKsASIBBEAgBCgCsAEgAUECdBDfBAsgBCgCnAEiAQRAIAQoAqABIAFBAnQQ3wQLICYEQCAjICZBAnQQ3wQLIBQEQCAiIBRBAnQQ3wQLIBwEQCAgIBxBAnQQ3wQLIBFFDQIgJCARQQJ0EN8EDAILQQAhFEHRzsUALQAAGkEBIRxBJEEBENYEIgFFDQIgHkEkNgIMIB4gATYCCCAeQoCAgIDIBDcCACABQSBqQZzewgAoAAA2AAAgAUEYakGU3sIAKQAANwAAIAFBEGpBjN7CACkAADcAACABQQhqQYTewgApAAA3AAAgAUH83cIAKQAANwAAQQQhIkEEISNBBCEkQQAhEQsgBCgCnAEiAQRAIAQoAqABIAFBAnQQ3wQLIAQoAngiAQRAIAQoAnwgAUECdBDfBAsgBCgCiAEiAQRAIAQoAowBIAFBAnQQ3wQLIAQoAlgiAQRAIAQoAlwgAUECdBDfBAsgBCgCaCIBBEAgBCgCbCABQQJ0EN8ECyAmBEAgIyAmQQJ0EN8ECyAUBEAgIiAUQQJ0EN8ECyAcBEAgICAcQQJ0EN8ECyARBEAgJCARQQJ0EN8ECyAEKAIwIgEEQCAEKAI0IAFBAnQQ3wQLIAQoAkAiAUUNACAEKAJEIAFBAnQQ3wQLIAQoAhAiAQRAIAQoAhQgAUECdBDfBAsgBCgCICIBBEAgBCgCJCABQQJ0EN8ECyAEQZAEaiQADAILQQFBJEHU2MIAEMgEAAsgFCARQfiBwAAQyAQACyAGLQB8IRIgBigCeCECIAYoAnQhDAJAIAYoAnAiE0GAgICAeEYEQCAGQeICaiAGQf8Aai0AACIBOgAAIAYgBi8AfSIDOwHgAiAAIBI6AAwgACACNgIIIAAgDDYCBCAAIAM7AA0gAEEPaiABOgAAIABBgICAgHg2AgAgBigCkAIiAARAIAYoApQCIABBAnQQ3wQLIAYoAqACIgAEQCAGKAKkAiAAQQJ0EN8ECyAnBEAgKyAnQQJ0EN8ECyAoBEAgLCAoQQJ0EN8ECyAGKAKAAiIABEAgBigChAIgAEECdBDfBAsgBigC4AEiAARAIAYoAuQBIABBAnQQ3wQLIAYoAvABIgBFDQEgBigC9AEgAEECdBDfBAwBCyAGKALEASEDIAYoAsABIQEgBi0ArAEhBCAGKAKoASEIIAYoAqQBIQcgBigCoAEhDSAGLQCcASEFIAYoApgBIQogBigClAEhDiAGKAKQASEPIAYtAIwBIREgBigCiAEhCyAGKAKEASEQIAYoAoABIRYgBigCsAEiCQRAIAYoArQBIAlBAnQQ3wQLIAEEQCADIAFBAnQQ3wQLQQAhAyACQf////8DSyACQQJ0IglB/P///wdLcg0GAn8gCUUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQMgCUEEENYEIgFFDQcgAgshAyAJBEAgASAMIAn8CgAACyAAIAI2AgggACABNgIEIAAgAzYCAEEAIQEgC0H/////A0sgC0ECdCICQfz///8HS3INBwJ/IAJFBEBBBCEDQQAMAQtB0c7FAC0AABpBBCEBIAJBBBDWBCIDRQ0IIAsLIQEgAgRAIAMgECAC/AoAAAsgACALNgIYIAAgAzYCFCAAIAE2AhBBACECIApB/////wNLIApBAnQiAUH8////B0tyDQgCfyABRQRAQQQhA0EADAELQdHOxQAtAAAaQQQhAiABQQQQ1gQiA0UNCSAKCyECIAEEQCADIA4gAfwKAAALIAAgCjYCKCAAIAM2AiQgACACNgIgQQAhAiAIQf////8DSyAIQQJ0IgFB/P///wdLcg0IAn8gAUUEQEEEIQNBAAwBC0HRzsUALQAAGkEEIQIgAUEEENYEIgNFDQkgCAshAiABBEAgAyAHIAH8CgAACyAAIAg2AjggACADNgI0IAAgAjYCMCAAIAQ6ADwgACAFOgAsIAAgEToAHCAAIBI6AAwgDwRAIA4gD0ECdBDfBAsgDQRAIAcgDUECdBDfBAsgEwRAIAwgE0ECdBDfBAsgFgRAIBAgFkECdBDfBAsgBigCkAIiAARAIAYoApQCIABBAnQQ3wQLIAYoAqACIgAEQCAGKAKkAiAAQQJ0EN8ECyAnBEAgKyAnQQJ0EN8ECyAoBEAgLCAoQQJ0EN8ECyAGKAKAAiIABEAgBigChAIgAEECdBDfBAsgBigC4AEiAARAIAYoAuQBIABBAnQQ3wQLIAYoAvABIgBFDQAgBigC9AEgAEECdBDfBAsgBhCmAwsgBkHwAmokAA8LIAggAUH4gcAAEMgEAAsgCyABQfiBwAAQyAQACyALIAFB+IHAABDIBAALIAEgAkH4gcAAEMgEAAsgAyAJQfiBwAAQyAQACyABIAJB+IHAABDIBAALIAIgAUH4gcAAEMgEAAuUJAIOfwN+IwBBkARrIgUkAAJAAkACQAJAIAMoAggiBkUEQEHRzsUALQAAGgwBCyAGrUIFhiADKAIEIAZBAnRqQQRrKAIAZ619QoAQVg0AQdHOxQAtAAAaAkACQCADKAIIDgICAAELIAMoAgQoAgBBAkkNAQsCQAJAAkAgASgCCCIGIAMoAggiB0YEQCAGQQJ0IQYgASgCBEEEayEKIAMoAgRBBGshCANAIAZFDQIgBiAIaiEMIAYgCmogBkEEayEGKAIAIgkgDCgCACIMRg0ACyAJIAxJDQMMAgsgBiAHTw0BDAILIAYNAQtB0c7FAC0AABpBI0EBENYEIgQEQCAAQSM2AgwgACAENgIIIABCgYCAgLAENwIAIARBH2pBwLPEACgAADYAACAEQRhqQbmzxAApAAA3AAAgBEEQakGxs8QAKQAANwAAIARBCGpBqbPEACkAADcAACAEQaGzxAApAAA3AAAMAwtBAUEjQayqxAAQyAQACwJAAkACQCAHIAIoAggiBkYEQCAHQQJ0IQYgAigCBEEEayEHIAMoAgRBBGshCgNAIAZFDQIgBiAKaiEIIAYgB2ogBkEEayEGKAIAIgwgCCgCACIIRg0ACyAIIAxNDQMMAgsgBiAHSQ0BDAILIAZFDQELQQAhBiAFQfgAakGMocQAKAIANgIAIAVBhKHEACkCADcDcCAFQfAAaiIHQeiixAAQpQMgBSgCdEGBgAQ2AgAgBUEIakEBNgIAIAUgBSkDcDcDACAHIAEgBSADEOMEIAUoAnQhByAFKAJ4IgogAigCCEYEQCAHIAIoAgQgCkECdBDxA0UhBgsgBSgCcCIKBEAgByAKQQJ0EN8ECyAGRQRAQdHOxQAtAAAaQTtBARDWBCIEBEAgAEE7NgIMIAAgBDYCCCAAQTs2AgQgBEE3akHzssQAKAAANgAAIARBMGpB7LLEACkAADcAACAEQShqQeSyxAApAAA3AAAgBEEgakHcssQAKQAANwAAIARBGGpB1LLEACkAADcAACAEQRBqQcyyxAApAAA3AAAgBEEIakHEssQAKQAANwAAIARBvLLEACkAADcAACAAQQE2AgAgBSgCACIARQ0EIAUoAgQgAEECdBDfBAwEC0EBQTtBrKrEABDIBAALIAEoAggiBkECdCEHQQAhCAJAAkACQAJAAkACQCAGQf////8DSyAHQfz///8HS3INACABKAIEIQkCfyAHRQRAQQQhCkEADAELQdHOxQAtAAAaQQQhCCAHQQQQ1gQiCkUNASAGCyEMIAcEQCAKIAkgB/wKAAALQdHOxQAtAAAaQZgDQQQQ1gQiB0UNASAFQQA2AhggBSAHNgIUIAVBETYCEEEQIQsDQAJAAkACQAJAIAYOAgABAgsgBUGIBGpBjKHEACgCADYCACAFQYShxAApAgA3A4AEDAILIAooAgAhB0HRzsUALQAAGkEEQQQQ1gQiBkUNBSAFQfgAaiIIQQE2AgAgBiAKKAIANgIAIAUgBjYCdCAFQQE2AnAgBUHwAGogBxCzAiAFQYgEaiAIKAIANgIAIAUgBSkCcDcDgAQMAQsgBUGABGogCiAGIAogBhDtAgsgBUHwAGogBUGABGogAxChASAFQTBqIg4gBUH4AGooAgA2AgAgBSAFKQJwNwMoIAUoAnwiBgRAIAUoAoABIAZBAnQQ3wQLIAVBHGogBUGABGogAxCKAiAFKAIkIgdBAnQhBkEAIQggB0H/////A0sgBkH8////B0tyDQQgBSgCICENAn8gBkUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQggBkEEENYEIglFDQUgBwshDyAGBEAgCSANIAb8CgAACyAFKAIYIgggBSgCEEYEQCAFQRBqQayyxAAQmQMLIAUoAhQgCEEYbGoiBiAFKQMoNwIAIAYgBzYCFCAGIAk2AhAgBiAPNgIMIAZBCGogDigCADYCACAFIAhBAWo2AhggDARAIAogDEECdBDfBAsgBSgCJCEGIAUoAiAhCiAFKAIcIQwgBSgCgAQiBwRAIAUoAoQEIAdBAnQQ3wQLIAtBAWsiCw0ACwJAAkAgBgRAIAEoAggiBw0BCyAFQUBrQYyhxAAoAgA2AgAgBUGEocQAKQIANwM4DAELIAEoAgQhCCAHQQFGBEAgCCgCACEGIAVB8ABqIgcgBUEcahC+AyAHIAYQswIgBUFAayAFQfgAaigCADYCACAFIAUpAnA3AzgMAQsgBkEBRgRAIAooAgAhBiAFQfAAaiIHIAEQvgMgByAGELMCIAVBQGsgBUH4AGooAgA2AgAgBSAFKQJwNwM4DAELIAVBOGogCiAGIAggBxDtAgsgBUHwAGogBUE4aiADEKEBIAVB0ABqIAVB+ABqKAIANgIAIAUgBSkCcDcDSCAFKAJ8IgYEQCAFKAKAASAGQQJ0EN8ECyAFQdQAaiAFQThqIAMQigIgBSgCGCIGIAUoAhBGBEAgBUEQakGMssQAEJkDCyAFKAIUIAZBGGxqIgcgBSkDSDcCACAHQQhqIAVB0ABqKQMANwIAIAdBEGogBUHYAGopAwA3AgAgBSAGQQFqNgIYIAVBADYCbCAFQoCAgIDAADcCZCAEDQQMBQsgCCAHQfiBwAAQyAQAC0EEQZgDQfyxxAAQyAQAC0EEQQRB+IHAABDIBAALIAggBkH4gcAAEMgEAAsgBUGABGohCEEAIQYjAEGgA2siBCQAIAQgAxCOAkHRzsUALQAAGgJAQaACQQQQ1gQiCwRAQeD2wAAoAgAhDSAEQZgDaiEOQdj2wAApAgAhFQNAIAQgBkEEdGoiBykDCCETIAcpAwAhFCAOIA02AgAgBCAVNwOQAyATIBSEUEUEQEEBIQdBACEJA0AgBCgCkAMgB0EBa0YEQCAEQZADakHc98AAEKUDCyAEKAKUAyAJaiAUPgIAIBRC/////w9WIBNCAFIgE1AgE0IghiAUQiCIhCEUIAlBBGohCSATQiCIIRMgBCAHNgKYAyAHQQFqIQcbDQALCyAEQYgDaiAOKAIAIgc2AgAgBCAEKQOQAyITNwOAAyALIAZBDGxqIglBCGogBzYCACAJIBM3AgAgBkEBaiIGQRhHDQALIAhBGDYCCCAIIAs2AgQgCEEYNgIAIARBoANqJAAMAQtBBEGgAkHsscQAEMgEAAsgBSAFKAKABDYCeCAFIAUoAoQEIgQ2AnAgBSAENgJ0IAUgBCAFKAKIBEEMbGo2AnwgBUHkAGogBUHwAGoQxwMLIAVB8ABqIAEQjgJB0c7FAC0AABoCQEGgAkEEENYEIggEQEEAIQRB4PbAACgCACELIAVBiARqIQlB2PbAACkCACEVA0AgBUHwAGogBEEEdGoiBikDCCETIAYpAwAhFCAJIAs2AgAgBSAVNwOABCATIBSEUEUEQEEBIQZBACEHA0AgBSgCgAQgBkEBa0YEQCAFQYAEakHc98AAEKUDCyAFKAKEBCAHaiAUPgIAIBRC/////w9WIBNCAFIgE1AgE0IghiAUQiCIhCEUIAdBBGohByATQiCIIRMgBSAGNgKIBCAGQQFqIQYbDQALCyAFQfgDaiAJKAIAIgY2AgAgBSAFKQOABCITNwPwAyAIIARBDGxqIgdBCGogBjYCACAHIBM3AgAgBEEBaiIEQRhHDQALIAUoAmQgBSgCbCIGa0EXTQRAIAVB5ABqIAZBGEEEQQwQiAMgBSgCbCEGCyAFKAJoIAZBDGxqIAhBoAL8CgAAIAUgBkEYajYCbCAIQaACEN8EIAVB8ABqIAIQjgJBACEEQdHOxQAtAAAaQaACQQQQ1gQiCEUNBkHg9sAAKAIAIQsgBUGIBGohCUHY9sAAKQIAIRUDQCAFQfAAaiAEQQR0aiIGKQMIIRMgBikDACEUIAkgCzYCACAFIBU3A4AEIBMgFIRQRQRAQQEhBkEAIQcDQCAFKAKABCAGQQFrRgRAIAVBgARqQdz3wAAQpQMLIAUoAoQEIAdqIBQ+AgAgFEL/////D1YgE0IAUiATUCATQiCGIBRCIIiEIRQgB0EEaiEHIBNCIIghEyAFIAY2AogEIAZBAWohBhsNAAsLIAVB+ANqIAkoAgAiBjYCACAFIAUpA4AEIhM3A/ADIAggBEEMbGoiB0EIaiAGNgIAIAcgEzcCACAEQQFqIgRBGEcNAAsgBSgCZCAFKAJsIgZrQRdNBEAgBUHkAGogBkEYQQRBDBCIAyAFKAJsIQYLIAUoAmggBkEMbGogCEGgAvwKAAAgBSAGQRhqNgJsIAhBoAIQ3wQgBSgCGCIEBEAgBSgCFCIIIARBGGxqIQ4gBUGIBGohCQNAIAVB8ABqIAgQjgJB0c7FAC0AABpBoAJBBBDWBCILRQ0IIAhBDGohDSAIQRhqIQhBACEEA0AgBUHwAGogBEEEdGoiBikDCCETIAYpAwAhFCAJQeD2wAAoAgAiDzYCACAFQdj2wAApAgAiFTcDgAQgEyAUhFBFBEBBASEGQQAhBwNAIAUoAoAEIAZBAWtGBEAgBUGABGpB3PfAABClAwsgBSgChAQgB2ogFD4CACAUQv////8PViATQgBSIBNQIBNCIIYgFEIgiIQhFCAHQQRqIQcgE0IgiCETIAUgBjYCiAQgBkEBaiEGGw0ACwsgBUH4A2oiECAJKAIAIgY2AgAgBSAFKQOABCITNwPwAyALIARBDGxqIgdBCGogBjYCACAHIBM3AgAgBEEBaiIEQRhHDQALIAUoAmQgBSgCbCIGa0EXTQRAIAVB5ABqIAZBGEEEQQwQiAMgBSgCbCEGCyAFKAJoIAZBDGxqIAtBoAL8CgAAIAUgBkEYajYCbCALQaACEN8EIAVB8ABqIA0QjgJB0c7FAC0AABpBoAJBBBDWBCILRQ0DQQAhBANAIAVB8ABqIARBBHRqIgYpAwghEyAGKQMAIRQgCSAPNgIAIAUgFTcDgAQgEyAUhFBFBEBBASEGQQAhBwNAIAUoAoAEIAZBAWtGBEAgBUGABGpB3PfAABClAwsgBSgChAQgB2ogFD4CACAUQv////8PViATQgBSIBNQIBNCIIYgFEIgiIQhFCAHQQRqIQcgE0IgiCETIAUgBjYCiAQgBkEBaiEGGw0ACwsgECAJKAIAIgY2AgAgBSAFKQOABCITNwPwAyALIARBDGxqIgdBCGogBjYCACAHIBM3AgAgBEEBaiIEQRhHDQALIAUoAmQgBSgCbCIGa0EXTQRAIAVB5ABqIAZBGEEEQQwQiAMgBSgCbCEGCyAFKAJoIAZBDGxqIAtBoAL8CgAAIAUgBkEYajYCbCALQaACEN8EIAggDkcNAAsLIAAgBSkCZDcCBCAAQQA2AgAgAEEMaiAFQewAaigCADYCACAFKAI4IgAEQCAFKAI8IABBAnQQ3wQLIAUoAhgiBwRAIAUoAhQhBgNAIAYoAgAiAARAIAZBBGooAgAgAEECdBDfBAsgBkEMaigCACIABEAgBkEQaigCACAAQQJ0EN8ECyAGQRhqIQYgB0EBayIHDQALCyAFKAIQIgAEQCAFKAIUIABBGGwQ3wQLIAwEQCAKIAxBAnQQ3wQLIAUoAgAiAEUNBCAFKAIEIABBAnQQ3wQMBAsMBQsMBAtB0c7FAC0AABpBKkEBENYEIgQEQCAAQSo2AgwgACAENgIIIABCgYCAgKAFNwIAIARBKGpBn7PEAC8AADsAACAEQSBqQZezxAApAAA3AAAgBEEYakGPs8QAKQAANwAAIARBEGpBh7PEACkAADcAACAEQQhqQf+yxAApAAA3AAAgBEH3ssQAKQAANwAADAILQQFBKkGsqsQAEMgEAAtB0c7FAC0AABpBN0EBENYEIgRFDQEgAEE3NgIMIAAgBDYCCCAAQoGAgIDwBjcCACAEQS9qQfOzxAApAAA3AAAgBEEoakHss8QAKQAANwAAIARBIGpB5LPEACkAADcAACAEQRhqQdyzxAApAAA3AAAgBEEQakHUs8QAKQAANwAAIARBCGpBzLPEACkAADcAACAEQcSzxAApAAA3AAALIAMoAgAiAARAIAMoAgQgAEECdBDfBAsgAigCACIABEAgAigCBCAAQQJ0EN8ECyABKAIAIgAEQCABKAIEIABBAnQQ3wQLIAVBkARqJAAPC0EBQTdBrKrEABDIBAALQQRBoAJB7LHEABDIBAAL0R4BDn8jAEHwHmsiAyQAIANBgBhqIgRBAEHgAPwLAAJAAkACQAJAAkACQAJAIAJBwAFqIgUgBEEwEPEDRQRAIAJB8AFqIANBsBhqQTAQ8QNFDQELIANBgBhqIgZBAEHgAPwLACABQcABaiIEIAZBMBDxA0UEQCABQfABaiADQbAYakEwEPEDRQ0CCyADIAJB4ABqIAQQPyADQeAAaiABQeAAaiIGIAUQPyADQcABaiIHIAIgBBA/IANBoAJqIgIgASAFED8gByACQTAQ8QNFBEAgA0HwAWogA0HQAmpBMBDxA0UNAwtBACIBRQRAIANBgBhqIANB4AD8CgAACyADQeAPaiADQYAYaiICIANB4ABqEI0BIAFFBEAgAiADQcABakHgAPwKAAALIANBwBBqIgIgA0GAGGoiBiADQaACaiIJEI0BIANBoBFqIgggBCAFED8gA0GAEmoiCiADQeAPaiIEIAQQPyADQeASaiIFIAIgAhA/IANBwBNqIgsgAiAFED8gA0GgFGoiByAFIAkQPyAGIAogCBA/IANBqBpqIgUgBiALEI0BIAYgByAHENUBIANBgBVqIgcgBSAGEI0BIAUgAiAHED8gAUUEQCADQcAWaiAEQeAA/AoAAAsgAUUEQCADQYAYaiADQYAVakHgAPwKAAALIANBoBdqIgIgA0GgFGogA0GAGGoiBBCNASADQeAVaiADQcAWaiACED8gAUUEQCAEIANB4ABqQeAA/AoAAAsgA0GgF2oiAiADQcATaiADQYAYaiIEED8gA0GIG2ogA0HgFWogAhCNASABRQRAIAQgA0GgEWpB4AD8CgAACyADQegbaiADQcATaiADQYAYaiIBED8gASADQagaahCvAiADKAKAGEUNA0GQjcUAQSsgA0HvHmpBgI3FAEHAksUAEMoDAAsgA0HwHGogAUEoaikDADcDACADQegcaiABQSBqKQMANwMAIANB4BxqIAFBGGopAwA3AwAgA0HYHGogAUEQaikDADcDACADQdAcaiABQQhqKQMANwMAIANBgB1qIAFBOGopAwA3AwAgA0GIHWogAUFAaykDADcDACADQZAdaiABQcgAaikDADcDACADQZgdaiABQdAAaikDADcDACADQaAdaiABQdgAaikDADcDACADIAEpAwA3A8gcIAMgASkDMDcD+BxBACICRQRAIANBgANqIANByBxqQeAA/AoAAAsgA0GoGGoiBCABQYgBaikDADcDACADQaAYaiIGIAFBgAFqKQMANwMAIANBmBhqIgUgAUH4AGopAwA3AwAgA0GQGGoiByABQfAAaikDADcDACADQYgYaiIJIAFB6ABqKQMANwMAIANBuBhqIgggAUGYAWopAwA3AwAgA0HAGGoiCiABQaABaikDADcDACADQcgYaiILIAFBqAFqKQMANwMAIANB0BhqIgwgAUGwAWopAwA3AwAgA0HYGGoiDSABQbgBaikDADcDACADIAEpA2A3A4AYIAMgASkDkAE3A7AYIAJFBEAgA0HIHGogA0GAGGpB4AD8CgAACyACRQRAIANB4ANqIANByBxqQeAA/AoAAAsgBCABQegBaikDADcDACAGIAFB4AFqKQMANwMAIAUgAUHYAWopAwA3AwAgByABQdABaikDADcDACAJIAFByAFqKQMANwMAIAggAUH4AWopAwA3AwAgCiABQYACaikDADcDACALIAFBiAJqKQMANwMAIAwgAUGQAmopAwA3AwAgDSABQZgCaikDADcDACADIAEpA8ABNwOAGCADIAEpA/ABNwOwGCACRQRAIANByBxqIANBgBhqQeAA/AoAAAsgAkUEQCADQcAEaiADQcgcakHgAPwKAAALIAAgA0GAA2pBoAL8CgAADAQLIANB0B1qIAJBKGopAwA3AwAgA0HIHWogAkEgaikDADcDACADQcAdaiACQRhqKQMANwMAIANBuB1qIAJBEGopAwA3AwAgA0GwHWogAkEIaikDADcDACADQeAdaiACQThqKQMANwMAIANB6B1qIAJBQGspAwA3AwAgA0HwHWogAkHIAGopAwA3AwAgA0H4HWogAkHQAGopAwA3AwAgA0GAHmogAkHYAGopAwA3AwAgAyACKQMANwOoHSADIAIpAzA3A9gdQQAiAUUEQCADQaAFaiADQagdakHgAPwKAAALIANBqBhqIgQgAkGIAWopAwA3AwAgA0GgGGoiBiACQYABaikDADcDACADQZgYaiIHIAJB+ABqKQMANwMAIANBkBhqIgkgAkHwAGopAwA3AwAgA0GIGGoiCCACQegAaikDADcDACADQbgYaiIKIAJBmAFqKQMANwMAIANBwBhqIgsgAkGgAWopAwA3AwAgA0HIGGoiDCACQagBaikDADcDACADQdAYaiINIAJBsAFqKQMANwMAIANB2BhqIg4gAkG4AWopAwA3AwAgAyACKQNgNwOAGCADIAIpA5ABNwOwGCABRQRAIANBqB1qIANBgBhqQeAA/AoAAAsgAUUEQCADQYAGaiADQagdakHgAPwKAAALIAQgBUEoaikDADcDACAGIAVBIGopAwA3AwAgByAFQRhqKQMANwMAIAkgBUEQaikDADcDACAIIAVBCGopAwA3AwAgCiACQfgBaikDADcDACALIAJBgAJqKQMANwMAIAwgAkGIAmopAwA3AwAgDSACQZACaikDADcDACAOIAJBmAJqKQMANwMAIAMgBSkDADcDgBggAyACKQPwATcDsBggAUUEQCADQagdaiADQYAYakHgAPwKAAALIAFFBEAgA0HgBmogA0GoHWpB4AD8CgAACyAAIANBoAVqQaAC/AoAAAwDCwJAIAMgA0HgAGpBMBDxAw0AIANBMGogA0GQAWpBMBDxAw0AIANBgBhqIgJBAEHgAPwLACAGIAJBMBDxAw0CIAFBkAFqIANBsBhqQTAQ8QMNAgtBACIBRQRAIANBqBpqQQBB4AD8CwALIANB2BdqQgA3AwAgA0HgF2pCADcDACADQegXakIANwMAIANB8BdqQgA3AwAgA0H4F2pCADcDACADQcgXakGgkcUAKQMANwMAIANBwBdqQZiRxQApAwA3AwAgA0G4F2pBkJHFACkDADcDACADQbAXakGIkcUAKQMANwMAIANBqBdqQYCRxQApAwA3AwAgA0IANwPQFyADQfiQxQApAwA3A6AXIAFFBEAgA0HoG2pBAEHgAPwLAAsgAUUEQCADQYgbaiADQaAXakHgAPwKAAALIANBgBhqIANBqBpqEK8CIAMoAoAYQQFGDQMgACADQYgYakGgAvwKAAAMAgsgACADQYgYakGgAvwKAAAMAQsgA0GAGGoiAkEAQeAA/AsAAkACQCAEIAJBMBDxA0UEQCABQfABaiICIANBsBhqQTAQ8QNFDQELIANBwAdqIgIgASABED8gA0GAGGoiBSACIAIQ1QEgA0GgCGogBSACENUBQQAiAkUEQCAFQQBB4AD8CwALIANBqBpqIgkgA0GAGGoiBSAEED8gBSAJIAQQPyADQYAJaiIHIAUgA0GgCGoQ1QEgA0HgCWoiCyAHIAcQPyADQcAKaiIHIAYgBBA/IANBoAtqIgQgByAHED8gA0GADGoiCCAHIAQQPyADQeAMaiIKIAggCBDVASADQcANaiIIIAogChDVASADQaAOaiAIIAgQ1QEgBSABIAYQPyADQYAPaiIBIAUgBxA/IANB4A9qIgggASABENUBIANBwBBqIgEgCCAIENUBIANBoBFqIgggASABENUBIANBgBJqIgEgCyAIEI0BIANB4BJqIAEgBxA/IAkgBiAGED8gAkUEQCAFIARB4AD8CgAACyADQcATaiIBIANBqBpqIgUgA0GAGGoQPyADQaAUaiIEIAEgARDVASADQYAVaiIBIAQgBBDVASADQeAVaiABIAEQ1QEgBSADQeASaiIBIAEQ1QEgAkUEQCADQcAWaiADQYAJakHgAPwKAAALIAJFBEAgA0GAGGogA0HAEGpB4AD8CgAACyADQaAXaiIEIANBgBhqIgEgA0GAEmoQjQEgASADQcAWaiAEED8gA0GIG2ogASADQeAVahCNASACRQRAIANB6BtqIANBoA5qQeAA/AoAAAsgA0GAGGogA0GoGmoQrwIgAygCgBhFDQFBkI3FAEErIANB7x5qQYCNxQBBoJLFABDKAwALIANBsB5qIAFBKGopAwA3AwAgA0GoHmogAUEgaikDADcDACADQaAeaiABQRhqKQMANwMAIANBmB5qIAFBEGopAwA3AwAgA0GQHmogAUEIaikDADcDACADQcAeaiABQThqKQMANwMAIANByB5qIAFBQGspAwA3AwAgA0HQHmogAUHIAGopAwA3AwAgA0HYHmogAUHQAGopAwA3AwAgA0HgHmogAUHYAGopAwA3AwAgAyABKQMANwOIHiADIAEpAzA3A7geQQAiBUUEQCADQYAYaiADQYgeakHgAPwKAAALIANB0BpqIgcgBkEoaikDADcDACADQcgaaiIJIAZBIGopAwA3AwAgA0HAGmoiCCAGQRhqKQMANwMAIANBuBpqIgogBkEQaikDADcDACADQbAaaiILIAZBCGopAwA3AwAgA0HgGmoiDCABQZgBaikDADcDACADQegaaiINIAFBoAFqKQMANwMAIANB8BpqIg4gAUGoAWopAwA3AwAgA0H4GmoiDyABQbABaikDADcDACADQYAbaiIQIAFBuAFqKQMANwMAIAMgBikDADcDqBogAyABKQOQATcD2BogBUUEQCADQYgeaiADQagaakHgAPwKAAALIAVFBEAgA0HgGGogA0GIHmpB4AD8CgAACyAHIARBKGopAwA3AwAgCSAEQSBqKQMANwMAIAggBEEYaikDADcDACAKIARBEGopAwA3AwAgCyAEQQhqKQMANwMAIAwgAkEIaikDADcDACANIAJBEGopAwA3AwAgDiACQRhqKQMANwMAIA8gAkEgaikDADcDACAQIAJBKGopAwA3AwAgAyAEKQMANwOoGiADIAIpAwA3A9gaIAVFBEAgA0GIHmogA0GoGmpB4AD8CgAACyAFRQRAIANBwBlqIANBiB5qQeAA/AoAAAsgACADQYAYakGgAvwKAAAMAQsgACADQYgYakGgAvwKAAALIANB8B5qJAAPC0GQjcUAQSsgA0HvHmpBgI3FAEGwksUAEMoDAAvqIQIPfxx+IwBBsAJrIgMkACADQQA2AgggA0KAgICAgAE3AgAgA0EANgIUIANCgICAgIABNwIMAkACQAJAIAJFDQAgAUEwaiIEQdizwgBBMBDxA0UNAiABIAJB6ABsaiEIIANBQGshBSADQZACaiEJIANByABqIQZBkLPCACkDACEiQYizwgApAwAhI0GAs8IAKQMAISRB+LLCACkDACElQfCywgApAwAhJkHossIAKQMAISdBsLTCACkDACEoQai0wgApAwAhKUGgtMIAKQMAISpBmLTCACkDACErQZC0wgApAwAhLEGItMIAKQMAIS0DQCADQZABakIANwMAIANBiAFqQgA3AwAgA0GAAWpCADcDACADQfgAakIANwMAIANCADcDcCADQgE3A5gBIANByAFqIARBKGopAwA3AwAgA0HAAWogBEEgaikDADcDACADQbgBaiAEQRhqKQMANwMAIANBsAFqIARBEGopAwA3AwAgA0GoAWogBEEIaikDADcDACADIAQpAwA3A6ABIANB+AFqICI3AwAgA0HwAWogIzcDACADQegBaiAkNwMAIANB4AFqICU3AwAgA0HYAWogJjcDACADICc3A9ABIANBqAJqIgogKDcDACADQaACaiILICk3AwAgA0GYAmoiDCAqNwMAIANBkAJqIg0gKzcDACADQYgCaiIOICw3AwAgAyAtNwOAAiADQeAAakIANwMAIANB2ABqQgA3AwAgA0HQAGpCADcDACADQcgAakIANwMAIAVCADcDACADQgA3AzggA0EwaiIPAn8CQCADQaABaiADQfAAakEwEPEDRQRAQq2q5qjb0M+8mn8hEkKqx6uW2fyjzBEhHwwBCyADQdABaiADQfAAakEwEPEDRQRAQgAhH0IAIRIgBgwCC0Kr1f7///+//7l/IRcDQCADLQDIAUEBcUUEQANAIANBoAFqEL8CIAMpA6gCIhJCAYNQRQRAIAMpA6ACIRMgAyASQtWqgYCAgMCAxgB9IhQ3A6gCIAMgE0L//8+K6///1R58IhUgEiAUVq18IhQ3A6ACIAMgAykDmAIiFkKk7MO1j9S0mOcAfCISIBQgFVQgEyAVVnKtfCIVNwOYAiADIAMpA5ACIhRCv6WUnM/w0rvkAHwiEyASIBZUIBIgFVZyrXwiFTcDkAIgAyADKQOIAiIWQtfZrprk9umNywB8IhIgEyAUVCATIBVWcq18IhM3A4gCIAMgAykDgAIgEiAWVCASIBNWcq18QprN/8ujvcSAGnw3A4ACCyADQYACahC/AiADLQDIAUEBcUUNAAsgAykD+AEhFwsgF6dBAXFFBEADQCADQdABahC/AiADKQNgIhJCAYNQRQRAIAMpA1ghEyADIBJC1aqBgICAwIDGAH0iFDcDYCADIBNC///Piuv//9UefCIVIBIgFFatfCIUNwNYIAMgAykDUCIWQqTsw7WP1LSY5wB8IhIgFCAVVCATIBVWcq18IhU3A1AgAyADKQNIIhRCv6WUnM/w0rvkAHwiEyASIBZUIBIgFVZyrXwiFTcDSCADIAMpA0AiFkLX2a6a5PbpjcsAfCISIBMgFFQgEyAVVnKtfCITNwNAIAMgAykDOCASIBZUIBIgE1ZyrXxCms3/y6O9xIAafDcDOAsgA0E4ahC/AiADKQP4ASIXQgGDUA0ACwsgAykDqAEhFQJAAkAgAwJ+AkACQAJAAn4gAykD0AEiHiADKQOgASIgUgRAIAMpA+ABIRQgAykD2AEhGCAeIRIgICEdIAMpA7ABDAELIAMpA+ABIRQgAykDsAEhEyAVIAMpA9gBIhhSBEAgGCESIBUhHSATDAELIBMgFFIEQCAVIRggFCESIBMhHSATDAELIAMpA+gBIhIgAykDuAEiHVIEQCATIRQgFSEYIBMMAQsgAykD8AEiFiADKQPAASIdUgRAIBMhFCAVIRggFiESIBMMAQsgFyADKQPIASIdUQ0BIBMhFCAVIRggFyESIBMLIRkgEiAdViADKQM4IR0gAykDgAIhHyADKQPwASEWIAMpA+gBIRIgAykDyAEhHCADKQPAASEaIAMpA7gBIRtFBEAgFCETDAILIAMgFyAcfSIhNwP4ASADIBYgGn0iEyAXIBxUrSIXfTcD8AEgAyASIBt9IhwgFiAaVCATIBdUcq0iE303A+gBIAMgFCAZfSIWIBIgG1QgEyAcVnKtIhJ9NwPgASADIBggFX0iEyAUIBlUIBIgFlZyrSISfTcD2AEgAyAeICB9IBUgGFYgEiATVnKtfTcD0AEgAykDQCEYAkACQCAdIB9SBEAgAykDkAIhFSADKQOIAiESIAMpA0ghGiAdIRcgHyEUDAELIAMpA5ACIRUgAykDSCEaIAMpA4gCIhIgGFIEQCAYIRcgEiEUDAELIBUgGlIEQCAYIRIgGiEXIBUhFAwBCyADKQNQIhYgAykDmAIiFFIEQCAaIRUgGCESIBYhFwwBCyADKQNYIhwgAykDoAIiFFIEQCAaIRUgGCESIBwhFwwBCyAaIRUgGCESIAMpA2AiFyEbIBwhGSAWIRMgFyADKQOoAiIUUQ0BCyAUIBdWIAMpA6gCIRcgAykDoAIhHCADKQOYAiEWIAMpA2AhGyADKQNYIRkgAykDUCETDQMLIAMgGyAXfTcDYCADIBkgHH0iFCAXIBtWrSIXfTcDWCADIBMgFn0iGyAZIBxUIBQgF1RyrSIUfTcDUCADIBogFX0iFyATIBZUIBQgG1ZyrSITfTcDSCADIBggEn0iFCATIBdWIBUgGlZyrSITfSIVNwNAIB0gH30gEyAUViASIBhWcq19DAMLIAMpAzghHSADKQOAAiEfIBUhGCAXIRwgFiEaIBIhGyATIRkLIAMgHCAXfTcDyAEgAyAaIBZ9IhQgFyAcVq0iHH03A8ABIAMgGyASfSIhIBQgHFQgFiAaVnKtIhR9NwO4ASADIBkgE30iFiAUICFWIBIgG1ZyrSISfTcDsAEgAyAVIBh9IhQgEyAZViASIBZWcq0iEn03A6gBIAMgICAefSAVIBhUIBIgFFZyrX03A6ABIAMpA4gCIRgCQAJAIB0gH1IEQCADKQNIIRYgAykDQCEVIAMpA5ACIRsgHyESIB0hHgwBCyADKQNIIRYgAykDkAIhGyADKQNAIhUgGFIEQCAYIRIgFSEeDAELIBYgG1IEQCAYIRUgGyESIBYhHgwBCyADKQOYAiIcIAMpA1AiHlIEQCAbIRYgGCEVIBwhEgwBCyADKQOgAiIaIAMpA1giHlIEQCAbIRYgGCEVIBohEgwBCyAbIRYgGCEVIAMpA6gCIhIhGSAaIRMgHCEUIBIgAykDYCIeUQ0BCyASIB5UIAMpA2AhEiADKQNYIRogAykDUCEcIAMpA6gCIRkgAykDoAIhEyADKQOYAiEUDQMLIAMgGSASfTcDqAIgAyATIBp9Ih4gEiAZVq0iEn03A6ACIAMgFCAcfSIZIBMgGlQgEiAeVnKtIhJ9NwOYAiADIBsgFn0iEyAUIBxUIBIgGVZyrSISfTcDkAIgAyAYIBV9IhQgEiATViAWIBtWcq0iE30iEjcDiAIgAyAfIB19IBMgFFYgFSAYVnKtfSIfNwOAAgwDCyADIBtCq9X+////v/+5fyAXfSIbfCIeNwNgIAMgGUL//8+K6///1R4gHH0iGSAXQqvV/v///7//uX9WrSIXfSIgfCIUIBsgHlatfCIbNwNYIANCpOzDtY/UtJjnACAWfSIeIBcgGVYgHEL//8+K6///1R5Wcq0iF30iGSATfCITIBQgIFQgFCAbVnKtfCIcNwNQIAMgGkK/pZScz/DSu+QAIBV9IhogFyAeViAWQqTsw7WP1LSY5wBWcq0iFn0iF3wiFCATIBlUIBMgHFZyrXwiGTcDSCADIBhC19mumuT26Y3LACASfSIYIBYgGlYgFUK/pZScz/DSu+QAVnKtIhZ9Ihp8IhMgFCAXVCAUIBlWcq18IhU3A0AgEyAaVCATIBVWcq0gHSAffSAWIBhWIBJC19mumuT26Y3LAFZyrX18QprN/8ujvcSAGnwLIh03AzggISEXDAELIAMgGUKr1f7///+//7l/IBJ9Ihl8Ih43A6gCIAMgE0L//8+K6///1R4gGn0iEyASQqvV/v///7//uX9WrSIgfSIhfCISIBkgHlatfCIZNwOgAiADIBRCpOzDtY/UtJjnACAcfSIUIBMgIFQgGkL//8+K6///1R5Wcq0iGn0iHnwiEyASICFUIBIgGVZyrXwiGTcDmAIgAyAbQr+llJzP8NK75AAgFn0iGyAUIBpUIBxCpOzDtY/UtJjnAFZyrSIUfSIafCISIBMgHlQgEyAZVnKtfCIZNwOQAiADIBhC19mumuT26Y3LACAVfSIYIBQgG1YgFkK/pZScz/DSu+QAVnKtIhR9IhZ8IhMgEiAaVCASIBlWcq18IhI3A4gCIAMgEiATVCATIBZUcq0gHyAdfSAUIBhWIBVC19mumuT26Y3LAFZyrX18QprN/8ujvcSAGnwiHzcDgAILIANBoAFqIANB8ABqIgJBMBDxA0UNASADQdABaiACQTAQ8QMNAAsgHSEfIBUhEiAGDAELIAkLIgJBGGopAwA3AwAgA0EoaiIQIAJBEGopAwA3AwAgA0EgaiIRIAJBCGopAwA3AwAgAyACKQMANwMYIAMoAggiByADKAIARgRAIANBhLrCABCcAwsgAygCBCAHQTBsaiICIBI3AwggAiAfNwMAIAIgAykDGDcDECACQRhqIBEpAwA3AwAgAkEgaiAQKQMANwMAIAJBKGogDykDADcDACADIAdBAWo2AgggA0E4aiABIAQQTCADKAI4QQFGDQIgCiAFQShqKQMANwMAIAsgBUEgaikDADcDACAMIAVBGGopAwA3AwAgDSAFQRBqKQMANwMAIA4gBUEIaikDADcDACADIAUpAwA3A4ACAn4gA0GAAmpB2LPCAEEwEPEDBEBC///Piuv//9UeIAMpA6ACIhN9IhUgAykDqAIiFEKr1f7///+//7l/Vq0iFn0hF0Kk7MO1j9S0mOcAIAMpA5gCIhp9IhkgFSAWVCATQv//z4rr///VHlZyrSITfSEdQr+llJzP8NK75AAgAykDkAIiFX0iFiATIBlWIBpCpOzDtY/UtJjnAFZyrSITfSEfQtfZrprk9umNywAgAykDiAIiGn0iGSATIBZWIBVCv6WUnM/w0rvkAFZyrSITfSEVQprN/8ujvcSAGiADKQOAAiATIBlWIBpC19mumuT26Y3LAFZyrXx9IRhCq9X+////v/+5fyAUfQwBCyADKQOgAiEXIAMpA5gCIR0gAykDkAIhHyADKQOIAiEVIAMpA4ACIRggAykDqAILIRYgAygCFCIEIAMoAgxGBEAgA0EMakGUusIAEJwDCyADKAIQIARBMGxqIgIgFjcDKCACIBc3AyAgAiAdNwMYIAIgHzcDECACIBU3AwggAiAYNwMAIAMgBEEBajYCFCABQegAaiICIAhGDQEgAUGYAWohBCACIQEgBEHYs8IAQTAQ8QMNAAsMAgsgACADKQIANwIAIAAgAykCDDcCDCAAQQhqIANBCGooAgA2AgAgAEEUaiADQRRqKAIANgIAIANBsAJqJAAPCyADIAMpA0g3A4gCIAMgAykDQDcDgAJBoLHCAEErIANBgAJqQaS6wgBBtLrCABDKAwALIAMgEjcDQCADQgI3AzhBoLHCAEErIANBOGpBpLrCAEHEusIAEMoDAAufJAIJfwF+IwBBEGsiCCQAAn8CQAJAAkACQAJAAkAgAEH1AU8EQEEAIABBzP97Sw0HGiAAQQtqIgFBeHEhBUGM0sUAKAIAIglFDQRBHyEHQQAgBWshBCAAQfT//wdNBEAgBUEGIAFBCHZnIgBrdkEBcSAAQQF0a0E+aiEHCyAHQQJ0QfDOxQBqKAIAIgFFBEBBACEADAILQQAhACAFQRkgB0EBdmtBACAHQR9HG3QhAwNAAkAgASgCBEF4cSIGIAVJDQAgBiAFayIGIARPDQAgASECIAYiBA0AQQAhBCABIQAMBAsgASgCFCIGIAAgBiABIANBHXZBBHFqKAIQIgFHGyAAIAYbIQAgA0EBdCEDIAENAAsMAQtBiNLFACgCACICQRAgAEELakH4A3EgAEELSRsiBUEDdiIAdiIBQQNxBEACQCABQX9zQQFxIABqIgZBA3QiAEGA0MUAaiIDIABBiNDFAGooAgAiASgCCCIERwRAIAQgAzYCDCADIAQ2AggMAQtBiNLFACACQX4gBndxNgIACyABIABBA3I2AgQgACABaiIAIAAoAgRBAXI2AgQgAUEIagwHCyAFQZDSxQAoAgBNDQMCQAJAIAFFBEBBjNLFACgCACIARQ0GIABoQQJ0QfDOxQBqKAIAIgIoAgRBeHEgBWshBCACIQEDQAJAIAIoAhAiAA0AIAIoAhQiAA0AIAEoAhghBwJAAkAgASABKAIMIgBGBEAgAUEUQRAgASgCFCIAG2ooAgAiAg0BQQAhAAwCCyABKAIIIgIgADYCDCAAIAI2AggMAQsgAUEUaiABQRBqIAAbIQMDQCADIQYgAiIAQRRqIABBEGogACgCFCICGyEDIABBFEEQIAIbaigCACICDQALIAZBADYCAAsgB0UNBAJAIAEoAhxBAnRB8M7FAGoiAigCACABRwRAIAEgBygCEEcEQCAHIAA2AhQgAA0CDAcLIAcgADYCECAADQEMBgsgAiAANgIAIABFDQQLIAAgBzYCGCABKAIQIgIEQCAAIAI2AhAgAiAANgIYCyABKAIUIgJFDQQgACACNgIUIAIgADYCGAwECyAAKAIEQXhxIAVrIgIgBCACIARJIgIbIQQgACABIAIbIQEgACECDAALAAsCQEECIAB0IgNBACADa3IgASAAdHFoIgZBA3QiAUGA0MUAaiIDIAFBiNDFAGooAgAiACgCCCIERwRAIAQgAzYCDCADIAQ2AggMAQtBiNLFACACQX4gBndxNgIACyAAIAVBA3I2AgQgACAFaiIGIAEgBWsiA0EBcjYCBCAAIAFqIAM2AgBBkNLFACgCACIEBEAgBEF4cUGA0MUAaiEBQZjSxQAoAgAhAgJ/QYjSxQAoAgAiBUEBIARBA3Z0IgRxRQRAQYjSxQAgBCAFcjYCACABDAELIAEoAggLIQQgASACNgIIIAQgAjYCDCACIAE2AgwgAiAENgIIC0GY0sUAIAY2AgBBkNLFACADNgIAIABBCGoMCAtBjNLFAEGM0sUAKAIAQX4gASgCHHdxNgIACwJAAkAgBEEQTwRAIAEgBUEDcjYCBCABIAVqIgMgBEEBcjYCBCADIARqIAQ2AgBBkNLFACgCACIGRQ0BIAZBeHFBgNDFAGohAEGY0sUAKAIAIQICf0GI0sUAKAIAIgVBASAGQQN2dCIGcUUEQEGI0sUAIAUgBnI2AgAgAAwBCyAAKAIICyEGIAAgAjYCCCAGIAI2AgwgAiAANgIMIAIgBjYCCAwBCyABIAQgBWoiAEEDcjYCBCAAIAFqIgAgACgCBEEBcjYCBAwBC0GY0sUAIAM2AgBBkNLFACAENgIACyABQQhqDAYLIAAgAnJFBEBBACECQQIgB3QiAEEAIABrciAJcSIARQ0DIABoQQJ0QfDOxQBqKAIAIQALIABFDQELA0AgACACIAAoAgRBeHEiAyAFayIGIARJIgcbIQkgACgCECIBRQRAIAAoAhQhAQsgAiAJIAMgBUkiABshAiAEIAYgBCAHGyAAGyEEIAEiAA0ACwsgAkUNACAFQZDSxQAoAgAiAE0gBCAAIAVrT3ENACACKAIYIQcCQAJAIAIgAigCDCIARgRAIAJBFEEQIAIoAhQiABtqKAIAIgENAUEAIQAMAgsgAigCCCIBIAA2AgwgACABNgIIDAELIAJBFGogAkEQaiAAGyEDA0AgAyEGIAEiAEEUaiAAQRBqIAAoAhQiARshAyAAQRRBECABG2ooAgAiAQ0ACyAGQQA2AgALIAdFDQICQCACKAIcQQJ0QfDOxQBqIgEoAgAgAkcEQCACIAcoAhBHBEAgByAANgIUIAANAgwFCyAHIAA2AhAgAA0BDAQLIAEgADYCACAARQ0CCyAAIAc2AhggAigCECIBBEAgACABNgIQIAEgADYCGAsgAigCFCIBRQ0CIAAgATYCFCABIAA2AhgMAgsCQAJAAkACQAJAIAVBkNLFACgCACIBSwRAIAVBlNLFACgCACIATwRAIAVBr4AEakGAgHxxIgJBEHZAACEAIAhBBGoiAUEANgIIIAFBACACQYCAfHEgAEF/RiICGzYCBCABQQAgAEEQdCACGzYCAEEAIAgoAgQiAUUNCRogCCgCDCEGQaDSxQAgCCgCCCIEQaDSxQAoAgBqIgA2AgBBpNLFACAAQaTSxQAoAgAiAiAAIAJLGzYCAAJAAkBBnNLFACgCACICBEBB8M/FACEAA0AgASAAKAIAIgMgACgCBCIHakYNAiAAKAIIIgANAAsMAgtBrNLFACgCACIAQQAgACABTRtFBEBBrNLFACABNgIAC0Gw0sUAQf8fNgIAQfzPxQAgBjYCAEH0z8UAIAQ2AgBB8M/FACABNgIAQYzQxQBBgNDFADYCAEGU0MUAQYjQxQA2AgBBiNDFAEGA0MUANgIAQZzQxQBBkNDFADYCAEGQ0MUAQYjQxQA2AgBBpNDFAEGY0MUANgIAQZjQxQBBkNDFADYCAEGs0MUAQaDQxQA2AgBBoNDFAEGY0MUANgIAQbTQxQBBqNDFADYCAEGo0MUAQaDQxQA2AgBBvNDFAEGw0MUANgIAQbDQxQBBqNDFADYCAEHE0MUAQbjQxQA2AgBBuNDFAEGw0MUANgIAQczQxQBBwNDFADYCAEHA0MUAQbjQxQA2AgBByNDFAEHA0MUANgIAQdTQxQBByNDFADYCAEHQ0MUAQcjQxQA2AgBB3NDFAEHQ0MUANgIAQdjQxQBB0NDFADYCAEHk0MUAQdjQxQA2AgBB4NDFAEHY0MUANgIAQezQxQBB4NDFADYCAEHo0MUAQeDQxQA2AgBB9NDFAEHo0MUANgIAQfDQxQBB6NDFADYCAEH80MUAQfDQxQA2AgBB+NDFAEHw0MUANgIAQYTRxQBB+NDFADYCAEGA0cUAQfjQxQA2AgBBjNHFAEGA0cUANgIAQZTRxQBBiNHFADYCAEGI0cUAQYDRxQA2AgBBnNHFAEGQ0cUANgIAQZDRxQBBiNHFADYCAEGk0cUAQZjRxQA2AgBBmNHFAEGQ0cUANgIAQazRxQBBoNHFADYCAEGg0cUAQZjRxQA2AgBBtNHFAEGo0cUANgIAQajRxQBBoNHFADYCAEG80cUAQbDRxQA2AgBBsNHFAEGo0cUANgIAQcTRxQBBuNHFADYCAEG40cUAQbDRxQA2AgBBzNHFAEHA0cUANgIAQcDRxQBBuNHFADYCAEHU0cUAQcjRxQA2AgBByNHFAEHA0cUANgIAQdzRxQBB0NHFADYCAEHQ0cUAQcjRxQA2AgBB5NHFAEHY0cUANgIAQdjRxQBB0NHFADYCAEHs0cUAQeDRxQA2AgBB4NHFAEHY0cUANgIAQfTRxQBB6NHFADYCAEHo0cUAQeDRxQA2AgBB/NHFAEHw0cUANgIAQfDRxQBB6NHFADYCAEGE0sUAQfjRxQA2AgBB+NHFAEHw0cUANgIAQZzSxQAgAUEPakF4cSIAQQhrIgI2AgBBgNLFAEH40cUANgIAQZTSxQAgBEEoayIDIAEgAGtqQQhqIgA2AgAgAiAAQQFyNgIEIAEgA2pBKDYCBEGo0sUAQYCAgAE2AgAMCAsgAiADSSABIAJNcg0AIAAoAgwiA0EBcQ0AIANBAXYgBkYNAwtBrNLFAEGs0sUAKAIAIgAgASAAIAFJGzYCACABIARqIQNB8M/FACEAAkACQANAIAMgACgCACIHRwRAIAAoAggiAA0BDAILCyAAKAIMIgNBAXENACADQQF2IAZGDQELQfDPxQAhAANAAkAgAiAAKAIAIgNPBEAgAiADIAAoAgRqIgdJDQELIAAoAgghAAwBCwtBnNLFACABQQ9qQXhxIgBBCGsiAzYCAEGU0sUAIARBKGsiCSABIABrakEIaiIANgIAIAMgAEEBcjYCBCABIAlqQSg2AgRBqNLFAEGAgIABNgIAIAIgB0Ega0F4cUEIayIAIAAgAkEQakkbIgNBGzYCBEHwz8UAKQIAIQogA0EQakH4z8UAKQIANwIAIAMgCjcCCEH8z8UAIAY2AgBB9M/FACAENgIAQfDPxQAgATYCAEH4z8UAIANBCGo2AgAgA0EcaiEAA0AgAEEHNgIAIABBBGoiACAHSQ0ACyACIANGDQcgAyADKAIEQX5xNgIEIAIgAyACayIAQQFyNgIEIAMgADYCACAAQYACTwRAIAIgABD7AgwICyAAQfgBcUGA0MUAaiEBAn9BiNLFACgCACIDQQEgAEEDdnQiAHFFBEBBiNLFACAAIANyNgIAIAEMAQsgASgCCAshACABIAI2AgggACACNgIMIAIgATYCDCACIAA2AggMBwsgACABNgIAIAAgACgCBCAEajYCBCABQQ9qQXhxQQhrIgIgBUEDcjYCBCAHQQ9qQXhxQQhrIgQgAiAFaiIAayEFIARBnNLFACgCAEYNAyAEQZjSxQAoAgBGDQQgBCgCBCIBQQNxQQFGBEAgBCABQXhxIgEQ4AIgASAFaiEFIAEgBGoiBCgCBCEBCyAEIAFBfnE2AgQgACAFQQFyNgIEIAAgBWogBTYCACAFQYACTwRAIAAgBRD7AgwGCyAFQfgBcUGA0MUAaiEBAn9BiNLFACgCACIDQQEgBUEDdnQiBHFFBEBBiNLFACADIARyNgIAIAEMAQsgASgCCAshAyABIAA2AgggAyAANgIMIAAgATYCDCAAIAM2AggMBQtBlNLFACAAIAVrIgE2AgBBnNLFAEGc0sUAKAIAIgAgBWoiAjYCACACIAFBAXI2AgQgACAFQQNyNgIEIABBCGoMCAtBmNLFACgCACEAAkAgASAFayICQQ9NBEBBmNLFAEEANgIAQZDSxQBBADYCACAAIAFBA3I2AgQgACABaiIBIAEoAgRBAXI2AgQMAQtBkNLFACACNgIAQZjSxQAgACAFaiIDNgIAIAMgAkEBcjYCBCAAIAFqIAI2AgAgACAFQQNyNgIECyAAQQhqDAcLIAAgBCAHajYCBEGc0sUAQZzSxQAoAgAiAEEPakF4cSIBQQhrIgI2AgBBlNLFAEGU0sUAKAIAIARqIgMgACABa2pBCGoiATYCACACIAFBAXI2AgQgACADakEoNgIEQajSxQBBgICAATYCAAwDC0Gc0sUAIAA2AgBBlNLFAEGU0sUAKAIAIAVqIgE2AgAgACABQQFyNgIEDAELQZjSxQAgADYCAEGQ0sUAQZDSxQAoAgAgBWoiATYCACAAIAFBAXI2AgQgACABaiABNgIACyACQQhqDAMLQQBBlNLFACgCACIAIAVNDQIaQZTSxQAgACAFayIBNgIAQZzSxQBBnNLFACgCACIAIAVqIgI2AgAgAiABQQFyNgIEIAAgBUEDcjYCBCAAQQhqDAILQYzSxQBBjNLFACgCAEF+IAIoAhx3cTYCAAsCQCAEQRBPBEAgAiAFQQNyNgIEIAIgBWoiACAEQQFyNgIEIAAgBGogBDYCACAEQYACTwRAIAAgBBD7AgwCCyAEQfgBcUGA0MUAaiEBAn9BiNLFACgCACIDQQEgBEEDdnQiBHFFBEBBiNLFACADIARyNgIAIAEMAQsgASgCCAshAyABIAA2AgggAyAANgIMIAAgATYCDCAAIAM2AggMAQsgAiAEIAVqIgBBA3I2AgQgACACaiIAIAAoAgRBAXI2AgQLIAJBCGoLIAhBEGokAAu5HQENfyMAQfAeayIDJAAgA0GAGGoiBkEAQeAA/AsAAkACQAJAAkACQCACQcABaiIFIAYQpgRFBEAgBkEAQeAA/AsAIAFBwAFqIgQgBhCmBA0BIAMgAkHgAGogBBA/IANB4ABqIAFB4ABqIgcgBRA/IANBwAFqIgkgAiAEED8gA0GgAmoiAiABIAUQPyAJIAIQpgQNA0EAIgFFBEAgBiADQeAA/AoAAAsgA0HgD2ogA0GAGGoiAiADQeAAahCNASABRQRAIAIgA0HAAWpB4AD8CgAACyADQcAQaiICIANBgBhqIgcgA0GgAmoiCRCNASADQaARaiIIIAQgBRA/IANBgBJqIgogA0HgD2oiBCAEED8gA0HgEmoiBSACIAIQPyADQcATaiILIAIgBRA/IANBoBRqIgYgBSAJED8gByAKIAgQPyADQagaaiIFIAcgCxCNASAHIAYgBhDVASADQYAVaiIGIAUgBxCNASAFIAIgBhA/IAFFBEAgA0HAFmogBEHgAPwKAAALIAFFBEAgA0GAGGogA0GAFWpB4AD8CgAACyADQaAXaiICIANBoBRqIANBgBhqIgQQjQEgA0HgFWogA0HAFmogAhA/IAFFBEAgBCADQeAAakHgAPwKAAALIANBoBdqIgIgA0HAE2ogA0GAGGoiBBA/IANBiBtqIANB4BVqIAIQjQEgAUUEQCAEIANBoBFqQeAA/AoAAAsgA0HoG2ogA0HAE2ogA0GAGGoiARA/IAEgA0GoGmoQmQIgAygCgBhFDQJBoLHCAEErIANB7x5qQZCxwgBBxLLCABDKAwALIANB8BxqIAFBKGopAwA3AwAgA0HoHGogAUEgaikDADcDACADQeAcaiABQRhqKQMANwMAIANB2BxqIAFBEGopAwA3AwAgA0HQHGogAUEIaikDADcDACADQYAdaiABQThqKQMANwMAIANBiB1qIAFBQGspAwA3AwAgA0GQHWogAUHIAGopAwA3AwAgA0GYHWogAUHQAGopAwA3AwAgA0GgHWogAUHYAGopAwA3AwAgAyABKQMANwPIHCADIAEpAzA3A/gcQQAiAkUEQCADQYADaiADQcgcakHgAPwKAAALIANBqBhqIgQgAUGIAWopAwA3AwAgA0GgGGoiByABQYABaikDADcDACADQZgYaiIFIAFB+ABqKQMANwMAIANBkBhqIgYgAUHwAGopAwA3AwAgA0GIGGoiCSABQegAaikDADcDACADQbgYaiIIIAFBmAFqKQMANwMAIANBwBhqIgogAUGgAWopAwA3AwAgA0HIGGoiCyABQagBaikDADcDACADQdAYaiIMIAFBsAFqKQMANwMAIANB2BhqIg0gAUG4AWopAwA3AwAgAyABKQNgNwOAGCADIAEpA5ABNwOwGCACRQRAIANByBxqIANBgBhqQeAA/AoAAAsgAkUEQCADQeADaiADQcgcakHgAPwKAAALIAQgAUHoAWopAwA3AwAgByABQeABaikDADcDACAFIAFB2AFqKQMANwMAIAYgAUHQAWopAwA3AwAgCSABQcgBaikDADcDACAIIAFB+AFqKQMANwMAIAogAUGAAmopAwA3AwAgCyABQYgCaikDADcDACAMIAFBkAJqKQMANwMAIA0gAUGYAmopAwA3AwAgAyABKQPAATcDgBggAyABKQPwATcDsBggAkUEQCADQcgcaiADQYAYakHgAPwKAAALIAJFBEAgA0HABGogA0HIHGpB4AD8CgAACyAAIANBgANqQaAC/AoAAAwDCyADQdAdaiACQShqKQMANwMAIANByB1qIAJBIGopAwA3AwAgA0HAHWogAkEYaikDADcDACADQbgdaiACQRBqKQMANwMAIANBsB1qIAJBCGopAwA3AwAgA0HgHWogAkE4aikDADcDACADQegdaiACQUBrKQMANwMAIANB8B1qIAJByABqKQMANwMAIANB+B1qIAJB0ABqKQMANwMAIANBgB5qIAJB2ABqKQMANwMAIAMgAikDADcDqB0gAyACKQMwNwPYHUEAIgFFBEAgA0GgBWogA0GoHWpB4AD8CgAACyADQagYaiIEIAJBiAFqKQMANwMAIANBoBhqIgcgAkGAAWopAwA3AwAgA0GYGGoiBiACQfgAaikDADcDACADQZAYaiIJIAJB8ABqKQMANwMAIANBiBhqIgggAkHoAGopAwA3AwAgA0G4GGoiCiACQZgBaikDADcDACADQcAYaiILIAJBoAFqKQMANwMAIANByBhqIgwgAkGoAWopAwA3AwAgA0HQGGoiDSACQbABaikDADcDACADQdgYaiIOIAJBuAFqKQMANwMAIAMgAikDYDcDgBggAyACKQOQATcDsBggAUUEQCADQagdaiADQYAYakHgAPwKAAALIAFFBEAgA0GABmogA0GoHWpB4AD8CgAACyAEIAVBKGopAwA3AwAgByAFQSBqKQMANwMAIAYgBUEYaikDADcDACAJIAVBEGopAwA3AwAgCCAFQQhqKQMANwMAIAogAkH4AWopAwA3AwAgCyACQYACaikDADcDACAMIAJBiAJqKQMANwMAIA0gAkGQAmopAwA3AwAgDiACQZgCaikDADcDACADIAUpAwA3A4AYIAMgAikD8AE3A7AYIAFFBEAgA0GoHWogA0GAGGpB4AD8CgAACyABRQRAIANB4AZqIANBqB1qQeAA/AoAAAsgACADQaAFakGgAvwKAAAMAgsgACADQYgYakGgAvwKAAAMAQsCQCADIANB4ABqEKYEBEAgA0GAGGoiAkEAQeAA/AsAIAcgAhCmBEUNAQtBACIBRQRAIANBqBpqQQBB4AD8CwALIANB2BdqQgA3AwAgA0HgF2pCADcDACADQegXakIANwMAIANB8BdqQgA3AwAgA0H4F2pCADcDACADQcgXakHgtMIAKQMANwMAIANBwBdqQdi0wgApAwA3AwAgA0G4F2pB0LTCACkDADcDACADQbAXakHItMIAKQMANwMAIANBqBdqQcC0wgApAwA3AwAgA0IANwPQFyADQbi0wgApAwA3A6AXIAFFBEAgA0HoG2pBAEHgAPwLAAsgAUUEQCADQYgbaiADQaAXakHgAPwKAAALIANBgBhqIANBqBpqEJkCIAMoAoAYQQFGDQIgACADQYgYakGgAvwKAAAMAQsgA0GAGGoiBUEAQeAA/AsAAkAgBCAFEKYERQRAIANBwAdqIgIgASABED8gBSACIAIQ1QEgA0GgCGogBSACENUBQQAiAkUEQCAFQQBB4AD8CwALIANBqBpqIgkgA0GAGGoiBSAEED8gBSAJIAQQPyADQYAJaiIGIAUgA0GgCGoQ1QEgA0HgCWoiCyAGIAYQPyADQcAKaiIGIAcgBBA/IANBoAtqIgQgBiAGED8gA0GADGoiCCAGIAQQPyADQeAMaiIKIAggCBDVASADQcANaiIIIAogChDVASADQaAOaiAIIAgQ1QEgBSABIAcQPyADQYAPaiIBIAUgBhA/IANB4A9qIgggASABENUBIANBwBBqIgEgCCAIENUBIANBoBFqIgggASABENUBIANBgBJqIgEgCyAIEI0BIANB4BJqIAEgBhA/IAkgByAHED8gAkUEQCAFIARB4AD8CgAACyADQcATaiIBIANBqBpqIgcgA0GAGGoQPyADQaAUaiIEIAEgARDVASADQYAVaiIBIAQgBBDVASADQeAVaiABIAEQ1QEgByADQeASaiIBIAEQ1QEgAkUEQCADQcAWaiADQYAJakHgAPwKAAALIAJFBEAgA0GAGGogA0HAEGpB4AD8CgAACyADQaAXaiIEIANBgBhqIgEgA0GAEmoQjQEgASADQcAWaiAEED8gA0GIG2ogASADQeAVahCNASACRQRAIANB6BtqIANBoA5qQeAA/AoAAAsgA0GAGGogA0GoGmoQmQIgAygCgBhFDQFBoLHCAEErIANB7x5qQZCxwgBBiLXCABDKAwALIANBsB5qIAFBKGopAwA3AwAgA0GoHmogAUEgaikDADcDACADQaAeaiABQRhqKQMANwMAIANBmB5qIAFBEGopAwA3AwAgA0GQHmogAUEIaikDADcDACADQcAeaiABQThqKQMANwMAIANByB5qIAFBQGspAwA3AwAgA0HQHmogAUHIAGopAwA3AwAgA0HYHmogAUHQAGopAwA3AwAgA0HgHmogAUHYAGopAwA3AwAgAyABKQMANwOIHiADIAEpAzA3A7geQQAiAkUEQCADQYAYaiADQYgeakHgAPwKAAALIANB0BpqIgUgB0EoaikDADcDACADQcgaaiIGIAdBIGopAwA3AwAgA0HAGmoiCSAHQRhqKQMANwMAIANBuBpqIgggB0EQaikDADcDACADQbAaaiIKIAdBCGopAwA3AwAgA0HgGmoiCyABQZgBaikDADcDACADQegaaiIMIAFBoAFqKQMANwMAIANB8BpqIg0gAUGoAWopAwA3AwAgA0H4GmoiDiABQbABaikDADcDACADQYAbaiIPIAFBuAFqKQMANwMAIAMgBykDADcDqBogAyABKQOQATcD2BogAkUEQCADQYgeaiADQagaakHgAPwKAAALIAJFBEAgA0HgGGogA0GIHmpB4AD8CgAACyAFIARBKGopAwA3AwAgBiAEQSBqKQMANwMAIAkgBEEYaikDADcDACAIIARBEGopAwA3AwAgCiAEQQhqKQMANwMAIAsgAUH4AWopAwA3AwAgDCABQYACaikDADcDACANIAFBiAJqKQMANwMAIA4gAUGQAmopAwA3AwAgDyABQZgCaikDADcDACADIAQpAwA3A6gaIAMgASkD8AE3A9gaIAJFBEAgA0GIHmogA0GoGmpB4AD8CgAACyACRQRAIANBwBlqIANBiB5qQeAA/AoAAAsgACADQYAYakGgAvwKAAAMAQsgACADQYgYakGgAvwKAAALIANB8B5qJAAPC0GgscIAQSsgA0HvHmpBkLHCAEHUssIAEMoDAAvHHgIFfxp+IwBB8ARrIgEkACABQdAEakHg+cEAQQEQtwIgAUGABGogASkD6AQiD0IAQqGhuoCg9AFCABDJAyABQZAEaiABKQPgBCIJQgBCoaG6gKD0AUIAEMkDIAFBoARqIAEpA9gEIhBCAEKhobqAoPQBQgAQyQMgAUGwBGogASkD0AQiEUIAQqGhuoCg9AFCABDJAyABQfADaiABKQOABCINQrHqlJHdo4KcWH4iBkIAQq/4//9vQgAQyQMgAUHgA2ogBkIAQn9CABDJAyABQdADaiAPIAEpA+ADIgYgASkDiAQiCyABKQOQBHwiCHwiByABKQP4AyANIAEpA/ADIhR8IBRUrXx8Ig18Ig9CseqUkd2jgpxYfiIUQgBCr/j//29CABDJAyABQcADaiAUQgBCf0IAEMkDIAFBsANqIAkgDSAPVq0iDnwiCSAGIAEpA5gEIAggC1StfCIWIAEpA6AEfCILfCIIIAcgDVatIAEpA+gDIg0gBiAHVq18fHwiDHwiFCABKQPAAyITfCIKIAEpA9gDIAEpA9ADIgcgD3wgB1StfHwiD0Kx6pSR3aOCnFh+IgdCAEKv+P//b0IAEMkDIAFBoANqIAdCAEJ/QgAQyQMgAUGQA2ogASkDoAMiByATIBAgBiABKQOoBCALIBZUrXwiEiABKQOwBHwiFnwiBiAIIAxWrSANIAggC1StfHx8Igt8IgggCSAOVK0gCSAUVq18fCIJfCIQIAogD1atIAEpA8gDIg4gCiAUVK18fHwiF3wiFCABKQO4AyAPIAEpA7ADIg98IA9UrXx8Ig9CseqUkd2jgpxYfiIKQgBCr/j//29CABDJAyABQYADaiAKQgBCf0IAEMkDAkAgASkDiAMiCiABKQOoAyIMIAcgESAGIAtWrSANIAYgFlStfHwiFSABKQO4BCASIBZWrXx8IgZ8Ig0gBlStIA0gDSAIIAtUrSAIIAlWrXx8Ig1WrXwiCCAGIBVUrXwiBiAOIA0gDSATfCINVq18IA0gDSAQIBdWrSAOIAkgEFatfHx8Ig1WrXx8Igl8IgsgCVStfCALIAwgDSAHIA18Ig1WrXwgDSAPIBRUrSAMIAcgFFatfHx8IhQgDVStfHwiByALVK18IgsgBiAIVK0gBiAJVq18fCINIAEpA4ADIgZ8IgkgDVStfCAJIAogByAGIAd8IgdWrXwgByAKIAYgBiAUfCIGVq18IAYgASkDmAMgDyABKQOQAyIPfCAPVK18fCIUIAZUrXx8IgYgB1StfHwiByAJVK18Ig8gCyANVq18IhYgD1ogFEKv+P//b1QiAiAGIAeDIBaDQn9ScnFFBEAgBkIBfCIPIAKtIgl9IQ0gB0IBfCILIAZCf1IgCSAPVnKtIgZ9IQ8gFiAHQn9SIAYgC1ZyrX1CAXwhFiAUQtGHgIAQfCEUDAELIAchDyAGIQ0LIAFB0ARqQeH5wQBBwAAQtwIgAUHAAmogASkD6AQiC0IAQqGhuoCg9AFCABDJAyABQdACaiABKQPgBCIIQgBCoaG6gKD0AUIAEMkDIAFB4AJqIAEpA9gEIhJCAEKhobqAoPQBQgAQyQMgAUHwAmogASkD0AQiGEIAQqGhuoCg9AFCABDJAyABQbACaiABKQPAAiIJQrHqlJHdo4KcWH4iBkIAQq/4//9vQgAQyQMgAUGgAmogBkIAQn9CABDJAyABQZACaiALIAEpA6ACIgYgASkDyAIiEyABKQPQAnwiCnwiByABKQO4AiAJIAEpA7ACIhB8IBBUrXx8Igl8IgtCseqUkd2jgpxYfiIQQgBCr/j//29CABDJAyABQYACaiAQQgBCf0IAEMkDIAFB8AFqIAggCSALVq0iF3wiCCAGIAEpA9gCIAogE1StfCIRIAEpA+ACfCITfCIKIAcgCVatIAEpA6gCIgkgBiAHVq18fHwiFXwiECABKQOAAiIOfCIMIAEpA5gCIAEpA5ACIgcgC3wgB1StfHwiC0Kx6pSR3aOCnFh+IgdCAEKv+P//b0IAEMkDIAFB4AFqIAdCAEJ/QgAQyQMgAUHQAWogASkD4AEiByAOIBIgBiABKQPoAiARIBNWrXwiGSABKQPwAnwiEXwiBiAKIBVWrSAJIAogE1StfHx8IhN8IgogCCAXVK0gCCAQVq18fCIIfCISIAsgDFStIAEpA4gCIhcgDCAQVK18fHwiGnwiECABKQP4ASALIAEpA/ABIgt8IAtUrXx8IgtCseqUkd2jgpxYfiIMQgBCr/j//29CABDJAyABQcABaiAMQgBCf0IAEMkDAkAgASkDyAEiDCABKQPoASIVIAcgGCAGIBNWrSAJIAYgEVStfHwiGyABKQP4AiARIBlUrXx8IgZ8IgkgBlStIAkgCSAKIBNUrSAIIApUrXx8IglWrXwiCiAGIBtUrXwiBiAXIAkgCSAOfCIJVq18IAkgCSASIBpWrSAXIAggElatfHx8IglWrXx8Igh8IhMgCFStfCATIBUgCSAHIAl8IglWrXwgCSALIBBUrSAVIAcgEFatfHx8IhAgCVStfHwiByATVK18Ig4gBiAKVK0gBiAIVq18fCIJIAEpA8ABIgZ8IgggCVStfCAIIAwgByAGIAd8IgdWrXwgByAMIAYgBiAQfCIGVq18IAYgASkD2AEgCyABKQPQASILfCALVK18fCITIAZUrXx8IgYgB1StfHwiByAIVK18IgsgCSAOVK18IhAgC1ogE0Kv+P//b1QiAiAGIAeDIBCDQn9ScnFFBEAgBkIBfCILIAKtIgh9IQkgB0IBfCIKIAZCf1IgCCALVnKtIgZ9IQsgECAHQn9SIAYgClZyrX1CAXwhECATQtGHgIAQfCETDAELIAchCyAGIQkLIAFB0ARqQaH6wQBBwAAQtwIgAUGAAWogASkD6AQiCkIAQqGhuoCg9AFCABDJAyABQZABaiABKQPgBCIOQgBCoaG6gKD0AUIAEMkDIAFBoAFqIAEpA9gEIhlCAEKhobqAoPQBQgAQyQMgAUGwAWogASkD0AQiHEIAQqGhuoCg9AFCABDJAyABQfAAaiABKQOAASIIQrHqlJHdo4KcWH4iBkIAQq/4//9vQgAQyQMgAUHgAGogBkIAQn9CABDJAyABQdAAaiAKIAEpA2AiBiABKQOIASIMIAEpA5ABfCIRfCIHIAEpA3ggCCABKQNwIhJ8IBJUrXx8Igh8IgpCseqUkd2jgpxYfiISQgBCr/j//29CABDJAyABQUBrIBJCAEJ/QgAQyQMgAUEwaiAOIAggClatIhp8Ig4gBiABKQOYASAMIBFWrXwiGCABKQOgAXwiDHwiESAHIAhWrSABKQNoIgggBiAHVq18fHwiG3wiEiABKQNAIhd8IhUgASkDWCABKQNQIgcgCnwgB1StfHwiCkKx6pSR3aOCnFh+IgdCAEKv+P//b0IAEMkDIAFBIGogB0IAQn9CABDJAyABQRBqIAEpAyAiByAXIBkgBiABKQOoASAMIBhUrXwiHSABKQOwAXwiGHwiBiARIBtWrSAIIAwgEVatfHx8Igx8IhEgDiAaVK0gDiASVq18fCIOfCIZIAogFVStIAEpA0giGiASIBVWrXx8fCIefCISIAEpAzggCiABKQMwIgp8IApUrXx8IgpCseqUkd2jgpxYfiIVQgBCr/j//29CABDJAyABIBVCAEJ/QgAQyQMCQCABKQMIIhUgASkDKCIbIAcgHCAGIAxWrSAIIAYgGFStfHwiHyABKQO4ASAYIB1UrXx8IgZ8IgggBlStIAggCCAMIBFWrSAOIBFUrXx8IghWrXwiESAGIB9UrXwiBiAaIAggCCAXfCIIVq18IAggCCAZIB5WrSAaIA4gGVatfHx8IghWrXx8Ig58IgwgDlStfCAMIBsgCCAHIAh8IghWrXwgCCAKIBJUrSAbIAcgElatfHx8IhIgCFStfHwiByAMVK18IgwgBiARVK0gBiAOVq18fCIIIAEpAwAiBnwiDiAIVK18IA4gFSAHIAYgB3wiB1atfCAHIBUgBiAGIBJ8IgZWrXwgBiABKQMYIAogASkDECIKfCAKVK18fCIKIAZUrXx8IgYgB1StfHwiByAOVK18IhEgCCAMVK18Ig4gEVogCkKv+P//b1QiAiAGIAeDIA6DQn9ScnFFBEAgBkIBfCIMIAKtIhF9IQggB0IBfCISIAZCf1IgDCARVHKtIgx9IQYgDiAHQn9SIAwgElZyrX1CAXwhDiAKQtGHgIAQfCEKDAELIAYhCCAHIQYLIAFB0ARqIgJB4frBAEHAAEEQEPEBAkACQCABKALQBEGAgICAeEcEQCABQcgEaiIFIAFB2ARqKAIANgIAIAEgASkC0AQ3A8AEEMcEIgNFDQEgAyADKQMAIgdCAXw3AwAgAykDCCEMIAJBofvBAEHAAEEQEPEBIAEtANQEIQMgASgC0AQiAkGAgICAeEYNAiAAIAEvANUEOwCVAiAAQZcCaiABQdcEai0AADoAACABKALYBCEEIABCADcDACAAQQI6ALgEIABBCGpCADcDACAAQRBqQgA3AwAgAEEYakIANwMAIABCADcDQCAAIBQ3AzggACANNwMwIAAgDzcDKCAAIBY3AyAgAEHIAGpCADcDACAAQdAAakIANwMAIABB2ABqQgA3AwAgAEHgAGpCADcDACAAQegAakIANwMAIABB8ABqQgA3AwAgAEH4AGpCADcDACAAQgA3A+ADIABCADcDmAMgACAKNwO4ASAAIAg3A7ABIAAgBjcDqAEgACAONwOgASAAIBM3A5gBIAAgCTcDkAEgACALNwOIASAAIBA3A4ABIABBATYCqAQgAEIANwOAAiAAQgA3A4gCIABCADcDwAEgAEHIAWpCADcDACAAQdABakIANwMAIABC85aAgDA3A9gBIAAgBzcD8AEgACAMNwP4ASAAQgE3A6gCIABBtARqIAUoAgA2AgAgACABKQPABDcCrAQgAEGAscIAKQMANwPgASAAQegBakGIscIAKQMANwMAIABBAkEBIAQbOgCcAiAAQgA3A6ACIAAgAzoAlAIgAEIANwOwAiAAIAQ2ApgCIAAgAjYCkAIgAUHwBGokAA8LIAEgAS0A1AQ6AMAEQYz3wQBBKyABQcAEakHk+8EAQaj8wQAQygMACxDwAwALIAEgAzoA0ARBjPfBAEErIAFB0ARqQeT7wQBBmPzBABDKAwAL5SECE38BfiMAQZABayIDJAAgAyACNgIAIANBBjYCBBDjASEEAkACQCACQfylwABBBhDxAwRAQQEhAiADQQE2AmggA0HErMAANgJkIANCATcCcCADIAOtQoCAgICgAoQ3AwggAyADQQhqNgJsIABBBGogA0HkAGoQ0gIMAQsCQAJAAkACQAJAAkACQAJAAkACQCAEQYABakEDdiAEQQdxQQBHaiIGQYCAAkkEQEHRzsUALQAAGkErQQEQ1gQiAkUNASACQSdqIgVBl67AACgAADYAACACQSBqIghBkK7AACkAADcAACACQRhqIgdBiK7AACkAADcAACACQRBqIglBgK7AACkAADcAACACQQhqIgpB+K3AACkAADcAACACQfCtwAApAAA3AAAgA0ErNgIcIAMgAjYCGCADQoCAgICwBTcCECADQoCAgIAQNwIIIAMgBjYCICADQQA2AjAgA0KAgICAEDcCKCAGQQR2IAZBD3FBAEdqIg5BgAJPDQJB0c7FAC0AABpBASENQStBARDWBCIERQ0DIAQgAikAADcAACAEQSdqIAUoAAA2AAAgBEEgaiAIKQAANwAAIARBGGogBykAADcAACAEQRBqIAkpAAA3AAAgBEEIaiAKKQAANwAAIANBKzYCbCADIAQ2AmggA0ErNgJkIANB5ABqQfiuwAAQtgMgAygCaCIIQSs6ACsgAygCZCEPIAYEQEHRzsUALQAAGiAGQQEQ1wQiDUUNBQsCfyAGRQRAQQEhBEEAIQJBAAwBCyADQQhqQQAgBkEBQQEQiAMgAygCDCEEIAMoAhAhAiADKAIICyAGRSIQRQRAIAIgBGogDSAG/AoAAAsgAyACIAZqIgI2AhAgAmtBH00EQCADQQhqIAJBIEEBQQEQiAMgAygCDCEEIAMoAhAhAgsgAiAEaiIFIAEpAAA3AAAgBUEYaiABQRhqKQAANwAAIAVBEGogAUEQaikAADcAACAFQQhqIAFBCGopAAA3AAAgAyACQSBqIgI2AhBB0c7FAC0AABpBAkEBENYEIgFFDQUgASAGQQF0IglBCHQgCUGA/gNxQQh2cjsAACADQQI2AjwgAyABNgI4IANBAjYCNCADQTRqIgVBgLDAABC2AyADKAI4QQA6AAJBAyEBIANBAzYCPCADKAI0QS9rQVRPBEAgBUEDQSxBAUEBEIgDIAMoAjwhAQsgAygCOCIHIAFqIgUgCCkAADcAACAFQQhqIAhBCGopAAA3AAAgBUEQaiAIQRBqKQAANwAAIAVBGGogCEEYaikAADcAACAFQSBqIAhBIGopAAA3AAAgBUEoaiAIQShqKAAANgAAIAMgAUEsaiIBNgI8IAMoAgggAmsgAUkEQCADQQhqIAIgAUEBQQEQiAMgAygCDCEEIAMoAhAhAgsgAQRAIAIgBGogByAB/AoAAAsgAyABIAJqIgI2AhAgA0HkAGogBCACEOEBQQAhAUHRzsUALQAAGkEgQQEQ1gQiBUUNDCAFIAMpAGQ3AAAgBUEYaiADQfwAaikAADcAACAFQRBqIANB9ABqKQAANwAAIAVBCGogA0HsAGopAAA3AAAgAkEASA0GIAIEQEHRzsUALQAAGkEBIQEgAkEBENYEIgRFDQcgAyACNgJIIAMgBDYCRCAEIAIQ3wQLIANBADYCSCADQoCAgIAQNwJAIANBQGsiBEEAQSBBAUEBEIgDIAMoAkgiAiADKAJEaiIBIAUpAAA3AAAgAUEYaiAFQRhqKQAANwAAIAFBEGogBUEQaikAADcAACABQQhqIAVBCGopAAA3AAAgAyACQSBqIgE2AkhB0c7FAC0AABpBAUEBENYEIgJFDQcgAkEBOgAAIANBATYCVCADIAI2AlAgA0EBNgJMIANBzABqQQFBLEEBQQEQiAMgAygCUCIHIAMoAlQiCmoiAiAIKQAANwAAIAJBCGogCEEIaikAADcAACACQRBqIAhBEGopAAA3AAAgAkEYaiAIQRhqKQAANwAAIAJBIGogCEEgaikAADcAACACQShqIAhBKGooAAA2AAAgAyAKQSxqIgI2AlQgAygCQCABayACSQRAIAQgASACQQFBARCIAyADKAJIIQELIAMoAkQhBCACBEAgASAEaiAHIAL8CgAACyADIAEgAmoiATYCSCADQeQAaiAEIAEQ4QFB0c7FAC0AABpBIEEBENYEIgJFDQwgAiADKQBkNwAAIAJBGGoiByADQfwAaikAADcAACACQRBqIgogA0H0AGopAAA3AAAgAkEIaiILIANB7ABqKQAANwAAIAMoAiggAygCMCIEa0EfTQRAIANBKGogBEEgQQFBARCIAyADKAIwIQQLIAMoAiwiDCAEaiIBIAIpAAA3AAAgAUEIaiALKQAANwAAIAFBEGogCikAADcAACABQRhqIAcpAAA3AAAgAyAEQSBqIgc2AjAgDkECSQRAIAIhBAwLCyADKAIQIhFBAEgNCEECIQsDQEHRzsUALQAAGkEgQQEQ1gQiAUUNCiABIAItAAAgBS0AAHM6AAAgASACLQABIAUtAAFzOgABIAEgAi0AAiAFLQACczoAAiABIAItAAMgBS0AA3M6AAMgASACLQAEIAUtAARzOgAEIAEgAi0ABSAFLQAFczoABSABIAItAAYgBS0ABnM6AAYgASACLQAHIAUtAAdzOgAHIAEgAi0ACCAFLQAIczoACCABIAItAAkgBS0ACXM6AAkgASACLQAKIAUtAApzOgAKIAEgAi0ACyAFLQALczoACyABIAItAAwgBS0ADHM6AAwgASACLQANIAUtAA1zOgANIAEgAi0ADiAFLQAOczoADiABIAItAA8gBS0AD3M6AA8gASACLQAQIAUtABBzOgAQIAEgAi0AESAFLQARczoAESABIAItABIgBS0AEnM6ABIgASACLQATIAUtABNzOgATIAEgAi0AFCAFLQAUczoAFCABIAItABUgBS0AFXM6ABUgASACLQAWIAUtABZzOgAWIAEgAi0AFyAFLQAXczoAFyABIAItABggBS0AGHM6ABggASACLQAZIAUtABlzOgAZIAEgAi0AGiAFLQAaczoAGiABIAItABsgBS0AG3M6ABsgASACLQAcIAUtABxzOgAcIAEgAi0AHSAFLQAdczoAHSABIAItAB4gBS0AHnM6AB4gASACLQAfIAUtAB9zOgAfIBEEQEHRzsUALQAAGgsgA0EANgJgIANCgICAgBA3AlggA0HYAGpBAEEgQQFBARCIAyADKAJcIgogAygCYCIHaiIEIAEpAAA3AAAgBEEYaiABQRhqKQAANwAAIARBEGogAUEQaikAADcAACAEQQhqIAFBCGopAAA3AAAgAyAHQSBqIgc2AmBB0c7FAC0AABpBAUEBENYEIgRFBEBBAUEBEP8EAAsgBCALOgAAIANBATYCjAEgAyAENgKIASADQQE2AoQBIANBhAFqQQFBLEEBQQEQiAMgAygCiAEiEiADKAKMASIMaiIEIAgpAAA3AAAgBEEIaiAIQQhqKQAANwAAIARBEGogCEEQaikAADcAACAEQRhqIAhBGGopAAA3AAAgBEEgaiAIQSBqKQAANwAAIARBKGogCEEoaigAADYAACADIAxBLGoiBDYCjAEgAygCWCAHayAESQRAIANB2ABqIAcgBEEBQQEQiAMgAygCXCEKIAMoAmAhBwsgBARAIAcgCmogEiAE/AoAAAsgAyAEIAdqIgQ2AmAgA0HkAGogCiAEEOEBQdHOxQAtAAAaQSBBARDWBCIERQ0NIAQgAykAZDcAACAEQRhqIhMgA0H8AGopAAA3AAAgBEEQaiIUIANB9ABqKQAANwAAIARBCGoiFSADQewAaikAADcAACACQSAQ3wQgAygCKCADKAIwIgdrQR9NBEAgA0EoaiAHQSBBAUEBEIgDIAMoAjAhBwsgAygCLCIMIAdqIgIgBCkAADcAACACQQhqIBUpAAA3AAAgAkEQaiAUKQAANwAAIAJBGGogEykAADcAACADIAdBIGoiBzYCMCADKAKEASICBEAgEiACEN8ECyADKAJYIgIEQCAKIAIQ3wQLIAFBIBDfBCAEIQIgDiALQQFqIgtPDQALDAoLIANBADYCdCADQQE2AmggA0HYrcAANgJkIANCBDcCbCADQeQAakHgrcAAEKgEAAtBAUErQYSkwAAQyAQACyADQQA2AnQgA0EBNgJoIANB2K/AADYCZCADQgQ3AmwgA0HkAGpB4K/AABCoBAALQQFBK0H4gcAAEMgEAAtBASAGQfCvwAAQyAQAC0EBQQJBhKTAABDIBAALIAEgAkH4gcAAEMgEAAtBAUEBEP8EAAtB0c7FAC0AABpBACARQfiBwAAQyAQAC0EBQSBBpK3AABDIBAALAkAgByAJTwRAIAZFBEBBASEBDAILQdHOxQAtAAAaIAlBARDWBCIBDQFBASAJQYSkwAAQyAQACyAJIAdBkLDAABDlBAALIAkEQCABIAwgCfwKAAALIARBIBDfBCADKAJMIgIEQCADKAJQIAIQ3wQLIAMoAkAiAgRAIAMoAkQgAhDfBAsgBUEgEN8EIAMoAjQiAgRAIAMoAjggAhDfBAsgBgRAIA0gBhDfBAsgDwRAIAggDxDfBAsgAygCKCICBEAgDCACEN8ECyADQQA2AmwgA0KAgICAwAA3AmQCQAJAIAYEQEHRzsUALQAAGiAGQQEQ1gQiAkUNASAQRQRAIAIgASAG/AoAAAsgA0HkAGpByK7AABCfAyADKAJoIgQgBjYCACAEIAY2AgggBCACNgIEQdHOxQAtAAAaIANBATYCbCAGQQEQ1gQiAkUNASAQRQRAIAIgASAGaiAG/AoAAAsgAygCbCIEIAMoAmRGBEAgA0HkAGpByK7AABCfAwsgAygCaCAEQQxsaiIFIAY2AgggBSACNgIEIAUgBjYCACADKAJoIQYgAygCZCEHIAEgCRDfBCADKAIIIgEEQCADKAIMIAEQ3wQLIAMoAhQiAQRAIAMoAhggARDfBAsgBEEBaiIBrUIwfiIWpyEFQQAhBCAWQiCIpyAFQfj///8HS3INAkEAIQJBCCEIIAUEQEHRzsUALQAAGkEIIQQgBUEIENYEIghFDQMgASEECyADQYwBaiIKQQA2AgAgAyAINgKIASADIAQ2AoQBIAMgBiABQQxsajYCcCADIAc2AmwgAyAGNgJoIAMgBjYCZCADIAg2AhAgA0EANgIMIAMgCjYCCCADQQhqIQgjAEEwayIFJAACQCADQeQAaiIHKAIEIgEgBygCDCIMRgRAIAgoAgQhCQwBCyAIKAIIIAgoAgQiCUEwbGohBgNAIAcgAUEMaiIENgIEIAEoAgAhDSAFIAFBBGooAgAiCyABQQhqKAIAEI4BIA0EQCALIA0Q3wQLIAYgBSkDADcDACAIIAlBAWoiCTYCBCAGQShqIAVBKGopAwA3AwAgBkEgaiAFQSBqKQMANwMAIAZBGGogBUEYaikDADcDACAGQRBqIAVBEGopAwA3AwAgBkEIaiAFQQhqKQMANwMAIAZBMGohBiAEIgEgDEcNAAsLIAgoAgAgCTYCACAHKAIIIgEEQCAHKAIAIAFBDGwQ3wQLIAVBMGokACAAQQRqIgFBCGogCigCADYCACABIAMpAoQBNwIADAMLQZuuwABBG0G4rsAAEP4DAAtBASAGQYSkwAAQyAQACyAEIAVB4IDAABDIBAALIAAgAjYCACADQZABaiQADwtBAUEgQYSkwAAQyAQAC/AiAgd/GX4jAEHgIWsiAiQAIAJByBlqIAFBCGopAwA3AwAgAkHQGWogAUEQaikDADcDACACQdgZaiABQRhqKQMANwMAIAJB4BlqIAFBIGopAwA3AwAgAkHoGWogAUEoaikDADcDACACQfgZaiABQThqKQMANwMAIAJBgBpqIAFBQGspAwA3AwAgAkGIGmogAUHIAGopAwA3AwAgAkGQGmogAUHQAGopAwA3AwAgAkGYGmogAUHYAGopAwA3AwAgAiABKQMANwPAGSACIAEpAzA3A/AZIAJByBpqIAFBqANqKQMANwMAIAJBwBpqIAFBoANqKQMANwMAIAJBuBpqIAFBmANqKQMANwMAIAJBsBpqIAFBkANqKQMANwMAIAJBqBpqIAFBiANqKQMANwMAIAJB+BpqIAFB2ANqKQMANwMAIAJB8BpqIAFB0ANqKQMANwMAIAJB6BpqIAFByANqKQMANwMAIAJB4BpqIAFBwANqKQMANwMAIAJB2BpqIAFBuANqKQMANwMAIAIgASkDgAM3A6AaIAIgASkDsAM3A9AaIAJBwAFqIgQgAkHAGWpB4AD8CgAAIAJBoAJqIAJBoBpqQeAA/AoAACACQcAHaiIFIARBwAH8CgAAIAIgBRCsAyACQYgbaiABQagCaikDADcDACACQZAbaiABQbACaikDADcDACACQZgbaiABQbgCaikDADcDACACQaAbaiABQcACaikDADcDACACQagbaiABQcgCaikDADcDACACQbgbaiABQdgCaikDADcDACACQcAbaiABQeACaikDADcDACACQcgbaiABQegCaikDADcDACACQdAbaiABQfACaikDADcDACACQdgbaiABQfgCaikDADcDACACIAEpA6ACNwOAGyACIAEpA9ACNwOwGyACQYgcaiABQegBaikDADcDACACQYAcaiABQeABaikDADcDACACQfgbaiABQdgBaikDADcDACACQfAbaiABQdABaikDADcDACACQegbaiABQcgBaikDADcDACACQbgcaiABQZgCaikDADcDACACQbAcaiABQZACaikDADcDACACQagcaiABQYgCaikDADcDACACQaAcaiABQYACaikDADcDACACQZgcaiABQfgBaikDADcDACACIAEpA8ABNwPgGyACIAEpA/ABNwOQHCACQcAEaiIEIAJBgBtqQeAA/AoAACACQaAFaiACQeAbakHgAPwKAAAgBSAEQcAB/AoAACACQYADaiIIIAUQrAMgAkHIHGogAUHoAGopAwA3AwAgAkHQHGogAUHwAGopAwA3AwAgAkHYHGogAUH4AGopAwA3AwAgAkHgHGogAUGAAWopAwA3AwAgAkHoHGogAUGIAWopAwA3AwAgAkH4HGogAUGYAWopAwA3AwAgAkGAHWogAUGgAWopAwA3AwAgAkGIHWogAUGoAWopAwA3AwAgAkGQHWogAUGwAWopAwA3AwAgAkGYHWogAUG4AWopAwA3AwAgAiABKQNgNwPAHCACIAEpA5ABNwPwHCACQcgdaiABQYgEaikDADcDACACQcAdaiABQYAEaikDADcDACACQbgdaiABQfgDaikDADcDACACQbAdaiABQfADaikDADcDACACQagdaiABQegDaikDADcDACACQfgdaiABQbgEaikDADcDACACQfAdaiABQbAEaikDADcDACACQegdaiABQagEaikDADcDACACQeAdaiABQaAEaikDADcDACACQdgdaiABQZgEaikDADcDACACIAEpA+ADNwOgHSACIAEpA5AENwPQHSACQYAJaiIEIAJBwBxqQeAA/AoAACACQeAJaiACQaAdakHgAPwKAAAgBSAEQcAB/AoAACACQYAGaiAFIgQQrAMgAkHACmoiBiIDIAIgARCNASAEIAMgAxDVASADIARB4AD8CgAAIAJBiB5qIAJBCGopAwA3AwAgAkGQHmogAkEQaikDADcDACACQZgeaiACQRhqKQMANwMAIAJBoB5qIAJBIGopAwA3AwAgAkGoHmogAkEoaikDADcDACACQbgeaiACQThqKQMANwMAIAJBwB5qIAJBQGspAwA3AwAgAkHIHmogAkHIAGopAwA3AwAgAkHQHmogAkHQAGopAwA3AwAgAkHYHmogAkHYAGopAwA3AwAgAiACKQMANwOAHiACIAIpAzA3A7AeIAJB4A9qIgcgAkGAHmpB4AD8CgAAIAQiAyAHIAYiBBDVASAEIANB4AD8CgAAIAJBoAtqIgYiAyAIIAFB4ABqEI0BIAUiBCADIAMQ1QEgAyAEQeAA/AoAACACQegeaiACQYgDaikDADcDACACQfAeaiACQZADaikDADcDACACQfgeaiACQZgDaikDADcDACACQYAfaiACQaADaikDADcDACACQYgfaiACQagDaikDADcDACACQZgfaiACQbgDaikDADcDACACQaAfaiACQcADaikDADcDACACQagfaiACQcgDaikDADcDACACQbAfaiACQdADaikDADcDACACQbgfaiACQdgDaikDADcDACACIAIpA4ADNwPgHiACIAIpA7ADNwOQHyAHIAJB4B5qQeAA/AoAACAEIgMgByAGIgQQ1QEgBCADQeAA/AoAACACQYAMaiIGIgMgAkHgAGogAUGAA2oQ1QEgBSIEIAMgAxDVASADIARB4AD8CgAAIAJByB9qIAJB6ABqKQMANwMAIAJB0B9qIAJB8ABqKQMANwMAIAJB2B9qIAJB+ABqKQMANwMAIAJB4B9qIAJBgAFqKQMANwMAIAJB6B9qIAJBiAFqKQMANwMAIAJB+B9qIAJBmAFqKQMANwMAIAJBgCBqIAJBoAFqKQMANwMAIAJBiCBqIAJBqAFqKQMANwMAIAJBkCBqIAJBsAFqKQMANwMAIAJBmCBqIAJBuAFqKQMANwMAIAIgAikDYDcDwB8gAiACKQOQATcD8B8gByACQcAfakHgAPwKAAAgBCIDIAcgBiIEENUBIAQgA0HgAPwKAAAgAkHgDGoiBiIDIAJB4ANqIAFB4ANqENUBIAUiBCADIAMQ1QEgAyAEQeAA/AoAACACQaggaiACQegDaikDADcDACACQbAgaiACQfADaikDADcDACACQbggaiACQfgDaikDADcDACACQcAgaiACQYAEaikDADcDACACQcggaiACQYgEaikDADcDACACQdggaiACQZgEaikDADcDACACQeAgaiACQaAEaikDADcDACACQeggaiACQagEaikDADcDACACQfAgaiACQbAEaikDADcDACACQfggaiACQbgEaikDADcDACACIAIpA+ADNwOgICACIAIpA5AENwPQICAHIAJBoCBqQeAA/AoAACAEIgMgByAGIgQQ1QEgBCADQeAA/AoAACACQcANaiEEIAJB4AZqIgMpAzAiGCEMIAMpAwAiGSEJAn4CQAJ+AkAgGCAZUg0AIAMpAzgiDSADKQMIIglSBEAgDSEMDAELIAMpA0AiDiADKQMQIglSBEAgDiEMDAELIAMpA0giCyADKQMYIglSBEAgCyEMDAELIAMpA1AiECADKQMgIglSBEAgECEMDAELIA0hDyAOIREgCyESIAMpA1giDCETIBAgDCADKQMoIglRDQEaCyAJIAxUDQEgAykDOCENIAMpAwghDyADKQNAIQ4gAykDECERIAMpA0ghCyADKQMYIRIgAykDUCEQIAMpA1ghDCADKQMoIRMgAykDIAsiCiAQfSIJIAwgE1atIhp9IRQgEiALfSIVIAogEFQgCSAaVHKtIgl9IRogESAOfSIWIAkgFVYgCyASVnKtIgl9IRUgDyANfSIXIAkgFlYgDiARVnKtIgl9IRYgCSAXViANIA9WciEDIBkgGH0hFyATIAx9DAELQqTsw7WP1LSY5wAgAykDSCILIAMpAxgiEn0iDSADKQNQIhAgAykDICIKVCAQIAp9Ig4gAykDWCIMIAMpAygiE1StIg9Ucq0iCX0iFH0iFSAOIA99Ig5C///Piuv//9UeVkL//8+K6///1R4gDn0iFyAMIBN9IhtCq9X+////v/+5f1atIhxUcq0iD30hGkK/pZScz/DSu+QAIAMpA0AiDiADKQMQIhF9IhYgCyASVCAJIA1Wcq0iCX0iHX0iHiAPIBVWIBRCpOzDtY/UtJjnAFZyrSIUfSEVQtfZrprk9umNywAgAykDOCINIAMpAwgiD30iHyAOIBFUIAkgFlZyrSIJfSIgfSIhIBQgHlYgHUK/pZScz/DSu+QAVnKtIhR9IRYgFCAhViAgQtfZrprk9umNywBWciEDIBcgHH0hFCANIA9UIAkgH1ZyrSAZIBh9fEKazf/Lo73EgBp8IRdCq9X+////v/+5fyAbfQshG0Kazf/Lo73EgBohCSANIA98Ig0gD1QgDSAOIBF8Ig4gEVQgDiALIBJ8IhEgElQgESAKIAogEHwiC1YgCyALIAwgE3wiDyATVK18IgtWcq18IhAgEVRyrXwiESAOVHKtfCISIA1Ucq0gGCAZfHwiDCEKAkACQAJAIAxCms3/y6O9xIAaUg0AQtfZrprk9umNywAhCSASIgpC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQkgESIKQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEJIBAiCkKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEJIAsiCkL//8+K6///1R5SDQBCq9X+////v/+5fyEJIA8iCkKr1f7///+//7l/UQ0BCyAJIApYDQAgEiEKIBEhDSAQIQkgCyEODAELIAtC///Piuv//9UefSIKIA9Cq9X+////v/+5f1StIg19IQ4gEEKk7MO1j9S0mOcAfSITIAtC///Piuv//9UeVCAKIA1Ucq0iCn0hCSARQr+llJzP8NK75AB9IgsgEEKk7MO1j9S0mOcAVCAKIBNWcq0iCn0hDSASQtfZrprk9umNywB9IhAgEUK/pZScz/DSu+QAVCAKIAtWcq0iC30hCiAMIBJC19mumuT26Y3LAFQgCyAQVnKtfUKazf/Lo73EgBp9IQwgD0LVqoGAgIDAgMYAfCEPCyAEIA83A1ggBCAONwNQIAQgCTcDSCAEIA03A0AgBCAKNwM4IAQgDDcDMCAEIBs3AyggBCAUNwMgIAQgGjcDGCAEIBU3AxAgBCAWNwMIIAQgFyADrX03AwAgAkGgDmoiBiIDIAQgAUGgAmoQ1QEgAkHAB2oiBSIEIAMgAxDVASADIARB4AD8CgAAIAJB4A9qIgggAkHADWpB4AD8CgAAIAUiAyAIIAYiBBDVASAEIANB4AD8CgAAIAJBgA9qIgMgAkGABmogAUHAAWoQjQEgBSIBIAMgAxDVASADIAFB4AD8CgAAIAJBiCFqIAJBiAZqKQMANwMAIAJBkCFqIAJBkAZqKQMANwMAIAJBmCFqIAJBmAZqKQMANwMAIAJBoCFqIAJBoAZqKQMANwMAIAJBqCFqIAJBqAZqKQMANwMAIAJBuCFqIAJBuAZqKQMANwMAIAJBwCFqIAJBwAZqKQMANwMAIAJByCFqIAJByAZqKQMANwMAIAJB0CFqIAJB0AZqKQMANwMAIAJB2CFqIAJB2AZqKQMANwMAIAIgAikDgAY3A4AhIAIgAikDsAY3A7AhIAggAkGAIWpB4AD8CgAAIAEgCCADENUBIAMgAUHgAPwKAAAgAkGAFWoiASACQcAKakHgAPwKAAAgAkHgFWogAkGgC2pB4AD8CgAAIAJBwBZqIANB4AD8CgAAIAJBoBdqIARB4AD8CgAAIAJBgBhqIAJBgAxqQeAA/AoAACACQeAYaiACQeAMakHgAPwKAAAgAkHAEGogAUGgAvwKAAAgAkHgEmogAkGgF2pBoAL8CgAAIAAgAkHAEGpBwAT8CgAAIAJB4CFqJAALxRoCAX8WfiMAQeADayIDJAACfyACQZCmxABBIBDxA0UEQEIBIQdCAiEFQQgMAQsgA0GQA2pCADcDACADQYgDakIANwMAIANCADcDgANCASELIANCATcDmAMgA0G4A2ogAkEYaikDADcDACADQbADaiACQRBqKQMANwMAIANBqANqIAJBCGopAwA3AwAgAyACKQMANwOgAyADQdgDakHopcQAKQMANwMAIANB0ANqQeClxAApAwA3AwAgA0HIA2pB2KXEACkDADcDACADQdClxAApAwA3A8ADAkAgA0GgA2ogA0GAA2pBIBDxA0UEQEKhobqAoPQBIQcMAQtCoaG6gKD0ASEHIAMpA7gDIQUgAykDoAMhFiADKQOoAyEGIAMpA7ADIRNCr/j//28hBEJ/IRdCfyEIQn8hEgNAIANBwANqIANBgANqQSAQ8QNFBEAgDyENIA4hCyAKIQcgESEQDAILIAWnQQFxRQRAA0AgE0I/hiAFQgGIhCEFAn4gB6dBAXFFBEAgEEI/hiANQj+GIQwgC0I/hiAHQgGIhCEHIBBCAYghECANQgGIhCENIAwgC0IBiIQMAQsgEEIBfSIUIA1CAFIgDUIBfSINIAtCAFIgC0IBfSIMIAdC0YeAgBB9IhUgB1StfCIJIAxUcq18IgwgDVRyrXwiB0IBiCILQoCAgICAgICAgH+EIg0gDSALIAcgFFQbIBBCAFIbIRAgB0I/hiAMQgGIhCENIAlCP4YgFUIBiIQhByAMQj+GIAlCAYiECyELIBZCP4YgBkI/hiATQgGIhCETIBZCAYghFiAGQgGIhCEGIAVCAYNQDQALIAMgEzcDsAMgAyAFNwO4AyADIAY3A6gDIAMgFjcDoAMLIASnQQFxRQRAA0AgEkI/hiAEQgGIhCEEAn4gCkIBg1BFBEAgEUIBfSIUIA9CAFIgD0IBfSIPIA5CAFIgDkIBfSIMIApC0YeAgBB9IhUgClStfCIJIAxUcq18IgwgD1RyrXwiCkIBiCIOQoCAgICAgICAgH+EIg8gDyAOIAogFFQbIBFCAFIbIREgCkI/hiAMQgGIhCEPIAlCP4YgFUIBiIQhCiAMQj+GIAlCAYiEDAELIBFCP4YgD0I/hiEMIA5CP4YgCkIBiIQhCiARQgGIIREgD0IBiIQhDyAMIA5CAYiECyEOIBdCP4YgCEI/hiASQgGIhCESIBdCAYghFyAIQgGIhCEIIARCAYNQDQALIAMgEjcD0AMgAyAENwPYAyADIAg3A8gDIAMgFzcDwAMLAkACQAJAAkACQCAWIgwgFyIJUg0AIAghCSAGIQwgBiAIUg0AIBMiDCASIglSDQAgBCEJIAUhDCAEIAVRDQELIAkgDFgNACADIAQgBX0iCTcD2AMgAyASIBN9IhQgBCAFVK0iBH0iDDcD0AMgAyAIIAZ9IhUgEiATVCAEIBRWcq0iBH0iFDcDyAMgAyAXIBZ9IAQgFVYgBiAIVnKtfSIXNwPAAwJAAkAgECIIIBEiBFINACANIgggDyIEUg0AIAsiCCAOIgRSDQAgByIIIAoiBFENAQsgBCAIVA0CCyARIBB9IA8gDX0iFSAOIAt9IhggByAKVq0iGVQgCyAOVnKtIg5UIA0gD1ZyrX0hESAKIAd9IQogDCESIBQhCCAJIQQgFSAOfSEPIBggGX0hDgwDCyADIAUgBH0iCTcDuAMgAyATIBJ9IhQgBCAFVq0iBX0iDDcDsAMgAyAGIAh9IhUgEiATViAFIBRWcq0iBX0iFDcDqAMgAyAWIBd9IAYgCFQgBSAVVnKtfSIWNwOgAwJAAkAgECIFIBEiBlINACANIgUgDyIGUg0AIAsiBSAOIgZSDQAgByIFIAoiBlENAQsgBSAGVA0CCyAQIBF9IA0gD1QgDSAPfSINIAsgDlQgCyAOfSILIAcgClStIhVUcq0iGFRyrX0hECAHIAp9IQcgDCETIBQhBiAJIQUgDSAYfSENIAsgFX0hCwwCCyARIBBCf4UgDUJ/hSIEIAtCf4UiCCAHQq/4//9vVq0iEVStIhJUrX18IA8gBCASfSIPfCIEIA9UIAQgDiAIIBF9Ig58IgggDlQgCEKv+P//byAHfSIOIAp8IgogDlStfCIOIAhUcq18Ig8gBFRyrXwhESAMIRIgFCEIIAkhBAwBCyAQIBFCf4V8IA9Cf4UiBSAOQn+FIgYgCkKv+P//b1atIhBUrSITVK19IA0gBSATfSINfCIFIA1UIAUgCyAGIBB9Igt8IgYgC1QgBkKv+P//byAKfSILIAd8IgcgC1StfCILIAZUcq18Ig0gBVRyrXwhECAMIRMgFCEGIAkhBQsgA0GgA2ogA0GAA2pBIBDxAw0ACwsgA0HwAmogASkDGCIEQgAgB0IAEMkDIANBwAJqIAEpAxAiBUIAIAdCABDJAyADQbACaiABKQMIIgZCACAHQgAQyQMgA0GgAmogASkDACIIQgAgB0IAEMkDIANB4AJqIAMpA/ACIgdCseqUkd2jgpxYfiIJQgBCr/j//29CABDJAyADQdACaiAJQgBCf0IAEMkDIANBkAJqIARCACALQgAQyQMgA0HgAWogBUIAIAtCABDJAyADQdABaiAGQgAgC0IAEMkDIANBwAFqIAhCACALQgAQyQMgA0GAAmogAykD0AIiCSADKQP4AiIOIAMpA8ACfCIPfCIMIAMpA+gCIAcgAykD4AIiCnwgClStfHwiByADKQOQAnwiCkKx6pSR3aOCnFh+IgtCAEKv+P//b0IAEMkDIANB8AFqIAtCAEJ/QgAQyQMgA0GwAWogBEIAIA1CABDJAyADQYABaiAFQgAgDUIAEMkDIANB8ABqIAZCACANQgAQyQMgA0HgAGogCEIAIA1CABDJAyADQaABaiADKQOYAiAHIApWrXwiEiADKQPgAXwiCyAJIAMpA8gCIA4gD1atfCIUIAMpA7ACfCINfCIOIAcgDFStIAMpA9gCIgcgCSAMVq18fHwiFnwiDCADKQPwASIPfCIRIAMpA4gCIAogAykDgAIiCnwgClStfHwiCiADKQOwAXwiE0Kx6pSR3aOCnFh+IhdCAEKv+P//b0IAEMkDIANBkAFqIBdCAEJ/QgAQyQMgA0HQAGogBEIAIBBCABDJAyADQSBqIAVCACAQQgAQyQMgA0EQaiAGQgAgEEIAEMkDIAMgCEIAIBBCABDJAyADQUBrIAMpA7gBIAogE1atfCIXIAMpA4ABfCIEIA8gCSADKQO4AiANIBRUrXwiFSADKQOgAnwiBXwiBiAOIBZWrSAHIA0gDlatfHx8IgggAykD0AF8IgkgCyAMVq0gAykD6AEgCyASVK18fHwiC3wiDSAKIBFUrSADKQP4ASIKIAwgEVatfHx8IhZ8IgwgAykDkAEiEHwiDiADKQOoASADKQOgASIRIBN8IBFUrXx8IhEgAykDUHwiE0Kx6pSR3aOCnFh+IhJCAEKv+P//b0IAEMkDIANBMGogEkIAQn9CABDJAwJAAkAgAykDOCISIAMpA5gBIhQgECAKIA8gBiAIVq0gByAFIAZWrXx8IgcgAykDqAIgBSAVVK18fCIFIAMpA8ABfCIGIAkgC1atIAMpA9gBIAggCVatfHx8Igh8IgkgCFStfCAJIAkgDSAWVq0gCiALIA1WrXx8fCIJVq18IgogBiAIVq0gAykDyAEgBSAGVq18fCILIAUgB1StfCIHfCIFIAMpA2B8IgYgAykDeCAJIAMpA3B8IgggCVStfCAIIAQgDFatIAMpA4gBIAQgF1StfHx8IgQgCFStfHwiCHwiCSAIVK18IAkgFCAEIAQgEHwiBFatfCAEIA4gEVatIBQgDCAOVq18fHwiDCAEVK18fCIEIAlUrXwiDSAGIAhWrSADKQNoIAUgBlatfHwiECAFIApUrSAHIAtUrXx8Igt8IgUgAykDAHwiCSADKQMYIAQgBCADKQMQfCIEVq18IAQgBCADKQMoIAMpA1ggESATVq18IgggAykDIHwiBiAIVK18IAYgBiAMfCIGVq18fCIEVq18fCIMIAMpAzAiCHwiByAMVK18IAcgEiAEIAQgCHwiBFatfCAEIBIgBiAGIAh8IgZWrXwgBiADKQNIIAMpA0AiCCATfCAIVK18fCIKIAZUrXx8IgYgBFStfHwiCCAHVK18IgQgCSAMVq0gAykDCCAFIAlWrXx8IgkgBSANVK0gCyAQVK18fCIFfCIHIARUIAUgCVRyDQAgB0J/UgRAIAYhBCAIIQUMAgsgCEJ/UgRAIAYhBCAIIQVCfyEHDAILQn8hBSAGQn9SBEAgBiEEQn8hBwwCC0J/IQQgCkKv+P//b1oNAEJ/IQcMAQsgBkIBfCIFIApCr/j//29UrSIJfSEEIAhCAXwiDCAGQn9SIAUgCVRyrSIGfSEFIAcgCEJ/UiAGIAxWcq19QgF8IQcgCkLRh4CAEHwhCgsgACAKNwMgIAAgBDcDGCAAIAc3AwhCACEHQRALIABqIAU3AwAgACAHNwMAIANB4ANqJAALkyECAX8UfiMAQYAJayIDJAAgA0GAB2ogASkDGCIJQgAgAikDGCIEQgAQyQMgA0GQB2ogASkDECIIQgAgBEIAEMkDIANBoAdqIAEpAwgiBkIAIARCABDJAyADQbAHaiABKQMAIg1CACAEQgAQyQMgA0HwBmogAykDgAciBUIAQgBCiceZpK7wgemHfxDJAyADQeAGaiADKQP4BiIEQgBCx/rzw+2Co5A8QgAQyQMgA0HQBmogBEIAQo2Vx8OW0trAl39CABDJAyADQfAFaiAEQgBC3bCFjOi2kai4f0IAEMkDIANBkAVqIARCAEKpwMaJrs6TsjBCABDJAyADQcAHaiACKQMQIgRCACAJQgAQyQMgA0HQB2ogBEIAIAhCABDJAyADQeAHaiAEQgAgBkIAEMkDIANB8AdqIARCACANQgAQyQMgA0HABmogAykD0AYiDiADKQOIByIMIAMpA5AHfCIHfCILIAMpA+gGIAUgAykD4AYiBHwgBFStfHwiBSADKQPAB3wiD0IAQgBCiceZpK7wgemHfxDJAyADQbAGaiADKQPIBiIEQgBCx/rzw+2Co5A8QgAQyQMgA0GgBmogBEIAQo2Vx8OW0trAl39CABDJAyADQZAGaiAEQgBC3bCFjOi2kai4f0IAEMkDIANBgAZqIARCAEKpwMaJrs6TsjBCABDJAyADQYAIaiACKQMIIgRCACAJQgAQyQMgA0GQCGogBEIAIAhCABDJAyADQaAIaiAEQgAgBkIAEMkDIANBsAhqIARCACANQgAQyQMgA0HgBWogAykDyAcgBSAPVq18IhEgAykD0Ad8IgogAykDmAcgByAMVK18IhAgAykDoAd8IgwgAykD8AV8IgcgBSALVK0gAykD2AYgCyAOVK18fHwiFHwiCyADKQOgBnwiBSADKQO4BiADKQOwBiIEIA98IARUrXx8Ig8gAykDgAh8Ig5CAEIAQonHmaSu8IHph38QyQMgA0HQBWogAykD6AUiBEIAQsf688PtgqOQPEIAEMkDIANBwAVqIARCAEKNlcfDltLawJd/QgAQyQMgA0GwBWogBEIAQt2whYzotpGouH9CABDJAyADQaAFaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0HACGogAikDACIEQgAgCUIAEMkDIANB0AhqIARCACAIQgAQyQMgA0HgCGogBEIAIAZCABDJAyADQfAIaiAEQgAgDUIAEMkDIANBgAVqIAMpA4gIIA4gD1StfCIVIAMpA5AIfCITIAMpA6gHIAwgEFStfCIWIAMpA7AHfCIQIAMpA5AFfCISIAcgFFatIAMpA/gFIAcgDFStfHx8IgwgAykD4Ad8IgcgCiALVq0gAykD2AcgCiARVK18fHwiCiADKQOQBnwiESAFIA9WrSADKQOoBiAFIAtUrXx8fCIUfCILIAMpA8AFfCIFIAMpA9gFIAMpA9AFIgQgDnwgBFStfHwiDyADKQPACHwiDkIAQgBCiceZpK7wgemHfxDJAyADQfAEaiADKQOIBSIEQgBCx/rzw+2Co5A8QgAQyQMgA0HgBGogBEIAQo2Vx8OW0trAl39CABDJAyADQdAEaiAEQgBC3bCFjOi2kai4f0IAEMkDIANBwARqIARCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDyAQgAykDqAUgAykDiAYgDCASVK0gAykDmAUgECASVq18fCADKQO4ByAQIBZUrXx8IhAgAykD8Ad8IgQgByAKVq0gAykD6AcgByAMVK18fHwiDCADKQOABnwiByAMVK18IAcgESAUVq0gAykDmAYgCiARVq18fHwiCiAHVK18IAQgDFatIAMpA/gHIAQgEFStfHx8IhAgAykDsAh8IgQgAykDqAggCiAKIAMpA6AIfCIKVq18IAogCiALIBNUrSADKQOYCCATIBVUrXx8fCIKVq18fCIMIAMpA6AFfCIHIAxUrXwgByADKQO4BSAKIAogAykDsAV8IgpWrXwgCiAFIA9WrSADKQPIBSAFIAtUrXx8fCIFIApUrXx8IgsgB1StfCAEIAxWrSADKQO4CCAEIBBUrXx8fCIHIAMpA/AIfCIKIAMpA+gIIAsgAykD4Ah8IgQgC1StfCAEIAQgAykD2AggAykDyAggDiAPVK18Ig8gAykD0Ah8IgsgD1StfCALIAUgC3wiC1atfHwiBFatfHwiDyADKQPABHwiBSAPVK18IAUgBSADKQPYBCAEIAQgAykD0AR8IgRWrXwgBCAEIAMpA+gEIAsgCyADKQPgBHwiC1atfCALIAMpA/gEIAMpA/AEIgwgDnwgDFStfHwiDCALVK18fCIEVq18fCIFVq18IAogD1atIAMpA/gIIAcgClatfHx8IgpCqcDGia7Ok7IwVg0AAkAgCkKpwMaJrs6TsjBRBEAgBULdsIWM6LaRqLh/Vg0CIAVC3bCFjOi2kai4f1IEQCAEIQsgBSEPQqnAxomuzpOyMCEKDAQLIARCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQ8gBEKNlcfDltLawJd/UQ0BIAQhC0KpwMaJrs6TsjAhCgwDCyAEIQsgBSEPDAILQo2Vx8OW0trAl38hCyAMQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhCgwBCyAEQvPquLzpraW/6AB8Ig8gDELH+vPD7YKjkDxUrSIHfSELIAVCo8/685fJ7tfHAHwiDiAEQo2Vx8OW0trAl39UIAcgD1ZyrSIEfSEPIAogBULdsIWM6LaRqLh/VCAEIA5Wcq19QqnAxomuzpOyMH0hCiAMQsf688PtgqOQPH0hDAsgA0HAA2ogAikDOCIEQgAgCUIAEMkDIANB0ANqIARCACAIQgAQyQMgA0HgA2ogBEIAIAZCABDJAyADQfADaiAEQgAgDUIAEMkDIANBsANqIAMpA8ADIgdCAEIAQonHmaSu8IHph38QyQMgA0GgA2ogAykDuAMiBEIAQsf688PtgqOQPEIAEMkDIANBkANqIARCAEKNlcfDltLawJd/QgAQyQMgA0GAA2ogBEIAQt2whYzotpGouH9CABDJAyADQfACaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0GwAmogAikDMCIEQgAgCUIAEMkDIANBwAJqIARCACAIQgAQyQMgA0HQAmogBEIAIAZCABDJAyADQeACaiAEQgAgDUIAEMkDIANBoAJqIAMpA5ADIhEgAykDyAMiECADKQPQA3wiEnwiBSADKQOoAyAHIAMpA6ADIgR8IARUrXx8IgcgAykDsAJ8Ig5CAEIAQonHmaSu8IHph38QyQMgA0GQAmogAykDqAIiBEIAQsf688PtgqOQPEIAEMkDIANBgAJqIARCAEKNlcfDltLawJd/QgAQyQMgA0HwAWogBEIAQt2whYzotpGouH9CABDJAyADQeABaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0GgAWogAikDKCIEQgAgCUIAEMkDIANBsAFqIARCACAIQgAQyQMgA0HAAWogBEIAIAZCABDJAyADQdABaiAEQgAgDUIAEMkDIANBkAFqIAMpA7gCIAcgDlatfCIUIAMpA8ACfCITIAMpA9gDIBAgElatfCIVIAMpA+ADfCIQIAMpA4ADfCISIAUgB1atIAMpA5gDIAUgEVStfHx8IhZ8IgUgAykDgAJ8IgcgAykDmAIgAykDkAIiBCAOfCAEVK18fCIOIAMpA6ABfCIRQgBCAEKJx5mkrvCB6Yd/EMkDIANBgAFqIAMpA5gBIgRCAELH+vPD7YKjkDxCABDJAyADQfAAaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANBEGogBEIAQt2whYzotpGouH9CABDJAyADIARCAEKpwMaJrs6TsjBCABDJAyADQYAEaiACKQMgIgRCACAJQgAQyQMgA0GQBGogBEIAIAhCABDJAyADQaAEaiAEQgAgBkIAEMkDIANBsARqIARCACANQgAQyQMgA0HgAGogAykDqAEgDiARVq18IhcgAykDsAF8IgkgAykD6AMgECAVVK18IhUgAykD8AN8IgggAykD8AJ8IgYgEiAWVq0gAykDiAMgECASVq18fHwiDSADKQPQAnwiECAFIBNUrSADKQPIAiATIBRUrXx8fCITIAMpA/ABfCISIAcgDlatIAMpA4gCIAUgB1atfHx8IhR8IgUgAykDcHwiByADKQOIASADKQOAASIEIBF8IARUrXx8Ig4gAykDgAR8IhFCAEIAQonHmaSu8IHph38QyQMgA0HQAGogAykDaCIEQgBCx/rzw+2Co5A8QgAQyQMgA0FAayAEQgBCjZXHw5bS2sCXf0IAEMkDIANBMGogBEIAQt2whYzotpGouH9CABDJAyADQSBqIARCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDKCADKQMIIAMpA+gBIAYgDVatIAMpA/gCIAYgCFStfHwgAykD+AMgCCAVVK18fCIVIAMpA+ACfCIEIBAgE1atIAMpA9gCIA0gEFatfHx8IgggAykD4AF8IgYgCFStfCAGIAYgEiAUVq0gAykD+AEgEiATVK18fHwiBlatfCAEIAhWrSADKQPoAiAEIBVUrXx8fCINIAMpA9ABfCIEIAMpA8gBIAYgAykDwAF8IgggBlStfCAIIAUgCVStIAMpA7gBIAkgF1StfHx8IgkgCFStfHwiCCADKQMAfCIGIAhUrXwgBiADKQMYIAkgCSADKQMQfCIJVq18IAkgCSAHIA5WrSADKQN4IAUgB1atfHx8IglWrXx8IgUgBlStfCAEIAhWrSADKQPYASAEIA1UrXx8fCIHIAMpA7AEfCIIIAMpA6gEIAUgAykDoAR8IgQgBVStfCAEIAQgAykDmAQgAykDiAQgDiARVq18IgYgAykDkAR8IgUgBlStfCAFIAUgCXwiBVatfHwiBFatfHwiBiADKQMgfCIJIAZUrXwgCSAJIAMpAzggBCAEIAMpAzB8IgRWrXwgBCAEIAMpA0ggBSAFIAMpA0B8IgVWrXwgBSADKQNYIAMpA1AiDSARfCANVK18fCINIAVUrXx8IgRWrXx8IglWrXwgBiAIVK0gAykDuAQgByAIVq18fHwiBkKpwMaJrs6TsjBWDQACQCAGQqnAxomuzpOyMFEEQCAJQt2whYzotpGouH9WDQIgCULdsIWM6LaRqLh/UgRAIAQhBSAJIQhCqcDGia7Ok7IwIQYMBAsgBEKNlcfDltLawJd/Vg0CQt2whYzotpGouH8hCCAEQo2Vx8OW0trAl39RDQEgBCEFQqnAxomuzpOyMCEGDAMLIAQhBSAJIQgMAgtCjZXHw5bS2sCXfyEFIA1Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEGDAELIARC8+q4vOmtpb/oAHwiCCANQsf688PtgqOQPFStIgd9IQUgCUKjz/rzl8nu18cAfCIOIARCjZXHw5bS2sCXf1QgByAIVnKtIgR9IQggBiAJQt2whYzotpGouH9UIAQgDlZyrX1CqcDGia7Ok7IwfSEGIA1Cx/rzw+2Co5A8fSENCyAAIA03AzggACAFNwMwIAAgCDcDKCAAIAY3AyAgACAMNwMYIAAgCzcDECAAIA83AwggACAKNwMAIANBgAlqJAAL/B4CAX8WfiMAQeAEayIDJAACfyACQZCmxABBIBDxA0UEQEIBIQxCAiEFQQgMAQsgA0GQBGpCADcDACADQYgEakIANwMAIANCADcDgAQgA0IBNwOYBCADQbgEaiACQRhqKQMANwMAIANBsARqIAJBEGopAwA3AwAgA0GoBGogAkEIaikDADcDACADIAIpAwA3A6AEIANB2ARqQcilxAApAwA3AwAgA0HQBGpBwKXEACkDADcDACADQcgEakG4pcQAKQMANwMAIANBsKXEACkDADcDwAQCQCADQaAEaiADQYAEakEgEPEDRQRAQqWJufqXlrSLAiEMQqfbhfHayLncGyEFQuOz8Zqe1o7/0wAhC0KFge6d1efgpIx/IQ0MAQtCpYm5+peWtIsCIQxChYHundXn4KSMfyENQuOz8Zqe1o7/0wAhC0Kn24Xx2si53BshBSADKQO4BCEHIAMpA6AEIRYgAykDqAQhBCADKQOwBCESQoGAgIC/sv3wwwAhCEKpwMaJrs6TsjAhF0LdsIWM6LaRqLh/IQZCkeHlzYeJ+pkoIRMDQCADQcAEaiADQYAEakEgEPEDRQRAIBAhDSAOIQsgESEFIA8hDAwCCyAHp0EBcUUEQANAIBJCP4YgB0IBiIQhBwJAIAVCAYNQBEAgDSEJIAshCiAFIRQMAQsgDCANQqPP+vOXye7XxwB9IgkgDVQgCSAJIAtCkeHlzYeJ+pkofCIKIAtUIAogCiAFQoGAgIC/sv3wwwB8IhQgBVStfCIKVnKtfCIJVnKtfEKpwMaJrs6TsjB8IQwLIBZCP4YgBEI/hiASQgGIhCESIBZCAYghFiAMQj+GIAlCAYiEIQ0gCUI/hiAKQgGIhCELIApCP4YgFEIBiIQhBSAMQgGIIQwgBEIBiIQhBCAHQgGDUA0ACyADIBI3A7AEIAMgBzcDuAQgAyAENwOoBCADIBY3A6AECyAIp0EBcUUEQANAIBNCP4YgCEIBiIQhCAJAIBFCAYNQBEAgECEJIA4hCiARIRQMAQsgDyAQQqPP+vOXye7XxwB9IgkgEFQgCSAJIA5CkeHlzYeJ+pkofCIKIA5UIAogCiARQoGAgIC/sv3wwwB8IhQgEVStfCIKVnKtfCIJVnKtfEKpwMaJrs6TsjB8IQ8LIBdCP4YgBkI/hiATQgGIhCETIBdCAYghFyAPQj+GIAlCAYiEIRAgCUI/hiAKQgGIhCEOIApCP4YgFEIBiIQhESAPQgGIIQ8gBkIBiIQhBiAIQgGDUA0ACyADIBM3A9AEIAMgCDcD2AQgAyAGNwPIBCADIBc3A8AECwJAAkACQAJAAkAgFiIKIBciCVINACAGIQkgBCEKIAQgBlINACASIgogEyIJUg0AIAghCSAHIQogByAIUQ0BCyAJIApYDQAgAyAIIAd9Igk3A9gEIAMgEyASfSIUIAcgCFatIgh9Igo3A9AEIAMgBiAEfSIVIAggFFYgEiATVnKtIgh9IhQ3A8gEIAMgFyAWfSAIIBVWIAQgBlZyrX0iFzcDwAQCQAJAIAwiBiAPIghSDQAgDSIGIBAiCFINACALIgYgDiIIUg0AIAUiBiARIghRDQELIAYgCFYNAgsgDyAMfSAQIA19IhUgDiALfSIYIAUgEVatIhlUIAsgDlZyrSIOVCANIBBWcq19IQ8gESAFfSERIAohEyAUIQYgCSEIIBUgDn0hECAYIBl9IQ4MAwsgAyAHIAh9Igk3A7gEIAMgEiATfSIUIAcgCFStIgd9Igo3A7AEIAMgBCAGfSIVIBIgE1QgByAUVnKtIgd9IhQ3A6gEIAMgFiAXfSAEIAZUIAcgFVZyrX0iFjcDoAQCQAJAIAwiByAPIgRSDQAgDSIHIBAiBFINACALIgcgDiIEUg0AIAUhByARIgQgBVENAQsgBCAHVg0CCyAMIA99IA0gEFQgDSAQfSINIAsgDlQgCyAOfSILIAUgEVStIhVUcq0iGFRyrX0hDCAFIBF9IQUgCiESIBQhBCAJIQcgDSAYfSENIAsgFX0hCwwCCyAPQt2whYzotpGouH8gDX0iBkKR4eXNh4n6mSggC30iCCAFQoGAgIC/sv3wwwBWrSIPVCALQpHh5c2HifqZKFZyrSITVCANQt2whYzotpGouH9Wcq0gDHx9IBAgBiATfSIQfCIGIBBUIAYgDiAIIA99Ig58IgggDlQgCEKBgICAv7L98MMAIAV9Ig4gEXwiESAOVK18Ig4gCFRyrXwiECAGVHKtfEKpwMaJrs6TsjB8IQ8gCiETIBQhBiAJIQgMAQsgDCAPfULdsIWM6LaRqLh/IBB9IgdCkeHlzYeJ+pkoIA59IgQgEUKBgICAv7L98MMAVq0iDFQgDkKR4eXNh4n6mShWcq0iElQgEELdsIWM6LaRqLh/VnKtfSANIAcgEn0iDXwiByANVCAHIAsgBCAMfSILfCIEIAtUIARCgYCAgL+y/fDDACARfSILIAV8IgUgC1StfCILIARUcq18Ig0gB1RyrXxCqcDGia7Ok7IwfCEMIAohEiAUIQQgCSEHCyADQaAEaiADQYAEakEgEPEDDQALCyADQfADaiABKQMYIgdCACAFQgAQyQMgA0GgA2ogASkDECIEQgAgBUIAEMkDIANBkANqIAEpAwgiBkIAIAVCABDJAyADQYADaiABKQMAIghCACAFQgAQyQMgA0HgA2ogAykD8AMiCkL/////vrL98EJ+IgVCAEKBgICAv7L98MMAQgAQyQMgA0HQA2ogBUIAQpHh5c2HifqZKEIAEMkDIANBwANqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GwA2ogBUIAQqnAxomuzpOyMEIAEMkDIANB8AJqIAdCACALQgAQyQMgA0GgAmogBEIAIAtCABDJAyADQZACaiAGQgAgC0IAEMkDIANBgAJqIAhCACALQgAQyQMgA0HgAmogAykD0AMiECADKQP4AyIRIAMpA6ADfCIOfCIJIAMpA+gDIAogAykD4AMiBXwgBVStfHwiCiADKQPwAnwiC0L/////vrL98EJ+IgVCAEKBgICAv7L98MMAQgAQyQMgA0HQAmogBUIAQpHh5c2HifqZKEIAEMkDIANBwAJqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GwAmogBUIAQqnAxomuzpOyMEIAEMkDIANB8AFqIAdCACANQgAQyQMgA0GgAWogBEIAIA1CABDJAyADQZABaiAGQgAgDUIAEMkDIANBgAFqIAhCACANQgAQyQMgA0HgAWogAykD+AIgCiALVq18Ig8gAykDoAJ8Ig0gAykDqAMgDiARVK18IhIgAykDkAN8IhEgAykDwAN8Ig4gCSAKVq0gAykD2AMgCSAQVK18fHwiE3wiCSADKQPQAnwiCiADKQPoAiADKQPgAiIFIAt8IAVUrXx8IgsgAykD8AF8IhBC/////76y/fBCfiIFQgBCgYCAgL+y/fDDAEIAEMkDIANB0AFqIAVCAEKR4eXNh4n6mShCABDJAyADQcABaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBsAFqIAVCAEKpwMaJrs6TsjBCABDJAyADQfAAaiAHQgAgDEIAEMkDIANBIGogBEIAIAxCABDJAyADQRBqIAZCACAMQgAQyQMgAyAIQgAgDEIAEMkDIANB4ABqIAMpA/gBIAsgEFatfCIMIAMpA6ABfCIEIAMpA5gDIBEgElStfCISIAMpA4ADfCIGIAMpA7ADfCIIIA4gE1atIAMpA8gDIA4gEVStfHx8IgUgAykDkAJ8IhEgCSANVK0gAykDqAIgDSAPVK18fHwiDSADKQPAAnwiDiAKIAtWrSADKQPYAiAJIApWrXx8fCIPfCIJIAMpA9ABfCIKIAMpA+gBIAMpA+ABIgcgEHwgB1StfHwiCyADKQNwfCIQQv////++sv3wQn4iB0IAQoGAgIC/sv3wwwBCABDJAyADQdAAaiAHQgBCkeHlzYeJ+pkoQgAQyQMgA0FAayAHQgBC3bCFjOi2kai4f0IAEMkDIANBMGogB0IAQqnAxomuzpOyMEIAEMkDAkACQCADKQM4IAMpA7gBIAMpA7gCIAUgCFStIAMpA7gDIAYgCFatfHwgAykDiAMgBiASVK18fCISIAMpA4ACfCIHIA0gEVStIAMpA5gCIAUgEVatfHx8IgYgAykDsAJ8IgggBlStfCAIIAggDiAPVq0gAykDyAIgDSAOVq18fHwiCFatfCAGIAdUrSADKQOIAiAHIBJUrXx8fCIFIAMpA4ABfCIHIAMpA5gBIAggAykDkAF8IgYgCFStfCAGIAQgCVatIAMpA6gBIAQgDFStfHx8IgQgBlStfHwiBiADKQOwAXwiCCAGVK18IAggAykDyAEgBCAEIAMpA8ABfCIEVq18IAQgCiALVq0gAykD2AEgCSAKVq18fHwiCSAEVK18fCIEIAhUrXwgBiAHVK0gAykDiAEgBSAHVq18fHwiCiADKQMAfCIHIAMpAxggBCAEIAMpAxB8IgRWrXwgBCAEIAMpAyggAykDeCALIBBWrXwiCCADKQMgfCIGIAhUrXwgBiAGIAl8IgZWrXx8IgRWrXx8IgggAykDMHwiBSAIVK18IAUgAykDSCAEIAQgAykDQHwiBFatfCAEIAQgAykDWCAGIAYgAykDUHwiBlatfCAGIAMpA2ggAykDYCIJIBB8IAlUrXx8IgwgBlStfHwiBFatfHwiBiAFVK18IAcgCFatIAMpAwggByAKVK18fHwiD0KpwMaJrs6TsjBWDQACQCAPQqnAxomuzpOyMFEEQCAGQt2whYzotpGouH9WDQIgBkLdsIWM6LaRqLh/UgRAIAQhByAGIQVCqcDGia7Ok7IwIQ8MBAsgBEKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyEFIARCkeHlzYeJ+pkoUQ0BIAQhB0KpwMaJrs6TsjAhDwwDCyAEIQcgBiEFDAILQpHh5c2HifqZKCEHIAxCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhDwwBCyAEQpHh5c2HifqZKH0iCCAMQoGAgIC/sv3wwwBUrSIFfSEHIAZCo8/685fJ7tfHAHwiCSAEQpHh5c2HifqZKFQgBSAIVnKtIgR9IQUgDyAGQt2whYzotpGouH9UIAQgCVZyrX1CqcDGia7Ok7IwfSEPIAxCgYCAgL+y/fDDAH0hDAsgACAMNwMgIAAgBzcDGCAAIA83AwhCACEMQRALIABqIAU3AwAgACAMNwMAIANB4ARqJAALgh8CAX8WfiMAQeAEayIDJAACfyACQZCmxABBIBDxA0UEQEIBIQxCAiEFQQgMAQsgA0GQBGpCADcDACADQYgEakIANwMAIANCADcDgAQgA0IBNwOYBCADQbgEaiACQRhqKQMANwMAIANBsARqIAJBEGopAwA3AwAgA0GoBGogAkEIaikDADcDACADIAIpAwA3A6AEIANB2ARqQailxAApAwA3AwAgA0HQBGpBoKXEACkDADcDACADQcgEakGYpcQAKQMANwMAIANBkKXEACkDADcDwAQCQCADQaAEaiADQYAEakEgEPEDRQRAQp/q4NWc7qfsBiEMQon1q5y1i7+WcyEFQvuDlKKdosbztX8hC0L2/4XS8N/H1ccAIQ0MAQtCn+rg1Zzup+wGIQxC9v+F0vDfx9XHACENQvuDlKKdosbztX8hC0KJ9auctYu/lnMhBSADKQO4BCEHIAMpA6AEIRYgAykDqAQhBCADKQOwBCESQsf688PtgqOQPCEIQqnAxomuzpOyMCEXQt2whYzotpGouH8hBkKNlcfDltLawJd/IRMDQCADQcAEaiADQYAEakEgEPEDRQRAIBAhDSAOIQsgESEFIA8hDAwCCyAHp0EBcUUEQANAIBJCP4YgB0IBiIQhBwJAIAVCAYNQBEAgDSEJIAshCiAFIRQMAQsgDCANQqPP+vOXye7XxwB9IgkgDVQgCSAJIAtC8+q4vOmtpb/oAH0iCiALVCAKIAogBULH+vPD7YKjkDx8IhQgBVStfCIKVnKtfCIJVnKtfEKpwMaJrs6TsjB8IQwLIBZCP4YgBEI/hiASQgGIhCESIBZCAYghFiAMQj+GIAlCAYiEIQ0gCUI/hiAKQgGIhCELIApCP4YgFEIBiIQhBSAMQgGIIQwgBEIBiIQhBCAHQgGDUA0ACyADIBI3A7AEIAMgBzcDuAQgAyAENwOoBCADIBY3A6AECyAIp0EBcUUEQANAIBNCP4YgCEIBiIQhCAJAIBFCAYNQBEAgECEJIA4hCiARIRQMAQsgDyAQQqPP+vOXye7XxwB9IgkgEFQgCSAJIA5C8+q4vOmtpb/oAH0iCiAOVCAKIAogEULH+vPD7YKjkDx8IhQgEVStfCIKVnKtfCIJVnKtfEKpwMaJrs6TsjB8IQ8LIBdCP4YgBkI/hiATQgGIhCETIBdCAYghFyAPQj+GIAlCAYiEIRAgCUI/hiAKQgGIhCEOIApCP4YgFEIBiIQhESAPQgGIIQ8gBkIBiIQhBiAIQgGDUA0ACyADIBM3A9AEIAMgCDcD2AQgAyAGNwPIBCADIBc3A8AECwJAAkACQAJAAkAgFiIKIBciCVINACAGIQkgBCEKIAQgBlINACASIgogEyIJUg0AIAghCSAHIQogByAIUQ0BCyAJIApYDQAgAyAIIAd9Igk3A9gEIAMgEyASfSIUIAcgCFatIgh9Igo3A9AEIAMgBiAEfSIVIAggFFYgEiATVnKtIgh9IhQ3A8gEIAMgFyAWfSAIIBVWIAQgBlZyrX0iFzcDwAQCQAJAIAwiBiAPIghSDQAgDSIGIBAiCFINACALIgYgDiIIUg0AIAUiBiARIghRDQELIAYgCFYNAgsgDyAMfSAQIA19IhUgDiALfSIYIAUgEVatIhlUIAsgDlZyrSIOVCANIBBWcq19IQ8gESAFfSERIAohEyAUIQYgCSEIIBUgDn0hECAYIBl9IQ4MAwsgAyAHIAh9Igk3A7gEIAMgEiATfSIUIAcgCFStIgd9Igo3A7AEIAMgBCAGfSIVIBIgE1QgByAUVnKtIgd9IhQ3A6gEIAMgFiAXfSAEIAZUIAcgFVZyrX0iFjcDoAQCQAJAIAwiByAPIgRSDQAgDSIHIBAiBFINACALIgcgDiIEUg0AIAUhByARIgQgBVENAQsgBCAHVg0CCyAMIA99IA0gEFQgDSAQfSINIAsgDlQgCyAOfSILIAUgEVStIhVUcq0iGFRyrX0hDCAFIBF9IQUgCiESIBQhBCAJIQcgDSAYfSENIAsgFX0hCwwCCyAPQt2whYzotpGouH8gDX0iBkKNlcfDltLawJd/IAt9IgggBULH+vPD7YKjkDxWrSIPVCALQo2Vx8OW0trAl39Wcq0iE1QgDULdsIWM6LaRqLh/VnKtIAx8fSAQIAYgE30iEHwiBiAQVCAGIA4gCCAPfSIOfCIIIA5UIAhCx/rzw+2Co5A8IAV9Ig4gEXwiESAOVK18Ig4gCFRyrXwiECAGVHKtfEKpwMaJrs6TsjB8IQ8gCiETIBQhBiAJIQgMAQsgDCAPfULdsIWM6LaRqLh/IBB9IgdCjZXHw5bS2sCXfyAOfSIEIBFCx/rzw+2Co5A8Vq0iDFQgDkKNlcfDltLawJd/VnKtIhJUIBBC3bCFjOi2kai4f1ZyrX0gDSAHIBJ9Ig18IgcgDVQgByALIAQgDH0iC3wiBCALVCAEQsf688PtgqOQPCARfSILIAV8IgUgC1StfCILIARUcq18Ig0gB1RyrXxCqcDGia7Ok7IwfCEMIAohEiAUIQQgCSEHCyADQaAEaiADQYAEakEgEPEDDQALCyADQfADaiABKQMYIgdCACAFQgAQyQMgA0GgA2ogASkDECIEQgAgBUIAEMkDIANBkANqIAEpAwgiBkIAIAVCABDJAyADQYADaiABKQMAIghCACAFQgAQyQMgA0HgA2ogAykD8AMiCkKJx5mkrvCB6Yd/fiIFQgBCx/rzw+2Co5A8QgAQyQMgA0HQA2ogBUIAQo2Vx8OW0trAl39CABDJAyADQcADaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBsANqIAVCAEKpwMaJrs6TsjBCABDJAyADQfACaiAHQgAgC0IAEMkDIANBoAJqIARCACALQgAQyQMgA0GQAmogBkIAIAtCABDJAyADQYACaiAIQgAgC0IAEMkDIANB4AJqIAMpA9ADIhAgAykD+AMiESADKQOgA3wiDnwiCSADKQPoAyAKIAMpA+ADIgV8IAVUrXx8IgogAykD8AJ8IgtCiceZpK7wgemHf34iBUIAQsf688PtgqOQPEIAEMkDIANB0AJqIAVCAEKNlcfDltLawJd/QgAQyQMgA0HAAmogBUIAQt2whYzotpGouH9CABDJAyADQbACaiAFQgBCqcDGia7Ok7IwQgAQyQMgA0HwAWogB0IAIA1CABDJAyADQaABaiAEQgAgDUIAEMkDIANBkAFqIAZCACANQgAQyQMgA0GAAWogCEIAIA1CABDJAyADQeABaiADKQP4AiAKIAtWrXwiDyADKQOgAnwiDSADKQOoAyAOIBFUrXwiEiADKQOQA3wiESADKQPAA3wiDiAJIApWrSADKQPYAyAJIBBUrXx8fCITfCIJIAMpA9ACfCIKIAMpA+gCIAMpA+ACIgUgC3wgBVStfHwiCyADKQPwAXwiEEKJx5mkrvCB6Yd/fiIFQgBCx/rzw+2Co5A8QgAQyQMgA0HQAWogBUIAQo2Vx8OW0trAl39CABDJAyADQcABaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBsAFqIAVCAEKpwMaJrs6TsjBCABDJAyADQfAAaiAHQgAgDEIAEMkDIANBIGogBEIAIAxCABDJAyADQRBqIAZCACAMQgAQyQMgAyAIQgAgDEIAEMkDIANB4ABqIAMpA/gBIAsgEFatfCIMIAMpA6ABfCIEIAMpA5gDIBEgElStfCISIAMpA4ADfCIGIAMpA7ADfCIIIA4gE1atIAMpA8gDIA4gEVStfHx8IgUgAykDkAJ8IhEgCSANVK0gAykDqAIgDSAPVK18fHwiDSADKQPAAnwiDiAKIAtWrSADKQPYAiAJIApWrXx8fCIPfCIJIAMpA9ABfCIKIAMpA+gBIAMpA+ABIgcgEHwgB1StfHwiCyADKQNwfCIQQonHmaSu8IHph39+IgdCAELH+vPD7YKjkDxCABDJAyADQdAAaiAHQgBCjZXHw5bS2sCXf0IAEMkDIANBQGsgB0IAQt2whYzotpGouH9CABDJAyADQTBqIAdCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDOCADKQO4ASADKQO4AiAFIAhUrSADKQO4AyAGIAhWrXx8IAMpA4gDIAYgElStfHwiEiADKQOAAnwiByANIBFUrSADKQOYAiAFIBFWrXx8fCIGIAMpA7ACfCIIIAZUrXwgCCAIIA4gD1atIAMpA8gCIA0gDlatfHx8IghWrXwgBiAHVK0gAykDiAIgByASVK18fHwiBSADKQOAAXwiByADKQOYASAIIAMpA5ABfCIGIAhUrXwgBiAEIAlWrSADKQOoASAEIAxUrXx8fCIEIAZUrXx8IgYgAykDsAF8IgggBlStfCAIIAMpA8gBIAQgBCADKQPAAXwiBFatfCAEIAogC1atIAMpA9gBIAkgClatfHx8IgkgBFStfHwiBCAIVK18IAYgB1StIAMpA4gBIAUgB1atfHx8IgogAykDAHwiByADKQMYIAQgBCADKQMQfCIEVq18IAQgBCADKQMoIAMpA3ggCyAQVq18IgggAykDIHwiBiAIVK18IAYgBiAJfCIGVq18fCIEVq18fCIIIAMpAzB8IgUgCFStfCAFIAMpA0ggBCAEIAMpA0B8IgRWrXwgBCAEIAMpA1ggBiAGIAMpA1B8IgZWrXwgBiADKQNoIAMpA2AiCSAQfCAJVK18fCIMIAZUrXx8IgRWrXx8IgYgBVStfCAHIAhWrSADKQMIIAcgClStfHx8Ig9CqcDGia7Ok7IwVg0AAkAgD0KpwMaJrs6TsjBRBEAgBkLdsIWM6LaRqLh/Vg0CIAZC3bCFjOi2kai4f1IEQCAEIQcgBiEFQqnAxomuzpOyMCEPDAQLIARCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQUgBEKNlcfDltLawJd/UQ0BIAQhB0KpwMaJrs6TsjAhDwwDCyAEIQcgBiEFDAILQo2Vx8OW0trAl38hByAMQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhDwwBCyAEQvPquLzpraW/6AB8IgggDELH+vPD7YKjkDxUrSIFfSEHIAZCo8/685fJ7tfHAHwiCSAEQo2Vx8OW0trAl39UIAUgCFZyrSIEfSEFIA8gBkLdsIWM6LaRqLh/VCAEIAlWcq19QqnAxomuzpOyMH0hDyAMQsf688PtgqOQPH0hDAsgACAMNwMgIAAgBzcDGCAAIA83AwhCACEMQRALIABqIAU3AwAgACAMNwMAIANB4ARqJAAL7RoCAX8WfiMAQaAEayIDJAACfyACQZCmxABBIBDxA0UEQEIBIQpCAiEGQQgMAQsgA0HQA2pCADcDACADQcgDakIANwMAIANCADcDwAMgA0IBNwPYAyADQfgDaiACQRhqKQMANwMAIANB8ANqIAJBEGopAwA3AwAgA0HoA2ogAkEIaikDADcDACADIAIpAwA3A+ADIANBmARqQYilxAApAwA3AwAgA0GQBGpBgKXEACkDADcDACADQYgEakH4pMQAKQMANwMAIANB8KTEACkDADcDgAQCQCADQeADaiADQcADakEgEPEDRQRAQqQLIQYMAQtCpAshBiADKQP4AyEFIAMpA+ADIRYgAykD6AMhByADKQPwAyESQm0hCUL///////////8AIRdCfyEEQn8hEwNAIANBgARqIANBwANqQSAQ8QNFBEAgDCELIA8hECAIIQYgESEKDAILIAWnQQFxRQRAA0AgEkI/hiAFQgGIhCEFAkAgBkIBg1AEQCALIQ0gECEOIAYhFAwBCyAKIAtCAFIgC0IBfSILIBBCAFIgEEIBfSINIAZCE30iFCAGVK18Ig4gDVRyrXwiDSALVHKtfEL///////////8AfCEKCyAWQj+GIAdCP4YgEkIBiIQhEiAWQgGIIRYgCkI/hiANQgGIhCELIA1CP4YgDkIBiIQhECAOQj+GIBRCAYiEIQYgCkIBiCEKIAdCAYiEIQcgBUIBg1ANAAsgAyASNwPwAyADIAU3A/gDIAMgBzcD6AMgAyAWNwPgAwsgCadBAXFFBEADQCATQj+GIAlCAYiEIQkCQCAIQgGDUARAIAwhDSAPIQ4gCCEUDAELIBEgDEIAUiAMQgF9IgwgD0IAUiAPQgF9Ig0gCEITfSIUIAhUrXwiDiANVHKtfCINIAxUcq18Qv///////////wB8IRELIBdCP4YgBEI/hiATQgGIhCETIBdCAYghFyARQj+GIA1CAYiEIQwgDUI/hiAOQgGIhCEPIA5CP4YgFEIBiIQhCCARQgGIIREgBEIBiIQhBCAJQgGDUA0ACyADIBM3A5AEIAMgCTcDmAQgAyAENwOIBCADIBc3A4AECwJAAkACQAJAAkAgFiIOIBciDVINACAEIQ0gByEOIAQgB1INACASIg4gEyINUg0AIAkhDSAFIQ4gBSAJUQ0BCyANIA5YDQAgAyAJIAV9IhQ3A5gEIAMgEyASfSIOIAUgCVatIgl9Ig03A5AEIAMgBCAHfSIVIAkgDlYgEiATVnKtIgl9Ig43A4gEIAMgFyAWfSAEIAdUIAkgFVZyrX0iFzcDgAQCQAJAIAoiBCARIglSDQAgDCEJIAwgCyIEUg0AIA8hCSAPIBAiBFINACAIIQkgCCAGIgRRDQELIAQgCVYNAgsgESAKfSAMIAt9IhkgDyAQfSIYIAYgCFatIhVUIA8gEFRyrSIPVCALIAxWcq19IREgCCAGfSEIIA0hEyAOIQQgFCEJIBkgD30hDCAYIBV9IQ8MAwsgAyAFIAl9IhQ3A/gDIAMgEiATfSIOIAUgCVStIgV9Ig03A/ADIAMgByAEfSIVIBIgE1QgBSAOVnKtIgV9Ig43A+gDIAMgFiAXfSAEIAdWIAUgFVZyrX0iFjcD4AMCQAJAIAoiBSARIgdSDQAgCyIFIAwiB1INACAQIgUgDyIHUg0AIAYiBSAIIgdRDQELIAUgB1QNAgsgCiARfSALIAxUIAsgDH0iCyAQIA99IhggBiAIVK0iFVQgDyAQVnKtIhBUcq19IQogBiAIfSEGIA0hEiAOIQcgFCEFIAsgEH0hCyAYIBV9IRAMAgsgEUJ/QgAgC0J/hSIRIBBCf4UiEyAGQm1WrSIJVK0iBFQbIAp9fCARIAR9IgQgDHwiDCAEVCAMIAwgEyAJfSIEIA98IgkgBFQgCUJtIAZ9IgQgCHwiCCAEVK18Ig8gCVRyrXwiDFZyrXxC////////////AHwhESANIRMgDiEEIBQhCQwBCyAKIBF9IAxCf4UiCiAPQn+FIhIgCEJtVq0iBVStIgdUrX0gCiAHfSIHIAt8IgsgB1QgCyALIBIgBX0iByAQfCIFIAdUIAVCbSAIfSIHIAZ8IgYgB1StfCIQIAVUcq18IgtWcq18Qv///////////wB8IQogDSESIA4hByAUIQULIANB4ANqIANBwANqQSAQ8QMNAAsLIANBsANqIAEpAxgiGEIAIAZCABDJAyADQfACaiABKQMQIhVCACAGQgAQyQMgA0HgAmogASkDCCIWQgAgBkIAEMkDIANB0AJqIAEpAwAiFEIAIAZCABDJAyADQaADaiADKQOwAyIFQpuUr8Pytajehn9+IgRCAEJtQgAQyQMgA0GQA2ogBEIAQn9CABDJAyADQYADaiAEQgBC////////////AEIAEMkDIANBwAJqIBhCACAQQgAQyQMgA0GAAmogFUIAIBBCABDJAyADQfABaiAWQgAgEEIAEMkDIANB4AFqIBRCACAQQgAQyQMgA0GwAmogAykDkAMiDyADKQO4AyIJIAMpA/ACfCIHfCIMIAMpA6gDIAUgAykDoAMiBHwgBFStfHwiBSADKQPAAnwiDkKblK/D8rWo3oZ/fiIEQgBCbUIAEMkDIANBoAJqIARCAEJ/QgAQyQMgA0GQAmogBEIAQv///////////wBCABDJAyADQdABaiAYQgAgC0IAEMkDIANBkAFqIBVCACALQgAQyQMgA0GAAWogFkIAIAtCABDJAyADQfAAaiAUQgAgC0IAEMkDIANBwAFqIAMpA8gCIAUgDlatfCINIAMpA4ACfCIXIA8gAykD+AIgByAJVK18IgggAykD4AJ8IhF8IgYgBSAMVK0gAykDmAMiBSAMIA9UrXx8fCIJfCISIAMpA6ACIgd8IgsgAykDuAIgAykDsAIiBCAOfCAEVK18fCIQIAMpA9ABfCITQpuUr8Pytajehn9+IgRCAEJtQgAQyQMgA0GwAWogBEIAQn9CABDJAyADQaABaiAEQgBC////////////AEIAEMkDIANB4ABqIBhCACAKQgAQyQMgA0EgaiAVQgAgCkIAEMkDIANBEGogFkIAIApCABDJAyADIBRCACAKQgAQyQMgA0HQAGogAykD2AEgECATVq18Ig4gAykDkAF8IhQgByADKQPoAiAIIBFWrXwiCCADKQPQAnwiDyADKQOAA3wiDCAGIAlWrSAFIAYgEVStfHx8IgogAykD8AF8IgYgEiAXVK0gAykDiAIgDSAXVq18fHwiEXwiDSALIBBWrSADKQOoAiIFIAsgElStfHx8Igl8IgsgAykDsAEiB3wiECADKQPIASADKQPAASIEIBN8IARUrXx8IhIgAykDYHwiE0KblK/D8rWo3oZ/fiIEQgBCbUIAEMkDIANBQGsgBEIAQn9CABDJAyADQTBqIARCAEL///////////8AQgAQyQMCQAJAIAMpAzggAykDqAEgAykDmAIgCiAMVK0gAykDiAMgDCAPVK18fCIEIAMpA9gCIAggD1atfHwiDyADKQPgAXwiDCAGIBFWrSADKQP4ASAGIApUrXx8fCIGIAMpA5ACfCIIIAZUrXwgCCAJIA1UrSAFIA0gEVStfHx8Ig0gCFStfCIIIAYgDFStIAMpA+gBIAwgD1StfHwiBSAEIA9WrXwiCXwiDyADKQNwfCIMIAMpA4gBIA0gAykDgAF8IgQgDVStfCAEIAsgFFStIAMpA5gBIA4gFFatfHx8Ig0gBFStfHwiBiADKQOgAXwiDiAGVK18IA4gAykDuAEiBCAHIA18IgcgDVStfCAHIAcgECASVq0gBCALIBBWrXx8fCIHVq18fCIEIA5UrXwiDSAGIAxUrSADKQN4IAwgD1StfHwiDiAIIA9WrSAFIAlWrXx8Igl8IgsgAykDAHwiECADKQMYIAQgAykDEHwiCCAEVK18IAggAykDKCADKQNoIBIgE1atfCIEIAMpAyB8IgUgBFStfCAFIAd8Ig8gBVStfHwiBSAIVK18fCIMIAMpAzB8IgYgDFStfCAGIAMpA0giByAFIAMpA0AiBHwiCCAFVK18IAggByAEIA98IgUgD1StfCAFIAMpA1ggAykDUCIEIBN8IARUrXx8IhEgBVStfHwiBCAIVK18fCIHIAZUrXwiCCAMIBBUrSADKQMIIAsgEFatfHwiBSALIA1UrSAJIA5UrXx8Igl8IgogCFQgBSAJVnIgCkIAU3INAAJAIApC////////////AFEEQEJ/IQYgB0J/UgRAIAQhCCAHIQZC////////////ACEKDAQLIARCf1ENASAEIQhC////////////ACEKDAMLIAQhCCAHIQYMAgtCfyEIIBFCbVoNAEL///////////8AIQoMAQsgBEIBfCIOIBFCbVStIgV9IQggB0IBfCIJIARCf1IgBSAOVnKtIgR9IQYgCiAHQn9SIAQgCVZyrX1C////////////AH0hCiARQhN8IRELIAAgETcDICAAIAg3AxggACAKNwMIQgAhCkEQCyAAaiAGNwMAIAAgCjcDACADQaAEaiQAC/scAgF/FH4jAEGABmsiAiQAIAJB4AVqIAEpAwAgASkDCBDNAiACQYAFaiABKQMQIAEpAxgQzQIgAkGgBWogASkDICABKQMoEM0CIAJBwAVqIAEpAzAgASkDOBDNAiACQYADaiACKQOYBSIDQgBCgICAgICAEUIAEMkDIAJBkANqIANCAEKAgICAgHxCABDJAyACQaADaiADQgBCf0IAEMkDIAJBsANqIANCAEL///////+gAkIAEMkDIAJB0AJqQgAgAikDgAMiBH1CAEKRgICAgICAgAhCABDJAyACQcADaiACKQOQBSIDQgBCgICAgICAEUIAEMkDIAJB0ANqIANCAEKAgICAgHxCABDJAyACQeADaiADQgBCf0IAEMkDIAJB8ANqIANCAEL///////+gAkIAEMkDIAJB4AJqQgAgBEKAgICAgIB/gyIDIAR9IANUrSIFIAIpA4gDIgggAikDkAN8Igd8IgQgAikDwAN8Igl9QgBCkYCAgICAgIAIQgAQyQMgAkGABGogAikDiAUiA0IAQoCAgICAgBFCABDJAyACQZAEaiADQgBCgICAgIB8QgAQyQMgAkGgBGogA0IAQn9CABDJAyACQbAEaiADQgBC////////oAJCABDJAyACQfACakIAIAlCAFKtIg0gBCAFVK0iCiACKQOYAyAHIAhUrXwiByACKQOgA3wiBnwiBSACKQPQA3wiCCACKQPIAyAEIAlWrXx8Igx8IgQgAikDgAR8Igl9QgBCkYCAgICAgIAIQgAQyQMgAkHABGogAikDgAUiA0IAQoCAgICAgBFCABDJAyACQdAEaiADQgBCgICAgIB8QgAQyQMgAkHgBGogA0IAQn9CABDJAyACQfAEaiADQgBC////////oAJCABDJAyACQcACakIAIAIpA4gEIAQgCVatfCIQIAIpA5AEfCIDIAIpA6gDIAYgB1StfCIOIAIpA7ADfCIHIAIpA9ACfCIGIAUgClStfCIKIAIpA+ADfCILIAggDFatIAIpA9gDIAUgCFatfHx8IgUgBCANVK18Igx8IgQgCUIAUq18IgkgAikDwAR8Igh9QgBCkYCAgICAgIAIQgAQyQMCQAJAIAIpA8gCIAIpA9gEIAIpA8gEIAggCVStfCIPIAIpA9AEfCINIA9UrXwgDSADIARWrSACKQOYBCADIBBUrXx8Ig8gAikDoAR8IgMgBSAMVq0iESACKQPgAnwiDCACKQO4AyAHIA5UrXwiDiACKQPwA3wiECAGIApWrSACKQPYAiAGIAdUrXx8fCIHIAUgC1StIAIpA+gDIAogC1atfHx8Igp8Igt8IgUgBCAJVq18IgZ8IgQgDVStfCINIAIpA+AEfCIJIAUgBlatIhIgAikD8AJ8IgYgByAKVq0gByAQVK0gAikD+AMgDiAQVq18fHwiECACKQOwBHwiByALIAxUrSACKQPoAiAMIBFUrXx8fCIKIAMgBVatIAIpA6gEIAMgD1StfHx8Igt8Igx8IgMgBCAEIAhCAFKtfCIEVq18IgggA1StIg4gAikDwAJ8IgUgDlStfCAFIAogC1atIAcgClatIAIpA7gEIAcgEFStfHx8IgsgAikD8AR8IgogBiAMVq0gAikD+AIgBiASVK18fHwiBiADIAlUrSACKQPoBCAJIA1UrXx8fCIDfCIHIAVUrXwgAyAGVK0gBiAKVK0gAikD+AQgCiALVK18fHx8IgZCkYCAgICAgIAIVg0AIAZCkYCAgICAgIAIUQRAIAQgCIQgB4RQRQ0BQgAhCUKRgICAgICAgAghBkIAIQVCACEDDAILIAchCSAIIQUgBCEDDAELIARCAX0hAyAIIARQrSIEfSEFIAcgBCAIVq0iBH0hCSAGIAQgB1atfUKRgICAgICAgAh9IQYLQpGAgICAgICACCEEIAIpA+gFIgggCXwiCSAIVCAJIAUgAikD8AUiBXwiCCAFVCAIIAggAyACKQP4BSIDfCIFIANUrXwiCFZyrXwiByAJVHKtIAIpA+AFIAZ8fCIGIQMCQAJAIAZCkYCAgICAgIAIUQRAIAcgCIRCAFINAUIBIQQgBSIDQgFRDQELIAMgBFoNACAHIQQgCCEDIAUhCQwBCyAFQgF9IQkgCCAFUK0iBH0hAyAHIAQgCFatIgV9IQRC7v////////93Qu//////////dyAFIAdWGyAGfCEGC0KRgICAgICAgAghCiAEIAQgACkDKHwiBFYgBCADIAMgACkDMHwiA1YgAyAJIAApAzh8IgUgCVStfCIIIANUcq18IgcgBFRyrSAAKQMgIAZ8fCIGIQQCQAJAIAZCkYCAgICAgIAIUQRAIAcgCIRCAFINAUIBIQogBSIEQgFRDQELIAQgCloNACAHIQQgCCEDIAUhCQwBCyAFQgF9IQkgCCAFUK0iBH0hAyAHIAQgCFatIgV9IQRC7v////////93Qu//////////dyAFIAdWGyAGfCEGCyAAIAk3AzggACADNwMwIAAgBDcDKCAAIAY3AyAgAkHwAGogAikD2AUiA0IAQoCAgICAgBFCABDJAyACQeAAaiADQgBCgICAgIB8QgAQyQMgAkHQAGogA0IAQn9CABDJAyACQUBrIANCAEL///////+gAkIAEMkDIAJBMGpCACACKQNwIgR9QgBCkYCAgICAgIAIQgAQyQMgAkGwAWogAikD0AUiA0IAQoCAgICAgBFCABDJAyACQaABaiADQgBCgICAgIB8QgAQyQMgAkGQAWogA0IAQn9CABDJAyACQYABaiADQgBC////////oAJCABDJAyACQSBqQgAgBEKAgICAgIB/gyIDIAR9IANUrSIFIAIpA3giCCACKQNgfCIHfCIEIAIpA7ABfCIJfUIAQpGAgICAgICACEIAEMkDIAJB8AFqIAIpA8gFIgNCAEKAgICAgIARQgAQyQMgAkHgAWogA0IAQoCAgICAfEIAEMkDIAJB0AFqIANCAEJ/QgAQyQMgAkHAAWogA0IAQv///////6ACQgAQyQMgAkEQakIAIAlCAFKtIg0gBCAFVK0iCiACKQNoIAcgCFStfCIHIAIpA1B8IgZ8IgUgAikDoAF8IgggAikDuAEgBCAJVq18fCIMfCIEIAIpA/ABfCIJfUIAQpGAgICAgICACEIAEMkDIAJBsAJqIAIpA8AFIgNCAEKAgICAgIARQgAQyQMgAkGgAmogA0IAQoCAgICAfEIAEMkDIAJBkAJqIANCAEJ/QgAQyQMgAkGAAmogA0IAQv///////6ACQgAQyQMgAkIAIAIpA/gBIAQgCVatfCIPIAIpA+ABfCIDIAIpA1ggBiAHVK18IhEgAikDQHwiByACKQMwfCIGIAUgClStfCIKIAIpA5ABfCILIAggDFatIAIpA6gBIAUgCFatfHx8IgUgBCANVK18IhJ8IgQgCUIAUq18IgkgAikDsAJ8Igh9QgBCkYCAgICAgIAIQgAQyQMgAikDuAUhDSACKQOwBSEMIAIpA6gFIRAgAikDoAUhFAJAAkAgAikDCCACKQOoAiACKQO4AiAIIAlUrXwiEyACKQOgAnwiDiATVK18IA4gAyAEVq0gAikD6AEgAyAPVK18fCITIAIpA9ABfCIDIAUgElatIhIgAikDIHwiDyACKQNIIAcgEVStfCIVIAIpA4ABfCIRIAYgClatIAIpAzggBiAHVK18fHwiByAFIAtUrSACKQOYASAKIAtWrXx8fCIKfCILfCIFIAQgCVatfCIGfCIEIA5UrXwiDiACKQOQAnwiCSAFIAZWrSIWIAIpAxB8IgYgByAKVq0gByARVK0gAikDiAEgESAVVK18fHwiESACKQPAAXwiByALIA9UrSACKQMoIA8gElStfHx8IgogAyAFVq0gAikD2AEgAyATVK18fHwiC3wiD3wiAyAEIAQgCEIAUq18IgRWrXwiCCADVK0iEiACKQMAfCIFIBJUrXwgBSAKIAtWrSAHIApWrSACKQPIASAHIBFUrXx8fCILIAIpA4ACfCIKIAYgD1atIAIpAxggBiAWVK18fHwiBiADIAlUrSACKQOYAiAJIA5UrXx8fCIDfCIHIAVUrXwgAyAGVK0gBiAKVK0gAikDiAIgCiALVK18fHx8IgZCkYCAgICAgIAIVg0AIAZCkYCAgICAgIAIUQRAIAQgCIQgB4RQRQ0BQgAhCUKRgICAgICAgAghBkIAIQVCACEDDAILIAchCSAIIQUgBCEDDAELIARCAX0hAyAIIARQrSIEfSEFIAcgBCAIVq0iBH0hCSAGIAQgB1atfUKRgICAgICAgAh9IQYLQpGAgICAgICACCEEIAkgEHwiCSAQVCAJIAUgDHwiCCAMVCAIIAggAyANfCIFIA1UrXwiCFZyrXwiByAJVHKtIAYgFHx8IgYhAwJAAkAgBkKRgICAgICAgAhRBEAgByAIhEIAUg0BQgEhBCAFIgNCAVENAQsgAyAEWg0AIAchBCAIIQMgBSEJDAELIAVCAX0hCSAIIAVQrSIEfSEDIAcgBCAIVq0iBX0hBELu/////////3dC7/////////93IAUgB1YbIAZ8IQYLIABBIGpCkYCAgICAgIAIIQogBCAEIAApA0h8IgRWIAQgAyADIAApA1B8IgNWIAMgCSAAKQNYfCIFIAlUrXwiCCADVHKtfCIHIARUcq0gACkDQCAGfHwiBiEEAkACQCAGQpGAgICAgICACFEEQCAHIAiEQgBSDQFCASEKIAUiBEIBUQ0BCyAEIApaDQAgByEEIAghAyAFIQkMAQsgBUIBfSEJIAggBVCtIgR9IQMgByAEIAhWrSIFfSEEQu7/////////d0Lv/////////3cgBSAHVhsgBnwhBgsgACAJNwNYIAAgAzcDUCAAIAQ3A0ggACAGNwNAEEYgAkGABmokAAvHIQIffgJ/IwBB0ANrIiEkACABKQMAIRogASkDCCEXIAEpAxAhGCABKQMYIRkgASkDICETIAEpAyghFEHYACEiA0AgIUHAAmogASAiaikDACIFQgAgFEIAEMkDICFB0AJqIAVCACATQgAQyQMgIUHgAmogBUIAIBlCABDJAyAhQfACaiAFQgAgGEIAEMkDICFBgANqIAVCACAXQgAQyQMgIUGQA2ogBUIAIBpCABDJAyAhQbACaiAhKQPAAiILIBV8Ig9CAEIAQv3/8//P///5iX8QyQMgIUGgAmogISkDuAIiBUIAQqvV/v///7//uX9CABDJAyAhQZACaiAFQgBC///Piuv//9UeQgAQyQMgIUGAAmogBUIAQqTsw7WP1LSY5wBCABDJAyAhQfABaiAFQgBCv6WUnM/w0rvkAEIAEMkDICFB4AFqIAVCAELX2a6a5PbpjcsAQgAQyQMgIUHQAWogBUIAQprN/8ujvcSAGkIAEMkDICEpA9gBICEpA5ADIgwgEnwiByAhKQOIAyAhKQOAAyIFIAZ8IgYgBVStfCAGICEpA/gCIAQgISkD8AIiBHwiBSAEVK18IAUgISkD6AIgAyAhKQPgAiIDfCIEIANUrXwgBCAhKQPYAiACICEpA9ACIgJ8IgMgAlStfCADICEpA8gCIAsgD1atfHwiAiADVK18fCIQIARUrXx8IgQgBVStfHwiAyAGVK18fCIIICEpA9ABfCILIAhUrXwgCyAhKQPoASADICEpA+ABfCIGIANUrXwgBiAhKQP4ASAEICEpA/ABfCIFIARUrXwgBSAhKQOIAiAQICEpA4ACfCIEIBBUrXwgBCAhKQOYAiACICEpA5ACIgJ8IgMgAlStfCADICEpA6gCICEpA6ACIgIgD3wgAlStfHwiFSADVK18fCICIARUrXx8IgMgBVStfHwiBCAGVK18fCIGIAtUrXwgByAIVq0gISkDmAMgByAMVK18fHwhEiAiQQhrIiJBKEcNAAsCQAJAIBJCms3/y6O9xIAaVg0AAkACQAJAAkAgEkKazf/Lo73EgBpSDQAgBkLX2a6a5PbpjcsAVg0EIAZC19mumuT26Y3LAFIEQEKazf/Lo73EgBohEgwBCyAEQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEbIARCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohEgwCCyADQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEcIANCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohEgwDCyACQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIR0gAkL//8+K6///1R5RDQNCms3/y6O9xIAaIRIgAiELDAULIAYhGwsgBCEcCyADIR0gAiELDAILQv//z4rr///VHiELIBVCqtX+////v/+5f1YNAEKazf/Lo73EgBohEgwBCyACQv//z4rr///VHn0iCCAVQqvV/v///7//uX9UrSIFfSELIANCpOzDtY/UtJjnAH0iDCACQv//z4rr///VHlQgBSAIVnKtIgJ9IR0gBEK/pZScz/DSu+QAfSIFIANCpOzDtY/UtJjnAFQgAiAMVnKtIgJ9IRwgBkLX2a6a5PbpjcsAfSIDIARCv6WUnM/w0rvkAFQgAiAFVnKtIgJ9IRsgEiAGQtfZrprk9umNywBUIAIgA1ZyrX1Cms3/y6O9xIAafSESIBVC1aqBgICAwIDGAHwhFQtCms3/y6O9xIAaIRYgFyABKQM4Ig18IgwgF1QgDCAYIAEpA0AiDnwiBCAYVCAEIAQgGSABKQNIIhF8IgMgGVQgAyATIAEpA1AiCXwiAiATVCACIBQgASkDWCIKfCIPIBRUrXwiBiACVHKtfCIFIANUcq18IgRWcq18IgMgDFRyrSABKQMwIgcgGnx8Ih4hAgJAAkACQCAeQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIRYgAyICQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEWIAQiAkK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhFiAFIgJCpOzDtY/UtJjnAFINAEL//8+K6///1R4hFiAGIgJC///Piuv//9UeUg0AQqvV/v///7//uX8hFiAPIgJCq9X+////v/+5f1ENAQsgAiAWWg0AIAYhFiAFIRAgBCEIIAMhDAwBCyAGQv//z4rr///VHn0iCCAPQqvV/v///7//uX9UrSICfSEWIAVCpOzDtY/UtJjnAH0iDCAGQv//z4rr///VHlQgAiAIVnKtIgJ9IRAgBEK/pZScz/DSu+QAfSIGIAVCpOzDtY/UtJjnAFQgAiAMVnKtIgJ9IQggA0LX2a6a5PbpjcsAfSIFIARCv6WUnM/w0rvkAFQgAiAGVnKtIgJ9IQwgHiADQtfZrprk9umNywBUIAIgBVZyrX1Cms3/y6O9xIAafSEeIA9C1aqBgICAwIDGAHwhDwsgIQJ+AkACQCAaIgMgByIFUg0AIBciAyANIgVSDQAgGCIDIA4iBVINACAZIgMgESIFUg0AIBMiAyAJIgVSDQAgFCIDIAoiBVENAQsgAyAFWg0AQqTsw7WP1LSY5wAgESAZfSIGIAkgE30iBSAKIBRUrSICVCAJIBNUcq0iA30iCX0iBCAFIAJ9IgJC///Piuv//9UeVkL//8+K6///1R4gAn0iHyAKIBR9IiBCq9X+////v/+5f1atIhNUcq0iAn0hBUK/pZScz/DSu+QAIA4gGH0iCiARIBlUIAMgBlZyrSIDfSIUfSIGIAIgBFYgCUKk7MO1j9S0mOcAVnKtIgJ9IQRC19mumuT26Y3LACANIBd9IhEgDiAYVCADIApWcq0iCX0iCn0iAyACIAZWIBRCv6WUnM/w0rvkAFZyrSICfSEGIAIgA1YgCkLX2a6a5PbpjcsAVnIhIiAfIBN9IQMgDSAXVCAJIBFWcq0gGiAHfXxCms3/y6O9xIAafCEOQqvV/v///7//uX8gIH0MAQsgEyAJfSIFIAogFFatIgJ9IQMgGSARfSIEIAkgE1YgAiAFVnKtIgJ9IQUgGCAOfSIGIBEgGVYgAiAEVnKtIgJ9IQQgFyANfSIJIA4gGFYgAiAGVnKtIgJ9IQYgDSAXViACIAlWciEiIBogB30hDiAUIAp9CzcDyAMgISADNwPAAyAhIAU3A7gDICEgBDcDsAMgISAGNwOoAyAhIA4gIq19NwOgA0EoISJCACENQgAhAkIAIQNCACEEQgAhBkIAIQUDQCAhQfAAaiAhQaADaiAiaikDACIHQgAgD0IAEMkDICFBgAFqIAdCACAWQgAQyQMgIUGQAWogB0IAIBBCABDJAyAhQaABaiAHQgAgCEIAEMkDICFBsAFqIAdCACAMQgAQyQMgIUHAAWogB0IAIB5CABDJAyAhQeAAaiAhKQNwIgogDXwiDUIAQgBC/f/z/8////mJfxDJAyAhQdAAaiAhKQNoIgdCAEKr1f7///+//7l/QgAQyQMgIUFAayAHQgBC///Piuv//9UeQgAQyQMgIUEwaiAHQgBCpOzDtY/UtJjnAEIAEMkDICFBIGogB0IAQr+llJzP8NK75ABCABDJAyAhQRBqIAdCAELX2a6a5PbpjcsAQgAQyQMgISAHQgBCms3/y6O9xIAaQgAQyQMgISkDCCAhKQPAASIHIAV8Ig4gISkDuAEgISkDsAEiBSAGfCIGIAVUrXwgBiAhKQOoASAEICEpA6ABIgR8IgUgBFStfCAFICEpA5gBIAMgISkDkAEiA3wiBCADVK18IAQgISkDiAEgAiAhKQOAASICfCIDIAJUrXwgAyAhKQN4IAogDVatfHwiAiADVK18fCIRIARUrXx8IgQgBVStfHwiAyAGVK18fCIJICEpAwB8IgogCVStfCAKICEpAxggAyAhKQMQfCIGIANUrXwgBiAhKQMoIAQgISkDIHwiBSAEVK18IAUgISkDOCARICEpAzB8IgQgEVStfCAEICEpA0ggAiAhKQNAIgJ8IgMgAlStfCADICEpA1ggISkDUCICIA18IAJUrXx8Ig0gA1StfHwiAiAEVK18fCIDIAVUrXx8IgQgBlStfHwiBiAKVK18IAkgDlStICEpA8gBIAcgDlatfHx8IQUgIkEIayIiQXhHDQALAkACQCAFQprN/8ujvcSAGlYNAAJAAkACQAJAIAVCms3/y6O9xIAaUg0AIAZC19mumuT26Y3LAFYNBCAGQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQUMAQsgBEK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhESAEQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQUMAgsgA0Kk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhCSADQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQUMAwsgAkL//8+K6///1R5WDQRCpOzDtY/UtJjnACEKIAJC///Piuv//9UeUQ0DQprN/8ujvcSAGiEFIAIhDAwFCyAGIRELIAQhCQsgAyEKIAIhDAwCC0L//8+K6///1R4hDCANQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQUMAQsgAkL//8+K6///1R59IgcgDUKr1f7///+//7l/VK0iCH0hDCADQqTsw7WP1LSY5wB9IhAgAkL//8+K6///1R5UIAcgCFRyrSICfSEKIARCv6WUnM/w0rvkAH0iCCADQqTsw7WP1LSY5wBUIAIgEFZyrSICfSEJIAZC19mumuT26Y3LAH0iAyAEQr+llJzP8NK75ABUIAIgCFZyrSICfSERIAUgBkLX2a6a5PbpjcsAVCACIANWcq19QprN/8ujvcSAGn0hBSANQtWqgYCAgMCAxgB8IQ0LQprN/8ujvcSAGiEDIBsgG3wiDyAbVCAPIBwgHHwiCCAcVCAIIAggHSAdfCIEIB1UIAQgCyALfCICIAtUIAIgFSAVfCIGIBVUrXwiByACVHKtfCIQIARUcq18IghWcq18IgsgD1RyrSASQgGGhCIOIQQCQAJAAkAgDkKazf/Lo73EgBpSDQBC19mumuT26Y3LACEDIAsiBELX2a6a5PbpjcsAUg0AQr+llJzP8NK75AAhAyAIIgRCv6WUnM/w0rvkAFINAEKk7MO1j9S0mOcAIQMgECIEQqTsw7WP1LSY5wBSDQBC///Piuv//9UeIQMgByIEQv//z4rr///VHlINAEKr1f7///+//7l/IQMgBiIEQqvV/v///7//uX9RDQELIAMgBFgNACALIQQgCCEDIBAhAiAHIQ8MAQsgB0L//8+K6///1R59IgMgBkKr1f7///+//7l/VK0iAn0hDyAQQqTsw7WP1LSY5wB9IgQgB0L//8+K6///1R5UIAIgA1ZyrSIDfSECIAhCv6WUnM/w0rvkAH0iByAQQqTsw7WP1LSY5wBUIAMgBFZyrSIEfSEDIAtC19mumuT26Y3LAH0iECAIQr+llJzP8NK75ABUIAQgB1ZyrSIIfSEEIA4gC0LX2a6a5PbpjcsAVCAIIBBWcq19QprN/8ujvcSAGn0hDiAGQtWqgYCAgMCAxgB8IQYLIAAgBjcDWCAAIA83A1AgACACNwNIIAAgAzcDQCAAIAQ3AzggACAONwMwIAAgDTcDKCAAIAw3AyAgACAKNwMYIAAgCTcDECAAIBE3AwggACAFNwMAICFB0ANqJAALvhgCAX8WfiMAQaADayIDJAACfyACQZCmxABBIBDxA0UEQEIBIQZCAiEFQQgMAQsgA0HQAmpCADcDACADQcgCakIANwMAIANCADcDwAIgA0IBNwPYAiADQfgCaiACQRhqKQMANwMAIANB8AJqIAJBEGopAwA3AwAgA0HoAmogAkEIaikDADcDACADIAIpAwA3A+ACIANBmANqQYimxAApAwA3AwAgA0GQA2pBgKbEACkDADcDACADQYgDakH4pcQAKQMANwMAIANB8KXEACkDADcDgAMCQCADQeACaiADQcACakEgEPEDRQRAQv3////PACEPQgMhDkL/////v38hBkJ+IQsMAQtC/f///88AIQ9CfiELQv////+/fyEGQgMhDiADKQP4AiEFIAMpA+ACIRcgAykD6AIhCCADKQPwAiERQn8hBEKBgICAcCEVQv////8PIRMDQCADQYADaiADQcACakEgEPEDRQRAIAwhCyAJIQYgEiEOIBAhDwwCCyAFp0EBcUUEQANAIBFCP4YgBUIBiIQhBQJ+IA6nQQFxRQRAIA9CP4YgC0I/hiEKIAZCP4YgDkIBiIQhDiAPQgGIIQ8gC0IBiIQhCyAKIAZCAYiEDAELIA9C/////w99IhYgCyAGQoCAgIAQfCIUUCAGQv////8PfCAGVHKtfCIGIAtUrXwiC0IBiCINQoCAgICAgICAgH+EIgogCiANIAsgFlQbIA8gFlYbIQ8gC0I/hiAGQgGIhCELIBRCP4YgDkIBfUIBiIQhDiAGQj+GIBRCAYiECyEGIBdCP4YgCEI/hiARQgGIhCERIBdCAYghFyAIQgGIhCEIIAVCAYNQDQALIAMgETcD8AIgAyAFNwP4AiADIAg3A+gCIAMgFzcD4AILIASnQQFxRQRAA0AgE0I/hiAEQgGIhCEEAn4gEkIBg1BFBEAgEEL/////D30iFiAMIAlCgICAgBB8IhRQIAlC/////w98IAlUcq18IgkgDFStfCIMQgGIIg1CgICAgICAgICAf4QiCiAKIA0gDCAWVBsgECAWVhshECAMQj+GIAlCAYiEIQwgFEI/hiASQgF9QgGIhCESIAlCP4YgFEIBiIQMAQsgEEI/hiAMQj+GIQogCUI/hiASQgGIhCESIBBCAYghECAMQgGIhCEMIAogCUIBiIQLIQkgFUI/hiAHQj+GIBNCAYiEIRMgFUIBiCEVIAdCAYiEIQcgBEIBg1ANAAsgAyATNwOQAyADIAQ3A5gDIAMgBzcDiAMgAyAVNwOAAwsCQAJAAkACQAJAIBciCiAVIg1SDQAgByENIAghCiAHIAhSDQAgESIKIBMiDVINACAEIQ0gBSEKIAQgBVENAQsgCiANWg0AIAMgBCAFfSIUNwOYAyADIBMgEX0iCiAEIAVUrSIEfSINNwOQAyADIAcgCH0iFiAEIApWIBEgE1ZyrSIEfSIKNwOIAyADIBUgF30gByAIVCAEIBZWcq19IhU3A4ADAkACQCAPIgcgECIEUg0AIAsiByAMIgRSDQAgCSEEIAYhByAGIAlSDQAgDiIHIBIiBFENAQsgBCAHVA0CCyAQIA99IAwgC30iGSAJIAZ9IhggDiASVq0iFlQgBiAJVnKtIglUIAsgDFZyrX0hECASIA59IRIgDSETIAohByAUIQQgGSAJfSEMIBggFn0hCQwDCyADIAUgBH0iFDcD+AIgAyARIBN9IgogBCAFVq0iBX0iDTcD8AIgAyAIIAd9IhYgESATVCAFIApWcq0iBX0iCjcD6AIgAyAXIBV9IAcgCFYgBSAWVnKtfSIXNwPgAgJAAkAgDyIFIBAiCFINACAMIQggDCALIgVSDQAgBiEFIAkhCCAGIAlSDQAgDiIFIBIiCFENAQsgBSAIVA0CCyAPIBB9IAsgDFQgCyAMfSIYIAYgCVQgBiAJfSIWIA4gElStIgZUcq0iC1RyrX0hDyAOIBJ9IQ4gDSERIAohCCAUIQUgGCALfSELIBYgBn0hBgwCCyAQIAtCAFJCACALfSIHIAZC/////w9WrSIEVHKtIA98fSAHIAR9IgQgDHwiEyAEVCATQv////8PIAZ9IgQgCXwiByAEVCAHIA5Cf4UiBCASfCISIARUrXwiCSAHVHKtfCIMIBNUcq18Qv////8PfSEQIA0hEyAKIQcgFCEEDAELIA8gEH0gDEIAUkIAIAx9IgUgCUL/////D1atIghUcq19IAUgCH0iCCALfCIRIAhUIBFC/////w8gCX0iCCAGfCIFIAhUIAUgEkJ/hSIIIA58Ig4gCFStfCIGIAVUcq18IgsgEVRyrXxC/////w99IQ8gDSERIAohCCAUIQULIANB4AJqIANBwAJqQSAQ8QMNAAsLIANBsAJqIAEpAxgiF0IAIA5CABDJAyADQZACaiABKQMQIhVCACAOQgAQyQMgA0GAAmogASkDCCIRQgAgDkIAEMkDIANB8AFqIAEpAwAiDUIAIA5CABDJAyADQaACaiADKQOwAiIFQgBCgYCAgHBCABDJAyADQeABaiAXQgAgBkIAEMkDIANBwAFqIBVCACAGQgAQyQMgA0GwAWogEUIAIAZCABDJAyADQaABaiANQgAgBkIAEMkDIANB0AFqIAMpA7gCIgQgAykDkAJ8IgcgBUIghnwiCCADKQPgAXwiCUIAQoGAgIBwQgAQyQMgA0GQAWogF0IAIAtCABDJAyADQfAAaiAVQgAgC0IAEMkDIANB4ABqIBFCACALQgAQyQMgA0HQAGogDUIAIAtCABDJAyADQYABaiAHIAhWrSAFQiCIfCIKIAMpA5gCIAQgB1atfCIHIAMpA4ACfCIEfCIMIAMpA8ABfCISIAMpA+gBIAggCVatfHwiECAJQiCGfCITIAMpA5ABfCIUQgBCgYCAgHBCABDJAyADQUBrIBdCACAPQgAQyQMgA0EgaiAVQgAgD0IAEMkDIANBEGogEUIAIA9CABDJAyADIA1CACAPQgAQyQMgA0EwaiADKQOYASATIBRWrXwiBSADKQNwfCIRIAMpA4gCIAQgB1StfCIIIAMpA/ABfCIOIAMpA6ACfCINIAogDFatfCIGIAMpA7ABfCILIBAgElStIAMpA8gBIAwgElatfHx8Ig8gECATVq0gCUIgiHx8Igd8IgwgFEIghnwiEiADKQNAfCIVQgBCgYCAgHBCABDJAwJAAkAgAykDOCADKQMoIAMpA0ggEiAVVq18IgQgAykDIHwiEyAEVK18IBMgDCARVK0gAykDeCAFIBFWrXx8IhEgAykDYHwiCSAHIA9UrSIKIAMpA9ABfCIQIAYgDVStIAMpA6gCIA0gDlStfHwiBSADKQP4ASAIIA5WrXx8Ig4gAykDoAF8Ig0gCyAPVq0gAykDuAEgBiALVq18fHwiCHwiB3wiDyAMIBJWrSAUQiCIfHwiBHwiDCATVK18IhIgAykDEHwiFCAEIA9UrSITIAMpA4ABfCIGIAcgEFStIAMpA9gBIAogEFatfHwiECAIIA1UrSADKQOoASANIA5UrXx8Ig0gBSAOVq18Igp8IgsgAykDUHwiDiAJIA9WrSADKQNoIAkgEVStfHx8IgV8Igh8Ig8gDCAVQiCGfCIJIAxUrSAVQiCIfHwiByAPVK0iBCADKQMwfCIMIARUrXwgDCAGIAhWrSADKQOIASAGIBNUrXx8IhEgBSAOVK0gAykDWCALIA5WrXx8IhMgCyAQVK0gCiANVK18fCINfCIQIAMpAwB8IgUgDyAUVK0gAykDGCASIBRWrXx8fCIEfCIIIAxUrXwiCiAEIAVUrSADKQMIIAUgEFStfHwiBSAQIBFUrSANIBNUrXx8IgR8IgYgClQgBCAFVHIgBkKBgICAcFZyDQACQCAGQoGAgIBwUQRAIAdC/////w9WDQJCACEFIAhCAFINAkL/////DyEEIAdC/////w9aDQEgByEEQoGAgIBwIQYMAwsgByEEIAghBQwCCyAJQn9RDQBCgYCAgHAhBgwBCyAHQv////8PfSIKIAlCf1KtIgV9IQQgCCAHQv////8PVCAFIApWcq0iB30hBSAGIAcgCFatfUL/////D3whBiAJQgF8IQkLIAAgCTcDICAAIAQ3AxggACAGNwMIQgAhBkEQCyAAaiAFNwMAIAAgBjcDACADQaADaiQAC/4gAhh/Bn4jAEHwAmsiByQAIAdBADYCCCAHQoCAgIDAADcCACAHQQA2AhQgB0KAgICAwAA3AgwgBARAIAMgBEEMbGohDyADQQxqIQggB0HIAGohDEGs/MAAKAIAIQ5BpPzAACkCACEjIAMhCgNAIAghCSAHQUBrIAoQ4gEgBykDWCEfIAcpA1AhISAHKQNIISAgBykDQCEiIAwgDjYCACAHICM3A0AgICAihFBFBEBBASEIQQAhCgNAIAcoAkAgCEEBa0YEQCAHQUBrQaj9wAAQpQMLIAcoAkQgCmogIj4CACAgQiCGICJCgICAgBBUIQ0gIFAhECAKQQRqIQogIEIgiCEgIAcgCDYCSCAIQQFqIQggIkIgiIQhIiANIBBxRQ0ACwsgB0EgaiIKIAwoAgA2AgAgByAHKQNANwMYIAcoAggiCCAHKAIARgRAIAdBnJTBABCfAwsgBygCBCAIQQxsaiINIAcpAxg3AgAgDUEIaiAKKAIANgIAIAcgCEEBajYCCCAMIA42AgAgByAjNwNAIB8gIYRQRQRAQQEhCEEAIQoDQCAHKAJAIAhBAWtGBEAgB0FAa0Go/cAAEKUDCyAHKAJEIApqICE+AgAgH0IghiAhQoCAgIAQVCENIB9QIRAgCkEEaiEKIB9CIIghHyAHIAg2AkggCEEBaiEIICFCIIiEISEgDSAQcUUNAAsLIAdBMGoiCiAMKAIANgIAIAcgBykDQDcDKCAHKAIUIgggBygCDEYEQCAHQQxqQayUwQAQnwMLIAcoAhAgCEEMbGoiDSAHKQMoNwIAIA1BCGogCigCADYCACAHIAhBAWo2AhQgCUEAQQwgCSAPRiING2ohCCAJIQogDUUNAAsLIAdBADYCPCAHQoCAgIDAADcCNCAGBEAgB0E0akG8lMEAEJ8DIAcoAjgiCEGk/MAAKQIANwIAIAhBCGpBrPzAACgCADYCACAHQQE2AjxBASELCyAFBEAgB0HIAGoiBUGs/MAAKAIANgIAIAdBpPzAACkCADcDQCACBEAgB0FAa0GY/cAAEKUDIAcoAkQgAjYCACAHQQE2AkgLIAdB0AFqIAUoAgA2AgAgByAHKQNANwPIASAHKAI0IAtGBEAgB0E0akG8lMEAEJ8DCyAHKAI4IAtBDGxqIgUgBykDyAE3AgAgBUEIaiAHQdABaigCADYCACAHIAtBAWo2AjwgAgRAIAEgAkHIAGxqIQUgASEIA0AgB0E0aiIKIAgQuAEgCiAIQSBqELgBIAhByABqIgggBUcNAAsLIAdByABqQaz8wAAoAgA2AgAgB0Gk/MAAKQIANwNAIAQEQCAHQUBrQZj9wAAQpQMgBygCRCAENgIAIAdBATYCSAsgB0HQAWoiCCAHQcgAaigCADYCACAHIAcpA0A3A8gBIAcoAjwiBSAHKAI0RgRAIAdBNGpBvJTBABCfAwsgBygCOCAFQQxsaiIKIAcpA8gBNwIAIApBCGogCCgCADYCACAHIAVBAWoiCDYCPAJAIARFDQBBBCEMQQAhCgJAAkACQANAIAogBygCCCIFTw0CIAcoAgQgDGoiCEEEaigCACILQQJ0IQlBACEFIAtB/////wNLIAlB/P///wdLcg0BIAgoAgAhDgJ/IAlFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEFIAlBBBDWBCIIRQ0CIAsLIQ8gCQRAIAggDiAJ/AoAAAsgBygCPCIFIAcoAjRGBEAgB0E0akG8lMEAEJ8DCyAHKAI4IAVBDGxqIgkgCzYCCCAJIAg2AgQgCSAPNgIAIAcgBUEBajYCPCAHKAIUIgUgCksEQCAHKAIQIAxqIghBBGooAgAiC0ECdCEJQQAhBSALQf////8DSyAJQfz///8HS3INBCAIKAIAIQ4CfyAJRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhBSAJQQQQ1gQiCEUNBSALCyEPIAkEQCAIIA4gCfwKAAALIAcoAjwiBSAHKAI0RgRAIAdBNGpBvJTBABCfAwsgBygCOCAFQQxsaiIJIAs2AgggCSAINgIEIAkgDzYCACAHIAVBAWoiCDYCPCAMQQxqIQwgBCAKQQFqIgpHDQEMBQsLIAogBUGMlMEAENkDAAsgBSAJQfiBwAAQyAQACyAKIAVB/JPBABDZAwALIAUgCUH4gcAAEMgEAAsgB0HIAGoiBUGs/MAAKAIANgIAIAdBpPzAACkCADcDQCAHQdABaiAFKAIANgIAIAcgBykDQDcDyAEgBygCNCAIRgRAIAdBNGpBvJTBABCfAwsgBygCOCAIQQxsaiIFIAcpA8gBNwIAIAVBCGogB0HQAWooAgA2AgAgByAIQQFqNgI8CwJAIAQgAiACIARLGyIKRQ0AIAdB6AFqIRggB0GUAWohDiAHQYgBaiEPIAdBrAFqIQ0gB0GgAWohEAJAA0AgB0FAayIZIQQjAEHgBmsiAiQAIAIQIUEBIQVBBCEIQQQhCUEBIQsCQAJAAkACQCACKAK0BCIMBEBB0c7FAC0AABogAigCsAQhESAMQQJ0IgtBBBDWBCIJRQ0BIAsEQCAJIBEgC/wKAAALQQIhCwsgAkHXBGpBADoAACACQQA7ANUEIAIgCzoA1AQgAiAMNgLQBCACIAk2AswEIAIgDDYCyAQgAygCCCIJBEBB0c7FAC0AABogAygCBCEMIAlBAnQiBUEEENYEIghFDQIgBQRAIAggDCAF/AoAAAtBAiEFCyACQecEakEAOgAAIAJBADsA5QQgAiAFOgDkBCACIAk2AuAEIAIgCDYC3AQgAiAJNgLYBAJAAkACQAJAIAIoApACIglBgICAgHhHBEAgAkHoBWogAkHIBGogAkHYBGogAkGQAmoQTyACQbAFaiIFIAJB9AVqKAIANgIAIAIgAikC7AU3A6gFIAIoAugFIgxBgICAgHhHDQIgBCACKQOoBTcCACAEQYCAgIB4NgJIIARBCGogBSgCADYCAAwBCyACQQI2AuwFIAJBgOHCADYC6AUgAkIBNwL0BSACIAJBuARqrUKAgICA4AuENwOoBSACIAJBqAVqNgLwBSAEIAJB6AVqENICIARBgICAgHg2AkgLIAIoAtgEIgQEQCACKALcBCAEQQJ0EN8ECyACKALIBCIEBEAgAigCzAQgBEECdBDfBAsgAigCrAQiBARAIAIoArAEIARBAnQQ3wQLAkAgAigC5AEiBEUNACAEIARBDGxBE2pBeHEiBWpBCWoiBEUNACACKALgASAFayAEEN8ECyACKAKQAiIJQYCAgIB4Rw0BDAILIAJBkAVqIAJBoAZqKQIANwMAIAJBiAVqIgggAkGYBmopAgA3AwAgAkGABWogAkGQBmopAgA3AwAgAkH4BGoiCyACQYgGaikCADcDACACQfAEaiACQYAGaikCADcDACACIAIpAvgFNwPoBCACQaQFaiAFKAIANgIAIAIgAikDqAU3ApwFIAIgDDYCmAUgCCgCACERIAsoAgAhEyACKAKMBSEaIAIoAvwEIRsgAigC7AQhHCACKALoBCEUIAJBqAVqIAJBmAVqEOcBIAJBtAVqIhUgAkHoBGoQ5wEgAkHABWoiFiALEOcBIAJBzAVqIhcgCBDnASACKALgBCILQQJ0IQhBACESIAtB/////wNLIAhB/P///wdLcg0EIAIoAtwEIR0gAi0A5AQhHgJ/IAhFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCESIAhBBBDWBCIFRQ0FIAsLIRIgCARAIAUgHSAI/AoAAAsgAiAeOgDkBSACIAs2AuAFIAIgBTYC3AUgAiASNgLYBSACQegFaiIFIAEgAkHYBWoQqAEgAkG4BmogAkGwBWooAgA2AgAgAkHEBmogFUEIaigCADYCACACQdAGaiAWQQhqKAIANgIAIAJB3AZqIBdBCGooAgA2AgAgAiACKQKoBTcDsAYgAiAVKQIANwK8BiACIBYpAgA3A8gGIAIgFykCADcC1AYgBCAFQfgA/AoAACARBEAgGiARQQJ0EN8ECyATBEAgGyATQQJ0EN8ECyAUBEAgHCAUQQJ0EN8ECyAMBEAgAigCnAUgDEECdBDfBAsgAigC2AQiBARAIAIoAtwEIARBAnQQ3wQLIAIoAsgEIgQEQCACKALMBCAEQQJ0EN8ECyACKAKsBCIEBEAgAigCsAQgBEECdBDfBAsgAigC5AEiBEUNACAEIARBDGxBE2pBeHEiBWpBCWoiBEUNACACKALgASAFayAEEN8ECyAJRQ0AIAIoApQCIAlBAnQQ3wQLIAJB4AZqJAAMAwtBBCALQfiBwAAQyAQAC0EEIAVB+IHAABDIBAALIBIgCEH4gcAAEMgEAAsgBygCiAFBgICAgHhGDQEgB0HIAWoiAiAZQcgA/AoAACAHQZgCaiIFIA9BCGooAgA2AgAgB0GoAmoiCCAOQQhqKAIANgIAIAdBuAJqIgkgEEEIaigCADYCACAHQcgCaiIMIA1BCGooAgA2AgAgByAPKQIANwOQAiAHIA4pAgA3A6ACIAcgECkCADcDsAIgByANKQIANwPAAiAHQTRqIgQgAhC4ASAEIBgQuAEgBygCPCICIAcoAjRGBEAgBEG8lMEAEJ8DCyAHKAI4IAJBDGxqIgQgBykDkAI3AgAgBEEIaiAFKAIANgIAIAcgAkEBaiIENgI8IAcoAjQgBEYEQCAHQTRqQbyUwQAQnwMLIAcoAjggBEEMbGoiBCAHKQOgAjcCACAEQQhqIAgoAgA2AgAgByACQQJqIgQ2AjwgBygCNCAERgRAIAdBNGpBvJTBABCfAwsgBygCOCAEQQxsaiIEIAcpA7ACNwIAIARBCGogCSgCADYCACAHIAJBA2oiBDYCPCAHKAI0IARGBEAgB0E0akG8lMEAEJ8DCyAHKAI4IARBDGxqIgQgBykDwAI3AgAgBEEIaiAMKAIANgIAIAcgAkEEajYCPCABQcgAaiEBIANBDGohAyAKQQFrIgoNAAsMAQsgB0HQAWogB0HIAGooAgA2AgAgByAHKQNANwPIAUHU/sAAQSsgB0HIAWpBkIXBAEHsk8EAEMoDAAsCQCAGRQ0AIAcoAjwhASAHQcgAakGs/MAAKAIAIgI2AgAgB0Gk/MAAKQIAIh83A0ACQAJAIAFBAWsiAUUEQCAHQdABaiACNgIAIAcgHzcDyAEMAQsgB0FAa0GY/cAAEKUDIAcoAkQgATYCACAHQdABakEBNgIAIAcgBykDQDcDyAEgBygCPEUNAQsgBygCOCIBKAIAIgIEQCABKAIEIAJBAnQQ3wQLIAEgBykDyAE3AgAgAUEIaiAHQdABaigCADYCAAwBC0EAQQBBzJPBABDZAwALIAAgBykCNDcCACAAQQhqIAdBPGooAgA2AgAgBygCFCIKBEAgBygCECEIA0AgCCgCACIABEAgCEEEaigCACAAQQJ0EN8ECyAIQQxqIQggCkEBayIKDQALCyAHKAIMIgAEQCAHKAIQIABBDGwQ3wQLIAcoAggiCgRAIAcoAgQhCANAIAgoAgAiAARAIAhBBGooAgAgAEECdBDfBAsgCEEMaiEIIApBAWsiCg0ACwsgBygCACIABEAgBygCBCAAQQxsEN8ECyAHQfACaiQAC/8cAgR/L34jAEGQB2siAiQAIAJBoAZqIAFBGGopAwA3AwAgAkGYBmogAUEQaikDADcDACACQZAGaiABQQhqKQMANwMAIAJBsAZqIAFBKGopAwA3AwAgAkG4BmogAUEwaikDADcDACACQcAGaiABQThqKQMANwMAIAIgASkDADcDiAYgAiABKQMgNwOoBiACQcgGaiACQYgGahCvAyACKALMBiEDIAIoAsgGIQUCQCACKALQBiIEQQJGBEAgAykDOCEOIAMpAzAhECADKQMoIREgAykDICEMIAMpAxghEyADKQMQIQ8gAykDCCENIAM1AgQhByADKAIAIQQgBQRAIAMgBUEFdBDfBAtCqcDGia7Ok7IwIQogDSARfCIJIA1UIAkgCSAPIBB8IgggD1QgCCAOIBN8IgYgE1StfCILIAhUcq18IglWcq0gDCAErSAHQiCGhCISfHwiCCEHAkACQAJAIAhCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hCiAJIgdC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQogCyIHQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQogBiEHIAZCx/rzw+2Co5A8UQ0BCyAHIApaDQAgCSEKIAshBwwBCyALQvPquLzpraW/6AB8IhQgBkLH+vPD7YKjkDxUrSIKfSEHIAlCo8/685fJ7tfHAHwiFSALQo2Vx8OW0trAl39UIAogFFZyrSILfSEKIAggCULdsIWM6LaRqLh/VCALIBVWcq19QqnAxomuzpOyMH0hCCAGQsf688PtgqOQPH0hBgsgAiAGNwPgBSACIAc3A9gFIAIgCjcD0AUgAiAINwPIBSABQUBrIQEgAgJ+AkACQCAMIgggEiIGUg0AIBEiCCANIgZSDQAgECIIIA8iBlINACAOIgggEyIGUQ0BCyAGIAhaDQBC3bCFjOi2kai4fyARIA19IhggECAPfSIHIA4gE1StIgZUIA8gEFZyrSIUfSIVfSIKIAcgBn0iBkKNlcfDltLawJd/VkKNlcfDltLawJd/IAZ9IgsgDiATfSIJQsf688PtgqOQPFatIgdUcq0iBn0hCCAGIApWIBVC3bCFjOi2kai4f1ZyIQQgCyAHfSEGIA0gEVYgFCAYVnKtIBIgDH18QqnAxomuzpOyMHwhC0LH+vPD7YKjkDwgCX0MAQsgDyAQfSIIIA4gE1atIgd9IQYgDSARfSIJIA8gEFQgByAIVnKtIgd9IQggDSARVCAHIAlWciEEIBIgDH0hCyATIA59CzcD4AYgAiAGNwPYBiACIAg3A9AGIAIgCyAErX03A8gGIAJBqAVqIgMgAkHIBWogAkHIBmoiBBB+IAJC19G0hZXV8ov6ADcD4AYgAkK5w9SKrq+wtR83A9gGIAJChKWvy+bJ+qUzNwPQBiACQo673vDM6NmPKjcDyAYgAkGwBGogDkIAIBNCABDJAyACQdADaiAOQgAgD0IAEMkDIAJBwANqIA5CACANQgAQyQMgAkGwA2ogDkIAIBJCABDJAyACQaAEaiACKQOwBCIJQgBCAEKJx5mkrvCB6Yd/EMkDIAJBkARqIAIpA6gEIgZCAELH+vPD7YKjkDxCABDJAyACQYAEaiAGQgBCjZXHw5bS2sCXf0IAEMkDIAJB8ANqIAZCAELdsIWM6LaRqLh/QgAQyQMgAkHgA2ogBkIAQqnAxomuzpOyMEIAEMkDIAJBoANqIBBCACATQgAQyQMgAkHAAmogEEIAIA9CABDJAyACQbACaiAQQgAgDUIAEMkDIAJBoAJqIBBCACASQgAQyQMgAkGQA2ogAikDgAQiCyACKQO4BCIIIAIpA9ADfCIHfCIUIAIpA5gEIAkgAikDkAQiBnwgBlStfHwiCiACKQOgA3wiBkIAQgBCiceZpK7wgemHfxDJAyACQYADaiACKQOYAyIJQgBCx/rzw+2Co5A8QgAQyQMgAkHwAmogCUIAQo2Vx8OW0trAl39CABDJAyACQeACaiAJQgBC3bCFjOi2kai4f0IAEMkDIAJB0AJqIAlCAEKpwMaJrs6TsjBCABDJAyACQZACaiARQgAgE0IAEMkDIAJBsAFqIBFCACAPQgAQyQMgAkGgAWogEUIAIA1CABDJAyACQZABaiARQgAgEkIAEMkDIAJBgAJqIAIpA6gDIAYgClStfCIJIAIpA8ACfCIVIAIpA9gDIAcgCFStfCIIIAIpA8ADfCIOIAIpA/ADfCIQIAogFFStIAIpA4gEIAsgFFatfHx8Igd8IhEgAikD8AJ8IgogAikDiAMgBiACKQOAAyIGfCAGVK18fCILIAIpA5ACfCIGQgBCAEKJx5mkrvCB6Yd/EMkDIAJB8AFqIAIpA4gCIhRCAELH+vPD7YKjkDxCABDJAyACQeABaiAUQgBCjZXHw5bS2sCXf0IAEMkDIAJB0AFqIBRCAELdsIWM6LaRqLh/QgAQyQMgAkHAAWogFEIAQqnAxomuzpOyMEIAEMkDIAJBgAFqIAxCACATQgAQyQMgAkEgaiAMQgAgD0IAEMkDIAJBEGogDEIAIA1CABDJAyACIAxCACASQgAQyQMgAkHwAGogAikDmAIgBiALVK18IiwgAikDsAF8IiAgAikDyAMgCCAOVq18Ii0gAikDsAN8IiEgAikD4AN8IiIgByAQVK0gAikD+AMgDiAQVq18fHwiIyACKQOwAnwiJCARIBVUrSACKQPIAiAJIBVWrXx8fCIlIAIpA+ACfCImIAogC1atIAIpA/gCIAogEVStfHx8Ii58IicgAikD4AF8IiggAikD+AEgBiACKQPwASIGfCAGVK18fCIpIAIpA4ABfCIqQgBCAEKJx5mkrvCB6Yd/EMkDIAJB4ABqIAIpA3giBkIAQsf688PtgqOQPEIAEMkDIAJB0ABqIAZCAEKNlcfDltLawJd/QgAQyQMgAkFAayAGQgBC3bCFjOi2kai4f0IAEMkDIAJBMGogBkIAQqnAxomuzpOyMEIAEMkDIAIpA+gCIS8gAikDuAIhMCACKQPoAyEZIAIpA7gDIQYgAikDoAIhGiACKQPQAiEWIAIpA6ABITEgAikDqAEhMiACKQO4ASEzIAIpA9gCIRsgAikDqAIhHCACKQOQASEXIAIpA8ABIR0gAikD0AEhNCACKQPYASEeIAIpA+gBIR8gAikDECEYIAIpAxghFCACKQOIASEVIAIpAyAhEyACKQMoIQ8gAikDyAEhByACKQOYASEIIAIpAwAhDSACKQMwIQ4gAikDOCEQIAIpA0AhESACKQNIIQwgAikDUCESIAIpA1ghCiACKQNgISsgAikDaCEJIAIpAwghCyACQYgFaiADIAQQfgJAAkAgECAOIA0gByAdIBcgGyAWIBogIiAjVq0gGSAhICJWrXx8IAYgISAtVK18fCIGfCIZICQgJVatIDAgIyAkVq18fHwiGnwiFiAaVK18IBYgFiAmIC5WrSAvICUgJlatfHx8IhZWrXwgGSAaVq0gHCAGIBlWrXx8fCIGfCIbIDIgFiAxfCIXIBZUrXwgFyAgICdWrSAzICAgLFStfHx8IhwgF1StfHwiF3wiHSAXVK18IB0gHiAcIDR8IgcgHFStfCAHIAcgKCApVq0gHyAnIChWrXx8fCIHVq18fCIeIB1UrXwgFyAbVK0gCCAGIBtWrXx8fCIIfCIfIBQgGCAefCIYIB5UrXwgGCAPIBMgFSApICpWrXwiBnwiDSAGVK18IAcgDXwiDyANVK18fCIGIBhUrXx8Ig18Ig4gDVStfCAOIAwgBiARfCIHIAZUrXwgByAHIAogDyASfCIGIA9UrXwgBiAJICogK3wgK1StfHwiEiAGVK18fCIHVq18fCIJIA5UrXwgDSAfVK0gCyAIIB9WrXx8fCIMQqnAxomuzpOyMFYNAAJAIAxCqcDGia7Ok7IwUQRAIAlC3bCFjOi2kai4f1YNAiAJQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIQwLIAkhCCAHIQYMAgsgB0KNlcfDltLawJd/Vg0AQt2whYzotpGouH8hCCAHQo2Vx8OW0trAl39SBEBCqcDGia7Ok7IwIQwgByEGDAILQo2Vx8OW0trAl38hBiASQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhDAwBCyAHQvPquLzpraW/6AB8IgogEkLH+vPD7YKjkDxUrSIIfSEGIAlCo8/685fJ7tfHAHwiCyAHQo2Vx8OW0trAl39UIAggClZyrSIHfSEIIAwgCULdsIWM6LaRqLh/VCAHIAtWcq19QqnAxomuzpOyMH0hDCASQsf688PtgqOQPH0hEgsgAiASNwPgBSACIAY3A9gFIAIgCDcD0AUgAiAMNwPIBSACQueo9ca8p8KHuH83A+AGIAJC5fHh0cWMhqqnfzcD2AYgAkKqmdmK5dzjo65/NwPQBiACQvK19tfrgqDtIzcDyAYgAkHoBGogAkHIBWoiAyACQcgGaiIEEH4gAkHQBGogAkGQBWopAwA3AwAgAkHYBGogAkGYBWopAwA3AwAgAkHgBGogAkGgBWopAwA3AwAgAiACKQOIBTcDyAQgAyABIAEQoAIgBCACQcgEaiADEJEDIAIpA9gGIQcgAikD0AYhBiACKALIBkEBRg0BIAAgAikD4AY3AxAgAEE4aiACQYgHaikDADcDACAAQTBqIAJBgAdqKQMANwMAIABBKGogAkH4BmopAwA3AwAgAEEgaiACQfAGaikDADcDACAAQRhqIAJB6AZqKQMANwMAIAAgBzcDCCAAIAY3AwAgAkGQB2okAA8LIAIgBDYC0AYgAiADNgLMBiACIAU2AsgGQYCLwABBKyACQcgGakHwisAAQaSNwAAQygMACyACIAc3A9AGIAIgBjcDyAZB1P7AAEErIAJByAZqQbCFwQBBwIXBABDKAwALjhgCDn8BfiMAQeAKayIDJAAgA0E4aiABQThqKQMANwMAIANBMGogAUEwaikDADcDACADQShqIAFBKGopAwA3AwAgA0EgaiABQSBqKQMANwMAIANBGGogAUEYaikDADcDACADQRBqIAFBEGopAwA3AwAgA0EIaiABQQhqKQMANwMAIANByABqIAJBCGopAwA3AwAgA0HQAGogAkEQaikDADcDACADQdgAaiACQRhqKQMANwMAIANB4ABqIAJBIGopAwA3AwAgA0HoAGogAkEoaikDADcDACADQfAAaiACQTBqKQMANwMAIANB+ABqIAJBOGopAwA3AwAgAyABKQMANwMAIAMgAikDADcDQCADQegBakIANwMAIANB4AFqQgA3AwAgA0HYAWpCADcDACADQdABakIANwMAIANByAFqQgA3AwAgA0HAAWpCADcDACADQbgBakIANwMAIANCADcDsAEgA0FAayEBAkACQAJAAkACQAJAIAMgA0GwAWoiAhCnBARAIAEgAhCnBA0BCyADQegBakIANwMAIANB4AFqQgA3AwAgA0HYAWpCADcDACADQdABakIANwMAIANByAFqQgA3AwAgA0HAAWpCADcDACADQbgBakIANwMAIANCADcDsAEgAyADQbABaiICEKcEBEAgASACEKcEDQELIANBsAFqECEgA0GQBmogA0HIAWopAwA3AwAgA0GIBmogA0HAAWopAwA3AwAgA0GABmogAykDuAE3AwAgA0GgBmogA0H4AWopAwA3AwAgA0GoBmogA0GAAmopAwA3AwAgA0GwBmogA0GIAmopAwA3AwAgA0HABmogA0GYAmopAwA3AwAgA0HIBmogA0GgAmopAwA3AwAgA0HQBmogA0GoAmopAwA3AwAgAyADKQOwATcD+AUgAyADKQPwATcDmAYgAyADKQOQAjcDuAYgA0HYBmoiCyABEEsgA0GgCWoiBiADQQhqIgIpAwA3AwAgA0GoCWoiCCADQRBqIgQpAwA3AwAgA0GwCWoiDCADQRhqIgUpAwA3AwAgA0G4CWoiDSADKQMgNwMAIANBwAlqIg4gA0EoaiIHKQMANwMAIANByAlqIg8gA0EwaiIJKQMANwMAIANB0AlqIhAgA0E4aiIKKQMANwMAIAMgAykDADcDmAkgA0GgCGogBikDADcDACADQagIaiAIKQMANwMAIANBsAhqIAwpAwA3AwAgA0G4CGogDSkDADcDACADQcAIaiAOKQMANwMAIANByAhqIA8pAwA3AwAgA0HQCGogECkDADcDACADIAMpA5gJNwOYCCADQdgIaiIGIANBmAhqEEsgA0HwCWogBSkDADcDACADQegJaiAEKQMANwMAIANB4AlqIAIpAwA3AwAgA0GACmogBykDADcDACADQYgKaiAJKQMANwMAIANBkApqIAopAwA3AwAgAyADKQMANwPYCSADIAMpAyA3A/gJIANB2AdqIgggBiADQdgJahA4IANBoApqIAIpAwA3AwAgA0GoCmogBCkDADcDACADQbAKaiAFKQMANwMAIANBwApqIAcpAwA3AwAgA0HICmogCSkDADcDACADQdAKaiAKKQMANwMAIAMgAykDADcDmAogAyADKQMgNwO4CiAGIANB+AVqIANBmApqEFkgA0GYB2oiAiAIIAYQoAIgBiACIANBmAZqEKACIAsgBhCnBCADKALcBSICBEAgAygC4AUgAkECdBDfBAsCQCADKAKUAyICRQ0AIAIgAkEMbEETakF4cSIFakEJaiICRQ0AIAMoApADIAVrIAIQ3wQLIAMoAsADIgJBgICAgHhGIAJFckUEQCADKALEAyACQQJ0EN8ECw0AIANB6AFqIANBOGopAwA3AwAgA0HgAWogA0EwaikDADcDACADQdgBaiADQShqKQMANwMAIANB0AFqIANBIGopAwA3AwAgA0HIAWogA0EYaikDADcDACADQcABaiADQRBqKQMANwMAIANBuAFqIANBCGopAwA3AwAgAyADKQMANwOwASADQZgKaiADQbABahCvAyADKAKcCiECIAMoApgKIQQgAygCoAoiBUECRw0BIANBoApqIAJBEGopAwA3AwAgA0GoCmogAkEYaikDADcDACADQbAKaiACQSBqKQMANwMAIANBuApqIAJBKGopAwA3AwAgA0HACmogAkEwaikDADcDACADQcgKaiACQThqKQMANwMAIAMgAikDCDcDmAogAigCBCEFIAIoAgAhByAEBEAgAiAEQQV0EN8ECyADQegJaiADQaAKaikDADcDACADQfAJaiADQagKaikDADcDACADQYAKaiADQbgKaikDADcDACADQYgKaiADQcAKaikDADcDACADQZAKaiADQcgKaikDADcDACADIAU2AtwJIAMgBzYC2AkgAyADKQOYCjcD4AkgAyADKQOwCjcD+AkgA0HoAWogAUE4aikDADcDACADQeABaiABQTBqKQMANwMAIANB2AFqIAFBKGopAwA3AwAgA0HQAWogAUEgaikDADcDACADQcgBaiABQRhqKQMANwMAIANBwAFqIAFBEGopAwA3AwAgA0G4AWogAUEIaikDADcDACADIAEpAwA3A7ABIANBmApqIANBsAFqEK8DIAMoApwKIQEgAygCmAohAiADKAKgCiIEQQJHDQIgA0GgCWogAUEQaikDADcDACADQagJaiABQRhqKQMANwMAIANBsAlqIAFBIGopAwA3AwAgA0G4CWogAUEoaikDADcDACADQcAJaiABQTBqKQMANwMAIANByAlqIAFBOGopAwA3AwAgAyABKQMINwOYCSABKAIEIQQgASgCACEFIAIEQCABIAJBBXQQ3wQLIANBqApqIANBoAlqIgEpAwA3AwAgA0GwCmogA0GoCWopAwA3AwAgA0HACmogA0G4CWopAwA3AwAgA0HICmogA0HACWopAwA3AwAgA0HQCmogA0HICWopAwA3AwAgAyAENgKcCiADIAU2ApgKIAMgAykDmAk3A6AKIAMgAykDsAk3A7gKIANBmAhqIgIgA0HYCWoQzQEgA0EANgKgCSADQoCAgIAQNwKYCSADQdD/wAA2ArQBIANCoICAgA43ArgBIAMgA0GYCWoiBDYCsAEgAiADQbABaiICENMCDQUgA0GIAWogASgCADYCACADIAMpApgJNwOAASADQdgIaiIFIANB+AlqEM0BIANBADYCoAkgA0KAgICAEDcCmAkgA0HQ/8AANgK0ASADQqCAgIAONwK4ASADIAQ2ArABIAUgAhDTAg0FIANBmAFqIAEoAgA2AgAgAyADKQKYCTcDkAEgBCADQZgKahDNASADQQA2AuAHIANCgICAgBA3AtgHIANB0P/AADYCtAEgA0KggICADjcCuAEgAyADQdgHaiIBNgKwASAEIAIQ0wINBSADQagBaiADQeAHaigCADYCACADIAMpAtgHNwOgASACIANBuApqEM0BIANBADYCoAYgA0KAgICAEDcCmAYgA0HQ/8AANgLcBiADQqCAgIAONwLgBiADIANBmAZqNgLYBiACIANB2AZqENMCDQUgA0GABmogA0GgBmooAgA2AgAgAyADKQKYBjcD+AUgA0EFNgKcByADQeyDwQA2ApgHIANCBDcCpAcgA0KAgICAwAQiESADQfgFaq2ENwPwByADIBEgA0GgAWqthDcD6AcgAyARIANBkAFqrYQ3A+AHIAMgESADQYABaq2ENwPYByADIAE2AqAHIABBBGogA0GYB2oQ0gIgAygC+AUiAQRAIAMoAvwFIAEQ3wQLIAMoAqABIgEEQCADKAKkASABEN8ECyADKAKQASIBBEAgAygClAEgARDfBAsgAygCgAEiAQRAIAMoAoQBIAEQ3wQLIABBATYCAAwDCyAAQQhqIANBgAH8CgAAIABBADYCAAwCCyADIAU2AqAKIAMgAjYCnAogAyAENgKYCgwCCyADIAQ2AqAKIAMgATYCnAogAyACNgKYCgwBCyADQeAKaiQADwtBgIvAAEErIANBmApqQfCKwABBpI3AABDKAwALQfj/wABBNyADQd8KakHo/8AAQfyAwQAQygMAC9AkAi1/DH4jAEGACWsiAiQAIwBBwAJrIgMkACADQbACakIDQgBCifWrnLWLv5ZzQgAQyQMgA0HwAWogAykDsAIiMUKJx5mkrvCB6Yd/fiIvQgBCx/rzw+2Co5A8QgAQyQMgA0HgAWogL0IAQo2Vx8OW0trAl39CABDJAyADQdABaiAvQgBC3bCFjOi2kai4f0IAEMkDIANBwAFqIC9CAEKpwMaJrs6TsjBCABDJAyADQaACakIDQgBC+4OUop2ixvO1f0IAEMkDIANBsAFqIAMpA+ABIjAgAykDuAJ8IjIgAykD+AEgMSADKQPwASIvfCAvVK18fCIxIAMpA6ACfCIvQonHmaSu8IHph39+IjNCAELH+vPD7YKjkDxCABDJAyADQaABaiAzQgBCjZXHw5bS2sCXf0IAEMkDIANBkAFqIDNCAELdsIWM6LaRqLh/QgAQyQMgA0GAAWogM0IAQqnAxomuzpOyMEIAEMkDIANBkAJqQgNCAEL2/4XS8N/H1ccAQgAQyQMgA0HwAGogAykDoAEiNiADKQOoAiAvIDFUrXwiMyAxIDJUrSADKQPoASAwIDJWrXx8IjIgAykD0AF8IjF8IjB8IjcgAykDuAEgLyADKQOwASIvfCAvVK18fCI0IAMpA5ACfCIvQonHmaSu8IHph39+IjVCAELH+vPD7YKjkDxCABDJAyADQeAAaiA1QgBCjZXHw5bS2sCXf0IAEMkDIANB0ABqIDVCAELdsIWM6LaRqLh/QgAQyQMgA0FAayA1QgBCqcDGia7Ok7IwQgAQyQMgA0GAAmpCA0IAQp/q4NWc7qfsBkIAEMkDIANBMGogAykDYCI1IDAgM1StIjMgAykD2AEgMSAyVK18IjIgAykDwAF8IjF8IjggAykDkAF8IjkgNCA3VK0gAykDqAEgNiA3Vq18fHwiOiADKQOYAiAvIDRUrXx8IjB8IjcgAykDeCAvIAMpA3AiL3wgL1StfHwiNCADKQOAAnwiNkKJx5mkrvCB6Yd/fiIvQgBCx/rzw+2Co5A8QgAQyQMgA0EgaiAvQgBCjZXHw5bS2sCXf0IAEMkDIANBEGogL0IAQt2whYzotpGouH9CABDJAyADIC9CAEKpwMaJrs6TsjBCABDJAwJAIAMpAwggAykDSCADKQOIASADKQOAASIvIAMpA8gBIDEgMlStfHwiMSAvVK18IDEgMSAzIDhWrXwiL1atfCAvIC8gOSA6Vq0gAykDmAEgOCA5Vq18fHwiMVatfCIvIAMpA0B8IjIgL1StfCAyIDIgMSAxIDAgOlStfCIwVq18IjFWrXwgMSAxIAMpA1ggMCAwIAMpA1B8Ii9WrXwgLyAvIDQgN1StIAMpA2ggNSA3Vq18fHwiMFatfHwiMlatfCIvIAMpAwB8IjEgL1StfCAxIDEgMiAwIDAgAykDiAIgNCA2Vq18fCIwVq18Ii8gMlStfCIyVq18IDIgMiADKQMYIC8gLyADKQMQfCIxVq18IDEgMSADKQMoIDAgAykDICIvfCIwIC9UrXwgMCADKQM4IAMpAzAiLyA2fCAvVK18fCI2IDBUrXx8IjBWrXx8IjRWrXwiNUKpwMaJrs6TsjBUBEAgMCEvDAELAkAgNELdsIWM6LaRqLh/Vg0AIDRC3bCFjOi2kai4f1IEQCAwIS9CqcDGia7Ok7IwITUMAgsgMEKNlcfDltLawJd/Vg0AAkAgMEKNlcfDltLawJd/UgRAIDAhLwwBC0KNlcfDltLawJd/IS8gNkLH+vPD7YKjkDxaDQELQt2whYzotpGouH8hNEKpwMaJrs6TsjAhNQwBCyAwQvPquLzpraW/6AB8IjMgNkLH+vPD7YKjkDxUrSIyfSEvIDRCo8/685fJ7tfHAHwiMSAwQo2Vx8OW0trAl39UIDIgM1ZyrSIwfSE0IDUgMCAxVq19QqnAxomuzpOyMH0hNSA2Qsf688PtgqOQPH0hNgsgAkIANwMgIAIgNjcDGCACIC83AxAgAiA0NwMIIAIgNTcDACACQShqQgA3AwAgAkEwakIANwMAIAJBOGpCADcDACADQcACaiQAIAJByAdqIhsgAUEIaiIsKQMANwMAIAJB0AdqIhwgAUEQaiItKQMANwMAIAJB2AdqIgUgAUEYaiIuKQMANwMAIAJB4AdqIgYgASkDIDcDACACQegHaiIHIAFBKGopAwA3AwAgAkHwB2oiCCABQTBqKQMANwMAIAJB+AdqIgkgAUE4aikDADcDACACIAEpAwA3A8AHIAJB2AFqIgogBSkDACIxNwMAIAJB0AFqIgsgHCkDACIwNwMAIAJByAFqIgwgGykDACIvNwMAIAJBiAhqIhkgLzcDACACQZAIaiIaIDA3AwAgAkGYCGoiFCAxNwMAIAIgAikDwAciLzcDwAEgAkGgCGoiDSAGKQMANwMAIAJBqAhqIg4gBykDADcDACACQbAIaiIPIAgpAwA3AwAgAkG4CGoiECAJKQMANwMAIAIgLzcDgAggAkHAAWoiBCACQYAIaiIREEsgECACQfgBaiIVKQMANwMAIA8gAkHwAWoiFikDADcDACAOIAJB6AFqIhcpAwA3AwAgDSACQeABaiIYKQMANwMAIBQgCikDADcDACAaIAspAwA3AwAgGSAMKQMANwMAIAIgAikDwAE3A4AIIAQgAkHAB2oiISAREDggCSAVKQMAIjM3AwAgCCAWKQMAIjI3AwAgByAXKQMAIjE3AwAgBiAYKQMAIjA3AwAgBSAKKQMAIi83AwAgAkHIA2oiEiAMKQMANwMAIAJB0ANqIhMgCykDADcDACACQdgDaiIdIC83AwAgAkHgA2oiHiAwNwMAIAJB6ANqIiAgMTcDACACQfADaiIiIDI3AwAgAkH4A2oiIyAzNwMAIAIgAikDwAEiLzcDwAcgAiAvNwPAAyAbIAFByABqKQMANwMAIBwgAUHQAGopAwA3AwAgBSABQdgAaikDADcDACAGIAEpA2A3AwAgByABQegAaikDADcDACAIIAFB8ABqKQMANwMAIAkgAUH4AGopAwA3AwAgAiABKQNANwPAByAKIAUpAwAiMTcDACALIBwpAwAiMDcDACAMIBspAwAiLzcDACAZIC83AwAgGiAwNwMAIBQgMTcDACACIAIpA8AHIi83A8ABIA0gBikDADcDACAOIAcpAwA3AwAgDyAIKQMANwMAIBAgCSkDADcDACACIC83A4AIIAQgERBLIBAgFSkDADcDACAPIBYpAwA3AwAgDiAXKQMANwMAIA0gGCkDADcDACAUIAopAwA3AwAgGiALKQMANwMAIBkgDCkDADcDACACIAIpA8ABNwOACCAEICEgERA4IAkgFSkDACIzNwMAIAggFikDACIyNwMAIAcgFykDACIxNwMAIAYgGCkDACIwNwMAIAUgCikDACIvNwMAIAJBiARqIiQgDCkDADcDACACQZAEaiIlIAspAwA3AwAgAkGYBGoiJiAvNwMAIAJBoARqIisgMDcDACACQagEaiInIDE3AwAgAkGwBGoiKCAyNwMAIAJBuARqIikgMzcDACACIAIpA8ABIi83A8AHIAIgLzcDgAQgBBD0AyARIAJBgARqIh8gBBA4IAJBgANqIgMgAkHAA2oiKiAREKACIBsgAUGIAWopAwA3AwAgHCABQZABaikDADcDACAFIAFBmAFqKQMANwMAIAYgASkDoAE3AwAgByABQagBaikDADcDACAIIAFBsAFqKQMANwMAIAkgAUG4AWopAwA3AwAgAiABKQOAATcDwAcgCiAFKQMAIjE3AwAgCyAcKQMAIjA3AwAgDCAbKQMAIi83AwAgGSAvNwMAIBogMDcDACAUIDE3AwAgAiACKQPAByIvNwPAASANIAYpAwA3AwAgDiAHKQMANwMAIA8gCCkDADcDACAQIAkpAwA3AwAgAiAvNwOACCAEIBEQSyAQIBUpAwA3AwAgDyAWKQMANwMAIA4gFykDADcDACANIBgpAwA3AwAgFCAKKQMANwMAIBogCykDADcDACAZIAwpAwA3AwAgAiACKQPAATcDgAggBCAhIBEQOCAJIBUpAwAiMzcDACAIIBYpAwAiMjcDACAHIBcpAwAiMTcDACAGIBgpAwAiMDcDACAFIAopAwAiLzcDACASIAwpAwA3AwAgEyALKQMANwMAIB0gLzcDACAeIDA3AwAgICAxNwMAICIgMjcDACAjIDM3AwAgAiACKQPAASIvNwPAByACIC83A8ADIB8Q9AMgGSAkKQMANwMAIBogJSkDADcDACAUICYpAwA3AwAgDSACKQOgBDcDACAOICcpAwA3AwAgDyAoKQMANwMAIBAgKSkDADcDACACIAIpA4AENwOACCAEIBEQSyAQIBUpAwAiMjcDACAPIBYpAwAiMTcDACAOIBcpAwAiMDcDACANIBgpAwAiLzcDACAbIAwpAwA3AwAgHCALKQMANwMAIAUgCikDADcDACAGIC83AwAgByAwNwMAIAggMTcDACAJIDI3AwAgAiACKQPAASIvNwOACCACIC83A8AHIAQgKiAhEDggKiADIAQQoAIgBCACIAEQOCARIAQgAUFAayIdEDggISARIAFBgAFqIh4QOCAEEPQDIBEgISAEEDggAkFAayIDICogERDcASAEIAMQLiACKQPQASEwIAIpA8gBIS8gAAJ+IAIoAsABQQFGBEAgACAwNwMQIAAgLzcDCEIBDAELIAJBuAFqIAJBgAJqIgMpAwA3AwAgAkGwAWogFSkDADcDACACQagBaiAWKQMANwMAIAJBoAFqIBcpAwA3AwAgAkGYAWogGCkDADcDACACIAIpA9gBNwOQASACIDA3A4gBIAIgLzcDgAEgGSAsKQMANwMAIBogLSkDADcDACAUIC4pAwA3AwAgDSABQSBqIh8pAwA3AwAgDiAfQQhqKQMANwMAIA8gH0EQaikDADcDACAQIB9BGGopAwA3AwAgAiABKQMANwOACCACQcABaiISIAJBgAhqIhMQSyAQIBUpAwAiMzcDACAPIBYpAwAiMjcDACAOIBcpAwAiMTcDACANIBgpAwAiMDcDACAUIAopAwAiLzcDACAkIAwpAwA3AwAgJSALKQMANwMAICYgLzcDACArIDA3AwAgJyAxNwMAICggMjcDACApIDM3AwAgAiACKQPAASIvNwOACCACIC83A4AEIBMgHSAeEDggEhD0AyACQcAHaiIgIBMgEhA4IBIgAkGABGoiIiAgENwBIAJBgANqIBIgAkGAAWoiHxA4IBIgARDwAiAiIBIgHRA4IBkgHkEIaikDADcDACAaIB5BEGopAwA3AwAgFCAeQRhqKQMANwMAIA0gAUGgAWoiIykDADcDACAOICNBCGopAwA3AwAgDyAjQRBqKQMANwMAIBAgI0EYaikDADcDACACIB4pAwA3A4AIIBIgExBLIBAgFSkDACIzNwMAIA8gFikDACIyNwMAIA4gFykDACIxNwMAIA0gGCkDACIwNwMAIBQgCikDACIvNwMAIBsgDCkDADcDACAcIAspAwA3AwAgBSAvNwMAIAYgMDcDACAHIDE3AwAgCCAyNwMAIAkgMzcDACACIAIpA8ABIi83A4AIIAIgLzcDwAcgEhD0AyATICAgEhA4ICAgIiATEKACIAMgICAfEDggEyABEPACIAJBwANqIgMgEyAeEDggGyAdQQhqKQMANwMAIBwgHUEQaikDADcDACAFIB1BGGopAwA3AwAgBiABQeAAaiIBKQMANwMAIAcgAUEIaikDADcDACAIIAFBEGopAwA3AwAgCSABQRhqKQMANwMAIAIgHSkDADcDwAcgEyAgEEsgCSAQKQMAIjM3AwAgCCAPKQMAIjI3AwAgByAOKQMAIjE3AwAgBiANKQMAIjA3AwAgBSAUKQMAIi83AwAgJCAZKQMANwMAICUgGikDADcDACAmIC83AwAgKyAwNwMAICcgMTcDACAoIDI3AwAgKSAzNwMAIAIgAikDgAgiLzcDwAcgAiAvNwOABCATIAMgIhCgAiACQcACaiATIB8QOCAMIAJBiANqKQMANwMAIAsgAkGQA2opAwA3AwAgCiACQZgDaikDADcDACAYIAJBoANqKQMANwMAIBcgAkGoA2opAwA3AwAgFiACQbADaikDADcDACAVIAJBuANqKQMANwMAIAIgAikDgAM3A8ABIABBCGogEkHAAfwKAABCAAs3AwAgAkGACWokAAuHGwIHfxR+IwBBkARrIgQkAAJAAkAgASgCDEUNACABKAIEIgcgASkDGCIMIAOtIguFQvPK0cunjNmy8ACFIg1CEIkgDSABKQMQIhJC4eSV89bs2bzsAIV8Ig2FIhQgDELt3pHzlszct+QAhSIMIBJC9crNg9es27fzAIV8IhJCIIl8IhYgC0KAgICAgICAgASEhSAMQg2JIBKFIgwgDXwiCyAMQhGJhSIMfCINIAxCDYmFIgwgFEIViSAWhSISIAtCIIlC/wGFfCILfCIUIAxCEYmFIgxCDYkgDCALIBJCEImFIgsgDUIgiXwiDXwiDIUiEkIRiSASIAtCFYkgDYUiCyAUQiCJfCINfCIShSIUQg2JIBQgC0IQiSANhSILIAxCIIl8Igx8hSINQhGJIAtCFYkgDIUiDEIQiSAMIBJCIIl8IgyFQhWJhSAMIA18IgxCIIiFIAyFIgyncSEFIAxCGYhC/wCDQoGChIiQoMCAAX4hCyABKAIAIghBEGshAQNAIAUgCGopAAAiDCALhSINQn+FIA1CgYKEiJCgwIABfYNCgIGChIiQoMCAf4MiDlBFBEADQCADIAEgDnqnQQN2IAVqIAdxIgpBBHRrKAIARg0EIA5CAX0gDoMiDlBFDQALCyAMIAxCAYaDQoCBgoSIkKDAgH+DUEUNASAFIAZBCGoiBmogB3EhBQwACwALQeSewQAQ6AQACyACKAIIIglBDE0EQEEAIQEgBEEANgKMBCAEQoCAgICAATcChARBCCEHAn9BACAJRQ0AGkEAIAhBACAKa0EEdGoiA0EEaygCACIGRQ0AGiADQQhrKAIAIgUgBkEMbGohByAFQQxqIQMgAigCBCEIIAkhBgNAIAMhAkIAIRJCACEUQgAhFkIAIRogBSgCCCIDBEAgBSgCBCEBIANBKGwhAwNAAkACQCAJIAEoAgAiBUsEQCAEQcADaiABQSBqKQMAIgxCACAIIAVBBXRqIgUpAxgiC0IAEMkDIARBwAJqIAFBGGopAwAiDUIAIAtCABDJAyAEQcABaiABQRBqKQMAIg9CACALQgAQyQMgBEFAayABQQhqKQMAIg5CACALQgAQyQMgBEGwA2ogBCkDwAMiEEKJx5mkrvCB6Yd/fiILQgBCx/rzw+2Co5A8QgAQyQMgBEGgA2ogC0IAQo2Vx8OW0trAl39CABDJAyAEQZADaiALQgBC3bCFjOi2kai4f0IAEMkDIARBgANqIAtCAEKpwMaJrs6TsjBCABDJAyAEQdADaiAFKQMQIgtCACAMQgAQyQMgBEHQAmogC0IAIA1CABDJAyAEQdABaiALQgAgD0IAEMkDIARB0ABqIAtCACAOQgAQyQMgBEGwAmogBCkDoAMiFyAEKQPIAyIYIAQpA8ACfCIZfCIRIAQpA7gDIBAgBCkDsAMiC3wgC1StfHwiECAEKQPQA3wiE0KJx5mkrvCB6Yd/fiILQgBCx/rzw+2Co5A8QgAQyQMgBEGgAmogC0IAQo2Vx8OW0trAl39CABDJAyAEQZACaiALQgBC3bCFjOi2kai4f0IAEMkDIARBgAJqIAtCAEKpwMaJrs6TsjBCABDJAyAEQeADaiAFKQMIIgtCACAMQgAQyQMgBEHgAmogC0IAIA1CABDJAyAEQeABaiALQgAgD0IAEMkDIARB4ABqIAtCACAOQgAQyQMgBEGwAWogBCkD2AMgECATVq18IhwgBCkD0AJ8IhUgBCkDyAIgGCAZVq18IhsgBCkDwAF8IhggBCkDkAN8IhkgECARVK0gBCkDqAMgESAXVK18fHwiHXwiESAEKQOgAnwiECAEKQO4AiAEKQOwAiILIBN8IAtUrXx8IhMgBCkD4AN8IhdCiceZpK7wgemHf34iC0IAQsf688PtgqOQPEIAEMkDIARBoAFqIAtCAEKNlcfDltLawJd/QgAQyQMgBEGQAWogC0IAQt2whYzotpGouH9CABDJAyAEQYABaiALQgBCqcDGia7Ok7IwQgAQyQMgBEHwA2ogBSkDACILQgAgDEIAEMkDIARB8AJqIAtCACANQgAQyQMgBEHwAWogC0IAIA9CABDJAyAEQfAAaiALQgAgDkIAEMkDIARBMGogBCkD6AMgEyAXVq18Ih4gBCkD4AJ8IgsgBCkDyAEgGCAbVK18IhsgBCkDQHwiDSAEKQOAA3wiDyAZIB1WrSAEKQOYAyAYIBlWrXx8fCIOIAQpA9ABfCIYIBEgFVStIAQpA9gCIBUgHFStfHx8IhUgBCkDkAJ8IhkgECATVq0gBCkDqAIgECARVK18fHwiHHwiESAEKQOgAXwiECAEKQO4ASAEKQOwASIMIBd8IAxUrXx8IhMgBCkD8AN8IhdCiceZpK7wgemHf34iDEIAQsf688PtgqOQPEIAEMkDIARBIGogDEIAQo2Vx8OW0trAl39CABDJAyAEQRBqIAxCAELdsIWM6LaRqLh/QgAQyQMgBCAMQgBCqcDGia7Ok7IwQgAQyQMCQCAEKQMIIAQpA4gBIAQpA4gCIA4gD1StIAQpA4gDIA0gD1atfHwgBCkDSCANIBtUrXx8IhsgBCkDUHwiDCAVIBhUrSAEKQPYASAOIBhWrXx8fCINIAQpA4ACfCIPIA1UrXwgDyAPIBkgHFatIAQpA5gCIBUgGVatfHx8Ig5WrXwgDCANVq0gBCkDWCAMIBtUrXx8fCIVIAQpA2B8IgwgBCkD6AEgDiAEKQPgAXwiDSAOVK18IA0gCyARVq0gBCkD6AIgCyAeVK18fHwiCyANVK18fCINIAQpA4ABfCIPIA1UrXwgDyAEKQOYASALIAsgBCkDkAF8Ig5WrXwgDiAOIBAgE1atIAQpA6gBIBAgEVStfHx8Ig5WrXx8IgsgD1StfCAMIA1WrSAEKQNoIAwgFVStfHx8IhUgBCkDcHwiDyAEKQP4ASALIAQpA/ABfCIMIAtUrXwgDCAMIAQpA/gCIAQpA/gDIBMgF1atfCINIAQpA/ACfCILIA1UrXwgCyALIA58Ig1WrXx8IgtWrXx8IhEgBCkDAHwiECARVK18IBAgECAEKQMYIAsgCyAEKQMQfCITVq18IBMgEyAEKQMoIA0gDSAEKQMgfCIMVq18IAwgBCkDOCAEKQMwIgsgF3wgC1StfHwiDiAMVK18fCIMVq18fCINVq18IA8gEVatIAQpA3ggDyAVVK18fHwiEUKpwMaJrs6TsjBWDQAgEUKpwMaJrs6TsjBSDQIgDULdsIWM6LaRqLh/Vg0AIA1C3bCFjOi2kai4f1IEQEKpwMaJrs6TsjAhEQwDCyAMQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEPIAxCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhESAMIQsMBAtCjZXHw5bS2sCXfyELIA5Cx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCERDAMLIAxC8+q4vOmtpb/oAHwiDyAOQsf688PtgqOQPFStIhB9IQsgDUKjz/rzl8nu18cAfCITIAxCjZXHw5bS2sCXf1QgDyAQVHKtIgx9IQ8gESANQt2whYzotpGouH9UIAwgE1ZyrX1CqcDGia7Ok7IwfSERIA5Cx/rzw+2Co5A8fSEODAILIAUgCUHIn8EAENkDAAsgDSEPIAwhCwtCqcDGia7Ok7IwIRAgDyAWfCIMIA9UIAwgCyALIBR8Ig1WIA0gDSAOIBJ8IhIgDlStfCILVnKtfCINIAxUcq0gESAafHwiGiEMAkACQAJAIBpCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hECANIgxC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IRAgCyEMIAtCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhECASIgxCx/rzw+2Co5A8UQ0BCyAMIBBaDQAgDSEWIAshFAwBCyALQvPquLzpraW/6AB8IgwgEkLH+vPD7YKjkDxUrSIWfSEUIA1Co8/685fJ7tfHAHwiDyALQo2Vx8OW0trAl39UIAwgFlRyrSIMfSEWIBogDULdsIWM6LaRqLh/VCAMIA9Wcq19QqnAxomuzpOyMH0hGiASQsf688PtgqOQPH0hEgsgAUEoaiEBIANBKGsiAw0ACyAEKAKMBCEBCyAEKAKEBCABRgRAIARBhARqQbifwQAQogMLIAQoAogEIAFBBXRqIgMgEjcDGCADIBQ3AxAgAyAWNwMIIAMgGjcDACAEIAFBAWoiATYCjAQgAkEAQQwgBkEBayIGRSACIAdGciIKG2ohAyACIQUgCkUNAAsgBCgCiAQhByAEKAKEBAshBiABQQV0IQUgASEDAkACQAJAA0AgBUUNASADQQFrIQMgBUEgayIFIAdqQdjDwgBBIBDxA0UNAAsgA0EBaiICIAEgASACSxshBQwBC0HRzsUALQAAGkEgQQgQ1gQiAUUNASABQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwBBfyEDQQEhBSAGBEAgByAGQQV0EN8ECyABIQdBASEGCyAAIAM2AgwgACAFNgIIIAAgBzYCBCAAIAY2AgAgBEGQBGokAA8LQQhBIBD/BAALQfSewQBBNEGon8EAEP4DAAuCHAIMfxZ+IwBBoAZrIgIkACACQeAEaiABQQhqKQMANwMAIAJB6ARqIAFBEGopAwA3AwAgAkHwBGogAUEYaikDADcDACACQfgEaiABQSBqKQMANwMAIAJBgAVqIAFBKGopAwA3AwAgAkGQBWogAUE4aikDADcDACACQZgFaiABQUBrKQMANwMAIAJBoAVqIAFByABqKQMANwMAIAJBqAVqIAFB0ABqKQMANwMAIAJBsAVqIAFB2ABqKQMANwMAIAIgASkDADcD2AQgAiABKQMwNwOIBSACQbgFaiIGIAJB2ARqEPcDIAIoArwFIQQgAigCuAUhAwJAAkACQAJAAkACQAJAIAIoAsAFIgVBAkYEQCAEKAIEIQcgBCgCACEIIAYgBEEIakHYAPwKAAAgAwRAIAQgA0EwbBDfBAsgAkHoAWoiBiACQcAFaikDADcDACACQfABaiIJIAJByAVqKQMANwMAIAJB+AFqIgogAkHQBWopAwA3AwAgAkGAAmoiCyACQdgFaikDADcDACACQZACaiIMIAJB6AVqKQMANwMAIAJBmAJqIg0gAkHwBWopAwA3AwAgAkGgAmoiBCACQfgFaikDADcDACACQagCaiIDIAJBgAZqKQMANwMAIAJBsAJqIgUgAkGIBmopAwA3AwAgAiAHNgLcASACIAg2AtgBIAIgAikDuAU3A+ABIAIgAikD4AU3A4gCQprN/8ujvcSAGiEYIAIpA+ABIhsgDCkDACIhfCIWIBtUIBYgBikDACIcIA0pAwAiInwiESAcVCARIAkpAwAiHSAEKQMAIhd8IhAgHVQgECAKKQMAIh4gAykDACIZfCIPIB5UIA8gCykDACIfIAUpAwAiGnwiDiAfVK18IhUgD1RyrXwiEiAQVHKtfCIUIBFUcq18IhEgFlRyrSACKQOIAiIgIAIpA9gBIiN8fCIPIRACQAJAAkAgD0Kazf/Lo73EgBpSDQBC19mumuT26Y3LACEYIBEhECARQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEYIBQiEEK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhGCASIhBCpOzDtY/UtJjnAFINAEL//8+K6///1R4hGCAVIhBC///Piuv//9UeUg0AQqvV/v///7//uX8hGCAOIRAgDkKr1f7///+//7l/UQ0BCyAQIBhaDQAgESEQIBQhGCASIRMgFSEWDAELIBVC///Piuv//9UefSITIA5Cq9X+////v/+5f1StIhB9IRYgEkKk7MO1j9S0mOcAfSIYIBVC///Piuv//9UeVCAQIBNWcq0iEH0hEyAUQr+llJzP8NK75AB9IhUgEkKk7MO1j9S0mOcAVCAQIBhWcq0iEH0hGCARQtfZrprk9umNywB9IhIgFEK/pZScz/DSu+QAVCAQIBVWcq0iFH0hECAPIBFC19mumuT26Y3LAFQgEiAUVHKtfUKazf/Lo73EgBp9IQ8gDkLVqoGAgIDAgMYAfCEOCyACIA43A6AEIAIgFjcDmAQgAiATNwOQBCACIBg3A4gEIAIgEDcDgAQgAiAPNwP4AyABQeAAaiEFIAICfgJAAkAgIyIOICAiD1INACAbIg4gISIPUg0AIBwiDiAiIg9SDQAgHSIOIBciD1INACAeIg4gGSIPUg0AIB8iDiAaIg9RDQELIA4gD1oNAEKk7MO1j9S0mOcAIBcgHX0iEiAZIB59Ig8gGiAfVK0iDlQgGSAeVHKtIhF9IhV9IhAgDyAOfSIOQv//z4rr///VHlZC///Piuv//9UeIA59IhggGiAffSIZQqvV/v///7//uX9WrSIaVHKtIg59IQ9Cv6WUnM/w0rvkACAiIBx9IhQgFyAdVCARIBJWcq0iEX0iFn0iEiAOIBBWIBVCpOzDtY/UtJjnAFZyrSIQfSEOQtfZrprk9umNywAgISAbfSITIBEgFFYgHCAiVnKtIhV9IhR9IhEgECASViAWQr+llJzP8NK75ABWcq0iEH0hFiAQIBFWIBRC19mumuT26Y3LAFZyIQMgGCAafSESIBMgFVQgGyAhVnKtICMgIH18QprN/8ujvcSAGnwhF0Kr1f7///+//7l/IBl9DAELIB4gGX0iDyAaIB9WrSIOfSESIB0gF30iECAZIB5WIA4gD1ZyrSIOfSEPIBwgIn0iFCAXIB1WIA4gEFZyrSIQfSEOIBsgIX0iESAcICJUIBAgFFZyrSIQfSEWIBsgIVQgECARVnIhAyAjICB9IRcgHyAafQs3A+AFIAIgEjcD2AUgAiAPNwPQBSACIA43A8gFIAIgFjcDwAUgAiAXIAOtfTcDuAUgAkHIA2oiASACQfgDaiACQbgFaiIDELIBIAJCodWmgICAwI5uNwPgBSACQoeA8MvehIDChn83A9gFIAJC6LvQ78D4iLzPADcD0AUgAkLRwLPPhr6cvp5/NwPIBSACQpnXtYOmi4Dv/QA3A8AFIAJChcGL5PeOvvANNwO4BSACQZgDaiABIAMQsgFB2AAhAUIAIRNCACEOQgAhFkIAIRVCACERQgAhFwNAIAJB8ABqIAJB2AFqIAFqKQMAIg9CACAfQgAQyQMgAkGAAWogD0IAIB5CABDJAyACQZABaiAPQgAgHUIAEMkDIAJBoAFqIA9CACAcQgAQyQMgAkGwAWogD0IAIBtCABDJAyACQcABaiAPQgAgI0IAEMkDIAJB4ABqIAIpA3AiECAXfCIZQgBCAEL9//P/z///+Yl/EMkDIAJB0ABqIAIpA2giD0IAQqvV/v///7//uX9CABDJAyACQUBrIA9CAEL//8+K6///1R5CABDJAyACQTBqIA9CAEKk7MO1j9S0mOcAQgAQyQMgAkEgaiAPQgBCv6WUnM/w0rvkAEIAEMkDIAJBEGogD0IAQtfZrprk9umNywBCABDJAyACIA9CAEKazf/Lo73EgBpCABDJAyACKQMIIAIpA8ABIg8gE3wiGiACKQO4ASAOIAIpA7ABIg58IhMgDlStfCATIAIpA6gBIAIpA6ABIg4gFnwiEiAOVK18IBIgAikDmAEgAikDkAEiDiAVfCIUIA5UrXwgFCACKQOIASACKQOAASIOIBF8IhEgDlStfCARIAIpA3ggECAZVq18fCIOIBFUrXx8IhUgFFStfHwiESASVK18fCIQIBNUrXx8IiAgAikDAHwiEyAgVK18IBMgAikDGCAQIAIpAxB8IhIgEFStfCASIAIpAyggESACKQMgfCIUIBFUrXwgFCACKQM4IBUgAikDMHwiESAVVK18IBEgESACKQNIIA4gAikDQCIOfCIQIA5UrXwgECACKQNYIAIpA1AiDiAZfCAOVK18fCIXIBBUrXx8IhFWrXx8IhUgFFStfHwiFiASVK18fCIOIBNUrXwgGiAgVq0gAikDyAEgDyAaVq18fHwhEyABQQhrIgFBKEcNAAsgE0Kazf/Lo73EgBpWDQYgE0Kazf/Lo73EgBpRDQEMAgsgAiAFNgLABSACIAQ2ArwFIAIgAzYCuAVBgIvAAEErIAJBuAVqQayLwABBpI3AABDKAwALIA5C19mumuT26Y3LAFYNBCAOQtfZrprk9umNywBSBEBCms3/y6O9xIAaIRMMAQsgFkK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhDyAWQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIRMMAgsgFUKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhFCAVQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIRMMAwsgEUL//8+K6///1R5WDQRCpOzDtY/UtJjnACESIBFC///Piuv//9UeUQ0DQprN/8ujvcSAGiETIBEhEAwFCyAOIQ8LIBYhFAsgFSESIBEhEAwCC0L//8+K6///1R4hECAXQqrV/v///7//uX9WDQBCms3/y6O9xIAaIRMMAQsgEUL//8+K6///1R59IhIgF0Kr1f7///+//7l/VK0iD30hECAVQqTsw7WP1LSY5wB9IhQgEUL//8+K6///1R5UIA8gElZyrSIPfSESIBZCv6WUnM/w0rvkAH0iESAVQqTsw7WP1LSY5wBUIA8gFFZyrSIPfSEUIA5C19mumuT26Y3LAH0iFSAWQr+llJzP8NK75ABUIA8gEVZyrSIRfSEPIBMgDkLX2a6a5PbpjcsAVCARIBVWcq19QprN/8ujvcSAGn0hEyAXQtWqgYCAgMCAxgB8IRcLIAIgFzcDoAQgAiAQNwOYBCACIBI3A5AEIAIgFDcDiAQgAiAPNwOABCACIBM3A/gDIAJCl9XOgICAwJ0iNwPgBSACQpCAkI3SiYCubjcD2AUgAkKsi92p8pzd3zc3A9AFIAJC49vSgr6L5sBYNwPIBSACQtvUvOznn5bQsH83A8AFIAJC8LSX/Mvgt+ABNwO4BSACQegCaiACQfgDaiIBIAJBuAVqIgMQsgEgAkHAAmogAkGgA2opAwA3AwAgAkHIAmogAkGoA2opAwA3AwAgAkHQAmogAkGwA2opAwA3AwAgAkHYAmogAkG4A2opAwA3AwAgAkHgAmogAkHAA2opAwA3AwAgAiACKQOYAzcDuAIgASAFIAUQ1QEgAyACQbgCaiABEMEDIAIpA8gFIQ8gAikDwAUhDiACKAK4BUEBRwRAIABBEGogAkHQBWpB0AD8CgAAIAAgDzcDCCAAIA43AwAgAkGgBmokAA8LIAIgDzcDwAUgAiAONwO4BUHU/sAAQSsgAkG4BWpBsIXBAEHAhcEAEMoDAAvCFwIYfwJ+IwBBwAdrIgIkACACEG0gAkHIAmoiBSABQShqKQMANwMAIAJBwAJqIgYgAUEgaikDADcDACACQbgCaiIEIAFBGGopAwA3AwAgAkGwAmoiByABQRBqKQMANwMAIAJBqAJqIgggAUEIaikDADcDACACQdgCaiIMIAFBOGopAwA3AwAgAkHgAmoiDSABQUBrKQMANwMAIAJB6AJqIg4gAUHIAGopAwA3AwAgAkHwAmoiDyABQdAAaikDADcDACACQfgCaiIQIAFB2ABqKQMANwMAIAIgASkDADcDoAIgAiABKQMwNwPQAkEARQRAIAJBgAZqIAJBoAJqQeAA/AoAAAsgBSACQagGaiIRKQMANwMAIAYgAkGgBmoiEykDADcDACAEIAJBmAZqIgkpAwA3AwAgByACQZAGaiISKQMANwMAIAggAkGIBmoiFCkDADcDACAMIAJBuAZqIhUpAwA3AwAgDSACQcAGaiIWKQMANwMAIA4gAkHIBmoiFykDADcDACAPIAJB0AZqIhgpAwA3AwAgECACQdgGaiIZKQMANwMAIAIgAikDgAY3A6ACIAIgAikDsAY3A9ACIANFBEAgAkHgBmogAkGgAmpB4AD8CgAACyACQaACaiIKIAJB4AZqIgsQXiADRQRAIAsgCkHgAPwKAAALIAJBoAJqIgogAkGABmoiCyACQeAGahA/IANFBEAgCyAKQeAA/AoAAAsgA0UEQCACQcAEaiACQYAGakHgAPwKAAALIAUgAUGIAWopAwA3AwAgBiABQYABaikDADcDACAEIAFB+ABqKQMANwMAIAcgAUHwAGopAwA3AwAgCCABQegAaikDADcDACAMIAFBmAFqKQMANwMAIA0gAUGgAWopAwA3AwAgDiABQagBaikDADcDACAPIAFBsAFqKQMANwMAIBAgAUG4AWopAwA3AwAgAiABKQNgNwOgAiACIAEpA5ABNwPQAiADRQRAIAJBgAZqIAJBoAJqQeAA/AoAAAsgBSARKQMANwMAIAYgEykDADcDACAEIAkpAwA3AwAgByASKQMANwMAIAggFCkDADcDACAMIBUpAwA3AwAgDSAWKQMANwMAIA4gFykDADcDACAPIBgpAwA3AwAgECAZKQMANwMAIAIgAikDgAY3A6ACIAIgAikDsAY3A9ACIANFBEAgAkHgBmogAkGgAmpB4AD8CgAACyACQaACaiIKIAJB4AZqIgsQXiADRQRAIAsgCkHgAPwKAAALIAJBoAJqIgogAkGABmoiCyACQeAGahA/IANFBEAgCyAKQeAA/AoAAAsgA0UEQCACQaAFaiACQYAGakHgAPwKAAALIAJBoAJqIgoQdSACQeAGaiILIAJBoAVqIAoQPyACQcABaiACQcAEaiALENUBIAUgAUHoAWopAwA3AwAgBiABQeABaikDADcDACAEIAFB2AFqKQMANwMAIAcgAUHQAWopAwA3AwAgCCABQcgBaikDADcDACAMIAFB+AFqKQMANwMAIA0gAUGAAmopAwA3AwAgDiABQYgCaikDADcDACAPIAFBkAJqKQMANwMAIBAgAUGYAmopAwA3AwAgAiABKQPAATcDoAIgAiABKQPwATcD0AIgA0UEQCACQYAGaiAKQeAA/AoAAAsgBSARKQMANwMAIAYgEykDADcDACAEIAkpAwA3AwAgByASKQMANwMAIAggFCkDADcDACAMIBUpAwA3AwAgDSAWKQMANwMAIA4gFykDADcDACAPIBgpAwA3AwAgECAZKQMANwMAIAIgAikDgAY3A6ACIAIgAikDsAY3A9ACIANFBEAgAkHgBmogAkGgAmpB4AD8CgAACyACQaACaiIJIAJB4AZqIhEQXiADRQRAIBEgCUHgAPwKAAALIAJBoAJqIgkgAkGABmoiESACQeAGahA/IANFBEAgESAJQeAA/AoAAAsgA0UEQCACQcAEaiACQYAGakHgAPwKAAALIAJBoAVqEHUgBSACQcgFaikDADcDACAGIAJBwAVqKQMANwMAIAQgAkG4BWopAwA3AwAgByACQbAFaikDADcDACAIIAJBqAVqKQMANwMAIAwgAkHYBWopAwA3AwAgDSACQeAFaikDADcDACAOIAJB6AVqKQMANwMAIA8gAkHwBWopAwA3AwAgECACQfgFaikDADcDACACIAIpA6AFNwOgAiACIAIpA9AFNwPQAiADRQRAIAJB4AZqIAJBoAJqQeAA/AoAAAsgAkGgAmoiBSACQeAGaiIGEF4gA0UEQCAGIAVB4AD8CgAACyADRQRAIAJBoAJqIAJB4AZqQeAA/AoAAAsgAkHgBmoiAyACQcAEaiIHIAJBoAJqIgQQPyAHIAJBwAFqIAMQ1QEgBCACIAEQPyADIAQgAUHgAGoiBRA/IAJBgAZqIgggAyABQcABaiIGED8gBBB1IAMgCCAEED8gAkHgAGoiCCAHIAMQjQEgBCAIED0gAikDsAIhGiACKQOoAiEbIAACfiACKAKgAkEBRgRAIAAgGjcDECAAIBs3AwhCAQwBCyACQdABaiACQbgCaiIEQdAA/AoAACACIBo3A8gBIAIgGzcDwAEgAkHIAmoiByABQShqKQMANwMAIAJBwAJqIgggAUEgaikDADcDACAEIAFBGGopAwA3AwAgAkGwAmoiDCABQRBqKQMANwMAIAJBqAJqIg0gAUEIaikDADcDACACQdgCaiIOIAFBMGoiA0EIaikDADcDACACQeACaiIPIANBEGopAwA3AwAgAkHoAmoiECADQRhqKQMANwMAIAJB8AJqIhEgA0EgaikDADcDACACQfgCaiITIANBKGopAwA3AwAgAiABKQMANwOgAiACIAMpAwA3A9ACQQAiA0UEQCACQeAGaiACQaACakHgAPwKAAALIAJBoAJqIgkgAkHgBmoiEhBeIANFBEAgEiAJQeAA/AoAAAsgA0UEQCACQaAFaiACQeAGakHgAPwKAAALIAJB4AZqIhIgBSAGED8gAkGgAmoiCRB1IAJBgAZqIhQgEiAJED8gCSACQaAFaiIVIBQQjQEgAkHABGogCSACQcABahA/IAkgARC0AiAVIAkgBRA/IAcgBkEoaikDADcDACAIIAZBIGopAwA3AwAgBCAGQRhqKQMANwMAIAwgBkEQaikDADcDACANIAZBCGopAwA3AwAgDiABQfABaiIEQQhqKQMANwMAIA8gBEEQaikDADcDACAQIARBGGopAwA3AwAgESAEQSBqKQMANwMAIBMgBEEoaikDADcDACACIAYpAwA3A6ACIAIgBCkDADcD0AIgA0UEQCASIAlB4AD8CgAACyACQaACaiIEIAJB4AZqIgcQXiADRQRAIAcgBEHgAPwKAAALIANFBEAgAkGABmogAkHgBmpB4AD8CgAACyACQaACaiIIEHUgAkHgBmoiBCACQYAGaiIHIAgQPyAHIAJBoAVqIgggBBDVASACQYADaiAHIAJBwAFqED8gBCABELQCIAggBCAGED8gAkGIB2ogBUEoaikDADcDACACQYAHaiAFQSBqKQMANwMAIAJB+AZqIAVBGGopAwA3AwAgAkHwBmogBUEQaikDADcDACACQegGaiAFQQhqKQMANwMAIAJBmAdqIAFBkAFqIgFBCGopAwA3AwAgAkGgB2ogAUEQaikDADcDACACQagHaiABQRhqKQMANwMAIAJBsAdqIAFBIGopAwA3AwAgAkG4B2ogAUEoaikDADcDACACIAUpAwA3A+AGIAIgASkDADcDkAcgA0UEQCAHIARB4AD8CgAACyACQeAGaiIBIAJBgAZqIgUQXiADRQRAIAUgAUHgAPwKAAALIANFBEAgAkHgBmogAkGABmpB4AD8CgAACyACQYAGaiIBIAJBoAVqIAJB4AZqENUBIAJB4ANqIAEgAkHAAWoQPyADRQRAIAJBoAJqIAJBwARqQeAA/AoAAAsgAEEIaiACQaACakGgAvwKAABCAAs3AwAgAkHAB2okAAveGgIVfxB+IwBBgARrIgMkAAJAAkACQCABKAIMIgRBf0cEQCACKAIMIgVBf0cNAQtB0c7FAC0AABpBIEEIENYEIgVFDQEgBUIANwMAIAVBGGpCADcDACAFQRBqQgA3AwAgBUEIakIANwMAQX8hCkEBIQ1BASEIDAILIAQgBWoiCkEBaiIIQQV0IQQCQCAIQf///z9LIARB+P///wdLcg0AAn8gBEUEQEEIIQVBAAwBC0HRzsUALQAAGkEIIQYgBEEIENYEIgVFDQEgCAshDQJAAkACQAJAIAhBAk8EQCAKQQdxIQYgCkEBa0EHTw0BIAUhBAwCCyAFIQQgCA0CDAMLIApBeHEhByAFIQQDQCAEQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgBEEgakIANwMAIARBKGpCADcDACAEQTBqQgA3AwAgBEE4akIANwMAIARBQGtCADcDACAEQcgAakIANwMAIARB0ABqQgA3AwAgBEHYAGpCADcDACAEQeAAakIANwMAIARB6ABqQgA3AwAgBEHwAGpCADcDACAEQfgAakIANwMAIARBmAFqQgA3AwAgBEGQAWpCADcDACAEQYgBakIANwMAIARBgAFqQgA3AwAgBEG4AWpCADcDACAEQbABakIANwMAIARBqAFqQgA3AwAgBEGgAWpCADcDACAEQcABakIANwMAIARByAFqQgA3AwAgBEHQAWpCADcDACAEQdgBakIANwMAIARB4AFqQgA3AwAgBEHoAWpCADcDACAEQfABakIANwMAIARB+AFqQgA3AwAgBEGAAmohBCAHQQhrIgcNAAsLIAZFDQADQCAEQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgBEEgaiEEIAZBAWsiBg0ACwsgBEIANwMAIARBGGpCADcDACAEQRBqQgA3AwAgBEEIakIANwMACyABKAIIIglFDQIgAigCCCIHRQ0CIAEoAgQiBiAJQQV0aiERIAIoAgQiDiAHQQV0aiESIA4gB0EAR0EFdGohEyAGQSBqIQQgCUEBa0H///8/cSEUIAdBAWtB////P3FBAWohFQNAIAYhCyAEIQYgDyIQQQFqIQ9BACEBIAwhAiATIQkgDiEEAkADQCAIIAEgEGoiB0sEQCAJIQcgA0HAA2ogCykDGCIaQgAgBCkDGCIYQgAQyQMgA0HAAmogCykDECIZQgAgGEIAEMkDIANBwAFqIAspAwgiG0IAIBhCABDJAyADQUBrIAspAwAiHUIAIBhCABDJAyADQbADaiADKQPAAyIeQonHmaSu8IHph39+IhhCAELH+vPD7YKjkDxCABDJAyADQaADaiAYQgBCjZXHw5bS2sCXf0IAEMkDIANBkANqIBhCAELdsIWM6LaRqLh/QgAQyQMgA0GAA2ogGEIAQqnAxomuzpOyMEIAEMkDIANB0ANqIAQpAxAiGEIAIBpCABDJAyADQdACaiAYQgAgGUIAEMkDIANB0AFqIBhCACAbQgAQyQMgA0HQAGogGEIAIB1CABDJAyADQbACaiADKQOgAyIgIAMpA8gDIiEgAykDwAJ8IiJ8IhwgAykDuAMgHiADKQOwAyIYfCAYVK18fCIeIAMpA9ADfCIfQonHmaSu8IHph39+IhhCAELH+vPD7YKjkDxCABDJAyADQaACaiAYQgBCjZXHw5bS2sCXf0IAEMkDIANBkAJqIBhCAELdsIWM6LaRqLh/QgAQyQMgA0GAAmogGEIAQqnAxomuzpOyMEIAEMkDIANB4ANqIAQpAwgiGEIAIBpCABDJAyADQeACaiAYQgAgGUIAEMkDIANB4AFqIBhCACAbQgAQyQMgA0HgAGogGEIAIB1CABDJAyADQbABaiADKQPYAyAeIB9WrXwiJSADKQPQAnwiIyADKQPIAiAhICJWrXwiJCADKQPAAXwiISADKQOQA3wiIiAcIB5WrSADKQOoAyAcICBUrXx8fCImfCIcIAMpA6ACfCIeIAMpA7gCIAMpA7ACIhggH3wgGFStfHwiHyADKQPgA3wiIEKJx5mkrvCB6Yd/fiIYQgBCx/rzw+2Co5A8QgAQyQMgA0GgAWogGEIAQo2Vx8OW0trAl39CABDJAyADQZABaiAYQgBC3bCFjOi2kai4f0IAEMkDIANBgAFqIBhCAEKpwMaJrs6TsjBCABDJAyADQfADaiAEKQMAIhhCACAaQgAQyQMgA0HwAmogGEIAIBlCABDJAyADQfABaiAYQgAgG0IAEMkDIANB8ABqIBhCACAdQgAQyQMgA0EwaiADKQPoAyAfICBWrXwiJyADKQPgAnwiGCADKQPIASAhICRUrXwiJCADKQNAfCIZIAMpA4ADfCIbICIgJlatIAMpA5gDICEgIlatfHx8Ih0gAykD0AF8IiEgHCAjVK0gAykD2AIgIyAlVK18fHwiIyADKQOQAnwiIiAeIB9WrSADKQOoAiAcIB5WrXx8fCIlfCIcIAMpA6ABfCIeIAMpA7gBIAMpA7ABIhogIHwgGlStfHwiHyADKQPwA3wiIEKJx5mkrvCB6Yd/fiIaQgBCx/rzw+2Co5A8QgAQyQMgA0EgaiAaQgBCjZXHw5bS2sCXf0IAEMkDIANBEGogGkIAQt2whYzotpGouH9CABDJAyADIBpCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDCCADKQOIASADKQOIAiAbIB1WrSADKQOIAyAZIBtWrXx8IAMpA0ggGSAkVK18fCIkIAMpA1B8IhogISAjVq0gAykD2AEgHSAhVq18fHwiGSADKQOAAnwiGyAZVK18IBsgGyAiICVWrSADKQOYAiAiICNUrXx8fCIbVq18IBkgGlStIAMpA1ggGiAkVK18fHwiHSADKQNgfCIaIAMpA+gBIBsgAykD4AF8IhkgG1StfCAZIBggHFatIAMpA+gCIBggJ1StfHx8IhggGVStfHwiGSADKQOAAXwiGyAZVK18IBsgAykDmAEgGCAYIAMpA5ABfCIYVq18IBggHiAfVq0gAykDqAEgHCAeVq18fHwiHCAYVK18fCIYIBtUrXwgGSAaVK0gAykDaCAaIB1UrXx8fCIeIAMpA3B8IhogAykD+AEgGCAYIAMpA/ABfCIYVq18IBggGCADKQP4AiADKQP4AyAfICBWrXwiGyADKQPwAnwiGSAbVK18IBkgGSAcfCIZVq18fCIYVq18fCIbIAMpAwB8Ih0gG1StfCAdIAMpAxggGCAYIAMpAxB8IhhWrXwgGCAYIAMpAyggGSAZIAMpAyB8IhlWrXwgGSADKQM4IAMpAzAiHCAgfCAcVK18fCIcIBlUrXx8IhhWrXx8IhkgHVStfCAaIBtWrSADKQN4IBogHlStfHx8IhtCqcDGia7Ok7IwVg0AAkAgG0KpwMaJrs6TsjBRBEAgGULdsIWM6LaRqLh/Vg0CIBlC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhGwsgGSEdIBghGgwCCyAYQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEdIBhCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhGyAYIRoMAgtCjZXHw5bS2sCXfyEaIBxCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEbDAELIBhC8+q4vOmtpb/oAHwiHSAcQsf688PtgqOQPFStIh59IRogGUKjz/rzl8nu18cAfCIfIBhCjZXHw5bS2sCXf1QgHSAeVHKtIhh9IR0gGyAZQt2whYzotpGouH9UIBggH1ZyrX1CqcDGia7Ok7IwfSEbIBxCx/rzw+2Co5A8fSEcC0KpwMaJrs6TsjAhHiACIAVqIgQpAwAgG3wgHSAEQQhqIgkpAwB8IhkgHVQgGSAZIBogGiAEQRBqIhYpAwB8IhpWIBogHCAEQRhqIhcpAwB8IhsgHFStfCIYIBpUcq18IhlWcq18IhwhGgJAAkACQCAcQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IR4gGSEaIBlC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IR4gGCEaIBhCjZXHw5bS2sCXf1INAELH+vPD7YKjkDwhHiAbIRogG0LH+vPD7YKjkDxRDQELIBogHloNACAZIRogGCEdDAELIBhC8+q4vOmtpb/oAHwiGiAbQsf688PtgqOQPFStIh59IR0gGUKjz/rzl8nu18cAfCIfIBhCjZXHw5bS2sCXf1QgGiAeVHKtIhh9IRogHCAZQt2whYzotpGouH9UIBggH1ZyrX1CqcDGia7Ok7IwfSEcIBtCx/rzw+2Co5A8fSEbCyAEIBw3AwAgFiAdNwMAIAkgGjcDACAXIBs3AwAgAkEgaiECIAcgByASR0EFdGohCSAHIQQgAUEBaiIBIBVHDQEMAgsLIAcgCEGMyMIAENkDAAsgDEEgaiEMIAYgBiARR0EFdGohBCAQIBRHDQALDAILIAYgBEH8x8IAEMgEAAtBCEEgEP8EAAsgACAKNgIMIAAgCDYCCCAAIAU2AgQgACANNgIAIANBgARqJAAL2g0CCH8JfkICIRAjAEHAB2siAiQAIAJByARqIgMgAUEIaikDACIKNwMAIAJB0ARqIgQgAUEQaikDACILNwMAIAJB4ARqIgUgASkDICIMNwMAIAJB6ARqIgYgAUEoaikDACINNwMAIAJB8ARqIgcgAUEwaikDACIONwMAIAJB+ARqIgggAUE4aikDACIPNwMAIAJB2ARqIgkgAUEYaikDACIRNwMAIAJBiANqIAo3AwAgAkGQA2ogCzcDACACQZgDaiARNwMAIAJBoANqIAw3AwAgAkGoA2ogDTcDACACQbADaiAONwMAIAJBuANqIA83AwAgAiABKQMAIgo3A8AEIAIgCjcDgAMgAyABQcgAaikDACIKNwMAIAQgAUHQAGopAwAiCzcDACAJIAFB2ABqKQMAIgw3AwAgBSABKQNgIg03AwAgBiABQegAaikDACIONwMAIAcgAUHwAGopAwAiDzcDACAIIAFB+ABqKQMAIhE3AwAgAkH4A2ogETcDACACQfADaiAPNwMAIAJB6ANqIA43AwAgAkHgA2ogDTcDACACQdgDaiAMNwMAIAJB0ANqIAs3AwAgAkHIA2ogCjcDACACIAEpA0AiCjcDwAQgAiAKNwPAAyACQdgBaiABQZgBaikDACIKNwMAIAJB0AFqIAFBkAFqKQMAIgs3AwAgAkHIAWogAUGIAWopAwAiDDcDACACQeABaiABKQOgASINNwMAIAJB6AFqIAFBqAFqKQMAIg43AwAgAkHwAWogAUGwAWopAwAiDzcDACACQfgBaiABQbgBaikDACIRNwMAIAIgASkDgAEiEjcDwAEgCCARNwMAIAcgDzcDACAGIA43AwAgBSANNwMAIAkgCjcDACAEIAs3AwAgAyAMNwMAIAIgEjcDwAQgAkG4BGogCCkDADcDACACQbAEaiAHKQMANwMAIAJBqARqIAYpAwA3AwAgAkGgBGogBSkDADcDACACQZgEaiAJKQMANwMAIAJBkARqIAQpAwA3AwAgAkGIBGogAykDADcDACACIAIpA8AENwOABCACIAJBgANqQcAB/AoAAANAIAJBgANqIgkiASACIAIQ6wEgAiABQcAB/AoAACAQQgKDIBBCAYghEFANAAsgAkHgBmoiASACKQMgIgo3AwAgAkGgA2ogCjcDACACQcgGaiIDIAJBCGopAwAiCjcDACACQdAGaiIEIAJBEGopAwAiCzcDACACQegGaiIFIAJBKGopAwAiDDcDACACQfAGaiIGIAJBMGopAwAiDTcDACACQfgGaiIHIAJBOGopAwAiDjcDACACQdgGaiIIIAJBGGopAwAiDzcDACACQYgDaiAKNwMAIAJBkANqIAs3AwAgAkGYA2ogDzcDACACQagDaiAMNwMAIAJBsANqIA03AwAgAkG4A2ogDjcDACACIAIpAwAiCjcDwAYgAiAKNwOAAyADIAJByABqKQMANwMAIAQgAkHQAGopAwA3AwAgCCACQdgAaikDADcDACABIAIpA2A3AwAgBSACQegAaikDADcDACAGIAJB8ABqKQMANwMAIAcgAkH4AGopAwA3AwAgAiACKQNANwPABiACQfgDaiAHKQMANwMAIAJB8ANqIAYpAwA3AwAgAkHoA2ogBSkDADcDACACQeADaiABKQMANwMAIAJB2ANqIAgpAwA3AwAgAkHQA2ogBCkDADcDACACQcgDaiADKQMANwMAIAIgAikDwAY3A8ADIAJB2AFqIAJBmAFqKQMAIgo3AwAgAkHQAWogAkGQAWopAwAiCzcDACACQcgBaiACQYgBaikDACIMNwMAIAIgAikDgAEiDTcDwAEgAkHgAWogAikDoAEiDjcDACACQegBaiACQagBaikDACIPNwMAIAJB8AFqIAJBsAFqKQMAIhE3AwAgAkH4AWogAkG4AWopAwAiEjcDACAHIBI3AwAgBiARNwMAIAUgDzcDACABIA43AwAgCCAKNwMAIAQgCzcDACADIAw3AwAgAiANNwPABiACQbgEaiAHKQMANwMAIAJBsARqIAYpAwA3AwAgAkGoBGogBSkDADcDACACQaAEaiABKQMANwMAIAJBmARqIAgpAwA3AwAgAkGQBGogBCkDADcDACACQYgEaiADKQMANwMAIAIgAikDwAY3A4AEIAJBwAFqIAlBwAH8CgAAIBBCAVIEQANAIAJBgANqIgMgAkHAAWoiASABEOsBIAEgA0HAAfwKAAAgEEICg1BFBEAgAkGAA2oiASACIAJBwAFqEOsBIAIgAUHAAfwKAAALIBBCBFQgEEIBiCEQRQ0ACwsgACACQcAB/AoAACACQcAHaiQAC6gcAgR/J34jAEEQayIFJAAgBUEEaiABEMYBQdHOxQAtAAAaAkACQAJAAkACQAJAAkACQAJAAkACQAJAQcAEQQgQ1gQiAwRAIAUoAgwiBEUNASAEQQFGDQICfiAFKAIIIgJBMGpB2LPCAEEwEPEDBEBC///Piuv//9UeIAIpA1AiIn0iESACKQNYIiNCq9X+////v/+5f1atIhJ9ISpCpOzDtY/UtJjnACACKQNIIgt9IhMgESASVCAiQv//z4rr///VHlZyrSIRfSEiQr+llJzP8NK75AAgAikDQCISfSIUIBEgE1YgC0Kk7MO1j9S0mOcAVnKtIgt9IRFC19mumuT26Y3LACACKQM4IhN9IgYgCyAUViASQr+llJzP8NK75ABWcq0iC30hEkKr1f7///+//7l/ICN9ISNCms3/y6O9xIAaIAIpAzAgBiALVCATQtfZrprk9umNywBWcq18fQwBCyACKQNYISMgAikDUCEqIAIpA0ghIiACKQNAIREgAikDOCESIAIpAzALIQsgBEECTQ0DIARBA0YNBAJ+IAJBkAFqQdizwgBBMBDxAwRAQv//z4rr///VHiACKQOwASIUfSIGIAIpA7gBIiRCq9X+////v/+5f1atIhV9IRNCpOzDtY/UtJjnACACKQOoASIMfSIWIAYgFVQgFEL//8+K6///1R5Wcq0iBn0hFEK/pZScz/DSu+QAIAIpA6ABIhV9IhcgBiAWViAMQqTsw7WP1LSY5wBWcq0iDH0hBkLX2a6a5PbpjcsAIAIpA5gBIhZ9IgcgDCAXViAVQr+llJzP8NK75ABWcq0iDH0hFUKr1f7///+//7l/ICR9ISRCms3/y6O9xIAaIAIpA5ABIAcgDFQgFkLX2a6a5PbpjcsAVnKtfH0MAQsgAikDuAEhJCACKQOwASETIAIpA6gBIRQgAikDoAEhBiACKQOYASEVIAIpA5ABCyEMIARBBE0NBSAEQQVGDQYCfiACQfABakHYs8IAQTAQ8QMEQEL//8+K6///1R4gAikDkAIiF30iByACKQOYAiIlQqvV/v///7//uX9WrSIYfSEWQqTsw7WP1LSY5wAgAikDiAIiDX0iGSAHIBhUIBdC///Piuv//9UeVnKtIgd9IRdCv6WUnM/w0rvkACACKQOAAiIYfSIaIAcgGVYgDUKk7MO1j9S0mOcAVnKtIg19IQdC19mumuT26Y3LACACKQP4ASIZfSIIIA0gGlYgGEK/pZScz/DSu+QAVnKtIg19IRhCq9X+////v/+5fyAlfSElQprN/8ujvcSAGiACKQPwASAIIA1UIBlC19mumuT26Y3LAFZyrXx9DAELIAIpA5gCISUgAikDkAIhFiACKQOIAiEXIAIpA4ACIQcgAikD+AEhGCACKQPwAQshDSAEQQZNDQcgBEEHRg0IAn4gAkHQAmpB2LPCAEEwEPEDBEBC///Piuv//9UeIAIpA/ACIhp9IgggAikD+AIiJkKr1f7///+//7l/Vq0iG30hGUKk7MO1j9S0mOcAIAIpA+gCIg59IhwgCCAbVCAaQv//z4rr///VHlZyrSIIfSEaQr+llJzP8NK75AAgAikD4AIiG30iHSAIIBxWIA5CpOzDtY/UtJjnAFZyrSIOfSEIQtfZrprk9umNywAgAikD2AIiHH0iCSAOIB1WIBtCv6WUnM/w0rvkAFZyrSIOfSEbQqvV/v///7//uX8gJn0hJkKazf/Lo73EgBogAikD0AIgCSAOVCAcQtfZrprk9umNywBWcq18fQwBCyACKQP4AiEmIAIpA/ACIRkgAikD6AIhGiACKQPgAiEIIAIpA9gCIRsgAikD0AILIQ4gBEEITQ0JIARBCUYNCgJ+IAJBsANqQdizwgBBMBDxAwRAQv//z4rr///VHiACKQPQAyIdfSIJIAIpA9gDIidCq9X+////v/+5f1atIh59IRxCpOzDtY/UtJjnACACKQPIAyIPfSIfIAkgHlQgHUL//8+K6///1R5Wcq0iCX0hHUK/pZScz/DSu+QAIAIpA8ADIh59IiAgCSAfViAPQqTsw7WP1LSY5wBWcq0iD30hCULX2a6a5PbpjcsAIAIpA7gDIh99IgogDyAgViAeQr+llJzP8NK75ABWcq0iD30hHkKr1f7///+//7l/ICd9ISdCms3/y6O9xIAaIAIpA7ADIAogD1QgH0LX2a6a5PbpjcsAVnKtfH0MAQsgAikD2AMhJyACKQPQAyEcIAIpA8gDIR0gAikDwAMhCSACKQO4AyEeIAIpA7ADCyEPIARBCk0NCyAEQQtHBEACfiACQZAEakHYs8IAQTAQ8QMEQEL//8+K6///1R4gAikDsAQiIH0iCiACKQO4BCIoQqvV/v///7//uX9WrSIhfSEfQqTsw7WP1LSY5wAgAikDqAQiEH0iKSAKICFUICBC///Piuv//9UeVnKtIgp9ISBCv6WUnM/w0rvkACACKQOgBCIhfSIrIAogKVYgEEKk7MO1j9S0mOcAVnKtIhB9IQpC19mumuT26Y3LACACKQOYBCIpfSIsIBAgK1YgIUK/pZScz/DSu+QAVnKtIhB9ISFCq9X+////v/+5fyAofSEoQprN/8ujvcSAGiACKQOQBCAQICxWIClC19mumuT26Y3LAFZyrXx9DAELIAIpA7gEISggAikDsAQhHyACKQOoBCEgIAIpA6AEIQogAikDmAQhISACKQOQBAshECADIAIpAwA3AwAgA0EoaiACQShqKQMANwMAIANBIGogAkEgaikDADcDACADQRhqIAJBGGopAwA3AwAgA0EQaiACQRBqKQMANwMAIANBCGogAkEIaikDADcDACADICM3A1ggAyAqNwNQIAMgIjcDSCADIBE3A0AgAyASNwM4IAMgCzcDMCADIAIpA2A3A2AgA0HoAGogAkHoAGopAwA3AwAgA0HwAGogAkHwAGopAwA3AwAgA0H4AGogAkH4AGopAwA3AwAgA0GAAWogAkGAAWopAwA3AwAgA0GIAWogAkGIAWopAwA3AwAgAyAkNwO4ASADIBM3A7ABIAMgFDcDqAEgAyAGNwOgASADIBU3A5gBIAMgDDcDkAEgA0HoAWogAkHoAWopAwA3AwAgA0HgAWogAkHgAWopAwA3AwAgA0HYAWogAkHYAWopAwA3AwAgA0HQAWogAkHQAWopAwA3AwAgA0HIAWogAkHIAWopAwA3AwAgAyACKQPAATcDwAEgAyAlNwOYAiADIBY3A5ACIAMgFzcDiAIgAyAHNwOAAiADIBg3A/gBIAMgDTcD8AEgA0HIAmogAkHIAmopAwA3AwAgA0HAAmogAkHAAmopAwA3AwAgA0G4AmogAkG4AmopAwA3AwAgA0GwAmogAkGwAmopAwA3AwAgA0GoAmogAkGoAmopAwA3AwAgAyACKQOgAjcDoAIgAyAmNwP4AiADIBk3A/ACIAMgGjcD6AIgAyAINwPgAiADIBs3A9gCIAMgDjcD0AIgA0GoA2ogAkGoA2opAwA3AwAgA0GgA2ogAkGgA2opAwA3AwAgA0GYA2ogAkGYA2opAwA3AwAgA0GQA2ogAkGQA2opAwA3AwAgA0GIA2ogAkGIA2opAwA3AwAgAyACKQOAAzcDgAMgAyAnNwPYAyADIBw3A9ADIAMgHTcDyAMgAyAJNwPAAyADIB43A7gDIAMgDzcDsAMgA0GIBGogAkGIBGopAwA3AwAgA0GABGogAkGABGopAwA3AwAgA0H4A2ogAkH4A2opAwA3AwAgA0HwA2ogAkHwA2opAwA3AwAgA0HoA2ogAkHoA2opAwA3AwAgAyACKQPgAzcD4AMgAyAoNwO4BCADIB83A7AEIAMgIDcDqAQgAyAKNwOgBCADICE3A5gEIAMgEDcDkARBDCECIAACfyADQZAEakH4w8IAQTAQ8QMEQEEMIQRBCwwBCyADQeADakH4w8IAQTAQ8QMEQEELIQRBCgwBCyADQbADakH4w8IAQTAQ8QMEQEEKIQRBCQwBCyADQYADakH4w8IAQTAQ8QMEQEEJIQRBCAwBCyADQdACakH4w8IAQTAQ8QMEQEEIIQRBBwwBCyADQaACakH4w8IAQTAQ8QMEQEEHIQRBBgwBCyADQfABakH4w8IAQTAQ8QMEQEEGIQRBBQwBCyADQcABakH4w8IAQTAQ8QMEQEEFIQRBBAwBCyADQZABakH4w8IAQTAQ8QMEQEEEIQRBAwwBCyADQeAAakH4w8IAQTAQ8QMEQEEDIQRBAgwBCyADQTBqQfjDwgBBMBDxAwRAQQIhBEEBDAELIANB+MPCAEEwEPEDBEBBASEEQQAMAQtB0c7FAC0AABpBMEEIENYEIgJFDQ4gAkIANwMAIAJBKGpCADcDACACQSBqQgA3AwAgAkEYakIANwMAIAJBEGpCADcDACACQQhqQgA3AwAgA0HABBDfBEEBIQQgAiEDQQEhAkF/CzYCDCAAIAQ2AgggACADNgIEIAAgAjYCACAFKAIEIgAEQCAFKAIIIABBMGwQ3wQLIAEoAgAiAARAIAEoAgQgAEEwbBDfBAsgBUEQaiQADwtBC0ELQfS5wgAQ2QMAC0EIQcAEEP8EAAtBAEEAQcS4wgAQ2QMAC0EBQQFB1LjCABDZAwALQQJBAkHkuMIAENkDAAtBA0EDQfS4wgAQ2QMAC0EEQQRBhLnCABDZAwALQQVBBUGUucIAENkDAAtBBkEGQaS5wgAQ2QMAC0EHQQdBtLnCABDZAwALQQhBCEHEucIAENkDAAtBCUEJQdS5wgAQ2QMAC0EKQQpB5LnCABDZAwALQQhBMBD/BAALxBYCJH8FfiMAQdAOayIBJAAgASAANgLQDSABIABBwAFqIhY2AtQNIAFBiANqIhEgAUHQDWoiEhC9AyABQUBrIhogAUHAA2oiBSkDACIlNwMAIAFBOGoiGyABQbgDaiIGKQMAIiY3AwAgAUEwaiIcIAFBsANqIgcpAwAiJzcDACABQShqIh0gAUGoA2oiCCkDACIoNwMAIAFBIGoiHiABQaADaiIJKQMAIik3AwAgAUGYDmoiAiABQZADaiIKKQMANwMAIAFBoA5qIgMgAUGYA2oiCykDADcDACABQagOaiIMICk3AwAgAUGwDmoiBCAoNwMAIAFBuA5qIg0gJzcDACABQcAOaiIOICY3AwAgAUHIDmoiDyAlNwMAIAEgASkDiAMiJTcDCCABICU3A5AOIAFBwAZqIhMgDykDADcDACABQbgGaiIQIA4pAwA3AwAgAUGwBmoiFCANKQMANwMAIAFBqAZqIhUgBCkDADcDACABQaAGaiIXIAwpAwA3AwAgAUGYBmoiGCADKQMANwMAIAFBkAZqIhkgAikDADcDACABIAEpA5AONwOIBiABQcAMaiATKQMANwMAIAFBuAxqIBApAwA3AwAgAUGwDGogFCkDADcDACABQagMaiAVKQMANwMAIAFBoAxqIBcpAwA3AwAgAUGYDGogGCkDADcDACABQZAMaiAZKQMANwMAIAEgASkDiAY3A4gMIBEgEhC9AyAaIAUpAwAiJTcDACAbIAYpAwAiJjcDACAcIAcpAwAiJzcDACAdIAgpAwAiKDcDACAeIAkpAwAiKTcDACACIAopAwA3AwAgAyALKQMANwMAIAwgKTcDACAEICg3AwAgDSAnNwMAIA4gJjcDACAPICU3AwAgASABKQOIAyIlNwMIIAEgJTcDkA4gEyAPKQMANwMAIBAgDikDADcDACAUIA0pAwA3AwAgFSAEKQMANwMAIBcgDCkDADcDACAYIAMpAwA3AwAgGSACKQMANwMAIAEgASkDkA43A4gGIAFBgA1qIBMpAwA3AwAgAUH4DGogECkDADcDACABQfAMaiAUKQMANwMAIAFB6AxqIBUpAwA3AwAgAUHgDGogFykDADcDACABQdgMaiAYKQMANwMAIAFB0AxqIBkpAwA3AwAgASABKQOIBjcDyAwgESASEL0DIBogBSkDACIlNwMAIBsgBikDACImNwMAIBwgBykDACInNwMAIB0gCCkDACIoNwMAIB4gCSkDACIpNwMAIAIgCikDADcDACADIAspAwA3AwAgDCApNwMAIAQgKDcDACANICc3AwAgDiAmNwMAIA8gJTcDACABIAEpA4gDIiU3AwggASAlNwOQDiATIA8pAwA3AwAgECAOKQMANwMAIBQgDSkDADcDACAVIAQpAwA3AwAgFyAMKQMANwMAIBggAykDADcDACAZIAIpAwA3AwAgASABKQOQDjcDiAYgAUHADWogEykDADcDACABQbgNaiAQKQMANwMAIAFBsA1qIBQpAwA3AwAgAUGoDWogFSkDADcDACABQaANaiAXKQMANwMAIAFBmA1qIBgpAwA3AwAgAUGQDWogGSkDADcDACABIAEpA4gGNwOIDUEARQRAIAFBiAlqIAFBiAxqQcAB/AoAAAsgASAAQYADajYCzA0gASAWNgLIDSABQQhqIiEgAUHIDWoiIhC9AyAPIBopAwAiJTcDACAOIBspAwAiJjcDACANIBwpAwAiJzcDACAEIB0pAwAiKDcDACAMIB4pAwAiKTcDACABQdgNaiIAIAFBEGoiIykDADcDACABQeANaiICIAFBGGoiJCkDADcDACABQegNaiIDICk3AwAgAUHwDWoiFiAoNwMAIAFB+A1qIhEgJzcDACABQYAOaiISICY3AwAgAUGIDmoiHyAlNwMAIAEgASkDCCIlNwOQDiABICU3A9ANIAUgHykDADcDACAGIBIpAwA3AwAgByARKQMANwMAIAggFikDADcDACAJIAMpAwA3AwAgCyACKQMANwMAIAogACkDADcDACABIAEpA9ANNwOIAyATIAUpAwA3AwAgECAGKQMANwMAIBQgBykDADcDACAVIAgpAwA3AwAgFyAJKQMANwMAIBggCykDADcDACAZIAopAwA3AwAgASABKQOIAzcDiAYgISAiEL0DIA8gGikDACIlNwMAIA4gGykDACImNwMAIA0gHCkDACInNwMAIAQgHSkDACIoNwMAIAwgHikDACIpNwMAIAAgIykDADcDACACICQpAwA3AwAgAyApNwMAIBYgKDcDACARICc3AwAgEiAmNwMAIB8gJTcDACABIAEpAwgiJTcDkA4gASAlNwPQDSAFIB8pAwA3AwAgBiASKQMANwMAIAcgESkDADcDACAIIBYpAwA3AwAgCSADKQMANwMAIAsgAikDADcDACAKIAApAwA3AwAgASABKQPQDTcDiAMgAUGAB2ogBSkDADcDACABQfgGaiAGKQMANwMAIAFB8AZqIAcpAwA3AwAgAUHoBmogCCkDADcDACABQeAGaiAJKQMANwMAIAFB2AZqIAspAwA3AwAgAUHQBmogCikDADcDACABIAEpA4gDNwPIBiAhICIQvQMgDyAaKQMAIiU3AwAgDiAbKQMAIiY3AwAgDSAcKQMAIic3AwAgBCAdKQMAIig3AwAgDCAeKQMAIik3AwAgACAjKQMANwMAIAIgJCkDADcDACADICk3AwAgFiAoNwMAIBEgJzcDACASICY3AwAgHyAlNwMAIAEgASkDCCIlNwOQDiABICU3A9ANIAUgHykDADcDACAGIBIpAwA3AwAgByARKQMANwMAIAggFikDADcDACAJIAMpAwA3AwAgCyACKQMANwMAIAogACkDADcDACABIAEpA9ANNwOIAyABQcAHaiAFKQMANwMAIAFBuAdqIAYpAwA3AwAgAUGwB2ogBykDADcDACABQagHaiAIKQMANwMAIAFBoAdqIAkpAwA3AwAgAUGYB2ogCykDADcDACABQZAHaiAKKQMANwMAIAEgASkDiAM3A4gHICBFBEAgAUGIDGogAUGIBmpBwAH8CgAACyAgRQRAIAFByApqIAFBiAxqQcAB/AoAAAsgAUEIaiABQYgJakGAA/wKAAAgAUHIB2ohBSABQcgGaiEGIAFByAVqIQcgAUHIAmohCCABQYgFaiEJIAFBiAJqIQogAUGIBGohCyABQYgBaiEMIAFByANqIQ0gAUHIAGohDiABQcgEaiEPIAFByAFqIRNBgLXCACkDACElQfi0wgApAwAhJkHwtMIAKQMAISdB6LTCACkDACEoQQAhAANAIAFBqA5qIhAgJTcDACABQaAOaiIUICY3AwAgAUGYDmoiFSAnNwMAIARCADcDACAEQQhqQgA3AwAgBEEQakIANwMAIARBGGpCADcDACABICg3A5AOIAZBAEGAAfwLACABQcAGaiABQcgOaikDADcDACABQbgGaiABQcAOaikDADcDACABQbAGaiABQbgOaikDADcDACABQagGaiABQbAOaikDADcDACABQaAGaiAQKQMANwMAIAFBmAZqIBQpAwA3AwAgAUGQBmogFSkDADcDACABIAEpA5AONwOIBiAFQQBBwAH8CwBBACIQRQRAIAFBiANqIAFBiAZqQYAD/AoAAAsCQAJAIAFBCGogAUGIA2oQpwRFDQAgDiANEKcERQ0AIAwgCxCnBEUNACATIA8QpwRFDQAgCiAJEKcERQ0AIAggBxCnBA0BCyABQYgGaiICIAFBCGoiAxBNIBBFBEAgAyACQYAD/AoAAAsgAEEBaiEADAELCyABQdAOaiQAIAAL8BoCEH8RfiMAQbADayIEJAACQAJAIAEoAgxFDQAgASgCBCIGIAEpAxgiFCADrSIVhULzytHLp4zZsvAAhSIWQhCJIBYgASkDECIYQuHklfPW7Nm87ACFfCIWhSIXIBRC7d6R85bM3LfkAIUiFCAYQvXKzYPXrNu38wCFfCIYQiCJfCIZIBVCgICAgICAgIAEhIUgFEINiSAYhSIUIBZ8IhUgFEIRiYUiFHwiFiAUQg2JhSIUIBdCFYkgGYUiGCAVQiCJQv8BhXwiFXwiFyAUQhGJhSIUQg2JIBQgFSAYQhCJhSIVIBZCIIl8IhZ8IhSFIhhCEYkgGCAVQhWJIBaFIhUgF0IgiXwiFnwiGIUiF0INiSAXIBVCEIkgFoUiFSAUQiCJfCIUfIUiFkIRiSAVQhWJIBSFIhRCEIkgFCAYQiCJfCIUhUIViYUgFCAWfCIUQiCIhSAUhSIUp3EhBSAUQhmIQv8Ag0KBgoSIkKDAgAF+IRUgASgCACIBQRBrIQgDQCABIAVqKQAAIhQgFYUiFkJ/hSAWQoGChIiQoMCAAX2DQoCBgoSIkKDAgH+DIhtQRQRAA0AgAyAIIBt6p0EDdiAFaiAGcSIJQQR0aygCAEYNBCAbQgF9IBuDIhtQRQ0ACwsgFCAUQgGGg0KAgYKEiJCgwIB/g1BFDQEgBSAHQQhqIgdqIAZxIQUMAAsAC0HknsEAEOgEAAsgAigCCCIIQQxNBEBBACEFIARBADYC5AEgBEKAgICAgAE3AtwBQQghAwJ/QQAgCEUNABpBACABQQAgCWtBBHRqIgFBBGsoAgAiBkUNABogAUEIaygCACIBIAZBDGxqIQ8gAUEMaiEGIAIoAgQhECAEQZACaiEJIARBiAJqIQsgBEGAAmohDCAEQfgBaiENIARB8AFqIQ4gCCEHA0AgCUIANwMAIAtCADcDACAMQgA3AwAgDUIANwMAIA5CADcDACAEQgA3A+gBIAEoAggiAgRAIAEoAgQiAyACQThsaiEKIANBOGohAQNAIAEhAgJAAkACQCAIIAMoAgAiAUsEQCAQIAFBMGxqIQUgA0EIaikDACEeIANBEGopAwAhHyADQRhqKQMAISAgA0EgaikDACEhQSghASADQShqKQMAISIgA0EwaikDACEjQgAhHEIAIRpCACEXQgAhFEIAIRVCACEdA0AgBEHwAGogASAFaikDACIWQgAgI0IAEMkDIARBgAFqIBZCACAiQgAQyQMgBEGQAWogFkIAICFCABDJAyAEQaABaiAWQgAgIEIAEMkDIARBsAFqIBZCACAfQgAQyQMgBEHAAWogFkIAIB5CABDJAyAEQeAAaiAEKQNwIhsgHXwiGEIAQgBC/f/z/8////mJfxDJAyAEQdAAaiAEKQNoIhZCAEKr1f7///+//7l/QgAQyQMgBEFAayAWQgBC///Piuv//9UeQgAQyQMgBEEwaiAWQgBCpOzDtY/UtJjnAEIAEMkDIARBIGogFkIAQr+llJzP8NK75ABCABDJAyAEQRBqIBZCAELX2a6a5PbpjcsAQgAQyQMgBCAWQgBCms3/y6O9xIAaQgAQyQMgBCkDCCAcIAQpA8ABIiR8IhYgBCkDuAEgGiAEKQOwASIcfCIZIBxUrXwgGSAEKQOoASAEKQOgASIaIBd8IhcgGlStfCAXIAQpA5gBIAQpA5ABIhogFHwiFCAaVK18IBQgFCAEKQOIASAEKQOAASIaIBV8IhUgGlStfCAVIAQpA3ggGCAbVK18fCIcIBVUrXx8IhVWrXx8IhQgF1StfHwiFyAZVK18fCIZIAQpAwB8IhsgGVStfCAbIAQpAxggFyAXIAQpAxB8IhpWrXwgGiAaIAQpAyggFCAUIAQpAyB8IhdWrXwgFyAXIAQpAzggFSAVIAQpAzB8IhRWrXwgFCAEKQNIIBwgBCkDQCIdfCIVIB1UrXwgFSAEKQNYIBggBCkDUCIcfCAcVK18fCIdIBVUrXx8IhUgFFStfHwiFFatfHwiF1atfHwiGiAbVK18IBYgGVatIAQpA8gBIBYgJFStfHx8IRwgAUEIayIBQXhHDQALIBxCms3/y6O9xIAaVg0CIBxCms3/y6O9xIAaUQ0BIBUhGCAUIRYgFyEZIBohGwwDCyABIAhByJ/BABDZAwALIBpC19mumuT26Y3LAFYNAAJAIBpC19mumuT26Y3LAFIEQCAVIRggFCEWIBchGSAaIRsMAQsgF0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhGyAXQr+llJzP8NK75ABSBEAgFSEYIBQhFiAXIRkMAQsgFEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhGSAUQqTsw7WP1LSY5wBSBEAgFSEYIBQhFgwBCyAVQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIRYgFUL//8+K6///1R5SBEAgFSEYDAELQv//z4rr///VHiEYIB1CqtX+////v/+5f1YNAQtCms3/y6O9xIAaIRwMAQsgFUL//8+K6///1R59IhYgHUKr1f7///+//7l/VK0iGX0hGCAUQqTsw7WP1LSY5wB9IhsgFUL//8+K6///1R5UIBYgGVRyrSIVfSEWIBdCv6WUnM/w0rvkAH0iHiAUQqTsw7WP1LSY5wBUIBUgG1ZyrSIUfSEZIBpC19mumuT26Y3LAH0iFSAXQr+llJzP8NK75ABUIBQgHlZyrSIUfSEbIBwgGkLX2a6a5PbpjcsAVCAUIBVWcq19QprN/8ujvcSAGn0hHCAdQtWqgYCAgMCAxgB8IR0LIAQgHTcDwAIgBCAYNwO4AiAEIBY3A7ACIAQgGTcDqAIgBCAbNwOgAiAEIBw3A5gCIARB+AJqIgEgBEGYAmoiAykDKCIVIARB6AFqIgUpAyh8IhY3AyggASADKQMgIhggBSkDIHwiFCAVIBZWrXwiFjcDICABIAMpAxgiFyAFKQMYfCIVIBQgGFQgFCAWVnKtfCIWNwMYIAEgAykDECIYIAUpAxB8IhQgFSAXVCAVIBZWcq18IhY3AxAgASADKQMIIhcgBSkDCHwiFSAUIBhUIBQgFlZyrXwiFjcDCCABIAMpAwAiGCAFKQMAfCIUIBUgF1QgFSAWVnKtfCIVNwMAIAEgFCAYVCAUIBVWcjoAMEKazf/Lo73EgBohFyAEKQOgAyEdIAQpA5gDIRggBCkDkAMhGSAEKQOIAyEaIAQpA4ADIRwgBCkD+AIiGyEUAkACQAJAIBtCms3/y6O9xIAaUg0AQtfZrprk9umNywAhFyAcIhRC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIRcgGiIUQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEXIBkiFEKk7MO1j9S0mOcAUg0AQv//z4rr///VHiEXIBgiFEL//8+K6///1R5SDQBCq9X+////v/+5fyEXIB0iFEKr1f7///+//7l/UQ0BCyAUIBdaDQAgHCEXIBohFCAZIRUgGCEWDAELIBhC///Piuv//9UefSIUIB1Cq9X+////v/+5f1StIhV9IRYgGUKk7MO1j9S0mOcAfSIXIBhC///Piuv//9UeVCAUIBVUcq0iFH0hFSAaQr+llJzP8NK75AB9IhggGUKk7MO1j9S0mOcAVCAUIBdWcq0iF30hFCAcQtfZrprk9umNywB9IhkgGkK/pZScz/DSu+QAVCAXIBhWcq0iGH0hFyAbIBxC19mumuT26Y3LAFQgGCAZVnKtfUKazf/Lo73EgBp9IRsgHULVqoGAgIDAgMYAfCEdCyAEIB03A5ACIAQgFjcDiAIgBCAVNwOAAiAEIBQ3A/gBIAQgFzcD8AEgBCAbNwPoASACQQBBOCACIApGIgUbaiEBIAIhAyAFRQ0ACyAEKALkASEFCyAEQfACaiICIAkpAwA3AwAgBEHoAmoiCiALKQMANwMAIARB4AJqIhEgDCkDADcDACAEQdgCaiISIA0pAwA3AwAgBEHQAmoiEyAOKQMANwMAIAQgBCkD6AE3A8gCIAQoAtwBIAVGBEAgBEHcAWpBuJ/BABCcAwsgBCgC4AEiAyAFQTBsaiIBIAQpA8gCNwMAIAFBCGogEykDADcDACABQRBqIBIpAwA3AwAgAUEYaiARKQMANwMAIAFBIGogCikDADcDACABQShqIAIpAwA3AwAgBCAFQQFqIgU2AuQBQQBBDCAHQQFrIgdFIAYiASAPRnIiAhsgAWohBiACRQ0ACyAEKALcAQshByAFQTBsIQEgBSEGAkACQAJAA0AgAUUNASAGQQFrIQYgAUEwayIBIANqQfjDwgBBMBDxA0UNAAsgBkEBaiIBIAUgASAFSRshBQwBC0HRzsUALQAAGkEwQQgQ1gQiAUUNASABQgA3AwAgAUEoakIANwMAIAFBIGpCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDAEF/IQZBASEFIAcEQCADIAdBMGwQ3wQLIAEhA0EBIQcLIAAgBjYCDCAAIAU2AgggACADNgIEIAAgBzYCACAEQbADaiQADwtBCEEwEP8EAAtB9J7BAEE0QaifwQAQ/gMAC9AUAg1/AX4jAEGwD2siAyQAQQBFBEAgAyABQeAA/AoAAAsgA0HgAGohASAERQRAIAEgAkHgAPwKAAALIARFBEAgA0HwAWpBAEHgAPwLAAsCQAJAAkACQAJAAkAgAyADQfABaiICEKYEBEAgASACEKYEDQELIANB8AFqIgJBAEHgAPwLACADIAIQpgQEQCABIAIQpgQNAQsgA0HwAWoQJiADQcAIaiADQbgCaikDADcDACADQbgIaiADQbACaikDADcDACADQbAIaiADQagCaikDADcDACADQagIaiADQaACaikDADcDACADQaAIaiADQZgCaikDADcDACADQdAIaiADQfgCaikDADcDACADQdgIaiADQYADaikDADcDACADQeAIaiADQYgDaikDADcDACADQegIaiADQZADaikDADcDACADQfAIaiADQZgDaikDADcDACADIAMpA5ACNwOYCCADIAMpA/ACNwPICCADQaAJaiADQcgDaikDADcDACADQZgJaiADQcADaikDADcDACADQZAJaiADQbgDaikDADcDACADQYgJaiADQbADaikDADcDACADQYAJaiADQagDaikDADcDACADIAMpA6ADNwP4CCADQagJaiIPIAEQXiADQZANaiADQQhqIgIpAwA3AwAgA0GYDWogA0EQaiIEKQMANwMAIANBoA1qIANBGGoiBSkDADcDACADQagNaiADQSBqIgcpAwA3AwAgA0GwDWogA0EoaiIJKQMANwMAIANBwA1qIANBOGoiCikDADcDACADQcgNaiADQUBrIgspAwA3AwAgA0HQDWogA0HIAGoiDCkDADcDACADQdgNaiADQdAAaiINKQMANwMAIANB4A1qIANB2ABqIg4pAwA3AwAgAyADKQMANwOIDSADIAMpAzA3A7gNIANByAtqIgggA0GIDWpB4AD8CgAAIANBqAxqIgYgCBBeIANBkA5qIAkpAwA3AwAgA0GIDmogBykDADcDACADQYAOaiAFKQMANwMAIANB+A1qIAQpAwA3AwAgA0HwDWogAikDADcDACADQaAOaiAKKQMANwMAIANBqA5qIAspAwA3AwAgA0GwDmogDCkDADcDACADQbgOaiANKQMANwMAIANBwA5qIA4pAwA3AwAgAyADKQMANwPoDSADIAMpAzA3A5gOIANB6ApqIgggBiADQegNahA/IANB0A5qIAIpAwA3AwAgA0HYDmogBCkDADcDACADQeAOaiAFKQMANwMAIANB6A5qIAcpAwA3AwAgA0HwDmogCSkDADcDACADQYAPaiAKKQMANwMAIANBiA9qIAspAwA3AwAgA0GQD2ogDCkDADcDACADQZgPaiANKQMANwMAIANBoA9qIA4pAwA3AwAgAyADKQMANwPIDiADIAMpAzA3A/gOIAYgA0GYCGogA0HIDmoQdyADQYgKaiICIAggBhDVASAGIAIgA0HICGoQ1QEgDyAGEKYEIAMoAvwHIgIEQCADKAKACCACQQJ0EN8ECwJAIAMoAvQBIgJFDQAgAiACQQxsQRNqQXhxIgVqQQlqIgJFDQAgAygC8AEgBWsgAhDfBAsgAygC8AQiAkGAgICAeEYgAkVyRQRAIAMoAvQEIAJBAnQQ3wQLDQAgA0HwAWoiAiADQeAA/AoAACADQcgOaiIGIAIQ9wMgAygCzA4hAiADKALIDiEEIAMoAtAOIgVBAkcNASACKAIEIQUgAigCACEHIAYgAkEIakHYAPwKAAAgBARAIAIgBEEwbBDfBAsgA0H4DWogA0HQDmopAwA3AwAgA0GADmogA0HYDmopAwA3AwAgA0GIDmogA0HgDmopAwA3AwAgA0GQDmogA0HoDmopAwA3AwAgA0GgDmogA0H4DmopAwA3AwAgA0GoDmogA0GAD2opAwA3AwAgA0GwDmogA0GID2opAwA3AwAgA0G4DmogA0GQD2opAwA3AwAgA0HADmogA0GYD2opAwA3AwAgAyAFNgLsDSADIAc2AugNIAMgAykDyA43A/ANIAMgAykD8A43A5gOIANB8AFqIgIgAUHgAPwKAAAgA0HIDmogAhD3AyADKALMDiEBIAMoAsgOIQIgAygC0A4iBEECRw0CIAEoAgQhBCABKAIAIQUgA0GIDWogAUEIakHYAPwKAAAgAgRAIAEgAkEwbBDfBAsgA0HYDmogA0GQDWoiASkDADcDACADQeAOaiADQZgNaikDADcDACADQegOaiADQaANaikDADcDACADQfAOaiADQagNaikDADcDACADQYAPaiADQbgNaikDADcDACADQYgPaiADQcANaikDADcDACADQZAPaiADQcgNaikDADcDACADQZgPaiADQdANaikDADcDACADQaAPaiADQdgNaikDADcDACADIAQ2AswOIAMgBTYCyA4gAyADKQOIDTcD0A4gAyADKQOwDTcD+A4gA0HIC2oiAiADQegNahCmASADQQA2ApANIANCgICAgBA3AogNIANB0P/AADYC9AEgA0KggICADjcC+AEgAyADQYgNaiIENgLwASACIANB8AFqIgIQxQINBSADQcgBaiABKAIANgIAIAMgAykCiA03A8ABIANBqAxqIgUgA0GYDmoQpgEgA0EANgKQDSADQoCAgIAQNwKIDSADQdD/wAA2AvQBIANCoICAgA43AvgBIAMgBDYC8AEgBSACEMUCDQUgA0HYAWogASgCADYCACADIAMpAogNNwPQASAEIANByA5qEKYBIANBADYC8AogA0KAgICAEDcC6AogA0HQ/8AANgL0ASADQqCAgIAONwL4ASADIANB6ApqIgE2AvABIAQgAhDFAg0FIANB6AFqIANB8ApqKAIANgIAIAMgAykC6Ao3A+ABIAIgA0H4DmoQpgEgA0EANgLQCCADQoCAgIAQNwLICCADQdD/wAA2AqwJIANCoICAgA43ArAJIAMgA0HICGo2AqgJIAIgA0GoCWoQxQINBSADQaAIaiADQdAIaigCADYCACADIAMpAsgINwOYCCADQQU2AowKIANB7IPBADYCiAogA0IENwKUCiADQoCAgIDABCIQIANBmAhqrYQ3A4ALIAMgECADQeABaq2ENwP4CiADIBAgA0HQAWqthDcD8AogAyAQIANBwAFqrYQ3A+gKIAMgATYCkAogAEEEaiADQYgKahDSAiADKAKYCCIBBEAgAygCnAggARDfBAsgAygC4AEiAQRAIAMoAuQBIAEQ3wQLIAMoAtABIgEEQCADKALUASABEN8ECyADKALAASIBBEAgAygCxAEgARDfBAsgAEEBNgIADAMLIABBCGogA0HAAfwKAAAgAEEANgIADAILIAMgBTYC0A4gAyACNgLMDiADIAQ2AsgODAILIAMgBDYC0A4gAyABNgLMDiADIAI2AsgODAELIANBsA9qJAAPC0GAi8AAQSsgA0HIDmpBrIvAAEGkjcAAEMoDAAtB+P/AAEE3IANBrw9qQej/wABB/IDBABDKAwALrxkCAX8bfiMAQYAGayIBJAAgAUHwBWpCA0IAQsau0OHB5sfvdEIAEMkDIAFB4AVqIAEpA/AFQn6DIgdCAEIAQv3/8//P///5iX8QyQMgAUHQBWogASkD6AUiAkIAQqvV/v///7//uX9CABDJAyABQcAFaiACQgBC///Piuv//9UeQgAQyQMgAUGwBWogAkIAQqTsw7WP1LSY5wBCABDJAyABQaAFaiACQgBCv6WUnM/w0rvkAEIAEMkDIAFBkAVqIAJCAELX2a6a5PbpjcsAQgAQyQMgAUGABWogAkIAQprN/8ujvcSAGkIAEMkDIAFB8ARqQgNCAELxicTO4NS5uwpCABDJAyABQeAEaiABKQPwBCIEIAEpA8AFIgUgASkD+AV8IgYgASkD2AUgASkD0AUiAiAHfCACVK18fCIDfCIHQgBCAEL9//P/z///+Yl/EMkDIAFB0ARqIAEpA+gEIgJCAEKr1f7///+//7l/QgAQyQMgAUHABGogAkIAQv//z4rr///VHkIAEMkDIAFBsARqIAJCAEKk7MO1j9S0mOcAQgAQyQMgAUGgBGogAkIAQr+llJzP8NK75ABCABDJAyABQZAEaiACQgBC19mumuT26Y3LAEIAEMkDIAFBgARqIAJCAEKazf/Lo73EgBpCABDJAyABQfADakIDQgBC1e3W5MTt0fKNf0IAEMkDIAFB4ANqIAEpA/ADIgggASkDwAQiCSABKQP4BCAEIAdWrXwiBCABKQOwBSIKIAMgBlStIAEpA8gFIAUgBlatfHx8IgV8IgN8IgYgASkD2AQgASkD0AQiAiAHfCACVK18fCILfCIHQgBCAEL9//P/z///+Yl/EMkDIAFB0ANqIAEpA+gDIgJCAEKr1f7///+//7l/QgAQyQMgAUHAA2ogAkIAQv//z4rr///VHkIAEMkDIAFBsANqIAJCAEKk7MO1j9S0mOcAQgAQyQMgAUGgA2ogAkIAQr+llJzP8NK75ABCABDJAyABQZADaiACQgBC19mumuT26Y3LAEIAEMkDIAFBgANqIAJCAEKazf/Lo73EgBpCABDJAyABQfACakIDQgBCwIf2nJmV4vXnAEIAEMkDIAFB4AJqIAEpA/ACIgwgASkDwAMiDSABKQP4AyAHIAhUrXwiCCADIARUrSIDIAEpA6AFIg4gASkDuAUgBSAKVK18fCIKfCIEIAEpA7AEfCIFIAYgC1atIAEpA8gEIAYgCVStfHx8Igl8Igt8IgYgASkD2AMgASkD0AMiAiAHfCACVK18fCIPfCIHQgBCAEL9//P/z///+Yl/EMkDIAFB0AJqIAEpA+gCIgJCAEKr1f7///+//7l/QgAQyQMgAUHAAmogAkIAQv//z4rr///VHkIAEMkDIAFBsAJqIAJCAEKk7MO1j9S0mOcAQgAQyQMgAUGgAmogAkIAQr+llJzP8NK75ABCABDJAyABQZACaiACQgBC19mumuT26Y3LAEIAEMkDIAFBgAJqIAJCAEKazf/Lo73EgBpCABDJAyABQfABakIDQgBCrarmqNvQz7yaf0IAEMkDIAFB4AFqIAEpA/ABIhAgASkDwAIiESABKQP4AiAHIAxUrXwiDCAIIAtWrSILIAMgBFatIhIgASkDkAUiEyABKQOoBSAKIA5UrXx8Igp8IgMgASkDoAR8IgggBSAJVq0gASkDuAQgBCAFVq18fHwiDnwiBCABKQOwA3wiBSAGIA9WrSABKQPIAyAGIA1UrXx8fCINfCIJfCIGIAEpA9gCIAEpA9ACIgIgB3wgAlStfHwiD3wiB0IAQgBC/f/z/8////mJfxDJAyABQdABaiABKQPoASICQgBCq9X+////v/+5f0IAEMkDIAFBwAFqIAJCAEL//8+K6///1R5CABDJAyABQbABaiACQgBCpOzDtY/UtJjnAEIAEMkDIAFBoAFqIAJCAEK/pZScz/DSu+QAQgAQyQMgAUGQAWogAkIAQtfZrprk9umNywBCABDJAyABQYABaiACQgBCms3/y6O9xIAaQgAQyQMgAUHwAGpCA0IAQqrHq5bZ/KPMEUIAEMkDIAFB4ABqIAEpA3AiFCABKQPAASIVIAEpA/gBIAcgEFStfCIQIAkgDFStIgwgBCALVK0iCyADIBJUrSISIAEpA4AFIhYgASkDmAUgCiATVK18fCITfCIJIAEpA5AEfCIKIAggDlatIAEpA6gEIAMgCFatfHx8Ig58IgMgASkDoAN8IgggBSANVq0gASkDuAMgBCAFVq18fHwiDXwiBCABKQOwAnwiBSAGIA9WrSABKQPIAiAGIBFUrXx8fCIPfCIRfCIGIAEpA9gBIAEpA9ABIgIgB3wgAlStfHwiF3wiB0IAQgBC/f/z/8////mJfxDJAyABQdAAaiABKQNoIgJCAEKr1f7///+//7l/QgAQyQMgAUFAayACQgBC///Piuv//9UeQgAQyQMgAUEwaiACQgBCpOzDtY/UtJjnAEIAEMkDIAFBIGogAkIAQr+llJzP8NK75ABCABDJAyABQRBqIAJCAELX2a6a5PbpjcsAQgAQyQMgASACQgBCms3/y6O9xIAaQgAQyQMCQCABKQMIIAEpAwAiGCABKQOIASABKQOAASIZIAEpA4gCIAEpA4ACIhogASkDiAMgASkDgAMiGyABKQOIBCABKQOABCIcIAkgElStIAEpA4gFIBMgFlStfHx8IgIgHFStfCACIAIgCiAOVq0gASkDmAQgCSAKVq18fHwiCVatfCAJIAMgC1StIgl8IgIgCVStfHwiCSAbVK18IAkgCSABKQOYAyACIAIgASkDkAN8IgpWrXwgCiAKIAggDVatIAEpA6gDIAMgCFatfHx8IgJWrXx8IgNWrXwgAyAEIAxUrSIIIAJ8IgIgCFStIgh8IgMgCFStfHwiCCAaVK18IAggASkDmAIgAyADIAEpA5ACfCIJVq18IAkgCSABKQOoAiACIAIgASkDoAJ8IgNWrXwgAyADIAUgD1atIAEpA7gCIAQgBVatfHx8IgJWrXx8IgRWrXx8IgUgCFStfCAFIAQgECARVq0iAyACfCICIANUrSIDfCIEIANUrSIDfCIFIANUrXx8IgMgGVStfCADIAEpA5gBIAUgBSABKQOQAXwiCFatfCAIIAEpA6gBIAQgBCABKQOgAXwiBVatfCAFIAUgASkDuAEgAiACIAEpA7ABfCIEVq18IAQgBCAGIBdWrSABKQPIASAGIBVUrXx8fCICVq18fCIGVq18fCIEIAhUrXx8IgUgA1StfCAFIAQgBiACIAEpA3ggByAUVK18IgN8IgkgA1StIgN8IgIgA1StIgN8IgYgA1StIgN8IgQgA1StfHwiAyAYVK18IAMgASkDGCAEIAQgASkDEHwiBFatfCAEIAEpAyggBiAGIAEpAyB8IghWrXwgCCAIIAEpAzggAiACIAEpAzB8IgZWrXwgBiAGIAEpA0ggCSABKQNAIgV8IgIgBVStfCACIAEpA1ggByABKQNQIgV8IAVUrXx8IgUgAlStfHwiBlatfHwiAlatfHwiByAEVK18fCIEIANUrXwiA0Kazf/Lo73EgBpSDQACQAJAIARC19mumuT26Y3LAFYNAEKazf/Lo73EgBohAyAEQtfZrprk9umNywBSDQIgB0K/pZScz/DSu+QAVg0AIAdCv6WUnM/w0rvkAFIEQELX2a6a5PbpjcsAIQQMAwsgAkKk7MO1j9S0mOcAVg0AIAJCpOzDtY/UtJjnAFINASAGQv//z4rr///VHlYNACAGQv//z4rr///VHlIEQEKk7MO1j9S0mOcAIQIMAgsgBUKr1f7///+//7l/Wg0AQv//z4rr///VHiEGQqTsw7WP1LSY5wAhAgwBC0J/QgAgBELX2a6a5PbpjcsAfSIEIAdCv6WUnM/w0rvkAFQgB0K/pZScz/DSu+QAfSIHIAJCpOzDtY/UtJjnAFQgAkKk7MO1j9S0mOcAfSICIAZC///Piuv//9UeVCAGQv//z4rr///VHn0iBiAFQqvV/v///7//uX9UrSIIVHKtIglUcq0iClRyrSILVBshAyAGIAh9IQYgAiAJfSECIAcgCn0hByAEIAt9IQQgBULVqoGAgIDAgMYAfCEFDAELQr+llJzP8NK75AAhB0LX2a6a5PbpjcsAIQQLIABCADcDMCAAIAU3AyggACAGNwMgIAAgAjcDGCAAIAc3AxAgACAENwMIIAAgAzcDACAAQThqQgA3AwAgAEFAa0IANwMAIABByABqQgA3AwAgAEHQAGpCADcDACAAQdgAakIANwMAIAFBgAZqJAALwBgCEn8QfiMAQdABayIEJAACQAJAAkAgASgCDCIDQX9HBEAgAigCDCIFQX9HDQELQdHOxQAtAAAaQTBBCBDWBCIFRQ0BIAVCADcDACAFQShqQgA3AwAgBUEgakIANwMAIAVBGGpCADcDACAFQRBqQgA3AwAgBUEIakIANwMAQX8hCkEBIQxBASEJDAILIAMgBWoiCkEBaiIJrUIwfiIVpyEDAkAgFUIgiKcgA0H4////B0tyDQACfyADRQRAQQghBUEADAELQdHOxQAtAAAaQQghBiADQQgQ1gQiBUUNASAJCyEMAkACQAJAAkAgCUECTwRAIApBB3EhBiAKQQFrQQdPDQEgBSEDDAILIAUhAyAJDQIMAwsgCkF4cSEIIAUhAwNAIANCADcDACADQShqQgA3AwAgA0EgakIANwMAIANBGGpCADcDACADQRBqQgA3AwAgA0EIakIANwMAIANBMGpCADcDACADQThqQgA3AwAgA0FAa0IANwMAIANByABqQgA3AwAgA0HQAGpCADcDACADQdgAakIANwMAIANB4ABqQgA3AwAgA0HoAGpCADcDACADQfAAakIANwMAIANB+ABqQgA3AwAgA0GAAWpCADcDACADQYgBakIANwMAIANBuAFqQgA3AwAgA0GwAWpCADcDACADQagBakIANwMAIANBoAFqQgA3AwAgA0GYAWpCADcDACADQZABakIANwMAIANBwAFqQgA3AwAgA0HIAWpCADcDACADQdABakIANwMAIANB2AFqQgA3AwAgA0HgAWpCADcDACADQegBakIANwMAIANB8AFqQgA3AwAgA0H4AWpCADcDACADQYACakIANwMAIANBiAJqQgA3AwAgA0GQAmpCADcDACADQZgCakIANwMAIANByAJqQgA3AwAgA0HAAmpCADcDACADQbgCakIANwMAIANBsAJqQgA3AwAgA0GoAmpCADcDACADQaACakIANwMAIANB+AJqQgA3AwAgA0HwAmpCADcDACADQegCakIANwMAIANB4AJqQgA3AwAgA0HYAmpCADcDACADQdACakIANwMAIANBgANqIQMgCEEIayIIDQALCyAGRQ0AA0AgA0IANwMAIANBKGpCADcDACADQSBqQgA3AwAgA0EYakIANwMAIANBEGpCADcDACADQQhqQgA3AwAgA0EwaiEDIAZBAWsiBg0ACwsgA0IANwMAIANBKGpCADcDACADQSBqQgA3AwAgA0EYakIANwMAIANBEGpCADcDACADQQhqQgA3AwALIAEoAggiB0UNAiACKAIIIgZFDQIgASgCBCIIIAdBMGxqIRAgAigCBCINQTBBACAGG2ohESANIAZBMGxqIRIgCEEwaiEDIAdBAWtB/////wBxIRMgBkEBa0H/////AHEhFANAIAghByADIQggDiIPQQFqIQ5BACEBIBEhAyANIQYDQCADIQICQAJAAkACQAJAAkACQCAJIAEgD2oiC0sEQCAHKQMAIR4gBykDCCEfIAcpAxAhICAHKQMYISEgBykDICEiIAcpAyghI0IAIRtBKCEDQgAhGEIAIRVCACEaQgAhFkIAIRkDQCAEQfAAaiADIAZqKQMAIhdCACAjQgAQyQMgBEGAAWogF0IAICJCABDJAyAEQZABaiAXQgAgIUIAEMkDIARBoAFqIBdCACAgQgAQyQMgBEGwAWogF0IAIB9CABDJAyAEQcABaiAXQgAgHkIAEMkDIARB4ABqIAQpA3AiHCAZfCIdQgBCAEL9//P/z///+Yl/EMkDIARB0ABqIAQpA2giF0IAQqvV/v///7//uX9CABDJAyAEQUBrIBdCAEL//8+K6///1R5CABDJAyAEQTBqIBdCAEKk7MO1j9S0mOcAQgAQyQMgBEEgaiAXQgBCv6WUnM/w0rvkAEIAEMkDIARBEGogF0IAQtfZrprk9umNywBCABDJAyAEIBdCAEKazf/Lo73EgBpCABDJAyAEKQMIIAQpA8ABIiQgG3wiFyAEKQO4ASAEKQOwASIZIBh8IhggGVStfCAYIBggBCkDqAEgBCkDoAEiGSAVfCIVIBlUrXwgFSAVIAQpA5gBIAQpA5ABIhkgGnwiGiAZVK18IBogBCkDiAEgBCkDgAEiGSAWfCIWIBlUrXwgFiAEKQN4IBwgHVatfHwiGSAWVK18fCIWIBpUrXx8IhVWrXx8IhhWrXx8IhwgBCkDAHwiGyAcVK18IBsgBCkDGCAYIBggBCkDEHwiGFatfCAYIAQpAyggFSAVIAQpAyB8IhVWrXwgFSAEKQM4IBYgFiAEKQMwfCIWVq18IBYgFiAEKQNIIBkgBCkDQCIZfCIaIBlUrXwgGiAEKQNYIB0gBCkDUCIdfCAdVK18fCIZIBpUrXx8IhZWrXx8IhogFVStfHwiFSAYVK18fCIYIBtUrXwgFyAcVq0gBCkDyAEgFyAkVK18fHwhGyADQQhrIgNBeEcNAAsgBSALQTBsaiEDIBtCms3/y6O9xIAaVg0GIBtCms3/y6O9xIAaUQ0BDAILIAsgCUGMyMIAENkDAAsgGELX2a6a5PbpjcsAVg0EIBhC19mumuT26Y3LAFIEQEKazf/Lo73EgBohGwwBCyAVQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEeIBVCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohGwwCCyAaQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEcIBpCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohGwwDCyAWQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIR0gFkL//8+K6///1R5RDQNCms3/y6O9xIAaIRsgFiEXDAULIBghHgsgFSEcCyAaIR0gFiEXDAILQv//z4rr///VHiEXIBlCqtX+////v/+5f1YNAEKazf/Lo73EgBohGwwBCyAWQv//z4rr///VHn0iHSAZQqvV/v///7//uX9UrSIcfSEXIBpCpOzDtY/UtJjnAH0iHiAWQv//z4rr///VHlQgHCAdVnKtIhZ9IR0gFUK/pZScz/DSu+QAfSIfIBpCpOzDtY/UtJjnAFQgFiAeVnKtIhZ9IRwgGELX2a6a5PbpjcsAfSIaIBVCv6WUnM/w0rvkAFQgFiAfVnKtIhV9IR4gGyAYQtfZrprk9umNywBUIBUgGlZyrX1Cms3/y6O9xIAafSEbIBlC1aqBgICAwIDGAHwhGQtCms3/y6O9xIAaIRYgAykDACAbfCAeIAMpAwh8IhUgHlQgFSAcIBwgAykDEHwiHFYgHCAcIB0gHSADKQMYfCIdViAdIBcgFyADKQMgfCIXViAXIBkgAykDKHwiGyAZVK18IhggF1RyrXwiGiAdVHKtfCIcVnKtfCIZIBVUcq18Ih4hFQJAAkACQCAeQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIRYgGSIVQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEWIBwiFUK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhFiAaIhVCpOzDtY/UtJjnAFINAEL//8+K6///1R4hFiAYIhVC///Piuv//9UeUg0AQqvV/v///7//uX8hFiAbIhVCq9X+////v/+5f1ENAQsgFSAWWg0AIBkhFSAcIRcgGiEWIBghHQwBCyAYQv//z4rr///VHn0iFSAbQqvV/v///7//uX9UrSIWfSEdIBpCpOzDtY/UtJjnAH0iFyAYQv//z4rr///VHlQgFSAWVHKtIhV9IRYgHEK/pZScz/DSu+QAfSIYIBpCpOzDtY/UtJjnAFQgFSAXVnKtIhV9IRcgGULX2a6a5PbpjcsAfSIaIBxCv6WUnM/w0rvkAFQgFSAYVnKtIhh9IRUgHiAZQtfZrprk9umNywBUIBggGlZyrX1Cms3/y6O9xIAafSEeIBtC1aqBgICAwIDGAHwhGwsgAyAbNwMoIAMgHTcDICADIBY3AxggAyAXNwMQIAMgFTcDCCADIB43AwAgAkEwQQAgAiASRxtqIQMgASAURiACIQYgAUEBaiEBRQ0ACyAIQTBBACAIIBBHG2ohAyAPIBNHDQALDAILIAYgA0H8x8IAEMgEAAtBCEEwEP8EAAsgACAKNgIMIAAgCTYCCCAAIAU2AgQgACAMNgIAIARB0AFqJAALmJ8DAokBfxR+IwBBkDlrIgckACAHIAE2AgwgB0EYaiACQQhqKAIANgIAIAcgAikCADcDECAHQShqIAJBFGooAgA2AgAgByACKQIMNwMgIAdBOGogAkEgaigCADYCACAHIAIpAhg3AzAgB0HIAGogAkEsaigCADYCACAHIAIpAiQ3A0AgB0HYAGogAkE4aigCADYCACAHIAIpAjA3A1AgB0HoAGogAkHEAGooAgA2AgAgByACKQI8NwNgIAdB+ABqIAJB0ABqKAIANgIAIAcgAikCSDcDcCAHQYgBaiACQdwAaigCADYCACAHIAIpAlQ3A4ABIAdBmAFqIAJB6ABqKAIANgIAIAcgAikCYDcDkAEgB0GoAWogAkH0AGooAgA2AgAgByACKQJsNwOgASAHQbgBaiACQYABaigCADYCACAHIAIpAng3A7ABIAdByAFqIAJBjAFqKAIANgIAIAcgAikChAE3A8ABAkACQAJAAkAgAQ4CAAECCyAHQZAGaiAHQRBqEPcCIAdBsAZqIgEgB0EgahD3AiAHQdAGaiAHQTBqEPcCIAdB8AZqIgIgB0FAaxD3AiAHQZAHaiAHQdAAahD3AiAHQbAHaiIDIAdB4ABqEPcCIAdBiAVqIAdByAZqKQMANwMAIAdBgAVqIAdBwAZqKQMANwMAIAdB+ARqIAdBuAZqKQMANwMAIAdB8ARqIAEpAwA3AwAgB0HoBGogB0GoBmopAwA3AwAgB0HgBGogB0GgBmopAwA3AwAgB0HYBGogB0GYBmopAwA3AwAgB0GYBWogB0HYBmopAwA3AwAgB0GgBWogB0HgBmopAwA3AwAgB0GoBWogB0HoBmopAwA3AwAgB0GwBWogAikDADcDACAHQbgFaiAHQfgGaikDADcDACAHQcAFaiAHQYAHaikDADcDACAHQcgFaiAHQYgHaikDADcDACAHIAcpA5AGNwPQBCAHIAcpA9AGNwOQBSAHQYgGaiAHQcgHaikDADcDACAHQYAGaiAHQcAHaikDADcDACAHQfgFaiAHQbgHaikDADcDACAHQfAFaiADKQMANwMAIAdB6AVqIAdBqAdqKQMANwMAIAdB4AVqIAdBoAdqKQMANwMAIAdB2AVqIAdBmAdqKQMANwMAIAcgBykDkAc3A9AFIAdBkAlqIAdB8ABqEPcCIAdBsAlqIgEgB0GAAWoQ9wIgB0HQCWogB0GQAWoQ9wIgB0HwCWoiAiAHQaABahD3AiAHQZAKaiAHQbABahD3AiAHQbAKaiIDIAdBwAFqEPcCIAdBiAhqIAdByAlqKQMANwMAIAdBgAhqIAdBwAlqKQMANwMAIAdB+AdqIAdBuAlqKQMANwMAIAdB8AdqIAEpAwA3AwAgB0HoB2ogB0GoCWopAwA3AwAgB0HgB2ogB0GgCWopAwA3AwAgB0HYB2ogB0GYCWopAwA3AwAgB0GYCGogB0HYCWopAwA3AwAgB0GgCGogB0HgCWopAwA3AwAgB0GoCGogB0HoCWopAwA3AwAgB0GwCGogAikDADcDACAHQbgIaiAHQfgJaikDADcDACAHQcAIaiAHQYAKaikDADcDACAHQcgIaiAHQYgKaikDADcDACAHIAcpA5AJNwPQByAHIAcpA9AJNwOQCCAHQYgJaiAHQcgKaikDADcDACAHQYAJaiAHQcAKaikDADcDACAHQfgIaiAHQbgKaikDADcDACAHQfAIaiADKQMANwMAIAdB6AhqIAdBqApqKQMANwMAIAdB4AhqIAdBoApqKQMANwMAIAdB2AhqIAdBmApqKQMANwMAIAcgBykDkAo3A9AIIAdB0AFqIhYgB0HQBGpBwAH8CgAAIAdBkANqIAdB0AdqQcAB/AoAACAHQZAnaiF6IwBB0C5rIgYkACAGQYgqakG0jcAAQcAAELcCIAZBgAdqIAYpA6AqIowBQgBCifWrnLWLv5ZzQgAQyQMgBkHAB2ogBikDmCoijgFCAEKJ9auctYu/lnNCABDJAyAGQYAIaiAGKQOQKiKNAUIAQon1q5y1i7+Wc0IAEMkDIAZBwAhqIAYpA4gqIpABQgBCifWrnLWLv5ZzQgAQyQMgBkHwBmogBikDgAcilAFCAEIAQonHmaSu8IHph38QyQMgBkHgBmogBikD+AYijwFCAELH+vPD7YKjkDxCABDJAyAGQdAGaiCPAUIAQo2Vx8OW0trAl39CABDJAyAGQfAFaiCPAUIAQt2whYzotpGouH9CABDJAyAGQZAFaiCPAUIAQqnAxomuzpOyMEIAEMkDIAZBkAdqIIwBQgBC+4OUop2ixvO1f0IAEMkDIAZB0AdqII4BQgBC+4OUop2ixvO1f0IAEMkDIAZBkAhqII0BQgBC+4OUop2ixvO1f0IAEMkDIAZB0AhqIJABQgBC+4OUop2ixvO1f0IAEMkDIAZBwAZqIAYpA9AGIpUBIAYpA4gHIpIBIAYpA8AHfCKTAXwilgEgBikD6AYglAEgBikD4AYijwF8II8BVK18fCKUASAGKQOQB3wikQFCAEIAQonHmaSu8IHph38QyQMgBkGwBmogBikDyAYijwFCAELH+vPD7YKjkDxCABDJAyAGQaAGaiCPAUIAQo2Vx8OW0trAl39CABDJAyAGQZAGaiCPAUIAQt2whYzotpGouH9CABDJAyAGQYAGaiCPAUIAQqnAxomuzpOyMEIAEMkDIAZBoAdqIIwBQgBC9v+F0vDfx9XHAEIAEMkDIAZB4AdqII4BQgBC9v+F0vDfx9XHAEIAEMkDIAZBoAhqII0BQgBC9v+F0vDfx9XHAEIAEMkDIAZB4AhqIJABQgBC9v+F0vDfx9XHAEIAEMkDIAZB4AVqIAYpA5gHIJEBIJQBVK18IpcBIAYpA9AHfCKYASAGKQPIByCSASCTAVatfCKZASAGKQOACHwikgEgBikD8AV8IpMBIJQBIJYBVK0gBikD2AYglQEglgFWrXx8fCKaAXwilgEgBikDoAZ8IpQBIAYpA7gGIAYpA7AGIo8BIJEBfCCPAVStfHwikQEgBikDoAd8IpUBQgBCAEKJx5mkrvCB6Yd/EMkDIAZB0AVqIAYpA+gFIo8BQgBCx/rzw+2Co5A8QgAQyQMgBkHABWogjwFCAEKNlcfDltLawJd/QgAQyQMgBkGwBWogjwFCAELdsIWM6LaRqLh/QgAQyQMgBkGgBWogjwFCAEKpwMaJrs6TsjBCABDJAyAGQbAHaiCMAUIAQp/q4NWc7qfsBkIAEMkDIAZB8AdqII4BQgBCn+rg1Zzup+wGQgAQyQMgBkGwCGogjQFCAEKf6uDVnO6n7AZCABDJAyAGQfAIaiCQAUIAQp/q4NWc7qfsBkIAEMkDIAZBgAVqIAYpA6gHIJEBIJUBVq18IpsBIAYpA+AHfCKOASAGKQOICCCSASCZAVStfCKZASAGKQPACHwijQEgBikDkAV8IpABIJMBIJoBVq0gBikD+AUgkgEgkwFWrXx8fCKPASAGKQOQCHwikgEglgEgmAFUrSAGKQPYByCXASCYAVatfHx8IpgBIAYpA5AGfCKTASCRASCUAVStIAYpA6gGIJQBIJYBVK18fHwilwF8IpYBIAYpA8AFfCKUASAGKQPYBSAGKQPQBSKMASCVAXwgjAFUrXx8IpEBIAYpA7AHfCKVAUIAQgBCiceZpK7wgemHfxDJAyAGQfAEaiAGKQOIBSKMAUIAQsf688PtgqOQPEIAEMkDIAZB4ARqIIwBQgBCjZXHw5bS2sCXf0IAEMkDIAZB0ARqIIwBQgBC3bCFjOi2kai4f0IAEMkDIAZBwARqIIwBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA8gEIAYpA+gIIAYpA+AIII8BIJABVK0gBikDmAUgjQEgkAFWrXx8IpABIAYpA8gIII0BIJkBVK18fCKMASCQAVSthCKQASAGKQPYCCCMASCMASAGKQPQCHwijQFWrXwgjQEgjQEgkgEgmAFWrSAGKQOYCCCPASCSAVatfHx8IowBVq18fCKNASCQAVStfCCNASCNASAGKQOIBiCMASCMASAGKQOABnwikAFWrXwgkAEgkAEgkwEglwFWrSAGKQOYBiCTASCYAVStfHx8IowBVq18fCKQAVatfCCQASAGKQOoCCCMASCMASAGKQOgCHwijQFWrXwgjQEgjQEgjgEglgFWrSAGKQPoByCOASCbAVStfHx8IowBVq18fCKOASCQAVStfCKSASAGKQPwCHwijQEgBikDqAUgjgEgjgEgBikDoAV8IpABVq18IJABIAYpA7gFIIwBIIwBIAYpA7AFfCKOAVatfCCOASCRASCUAVStIAYpA8gFIJQBIJYBVK18fHwijwEgjgFUrXx8IowBIJABVK18fCKQASAGKQO4CCCMASCMASAGKQOwCHwijgFWrXwgjgEgjgEgBikD+AcgBikDuAcgkQEglQFWrXwilgEgBikD8Ad8IowBIJYBVK18IIwBIIwBII8BfCKPAVatfHwijAFWrXx8IpYBIAYpA8AEfCKUASCWAVStfCCUASCUASAGKQPYBCCMASCMASAGKQPQBHwijgFWrXwgjgEgjgEgBikD6AQgjwEgjwEgBikD4AR8IowBVq18IIwBIAYpA/gEIAYpA/AEIo8BIJUBfCCPAVStfHwimAEgjAFUrXx8IowBVq18fCKOAVatfCCQASCWAVatII0BIJABVq0gBikD+AggjQEgkgFUrXx8fHwilAFCqcDGia7Ok7IwVg0AAkAglAFCqcDGia7Ok7IwUQRAII4BQt2whYzotpGouH9WDQIgjgFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhlAELII4BIZYBIIwBIZABDAILIIwBQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyGWASCMAUKNlcfDltLawJd/UgRAQqnAxomuzpOyMCGUASCMASGQAQwCC0KNlcfDltLawJd/IZABIJgBQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhlAEMAQsgjAFC8+q4vOmtpb/oAHwijQEgmAFCx/rzw+2Co5A8VK0ijwF9IZABII4BQqPP+vOXye7XxwB8IpEBIIwBQo2Vx8OW0trAl39UII0BII8BVHKtIowBfSGWASCUASCOAULdsIWM6LaRqLh/VCCMASCRAVZyrX1CqcDGia7Ok7IwfSGUASCYAULH+vPD7YKjkDx9IZgBCyAGQYgqakH0jcAAQcAAELcCIAZBwAJqIAYpA6AqIowBQgBCifWrnLWLv5ZzQgAQyQMgBkGAA2ogBikDmCoijgFCAEKJ9auctYu/lnNCABDJAyAGQcADaiAGKQOQKiKNAUIAQon1q5y1i7+Wc0IAEMkDIAZBgARqIAYpA4gqIo8BQgBCifWrnLWLv5ZzQgAQyQMgBkGwAmogBikDwAIikwFCAEIAQonHmaSu8IHph38QyQMgBkGgAmogBikDuAIikQFCAELH+vPD7YKjkDxCABDJAyAGQZACaiCRAUIAQo2Vx8OW0trAl39CABDJAyAGQbABaiCRAUIAQt2whYzotpGouH9CABDJAyAGQdAAaiCRAUIAQqnAxomuzpOyMEIAEMkDIAZB0AJqIIwBQgBC+4OUop2ixvO1f0IAEMkDIAZBkANqII4BQgBC+4OUop2ixvO1f0IAEMkDIAZB0ANqII0BQgBC+4OUop2ixvO1f0IAEMkDIAZBkARqII8BQgBC+4OUop2ixvO1f0IAEMkDIAZBgAJqIAYpA5ACIpsBIAYpA8gCIpkBIAYpA4ADfCKaAXwikgEgBikDqAIgkwEgBikDoAIikQF8IJEBVK18fCKTASAGKQPQAnwilQFCAEIAQonHmaSu8IHph38QyQMgBkHwAWogBikDiAIikQFCAELH+vPD7YKjkDxCABDJAyAGQeABaiCRAUIAQo2Vx8OW0trAl39CABDJAyAGQdABaiCRAUIAQt2whYzotpGouH9CABDJAyAGQcABaiCRAUIAQqnAxomuzpOyMEIAEMkDIAZB4AJqIIwBQgBC9v+F0vDfx9XHAEIAEMkDIAZBoANqII4BQgBC9v+F0vDfx9XHAEIAEMkDIAZB4ANqII0BQgBC9v+F0vDfx9XHAEIAEMkDIAZBoARqII8BQgBC9v+F0vDfx9XHAEIAEMkDIAZBoAFqIAYpA9gCIJMBIJUBVq18IpwBIAYpA5ADfCKXASAGKQOIAyCZASCaAVatfCKdASAGKQPAA3wimQEgBikDsAF8IpoBIJIBIJMBVq0gBikDmAIgkgEgmwFUrXx8fCKeAXwikgEgBikD4AF8IpMBIAYpA/gBIAYpA/ABIpEBIJUBfCCRAVStfHwilQEgBikD4AJ8IpsBQgBCAEKJx5mkrvCB6Yd/EMkDIAZBkAFqIAYpA6gBIpEBQgBCx/rzw+2Co5A8QgAQyQMgBkGAAWogkQFCAEKNlcfDltLawJd/QgAQyQMgBkHwAGogkQFCAELdsIWM6LaRqLh/QgAQyQMgBkHgAGogkQFCAEKpwMaJrs6TsjBCABDJAyAGQfACaiCMAUIAQp/q4NWc7qfsBkIAEMkDIAZBsANqII4BQgBCn+rg1Zzup+wGQgAQyQMgBkHwA2ogjQFCAEKf6uDVnO6n7AZCABDJAyAGQbAEaiCPAUIAQp/q4NWc7qfsBkIAEMkDIAZBQGsgBikD6AIglQEgmwFWrXwinwEgBikDoAN8Io4BIAYpA8gDIJkBIJ0BVK18Ip0BIAYpA4AEfCKNASAGKQNQfCKPASCaASCeAVatIAYpA7gBIJkBIJoBVq18fHwikQEgBikD0AN8IpkBIJIBIJcBVK0gBikDmAMglwEgnAFUrXx8fCKXASAGKQPQAXwimgEgkwEglQFWrSAGKQPoASCSASCTAVatfHx8IpwBfCKSASAGKQOAAXwikwEgBikDmAEgBikDkAEijAEgmwF8IIwBVK18fCKVASAGKQPwAnwimwFCAEIAQonHmaSu8IHph38QyQMgBkEwaiAGKQNIIowBQgBCx/rzw+2Co5A8QgAQyQMgBkEgaiCMAUIAQo2Vx8OW0trAl39CABDJAyAGQRBqIIwBQgBC3bCFjOi2kai4f0IAEMkDIAYgjAFCAEKpwMaJrs6TsjBCABDJAwJAAkAgBikDCCAGKQOoBCAGKQOgBCCPASCRAVatIAYpA1ggjQEgjwFWrXx8Io8BIAYpA4gEII0BIJ0BVK18fCKMASCPAVSthCKPASAGKQOYBCCMASCMASAGKQOQBHwijQFWrXwgjQEgjQEglwEgmQFUrSAGKQPYAyCRASCZAVatfHx8IowBVq18fCKNASCPAVStfCCNASCNASAGKQPIASCMASCMASAGKQPAAXwijwFWrXwgjwEgjwEgmgEgnAFWrSAGKQPYASCXASCaAVatfHx8IowBVq18fCKPAVatfCCPASAGKQPoAyCMASCMASAGKQPgA3wijQFWrXwgjQEgjQEgjgEgkgFWrSAGKQOoAyCOASCfAVStfHx8IowBVq18fCKOASCPAVStfCKXASAGKQOwBHwijwEgBikDaCCOASCOASAGKQNgfCKNAVatfCCNASAGKQN4IIwBIIwBIAYpA3B8Io4BVq18II4BIJMBIJUBVq0gBikDiAEgkgEgkwFWrXx8fCKRASCOAVStfHwijAEgjQFUrXx8Io4BIAYpA/gDIIwBIIwBIAYpA/ADfCKNAVatfCCNASCNASAGKQO4AyAGKQP4AiCVASCbAVatfCKSASAGKQOwA3wijAEgkgFUrXwgjAEgjAEgkQF8IpEBVq18fCKMAVatfHwikwEgBikDAHwilQEgkwFUrXwglQEglQEgBikDGCCMASCMASAGKQMQfCKNAVatfCCNASCNASAGKQMoIJEBIJEBIAYpAyB8IowBVq18IIwBIAYpAzggBikDMCKRASCbAXwgkQFUrXx8IpIBIIwBVK18fCKMAVatfHwijQFWrXwgjgEgkwFWrSCOASCPAVStIAYpA7gEII8BIJcBVK18fHx8IpEBQqnAxomuzpOyMFYNAAJAIJEBQqnAxomuzpOyMFEEQCCNAULdsIWM6LaRqLh/Vg0CII0BQt2whYzotpGouH9SBEAgjAEhjgEgjQEhjwFCqcDGia7Ok7IwIZEBDAQLIIwBQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyGPASCMAUKNlcfDltLawJd/UQ0BIIwBIY4BQqnAxomuzpOyMCGRAQwDCyCMASGOASCNASGPAQwCC0KNlcfDltLawJd/IY4BIJIBQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhkQEMAQsgjAFC8+q4vOmtpb/oAHwijwEgkgFCx/rzw+2Co5A8VK0ikwF9IY4BII0BQqPP+vOXye7XxwB8IpUBIIwBQo2Vx8OW0trAl39UII8BIJMBVHKtIowBfSGPASCRASCNAULdsIWM6LaRqLh/VCCMASCVAVZyrX1CqcDGia7Ok7IwfSGRASCSAULH+vPD7YKjkDx9IZIBCyAGQYgJakEAQYAB/AsAIAZByApqQQBBwAH8CwAgBiCSATcDwAogBiCOATcDuAogBiCPATcDsAogBiCRATcDqAogBiCYATcDoAogBiCQATcDmAogBiCWATcDkAogBiCUATcDiAogBiAWNgKIHiAGIBZBwAFqIiE2AoweIAZBiCdqIgoiGSAGQYgeaiIeEL0DIAZBwCRqIiQgBkHAJ2oiASkDACKMATcDACAGQbgkaiInIAZBuCdqIgIpAwAijgE3AwAgBkGwJGoiKCAGQbAnaiIDKQMAIo0BNwMAIAZBqCRqIikgBkGoJ2oiBCkDACKQATcDACAGQZAhaiIiIAZBkCdqIgUpAwA3AwAgBkGYIWoiIyAGQZgnaiIRKQMANwMAIAZBoCFqIiUgBkGgJ2oiCCkDADcDACAGQaghaiIPIJABNwMAIAZBsCFqIhQgjQE3AwAgBkG4IWoiCyCOATcDACAGQcAhaiIJIIwBNwMAIAYgBikDiCcijAE3A4gkIAYgjAE3A4ghIAZBwCpqIhcgCSkDADcDACAGQbgqaiIYIAspAwA3AwAgBkGwKmoiGyAUKQMANwMAIAZBqCpqIhwgDykDADcDACAGQaAqaiIdICUpAwA3AwAgBkGYKmoiHyAjKQMANwMAIAZBkCpqIiAgIikDADcDACAGIAYpA4ghNwOIKiAGQcgtaiAXKQMANwMAIAZBwC1qIBgpAwA3AwAgBkG4LWogGykDADcDACAGQbAtaiAcKQMANwMAIAZBqC1qIB0pAwA3AwAgBkGgLWogHykDADcDACAGQZgtaiAgKQMANwMAIAYgBikDiCo3A5AtIBkgHhC9AyAkIAEpAwAijAE3AwAgJyACKQMAIo4BNwMAICggAykDACKNATcDACApIAQpAwAikAE3AwAgIiAFKQMANwMAICMgESkDADcDACAlIAgpAwA3AwAgDyCQATcDACAUII0BNwMAIAsgjgE3AwAgCSCMATcDACAGIAYpA4gnIowBNwOIJCAGIIwBNwOIISAXIAkpAwA3AwAgGCALKQMANwMAIBsgFCkDADcDACAcIA8pAwA3AwAgHSAlKQMANwMAIB8gIykDADcDACAgICIpAwA3AwAgBiAGKQOIITcDiCogBkGILmogFykDADcDACAGQYAuaiAYKQMANwMAIAZB+C1qIBspAwA3AwAgBkHwLWogHCkDADcDACAGQegtaiAdKQMANwMAIAZB4C1qIB8pAwA3AwAgBkHYLWogICkDADcDACAGIAYpA4gqNwPQLSAZIB4QvQMgJCABKQMAIowBNwMAICcgAikDACKOATcDACAoIAMpAwAijQE3AwAgKSAEKQMAIpABNwMAICIgBSkDADcDACAjIBEpAwA3AwAgJSAIKQMANwMAIA8gkAE3AwAgFCCNATcDACALII4BNwMAIAkgjAE3AwAgBiAGKQOIJyKMATcDiCQgBiCMATcDiCEgFyAJKQMANwMAIBggCykDADcDACAbIBQpAwA3AwAgHCAPKQMANwMAIB0gJSkDADcDACAfICMpAwA3AwAgICAiKQMANwMAIAYgBikDiCE3A4gqIAZByC5qIBcpAwA3AwAgBkHALmogGCkDADcDACAGQbguaiAbKQMANwMAIAZBsC5qIBwpAwA3AwAgBkGoLmogHSkDADcDACAGQaAuaiAfKQMANwMAIAZBmC5qICApAwA3AwAgBiAGKQOIKjcDkC4gBkGIGGoiNCAGQZAtaiIvQcAB/AoAACAGIBZBgANqNgKMGyAGICE2AogbIAZBiCRqInsiLSAGQYgbaiIwEL0DIAkgJCkDACKMATcDACALICcpAwAijgE3AwAgFCAoKQMAIo0BNwMAIA8gKSkDACKQATcDACAGQZAeaiIWIAZBkCRqIjEpAwA3AwAgBkGYHmoiGSAGQZgkaiIyKQMANwMAIAZBoB5qIh4gBkGgJGoiMykDADcDACAGQageaiIhIJABNwMAIAZBsB5qIiYgjQE3AwAgBkG4HmoiKiCOATcDACAGQcAeaiIsIIwBNwMAIAYgBikDiCQijAE3A4ghIAYgjAE3A4geIAEgLCkDADcDACACICopAwA3AwAgAyAmKQMANwMAIAQgISkDADcDACAIIB4pAwA3AwAgESAZKQMANwMAIAUgFikDADcDACAGIAYpA4geNwOIJyAXIAEpAwA3AwAgGCACKQMANwMAIBsgAykDADcDACAcIAQpAwA3AwAgHSAIKQMANwMAIB8gESkDADcDACAgIAUpAwA3AwAgBiAGKQOIJzcDiCogLSAwEL0DIAkgJCkDACKMATcDACALICcpAwAijgE3AwAgFCAoKQMAIo0BNwMAIA8gKSkDACKQATcDACAWIDEpAwA3AwAgGSAyKQMANwMAIB4gMykDADcDACAhIJABNwMAICYgjQE3AwAgKiCOATcDACAsIIwBNwMAIAYgBikDiCQijAE3A4ghIAYgjAE3A4geIAEgLCkDADcDACACICopAwA3AwAgAyAmKQMANwMAIAQgISkDADcDACAIIB4pAwA3AwAgESAZKQMANwMAIAUgFikDADcDACAGIAYpA4geNwOIJyAGQYAraiABKQMANwMAIAZB+CpqIAIpAwA3AwAgBkHwKmogAykDADcDACAGQegqaiAEKQMANwMAIAZB4CpqIAgpAwA3AwAgBkHYKmogESkDADcDACAGQdAqaiAFKQMANwMAIAYgBikDiCc3A8gqIC0gMBC9AyAJICQpAwAijAE3AwAgCyAnKQMAIo4BNwMAIBQgKCkDACKNATcDACAPICkpAwAikAE3AwAgFiAxKQMANwMAIBkgMikDADcDACAeIDMpAwA3AwAgISCQATcDACAmII0BNwMAICogjgE3AwAgLCCMATcDACAGIAYpA4gkIowBNwOIISAGIIwBNwOIHiABICwpAwA3AwAgAiAqKQMANwMAIAMgJikDADcDACAEICEpAwA3AwAgCCAeKQMANwMAIBEgGSkDADcDACAFIBYpAwA3AwAgBiAGKQOIHjcDiCcgBkHAK2ogASkDADcDACAGQbgraiACKQMANwMAIAZBsCtqIAMpAwA3AwAgBkGoK2ogBCkDADcDACAGQaAraiAIKQMANwMAIAZBmCtqIBEpAwA3AwAgBkGQK2ogBSkDADcDACAGIAYpA4gnNwOIKyAvIAZBiCpqInxBwAH8CgAAIAZByBlqIC9BwAH8CgAAIAZBiAxqIn0gNEGAA/wKAAAgCEGAtcIAKQMAIowBNwMAIBFB+LTCACkDACKOATcDACAFQfC0wgApAwAijQE3AwAgBEIANwMAIANCADcDACACQgA3AwAgAUIANwMAIAZB6LTCACkDACKQATcDiCcgBkHIKmoiJEEAQYAB/AsAIBcgASkDADcDACAYIAIpAwA3AwAgGyADKQMANwMAIBwgBCkDADcDACAdIAgpAwA3AwAgHyARKQMANwMAICAgBSkDADcDACAGIAYpA4gnNwOIKiAGQcgraiIBQQBBwAH8CwAgBkGID2ogfCICQYAD/AoAACB7IgMgfRAeICUgjAE3AwAgIyCOATcDACAiII0BNwMAIA9CADcDACAUQgA3AwAgC0IANwMAIAlCADcDACAGIJABNwOIISAkQQBBgAH8CwAgFyAJKQMANwMAIBggCykDADcDACAbIBQpAwA3AwAgHCAPKQMANwMAIB0gJSkDADcDACAfICMpAwA3AwAgICAiKQMANwMAIAYgBikDiCE3A4gqIAFBAEHAAfwLACAKIgEgAkGAA/wKAAACQAJAIAMgARCnBEUNACAGQcgkaiAGQcgnahCnBEUNACAGQYglaiAGQYgoahCnBEUNACAGQcglaiAGQcgoahCnBEUNACAGQYgmaiAGQYgpahCnBEUNACAGQcgmaiAGQcgpahCnBA0BCyAGQYgqaiIBIAZBiAxqIgIgBkGICWoiAxD2ASACIAFBgAP8CgAAIAEgBkGID2oiBCADEPYBIAQgAUGAA/wKAAAgBkGIJGoiAyACEB4gBkGgIWoiAkGAtcIAKQMANwMAIAZBmCFqIgRB+LTCACkDADcDACAGQZAhaiIFQfC0wgApAwA3AwAgBkGoIWoiEUIANwMAIAZBsCFqIghCADcDACAGQbghaiIPQgA3AwAgBkHAIWoiFEIANwMAIAZB6LTCACkDADcDiCEgBkHIKmpBAEGAAfwLACAGQcAqaiAUKQMANwMAIAZBuCpqIA8pAwA3AwAgBkGwKmogCCkDADcDACAGQagqaiARKQMANwMAIAZBoCpqIAIpAwA3AwAgBkGYKmogBCkDADcDACAGQZAqaiAFKQMANwMAIAYgBikDiCE3A4gqIAZByCtqQQBBwAH8CwAgBkGIJ2oiAiABQYAD/AoAAAJAIAMgAhCnBEUNACAGQcgkaiAGQcgnahCnBEUNACAGQYglaiAGQYgoahCnBEUNACAGQcglaiAGQcgoahCnBEUNACAGQYgmaiAGQYgpahCnBEUNACAGQcgmaiAGQcgpahCnBA0BCyAGQYgqaiIBIAZBiAxqIgIgBkGICWoiAxD2ASACIAFBgAP8CgAAIAEgBkGID2oiAiADEPYBIAIgAUGAA/wKAAALIwBBwP4IayICJAAgAiAGQYgMaiKJASIeNgKA6wggAiAeQcABaiIqNgKE6wggAkGA9AhqIgoiISACQYDrCGoieyImEL0DIAJBuPEIaiIlIAJBuPQIaiIBKQMAIowBNwMAIAJBsPEIaiIkIAJBsPQIaiIDKQMAIo4BNwMAIAJBqPEIaiInIAJBqPQIaiIEKQMAIo0BNwMAIAJBoPEIaiIoIAJBoPQIaiIFKQMAIpABNwMAIAJBmPEIaiIpIAJBmPQIaiIRKQMAIo8BNwMAIAJBiO4IaiIWIAJBiPQIaiIIKQMANwMAIAJBkO4IaiIZIAJBkPQIaiIPKQMANwMAIAJBmO4IaiIUII8BNwMAIAJBoO4IaiILIJABNwMAIAJBqO4IaiIJII0BNwMAIAJBsO4IaiIXII4BNwMAIAJBuO4IaiIYIIwBNwMAIAIgAikDgPQIIowBNwOA8QggAiCMATcDgO4IIAJBuPcIaiIbIBgpAwA3AwAgAkGw9whqIhwgFykDADcDACACQaj3CGoiHSAJKQMANwMAIAJBoPcIaiIfIAspAwA3AwAgAkGY9whqIiAgFCkDADcDACACQZD3CGoiIiAZKQMANwMAIAJBiPcIaiIjIBYpAwA3AwAgAiACKQOA7gg3A4D3CCACQbj9CGogGykDADcDACACQbD9CGogHCkDADcDACACQaj9CGogHSkDADcDACACQaD9CGogHykDADcDACACQZj9CGogICkDADcDACACQZD9CGogIikDADcDACACQYj9CGogIykDADcDACACIAIpA4D3CDcDgP0IICEgJhC9AyAlIAEpAwAijAE3AwAgJCADKQMAIo4BNwMAICcgBCkDACKNATcDACAoIAUpAwAikAE3AwAgKSARKQMAIo8BNwMAIBYgCCkDADcDACAZIA8pAwA3AwAgFCCPATcDACALIJABNwMAIAkgjQE3AwAgFyCOATcDACAYIIwBNwMAIAIgAikDgPQIIowBNwOA8QggAiCMATcDgO4IIBsgGCkDADcDACAcIBcpAwA3AwAgHSAJKQMANwMAIB8gCykDADcDACAgIBQpAwA3AwAgIiAZKQMANwMAICMgFikDADcDACACIAIpA4DuCDcDgPcIIAJB+P0IaiAbKQMANwMAIAJB8P0IaiAcKQMANwMAIAJB6P0IaiAdKQMANwMAIAJB4P0IaiAfKQMANwMAIAJB2P0IaiAgKQMANwMAIAJB0P0IaiAiKQMANwMAIAJByP0IaiAjKQMANwMAIAIgAikDgPcINwPA/QggISAmEL0DICUgASkDACKMATcDACAkIAMpAwAijgE3AwAgJyAEKQMAIo0BNwMAICggBSkDACKQATcDACApIBEpAwAijwE3AwAgFiAIKQMANwMAIBkgDykDADcDACAUII8BNwMAIAsgkAE3AwAgCSCNATcDACAXII4BNwMAIBggjAE3AwAgAiACKQOA9AgijAE3A4DxCCACIIwBNwOA7gggGyAYKQMANwMAIBwgFykDADcDACAdIAkpAwA3AwAgHyALKQMANwMAICAgFCkDADcDACAiIBkpAwA3AwAgIyAWKQMANwMAIAIgAikDgO4INwOA9wggAkG4/ghqIBspAwA3AwAgAkGw/ghqIBwpAwA3AwAgAkGo/ghqIB0pAwA3AwAgAkGg/ghqIB8pAwA3AwAgAkGY/ghqICApAwA3AwAgAkGQ/ghqICIpAwA3AwAgAkGI/ghqICMpAwA3AwAgAiACKQOA9wg3A4D+CCACQYD6CGoiMyACQYD9CGoiL0HAAfwKAAAgAiAeQYADajYChOgIIAIgKjYCgOgIIAJBgPEIaiJ8Ii0gAkGA6AhqIn0iMBC9AyAYICUpAwAijAE3AwAgFyAkKQMAIo4BNwMAIAkgJykDACKNATcDACALICgpAwAikAE3AwAgFCApKQMAIo8BNwMAIAJBiOsIaiIWIAJBiPEIaiIxKQMANwMAIAJBkOsIaiIZIAJBkPEIaiIyKQMANwMAIAJBmOsIaiIeII8BNwMAIAJBoOsIaiIhIJABNwMAIAJBqOsIaiImII0BNwMAIAJBsOsIaiIqII4BNwMAIAJBuOsIaiIsIIwBNwMAIAIgAikDgPEIIowBNwOA7gggAiCMATcDgOsIIAEgLCkDADcDACADICopAwA3AwAgBCAmKQMANwMAIAUgISkDADcDACARIB4pAwA3AwAgDyAZKQMANwMAIAggFikDADcDACACIAIpA4DrCDcDgPQIIBsgASkDADcDACAcIAMpAwA3AwAgHSAEKQMANwMAIB8gBSkDADcDACAgIBEpAwA3AwAgIiAPKQMANwMAICMgCCkDADcDACACIAIpA4D0CDcDgPcIIC0gMBC9AyAYICUpAwAijAE3AwAgFyAkKQMAIo4BNwMAIAkgJykDACKNATcDACALICgpAwAikAE3AwAgFCApKQMAIo8BNwMAIBYgMSkDADcDACAZIDIpAwA3AwAgHiCPATcDACAhIJABNwMAICYgjQE3AwAgKiCOATcDACAsIIwBNwMAIAIgAikDgPEIIowBNwOA7gggAiCMATcDgOsIIAEgLCkDADcDACADICopAwA3AwAgBCAmKQMANwMAIAUgISkDADcDACARIB4pAwA3AwAgDyAZKQMANwMAIAggFikDADcDACACIAIpA4DrCDcDgPQIIAJB+PcIaiABKQMANwMAIAJB8PcIaiADKQMANwMAIAJB6PcIaiAEKQMANwMAIAJB4PcIaiAFKQMANwMAIAJB2PcIaiARKQMANwMAIAJB0PcIaiAPKQMANwMAIAJByPcIaiAIKQMANwMAIAIgAikDgPQINwPA9wggLSAwEL0DIBggJSkDACKMATcDACAXICQpAwAijgE3AwAgCSAnKQMAIo0BNwMAIAsgKCkDACKQATcDACAUICkpAwAijwE3AwAgFiAxKQMANwMAIBkgMikDADcDACAeII8BNwMAICEgkAE3AwAgJiCNATcDACAqII4BNwMAICwgjAE3AwAgAiACKQOA8QgijAE3A4DuCCACIIwBNwOA6wggASAsKQMANwMAIAMgKikDADcDACAEICYpAwA3AwAgBSAhKQMANwMAIBEgHikDADcDACAPIBkpAwA3AwAgCCAWKQMANwMAIAIgAikDgOsINwOA9AggAkG4+AhqIAEpAwA3AwAgAkGw+AhqIAMpAwA3AwAgAkGo+AhqIAQpAwA3AwAgAkGg+AhqIAUpAwA3AwAgAkGY+AhqIBEpAwA3AwAgAkGQ+AhqIA8pAwA3AwAgAkGI+AhqIAgpAwA3AwAgAiACKQOA9Ag3A4D4CCAvIAJBgPcIaiIFQcAB/AoAACACQcD7CGogL0HAAfwKAAAgAiAzQYAD/AoAACACQYAGaiIDIAJBARB0IAJBgANqIgEgA0GAA/wKAAAgAkGACWoiDyACIAEQ9gEgAkGADGoiAyACIA8Q9gEgAkGAD2oifiACIAMQ9gEgAkGAEmoiLSABIH4Q9gEgAkGAFWoiGyABIC0Q9gEgAkGAGGoiIyABIBsQ9gEgAkGAG2oifyABICMQ9gEgAkGAHmoiJSABIH8Q9gEgAkGAIWoiHCABICUQ9gEgAkGAJGoiQSABIBwQ9gEgAkGAJ2oiQiABIEEQ9gEgAkGAKmoiMCABIEIQ9gEgAkGALWoiUyABIDAQ9gEgAkGAMGoiJCABIFMQ9gEgAkGAM2oiJyABICQQ9gEgAkGANmoiVCABICcQ9gEgAkGAOWoiOCABIFQQ9gEgAkGAPGoiHSABIDgQ9gEgAkGAP2oiDCABIB0Q9gEgAkGAwgBqIkMgASAMEPYBIAJBgMUAaiJpIAEgQxD2ASACQYDIAGoiSyABIGkQ9gEgAkGAywBqIhQgASBLEPYBIAJBgM4AaiJVIAEgFBD2ASACQYDRAGoiRCABIFUQ9gEgAkGA1ABqIkUgASBEEPYBIAJBgNcAaiKAASABIEUQ9gEgAkGA2gBqIiggASCAARD2ASACQYDdAGoiViABICgQ9gEgAkGA4ABqIjEgASBWEPYBIAJBgOMAaiJqIAEgMRD2ASACQYDmAGoiayABIGoQ9gEgAkGA6QBqImwgASBrEPYBIAJBgOwAaiIrIAEgbBD2ASACQYDvAGoibSABICsQ9gEgAkGA8gBqIjIgASBtEPYBIAJBgPUAaiIfIAEgMhD2ASACQYD4AGoiiAEgASAfEPYBIAJBgPsAaiIpIAEgiAEQ9gEgAkGA/gBqIm4gASApEPYBIAJBgIEBaiJGIAEgbhD2ASACQYCEAWoiFiABIEYQ9gEgAkGAhwFqIjMgASAWEPYBIAJBgIoBaiJvIAEgMxD2ASACQYCNAWoigQEgASBvEPYBIAJBgJABaiIZIAEggQEQ9gEgAkGAkwFqIjQgASAZEPYBIAJBgJYBaiJwIAEgNBD2ASACQYCZAWoiESABIHAQ9gEgAkGAnAFqInEgASAREPYBIAJBgJ8BaiJyIAEgcRD2ASACQYCiAWoiGiABIHIQ9gEgAkGApQFqInMgASAaEPYBIAJBgKgBaiILIAEgcxD2ASACQYCrAWoiNSABIAsQ9gEgAkGArgFqIh4gASA1EPYBIAJBgLEBaiJ0IAEgHhD2ASACQYC0AWoiVyABIHQQ9gEgAkGAtwFqIlggASBXEPYBIAJBgLoBaiJZIAEgWBD2ASACQYC9AWoiRyABIFkQ9gEgAkGAwAFqIoIBIAEgRxD2ASACQYDDAWoiNiABIIIBEPYBIAJBgMYBaiJJIAEgNhD2ASACQYDJAWoidSABIEkQ9gEgAkGAzAFqIkogASB1EPYBIAJBgM8BaiKDASABIEoQ9gEgAkGA0gFqIlogASCDARD2ASACQYDVAWoiCSABIFoQ9gEgAkGA2AFqIg4gASAJEPYBIAJBgNsBaiJbIAEgDhD2ASACQYDeAWoiDSABIFsQ9gEgAkGA4QFqIlwgASANEPYBIAJBgOQBaiJdIAEgXBD2ASACQYDnAWoiTCABIF0Q9gEgAkGA6gFqIoQBIAEgTBD2ASACQYDtAWoiXiABIIQBEPYBIAJBgPABaiIXIAEgXhD2ASACQYDzAWoidiABIBcQ9gEgAkGA9gFqIncgASB2EPYBIAJBgPkBaiI3IAEgdxD2ASACQYD8AWoiOSABIDcQ9gEgAkGA/wFqIk0gASA5EPYBIAJBgIICaiJfIAEgTRD2ASACQYCFAmoiTiABIF8Q9gEgAkGAiAJqIhIgASBOEPYBIAJBgIsCaiIgIAEgEhD2ASACQYCOAmoieCABICAQ9gEgAkGAkQJqIoUBIAEgeBD2ASACQYCUAmoiISABIIUBEPYBIAJBgJcCaiKGASABICEQ9gEgAkGAmgJqInkgASCGARD2ASACQYCdAmoiYCABIHkQ9gEgAkGAoAJqIiIgASBgEPYBIAJBgKMCaiImIAEgIhD2ASACQYCmAmoiGCABICYQ9gEgAkGAqQJqIhAgASAYEPYBIAJBgKwCaiJPIAEgEBD2ASACQYCvAmoiigEgASBPEPYBIAJBgLICaiJhIAEgigEQ9gEgAkGAtQJqIlAgASBhEPYBIAJBgLgCaiIqIAEgUBD2ASACQYC7AmoiYiABICoQ9gEgAkGAvgJqImMgASBiEPYBIAJBgMECaiI6IAEgYxD2ASACQYDEAmoiZCABIDoQ9gEgAkGAxwJqIkggAyBkEPYBIAJBgMoCaiJlIAEgSBD2ASACQYDNAmoiZiABIGUQ9gEgAkGA0AJqIosBIAEgZhD2ASACQYDTAmoiOyABIIsBEPYBIAJBgNYCaiJnIAEgOxD2ASACQYDZAmoiLCABIGcQ9gEgAkGA3AJqIi8gASAsEPYBIAJBgN8CaiI8IAEgLxD2ASACQYDiAmoiLiABIDwQ9gEgAkGA5QJqIj0gASAuEPYBIAJBgOgCaiI+IAEgPRD2ASACQYDrAmoiaCABID4Q9gEgAkGA7gJqIlEgASBoEPYBIAJBgPECaiITIAEgURD2ASACQYD0AmoiPyABIBMQ9gEgAkGA9wJqIgggASA/EPYBIAJBgPoCaiJSIAEgCBD2ASACQYD9AmoiQCABIFIQ9gEgAkGAgANqIocBIAEgQBD2ASACQYCDA2oiFSABIIcBEPYBIAJBgO4IaiIBIA8gFRD2ASB8IgMgAUEHEHQgCiIEIAMgORD2ASAFIARBCBB0IAJBgIYDaiIKIAUgZBD2ASABIApBCRB0IAMgASBXEPYBIAQgA0EJEHQgBSAEIE4Q9gEgAkGAiQNqIgogBUEIEHQgASBLIAoQ9gEgAyABQQsQdCAEIAMgHRD2ASAFIARBCxB0IAJBgIwDaiIKIAUgLBD2ASABIApBCBB0IAMgASAXEPYBIAQgA0EIEHQgBSAEIBAQ9gEgAkGAjwNqIgogBUEMEHQgASAIIAoQ9gEgAyABQQkQdCAEIAMgWhD2ASAFIARBDhB0IAJBgJIDaiIKIAUgNxD2ASABIApBBRB0IAMgASAnEPYBIAQgA0EJEHQgBSAEIEIQ9gEgAkGAlQNqIgogBUEHEHQgASAjIAoQ9gEgAyABQQoQdCAEIAMgHRD2ASAFIARBBxB0IAJBgJgDaiIKIAUgVBD2ASABIApBDBB0IAMgASAYEPYBIAQgA0EIEHQgBSAEICsQ9gEgAkGAmwNqIgogBUEKEHQgASBwIAoQ9gEgAyABQQgQdCAEIAMgERD2ASAFIARBCxB0IAJBgJ4DaiIKIAUgFRD2ASABIApBChB0IAMgASBlEPYBIAQgA0EKEHQgBSAEIBwQ9gEgAkGAoQNqIgogBUENEHQgASAyIAoQ9gEgAyABQQYQdCAEIAMgMBD2ASAFIARBDxB0IAJBgKQDaiIKIAUgNRD2ASABIApBDBB0IAMgASAsEPYBIAQgA0EHEHQgBSAEIIIBEPYBIAJBgKcDaiIKIAVBCRB0IAEgQCAKEPYBIAMgAUEIEHQgBCADIEAQ9gEgBSAEQQkQdCACQYCqA2oiCiAFIBIQ9gEgASAKQQsQdCADIAEgGBD2ASAEIANBCRB0IAUgBCAXEPYBIAJBgK0DaiIKIAVBBxB0IAEgGiAKEPYBIAMgAUEIEHQgBCADIB4Q9gEgBSAEQQcQdCACQYCwA2oiCiAFIFUQ9gEgASAKQQoQdCADIAEgTxD2ASAEIANBBhB0IAUgBCAkEPYBIAJBgLMDaiIKIAVBCxB0IAEgGCAKEPYBIAMgAUEJEHQgBCADIEwQ9gEgBSAEQQsQdCACQYC2A2oiCiAFIE0Q9gEgASAKQQkQdCADIAEgKRD2ASAEIANBCRB0IAUgBCAREPYBIAJBgLkDaiIKIAVBBxB0IAEgKCAKEPYBIAMgAUEHEHQgBCADIDAQ9gEgBSAEQQwQdCACQYC8A2oiCiAFICcQ9gEgASAKQQsQdCADIAEgPBD2ASAEIANBBhB0IAUgBCBDEPYBIAJBgL8DaiIKIAVBChB0IAEgQyAKEPYBIAMgAUEMEHQgBCADICEQ9gEgBSAEQQcQdCACQYDCA2oiCiAFIDYQ9gEgASAKQQwQdCADIAEgTRD2ASAEIANBCBB0IAUgBCATEPYBIAJBgMUDaiIKIAVBBBB0IAEgGyAKEPYBIAMgAUENEHQgBCADIA4Q9gEgBSAEQQgQdCACQYDIA2oiCiAFICkQ9gEgASAKQQUQdCADIAEgGxD2ASAEIANBDBB0IAUgBCA5EPYBIAJBgMsDaiIKIAVBCBB0IAEgWyAKEPYBIAMgAUEHEHQgBCADIDMQ9gEgBSAEQQgQdCACQYDOA2oiCiAFIB8Q9gEgASAKQQUQdCADIAEgIxD2ASAEIANBDRB0IAUgBCAfEPYBIAJBgNEDaiIKIAVBDRB0IAEgISAKEPYBIAMgAUEIEHQgBCADIGIQ9gEgBSAEQQcQdCACQYDUA2oiCiAFIBYQ9gEgASAKQQsQdCADIAEgHhD2ASAEIANBChB0IAUgBCB1EPYBIAJBgNcDaiIKIAVBCRB0IAEgIiAKEPYBIAMgAUELEHQgBCADIDwQ9gEgBSAEQQgQdCACQYDaA2oiCiAFID0Q9gEgASAKQQIQdCADIAEgDxD2ASAEIANBDRB0IAUgBCAzEPYBIAJBgN0DaiIKIAVBBxB0IAEgFCAKEPYBIAMgAUEMEHQgBCADIBIQ9gEgBSAEQQ0QdCACQYDgA2oiCiAFIDEQ9gEgASAKQQcQdCADIAEgJxD2ASAEIANBBxB0IAUgBCAlEPYBIAJBgOMDaiIKIAVBCRB0IAEgQSAKEPYBIAMgAUEKEHQgBCADIDgQ9gEgBSAEQQwQdCACQYDmA2oiCiAFIEsQ9gEgASAKQQoQdCADIAEgLBD2ASAEIANBChB0IAUgBCAiEPYBIAJBgOkDaiIKIAVBCRB0IAEgYyAKEPYBIAMgAUEKEHQgBCADICAQ9gEgBSAEQQcQdCACQYDsA2oiCiAFIG4Q9gEgASAKQQoQdCADIAEgExD2ASAEIANBCBB0IAUgBCAJEPYBIAJBgO8DaiIKIAVBCBB0IAEgdiAKEPYBIAMgAUEIEHQgBCADIAkQ9gEgBSAEQQgQdCACQYDyA2oiCiAFIAsQ9gEgASAKQQcQdCADIAEgMRD2ASAEIANBDBB0IAUgBCBtEPYBIAJBgPUDaiIKIAVBCxB0IAEgFyAKEPYBIAMgAUEKEHQgBCADIFYQ9gEgBSAEQQsQdCACQYD4A2oiCiAFICIQ9gEgASAKQQsQdCADIAEgIhD2ASAEIANBChB0IAUgBCBmEPYBIAJBgPsDaiIKIAVBDBB0IAEgdyAKEPYBIAMgAUEMEHQgBCADIDwQ9gEgBSAEQQcQdCACQYD+A2oiCiAFIDIQ9gEgASAKQQkQdCADIAEgDRD2ASAEIANBChB0IAUgBCBREPYBIAJBgIEEaiIKIAVBChB0IAEgCSAKEPYBIAMgAUEIEHQgBCADIEoQ9gEgBSAEQQgQdCACQYCEBGoiCiAFIAkQ9gEgASAKQQYQdCADIAEgQxD2ASAEIANBCxB0IAUgBCAXEPYBIAJBgIcEaiIKIAVBCBB0IAEgLiAKEPYBIAMgAUENEHQgBCADIFkQ9gEgBSAEQQcQdCACQYCKBGoiCiAFIB0Q9gEgASAKQQsQdCADIAEgERD2ASAEIANBCRB0IAUgBCAIEPYBIAJBgI0EaiIKIAVBCRB0IAEgGSAKEPYBIAMgAUEKEHQgBCADIGcQ9gEgBSAEQQcQdCACQYCQBGoiCiAFIHEQ9gEgASAKQQkQdCADIAEgOhD2ASAEIANBCBB0IAUgBCBhEPYBIAJBgJMEaiIKIAVBCRB0IAEgTCAKEPYBIAMgAUEOEHQgBCADIDoQ9gEgBSAEQQkQdCACQYCWBGoiCiAFICkQ9gEgASAKQQgQdCADIAEgRhD2ASAEIANBDBB0IAUgBCAZEPYBIAJBgJkEaiIKIAVBCRB0IAEgHiAKEPYBIAMgAUEIEHQgBCADIGoQ9gEgBSAEQQoQdCACQYCcBGoiCiAFIBYQ9gEgASAKQQwQdCADIAEgIBD2ASAEIANBCBB0IAUgBCAXEPYBIAJBgJ8EaiIKIAVBCBB0IAEgNyAKEPYBIAMgAUEIEHQgBCADIA0Q9gEgBSAEQQ4QdCACQYCiBGoiCiAFIDYQ9gEgASAKQQcQdCADIAEgHRD2ASAEIANBCRB0IAUgBCAyEPYBIAJBgKUEaiIKIAVBCBB0IAEgESAKEPYBIAMgAUEJEHQgBCADIFcQ9gEgBSAEQQkQdCACQYCoBGoiCiAFIFEQ9gEgASAKQQcQdCADIAEgGhD2ASAEIANBChB0IAUgBCA+EPYBIAJBgKsEaiIKIAVBCBB0IAEgNSAKEPYBIAMgAUEIEHQgBCADIFMQ9gEgBSAEQQkQdCACQYCuBGoiCiAFIEQQ9gEgASAKQQkQdCADIAEgKxD2ASAEIANBChB0IAUgBCArEPYBIAJBgLEEaiIKIAVBDRB0IAEgYiAKEPYBIAMgAUEMEHQgBCADIHQQ9gEgBSAEQQwQdCACQYC0BGoiCiAFIBIQ9gEgASAKQQQQdCADIAEgIxD2ASAEIANBDBB0IAUgBCAiEPYBIAJBgLcEaiIKIAVBCBB0IAEgZiAKEPYBIAMgAUEHEHQgBCADIDMQ9gEgBSAEQQkQdCACQYC6BGoiCiAFID4Q9gEgASAKQQgQdCADIAEgKhD2ASAEIANBBxB0IAUgBCA2EPYBIAJBgL0EaiIKIAVBChB0IAEgLyAKEPYBIAMgAUEHEHQgBCADIAsQ9gEgBSAEQQoQdCACQYDABGoiCiAFICAQ9gEgASAKQQgQdCADIAEgbBD2ASAEIANBCRB0IAUgBCAqEPYBIAJBgMMEaiIKIAVBCBB0IAEgKiAKEPYBIAMgAUEDEHQgBCADIC0Q9gEgBSAEQQ0QdCACQYDGBGoiCiAFIDsQ9gEgASAKQQgQdCADIAEgHRD2ASAEIANBDBB0IAUgBCA8EPYBIAJBgMkEaiIKIAVBCRB0IAEgDSAKEPYBIAMgAUEGEHQgBCADIIABEPYBIAUgBEEJEHQgAkGAzARqIgogBSBJEPYBIAEgCkEKEHQgAyABICYQ9gEgBCADQQgQdCAFIAQgWxD2ASACQYDPBGoiCiAFQQcQdCABIAsgChD2ASADIAFBChB0IAQgAyA+EPYBIAUgBEEKEHQgAkGA0gRqIgogBSANEPYBIAEgCkEJEHQgAyABID8Q9gEgBCADQQgQdCAFIAQgYRD2ASACQYDVBGoiCiAFQQQQdCABICUgChD2ASADIAFBDBB0IAQgAyB5EPYBIAUgBEEHEHQgAkGA2ARqIgogBSAcEPYBIAEgCkEMEHQgAyABIC4Q9gEgBCADQQYQdCAFIAQgahD2ASACQYDbBGoiLiAFQQMQdCABIAIgLhD2ASADIAFBDhB0IAQgAyALEPYBIAUgBEEIEHQgAkGA3gRqIi4gBSAxEPYBIAEgLkELEHQgAyABIGUQ9gEgBCADQQcQdCAFIAQgERD2ASACQYDhBGoiLiAFQQcQdCABIEQgLhD2ASADIAFBChB0IAQgAyBhEPYBIAUgBEEIEHQgAkGA5ARqIi4gBSAIEPYBIAEgLkEGEHQgAyABICQQ9gEgBCADQQwQdCAFIAQgIRD2ASACQYDnBGoiLiAFQQYQdCABIFQgLhD2ASADIAFBCxB0IAQgAyA1EPYBIAUgBEEJEHQgAkGA6gRqIi4gBSAhEPYBIAEgLkEIEHQgAyABIDoQ9gEgBCADQQUQdCAFIAQgQRD2ASACQYDtBGoiLiAFQQsQdCABIAkgLhD2ASADIAFBBRB0IAQgAyBTEPYBIAUgBEELEHQgAkGA8ARqIi4gBSA7EPYBIAEgLkEIEHQgAyABIFAQ9gEgBCADQQgQdCAFIAQgUhD2ASACQYDzBGoiLiAFQQgQdCABIHggLhD2ASADIAFBCxB0IAQgAyBgEPYBIAUgBEEIEHQgAkGA9gRqIi4gBSAfEPYBIAEgLkEKEHQgAyABIDwQ9gEgBCADQQkQdCAFIAQgJhD2ASACQYD5BGoiLiAFQQgQdCABID0gLhD2ASADIAFBCBB0IAQgAyBHEPYBIAUgBEEKEHQgAkGA/ARqIi4gBSAREPYBIAEgLkEJEHQgAyABIEgQ9gEgBCADQQoQdCAFIAQgORD2ASACQYD/BGoiLiAFQQcQdCABIDYgLhD2ASADIAFBCRB0IAQgAyBPEPYBIAUgBEEIEHQgAkGAggVqIk8gBSAfEPYBIAEgT0EJEHQgAyABIGwQ9gEgBCADQQwQdCAFIAQgUBD2ASACQYCFBWoiTyAFQQMQdCABIC0gTxD2ASADIAFBEhB0IAQgAyBeEPYBIAUgBEEHEHQgAkGAiAVqIk8gBSBvEPYBIAEgT0EJEHQgAyABIGcQ9gEgBCADQQgQdCAFIAQgPxD2ASACQYCLBWoiTyAFQQkQdCABIBcgTxD2ASADIAFBCBB0IAQgAyBKEPYBIAUgBEEIEHQgAkGAjgVqIk8gBSApEPYBIAEgT0EIEHQgAyABIEMQ9gEgBCADQQkQdCAFIAQgERD2ASACQYCRBWoiTyAFQQkQdCABIDkgTxD2ASADIAFBCBB0IAQgAyArEPYBIAUgBEELEHQgAkGAlAVqIisgBSAcEPYBIAEgK0ESEHQgAyABIEcQ9gEgBCADQQkQdCAFIAQgVhD2ASACQYCXBWoiKyAFQQ0QdCABID0gKxD2ASADIAFBBxB0IAQgAyA0EPYBIAUgBEEIEHQgAkGAmgVqIisgBSApEPYBIAEgK0EKEHQgAyABIFoQ9gEgBCADQQgQdCAFIAQgUBD2ASACQYCdBWoiKyAFQQIQdCABIA8gKxD2ASADIAFBDRB0IAQgAyAZEPYBIAUgBEEIEHQgAkGAoAVqIisgBSAzEPYBIAEgK0EJEHQgAyABIB0Q9gEgBCADQQkQdCAFIAQgahD2ASACQYCjBWoiKyAFQQkQdCABIBwgKxD2ASADIAFBDhB0IAQgAyBdEPYBIAUgBEEHEHQgAkGApgVqIisgBSApEPYBIAEgK0EDEHQgAyABIAIQ9gEgBCADQRIQdCAFIAQgRRD2ASACQYCpBWoiKyAFQQgQdCABIEUgKxD2ASADIAFBChB0IAQgAyBfEPYBIAUgBEEGEHQgAkGArAVqIisgBSAkEPYBIAEgK0EIEHQgAyABICcQ9gEgBCADQQwQdCAFIAQgeBD2ASACQYCvBWoiKyAFQQgQdCABIBQgKxD2ASADIAFBChB0IAQgAyB4EPYBIAUgBEEKEHQgAkGAsgVqIisgBSAvEPYBIAEgK0EHEHQgAyABICgQ9gEgBCADQQoQdCAFIAQghQEQ9gEgAkGAtQVqIisgBUEGEHQgASAUICsQ9gEgAyABQQsQdCAEIAMgCRD2ASAFIARBBhB0IAJBgLgFaiIrIAUgGxD2ASABICtBCRB0IAMgASAnEPYBIAQgA0EMEHQgBSAEIEsQ9gEgAkGAuwVqIisgBUEKEHQgASA4ICsQ9gEgAyABQQsQdCAEIAMgDRD2ASAFIARBBhB0IAJBgL4FaiINIAUgaRD2ASABIA1BDBB0IAMgASAmEPYBIAQgA0EIEHQgBSAEICIQ9gEgAkGAwQVqIg0gBUEJEHQgASAUIA0Q9gEgAyABQQoQdCAEIAMgThD2ASAFIARBBxB0IAJBgMQFaiINIAUgVxD2ASABIA1BCRB0IAMgASB1EPYBIAQgA0EHEHQgBSAEIEsQ9gEgAkGAxwVqIg0gBUELEHQgASCGASANEPYBIAMgAUEIEHQgBCADIFgQ9gEgBSAEQQkQdCACQYDKBWoiDSAFIFsQ9gEgASANQQgQdCADIAEgUhD2ASAEIANBCBB0IAUgBCBYEPYBIAJBgM0FaiINIAVBCBB0IAEgJSANEPYBIAMgAUEGEHQgBCADIA8Q9gEgBSAEQQ4QdCACQYDQBWoiDSAFIHAQ9gEgASANQQUQdCADIAEgJRD2ASAEIANBCxB0IAUgBCByEPYBIAJBgNMFaiINIAVBAxB0IAEgDyANEPYBIAMgAUENEHQgBCADIBkQ9gEgBSAEQQ0QdCACQYDWBWoiDSAFIAkQ9gEgASANQQgQdCADIAEgWhD2ASAEIANBCBB0IAUgBCA3EPYBIAJBgNkFaiINIAVBCBB0IAEgYiANEPYBIAMgAUEIEHQgBCADIDIQ9gEgBSAEQQgQdCACQYDcBWoiDSAFIB4Q9gEgASANQQsQdCADIAEgXBD2ASAEIANBCBB0IAUgBCCBARD2ASACQYDfBWoiDSAFQQgQdCABIDggDRD2ASADIAFBCRB0IAQgAyBzEPYBIAUgBEEKEHQgAkGA4gVqIg0gBSBkEPYBIAEgDUEIEHQgAyABIBMQ9gEgBCADQQgQdCAFIAQgKBD2ASACQYDlBWoiDSAFQQoQdCABIFUgDRD2ASADIAFBCxB0IAQgAyBnEPYBIAUgBEEIEHQgAkGA6AVqIg0gBSBaEPYBIAEgDUEFEHQgAyABIDAQ9gEgBCADQQwQdCAFIAQgGBD2ASACQYDrBWoiDSAFQQcQdCABIFcgDRD2ASADIAFBChB0IAQgAyAIEPYBIAUgBEEMEHQgAkGA7gVqIg0gBSAhEPYBIAEgDUEIEHQgAyABIBgQ9gEgBCADQQcQdCAFIAQgFhD2ASACQYDxBWoiDSAFQQkQdCABIHIgDRD2ASADIAFBCRB0IAQgAyB1EPYBIAUgBEEJEHQgAkGA9AVqIg0gBSAgEPYBIAEgDUEGEHQgAyABICQQ9gEgBCADQQsQdCAFIAQgJhD2ASACQYD3BWoiDSAFQQgQdCABIGcgDRD2ASADIAFBBxB0IAQgAyBHEPYBIAUgBEEJEHQgAkGA+gVqIg0gBSBZEPYBIAEgDUEKEHQgAyABIFIQ9gEgBCADQQYQdCAFIAQgQRD2ASACQYD9BWoiDSAFQQsQdCABID8gDRD2ASADIAFBBxB0IAQgAyAMEPYBIAUgBEELEHQgAkGAgAZqIg0gBSBoEPYBIAEgDUELEHQgAyABIBoQ9gEgBCADQQoQdCAFIAQgdBD2ASACQYCDBmoiDSAFQQ0QdCABIHEgDRD2ASADIAFBDBB0IAQgAyAIEPYBIAUgBEEGEHQgAkGAhgZqIg0gBSAxEPYBIAEgDUEMEHQgAyABIFwQ9gEgBCADQQcQdCAFIAQgWBD2ASACQYCJBmoiDSAFQQ0QdCABIC8gDRD2ASADIAFBBxB0IAQgAyBvEPYBIAUgBEEJEHQgAkGAjAZqIg0gBSAaEPYBIAEgDUEJEHQgAyABID8Q9gEgBCADQQkQdCAFIAQgFhD2ASACQYCPBmoiDSAFQQYQdCABIBwgDRD2ASADIAFBCRB0IAQgAyAUEPYBIAUgBEEOEHQgAkGAkgZqIg0gBSBzEPYBIAEgDUEJEHQgAyABIE0Q9gEgBCADQQQQdCAFIAQgfhD2ASACQYCVBmoiDSAFQQwQdCABIEYgDRD2ASADIAFBAxB0IAQgAyACEPYBIAUgBEEMEHQgAkGAmAZqIg0gBSAkEPYBIAEgDUEOEHQgAyABIGUQ9gEgBCADQQwQdCAFIAQgCxD2ASACQYCbBmoiDSAFQQgQdCABIB4gDRD2ASADIAFBCRB0IAQgAyB5EPYBIAUgBEEHEHQgAkGAngZqIg0gBSBEEPYBIAEgDUEKEHQgAyABIAgQ9gEgBCADQQgQdCAFIAQgFRD2ASACQYChBmoiDSAFQQ4QdCABIE4gDRD2ASADIAFBCRB0IAQgAyA6EPYBIAUgBEEHEHQgAkGApAZqIg0gBSAZEPYBIAEgDUEJEHQgAyABIF8Q9gEgBCADQQQQdCAFIAQgJRD2ASACQYCnBmoiDSAFQQwQdCABIAwgDRD2ASADIAFBDxB0IAQgAyB3EPYBIAUgBEEIEHQgAkGAqgZqIg0gBSAqEPYBIAEgDUEJEHQgAyABIIoBEPYBIAQgA0EIEHQgBSAEIGgQ9gEgAkGArQZqIg0gBUELEHQgASA+IA0Q9gEgAyABQQYQdCAEIAMgDBD2ASAFIARBCxB0IAJBgLAGaiINIAUgDhD2ASABIA1BBxB0IAMgASBGEPYBIAQgA0EJEHQgBSAEIIEBEPYBIAJBgLMGaiINIAVBCRB0IAEgCSANEPYBIAMgAUEIEHQgBCADID0Q9gEgBSAEQQcQdCACQYC2BmoiDSAFIG0Q9gEgASANQQsQdCADIAEgFhD2ASAEIANBCBB0IAUgBCBuEPYBIAJBgLkGaiINIAVBDBB0IAEgHiANEPYBIAMgAUEKEHQgBCADIIcBEPYBIAUgBEEIEHQgAkGAvAZqIg0gBSAaEPYBIAEgDUEIEHQgAyABIGwQ9gEgBCADQQMQdCAFIAQgDxD2ASACQYC/BmoiGiAFQQ4QdCABICAgGhD2ASADIAFBCBB0IAQgAyBeEPYBIAUgBEEEEHQgAkGAwgZqIhogBSAjEPYBIAEgGkEOEHQgAyABIBMQ9gEgBCADQQgQdCAFIAQgThD2ASACQYDFBmoiGiAFQQQQdCABIH8gGhD2ASADIAFBCxB0IAQgAyAoEPYBIAUgBEEKEHQgAkGAyAZqIhogBSA7EPYBIAEgGkEJEHQgAyABIF0Q9gEgBCADQQYQdCAFIAQgQhD2ASACQYDLBmoiGiAFQQoQdCABIHMgGhD2ASADIAFBDBB0IAQgAyAXEPYBIAUgBEEGEHQgAkGAzgZqIhogBSAoEPYBIAEgGkEKEHQgAyABIGEQ9gEgBCADQQYQdCAFIAQgJBD2ASACQYDRBmoiGiAFQQ0QdCABIEggGhD2ASADIAFBBxB0IAQgAyAfEPYBIAUgBEEJEHQgAkGA1AZqIhogBSAsEPYBIAEgGkEIEHQgAyABICcQ9gEgBCADQQsQdCAFIAQgQBD2ASACQYDXBmoiGiAFQQkQdCABIBggGhD2ASADIAFBCBB0IAQgAyA5EPYBIAUgBEEFEHQgAkGA2gZqIhogBSB/EPYBIAEgGkELEHQgAyABIHQQ9gEgBCADQQkQdCAFIAQgJhD2ASACQYDdBmoiGiAFQQgQdCABICIgGhD2ASADIAFBCRB0IAQgAyBbEPYBIAUgBEEIEHQgAkGA4AZqIhogBSA3EPYBIAEgGkEJEHQgAyABIFIQ9gEgBCADQQsQdCAFIAQgGBD2ASACQYDjBmoiGiAFQQgQdCABIFIgGhD2ASADIAFBBRB0IAQgAyAtEPYBIAUgBEEREHQgAkGA5gZqIhogBSAJEPYBIAEgGkEEEHQgAyABIBsQ9gEgBCADQQwQdCAFIAQgRxD2ASACQYDpBmoiCSAFQQUQdCABIBsgCRD2ASADIAFBDhB0IAQgAyAmEPYBIAUgBEEJEHQgAkGA7AZqIgkgBSAVEPYBIAEgCUEIEHQgAyABIBIQ9gEgBCADQQgQdCAFIAQgIBD2ASACQYDvBmoiCSAFQQoQdCABIFUgCRD2ASADIAFBCxB0IAQgAyBFEPYBIAUgBEEIEHQgAkGA8gZqIgkgBSAUEPYBIAEgCUEJEHQgAyABIBEQ9gEgBCADQQkQdCAFIAQgYBD2ASACQYD1BmoiCSAFQQcQdCABIDggCRD2ASADIAFBDBB0IAQgAyBREPYBIAUgBEEIEHQgAkGA+AZqIgkgBSAgEPYBIAEgCUELEHQgAyABICIQ9gEgBCADQQcQdCAFIAQgggEQ9gEgAkGA+wZqIgkgBUEIEHQgASA1IAkQ9gEgAyABQQoQdCAEIAMgTRD2ASAFIARBCBB0IAJBgP4GaiIJIAUgWRD2ASABIAlBCxB0IAMgASAvEPYBIAQgA0EEEHQgBSAEIC0Q9gEgAkGAgQdqIgkgBUENEHQgASBxIAkQ9gEgAyABQQkQdCAEIAMgaxD2ASAFIARBChB0IAJBgIQHaiIJIAUgXRD2ASABIAlBCRB0IAMgASBAEPYBIAQgA0EIEHQgBSAEIEkQ9gEgAkGAhwdqIgkgBUEJEHQgASBMIAkQ9gEgAyABQQgQdCAEIAMgTBD2ASAFIARBBRB0IAJBgIoHaiIJIAUgQRD2ASABIAlBCxB0IAMgASA1EPYBIAQgA0EIEHQgBSAEIDIQ9gEgAkGAjQdqIgkgBUEMEHQgASAQIAkQ9gEgAyABQQgQdCAEIAMgHhD2ASAFIARBCBB0IAJBgJAHaiIJIAUgERD2ASABIAlBChB0IAMgASB2EPYBIAQgA0EIEHQgBSAEIBAQ9gEgAkGAkwdqIgkgBUEJEHQgASAWIAkQ9gEgAyABQQcQdCAEIAMgaxD2ASAFIARBCRB0IAJBgJYHaiIJIAUgaRD2ASABIAlBChB0IAMgASA6EPYBIAQgA0EJEHQgBSAEIAgQ9gEgAkGAmQdqIgkgBUEGEHQgASBWIAkQ9gEgAyABQQQQdCAEIAMgDxD2ASAFIARBDRB0IAJBgJwHaiIJIAUgHxD2ASABIAlBCBB0IAMgASBGEPYBIAQgA0EJEHQgBSAEID0Q9gEgAkGAnwdqIgkgBUEJEHQgASBNIAkQ9gEgAyABQQoQdCAEIAMgLxD2ASAFIARBCBB0IAJBgKIHaiIJIAUgHBD2ASABIAlBCxB0IAMgASAXEPYBIAQgA0EIEHQgBSAEIA4Q9gEgAkGApQdqIgkgBUEHEHQgASBJIAkQ9gEgAyABQQcQdCAEIAMgHRD2ASAFIARBChB0IAJBgKgHaiIJIAUgCxD2ASABIAlBCRB0IAMgASBcEPYBIAQgA0EFEHQgBSAEIEEQ9gEgAkGAqwdqIgkgBUEKEHQgASAcIAkQ9gEgAyABQREQdCAEIAMggwEQ9gEgBSAEQQgQdCACQYCuB2oiCSAFIGMQ9gEgASAJQQcQdCADIAEgMhD2ASAEIANBCRB0IAUgBCBmEPYBIAJBgLEHaiIJIAVBCRB0IAEgdiAJEPYBIAMgAUEGEHQgBCADIBQQ9gEgBSAEQQoQdCACQYC0B2oiCSAFIFYQ9gEgASAJQQoQdCADIAEgVBD2ASAEIANBCRB0IAUgBCBFEPYBIAJBgLcHaiIJIAVBBxB0IAEgQiAJEPYBIAMgAUELEHQgBCADICUQ9gEgBSAEQQ8QdCACQYC6B2oiCSAFIEAQ9gEgASAJQQcQdCADIAEgKRD2ASAEIANBBhB0IAUgBCBTEPYBIAJBgL0HaiIJIAVBCxB0IAEgCCAJEPYBIAMgAUENEHQgBCADIEkQ9gEgBSAEQQkQdCACQYDAB2oiCSAFIEoQ9gEgASAJQQoQdCADIAEgLBD2ASAEIANBChB0IAUgBCBkEPYBIAJBgMMHaiIJIAVBBhB0IAEgMSAJEPYBIAMgAUEKEHQgBCADIBUQ9gEgBSAEQQQQdCACQYDGB2oiCSAFIBsQ9gEgASAJQQwQdCADIAEgGBD2ASAEIANBCBB0IAUgBCBEEPYBIAJBgMkHaiIJIAVBChB0IAEgYyAJEPYBIAMgAUEGEHQgBCADIGsQ9gEgBSAEQQoQdCACQYDMB2oiCSAFICQQ9gEgASAJQQsQdCADIAEgURD2ASAEIANBBxB0IAUgBCBJEPYBIAJBgM8HaiIJIAVBAxB0IAEgDyAJEPYBIAMgAUENEHQgBCADIEYQ9gEgBSAEQQsQdCACQYDSB2oiCSAFIGgQ9gEgASAJQQYQdCADIAEgVRD2ASAEIANBCxB0IAUgBCBIEPYBIAJBgNUHaiIJIAVBCRB0IAEgICAJEPYBIAMgAUELEHQgBCADIGUQ9gEgBSAEQQcQdCACQYDYB2oiCSAFIDQQ9gEgASAJQQkQdCADIAEgEhD2ASAEIANBCBB0IAUgBCCEARD2ASACQYDbB2oiCSAFQQYQdCABIAwgCRD2ASADIAFBDBB0IAQgAyBiEPYBIAUgBEEMEHQgAkGA3gdqIgkgBSBKEPYBIAEgCUEHEHQgAyABIAsQ9gEgBCADQQoQdCAFIAQgIRD2ASACQYDhB2oiCSAFQQwQdCABIBEgCRD2ASADIAFBCRB0IAQgAyAfEPYBIAUgBEEFEHQgAkGA5AdqIgkgBSAjEPYBIAEgCUEMEHQgAyABIC8Q9gEgBCADQQgQdCAFIAQgKBD2ASACQYDnB2oiCSAFQQwQdCABIBUgCRD2ASADIAFBCRB0IAQgAyBREPYBIAUgBEEJEHQgAkGA6gdqIgkgBSA+EPYBIAEgCUEJEHQgAyABIDwQ9gEgBCADQQcQdCAFIAQgchD2ASACQYDtB2oiCSAFQQkQdCABIAsgCRD2ASADIAFBBBB0IAQgAyAPEPYBIAUgBEEQEHQgAkGA8AdqIgkgBSAqEPYBIAEgCUEHEHQgAyABIDMQ9gEgBCADQQoQdCAFIAQgXxD2ASACQYDzB2oiCSAFQQgQdCABIDcgCRD2ASADIAFBBBB0IAQgAyAlEPYBIAUgBEELEHQgAkGA9gdqIgkgBSA0EPYBIAEgCUEKEHQgAyABICYQ9gEgBCADQQoQdCAFIAQghwEQ9gEgAkGA+QdqIgkgBUEHEHQgASAZIAkQ9gEgAyABQQgQdCAEIAMgcBD2ASAFIARBBxB0IAJBgPwHaiIJIAUggAEQ9gEgASAJQQoQdCADIAEghQEQ9gEgBCADQQgQdCAFIAQgZBD2ASACQYD/B2oiCSAFQQkQdCABIGYgCRD2ASADIAFBChB0IAQgAyA+EPYBIAUgBEEJEHQgAkGAgghqIgkgBSAWEPYBIAEgCUEDEHQgAyABIA8Q9gEgBCADQQ0QdCAFIAQgbhD2ASACQYCFCGoiDyAFQQoQdCABIDMgDxD2ASADIAFBCRB0IAQgAyA5EPYBIAUgBEEJEHQgAkGAiAhqIg8gBSAIEPYBIAEgD0EIEHQgAyABIBMQ9gEgBCADQQcQdCAFIAQgGRD2ASACQYCLCGoiDyAFQQcQdCABIDEgDxD2ASADIAFBChB0IAQgAyBIEPYBIAUgBEEEEHQgAkGAjghqIg8gBSAjEPYBIAEgD0EMEHQgAyABIG0Q9gEgBCADQQsQdCAFIAQgCBD2ASACQYCRCGoiDyAFQQQQdCABIBsgDxD2ASADIAFBDRB0IAQgAyBjEPYBIAUgBEEIEHQgAkGAlAhqIg8gBSAqEPYBIAEgD0EJEHQgAyABIIQBEPYBIAQgA0EJEHQgBSAEIEIQ9gEgAkGAlwhqIg8gBUELEHQgASB3IA8Q9gEgAyABQQkQdCAEIAMgiwEQ9gEgBSAEQQcQdCACQYCaCGoiDyAFIAsQ9gEgASAPQQcQdCADIAEgHRD2ASAEIANBChB0IAUgBCBgEPYBIAJBgJ0IaiIPIAVBBxB0IAEgiAEgDxD2ASADIAFBCBB0IAQgAyBFEPYBIAUgBEEKEHQgAkGAoAhqIg8gBSAsEPYBIAEgD0EIEHQgAyABIFAQ9gEgBCADQQkQdCAFIAQgFxD2ASACQYCjCGoiDyAFQQkQdCABIF8gDxD2ASADIAFBCBB0IAQgAyAqEPYBIAUgBEEIEHQgAkGApghqIg8gBSBeEPYBIAEgD0EHEHQgAyABIFQQ9gEgBCADQQsQdCAFIAQgCBD2ASACQYCpCGoiCCAFQQkQdCABIC8gCBD2ASADIAFBCRB0IAQgAyBIEPYBIAUgBEEIEHQgAkGArAhqIgggBSBeEPYBIAEgCEEGEHQgAyABICcQ9gEgBCADQQwQdCAFIAQgPRD2ASACQYCvCGoiCCAFQQgQdCABIEcgCBD2ASADIAFBCRB0IAQgAyB5EPYBIAUgBEELEHQgAkGAsghqIgggBSA3EPYBIAEgCEEJEHQgAyABIGAQ9gEgBCADQQgQdCAFIAQgUBD2ASACQYC1CGoiCCAFQQQQdCABICMgCBD2ASADIAFBDRB0IAQgAyA/EPYBIAUgBEEHEHQgAkGAuAhqIgggBSAfEPYBIAEgCEEIEHQgAyABIDQQ9gEgBCADQQYQdCAFIAQgMBD2ASACQYC7CGoiCCAFQQsQdCABIEwgCBD2ASADIAFBCRB0IAQgAyA0EPYBIAUgBEEKEHQgAkGAvghqIgggBSA/EPYBIAEgCEEFEHQgAyABIBsQ9gEgBCADQQsQdCAFIAQgWRD2ASACQYDBCGoiCCAFQQwQdCABICEgCBD2ASADIAFBCBB0IAQgAyCGARD2ASAFIARBBRB0IAJBgMQIaiIIIAUgMBD2ASABIAhBDBB0IAMgASA7EPYBIAQgA0EKEHQgBSAEIEAQ9gEgAkGAxwhqIgggBUEIEHQgASASIAgQ9gEgAyABQQgQdCAEIAMgOhD2ASAFIARBCRB0IAJBgMoIaiIIIAUgShD2ASABIAhBCRB0IAMgASA7EPYBIAQgA0ELEHQgBSAEIG8Q9gEgAkGAzQhqIgggBUEHEHQgASBEIAgQ9gEgAyABQQUQdCAEIAMgLRD2ASAFIARBDhB0IAJBgNAIaiIIIAUgOxD2ASABIAhBBhB0IAMgASAUEPYBIAQgA0EJEHQgBSAEIDUQ9gEgAkGA0whqIgggBUEHEHQgASAoIAgQ9gEgAyABQQkQdCAEIAMgHBD2ASAFIARBDRB0IAJBgNYIaiIIIAUgLBD2ASABIAhBCBB0IAMgASBcEPYBIAQgA0EFEHQgBSAEIFMQ9gEgAkGA2QhqIgggBUEJEHQgASAUIAgQ9gEgAyABQQoQdCAEIAMgNBD2ASAFIARBCBB0IAJBgNwIaiIIIAUgWBD2ASABIAhBChB0IAMgASBOEPYBIAQgA0ELEHQgBSAEIIMBEPYBIAJBgN8IaiIIIAVBAxB0IAEgLSAIEPYBIAMgAUEKEHQgBCADIEIQ9gEgBSAEQQ4QdCACQYDiCGoiCCAFIGkQ9gEgASAIQQoQdCADIAEgERD2ASAEIANBCRB0IAUgBCBdEPYBIAJBgOUIaiIRIAVBBxB0IAEgQyAREPYBIAMgAUEKEHQgBCADIBgQ9gEgBSAEQQcQdCB9IhEgBSA2EPYBIAEgEUEMEHQgAyABIGgQ9gEgBCADQQkQdCAFIAQgNhD2ASB7IgEgBUEIEHQgBkGIKmoiBCIDIDAgARD2ASACQcD+CGokACCJASADQYAD/AoAACAGQYgSaiIBIIkBQYAD/AoAACAGQYgVaiIDIAZBiAlqQYAD/AoAACAEIgIgARD5ASAGKQOYKiGMASAGKQOQKiGOAQJAIAYoAogqQQFHBEAgBkGYG2ogBkGgKmpB8AL8CgAAIAYgjAE3A5AbIAYgjgE3A4gbIAZBiB5qIAMQHyAGQYghaiIDIAEQHyACIAMQTSAGQYgnaiIBIAIgBkGIG2oQ9gEgARBqBEADQCAGQYgqaiIBIAZBiCFqIgIgBkGIHmoQ9gEgAiABQYAD/AoAACABIAIQTSAGQYgnaiICIAFBgAP8CgAAIAEgAiAGQYgbahD2ASAGQYgkaiICIAFBgAP8CgAAIAIQag0ACwsgeiAGQYghakGAA/wKAAAgekGAA2ogBkGID2pBgAP8CgAAIAZB0C5qJAAMAQsgBiCMATcDkCogBiCOATcDiCpBgIvAAEErIAZBiCpqQdyLwABB/I7AABDKAwALIAdB0ApqIgEgekGAA/wKAAAgB0HQDWoiAiAHQZAqakGAA/wKAAAgACABELQDIABBkAFqIAIQtAMMAgsgB0GwF2oiASAHQRBqEPYCIAdB4BdqIAdBIGoQ9gIgB0GQGGoiAiAHQTBqEPYCIAdBwBhqIAdBQGsQ9gIgB0HwGGoiAyAHQdAAahD2AiAHQaAZaiAHQeAAahD2AiAHQZAVaiIGIAFB4AD8CgAAIAdB8BVqIAJB4AD8CgAAIAdB0BZqIANB4AD8CgAAIAdB8BtqIgEgB0HwAGoQ9gIgB0GgHGogB0GAAWoQ9gIgB0HQHGoiAiAHQZABahD2AiAHQYAdaiAHQaABahD2AiAHQbAdaiIDIAdBsAFqEPYCIAdB4B1qIAdBwAFqEPYCIAdB0BlqIgQgAUHgAPwKAAAgB0GwGmogAkHgAPwKAAAgB0GQG2ogA0HgAPwKAAAgB0HQEGoiUiAGQaAC/AoAACAHQfASaiAEQaAC/AoAACMAQeCvC2siBSQAIAUgUjYCwJILIAUgUkGgAmoiETYCxJILIAVBgKALaiIWIgEgBUHAkgtqIgoiBhCQAyAFQcCbC2oieyICIAFB4AD8CgAAIAVBgJcLaiJ8IgMgAkHgAPwKAAAgBUHApAtqIn0iBCADQeAA/AoAACAFQcCtC2oiCCAEQeAA/AoAACABIAYQkAMgAiABQeAA/AoAACADIAJB4AD8CgAAIAQgA0HgAPwKAAAgBUGgrgtqIARB4AD8CgAAIAEgBhCQAyACIAFB4AD8CgAAIAMgAkHgAPwKAAAgBCADQeAA/AoAACAFQYCvC2ogBEHgAPwKAAAgBUGAqQtqIgkgCEGgAvwKAAAgBSBSQcAEajYChI4LIAUgETYCgI4LIHsiASAFQYCOC2oiiAEiBhCQAyB8IgIgAUHgAPwKAAAgCiIDIAJB4AD8CgAAIBYiBCADQeAA/AoAACB9IhEgBEHgAPwKAAAgASAGEJADIAIgAUHgAPwKAAAgAyACQeAA/AoAACAEIANB4AD8CgAAIAVBoKULaiAEQeAA/AoAACABIAYQkAMgAiABQeAA/AoAACADIAJB4AD8CgAAIAQgA0HgAPwKAAAgBUGApgtqIARB4AD8CgAAIAgiASARQaAC/AoAACAFQaCrC2ogAUGgAvwKAAAgBSAJQcAE/AoAACAFQYAJaiICIAVBARDkASAFQcAEaiIBIAJBwAT8CgAAIAVBwA1qIjsgBSABEJsCIAVBgBJqIh8gASA7EJsCIAVBwBZqIhUgASAfEJsCIAVBgBtqImwgASAVEJsCIAVBwB9qIjwgASBsEJsCIAVBgCRqIlMgASA8EJsCIAVBwChqIj0gASBTEJsCIAVBgC1qIhEgASA9EJsCIAVBwDFqIj4gASAREJsCIAVBgDZqIg8gASA+EJsCIAVBwDpqIhAgASAPEJsCIAVBgD9qIiAgASAQEJsCIAVBwMMAaiIqIAEgIBCbAiAFQYDIAGoiPyABICoQmwIgBUHAzABqIn8gASA/EJsCIAVBgNEAaiJAIAEgfxCbAiAFQcDVAGoiLCABIEAQmwIgBUGA2gBqIiIgASAsEJsCIAVBwN4AaiICIAUgIhCbAiAFQYDjAGoiIyAFIAIQmwIgBUHA5wBqIi8gASAjEJsCIAVBgOwAaiJtIAEgLxCbAiAFQcDwAGoiVCABIG0QmwIgBUGA9QBqIi0gPCACEJsCIAVBwPkAaiIlIAEgLRCbAiAFQYD+AGoiOCABICUQmwIgBUHAggFqIm4gASA4EJsCIAVBgIcBaiJvIAEgbhCbAiAFQcCLAWoiDCABIG8QmwIgBUGAkAFqIoABIAEgDBCbAiAFQcCUAWoiMCABIIABEJsCIAVBgJkBaiIxIAEgMBCbAiAFQcCdAWoiQSABIDEQmwIgBUGAogFqIhQgASBBEJsCIAVBwKYBaiKBASABIBQQmwIgBUGAqwFqIksgASCBARCbAiAFQcCvAWoiJCABIEsQmwIgBUGAtAFqInAgASAkEJsCIAVBwLgBaiJVIAEgcBCbAiAFQYC9AWoiQiABIFUQmwIgBUHAwQFqIicgASBCEJsCIAVBgMYBaiJWIAEgJxCbAiAFQcDKAWoiMiABIFYQmwIgBUGAzwFqIkMgASAyEJsCIAVBwNMBaiJxIAEgQxCbAiAFQYDYAWoiRCABIHEQmwIgBUHA3AFqIkUgASBEEJsCIAVBgOEBaiJGIAEgRRCbAiAFQcDlAWoiMyABIEYQmwIgBUGA6gFqIoIBIAEgMxCbAiAFQcDuAWoiNCABIIIBEJsCIAVBgPMBaiIoIAEgNBCbAiAFQcD3AWoiKSABICgQmwIgBUGA/AFqIhogASApEJsCIAVBwIACaiJHIAEgGhCbAiAFQYCFAmoiciABIEcQmwIgBUHAiQJqInMgASByEJsCIAVBgI4CaiJ0IAEgcxCbAiAFQcCSAmoiSSABIHQQmwIgBUGAlwJqIkogASBJEJsCIAVBwJsCaiILIAEgShCbAiAFQYCgAmoiCSABIAsQmwIgBUHApAJqIisgASAJEJsCIAVBgKkCaiI1IAEgKxCbAiAFQcCtAmoiDSABIDUQmwIgBUGAsgJqIlcgASANEJsCIAVBwLYCaiJMIAEgVxCbAiAFQYC7AmoiNiABIEwQmwIgBUHAvwJqIlggASA2EJsCIAVBgMQCaiJZIAEgWBCbAiAFQcDIAmoiWiABIFkQmwIgBUGAzQJqIoMBIAEgWhCbAiAFQcDRAmoiWyABIIMBEJsCIAVBgNYCaiJcIAEgWxCbAiAFQcDaAmoiTSABIFwQmwIgBUGA3wJqIl0gASBNEJsCIAVBwOMCaiJ1IAEgXRCbAiAFQYDoAmoiXiABIHUQmwIgBUHA7AJqIhcgASBeEJsCIAVBgPECaiKEASABIBcQmwIgBUHA9QJqIhYgASCEARCbAiAFQYD6AmoihQEgASAWEJsCIAVBwP4CaiJfIAEghQEQmwIgBUGAgwNqIk4gASBfEJsCIAVBwIcDaiIOIAEgThCbAiAFQYCMA2oiGCABIA4QmwIgBUHAkANqIhsgASAYEJsCIAVBgJUDaiJgIAEgGxCbAiAFQcCZA2oiNyABIGAQmwIgBUGAngNqIlAgASA3EJsCIAVBwKIDaiJhIAEgUBCbAiAFQYCnA2oiYiABIGEQmwIgBUHAqwNqImMgASBiEJsCIAVBgLADaiJkIAEgYxCbAiAFQcC0A2oihgEgASBkEJsCIAVBgLkDaiJPIAEghgEQmwIgBUHAvQNqIhkgASBPEJsCIAVBgMIDaiJ2IAEgGRCbAiAFQcDGA2oidyABIHYQmwIgBUGAywNqIjkgASB3EJsCIAVBwM8DaiIeIAEgORCbAiAFQYDUA2oiZSABIB4QmwIgBUHA2ANqImYgASBlEJsCIAVBgN0DaiJIIAEgZhCbAiAFQcDhA2oiEiABIEgQmwIgBUGA5gNqInggASASEJsCIAVBwOoDaiJnIAEgeBCbAiAFQYDvA2oiBiABIGcQmwIgBUHA8wNqIi4gASAGEJsCIAVBgPgDaiJoIAEgLhCbAiAFQcD8A2oieSABIGgQmwIgBUGAgQRqIiEgASB5EJsCIAVBwIUEaiKHASABICEQmwIgBUGAigRqIlEgASCHARCbAiAFQcCOBGoiaSABIFEQmwIgBUGAkwRqIgggASBpEJsCIAVBwJcEaiI6IAEgCBCbAiAFQYCcBGoieiABIDoQmwIgBUHAoARqImogASB6EJsCIAVBgKUEaiIcIAIgZhCbAiAFQcCpBGoiHSABIBwQmwIgBUGArgRqIhMgASAdEJsCIAVBwLIEaiImIAIgZxCbAiAFQYC3BGoiayABICYQmwIgfCIBIC0gaxCbAiB7IgIgAUEHEOQBIAQiAyACIGUQmwIgfSIEIANBChDkASAFQcC7BGoifiAEIF8QmwIgASB+QQkQ5AEgAiABICQQmwIgAyACQQgQ5AEgBCADIEMQmwIgBUGAwARqIn4gBEEIEOQBIAEgQCB+EJsCIAIgAUEKEOQBIAMgAiAQEJsCIAQgA0EOEOQBIAVBwMQEaiIQIAQgCRCbAiABIBBBCxDkASACIAEggQEQmwIgAyACQQkQ5AEgBCADICYQmwIgBUGAyQRqIhAgBEEHEOQBIAEgKSAQEJsCIAIgAUEKEOQBIAMgAiAGEJsCIAQgA0EHEOQBIAVBwM0EaiIQIAQgRRCbAiABIBBBCBDkASACIAEgKRCbAiADIAJBCRDkASAEIAMgVRCbAiAFQYDSBGoiECAEQQcQ5AEgASAvIBAQmwIgAiABQQoQ5AEgAyACIBYQmwIgBCADQQgQ5AEgBUHA1gRqIhAgBCA6EJsCIAEgEEEJEOQBIAIgASAuEJsCIAMgAkEGEOQBIAQgAyAwEJsCIAVBgNsEaiIQIARBCRDkASABICMgEBCbAiACIAFBCRDkASADIAIgQxCbAiAEIANBCRDkASAFQcDfBGoiECAEIHYQmwIgASAQQQcQ5AEgAiABIEcQmwIgAyACQQkQ5AEgBCADIFsQmwIgBUGA5ARqIhAgBEEIEOQBIAEgNiAQEJsCIAIgAUEJEOQBIAMgAiAIEJsCIAQgA0EIEOQBIAVBwOgEaiIQIAQgJxCbAiABIBBBAxDkASACIAEgOxCbAiADIAJBDxDkASAEIAMgdBCbAiAFQYDtBGoiECAEQQkQ5AEgASBhIBAQmwIgAiABQQUQ5AEgAyACIBEQmwIgBCADQQwQ5AEgBUHA8QRqIhAgBCBNEJsCIAEgEEEJEOQBIAIgASBOEJsCIAMgAkEJEOQBIAQgAyBfEJsCIAVBgPYEaiIQIARBBhDkASABIA8gEBCbAiACIAFBCRDkASADIAIgDxCbAiAEIANBCxDkASAFQcD6BGoiECAEIA4QmwIgASAQQQQQ5AEgAiABIB8QmwIgAyACQQ0Q5AEgBCADIFkQmwIgBUGA/wRqIhAgBEEIEOQBIAEgFiAQEJsCIAIgAUEIEOQBIAMgAiBoEJsCIAQgA0EGEOQBIAVBwIMFaiIQIAQgPhCbAiABIBBBCxDkASACIAEgRxCbAiADIAJBCBDkASAEIAMgLxCbAiAFQYCIBWoiECAEQQkQ5AEgASBwIBAQmwIgAiABQQsQ5AEgAyACIGIQmwIgBCADQQgQ5AEgBUHAjAVqIhAgBCAZEJsCIAEgEEEJEOQBIAIgASBpEJsCIAMgAkEKEOQBIAQgAyASEJsCIAVBgJEFaiIQIARBAxDkASABIB8gEBCbAiACIAFBDRDkASADIAIgNxCbAiAEIANBCBDkASAFQcCVBWoiECAEIGgQmwIgASAQQQgQ5AEgAiABIEEQmwIgAyACQQwQ5AEgBCADIBsQmwIgBUGAmgVqIhAgBEEJEOQBIAEggwEgEBCbAiACIAFBCRDkASADIAIgNRCbAiAEIANBBhDkASAFQcCeBWoiECAEICIQmwIgASAQQQgQ5AEgAiABICIQmwIgAyACQQoQ5AEgBCADIDQQmwIgBUGAowVqIhAgBEEJEOQBIAEgRiAQEJsCIAIgAUEJEOQBIAMgAiBQEJsCIAQgA0EHEOQBIAVBwKcFaiIQIAQgJRCbAiABIBBBCBDkASACIAEgVBCbAiADIAJBChDkASAEIAMgGhCbAiAFQYCsBWoiECAEQQgQ5AEgASBJIBAQmwIgAiABQQkQ5AEgAyACICkQmwIgBCADQQkQ5AEgBUHAsAVqIhAgBCAeEJsCIAEgEEEEEOQBIAIgASBsEJsCIAMgAkEJEOQBIAQgAyA+EJsCIAVBgLUFaiIQIARBDxDkASABIBkgEBCbAiACIAFBChDkASADIAIgNhCbAiAEIANBBxDkASAFQcC5BWoiECAEIEQQmwIgASAQQQkQ5AEgAiABIBcQmwIgAyACQQgQ5AEgBCADIDQQmwIgBUGAvgVqIhAgBEEKEOQBIAEgUSAQEJsCIAIgAUEJEOQBIAMgAiAbEJsCIAQgA0EJEOQBIAVBwMIFaiIQIAQgWhCbAiABIBBBBxDkASACIAEgLRCbAiADIAJBCRDkASAEIAMgSRCbAiAFQYDHBWoiECAEQQoQ5AEgASAzIBAQmwIgAiABQQkQ5AEgAyACIFYQmwIgBCADQQkQ5AEgBUHAywVqIhAgBCAdEJsCIAEgEEEKEOQBIAIgASAWEJsCIAMgAkEKEOQBIAQgAyAcEJsCIAVBgNAFaiIQIARBCBDkASABIGogEBCbAiACIAFBDBDkASADIAIgIRCbAiAEIANBCBDkASAFQcDUBWoiECAEIDUQmwIgASAQQQUQ5AEgAiABIA8QmwIgAyACQQsQ5AEgBCADIAkQmwIgBUGA2QVqIhAgBEEOEOQBIAEgCCAQEJsCIAIgAUEHEOQBIAMgAiBzEJsCIAQgA0EJEOQBIAVBwN0FaiIQIAQgdhCbAiABIBBBCxDkASACIAEgJBCbAiADIAJBCRDkASAEIAMgDhCbAiAFQYDiBWoiDiAEQQYQ5AEgASAMIA4QmwIgAiABQQsQ5AEgAyACIIABEJsCIAQgA0EKEOQBIAVBwOYFaiIOIAQgXhCbAiABIA5BCBDkASACIAEgDRCbAiADIAJBCBDkASAEIAMgZxCbAiAFQYDrBWoiDiAEQQkQ5AEgASBIIA4QmwIgAiABQQgQ5AEgAyACIAYQmwIgBCADQQoQ5AEgBUHA7wVqIg4gBCBOEJsCIAEgDkEFEOQBIAIgASA+EJsCIAMgAkEMEOQBIAQgAyASEJsCIAVBgPQFaiIOIARBCRDkASABIBggDhCbAiACIAFBCBDkASADIAIgHBCbAiAEIANBCBDkASAFQcD4BWoiDiAEIFcQmwIgASAOQQcQ5AEgAiABIAsQmwIgAyACQQgQ5AEgBCADIHIQmwIgBUGA/QVqIg4gBEEIEOQBIAEgCyAOEJsCIAIgAUEJEOQBIAMgAiBIEJsCIAQgA0EJEOQBIAVBwIEGaiIOIAQgJhCbAiABIA5BBxDkASACIAEgGhCbAiADIAJBCBDkASAEIAMgCxCbAiAFQYCGBmoiDiAEQQsQ5AEgASBqIA4QmwIgAiABQQgQ5AEgAyACIHoQmwIgBCADQQkQ5AEgBUHAigZqIg4gBCATEJsCIAEgDkEKEOQBIAIgASANEJsCIAMgAkEIEOQBIAQgAyAdEJsCIAVBgI8GaiIOIARBCRDkASABIFQgDhCbAiACIAFBCBDkASADIAIgIhCbAiAEIANBDBDkASAFQcCTBmoiDiAEIAkQmwIgASAOQQoQ5AEgAiABICQQmwIgAyACQQsQ5AEgBCADIAYQmwIgBUGAmAZqIg4gBEEJEOQBIAEgIiAOEJsCIAIgAUEKEOQBIAMgAiBYEJsCIAQgA0EJEOQBIAVBwJwGaiIOIAQgahCbAiABIA5BCBDkASACIAEgMhCbAiADIAJBCBDkASAEIAMgMhCbAiAFQYChBmoiDiAEQQUQ5AEgASAVIA4QmwIgAiABQQwQ5AEgAyACIEsQmwIgBCADQQkQ5AEgBUHApQZqIg4gBCBMEJsCIAEgDkEHEOQBIAIgASArEJsCIAMgAkEHEOQBIAQgAyAqEJsCIAVBgKoGaiIOIARBChDkASABIAsgDhCbAiACIAFBChDkASADIAIgXhCbAiAEIANBCBDkASAFQcCuBmoiDiAEIAYQmwIgASAOQQYQ5AEgAiABICAQmwIgAyACQQsQ5AEgBCADIGQQmwIgBUGAswZqIg4gBEEKEOQBIAEgCSAOEJsCIAIgAUEMEOQBIAMgAiBIEJsCIAQgA0EIEOQBIAVBwLcGaiIOIAQgEhCbAiABIA5BCBDkASACIAEgGRCbAiADIAJBCBDkASAEIAMgWxCbAiAFQYC8BmoiDiAEQQgQ5AEgASBdIA4QmwIgAiABQQcQ5AEgAyACIEkQmwIgBCADQQUQ5AEgBUHAwAZqIg4gBCA8EJsCIAEgDkESEOQBIAIgASBZEJsCIAMgAkEJEOQBIAQgAyAYEJsCIAVBgMUGaiIOIARBBxDkASABIIIBIA4QmwIgAiABQQgQ5AEgAyACIEsQmwIgBCADQQgQ5AEgBUHAyQZqIg4gBCArEJsCIAEgDkEKEOQBIAIgASBcEJsCIAMgAkEKEOQBIAQgAyAsEJsCIAVBgM4GaiIOIARBCxDkASABIGkgDhCbAiACIAFBBxDkASADIAIgRxCbAiAEIANBCxDkASAFQcDSBmoiDiAEIDEQmwIgASAOQQkQ5AEgAiABIBYQmwIgAyACQQoQ5AEgBCADIE0QmwIgBUGA1wZqIg4gBEEIEOQBIAEgCCAOEJsCIAIgAUEJEOQBIAMgAiAJEJsCIAQgA0EHEOQBIAVBwNsGaiIOIAQgJRCbAiABIA5BCBDkASACIAEgOBCbAiADIAJBDBDkASAEIAMgJxCbAiAFQYDgBmoiDiAEQQoQ5AEgASAoIA4QmwIgAiABQQkQ5AEgAyACIDEQmwIgBCADQQsQ5AEgBUHA5AZqIg4gBCBmEJsCIAEgDkEGEOQBIAIgASAtEJsCIAMgAkEKEOQBIAQgAyASEJsCIAVBgOkGaiIOIARBCBDkASABIB4gDhCbAiACIAFBDRDkASADIAIgCBCbAiAEIANBCBDkASAFQcDtBmoiDiAEIE0QmwIgASAOQQcQ5AEgAiABIAsQmwIgAyACQQoQ5AEgBCADIDkQmwIgBUGA8gZqIg4gBEEIEOQBIAEgJiAOEJsCIAIgAUEHEOQBIAMgAiBxEJsCIAQgA0EMEOQBIAVBwPYGaiIOIAQgMhCbAiABIA5BCxDkASACIAEgPxCbAiADIAJBCRDkASAEIAMgLRCbAiAFQYD7BmoiDiAEQQoQ5AEgASBiIA4QmwIgAiABQQgQ5AEgAyACIF0QmwIgBCADQQgQ5AEgBUHA/wZqIg4gBCBQEJsCIAEgDkELEOQBIAIgASAWEJsCIAMgAkEHEOQBIAQgAyBWEJsCIAVBgIQHaiIOIARBCRDkASABIB4gDhCbAiACIAFBCRDkASADIAIgYRCbAiAEIANBBRDkASAFQcCIB2oiDiAEIBEQmwIgASAOQQsQ5AEgAiABICkQmwIgAyACQQkQ5AEgBCADICwQmwIgBUGAjQdqIg4gBEEKEOQBIAEgHSAOEJsCIAIgAUEKEOQBIAMgAiBEEJsCIAQgA0EHEOQBIAVBwJEHaiIOIAQgKhCbAiABIA5BChDkASACIAEgSxCbAiADIAJBBhDkASAEIAMgIBCbAiAFQYCWB2oiSyAEQQsQ5AEgASB1IEsQmwIgAiABQQgQ5AEgAyACIDQQmwIgBCADQQ0Q5AEgBUHAmgdqIksgBCA5EJsCIAEgS0EIEOQBIAIgASAdEJsCIAMgAkEIEOQBIAQgAyBREJsCIAVBgJ8HaiJLIARBCBDkASABIGMgSxCbAiACIAFBBxDkASADIAIgbxCbAiAEIANBDxDkASAFQcCjB2oiSyAEIDoQmwIgASBLQQkQ5AEgAiABIBIQmwIgAyACQQYQ5AEgBCADIBEQmwIgBUGAqAdqIhIgBEEJEOQBIAEgbiASEJsCIAIgAUEKEOQBIAMgAiAIEJsCIAQgA0EMEOQBIAVBwKwHaiISIAQghwEQmwIgASASQQcQ5AEgAiABICcQmwIgAyACQQkQ5AEgBCADIBsQmwIgBUGAsQdqIhIgBEEJEOQBIAEgESASEJsCIAIgAUEUEOQBIAMgAiBrEJsCIAQgA0EJEOQBIAVBwLUHaiISIAQgExCbAiABIBJBCBDkASACIAEgFxCbAiADIAJBCBDkASAEIAMgLxCbAiAFQYC6B2oiEiAEQQwQ5AEgASA3IBIQmwIgAiABQQcQ5AEgAyACIEQQmwIgBCADQQoQ5AEgBUHAvgdqIhIgBCCGARCbAiABIBJBCBDkASACIAEgJhCbAiADIAJBCBDkASAEIAMgBhCbAiAFQYDDB2oiEiAEQQcQ5AEgASBFIBIQmwIgAiABQQgQ5AEgAyACICwQmwIgBCADQQoQ5AEgBUHAxwdqIhIgBCBeEJsCIAEgEkEIEOQBIAIgASAIEJsCIAMgAkEKEOQBIAQgAyBOEJsCIAVBgMwHaiISIARBBBDkASABIBUgEhCbAiACIAFBDhDkASADIAIgXBCbAiAEIANBBxDkASAFQcDQB2oiEiAEIG0QmwIgASASQQkQ5AEgAiABICsQmwIgAyACQQUQ5AEgBCADIDwQmwIgBUGA1QdqIhIgBEEKEOQBIAEgVCASEJsCIAIgAUELEOQBIAMgAiAUEJsCIAQgA0EHEOQBIAVBwNkHaiISIAQgPxCbAiABIBJBCxDkASACIAEgGxCbAiADIAJBBBDkASAEIAMgOxCbAiAFQYDeB2oiEiAEQQ0Q5AEgASBuIBIQmwIgAiABQQoQ5AEgAyACIDcQmwIgBCADQQsQ5AEgBUHA4gdqIhIgBCA0EJsCIAEgEkEKEOQBIAIgASAoEJsCIAMgAkEJEOQBIAQgAyBtEJsCIAVBgOcHaiISIARBCxDkASABICggEhCbAiACIAFBCBDkASADIAIgMxCbAiAEIANBCxDkASAFQcDrB2oiEiAEIF0QmwIgASASQQQQ5AEgAiABIFMQmwIgAyACQQ8Q5AEgBCADIAsQmwIgBUGA8AdqIhIgBEEHEOQBIAEgKiASEJsCIAIgAUEIEOQBIAMgAiAPEJsCIAQgA0ELEOQBIAVBwPQHaiISIAQgZBCbAiABIBJBBhDkASACIAEgJRCbAiADIAJBBxDkASAEIAMgfxCbAiAFQYD5B2oiEiAEQQsQ5AEgASBRIBIQmwIgAiABQQgQ5AEgAyACIG8QmwIgBCADQQoQ5AEgBUHA/QdqIhIgBCAbEJsCIAEgEkEIEOQBIAIgASBMEJsCIAMgAkEHEOQBIAQgAyAlEJsCIAVBgIIIaiISIARBCxDkASABIFEgEhCbAiACIAFBChDkASADIAIgZxCbAiAEIANBCxDkASAFQcCGCGoiEiAEIDUQmwIgASASQQYQ5AEgAiABIC0QmwIgAyACQQwQ5AEgBCADICEQmwIgBUGAiwhqIi0gBEEKEOQBIAEgRSAtEJsCIAIgAUEJEOQBIAMgAiBlEJsCIAQgA0EKEOQBIAVBwI8IaiItIAQgCxCbAiABIC1BCBDkASACIAEgMxCbAiADIAJBCBDkASAEIAMgOBCbAiAFQYCUCGoiCyAEQQwQ5AEgASAbIAsQmwIgAiABQQgQ5AEgAyACIFsQmwIgBCADQQsQ5AEgBUHAmAhqIgsgBCAGEJsCIAEgC0EJEOQBIAIgASA0EJsCIAMgAkEKEOQBIAQgAyAYEJsCIAVBgJ0IaiILIARBBRDkASABICogCxCbAiACIAFBCxDkASADIAIgVBCbAiAEIANBChDkASAFQcChCGoiCyAEIFUQmwIgASALQQkQ5AEgAiABIBwQmwIgAyACQQcQ5AEgBCADIEoQmwIgBUGApghqIgsgBEEJEOQBIAEgYCALEJsCIAIgAUEDEOQBIAMgAiAfEJsCIAQgA0EQEOQBIAVBwKoIaiILIAQgFxCbAiABIAtBBxDkASACIAEgRBCbAiADIAJBBhDkASAEIAMgIBCbAiAFQYCvCGoiCyAEQQkQ5AEgASAsIAsQmwIgAiABQQoQ5AEgAyACIGQQmwIgBCADQQkQ5AEgBUHAswhqIgsgBCAkEJsCIAEgC0EGEOQBIAIgASA+EJsCIAMgAkEMEOQBIAQgAyATEJsCIAVBgLgIaiILIARBBhDkASABIC8gCxCbAiACIAFBDRDkASADIAIgWRCbAiAEIANBBhDkASAFQcC8CGoiCyAEIAwQmwIgASALQQsQ5AEgAiABIDYQmwIgAyACQQ8Q5AEgBCADIBMQmwIgBUGAwQhqIgsgBEEHEOQBIAEgDCALEJsCIAIgAUEJEOQBIAMgAiAPEJsCIAQgA0ENEOQBIAVBwMUIaiILIAQgYxCbAiABIAtBCRDkASACIAEgHhCbAiADIAJBBBDkASAEIAMgPRCbAiAFQYDKCGoiCyAEQQ4Q5AEgASA2IAsQmwIgAiABQQ0Q5AEgAyACIHUQmwIgBCADQQkQ5AEgBUHAzghqIgsgBCAjEJsCIAEgC0EKEOQBIAIgASAcEJsCIAMgAkEHEOQBIAQgAyBJEJsCIAVBgNMIaiILIARBCBDkASABIEYgCxCbAiACIAFBChDkASADIAIgaxCbAiAEIANBChDkASAFQcDXCGoiCyAEIEMQmwIgASALQQkQ5AEgAiABIGUQmwIgAyACQQcQ5AEgBCADIEEQmwIgBUGA3AhqIgsgBEEKEOQBIAEgdyALEJsCIAIgAUEIEOQBIAMgAiBgEJsCIAQgA0EIEOQBIAVBwOAIaiILIAQgHhCbAiABIAtBBRDkASACIAEgERCbAiADIAJBCBDkASAEIAMgIBCbAiAFQYDlCGoiCyAEQQ0Q5AEgASAaIAsQmwIgAiABQQkQ5AEgAyACIA0QmwIgBCADQQgQ5AEgBUHA6QhqIgsgBCAZEJsCIAEgC0EJEOQBIAIgASAIEJsCIAMgAkEJEOQBIAQgAyAXEJsCIAVBgO4IaiILIARBCBDkASABIDcgCxCbAiACIAFBAxDkASADIAIgOxCbAiAEIANBDRDkASAFQcDyCGoiCyAEIDEQmwIgASALQQoQ5AEgAiABICcQmwIgAyACQQgQ5AEgBCADIDIQmwIgBUGA9whqIgsgBEEJEOQBIAEgFCALEJsCIAIgAUELEOQBIAMgAiA5EJsCIAQgA0EJEOQBIAVBwPsIaiILIAQgFBCbAiABIAtBCBDkASACIAEgQhCbAiADIAJBAxDkASAEIAMgOxCbAiAFQYCACWoiCyAEQQ0Q5AEgASAkIAsQmwIgAiABQQkQ5AEgAyACIBQQmwIgBCADQQgQ5AEgBUHAhAlqIgsgBCBzEJsCIAEgC0EKEOQBIAIgASBQEJsCIAMgAkEJEOQBIAQgAyAYEJsCIAVBgIkJaiILIARBBxDkASABIEIgCxCbAiACIAFBDBDkASADIAIgWhCbAiAEIANBBBDkASAFQcCNCWoiCyAEIFMQmwIgASALQQwQ5AEgAiABIEwQmwIgAyACQQcQ5AEgBCADICMQmwIgBUGAkglqIgsgBEEJEOQBIAEgdCALEJsCIAIgAUEJEOQBIAMgAiAxEJsCIAQgA0EKEOQBIAVBwJYJaiILIAQgJhCbAiABIAtBCRDkASACIAEgTxCbAiADIAJBCBDkASAEIAMgcRCbAiAFQYCbCWoiCyAEQQoQ5AEgASAoIAsQmwIgAiABQQkQ5AEgAyACIDUQmwIgBCADQQgQ5AEgBUHAnwlqIgsgBCB3EJsCIAEgC0EIEOQBIAIgASANEJsCIAMgAkEIEOQBIAQgAyA3EJsCIAVBgKQJaiILIARBDBDkASABIBcgCxCbAiACIAFBCBDkASADIAIgFBCbAiAEIANBBRDkASAFQcCoCWoiCyAEIDwQmwIgASALQQsQ5AEgAiABIEoQmwIgAyACQQoQ5AEgBCADIBkQmwIgBUGArQlqIgsgBEEIEOQBIAEgFyALEJsCIAIgAUELEOQBIAMgAiAREJsCIAQgA0EIEOQBIAVBwLEJaiILIAQgHxCbAiABIAtBDRDkASACIAEgRhCbAiADIAJBBxDkASAEIAMgQBCbAiAFQYC2CWoiCyAEQQgQ5AEgASAsIAsQmwIgAiABQQoQ5AEgAyACIBcQmwIgBCADQQgQ5AEgBUHAuglqIgsgBCAoEJsCIAEgC0EHEOQBIAIgASAiEJsCIAMgAkEKEOQBIAQgAyAdEJsCIAVBgL8JaiILIARBCRDkASABIHIgCxCbAiACIAFBCRDkASADIAIgLxCbAiAEIANBCRDkASAFQcDDCWoiCyAEICAQmwIgASALQQ4Q5AEgAiABIAYQmwIgAyACQQoQ5AEgBCADIBgQmwIgBUGAyAlqIgsgBEEHEOQBIAEgIyALEJsCIAIgAUEJEOQBIAMgAiA/EJsCIAQgA0ELEOQBIAVBwMwJaiILIAQgahCbAiABIAtBCRDkASACIAEgIRCbAiADIAJBCBDkASAEIAMgSBCbAiAFQYDRCWoiCyAEQQYQ5AEgASAiIAsQmwIgAiABQQsQ5AEgAyACIAYQmwIgBCADQQoQ5AEgBUHA1QlqIgsgBCAIEJsCIAEgC0EIEOQBIAIgASBrEJsCIAMgAkEIEOQBIAQgAyAdEJsCIAVBgNoJaiIIIARBCBDkASABIBsgCBCbAiACIAFBBRDkASADIAIgDxCbAiAEIANBDBDkASAFQcDeCWoiCCAEIIQBEJsCIAEgCEEIEOQBIAIgASB4EJsCIAMgAkEJEOQBIAQgAyA1EJsCIAVBgOMJaiIIIARBBxDkASABIEIgCBCbAiACIAFBCRDkASADIAIgGhCbAiAEIANBChDkASAFQcDnCWoiCCAEIEEQmwIgASAIQQgQ5AEgAiABICcQmwIgAyACQQgQ5AEgBCADIHAQmwIgBUGA7AlqIgggBEEIEOQBIAEgMyAIEJsCIAIgAUELEOQBIAMgAiAmEJsCIAQgA0EIEOQBIAVBwPAJaiIIIAQgIRCbAiABIAhBDBDkASACIAEgZhCbAiADIAJBBRDkASAEIAMgUxCbAiAFQYD1CWoiCCAEQQ4Q5AEgASCFASAIEJsCIAIgAUEHEOQBIAMgAiBVEJsCIAQgA0EKEOQBIAVBwPkJaiIIIAQgYRCbAiABIAhBDBDkASACIAEgaRCbAiADIAJBCxDkASAEIAMgIRCbAiAFQYD+CWoiCCAEQQcQ5AEgASBWIAgQmwIgAiABQQgQ5AEgAyACICoQmwIgBCADQQsQ5AEgBUHAggpqIgggBCA6EJsCIAEgCEEIEOQBIAIgASBQEJsCIAMgAkEIEOQBIAQgAyAjEJsCIAVBgIcKaiIIIARBCxDkASABIB4gCBCbAiACIAFBCRDkASADIAIgYBCbAiAEIANBCBDkASAFQcCLCmoiCCAEIFgQmwIgASAIQQQQ5AEgAiABID0QmwIgAyACQQcQ5AEgBCADIB8QmwIgBUGAkApqIgggBEENEOQBIAEgYiAIEJsCIAIgAUEIEOQBIAMgAiAYEJsCIAQgA0EIEOQBIAVBwJQKaiIIIAQgXxCbAiABIAhBCBDkASACIAEgXBCbAiADIAJBCRDkASAEIAMgHBCbAiAFQYCZCmoiCCAEQQgQ5AEgASA5IAgQmwIgAiABQQgQ5AEgAyACIBgQmwIgBCADQQgQ5AEgBUHAnQpqIgggBCAoEJsCIAEgCEEREOQBIAIgASBGEJsCIAMgAkEIEOQBIAQgAyAkEJsCIAVBgKIKaiIIIARBCRDkASABIBEgCBCbAiACIAFBCxDkASADIAIgORCbAiAEIANBBxDkASAFQcCmCmoiCCAEIDAQmwIgASAIQQ4Q5AEgAiABIBMQmwIgAyACQQgQ5AEgBCADIDoQmwIgBUGAqwpqIgggBEEIEOQBIAEgKSAIEJsCIAIgAUEMEOQBIAMgAiBaEJsCIAQgA0ENEOQBIAVBwK8KaiIIIAQgQRCbAiABIAhBCBDkASACIAEgQxCbAiADIAJBChDkASAEIAMgKRCbAiAFQYC0CmoiCCAEQQsQ5AEgASAdIAgQmwIgAiABQQcQ5AEgAyACIEoQmwIgBCADQQQQ5AEgBUHAuApqIgggBCAfEJsCIAEgCEEMEOQBIAIgASBAEJsCIAMgAkEHEOQBIAQgAyAPEJsCIAVBgL0KaiIIIARBCxDkASABIDYgCBCbAiACIAFBCBDkASADIAIgYxCbAiAEIANBCBDkASAFQcDBCmoiCCAEIBQQmwIgASAIQQsQ5AEgAiABIDgQmwIgAyACQQwQ5AEgBCADICAQmwIgBUGAxgpqIgggBEEKEOQBIAEgRSAIEJsCIAIgAUEIEOQBIAMgAiAJEJsCIAQgA0EHEOQBIAVBwMoKaiIIIAQgQBCbAiABIAhBCxDkASACIAEgOhCbAiADIAJBBhDkASAEIAMgMBCbAiAFQYDPCmoiCCAEQQsQ5AEgASBNIAgQmwIgAiABQQoQ5AEgAyACIEIQmwIgBCADQQkQ5AEgBUHA0wpqIgggBCAcEJsCIAEgCEEGEOQBIAIgASAlEJsCIAMgAkEKEOQBIAQgAyBOEJsCIAVBgNgKaiIIIARBAhDkASABIAUgCBCbAiACIAFBEBDkASADIAIgFhCbAiAEIANBBhDkASAFQcDcCmoiCCAEIDAQmwIgASAIQQcQ5AEgAiABIBEQmwIgAyACQQoQ5AEgBCADIDMQmwIgBUGA4QpqIgggBEELEOQBIAEgRyAIEJsCIAIgAUEJEOQBIAMgAiBXEJsCIAQgA0EGEOQBIAVBwOUKaiIIIAQgIxCbAiABIAhBDRDkASACIAEgMBCbAiADIAJBChDkASAEIAMgaBCbAiAFQYDqCmoiCCAEQQIQ5AEgASAFIAgQmwIgAiABQQ4Q5AEgAyACIBQQmwIgBCADQQUQ5AEgBUHA7gpqIgggBCA9EJsCIAEgCEEOEOQBIAIgASBMEJsCIAMgAkEIEOQBIAQgAyAcEJsCIAVBgPMKaiIIIARBCBDkASABIAYgCBCbAiACIAFBCBDkASADIAIgeRCbAiAEIANBCxDkASAFQcD3CmoiCCAEIBkQmwIgASAIQQcQ5AEgAiABIAkQmwIgAyACQQkQ5AEgBCADIFgQmwIgBUGA/ApqIgggBEEIEOQBIAEgJyAIEJsCIAIgAUEJEOQBIAMgAiAxEJsCIAQgA0EIEOQBIAVBwIALaiIIIAQgJRCbAiABIAhBCxDkASACIAEgShCbAiADIAJBCRDkASAEIAMgIRCbAiAFQYCFC2oiCCAEQQUQ5AEgASA/IAgQmwIgAiABQQwQ5AEgAyACIFcQmwIgBCADQQcQ5AEgBUHAiQtqIgggBCAyEJsCIAEgCEEKEOQBIAIgASB4EJsCIAMgAkELEOQBIAQgAyAGEJsCIIgBIgYgBEEIEOQBIAEgeSAGEJsCIAIgAUEEEOQBIAMgAiAVEJsCIAQgA0EMEOQBIAoiBiAEIBEQmwIgASAGQQcQ5AEgAiABIGwQmwIgAyACQQgQ5AEgBCADID0QmwIgB0GQMGoiUyAEQQQQ5AEgBUHgrwtqJAAgB0HQNGoiBiBTIFIQmwIjAEGgiQprIgUkACAFIAY2AoDsCSAFIAZBoAJqIgg2AoTsCSAFQcD5CWoiASAFQYDsCWoiERCQAyAFQYD1CWoiAiABQeAA/AoAACAFQcDwCWoiAyACQeAA/AoAACAFQYD+CWoiBCADQeAA/AoAACAFQYCHCmoiDyAEQeAA/AoAACABIBEQkAMgAiABQeAA/AoAACADIAJB4AD8CgAAIAQgA0HgAPwKAAAgBUHghwpqIARB4AD8CgAAIAEgERCQAyACIAFB4AD8CgAAIAMgAkHgAPwKAAAgBCADQeAA/AoAACAFQcCICmogBEHgAPwKAAAgBUHAggpqIA9BoAL8CgAAIAUgBkHABGo2AsTnCSAFIAg2AsDnCSAFQYD1CWoiAyAFQcDnCWoiURCQAyAFQcDwCWoiBCADQeAA/AoAACAFQYDsCWoiQyAEQeAA/AoAACAFQcD5CWoiAiBDQeAA/AoAACAFQYD+CWoiASACQeAA/AoAACADIFEQkAMgBCADQeAA/AoAACBDIARB4AD8CgAAIAIgQ0HgAPwKAAAgBUHg/glqIAJB4AD8CgAAIAMgURCQAyAEIANB4AD8CgAAIEMgBEHgAPwKAAAgAiBDQeAA/AoAACAFQcD/CWogAkHgAPwKAAAgBUGAhwpqIgYgAUGgAvwKAAAgBUHghApqIAZBoAL8CgAAIAUgBUHAggpqQcAE/AoAACAFQcAEaiIGIAVBARDkASAFQYAJaiIpIAUgBhCbAiAFQcANaiIdIAYgKRCbAiAFQYASaiI5IAYgHRCbAiAFQcAWaiIqIAYgORCbAiAFQYAbaiIsIAYgKhCbAiAFQcAfaiIRIAYgLBCbAiAFQYAkaiJEIAYgERCbAiAFQcAoaiJMIAYgRBCbAiAFQYAtaiIWIAYgTBCbAiAFQcAxaiIJIAYgFhCbAiAFQYA2aiIZIAYgCRCbAiAFQcA6aiISIAYgGRCbAiAFQYA/aiIvIAYgEhCbAiAFQcDDAGoiOiAGIC8QmwIgBUGAyABqIjsgBiA6EJsCIAVBwMwAaiJFIAYgOxCbAiAFQYDRAGoiPCAGIEUQmwIgBUHA1QBqIh8gBiA8EJsCIAVBgNoAaiJGIAYgHxCbAiAFQcDeAGoiLSAGIEYQmwIgBUGA4wBqIhQgBiAtEJsCIAVBwOcAaiIXIAYgFBCbAiAFQYDsAGoiMCAGIBcQmwIgBUHA8ABqIh4gBiAwEJsCIAVBgPUAaiIhIAYgHhCbAiAFQcD5AGoiGCAGICEQmwIgBUGA/gBqIk0gBiAYEJsCIAVBwIIBaiIxIAYgTRCbAiAFQYCHAWoiICAGIDEQmwIgBUHAiwFqIhogBiAgEJsCIAVBgJABaiIVIAYgGhCbAiAFQcCUAWoiPSAGIBUQmwIgBUGAmQFqIiIgBiA9EJsCIAVBwJ0BaiJOIAYgIhCbAiAFQYCiAWoiGyAGIE4QmwIgBUHApgFqIjIgBiAbEJsCIAVBgKsBaiJJIAYgMhCbAiAFQcCvAWoiPiAGIEkQmwIgBUGAtAFqIhMgBiA+EJsCIAVBwLgBaiIjIAYgExCbAiAFQYC9AWoiMyAGICMQmwIgBUHAwQFqIj8gBiAzEJsCIAVBgMYBaiILIAYgPxCbAiAFQcDKAWoiRyAGIAsQmwIgBUGAzwFqIiUgBiBHEJsCIAVBwNMBaiIIIAYgJRCbAiAFQYDYAWoiSiAGIAgQmwIgBUHA3AFqIiQgBiBKEJsCIAVBgOEBaiInIAYgJBCbAiAFQcDlAWoiQCAGICcQmwIgBUGA6gFqIlAgBiBAEJsCIAVBwO4BaiI0IAYgUBCbAiAFQYDzAWoiNSAGIDQQmwIgBUHA9wFqIiggBiA1EJsCIAVBgPwBaiI2IAYgKBCbAiAFQcCAAmoiQSAGIDYQmwIgBUGAhQJqIiYgBiBBEJsCIAVBwIkCaiJCIAYgJhCbAiAFQYCOAmoiDyAGIEIQmwIgBUHAkgJqIjcgBiAPEJsCIAVBgJcCaiIcIAYgNxCbAiAFQcCbAmoiDSAGIBwQmwIgBUGAoAJqIlIgBiANEJsCIAVBwKQCaiJIIFJBARDkASAFQYCpAmoiBiAFIEgQmwIgASAGQQEQ5AEgBUHArQJqIkggASAFEJsCIAVBgLICaiI4IEEgSBCbAiABIEhBARDkASAFQcC2AmoiVCABIAUQmwIgBUGAuwJqIgwgOEEBEOQBIAEgVEEBEOQBIAVBwL8CaiI4IAEgBRCbAiAEIAxBAhDkASADIAQgLRCbAiACIANBCBDkASABIAIgPBCbAiAFQYDEAmoiDCABQQkQ5AEgBCBAIAwQmwIgAyAEQQcQ5AEgAiADIEAQmwIgASACQQ0Q5AEgBUHAyAJqIgwgASA1EJsCIAQgDEEHEOQBIAMgBCALEJsCIAIgA0EEEOQBIAEgAiAdEJsCIAVBgM0CaiIMIAFBCRDkASAEIB0gDBCbAiADIARBDRDkASACIAMgDxCbAiABIAJBBxDkASAFQcDRAmoiDCABIEwQmwIgBCAMQQkQ5AEgAyAEIEUQmwIgAiADQQcQ5AEgASACIEUQmwIgBUGA1gJqIgwgAUEHEOQBIAQgFCAMEJsCIAMgBEEHEOQBIAIgAyApEJsCIAEgAkEQEOQBIAVBwNoCaiIMIAEgMRCbAiAEIAxBCBDkASADIAQgLRCbAiACIANBCBDkASABIAIgIBCbAiAFQYDfAmoiDCABQQoQ5AEgBCAzIAwQmwIgAyAEQQcQ5AEgAiADIDIQmwIgASACQQYQ5AEgBUHA4wJqIgwgASAtEJsCIAQgDEEJEOQBIAMgBCALEJsCIAIgA0EHEOQBIAEgAiAREJsCIAVBgOgCaiIMIAFBChDkASAEICcgDBCbAiADIARBBxDkASACIAMgFBCbAiABIAJBChDkASAFQcDsAmoiDCABIA8QmwIgBCAMQQcQ5AEgAyAEIEEQmwIgAiADQQcQ5AEgASACIDoQmwIgBUGA8QJqIgwgAUEJEOQBIAQgGyAMEJsCIAMgBEEIEOQBIAIgAyAIEJsCIAEgAkEHEOQBIAVBwPUCaiIMIAEgERCbAiAEIAxBCRDkASADIAQgGBCbAiACIANBChDkASABIAIgNxCbAiAFQYD6AmoiDCABQQoQ5AEgBCAYIAwQmwIgAyAEQQoQ5AEgAiADIDYQmwIgASACQQcQ5AEgBUHA/gJqIgwgASAoEJsCIAQgDEEIEOQBIAMgBCBEEJsCIAIgA0ELEOQBIAEgAiAlEJsCIAVBgIMDaiIMIAFBBxDkASAEIA8gDBCbAiADIARBCBDkASACIAMgFBCbAiABIAJBChDkASAFQcCHA2oiDCABICIQmwIgBCAMQQcQ5AEgAyAEIAsQmwIgAiADQQYQ5AEgASACIB8QmwIgBUGAjANqIgwgAUEJEOQBIAQgIyAMEJsCIAMgBEEFEOQBIAIgAyAsEJsCIAEgAkEIEOQBIAVBwJADaiIMIAEgKhCbAiAEIAxBDBDkASADIAQgSRCbAiACIANBCBDkASABIAIgIxCbAiAFQYCVA2oiDCABQQcQ5AEgBCA2IAwQmwIgAyAEQQgQ5AEgAiADICMQmwIgASACQQgQ5AEgBUHAmQNqIgwgASAPEJsCIAQgDEEIEOQBIAMgBCAyEJsCIAIgA0EFEOQBIAEgAiA6EJsCIAVBgJ4DaiIMIAFBChDkASAEIDAgDBCbAiADIARBCBDkASACIAMgPhCbAiABIAJBBRDkASAFQcCiA2oiDCABIEwQmwIgBCAMQQkQ5AEgAyAEIAgQmwIgAiADQQ0Q5AEgASACICEQmwIgBUGApwNqIgwgAUEHEOQBIAQgHiAMEJsCIAMgBEEGEOQBIAIgAyAvEJsCIAEgAkEJEOQBIAVBwKsDaiIMIAEgUBCbAiAEIAxBBxDkASADIAQgERCbAiACIANBChDkASABIAIgGxCbAiAFQYCwA2oiDCABQQUQ5AEgBCBMIAwQmwIgAyAEQQoQ5AEgAiADID0QmwIgASACQQgQ5AEgBUHAtANqIgwgASAnEJsCIAQgDEEKEOQBIAMgBCAcEJsCIAIgA0EIEOQBIAEgAiA+EJsCIAVBgLkDaiIMIAFBBxDkASAEIEIgDBCbAiADIARBCRDkASACIAMgIhCbAiABIAJBBBDkASAFQcC9A2oiDCABIBEQmwIgBCAMQQ4Q5AEgAyAEID8QmwIgAiADQQYQ5AEgASACIBoQmwIgBUGAwgNqIgwgAUEFEOQBIAQgOSAMEJsCIAMgBEEKEOQBIAIgAyBNEJsCIAEgAkEJEOQBIAVBwMYDaiIMIAEgNBCbAiAEIAxBBxDkASADIAQgQBCbAiACIANBAxDkASABIAIgKRCbAiAFQYDLA2oiDCABQQ0Q5AEgBCAzIAwQmwIgAyAEQQQQ5AEgAiADICkQmwIgASACQQsQ5AEgBUHAzwNqIgwgASASEJsCIAQgDEEJEOQBIAMgBCBGEJsCIAIgA0EIEOQBIAEgAiAcEJsCIAVBgNQDaiIMIAFBBxDkASAEIFAgDBCbAiADIARBAhDkASACIAMgKRCbAiABIAJBERDkASAFQcDYA2oiDCABIDgQmwIgBCAMQQcQ5AEgAyAEIDAQmwIgAiADQQoQ5AEgASACIDUQmwIgBUGA3QNqIgwgAUEIEOQBIAQgEyAMEJsCIAMgBEEHEOQBIAIgAyAxEJsCIAEgAkEKEOQBIAVBwOEDaiIMIAEgBhCbAiAEIAxBCBDkASADIAQgRhCbAiACIANBCBDkASABIAIgIRCbAiAFQYDmA2oiDCABQQgQ5AEgBCAZIAwQmwIgAyAEQQYQ5AEgAiADIBEQmwIgASACQQkQ5AEgBUHA6gNqIgwgASAvEJsCIAQgDEEJEOQBIAMgBCAYEJsCIAIgA0EGEOQBIAEgAiA6EJsCIAVBgO8DaiIMIAFBCBDkASAEIDwgDBCbAiADIARBChDkASACIAMgHhCbAiABIAJBCBDkASAFQcDzA2oiDCABIAkQmwIgBCAMQQoQ5AEgAyAEICMQmwIgAiADQQcQ5AEgASACIBUQmwIgBUGA+ANqIgwgAUEHEOQBIAQgFyAMEJsCIAMgBEEJEOQBIAIgAyAvEJsCIAEgAkEJEOQBIAVBwPwDaiIMIAEgMBCbAiAEIAxBCBDkASADIAQgMhCbAiACIANBBhDkASABIAIgMRCbAiAFQYCBBGoiDCABQQgQ5AEgBCBNIAwQmwIgAyAEQQgQ5AEgAiADID8QmwIgASACQQcQ5AEgBUHAhQRqIgwgASA3EJsCIAQgDEEGEOQBIAMgBCAgEJsCIAIgA0EIEOQBIAEgAiAnEJsCIAVBgIoEaiIMIAFBBBDkASAEIBEgDBCbAiADIARBDRDkASACIAMgHBCbAiABIAJBBhDkASAFQcCOBGoiDCABIB4QmwIgBCAMQQgQ5AEgAyAEICgQmwIgAiADQQcQ5AEgASACID0QmwIgBUGAkwRqIgwgAUEHEOQBIAQgJCAMEJsCIAMgBEEGEOQBIAIgAyAgEJsCIAEgAkEHEOQBIAVBwJcEaiIMIAEgRhCbAiAEIAxBCBDkASADIAQgFhCbAiACIANBCxDkASABIAIgUhCbAiAFQYCcBGoiDCABQQkQ5AEgBCA+IAwQmwIgAyAEQQYQ5AEgAiADIBQQmwIgASACQQgQ5AEgBUHAoARqIgwgASAlEJsCIAQgDEEHEOQBIAMgBCAPEJsCIAIgA0EHEOQBIAEgAiBJEJsCIAVBgKUEaiIMIAFBBxDkASAEIBggDBCbAiADIARBCBDkASACIAMgShCbAiABIAJBChDkASAFQcCpBGoiDCABIDYQmwIgBCAMQQcQ5AEgAyAEIBcQmwIgAiADQQUQ5AEgASACIDkQmwIgBUGArgRqIgwgAUEPEOQBIAQgPSAMEJsCIAMgBEEIEOQBIAIgAyBBEJsCIAEgAkEDEOQBIAVBwLIEaiIMIAEgBRCbAiAEIAxBDxDkASADIAQgHhCbAiACIANBCBDkASABIAIgJBCbAiAFQYC3BGoiDCABQQkQ5AEgBCAcIAwQmwIgAyAEQQcQ5AEgAiADIBYQmwIgASACQQoQ5AEgBUHAuwRqIgwgASAIEJsCIAQgDEEIEOQBIAMgBCAPEJsCIAIgA0EFEOQBIAEgAiAZEJsCIAVBgMAEaiIMIAFBBhDkASAEICwgDBCbAiADIARBBhDkASACIAMgKRCbAiABIAJBDhDkASAFQcDEBGoiDCABIDgQmwIgBCAMQQEQ5AEgAyAEIAUQmwIgAiADQQgQ5AEgASACIEcQmwIgBUGAyQRqIjggAUEJEOQBIAQgQiA4EJsCIAMgBEEJEOQBIAIgAyAcEJsCIAEgAkEKEOQBIAVBwM0EaiI4IAEgNRCbAiAEIDhBCBDkASADIAQgHxCbAiACIANBAxDkASABIAIgBRCbAiAFQYDSBGoiOCABQQkQ5AEgBCAGIDgQmwIgAyAEQQsQ5AEgAiADIBQQmwIgASACQQcQ5AEgBUHA1gRqIjggASAhEJsCIAQgOEEHEOQBIAMgBCAVEJsCIAIgA0EHEOQBIAEgAiAUEJsCIAVBgNsEaiIVIAFBBxDkASAEIB8gFRCbAiADIARBDRDkASACIAMgPRCbAiABIAJBChDkASAFQcDfBGoiFSABID4QmwIgBCAVQQgQ5AEgAyAEIEAQmwIgAiADQQgQ5AEgASACID8QmwIgBUGA5ARqIhUgAUEGEOQBIAQgHyAVEJsCIAMgBEEJEOQBIAIgAyAjEJsCIAEgAkEIEOQBIAVBwOgEaiIVIAEgCBCbAiAEIBVBBhDkASADIAQgIBCbAiACIANBCBDkASABIAIgShCbAiAFQYDtBGoiFSABQQoQ5AEgBCAIIBUQmwIgAyAEQQcQ5AEgAiADIBMQmwIgASACQQgQ5AEgBUHA8QRqIhUgASA3EJsCIAQgFUEIEOQBIAMgBCAkEJsCIAIgA0EHEOQBIAEgAiALEJsCIAVBgPYEaiIVIAFBCBDkASAEIDIgFRCbAiADIARBBxDkASACIAMgGxCbAiABIAJBChDkASAFQcD6BGoiFSABIDIQmwIgBCAVQQwQ5AEgAyAEIAgQmwIgAiADQQkQ5AEgASACIEIQmwIgBUGA/wRqIhUgAUEKEOQBIAQgGiAVEJsCIAMgBEEIEOQBIAIgAyAgEJsCIAEgAkEHEOQBIAVBwIMFaiIVIAEgGhCbAiAEIBVBBhDkASADIAQgLxCbAiACIANBCRDkASABIAIgNRCbAiAFQYCIBWoiFSABQQUQ5AEgBCAvIBUQmwIgAyAEQQoQ5AEgAiADIEkQmwIgASACQQoQ5AEgBUHAjAVqIhUgASAyEJsCIAQgFUEEEOQBIAMgBCBEEJsCIAIgA0ELEOQBIAEgAiAiEJsCIAVBgJEFaiIVIAFBBxDkASAEIAkgFRCbAiADIARBCRDkASACIAMgMRCbAiABIAJBCRDkASAFQcCVBWoiFSABICIQmwIgBCAVQQUQ5AEgAyAEIBYQmwIgAiADQQoQ5AEgASACIEcQmwIgBUGAmgVqIhUgAUEJEOQBIAQgJiAVEJsCIAMgBEEIEOQBIAIgAyAkEJsCIAEgAkEGEOQBIAVBwJ4FaiIVIAEgIRCbAiAEIBVBCRDkASADIAQgHhCbAiACIANBBxDkASABIAIgFxCbAiAFQYCjBWoiFSABQQsQ5AEgBCBQIBUQmwIgAyAEQQgQ5AEgAiADICUQmwIgASACQQwQ5AEgBUHApwVqIhUgASAoEJsCIAQgFUELEOQBIAMgBCAiEJsCIAIgA0EHEOQBIAEgAiAPEJsCIAVBgKwFaiIVIAFBCRDkASAEIDQgFRCbAiADIARBBBDkASACIAMgLBCbAiABIAJBCxDkASAFQcCwBWoiFSABICcQmwIgBCAVQQQQ5AEgAyAEICoQmwIgAiADQQsQ5AEgASACIBMQmwIgBUGAtQVqIhMgAUEFEOQBIAQgGSATEJsCIAMgBEEGEOQBIAIgAyAqEJsCIAEgAkEKEOQBIAVBwLkFaiITIAEgSRCbAiAEIBNBCBDkASADIAQgJRCbAiACIANBBBDkASABIAIgKhCbAiAFQYC+BWoiEyABQQkQ5AEgBCAfIBMQmwIgAyAEQQoQ5AEgAiADIAYQmwIgASACQQcQ5AEgBUHAwgVqIhMgASAUEJsCIAQgE0EKEOQBIAMgBCBEEJsCIAIgA0EKEOQBIAEgAiAlEJsCIAVBgMcFaiITIAFBBhDkASAEIDEgExCbAiADIARBCRDkASACIAMgNBCbAiABIAJBBhDkASAFQcDLBWoiEyABIDAQmwIgBCATQQcQ5AEgAyAEIBYQmwIgAiADQQkQ5AEgASACICYQmwIgBUGA0AVqIhMgAUEHEOQBIAQgJiATEJsCIAMgBEEKEOQBIAIgAyAXEJsCIAEgAkEMEOQBIAVBwNQFaiITIAEgQRCbAiAEIBNBBhDkASADIAQgKRCbAiACIANBDBDkASABIAIgKBCbAiAFQYDZBWoiEyABQQgQ5AEgBCAhIBMQmwIgAyAEQQYQ5AEgAiADIBkQmwIgASACQQkQ5AEgBUHA3QVqIhMgASAlEJsCIAQgE0EKEOQBIAMgBCAbEJsCIAIgA0EHEOQBIAEgAiAcEJsCIAVBgOIFaiITIAFBCRDkASAEIFIgExCbAiADIARBCxDkASACIAMgQRCbAiABIAJBBxDkASAFQcDmBWoiEyABIDYQmwIgBCATQQkQ5AEgAyAEID4QmwIgAiADQQcQ5AEgASACIBsQmwIgBUGA6wVqIhMgAUEGEOQBIAQgLCATEJsCIAMgBEELEOQBIAIgAyAjEJsCIAEgAkEGEOQBIAVBwO8FaiITIAEgEhCbAiAEIBNBChDkASADIAQgNBCbAiACIANBCBDkASABIAIgCxCbAiAFQYD0BWoiEyABQQUQ5AEgBCAZIBMQmwIgAyAEQQYQ5AEgAiADIB0QmwIgASACQQsQ5AEgBUHA+AVqIhMgASAzEJsCIAQgE0EGEOQBIAMgBCAYEJsCIAIgA0EFEOQBIAEgAiAREJsCIAVBgP0FaiITIAFBCxDkASAEIBggExCbAiADIARBCBDkASACIAMgEhCbAiABIAJBChDkASAFQcCBBmoiEyABIBwQmwIgBCATQQgQ5AEgAyAEIA8QmwIgAiADQQYQ5AEgASACICwQmwIgBUGAhgZqIhMgAUEIEOQBIAQgEiATEJsCIAMgBEEJEOQBIAIgAyAGEJsCIAEgAkEIEOQBIAVBwIoGaiITIAEgShCbAiAEIBNBBhDkASADIAQgRBCbAiACIANBDRDkASABIAIgJBCbAiAFQYCPBmoiEyABQQgQ5AEgBCAkIBMQmwIgAyAEQQUQ5AEgAiADIBIQmwIgASACQQkQ5AEgBUHAkwZqIhMgASA0EJsCIAQgE0EJEOQBIAMgBCALEJsCIAIgA0EDEOQBIAEgAiA5EJsCIAVBgJgGaiITIAFBDBDkASAEICIgExCbAiADIARBBhDkASACIAMgPBCbAiABIAJBCBDkASAFQcCcBmoiEyABIEoQmwIgBCATQQoQ5AEgAyAEICAQmwIgAiADQQoQ5AEgASACIBQQmwIgBUGAoQZqIhMgAUEKEOQBIAQgBiATEJsCIAMgBEEJEOQBIAIgAyAaEJsCIAEgAkEHEOQBIAVBwKUGaiIGIAEgOxCbAiAEIAZBBxDkASADIAQgEhCbAiACIANBCRDkASABIAIgCRCbAiAFQYCqBmoiBiABQQoQ5AEgBCA3IAYQmwIgAyAEQQkQ5AEgAiADID8QmwIgASACQQgQ5AEgBUHArgZqIgYgASAJEJsCIAQgBkEJEOQBIAMgBCBBEJsCIAIgA0EFEOQBIAEgAiAqEJsCIAVBgLMGaiIGIAFBBxDkASAEICwgBhCbAiADIARBDBDkASACIAMgCBCbAiABIAJBBxDkASAFQcC3BmoiBiABICIQmwIgBCAGQQkQ5AEgAyAEIEcQmwIgAiADQQkQ5AEgASACIEAQmwIgBUGAvAZqIgYgAUEHEOQBIAQgCyAGEJsCIAMgBEEKEOQBIAIgAyA7EJsCIAEgAkEIEOQBIAVBwMAGaiIGIAEgOxCbAiAEIAZBBxDkASADIAQgGRCbAiACIANBChDkASABIAIgJhCbAiAFQYDFBmoiBiABQQUQ5AEgBCAZIAYQmwIgAyAEQQkQ5AEgAiADIB8QmwIgASACQQoQ5AEgBUHAyQZqIgYgASAIEJsCIAQgBkEEEOQBIAMgBCBEEJsCIAIgA0ELEOQBIAEgAiAzEJsCIAVBgM4GaiIGIAFBBxDkASAEID0gBhCbAiADIARBCRDkASACIAMgNxCbAiABIAJBChDkASAFQcDSBmoiBiABIEAQmwIgBCAGQQEQ5AEgAyAEIAUQmwIgAiADQREQ5AEgASACID0QmwIgBUGA1wZqIgYgAUEIEOQBIAQgCCAGEJsCIAMgBEEHEOQBIAIgAyA/EJsCIAEgAkEGEOQBIAVBwNsGaiIGIAEgIBCbAiAEIAZBCBDkASADIAQgJxCbAiACIANBBRDkASABIAIgLxCbAiAFQYDgBmoiBiABQQwQ5AEgBCA1IAYQmwIgAyAEQQgQ5AEgAiADIDYQmwIgASACQQgQ5AEgBUHA5AZqIgYgASAbEJsCIAQgBkECEOQBIAMgBCAFEJsCIAIgA0EKEOQBIAEgAiBIEJsCIAVBgOkGaiIGIAFBBxDkASAEIBcgBhCbAiADIARBAxDkASACIAMgKRCbAiABIAJBDBDkASAFQcDtBmoiBiABIA8QmwIgBCAGQQYQ5AEgAyAEIAUQmwIgAiADQQwQ5AEgASACIEYQmwIgBUGA8gZqIgYgAUEJEOQBIAQgIyAGEJsCIAMgBEEGEOQBIAIgAyAhEJsCIAEgAkELEOQBIAVBwPYGaiIGIAEgJxCbAiAEIAZBBhDkASADIAQgMBCbAiACIANBCxDkASABIAIgJhCbAiAFQYD7BmoiBiABQQMQ5AEgBCA5IAYQmwIgAyAEQQsQ5AEgAiADIAsQmwIgASACQQUQ5AEgBUHA/wZqIgYgASA6EJsCIAQgBkEJEOQBIAMgBCAmEJsCIAIgA0EFEOQBIAEgAiAREJsCIAVBgIQHaiIGIAFBCxDkASAEIEggBhCbAiADIARBBhDkASACIAMgFhCbAiABIAJBCxDkASAFQcCIB2oiBiABIDUQmwIgBCAGQQcQ5AEgAyAEIA8QmwIgAiADQQYQ5AEgASACIBYQmwIgBUGAjQdqIgYgAUEJEOQBIAQgNiAGEJsCIAMgBEEKEOQBIAIgAyAnEJsCIAEgAkEHEOQBIAVBwJEHaiIGIAEgGxCbAiAEIAZBAxDkASADIAQgORCbAiACIANBDBDkASABIAIgNxCbAiAFQYCWB2oiBiABQQEQ5AEgBCAFIAYQmwIgAyAEQQ8Q5AEgAiADIBoQmwIgASACQQgQ5AEgBUHAmgdqIgYgASA2EJsCIAQgBkEFEOQBIAMgBCAREJsCIAIgA0EKEOQBIAEgAiBHEJsCIAVBgJ8HaiIGIAFBChDkASAEIDUgBhCbAiADIARBBhDkASACIAMgTRCbAiABIAJBCxDkASAFQcCjB2oiBiABIBYQmwIgBCAGQQwQ5AEgAyAEIBwQmwIgAiADQQgQ5AEgASACICQQmwIgBUGAqAdqIgYgAUEGEOQBIAQgCSAGEJsCIAMgBEEJEOQBIAIgAyAlEJsCIAEgAkEIEOQBIAVBwKwHaiIGIAEgCxCbAiAEIAZBBRDkASADIAQgOhCbAiACIANBCBDkASABIAIgRRCbAiAFQYCxB2oiBiABQQgQ5AEgBCAoIAYQmwIgAyAEQQgQ5AEgAiADID4QmwIgASACQQgQ5AEgBUHAtQdqIgYgASAfEJsCIAQgBkEMEOQBIAMgBCANEJsCIAIgA0EJEOQBIAEgAiAiEJsCIAVBgLoHaiIGIAFBARDkASAEIAUgBhCbAiADIARBCxDkASACIAMgVBCbAiABIAJBCRDkASAFQcC+B2oiBiABIA8QmwIgBCAGQQcQ5AEgAyAEIBQQmwIgAiADQQgQ5AEgASACIEIQmwIgBUGAwwdqIgYgAUEEEOQBIAQgRCAGEJsCIAMgBEEKEOQBIAIgAyBOEJsCIAEgAkEHEOQBIAVBwMcHaiIGIAEgGhCbAiAEIAZBCRDkASADIAQgKBCbAiACIANBBhDkASABIAIgGBCbAiAFQYDMB2oiBiABQQYQ5AEgBCA6IAYQmwIgAyAEQQgQ5AEgAiADIB0QmwIgASACQQsQ5AEgBUHA0AdqIgYgASA+EJsCIAQgBkEJEOQBIAMgBCAbEJsCIAIgA0ECEOQBIAEgAiApEJsCIAVBgNUHaiIGIAFBDBDkASAEIA8gBhCbAiADIARBBhDkASACIAMgIBCbAiABIAJBBhDkASAFQcDZB2oiBiABIAkQmwIgBCAGQQkQ5AEgAyAEIEUQmwIgAiADQQcQ5AEgASACIBcQmwIgBUGA3gdqIgYgAUEJEOQBIAQgNCAGEJsCIAMgBEEHEOQBIAIgAyAtEJsCIAEgAkEIEOQBIAVBwOIHaiIGIAEgFxCbAiAEIAZBCBDkASADIAQgThCbAiACIANBBBDkASABIAIgKhCbAiAFQYDnB2oiBiABQQsQ5AEgBCA3IAYQmwIgAyAEQQcQ5AEgAiADIB4QmwIgASACQQcQ5AEgBUHA6wdqIgYgASA8EJsCIAQgBkEMEOQBIAMgBCBHEJsCIAIgA0EEEOQBIAEgAiAREJsCIAVBgPAHaiIGIAFBCxDkASAEICcgBhCbAiADIARBBRDkASACIAMgOxCbAiABIAJBCRDkASAFQcD0B2oiBiABIDEQmwIgBCAGQQgQ5AEgAyAEIDMQmwIgAiADQQcQ5AEgASACICcQmwIgBUGA+QdqIgYgAUEHEOQBIAQgFyAGEJsCIAMgBEEIEOQBIAIgAyA2EJsCIAEgAkEGEOQBIAVBwP0HaiIGIAEgRhCbAiAEIAZBCBDkASADIAQgThCbAiACIANBCRDkASABIAIgRRCbAiAFQYCCCGoiBiABQQkQ5AEgBCALIAYQmwIgAyAEQQcQ5AEgAiADICgQmwIgASACQQoQ5AEgBUHAhghqIgYgASAkEJsCIAQgBkEKEOQBIAMgBCAfEJsCIAIgA0EHEOQBIAEgAiAwEJsCIAVBgIsIaiIGIAFBBhDkASAEIDsgBhCbAiADIARBCRDkASACIAMgFxCbAiABIAJBChDkASAFQcCPCGoiBiABIDQQmwIgBCAGQQcQ5AEgAyAEIBcQmwIgAiADQQgQ5AEgASACIA8QmwIgBUGAlAhqIgYgAUEHEOQBIAQgPCAGEJsCIAMgBEEIEOQBIAIgAyAbEJsCIAEgAkEHEOQBIAVBwJgIaiIGIAEgGBCbAiAEIAZBCBDkASADIAQgQhCbAiACIANBBxDkASABIAIgIxCbAiAFQYCdCGoiBiABQQYQ5AEgBCAtIAYQmwIgAyAEQQYQ5AEgAiADIEwQmwIgASACQQcQ5AEgBUHAoQhqIgYgASAZEJsCIAQgBkEJEOQBIAMgBCAmEJsCIAIgA0EIEOQBIAEgAiAeEJsCIAVBgKYIaiIGIAFBBxDkASAEIB8gBhCbAiADIARBCBDkASACIAMgMxCbAiABIAJBCRDkASAFQcCqCGoiBiABIFAQmwIgBCAGQQcQ5AEgAyAEICIQmwIgAiADQQoQ5AEgASACIBwQmwIgBUGArwhqIgYgAUEHEOQBIAQgHSAGEJsCIAMgBEEMEOQBIAIgAyA3EJsCIAEgAkEHEOQBIAVBwLMIaiIGIAEgNRCbAiAEIAZBBhDkASADIAQgIRCbAiACIANBCRDkASABIAIgCRCbAiAFQYC4CGoiBiABQQYQ5AEgBCAdIAYQmwIgAyAEQQ0Q5AEgAiADIBkQmwIgASACQQoQ5AEgBUHAvAhqIgYgASAIEJsCIAQgBkEFEOQBIAMgBCAqEJsCIAIgA0EMEOQBIAEgAiBFEJsCIAVBgMEIaiIGIAFBBhDkASAEICogBhCbAiADIARBCRDkASACIAMgOxCbAiABIAJBDBDkASAFQcDFCGoiBiABIA0QmwIgBCAGQQoQ5AEgAyAEIAgQmwIgAiADQQwQ5AEgASACIA0QmwIgBUGAyghqIgYgAUEJEOQBIAQgMiAGEJsCIAMgBEEHEOQBIAIgAyAUEJsCIAEgAkEJEOQBIAVBwM4IaiIGIAEgRhCbAiAEIAZBCRDkASADIAQgLxCbAiACIANBCRDkASABIAIgJxCbAiAFQYDTCGoiBiABQQkQ5AEgBCA/IAYQmwIgAyAEQQYQ5AEgAiADIB4QmwIgASACQQgQ5AEgBUHA1whqIgYgASAoEJsCIAQgBkEHEOQBIAMgBCAYEJsCIAIgA0EIEOQBIAEgAiAbEJsCIAVBgNwIaiIGIAFBBhDkASAEIBQgBhCbAiADIARBChDkASACIAMgLxCbAiABIAJBCRDkASAFQcDgCGoiBiABIBQQmwIgBCAGQQUQ5AEgAyAEIB0QmwIgAiADQQgQ5AEgASACIDkQmwIgBUGA5QhqIgYgAUEKEOQBIAQgOiAGEJsCIAMgBEEKEOQBIAIgAyAmEJsCIAEgAkELEOQBIAVBwOkIaiIGIAEgLRCbAiAEIAZBBxDkASADIAQgIBCbAiACIANBDhDkASABIAIgMBCbAiAFQYDuCGoiBiABQQIQ5AEgBCAFIAYQmwIgAyAEQQ4Q5AEgAiADIEoQmwIgASACQQcQ5AEgBUHA8ghqIgYgASAoEJsCIAQgBkEHEOQBIAMgBCBCEJsCIAIgA0EEEOQBIAEgAiAdEJsCIAVBgPcIaiIGIAFBDBDkASAEIB4gBhCbAiADIARBBRDkASACIAMgERCbAiABIAJBCxDkASAFQcD7CGoiBiABIEcQmwIgBCAGQQcQ5AEgAyAEICUQmwIgAiADQQYQ5AEgASACICEQmwIgBUGAgAlqIgYgAUEJEOQBIAQgGCAGEJsCIAMgBEEPEOQBIAIgAyAkEJsCIAEgAkEHEOQBIAVBwIQJaiIGIAEgLRCbAiAEIAZBCRDkASADIAQgSRCbAiACIANBBxDkASABIAIgIRCbAiAFQYCJCWoiBiABQQcQ5AEgBCAJIAYQmwIgAyAEQQYQ5AEgAiADIBEQmwIgASACQQkQ5AEgBUHAjQlqIgYgASAtEJsCIAQgBkEJEOQBIAMgBCAzEJsCIAIgA0EJEOQBIAEgAiBSEJsCIAVBgJIJaiIGIAFBCBDkASAEID8gBhCbAiADIARBBRDkASACIAMgCRCbAiABIAJBChDkASAFQcCWCWoiBiABIBsQmwIgBCAGQQgQ5AEgAyAEIBgQmwIgAiADQQQQ5AEgASACIB0QmwIgBUGAmwlqIgYgAUEKEOQBIAQgMSAGEJsCIAMgBEEIEOQBIAIgAyASEJsCIAEgAkEJEOQBIAVBwJ8JaiIGIAEgCBCbAiAEIAZBBxDkASADIAQgKBCbAiACIANBCxDkASABIAIgQRCbAiAFQYCkCWoiBiABQQcQ5AEgBCAkIAYQmwIgAyAEQQIQ5AEgAiADICkQmwIgASACQQ8Q5AEgBUHAqAlqIgYgASAjEJsCIAQgBkEFEOQBIAMgBCAREJsCIAIgA0EIEOQBIAEgAiAWEJsCIAVBgK0JaiIGIAFBCRDkASAEIDMgBhCbAiADIARBBxDkASACIAMgQhCbAiABIAJBBxDkASAFQcCxCWoiBiABIAsQmwIgBCAGQQgQ5AEgAyAEICMQmwIgAiADQQgQ5AEgASACIBcQmwIgBUGAtglqIgYgAUELEOQBIAQgQCAGEJsCIAMgBEEHEOQBIAIgAyAwEJsCIAEgAkEJEOQBIAVBwLoJaiIGIAEgIBCbAiAEIAZBBhDkASADIAQgOxCbAiACIANBBhDkASABIAIgLBCbAiAFQYC/CWoiBiABQQsQ5AEgBCA9IAYQmwIgAyAEQQcQ5AEgAiADIDQQmwIgASACQQQQ5AEgBUHAwwlqIgYgASAsEJsCIAQgBkEKEOQBIAMgBCANEJsCIAIgA0EDEOQBIAEgAiAFEJsCIAVBgMgJaiIGIAFBDBDkASAEIDEgBhCbAiADIARBCRDkASACIAMgThCbAiABIAJBBxDkASAFQcDMCWoiBiABIBwQmwIgBCAGQQcQ5AEgAyAEICYQmwIgAiADQQYQ5AEgASACIDwQmwIgBUGA0QlqIgYgAUEIEOQBIAQgMiAGEJsCIAMgBEEIEOQBIAIgAyAIEJsCIAEgAkEFEOQBIAVBwNUJaiIGIAEgHRCbAiAEIAZBCxDkASADIAQgHBCbAiACIANBBRDkASABIAIgCRCbAiAFQYDaCWoiBiABQQkQ5AEgBCAiIAYQmwIgAyAEQQUQ5AEgAiADIAkQmwIgASACQQgQ5AEgBUHA3glqIgYgASAfEJsCIAQgBkEGEOQBIAMgBCAWEJsCIAIgA0EIEOQBIAEgAiBNEJsCIAVBgOMJaiIGIAFBDxDkASAEICUgBhCbAiADIARBBBDkASACIAMgORCbAiABIAJBDBDkASBRIAEgSBCbAiAEIFFBCBDkASADIAQgDRCbAiACIANBCBDkASABIAIgCxCbAiBDIAFBBxDkASACICUgQxCbAiABIAJBChDkASAHQZAnaiIDIAEgPBCbAiAFQaCJCmokACAHQdAraiIBIFNBwAT8CgAAIAdBkB5qIgIgA0HABPwKAAAgB0HQImoiAyABQcAE/AoAACAAIAIQtQMgAEGQAWogAxC1AwwBCyAHQQI2ApQnIAdB0MnBADYCkCcgB0IBNwKcJyAHIAdBDGqtQoCAgIDgAYQ3A9A0IAcgB0HQNGo2ApgnIAdBkCdqQZTKwQAQqAQACyAHKALAASIABEAgBygCxAEgAEECdBDfBAsgBygCsAEiAARAIAcoArQBIABBAnQQ3wQLIAcoAqABIgAEQCAHKAKkASAAQQJ0EN8ECyAHKAKQASIABEAgBygClAEgAEECdBDfBAsgBygCgAEiAARAIAcoAoQBIABBAnQQ3wQLIAcoAnAiAARAIAcoAnQgAEECdBDfBAsgBygCYCIABEAgBygCZCAAQQJ0EN8ECyAHKAJQIgAEQCAHKAJUIABBAnQQ3wQLIAcoAkAiAARAIAcoAkQgAEECdBDfBAsgBygCMCIABEAgBygCNCAAQQJ0EN8ECyAHKAIgIgAEQCAHKAIkIABBAnQQ3wQLIAcoAhAiAARAIAcoAhQgAEECdBDfBAsgB0GQOWokAAvFFQIIfxh+IwBB0AFrIgMkACADQQA2AgggA0KAgICAgAE3AgAgA0EANgIUIANCgICAgIABNwIMAkACQAJAIAJFDQAgAUEgaiIEQbizwgBBIBDxA0UNAiABIAJByABsaiEIIANBMGohBiADQcABaiEHIANBOGohCUGws8IAKQMAIR9BqLPCACkDACEgQaCzwgApAwAhIUGYs8IAKQMAISIDQEIAIRQgA0HgAGpCADcDACADQdgAakIANwMAIANCADcDUCADQgE3A2ggA0GIAWogBEEYaikDADcDACADQYABaiAEQRBqKQMANwMAIANB+ABqIARBCGopAwA3AwAgAyAEKQMANwNwIANBqAFqIB83AwAgA0GgAWogIDcDACADQZgBaiAhNwMAIAMgIjcDkAEgA0GwAWohBQJ/IANB8ABqIANB0ABqQSAQ8QNFBEBCifWrnLWLv5ZzIRVC+4OUop2ixvO1fyEXQvb/hdLw38fVxwAhDUKf6uDVnO6n7AYhFkIAIRhCACETIAcMAQtCifWrnLWLv5ZzIRVC+4OUop2ixvO1fyEXQvb/hdLw38fVxwAhEkKf6uDVnO6n7AYhFkKNlcfDltLawJd/IRlC3bCFjOi2kai4fyEOQqnAxomuzpOyMCEcQsf688PtgqOQPCELIAMpA4gBIQwgAykDcCEdIAMpA3ghDyADKQOAASEaQgAhDUIAIRhCACETA0AgA0GQAWogA0HQAGpBIBDxA0UEQCADQShqIQUgCQwCCyAMp0EBcUUEQANAIBpCP4YgDEIBiIQhDAJAIBVCAYNQBEAgEiEQIBchESAVIRsMAQsgFiASQqPP+vOXye7XxwB9IhAgElQgECAQIBdC8+q4vOmtpb/oAH0iESAXVCARIBEgFULH+vPD7YKjkDx8IhsgFVStfCIRVnKtfCIQVnKtfEKpwMaJrs6TsjB8IRYLIB1CP4YgD0I/hiAaQgGIhCEaIB1CAYghHSAWQj+GIBBCAYiEIRIgEEI/hiARQgGIhCEXIBFCP4YgG0IBiIQhFSAWQgGIIRYgD0IBiIQhDyAMQgGDUA0ACyADIBo3A4ABIAMgDDcDiAEgAyAPNwN4IAMgHTcDcAsgC6dBAXFFBEADQCAZQj+GIAtCAYiEIQsCQCATQgGDUARAIA0hECAYIREgEyEbDAELIBQgDUKjz/rzl8nu18cAfSIQIA1UIBAgECAYQvPquLzpraW/6AB9IhEgGFQgESARIBNCx/rzw+2Co5A8fCIbIBNUrXwiEVZyrXwiEFZyrXxCqcDGia7Ok7IwfCEUCyAcQj+GIA5CP4YgGUIBiIQhGSAcQgGIIRwgFEI/hiAQQgGIhCENIBBCP4YgEUIBiIQhGCARQj+GIBtCAYiEIRMgFEIBiCEUIA5CAYiEIQ4gC0IBg1ANAAsgAyAZNwOgASADIAs3A6gBIAMgDjcDmAEgAyAcNwOQAQsCQAJAAkACQAJAAkACQCAcIhAgHSIRUg0AIA4hECAPIREgDiAPUg0AIBkiECAaIhFSDQAgCyEQIAwhESALIAxRDQELIBAgEVgNACADIAsgDH0iEDcDqAEgAyAZIBp9IhsgCyAMVK0iC30iETcDoAEgAyAOIA99Ih4gGSAaVCALIBtWcq0iC30iGzcDmAEgAyAcIB19IA4gD1QgCyAeVnKtfSIcNwOQAQJAAkAgFCILIBYiDlINACANIQsgEiIOIA1SDQAgFyIOIBgiC1INACAVIg4gEyILUQ0BCyALIA5UDQILIBQgFn0gDSASVCANIBJ9Ig4gGCAXfSILIBMgFVStIg1UIBcgGFZyrSIZVHKtfSEUIBMgFX0hEyALIA19IRggDiAZfSENDAILIAMgDCALfSIQNwOIASADIBogGX0iGyALIAxWrSIMfSIRNwOAASADIA8gDn0iHiAMIBtWIBkgGlZyrSIMfSIbNwN4IAMgHSAcfSAMIB5WIA4gD1ZyrX0iHTcDcAJAAkAgFCIPIBYiDFINACANIQ8gEiIMIA1SDQAgFyIMIBgiD1INACAVIgwgEyIPUQ0BCyAMIA9UDQMLIBYgFH0gEiANfSIPIBcgGFQgFyAYfSIMIBMgFVatIhdUcq0iGlQgDSASVnKtfSEWIBUgE30hFSAMIBd9IRcgDyAafSESDAMLIBQgFn1C3bCFjOi2kai4fyASfSIOQo2Vx8OW0trAl38gF30iCyAVQsf688PtgqOQPFatIhRUIBdCjZXHw5bS2sCXf1ZyrSIZVCASQt2whYzotpGouH9Wcq19IA0gDiAZfSINfCIOIA1UIA4gCyAUfSINIBh8IgsgDVQgC0LH+vPD7YKjkDwgFX0iDSATfCITIA1UrXwiGCALVHKtfCINIA5Ucq18QqnAxomuzpOyMHwhFAsgESEZIBshDiAQIQsMAgsgFiAUfULdsIWM6LaRqLh/IA19Ig9CjZXHw5bS2sCXfyAYfSIMIBNCx/rzw+2Co5A8Vq0iFlQgGEKNlcfDltLawJd/VnKtIhpUIA1C3bCFjOi2kai4f1ZyrX0gEiAPIBp9IhJ8Ig8gElQgDyAMIBZ9IhIgF3wiDCASVCAMQsf688PtgqOQPCATfSISIBV8IhUgElStfCIXIAxUcq18IhIgD1RyrXxCqcDGia7Ok7IwfCEWCyARIRogGyEPIBAhDAsgA0HwAGogA0HQAGpBIBDxAw0ACyASIQ0gBwshAiADIBM3A0AgAyAYNwM4IAMgFzcDwAEgAyAVNwPIASADQSBqIgogAkEIaikDADcDACADIBY3A7ABIAMgFDcDKCADIAIpAwA3AxggBSkDACEOIAMoAggiBSADKAIARgRAIANBhLrCABCiAwsgAygCBCAFQQV0aiICIA03AwggAiAONwMAIAIgAykDGDcDECACQRhqIAopAwA3AwAgAyAFQQFqNgIIIANBKGogASAEEFsgAygCKEEBRg0CIANByAFqIAZBGGopAwA3AwAgA0HAAWogBkEQaikDADcDACADQbgBaiAGQQhqKQMANwMAIAMgBikDADcDsAECfiADQbABakG4s8IAQSAQ8QMEQEKNlcfDltLawJd/IAMpA8ABIg59Ig8gAykDyAEiC0LH+vPD7YKjkDxWrSIMfSEUQt2whYzotpGouH8gAykDuAEiEH0iESAMIA9WIA5CjZXHw5bS2sCXf1ZyrSIOfSEWQsf688PtgqOQPCALfSETQqnAxomuzpOyMCADKQOwASAOIBFWIBBC3bCFjOi2kai4f1ZyrXx9DAELIAMpA8gBIRMgAykDwAEhFCADKQO4ASEWIAMpA7ABCyEVIAMoAhQiBCADKAIMRgRAIANBDGpBlLrCABCiAwsgAygCECAEQQV0aiICIBM3AxggAiAUNwMQIAIgFjcDCCACIBU3AwAgAyAEQQFqNgIUIAFByABqIgIgCEYNASABQegAaiEEIAIhASAEQbizwgBBIBDxAw0ACwwCCyAAIAMpAgA3AgAgACADKQIMNwIMIABBCGogA0EIaigCADYCACAAQRRqIANBFGooAgA2AgAgA0HQAWokAA8LIAMgAykDODcDuAEgAyADKQMwNwOwAUGgscIAQSsgA0GwAWpBpLrCAEG0usIAEMoDAAsgAyANNwMwIANCAjcDKEGgscIAQSsgA0EoakGkusIAQcS6wgAQygMAC/sLAg5/An5CAiEQIwBBgAlrIgIkACACQegGaiABQQhqKQMANwMAIAJB8AZqIAFBEGopAwA3AwAgAkH4BmogAUEYaikDADcDACACQYAHaiABQSBqKQMANwMAIAJBiAdqIAFBKGopAwA3AwAgAkGYB2ogAUE4aikDADcDACACQaAHaiABQUBrKQMANwMAIAJBqAdqIAFByABqKQMANwMAIAJBsAdqIAFB0ABqKQMANwMAIAJBuAdqIAFB2ABqKQMANwMAIAIgASkDADcD4AYgAiABKQMwNwOQByACQcAEaiIFIAJB4AZqIgNB4AD8CgAAIAJByAJqIgQgAUGIAWopAwA3AwAgAkHAAmoiBiABQYABaikDADcDACACQbgCaiIHIAFB+ABqKQMANwMAIAJBsAJqIgggAUHwAGopAwA3AwAgAkGoAmoiCSABQegAaikDADcDACACQdgCaiIKIAFBmAFqKQMANwMAIAJB4AJqIgsgAUGgAWopAwA3AwAgAkHoAmoiDCABQagBaikDADcDACACQfACaiINIAFBsAFqKQMANwMAIAJB+AJqIg4gAUG4AWopAwA3AwAgAiABKQNgNwOgAiACIAEpA5ABNwPQAiADIAJBoAJqIg9B4AD8CgAAIAJBoAVqIANB4AD8CgAAIAQgAUHoAWopAwA3AwAgBiABQeABaikDADcDACAHIAFB2AFqKQMANwMAIAggAUHQAWopAwA3AwAgCSABQcgBaikDADcDACAKIAFB+AFqKQMANwMAIAsgAUGAAmopAwA3AwAgDCABQYgCaikDADcDACANIAFBkAJqKQMANwMAIA4gAUGYAmopAwA3AwAgAiABKQPAATcDoAIgAiABKQPwATcD0AIgAyAPQeAA/AoAACACQYAGaiADQeAA/AoAACACIAVBoAL8CgAAA0AgAkHABGoiASACIAIQuQIgAiABQaAC/AoAACAQQgKDIBBCAYghEFANAAsgAkGoCGogAkEIaikDADcDACACQbAIaiACQRBqKQMANwMAIAJBuAhqIAJBGGopAwA3AwAgAkHACGogAkEgaikDADcDACACQcgIaiACQShqKQMANwMAIAJB2AhqIAJBOGopAwA3AwAgAkHgCGogAkFAaykDADcDACACQegIaiACQcgAaikDADcDACACQfAIaiACQdAAaikDADcDACACQfgIaiACQdgAaikDADcDACACIAIpAwA3A6AIIAIgAikDMDcD0AggASACQaAIakHgAPwKAAAgAkHIAmoiASACQYgBaikDADcDACACQcACaiIEIAJBgAFqKQMANwMAIAJBuAJqIgYgAkH4AGopAwA3AwAgAkGwAmoiByACQfAAaikDADcDACACQagCaiIIIAJB6ABqKQMANwMAIAJB2AJqIgkgAkGYAWopAwA3AwAgAkHgAmoiCiACQaABaikDADcDACACQegCaiILIAJBqAFqKQMANwMAIAJB8AJqIgwgAkGwAWopAwA3AwAgAkH4AmoiDSACQbgBaikDADcDACACIAIpA2A3A6ACIAIgAikDkAE3A9ACIAJBoAhqIgMgAkGgAmoiBUHgAPwKAAAgAkGgBWogA0HgAPwKAAAgASACQegBaikDADcDACAEIAJB4AFqKQMANwMAIAYgAkHYAWopAwA3AwAgByACQdABaikDADcDACAIIAJByAFqKQMANwMAIAkgAkH4AWopAwA3AwAgCiACQYACaikDADcDACALIAJBiAJqKQMANwMAIAwgAkGQAmopAwA3AwAgDSACQZgCaikDADcDACACIAIpA8ABNwOgAiACIAIpA/ABNwPQAiADIAVB4AD8CgAAIAJBgAZqIANB4AD8CgAAIAUgAkHABGpBoAL8CgAAIBBCAVIEQANAIAJBwARqIgQgAkGgAmoiASABELkCIAEgBEGgAvwKAAAgEEICg1BFBEAgAkHABGoiASACIAJBoAJqELkCIAIgAUGgAvwKAAALIBBCBFQgEEIBiCEQRQ0ACwsgACACQaAC/AoAACACQYAJaiQAC+IZAwp/CX4CfCMAQfAAayICJAAgASgCBCEFQQQhCSABKAIIIgMhBAJAAkACQAJAAkACQAJAAkAgAw4CBQABCyAFKAIAQQFGDQMgBUEEaiEEDAELIAUgA0ECdCIJaiEEIANBAWtB/v///wNxDQELA0AgBTUCACANhiAPfCEPIA1CIHwhDSAFQQRqIgUgBEcNAAsCfgJAAkACQAJAAkAgD0IEWgRAIA+6n/wHIg5QDQEgDiAPIA6AIA58QgGIIhBUDQIgECEMDAMLIA9CAFKtIQ4MAwtBgIzFABCaBAALA0AgECAPIBCAIBB8QgGIIgxUIBAhDiAMIRANAAsLIAwgDloNAANAIAwiDlANAiAOIA8gDIAgDHxCAYgiDFYNAAsLIA4MAQtBgIzFABCaBAALIQ1BACEJIAJB4ABqIgNBtLzEACgCADYCACACQay8xAApAgA3A1ggDVBFBEBBASEFA0AgAigCWCAFQQFrRgRAIAJB2ABqQaC9xAAQpQMLIAIoAlwgCWogDT4CACAJQQRqIQkgAiAFNgJgIAVBAWohBSANQoCAgIAQVCANQiCIIQ1FDQALCyAAIAIpA1g3AgAgAEEIaiADKAIANgIADAMLIAOtQgWGIARBBGsoAgBnrSIMfSIUQgGIIRAgBUEEayEDQgAgDH0hEgNAIBJCAX1CH4MiDEIBfCITQsAAIA99Ig4gDiATVhshESADIAlqIQYgD0LAAFIEQCANIBGGIAY1AgAgEyARfYiEIQ0LIAwgDloEQCANIAY1AgAgESATfYZCAFKthCENCyASIBF9IRIgDyARfCEPIAlBBGsiCQ0AC0QAAAAAAAAAQCEVRAAAAAAAAABARAAAAAAAAPA/IBQgDXl8QkB8IgynIgZBH3UiAyAGcyADayIIQQFxGyEWIAhBAk8EQANAIBYgFSAVoiIVoiAWIAhBAnEbIRYgCEEDSyAIQQF2IQgNAAsLRAAAAAAAAPA/IBajIBYgBkEASBshFQJAAkACQAJAIAxCgAhYBEAgFSANuqIiFb1C////////////AINC//////////f/AFgNAQsgAiABNgJcIAJBgICAgHg2AlggAkHIAGoiBiACQdgAakF/IBRC/gd9IgxCBYinIAxCgICAgIAEWhsgDKciA0EecRDsASACQThqIAYQciACKAJAIQggAigCPCEKAkACQCACKAI4IgZBgICAgHhHBEAgCA0BIAJBADYCECACIAo2AgwgAiAGNgIIDAILIAooAggNACACQQhqIAoQwAMMAQsgDEKAgICAgAhaDQQgAiAINgJgIAIgCjYCXCACIAY2AlggAkEIaiACQdgAaiAMQgaIpyADQQF2QR9xEM8BCyACKAJIIgNFDQEgAigCTCADQQJ0EN8EDAELIAJB2ABqIQojAEEgayIEJAACQCAVnyIVvUL///////////8Ag0KAgICAgICA+P8AWgRAIApBgICAgHg2AgAMAQsCfwJAIBWdIhVEAAAAAAAAAABiBEAgFb0iDEIAUwRAIApBgICAgHg2AgAMBAsgDEI0iKdB/w9xIgZBswhrIQggBEEYakG0vMQAKAIANgIAIARBrLzEACkCADcDECAMQv////////8Hg0KAgICAgICACIQgDEIBhkL+////////D4MgBhsiDFAEQEEEIQNBAAwDCwNAIAQoAhAgC0YEQCAEQRBqQaC9xAAQpQMLIAQoAhQgB2ogDD4CACAEIAtBAWoiCzYCGCAHQQRqIQcgDEKAgICAEFQgDEIgiCEMRQ0ACwwBCyAKQQhqQbS8xAAoAgA2AgAgCkGsvMQAKQIANwIADAILIAQoAhQhAyAEKAIQCyEHAkACQAJAIAhBAEogCEEASGtB/wFxDgICAQALIAQgCzYCGCAEIAM2AhQgBCAHNgIQAkACQCAHQYCAgIB4RwRAIAsNASAEQQhqIARBGGooAgA2AgAgBCAEKQIQNwMADAILIAMoAggNACAEIAMQwAMMAQsgBCAEQRBqQbMIIAZrIgNBBXYgA0EfcRDsAQsgBCgCACEHIAQoAgQhAyAEKAIIIQsMAQsCQAJAIAdBgICAgHhHBEAgCw0BIARBADYCCCAEIAM2AgQgBCAHNgIADAILIAMoAggNACAEIAMQwAMMAQsgBCALNgIYIAQgAzYCFCAEIAc2AhAgBCAEQRBqIAhBBXYgCEEfcRDPAQsgBCgCCCELIAQoAgQhAyAEKAIAIQcLIAogCzYCCCAKIAM2AgQgCiAHNgIACyAEQSBqJAAgAigCWEGAgICAeEYNASACQRBqIAJB4ABqKAIANgIAIAIgAikCWDcDCAsgAkEgaiACQRBqKAIANgIAIAIgAikDCDcDGCACQdgAaiABIAJBGGoQoQEgAkHQAGogAkHgAGooAgA2AgAgAiACKQJYNwNIIAIoAmQiAwRAIAIoAmggA0ECdBDfBAsgEEIBfCEMIAJB2ABqIAJByABqIAJBGGoQygECQAJAIAIoAlhBgICAgHhHBEAgAigCYA0BIAJBMGogAkHgAGooAgA2AgAgAiACKQJYNwMoDAILIAIoAlwoAggNACACQQA2AjAgAkKAgICAwAA3AygMAQsgAkEoaiACQdgAakEAQQEQ7AELIAynQR9xIQsgDEIFiKchCgNAAkACQAJAAkACQAJAIAIoAiAiByACKAIwIgRGBEAgAigCHEEEayEIIAdBAnQhBSACKAIsIQkDQCAFRQ0CIAUgCGooAgAiBiAFQQRrIgUgCWooAgAiA0YNAAsgAyAGTQ0CDAMLIAQgB00NASACKAIsIQkMAwsgBQ0BCwNAAkACQCAEIAdGBEAgAigCHEEEayELIARBAnQhBSACKAIsQQRrIQoDQCAFRQ0DIAUgCmohCCAFIAtqIAVBBGshBSgCACIGIAgoAgAiA0YNAAsgAyAGSQ0BDAILIAQgB08NAQsgAigCGCIDBEAgAigCHCADQQJ0EN8ECyACQSBqIAJBMGooAgA2AgAgAiACKQMoNwMYIAJB2ABqIAEgAkEYahChASACQdAAaiACQeAAaigCADYCACACIAIpAlg3A0ggAigCZCIDBEAgAigCaCADQQJ0EN8ECyACQdgAaiACQcgAaiACQRhqEMoBAkACQCACKAJYQYCAgIB4RwRAIAIoAmANASACQUBrIAJB4ABqKAIANgIAIAIgAikCWDcDOAwCCyACKAJcKAIIDQAgAkEANgJAIAJCgICAgMAANwM4DAELIAJBOGogAkHYAGpBAEEBEOwBCyACQTBqIAJBQGsoAgAiBDYCACACIAIpAzg3AyggAigCICEHDAELCyAAIAIpAxg3AgAgAEEIaiACQSBqKAIANgIAIAIoAigiAEUNCSACKAIsIABBAnQQ3wQMCQsgB0UNAQsgBK1CBYYgCSAEQQJ0akEEaygCAGetfSAMWA0AQdHOxQAtAAAaQQRBBBDWBCIDBEAgA0EBNgIAIAJBATYCYCACIAM2AlwgAkEBNgJYIAJByABqIAJB2ABqIAogCxDPASACKAIYIgMEQCACKAIcIANBAnQQ3wQLIAJBIGogAkHQAGoiAygCADYCACACIAIpAkg3AxggAkHYAGogASACQRhqEKEBIAMgAkHgAGoiBigCADYCACACIAIpAlg3A0ggAigCZCIDBEAgAigCaCADQQJ0EN8ECyACQdgAaiACQcgAaiACQRhqEMoBAkACQCACKAJYQYCAgIB4RwRAIAIoAmANASACQUBrIAYoAgA2AgAgAiACKQJYNwM4DAILIAIoAlwoAggNACACQQA2AkAgAkKAgICAwAA3AzgMAQsgAkE4aiACQdgAakEAQQEQ7AELIAIoAigiA0UNAiAJIANBAnQQ3wQMAgtBBEEEEP8EAAsgAigCGCIDBEAgAigCHCADQQJ0EN8ECyACQSBqIAJBMGooAgA2AgAgAiACKQMoNwMYIAJB2ABqIAEgAkEYahChASACQdAAaiACQeAAaiIGKAIANgIAIAIgAikCWDcDSCACKAJkIgMEQCACKAJoIANBAnQQ3wQLIAJB2ABqIAJByABqIAJBGGoQygECQCACKAJYQYCAgIB4RwRAIAIoAmANASACQUBrIAYoAgA2AgAgAiACKQJYNwM4DAILIAIoAlwoAggNACACQQA2AkAgAkKAgICAwAA3AzgMAQsgAkE4aiACQdgAakEAQQEQ7AELIAJBMGogAkFAaygCADYCACACIAIpAzg3AygMAAsAC0H8wMQAEOgEAAtB2MDEAEERQezAxAAQ6AMAC0HRzsUALQAAGkEEIQRBBEEEENYEIglFDQILIAQEQCAJIAUgBPwKAAALIAAgAzYCCCAAIAk2AgQgACADNgIACyACQfAAaiQADwtBBEEEQaSDxQAQyAQAC+cUAg5/FH4jAEGABGsiAiQAIAEoAgQhAyABKAIAAkAgACgCFCIIIAAoAhAiBE0NACABKAIIIQkgACgCBCILBEAgACgCDCEGIAAoAgAhDCAAKAIIQQRqIQ0DQCAEQQFqIQ5BACEHIARBBXQhDyAMIQAgDSEBQgAhHUIAIRlCACEeQgAhGAJAA0AgBiAHRg0BAn4CQCABQQRqKAIAIgUgBEsEQCACQcADaiAAQRhqKQMAIhBCACABKAIAIA9qIgUpAxgiEkIAEMkDIAJB0ANqIBBCACAFKQMQIhNCABDJAyACQeADaiAQQgAgBSkDCCIUQgAQyQMgAkHwA2ogEEIAIAUpAwAiEEIAEMkDIAJBsANqIAIpA8ADIhVC/////76y/fBCfiIRQgBCgYCAgL+y/fDDAEIAEMkDIAJBoANqIBFCAEKR4eXNh4n6mShCABDJAyACQZADaiARQgBC3bCFjOi2kai4f0IAEMkDIAJBgANqIBFCAEKpwMaJrs6TsjBCABDJAyACQcACaiAAQRBqKQMAIhFCACASQgAQyQMgAkHQAmogEUIAIBNCABDJAyACQeACaiARQgAgFEIAEMkDIAJB8AJqIBFCACAQQgAQyQMgAkGwAmogAikDoAMiGiACKQPIAyIbIAIpA9ADfCIcfCIWIAIpA7gDIBUgAikDsAMiEXwgEVStfHwiFSACKQPAAnwiF0L/////vrL98EJ+IhFCAEKBgICAv7L98MMAQgAQyQMgAkGgAmogEUIAQpHh5c2HifqZKEIAEMkDIAJBkAJqIBFCAELdsIWM6LaRqLh/QgAQyQMgAkGAAmogEUIAQqnAxomuzpOyMEIAEMkDIAJBwAFqIABBCGopAwAiEUIAIBJCABDJAyACQdABaiARQgAgE0IAEMkDIAJB4AFqIBFCACAUQgAQyQMgAkHwAWogEUIAIBBCABDJAyACQbABaiACKQPIAiAVIBdWrXwiISACKQPQAnwiHyACKQPYAyAbIBxWrXwiICACKQPgA3wiGyACKQOQA3wiHCAVIBZUrSACKQOoAyAWIBpUrXx8fCIifCIWIAIpA6ACfCIVIAIpA7gCIAIpA7ACIhEgF3wgEVStfHwiFyACKQPAAXwiGkL/////vrL98EJ+IhFCAEKBgICAv7L98MMAQgAQyQMgAkGgAWogEUIAQpHh5c2HifqZKEIAEMkDIAJBkAFqIBFCAELdsIWM6LaRqLh/QgAQyQMgAkGAAWogEUIAQqnAxomuzpOyMEIAEMkDIAJBQGsgACkDACIRQgAgEkIAEMkDIAJB0ABqIBFCACATQgAQyQMgAkHgAGogEUIAIBRCABDJAyACQfAAaiARQgAgEEIAEMkDIAJBMGogAikDyAEgFyAaVq18IiMgAikD0AF8IhIgAikD6AMgGyAgVK18IiAgAikD8AN8IhMgAikDgAN8IhQgHCAiVq0gAikDmAMgGyAcVq18fHwiESACKQPgAnwiGyAWIB9UrSACKQPYAiAfICFUrXx8fCIfIAIpA5ACfCIcIBUgF1atIAIpA6gCIBUgFlStfHx8IiF8IhYgAikDoAF8IhUgAikDuAEgAikDsAEiECAafCAQVK18fCIXIAIpA0B8IhpC/////76y/fBCfiIQQgBCgYCAgL+y/fDDAEIAEMkDIAJBIGogEEIAQpHh5c2HifqZKEIAEMkDIAJBEGogEEIAQt2whYzotpGouH9CABDJAyACIBBCAEKpwMaJrs6TsjBCABDJAwJAAkAgAikDCCACKQOIASACKQOIAiARIBRUrSACKQOIAyATIBRWrXx8IAIpA/gDIBMgIFStfHwiICACKQPwAnwiECAbIB9WrSACKQPoAiARIBtWrXx8fCITIAIpA4ACfCIUIBNUrXwgFCAUIBwgIVatIAIpA5gCIBwgH1StfHx8IhRWrXwgECATVq0gAikD+AIgECAgVK18fHwiESACKQPwAXwiECACKQPoASAUIAIpA+ABfCITIBRUrXwgEyASIBZWrSACKQPYASASICNUrXx8fCISIBNUrXx8IhMgAikDgAF8IhQgE1StfCAUIAIpA5gBIBIgEiACKQOQAXwiElatfCASIBUgF1atIAIpA6gBIBUgFlStfHx8IhYgElStfHwiEiAUVK18IBAgE1atIAIpA/gBIBAgEVStfHx8IhUgAikDcHwiFCACKQNoIBIgAikDYHwiECASVK18IBAgECACKQNYIAIpA0ggFyAaVq18IhMgAikDUHwiEiATVK18IBIgEiAWfCISVq18fCIQVq18fCIRIAIpAwB8IhMgEVStfCATIBMgAikDGCAQIBAgAikDEHwiEFatfCAQIBAgAikDKCASIBIgAikDIHwiElatfCASIAIpAzggAikDMCIWIBp8IBZUrXx8IhYgElStfHwiEFatfHwiE1atfCARIBRUrSACKQN4IBQgFVStfHx8IhFCqcDGia7Ok7IwVg0AAkAgEUKpwMaJrs6TsjBRBEAgE0LdsIWM6LaRqLh/Vg0CIBNC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhEQsgEyEUIBAhEgwCCyAQQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IRQgEEKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIREgECESDAILQpHh5c2HifqZKCESIBZCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhEQwBCyAQQpHh5c2HifqZKH0iFCAWQoGAgIC/sv3wwwBUrSIVfSESIBNCo8/685fJ7tfHAHwiFyAQQpHh5c2HifqZKFQgFCAVVHKtIhB9IRQgESATQt2whYzotpGouH9UIBAgF1ZyrX1CqcDGia7Ok7IwfSERIBZCgYCAgL+y/fDDAH0hFgtCqcDGia7Ok7IwIRUgFCAZfCIQIBlUIBAgEiAefCITIB5UIBMgFiAYfCISIBhUrXwiGCATVHKtfCITIBBUcq0gESAdfHwiHSEQAkAgHUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEVIBMiEELdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCEVIBgiEEKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACEVIBIiEEKBgICAv7L98MMAUQ0CCyAQIBVaDQEgEyEZIBghHiASDAILIAQgBUH0+cAAENkDAAsgGEKR4eXNh4n6mSh9IhAgEkKBgICAv7L98MMAVK0iGX0hHiATQqPP+vOXye7XxwB8IhQgGEKR4eXNh4n6mShUIBAgGVRyrSIQfSEZIB0gE0LdsIWM6LaRqLh/VCAQIBRWcq19QqnAxomuzpOyMH0hHSASQoGAgIC/sv3wwwB9CyEYIABBIGohACABQQxqIQEgCyAHQQFqIgdHDQALIAkgA0EFdGoiACAYNwMYIAAgHjcDECAAIBk3AwggACAdNwMAIANBAWohAyAOIgQgCEcNAQwDCwsgBiAGQeT5wAAQ2QMACyAIIARrIgBBBXQiAQRAIAkgA0EFdGpBACAB/AsACyAAIANqIQMLIAM2AgAgAkGABGokAAvCEgIjfwR+IwBBkAxrIgMkACADIAE2AtAKIAMgAUHAAWoiFDYC1AogA0EIaiIHIANB0ApqIggQvQMgA0GIDGoiHCADQUBrIgkpAwAiJjcDACADQYAMaiIdIANBOGoiCikDACInNwMAIANB+AtqIh4gA0EwaiILKQMAIig3AwAgA0HwC2oiHyADQShqIgwpAwAiKTcDACADQZgLaiIEIANBEGoiDSkDADcDACADQaALaiIFIANBGGoiDikDADcDACADQagLaiIGIANBIGoiDykDADcDACADQbALaiIQICk3AwAgA0G4C2oiESAoNwMAIANBwAtqIhIgJzcDACADQcgLaiITICY3AwAgAyADKQMIIiY3A9ALIAMgJjcDkAsgA0HAA2oiFSATKQMANwMAIANBuANqIhYgEikDADcDACADQbADaiIXIBEpAwA3AwAgA0GoA2oiGCAQKQMANwMAIANBoANqIhkgBikDADcDACADQZgDaiIaIAUpAwA3AwAgA0GQA2oiGyAEKQMANwMAIAMgAykDkAs3A4gDIANBwAlqIBUpAwA3AwAgA0G4CWogFikDADcDACADQbAJaiAXKQMANwMAIANBqAlqIBgpAwA3AwAgA0GgCWogGSkDADcDACADQZgJaiAaKQMANwMAIANBkAlqIBspAwA3AwAgAyADKQOIAzcDiAkgByAIEL0DIBwgCSkDACImNwMAIB0gCikDACInNwMAIB4gCykDACIoNwMAIB8gDCkDACIpNwMAIAQgDSkDADcDACAFIA4pAwA3AwAgBiAPKQMANwMAIBAgKTcDACARICg3AwAgEiAnNwMAIBMgJjcDACADIAMpAwgiJjcD0AsgAyAmNwOQCyAVIBMpAwA3AwAgFiASKQMANwMAIBcgESkDADcDACAYIBApAwA3AwAgGSAGKQMANwMAIBogBSkDADcDACAbIAQpAwA3AwAgAyADKQOQCzcDiAMgA0GACmogFSkDADcDACADQfgJaiAWKQMANwMAIANB8AlqIBcpAwA3AwAgA0HoCWogGCkDADcDACADQeAJaiAZKQMANwMAIANB2AlqIBopAwA3AwAgA0HQCWogGykDADcDACADIAMpA4gDNwPICSAHIAgQvQMgHCAJKQMAIiY3AwAgHSAKKQMAIic3AwAgHiALKQMAIig3AwAgHyAMKQMAIik3AwAgBCANKQMANwMAIAUgDikDADcDACAGIA8pAwA3AwAgECApNwMAIBEgKDcDACASICc3AwAgEyAmNwMAIAMgAykDCCImNwPQCyADICY3A5ALIBUgEykDADcDACAWIBIpAwA3AwAgFyARKQMANwMAIBggECkDADcDACAZIAYpAwA3AwAgGiAFKQMANwMAIBsgBCkDADcDACADIAMpA5ALNwOIAyADQcAKaiAVKQMANwMAIANBuApqIBYpAwA3AwAgA0GwCmogFykDADcDACADQagKaiAYKQMANwMAIANBoApqIBkpAwA3AwAgA0GYCmogGikDADcDACADQZAKaiAbKQMANwMAIAMgAykDiAM3A4gKQQBFBEAgA0GIBmogA0GICWpBwAH8CgAACyADIAFBgANqNgLMCiADIBQ2AsgKIANB0AtqIiEgA0HICmoiIhC9AyATIBwpAwAiJjcDACASIB0pAwAiJzcDACARIB4pAwAiKDcDACAQIB8pAwAiKTcDACADQdgKaiIBIANB2AtqIiMpAwA3AwAgA0HgCmoiBCADQeALaiIkKQMANwMAIANB6ApqIgUgA0HoC2oiJSkDADcDACADQfAKaiIGICk3AwAgA0H4CmoiFCAoNwMAIANBgAtqIgcgJzcDACADQYgLaiIIICY3AwAgAyADKQPQCyImNwOQCyADICY3A9AKIAkgCCkDADcDACAKIAcpAwA3AwAgCyAUKQMANwMAIAwgBikDADcDACAPIAUpAwA3AwAgDiAEKQMANwMAIA0gASkDADcDACADIAMpA9AKNwMIIBUgCSkDADcDACAWIAopAwA3AwAgFyALKQMANwMAIBggDCkDADcDACAZIA8pAwA3AwAgGiAOKQMANwMAIBsgDSkDADcDACADIAMpAwg3A4gDICEgIhC9AyATIBwpAwAiJjcDACASIB0pAwAiJzcDACARIB4pAwAiKDcDACAQIB8pAwAiKTcDACABICMpAwA3AwAgBCAkKQMANwMAIAUgJSkDADcDACAGICk3AwAgFCAoNwMAIAcgJzcDACAIICY3AwAgAyADKQPQCyImNwOQCyADICY3A9AKIAkgCCkDADcDACAKIAcpAwA3AwAgCyAUKQMANwMAIAwgBikDADcDACAPIAUpAwA3AwAgDiAEKQMANwMAIA0gASkDADcDACADIAMpA9AKNwMIIANBgARqIAkpAwA3AwAgA0H4A2ogCikDADcDACADQfADaiALKQMANwMAIANB6ANqIAwpAwA3AwAgA0HgA2ogDykDADcDACADQdgDaiAOKQMANwMAIANB0ANqIA0pAwA3AwAgAyADKQMINwPIAyAhICIQvQMgEyAcKQMAIiY3AwAgEiAdKQMAIic3AwAgESAeKQMAIig3AwAgECAfKQMAIik3AwAgASAjKQMANwMAIAQgJCkDADcDACAFICUpAwA3AwAgBiApNwMAIBQgKDcDACAHICc3AwAgCCAmNwMAIAMgAykD0AsiJjcDkAsgAyAmNwPQCiAJIAgpAwA3AwAgCiAHKQMANwMAIAsgFCkDADcDACAMIAYpAwA3AwAgDyAFKQMANwMAIA4gBCkDADcDACANIAEpAwA3AwAgAyADKQPQCjcDCCADQcAEaiAJKQMANwMAIANBuARqIAopAwA3AwAgA0GwBGogCykDADcDACADQagEaiAMKQMANwMAIANBoARqIA8pAwA3AwAgA0GYBGogDikDADcDACADQZAEaiANKQMANwMAIAMgAykDCDcDiAQgIEUEQCADQYgJaiADQYgDakHAAfwKAAALICBFBEAgA0HIB2ogA0GICWpBwAH8CgAACyADQQhqIANBiAZqQYAD/AoAACACBEADQCADQYgDaiIBIANBCGoiBBCqASAEIAFBgAP8CgAAIAJBAWsiAg0ACwsgACADQQhqQYAD/AoAACADQZAMaiQAC/sVAgJ/GH4jAEHQA2siASQAIAFBoANqQcChxQBBARCnAkEoIQIgASkDoAMhFyABKQOoAyEYIAEpA7ADIRAgASkDuAMhESABKQPAAyESIAEpA8gDIQ8DQCABQcACaiACQeCgxQBqKQMAIgNCACAPQgAQyQMgAUHQAmogA0IAIBJCABDJAyABQeACaiADQgAgEUIAEMkDIAFB8AJqIANCACAQQgAQyQMgAUGAA2ogA0IAIBhCABDJAyABQZADaiADQgAgF0IAEMkDIAFBsAJqIAEpA8ACIgkgDnwiE0IAQgBC/f/z/8////mJfxDJAyABQaACaiABKQO4AiIDQgBCq9X+////v/+5f0IAEMkDIAFBkAJqIANCAEL//8+K6///1R5CABDJAyABQYACaiADQgBCpOzDtY/UtJjnAEIAEMkDIAFB8AFqIANCAEK/pZScz/DSu+QAQgAQyQMgAUHgAWogA0IAQtfZrprk9umNywBCABDJAyABQdABaiADQgBCms3/y6O9xIAaQgAQyQMgASkD2AEgASkDkAMiDCALfCIUIAEpA4gDIAEpA4ADIgMgB3wiByADVK18IAcgASkD+AIgASkD8AIiAyAGfCIGIANUrXwgBiABKQPoAiABKQPgAiIDIAV8IgUgA1StfCAFIAEpA9gCIAQgASkD0AIiBHwiAyAEVK18IAMgASkDyAIgCSATVq18fCIEIANUrXx8IhUgBVStfHwiBSAGVK18fCIDIAdUrXx8IhYgASkD0AF8IgcgFlStfCAHIAcgASkD6AEgAyABKQPgAXwiCSADVK18IAkgASkD+AEgBSABKQPwAXwiBiAFVK18IAYgASkDiAIgFSABKQOAAnwiBSAVVK18IAUgASkDmAIgBCABKQOQAiIEfCIDIARUrXwgAyABKQOoAiABKQOgAiIEIBN8IARUrXx8Ig4gA1StfHwiBCAFVK18fCIFIAZUrXx8IgYgCVStfHwiB1atfCIJIAggFCAWVq0gASkDmAMgDCAUVq18fCIIfCIDfCILIAlUrSADIAhUrXwhCCACQQhrIgJBeEcNAAsCQAJAAkACQCAIQgBSIAtCms3/y6O9xIAaVnINAAJAIAtCms3/y6O9xIAaUQRAIAdC19mumuT26Y3LAFYNAiAHQtfZrprk9umNywBRDQFCms3/y6O9xIAaIQsLIAchEAwCCyAGQr+llJzP8NK75ABWDQBC19mumuT26Y3LACEQIAZCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohCwwCCyAFQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACERIAVCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohCwwDCyAEQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIRIgBEL//8+K6///1R5SBEBCms3/y6O9xIAaIQsgBCEPDAQLQv//z4rr///VHiEPIA5Cq9X+////v/+5f1oNAEKazf/Lo73EgBohCwwDCyAEQv//z4rr///VHn0iCSAOQqvV/v///7//uX9UrSIIfSEPIAVCpOzDtY/UtJjnAH0iAyAEQv//z4rr///VHlQgCCAJVnKtIgR9IRIgBkK/pZScz/DSu+QAfSIIIAVCpOzDtY/UtJjnAFQgAyAEVHKtIgR9IREgB0LX2a6a5PbpjcsAfSIDIAZCv6WUnM/w0rvkAFQgBCAIVnKtIgR9IRAgCyAHQtfZrprk9umNywBUIAMgBFRyrX1Cms3/y6O9xIAafSELIA5C1aqBgICAwIDGAHwhDgwCCyAGIRELIAUhEiAEIQ8LIAFBoANqQcChxQBBARCnAkEoIQIgASkDoAMhEyABKQOoAyEUIAEpA7ADIRUgASkDuAMhFiABKQPAAyEXIAEpA8gDIRhCACEHQgAhBkIAIQVCACEEQgAhCANAIAFB8ABqIAJB4KDFAGopAwAiA0IAIBhCABDJAyABQYABaiADQgAgF0IAEMkDIAFBkAFqIANCACAWQgAQyQMgAUGgAWogA0IAIBVCABDJAyABQbABaiADQgAgFEIAEMkDIAFBwAFqIANCACATQgAQyQMgAUHgAGogASkDcCIJIA18IhlCAEIAQv3/8//P///5iX8QyQMgAUHQAGogASkDaCIDQgBCq9X+////v/+5f0IAEMkDIAFBQGsgA0IAQv//z4rr///VHkIAEMkDIAFBMGogA0IAQqTsw7WP1LSY5wBCABDJAyABQSBqIANCAEK/pZScz/DSu+QAQgAQyQMgAUEQaiADQgBC19mumuT26Y3LAEIAEMkDIAEgA0IAQprN/8ujvcSAGkIAEMkDIAEpAwggASkDwAEiDCAKfCIaIAEpA7gBIAEpA7ABIgMgB3wiByADVK18IAcgASkDqAEgASkDoAEiAyAGfCIGIANUrXwgBiABKQOYASABKQOQASIDIAV8IgUgA1StfCAFIAEpA4gBIAQgASkDgAEiBHwiAyAEVK18IAMgASkDeCAJIBlWrXx8IgQgA1StfHwiDSAFVK18fCIFIAZUrXx8IgMgB1StfHwiCiABKQMAfCIHIApUrXwgByAHIAEpAxggAyABKQMQfCIJIANUrXwgCSABKQMoIAUgASkDIHwiBiAFVK18IAYgASkDOCANIAEpAzB8IgUgDVStfCAFIAEpA0ggBCABKQNAIgR8IgMgBFStfCADIAEpA1ggASkDUCIEIBl8IARUrXx8Ig0gA1StfHwiBCAFVK18fCIFIAZUrXx8IgYgCVStfHwiB1atfCIJIAggCiAaVK0gASkDyAEgDCAaVq18fCIIfCIDfCIKIAlUrSADIAhUrXwhCCACQQhrIgJBeEcNAAsCQAJAIAhCAFIgCkKazf/Lo73EgBpWcg0AAkAgCkKazf/Lo73EgBpRBEAgB0LX2a6a5PbpjcsAVg0CIAdC19mumuT26Y3LAFIEQCAEIQMgBSEIIAYhCSAHIQxCms3/y6O9xIAaIQoMBAsgBkK/pZScz/DSu+QAVg0CQtfZrprk9umNywAhDCAGQr+llJzP8NK75ABSBEAgBCEDIAUhCCAGIQlCms3/y6O9xIAaIQoMBAsgBUKk7MO1j9S0mOcAVg0CQr+llJzP8NK75AAhCSAFQqTsw7WP1LSY5wBSBEAgBCEDIAUhCEKazf/Lo73EgBohCgwECyAEQv//z4rr///VHlYNAkKk7MO1j9S0mOcAIQggBEL//8+K6///1R5RDQEgBCEDQprN/8ujvcSAGiEKDAMLIAQhAyAFIQggBiEJIAchDAwCC0L//8+K6///1R4hAyANQqvV/v///7//uX9aDQBCms3/y6O9xIAaIQoMAQsgBEL//8+K6///1R59IgwgDUKr1f7///+//7l/VK0iCH0hAyAFQqTsw7WP1LSY5wB9IgkgBEL//8+K6///1R5UIAggDFZyrSIEfSEIIAZCv6WUnM/w0rvkAH0iDCAFQqTsw7WP1LSY5wBUIAQgCVZyrSIEfSEJIAdC19mumuT26Y3LAH0iBSAGQr+llJzP8NK75ABUIAQgDFZyrSIEfSEMIAogB0LX2a6a5PbpjcsAVCAEIAVWcq19QprN/8ujvcSAGn0hCiANQtWqgYCAgMCAxgB8IQ0LIAAgDTcDWCAAIAM3A1AgACAINwNIIAAgCTcDQCAAIAw3AzggACAKNwMwIAAgDjcDKCAAIA83AyAgACASNwMYIAAgETcDECAAIBA3AwggACALNwMAIAFB0ANqJAALthQCBX8bfiMAQRBrIgYkACAGQQRqIAEQ9wFB0c7FAC0AABoCQAJAAkACQAJAAkACQAJAAkACQAJAAkBBgANBCBDWBCIDBEAgBigCDCIERQ0BIARBAUYNAgJ+IAYoAggiAkEgakG4s8IAQSAQ8QMEQEKNlcfDltLawJd/IAIpAzAiEn0iESACKQM4IhNCx/rzw+2Co5A8Vq0iFH0hHkLdsIWM6LaRqLh/IAIpAygiDH0iByARIBRUIBJCjZXHw5bS2sCXf1ZyrSIRfSESQsf688PtgqOQPCATfSETQqnAxomuzpOyMCACKQMgIAcgEVQgDELdsIWM6LaRqLh/VnKtfH0MAQsgAikDOCETIAIpAzAhHiACKQMoIRIgAikDIAshESAEQQJNDQMgBEEDRg0EAn4gAkHgAGpBuLPCAEEgEPEDBEBCjZXHw5bS2sCXfyACKQNwIgx9IgcgAikDeCIVQsf688PtgqOQPFatIhZ9IRRC3bCFjOi2kai4fyACKQNoIg19IgggByAWVCAMQo2Vx8OW0trAl39Wcq0iB30hDELH+vPD7YKjkDwgFX0hFUKpwMaJrs6TsjAgAikDYCAHIAhWIA1C3bCFjOi2kai4f1ZyrXx9DAELIAIpA3ghFSACKQNwIRQgAikDaCEMIAIpA2ALIQcgBEEETQ0FIARBBUYNBgJ+IAJBoAFqQbizwgBBIBDxAwRAQo2Vx8OW0trAl38gAikDsAEiDX0iCCACKQO4ASIXQsf688PtgqOQPFatIhh9IRZC3bCFjOi2kai4fyACKQOoASIOfSIJIAggGFQgDUKNlcfDltLawJd/VnKtIgh9IQ1Cx/rzw+2Co5A8IBd9IRdCqcDGia7Ok7IwIAIpA6ABIAggCVYgDkLdsIWM6LaRqLh/VnKtfH0MAQsgAikDuAEhFyACKQOwASEWIAIpA6gBIQ0gAikDoAELIQggBEEGTQ0HIARBB0YNCAJ+IAJB4AFqQbizwgBBIBDxAwRAQo2Vx8OW0trAl38gAikD8AEiDn0iCSACKQP4ASIZQsf688PtgqOQPFatIhp9IRhC3bCFjOi2kai4fyACKQPoASIPfSIKIAkgGlQgDkKNlcfDltLawJd/VnKtIgl9IQ5Cx/rzw+2Co5A8IBl9IRlCqcDGia7Ok7IwIAIpA+ABIAkgClYgD0LdsIWM6LaRqLh/VnKtfH0MAQsgAikD+AEhGSACKQPwASEYIAIpA+gBIQ4gAikD4AELIQkgBEEITQ0JIARBCUYNCgJ+IAJBoAJqQbizwgBBIBDxAwRAQo2Vx8OW0trAl38gAikDsAIiD30iCiACKQO4AiIbQsf688PtgqOQPFatIhx9IRpC3bCFjOi2kai4fyACKQOoAiIQfSILIAogHFQgD0KNlcfDltLawJd/VnKtIgp9IQ9Cx/rzw+2Co5A8IBt9IRtCqcDGia7Ok7IwIAIpA6ACIAogC1YgEELdsIWM6LaRqLh/VnKtfH0MAQsgAikDuAIhGyACKQOwAiEaIAIpA6gCIQ8gAikDoAILIQogBEEKTQ0LIARBC0cEQAJ+IAJB4AJqQbizwgBBIBDxAwRAQo2Vx8OW0trAl38gAikD8AIiEH0iCyACKQP4AiIdQsf688PtgqOQPFatIh99IRxC3bCFjOi2kai4fyACKQPoAiIgfSIhIAsgH1QgEEKNlcfDltLawJd/VnKtIgt9IRBCx/rzw+2Co5A8IB19IR1CqcDGia7Ok7IwIAIpA+ACIAsgIVYgIELdsIWM6LaRqLh/VnKtfH0MAQsgAikD+AIhHSACKQPwAiEcIAIpA+gCIRAgAikD4AILIQsgAyACKQMANwMAIANBGGogAkEYaikDADcDACADQRBqIAJBEGopAwA3AwAgA0EIaiACQQhqKQMANwMAIAMgEzcDOCADIB43AzAgAyASNwMoIAMgETcDICADIAIpA0A3A0AgA0HIAGogAkHIAGopAwA3AwAgA0HQAGogAkHQAGopAwA3AwAgA0HYAGogAkHYAGopAwA3AwAgAyAVNwN4IAMgFDcDcCADIAw3A2ggAyAHNwNgIAMgAikDgAE3A4ABIANBiAFqIAJBiAFqKQMANwMAIANBkAFqIAJBkAFqKQMANwMAIANBmAFqIAJBmAFqKQMANwMAIAMgFzcDuAEgAyAWNwOwASADIA03A6gBIAMgCDcDoAEgA0HYAWogAkHYAWopAwA3AwAgA0HQAWogAkHQAWopAwA3AwAgA0HIAWogAkHIAWopAwA3AwAgAyACKQPAATcDwAEgAyAJNwPgASADIA43A+gBIAMgGDcD8AEgAyAZNwP4ASADQZgCaiACQZgCaikDADcDACADQZACaiACQZACaikDADcDACADQYgCaiACQYgCaikDADcDACADIAIpA4ACNwOAAiADIAo3A6ACIAMgDzcDqAIgAyAaNwOwAiADIBs3A7gCIANB2AJqIAJB2AJqKQMANwMAIANB0AJqIAJB0AJqKQMANwMAIANByAJqIAJByAJqKQMANwMAIAMgAikDwAI3A8ACIAMgCzcD4AIgAyAQNwPoAiADIBw3A/ACIAMgHTcD+AJBDCEEIAACfyADQeACakHYw8IAQSAQ8QMEQEEMIQVBCwwBCyADQcACakHYw8IAQSAQ8QMEQEELIQVBCgwBCyADQaACakHYw8IAQSAQ8QMEQEEKIQVBCQwBCyADQYACakHYw8IAQSAQ8QMEQEEJIQVBCAwBCyADQeABakHYw8IAQSAQ8QMEQEEIIQVBBwwBCyADQcABakHYw8IAQSAQ8QMEQEEHIQVBBgwBCyADQaABakHYw8IAQSAQ8QMEQEEGIQVBBQwBCyADQYABakHYw8IAQSAQ8QMEQEEFIQVBBAwBCyADQeAAakHYw8IAQSAQ8QMEQEEEIQVBAwwBCyADQUBrQdjDwgBBIBDxAwRAQQMhBUECDAELIANBIGpB2MPCAEEgEPEDBEBBAiEFQQEMAQsgA0HYw8IAQSAQ8QMEQEEBIQVBAAwBC0HRzsUALQAAGkEgQQgQ1gQiBEUNDiAEQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgA0GAAxDfBEEBIQUgBCEDQQEhBEF/CzYCDCAAIAU2AgggACADNgIEIAAgBDYCACAGKAIEIgAEQCACIABBBXQQ3wQLIAEoAgAiAARAIAEoAgQgAEEFdBDfBAsgBkEQaiQADwtBC0ELQfS5wgAQ2QMAC0EIQYADEP8EAAtBAEEAQcS4wgAQ2QMAC0EBQQFB1LjCABDZAwALQQJBAkHkuMIAENkDAAtBA0EDQfS4wgAQ2QMAC0EEQQRBhLnCABDZAwALQQVBBUGUucIAENkDAAtBBkEGQaS5wgAQ2QMAC0EHQQdBtLnCABDZAwALQQhBCEHEucIAENkDAAtBCUEJQdS5wgAQ2QMAC0EKQQpB5LnCABDZAwALQQhBIBD/BAAL/xMCAX8WfiMAQYADayIDJAAgASkDACEOIAEpAwghDyABKQMQIREgASkDGCEVIAEpAyAhFiABKQMoIRdBKCEBA0AgA0GgAmogASACaikDACIJQgAgF0IAEMkDIANBsAJqIAlCACAWQgAQyQMgA0HAAmogCUIAIBVCABDJAyADQdACaiAJQgAgEUIAEMkDIANB4AJqIAlCACAPQgAQyQMgA0HwAmogCUIAIA5CABDJAyADQZACaiADKQOgAiIMIBJ8IgdC/f/z/8////mJf34iCUIAQqvV/v///7//uX9CABDJAyADQYACaiAJQgBC///Piuv//9UeQgAQyQMgA0HwAWogCUIAQqTsw7WP1LSY5wBCABDJAyADQeABaiAJQgBCv6WUnM/w0rvkAEIAEMkDIANB0AFqIAlCAELX2a6a5PbpjcsAQgAQyQMgA0HAAWogCUIAQprN/8ujvcSAGkIAEMkDIAMpA8gBIAMpA/ACIhMgEHwiCSADKQPoAiADKQPgAiIKIAh8IgggClStfCAIIAMpA9gCIAMpA9ACIgogBnwiBiAKVK18IAYgAykDyAIgAykDwAIiCiAFfCIFIApUrXwgBSADKQO4AiADKQOwAiIKIAR8IgQgClStfCAEIAMpA6gCIAcgDFStfHwiCiAEVK18fCIEIAVUrXx8IgUgBlStfHwiBiAIVK18fCIMIAMpA8ABfCIIIAxUrXwgCCAIIAMpA9gBIAYgBiADKQPQAXwiBlatfCAGIAYgAykD6AEgBSAFIAMpA+ABfCIFVq18IAUgBSADKQP4ASAEIAQgAykD8AF8IgRWrXwgBCAEIAMpA4gCIAMpA4ACIhAgCnwiCiAQVK18IAogAykDmAIgByADKQOQAiIHfCAHVK18fCISIApUrXx8IgRWrXx8IgVWrXx8IgZWrXx8IghWrXwgCSAMVq0gAykD+AIgCSATVK18fHwhECABQQhrIgFBeEcNAAsCQAJAIBBCms3/y6O9xIAaVg0AIBBCms3/y6O9xIAaUgRAIAQhCSAFIQwgBiEKIAghEwwCCyAIQtfZrprk9umNywBWDQACQCAIQtfZrprk9umNywBSBEAgBCEJIAUhDCAGIQogCCETDAELIAZCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIRMgBkK/pZScz/DSu+QAUgRAIAQhCSAFIQwgBiEKDAELIAVCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQogBUKk7MO1j9S0mOcAUgRAIAQhCSAFIQwMAQsgBEL//8+K6///1R5WDQFCpOzDtY/UtJjnACEMIARC///Piuv//9UeUgRAIAQhCQwBC0L//8+K6///1R4hCSASQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEQDAELIARC///Piuv//9UefSIHIBJCq9X+////v/+5f1StIgx9IQkgBUKk7MO1j9S0mOcAfSIKIARC///Piuv//9UeVCAHIAxUcq0iBH0hDCAGQr+llJzP8NK75AB9IgcgBUKk7MO1j9S0mOcAVCAEIApWcq0iBH0hCiAIQtfZrprk9umNywB9IgUgBkK/pZScz/DSu+QAVCAEIAdWcq0iBH0hEyAQIAhC19mumuT26Y3LAFQgBCAFVnKtfUKazf/Lo73EgBp9IRAgEkLVqoGAgIDAgMYAfCESC0HYACEBQgAhCEIAIQZCACEFQgAhBANAIANB4ABqIAEgAmopAwAiB0IAIBdCABDJAyADQfAAaiAHQgAgFkIAEMkDIANBgAFqIAdCACAVQgAQyQMgA0GQAWogB0IAIBFCABDJAyADQaABaiAHQgAgD0IAEMkDIANBsAFqIAdCACAOQgAQyQMgA0HQAGogAykDYCIUIA18Ig1C/f/z/8////mJf34iB0IAQqvV/v///7//uX9CABDJAyADQUBrIAdCAEL//8+K6///1R5CABDJAyADQTBqIAdCAEKk7MO1j9S0mOcAQgAQyQMgA0EgaiAHQgBCv6WUnM/w0rvkAEIAEMkDIANBEGogB0IAQtfZrprk9umNywBCABDJAyADIAdCAEKazf/Lo73EgBpCABDJAyADKQMIIAMpA7ABIhggC3wiByADKQOoASADKQOgASILIAh8IgggC1StfCAIIAMpA5gBIAMpA5ABIgsgBnwiBiALVK18IAYgAykDiAEgAykDgAEiCyAFfCIFIAtUrXwgBSADKQN4IAMpA3AiCyAEfCIEIAtUrXwgBCADKQNoIA0gFFStfHwiFCAEVK18fCIEIAVUrXx8IgUgBlStfHwiBiAIVK18fCILIAMpAwB8IgggC1StfCAIIAggAykDGCAGIAYgAykDEHwiBlatfCAGIAYgAykDKCAFIAUgAykDIHwiBVatfCAFIAUgAykDOCAEIAQgAykDMHwiBFatfCAEIAQgAykDSCADKQNAIhkgFHwiFCAZVK18IBQgAykDWCANIAMpA1AiDXwgDVStfHwiDSAUVK18fCIEVq18fCIFVq18fCIGVq18fCIIVq18IAcgC1atIAMpA7gBIAcgGFStfHx8IQsgAUEIayIBQShHDQALAkACQCALQprN/8ujvcSAGlYNACALQprN/8ujvcSAGlIEQCAEIQcgBSEOIAYhDyAIIREMAgsgCELX2a6a5PbpjcsAVg0AAkAgCELX2a6a5PbpjcsAUgRAIAQhByAFIQ4gBiEPIAghEQwBCyAGQr+llJzP8NK75ABWDQFC19mumuT26Y3LACERIAZCv6WUnM/w0rvkAFIEQCAEIQcgBSEOIAYhDwwBCyAFQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEPIAVCpOzDtY/UtJjnAFIEQCAEIQcgBSEODAELIARC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhDiAEQv//z4rr///VHlIEQCAEIQcMAQtC///Piuv//9UeIQcgDUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohCwwBCyAEQv//z4rr///VHn0iDiANQqvV/v///7//uX9UrSIPfSEHIAVCpOzDtY/UtJjnAH0iESAEQv//z4rr///VHlQgDiAPVHKtIgR9IQ4gBkK/pZScz/DSu+QAfSIVIAVCpOzDtY/UtJjnAFQgBCARVnKtIgR9IQ8gCELX2a6a5PbpjcsAfSIFIAZCv6WUnM/w0rvkAFQgBCAVVnKtIgR9IREgCyAIQtfZrprk9umNywBUIAQgBVZyrX1Cms3/y6O9xIAafSELIA1C1aqBgICAwIDGAHwhDQsgACANNwNYIAAgBzcDUCAAIA43A0ggACAPNwNAIAAgETcDOCAAIAs3AzAgACASNwMoIAAgCTcDICAAIAw3AxggACAKNwMQIAAgEzcDCCAAIBA3AwAgA0GAA2okAAucDgESfyMAQSBrIgskAAJAAkACQCACRQ0AIAEgAkECdCIFakEEaygCAARAIAIhCQwBCyABQQRrIQcgAkH/////A3EhBgNAIAVFDQEgBkEBayEGIAUgB2ogBUEEayEFKAIARQ0ACyAGQQFqIgkgAksNAQsgAyAEQQJ0IgVqQQRrKAIADQEgA0EEayEKIAQhBgNAIAVFBEBBACEEDAMLIAZBAWshBiAFIApqIAVBBGshBSgCAEUNAAsgBCAGQQFqIgJPBEAgAiEEDAILIAIgBEGUycQAEOUEAAsgCSACQYTJxAAQ5QQACwJAAkACQAJAAkACQAJAAkACQAJAAn8gBCAJRgRAIAFBBGshBiADQQRrIQcgCUECdCEFAkADQCAFRQ0BIAUgB2ohCiAFIAZqIAVBBGshBSgCACIIIAooAgAiAkYNAAsgAiAISSACIAhLawwCC0F/QQAgBRsMAQsgBCAJSSAEIAlLawtB/wFxDgIBAgALQQAhBSAEQf////8DSyAEQQJ0IgJB/P///wdLcg0CAn8gAkUEQEEEIQhBAAwBC0HRzsUALQAAGkEEIQUgAkEEENYEIghFDQMgBAshCiACBEAgCCADIAL8CgAACyAJIAQgBCAJSxsiDEECdCEOAkAgDEUNACAMQQFxAkAgDEEBRgRAQQAhBwwBCyAMQf7///8DcSEQQQAhByABIQYgCCEFA0AgBSAFKAIAIhEgBigCACISayITIAdrNgIAIAVBBGoiAyADKAIAIhQgBkEEaigCACIVayIWIBEgEkkgByATS3IiA2s2AgAgFCAVSSADIBZLciEHIAZBCGohBiAFQQhqIQUgECANQQJqIg1HDQALCwR/IAggDUECdCIFaiIDIAMoAgAiBiABIAVqKAIAIgVrIgMgB2s2AgAgAyAHSSAFIAZLcgUgBwtBAXFFDQAgCCAOaiEFIAIgDEECdGshBgNAIAZFDQogBSAFKAIAIgNBAWs2AgAgBkEEayEGIAVBBGohBSADRQ0ACwsgASAOaiEGIAlBAnQgDmshBQJAA0AgBUUNASAFQQRrIQUgBigCACAGQQRqIQZFDQALDAkLQQAhByAERQ0FIAggBEECdGpBBGsoAgAEQCAEIQcMBgsgCEEEayEDIAQhBQNAIAJFDQYgBUEBayEFIAIgA2ogAkEEayECKAIARQ0ACyAFQQFqIgEgBCABIARJGyEHDAULIABBAToAACAAQejIxAApAgA3AgQgAEEMakHwyMQAKAIANgIADAULQQAhBSAJQf////8DSyAJQQJ0IgJB/P///wdLcg0BAn8gAkUEQEEEIQhBAAwBC0HRzsUALQAAGkEEIQUgAkEEENYEIghFDQIgCQshCiACBEAgCCABIAL8CgAACyAEIAkgBCAJSRsiDEECdCEOAkAgDEUNACAMQQFxAkAgDEEBRgRAQQAhBwwBCyAMQf7///8DcSEQQQAhByADIQYgCCEFA0AgBSAFKAIAIhEgBigCACISayITIAdrNgIAIAVBBGoiASABKAIAIhQgBkEEaigCACIVayIWIBEgEkkgByATS3IiAWs2AgAgFCAVSSABIBZLciEHIAZBCGohBiAFQQhqIQUgECANQQJqIg1HDQALCwR/IAggDUECdCIFaiIBIAEoAgAiBiADIAVqKAIAIgVrIgEgB2s2AgAgASAHSSAFIAZLcgUgBwtBAXFFDQAgCCAOaiEFIAIgDEECdGshBgNAIAZFDQggBSAFKAIAIgFBAWs2AgAgBkEEayEGIAVBBGohBSABRQ0ACwsgAyAOaiEGIARBAnQgDmshBQJAA0AgBUUNASAFQQRrIQUgBigCACAGQQRqIQZFDQALDAcLQQAhByAJRQ0CIAggCUECdGpBBGsoAgAEQCAJIQcMAwsgCEEEayEDIAkhBQNAIAJFDQMgBUEBayEFIAIgA2ogAkEEayECKAIARQ0ACyAFQQFqIgEgCSABIAlJGyEHDAILIAUgAkH4wsQAEMgEAAsgBSACQfjCxAAQyAQACwJAAkAgByAKQQJ2Tw0AIApFBEBBACEKDAELIApBAnQhASAHRQRAIAggARDfBEEEIQhBACEKDAELIAchCiAIIAFBBCAHQQJ0IgEQzgQiCEUNAQsgACAHNgIMIAAgCDYCCCAAIAo2AgQgAEECOgAADAILQQQgAUG0ycQAEMgEAAsCQCAHIApBAnZPDQAgCkUEQEEAIQoMAQsgCkECdCEBIAdFBEAgCCABEN8EQQQhCEEAIQoMAQsgByEKIAggAUEEIAdBAnQiARDOBCIIRQ0CCyAAIAc2AgwgACAINgIIIAAgCjYCBCAAQQA6AAALIAtBIGokAA8LQQQgAUG0ycQAEMgEAAsgC0EANgIYIAtBATYCDCALQcSKxQA2AgggC0IENwIQIAtBCGpBzIrFABCoBAALthECAX8QfiMAQbAEayIDJAAgA0GIBGogASACELECQQEhAgJAIAMtAIgEQQFGBEAgACADLQCJBDoAAQwBCyADQYACaiADKQOoBCIEQgBCifWrnLWLv5ZzQgAQyQMgA0HAAmogAykDoAQiB0IAQon1q5y1i7+Wc0IAEMkDIANBgANqIAMpA5gEIgZCAEKJ9auctYu/lnNCABDJAyADQcADaiADKQOQBCIIQgBCifWrnLWLv5ZzQgAQyQMgA0HwAWogAykDgAIiCkKJx5mkrvCB6Yd/fiIFQgBCx/rzw+2Co5A8QgAQyQMgA0HgAWogBUIAQo2Vx8OW0trAl39CABDJAyADQZABaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBQGsgBUIAQqnAxomuzpOyMEIAEMkDIANBkAJqIARCAEL7g5SinaLG87V/QgAQyQMgA0HQAmogB0IAQvuDlKKdosbztX9CABDJAyADQZADaiAGQgBC+4OUop2ixvO1f0IAEMkDIANB0ANqIAhCAEL7g5SinaLG87V/QgAQyQMgA0HQAWogAykD4AEiDCADKQOIAiINIAMpA8ACfCIOfCIJIAMpA/gBIAogAykD8AEiBXwgBVStfHwiCiADKQOQAnwiC0KJx5mkrvCB6Yd/fiIFQgBCx/rzw+2Co5A8QgAQyQMgA0HAAWogBUIAQo2Vx8OW0trAl39CABDJAyADQbABaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBoAFqIAVCAEKpwMaJrs6TsjBCABDJAyADQaACaiAEQgBC9v+F0vDfx9XHAEIAEMkDIANB4AJqIAdCAEL2/4XS8N/H1ccAQgAQyQMgA0GgA2ogBkIAQvb/hdLw38fVxwBCABDJAyADQeADaiAIQgBC9v+F0vDfx9XHAEIAEMkDIANBgAFqIAMpA5gCIAogC1atfCIQIAMpA9ACfCIPIAMpA8gCIA0gDlatfCIRIAMpA4ADfCINIAMpA5ABfCIOIAkgClatIAMpA+gBIAkgDFStfHx8IhJ8IgkgAykDwAF8IgogAykD2AEgAykD0AEiBSALfCAFVK18fCILIAMpA6ACfCIMQonHmaSu8IHph39+IgVCAELH+vPD7YKjkDxCABDJAyADQfAAaiAFQgBCjZXHw5bS2sCXf0IAEMkDIANB4ABqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0HQAGogBUIAQqnAxomuzpOyMEIAEMkDIANBsAJqIARCAEKf6uDVnO6n7AZCABDJAyADQfACaiAHQgBCn+rg1Zzup+wGQgAQyQMgA0GwA2ogBkIAQp/q4NWc7qfsBkIAEMkDIANB8ANqIAhCAEKf6uDVnO6n7AZCABDJAyADQTBqIAMpA6gCIAsgDFatfCITIAMpA+ACfCIHIAMpA4gDIA0gEVStfCIRIAMpA8ADfCIGIAMpA0B8IgggDiASVq0gAykDmAEgDSAOVq18fHwiBSADKQOQA3wiDSAJIA9UrSADKQPYAiAPIBBUrXx8fCIPIAMpA7ABfCIOIAogC1atIAMpA8gBIAkgClatfHx8IhB8IgkgAykDcHwiCiADKQOIASADKQOAASIEIAx8IARUrXx8IgsgAykDsAJ8IgxCiceZpK7wgemHf34iBEIAQsf688PtgqOQPEIAEMkDIANBIGogBEIAQo2Vx8OW0trAl39CABDJAyADQRBqIARCAELdsIWM6LaRqLh/QgAQyQMgAyAEQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgAykDCCADKQPoAyADKQPgAyAFIAhUrSADKQNIIAYgCFatfHwiCCADKQPIAyAGIBFUrXx8IgQgCFSthCIIIAMpA9gDIAQgBCADKQPQA3wiBFatfCAEIAQgDSAPVq0gAykDmAMgBSANVq18fHwiBFatfHwiBiAIVK18IAYgBiADKQOoASAEIAQgAykDoAF8IgRWrXwgBCAEIA4gEFatIAMpA7gBIA4gD1StfHx8IgRWrXx8IgZWrXwgBiADKQOoAyAEIAQgAykDoAN8IgRWrXwgBCAEIAcgCVatIAMpA+gCIAcgE1StfHx8IgRWrXx8IgcgBlStfCIPIAMpA/ADfCIIIAMpA1ggByAHIAMpA1B8IgdWrXwgByADKQNoIAQgBCADKQNgfCIEVq18IAQgCiALVq0gAykDeCAJIApWrXx8fCIFIARUrXx8IgQgB1StfHwiByADKQO4AyAEIAQgAykDsAN8IgRWrXwgBCAEIAMpA/gCIAMpA7gCIAsgDFatfCIJIAMpA/ACfCIGIAlUrXwgBiAFIAZ8IgZWrXx8IgRWrXx8IgUgAykDAHwiCiAFVK18IAogAykDGCAEIAQgAykDEHwiBFatfCAEIAQgAykDKCAGIAYgAykDIHwiBlatfCAGIAMpAzggAykDMCIJIAx8IAlUrXx8IgkgBlStfHwiBFatfHwiBiAKVK18IAUgB1StIAcgCFStIAMpA/gDIAggD1StfHx8fCIFQqnAxomuzpOyMFYNAAJAIAVCqcDGia7Ok7IwUg0AIAZC3bCFjOi2kai4f1YNASAGQt2whYzotpGouH9SBEBCqcDGia7Ok7IwIQUMAQsgBEKNlcfDltLawJd/Vg0BQt2whYzotpGouH8hCCAEQo2Vx8OW0trAl39SIAlCx/rzw+2Co5A8VHINAgwBCyAGIQggBCEHDAILIARC8+q4vOmtpb/oAHwiCCAJQsf688PtgqOQPFStIgp9IQcgBkKjz/rzl8nu18cAfCILIARCjZXHw5bS2sCXf1QgCCAKVHKtIgR9IQggBSAGQt2whYzotpGouH9UIAQgC1ZyrX1CqcDGia7Ok7IwfSEFIAlCx/rzw+2Co5A8fSEJDAELQqnAxomuzpOyMCEFIAQhBwsgACAJNwMgIAAgBzcDGCAAIAg3AxAgACAFNwMIQQAhAgsgACACOgAAIANBsARqJAAL2g4CD38BfiMAQUBqIgMkAAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIAItAAwiDkEBRwRAAkACQCABLQAMIhBFBEAgASgCCCIEQQJ0IQYgBEH/////A0sgBkH8////B0tyDQcgASgCBCEHAn8gBkUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQUgBkEEENYEIgFFDQggBAshBSAGBEAgASAHIAb8CgAACyAEDQEgA0EQakGozMIAKQIANwMAIANBoMzCACkCADcDCCAFRQ0CIAEgBUECdBDfBAwCCyABKAIIIgRBAnQhBiAEQf////8DSyAGQfz///8HS3INByABKAIEIQcCfyAGRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhBSAGQQQQ1gQiAUUNCCAECyEFIAYEQCABIAcgBvwKAAALIAMgEDoAFCADIAQ2AhAgAyABNgIMIAMgBTYCCAwBCyADQQI6ABQgAyAENgIQIAMgATYCDCADIAU2AggLAkACQCAORQRAIAIoAggiAUECdCEFQQAhBCABQf////8DSyAFQfz///8HS3INCSACKAIEIQoCfyAFRQRAQQQhAkEADAELQdHOxQAtAAAaQQQhBCAFQQQQ1gQiAkUNCiABCyEEIAUEQCACIAogBfwKAAALIAENAUEAIQEgA0EgakGozMIAKQIANwMAIANBoMzCACkCADcDGCAERQ0CIAIgBEECdBDfBAwCCyACKAIIIgFBAnQhBUEAIQQgAUH/////A0sgBUH8////B0tyDQkgAigCBCEKAn8gBUUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQQgBUEEENYEIgJFDQogAQshBCAFBEAgAiAKIAX8CgAACyADIA46ACQgAyABNgIgIAMgAjYCHCADIAQ2AhgMAQsgA0ECOgAkIAMgATYCICADIAI2AhwgAyAENgIYCyADQShqIANBCGogA0EYahChASADKQI0IhJCIIinIQQgAygCLCEFIAMoAighAiASpyEHAkAgAy0AFCIJQQFHBEAgCUEBIAMoAjwiDBshBiAJQQEgAygCMCIPGyEJDAELIAJBBE8EQCAFIAJBAnQQ3wRBBCEFQQAhAgtBASEJIAdBBE8EQCAEIAdBAnQQ3wRBACEHQQQhBAtBASEGCyADLQAkIREgAygCGCIIBEAgAygCHCAIQQJ0EN8ECyADKAIIIggEQCADKAIMIAhBAnQQ3wQLIAMgDDYCMCADIAQ2AiwgAyAHNgIoIANBKGpBAhCzAkEBIQcgAygCLCEMIAMoAighDQJAIAZBAUcEQCAGQQEgAygCMCILGyEHDAELIA1BBEkNACAMIA1BAnQQ3wRBACENQQQhDAsgAUECdCEEAn8CQCAORQRAIAFB/////wFLBEBBACEGDBELIAFFDQFB0c7FAC0AABpBBCEGIARBBBDWBCIIRQ0QIAQEQCAIIAogBPwKAAALIAEhBkECDAILIAFB/////wFLBEBBACEGDA8LAkAgAUUEQEEEIQgMAQtB0c7FAC0AABpBBCEGIARBBBDWBCIIRQ0PCyAEBEAgCCAKIAT8CgAACyABIQYgDgwBC0EEIQggBARAQQQgCiAE/AoAAAtBACEGQQELIQQgCUECIAlrIBEbIQkgBCAHRw0CIAdBAkcNAyABIAtHDQEgDEEEayEEIAtBAnQhASAIQQRrIQcDQCABRQ0EIAEgB2ohCiABIARqIAFBBGshASgCACILIAooAgAiCkYNAAsgCiALSw0JDAMLQdHOxQAtAAAaQR1BARDWBCIBRQ0HIABBHTYCDCAAIAE2AgggAEKAgICA2AM3AgAgAUEVakGC4MIAKQAANwAAIAFBEGpB/d/CACkAADcAACABQQhqQfXfwgApAAA3AAAgAUHt38IAKQAANwAADAoLIAEgC00NAQwHCyAEIAdLDQYLIAYEQCAIIAZBAnQQ3wQLIA0EQCAMIA1BAnQQ3wQLIAMgCToAJCADIA82AiAgAyAFNgIcIAMgAjYCGCADQShqIANBGGpBARC9ASADQQZqIANBN2otAAA6AAAgAyADLwA1OwEEIAMtADQhCSADKAIwIQ8gAygCLCEFIAMoAighAgwGCyAFIAZB+IHAABDIBAALIAUgBkH4gcAAEMgEAAsgBCAFQfiBwAAQyAQACyAEIAVB+IHAABDIBAALQQFBHUHU2MIAEMgEAAsgBgRAIAggBkECdBDfBAsgDUUNACAMIA1BAnQQ3wQLQQAhByAAQQ1qIQEgDkEBSyAORWsgEEEBSyAQRWsgByAQQQFHG3NBAE4EQCAAIAk6AAwgACAPNgIIIAAgBTYCBCAAIAI2AgAgASADLwEEOwAAIAFBAmogA0EGai0AADoAAAwBCyAAIA82AgggACAFNgIEIAAgAjYCACABIAMvAQQ7AAAgAEECIAlrOgAMIAFBAmogA0EGai0AADoAAAsgA0FAayQADwsgBiAEQfiBwAAQyAQACyAGIARB+IHAABDIBAAL0A0CHH8HfiMAQSBrIg4kACADQQFrIRQCQCADBEAgA0ECayEHAkACQCADQQFHBEAgASgCCCIQIANrIgRBAWoiDEECdCEJIAxB/////wNLIAlB/P///wdLcg0CIAIgFEECdGooAgAhFiACIAdBAnRqNQIAISQCfyAJRQRAQQQhC0EADAELQdHOxQAtAAAaQQQhBSAJQQQQ1wQiC0UNAyAMCyEJIAwNASABKAIAIQQgECEHDAQLIAdBAUGY98QAENkDAAsgASgCBCIRIBBBAnQiByADQQJ0a2ohEiADQQFxIRcgByARaiEVQQAgA0F+cWshG0EAIANB/v///wNxayEcQgAgFq0iI0IghiIlfSEmIANB/////wNxQQFGIR0gECEHAkACQANAIAQhDwJ/AkACQAJAIAdFDQAgESAHQQJ0IgVqQQRrIgRFDQAgB0ECayEGIAdBAU0NASAEKAIAIQQgESAGQQJ0ajUCACEiIAogFkkNAiAErSAKrXwhIUF/DAMLQcj3xAAQ6AQACyAGQQFB2PfEABDZAwALIAStIAqtQiCGhCIgICAgI4AiICAjfn0hISAgpwshDQJAICFC/////w9WDQAgJiAhQiCGfCAifCEgA0AgICAlfCIgIA2tICR+Wg0BIA1BAWshDSAhICN8IiFCgICAgBBUDQALCyAHIA9JDQECQCAFIA9BAnQiGEYNACANrSEiAn8gHQRAQoCAgIBwISBBAAwBC0L/////DyEhQQAhBSASIQQgAiEGA0AgBCAhIAQ1AgB8ICIgBjUCAH59Qv////8ffSIgPgIAIARBBGoiCCAINQIAICBCIIh8ICIgBkEEajUCAH59Qv////8ffSIgPgIAICBCIIghISAEQQhqIQQgBkEIaiEGIBwgBUECayIFRw0ACyAhQv////8ffSEgQQAgBWsLIQQgESAYaiEZIAogFwR+IBkgBEECdCIEaiIGICAgBjUCAHwgIiACIARqNQIAfn0iID4CACAgQiCIBSAhC6dBf3NPDQAgAyAHIA9rIh5LDQMCfyAURQRAQQAhCEEADAELQQAhBEEAIQpBACEIA0AgBCASaiIFIAUoAgAiHyACIARqIhMoAgBqIhogCGoiCDYCACAFQQRqIgUgBSgCACIGIBNBBGooAgBqIhMgGiAfSSAIIBpJcmoiBTYCACAFIBNJIAYgE0tyIgYhCCAEQQhqIQQgGyAKQQJrIgpHDQALQQAgCmsLIQQgDUEBayENIBcEfyAZIARBAnQiBmoiBCAEKAIAIgUgAiAGaigCAGoiBiAIaiIENgIAIAQgBkkgBSAGS3IFIAYLQQFxRSADIB5Gcg0AQQAhBANAIAQgFWoiBSAFKAIAQQFqIgU2AgAgBQ0BIARBfEcgBEEEaiEEDQALCyALIBhqIA02AgAgASAHQQFrIgc2AgggFUEEayEVIBJBBGshEiAPQQFrIQQgESAHQQJ0aigCACEKIA8NAAsgASgCACEEDAQLIA8gB0Ho98QAEOQEAAsgDkEANgIYIA5BATYCDCAOQZjyxAA2AgggDkIENwIQIA5BCGpBiPPEABCoBAALIAUgCUGo98QAEMgEAAsgFEEAQYj3xAAQ2QMACwJAIAQgB0YEQCABQbj3xAAQpQMgASgCBCAEQQJ0aiAKNgIAIAEoAgQhBQwBCyABKAIEIgUgB0ECdGogCjYCACAHIQQLIAEgBEEBaiIINgIIAkAgBSAIQQJ0akEEaygCAA0AIARBAmohBiAEQQJ0IQQCQANAIARBfEYEQEEAIQYMAgsgBkEBayEGIAQgBWogBEEEayEEKAIARQ0ACyAGIAhLDQELIAEgBjYCCCAGIQgLAkACQCAIIAEoAgAiAkECdk8gAkVyRQRAIAJBAnQhAgJAIAhFBEBBBCEGIAUgAhDfBAwBCyAFIAJBBCAIQQJ0IgIQzgQiBkUNAgsgASAINgIAIAEgBjYCBAtBACEFIAxFDQEgCyAMQQJ0akEEaygCAARAIAwhBQwCCyAQQQJ0IANBAnRrIQQgECADa0ECaiEGA0AgBEF8Rg0CIAZBAWshBiAEIAtqIARBBGshBCgCAEUNAAsgBiAMIAYgDEkbIQUMAQtBBCACQfj3xAAQyAQACwJAAkAgBSAJQQJ2Tw0AIAlFBEBBACEJDAELIAlBAnQhAiAFRQRAIAsgAhDfBEEEIQtBACEJDAELIAUhCSALIAJBBCAFQQJ0IgIQzgQiC0UNAQsgACAFNgIIIAAgCzYCBCAAIAk2AgAgACABKQIANwIMIABBFGogAUEIaigCADYCACAOQSBqJAAPC0EEIAJB+PfEABDIBAALkQ4CAX8SfiMAQcADayIDJAAgA0HAAWogASkDGCIFQgAgAikDGCIEQgAQyQMgA0HQAWogASkDECIIQgAgBEIAEMkDIANB4AFqIAEpAwgiB0IAIARCABDJAyADQfABaiABKQMAIgZCACAEQgAQyQMgA0GwAWogAykDwAEiCkKblK/D8rWo3oZ/fiIEQgBCbUIAEMkDIANBoAFqIARCAEJ/QgAQyQMgA0EwaiAEQgBC////////////AEIAEMkDIANBgAJqIAIpAxAiBEIAIAVCABDJAyADQbACaiAEQgAgCEIAEMkDIANB4AJqIARCACAHQgAQyQMgA0GQA2ogBEIAIAZCABDJAyADQZABaiADKQOgASIJIAMpA8gBIg0gAykD0AF8Igx8IgsgAykDuAEgCiADKQOwASIEfCAEVK18fCIKIAMpA4ACfCIPQpuUr8Pytajehn9+IgRCAEJtQgAQyQMgA0GAAWogBEIAQn9CABDJAyADQUBrIARCAEL///////////8AQgAQyQMgA0GQAmogAikDCCIEQgAgBUIAEMkDIANBwAJqIARCACAIQgAQyQMgA0HwAmogBEIAIAdCABDJAyADQaADaiAEQgAgBkIAEMkDIANB8ABqIAMpA4gCIAogD1atfCIQIAMpA7ACfCIOIAkgAykD2AEgDCANVK18IhEgAykD4AF8Ig18IgwgCiALVK0gAykDqAEiEiAJIAtWrXx8fCITfCIJIAMpA4ABIhR8IgsgAykDmAEgAykDkAEiBCAPfCAEVK18fCIKIAMpA5ACfCIPQpuUr8Pytajehn9+IgRCAEJtQgAQyQMgA0HgAGogBEIAQn9CABDJAyADQdAAaiAEQgBC////////////AEIAEMkDIANBoAJqIAIpAwAiBEIAIAVCABDJAyADQdACaiAEQgAgCEIAEMkDIANBgANqIARCACAHQgAQyQMgA0GwA2ogBEIAIAZCABDJAyADQSBqIAMpA5gCIAogD1atfCIVIAMpA8ACfCIFIBQgAykD6AEgDSARVK18IhEgAykD8AF8IgQgAykDMHwiCCAMIBNWrSASIAwgDVStfHx8IgcgAykD4AJ8IgYgCSAOVK0gAykDuAIgDiAQVK18fHwiDnwiDSAKIAtUrSADKQOIASIQIAkgC1atfHx8IhJ8IgkgAykDYCITfCILIAMpA3ggAykDcCIKIA98IApUrXx8IgogAykDoAJ8Ig9Cm5Svw/K1qN6Gf34iDEIAQm1CABDJAyADQRBqIAxCAEJ/QgAQyQMgAyAMQgBC////////////AEIAEMkDAkACQCADKQMIIAMpA1ggAykDSCAHIAhUrSADKQM4IAQgCFatfHwiDCADKQP4ASAEIBFUrXx8IgQgAykDkAN8IgggBiAOVq0gAykD6AIgBiAHVK18fHwiByADKQNAfCIGIAdUrXwgBiAGIA0gElatIBAgDSAOVK18fHwiBlatfCIOIAcgCFStIAMpA5gDIAQgCFatfHwiDSAEIAxUrXwiDHwiBCADKQOgA3wiCCADKQP4AiAGIAMpA/ACfCIHIAZUrXwgByAFIAlWrSADKQPIAiAFIBVUrXx8fCIFIAdUrXx8IgcgAykDUHwiBiAHVK18IAYgAykDaCIQIAUgBSATfCIFVq18IAUgCiALVK0gECAJIAtWrXx8fCIJIAVUrXx8IgUgBlStfCIQIAcgCFStIAMpA6gDIAQgCFatfHwiESAEIA5UrSAMIA1UrXx8Ig58IgQgAykDsAN8IgcgAykDiAMgBSAFIAMpA4ADfCIFVq18IAUgBSADKQPYAiADKQOoAiAKIA9WrXwiBiADKQPQAnwiCCAGVK18IAggCCAJfCIIVq18fCIFVq18fCIGIAMpAwB8IgsgBlStfCALIAMpAxgiCSAFIAUgAykDECIKfCIFVq18IAUgBSAJIAggCCAKfCIIVq18IAggAykDKCADKQMgIgkgD3wgCVStfHwiCSAIVK18fCIFVq18fCIIIAtUrXwiCyAGIAdUrSADKQO4AyAEIAdWrXx8IgcgBCAQVK0gDiARVK18fCIEfCIGIAtUIAQgB1RyIAZCAFNyDQACQCAGQv///////////wBRBEBCfyEHIAhCf1IEQCAFIQQgCCEHQv///////////wAhBgwECyAFQn9RDQEgBSEEQv///////////wAhBgwDCyAFIQQgCCEHDAILQn8hBCAJQm1aDQBC////////////ACEGDAELIAVCAXwiByAJQm1UrSILfSEEIAhCAXwiCiAFQn9SIAcgC1RyrSIFfSEHIAYgCEJ/UiAFIApWcq19Qv///////////wB9IQYgCUITfCEJCyAAIAk3AxggACAENwMQIAAgBzcDCCAAIAY3AwAgA0HAA2okAAuFEAIBfxB+IwBBgARrIgMkACADQYACaiABKQMYIgVCACACKQMYIgRCABDJAyADQZACaiABKQMQIgZCACAEQgAQyQMgA0GgAmogASkDCCIHQgAgBEIAEMkDIANBsAJqIAEpAwAiCEIAIARCABDJAyADQfABaiADKQOAAiIKQv////++sv3wQn4iBEIAQoGAgIC/sv3wwwBCABDJAyADQeABaiAEQgBCkeHlzYeJ+pkoQgAQyQMgA0GQAWogBEIAQt2whYzotpGouH9CABDJAyADQUBrIARCAEKpwMaJrs6TsjBCABDJAyADQcACaiACKQMQIgRCACAFQgAQyQMgA0HwAmogBEIAIAZCABDJAyADQaADaiAEQgAgB0IAEMkDIANB0ANqIARCACAIQgAQyQMgA0HQAWogAykD4AEiDCADKQOIAiINIAMpA5ACfCIOfCIJIAMpA/gBIAogAykD8AEiBHwgBFStfHwiCiADKQPAAnwiC0L/////vrL98EJ+IgRCAEKBgICAv7L98MMAQgAQyQMgA0HAAWogBEIAQpHh5c2HifqZKEIAEMkDIANBsAFqIARCAELdsIWM6LaRqLh/QgAQyQMgA0GgAWogBEIAQqnAxomuzpOyMEIAEMkDIANB0AJqIAIpAwgiBEIAIAVCABDJAyADQYADaiAEQgAgBkIAEMkDIANBsANqIARCACAHQgAQyQMgA0HgA2ogBEIAIAhCABDJAyADQYABaiADKQPIAiAKIAtWrXwiESADKQPwAnwiDyADKQOYAiANIA5WrXwiECADKQOgAnwiDSADKQOQAXwiDiAJIApWrSADKQPoASAJIAxUrXx8fCISfCIJIAMpA8ABfCIKIAMpA9gBIAMpA9ABIgQgC3wgBFStfHwiCyADKQPQAnwiDEL/////vrL98EJ+IgRCAEKBgICAv7L98MMAQgAQyQMgA0HwAGogBEIAQpHh5c2HifqZKEIAEMkDIANB4ABqIARCAELdsIWM6LaRqLh/QgAQyQMgA0HQAGogBEIAQqnAxomuzpOyMEIAEMkDIANB4AJqIAIpAwAiBEIAIAVCABDJAyADQZADaiAEQgAgBkIAEMkDIANBwANqIARCACAHQgAQyQMgA0HwA2ogBEIAIAhCABDJAyADQTBqIAMpA9gCIAsgDFatfCITIAMpA4ADfCIEIAMpA6gCIA0gEFStfCIQIAMpA7ACfCIGIAMpA0B8IgcgDiASVq0gAykDmAEgDSAOVq18fHwiCCADKQOgA3wiDSAJIA9UrSADKQP4AiAPIBFUrXx8fCIPIAMpA7ABfCIOIAogC1atIAMpA8gBIAkgClatfHx8IhF8IgkgAykDcHwiCiADKQOIASADKQOAASIFIAx8IAVUrXx8IgsgAykD4AJ8IgxC/////76y/fBCfiIFQgBCgYCAgL+y/fDDAEIAEMkDIANBIGogBUIAQpHh5c2HifqZKEIAEMkDIANBEGogBUIAQt2whYzotpGouH9CABDJAyADIAVCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDCCADKQNYIAMpA6gBIAcgCFatIAMpA0ggBiAHVq18fCADKQO4AiAGIBBUrXx8IhAgAykD0AN8IgUgDSAPVq0gAykDqAMgCCANVq18fHwiBiADKQOgAXwiByAGVK18IAcgByAOIBFWrSADKQO4ASAOIA9UrXx8fCIHVq18IAUgBlatIAMpA9gDIAUgEFStfHx8IgggAykD4AN8IgUgAykDuAMgByADKQOwA3wiBiAHVK18IAYgBCAJVq0gAykDiAMgBCATVK18fHwiBCAGVK18fCIGIAMpA1B8IgcgBlStfCAHIAMpA2ggBCAEIAMpA2B8IgRWrXwgBCAKIAtWrSADKQN4IAkgClatfHx8IgkgBFStfHwiBCAHVK18IAUgBlatIAMpA+gDIAUgCFStfHx8IgogAykD8AN8IgcgAykDyAMgBCADKQPAA3wiBSAEVK18IAUgBSADKQOYAyADKQPoAiALIAxWrXwiBiADKQOQA3wiBCAGVK18IAQgBCAJfCIEVq18fCIFVq18fCIIIAMpAwB8IgYgCFStfCAGIAYgAykDGCAFIAUgAykDEHwiBVatfCAFIAUgAykDKCAEIAQgAykDIHwiBFatfCAEIAMpAzggAykDMCIJIAx8IAlUrXx8IgkgBFStfHwiBVatfHwiBlatfCAHIAhWrSADKQP4AyAHIApUrXx8fCIIQqnAxomuzpOyMFYNAAJAIAhCqcDGia7Ok7IwUQRAIAZC3bCFjOi2kai4f1YNAiAGQt2whYzotpGouH9SBEAgBSEEIAYhB0KpwMaJrs6TsjAhCAwECyAFQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IQcgBUKR4eXNh4n6mShRDQEgBSEEQqnAxomuzpOyMCEIDAMLIAUhBCAGIQcMAgtCkeHlzYeJ+pkoIQQgCUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCEIDAELIAVCkeHlzYeJ+pkofSIHIAlCgYCAgL+y/fDDAFStIgp9IQQgBkKjz/rzl8nu18cAfCILIAVCkeHlzYeJ+pkoVCAHIApUcq0iBX0hByAIIAZC3bCFjOi2kai4f1QgBSALVnKtfUKpwMaJrs6TsjB9IQggCUKBgICAv7L98MMAfSEJCyAAIAk3AxggACAENwMQIAAgBzcDCCAAIAg3AwAgA0GABGokAAuLEAIBfxB+IwBBgARrIgMkACADQYACaiABKQMYIgVCACACKQMYIgRCABDJAyADQZACaiABKQMQIgZCACAEQgAQyQMgA0GgAmogASkDCCIHQgAgBEIAEMkDIANBsAJqIAEpAwAiCEIAIARCABDJAyADQfABaiADKQOAAiIKQonHmaSu8IHph39+IgRCAELH+vPD7YKjkDxCABDJAyADQeABaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANBkAFqIARCAELdsIWM6LaRqLh/QgAQyQMgA0FAayAEQgBCqcDGia7Ok7IwQgAQyQMgA0HAAmogAikDECIEQgAgBUIAEMkDIANB8AJqIARCACAGQgAQyQMgA0GgA2ogBEIAIAdCABDJAyADQdADaiAEQgAgCEIAEMkDIANB0AFqIAMpA+ABIgwgAykDiAIiDSADKQOQAnwiDnwiCSADKQP4ASAKIAMpA/ABIgR8IARUrXx8IgogAykDwAJ8IgtCiceZpK7wgemHf34iBEIAQsf688PtgqOQPEIAEMkDIANBwAFqIARCAEKNlcfDltLawJd/QgAQyQMgA0GwAWogBEIAQt2whYzotpGouH9CABDJAyADQaABaiAEQgBCqcDGia7Ok7IwQgAQyQMgA0HQAmogAikDCCIEQgAgBUIAEMkDIANBgANqIARCACAGQgAQyQMgA0GwA2ogBEIAIAdCABDJAyADQeADaiAEQgAgCEIAEMkDIANBgAFqIAMpA8gCIAogC1atfCIRIAMpA/ACfCIPIAMpA5gCIA0gDlatfCIQIAMpA6ACfCINIAMpA5ABfCIOIAkgClatIAMpA+gBIAkgDFStfHx8IhJ8IgkgAykDwAF8IgogAykD2AEgAykD0AEiBCALfCAEVK18fCILIAMpA9ACfCIMQonHmaSu8IHph39+IgRCAELH+vPD7YKjkDxCABDJAyADQfAAaiAEQgBCjZXHw5bS2sCXf0IAEMkDIANB4ABqIARCAELdsIWM6LaRqLh/QgAQyQMgA0HQAGogBEIAQqnAxomuzpOyMEIAEMkDIANB4AJqIAIpAwAiBEIAIAVCABDJAyADQZADaiAEQgAgBkIAEMkDIANBwANqIARCACAHQgAQyQMgA0HwA2ogBEIAIAhCABDJAyADQTBqIAMpA9gCIAsgDFatfCITIAMpA4ADfCIEIAMpA6gCIA0gEFStfCIQIAMpA7ACfCIGIAMpA0B8IgcgDiASVq0gAykDmAEgDSAOVq18fHwiCCADKQOgA3wiDSAJIA9UrSADKQP4AiAPIBFUrXx8fCIPIAMpA7ABfCIOIAogC1atIAMpA8gBIAkgClatfHx8IhF8IgkgAykDcHwiCiADKQOIASADKQOAASIFIAx8IAVUrXx8IgsgAykD4AJ8IgxCiceZpK7wgemHf34iBUIAQsf688PtgqOQPEIAEMkDIANBIGogBUIAQo2Vx8OW0trAl39CABDJAyADQRBqIAVCAELdsIWM6LaRqLh/QgAQyQMgAyAFQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpAwggAykDWCADKQOoASAHIAhWrSADKQNIIAYgB1atfHwgAykDuAIgBiAQVK18fCIQIAMpA9ADfCIFIA0gD1atIAMpA6gDIAggDVatfHx8IgYgAykDoAF8IgcgBlStfCAHIAcgDiARVq0gAykDuAEgDiAPVK18fHwiB1atfCAFIAZWrSADKQPYAyAFIBBUrXx8fCIIIAMpA+ADfCIFIAMpA7gDIAcgAykDsAN8IgYgB1StfCAGIAQgCVatIAMpA4gDIAQgE1StfHx8IgQgBlStfHwiBiADKQNQfCIHIAZUrXwgByADKQNoIAQgBCADKQNgfCIEVq18IAQgCiALVq0gAykDeCAJIApWrXx8fCIJIARUrXx8IgQgB1StfCAFIAZWrSADKQPoAyAFIAhUrXx8fCIKIAMpA/ADfCIHIAMpA8gDIAQgAykDwAN8IgUgBFStfCAFIAUgAykDmAMgAykD6AIgCyAMVq18IgYgAykDkAN8IgQgBlStfCAEIAQgCXwiBFatfHwiBVatfHwiCCADKQMAfCIGIAhUrXwgBiAGIAMpAxggBSAFIAMpAxB8IgVWrXwgBSAFIAMpAyggBCAEIAMpAyB8IgRWrXwgBCADKQM4IAMpAzAiCSAMfCAJVK18fCIJIARUrXx8IgVWrXx8IgZWrXwgByAIVq0gAykD+AMgByAKVK18fHwiCEKpwMaJrs6TsjBWDQACQCAIQqnAxomuzpOyMFEEQCAGQt2whYzotpGouH9WDQIgBkLdsIWM6LaRqLh/UgRAIAUhBCAGIQdCqcDGia7Ok7IwIQgMBAsgBUKNlcfDltLawJd/Vg0CQt2whYzotpGouH8hByAFQo2Vx8OW0trAl39RDQEgBSEEQqnAxomuzpOyMCEIDAMLIAUhBCAGIQcMAgtCjZXHw5bS2sCXfyEEIAlCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEIDAELIAVC8+q4vOmtpb/oAHwiByAJQsf688PtgqOQPFStIgp9IQQgBkKjz/rzl8nu18cAfCILIAVCjZXHw5bS2sCXf1QgByAKVHKtIgV9IQcgCCAGQt2whYzotpGouH9UIAUgC1ZyrX1CqcDGia7Ok7IwfSEIIAlCx/rzw+2Co5A8fSEJCyAAIAk3AxggACAENwMQIAAgBzcDCCAAIAg3AwAgA0GABGokAAvIDQEMfyMAQUBqIgQkAAJAAkACQAJAAkACfwJAAkACQAJAAkACQCACRQRAIARBEGpBkJLCACgCADYCACAEQYiSwgApAgA3AwgMAQsgAkEASA0BQdHOxQAtAAAaQQEhAyACQQEQ1gQiB0UNASACBEAgByABIAL8CgAACwJAIAJBAUYNACACIAdqIQVBACEBIAJBAXYiBkEBRwRAIAJBAWshAyAGQf7///8DcSEJA0AgAyAHaiIGLQAAIQggBiABIAdqIgYtAAA6AAAgBiAIOgAAIAUgAUF+c2oiCC0AACEKIAggBkEBaiIGLQAAOgAAIAYgCjoAACADQQJrIQMgCSABQQJqIgFHDQALCyACIgNBAnFFDQAgASAHaiIGLQAAIQkgBiAFIAFBf3NqIgEtAAA6AAAgASAJOgAACyAEQQhqIAcgA0EIEM8CIAcgAhDfBAsgBEE4akGQksIAKAIANgIAIARBiJLCACkCADcDMCAEQTBqQYyTwgAQpQMgBCgCNEEBNgIAIAQoAjQhAQJAAkAgBCgCMCICQYCAgIB4Rw0AIAEoAggNACAEQQA2AiAgBEKAgICAwAA3AhgMAQsgBEEBNgI4IAQgATYCNCAEIAI2AjAgBEEYaiAEQTBqQQRBABDPAQsgBEE4aiIBIARBIGooAgA2AgAgBCAEKQIYNwMwIARBMGpBARDDAiAEKAI0IQkgBCgCMCENAn8CQCAEKAIQIgcgASgCACICSwRAIAJBAnQhASACRQ0BQdHOxQAtAAAaIAFBBBDWBCIFRQ0EIAEEQCAFIAkgAfwKAAALIAJBA3EhBkEAIQEgBCgCDCELIAJBBE8EQCACQQJ0QXBxIQ5BACEDA0AgAyAFaiIIIAgoAgAgAyALaiIKKAIAcTYCACAIQQRqIgwgDCgCACAKQQRqKAIAcTYCACAIQQhqIgwgDCgCACAKQQhqKAIAcTYCACAIQQxqIgggCCgCACAKQQxqKAIAcTYCACABQQRqIQEgDiADQRBqIgNHDQALCyAGBEAgBSABQQJ0IgNqIQEgAyALaiEDA0AgASABKAIAIAMoAgBxNgIAIAFBBGohASADQQRqIQMgBkEBayIGDQALCyAFIAJBAnQiAWpBBGsoAgAEQCAFIQMgAiEBDAsLIAIhAwNAIAFFBEBBACEBDAkLIANBAWshAyABQQRrIgEgBWooAgBFDQALIANBAWoiASACIAEgAkkbIQEMBwsgB0ECdCEBIAQoAgwhAiAHBEBB0c7FAC0AABogAUEEENYEIgVFDQUgAQRAIAUgAiAB/AoAAAsgB0EDcSEGQQAhASAHQQRPBEAgB0ECdEFwcSEKQQAhAwNAIAMgBWoiAiACKAIAIAMgCWoiCCgCAHE2AgAgAkEEaiILIAsoAgAgCEEEaigCAHE2AgAgAkEIaiILIAsoAgAgCEEIaigCAHE2AgAgAkEMaiICIAIoAgAgCEEMaigCAHE2AgAgAUEEaiEBIAogA0EQaiIDRw0ACwsgBgRAIAUgAUECdCICaiEBIAIgCWohAwNAIAEgASgCACADKAIAcTYCACABQQRqIQEgA0EEaiEDIAZBAWsiBg0ACwsgBSAHQQJ0IgFqQQRrKAIABEAgBSEDIAcMAwsgByEDA0AgAUUEQEEAIQEMCAsgA0EBayEDIAFBBGsiASAFaigCAEUNAAsgA0EBaiIBIAcgASAHSRshAQwGC0EEIQMgAQRAQQQgAiAB/AoAAAtBACEBQQAhAgwKC0EEIQMgAQRAQQQgCSAB/AoAAAtBAAshASAEQYCAgIB4NgIwIAQgBEEIajYCNCABIQIMCQsgAyACQaSbwgAQyAQAC0EEIAFB+IHAABDIBAALQQQgAUH4gcAAEMgEAAsgB0ECdiABTQRAIAchAiAFIQMMBAsgB0ECdCEGIAFFBEAgBSAGEN8EQQQMAgsgASECIAUgBkEEIAFBAnQiBRDOBCIDDQNBBCAFQZSSwgAQyAQACyACQQJ2IAFNBEAgBSEDDAMLIAJBAnQhBiABDQEgBSAGEN8EQQQLIQNBACECQQAhAQwBCyABIQIgBSAGQQQgAUECdCIFEM4EIgMNAEEEIAVBlJLCABDIBAALIARBgICAgHg2AjAgBCAEQQhqNgI0IAcNAQsgBEEANgIsIARCgICAgMAANwIkDAELIARBJGogBEEwakEEQQAQ7AELIAAgATYCCCAAIAM2AgQgACACNgIAIAAgBCkCJDcCDCAAQRRqIARBLGooAgA2AgAgDQRAIAkgDUECdBDfBAsgBCgCCCIABEAgBCgCDCAAQQJ0EN8ECyAEQUBrJAAL7AwCAX8UfiMAQYADayIDJAAgA0GAAWogASkDGCIEQgAgAikDGCIFQgAQyQMgA0GQAWogASkDECIJQgAgBUIAEMkDIANBoAFqIAEpAwgiB0IAIAVCABDJAyADQbABaiABKQMAIghCACAFQgAQyQMgA0HwAGogAykDgAEiBkKx6pSR3aOCnFh+IgVCAEKv+P//b0IAEMkDIANB4ABqIAVCAEJ/QgAQyQMgA0HAAWogAikDECIFQgAgBEIAEMkDIANB8AFqIAVCACAJQgAQyQMgA0GgAmogBUIAIAdCABDJAyADQdACaiAFQgAgCEIAEMkDIANB0ABqIAMpA2AiBSADKQOIASINIAMpA5ABfCIOfCIKIAMpA3ggBiADKQNwIgt8IAtUrXx8IgsgAykDwAF8IgxCseqUkd2jgpxYfiIGQgBCr/j//29CABDJAyADQUBrIAZCAEJ/QgAQyQMgA0HQAWogAikDCCIGQgAgBEIAEMkDIANBgAJqIAZCACAJQgAQyQMgA0GwAmogBkIAIAdCABDJAyADQeACaiAGQgAgCEIAEMkDIANBMGogAykDyAEgCyAMVq18IhEgAykD8AF8Ig8gBSADKQOYASANIA5WrXwiEyADKQOgAXwiDXwiDiAKIAtWrSADKQNoIgsgBSAKVq18fHwiFHwiCiADKQNAIhV8IhAgAykDWCADKQNQIgYgDHwgBlStfHwiDCADKQPQAXwiEkKx6pSR3aOCnFh+IgZCAEKv+P//b0IAEMkDIANBIGogBkIAQn9CABDJAyADQeABaiACKQMAIgZCACAEQgAQyQMgA0GQAmogBkIAIAlCABDJAyADQcACaiAGQgAgB0IAEMkDIANB8AJqIAZCACAIQgAQyQMgA0EQaiADKQPYASAMIBJWrXwiFiADKQOAAnwiBCAVIAUgAykDqAEgDSATVK18IhcgAykDsAF8Igl8IgUgDiAUVq0gCyANIA5WrXx8fCIHIAMpA6ACfCIIIAogD1StIAMpA/gBIA8gEVStfHx8IgZ8Ig8gDCAQVK0gAykDSCIMIAogEFatfHx8IhR8IgogAykDICINfCIOIAMpAzggAykDMCIQIBJ8IBBUrXx8IhAgAykD4AF8IhJCseqUkd2jgpxYfiIRQgBCr/j//29CABDJAyADIBFCAEJ/QgAQyQMCQAJAIAMpAwgiESADKQMoIhMgDSAMIBUgBSAHVq0gCyAFIAlUrXx8IgsgAykDuAEgCSAXVK18fCIFIAMpA9ACfCIJIAYgCFStIAMpA6gCIAcgCFatfHx8Igd8IgggB1StfCAIIAggDyAUVq0gDCAGIA9WrXx8fCIIVq18IgYgByAJVK0gAykD2AIgBSAJVq18fCIMIAUgC1StfCILfCIFIAMpA+ACfCIJIAMpA7gCIAggAykDsAJ8IgcgCFStfCAHIAQgClatIAMpA4gCIAQgFlStfHx8IgQgB1StfHwiB3wiCCAHVK18IAggEyAEIAQgDXwiBFatfCAEIA4gEFatIBMgCiAOVq18fHwiCiAEVK18fCIEIAhUrXwiDyAHIAlUrSADKQPoAiAFIAlWrXx8Ig0gBSAGVK0gCyAMVK18fCILfCIFIAMpA/ACfCIHIAMpA8gCIAQgBCADKQPAAnwiBFatfCAEIAQgAykDmAIgAykD6AEgECASVq18IgggAykDkAJ8IgkgCFStfCAJIAkgCnwiCVatfHwiBFatfHwiCCADKQMAIgZ8IgogCFStfCAKIBEgBCAEIAZ8IgRWrXwgBCAEIBEgCSAGIAl8IglWrXwgCSADKQMYIAMpAxAiBiASfCAGVK18fCIGIAlUrXx8IgRWrXx8IgkgClStfCIKIAcgCFatIAMpA/gCIAUgB1atfHwiByAFIA9UrSALIA1UrXx8IgV8IgggClQgBSAHVHINACAIQn9SBEAgBCEFIAkhBwwCCyAJQn9SBEAgBCEFIAkhB0J/IQgMAgtCfyEHIARCf1IEQCAEIQVCfyEIDAILQn8hBSAGQq/4//9vWg0AQn8hCAwBCyAEQgF8IgcgBkKv+P//b1StIgp9IQUgCUIBfCILIARCf1IgByAKVHKtIgR9IQcgCCAJQn9SIAQgC1ZyrX1CAXwhCCAGQtGHgIAQfCEGCyAAIAY3AxggACAFNwMQIAAgBzcDCCAAIAg3AwAgA0GAA2okAAufGQIIfxJ+IwBBsAFrIgMkACADQeAAakIANwMAIANB2ABqQgA3AwAgA0IANwNQIANCATcDaCADQThqIgVCfzcDACADQTBqIgdCfzcDACADQn83AyggA0Ku+P//bzcDQCADQZABaiADQShqQf8BELICIANB+ABqIgZCADcDACADQYABaiIJQgA3AwAgA0IANwNwIAMgAykDqAFCAYM3A4gBAkAgA0HwAGogA0HQAGpBIBDxA0UEQEGAAiEEDAELQYACIQQDQCAFQn83AwAgB0J/NwMAIANCfzcDKCADQq74//9vNwNAIANBkAFqIANBKGogBEECaxCyAiAGQgA3AwAgCUIANwMAIANCADcDcCADIAMpA6gBQgGDNwOIASAEQQFrIQQgA0HwAGogA0HQAGpBIBDxAw0ACwtBACEFAkACQAJAAkACQAJAIAIgBEEDdiAEQQdxQQBHaiIETQRAAkAgBCACayIERQRAQQEhBQwBC0HRzsUALQAAGiAEQQEQ1wQiBUUNBAsgAyAENgKYASADIAU2ApQBIAMgBDYCkAEgAgRAIANBkAFqIAQgAkEBQQEQiAMgAygCmAEhBCADKAKUASEFCyACBEAgBCAFaiABIAL8CgAACyMAQcABayIBJAAgA0EoaiIHAn8gAiAEakEfTQRAIAdBADoAAUEBDAELIAFBoAFqIAUpABgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIQQgBCoaG6gKD0AUIAEMkDIAFBsAFqIAUpABAiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIOQgBCoaG6gKD0AUIAEMkDIAFB0ABqIAUpAAgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIVQgBCoaG6gKD0AUIAEMkDIAFBIGogBSkAACILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEIhlCAEKhobqAoPQBQgAQyQMgAUGQAWogASkDoAEiDEKx6pSR3aOCnFh+IgtCAEKv+P//b0IAEMkDIAFBgAFqIAtCAEJ/QgAQyQMgAUHwAGogECABKQOAASILIAEpA6gBIg8gASkDsAF8IhF8Ig0gASkDmAEgDCABKQOQASISfCASVK18fCIMfCIQQrHqlJHdo4KcWH4iEkIAQq/4//9vQgAQyQMgAUHgAGogEkIAQn9CABDJAyABQUBrIAwgEFatIhYgDnwiDiALIAEpA7gBIA8gEVatfCIUIAEpA1B8Ig98IhEgDCANVK0gASkDiAEiDCALIA1WrXx8fCIXfCISIAEpA2AiGHwiEyABKQN4IAEpA3AiDSAQfCANVK18fCIQQrHqlJHdo4KcWH4iDUIAQq/4//9vQgAQyQMgAUEwaiANQgBCf0IAEMkDIAFBEGogASkDMCINIBggFSALIAEpA1ggDyAUVK18IhogASkDIHwiFHwiCyARIBdWrSAMIA8gEVatfHx8Ig98IhEgDiAWVK0gDiASVq18fCIOfCIVIBAgE1StIAEpA2giFiASIBNWrXx8fCIbfCISIAEpA0ggECABKQNAIhN8IBNUrXx8IhBCseqUkd2jgpxYfiITQgBCr/j//29CABDJAyABIBNCAEJ/QgAQyQMCQAJAAkAgASkDCCITIAEpAzgiFyANIBkgCyAPVq0gDCALIBRUrXx8IhwgASkDKCAUIBpUrXx8Igt8IgwgC1StIAwgDCAPIBFWrSAOIBFUrXx8Ig9WrXwiFCALIBxUrXwiCyAWIA8gDyAYfCIMVq18IAwgDCAVIBtWrSAWIA4gFVatfHx8Ig5WrXx8Igx8Ig8gDFStfCAPIBcgDiANIA58IhFWrXwgESAQIBJUrSAXIA0gElatfHx8IhIgEVStfHwiDSAPVK18IhggCyAUVK0gCyAMVq18fCIOIAEpAwAiC3wiESAOVK18IBEgESATIA0gCyANfCIMVq18IAwgEyALIAsgEnwiDVatfCANIAEpAxggECABKQMQIgt8IAtUrXx8Ig8gDVStfHwiCyAMVK18fCIMVq18Ig0gDiAYVK18Ig4gDVQNACAOQn9SDQEgDEJ/UgRAQn8hDgwCC0J/IRAgC0J/UgRAQn8hDiALIQ0MAwsgD0Kv+P//b1oNAEJ/IQ5CfyENDAILIAtCAXwiECAPQq/4//9vVK0iEX0hDSAMQgF8IhIgC0J/UiAQIBFUcq0iC30hECAOIAxCf1IgCyASVnKtfUIBfCEOIA9C0YeAgBB8IQ8MAQsgDCEQIAshDQsgByAPNwMgIAcgDTcDGCAHIBA3AxAgByAONwMIQQALOgAAIAFBwAFqJAAgAy0AKEUNASADIAMtACk6AHBB5NjCAEErIANB8ABqQaTawgBBtNrCABDKAwALIAJBAEgNA0HRzsUALQAAGkEBIQUgAkEBENYEIgdFDQMgAgRAIAcgASAC/AoAAAsgA0EMaiAHAn9BASACQQFGDQAaIAIgB2ohAUEAIQQgAkEBdiIGQQFHBEAgAkEBayEFIAZB/v///wNxIQkDQCAFIAdqIgYtAAAhCCAGIAQgB2oiBi0AADoAACAGIAg6AAAgASAEQX5zaiIILQAAIQogCCAGQQFqIgYtAAA6AAAgBiAKOgAAIAVBAmshBSAJIARBAmoiBEcNAAsLIAIgAkECcUUNABogBCAHaiIFLQAAIQYgBSABIARBf3NqIgEtAAA6AAAgASAGOgAAIAILQQgQzwIgByACEN8EAkBB2NPBAEHo0cEAQSAQ8QMEQCADQThqQn83AwAgA0EwakJ/NwMAIANCfzcDKCADQt7w//9fNwNADAELIANBQGtB8NPBACkDADcDACADQThqQejTwQApAwA3AwAgA0EwakHg08EAKQMANwMAIANB2NPBACkDADcDKAsgA0GQAWoiAiADQShqIgEQ9QEgA0EANgJ4IANCgICAgBA3AnAgA0Hc08IANgIsIANCoICAgA43AjAgAyADQfAAajYCKCACIAEQ0wINBCADKAJwIQIgASADKAJ0IgcgAygCeBCVAyADKAIwIgVFBEAgAygCKEUEQCABQcjQwgAQpQMLIAMoAixBADYCACADQQE2AjBBASEFCyADKAIsIgEgASgCAEEBaiIENgIAAkAgBA0AIAVBAUcEQCAFQQJ0QQRrIQUgAUEEaiEEA0AgBCAEKAIAQQFqIgE2AgAgAQ0CIARBBGohBCAFQQRrIgUNAAsLIAMoAjAiASADKAIoRgRAIANBKGpB2NDCABClAwsgAygCLCABQQJ0akEBNgIAIAMgAUEBajYCMAsgA0EgaiADQTBqKAIANgIAIAMgAykCKDcDGCACBEAgByACEN8ECyADQShqIANBDGogA0EYahDvAQJAAkAgAygCMEUEQEHRzsUALQAAGkEBIQRBAUEBENYEIgFFDQggAUEAOgAAIAAgAUEBEIEBDAELIANBkAFqIANBKGpBCBCwAiADKAKUASEBAkAgAygCmAEiAkECSQ0AIAEgAmohB0EAIQQgAkEBdiIGQQFHBEAgAkEBayEFIAZB/v///wdxIQkDQCABIAVqIgYtAAAhCCAGIAEgBGoiBi0AADoAACAGIAg6AAAgByAEQX5zaiIILQAAIQogCCAGQQFqIgYtAAA6AAAgBiAKOgAAIAVBAmshBSAJIARBAmoiBEcNAAsLIAJBAnFFDQAgASAEaiIFLQAAIQYgBSAHIARBf3NqIgUtAAA6AAAgBSAGOgAACyADKAKQASEEIAAgASACEIEBIARFDQELIAEgBBDfBAsgAygCKCIARQ0BIAMoAiwgAEECdBDfBAwBCyAAIAMpAzA3AwAgAEEYaiADQcgAaikDADcDACAAQRBqIANBQGspAwA3AwAgAEEIaiADQThqKQMANwMAIAMoApABIgBFDQAgBSAAEN8ECyADQbABaiQADwtBASAEQZTawgAQyAQACyAFIAJB1NjCABDIBAALQYTUwgBBNyADQdAAakH008IAQYjVwgAQygMAC0EBQQEQ/wQAC8gMAgZ+DX8jAEEgayIOJABBAUECIAAoAgwbIgogACgCCCIISwRAIA5BGGogACAKIABBEGoQogEgACgCCCEICyAAKQMYIgIgASgCACINrSIDhULzytHLp4zZsvAAhSIEQhCJIAQgACkDECIFQuHklfPW7Nm87ACFfCIEhSIGIAJC7d6R85bM3LfkAIUiAiAFQvXKzYPXrNu38wCFfCIFQiCJfCIHIANCgICAgICAgIAEhIUgAkINiSAFhSICIAR8IgMgAkIRiYUiAnwiBCACQg2JhSICIAZCFYkgB4UiBSADQiCJQv8BhXwiA3wiBiACQhGJhSICQg2JIAIgAyAFQhCJhSIDIARCIIl8IgR8IgKFIgVCEYkgBSADQhWJIASFIgMgBkIgiXwiBHwiBYUiBkINiSAGIANCEIkgBIUiAyACQiCJfCICfIUiBEIRiSADQhWJIAKFIgJCEIkgAiAFQiCJfCIChUIViYUgAiAEfCICQiCIhSAChSECIAEoAhQhECABKAIQIREgASgCDCEPIAEoAgghEiABKAIEIRMgCEUEQCAOQRBqIABBASAAQRBqEKIBCyAAKAIEIgwgAqdxIQggAkIZiCIEQv8Ag0KBgoSIkKDAgAF+IQUgACgCACEJQQAhAQJAAkADQCAIIAlqKQAAIgMgBYUiAkJ/hSACQoGChIiQoMCAAX2DQoCBgoSIkKDAgH+DIgJQRQRAA0AgDSAJIAJ6p0EDdiAIaiAMcUF0bGoiCkEMaygCAEYNAyACQgF9IAKDIgJQRQ0ACwsgA0KAgYKEiJCgwIB/gyECQQEhCiABQQFHBEAgAnqnQQN2IAhqIAxxIQsgAkIAUiEKCyACIANCAYaDUARAIAggFEEIaiIUaiAMcSEIIAohAQwBCwsgCSALaiwAACIIQQBOBEAgCSAJKQMAQoCBgoSIkKDAgH+DeqdBA3YiC2otAAAhCAsgCSALaiAEp0H/AHEiAToAACAJIAtBCGsgDHFqQQhqIAE6AAAgACAAKAIIIAhBAXFrNgIIIAAgACgCDEEBajYCDCAJIAtBdGxqIgFBDGsgDTYCACABQQhrIBM2AgAgAUEEayASNgIADAELIApBBGsgEjYCACAKQQhrIBM2AgALIAApAxgiAiAPrSIDhULzytHLp4zZsvAAhSIEQhCJIAQgACkDECIFQuHklfPW7Nm87ACFfCIEhSIGIAJC7d6R85bM3LfkAIUiAiAFQvXKzYPXrNu38wCFfCIFQiCJfCIHIANCgICAgICAgIAEhIUgAkINiSAFhSICIAR8IgMgAkIRiYUiAnwiBCACQg2JhSICIAZCFYkgB4UiBSADQiCJQv8BhXwiA3wiBiACQhGJhSICQg2JIAIgAyAFQhCJhSIDIARCIIl8IgR8IgKFIgVCEYkgBSADQhWJIASFIgMgBkIgiXwiBHwiBYUiBkINiSAGIANCEIkgBIUiAyACQiCJfCICfIUiBEIRiSADQhWJIAKFIgJCEIkgAiAFQiCJfCIChUIViYUgAiAEfCICQiCIhSAChSECIAAoAghFBEAgDkEIaiAAQQEgAEEQahCiAQsgACgCBCIMIAKncSEIIAJCGYgiBEL/AINCgYKEiJCgwIABfiEFIAAoAgAhCUEAIQ1BACEBAkADQAJAIAggCWopAAAiAyAFhSICQn+FIAJCgYKEiJCgwIABfYNCgIGChIiQoMCAf4MiAlBFBEADQCAPIAkgAnqnQQN2IAhqIAxxQXRsaiIKQQxrKAIARg0CIAJCAX0gAoMiAlBFDQALCyADQoCBgoSIkKDAgH+DIQJBASEKIAFBAUcEQCACeqdBA3YgCGogDHEhCyACQgBSIQoLIAIgA0IBhoNQBEAgCCANQQhqIg1qIAxxIQggCiEBDAIFIAkgC2osAAAiCEEATgRAIAkgCSkDAEKAgYKEiJCgwIB/g3qnQQN2IgtqLQAAIQgLIAkgC2ogBKdB/wBxIgE6AAAgCSALQQhrIAxxakEIaiABOgAAIAAgACgCCCAIQQFxazYCCCAAIAAoAgxBAWo2AgwgCSALQXRsaiIAQQxrIA82AgAgAEEIayARNgIAIABBBGsgEDYCAAwDCwALCyAKQQRrIBA2AgAgCkEIayARNgIACyAOQSBqJAALuw4CBX8RfiMAQZACayIDJABBAyEEIAACfwJAAkACQAJAAkACQAJAAkACQCACQQNPBEACfyABLAAAIgRBAE4EQCAEQf8BcSEEIAFBAWoMAQsgAS0AAUE/cSEGIARBH3EhBSAEQV9NBEAgBUEGdCAGciEEIAFBAmoMAQsgAS0AAkE/cSAGQQZ0ciEGIARBcEkEQCAGIAVBDHRyIQQgAUEDagwBCyAFQRJ0QYCA8ABxIAEtAANBP3EgBkEGdHJyIQQgAUEEagshBSAEQTBHDQEgBSABIAJqRg0FAn8gBSwAACIEQQBOBEAgBEH/AXEMAQsgBS0AAUE/cSEHIARBH3EhBiAGQQZ0IAdyIARBX00NABogBS0AAkE/cSAHQQZ0ciEHIAcgBkEMdHIgBEFwSQ0AGiAGQRJ0QYCA8ABxIAUtAANBP3EgB0EGdHJyC0H4AEcNASABLAACQb9/SgRAIAJBAmshAiABQQJqIQEMAgsgASACQQIgAkHw1sEAENIEAAsgAkUNAQtBACEEAkADQAJAIAEgBGotAAAiBUEwa0H/AXFBCkkNACAFQcEAaw4mAAAAAAAAAgICAgICAgICAgICAgICAgICAgICAgICAgIAAAAAAAACCyACIARBAWoiBEcNAAtBAiEEIAJB4ABLDQEgA0HgAWogASACEKYCIAMpA4gCIRIgAykDgAIhEyADKQP4ASEUIAMpA/ABIRUgAykD6AEhFiADKQPgASEXQSghBANAIANB8ABqIARBqNTBAGopAwAiCUIAIBJCABDJAyADQYABaiAJQgAgE0IAEMkDIANBkAFqIAlCACAUQgAQyQMgA0GgAWogCUIAIBVCABDJAyADQbABaiAJQgAgFkIAEMkDIANBwAFqIAlCACAXQgAQyQMgA0HgAGogAykDcCIRIA98Ig5CAEIAQv3/8//P///5iX8QyQMgA0HQAGogAykDaCIJQgBCq9X+////v/+5f0IAEMkDIANBQGsgCUIAQv//z4rr///VHkIAEMkDIANBMGogCUIAQqTsw7WP1LSY5wBCABDJAyADQSBqIAlCAEK/pZScz/DSu+QAQgAQyQMgA0EQaiAJQgBC19mumuT26Y3LAEIAEMkDIAMgCUIAQprN/8ujvcSAGkIAEMkDIAMpAwggAykDwAEiGCAIfCIJIAMpA7gBIAMpA7ABIgggDXwiDSAIVK18IA0gAykDqAEgAykDoAEiCCAMfCIMIAhUrXwgDCADKQOYASADKQOQASIIIAt8IgsgCFStfCALIAMpA4gBIAMpA4ABIgggCnwiCiAIVK18IAogAykDeCAOIBFUrXx8IgggClStfHwiCiALVK18fCILIAxUrXx8IgwgDVStfHwiESADKQMAfCINIBFUrXwgDSANIAMpAxggDCAMIAMpAxB8IgxWrXwgDCAMIAMpAyggCyALIAMpAyB8IgtWrXwgCyALIAMpAzggCiAKIAMpAzB8IgpWrXwgCiAKIAMpA0ggAykDQCIPIAh8IgggD1StfCAIIAMpA1ggDiADKQNQIg58IA5UrXx8Ig8gCFStfHwiClatfHwiC1atfHwiDFatfHwiDVatfCIOIBAgCSARVq0gAykDyAEgCSAYVK18fCIQfCIJfCIIIA5UrSAJIBBUrXwhECAEQQhrIgRBeEcNAAsgEEIAUiAIQprN/8ujvcSAGlZyDQMgCEKazf/Lo73EgBpRBEAgDULX2a6a5PbpjcsAVg0EIA1C19mumuT26Y3LAFENA0Kazf/Lo73EgBohCAsgDSEJDAYLQQAhBAsgACAEOgABQQEMBwsgDEK/pZScz/DSu+QAVg0AQtfZrprk9umNywAhCSAMQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQgMBAsgC0Kk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhDiALQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQgMBQsgCkL//8+K6///1R5WDQBCpOzDtY/UtJjnACERIApC///Piuv//9UeUiAPQqrV/v///7//uX9Ycg0CCyAKQv//z4rr///VHn0iCSAPQqvV/v///7//uX9UrSIOfSEQIAtCpOzDtY/UtJjnAH0iEiAKQv//z4rr///VHlQgCSAOVHKtIgp9IREgDEK/pZScz/DSu+QAfSIJIAtCpOzDtY/UtJjnAFQgCiASVnKtIgp9IQ4gDULX2a6a5PbpjcsAfSILIAxCv6WUnM/w0rvkAFQgCSAKVHKtIgp9IQkgCCANQtfZrprk9umNywBUIAogC1ZyrX1Cms3/y6O9xIAafSEIIA9C1aqBgICAwIDGAHwhDwwEC0Hg1sEAEOgEAAtCms3/y6O9xIAaIQggCiEQDAILIAwhDgsgCyERIAohEAsgACAPNwMwIAAgEDcDKCAAIBE3AyAgACAONwMYIAAgCTcDECAAIAg3AwhBAAs6AAAgA0GQAmokAAvEDAIJfwF+IwBB0ABrIgMkAAJAAkAgAi0ADCIJRQRAIANBOGogAhDYAyADKAI4RQ0BIAMpA0BQIQQLIANBgICAgHg2AjggAyACNgI8AkAgAigCCEUEQCADQQA2AiAgA0KAgICAwAA3AhgMAQsgA0EYaiADQThqQQBBARDsAQsCfyAERQRAIAMoAiAhBCADKAIYIQUgAygCHAwBCyADQUBrIANBIGooAgAiBDYCACADIAMpAhg3AzggBEUEQCADKAI4RQRAIANBOGpByNDCABClAwsgAygCPEEANgIAIANBATYCQEEBIQQLIAMoAjwiBSAFKAIAQQFqIgY2AgACQCAGDQAgBEEBRwRAIARBAnRBBGshBiAFQQRqIQQDQCAEIAQoAgBBAWoiBTYCACAFDQIgBEEEaiEEIAZBBGsiBg0ACwsgAygCQCIGIAMoAjhGBEAgA0E4akHY0MIAEKUDCyADKAI8IAZBAnRqQQE2AgAgAyAGQQFqNgJACyADKAJAIQQgAygCOCEFIAMoAjwLIQZBASEHAkAgCUEBRwRAIAlBASAEGyEHDAELQQAhBCAFQQRJDQAgBiAFQQJ0EN8EQQAhBUEEIQYLIAMgBzoAFCADIAQ2AhAgAyAGNgIMIAMgBTYCCAJAIAEtAAwEQCADQRhqIgQgASADQQhqEJoBIANBOGogBCACEKEBIAMpAkQiDEIgiKchByADKAI8IQYgAygCOCECIAynIQQCQCADLQAkIgFBAUcEQCABQQEgAygCQCIBGyEFDAELIAJBBE8EQCAGIAJBAnQQ3wRBBCEGQQAhAgtBASEFQQAhASAEQQRJDQAgByAEQQJ0EN8EQQAhBEEEIQcLIAAgATYCCCAAIAY2AgQgACACNgIAIAAgBUECIAVrIAkbOgAMIAQEQCAHIARBAnQQ3wQLIAMoAhgiAEUNASADKAIcIABBAnQQ3wQMAQsgASgCCCIGQQJ0IQRBACEFIAZB/////wNLIARB/P///wdLcg0CIAEoAgQhCAJ/IARFBEBBBCEHQQAMAQtB0c7FAC0AABpBBCEFIARBBBDWBCIHRQ0DIAYLIQEgBARAIAcgCCAE/AoAAAsCQAJAAkACQCADLQAUDgIBAAILQQIhBSADQQI6ACQgAyAGNgIgIAMgBzYCHCADIAE2AhgMAgsCQAJAAkACfyADKAIQIgUgBkYEQCAHQQRrIQogAygCDEEEayELA0AgBEUNAyAEIAtqIQggBCAKaiAEQQRrIQQoAgAiBSAIKAIAIghGDQALIAUgCEsgBSAISWsMAQsgBSAGSSAFIAZLawtB/wFxDgIAAgELIANBIGpBqMzCACkCADcDACADQaDMwgApAgA3AxhBASEFIAFFDQMgByABQQJ0EN8EDAMLIAMgBjYCQCADIAc2AjwgAyABNgI4IANBLGogA0EIaiADQThqEJ4BIANBIGogA0E0aigCACIBNgIAIAMgAykCLDcDGCADIAFFIgU6ACQMAgsgAyAGNgJAIAMgBzYCPCADIAE2AjggA0EsaiADQThqIANBCGoQhwIgA0EgaiADQTRqKAIAIgE2AgAgAyADKQIsNwMYIANBAkEBIAEbIgU6ACQMAQsgAyAGNgJAIAMgBzYCPCADIAE2AjggA0EsaiADQThqIANBCGoQygEgAygCNEUEQCADQSBqIANBNGooAgA2AgBBASEFIANBAToAJCADIAMpAiw3AxgMAQsgA0EgaiADQTRqKAIANgIAQQIhBSADQQI6ACQgAyADKQIsNwMYCyADQThqIANBGGogAhChASADKQJEIgxCIIinIQcgAygCPCEGIAMoAjghAiAMpyEEAkAgBUEBRwRAIAVBASADKAJAIgEbIQUMAQsgAkEETwRAIAYgAkECdBDfBEEEIQZBACECC0EBIQVBACEBIARBBEkNACAHIARBAnQQ3wRBACEEQQQhBwsgBARAIAcgBEECdBDfBAsgAygCGCIEBEAgAygCHCAEQQJ0EN8ECyAAIAE2AgggACAGNgIEIAAgAjYCACAAQQIgBWsgBSAJGzoADAsgAygCCCIABEAgAygCDCAAQQJ0EN8ECyADQdAAaiQADwtBtM3CAEEcQbTOwgAQ6AMACyAFIARB+IHAABDIBAAL3QsCDX8BfiMAQaAEayICJABB0c7FAC0AABoCQAJAAkACQEHAAUEIENYEIgMEQCADIAFBwAH8CgAAIAMpAwAhDyACQcABaiIBIANBCGpBuAH8CgAAIANBwAEQ3wQgAkEQaiACQcgBaikDADcDACACQRhqIAJB0AFqKQMANwMAIAJBIGogAkHYAWopAwA3AwAgAkEoaiACQeABaikDADcDACACQTBqIAJB6AFqKQMANwMAIAJBOGogAkHwAWopAwA3AwAgAkHIAGogAkGAAmopAwA3AwAgAkHQAGogAkGIAmopAwA3AwAgAkHYAGogAkGQAmopAwA3AwAgAkHgAGogAkGYAmopAwA3AwAgAkHoAGogAkGgAmopAwA3AwAgAkHwAGogAkGoAmopAwA3AwAgAkH4AGogAkGwAmopAwA3AwAgAiAPNwMAIAIgAikDwAE3AwggAiACKQP4ATcDQCACQbgBaiACQfACaikDADcDACACQbABaiACQegCaikDADcDACACQagBaiACQeACaikDADcDACACQaABaiACQdgCaikDADcDACACQZgBaiACQdACaikDADcDACACQZABaiACQcgCaikDADcDACACQYgBaiACQcACaikDADcDACACIAIpA7gCNwOAASABIAIQrwMgAigCxAEhASACKALAASEDIAIoAsgBIgRBAkcNASACQYADaiABQRBqKQMANwMAIAJBiANqIAFBGGopAwA3AwAgAkGQA2ogAUEgaikDADcDACACQZgDaiABQShqKQMANwMAIAJBoANqIAFBMGopAwA3AwAgAkGoA2ogAUE4aikDADcDACACIAEpAwg3A/gCIAEoAgQhBCABKAIAIQcgAwRAIAEgA0EFdBDfBAsgAkHAAWogAkFAaxCvAyACKALEASEBIAIoAsABIQMgAigCyAEiBUECRw0CIAJBuANqIAFBEGopAwA3AwAgAkHAA2ogAUEYaikDADcDACACQcgDaiABQSBqKQMANwMAIAJB0ANqIAFBKGopAwA3AwAgAkHYA2ogAUEwaikDADcDACACQeADaiABQThqKQMANwMAIAIgASkDCDcDsAMgASgCBCEFIAEoAgAhCCADBEAgASADQQV0EN8ECyACQcABaiACQYABahCvAyACKALEASEBIAIoAsABIQMgAigCyAEiBkECRw0DIAJB8ANqIgYgAUEQaikDADcDACACQfgDaiIJIAFBGGopAwA3AwAgAkGABGogAUEgaikDADcDACACQYgEaiIKIAFBKGopAwA3AwAgAkGQBGoiCyABQTBqKQMANwMAIAJBmARqIgwgAUE4aikDADcDACACIAEpAwg3A+gDIAEoAgQhDSABKAIAIQ4gAwRAIAEgA0EFdBDfBAsgACACKQPoAzcDiAEgACACKQOABDcDoAEgACANNgKEASAAIA42AoABIAAgBDYCBCAAIAc2AgAgAEGYAWogCSkDADcDACAAQZABaiAGKQMANwMAIABBqAFqIAopAwA3AwAgAEGwAWogCykDADcDACAAQbgBaiAMKQMANwMAIAAgBTYCRCAAIAg2AkAgAEEYaiACQYgDaikDADcDACAAQRBqIAJBgANqKQMANwMAIAAgAikD+AI3AwggAEE4aiACQagDaikDADcDACAAQTBqIAJBoANqKQMANwMAIABBKGogAkGYA2opAwA3AwAgACACKQOQAzcDICAAIAIpA7ADNwNIIABB0ABqIAJBuANqKQMANwMAIABB2ABqIAJBwANqKQMANwMAIABB+ABqIAJB4ANqKQMANwMAIABB8ABqIAJB2ANqKQMANwMAIABB6ABqIAJB0ANqKQMANwMAIAAgAikDyAM3A2AgAkGgBGokAA8LQQhBwAFB8LXCABDIBAALIAIgBDYCyAEMAgsgAiAFNgLIAQwBCyACIAY2AsgBCyACIAE2AsQBIAIgAzYCwAFBgIvAAEErIAJBwAFqQfCKwABBpI3AABDKAwALhB4CCH8PfiMAQbABayIDJAAgA0HgAGpCADcDACADQdgAakIANwMAIANCADcDUCADQgE3A2ggA0E4akIANwMAIANBQGtCADcDACADQgA3AzAgA0KRgICAgICAgAg3AyggA0GQAWogA0EoakH/ARCyAiADQfgAaiIHQgA3AwAgA0GAAWoiBkIANwMAIANCADcDcCADIAMpA6gBQgGDNwOIAQJAIANB8ABqIANB0ABqQSAQ8QNFBEBBgAIhBAwBCyADQTBqIQVBgAIhBANAIAVCADcDACAFQQhqQgA3AwAgBUEQakIANwMAIANCkYCAgICAgIAINwMoIANBkAFqIANBKGogBEECaxCyAiAHQgA3AwAgBkIANwMAIANCADcDcCADIAMpA6gBQgGDNwOIASAEQQFrIQQgA0HwAGogA0HQAGpBIBDxAw0ACwtBACEFAkACQAJAAkACQAJAIAIgBEEDdiAEQQdxQQBHaiIETQRAAkAgBCACayIERQRAQQEhBQwBC0HRzsUALQAAGiAEQQEQ1wQiBUUNBAsgAyAENgKYASADIAU2ApQBIAMgBDYCkAEgAgRAIANBkAFqIAQgAkEBQQEQiAMgAygCmAEhBCADKAKUASEFCyACBEAgBCAFaiABIAL8CgAACyMAQcACayIBJAAgA0EoaiIHAn8gAiAEakEfTQRAIAdBADoAAUEBDAELIAFB8AFqIAUpABgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCINQgBCgYiA8Leuf0IAEMkDIAFBsAJqIAUpABAiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIOQgBCgYiA8Leuf0IAEMkDIAFBkAFqIAUpAAgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIQQgBCgYiA8Leuf0IAEMkDIAFBQGsgBSkAACILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEIgtCAEKBiIDwt65/QgAQyQMgAUHgAWpCACABKQPwASIMfUIAQpGAgICAgICACEIAEMkDIAFB0AFqIA1CAEL//7+YE0IAEMkDIAFBoAJqIA5CAEL//7+YE0IAEMkDIAFB8ABqIBBCAEL//7+YE0IAEMkDIAFBIGogC0IAQv//v5gTQgAQyQMgAUHAAWpCACAMQgBSrSIRIAEpA/gBIhMgASkDsAJ8IhJ8IgwgASkD0AF8Ig99QgBCkYCAgICAgIAIQgAQyQMgAUGwAWogDUIAQoCAvntCABDJAyABQZACaiAOQgBCgIC+e0IAEMkDIAFB4ABqIBBCAEKAgL57QgAQyQMgAUEQaiALQgBCgIC+e0IAEMkDIAFBgAFqQgAgD0IAUq0iFCAMIBFUrSIXIAEpA7gCIBIgE1StfCISIAEpA5ABfCIVfCIRIAEpA6ACfCITIAEpA9gBIAwgD1atfHwiGHwiDCABKQOwAXwiD31CAEKRgICAgICAgAhCABDJAyABQaABaiANQgBCkJCC8LWV9f8HQgAQyQMgAUGAAmogDkIAQpCQgvC1lfX/B0IAEMkDIAFB0ABqIBBCAEKQkILwtZX1/wdCABDJAyABIAtCAEKQkILwtZX1/wdCABDJAyABQTBqQgAgASkDuAEgDCAPVq18IhYgASkDkAJ8IgsgASkDmAEgEiAVVq18IhUgASkDQHwiDSABKQPgAXwiDiARIBdUrXwiECABKQNwfCISIBMgGFatIAEpA6gCIBEgE1atfHx8IhEgDCAUVK18IhR8IgwgD0IAUq18Ig8gASkDoAF8IhN9QgBCkYCAgICAgIAIQgAQyQMCQAJAIAEpAwggASkDiAEgCyAMVq0gASkDmAIgCyAWVK18fCIXIAEpA2B8IgsgESAUVq0iGCABKQPAAXwiFCAOIBBWrSABKQPoASANIA5WrXx8IhYgASkDSCANIBVUrXx8Ig0gASkDIHwiDiARIBJUrSABKQN4IBAgElatfHx8IhF8IhJ8IhAgDCAPVq18IhUgEFStIhkgASkDgAF8IgwgGVStfCAMIAwgASkDECANIBZUrYQiFiAOIBFWrSABKQMoIA0gDlatfHx8Ig0gEiAUVK0gASkDyAEgFCAYVK18fHwiDiALIBBWrSABKQNoIAsgF1StfHx8Igt8IhFWrXwiEiALIA5UrSANIA5WrSABKQMYIA0gFlStfHx8fCILIAEpAwB8Ig0gC1StfCANIAEpA1ggASkDiAIgASkDqAEgDyATVq18IhAgASkDgAJ8Ig4gEFStfCAOIA4gFXwiEFatfCIMIAEpA1B8Ig4gDFStfCAOIA4gEXwiDFatfHwiDiANVK18IAsgElStfCABKQM4IAwgECATQgBSrXwiCyAQVK18Ig0gDFStIgwgASkDMHwiECAMVK18IBAgDiAQfCIOVq18fCIRQpGAgICAgICACFYNACARQpGAgICAgICACFIEQCAOIRAgDSEMIAshDwwCCyALIA2EIA6EUEUNAEIAIRBCkYCAgICAgIAIIRFCACEMQgAhDwwBCyALQgF9IQ8gDSALUK0iC30hDCAOIAsgDVatIgt9IRAgESALIA5WrX1CkYCAgICAgIAIfSERCyAHIA83AyAgByAMNwMYIAcgEDcDECAHIBE3AwhBAAs6AAAgAUHAAmokACADLQAoRQ0BIAMgAy0AKToAcEHk2MIAQSsgA0HwAGpBpNrCAEG02sIAEMoDAAsgAkEASA0DQdHOxQAtAAAaQQEhBSACQQEQ1gQiB0UNAyACBEAgByABIAL8CgAACyADQQxqIAcCf0EBIAJBAUYNABogAiAHaiEBQQAhBCACQQF2IgZBAUcEQCACQQFrIQUgBkH+////A3EhCQNAIAUgB2oiBi0AACEIIAYgBCAHaiIGLQAAOgAAIAYgCDoAACABIARBfnNqIggtAAAhCiAIIAZBAWoiBi0AADoAACAGIAo6AAAgBUECayEFIAkgBEECaiIERw0ACwsgAiACQQJxRQ0AGiAEIAdqIgUtAAAhBiAFIAEgBEF/c2oiAS0AADoAACABIAY6AAAgAgtBCBDPAiAHIAIQ3wQjAEEwayIBJABCkYCAgICAgIAIIRAgAUEgakIAQn9B+NLBAEHo0cEAQSAQ8QMiBRsiC0J/hSIMQgBCkYCAgICAgIAIQgAQyQMgAUEQakIAIAwgC0IBfCINfCANVK0iDCANUK0iDyALfCIRfCINfUIAQpGAgICAgICACEIAEMkDIAFCACANQgBSrSITIAwgDVatIgwgDyARVq0iDSALfCIPfCIRfCILfUIAQpGAgICAgICACEIAEMkDIANBKGoiAgJ+IAEpAwggASkDGCABKQMoIA0gD1atQpCAgICAgICACEIAIAUbhCIPIAEpAyB8Ig0gD1StfCANIAwgEVatfCIMIA1UrXwiDyABKQMQfCINIA9UrXwgDSAMIAsgE1StIgx8Ig8gDFStfCIMIA1UrXwiESABKQMAfCINIBFUrXwgDSANIAwgC0IAUq0iCyAPfCIPIAtUrSIMfCILIAxUrXwiDVatfCIMQpGAgICAgICACFIEQCAMIRAgDSEOIAshDCAPDAELQgAhDEIAIAsgD4QgDYRQDQAaQn9CACANIAsgD1CtIg5UrSIRVBshECALIA59IQwgDSARfSEOIA9CAX0LNwMYIAIgDDcDECACIA43AwggAiAQNwMAIAFBMGokACADQQA2AnggA0KAgICAEDcCcCADQdzTwgA2ApQBIANCoICAgA43ApgBIAMgA0HwAGo2ApABIAIgA0GQAWoiARDTAg0EIAMoAnAhAiABIAMoAnQiByADKAJ4EJUDIAMoApgBIgVFBEAgAygCkAFFBEAgAUHI0MIAEKUDCyADKAKUAUEANgIAIANBATYCmAFBASEFCyADKAKUASIBIAEoAgBBAWoiBDYCAAJAIAQNACAFQQFHBEAgBUECdEEEayEFIAFBBGohBANAIAQgBCgCAEEBaiIBNgIAIAENAiAEQQRqIQQgBUEEayIFDQALCyADKAKYASIBIAMoApABRgRAIANBkAFqQdjQwgAQpQMLIAMoApQBIAFBAnRqQQE2AgAgAyABQQFqNgKYAQsgA0EgaiADQZgBaigCADYCACADIAMpApABNwMYIAIEQCAHIAIQ3wQLIANBKGogA0EMaiADQRhqEO8BAkACQCADKAIwRQRAQdHOxQAtAAAaQQEhBEEBQQEQ1gQiAUUNCCABQQA6AAAgACABQQEQhgEMAQsgA0GQAWogA0EoakEIELACIAMoApQBIQECQCADKAKYASICQQJJDQAgASACaiEHQQAhBCACQQF2IgZBAUcEQCACQQFrIQUgBkH+////B3EhCQNAIAEgBWoiBi0AACEIIAYgASAEaiIGLQAAOgAAIAYgCDoAACAHIARBfnNqIggtAAAhCiAIIAZBAWoiBi0AADoAACAGIAo6AAAgBUECayEFIAkgBEECaiIERw0ACwsgAkECcUUNACABIARqIgUtAAAhBiAFIAcgBEF/c2oiBS0AADoAACAFIAY6AAALIAMoApABIQQgACABIAIQhgEgBEUNAQsgASAEEN8ECyADKAIoIgBFDQEgAygCLCAAQQJ0EN8EDAELIAAgAykDMDcDACAAQRhqIANByABqKQMANwMAIABBEGogA0FAaykDADcDACAAQQhqIANBOGopAwA3AwAgAygCkAEiAEUNACAFIAAQ3wQLIANBsAFqJAAPC0EBIARBlNrCABDIBAALIAUgAkHU2MIAEMgEAAtBhNTCAEE3IANB0ABqQfTTwgBBiNXCABDKAwALQQFBARD/BAAL0BgCCH8MfiMAQbABayIDJAAgA0HgAGpCADcDACADQdgAakIANwMAIANCADcDUCADQgE3A2ggA0EwaiEHQYACIQUDQCAHQn83AwAgB0EIakJ/NwMAIANC////////////ADcDKCADQmw3A0AgA0GQAWogA0EoaiAFQQFrIgYQsgIgA0H4AGpCADcDACADQYABakIANwMAIANCADcDcCADIAMpA6gBQgGDNwOIASADQfAAaiADQdAAakEgEPEDBEAgBiEFDAELC0EAIQYCQAJAAkACQAJAAkAgAiAFQQN2IAVBB3FBAEdqIgVNBEACQCAFIAJrIgVFBEBBASEGDAELQdHOxQAtAAAaIAVBARDXBCIGRQ0ECyADIAU2ApgBIAMgBjYClAEgAyAFNgKQASACBEAgA0GQAWogBSACQQFBARCIAyADKAKYASEFIAMoApQBIQYLIAIEQCAFIAZqIAEgAvwKAAALIAYhASMAQYACayIEJAAgA0EoaiIHAn8gAiAFakEfTQRAIAdBADoAAUEBDAELIARB4AFqIAEpABgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhEIAQqQLQgAQyQMgBEHwAWogASkAECILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEQgBCpAtCABDJAyAEQfAAaiABKQAIIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIRCAEKkC0IAEMkDIARBMGogASkAACILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEQgBCpAtCABDJAyAEQdABaiAEKQPgASINQpuUr8Pytajehn9+IgtCAEJtQgAQyQMgBEHAAWogC0IAQn9CABDJAyAEQYABaiALQgBC////////////AEIAEMkDIARBsAFqIAQpA8ABIhMgBCkD6AEiDiAEKQPwAXwiDHwiECAEKQPYASAEKQPQASILIA1CfIN8IAtUrXx8Ig9Cm5Svw/K1qN6Gf34iC0IAQm1CABDJAyAEQaABaiALQgBCf0IAEMkDIARBkAFqIAtCAEL///////////8AQgAQyQMgBEHgAGogBCkDoAEiFCATIAQpA/gBIAwgDlStfCINIAQpA3B8IhF8IhIgDyAQVK0gBCkDyAEiDiAQIBNUrXx8fCIMfCIQIAQpA7gBIAQpA7ABIgsgD3wgC1StfHwiD0KblK/D8rWo3oZ/fiILQgBCbUIAEMkDIARB0ABqIAtCAEJ/QgAQyQMgBEFAayALQgBC////////////AEIAEMkDIARBIGogBCkDUCIVIBQgBCkDeCANIBFWrXwiDSAEKQMwfCIWIAQpA4ABfCITIAwgElStIA4gESASVq18fHwiEXwiEiAPIBBUrSAEKQOoASIOIBAgFFStfHx8Igx8IhAgBCkDaCAPIAQpA2AiC3wgC1StfHwiD0KblK/D8rWo3oZ/fiILQgBCbUIAEMkDIARBEGogC0IAQn9CABDJAyAEIAtCAEL///////////8AQgAQyQMCQAJAIAQpAwggBCkDSCAEKQOYASAEKQOQASILIAQpAzggDSAWVq18fCINIAtUrXwgDSANIBEgE1StIAQpA4gBIBMgFlStfHx8IgtWrXwgCyALIAwgElStIA4gESASVq18fHwiDVatfCILIAQpA0B8Ig4gC1StfCAOIAQpA1giCyANIA0gFXwiDFatfCAMIAwgDyAQVK0gCyAQIBVUrXx8fCIMVq18fCISIA5UrXwiCyAEKQMAfCIQIAtUrXwgECAQIAQpAxgiCyASIBIgBCkDECINfCIOVq18IA4gDiALIA0gDCANfCIMVq18IAwgBCkDKCAPIAQpAyAiC3wgC1StfHwiDyAMVK18fCIMVq18fCINVq18IhFCAFMNAAJAAkAgEUL///////////8AVA0AQn8hDiANQn9SBEBC////////////ACERDAELIAxCf1ENAUL///////////8AIREgDCELDAMLIA0hDiAMIQsMAgsgD0JtWg0AQv///////////wAhEUJ/IQsMAQsgDEIBfCISIA9CbVStIg59IQsgDUIBfCIQIAxCf1IgDiASVnKtIgx9IQ4gESANQn9SIAwgEFZyrX1C////////////AH0hESAPQhN8IQ8LIAcgDzcDICAHIAs3AxggByAONwMQIAcgETcDCEEACzoAACAEQYACaiQAIAMtAChFDQEgAyADLQApOgBwQeTYwgBBKyADQfAAakGk2sIAQbTawgAQygMACyACQQBIDQNB0c7FAC0AABpBASEGIAJBARDWBCIIRQ0DIAIEQCAIIAEgAvwKAAALIANBDGogCAJ/QQEgAkEBRg0AGiACIAhqIQlBACEFIAJBAXYiAUEBRwRAIAJBAWshBiABQf7///8DcSEEA0AgBiAIaiIHLQAAIQEgByAFIAhqIgotAAA6AAAgCiABOgAAIAkgBUF+c2oiAS0AACEHIAEgCkEBaiIBLQAAOgAAIAEgBzoAACAGQQJrIQYgBCAFQQJqIgVHDQALCyACIAJBAnFFDQAaIAUgCGoiAS0AACEGIAEgCSAFQX9zaiIBLQAAOgAAIAEgBjoAACACC0EIEM8CIAggAhDfBAJAQZjTwQBB6NHBAEEgEPEDBEAgA0E4akJ/NwMAIANCfzcDMCADQv///////////wA3AyggA0JHNwNADAELIANBQGtBsNPBACkDADcDACADQThqQajTwQApAwA3AwAgA0EwakGg08EAKQMANwMAIANBmNPBACkDADcDKAsgA0GQAWoiASADQShqIgUQ2AEgA0EANgJ4IANCgICAgBA3AnAgA0Hc08IANgIsIANCoICAgA43AjAgAyADQfAAajYCKCABIAUQ0wINBCADKAJwIQcgBSADKAJ0IgIgAygCeBCVAyADKAIwIgZFBEAgAygCKEUEQCAFQcjQwgAQpQMLIAMoAixBADYCACADQQE2AjBBASEGCyADKAIsIgUgBSgCAEEBaiIBNgIAAkAgAQ0AIAZBAUcEQCAGQQJ0QQRrIQYgBUEEaiEFA0AgBSAFKAIAQQFqIgE2AgAgAQ0CIAVBBGohBSAGQQRrIgYNAAsLIAMoAjAiASADKAIoRgRAIANBKGpB2NDCABClAwsgAygCLCABQQJ0akEBNgIAIAMgAUEBajYCMAsgA0EgaiADQTBqKAIANgIAIAMgAykCKDcDGCAHBEAgAiAHEN8ECyADQShqIANBDGogA0EYahDvAQJAAkAgAygCMEUEQEHRzsUALQAAGkEBIQVBAUEBENYEIgFFDQggAUEAOgAAIAAgAUEBEIcBDAELIANBkAFqIANBKGpBCBCwAiADKAKUASEBAkAgAygCmAEiCEECSQ0AIAEgCGohCUEAIQUgCEEBdiICQQFHBEAgCEEBayEGIAJB/v///wdxIQQDQCABIAZqIgctAAAhAiAHIAEgBWoiCi0AADoAACAKIAI6AAAgCSAFQX5zaiICLQAAIQcgAiAKQQFqIgItAAA6AAAgAiAHOgAAIAZBAmshBiAEIAVBAmoiBUcNAAsLIAhBAnFFDQAgASAFaiICLQAAIQYgAiAJIAVBf3NqIgItAAA6AAAgAiAGOgAACyADKAKQASEFIAAgASAIEIcBIAVFDQELIAEgBRDfBAsgAygCKCIARQ0BIAMoAiwgAEECdBDfBAwBCyAAIAMpAzA3AwAgAEEYaiADQcgAaikDADcDACAAQRBqIANBQGspAwA3AwAgAEEIaiADQThqKQMANwMAIAMoApABIgBFDQAgBiAAEN8ECyADQbABaiQADwtBASAFQZTawgAQyAQACyAGIAJB1NjCABDIBAALQYTUwgBBNyADQdAAakH008IAQYjVwgAQygMAC0EBQQEQ/wQAC4oNAgl/AX4jAEGABmsiAiQAIAJBQGsiA0EAQcgB/AsAIAJBkAJqQQBBiQH8CwAgAkEYNgKIAiADIAEoAgQgASgCCBD7ASACQaADaiADQeAC/AoAACACLQD4BSIDIAJB8ARqaiEBQYgBIANrIgMEQCABQQAgA/wLAAsgAkEAOgD4BSABQQE6AAAgAkGoA2oiASABKQMAIAIpA/gEhTcDACACQbADaiIDIAMpAwAgAikDgAWFNwMAIAJBuANqIgcgBykDACACKQOIBYU3AwAgAiACLQD3BUGAAXI6APcFIAIgAikDoAMgAikD8ASFNwOgAyACIAIpA8ADIAIpA5AFhTcDwAMgAiACKQPIAyACKQOYBYU3A8gDIAIgAikD0AMgAikDoAWFNwPQAyACIAIpA9gDIAIpA6gFhTcD2AMgAiACKQPgAyACKQOwBYU3A+ADIAIgAikD6AMgAikDuAWFNwPoAyACIAIpA/ADIAIpA8AFhTcD8AMgAiACKQP4AyACKQPIBYU3A/gDIAIgAikDgAQgAikD0AWFNwOABCACIAIpA4gEIAIpA9gFhTcDiAQgAiACKQOQBCACKQPgBYU3A5AEIAIgAikDmAQgAikD6AWFNwOYBCACIAIpA6AEIAIpA/AFhTcDoAQgAkGgA2oiCCACKALoBBCCBSACQSBqIgQgBykDADcDACACQRhqIgUgAykDADcDACACQRBqIgYgASkDADcDACACIAIpA6ADNwMIQdHOxQAtAAAaAkACQEEgQQEQ1gQiAQRAIAFBGGoiAyAEKQMANwAAIAEgAikDCCILNwAAIAFBEGoiByAFKQMANwAAIAFBCGoiBSAGKQMANwAAIAEgAUEfaiIGLQAAOgAAIAYgCzwAACABLQABIQYgASABQR5qIgQtAAA6AAEgBCAGOgAAIAFBHWoiBi0AACEEIAYgAS0AAjoAACABIAQ6AAIgAUEcaiIGLQAAIQQgBiABLQADOgAAIAEgBDoAAyABQRtqIgYtAAAhBCAGIAEtAAQ6AAAgASAEOgAEIAFBGmoiBi0AACEEIAYgAS0ABToAACABIAQ6AAUgAUEZaiIGLQAAIQQgBiABLQAGOgAAIAEgBDoABiADLQAAIQYgAyABLQAHOgAAIAEgBjoAByABQRdqIgMtAAAhBiADIAUtAAA6AAAgBSAGOgAAIAFBFmoiAy0AACEFIAMgAS0ACToAACABIAU6AAkgAUEVaiIDLQAAIQUgAyABLQAKOgAAIAEgBToACiABQRRqIgMtAAAhBSADIAEtAAs6AAAgASAFOgALIAFBE2oiAy0AACEFIAMgAS0ADDoAACABIAU6AAwgAUESaiIDLQAAIQUgAyABLQANOgAAIAEgBToADSABQRFqIgMtAAAhBSADIAEtAA46AAAgASAFOgAOIActAAAhAyAHIAEtAA86AAAgASADOgAPIAJBKGoiAyABQSBBCBDPAiABQSAQ3wQgCEHEm8IAQcAAEJICIAIoAqADDQIgCCACKAKkAyACKAKoA0EQEPEBIAIoAqADIgFBgICAgHhGDQIgAiACKQKkAzcCOCACIAE2AjQgAkFAayADIAJBNGoQ7gECQAJAIAIoAkhFBEBB0c7FAC0AABpBASEBQQFBARDWBCIDRQ0EIANBADoAACACQQE2AqgDIAIgAzYCpAMgAkEBNgKgAwwBCyACQaADaiACQUBrQQgQsAIgAigCqAMiAUECSQ0AIAIoAqQDIgcgAWohBkEAIQMgAUEBdiIEQQFHBEAgAUEBayEFIARB/v///wdxIQkDQCAFIAdqIgQtAAAhCCAEIAMgB2oiBC0AADoAACAEIAg6AAAgBiADQX5zaiIILQAAIQogCCAEQQFqIgQtAAA6AAAgBCAKOgAAIAVBAmshBSAJIANBAmoiA0cNAAsLIAFBAnEEQCADIAdqIgctAAAhBSAHIAYgA0F/c2oiAy0AADoAACADIAU6AAALIAFBH0sNAQsDQCACKAKgAyABRgRAIAJBoANqQdCewgAQtgMLIAIoAqQDIQMgAQRAIANBAWogAyAB/AoAAAsgA0EAOgAAIAIgAUEBaiIDNgKoAyABQR9JIAMhAQ0ACwsgACACKQKgAzcCACAAQQhqIAJBqANqKAIANgIAIAIoAkAiAARAIAIoAkQgAEECdBDfBAsgAkGABmokAA8LQQFBIEGkm8IAEMgEAAtBAUEBEP8EAAtBwJ7CABDoBAALqRoCCH8RfiMAQbABayIDJAAgA0HgAGpCADcDACADQdgAakIANwMAIANCADcDUCADQgE3A2hBgAIhBQNAIANCfjcDQCADQv////8PNwM4IANCADcDMCADQoGAgIBwNwMoIANBkAFqIANBKGogBUEBayIGELICIANB+ABqQgA3AwAgA0GAAWpCADcDACADQgA3A3AgAyADKQOoAUIBgzcDiAEgA0HwAGogA0HQAGpBIBDxAwRAIAYhBQwBCwtBACEGAkACQAJAAkACQAJAIAIgBUEDdiAFQQdxQQBHaiIFTQRAAkAgBSACayIFRQRAQQEhBgwBC0HRzsUALQAAGiAFQQEQ1wQiBkUNBAsgAyAFNgKYASADIAY2ApQBIAMgBTYCkAEgAgRAIANBkAFqIAUgAkEBQQEQiAMgAygCmAEhBSADKAKUASEGCyACBEAgBSAGaiABIAL8CgAACyAGIQEjAEHAAmsiBCQAIANBKGoiBwJ/IAIgBWpBH00EQCAHQQA6AAFBAQwBCyAEQfABaiABKQAYIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIQiFEIAQgNCABDJAyAEQbACaiABKQAQIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIQiFUIAQgNCABDJAyAEQZABaiABKQAIIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIQiFkIAQgNCABDJAyAEQUBrIAEpAAAiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIXQgBCA0IAEMkDIARB4AFqIAQpA/ABIg1CAEKBgICAcEIAEMkDIARB0AFqIBRCAEL/////v39CABDJAyAEQaACaiAVQgBC/////79/QgAQyQMgBEHwAGogFkIAQv////+/f0IAEMkDIARBIGogF0IAQv////+/f0IAEMkDIARBwAFqIA1CIIYiESAEKQP4ASIPIAQpA7ACfCIOfCIQIAQpA9ABfCIMQgBCgYCAgHBCABDJAyAEQbABaiAUQgBCfkIAEMkDIARBkAJqIBVCAEJ+QgAQyQMgBEHgAGogFkIAQn5CABDJAyAEQRBqIBdCAEJ+QgAQyQMgBEGAAWogDEIghiILIBAgEVStIA1CIIh8Ig0gBCkDuAIgDiAPVK18IhEgBCkDkAF8Ig98IhggBCkDoAJ8IhMgBCkD2AEgDCAQVK18fCIOfCISIAQpA7ABfCIZQgBCgYCAgHBCABDJAyAEQaABaiAUQgBC/f///88AQgAQyQMgBEGAAmogFUIAQv3////PAEIAEMkDIARB0ABqIBZCAEL9////zwBCABDJAyAEIBdCAEL9////zwBCABDJAyAEQTBqIBlCIIYiECALIBJWrSAMQiCIfCILIAQpA5gBIA8gEVStfCIPIAQpA0B8IhsgBCkD4AF8IgwgDSAYVq18IhQgBCkDcHwiFSAOIBNUrSAEKQOoAiATIBhUrXx8fCIOfCIWIAQpA5ACfCIXIAQpA7gBIBIgGVatfHwiDXwiGCAEKQOgAXwiGkIAQoGAgIBwQgAQyQMCQAJAIAQpAwggBCkDGCAEKQPIASALIBZWrSILIAQpA8ABfCITIAtUrXwgEyAEKQNIIA8gG1atfCIRIAQpAyB8IhIgDCAUVq0gBCkD6AEgDCAbVK18fHwiDCAOIBVUrSAEKQN4IBQgFVatfHx8Igt8Ig8gE1StfCIOIAsgDFStIAwgElStIAQpAyggESASVq18fHx8IhIgBCkDEHwiDCASVK18IAwgBCkDaCANIBdUrSAEKQOYAiAWIBdWrXx8IgsgBCkDYHwiESALVK18IBEgDyARfCILVq18fCIPIAxUrXwiESAOIBJWrXwiEyAEKQOIASALIBAgGFatIBlCIIh8fCIOIAtUrSILIAQpA4ABfCINIAtUrXwgDSAPfCIPIA1UrXx8IhIgBCkDAHwiDCASVK18IAwgDCAEKQNYIAQpA4gCIAQpA6gBIBggGlatfCILIAQpA4ACfCINIAtUrXwgDSAOfCIOIA1UrXwiCyAEKQNQfCIQIAtUrXwgECAPIBB8Ig1WrXx8Ig9WrXwiCyARIBNWrSASIBNUrXx8IhAgC1StIBAgECAEKQM4IA0gGkIghiILIA58IgwgC1StIBpCIIh8fCIOIA1UrSILIAQpAzB8Ig0gC1StfCANIA0gD3wiEVatfHwiEFatfEIAUiAQQoGAgIBwVnINAAJAIBBCgYCAgHBRBEAgDkL/////D1YNAkIAIQ8gEUIAUg0CQv////8PIQsgDkL/////D1oNAUKBgICAcCEQIA4hCwwDCyARIQ8gDiELDAILIAxCf1ENAEKBgICAcCEQDAELIA5C/////w99Ig0gDEJ/Uq0iD30hCyARIA5C/////w9UIA0gD1RyrSIOfSEPIBAgDiARVq19Qv////8PfCEQIAxCAXwhDAsgByAMNwMgIAcgCzcDGCAHIA83AxAgByAQNwMIQQALOgAAIARBwAJqJAAgAy0AKEUNASADIAMtACk6AHBB5NjCAEErIANB8ABqQaTawgBBtNrCABDKAwALIAJBAEgNA0HRzsUALQAAGkEBIQYgAkEBENYEIghFDQMgAgRAIAggASAC/AoAAAsgA0EMaiAIAn9BASACQQFGDQAaIAIgCGohCUEAIQUgAkEBdiIBQQFHBEAgAkEBayEGIAFB/v///wNxIQQDQCAGIAhqIgctAAAhASAHIAUgCGoiCi0AADoAACAKIAE6AAAgCSAFQX5zaiIBLQAAIQcgASAKQQFqIgEtAAA6AAAgASAHOgAAIAZBAmshBiAEIAVBAmoiBUcNAAsLIAIgAkECcUUNABogBSAIaiIBLQAAIQYgASAJIAVBf3NqIgEtAAA6AAAgASAGOgAAIAILQQgQzwIgCCACEN8EAkBBuNLBAEHo0cEAQSAQ8QMEQCADQn43A0AgA0L/////HzcDOCADQgA3AzAgA0KCgICAYDcDKAwBCyADQUBrQdDSwQApAwA3AwAgA0E4akHI0sEAKQMANwMAIANBMGpBwNLBACkDADcDACADQbjSwQApAwA3AygLIANBkAFqIgEgA0EoaiICEKMCIANBADYCeCADQoCAgIAQNwJwIANB3NPCADYCLCADQqCAgIAONwIwIAMgA0HwAGo2AiggASACENMCDQQgAygCcCEEIAIgAygCdCIHIAMoAngQlQMgAygCMCIGRQRAIAMoAihFBEAgAkHI0MIAEKUDCyADKAIsQQA2AgAgA0EBNgIwQQEhBgsgAygCLCICIAIoAgBBAWoiATYCAAJAIAENACAGQQFHBEAgBkECdEEEayEBIAJBBGohBQNAIAUgBSgCAEEBaiICNgIAIAINAiAFQQRqIQUgAUEEayIBDQALCyADKAIwIgEgAygCKEYEQCADQShqQdjQwgAQpQMLIAMoAiwgAUECdGpBATYCACADIAFBAWo2AjALIANBIGogA0EwaigCADYCACADIAMpAig3AxggBARAIAcgBBDfBAsgA0EoaiADQQxqIANBGGoQ7wECQAJAIAMoAjBFBEBB0c7FAC0AABpBASEFQQFBARDWBCIBRQ0IIAFBADoAACAAIAFBARCJAQwBCyADQZABaiADQShqQQgQsAIgAygClAEhAQJAIAMoApgBIghBAkkNACABIAhqIQlBACEFIAhBAXYiAkEBRwRAIAhBAWshBiACQf7///8HcSEEA0AgASAGaiIHLQAAIQIgByABIAVqIgotAAA6AAAgCiACOgAAIAkgBUF+c2oiAi0AACEHIAIgCkEBaiICLQAAOgAAIAIgBzoAACAGQQJrIQYgBCAFQQJqIgVHDQALCyAIQQJxRQ0AIAEgBWoiAi0AACEGIAIgCSAFQX9zaiICLQAAOgAAIAIgBjoAAAsgAygCkAEhBSAAIAEgCBCJASAFRQ0BCyABIAUQ3wQLIAMoAigiAEUNASADKAIsIABBAnQQ3wQMAQsgACADKQMwNwMAIABBGGogA0HIAGopAwA3AwAgAEEQaiADQUBrKQMANwMAIABBCGogA0E4aikDADcDACADKAKQASIARQ0AIAYgABDfBAsgA0GwAWokAA8LQQEgBUGU2sIAEMgEAAsgBiACQdTYwgAQyAQAC0GE1MIAQTcgA0HQAGpB9NPCAEGI1cIAEMoDAAtBAUEBEP8EAAuFIQIIfxB+IwBBsAFrIgQkACAEQeAAakIANwMAIARB2ABqQgA3AwAgBEIANwNQIARCATcDaEGAAiEFA0AgBELG+vPD7YKjkDw3A0AgBEKNlcfDltLawJd/NwM4IARC3bCFjOi2kai4fzcDMCAEQqnAxomuzpOyMDcDKCAEQZABaiAEQShqIAVBAWsiBhCyAiAEQfgAakIANwMAIARBgAFqQgA3AwAgBEIANwNwIAQgBCkDqAFCAYM3A4gBIARB8ABqIARB0ABqQSAQ8QMEQCAGIQUMAQsLQQAhBgJAAkACQAJAAkACQCACIAVBA3YgBUEHcUEAR2oiBU0EQAJAIAUgAmsiBUUEQEEBIQYMAQtB0c7FAC0AABogBUEBENcEIgZFDQQLIAQgBTYCmAEgBCAGNgKUASAEIAU2ApABIAIEQCAEQZABaiAFIAJBAUEBEIgDIAQoApgBIQUgBCgClAEhBgsgAgRAIAUgBmogASAC/AoAAAsgBiEBIwBBgARrIgMkACAEQShqIgcCfyACIAVqQR9NBEAgB0EAOgABQQEMAQsgA0GwA2ogASkAGCILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEIhRCAEKJ9auctYu/lnNCABDJAyADQfADaiABKQAQIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIQiFUIAQon1q5y1i7+Wc0IAEMkDIANB8AFqIAEpAAgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIWQgBCifWrnLWLv5ZzQgAQyQMgA0HwAGogASkAACILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEIhdCAEKJ9auctYu/lnNCABDJAyADQaADaiADKQOwAyIPQonHmaSu8IHph39+IgtCAELH+vPD7YKjkDxCABDJAyADQZADaiALQgBCjZXHw5bS2sCXf0IAEMkDIANBgANqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0HwAmogC0IAQqnAxomuzpOyMEIAEMkDIANB4AJqIBRCAEL7g5SinaLG87V/QgAQyQMgA0HgA2ogFUIAQvuDlKKdosbztX9CABDJAyADQaABaiAWQgBC+4OUop2ixvO1f0IAEMkDIANBIGogF0IAQvuDlKKdosbztX9CABDJAyADQdACaiADKQOQAyINIAMpA7gDIg4gAykD8AN8Igx8IhAgAykDqAMgDyADKQOgAyILfCALVK18fCISIAMpA+ACfCILQonHmaSu8IHph39+Ig9CAELH+vPD7YKjkDxCABDJAyADQcACaiAPQgBCjZXHw5bS2sCXf0IAEMkDIANBsAJqIA9CAELdsIWM6LaRqLh/QgAQyQMgA0GgAmogD0IAQqnAxomuzpOyMEIAEMkDIANBkAJqIBRCAEL2/4XS8N/H1ccAQgAQyQMgA0HQA2ogFUIAQvb/hdLw38fVxwBCABDJAyADQZABaiAWQgBC9v+F0vDfx9XHAEIAEMkDIANBEGogF0IAQvb/hdLw38fVxwBCABDJAyADQeABaiADKQPoAiALIBJUrXwiDyADKQPgA3wiGCADKQP4AyAMIA5UrXwiDiADKQPwAXwiGSADKQOAA3wiEyAQIBJWrSADKQOYAyANIBBWrXx8fCIMfCIRIAMpA8ACfCIQIAMpA9gCIAsgAykD0AIiC3wgC1StfHwiEiADKQOQAnwiC0KJx5mkrvCB6Yd/fiINQgBCx/rzw+2Co5A8QgAQyQMgA0HQAWogDUIAQo2Vx8OW0trAl39CABDJAyADQcABaiANQgBC3bCFjOi2kai4f0IAEMkDIANBsAFqIA1CAEKpwMaJrs6TsjBCABDJAyADQYACaiAUQgBCn+rg1Zzup+wGQgAQyQMgA0HAA2ogFUIAQp/q4NWc7qfsBkIAEMkDIANBgAFqIBZCAEKf6uDVnO6n7AZCABDJAyADIBdCAEKf6uDVnO6n7AZCABDJAyADQeAAaiADKQOYAiALIBJUrXwiDSADKQPQA3wiGiADKQP4ASAOIBlWrXwiDiADKQNwfCIUIAMpA/ACfCIVIAwgE1StIAMpA4gDIBMgGVStfHx8IhYgAykDoAF8IhcgESAYVK0gAykD6AMgDyAYVq18fHwiGCADKQOwAnwiEyAQIBJWrSADKQPIAiAQIBFUrXx8fCIMfCIRIAMpA9ABfCIQIAMpA+gBIAsgAykD4AEiC3wgC1StfHwiEiADKQOAAnwiGUKJx5mkrvCB6Yd/fiILQgBCx/rzw+2Co5A8QgAQyQMgA0HQAGogC0IAQo2Vx8OW0trAl39CABDJAyADQUBrIAtCAELdsIWM6LaRqLh/QgAQyQMgA0EwaiALQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpAzggAykDGCADKQMQIBUgFlatIAMpA/gCIBQgFVatfHwiCyADKQN4IA4gFFatfHwiDiALVK2EIgsgAykDKCAOIA4gAykDIHwiD1atfCAPIA8gFyAYVq0gAykDqAEgFiAXVq18fHwiDlatfHwiDyALVK18IA8gDyADKQOoAiAOIA4gAykDoAJ8IgtWrXwgCyALIAwgE1StIAMpA7gCIBMgGFStfHx8IgxWrXx8Ig5WrXwgDiADKQOYASAMIAwgAykDkAF8IgtWrXwgCyALIBEgGlStIAMpA9gDIA0gGlatfHx8IgxWrXx8IgsgDlStfCIOIAMpAwB8IhMgAykDuAEgCyALIAMpA7ABfCINVq18IA0gAykDyAEgDCAMIAMpA8ABfCILVq18IAsgECASVq0gAykD2AEgECARVK18fHwiDCALVK18fCILIA1UrXx8IhEgAykDiAEgCyALIAMpA4ABfCIPVq18IA8gDyADKQPIAyADKQOIAiASIBlWrXwiCyADKQPAA3wiDSALVK18IA0gDCANfCIQVq18fCILVq18fCISIAMpAzB8Ig8gElStfCAPIAMpA0ggCyALIAMpA0B8Ig1WrXwgDSANIAMpA1ggECAQIAMpA1B8IgxWrXwgDCADKQNoIAMpA2AiCyAZfCALVK18fCIQIAxUrXx8IgxWrXx8Ig0gD1StfCARIBJWrSARIBNUrSADKQMIIA4gE1atfHx8fCIRQqnAxomuzpOyMFYNAAJAAkAgEUKpwMaJrs6TsjBSDQAgDULdsIWM6LaRqLh/Vg0CIA1C3bCFjOi2kai4f1IEQEKpwMaJrs6TsjAhEQwBCyAMQo2Vx8OW0trAl39WDQJC3bCFjOi2kai4fyEOIAxCjZXHw5bS2sCXf1ENAUKpwMaJrs6TsjAhESAMIQsMAwsgDSEOIAwhCwwCC0KNlcfDltLawJd/IQsgEELH+vPD7YKjkDxaDQBCqcDGia7Ok7IwIREMAQsgDELz6ri86a2lv+gAfCISIBBCx/rzw+2Co5A8VK0iDn0hCyANQqPP+vOXye7XxwB8Ig8gDEKNlcfDltLawJd/VCAOIBJWcq0iDH0hDiARIA1C3bCFjOi2kai4f1QgDCAPVnKtfUKpwMaJrs6TsjB9IREgEELH+vPD7YKjkDx9IRALIAcgEDcDICAHIAs3AxggByAONwMQIAcgETcDCEEACzoAACADQYAEaiQAIAQtAChFDQEgBCAELQApOgBwQeTYwgBBKyAEQfAAakGk2sIAQbTawgAQygMACyACQQBIDQNB0c7FAC0AABpBASEGIAJBARDWBCIIRQ0DIAIEQCAIIAEgAvwKAAALIARBDGogCAJ/QQEgAkEBRg0AGiACIAhqIQlBACEFIAJBAXYiAUEBRwRAIAJBAWshBiABQf7///8DcSEDA0AgBiAIaiIHLQAAIQEgByAFIAhqIgotAAA6AAAgCiABOgAAIAkgBUF+c2oiAS0AACEHIAEgCkEBaiIBLQAAOgAAIAEgBzoAACAGQQJrIQYgAyAFQQJqIgVHDQALCyACIAJBAnFFDQAaIAUgCGoiAS0AACEGIAEgCSAFQX9zaiIBLQAAOgAAIAEgBjoAACACC0EIEM8CIAggAhDfBAJAQbjTwQBB6NHBAEEgEPEDBEAgBEKq37eXkZHS4egANwNAIARCz/6qlYftn4SNfzcDOCAEQrGkoMjwyOjw0QA3AzAgBEL6gae5lNb1rCI3AygMAQsgBEFAa0HQ08EAKQMANwMAIARBOGpByNPBACkDADcDACAEQTBqQcDTwQApAwA3AwAgBEG408EAKQMANwMoCyAEQZABaiIBIARBKGoiAhDNASAEQQA2AnggBEKAgICAEDcCcCAEQdzTwgA2AiwgBEKggICADjcCMCAEIARB8ABqNgIoIAEgAhDTAg0EIAQoAnAhAyACIAQoAnQiByAEKAJ4EJUDIAQoAjAiBkUEQCAEKAIoRQRAIAJByNDCABClAwsgBCgCLEEANgIAIARBATYCMEEBIQYLIAQoAiwiAiACKAIAQQFqIgE2AgACQCABDQAgBkEBRwRAIAZBAnRBBGshASACQQRqIQUDQCAFIAUoAgBBAWoiAjYCACACDQIgBUEEaiEFIAFBBGsiAQ0ACwsgBCgCMCIBIAQoAihGBEAgBEEoakHY0MIAEKUDCyAEKAIsIAFBAnRqQQE2AgAgBCABQQFqNgIwCyAEQSBqIARBMGooAgA2AgAgBCAEKQIoNwMYIAMEQCAHIAMQ3wQLIARBKGogBEEMaiAEQRhqEO8BAkACQCAEKAIwRQRAQdHOxQAtAAAaQQEhBUEBQQEQ1gQiAUUNCCABQQA6AAAgACABQQEQigEMAQsgBEGQAWogBEEoakEIELACIAQoApQBIQECQCAEKAKYASIIQQJJDQAgASAIaiEJQQAhBSAIQQF2IgJBAUcEQCAIQQFrIQYgAkH+////B3EhAwNAIAEgBmoiBy0AACECIAcgASAFaiIKLQAAOgAAIAogAjoAACAJIAVBfnNqIgItAAAhByACIApBAWoiAi0AADoAACACIAc6AAAgBkECayEGIAMgBUECaiIFRw0ACwsgCEECcUUNACABIAVqIgItAAAhBiACIAkgBUF/c2oiAi0AADoAACACIAY6AAALIAQoApABIQUgACABIAgQigEgBUUNAQsgASAFEN8ECyAEKAIoIgBFDQEgBCgCLCAAQQJ0EN8EDAELIAAgBCkDMDcDACAAQRhqIARByABqKQMANwMAIABBEGogBEFAaykDADcDACAAQQhqIARBOGopAwA3AwAgBCgCkAEiAEUNACAGIAAQ3wQLIARBsAFqJAAPC0EBIAVBlNrCABDIBAALIAYgAkHU2MIAEMgEAAtBhNTCAEE3IARB0ABqQfTTwgBBiNXCABDKAwALQQFBARD/BAAL/iACCH8QfiMAQbABayIEJAAgBEHgAGpCADcDACAEQdgAakIANwMAIARCADcDUCAEQgE3A2hBgAIhBQNAIARCgICAgL+y/fDDADcDQCAEQpHh5c2HifqZKDcDOCAEQt2whYzotpGouH83AzAgBEKpwMaJrs6TsjA3AyggBEGQAWogBEEoaiAFQQFrIgYQsgIgBEH4AGpCADcDACAEQYABakIANwMAIARCADcDcCAEIAQpA6gBQgGDNwOIASAEQfAAaiAEQdAAakEgEPEDBEAgBiEFDAELC0EAIQYCQAJAAkACQAJAAkAgAiAFQQN2IAVBB3FBAEdqIgVNBEACQCAFIAJrIgVFBEBBASEGDAELQdHOxQAtAAAaIAVBARDXBCIGRQ0ECyAEIAU2ApgBIAQgBjYClAEgBCAFNgKQASACBEAgBEGQAWogBSACQQFBARCIAyAEKAKYASEFIAQoApQBIQYLIAIEQCAFIAZqIAEgAvwKAAALIAYhASMAQYAEayIDJAAgBEEoaiIHAn8gAiAFakEfTQRAIAdBADoAAUEBDAELIANBsANqIAEpABgiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIUQgBCp9uF8drIudwbQgAQyQMgA0HwA2ogASkAECILQjiGIAtCgP4Dg0IohoQgC0KAgPwHg0IYhiALQoCAgPgPg0IIhoSEIAtCCIhCgICA+A+DIAtCGIhCgID8B4OEIAtCKIhCgP4DgyALQjiIhISEIhVCAEKn24Xx2si53BtCABDJAyADQfABaiABKQAIIgtCOIYgC0KA/gODQiiGhCALQoCA/AeDQhiGIAtCgICA+A+DQgiGhIQgC0IIiEKAgID4D4MgC0IYiEKAgPwHg4QgC0IoiEKA/gODIAtCOIiEhIQiFkIAQqfbhfHayLncG0IAEMkDIANB8ABqIAEpAAAiC0I4hiALQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCALQgiIQoCAgPgPgyALQhiIQoCA/AeDhCALQiiIQoD+A4MgC0I4iISEhCIXQgBCp9uF8drIudwbQgAQyQMgA0GgA2ogAykDsAMiD0L/////vrL98EJ+IgtCAEKBgICAv7L98MMAQgAQyQMgA0GQA2ogC0IAQpHh5c2HifqZKEIAEMkDIANBgANqIAtCAELdsIWM6LaRqLh/QgAQyQMgA0HwAmogC0IAQqnAxomuzpOyMEIAEMkDIANB4AJqIBRCAELjs/GantaO/9MAQgAQyQMgA0HgA2ogFUIAQuOz8Zqe1o7/0wBCABDJAyADQaABaiAWQgBC47Pxmp7Wjv/TAEIAEMkDIANBIGogF0IAQuOz8Zqe1o7/0wBCABDJAyADQdACaiADKQOQAyINIAMpA7gDIg4gAykD8AN8Igx8IhAgAykDqAMgDyADKQOgAyILfCALVK18fCISIAMpA+ACfCILQv////++sv3wQn4iD0IAQoGAgIC/sv3wwwBCABDJAyADQcACaiAPQgBCkeHlzYeJ+pkoQgAQyQMgA0GwAmogD0IAQt2whYzotpGouH9CABDJAyADQaACaiAPQgBCqcDGia7Ok7IwQgAQyQMgA0GQAmogFEIAQoWB7p3V5+CkjH9CABDJAyADQdADaiAVQgBChYHundXn4KSMf0IAEMkDIANBkAFqIBZCAEKFge6d1efgpIx/QgAQyQMgA0EQaiAXQgBChYHundXn4KSMf0IAEMkDIANB4AFqIAMpA+gCIAsgElStfCIPIAMpA+ADfCIYIAMpA/gDIAwgDlStfCIOIAMpA/ABfCIZIAMpA4ADfCITIBAgElatIAMpA5gDIA0gEFatfHx8Igx8IhEgAykDwAJ8IhAgAykD2AIgCyADKQPQAiILfCALVK18fCISIAMpA5ACfCILQv////++sv3wQn4iDUIAQoGAgIC/sv3wwwBCABDJAyADQdABaiANQgBCkeHlzYeJ+pkoQgAQyQMgA0HAAWogDUIAQt2whYzotpGouH9CABDJAyADQbABaiANQgBCqcDGia7Ok7IwQgAQyQMgA0GAAmogFEIAQqWJufqXlrSLAkIAEMkDIANBwANqIBVCAEKlibn6l5a0iwJCABDJAyADQYABaiAWQgBCpYm5+peWtIsCQgAQyQMgAyAXQgBCpYm5+peWtIsCQgAQyQMgA0HgAGogAykDmAIgCyASVK18Ig0gAykD0AN8IhogAykD+AEgDiAZVq18Ig4gAykDcHwiFCADKQPwAnwiFSAMIBNUrSADKQOIAyATIBlUrXx8fCIWIAMpA6ABfCIXIBEgGFStIAMpA+gDIA8gGFatfHx8IhggAykDsAJ8IhMgECASVq0gAykDyAIgECARVK18fHwiDHwiESADKQPQAXwiECADKQPoASALIAMpA+ABIgt8IAtUrXx8IhIgAykDgAJ8IhlC/////76y/fBCfiILQgBCgYCAgL+y/fDDAEIAEMkDIANB0ABqIAtCAEKR4eXNh4n6mShCABDJAyADQUBrIAtCAELdsIWM6LaRqLh/QgAQyQMgA0EwaiALQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpAzggAykDGCADKQMoIAMpA3ggDiAUVq18IgsgAykDIHwiDiALVK18IA4gDiAVIBZWrSADKQP4AiAUIBVWrXx8fCILVq18IAsgCyAXIBhWrSADKQOoASAWIBdWrXx8fCIOVq18IgsgAykDEHwiDyALVK18IA8gDyADKQOoAiAOIA4gAykDoAJ8IgtWrXwgCyALIAwgE1StIAMpA7gCIBMgGFStfHx8IgxWrXx8Ig5WrXwgDiADKQOYASAMIAwgAykDkAF8IgtWrXwgCyALIBEgGlStIAMpA9gDIA0gGlatfHx8IgxWrXx8IgsgDlStfCIOIAMpAwB8IhMgAykDuAEgCyALIAMpA7ABfCINVq18IA0gAykDyAEgDCAMIAMpA8ABfCILVq18IAsgECASVq0gAykD2AEgECARVK18fHwiDCALVK18fCILIA1UrXx8IhEgAykDiAEgCyALIAMpA4ABfCIPVq18IA8gDyADKQPIAyADKQOIAiASIBlWrXwiCyADKQPAA3wiDSALVK18IA0gDCANfCIQVq18fCILVq18fCISIAMpAzB8Ig8gElStfCAPIAMpA0ggCyALIAMpA0B8Ig1WrXwgDSANIAMpA1ggECAQIAMpA1B8IgxWrXwgDCADKQNoIAMpA2AiCyAZfCALVK18fCIQIAxUrXx8IgxWrXx8Ig0gD1StfCARIBJWrSARIBNUrSADKQMIIA4gE1atfHx8fCIRQqnAxomuzpOyMFYNAAJAAkAgEUKpwMaJrs6TsjBSDQAgDULdsIWM6LaRqLh/Vg0CIA1C3bCFjOi2kai4f1IEQEKpwMaJrs6TsjAhEQwBCyAMQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IQ4gDEKR4eXNh4n6mShRDQFCqcDGia7Ok7IwIREgDCELDAMLIA0hDiAMIQsMAgtCkeHlzYeJ+pkoIQsgEEKBgICAv7L98MMAWg0AQqnAxomuzpOyMCERDAELIAxCkeHlzYeJ+pkofSISIBBCgYCAgL+y/fDDAFStIg59IQsgDUKjz/rzl8nu18cAfCIPIAxCkeHlzYeJ+pkoVCAOIBJWcq0iDH0hDiARIA1C3bCFjOi2kai4f1QgDCAPVnKtfUKpwMaJrs6TsjB9IREgEEKBgICAv7L98MMAfSEQCyAHIBA3AyAgByALNwMYIAcgDjcDECAHIBE3AwhBAAs6AAAgA0GABGokACAELQAoRQ0BIAQgBC0AKToAcEHk2MIAQSsgBEHwAGpBpNrCAEG02sIAEMoDAAsgAkEASA0DQdHOxQAtAAAaQQEhBiACQQEQ1gQiCEUNAyACBEAgCCABIAL8CgAACyAEQQxqIAgCf0EBIAJBAUYNABogAiAIaiEJQQAhBSACQQF2IgFBAUcEQCACQQFrIQYgAUH+////A3EhAwNAIAYgCGoiBy0AACEBIAcgBSAIaiIKLQAAOgAAIAogAToAACAJIAVBfnNqIgEtAAAhByABIApBAWoiAS0AADoAACABIAc6AAAgBkECayEGIAMgBUECaiIFRw0ACwsgAiACQQJxRQ0AGiAFIAhqIgEtAAAhBiABIAkgBUF/c2oiAS0AADoAACABIAY6AAAgAgtBCBDPAiAIIAIQ3wQCQEHY0sEAQejRwQBBIBDxAwRAIARChoCAgPqu8KWXfzcDQCAEQufG4tKtttybcTcDOCAEQq6koMjwyOjw0QA3AzAgBEL6gae5lNb1rCI3AygMAQsgBEFAa0Hw0sEAKQMANwMAIARBOGpB6NLBACkDADcDACAEQTBqQeDSwQApAwA3AwAgBEHY0sEAKQMANwMoCyAEQZABaiIBIARBKGoiAhDMASAEQQA2AnggBEKAgICAEDcCcCAEQdzTwgA2AiwgBEKggICADjcCMCAEIARB8ABqNgIoIAEgAhDTAg0EIAQoAnAhAyACIAQoAnQiByAEKAJ4EJUDIAQoAjAiBkUEQCAEKAIoRQRAIAJByNDCABClAwsgBCgCLEEANgIAIARBATYCMEEBIQYLIAQoAiwiAiACKAIAQQFqIgE2AgACQCABDQAgBkEBRwRAIAZBAnRBBGshASACQQRqIQUDQCAFIAUoAgBBAWoiAjYCACACDQIgBUEEaiEFIAFBBGsiAQ0ACwsgBCgCMCIBIAQoAihGBEAgBEEoakHY0MIAEKUDCyAEKAIsIAFBAnRqQQE2AgAgBCABQQFqNgIwCyAEQSBqIARBMGooAgA2AgAgBCAEKQIoNwMYIAMEQCAHIAMQ3wQLIARBKGogBEEMaiAEQRhqEO8BAkACQCAEKAIwRQRAQdHOxQAtAAAaQQEhBUEBQQEQ1gQiAUUNCCABQQA6AAAgACABQQEQiwEMAQsgBEGQAWogBEEoakEIELACIAQoApQBIQECQCAEKAKYASIIQQJJDQAgASAIaiEJQQAhBSAIQQF2IgJBAUcEQCAIQQFrIQYgAkH+////B3EhAwNAIAEgBmoiBy0AACECIAcgASAFaiIKLQAAOgAAIAogAjoAACAJIAVBfnNqIgItAAAhByACIApBAWoiAi0AADoAACACIAc6AAAgBkECayEGIAMgBUECaiIFRw0ACwsgCEECcUUNACABIAVqIgItAAAhBiACIAkgBUF/c2oiAi0AADoAACACIAY6AAALIAQoApABIQUgACABIAgQiwEgBUUNAQsgASAFEN8ECyAEKAIoIgBFDQEgBCgCLCAAQQJ0EN8EDAELIAAgBCkDMDcDACAAQRhqIARByABqKQMANwMAIABBEGogBEFAaykDADcDACAAQQhqIARBOGopAwA3AwAgBCgCkAEiAEUNACAGIAAQ3wQLIARBsAFqJAAPC0EBIAVBlNrCABDIBAALIAYgAkHU2MIAEMgEAAtBhNTCAEE3IARB0ABqQfTTwgBBiNXCABDKAwALQQFBARD/BAAL/woBAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECyAAKAIMIgEEQCAAKAIQIAFBAnQQ3wQLIAAoAhgiAQRAIAAoAhwgAUECdBDfBAsgACgCJCIBBEAgACgCKCABQQJ0EN8ECyAAKAIwIgEEQCAAKAI0IAFBAnQQ3wQLIAAoAjwiAQRAIAAoAkAgAUECdBDfBAsgACgCSCIBBEAgACgCTCABQQJ0EN8ECyAAKAJUIgEEQCAAKAJYIAFBAnQQ3wQLIAAoAmAiAQRAIAAoAmQgAUECdBDfBAsgACgCbCIBBEAgACgCcCABQQJ0EN8ECyAAKAJ4IgEEQCAAKAJ8IAFBAnQQ3wQLIAAoAoQBIgEEQCAAKAKIASABQQJ0EN8ECyAAKAKQASIBBEAgACgClAEgAUECdBDfBAsgACgCnAEiAQRAIAAoAqABIAFBAnQQ3wQLIAAoAqgBIgEEQCAAKAKsASABQQJ0EN8ECyAAKAK0ASIBBEAgACgCuAEgAUECdBDfBAsgACgCwAEiAQRAIAAoAsQBIAFBAnQQ3wQLIAAoAswBIgEEQCAAKALQASABQQJ0EN8ECyAAKALYASIBBEAgACgC3AEgAUECdBDfBAsgACgC5AEiAQRAIAAoAugBIAFBAnQQ3wQLIAAoAvABIgEEQCAAKAL0ASABQQJ0EN8ECyAAKAL8ASIBBEAgACgCgAIgAUECdBDfBAsgACgCiAIiAQRAIAAoAowCIAFBAnQQ3wQLIAAoApQCIgEEQCAAKAKYAiABQQJ0EN8ECyAAKAKgAiIBBEAgACgCpAIgAUECdBDfBAsgACgCrAIiAQRAIAAoArACIAFBAnQQ3wQLIAAoArgCIgEEQCAAKAK8AiABQQJ0EN8ECyAAKALEAiIBBEAgACgCyAIgAUECdBDfBAsgACgC0AIiAQRAIAAoAtQCIAFBAnQQ3wQLIAAoAtwCIgEEQCAAKALgAiABQQJ0EN8ECyAAKALoAiIBBEAgACgC7AIgAUECdBDfBAsgACgC9AIiAQRAIAAoAvgCIAFBAnQQ3wQLIAAoAoADIgEEQCAAKAKEAyABQQJ0EN8ECyAAKAKMAyIBBEAgACgCkAMgAUECdBDfBAsgACgCmAMiAQRAIAAoApwDIAFBAnQQ3wQLIAAoAqQDIgEEQCAAKAKoAyABQQJ0EN8ECyAAKAKwAyIBBEAgACgCtAMgAUECdBDfBAsgACgCvAMiAQRAIAAoAsADIAFBAnQQ3wQLIAAoAsgDIgEEQCAAKALMAyABQQJ0EN8ECyAAKALUAyIBBEAgACgC2AMgAUECdBDfBAsgACgC4AMiAQRAIAAoAuQDIAFBAnQQ3wQLIAAoAuwDIgEEQCAAKALwAyABQQJ0EN8ECyAAKAL4AyIBBEAgACgC/AMgAUECdBDfBAsgACgChAQiAQRAIAAoAogEIAFBAnQQ3wQLIAAoApAEIgEEQCAAKAKUBCABQQJ0EN8ECyAAKAKcBCIBBEAgACgCoAQgAUECdBDfBAsgACgCqAQiAQRAIAAoAqwEIAFBAnQQ3wQLIAAoArQEIgEEQCAAKAK4BCABQQJ0EN8ECyAAKALABCIBBEAgACgCxAQgAUECdBDfBAsgACgCzAQiAQRAIAAoAtAEIAFBAnQQ3wQLIAAoAtgEIgEEQCAAKALcBCABQQJ0EN8ECyAAKALkBCIBBEAgACgC6AQgAUECdBDfBAsgACgC8AQiAQRAIAAoAvQEIAFBAnQQ3wQLIAAoAvwEIgEEQCAAKAKABSABQQJ0EN8ECyAAKAKIBSIBBEAgACgCjAUgAUECdBDfBAsgACgClAUiAQRAIAAoApgFIAFBAnQQ3wQLIAAoAqAFIgEEQCAAKAKkBSABQQJ0EN8ECwuMDAIXfgF/IAIpAwAiEyEDIAEpAwAiDyEJAn4CQAJ+AkAgDyATUg0AIAIpAwgiBCABKQMIIglSBEAgBCEDDAELIAIpAxAiCyABKQMQIglSBEAgCyEDDAELIAIpAxgiDSABKQMYIglSBEAgDSEDDAELIAIpAyAiDiABKQMgIglSBEAgDiEDDAELIAQhEiALIRQgDSEGIAIpAygiAyEIIA4gAyABKQMoIglRDQEaCyADIAlWDQEgAikDCCEEIAEpAwghEiACKQMQIQsgASkDECEUIAIpAxghDSABKQMYIQYgAikDICEOIAIpAyghAyABKQMoIQggASkDIAsiBSAOfSIMIAMgCFatIgd9IRggBiANfSIKIAUgDlQgByAMVnKtIgV9IQ4gFCALfSIHIAYgDVQgBSAKVnKtIgV9IQ0gEiAEfSIGIAUgB1YgCyAUVnKtIgV9IQsgBSAGViAEIBJWciEaIA8gE30hEiAIIAN9DAELQqTsw7WP1LSY5wAgAikDGCIKIAEpAxgiB30iCyACKQMgIgQgASkDICIDVCAEIAN9Ig4gAikDKCIGIAEpAygiBVStIgNUcq0iBH0iCH0iDSAOIAN9IgNC///Piuv//9UeVkL//8+K6///1R4gA30iEiAGIAV9IhBCq9X+////v/+5f1atIhRUcq0iA30hDkK/pZScz/DSu+QAIAIpAxAiESABKQMQIgZ9IgUgByAKViAEIAtWcq0iBH0iDH0iCyADIA1WIAhCpOzDtY/UtJjnAFZyrSIDfSENQtfZrprk9umNywAgAikDCCIKIAEpAwgiB30iCCAGIBFWIAQgBVZyrSIGfSIFfSIEIAMgC1YgDEK/pZScz/DSu+QAVnKtIgN9IQsgAyAEViAFQtfZrprk9umNywBWciEaIBIgFH0hGCAHIApWIAYgCFZyrSAPIBN9fEKazf/Lo73EgBp8IRJCq9X+////v/+5fyAQfQshFCACKQMwIhYhAyABKQMwIhchCSAAAn4CQAJ+AkAgFiAXUg0AIAIpAzgiBCABKQM4IglSBEAgBCEDDAELIAIpA0AiCCABKQNAIglSBEAgCCEDDAELIAIpA0giBSABKQNIIglSBEAgBSEDDAELIAIpA1AiBiABKQNQIglSBEAgBiEDDAELIAQhESAIIQwgBSEKIAIpA1giAyEVIAYgAyABKQNYIglRDQEaCyADIAlWDQEgAikDOCEEIAEpAzghESACKQNAIQggASkDQCEMIAIpA0ghBSABKQNIIQogAikDUCEGIAIpA1ghAyABKQNYIRUgASkDUAsiByAGfSITIAMgFVatIhB9IQkgCiAFfSIPIBAgE1YgBiAHVnKtIgd9IQYgDCAIfSIQIAcgD1YgBSAKVnKtIgd9IQUgESAEfSIKIAcgEFYgCCAMVnKtIgd9IQggByAKViAEIBFWciECIBcgFn0hBCAVIAN9DAELQqTsw7WP1LSY5wAgAikDSCIPIAEpA0giEH0iESACKQNQIgQgASkDUCIDVCAEIAN9IgcgAikDWCIIIAEpA1giBlStIgNUcq0iBH0iDH0iBSAHIAN9IgNC///Piuv//9UeVkL//8+K6///1R4gA30iCSAIIAZ9IhlCq9X+////v/+5f1atIhVUcq0iA30hBkK/pZScz/DSu+QAIAIpA0AiEyABKQNAIgp9IgcgDyAQVCAEIBFWcq0iBH0iD30iCCADIAVWIAxCpOzDtY/UtJjnAFZyrSIDfSEFQtfZrprk9umNywAgAikDOCIQIAEpAzgiEX0iDCAKIBNWIAQgB1ZyrSIKfSIHfSIEIAMgCFYgD0K/pZScz/DSu+QAVnKtIgN9IQggAyAEViAHQtfZrprk9umNywBWciECIAkgFX0hCSAQIBFUIAogDFZyrSAXIBZ9fEKazf/Lo73EgBp8IQRCq9X+////v/+5fyAZfQs3A1ggACAJNwNQIAAgBjcDSCAAIAU3A0AgACAINwM4IAAgFDcDKCAAIBg3AyAgACAONwMYIAAgDTcDECAAIAs3AwggACAEIAKtfTcDMCAAIBIgGq19NwMAC/YaAhJ+CH8jAEGgAWsiFSQAAkACQAJAAkACQAJAIAIQ4wEiFkEDdiAWQQdxQQBHaiIWTQRAAkAgFiACayIWRQRAQQEhFwwBC0HRzsUALQAAGiAWQQEQ1wQiF0UNBAsgFSAWNgIwIBUgFzYCLCAVIBY2AiggAgRAIBVBKGogFiACQQFBARCIAyAVKAIwIRYgFSgCLCEXCyACBEAgFiAXaiABIAL8CgAACyMAQdABayIBJAAgFUHYAGoiGQJ/IAIgFmpBL00EQCAZQQA6AAFBAQwBCyAXKQAoIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhDSAXKQAAIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhDiAXKQAIIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhDyAXKQAQIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhECAXKQAYIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhESAXKQAgIgNCOIYgA0KA/gODQiiGhCADQoCA/AeDQhiGIANCgICA+A+DQgiGhIQgA0IIiEKAgID4D4MgA0IYiEKAgPwHg4QgA0IoiEKA/gODIANCOIiEhIQhEkEoIQIDQCABQfAAaiACQeCmxABqKQMAIgNCACANQgAQyQMgAUGAAWogA0IAIBJCABDJAyABQZABaiADQgAgEUIAEMkDIAFBoAFqIANCACAQQgAQyQMgAUGwAWogA0IAIA9CABDJAyABQcABaiADQgAgDkIAEMkDIAFB4ABqIAEpA3AiDCALfCIJQgBCAEL9//P/z///+Yl/EMkDIAFB0ABqIAEpA2giA0IAQqvV/v///7//uX9CABDJAyABQUBrIANCAEL//8+K6///1R5CABDJAyABQTBqIANCAEKk7MO1j9S0mOcAQgAQyQMgAUEgaiADQgBCv6WUnM/w0rvkAEIAEMkDIAFBEGogA0IAQtfZrprk9umNywBCABDJAyABIANCAEKazf/Lo73EgBpCABDJAyABKQMIIAEpA8ABIhMgBHwiAyABKQO4ASABKQOwASIEIAd8IgcgBFStfCAHIAcgASkDqAEgASkDoAEiBCAFfCIFIARUrXwgBSAFIAEpA5gBIAEpA5ABIgQgCHwiCCAEVK18IAggASkDiAEgASkDgAEiBCAGfCIGIARUrXwgBiABKQN4IAkgDFStfHwiCyAGVK18fCIGIAhUrXx8IgVWrXx8IgdWrXx8IgwgASkDAHwiBCAMVK18IAQgASkDGCAHIAcgASkDEHwiB1atfCAHIAEpAyggBSAFIAEpAyB8IgVWrXwgBSABKQM4IAYgBiABKQMwfCIGVq18IAYgBiABKQNIIAsgASkDQCIUfCIIIBRUrXwgCCABKQNYIAkgASkDUCIJfCAJVK18fCILIAhUrXx8IgZWrXx8IgggBVStfHwiBSAHVK18fCIHIARUrXwiCSADIAxWrSABKQPIASADIBNUrXx8IgMgCnwiCnwiBCAJVK0gAyAKVq18IQogAkEIayICQXhHDQALAkACQCAKQgBSIARCms3/y6O9xIAaVnINAAJAAkAgBEKazf/Lo73EgBpSBEAgBSEDIAchCQwBCyAHQtfZrprk9umNywBWDQICQCAHQtfZrprk9umNywBSBEAgBSEDIAchCQwBCyAFQr+llJzP8NK75ABWDQNC19mumuT26Y3LACEJIAVCv6WUnM/w0rvkAFIEQCAFIQMMAQsgCEKk7MO1j9S0mOcAVg0DQr+llJzP8NK75AAhAyAIQqTsw7WP1LSY5wBRDQILQprN/8ujvcSAGiEECyAIIQwgBiEKDAILIAZC///Piuv//9UeVg0AQqTsw7WP1LSY5wAhDCAGQv//z4rr///VHlIEQEKazf/Lo73EgBohBCAGIQoMAgtC///Piuv//9UeIQogC0Kr1f7///+//7l/Wg0AQprN/8ujvcSAGiEEDAELIAZC///Piuv//9UefSIDIAtCq9X+////v/+5f1StIgl9IQogCEKk7MO1j9S0mOcAfSINIAZC///Piuv//9UeVCADIAlUcq0iA30hDCAFQr+llJzP8NK75AB9IgYgCEKk7MO1j9S0mOcAVCADIA1Wcq0iCX0hAyAHQtfZrprk9umNywB9IgggBUK/pZScz/DSu+QAVCAGIAlUcq0iBX0hCSAEIAdC19mumuT26Y3LAFQgBSAIVnKtfUKazf/Lo73EgBp9IQQgC0LVqoGAgIDAgMYAfCELCyAZIAs3AzAgGSAKNwMoIBkgDDcDICAZIAM3AxggGSAJNwMQIBkgBDcDCEEACzoAACABQdABaiQAIBUtAFhFDQEgFSAVLQBZOgCQAUHk2MIAQSsgFUGQAWpBpNrCAEG02sIAEMoDAAsgAkEASA0DQdHOxQAtAAAaQQEhFyACQQEQ1gQiGUUNAyACBEAgGSABIAL8CgAACyAVQQxqIBkCf0EBIAJBAUYNABogAiAZaiEBQQAhFiACQQF2IhhBAUcEQCACQQFrIRcgGEH+////A3EhGwNAIBcgGWoiGC0AACEaIBggFiAZaiIYLQAAOgAAIBggGjoAACABIBZBfnNqIhotAAAhHCAaIBhBAWoiGC0AADoAACAYIBw6AAAgF0ECayEXIBsgFkECaiIWRw0ACwsgAiACQQJxRQ0AGiAWIBlqIhctAAAhGCAXIAEgFkF/c2oiAS0AADoAACABIBg6AAAgAgtBCBDPAiAZIAIQ3wQCQEH408EAQYjSwQBBMBDxAwRAIBVCrtXy//////rDADcDgAEgFUL9/5/qrv7/2zI3A3ggFULpuqaXmsmO9Ac3A3AgFUL69sqZmOa81Gw3A2ggFULpgNOH6qOjim83A2AgFUKGhPz34+SshQQ3A1gMAQsgFUGAAWpBoNTBACkDADcDACAVQfgAakGY1MEAKQMANwMAIBVB8ABqQZDUwQApAwA3AwAgFUHoAGpBiNTBACkDADcDACAVQeAAakGA1MEAKQMANwMAIBVB+NPBACkDADcDWAsgFUEoaiICIBVB2ABqIgEQpgEgFUEANgKYASAVQoCAgIAQNwKQASAVQdzTwgA2AlwgFUKggICADjcCYCAVIBVBkAFqNgJYIAIgARDFAg0EIBUoApABIQIgASAVKAKUASIZIBUoApgBEJUDIBUoAmAiF0UEQCAVKAJYRQRAIAFByNDCABClAwsgFSgCXEEANgIAIBVBATYCYEEBIRcLIBUoAlwiFiAWKAIAQQFqIgE2AgACQCABDQAgF0EBRwRAIBdBAnRBBGshASAWQQRqIRYDQCAWIBYoAgBBAWoiFzYCACAXDQIgFkEEaiEWIAFBBGsiAQ0ACwsgFSgCYCIBIBUoAlhGBEAgFUHYAGpB2NDCABClAwsgFSgCXCABQQJ0akEBNgIAIBUgAUEBajYCYAsgFUEgaiAVQeAAaigCADYCACAVIBUpAlg3AxggAgRAIBkgAhDfBAsgFUHYAGogFUEMaiAVQRhqEO8BAkACQCAVKAJgRQRAQdHOxQAtAAAaQQEhFkEBQQEQ1gQiAUUNCCABQQA6AAAgACABQQEQjgEMAQsgFUEoaiAVQdgAakEIELACIBUoAiwhAQJAIBUoAjAiAkECSQ0AIAEgAmohGUEAIRYgAkEBdiIYQQFHBEAgAkEBayEXIBhB/v///wdxIRsDQCABIBdqIhgtAAAhGiAYIAEgFmoiGC0AADoAACAYIBo6AAAgGSAWQX5zaiIaLQAAIRwgGiAYQQFqIhgtAAA6AAAgGCAcOgAAIBdBAmshFyAbIBZBAmoiFkcNAAsLIAJBAnFFDQAgASAWaiIXLQAAIRggFyAZIBZBf3NqIhctAAA6AAAgFyAYOgAACyAVKAIoIRYgACABIAIQjgEgFkUNAQsgASAWEN8ECyAVKAJYIgBFDQEgFSgCXCAAQQJ0EN8EDAELIAAgFSkDYDcDACAAQShqIBVBiAFqKQMANwMAIABBIGogFUGAAWopAwA3AwAgAEEYaiAVQfgAaikDADcDACAAQRBqIBVB8ABqKQMANwMAIABBCGogFUHoAGopAwA3AwAgFSgCKCIARQ0AIBcgABDfBAsgFUGgAWokAA8LQQEgFkGU2sIAEMgEAAsgFyACQdTYwgAQyAQAC0GE1MIAQTcgFUGfAWpB9NPCAEGI1cIAEMoDAAtBAUEBEP8EAAuDCwIOfwh+IwBB0AJrIgIkACACQYACaiABIAEoAgwQ/AECQAJAAkACQAJAIAItAMACIgVBA0YNACACQfgBaiIDIAJBuAJqKQMANwMAIAJB8AFqIgYgAkGwAmopAwA3AwAgAkHoAWoiBCACQagCaikDADcDACACQeABaiIJIAJBoAJqKQMANwMAIAJB2AFqIgogAkGYAmopAwA3AwAgAkHQAWoiByACQZACaikDADcDACACQcgBaiIIIAJBiAJqKQMANwMAIAIgAikDgAI3A8ABIAIgAigAwQI2AnggAiACQcQCaigAADYAeyAFQQJGDQAgAkHYAGogAykDADcDACACQdAAaiAGKQMANwMAIAJByABqIAQpAwA3AwAgAkFAayAJKQMANwMAIAJBOGogCikDADcDACACQTBqIAcpAwA3AwAgAkEoaiAIKQMANwMAIAIgAikDwAE3AyAgAiACKAJ4NgIYIAIgAigAezYAGwJAIAEoAgwoAgBBgICAgHhHDQAgASgCBEUNACABKAIIRQ0DC0HRzsUALQAAGkGgAkEIENYEIgNFDQMgAyACKQMgNwMAIAMgBToAQCADIAIoAhg2AEEgA0HEAGogAigAGzYAACADQThqIAJB2ABqKQMANwMAIANBMGogAkHQAGopAwA3AwAgA0EoaiACQcgAaikDADcDACADQSBqIAJBQGspAwA3AwAgA0EYaiACQThqKQMANwMAIANBEGogAkEwaikDADcDACADQQhqIAJBKGopAwA3AwAgAkEBNgIUIAIgAzYCECACQQQ2AgwgAkHoAGogAUEIaikCADcDACACIAEpAgA3A2AgAkGAAmogAkHgAGogAigCbBD8AQJAIAItAMACIgFBA0YNAEGJASEGIAJBwQJqIglBA2ohCkEBIQUDQCACQfgBaiIEIAJBuAJqKQMANwMAIAJB8AFqIgcgAkGwAmopAwA3AwAgAkHoAWoiCCACQagCaikDADcDACACQeABaiILIAJBoAJqKQMANwMAIAJB2AFqIgwgAkGYAmopAwA3AwAgAkHQAWoiDSACQZACaikDADcDACACQcgBaiIOIAJBiAJqKQMANwMAIAIgAikDgAI3A8ABIAIgCSgAADYCuAEgAiAKKAAANgC7ASABQf8BcUECRg0BIAJBsAFqIg8gBCkDADcDACACQagBaiIEIAcpAwA3AwAgAkGgAWoiByAIKQMANwMAIAJBmAFqIgggCykDADcDACACQZABaiILIAwpAwA3AwAgAkGIAWoiDCANKQMANwMAIAJBgAFqIg0gDikDADcDACACIAIpA8ABNwN4IAIgAigCuAE2AnAgAiACKAC7ATYAcyACKAIMIAVGBEACQCACKAJsKAIAQYCAgIB4Rw0AIAIoAmRFDQAgAigCaEUNCAsgAkEMaiAFQQFBCEHIABCIAyACKAIQIQMLIA0pAwAhECAMKQMAIREgCykDACESIAgpAwAhEyAHKQMAIRQgBCkDACEVIA8pAwAhFiACKQN4IRcgAyAGaiIEQQFrIAE6AAAgBEHBAGsiASAXNwMAIAQgAigCcDYAACAEQQNqIAIoAHM2AAAgAUE4aiAWNwMAIAFBMGogFTcDACABQShqIBQ3AwAgAUEgaiATNwMAIAFBGGogEjcDACABQRBqIBE3AwAgAUEIaiAQNwMAIAIgBUEBaiIFNgIUIAJBgAJqIAJB4ABqIAIoAmwQ/AEgBkHIAGohBiACLQDAAiIBQQNHDQALCyAAQQhqIAJBFGooAgA2AgAgACACKQIMNwIADAELIABBADYCCCAAQoCAgICAATcCAAsgAkHQAmokAA8LQbSbwgAQmgQAC0EIQaACQZCWwgAQyAQAC0G0m8IAEJoEAAv8CgISfwJ+IwBB0ABrIgYkACAGIAI2AgwgBiABNgIIIAYgAzYCECAGIAU2AhQCQAJAIAEoAgggBUcNACACKAIIIAVHDQAgAygCCCAFRw0AIAZBIGoiCEGI+sQAKAIANgIAIAZBgPrEACkCADcDGEEBIQcgBkEYakEAIAVBAXQiEBCJAyAGKAIcIgogCCgCACIJQQJ0aiELIAVBA3RBBGsiDQRAIAtBACAN/AsACyALIA1qQQA2AgAgCCAJIBBqIgk2AgAgBUEBcSETIAVB/v///wFxIRQgBUEBayEVIAMoAgQhDSABKAIEIRAgAigCBCEWIAohCEEAIQEDQCAJIAEgBWoiEUkEQCARIAlB0PzEABDlBAALIAchCyAWIAFBAnQiDmo1AgAhGEEAIQICQCAVRQRAQQAhAwwBCyAQIQcgCCEBQQAhAwNAIAEgAiABNQIAIAc1AgAgGH58IhmnaiIMNgIAIAFBBGoiDyAZQiCIpyACIAxLaiICIA81AgAgB0EEajUCACAYfnwiGadqIgw2AgAgGUIgiKcgAiAMS2ohAiAHQQhqIQcgAUEIaiEBIBQgA0ECaiIDRw0ACwsgCiAOaiEMIBMEQCAMIANBAnQiAWoiAyACIAM1AgAgASAQajUCACAYfnwiGKdqIgE2AgAgGEIgiKcgASACSWohAgsgDCgCACAEbK0hGEEAIQMCQCAVRQRAQQAhDgwBCyANIQcgCCEBQQAhDgNAIAEgAyABNQIAIAc1AgAgGH58IhmnaiIPNgIAIAFBBGoiFyAZQiCIpyADIA9LaiIDIBc1AgAgB0EEajUCACAYfnwiGadqIg82AgAgGUIgiKcgAyAPS2ohAyAHQQhqIQcgAUEIaiEBIBQgDkECaiIORw0ACwsgEwRAIAwgDkECdCIBaiIHIAMgBzUCACABIA1qNQIAIBh+fCIYp2oiATYCACAYQiCIpyABIANJaiEDCyAJIBFLBEAgCiARQQJ0aiADIAIgEmoiAWoiBzYCACABIAJJIAMgB0tyIRIgCEEEaiEIIAsgBSALSyICaiEHIAshASACRQ0DDAELCyARIAlB4PzEABDZAwALIAZBBDYCHCAGQez7xAA2AhggBkIENwIkIAYgBkEUaq1CgICAgOABhDcDSCAGQoCAgIDwDiIYIAZBEGqthDcDQCAGIBggBkEMaq2ENwM4IAYgGCAGQQhqrYQ3AzAgBiAGQTBqNgIgIAZBGGpBjPzEABCoBAALAkACQAJAAkACQAJAIBJFBEAgBSAJSw0CIAkgBWsiAUECdCEEQQAhAyABQf////8DSyAEQfz///8HS3INAQJ/IARFBEBBBCECQQAMAQtB0c7FAC0AABpBBCEDIARBBBDWBCICRQ0CIAELIQMgBARAIAIgCiAFQQJ0aiAE/AoAAAsgBigCGCIHRQ0GDAULIAUgCUsNAyAFIAkgBWsiASABIAVLG0ECdCECIAogBUECdCIDaiEEQQAhAUEAIQcDQCABIAJHBEAgASAKaiABIARqKAIAIgggByABIA1qIgcoAgBqayILNgIAIAcoAgAiByAIQX9zIghyIAtxIAcgCHFyQR92IQcgAyABQQRqIgFHDQELC0HRzsUALQAAGiADQQQQ1gQiAkUNAiADBEAgAiAKIAP8CgAACyAFIQMgBSEBIAYoAhgiBw0EDAULIAMgBEHU+MQAEMgEAAsgBSAJQZz8xAAQ5AQAC0EEIANB1PjEABDIBAALIAZBADYCQCAGQQE2AjQgBkG4/MQANgIwIAZCBDcCOCAGQTBqQcD8xAAQqAQACyAKIAdBAnQQ3wQLIABBCGogATYCACAGIAI2AhwgBiADNgIYIAAgBikDGDcCACAGQdAAaiQAC+MKAgF/EX4jAEHAAmsiAyQAIANBQGsgASkDGCIJQgAgAikDGCIEQgAQyQMgA0HQAGogASkDECIHQgAgBEIAEMkDIANB4ABqIAEpAwgiBUIAIARCABDJAyADQfAAaiABKQMAIghCACAEQgAQyQMgA0EQaiADKQNAIgZCAEKBgICAcEIAEMkDIANBgAFqIAIpAxAiBEIAIAlCABDJAyADQbABaiAEQgAgB0IAEMkDIANB4AFqIARCACAFQgAQyQMgA0GQAmogBEIAIAhCABDJAyADQSBqIAZCIIYiCyADKQNIIg0gAykDUHwiDnwiDCADKQOAAXwiBEIAQoGAgIBwQgAQyQMgA0GQAWogAikDCCIKQgAgCUIAEMkDIANBwAFqIApCACAHQgAQyQMgA0HwAWogCkIAIAVCABDJAyADQaACaiAKQgAgCEIAEMkDIANBMGogBEIghiIPIAsgDFatIAZCIIh8IhAgAykDWCANIA5WrXwiDiADKQNgfCIRfCILIAMpA7ABfCINIAMpA4gBIAQgDFStfHwiEnwiDCADKQOQAXwiCkIAQoGAgIBwQgAQyQMgA0GgAWogAikDACIGQgAgCUIAEMkDIANB0AFqIAZCACAHQgAQyQMgA0GAAmogBkIAIAVCABDJAyADQbACaiAGQgAgCEIAEMkDIAMgCkIghiITIAwgD1StIARCIIh8Ig8gAykDaCAOIBFWrXwiDiADKQNwfCIEIAMpAxB8IgcgCyAQVK18IgUgAykD4AF8IgggDSASVq0gAykDuAEgCyANVq18fHwiEHwiBiADKQPAAXwiCyADKQOYASAKIAxUrXx8IhF8IgwgAykDoAF8IglCAEKBgICAcEIAEMkDAkACQCADKQMIIAMpA9gBIAMpA6gBIAkgDFStfCISIAMpA9ABfCINIBJUrXwgDSANIAsgEVatIAMpA8gBIAYgC1atfHwiESADKQPwAXwiCyAGIA9UrSIPIAMpAyB8IgYgBSAHVK0gAykDGCAEIAdWrXx8IhIgAykDeCAEIA5UrXx8IgQgAykDkAJ8IgcgCCAQVq0gAykD6AEgBSAIVq18fHwiDnwiEHwiBSAMIBNUrSAKQiCIfHwiCnwiDVatfCITIAMpA4ACfCIIIAUgClatIhQgAykDMHwiDCAGIBBWrSADKQMoIAYgD1StfHwiDyAHIA5WrSADKQOYAiAEIAdWrXx8Ig4gBCASVK18IhB8IgQgAykDoAJ8IgcgBSALVK0gAykD+AEgCyARVK18fHwiC3wiEXwiBSAJQiCGIgYgDXwiCiAGVK0gCUIgiHx8IgkgBVStIg0gAykDAHwiBiANVK18IAYgDCARVq0gAykDOCAMIBRUrXx8Ig0gByALVq0gAykDqAIgBCAHVq18fCILIAQgD1StIA4gEFatfHwiDnwiBCADKQOwAnwiDCAFIAhUrSADKQOIAiAIIBNUrXx8fCIFfCIHIAZUrXwiBiAFIAxUrSADKQO4AiAEIAxWrXx8IgUgBCANVK0gCyAOVq18fCIEfCIIIAZUIAQgBVRyIAhCgYCAgHBWcg0AAkAgCEKBgICAcFEEQCAJQv////8PVg0CQgAhBSAHQgBSDQJC/////w8hBCAJQv////8PWg0BIAkhBEKBgICAcCEIDAMLIAkhBCAHIQUMAgsgCkJ/UQ0AQoGAgIBwIQgMAQsgCUL/////D30iBSAKQn9SrSIGfSEEIAcgCUL/////D1QgBSAGVHKtIgl9IQUgCCAHIAlUrX1C/////w98IQggCkIBfCEKCyAAIAo3AxggACAENwMQIAAgBTcDCCAAIAg3AwAgA0HAAmokAAvACwEJfyMAQTBrIgMkACABLQAMIQgCQCACLQAMIgZBAUYEQCABKAIIIgJBAnQhBAJAIAJB/////wNLIARB/P///wdLcg0AIAEoAgQhBgJ/IARFBEBBBCEBQQAMAQtB0c7FAC0AABpBBCEFIARBBBDWBCIBRQ0BIAILIQUgBARAIAEgBiAE/AoAAAsgACAIOgAMIAAgAjYCCCAAIAE2AgQgACAFNgIADAILIAUgBEH4gcAAEMgEAAsCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQCAIQQFrDgIPAQALIAZFDQEMAgsgBkUNAQsCfyABKAIIIgQgAigCCCIGRgRAIARBAnQhByABKAIEQQRrIQogAigCBEEEayELAkADQCAHRQ0BIAcgC2ohCSAHIApqIAdBBGshBygCACIFIAkoAgAiCUYNAAsgBSAJSyAFIAlJawwCC0F/QQAgBxsMAQsgBCAGSyAEIAZJawtB/wFxDgIBAgMLAkAgASgCCCIFIAIoAggiBEkEQEHRzsUALQAAGiACKAIEIQYgBEECdCICQQQQ1gQiBUUNByACBEAgBSAGIAL8CgAACyADIAQ2AiwgAyAFNgIoIAMgBDYCJCADQRhqIANBJGogARDKAQwBCyAFQQJ0IQQgASgCBCEGAkAgBUUEQEEEIQEMAQtB0c7FAC0AABogBEEEENYEIgFFDQgLIAQEQCABIAYgBPwKAAALIAMgBTYCLCADIAE2AiggAyAFNgIkIANBGGogA0EkaiACEMoBC0EBIQcCQCAIQQFHBEAgCEEBIAMoAiAbIQcMAQsgA0EANgIgIAMoAhgiAUEESQ0AIAMoAhwgAUECdBDfBCADQoCAgIDAADcCGAsgACADKQIYNwIAIAAgBzoADCAAQQhqIANBIGooAgA2AgAMDAsgAEEIakGozMIAKQIANwIAIABBoMzCACkCADcCAAwLC0EAIQUgBEH/////A0sgBEECdCIGQfz///8HS3INBSABKAIEIQcCfyAGRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhBSAGQQQQ1gQiAUUNBiAECyEFIAYEQCABIAcgBvwKAAALIAMgBDYCLCADIAE2AiggAyAFNgIkIANBGGogA0EkaiACEIcCQQEhByAIQQFGDQEgCEEBIAMoAiAbIQcMAgtBACEFIAZB/////wNLIAZBAnQiBEH8////B0tyDQUgAigCBCEHAn8gBEUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQUgBEEEENYEIgJFDQYgBgshBSAEBEAgAiAHIAT8CgAAC0ECIAhrIQcgAyAGNgIsIAMgAjYCKCADIAU2AiQgA0EYaiADQSRqIAEQhwICQCAIQQFxRQRAIAdBASADKAIgGyEHDAELIANBADYCICADKAIYQQRJDQAgA0EIaiADQRhqQQAQ0wMgAygCCCIBQYGAgIB4Rw0HCyAAIAMpAhg3AgAgACAHOgAMIABBCGogA0EgaigCADYCAAwJCyADQQA2AiAgAygCGEEESQ0AIANBEGogA0EYakEAENMDIAMoAhAiAUGBgICAeEcNBgsgACADKQIYNwIAIAAgBzoADCAAQQhqIANBIGooAgA2AgAMBwtBBCACQfiBwAAQyAQAC0EEIARB+IHAABDIBAALIAUgBkH4gcAAEMgEAAsgBSAEQfiBwAAQyAQACyABIAMoAgxB0M/CABDIBAALIAEgAygCFEHQz8IAEMgEAAsgAigCCCIFQQJ0IQRBACEBAkAgBUH/////A0sgBEH8////B0tyDQAgAigCBCEHAn8gBEUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQEgBEEEENYEIgJFDQEgBQshASAEBEAgAiAHIAT8CgAACyAAQQIgBms6AAwgACAFNgIIIAAgAjYCBCAAIAE2AgAMAQsgASAEQfiBwAAQyAQACyADQTBqJAALwAsBCX8jAEEwayIDJAAgAS0ADCEIAkAgAi0ADCIGQQFGBEAgASgCCCICQQJ0IQQCQCACQf////8DSyAEQfz///8HS3INACABKAIEIQYCfyAERQRAQQQhAUEADAELQdHOxQAtAAAaQQQhBSAEQQQQ1gQiAUUNASACCyEFIAQEQCABIAYgBPwKAAALIAAgCDoADCAAIAI2AgggACABNgIEIAAgBTYCAAwCCyAFIARBpIPFABDIBAALAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgCEEBaw4CDwEACyAGRQ0BDAILIAZFDQELAn8gASgCCCIEIAIoAggiBkYEQCAEQQJ0IQcgASgCBEEEayEKIAIoAgRBBGshCwJAA0AgB0UNASAHIAtqIQkgByAKaiAHQQRrIQcoAgAiBSAJKAIAIglGDQALIAUgCUsgBSAJSWsMAgtBf0EAIAcbDAELIAQgBksgBCAGSWsLQf8BcQ4CAQIDCwJAIAEoAggiBSACKAIIIgRJBEBB0c7FAC0AABogAigCBCEGIARBAnQiAkEEENYEIgVFDQcgAgRAIAUgBiAC/AoAAAsgAyAENgIsIAMgBTYCKCADIAQ2AiQgA0EYaiADQSRqIAEQygEMAQsgBUECdCEEIAEoAgQhBgJAIAVFBEBBBCEBDAELQdHOxQAtAAAaIARBBBDWBCIBRQ0ICyAEBEAgASAGIAT8CgAACyADIAU2AiwgAyABNgIoIAMgBTYCJCADQRhqIANBJGogAhDKAQtBASEHAkAgCEEBRwRAIAhBASADKAIgGyEHDAELIANBADYCICADKAIYIgFBBEkNACADKAIcIAFBAnQQ3wQgA0KAgICAwAA3AhgLIAAgAykCGDcCACAAIAc6AAwgAEEIaiADQSBqKAIANgIADAwLIABBCGpBgMTEACkCADcCACAAQfjDxAApAgA3AgAMCwtBACEFIARB/////wNLIARBAnQiBkH8////B0tyDQUgASgCBCEHAn8gBkUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQUgBkEEENYEIgFFDQYgBAshBSAGBEAgASAHIAb8CgAACyADIAQ2AiwgAyABNgIoIAMgBTYCJCADQRhqIANBJGogAhCHAkEBIQcgCEEBRg0BIAhBASADKAIgGyEHDAILQQAhBSAGQf////8DSyAGQQJ0IgRB/P///wdLcg0FIAIoAgQhBwJ/IARFBEBBBCECQQAMAQtB0c7FAC0AABpBBCEFIARBBBDWBCICRQ0GIAYLIQUgBARAIAIgByAE/AoAAAtBAiAIayEHIAMgBjYCLCADIAI2AiggAyAFNgIkIANBGGogA0EkaiABEIcCAkAgCEEBcUUEQCAHQQEgAygCIBshBwwBCyADQQA2AiAgAygCGEEESQ0AIANBCGogA0EYakEAENMDIAMoAggiAUGBgICAeEcNBwsgACADKQIYNwIAIAAgBzoADCAAQQhqIANBIGooAgA2AgAMCQsgA0EANgIgIAMoAhhBBEkNACADQRBqIANBGGpBABDTAyADKAIQIgFBgYCAgHhHDQYLIAAgAykCGDcCACAAIAc6AAwgAEEIaiADQSBqKAIANgIADAcLQQQgAkGkg8UAEMgEAAtBBCAEQaSDxQAQyAQACyAFIAZBpIPFABDIBAALIAUgBEGkg8UAEMgEAAsgASADKAIMQbTJxAAQyAQACyABIAMoAhRBtMnEABDIBAALIAIoAggiBUECdCEEQQAhAQJAIAVB/////wNLIARB/P///wdLcg0AIAIoAgQhBwJ/IARFBEBBBCECQQAMAQtB0c7FAC0AABpBBCEBIARBBBDWBCICRQ0BIAULIQEgBARAIAIgByAE/AoAAAsgAEECIAZrOgAMIAAgBTYCCCAAIAI2AgQgACABNgIADAELIAEgBEGkg8UAEMgEAAsgA0EwaiQAC+YKAgd/An4jAEHQAGsiAyQAAkAgAi0ADCIFQQFGBEAgACABKQIANwIAIABBCGogAUEIaikCADcCACACKAIAIgBFDQEgAigCBCAAQQJ0EN8EDAELAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgAS0ADCIGQQFrDgILAQALIAVFDQEMAgsgBUUNAQsCfyABKAIIIgQgAigCCCIFRgRAIARBAnQhBCABKAIEQQRrIQggAigCBEEEayEJAkADQCAERQ0BIAQgCWohByAEIAhqIARBBGshBCgCACIFIAcoAgAiB0YNAAsgBSAHSyAFIAdJawwCC0F/QQAgBBsMAQsgBCAFSyAEIAVJawtB/wFxDgIBAgMLIANBKGogAUEIaiIIKAIANgIAIAMgASkCACIKNwMgIANBOGogAkEIaiIJKAIANgIAIAMgAikCACILNwMwAn8gCqciBCALpyIFSQRAIANByABqIAkoAgA2AgAgAyACKQIANwNAIANBFGogA0FAayADQSBqEMoBIANBJGoMAQsgA0HIAGogCCgCADYCACADIAEpAgA3A0AgA0EUaiADQUBrIANBMGoQygEgBSEEIANBNGoLIQcgBARAIAcoAgAgBEECdBDfBAsCQCAGQQFHBEAgAygCHA0BIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAsLIANBADYCHCADKAIUIgFBBE8EQCADKAIYIAFBAnQQ3wQgA0KAgICAwAA3AhQLIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAoLIAAgBjoADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAkLIABBCGpBqMzCACkCADcCACAAQaDMwgApAgA3AgAgAigCACIARQ0HIAIoAgQgAEECdBDfBAwHCyADQThqIAFBCGooAgA2AgAgAyABKQIANwMwIANByABqIAJBCGooAgA2AgAgAyACKQIANwNAIANBIGogA0EwaiADQUBrEIcCIAMoAkAiAQRAIAMoAkQgAUECdBDfBAtBASEEIAZBAUYNASAGQQEgAygCKBshBAwCCyADQThqIAJBCGooAgA2AgAgAyACKQIANwMwIANByABqIAFBCGooAgA2AgAgAyABKQIANwNAIANBIGogA0EwaiADQUBrEIcCIAMoAkAiAQRAIAMoAkQgAUECdBDfBAtBAiAGayEEAkAgBkEBcUUEQCAEQQEgAygCKBshBAwBCyADQQA2AiggAygCIEEESQ0AIAMgA0EgakEAENMDIAMoAgAiAUGBgICAeEcNAwsgACADKQIgNwIAIAAgBDoADCAAQQhqIANBKGooAgA2AgAMBgsgA0EANgIoIAMoAiBBBEkNACADQQhqIANBIGpBABDTAyADKAIIIgFBgYCAgHhHDQILIAAgAykCIDcCACAAIAQ6AAwgAEEIaiADQShqKAIANgIADAQLIAEgAygCBEHQz8IAEMgEAAsgASADKAIMQdDPwgAQyAQACyACQQ1qIQQCQAJAAkAgBUEBaw4CAAECCyAAQQE6AAwgACACKQIANwIAIAAgBC8AADsADSAAQQhqIAJBCGooAgA2AgAgAEEPaiAEQQJqLQAAOgAADAILIABBADoADCAAIAIpAgA3AgAgACAELwAAOwANIABBCGogAkEIaigCADYCACAAQQ9qIARBAmotAAA6AAAMAQsgAEECOgAMIAAgAikCADcCACAAIAQvAAA7AA0gAEEIaiACQQhqKAIANgIAIABBD2ogBEECai0AADoAAAsgASgCACIARQ0AIAEoAgQgAEECdBDfBAsgA0HQAGokAAuRCwIBfw9+IwBB8AJrIgMkACADQcgCaiABIAIQsQJBASECAkAgAy0AyAJBAUYEQCAAIAMtAMkCOgABDAELIANBQGsgAykD6AIiBUIAQoGIgPC3rn9CABDJAyADQYABaiADKQPgAiIIQgBCgYiA8Leuf0IAEMkDIANBwAFqIAMpA9gCIgRCAEKBiIDwt65/QgAQyQMgA0GAAmogAykD0AIiBkIAQoGIgPC3rn9CABDJAyADQRBqQgAgAykDQCIHfUIAQpGAgICAgICACEIAEMkDIANB0ABqIAVCAEL//7+YE0IAEMkDIANBkAFqIAhCAEL//7+YE0IAEMkDIANB0AFqIARCAEL//7+YE0IAEMkDIANBkAJqIAZCAEL//7+YE0IAEMkDIANBIGpCACAHQgBSrSIJIAMpA0giDCADKQOAAXwiC3wiByADKQNQfCIKfUIAQpGAgICAgICACEIAEMkDIANB4ABqIAVCAEKAgL57QgAQyQMgA0GgAWogCEIAQoCAvntCABDJAyADQeABaiAEQgBCgIC+e0IAEMkDIANBoAJqIAZCAEKAgL57QgAQyQMgA0EwakIAIApCAFKtIg0gByAJVK0iECADKQOIASALIAxUrXwiCyADKQPAAXwiDnwiCSADKQOQAXwiDCADKQNYIAcgClatfHwiEXwiByADKQNgfCIKfUIAQpGAgICAgICACEIAEMkDIANB8ABqIAVCAEKQkILwtZX1/wdCABDJAyADQbABaiAIQgBCkJCC8LWV9f8HQgAQyQMgA0HwAWogBEIAQpCQgvC1lfX/B0IAEMkDIANBsAJqIAZCAEKQkILwtZX1/wdCABDJAyADQgAgAykDaCAHIApWrXwiDyADKQOgAXwiBSADKQPIASALIA5WrXwiDiADKQOAAnwiCCADKQMQfCIEIAkgEFStfCIGIAMpA9ABfCILIAwgEVatIAMpA5gBIAkgDFatfHx8IgkgByANVK18Ig18IgcgCkIAUq18IgogAykDcHwiDH1CAEKRgICAgICAgAhCABDJAwJAAkAgAykDuAIgAykDOCAFIAdWrSADKQOoASAFIA9UrXx8IhAgAykD4AF8IgUgCSANVq0iESADKQMgfCINIAQgBlatIAMpAxggBCAIVK18fCIPIAMpA4gCIAggDlStfHwiCCADKQOQAnwiBCAJIAtUrSADKQPYASAGIAtWrXx8fCIJfCILfCIGIAcgClatfCIOIAZUrSISIAMpAzB8IgcgElStfCAHIAcgAykDoAIgCCAPVK2EIg8gBCAJVq0gAykDmAIgBCAIVK18fHwiCCALIA1UrSADKQMoIA0gEVStfHx8IgQgBSAGVq0gAykD6AEgBSAQVK18fHwiBXwiB1atfCIJIAQgBVatIAQgCFStIAMpA6gCIAggD1StfHx8fCIFIAMpA7ACfCIIIAVUrXwgCCADKQP4ASADKQO4ASADKQN4IAogDFatfCIGIAMpA7ABfCIEIAZUrXwgBCAEIA58IgRWrXwiCiADKQPwAXwiBiAKVK18IAYgBiAHfCIGVq18fCIHIAhUrXwgBSAJVK18IAMpAwggBiAEIAxCAFKtfCIFIARUrXwiCCAGVK0iBiADKQMAfCIEIAZUrXwgBCAEIAd8IgRWrXx8IglCkYCAgICAgIAIVg0AIAlCkYCAgICAgIAIUgRAIAQhBiAIIQcgBSEKDAILIAUgCIQgBIRQRQ0AQgAhBkKRgICAgICAgAghCUIAIQdCACEKDAELIAVCAX0hCiAIIAVQrSIFfSEHIAQgBSAIVq0iBX0hBiAJIAQgBVStfUKRgICAgICAgAh9IQkLIAAgCjcDICAAIAc3AxggACAGNwMQIAAgCTcDCEEAIQILIAAgAjoAACADQfACaiQAC7EMAgN/EH4jAEGwAmsiAyQAAkAgASgCDCIEQX9GBEAgAEIANwMAIABBKGpCADcDACAAQSBqQgA3AwAgAEEYakIANwMAIABBEGpCADcDACAAQQhqQgA3AwAMAQsgASgCCCIFIARNBEAgBCAFQdzHwgAQ2QMACyABKAIEIgUgBEEwbGoiASkDKCEMIAEpAyAhDiABKQMYIQ8gASkDECERIAEpAwghEiABKQMAIRMgBARAA0BBKCEBQgAhCUIAIQtCACEKQgAhCEIAIQZCACENA0AgA0HwAGogASACaikDACIHQgAgDEIAEMkDIANBgAFqIAdCACAOQgAQyQMgA0GQAWogB0IAIA9CABDJAyADQaABaiAHQgAgEUIAEMkDIANBsAFqIAdCACASQgAQyQMgA0HAAWogB0IAIBNCABDJAyADQeAAaiADKQNwIhAgDXwiDUIAQgBC/f/z/8////mJfxDJAyADQdAAaiADKQNoIgdCAEKr1f7///+//7l/QgAQyQMgA0FAayAHQgBC///Piuv//9UeQgAQyQMgA0EwaiAHQgBCpOzDtY/UtJjnAEIAEMkDIANBIGogB0IAQr+llJzP8NK75ABCABDJAyADQRBqIAdCAELX2a6a5PbpjcsAQgAQyQMgAyAHQgBCms3/y6O9xIAaQgAQyQMgAykDCCADKQPAASIUIAl8IgcgAykDuAEgAykDsAEiCSALfCILIAlUrXwgCyADKQOoASADKQOgASIJIAp8IgogCVStfCAKIAMpA5gBIAMpA5ABIgkgCHwiCCAJVK18IAggAykDiAEgAykDgAEiCSAGfCIGIAlUrXwgBiADKQN4IA0gEFStfHwiECAGVK18fCIGIAhUrXx8IgggClStfHwiCiALVK18fCIJIAMpAwB8IgsgCVStfCALIAsgAykDGCAKIAogAykDEHwiClatfCAKIAogAykDKCAIIAggAykDIHwiCFatfCAIIAggAykDOCAGIAYgAykDMHwiBlatfCAGIAYgAykDSCADKQNAIhUgEHwiECAVVK18IBAgAykDWCANIAMpA1AiDXwgDVStfHwiDSAQVK18fCIGVq18fCIIVq18fCIKVq18fCILVq18IAcgCVatIAMpA8gBIAcgFFStfHx8IQkgAUEIayIBQXhHDQALAkACQCAJQprN/8ujvcSAGlYNACAJQprN/8ujvcSAGlIEQCAGIQcgCCEMIAohDiALIQ8MAgsgC0LX2a6a5PbpjcsAVg0AAkAgC0LX2a6a5PbpjcsAUgRAIAYhByAIIQwgCiEOIAshDwwBCyAKQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEPIApCv6WUnM/w0rvkAFIEQCAGIQcgCCEMIAohDgwBCyAIQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEOIAhCpOzDtY/UtJjnAFIEQCAGIQcgCCEMDAELIAZC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhDCAGQv//z4rr///VHlIEQCAGIQcMAQtC///Piuv//9UeIQcgDUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohCQwBCyAGQv//z4rr///VHn0iDCANQqvV/v///7//uX9UrSIOfSEHIAhCpOzDtY/UtJjnAH0iDyAGQv//z4rr///VHlQgDCAOVHKtIgZ9IQwgCkK/pZScz/DSu+QAfSIRIAhCpOzDtY/UtJjnAFQgBiAPVnKtIgZ9IQ4gC0LX2a6a5PbpjcsAfSIIIApCv6WUnM/w0rvkAFQgBiARVnKtIgZ9IQ8gCSALQtfZrprk9umNywBUIAYgCFZyrX1Cms3/y6O9xIAafSEJIA1C1aqBgICAwIDGAHwhDQsgAyANNwOoAiADIAc3A6ACIAMgDDcDmAIgAyAONwOQAiADIA83A4gCIAMgCTcDgAIgA0HQAWogA0GAAmogBSAEQQFrIgRBMGxqEL0CIAMpA9ABIRMgAykD2AEhEiADKQPgASERIAMpA+gBIQ8gAykD8AEhDiADKQP4ASEMIAQNAAsLIAAgDDcDKCAAIA43AyAgACAPNwMYIAAgETcDECAAIBI3AwggACATNwMACyADQbACaiQAC6wKAgd/An4jAEHQAGsiAyQAAkAgAi0ADCIFQQFGBEAgACABKQIANwIAIABBCGogAUEIaikCADcCACACKAIAIgBFDQEgAigCBCAAQQJ0EN8EDAELAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgAS0ADCIGQQFrDgILAQALIAVFDQEMAgsgBUUNAQsCfyABKAIIIgQgAigCCCIFRgRAIARBAnQhBCABKAIEQQRrIQggAigCBEEEayEJAkADQCAERQ0BIAQgCWohByAEIAhqIARBBGshBCgCACIFIAcoAgAiB0YNAAsgBSAHSyAFIAdJawwCC0F/QQAgBBsMAQsgBCAFSyAEIAVJawtB/wFxDgIBAgMLIANBKGogAUEIaiIIKAIANgIAIAMgASkCACIKNwMgIANBOGogAkEIaiIJKAIANgIAIAMgAikCACILNwMwAn8gCqciBCALpyIFSQRAIANByABqIAkoAgA2AgAgAyACKQIANwNAIANBFGogA0FAayADQSBqEMoBIANBJGoMAQsgA0HIAGogCCgCADYCACADIAEpAgA3A0AgA0EUaiADQUBrIANBMGoQygEgBSEEIANBNGoLIQcgBARAIAcoAgAgBEECdBDfBAsCQCAGQQFHBEAgAygCHA0BIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAsLIANBADYCHCADKAIUIgFBBE8EQCADKAIYIAFBAnQQ3wQgA0KAgICAwAA3AhQLIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAoLIAAgBjoADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAkLIABBCGpBgMTEACkCADcCACAAQfjDxAApAgA3AgAgAigCACIARQ0HIAIoAgQgAEECdBDfBAwHCyADQcgAaiABQQhqKAIANgIAIAMgASkCADcDQCADQTBqIANBQGsgAhCHAiACKAIAIgEEQCACKAIEIAFBAnQQ3wQLQQEhBCAGQQFGDQEgBkEBIAMoAjgbIQQMAgsgA0HIAGogAkEIaigCADYCACADIAIpAgA3A0AgA0EwaiADQUBrIAEQhwIgASgCACICBEAgASgCBCACQQJ0EN8EC0ECIAZrIQQCQCAGQQFxRQRAIARBASADKAI4GyEEDAELIANBADYCOCADKAIwQQRJDQAgAyADQTBqQQAQ0wMgAygCACIBQYGAgIB4Rw0DCyAAIAMpAjA3AgAgACAEOgAMIABBCGogA0E4aigCADYCAAwGCyADQQA2AjggAygCMEEESQ0AIANBCGogA0EwakEAENMDIAMoAggiAUGBgICAeEcNAgsgACADKQIwNwIAIAAgBDoADCAAQQhqIANBOGooAgA2AgAMBAsgASADKAIEQbTJxAAQyAQACyABIAMoAgxBtMnEABDIBAALIAJBDWohBAJAAkACQCAFQQFrDgIAAQILIABBAToADCAAIAIpAgA3AgAgACAELwAAOwANIABBCGogAkEIaigCADYCACAAQQ9qIARBAmotAAA6AAAMAgsgAEEAOgAMIAAgAikCADcCACAAIAQvAAA7AA0gAEEIaiACQQhqKAIANgIAIABBD2ogBEECai0AADoAAAwBCyAAQQI6AAwgACACKQIANwIAIAAgBC8AADsADSAAQQhqIAJBCGooAgA2AgAgAEEPaiAEQQJqLQAAOgAACyABKAIAIgBFDQAgASgCBCAAQQJ0EN8ECyADQdAAaiQAC68KAQp/IwBBkAVrIgMkAAJAIAEoAgQiBARAIAEgBCABKAIIIgYgBCAEIAZLGyIFazYCBCABIAEoAgAiBCAFQQV0ajYCAAJAAkACQAJAAkAgBgRAIANBqANqIARBGGopAwA3AwAgA0GgA2ogBEEQaikDADcDACADQZgDaiAEQQhqKQMANwMAIAMgBCkDADcDkAMgBUEBRg0BIANB6ANqIARBOGopAwA3AwAgA0HgA2ogBEEwaikDADcDACADQdgDaiIGIARBKGopAwA3AwAgAyAEKQMgNwPQAyADIANBkANqIANB0ANqEEMCQAJAAkAgAy0AQCIBQQJGBEAgBiADQQhqKAIANgIAIAMgAykDADcD0AMMAQsgA0HAAmoiBiADQThqKQMANwMAIANBuAJqIgcgA0EwaikDADcDACADQbACaiIIIANBKGopAwA3AwAgA0GoAmoiCSADQSBqKQMANwMAIANBoAJqIgogA0EYaikDADcDACADQZgCaiILIANBEGopAwA3AwAgA0GQAmoiDCADQQhqKQMANwMAIAMgAykDADcDiAIgAyADKABBNgLAASADIANBxABqKAAANgDDASADQdABaiAMKQMANwMAIANB2AFqIAspAwA3AwAgA0HgAWogCikDADcDACADQegBaiAJKQMANwMAIANB8AFqIAgpAwA3AwAgA0H4AWogBykDADcDACADQYACaiAGKQMANwMAIAMgAykDiAI3A8gBIAVBA0kNBSAFQQNGDQYgA0HIA2ogBEH4AGopAwA3AwAgA0HAA2ogBEHwAGopAwA3AwAgA0G4A2ogBEHoAGopAwA3AwAgA0GYA2ogBEHIAGopAwA3AwAgA0GgA2ogBEHQAGopAwA3AwAgA0GoA2ogBEHYAGopAwA3AwAgAyAEKQNgNwOwAyADIAQpA0A3A5ADIAVBBE0NByAFQQVGDQggA0GIBGogBEG4AWopAwA3AwAgA0GABGogBEGwAWopAwA3AwAgA0H4A2ogBEGoAWopAwA3AwAgA0HYA2oiBSAEQYgBaikDADcDACADQeADaiAEQZABaikDADcDACADQegDaiAEQZgBaikDADcDACADIAQpA6ABNwPwAyADIAQpA4ABNwPQAyADIANBkANqIANB0ANqEGIgAygCAEUNASAFIANBDGooAgA2AgAgAyADKQIENwPQAwsgAigCACIBQYCAgIB4RiABRXJFBEAgAigCBCABEN8ECyACIAMpA9ADNwIAIAJBCGogA0HYA2ooAgA2AgBBAiEBDAELIANBjAJqIQIgAiADQQhqQYAB/AoAACADQdADaiIEIAJBgAH8CgAAIANB2ARqIANB0AFqKQMANwMAIANB4ARqIANB2AFqKQMANwMAIANB6ARqIANB4AFqKQMANwMAIANB8ARqIANB6AFqKQMANwMAIANB+ARqIANB8AFqKQMANwMAIANBgAVqIANB+AFqKQMANwMAIANBiAVqIANBgAJqKQMANwMAIAMgAykDyAE3A9AEIAMgAygCwAE2ApADIAMgAygAwwE2AJMDIAMgBEHAAfwKAAALIAAgA0HAAfwKAAAgACABOgDAASAAIAMoApADNgDBASAAQcQBaiADKACTAzYAAAwHC0EAQQBBwPrAABDZAwALQQFBAUHQ+sAAENkDAAtBAkECQeD6wAAQ2QMAC0EDQQNB8PrAABDZAwALQQRBBEGA+8AAENkDAAtBBUEFQZD7wAAQ2QMACyAAQQM6AMABCyADQZAFaiQAC74IAhJ/An4jAEHQBmsiBSQAIAVBiAVqIgkgAUFAayIIIAJBQGsQ3AEgBUHIBWoiByABIAIQ3AEgBUGIBmoiBiAJIAcQkQMgBSkDmAYhFyAFKQOQBiEYAkAgBSgCiAZBAUcEQCAFQRhqIgogBSkDoAY3AwAgBUFAayILIAVByAZqKQMANwMAIAVBOGoiDiAFQcAGaiIPKQMANwMAIAVBMGoiECAFQbgGaiIRKQMANwMAIAVBKGoiEiAFQbAGaiITKQMANwMAIAVBIGoiFCAFQagGaiIVKQMANwMAIAVBEGoiFiAXNwMAIAUgGDcDCCAHIAVBCGoiDCAMEDggBiABIAIQoAIgBUHIAGoiDSAHIAYQ3AEgBUGQBGogFikDADcDACAFQZgEaiAKKQMANwMAIAVBoARqIBQpAwA3AwAgBUGwBGogECkDADcDACAFQbgEaiAOKQMANwMAIAVBwARqIAspAwA3AwAgBSAFKQMINwOIBCAFIBIpAwA3A6gEIAYgDCABEDggBUGIAWoiCiAGIAgQ3AEgBUHIAWoiAiAIIAgQoAIgBUGIAmoiCyANIAEQ3AEgBiACIAsQkQMgBSkDmAYhFyAFKQOQBiEYIAUoAogGQQFGDQEgBUGABmogBUHIBmopAwA3AwAgBUH4BWogDykDADcDACAFQfAFaiARKQMANwMAIAVB6AVqIBMpAwA3AwAgBUHgBWogFSkDADcDACAFIAUpA6AGNwPYBSAFIBc3A9AFIAUgGDcDyAUgBiAMIAcQoAIgBUHIAmoiAiAGEPACIAYgAiACEDggByAGIAEQ3AEgCSAHIA0Q3AEgBiABIAkQ3AEgByACIAYQOCAFQcgDaiAHIAgQ3AEgBUGQA2ogBUGQBWopAwA3AwAgBUGYA2ogBUGYBWopAwA3AwAgBUGgA2ogBUGgBWopAwA3AwAgBUGoA2ogBUGoBWopAwA3AwAgBUGwA2ogBUGwBWopAwA3AwAgBUG4A2ogBUG4BWopAwA3AwAgBUHAA2ogBUHABWopAwA3AwAgBUHQBGogBUHQAmopAwA3AwAgBUHYBGogBUHYAmopAwA3AwAgBUHgBGogBUHgAmopAwA3AwAgBSAFKQOIBTcDiAMgBSAFKQPIAjcDyAQgBUGABWogBUGAA2opAwA3AwAgBUH4BGogBUH4AmopAwA3AwAgBUHwBGogBUHwAmopAwA3AwAgBSAFKQPoAjcD6AQgBiACIAEQOCAHIAYgCBDcASAAIAVBiARqIAogAyAEEBkgAEGQAWogBUHIBGogByADIAQQGSAAQRBqIAVBiANqQYAB/AoAACAFQdAGaiQADwsgBSAXNwOQBiAFIBg3A4gGQdT+wABBKyAFQYgGakGwhcEAQdCFwQAQygMACyAFIBc3A5AGIAUgGDcDiAZBoLHCAEErIAVBiAZqQaS6wgBB9LrCABDKAwALxgoBCn8jAEEwayIEJAAgAS0ADCEHAkACQCACLQAMIghBAUYEQCABKAIIIgJBAnQhBQJAIAJB/////wNLIAVB/P///wdLcg0AIAEoAgQhBgJ/IAVFBEBBBCEBQQAMAQtB0c7FAC0AABpBBCEDIAVBBBDWBCIBRQ0BIAILIQMgBQRAIAEgBiAF/AoAAAsgACAHOgAMIAAgAjYCCCAAIAE2AgQgACADNgIADAILDAILAkACQAJAAkACQAJAAkACQAJAAkACQCAHQQFrDgIKAQALIAhFDQEMAgsgCEUNAQsCQCABKAIIIgMgAigCCCIFSQRAQdHOxQAtAAAaIAIoAgQhBiAFQQJ0IgJBBBDWBCIDRQ0FIAIEQCADIAYgAvwKAAALIAQgBTYCLCAEIAM2AiggBCAFNgIkIARBGGogBEEkaiABEMoBDAELIANBAnQhBSABKAIEIQYCQCADRQRAQQQhAQwBC0HRzsUALQAAGiAFQQQQ1gQiAUUNBgsgBQRAIAEgBiAF/AoAAAsgBCADNgIsIAQgATYCKCAEIAM2AiQgBEEYaiAEQSRqIAIQygELQQEhAyAHQQFGDQEgB0EBIAQoAiAbIQMMAgsCQAJAAkACQAJAAn8gASgCCCIFIAIoAggiBkYEQCAFQQJ0IQMgASgCBEEEayELIAIoAgRBBGshDAJAA0AgA0UNASADIAxqIQkgAyALaiADQQRrIQMoAgAiCiAJKAIAIglGDQALIAkgCkkgCSAKS2sMAgtBf0EAIAMbDAELIAUgBksgBSAGSWsLQf8BcQ4CAAECCyAAQQhqQajMwgApAgA3AgAgAEGgzMIAKQIANwIADAsLQQAhAyAFQf////8DSyAFQQJ0IgZB/P///wdLcg0HIAEoAgQhCAJ/IAZFBEBBBCEBQQAMAQtB0c7FAC0AABpBBCEDIAZBBBDWBCIBRQ0IIAULIQMgBgRAIAEgCCAG/AoAAAsgBCAFNgIsIAQgATYCKCAEIAM2AiQgBEEYaiAEQSRqIAIQhwJBASEDIAdBAUYNASAHQQEgBCgCIBshAwwCC0EAIQMgBkH/////A0sgBkECdCIFQfz///8HS3INCiACKAIEIQcCfyAFRQRAQQQhAkEADAELQdHOxQAtAAAaQQQhAyAFQQQQ1gQiAkUNCyAGCyEDIAUEQCACIAcgBfwKAAALIAQgBjYCLCAEIAI2AiggBCADNgIkIARBDGogBEEkaiABEIcCIAAgBCkCDDcCACAAQQhqIARBFGooAgAiATYCACAAIAhBASABGzoADAwJCyAEQQA2AiAgBCgCGEEESQ0AIAQgBEEYakEAENMDIAQoAgAiAUGBgICAeEcNBgsgACAEKQIYNwIAIAAgAzoADCAAQQhqIARBIGooAgA2AgAMBwsgBEEANgIgIAQoAhgiAUEESQ0AIAQoAhwgAUECdBDfBCAEQoCAgIDAADcCGAsgACAEKQIYNwIAIAAgAzoADCAAQQhqIARBIGooAgA2AgAMBQtBBCACQfiBwAAQyAQAC0EEIAVB+IHAABDIBAALIAMgBkH4gcAAEMgEAAsgASAEKAIEQdDPwgAQyAQACyACKAIIIgFBAnQhBQJAIAFB/////wNLIAVB/P///wdLcg0AIAIoAgQhBgJ/IAVFBEBBBCECQQAMAQtB0c7FAC0AABpBBCEDIAVBBBDWBCICRQ0BIAELIQMgBQRAIAIgBiAF/AoAAAsgACAIOgAMIAAgATYCCCAAIAI2AgQgACADNgIADAELDAELIARBMGokAA8LIAMgBUH4gcAAEMgEAAvGCgEKfyMAQTBrIgQkACABLQAMIQcCQAJAIAItAAwiCEEBRgRAIAEoAggiAkECdCEFAkAgAkH/////A0sgBUH8////B0tyDQAgASgCBCEGAn8gBUUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQMgBUEEENYEIgFFDQEgAgshAyAFBEAgASAGIAX8CgAACyAAIAc6AAwgACACNgIIIAAgATYCBCAAIAM2AgAMAgsMAgsCQAJAAkACQAJAAkACQAJAAkACQAJAIAdBAWsOAgoBAAsgCEUNAQwCCyAIRQ0BCwJAIAEoAggiAyACKAIIIgVJBEBB0c7FAC0AABogAigCBCEGIAVBAnQiAkEEENYEIgNFDQUgAgRAIAMgBiAC/AoAAAsgBCAFNgIsIAQgAzYCKCAEIAU2AiQgBEEYaiAEQSRqIAEQygEMAQsgA0ECdCEFIAEoAgQhBgJAIANFBEBBBCEBDAELQdHOxQAtAAAaIAVBBBDWBCIBRQ0GCyAFBEAgASAGIAX8CgAACyAEIAM2AiwgBCABNgIoIAQgAzYCJCAEQRhqIARBJGogAhDKAQtBASEDIAdBAUYNASAHQQEgBCgCIBshAwwCCwJAAkACQAJAAkACfyABKAIIIgUgAigCCCIGRgRAIAVBAnQhAyABKAIEQQRrIQsgAigCBEEEayEMAkADQCADRQ0BIAMgDGohCSADIAtqIANBBGshAygCACIKIAkoAgAiCUYNAAsgCSAKSSAJIApLawwCC0F/QQAgAxsMAQsgBSAGSyAFIAZJawtB/wFxDgIAAQILIABBCGpBgMTEACkCADcCACAAQfjDxAApAgA3AgAMCwtBACEDIAVB/////wNLIAVBAnQiBkH8////B0tyDQcgASgCBCEIAn8gBkUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQMgBkEEENYEIgFFDQggBQshAyAGBEAgASAIIAb8CgAACyAEIAU2AiwgBCABNgIoIAQgAzYCJCAEQRhqIARBJGogAhCHAkEBIQMgB0EBRg0BIAdBASAEKAIgGyEDDAILQQAhAyAGQf////8DSyAGQQJ0IgVB/P///wdLcg0KIAIoAgQhBwJ/IAVFBEBBBCECQQAMAQtB0c7FAC0AABpBBCEDIAVBBBDWBCICRQ0LIAYLIQMgBQRAIAIgByAF/AoAAAsgBCAGNgIsIAQgAjYCKCAEIAM2AiQgBEEMaiAEQSRqIAEQhwIgACAEKQIMNwIAIABBCGogBEEUaigCACIBNgIAIAAgCEEBIAEbOgAMDAkLIARBADYCICAEKAIYQQRJDQAgBCAEQRhqQQAQ0wMgBCgCACIBQYGAgIB4Rw0GCyAAIAQpAhg3AgAgACADOgAMIABBCGogBEEgaigCADYCAAwHCyAEQQA2AiAgBCgCGCIBQQRJDQAgBCgCHCABQQJ0EN8EIARCgICAgMAANwIYCyAAIAQpAhg3AgAgACADOgAMIABBCGogBEEgaigCADYCAAwFC0EEIAJBpIPFABDIBAALQQQgBUGkg8UAEMgEAAsgAyAGQaSDxQAQyAQACyABIAQoAgRBtMnEABDIBAALIAIoAggiAUECdCEFAkAgAUH/////A0sgBUH8////B0tyDQAgAigCBCEGAn8gBUUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQMgBUEEENYEIgJFDQEgAQshAyAFBEAgAiAGIAX8CgAACyAAIAg6AAwgACABNgIIIAAgAjYCBCAAIAM2AgAMAQsMAQsgBEEwaiQADwsgAyAFQaSDxQAQyAQAC7gKAgh/AX4jAEHgAGsiAyQAAkAgAigCCCIFBEAgASgCCCIJRQRAIABBCGpB7PTEACgCACIENgIAIABB5PTEACkCACILNwIAIAAgCzcCDCAAQRRqIAQ2AgAgAigCACIABEAgAigCBCAAQQJ0EN8ECyABKAIAIgBFDQIgASgCBCAAQQJ0EN8EDAILAkACQAJAAkACQCAFQQFGBEAgAigCBCIEKAAAQQFHDQEgACABKQIANwIAIABB5PTEACkCADcCDCAAQRRqQez0xAAoAgA2AgAgAEEIaiABQQhqKAIANgIAIAIoAgAiAEUNByAEIABBAnQQ3wQMBwsCfyAFIAlGBEAgBUECdCEEIAEoAgRBBGshCCACKAIEQQRrIQoDQCAERQ0FIAQgCmohByAEIAhqIARBBGshBCgCACIGIAcoAgAiB0YNAAsgBiAHSyAGIAdJawwBCyAFIAlJIAUgCUtrC0H/AXEOAgIEAQsgA0EoaiABIAQoAgAQggIgA0EQaiIFIANBMGooAgA2AgAgAyADKQIoNwMIIAMoAjQhASACQQA2AggCQCABRQ0AIAIoAgAEfyAEBSACQZjzxAAQpQMgAigCBAtBADYCACACQQE2AgggAigCBCIEIAEgBCgCACIBaiIENgIAIAEgBE0NACACKAIIIgEgAigCAEYEQCACQajzxAAQpQMLIAIoAgQgAUECdGpBATYCACACIAFBAWo2AggLIAAgAykDCDcCACAAIAIpAgA3AgwgAEEUaiACQQhqKAIANgIAIABBCGogBSgCADYCAAwFCyAAIAEpAgA3AgwgAEEUaiABQQhqKAIANgIADAELIAFBADYCCCABKAIARQRAIAFB0PXEABClAwsgASgCBEEBNgIAIABBCGpBATYCACABQQhqQQE2AgAgACABKQIANwIAIABBDGohAAsgAEEIakHs9MQAKAIANgIAIABB5PTEACkCADcCACACKAIAIgBFDQIgAigCBCAAQQJ0EN8EDAILIAIoAgQiBiAFQQJ0akEEaygCACIEZyIHRQRAIANBMGogAUEIaigCADYCACADIAEpAgA3AyggACADQShqIAYgBRB7IAIoAgAiAEUNAiAGIABBAnQQ3wQMAgsgASgCBCEIAkACQCABKAIAIgFBgICAgHhHDQAgCCgCCA0AIANB0ABqIAgQwAMMAQsgAyAJNgIwIAMgCDYCLCADIAE2AiggA0HQAGogA0EoaiAERSAHQQAgBBsQzwELAkACQCACKAIAIgFBgICAgHhHDQAgBigCCA0AIANBxABqIAYQwAMMAQsgAyAFNgIwIAMgBjYCLCADIAE2AiggA0HEAGogA0EoaiAERSAHQQAgBBsQzwELIANBKGogA0HQAGogAygCSCIBIAMoAkwQeyADQSBqIANBMGooAgA2AgAgAyADKQIoNwMYIANB2ABqIANBPGooAgA2AgAgAyADKQI0NwNQIAMoAkQiAgRAIAEgAkECdBDfBAsCQAJAIAMoAlBBgICAgHhHBEAgAygCWA0BIANBMGogA0HYAGooAgA2AgAgAyADKQNQNwMoDAILIAMoAlQiASgCCA0AIANBKGogARDAAwwBCyADQShqIANB0ABqIARFIAdBACAEGxDsAQsgACADKQMYNwIAIAAgAykDKDcCDCAAQQhqIANBIGooAgA2AgAgAEEUaiADQTBqKAIANgIADAELIANBADYCOCADQQE2AiwgA0HU88QANgIoIANCBDcCMCADQShqQdT0xAAQqAQACyADQeAAaiQAC7wKAQd/IwBBMGsiAyQAIAEtAAwhBQJAAkAgAi0ADCIEQQFGBEAgASgCCCIGQQJ0IQQCQCAGQf////8DSyAEQfz///8HS3INACABKAIEIQgCfyAERQRAQQQhAUEADAELQdHOxQAtAAAaQQQhByAEQQQQ1gQiAUUNASAGCyEHIAQEQCABIAggBPwKAAALIAAgBToADCAAIAY2AgggACABNgIEIAAgBzYCAAwCCyAHIARB+IHAABDIBAALAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkAgBUEBaw4CDAEACyAERQ0BDAILIARFDQELAn8gASgCCCIEIAIoAggiBkYEQCAEQQJ0IQQgASgCBEEEayEIIAIoAgRBBGshCQJAA0AgBEUNASAEIAlqIQcgBCAIaiAEQQRrIQQoAgAiBiAHKAIAIgdGDQALIAYgB0sgBiAHSWsMAgtBf0EAIAQbDAELIAQgBksgBCAGSWsLQf8BcQ4CAgYBCyADQShqIAJBCGooAgA2AgAgAyACKQIANwMgIANBFGogA0EgaiABEMoBIAMoAhxFBEAgAEEBOgAMIAAgAykCFDcCACAAQQhqIANBHGooAgA2AgAMCwsgACAFOgAMIAAgAykCFDcCACAAQQhqIANBHGooAgA2AgAMCgtBAiEEIAVBAWsOAgMBAgsgAEEIakGozMIAKQIANwIAIABBoMzCACkCADcCAAwHC0EAIQQLIANBKGogAkEIaigCADYCACADIAIpAgA3AyAgA0EUaiADQSBqIAEQhwIgBEEBIAMoAhwbIQQMAwsgA0EoaiACQQhqKAIANgIAIAMgAikCADcDICADQRRqIgIgA0EgaiABEIcCQQAhASADQQA2AhwgAiACKAIAIAIoAggiBWtBAEkEfyACIAVBAEEEQQQQiAMgAigCCAUgBQs2AgggAygCHCIFRQ0BIAMoAhgiASAFQQJ0IgRqQQRrKAIABEAgBSEBDAILIAFBBGshASAFQf////8DcSECAkADQCAERQRAQQAhBAwCCyACQQFrIQIgASAEaiAEQQRrIQQoAgBFDQALIAUiASACQQFqIgRJDQILIAMgBDYCHCAEIQEMAQsgA0EoaiACQQhqKAIANgIAIAMgAikCADcDICADQRRqIAEgA0EgahCeAUEBIQQCQAJAIAVBAUcEQCAFQQEgAygCHBshBAwBCyADQQA2AhwgAygCFEEESQ0AIANBCGogA0EUakEAENMDIAMoAggiAUGBgICAeEcNAQsgACADKQIUNwIAIAAgBDoADCAAQQhqIANBHGooAgA2AgAMBQsgASADKAIMQdDPwgAQyAQAC0EBIQQgASADKAIUQQJ2Tw0AIAMgA0EUaiABENMDIAMoAgAiAUGBgICAeEYNACABIAMoAgRB0M/CABDIBAALIAAgAykCFDcCACAAIAQ6AAwgAEEIaiADQRxqKAIANgIADAILIAJBDWohAQJAAkACQCAEQQFrDgIBAgALIABBAjoADCAAIAIpAgA3AgAgACABLwAAOwANIABBCGogAkEIaigCADYCACAAQQ9qIAFBAmotAAA6AAAMAwsgAEEBOgAMIAAgAikCADcCACAAIAEvAAA7AA0gAEEIaiACQQhqKAIANgIAIABBD2ogAUECai0AADoAAAwCCyAAQQA6AAwgACACKQIANwIAIAAgAS8AADsADSAAQQhqIAJBCGooAgA2AgAgAEEPaiABQQJqLQAAOgAADAELIAIoAgAiAEUNACACKAIEIABBAnQQ3wQLIANBMGokAAukCQERfyMAQSBrIgkkACACKAIEIQcgASgCBCEGAkACQAJAAkAgASgCCCIIIAIoAggiBE0EQAJAIAgEQCAIQQFxAkAgCEEBRgRADAELIAhB/v///wFxIQ4gByEBIAYhAwNAIAEgAygCACIPIAEoAgAiEGsiESAFazYCACABQQRqIgsgA0EEaigCACIMIAsoAgAiC2siEiAPIBBJIAUgEUtyIgVrNgIAIAsgDEsgBSASS3IhBSABQQhqIQEgA0EIaiEDIA4gCkECaiIKRw0ACwsEfyAHIApBAnQiAWoiAyABIAZqKAIAIgEgAygCACIDayIGIAVrNgIAIAEgA0kgBSAGS3IFIAULQQFxDQELIAQgCE0NAiAIQQJ0IQEgBEECdCEDA0AgASAHaigCAA0BIAFBBGoiASADRw0ACwwCCyAJQQA2AhggCUEBNgIMIAlBxIrFADYCCCAJQgQ3AhAgCUEIakHcisUAEKgEAAsgBiAEQQJ0aiENAkACQCAEBEAgBEEBcSEOIARBAUcNAQwCC0EAIQEgAigCACAISQRAIAJBACAIEIkDIAIoAgQhByACKAIIIQELIAhBAnQiAwRAIAcgAUECdGogDSAD/AoAAAsgAiABIAhqIgQ2AgggAigCACEFDAMLIARB/v///wFxIQ8gByEBIAYhAwNAIAEgAygCACIQIAEoAgAiEWsiCyAFazYCACABQQRqIgwgA0EEaigCACISIAwoAgAiDGsiEyAQIBFJIAUgC0tyIgVrNgIAIAwgEksgBSATS3IhBSABQQhqIQEgA0EIaiEDIA8gCkECaiIKRw0ACwsgDgRAIAcgCkECdCIBaiIDIAEgBmooAgAiASADKAIAIgNrIgYgBWs2AgAgASADSSAFIAZLciEFCyAIIARrIgFBAnQhBiAEIQMgAigCACAEayABSQRAIAIgBCABEIkDIAIoAgQhByACKAIIIQMLIAYEQCAHIANBAnRqIA0gBvwKAAALIAIgASADaiIGNgIIAkAgBUEBcUUNACAEIAZNBEACQCAEIAZGDQAgByAEQQJ0aiIBIAEoAgAiBUEBazYCACAFDQIgASAEIAZHIgVBAnRqIQEgAyAIakECdCAFQQJ0ayAEQQN0ayEDA0AgA0UNASABIAEoAgAiBEEBazYCACADQQRrIQMgAUEEaiEBIARFDQALDAILIAlBADYCGCAJQQE2AgwgCUHEisUANgIIIAlCBDcCECAJQQhqQcyKxQAQqAQACyAEIAZBnL7EABDkBAALIAYhBAsgAigCACEFIARFDQELIAcgBEECdCIBakEEaygCAA0BIARB/////wNxIQMDQCABRQ0BIANBAWshAyABQQRrIgEgB2ooAgBFDQALIANBAWoiASAEIAEgBEkbIQQMAQtBACEECwJAAkAgBUECdiAETQRAIAchAyAFIQEMAQtBACEBIAVFBEAgByEDDAELIAVBAnQhAiAERQRAQQQhAyAHIAIQ3wQMAQsgByACQQQgBCIBQQJ0IgIQzgQiA0UNAQsgACAENgIIIAAgAzYCBCAAIAE2AgAgCUEgaiQADwtBBCACQYzBxAAQyAQAC+MLAgF/EX4jAEHgAmsiAiQAIAJBoAJqQgA3AwAgAkGYAmpCADcDACACQZACakIANwMAIAJBiAJqQgA3AwAgAkIANwOAAiACQgE3A6gCIAEpAwAhDSABKQMIIQ4gASkDECEPIAEpAxghECABKQMgIREgASkDKCESQSghAQNAIAJB8ABqIAJBgAJqIAFqKQMAIgVCACASQgAQyQMgAkGAAWogBUIAIBFCABDJAyACQZABaiAFQgAgEEIAEMkDIAJBoAFqIAVCACAPQgAQyQMgAkGwAWogBUIAIA5CABDJAyACQcABaiAFQgAgDUIAEMkDIAJB4ABqIAIpA3AiCyAMfCIKQgBCAEL9//P/z///+Yl/EMkDIAJB0ABqIAIpA2giBUIAQqvV/v///7//uX9CABDJAyACQUBrIAVCAEL//8+K6///1R5CABDJAyACQTBqIAVCAEKk7MO1j9S0mOcAQgAQyQMgAkEgaiAFQgBCv6WUnM/w0rvkAEIAEMkDIAJBEGogBUIAQtfZrprk9umNywBCABDJAyACIAVCAEKazf/Lo73EgBpCABDJAyACKQMIIAIpA8ABIhMgBHwiBSACKQO4ASACKQOwASIEIAh8IgggBFStfCAIIAIpA6gBIAIpA6ABIgQgB3wiByAEVK18IAcgAikDmAEgAikDkAEiBCAGfCIGIARUrXwgBiACKQOIASACKQOAASIEIAN8IgMgBFStfCADIAIpA3ggCiALVK18fCIEIANUrXx8IgMgBlStfHwiBiAHVK18fCIHIAhUrXx8IgsgAikDAHwiCCALVK18IAggCCACKQMYIAcgByACKQMQfCIHVq18IAcgByACKQMoIAYgBiACKQMgfCIGVq18IAYgBiACKQM4IAMgAyACKQMwfCIDVq18IAMgAyACKQNIIAIpA0AiDCAEfCIEIAxUrXwgBCACKQNYIAogAikDUCIKfCAKVK18fCIMIARUrXx8IgNWrXx8IgZWrXx8IgdWrXx8IghWrXwiCiAFIAtWrSACKQPIASAFIBNUrXx8IgUgCXwiCXwiBCAKVK0gBSAJVq18IQkgAUEIayIBQXhHDQALAkACQCAJQgBSIARCms3/y6O9xIAaVnINAAJAIARCms3/y6O9xIAaUQRAIAhC19mumuT26Y3LAFYNAiAIQtfZrprk9umNywBSBEAgAyEFIAYhCSAHIQogCCELQprN/8ujvcSAGiEEDAQLIAdCv6WUnM/w0rvkAFYNAkLX2a6a5PbpjcsAIQsgB0K/pZScz/DSu+QAUgRAIAMhBSAGIQkgByEKQprN/8ujvcSAGiEEDAQLIAZCpOzDtY/UtJjnAFYNAkK/pZScz/DSu+QAIQogBkKk7MO1j9S0mOcAUgRAIAMhBSAGIQlCms3/y6O9xIAaIQQMBAsgA0L//8+K6///1R5WDQJCpOzDtY/UtJjnACEJIANC///Piuv//9UeUQ0BIAMhBUKazf/Lo73EgBohBAwDCyADIQUgBiEJIAchCiAIIQsMAgtC///Piuv//9UeIQUgDEKr1f7///+//7l/Wg0AQprN/8ujvcSAGiEEDAELIANC///Piuv//9UefSIJIAxCq9X+////v/+5f1StIgp9IQUgBkKk7MO1j9S0mOcAfSILIANC///Piuv//9UeVCAJIApUcq0iA30hCSAHQr+llJzP8NK75AB9Ig0gBkKk7MO1j9S0mOcAVCADIAtWcq0iA30hCiAIQtfZrprk9umNywB9IgYgB0K/pZScz/DSu+QAVCADIA1Wcq0iA30hCyAEIAhC19mumuT26Y3LAFQgAyAGVnKtfUKazf/Lo73EgBp9IQQgDELVqoGAgIDAgMYAfCEMCyACIAw3A/gBIAIgBTcD8AEgAiAJNwPoASACIAo3A+ABIAIgCzcD2AEgAiAENwPQASACIAJBgAJqNgLcAiACQQA2AsQCIAJBADYCsAIgAiACQdABajYC2AIgACACQbACahCtAiACQeACaiQAC4kKAiB/AX4jAEHABGsiAiQAQdHOxQAtAAAaQcAEQQgQ1gQiAwRAIAMgAUHABPwKAAAgAykDACEiIANBwAQQ3wQgAiAiNwMAIAJBCGogAUEIakGYAvwKAAAgAkGgAmoiBCACEKQBIABBKGogAkHIAmoiAykDADcDACAAQSBqIAJBwAJqIgUpAwA3AwAgAEEYaiACQbgCaiIGKQMANwMAIABBEGogAkGwAmoiBykDADcDACAAQQhqIAJBqAJqIggpAwA3AwAgACACKQOgAjcDACAAIAIpA9ACNwMwIABBOGogAkHYAmoiCSkDADcDACAAQUBrIAJB4AJqIgopAwA3AwAgAEHIAGogAkHoAmoiCykDADcDACAAQdAAaiACQfACaiIMKQMANwMAIABB2ABqIAJB+AJqIg0pAwA3AwAgAEGIAWogAkGoA2oiDikDADcDACAAQYABaiACQaADaiIPKQMANwMAIABB+ABqIAJBmANqIhApAwA3AwAgAEHwAGogAkGQA2oiESkDADcDACAAQegAaiACQYgDaiISKQMANwMAIAAgAikDgAM3A2AgAEG4AWogAkHYA2oiEykDADcDACAAQbABaiACQdADaiIUKQMANwMAIABBqAFqIAJByANqIhUpAwA3AwAgAEGgAWogAkHAA2oiFikDADcDACAAQZgBaiACQbgDaiIXKQMANwMAIAAgAikDsAM3A5ABIABB6AFqIAJBiARqIhgpAwA3AwAgAEHgAWogAkGABGoiGSkDADcDACAAQdgBaiACQfgDaiIaKQMANwMAIABB0AFqIAJB8ANqIhspAwA3AwAgAEHIAWogAkHoA2oiHCkDADcDACAAIAIpA+ADNwPAASAAQZgCaiACQbgEaiIdKQMANwMAIABBkAJqIAJBsARqIh4pAwA3AwAgAEGIAmogAkGoBGoiHykDADcDACAAQYACaiACQaAEaiIgKQMANwMAIABB+AFqIAJBmARqIiEpAwA3AwAgACACKQOQBDcD8AEgBCABQaACahCkASAAQcgCaiADKQMANwMAIABBwAJqIAUpAwA3AwAgAEG4AmogBikDADcDACAAQbACaiAHKQMANwMAIABBqAJqIAgpAwA3AwAgACACKQOgAjcDoAIgACACKQPQAjcD0AIgAEHYAmogCSkDADcDACAAQeACaiAKKQMANwMAIABB6AJqIAspAwA3AwAgAEHwAmogDCkDADcDACAAQfgCaiANKQMANwMAIABBqANqIA4pAwA3AwAgAEGgA2ogDykDADcDACAAQZgDaiAQKQMANwMAIABBkANqIBEpAwA3AwAgAEGIA2ogEikDADcDACAAIAIpA4ADNwOAAyAAQdgDaiATKQMANwMAIABB0ANqIBQpAwA3AwAgAEHIA2ogFSkDADcDACAAQcADaiAWKQMANwMAIABBuANqIBcpAwA3AwAgACACKQOwAzcDsAMgAEGIBGogGCkDADcDACAAQYAEaiAZKQMANwMAIABB+ANqIBopAwA3AwAgAEHwA2ogGykDADcDACAAQegDaiAcKQMANwMAIAAgAikD4AM3A+ADIABBuARqIB0pAwA3AwAgAEGwBGogHikDADcDACAAQagEaiAfKQMANwMAIABBoARqICApAwA3AwAgAEGYBGogISkDADcDACAAIAIpA5AENwOQBCACQcAEaiQADwtBCEHABEHwtcIAEMgEAAuICgIJfwF+IwBB4ABrIgMkAAJAAkACQAJAAkAgAigCCCIGBEAgASgCCCIFRQRAIABBCGpB7PTEACgCACIBNgIAIABB5PTEACkCACIMNwIAIAAgDDcCDCAAQRRqIAE2AgAMBQsgAigCBCEHAkACQAJAIAZBAUcEQAJ/IAUgBkYEQCAGQQJ0IQQgB0EEayEKIAEoAgRBBGshCwNAIARFDQUgBCAKaiEJIAQgC2ogBEEEayEEKAIAIgggCSgCACIJRg0ACyAIIAlLIAggCUlrDAELIAUgBksgBSAGSWsLQf8BcQ4CAgMBCyAHKAAAQQFGDQZB0c7FAC0AABogASgCBCEEIAVBAnQiAUEEENYEIgJFDQggAQRAIAIgBCAB/AoAAAsgAyAFNgJYIAMgAjYCVCADIAU2AlAgA0EoaiIEIANB0ABqIAcoAgAQggIgA0EQaiIFIANBMGoiASgCADYCACADIAMpAig3AwggAygCNCECIAFB7PTEACgCADYCACADQeT0xAApAgA3AyggAgRAIARB6PbEABClAyADKAIsIAI2AgAgA0EBNgIwCyAAIAMpAyg3AgwgAEEUaiABKAIANgIAIABBCGogBSgCADYCACAAIAMpAwg3AgAMBwtB0c7FAC0AABogASgCBCEEIAVBAnQiAUEEENYEIgJFDQcgAQRAIAIgBCAB/AoAAAsgACAFNgIUIAAgAjYCECAAIAU2AgwgAEHk9MQAKQIANwIAIABBCGpB7PTEACgCADYCAAwGC0HRzsUALQAAGkEEQQQQ1gQiAUUNAiAAQQE2AgggACABNgIEIABBATYCACABQQE2AgAgAEHk9MQAKQIANwIMIABBFGpB7PTEACgCADYCAAwFCyAHIAZBAnRqQQRrIgRFDQIgBCgCACIEZyIIRQRAQdHOxQAtAAAaIAEoAgQhBCAFQQJ0IgFBBBDWBCICRQ0GIAEEQCACIAQgAfwKAAALIAMgBTYCMCADIAI2AiwgAyAFNgIoIAAgA0EoaiAHIAYQewwFCyADIAE2AiwgA0GAgICAeDYCKCADQdAAaiIHIANBKGoiBiAERSIBIAhBACAEGyIFEM8BIAMgAjYCLCADQYCAgIB4NgIoIANBxABqIAYgASAFEM8BIAYgByADKAJIIgIgAygCTBB7IANBIGogA0EwaigCADYCACADIAMpAig3AxggA0HYAGogA0E8aigCADYCACADIAMpAjQ3A1AgAygCRCIEBEAgAiAEQQJ0EN8ECwJAAkAgAygCUEGAgICAeEcEQCADKAJYDQEgA0EwaiADQdgAaigCADYCACADIAMpA1A3AygMAgsgAygCVCICKAIIDQAgA0EoaiACEMADDAELIANBKGogA0HQAGogASAFEOwBCyAAIAMpAxg3AgAgACADKQMoNwIMIABBCGogA0EgaigCADYCACAAQRRqIANBMGooAgA2AgAMBAsgA0EANgI4IANBATYCLCADQdTzxAA2AiggA0IENwIwIANBKGpB4PXEABCoBAALQQRBBBD/BAALQfj2xAAQ6AQAC0HRzsUALQAAGiABKAIEIQQgBUECdCIBQQQQ1gQiAgRAIAEEQCACIAQgAfwKAAALIAAgBTYCCCAAIAI2AgQgACAFNgIAIABB5PTEACkCADcCDCAAQRRqQez0xAAoAgA2AgAMAQsMAQsgA0HgAGokAA8LQQQgAUGkg8UAEMgEAAumCQIHfg9/IwBBMGsiCyQAIAsgAzYCKCABKAIMIRAgCyALQShqNgIsAkACQAJAAn8CQCAQIAIgEGoiA00EQCABKAIEIhEgEUEBakEDdkEHbCARQQhJGyICQQF2IANJBEAgAkEBaiICIAMgAiADSxsiAkEISQ0CQX8gAkEDdEEHbkEBa2d2QQFqIAJB/////wFNDQMaEPUDIAsoAiQhAyALKAIgIQIMBgsgASALQSxqQTpBDBDEAUGBgICAeCECDAULEPUDIAsoAgwhAyALKAIIIQIMBAtBBEEIIAJBBEkbCyIDrUIMfiIFQiCIpw0AIAWnIgJBeEsNACACQQdqQXhxIg4gA0EIaiISaiICIA5JIAJB+P///wdLcg0AQdHOxQAtAAAaIAJBCBDWBCINDQEgAhC+BCALKAIcIQMgCygCGCECDAILEPUDIAsoAhQhAyALKAIQIQIMAQsgDSAOaiENIBIEQCANQf8BIBL8CwALIANBAWsiEyADQQN2QQdsIANBCUkbIRUCQCAQRQRAIAEoAgAhDgwBCyANQQhqIRYgASgCACIOQQxrIRcgDikDAEJ/hUKAgYKEiJCgwIB/gyEFIAsoAighFEEAIQMgECESIA4hAgNAIAVQBEADQCADQQhqIQMgAkEIaiICKQMAQoCBgoSIkKDAgH+DIgVCgIGChIiQoMCAf1ENAAsgBUKAgYKEiJCgwIB/hSEFCyANIBMgFCkDCCIEIBcgBXqnQQN2IANqIhhBdGxqNQIAQoCAgICAgICABIQiBoVC88rRy6eM2bL0AIUiB0IQiSAHIBQpAwAiCELh5JXz1uzZvOwAhXwiB4UiCUIViSAJIARC7d6R85bM3LfkAIUiBCAIQvXKzYPXrNu38wCFfCIIQiCJfCIJhSIKQhCJIAogByAEQg2JIAiFIgR8IgdCIIlC/wGFfCIIhSIKQhWJIAogByAEQhGJhSIEIAYgCYV8IgZCIIl8IgeFIglCEIkgCSAGIARCDYmFIgQgCHwiBkIgiXwiCIUiCUIViSAJIAYgBEIRiYUiBCAHfCIGQiCJfCIHhSIJQhCJIAkgBEINiSAGhSIEIAh8IgZCIIl8IgiFQhWJIARCEYkgBoUiBEINiSAEIAd8hSIEQhGJhSAEIAh8IgRCIIiFIASFpyIZcSIMaikAAEKAgYKEiJCgwIB/gyIEUARAQQghDwNAIAwgD2ohDCAPQQhqIQ8gDSAMIBNxIgxqKQAAQoCBgoSIkKDAgH+DIgRQDQALCyAFQgF9IAWDIQUgDSAEeqdBA3YgDGogE3EiDGosAABBAE4EQCANKQMAQoCBgoSIkKDAgH+DeqdBA3YhDAsgDCANaiAZQRl2Ig86AAAgFiAMQQhrIBNxaiAPOgAAIA0gDEF/c0EMbGoiDEEIaiAOIBhBf3NBDGxqIg9BCGooAAA2AAAgDCAPKQAANwAAIBJBAWsiEg0ACwsgASATNgIEIAEgDTYCACABIBUgEGs2AghBgYCAgHghAiARRQ0AIBEgEUEMbEETakF4cSIDakEJaiIBRQ0AIA4gA2sgARDfBAsgACADNgIEIAAgAjYCACALQTBqJAALzgkCCn8DfiMAQfAAayIEJAAgAwRAIARBCGoiA0Gs/MAAKAIANgIAIARBpPzAACkCADcDACACBEAgBEGY/cAAEKUDIAQoAgQgAjYCACAEQQE2AggLIARB6ABqIAMoAgA2AgAgBCAEKQMANwNgIAAoAggiAyAAKAIARgRAIABBtJLBABCfAwsgACgCBCADQQxsaiIGIAQpA2A3AgAgBkEIaiAEQegAaigCADYCACAAIANBAWo2AggLIAIEQCABIAJBMGxqIQsgBEHoAGohBkGs/MAAKAIAIQpBpPzAACkCACEQA0AgBCABEN8BIAQpAwghDiAEKQMAIQ8gBiAKNgIAIAQgEDcDYCAOIA+EUEUEQEEBIQJBACEDA0AgBCgCYCACQQFrRgRAIARB4ABqQaj9wAAQpQMLIAQoAmQgA2ogDz4CACAPQv////8PViAOQgBSIA5QIA5CIIYgD0IgiIQhDyADQQRqIQMgDkIgiCEOIAQgAjYCaCACQQFqIQIbDQALCyAEQdgAaiIHIAYoAgA2AgAgBCAEKQNgNwNQIAAoAggiAiAAKAIARgRAIABBtJLBABCfAwsgACgCBCACQQxsaiIDIAQpA1A3AgAgA0EIaiAHKAIANgIAIAAgAkEBaiIFNgIIIAQpAxghDiAEKQMQIQ8gBiAKNgIAIAQgEDcDYCAOIA+EUEUEQEEBIQJBACEDA0AgBCgCYCACQQFrRgRAIARB4ABqQaj9wAAQpQMLIAQoAmQgA2ogDz4CACAPQv////8PViAOQgBSIA5QIA5CIIYgD0IgiIQhDyADQQRqIQMgDkIgiCEOIAQgAjYCaCACQQFqIQIbDQALIAAoAgghBQsgByAGKAIANgIAIAQgBCkDYDcDUCAAKAIAIAVGBEAgAEG0ksEAEJ8DCyAAKAIEIAVBDGxqIgIgBCkDUDcCACACQQhqIAcoAgA2AgAgACAFQQFqIgg2AgggBCkDKCEOIAQpAyAhDyAGIAo2AgAgBCAQNwNgIA4gD4RQRQRAQQEhAkEAIQMDQCAEKAJgIAJBAWtGBEAgBEHgAGpBqP3AABClAwsgBCgCZCADaiAPPgIAIA9C/////w9WIA5CAFIgDlAgDkIghiAPQiCIhCEPIANBBGohAyAOQiCIIQ4gBCACNgJoIAJBAWohAhsNAAsLIAcgBigCADYCACAEIAQpA2A3A1AgACgCACAIRgRAIABBtJLBABCfAwsgACgCBCAIQQxsaiICIAQpA1A3AgAgAkEIaiAHKAIANgIAIAAgBUECaiICNgIIIAQpAzghDiAEKQMwIQ8gBiAKNgIAIAQgEDcDYCAOIA+EUEUEQEEBIQJBACEDA0AgBCgCYCACQQFrRgRAIARB4ABqQaj9wAAQpQMLIAQoAmQgA2ogDz4CACAPQv////8PViAOQgBSIA5QIA5CIIYgD0IgiIQhDyADQQRqIQMgDkIgiCEOIAQgAjYCaCACQQFqIQIbDQALIAAoAgghAgsgByAGKAIANgIAIAQgBCkDYDcDUCAAKAIAIAJGBEAgAEG0ksEAEJ8DCyAAKAIEIAJBDGxqIgMgBCkDUDcCACADQQhqIAcoAgA2AgAgACACQQFqNgIIIAFBMGoiASALRw0ACwsgBEHwAGokAAv8CAIIfwF+IwBBwAZrIgIkAEHRzsUALQAAGgJAAkACQAJAQaACQQgQ1gQiAwRAIAMgAUGgAvwKAABBACIBRQRAIANBwAFqIgQgBEHgAPwKAAALIAMpAwAhCiACQaACaiIEIANBCGpBmAL8CgAAIANBoAIQ3wQgAiAKNwMAIAJBCGogBEHYAPwKAAAgAUUEQCACQeAAaiACQfgCakHgAPwKAAALIAFFBEAgAkHAAWogAkHYA2pB4AD8CgAACyACQaACaiACEPcDIAIoAqQCIQEgAigCoAIhAyACKAKoAiIEQQJHDQEgASgCBCEEIAEoAgAhByACQbgEaiABQQhqQdgA/AoAACADBEAgASADQTBsEN8ECyACQaACaiACQeAAahD3AyACKAKkAiEBIAIoAqACIQMgAigCqAIiBUECRw0CIAEoAgQhBSABKAIAIQggAkGQBWogAUEIakHYAPwKAAAgAwRAIAEgA0EwbBDfBAsgAkGgAmogAkHAAWoQ9wMgAigCpAIhASACKAKgAiEDIAIoAqgCIgZBAkcNAyABKAIEIQYgASgCACEJIAJB6AVqIAFBCGpB2AD8CgAAIAMEQCABIANBMGwQ3wQLIAAgAikD6AU3A8gBIAAgAikDkAY3A/ABIABB6AFqIAJBiAZqKQMANwMAIABB4AFqIAJBgAZqKQMANwMAIABB2AFqIAJB+AVqKQMANwMAIABB0AFqIAJB8AVqKQMANwMAIABB+AFqIAJBmAZqKQMANwMAIABBgAJqIAJBoAZqKQMANwMAIABBiAJqIAJBqAZqKQMANwMAIABBkAJqIAJBsAZqKQMANwMAIABBmAJqIAJBuAZqKQMANwMAIAAgBjYCxAEgACAJNgLAASAAIAc2AgAgACAENgIEIAAgAikDuAQ3AwggAEEQaiACQcAEaikDADcDACAAQRhqIAJByARqKQMANwMAIABBIGogAkHQBGopAwA3AwAgAEEoaiACQdgEaikDADcDACAAQdgAaiACQYgFaikDADcDACAAQdAAaiACQYAFaikDADcDACAAQcgAaiACQfgEaikDADcDACAAQUBrIAJB8ARqKQMANwMAIABBOGogAkHoBGopAwA3AwAgACACKQPgBDcDMCAAIAU2AmQgACAINgJgIABBiAFqIAJBsAVqKQMANwMAIABBgAFqIAJBqAVqKQMANwMAIABB+ABqIAJBoAVqKQMANwMAIABB8ABqIAJBmAVqKQMANwMAIAAgAikDkAU3A2ggAEG4AWogAkHgBWopAwA3AwAgAEGwAWogAkHYBWopAwA3AwAgAEGoAWogAkHQBWopAwA3AwAgAEGgAWogAkHIBWopAwA3AwAgAEGYAWogAkHABWopAwA3AwAgACACKQO4BTcDkAEgAkHABmokAA8LQQhBoAJB8LXCABDIBAALIAIgBDYCqAIMAgsgAiAFNgKoAgwBCyACIAY2AqgCCyACIAE2AqQCIAIgAzYCoAJBgIvAAEErIAJBoAJqQayLwABBpI3AABDKAwALmgkCB34PfyMAQTBrIgskACALIAM2AiggASgCDCEQIAsgC0EoajYCLAJAAkACQAJ/AkAgECACIBBqIgNNBEAgASgCBCIRIBFBAWpBA3ZBB2wgEUEISRsiAkEBdiADSQRAIAJBAWoiAiADIAIgA0sbIgJBCEkNAiACQf////8BTQRAQX8gAkEDdEEHbkEBa2d2IgJB/v///wBLDQUgAkEBagwECxD1AyALKAIkIQMgCygCICECDAYLIAEgC0EsakE5QRAQxAFBgYCAgHghAgwFCxD1AyALKAIMIQMgCygCCCECDAQLQQRBCCACQQRJGwsiA0EEdCIOIANBCGoiEmoiAiAOSSACQfj///8HS3INAEHRzsUALQAAGiACQQgQ1gQiDQ0BIAIQvgQgCygCHCEDIAsoAhghAgwCCxD1AyALKAIUIQMgCygCECECDAELIA0gDmohDSASBEAgDUH/ASAS/AsACyADQQFrIhMgA0EDdkEHbCADQQlJGyEVAkAgEEUEQCABKAIAIQ4MAQsgDUEIaiEWIAEoAgAiDkEQayEXIA4pAwBCf4VCgIGChIiQoMCAf4MhBSALKAIoIRRBACEDIBAhEiAOIQIDQCAFUARAA0AgA0EIaiEDIAJBCGoiAikDAEKAgYKEiJCgwIB/gyIFQoCBgoSIkKDAgH9RDQALIAVCgIGChIiQoMCAf4UhBQsgDSATIBQpAwgiBCAXIAV6p0EDdiADaiIYQQR0azUCAEKAgICAgICAgASEIgaFQvPK0cunjNmy9ACFIgdCEIkgByAUKQMAIghC4eSV89bs2bzsAIV8IgeFIglCFYkgCSAEQu3ekfOWzNy35ACFIgQgCEL1ys2D16zbt/MAhXwiCEIgiXwiCYUiCkIQiSAKIAcgBEINiSAIhSIEfCIHQiCJQv8BhXwiCIUiCkIViSAKIAcgBEIRiYUiBCAGIAmFfCIGQiCJfCIHhSIJQhCJIAkgBiAEQg2JhSIEIAh8IgZCIIl8IgiFIglCFYkgCSAGIARCEYmFIgQgB3wiBkIgiXwiB4UiCUIQiSAJIARCDYkgBoUiBCAIfCIGQiCJfCIIhUIViSAEQhGJIAaFIgRCDYkgBCAHfIUiBEIRiYUgBCAIfCIEQiCIhSAEhaciGXEiDGopAABCgIGChIiQoMCAf4MiBFAEQEEIIQ8DQCAMIA9qIQwgD0EIaiEPIA0gDCATcSIMaikAAEKAgYKEiJCgwIB/gyIEUA0ACwsgBUIBfSAFgyEFIA0gBHqnQQN2IAxqIBNxIgxqLAAAQQBOBEAgDSkDAEKAgYKEiJCgwIB/g3qnQQN2IQwLIAwgDWogGUEZdiIPOgAAIBYgDEEIayATcWogDzoAACANIAxBf3NBBHRqIgxBCGogDiAYQX9zQQR0aiIPQQhqKQAANwAAIAwgDykAADcAACASQQFrIhINAAsLIAEgEzYCBCABIA02AgAgASAVIBBrNgIIQYGAgIB4IQIgEUUNACARIBFBBHRBF2pBcHEiA2pBCWoiAUUNACAOIANrIAEQ3wQLIAAgAzYCBCAAIAI2AgAgC0EwaiQAC5ELAgF/EX4jAEGAAmsiAiQAIAJB8AFqQgA3AwAgAkHoAWpCADcDACACQeABakIANwMAIAJB2AFqQgA3AwAgAkIANwPQASACQgE3A/gBIAEpAwAhDSABKQMIIQ4gASkDECEPIAEpAxghECABKQMgIREgASkDKCESQSghAQNAIAJB8ABqIAJB0AFqIAFqKQMAIgRCACASQgAQyQMgAkGAAWogBEIAIBFCABDJAyACQZABaiAEQgAgEEIAEMkDIAJBoAFqIARCACAPQgAQyQMgAkGwAWogBEIAIA5CABDJAyACQcABaiAEQgAgDUIAEMkDIAJB4ABqIAIpA3AiCyAMfCIJQgBCAEL9//P/z///+Yl/EMkDIAJB0ABqIAIpA2giBEIAQqvV/v///7//uX9CABDJAyACQUBrIARCAEL//8+K6///1R5CABDJAyACQTBqIARCAEKk7MO1j9S0mOcAQgAQyQMgAkEgaiAEQgBCv6WUnM/w0rvkAEIAEMkDIAJBEGogBEIAQtfZrprk9umNywBCABDJAyACIARCAEKazf/Lo73EgBpCABDJAyACKQMIIAIpA8ABIhMgBXwiBCACKQO4ASACKQOwASIFIAh8IgggBVStfCAIIAIpA6gBIAIpA6ABIgUgB3wiByAFVK18IAcgAikDmAEgAikDkAEiBSAGfCIGIAVUrXwgBiACKQOIASACKQOAASIFIAN8IgMgBVStfCADIAIpA3ggCSALVK18fCIFIANUrXx8IgMgBlStfHwiBiAHVK18fCIHIAhUrXx8IgsgAikDAHwiCCALVK18IAggCCACKQMYIAcgByACKQMQfCIHVq18IAcgByACKQMoIAYgBiACKQMgfCIGVq18IAYgBiACKQM4IAMgAyACKQMwfCIDVq18IAMgAyACKQNIIAIpA0AiDCAFfCIFIAxUrXwgBSACKQNYIAkgAikDUCIJfCAJVK18fCIMIAVUrXx8IgNWrXx8IgZWrXx8IgdWrXx8IghWrXwiCSAKIAQgC1atIAIpA8gBIAQgE1StfHwiCnwiBHwiBSAJVK0gBCAKVK18IQogAUEIayIBQXhHDQALAkACQAJAAkAgCkIAUiAFQprN/8ujvcSAGlZyDQAgBUKazf/Lo73EgBpSDQEgCELX2a6a5PbpjcsAVg0AIAhC19mumuT26Y3LAFIEQCADIQogBiEEIAchCSAIIQtCms3/y6O9xIAaIQUMBAsgB0K/pZScz/DSu+QAVg0AQtfZrprk9umNywAhCyAHQr+llJzP8NK75ABSBEAgAyEKIAYhBCAHIQlCms3/y6O9xIAaIQUMBAsgBkKk7MO1j9S0mOcAVg0AQr+llJzP8NK75AAhCSAGQqTsw7WP1LSY5wBSBEAgAyEKIAYhBEKazf/Lo73EgBohBQwECyADQv//z4rr///VHlYNAEKk7MO1j9S0mOcAIQQgA0L//8+K6///1R5SIAxCqtX+////v/+5f1hyDQILIANC///Piuv//9UefSIEIAxCq9X+////v/+5f1StIgl9IQogBkKk7MO1j9S0mOcAfSILIANC///Piuv//9UeVCAEIAlUcq0iA30hBCAHQr+llJzP8NK75AB9Ig0gBkKk7MO1j9S0mOcAVCADIAtWcq0iA30hCSAIQtfZrprk9umNywB9IgYgB0K/pZScz/DSu+QAVCADIA1Wcq0iA30hCyAFIAhC19mumuT26Y3LAFQgAyAGVnKtfUKazf/Lo73EgBp9IQUgDELVqoGAgIDAgMYAfCEMDAILIAMhCiAGIQQgByEJIAghCwwBCyADIQpCms3/y6O9xIAaIQULIAAgDDcDKCAAIAo3AyAgACAENwMYIAAgCTcDECAAIAs3AwggACAFNwMAIAJBgAJqJAAL+w0CC38KfiMAQdACayIDJAACQAJAAkACQAJAAkACQCABQYjSwQBBMBDxA0UEQCABQTBqIgRBiNLBAEEwEPEDRQ0BCwJAAkAgAi0ADCIJQQFHBEAgAS0AYCEEIANBCGpBAEHgAPwLACADIAQ6AGggA0HIAWogAUHYAGopAwA3AwAgA0HAAWogAUHQAGopAwA3AwAgA0G4AWogAUHIAGopAwA3AwAgA0GwAWogAUFAaykDADcDACADQagBaiABQThqKQMANwMAIANB+ABqIAFBCGopAwA3AwAgA0GAAWogAUEQaikDADcDACADQYgBaiABQRhqKQMANwMAIANBkAFqIAFBIGopAwA3AwAgA0GYAWogAUEoaikDADcDACADIAEpAzA3A6ABIAMgASkDADcDcCADIAQ6ANABIAIoAgQhCiACKAIAIQtBBCEFIAkOAwECAQILIAEtAGAhASAAQQBB4AD8CwAgACABOgBgDAMLIAIoAggiB0ECdCEBIAdB/////wNLIAFB/P///wdLcg0DIAEEf0HRzsUALQAAGkEEIQYgAUEEENYEIgVFDQQgBwVBAAshBiABRQ0AIAUgCiAB/AoAAAsgB0UNBUHg98EAKAIAIQ0gA0HgAWohBEHY98EAKQIAIRMDQCAEIA02AgAgAyATNwPYASADQdgBakHM+MEAEKUDIAMoAtwBQQE2AgAgAygC3AEhCCADKALYASEMAn8gB0EBRwRAQdHOxQAtAAAaQQRBBBDWBCIBRQ0GIAEgCCgCACICNgIAIAIgBSgCAHEMAQtB0c7FAC0AABpBBEEEENYEIgFFDQYgASAFKAIAIgI2AgAgAiAIKAIAcQshAiABIAI2AgAgDARAIAggDEECdBDfBAsgAUEEEN8EIAIEQCADQdgBaiICIANBCGoiASADQfAAahAnIAEgAkHoAPwKAAALIANB2AFqIgEgA0HwAGoiAiACECcgAiABQegA/AoAACADIAc2AuABIAMgBTYC3AEgAyAGNgLYAQJAAkAgBkGAgICAeEcNACAFKAIIDQAgA0EANgLMAiADQoCAgIDAADcCxAIMAQsgA0HEAmogA0HYAWpBAEEBEOwBCyADKALEAiEGIAMoAsgCIQUgAygCzAIiBw0ACwwFCyAAIAQpAwA3AzAgACABKQMANwMAIABB2ABqIARBKGopAwA3AwAgAEHQAGogBEEgaikDADcDACAAQcgAaiAEQRhqKQMANwMAIABBQGsgBEEQaikDADcDACAAQThqIARBCGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwAgAEEgaiABQSBqKQMANwMAIABBKGogAUEoaikDADcDACAAIAEtAGA6AGALIAIoAgAiAEUNBCACKAIEIABBAnQQ3wQMBAsgBiABQfiBwAAQyAQAC0EEQQRB+IHAABDIBAALQQRBBEH4gcAAEMgEAAsgCUUEQCADQdgBaiECAkACQCADQQhqIgFBiNLBAEEwEPEDRQRAIAFBMGoiBEGI0sEAQTAQ8QNFDQELIAEpA1ghFCABKQNQIRAgASkDSCERIAEpA0AhEiABKQM4IRYgASkDMCEXAkAgAUEwakGI0sEAQTAQ8QNFBEAgFiEOIBIhDyARIRUgECETDAELQv//z4rr///VHiAQfSIPIBRCq9X+////v/+5f1atIhV9IRNCpOzDtY/UtJjnACARfSIOIA8gFVQgEEL//8+K6///1R5Wcq0iD30hFUK/pZScz/DSu+QAIBJ9IhAgDiAPVCARQqTsw7WP1LSY5wBWcq0iDn0hD0LX2a6a5PbpjcsAIBZ9IhEgDiAQViASQr+llJzP8NK75ABWcq0iEn0hDkKazf/Lo73EgBogESASVCAWQtfZrprk9umNywBWcq0gF3x9IRdCq9X+////v/+5fyAUfSEUCyACIBQ3A1ggAiATNwNQIAIgFTcDSCACIA83A0AgAiAONwM4IAIgFzcDMCACIAEpAwA3AwAMAQsgAiAEKQMANwMwIAIgASkDADcDACACQdgAaiAEQShqKQMANwMAIAJB0ABqIARBIGopAwA3AwAgAkHIAGogBEEYaikDADcDACACQUBrIARBEGopAwA3AwAgAkE4aiAEQQhqKQMANwMACyACQQhqIAFBCGopAwA3AwAgAkEQaiABQRBqKQMANwMAIAJBGGogAUEYaikDADcDACACQSBqIAFBIGopAwA3AwAgAkEoaiABQShqKQMANwMAIAIgAS0AYDoAYCABIAJB6AD8CgAACyAAIANBCGpB6AD8CgAAIAYEQCAFIAZBAnQQ3wQLIAtFDQAgCiALQQJ0EN8ECyADQdACaiQAC6kJAgt/AX4jAEHwAWsiAyQAAkACQAJAAkACQAJAAkAgAUHo0cEAQSAQ8QNFBEAgAUEgaiIEQejRwQBBIBDxA0UNAQsCQAJAIAItAAwiCEEBRwRAIANBEGpCADcDACADQRhqQgA3AwAgA0EgakIANwMAIANBKGpCADcDACADQTBqQgA3AwAgA0E4akIANwMAIANBQGtCADcDACADQgA3AwggAyABLQBAIgQ6AEggA0GIAWogAUE4aikDADcDACADQYABaiABQTBqKQMANwMAIANB+ABqIAFBKGopAwA3AwAgA0HYAGogAUEIaikDADcDACADQeAAaiABQRBqKQMANwMAIANB6ABqIAFBGGopAwA3AwAgAyAEOgCQASADIAEpAyA3A3AgAyABKQMANwNQIAIoAgQhCSACKAIAIQpBBCEFQQAhBCAIDgMBAgECCyAAQgA3AwAgAEEIakIANwMAIABBEGpCADcDACAAQRhqQgA3AwAgAEEgakIANwMAIABBKGpCADcDACAAQTBqQgA3AwAgAEE4akIANwMADAMLIAIoAggiBkECdCEBIAZB/////wNLIAFB/P///wdLcg0DAn8gAUUEQEEADAELQdHOxQAtAAAaQQQhBCABQQQQ1gQiBUUNBCAGCyEEIAFFDQAgBSAJIAH8CgAACyAGRQ0FQeD3wQAoAgAhDCADQaABaiENQdj3wQApAgAhDgNAIA0gDDYCACADIA43A5gBIANBmAFqQcz4wQAQpQMgAygCnAFBATYCACADKAKcASEHIAMoApgBIQsCfyAGQQFHBEBB0c7FAC0AABpBBEEEENYEIgFFDQYgASAHKAIAIgI2AgAgAiAFKAIAcQwBC0HRzsUALQAAGkEEQQQQ1gQiAUUNBiABIAUoAgAiAjYCACACIAcoAgBxCyECIAEgAjYCACALBEAgByALQQJ0EN8ECyABQQQQ3wQgAgRAIANBmAFqIgEgA0EIaiICIANB0ABqEDYgAiABQcgA/AoAAAsgA0GYAWoiAiADQdAAaiIBIAEQNiABIAJByAD8CgAAIAMgBjYCoAEgAyAFNgKcASADIAQ2ApgBAkACQCAEQYCAgIB4Rw0AIAUoAggNACADQQA2AuwBIANCgICAgMAANwLkAQwBCyADQeQBaiADQZgBakEAQQEQ7AELIAMoAuQBIQQgAygC6AEhBSADKALsASIGDQALDAULIAAgBCkDADcDICAAIAEpAwA3AwAgAEE4aiAEQRhqKQMANwMAIABBMGogBEEQaikDADcDACAAQShqIARBCGopAwA3AwAgAEEIaiABQQhqKQMANwMAIABBEGogAUEQaikDADcDACAAQRhqIAFBGGopAwA3AwALIAAgAS0AQDoAQCACKAIAIgBFDQQgAigCBCAAQQJ0EN8EDAQLIAQgAUH4gcAAEMgEAAtBBEEEQfiBwAAQyAQAC0EEQQRB+IHAABDIBAALIAhFBEAgA0GYAWoiASADQQhqIgIQ3QIgAiABQcgA/AoAAAsgACADQQhqQcgA/AoAACAEBEAgBSAEQQJ0EN8ECyAKRQ0AIAkgCkECdBDfBAsgA0HwAWokAAu3BwIKfwJ+IwBB8AlrIgUkACAFQcgHaiIKIAFB4ABqIgggAkHgAGoQjQEgBUGoCGoiByABIAIQjQEgBUGICWoiBiAKIAcQwQMgBSkDmAkhDyAFKQOQCSEQAkAgBSgCiAlBAUcEQCAFQRhqIgsgBUGgCWoiDkHQAPwKAAAgBUEQaiIMIA83AwAgBSAQNwMIIAcgBUEIaiIJIAkQPyAGIAEgAhDVASAFQegAaiINIAcgBhCNASAFQZAGaiAMKQMANwMAIAVBmAZqIAspAwA3AwAgBUGgBmogBUEgaikDADcDACAFQagGaiAFQShqKQMANwMAIAVBsAZqIAVBMGopAwA3AwAgBUHABmogBUFAaykDADcDACAFQcgGaiAFQcgAaikDADcDACAFQdAGaiAFQdAAaikDADcDACAFQdgGaiAFQdgAaikDADcDACAFQeAGaiAFQeAAaikDADcDACAFIAUpAwg3A4gGIAUgBSkDODcDuAYgBiAJIAEQPyAFQcgBaiILIAYgCBCNASAFQagCaiICIAggCBDVASAFQYgDaiIMIA0gARCNASAGIAIgDBDBAyAFKQOYCSEPIAUpA5AJIRAgBSgCiAlBAUYNASAFQbgIaiAOQdAA/AoAACAFIA83A7AIIAUgEDcDqAggBiAJIAcQ1QEgBUHoA2oiAiAGELQCIAYgAiACED8gByAGIAEQjQEgCiAHIA0QjQEgBiABIAoQjQEgByACIAYQPyAFQagFaiAHIAgQjQEgBUHIBGoiCSAKQeAA/AoAACAFQZAHaiAFQZAEaikDADcDACAFQYgHaiAFQYgEaikDADcDACAFQYAHaiAFQYAEaikDADcDACAFQfgGaiAFQfgDaikDADcDACAFQfAGaiAFQfADaikDADcDACAFQaAHaiAFQaAEaikDADcDACAFQagHaiAFQagEaikDADcDACAFQbAHaiAFQbAEaikDADcDACAFQbgHaiAFQbgEaikDADcDACAFQcAHaiAFQcAEaikDADcDACAFIAUpA+gDNwPoBiAFIAUpA5gENwOYByAGIAIgARA/IAcgBiAIEI0BIAAgBUGIBmogCyADIAQQICAAQdABaiAFQegGaiAHIAMgBBAgIABBEGogCUHAAfwKAAAgBUHwCWokAA8LIAUgDzcDkAkgBSAQNwOICUHU/sAAQSsgBUGICWpBsIXBAEHQhcEAEMoDAAsgBSAPNwOQCSAFIBA3A4gJQaCxwgBBKyAFQYgJakGkusIAQfS6wgAQygMAC6AIAg9/BH4jAEGACWsiAiQAIAIgASABQcABaiIDEOsBIAJBwAFqIgUgASADEKACIAJBgAJqIAFBQGsiBiABQYACahCgAiACQcACaiABQYABaiIHIAFBwAJqEKACIAJBiAZqQgA3AwAgAkGQBmpCADcDACACQZgGakIANwMAIAJBoAZqQgA3AwAgAkGoBmpCADcDACACQbAGakIANwMAIAJBuAZqQgA3AwAgAkHYBGoiCEHAg8AAKQMAIhE3AwAgAkHQBGoiCUG4g8AAKQMAIhI3AwAgAkHIBGoiCkGwg8AAKQMAIhM3AwAgAkHgBGoiC0IANwMAIAJB6ARqIgxCADcDACACQfAEaiINQgA3AwAgAkH4BGoiDkIANwMAIAJCADcDgAYgAkGog8AAKQMAIhQ3A8AEIAJB+AZqIA4pAwA3AwAgAkHwBmogDSkDADcDACACQegGaiAMKQMANwMAIAJB4AZqIAspAwA3AwAgAkHYBmogCCkDADcDACACQdAGaiAJKQMANwMAIAJByAZqIAopAwA3AwAgAiACKQPABDcDwAYgAkG4B2pCADcDACACQbAHakIANwMAIAJBqAdqQgA3AwAgAkGgB2pCADcDACACQZgHakIANwMAIAJBkAdqQgA3AwAgAkGIB2pCADcDACACQgA3A4AHIAJBwARqIgQgAkGABmogAxDrASACQYADaiIPIAEgBBCgAiACQcADaiIBIAYgAkGABWoiAxCgAiACQYAEaiIGIAcgAkHABWoiBxCgAiAEIAUgDxDrASAPIAQgAhDcASABIAMgAkFAayIFENwBIAYgByACQYABaiIQENwBIAJByAdqQgA3AwAgAkHQB2pCADcDACACQdgHakIANwMAIAJB4AdqQgA3AwAgAkHoB2pCADcDACACQfAHakIANwMAIAJB+AdqQgA3AwAgCCARNwMAIAkgEjcDACAKIBM3AwAgC0IANwMAIAxCADcDACANQgA3AwAgDkIANwMAIAJCADcDwAcgAiAUNwPABCACQbgIaiAOKQMANwMAIAJBsAhqIA0pAwA3AwAgAkGoCGogDCkDADcDACACQaAIaiALKQMANwMAIAJBmAhqIAgpAwA3AwAgAkGQCGogCSkDADcDACACQYgIaiAKKQMANwMAIAIgAikDwAQ3A4AIIAJB+AhqQgA3AwAgAkHwCGpCADcDACACQegIakIANwMAIAJB4AhqQgA3AwAgAkHYCGpCADcDACACQdAIakIANwMAIAJByAhqQgA3AwAgAkIANwPACCAEIAJBwAdqIAIQ6wEgACAPIAQQ3AEgAEFAayABIAMQ3AEgAEGAAWogBiAHENwBIABBwAFqIAIgAhCgAiAAQYACaiAFIAUQoAIgAEHAAmogECAQEKACIAJBgAlqJAALpQkCC38HfiMAQeAAayIFJAAgBUEYaiABEOABIAUpAiAhFiAFKAIcIQ8gBSgCGCENIAVBEGogBUEwaikCADcDACAFIAUpAig3AwggBUE4aiAFQQhqEMYBAkACQCACKAIAIgdBgICAgHhGDQAgAigCBCEJIAIoAgghASAFKAI8IQogBSAFKAJAIgg2AlwgBSABNgJYIAEgCEcNASAFQQA2AiAgBUKAgICAgAE3AhggCARAQQAhAQNAQgAhEEIAIRFCACESQgAhE0IAIRRCACEVIAEgCWotAAAEQCAGIApqIgIpAwAhECACQShqKQMAIRUgAkEgaikDACEUIAJBGGopAwAhEyACQRBqKQMAIRIgAkEIaikDACERCyAFKAIYIAFGBEAgBUEYakHEt8IAEJwDCyAFKAIcIAZqIgIgEDcDACACQShqIBU3AwAgAkEgaiAUNwMAIAJBGGogEzcDACACQRBqIBI3AwAgAkEIaiARNwMAIAUgAUEBaiIBNgIgIAZBMGohBiABIAhHDQALCyAFQdAAaiIBIAVBIGooAgA2AgAgBSAFKQIYNwNIIAUoAjgiAgRAIAogAkEwbBDfBAsgBUFAayABKAIANgIAIAUgBSkDSDcDOCAHRQ0AIAkgBxDfBAsgBSgCQCIGQTBsIQIgBSgCPCEIIAUoAjghDCAGIQECQAJAAkACQANAIAJFDQEgAUEBayEBIAJBMGsiAiAIakH4w8IAQTAQ8QNFDQALIAFBAWoiAiAGIAIgBkkbIQYMAQtB0c7FAC0AABpBMEEIENYEIgJFDQEgAkIANwMAIAJBKGpCADcDACACQSBqQgA3AwAgAkEYakIANwMAIAJBEGpCADcDACACQQhqQgA3AwBBfyEBQQEhBiAMBEAgCCAMQTBsEN8ECyACIQhBASEMCyADBEAgAygCCCICIAMoAgBGBEAgA0H0t8IAEKMDCyADKAIEIAJBBHRqIgcgFjcCCCAHIA82AgQgByANNgIAIAMgAkEBajYCCAsgBARAIAatQjB+IhCnIQdBACECIBBCIIinIAdB+P///wdLcg0CAkAgB0UEQEEIIQ4MAQtB0c7FAC0AABpBCCECIAdBCBDWBCIORQ0DIAZFDQBBACEJIAYhAgNAIAcgCUYNASAJIA5qIgogCCAJaiILKQMANwMAIApBKGogC0EoaikDADcDACAKQSBqIAtBIGopAwA3AwAgCkEYaiALQRhqKQMANwMAIApBEGogC0EQaikDADcDACAKQQhqIAtBCGopAwA3AwAgCUEwaiEJIAJBAWsiAg0ACwsgBCgCCCIHIAQoAgBGBEAgBEGEuMIAEKMDCyAEKAIEIAdBBHRqIgIgATYCDCACIAY2AgggAiAONgIEIAIgBjYCACAEIAdBAWo2AggLIAAgATYCDCAAIAY2AgggACAINgIEIAAgDDYCACAFKAIIIgAEQCAFKAIMIABBMGwQ3wQLIAMgDUVyRQRAIA8gDUEwbBDfBAsgBUHgAGokAA8LQQhBMBD/BAALIAIgB0HogcAAEMgEAAsgBUEANgIYIAVB2ABqIAVB3ABqIAVBGGpBtLfCABCXBAALtgkBBH8jAEHQB2siAyQAAkAgASgCBCIEBEAgASAEIAEoAggiBiAEIAQgBksbIgVrNgIEIAEgASgCACIEIAVBMGxqNgIAAkACQAJAAkACQCAGBEAgA0H4BGogBEEoaikDADcDACADQfAEaiAEQSBqKQMANwMAIANB6ARqIARBGGopAwA3AwAgA0HgBGogBEEQaikDADcDACADQdgEaiAEQQhqKQMANwMAIAMgBCkDADcD0AQgBUEBRg0BIANB2AVqIARB2ABqKQMANwMAIANB0AVqIARB0ABqKQMANwMAIANByAVqIARByABqKQMANwMAIANBwAVqIARBQGspAwA3AwAgA0G4BWoiBiAEQThqKQMANwMAIAMgBCkDMDcDsAUgAyADQdAEaiADQbAFakEAEDECQAJAAkAgAy0AYCIBQQJGBEAgBiADQQhqKAIANgIAIAMgAykDADcDsAUMAQsgA0GIA2ogA0HgAPwKAAAgAyADQeQAaigAADYAowIgAyADKABhNgKgAiADQagCaiADQYgDakHgAPwKAAAgBUEDSQ0FIAVBA0YNBiADQagFaiAEQbgBaikDADcDACADQaAFaiAEQbABaikDADcDACADQZgFaiAEQagBaikDADcDACADQZAFaiAEQaABaikDADcDACADQYgFaiAEQZgBaikDADcDACADQdgEaiAEQegAaikDADcDACADQeAEaiAEQfAAaikDADcDACADQegEaiAEQfgAaikDADcDACADQfAEaiAEQYABaikDADcDACADQfgEaiAEQYgBaikDADcDACADIAQpA5ABNwOABSADIAQpA2A3A9AEIAVBBE0NByAFQQVGDQggA0GIBmogBEGYAmopAwA3AwAgA0GABmogBEGQAmopAwA3AwAgA0H4BWogBEGIAmopAwA3AwAgA0HwBWogBEGAAmopAwA3AwAgA0HoBWogBEH4AWopAwA3AwAgA0G4BWoiBSAEQcgBaikDADcDACADQcAFaiAEQdABaikDADcDACADQcgFaiAEQdgBaikDADcDACADQdAFaiAEQeABaikDADcDACADQdgFaiAEQegBaikDADcDACADIAQpA/ABNwPgBSADIAQpA8ABNwOwBSADIANB0ARqIANBsAVqEGwgAygCAEUNASAFIANBDGooAgA2AgAgAyADKQIENwOwBQsgAigCACIBQYCAgIB4RiABRXJFBEAgAigCBCABEN8ECyACIAMpA7AFNwIAIAJBCGogA0G4BWooAgA2AgBBAiEBDAELIANBjANqIQIgAiADQQhqQcAB/AoAACADQbAFaiIEIAJBwAH8CgAAIANB8AZqIANBqAJqQeAA/AoAACADIAMoAKMCNgCLAyADIAMoAqACNgKIAyADIARBoAL8CgAACyAAIANBoAL8CgAAIAAgAToAoAIgACADKAKIAzYAoQIgAEGkAmogAygAiwM2AAAMBwtBAEEAQcD6wAAQ2QMAC0EBQQFB0PrAABDZAwALQQJBAkHg+sAAENkDAAtBA0EDQfD6wAAQ2QMAC0EEQQRBgPvAABDZAwALQQVBBUGQ+8AAENkDAAsgAEEDOgCgAgsgA0HQB2okAAvtBwIJfwh+IwBBEGsiByQAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASECQQFBARDWBCIGRQ0CIAZBADoAACAHQQE2AgQMAQsgB0EEaiABQQgQsAIgBygCCCEGIAcoAgwiAkECSQ0AIAIgBmohBEEAIQEgAkEBdiIFQQFHBEAgAkEBayEDIAVB/v///wdxIQkDQCADIAZqIgUtAAAhCCAFIAEgBmoiBS0AADoAACAFIAg6AAAgBCABQX5zaiIILQAAIQogCCAFQQFqIgUtAAA6AAAgBSAKOgAAIANBAmshAyAJIAFBAmoiAUcNAAsLIAJBAnEEQCABIAZqIgMtAAAhBSADIAQgAUF/c2oiAS0AADoAACABIAU6AAALIAJBMU8NAgsCQCACIAJBDGsiAUEAIAEgAk0bIgVGDQAgBSAGaiEBQQwgAiACQQxPGyIEQQNxIQMCQCAEQQFrQQNJBEAMAQsgBEEMcSEEA0AgC0IgiEKAgPz/D4MgDUIghoQgC0IQhiILQjCIhCENIAFBA2oxAAAgAUEBajEAACALIAExAABCCIaEhEIQhiABQQJqMQAAQgiGhIQhCyABQQRqIQEgBEEEayIEDQALCyADRQ0AA0AgDUIIhiALQjiIhCENIAExAAAgC0IIhoQhCyABQQFqIQEgA0EBayIDDQALCyACQRhrIgFBACABIAJNGyIEIAVHBEAgBCAGaiEBQRggAiACQRhPG0EMIAIgAkEMTxtrIQMDQCARQgiGIA9COIiEIREgATEAACAPQgiGhCEPIAFBAWohASADQQFrIgMNAAsLIAQgAkEkayIBQQAgASACTRsiBEcEQEEkIAIgAkEkTxtBGCACIAJBGE8bayEDIAQgBmohAQNAIBJCCIYgEEI4iIQhEiABMQAAIBBCCIaEIRAgAUEBaiEBIANBAWsiAw0ACwsCQCACQSVJDQAgBEEDcSEDAkAgAkEla0EDSQRAIAYhAQwBCyAEQRxxIQQgBiEBA0AgDEIgiEKAgPz/D4MgDkIghoQgDEIQhiIMQjCIhCEOIAFBA2oxAAAgAUEBajEAACAMIAExAABCCIaEhEIQhiABQQJqMQAAQgiGhIQhDCABQQRqIQEgBEEEayIEDQALCyADRQ0AA0AgDkIIhiAMQjiIhCEOIAExAAAgDEIIhoQhDCABQQFqIQEgA0EBayIDDQALCyAAIAw3AzAgACAQNwMgIAAgDzcDECAAIAs3AwAgACAONwM4IAAgEjcDKCAAIBE3AxggACANNwMIIAcoAgQiAARAIAYgABDfBAsgB0EQaiQADwtBAUEBEP8EAAtB1NrCAEEtQYTbwgAQ/gMAC9sIAgh/An4jAEHQAGsiAyQAAkAgAi0ADCIHQQFGBEAgACABKQIANwIAIABBCGogAUEIaikCADcCACACKAIAIgBFDQEgAigCBCAAQQJ0EN8EDAELAkACQAJAAkACQAJAAkACQAJAIAEtAAwiCEEBaw4CAAIBCyAAIAIpAgA3AgAgAEEIaiACQQhqKQIANwIADAYLIAdFDQEMAgsgB0UNAQsgA0EoaiABQQhqIgYoAgA2AgAgAyABKQIAIgs3AyAgA0E4aiACQQhqIgkoAgA2AgAgAyACKQIAIgw3AzACfyALpyIEIAynIgdJBEAgA0HIAGogCSgCADYCACADIAIpAgA3A0AgA0EUaiADQUBrIANBIGoQygEgA0EkagwBCyADQcgAaiAGKAIANgIAIAMgASkCADcDQCADQRRqIANBQGsgA0EwahDKASAHIQQgA0E0agshBSAEBEAgBSgCACAEQQJ0EN8ECyAIQQFGDQEgAygCHA0CIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAULAkACQAJAAn8gASgCCCIEIAIoAggiBUYEQCAEQQJ0IQQgASgCBEEEayEJIAIoAgRBBGshCgJAA0AgBEUNASAEIApqIQYgBCAJaiAEQQRrIQQoAgAiBSAGKAIAIgZGDQALIAUgBksgBSAGSWsMAgtBf0EAIAQbDAELIAQgBUsgBCAFSWsLQf8BcQ4CAQIACyADQThqIAJBCGooAgA2AgAgAyACKQIANwMwIANByABqIAFBCGooAgA2AgAgAyABKQIANwNAIANBIGogA0EwaiADQUBrEIcCIAMoAkAiAQRAIAMoAkQgAUECdBDfBAsgACADKQIgNwIAIABBCGogA0EoaigCACIBNgIAIAAgB0EBIAEbOgAMDAYLIABBCGpBqMzCACkCADcCACAAQaDMwgApAgA3AgAgAigCACIARQ0DIAIoAgQgAEECdBDfBAwDCyADQThqIAFBCGooAgA2AgAgAyABKQIANwMwIANByABqIAJBCGooAgA2AgAgAyACKQIANwNAIANBIGogA0EwaiADQUBrEIcCIAMoAkAiAQRAIAMoAkQgAUECdBDfBAtBASEEAkAgCEEBRwRAIAhBASADKAIoGyEEDAELIANBADYCKCADKAIgQQRJDQAgA0EIaiADQSBqQQAQ0wMgAygCCCIBQYGAgIB4Rw0ECyAAIAMpAiA3AgAgACAEOgAMIABBCGogA0EoaigCADYCAAwECyADQQA2AhwgAygCFCIBQQRPBEAgAygCGCABQQJ0EN8EIANCgICAgMAANwIUCyAAQQE6AAwgACADKQIUNwIAIABBCGogA0EcaigCADYCAAwDCyAAIAg6AAwgACADKQIUNwIAIABBCGogA0EcaigCADYCAAwCCyABKAIAIgBFDQEgASgCBCAAQQJ0EN8EDAELIAEgAygCDEHQz8IAEMgEAAsgA0HQAGokAAvnCAEPfyMAQcACayICJAAgAkE4akIANwMAIAJBMGpCADcDACACQShqQgA3AwAgAkEgakIANwMAIAJBGGpCADcDACACQRBqQgA3AwAgAkEIakIANwMAIAJCADcDAAJAAkAgASACEKcEBEAgAUFAayIDIAIQpwQNAQsgAkHgAGoiAyABKQMgNwMAIAJB2ABqIgQgAUEYaikDADcDACACQdAAaiIFIAFBEGopAwA3AwAgAkHIAGoiBiABQQhqKQMANwMAIAJB6ABqIgcgAUEoaikDADcDACACQfAAaiIIIAFBMGopAwA3AwAgAkH4AGoiCSABQThqKQMANwMAIAIgASkDADcDQCACQZgBaiIKIAFB2ABqKQMANwMAIAJBkAFqIgsgAUHQAGopAwA3AwAgAkGIAWoiDCABQcgAaikDADcDACACIAEpA0A3A4ABIAJBuAFqIg0gAUH4AGopAwA3AwAgAkGwAWoiDiABQfAAaikDADcDACACQagBaiIPIAFB6ABqKQMANwMAIAJBoAFqIhAgASkDYDcDACACQQhqIAwpAwA3AwAgAkEQaiALKQMANwMAIAJBGGogCikDADcDACACQSBqIBApAwA3AwAgAkEoaiAPKQMANwMAIAJBMGogDikDADcDACACQThqIA0pAwA3AwAgAiACKQOAATcDACAAQUBrIAIQ8AIgAEE4aiAJKQMANwMAIABBMGogCCkDADcDACAAQShqIAcpAwA3AwAgAEEgaiADKQMANwMAIABBGGogBCkDADcDACAAQRBqIAUpAwA3AwAgAEEIaiAGKQMANwMAIAAgAikDQDcDAAwBCyACQeABaiIEIAEpAyA3AwAgAkHYAWoiBSABQRhqKQMANwMAIAJB0AFqIgYgAUEQaikDADcDACACQcgBaiIHIAFBCGopAwA3AwAgAkHoAWoiCCABQShqKQMANwMAIAJB8AFqIgkgAUEwaikDADcDACACQfgBaiIKIAFBOGopAwA3AwAgAkGIAmoiCyADQQhqKQMANwMAIAJBkAJqIgwgA0EQaikDADcDACACQZgCaiINIANBGGopAwA3AwAgAiABKQMANwPAASACIAMpAwA3A4ACIAJBuAJqIgMgAUH4AGopAwA3AwAgAkGwAmoiDiABQfAAaikDADcDACACQagCaiIPIAFB6ABqKQMANwMAIAJBoAJqIhAgASkDYDcDACAAQThqIAopAwA3AwAgAEEwaiAJKQMANwMAIABBKGogCCkDADcDACAAQSBqIAQpAwA3AwAgAEEYaiAFKQMANwMAIABBEGogBikDADcDACAAQQhqIAcpAwA3AwAgACACKQPAATcDACAAQfgAaiADKQMANwMAIABB8ABqIA4pAwA3AwAgAEHoAGogDykDADcDACAAQeAAaiAQKQMANwMAIABB2ABqIA0pAwA3AwAgAEHQAGogDCkDADcDACAAQcgAaiALKQMANwMAIAAgAikDgAI3A0ALIAJBwAJqJAAL/QgCAX8MfiMAQbACayICJAAgAkGIAmogAUHAABCxAkEBIQECQCACLQCIAkEBRgRAIAAgAi0AiQI6AAEMAQsgAkHAAWogAikDqAJCAEKkC0IAEMkDIAJB0AFqIAIpA6ACQgBCpAtCABDJAyACQeABaiACKQOYAkIAQqQLQgAQyQMgAkHwAWogAikDkAJCAEKkC0IAEMkDIAJBsAFqIAIpA8ABIgdCm5Svw/K1qN6Gf34iBEIAQm1CABDJAyACQaABaiAEQgBCf0IAEMkDIAJBMGogBEIAQv///////////wBCABDJAyACQZABaiACKQOgASIEIAIpA8gBIgYgAikD0AF8IgV8IgggAikDuAEgAikDsAEiAyAHQnyDfCADVK18fCIHQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAkGAAWogA0IAQn9CABDJAyACQUBrIANCAEL///////////8AQgAQyQMgAkHwAGogAikDgAEiAyAEIAIpA9gBIAUgBlStfCIJIAIpA+ABfCIGfCIFIAcgCFStIAIpA6gBIgsgBCAIVq18fHwiDHwiBCACKQOYASACKQOQASIIIAd8IAhUrXx8IghCm5Svw/K1qN6Gf34iB0IAQm1CABDJAyACQeAAaiAHQgBCf0IAEMkDIAJB0ABqIAdCAEL///////////8AQgAQyQMgAkEgaiACKQNgIgcgAyACKQPoASAGIAlUrXwiDSACKQPwAXwiCSACKQMwfCIKIAUgDFatIAsgBSAGVK18fHwiBnwiBSAEIAhWrSACKQOIASILIAMgBFatfHx8Igx8IgQgAikDeCAIIAIpA3AiA3wgA1StfHwiCEKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAJBEGogA0IAQn9CABDJAyACIANCAEL///////////8AQgAQyQMCQAJAIAIpAwggAikDWCACKQNIIAIpA0AiDiACKQP4ASAJIA1UrXx8IgMgDlStfCADIAMgBiAKVK0gAikDOCAJIApWrXx8fCIJVq18IAkgCSAFIAxWrSALIAUgBlStfHx8IgNWrXwiBSACKQNQfCIGIAVUrXwgBiACKQNoIgkgAyADIAd8IgVWrXwgBSAEIAhWrSAJIAQgB1StfHx8IgkgBVStfHwiBCAGVK18IgMgAikDAHwiByADVK18IAcgAikDGCIGIAQgBCACKQMQIgN8IgVWrXwgBSAFIAYgAyADIAl8IgRWrXwgBCACKQMoIAggAikDICIDfCADVK18fCIGIARUrXx8IgRWrXx8IgggB1StfCIFQgBZBEAgBUL///////////8AUiAGQm1UciAEIAiDQn9Scg0BCyAEQgF8IgMgBkJtVK0iCX0hByAIQgF8IgogBEJ/UiADIAlUcq0iBH0hAyAFIAhCf1IgBCAKVnKtfUL///////////8AfSEFIAZCE3whBgwBCyAIIQMgBCEHCyAAIAY3AyAgACAHNwMYIAAgAzcDECAAIAU3AwhBACEBCyAAIAE6AAAgAkGwAmokAAvkCAEHfyMAQTBrIgMkAAJAIAItAAwiB0EBRgRAIAAgASkCADcCACAAQQhqIAFBCGopAgA3AgAMAQsCQAJAAkACQAJAAkACQAJAAkACQAJAAkACQCABLQAMIgZBAWsOAgoBAAsgB0UNAQwCCyAHRQ0BCwJ/IAEoAggiBCACKAIIIgVGBEAgBEECdCEEIAEoAgRBBGshCCACKAIEQQRrIQkCQANAIARFDQEgBCAJaiEHIAQgCGogBEEEayEEKAIAIgUgBygCACIHRg0ACyAFIAdLIAUgB0lrDAILQX9BACAEGwwBCyAEIAVLIAQgBUlrC0H/AXEOAgMCAQsgA0EoaiABQQhqKAIANgIAIAMgASkCADcDICADQRRqIANBIGogAhDKASADKAIcRQRAIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAoLIAAgBjoADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAkLQQIhBAJAAkACQCAGQQFrDgICAAELQQAhBAsgA0EoaiABQQhqKAIANgIAIAMgASkCADcDICADQRRqIAIgA0EgahCeASAEQQEgAygCHBshBAwFCyADQShqIAFBCGooAgA2AgAgAyABKQIANwMgIANBFGoiASACIANBIGoQngFBACECIANBADYCHCABEOUDIAMoAhwiBkUNAyADKAIYIgEgBkECdCIEakEEaygCAARAIAYhAgwECyABQQRrIQIgBkH/////A3EhAQJAA0AgBEUEQEEAIQQMAgsgAUEBayEBIAIgBGogBEEEayEEKAIARQ0ACyAGIgIgAUEBaiIESQ0ECyADIAQ2AhwgBCECDAMLIANBKGogAUEIaigCADYCACADIAEpAgA3AyAgA0EUaiADQSBqIAIQhwJBASEEAkAgBkEBRwRAIAZBASADKAIcGyEEDAELIANBADYCHCADKAIUQQRJDQAgA0EIaiADQRRqQQAQ0wMgAygCCCIBQYGAgIB4Rw0CCyAAIAMpAhQ3AgAgACAEOgAMIABBCGogA0EcaigCADYCAAwHCyAAQQhqQYDExAApAgA3AgAgAEH4w8QAKQIANwIADAQLIAEgAygCDEG0ycQAEMgEAAtBASEEIAIgAygCFEECdk8NACADIANBFGogAhDTAyADKAIAIgFBgYCAgHhGDQAgASADKAIEQbTJxAAQyAQACyAAIAMpAhQ3AgAgACAEOgAMIABBCGogA0EcaigCADYCAAwDCyACKAIIIgRBAnQhBUEAIQYgBEH/////A0sgBUH8////B0tyDQEgAigCBCEIAn8gBUUEQEEEIQJBAAwBC0HRzsUALQAAGkEEIQYgBUEEENYEIgJFDQIgBAshBiAFBEAgAiAIIAX8CgAACyAAQQIgB2s6AAwgACAENgIIIAAgAjYCBCAAIAY2AgALIAEoAgAiAEUNASABKAIEIABBAnQQ3wQMAQsgBiAFQaSDxQAQyAQACyADQTBqJAALnwoCAX8QfiMAQdABayIDJAAgASkDACEOIAEpAwghDyABKQMQIRAgASkDGCERIAEpAyAhEiABKQMoIRNBKCEBA0AgA0HwAGogASACaikDACIFQgAgE0IAEMkDIANBgAFqIAVCACASQgAQyQMgA0GQAWogBUIAIBFCABDJAyADQaABaiAFQgAgEEIAEMkDIANBsAFqIAVCACAPQgAQyQMgA0HAAWogBUIAIA5CABDJAyADQeAAaiADKQNwIgkgDXwiCkIAQgBC/f/z/8////mJfxDJAyADQdAAaiADKQNoIgVCAEKr1f7///+//7l/QgAQyQMgA0FAayAFQgBC///Piuv//9UeQgAQyQMgA0EwaiAFQgBCpOzDtY/UtJjnAEIAEMkDIANBIGogBUIAQr+llJzP8NK75ABCABDJAyADQRBqIAVCAELX2a6a5PbpjcsAQgAQyQMgAyAFQgBCms3/y6O9xIAaQgAQyQMgAykDCCAMIAMpA8ABIgx8IgUgAykDuAEgByADKQOwASIHfCILIAdUrXwgCyADKQOoASADKQOgASIHIAh8IgggB1StfCAIIAMpA5gBIAMpA5ABIgcgBnwiBiAHVK18IAYgAykDiAEgAykDgAEiByAEfCIEIAdUrXwgBCADKQN4IAkgClatfHwiCSAEVK18fCIEIAZUrXx8IgYgCFStfHwiCCALVK18fCILIAMpAwB8IgcgC1StfCAHIAcgAykDGCAIIAggAykDEHwiCFatfCAIIAggAykDKCAGIAYgAykDIHwiBlatfCAGIAYgAykDOCAEIAQgAykDMHwiBFatfCAEIAQgAykDSCADKQNAIg0gCXwiCSANVK18IAkgAykDWCAKIAMpA1AiCnwgClStfHwiDSAJVK18fCIEVq18fCIGVq18fCIIVq18fCIHVq18IAUgC1atIAMpA8gBIAUgDFStfHx8IQwgAUEIayIBQXhHDQALAkACQCAMQprN/8ujvcSAGlYNACAMQprN/8ujvcSAGlIEQCAEIQUgBiEKIAghCyAHIQkMAgsgB0LX2a6a5PbpjcsAVg0AAkAgB0LX2a6a5PbpjcsAUgRAIAQhBSAGIQogCCELIAchCQwBCyAIQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEJIAhCv6WUnM/w0rvkAFIEQCAEIQUgBiEKIAghCwwBCyAGQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACELIAZCpOzDtY/UtJjnAFIEQCAEIQUgBiEKDAELIARC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhCiAEQv//z4rr///VHlIEQCAEIQUMAQtC///Piuv//9UeIQUgDUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDAwBCyAEQv//z4rr///VHn0iCiANQqvV/v///7//uX9UrSILfSEFIAZCpOzDtY/UtJjnAH0iCSAEQv//z4rr///VHlQgCiALVHKtIgR9IQogCEK/pZScz/DSu+QAfSIOIAZCpOzDtY/UtJjnAFQgBCAJVnKtIgR9IQsgB0LX2a6a5PbpjcsAfSIGIAhCv6WUnM/w0rvkAFQgBCAOVnKtIgR9IQkgDCAHQtfZrprk9umNywBUIAQgBlZyrX1Cms3/y6O9xIAafSEMIA1C1aqBgICAwIDGAHwhDQsgACANNwMoIAAgBTcDICAAIAo3AxggACALNwMQIAAgCTcDCCAAIAw3AwAgA0HQAWokAAutDgIIfwh+IwBB8ABrIgIkACMAQRBrIggkACAIQQRqIAEQvwECQCAIKAIMIgNBMUkEQCAIKAIIIQQCQCADIANBDGsiAUEAIAEgA00bIglGDQAgBCAJaiEBQQwgAyADQQxPGyIGQQNxIQUgBkEBa0EDTwRAIAZBDHEhBgNAIApCIIhCgID8/w+DIAxCIIaEIApCEIYiCkIwiIQhDCABQQNqMQAAIAFBAWoxAAAgCiABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQogAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIAxCCIYgCkI4iIQhDCABMQAAIApCCIaEIQogAUEBaiEBIAVBAWsiBQ0ACwsgCSADQRhrIgFBACABIANNGyIJRwRAIAQgCWohAUEYIAMgA0EYTxtBDCADIANBDE8bayEFA0AgEEIIhiAOQjiIhCEQIAExAAAgDkIIhoQhDiABQQFqIQEgBUEBayIFDQALCyAJIANBJGsiAUEAIAEgA00bIgZHBEBBJCADIANBJE8bQRggAyADQRhPG2shBSAEIAZqIQEDQCARQgiGIA9COIiEIREgATEAACAPQgiGhCEPIAFBAWohASAFQQFrIgUNAAsLAkAgA0ElSQ0AIAZBA3EhBQJAIANBJWtBA0kEQCAEIQEMAQsgBkEccSEGIAQhAQNAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIAVBAWsiBQ0ACwsgAiALNwMwIAIgDzcDICACIA43AxAgAiAKNwMAIAIgDTcDOCACIBE3AyggAiAQNwMYIAIgDDcDCCAIKAIEIgEEQCAEIAEQ3wQLIAhBEGokAAwBC0HU2sIAQS1BhNvCABD+AwALIAJCgICAgMAANwNAIAIpAwghCiACKQMAIQsgAkHoAGoiBEGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAJB2ABqIAQoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQMYIQogAikDECELQQAhByACQegAaiIDQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAogC4RQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIAdqIAs+AgAgC0L/////D1YgCkIAUiAKUCAKQiCGIAtCIIiEIQsgB0EEaiEHIApCIIghCiACIAE2AmggAUEBaiEBGw0ACwsgBCADKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiBCACKQNQNwIAIARBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDKCEKIAIpAyAhC0EAIQcgAkHoAGoiA0Gs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAQgAygCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgQgAikDUDcCACAEQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAzghCiACKQMwIQtBACEHIAJB6ABqIgNBrPzAACgCADYCACACQaT8wAApAgA3A2AgCiALhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgB2ogCz4CACALQv////8PViAKQgBSIApQIApCIIYgC0IgiIQhCyAHQQRqIQcgCkIgiCEKIAIgATYCaCABQQFqIQEbDQALCyAEIAMoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaigCADYCACAAIAFBAWo2AgggAkHwAGokAAutDgIIfwh+IwBB8ABrIgIkACMAQRBrIggkACAIQQRqIAEQyQECQCAIKAIMIgNBMUkEQCAIKAIIIQQCQCADIANBDGsiAUEAIAEgA00bIglGDQAgBCAJaiEBQQwgAyADQQxPGyIGQQNxIQUgBkEBa0EDTwRAIAZBDHEhBgNAIApCIIhCgID8/w+DIAxCIIaEIApCEIYiCkIwiIQhDCABQQNqMQAAIAFBAWoxAAAgCiABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQogAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIAxCCIYgCkI4iIQhDCABMQAAIApCCIaEIQogAUEBaiEBIAVBAWsiBQ0ACwsgCSADQRhrIgFBACABIANNGyIJRwRAIAQgCWohAUEYIAMgA0EYTxtBDCADIANBDE8bayEFA0AgEEIIhiAOQjiIhCEQIAExAAAgDkIIhoQhDiABQQFqIQEgBUEBayIFDQALCyAJIANBJGsiAUEAIAEgA00bIgZHBEBBJCADIANBJE8bQRggAyADQRhPG2shBSAEIAZqIQEDQCARQgiGIA9COIiEIREgATEAACAPQgiGhCEPIAFBAWohASAFQQFrIgUNAAsLAkAgA0ElSQ0AIAZBA3EhBQJAIANBJWtBA0kEQCAEIQEMAQsgBkEccSEGIAQhAQNAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIAVBAWsiBQ0ACwsgAiALNwMwIAIgDzcDICACIA43AxAgAiAKNwMAIAIgDTcDOCACIBE3AyggAiAQNwMYIAIgDDcDCCAIKAIEIgEEQCAEIAEQ3wQLIAhBEGokAAwBC0HU2sIAQS1BhNvCABD+AwALIAJCgICAgMAANwNAIAIpAwghCiACKQMAIQsgAkHoAGoiBEGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAJB2ABqIAQoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQMYIQogAikDECELQQAhByACQegAaiIDQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAogC4RQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIAdqIAs+AgAgC0L/////D1YgCkIAUiAKUCAKQiCGIAtCIIiEIQsgB0EEaiEHIApCIIghCiACIAE2AmggAUEBaiEBGw0ACwsgBCADKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiBCACKQNQNwIAIARBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDKCEKIAIpAyAhC0EAIQcgAkHoAGoiA0Gs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAQgAygCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgQgAikDUDcCACAEQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAzghCiACKQMwIQtBACEHIAJB6ABqIgNBrPzAACgCADYCACACQaT8wAApAgA3A2AgCiALhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgB2ogCz4CACALQv////8PViAKQgBSIApQIApCIIYgC0IgiIQhCyAHQQRqIQcgCkIgiCEKIAIgATYCaCABQQFqIQEbDQALCyAEIAMoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaigCADYCACAAIAFBAWo2AgggAkHwAGokAAutDgIIfwh+IwBB8ABrIgIkACMAQRBrIggkACAIQQRqIAEQlAICQCAIKAIMIgNBMUkEQCAIKAIIIQQCQCADIANBDGsiAUEAIAEgA00bIglGDQAgBCAJaiEBQQwgAyADQQxPGyIGQQNxIQUgBkEBa0EDTwRAIAZBDHEhBgNAIApCIIhCgID8/w+DIAxCIIaEIApCEIYiCkIwiIQhDCABQQNqMQAAIAFBAWoxAAAgCiABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQogAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIAxCCIYgCkI4iIQhDCABMQAAIApCCIaEIQogAUEBaiEBIAVBAWsiBQ0ACwsgCSADQRhrIgFBACABIANNGyIJRwRAIAQgCWohAUEYIAMgA0EYTxtBDCADIANBDE8bayEFA0AgEEIIhiAOQjiIhCEQIAExAAAgDkIIhoQhDiABQQFqIQEgBUEBayIFDQALCyAJIANBJGsiAUEAIAEgA00bIgZHBEBBJCADIANBJE8bQRggAyADQRhPG2shBSAEIAZqIQEDQCARQgiGIA9COIiEIREgATEAACAPQgiGhCEPIAFBAWohASAFQQFrIgUNAAsLAkAgA0ElSQ0AIAZBA3EhBQJAIANBJWtBA0kEQCAEIQEMAQsgBkEccSEGIAQhAQNAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIAVBAWsiBQ0ACwsgAiALNwMwIAIgDzcDICACIA43AxAgAiAKNwMAIAIgDTcDOCACIBE3AyggAiAQNwMYIAIgDDcDCCAIKAIEIgEEQCAEIAEQ3wQLIAhBEGokAAwBC0HU2sIAQS1BhNvCABD+AwALIAJCgICAgMAANwNAIAIpAwghCiACKQMAIQsgAkHoAGoiBEGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAJB2ABqIAQoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQMYIQogAikDECELQQAhByACQegAaiIDQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAogC4RQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIAdqIAs+AgAgC0L/////D1YgCkIAUiAKUCAKQiCGIAtCIIiEIQsgB0EEaiEHIApCIIghCiACIAE2AmggAUEBaiEBGw0ACwsgBCADKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiBCACKQNQNwIAIARBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDKCEKIAIpAyAhC0EAIQcgAkHoAGoiA0Gs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAQgAygCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgQgAikDUDcCACAEQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAzghCiACKQMwIQtBACEHIAJB6ABqIgNBrPzAACgCADYCACACQaT8wAApAgA3A2AgCiALhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgB2ogCz4CACALQv////8PViAKQgBSIApQIApCIIYgC0IgiIQhCyAHQQRqIQcgCkIgiCEKIAIgATYCaCABQQFqIQEbDQALCyAEIAMoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaigCADYCACAAIAFBAWo2AgggAkHwAGokAAutDgIIfwh+IwBB8ABrIgIkACMAQRBrIggkACAIQQRqIAEQ6gECQCAIKAIMIgNBMUkEQCAIKAIIIQQCQCADIANBDGsiAUEAIAEgA00bIglGDQAgBCAJaiEBQQwgAyADQQxPGyIGQQNxIQUgBkEBa0EDTwRAIAZBDHEhBgNAIApCIIhCgID8/w+DIAxCIIaEIApCEIYiCkIwiIQhDCABQQNqMQAAIAFBAWoxAAAgCiABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQogAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIAxCCIYgCkI4iIQhDCABMQAAIApCCIaEIQogAUEBaiEBIAVBAWsiBQ0ACwsgCSADQRhrIgFBACABIANNGyIJRwRAIAQgCWohAUEYIAMgA0EYTxtBDCADIANBDE8bayEFA0AgEEIIhiAOQjiIhCEQIAExAAAgDkIIhoQhDiABQQFqIQEgBUEBayIFDQALCyAJIANBJGsiAUEAIAEgA00bIgZHBEBBJCADIANBJE8bQRggAyADQRhPG2shBSAEIAZqIQEDQCARQgiGIA9COIiEIREgATEAACAPQgiGhCEPIAFBAWohASAFQQFrIgUNAAsLAkAgA0ElSQ0AIAZBA3EhBQJAIANBJWtBA0kEQCAEIQEMAQsgBkEccSEGIAQhAQNAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIAZBBGsiBg0ACwsgBUUNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIAVBAWsiBQ0ACwsgAiALNwMwIAIgDzcDICACIA43AxAgAiAKNwMAIAIgDTcDOCACIBE3AyggAiAQNwMYIAIgDDcDCCAIKAIEIgEEQCAEIAEQ3wQLIAhBEGokAAwBC0HU2sIAQS1BhNvCABD+AwALIAJCgICAgMAANwNAIAIpAwghCiACKQMAIQsgAkHoAGoiBEGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAJB2ABqIAQoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQMYIQogAikDECELQQAhByACQegAaiIDQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAogC4RQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIAdqIAs+AgAgC0L/////D1YgCkIAUiAKUCAKQiCGIAtCIIiEIQsgB0EEaiEHIApCIIghCiACIAE2AmggAUEBaiEBGw0ACwsgBCADKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiBCACKQNQNwIAIARBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDKCEKIAIpAyAhC0EAIQcgAkHoAGoiA0Gs/MAAKAIANgIAIAJBpPzAACkCADcDYCAKIAuEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCAHaiALPgIAIAtC/////w9WIApCAFIgClAgCkIghiALQiCIhCELIAdBBGohByAKQiCIIQogAiABNgJoIAFBAWohARsNAAsLIAQgAygCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgQgAikDUDcCACAEQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAzghCiACKQMwIQtBACEHIAJB6ABqIgNBrPzAACgCADYCACACQaT8wAApAgA3A2AgCiALhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgB2ogCz4CACALQv////8PViAKQgBSIApQIApCIIYgC0IgiIQhCyAHQQRqIQcgCkIgiCEKIAIgATYCaCABQQFqIQEbDQALCyAEIAMoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIEIAIpA1A3AgAgBEEIaiACQdgAaigCADYCACAAIAFBAWo2AgggAkHwAGokAAvNCAIHfwJ+IwBB8ABrIgIkACACIAEQ3wEgAkKAgICAwAA3A0AgAikDCCEJIAIpAwAhCiACQegAaiIEQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAkgCoRQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIANqIAo+AgAgCkL/////D1YgCUIAUiAJUCAJQiCGIApCIIiEIQogA0EEaiEDIAlCIIghCSACIAE2AmggAUEBaiEBGw0ACwsgAkHYAGogBCgCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgMgAikDUDcCACADQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAxghCSACKQMQIQpBACEDIAJB6ABqIgVBrPzAACgCADYCACACQaT8wAApAgA3A2AgCSAKhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgA2ogCj4CACAKQv////8PViAJQgBSIAlQIAlCIIYgCkIgiIQhCiADQQRqIQMgCUIgiCEJIAIgATYCaCABQQFqIQEbDQALCyAEIAUoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIDIAIpA1A3AgAgA0EIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQMoIQkgAikDICEKQQAhAyACQegAaiIFQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAkgCoRQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIANqIAo+AgAgCkL/////D1YgCUIAUiAJUCAJQiCGIApCIIiEIQogA0EEaiEDIAlCIIghCSACIAE2AmggAUEBaiEBGw0ACwsgBCAFKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiAyACKQNQNwIAIANBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDOCEJIAIpAzAhCkEAIQMgAkHoAGoiBUGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAJIAqEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCADaiAKPgIAIApC/////w9WIAlCAFIgCVAgCUIghiAKQiCIhCEKIANBBGohAyAJQiCIIQkgAiABNgJoIAFBAWohARsNAAsLIAQgBSgCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgMgAikDUDcCACADQQhqIAJB2ABqKAIANgIAIAAgAUEBajYCCCACQfAAaiQAC80IAgd/An4jAEHwAGsiAiQAIAIgARDeASACQoCAgIDAADcDQCACKQMIIQkgAikDACEKIAJB6ABqIgRBrPzAACgCADYCACACQaT8wAApAgA3A2AgCSAKhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgA2ogCj4CACAKQv////8PViAJQgBSIAlQIAlCIIYgCkIgiIQhCiADQQRqIQMgCUIgiCEJIAIgATYCaCABQQFqIQEbDQALCyACQdgAaiAEKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiAyACKQNQNwIAIANBCGogAkHYAGoiBCgCADYCACAAIAFBAWo2AgggAikDGCEJIAIpAxAhCkEAIQMgAkHoAGoiBUGs/MAAKAIANgIAIAJBpPzAACkCADcDYCAJIAqEUEUEQEEBIQEDQCACKAJgIAFBAWtGBEAgAkHgAGpBqP3AABClAwsgAigCZCADaiAKPgIAIApC/////w9WIAlCAFIgCVAgCUIghiAKQiCIhCEKIANBBGohAyAJQiCIIQkgAiABNgJoIAFBAWohARsNAAsLIAQgBSgCADYCACACIAIpA2A3A1AgACgCCCIBIAAoAgBGBEAgAEG8lMEAEJ8DCyAAKAIEIAFBDGxqIgMgAikDUDcCACADQQhqIAJB2ABqIgQoAgA2AgAgACABQQFqNgIIIAIpAyghCSACKQMgIQpBACEDIAJB6ABqIgVBrPzAACgCADYCACACQaT8wAApAgA3A2AgCSAKhFBFBEBBASEBA0AgAigCYCABQQFrRgRAIAJB4ABqQaj9wAAQpQMLIAIoAmQgA2ogCj4CACAKQv////8PViAJQgBSIAlQIAlCIIYgCkIgiIQhCiADQQRqIQMgCUIgiCEJIAIgATYCaCABQQFqIQEbDQALCyAEIAUoAgA2AgAgAiACKQNgNwNQIAAoAggiASAAKAIARgRAIABBvJTBABCfAwsgACgCBCABQQxsaiIDIAIpA1A3AgAgA0EIaiACQdgAaiIEKAIANgIAIAAgAUEBajYCCCACKQM4IQkgAikDMCEKQQAhAyACQegAaiIFQaz8wAAoAgA2AgAgAkGk/MAAKQIANwNgIAkgCoRQRQRAQQEhAQNAIAIoAmAgAUEBa0YEQCACQeAAakGo/cAAEKUDCyACKAJkIANqIAo+AgAgCkL/////D1YgCUIAUiAJUCAJQiCGIApCIIiEIQogA0EEaiEDIAlCIIghCSACIAE2AmggAUEBaiEBGw0ACwsgBCAFKAIANgIAIAIgAikDYDcDUCAAKAIIIgEgACgCAEYEQCAAQbyUwQAQnwMLIAAoAgQgAUEMbGoiAyACKQNQNwIAIANBCGogAkHYAGooAgA2AgAgACABQQFqNgIIIAJB8ABqJAAL5wcCB38EfiMAQSBrIgIkACACQRBqIAEQvgEgAigCGCIFQSFJBEAgAigCFCEEAkAgBSAFQRBrIgFBACABIAVNGyIHRg0AIAQgB2ohAUEQIAUgBUEQTxsiCEEDcSEDAkAgCEEBa0EDSQRADAELIAhBHHEhBgNAIApCIIhCgID8/w+DIAxCIIaEIApCEIYiCUIwiIQhDCABQQNqMQAAIAFBAWoxAAAgCSABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQogAUEEaiEBIAZBBGsiBg0ACwsgAwRAA0AgDEIIhiAKQjiIhCEMIAExAAAgCkIIhoQhCiABQQFqIQEgA0EBayIDDQALC0IAIQkgBUERSQRADAELIAdBA3EhAwJAIAggBWtBfEsEQCAEIQEMAQsgB0E8cSEGIAQhAQNAIAlCIIhCgID8/w+DIAtCIIaEIAlCEIYiCUIwiIQhCyABQQNqMQAAIAFBAWoxAAAgCSABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQkgAUEEaiEBIAZBBGsiBg0ACwsgA0UNAANAIAtCCIYgCUI4iIQhCyABMQAAIAlCCIaEIQkgAUEBaiEBIANBAWsiAw0ACwsgAigCECIBBEAgBCABEN8EC0EAIQMgAkEYaiIEQZCSwgAoAgA2AgAgAkGIksIAKQIANwMQIAogDIRQRQRAQQEhAQNAIAIoAhAgAUEBa0YEQCACQRBqQZyTwgAQpQMLIAIoAhQgA2ogCj4CACAKQv////8PViAMQgBSIAxQIAxCIIYgCkIgiIQhCiADQQRqIQMgDEIgiCEMIAIgATYCGCABQQFqIQEbDQALCyACQQhqIAQoAgA2AgAgAiACKQMQNwMAIAAoAggiASAAKAIARgRAIABB6KvCABCfAwsgACgCBCABQQxsaiIEIAIpAwA3AgAgBEEIaiACQQhqIgQoAgA2AgAgACABQQFqNgIIQQAhAyACQRhqIgVBkJLCACgCADYCACACQYiSwgApAgA3AxAgCSALhFBFBEBBASEBA0AgAigCECABQQFrRgRAIAJBEGpBnJPCABClAwsgAigCFCADaiAJPgIAIAlC/////w9WIAtCAFIgC1AgC0IghiAJQiCIhCEJIANBBGohAyALQiCIIQsgAiABNgIYIAFBAWohARsNAAsLIAQgBSgCADYCACACIAIpAxA3AwAgACgCCCIBIAAoAgBGBEAgAEHoq8IAEJ8DCyAAKAIEIAFBDGxqIgQgAikDADcCACAEQQhqIAJBCGooAgA2AgAgACABQQFqNgIIIAJBIGokAA8LQdTawgBBLUGE28IAEP4DAAvnBwIHfwR+IwBBIGsiAiQAIAJBEGogARC/ASACKAIYIgVBIUkEQCACKAIUIQQCQCAFIAVBEGsiAUEAIAEgBU0bIgdGDQAgBCAHaiEBQRAgBSAFQRBPGyIIQQNxIQMCQCAIQQFrQQNJBEAMAQsgCEEccSEGA0AgCkIgiEKAgPz/D4MgDEIghoQgCkIQhiIJQjCIhCEMIAFBA2oxAAAgAUEBajEAACAJIAExAABCCIaEhEIQhiABQQJqMQAAQgiGhIQhCiABQQRqIQEgBkEEayIGDQALCyADBEADQCAMQgiGIApCOIiEIQwgATEAACAKQgiGhCEKIAFBAWohASADQQFrIgMNAAsLQgAhCSAFQRFJBEAMAQsgB0EDcSEDAkAgCCAFa0F8SwRAIAQhAQwBCyAHQTxxIQYgBCEBA0AgCUIgiEKAgPz/D4MgC0IghoQgCUIQhiIJQjCIhCELIAFBA2oxAAAgAUEBajEAACAJIAExAABCCIaEhEIQhiABQQJqMQAAQgiGhIQhCSABQQRqIQEgBkEEayIGDQALCyADRQ0AA0AgC0IIhiAJQjiIhCELIAExAAAgCUIIhoQhCSABQQFqIQEgA0EBayIDDQALCyACKAIQIgEEQCAEIAEQ3wQLQQAhAyACQRhqIgRBkJLCACgCADYCACACQYiSwgApAgA3AxAgCiAMhFBFBEBBASEBA0AgAigCECABQQFrRgRAIAJBEGpBnJPCABClAwsgAigCFCADaiAKPgIAIApC/////w9WIAxCAFIgDFAgDEIghiAKQiCIhCEKIANBBGohAyAMQiCIIQwgAiABNgIYIAFBAWohARsNAAsLIAJBCGogBCgCADYCACACIAIpAxA3AwAgACgCCCIBIAAoAgBGBEAgAEHoq8IAEJ8DCyAAKAIEIAFBDGxqIgQgAikDADcCACAEQQhqIAJBCGoiBCgCADYCACAAIAFBAWo2AghBACEDIAJBGGoiBUGQksIAKAIANgIAIAJBiJLCACkCADcDECAJIAuEUEUEQEEBIQEDQCACKAIQIAFBAWtGBEAgAkEQakGck8IAEKUDCyACKAIUIANqIAk+AgAgCUL/////D1YgC0IAUiALUCALQiCGIAlCIIiEIQkgA0EEaiEDIAtCIIghCyACIAE2AhggAUEBaiEBGw0ACwsgBCAFKAIANgIAIAIgAikDEDcDACAAKAIIIgEgACgCAEYEQCAAQeirwgAQnwMLIAAoAgQgAUEMbGoiBCACKQMANwIAIARBCGogAkEIaigCADYCACAAIAFBAWo2AgggAkEgaiQADwtB1NrCAEEtQYTbwgAQ/gMAC4wKAgF/EH4jAEHAAWsiAyQAIAEpAwAhDiABKQMIIQ8gASkDECEQIAEpAxghESABKQMgIRIgASkDKCETQSghAQNAIANB4ABqIAEgAmopAwAiBUIAIBNCABDJAyADQfAAaiAFQgAgEkIAEMkDIANBgAFqIAVCACARQgAQyQMgA0GQAWogBUIAIBBCABDJAyADQaABaiAFQgAgD0IAEMkDIANBsAFqIAVCACAOQgAQyQMgA0HQAGogAykDYCIJIA18IgpC/f/z/8////mJf34iBUIAQqvV/v///7//uX9CABDJAyADQUBrIAVCAEL//8+K6///1R5CABDJAyADQTBqIAVCAEKk7MO1j9S0mOcAQgAQyQMgA0EgaiAFQgBCv6WUnM/w0rvkAEIAEMkDIANBEGogBUIAQtfZrprk9umNywBCABDJAyADIAVCAEKazf/Lo73EgBpCABDJAyADKQMIIAwgAykDsAEiDHwiBSADKQOoASAHIAMpA6ABIgd8IgsgB1StfCALIAMpA5gBIAMpA5ABIgcgCHwiCCAHVK18IAggAykDiAEgAykDgAEiByAGfCIGIAdUrXwgBiADKQN4IAMpA3AiByAEfCIEIAdUrXwgBCADKQNoIAkgClatfHwiCSAEVK18fCIEIAZUrXx8IgYgCFStfHwiCCALVK18fCILIAMpAwB8IgcgC1StfCAHIAcgAykDGCAIIAggAykDEHwiCFatfCAIIAggAykDKCAGIAYgAykDIHwiBlatfCAGIAYgAykDOCAEIAQgAykDMHwiBFatfCAEIAQgAykDSCADKQNAIg0gCXwiCSANVK18IAkgAykDWCAKIAMpA1AiCnwgClStfHwiDSAJVK18fCIEVq18fCIGVq18fCIIVq18fCIHVq18IAUgC1atIAMpA7gBIAUgDFStfHx8IQwgAUEIayIBQXhHDQALAkACQCAMQprN/8ujvcSAGlYNACAMQprN/8ujvcSAGlIEQCAEIQUgBiEKIAghCyAHIQkMAgsgB0LX2a6a5PbpjcsAVg0AAkAgB0LX2a6a5PbpjcsAUgRAIAQhBSAGIQogCCELIAchCQwBCyAIQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEJIAhCv6WUnM/w0rvkAFIEQCAEIQUgBiEKIAghCwwBCyAGQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACELIAZCpOzDtY/UtJjnAFIEQCAEIQUgBiEKDAELIARC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhCiAEQv//z4rr///VHlIEQCAEIQUMAQtC///Piuv//9UeIQUgDUKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDAwBCyAEQv//z4rr///VHn0iCiANQqvV/v///7//uX9UrSILfSEFIAZCpOzDtY/UtJjnAH0iCSAEQv//z4rr///VHlQgCiALVHKtIgR9IQogCEK/pZScz/DSu+QAfSIOIAZCpOzDtY/UtJjnAFQgBCAJVnKtIgR9IQsgB0LX2a6a5PbpjcsAfSIGIAhCv6WUnM/w0rvkAFQgBCAOVnKtIgR9IQkgDCAHQtfZrprk9umNywBUIAQgBlZyrX1Cms3/y6O9xIAafSEMIA1C1aqBgICAwIDGAHwhDQsgACANNwMoIAAgBTcDICAAIAo3AxggACALNwMQIAAgCTcDCCAAIAw3AwAgA0HAAWokAAvoBgIKfwJ+IwBBkAZrIgQkACAEQQhqIgcgARBhIARB4ARqIARBIGopAwA3AwAgBEHYBGogBEEYaikDADcDACAEQdAEaiAEQRBqKQMANwMAIARB8ARqIARBMGopAwA3AwAgBEH4BGogBEE4aikDADcDACAEQYAFaiAEQUBrKQMANwMAIAQgBCkDCDcDyAQgBCAEKQMoNwPoBCAEQcgFaiIFIAcgARA4IARByABqIg0gBSABQUBrIggQ3AEgBEGIA2oiBiAHIAcQOCAFIAEgARCgAiAEQYgBaiILIAYgBRDcASAEQcgCaiIKIAggCBCgAiAGIAEgCxDcASAFIAogBhCRAyAEKQPYBSEOIAQpA9AFIQ8gBCgCyAVBAUcEQCAEQcACaiAEQYgGaikDADcDACAEQbgCaiAEQYAGaikDADcDACAEQbACaiAEQfgFaikDADcDACAEQagCaiAEQfAFaikDADcDACAEQaACaiAEQegFaikDADcDACAEIAQpA+AFNwOYAiAEIA43A5ACIAQgDzcDiAIgBEHIAWoiCSAEQYgCaiIMIAcQ3AEgBEGQBWogBEHQAWopAwA3AwAgBEGYBWogBEHYAWopAwA3AwAgBEGgBWogBEHgAWopAwA3AwAgBEGwBWogBEHwAWopAwA3AwAgBEG4BWogBEH4AWopAwA3AwAgBEHABWogBEGAAmopAwA3AwAgBCAEKQPIATcDiAUgBCAEKQPoATcDqAUgBSAJIAEQOCAMIAUgCBDcASAGIAkgCRA4IAUgASALEKACIAogBiAFENwBIAUgASAKENwBIAYgCSAFEDggBEGIBGogBiAIENwBIARB0ANqIARB0AJqKQMANwMAIARB2ANqIARB2AJqKQMANwMAIARB4ANqIARB4AJqKQMANwMAIARB6ANqIARB6AJqKQMANwMAIARB8ANqIARB8AJqKQMANwMAIARB+ANqIARB+AJqKQMANwMAIARBgARqIARBgANqKQMANwMAIAQgBCkDyAI3A8gDIAAgBEHIBGogDSACIAMQGSAAQZABaiAEQYgFaiAMIAIgAxAZIABBEGogBEHIA2pBgAH8CgAAIARBkAZqJAAPCyAEIA43A9AFIAQgDzcDyAVBoLHCAEErIARByAVqQaS6wgBBhLvCABDKAwAL7wgBCn8jAEEgayIDJAACQAJAAkACQAJ/AkACQAJAAkACfwJAAkACQAJ/AkACQAJAAkAgAS0ADEEBaw4CAQIACyADQRhqQbjMwgAoAgA2AgAgA0GwzMIAKQIANwMQIAINAkEEDAMLIAINAyAAQQhqQajMwgApAgA3AgAgAEGgzMIAKQIANwIADAwLIANBGGogAUEIaigCADYCACADIAEpAgA3AxACQCACRQ0AIAMoAhgiBEUEQCADKAIQRQRAIANBEGpByNDCABClAwsgAygCFEEANgIAIANBATYCGEEBIQQLIAMoAhQiASACIAEoAgAiAmoiBTYCACACIAVNDQAgBEEBRwRAIARBAnRBBGshBCABQQRqIQEDQCABIAEoAgBBAWoiAjYCACACDQIgAUEEaiEBIARBBGsiBA0ACwsgAygCGCIBIAMoAhBGBEAgA0EQakHY0MIAEKUDCyADKAIUIAFBAnRqQQE2AgAgAyABQQFqNgIYCyADKAIUIQIgAygCECEBIAMoAhgiBA0DIABBCGpBqMzCACkCADcCACAAQaDMwgApAgA3AgAgAUUNDiACIAFBAnQQ3wQMDgsgA0EQakGkzcIAEKUDIAMoAhQgAjYCAEEBIQQgAygCECEHIAMoAhQLIQggBCABKAIIIgVGBEAgCCAEQQJ0IgVqIQQgAkUEQCAEIQkMBAsgASgCBCIKIAVqIgtBBGsiDCgCACIFIARBBGsiCSgCACIGRgRAIAogDEYNBCAEQQhrKAIAIQYgC0EIaygCACEFCyAFIAZLIAUgBklrDAQLIAQgBUkgBCAFS2sMAwsgA0EYakG4zMIAKAIANgIAIANBsMzCACkCADcDECADQRBqQaTNwgAQpQMgAygCFCACNgIAIABBCGpBATYCACAAIAMpAxA3AgAgAEECOgAMDAgLIABBAjoADCAAIAQ2AgggACACNgIEIAAgATYCAAwKC0F/QQAgCCAJRxsLQf8BcQ4CAAECCyAAQQhqQajMwgApAgA3AgAgAEGgzMIAKQIANwIAIAdFDQQgCCAHQQJ0EN8EDAQLIANBGGoiBCABQQhqKAIANgIAIAMgASkCADcDECADQRBqIAIQwwIgAygCFCECIAMoAhAhASAEKAIAIglFDQEgASEEQQAhBiACDAILIANBGGogAUEIaigCADYCACADIAEpAgA3AxAgA0EEaiACIANBEGoQ+QIgAygCDEUNAyAAIAMpAgQ3AgAgAEECOgAMIABBCGogA0EMaigCADYCAAwEC0EBIQZBACEEQQQgAUUNABogAiABQQJ0EN8EQQQLIQUgAEEAOwANIAAgBjoADCAAIAk2AgggACAFNgIEIAAgBDYCACAAQQ9qQQA6AAAMAgsgASgCACIARQ0CIAEoAgQgAEECdBDfBAwCCyAAQQhqQajMwgApAgA3AgAgAEGgzMIAKQIANwIAIAMoAgQiAEUNACADKAIIIABBAnQQ3wQLIAdFDQAgCCAHQQJ0EN8ECyADQSBqJAALtQoCAX8KfiMAQdACayICJAAgAkHwAWogASkDGCIEQonHmaSu8IHph39+IgNCAELH+vPD7YKjkDxCABDJAyACQeABaiADQgBCjZXHw5bS2sCXf0IAEMkDIAJB0AFqIANCAELdsIWM6LaRqLh/QgAQyQMgAkHAAWogA0IAQqnAxomuzpOyMEIAEMkDIAJBsAFqIAIpA+ABIgYgASkDEHwiByACKQP4ASAEIAIpA/ABIgN8IANUrXx8IgRCiceZpK7wgemHf34iA0IAQsf688PtgqOQPEIAEMkDIAJBoAFqIANCAEKNlcfDltLawJd/QgAQyQMgAkHQAGogA0IAQt2whYzotpGouH9CABDJAyACIANCAEKpwMaJrs6TsjBCABDJAyACQZABaiACKQOgASIJIAIpA9ABIgggASkDCHwiBSAEIAdUrSACKQPoASAGIAdWrXx8fCIKfCIHIAIpA7gBIAIpA7ABIgMgBHwgA1StfHwiBEKJx5mkrvCB6Yd/fiIDQgBCx/rzw+2Co5A8QgAQyQMgAkGAAWogA0IAQo2Vx8OW0trAl39CABDJAyACQfAAaiADQgBC3bCFjOi2kai4f0IAEMkDIAJB4ABqIANCAEKpwMaJrs6TsjBCABDJAyACQUBrIAIpA4ABIgsgAikDwAEiDCABKQMAfCIGIAUgClatIAIpA9gBIAUgCFStfHx8IgUgAikDUHwiCCAEIAdUrSACKQOoASAHIAlUrXx8fCIJfCIHIAIpA5gBIAIpA5ABIgMgBHwgA1StfHwiBEKJx5mkrvCB6Yd/fiIDQgBCx/rzw+2Co5A8QgAQyQMgAkEwaiADQgBCjZXHw5bS2sCXf0IAEMkDIAJBIGogA0IAQt2whYzotpGouH9CABDJAyACQRBqIANCAEKpwMaJrs6TsjBCABDJAwJAIAIpAxggAikDaCACKQMIIAUgBlStIAIpA8gBIAYgDFStfHwiBiACKQMAfCIDIAZUrXwgAyADIAggCVatIAIpA1ggBSAIVq18fHwiA1atfCIGIAIpA2B8IgUgBlStfCAFIAIpA3ggAyADIAIpA3B8IgNWrXwgAyAEIAdUrSACKQOIASAHIAtUrXx8fCIGIANUrXx8IgMgBVStfCIFIAIpAxB8IgcgBVStfCAHIAIpAyggAyADIAIpAyB8IgNWrXwgAyADIAIpAzggBiACKQMwIgZ8IgUgBlStfCAFIAUgAikDSCAEIAIpA0AiBHwgBFStfHwiBVatfHwiA1atfHwiBCAHVK18IgZCqcDGia7Ok7IwVARAIAMhBwwBCwJAIARC3bCFjOi2kai4f1YNACAEQt2whYzotpGouH9SBEAgAyEHQqnAxomuzpOyMCEGDAILIANCjZXHw5bS2sCXf1YNAAJAIANCjZXHw5bS2sCXf1IEQCADIQcMAQtCjZXHw5bS2sCXfyEHIAVCx/rzw+2Co5A8Wg0BC0LdsIWM6LaRqLh/IQRCqcDGia7Ok7IwIQYMAQsgA0Lz6ri86a2lv+gAfCIIIAVCx/rzw+2Co5A8VK0iCX0hByAEQqPP+vOXye7XxwB8IgogA0KNlcfDltLawJd/VCAIIAlUcq0iA30hBCAGIAMgClatfUKpwMaJrs6TsjB9IQYgBULH+vPD7YKjkDx9IQULIAIgBTcDmAIgAiAHNwOQAiACIAQ3A4gCIAIgBjcDgAIgAiACQaACaiIBNgLMAiACQQA2ArQCIAJBADYCoAIgAiACQYACajYCyAIgACABEK0CIAJB0AJqJAALrwoCAX8KfiMAQdACayICJAAgAkHwAWogASkDGCIEQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyACQeABaiADQgBCkeHlzYeJ+pkoQgAQyQMgAkHQAWogA0IAQt2whYzotpGouH9CABDJAyACQcABaiADQgBCqcDGia7Ok7IwQgAQyQMgAkGwAWogAikD4AEiBiABKQMQfCIHIAIpA/gBIAQgAikD8AEiA3wgA1StfHwiBEL/////vrL98EJ+IgNCAEKBgICAv7L98MMAQgAQyQMgAkGgAWogA0IAQpHh5c2HifqZKEIAEMkDIAJB0ABqIANCAELdsIWM6LaRqLh/QgAQyQMgAiADQgBCqcDGia7Ok7IwQgAQyQMgAkGQAWogAikDoAEiCSACKQPQASIIIAEpAwh8IgUgBCAHVK0gAikD6AEgBiAHVq18fHwiCnwiByACKQO4ASACKQOwASIDIAR8IANUrXx8IgRC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJBgAFqIANCAEKR4eXNh4n6mShCABDJAyACQfAAaiADQgBC3bCFjOi2kai4f0IAEMkDIAJB4ABqIANCAEKpwMaJrs6TsjBCABDJAyACQUBrIAIpA4ABIgsgAikDwAEiDCABKQMAfCIGIAUgClatIAIpA9gBIAUgCFStfHx8IgUgAikDUHwiCCAEIAdUrSACKQOoASAHIAlUrXx8fCIJfCIHIAIpA5gBIAIpA5ABIgMgBHwgA1StfHwiBEL/////vrL98EJ+IgNCAEKBgICAv7L98MMAQgAQyQMgAkEwaiADQgBCkeHlzYeJ+pkoQgAQyQMgAkEgaiADQgBC3bCFjOi2kai4f0IAEMkDIAJBEGogA0IAQqnAxomuzpOyMEIAEMkDAkAgAikDGCACKQNoIAIpAwggBSAGVK0gAikDyAEgBiAMVK18fCIGIAIpAwB8IgMgBlStfCADIAMgCCAJVq0gAikDWCAFIAhWrXx8fCIDVq18IgYgAikDYHwiBSAGVK18IAUgAikDeCADIAMgAikDcHwiA1atfCADIAQgB1StIAIpA4gBIAcgC1StfHx8IgYgA1StfHwiAyAFVK18IgUgAikDEHwiByAFVK18IAcgAikDKCADIAMgAikDIHwiA1atfCADIAMgAikDOCAGIAIpAzAiBnwiBSAGVK18IAUgBSACKQNIIAQgAikDQCIEfCAEVK18fCIFVq18fCIDVq18fCIEIAdUrXwiBkKpwMaJrs6TsjBUBEAgAyEHDAELAkAgBELdsIWM6LaRqLh/Vg0AIARC3bCFjOi2kai4f1IEQCADIQdCqcDGia7Ok7IwIQYMAgsgA0KR4eXNh4n6mShWDQACQCADQpHh5c2HifqZKFIEQCADIQcMAQtCkeHlzYeJ+pkoIQcgBUKBgICAv7L98MMAWg0BC0LdsIWM6LaRqLh/IQRCqcDGia7Ok7IwIQYMAQsgA0KR4eXNh4n6mSh9IgggBUKBgICAv7L98MMAVK0iCX0hByAEQqPP+vOXye7XxwB8IgogA0KR4eXNh4n6mShUIAggCVRyrSIDfSEEIAYgAyAKVq19QqnAxomuzpOyMH0hBiAFQoGAgIC/sv3wwwB9IQULIAIgBTcDmAIgAiAHNwOQAiACIAQ3A4gCIAIgBjcDgAIgAiACQaACaiIBNgLMAiACQQA2ArQCIAJBADYCoAIgAiACQYACajYCyAIgACABEK0CIAJB0AJqJAALoQgCCH8CfiMAQdAAayIDJAACQCACLQAMIgdBAUYEQCAAIAEpAgA3AgAgAEEIaiABQQhqKQIANwIAIAIoAgAiAEUNASACKAIEIABBAnQQ3wQMAQsCQAJAAkACQAJAAkACQAJAAkAgAS0ADCIIQQFrDgIAAgELIAAgAikCADcCACAAQQhqIAJBCGopAgA3AgAMBgsgB0UNAQwCCyAHRQ0BCyADQShqIAFBCGoiBigCADYCACADIAEpAgAiCzcDICADQThqIAJBCGoiCSgCADYCACADIAIpAgAiDDcDMAJ/IAunIgQgDKciB0kEQCADQcgAaiAJKAIANgIAIAMgAikCADcDQCADQRRqIANBQGsgA0EgahDKASADQSRqDAELIANByABqIAYoAgA2AgAgAyABKQIANwNAIANBFGogA0FAayADQTBqEMoBIAchBCADQTRqCyEFIAQEQCAFKAIAIARBAnQQ3wQLIAhBAUYNASADKAIcDQIgAEEBOgAMIAAgAykCFDcCACAAQQhqIANBHGooAgA2AgAMBQsCQAJAAkACfyABKAIIIgQgAigCCCIFRgRAIARBAnQhBCABKAIEQQRrIQkgAigCBEEEayEKAkADQCAERQ0BIAQgCmohBiAEIAlqIARBBGshBCgCACIFIAYoAgAiBkYNAAsgBSAGSyAFIAZJawwCC0F/QQAgBBsMAQsgBCAFSyAEIAVJawtB/wFxDgIBAgALIANByABqIAJBCGooAgA2AgAgAyACKQIANwNAIANBMGogA0FAayABEIcCIAEoAgAiAgRAIAEoAgQgAkECdBDfBAsgACADKQIwNwIAIABBCGogA0E4aigCACIBNgIAIAAgB0EBIAEbOgAMDAYLIABBCGpBgMTEACkCADcCACAAQfjDxAApAgA3AgAgAigCACIARQ0DIAIoAgQgAEECdBDfBAwDCyADQcgAaiABQQhqKAIANgIAIAMgASkCADcDQCADQTBqIANBQGsgAhCHAiACKAIAIgEEQCACKAIEIAFBAnQQ3wQLQQEhBAJAIAhBAUcEQCAIQQEgAygCOBshBAwBCyADQQA2AjggAygCMEEESQ0AIANBCGogA0EwakEAENMDIAMoAggiAUGBgICAeEcNBAsgACADKQIwNwIAIAAgBDoADCAAQQhqIANBOGooAgA2AgAMBAsgA0EANgIcIAMoAhQiAUEETwRAIAMoAhggAUECdBDfBCADQoCAgIDAADcCFAsgAEEBOgAMIAAgAykCFDcCACAAQQhqIANBHGooAgA2AgAMAwsgACAIOgAMIAAgAykCFDcCACAAQQhqIANBHGooAgA2AgAMAgsgASgCACIARQ0BIAEoAgQgAEECdBDfBAwBCyABIAMoAgxBtMnEABDIBAALIANB0ABqJAALvQgCC38FfiMAQeAAayIFJAAgBUEYaiABEOYBIAUpAiAhFCAFKAIcIQ8gBSgCGCELIAVBEGogBUEwaikCADcDACAFIAUpAig3AwggBUE4aiAFQQhqEPcBAkACQCACKAIAIgdBgICAgHhGDQAgAigCBCEJIAIoAgghAiAFKAI8IQogBSAFKAJAIgE2AlwgBSACNgJYIAEgAkcNASAFQQA2AiAgBUKAgICAgAE3AhggAQRAQQAhAgNAQgAhEUIAIRBCACESQgAhEyACIAlqLQAABEAgCCAKaiIGKQMAIREgBkEYaikDACETIAZBEGopAwAhEiAGQQhqKQMAIRALIAUoAhggAkYEQCAFQRhqQcS3wgAQogMLIAUoAhwgCGoiBiARNwMAIAZBGGogEzcDACAGQRBqIBI3AwAgBkEIaiAQNwMAIAUgAkEBaiICNgIgIAhBIGohCCABIAJHDQALCyAFQdAAaiIBIAVBIGooAgA2AgAgBSAFKQIYNwNIIAUoAjgiAgRAIAogAkEFdBDfBAsgBUFAayABKAIANgIAIAUgBSkDSDcDOCAHRQ0AIAkgBxDfBAsgBSgCQCIGQQV0IQIgBSgCPCEIIAUoAjghCSAGIQECQAJAAkACQANAIAJFDQEgAUEBayEBIAJBIGsiAiAIakHYw8IAQSAQ8QNFDQALIAFBAWoiAiAGIAIgBkkbIQYMAQtB0c7FAC0AABpBIEEIENYEIgJFDQEgAkIANwMAIAJBGGpCADcDACACQRBqQgA3AwAgAkEIakIANwMAQX8hAUEBIQYgCQRAIAggCUEFdBDfBAsgAiEIQQEhCQsgAwRAIAMoAggiAiADKAIARgRAIANB9LfCABCjAwsgAygCBCACQQR0aiIHIBQ3AgggByAPNgIEIAcgCzYCACADIAJBAWo2AggLIAQEQEEAIQIgBkH///8/SyAGQQV0IgpB+P///wdLcg0CAkAgCkUEQEEIIQwMAQtB0c7FAC0AABpBCCECIApBCBDWBCIMRQ0DIAZFDQBBACECIAYhBwNAIAIgCkYNASACIAxqIg0gAiAIaiIOKQMANwMAIA1BGGogDkEYaikDADcDACANQRBqIA5BEGopAwA3AwAgDUEIaiAOQQhqKQMANwMAIAJBIGohAiAHQQFrIgcNAAsLIAQoAggiByAEKAIARgRAIARBhLjCABCjAwsgBCgCBCAHQQR0aiICIAE2AgwgAiAGNgIIIAIgDDYCBCACIAY2AgAgBCAHQQFqNgIICyAAIAE2AgwgACAGNgIIIAAgCDYCBCAAIAk2AgAgBSgCCCIABEAgBSgCDCAAQQV0EN8ECyADIAtFckUEQCAPIAtBBXQQ3wQLIAVB4ABqJAAPC0EIQSAQ/wQACyACIApB6IHAABDIBAALIAVBADYCGCAFQdgAaiAFQdwAaiAFQRhqQbS3wgAQlwQAC44IAgd/An4jAEEgayIHJAACQAJAAkACfwJAAkACQAJAAkACQAJAAkAgAi0ADEEBaw4CBQABCyACKAIIIgNFDQQgA0EBayIDQf7///8DcQ0FIANB/////wNxIglBAWoiCEEDcSEFIAIoAgQiBiEEIAlBA08EQCAIQfz///8HcSEDA0AgCkKAAXwhCiAEQRBqIQQgA0EEayIDDQALCyAFBEAgBSEDA0AgBDUCACAKhiALfCELIApCIHwhCiAEQQRqIQQgA0EBayIDDQALCyALQoCAgIAQVA0EQgAhCiAJQQNPBEAgCEH8////B3EhBANAIApCgAF8IQogBkEQaiEGIARBBGsiBA0ACwsgCEEDcQ0BDAILIAIoAggiAwRAIANBAWsiA0H+////A3ENBSACKAIEIQQgA0H/////A3EiA0EBaiIFQQNxIQYgA0EDTwRAIAVB/P///wdxIQMDQCAKQoABfCEKIARBEGohBCADQQRrIgMNAAsLIAYEQANAIAQ1AgAgCoYgC3whCyAKQiB8IQogBEEEaiEEIAZBAWsiBg0ACwsgC0IAUw0FC0IAIAt9IQsMAgtCACELA0AgBjUCACAKhiALfCELIApCIHwhCiAGQQRqIQYgBUEBayIFDQALCyALQgBTDQILIAtCgICAgAh8QoCAgIAQWg0BIAEoAggiA0ECdCEEQQAhBSADQf////8DSyAEQfz///8HS3INBiABKAIEIQYgAS0ADCEBIAQNAkEEIQJBAAwDCyABKAIIIgJBAnQhBUEAIQMgAkH/////A0sgBUH8////B0tyDQQgASgCBCEEIAEtAAwhBgJ/IAVFBEBBBCEBQQAMAQtB0c7FAC0AABpBBCEDIAVBBBDWBCIBRQ0FIAILIQMgBQRAIAEgBCAF/AoAAAsgByAGOgAUIAcgAjYCECAHIAE2AgwgByADNgIIIAAgB0EIaiALpxCcAgwDCyAHQQhqIAEgAhChASAHKAIYIQIgBygCFCEGIAcoAgwhAyAHKAIIIQQCQCABLQAMIgFBAUcEQCABQQEgBygCHCIBGyEFDAELIARBBE8EQCADIARBAnQQ3wRBACEEQQQhAwtBASEFQQAhASAGQQRJDQAgAiAGQQJ0EN8EQQAhBkEEIQILIAAgBToADCAAIAE2AgggACACNgIEIAAgBjYCACAERQ0CIAMgBEECdBDfBAwCC0HRzsUALQAAGkEEIQUgBEEEENYEIgJFDQMgAwshBSAEBEAgAiAGIAT8CgAACyAHIAE6ABQgByADNgIQIAcgAjYCDCAHIAU2AgggACAHQQhqQQAgC6ciAGsgACALQgBTGxCcAgsgB0EgaiQADwsgAyAFQfiBwAAQyAQACyAFIARB+IHAABDIBAAL5gcCBX8BfiMAQdAAayICJAAgAkEMaiABEIUCAkACQCACKAIMQYCAgIB4RwRAIAEoAgAEQCABKAIMIAEoAgRrQQxuIQULQQMgASgCEAR/IAEoAhwgASgCFGtBDG4FQQALIAVqIgMgA0EDTRtBAWoiBa1CDH4iB6chAyAHQiCIpyADQfz///8HS3INAgJAIANFBEBBBCEEQQAhBQwBC0HRzsUALQAAGkEEIQYgA0EEENYEIgRFDQMLIAQgAikCDDcCACAEQQhqIAJBFGooAgA2AgAgAkEBNgIIIAIgBDYCBCACIAU2AgAgAkE4aiABQSBqKQIANwMAIAJBMGogAUEYaikCADcDACACQShqIAFBEGopAgA3AwAgAkEgaiABQQhqKQIANwMAIAIgASkCADcDGCACQcQAaiACQRhqEIUCIAIoAkRBgICAgHhHBEBBDCEFQQEhAwNAIAIoAgAgA0YEQCACIAMgAigCGAR/IAIoAiQgAigCHGtBDG5BAWoFQQELIAIoAigEfyACKAI0IAIoAixrQQxuBUEAC2pBBEEMEIgDIAIoAgQhBAsgBCAFaiIBIAIpAkQ3AgAgAUEIaiACQcwAaigCADYCACACIANBAWoiAzYCCCAFQQxqIQUgAkHEAGogAkEYahCFAiACKAJEQYCAgIB4Rw0ACwsCQCACKAIYIgFFDQAgAigCJCIEIAIoAhwiA2tBDG4hBSADIARHBEADQCADKAIAIgQEQCADQQRqKAIAIARBAnQQ3wQLIANBDGohAyAFQQFrIgUNAAsLIAIoAiAiA0UNACABIANBDGwQ3wQLAkAgAigCKCIBRQ0AIAIoAjQiBCACKAIsIgNrQQxuIQUgAyAERwRAA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgBUEBayIFDQALCyACKAIwIgNFDQAgASADQQxsEN8ECyAAIAIpAgA3AgAgAEEIaiACQQhqKAIANgIADAELIABBADYCCCAAQoCAgIDAADcCAAJAIAEoAgAiAEUNACABKAIMIgQgASgCBCIDa0EMbiEFIAMgBEcEQANAIAMoAgAiBARAIANBBGooAgAgBEECdBDfBAsgA0EMaiEDIAVBAWsiBQ0ACwsgASgCCCIDRQ0AIAAgA0EMbBDfBAsgASgCECIARQ0AIAEoAhwiBCABKAIUIgNrQQxuIQUgAyAERwRAA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgBUEBayIFDQALCyABKAIYIgFFDQAgACABQQxsEN8ECyACQdAAaiQADwsgBiADQaStwAAQyAQAC50IAhJ/AX4gACgCACEFAkAgACgCBEEBaiIMQQN2IAxBB3FBAEdqIgpFDQAgCkEBRwRAIApB/v///wNxIQ0DQCAEIAVqIgcgBykDACIWQn+FQgeIQoGChIiQoMCAAYMgFkL//v379+/fv/8AhHw3AwAgB0EIaiIHIAcpAwAiFkJ/hUIHiEKBgoSIkKDAgAGDIBZC//79+/fv37//AIR8NwMAIARBEGohBCANQQJrIg0NAAsLIApBAXFFDQAgBCAFaiIEIAQpAwAiFkJ/hUIHiEKBgoSIkKDAgAGDIBZC//79+/fv37//AIR8NwMACyAAAn8CQCAMQQhPBEAgBSAMaiAFKQAANwAADAELIAwEQCAFQQhqIAUgDPwKAAALIAwNAEEADAELQQQgA2shDUEAIANrIQ8gA0EccSESIANBA3EhEUEBIQVBACEKA0AgCiELIAUhCgJAIAsgACgCACIEai0AAEGAAUcNACAEIA1qIRMgBCAPaiEUIAQgAyALQX9zbGohFQNAIAEgACALIAIREAAhFiAAKAIEIgggFqciDnEiBSEEIAAoAgAiByAFaikAAEKAgYKEiJCgwIB/gyIWUARAQQghBgNAIAQgBmohBCAGQQhqIQYgByAEIAhxIgRqKQAAQoCBgoSIkKDAgH+DIhZQDQALCyAHIBZ6p0EDdiAEaiAIcSIEaiwAAEEATgRAIAcpAwBCgIGChIiQoMCAf4N6p0EDdiEECwJAIAQgBWsgCyAFa3MgCHFBCE8EQCAEIAdqIgUtAAAgBSAOQRl2IgU6AAAgACgCACAEQQhrIAhxakEIaiAFOgAAIAcgAyAEQX9zbGohDkH/AUcEQCAOQQRqIQRBACEIIBMhBwNAIAggFGoiBS0AACEJIAUgCCAOaiIGLQAAOgAAIAYgCToAACAFQQFqIgktAAAhECAJIAZBAWoiCS0AADoAACAJIBA6AAAgBUECaiIJLQAAIRAgCSAGQQJqIgktAAA6AAAgCSAQOgAAIAVBA2oiBS0AACEJIAUgBkEDaiIFLQAAOgAAIAUgCToAACAHIgVBBGohByAEIgZBBGohBCASIAhBBGoiCEcNAAsMAgsgACgCBCEEIAAoAgAgC2pB/wE6AAAgACgCACAEIAtBCGtxakEIakH/AToAACADRQ0DIA4gFSAD/AoAAAwDCyAHIAtqIA5BGXYiBDoAACAAKAIAIAggC0EIa3FqQQhqIAQ6AAAMAgsgEUUNACARIQgDQCAFLQAAIQQgBSAGLQAAOgAAIAYgBDoAACAFQQFqIQUgBkEBaiEGIAhBAWsiCA0ACwwACwALIA0gA2shDSAPIANrIQ8gCiAKIAxJIgRqIQUgBA0ACyAAKAIEIgEgAUEBakEDdkEHbCABQQhJGwsgACgCDGs2AggL1gcBAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECyAAKAIMIgEEQCAAKAIQIAFBAnQQ3wQLIAAoAhgiAQRAIAAoAhwgAUECdBDfBAsgACgCJCIBBEAgACgCKCABQQJ0EN8ECyAAKAIwIgEEQCAAKAI0IAFBAnQQ3wQLIAAoAjwiAQRAIAAoAkAgAUECdBDfBAsgACgCSCIBBEAgACgCTCABQQJ0EN8ECyAAKAJUIgEEQCAAKAJYIAFBAnQQ3wQLIAAoAmAiAQRAIAAoAmQgAUECdBDfBAsgACgCbCIBBEAgACgCcCABQQJ0EN8ECyAAKAJ4IgEEQCAAKAJ8IAFBAnQQ3wQLIAAoAoQBIgEEQCAAKAKIASABQQJ0EN8ECyAAKAKQASIBBEAgACgClAEgAUECdBDfBAsgACgCnAEiAQRAIAAoAqABIAFBAnQQ3wQLIAAoAqgBIgEEQCAAKAKsASABQQJ0EN8ECyAAKAK0ASIBBEAgACgCuAEgAUECdBDfBAsgACgCwAEiAQRAIAAoAsQBIAFBAnQQ3wQLIAAoAswBIgEEQCAAKALQASABQQJ0EN8ECyAAKALYASIBBEAgACgC3AEgAUECdBDfBAsgACgC5AEiAQRAIAAoAugBIAFBAnQQ3wQLIAAoAvABIgEEQCAAKAL0ASABQQJ0EN8ECyAAKAL8ASIBBEAgACgCgAIgAUECdBDfBAsgACgCiAIiAQRAIAAoAowCIAFBAnQQ3wQLIAAoApQCIgEEQCAAKAKYAiABQQJ0EN8ECyAAKAKgAiIBBEAgACgCpAIgAUECdBDfBAsgACgCrAIiAQRAIAAoArACIAFBAnQQ3wQLIAAoArgCIgEEQCAAKAK8AiABQQJ0EN8ECyAAKALEAiIBBEAgACgCyAIgAUECdBDfBAsgACgC0AIiAQRAIAAoAtQCIAFBAnQQ3wQLIAAoAtwCIgEEQCAAKALgAiABQQJ0EN8ECyAAKALoAiIBBEAgACgC7AIgAUECdBDfBAsgACgC9AIiAQRAIAAoAvgCIAFBAnQQ3wQLIAAoAoADIgEEQCAAKAKEAyABQQJ0EN8ECyAAKAKMAyIBBEAgACgCkAMgAUECdBDfBAsgACgCmAMiAQRAIAAoApwDIAFBAnQQ3wQLIAAoAqQDIgEEQCAAKAKoAyABQQJ0EN8ECyAAKAKwAyIBBEAgACgCtAMgAUECdBDfBAsgACgCvAMiAQRAIAAoAsADIAFBAnQQ3wQLIAAoAsgDIgEEQCAAKALMAyABQQJ0EN8ECyAAKALUAyIBBEAgACgC2AMgAUECdBDfBAsLrggBCX9BDCEGIwBBEGsiBCQAAkAgASgCCCICQQxNBEACQCACRQRAQQghBQwBCyABKAIEIQlB0c7FAC0AABogAkEwbCIKIgFBCBDWBCIFRQ0CIAIhAQNAIAcgCkYNASAFIAdqIgMgByAJaiIIKQMANwMAIANBKGogCEEoaikDADcDACADQSBqIAhBIGopAwA3AwAgA0EYaiAIQRhqKQMANwMAIANBEGogCEEQaikDADcDACADQQhqIAhBCGopAwA3AwAgB0EwaiEHIAFBAWsiAQ0ACwsgBCACNgIMIAQgBTYCCCAEIAI2AgQgAkEMSQRAIARBBGogAkEMIAJrIgNBCEEwEIgDIAQoAgggBCgCDCIFQTBsaiEBIANBAk8EQCACQX9zQQxqIgJBB3EhBiADQQJrQQdPBEAgAkF4cSEHA0AgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgAUEwakIANwMAIAFBOGpCADcDACABQUBrQgA3AwAgAUHIAGpCADcDACABQdAAakIANwMAIAFB2ABqQgA3AwAgAUHgAGpCADcDACABQegAakIANwMAIAFB8ABqQgA3AwAgAUH4AGpCADcDACABQYABakIANwMAIAFBiAFqQgA3AwAgAUG4AWpCADcDACABQbABakIANwMAIAFBqAFqQgA3AwAgAUGgAWpCADcDACABQZgBakIANwMAIAFBkAFqQgA3AwAgAUHAAWpCADcDACABQcgBakIANwMAIAFB0AFqQgA3AwAgAUHYAWpCADcDACABQeABakIANwMAIAFB6AFqQgA3AwAgAUHwAWpCADcDACABQfgBakIANwMAIAFBgAJqQgA3AwAgAUGIAmpCADcDACABQZACakIANwMAIAFBmAJqQgA3AwAgAUHIAmpCADcDACABQcACakIANwMAIAFBuAJqQgA3AwAgAUGwAmpCADcDACABQagCakIANwMAIAFBoAJqQgA3AwAgAUH4AmpCADcDACABQfACakIANwMAIAFB6AJqQgA3AwAgAUHgAmpCADcDACABQdgCakIANwMAIAFB0AJqQgA3AwAgAUGAA2ohASAHQQhrIgcNAAsLIAYEQANAIAFCADcDACABQShqQgA3AwAgAUEgakIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIAFBMGohASAGQQFrIgYNAAsLIAMgBWpBAWshBQsgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgBUEBaiEGCyAAIAQpAgQ3AgAgAEEIaiAGNgIAIARBEGokAA8LQezGwgBBN0HMx8IAEP4DAAtBCCABQeiBwAAQyAQAC6kGAgp/An4jAEGQCWsiBCQAIARBCGoiByABEGUgBEGQB2ogBEEwaikDADcDACAEQYgHaiAEQShqKQMANwMAIARBgAdqIARBIGopAwA3AwAgBEH4BmogBEEYaikDADcDACAEQfAGaiAEQRBqKQMANwMAIARBoAdqIARBQGspAwA3AwAgBEGoB2ogBEHIAGopAwA3AwAgBEGwB2ogBEHQAGopAwA3AwAgBEG4B2ogBEHYAGopAwA3AwAgBEHAB2ogBEHgAGopAwA3AwAgBCAEKQMINwPoBiAEIAQpAzg3A5gHIARBqAhqIgUgByABED8gBEHoAGoiDSAFIAFB4ABqIggQjQEgBEHIBGoiBiAHIAcQPyAFIAEgARDVASAEQcgBaiILIAYgBRCNASAEQegDaiIJIAggCBDVASAGIAEgCxCNASAFIAkgBhDBAyAEKQO4CCEOIAQpA7AIIQ8gBCgCqAhBAUcEQCAEQZgDaiAEQcAIakHQAPwKAAAgBCAONwOQAyAEIA83A4gDIARBqAJqIgogBEGIA2oiDCAHEI0BIARB0AdqIARBsAJqKQMANwMAIARB2AdqIARBuAJqKQMANwMAIARB4AdqIARBwAJqKQMANwMAIARB6AdqIARByAJqKQMANwMAIARB8AdqIARB0AJqKQMANwMAIARBgAhqIARB4AJqKQMANwMAIARBiAhqIARB6AJqKQMANwMAIARBkAhqIARB8AJqKQMANwMAIARBmAhqIARB+AJqKQMANwMAIARBoAhqIARBgANqKQMANwMAIAQgBCkDqAI3A8gHIAQgBCkD2AI3A/gHIAUgCiABED8gDCAFIAgQjQEgBiAKIAoQPyAFIAEgCxDVASAJIAYgBRCNASAFIAEgCRCNASAGIAogBRA/IARBiAZqIAYgCBCNASAEQagFaiIBIAlB4AD8CgAAIAAgBEHoBmogDSACIAMQICAAQdABaiAEQcgHaiAMIAIgAxAgIABBEGogAUHAAfwKAAAgBEGQCWokAA8LIAQgDjcDsAggBCAPNwOoCEGgscIAQSsgBEGoCGpBpLrCAEGEu8IAEMoDAAu6BwECfyMAQeADayICJAAgAkEAQeAA/AsAAkACQCABIAIQpgQEQCABQeAAaiIDIAIQpgQNAQsgAkGIAWogAUEoaikDADcDACACQYABaiABQSBqKQMANwMAIAJB+ABqIAFBGGopAwA3AwAgAkHwAGogAUEQaikDADcDACACQegAaiABQQhqKQMANwMAIAJBmAFqIAFBOGopAwA3AwAgAkGgAWogAUFAaykDADcDACACQagBaiABQcgAaikDADcDACACQbABaiABQdAAaikDADcDACACQbgBaiABQdgAaikDADcDACACIAEpAwA3A2AgAiABKQMwNwOQASACQegBaiABQYgBaikDADcDACACQeABaiABQYABaikDADcDACACQdgBaiABQfgAaikDADcDACACQdABaiABQfAAaikDADcDACACQcgBaiABQegAaikDADcDACACQZgCaiABQbgBaikDADcDACACQZACaiABQbABaikDADcDACACQYgCaiABQagBaikDADcDACACQYACaiABQaABaikDADcDACACQfgBaiABQZgBaikDADcDACACIAEpA2A3A8ABIAIgASkDkAE3A/ABQQAiAUUEQCACIAJBwAFqQeAA/AoAAAsgAEHgAGogAhC0AiABDQEgACACQeAAakHgAPwKAAAMAQsgAkHIAmogAUEoaikDADcDACACQcACaiABQSBqKQMANwMAIAJBuAJqIAFBGGopAwA3AwAgAkGwAmogAUEQaikDADcDACACQagCaiABQQhqKQMANwMAIAJB2AJqIAFBOGopAwA3AwAgAkHgAmogAUFAaykDADcDACACQegCaiABQcgAaikDADcDACACQfACaiABQdAAaikDADcDACACQfgCaiABQdgAaikDADcDACACIAEpAwA3A6ACIAIgASkDMDcD0AIgAkGoA2ogA0EoaikDADcDACACQaADaiADQSBqKQMANwMAIAJBmANqIANBGGopAwA3AwAgAkGQA2ogA0EQaikDADcDACACQYgDaiADQQhqKQMANwMAIAJB2ANqIAFBuAFqKQMANwMAIAJB0ANqIAFBsAFqKQMANwMAIAJByANqIAFBqAFqKQMANwMAIAJBwANqIAFBoAFqKQMANwMAIAJBuANqIAFBmAFqKQMANwMAIAIgAykDADcDgAMgAiABKQOQATcDsANBACIBRQRAIAAgAkGgAmpB4AD8CgAACyABDQAgAEHgAGogAkGAA2pB4AD8CgAACyACQeADaiQAC6EIAgF/Cn4jAEGQAmsiAiQAIAJBsAFqIAEpAxgiBUKblK/D8rWo3oZ/fiIEQgBCbUIAEMkDIAJBoAFqIARCAEJ/QgAQyQMgAkGQAWogBEIAQv///////////wBCABDJAyACQYABaiACKQOgASIEIAEpAxB8IgcgAikDuAEgBSACKQOwASIDfCADVK18fCIFQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAkHwAGogA0IAQn9CABDJAyACIANCAEL///////////8AQgAQyQMgAkHgAGogAikDcCIDIAQgASkDCHwiBiAFIAdUrSACKQOoASIKIAQgB1atfHx8Igt8IgcgAikDiAEgBSACKQOAASIFfCAFVK18fCIFQpuUr8Pytajehn9+IghCAEJtQgAQyQMgAkHQAGogCEIAQn9CABDJAyACQRBqIAhCAEL///////////8AQgAQyQMgAkFAayACKQNQIgggAyACKQOQASIMIAEpAwB8IgkgBiALVq0gCiAEIAZWrXx8fCIEfCIGIAUgB1StIAIpA3giCiADIAdWrXx8fCILfCIHIAIpA2ggBSACKQNgIgV8IAVUrXx8IgVCm5Svw/K1qN6Gf34iA0IAQm1CABDJAyACQTBqIANCAEJ/QgAQyQMgAkEgaiADQgBC////////////AEIAEMkDAkACQCACKQMoIAIpAxggAikDCCAEIAlUrSACKQOYASAJIAxUrXx8IgkgAikDAHwiAyAJVK18IAMgBiALVq0gCiAEIAZWrXx8fCIEIANUrXwiBiACKQMQfCIDIAZUrXwgAyACKQNYIgYgBCAEIAh8IgRWrXwgBCAFIAdUrSAGIAcgCFStfHx8IgYgBFStfHwiBCADVK18IgMgAikDIHwiByADVK18IAcgAikDOCIIIAQgBCACKQMwIgN8IgRWrXwgBCAEIAggAyADIAZ8IgNWrXwgAyACKQNIIAUgAikDQCIFfCAFVK18fCIIIANUrXx8IgRWrXx8IgUgB1StfCIGQgBTDQACQCAGQv///////////wBaBEBCfyEDIAVCf1IEQCAEIQcgBSEDQv///////////wAhBgwECyAEQn9RDQEgBCEHQv///////////wAhBgwDCyAEIQcgBSEDDAILQn8hByAIQm1aDQBC////////////ACEGDAELIARCAXwiAyAIQm1UrSIJfSEHIAVCAXwiCiAEQn9SIAMgCVRyrSIEfSEDIAYgBUJ/UiAEIApWcq19Qv///////////wB9IQYgCEITfCEICyACIAg3A9gBIAIgBzcD0AEgAiADNwPIASACIAY3A8ABIAIgAkHgAWoiATYCjAIgAkEANgL0ASACQQA2AuABIAIgAkHAAWo2AogCIAAgARCtAiACQZACaiQAC5AHAQ9/IwBBIGsiCyQAIAEoAgQhCSACKAIEIQYCQAJAIAIoAggiCCABKAIIIgVNBEAgCEUNAiAIQQFxAkAgCEEBRgRADAELIAhB/v///wFxIRAgBiEDIAkhAgNAIAIgAigCACIRIAMoAgBqIg0gB2oiBzYCACACQQRqIgQgBCgCACIMIANBBGooAgBqIg4gDSARSSAHIA1JcmoiBDYCACAEIA5JIAwgDktyIgQhByADQQhqIQMgAkEIaiECIBAgCkECaiIKRw0ACwsEfyAJIApBAnQiBGoiAiACKAIAIgMgBCAGaigCAGoiBiAHaiICNgIAIAIgBkkgAyAGS3IFIAQLQQFxRQ0CIAUgCEYNASAFQQJ0IQYgCEECdCECA0AgAiAJaiIDIAMoAgBBAWoiAzYCACADDQMgBiACQQRqIgJHDQALIAUhCAwBCwJAIAVFBEAMAQsgBUEBcQJAIAVBAUYEQAwBCyAFQf7///8BcSEQIAYhAyAJIQIDQCACIAIoAgAiESADKAIAaiINIAdqIgc2AgAgAkEEaiIEIAQoAgAiDCADQQRqKAIAaiIOIA0gEUkgByANSXJqIgQ2AgAgBCAOSSAMIA5LciEHIANBCGohAyACQQhqIQIgECAKQQJqIgpHDQALC0UNACAJIApBAnQiBGoiAiACKAIAIgMgBCAGaigCAGoiBCAHaiICNgIAIAIgBEkgAyAES3IhBwsgCCAFayIEQQJ0IQIgBSEDIAEoAgAgBWsgBEkEQCABIAUgBBCJAyABKAIEIQkgASgCCCEDCyACBEAgCSADQQJ0aiAGIAVBAnRqIAL8CgAACyABIAMgBGoiBjYCCAJAIAUgBk0EQCAFIAZGDQEgCSAFQQJ0aiIMIAwoAgAiBCAHaiICNgIAIAIgBE8NAyAGIAVrQQFGBEAgBiEIDAMLIAMgCGpBAnQgBUEDdGtBBGshBCAMQQRqIQIDQCACIAIoAgBBAWoiAzYCACADDQQgAkEEaiECIARBBGsiBA0ACyAGIQgMAgsgBSAGQZy8xAAQ5AQACyALQQA2AhggC0EBNgIMIAtBjLvEADYCCCALQgQ3AhAgC0EIakH8u8QAEKgEAAsgASgCACAIRgR/IAFBjLzEABClAyABKAIEBSAJCyAIQQJ0akEBNgIAIAEgCEEBajYCCAsgACABKQIANwIAIABBCGogAUEIaigCADYCACALQSBqJAAL/QYCCX8GfiMAQRBrIgckAAJAAkACQCABKAIIRQRAQdHOxQAtAAAaQQEhAkEBQQEQ1gQiBkUNAiAGQQA6AAAgB0EBNgIEDAELIAdBBGogAUEIELACIAcoAgghBiAHKAIMIgJBAkkNACACIAZqIQRBACEBIAJBAXYiBUEBRwRAIAJBAWshAyAFQf7///8HcSEJA0AgAyAGaiIFLQAAIQggBSABIAZqIgUtAAA6AAAgBSAIOgAAIAQgAUF+c2oiCC0AACEKIAggBUEBaiIFLQAAOgAAIAUgCjoAACADQQJrIQMgCSABQQJqIgFHDQALCyACQQJxBEAgASAGaiIDLQAAIQUgAyAEIAFBf3NqIgEtAAA6AAAgASAFOgAACyACQSVPDQILAkAgAiACQQxrIgFBACABIAJNGyIFRg0AIAUgBmohAUEMIAIgAkEMTxsiBEEDcSEDAkAgBEEBa0EDSQRADAELIARBDHEhBANAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIARBBGsiBA0ACwsgA0UNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIANBAWsiAw0ACwsgAkEYayIBQQAgASACTRsiBCAFRwRAQRggAiACQRhPG0EMIAIgAkEMTxtrIQMgBCAGaiEBA0AgEEIIhiAPQjiIhCEQIAExAAAgD0IIhoQhDyABQQFqIQEgA0EBayIDDQALCwJAIAJBGUkNACAEQQNxIQMCQCACQRlrQQNJBEAgBiEBDAELIARBPHEhBCAGIQEDQCAMQiCIQoCA/P8PgyAOQiCGhCAMQhCGIgxCMIiEIQ4gAUEDajEAACABQQFqMQAAIAwgATEAAEIIhoSEQhCGIAFBAmoxAABCCIaEhCEMIAFBBGohASAEQQRrIgQNAAsLIANFDQADQCAOQgiGIAxCOIiEIQ4gATEAACAMQgiGhCEMIAFBAWohASADQQFrIgMNAAsLIAAgDDcDICAAIA83AxAgACALNwMAIAAgDjcDKCAAIBA3AxggACANNwMIIAcoAgQiAARAIAYgABDfBAsgB0EQaiQADwtBAUEBEP8EAAtB1NrCAEEtQYTbwgAQ/gMAC9AJAgF/Cn4jAEGAAmsiAiQAIAJB8AFqIAEpAxgiBUL/////vrL98EJ+IgNCAEKBgICAv7L98MMAQgAQyQMgAkHgAWogA0IAQpHh5c2HifqZKEIAEMkDIAJB0AFqIANCAELdsIWM6LaRqLh/QgAQyQMgAkHAAWogA0IAQqnAxomuzpOyMEIAEMkDIAJBsAFqIAIpA+ABIgcgASkDEHwiBCACKQP4ASAFIAIpA/ABIgN8IANUrXx8IgVC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJBoAFqIANCAEKR4eXNh4n6mShCABDJAyACQdAAaiADQgBC3bCFjOi2kai4f0IAEMkDIAIgA0IAQqnAxomuzpOyMEIAEMkDIAJBkAFqIAIpA6ABIgkgAikD0AEiCCABKQMIfCIGIAQgBVatIAIpA+gBIAQgB1StfHx8Igp8IgQgAikDuAEgAikDsAEiAyAFfCADVK18fCIFQv////++sv3wQn4iA0IAQoGAgIC/sv3wwwBCABDJAyACQYABaiADQgBCkeHlzYeJ+pkoQgAQyQMgAkHwAGogA0IAQt2whYzotpGouH9CABDJAyACQeAAaiADQgBCqcDGia7Ok7IwQgAQyQMgAkFAayACKQOAASILIAIpA8ABIgwgASkDAHwiByAGIApWrSACKQPYASAGIAhUrXx8fCIGIAIpA1B8IgggBCAFVq0gAikDqAEgBCAJVK18fHwiCXwiBCACKQOYASACKQOQASIDIAV8IANUrXx8IgVC/////76y/fBCfiIDQgBCgYCAgL+y/fDDAEIAEMkDIAJBMGogA0IAQpHh5c2HifqZKEIAEMkDIAJBIGogA0IAQt2whYzotpGouH9CABDJAyACQRBqIANCAEKpwMaJrs6TsjBCABDJAwJAIAIpAxggAikDaCACKQMIIAYgB1StIAIpA8gBIAcgDFStfHwiByACKQMAfCIDIAdUrXwgAyADIAggCVatIAIpA1ggBiAIVq18fHwiA1atfCIHIAIpA2B8IgYgB1StfCAGIAIpA3ggAyADIAIpA3B8IgNWrXwgAyAEIAVWrSACKQOIASAEIAtUrXx8fCIEIANUrXx8IgMgBlStfCIHIAIpAxB8IgYgB1StfCAGIAIpAyggAyADIAIpAyB8IgNWrXwgAyACKQM4IAIpAzAiByAEfCIEIAdUrXwgBCACKQNIIAUgAikDQCIFfCAFVK18fCIFIARUrXx8IgQgA1StfHwiAyAGVK18IgZCqcDGia7Ok7IwUg0AAkAgA0LdsIWM6LaRqLh/Vg0AQqnAxomuzpOyMCEGIANC3bCFjOi2kai4f1INASAEQpHh5c2HifqZKFYNACAFQoGAgIC/sv3wwwBUBEBC3bCFjOi2kai4fyEDDAILIARCkeHlzYeJ+pkoUQ0AQt2whYzotpGouH8hAwwBC0J/QgAgA0Kjz/rzl8nu18cAfCIDIARCkeHlzYeJ+pkoVCAEQpHh5c2HifqZKH0iBCAFQoGAgIC/sv3wwwBUrSIHVHKtIghUGyEGIAQgB30hBCADIAh9IQMgBUKBgICAv7L98MMAfSEFCyAAIAU3AxggACAENwMQIAAgAzcDCCAAIAY3AwAgAkGAAmokAAvVCQIBfwp+IwBBgAJrIgIkACACQfABaiABKQMYIgVCiceZpK7wgemHf34iA0IAQsf688PtgqOQPEIAEMkDIAJB4AFqIANCAEKNlcfDltLawJd/QgAQyQMgAkHQAWogA0IAQt2whYzotpGouH9CABDJAyACQcABaiADQgBCqcDGia7Ok7IwQgAQyQMgAkGwAWogAikD4AEiByABKQMQfCIEIAIpA/gBIAUgAikD8AEiA3wgA1StfHwiBUKJx5mkrvCB6Yd/fiIDQgBCx/rzw+2Co5A8QgAQyQMgAkGgAWogA0IAQo2Vx8OW0trAl39CABDJAyACQdAAaiADQgBC3bCFjOi2kai4f0IAEMkDIAIgA0IAQqnAxomuzpOyMEIAEMkDIAJBkAFqIAIpA6ABIgkgAikD0AEiCCABKQMIfCIGIAQgBVatIAIpA+gBIAQgB1StfHx8Igp8IgQgAikDuAEgAikDsAEiAyAFfCADVK18fCIFQonHmaSu8IHph39+IgNCAELH+vPD7YKjkDxCABDJAyACQYABaiADQgBCjZXHw5bS2sCXf0IAEMkDIAJB8ABqIANCAELdsIWM6LaRqLh/QgAQyQMgAkHgAGogA0IAQqnAxomuzpOyMEIAEMkDIAJBQGsgAikDgAEiCyACKQPAASIMIAEpAwB8IgcgBiAKVq0gAikD2AEgBiAIVK18fHwiBiACKQNQfCIIIAQgBVatIAIpA6gBIAQgCVStfHx8Igl8IgQgAikDmAEgAikDkAEiAyAFfCADVK18fCIFQonHmaSu8IHph39+IgNCAELH+vPD7YKjkDxCABDJAyACQTBqIANCAEKNlcfDltLawJd/QgAQyQMgAkEgaiADQgBC3bCFjOi2kai4f0IAEMkDIAJBEGogA0IAQqnAxomuzpOyMEIAEMkDAkAgAikDGCACKQNoIAIpAwggBiAHVK0gAikDyAEgByAMVK18fCIHIAIpAwB8IgMgB1StfCADIAMgCCAJVq0gAikDWCAGIAhWrXx8fCIDVq18IgcgAikDYHwiBiAHVK18IAYgAikDeCADIAMgAikDcHwiA1atfCADIAQgBVatIAIpA4gBIAQgC1StfHx8IgQgA1StfHwiAyAGVK18IgcgAikDEHwiBiAHVK18IAYgAikDKCADIAMgAikDIHwiA1atfCADIAIpAzggAikDMCIHIAR8IgQgB1StfCAEIAIpA0ggBSACKQNAIgV8IAVUrXx8IgUgBFStfHwiBCADVK18fCIDIAZUrXwiBkKpwMaJrs6TsjBSDQACQCADQt2whYzotpGouH9WDQBCqcDGia7Ok7IwIQYgA0LdsIWM6LaRqLh/Ug0BIARCjZXHw5bS2sCXf1YNACAFQsf688PtgqOQPFQEQELdsIWM6LaRqLh/IQMMAgsgBEKNlcfDltLawJd/UQ0AQt2whYzotpGouH8hAwwBC0J/QgAgA0Kjz/rzl8nu18cAfCIDIARCjZXHw5bS2sCXf1QgBELz6ri86a2lv+gAfCIEIAVCx/rzw+2Co5A8VK0iB1RyrSIIVBshBiAEIAd9IQQgAyAIfSEDIAVCx/rzw+2Co5A8fSEFCyAAIAU3AxggACAENwMQIAAgAzcDCCAAIAY3AwAgAkGAAmokAAvEBwIMfwF+IwBBoAJrIgMkACACpyEEAkACQAJAAkACQCACQgFYBEAgBEEBaw0EDAELIANBKGoiBSABQShqKQMANwMAIANBIGoiBiABQSBqKQMANwMAIANBGGoiByABQRhqKQMANwMAIANBEGoiCCABQRBqKQMANwMAIANBCGoiCSABQQhqKQMANwMAIANBOGoiCiABQThqKQMANwMAIANBQGsiCyABQUBrKQMANwMAIANByABqIgwgAUHIAGopAwA3AwAgA0HQAGoiDSABQdAAaikDADcDACADQdgAaiIOIAFB2ABqKQMANwMAIAMgASkDADcDACADIAEpAzA3AzAgBEEBcUUNAQwCCyADQYgBaiABQShqKQMANwMAIANBgAFqIAFBIGopAwA3AwAgA0H4AGogAUEYaikDADcDACADQfAAaiABQRBqKQMANwMAIANB6ABqIAFBCGopAwA3AwAgA0GYAWogAUE4aikDADcDACADQaABaiABQUBrKQMANwMAIANBqAFqIAFByABqKQMANwMAIANBsAFqIAFB0ABqKQMANwMAIANBuAFqIAFB2ABqKQMANwMAIAMgASkDADcDYCADIAEpAzA3A5ABIAAgA0HgAGpB4AD8CgAADAMLA0AgA0HgAGoiASADEF4gAyABQeAA/AoAACACQgKDIAJCAYghAlANAAsLIANB6AFqIAUpAwA3AwAgA0HgAWogBikDADcDACADQdgBaiAHKQMANwMAIANB0AFqIAgpAwA3AwAgA0HIAWogCSkDADcDACADQfgBaiAKKQMANwMAIANBgAJqIAspAwA3AwAgA0GIAmogDCkDADcDACADQZACaiANKQMANwMAIANBmAJqIA4pAwA3AwAgAyADKQMANwPAASADIAMpAzA3A/ABIAJCAVIEQANAIANB4ABqIgQgA0HAAWoiBRBeQQAiAUUEQCAFIARB4AD8CgAACwJAIAJCAoNQDQAgA0HgAGoiBCADIANBwAFqED8gAQ0AIAMgBEHgAPwKAAALIAJCBFQgAkIBiCECRQ0ACwsgACADQeAA/AoAAAwBCyAAQgA3AzAgAEEoakG4ocUAKQMANwMAIABBIGpBsKHFACkDADcDACAAQRhqQaihxQApAwA3AwAgAEEQakGgocUAKQMANwMAIABBCGpBmKHFACkDADcDACAAQZChxQApAwA3AwAgAEE4akIANwMAIABBQGtCADcDACAAQcgAakIANwMAIABB0ABqQgA3AwAgAEHYAGpCADcDAAsgA0GgAmokAAvbBwEJfyMAQSBrIgckACABKAIAIQoCQAJAAkACQAJAAkACQCACRQRAIAEoAgQhCyAKQYCAgIB4Rg0BIAEoAgghASAKIQQgCyEFDAILQX8gASgCBCILIAEgCkGAgICAeEYbIggoAgggAmpBAWoiASABIAJJGyIGQQJ0IQUgBkH/////A0sgBUH8////B0tyDQNB0c7FAC0AABpBBCEEIAVBBBDWBCIBRQ0DIAcgATYCGCAHIAY2AhQgASEFIAJBAUcEfyACQQJ0QQRrIgUEQCABQQAgBfwLAAsgASAFagUgBQtBADYCACAIKAIIIgVBAnQhCSAHIAI2AhwgCCgCBCEIIAYgAiIEayAFSQRAIAdBFGogBCAFEIkDIAcoAhwhBCAHKAIYIQELIAkEQCABIARBAnRqIAggCfwKAAALIAdBEGogBCAFajYCACAHIAcpAhQ3AwgMAgsgCygCCCIBQQJ0IQYgAUH/////A0sgBkH8////B0tyDQMgCygCBCEIAn8gBkUEQEEEIQVBAAwBC0HRzsUALQAAGkEEIQQgBkEEENYEIgVFDQQgAQshBCAGRQ0AIAUgCCAG/AoAAAsgByABNgIQIAcgBTYCDCAHIAQ2AggLIANB/wFxRQRAIAcoAhAhBAwECyACIAcoAhAiBksNAiAGIAIiBEYNAyAHKAIMIQUgBkECdCEEIAJBAnQhASADQR9xIQhBACADa0EfcSEJQQAhAwNAIAEgBWoiDCADIAwoAgAiAyAIdHI2AgAgAyAJdiEDIAQgAUEEaiIBRw0ACyADRQRAIAYhBAwECyAHKAIIIAZGBH8gB0EIakHohcUAEKUDIAcoAgwFIAULIAZBAnRqIAM2AgAgByAGQQFqIgQ2AhAMAwsgBCAFQdiFxQAQyAQACyAEIAZBpIPFABDIBAALIAIgBkH4hcUAEOQEAAtBACEFIAcoAgwhBiAHKAIIIQgCQCAERQ0AIAYgBEECdCIBakEEaygCAARAIAQhBQwBCyAGQQRrIQkgBEH/////A3EhAwNAIAFFDQEgA0EBayEDIAEgCWogAUEEayEBKAIARQ0ACyADQQFqIgEgBCABIARJGyEFCwJAAkACQCAIQQJ2IAVNBEAgBiEDIAghAQwBC0EAIQEgCEUEQCAGIQMMAQsgCEECdCEEIAVFBEBBBCEDIAYgBBDfBAwBCyAGIARBBCAFIgFBAnQiBBDOBCIDRQ0BCyAAIAU2AgggACADNgIEIAAgATYCACACRSAKQf////8HcUVyDQEgCyAKQQJ0EN8EDAELQQQgBEGIhsUAEMgEAAsgB0EgaiQAC/4HAgp/AX4jAEHQA2siCiQAQdHOxQAtAAAaAkACQAJAAkACQAJAAkBBIEEEENYEIgwEQCABKAIIIgutQjB+IhSnIREgFEIgiKcgEUH4////B0tyDQEgEUUEQCAMIAs2AghBCCESIAxBCDYCBCAMIAs2AgAgASgCDCEBDAULIAEoAgQhE0HRzsUALQAAGkEIIQ0gEUEIENYEIhJFDQEgC0UNAiALIQ0DQCAOIBFHBEAgDiASaiIPIA4gE2oiECkDADcDACAPQShqIBBBKGopAwA3AwAgD0EgaiAQQSBqKQMANwMAIA9BGGogEEEYaikDADcDACAPQRBqIBBBEGopAwA3AwAgD0EIaiAQQQhqKQMANwMAIA5BMGohDiANQQFrIg0NAQsLIAwgCzYCCCAMIBI2AgQgDCALNgIADAMLQQRBIBD/BAALIA0gEUHogcAAEMgEAAsgDEEANgIIIAwgEjYCBCAMQQA2AgALQdHOxQAtAAAaIAEoAgwhASARQQgQ1gQiEkUNASALRQ0AQQAhDiALIQ0DQCAOIBFGDQEgDiASaiIPIA4gE2oiECkDADcDACAPQShqIBBBKGopAwA3AwAgD0EgaiAQQSBqKQMANwMAIA9BGGogEEEYaikDADcDACAPQRBqIBBBEGopAwA3AwAgD0EIaiAQQQhqKQMANwMAIA5BMGohDiANQQFrIg0NAAsLIAwgCzYCGCAMIBI2AhQgDCALNgIQIAwgATYCHCAMIAE2AgwgCkECNgIQIAogDDYCDCAKQQI2AghBACENIApBADYCHCAKQoCAgICAATcCFCADBEAgCkGwA2ohAQNAIAUgDUYNAyAHIA1GDQQgCkHwAWoiCyACIAQgBhDGAkEAIgxFBEAgCkEgaiALQcAB/AoAAAsgCkHoAWoiDiABQQhqKQIANwMAIAogASkCADcD4AEgCigCECILIAooAghGBEAgCkEIakGAkcAAEKMDCyAKKAIMIAtBBHRqIhEgCikD4AE3AgAgEUEIaiAOKQMANwIAIAogC0EBajYCECAKKAIcIgsgCigCFEYEQCAKQRRqQZCRwAAQnQMLIAxFBEAgCigCGCALQcABbGogCkEgakHAAfwKAAALIAogC0EBajYCHCACQcABaiECIAZBMGohBiAEQTBqIQQgAyANQQFqIg1HDQALCyAKQcgDaiAKQRBqKAIANgIAIAogCikCCDcDwAMgCkGAgICAeDYC8AEgACAKQcADaiAKQfABaiAIIAkQqwEgAEEYaiAKQRxqKAIANgIAIAAgCikCFDcCECAKQdADaiQADwtBCCARQeiBwAAQyAQACyAFIAVB4JDAABDZAwALIAcgB0HwkMAAENkDAAvhDAIKfwh+IwBB4ABrIgQkACADBEAgBEEIaiIDQaz8wAAoAgA2AgAgBEGk/MAAKQIANwMAIAIEQCAEQZj9wAAQpQMgBCgCBCACNgIAIARBATYCCAsgBEHYAGogAygCADYCACAEIAQpAwA3A1AgACgCCCIFIAAoAgBGBEAgAEG0ksEAEJ8DCyAAKAIEIAVBDGxqIgMgBCkDUDcCACADQQhqIARB2ABqKAIANgIAIAAgBUEBajYCCAsgAgRAIAEgAkEFdGohDSAEQdgAaiEKQaz8wAAoAgAhDEGk/MAAKQIAIRUDQEIAIRBCACERQgAhEkIAIRNCACEUQgAhDiMAQRBrIggkACAIQQRqIAEQvgECQCAIKAIMIgZBJUkEQCAIKAIIIQICQCAGIAZBDGsiA0EAIAMgBk0bIglGDQAgAiAJaiEDQQwgBiAGQQxPGyIFQQNxIQcgBUEBa0EDTwRAIAVBDHEhBQNAIBBCIIhCgID8/w+DIBJCIIaEIBBCEIYiD0IwiIQhEiADQQNqMQAAIANBAWoxAAAgDyADMQAAQgiGhIRCEIYgA0ECajEAAEIIhoSEIRAgA0EEaiEDIAVBBGsiBQ0ACwsgB0UNAANAIBJCCIYgEEI4iIQhEiADMQAAIBBCCIaEIRAgA0EBaiEDIAdBAWsiBw0ACwsgBkEYayIDQQAgAyAGTRsiBSAJRwRAQRggBiAGQRhPG0EMIAYgBkEMTxtrIQcgAiAFaiEDA0AgDkIIhiAUQjiIhCEOIAMxAAAgFEIIhoQhFCADQQFqIQMgB0EBayIHDQALCwJAIAZBGUkNACAFQQNxIQcCQCAGQRlrQQNJBEAgAiEDDAELIAVBPHEhBSACIQMDQCARQiCIQoCA/P8PgyATQiCGhCARQhCGIg9CMIiEIRMgA0EDajEAACADQQFqMQAAIA8gAzEAAEIIhoSEQhCGIANBAmoxAABCCIaEhCERIANBBGohAyAFQQRrIgUNAAsLIAdFDQADQCATQgiGIBFCOIiEIRMgAzEAACARQgiGhCERIANBAWohAyAHQQFrIgcNAAsLIAQgETcDICAEIBQ3AxAgBCAQNwMAIAQgEzcDKCAEIA43AxggBCASNwMIIAgoAgQiAwRAIAIgAxDfBAsgCEEQaiQADAELQdTawgBBLUGE28IAEP4DAAsgBCkDCCEOIAQpAwAhDyAKIAw2AgAgBCAVNwNQIA4gD4RQRQRAQQEhAkEAIQMDQCAEKAJQIAJBAWtGBEAgBEHQAGpBqP3AABClAwsgBCgCVCADaiAPPgIAIA9C/////w9WIA5CAFIgDlAgDkIghiAPQiCIhCEPIANBBGohAyAOQiCIIQ4gBCACNgJYIAJBAWohAhsNAAsLIARByABqIgsgCigCADYCACAEIAQpA1A3A0AgACgCCCIDIAAoAgBGBEAgAEG0ksEAEJ8DCyAAKAIEIANBDGxqIgIgBCkDQDcCACACQQhqIAsoAgA2AgAgACADQQFqIgY2AgggBCkDGCEOIAQpAxAhDyAKIAw2AgAgBCAVNwNQIA4gD4RQRQRAQQEhAkEAIQMDQCAEKAJQIAJBAWtGBEAgBEHQAGpBqP3AABClAwsgBCgCVCADaiAPPgIAIA9C/////w9WIA5CAFIgDlAgDkIghiAPQiCIhCEPIANBBGohAyAOQiCIIQ4gBCACNgJYIAJBAWohAhsNAAsgACgCCCEGCyALIAooAgA2AgAgBCAEKQNQNwNAIAAoAgAgBkYEQCAAQbSSwQAQnwMLIAAoAgQgBkEMbGoiAiAEKQNANwIAIAJBCGogCygCADYCACAAIAZBAWoiBzYCCCAEKQMoIQ4gBCkDICEPIAogDDYCACAEIBU3A1AgDiAPhFBFBEBBASECQQAhAwNAIAQoAlAgAkEBa0YEQCAEQdAAakGo/cAAEKUDCyAEKAJUIANqIA8+AgAgD0L/////D1YgDkIAUiAOUCAOQiCGIA9CIIiEIQ8gA0EEaiEDIA5CIIghDiAEIAI2AlggAkEBaiECGw0ACwsgCyAKKAIANgIAIAQgBCkDUDcDQCAAKAIAIAdGBEAgAEG0ksEAEJ8DCyAAKAIEIAdBDGxqIgIgBCkDQDcCACACQQhqIAsoAgA2AgAgACAGQQJqNgIIIAFBIGoiASANRw0ACwsgBEHgAGokAAv+BwIKfwF+IwBB0ANrIggkAEHRzsUALQAAGgJAAkACQAJAAkACQAJAQSBBBBDWBCIKBEAgASgCCCIJrUIwfiISpyEPIBJCIIinIA9B+P///wdLcg0BIA9FBEAgCiAJNgIIQQghECAKQQg2AgQgCiAJNgIAIAEoAgwhAQwFCyABKAIEIRFB0c7FAC0AABpBCCELIA9BCBDWBCIQRQ0BIAlFDQIgCSELA0AgDCAPRwRAIAwgEGoiDSAMIBFqIg4pAwA3AwAgDUEoaiAOQShqKQMANwMAIA1BIGogDkEgaikDADcDACANQRhqIA5BGGopAwA3AwAgDUEQaiAOQRBqKQMANwMAIA1BCGogDkEIaikDADcDACAMQTBqIQwgC0EBayILDQELCyAKIAk2AgggCiAQNgIEIAogCTYCAAwDC0EEQSAQ/wQACyALIA9B6IHAABDIBAALIApBADYCCCAKIBA2AgQgCkEANgIAC0HRzsUALQAAGiABKAIMIQEgD0EIENYEIhBFDQEgCUUNAEEAIQwgCSELA0AgDCAPRg0BIAwgEGoiDSAMIBFqIg4pAwA3AwAgDUEoaiAOQShqKQMANwMAIA1BIGogDkEgaikDADcDACANQRhqIA5BGGopAwA3AwAgDUEQaiAOQRBqKQMANwMAIA1BCGogDkEIaikDADcDACAMQTBqIQwgC0EBayILDQALCyAKIAk2AhggCiAQNgIUIAogCTYCECAKIAE2AhwgCiABNgIMIAhBAjYCECAIIAo2AgwgCEECNgIIQQAhCyAIQQA2AhwgCEKAgICAgAE3AhQgAwRAIAhBsANqIQEDQCAFIAtGDQMgByALRg0EIAhB8AFqIgkgAiAEIAYQxgJBACIKRQRAIAhBIGogCUHAAfwKAAALIAhB6AFqIgwgAUEIaikCADcDACAIIAEpAgA3A+ABIAgoAhAiCSAIKAIIRgRAIAhBCGpBtLvCABCjAwsgCCgCDCAJQQR0aiIPIAgpA+ABNwIAIA9BCGogDCkDADcCACAIIAlBAWo2AhAgCCgCHCIJIAgoAhRGBEAgCEEUakHEu8IAEJ0DCyAKRQRAIAgoAhggCUHAAWxqIAhBIGpBwAH8CgAACyAIIAlBAWo2AhwgAkHAAWohAiAGQTBqIQYgBEEwaiEEIAMgC0EBaiILRw0ACwsgCEHIA2ogCEEQaigCADYCACAIIAgpAgg3A8ADIAhBgICAgHg2AvABIAAgCEHAA2ogCEHwAWpBAEEAEKsBIABBGGogCEEcaigCADYCACAAIAgpAhQ3AhAgCEHQA2okAA8LQQggD0HogcAAEMgEAAsgBSAFQZS7wgAQ2QMACyAHIAdBpLvCABDZAwALjggBBn8jAEEgayIDJAACQAJAAkACQAJAIAEtAAxBAWsOAgECAAsgA0EYaiABQQhqKAIAIgQ2AgAgAyABKQIANwMQIARFBEAgAygCEEUEQCADQRBqQcjQwgAQpQMLIAMoAhRBADYCACADQQE2AhhBASEECyADKAIUIgUgAiAFKAIAIgJqIgE2AgACfwJAAkAgASACTw0AIARBAUYNASAEQQJ0QQRrIQQgBUEEaiEBA0AgASABKAIAQQFqIgI2AgAgAg0BIAFBBGohASAEQQRrIgQNAAsMAQsgAygCGAwBCyADKAIYIgEgAygCEEYEQCADQRBqQdjQwgAQpQMLIAMoAhQgAUECdGpBATYCACABQQFqCyEBIAMoAhQhAiADKAIQIQYCfyABBEAgBiEEIAIMAQtBASEHQQAhBEEEIAZFDQAaIAIgBkECdBDfBEEECyEFIABBADsADSAAIAc6AAwgACABNgIIIAAgBTYCBCAAIAQ2AgAgAEEPakEAOgAADAMLIANBGGpBuMzCACgCADYCACADQbDMwgApAgA3AxAgA0EQakGkzcIAEKUDIAMoAhQgAjYCACAAQQhqQQE2AgAgACADKQMQNwIAIABBADoADAwBCyADQRhqQbjMwgAoAgA2AgAgA0GwzMIAKQIANwMQIANBEGpBpM3CABClAyADKAIUIAI2AgAgAygCFCEHAkAgASgCCCIFQQFHBEAgBUEBSyAFRWshBAwBCyABKAIEKAIAIgYgBygCACIFRg0AIAUgBkkgBSAGS2shBAsgAygCECEIAkACQAJAAkACQAJAIARB/wFxDgIAAgELIABBCGpBqMzCACkCADcCACAAQaDMwgApAgA3AgAgCEUNBSAHIAhBAnQQ3wQMBQsgA0EYaiIFIAFBCGooAgA2AgAgAyABKQIANwMQIANBBGogAiADQRBqEPkCIAMoAgxFDQEgBSADQQxqKAIANgIAIAMgAykCBDcDEEEAIQEMAgsgA0EYaiIFIAFBCGooAgA2AgAgAyABKQIANwMQIANBEGogAhDDAiADKAIUIQIgAygCECEGIAUoAgAiAQRAIABBAjoADCAAIAE2AgggACACNgIEIAAgBjYCAAwDCyAAQQhqQajMwgApAgA3AgAgAEGgzMIAKQIANwIAIAZFDQIgAiAGQQJ0EN8EDAILIAVBqMzCACgCADYCACADQaDMwgApAgA3AxBBASEBIAMoAgQiAkUNACADKAIIIAJBAnQQ3wQLIAAgAykDEDcCACAAQQA7AA0gACABOgAMIABBD2pBADoAACAAQQhqIANBGGooAgA2AgALIAhFDQEgByAIQQJ0EN8EDAELIAEoAgAiAEUNACABKAIEIABBAnQQ3wQLIANBIGokAAufBwIHfwh+IwBB0ABrIgIkACABKQM4IQwgASkDMCENIAEpAyghCSABKQMgIQ4gASkDGCEKIAEpAxAhDyABKQMIIQsgASkDACEQIAJByABqIgRB4PbAACgCADYCACACQdj2wAApAgA3A0AgCyAQhFBFBEBBASEBA0AgAigCQCABQQFrRgRAIAJBQGtB3PfAABClAwsgAigCRCADaiAQPgIAIBBC/////w9WIAtCAFIgC1AgC0IghiAQQiCIhCEQIANBBGohAyALQiCIIQsgAiABNgJIIAFBAWohARsNAAsLIAJBOGogBCgCACIBNgIAIAJBCGogATYCACACIAIpA0AiCzcDMCACIAs3AwBBACEDIARB4PbAACgCADYCACACQdj2wAApAgA3A0AgCiAPhFBFBEBBASEBA0AgAigCQCABQQFrRgRAIAJBQGtB3PfAABClAwsgAigCRCADaiAPPgIAIA9C/////w9WIApCAFIgClAgCkIghiAPQiCIhCEPIANBBGohAyAKQiCIIQogAiABNgJIIAFBAWohARsNAAsLIAJBOGoiBSACQcgAaiIEKAIAIgE2AgAgAkEUaiABNgIAIAIgAikDQCIKNwMwIAIgCjcCDEEAIQMgBEHg9sAAKAIANgIAIAJB2PbAACkCADcDQCAJIA6EUEUEQEEBIQEDQCACKAJAIAFBAWtGBEAgAkFAa0Hc98AAEKUDCyACKAJEIANqIA4+AgAgDkL/////D1YgCUIAUiAJUCAJQiCGIA5CIIiEIQ4gA0EEaiEDIAlCIIghCSACIAE2AkggAUEBaiEBGw0ACwsgBSAEKAIAIgE2AgAgAkEgaiIFIAE2AgAgAiACKQNAIgk3AzAgAiAJNwMYQQAhAyAEQeD2wAAoAgA2AgAgAkHY9sAAKQIANwNAIAwgDYRQRQRAQQEhAQNAIAIoAkAgAUEBa0YEQCACQUBrQdz3wAAQpQMLIAIoAkQgA2ogDT4CACANQv////8PViAMQgBSIAxQIAxCIIYgDUIgiIQhDSADQQRqIQMgDEIgiCEMIAIgATYCSCABQQFqIQEbDQALCyACQSxqIAJByABqKAIANgIAIAIgAikDQDcCJCAAQShqIAJBKGopAwA3AgAgAEEgaiAFKQMANwIAIABBGGogAkEYaikDADcCACAAQRBqIAJBEGopAwA3AgAgAEEIaiACQQhqKQMANwIAIAAgAikDADcCACACQdAAaiQAC9QJARB+QprN/8ujvcSAGiELIAEpAwgiAyACKQMIfCIIIANUIAggASkDECIDIAIpAxB8IgogA1QgCiABKQMYIgMgAikDGHwiBCADVCAEIAEpAyAiAyACKQMgfCIFIANUIAUgASkDKCIDIAIpAyh8IgwgA1StfCIGIAVUcq18IgcgBFRyrXwiBCAKVHKtfCIFIAhUcq0gAikDACABKQMAfHwiDiEDAkACQAJAIA5Cms3/y6O9xIAaUg0AQtfZrprk9umNywAhCyAFIgNC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQsgBCIDQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACELIAciA0Kk7MO1j9S0mOcAUg0AQv//z4rr///VHiELIAYiA0L//8+K6///1R5SDQBCq9X+////v/+5fyELIAwiA0Kr1f7///+//7l/UQ0BCyADIAtaDQAgBSEQIAQhESAHIRIgBiELDAELIAZC///Piuv//9UefSIIIAxCq9X+////v/+5f1StIgN9IQsgB0Kk7MO1j9S0mOcAfSIKIAZC///Piuv//9UeVCADIAhWcq0iA30hEiAEQr+llJzP8NK75AB9IgYgB0Kk7MO1j9S0mOcAVCADIApWcq0iA30hESAFQtfZrprk9umNywB9IgcgBEK/pZScz/DSu+QAVCADIAZWcq0iA30hECAOIAVC19mumuT26Y3LAFQgAyAHVnKtfUKazf/Lo73EgBp9IQ4gDELVqoGAgIDAgMYAfCEMC0Kazf/Lo73EgBohCSABKQM4IgMgAikDOHwiCCADVCAIIAEpA0AiAyACKQNAfCIKIANUIAogASkDSCIDIAIpA0h8IgQgA1QgBCABKQNQIgMgAikDUHwiBSADVCAFIAEpA1giAyACKQNYfCINIANUrXwiBiAFVHKtfCIHIARUcq18IgQgClRyrXwiBSAIVHKtIAIpAzAgASkDMHx8Ig8hAwJAAkACQCAPQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIQkgBSIDQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEJIAQiA0K/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhCSAHIgNCpOzDtY/UtJjnAFINAEL//8+K6///1R4hCSAGIgNC///Piuv//9UeUg0AQqvV/v///7//uX8hCSANIgNCq9X+////v/+5f1ENAQsgAyAJWg0AIAUhAyAEIQkgByEIIAYhCgwBCyAGQv//z4rr///VHn0iCCANQqvV/v///7//uX9UrSIDfSEKIAdCpOzDtY/UtJjnAH0iCSAGQv//z4rr///VHlQgAyAIVnKtIgN9IQggBEK/pZScz/DSu+QAfSIGIAdCpOzDtY/UtJjnAFQgAyAJVnKtIgN9IQkgBULX2a6a5PbpjcsAfSIHIARCv6WUnM/w0rvkAFQgAyAGVnKtIgR9IQMgDyAFQtfZrprk9umNywBUIAQgB1ZyrX1Cms3/y6O9xIAafSEPIA1C1aqBgICAwIDGAHwhDQsgACANNwNYIAAgCjcDUCAAIAg3A0ggACAJNwNAIAAgAzcDOCAAIA83AzAgACAMNwMoIAAgCzcDICAAIBI3AxggACARNwMQIAAgEDcDCCAAIA43AwALnwcBAn8jAEEQayICJAAgAkEEaiIDIAEQqgQgAiAANgIMIAMgAkEMakHYlcEAEI4DIAIgAEEBajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBAmo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQQNqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEEajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBBWo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQQZqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEHajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBCGo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQQlqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEKajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBC2o2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQQxqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEENajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBDmo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQQ9qNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEQajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBEWo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQRJqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEETajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBFGo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQRVqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEWajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBF2o2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQRhqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEZajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBGmo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQRtqNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEcajYCDCACQQRqIAJBDGpB2JXBABCOAyACIABBHWo2AgwgAkEEaiACQQxqQdiVwQAQjgMgAiAAQR5qNgIMIAJBBGogAkEMakHYlcEAEI4DIAIgAEEfajYCDCACQQRqIAJBDGpB2JXBABCOAyADEKEEIAJBEGokAAvPBgEIfwJAAkAgASAAQQNqQXxxIgMgAGsiCEkNACABIAhrIgZBBEkNACAGQQNxIQdBACEBAkAgACADRiIJDQACQCAAIANrIgVBfEsEQEEAIQMMAQtBACEDA0AgASAAIANqIgIsAABBv39KaiACQQFqLAAAQb9/SmogAkECaiwAAEG/f0pqIAJBA2osAABBv39KaiEBIANBBGoiAw0ACwsgCQ0AIAAgA2ohAgNAIAEgAiwAAEG/f0pqIQEgAkEBaiECIAVBAWoiBQ0ACwsgACAIaiEAAkAgB0UNACAAIAZBfHFqIgMsAABBv39KIQQgB0EBRg0AIAQgAywAAUG/f0pqIQQgB0ECRg0AIAQgAywAAkG/f0pqIQQLIAZBAnYhBSABIARqIQQDQCAAIQMgBUUNAkHAASAFIAVBwAFPGyIGQQNxIQcgBkECdCEIQQAhAiAFQQRPBEAgACAIQfAHcWohCSAAIQEDQCABKAIAIgBBf3NBB3YgAEEGdnJBgYKECHEgAmogAUEEaigCACIAQX9zQQd2IABBBnZyQYGChAhxaiABQQhqKAIAIgBBf3NBB3YgAEEGdnJBgYKECHFqIAFBDGooAgAiAEF/c0EHdiAAQQZ2ckGBgoQIcWohAiABQRBqIgEgCUcNAAsLIAUgBmshBSADIAhqIQAgAkEIdkH/gfwHcSACQf+B/AdxakGBgARsQRB2IARqIQQgB0UNAAsCfyADIAZB/AFxQQJ0aiIAKAIAIgFBf3NBB3YgAUEGdnJBgYKECHEiASAHQQFGDQAaIAEgACgCBCIBQX9zQQd2IAFBBnZyQYGChAhxaiIBIAdBAkYNABogACgCCCIAQX9zQQd2IABBBnZyQYGChAhxIAFqCyIBQQh2Qf+BHHEgAUH/gfwHcWpBgYAEbEEQdiAEag8LIAFFBEBBAA8LIAFBA3EhAwJAIAFBBEkEQAwBCyABQXxxIQUDQCAEIAAgAmoiASwAAEG/f0pqIAFBAWosAABBv39KaiABQQJqLAAAQb9/SmogAUEDaiwAAEG/f0pqIQQgBSACQQRqIgJHDQALCyADRQ0AIAAgAmohAQNAIAQgASwAAEG/f0pqIQQgAUEBaiEBIANBAWsiAw0ACwsgBAuhBwIBfwp+IwBBwAFrIgIkACACQbABaiABKQMYIgVCm5Svw/K1qN6Gf34iBEIAQm1CABDJAyACQaABaiAEQgBCf0IAEMkDIAJBkAFqIARCAEL///////////8AQgAQyQMgAkGAAWogAikDoAEiBCABKQMQfCIHIAIpA7gBIAUgAikDsAEiA3wgA1StfHwiBUKblK/D8rWo3oZ/fiIDQgBCbUIAEMkDIAJB8ABqIANCAEJ/QgAQyQMgAiADQgBC////////////AEIAEMkDIAJB4ABqIAIpA3AiAyAEIAEpAwh8IgYgBSAHVK0gAikDqAEiCiAEIAdWrXx8fCILfCIHIAIpA4gBIAUgAikDgAEiBXwgBVStfHwiBUKblK/D8rWo3oZ/fiIIQgBCbUIAEMkDIAJB0ABqIAhCAEJ/QgAQyQMgAkEQaiAIQgBC////////////AEIAEMkDIAJBQGsgAikDUCIIIAMgAikDkAEiDCABKQMAfCIJIAYgC1atIAogBCAGVq18fHwiBHwiBiAFIAdUrSACKQN4IgogAyAHVq18fHwiC3wiByACKQNoIAUgAikDYCIFfCAFVK18fCIFQpuUr8Pytajehn9+IgNCAEJtQgAQyQMgAkEwaiADQgBCf0IAEMkDIAJBIGogA0IAQv///////////wBCABDJAwJAAkAgAikDKCACKQMYIAIpAwggBCAJVK0gAikDmAEgCSAMVK18fCIJIAIpAwB8IgMgCVStfCADIAYgC1atIAogBCAGVq18fHwiBCADVK18IgYgAikDEHwiAyAGVK18IAMgAikDWCIGIAQgBCAIfCIEVq18IAQgBSAHVK0gBiAHIAhUrXx8fCIGIARUrXx8IgQgA1StfCIDIAIpAyB8IgcgA1StfCAHIAcgAikDOCIIIAQgBCACKQMwIgN8IgRWrXwgBCAEIAggAyADIAZ8IgNWrXwgAyACKQNIIAUgAikDQCIFfCAFVK18fCIGIANUrXx8IgRWrXx8IgdWrXwiCEIAWQRAIAhC////////////AFIgBkJtVHIgBCAHg0J/UnINAQsgBEIBfCIDIAZCbVStIgl9IQUgB0IBfCIKIARCf1IgAyAJVHKtIgR9IQMgCCAHQn9SIAQgClZyrX1C////////////AH0hCCAGQhN8IQYMAQsgByEDIAQhBQsgACAGNwMYIAAgBTcDECAAIAM3AwggACAINwMAIAJBwAFqJAAL4AsCCn4NfyMAQaABayINJAACQCABKAIMIhVBf0YEQCAAIAIpAgA3AgAgAEEIaiACQQhqKQIANwIAIAEoAgAiAEUNASABKAIEIABBMGwQ3wQMAQsgAigCDCIWQX9HBEAgASACIBUgFkgiDxsiEigCACEYIBIoAgQhFCACIAEgDxsiASgCACEXIAEoAgQhDyABKAIIIQ4CQAJAAkAgEigCCCIBBEAgAUEwbCEZIA1BBGohECANQfAAaiERQX8hEiAPIQIgFCEBA0AgESABKQIANwIAIBFBKGogAUEoaikCADcCACARQSBqIAFBIGopAgA3AgAgEUEYaiABQRhqKQIANwIAIBFBEGogAUEQaikCADcCACARQQhqIAFBCGopAgA3AgAgDUEIaiANQfQAaikCADcDACANQRBqIA1B/ABqKQIANwMAIA1BGGogDUGEAWopAgA3AwAgDUEgaiANQYwBaikCADcDACANQShqIA1BlAFqKQIANwMAIA1BMGogDUGcAWooAgA2AgAgDSANKQJsNwMAIA1BQGsgEEEIaikCADcDACANQcgAaiAQQRBqKQIANwMAIA1B0ABqIBBBGGopAgA3AwAgDUHYAGogEEEgaikCADcDACANQeAAaiAQQShqKQIANwMAIA0gECkCADcDOCAOIBJBAWoiEkYNAkKazf/Lo73EgBohBCANQThqIhMpAwgiAyACKQMIfCIGIANUIAYgEykDECIDIAIpAxB8IgogA1QgCiATKQMYIgMgAikDGHwiBSADVCAFIBMpAyAiAyACKQMgfCIHIANUIAcgEykDKCIDIAIpAyh8IgsgA1StfCIIIAdUcq18IgkgBVRyrXwiBSAKVHKtfCIHIAZUcq0gAikDACATKQMAfHwiDCEDAkACQAJAIAxCms3/y6O9xIAaUg0AQtfZrprk9umNywAhBCAHIgNC19mumuT26Y3LAFINAEK/pZScz/DSu+QAIQQgBSIDQr+llJzP8NK75ABSDQBCpOzDtY/UtJjnACEEIAkiA0Kk7MO1j9S0mOcAUg0AQv//z4rr///VHiEEIAgiA0L//8+K6///1R5SDQBCq9X+////v/+5fyEEIAsiA0Kr1f7///+//7l/UQ0BCyADIARaDQAgByEDIAUhBCAJIQYgCCEKDAELIAhC///Piuv//9UefSIGIAtCq9X+////v/+5f1StIgN9IQogCUKk7MO1j9S0mOcAfSIEIAhC///Piuv//9UeVCADIAZWcq0iA30hBiAFQr+llJzP8NK75AB9IgggCUKk7MO1j9S0mOcAVCADIARWcq0iA30hBCAHQtfZrprk9umNywB9IgkgBUK/pZScz/DSu+QAVCADIAhWcq0iBX0hAyAMIAdC19mumuT26Y3LAFQgBSAJVnKtfUKazf/Lo73EgBp9IQwgC0LVqoGAgIDAgMYAfCELCyACIAs3AyggAiAKNwMgIAIgBjcDGCACIAQ3AxAgAiADNwMIIAIgDDcDACABQTBqIQEgAkEwaiECIBlBMGsiGQ0ACwsgFSAWIBUgFkobIQEgGARAIBQgGEEwbBDfBAsCQCABQQBIDQAgASAOTw0CIA8gAUEwbGohAgNAIAJB+MPCAEEwEPEDDQEgAkEwayECIAFBAEogAUEBayEBDQALQdHOxQAtAAAaQTBBCBDWBCIBRQ0DIAFCADcDACAAQoGAgIBwNwIIIAAgATYCBCAAQQE2AgAgAUEoakIANwMAIAFBIGpCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACAXRQ0FIA8gF0EwbBDfBAwFCyAAIAE2AgwgACAPNgIEIAAgFzYCACAAIAFBAWoiACAOIAAgDkkbNgIIDAQLIA4gDkHUysIAENkDAAsgASAOQcTKwgAQ2QMAC0EIQTAQ/wQACyAAIAEpAgA3AgAgAEEIaiABQQhqKQIANwIAIAIoAgAiAEUNACACKAIEIABBMGwQ3wQLIA1BoAFqJAALvQcBCn8jAEHQAmsiCiQAQdHOxQAtAAAaAkACQAJAAkACQAJAAkBBIEEEENYEIg0EQCABKAIIIgxBBXQhDiAMQf///z9LIA5B+P///wdLcg0BIA5FBEAgDSAMNgIIQQghDyANQQg2AgQgDSAMNgIAIAEoAgwhAQwFCyABKAIEIRNB0c7FAC0AABpBCCELIA5BCBDWBCIPRQ0BIAxFDQJBACELIAwhEANAIAsgDkcEQCALIA9qIhEgCyATaiISKQMANwMAIBFBGGogEkEYaikDADcDACARQRBqIBJBEGopAwA3AwAgEUEIaiASQQhqKQMANwMAIAtBIGohCyAQQQFrIhANAQsLIA0gDDYCCCANIA82AgQgDSAMNgIADAMLQQRBIBD/BAALIAsgDkHogcAAEMgEAAsgDUEANgIIIA0gDzYCBCANQQA2AgALQdHOxQAtAAAaIAEoAgwhASAOQQgQ1gQiD0UNASAMRQ0AQQAhCyAMIRADQCALIA5GDQEgCyAPaiIRIAsgE2oiEikDADcDACARQRhqIBJBGGopAwA3AwAgEUEQaiASQRBqKQMANwMAIBFBCGogEkEIaikDADcDACALQSBqIQsgEEEBayIQDQALCyANIAw2AhggDSAPNgIUIA0gDDYCECANIAE2AhwgDSABNgIMIApBAjYCECAKIA02AgwgCkECNgIIQQAhCyAKQQA2AhwgCkKAgICAgAE3AhQgAwRAIApBsAJqIQEDQCAFIAtGDQMgByALRg0EIApBsAFqIgwgAiAEIAYQtQJBACIQRQRAIApBIGogDEGAAfwKAAALIApBqAFqIg0gAUEIaikCADcDACAKIAEpAgA3A6ABIAooAhAiDCAKKAIIRgRAIApBCGpBgJHAABCjAwsgCigCDCAMQQR0aiIOIAopA6ABNwIAIA5BCGogDSkDADcCACAKIAxBAWo2AhAgCigCHCIMIAooAhRGBEAgCkEUakGQkcAAEKQDCyAQRQRAIAooAhggDEEHdGogCkEgakGAAfwKAAALIAogDEEBajYCHCACQYABaiECIAZBIGohBiAEQSBqIQQgAyALQQFqIgtHDQALCyAKQcgCaiAKQRBqKAIANgIAIAogCikCCDcDwAIgCkGAgICAeDYCsAEgACAKQcACaiAKQbABaiAIIAkQwQEgAEEYaiAKQRxqKAIANgIAIAAgCikCFDcCECAKQdACaiQADwtBCCAOQeiBwAAQyAQACyAFIAVB4JDAABDZAwALIAcgB0HwkMAAENkDAAu9BwEKfyMAQdACayIIJABB0c7FAC0AABoCQAJAAkACQAJAAkACQEEgQQQQ1gQiCwRAIAEoAggiCkEFdCEMIApB////P0sgDEH4////B0tyDQEgDEUEQCALIAo2AghBCCENIAtBCDYCBCALIAo2AgAgASgCDCEBDAULIAEoAgQhEUHRzsUALQAAGkEIIQkgDEEIENYEIg1FDQEgCkUNAkEAIQkgCiEOA0AgCSAMRwRAIAkgDWoiDyAJIBFqIhApAwA3AwAgD0EYaiAQQRhqKQMANwMAIA9BEGogEEEQaikDADcDACAPQQhqIBBBCGopAwA3AwAgCUEgaiEJIA5BAWsiDg0BCwsgCyAKNgIIIAsgDTYCBCALIAo2AgAMAwtBBEEgEP8EAAsgCSAMQeiBwAAQyAQACyALQQA2AgggCyANNgIEIAtBADYCAAtB0c7FAC0AABogASgCDCEBIAxBCBDWBCINRQ0BIApFDQBBACEJIAohDgNAIAkgDEYNASAJIA1qIg8gCSARaiIQKQMANwMAIA9BGGogEEEYaikDADcDACAPQRBqIBBBEGopAwA3AwAgD0EIaiAQQQhqKQMANwMAIAlBIGohCSAOQQFrIg4NAAsLIAsgCjYCGCALIA02AhQgCyAKNgIQIAsgATYCHCALIAE2AgwgCEECNgIQIAggCzYCDCAIQQI2AghBACEJIAhBADYCHCAIQoCAgICAATcCFCADBEAgCEGwAmohAQNAIAUgCUYNAyAHIAlGDQQgCEGwAWoiCiACIAQgBhC1AkEAIg5FBEAgCEEgaiAKQYAB/AoAAAsgCEGoAWoiCyABQQhqKQIANwMAIAggASkCADcDoAEgCCgCECIKIAgoAghGBEAgCEEIakG0u8IAEKMDCyAIKAIMIApBBHRqIgwgCCkDoAE3AgAgDEEIaiALKQMANwIAIAggCkEBajYCECAIKAIcIgogCCgCFEYEQCAIQRRqQcS7wgAQpAMLIA5FBEAgCCgCGCAKQQd0aiAIQSBqQYAB/AoAAAsgCCAKQQFqNgIcIAJBgAFqIQIgBkEgaiEGIARBIGohBCADIAlBAWoiCUcNAAsLIAhByAJqIAhBEGooAgA2AgAgCCAIKQIINwPAAiAIQYCAgIB4NgKwASAAIAhBwAJqIAhBsAFqQQBBABDBASAAQRhqIAhBHGooAgA2AgAgACAIKQIUNwIQIAhB0AJqJAAPC0EIIAxB6IHAABDIBAALIAUgBUGUu8IAENkDAAsgByAHQaS7wgAQ2QMAC8QHAhJ+AX8gAikDACINIQQgASkDACIOIQcCfgJAAn4CQCANIA5SDQAgAikDCCIDIAEpAwgiB1IEQCADIQQMAQsgAikDECIFIAEpAxAiB1IEQCAFIQQMAQsgAyEJIAIpAxgiBCEMIAUgBCABKQMYIgdRDQEaCyAEIAdWDQEgAikDCCEDIAEpAwghCSACKQMQIQUgAikDGCEEIAEpAxghDCABKQMQCyIRIAV9IgogBCAMVq0iCH0hFCAJIAN9IgYgCCAKViAFIBFWcq0iBX0hESAFIAZWIAMgCVZyIRUgDCAEfSEMIA4gDX0MAQtC3bCFjOi2kai4fyACKQMIIgsgASkDCCIPfSIQIAIpAxAiBSABKQMQIgNUIAUgA30iBiACKQMYIgQgASkDGCIFVK0iA1RyrSIKfSIJfSIIIAYgA30iA0KNlcfDltLawJd/VkKNlcfDltLawJd/IAN9IgYgBCAFfSIEQsf688PtgqOQPFatIgVUcq0iA30hESADIAhWIAlC3bCFjOi2kai4f1ZyIRUgBiAFfSEUQsf688PtgqOQPCAEfSEMIAsgD1QgCiAQVnKtIA4gDX18QqnAxomuzpOyMHwLIQkgAikDICISIQQgASkDICITIQcCfgJAAn4CQCASIBNSDQAgAikDKCIDIAEpAygiB1IEQCADIQQMAQsgAikDMCIFIAEpAzAiB1IEQCAFIQQMAQsgAyEIIAIpAzgiBCELIAUgBCABKQM4IgdRDQEaCyAEIAdWDQEgAikDKCEDIAEpAyghCCACKQMwIQUgAikDOCEEIAEpAzghCyABKQMwCyIGIAV9Ig8gBCALVq0iEH0hByAIIAN9IgogDyAQVCAFIAZWcq0iBn0hBSAGIApWIAMgCFZyIQIgCyAEfSEEIBMgEn0MAQtC3bCFjOi2kai4fyACKQMoIg0gASkDKCIOfSILIAIpAzAiBSABKQMwIgNUIAUgA30iBiACKQM4IgQgASkDOCIFVK0iA1RyrSIPfSIQfSIKIAYgA30iA0KNlcfDltLawJd/VkKNlcfDltLawJd/IAN9IgggBCAFfSIGQsf688PtgqOQPFatIgRUcq0iA30hBSAQQt2whYzotpGouH9WIAMgClZyIQIgCCAEfSEHQsf688PtgqOQPCAGfSEEIA0gDlQgCyAPVHKtIBMgEn18QqnAxomuzpOyMHwLIQMgACAENwM4IAAgBzcDMCAAIAU3AyggACAMNwMYIAAgFDcDECAAIBE3AwggACADIAKtfTcDICAAIAkgFa19NwMAC/YGAgd/A34jAEGgAmsiAyQAIANBKGoiBUEAQcEA/AsAIANBGGpByILBACkDADcDACADQRBqQcCCwQApAwA3AwAgA0EIakG4gsEAKQMANwMAIANCADcDICADQbCCwQApAwA3AwACQCACQcAATwRAIAMgAkEGdiIErTcDICADIAEgBBAtIAJBP3EiBEUEQCAEIQIMAgsgBSABIAJBQHFqIAT8CgAAIAQhAgwBCyACRQ0AIAUgASAC/AoAAAsgAyACOgBoIANB8ABqIANB8AD8CgAAIANBmAFqIgIgAy0A2AEiAWoiBEGAAToAACABrSILQjuGIAMpA5ABIgpCCYYiDCALQgOGhCILQoD+A4NCKIaEIAtCgID8B4NCGIYgC0KAgID4D4NCCIaEhCAKQgGGQoCAgPgPgyAKQg+IQoCA/AeDhCAKQh+IQoD+A4MgDEI4iISEhCEKAkACQCABQT9HBEAgAUE/cyIFBEAgBEEBakEAIAX8CwALIAFBOHNBB0sNAQsgA0HwAGoiASACQQEQLSADQZACakIANwMAIANBiAJqQgA3AwAgA0GAAmpCADcDACADQfgBakIANwMAIANB8AFqQgA3AwAgA0HoAWpCADcDACADQgA3A+ABIAMgCjcDmAIgASADQeABakEBEC0MAQsgAyAKNwPQASADQfAAaiACQQEQLQsgAygCcCEBIAMoAnQhAiADKAJ4IQQgAygCfCEFIAMoAoABIQYgAygChAEhByADKAKIASEIIAAgAygCjAEiCUEYdCAJQYD+A3FBCHRyIAlBCHZBgP4DcSAJQRh2cnI2ABwgACAIQRh0IAhBgP4DcUEIdHIgCEEIdkGA/gNxIAhBGHZycjYAGCAAIAdBGHQgB0GA/gNxQQh0ciAHQQh2QYD+A3EgB0EYdnJyNgAUIAAgBkEYdCAGQYD+A3FBCHRyIAZBCHZBgP4DcSAGQRh2cnI2ABAgACAFQRh0IAVBgP4DcUEIdHIgBUEIdkGA/gNxIAVBGHZycjYADCAAIARBGHQgBEGA/gNxQQh0ciAEQQh2QYD+A3EgBEEYdnJyNgAIIAAgAkEYdCACQYD+A3FBCHRyIAJBCHZBgP4DcSACQRh2cnI2AAQgACABQRh0IAFBgP4DcUEIdHIgAUEIdkGA/gNxIAFBGHZycjYAACADQaACaiQAC+4FAgZ/CH4jAEEQayIGJAAgBkEEaiABEL4BIAYoAgwiAkExSQRAIAYoAgghBQJAIAIgAkEMayIBQQAgASACTRsiB0YNACAFIAdqIQFBDCACIAJBDE8bIgNBA3EhBAJAIANBAWtBA0kEQAwBCyADQQxxIQMDQCAIQiCIQoCA/P8PgyAKQiCGhCAIQhCGIghCMIiEIQogAUEDajEAACABQQFqMQAAIAggATEAAEIIhoSEQhCGIAFBAmoxAABCCIaEhCEIIAFBBGohASADQQRrIgMNAAsLIARFDQADQCAKQgiGIAhCOIiEIQogATEAACAIQgiGhCEIIAFBAWohASAEQQFrIgQNAAsLIAJBGGsiAUEAIAEgAk0bIgMgB0cEQCADIAVqIQFBGCACIAJBGE8bQQwgAiACQQxPG2shBANAIA5CCIYgDEI4iIQhDiABMQAAIAxCCIaEIQwgAUEBaiEBIARBAWsiBA0ACwsgAyACQSRrIgFBACABIAJNGyIDRwRAQSQgAiACQSRPG0EYIAIgAkEYTxtrIQQgAyAFaiEBA0AgD0IIhiANQjiIhCEPIAExAAAgDUIIhoQhDSABQQFqIQEgBEEBayIEDQALCwJAIAJBJUkNACADQQNxIQQCQCACQSVrQQNJBEAgBSEBDAELIANBHHEhAyAFIQEDQCAJQiCIQoCA/P8PgyALQiCGhCAJQhCGIglCMIiEIQsgAUEDajEAACABQQFqMQAAIAkgATEAAEIIhoSEQhCGIAFBAmoxAABCCIaEhCEJIAFBBGohASADQQRrIgMNAAsLIARFDQADQCALQgiGIAlCOIiEIQsgATEAACAJQgiGhCEJIAFBAWohASAEQQFrIgQNAAsLIAAgCTcDMCAAIA03AyAgACAMNwMQIAAgCDcDACAAIAs3AzggACAPNwMoIAAgDjcDGCAAIAo3AwggBigCBCIABEAgBSAAEN8ECyAGQRBqJAAPC0HU2sIAQS1BhNvCABD+AwAL7gUCBn8IfiMAQRBrIgYkACAGQQRqIAEQnwEgBigCDCICQTFJBEAgBigCCCEFAkAgAiACQQxrIgFBACABIAJNGyIHRg0AIAUgB2ohAUEMIAIgAkEMTxsiA0EDcSEEAkAgA0EBa0EDSQRADAELIANBDHEhAwNAIAhCIIhCgID8/w+DIApCIIaEIAhCEIYiCEIwiIQhCiABQQNqMQAAIAFBAWoxAAAgCCABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQggAUEEaiEBIANBBGsiAw0ACwsgBEUNAANAIApCCIYgCEI4iIQhCiABMQAAIAhCCIaEIQggAUEBaiEBIARBAWsiBA0ACwsgAkEYayIBQQAgASACTRsiAyAHRwRAIAMgBWohAUEYIAIgAkEYTxtBDCACIAJBDE8bayEEA0AgDkIIhiAMQjiIhCEOIAExAAAgDEIIhoQhDCABQQFqIQEgBEEBayIEDQALCyADIAJBJGsiAUEAIAEgAk0bIgNHBEBBJCACIAJBJE8bQRggAiACQRhPG2shBCADIAVqIQEDQCAPQgiGIA1COIiEIQ8gATEAACANQgiGhCENIAFBAWohASAEQQFrIgQNAAsLAkAgAkElSQ0AIANBA3EhBAJAIAJBJWtBA0kEQCAFIQEMAQsgA0EccSEDIAUhAQNAIAlCIIhCgID8/w+DIAtCIIaEIAlCEIYiCUIwiIQhCyABQQNqMQAAIAFBAWoxAAAgCSABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQkgAUEEaiEBIANBBGsiAw0ACwsgBEUNAANAIAtCCIYgCUI4iIQhCyABMQAAIAlCCIaEIQkgAUEBaiEBIARBAWsiBA0ACwsgACAJNwMwIAAgDTcDICAAIAw3AxAgACAINwMAIAAgCzcDOCAAIA83AyggACAONwMYIAAgCjcDCCAGKAIEIgAEQCAFIAAQ3wQLIAZBEGokAA8LQdTawgBBLUGE28IAEP4DAAvTlQECHH8bfiMAQeAAayIIJABB0c7FAC0AABoCQAJAQTBBCBDWBCIEBEAgBEEoakGgxcIAKQMANwMAIARBIGpBmMXCACkDADcDACAEQRhqQZDFwgApAwA3AwAgBEEQakGIxcIAKQMANwMAIARBCGpBgMXCACkDADcDACAEQfjEwgApAwA3AwAgCEIBNwIIIAggBDYCBCAIQQE2AgAgASgCBCIJIAEoAggiAkEEdGohBSABKAIAIQcgCSEEAkAgAgRAIAhB1ABqIgFBCGohAgNAIAQoAgAiBkGAgICAeEcEQCAIIAY2AlAgASAEQQRqKQIANwIAIAIgBEEMaigCADYCACAIQTBqIAggCEHQAGoQbiAIKAIAIgYEQCAIKAIEIAZBMGwQ3wQLIAhBCGogCEE4aikCADcDACAIIAgpAjA3AwAgCCgCUCIGBEAgCCgCVCAGQTBsEN8ECyAEQRBqIgQgBUcNAQwDCwsgBEEQaiEECyAEIAVGDQAgBSAEa0EEdiEBA0AgBCgCACIFBEAgBEEEaigCACAFQTBsEN8ECyAEQRBqIQQgAUEBayIBDQALCyAHBEAgCSAHQQR0EN8ECyAIQRBqIQUjAEGgBmsiBiQAIAYQJgJAAkACQCAGKAIMRQ0AIAYoAgQiASAGKQMYIh9C/8rRy6eM2bLwAIUiHkIQiSAeIAYpAxAiIELh5JXz1uzZvOwAhXwiHoUiIiAfQu3ekfOWzNy35ACFIh8gIEL1ys2D16zbt/MAhXwiIEIgiXwiIUKMgICAgICAgASFIB9CDYkgIIUiHyAefCIeIB9CEYmFIh98IiAgH0INiYUiHyAiQhWJICGFIiIgHkIgiUL/AYV8Ih58IiEgH0IRiYUiH0INiSAfIB4gIkIQiYUiHiAgQiCJfCIgfCIfhSIiQhGJICIgHkIViSAghSIeICFCIIl8IiB8IiKFIiFCDYkgISAeQhCJICCFIh4gH0IgiXwiH3yFIiBCEYkgHkIViSAfhSIfQhCJIB8gIkIgiXwiH4VCFYmFIB8gIHwiH0IgiIUgH4UiH6dxIQMgH0IZiEL/AINCgYKEiJCgwIABfiEgIAYoAgAiBEEMayEJA0ACQCADIARqKQAAIh4gIIUiH0J/hSAfQoGChIiQoMCAAX2DQoCBgoSIkKDAgH+DIh9QRQRAA0AgCUEAIB96p0EDdiADaiABcWsiB0EMbGooAgBBDEYNAiAfQgF9IB+DIh9QRQ0ACwsgHiAeQgGGg0KAgYKEiJCgwIB/g1BFDQIgAyAKQQhqIgpqIAFxIQMMAQsLIAQgB0EMbGoiB0EEaygCACEJIAdBCGsoAgAhAyAGKAKMBiIHBEAgBigCkAYgB0ECdBDfBAsCQCABRQ0AIAEgAUEMbEETakF4cSIHakEJaiIBRQ0AIAQgB2sgARDfBAsgBigCgAMiAUGAgICAeEYgAUVyRQRAIAYoAoQDIAFBAnQQ3wQLIAmtQjB+Ih+nIQxBACEBIB9CIIinIAxB+P///wdLcg0BAn8gDEUEQEEIIQRBAAwBC0HRzsUALQAAGkEIIQEgDEEIENYEIgRFDQIgCQshCiAJBEAgBCEBIAkhBwNAIAMtAAAhCyMAQbAMayICJAACQAJAAkAgC8BBAEgEQCACQfALakEAIAtrrcIiH0IAQsau0OHB5sfvdEIAEMkDIAJB4AtqIAIpA/ALQn6DIiJCAEIAQv3/8//P///5iX8QyQMgAkHQC2ogAikD6AsiHkIAQqvV/v///7//uX9CABDJAyACQcALaiAeQgBC///Piuv//9UeQgAQyQMgAkGwC2ogHkIAQqTsw7WP1LSY5wBCABDJAyACQaALaiAeQgBCv6WUnM/w0rvkAEIAEMkDIAJBkAtqIB5CAELX2a6a5PbpjcsAQgAQyQMgAkGAC2ogHkIAQprN/8ujvcSAGkIAEMkDIAJB8ApqIB9CAELxicTO4NS5uwpCABDJAyACQeAKaiACKQPwCiIhIAIpA8ALIiMgAikD+At8IiAgAikD2AsgAikD0AsiHiAifCAeVK18fCIlfCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0ApqIAIpA+gKIh5CAEKr1f7///+//7l/QgAQyQMgAkHACmogHkIAQv//z4rr///VHkIAEMkDIAJBsApqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgCmogHkIAQr+llJzP8NK75ABCABDJAyACQZAKaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgApqIB5CAEKazf/Lo73EgBpCABDJAyACQfAJaiAfQgBC1e3W5MTt0fKNf0IAEMkDIAJB4AlqIAIpA/AJIiQgAikDwAoiJiACKQP4CiAhICJWrXwiISACKQOwCyInICAgJVatIAIpA8gLICAgI1StfHx8IiN8IiV8IiAgAikD2AogAikD0AoiHiAifCAeVK18fCIofCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0AlqIAIpA+gJIh5CAEKr1f7///+//7l/QgAQyQMgAkHACWogHkIAQv//z4rr///VHkIAEMkDIAJBsAlqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgCWogHkIAQr+llJzP8NK75ABCABDJAyACQZAJaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgAlqIB5CAEKazf/Lo73EgBpCABDJAyACQfAIaiAfQgBCwIf2nJmV4vXnAEIAEMkDIAJB4AhqIAIpA/AIIiogAikDwAkiKyACKQP4CSAiICRUrXwiJCAhICVWrSIlIAIpA6ALIikgAikDuAsgIyAnVK18fCInfCIhIAIpA7AKfCIjICAgKFatIAIpA8gKICAgJlStfHx8IiZ8Iih8IiAgAikD2AkgAikD0AkiHiAifCAeVK18fCIsfCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0AhqIAIpA+gIIh5CAEKr1f7///+//7l/QgAQyQMgAkHACGogHkIAQv//z4rr///VHkIAEMkDIAJBsAhqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgCGogHkIAQr+llJzP8NK75ABCABDJAyACQZAIaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgAhqIB5CAEKazf/Lo73EgBpCABDJAyACQfAHaiAfQgBCrarmqNvQz7yaf0IAEMkDIAJB4AdqIAIpA/AHIi0gAikDwAgiLiACKQP4CCAiICpUrXwiKiAkIChWrSIoICEgJVStIi8gAikDkAsiMCACKQOoCyAnIClUrXx8Iid8IiUgAikDoAp8IiQgIyAmVq0gAikDuAogISAjVq18fHwiKXwiISACKQOwCXwiIyAgICxWrSACKQPICSAgICtUrXx8fCIrfCImfCIgIAIpA9gIIAIpA9AIIh4gInwgHlStfHwiLHwiIkIAQgBC/f/z/8////mJfxDJAyACQdAHaiACKQPoByIeQgBCq9X+////v/+5f0IAEMkDIAJBwAdqIB5CAEL//8+K6///1R5CABDJAyACQbAHaiAeQgBCpOzDtY/UtJjnAEIAEMkDIAJBoAdqIB5CAEK/pZScz/DSu+QAQgAQyQMgAkGQB2ogHkIAQtfZrprk9umNywBCABDJAyACQYAHaiAeQgBCms3/y6O9xIAaQgAQyQMgAkHwBmogH0IAQqrHq5bZ/KPMEUIAEMkDIAJB4AZqIAIpA/AGIjEgAikDwAciMiACKQP4ByAiIC1UrXwiLSAmICpUrSIqICEgKFStIiggJSAvVK0iLyACKQOACyIzIAIpA5gLICcgMFStfHwiJ3wiHiACKQOQCnwiJiAkIClWrSACKQOoCiAkICVUrXx8fCIpfCIlIAIpA6AJfCIkICMgK1atIAIpA7gJICEgI1atfHx8Iit8IiEgAikDsAh8IiMgICAsVq0gAikDyAggICAuVK18fHwiLHwiLnwiICACKQPYByACKQPQByIfICJ8IB9UrXx8IjB8IiJCAEIAQv3/8//P///5iX8QyQMgAkHQBmogAikD6AYiH0IAQqvV/v///7//uX9CABDJAyACQcAGaiAfQgBC///Piuv//9UeQgAQyQMgAkGwBmogH0IAQqTsw7WP1LSY5wBCABDJAyACQaAGaiAfQgBCv6WUnM/w0rvkAEIAEMkDIAJBkAZqIB9CAELX2a6a5PbpjcsAQgAQyQMgAkGABmogH0IAQprN/8ujvcSAGkIAEMkDIAIpA4gGIAIpA4AGIjQgAikDiAcgAikDgAciNSACKQOICCACKQOACCI2IAIpA4gJIAIpA4AJIjcgAikDiAogAikDgAoiOCAeIC9UrSACKQOICyAnIDNUrXx8fCIfIDhUrXwgHyAfICYgKVatIAIpA5gKIB4gJlatfHx8Ih5WrXwgHiAlIChUrSImfCIfICZUrXx8Ih4gN1StfCAeIB4gAikDmAkgHyAfIAIpA5AJfCImVq18ICYgJiAkICtWrSACKQOoCSAkICVUrXx8fCIfVq18fCIlVq18ICUgISAqVK0iHiAffCIfIB5UrSIkfCIeICRUrXx8IiUgNlStfCAlIAIpA5gIIB4gHiACKQOQCHwiJFatfCAkICQgAikDqAggHyAfIAIpA6AIfCIeVq18IB4gHiAjICxWrSACKQO4CCAhICNWrXx8fCIfVq18fCIeVq18fCIhICVUrXwgISAeIC0gLlatIiMgH3wiHyAjVK0iI3wiHiAjVK0iI3wiISAjVK18fCIjIDVUrXwgIyACKQOYByAhICEgAikDkAd8IiVWrXwgJSACKQOoByAeIB4gAikDoAd8IiFWrXwgISAhIAIpA7gHIB8gHyACKQOwB3wiHlatfCAeIB4gICAwVq0gAikDyAcgICAyVK18fHwiH1atfHwiHlatfHwiICAlVK18fCIhICNUrXwgISAgIB4gHyACKQP4BiAiIDFUrXwiI3wiJCAjVK0iI3wiHyAjVK0iI3wiHiAjVK0iI3wiICAjVK18fCIhIDRUrXwgISACKQOYBiAgIAIpA5AGfCIjICBUrXwgIyACKQOoBiAeIB4gAikDoAZ8IiVWrXwgJSAlIAIpA7gGIB8gHyACKQOwBnwiHlatfCAeIAIpA8gGICQgAikDwAYiIHwiHyAgVK18IB8gAikD2AYgIiACKQPQBiIgfCAgVK18fCImIB9UrXx8IiIgHlStfHwiIFatfHwiHyAjVK18fCIeICFUrXwiJ0Kazf/Lo73EgBpSDQICQCAeQtfZrprk9umNywBWDQBCms3/y6O9xIAaIScgHkLX2a6a5PbpjcsAUg0DIB9Cv6WUnM/w0rvkAFYNACAfQr+llJzP8NK75ABSBEBC19mumuT26Y3LACEeDAQLICBCpOzDtY/UtJjnAFYNACAgQqTsw7WP1LSY5wBSDQIgIkL//8+K6///1R5WDQAgIkL//8+K6///1R5SBEBCpOzDtY/UtJjnACEgDAMLICZCq9X+////v/+5f1oNAEL//8+K6///1R4hIkKk7MO1j9S0mOcAISAMAgtCf0IAIB5C19mumuT26Y3LAH0iHiAfQr+llJzP8NK75ABUIB9Cv6WUnM/w0rvkAH0iHyAgQqTsw7WP1LSY5wBUICBCpOzDtY/UtJjnAH0iICAiQv//z4rr///VHlQgIkL//8+K6///1R59IiIgJkKr1f7///+//7l/VK0iIVRyrSIjVHKtIiVUcq0iJFQbIScgIiAhfSEiICAgI30hICAfICV9IR8gHiAkfSEeICZC1aqBgICAwIDGAHwhJgwCCyACQaAFaiALrUL/AYMiH0IAQsau0OHB5sfvdEIAEMkDIAJBkAVqIAIpA6AFQn6DIiJCAEIAQv3/8//P///5iX8QyQMgAkGABWogAikDmAUiHkIAQqvV/v///7//uX9CABDJAyACQfAEaiAeQgBC///Piuv//9UeQgAQyQMgAkHwA2ogHkIAQqTsw7WP1LSY5wBCABDJAyACQfACaiAeQgBCv6WUnM/w0rvkAEIAEMkDIAJB8AFqIB5CAELX2a6a5PbpjcsAQgAQyQMgAkHwAGogHkIAQprN/8ujvcSAGkIAEMkDIAJBsAVqIB9CAELxicTO4NS5uwpCABDJAyACQeAEaiACKQOwBSIhIAIpA/AEIiMgAikDqAV8IiAgAikDiAUgAikDgAUiHiAifCAeVK18fCIlfCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0ARqIAIpA+gEIh5CAEKr1f7///+//7l/QgAQyQMgAkHABGogHkIAQv//z4rr///VHkIAEMkDIAJBsARqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgBGogHkIAQr+llJzP8NK75ABCABDJAyACQZAEaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgARqIB5CAEKazf/Lo73EgBpCABDJAyACQcAFaiAfQgBC1e3W5MTt0fKNf0IAEMkDIAJB4ANqIAIpA8AFIiQgAikDwAQiJiACKQO4BSAhICJWrXwiISACKQPwAyInICAgJVatIAIpA/gEICAgI1StfHx8IiN8IiV8IiAgAikD2AQgAikD0AQiHiAifCAeVK18fCIofCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0ANqIAIpA+gDIh5CAEKr1f7///+//7l/QgAQyQMgAkHAA2ogHkIAQv//z4rr///VHkIAEMkDIAJBsANqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgA2ogHkIAQr+llJzP8NK75ABCABDJAyACQZADaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgANqIB5CAEKazf/Lo73EgBpCABDJAyACQdAFaiAfQgBCwIf2nJmV4vXnAEIAEMkDIAJB4AJqIAIpA9AFIiogAikDwAMiKyACKQPIBSAiICRUrXwiJCAhICVWrSIlIAIpA/ACIikgAikD+AMgIyAnVK18fCInfCIhIAIpA7AEfCIjICAgKFatIAIpA8gEICAgJlStfHx8IiZ8Iih8IiAgAikD2AMgAikD0AMiHiAifCAeVK18fCIsfCIiQgBCAEL9//P/z///+Yl/EMkDIAJB0AJqIAIpA+gCIh5CAEKr1f7///+//7l/QgAQyQMgAkHAAmogHkIAQv//z4rr///VHkIAEMkDIAJBsAJqIB5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgAmogHkIAQr+llJzP8NK75ABCABDJAyACQZACaiAeQgBC19mumuT26Y3LAEIAEMkDIAJBgAJqIB5CAEKazf/Lo73EgBpCABDJAyACQeAFaiAfQgBCrarmqNvQz7yaf0IAEMkDIAJB4AFqIAIpA+AFIi0gAikDwAIiLiACKQPYBSAiICpUrXwiKiAkIChWrSIoICEgJVStIi8gAikD8AEiMCACKQP4AiAnIClUrXx8Iid8IiUgAikDoAR8IiQgIyAmVq0gAikDuAQgISAjVq18fHwiKXwiISACKQOwA3wiIyAgICxWrSACKQPIAyAgICtUrXx8fCIrfCImfCIgIAIpA9gCIAIpA9ACIh4gInwgHlStfHwiLHwiIkIAQgBC/f/z/8////mJfxDJAyACQdABaiACKQPoASIeQgBCq9X+////v/+5f0IAEMkDIAJBwAFqIB5CAEL//8+K6///1R5CABDJAyACQbABaiAeQgBCpOzDtY/UtJjnAEIAEMkDIAJBoAFqIB5CAEK/pZScz/DSu+QAQgAQyQMgAkGQAWogHkIAQtfZrprk9umNywBCABDJAyACQYABaiAeQgBCms3/y6O9xIAaQgAQyQMgAkHwBWogH0IAQqrHq5bZ/KPMEUIAEMkDIAJB4ABqIAIpA/AFIjEgAikDwAEiMiACKQPoBSAiIC1UrXwiLSAmICpUrSIqICEgKFStIiggJSAvVK0iLyACKQNwIjMgAikD+AEgJyAwVK18fCInfCIeIAIpA5AEfCImICQgKVatIAIpA6gEICQgJVStfHx8Iil8IiUgAikDoAN8IiQgIyArVq0gAikDuAMgISAjVq18fHwiK3wiISACKQOwAnwiIyAgICxWrSACKQPIAiAgIC5UrXx8fCIsfCIufCIgIAIpA9gBIAIpA9ABIh8gInwgH1StfHwiMHwiIkIAQgBC/f/z/8////mJfxDJAyACQdAAaiACKQNoIh9CAEKr1f7///+//7l/QgAQyQMgAkFAayAfQgBC///Piuv//9UeQgAQyQMgAkEwaiAfQgBCpOzDtY/UtJjnAEIAEMkDIAJBIGogH0IAQr+llJzP8NK75ABCABDJAyACQRBqIB9CAELX2a6a5PbpjcsAQgAQyQMgAiAfQgBCms3/y6O9xIAaQgAQyQMCQCACKQMIIAIpAwAiNCACKQOIASACKQOAASI1IAIpA4gCIAIpA4ACIjYgAikDiAMgAikDgAMiNyACKQOIBCACKQOABCI4IB4gL1StIAIpA3ggJyAzVK18fHwiHyA4VK18IB8gHyAmIClWrSACKQOYBCAeICZWrXx8fCIeVq18IB4gJSAoVK0iJnwiHyAmVK18fCIeIDdUrXwgHiAeIAIpA5gDIB8gHyACKQOQA3wiJlatfCAmICYgJCArVq0gAikDqAMgJCAlVK18fHwiH1atfHwiJVatfCAlICEgKlStIh4gH3wiHyAeVK0iJHwiHiAkVK18fCIlIDZUrXwgJSACKQOYAiAeIB4gAikDkAJ8IiRWrXwgJCAkIAIpA6gCIB8gHyACKQOgAnwiHlatfCAeIB4gIyAsVq0gAikDuAIgISAjVq18fHwiH1atfHwiHlatfHwiISAlVK18ICEgHiAtIC5WrSIjIB98Ih8gI1StIiN8Ih4gI1StIiN8IiEgI1StfHwiIyA1VK18ICMgAikDmAEgISAhIAIpA5ABfCIlVq18ICUgAikDqAEgHiAeIAIpA6ABfCIhVq18ICEgISACKQO4ASAfIB8gAikDsAF8Ih5WrXwgHiAeICAgMFatIAIpA8gBICAgMlStfHx8Ih9WrXx8Ih5WrXx8IiAgJVStfHwiISAjVK18ICEgICAeIB8gAikD+AUgIiAxVK18IiN8IiQgI1StIiN8Ih8gI1StIiN8Ih4gI1StIiN8IiAgI1StfHwiISA0VK18ICEgAikDGCAgIAIpAxB8IiMgIFStfCAjIAIpAyggHiAeIAIpAyB8IiVWrXwgJSACKQM4IB8gHyACKQMwfCIeVq18IB4gHiACKQNIICQgAikDQCIgfCIfICBUrXwgHyAfIAIpA1ggIiACKQNQIiB8ICBUrXx8IiBWrXx8Ih9WrXx8IicgJVStfHwiHiAjVK18fCImICFUrXwiIkKazf/Lo73EgBpSDQACQAJAICZC19mumuT26Y3LAFYNAEKazf/Lo73EgBohIiAmQtfZrprk9umNywBSDQIgHkK/pZScz/DSu+QAVg0AIB5Cv6WUnM/w0rvkAFIEQELX2a6a5PbpjcsAISYMAwsgJ0Kk7MO1j9S0mOcAVg0AICdCpOzDtY/UtJjnAFINASAfQv//z4rr///VHlYNACAfQv//z4rr///VHlIEQEKk7MO1j9S0mOcAIScMAgsgIEKr1f7///+//7l/Wg0AQv//z4rr///VHiEfQqTsw7WP1LSY5wAhJwwBC0J/QgAgJkLX2a6a5PbpjcsAfSIhIB5Cv6WUnM/w0rvkAFQgHkK/pZScz/DSu+QAfSIeICdCpOzDtY/UtJjnAFQgJ0Kk7MO1j9S0mOcAfSIjIB9C///Piuv//9UeVCAfQv//z4rr///VHn0iHyAgQqvV/v///7//uX9UrSIlVHKtIiRUcq0iJlRyrSIoVBshIiAfICV9IR8gIyAkfSEnIB4gJn0hHiAhICh9ISYgIELVqoGAgIDAgMYAfCEgDAELQr+llJzP8NK75AAhHkLX2a6a5PbpjcsAISYLIAYgIDcDKCAGIB83AyAgBiAnNwMYIAYgHjcDECAGICY3AwggBiAiNwMADAILQr+llJzP8NK75AAhH0LX2a6a5PbpjcsAIR4LIAIgJjcDqAwgAiAiNwOgDCACICA3A5gMIAIgHzcDkAwgAiAeNwOIDCACICc3A4AMAkAgAkGADGpB+JTBAEEwEPEDRQRAIB4hISAfISMgICElICIhJAwBC0L//8+K6///1R4gIn0iISAmQqvV/v///7//uX9WrSIjfSEkQqTsw7WP1LSY5wAgIH0iKCAhICNUICJC///Piuv//9UeVnKtIiJ9ISVCv6WUnM/w0rvkACAffSIhICIgKFYgIEKk7MO1j9S0mOcAVnKtIiB9ISNC19mumuT26Y3LACAefSIiICAgIVYgH0K/pZScz/DSu+QAVnKtIh99ISFCms3/y6O9xIAaIB8gIlYgHkLX2a6a5PbpjcsAVnKtICd8fSEnQqvV/v///7//uX8gJn0hJgsgBiAmNwMoIAYgJDcDICAGICU3AxggBiAjNwMQIAYgITcDCCAGICc3AwALIAJBsAxqJAAgAUEoaiAGQShqKQMANwMAIAFBIGogBkEgaikDADcDACABQRhqIAZBGGopAwA3AwAgAUEQaiAGQRBqKQMANwMAIAFBCGogBkEIaikDADcDACABIAYpAwA3AwAgA0EBaiEDIAFBMGohASAHQQFrIgcNAAsLIAkhAQJAAkADQCAMRQ0BIAFBAWshASAMQTBrIgwgBGpB+MPCAEEwEPEDRQ0ACyABQQFqIgcgCSAHIAlJGyEMDAELQdHOxQAtAAAaQTBBCBDWBCIJRQ0GIAlCADcDACAJQShqQgA3AwAgCUEgakIANwMAIAlBGGpCADcDACAJQRBqQgA3AwAgCUEIakIANwMAQX8hAUEBIQwgCgRAIAQgCkEwbBDfBAsgCSEEQQEhCgsgBSABNgIMIAUgDDYCCCAFIAQ2AgQgBSAKNgIAIAZBoAZqJAAMAgtB0JrBAEEWQYibwQAQ6AMACyABIAxBiJnBABDIBAALIAhB2ABqIhggCEEIaikDADcDACAIIAgpAwA3A1AgCEEwaiEOIAhB0ABqIRFBACEBQgAhKkEAIQcjAEHgBGsiAyQAAkACQAJAAkACQCAFIgwoAgwiD0F/RwRAIBEoAggiBK1CMH4iH6chCQJAIB9CIIinIAlB+P///wdLcg0AIBEoAgwhCiARKAIEIRcCQCAJRQRAQQghCwwBC0HRzsUALQAAGkEIIQEgCUEIENYEIgtFDQEgBEUNACAEIQEDQCAHIAlGDQEgByALaiIFIAcgF2oiAikDADcDACAFQShqIAJBKGopAwA3AwAgBUEgaiACQSBqKQMANwMAIAVBGGogAkEYaikDADcDACAFQRBqIAJBEGopAwA3AwAgBUEIaiACQQhqKQMANwMAIAdBMGohByABQQFrIgENAAsLIAMgBDYC2AEgAyALNgLUASADIAQ2AtABIAMgCjYC3AEgCiAPSA0DIAogD2siFEEBaiISrUIwfiIfpyEBQQAhBAJAIB9CIIinIAFB+P///wdLcg0AAn8gAUUEQEEIIQlBAAwBC0HRzsUALQAAGkEIIQQgAUEIENYEIglFDQEgEgshGQJAAkACQAJAIBJBAk8EQCAUQQdxIQQgDyAKa0F4TQ0BIAkhAQwCCyAJIQEgEg0CDAMLIBRBeHEhByAJIQEDQCABQgA3AwAgAUEoakIANwMAIAFBIGpCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACABQTBqQgA3AwAgAUE4akIANwMAIAFBQGtCADcDACABQcgAakIANwMAIAFB0ABqQgA3AwAgAUHYAGpCADcDACABQeAAakIANwMAIAFB6ABqQgA3AwAgAUHwAGpCADcDACABQfgAakIANwMAIAFBgAFqQgA3AwAgAUGIAWpCADcDACABQbgBakIANwMAIAFBsAFqQgA3AwAgAUGoAWpCADcDACABQaABakIANwMAIAFBmAFqQgA3AwAgAUGQAWpCADcDACABQcABakIANwMAIAFByAFqQgA3AwAgAUHQAWpCADcDACABQdgBakIANwMAIAFB4AFqQgA3AwAgAUHoAWpCADcDACABQfABakIANwMAIAFB+AFqQgA3AwAgAUGAAmpCADcDACABQYgCakIANwMAIAFBkAJqQgA3AwAgAUGYAmpCADcDACABQcgCakIANwMAIAFBwAJqQgA3AwAgAUG4AmpCADcDACABQbACakIANwMAIAFBqAJqQgA3AwAgAUGgAmpCADcDACABQfgCakIANwMAIAFB8AJqQgA3AwAgAUHoAmpCADcDACABQeACakIANwMAIAFB2AJqQgA3AwAgAUHQAmpCADcDACABQYADaiEBIAdBCGsiBw0ACwsgBEUNAANAIAFCADcDACABQShqQgA3AwAgAUEgakIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIAFBMGohASAEQQFrIgQNAAsLIAFCADcDACABQShqQgA3AwAgAUEgakIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMACyAMKAIIIgEgD0sEQCADQZgCaiIEIAwoAgQgD0EwbGoiAUEIaikDADcDACADQaACaiIFIAFBEGopAwA3AwAgA0GoAmoiByABQRhqKQMANwMAIANBsAJqIgIgAUEgaikDADcDACADQbgCaiIGIAFBKGopAwA3AwAgAyABKQMANwOQAiABQfjDwgBBMBDxA0UNBCADQZADakIANwMAIANBiANqQgA3AwAgA0GAA2pCADcDACADQfgCakIANwMAIANCADcD8AIgA0IBNwOYAyADQcgDaiAGKQMANwMAIANBwANqIAIpAwA3AwAgA0G4A2ogBykDADcDACADQbADaiAFKQMANwMAIANBqANqIAQpAwA3AwAgAyADKQOQAjcDoAMgA0H4A2pBsMPCACkDADcDACADQfADakGow8IAKQMANwMAIANB6ANqQaDDwgApAwA3AwAgA0HgA2pBmMPCACkDADcDACADQdgDakGQw8IAKQMANwMAIANBiMPCACkDADcD0AMgA0GoBGpB0MTCACkDADcDACADQaAEakHIxMIAKQMANwMAIANBmARqQcDEwgApAwA3AwAgA0GQBGoiBEG4xMIAKQMANwMAIANBiARqQbDEwgApAwA3AwAgA0GoxMIAKQMANwOABCADQdgEakIANwMAIANB0ARqQgA3AwAgA0HIBGpCADcDACADQcAEaiIBQgA3AwAgA0G4BGpCADcDACADQgA3A7AEIANBoANqIANB8AJqQTAQ8QNFBEBCrarmqNvQz7yafyEfQqrHq5bZ/KPMESEqDAcLIANB0ANqIANB8AJqQTAQ8QNFBEAgASEEQgAhHwwHC0Kr1f7///+//7l/ISADQCADLQDIA0EBcUUEQANAIANBoANqEL8CIAMpA6gEIh9CAYNQRQRAIAMpA6AEIR4gAyAfQtWqgYCAgMCAxgB9IiI3A6gEIAMgHkL//8+K6///1R58IiAgHyAiVq18IiI3A6AEIAMgAykDmAQiIUKk7MO1j9S0mOcAfCIfIB4gIFYgICAiVnKtfCIgNwOYBCADIAMpA5AEIiJCv6WUnM/w0rvkAHwiHiAfICFUIB8gIFZyrXwiIDcDkAQgAyADKQOIBCIhQtfZrprk9umNywB8Ih8gHiAiVCAeICBWcq18Ih43A4gEIAMgAykDgAQgHiAfVCAfICFUcq18QprN/8ujvcSAGnw3A4AECyADQYAEahC/AiADLQDIA0EBcUUNAAsgAykD+AMhIAsgIKdBAXFFBEADQCADQdADahC/AiADKQPYBCIfQgGDUEUEQCADKQPQBCEeIAMgH0LVqoGAgIDAgMYAfSIiNwPYBCADIB5C///Piuv//9UefCIgIB8gIlatfCIiNwPQBCADIAMpA8gEIiFCpOzDtY/UtJjnAHwiHyAeICBWICAgIlZyrXwiIDcDyAQgAyADKQPABCIiQr+llJzP8NK75AB8Ih4gHyAhVCAfICBWcq18IiA3A8AEIAMgAykDuAQiIULX2a6a5PbpjcsAfCIfIB4gIlQgHiAgVnKtfCIeNwO4BCADIAMpA7AEIB4gH1QgHyAhVHKtfEKazf/Lo73EgBp8NwOwBAsgA0GwBGoQvwIgAykD+AMiIEIBg1ANAAsLIAMpA6gDIR4CQAJAIAMCfgJAAkACQAJ+IAMpA9ADIisgAykDoAMiLFIEQCADKQPgAyEiIAMpA9gDISQgKyEfICwhJyADKQOwAwwBCyADKQPgAyEiIAMpA7ADISUgHiADKQPYAyIkUgRAICQhHyAeIScgJQwBCyAiICVSBEAgHiEkICIhHyAlIScgJQwBCyADKQPoAyIfIAMpA7gDIidSBEAgHiEkICUiIgwBCyADKQPwAyIjIAMpA8ADIidSBEAgHiEkICMhHyAlIiIMAQsgICADKQPIAyInUQ0BIB4hJCAgIR8gJSIiCyEoIB8gJ1YgAykDsAQhJyADKQOABCEqIAMpA/ADISMgAykD6AMhHyADKQPIAyEhIAMpA8ADISYgAykDuAMhKUUEQCAiISUMAgsgAyAgICF9Ii03A/gDIAMgIyAmfSIlICAgIVStIiB9NwPwAyADIB8gKX0iISAjICZUICAgJVZyrSIgfTcD6AMgAyAiICh9IiMgHyApVCAgICFWcq0iH303A+ADIAMgJCAefSIgICIgKFQgHyAjVnKtIh99NwPYAyADICsgLH0gHiAkViAfICBWcq19NwPQAyADKQO4BCEkAkACQCAnICpSBEAgAykDkAQhHiADKQOIBCEfIAMpA8AEISEgJyEgICohIgwBCyADKQOQBCEeIAMpA8AEISEgAykDiAQiHyAkUgRAICQhICAfISIMAQsgHiAhUgRAICQhHyAhISAgHiEiDAELIAMpA8gEIiMgAykDmAQiIlIEQCAhIR4gJCEfICMhIAwBCyADKQPQBCIoIAMpA6AEIiJSBEAgISEeICQhHyAoISAMAQsgISEeICQhHyADKQPYBCIgISYgKCEpICMhJSAgIAMpA6gEIiJRDQELICAgIlQgAykDqAQhICADKQOgBCEoIAMpA5gEISMgAykD2AQhJiADKQPQBCEpIAMpA8gEISUNAwsgAyAmICB9NwPYBCADICkgKH0iIiAgICZWrSIgfTcD0AQgAyAlICN9IiYgKCApViAgICJWcq0iIH03A8gEIAMgISAefSIiICAgJlYgIyAlVnKtIiB9NwPABCADICQgH30iIyAgICJWIB4gIVZyrSIgfSIeNwO4BCAnICp9ICAgI1YgHyAkVnKtfQwDCyADKQOwBCEnIAMpA4AEISogHiEkICAhISAjISYgHyEpICUhKAsgAyAhICB9NwPIAyADICYgI30iIiAgICFWrSIhfTcDwAMgAyApIB99Ii0gISAiViAjICZWcq0iIn03A7gDIAMgKCAlfSIhICIgLVYgHyApVnKtIh99NwOwAyADIB4gJH0iIiAfICFWICUgKFZyrSIffTcDqAMgAyAsICt9IB4gJFQgHyAiVnKtfTcDoAMgAykDiAQhJAJAAkAgJyAqUgRAIAMpA8AEISMgAykDuAQhHiADKQOQBCEmICohHyAnISsMAQsgAykDwAQhIyADKQOQBCEmIAMpA7gEIh4gJFIEQCAkIR8gHiErDAELICMgJlIEQCAkIR4gJiEfICMhKwwBCyADKQOYBCIoIAMpA8gEIitSBEAgJiEjICQhHiAoIR8MAQsgAykDoAQiISADKQPQBCIrUgRAICYhIyAkIR4gISEfDAELICYhIyAkIR4gAykDqAQiHyEpICEhJSAoISIgHyADKQPYBCIrUQ0BCyAfICtUIAMpA9gEIR8gAykD0AQhISADKQPIBCEoIAMpA6gEISkgAykDoAQhJSADKQOYBCEiDQMLIAMgKSAffTcDqAQgAyAlICF9IisgHyApVq0iH303A6AEIAMgIiAofSIpIB8gK1YgISAlVnKtIh99NwOYBCADICYgI30iISAiIChUIB8gKVZyrSIffTcDkAQgAyAkIB59IiIgHyAhViAjICZWcq0iIX0iHzcDiAQgAyAqICd9ICEgIlYgHiAkVnKtfSIqNwOABAwDCyADQqvV/v///7//uX8gIH0iIiAmfCImNwPYBCADIClC///Piuv//9UeICh9IisgIEKr1f7///+//7l/Vq0iLH0iLnwiICAiICZWrXwiJjcD0AQgAyAlQqTsw7WP1LSY5wAgI30iKSArICxUIChC///Piuv//9UeVnKtIih9Iit8IiIgICAuVCAgICZWcq18IiU3A8gEIAMgIUK/pZScz/DSu+QAIB59IiYgKCApViAjQqTsw7WP1LSY5wBWcq0iI30iKHwiICAiICtUICIgJVZyrXwiITcDwAQgAyAkQtfZrprk9umNywAgH30iJSAjICZWIB5Cv6WUnM/w0rvkAFZyrSIjfSImfCIiICAgKFQgICAhVnKtfCIeNwO4BCAeICJUICIgJlRyrSAnICp9ICMgJVYgH0LX2a6a5PbpjcsAVnKtfXxCms3/y6O9xIAafAsiJzcDsAQgLSEgDAELIANCq9X+////v/+5fyAffSIrICl8Iik3A6gEIAMgJUL//8+K6///1R4gIX0iLCAfQqvV/v///7//uX9WrSItfSIufCIfICkgK1StfCIlNwOgBCADICJCpOzDtY/UtJjnACAofSIrICwgLVQgIUL//8+K6///1R5Wcq0iIX0iKXwiIiAfIC5UIB8gJVZyrXwiJTcDmAQgAyAmQr+llJzP8NK75AAgI30iLCAhICtWIChCpOzDtY/UtJjnAFZyrSIhfSIofCIfICIgKVQgIiAlVnKtfCIlNwOQBCADICRC19mumuT26Y3LACAefSImICEgLFYgI0K/pZScz/DSu+QAVnKtIiF9IiN8IiIgHyAoVCAfICVWcq18Ih83A4gEIAMgHyAiVCAiICNUcq0gKiAnfSAhICZWIB5C19mumuT26Y3LAFZyrX18QprN/8ujvcSAGnwiKjcDgAQLIANBoANqIANB8AJqIgVBMBDxA0UNByADQdADaiAFQTAQ8QMNAAsgASEEICchKiAeIR8MBgsgDyABQezHwgAQ2QMACyAEIAFB0MjCABDIBAALIAEgCUHogcAAEMgEAAsgA0EANgLABCADQQE2ArQEIANBuMjCADYCsAQgA0IENwK4BCADQbAEakHAyMIAEKgEAAsgA0ICNwOwBEGQycIAQSsgA0GwBGpBgMnCAEG8ycIAEMoDAAtB0c7FAC0AABpBMEEIENYEIgEEQCABQgA3AwAgDkKBgICAcDcCCCAOIAE2AgQgDkEBNgIAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgDiARKQIANwIQIA5BGGogEUEIaikCADcCACAERQ0CIAsgCRDfBAwCCwwFCyADQegCaiAEQRhqKQMAIh43AwAgA0HgAmogBEEQaikDACIgNwMAIANB2AJqIARBCGopAwAiIjcDACADQfgBaiAiNwMAIANBgAJqICA3AwAgA0GIAmogHjcDACADIAQpAwAiHjcD0AIgAyAfNwPoASADICo3A+ABIAMgHjcD8AEgD0F/cyEaAkADQAJAAkACQAJAAkACQAJAIAMoAtgBIgEgCksEQCAKIA9rIQIgAygC1AEgCkEwbGoiASkDACEoIAEpAwghKyABKQMQISkgASkDGCEsIAEpAyAhLSABKQMoIS5CACEfQSghAUIAISFCACEkQgAhHkIAISpCACEnA0AgA0HwAGogA0HgAWogAWopAwAiIEIAIC5CABDJAyADQYABaiAgQgAgLUIAEMkDIANBkAFqICBCACAsQgAQyQMgA0GgAWogIEIAIClCABDJAyADQbABaiAgQgAgK0IAEMkDIANBwAFqICBCACAoQgAQyQMgA0HgAGogAykDcCIlIB98IiBCAEIAQv3/8//P///5iX8QyQMgA0HQAGogAykDaCIfQgBCq9X+////v/+5f0IAEMkDIANBQGsgH0IAQv//z4rr///VHkIAEMkDIANBMGogH0IAQqTsw7WP1LSY5wBCABDJAyADQSBqIB9CAEK/pZScz/DSu+QAQgAQyQMgA0EQaiAfQgBC19mumuT26Y3LAEIAEMkDIAMgH0IAQprN/8ujvcSAGkIAEMkDIAMpAwggJyADKQPAASIvfCIiIAMpA7gBIAMpA7ABIiMgKnwiHyAjVK18IB8gHyADKQOoASADKQOgASIjIB58Ih4gI1StfCAeIB4gAykDmAEgJCADKQOQASIkfCIjICRUrXwgIyADKQOIASADKQOAASIkICF8IiEgJFStfCAhICEgAykDeCAgICVUrXx8IiRWrXx8IiEgI1StfHwiI1atfHwiHlatfHwiJSADKQMAfCImICVUrXwgJiADKQMYIB4gHiADKQMQfCInVq18ICcgJyADKQMoICMgIyADKQMgfCIeVq18IB4gHiADKQM4ICEgISADKQMwfCIjVq18ICMgIyADKQNIICQgAykDQCIffCIhIB9UrXwgISAhIAMpA1ggICADKQNQIh98IB9UrXx8Ih9WrXx8IiFWrXx8IiRWrXx8Ih5WrXx8IiogJlStfCAiICVWrSADKQPIASAiIC9UrXx8fCEnIAFBCGsiAUF4Rw0ACyAnQprN/8ujvcSAGlYNBiAnQprN/8ujvcSAGlENAQwCCyAKIAFB4MjCABDZAwALICpC19mumuT26Y3LAFYNBCAqQtfZrprk9umNywBSBEBCms3/y6O9xIAaIScMAQsgHkK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhICAeQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIScMAgsgJEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhIyAkQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIScMAwsgIUL//8+K6///1R5WDQRCpOzDtY/UtJjnACEoICFC///Piuv//9UeUQ0DQprN/8ujvcSAGiEnICEhJgwFCyAqISALIB4hIwsgJCEoICEhJgwCC0L//8+K6///1R4hJiAfQqrV/v///7//uX9WDQBCms3/y6O9xIAaIScMAQsgIUL//8+K6///1R59IiAgH0Kr1f7///+//7l/VK0iIn0hJiAkQqTsw7WP1LSY5wB9IiMgIUL//8+K6///1R5UICAgIlRyrSIgfSEoIB5Cv6WUnM/w0rvkAH0iIiAkQqTsw7WP1LSY5wBUICAgI1ZyrSIgfSEjICpC19mumuT26Y3LAH0iISAeQr+llJzP8NK75ABUICAgIlZyrSIefSEgICcgKkLX2a6a5PbpjcsAVCAeICFWcq19QprN/8ujvcSAGn0hJyAfQtWqgYCAgMCAxgB8IR8LIAMgHzcD2AQgAyAmNwPQBCADICg3A8gEIAMgIzcDwAQgAyAgNwO4BCADICc3A7AEAkACQAJAAkACQAJAIAIgEkkEQCADQbgEaikDACEfIANBwARqKQMAIR4gA0HIBGopAwAhICADQdAEaikDACEiIANB2ARqKQMAISEgCSACQTBsaiIBIAMpA7AENwMAIAFBKGogITcDACABQSBqICI3AwAgAUEYaiAgNwMAIAFBEGogHjcDACABQQhqIB83AwAgA0GABGohByMAQTBrIgUkACAFIANBsARqIgE2AggCQAJAAkAgAUH4w8IAQTAQ8QMEQCAMKAIMIg1Bf0cEQCAMKAIIIgZBMGwhASAMKAIEIQtBCCEEIAYEQEHRzsUALQAAGiABQQgQ1gQiBEUNBAsgBUEUaiIQQQA2AgAgBSAENgIQIAUgBjYCDCAFIAEgC2o2AhwgBSALNgIYIAUgBUEIajYCICAFIAQ2AiwgBUEANgIoIAUgEDYCJCMAQdABayIBJAAgBUEkaiIEKAIEIQYgBCgCACAFQRhqIgsoAgAiEyALKAIEIhZHBEAgBCgCCCEbIAsoAgghHCAWIBNrQTBuIRZBACELA0AgEyALQTBsaiIEKQMAIScgBCkDCCEoIAQpAxAhKiAEKQMYISsgBCkDICEsIAQpAyghLSAcKAIAIR1BKCEEQgAhKUIAISRCACEhQgAhIEIAIR5CACEmA0AgAUHwAGogBCAdaikDACIfQgAgLUIAEMkDIAFBgAFqIB9CACAsQgAQyQMgAUGQAWogH0IAICtCABDJAyABQaABaiAfQgAgKkIAEMkDIAFBsAFqIB9CACAoQgAQyQMgAUHAAWogH0IAICdCABDJAyABQeAAaiABKQNwIiUgJnwiIkIAQgBC/f/z/8////mJfxDJAyABQdAAaiABKQNoIh9CAEKr1f7///+//7l/QgAQyQMgAUFAayAfQgBC///Piuv//9UeQgAQyQMgAUEwaiAfQgBCpOzDtY/UtJjnAEIAEMkDIAFBIGogH0IAQr+llJzP8NK75ABCABDJAyABQRBqIB9CAELX2a6a5PbpjcsAQgAQyQMgASAfQgBCms3/y6O9xIAaQgAQyQMgASkDCCApIAEpA8ABIi58Ih8gASkDuAEgJCABKQOwASImfCIjICZUrXwgIyABKQOoASABKQOgASIkICF8IiEgJFStfCAhIAEpA5gBIAEpA5ABIiQgIHwiICAkVK18ICAgASkDiAEgASkDgAEiJCAefCIeICRUrXwgHiABKQN4ICIgJVStfHwiJiAeVK18fCIeICBUrXx8IiAgIVStfHwiISAjVK18fCIjIAEpAwB8IiUgI1StfCAlICUgASkDGCAhICEgASkDEHwiJFatfCAkICQgASkDKCAgICAgASkDIHwiIVatfCAhICEgASkDOCAeIB4gASkDMHwiIFatfCAgICAgASkDSCAmIAEpA0AiKXwiHiApVK18IB4gASkDWCAiIAEpA1AiJnwgJlStfHwiJiAeVK18fCIeVq18fCIgVq18fCIhVq18fCIkVq18IB8gI1atIAEpA8gBIB8gLlStfHx8ISkgBEEIayIEQXhHDQALAkACQCApQprN/8ujvcSAGlYNACApQprN/8ujvcSAGlIEQCAeIR8gICEiICEhIyAkISUMAgsgJELX2a6a5PbpjcsAVg0AAkAgJELX2a6a5PbpjcsAUgRAIB4hHyAgISIgISEjICQhJQwBCyAhQr+llJzP8NK75ABWDQFC19mumuT26Y3LACElICFCv6WUnM/w0rvkAFIEQCAeIR8gICEiICEhIwwBCyAgQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEjICBCpOzDtY/UtJjnAFIEQCAeIR8gICEiDAELIB5C///Piuv//9UeVg0BQqTsw7WP1LSY5wAhIiAeQv//z4rr///VHlIEQCAeIR8MAQtC///Piuv//9UeIR8gJkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohKQwBCyAeQv//z4rr///VHn0iIiAmQqvV/v///7//uX9UrSIjfSEfICBCpOzDtY/UtJjnAH0iJSAeQv//z4rr///VHlQgIiAjVHKtIh59ISIgIUK/pZScz/DSu+QAfSInICBCpOzDtY/UtJjnAFQgHiAlVnKtIh59ISMgJELX2a6a5PbpjcsAfSIgICFCv6WUnM/w0rvkAFQgHiAnVnKtIh59ISUgKSAkQtfZrprk9umNywBUIB4gIFZyrX1Cms3/y6O9xIAafSEpICZC1aqBgICAwIDGAHwhJgsgGyAGQTBsaiIEICY3AyggBCAfNwMgIAQgIjcDGCAEICM3AxAgBCAlNwMIIAQgKTcDACAGQQFqIQYgC0EBaiILIBZHDQALCyAGNgIAIAFB0AFqJAAgB0EIaiAQKAIANgIAIAcgBSkCDDcCAAwCCwtB0c7FAC0AABpBMEEIENYEIgFFDRAgAUIANwMAIAdBATYCCCAHIAE2AgQgB0EBNgIAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwBBfyENCyAHIA02AgwgBUEwaiQADAELQQggAUG0ysIAEMgEAAsgAygCjAQiE0F/RgRAQdHOxQAtAAAaQTBBCBDWBCIBRQ0OIAFCADcDACABQShqQgA3AwAgAUEgakIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIANCgYCAgHA3A8gCIAMgATYCxAIgA0EBNgLAAgwGCyACrUIwfiIfpyEBQQAhBCAfQiCIpyABQfj///8HS3INAQJ/IAFFBEBBCCEFQQAMAQtB0c7FAC0AABpBCCEEIAFBCBDWBCIFRQ0CIAILIRAgAkECSQ0CIAogGmoiB0EHcSEEIAUhASAKIA9rQQJrQQdPBEAgB0F4cSEKA0AgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgAUEwakIANwMAIAFBOGpCADcDACABQUBrQgA3AwAgAUHIAGpCADcDACABQdAAakIANwMAIAFB2ABqQgA3AwAgAUHgAGpCADcDACABQegAakIANwMAIAFB8ABqQgA3AwAgAUH4AGpCADcDACABQYABakIANwMAIAFBiAFqQgA3AwAgAUG4AWpCADcDACABQbABakIANwMAIAFBqAFqQgA3AwAgAUGgAWpCADcDACABQZgBakIANwMAIAFBkAFqQgA3AwAgAUHAAWpCADcDACABQcgBakIANwMAIAFB0AFqQgA3AwAgAUHYAWpCADcDACABQeABakIANwMAIAFB6AFqQgA3AwAgAUHwAWpCADcDACABQfgBakIANwMAIAFBgAJqQgA3AwAgAUGIAmpCADcDACABQZACakIANwMAIAFBmAJqQgA3AwAgAUHIAmpCADcDACABQcACakIANwMAIAFBuAJqQgA3AwAgAUGwAmpCADcDACABQagCakIANwMAIAFBoAJqQgA3AwAgAUH4AmpCADcDACABQfACakIANwMAIAFB6AJqQgA3AwAgAUHgAmpCADcDACABQdgCakIANwMAIAFB0AJqQgA3AwAgAUGAA2ohASAKQQhrIgoNAAsLIARFDQMDQCABQgA3AwAgAUEoakIANwMAIAFBIGpCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACABQTBqIQEgBEEBayIEDQALDAMLIAIgEkHwyMIAENkDAAsgBCABQczJwgAQyAQACyAFIQEgAkUNAQsgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwALIAMgAjYC2AMgAyAFNgLUAyADIBA2AtADIAMoAogEIgatQjB+Ih+nIQRBACEBIB9CIIinIARB+P///wdLcg0BAkAgBEUEQEEIIQsMAQsgAygChAQhFUHRzsUALQAAGkEIIQEgBEEIENYEIgtFDQIgBkUNAEEAIQogBiEHA0AgBCAKRg0BIAogC2oiASAKIBVqIg0pAwA3AwAgAUEoaiANQShqKQMANwMAIAFBIGogDUEgaikDADcDACABQRhqIA1BGGopAwA3AwAgAUEQaiANQRBqKQMANwMAIAFBCGogDUEIaikDADcDACAKQTBqIQogB0EBayIHDQALCyAQIAIiBGsgBkkEQCADQdADaiACIAZBCEEwEIgDIAMoAtQDIQUgAygC2AMhBAsgBkEwbCIBBEAgBSAEQTBsaiALIAH8CgAACyADIAQgBmo2AtgDIAYEQCALIAEQ3wQLIANByAJqIANB2ANqKAIANgIAIAMgAykC0AM3A8ACIAMgAiATajYCzAILIAMoAoAEIgEEQCADKAKEBCABQTBsEN8ECyADQYgEaiADQdgBaikCADcDACADIAMpAtABNwOABCADQdABaiEFIANBwAJqIQQjAEEwayIBJAACQAJAAkACQCADQYAEaiIHKAIMQX9GBEAgBCgCBCECIAQoAgAhCgJAIAQoAgwiEEF/RgRAQdHOxQAtAAAaQTBBCBDWBCIERQ0OIARCADcDACAFQQE2AgggBSAENgIEIAVBATYCACAEQShqQgA3AwAgBEEgakIANwMAIARBGGpCADcDACAEQRBqQgA3AwAgBEEIakIANwMADAELIAQoAggiC0EwbCEGQQghBCALBEBB0c7FAC0AABogBkEIENYEIgRFDQMLIAFBLGoiDUEANgIAIAEgBDYCKCABIAs2AiQgASAENgIQIAFBADYCDCABIA02AgggAiACIAZqIAFBCGoQzAIgBUEIaiANKAIANgIAIAUgASkCJDcCAAsgBSAQNgIMIAoEQCACIApBMGwQ3wQLIAcoAgAiBEUNBCAHKAIEIARBMGwQ3wQMBAsgBCgCDCIQQX9GDQIgBCgCCCIKQTBsIQIgBCgCBCEGIAQoAgAhC0EIIQQgCgRAQdHOxQAtAAAaIAJBCBDWBCIERQ0CCyABQSBqIg1BADYCACABIAQ2AhwgASAKNgIYIAEgBDYCLCABQQA2AiggASANNgIkIAYgAiAGaiABQSRqEMwCIAFBEGogDSgCADYCACABIAEpAhg3AwggASAQNgIUIAsEQCAGIAtBMGwQ3wQLIAUgByABQQhqENkBDAMLQQggBkG0ysIAEMgEAAtBCCACQbTKwgAQyAQACyAFIAcpAgA3AgAgBUEIaiAHQQhqKQIANwIAIAQoAgAiBUUNACAEKAIEIAVBMGwQ3wQLIAFBMGokACADKALcASIKIA9IDQIMAQsLIAEgBEHogcAAEMgEAAsgDiASNgIIIA4gCTYCBCAOIBk2AgAgDiADKQLQATcCECAOIBQ2AgwgDkEYaiADQdgBaikCADcCACARKAIAIgFFDQAgFyABQTBsEN8ECyADQeAEaiQADAALIAhBKGogCEE4aikCADcDACAIIAgpAjA3AyAgGCAIQcgAaikCACIfNwMAIAggCCkCQDcDUCAfpyIJQQxLDQEgCUEMSQRAQQwgCSIEayIFIAgoAlAgBGtLBEAgESAEIAVBCEEwEIgDIAgoAlghBAsgCCgCVCIHIARBMGxqIQEgBUECTwRAIAlBf3NBDGpBMGwiAgRAIAFBACAC/AsACyAHIAlBUGxqIARBMGxqQZAEaiEBIAQgBWpBAWshBAsgAUIANwMAIAFBKGpCADcDACABQSBqQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgCCAEQQFqNgJYCyAAIAgpA1A3AhAgACAIKQMgNwIAIABBGGogCEHYAGopAwA3AgAgAEEIaiAIQShqKQMANwIAIAgoAhAiAARAIAgoAhQgAEEwbBDfBAsgCEHgAGokAA8LDAELQciFwABBOkGshsAAEP4DAAtBCEEwEP8EAAvoBgIDfwN+IwBBoAJrIgMkACADQShqIgVBAEHBAPwLACADQRhqQbCjwAApAwA3AwAgA0EQakGoo8AAKQMANwMAIANBCGpBoKPAACkDADcDACADQgA3AyAgA0GYo8AAKQMANwMAAkAgAkHAAE8EQCADIAJBBnYiBK03AyAgAyABIAQQLSACQT9xIgRFBEAgBCECDAILIAUgASACQUBxaiAE/AoAACAEIQIMAQsgAkUNACAFIAEgAvwKAAALIAMgAjoAaCADQfAAaiADQfAA/AoAACADQZgBaiICIAMtANgBIgFqIgRBgAE6AAAgAa0iB0I7hiADKQOQASIGQgmGIgggB0IDhoQiB0KA/gODQiiGhCAHQoCA/AeDQhiGIAdCgICA+A+DQgiGhIQgBkIBhkKAgID4D4MgBkIPiEKAgPwHg4QgBkIfiEKA/gODIAhCOIiEhIQhBgJAAkAgAUE/RwRAIAFBP3MiBQRAIARBAWpBACAF/AsACyABQThzQQdLDQELIANB8ABqIgEgAkEBEC0gA0GQAmpCADcDACADQYgCakIANwMAIANBgAJqQgA3AwAgA0H4AWpCADcDACADQfABakIANwMAIANB6AFqQgA3AwAgA0IANwPgASADIAY3A5gCIAEgA0HgAWpBARAtDAELIAMgBjcD0AEgA0HwAGogAkEBEC0LIAAgAygCjAEiAUEYdCABQYD+A3FBCHRyIAFBCHZBgP4DcSABQRh2cnI2ABwgACADKAKIASIBQRh0IAFBgP4DcUEIdHIgAUEIdkGA/gNxIAFBGHZycjYAGCAAIAMoAoQBIgFBGHQgAUGA/gNxQQh0ciABQQh2QYD+A3EgAUEYdnJyNgAUIAAgAygCgAEiAUEYdCABQYD+A3FBCHRyIAFBCHZBgP4DcSABQRh2cnI2ABAgACADKAJ8IgFBGHQgAUGA/gNxQQh0ciABQQh2QYD+A3EgAUEYdnJyNgAMIAAgAygCeCIBQRh0IAFBgP4DcUEIdHIgAUEIdkGA/gNxIAFBGHZycjYACCAAIAMoAnQiAUEYdCABQYD+A3FBCHRyIAFBCHZBgP4DcSABQRh2cnI2AAQgACADKAJwIgBBGHQgAEGA/gNxQQh0ciAAQQh2QYD+A3EgAEEYdnJyNgAAIANBoAJqJAALkQYCCX8EfiMAQRBrIgckAAJAAkACQCABKAIIRQRAQdHOxQAtAAAaQQEhA0EBQQEQ1gQiBUUNAiAFQQA6AAAgB0EBNgIEDAELIAdBBGogAUEIELACIAcoAgghBSAHKAIMIgNBAkkNACADIAVqIQZBACEBIANBAXYiAkEBRwRAIANBAWshBCACQf7///8HcSEIA0AgBCAFaiICLQAAIQkgAiABIAVqIgItAAA6AAAgAiAJOgAAIAYgAUF+c2oiCS0AACEKIAkgAkEBaiICLQAAOgAAIAIgCjoAACAEQQJrIQQgCCABQQJqIgFHDQALCyADQQJxBEAgASAFaiIELQAAIQIgBCAGIAFBf3NqIgEtAAA6AAAgASACOgAACyADQSFPDQILAkAgAyADQRBrIgFBACABIANNGyICRg0AIAIgBWohAUEQIAMgA0EQTxsiCEEDcSEEAkAgCEEBa0EDSQRADAELIAhBHHEhBgNAIAxCIIhCgID8/w+DIA5CIIaEIAxCEIYiC0IwiIQhDiABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQwgAUEEaiEBIAZBBGsiBg0ACwsgBARAA0AgDkIIhiAMQjiIhCEOIAExAAAgDEIIhoQhDCABQQFqIQEgBEEBayIEDQALC0IAIQsgA0ERSQRADAELIAJBA3EhBAJAIAggA2tBfEsEQCAFIQEMAQsgAkE8cSEGIAUhAQNAIAtCIIhCgID8/w+DIA1CIIaEIAtCEIYiC0IwiIQhDSABQQNqMQAAIAFBAWoxAAAgCyABMQAAQgiGhIRCEIYgAUECajEAAEIIhoSEIQsgAUEEaiEBIAZBBGsiBg0ACwsgBEUNAANAIA1CCIYgC0I4iIQhDSABMQAAIAtCCIaEIQsgAUEBaiEBIARBAWsiBA0ACwsgACALNwMQIAAgDDcDACAAIA03AxggACAONwMIIAcoAgQiAARAIAUgABDfBAsgB0EQaiQADwtBAUEBEP8EAAtB1NrCAEEtQYTbwgAQ/gMAC60HAgl/An4jAEGQAWsiACQAIABBIGpCADcDACAAQRhqQgA3AwAgAEEQakIANwMAIABBCGpCADcDACAAQgA3AwAgAEIBNwMoQYF9IQYgAEGIAWohCEGAAyEHA0ACQCAIQgA3AwAgAEGAAWpCADcDACAAQfgAakIANwMAIABB8ABqQgA3AwAgAEHoAGpCADcDACAAQgA3A2AgB0EBayIEQQZ2IQECQCAEQT9xIgJFBEAgAUEGRg0BIARB/wJLDQIgAEHgAGogAUEDdGpCms3/y6O9xIAaNwMAIAFBBUYNASABQQFqIQJBBiABayIDQQAgA0EGTRsiA0EBRgRAIAIhAQwDCyAAQeAAaiACQQN0akLX2a6a5PbpjcsANwMAIAFBBEYNASABQQJqIQIgA0ECRgRAIAIhAQwDCyAAQeAAaiACQQN0akK/pZScz/DSu+QANwMAIAFBA0YNASABQQNqIQIgA0EDRgRAIAIhAQwDCyAAQeAAaiACQQN0akKk7MO1j9S0mOcANwMAIAFBAkYNASABQQRqIQIgA0EERgRAIAIhAQwDCyAAQeAAaiIFIAJBA3RqQv//z4rr///VHjcDACABQQFGDQEgAUEFaiEBIANBBUYNAiABQQN0IAVqQqrV/v///7//uX83AwAgBEHAAEkNAUEGQQZBgNfBABDZAwALIARBgANPBEAgAUEGQaDXwQAQ2QMACyAAQeAAaiIFIAFBA3RqIgNCms3/y6O9xIAaIAKtIgmINwMAIARBvwJLDQAgAUEBaiICQQN0IAVqQprN/8ujvcSAGiAGQT9xrSIKhkLX2a6a5PbpjcsAIAmIhDcDACACQQVGDQAgAUECaiICQQN0IAVqQtfZrprk9umNywAgCoZCv6WUnM/w0rvkACAJiIQ3AwAgAkEFRg0AIAFBA2oiAkEDdCAFakK/pZScz/DSu+QAIAqGQqTsw7WP1LSY5wAgCYiENwMAIAJBBUYNACABQQRqIgFBA3QgBWpCpOzDtY/UtJjnACAKhkL//8+K6///1R4gCYiENwMAIAFBBUYNACADQv//z4rr///VHiAKhkKq1f7///+//7l/IAmIhDcDKAsgAEE4akIANwMAIABBQGtCADcDACAAQcgAakIANwMAIABB0ABqQgA3AwAgAEIANwMwIAAgACkDiAFCAYM3A1ggAEEwaiAAQTAQ8QMEQCAGQQFqIQYgBCEHDAIFIABBkAFqJAAgBw8LAAsLIAFBBkGQ18EAENkDAAv4BgEEfyMAQZASayIDJAAgAyABNgLwDyADIAFBoAJqIgY2AvQPIANBCGoiBSADQfAPahCQA0EARQRAIANBsBFqIAVB4AD8CgAACyAERQRAIANB0BBqIANBsBFqQeAA/AoAAAsgBEUEQCADQcgEaiADQdAQakHgAPwKAAALIARFBEAgA0HIDWogA0HIBGpB4AD8CgAACyADQQhqIgUgA0HwD2oQkAMgBEUEQCADQbARaiAFQeAA/AoAAAsgBEUEQCADQdAQaiADQbARakHgAPwKAAALIARFBEAgA0HIBGogA0HQEGpB4AD8CgAACyAERQRAIANBqA5qIANByARqQeAA/AoAAAsgA0EIaiIFIANB8A9qEJADIARFBEAgA0GwEWogBUHgAPwKAAALIARFBEAgA0HQEGogA0GwEWpB4AD8CgAACyAERQRAIANByARqIANB0BBqQeAA/AoAAAsgBEUEQCADQYgPaiADQcgEakHgAPwKAAALQQAiBUUEQCADQYgJaiADQcgNakGgAvwKAAALIAMgAUHABGo2AuwPIAMgBjYC6A8gA0GwEWoiASADQegPahCQAyAERQRAIANB0BBqIAFB4AD8CgAACyAERQRAIANB8A9qIANB0BBqQeAA/AoAAAsgBEUEQCADQQhqIANB8A9qQeAA/AoAAAsgBEUEQCADQcgEaiADQQhqQeAA/AoAAAsgA0GwEWoiASADQegPahCQAyAERQRAIANB0BBqIAFB4AD8CgAACyAERQRAIANB8A9qIANB0BBqQeAA/AoAAAsgBEUEQCADQQhqIANB8A9qQeAA/AoAAAsgBEUEQCADQagFaiADQQhqQeAA/AoAAAsgA0GwEWoiASADQegPahCQAyAERQRAIANB0BBqIAFB4AD8CgAACyAERQRAIANB8A9qIANB0BBqQeAA/AoAAAsgBEUEQCADQQhqIANB8A9qQeAA/AoAAAsgBEUEQCADQYgGaiADQQhqQeAA/AoAAAsgBUUEQCADQcgNaiADQcgEakGgAvwKAAALIAVFBEAgA0GoC2ogA0HIDWpBoAL8CgAACyADQQhqIANBiAlqQcAE/AoAACACBEADQCADQcgEaiIBIANBCGoiBBCNAiAEIAFBwAT8CgAAIAJBAWsiAg0ACwsgACADQQhqQcAE/AoAACADQZASaiQAC7YHAgh+DH8CQCABKAIMIhBBf0YEQCAAIAIpAgA3AgAgAEEIaiACQQhqKQIANwIAIAEoAgAiAEUNASABKAIEIABBBXQQ3wQMAQsgAigCDCIRQX9HBEAgASACIBAgEUgiDBsiDSgCACETIA0oAgQhFCACIAEgDBsiASgCACESIAEoAgQhDiABKAIIIQsCQCANKAIIIgFFDQAgAUEFdCEWQX8hFUEAIQIDQCAVQQFqIhUgC0cEQEKpwMaJrs6TsjAhBCACIA5qIg8pAwAgAiAUaiIBKQMAfCABQQhqKQMAIgMgD0EIaiINKQMAfCIIIANUIAggAUEQaikDACIDIA9BEGoiDCkDAHwiBSADVCAFIAFBGGopAwAiAyAPQRhqIgEpAwB8IgcgA1StfCIGIAVUcq18IgUgCFRyrXwiCSEDAkACQAJAIAlCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hBCAFIQMgBULdsIWM6LaRqLh/Ug0AQo2Vx8OW0trAl38hBCAGIQMgBkKNlcfDltLawJd/Ug0AQsf688PtgqOQPCEEIAciA0LH+vPD7YKjkDxRDQELIAMgBFoNACAFIQQgBiEDDAELIAZC8+q4vOmtpb/oAHwiCiAHQsf688PtgqOQPFStIgR9IQMgBUKjz/rzl8nu18cAfCIIIAZCjZXHw5bS2sCXf1QgBCAKVnKtIgZ9IQQgCSAFQt2whYzotpGouH9UIAYgCFZyrX1CqcDGia7Ok7IwfSEJIAdCx/rzw+2Co5A8fSEHCyAPIAk3AwAgDSAENwMAIAwgAzcDACABIAc3AwAgFiACQSBqIgJHDQEMAgsLIAsgC0HUysIAENkDAAsgECARIBAgEUobIQEgEwRAIBQgE0EFdBDfBAsCQAJAAkAgAUEASA0AIAEgC08NASAOIAFBBXRqIQIDQCACQdjDwgBBIBDxAw0BIAJBIGshAiABQQBKIAFBAWshAQ0AC0HRzsUALQAAGkEgQQgQ1gQiAUUNAiABQgA3AwAgAEKBgICAcDcCCCAAIAE2AgQgAEEBNgIAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIBJFDQQgDiASQQV0EN8EDwsgACABNgIMIAAgDjYCBCAAIBI2AgAgACABQQFqIgAgCyAAIAtJGzYCCA8LIAEgC0HEysIAENkDAAtBCEEgEP8EAAsgACABKQIANwIAIABBCGogAUEIaikCADcCACACKAIAIgBFDQAgAigCBCAAQQV0EN8ECwvscwIWfiJ/IwBB4ABrIh0kAEHRzsUALQAAGgJAAkBBIEEIENYEIhsEQCAbQRhqQfDEwgApAwA3AwAgG0EQakHoxMIAKQMANwMAIBtBCGpB4MTCACkDADcDACAbQdjEwgApAwA3AwAgHUIBNwIIIB0gGzYCBCAdQQE2AgAgASgCBCIaIAEoAggiGUEEdGohHCABKAIAIR8gGiEbAkAgGQRAIB1B1ABqIgFBCGohGQNAIBsoAgAiIEGAgICAeEcEQCAdICA2AlAgASAbQQRqKQIANwIAIBkgG0EMaigCADYCACAdQTBqIB0gHUHQAGoQZyAdKAIAIiAEQCAdKAIEICBBBXQQ3wQLIB1BCGogHUE4aikCADcDACAdIB0pAjA3AwAgHSgCUCIgBEAgHSgCVCAgQQV0EN8ECyAbQRBqIhsgHEcNAQwDCwsgG0EQaiEbCyAbIBxGDQAgHCAba0EEdiEBA0AgGygCACIcBEAgG0EEaigCACAcQQV0EN8ECyAbQRBqIRsgAUEBayIBDQALCyAfBEAgGiAfQQR0EN8ECyAdQRBqIRwjAEHABGsiICQAICAQIQJAAkACQCAgKALsAUUNACAgKALkASIBICApA/gBIgNC/8rRy6eM2bLwAIUiAkIQiSACICApA/ABIgRC4eSV89bs2bzsAIV8IgKFIgUgA0Lt3pHzlszct+QAhSIDIARC9crNg9es27fzAIV8IgRCIIl8IgZCjICAgICAgIAEhSADQg2JIASFIgMgAnwiAiADQhGJhSIDfCIEIANCDYmFIgMgBUIViSAGhSIFIAJCIIlC/wGFfCICfCIGIANCEYmFIgNCDYkgAyACIAVCEImFIgIgBEIgiXwiBHwiA4UiBUIRiSAFIAJCFYkgBIUiAiAGQiCJfCIEfCIFhSIGQg2JIAYgAkIQiSAEhSICIANCIIl8IgN8hSIEQhGJIAJCFYkgA4UiA0IQiSADIAVCIIl8IgOFQhWJhSADIAR8IgNCIIiFIAOFIgOncSEeIANCGYhC/wCDQoGChIiQoMCAAX4hBCAgKALgASIbQQxrIRoDQAJAIBsgHmopAAAiAiAEhSIDQn+FIANCgYKEiJCgwIABfYNCgIGChIiQoMCAf4MiA1BFBEADQCAaQQAgA3qnQQN2IB5qIAFxayIfQQxsaigCAEEMRg0CIANCAX0gA4MiA1BFDQALCyACIAJCAYaDQoCBgoSIkKDAgH+DUEUNAiAeICFBCGoiIWogAXEhHgwBCwsgGyAfQQxsaiIfQQRrKAIAIRogH0EIaygCACEeICAoAqwEIh8EQCAgKAKwBCAfQQJ0EN8ECwJAIAFFDQAgASABQQxsQRNqQXhxIh9qQQlqIgFFDQAgGyAfayABEN8ECyAgKAKQAiIBQYCAgIB4RiABRXJFBEAgICgClAIgAUECdBDfBAtBACEbIBpB////P0sgGkEFdCIYQfj///8HS3INAQJ/IBhFBEBBCCEBQQAMAQtB0c7FAC0AABpBCCEbIBhBCBDWBCIBRQ0CIBoLISEgGgRAIAEhGyAaIR8DQCAeLQAAISQjAEGgBmsiGSQAAkAgJMBBAEgEQCAZQfAFakEAICRrrcIiA0IAQon1q5y1i7+Wc0IAEMkDIBlB4AVqIBkpA/AFIgVCAEIAQonHmaSu8IHph38QyQMgGUHQBWogGSkD6AUiAkIAQsf688PtgqOQPEIAEMkDIBlBwAVqIAJCAEKNlcfDltLawJd/QgAQyQMgGUGwBWogAkIAQt2whYzotpGouH9CABDJAyAZQaAFaiACQgBCqcDGia7Ok7IwQgAQyQMgGUGQBWogA0IAQvuDlKKdosbztX9CABDJAyAZQYAFaiAZKQPABSIHIBkpA/gFfCIEIBkpA9gFIAUgGSkD0AUiAnwgAlStfHwiBSAZKQOQBXwiBkIAQgBCiceZpK7wgemHfxDJAyAZQfAEaiAZKQOIBSICQgBCx/rzw+2Co5A8QgAQyQMgGUHgBGogAkIAQo2Vx8OW0trAl39CABDJAyAZQdAEaiACQgBC3bCFjOi2kai4f0IAEMkDIBlBwARqIAJCAEKpwMaJrs6TsjBCABDJAyAZQbAEaiADQgBC9v+F0vDfx9XHAEIAEMkDIBlBoARqIBkpA+AEIgggGSkDmAUgBSAGVq18IgkgBCAFVq0gGSkDyAUgBCAHVK18fCIHIBkpA7AFfCIKfCINfCIEIBkpA/gEIAYgGSkD8AQiAnwgAlStfHwiBSAZKQOwBHwiBkIAQgBCiceZpK7wgemHfxDJAyAZQZAEaiAZKQOoBCICQgBCx/rzw+2Co5A8QgAQyQMgGUGABGogAkIAQo2Vx8OW0trAl39CABDJAyAZQfADaiACQgBC3bCFjOi2kai4f0IAEMkDIBlB4ANqIAJCAEKpwMaJrs6TsjBCABDJAyAZQdADaiADQgBCn+rg1Zzup+wGQgAQyQMgGUHAA2ogGSkDgAQiDiAJIA1WrSIJIBkpA7gFIAcgClatfCIKIBkpA6AFfCINfCICIBkpA9AEfCIHIAQgBVatIBkpA+gEIAQgCFStfHx8IgQgGSkDuAQgBSAGVq18fCIQfCIFIBkpA5gEIAYgGSkDkAQiA3wgA1StfHwiBiAZKQPQA3wiCEIAQgBCiceZpK7wgemHfxDJAyAZQbADaiAZKQPIAyIDQgBCx/rzw+2Co5A8QgAQyQMgGUGgA2ogA0IAQo2Vx8OW0trAl39CABDJAyAZQZADaiADQgBC3bCFjOi2kai4f0IAEMkDIBlBgANqIANCAEKpwMaJrs6TsjBCABDJAwJAIBkpA4gDIBkpA+gDIBkpA8gEIBkpA8AEIgsgGSkDqAUgCiANVq18fCIDIAtUrXwgAyADIAIgCVStfCIDVq18IAMgAyAEIAdUrSAZKQPYBCACIAdWrXx8fCIDVq18IgcgGSkD4AN8IgIgB1StfCACIAIgAyADIAQgEFatfCIEVq18IgNWrXwgAyADIBkpA/gDIAQgBCAZKQPwA3wiAlatfCACIAIgBSAGVq0gGSkDiAQgBSAOVK18fHwiAlatfHwiBFatfCIFIBkpA4ADfCIDIAVUrXwgAyADIAQgBCACIAIgGSkD2AMgBiAIVq18fCIFVq18IgJWrXwiA1atfCADIAMgGSkDmAMgAiACIBkpA5ADfCICVq18IAIgAiAZKQOoAyAFIBkpA6ADIgZ8IgQgBlStfCAEIBkpA7gDIBkpA7ADIgUgCHwgBVStfHwiBiAEVK18fCICVq18fCIEVq18IgdCqcDGia7Ok7IwVARAIAIhAwwBCwJAIARC3bCFjOi2kai4f1YNACAEQt2whYzotpGouH9SBEAgAiEDQqnAxomuzpOyMCEHDAILIAJCjZXHw5bS2sCXf1YNAAJAIAJCjZXHw5bS2sCXf1IEQCACIQMMAQtCjZXHw5bS2sCXfyEDIAZCx/rzw+2Co5A8Wg0BC0LdsIWM6LaRqLh/IQRCqcDGia7Ok7IwIQcMAQsgAkLz6ri86a2lv+gAfCIFIAZCx/rzw+2Co5A8VK0iCH0hAyAEQqPP+vOXye7XxwB8IgkgAkKNlcfDltLawJd/VCAFIAhUcq0iAn0hBCAHIAIgCVatfUKpwMaJrs6TsjB9IQcgBkLH+vPD7YKjkDx9IQYLIBkgBjcDmAYgGSADNwOQBiAZIAQ3A4gGIBkgBzcDgAYCQCAZQYAGakGolcEAQSAQ8QNFBEAgBCECIAMhBQwBC0KNlcfDltLawJd/IAN9IgIgBkLH+vPD7YKjkDxWrSIIfSEFQt2whYzotpGouH8gBH0iCSACIAhUIANCjZXHw5bS2sCXf1ZyrSIDfSECQqnAxomuzpOyMCADIAlWIARC3bCFjOi2kai4f1ZyrSAHfH0hB0LH+vPD7YKjkDwgBn0hBgsgICAGNwMYICAgBTcDECAgIAI3AwgMAQsgGUHAAmogJK1C/wGDIgNCAEKJ9auctYu/lnNCABDJAyAZQbACaiAZKQPAAiIFQgBCAEKJx5mkrvCB6Yd/EMkDIBlBoAJqIBkpA7gCIgJCAELH+vPD7YKjkDxCABDJAyAZQZACaiACQgBCjZXHw5bS2sCXf0IAEMkDIBlBsAFqIAJCAELdsIWM6LaRqLh/QgAQyQMgGUHQAGogAkIAQqnAxomuzpOyMEIAEMkDIBlB0AJqIANCAEL7g5SinaLG87V/QgAQyQMgGUGAAmogGSkDkAIiByAZKQPIAnwiBCAZKQOoAiAFIBkpA6ACIgJ8IAJUrXx8IgUgGSkD0AJ8IgZCAEIAQonHmaSu8IHph38QyQMgGUHwAWogGSkDiAIiAkIAQsf688PtgqOQPEIAEMkDIBlB4AFqIAJCAEKNlcfDltLawJd/QgAQyQMgGUHQAWogAkIAQt2whYzotpGouH9CABDJAyAZQcABaiACQgBCqcDGia7Ok7IwQgAQyQMgGUHgAmogA0IAQvb/hdLw38fVxwBCABDJAyAZQaABaiAZKQPgASIIIBkpA9gCIAUgBlatfCIJIAQgBVatIBkpA5gCIAQgB1StfHwiByAZKQOwAXwiCnwiDXwiBCAZKQP4ASAGIBkpA/ABIgJ8IAJUrXx8IgUgGSkD4AJ8IgZCAEIAQonHmaSu8IHph38QyQMgGUGQAWogGSkDqAEiAkIAQsf688PtgqOQPEIAEMkDIBlBgAFqIAJCAEKNlcfDltLawJd/QgAQyQMgGUHwAGogAkIAQt2whYzotpGouH9CABDJAyAZQeAAaiACQgBCqcDGia7Ok7IwQgAQyQMgGUHwAmogA0IAQp/q4NWc7qfsBkIAEMkDIBlBQGsgGSkDgAEiDiAJIA1WrSIJIBkpA7gBIAcgClatfCIKIBkpA1B8Ig18IgIgGSkD0AF8IgcgBCAFVq0gGSkD6AEgBCAIVK18fHwiBCAZKQPoAiAFIAZWrXx8IhB8IgUgGSkDmAEgBiAZKQOQASIDfCADVK18fCIGIBkpA/ACfCIIQgBCAEKJx5mkrvCB6Yd/EMkDIBlBMGogGSkDSCIDQgBCx/rzw+2Co5A8QgAQyQMgGUEgaiADQgBCjZXHw5bS2sCXf0IAEMkDIBlBEGogA0IAQt2whYzotpGouH9CABDJAyAZIANCAEKpwMaJrs6TsjBCABDJAwJAIBkpAwggGSkDaCAZKQPIASAZKQPAASILIBkpA1ggCiANVq18fCIDIAtUrXwgAyADIAIgCVStfCIDVq18IAMgAyAEIAdUrSAZKQPYASACIAdWrXx8fCIDVq18IgcgGSkDYHwiAiAHVK18IAIgAiADIAMgBCAQVq18IgRWrXwiA1atfCADIAMgGSkDeCAEIAQgGSkDcHwiAlatfCACIAIgBSAGVq0gGSkDiAEgBSAOVK18fHwiAlatfHwiBFatfCIFIBkpAwB8IgMgBVStfCADIAMgBCAEIAIgAiAZKQP4AiAGIAhWrXx8IgVWrXwiAlatfCIDVq18IAMgGSkDGCACIAIgGSkDEHwiAlatfCACIAIgGSkDKCAFIBkpAyAiBnwiBCAGVK18IAQgBCAZKQM4IBkpAzAiBSAIfCAFVK18fCIEVq18fCICVq18fCIGIANUrXwiB0KpwMaJrs6TsjBUBEAgAiEDDAELAkAgBkLdsIWM6LaRqLh/Vg0AIAZC3bCFjOi2kai4f1IEQCACIQNCqcDGia7Ok7IwIQcMAgsgAkKNlcfDltLawJd/Vg0AAkAgAkKNlcfDltLawJd/UgRAIAIhAwwBC0KNlcfDltLawJd/IQMgBELH+vPD7YKjkDxaDQELQt2whYzotpGouH8hBkKpwMaJrs6TsjAhBwwBCyACQvPquLzpraW/6AB8IgUgBELH+vPD7YKjkDxUrSIIfSEDIAZCo8/685fJ7tfHAHwiCSACQo2Vx8OW0trAl39UIAUgCFRyrSICfSEGIAcgAiAJVq19QqnAxomuzpOyMH0hByAEQsf688PtgqOQPH0hBAsgICAENwMYICAgAzcDECAgIAY3AwgLICAgBzcDACAZQaAGaiQAIBtBGGogIEEYaikDADcDACAbQRBqICBBEGopAwA3AwAgG0EIaiAgQQhqKQMANwMAIBsgICkDADcDACAeQQFqIR4gG0EgaiEbIB9BAWsiHw0ACwsgGiEbAkACQANAIBhFDQEgG0EBayEbIBhBIGsiGCABakHYw8IAQSAQ8QNFDQALIBtBAWoiHyAaIBogH0sbIRgMAQtB0c7FAC0AABpBIEEIENYEIhpFDQYgGkIANwMAIBpBGGpCADcDACAaQRBqQgA3AwAgGkEIakIANwMAQX8hG0EBIRggIQRAIAEgIUEFdBDfBAsgGiEBQQEhIQsgHCAbNgIMIBwgGDYCCCAcIAE2AgQgHCAhNgIAICBBwARqJAAMAgtB0JrBAEEWQYibwQAQ6AMACyAbIBhBiJnBABDIBAALIB1B2ABqIi8gHUEIaikDADcDACAdIB0pAwA3A1AgHUEwaiEkIB1B0ABqIShBACEBQgAhCkIAIQlCACELQgAhCEEAIRkjAEGABWsiGCQAAkACQAJAAkACQAJAIBwiICgCDCInQX9HBEAgKCgCCCIaQQV0IRwCQCAaQf///z9LIBxB+P///wdLcg0AICgoAgwhHiAoKAIEISwCQCAcRQRAQQghIQwBC0HRzsUALQAAGkEIIQEgHEEIENYEIiFFDQEgGkUNAEEAIQEgGiEbA0AgASAcRg0BIAEgIWoiHyABICxqIiYpAwA3AwAgH0EYaiAmQRhqKQMANwMAIB9BEGogJkEQaikDADcDACAfQQhqICZBCGopAwA3AwAgAUEgaiEBIBtBAWsiGw0ACwsgGCAaNgKIBCAYICE2AoQEIBggGjYCgAQgGCAeNgKMBCAeICdIDQUgHiAnayIrQQFqIiZBBXQhAQJAICZB////P0sgAUH4////B0tyDQACfyABRQRAQQghG0EADAELQdHOxQAtAAAaQQghGSABQQgQ1gQiG0UNASAmCyEwAkACQAJAAkAgJkECTwRAICtBB3EhGSAnIB5rQXhNDQEgGyEBDAILIBshASAmDQIMAwsgK0F4cSEcIBshAQNAIAFCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACABQSBqQgA3AwAgAUEoakIANwMAIAFBMGpCADcDACABQThqQgA3AwAgAUFAa0IANwMAIAFByABqQgA3AwAgAUHQAGpCADcDACABQdgAakIANwMAIAFB4ABqQgA3AwAgAUHoAGpCADcDACABQfAAakIANwMAIAFB+ABqQgA3AwAgAUGYAWpCADcDACABQZABakIANwMAIAFBiAFqQgA3AwAgAUGAAWpCADcDACABQbgBakIANwMAIAFBsAFqQgA3AwAgAUGoAWpCADcDACABQaABakIANwMAIAFBwAFqQgA3AwAgAUHIAWpCADcDACABQdABakIANwMAIAFB2AFqQgA3AwAgAUHgAWpCADcDACABQegBakIANwMAIAFB8AFqQgA3AwAgAUH4AWpCADcDACABQYACaiEBIBxBCGsiHA0ACwsgGUUNAANAIAFCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACABQSBqIQEgGUEBayIZDQALCyABQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwALICAoAggiASAnSwRAICAoAgQgJ0EFdGoiAUHYw8IAQSAQ8QNFDQYgGEGwBGpCADcDACAYQagEaiIxQgA3AwAgGEIANwOgBCAYQgE3A7gEIBhB2ARqIAFBGGopAwA3AwAgGEHQBGogAUEQaikDADcDACAYQcgEaiIyIAFBCGopAwA3AwAgGCABKQMANwPABCAYQfgEaiIzQdDDwgApAwA3AwAgGEHwBGoiNEHIw8IAKQMANwMAIBhB6ARqIjVBwMPCACkDADcDACAYQbjDwgApAwA3A+AEAkAgGEHABGogGEGgBGpBIBDxA0UEQEKf6uDVnO6n7AYhE0KJ9auctYu/lnMhDUL7g5SinaLG87V/IQ5C9v+F0vDfx9XHACEQDAELQp/q4NWc7qfsBiETQvb/hdLw38fVxwAhEEL7g5SinaLG87V/IQ5CifWrnLWLv5ZzIQ0gGCkD2AQhBCAYKQPABCEPIBgpA8gEIQIgGCkD0AQhDELH+vPD7YKjkDwhA0KpwMaJrs6TsjAhFULdsIWM6LaRqLh/IQVCjZXHw5bS2sCXfyESA0AgGEHgBGogGEGgBGpBIBDxA0UEQCAJIRAgCiEOIAghDSALIRMMAgsgBKdBAXFFBEADQCAMQj+GIARCAYiEIQQCQCANQgGDUARAIBAhBiAOIQcgDSERDAELIBMgECAQQqPP+vOXye7XxwB9IhRWIBQgFCAOQvPquLzpraW/6AB9IgYgDlQgBiAGIA1Cx/rzw+2Co5A8fCIRIA1UrXwiB1ZyrXwiBlZyrXxCqcDGia7Ok7IwfCETCyAPQj+GIAJCP4YgDEIBiIQhDCAPQgGIIQ8gE0I/hiAGQgGIhCEQIAZCP4YgB0IBiIQhDiAHQj+GIBFCAYiEIQ0gE0IBiCETIAJCAYiEIQIgBEIBg1ANAAsgGCAMNwPQBCAYIAQ3A9gEIBggAjcDyAQgGCAPNwPABAsgA6dBAXFFBEADQCASQj+GIANCAYiEIQMCQCAIQgGDUARAIAkhBiAKIQcgCCERDAELIAsgCSAJQqPP+vOXye7XxwB9IhRWIBQgFCAKQvPquLzpraW/6AB9IgYgClQgBiAGIAhCx/rzw+2Co5A8fCIRIAhUrXwiB1ZyrXwiBlZyrXxCqcDGia7Ok7IwfCELCyAVQj+GIAVCP4YgEkIBiIQhEiAVQgGIIRUgC0I/hiAGQgGIhCEJIAZCP4YgB0IBiIQhCiAHQj+GIBFCAYiEIQggC0IBiCELIAVCAYiEIQUgA0IBg1ANAAsgGCASNwPwBCAYIAM3A/gEIBggBTcD6AQgGCAVNwPgBAsCQAJAAkACQAJAIA8iByAVIgZSDQAgAiEHIAIgBSIGUg0AIAwiByASIgZSDQAgBCIHIAMiBlENAQsgBiAHWA0AIBggAyAEfSIGNwP4BCAYIBIgDH0iESADIARUrSIDfSIHNwPwBCAYIAUgAn0iFCADIBFWIAwgElZyrSIDfSIRNwPoBCAYIBUgD30gAiAFViADIBRWcq19IhU3A+AEAkACQCATIgUgCyIDUg0AIBAiBSAJIgNSDQAgDiIFIAoiA1INACAIIgMgDSIFUQ0BCyADIAVUDQILIAsgE30gCSAQfSIUIAogDn0iFiAIIA1UrSIXVCAKIA5Ucq0iClQgCSAQVHKtfSELIAggDX0hCCAHIRIgESEFIAYhAyAUIAp9IQkgFiAXfSEKDAMLIBggBCADfSIGNwPYBCAYIAwgEn0iESADIARWrSIEfSIHNwPQBCAYIAIgBX0iFCAMIBJUIAQgEVZyrSIEfSIRNwPIBCAYIA8gFX0gAiAFVCAEIBRWcq19Ig83A8AEAkACQCATIgQgCyICUg0AIBAiBCAJIgJSDQAgDiIEIAoiAlINACAIIgIgDSIEUQ0BCyACIARWDQILIBMgC30gECAJfSIUIA4gCn0iFiAIIA1WrSIXVCAKIA5Wcq0iDlQgCSAQVnKtfSETIA0gCH0hDSAHIQwgESECIAYhBCAUIA59IRAgFiAXfSEODAILIAtC3bCFjOi2kai4fyAQfSIDQo2Vx8OW0trAl38gDn0iBSANQsf688PtgqOQPFatIgtUIA5CjZXHw5bS2sCXf1ZyrSISVCAQQt2whYzotpGouH9Wcq0gE3x9IAkgAyASfSISfCIDIBJUIAMgAyAFIAt9IgkgCnwiBSAJVCAFQsf688PtgqOQPCANfSIJIAh8IgggCVStfCIKIAVUcq18IglWcq18QqnAxomuzpOyMHwhCyAHIRIgESEFIAYhAwwBCyATIAt9Qt2whYzotpGouH8gCX0iAkKNlcfDltLawJd/IAp9IgQgCELH+vPD7YKjkDxWrSITVCAKQo2Vx8OW0trAl39Wcq0iDFQgCULdsIWM6LaRqLh/VnKtfSAQIAIgDH0iDHwiAiAMVCACIAIgDiAEIBN9IhB8IgQgEFQgBELH+vPD7YKjkDwgCH0iDiANfCINIA5UrXwiDiAEVHKtfCIQVnKtfEKpwMaJrs6TsjB8IRMgByEMIBEhAiAGIQQLIBhBwARqIBhBoARqQSAQ8QMNAAsLICdBf3MhNgNAAkACQCAYKAKIBCIBIB5LBEAgGEHAA2ogGCgChAQgHkEFdGoiASkDGCIDQgAgDUIAEMkDIBhBwAJqIAEpAxAiAkIAIA1CABDJAyAYQcABaiABKQMIIgRCACANQgAQyQMgGEFAayABKQMAIgVCACANQgAQyQMgGEGwA2ogGCkDwAMiCEKJx5mkrvCB6Yd/fiIGQgBCx/rzw+2Co5A8QgAQyQMgGEGgA2ogBkIAQo2Vx8OW0trAl39CABDJAyAYQZADaiAGQgBC3bCFjOi2kai4f0IAEMkDIBhBgANqIAZCAEKpwMaJrs6TsjBCABDJAyAYQdADaiADQgAgDkIAEMkDIBhB0AJqIAJCACAOQgAQyQMgGEHQAWogBEIAIA5CABDJAyAYQdAAaiAFQgAgDkIAEMkDIBhBsAJqIBgpA6ADIgwgGCkDyAMiCyAYKQPAAnwiD3wiByAYKQO4AyAIIBgpA7ADIgZ8IAZUrXx8IgggGCkD0AN8IglCiceZpK7wgemHf34iBkIAQsf688PtgqOQPEIAEMkDIBhBoAJqIAZCAEKNlcfDltLawJd/QgAQyQMgGEGQAmogBkIAQt2whYzotpGouH9CABDJAyAYQYACaiAGQgBCqcDGia7Ok7IwQgAQyQMgGEHgA2ogA0IAIBBCABDJAyAYQeACaiACQgAgEEIAEMkDIBhB4AFqIARCACAQQgAQyQMgGEHgAGogBUIAIBBCABDJAyAYQbABaiAYKQPYAyAIIAlWrXwiEiAYKQPQAnwiCiAYKQPIAiALIA9WrXwiESAYKQPAAXwiCyAYKQOQA3wiDyAHIAhWrSAYKQOoAyAHIAxUrXx8fCIVfCIHIBgpA6ACfCIIIBgpA7gCIAkgGCkDsAIiBnwgBlStfHwiCSAYKQPgA3wiDEKJx5mkrvCB6Yd/fiIGQgBCx/rzw+2Co5A8QgAQyQMgGEGgAWogBkIAQo2Vx8OW0trAl39CABDJAyAYQZABaiAGQgBC3bCFjOi2kai4f0IAEMkDIBhBgAFqIAZCAEKpwMaJrs6TsjBCABDJAyAYQfADaiADQgAgE0IAEMkDIBhB8AJqIAJCACATQgAQyQMgGEHwAWogBEIAIBNCABDJAyAYQfAAaiAFQgAgE0IAEMkDIBhBMGogGCkD6AMgCSAMVq18IhQgGCkD4AJ8IgIgGCkDyAEgCyARVK18IhEgGCkDQHwiBCAYKQOAA3wiBSAPIBVWrSAYKQOYAyALIA9WrXx8fCIGIBgpA9ABfCILIAcgClStIBgpA9gCIAogElStfHx8IgogGCkDkAJ8Ig8gCCAJVq0gGCkDqAIgByAIVq18fHwiEnwiByAYKQOgAXwiCCAYKQO4ASAMIBgpA7ABIgN8IANUrXx8IgkgGCkD8AN8IgxCiceZpK7wgemHf34iA0IAQsf688PtgqOQPEIAEMkDIBhBIGogA0IAQo2Vx8OW0trAl39CABDJAyAYQRBqIANCAELdsIWM6LaRqLh/QgAQyQMgGCADQgBCqcDGia7Ok7IwQgAQyQMCQCAYKQMIIBgpA4gBIBgpA4gCIAUgBlatIBgpA4gDIAQgBVatfHwgGCkDSCAEIBFUrXx8IhEgGCkDUHwiAyAKIAtUrSAYKQPYASAGIAtWrXx8fCIEIBgpA4ACfCIFIARUrXwgBSAFIA8gElatIBgpA5gCIAogD1atfHx8IgZWrXwgAyAEVq0gGCkDWCADIBFUrXx8fCIKIBgpA2B8IgMgGCkD6AEgBiAGIBgpA+ABfCIEVq18IAQgBCACIAdWrSAYKQPoAiACIBRUrXx8fCICVq18fCIEIBgpA4ABfCIFIARUrXwgBSAYKQOYASACIAIgGCkDkAF8IgZWrXwgBiAGIAggCVatIBgpA6gBIAcgCFatfHx8IgdWrXx8IgIgBVStfCADIARWrSAYKQNoIAMgClStfHx8IgggGCkDcHwiAyAYKQP4ASACIAIgGCkD8AF8IgRWrXwgBCAEIBgpA/gCIBgpA/gDIAkgDFatfCIFIBgpA/ACfCICIAVUrXwgAiACIAd8IgVWrXx8IgJWrXx8IgYgGCkDAHwiBCAGVK18IAQgBCAYKQMYIAIgAiAYKQMQfCIHVq18IAcgByAYKQMoIAUgBSAYKQMgfCICVq18IAIgGCkDOCAYKQMwIgUgDHwgBVStfHwiCyACVK18fCICVq18fCIEVq18IAMgBlatIBgpA3ggAyAIVK18fHwiCEKpwMaJrs6TsjBWDQAgCEKpwMaJrs6TsjBSDQIgBELdsIWM6LaRqLh/Vg0AIARC3bCFjOi2kai4f1IEQEKpwMaJrs6TsjAhCAwDCyACQo2Vx8OW0trAl39WDQBC3bCFjOi2kai4fyEDIAJCjZXHw5bS2sCXf1IEQEKpwMaJrs6TsjAhCCACIQ8MBAtCjZXHw5bS2sCXfyEPIAtCx/rzw+2Co5A8Wg0AQqnAxomuzpOyMCEIDAMLIAJC8+q4vOmtpb/oAHwiAyALQsf688PtgqOQPFStIgV9IQ8gBEKjz/rzl8nu18cAfCIGIAJCjZXHw5bS2sCXf1QgAyAFVHKtIgJ9IQMgCCAEQt2whYzotpGouH9UIAIgBlZyrX1CqcDGia7Ok7IwfSEIIAtCx/rzw+2Co5A8fSELDAILIB4gAUHgyMIAENkDAAsgBCEDIAIhDwsgGCALNwP4BCAYIA83A/AEIBggAzcD6AQgGCAINwPgBAJAAkACQAJAAkAgJiAeICdrIh9LBEAgNSkDACEDIDQpAwAhAiAzKQMAIQQgGyAfQQV0IiVqIgEgGCkD4AQ3AwAgAUEYaiAENwMAIAFBEGogAjcDACABQQhqIAM3AwAgGEHABGohIiMAQTBrIhkkACAZIBhB4ARqIgE2AggCQAJAAkAgAUHYw8IAQSAQ8QMEQCAgKAIMIipBf0cEQCAgKAIIIhxBBXQhASAgKAIEISFBCCEaIBwEQEHRzsUALQAAGiABQQgQ1gQiGkUNBAsgGUEUaiItQQA2AgAgGSAaNgIQIBkgHDYCDCAZIAEgIWo2AhwgGSAhNgIYIBkgGUEIajYCICAZIBo2AiwgGUEANgIoIBkgLTYCJCMAQYAEayIBJAAgGUEkaiIaKAIEISEgGigCACAZQRhqIhwoAgAiLiAcKAIEIiNHBEAgHCgCCCE4IBooAgggIUEFdGohOSAhICMgLmtBBXYiHGohIUEAIRoDQCABQcADaiAaIC5qIiNBGGopAwAiA0IAIDgoAgAiKSkDGCICQgAQyQMgAUHQA2ogI0EQaikDACIEQgAgAkIAEMkDIAFB4ANqICNBCGopAwAiBUIAIAJCABDJAyABQfADaiAjKQMAIgZCACACQgAQyQMgAUGwA2ogASkDwAMiCEKJx5mkrvCB6Yd/fiICQgBCx/rzw+2Co5A8QgAQyQMgAUGgA2ogAkIAQo2Vx8OW0trAl39CABDJAyABQZADaiACQgBC3bCFjOi2kai4f0IAEMkDIAFBgANqIAJCAEKpwMaJrs6TsjBCABDJAyABQcACaiApKQMQIgJCACADQgAQyQMgAUHQAmogAkIAIARCABDJAyABQeACaiACQgAgBUIAEMkDIAFB8AJqIAJCACAGQgAQyQMgAUGwAmogASkDoAMiDCABKQPIAyILIAEpA9ADfCIPfCIHIAEpA7gDIAggASkDsAMiAnwgAlStfHwiCCABKQPAAnwiCUKJx5mkrvCB6Yd/fiICQgBCx/rzw+2Co5A8QgAQyQMgAUGgAmogAkIAQo2Vx8OW0trAl39CABDJAyABQZACaiACQgBC3bCFjOi2kai4f0IAEMkDIAFBgAJqIAJCAEKpwMaJrs6TsjBCABDJAyABQcABaiApKQMIIgJCACADQgAQyQMgAUHQAWogAkIAIARCABDJAyABQeABaiACQgAgBUIAEMkDIAFB8AFqIAJCACAGQgAQyQMgAUGwAWogASkDyAIgCCAJVq18IhIgASkD0AJ8IgogASkD2AMgCyAPVq18IhEgASkD4AN8IgsgASkDkAN8Ig8gByAIVq0gASkDqAMgByAMVK18fHwiFXwiByABKQOgAnwiCCABKQO4AiAJIAEpA7ACIgJ8IAJUrXx8IgkgASkDwAF8IgxCiceZpK7wgemHf34iAkIAQsf688PtgqOQPEIAEMkDIAFBoAFqIAJCAEKNlcfDltLawJd/QgAQyQMgAUGQAWogAkIAQt2whYzotpGouH9CABDJAyABQYABaiACQgBCqcDGia7Ok7IwQgAQyQMgAUFAayApKQMAIgJCACADQgAQyQMgAUHQAGogAkIAIARCABDJAyABQeAAaiACQgAgBUIAEMkDIAFB8ABqIAJCACAGQgAQyQMgAUEwaiABKQPIASAJIAxWrXwiFCABKQPQAXwiAiABKQPoAyALIBFUrXwiESABKQPwA3wiBCABKQOAA3wiBSAPIBVWrSABKQOYAyALIA9WrXx8fCIGIAEpA+ACfCILIAcgClStIAEpA9gCIAogElStfHx8IgogASkDkAJ8Ig8gCCAJVq0gASkDqAIgByAIVq18fHwiEnwiByABKQOgAXwiCCABKQO4ASAMIAEpA7ABIgN8IANUrXx8IgkgASkDQHwiDEKJx5mkrvCB6Yd/fiIDQgBCx/rzw+2Co5A8QgAQyQMgAUEgaiADQgBCjZXHw5bS2sCXf0IAEMkDIAFBEGogA0IAQt2whYzotpGouH9CABDJAyABIANCAEKpwMaJrs6TsjBCABDJAwJAAkAgASkDCCABKQOIASABKQOIAiAFIAZWrSABKQOIAyAEIAVWrXx8IAEpA/gDIAQgEVStfHwiESABKQPwAnwiAyAKIAtUrSABKQPoAiAGIAtWrXx8fCIEIAEpA4ACfCIFIARUrXwgBSAFIA8gElatIAEpA5gCIAogD1atfHx8IgZWrXwgAyAEVq0gASkD+AIgAyARVK18fHwiCiABKQPwAXwiAyABKQPoASAGIAYgASkD4AF8IgRWrXwgBCACIAdWrSABKQPYASACIBRUrXx8fCICIARUrXx8IgQgASkDgAF8IgUgBFStfCAFIAEpA5gBIAIgAiABKQOQAXwiBlatfCAGIAYgCCAJVq0gASkDqAEgByAIVq18fHwiB1atfHwiAiAFVK18IAMgBFatIAEpA/gBIAMgClStfHx8IgggASkDcHwiAyABKQNoIAIgAiABKQNgfCICVq18IAIgAiABKQNYIAEpA0ggCSAMVq18IgUgASkDUHwiBCAFVK18IAQgBCAHfCIFVq18fCIEVq18fCICIAEpAwB8IgYgAlStfCAGIAYgASkDGCAEIAQgASkDEHwiB1atfCAHIAcgASkDKCAFIAUgASkDIHwiBFatfCAEIAEpAzggASkDMCIFIAx8IAVUrXx8IgogBFStfHwiBFatfHwiBVatfCACIANUrSABKQN4IAMgCFStfHx8IglCqcDGia7Ok7IwVg0AAkAgCUKpwMaJrs6TsjBRBEAgBULdsIWM6LaRqLh/Vg0CIAVC3bCFjOi2kai4f1IEQCAEIQMgBSECQqnAxomuzpOyMCEJDAQLIARCjZXHw5bS2sCXf1YNAkLdsIWM6LaRqLh/IQIgBEKNlcfDltLawJd/UQ0BIAQhA0KpwMaJrs6TsjAhCQwDCyAEIQMgBSECDAILQo2Vx8OW0trAl38hAyAKQsf688PtgqOQPFoNAEKpwMaJrs6TsjAhCQwBCyAEQvPquLzpraW/6AB8IgIgCkLH+vPD7YKjkDxUrSIGfSEDIAVCo8/685fJ7tfHAHwiByAEQo2Vx8OW0trAl39UIAIgBlRyrSIEfSECIAkgBULdsIWM6LaRqLh/VCAEIAdWcq19QqnAxomuzpOyMH0hCSAKQsf688PtgqOQPH0hCgsgGiA5aiIjIAk3AwAgI0EYaiAKNwMAICNBEGogAzcDACAjQQhqIAI3AwAgGkEgaiEaIBxBAWsiHA0ACwsgITYCACABQYAEaiQAICJBCGogLSgCADYCACAiIBkpAgw3AgAMAgsLQdHOxQAtAAAaQSBBCBDWBCIBRQ0WIAFCADcDACAiQQE2AgggIiABNgIEICJBATYCACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDAEF/ISoLICIgKjYCDCAZQTBqJAAMAQtBCCABQbTKwgAQyAQACyAYKALMBCIpQX9GBEBB0c7FAC0AABpBIEEIENYEIgFFDRQgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIBhCgYCAgHA3A5gEIBggATYClAQgGEEBNgKQBAwFCyAlQfj///8HSwRAQQAhAQwMCwJ/ICVFBEBBCCEaQQAMAQtB0c7FAC0AABpBCCEBICVBCBDWBCIaRQ0MIB8LISMgH0ECSQ0BIB4gNmoiHEEHcSEZIBohASAeICdrQQJrQQdPBEAgHEF4cSEeA0AgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIAFBIGpCADcDACABQShqQgA3AwAgAUEwakIANwMAIAFBOGpCADcDACABQUBrQgA3AwAgAUHIAGpCADcDACABQdAAakIANwMAIAFB2ABqQgA3AwAgAUHgAGpCADcDACABQegAakIANwMAIAFB8ABqQgA3AwAgAUH4AGpCADcDACABQZgBakIANwMAIAFBkAFqQgA3AwAgAUGIAWpCADcDACABQYABakIANwMAIAFBuAFqQgA3AwAgAUGwAWpCADcDACABQagBakIANwMAIAFBoAFqQgA3AwAgAUHAAWpCADcDACABQcgBakIANwMAIAFB0AFqQgA3AwAgAUHYAWpCADcDACABQeABakIANwMAIAFB6AFqQgA3AwAgAUHwAWpCADcDACABQfgBakIANwMAIAFBgAJqIQEgHkEIayIeDQALCyAZRQ0CA0AgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIAFBIGohASAZQQFrIhkNAAsMAgsgHyAmQfDIwgAQ2QMACyAaIQEgH0UNAQsgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMACyAYIB82AqgEIBggGjYCpAQgGCAjNgKgBCAYKALIBCIZQQV0IR5BACEBIBlB////P0sgHkH4////B0tyDQECQCAeRQRAQQghIQwBCyAYKALEBCEqQdHOxQAtAAAaQQghASAeQQgQ1gQiIUUNAiAZRQ0AQQAhASAZIRwDQCABIB5GDQEgASAhaiIiIAEgKmoiJSkDADcDACAiQRhqICVBGGopAwA3AwAgIkEQaiAlQRBqKQMANwMAICJBCGogJUEIaikDADcDACABQSBqIQEgHEEBayIcDQALCyAjIB8iAWsgGUkEQCAYQaAEaiABIBlBCEEgEIgDIBgoAqQEIRogGCgCqAQhAQsgHgRAIBogAUEFdGogISAe/AoAAAsgGCABIBlqNgKoBCAZBEAgISAeEN8ECyAYQZgEaiAxKAIANgIAIBggGCkCoAQ3A5AEIBggHyApajYCnAQLIBgoAsAEIgEEQCAYKALEBCABQQV0EN8ECyAyIBhBiARqKQIANwMAIBggGCkCgAQ3A8AEIBhBgARqIRwgGEGQBGohGiMAQTBrIgEkAAJAAkACQAJAIBhBwARqIh8oAgxBf0YEQCAaKAIEIRkgGigCACEhAkAgGigCDCIjQX9GBEBB0c7FAC0AABpBIEEIENYEIhpFDRUgGkIANwMAIBxBATYCCCAcIBo2AgQgHEEBNgIAIBpBGGpCADcDACAaQRBqQgA3AwAgGkEIakIANwMADAELIBooAggiIkEFdCEeQQghGiAiBEBB0c7FAC0AABogHkEIENYEIhpFDQMLIAFBLGoiJUEANgIAIAEgGjYCKCABICI2AiQgASAaNgIQIAFBADYCDCABICU2AgggGSAZIB5qIAFBCGoQ/gIgHEEIaiAlKAIANgIAIBwgASkCJDcCAAsgHCAjNgIMICEEQCAZICFBBXQQ3wQLIB8oAgAiGkUNBCAfKAIEIBpBBXQQ3wQMBAsgGigCDCIjQX9GDQIgGigCCCIhQQV0IRkgGigCBCEeIBooAgAhIkEIIRogIQRAQdHOxQAtAAAaIBlBCBDWBCIaRQ0CCyABQSBqIiVBADYCACABIBo2AhwgASAhNgIYIAEgGjYCLCABQQA2AiggASAlNgIkIB4gGSAeaiABQSRqEP4CIAFBEGogJSgCADYCACABIAEpAhg3AwggASAjNgIUICIEQCAeICJBBXQQ3wQLIBwgHyABQQhqEOUBDAMLQQggHkG0ysIAEMgEAAtBCCAZQbTKwgAQyAQACyAcIB8pAgA3AgAgHEEIaiAfQQhqKQIANwIAIBooAgAiHEUNACAaKAIEIBxBBXQQ3wQLIAFBMGokACAYKAKMBCIeICdIDQcMAQsLIAEgHkHogcAAEMgEAAsgJyABQezHwgAQ2QMACyAZIAFB0MjCABDIBAALIAEgHEHogcAAEMgEAAsgGEEANgLwBCAYQQE2AuQEIBhBuMjCADYC4AQgGEIENwLoBCAYQeAEakHAyMIAEKgEAAsgASAlQczJwgAQyAQACyAkICY2AgggJCAbNgIEICQgMDYCACAkIBgpAoAENwIQICQgKzYCDCAkQRhqIBhBiARqKQIANwIAICgoAgAiAUUNAiAsIAFBBXQQ3wQMAgsgGEICNwPgBEGQycIAQSsgGEHgBGpBgMnCAEG8ycIAEMoDAAtB0c7FAC0AABpBIEEIENYEIgFFDQQgAUIANwMAICRCgYCAgHA3AgggJCABNgIEICRBATYCACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACAkICgpAgA3AhAgJEEYaiAoQQhqKQIANwIAIBpFDQAgISAcEN8ECyAYQYAFaiQADAALIB1BKGogHUE4aikCADcDACAdIB0pAjA3AyAgLyAdQcgAaikCACIDNwMAIB0gHSkCQDcDUCADpyIaQQxLDQEgGkEMSQRAQQwgGiIbayIcIB0oAlAgGmtLBEAgKCAaIBxBCEEgEIgDIB0oAlghGwsgHSgCVCIfIBtBBXRqIQEgHEECTwRAIBpBf3NBDGpBBXQiGQRAIAFBACAZ/AsACyAbQQV0IBpBBXRrIB9qQeACaiEBIBsgHGpBAWshGwsgAUIANwMAIAFBGGpCADcDACABQRBqQgA3AwAgAUEIakIANwMAIB0gG0EBajYCWAsgACAdKQNQNwIQIAAgHSkDIDcCACAAQRhqIB1B2ABqKQMANwIAIABBCGogHUEoaikDADcCACAdKAIQIgAEQCAdKAIUIABBBXQQ3wQLIB1B4ABqJAAPCwwBC0HIhcAAQTpBrIbAABD+AwALQQhBIBD/BAAL8gYBCn8jAEEwayICJAAgAkEoakG4zMIAKAIANgIAIAJBsMzCACkCADcDICACQSBqQaTNwgAQpQMgAigCJEEBNgIAIAIoAiQhAwJAAkACQAJAAkACQAJ/AkACQAJAIAIoAiAiBkGAgICAeEcNACADKAIIDQBBBCEKDAELIAJBATYCKCACIAM2AiQgAiAGNgIgIAJBFGogAkEgakEEQQAQzwEgAigCGCEKIAIoAhQhCSACKAIcIgYNAQtBBCEIQQAhBkEBDAELQdHOxQAtAAAaIAZBAnQiA0EEENYEIghFDQEgAwRAIAggCiAD/AoAAAtBAAshBwJ/AkAgAAJ/An8CQCABLQAMIgUEQEGwzMIAIAVBAkcNAxogASgCCCIDQQJ0IQRBACEFIANB/////wNLIARB/P///wdLcg0IIAEoAgQhCyAEDQFBBCEBQQAMAgsgASgCCCIDQQJ0IQRBACEFIANB/////wNLIARB/P///wdLcg0GIAEoAgQhASAEBEBB0c7FAC0AABpBBCEFIARBBBDWBCIHRQ0HIARFIgtFBEAgByABIAT8CgAACyADDQRBBCEHQQAMBQtBBCEFIAQEQEEEIAEgBPwKAAALQQQhB0EADAQLQdHOxQAtAAAaQQQhBSAEQQQQ1gQiAUUNBiADCyEFIAQEQCABIAsgBPwKAAALIAIgAzYCKCACIAE2AiQgAiAFNgIgIAJBIGoLIgMpAgA3AgAgAEEIaiADQQhqKAIANgIAIAcNBwwGC0HRzsUALQAAGiAEQQQQ1gQiBUUNBCALRQRAIAUgByAE/AoAAAsgAwshASACIAM2AhAgAiAFNgIMIAIgAzYCCCACIAY2AhwgAiAINgIYIAIgBjYCFAJ/IAMgBkkEQCACIAY2AiggAiAINgIkIAIgBjYCICAAIAJBIGogAkEIahDKASACQQxqDAELIAJBKGogAkEQaigCADYCACACIAIpAgg3AyAgACACQSBqIAJBFGoQygEgBiEDIAJBGGoLIQUgAwRAIAUoAgAgA0ECdBDfBAsgASEGIAchCCABDQQMBQtBBCADQfiBwAAQyAQACyAFIARB+IHAABDIBAALIAUgBEH4gcAAEMgEAAtBBCAEQfiBwAAQyAQACyAIIAZBAnQQ3wQLIAkEQCAKIAlBAnQQ3wQLIAJBMGokAAvxBgIUfwF+IwBBgANrIgIkAEHRzsUALQAAGkGAA0EIENYEIgMEQCADIAFBgAP8CgAAIAMpAwAhFiADQYADEN8EIAIgFjcDACACQQhqIAFBCGpBuAH8CgAAIAJBwAFqIgQgAhCFASAAQRhqIAJB2AFqIgMpAwA3AwAgAEEQaiACQdABaiIFKQMANwMAIABBCGogAkHIAWoiBikDADcDACAAIAIpA8ABNwMAIAAgAikD4AE3AyAgAEEoaiACQegBaiIHKQMANwMAIABBMGogAkHwAWoiCCkDADcDACAAQThqIAJB+AFqIgkpAwA3AwAgACACKQOAAjcDQCAAQcgAaiACQYgCaiIKKQMANwMAIABB0ABqIAJBkAJqIgspAwA3AwAgAEHYAGogAkGYAmoiDCkDADcDACAAQfgAaiACQbgCaiINKQMANwMAIABB8ABqIAJBsAJqIg4pAwA3AwAgAEHoAGogAkGoAmoiDykDADcDACAAIAIpA6ACNwNgIABBmAFqIAJB2AJqIhApAwA3AwAgAEGQAWogAkHQAmoiESkDADcDACAAQYgBaiACQcgCaiISKQMANwMAIAAgAikDwAI3A4ABIABBuAFqIAJB+AJqIhMpAwA3AwAgAEGwAWogAkHwAmoiFCkDADcDACAAQagBaiACQegCaiIVKQMANwMAIAAgAikD4AI3A6ABIAQgAUHAAWoQhQEgAEHYAWogAykDADcDACAAQdABaiAFKQMANwMAIABByAFqIAYpAwA3AwAgACACKQPAATcDwAEgACACKQPgATcD4AEgAEHoAWogBykDADcDACAAQfABaiAIKQMANwMAIABB+AFqIAkpAwA3AwAgACACKQOAAjcDgAIgAEGIAmogCikDADcDACAAQZACaiALKQMANwMAIABBmAJqIAwpAwA3AwAgAEG4AmogDSkDADcDACAAQbACaiAOKQMANwMAIABBqAJqIA8pAwA3AwAgACACKQOgAjcDoAIgAEHYAmogECkDADcDACAAQdACaiARKQMANwMAIABByAJqIBIpAwA3AwAgACACKQPAAjcDwAIgAEH4AmogEykDADcDACAAQfACaiAUKQMANwMAIABB6AJqIBUpAwA3AwAgACACKQPgAjcD4AIgAkGAA2okAA8LQQhBgANB8LXCABDIBAALuAYCBn4IfyMAQRBrIhAkACABKQMYIgQgAq0iBYVC88rRy6eM2bLwAIUiBkIQiSAGIAEpAxAiB0Lh5JXz1uzZvOwAhXwiBoUiCCAEQu3ekfOWzNy35ACFIgQgB0L1ys2D16zbt/MAhXwiB0IgiXwiCSAFQoCAgICAgICABISFIARCDYkgB4UiBCAGfCIFIARCEYmFIgR8IgYgBEINiYUiBCAIQhWJIAmFIgcgBUIgiUL/AYV8IgV8IgggBEIRiYUiBEINiSAEIAUgB0IQiYUiBSAGQiCJfCIGfCIEhSIHQhGJIAcgBUIViSAGhSIFIAhCIIl8IgZ8IgeFIghCDYkgCCAFQhCJIAaFIgUgBEIgiXwiBHyFIgZCEYkgBUIViSAEhSIEQhCJIAQgB0IgiXwiBIVCFYmFIAQgBnwiBEIgiIUgBIUhBCABKAIIRQRAIBBBCGogAUEBIAFBEGoQpQELIAEoAgQiDiAEp3EhCiAEQhmIIgZC/wCDQoGChIiQoMCAAX4hByABKAIAIQsCQAJAA0AgCiALaikAACIFIAeFIgRCf4UgBEKBgoSIkKDAgAF9g0KAgYKEiJCgwIB/gyIEUEUEQANAIAIgCyAEeqdBA3YgCmogDnFBBHRrIgxBEGsoAgBGDQMgBEIBfSAEgyIEUEUNAAsLIAVCgIGChIiQoMCAf4MhBEEBIQwgD0EBRwRAIAR6p0EDdiAKaiAOcSENIARCAFIhDAsgBCAFQgGGg1AEQCAKIBFBCGoiEWogDnEhCiAMIQ8MAQsLIAsgDWosAAAiCkEATgRAIAsgCykDAEKAgYKEiJCgwIB/g3qnQQN2Ig1qLQAAIQoLIAsgDWogBqdB/wBxIg86AAAgCyANQQhrIA5xakEIaiAPOgAAIABBgICAgHg2AgAgASABKAIIIApBAXFrNgIIIAEgASgCDEEBajYCDCALIA1BBHRrIgBBDGsiAUEIaiADQQhqKAIANgIAIAEgAykCADcCACAAQRBrIAI2AgAMAQsgACAMQQxrIgEpAgA3AgAgASADKQIANwIAIABBCGogAUEIaiIAKAIANgIAIAAgA0EIaigCADYCAAsgEEEQaiQAC6oGAgF/DX4jAEHQAWsiAiQAIAJB8ABqIAEpAxgiBEKx6pSR3aOCnFh+IgNCAEKv+P//b0IAEMkDIAJB4ABqIANCAEJ/QgAQyQMgAkHQAGogAikDYCIDIAEpAxB8IgUgAikDeCAEIAIpA3AiBnwgBlStfHwiBkKx6pSR3aOCnFh+IgRCAEKv+P//b0IAEMkDIAJBQGsgBEIAQn9CABDJAyACQTBqIAIpA0AiBCADIAEpAwh8IgcgBSAGVq0gAikDaCIIIAMgBVatfHx8Igp8IgkgAikDWCACKQNQIgUgBnwgBVStfHwiBkKx6pSR3aOCnFh+IgVCAEKv+P//b0IAEMkDIAJBIGogBUIAQn9CABDJAyACQRBqIAIpAyAiBSAEIAMgASkDAHwiDCAHIApWrSAIIAMgB1atfHx8Igd8IgogBiAJVK0gAikDSCINIAQgCVatfHx8Ig98IgkgAikDOCAGIAIpAzAiBnwgBlStfHwiBkKx6pSR3aOCnFh+IgtCAEKv+P//b0IAEMkDIAIgC0IAQn9CABDJAwJAIAIpAwgiCyACKQMoIg4gBSANIAQgByAMVK0gCCADIAxWrXx8Igh8IgMgCFStfCADIAMgCiAPVq0gDSAHIApWrXx8fCIDVq18Igd8IgQgB1StfCAEIAQgDiADIAMgBXwiA1atfCADIAYgCVStIA4gBSAJVq18fHwiBSADVK18fCIEVq18IgggAikDACIDfCIHIAhUrXwgByALIAQgAyAEfCIEVq18IAQgCyADIAMgBXwiA1atfCADIAIpAxggAikDECIFIAZ8IAVUrXx8IgUgA1StfHwiBiAEVK18fCIDIAdUrXwiBEJ/Ug0AIANCf1IEQEJ/IQQMAQtCfyEDIAZCf1IEQEJ/IQQMAQtCfyEGIAVCr/j//29UBEBCfyEEDAELIAVC0YeAgBB8IQVCACEGQgAhA0IAIQQLIAIgBTcDmAEgAiAGNwOQASACIAM3A4gBIAIgBDcDgAEgAiACQaABaiIBNgLMASACQQA2ArQBIAJBADYCoAEgAiACQYABajYCyAEgACABEK0CIAJB0AFqJAALkgUBC38jAEHAA2siAyQAIAMgASACEDggA0FAayIHIAFBQGsiCCACQUBrIgkQOCADQYABaiIMIAFBgAFqIgogAkGAAWoiCxA4IANBwAFqIg0Q9AMgA0HAAmoiBSAIIAoQoAIgA0GAA2oiBCAJIAsQoAIgA0GAAmoiBiAFIAQQOCAEIAYgBxDcASAFIAQgDBDcASAEIA0gBRA4IAAgAyAEEKACIAUgASAIEKACIAQgAiAJEKACIAYgBSAEEDggBCAGIAMQ3AEgBiAEIAcQ3AEgBBD0AyAFIAQgDBA4IABBQGsgBiAFEKACIAUgASAKEKACIAQgAiALEKACIAYgBSAEEDggA0G4A2oiASADQThqKQMANwMAIANBsANqIgIgA0EwaikDADcDACADQagDaiIIIANBKGopAwA3AwAgA0GgA2oiCSADQSBqKQMANwMAIANBmANqIgogA0EYaikDADcDACADQZADaiILIANBEGopAwA3AwAgA0GIA2oiByADQQhqKQMANwMAIAMgAykDADcDgAMgBSAGIAQQ3AEgASADQfgAaikDADcDACACIANB8ABqKQMANwMAIAggA0HoAGopAwA3AwAgCSADQeAAaikDADcDACAKIANB2ABqKQMANwMAIAsgA0HQAGopAwA3AwAgByADQcgAaikDADcDACADIAMpA0A3A4ADIAYgBSAEEKACIAEgA0G4AWopAwA3AwAgAiADQbABaikDADcDACAIIANBqAFqKQMANwMAIAkgA0GgAWopAwA3AwAgCiADQZgBaikDADcDACALIANBkAFqKQMANwMAIAcgA0GIAWopAwA3AwAgAyADKQOAATcDgAMgAEGAAWogBiAEENwBIANBwANqJAALqAYBB38CQAJAAkACQAJAAkAgAAJ+AkACQCABKAIAIglBgICAgHhHBEAgASgCCCIEIAJNDQIgBCACayEFIAEoAgQhBiACRQ0BIAVBAnQiAUUNASAGIAYgAkECdGogAfwKAAAMAQsgAiABKAIEIgQoAggiAU8EQCABQQJ0IQIgBCgCBCEEAkAgAUUEQEEEIQMMAQtB0c7FAC0AABogAkEEENYEIgNFDQYLIAIEQCADIAQgAvwKAAALIAGtIAOtQiCGhAwDC0HRzsUALQAAGiAEKAIEIQQgASACayIFQQJ0IgFBBBDWBCIGRQ0FIAEEQCAGIAQgAkECdGogAfwKAAALIAUhCQsgA0H/AXFFDQYgBQ0CQQAhBAwHCyABKQIACzcCACAAQQA2AggPCyADQR9xIQJBACEEQQAgA2tBH3EhByAGIAVBAnRqIQEgBUEBa0H/////A3EiCkEBaiIIQQNxIQMgCkEDSQ0CIAhB/P///wdxIQoDQCABQQRrIgggBCAIKAIAIgQgAnZyNgIAIAFBCGsiCCAEIAd0IAgoAgAiBCACdnI2AgAgAUEMayIIIAQgB3QgCCgCACIEIAJ2cjYCACABQRBrIgEgBCAHdCABKAIAIgQgAnZyNgIAIAQgB3QhBCAKQQRrIgoNAAsMAgtBBCACQaSDxQAQyAQAC0EEIAFBpIPFABDIBAALIANFDQAgAUEEayEBA0AgASAEIAEoAgAiBCACdnI2AgAgAUEEayEBIAQgB3QhBCADQQFrIgMNAAsLQQAhBCAFRQ0AIAYgBUECdCIBakEEaygCAARAIAUhBAwBCyAGQQRrIQMgBUH/////A3EhAgNAIAFFDQEgAkEBayECIAEgA2ogAUEEayEBKAIARQ0ACyACQQFqIgEgBSABIAVJGyEECwJAAkAgCUECdiAETQRAIAYhAiAJIQEMAQtBACEBIAlFBEAgBiECDAELIAlBAnQhAyAERQRAQQQhAiAGIAMQ3wQMAQsgBiADQQQgBCIBQQJ0IgMQzgQiAkUNAQsgACACNgIEIAAgATYCACAAIAQ2AggPC0EEIANBiIbFABDIBAALsQYCB38DfiMAQUBqIgQkAAJAAkACQAJ/AkACQCACKAIIIgNFDQACQCADQQFrIgNB/v///wNxRQRAIANB/////wNxIgZBAWoiB0EDcSEFIAIoAgQiCCEDIAZBA08EQCAHQfz///8HcSEGA0AgCkKAAXwhCiADQRBqIQMgBkEEayIGDQALCyAFBEADQCADNQIAIAqGIAt8IQsgCkIgfCEKIANBBGohAyAFQQFrIgUNAAsLIAtCgICAgBBUDQELIARBEGogAUEIaigCADYCACAEIAEpAgA3AwggBEEgaiACQQhqKAIANgIAIAQgAikCADcDGCAEQShqIARBCGogBEEYahCcASAAQQhqIARBPGooAgA2AgAgACAEKQI0NwIAIAQoAigiAEUNBiAEKAIsIABBAnQQ3wQMBgsgC1ANACABKAIIIQMgASgCBCEGAkACQCALQoCABFoEQCADRQ0CIANB/////wNqIQcgA0ECdCEFIANB/////wNxQQFHDQEgBSAGagwFCyADRQ0BIAunIQcgBkEEayEJIANBAnQhA0EAIQUDQCAFQRB0IAMgCWooAgAiBUEQdnIgB3BBEHQgBUH//wNxciAHcCEFIANBBGsiAw0ACwwFCyAFIAZqQQhrIQMgB0H/////A3FBAWpB/v///wdxIQVCACEKA0AgAzUCACADQQRqNQIAIApCIIaEIAuCQiCGhCALgiEKIANBCGshAyAFQQJrIgUNAAsMAgsgBEEwakHcmsAAKAIANgIAIARB1JrAACkCADcDKAwECyAEQQA2AjggBEEBNgIsIARBhJzAADYCKCAEQgQ3AjAgBEEoakH0nMAAEKgEAAsgCkIghiEMIANBCGoLIQMgB0EBcQR+IAoFIAwgA0EEazUCAIQgC4ILpyEFCyAEQTBqQdyawAAoAgA2AgAgBEHUmsAAKQIANwMoIAVFDQAgBEEoakHIm8AAEKUDIAQoAiwgBTYCACAEQQE2AjALIAAgBCkDKDcCACAAQQhqIARBMGooAgA2AgAgAigCACIABEAgCCAAQQJ0EN8ECyABKAIAIgBFDQAgBiAAQQJ0EN8ECyAEQUBrJAALsQYCB38DfiMAQUBqIgQkAAJAAkACQAJ/AkACQCACKAIIIgNFDQACQCADQQFrIgNB/v///wNxRQRAIANB/////wNxIgZBAWoiB0EDcSEFIAIoAgQiCCEDIAZBA08EQCAHQfz///8HcSEGA0AgCkKAAXwhCiADQRBqIQMgBkEEayIGDQALCyAFBEADQCADNQIAIAqGIAt8IQsgCkIgfCEKIANBBGohAyAFQQFrIgUNAAsLIAtCgICAgBBUDQELIARBEGogAUEIaigCADYCACAEIAEpAgA3AwggBEEgaiACQQhqKAIANgIAIAQgAikCADcDGCAEQShqIARBCGogBEEYahCcASAAQQhqIARBPGooAgA2AgAgACAEKQI0NwIAIAQoAigiAEUNBiAEKAIsIABBAnQQ3wQMBgsgC1ANACABKAIIIQMgASgCBCEGAkACQCALQoCABFoEQCADRQ0CIANB/////wNqIQcgA0ECdCEFIANB/////wNxQQFHDQEgBSAGagwFCyADRQ0BIAunIQcgBkEEayEJIANBAnQhA0EAIQUDQCAFQRB0IAMgCWooAgAiBUEQdnIgB3BBEHQgBUH//wNxciAHcCEFIANBBGsiAw0ACwwFCyAFIAZqQQhrIQMgB0H/////A3FBAWpB/v///wdxIQVCACEKA0AgAzUCACADQQRqNQIAIApCIIaEIAuCQiCGhCALgiEKIANBCGshAyAFQQJrIgUNAAsMAgsgBEEwakGQksIAKAIANgIAIARBiJLCACkCADcDKAwECyAEQQA2AjggBEEBNgIsIARByJPCADYCKCAEQgQ3AjAgBEEoakG4lMIAEKgEAAsgCkIghiEMIANBCGoLIQMgB0EBcQR+IAoFIAwgA0EEazUCAIQgC4ILpyEFCyAEQTBqQZCSwgAoAgA2AgAgBEGIksIAKQIANwMoIAVFDQAgBEEoakGMk8IAEKUDIAQoAiwgBTYCACAEQQE2AjALIAAgBCkDKDcCACAAQQhqIARBMGooAgA2AgAgAigCACIABEAgCCAAQQJ0EN8ECyABKAIAIgBFDQAgBiAAQQJ0EN8ECyAEQUBrJAALsQYCB38DfiMAQUBqIgQkAAJAAkACQAJ/AkACQCACKAIIIgNFDQACQCADQQFrIgNB/v///wNxRQRAIANB/////wNxIgZBAWoiB0EDcSEFIAIoAgQiCCEDIAZBA08EQCAHQfz///8HcSEGA0AgCkKAAXwhCiADQRBqIQMgBkEEayIGDQALCyAFBEADQCADNQIAIAqGIAt8IQsgCkIgfCEKIANBBGohAyAFQQFrIgUNAAsLIAtCgICAgBBUDQELIARBEGogAUEIaigCADYCACAEIAEpAgA3AwggBEEgaiACQQhqKAIANgIAIAQgAikCADcDGCAEQShqIARBCGogBEEYahCcASAAQQhqIARBPGooAgA2AgAgACAEKQI0NwIAIAQoAigiAEUNBiAEKAIsIABBAnQQ3wQMBgsgC1ANACABKAIIIQMgASgCBCEGAkACQCALQoCABFoEQCADRQ0CIANB/////wNqIQcgA0ECdCEFIANB/////wNxQQFHDQEgBSAGagwFCyADRQ0BIAunIQcgBkEEayEJIANBAnQhA0EAIQUDQCAFQRB0IAMgCWooAgAiBUEQdnIgB3BBEHQgBUH//wNxciAHcCEFIANBBGsiAw0ACwwFCyAFIAZqQQhrIQMgB0H/////A3FBAWpB/v///wdxIQVCACEKA0AgAzUCACADQQRqNQIAIApCIIaEIAuCQiCGhCALgiEKIANBCGshAyAFQQJrIgUNAAsMAgsgBEEwakG4zMIAKAIANgIAIARBsMzCACkCADcDKAwECyAEQQA2AjggBEEBNgIsIARBhNHCADYCKCAEQgQ3AjAgBEEoakH00cIAEKgEAAsgCkIghiEMIANBCGoLIQMgB0EBcQR+IAoFIAwgA0EEazUCAIQgC4ILpyEFCyAEQTBqQbjMwgAoAgA2AgAgBEGwzMIAKQIANwMoIAVFDQAgBEEoakGkzcIAEKUDIAQoAiwgBTYCACAEQQE2AjALIAAgBCkDKDcCACAAQQhqIARBMGooAgA2AgAgAigCACIABEAgCCAAQQJ0EN8ECyABKAIAIgBFDQAgBiAAQQJ0EN8ECyAEQUBrJAALsQYCB38DfiMAQUBqIgQkAAJAAkACQAJ/AkACQCACKAIIIgNFDQACQCADQQFrIgNB/v///wNxRQRAIANB/////wNxIgZBAWoiB0EDcSEFIAIoAgQiCCEDIAZBA08EQCAHQfz///8HcSEGA0AgCkKAAXwhCiADQRBqIQMgBkEEayIGDQALCyAFBEADQCADNQIAIAqGIAt8IQsgCkIgfCEKIANBBGohAyAFQQFrIgUNAAsLIAtCgICAgBBUDQELIARBEGogAUEIaigCADYCACAEIAEpAgA3AwggBEEgaiACQQhqKAIANgIAIAQgAikCADcDGCAEQShqIARBCGogBEEYahCcASAAQQhqIARBPGooAgA2AgAgACAEKQI0NwIAIAQoAigiAEUNBiAEKAIsIABBAnQQ3wQMBgsgC1ANACABKAIIIQMgASgCBCEGAkACQCALQoCABFoEQCADRQ0CIANB/////wNqIQcgA0ECdCEFIANB/////wNxQQFHDQEgBSAGagwFCyADRQ0BIAunIQcgBkEEayEJIANBAnQhA0EAIQUDQCAFQRB0IAMgCWooAgAiBUEQdnIgB3BBEHQgBUH//wNxciAHcCEFIANBBGsiAw0ACwwFCyAFIAZqQQhrIQMgB0H/////A3FBAWpB/v///wdxIQVCACEKA0AgAzUCACADQQRqNQIAIApCIIaEIAuCQiCGhCALgiEKIANBCGshAyAFQQJrIgUNAAsMAgsgBEEwakGMocQAKAIANgIAIARBhKHEACkCADcDKAwECyAEQQA2AjggBEEBNgIsIARBlKPEADYCKCAEQgQ3AjAgBEEoakGEpMQAEKgEAAsgCkIghiEMIANBCGoLIQMgB0EBcQR+IAoFIAwgA0EEazUCAIQgC4ILpyEFCyAEQTBqQYyhxAAoAgA2AgAgBEGEocQAKQIANwMoIAVFDQAgBEEoakHoosQAEKUDIAQoAiwgBTYCACAEQQE2AjALIAAgBCkDKDcCACAAQQhqIARBMGooAgA2AgAgAigCACIABEAgCCAAQQJ0EN8ECyABKAIAIgBFDQAgBiAAQQJ0EN8ECyAEQUBrJAALyxUDDX8CfgF8IwBBMGsiCSQAAkACQCADQQJrQSNJBEACQCACRQ0AIAEtAAAiBkErRgRAIAJBAWsiBEUNASABIAFBAWogAS0AASIGQStGIgcbIQEgAiAEIAcbIQILAkAgBkH/AXFB3wBHBEAgAkEASA0BQQAhBkHRzsUALQAAGkEBIQUgAkEBENYEIgRFDQEgCUEANgIUIAkgBDYCECAJIAI2AgwDQAJAAkACQAJAIAEtAAAiBEEwayIFQf8BcUEKSQ0AIARB4QBrQf8BcUEaTwRAIARBwQBrQf8BcUEaTwRAIARB3wBGDQUgCSgCDCEEDAMLIARBN2shBQwBCyAEQdcAayEFCyAJKAIMIQQgBUH/AXEgA0H/AXFJDQELIABBgICAgHg2AgAgAEEBOgAEIARFDQggCSgCECAEEN8EDAgLIAQgBkYEQCAJQQxqQfS+xAAQtgMLIAkoAhAgBmogBToAACAJIAZBAWoiBjYCFAsgAUEBaiEBIAJBAWsiAg0ACwwECyAAQYCAgIB4NgIAIABBAToABAwECyAFIAJB5L7EABDIBAALIABBgICAgHg2AgAgAEEAOgAEDAILIAlBADYCHCAJQQE2AhAgCUHMvsQANgIMIAlCBDcCFCAJQQxqQdS+xAAQqAQACwJAIANpQQFGBEAgCSgCECEEIAZBAk8EQCAEIAZqIQJBACEBIAZBAXYiB0EBRwRAIAZBAWshBSAHQf7///8HcSEIA0AgBCAFaiIHLQAAIQogByABIARqIgctAAA6AAAgByAKOgAAIAIgAUF+c2oiCi0AACELIAogB0EBaiIHLQAAOgAAIAcgCzoAACAFQQJrIQUgCCABQQJqIgFHDQALCyAGQQJxBEAgASAEaiIELQAAIQYgBCACIAFBf3NqIgEtAAA6AAAgASAGOgAACyAJKAIUIQYgCSgCECEEC0EgQR8gA2drIgpB/wFxcEUEQCAJQSRqIAQgBiAKEM8CDAILIAlBJGohCyAEIQFBACEFQQAhAiMAQRBrIggkAEF/IAatIAqtQv8Bg34iEUIFiCARQh+DQgBSrXwiEaciByARQoCAgIAQWhsiBEECdCEDAkACQAJAIARB/////wNLIANB/P///wdLcg0AAkAgA0UEQEEEIQRBACEHDAELQdHOxQAtAAAaQQQhBSADQQQQ1gQiBEUNAQsgCEEANgIMIAggBDYCCCAIIAc2AgQgBkUNAkEAIQVBACEEQQAhAwNAIAEtAAAiByADdCAEciEEAn8gAyAKaiICQf8BcUEfTQRAIAIMAQsgCCgCBCAFRgRAIAhBBGpBqM3EABClAwsgCCgCCCAFQQJ0aiAENgIAIAggBUEBaiIFNgIMIAdBACADa3YhBCACQSBrCyEDIAFBAWohASAGQQFrIgYNAAsMAQsgBSADQYjNxAAQyAQACyADQf8BcQRAIAgoAgQgBUYEQCAIQQRqQZjNxAAQpQMLIAgoAgggBUECdGogBDYCACAIIAVBAWoiBTYCDAtBACECIAgoAgghBCAIKAIEIQcgBUUNACAEIAVBAnQiA2pBBGsoAgAEQCAFIQIMAQsgBUH/////A3EhAQNAIANFDQEgAUEBayEBIANBBGsiAyAEaigCAEUNAAsgAUEBaiIBIAUgASAFSRshAgsCQAJAAkAgB0ECdiACTQRAIAQhASAHIQMMAQtBACEDIAdFBEAgBCEBDAELIAdBAnQhBiACRQRAQQQhASAEIAYQ3wQMAQsgBCAGQQQgAiIDQQJ0IgQQzgQiAUUNAQsgCyACNgIIIAsgATYCBCALIAM2AgAgCEEQaiQADAELQQQgBEH88cQAEMgEAAsMAQsgCUEkaiENIAkoAhAhDEEAIQEjAEEwayIFJAACQAJAAkACQAJ/QQAgA7gQ5wIgBriiRAAAAAAAAKA/opsiE0QAAAAAAADwv2RFDQAaQQAgE0QAAAAAAADwQWNFDQAaIBOrCyIKQf////8DSyAKQQJ0IgJB/P///wdLcg0AAkAgAkUEQEEEIQ5BACEKDAELQdHOxQAtAAAaQQQhASACQQQQ1gQiDkUNAQsgBUEANgIUIAUgDjYCECAFIAo2AgwgA0GAAk0EQAJAAkACQCADQQN0Ig9B8NHEAGooAgAiCwRAIAYgBiALcCIBIAsgARsiCEkNASAIQQNxIQQgCEEETw0CQQAhAkEAIQEMAwtB2M3EABCbBAALIAVBADYCKCAFQQE2AhwgBUHQycQANgIYIAVCBDcCICAFQRhqQejNxAAQqAQACyAIQXxxIRBBACECQQAhAQNAIAEgDGoiBy0AACACIANsaiADbCAHQQFqLQAAaiADbCAHQQJqLQAAaiADbCAHQQNqLQAAaiECIBAgAUEEaiIBRw0ACwsgBARAIAEgDGohAQNAIAEtAAAgAiADbGohAiABQQFqIQEgBEEBayIEDQALCyAPQezRxABqNQIAIRIgBiAIayEHIAoEfyAOBSAFQQxqQfjNxAAQpQMgBSgCEAsgAjYCAEEBIQQgBUEBNgIUIAdFBEAgBSgCECEBIAUoAgwhBgwDCyAIIAxqIQYCQANAIAUoAhQiBEECdCEKIAUoAhAhAiALIAcgByALSxshCAJAAkACQCAERQ0AIAIgCmoiAUEEayIMRQ0AIAwoAgBFDQELIAUoAgwgBEYEfyAFQQxqQYjOxAAQpQMgBSgCEAUgAgsgCmpBADYCACAFIARBAWoiATYCFCABRQ0BIAUoAhAiAiABQQJ0aiEBC0IAIREDQCACIAI1AgAgEn4gEXwiET4CACARQiCIIREgAkEEaiICIAFHDQALCyAIQQNxIQRBACECQQAhASAIQQRPBEAgCEF8cSEMA0AgASAGaiIKLQAAIAIgA2xqIANsIApBAWotAABqIANsIApBAmotAABqIANsIApBA2otAABqIQIgDCABQQRqIgFHDQALCyAEBEAgASAGaiEBA0AgAS0AACACIANsaiECIAFBAWohASAEQQFrIgQNAAsLIAUoAhQiAUUNASAHIAhrIQcgBSgCECIEIAIgBCgCACIKaiICNgIAAkAgAUEBRiACIApPcg0AIARBBGohAiABQQJ0QQhrIQEDQCACIAIoAgBBAWoiBDYCACAEDQEgAkEEaiECIAEiBEEEayEBIAQNAAsLIAYgCGohBiAHDQALIAUoAhAhASAFKAIMIQYgBSgCFCIEDQMMBAsgBUEANgIoIAVBATYCHCAFQZSHxQA2AhggBUIENwIgIAVBGGpBhIjFABCoBAALIANBgQJByM3EABDZAwALIAEgAkG4zcQAEMgEAAsgASAEQQJ0IgNqQQRrKAIADQEgBEH/////A3EhAgNAIANFDQEgAkEBayECIANBBGsiAyABaigCAEUNAAsgAkEBaiICIAQgAiAESRshBAwBC0EAIQQLAkACQAJAIAZBAnYgBE0EQCABIQIgBiEDDAELQQAhAyAGRQRAIAEhAgwBCyAGQQJ0IQYgBEUEQEEEIQIgASAGEN8EDAELIAEgBkEEIAQiA0ECdCIBEM4EIgJFDQELIA0gBDYCCCANIAI2AgQgDSADNgIAIAVBMGokAAwBC0EEIAFB/PHEABDIBAALCyAAIAkpAiQ3AgAgAEEIaiAJQSxqKAIANgIAIAkoAgwiAEUNACAJKAIQIAAQ3wQLIAlBMGokAAuhBwELfyMAQTBrIgIkACACIAE2AiQCQCACQSRqEOEERQRAQYfwwABBHhDNBCEDIAFBhAFPBEAgARCrAwsgAEGAgICAeDYCACAAIAM2AgQMAQsgAiABNgIYIAJBhfDAAEEBEM0EIgM2AiQgAkEQaiACQRhqIAJBJGoQgAQgAigCFCEBIAIoAhAhBCADQYQBTwRAIAMQqwMLAkACQAJAAkAgBEEBcQRAIAEhAwwBCyACIAE2AiQgAkEkahDgBA0BQaXwwABBERDNBCEDIAFBhAFJDQAgARCrAwsgAEGAgICAeDYCACAAIAM2AgQMAQsgAiABNgIcIAJBhvDAAEEBEM0EIgM2AiQgAkEIaiACQRhqIAJBJGoQgAQgAigCDCEBIAIoAgghBCADQYQBTwRAIAMQqwMLAkACQAJAIARBAXEEQCABIQMMAQsgAiABNgIkIAJBJGoQ4AQNAUG28MAAQREQzQQhAyABQYQBSQ0AIAEQqwMLIABBgICAgHg2AgAgACADNgIEDAELIAIgATYCICACQSRqIAJBHGpBABD3BBDsAiACKAIoIQMCQCACKAIkIgRBgICAgHhGBEAgAEGAgICAeDYCACAAIAM2AgQMAQsgAigCLCEJIAJBJGogAkEcakEBEPcEEOwCIAIoAighAQJAIAIoAiQiBUGAgICAeEYEQCAAQYCAgIB4NgIAIAAgATYCBAwBCyACKAIsIQogAkEkaiACQSBqQQAQ9wQQ7AIgAigCKCEGAkAgAigCJCIHQYCAgIB4RgRAIABBgICAgHg2AgAgACAGNgIEDAELIAIoAiwhCyACQSRqIAJBIGpBARD3BBDsAiACKAIoIQggAigCJCIMQYCAgIB4Rw0FIABBgICAgHg2AgAgACAINgIEIAdFDQAgBiAHQQJ0EN8ECyAFRQ0AIAEgBUECdBDfBAsgBARAIAMgBEECdBDfBAsgAigCICEBCyABQYQBSQ0AIAEQqwMLIAIoAhwiAEGEAUkNACAAEKsDCyACKAIYIgBBhAFJDQEgABCrAwwBCyAAIAIoAiw2AiwgACAINgIoIAAgDDYCJCAAIAs2AiAgACAGNgIcIAAgBzYCGCAAIAo2AhQgACABNgIQIAAgBTYCDCAAIAk2AgggACADNgIEIAAgBDYCACACKAIgIgBBhAFPBEAgABCrAwsgAigCHCIAQYQBTwRAIAAQqwMLIAIoAhgiAEGEAUkNACAAEKsDCyACQTBqJAALygYCCn8BfiMAQfABayICJABB0c7FAC0AABpBASEGQQIhBAJAQQJBARDWBCIIBEAgCEGw8AE7AAAgAkECNgIMIAIgCDYCCCACQQI2AgQgASgCBCEJAn8gASgCCCIHRQRAQQIMAQsgAkHcAGqtQoCAgIDwBIQhDCAJIQQDQCACIAQ2AkAgAiADNgI8IAIgBjYCOCACIAU2AjQgAiAENgJcIAIgDDcDYCACQQE2AnwgAkEBNgJsIAJBoIvBADYCaCACQQE2AnQgAkKAgICAgISAgGk3AqABIAJCgIAINwKYASACQQI7AZABIAIgAkGQAWo2AnggAiACQeAAajYCcCACQTRqQdD/wAAgAkHoAGoQqwINAyAEQQFqIQQgAigCNCEFIAIoAjghBiACKAI8IQMgB0EBayIHDQALIANFBEBBAiEEQQAhA0ECDAELIAJBBGpBAiADQQFBARCIAyACKAIEIQQgAigCCCEIIAIoAgwLIQcgAwRAIAcgCGogBiAD/AoAAAsgBQRAIAYgBRDfBAsCQCACIAMgB2oiAwR/IAJBkAFqIAggAxCVASACLQCQAUEBRw0BIAItAJEBBUEDCzoAkAFB1P7AAEErIAJBkAFqQaSPwQBB+JHBABDKAwALIAJBwgBqIAJBoAFqIgUpAwAiDDcBACACQRhqIgMgDDcDACACQShqIgcgAkGwAWoiCikDADcDACACQSBqIgYgAkGoAWoiCykDADcDACACIAIpA5gBNwMQIAJByAFqQgA3AwAgAkHAAWpCADcDACACQbgBakIANwMAIApCADcDACALQgA3AwAgBUIANwMAIAJBmAFqQgA3AwAgAkIANwOQASACQdgBaiADKQMANwMAIAJB4AFqIAYpAwA3AwAgAkHoAWogBykDADcDACACIAIpAxA3A9ABIAJBkAFqIgUQRiAAQSBqIAVB4AD8CgAAIABBGGogBykDADcDACAAQRBqIAYpAwA3AwAgAEEIaiADKQMANwMAIAAgAikDEDcDACAEBEAgCCAEEN8ECyABKAIAIgAEQCAJIAAQ3wQLIAJB8AFqJAAPC0EBQQJBrIPBABDIBAALQdT+wABBKyACQegAakHo/8AAQYiSwQAQygMAC7oGAQh/IwBBMGsiAyQAIAEtAAwhCAJAAkAgAi0ADCIGQQFGBEAgASgCCCIGQQJ0IQUCQCAGQf////8DSyAFQfz///8HS3INACABKAIEIQcCfyAFRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhBCAFQQQQ1gQiAUUNASAGCyEEIAUEQCABIAcgBfwKAAALIAAgCDoADCAAIAY2AgggACABNgIEIAAgBDYCAAwCCyAEIAVB+IHAABDIBAALAkACQAJAAkACQAJAIAhBAWsOAgECAAsgBg0CDAMLIAAgAikCADcCACAAQQhqIAJBCGopAgA3AgAMBQsgBg0BCwJAAkACQAJ/IAEoAggiBCACKAIIIgVGBEAgBEECdCEEIAEoAgRBBGshCSACKAIEQQRrIQoCQANAIARFDQEgBCAKaiEHIAQgCWogBEEEayEEKAIAIgUgBygCACIHRg0ACyAFIAdLIAUgB0lrDAILQX9BACAEGwwBCyAEIAVLIAQgBUlrC0H/AXEOAgACAQsgAEEIakGozMIAKQIANwIAIABBoMzCACkCADcCAAwECyADQShqIAJBCGooAgA2AgAgAyACKQIANwMgIANBCGogA0EgaiABEIcCIAAgAykCCDcCACAAQQhqIANBEGooAgAiATYCACAAIAZBASABGzoADAwECyADQShqIAJBCGooAgA2AgAgAyACKQIANwMgIANBFGogASADQSBqEJ4BQQEhBAJAIAhBAUcEQCAIQQEgAygCHBshBAwBCyADQQA2AhwgAygCFEEESQ0AIAMgA0EUakEAENMDIAMoAgAiAUGBgICAeEcNAgsgACADKQIUNwIAIAAgBDoADCAAQQhqIANBHGooAgA2AgAMAwsgA0EoaiACQQhqKAIANgIAIAMgAikCADcDICADQRRqIANBIGogARDKASADKAIcRQRAIABBAToADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAMLIAAgCDoADCAAIAMpAhQ3AgAgAEEIaiADQRxqKAIANgIADAILIAEgAygCBEHQz8IAEMgEAAsgAigCACIARQ0AIAIoAgQgAEECdBDfBAsgA0EwaiQAC/4FAg1+AX8jAEGAAWsiDyQAIA9B8ABqIAEpAxgiA0Kx6pSR3aOCnFh+IgJCAEKv+P//b0IAEMkDIA9B4ABqIAJCAEJ/QgAQyQMgD0HQAGogDykDYCICIAEpAxB8IgQgDykDeCADIA8pA3AiBXwgBVStfHwiBUKx6pSR3aOCnFh+IgNCAEKv+P//b0IAEMkDIA9BQGsgA0IAQn9CABDJAyAPQTBqIA8pA0AiAyACIAEpAwh8IgYgBCAFVq0gDykDaCIHIAIgBFatfHx8Igl8IgggDykDWCAPKQNQIgQgBXwgBFStfHwiBUKx6pSR3aOCnFh+IgRCAEKv+P//b0IAEMkDIA9BIGogBEIAQn9CABDJAyAPQRBqIA8pAyAiBCADIAIgASkDAHwiCyAGIAlWrSAHIAIgBlatfHx8IgZ8IgkgBSAIVK0gDykDSCIMIAMgCFatfHx8Ig58IgggDykDOCAFIA8pAzAiBXwgBVStfHwiBUKx6pSR3aOCnFh+IgpCAEKv+P//b0IAEMkDIA8gCkIAQn9CABDJAyAPKQMIIgogDykDKCINIAQgDCADIAYgC1StIAcgAiALVq18fCIHfCICIAdUrXwgAiACIAkgDlatIAwgBiAJVq18fHwiAlatfCIGfCIDIAZUrXwgAyADIA0gAiACIAR8IgJWrXwgAiAFIAhUrSANIAQgCFatfHx8IgQgAlStfHwiA1atfCIHIA8pAwAiAnwiBiAHVK18IAYgCiADIAIgA3wiA1atfCADIAogAiACIAR8IgJWrXwgAiAPKQMYIA8pAxAiBCAFfCAEVK18fCIFIAJUrXx8IgQgA1StfHwiAiAGVK18IQYCQCAFQq/4//9vVARAIAIhAwwBCyACIASDIAaDQn9SBEAgAiEDDAELIAJCAXwiBiAEQn9SrSIHfSEDQgAgAkJ/UiAGIAdUcq19IQYgBEIBfCEEIAVC0YeAgBB8IQULIAAgBTcDGCAAIAQ3AxAgACADNwMIIAAgBjcDACAPQYABaiQAC4sGAQh/IwBBgAlrIgMkACADQZgGaiIFQcCDwAApAwA3AwAgA0GQBmoiBkG4g8AAKQMANwMAIANBiAZqIgdBsIPAACkDADcDACADQaAGakIANwMAIANBqAZqIghCADcDACADQbAGaiIEQgA3AwAgA0G4BmoiCUIANwMAIANByAdqQgA3AwAgA0HQB2pCADcDACADQdgHakIANwMAIANB4AdqQgA3AwAgA0HoB2pCADcDACADQfAHakIANwMAIANB+AdqQgA3AwAgA0IANwPAByADQaiDwAApAwA3A4AGIANBoAhqQgA3AwAgA0H4CGpCADcDACADQfAIakIANwMAIANB6AhqQgA3AwAgA0HgCGpCADcDACADQdgIakIANwMAIANB0AhqQgA3AwAgA0HICGpCADcDACADQbgIaiAJKQMANwMAIANBsAhqIAQpAwA3AwAgA0GoCGogCCkDADcDACADQZgIaiAFKQMANwMAIANBkAhqIAYpAwA3AwAgA0GICGogBykDADcDACADQgA3A8AIIAMgAykDgAY3A4AIIAMgASACEOsBIANBwAFqIgkgAUHAAWoiBSACQcABaiIIEOsBIANBwARqIgogASAFEKACIANBgAVqIgYgAUFAayABQYACahCgAiADQcAFaiIHIAFBgAFqIAFBwAJqEKACIANBgAZqIgQgAiAIEKACIANBwAZqIgEgAkFAayACQYACahCgAiADQYAHaiIFIAJBgAFqIAJBwAJqEKACIANBgANqIAogBBDrASAEIAkgA0HAB2oQ6wEgACADIAQQoAIgAEFAayADQUBrIAEQoAIgAEGAAWogA0GAAWogBRCgAkEAIgJFBEAgBCADQcAB/AoAAAsgA0HABGogA0GAA2ogA0GABmoiBBDcASAGIANBwANqIAEQ3AEgByADQYAEaiAFENwBIAJFBEAgBCADQcABakHAAfwKAAALIABBwAFqIANBwARqIANBgAZqENwBIABBgAJqIAYgARDcASAAQcACaiAHIAUQ3AEgA0GACWokAAuyBgEIf0EMIQYjAEEQayIEJAACQCABKAIIIgJBDE0EQAJAIAJFBEBBCCEFDAELIAEoAgQhCUEAIQFB0c7FAC0AABogAkEFdCIIIgNBCBDWBCIFRQ0CA0AgASAIRg0BIAEgBWoiAyABIAlqIgcpAwA3AwAgA0EYaiAHQRhqKQMANwMAIANBEGogB0EQaikDADcDACADQQhqIAdBCGopAwA3AwAgCCABQSBqIgFHDQALCyAEIAI2AgwgBCAFNgIIIAQgAjYCBCACQQxJBEAgBEEEaiACQQwgAmsiA0EIQSAQiAMgBCgCCCAEKAIMIgVBBXRqIQEgA0ECTwRAIAJBf3NBDGoiAkEHcSEGIANBAmtBB08EQCACQXhxIQIDQCABQgA3AwAgAUEYakIANwMAIAFBEGpCADcDACABQQhqQgA3AwAgAUEgakIANwMAIAFBKGpCADcDACABQTBqQgA3AwAgAUE4akIANwMAIAFBQGtCADcDACABQcgAakIANwMAIAFB0ABqQgA3AwAgAUHYAGpCADcDACABQeAAakIANwMAIAFB6ABqQgA3AwAgAUHwAGpCADcDACABQfgAakIANwMAIAFBmAFqQgA3AwAgAUGQAWpCADcDACABQYgBakIANwMAIAFBgAFqQgA3AwAgAUG4AWpCADcDACABQbABakIANwMAIAFBqAFqQgA3AwAgAUGgAWpCADcDACABQcABakIANwMAIAFByAFqQgA3AwAgAUHQAWpCADcDACABQdgBakIANwMAIAFB4AFqQgA3AwAgAUHoAWpCADcDACABQfABakIANwMAIAFB+AFqQgA3AwAgAUGAAmohASACQQhrIgINAAsLIAYEQANAIAFCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACABQSBqIQEgBkEBayIGDQALCyADIAVqQQFrIQULIAFCADcDACABQRhqQgA3AwAgAUEQakIANwMAIAFBCGpCADcDACAFQQFqIQYLIAAgBCkCBDcCACAAQQhqIAY2AgAgBEEQaiQADwtB7MbCAEE3QczHwgAQ/gMAC0EIIANB6IHAABDIBAALvAYCCX8BfgJAAkACQAJAAkACQCABKAIAIgcEQAJAIAEoAgQiAyABKAIMIgRGBEAgAyECDAELIAEgA0EMaiICNgIEIAMoAgAiBUGAgICAeEcNAgsgBCACa0EMbiEDIAIgBEcEQANAIAIoAgAiBQRAIAJBBGooAgAgBUECdBDfBAsgAkEMaiECIANBAWsiAw0ACwsgASgCCCICBEAgByACQQxsEN8ECyABQQA2AgALIAEoAiAiAkUNAgJAIAEoAigiA0UEQCACIAEoAiRHDQEMBAsgAUEANgIoIAMgASgCJCIFIAJrQRhuTw0CIAIgA0EYbGohAgsgASACQRhqNgIgQQAhBUHRzsUALQAAGkEYQQQQ1gQiA0UNAyACKAIIIgdBAnQhBCAHQf////8DSyAEQfz///8HS3INBCACKAIEIQgCfyAERQRAQQQhCUEADAELQdHOxQAtAAAaQQQhBSAEQQQQ1gQiCUUNBSAHCyEFIAQEQCAJIAggBPwKAAALIAIoAhQiCEECdCEGQQAhBCAIQf////8DSyAGQfz///8HS3INBSACKAIQIQoCfyAGRQRAQQQhAkEADAELQdHOxQAtAAAaQQQhBCAGQQQQ1gQiAkUNBiAICyEEIAYEQCACIAogBvwKAAALIAMgCDYCFCADIAI2AhAgAyAENgIMIAMgBzYCCCADIAk2AgQgAyAFNgIAIAEgA0EYajYCDCABQQI2AgggASADNgIAIAEgA0EMajYCBAsgACAFNgIAIAAgAykCBDcCBA8LIAEgBTYCIAsCQAJAAkAgASgCECIEBEAgASgCFCIDIAEoAhwiBUcNASADIQIMAgsgAEGAgICAeDYCAA8LIAEgA0EMaiICNgIUIAMpAgQhCyADKAIAIgNBgICAgHhHDQELIAUgAmtBDG4hAyACIAVHBEADQCACKAIAIgUEQCACQQRqKAIAIAVBAnQQ3wQLIAJBDGohAiADQQFrIgMNAAsLIAEoAhgiAgRAIAQgAkEMbBDfBAsgAUEANgIQQYCAgIB4IQMLIAAgCzcCBCAAIAM2AgAPC0EEQRgQ/wQACyAFIARB+IHAABDIBAALIAQgBkH4gcAAEMgEAAvQBQIIfwJ+IwBBwAprIgIkACACQYAGaiIIIAEQaCACQYgJakIANwMAIAJBkAlqQgA3AwAgAkGYCWpCADcDACACQaAJakIANwMAIAJBqAlqQgA3AwAgAkGwCWpCADcDACACQbgJakIANwMAIAJBmANqIgRBwIPAACkDADcDACACQZADaiIFQbiDwAApAwA3AwAgAkGIA2oiA0Gwg8AAKQMANwMAIAJBoANqQgA3AwAgAkGoA2oiBkIANwMAIAJBsANqIgdCADcDACACQbgDaiIJQgA3AwAgAkIANwOACSACQaiDwAApAwA3A4ADIAJB4AlqQgA3AwAgAkGICmpCADcDACACQZAKakIANwMAIAJBmApqQgA3AwAgAkGgCmpCADcDACACQagKakIANwMAIAJBsApqQgA3AwAgAkG4CmpCADcDACACQfgJaiAJKQMANwMAIAJB8AlqIAcpAwA3AwAgAkHoCWogBikDADcDACACQdgJaiAEKQMANwMAIAJB0AlqIAUpAwA3AwAgAkHICWogAykDADcDACACQgA3A4AKIAIgAikDgAM3A8AJIAJBgANqIgMgAUHAAWoiBRBoIAJBwAdqIgYgAkGACWogAxDrASACQcABaiIHIAggBhDcASACQYACaiACQcAGaiACQYAIahDcASACQcACaiACQYAHaiACQcAIahDcASADIAcQYyACKQOQAyEKIAIpA4gDIQsgAAJ+IAIoAoADQQFGBEAgACAKNwMQIAAgCzcDCEIBDAELIAJBEGogBEGwAfwKAAAgAiAKNwMIIAIgCzcDACACQYADaiIEIAEgAhDrASACQYAGaiIDIAUQ8AIgAkHABmogAUGAAmoQ8AIgAkGAB2ogAUHAAmoQ8AIgAkHAB2oiASACQcAB/AoAACACQcAEaiADIAEQ6wEgAEEIaiAEQYAD/AoAAEIACzcDACACQcAKaiQAC4AGAgN/AX4jAEHAA2siAiQAIAJB2AJqQgA3AwAgAkHQAmpCADcDACACQcgCakIANwMAIAJBwAJqQgA3AwAgAkG4AmpCADcDACACQegCakGAkcUAKQMANwMAIAJB8AJqQYiRxQApAwA3AwAgAkH4AmpBkJHFACkDADcDACACQYADakGYkcUAKQMANwMAIAJBiANqQaCRxQApAwA3AwAgAkIANwOwAiACQfiQxQApAwA3A+ACIAJBuANqQgA3AwAgAkGwA2pCADcDACACQagDakIANwMAIAJBoANqQgA3AwAgAkGYA2pCADcDACACQgA3A5ADIAJBmAFqIAJBsAJqEPICIAIoApgBQQFHBEAgAkGgAWohA0EARQRAIAJBCGogA0GQAfwKAAALIAJBwAFqIAFBKGopAwA3AwAgAkG4AWogAUEgaikDADcDACACQbABaiABQRhqKQMANwMAIAJBqAFqIAFBEGopAwA3AwAgAyABQQhqKQMANwMAIAJB0AFqIAFBOGopAwA3AwAgAkHYAWogAUFAaykDADcDACACQeABaiABQcgAaikDADcDACACQegBaiABQdAAaikDADcDACACQfABaiABQdgAaikDADcDACACIAEpAwA3A5gBIAIgASkDMDcDyAEgAkGgAmogAUGIAWopAwA3AwAgAkGYAmogAUGAAWopAwA3AwAgAkGQAmogAUH4AGopAwA3AwAgAkGIAmogAUHwAGopAwA3AwAgAkGAAmogAUHoAGopAwA3AwAgAiABKQNgNwP4ASAERQRAIAJBsAJqIAJBmAFqQZAB/AoAAAtCgICEgICAwIBSIQUDQCAFQgGDUEUEQCACQZgBaiIBIAJBCGoiAyACQbACahAVIAMgAUGQAfwKAAALIAJBmAFqIgMgAkGwAmoiASABEBUgASADQZAB/AoAACAFQgJUIAVCAYghBUUNAAsgACACQQhqQZAB/AoAACACQcADaiQADwtBkI3FAEErIAJBsAJqQYCNxQBBsJLFABDKAwAL1gYBA38gAEHQAWohBQJAAkACQEGIASAALQDYAiIDayIEIAJNBEAgA0UNASAEBEAgAyAFaiABIAT8CgAACyAAIAApAwAgACkD0AGFNwMAIAAgACkDCCAAKQPYAYU3AwggACAAKQMQIAApA+ABhTcDECAAIAApAxggACkD6AGFNwMYIAAgACkDICAAKQPwAYU3AyAgACAAKQMoIAApA/gBhTcDKCAAIAApAzAgACkDgAKFNwMwIAAgACkDOCAAKQOIAoU3AzggACAAKQNAIAApA5AChTcDQCAAIAApA0ggACkDmAKFNwNIIAAgACkDUCAAKQOgAoU3A1AgACAAKQNYIAApA6gChTcDWCAAIAApA2AgACkDsAKFNwNgIAAgACkDaCAAKQO4AoU3A2ggACAAKQNwIAApA8AChTcDcCAAIAApA3ggACkDyAKFNwN4IAAgACkDgAEgACkD0AKFNwOAASAAIAAoAsgBEIIFIAIgBGshAiABIARqIQEMAQsgAgRAIAMgBWogASAC/AoAAAsgAiADaiEDDAELIAEgAkGIAW5BiAFsIgNqIQQgAiADayEDIAJBiAFPBEADQCAAIAApAwAgASkAAIU3AwAgACAAKQMIIAFBCGopAACFNwMIIAAgACkDECABQRBqKQAAhTcDECAAIAApAxggAUEYaikAAIU3AxggACAAKQMgIAFBIGopAACFNwMgIAAgACkDKCABQShqKQAAhTcDKCAAIAApAzAgAUEwaikAAIU3AzAgACAAKQM4IAFBOGopAACFNwM4IAAgACkDQCABQUBrKQAAhTcDQCAAIAApA0ggAUHIAGopAACFNwNIIAAgACkDUCABQdAAaikAAIU3A1AgACAAKQNYIAFB2ABqKQAAhTcDWCAAIAApA2AgAUHgAGopAACFNwNgIAAgACkDaCABQegAaikAAIU3A2ggACAAKQNwIAFB8ABqKQAAhTcDcCAAIAApA3ggAUH4AGopAACFNwN4IAAgACkDgAEgAUGAAWopAACFNwOAASAAIAAoAsgBEIIFIAFBiAFqIgEgBEcNAAsLIANBiQFPDQEgA0UNACAFIAQgA/wKAAAgACADOgDYAg8LIAAgAzoA2AIPCyADQYgBQaiVwgAQ5QQAC7MFAQd/IwBB0AFrIgMkAAJAAkACQCABKAIEIgUEQCABKAIIIgZFDQIgA0GJAWohByABKAIAIQQDQCABIAUgBiAFIAUgBksbIghrIgU2AgQgASAEIAhBBXRqIgk2AgAgA0GoAWogBEEYaikDADcDACADQaABaiAEQRBqKQMANwMAIANBmAFqIARBCGopAwA3AwAgAyAEKQMANwOQASAIQQFGDQQgA0HIAWogBEE4aikDADcDACADQcABaiAEQTBqKQMANwMAIANBuAFqIARBKGopAwA3AwAgAyAEKQMgNwOwASADQcgAaiADQZABaiADQbABahBDAkACQCADLQCIASIEQQJGBEAgAigCACIBQYCAgIB4RiABRXJFBEAgAigCBCABEN8ECyACIAMpA0g3AgAgAkEIaiADQdAAaigCADYCAAwBCyADQRBqIANB0ABqKQMANwMAIANBGGogA0HYAGopAwA3AwAgA0EgaiADQeAAaikDADcDACADQShqIANB6ABqKQMANwMAIANBMGogA0HwAGopAwA3AwAgA0E4aiADQfgAaikDADcDACADQUBrIANBgAFqKQMANwMAIAMgAykDSDcDCCADIAcoAAA2AgAgAyAHQQNqKAAANgADIARBA0YNAQsgACADKQMINwMAIAAgAygCADYAQSAAQcQAaiADKAADNgAAIABBOGogA0FAaykDADcDACAAQTBqIANBOGopAwA3AwAgAEEoaiADQTBqKQMANwMAIABBIGogA0EoaikDADcDACAAQRhqIANBIGopAwA3AwAgAEEQaiADQRhqKQMANwMAIABBCGogA0EQaikDADcDAAwDCyAJIQQgBQ0ACwtBAyEECyAAIAQ6AEAgA0HQAWokAA8LQQBBAEGg+sAAENkDAAtBAUEBQbD6wAAQ2QMAC7MFAQd/IwBB0AFrIgMkAAJAAkACQCABKAIEIgUEQCABKAIIIgZFDQIgA0GJAWohByABKAIAIQQDQCABIAUgBiAFIAUgBksbIghrIgU2AgQgASAEIAhBBXRqIgk2AgAgA0GoAWogBEEYaikDADcDACADQaABaiAEQRBqKQMANwMAIANBmAFqIARBCGopAwA3AwAgAyAEKQMANwOQASAIQQFGDQQgA0HIAWogBEE4aikDADcDACADQcABaiAEQTBqKQMANwMAIANBuAFqIARBKGopAwA3AwAgAyAEKQMgNwOwASADQcgAaiADQZABaiADQbABahBFAkACQCADLQCIASIEQQJGBEAgAigCACIBQYCAgIB4RiABRXJFBEAgAigCBCABEN8ECyACIAMpA0g3AgAgAkEIaiADQdAAaigCADYCAAwBCyADQRBqIANB0ABqKQMANwMAIANBGGogA0HYAGopAwA3AwAgA0EgaiADQeAAaikDADcDACADQShqIANB6ABqKQMANwMAIANBMGogA0HwAGopAwA3AwAgA0E4aiADQfgAaikDADcDACADQUBrIANBgAFqKQMANwMAIAMgAykDSDcDCCADIAcoAAA2AgAgAyAHQQNqKAAANgADIARBA0YNAQsgACADKQMINwMAIAAgAygCADYAQSAAQcQAaiADKAADNgAAIABBOGogA0FAaykDADcDACAAQTBqIANBOGopAwA3AwAgAEEoaiADQTBqKQMANwMAIABBIGogA0EoaikDADcDACAAQRhqIANBIGopAwA3AwAgAEEQaiADQRhqKQMANwMAIABBCGogA0EQaikDADcDAAwDCyAJIQQgBQ0ACwtBAyEECyAAIAQ6AEAgA0HQAWokAA8LQQBBAEGg+sAAENkDAAtBAUEBQbD6wAAQ2QMAC5QmAhF/D34jAEHQAWsiBCQAAkACQAJAIAEoAgQiCQRAIAEoAggiDEUNAiAEQYkBaiENIAEoAgAhAwNAIAEgCSAMIAkgCSAMSxsiBWsiCTYCBCABIAMgBUEFdGoiDzYCACAEQagBaiADQRhqKQMANwMAIARBoAFqIANBEGopAwA3AwAgBEGYAWogA0EIaikDADcDACAEIAMpAwA3A5ABIAVBAUYNBCAEQcgBaiADQThqKQMANwMAIARBwAFqIANBMGopAwA3AwAgBEG4AWogA0EoaikDADcDACAEIAMpAyA3A7ABIARByABqIQtBACEHIwBBoAprIgMkACADQeADaiAEQZABaiIFQRhqKQMANwMAIANB2ANqIAVBEGopAwA3AwAgA0HQA2ogBUEIaikDADcDACADQfADaiAEQbABaiIGQQhqKQMANwMAIANB+ANqIAZBEGopAwA3AwAgA0GABGogBkEYaikDADcDACADQQA6AIgEIAMgBSkDADcDyAMgAyAGKQMANwPoAyADQegDaiEOAkACQAJAAkACQCADQcgDakHo0cEAQSAQ8QNFBEAgDkHo0cEAQSAQ8QNFDQELIANBsARqIgYQPiADQdAEaiEIIANBkApqIAZBGGopAwA3AwAgA0GICmogBkEQaikDADcDACADQYAKaiAGQQhqKQMANwMAIAMgBikDADcD+AkgA0HQAmogAykD+AMiFUIAIAMpA4AEIhRCABDJAyADQcACaiADKQPwAyIWQgAgFEIAEMkDIANBsAJqIAMpA+gDIhhCACAUQgAQyQMgA0GAA2ogFkIAIBVCABDJAyADQfACaiAYQgAgFUIAEMkDIANBoANqIBhCACAWQgAQyQMgA0GgAmogFEIAIBRCABDJAyADQeACaiAVQgAgFUIAEMkDIANBkANqIBZCACAWQgAQyQMgA0GwA2ogGEIAIBhCABDJAyADQZACaiADKQOgAiIaQn2DIhtCAEKBgICAcEIAEMkDIAMpA6gDIAMpA/gCIAMpA7gCIAMpA8gCIAMpA9gCIhQgAykDwAJ8IhUgFFStfCIWIAMpA7ACfCIUIBZUrXwiGCADKQPwAnwiFiAYVK18IBYgFiADKQOIAyAUIBQgAykDgAN8IhRWrXx8IhZWrXwiGSADKQOgA3wiGCAZVK18IhlCP4ggAykDuAMgAykDsAMiHCAZQgGGIBhCP4iEfCIXIBxUrXwgFyAXIAMpA5gDIAMpA+gCIAMpA+ACIhwgFUIBhiADKQPQAiIeQj+IhHwiGSAcVK18IBkgAykDqAIiHCAeQgGGfCIeIBxUrXwiHCAZVK18IhkgFEIBhiAVQj+IhHwiHyAZVK0iGSADKQOQA3wiFSAZVK18IBUgFSAWQgGGIBRCP4iEfCIUVq18IhUgGEIBhiAWQj+IhHwiFiAVVK18IhlWrXx8IRgCfwJAIAMpA5gCIBtCIIYiFyAefCIVIBdUrSAaQiCIfCIXIBx8IhogF1StIhsgAykDkAJ8IhcgG1StfCAXIB98IhsgF1StfCIXUA0AIBQgF3wiFCAXVCIGRQ0AIAatIhcgFnwiFiAXWg0AIBYgF1StIhcgGXwiGSAXWg0AIBcgGVatIhcgGHwiGCAXVAwBC0EACyEKIAgpAwAhHCAIKQMIIR4gCCkDECEfIAgpAxghISADQYACaiAVQgBCgYCAgHBCABDJAwJAIAMpA4gCIBogFUIghiIafCIXIBpUrSAVQiCIfCIVIBt8IhogFVStIhsgAykDgAJ8IhUgG1StfCAUIBV8IhQgFVStfCIVUA0AIBUgFnwiFiAVWg0AIBUgFlatIhUgGXwiGSAVWg0AIBUgGVatIhUgGHwiGCAVVCEHCyADQfABaiAXQgBCgYCAgHBCABDJA0EAIQYgAykD+AEgFCAXQiCGIhQgGnwiFSAUVK0gF0IgiHwiFHwiFyAUVK0iGiADKQPwAXwiFCAaVK18IBQgFnwiFiAUVK18IhRQRQRAIBQgGXwiGSAUVCIGrSIUIBh8IhogGCAGGyEYIAYgFCAaVnEhBgsgA0HgAWogFUIAQoGAgIBwQgAQyQMgAykD6AEgFUIghiIUIBd8IhcgFFStIBVCIIh8IhQgFnwiFSAUVK0iFiADKQPgAXwiFCAWVK18IBQgFCAZfCIWVq18IhQgGHwiGSAYIBRCAFIiCBshGAJAAkACQCAHIApyIAZyIBQgGVYiB60gFCAIG0IAUnIgByAIcSAYQoGAgIBwVnJyDQAgGEKBgICAcFINAkIAIRkgFkIAUg0AQv////8PIRQgFUL/////D1YEQCAVIRQMAgsgFUL/////D1IgF0J/UnINAgwBCyAWIRkgFSEUCyAUQv////8PfSIWIBdCf1KtIhp9IRUgGSAUQv////8PVCAWIBpUcq0iFH0hFiAYIBQgGVatfUL/////D3whGCAXQgF8IRcLIAMgFzcDkAkgAyAVNwOICSADIBY3A4AJIAMgGDcD+AggA0HwAGogAykD2AMiFUIAIAMpA+ADIhRCABDJAyADQeAAaiADKQPQAyIWQgAgFEIAEMkDIANB0ABqIAMpA8gDIhhCACAUQgAQyQMgA0GgAWogFkIAIBVCABDJAyADQZABaiAYQgAgFUIAEMkDIANBwAFqIBhCACAWQgAQyQMgA0FAayAUQgAgFEIAEMkDIANBgAFqIBVCACAVQgAQyQMgA0GwAWogFkIAIBZCABDJAyADQdABaiAYQgAgGEIAEMkDIANBMGogAykDQCIaQn2DIhtCAEKBgICAcEIAEMkDIAMpA8gBIAMpA5gBIAMpA1ggAykDaCADKQN4IhQgAykDYHwiFSAUVK18IhYgAykDUHwiFCAWVK18IhggAykDkAF8IhYgGFStfCAWIBYgAykDqAEgFCAUIAMpA6ABfCIUVq18fCIWVq18IhkgAykDwAF8IhggGVStfCIZQj+IIAMpA9gBIAMpA9ABIh0gGUIBhiAYQj+IhHwiFyAdVK18IBcgFyADKQO4ASADKQOIASADKQOAASIdIBVCAYYgAykDcCIgQj+IhHwiGSAdVK18IBkgAykDSCIdICBCAYZ8IiAgHVStfCIdIBlUrXwiGSAUQgGGIBVCP4iEfCIiIBlUrSIZIAMpA7ABfCIVIBlUrXwgFSAVIBZCAYYgFEI/iIR8IhRWrXwiFSAYQgGGIBZCP4iEfCIWIBVUrXwiGVatfHwhGEEAIQcCfwJAIAMpAzggG0IghiIXICB8IhUgF1StIBpCIIh8IhcgHXwiGiAXVK0iGyADKQMwfCIXIBtUrXwgFyAifCIbIBdUrXwiF1ANACAUIBd8IhQgF1QiBkUNACAGrSIXIBZ8IhYgF1oNACAWIBdUrSIXIBl8IhkgF1oNACAXIBlWrSIXIBh8IhggF1QMAQtBAAshCiADQSBqIBVCAEKBgICAcEIAEMkDAkAgAykDKCAaIBVCIIYiGnwiFyAaVK0gFUIgiHwiFSAbfCIaIBVUrSIbIAMpAyB8IhUgG1StfCAUIBV8IhQgFVStfCIVUA0AIBUgFnwiFiAVWg0AIBUgFlatIhUgGXwiGSAVWg0AIBUgGVatIhUgGHwiGCAVVCEHCyADQRBqIBdCAEKBgICAcEIAEMkDQQAhBiADKQMYIBQgF0IghiIUIBp8IhUgFFStIBdCIIh8IhR8IhcgFFStIhogAykDEHwiFCAaVK18IBQgFnwiFiAUVK18IhRQRQRAIBQgGXwiGSAUVCIGrSIUIBh8IhogGCAGGyEYIAYgFCAaVnEhBgsgAyAVQgBCgYCAgHBCABDJAyADKQMIIBVCIIYiFCAXfCIXIBRUrSAVQiCIfCIUIBZ8IhUgFFStIhYgAykDAHwiFCAWVK18IBQgFCAZfCIWVq18IhQgGHwiGSAYIBRCAFIiCBshGAJAAkACQCAHIApyIAZyIBQgGVYiB60gFCAIG0IAUnIgByAIcSAYQoGAgIBwVnJyDQAgGEKBgICAcFINAkIAIRkgFkIAUg0AQv////8PIRQgFUL/////D1YEQCAVIRQMAgsgFUL/////D1IgF0J/UnINAgwBCyAWIRkgFSEUCyAUQv////8PfSIWIBdCf1KtIhp9IRUgGSAUQv////8PVCAWIBpUcq0iFH0hFiAYIBQgGVatfUL/////D3whGCAXQgF8IRcLIAMgFzcD0AkgAyAVNwPICSADIBY3A8AJIAMgGDcDuAkgA0HwCWoiByAFQRhqIgYpAwA3AwAgA0HoCWoiCCAFQRBqIgopAwA3AwAgA0HgCWoiECAFQQhqIhEpAwA3AwAgAyAFKQMANwPYCSADQZgJaiADQbgJaiISIANB2AlqIhMQkQEgByAGKQMANwMAIAggCikDADcDACAQIBEpAwA3AwAgAyAFKQMANwPYCSASIANB+AlqIBMQkQECQAJAIAMpA5gJIhogAykDuAl8IhUgAykDoAkiFCADKQPACXwiFiAUVCAWIBYgAykDqAkiFCADKQPICXwiGCAUVCAYIBggAykDsAkiFCADKQPQCXwiFyAUVK18IhRWcq18IhlWcq18IhggFVQgFSAaVHINAEKBgICAcCEWAkAgGCIVQoGAgIBwUg0AIBlCAFINAUL/////DyEWIBQiFUL/////D1INACAXQn9RDQFCACEVQoGAgIBwIRgMAgsgFSAWWg0AIBkhFSAUIRYMAQsgFEL/////D30iFSAXQn9SrSIafSEWIBkgFEL/////D1QgFSAaVHKtIhR9IRUgGEL+////D0L/////DyAUIBlWG3whGCAXQgF8IRcLAkACQCAYIBx8IhogFSAVIB58IhVWIBUgFiAffCIUIBZUIBQgFCAXICF8IhkgF1StfCIUVnKtfCIWIBVUcq18IhcgGlQgGCAaVnINAEKBgICAcCEYAkAgFyIVQoGAgIBwUg0AIBZCAFINAUL/////DyEYIBQiFUL/////D1INACAZQn9RDQFCACEVQoGAgIBwIRcMAgsgFSAYWg0AIBYhFSAUIRgMAQsgFEL/////D30iFSAZQn9SrSIafSEYIBYgFEL/////D1QgFSAaVHKtIhR9IRUgF0L+////D0L/////DyAUIBZWG3whFyAZQgF8IRkLIAMgGTcD8AkgAyAYNwPoCSADIBU3A+AJIAMgFzcD2AkgA0H4CGogA0HYCWpBIBDxAyADKALcCCIFBEAgAygC4AggBUECdBDfBAsCQCADKAKUBiIFRQ0AIAUgBUEMbEETakF4cSIGakEJaiIFRQ0AIAMoApAGIAZrIAUQ3wQLIAMoAsAGIgVBgICAgHhGIAVFckUEQCADKALEBiAFQQJ0EN8ECw0BCyALIANByANqQcgA/AoAAAwBCyADQfgJaiIFIANByANqEKMCIANBADYC4AkgA0KAgICAEDcC2AkgA0Gw18EANgK0BCADQqCAgIAONwK4BCADIANB2AlqIgc2ArAEIAUgA0GwBGoiBRDTAg0BIANBmARqIANB4AlqKAIANgIAIAMgAykC2Ak3A5AEIAUgDhCjAiADQQA2AoAJIANCgICAgBA3AvgIIANBsNfBADYCvAkgA0KggICADjcCwAkgAyADQfgIajYCuAkgBSADQbgJahDTAg0BIANBqARqIANBgAlqKAIANgIAIAMgAykC+Ag3A6AEIANBAzYC3AkgA0Ho9cEANgLYCSADQgI3AuQJIAMgA0GgBGqtQoCAgIDAB4Q3A6AJIAMgA0GQBGqtQoCAgIDAB4Q3A5gJIAMgA0GYCWo2AuAJIAsgBxDSAiADKAKgBCIFBEAgAygCpAQgBRDfBAsgAygCkAQiBQRAIAMoApQEIAUQ3wQLIAtBAjoAQAsgA0GgCmokAAwBC0HY18EAQTcgA0GfCmpByNfBAEHc2MEAEMoDAAsCQAJAIAQtAIgBIgNBAkYEQCACKAIAIgFBgICAgHhGIAFFckUEQCACKAIEIAEQ3wQLIAIgBCkDSDcCACACQQhqIARB0ABqKAIANgIADAELIARBEGogBEHQAGopAwA3AwAgBEEYaiAEQdgAaikDADcDACAEQSBqIARB4ABqKQMANwMAIARBKGogBEHoAGopAwA3AwAgBEEwaiAEQfAAaikDADcDACAEQThqIARB+ABqKQMANwMAIARBQGsgBEGAAWopAwA3AwAgBCAEKQNINwMIIAQgDSgAADYCACAEIA1BA2ooAAA2AAMgA0EDRg0BCyAAIAQpAwg3AwAgACAEKAIANgBBIABBxABqIAQoAAM2AAAgAEE4aiAEQUBrKQMANwMAIABBMGogBEE4aikDADcDACAAQShqIARBMGopAwA3AwAgAEEgaiAEQShqKQMANwMAIABBGGogBEEgaikDADcDACAAQRBqIARBGGopAwA3AwAgAEEIaiAEQRBqKQMANwMADAMLIA8hAyAJDQALC0EDIQMLIAAgAzoAQCAEQdABaiQADwtBAEEAQaD6wAAQ2QMAC0EBQQFBsPrAABDZAwAL9DICEX8PfiMAQdABayIFJAACQAJAAkAgASgCBCIKBEAgASgCCCIMRQ0CIAVBiQFqIQ0gASgCACEEA0AgASAKIAwgCiAKIAxLGyIGayIKNgIEIAEgBCAGQQV0aiIPNgIAIAVBqAFqIARBGGopAwA3AwAgBUGgAWogBEEQaikDADcDACAFQZgBaiAEQQhqKQMANwMAIAUgBCkDADcDkAEgBkEBRg0EIAVByAFqIARBOGopAwA3AwAgBUHAAWogBEEwaikDADcDACAFQbgBaiAEQShqKQMANwMAIAUgBCkDIDcDsAEgBUHIAGohC0EAIQkjAEGgDWsiAyQAIANB4AZqIAVBkAFqIghBGGopAwA3AwAgA0HYBmogCEEQaikDADcDACADQdAGaiAIQQhqKQMANwMAIANB8AZqIAVBsAFqIgRBCGopAwA3AwAgA0H4BmogBEEQaikDADcDACADQYAHaiAEQRhqKQMANwMAIANBADoAiAcgAyAIKQMANwPIBiADIAQpAwA3A+gGIANB6AZqIQ4CQAJAAkACQAJAIANByAZqQejRwQBBIBDxA0UEQCAOQejRwQBBIBDxA0UNAQsgA0GwB2oiBBA6IANB0AdqIQYgA0GQDWogBEEYaikDADcDACADQYgNaiAEQRBqKQMANwMAIANBgA1qIARBCGopAwA3AwAgAyAEKQMANwP4DCADQdAFaiADKQP4BiIWQgAgAykDgAciF0IAEMkDIANBwAVqIAMpA/AGIhVCACAXQgAQyQMgA0GwBWogAykD6AYiFEIAIBdCABDJAyADQYAGaiAVQgAgFkIAEMkDIANB8AVqIBRCACAWQgAQyQMgA0GgBmogFEIAIBVCABDJAyADQaAFaiAXQgAgF0IAEMkDIANB4AVqIBZCACAWQgAQyQMgA0GQBmogFUIAIBVCABDJAyADQbAGaiAUQgAgFEIAEMkDIANBkAVqIAMpA6AFIhxC/////76y/fBCfiIUQgBCgYCAgL+y/fDDAEIAEMkDIANBgAVqIBRCAEKR4eXNh4n6mShCABDJAyADQfAEaiAUQgBC3bCFjOi2kai4f0IAEMkDIANB4ARqIBRCAEKpwMaJrs6TsjBCABDJAyADKQOoBiADKQP4BSADKQO4BSADKQPIBSADKQPYBSIUIAMpA8AFfCIYIBRUrXwiFCADKQOwBXwiFyAUVK18IhQgAykD8AV8IhUgFFStfCAVIBUgAykDiAYgFyAXIAMpA4AGfCIdVq18fCIeVq18IhQgAykDoAZ8IhYgFFStfCIVQj+IIAMpA7gGIAMpA7AGIhQgFUIBhiAWQj+IhHwiGSAUVK18IBkgAykDmAYgAykD6AUgAykD4AUiFCAYQgGGIAMpA9AFIhVCP4iEfCIXIBRUrXwgFyADKQOoBSIUIBVCAYZ8IhsgFFStfCIaIBdUrXwiFCAdQgGGIBhCP4iEfCIYIBRUrSIUIAMpA5AGfCIVIBRUrXwgFSAVIB5CAYYgHUI/iIR8IhVWrXwiFCAWQgGGIB5CP4iEfCIWIBRUrXwiFyAZVK18fCEZAn8CQCADKQPoBCADKQP4BCADKQOIBSADKQOYBSADKQOQBSIUIBxCfYN8IBRUrXwiFCADKQOABXwiHCAUVK18IBwgGyAcfCIcVq18IhQgAykD8AR8IhsgFFStfCAaIBt8IhogG1StfCIUIAMpA+AEfCIbIBRUrXwgGCAbfCIYIBtUrXwiFFANACAUIBV8IhUgFFQiBEUNACAErSIUIBZ8IhYgFFoNACAUIBZWrSIUIBd8IhcgFFoNACAUIBdWrSIUIBl8IhkgFFQMAQtBAAshBCAGKQMAISEgBikDCCEiIAYpAxAhHSAGKQMYIR4gA0HQBGogHEL/////vrL98EJ+IhRCAEKBgICAv7L98MMAQgAQyQMgA0HABGogFEIAQpHh5c2HifqZKEIAEMkDIANBsARqIBRCAELdsIWM6LaRqLh/QgAQyQMgA0GgBGogFEIAQqnAxomuzpOyMEIAEMkDAkAgAykDqAQgAykDuAQgAykDyAQgAykD2AQgAykD0AQiFCAcfCAUVK18IhQgAykDwAR8IhsgFFStfCAbIBogG3wiG1atfCIUIAMpA7AEfCIaIBRUrXwgGCAafCIYIBpUrXwiFCADKQOgBHwiGiAUVK18IBUgGnwiFSAaVK18IhRQDQAgFCAWfCIWIBRaDQAgFCAWVq0iFCAXfCIXIBRaDQAgFCAXVq0iFCAZfCIZIBRUIQkLIANBkARqIBtC/////76y/fBCfiIUQgBCgYCAgL+y/fDDAEIAEMkDIANBgARqIBRCAEKR4eXNh4n6mShCABDJAyADQfADaiAUQgBC3bCFjOi2kai4f0IAEMkDIANB4ANqIBRCAEKpwMaJrs6TsjBCABDJA0EAIQcgAykD6AMgAykD+AMgAykDiAQgAykDmAQgAykDkAQiFCAbfCAUVK18IhQgAykDgAR8IhogFFStfCAaIBggGnwiGlatfCIUIAMpA/ADfCIYIBRUrXwgGCAVIBh8IhhWrXwiFCADKQPgA3wiFSAUVK18IBUgFnwiFiAVVK18IhRQRQRAIBQgF3wiFyAUVCIGrSIVIBl8IhQgGSAGGyEZIAYgFCAVVHEhBwsgA0HQA2ogGkL/////vrL98EJ+IhRCAEKBgICAv7L98MMAQgAQyQMgA0HAA2ogFEIAQpHh5c2HifqZKEIAEMkDIANBsANqIBRCAELdsIWM6LaRqLh/QgAQyQMgA0GgA2ogFEIAQqnAxomuzpOyMEIAEMkDIAMpA6gDIAMpA7gDIAMpA8gDIAMpA9gDIAMpA9ADIhQgGnwgFFStfCIUIAMpA8ADfCIVIBRUrXwgFSAYfCIYIBVUrXwiFCADKQOwA3wiFSAUVK18IBUgFSAWfCIVVq18IhQgAykDoAN8IhYgFFStfCAWIBYgF3wiFlatfCIXIBl8IhQgGSAXQgBSIgYbIRkCQAJAAkAgBCAJciAHciAUIBdUIgStIBcgBhtCAFJyIAQgBnEgGUKpwMaJrs6TsjBWcnINACAZQqnAxomuzpOyMFIEQCAVIRQMAwsgFkLdsIWM6LaRqLh/Vg0AIBZC3bCFjOi2kai4f1IEQCAVIRQMAwtC3bCFjOi2kai4fyEXIBVCkeHlzYeJ+pkoVg0BIBVCkeHlzYeJ+pkoUgRAIBUhFAwDCyAYQoCAgIC/sv3wwwBWDQEgFSEUDAILIBYhFwsgFUKR4eXNh4n6mSh9IhsgGEKBgICAv7L98MMAVK0iFn0hFCAXQqPP+vOXye7XxwB8IhogFUKR4eXNh4n6mShUIBYgG1ZyrSIVfSEWIBkgF0LdsIWM6LaRqLh/VCAVIBpWcq19QqnAxomuzpOyMH0hGSAYQoGAgIC/sv3wwwB9IRgLIAMgGDcDkAwgAyAUNwOIDCADIBY3A4AMIAMgGTcD+AsgA0GwAmogAykD2AYiFkIAIAMpA+AGIhdCABDJAyADQaACaiADKQPQBiIVQgAgF0IAEMkDIANBkAJqIAMpA8gGIhRCACAXQgAQyQMgA0HgAmogFUIAIBZCABDJAyADQdACaiAUQgAgFkIAEMkDIANBgANqIBRCACAVQgAQyQMgA0GAAmogF0IAIBdCABDJAyADQcACaiAWQgAgFkIAEMkDIANB8AJqIBVCACAVQgAQyQMgA0GQA2ogFEIAIBRCABDJAyADQfABaiADKQOAAiIcQv////++sv3wQn4iFEIAQoGAgIC/sv3wwwBCABDJAyADQeABaiAUQgBCkeHlzYeJ+pkoQgAQyQMgA0HQAWogFEIAQt2whYzotpGouH9CABDJAyADQcABaiAUQgBCqcDGia7Ok7IwQgAQyQMgAykDiAMgAykD2AIgAykDmAIgAykDqAIgAykDuAIiFCADKQOgAnwiGCAUVK18IhQgAykDkAJ8IhcgFFStfCIUIAMpA9ACfCIVIBRUrXwgFSAVIAMpA+gCIBcgFyADKQPgAnwiH1atfHwiIFatfCIUIAMpA4ADfCIWIBRUrXwiFUI/iCADKQOYAyADKQOQAyIUIBVCAYYgFkI/iIR8IhkgFFStfCAZIAMpA/gCIAMpA8gCIAMpA8ACIhQgGEIBhiADKQOwAiIVQj+IhHwiFyAUVK18IBcgAykDiAIiFCAVQgGGfCIbIBRUrXwiGiAXVK18IhQgH0IBhiAYQj+IhHwiGCAUVK0iFCADKQPwAnwiFSAUVK18IBUgFSAgQgGGIB9CP4iEfCIVVq18IhQgFkIBhiAgQj+IhHwiFiAUVK18IhcgGVStfHwhGUEAIQkCfwJAIAMpA8gBIAMpA9gBIAMpA+gBIAMpA/gBIAMpA/ABIhQgHEJ9g3wgFFStfCIUIAMpA+ABfCIcIBRUrXwgHCAbIBx8IhxWrXwiFCADKQPQAXwiGyAUVK18IBogG3wiGiAbVK18IhQgAykDwAF8IhsgFFStfCAYIBt8IhggG1StfCIUUA0AIBQgFXwiFSAUVCIERQ0AIAStIhQgFnwiFiAUWg0AIBQgFlatIhQgF3wiFyAUWg0AIBQgF1atIhQgGXwiGSAUVAwBC0EACyEEIANBsAFqIBxC/////76y/fBCfiIUQgBCgYCAgL+y/fDDAEIAEMkDIANBoAFqIBRCAEKR4eXNh4n6mShCABDJAyADQZABaiAUQgBC3bCFjOi2kai4f0IAEMkDIANBgAFqIBRCAEKpwMaJrs6TsjBCABDJAwJAIAMpA4gBIAMpA5gBIAMpA6gBIAMpA7gBIAMpA7ABIhQgHHwgFFStfCIUIAMpA6ABfCIbIBRUrXwgGyAaIBt8IhtWrXwiFCADKQOQAXwiGiAUVK18IBggGnwiGCAaVK18IhQgAykDgAF8IhogFFStfCAVIBp8IhUgGlStfCIUUA0AIBQgFnwiFiAUWg0AIBQgFlatIhQgF3wiFyAUWg0AIBQgF1atIhQgGXwiGSAUVCEJCyADQfAAaiAbQv////++sv3wQn4iFEIAQoGAgIC/sv3wwwBCABDJAyADQeAAaiAUQgBCkeHlzYeJ+pkoQgAQyQMgA0HQAGogFEIAQt2whYzotpGouH9CABDJAyADQUBrIBRCAEKpwMaJrs6TsjBCABDJA0EAIQcgAykDSCADKQNYIAMpA2ggAykDeCADKQNwIhQgG3wgFFStfCIUIAMpA2B8IhogFFStfCAaIBggGnwiGlatfCIUIAMpA1B8IhggFFStfCAYIBUgGHwiGFatfCIUIAMpA0B8IhUgFFStfCAVIBZ8IhYgFVStfCIUUEUEQCAUIBd8IhcgFFQiBq0iFSAZfCIUIBkgBhshGSAGIBQgFVRxIQcLIANBMGogGkL/////vrL98EJ+IhRCAEKBgICAv7L98MMAQgAQyQMgA0EgaiAUQgBCkeHlzYeJ+pkoQgAQyQMgA0EQaiAUQgBC3bCFjOi2kai4f0IAEMkDIAMgFEIAQqnAxomuzpOyMEIAEMkDIAMpAwggAykDGCADKQMoIAMpAzggAykDMCIUIBp8IBRUrXwiFCADKQMgfCIVIBRUrXwgFSAYfCIYIBVUrXwiFCADKQMQfCIVIBRUrXwgFSAVIBZ8IhVWrXwiFCADKQMAfCIWIBRUrXwgFiAWIBd8IhZWrXwiFyAZfCIUIBkgF0IAUiIGGyEZAkACQAJAIAQgCXIgB3IgFCAXVCIErSAXIAYbQgBSciAEIAZxIBlCqcDGia7Ok7IwVnJyDQAgGUKpwMaJrs6TsjBSBEAgFSEUDAMLIBZC3bCFjOi2kai4f1YNACAWQt2whYzotpGouH9SBEAgFSEUDAMLQt2whYzotpGouH8hFyAVQpHh5c2HifqZKFYNASAVQpHh5c2HifqZKFIEQCAVIRQMAwsgGEKAgICAv7L98MMAVg0BIBUhFAwCCyAWIRcLIBVCkeHlzYeJ+pkofSIbIBhCgYCAgL+y/fDDAFStIhZ9IRQgF0Kjz/rzl8nu18cAfCIaIBVCkeHlzYeJ+pkoVCAWIBtWcq0iFX0hFiAZIBdC3bCFjOi2kai4f1QgFSAaVnKtfUKpwMaJrs6TsjB9IRkgGEKBgICAv7L98MMAfSEYCyADIBg3A9AMIAMgFDcDyAwgAyAWNwPADCADIBk3A7gMIANB8AxqIhAgCEEYaiIRKQMANwMAIANB6AxqIhIgCEEQaiITKQMANwMAIANB4AxqIgkgCEEIaiIHKQMANwMAIAMgCCkDADcD2AwgA0GYDGogA0G4DGoiBiADQdgMaiIEEH0gECARKQMANwMAIBIgEykDADcDACAJIAcpAwA3AwAgAyAIKQMANwPYDCAGIANB+AxqIAQQfUKpwMaJrs6TsjAhFCADKQOgDCIVIAMpA8AMfCIYIBVUIBggAykDqAwiFSADKQPIDHwiFyAVVCAXIBcgAykDsAwiFSADKQPQDHwiGSAVVK18IhZWcq18IhcgGFRyrSADKQO4DCADKQOYDHx8IhghFQJAAkACQCAYQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRQgFyIVQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIRQgFiIVQpHh5c2HifqZKFINAEKBgICAv7L98MMAIRQgGSIVQoGAgIC/sv3wwwBRDQELIBQgFVgNACAXIRQgFiEVDAELIBZCkeHlzYeJ+pkofSIbIBlCgYCAgL+y/fDDAFStIhR9IRUgF0Kjz/rzl8nu18cAfCIaIBZCkeHlzYeJ+pkoVCAUIBtWcq0iFn0hFCAYIBdC3bCFjOi2kai4f1QgFiAaVnKtfUKpwMaJrs6TsjB9IRggGUKBgICAv7L98MMAfSEZC0KpwMaJrs6TsjAhGyAYICF8IBQgFCAifCIaViAaIBogFSAVIB18IhRWIBQgGSAefCIYIBlUrXwiFiAUVHKtfCIXVnKtfCIZIRQCQAJAAkAgGUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEbIBciFELdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCEbIBYiFEKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACEbIBgiFEKBgICAv7L98MMAUQ0BCyAUIBtaDQAgFyEUIBYhFQwBCyAWQpHh5c2HifqZKH0iGyAYQoGAgIC/sv3wwwBUrSIUfSEVIBdCo8/685fJ7tfHAHwiGiAWQpHh5c2HifqZKFQgFCAbVnKtIhZ9IRQgGSAXQt2whYzotpGouH9UIBYgGlZyrX1CqcDGia7Ok7IwfSEZIBhCgYCAgL+y/fDDAH0hGAsgAyAYNwPwDCADIBU3A+gMIAMgFDcD4AwgAyAZNwPYDCADQfgLaiADQdgMakEgEPEDIAMoAtwLIgQEQCADKALgCyAEQQJ0EN8ECwJAIAMoApQJIgRFDQAgBCAEQQxsQRNqQXhxIgZqQQlqIgRFDQAgAygCkAkgBmsgBBDfBAsgAygCwAkiBEGAgICAeEYgBEVyRQRAIAMoAsQJIARBAnQQ3wQLDQELIAsgA0HIBmpByAD8CgAADAELIANB+AxqIgYgA0HIBmoQzAEgA0EANgLgDCADQoCAgIAQNwLYDCADQbDXwQA2ArQHIANCoICAgA43ArgHIAMgA0HYDGoiBDYCsAcgBiADQbAHaiIGENMCDQEgA0GYB2ogA0HgDGooAgA2AgAgAyADKQLYDDcDkAcgBiAOEMwBIANBADYCgAwgA0KAgICAEDcC+AsgA0Gw18EANgK8DCADQqCAgIAONwLADCADIANB+AtqNgK4DCAGIANBuAxqENMCDQEgA0GoB2ogA0GADGooAgA2AgAgAyADKQL4CzcDoAcgA0EDNgLcDCADQej1wQA2AtgMIANCAjcC5AwgAyADQaAHaq1CgICAgMAHhDcDoAwgAyADQZAHaq1CgICAgMAHhDcDmAwgAyADQZgMajYC4AwgCyAEENICIAMoAqAHIgQEQCADKAKkByAEEN8ECyADKAKQByIEBEAgAygClAcgBBDfBAsgC0ECOgBACyADQaANaiQADAELQdjXwQBBNyADQZ8NakHI18EAQdzYwQAQygMACwJAAkAgBS0AiAEiBEECRgRAIAIoAgAiAUGAgICAeEYgAUVyRQRAIAIoAgQgARDfBAsgAiAFKQNINwIAIAJBCGogBUHQAGooAgA2AgAMAQsgBUEQaiAFQdAAaikDADcDACAFQRhqIAVB2ABqKQMANwMAIAVBIGogBUHgAGopAwA3AwAgBUEoaiAFQegAaikDADcDACAFQTBqIAVB8ABqKQMANwMAIAVBOGogBUH4AGopAwA3AwAgBUFAayAFQYABaikDADcDACAFIAUpA0g3AwggBSANKAAANgIAIAUgDUEDaigAADYAAyAEQQNGDQELIAAgBSkDCDcDACAAIAUoAgA2AEEgAEHEAGogBSgAAzYAACAAQThqIAVBQGspAwA3AwAgAEEwaiAFQThqKQMANwMAIABBKGogBUEwaikDADcDACAAQSBqIAVBKGopAwA3AwAgAEEYaiAFQSBqKQMANwMAIABBEGogBUEYaikDADcDACAAQQhqIAVBEGopAwA3AwAMAwsgDyEEIAoNAAsLQQMhBAsgACAEOgBAIAVB0AFqJAAPC0EAQQBBoPrAABDZAwALQQFBAUGw+sAAENkDAAv8KQIRfw9+IwBB0AFrIgQkAAJAAkACQCABKAIEIgkEQCABKAIIIgxFDQIgBEGJAWohDSABKAIAIQMDQCABIAkgDCAJIAkgDEsbIgVrIgk2AgQgASADIAVBBXRqIg82AgAgBEGoAWogA0EYaikDADcDACAEQaABaiADQRBqKQMANwMAIARBmAFqIANBCGopAwA3AwAgBCADKQMANwOQASAFQQFGDQQgBEHIAWogA0E4aikDADcDACAEQcABaiADQTBqKQMANwMAIARBuAFqIANBKGopAwA3AwAgBCADKQMgNwOwASAEQcgAaiELQQAhByMAQaALayIDJAAgA0HgBGogBEGQAWoiBUEYaikDADcDACADQdgEaiAFQRBqKQMANwMAIANB0ARqIAVBCGopAwA3AwAgA0HwBGogBEGwAWoiBkEIaikDADcDACADQfgEaiAGQRBqKQMANwMAIANBgAVqIAZBGGopAwA3AwAgA0EAOgCIBSADIAUpAwA3A8gEIAMgBikDADcD6AQgA0HoBGohDgJAAkACQAJAAkAgA0HIBGpB6NHBAEEgEPEDRQRAIA5B6NHBAEEgEPEDRQ0BCyADQbAFaiIGEFUgA0HQBWohCCADQZALaiAGQRhqKQMANwMAIANBiAtqIAZBEGopAwA3AwAgA0GAC2ogBkEIaikDADcDACADIAYpAwA3A/gKIANB0ANqIAMpA/gEIhVCACADKQOABSIXQgAQyQMgA0HAA2ogAykD8AQiFEIAIBdCABDJAyADQbADaiADKQPoBCIYQgAgF0IAEMkDIANBgARqIBRCACAVQgAQyQMgA0HwA2ogGEIAIBVCABDJAyADQaAEaiAYQgAgFEIAEMkDIANBoANqIBdCACAXQgAQyQMgA0HgA2ogFUIAIBVCABDJAyADQZAEaiAUQgAgFEIAEMkDIANBsARqIBhCACAYQgAQyQMgA0GQA2ogAykDoAMiGUKx6pSR3aOCnFh+IhVCAEKv+P//b0IAEMkDIANBgANqIBVCAEJ/QgAQyQMgAykDqAQgAykD+AMgAykDuAMgAykDyAMgAykD2AMiFyADKQPAA3wiFSAXVK18IhQgAykDsAN8IhcgFFStfCIYIAMpA/ADfCIUIBhUrXwgFCAUIAMpA4gEIBcgFyADKQOABHwiGFatfHwiF1atfCIWIAMpA6AEfCIUIBZUrXwiFkI/iCADKQO4BCADKQOwBCIaIBZCAYYgFEI/iIR8IhYgGlStfCAWIAMpA5gEIAMpA+gDIAMpA+ADIhsgFUIBhiADKQPQAyIcQj+IhHwiGiAbVK18IBogAykDqAMiGyAcQgGGfCIcIBtUrXwiHSAaVK18IhogGEIBhiAVQj+IhHwiHiAaVK0iFSADKQOQBHwiGiAVVK18IBogGiAXQgGGIBhCP4iEfCIVVq18IhggFEIBhiAXQj+IhHwiGiAYVK18IhcgFlStfHwhGAJ/AkAgAykDiAMiFCAUIBQgAykDmAMgAykDkAMiFiAZQn2DfCAWVK18IhsgAykDgAMiFnwiGSAbVK18IBkgGSAcfCIbVq18IhwgFnwiGSAcVK18IBkgGSAdfCIcVq18IhkgFnwiFCAZVK18IBQgHnwiHSAUVK18IhRQDQAgFCAVfCIVIBRUIgZFDQAgBq0iFCAafCIaIBRaDQAgFCAaVq0iFCAXfCIXIBRaDQAgFCAXVq0iFCAYfCIYIBRUDAELQQALIQogCCkDACEeIAgpAwghHyAIKQMQISAgCCkDGCEhIANB8AJqIBtCseqUkd2jgpxYfiIUQgBCr/j//29CABDJAyADQeACaiAUQgBCf0IAEMkDAkAgAykD6AIiFCAUIBQgAykD+AIgAykD8AIiFiAbfCAWVK18IhsgAykD4AIiFnwiGSAbVK18IBkgGSAcfCIbVq18IhwgFnwiGSAcVK18IBkgGSAdfCIcVq18IhkgFnwiFCAZVK18IBQgFXwiHSAUVK18IhVQDQAgFSAafCIaIBVaDQAgFSAaVq0iFSAXfCIXIBVaDQAgFSAXVq0iFSAYfCIYIBVUIQcLIANB0AJqIBtCseqUkd2jgpxYfiIVQgBCr/j//29CABDJAyADQcACaiAVQgBCf0IAEMkDQQAhBiADKQPIAiIVIBUgFSADKQPYAiADKQPQAiIUIBt8IBRUrXwiGSADKQPAAiIUfCIWIBlUrXwgFiAWIBx8IhlWrXwiGyAUfCIWIBtUrXwgFiAWIB18IhtWrXwiFiAUfCIVIBZUrXwgFSAafCIcIBVUrXwiFVBFBEAgFSAXfCIXIBVUIgatIhUgGHwiFCAYIAYbIRggBiAUIBVUcSEGCyADQbACaiAZQrHqlJHdo4KcWH4iFUIAQq/4//9vQgAQyQMgA0GgAmogFUIAQn9CABDJAyADKQOoAiIVIBUgFSADKQO4AiADKQOwAiIUIBl8IBRUrXwiGiADKQOgAiIUfCIWIBpUrXwgFiAbfCIaIBZUrXwiGSAUfCIWIBlUrXwgFiAcfCIVIBZUrXwiGSAUfCIWIBlUrXwgFiAWIBd8IhRWrXwiFyAYfCIWIBggF0IAUiIIGyEYAkACQCAHIApyIAZyIBYgF1QiB60gFyAIG0IAUnIgByAIcXJFBEAgFUJ/UiAaQq/4//9vVHIgFCAYg0J/UnINAQsgFUIBfCIWIBpCr/j//29UrSIZfSEXIBRCAXwiGyAVQn9SIBYgGVRyrSIWfSEVIBggFEJ/UiAWIBtWcq19QgF8IRggGkLRh4CAEHwhGgwBCyAVIRcgFCEVCyADIBo3A5AKIAMgFzcDiAogAyAVNwOACiADIBg3A/gJIANBsAFqIAMpA9gEIhVCACADKQPgBCIXQgAQyQMgA0GgAWogAykD0AQiFEIAIBdCABDJAyADQZABaiADKQPIBCIYQgAgF0IAEMkDIANB4AFqIBRCACAVQgAQyQMgA0HQAWogGEIAIBVCABDJAyADQYACaiAYQgAgFEIAEMkDIANBgAFqIBdCACAXQgAQyQMgA0HAAWogFUIAIBVCABDJAyADQfABaiAUQgAgFEIAEMkDIANBkAJqIBhCACAYQgAQyQMgA0HwAGogAykDgAEiGUKx6pSR3aOCnFh+IhVCAEKv+P//b0IAEMkDIANB4ABqIBVCAEJ/QgAQyQMgAykDiAIgAykD2AEgAykDmAEgAykDqAEgAykDuAEiFyADKQOgAXwiFSAXVK18IhQgAykDkAF8IhcgFFStfCIYIAMpA9ABfCIUIBhUrXwgFCAUIAMpA+gBIBcgFyADKQPgAXwiGFatfHwiF1atfCIWIAMpA4ACfCIUIBZUrXwiFkI/iCADKQOYAiADKQOQAiIaIBZCAYYgFEI/iIR8IhYgGlStfCAWIAMpA/gBIAMpA8gBIAMpA8ABIhsgFUIBhiADKQOwASIcQj+IhHwiGiAbVK18IBogAykDiAEiGyAcQgGGfCIcIBtUrXwiHSAaVK18IhogGEIBhiAVQj+IhHwiIiAaVK0iFSADKQPwAXwiGiAVVK18IBogGiAXQgGGIBhCP4iEfCIVVq18IhggFEIBhiAXQj+IhHwiGiAYVK18IhcgFlStfHwhGEEAIQcCfwJAIAMpA2giFCAUIBQgAykDeCADKQNwIhYgGUJ9g3wgFlStfCIbIAMpA2AiFnwiGSAbVK18IBkgGSAcfCIbVq18IhwgFnwiGSAcVK18IBkgGSAdfCIcVq18IhkgFnwiFCAZVK18IBQgInwiHSAUVK18IhRQDQAgFCAVfCIVIBRUIgZFDQAgBq0iFCAafCIaIBRaDQAgFCAaVq0iFCAXfCIXIBRaDQAgFCAXVq0iFCAYfCIYIBRUDAELQQALIQogA0HQAGogG0Kx6pSR3aOCnFh+IhRCAEKv+P//b0IAEMkDIANBQGsgFEIAQn9CABDJAwJAIAMpA0giFCAUIBQgAykDWCADKQNQIhYgG3wgFlStfCIbIAMpA0AiFnwiGSAbVK18IBkgGSAcfCIbVq18IhwgFnwiGSAcVK18IBkgGSAdfCIcVq18IhkgFnwiFCAZVK18IBQgFXwiHSAUVK18IhVQDQAgFSAafCIaIBVaDQAgFSAaVq0iFSAXfCIXIBVaDQAgFSAXVq0iFSAYfCIYIBVUIQcLIANBMGogG0Kx6pSR3aOCnFh+IhVCAEKv+P//b0IAEMkDIANBIGogFUIAQn9CABDJA0EAIQYgAykDKCIVIBUgFSADKQM4IAMpAzAiFCAbfCAUVK18IhkgAykDICIUfCIWIBlUrXwgFiAWIBx8IhlWrXwiGyAUfCIWIBtUrXwgFiAWIB18IhtWrXwiFiAUfCIVIBZUrXwgFSAafCIcIBVUrXwiFVBFBEAgFSAXfCIXIBVUIgatIhUgGHwiFCAYIAYbIRggBiAUIBVUcSEGCyADQRBqIBlCseqUkd2jgpxYfiIVQgBCr/j//29CABDJAyADIBVCAEJ/QgAQyQMgAykDCCIVIBUgFSADKQMYIAMpAxAiFCAZfCAUVK18IhogAykDACIUfCIWIBpUrXwgFiAbfCIaIBZUrXwiGSAUfCIWIBlUrXwgFiAcfCIVIBZUrXwiGSAUfCIWIBlUrXwgFiAWIBd8IhRWrXwiFyAYfCIWIBggF0IAUiIIGyEYAkACQCAHIApyIAZyIBYgF1QiB60gFyAIG0IAUnIgByAIcXJFBEAgFUJ/UiAaQq/4//9vVHIgFCAYg0J/UnINAQsgFUIBfCIWIBpCr/j//29UrSIZfSEXIBRCAXwiGyAVQn9SIBYgGVRyrSIWfSEVIBggFEJ/UiAWIBtWcq19QgF8IRggGkLRh4CAEHwhGgwBCyAVIRcgFCEVCyADIBo3A9AKIAMgFzcDyAogAyAVNwPACiADIBg3A7gKIANB8ApqIgcgBUEYaiIGKQMANwMAIANB6ApqIgggBUEQaiIKKQMANwMAIANB4ApqIhAgBUEIaiIRKQMANwMAIAMgBSkDADcD2AogA0GYCmogA0G4CmoiEiADQdgKaiITEIABIAcgBikDADcDACAIIAopAwA3AwAgECARKQMANwMAIAMgBSkDADcD2AogEiADQfgKaiATEIABAkACQAJAIAMpA5gKIhkgAykDuAp8IhUgAykDoAoiFCADKQPACnwiFyAUVCAXIAMpA6gKIhQgAykDyAp8IhggFFQgGCAYIAMpA7AKIhQgAykD0Ap8IhogFFStfCIUVnKtfCIWIBdUcq18IhggFVQgFSAZVHINACAYQn9SDQEgFkJ/UgRAQn8hGAwCC0J/IRcgFEJ/UgRAQn8hGCAUIRUMAwsgGkKv+P//b1oNAEJ/IRhCfyEVDAILIBRCAXwiFyAaQq/4//9vVK0iGX0hFSAWQgF8IhsgFEJ/UiAXIBlUcq0iFH0hFyAYIBZCf1IgFCAbVnKtfUIBfCEYIBpC0YeAgBB8IRoMAQsgFiEXIBQhFQsCQAJAAkAgGCAefCIZIBcgH3wiGyAXVCAbIBsgFSAVICB8IhZWIBYgFiAaICF8IhcgGlStfCIUVnKtfCIWVnKtfCIaIBlUIBggGVZyDQAgGkJ/Ug0BIBZCf1IEQEJ/IRoMAgtCfyEYIBRCf1IEQEJ/IRogFCEVDAMLIBdCr/j//29aDQBCfyEaQn8hFQwCCyAUQgF8IhggF0Kv+P//b1StIhl9IRUgFkIBfCIbIBRCf1IgGCAZVHKtIhR9IRggGiAWQn9SIBQgG1ZyrX1CAXwhGiAXQtGHgIAQfCEXDAELIBYhGCAUIRULIAMgFzcD8AogAyAVNwPoCiADIBg3A+AKIAMgGjcD2AogA0H4CWogA0HYCmpBIBDxAyADKALcCSIFBEAgAygC4AkgBUECdBDfBAsCQCADKAKUByIFRQ0AIAUgBUEMbEETakF4cSIGakEJaiIFRQ0AIAMoApAHIAZrIAUQ3wQLIAMoAsAHIgVBgICAgHhGIAVFckUEQCADKALEByAFQQJ0EN8ECw0BCyALIANByARqQcgA/AoAAAwBCyADQfgKaiIFIANByARqEPUBIANBADYC4AogA0KAgICAEDcC2AogA0Gw18EANgK0BSADQqCAgIAONwK4BSADIANB2ApqIgc2ArAFIAUgA0GwBWoiBRDTAg0BIANBmAVqIANB4ApqKAIANgIAIAMgAykC2Ao3A5AFIAUgDhD1ASADQQA2AoAKIANCgICAgBA3AvgJIANBsNfBADYCvAogA0KggICADjcCwAogAyADQfgJajYCuAogBSADQbgKahDTAg0BIANBqAVqIANBgApqKAIANgIAIAMgAykC+Ak3A6AFIANBAzYC3AogA0Ho9cEANgLYCiADQgI3AuQKIAMgA0GgBWqtQoCAgIDAB4Q3A6AKIAMgA0GQBWqtQoCAgIDAB4Q3A5gKIAMgA0GYCmo2AuAKIAsgBxDSAiADKAKgBSIFBEAgAygCpAUgBRDfBAsgAygCkAUiBQRAIAMoApQFIAUQ3wQLIAtBAjoAQAsgA0GgC2okAAwBC0HY18EAQTcgA0GfC2pByNfBAEHc2MEAEMoDAAsCQAJAIAQtAIgBIgNBAkYEQCACKAIAIgFBgICAgHhGIAFFckUEQCACKAIEIAEQ3wQLIAIgBCkDSDcCACACQQhqIARB0ABqKAIANgIADAELIARBEGogBEHQAGopAwA3AwAgBEEYaiAEQdgAaikDADcDACAEQSBqIARB4ABqKQMANwMAIARBKGogBEHoAGopAwA3AwAgBEEwaiAEQfAAaikDADcDACAEQThqIARB+ABqKQMANwMAIARBQGsgBEGAAWopAwA3AwAgBCAEKQNINwMIIAQgDSgAADYCACAEIA1BA2ooAAA2AAMgA0EDRg0BCyAAIAQpAwg3AwAgACAEKAIANgBBIABBxABqIAQoAAM2AAAgAEE4aiAEQUBrKQMANwMAIABBMGogBEE4aikDADcDACAAQShqIARBMGopAwA3AwAgAEEgaiAEQShqKQMANwMAIABBGGogBEEgaikDADcDACAAQRBqIARBGGopAwA3AwAgAEEIaiAEQRBqKQMANwMADAMLIA8hAyAJDQALC0EDIQMLIAAgAzoAQCAEQdABaiQADwtBAEEAQaD6wAAQ2QMAC0EBQQFBsPrAABDZAwALjgYBAX8jAEGgBmsiAiQAAkACQAJAAkACQAJAAkAgAUH/AXFBAWsOBQECAwQFAAsgAhAhIABBCGogAkG0BGooAgA2AgAgACACKQKsBDcCAAJAIAIoAuQBIgBFDQAgACAAQQxsQRNqQXhxIgFqQQlqIgBFDQAgAigC4AEgAWsgABDfBAsgAigCkAIiAEGAgICAeEYgAEVyDQUgAigClAIgAEECdBDfBAwFCyACECYgAEEIaiACQZQGaigCADYCACAAIAIpAowGNwIAAkAgAigCBCIARQ0AIAAgAEEMbEETakF4cSIBakEJaiIARQ0AIAIoAgAgAWsgABDfBAsgAigCgAMiAEGAgICAeEYgAEVyDQQgAigChAMgAEECdBDfBAwECyACEFUgAEEIaiACQbQEaigCADYCACAAIAIpAqwENwIAAkAgAigC5AEiAEUNACAAIABBDGxBE2pBeHEiAWpBCWoiAEUNACACKALgASABayAAEN8ECyACKAKQAiIAQYCAgIB4RiAARXINAyACKAKUAiAAQQJ0EN8EDAMLIAIQPiAAQQhqIAJBtARqKAIANgIAIAAgAikCrAQ3AgACQCACKALkASIARQ0AIAAgAEEMbEETakF4cSIBakEJaiIARQ0AIAIoAuABIAFrIAAQ3wQLIAIoApACIgBBgICAgHhGIABFcg0CIAIoApQCIABBAnQQ3wQMAgsgAhBJIABBCGogAkG0BGooAgA2AgAgACACKQKsBDcCAAJAIAIoAuQBIgBFDQAgACAAQQxsQRNqQXhxIgFqQQlqIgBFDQAgAigC4AEgAWsgABDfBAsgAigCkAIiAEGAgICAeEYgAEVyDQEgAigClAIgAEECdBDfBAwBCyACEDogAEEIaiACQbQEaigCADYCACAAIAIpAqwENwIAAkAgAigC5AEiAEUNACAAIABBDGxBE2pBeHEiAWpBCWoiAEUNACACKALgASABayAAEN8ECyACKAKQAiIAQYCAgIB4RiAARXINACACKAKUAiAAQQJ0EN8ECyACQaAGaiQAC8EFAgl/A34jAEEgayIIJAACQAJAAn8CQAJAIAIEQCABKAIIIQUgASgCBCEGAkAgAkGAgARPBEAgBUUNAyAFQf////8DaiEHIAVBAnQhAyACrSEOIAVB/////wNxQQFHDQEgAyAGagwFCyAFRQ0CIAZBBGshCyAFQQJ0IQMDQCADIAtqIgQgBCgCACIHQRB2IgQgBCAJQRB0ciACbiIKIAJsa0EQdCAHQf//A3FyIgcgAm4iBCAKQRB0cjYCACAHIAIgBGxrIQkgA0EEayIDDQALDAULIAMgBmpBCGshAiAHQf////8DcUEBakH+////B3EhAwNAIAJBBGoiBCAENQIAIAxCIIaEIgwgDoAiDT4CACACIAI1AgAgDCANIA5+fUIghoQiDCAOgCINPgIAIAwgDSAOfn0hDCACQQhrIQIgA0ECayIDDQALDAILIAhBADYCGCAIQQE2AgwgCEHU88QANgIIIAhCBDcCECAIQQhqQcT0xAAQqAQACyABKAIAIQRBACEBDAMLIAxCIIYhDSACQQhqCyECIAdBAXEEfiAMBSACQQRrIgIgDSACNQIAhCIMIA6AIg0+AgAgDCANIA5+fQunIQkLIAEoAgAhBEEAIQEgBUUNACAGIAVBAnQiAmpBBGsoAgAEQCAFIQEMAQsgBkEEayEKIAVB/////wNxIQMDQCACRQ0BIANBAWshAyACIApqIAJBBGshAigCAEUNAAsgA0EBaiIBIAUgASAFSRshAQsCQAJAIARBAnYgAU0EQCAGIQMgBCECDAELQQAhAiAERQRAIAYhAwwBCyAEQQJ0IQQgAUUEQEEEIQMgBiAEEN8EDAELIAYgBEEEIAEiAkECdCIGEM4EIgNFDQELIAAgCTYCDCAAIAE2AgggACADNgIEIAAgAjYCACAIQSBqJAAPC0EEIAZB+PfEABDIBAALhwYBEn4gAikDACIPIQMgASkDACIQIQYgAAJ+AkACfgJAIA8gEFINACACKQMIIgQgASkDCCIGUgRAIAQhAwwBCyACKQMQIgcgASkDECIGUgRAIAchAwwBCyACKQMYIgogASkDGCIGUgRAIAohAwwBCyACKQMgIgUgASkDICIGUgRAIAUhAwwBCyAHIQsgCiEIIAUhCSACKQMoIgMhDCAEIAMgASkDKCIGUQ0BGgsgAyAGVg0BIAIpAwghBCACKQMQIQcgASkDECELIAIpAxghCiABKQMYIQggAikDICEFIAEpAyAhCSACKQMoIQMgASkDKCEMIAEpAwgLIQ4gCSAFfSINIAMgDFatIhF9IQYgCCAKfSISIA0gEVQgBSAJVnKtIgl9IQUgCyAHfSINIAggClQgCSASVnKtIgh9IQogDiAEfSIJIAggDVYgByALVnKtIgt9IQcgCSALVCAEIA5WciECIBAgD30hBCAMIAN9DAELQqTsw7WP1LSY5wAgAikDGCIDIAEpAxgiB30iCiACKQMgIgUgASkDICIEVCAFIAR9IgUgAikDKCIEIAEpAygiDlStIgtUcq0iCH0iCX0iBiAFIAt9IgVC///Piuv//9UeVkL//8+K6///1R4gBX0iCyAEIA59Ig5Cq9X+////v/+5f1atIgRUcq0iDH0hBUK/pZScz/DSu+QAIAIpAxAiDSABKQMQIhF9IhIgAyAHVCAIIApWcq0iA30iB30iCCAGIAxUIAlCpOzDtY/UtJjnAFZyrSIJfSEKQtfZrprk9umNywAgAikDCCIMIAEpAwgiE30iFCANIBFUIAMgElZyrSIDfSIGfSINIAggCVQgB0K/pZScz/DSu+QAVnKtIgh9IQcgCCANViAGQtfZrprk9umNywBWciECIAsgBH0hBiAMIBNUIAMgFFZyrSAQIA99fEKazf/Lo73EgBp8IQRCq9X+////v/+5fyAOfQs3AyggACAGNwMgIAAgBTcDGCAAIAo3AxAgACAHNwMIIAAgBCACrX03AwAL0CYCG38BfiMAQTBrIg4kAAJAAkACQAJAAkAgA0EGbiIKQQZsIANHBEBB0c7FAC0AABpBK0EBENYEIgFFDQEgAEErNgIMIAAgATYCCCAAQoGAgICwBTcCACABQSdqQa+MwQAoAAA2AAAgAUEgakGojMEAKQAANwAAIAFBGGpBoIzBACkAADcAACABQRBqQZiMwQApAAA3AAAgAUEIakGQjMEAKQAANwAAIAFBiIzBACkAADcAAAwFCwJAAkAgA0EMTwRAIAYOBwIBAQEBAQIBC0HRzsUALQAAGkEnQQEQ1gQiAUUNAyAAQSc2AgwgACABNgIIIABCgYCAgPAENwIAIAFBH2pBw43BACkAADcAACABQRhqQbyNwQApAAA3AAAgAUEQakG0jcEAKQAANwAAIAFBCGpBrI3BACkAADcAACABQaSNwQApAAA3AAAMBgtB0c7FAC0AABpBKEEBENYEIgFFDQMgAEEoNgIMIAAgATYCCCAAQoGAgICABTcCACABQSBqQZyNwQApAAA3AAAgAUEYakGUjcEAKQAANwAAIAFBEGpBjI3BACkAADcAACABQQhqQYSNwQApAAA3AAAgAUH8jMEAKQAANwAADAULAkAgBCAKTQRAIA4gATYCDCABQQVNDQEgDkEBNgIUIA5ByJrBADYCECAOQgE3AhwgDiAOQQxqrUKAgICA4AGENwMoIA4gDkEoajYCGCAOIA5BEGoQ0gIgDi0ABCEBIA4oAgAiCkGAgICAeEYNASAAIA4oAAU2AAkgAEEMaiAOQQhqKAAANgAAIAAgAToACCAAIAo2AgQgAEEBNgIADAYLQdHOxQAtAAAaQThBARDWBCIBRQ0EIABBODYCDCAAIAE2AgggAEKBgICAgAc3AgAgAUEwakH0jMEAKQAANwAAIAFBKGpB7IzBACkAADcAACABQSBqQeSMwQApAAA3AAAgAUEYakHcjMEAKQAANwAAIAFBEGpB1IzBACkAADcAACABQQhqQcyMwQApAAA3AAAgAUHEjMEAKQAANwAADAULAkACQAJAIAFB/wFxDgIBAgALIABBBGohAUHRzsUALQAAGkERQQEQ1gQiAkUEQEEBQRFBrIPBABDIBAALIAFBETYCCCABIAI2AgQgAUERNgIAIAJBEGpBw4zBAC0AADoAACACQQhqQbuMwQApAAA3AAAgAkGzjMEAKQAANwAAIABBATYCAAwGCyAAIQ1BACEKIwBB0AVrIgckAAJAAkACQCADQf///z9LIANBBXQiFEH4////B0tyDQBB0c7FAC0AABpBCCEKIBRBCBDWBCIBRQ0AIAEhCiADIQADQCAHQQhqIg8gAhD3AiAKQRhqIAdBIGopAwA3AwAgCkEQaiAHQRhqKQMANwMAIApBCGogB0EQaikDADcDACAKIAcpAwg3AwAgCkEgaiEKIAJBDGohAiAAQQFrIgANAAsgB0GAgICAeDYC0AMgB0EGNgIQIAcgAzYCDCAHIAE2AgggByAHQdADajYCFCAHQdABaiAPEJACAkAgBygC0AMiCkGAgICAeEcEQCAHKALYAyEDIAcoAtQDIQIgBygC0AEiAARAIAcoAtQBIABByAFsEN8ECyANIAM2AgwgDSACNgIIIA0gCjYCBCANQQE2AgAMAQsgBygC2AEhGCAHKALUASEVIAcoAtABIRMCQCAGQQZGBEBB0c7FAC0AABpBwAFBCBDWBCILRQ0EIAdB0AFqIgYgBRD3AiALQRhqIAdB6AFqIgMpAwA3AwAgC0EQaiAHQeABaiICKQMANwMAIAtBCGogB0HYAWoiACkDADcDACALIAcpA9ABNwMAIAYgBUEMahD3AiALQThqIAMpAwA3AwAgC0EwaiACKQMANwMAIAtBKGogACkDADcDACALIAcpA9ABNwMgIAYgBUEYahD3AiALQdgAaiADKQMANwMAIAtB0ABqIAIpAwA3AwAgC0HIAGogACkDADcDACALIAcpA9ABNwNAIAYgBUEkahD3AiALQfgAaiADKQMANwMAIAtB8ABqIAIpAwA3AwAgC0HoAGogACkDADcDACALIAcpA9ABNwNgIAYgBUEwahD3AiALQZgBaiADKQMANwMAIAtBkAFqIAIpAwA3AwAgC0GIAWogACkDADcDACALIAcpA9ABNwOAASAGIAVBPGoQ9wIgC0G4AWogAykDADcDACALQbABaiACKQMANwMAIAtBqAFqIAApAwA3AwAgCyAHKQPQATcDoAEgB0GAgICAeDYCkAUgB0KGgICA4AA3AtQBIAcgCzYC0AEgByAHQZAFajYC3AEgB0HQA2ogBhCQAiAHKAKQBSIFQYCAgIB4RwRAIAcoApgFIQMgBygClAUhAiAHKALQAyIABEAgBygC1AMgAEHIAWwQ3wQLIA0gAzYCDCANIAI2AgggDSAFNgIEIA1BATYCACALQcABEN8EIBNFDQMgFSATQcgBbBDfBAwDCyAHKALYAwRAIAcoAtADIRcgB0GoA2oiGSAHKALUAyIMQZgBaikDADcDACAHQaADaiIaIAxBkAFqKQMANwMAIAdBmANqIhsgDEGIAWopAwA3AwAgB0GwA2oiHCAMKQOgATcDACAHQbgDaiIdIAxBqAFqKQMANwMAIAdBwANqIh4gDEGwAWopAwA3AwAgB0HIA2oiHyAMQbgBaikDADcDACAHIAwpA4ABNwOQAyAMLQDAASEgIAdB2ARqIiEgDEEIaikDADcDACAHQeAEaiIIIAxBEGopAwA3AwAgB0HoBGoiCSAMQRhqKQMANwMAIAdB8ARqIhAgDCkDIDcDACAHQfgEaiIRIAxBKGopAwA3AwAgB0GABWoiEiAMQTBqKQMANwMAIAdBiAVqIhYgDEE4aikDADcDACAHQZgFaiIPIAxByABqKQMANwMAIAdBoAVqIgogDEHQAGopAwA3AwAgB0GoBWoiBiAMQdgAaikDADcDACAHIAwpAwA3A9AEIAcgDCkDQDcDkAUgB0HIBWoiBSAMQfgAaikDADcDACAHQcAFaiIDIAxB8ABqKQMANwMAIAdBuAVqIgIgDEHoAGopAwA3AwAgB0GwBWoiACAMKQNgNwMAIAdBiARqIBYpAwA3AwAgB0GABGogEikDADcDACAHQfgDaiARKQMANwMAIAdB8ANqIBApAwA3AwAgB0HoA2ogCSkDADcDACAHQeADaiAIKQMANwMAIAdB2ANqICEpAwA3AwAgByAHKQPQBDcD0AMgB0HIBGogBSkDADcDACAHQcAEaiADKQMANwMAIAdBuARqIAIpAwA3AwAgB0GwBGogACkDADcDACAHQagEaiAGKQMANwMAIAdBoARqIAopAwA3AwAgB0GYBGogDykDADcDACAHIAcpA5AFNwOQBCAHQYgDaiAfKQMANwMAIAdBgANqIB4pAwA3AwAgB0H4AmogHSkDADcDACAHQfACaiAcKQMANwMAIAdB6AJqIBkpAwA3AwAgB0HgAmogGikDADcDACAHQdgCaiAbKQMANwMAIAcgBykDkAM3A9ACIAdB0AFqIgAgB0HQA2pBgAH8CgAAIAdBCGogAEHAAfwKAAAgByAgOgDIASAXBEAgDCAXQcgBbBDfBAsgC0HAARDfBAwCC0EAQQBB+I3BABDZAwALIAdBAjoAyAELIA0gFSAYIAQgB0EIahA3IBNFDQAgFSATQcgBbBDfBAsgASAUEN8EIAdB0AVqJAAMAgsgCiAUQbyKwQAQyAQAC0EIQcABQbyKwQAQyAQACwwFCyAAIQ1BACEBIwBBsAhrIggkACADrUIwfiIipyEKAkACQAJAICJCIIinIApB+P///wdLcg0AAn8gCkUEQEEIIQBBAAwBC0HRzsUALQAAGkEIIQEgCkEIENYEIgBFDQEgAwshFiAAIQogAyEBA0AgCEEIaiIPIAIQ9gIgCkEoaiAIQTBqKQMANwMAIApBIGogCEEoaikDADcDACAKQRhqIAhBIGopAwA3AwAgCkEQaiAIQRhqKQMANwMAIApBCGogCEEQaikDADcDACAKIAgpAwg3AwAgCkEwaiEKIAJBDGohAiABQQFrIgENAAsgCEGAgICAeDYCsAUgCEEGNgIQIAggAzYCDCAIIAA2AgggCCAIQbAFajYCFCAIQbACaiAPEJECAkAgCCgCsAUiCkGAgICAeEcEQCAIKAK4BSEDIAgoArQFIQIgCCgCsAIiAQRAIAgoArQCIAFBqAJsEN8ECyANIAM2AgwgDSACNgIIIA0gCjYCBCANQQE2AgAMAQsgCCgCuAIhAyAIKAK0AiEKIAgoArACIQ8CQCAGQQZGBEBB0c7FAC0AABpBoAJBCBDWBCIJRQ0EIAhBsAJqIhAgBRD2AiAJQShqIAhB2AJqIhEpAwA3AwAgCUEgaiAIQdACaiISKQMANwMAIAlBGGogCEHIAmoiBikDADcDACAJQRBqIAhBwAJqIgIpAwA3AwAgCUEIaiAIQbgCaiIBKQMANwMAIAkgCCkDsAI3AwAgECAFQQxqEPYCIAlB2ABqIBEpAwA3AwAgCUHQAGogEikDADcDACAJQcgAaiAGKQMANwMAIAlBQGsgAikDADcDACAJQThqIAEpAwA3AwAgCSAIKQOwAjcDMCAQIAVBGGoQ9gIgCUGIAWogESkDADcDACAJQYABaiASKQMANwMAIAlB+ABqIAYpAwA3AwAgCUHwAGogAikDADcDACAJQegAaiABKQMANwMAIAkgCCkDsAI3A2AgECAFQSRqEPYCIAlBuAFqIBEpAwA3AwAgCUGwAWogEikDADcDACAJQagBaiAGKQMANwMAIAlBoAFqIAIpAwA3AwAgCUGYAWogASkDADcDACAJIAgpA7ACNwOQASAQIAVBMGoQ9gIgCUHoAWogESkDADcDACAJQeABaiASKQMANwMAIAlB2AFqIAYpAwA3AwAgCUHQAWogAikDADcDACAJQcgBaiABKQMANwMAIAkgCCkDsAI3A8ABIBAgBUE8ahD2AiAJQZgCaiARKQMANwMAIAlBkAJqIBIpAwA3AwAgCUGIAmogBikDADcDACAJQYACaiACKQMANwMAIAlB+AFqIAEpAwA3AwAgCSAIKQOwAjcD8AEgCEGAgICAeDYC0AcgCEKGgICA4AA3ArQCIAggCTYCsAIgCCAIQdAHajYCvAIgCEGwBWogEBCRAiAIKALQByIFQYCAgIB4RwRAIAgoAtgHIQMgCCgC1AchAiAIKAKwBSIBBEAgCCgCtAUgAUGoAmwQ3wQLIA0gAzYCDCANIAI2AgggDSAFNgIEIA1BATYCACAJQaACEN8EIA9FDQMgCiAPQagCbBDfBAwDCyAIKAK4BQRAIAgoArAFIQUgCEH4BGogCCgCtAUiBkHoAWopAwA3AwAgCEHwBGogBkHgAWopAwA3AwAgCEHoBGogBkHYAWopAwA3AwAgCEHgBGogBkHQAWopAwA3AwAgCEHYBGogBkHIAWopAwA3AwAgCEGIBWogBkH4AWopAwA3AwAgCEGQBWogBkGAAmopAwA3AwAgCEGYBWogBkGIAmopAwA3AwAgCEGgBWogBkGQAmopAwA3AwAgCEGoBWogBkGYAmopAwA3AwAgCCAGKQPAATcD0AQgCCAGKQPwATcDgAUgBi0AoAIhAiAIQfgGaiAGQQhqKQMANwMAIAhBgAdqIAZBEGopAwA3AwAgCEGIB2ogBkEYaikDADcDACAIQZAHaiAGQSBqKQMANwMAIAhBmAdqIAZBKGopAwA3AwAgCEGoB2ogBkE4aikDADcDACAIQbAHaiAGQUBrKQMANwMAIAhBuAdqIAZByABqKQMANwMAIAhBwAdqIAZB0ABqKQMANwMAIAhByAdqIAZB2ABqKQMANwMAIAggBikDADcD8AYgCCAGKQMwNwOgByAIQfgHaiAGQYgBaikDADcDACAIQfAHaiAGQYABaikDADcDACAIQegHaiAGQfgAaikDADcDACAIQeAHaiAGQfAAaikDADcDACAIQdgHaiAGQegAaikDADcDACAIQagIaiAGQbgBaikDADcDACAIQaAIaiAGQbABaikDADcDACAIQZgIaiAGQagBaikDADcDACAIQZAIaiAGQaABaikDADcDACAIQYgIaiAGQZgBaikDADcDACAIIAYpA2A3A9AHIAggBikDkAE3A4AIIAhBsAVqIAhB8AZqQeAA/AoAACAIQZAGaiAIQdAHakHgAPwKAAAgCEHwA2ogCEHQBGpB4AD8CgAAIAhBsAJqIgEgCEGwBWpBwAH8CgAAIAhBCGogAUGgAvwKAAAgCCACOgCoAiAFBEAgBiAFQagCbBDfBAsgCUGgAhDfBAwCC0EAQQBB+I3BABDZAwALIAhBAjoAqAILIA0gCiADIAQgCEEIahAyIA9FDQAgCiAPQagCbBDfBAsgACAWQTBsEN8EIAhBsAhqJAAMAgsgASAKQbyKwQAQyAQAC0EIQaACQbyKwQAQyAQACwwEC0EBQStBrIPBABDIBAALQQFBJ0Gsg8EAEMgEAAtBAUEoQayDwQAQyAQAC0EBQThBrIPBABDIBAALIA5BMGokAAv/BQIJfwF+AkACQAJAAkACQCABKAIAIgcEQAJAIAEoAgQiAyABKAIMIgRGBEAgAyECDAELIAEgA0EMaiICNgIEIAMoAgAiBUGAgICAeEcNAgsgBCACa0EMbiEDIAIgBEcEQANAIAIoAgAiBQRAIAJBBGooAgAgBUECdBDfBAsgAkEMaiECIANBAWsiAw0ACwsgASgCCCICBEAgByACQQxsEN8ECyABQQA2AgALIAEoAiAiAkUNASACIAEoAiRGDQEgASACQRhqNgIgQQAhBUHRzsUALQAAGkEYQQQQ1gQiA0UNAiACKAIIIgdBAnQhBCAHQf////8DSyAEQfz///8HS3INAyACKAIEIQgCfyAERQRAQQQhCUEADAELQdHOxQAtAAAaQQQhBSAEQQQQ1gQiCUUNBCAHCyEFIAQEQCAJIAggBPwKAAALIAIoAhQiCEECdCEGQQAhBCAIQf////8DSyAGQfz///8HS3INBCACKAIQIQoCfyAGRQRAQQQhAkEADAELQdHOxQAtAAAaQQQhBCAGQQQQ1gQiAkUNBSAICyEEIAYEQCACIAogBvwKAAALIAMgCDYCFCADIAI2AhAgAyAENgIMIAMgBzYCCCADIAk2AgQgAyAFNgIAIAEgA0EYajYCDCABQQI2AgggASADNgIAIAEgA0EMajYCBAsgACAFNgIAIAAgAykCBDcCBA8LAkACQAJAIAEoAhAiBARAIAEoAhQiAyABKAIcIgVHDQEgAyECDAILIABBgICAgHg2AgAPCyABIANBDGoiAjYCFCADKQIEIQsgAygCACIDQYCAgIB4Rw0BCyAFIAJrQQxuIQMgAiAFRwRAA0AgAigCACIFBEAgAkEEaigCACAFQQJ0EN8ECyACQQxqIQIgA0EBayIDDQALCyABKAIYIgIEQCAEIAJBDGwQ3wQLIAFBADYCEEGAgICAeCEDCyAAIAs3AgQgACADNgIADwtBBEEYEP8EAAsgBSAEQfiBwAAQyAQACyAEIAZB+IHAABDIBAAL8QUBB38jAEEgayICJAAgACgCACIEKAIEIQMCQAJAAkACQAJAIAQoAggiBQ4CAAECCyACQRBqQbiAxQAoAgA2AgAgAkGwgMUAKQIANwMIDAILIAMoAgAhBkHRzsUALQAAGkEEQQQQ1gQiBUUNAiACQRxqIgdBATYCACAFIAMoAgA2AgAgAiAFNgIYIAJBATYCFCACQRRqIAYQswIgAkEQaiAHKAIANgIAIAIgAikCFDcDCAwBCyACQQhqIAMgBSADIAUQ7QILIAJBFGogAkEIaiAAKAIEIgcoAgAQjAIgAigCCCIDBEAgAigCDCADQQJ0EN8ECyAEKAIAIgMEQCAEKAIEIANBAnQQ3wQLIAQgAikCFDcCACAEQQhqIAJBHGooAgA2AgACQCABBEACQCAAKAIIIgMoAggiAUUNACAEKAIEIQUCQAJAAkAgBCgCCCIADgIAAQILIANBADYCCAwCCyADIAUoAgAQswIMAQsgAygCBCEGIAFBAUYEQEEAIQEgAEH/////A0sgAEECdCIEQfz///8HS3INAyAGKAIAIQgCfyAERQRAQQQhBkEADAELQdHOxQAtAAAaQQQhASAEQQQQ1gQiBkUNBCAACyEBIAQEQCAGIAUgBPwKAAALIAJBHGoiBCAANgIAIAIgBjYCGCACIAE2AhQgAkEUaiAIELMCIAJBEGoiACAEKAIANgIAIAIgAikCFDcDCCADKAIAIgEEQCADKAIEIAFBAnQQ3wQLIAMgAikDCDcCACADQQhqIAAoAgA2AgAMAQsgAkEUaiAGIAEgBSAAEO0CIAMoAgAiAARAIAMoAgQgAEECdBDfBAsgAyACKQIUNwIAIANBCGogAkEcaigCADYCAAsgAkEUaiADIAcoAgAQjAIgAygCACIABEAgAygCBCAAQQJ0EN8ECyADIAIpAhQ3AgAgA0EIaiACQRxqKAIANgIACyACQSBqJAAPCyABIARBpIPFABDIBAALQQRBBEGkg8UAEMgEAAukBQETfyMAQSBrIgkkACACKAIIIg0gASgCCCIEIAQgDUsbIgpBAnQhDCACKAIEIQYgASgCBCEHAkACQAJAIApFDQAgCkEBcQJAIApBAUYEQAwBCyAKQX5xIQ8gBiEDIAchAgNAIAIgAigCACIQIAMoAgAiEWsiEiAIazYCACACQQRqIgUgBSgCACITIANBBGooAgAiFGsiFSAQIBFJIAggEktyIgVrNgIAIBMgFEkgBSAVS3IhCCADQQhqIQMgAkEIaiECIA8gC0ECaiILRw0ACwsEfyAHIAtBAnQiA2oiAiACKAIAIgUgAyAGaigCACIDayICIAhrNgIAIAIgCEkgAyAFS3IFIAgLRQ0AIAcgDGohAiAEQQJ0IApBAnRrIQMDQCADRQ0CIAIgAigCACIFQQFrNgIAIANBBGshAyACQQRqIQIgBUUNAAsLIAYgDGohAyANQQJ0IAxrIQIDQCACRQ0CIAJBBGshAiADKAIAIANBBGohA0UNAAsLIAlBADYCGCAJQQE2AgwgCUHEisUANgIIIAlCBDcCECAJQQhqQcyKxQAQqAQACwJAIARFBEBBACEEDAELIAcgBEECdCICakEEaygCAA0AIAdBBGshBSAEQf////8DcSEDAkADQCACRQRAQQAhAgwCCyADQQFrIQMgAiAFaiACQQRrIQIoAgBFDQALIANBAWoiAiAESw0BCyABIAI2AgggAiEECwJAIAQgASgCACICQQJ2TyACRXJFBEAgAkECdCECAkAgBEUEQEEEIQMgByACEN8EDAELIAcgAkEEIARBAnQiAhDOBCIDRQ0CCyABIAQ2AgAgASADNgIECyAAIAEpAgA3AgAgAEEIaiABQQhqKAIANgIAIAlBIGokAA8LQQQgAkGMwcQAEMgEAAvCCwEFfyMAQSBrIgQkAAJAAkACQAJAAkACQAJAAkACQAJAAkACQCABDigGAQEBAQEBAQECBAEBAwEBAQEBAQEBAQEBAQEBAQEBAQEBCAEBAQEHAAsgAUHcAEYNBAsgAkEBcUUgAUH/BU1yDQcCfwJAQRFBACABQa+wBE8bIgIgAkEIciIDIAFBC3QiAiADQQJ0QdTMxQBqKAIAQQt0SRsiAyADQQRyIgMgA0ECdEHUzMUAaigCAEELdCACSxsiAyADQQJyIgMgA0ECdEHUzMUAaigCAEELdCACSxsiAyADQQFqIgMgA0ECdEHUzMUAaigCAEELdCACSxsiAyADQQFqIgMgA0ECdEHUzMUAaigCAEELdCACSxsiA0ECdEHUzMUAaigCAEELdCIFIAJGIAIgBUtqIANqIgNBIU0EQCADQQJ0QdTMxQBqIgYoAgBBFXYhAkHvBSEFAn8CQCADQSFGDQAgBigCBEEVdiEFIAMNAEEADAELIAZBBGsoAgBB////AHELIQMCQCAFIAJBf3NqRQ0AIAEgA2shB0HvBSACIAJB7wVNGyEGIAVBAWshA0EAIQUDQCACIAZGDQMgBSACQZyvxQBqLQAAaiIFIAdLDQEgAyACQQFqIgJHDQALIAMhAgsgAkEBcQwCCyADQSJBtMrFABDZAwALIAZB7wVBxMrFABDZAwALRQ0HIARBADoACiAEQQA7AQggBCABQRR2QY61xQBqLQAAOgALIAQgAUEEdkEPcUGOtcUAai0AADoADyAEIAFBCHZBD3FBjrXFAGotAAA6AA4gBCABQQx2QQ9xQY61xQBqLQAAOgANIAQgAUEQdkEPcUGOtcUAai0AADoADCABQQFyZ0ECdiICIARBCGoiA2oiBUH7ADoAACAFQQFrQfUAOgAAIAMgAkECayICakHcADoAACAEQRBqIgMgAUEPcUGOtcUAai0AADoAACAAQQo6AAsgACACOgAKIAAgBCkCCDcCACAEQf0AOgARIABBCGogAy8BADsBAAwJCyAAQYAEOwEKIABCADcBAiAAQdzoATsBAAwICyAAQYAEOwEKIABCADcBAiAAQdzkATsBAAwHCyAAQYAEOwEKIABCADcBAiAAQdzcATsBAAwGCyAAQYAEOwEKIABCADcBAiAAQdy4ATsBAAwFCyAAQYAEOwEKIABCADcBAiAAQdzgADsBAAwECyACQYACcUUNASAAQYAEOwEKIABCADcBAiAAQdzOADsBAAwDCyACQf///wdxQYCABE8NAQsCf0EAIAFBIEkNABpBASABQf8ASQ0AGiABQYCABE8EQCABQeD//wBxQeDNCkcgAUH+//8AcUGe8ApHcSABQcDuCmtBeklxIAFBsJ0La0FySXEgAUHw1wtrQXFJcSABQYDwC2tB3mxJcSABQYCADGtBnnRJcSABQdCmDGtBe0lxIAFBgII4a0GwxVRJcSABQfCDOElxIAFBgIAITw0BGiABQeC+xQBBLEG4v8UAQdABQYjBxQBB5gMQ6gIMAQsgAUHuxMUAQShBvsXFAEGiAkHgx8UAQakCEOoCC0UEQCAEQQA6ABYgBEEAOwEUIAQgAUEUdkGOtcUAai0AADoAFyAEIAFBBHZBD3FBjrXFAGotAAA6ABsgBCABQQh2QQ9xQY61xQBqLQAAOgAaIAQgAUEMdkEPcUGOtcUAai0AADoAGSAEIAFBEHZBD3FBjrXFAGotAAA6ABggAUEBcmdBAnYiAiAEQRRqIgNqIgVB+wA6AAAgBUEBa0H1ADoAACADIAJBAmsiAmpB3AA6AAAgBEEcaiIDIAFBD3FBjrXFAGotAAA6AAAgAEEKOgALIAAgAjoACiAAIAQpAhQ3AgAgBEH9ADoAHSAAQQhqIAMvAQA7AQAMAgsgACABNgIEIABBgAE6AAAMAQsgAEGABDsBCiAAQgA3AQIgAEHcxAA7AQALIARBIGokAAvUBQIHfwF+An8gAUUEQCAAKAIIIQdBLSELIAVBAWoMAQtBK0GAgMQAIAAoAggiB0GAgIABcSIBGyELIAFBFXYgBWoLIQgCQCAHQYCAgARxRQRAQQAhAgwBCyADQRBPBEAgAiADENcBIAhqIQgMAQsgA0UNACADQQNxIQoCQCADQQRJBEBBACEBDAELIANBDHEhDEEAIQEDQCABIAIgCWoiBiwAAEG/f0pqIAZBAWosAABBv39KaiAGQQJqLAAAQb9/SmogBkEDaiwAAEG/f0pqIQEgDCAJQQRqIglHDQALCyAKBEAgAiAJaiEGA0AgASAGLAAAQb9/SmohASAGQQFqIQYgCkEBayIKDQALCyABIAhqIQgLAkAgAC8BDCIJIAhLBEACQAJAIAdBgICACHFFBEAgCSAIayEJQQAhAUEAIQgCQAJAAkAgB0EddkEDcUEBaw4DAAEAAgsgCSEIDAELIAlB/v8DcUEBdiEICyAHQf///wBxIQogACgCBCEHIAAoAgAhAANAIAFB//8DcSAIQf//A3FPDQJBASEGIAFBAWohASAAIAogBygCEBECAEUNAAsMBAsgACAAKQIIIg2nQYCAgP95cUGwgICAAnI2AghBASEGIAAoAgAiByAAKAIEIgogCyACIAMQjgQNA0EAIQEgCSAIa0H//wNxIQIDQCABQf//A3EgAk8NAiABQQFqIQEgB0EwIAooAhARAgBFDQALDAMLQQEhBiAAIAcgCyACIAMQjgQNAiAAIAQgBSAHKAIMEQMADQJBACEBIAkgCGtB//8DcSECA0AgAUH//wNxIgMgAkkhBiACIANNDQMgAUEBaiEBIAAgCiAHKAIQEQIARQ0ACwwCCyAHIAQgBSAKKAIMEQMADQEgACANNwIIQQAPC0EBIQYgACgCACIBIAAoAgQiACALIAIgAxCOBA0AIAEgBCAFIAAoAgwRAwAhBgsgBgvNBQIFfwN+IwBBIGsiBCQAAkACQAJAAn8CQAJAIAIoAggiA0UNAAJAIANBAWsiBUH+////A3FFBEAgAigCBCEDIAVB/////wNxIgZBAWoiB0EDcSEFIAZBA08EQCAHQfz///8HcSEGA0AgCEKAAXwhCCADQRBqIQMgBkEEayIGDQALCyAFBEADQCADNQIAIAiGIAl8IQkgCEIgfCEIIANBBGohAyAFQQFrIgUNAAsLIAlCgICAgBBUDQELIARBCGogASACEKEBIABBCGogBEEcaigCADYCACAAIAQpAhQ3AgAgBCgCCCIARQ0GIAQoAgwgAEECdBDfBAwGCyAJUA0AIAEoAgghAiABKAIEIQECQAJAIAlCgIAEWgRAIAJFDQIgAkH/////A2ohBiACQQJ0IQMgAkH/////A3FBAUcNASABIANqDAULIAJFDQEgCachBiABQQRrIQEgAkECdCEDQQAhBQNAIAVBEHQgASADaigCACICQRB2ciAGcEEQdCACQf//A3FyIAZwIQUgA0EEayIDDQALDAULIAEgA2pBCGshAyAGQf////8DcUEBakH+////B3EhBUIAIQgDQCADNQIAIANBBGo1AgAgCEIghoQgCYJCIIaEIAmCIQggA0EIayEDIAVBAmsiBQ0ACwwCCyAEQRBqQYyhxAAoAgA2AgAgBEGEocQAKQIANwMIDAQLIARBADYCGCAEQQE2AgwgBEGUo8QANgIIIARCBDcCECAEQQhqQYSkxAAQqAQACyAIQiCGIQogA0EIagshAyAGQQFxBH4gCAUgCiADQQRrNQIAhCAJggunIQULIARBEGpBjKHEACgCADYCACAEQYShxAApAgA3AwggBUUNACAEQQhqQeiixAAQpQMgBCgCDCAFNgIAIARBATYCEAsgACAEKQMINwIAIABBCGogBEEQaigCADYCAAsgBEEgaiQAC80FAgV/A34jAEEgayIEJAACQAJAAkACfwJAAkAgAigCCCIDRQ0AAkAgA0EBayIFQf7///8DcUUEQCACKAIEIQMgBUH/////A3EiBkEBaiIHQQNxIQUgBkEDTwRAIAdB/P///wdxIQYDQCAIQoABfCEIIANBEGohAyAGQQRrIgYNAAsLIAUEQANAIAM1AgAgCIYgCXwhCSAIQiB8IQggA0EEaiEDIAVBAWsiBQ0ACwsgCUKAgICAEFQNAQsgBEEIaiABIAIQoQEgAEEIaiAEQRxqKAIANgIAIAAgBCkCFDcCACAEKAIIIgBFDQYgBCgCDCAAQQJ0EN8EDAYLIAlQDQAgASgCCCECIAEoAgQhAQJAAkAgCUKAgARaBEAgAkUNAiACQf////8DaiEGIAJBAnQhAyACQf////8DcUEBRw0BIAEgA2oMBQsgAkUNASAJpyEGIAFBBGshASACQQJ0IQNBACEFA0AgBUEQdCABIANqKAIAIgJBEHZyIAZwQRB0IAJB//8DcXIgBnAhBSADQQRrIgMNAAsMBQsgASADakEIayEDIAZB/////wNxQQFqQf7///8HcSEFQgAhCANAIAM1AgAgA0EEajUCACAIQiCGhCAJgkIghoQgCYIhCCADQQhrIQMgBUECayIFDQALDAILIARBEGpBiPrEACgCADYCACAEQYD6xAApAgA3AwgMBAsgBEEANgIYIARBATYCDCAEQYD5xAA2AgggBEIENwIQIARBCGpB8PnEABCoBAALIAhCIIYhCiADQQhqCyEDIAZBAXEEfiAIBSAKIANBBGs1AgCEIAmCC6chBQsgBEEQakGI+sQAKAIANgIAIARBgPrEACkCADcDCCAFRQ0AIARBCGpB9PrEABClAyAEKAIMIAU2AgAgBEEBNgIQCyAAIAQpAwg3AgAgAEEIaiAEQRBqKAIANgIACyAEQSBqJAALzQUCBX8DfiMAQSBrIgQkAAJAAkACQAJ/AkACQCACKAIIIgNFDQACQCADQQFrIgVB/v///wNxRQRAIAIoAgQhAyAFQf////8DcSIGQQFqIgdBA3EhBSAGQQNPBEAgB0H8////B3EhBgNAIAhCgAF8IQggA0EQaiEDIAZBBGsiBg0ACwsgBQRAA0AgAzUCACAIhiAJfCEJIAhCIHwhCCADQQRqIQMgBUEBayIFDQALCyAJQoCAgIAQVA0BCyAEQQhqIAEgAhChASAAQQhqIARBHGooAgA2AgAgACAEKQIUNwIAIAQoAggiAEUNBiAEKAIMIABBAnQQ3wQMBgsgCVANACABKAIIIQIgASgCBCEBAkACQCAJQoCABFoEQCACRQ0CIAJB/////wNqIQYgAkECdCEDIAJB/////wNxQQFHDQEgASADagwFCyACRQ0BIAmnIQYgAUEEayEBIAJBAnQhA0EAIQUDQCAFQRB0IAEgA2ooAgAiAkEQdnIgBnBBEHQgAkH//wNxciAGcCEFIANBBGsiAw0ACwwFCyABIANqQQhrIQMgBkH/////A3FBAWpB/v///wdxIQVCACEIA0AgAzUCACADQQRqNQIAIAhCIIaEIAmCQiCGhCAJgiEIIANBCGshAyAFQQJrIgUNAAsMAgsgBEEQakG4gMUAKAIANgIAIARBsIDFACkCADcDCAwECyAEQQA2AhggBEEBNgIMIARBsP/EADYCCCAEQgQ3AhAgBEEIakGggMUAEKgEAAsgCEIghiEKIANBCGoLIQMgBkEBcQR+IAgFIAogA0EEazUCAIQgCYILpyEFCyAEQRBqQbiAxQAoAgA2AgAgBEGwgMUAKQIANwMIIAVFDQAgBEEIakGkgcUAEKUDIAQoAgwgBTYCACAEQQE2AhALIAAgBCkDCDcCACAAQQhqIARBEGooAgA2AgALIARBIGokAAvdBQIRfwZ+IwBBwA1rIgIkACACIAEgAUGgAmoiBRC5AiACQaACaiABIAUQ1QEgAkGAA2ogAUHgAGoiByABQYADahDVASACQeADaiABQcABaiIIIAFB4ANqENUBIAJBiAdqIglB8IPAACkDACITNwMAIAJBgAdqIgpB6IPAACkDACIUNwMAIAJB+AZqIgtB4IPAACkDACIVNwMAIAJB8AZqIgxB2IPAACkDACIWNwMAIAJB6AZqIg1B0IPAACkDACIXNwMAIAJBmAdqIg5CADcDACACQaAHaiIPQgA3AwAgAkGoB2oiEEIANwMAIAJBsAdqIhFCADcDACACQbgHaiISQgA3AwAgAkHIg8AAKQMAIhg3A+AGIAJCADcDkAdBAEUEQCACQYAJakEAQeAA/AsACyADRQRAIAJB4AlqIAJB4AZqQeAA/AoAAAsgA0UEQCACQcAKakEAQeAA/AsACyACQeAGaiIEIAJBgAlqIAUQuQIgAkHABGoiBiABIAQQ1QEgAkGgBWoiASAHIAJBwAdqIgUQ1QEgAkGABmoiByAIIAJBoAhqIggQ1QEgBCACQaACaiAGELkCIAYgBCACEI0BIAEgBSACQeAAaiIEEI0BIAcgCCACQcABaiIGEI0BIAkgEzcDACAKIBQ3AwAgCyAVNwMAIAwgFjcDACANIBc3AwAgDkIANwMAIA9CADcDACAQQgA3AwAgEUIANwMAIBJCADcDACACIBg3A+AGIAJCADcDkAcgA0UEQCACQaALakEAQeAA/AsACyADRQRAIAJBgAxqIAJB4AZqQeAA/AoAAAsgA0UEQCACQeAMakEAQeAA/AsACyACQeAGaiIDIAJBoAtqIAIQuQIgACACQcAEaiADEI0BIABB4ABqIAEgBRCNASAAQcABaiAHIAgQjQEgAEGgAmogAiACENUBIABBgANqIAQgBBDVASAAQeADaiAGIAYQ1QEgAkHADWokAAuLBQIJfwJ+IwBBkANrIgUkAAJAAkACQCABKAIIRQRAQdHOxQAtAAAaQQEhBEEBQQEQ1gQiBkUNAiAGQQA6AAAgBUEBNgIEDAELIAVBBGogAUEIELACIAUoAgghBiAFKAIMIgRBAkkNACAEIAZqIQlBACEBIARBAXYiAkEBRwRAIARBAWshByACQf7///8HcSEIA0AgBiAHaiIDLQAAIQIgAyABIAZqIgotAAA6AAAgCiACOgAAIAkgAUF+c2oiAi0AACEDIAIgCkEBaiICLQAAOgAAIAIgAzoAACAHQQJrIQcgCCABQQJqIgFHDQALCyAEQQJxBEAgASAGaiIDLQAAIQIgAyAJIAFBf3NqIgEtAAA6AAAgASACOgAACyAEQaECTw0CC0EAIQEgBUEQakEAQYAD/AsAQRghCANAIAEhA0IAIQtCACEMAkAgBCICIAJBDGsiAUEAIAEgAk0bIgRGDQAgBCAGaiEBQQwgAiACQQxPGyICQQNxIQcCQCACQQFrQQNJBEAMAQsgAkEMcSECA0AgC0IgiEKAgPz/D4MgDEIghoQgC0IQhiILQjCIhCEMIAFBA2oxAAAgAUEBajEAACALIAExAABCCIaEhEIQhiABQQJqMQAAQgiGhIQhCyABQQRqIQEgAkEEayICDQALCyAHRQ0AA0AgDEIIhiALQjiIhCEMIAExAAAgC0IIhoQhCyABQQFqIQEgB0EBayIHDQALCyADQRBqIQEgAyAFQRBqIgNqIgIgCzcDACACIAw3AwggCEEBayIIDQALIAAgA0GAA/wKAAAgBSgCBCIABEAgBiAAEN8ECyAFQZADaiQADwtBAUEBEP8EAAtB1NrCAEEtQYTbwgAQ/gMAC9UFAQd/IwBB0ANrIgIkACACQeACaiIDIAEgASgCDBCpAgJAAkACQAJAAkAgAi0AwAMiBEEDRg0AIAJBgAJqIgUgA0HgAPwKAAAgAiACQcQDaigAADYAmwEgAiACKADBAzYCmAEgBEECRg0AIAJBIGogBUHgAPwKAAAgAiACKACbATYAGyACIAIoApgBNgIYAkAgASgCDCgCAEGAgICAeEcNACABKAIERQ0AIAEoAghFDQMLQdHOxQAtAAAaQaADQQgQ1gQiA0UNAyADIAJBIGpB4AD8CgAAIAMgBDoAYCADIAIoAhg2AGEgA0HkAGogAigAGzYAACACQQE2AhQgAiADNgIQIAJBBDYCDCACQYgBaiABQQhqKQIANwMAIAIgASkCADcDgAEgAkHgAmogAkGAAWogAigCjAEQqQICQCACLQDAAyIFQQNGDQBByQEhBiACQcEDaiIHQQNqIQhBASEBA0AgAkGAAmoiBCACQeACakHgAPwKAAAgAiAIKAAANgD7ASACIAcoAAA2AvgBIAVBAkYNASACQZgBaiAEQeAA/AoAACACIAIoAPsBNgCTASACIAIoAvgBNgKQASACKAIMIAFGBEACQCACKAKMASgCAEGAgICAeEcNACACKAKEAUUNACACKAKIAUUNCAsgAkEMaiABQQFBCEHoABCIAyACKAIQIQMLIAMgBmoiBEHhAGsgAkGYAWpB4AD8CgAAIARBAWsgBToAACAEIAIoApABNgAAIARBA2ogAigAkwE2AAAgAiABQQFqIgE2AhQgAkHgAmogAkGAAWogAigCjAEQqQIgBkHoAGohBiACLQDAAyIFQQNHDQALCyAAQQhqIAJBFGooAgA2AgAgACACKQIMNwIADAELIABBADYCCCAAQoCAgICAATcCAAsgAkHQA2okAA8LQbSbwgAQmgQAC0EIQaADQZCWwgAQyAQAC0G0m8IAEJoEAAvXBQEHfyMAQdAGayICJAAgAkGABWoiAyABIAEoAgwQmAECQAJAAkACQAJAIAItAMAGIgRBA0YNACACQcADaiIFIANBwAH8CgAAIAIgAkHEBmooAAA2APsBIAIgAigAwQY2AvgBIARBAkYNACACQSBqIAVBwAH8CgAAIAIgAigA+wE2ABsgAiACKAL4ATYCGAJAIAEoAgwoAgBBgICAgHhHDQAgASgCBEUNACABKAIIRQ0DC0HRzsUALQAAGkGgBkEIENYEIgNFDQMgAyACQSBqQcAB/AoAACADIAQ6AMABIAMgAigCGDYAwQEgA0HEAWogAigAGzYAACACQQE2AhQgAiADNgIQIAJBBDYCDCACQegBaiABQQhqKQIANwMAIAIgASkCADcD4AEgAkGABWogAkHgAWogAigC7AEQmAECQCACLQDABiIFQQNGDQBBiQMhBiACQcEGaiIHQQNqIQhBASEBA0AgAkHAA2oiBCACQYAFakHAAfwKAAAgAiAIKAAANgC7AyACIAcoAAA2ArgDIAVBAkYNASACQfgBaiAEQcAB/AoAACACIAIoALsDNgDzASACIAIoArgDNgLwASACKAIMIAFGBEACQCACKALsASgCAEGAgICAeEcNACACKALkAUUNACACKALoAUUNCAsgAkEMaiABQQFBCEHIARCIAyACKAIQIQMLIAMgBmoiBEHBAWsgAkH4AWpBwAH8CgAAIARBAWsgBToAACAEIAIoAvABNgAAIARBA2ogAigA8wE2AAAgAiABQQFqIgE2AhQgAkGABWogAkHgAWogAigC7AEQmAEgBkHIAWohBiACLQDABiIFQQNHDQALCyAAQQhqIAJBFGooAgA2AgAgACACKQIMNwIADAELIABBADYCCCAAQoCAgICAATcCAAsgAkHQBmokAA8LQbSbwgAQmgQAC0EIQaAGQZCWwgAQyAQAC0G0m8IAEJoEAAvXBQEHfyMAQdAJayICJAAgAkGgB2oiAyABIAEoAgwQrAECQAJAAkACQAJAIAItAMAJIgRBA0YNACACQYAFaiIFIANBoAL8CgAAIAIgAkHECWooAAA2ANsCIAIgAigAwQk2AtgCIARBAkYNACACQSBqIAVBoAL8CgAAIAIgAigA2wI2ABsgAiACKALYAjYCGAJAIAEoAgwoAgBBgICAgHhHDQAgASgCBEUNACABKAIIRQ0DC0HRzsUALQAAGkGgCUEIENYEIgNFDQMgAyACQSBqQaAC/AoAACADIAQ6AKACIAMgAigCGDYAoQIgA0GkAmogAigAGzYAACACQQE2AhQgAiADNgIQIAJBBDYCDCACQcgCaiABQQhqKQIANwMAIAIgASkCADcDwAIgAkGgB2ogAkHAAmogAigCzAIQrAECQCACLQDACSIFQQNGDQBByQQhBiACQcEJaiIHQQNqIQhBASEBA0AgAkGABWoiBCACQaAHakGgAvwKAAAgAiAIKAAANgD7BCACIAcoAAA2AvgEIAVBAkYNASACQdgCaiAEQaAC/AoAACACIAIoAPsENgDTAiACIAIoAvgENgLQAiACKAIMIAFGBEACQCACKALMAigCAEGAgICAeEcNACACKALEAkUNACACKALIAkUNCAsgAkEMaiABQQFBCEGoAhCIAyACKAIQIQMLIAMgBmoiBEGhAmsgAkHYAmpBoAL8CgAAIARBAWsgBToAACAEIAIoAtACNgAAIARBA2ogAigA0wI2AAAgAiABQQFqIgE2AhQgAkGgB2ogAkHAAmogAigCzAIQrAEgBkGoAmohBiACLQDACSIFQQNHDQALCyAAQQhqIAJBFGooAgA2AgAgACACKQIMNwIADAELIABBADYCCCAAQoCAgICAATcCAAsgAkHQCWokAA8LQbSbwgAQmgQAC0EIQaAJQZCWwgAQyAQAC0G0m8IAEJoEAAvQBQIGfwJ+AkAgAkUNACACQQdrIgNBACACIANPGyEHIAFBA2pBfHEgAWshCEEAIQMDQAJAAkACQCABIANqLQAAIgXAIgZBAE4EQCAIIANrQQNxDQEgAyAHTw0CA0AgASADaiIEQQRqKAIAIAQoAgByQYCBgoR4cQ0DIANBCGoiAyAHSQ0ACwwCC0KAgICAgCAhCkKAgICAECEJAkACQAJ+AkACQAJAAkACQAJAAkACQAJAIAVBp7rFAGotAABBAmsOAwABAgoLIANBAWoiBCACSQ0CQgAhCkIAIQkMCQtCACEKIANBAWoiBCACSQ0CQgAhCQwIC0IAIQogA0EBaiIEIAJJDQJCACEJDAcLIAEgBGosAABBv39KDQYMBwsgASAEaiwAACEEAkACQCAFQeABayIFBEAgBUENRgRADAIFDAMLAAsgBEFgcUGgf0YNBAwDCyAEQZ9/Sg0CDAMLIAZBH2pB/wFxQQxPBEAgBkF+cUFuRw0CIARBQEgNAwwCCyAEQUBIDQIMAQsgASAEaiwAACEEAkACQAJAAkAgBUHwAWsOBQEAAAACAAsgBkEPakH/AXFBAksgBEFATnINAwwCCyAEQfAAakH/AXFBME8NAgwBCyAEQY9/Sg0BCyACIANBAmoiBE0EQEIAIQkMBQsgASAEaiwAAEG/f0oNAkIAIQkgA0EDaiIEIAJPDQQgASAEaiwAAEFASA0FQoCAgICA4AAMAwtCgICAgIAgDAILQgAhCSADQQJqIgQgAk8NAiABIARqLAAAQb9/TA0DC0KAgICAgMAACyEKQoCAgIAQIQkLIAAgCiADrYQgCYQ3AgQgAEEBNgIADwsgBEEBaiEDDAILIANBAWohAwwBCyACIANNDQADQCABIANqLAAAQQBIDQEgAiADQQFqIgNHDQALDAILIAIgA0sNAAsLIAAgAjYCCCAAIAE2AgQgAEEANgIAC4EGAQV/IABBCGsiASAAQQRrKAIAIgNBeHEiAGohAgJAAkAgA0EBcQ0AIANBAnFFDQEgASgCACIDIABqIQAgASADayIBQZjSxQAoAgBGBEAgAigCBEEDcUEDRw0BQZDSxQAgADYCACACIAIoAgRBfnE2AgQgASAAQQFyNgIEIAIgADYCAA8LIAEgAxDgAgsCQAJAAkACQAJAIAIoAgQiA0ECcUUEQCACQZzSxQAoAgBGDQIgAkGY0sUAKAIARg0DIAIgA0F4cSICEOACIAEgACACaiIAQQFyNgIEIAAgAWogADYCACABQZjSxQAoAgBHDQFBkNLFACAANgIADwsgAiADQX5xNgIEIAEgAEEBcjYCBCAAIAFqIAA2AgALIABBgAJJDQIgASAAEPsCQQAhAUGw0sUAQbDSxQAoAgBBAWsiADYCACAADQRB+M/FACgCACIABEADQCABQQFqIQEgACgCCCIADQALC0Gw0sUAQf8fIAEgAUH/H00bNgIADwtBnNLFACABNgIAQZTSxQBBlNLFACgCACAAaiIANgIAIAEgAEEBcjYCBEGY0sUAKAIAIAFGBEBBkNLFAEEANgIAQZjSxQBBADYCAAsgAEGo0sUAKAIAIgNNDQNBnNLFACgCACICRQ0DQQAhAEGU0sUAKAIAIgRBKUkNAkHwz8UAIQEDQCACIAEoAgAiBU8EQCACIAUgASgCBGpJDQQLIAEoAgghAQwACwALQZjSxQAgATYCAEGQ0sUAQZDSxQAoAgAgAGoiADYCACABIABBAXI2AgQgACABaiAANgIADwsgAEH4AXFBgNDFAGohAgJ/QYjSxQAoAgAiA0EBIABBA3Z0IgBxRQRAQYjSxQAgACADcjYCACACDAELIAIoAggLIQAgAiABNgIIIAAgATYCDCABIAI2AgwgASAANgIIDwtB+M/FACgCACIBBEADQCAAQQFqIQAgASgCCCIBDQALC0Gw0sUAQf8fIAAgAEH/H00bNgIAIAMgBE8NAEGo0sUAQX82AgALC4gFAgF/CH4jAEGgAWsiAiQAIAJBMGogASkDGCIEQgBC/////w9CABDJAyACQUBrIARCAEKBgICAcEIAEMkDIAIgBCABKQMQIgN8IgUgAikDMHwiBEIAQoGAgIBwQgAQyQMgAkEQaiAEQiCGIgcgBCAFVK0gAikDOCADIAVWrXx8IgYgASkDCHwiCHwiBUIAQoGAgIBwQgAQyQMgAkEgaiAFQiCGIgkgBSAHVK0gBEIgiHwiByACKQNAIgogASkDAHwiAyAGIAhWrXwiBnwiCHwiBEIAQoGAgIBwQgAQyQMCQCACKQMoIAIpAxggAikDCCADIAZWrSACKQNIIAMgClStfHwiBiACKQMAfCIDIAZUrXwgAyAHIAhWrXwiByADVK18IgYgAikDEHwiAyAGVK18IAMgAyAEIAlUrSAFQiCIfCIFIAd8IgcgBVStfCIDVq18IgYgAikDIHwiBSAGVK18IAUgAyAEQiCGIgMgB3wiBiADVK0gBEIgiHwiA3wiBCADVK18IgMgBVStfCIIQoGAgIBwVARAIAQhBSADIQcMAQsCQCAEQv////8PVg0AQgAhByADQgBSDQBC/////w8hBSAEQv////8PVARAIAQhBUKBgICAcCEIDAILIAZCf1ENAEKBgICAcCEIDAELIARC/////w99IgcgBkJ/Uq0iCX0hBSADIARC/////w9UIAcgCVRyrSIEfSEHIAggAyAEVK19Qv////8PfCEIIAZCAXwhBgsgAiAGNwNoIAIgBTcDYCACIAc3A1ggAiAINwNQIAIgAkHwAGoiATYCnAEgAkEANgKEASACQQA2AnAgAiACQdAAajYCmAEgACABEK0CIAJBoAFqJAAL4gQBBn8CQAJAIAAoAggiB0GAgIDAAXFFDQACQAJAIAdBgICAgAFxRQRAIAJBEEkNASABIAIQ1wEhAwwCCwJAAkAgAC8BDiIDRQRAQQAhAgwBCyABIAJqIQhBACECIAMhBSABIQQDQCAEIgYgCEYNAgJ/IAZBAWogBiwAACIEQQBODQAaIAZBAmogBEFgSQ0AGiAGQQNqIARBcEkNABogBkEEagsiBCAGayACaiECIAVBAWsiBQ0ACwtBACEFCyADIAVrIQMMAQsgAkUEQEEAIQIMAQsgAkEDcSEGAkAgAkEESQRADAELIAJBDHEhCANAIAMgASAFaiIELAAAQb9/SmogBEEBaiwAAEG/f0pqIARBAmosAABBv39KaiAEQQNqLAAAQb9/SmohAyAIIAVBBGoiBUcNAAsLIAZFDQAgASAFaiEEA0AgAyAELAAAQb9/SmohAyAEQQFqIQQgBkEBayIGDQALCyADIAAvAQwiBE8NACAEIANrIQZBACEDQQAhBQJAAkACQCAHQR12QQNxQQFrDgIAAQILIAYhBQwBCyAGQf7/A3FBAXYhBQsgB0H///8AcSEIIAAoAgQhByAAKAIAIQADQCADQf//A3EgBUH//wNxSQRAQQEhBCADQQFqIQMgACAIIAcoAhARAgBFDQEMAwsLQQEhBCAAIAEgAiAHKAIMEQMADQFBACEDIAYgBWtB//8DcSEBA0AgA0H//wNxIgIgAUkhBCABIAJNDQIgA0EBaiEDIAAgCCAHKAIQEQIARQ0ACwwBCyAAKAIAIAEgAiAAKAIEKAIMEQMAIQQLIAQLkgUCCX8BfiMAQSBrIgQkACABKAIEIQIgASgCDCEGIAEoAhAhBQJAA0ACQCACIAZHBEAgASACQQRqIgM2AgQgBEEUaiACKAIAEOwCIAQpAhghCyAEKAIUIgdBgICAgHhHDQEgC6chBwJAIAUoAgBFDQAgBSgCBCIDQYQBSQ0AIAMQqwMLIAUgBzYCBCAFQQE2AgAgAkEEaiECCyAAQQA2AgggAEKAgICAwAA3AgAgAiAGRwRAIAYgAmtBAnYhAwNAIAIoAgAiAEGEAU8EQCAAEKsDCyACQQRqIQIgA0EBayIDDQALCyABKAIIIgBFDQIgASgCACAAQQJ0EN8EDAILIAMhAiAHQYGAgIB4Rg0AC0HRzsUALQAAGkEwQQQQ1gQiAgRAIAIgCzcCBCACIAc2AgAgBEEBNgIQIAQgAjYCDCAEQQQ2AgggASgCCCEIIAEoAgAhCkEBIQEDQAJAIAMgBkcEQCAEQRRqIAMoAgAQ7AIgBCkCGCELIAQoAhQiCUGAgICAeEcNASALpyECAkAgBSgCAEUNACAFKAIEIgFBhAFJDQAgARCrAwsgBSACNgIEIAVBATYCACADQQRqIQMLIAMgBkcEQCAGIANrQQJ2IQIDQCADKAIAIgFBhAFPBEAgARCrAwsgA0EEaiEDIAJBAWsiAg0ACwsgCARAIAogCEECdBDfBAsgACAEKQIINwIAIABBCGogBEEQaigCADYCAAwDCyADQQRqIQMgCUGBgICAeEYNACAEKAIIIAFGBEAgBEEIaiABQQFBBEEMEIgDIAQoAgwhAgsgAiABQQxsaiIHIAs3AgQgByAJNgIAIAQgAUEBaiIBNgIQDAALAAtBBEEwQfCAwAAQyAQACyAEQSBqJAALiwUBB38jAEEgayIDJABBASEJQQEhBgJAIAEtAAwiBUEBRg0AAkACQAJAAkAgAi0ADCIGQQFrDgIEAQALIAUNAQwCCyAFDQELQQAhCUEAIQYMAQtBAiEGQQAhCQsCQAJAAkACQCABKAIIIgUEQCACKAIIIgQNAQsgA0EQakG4zMIAKAIANgIAIANBsMzCACkCADcDCAwBCyACKAIEIQcgASgCBCEIIARBAUYEQEEAIQEgBUH/////A0sgBUECdCIEQfz///8HS3INAiAHKAIAIQcCfyAERQRAQQQhAkEADAELQdHOxQAtAAAaQQQhASAEQQQQ1gQiAkUNAyAFCyEBIAQEQCACIAggBPwKAAALIANBHGoiBCAFNgIAIAMgAjYCGCADIAE2AhQgA0EUaiAHELMCIANBEGogBCgCADYCACADIAMpAhQ3AwgMAQsgBUEBRgRAQQAhASAEQf////8DSyAEQQJ0IgJB/P///wdLcg0DIAgoAgAhCAJ/IAJFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEBIAJBBBDWBCIFRQ0EIAQLIQEgAgRAIAUgByAC/AoAAAsgA0EcaiICIAQ2AgAgAyAFNgIYIAMgATYCFCADQRRqIAgQswIgA0EQaiACKAIANgIAIAMgAykCFDcDCAwBCyADQQhqIAggBSAHIAQQ7QILAkAgCUUEQCAGQQEgAygCEBshBgwBCyADQQA2AhAgAygCCCIBQQRJDQAgAygCDCABQQJ0EN8EIANCgICAgMAANwMICyAAIAMpAwg3AgAgACAGOgAMIABBCGogA0EQaigCADYCACADQSBqJAAPCyABIARB+IHAABDIBAALIAEgAkH4gcAAEMgEAAv7BAEGfyMAQSBrIgUkAAJ/IAEoAgAiAwRAIAEoAgQhAiABKAIMIQZBAAwBC0EBCyEEA0ACQAJAAkAgBEUEQCACIAZHDQEgASgCCCIEBEAgAyAEQQV0EN8ECyABQQA2AgBBASEEDAQLAkAgASgCICIERQ0AIAEoAiQiAiABKAIoTw0AIAEgAkEBajYCJAJAAkAgBCgCCCIGIAJLBEBBACEGAkAgBCgCBCACQQxsaiIHKAIIIgRB////P0sNACAEQQV0IgJB+P///wdLDQBBCCEDIAJFDQMgBygCBCEHQdHOxQAtAAAaQQghBiACQQgQ1gQiAw0CIAIhAwsgBiADQfiBwAAQyAQACyACIAZByILAABDZAwALIAJFDQAgAyAHIAL8CgAACyABIAQ2AgggASADNgIEIAEgAzYCACABIAMgBEEFdGoiBjYCDCADIQIMAgsgAAJ+AkAgASgCECICBEAgASgCFCIDIAEoAhxGDQEgASADQSBqNgIUIAVBCGogA0EIaikDADcDACAFQRBqIANBEGopAwA3AwAgBUEYaiADQRhqKQMANwMAIAUgAykDADcDAEIBDAILIABCADcDAAwECyABKAIYIgMEQCACIANBBXQQ3wQLIAFBADYCEEIACzcDACAAIAUpAwA3AwggAEEQaiAFQQhqKQMANwMAIABBGGogBUEQaikDADcDACAAQSBqIAVBGGopAwA3AwAMAgsgASACQSBqNgIEIAAgAikDADcDCCAAQRBqIAJBCGopAwA3AwAgAEEYaiACQRBqKQMANwMAIABBIGogAkEYaikDADcDACAAQgE3AwAMAQtBACEEDAELCyAFQSBqJAALrAQCB38BfiMAQeAGayICJAAgAkGABmoiA0EAQeAA/AsAAkACQCABQcABaiIEIAMQpgRFBEAgAyABQeAAahBeIAJBgANqIAMgBBA/IAJB4ANqIAEQXkEARQRAIAJBoAVqQQBB4AD8CwALIAJBgAZqIgMgBBBeIAJBwARqIgUgAkGgBWoiBiADED8gAyACQeADaiIHIAUQ1QEgByADIAEQPyAGEO4DIAMgBBBeIAUgBiADED8gAyAFIAQQPyAGIAcgAxDVASAFIAJBgANqIAYQjQEgCEUEQCADQQBB4AD8CwALIAJBwARqIAJBgAZqEKYEDQELIAJBgAZqIgNBAEHgAPwLAEIBIQkgASADEKYERQ0BIANBAEHgAPwLACAEIAMQpgRFDQFBACIBRQRAIAJBAEHgAPwLAAsgAkHYAmpCADcDACACQeACakIANwMAIAJB6AJqQgA3AwAgAkHwAmpCADcDACACQfgCakIANwMAIAJByAJqQeC0wgApAwA3AwAgAkHAAmpB2LTCACkDADcDACACQbgCakHQtMIAKQMANwMAIAJBsAJqQci0wgApAwA3AwAgAkGoAmpBwLTCACkDADcDACACQgA3A9ACIAJBuLTCACkDADcDoAIgAUUEQCACQcABakEAQeAA/AsACyABRQRAIAJB4ABqIAJBoAJqQeAA/AoAAAsgAiEBCyAAQQhqIAFBoAL8CgAAQgAhCQsgACAJNwMAIAJB4AZqJAALxgQBC38jAEEQayIGJAAgAC0ADCEKAkACQAJAAkAgACgCCEUEQEHRzsUALQAAGkEBIQJBAUEBENYEIgMNAUEBQQEQ/wQACyAGQQRqIABBChBAIAYoAgghAyAGKAIMIgUEQCADIQAgBUEDcSICBEADQCAAIAAtAAAiB0EwciAHQdcAaiAHQQpJGzoAACAAQQFqIQAgAkEBayICDQALCyADIAVqIQcgBUEETwRAA0AgACAALQAAIgJBMHIgAkHXAGogAkEKSRs6AAAgAEEBaiICIAItAAAiAkEwciACQdcAaiACQQpJGzoAACAAQQJqIgIgAi0AACICQTByIAJB1wBqIAJBCkkbOgAAIABBA2oiAiACLQAAIgJBMHIgAkHXAGogAkEKSRs6AAAgAEEEaiIAIAdHDQALCyAGKAIEIQIgBUEBRg0CQQAhACAFQQF2IgRBAUcEQCAFQQFrIQggBEH+////B3EhCwNAIAMgCGoiBC0AACEJIAQgACADaiIELQAAOgAAIAQgCToAACAHIABBfnNqIgktAAAhDCAJIARBAWoiBC0AADoAACAEIAw6AAAgCEECayEIIAsgAEECaiIARw0ACwsgBUECcUUNAiAAIANqIggtAAAhBCAIIAcgAEF/c2oiAC0AADoAACAAIAQ6AAAMAgsgBigCBCECDAELIANBMDoAACABIApBAEdBAUEAIANBARCJAiEADAELIAEgCkEAR0EBQQAgAyAFEIkCIQAgAkUNAQsgAyACEN8ECyAGQRBqJAAgAAvkBAEIfyMAQcANayIDJAAgA0GoCWpB8IPAACkDADcDACADQaAJakHog8AAKQMANwMAIANBmAlqQeCDwAApAwA3AwAgA0GQCWpB2IPAACkDADcDACADQYgJakHQg8AAKQMANwMAIANBuAlqQgA3AwAgA0HACWpCADcDACADQcgJakIANwMAIANB0AlqQgA3AwAgA0HYCWpCADcDACADQgA3A7AJIANByIPAACkDADcDgAlBAEUEQCADQaALakEAQeAA/AsACyAERQRAIANBgAxqIANBgAlqQeAA/AoAAAsgBEUEQCADQeAMakEAQeAA/AsACyADIAEgAhC5AiADQaACaiIIIAFBoAJqIgQgAkGgAmoiCRC5AiADQeAGaiIKIAEgBBDVASADQcAHaiIGIAFB4ABqIAFBgANqENUBIANBoAhqIgcgAUHAAWogAUHgA2oQ1QEgA0GACWoiBSACIAkQ1QEgA0HgCWoiASACQeAAaiACQYADahDVASADQcAKaiIEIAJBwAFqIAJB4ANqENUBIANBwARqIAogBRC5AiAFIAggA0GgC2oQuQIgACADIAUQ1QEgAEHgAGogA0HgAGogARDVASAAQcABaiADQcABaiAEENUBQQAiAkUEQCAFIANBoAL8CgAACyADQeAGaiADQcAEaiADQYAJaiIFEI0BIAYgA0GgBWogARCNASAHIANBgAZqIAQQjQEgAkUEQCAFIANBoAJqQaAC/AoAAAsgAEGgAmogA0HgBmogA0GACWoQjQEgAEGAA2ogBiABEI0BIABB4ANqIAcgBBCNASADQcANaiQAC8MEAgd/A34jAEEgayIFJAACfwJAAn8CQAJ/AkAgAgRAIAEoAgghBCABKAIEIQggAS0ADCEJAkACQCACQYCABE8EQCAERQ0CIARB/////wNqIQcgBEECdCEGIAKtIQsgBEH/////A3FBAUcNASAGIAhqDAULIARFDQEgCEEEayEHIARBAnQhAwNAIAZBEHQgAyAHaigCACIEQRB2ciACcEEQdCAEQf//A3FyIAJwIQYgA0EEayIDDQALDAULIAYgCGpBCGshAyAHQf////8DcUEBakH+////B3EhAgNAIAM1AgAgA0EEajUCACAKQiCGhCALgkIghoQgC4IhCiADQQhrIQMgAkECayICDQALDAILQQQMBAsgBUEANgIYIAVBATYCDCAFQYScwAA2AgggBUIENwIQIAVBCGpB9JzAABCoBAALIApCIIYhDCADQQhqCyEDIAdBAXEEfiAKBSAMIANBBGs1AgCEIAuCC6chBgtBACEDIAVBEGpB3JrAACgCADYCACAFQdSawAApAgA3AwggBg0BQQQLIQRBASEHQQAMAQsgBUEIakHIm8AAEKUDIAUoAgwgBjYCAEEBIQMgBSgCDCEEIAkhByAFKAIICyECIAEoAgAiAQRAIAggAUECdBDfBAtBASEGAkAgCUEBRwRAIAQhASAHIQYMAQtBBCEBQQAhAyACQQRJBEAgBCEBDAELIAQgAkECdBDfBEEAIQILIAAgBjoADCAAIAM2AgggACABNgIEIAAgAjYCACAFQSBqJAALwwQCB38DfiMAQSBrIgUkAAJ/AkACfwJAAn8CQCACBEAgASgCCCEEIAEoAgQhCCABLQAMIQkCQAJAIAJBgIAETwRAIARFDQIgBEH/////A2ohByAEQQJ0IQYgAq0hCyAEQf////8DcUEBRw0BIAYgCGoMBQsgBEUNASAIQQRrIQcgBEECdCEDA0AgBkEQdCADIAdqKAIAIgRBEHZyIAJwQRB0IARB//8DcXIgAnAhBiADQQRrIgMNAAsMBQsgBiAIakEIayEDIAdB/////wNxQQFqQf7///8HcSECA0AgAzUCACADQQRqNQIAIApCIIaEIAuCQiCGhCALgiEKIANBCGshAyACQQJrIgINAAsMAgtBBAwECyAFQQA2AhggBUEBNgIMIAVBhNHCADYCCCAFQgQ3AhAgBUEIakH00cIAEKgEAAsgCkIghiEMIANBCGoLIQMgB0EBcQR+IAoFIAwgA0EEazUCAIQgC4ILpyEGC0EAIQMgBUEQakG4zMIAKAIANgIAIAVBsMzCACkCADcDCCAGDQFBBAshBEEBIQdBAAwBCyAFQQhqQaTNwgAQpQMgBSgCDCAGNgIAQQEhAyAFKAIMIQQgCSEHIAUoAggLIQIgASgCACIBBEAgCCABQQJ0EN8EC0EBIQYCQCAJQQFHBEAgBCEBIAchBgwBC0EEIQFBACEDIAJBBEkEQCAEIQEMAQsgBCACQQJ0EN8EQQAhAgsgACAGOgAMIAAgAzYCCCAAIAE2AgQgACACNgIAIAVBIGokAAvkBAEIfyMAQcANayIDJAAgA0GoCWpB0JzFACkDADcDACADQaAJakHInMUAKQMANwMAIANBmAlqQcCcxQApAwA3AwAgA0GQCWpBuJzFACkDADcDACADQYgJakGwnMUAKQMANwMAIANBuAlqQgA3AwAgA0HACWpCADcDACADQcgJakIANwMAIANB0AlqQgA3AwAgA0HYCWpCADcDACADQgA3A7AJIANBqJzFACkDADcDgAlBAEUEQCADQaALakEAQeAA/AsACyAERQRAIANBgAxqIANBgAlqQeAA/AoAAAsgBEUEQCADQeAMakEAQeAA/AsACyADIAEgAhC5AiADQaACaiIIIAFBoAJqIgQgAkGgAmoiCRC5AiADQeAGaiIKIAEgBBDVASADQcAHaiIGIAFB4ABqIAFBgANqENUBIANBoAhqIgcgAUHAAWogAUHgA2oQ1QEgA0GACWoiBSACIAkQ1QEgA0HgCWoiASACQeAAaiACQYADahDVASADQcAKaiIEIAJBwAFqIAJB4ANqENUBIANBwARqIAogBRC5AiAFIAggA0GgC2oQuQIgACADIAUQ1QEgAEHgAGogA0HgAGogARDVASAAQcABaiADQcABaiAEENUBQQAiAkUEQCAFIANBoAL8CgAACyADQeAGaiADQcAEaiADQYAJaiIFEI0BIAYgA0GgBWogARCNASAHIANBgAZqIAQQjQEgAkUEQCAFIANBoAJqQaAC/AoAAAsgAEGgAmogA0HgBmogA0GACWoQjQEgAEGAA2ogBiABEI0BIABB4ANqIAcgBBCNASADQcANaiQAC74EAQp/IwBBEGsiBiQAAkACQAJAAkAgACgCACIAKAIIRQRAQdHOxQAtAAAaQQEhAkEBQQEQ1gQiAw0BQQFBARD/BAALIAZBBGogAEEKEEAgBigCCCEDIAYoAgwiBQRAIAMhACAFQQNxIgIEQANAIAAgAC0AACIHQTByIAdB1wBqIAdBCkkbOgAAIABBAWohACACQQFrIgINAAsLIAMgBWohByAFQQRPBEADQCAAIAAtAAAiAkEwciACQdcAaiACQQpJGzoAACAAQQFqIgIgAi0AACICQTByIAJB1wBqIAJBCkkbOgAAIABBAmoiAiACLQAAIgJBMHIgAkHXAGogAkEKSRs6AAAgAEEDaiICIAItAAAiAkEwciACQdcAaiACQQpJGzoAACAAQQRqIgAgB0cNAAsLIAYoAgQhAiAFQQFGDQJBACEAIAVBAXYiBEEBRwRAIAVBAWshCCAEQf7///8HcSEKA0AgAyAIaiIELQAAIQkgBCAAIANqIgQtAAA6AAAgBCAJOgAAIAcgAEF+c2oiCS0AACELIAkgBEEBaiIELQAAOgAAIAQgCzoAACAIQQJrIQggCiAAQQJqIgBHDQALCyAFQQJxRQ0CIAAgA2oiCC0AACEEIAggByAAQX9zaiIALQAAOgAAIAAgBDoAAAwCCyAGKAIEIQIMAQsgA0EwOgAAIAFBAUEBQQAgA0EBEIkCIQAMAQsgAUEBQQFBACADIAUQiQIhACACRQ0BCyADIAIQ3wQLIAZBEGokACAAC5gGAQx+QqnAxomuzpOyMCEGIAEpAwgiAyACKQMIfCIJIANUIAkgASkDECIDIAIpAxB8IgQgA1QgBCABKQMYIgMgAikDGHwiCiADVK18IgUgBFRyrXwiBCAJVHKtIAIpAwAgASkDAHx8IgshAwJAAkACQCALQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IQYgBCEDIARC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQYgBSIDQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQYgCiIDQsf688PtgqOQPFENAQsgAyAGWg0AIAQhBiAFIQkMAQsgBULz6ri86a2lv+gAfCIGIApCx/rzw+2Co5A8VK0iA30hCSAEQqPP+vOXye7XxwB8IgggBUKNlcfDltLawJd/VCADIAZWcq0iA30hBiALIARC3bCFjOi2kai4f1QgAyAIVnKtfUKpwMaJrs6TsjB9IQsgCkLH+vPD7YKjkDx9IQoLQqnAxomuzpOyMCEHIAEpAygiAyACKQMofCIMIANUIAwgASkDMCIDIAIpAzB8IgQgA1QgBCABKQM4IgMgAikDOHwiCCADVK18IgUgBFRyrXwiBCAMVHKtIAIpAyAgASkDIHx8Ig0hAwJAAkACQCANQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IQcgBCEDIARC3bCFjOi2kai4f1INAEKNlcfDltLawJd/IQcgBSIDQo2Vx8OW0trAl39SDQBCx/rzw+2Co5A8IQcgCCIDQsf688PtgqOQPFENAQsgAyAHWg0AIAQhByAFIQMMAQsgBULz6ri86a2lv+gAfCIOIAhCx/rzw+2Co5A8VK0iB30hAyAEQqPP+vOXye7XxwB8IgwgBUKNlcfDltLawJd/VCAHIA5Wcq0iBX0hByANIARC3bCFjOi2kai4f1QgBSAMVnKtfUKpwMaJrs6TsjB9IQ0gCELH+vPD7YKjkDx9IQgLIAAgCDcDOCAAIAM3AzAgACAHNwMoIAAgDTcDICAAIAo3AxggACAJNwMQIAAgBjcDCCAAIAs3AwALnwQBBn8jAEHgAWsiAiQAIAJB+ABqIgMgARAqAkACQAJAIAIoAnhBAUYEQCACQTBqIAJBqAFqKQMANwMAIAJBKGogAkGgAWopAwA3AwAgAkEgaiACQZgBaikDADcDACACQRhqIAJBkAFqKQMANwMAIAJBEGogAkGIAWopAwA3AwAgAiACKQOAATcDCCACQeAAaiACQdgBaikDADcDACACQdgAaiACQdABaikDADcDACACQdAAaiACQcgBaikDADcDACACQcgAaiACQcABaikDADcDACACQUBrIAJBuAFqKQMANwMAIAIgAikDsAE3AzggAkHsAGogAkEIahDYAiADIAJBOGoQ2AIgAigCdCIBIAIoAoABIgRHDQEgAigCcEEEayEEIAFBAnQhASACKAJ8QQRrIQcDQCACQThqIQMgAUUNBCABIAdqIQUgASAEaiABQQRrIQEoAgAiBiAFKAIAIgVGDQALIAUgBkkNAgwDC0HorsAAEOgEAAsgAkE4aiEDIAEgBE0NAQsgAkEIaiEDCyACKAJ4IgEEQCACKAJ8IAFBAnQQ3wQLIAIoAmwiAQRAIAIoAnAgAUECdBDfBAsgACADKQMANwMAIABBKGogA0EoaikDADcDACAAQSBqIANBIGopAwA3AwAgAEEYaiADQRhqKQMANwMAIABBEGogA0EQaikDADcDACAAQQhqIANBCGopAwA3AwAgAkHgAWokAAu5BAEKfyMAQRBrIgYkAAJAAkACQAJAIAAoAghFBEBB0c7FAC0AABpBASECQQFBARDWBCIDDQFBAUEBEP8EAAsgBkEEaiAAQQoQQCAGKAIIIQMgBigCDCIFBEAgAyEAIAVBA3EiAgRAA0AgACAALQAAIgdBMHIgB0HXAGogB0EKSRs6AAAgAEEBaiEAIAJBAWsiAg0ACwsgAyAFaiEHIAVBBE8EQANAIAAgAC0AACICQTByIAJB1wBqIAJBCkkbOgAAIABBAWoiAiACLQAAIgJBMHIgAkHXAGogAkEKSRs6AAAgAEECaiICIAItAAAiAkEwciACQdcAaiACQQpJGzoAACAAQQNqIgIgAi0AACICQTByIAJB1wBqIAJBCkkbOgAAIABBBGoiACAHRw0ACwsgBigCBCECIAVBAUYNAkEAIQAgBUEBdiIEQQFHBEAgBUEBayEIIARB/v///wdxIQoDQCADIAhqIgQtAAAhCSAEIAAgA2oiBC0AADoAACAEIAk6AAAgByAAQX5zaiIJLQAAIQsgCSAEQQFqIgQtAAA6AAAgBCALOgAAIAhBAmshCCAKIABBAmoiAEcNAAsLIAVBAnFFDQIgACADaiIILQAAIQQgCCAHIABBf3NqIgAtAAA6AAAgACAEOgAADAILIAYoAgQhAgwBCyADQTA6AAAgAUEBQQFBACADQQEQiQIhAAwBCyABQQFBAUEAIAMgBRCJAiEAIAJFDQELIAMgAhDfBAsgBkEQaiQAIAALtAQCCH4BfyMAQdAAayIKJAAgCkEwaiABKQMYIgNCAEL/////D0IAEMkDIApBQGsgA0IAQoGAgIBwQgAQyQMgCiADIAEpAxAiAnwiBCAKKQMwfCIDQgBCgYCAgHBCABDJAyAKQRBqIANCIIYiBSADIARUrSAKKQM4IAIgBFatfHwiBiABKQMIfCIHfCIEQgBCgYCAgHBCABDJAyAKQSBqIARCIIYiCCAEIAVUrSADQiCIfCIFIAopA0AiCSABKQMAfCICIAYgB1atfCIGfCIHfCIDQgBCgYCAgHBCABDJAwJAIAopAyggCikDGCAKKQMIIAIgBlatIAopA0ggAiAJVK18fCIGIAopAwB8IgIgBlStfCACIAUgB1atfCIFIAJUrXwiBiAKKQMQfCICIAZUrXwgAiACIAMgCFStIARCIIh8IgQgBXwiBSAEVK18IgJWrXwiBiAKKQMgfCIEIAZUrXwgBCACIANCIIYiAiAFfCIFIAJUrSADQiCIfCIDfCICIANUrXwiAyAEVK18IgZCgYCAgHBSBEAgAyEEDAELAkAgAkL/////D1YNAEIAIQQgA0IAUg0AQoGAgIBwIQYgBUJ/UiACQv////8PUnINAQtCf0IAIAMgAkL/////D1QgAkL/////D30iBCAFQn9SrSICVHKtIgdUGyEGIAQgAn0hAiADIAd9IQQgBUIBfCEFCyAAIAU3AxggACACNwMQIAAgBDcDCCAAIAY3AwAgCkHQAGokAAuDBAEGfyMAQdABayIEJAACQCABKAIAIgIgASgCBCIGRwRAIARBiQFqIQUDQCABIAJBGGoiBzYCACAEQZABaiIIIAIQ9wIgBEGwAWoiCSACQQxqEPcCIARByABqIAggCRBDAkACQCAELQCIASICQQJGBEAgAygCACIBQYCAgIB4RiABRXJFBEAgAygCBCABEN8ECyADIAQpA0g3AgAgA0EIaiAEQdAAaigCADYCAAwBCyAEQRBqIARB0ABqKQMANwMAIARBGGogBEHYAGopAwA3AwAgBEEgaiAEQeAAaikDADcDACAEQShqIARB6ABqKQMANwMAIARBMGogBEHwAGopAwA3AwAgBEE4aiAEQfgAaikDADcDACAEQUBrIARBgAFqKQMANwMAIAQgBCkDSDcDCCAEIAUoAAA2AgAgBCAFQQNqKAAANgADIAJBA0YNAQsgACAEKQMINwMAIAAgBCgCADYAQSAAQcQAaiAEKAADNgAAIABBOGogBEFAaykDADcDACAAQTBqIARBOGopAwA3AwAgAEEoaiAEQTBqKQMANwMAIABBIGogBEEoaikDADcDACAAQRhqIARBIGopAwA3AwAgAEEQaiAEQRhqKQMANwMAIABBCGogBEEQaikDADcDAAwDCyAHIgIgBkcNAAsLQQMhAgsgACACOgBAIARB0AFqJAALqAQBBH8jAEGAAWsiBCQAAkACQAJAIAEoAggiAkGAgIAQcUUEQCACQYCAgCBxDQFBASECIAAoAgBBASABEN4CRQ0CDAMLIAAoAgAhAgNAIAMgBGpB/wBqIAJBD3EiBUEwciAFQdcAaiAFQQpJGzoAACADQQFrIQMgAkEQSSACQQR2IQJFDQALQQEhAiABQQFB+7fFAEECIAMgBGpBgAFqQQAgA2sQiQJFDQEMAgsgACgCACECA0AgAyAEakH/AGogAkEPcSIFQTByIAVBN2ogBUEKSRs6AAAgA0EBayEDIAJBD0sgAkEEdiECDQALQQEhAiABQQFB+7fFAEECIAMgBGpBgAFqQQAgA2sQiQINAQsgASgCAEGMtcUAQQIgASgCBCgCDBEDAA0AAkAgASgCCCICQYCAgBBxRQRAIAJBgICAIHENASAAKAIEQQEgARDeAiECDAILIAAoAgQhAkEAIQMDQCADIARqQf8AaiACQQ9xIgBBMHIgAEHXAGogAEEKSRs6AAAgA0EBayEDIAJBD0sgAkEEdiECDQALIAFBAUH7t8UAQQIgAyAEakGAAWpBACADaxCJAiECDAELIAAoAgQhAkEAIQMDQCADIARqQf8AaiACQQ9xIgBBMHIgAEE3aiAAQQpJGzoAACADQQFrIQMgAkEPSyACQQR2IQINAAsgAUEBQfu3xQBBAiADIARqQYABakEAIANrEIkCIQILIARBgAFqJAAgAguJBAIGfwJ+IwBB0ABrIgMkACADQTBqQgA3AwAgA0EoakIANwMAIANBIGpCADcDACADQRhqQgA3AwAgA0EQakIANwMAIANCADcDCAJAAkAgAkECSwRAIAEtAABBMEcNASABLQABQfgARkEBdCEGC0EFIQQgAiAGTQ0BCyACQQFrIQVBBSEEAkACQANAAn4CQCACIAUiCEsEQCABIAVqLQAAIgVBMGtB/wFxQQpPDQFCUAwCCyAIIAJBjNbBABDZAwALQql/IAVB4QBrQf8BcUEGSQ0AGiAFQcEAa0H/AXFBBk8NAkJJCyAFrUL/AYN8IAdBP3GthiAJhCEJAkAgBEUgB0EEaiIHQcAAR3JFBEAgBEEGTw0BIANBCGogBEEDdGogCTcDAEIAIQlBACEHIARBAWshBAsgCEEBayEFIAYgCE8NAwwBCwsgBEEGQdDWwQAQ2QMACyADQQA2AkggA0EBNgI8IANBuNbBADYCOCADQgQ3AkAgA0E4akHA1sEAEKgEAAsgBEEGSQ0AIARBBkH81cEAENkDAAsgA0EIaiAEQQN0aiAJNwMAIAAgAykDCDcDACAAQQhqIANBEGopAwA3AwAgAEEQaiADQRhqKQMANwMAIABBGGogA0EgaikDADcDACAAQSBqIANBKGopAwA3AwAgAEEoaiADQTBqKQMANwMAIANB0ABqJAALiQQCBn8CfiMAQdAAayIDJAAgA0EwakIANwMAIANBKGpCADcDACADQSBqQgA3AwAgA0EYakIANwMAIANBEGpCADcDACADQgA3AwgCQAJAIAJBAksEQCABLQAAQTBHDQEgAS0AAUH4AEZBAXQhBgtBBSEEIAIgBk0NAQsgAkEBayEFQQUhBAJAAkADQAJ+AkAgAiAFIghLBEAgASAFai0AACIFQTBrQf8BcUEKTw0BQlAMAgsgCCACQaifxQAQ2QMAC0KpfyAFQeEAa0H/AXFBBkkNABogBUHBAGtB/wFxQQZPDQJCSQsgBa1C/wGDfCAHQT9xrYYgCYQhCQJAIARFIAdBBGoiB0HAAEdyRQRAIARBBk8NASADQQhqIARBA3RqIAk3AwBCACEJQQAhByAEQQFrIQQLIAhBAWshBSAGIAhPDQMMAQsLIARBBkHsn8UAENkDAAsgA0EANgJIIANBATYCPCADQdSfxQA2AjggA0IENwJAIANBOGpB3J/FABCoBAALIARBBkkNACAEQQZBmJ/FABDZAwALIANBCGogBEEDdGogCTcDACAAIAMpAwg3AwAgAEEIaiADQRBqKQMANwMAIABBEGogA0EYaikDADcDACAAQRhqIANBIGopAwA3AwAgAEEgaiADQShqKQMANwMAIABBKGogA0EwaikDADcDACADQdAAaiQAC8sEAQZ/QdHOxQAtAAAaAkACQEEwQQQQ1gQiBgRAIAEoAggiBEECdCECIARB/////wNLIAJB/P///wdLcg0CIAEoAgQhBwJ/IAJFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEDIAJBBBDWBCIFRQ0DIAQLIQMgAgRAIAUgByAC/AoAAAsgBiAENgIIIAYgBTYCBCAGIAM2AgAgASgCFCIEQQJ0IQJBACEDIARB/////wNLIAJB/P///wdLcg0CIAEoAhAhBwJ/IAJFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEDIAJBBBDWBCIFRQ0DIAQLIQMgAgRAIAUgByAC/AoAAAsgBiAENgIUIAYgBTYCECAGIAM2AgwgASgCICIEQQJ0IQJBACEDIARB/////wNLIAJB/P///wdLcg0CIAEoAhwhBwJ/IAJFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEDIAJBBBDWBCIFRQ0DIAQLIQMgAgRAIAUgByAC/AoAAAsgBiAENgIgIAYgBTYCHCAGIAM2AhggASgCLCIDQQJ0IQRBACEFIANB/////wNLIARB/P///wdLcg0BIAEoAighAgJ/IARFBEBBBCEBQQAMAQtB0c7FAC0AABpBBCEFIARBBBDWBCIBRQ0CIAMLIQUgBARAIAEgAiAE/AoAAAsgBiADNgIsIAYgATYCKCAGIAU2AiQgAEEENgIIIAAgBjYCBCAAQQQ2AgAPC0EEQTAQ/wQACyAFIARB+IHAABDIBAALIAMgAkH4gcAAEMgEAAuhBAEHfyMAQbACayIDJAACQAJAAkAgASgCBCIFBEAgASgCCCIGRQ0CIANByQFqIQcgASgCACEEA0AgASAFIAYgBSAFIAZLGyIIayIFNgIEIAEgBCAIQTBsaiIJNgIAIANB+AFqIARBKGopAwA3AwAgA0HwAWogBEEgaikDADcDACADQegBaiAEQRhqKQMANwMAIANB4AFqIARBEGopAwA3AwAgA0HYAWogBEEIaikDADcDACADIAQpAwA3A9ABIAhBAUYNBCADQagCaiAEQdgAaikDADcDACADQaACaiAEQdAAaikDADcDACADQZgCaiAEQcgAaikDADcDACADQZACaiAEQUBrKQMANwMAIANBiAJqIARBOGopAwA3AwAgAyAEKQMwNwOAAiADQegAaiADQdABaiADQYACakEAEDECQAJAIAMtAMgBIgRBAkYEQCACKAIAIgFBgICAgHhGIAFFckUEQCACKAIEIAEQ3wQLIAIgAykDaDcCACACQQhqIANB8ABqKAIANgIADAELIAMgBygAADYCACADIAdBA2ooAAA2AAMgA0EIaiADQegAakHgAPwKAAAgBEEDRg0BCyAAIANBCGpB4AD8CgAAIABB5ABqIAMoAAM2AAAgACADKAIANgBhDAMLIAkhBCAFDQALC0EDIQQLIAAgBDoAYCADQbACaiQADwtBAEEAQaD6wAAQ2QMAC0EBQQFBsPrAABDZAwALxAQCBX8BfiMAQSBrIgIkACABLQAMIgVFBEACQCABKAIIIgQEQCABKAIEIQMgBEECdCEEA0AgAygCAA0CIAdCIHwhByADQQRqIQMgBEEEayIEDQALC0GUiMUAQRxBlInFABDoAwALIAcgAygCAGithFAhAwsCQAJAIAEoAgBBgICAgHhHBEAgASgCCA0BIAJBCGogAUEIaigCADYCACACIAEpAgA3AwAMAgsgASgCBCgCCA0AIAJBADYCCCACQoCAgIDAADcDAAwBCyACIAFBAEEBEOwBCwJ/IANFBEAgAigCCCEDIAIoAgAhBCACKAIEDAELIAJBGGogAkEIaigCACIDNgIAIAIgAikDADcDECADRQRAIAIoAhBFBEAgAkEQakGUxcQAEKUDCyACKAIUQQA2AgAgAkEBNgIYQQEhAwsgAigCFCIEIAQoAgBBAWoiATYCAAJ/AkACQCABDQAgA0EBRg0BIANBAnRBBGshASAEQQRqIQMDQCADIAMoAgBBAWoiBDYCACAEDQEgA0EEaiEDIAFBBGsiAQ0ACwwBCyACKAIYDAELIAIoAhgiASACKAIQRgRAIAJBEGpBpMXEABClAwsgAigCFCABQQJ0akEBNgIAIAFBAWoLIQMgAigCECEEIAIoAhQLIQFBASEGAkAgBUEBRwRAIAVBASADGyEGDAELQQAhAyAEQQRJDQAgASAEQQJ0EN8EQQQhAUEAIQQLIAAgBjoADCAAIAM2AgggACABNgIEIAAgBDYCACACQSBqJAALvQQBCH8jAEEQayIDJAAgAyABNgIEIAMgADYCACADQqCAgIAONwIIAn8CQAJAAkAgAigCECIJBEAgAigCFCIADQEMAgsgAigCDCIARQ0BIAIoAggiASAAQQN0aiEEIABBAWtB/////wFxQQFqIQYgAigCACEAA0ACQCAAQQRqKAIAIgVFDQAgAygCACAAKAIAIAUgAygCBCgCDBEDAEUNAEEBDAULQQEgASgCACADIAFBBGooAgARAgANBBogAEEIaiEAIAQgAUEIaiIBRw0ACwwCCyAAQRhsIQogAEEBa0H/////AXFBAWohBiACKAIIIQQgAigCACEAA0ACQCAAQQRqKAIAIgFFDQAgAygCACAAKAIAIAEgAygCBCgCDBEDAEUNAEEBDAQLQQAhB0EAIQgCQAJAAkAgBSAJaiIBQQhqLwEAQQFrDgIBAgALIAFBCmovAQAhCAwBCyAEIAFBDGooAgBBA3RqLwEEIQgLAkACQAJAIAEvAQBBAWsOAgECAAsgAUECai8BACEHDAELIAQgAUEEaigCAEEDdGovAQQhBwsgAyAHOwEOIAMgCDsBDCADIAFBFGooAgA2AghBASAEIAFBEGooAgBBA3RqIgEoAgAgAyABQQRqKAIAEQIADQMaIABBCGohACAFQRhqIgUgCkcNAAsMAQsLAkAgBiACKAIETw0AIAMoAgAgAigCACAGQQN0aiIAKAIAIAAoAgQgAygCBCgCDBEDAEUNAEEBDAELQQALIANBEGokAAuVBAEMfyABQQFrIQ4gACgCBCEKIAAoAgAhCyAAKAIIIQwCQANAIAUNAQJ/AkAgAiADSQ0AA0AgASADaiEFAkACQAJAIAIgA2siB0EHTQRAIAIgA0cNASACIQMMBQsCQCAFQQNqQXxxIgYgBWsiBARAQQAhAANAIAAgBWotAABBCkYNBSAEIABBAWoiAEcNAAsgBCAHQQhrIgBNDQEMAwsgB0EIayEACwNAQYCChAggBigCACIJQYqUqNAAc2sgCXJBgIKECCAGQQRqKAIAIglBipSo0ABzayAJcnFBgIGChHhxQYCBgoR4Rw0CIAZBCGohBiAEQQhqIgQgAE0NAAsMAQtBACEAA0AgACAFai0AAEEKRg0CIAcgAEEBaiIARw0ACyACIQMMAwsgBCAHRgRAIAIhAwwDCwNAIAQgBWotAABBCkYEQCAEIQAMAgsgByAEQQFqIgRHDQALIAIhAwwCCyAAIANqIgZBAWohAwJAIAIgBk0NACAAIAVqLQAAQQpHDQBBACEFIAMhBiADDAMLIAIgA08NAAsLIAIgCEYNAkEBIQUgCCEGIAILIQACQCAMLQAABEAgC0Hkt8UAQQQgCigCDBEDAA0BC0EAIQQgACAIRwRAIAAgDmotAABBCkYhBAsgACAIayEAIAEgCGohByAMIAQ6AAAgBiEIIAsgByAAIAooAgwRAwBFDQELC0EBIQ0LIA0LpgQCEH8CfiMAQSBrIgIkAAJAIAEoAhAiDCABKAIMIgprIgVBACABKAIAIg4bIgQgASgCJCILIAEoAiAiCGsiDUEAIAEoAhQiDxtqIgMgBEkNACADIAEoAiwiECABKAIoIglrIhFBACAJGyADaiIESw0AAkAgBEEASA0AAkAgBEUEQEEBIQcMAQtB0c7FAC0AABpBASEGIARBARDWBCIHRQ0BCyABKQIYIRNBACEDIA4EQCACIAEpAgQ3AwggAiAKNgIQIAIgDDYCFCAFRSAKIAxGckUEQCAHIAJBCGogCmogBfwKAAALIAUhAwsgCUUgCSAQRnJFBEAgAyAHaiEFIBFBA3YhBkEAIQEDQCABIAVqIAEgCWopAwAiEkI4hiASQoD+A4NCKIaEIBJCgID8B4NCGIYgEkKAgID4D4NCCIaEhCASQgiIQoCAgPgPgyASQhiIQoCA/AeDhCASQiiIQoD+A4MgEkI4iISEhDcAACABQQhqIQEgBkEBayIGDQALIAEgA2ohAwsCQCAPRQ0AIAIgEzcDCCACIAg2AhAgAiALNgIUIAggC0YNACANBEAgAyAHaiACQQhqIAhqIA38CgAACyADIAtqIAhrIQMLIAAgAzYCCCAAIAc2AgQgACAENgIAIAJBIGokAA8LIAYgBEG40cEAEMgEAAsgAkEANgIYIAJBATYCDCACQZSBwAA2AgggAkIENwIQIAJBCGpBuNHBABCoBAALgAQBBn8jAEEwayIDJAAgA0EgakIANwMAIANBGGpCADcDACADQRBqQgA3AwAgA0IANwMIAkACQCABLAACQUBIBEBBAiECDAELIAEgAS0AAEErRiIEaiIFLQAAIgJBwQBrQV9xQQpqIAJBMGsgAkE5SxsiAkEPSw0BIAMgBAR/IAIFIAUtAAEiBEHBAGtBX3FBCmogBEEwayAEQTlLGyIEQQ9LDQIgAkEEdCAEcgs6AAggA0EIakEBciEEQQQhAgNAAkACQAJAIAEgAmoiBkECayIHLAAAIgVBQEgNACABIAIgAkHAAEcEfyAGLAAAQUBIDQEgBy0AAAUgBQtB/wFxQStGIgZqaiIHQQJrLQAAIgVBwQBrQV9xQQpqIAVBMGsgBUE5SxsiBUEPSw0FIAYNAiAHQQFrLQAAIgZBwQBrQV9xQQpqIAZBMGsgBkE5SxsiBkEPTQ0BDAULIAJBAmshBAwDCyAFQQR0IAZyIQULIAQgBToAACAEQQFqIQQgAkECaiICQcIARw0ACyAAIAMpAwg3AAAgAEEYaiADQSBqKQMANwAAIABBEGogA0EYaikDADcAACAAQQhqIANBEGopAwA3AAAgA0EwaiQADwsgAUHAACAEIAJBhOrAABDSBAALIANBAToAL0GEncAAQSsgA0EvakGU6sAAQaTqwAAQygMAC8UGAgd/AX4jAEHABGsiAiQAIAJB4ABqIgNBAEHgAPwLAAJAAkACQCABQcABaiIFIANBMBDxA0UEQCABQfABaiACQZABakEwEPEDRQ0BCyMAQeADayIDJAAgA0GAA2oiBCABQeAAahBeIAMgBCAFED8gA0HgAGoiByABEF4gA0GgAmoiBkEAQeAA/AsAIAQgBRBeIANBwAFqIgggBiAEED8gBCAHIAgQ1QEgByAEIAEQPyADQvP/s4CAgMCTqn83A/gCIANCioDQ4a+GgObTADcD8AIgA0L/gKrYpq/6x8cANwPoAiADQtfJ6LXu19/psX83A+ACIANCr9bi+7vn3OSOfzcD2AIgA0L+vI/sk6qR6wk3A9ACIANC8/+zgICAwJOqfzcDyAIgA0KKgNDhr4aA5tMANwPAAiADQv+Aqtimr/rHxwA3A7gCIANC18note7X3+mxfzcDsAIgA0Kv1uL7u+fc5I5/NwOoAiADQv68j+yTqpHrCTcDoAIgBCAFEF4gCCAGIAQQPyAEIAggBRA/IAYgByAEENUBIAIgAyAGEI0BIANB4ANqJAAgAkHgAGoiA0EAQeAA/AsAIAIgA0EwEPEDDQAgAkEwaiACQZABakEwEPEDRQ0BCyACQeAAaiIDQQBB4AD8CwAgASADQTAQ8QMEQEIBIQkMAgtCASEJIAFBMGogAkGQAWoiA0EwEPEDDQEgAkHgAGoiBEEAQeAA/AsAIAUgBEEwEPEDDQEgAUHwAWogA0EwEPEDDQEgAkHAAWpBAEHgAPwLAEIAIQkgAkGYBGpCADcDACACQaAEakIANwMAIAJBqARqQgA3AwAgAkGwBGpCADcDACACQbgEakIANwMAIAJBiARqQaCRxQApAwA3AwAgAkGABGpBmJHFACkDADcDACACQfgDakGQkcUAKQMANwMAIAJB8ANqQYiRxQApAwA3AwAgAkHoA2pBgJHFACkDADcDACACQgA3A5AEIAJB+JDFACkDADcD4AMgAkGAA2pBAEHgAPwLACACQaACaiACQeADakHgAPwKAAAgAEEIaiACQcABakGgAvwKAAAMAQsgAEEIaiABQaAC/AoAAAsgACAJNwMAIAJBwARqJAAL+AMCCH8DfiMAQRBrIgMkACACQf8BcSIFBEBBICAFbiEJIAEoAgQhBSABKAIIIgEEQCABrUIFhiAFIAFBAnRqQQRrKAIAZ619IQsLAkBBfyALIAKtQv8BgyIMgCINIAsgDCANflKtfCILpyIHIAtCgICAgBBaGyIEQQBIDQACQCAERQRAQQEhCEEAIQcMAQtB0c7FAC0AABpBASEGIARBARDWBCIIRQ0BCyABQQFrIQQgA0EANgIMIAMgCDYCCCADIAc2AgQgAQRAIAJBH3EhBkF/IAJ0QX9zIQcgBSAEQQJ0aiEIQQAhASAERSACQf8BcUEgS3JFBEADQCAFKAIAIQJBASEEA0AgAygCBCABRgRAIANBBGpB5M7EABC2AwsgAygCCCABaiACIAdxOgAAIAMgAUEBaiIBNgIMIAIgBnYhAiAEQf8BcSEKIARBAWohBCAJIApLDQALIAVBBGoiBSAIRw0ACwsgCCgCACICBEADQCADKAIEIAFGBEAgA0EEakHUzsQAELYDCyADKAIIIAFqIAIgB3E6AAAgAyABQQFqIgE2AgwgAiAGdiICDQALCyAAIAMpAgQ3AgAgAEEIaiADQQxqKAIANgIAIANBEGokAA8LIARBAEHEzsQAEOUEAAsgBiAEQbTOxAAQyAQAC0GkzsQAEJoEAAuNBAEEfwJAAkACQAJAIAJBA08EQAJ/IAEsAAAiA0EATgRAIANB/wFxIQMgAUEBagwBCyABLQABQT9xIQUgA0EfcSEEIANBX00EQCAEQQZ0IAVyIQMgAUECagwBCyABLQACQT9xIAVBBnRyIQUgA0FwSQRAIAUgBEEMdHIhAyABQQNqDAELIARBEnRBgIDwAHEgAS0AA0E/cSAFQQZ0cnIhAyABQQRqCyEEIANBMEcNASAEIAEgAmpGDQICfyAELAAAIgNBAE4EQCADQf8BcQwBCyAELQABQT9xIQYgA0EfcSEFIAVBBnQgBnIgA0FfTQ0AGiAELQACQT9xIAZBBnRyIQYgBiAFQQx0ciADQXBJDQAaIAVBEnRBgIDwAHEgBC0AA0E/cSAGQQZ0cnILQfgARw0BIAEsAAJBv39KBEAgAkECayECIAFBAmohAQwCCyABIAJBAiACQfDWwQAQ0gQACyACRQ0CC0EAIQMDQAJAIAEgA2otAAAiBEEwa0H/AXFBCkkNAAJAIARBwQBrDiYBAQEBAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEBAQEBAQALIABBADoAAQwECyACIANBAWoiA0cNAAsgAkHAAE0EQCAAQQhqIAEgAhC3AiAAQQA6AAAPCyAAQQI6AAEMAgtB4NbBABDoBAALIABBAzoAAQsgAEEBOgAAC/0DAgR/A34jAEEgayIEJAAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgBEIANwMAIAJBBnYhAwJAAkAgAkE/cSIFRQRAIANBBEYNASACQf8BSw0CIAQgA0EDdGogASkDADcDACADQQNGDQEgA0EBaiEFQQQgA2siBkEAIAZBBE0bIgZBAUYEQCAFIQMMAwsgBCAFQQN0aiABKQMINwMAIANBAkYNASADQQJqIQUgBkECRgRAIAUhAwwDCyAEIAVBA3RqIAEpAxA3AwAgA0EBRg0BIANBA2ohAyAGQQNGDQIgBCADQQN0aiABKQMYNwMAIAJBwABJDQFBBEEEQYDXwQAQ2QMACyACQYACTwRAIANBBEGg18EAENkDAAsgBCADQQN0aiIGIAEpAwAiByAFrSIIiDcDACACQb8BSw0AIAQgA0EBaiIFQQN0aiAHQQAgAmtBP3GtIgeGIAEpAwgiCSAIiIQ3AwAgBUEDRg0AIAQgA0ECaiICQQN0aiAJIAeGIAEpAxAiCSAIiIQ3AwAgAkEDRg0AIAYgCSAHhiABKQMYIAiIhDcDGAsgACAEKQMANwMAIABBGGogBEEYaikDADcDACAAQRBqIARBEGopAwA3AwAgAEEIaiAEQQhqKQMANwMAIARBIGokAA8LIANBBEGQ18EAENkDAAuNBAIGfwN+IwBBIGsiAiQAAkACQAJAIAEOAgACAQsgAEEANgIIDAELIAFpQQFHBEAgACgCCCIDRQ0BIAAoAgQhBCADQQFrQf////8DcSIHQQFqIgVBA3EhBiABrSEJAkAgB0EDSQRAIAQhAQwBCyAFQfz///8HcSEHIAQhAQNAIAEgATUCACAJfiAIfCIIPgIAIAFBBGoiBSAFNQIAIAl+IAhCIIh8Igg+AgAgAUEIaiIFIAU1AgAgCX4gCEIgiHwiCD4CACABQQxqIgUgBTUCACAJfiAIQiCIfCIKPgIAIApCIIghCCABQRBqIQEgB0EEayIHDQALCyAGBEADQCABIAE1AgAgCX4gCHwiCj4CACABQQRqIQEgCkIgiCEIIAZBAWsiBg0ACwsgCkKAgICAEFQNASAAKAIAIANGBH8gAEH0yMQAEKUDIAAoAgQFIAQLIANBAnRqIAg+AgAgACADQQFqNgIIDAELIAAoAgghAyAAKAIEIQQCQAJAIAAoAgAiBkGAgICAeEcEQCADDQEgAkEANgIQIAIgBDYCDCACIAY2AggMAgsgBCgCCA0AIAJBADYCECACQoCAgIDAADcCCAwBCyACIAM2AhwgAiAENgIYIAIgBjYCFCACQQhqIAJBFGpBACABaBDPAQsgACACKQIINwIAIABBCGogAkEQaigCADYCAAsgAkEgaiQAC7UFAQ9+An4gAUGAoMUAQTAQ8QMEQEL//8+K6///1R4gASkDICIKfSIFIAEpAygiC0Kr1f7///+//7l/Vq0iBn0hDkKk7MO1j9S0mOcAIAEpAxgiA30iByAFIAZUIApC///Piuv//9UeVnKtIgV9IQpCv6WUnM/w0rvkACABKQMQIgZ9IgggBSAHViADQqTsw7WP1LSY5wBWcq0iA30hBULX2a6a5PbpjcsAIAEpAwgiB30iAiADIAhWIAZCv6WUnM/w0rvkAFZyrSIDfSEGQqvV/v///7//uX8gC30hC0Kazf/Lo73EgBogASkDACACIANUIAdC19mumuT26Y3LAFZyrXx9DAELIAEpAyghCyABKQMgIQ4gASkDGCEKIAEpAxAhBSABKQMIIQYgASkDAAshAwJ+IAFBMGpBgKDFAEEwEPEDBEBC///Piuv//9UeIAEpA1AiCH0iAiABKQNYIgxCq9X+////v/+5f1atIgl9IQdCpOzDtY/UtJjnACABKQNIIgR9Ig0gAiAJVCAIQv//z4rr///VHlZyrSICfSEIQr+llJzP8NK75AAgASkDQCIJfSIPIAIgDVYgBEKk7MO1j9S0mOcAVnKtIgR9IQJC19mumuT26Y3LACABKQM4Ig19IhAgBCAPViAJQr+llJzP8NK75ABWcq0iBH0hCUKr1f7///+//7l/IAx9IQxCms3/y6O9xIAaIAEpAzAgBCAQViANQtfZrprk9umNywBWcq18fQwBCyABKQNYIQwgASkDUCEHIAEpA0ghCCABKQNAIQIgASkDOCEJIAEpAzALIQQgACAMNwNYIAAgBzcDUCAAIAg3A0ggACACNwNAIAAgCTcDOCAAIAQ3AzAgACALNwMoIAAgDjcDICAAIAo3AxggACAFNwMQIAAgBjcDCCAAIAM3AwALowMBBH8jAEHAA2siBCQAIAQgARBhIARBgAJqIgUgBCAEEDggBEHAAmoiBiABIAEQoAIgBEFAayIHIAUgBhDcASAGIAEgBxDcASAFIAQgBhA4IARBwAFqIAUgAUFAayIHENwBIARBiAFqIARByABqKQMANwMAIARBkAFqIARB0ABqKQMANwMAIARBmAFqIARB2ABqKQMANwMAIARBoAFqIARB4ABqKQMANwMAIARBqAFqIARB6ABqKQMANwMAIARBsAFqIARB8ABqKQMANwMAIARBuAFqIARB+ABqKQMANwMAIARBiANqIARBCGopAwA3AwAgBEGQA2ogBEEQaikDADcDACAEQZgDaiAEQRhqKQMANwMAIAQgBCkDQDcDgAEgBCAEKQMANwOAAyAEQbgDaiAEQThqKQMANwMAIARBsANqIARBMGopAwA3AwAgBEGoA2ogBEEoaikDADcDACAEIAQpAyA3A6ADIAYgBCABEDggBSAGIAcQ3AEgAEGAAWogBEGAA2ogBSACIAMQGSAAIARBgAFqQYAB/AoAACAEQcADaiQAC+0DAQl/IwBBEGsiAyQAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASEBQQFBARDWBCICRQ0DIAJBADoAACADQQE2AgwgAyACNgIIIANBATYCBAwBCyADQQRqIAFBCBCwAiADKAIMIgFBAkkNACADKAIIIgUgAWohCCABQQF2IgRBAUcEQCABQQFrIQYgBEH+////B3EhCQNAIAUgBmoiBC0AACEHIAQgAiAFaiIELQAAOgAAIAQgBzoAACAIIAJBfnNqIgctAAAhCiAHIARBAWoiBC0AADoAACAEIAo6AAAgBkECayEGIAkgAkECaiICRw0ACwsgAUECcQRAIAIgBWoiBi0AACEEIAYgCCACQX9zaiICLQAAOgAAIAIgBDoAAAsgAUEfSw0BCwNAIAMoAgQgAUYEQCADQQRqQbCewgAQtgMLIAMoAgghAiABBEAgAkEBaiACIAH8CgAACyACQQA6AAAgAyABQQFqIgI2AgwgAUEfSSACIQENAAsgAygCCCEFCyAAKAIAIAAoAggiAmsgAUkEQCAAIAIgAUEBQQEQiAMgACgCCCECCyABBEAgACgCBCACaiAFIAH8CgAACyAAIAEgAmo2AgggAygCBCIABEAgAygCCCAAEN8ECyADQRBqJAAPC0EBQQEQ/wQAC9MDAgZ/An4jAEFAaiIDJAAgA0EgakIANwMAIANBGGpCADcDACADQRBqQgA3AwAgA0IANwMIAkACQCACQQJLBEAgAS0AAEEwRw0BIAEtAAFB+ABGQQF0IQYLQQMhBCACIAZNDQELIAJBAWshBUEDIQQCQAJAA0ACfgJAIAIgBSIISwRAIAEgBWotAAAiBUEwa0H/AXFBCk8NAUJQDAILIAggAkGM1sEAENkDAAtCqX8gBUHhAGtB/wFxQQZJDQAaIAVBwQBrQf8BcUEGTw0CQkkLIAWtQv8Bg3wgB0E/ca2GIAmEIQkCQCAERSAHQQRqIgdBwABHckUEQCAEQQRPDQEgA0EIaiAEQQN0aiAJNwMAQgAhCUEAIQcgBEEBayEECyAIQQFrIQUgBiAITw0DDAELCyAEQQRB0NbBABDZAwALIANBADYCOCADQQE2AiwgA0G41sEANgIoIANCBDcCMCADQShqQcDWwQAQqAQACyAEQQRJDQAgBEEEQfzVwQAQ2QMACyADQQhqIARBA3RqIAk3AwAgACADKQMINwMAIABBCGogA0EQaikDADcDACAAQRBqIANBGGopAwA3AwAgAEEYaiADQSBqKQMANwMAIANBQGskAAvGBAIEfwp+IwBB8ABrIgIkACACQeQAaiABEPcDIAIoAmghAyACKAJkIQQgAigCbCIBQQJGBEAgAygCBCEFIAMoAgAhASACQQhqIANBCGpB2AD8CgAAIAQEQCADIARBMGwQ3wQLIAIpA1ghCyACKQNQIQggAikDSCEJIAIpA0AhCiACKQM4IQ0gAikDMCEOAkAgAkEwakHYgsAAQTAQ8QNFBEAgDSEGIAohByAJIQwgCCEPDAELQv//z4rr///VHiAIfSIHIAtCq9X+////v/+5f1atIgx9IQ9CpOzDtY/UtJjnACAJfSIGIAcgDFQgCEL//8+K6///1R5Wcq0iB30hDEK/pZScz/DSu+QAIAp9IgggBiAHVCAJQqTsw7WP1LSY5wBWcq0iBn0hB0LX2a6a5PbpjcsAIA19IgkgBiAIViAKQr+llJzP8NK75ABWcq0iCn0hBkKazf/Lo73EgBogCSAKVCANQtfZrprk9umNywBWcq0gDnx9IQ5Cq9X+////v/+5fyALfSELCyAAIAU2AgQgACABNgIAIAAgAikDCDcDCCAAIAs3A1ggACAPNwNQIAAgDDcDSCAAIAc3A0AgACAGNwM4IAAgDjcDMCAAQRBqIAJBEGopAwA3AwAgAEEYaiACQRhqKQMANwMAIABBIGogAkEgaikDADcDACAAQShqIAJBKGopAwA3AwAgAkHwAGokAA8LIAIgATYCbCACIAM2AmggAiAENgJkQYCLwABBKyACQeQAakGsi8AAQaSNwAAQygMAC4oDAQt/IwBBoAVrIgMkACADIAEgAhA/IANB4ABqIgcgAUHgAGoiCCACQeAAaiIJED8gA0HAAWoiCiABQcABaiILIAJBwAFqIgwQPyADQaACaiINEHUgA0HgA2oiBSAIIAsQ1QEgA0HABGoiBCAJIAwQ1QEgA0GAA2oiBiAFIAQQPyAEIAYgBxCNASAFIAQgChCNASAEIA0gBRA/IAAgAyAEENUBIAUgASAIENUBIAQgAiAJENUBIAYgBSAEED8gBCAGIAMQjQEgBiAEIAcQjQEgBBB1IAUgBCAKED8gAEHgAGogBiAFENUBIAUgASALENUBIAQgAiAMENUBIAYgBSAEED9BACIBRQRAIAQgA0HgAPwKAAALIANB4ANqIANBgANqIANBwARqIgIQjQEgAUUEQCACIANB4ABqQeAA/AoAAAsgA0GAA2ogA0HgA2ogA0HABGoiAhDVASABRQRAIAIgA0HAAWpB4AD8CgAACyAAQcABaiADQYADaiADQcAEahCNASADQaAFaiQAC8IDAQR/IAAoAgAiAQRAIAAoAgQgAUECdBDfBAsgACgCDCIBBEAgACgCECABQQJ0EN8ECyAAKAIYIgEEQCAAKAIcIAFBAnQQ3wQLIAAoAiQiAQRAIAAoAiggAUECdBDfBAsgACgCMCIBBEAgACgCNCABQQJ0EN8ECyAAKAI8IgEEQCAAKAJAIAFBAnQQ3wQLIAAoAkgiAQRAIAAoAkwgAUECdBDfBAsgACgCVCIBBEAgACgCWCABQQJ0EN8ECyAAKAJgIgEEQCAAKAJkIAFBAnQQ3wQLIAAoAmwiAQRAIAAoAnAgAUECdBDfBAsgACgCeCIBBEAgACgCfCABQQJ0EN8ECyAAKAKEASIBBEAgACgCiAEgAUECdBDfBAsgACgCkAEiAQRAIAAoApQBIAFBAnQQ3wQLIAAoApwBIgEEQCAAKAKgASABQQJ0EN8ECyAAKAKsASEBIAAoArABIgQEQCABIQIDQCACKAIAIgMEQCACQQRqKAIAIANBAnQQ3wQLIAJBDGooAgAiAwRAIAJBEGooAgAgA0ECdBDfBAsgAkEYaiECIARBAWsiBA0ACwsgACgCqAEiAARAIAEgAEEYbBDfBAsL0AQCCH4KfyABKAIEIQsgASgCACAAKAIAIg0gACgCBCIKRwRAIAAoAhQhESAAKAIQIQ4gACgCDCESIAAoAgghDCABKAIIIAtBBXRqIRMgCiANa0EFdiEPQQAhAANAAkACQCAOIAwgESgCAGoiCksEQEKpwMaJrs6TsjAhBCAAIA1qIgEpAwAgEiAKQQV0aiIKKQMAfCABQQhqKQMAIgIgCikDCHwiAyACVCADIAFBEGopAwAiBSAKKQMQfCICIAVUIAIgAiABQRhqKQMAIgUgCikDGHwiBiAFVK18IgJWcq18IgUgA1RyrXwiByEDAkAgB0KpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEEIAUhAyAFQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIQQgAiEDIAJCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhBCAGIQMgBkKBgICAv7L98MMAUQ0CCyADIARaDQEgBSEEIAIhAwwCCyAKIA5B1PnAABDZAwALIAJCkeHlzYeJ+pkofSIEIAZCgYCAgL+y/fDDAFStIgh9IQMgBUKjz/rzl8nu18cAfCIJIAJCkeHlzYeJ+pkoVCAEIAhUcq0iAn0hBCAHIAVC3bCFjOi2kai4f1QgAiAJVnKtfUKpwMaJrs6TsjB9IQcgBkKBgICAv7L98MMAfSEGCyAAIBNqIgEgBzcDACABQRhqIAY3AwAgAUEQaiADNwMAIAFBCGogBDcDACAAQSBqIQAgDEEBaiEMIAtBAWohCyAPQQFrIg8NAAsLIAs2AgALigQCBH8BfiMAQSBrIgIkAAJAAn9BACAALQAMDQAaIAJBEGogABDYAyACKAIQQQFHDQFBACABUA0AGiACKQMYIAFUCyEEIAApAgAhBiAAQbDMwgApAgA3AgAgAkEYaiIFIABBCGoiAygCADYCACADQbjMwgAoAgA2AgAgAiAGNwMQAkACQCAGp0GAgICAeEcEQCACKAIYDQEgAkEIaiAFKAIANgIAIAIgAikDEDcDAAwCCyACKAIUKAIIDQAgAkEANgIIIAJCgICAgMAANwMADAELIAIgAkEQaiABQgWIpyABp0EfcRDsASAAKAIAIgNFDQAgACgCBCADQQJ0EN8ECyAAIAIpAwA3AgAgAEEIaiIDIAJBCGooAgA2AgAgAygCACEDAkAgBEUEQCADDQEgAEEBOgAMDAELIANFBEAgACgCAEUEQCAAQcjQwgAQpQMLIAAoAgRBADYCACAAQQE2AghBASEDCyAAKAIEIgQgBCgCAEEBaiIFNgIAIAUNACADQQFHBEAgA0ECdEEEayEDIARBBGohBANAIAQgBCgCAEEBaiIFNgIAIAUNAiAEQQRqIQQgA0EEayIDDQALCyAAKAIIIgQgACgCAEYEQCAAQdjQwgAQpQMLIAAoAgQgBEECdGpBATYCACAAIARBAWo2AggLIAJBIGokAA8LQbTNwgBBHEG0zsIAEOgDAAvsBAEKfkKazf/Lo73EgBohBCABKQMIIgMgAikDCHwiBiADVCAGIAEpAxAiAyACKQMQfCIKIANUIAogASkDGCIDIAIpAxh8IgUgA1QgBSABKQMgIgMgAikDIHwiByADVCAHIAEpAygiAyACKQMofCILIANUrXwiCCAHVHKtfCIJIAVUcq18IgUgClRyrXwiByAGVHKtIAIpAwAgASkDAHx8IgwhAwJAAkACQCAMQprN/8ujvcSAGlINAELX2a6a5PbpjcsAIQQgByIDQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEEIAUiA0K/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhBCAJIgNCpOzDtY/UtJjnAFINAEL//8+K6///1R4hBCAIIgNC///Piuv//9UeUg0AQqvV/v///7//uX8hBCALIgNCq9X+////v/+5f1ENAQsgAyAEWg0AIAchAyAFIQQgCSEGIAghCgwBCyAIQv//z4rr///VHn0iBiALQqvV/v///7//uX9UrSIDfSEKIAlCpOzDtY/UtJjnAH0iBCAIQv//z4rr///VHlQgAyAGVnKtIgN9IQYgBUK/pZScz/DSu+QAfSIIIAlCpOzDtY/UtJjnAFQgAyAEVnKtIgN9IQQgB0LX2a6a5PbpjcsAfSIJIAVCv6WUnM/w0rvkAFQgAyAIVnKtIgV9IQMgDCAHQtfZrprk9umNywBUIAUgCVZyrX1Cms3/y6O9xIAafSEMIAtC1aqBgICAwIDGAHwhCwsgACALNwMoIAAgCjcDICAAIAY3AxggACAENwMQIAAgAzcDCCAAIAw3AwALhgQCBX8IfiMAQdAAayICJAAgAkHEAGogARCvAyACKAJIIQEgAigCRCEDIAIoAkwiBEECRgRAIAJBEGogAUEQaikDADcDACACQRhqIAFBGGopAwA3AwAgAkEgaiIEIAFBIGopAwA3AwAgAkEoaiABQShqKQMANwMAIAJBMGogAUEwaikDADcDACACQThqIAFBOGopAwA3AwAgAiABKQMINwMIIAEoAgQhBSABKAIAIQYgAwRAIAEgA0EFdBDfBAsgAikDOCEIIAIpAzAhByACKQMoIQogAikDICELAkAgBEGIg8AAQSAQ8QNFBEAgCiEJIAchDAwBC0KNlcfDltLawJd/IAd9IgkgCELH+vPD7YKjkDxWrSINfSEMQt2whYzotpGouH8gCn0iDiAJIA1UIAdCjZXHw5bS2sCXf1ZyrSIHfSEJQqnAxomuzpOyMCAHIA5WIApC3bCFjOi2kai4f1ZyrSALfH0hC0LH+vPD7YKjkDwgCH0hCAsgACAFNgIEIAAgBjYCACAAIAIpAwg3AwggACAINwM4IAAgDDcDMCAAIAk3AyggACALNwMgIABBEGogAkEQaikDADcDACAAQRhqIAJBGGopAwA3AwAgAkHQAGokAA8LIAIgBDYCTCACIAE2AkggAiADNgJEQYCLwABBKyACQcQAakHwisAAQaSNwAAQygMAC5cBAgF/AX4CQCAAIABBIGoiASkDAEI/hiAAQShqKQMAQgGIhDcDKCAAIABBGGopAwAiAkI/hiABKQMAQgGIhDcDICAAIABBEGoiASkDAEI/hiACQgGIhDcDGCAAIABBCGopAwAiAkI/hiABKQMAQgGIhDcDECAAIAApAwBCP4YgAkIBiIQ3AwggACAAKQMAQgGINwMADAALC5cDAQ9/IwBBIGsiByQAIAMgASABIANLGyIJQQJ0IQoCQAJAAkAgCUUNACAJQQFxAkAgCUEBRgRADAELIAlBfnEhDSACIQUgACEEA0AgBCAEKAIAIg4gBSgCACIPayIQIAZrNgIAIARBBGoiCyALKAIAIgsgBUEEaigCACIRayISIA4gD0kgBiAQS3IiBms2AgAgCyARSSAGIBJLciEGIAVBCGohBSAEQQhqIQQgDSAIQQJqIghHDQALCwR/IAAgCEECdCIEaiIFIAUoAgAiBSACIARqKAIAIgRrIgggBms2AgAgBCAFSyAGIAhLcgUgBgtFDQAgACAKaiEEIAFBAnQgCUECdGshBQNAIAVFDQIgBCAEKAIAIgBBAWs2AgAgBUEEayEFIARBBGohBCAARQ0ACwsgAiAKaiEFIANBAnQgCmshBANAIARFDQIgBEEEayEEIAUoAgAgBUEEaiEFRQ0ACwsgB0EANgIYIAdBATYCDCAHQcSKxQA2AgggB0IENwIQIAdBCGpBzIrFABCoBAALIAdBIGokAAvhAwENfiACKQMAIgohBiABKQMAIgshBCAAAn4CQAJ+AkAgCiALUg0AIAIpAwgiByABKQMIIgRSBEAgByEGDAELIAIpAxAiAyABKQMQIgRSBEAgAyEGDAELIAMhBSACKQMYIgYhCCAHIAYgASkDGCIEUQ0BGgsgBCAGVA0BIAIpAwghByACKQMQIQMgASkDECEFIAIpAxghBiABKQMYIQggASkDCAshCSAFIAN9IgwgBiAIVq0iDX0hBCAJIAd9Ig4gDCANVCADIAVWcq0iBX0hAyAFIA5WIAcgCVZyIQIgCyAKfSEHIAggBn0MAQtC3bCFjOi2kai4fyACKQMIIgYgASkDCCIHfSIJIAIpAxAiAyABKQMQIgVUIAMgBX0iAyACKQMYIgUgASkDGCIEVK0iCFRyrSIMfSINfSIOIAMgCH0iA0KR4eXNh4n6mShWQpHh5c2HifqZKCADfSIIIAUgBH0iBUKBgICAv7L98MMAVq0iBFRyrSIPfSEDIA4gD1QgDULdsIWM6LaRqLh/VnIhAiAIIAR9IQQgBiAHVCAJIAxUcq0gCyAKfXxCqcDGia7Ok7IwfCEHQoGAgIC/sv3wwwAgBX0LNwMYIAAgBDcDECAAIAM3AwggACAHIAKtfTcDAAvhAwENfiACKQMAIgohBiABKQMAIgshBCAAAn4CQAJ+AkAgCiALUg0AIAIpAwgiByABKQMIIgRSBEAgByEGDAELIAIpAxAiAyABKQMQIgRSBEAgAyEGDAELIAMhBSACKQMYIgYhCCAHIAYgASkDGCIEUQ0BGgsgBCAGVA0BIAIpAwghByACKQMQIQMgASkDECEFIAIpAxghBiABKQMYIQggASkDCAshCSAFIAN9IgwgBiAIVq0iDX0hBCAJIAd9Ig4gDCANVCADIAVWcq0iBX0hAyAFIA5WIAcgCVZyIQIgCyAKfSEHIAggBn0MAQtC3bCFjOi2kai4fyACKQMIIgYgASkDCCIHfSIJIAIpAxAiAyABKQMQIgVUIAMgBX0iAyACKQMYIgUgASkDGCIEVK0iCFRyrSIMfSINfSIOIAMgCH0iA0KNlcfDltLawJd/VkKNlcfDltLawJd/IAN9IgggBSAEfSIFQsf688PtgqOQPFatIgRUcq0iD30hAyAOIA9UIA1C3bCFjOi2kai4f1ZyIQIgCCAEfSEEIAYgB1QgCSAMVHKtIAsgCn18QqnAxomuzpOyMHwhB0LH+vPD7YKjkDwgBX0LNwMYIAAgBDcDECAAIAM3AwggACAHIAKtfTcDAAu+AwEGfyMAQSBrIgQkACAAKAIEIQUgACgCCCEDIAQgATYCBCADQQBHIgZBAnQhAgJAAkACQCADRQ0AIAUgBSgCACIHIAFrNgIAIAEgB00NACACIAVqIQEgA0ECdCAGQQJ0ayEGA0AgBkUNAiABIAEoAgAiB0EBazYCACAGQQRrIQYgAUEEaiEBIAdFDQALCwNAIAJBBEYNAiAEQQRqIAJqIAJBBGohAigCAEUNAAsLIARBADYCGCAEQQE2AgwgBEHEisUANgIIIARCBDcCECAEQQhqQcyKxQAQqAQACwJAIANFBEBBACEDDAELIAUgA0ECdCICakEEaygCAA0AIAVBBGshBiADQf////8DcSEBAkADQCACRQRAQQAhAgwCCyABQQFrIQEgAiAGaiACQQRrIQIoAgBFDQALIAFBAWoiAiADSw0BCyAAIAI2AgggAiEDCwJAIAMgACgCACIBQQJ2TyABRXJFBEAgAUECdCECAkAgA0UEQEEEIQEgBSACEN8EDAELIAUgAkEEIANBAnQiAhDOBCIBRQ0CCyAAIAM2AgAgACABNgIECyAEQSBqJAAPC0EEIAJBjMHEABDIBAAL/AMBAn8gACABaiECAkACQCAAKAIEIgNBAXENACADQQJxRQ0BIAAoAgAiAyABaiEBIAAgA2siAEGY0sUAKAIARgRAIAIoAgRBA3FBA0cNAUGQ0sUAIAE2AgAgAiACKAIEQX5xNgIEIAAgAUEBcjYCBCACIAE2AgAMAgsgACADEOACCwJAAkACQCACKAIEIgNBAnFFBEAgAkGc0sUAKAIARg0CIAJBmNLFACgCAEYNAyACIANBeHEiAhDgAiAAIAEgAmoiAUEBcjYCBCAAIAFqIAE2AgAgAEGY0sUAKAIARw0BQZDSxQAgATYCAA8LIAIgA0F+cTYCBCAAIAFBAXI2AgQgACABaiABNgIACyABQYACTwRAIAAgARD7Ag8LIAFB+AFxQYDQxQBqIQICf0GI0sUAKAIAIgNBASABQQN2dCIBcUUEQEGI0sUAIAEgA3I2AgAgAgwBCyACKAIICyEBIAIgADYCCCABIAA2AgwgACACNgIMIAAgATYCCA8LQZzSxQAgADYCAEGU0sUAQZTSxQAoAgAgAWoiATYCACAAIAFBAXI2AgQgAEGY0sUAKAIARw0BQZDSxQBBADYCAEGY0sUAQQA2AgAPC0GY0sUAIAA2AgBBkNLFAEGQ0sUAKAIAIAFqIgE2AgAgACABQQFyNgIEIAAgAWogATYCAAsLyQMCBX8BfiMAQUBqIgIkAAJAAkACQAJAAn8gACkDAFBFBEBBCCEDIAAMAQsgACkDCFBFBEBBECEDIABBCGoMAQsgACkDEFBFBEBBGCEDIABBEGoMAQsgACkDGFBFBEBBICEDIABBGGoMAQsgACkDIFBFBEBBKCEDIABBIGoMAQsgACkDKFANAUEwIQMgAEEoagshBiABKAIAIgRBqM/BAEECIAEoAgQiBSgCDBEDAEUNAUEBIQEMAwsgASgCAEG0z8EAQQMgASgCBCgCDBEDAEUNAUEBIQEMAgsgAiAGNgIgQQEhASACQQE2AiwgAkGsz8EANgIoIAJCATcCNCACQoCAgICwByIHIAJBIGqthDcDCCACIAJBCGo2AjAgBCAFIAJBKGoQqwINASAHIAJBBGqthCEHA0AgA0EwRg0BIAIgACADajYCBCACIAc3AyAgAkEBNgIcIAJBATYCDCACQazPwQA2AgggAkEBNgIUIAJCgICAgICEgIBpNwI4IAJCgIDAADcCMCACQQI7ASggA0EIaiEDIAIgAkEoajYCGCACIAJBIGo2AhAgBCAFIAJBCGoQqwJFDQALDAELQQAhAQsgAkFAayQAIAEL8AIBBn8jAEGgBWsiBCQAIAQgARBlIARBgANqIgUgBCAEED8gBEHgA2oiBiABIAEQ1QEgBEHgAGoiByAFIAYQjQEgBiABIAcQjQEgBSAEIAYQPyAEQaACaiAFIAFB4ABqIggQjQEgBEHAAWoiCSAHQeAA/AoAACAEQegEaiAEQShqKQMANwMAIARB4ARqIARBIGopAwA3AwAgBEHYBGogBEEYaikDADcDACAEQdAEaiAEQRBqKQMANwMAIARByARqIARBCGopAwA3AwAgBEH4BGogBEE4aikDADcDACAEQYAFaiAEQUBrKQMANwMAIARBiAVqIARByABqKQMANwMAIARBkAVqIARB0ABqKQMANwMAIARBmAVqIARB2ABqKQMANwMAIAQgBCkDADcDwAQgBCAEKQMwNwPwBCAGIAQgARA/IAUgBiAIEI0BIABBwAFqIARBwARqIAUgAiADECAgACAJQcAB/AoAACAEQaAFaiQAC/ADAQZ/IwBBMGsiAiQAIAIgATYCIAJAIAJBIGoQ4QRFBEBB5+/AAEEeEM0EIQMgAUGEAU8EQCABEKsDCyAAQYCAgIB4NgIAIAAgAzYCBAwBCyACIAE2AhwgAkGF8MAAQQEQzQQiATYCLCACQRBqIAJBHGogAkEsahCABCACKAIUIQMgAigCECEEIAFBhAFPBEAgARCrAwsCQAJAIARBAXEEQCAAQYCAgIB4NgIAIAAgAzYCBAwBCyACQSBqIAMQ7AIgAigCJCEBIAIoAiAiA0GAgICAeEYEQCAAQYCAgIB4NgIAIAAgATYCBAwBCyACKAIoIQYgAkGG8MAAQQEQzQQiBDYCLCACQQhqIAJBHGogAkEsahCABCACKAIMIQUgAigCCCEHIARBhAFPBEAgBBCrAwsCQCAHQQFxBEAgAEGAgICAeDYCACAAIAU2AgQMAQsgAkEgaiAFEOwCIAIoAiQhBCACKAIgIgVBgICAgHhHDQIgAEGAgICAeDYCACAAIAQ2AgQLIANFDQAgASADQQJ0EN8ECyACKAIcIgBBhAFJDQEgABCrAwwBCyAAIAIoAig2AhQgACAENgIQIAAgBTYCDCAAIAY2AgggACABNgIEIAAgAzYCACACKAIcIgBBhAFJDQAgABCrAwsgAkEwaiQAC54DAQx+IAIpAwAiCiEDIAEpAwAiCyEGIAACfgJAAn4CQCAKIAtSDQAgAikDCCIEIAEpAwgiBlIEQCAEIQMMAQsgAikDECIFIAEpAxAiBlIEQCAFIQMMAQsgBSEHIAIpAxgiAyEJIAQgAyABKQMYIgZRDQEaCyADIAZWDQEgAikDCCEEIAIpAxAhBSABKQMQIQcgAikDGCEDIAEpAxghCSABKQMICyEIIAcgBX0iDCADIAlWrSINfSEGIAggBH0iDiAMIA1UIAUgB1ZyrSIHfSEFIAcgDlYgBCAIVnIhAiALIAp9IQQgCSADfQwBCyACKQMQIgMgASkDECIFVCADIAV9IgMgAikDGCIFIAEpAxgiBFStIghUcq0iByACKQMIIgkgASkDCCIMfSINQn+FfCIGIANCf4UgCHwiAyAFIAR9IghCbVatIgRUrSIOfSEFIAYgDlQhAiADIAR9IQYgCSAMVCAHIA1Wcq0gCyAKfXxC////////////AHwhBEJtIAh9CzcDGCAAIAY3AxAgACAFNwMIIAAgBCACrX03AwALnQMBDH4gAikDACIKIQMgASkDACILIQYgAAJ+AkACfgJAIAogC1INACACKQMIIgQgASkDCCIGUgRAIAQhAwwBCyACKQMQIgUgASkDECIGUgRAIAUhAwwBCyAFIQcgAikDGCIDIQkgBCADIAEpAxgiBlENARoLIAMgBlYNASACKQMIIQQgAikDECEFIAEpAxAhByACKQMYIQMgASkDGCEJIAEpAwgLIQggByAFfSIMIAMgCVatIg19IQYgCCAEfSIOIAwgDVQgBSAHVnKtIgd9IQUgByAOViAEIAhWciECIAsgCn0hBCAJIAN9DAELIAIpAxAiAyABKQMQIgVUIAMgBX0iAyACKQMYIgUgASkDGCIEVK0iCFRyrSIHIAIpAwgiCSABKQMIIgx9Ig1Cf4V8IgYgA0J/hSAIfCIDIAUgBH0iCEKv+P//b1atIgRUrSIOfSEFIAYgDlQhAiADIAR9IQYgCSAMVCAHIA1Wcq0gCyAKQn+FfHwhBEKv+P//byAIfQs3AxggACAGNwMQIAAgBTcDCCAAIAQgAq19NwMAC5kDAQx+IAIpAwAiCiEDIAEpAwAiCyEFIAACfgJAAn4CQCAKIAtSDQAgAikDCCIGIAEpAwgiBVIEQCAGIQMMAQsgAikDECIEIAEpAxAiBVIEQCAEIQMMAQsgBCEHIAIpAxgiAyEIIAYgAyABKQMYIgVRDQEaCyADIAVWDQEgAikDCCEGIAIpAxAhBCABKQMQIQcgAikDGCEDIAEpAxghCCABKQMICyEJIAcgBH0iDCADIAhWrSINfSEFIAkgBn0iDiAMIA1UIAQgB1ZyrSIHfSEEIAcgDlYgBiAJVnIhAiALIAp9IQYgCCADfQwBCyACKQMQIgMgASkDECIEVCADIAR9IgQgAikDGCIJIAEpAxgiB1StIgVUcq0iAyACKQMIIgggASkDCCIMfSIGfSINIAQgBX0iBUL/////D1atIg59IQQgAyAGUiANIA5UciECQv////8PIAV9IQUgCCAMVCADIAZWcq0gCyAKfXxC/////w99IQYgByAJQn+FfAs3AxggACAFNwMQIAAgBDcDCCAAIAYgAq19NwMAC/4CAQF/IAAoAgAiAQRAIAAoAgQgAUECdBDfBAsgACgCDCIBBEAgACgCECABQQJ0EN8ECyAAKAIYIgEEQCAAKAIcIAFBAnQQ3wQLIAAoAiQiAQRAIAAoAiggAUECdBDfBAsgACgCMCIBBEAgACgCNCABQQJ0EN8ECyAAKAI8IgEEQCAAKAJAIAFBAnQQ3wQLIAAoAkgiAQRAIAAoAkwgAUECdBDfBAsgACgCVCIBBEAgACgCWCABQQJ0EN8ECyAAKAJgIgEEQCAAKAJkIAFBAnQQ3wQLIAAoAmwiAQRAIAAoAnAgAUECdBDfBAsgACgCeCIBBEAgACgCfCABQQJ0EN8ECyAAKAKEASIBBEAgACgCiAEgAUECdBDfBAsgACgCkAEiAQRAIAAoApQBIAFBAnQQ3wQLIAAoApwBIgEEQCAAKAKgASABQQJ0EN8ECyAAKAKoASIBBEAgACgCrAEgAUECdBDfBAsgACgCtAEiAQRAIAAoArgBIAFBAnQQ3wQLC+ADAgl+BH8gAigCBCEMIAIoAgAgACABRwRAIAIoAgggDEEwbGohDyAMIAEgAGtBMG4iDWohDEEAIQEDQAJ+IAAgAWoiAkHw98AAQTAQ8QMEQEL//8+K6///1R4gAkEgaikDACIGfSIEIAJBKGopAwAiB0Kr1f7///+//7l/Vq0iBX0hCUKk7MO1j9S0mOcAIAJBGGopAwAiA30iCCAEIAVUIAZC///Piuv//9UeVnKtIgR9IQZCv6WUnM/w0rvkACACQRBqKQMAIgV9IgogBCAIViADQqTsw7WP1LSY5wBWcq0iA30hBELX2a6a5PbpjcsAIAJBCGopAwAiCH0iCyADIApWIAVCv6WUnM/w0rvkAFZyrSIDfSEFQqvV/v///7//uX8gB30hB0Kazf/Lo73EgBogAikDACADIAtWIAhC19mumuT26Y3LAFZyrXx9DAELIAJBKGopAwAhByACQSBqKQMAIQkgAkEYaikDACEGIAJBEGopAwAhBCACQQhqKQMAIQUgAikDAAshAyABIA9qIgIgAzcDACACQShqIAc3AwAgAkEgaiAJNwMAIAJBGGogBjcDACACQRBqIAQ3AwAgAkEIaiAFNwMAIAFBMGohASANQQFrIg0NAAsLIAw2AgALgwMCCX8BfiMAQRBrIgUkACAFQQA2AgwgBUKAgICAEDcCBAJ/QQEgASAChFANABoDQCAFKAIEIARGBEAgBUEEakHE2sIAELYDCyAFKAIIIARqIAE8AAAgBSAEQQFqIgQ2AgwgAkI4hiABQoACVCEDIAJQIQYgAkIIiCECIAFCCIiEIQEgAyAGcUUNAAtBASEDIAUoAggiBiAEQQFGDQAaQQAhAyAEQQF2IgdBAUcEQCAEQQFrIQggB0H+////B3EhCgNAIAYgCGoiBy0AACEJIAcgAyAGaiIHLQAAOgAAIAcgCToAACAGIANBfnNqIARqIgktAAAhCyAJIAdBAWoiBy0AADoAACAHIAs6AAAgCEECayEIIAogA0ECaiIDRw0ACwsgBEECcQRAIAMgBmoiCC0AACEHIAggBiADayAEakEBayIDLQAAOgAAIAMgBzoAAAsgBSgCDCEDIAUoAggLIQYgBSgCBCEEIAAgBiADEIYBIAQEQCAGIAQQ3wQLIAVBEGokAAvjAgELfyMAQSBrIgckACABIANPBEACQCADRQ0AIANBAXECQCADQQFGBEAMAQsgA0F+cSELIAIhBSAAIQQDQCAEIAYgBCgCACIMIAUoAgBqIgZqIg02AgAgBEEEaiIIIAgoAgAiDiAFQQRqKAIAaiIIIAYgDEkgBiANS3JqIgY2AgAgCCAOSSAGIAhJciIIIQYgBUEIaiEFIARBCGohBCALIAlBAmoiCUcNAAsLBH8gACAJQQJ0IgVqIgQgBCgCACIEIAIgBWooAgBqIgIgBmoiBTYCACACIARJIAIgBUtyBSAIC0UgASADRnINACAAIANBAnQiAmohBCABQQJ0IAJrQQRrIQUDQCAEIAQoAgBBAWoiADYCACAADQEgBEEEaiEEIAUgBUEEayEFDQALCyAHQSBqJAAPCyAHQQA2AhggB0EBNgIMIAdBlIfFADYCCCAHQgQ3AhAgB0EIakGEiMUAEKgEAAuBBwEMfyMAQTBrIgQkACAEIAM6AAcCQAJAIANB/wFxIgMEQCADQSBLDQEgBCACNgIMIAQgATYCCCAEQSAgA242AhAgBCAEQQdqNgIUIARBGGohDEEAIQEjAEEQayIFJAAgBEEIaiICKAIIIQYCQAJAAkACQCACKAIEIgMEQCAGRQ0BIAMgBm4gAyAGcEEAR2ohAQsgAUH/////A0sgAUECdCIHQfz///8HS3INAQJAIAdFBEBBBCEKQQAhAQwBC0HRzsUALQAAGkEEIQggB0EEENYEIgpFDQILIAVBADYCDCAFIAo2AgggBSABNgIEIAMEQCAGRQ0DIAIoAgwhDyACKAIAIQ0gASADIAZuIgIgAyACIAZsR2oiAkkEQCAFQQRqQQAgAhCJAyAFKAIIIQogBSgCDCEJCwNAIA8tAABBH3EhByAGIAMgAyAGSxsiC0EDcSEIQQAhASALIA1qIg0hAiALQQRPBEAgC0F8cSEOA0AgAkEDay0AACACQQJrLQAAIAJBAWstAAAgASAHdHIgB3RyIAd0ciAHdCACQQRrIgItAAByIQEgDkEEayIODQALCyAIBEAgAkEBayECA0AgAi0AACABIAd0ciEBIAJBAWshAiAIQQFrIggNAAsLIAogCUECdGogATYCACAJQQFqIQkgAyALayIDDQALCyAMIAUpAgQ3AgAgDEEIaiAJNgIAIAVBEGokAAwDC0GEhMUAEJoEAAsgCCAHQfjMxAAQyAQAC0GEhMUAEJoEAAsgBCgCICIBRQRAQQAhAQwDCyAEKAIcIgIgAUECdCIDakEEaygCAA0CIAJBBGshBSABQf////8DcSECAkADQCADRQRAQQAhAwwCCyACQQFrIQIgAyAFaiADQQRrIQMoAgBFDQALIAJBAWoiAyABSw0DCyAEIAM2AiAgAyEBDAILQdzLxAAQmgQACyAEQQA2AiggBEEBNgIcIARBiMzEADYCGCAEQgQ3AiAgBEEYakGQzMQAEKgEAAsCQCABIAQoAhgiAkECdk8gAkVyRQRAIAQoAhwhAyACQQJ0IQUCQCABRQRAQQQhAiADIAUQ3wQMAQsgAyAFQQQgAUECdCIDEM4EIgJFDQILIAQgATYCGCAEIAI2AhwLIAAgBCkCGDcCACAAQQhqIARBIGooAgA2AgAgBEEwaiQADwtBBCADQfzxxAAQyAQAC4IDAQR/IAAoAgAiAQRAIAAoAgQgAUECdBDfBAsgACgCDCIBBEAgACgCECABQQJ0EN8ECyAAKAIYIgEEQCAAKAIcIAFBAnQQ3wQLIAAoAiQiAQRAIAAoAiggAUECdBDfBAsgACgCMCIBBEAgACgCNCABQQJ0EN8ECyAAKAI8IgEEQCAAKAJAIAFBAnQQ3wQLIAAoAkgiAQRAIAAoAkwgAUECdBDfBAsgACgCVCIBBEAgACgCWCABQQJ0EN8ECyAAKAJkIQEgACgCaCIDBEAgASECA0AgAigCACIEBEAgAkEEaigCACAEQQJ0EN8ECyACQQxqIQIgA0EBayIDDQALCyAAKAJgIgIEQCABIAJBDGwQ3wQLAkAgACgCbCIBQYCAgIB4Rg0AIAEEQCAAKAJwIAEQ3wQLIAAoAngiAUUNACAAKAJ8IAEQ3wQLAkAgACgChAEiAUGAgICAeEYNACABBEAgACgCiAEgARDfBAsgACgCkAEiAUUNACAAKAKUASABEN8ECwuWBwIJfgJ/IwBBIGsiDCQAIwBBQGoiCyQAQpGAgICAgICACCEJIAtBMGpCACABKQMYfSICQgBCkYCAgICAgIAIQgAQyQMgC0IAIAJCAFKtIgQgASkDEHwiAn1CAEKRgICAgICAgAhCABDJAyALQRBqQgAgAkIAUq0iAyACIARUrSIEIAEpAwh8IgV8IgJ9QgBCkYCAgICAgIAIQgAQyQMgC0EgakIAIAJCAFKtIgcgAiADVK0iAyALKQMwIgggASkDAHwiAiAEIAVWrXwiBXwiCnwiBH1CAEKRgICAgICAgAhCABDJAwJAIAspAyggCykDGCALKQMIIAIgBVatIAspAzggAiAIVK18fCIFIAspAwB8IgIgBVStfCACIAMgClatfCIDIAJUrXwiBSALKQMQfCICIAVUrXwgAiACIAMgBCAHVK0iA3wiByADVK18IgJWrXwiAyALKQMgfCIFIANUrXwgBSAFIAIgBEIAUq0iBCAHfCICIARUrSIDfCIEIANUrXwiA1atfCIIQpGAgICAgICACFQEQCACIQYgBCEFIAMhByAIIQkMAQtCACEFQgAhByACIASEIAOEUA0AIAJCAX0hBiAEIAJQrSICfSEFIAMgAiAEVq0iAn0hByAIIAIgA1atfUKRgICAgICAgAh9IQkLIAwgBjcDGCAMIAU3AxAgDCAHNwMIIAwgCTcDACALQUBrJAAgDCkDACECIAwpAwghBCAMKQMQIQMgACAMKQMYIgZCOIYgBkKA/gODQiiGhCAGQoCA/AeDQhiGIAZCgICA+A+DQgiGhIQgBkIIiEKAgID4D4MgBkIYiEKAgPwHg4QgBkIoiEKA/gODIAZCOIiEhIQ3ABggACADQjiGIANCgP4Dg0IohoQgA0KAgPwHg0IYhiADQoCAgPgPg0IIhoSEIANCCIhCgICA+A+DIANCGIhCgID8B4OEIANCKIhCgP4DgyADQjiIhISENwAQIAAgBEI4hiAEQoD+A4NCKIaEIARCgID8B4NCGIYgBEKAgID4D4NCCIaEhCAEQgiIQoCAgPgPgyAEQhiIQoCA/AeDhCAEQiiIQoD+A4MgBEI4iISEhDcACCAAIAJCOIYgAkKA/gODQiiGhCACQoCA/AeDQhiGIAJCgICA+A+DQgiGhIQgAkIIiEKAgID4D4MgAkIYiEKAgPwHg4QgAkIoiEKA/gODIAJCOIiEhIQ3AAAgDEEgaiQAC5EDAQd/IwBBEGsiBCQAAkACQAJAAkAgASgCBCICBEAgASgCACEHIAJBA3EhBQJAIAJBBEkEQEEAIQIMAQsgB0EcaiEDIAJBfHEhCEEAIQIDQCADKAIAIANBCGsoAgAgA0EQaygCACADQRhrKAIAIAJqampqIQIgA0EgaiEDIAggBkEEaiIGRw0ACwsgBQRAIAZBA3QgB2pBBGohAwNAIAMoAgAgAmohAiADQQhqIQMgBUEBayIFDQALCyABKAIMRQ0CIAJBD0sNASAHKAIEDQEMAwtBACECIAEoAgxFDQILIAJBACACQQBKG0EBdCECC0EAIQUgAkEATgRAIAJFDQFB0c7FAC0AABpBASEFIAJBARDWBCIDDQILIAUgAkH8rMUAEMgEAAtBASEDQQAhAgsgBEEANgIIIAQgAzYCBCAEIAI2AgAgBEH8q8UAIAEQqwJFBEAgACAEKQIANwIAIABBCGogBEEIaigCADYCACAEQRBqJAAPC0GcrcUAQdYAIARBD2pBjK3FAEGMrsUAEMoDAAufAwIFfwF+IwBBQGoiAiQAAkACQAJAAkACfyAAKQMAUEUEQEEIIQMgAAwBCyAAKQMIUEUEQEEQIQMgAEEIagwBCyAAKQMQUEUEQEEYIQMgAEEQagwBCyAAKQMYUA0BQSAhAyAAQRhqCyEGIAEoAgAiBEGoz8EAQQIgASgCBCIFKAIMEQMARQ0BQQEhAQwDCyABKAIAQbTPwQBBAyABKAIEKAIMEQMARQ0BQQEhAQwCCyACIAY2AiBBASEBIAJBATYCLCACQazPwQA2AiggAkIBNwI0IAJCgICAgLAHIgcgAkEgaq2ENwMIIAIgAkEIajYCMCAEIAUgAkEoahCrAg0BIAcgAkEEaq2EIQcDQCADQSBGDQEgAiAAIANqNgIEIAIgBzcDICACQQE2AhwgAkEBNgIMIAJBrM/BADYCCCACQQE2AhQgAkKAgICAgISAgGk3AjggAkKAgMAANwIwIAJBAjsBKCADQQhqIQMgAiACQShqNgIYIAIgAkEgajYCECAEIAUgAkEIahCrAkUNAAsMAQtBACEBCyACQUBrJAAgAQvpAgEFfwJAIAFBzf97QRAgACAAQRBNGyIAa08NACAAQRAgAUELakF4cSABQQtJGyIEakEMahBTIgJFDQAgAkEIayEBAkAgAEEBayIDIAJxRQRAIAEhAAwBCyACQQRrIgUoAgAiBkF4cSACIANqQQAgAGtxQQhrIgIgAEEAIAIgAWtBEE0baiIAIAFrIgJrIQMgBkEDcQRAIAAgAyAAKAIEQQFxckECcjYCBCAAIANqIgMgAygCBEEBcjYCBCAFIAIgBSgCAEEBcXJBAnI2AgAgASACaiIDIAMoAgRBAXI2AgQgASACEMQCDAELIAEoAgAhASAAIAM2AgQgACABIAJqNgIACwJAIAAoAgQiAUEDcUUNACABQXhxIgIgBEEQak0NACAAIAQgAUEBcXJBAnI2AgQgACAEaiIBIAIgBGsiBEEDcjYCBCAAIAJqIgIgAigCBEEBcjYCBCABIAQQxAILIABBCGohAwsgAwuFAwEEfyMAQbABayICJAAgAkEANgIQIAJCgICAgMAANwIIIAJBFGogAS0AMBDpAyACQQhqIgVB3N/AABCfAyACKAIMIgMgAikCFDcCACADQQhqIAJBHGooAgA2AgAgAkEBNgIQIAJBIGoiBCABEN8BIAJB+ABqIAQQ1AEgAigCCCACKAIQIgRrQQNNBEAgBSAEQQRBBEEMEIgDIAIoAhAhBAsgAigCDCAEQQxsaiIDIAIpAng3AgAgA0EIaiACQYABaikCADcCACADQRBqIAJBiAFqKQIANwIAIANBGGogAkGQAWopAgA3AgAgA0EgaiACQZgBaikCADcCACADQShqIAJBoAFqKQIANwIAIAIgBEEEajYCECACQewAaiABLQAxEOkDIAIoAhAiASACKAIIRgRAIAJBCGpB7N/AABCfAwsgAigCDCABQQxsaiIDIAIpAmw3AgAgA0EIaiACQfQAaigCADYCACAAQQhqIAFBAWo2AgAgACACKQIINwIAIAJBsAFqJAALhwMBBn8CQAJAIAJB/////wNLIAJBAnQiA0H8////B0tyDQACfyADRQRAQQQhBEEADAELQdHOxQAtAAAaQQQhBSADQQQQ1gQiBEUNASACCyEGIAMEQCAEIAEgA/wKAAALQQAhASACRQ0BIAQgAkECdGpBBGsoAgAEQCACIQEMAgsgBEEEayEHIAIhBQNAIANFDQIgBUEBayEFIAMgB2ogA0EEayEDKAIARQ0ACyAFQQFqIgEgAiABIAJJGyEBDAELIAUgA0H4wsQAEMgEAAsCQAJAAkAgBkECdiABTQRAIAENASAAQQhqQYDExAApAgA3AgAgAEH4w8QAKQIANwIAIAZFDQIgBCAGQQJ0EN8EDwsgBkECdCECIAFFBEAgBCACEN8EIABBCGpBgMTEACkCADcCACAAQfjDxAApAgA3AgAPCyABIQYgBCACQQQgAUECdCICEM4EIgRFDQILIABBAjoADCAAIAE2AgggACAENgIEIAAgBjYCAAsPC0EEIAJBtMnEABDIBAAL/QIBCX8jAEEQayIFJAAgBUEEaiABEOoBIAUoAgghBwJAAkAgBSgCDCICRQRAIABBCGpBuMzCACgCADYCACAAQbDMwgApAgA3AgAMAQtBACEBIAJBAEgNAUHRzsUALQAAGkEBIQEgAkEBENYEIgRFDQEgAgRAIAQgByAC/AoAAAsgACAEAn9BASACQQFGDQAaIAIgBGohCEEAIQEgAkEBdiIDQQFHBEAgAkEBayEAIANB/v///wNxIQoDQCAAIARqIgYtAAAhAyAGIAEgBGoiCS0AADoAACAJIAM6AAAgCCABQX5zaiIDLQAAIQYgAyAJQQFqIgMtAAA6AAAgAyAGOgAAIABBAmshACAKIAFBAmoiAUcNAAsLIAIgAkECcUUNABogASAEaiIDLQAAIQAgAyAIIAFBf3NqIgEtAAA6AAAgASAAOgAAIAILQQgQzwIgBCACEN8ECyAFKAIEIgAEQCAHIAAQ3wQLIAVBEGokAA8LIAEgAkHU2MIAEMgEAAv9AgEJfyMAQRBrIgUkACAFQQRqIAEQnwEgBSgCCCEHAkACQCAFKAIMIgJFBEAgAEEIakG4zMIAKAIANgIAIABBsMzCACkCADcCAAwBC0EAIQEgAkEASA0BQdHOxQAtAAAaQQEhASACQQEQ1gQiBEUNASACBEAgBCAHIAL8CgAACyAAIAQCf0EBIAJBAUYNABogAiAEaiEIQQAhASACQQF2IgNBAUcEQCACQQFrIQAgA0H+////A3EhCgNAIAAgBGoiBi0AACEDIAYgASAEaiIJLQAAOgAAIAkgAzoAACAIIAFBfnNqIgMtAAAhBiADIAlBAWoiAy0AADoAACADIAY6AAAgAEECayEAIAogAUECaiIBRw0ACwsgAiACQQJxRQ0AGiABIARqIgMtAAAhACADIAggAUF/c2oiAS0AADoAACABIAA6AAAgAgtBCBDPAiAEIAIQ3wQLIAUoAgQiAARAIAcgABDfBAsgBUEQaiQADwsgASACQdTYwgAQyAQAC/0CAQl/IwBBEGsiBSQAIAVBBGogARDJASAFKAIIIQcCQAJAIAUoAgwiAkUEQCAAQQhqQbjMwgAoAgA2AgAgAEGwzMIAKQIANwIADAELQQAhASACQQBIDQFB0c7FAC0AABpBASEBIAJBARDWBCIERQ0BIAIEQCAEIAcgAvwKAAALIAAgBAJ/QQEgAkEBRg0AGiACIARqIQhBACEBIAJBAXYiA0EBRwRAIAJBAWshACADQf7///8DcSEKA0AgACAEaiIGLQAAIQMgBiABIARqIgktAAA6AAAgCSADOgAAIAggAUF+c2oiAy0AACEGIAMgCUEBaiIDLQAAOgAAIAMgBjoAACAAQQJrIQAgCiABQQJqIgFHDQALCyACIAJBAnFFDQAaIAEgBGoiAy0AACEAIAMgCCABQX9zaiIBLQAAOgAAIAEgADoAACACC0EIEM8CIAQgAhDfBAsgBSgCBCIABEAgByAAEN8ECyAFQRBqJAAPCyABIAJB1NjCABDIBAAL/QIBCX8jAEEQayIFJAAgBUEEaiABEL4BIAUoAgghBwJAAkAgBSgCDCICRQRAIABBCGpBuMzCACgCADYCACAAQbDMwgApAgA3AgAMAQtBACEBIAJBAEgNAUHRzsUALQAAGkEBIQEgAkEBENYEIgRFDQEgAgRAIAQgByAC/AoAAAsgACAEAn9BASACQQFGDQAaIAIgBGohCEEAIQEgAkEBdiIDQQFHBEAgAkEBayEAIANB/v///wNxIQoDQCAAIARqIgYtAAAhAyAGIAEgBGoiCS0AADoAACAJIAM6AAAgCCABQX5zaiIDLQAAIQYgAyAJQQFqIgMtAAA6AAAgAyAGOgAAIABBAmshACAKIAFBAmoiAUcNAAsLIAIgAkECcUUNABogASAEaiIDLQAAIQAgAyAIIAFBf3NqIgEtAAA6AAAgASAAOgAAIAILQQgQzwIgBCACEN8ECyAFKAIEIgAEQCAHIAAQ3wQLIAVBEGokAA8LIAEgAkHU2MIAEMgEAAv9AgEJfyMAQRBrIgUkACAFQQRqIAEQlAIgBSgCCCEHAkACQCAFKAIMIgJFBEAgAEEIakG4zMIAKAIANgIAIABBsMzCACkCADcCAAwBC0EAIQEgAkEASA0BQdHOxQAtAAAaQQEhASACQQEQ1gQiBEUNASACBEAgBCAHIAL8CgAACyAAIAQCf0EBIAJBAUYNABogAiAEaiEIQQAhASACQQF2IgNBAUcEQCACQQFrIQAgA0H+////A3EhCgNAIAAgBGoiBi0AACEDIAYgASAEaiIJLQAAOgAAIAkgAzoAACAIIAFBfnNqIgMtAAAhBiADIAlBAWoiAy0AADoAACADIAY6AAAgAEECayEAIAogAUECaiIBRw0ACwsgAiACQQJxRQ0AGiABIARqIgMtAAAhACADIAggAUF/c2oiAS0AADoAACABIAA6AAAgAgtBCBDPAiAEIAIQ3wQLIAUoAgQiAARAIAcgABDfBAsgBUEQaiQADwsgASACQdTYwgAQyAQAC/0CAQl/IwBBEGsiBSQAIAVBBGogARC/ASAFKAIIIQcCQAJAIAUoAgwiAkUEQCAAQQhqQbjMwgAoAgA2AgAgAEGwzMIAKQIANwIADAELQQAhASACQQBIDQFB0c7FAC0AABpBASEBIAJBARDWBCIERQ0BIAIEQCAEIAcgAvwKAAALIAAgBAJ/QQEgAkEBRg0AGiACIARqIQhBACEBIAJBAXYiA0EBRwRAIAJBAWshACADQf7///8DcSEKA0AgACAEaiIGLQAAIQMgBiABIARqIgktAAA6AAAgCSADOgAAIAggAUF+c2oiAy0AACEGIAMgCUEBaiIDLQAAOgAAIAMgBjoAACAAQQJrIQAgCiABQQJqIgFHDQALCyACIAJBAnFFDQAaIAEgBGoiAy0AACEAIAMgCCABQX9zaiIBLQAAOgAAIAEgADoAACACC0EIEM8CIAQgAhDfBAsgBSgCBCIABEAgByAAEN8ECyAFQRBqJAAPCyABIAJB1NjCABDIBAALkwMCCH4BfwJAAkAgAUHo0cEAQSAQ8QNFBEAgAUEgaiIKQejRwQBBIBDxA0UNAQsgASkDOCEDIAEpAzAhAiABKQMoIQUgASkDICEGAkAgAUEgakHo0cEAQSAQ8QNFBEAgBSEEIAIhBwwBC0KNlcfDltLawJd/IAJ9IgQgA0LH+vPD7YKjkDxWrSIIfSEHQt2whYzotpGouH8gBX0iCSAEIAhUIAJCjZXHw5bS2sCXf1ZyrSICfSEEQqnAxomuzpOyMCACIAlWIAVC3bCFjOi2kai4f1ZyrSAGfH0hBkLH+vPD7YKjkDwgA30hAwsgACADNwM4IAAgBzcDMCAAIAQ3AyggACAGNwMgIAAgASkDADcDAAwBCyAAIAopAwA3AyAgACABKQMANwMAIABBOGogCkEYaikDADcDACAAQTBqIApBEGopAwA3AwAgAEEoaiAKQQhqKQMANwMACyAAQQhqIAFBCGopAwA3AwAgAEEQaiABQRBqKQMANwMAIABBGGogAUEYaikDADcDACAAIAEtAEA6AEAL5wIBCH8jAEEQayIGJABBCiEDIAAiBEHoB08EQCAEIQUDQCAGQQZqIANqIgdBA2sgBSAFQZDOAG4iBEGQzgBsayIIQf//A3FB5ABuIglBAXQiCkH+t8UAai0AADoAACAHQQRrIApB/bfFAGotAAA6AAAgB0EBayAIIAlB5ABsa0H//wNxQQF0IghB/rfFAGotAAA6AAAgB0ECayAIQf23xQBqLQAAOgAAIANBBGshAyAFQf+s4gRLIAQhBQ0ACwsCQCAEQQlNBEAgBCEFDAELIAMgBmpBBWogBCAEQf//A3FB5ABuIgVB5ABsa0H//wNxQQF0IgRB/rfFAGotAAA6AAAgA0ECayIDIAZBBmpqIARB/bfFAGotAAA6AAALQQAgACAFG0UEQCADQQFrIgMgBkEGamogBUEBdEEecUH+t8UAai0AADoAAAsgAiABQQFBACAGQQZqIANqQQogA2sQiQIgBkEQaiQAC+ECAQJ/IwBBEGsiAiQAAkAgAUGAAU8EQCACQQA2AgwCfyABQYAQTwRAIAFBgIAETwRAIAIgAUE/cUGAAXI6AA8gAiABQRJ2QfABcjoADCACIAFBBnZBP3FBgAFyOgAOIAIgAUEMdkE/cUGAAXI6AA0gAkEQagwCCyACIAFBP3FBgAFyOgAOIAIgAUEMdkHgAXI6AAwgAiABQQZ2QT9xQYABcjoADSACQQxqQQNyDAELIAIgAUE/cUGAAXI6AA0gAiABQQZ2QcABcjoADCACQQxqQQJyCyACQQxqayIBIAAoAgAgACgCCCIDa0sEQCAAIAMgAUEBQQEQiAMgACgCCCEDCyABBEAgACgCBCADaiACQQxqIAH8CgAACyAAIAEgA2o2AggMAQsgACgCCCIDIAAoAgBGBEAgAEH02MEAELYDCyAAKAIEIANqIAE6AAAgACADQQFqNgIICyACQRBqJABBAAuCAwEEfyAAKAIMIQICQAJAAkAgAUGAAk8EQCAAKAIYIQMCQAJAIAAgAkYEQCAAQRRBECAAKAIUIgIbaigCACIBDQFBACECDAILIAAoAggiASACNgIMIAIgATYCCAwBCyAAQRRqIABBEGogAhshBANAIAQhBSABIgJBFGogAkEQaiACKAIUIgEbIQQgAkEUQRAgARtqKAIAIgENAAsgBUEANgIACyADRQ0CAkAgACgCHEECdEHwzsUAaiIBKAIAIABHBEAgAygCECAARg0BIAMgAjYCFCACDQMMBAsgASACNgIAIAJFDQQMAgsgAyACNgIQIAINAQwCCyAAKAIIIgAgAkcEQCAAIAI2AgwgAiAANgIIDwtBiNLFAEGI0sUAKAIAQX4gAUEDdndxNgIADwsgAiADNgIYIAAoAhAiAQRAIAIgATYCECABIAI2AhgLIAAoAhQiAEUNACACIAA2AhQgACACNgIYDwsPC0GM0sUAQYzSxQAoAgBBfiAAKAIcd3E2AgAL4gIBBH8jAEEQayICJAACQCABQYABTwRAIAJBDGoiBEECciEDIAJBADYCDAJAIAFBgBBPBEAgBEEDciEFIAFBgIAETwRAIAJBEGohAyACIAFBEnZB8AFyOgAMIAIgAUEGdkE/cUGAAXI6AA4gAiABQQx2QT9xQYABcjoADSAFIQQMAgsgAiABQQx2QeABcjoADCACIAFBBnZBP3FBgAFyOgANIAMhBCAFIQMMAQsgAkEMakEBciEEIAIgAUEGdkHAAXI6AAwLIAQgAUE/cUGAAXI6AAAgAyACQQxqayIBIAAoAgAgACgCCCIDa0sEQCAAIAMgAUEBQQEQiAMgACgCCCEDCyABBEAgACgCBCADaiACQQxqIAH8CgAACyAAIAEgA2o2AggMAQsgACgCCCIDIAAoAgBGBEAgAEGEosAAELYDCyAAKAIEIANqIAE6AAAgACADQQFqNgIICyACQRBqJABBAAviAgEEfyMAQRBrIgIkAAJAIAFBgAFPBEAgAkEMaiIEQQJyIQMgAkEANgIMAkAgAUGAEE8EQCAEQQNyIQUgAUGAgARPBEAgAkEQaiEDIAIgAUESdkHwAXI6AAwgAiABQQZ2QT9xQYABcjoADiACIAFBDHZBP3FBgAFyOgANIAUhBAwCCyACIAFBDHZB4AFyOgAMIAIgAUEGdkE/cUGAAXI6AA0gAyEEIAUhAwwBCyACQQxqQQFyIQQgAiABQQZ2QcABcjoADAsgBCABQT9xQYABcjoAACADIAJBDGprIgEgACgCACAAKAIIIgNrSwRAIAAgAyABQQFBARCIAyAAKAIIIQMLIAEEQCAAKAIEIANqIAJBDGogAfwKAAALIAAgASADajYCCAwBCyAAKAIIIgMgACgCAEYEQCAAQZSBwQAQtgMLIAAoAgQgA2ogAToAACAAIANBAWo2AggLIAJBEGokAEEAC+ICAQR/IwBBEGsiAiQAAkAgAUGAAU8EQCACQQxqIgRBAnIhAyACQQA2AgwCQCABQYAQTwRAIARBA3IhBSABQYCABE8EQCACQRBqIQMgAiABQRJ2QfABcjoADCACIAFBBnZBP3FBgAFyOgAOIAIgAUEMdkE/cUGAAXI6AA0gBSEEDAILIAIgAUEMdkHgAXI6AAwgAiABQQZ2QT9xQYABcjoADSADIQQgBSEDDAELIAJBDGpBAXIhBCACIAFBBnZBwAFyOgAMCyAEIAFBP3FBgAFyOgAAIAMgAkEMamsiASAAKAIAIAAoAggiA2tLBEAgACADIAFBAUEBEIgDIAAoAgghAwsgAQRAIAAoAgQgA2ogAkEMaiAB/AoAAAsgACABIANqNgIIDAELIAAoAggiAyAAKAIARgRAIABB/JnCABC2AwsgACgCBCADaiABOgAAIAAgA0EBajYCCAsgAkEQaiQAQQAL4gIBBH8jAEEQayICJAACQCABQYABTwRAIAJBDGoiBEECciEDIAJBADYCDAJAIAFBgBBPBEAgBEEDciEFIAFBgIAETwRAIAJBEGohAyACIAFBEnZB8AFyOgAMIAIgAUEGdkE/cUGAAXI6AA4gAiABQQx2QT9xQYABcjoADSAFIQQMAgsgAiABQQx2QeABcjoADCACIAFBBnZBP3FBgAFyOgANIAMhBCAFIQMMAQsgAkEMakEBciEEIAIgAUEGdkHAAXI6AAwLIAQgAUE/cUGAAXI6AAAgAyACQQxqayIBIAAoAgAgACgCCCIDa0sEQCAAIAMgAUEBQQEQiAMgACgCCCEDCyABBEAgACgCBCADaiACQQxqIAH8CgAACyAAIAEgA2o2AggMAQsgACgCCCIDIAAoAgBGBEAgAEGg1cIAELYDCyAAKAIEIANqIAE6AAAgACADQQFqNgIICyACQRBqJABBAAv1CgEPfyMAQSBrIgckACABKAIIIgRBAnQhAgJAIARB/////wNLIAJB/P///wdLcg0AIAEtAAwhDiABKAIEIQMCfyACRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhCCACQQQQ1gQiAUUNASAECyEIIAIEQCABIAMgAvwKAAALIAcgBDYCHCAHIAE2AhggByAINgIUIAdBCGohCkECIQgjAEEwayIBJAAgB0EUaiIDKAIIIQIgAygCBCEEIAMoAgAhCSABQSBqIQMCQAJAAkACQAJAA0ACQAJAAkACQCACDgIAAQILIANBtLzEACgCADYCACABQay8xAApAgA3AxgMAgsgBCgCACEGQdHOxQAtAAAaQQRBBBDWBCICRQ0DIAFBLGoiBUEBNgIAIAIgBCgCADYCACABIAI2AiggAUEBNgIkIAFBJGogBhCzAiADIAUoAgA2AgAgASABKQIkNwMYDAELIAFBGGogBCACIAQgAhDtAgsgCQRAIAQgCUECdBDfBAsgCEECcSABKAIgIQIgASgCHCEEIAEoAhghCSAIQQF2IQhFDQALIAhBAUYEQCAKIAI2AgggCiAENgIEIAogCTYCAAwFC0EAIQUgAkH/////A0sgAkECdCIDQfz///8HS3INAQJ/IANFBEBBBCEGQQAMAQtB0c7FAC0AABpBBCEFIANBBBDWBCIGRQ0CIAILIQUgAwRAIAYgBCAD/AoAAAsgASACNgIUIAEgBjYCECABIAU2AgwgCEUNAyABQSBqIQ8DQAJAAkACQAJAIAIOAgABAgsgD0G0vMQAKAIANgIAIAFBrLzEACkCADcDGAwCCyAEKAIAIQNB0c7FAC0AABpBBEEEENYEIgJFDQUgAUEsaiIGQQE2AgAgAiAEKAIANgIAIAEgAjYCKCABQQE2AiQgAUEkaiADELMCIA8gBigCADYCACABIAEpAiQ3AxgMAQsgAUEYaiAEIAIgBCACEO0CCyAJBEAgBCAJQQJ0EN8ECyABKAIgIQIgASgCHCEEIAEoAhghCSAIQQJxBEACQCMAQSBrIgMkAAJAAkAgAUEMaiIGKAIIIgVFDQACQAJAAkAgAg4CAAECCyAGQQA2AggMAgsgBiAEKAIAELMCDAELIAYoAgQhDCAFQQFGBEBBACENIAJB/////wNLIAJBAnQiBUH8////B0tyDQIgDCgCACEQAn8gBUUEQEEEIQtBAAwBC0HRzsUALQAAGkEEIQ0gBUEEENYEIgtFDQMgAgshDSAFBEAgCyAEIAX8CgAACyADQRxqIgUgAjYCACADIAs2AhggAyANNgIUIANBFGogEBCzAiADQRBqIgsgBSgCADYCACADIAMpAhQ3AwggBigCACIFBEAgDCAFQQJ0EN8ECyAGIAMpAwg3AgAgBkEIaiALKAIANgIADAELIANBFGogDCAFIAQgAhDtAiAGKAIAIgUEQCAMIAVBAnQQ3wQLIAYgAykCFDcCACAGQQhqIANBHGooAgA2AgALIANBIGokAAwBCyANIAVBpIPFABDIBAALCyAIQQNLIAhBAXYhCA0ACwwDC0EEQQRBpIPFABDIBAALIAUgA0Gkg8UAEMgEAAtBBEEEQaSDxQAQyAQACyAKIAEpAgw3AgAgCkEIaiABQRRqKAIANgIAIAlFDQAgBCAJQQJ0EN8ECyABQTBqJABBASEBAkAgDkECIA4bIgJBAUcEQCACQQEgBygCEBshAQwBCyAHQQA2AhAgBygCCCICQQRJDQAgBygCDCACQQJ0EN8EIAdCgICAgMAANwIICyAAIAcpAgg3AgAgACABOgAMIABBCGogB0EQaigCADYCACAHQSBqJAAPCyAIIAJBpIPFABDIBAALswIBAX8jAEHwAGsiBiQAIAYgATYCDCAGIAA2AgggBiADNgIUIAYgAjYCECAGQejNxQAoAgA2AhwgBkHczcUAKAIANgIYAkAgBCgCAARAIAZBMGogBEEQaikCADcDACAGQShqIARBCGopAgA3AwAgBiAEKQIANwMgIAZBBDYCXCAGQZi3xQA2AlggBkIENwJkIAYgBkEQaq1CgICAgLAShDcDUCAGIAZBCGqtQoCAgICwEoQ3A0ggBiAGQSBqrUKAgICA0BKENwNADAELIAZBAzYCXCAGQeS2xQA2AlggBkIDNwJkIAYgBkEQaq1CgICAgLAShDcDSCAGIAZBCGqtQoCAgICwEoQ3A0ALIAYgBkEYaq1CgICAgMAShDcDOCAGIAZBOGo2AmAgBkHYAGogBRCoBAALxwMDAn4FfAJ/AkACQAJ/IAC9IgFCgICAgICAgAhZBEAgAUL/////////9/8AVg0DQYF4IQkgAUIgiCICQoCAwP8DUgRAIAKnDAILQYCAwP8DIAGnDQEaRAAAAAAAAAAADwsgAEQAAAAAAAAAAGEEQEQAAAAAAADwvyAAIACiow8LIAFCAFMNAUHLdyEJIABEAAAAAAAAUEOivSIBQiCIpwshCCABQv////8PgyAIQeK+JWoiCEH//z9xQZ7Bmv8Daq1CIIaEv0QAAAAAAADwv6AiACAAIABEAAAAAAAA4D+ioiIDob1CgICAgHCDvyIERAAAIGVHFfc/oiIFIAhBFHYgCWq3IgagIgcgBSAGIAehoCAAIAShIAOhIAAgAEQAAAAAAAAAQKCjIgAgAyAAIACiIgMgA6IiACAAIABEn8Z40Amawz+iRK94jh3Fccw/oKJEBPqXmZmZ2T+goiADIAAgACAARERSPt8S8cI/okTeA8uWZEbHP6CiRFmTIpQkSdI/oKJEk1VVVVVV5T+goqCgoqAiAEQAACBlRxX3P6IgACAEoEQAou8u/AXnPaKgoKAPCyAAIAChRAAAAAAAAAAAoyEACyAAC80CAQZ+IAAoAgAoAgAiACkDCCIDIAEoAgAgAkF0bGpBDGs1AgBCgICAgICAgIAEhCIEhULzytHLp4zZsvQAhSIFQhCJIAUgACkDACIGQuHklfPW7Nm87ACFfCIFhSIHQhWJIAcgA0Lt3pHzlszct+QAhSIDIAZC9crNg9es27fzAIV8IgZCIIl8IgeFIghCEIkgCCAFIANCDYkgBoUiA3wiBUIgiUL/AYV8IgaFIghCFYkgCCAFIANCEYmFIgMgBCAHhXwiBEIgiXwiBYUiB0IQiSAHIAQgA0INiYUiAyAGfCIEQiCJfCIGhSIHQhWJIAcgBCADQhGJhSIDIAV8IgRCIIl8IgWFIgdCEIkgByADQg2JIASFIgMgBnwiBEIgiXwiBoVCFYkgA0IRiSAEhSIDQg2JIAMgBXyFIgNCEYmFIAMgBnwiA0IgiYUgA4ULzQIBBn4gACgCACgCACIAKQMIIgMgASgCACACQQR0a0EQazUCAEKAgICAgICAgASEIgSFQvPK0cunjNmy9ACFIgVCEIkgBSAAKQMAIgZC4eSV89bs2bzsAIV8IgWFIgdCFYkgByADQu3ekfOWzNy35ACFIgMgBkL1ys2D16zbt/MAhXwiBkIgiXwiB4UiCEIQiSAIIAUgA0INiSAGhSIDfCIFQiCJQv8BhXwiBoUiCEIViSAIIAUgA0IRiYUiAyAEIAeFfCIEQiCJfCIFhSIHQhCJIAcgBCADQg2JhSIDIAZ8IgRCIIl8IgaFIgdCFYkgByAEIANCEYmFIgMgBXwiBEIgiXwiBYUiB0IQiSAHIANCDYkgBIUiAyAGfCIEQiCJfCIGhUIViSADQhGJIASFIgNCDYkgAyAFfIUiA0IRiYUgAyAGfCIDQiCJhSADhQvKAgEGfyABIAJBAXRqIQkgAEGA/gNxQQh2IQogAEH/AXEhDAJAAkACQAJAA0AgAUECaiELIAcgAS0AASICaiEIIAogAS0AACIBRwRAIAEgCksNBCAIIQcgCyIBIAlHDQEMBAsgByAISw0BIAQgCEkNAiADIAdqIQEDQCACRQRAIAghByALIgEgCUcNAgwFCyACQQFrIQIgAS0AACABQQFqIQEgDEcNAAsLQQAhAgwDCyAHIAhB0L7FABDmBAALIAggBEHQvsUAEOUEAAsgAEH//wNxIQcgBSAGaiEDQQEhAgNAIAVBAWohAAJAIAUsAAAiAUEATgRAIAAhBQwBCyAAIANHBEAgBS0AASABQf8AcUEIdHIhASAFQQJqIQUMAQtBwL7FABDoBAALIAcgAWsiB0EASA0BIAJBAXMhAiADIAVHDQALCyACQQFxC7ECAQJ/IAAoAggiAgRAIAAoAgQhAANAIAAoAgAiAQRAIABBBGooAgAgAUECdBDfBAsgAEEMaigCACIBBEAgAEEQaigCACABQQJ0EN8ECyAAQRhqKAIAIgEEQCAAQRxqKAIAIAFBAnQQ3wQLIABBJGooAgAiAQRAIABBKGooAgAgAUECdBDfBAsgAEEwaigCACIBBEAgAEE0aigCACABQQJ0EN8ECyAAQTxqKAIAIgEEQCAAQUBrKAIAIAFBAnQQ3wQLIABByABqKAIAIgEEQCAAQcwAaigCACABQQJ0EN8ECyAAQdQAaigCACIBBEAgAEHYAGooAgAgAUECdBDfBAsgAEHgAGooAgAiAQRAIABB5ABqKAIAIAFBAnQQ3wQLIABB7ABqIQAgAkEBayICDQALCwv7AgIFfwFvIwBBIGsiBCQAQQFBABDNBCICJQEgASUBEAEhBxCtAyIDIAcmASABQYQBTwRAIAEQqwMLIAJBhAFPBEAgAhCrAwsgBEEIaiADJQEQAgJAAn8CQAJAIAQoAggiAQRAIAQoAgwhAiADQYQBTwRAIAMQqwMLQQohBSACQQJPDQEMAgtB7O7AAEEjEM0EIQEgAEGAgICAeDYCACAAIAE2AgQgA0GEAUkNAyADEKsDDAMLIAEvAABBsPABRwRAIAEvAABBsLABRw0BCyABQQJqIQNBECEFQQAgAkECRg0BGiACQQJrIAMsAABBQE4NARogASACQQIgAkG078AAENIEAAsgASEDIAILIQYgBEEUaiADIAYgBRDxAQJAIAQoAhRBgICAgHhGBEBBxO/AAEEjEM0EIQMgAEGAgICAeDYCACAAIAM2AgQMAQsgACAEKQIUNwIAIABBCGogBEEcaigCADYCAAsgAkUNACABIAIQ3wQLIARBIGokAAvIAgEGfyACIARqIgpBAWoiB0ECdCEJAkACQCAHQf////8DSyAJQfz///8HS3INAAJ/IAlFBEBBBCEGQQAMAQtB0c7FAC0AABpBBCEFIAlBBBDXBCIGRQ0BIAcLIQUgBiAHIAEgAiADIAQQKSAHRQ0BIAYgB0ECdGpBBGsoAgAEQCAHIQgMAgsgCkECaiEEIApBAnQhAgNAIAJBfEYNAiAEQQFrIQQgAiAGaiACQQRrIQIoAgBFDQALIAQgByAEIAdJGyEIDAELIAUgCUHYyMQAEMgEAAsCQAJAIAggBUECdk8NACAFRQRAQQAhBQwBCyAFQQJ0IQEgCEUEQCAGIAEQ3wRBBCEGQQAhBQwBCyAGIAFBBCAIIgVBAnQiARDOBCIGRQ0BCyAAIAg2AgggACAGNgIEIAAgBTYCAA8LQQQgAUG0ycQAEMgEAAvMAgEDfyMAQRBrIgIkAAJAIAFBgAFPBEAgAkEANgIMAn8gAUGAEE8EQCABQYCABE8EQCACQQxqQQNyIQQgAiABQRJ2QfABcjoADCACIAFBBnZBP3FBgAFyOgAOIAIgAUEMdkE/cUGAAXI6AA1BBAwCCyACQQxqQQJyIQQgAiABQQx2QeABcjoADCACIAFBBnZBP3FBgAFyOgANQQMMAQsgAkEMakEBciEEIAIgAUEGdkHAAXI6AAxBAgshAyAEIAFBP3FBgAFyOgAAIAAoAgAgACgCCCIBayADSQRAIAAgASADEKADIAAoAgghAQsgAwRAIAAoAgQgAWogAkEMaiAD/AoAAAsgACABIANqNgIIDAELIAAoAggiAyAAKAIARgRAIABByK7FABC2AwsgACADQQFqNgIIIAAoAgQgA2ogAToAAAsgAkEQaiQAQQALgAMBCH8jAEEgayIDJAAgA0EIaiABIAIQoQEgAygCHCEJIAMoAhghCiADKAIUIQcgAygCDCEFIAMoAgghBAJAIAMoAhAiBgRAQQIhCAwBC0EBIQggBEUEQEEEIQVBACEEDAELIAUgBEECdBDfBEEAIQRBBCEFCyACLQAMIQICQAJAAkACQAJAAkACQCABLQAMQQFrDgIBAgALIAJBAWsOAgMEAgsgAkEBaw4CAgEDCyACQQFrDgIBAAILIABBADsADSAAIAg6AAwgACAGNgIIIAAgBTYCBCAAIAQ2AgAgAEEPakEAOgAADAILQdvVwgBBKEHg1sIAEP4DAAsgCQRAIANBF2pBADoAACADQQA7ABUgAyAFNgIMIAMgBDYCCCADIAY2AhAgAyAGRToAFCAAIANBCGpBARDTAQwBCyAAQQA7AA0gACAGNgIIIAAgBTYCBCAAIAQ2AgAgACAGRToADCAAQQ9qQQA6AAALIAcEQCAKIAdBAnQQ3wQLIANBIGokAAvBAwELfgJ+IAFByKXFAEEgEPEDBEBCjZXHw5bS2sCXfyABKQMQIgV9IgQgASkDGCIGQsf688PtgqOQPFatIgd9IQlC3bCFjOi2kai4fyABKQMIIgN9IgIgBCAHVCAFQo2Vx8OW0trAl39Wcq0iBH0hBULH+vPD7YKjkDwgBn0hBkKpwMaJrs6TsjAgASkDACACIARUIANC3bCFjOi2kai4f1ZyrXx9DAELIAEpAxghBiABKQMQIQkgASkDCCEFIAEpAwALIQQCfiABQSBqQcilxQBBIBDxAwRAQo2Vx8OW0trAl38gASkDMCIDfSICIAEpAzgiCELH+vPD7YKjkDxWrSIKfSEHQt2whYzotpGouH8gASkDKCILfSIMIAIgClQgA0KNlcfDltLawJd/VnKtIgJ9IQNCx/rzw+2Co5A8IAh9IQhCqcDGia7Ok7IwIAEpAyAgAiAMViALQt2whYzotpGouH9Wcq18fQwBCyABKQM4IQggASkDMCEHIAEpAyghAyABKQMgCyECIAAgCDcDOCAAIAc3AzAgACADNwMoIAAgAjcDICAAIAY3AxggACAJNwMQIAAgBTcDCCAAIAQ3AwALogMCAn8DfiMAQZABayIBJAACQEH408EAQYjSwQBBMBDxAwRAIAFCrtXy//////rDADcDiAEgAUL9/5/qrv7/2zI3A4ABIAFC6bqml5rJjvQHNwN4IAFC+vbKmZjmvNRsNwNwIAFC6YDTh+qjo4pvNwNoIAFChoT89+PkrIUENwNgDAELIAFBiAFqQaDUwQApAwA3AwAgAUGAAWpBmNTBACkDADcDACABQfgAakGQ1MEAKQMANwMAIAFB8ABqQYjUwQApAwA3AwAgAUHoAGpBgNTBACkDADcDACABQfjTwQApAwA3A2ALIAFBMGogAUHgAGoiAhCmASABIAEpAzAiBUIBiDcDACABIAEpA1AiA0I/hiABKQNYQgGIhDcDKCABIAEpA0giBEI/hiADQgGIhDcDICABIAEpA0AiA0I/hiAEQgGIhDcDGCABIAEpAzgiBEI/hiADQgGIhDcDECABIAVCP4YgBEIBiIQ3AwggAiAAIAEQLCACQYjSwQBBMBDxAwR/IAFB4ABqQfjTwQBBMBDxA0VBAXQFQQELIAFBkAFqJAAL5oYBAgl/G34jAEHAAWsiBCQAAkACQCABQeAAaiIIQcCNxQBBMBDxAwRAIwBB0B1rIgIkACACQZAZaiABQTBqIgYpAyAiD0IAIAYpAygiC0IAEMkDIAJBoBlqIAYpAxgiDkIAIAtCABDJAyACQbAZaiAGKQMQIgxCACALQgAQyQMgAkHAGWogBikDCCINQgAgC0IAEMkDIAJB0BlqIAYpAwAiEUIAIAtCABDJAyACQfAZaiAOQgAgD0IAEMkDIAJBgBpqIAxCACAPQgAQyQMgAkGQGmogDUIAIA9CABDJAyACQaAaaiARQgAgD0IAEMkDIAJBwBpqIAxCACAOQgAQyQMgAkHQGmogDUIAIA5CABDJAyACQeAaaiARQgAgDkIAEMkDIAJBgBtqIA1CACAMQgAQyQMgAkGQG2ogEUIAIAxCABDJAyACQbAbaiARQgAgDUIAEMkDIAJB4BlqIAtCACALQgAQyQMgAkGwGmogD0IAIA9CABDJAyACQfAaaiAOQgAgDkIAEMkDIAJBoBtqIAxCACAMQgAQyQMgAkHAG2ogDUIAIA1CABDJAyACQdAbaiARQgAgEUIAEMkDIAJBgBlqIAIpA+AZIhRC/f/z/8////mJf34iD0IAQqvV/v///7//uX9CABDJAyACQfAYaiAPQgBC///Piuv//9UeQgAQyQMgAkHgGGogD0IAQqTsw7WP1LSY5wBCABDJAyACQdAYaiAPQgBCv6WUnM/w0rvkAEIAEMkDIAJBwBhqIA9CAELX2a6a5PbpjcsAQgAQyQMgAkGwGGogD0IAQprN/8ujvcSAGkIAEMkDIAIpA7gbIAIpA5gbIAIpA4gbIAIpA9gaIAIpA8gaIAIpA4gaIAIpA/gZIAIpA6gZIAIpA5gZIgsgAikDoBl8Ig8gC1StfCIMIAIpA7AZfCILIAIpA/AZfCIOIAtUrXwiDSACKQO4GSALIAxUrXwiESACKQPAGXwiEnwiCyANVK18IAsgCyACKQOAGnwiDFatfCIQIAIpA8gZIBEgElatfCISIAIpA9AZfCITfCILIAIpA5AafCINIAIpA8AafCIRIA1UrXwiFSALIA1WrSACKQOYGiALIBBUrXx8IhAgAikD2BkgEiATVq18fCILIAIpA6AafCITfCINIBVUrXwgDSANIAIpA9AafCISVq18IhUgCyATVq0gAikDqBogCyAQVK18fHwiCyACKQPgGnwiDSACKQOAG3wiECANVK18IhMgCyANVq0gAikD6BogCyAVVK18fHwiCyATVK18IAsgAikDkBt8Ig0gC1StfCILIAIpA7AbfCITIAtUrXwiFUI/iCACKQPYGyACKQPIGyACKQOoGyACKQP4GiACKQO4GiACKQPoGSILIAIpA5AZIhdCAYZ8IhsgC1StIhogD0IBhiAXQj+IhHwiCyAaVK18IAsgAikDsBp8IhcgC1StfCILIA5CAYYgD0I/iIR8IhogC1StIgsgDEIBhiAOQj+IhHwiDyALVK18IA8gAikD8Bp8Ih0gD1StfCIPIBFCAYYgDEI/iIR8IhYgD1StIgsgEkIBhiARQj+IhHwiDyALVK18IA8gAikDoBt8IgwgD1StfCIPIBBCAYYgEkI/iIR8Ig4gD1StIgsgDUIBhiAQQj+IhHwiDyALVK18IA8gAikDwBt8IgsgD1StfCIPIBNCAYYgDUI/iIR8IhIgD1StIg0gFUIBhiATQj+IhHwiDyANVK18IA8gAikD0Bt8IhEgD1StfHwhDwJ/AkAgAikDuBggAikDyBggAikD2BggAikD6BggAikD+BggAikDiBkgAikDgBkiDSAUQn2DfCANVK18IhAgAikD8Bh8Ig0gEFStfCANIBt8IhAgDVStfCITIAIpA+AYfCINIBNUrXwgDSAXfCITIA1UrXwiFCACKQPQGHwiDSAUVK18IA0gGnwiFCANVK18IhUgAikDwBh8Ig0gFVStfCANIB18IhUgDVStfCIXIAIpA7AYfCINIBdUrXwgDSAWfCIXIA1UrXwiDVANACAMIA18IgwgDVQiBkUNACAGrSINIA58Ig4gDVoNACANIA5WrSINIAt8IgsgDVoNACALIA1UrSINIBJ8IhIgDVoNACANIBJWrSINIBF8IhEgDVoNACANIBFWrSINIA98Ig8gDVQMAQtBAAshCSACQaAYaiAQQv3/8//P///5iX9+Ig1CAEKr1f7///+//7l/QgAQyQMgAkGQGGogDUIAQv//z4rr///VHkIAEMkDIAJBgBhqIA1CAEKk7MO1j9S0mOcAQgAQyQMgAkHwF2ogDUIAQr+llJzP8NK75ABCABDJAyACQeAXaiANQgBC19mumuT26Y3LAEIAEMkDIAJB0BdqIA1CAEKazf/Lo73EgBpCABDJAwJAIAIpA9gXIAIpA+gXIAIpA/gXIAIpA4gYIAIpA5gYIAIpA6gYIAIpA6AYIg0gEHwgDVStfCIQIAIpA5AYfCINIBBUrXwgDSANIBN8IhBWrXwiEyACKQOAGHwiDSATVK18IA0gFHwiEyANVK18IhQgAikD8Bd8Ig0gFFStfCANIBV8IhQgDVStfCIVIAIpA+AXfCINIBVUrXwgDSAXfCIVIA1UrXwiFyACKQPQF3wiDSAXVK18IA0gDCANfCIXVq18IgxQDQAgDCAOfCIOIAxaDQAgDCAOVq0iDCALfCILIAxaDQAgCyAMVK0iDCASfCISIAxaDQAgDCASVq0iDCARfCIRIAxaDQAgDCARVq0iDCAPfCIPIAxUIQULIAJBwBdqIBBC/f/z/8////mJf34iDEIAQqvV/v///7//uX9CABDJAyACQbAXaiAMQgBC///Piuv//9UeQgAQyQMgAkGgF2ogDEIAQqTsw7WP1LSY5wBCABDJAyACQZAXaiAMQgBCv6WUnM/w0rvkAEIAEMkDIAJBgBdqIAxCAELX2a6a5PbpjcsAQgAQyQMgAkHwFmogDEIAQprN/8ujvcSAGkIAEMkDAn9BACACKQP4FiACKQOIFyACKQOYFyACKQOoFyACKQO4FyACKQPIFyACKQPAFyIMIBB8IAxUrXwiDSACKQOwF3wiDCANVK18IAwgDCATfCINVq18IhAgAikDoBd8IgwgEFStfCAMIBR8IhAgDFStfCITIAIpA5AXfCIMIBNUrXwgDCAVfCITIAxUrXwiFCACKQOAF3wiDCAUVK18IAwgF3wiFCAMVK18IhUgAikD8BZ8IgwgFVStfCAMIAwgDnwiFVatfCIOUA0AGkEAIA4gCyAOfCILWA0AGkEAIAsgDlStIg4gEnwiEiAOWg0AGkEAIA4gElatIg4gEXwiESAOWg0AGiAOIBFWrSIOIA98Ig8gDlQLIQogAkHgFmogDUL9//P/z///+Yl/fiIOQgBCq9X+////v/+5f0IAEMkDIAJB0BZqIA5CAEL//8+K6///1R5CABDJAyACQcAWaiAOQgBCpOzDtY/UtJjnAEIAEMkDIAJBsBZqIA5CAEK/pZScz/DSu+QAQgAQyQMgAkGgFmogDkIAQtfZrprk9umNywBCABDJAyACQZAWaiAOQgBCms3/y6O9xIAaQgAQyQMCQCACKQOYFiACKQOoFiACKQO4FiACKQPIFiACKQPYFiACKQPoFiACKQPgFiIOIA18IA5UrXwiDCACKQPQFnwiDiAMVK18IA4gDiAQfCIMVq18Ig0gAikDwBZ8Ig4gDVStfCAOIBN8Ig0gDlStfCIQIAIpA7AWfCIOIBBUrXwgDiAUfCIQIA5UrXwiEyACKQOgFnwiDiATVK18IA4gFXwiEyAOVK18IhQgAikDkBZ8Ig4gFFStfCAOIAsgDnwiFFatfCILUA0AIAsgEnwiEiALWg0AIAsgElatIgsgEXwiESALWg0AIAsgEVatIgsgD3wiDyALVCEHCyACQYAWaiAMQv3/8//P///5iX9+IgtCAEKr1f7///+//7l/QgAQyQMgAkHwFWogC0IAQv//z4rr///VHkIAEMkDIAJB4BVqIAtCAEKk7MO1j9S0mOcAQgAQyQMgAkHQFWogC0IAQr+llJzP8NK75ABCABDJAyACQcAVaiALQgBC19mumuT26Y3LAEIAEMkDIAJBsBVqIAtCAEKazf/Lo73EgBpCABDJAyACKQO4FSACKQPIFSACKQPYFSACKQPoFSACKQP4FSACKQOIFiACKQOAFiILIAx8IAtUrXwiDiACKQPwFXwiCyAOVK18IAsgDXwiDiALVK18IgwgAikD4BV8IgsgDFStfCALIBB8IgwgC1StfCINIAIpA9AVfCILIA1UrXwgCyATfCINIAtUrXwiECACKQPAFXwiCyAQVK18IAsgFHwiECALVK18IhMgAikDsBV8IgsgE1StfCALIBJ8IhMgC1StfCILUEUEQCALIBF8IhEgC1QiA60iCyAPfCISIA8gAxshDyADIAsgElZxIQMLIAJBoBVqIA5C/f/z/8////mJf34iC0IAQqvV/v///7//uX9CABDJAyACQZAVaiALQgBC///Piuv//9UeQgAQyQMgAkGAFWogC0IAQqTsw7WP1LSY5wBCABDJAyACQfAUaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJB4BRqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkHQFGogC0IAQprN/8ujvcSAGkIAEMkDIAIpA9gUIAIpA+gUIAIpA/gUIAIpA4gVIAIpA5gVIAIpA6gVIAIpA6AVIgsgDnwgC1StfCIOIAIpA5AVfCILIA5UrXwgCyAMfCISIAtUrXwiCyACKQOAFXwiDiALVK18IA4gDSAOfCILVq18Ig4gAikD8BR8IgwgDlStfCAMIAwgEHwiDlatfCINIAIpA+AUfCIMIA1UrXwgDCATfCINIAxUrXwiECACKQPQFHwiDCAQVK18IAwgEXwiESAMVK18IgwgD3wiEyAPIAxCAFIiBhshEAJAAkAgBSAJciAKciAHciADciAMIBNWIgOtIAwgBhtCAFJyIAMgBnEgEEKazf/Lo73EgBpWcnINAAJAIBBCms3/y6O9xIAaUg0AIBFC19mumuT26Y3LAFYNASARQtfZrprk9umNywBSDQAgDUK/pZScz/DSu+QAVg0BIA1Cv6WUnM/w0rvkAFINACAOQqTsw7WP1LSY5wBWDQEgDkKk7MO1j9S0mOcAUg0AIAtC///Piuv//9UeVg0BIAtC///Piuv//9UeUg0AIBJCqtX+////v/+5f1YNAQsgCyEPIA4hCyANIQwgESEODAELIAtC///Piuv//9UefSIMIBJCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIUIAtC///Piuv//9UeVCAMIBNUcq0iDH0hCyANQr+llJzP8NK75AB9IhMgDkKk7MO1j9S0mOcAVCAMIBRWcq0iDn0hDCARQtfZrprk9umNywB9IhQgDUK/pZScz/DSu+QAVCAOIBNWcq0iDX0hDiAQIBFC19mumuT26Y3LAFQgDSAUVnKtfUKazf/Lo73EgBp9IRAgEkLVqoGAgIDAgMYAfCESCyACIBI3A8gdIAIgDzcDwB0gAiALNwO4HSACIAw3A7AdIAIgDjcDqB0gAiAQNwOgHSACQeAbaiACQaAdaiAIELsBIAJBwBNqIAEpAyAiD0IAIAEpAygiC0IAEMkDIAJBkBNqIAEpAxgiDkIAIAtCABDJAyACQdASaiABKQMQIgxCACALQgAQyQMgAkGAEmogASkDCCINQgAgC0IAEMkDIAJBoBFqIAEpAwAiEUIAIAtCABDJAyACQaATaiAOQgAgD0IAEMkDIAJB4BJqIAxCACAPQgAQyQMgAkGQEmogDUIAIA9CABDJAyACQbARaiARQgAgD0IAEMkDIAJB8BJqIAxCACAOQgAQyQMgAkGgEmogDUIAIA5CABDJAyACQcARaiARQgAgDkIAEMkDIAJBsBJqIA1CACAMQgAQyQMgAkHQEWogEUIAIAxCABDJAyACQeARaiARQgAgDUIAEMkDIAJBwBRqIAtCACALQgAQyQMgAkHQE2ogD0IAIA9CABDJAyACQbATaiAOQgAgDkIAEMkDIAJBgBNqIAxCACAMQgAQyQMgAkHAEmogDUIAIA1CABDJAyACQfARaiARQgAgEUIAEMkDIAJBsBRqIAIpA8AUIhRC/f/z/8////mJf34iD0IAQqvV/v///7//uX9CABDJAyACQaAUaiAPQgBC///Piuv//9UeQgAQyQMgAkGQFGogD0IAQqTsw7WP1LSY5wBCABDJAyACQYAUaiAPQgBCv6WUnM/w0rvkAEIAEMkDIAJB8BNqIA9CAELX2a6a5PbpjcsAQgAQyQMgAkHgE2ogD0IAQprN/8ujvcSAGkIAEMkDIAIpA+gRIAIpA9gRIAIpA7gSIAIpA6gSIAIpA/gSIAIpA+gSIAIpA6gTIAIpA5gTIAIpA8gTIgsgAikDkBN8Ig8gC1StfCIMIAIpA9ASfCILIAIpA6ATfCIOIAtUrXwiDSACKQPYEiALIAxUrXwiESACKQOAEnwiEnwiCyANVK18IAsgCyACKQPgEnwiDFatfCIQIAIpA4gSIBEgElatfCISIAIpA6ARfCITfCILIAIpA5ASfCINIAIpA/ASfCIRIA1UrXwiFSALIA1WrSACKQOYEiALIBBUrXx8IhAgAikDqBEgEiATVq18fCILIAIpA7ARfCITfCINIBVUrXwgDSANIAIpA6ASfCISVq18IhUgCyATVq0gAikDuBEgCyAQVK18fHwiCyACKQPAEXwiDSACKQOwEnwiECANVK18IhMgCyANVq0gAikDyBEgCyAVVK18fHwiCyATVK18IAsgAikD0BF8Ig0gC1StfCILIAIpA+ARfCITIAtUrXwiFUI/iCACKQP4ESACKQPIEiACKQOIEyACKQO4EyACKQPYEyACKQPIFCILIAIpA8ATIhdCAYZ8IhsgC1StIhogD0IBhiAXQj+IhHwiCyAaVK18IAsgAikD0BN8IhcgC1StfCILIA5CAYYgD0I/iIR8IhogC1StIgsgDEIBhiAOQj+IhHwiDyALVK18IA8gAikDsBN8Ih0gD1StfCIPIBFCAYYgDEI/iIR8IhYgD1StIgsgEkIBhiARQj+IhHwiDyALVK18IA8gAikDgBN8IgwgD1StfCIPIBBCAYYgEkI/iIR8Ig4gD1StIgsgDUIBhiAQQj+IhHwiDyALVK18IA8gAikDwBJ8IgsgD1StfCIPIBNCAYYgDUI/iIR8IhIgD1StIg0gFUIBhiATQj+IhHwiDyANVK18IA8gAikD8BF8IhEgD1StfHwhD0EAIQUCfwJAIAIpA+gTIAIpA/gTIAIpA4gUIAIpA5gUIAIpA6gUIAIpA7gUIAIpA7AUIg0gFEJ9g3wgDVStfCIQIAIpA6AUfCINIBBUrXwgDSAbfCIQIA1UrXwiEyACKQOQFHwiDSATVK18IA0gF3wiEyANVK18IhQgAikDgBR8Ig0gFFStfCANIBp8IhQgDVStfCIVIAIpA/ATfCINIBVUrXwgDSAdfCIVIA1UrXwiFyACKQPgE3wiDSAXVK18IA0gFnwiFyANVK18Ig1QDQAgDCANfCIMIA1UIgNFDQAgA60iDSAOfCIOIA1aDQAgDSAOVq0iDSALfCILIA1aDQAgCyANVK0iDSASfCISIA1aDQAgDSASVq0iDSARfCIRIA1aDQAgDSARVq0iDSAPfCIPIA1UDAELQQALIQkgAkGQEWogEEL9//P/z///+Yl/fiINQgBCq9X+////v/+5f0IAEMkDIAJBgBFqIA1CAEL//8+K6///1R5CABDJAyACQfAQaiANQgBCpOzDtY/UtJjnAEIAEMkDIAJB4BBqIA1CAEK/pZScz/DSu+QAQgAQyQMgAkHQEGogDUIAQtfZrprk9umNywBCABDJAyACQcAQaiANQgBCms3/y6O9xIAaQgAQyQMCQCACKQPIECACKQPYECACKQPoECACKQP4ECACKQOIESACKQOYESACKQOQESINIBB8IA1UrXwiECACKQOAEXwiDSAQVK18IA0gDSATfCIQVq18IhMgAikD8BB8Ig0gE1StfCANIBR8IhMgDVStfCIUIAIpA+AQfCINIBRUrXwgDSAVfCIUIA1UrXwiFSACKQPQEHwiDSAVVK18IA0gF3wiFSANVK18IhcgAikDwBB8Ig0gF1StfCANIAwgDXwiF1atfCIMUA0AIAwgDnwiDiAMWg0AIAwgDlatIgwgC3wiCyAMWg0AIAsgDFStIgwgEnwiEiAMWg0AIAwgElatIgwgEXwiESAMWg0AIAwgEVatIgwgD3wiDyAMVCEFCyACQbAQaiAQQv3/8//P///5iX9+IgxCAEKr1f7///+//7l/QgAQyQMgAkGgEGogDEIAQv//z4rr///VHkIAEMkDIAJBkBBqIAxCAEKk7MO1j9S0mOcAQgAQyQMgAkGAEGogDEIAQr+llJzP8NK75ABCABDJAyACQfAPaiAMQgBC19mumuT26Y3LAEIAEMkDIAJB4A9qIAxCAEKazf/Lo73EgBpCABDJA0EAIQcCf0EAIAIpA+gPIAIpA/gPIAIpA4gQIAIpA5gQIAIpA6gQIAIpA7gQIAIpA7AQIgwgEHwgDFStfCINIAIpA6AQfCIMIA1UrXwgDCAMIBN8Ig1WrXwiECACKQOQEHwiDCAQVK18IAwgFHwiECAMVK18IhMgAikDgBB8IgwgE1StfCAMIBV8IhMgDFStfCIUIAIpA/APfCIMIBRUrXwgDCAXfCIUIAxUrXwiFSACKQPgD3wiDCAVVK18IAwgDCAOfCIVVq18Ig5QDQAaQQAgDiALIA58IgtYDQAaQQAgCyAOVK0iDiASfCISIA5aDQAaQQAgDiASVq0iDiARfCIRIA5aDQAaIA4gEVatIg4gD3wiDyAOVAshCiACQdAPaiANQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgAkHAD2ogDkIAQv//z4rr///VHkIAEMkDIAJBsA9qIA5CAEKk7MO1j9S0mOcAQgAQyQMgAkGgD2ogDkIAQr+llJzP8NK75ABCABDJAyACQZAPaiAOQgBC19mumuT26Y3LAEIAEMkDIAJBgA9qIA5CAEKazf/Lo73EgBpCABDJAwJAIAIpA4gPIAIpA5gPIAIpA6gPIAIpA7gPIAIpA8gPIAIpA9gPIAIpA9APIg4gDXwgDlStfCIMIAIpA8APfCIOIAxUrXwgDiAOIBB8IgxWrXwiDSACKQOwD3wiDiANVK18IA4gE3wiDSAOVK18IhAgAikDoA98Ig4gEFStfCAOIBR8IhAgDlStfCITIAIpA5APfCIOIBNUrXwgDiAVfCITIA5UrXwiFCACKQOAD3wiDiAUVK18IA4gCyAOfCIUVq18IgtQDQAgCyASfCISIAtaDQAgCyASVq0iCyARfCIRIAtaDQAgCyARVq0iCyAPfCIPIAtUIQcLIAJB8A5qIAxC/f/z/8////mJf34iC0IAQqvV/v///7//uX9CABDJAyACQeAOaiALQgBC///Piuv//9UeQgAQyQMgAkHQDmogC0IAQqTsw7WP1LSY5wBCABDJAyACQcAOaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJBsA5qIAtCAELX2a6a5PbpjcsAQgAQyQMgAkGgDmogC0IAQprN/8ujvcSAGkIAEMkDQQAhAyACKQOoDiACKQO4DiACKQPIDiACKQPYDiACKQPoDiACKQP4DiACKQPwDiILIAx8IAtUrXwiDiACKQPgDnwiCyAOVK18IAsgDXwiDiALVK18IgwgAikD0A58IgsgDFStfCALIBB8IgwgC1StfCINIAIpA8AOfCILIA1UrXwgCyATfCINIAtUrXwiECACKQOwDnwiCyAQVK18IAsgFHwiECALVK18IhMgAikDoA58IgsgE1StfCALIBJ8IhMgC1StfCILUEUEQCALIBF8IhEgC1QiA60iCyAPfCISIA8gAxshDyADIAsgElZxIQMLIAJBkA5qIA5C/f/z/8////mJf34iC0IAQqvV/v///7//uX9CABDJAyACQYAOaiALQgBC///Piuv//9UeQgAQyQMgAkHwDWogC0IAQqTsw7WP1LSY5wBCABDJAyACQeANaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJB0A1qIAtCAELX2a6a5PbpjcsAQgAQyQMgAkHADWogC0IAQprN/8ujvcSAGkIAEMkDIAIpA8gNIAIpA9gNIAIpA+gNIAIpA/gNIAIpA4gOIAIpA5gOIAIpA5AOIgsgDnwgC1StfCIOIAIpA4AOfCILIA5UrXwgCyAMfCISIAtUrXwiCyACKQPwDXwiDiALVK18IA4gDSAOfCILVq18Ig4gAikD4A18IgwgDlStfCAMIAwgEHwiDlatfCINIAIpA9ANfCIMIA1UrXwgDCATfCINIAxUrXwiECACKQPADXwiDCAQVK18IAwgEXwiESAMVK18IgwgD3wiEyAPIAxCAFIiBhshEAJAAkAgBSAJciAKciAHciADciAMIBNWIgOtIAwgBhtCAFJyIAMgBnEgEEKazf/Lo73EgBpWcnINAAJAIBBCms3/y6O9xIAaUg0AIBFC19mumuT26Y3LAFYNASARQtfZrprk9umNywBSDQAgDUK/pZScz/DSu+QAVg0BIA1Cv6WUnM/w0rvkAFINACAOQqTsw7WP1LSY5wBWDQEgDkKk7MO1j9S0mOcAUg0AIAtC///Piuv//9UeVg0BIAtC///Piuv//9UeUg0AIBJCqtX+////v/+5f1YNAQsgCyEPIA4hCyANIQwgESEODAELIAtC///Piuv//9UefSIMIBJCq9X+////v/+5f1StIhN9IQ8gDkKk7MO1j9S0mOcAfSIUIAtC///Piuv//9UeVCAMIBNUcq0iDH0hCyANQr+llJzP8NK75AB9IhMgDkKk7MO1j9S0mOcAVCAMIBRWcq0iDn0hDCARQtfZrprk9umNywB9IhQgDUK/pZScz/DSu+QAVCAOIBNWcq0iDX0hDiAQIBFC19mumuT26Y3LAFQgDSAUVnKtfUKazf/Lo73EgBp9IRAgEkLVqoGAgIDAgMYAfCESCyACIBI3A7gcIAIgDzcDsBwgAiALNwOoHCACIAw3A6AcIAIgDjcDmBwgAiAQNwOQHCACQZgdakIANwMAIAJBkB1qQgA3AwAgAkGIHWpCADcDACACQYAdakIANwMAIAJB+BxqQgA3AwAgAkIANwPwHCACQbAMaiAIKQMgIg9CACAIKQMoIgtCABDJAyACQYAMaiAIKQMYIg5CACALQgAQyQMgAkHAC2ogCCkDECIMQgAgC0IAEMkDIAJB8ApqIAgpAwgiDUIAIAtCABDJAyACQZAKaiAIKQMAIhFCACALQgAQyQMgAkGQDGogDkIAIA9CABDJAyACQdALaiAMQgAgD0IAEMkDIAJBgAtqIA1CACAPQgAQyQMgAkGgCmogEUIAIA9CABDJAyACQeALaiAMQgAgDkIAEMkDIAJBkAtqIA1CACAOQgAQyQMgAkGwCmogEUIAIA5CABDJAyACQaALaiANQgAgDEIAEMkDIAJBwApqIBFCACAMQgAQyQMgAkHQCmogEUIAIA1CABDJAyACQbANaiALQgAgC0IAEMkDIAJBwAxqIA9CACAPQgAQyQMgAkGgDGogDkIAIA5CABDJAyACQfALaiAMQgAgDEIAEMkDIAJBsAtqIA1CACANQgAQyQMgAkHgCmogEUIAIBFCABDJAyACQaANaiACKQOwDSITQv3/8//P///5iX9+Ig9CAEKr1f7///+//7l/QgAQyQMgAkGQDWogD0IAQv//z4rr///VHkIAEMkDIAJBgA1qIA9CAEKk7MO1j9S0mOcAQgAQyQMgAkHwDGogD0IAQr+llJzP8NK75ABCABDJAyACQeAMaiAPQgBC19mumuT26Y3LAEIAEMkDIAJB0AxqIA9CAEKazf/Lo73EgBpCABDJAyACKQPYCiACKQPICiACKQOoCyACKQOYCyACKQPoCyACKQPYCyACKQOYDCACKQOIDCACKQO4DCILIAIpA4AMfCIPIAtUrXwiDCACKQPAC3wiCyACKQOQDHwiDiALVK18Ig0gAikDyAsgCyAMVK18IhEgAikD8Ap8IhJ8IgsgDVStfCALIAsgAikD0At8IgxWrXwiECACKQP4CiARIBJWrXwiEiACKQOQCnwiFHwiCyACKQOAC3wiDSACKQPgC3wiESANVK18IhUgCyANVq0gAikDiAsgCyAQVK18fCIQIAIpA5gKIBIgFFatfHwiCyACKQOgCnwiFHwiDSAVVK18IA0gDSACKQOQC3wiElatfCIVIAsgFFatIAIpA6gKIAsgEFStfHx8IgsgAikDsAp8Ig0gAikDoAt8IhAgDVStfCIUIAsgDVatIAIpA7gKIAsgFVStfHx8IgsgFFStfCALIAIpA8AKfCINIAtUrXwiCyACKQPQCnwiFSALVK18IhZCP4ggAikD6AoiHyACKQO4CyIgIAIpA/gLIiEgAikDqAwiIiACKQPIDCIjIAIpA7gNIhQgAikDsAwiC0IBhnwiGCAUVK0iFyAPQgGGIAtCP4iEfCILIBdUrXwgCyACKQPADCIXfCIZIAtUrXwiCyAOQgGGIA9CP4iEfCIcIAtUrSILIAxCAYYgDkI/iIR8Ig8gC1StfCAPIAIpA6AMIht8IiQgD1StfCIPIBFCAYYgDEI/iIR8IiUgD1StIgsgEkIBhiARQj+IhHwiDyALVK18IA8gAikD8AsiGnwiDCAPVK18Ig8gEEIBhiASQj+IhHwiDiAPVK0iCyANQgGGIBBCP4iEfCIPIAtUrXwgDyACKQOwCyIdfCILIA9UrXwiDyAVQgGGIA1CP4iEfCISIA9UrSINIBZCAYYgFUI/iIR8Ig8gDVStfCAPIAIpA+AKIhV8IhEgD1StfHwhD0EAIQUCfwJAIAIpA9gMIAIpA+gMIAIpA/gMIAIpA4gNIAIpA5gNIAIpA6gNIAIpA6ANIg0gE0J9g3wgDVStfCIQIAIpA5ANfCINIBBUrXwgDSAYfCIQIA1UrXwiFiACKQOADXwiDSAWVK18IA0gGXwiFiANVK18IhggAikD8Ax8Ig0gGFStfCANIBx8IhggDVStfCIZIAIpA+AMfCINIBlUrXwgDSAkfCIZIA1UrXwiHCACKQPQDHwiDSAcVK18IA0gJXwiHCANVK18Ig1QDQAgDCANfCIMIA1UIgNFDQAgA60iDSAOfCIOIA1aDQAgDSAOVq0iDSALfCILIA1aDQAgCyANVK0iDSASfCISIA1aDQAgDSASVq0iDSARfCIRIA1aDQAgDSARVq0iDSAPfCIPIA1UDAELQQALIQkgAkGACmogEEL9//P/z///+Yl/fiINQgBCq9X+////v/+5f0IAEMkDIAJB8AlqIA1CAEL//8+K6///1R5CABDJAyACQeAJaiANQgBCpOzDtY/UtJjnAEIAEMkDIAJB0AlqIA1CAEK/pZScz/DSu+QAQgAQyQMgAkHACWogDUIAQtfZrprk9umNywBCABDJAyACQbAJaiANQgBCms3/y6O9xIAaQgAQyQMCQCACKQO4CSACKQPICSACKQPYCSACKQPoCSACKQP4CSACKQOICiACKQOACiINIBB8IA1UrXwiECACKQPwCXwiDSAQVK18IA0gDSAWfCIQVq18IhYgAikD4Al8Ig0gFlStfCANIBh8IhYgDVStfCIYIAIpA9AJfCINIBhUrXwgDSAZfCIYIA1UrXwiGSACKQPACXwiDSAZVK18IA0gHHwiGSANVK18IhwgAikDsAl8Ig0gHFStfCANIAwgDXwiHFatfCIMUA0AIAwgDnwiDiAMWg0AIAwgDlatIgwgC3wiCyAMWg0AIAsgDFStIgwgEnwiEiAMWg0AIAwgElatIgwgEXwiESAMWg0AIAwgEVatIgwgD3wiDyAMVCEFCyACQaAJaiAQQv3/8//P///5iX9+IgxCAEKr1f7///+//7l/QgAQyQMgAkGQCWogDEIAQv//z4rr///VHkIAEMkDIAJBgAlqIAxCAEKk7MO1j9S0mOcAQgAQyQMgAkHwCGogDEIAQr+llJzP8NK75ABCABDJAyACQeAIaiAMQgBC19mumuT26Y3LAEIAEMkDIAJB0AhqIAxCAEKazf/Lo73EgBpCABDJA0EAIQcCf0EAIAIpA9gIIAIpA+gIIAIpA/gIIAIpA4gJIAIpA5gJIAIpA6gJIAIpA6AJIgwgEHwgDFStfCINIAIpA5AJfCIMIA1UrXwgDCAMIBZ8Ig1WrXwiECACKQOACXwiDCAQVK18IAwgGHwiECAMVK18IhYgAikD8Ah8IgwgFlStfCAMIBl8IhYgDFStfCIYIAIpA+AIfCIMIBhUrXwgDCAcfCIYIAxUrXwiGSACKQPQCHwiDCAZVK18IAwgDCAOfCIZVq18Ig5QDQAaQQAgDiALIA58IgtYDQAaQQAgCyAOVK0iDiASfCISIA5aDQAaQQAgDiASVq0iDiARfCIRIA5aDQAaIA4gEVatIg4gD3wiDyAOVAshCiACQcAIaiANQv3/8//P///5iX9+Ig5CAEKr1f7///+//7l/QgAQyQMgAkGwCGogDkIAQv//z4rr///VHkIAEMkDIAJBoAhqIA5CAEKk7MO1j9S0mOcAQgAQyQMgAkGQCGogDkIAQr+llJzP8NK75ABCABDJAyACQYAIaiAOQgBC19mumuT26Y3LAEIAEMkDIAJB8AdqIA5CAEKazf/Lo73EgBpCABDJAwJAIAIpA/gHIAIpA4gIIAIpA5gIIAIpA6gIIAIpA7gIIAIpA8gIIAIpA8AIIg4gDXwgDlStfCIMIAIpA7AIfCIOIAxUrXwgDiAOIBB8IgxWrXwiDSACKQOgCHwiDiANVK18IA4gFnwiDSAOVK18IhAgAikDkAh8Ig4gEFStfCAOIBh8IhAgDlStfCIWIAIpA4AIfCIOIBZUrXwgDiAZfCIWIA5UrXwiGCACKQPwB3wiDiAYVK18IA4gCyAOfCIYVq18IgtQDQAgCyASfCISIAtaDQAgCyASVq0iCyARfCIRIAtaDQAgCyARVq0iCyAPfCIPIAtUIQcLIAJB4AdqIAxC/f/z/8////mJf34iC0IAQqvV/v///7//uX9CABDJAyACQdAHaiALQgBC///Piuv//9UeQgAQyQMgAkHAB2ogC0IAQqTsw7WP1LSY5wBCABDJAyACQbAHaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJBoAdqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkGQB2ogC0IAQprN/8ujvcSAGkIAEMkDQQAhAyACKQOYByACKQOoByACKQO4ByACKQPIByACKQPYByACKQPoByACKQPgByILIAx8IAtUrXwiDiACKQPQB3wiCyAOVK18IAsgDXwiDiALVK18IgwgAikDwAd8IgsgDFStfCALIBB8IgwgC1StfCINIAIpA7AHfCILIA1UrXwgCyAWfCINIAtUrXwiECACKQOgB3wiCyAQVK18IAsgGHwiECALVK18IhYgAikDkAd8IgsgFlStfCALIBJ8IhYgC1StfCILUEUEQCALIBF8IhEgC1QiA60iCyAPfCISIA8gAxshDyADIAsgElZxIQMLIAJBgAdqIA5C/f/z/8////mJf34iC0IAQqvV/v///7//uX9CABDJAyACQfAGaiALQgBC///Piuv//9UeQgAQyQMgAkHgBmogC0IAQqTsw7WP1LSY5wBCABDJAyACQdAGaiALQgBCv6WUnM/w0rvkAEIAEMkDIAJBwAZqIAtCAELX2a6a5PbpjcsAQgAQyQMgAkGwBmogC0IAQprN/8ujvcSAGkIAEMkDIAIpA7gGIAIpA8gGIAIpA9gGIAIpA+gGIAIpA/gGIAIpA4gHIAIpA4AHIgsgDnwgC1StfCIOIAIpA/AGfCILIA5UrXwgCyAMfCISIAtUrXwiCyACKQPgBnwiDiALVK18IA4gDSAOfCILVq18Ig4gAikD0AZ8IgwgDlStfCAMIAwgEHwiDlatfCINIAIpA8AGfCIMIA1UrXwgDCAWfCINIAxUrXwiECACKQOwBnwiDCAQVK18IAwgEXwiESAMVK18IgwgD3wiFiAPIAxCAFIiBhshEAJAAkAgBSAJciAKciAHciADciAMIBZWIgOtIAwgBhtCAFJyIAMgBnEgEEKazf/Lo73EgBpWcnINAAJAIBBCms3/y6O9xIAaUg0AIBFC19mumuT26Y3LAFYNASARQtfZrprk9umNywBSDQAgDUK/pZScz/DSu+QAVg0BIA1Cv6WUnM/w0rvkAFINACAOQqTsw7WP1LSY5wBWDQEgDkKk7MO1j9S0mOcAUg0AIAtC///Piuv//9UeVg0BIAtC///Piuv//9UeUg0AIBJCqtX+////v/+5f1YNAQsgCyEPIA4hCyANIQwgESEODAELIAtC///Piuv//9UefSIMIBJCq9X+////v/+5f1StIhZ9IQ8gDkKk7MO1j9S0mOcAfSIYIAtC///Piuv//9UeVCAMIBZUcq0iDH0hCyANQr+llJzP8NK75AB9IhYgDkKk7MO1j9S0mOcAVCAMIBhWcq0iDn0hDCARQtfZrprk9umNywB9IhggDUK/pZScz/DSu+QAVCAOIBZWcq0iDX0hDiAQIBFC19mumuT26Y3LAFQgDSAYVnKtfUKazf/Lo73EgBp9IRAgEkLVqoGAgIDAgMYAfCESCyACIBI3A8gdIAIgDzcDwB0gAiALNwO4HSACIAw3A7AdIAIgDjcDqB0gAiAQNwOgHSACQcAcaiIHIAJB8BxqIAJBoB1qIgMQuwEgAyACQZAcaiIFIAcQvQIgBSADIAEQuwEgAkLz/7OAgIDAk6p/NwOYHSACQoqA0OGvhoDm0wA3A5AdIAJC/4Cq2Kav+sfHADcDiB0gAkLXyei17tff6bF/NwOAHSACQq/W4vu759zkjn83A/gcIAJC/ryP7JOqkesJNwPwHCACQaAGaiAIKQMgIg9CACAIKQMoIgtCABDJAyACQYAGaiAIKQMYIg5CACALQgAQyQMgAkHQBWogCCkDECIMQgAgC0IAEMkDIAJBkAVqIAgpAwgiDUIAIAtCABDJAyACQcAEaiAIKQMAIhFCACALQgAQyQMgAkGQBmogDkIAIA9CABDJAyACQeAFaiAMQgAgD0IAEMkDIAJBoAVqIA1CACAPQgAQyQMgAkHQBGogEUIAIA9CABDJAyACQfAFaiAMQgAgDkIAEMkDIAJBsAVqIA1CACAOQgAQyQMgAkHgBGogEUIAIA5CABDJAyACQcAFaiANQgAgDEIAEMkDIAJB8ARqIBFCACAMQgAQyQMgAkGABWogEUIAIA1CABDJAyACQbAEaiATQv3/8//P///5iX9+Ig9CAEKr1f7///+//7l/QgAQyQMgAkGgBGogD0IAQv//z4rr///VHkIAEMkDIAJBkARqIA9CAEKk7MO1j9S0mOcAQgAQyQMgAkGABGogD0IAQr+llJzP8NK75ABCABDJAyACQfADaiAPQgBC19mumuT26Y3LAEIAEMkDIAJB4ANqIA9CAEKazf/Lo73EgBpCABDJAyACKQOIBSACKQP4BCACKQPIBSACKQO4BSACKQP4BSACKQPoBSACKQOYBiACKQOIBiACKQOoBiILIAIpA4AGfCIPIAtUrXwiDCACKQPQBXwiCyACKQOQBnwiDiALVK18Ig0gAikD2AUgCyAMVK18IhEgAikDkAV8IhJ8IgsgDVStfCALIAsgAikD4AV8IgxWrXwiECACKQOYBSARIBJWrXwiEiACKQPABHwiFnwiCyACKQOgBXwiDSACKQPwBXwiESANVK18IhggCyANVq0gAikDqAUgCyAQVK18fCIQIAIpA8gEIBIgFlatfHwiCyACKQPQBHwiFnwiDSAYVK18IA0gAikDsAV8IhIgDVStfCIYIAsgFlatIAIpA9gEIAsgEFStfHx8IgsgAikD4AR8Ig0gAikDwAV8IhAgDVStfCIWIAsgDVatIAIpA+gEIAsgGFStfHx8IgsgFlStfCALIAsgAikD8AR8IhZWrXwiCyACKQOABXwiGCALVK18IgtCP4ggHyAVIBUgC0IBhiAYQj+IhHwiGVatfCAZICAgHSAdIBZCAYYgEEI/iIR8IgtWrXwgCyALICEgGiASQgGGIBFCP4iEfCIVIBpUrXwgFSAVICIgGyAbIAxCAYYgDkI/iIR8Ig1WrXwgDSANICMgFyAXIA9CAYYgAikDoAYiGkI/iIR8IhtWrXwgGyAbIBQgFCAaQgGGfCIXVq18IhRWrXwiGyAOQgGGIA9CP4iEfCIaIBtUrXwiG1atfCIPIBFCAYYgDEI/iIR8Ih0gD1StfCINVq18Ig8gEEIBhiASQj+IhHwiDiAPVK18IgtWrXwiDyAYQgGGIBZCP4iEfCISIA9UrXwiESAZVK18fCEPQQAhBwJ/AkAgAikD6AMgAikD+AMgAikDiAQgAikDmAQgAikDqAQgAikDuAQgAikDsAQiDCATQn2DfCAMVK18IhAgAikDoAR8IgwgEFStfCAMIBd8IhAgDFStfCITIAIpA5AEfCIMIBNUrXwgDCAUfCITIAxUrXwiFCACKQOABHwiDCAUVK18IAwgGnwiFCAMVK18IhUgAikD8AN8IgwgFVStfCAMIBt8IhUgDFStfCIXIAIpA+ADfCIMIBdUrXwgDCAdfCIXIAxUrXwiDFANACAMIA18Ig0gDFQiA0UNACADrSIMIA58Ig4gDFoNACAMIA5WrSIMIAt8IgsgDFoNACALIAxUrSIMIBJ8IhIgDFoNACAMIBJWrSIMIBF8IhEgDFoNACAMIBFWrSIMIA98Ig8gDFQMAQtBAAshCSACQdADaiAQQv3/8//P///5iX9+IgxCAEKr1f7///+//7l/QgAQyQMgAkHAA2ogDEIAQv//z4rr///VHkIAEMkDIAJBsANqIAxCAEKk7MO1j9S0mOcAQgAQyQMgAkGgA2ogDEIAQr+llJzP8NK75ABCABDJAyACQZADaiAMQgBC19mumuT26Y3LAEIAEMkDIAJBgANqIAxCAEKazf/Lo73EgBpCABDJAwJAIAIpA4gDIAIpA5gDIAIpA6gDIAIpA7gDIAIpA8gDIAIpA9gDIAIpA9ADIgwgEHwgDFStfCIQIAIpA8ADfCIMIBBUrXwgDCATfCIQIAxUrXwiEyACKQOwA3wiDCATVK18IAwgFHwiEyAMVK18IhQgAikDoAN8IgwgFFStfCAMIBV8IhQgDFStfCIVIAIpA5ADfCIMIBVUrXwgDCAXfCIVIAxUrXwiFyACKQOAA3wiDCAXVK18IAwgDXwiFyAMVK18IgxQDQAgDCAOfCIOIAxaDQAgDCAOVq0iDCALfCILIAxaDQAgCyAMVK0iDCASfCISIAxaDQAgDCASVq0iDCARfCIRIAxaDQAgDCARVq0iDCAPfCIPIAxUIQcLIAJB8AJqIBBC/f/z/8////mJf34iDEIAQqvV/v///7//uX9CABDJAyACQeACaiAMQgBC///Piuv//9UeQgAQyQMgAkHQAmogDEIAQqTsw7WP1LSY5wBCABDJAyACQcACaiAMQgBCv6WUnM/w0rvkAEIAEMkDIAJBsAJqIAxCAELX2a6a5PbpjcsAQgAQyQMgAkGgAmogDEIAQprN/8ujvcSAGkIAEMkDQQAhAwJ/QQAgAikDqAIgAikDuAIgAikDyAIgAikD2AIgAikD6AIgAikD+AIgAikD8AIiDCAQfCAMVK18Ig0gAikD4AJ8IgwgDVStfCAMIAwgE3wiDVatfCIQIAIpA9ACfCIMIBBUrXwgDCAUfCIQIAxUrXwiEyACKQPAAnwiDCATVK18IAwgFXwiEyAMVK18IhQgAikDsAJ8IgwgFFStfCAMIBd8IhQgDFStfCIVIAIpA6ACfCIMIBVUrXwgDCAMIA58IhVWrXwiDlANABpBACAOIAsgDnwiC1gNABpBACALIA5UrSIOIBJ8IhIgDloNABpBACAOIBJWrSIOIBF8IhEgDloNABogDiARVq0iDiAPfCIPIA5UCyEKIAJBkAJqIA1C/f/z/8////mJf34iDkIAQqvV/v///7//uX9CABDJAyACQYACaiAOQgBC///Piuv//9UeQgAQyQMgAkHwAWogDkIAQqTsw7WP1LSY5wBCABDJAyACQeABaiAOQgBCv6WUnM/w0rvkAEIAEMkDIAJB0AFqIA5CAELX2a6a5PbpjcsAQgAQyQMgAkHAAWogDkIAQprN/8ujvcSAGkIAEMkDAkAgAikDyAEgAikD2AEgAikD6AEgAikD+AEgAikDiAIgAikDmAIgAikDkAIiDiANfCAOVK18IgwgAikDgAJ8Ig4gDFStfCAOIA4gEHwiDFatfCINIAIpA/ABfCIOIA1UrXwgDiATfCINIA5UrXwiECACKQPgAXwiDiAQVK18IA4gFHwiECAOVK18IhMgAikD0AF8Ig4gE1StfCAOIBV8IhMgDlStfCIUIAIpA8ABfCIOIBRUrXwgDiALIA58IhRWrXwiC1ANACALIBJ8IhIgC1oNACALIBJWrSILIBF8IhEgC1oNACALIBFWrSILIA98Ig8gC1QhAwsgAkGwAWogDEL9//P/z///+Yl/fiILQgBCq9X+////v/+5f0IAEMkDIAJBoAFqIAtCAEL//8+K6///1R5CABDJAyACQZABaiALQgBCpOzDtY/UtJjnAEIAEMkDIAJBgAFqIAtCAEK/pZScz/DSu+QAQgAQyQMgAkHwAGogC0IAQtfZrprk9umNywBCABDJAyACQeAAaiALQgBCms3/y6O9xIAaQgAQyQNBACEFIAIpA2ggAikDeCACKQOIASACKQOYASACKQOoASACKQO4ASACKQOwASILIAx8IAtUrXwiDiACKQOgAXwiCyAOVK18IAsgDXwiDiALVK18IgwgAikDkAF8IgsgDFStfCALIBB8IgwgC1StfCINIAIpA4ABfCILIA1UrXwgCyATfCINIAtUrXwiECACKQNwfCILIBBUrXwgCyAUfCIQIAtUrXwiEyACKQNgfCILIBNUrXwgCyASfCITIAtUrXwiC1BFBEAgCyARfCIRIAtUIgWtIgsgD3wiEiAPIAUbIQ8gBSALIBJWcSEFCyACQdAAaiAOQv3/8//P///5iX9+IgtCAEKr1f7///+//7l/QgAQyQMgAkFAayALQgBC///Piuv//9UeQgAQyQMgAkEwaiALQgBCpOzDtY/UtJjnAEIAEMkDIAJBIGogC0IAQr+llJzP8NK75ABCABDJAyACQRBqIAtCAELX2a6a5PbpjcsAQgAQyQMgAiALQgBCms3/y6O9xIAaQgAQyQMgAikDCCACKQMYIAIpAyggAikDOCACKQNIIAIpA1ggAikDUCILIA58IAtUrXwiDiACKQNAfCILIA5UrXwgCyAMfCISIAtUrXwiCyACKQMwfCIOIAtUrXwgDiANIA58IgtWrXwiDiACKQMgfCIMIA5UrXwgDCAMIBB8Ig5WrXwiDSACKQMQfCIMIA1UrXwgDCATfCINIAxUrXwiECACKQMAfCIMIBBUrXwgDCARfCIRIAxUrXwiDCAPfCITIA8gDEIAUiIGGyEQAkACQCAHIAlyIApyIANyIAVyIAwgE1YiA60gDCAGG0IAUnIgAyAGcSAQQprN/8ujvcSAGlZycg0AAkAgEEKazf/Lo73EgBpSDQAgEULX2a6a5PbpjcsAVg0BIBFC19mumuT26Y3LAFINACANQr+llJzP8NK75ABWDQEgDUK/pZScz/DSu+QAUg0AIA5CpOzDtY/UtJjnAFYNASAOQqTsw7WP1LSY5wBSDQAgC0L//8+K6///1R5WDQEgC0L//8+K6///1R5SDQAgEkKq1f7///+//7l/Vg0BCyALIQ8gDiELIA0hDCARIQ4MAQsgC0L//8+K6///1R59IgwgEkKr1f7///+//7l/VK0iE30hDyAOQqTsw7WP1LSY5wB9IhQgC0L//8+K6///1R5UIAwgE1RyrSIMfSELIA1Cv6WUnM/w0rvkAH0iEyAOQqTsw7WP1LSY5wBUIAwgFFZyrSIOfSEMIBFC19mumuT26Y3LAH0iFCANQr+llJzP8NK75ABUIA4gE1ZyrSINfSEOIBAgEULX2a6a5PbpjcsAVCANIBRWcq19QprN/8ujvcSAGn0hECASQtWqgYCAgMCAxgB8IRILIAIgEjcDyB0gAiAPNwPAHSACIAs3A7gdIAIgDDcDsB0gAiAONwOoHSACIBA3A6AdIAJBwBxqIgUgAkHwHGoiAyACQaAdaiIHELsBIAcgBSAIELsBIAMgAkGQHGogBxC9AiAEIAJB4BtqIAMQgwIgAkHQHWokACAEQcCNxQBBMBDxA0UNAQtCASEeIAFBwI3FAEEwEPEDDQEgCEHAjcUAQTAQ8QMNAUIAIR4gBEHYAGpCADcDACAEQdAAakIANwMAIARByABqQgA3AwAgBEFAa0IANwMAIARBOGpCADcDACAEQegAakGAkcUAKQMANwMAIARB8ABqQYiRxQApAwA3AwAgBEH4AGpBkJHFACkDADcDACAEQYABakGYkcUAKQMANwMAIARBiAFqQaCRxQApAwA3AwAgBEIANwMwIARB+JDFACkDADcDYCAEQbgBakIANwMAIARBsAFqQgA3AwAgBEGoAWpCADcDACAEQaABakIANwMAIARBmAFqQgA3AwAgBEIANwOQASAAQQhqIARBMGpBkAH8CgAADAELIABBCGogAUGQAfwKAAALIAAgHjcDACAEQcABaiQAC8gCAQJ/IwBBEGsiAiQAAkAgAUGAAU8EQCACQQA2AgwCfyABQYAQTwRAIAFBgIAETwRAIAIgAUE/cUGAAXI6AA8gAiABQRJ2QfABcjoADCACIAFBBnZBP3FBgAFyOgAOIAIgAUEMdkE/cUGAAXI6AA1BBAwCCyACIAFBP3FBgAFyOgAOIAIgAUEMdkHgAXI6AAwgAiABQQZ2QT9xQYABcjoADUEDDAELIAIgAUE/cUGAAXI6AA0gAiABQQZ2QcABcjoADEECCyIBIAAoAgAgACgCCCIDa0sEQCAAIAMgARCLAyAAKAIIIQMLIAEEQCAAKAIEIANqIAJBDGogAfwKAAALIAAgASADajYCCAwBCyAAKAIIIgMgACgCAEYEQCAAQdSmxQAQtgMLIAAoAgQgA2ogAToAACAAIANBAWo2AggLIAJBEGokAEEAC8wCAQl/IwBBEGsiBCQAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASEBQQFBARDWBCIDRQ0DIANBADoAACAAIANBARCLAQwBCyAEQQRqIAFBCBCwAiAEKAIIIQMCQCAEKAIMIgVBAkkNACADIAVqIQhBACEBIAVBAXYiAkEBRwRAIAVBAWshBiACQf7///8HcSEJA0AgAyAGaiICLQAAIQcgAiABIANqIgItAAA6AAAgAiAHOgAAIAggAUF+c2oiBy0AACEKIAcgAkEBaiICLQAAOgAAIAIgCjoAACAGQQJrIQYgCSABQQJqIgFHDQALCyAFQQJxRQ0AIAEgA2oiBi0AACECIAYgCCABQX9zaiIBLQAAOgAAIAEgAjoAAAsgBCgCBCEBIAAgAyAFEIsBIAFFDQELIAMgARDfBAsgBEEQaiQADwtBAUEBEP8EAAvMAgEJfyMAQRBrIgQkAAJAAkACQCABKAIIRQRAQdHOxQAtAAAaQQEhAUEBQQEQ1gQiA0UNAyADQQA6AAAgACADQQEQhwEMAQsgBEEEaiABQQgQsAIgBCgCCCEDAkAgBCgCDCIFQQJJDQAgAyAFaiEIQQAhASAFQQF2IgJBAUcEQCAFQQFrIQYgAkH+////B3EhCQNAIAMgBmoiAi0AACEHIAIgASADaiICLQAAOgAAIAIgBzoAACAIIAFBfnNqIgctAAAhCiAHIAJBAWoiAi0AADoAACACIAo6AAAgBkECayEGIAkgAUECaiIBRw0ACwsgBUECcUUNACABIANqIgYtAAAhAiAGIAggAUF/c2oiAS0AADoAACABIAI6AAALIAQoAgQhASAAIAMgBRCHASABRQ0BCyADIAEQ3wQLIARBEGokAA8LQQFBARD/BAALzAIBCX8jAEEQayIEJAACQAJAAkAgASgCCEUEQEHRzsUALQAAGkEBIQFBAUEBENYEIgNFDQMgA0EAOgAAIAAgA0EBEI4BDAELIARBBGogAUEIELACIAQoAgghAwJAIAQoAgwiBUECSQ0AIAMgBWohCEEAIQEgBUEBdiICQQFHBEAgBUEBayEGIAJB/v///wdxIQkDQCADIAZqIgItAAAhByACIAEgA2oiAi0AADoAACACIAc6AAAgCCABQX5zaiIHLQAAIQogByACQQFqIgItAAA6AAAgAiAKOgAAIAZBAmshBiAJIAFBAmoiAUcNAAsLIAVBAnFFDQAgASADaiIGLQAAIQIgBiAIIAFBf3NqIgEtAAA6AAAgASACOgAACyAEKAIEIQEgACADIAUQjgEgAUUNAQsgAyABEN8ECyAEQRBqJAAPC0EBQQEQ/wQAC8wCAQl/IwBBEGsiBCQAAkACQAJAIAEoAghFBEBB0c7FAC0AABpBASEBQQFBARDWBCIDRQ0DIANBADoAACAAIANBARCKAQwBCyAEQQRqIAFBCBCwAiAEKAIIIQMCQCAEKAIMIgVBAkkNACADIAVqIQhBACEBIAVBAXYiAkEBRwRAIAVBAWshBiACQf7///8HcSEJA0AgAyAGaiICLQAAIQcgAiABIANqIgItAAA6AAAgAiAHOgAAIAggAUF+c2oiBy0AACEKIAcgAkEBaiICLQAAOgAAIAIgCjoAACAGQQJrIQYgCSABQQJqIgFHDQALCyAFQQJxRQ0AIAEgA2oiBi0AACECIAYgCCABQX9zaiIBLQAAOgAAIAEgAjoAAAsgBCgCBCEBIAAgAyAFEIoBIAFFDQELIAMgARDfBAsgBEEQaiQADwtBAUEBEP8EAAvMAgEJfyMAQRBrIgQkAAJAAkACQCABKAIIRQRAQdHOxQAtAAAaQQEhAUEBQQEQ1gQiA0UNAyADQQA6AAAgACADQQEQhgEMAQsgBEEEaiABQQgQsAIgBCgCCCEDAkAgBCgCDCIFQQJJDQAgAyAFaiEIQQAhASAFQQF2IgJBAUcEQCAFQQFrIQYgAkH+////B3EhCQNAIAMgBmoiAi0AACEHIAIgASADaiICLQAAOgAAIAIgBzoAACAIIAFBfnNqIgctAAAhCiAHIAJBAWoiAi0AADoAACACIAo6AAAgBkECayEGIAkgAUECaiIBRw0ACwsgBUECcUUNACABIANqIgYtAAAhAiAGIAggAUF/c2oiAS0AADoAACABIAI6AAALIAQoAgQhASAAIAMgBRCGASABRQ0BCyADIAEQ3wQLIARBEGokAA8LQQFBARD/BAALswUBEH8jAEEQayIKJAACQCACKAIIIgRFBEAgAigCAEUEQCACQbDPwgAQpQMLIAIoAgQgATYCAEEBIQQgAkEBNgIIIAIoAgQhBQwBCyAKIAE2AgwgCkEMaiEHIAIoAgQhBSMAQSBrIggkAAJAAkACQAJAQQEgBCAEGyIJBEAgCUEBRwRAIAlBfnEhDSAFIQEgByEDA0AgASADKAIAIg4gASgCACIPayIQIAZrNgIAIAFBBGoiDCADQQRqKAIAIhEgDCgCACIMayISIA4gD0kgBiAQS3IiBms2AgAgDCARSyAGIBJLciEGIAFBCGohASADQQhqIQMgDSALQQJqIgtHDQALCyAJQQFxBEAgBSALQQJ0IgFqIgMgASAHaigCACIBIAMoAgAiA2siByAGazYCACABIANJIAYgB0tyIQYLIARFDQIgBkUNAQwDCyAERQ0BCyAEQQFLBEAgBSAJQQJ0IgNqIQEgBEECdCADayEDA0AgASgCAA0DIAFBBGohASADQQRrIgMNAAsLIAhBIGokAAwCC0HsisUAQSFBkIvFABD+AwALIAhBADYCGCAIQQE2AgwgCEHEisUANgIIIAhCBDcCECAIQQhqQdyKxQAQqAQACwsgAigCACEDAkAgBSAEQQJ0IgJqQQRrKAIADQAgBUEEayEHIAQhAQNAIAJFBEBBACEEDAILIAFBAWshASACIAdqIAJBBGshAigCAEUNAAsgAUEBaiIBIAQgASAESRshBAsCQCADQQJ2IARNBEAgBSEBIAMhAgwBC0EAIQIgA0UEQCAFIQEMAQsgA0ECdCEDIARFBEBBBCEBIAUgAxDfBAwBCyAFIANBBCAEIgJBAnQiBRDOBCIBDQBBBCAFQdDPwgAQyAQACyAAIAQ2AgggACABNgIEIAAgAjYCACAKQRBqJAALggMBBH8jAEEgayIBJAACQAJAAkACQAJAAkACQEGszsUALQAAQQFrDgMEAwEAC0GszsUAQQI6AAAgACgCACICKAIAIQAgAkEANgIAIABFDQQgACgCACECQdHOxQAtAAAaQSRBBBDWBCIARQ0BIAFBCGoiA0HklcMAQfyVwwBBmPnAABChAyAAQQhqIAFBEGoiBCgCADYCACAAIAEpAgg3AgAgA0H8lcMAQZSWwwBBmPnAABChAyAAQRRqIAQoAgA2AgAgACABKQIINwIMIANBlJbDAEGslsMAQZj5wAAQoQMgAEEgaiAEKAIANgIAIAAgASkCCDcCGCACQQM2AgggAiAANgIEIAJBAzYCAEGszsUAQQM6AAALIAFBIGokAA8LQQRBJEHo2cIAEMgEAAsgAUEANgIYIAFBATYCDCABQfDSwgA2AggMAgsgAUEANgIYIAFBATYCDCABQbDSwgA2AggMAQtBzNPCABDoBAALIAFCBDcCECABQQhqQfTMwQAQqAQAC8QCAQR/IABCADcCECAAAn9BACABQYACSQ0AGkEfIAFB////B0sNABogAUEGIAFBCHZnIgNrdkEBcSADQQF0a0E+agsiAjYCHCACQQJ0QfDOxQBqIQRBASACdCIDQYzSxQAoAgBxRQRAIAQgADYCACAAIAQ2AhggACAANgIMIAAgADYCCEGM0sUAQYzSxQAoAgAgA3I2AgAPCwJAAkAgASAEKAIAIgMoAgRBeHFGBEAgAyECDAELIAFBGSACQQF2a0EAIAJBH0cbdCEFA0AgAyAFQR12QQRxaiIEKAIQIgJFDQIgBUEBdCEFIAIhAyACKAIEQXhxIAFHDQALCyACKAIIIgEgADYCDCACIAA2AgggAEEANgIYIAAgAjYCDCAAIAE2AggPCyAEQRBqIAA2AgAgACADNgIYIAAgADYCDCAAIAA2AggLmgIBAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECyAAKAIMIgEEQCAAKAIQIAFBAnQQ3wQLIAAoAhgiAQRAIAAoAhwgAUECdBDfBAsgACgCJCIBBEAgACgCKCABQQJ0EN8ECyAAKAIwIgEEQCAAKAI0IAFBAnQQ3wQLIAAoAjwiAQRAIAAoAkAgAUECdBDfBAsgACgCSCIBBEAgACgCTCABQQJ0EN8ECyAAKAJUIgEEQCAAKAJYIAFBAnQQ3wQLIAAoAmAiAQRAIAAoAmQgAUECdBDfBAsgACgCbCIBBEAgACgCcCABQQJ0EN8ECyAAKAJ4IgEEQCAAKAJ8IAFBAnQQ3wQLIAAoAoQBIgEEQCAAKAKIASABQQJ0EN8ECwvPAgEGf0HRzsUALQAAGgJAAkBBGEEEENYEIgQEQCABKAIIIgVBAnQhByAFQf////8DSyAHQfz///8HS3INASABKAIEIQICfyAHRQRAQQQhA0EADAELQdHOxQAtAAAaQQQhBiAHQQQQ1gQiA0UNAiAFCyEGIAcEQCADIAIgB/wKAAALIAQgBTYCCCAEIAM2AgQgBCAGNgIAIAEoAhQiBUECdCECQQAhAyAFQf////8DSyACQfz///8HS3INAiABKAIQIQYCfyACRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhAyACQQQQ1gQiAUUNAyAFCyEDIAIEQCABIAYgAvwKAAALIAQgBTYCFCAEIAE2AhAgBCADNgIMIABBAjYCCCAAIAQ2AgQgAEECNgIADwtBBEEYEP8EAAsgBiAHQfiBwAAQyAQACyADIAJB+IHAABDIBAAL1AICB34EfyACKAIEIQogAigCACAAIAFHBEAgAigCCCAKQQV0aiENIAogASAAa0EFdiILaiEKQQAhAQNAAn4gACABaiICQaD4wABBIBDxAwRAQo2Vx8OW0trAl38gAkEQaikDACIEfSIDIAJBGGopAwAiBULH+vPD7YKjkDxWrSIHfSEGQt2whYzotpGouH8gAkEIaikDACIIfSIJIAMgB1QgBEKNlcfDltLawJd/VnKtIgN9IQRCx/rzw+2Co5A8IAV9IQVCqcDGia7Ok7IwIAIpAwAgAyAJViAIQt2whYzotpGouH9Wcq18fQwBCyACQRhqKQMAIQUgAkEQaikDACEGIAJBCGopAwAhBCACKQMACyEDIAEgDWoiAiADNwMAIAJBGGogBTcDACACQRBqIAY3AwAgAkEIaiAENwMAIAFBIGohASALQQFrIgsNAAsLIAo2AgALpQIBAn8jAEEQayICJAAgACgCACEAIAJBBGoiAyABEKoEIAIgADYCDCADIAJBDGpByJXBABCOAyACIABBDGo2AgwgAkEEaiACQQxqQciVwQAQjgMgAiAAQRhqNgIMIAJBBGogAkEMakHIlcEAEI4DIAIgAEEkajYCDCACQQRqIAJBDGpByJXBABCOAyACIABBMGo2AgwgAkEEaiACQQxqQciVwQAQjgMgAiAAQTxqNgIMIAJBBGogAkEMakHIlcEAEI4DIAIgAEHIAGo2AgwgAkEEaiACQQxqQciVwQAQjgMgAiAAQdQAajYCDCACQQRqIAJBDGpByJXBABCOAyACIABB4ABqNgIMIAJBBGogAkEMakHIlcEAEI4DIAMQoQQgAkEQaiQAC7wCAQV/IwBBEGsiAyQAIAIoAgQhBAJAAkACQAJAIAEoAggiBQRAIAIoAggiBg0BCyAAQQhqQfDIxAAoAgA2AgAgAEHoyMQAKQIANwIADAELIAZBAUYEQCAEKAIAIQQgA0EIaiIFIAFBCGooAgA2AgAgAyABKQIANwMAIAMgBBCzAiAAQQhqIAUoAgA2AgAgACADKQMANwIADAMLIAEoAgQhByAFQQFGDQEgACAHIAUgBCAGEO0CCyACKAIAIgBFBEAgASECDAILIAQgAEECdBDfBCABIQIMAQsgBygCACEEIANBCGoiBSACQQhqKAIANgIAIAMgAikCADcDACADIAQQswIgAEEIaiAFKAIANgIAIAAgAykDADcCACABIQILIAIoAgAiAARAIAIoAgQgAEECdBDfBAsgA0EQaiQAC8ACAQZ/IwBBMGsiAyQAIANBGGogASACEKEBIAMoAiwhBSADKAIoIQcgAygCJCEGIAMoAhgiBARAIAMoAhwgBEECdBDfBAtBASEIAkAgAi0ADCIEQQFHBEAgBEEBIAUbIQgMAQtBACEFIAZBBEkNACAHIAZBAnQQ3wRBBCEHQQAhBgsgAyAIOgAUIAMgBTYCECADIAc2AgwgAyAGNgIIAkACQAJAAkACQAJAAkAgAS0ADEEBaw4CAQIACyAEQQFrDgIDBAILIARBAWsOAgIBAwsgBEEBaw4CAQACCyAAIAMpAgg3AgAgAEEIaiADQRBqKQIANwIADAILQdvVwgBBKEHw1sIAEP4DAAsgCEEBRwRAIAAgAiADQQhqEJ0BDAELIAAgAykCCDcCACAAQQhqIANBEGopAgA3AgALIANBMGokAAvQAgEEfyMAQSBrIgUkAEEBIQcCQCAALQAEDQAgAC0ABSEIIAAoAgAiBi0ACkGAAXFFBEAgBigCAEHrt8UAQei3xQAgCEEBcSIIG0ECQQMgCBsgBigCBCgCDBEDAA0BIAYoAgAgASACIAYoAgQoAgwRAwANASAGKAIAQbi3xQBBAiAGKAIEKAIMEQMADQEgAyAGIAQoAgwRAgAhBwwBCyAIQQFxRQRAIAYoAgBB7bfFAEEDIAYoAgQoAgwRAwANAQsgBUEBOgAPIAVBzLfFADYCFCAFIAYpAgA3AgAgBSAGKQIINwIYIAUgBUEPajYCCCAFIAU2AhAgBSABIAIQrAINACAFQbi3xQBBAhCsAg0AIAMgBUEQaiAEKAIMEQIADQAgBSgCEEHwt8UAQQIgBSgCFCgCDBEDACEHCyAAQQE6AAUgACAHOgAEIAVBIGokACAAC/cCAQR/IwBBMGsiACQAAkACQEH0zcUAKAIARQRAQYzOxQAoAgAhAUGMzsUAQQA2AgAgAUUNASAAQRhqIAERBAAgAEEQaiICIABBJGopAgA3AwAgACAAKQIcNwMIIAAoAhghAUH0zcUAKAIAIgMNAgJAIANFDQBB+M3FACgCACICRQ0AQfzNxQAoAgAgAkECdBDfBAtB+M3FACABNgIAQfTNxQBBATYCAEH8zcUAIAApAwg3AgBBhM7FACAAQRBqKQMANwIACyAAQTBqJABB+M3FAA8LIABBADYCKCAAQQE2AhwgAEHctsQANgIYIABCBDcCICAAQRhqQcC3xAAQqAQACyAAQShqIAIpAwA3AgAgACAAKQMINwIgIAAgATYCHCAAQQE2AhgCQCAAQRhqIgEoAgBFDQAgASgCBCICRQ0AIAEoAgggAkECdBDfBAsgAEEANgIoIABBATYCHCAAQeC3xAA2AhggAEIENwIgIAFB6LfEABCoBAALigIBBX8CQAJAAkACQCABQQNqQXxxIgMgAUYNACACIAMgAWsiAyACIANJGyIERQ0AQQAhA0EBIQUDQCABIANqLQAAQf8BRg0EIAQgA0EBaiIDRw0ACyAEIAJBCGsiBksNAgwBCyACQQhrIQZBACEEC0F/IQMDQEGAgoQIIAEgBGoiBygCAEF/cyIFayAFckGAgoQIIAdBBGooAgBBf3MiBWsgBXJxQYCBgoR4cUGAgYKEeEcNASAEQQhqIgQgBk0NAAsLIAIgBEcEQEH/ASEDQQEhBQNAIAEgBGotAABB/wFGBEAgBCEDDAMLIAIgBEEBaiIERw0ACwtBACEFCyAAIAM2AgQgACAFNgIAC6sCAQh/IAIgAWtBDG4iByAAKAIAIAAoAggiBGtLBEAgACAEIAdBBEEMEIgDIAAoAgghBAsCQCABIAJHBEAgACgCBCAEQQxsaiEKQQAhAgNAQYCAgIB4IQUCQCABIAJqIgYoAgBBgICAgHhGDQAgBkEIaigCACIIQQJ0IQNBACEFIAhB/////wNLIANB/P///wdLcg0DIAZBBGooAgAhBgJ/IANFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEFIANBBBDWBCIJRQ0EIAgLIQUgA0UNACAJIAYgA/wKAAALIAIgCmoiAyAFNgIAIANBCGogCDYCACADQQRqIAk2AgAgAkEMaiECIARBAWohBCAHQQFrIgcNAAsLIAAgBDYCCA8LIAUgA0H4gcAAEMgEAAuPAgEDfyMAQYABayIEJAAgACgCACEAAn8CQCABKAIIIgJBgICAEHFFBEAgAkGAgIAgcQ0BIAAoAgBBASABEN4CDAILIAAoAgAhAEEAIQIDQCACIARqQf8AaiAAQQ9xIgNBMHIgA0HXAGogA0EKSRs6AAAgAkEBayECIABBD0sgAEEEdiEADQALIAFBAUH7t8UAQQIgAiAEakGAAWpBACACaxCJAgwBCyAAKAIAIQBBACECA0AgAiAEakH/AGogAEEPcSIDQTByIANBN2ogA0EKSRs6AAAgAkEBayECIABBD0sgAEEEdiEADQALIAFBAUH7t8UAQQIgAiAEakGAAWpBACACaxCJAgsgBEGAAWokAAutAgECfyMAQYAIayIBJAAgARAmAkACQCABKAK4BEEBcQRAIAEoAqAFQQFxRQ0BIAFBqAZqIAFBwARqIAFBqAVqEGwgASgCqAYNAiAAIAFBsAZqQcAB/AoAACABKAKMBiIABEAgASgCkAYgAEECdBDfBAsCQCABKAIEIgBFDQAgACAAQQxsQRNqQXhxIgJqQQlqIgBFDQAgASgCACACayAAEN8ECyABKAKAAyIAQYCAgIB4RiAARXJFBEAgASgChAMgAEECdBDfBAsgAUGACGokAA8LQZSEwQBBM0HwhMEAEOgDAAtBlITBAEEzQYCFwQAQ6AMACyABQfgHaiABQbQGaigCADYCACABIAEpAqwGNwPwB0HU/sAAQSsgAUHwB2pBkIXBAEGghcEAEMoDAAv9AQIEfwF+IwBBIGsiBSQAAkACQCAERQ0AIAEgASACaiICSw0AIAMgBGpBAWtBACADa3GtIAIgACgCACIBQQF0IgYgAiAGSxsiAkEIQQRBASAEQYEISRsgBEEBRhsiBiACIAZLGyIGrX4iCUIgiFBFDQAgCaciCEGAgICAeCADa0sNAEEAIQIgBSABBH8gBSABIARsNgIcIAUgACgCBDYCFCADBSACCzYCGCAFQQhqIAMgCCAFQRRqELgDIAUoAghBAUcNASAFKAIQIQIgBSgCDCEHCyAHIAJB5M7BABDIBAALIAUoAgwhASAAIAY2AgAgACABNgIEIAVBIGokAAvRAQIEfwF+IwBBIGsiAyQAAkACQCABIAEgAmoiAksNAEEEIAIgACgCACIBQQF0IgQgAiAESxsiAiACQQRNGyIErUIChiIHQiCIUEUNACAHpyIFQfz///8HSw0AIAMgAQR/IAMgAUECdDYCHCADIAAoAgQ2AhRBBAVBAAs2AhggA0EIakEEIAUgA0EUahC4AyADKAIIQQFHDQEgAygCECECIAMoAgwhBgsgBiACQeiGxQAQyAQACyADKAIMIQEgACAENgIAIAAgATYCBCADQSBqJAALqwICA38BfiMAQUBqIgIkACABKAIAQYCAgIB4RgRAIAEoAgwhAyACQSRqIgRBADYCACACQoCAgIAQNwIcIAJBMGogAygCACIDQQhqKQIANwMAIAJBOGogA0EQaikCADcDACACIAMpAgA3AyggAkEcakHEp8UAIAJBKGoQqwIaIAJBGGogBCgCACIDNgIAIAIgAikCHCIFNwMQIAFBCGogAzYCACABIAU3AgALIAEpAgAhBSABQoCAgIAQNwIAIAJBCGoiAyABQQhqIgEoAgA2AgAgAUEANgIAQdHOxQAtAAAaIAIgBTcDAEEMQQQQ1gQiAUUEQEEEQQwQ/wQACyABIAIpAwA3AgAgAUEIaiADKAIANgIAIABBvKrFADYCBCAAIAE2AgAgAkFAayQAC9YBAgR/AX4jAEEgayIDJAACQAJAIAEgASACaiICSwRAQQAhAQwBC0EAIQFBCCACIAAoAgAiBUEBdCIEIAIgBEsbIgIgAkEITRsiBK0iB0IgiFBFDQAgB6ciBkH/////B0sNACADIAUEfyADIAU2AhwgAyAAKAIENgIUQQEFQQALNgIYIANBCGpBASAGIANBFGoQuAMgAygCCEEBRw0BIAMoAhAhAiADKAIMIQELIAEgAkG0p8UAEMgEAAsgAygCDCEBIAAgBDYCACAAIAE2AgQgA0EgaiQAC/wBAQV/IwBBIGsiBCQAIAIgAWsiBUEMbiIGQQV0IQMCQCAFQfT///8FSyADQfj///8HS3INAAJ/IANFBEBBCCEFQQAMAQtB0c7FAC0AABpBCCEHIANBCBDWBCIFRQ0BIAYLIQcgACABIAJHBH8gBSEDIAYhAgNAIAQgARD0AiADQRhqIARBGGopAwA3AwAgA0EQaiAEQRBqKQMANwMAIANBCGogBEEIaikDADcDACADIAQpAwA3AwAgA0EgaiEDIAFBDGohASACQQFrIgINAAsgBgVBAAs2AgggACAFNgIEIAAgBzYCACAEQSBqJAAPCyAHIANBkJbCABDIBAALogIBBH8jAEEgayIFJABBASEGAkAgACgCACIHIAEgAiAAKAIEIggoAgwiAREDAA0AAkAgAC0ACkGAAXFFBEAgB0H1t8UAQQEgAREDAA0CIAMgACAEKAIMEQIARQ0BDAILIAdB9rfFAEECIAERAwANASAFQQE6AA8gBSAINgIEIAUgBzYCACAFQcy3xQA2AhQgBSAAKQIINwIYIAUgBUEPajYCCCAFIAU2AhAgAyAFQRBqIAQoAgwRAgANASAFKAIQQfC3xQBBAiAFKAIUKAIMEQMADQELAkAgAg0AIAAtAApBgAFxDQAgACgCAEH4t8UAQQEgACgCBCgCDBEDAA0BCyAAKAIAQYu1xQBBASAAKAIEKAIMEQMAIQYLIAVBIGokACAGC4ICAQR/IwBBIGsiAyQAQQEhBQJAIAAtAAQNACAALQAFIQYCQCAAKAIAIgQtAApBgAFxRQRAIAZBAXFFDQEgBCgCAEHrt8UAQQIgBCgCBCgCDBEDAEUNAQwCCyAGQQFxRQRAIAQoAgBB+bfFAEEBIAQoAgQoAgwRAwANAgsgA0EBOgAPIANBzLfFADYCFCADIAQpAgA3AgAgAyAEKQIINwIYIAMgA0EPajYCCCADIAM2AhAgASADQRBqIAIoAgwRAgANASADKAIQQfC3xQBBAiADKAIUKAIMEQMAIQUMAQsgASAEIAIoAgwRAgAhBQsgAEEBOgAFIAAgBToABCADQSBqJAAL8AEBBn8jAEEQayIFJAAgASgCCCEHIAEoAgAhBgJAIAEoAgQiAiABKAIMIgNGBEAgBiEEDAELIAYhBANAIAVBCGogAkEIaigCADYCACAFIAIpAgA3AwAgBCAFELsDNgIAIARBBGohBCACQQxqIgIgA0cNAAsLIAFChICAgMAANwIAIAFCgICAgMAANwIIIAMgAmtBDG4hASACIANHBEADQCACKAIAIgMEQCACQQRqKAIAIANBAnQQ3wQLIAJBDGohAiABQQFrIgENAAsLIAAgBjYCBCAAIAdBA2w2AgAgACAEIAZrQQJ2NgIIIAVBEGokAAvfAQEBfyABIAEoAgAiAUHgAGo2AgAjAEHgAGsiAkEoaiABQShqKQMANwMAIAJBIGogAUEgaikDADcDACACQRhqIAFBGGopAwA3AwAgAkEQaiABQRBqKQMANwMAIAJBCGogAUEIaikDADcDACACQThqIAFBOGopAwA3AwAgAkFAayABQUBrKQMANwMAIAJByABqIAFByABqKQMANwMAIAJB0ABqIAFB0ABqKQMANwMAIAJB2ABqIAFB2ABqKQMANwMAIAIgASkDADcDACACIAEpAzA3AzAgACACQeAA/AoAAAvBAQEBfyMAQZABayIDJAAgA0HIAGogAhAuIAACfiADKAJIQQFGBEAgAEIANwMIQgEMAQsgA0EgaiADQegAaikDADcDACADQShqIANB8ABqKQMANwMAIANBMGogA0H4AGopAwA3AwAgA0E4aiADQYABaikDADcDACADQUBrIANBiAFqKQMANwMAIAMgAykDYDcDGCADIAMpA1g3AxAgAyADKQNQNwMIIABBCGogASADQQhqEDhCAAs3AwAgA0GQAWokAAvVAQEHfwJAIAEEQCABQQJ0IQQDQAJAIAAoAgAiAkGEAUkNACAC0G8mARCDAyIBKAIMIQcgASgCECEDIAFCADcCDCABKAIIIQUgASgCBCEGIAFCBDcCBCABKAIAIQggAUEANgIAIAIgA0kNAyACIANrIgIgBU8NAyAGIAJBAnRqIAc2AgAgASADNgIQIAEgAjYCDCABIAU2AgggASgCBCABIAY2AgQgASgCACECIAEgCDYCACACRQ0AIAJBAnQQ3wQLIABBBGohACAEQQRrIgQNAAsLDwsAC84BAQJ/IwBBEGsiAiQAIAAoAgAhACACQQRqIgMgARCqBCACIAA2AgwgAyACQQxqQeiVwQAQjgMgAiAAQQhqNgIMIAJBBGogAkEMakHolcEAEI4DIAIgAEEQajYCDCACQQRqIAJBDGpB6JXBABCOAyACIABBGGo2AgwgAkEEaiACQQxqQeiVwQAQjgMgAiAAQSBqNgIMIAJBBGogAkEMakHolcEAEI4DIAIgAEEoajYCDCACQQRqIAJBDGpB6JXBABCOAyADEKEEIAJBEGokAAvIAQEEfyMAQRBrIgIkAEEDIQMgACwAACIEIATAQQd1IgBzIABrIgBB/wFxIgVBCk8EQEEBIQMgAiAAQQF0IgAgAEE4aiAFQeQASRtB/gFxIgBB/rfFAGotAAA6AA8gAiAAQf23xQBqLQAAOgAOIAVB4wBLIQALQQAgBCAAQf8BcRtFBEAgA0EBayIDIAJBDWpqIABBAXRB/gFxQf63xQBqLQAAOgAACyABIARBAE5BAUEAIAJBDWogA2pBAyADaxCJAiACQRBqJAAL2gEBA38jAEEwayIDJAAgAyACNgIMIAMgATYCCCADQRBqIgUgAkECTwR/IAIgAkECa0GU28IAIAFBAhDxAyIEGyECIARFQQF0BSAECyABaiACEJICAkAgAygCEA0AIAUgAygCFCADKAIYQRAQ8QEgAygCECIBQYCAgIB4Rg0AIAAgAykCFDcCBCAAIAE2AgAgA0EwaiQADwsgA0EBNgIUIANBrNvCADYCECADQgE3AhwgAyADQQhqrUKAgICAoAKENwMoIAMgA0EoajYCGCADQRBqQbTbwgAQqAQAC9wBAQN/IwBBIGsiAyQAIANBGGoiBEGQksIAKAIANgIAIANBiJLCACkCADcDECACBEAgA0EQakGMk8IAEKUDIAMoAhQgAjYCACADQQE2AhgLIANBCGogBCgCADYCACADIAMpAxA3AwAgACgCCCIEIAAoAgBGBEAgAEHoq8IAEJ8DCyAAKAIEIARBDGxqIgUgAykDADcCACAFQQhqIANBCGooAgA2AgAgACAEQQFqNgIIIAIEQCACQQV0IQIDQCAAIAEQugEgAUEgaiEBIAJBIGsiAg0ACwsgA0EgaiQAC+wBAQJ/IwBBIGsiASQAAkACQAJAAkACQAJAQZzOxQAtAABBAWsOAwIEAQALQZzOxQBBAjoAACAAKAIAIgIoAgAhACACQQA2AgAgAEUNAiAAKAIAIQAgAUEIakGIjMMAQZCRwwBB6NnCABChAyAAQQhqIAFBEGooAgA2AgAgACABKQIINwIAQZzOxQBBAzoAAAsgAUEgaiQADwsgAUEANgIYIAFBATYCDCABQbDSwgA2AggMAgtBzNPCABDoBAALIAFBADYCGCABQQE2AgwgAUHw0sIANgIICyABQgQ3AhAgAUEIakH0zMEAEKgEAAuVAgECfyMAQSBrIgUkAEHszsUAQezOxQAoAgAiBkEBajYCAAJ/QQAgBkEASA0AGkEBQbjSxQAtAAANABpBuNLFAEEBOgAAQbTSxQBBtNLFACgCAEEBajYCAEECC0H/AXEiBkECRwRAIAZBAXEEQCAFQQhqIAAgASgCGBEAAAsACwJAQeDOxQAoAgAiBkEATgRAQeDOxQAgBkEBajYCAEHkzsUAKAIABEAgBSAAIAEoAhQRAAAgBSAEOgAdIAUgAzoAHCAFIAI2AhggBSAFKQMANwIQQeTOxQAoAgAgBUEQakHozsUAKAIAKAIUEQAAC0HgzsUAQeDOxQAoAgBBAWs2AgBBuNLFAEEAOgAAIANFDQEACwALAAvFAQIGfwF+IwBBIGsiAiQAQQQgACgCACIFQQF0IgMgA0EETRsiBq1CGH4iCEIgiFBFBEBBAEEAIAEQyAQACwJAIAinIgdB/P///wdNBEBBACEDIAIgBQR/IAIgBUEYbDYCHCACIAAoAgQ2AhRBBAUgAws2AhggAkEIakEEIAcgAkEUahC4AyACKAIIQQFHDQEgAigCDCEEIAIoAhAhAwsgBCADIAEQyAQACyACKAIMIQEgACAGNgIAIAAgATYCBCACQSBqJAALxwECBn8BfiMAQSBrIgIkAEEEIAAoAgAiBUEBdCIDIANBBE0bIgatQsgAfiIIQiCIUEUEQEEAQQAgARDIBAALAkAgCKciB0H4////B00EQEEAIQMgAiAFBH8gAiAFQcgAbDYCHCACIAAoAgQ2AhRBCAUgAws2AhggAkEIakEIIAcgAkEUahC4AyACKAIIQQFHDQEgAigCDCEEIAIoAhAhAwsgBCADIAEQyAQACyACKAIMIQEgACAGNgIAIAAgATYCBCACQSBqJAALxwECBn8BfiMAQSBrIgIkAEEEIAAoAgAiBUEBdCIDIANBBE0bIgatQuwAfiIIQiCIUEUEQEEAQQAgARDIBAALAkAgCKciB0H8////B00EQEEAIQMgAiAFBH8gAiAFQewAbDYCHCACIAAoAgQ2AhRBBAUgAws2AhggAkEIakEEIAcgAkEUahC4AyACKAIIQQFHDQEgAigCDCEEIAIoAhAhAwsgBCADIAEQyAQACyACKAIMIQEgACAGNgIAIAAgATYCBCACQSBqJAALxQECBn8BfiMAQSBrIgIkAEEEIAAoAgAiBUEBdCIDIANBBE0bIgatQjB+IghCIIhQRQRAQQBBACABEMgEAAsCQCAIpyIHQfj///8HTQRAQQAhAyACIAUEfyACIAVBMGw2AhwgAiAAKAIENgIUQQgFIAMLNgIYIAJBCGpBCCAHIAJBFGoQuAMgAigCCEEBRw0BIAIoAgwhBCACKAIQIQMLIAQgAyABEMgEAAsgAigCDCEBIAAgBjYCACAAIAE2AgQgAkEgaiQAC8cBAgZ/AX4jAEEgayICJABBBCAAKAIAIgVBAXQiAyADQQRNGyIGrULAAX4iCEIgiFBFBEBBAEEAIAEQyAQACwJAIAinIgdB+P///wdNBEBBACEDIAIgBQR/IAIgBUHAAWw2AhwgAiAAKAIENgIUQQgFIAMLNgIYIAJBCGpBCCAHIAJBFGoQuAMgAigCCEEBRw0BIAIoAgwhBCACKAIQIQMLIAQgAyABEMgEAAsgAigCDCEBIAAgBjYCACAAIAE2AgQgAkEgaiQAC8kBAgZ/AX4jAEEgayIBJABBBCAAKAIAIgNBAXQiAiACQQRNGyIErULgAH4iB0IgiFBFBEBBAEEAQYDMwQAQyAQACwJAIAenIgVB+P///wdNBEAgASADBH8gASADQeAAbDYCHCABIAAoAgQ2AhRBCAVBAAs2AhggAUEIakEIIAUgAUEUahC4AyABKAIIQQFHDQEgASgCDCEGIAEoAhAhAgsgBiACQYDMwQAQyAQACyABKAIMIQIgACAENgIAIAAgAjYCBCABQSBqJAALxQECBn8BfiMAQSBrIgIkAEEEIAAoAgAiBUEBdCIDIANBBE0bIgatQgx+IghCIIhQRQRAQQBBACABEMgEAAsCQCAIpyIHQfz///8HTQRAQQAhAyACIAUEfyACIAVBDGw2AhwgAiAAKAIENgIUQQQFIAMLNgIYIAJBCGpBBCAHIAJBFGoQuAMgAigCCEEBRw0BIAIoAgwhBCACKAIQIQMLIAQgAyABEMgEAAsgAigCDCEBIAAgBjYCACAAIAE2AgQgAkEgaiQAC7wBAQJ/IwBBIGsiAyQAAkACf0EAIAEgASACaiICSw0AGkEAQQggAiAAKAIAIgFBAXQiBCACIARLGyICIAJBCE0bIgRBAEgNABpBACECIAMgAQR/IAMgATYCHCADIAAoAgQ2AhRBAQUgAgs2AhggA0EIakEBIAQgA0EUahC4AyADKAIIQQFHDQEgAygCECEAIAMoAgwLIABB0KzFABDIBAALIAMoAgwhASAAIAQ2AgAgACABNgIEIANBIGokAAu5EwIQfgV/IwBBIGsiFSQAIAIgAWsiGEECdCEUAkAgGEH4////A0sgFEH4////B0tyDQBBCCEWIBQEQEHRzsUALQAAGkEIIRcgFEEIENYEIhZFDQEgGEEDdiEXCyAVQRBqIhhBADYCACAVIBY2AgwgFSAXNgIIIBUgFjYCHCAVQQA2AhggFSAYNgIUIwBBoARrIgMkACAVQRRqIhQoAgQhFiAUKAIAIAEgAkcEQCAUKAIIIBZBBXRqIRQgFiACIAFrQQN2IgJqIRYDQCADQYAEaiABKAIAIAFBBGooAgAQtwIgA0GAAmogAykDmAQiBEIAQqfbhfHayLncG0IAEMkDIANBwAJqIAMpA5AEIghCAEKn24Xx2si53BtCABDJAyADQYADaiADKQOIBCIGQgBCp9uF8drIudwbQgAQyQMgA0HAA2ogAykDgAQiB0IAQqfbhfHayLncG0IAEMkDIANB8AFqIAMpA4ACIgpC/////76y/fBCfiIFQgBCgYCAgL+y/fDDAEIAEMkDIANB4AFqIAVCAEKR4eXNh4n6mShCABDJAyADQZABaiAFQgBC3bCFjOi2kai4f0IAEMkDIANBQGsgBUIAQqnAxomuzpOyMEIAEMkDIANBkAJqIARCAELjs/GantaO/9MAQgAQyQMgA0HQAmogCEIAQuOz8Zqe1o7/0wBCABDJAyADQZADaiAGQgBC47Pxmp7Wjv/TAEIAEMkDIANB0ANqIAdCAELjs/GantaO/9MAQgAQyQMgA0HQAWogAykD4AEiDCADKQOIAiINIAMpA8ACfCIOfCIJIAMpA/gBIAogAykD8AEiBXwgBVStfHwiCiADKQOQAnwiC0L/////vrL98EJ+IgVCAEKBgICAv7L98MMAQgAQyQMgA0HAAWogBUIAQpHh5c2HifqZKEIAEMkDIANBsAFqIAVCAELdsIWM6LaRqLh/QgAQyQMgA0GgAWogBUIAQqnAxomuzpOyMEIAEMkDIANBoAJqIARCAEKFge6d1efgpIx/QgAQyQMgA0HgAmogCEIAQoWB7p3V5+CkjH9CABDJAyADQaADaiAGQgBChYHundXn4KSMf0IAEMkDIANB4ANqIAdCAEKFge6d1efgpIx/QgAQyQMgA0GAAWogAykDmAIgCiALVq18IhEgAykD0AJ8Ig8gAykDyAIgDSAOVq18IhAgAykDgAN8Ig0gAykDkAF8Ig4gCSAKVq0gAykD6AEgCSAMVK18fHwiEnwiCSADKQPAAXwiCiADKQPYASADKQPQASIFIAt8IAVUrXx8IgsgAykDoAJ8IgxC/////76y/fBCfiIFQgBCgYCAgL+y/fDDAEIAEMkDIANB8ABqIAVCAEKR4eXNh4n6mShCABDJAyADQeAAaiAFQgBC3bCFjOi2kai4f0IAEMkDIANB0ABqIAVCAEKpwMaJrs6TsjBCABDJAyADQbACaiAEQgBCpYm5+peWtIsCQgAQyQMgA0HwAmogCEIAQqWJufqXlrSLAkIAEMkDIANBsANqIAZCAEKlibn6l5a0iwJCABDJAyADQfADaiAHQgBCpYm5+peWtIsCQgAQyQMgA0EwaiADKQOoAiALIAxWrXwiEyADKQPgAnwiCCADKQOIAyANIBBUrXwiECADKQPAA3wiBiADKQNAfCIHIA4gElatIAMpA5gBIA0gDlatfHx8IgUgAykDkAN8Ig0gCSAPVK0gAykD2AIgDyARVK18fHwiDyADKQOwAXwiDiAKIAtWrSADKQPIASAJIApWrXx8fCIRfCIJIAMpA3B8IgogAykDiAEgAykDgAEiBCAMfCAEVK18fCILIAMpA7ACfCIMQv////++sv3wQn4iBEIAQoGAgIC/sv3wwwBCABDJAyADQSBqIARCAEKR4eXNh4n6mShCABDJAyADQRBqIARCAELdsIWM6LaRqLh/QgAQyQMgAyAEQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpAwggAykD6AMgAykD2AMgAykDyAMgBiAQVK18IhAgAykD0AN8IgQgEFStfCAEIAQgBSAHVK0gAykDSCAGIAdWrXx8fCIGVq18IAYgBiANIA9WrSADKQOYAyAFIA1WrXx8fCIEVq18IgcgAykD4AN8IgYgB1StfCAGIAYgAykDqAEgBCAEIAMpA6ABfCIHVq18IAcgByAOIBFWrSADKQO4ASAOIA9UrXx8fCIEVq18fCIHVq18IAcgAykDqAMgBCAEIAMpA6ADfCIGVq18IAYgBiAIIAlWrSADKQPoAiAIIBNUrXx8fCIEVq18fCIIIAdUrXwiDyADKQPwA3wiByADKQNYIAggCCADKQNQfCIGVq18IAYgAykDaCAEIAQgAykDYHwiCFatfCAIIAogC1atIAMpA3ggCSAKVq18fHwiBSAIVK18fCIEIAZUrXx8IgggAykDuAMgBCAEIAMpA7ADfCIGVq18IAYgBiADKQP4AiADKQO4AiALIAxWrXwiCSADKQPwAnwiBCAJVK18IAQgBCAFfCIFVq18fCIEVq18fCIKIAMpAwB8IgYgClStfCAGIAYgAykDGCAEIAQgAykDEHwiC1atfCALIAsgAykDKCAFIAUgAykDIHwiBFatfCAEIAMpAzggAykDMCIFIAx8IAVUrXx8IgkgBFStfHwiBFatfHwiBlatfCAIIApWrSAHIAhWrSADKQP4AyAHIA9UrXx8fHwiBUKpwMaJrs6TsjBWDQACQCAFQqnAxomuzpOyMFEEQCAGQt2whYzotpGouH9WDQIgBkLdsIWM6LaRqLh/UgRAIAQhCCAGIQdCqcDGia7Ok7IwIQUMBAsgBEKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyEHIARCkeHlzYeJ+pkoUQ0BIAQhCEKpwMaJrs6TsjAhBQwDCyAEIQggBiEHDAILQpHh5c2HifqZKCEIIAlCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhBQwBCyAEQpHh5c2HifqZKH0iByAJQoGAgIC/sv3wwwBUrSIKfSEIIAZCo8/685fJ7tfHAHwiCyAEQpHh5c2HifqZKFQgByAKVHKtIgR9IQcgBSAGQt2whYzotpGouH9UIAQgC1ZyrX1CqcDGia7Ok7IwfSEFIAlCgYCAgL+y/fDDAH0hCQsgFCAFNwMAIBRBGGogCTcDACAUQRBqIAg3AwAgFEEIaiAHNwMAIAFBCGohASAUQSBqIRQgAkEBayICDQALCyAWNgIAIANBoARqJAAgAEEIaiAYKAIANgIAIAAgFSkCCDcCACAVQSBqJAAPCyAXIBQgAxDIBAALuwEBBX8jAEEgayICJAAgACgCACIEQf///x9LBEBBAEEAIAEQyAQACwJAQQQgBEEBdCIFIAVBBE0bIgVBBXQiBkH4////B00EfyACIAQEfyACIARBBXQ2AhwgAiAAKAIENgIUQQgFIAMLNgIYIAJBCGpBCCAGIAJBFGoQuAMgAigCCEEBRw0BIAIoAhAhAyACKAIMBSADCyADIAEQyAQACyACKAIMIQEgACAFNgIAIAAgATYCBCACQSBqJAALuwEBBX8jAEEgayICJAAgACgCACIEQf///z9LBEBBAEEAIAEQyAQACwJAQQQgBEEBdCIFIAVBBE0bIgVBBHQiBkH8////B00EfyACIAQEfyACIARBBHQ2AhwgAiAAKAIENgIUQQQFIAMLNgIYIAJBCGpBBCAGIAJBFGoQuAMgAigCCEEBRw0BIAIoAhAhAyACKAIMBSADCyADIAEQyAQACyACKAIMIQEgACAFNgIAIAAgATYCBCACQSBqJAALuwEBBX8jAEEgayICJAAgACgCACIEQf///wdLBEBBAEEAIAEQyAQACwJAQQQgBEEBdCIFIAVBBE0bIgVBB3QiBkH4////B00EfyACIAQEfyACIARBB3Q2AhwgAiAAKAIENgIUQQgFIAMLNgIYIAJBCGpBCCAGIAJBFGoQuAMgAigCCEEBRw0BIAIoAhAhAyACKAIMBSADCyADIAEQyAQACyACKAIMIQEgACAFNgIAIAAgATYCBCACQSBqJAALvAEBBX8jAEEgayICJAAgACgCACIEQf////8BSwRAQQBBACABEMgEAAsCQEEEIARBAXQiBSAFQQRNGyIFQQJ0IgZB/P///wdNBH8gAiAEBH8gAiAEQQJ0NgIcIAIgACgCBDYCFEEEBSADCzYCGCACQQhqQQQgBiACQRRqELgDIAIoAghBAUcNASACKAIQIQMgAigCDAUgAwsgAyABEMgEAAsgAigCDCEBIAAgBTYCACAAIAE2AgQgAkEgaiQAC6UBAQF/IAAoAgAiAQRAIAAoAgQgAUECdBDfBAsgACgCECIBBEAgACgCFCABQQJ0EN8ECyAAKAIgIgEEQCAAKAIkIAFBAnQQ3wQLIAAoAjAiAQRAIAAoAjQgAUECdBDfBAsgACgCQCIBBEAgACgCRCABQQJ0EN8ECyAAKAJQIgEEQCAAKAJUIAFBAnQQ3wQLIAAoAmAiAQRAIAAoAmQgAUECdBDfBAsL2wsCD38IfiMAQTBrIgMkACADQYCAgIB4NgIMIAMgAjYCKCADIAE2AiQgAyADQQxqNgIsIANBGGohDyMAQdACayIBJAAgAUGAAmoiCiADQSRqIgQgAUHPAmoiBSAEKAIIEKQCAkACQAJAAkAgAS0AwAIiBkEDRg0AIAFB+AFqIgIgAUG4AmopAwA3AwAgAUHwAWoiCyABQbACaikDADcDACABQegBaiIMIAFBqAJqKQMANwMAIAFB4AFqIgcgAUGgAmopAwA3AwAgAUHYAWoiCCABQZgCaikDADcDACABQdABaiIJIAFBkAJqKQMANwMAIAFByAFqIg0gAUGIAmopAwA3AwAgASABKQOAAjcDwAEgASABKADBAjYCeCABIAFBxAJqKAAANgB7IAZBAkYNACABQdgAaiIOIAIpAwA3AwAgAUHQAGoiECALKQMANwMAIAFByABqIgsgDCkDADcDACABQUBrIgwgBykDADcDACABQThqIgcgCCkDADcDACABQTBqIgggCSkDADcDACABQShqIgkgDSkDADcDACABIAEpA8ABNwMgIAEgASgCeDYCGCABIAEoAHs2ABtB0c7FAC0AABpBoAJBCBDWBCICRQ0CIAIgASkDIDcDACACIAY6AEAgAiABKAIYNgBBIAJBxABqIAEoABs2AAAgAkE4aiAOKQMANwMAIAJBMGogECkDADcDACACQShqIAspAwA3AwAgAkEgaiAMKQMANwMAIAJBGGogBykDADcDACACQRBqIAgpAwA3AwAgAkEIaiAJKQMANwMAIAFBATYCFCABIAI2AhAgAUEENgIMIAFB6ABqIARBCGooAgAiBjYCACABIAQpAgA3A2AgCiABQeAAaiAFIAYQpAICQCABLQDAAiIEQQNGDQBBiQEhCiABQcECaiILQQNqIQxBASEGA0AgAUH4AWoiBSABQbgCaikDADcDACABQfABaiIHIAFBsAJqKQMANwMAIAFB6AFqIgggAUGoAmopAwA3AwAgAUHgAWoiCSABQaACaikDADcDACABQdgBaiINIAFBmAJqKQMANwMAIAFB0AFqIg4gAUGQAmopAwA3AwAgAUHIAWoiECABQYgCaikDADcDACABIAEpA4ACNwPAASABIAsoAAA2ArgBIAEgDCgAADYAuwEgBEECRg0BIAFBsAFqIhEgBSkDADcDACABQagBaiIFIAcpAwA3AwAgAUGgAWoiByAIKQMANwMAIAFBmAFqIgggCSkDADcDACABQZABaiIJIA0pAwA3AwAgAUGIAWoiDSAOKQMANwMAIAFBgAFqIg4gECkDADcDACABIAEpA8ABNwN4IAEgASgCuAE2AnAgASABKAC7ATYAcyABKAIMIAZGBEAgAUEMaiAGQQFBCEHIABCIAyABKAIQIQILIA4pAwAhEiANKQMAIRMgCSkDACEUIAgpAwAhFSAHKQMAIRYgBSkDACEXIBEpAwAhGCABKQN4IRkgAiAKaiIFQQFrIAQ6AAAgBUHBAGsiBCAZNwMAIAUgASgCcDYAACAFQQNqIAEoAHM2AAAgBEE4aiAYNwMAIARBMGogFzcDACAEQShqIBY3AwAgBEEgaiAVNwMAIARBGGogFDcDACAEQRBqIBM3AwAgBEEIaiASNwMAIAEgBkEBaiIGNgIUIAFBgAJqIAFB4ABqIAFBzwJqIAEoAmgQpAIgCkHIAGohCiABLQDAAiIEQQNHDQALCyAPQQhqIAFBFGooAgA2AgAgDyABKQIMNwIADAELIA9BADYCCCAPQoCAgICAATcCAAsgAUHQAmokAAwBC0EIQaACQZCWwgAQyAQACyAAQQRqIQECQCADKAIMQYCAgIB4RwRAIAEgAykCDDcCACABQQhqIANBFGooAgA2AgBBASECIAMoAhgiAUUNASADKAIcIAFByABsEN8EDAELIAEgAykCGDcCACABQQhqIANBIGooAgA2AgBBACECCyAAIAI2AgAgA0EwaiQAC78BAQJ/IwBBIGsiAiQAIAEtAAwiAwRAIAJBCGogARByQQEhAQJAIANBAUcEQEECQQEgAigCEBshAQwBCyACQQA2AhAgAigCCCIDQQRJDQAgAigCDCADQQJ0EN8EIAJCgICAgMAANwIICyAAIAIpAgg3AgAgACABOgAMIABBCGogAkEQaigCADYCACACQSBqJAAPCyACQQA2AhggAkEBNgIMIAJBlMLEADYCCCACQgQ3AhAgAkEIakGcwsQAEKgEAAvCAQIDfwF+IwBBMGsiAiQAIAEoAgBBgICAgHhGBEAgASgCDCEDIAJBFGoiBEEANgIAIAJCgICAgBA3AgwgAkEgaiADKAIAIgNBCGopAgA3AwAgAkEoaiADQRBqKQIANwMAIAIgAykCADcDGCACQQxqQcSnxQAgAkEYahCrAhogAkEIaiAEKAIAIgM2AgAgAiACKQIMIgU3AwAgAUEIaiADNgIAIAEgBTcCAAsgAEG8qsUANgIEIAAgATYCACACQTBqJAALyAEBAX8jAEEQayILJAAgACgCACABIAIgACgCBCgCDBEDACEBIAtBADoADSALIAE6AAwgCyAANgIIIAtBCGogAyAEIAUgBhCCAyAHIAggCSAKEIIDIQEgCy0ADSICIAstAAwiA3IhAAJAIANBAXEgAkEBR3INACABKAIAIgAtAApBgAFxRQRAIAAoAgBB87fFAEECIAAoAgQoAgwRAwAhAAwBCyAAKAIAQfK3xQBBASAAKAIEKAIMEQMAIQALIAtBEGokACAAQQFxC7EBAQZ/AkACQCAAQYQBSQ0AIADQbyYBEIMDIgEoAgwhBSABKAIQIQIgAUIANwIMIAEoAgghAyABKAIEIQQgAUIENwIEIAEoAgAhBiABQQA2AgAgACACSQ0BIAAgAmsiACADTw0BIAQgAEECdGogBTYCACABIAI2AhAgASAANgIMIAEgAzYCCCABKAIEIAEgBDYCBCABKAIAIQAgASAGNgIAIABFDQAgAEECdBDfBAsPCwALhwEBBX8jAEGAA2siAiQAIAIgASABQeAAaiIGED8gAkHgAGoiBSABIAYQ1QEgAkGgAmoiAxB1IAJBwAFqIgQgAyAGED8gAyABIAQQ1QEgBCAFIAMQPyAFIAQgAhCNASADEHUgBCADIAIQPyAAIAUgBBCNASAAQeAAaiACIAIQ1QEgAkGAA2okAAvRAwIMfwF+IwBBIGsiBCQAIARBGGoiCRCDAyIFQRBqIgcoAgA2AgAgBEEQaiIKIAVBCGoiCCkCADcDACAHQQA2AgAgCEIANwIAIAUpAgAhDCAFQoCAgIDAADcCACAEIAw3AwgCfyMAQSBrIgMkAAJAAkAgBEEIaiIAKAIMIgEgACgCCCICRgRAAkAgACgCACICIAFGBEDQb0GAASABIAFBgAFNGyIG/A8BIgJBf0YNBAJAIAAoAhAiC0UEQCAAIAI2AhAMAQsgASALaiACRw0FCyABIAZqIgJB/////wFLDQQgAyABBH8gAyABQQJ0NgIcIAMgACgCBDYCFEEEBUEACzYCGCADQQhqQQQgAkECdCADQRRqELgDIAMoAghBAUYNBCADKAIMIQYgACACNgIAIAAgBjYCBAwBCyABIAJPDQMLIAAgAUEBaiICNgIIIAAoAgQgAUECdGogAjYCAAwBCyABIAJPDQELIAAgACgCBCABQQJ0aigCADYCDCAAKAIQIANBIGokACABagwBCwALIAggCikDADcCACAHIAkoAgA2AgAgBSgCBCEDIAUoAgAhASAFIAQpAwg3AgAgAQRAIAMgAUECdBDfBAsgBEEgaiQAC7kBAQN/IAEoAgwhAgJAAkACQAJAAkACQCABKAIEDgIAAQILIAINAUEBIQNBACEBQQEhAgwDCyACRQ0BCyAAIAEQ0gIPCyABKAIAIgIoAgQiAUEASA0BIAIoAgAhAyABRQRAQQEhAkEAIQEMAQtB0c7FAC0AABpBASEEIAFBARDWBCICRQ0BCyABBEAgAiADIAH8CgAACyAAIAE2AgggACACNgIEIAAgATYCAA8LIAQgAUGkm8IAEMgEAAu4AQEBf0HRzsUALQAAGkHAAEEIENYEIgJFBEBBCEHAAEGwncUAEMgEAAsgAEECNgIIIAAgAjYCBCAAQQI2AgAgAiABKQMANwMAIAJBOGogAUE4aikDADcDACACQTBqIAFBMGopAwA3AwAgAkEoaiABQShqKQMANwMAIAJBIGogAUEgaikDADcDACACQRhqIAFBGGopAwA3AwAgAkEQaiABQRBqKQMANwMAIAJBCGogAUEIaikDADcDAAu9AQEBfyMAQRBrIgckACAAKAIAIAEgAiAAKAIEKAIMEQMAIQEgB0EAOgANIAcgAToADCAHIAA2AgggB0EIaiADIAQgBSAGEIIDIQEgBy0ADSICIActAAwiA3IhAAJAIANBAXEgAkEBR3INACABKAIAIgAtAApBgAFxRQRAIAAoAgBB87fFAEECIAAoAgQoAgwRAwAhAAwBCyAAKAIAQfK3xQBBASAAKAIEKAIMEQMAIQALIAdBEGokACAAQQFxC7YBAQJ/IwBBIGsiAiQAIAJBGGoiA0GQksIAKAIANgIAIAJBiJLCACkCADcDECABBEAgAkEQakGMk8IAEKUDIAIoAhQgATYCACACQQE2AhgLIAJBCGogAygCADYCACACIAIpAxA3AwAgACgCCCIBIAAoAgBGBEAgAEHoq8IAEJ8DCyAAKAIEIAFBDGxqIgMgAikDADcCACADQQhqIAJBCGooAgA2AgAgACABQQFqNgIIIAJBIGokAAulAQEBfyMAQRBrIgYkAAJAIAEEQCAGQQRqIAEgAyAEIAUgAigCEBEHAAJAIAYoAgQiAiAGKAIMIgFNBEAgBigCCCEFDAELIAJBAnQhAiAGKAIIIQMgAUUEQEEEIQUgAyACEN8EDAELIAMgAkEEIAFBAnQiAhDOBCIFRQ0CCyAAIAE2AgQgACAFNgIAIAZBEGokAA8LEPgEAAtBBCACQfC1xAAQyAQAC5wBAQR/AkACQAJAAkACQCAAQQRPBEAgALif/AMiAUUNASABIAAgAW4gAWpBAXYiAkkNAiACIQMMAwsgAEEARyEBDAMLQZCMxQAQmgQACwNAIAIgACACbiACakEBdiIDSSACIQEgAyECDQALCyABIANNDQADQCADIgFFDQIgASAAIAFuIAFqQQF2IgNLDQALCyABDwtBkIzFABCaBAALpwEAIAAgARDaAiAAQQxqIAFBIGoQ2gIgAEEYaiABQUBrENoCIABBJGogAUHgAGoQ2gIgAEEwaiABQYABahDaAiAAQTxqIAFBoAFqENoCIABByABqIAFBwAFqENoCIABB1ABqIAFB4AFqENoCIABB4ABqIAFBgAJqENoCIABB7ABqIAFBoAJqENoCIABB+ABqIAFBwAJqENoCIABBhAFqIAFB4AJqENoCC6gBACAAIAEQ2AIgAEEMaiABQTBqENgCIABBGGogAUHgAGoQ2AIgAEEkaiABQZABahDYAiAAQTBqIAFBwAFqENgCIABBPGogAUHwAWoQ2AIgAEHIAGogAUGgAmoQ2AIgAEHUAGogAUHQAmoQ2AIgAEHgAGogAUGAA2oQ2AIgAEHsAGogAUGwA2oQ2AIgAEH4AGogAUHgA2oQ2AIgAEGEAWogAUGQBGoQ2AILmwEBBH8jAEEgayICJABBCCAAKAIAIgRBAXQiAyADQQhNGyIDQQBIBEBBAEEAIAEQyAQACyACIAQEfyACIAQ2AhwgAiAAKAIENgIUQQEFIAULNgIYIAJBCGpBASADIAJBFGoQuAMgAigCCEEBRgRAIAIoAgwgAigCECABEMgEAAsgAigCDCEBIAAgAzYCACAAIAE2AgQgAkEgaiQAC6UBAQF/IwBBQGoiAiQAIAAoAgAhACACQgA3AzggAkE4aiAAJQEQESACIAIoAjwiADYCNCACIAIoAjg2AjAgAiAANgIsIAIgAkEsaq1CgICAgNAOhDcDICACQQI2AgwgAkGEuMQANgIIIAJCATcCFCACIAJBIGo2AhAgASgCACABKAIEIAJBCGoQqwIgAigCLCIBBEAgAigCMCABEN8ECyACQUBrJAALjwEBAX8gAkEATgRAAn8gAygCBARAAkAgAygCCCIERQRADAELIAMoAgAgBCABIAIQzgQMAgsLIAEgAkUNABpB0c7FAC0AABogAiABENYECyIDRQRAIAAgAjYCCCAAIAE2AgQgAEEBNgIADwsgACACNgIIIAAgAzYCBCAAQQA2AgAPCyAAQQA2AgQgAEEBNgIAC5YBAQJ/IwBBEGsiAiQAIAAoAgAhACACQQRqIgMgARCqBCACIAA2AgwgAyACQQxqQeiVwQAQjgMgAiAAQQhqNgIMIAJBBGogAkEMakHolcEAEI4DIAIgAEEQajYCDCACQQRqIAJBDGpB6JXBABCOAyACIABBGGo2AgwgAkEEaiACQQxqQeiVwQAQjgMgAxChBCACQRBqJAALzwECBX8BbwJAIAEoAgAiBRCHBSIDQQBIDQACQCADRQRAQQEhBAwBC0HRzsUALQAAGkEBIQIgA0EBENYEIgRFDQELEBMhBxCtAyIBIAcmASABIgYlARAMIQcQrQMiASAHJgEgASUBEA0hBxCtAyICIAcmASABQYQBTwRAIAEQqwMLIAIlASAFJQEgBBAOIAJBhAFPBEAgAhCrAwsgBkGEAU8EQCAGEKsDCyAAIAUQhwU2AgggACAENgIEIAAgAzYCAA8LIAIgA0H0tMQAEMgEAAuyAQIEfwFvIwBBIGsiASQAIAFBADYCCCABQoCAgIAQNwIAIAFB2J/AADYCECABQqCAgIAONwIUIAEgATYCDCAAIAFBDGoQogJFBEAgASgCACECIAEoAgQiAyABKAIIEAMhBRCtAyIEIAUmASACBEAgAyACEN8ECyAAKAIAIgIEQCAAKAIEIAJBAnQQ3wQLIAFBIGokACAEDwtBgKDAAEE3IAFBH2pB8J/AAEGEocAAEMoDAAuVAQEDfyMAQRBrIgIkAAJ/QQEgASgCACIDQScgASgCBCIEKAIQIgERAgANABogAkEEaiAAKAIAQYECEIgCAkAgAi0ABEGAAUYEQCADIAIoAgggARECAEUNAUEBDAILIAMgAi0ADiIAIAJBBGpqIAItAA8gAGsgBCgCDBEDAEUNAEEBDAELIANBJyABEQIACyACQRBqJAALiAEAIAEgASgCACIBQUBrNgIAIAAgASkDADcDACAAQQhqIAFBCGopAwA3AwAgAEEQaiABQRBqKQMANwMAIABBGGogAUEYaikDADcDACAAQSBqIAEpAyA3AwAgAEEoaiABQShqKQMANwMAIABBMGogAUEwaikDADcDACAAQThqIAFBOGopAwA3AwALjwEBBH8gASgCCCIEQQJ0IQICQCAEQf////8DSyACQfz///8HS3INACABKAIEIQUCfyACRQRAQQQhAUEADAELQdHOxQAtAAAaQQQhAyACQQQQ1gQiAUUNASAECyEDIAIEQCABIAUgAvwKAAALIAAgBDYCCCAAIAE2AgQgACADNgIADwsgAyACQfiBwAAQyAQAC3cBBH8gACgCBCEDIAAoAggiBARAIAMhAQNAIAEoAgAiAgRAIAFBBGooAgAgAkECdBDfBAsgAUEMaigCACICBEAgAUEQaigCACACQQJ0EN8ECyABQRhqIQEgBEEBayIEDQALCyAAKAIAIgAEQCADIABBGGwQ3wQLC48BAQR/IAEoAggiBEECdCECAkAgBEH/////A0sgAkH8////B0tyDQAgASgCBCEFAn8gAkUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQMgAkEEENYEIgFFDQEgBAshAyACBEAgASAFIAL8CgAACyAAIAQ2AgggACABNgIEIAAgAzYCAA8LIAMgAkGkg8UAEMgEAAt+AgF/An4jAEHQAWsiAyQAIANB6ABqIAIQPSAAAn4gAygCaEEBRgRAIABCADcDCEIBDAELIAMpA3AhBCADKQN4IQUgA0EYaiADQYABakHQAPwKAAAgAyAFNwMQIAMgBDcDCCAAQQhqIAEgA0EIahA/QgALNwMAIANB0AFqJAALeAEDfyMAQYABayIDJAAgAC0AACEEQQAhAANAIAAgA2pB/wBqIARBD3EiAkEwciACQTdqIAJBCkkbOgAAIABBAWshACAEIgJBBHYhBCACQQ9LDQALIAFBAUH7t8UAQQIgACADakGAAWpBACAAaxCJAiADQYABaiQAC3oCAX4CfyMAQYABayIEJAAgACkDACECQQAhAANAIAAgBGpB/wBqIAKnQQ9xIgNBMHIgA0HXAGogA0EKSRs6AAAgAEEBayEAIAJCD1YgAkIEiCECDQALIAFBAUH7t8UAQQIgACAEakGAAWpBACAAaxCJAiAEQYABaiQAC3MBA38jAEGAAWsiBCQAIAAoAgAhAANAIAIgBGpB/wBqIABBD3EiA0EwciADQdcAaiADQQpJGzoAACACQQFrIQIgAEEPSyAAQQR2IQANAAsgAUEBQfu3xQBBAiACIARqQYABakEAIAJrEIkCIARBgAFqJAALcgEDfyMAQYABayIEJAAgACgCACEAA0AgAiAEakH/AGogAEEPcSIDQTByIANBN2ogA0EKSRs6AAAgAkEBayECIABBD0sgAEEEdiEADQALIAFBAUH7t8UAQQIgAiAEakGAAWpBACACaxCJAiAEQYABaiQAC4EBAQR/IAEoAgwgASgCBCIDayIEQcgAbiIFIAAoAgAgACgCCCICa0sEQCAAIAIgBUEIQcgAEIgDIAAoAgghAgsgBARAIAAoAgQgAkHIAGxqIAMgBPwKAAALIAEgAzYCDCAAIAIgBWo2AgggASgCCCIABEAgASgCACAAQcgAbBDfBAsLfQEEfyABKAIMIAEoAgQiA2siBEEMbiIFIAAoAgAgACgCCCICa0sEQCAAIAIgBUEEQQwQiAMgACgCCCECCyAEBEAgACgCBCACQQxsaiADIAT8CgAACyABIAM2AgwgACACIAVqNgIIIAEoAggiAARAIAEoAgAgAEEMbBDfBAsLewEBfyMAQSBrIgIkAAJ/IAAoAgBBgICAgHhHBEAgASAAKAIEIAAoAggQ0AQMAQsgAkEQaiAAKAIMKAIAIgBBCGopAgA3AwAgAkEYaiAAQRBqKQIANwMAIAIgACkCADcDCCABKAIAIAEoAgQgAkEIahCrAgsgAkEgaiQAC24BBn4gACADQv////8PgyIFIAFC/////w+DIgZ+IgcgBiADQiCIIgZ+IgggBSABQiCIIgl+fCIFQiCGfCIKNwMAIAAgByAKVq0gBiAJfiAFIAhUrUIghiAFQiCIhHx8IAEgBH4gAiADfnx8NwMIC3wBAX8jAEFAaiIFJAAgBSABNgIMIAUgADYCCCAFIAM2AhQgBSACNgIQIAVBAjYCHCAFQby3xQA2AhggBUICNwIkIAUgBUEQaq1CgICAgLAShDcDOCAFIAVBCGqtQoCAgIDAEoQ3AzAgBSAFQTBqNgIgIAVBGGogBBCoBAALbAECfyMAQRBrIgIkACAAKAIIIQMgACgCBCEAIAJBBGogARCqBCADBEAgA0EFdCEBA0AgAiAANgIMIAJBBGogAkEMakHolsEAEI4DIABBIGohACABQSBrIgENAAsLIAJBBGoQoQQgAkEQaiQAC2wBAn8jAEEQayICJAAgACgCCCEDIAAoAgQhACACQQRqIAEQqgQgAwRAIANBDGwhAQNAIAIgADYCDCACQQRqIAJBDGpBuJbBABCOAyAAQQxqIQAgAUEMayIBDQALCyACQQRqEKEEIAJBEGokAAtsAQJ/IwBBEGsiAiQAIAAoAgghAyAAKAIEIQAgAkEEaiABEKoEIAMEQCADQQV0IQEDQCACIAA2AgwgAkEEaiACQQxqQZiWwQAQjgMgAEEgaiEAIAFBIGsiAQ0ACwsgAkEEahChBCACQRBqJAALbwECfyMAQRBrIgIkACAAKAIIIQMgACgCBCEAIAJBBGogARCqBCADBEAgA0HsAGwhAQNAIAIgADYCDCACQQRqIAJBDGpByJbBABCOAyAAQewAaiEAIAFB7ABrIgENAAsLIAJBBGoQoQQgAkEQaiQAC2wBAn8jAEEQayICJAAgACgCCCEDIAAoAgQhACACQQRqIAEQqgQgAwRAIANBGGwhAQNAIAIgADYCDCACQQRqIAJBDGpB2JbBABCOAyAAQRhqIQAgAUEYayIBDQALCyACQQRqEKEEIAJBEGokAAtsAQJ/IwBBEGsiAiQAIAAoAgghAyAAKAIEIQAgAkEEaiABEKoEIAMEQCADQTBsIQEDQCACIAA2AgwgAkEEaiACQQxqQaiWwQAQjgMgAEEwaiEAIAFBMGsiAQ0ACwsgAkEEahChBCACQRBqJAALbAECfyMAQRBrIgIkACAAKAIIIQMgACgCBCEAIAJBBGogARCqBCADBEAgA0EMbCEBA0AgAiAANgIMIAJBBGogAkEMakHIlcEAEI4DIABBDGohACABQQxrIgENAAsLIAJBBGoQoQQgAkEQaiQAC34CAn4Bf0EBIQMCQAJAQcCnwgApAwAiASAAKQMAIgJUDQAgASACVg0BQcinwgApAwAiASAAKQMIIgJUDQAgASACVgRAQQAPC0HQp8IAKQMAIgEgACkDECICVA0AQQAhAyABIAJWDQBB2KfCACkDACAAKQMYWCEDCyADDwtBAAt2AQR/QQQhBUEEIQYCQCABKAIAIgQEQCABKAIEIQMgBEECdCEEAkAgAkUEQCADIAQQ3wRBBCEDDAELIAMgBEEEIAJBAnQiBRDOBCIDRQ0CCyABIAI2AgAgASADNgIEC0GBgICAeCEGCyAAIAU2AgQgACAGNgIAC3QBA38CQCABKAIIIgJBAEgNACABKAIEIQQCQCACRQRAQQEhAQwBC0HRzsUALQAAGkEBIQMgAkEBENYEIgFFDQELIAIEQCABIAQgAvwKAAALIAAgAjYCCCAAIAE2AgQgACACNgIADwsgAyACQbiuxQAQyAQAC2UBAn8jAEEQayICJAAgACgCCCEDIAAoAgQhACACQQRqIAEQqgQgAwRAA0AgAiAANgIMIAJBBGogAkEMakHYlcEAEI4DIABBAWohACADQQFrIgMNAAsLIAJBBGoQoQQgAkEQaiQAC2ABAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECyAAKAIMIgEEQCAAKAIQIAFBAnQQ3wQLIAAoAhgiAQRAIAAoAhwgAUECdBDfBAsgACgCJCIBBEAgACgCKCABQQJ0EN8ECwtmAQR/IAAoAgQhAiAAKAIIIgMEQCACIQEDQCABKAIAIgRBgICAgHhGIARFckUEQCABQQRqKAIAIARBAnQQ3wQLIAFBDGohASADQQFrIgMNAAsLIAAoAgAiAARAIAIgAEEMbBDfBAsLaQIBfwF+IAEoAggiAkUEQCAAQgA3AwAPCyABKAIEIQEgAkECdCECAkADQCABKAIADQEgA0IgfSEDIAFBBGohASACQQRrIgINAAsgAEIANwMADwsgACABKAIAaK0gA303AwggAEIBNwMAC2oCAX8BfiMAQTBrIgMkACADIAE2AgQgAyAANgIAIANBAjYCDCADQYi2xQA2AgggA0ICNwIUIANCgICAgOABIgQgA62ENwMoIAMgBCADQQRqrYQ3AyAgAyADQSBqNgIQIANBCGogAhCoBAALWgEEfyAAKAIEIQIgACgCCCIDBEAgAiEBA0AgASgCACIEBEAgAUEEaigCACAEQQJ0EN8ECyABQQxqIQEgA0EBayIDDQALCyAAKAIAIgAEQCACIABBDGwQ3wQLC2kAIwBBMGsiACQAQdDOxQAtAABFBEAgAEEwaiQADwsgAEECNgIMIABBhKrFADYCCCAAQgE3AhQgACABNgIsIAAgAEEsaq1CgICAgOABhDcDICAAIABBIGo2AhAgAEEIakGsqsUAEKgEAAtpAQF/IwBBEGsiAiQAAn8CQAJAAkAgACgCAEEBaw4CAQIACyABQfyEwABBDhDQBAwCCyACIABBCGo2AgwgAUGchcAAQRAgAkEMakGMhcAAEI0DDAELIAFBrIXAAEEMENAECyACQRBqJAALaQEBfyMAQRBrIgIkAAJ/AkACQAJAIAAoAgBBAWsOAgECAAsgAUHZosAAQQ4Q0AQMAgsgAiAAQQhqNgIMIAFB+KLAAEEQIAJBDGpB6KLAABCNAwwBCyABQYijwABBDBDQBAsgAkEQaiQAC1IBBH8jAEEQayIBJAAgAUEEaiAAENQDIAEoAggiAiABKAIMEM0EIAEoAgQiBARAIAIgBBDfBAsgACgCACICBEAgACgCBCACEN8ECyABQRBqJAALaQEBfyMAQRBrIgIkAAJ/AkACQAJAIAAoAgBBAWsOAgECAAsgAUG2gcEAQQ4Q0AQMAgsgAiAAQQhqNgIMIAFBkILBAEEQIAJBDGpBgILBABCNAwwBCyABQaCCwQBBDBDQBAsgAkEQaiQAC2kBAX8jAEEQayICJAACfwJAAkACQCAAKAIAQQFrDgIBAgALIAFBjPXBAEEOENAEDAILIAIgAEEIajYCDCABQaz1wQBBECACQQxqQZz1wQAQjQMMAQsgAUG89cEAQQwQ0AQLIAJBEGokAAtpAQF/IwBBEGsiAiQAAn8CQAJAAkAgACgCAEEBaw4CAQIACyABQYyawgBBDhDQBAwCCyACIABBCGo2AgwgAUGsmsIAQRAgAkEMakGcmsIAEI0DDAELIAFBvJrCAEEMENAECyACQRBqJAALaQEBfyMAQRBrIgIkAAJ/AkACQAJAIAAoAgBBAWsOAgECAAsgAUG8tsIAQQ4Q0AQMAgsgAiAAQQhqNgIMIAFB3LbCAEEQIAJBDGpBzLbCABCNAwwBCyABQey2wgBBDBDQBAsgAkEQaiQAC2kBAX8jAEEQayICJAACfwJAAkACQCAAKAIAQQFrDgIBAgALIAFBqMXCAEEOENAEDAILIAIgAEEIajYCDCABQcjFwgBBECACQQxqQbjFwgAQjQMMAQsgAUHYxcIAQQwQ0AQLIAJBEGokAAtpAQF/IwBBEGsiAiQAAn8CQAJAAkAgACgCAEEBaw4CAQIACyABQYSpxABBDhDQBAwCCyACIABBCGo2AgwgAUGkqcQAQRAgAkEMakGUqcQAEI0DDAELIAFBtKnEAEEMENAECyACQRBqJAALLQEBfyAAIAAoAgAgACgCCCIBa0EASQR/IAAgAUEAEIkDIAAoAggFIAELNgIIC2kBAX8jAEEQayICJAACfwJAAkACQCAAKAIAQQFrDgIBAgALIAFB6JvFAEEOENAEDAILIAIgAEEIajYCDCABQYicxQBBECACQQxqQfibxQAQjQMMAQsgAUGYnMUAQQwQ0AQLIAJBEGokAAtpAQF/IwBBEGsiAiQAAn8CQAJAAkAgACgCAEEBaw4CAQIACyABQeikxQBBDhDQBAwCCyACIABBCGo2AgwgAUGIpcUAQRAgAkEMakH4pMUAEI0DDAELIAFBmKXFAEEMENAECyACQRBqJAALWwEBfyMAQTBrIgMkACADIAE2AgwgAyAANgIIIANBATYCFCADQaC1xQA2AhAgA0IBNwIcIAMgA0EIaq1CgICAgMAShDcDKCADIANBKGo2AhggA0EQaiACEKgEAAtgACABRQRAIABBCGpBtLzEACgCADYCACAAQay8xAApAgA3AgAPC0HRzsUALQAAGkEEQQQQ1gQiAQRAIABBATYCCCAAIAE2AgQgAEEBNgIAIAFBATYCAA8LQQRBBBD/BAALWAEBfyMAQRBrIgQkACAEIAIgAxDNBCICNgIMIAQgASAEQQxqEIAEIAQoAgQhASAEKAIAIQMgAkGEAU8EQCACEKsDCyAAIAE2AgQgACADNgIAIARBEGokAAtWAQF/IwBBEGsiAiQAAn8gACgCACIAKAIAQYCAgIB4RwRAIAIgADYCDCABQfiEwABBBCACQQxqQeiEwAAQjQMMAQsgAUHkhMAAQQQQ0AQLIAJBEGokAAtMAQF/IAAoAgAgACgCCCIDayACSQRAIAAgAyACQQFBARCIAyAAKAIIIQMLIAIEQCAAKAIEIANqIAEgAvwKAAALIAAgAiADajYCCEEAC4kCAQR/IwBBEGsiAyQAIAMgAEHgAGo2AgwjAEEQayICJAAgASgCAEGo8cAAQQcgASgCBCgCDBEDACEEIAJBADoADSACIAQ6AAwgAiABNgIIIAJBCGpBhfDAAEEBIABBiPHAABCCA0GG8MAAQQEgAEEwakGI8cAAEIIDQa/xwABBCSADQQxqQZjxwAAQggMhASACLQANIgQgAi0ADCIFciEAAkAgBUEBcSAEQQFHcg0AIAEoAgAiAC0ACkGAAXFFBEAgACgCAEHzt8UAQQIgACgCBCgCDBEDACEADAELIAAoAgBB8rfFAEEBIAAoAgQoAgwRAwAhAAsgAkEQaiQAIABBAXEgA0EQaiQAC8ABACAAQvP/s4CAgMCTqn83A1ggAEKKgNDhr4aA5tMANwNQIABC/4Cq2Kav+sfHADcDSCAAQtfJ6LXu19/psX83A0AgAEKv1uL7u+fc5I5/NwM4IABC/ryP7JOqkesJNwMwIABC8/+zgICAwJOqfzcDKCAAQoqA0OGvhoDm0wA3AyAgAEL/gKrYpq/6x8cANwMYIABC18note7X3+mxfzcDECAAQq/W4vu759zkjn83AwggAEL+vI/sk6qR6wk3AwALSAEBfyAAKAIAIAAoAggiA2sgAkkEQCAAIAMgAhCLAyAAKAIIIQMLIAIEQCAAKAIEIANqIAEgAvwKAAALIAAgAiADajYCCEEAC1ABAX8jAEEwayIAJAAgAEEBNgIMIABB2KnFADYCCCAAQgE3AhQgACAAQS9qrUKAgICA0A+ENwMgIAAgAEEgajYCECAAQQhqQbCXwgAQqAQAC0MBA38CQCACRQ0AA0AgAC0AACIEIAEtAAAiBUYEQCAAQQFqIQAgAUEBaiEBIAJBAWsiAg0BDAILCyAEIAVrIQMLIAMLQgECfyAAKAIIIgEEQCAAKAIEIQADQCAAKAIAIgIEQCAAQQRqKAIAIAJBBXQQ3wQLIABBDGohACABQQFrIgENAAsLC0IBAn8gACgCCCIBBEAgACgCBCEAA0AgACgCACICBEAgAEEEaigCACACQQJ0EN8ECyAAQQxqIQAgAUEBayIBDQALCwt7ACAAQvf/tYjk+ZGDdjcDGCAAQpGg75jd6dueLzcDECAAQtGNg8rj78yhKTcDCCAAQtewjr+KnebKHTcDACAAQeilxQApAwA3AyAgAEEoakHwpcUAKQMANwMAIABBMGpB+KXFACkDADcDACAAQThqQYCmxQApAwA3AwALOgEBfyMAQSBrIgAkACAAQQA2AhggAEEBNgIMIABBsKvFADYCCCAAQgQ3AhAgAEEIakHkq8UAEKgEAAtIAQF/IAAoAgAgACgCCCIDayACSQRAIAAgAyACEKADIAAoAgghAwsgAgRAIAAoAgQgA2ogASAC/AoAAAsgACACIANqNgIIQQALSQEBf0HRzsUALQAAGkHgAEEIENYEIgIEQCACIAFB4AD8CgAAIABBAjYCCCAAIAI2AgQgAEECNgIADwtBCEHgAEGwncUAEMgEAAtPAQJ/IAAoAgQhAiAAKAIAIQMCQCAAKAIIIgAtAABFDQAgA0Hkt8UAQQQgAigCDBEDAEUNAEEBDwsgACABQQpGOgAAIAMgASACKAIQEQIAC04BAX8jAEEQayICJAAgAiAAKAIAIgBBDGo2AgwgAUG0msAAQQ5BwprAAEEBIABBpJrAAEHDmsAAQQEgAkEMakHohMAAEKoDIAJBEGokAAtOAQF/IwBBEGsiAiQAIAIgACgCACIAQQxqNgIMIAFBhMvCAEEKQY7LwgBBDCAAQaDLwgBBmsvCAEEGIAJBDGpB9MrCABCqAyACQRBqJAALTgEBfyMAQRBrIgIkACACIAAoAgAiAEEMajYCDCABQYTLwgBBCkGOy8IAQQwgAEGwy8IAQZrLwgBBBiACQQxqQfTKwgAQqgMgAkEQaiQAC0IBAX8gASgCBCICIAEoAghPBH9BAAUgASACQQFqNgIEIAEoAgAoAgAgAhDKBCEBQQELIQIgACABNgIEIAAgAjYCAAtPAQJ/QdHOxQAtAAAaIAEoAgQhAiABKAIAIQNBCEEEENYEIgFFBEBBBEEIEP8EAAsgASACNgIEIAEgAzYCACAAQcyqxQA2AgQgACABNgIAC0IBAX8jAEEgayIDJAAgA0EANgIQIANBATYCBCADQgQ3AgggAyABNgIcIAMgADYCGCADIANBGGo2AgAgAyACEKgEAAs2AQJ/AkAgACgCBCIBRQ0AIAEgAUEMbEETakF4cSICakEJaiIBRQ0AIAAoAgAgAmsgARDfBAsLVwIBbwF/IAEoAgAlASACKAIAJQEQCSEDEK0DIgEgAyYBQdjOxQAoAgAhAkHUzsUAKAIAIQRB1M7FAEIANwIAIAAgAiABIARBAUYiARs2AgQgACABNgIAC7M4Ahh/BH4jAEEQayIVJAAQrQMiCSAAJgEQrQMiCCABJgEQrQMiFCADJgEQrQMiEyAEJgEQrQMiCiAFJgEjAEEQayIXJAAgF0EEaiEQIAIhCyAGQQBHIRojAEHgAGsiDCQAIAxBDGogCRDsAiAMKAIQIQ0CQAJAAkACQAJAAkAgDCgCDCIJQYCAgIB4RgRAIBBBgICAgHg2AgAgECANNgIEQQEhBkEBIQcMAQsgDCgCFCEbIAxBDGogCBDsAiAMKAIQIQ4CQCAMKAIMIg9BgICAgHhGBEAgEEGAgICAeDYCACAQIA42AgRBASECQQEhBkEBIQcMAQsCQAJAAkAgC0GAAk8EQEH48cAAQR0QzQQhAiAQQYCAgIB4NgIAIBAgAjYCBAwBCyAMKAIUIRwgDEEMaiAUEOwCIAwoAhAhESAMKAIMIhZBgICAgHhHDQEgEEGAgICAeDYCACAQIBE2AgQLQQEhBkEBIQIMAQsgDCgCFCEdIAxBDGogExDsAiAMKAIQIQYCQCAMKAIMIgJBgICAgHhGBEAgEEGAgICAeDYCACAQIAY2AgQMAQsgDCgCFCEeIAxBDGoiEiAKEOwCIAwoAhAhGSAMKAIMIh9BgICAgHhHBEAgDCAMKAIUNgIIIAwgGTYCBCAMIB82AgAgDCAbNgIkIAwgDTYCICAMIAk2AhwgDCAcNgIwIAwgDjYCLCAMIA82AiggDCAdNgI8IAwgETYCOCAMIBY2AjQgDCAeNgJYIAwgBjYCVCAMIAI2AlAgDEEoaiECIAxBNGohEyAMQdAAaiEUIwBB0AdrIggkACAIQQA2AgwgCEKAgICAwAA3AgQgGgRAIAhBQGsiBiATEK0BIAhB4AZqIAYQ1AEgCCgCBCAIKAIMIgprQQNNBEAgCEEEaiAKQQRBBEEMEIgDIAgoAgwhCgsgCCgCCCAKQQxsaiIGIAgpAuAGNwIAIAZBCGogCEHoBmoiCSkCADcCACAGQRBqIAhB8AZqIg0pAgA3AgAgBkEYaiAIQfgGaiIOKQIANwIAIAZBIGogCEGAB2oiDykCADcCACAGQShqIAhBiAdqIhEpAgA3AgAgCCAKQQRqNgIMIAhBQGsiBiAUEK0BIAhB4AZqIAYQ1AEgCCgCBCAIKAIMIgprQQNNBEAgCEEEaiAKQQRBBEEMEIgDIAgoAgwhCgsgCCgCCCAKQQxsaiIGIAgpAuAGNwIAIAZBCGogCSkCADcCACAGQRBqIA0pAgA3AgAgBkEYaiAOKQIANwIAIAZBIGogDykCADcCACAGQShqIBEpAgA3AgAgCCAKQQRqNgIMCyAIQUBrIgogDEEcaiIGEK0BIAhB4AZqIAoQ1AEgCCgCBCAIKAIMIgprQQNNBEAgCEEEaiAKQQRBBEEMEIgDIAgoAgwhCgsgCCgCCCAKQQxsaiIJIAgpAuAGNwIAIAlBCGogCEHoBmoiDSkCADcCACAJQRBqIAhB8AZqKQIANwIAIAlBGGogCEH4BmopAgA3AgAgCUEgaiAIQYAHaikCADcCACAJQShqIAhBiAdqKQIANwIAIAggCkEEajYCDCAIQUBrIAIQ4gEgCCkDWCEhIAgpA1AhIiAIKQNIISAgCCkDQCEjQQAhCiAIQaAHaiIOQeD2wAAoAgA2AgAgCEHY9sAAKQIANwOYByAgICOEUEUEQEEBIQkDQCAIKAKYByAJQQFrRgRAIAhBmAdqQdz3wAAQpQMLIAgoApwHIApqICM+AgAgI0L/////D1YgIEIAUiAgUCAgQiCGICNCIIiEISMgCkEEaiEKICBCIIghICAIIAk2AqAHIAlBAWohCRsNAAsLIAhBuAdqIA4oAgAiCjYCACANIAo2AgAgCCAIKQOYByIgNwOwByAIICA3A+AGQQAhCiAIQcgHakHg9sAAKAIANgIAIAhB2PbAACkCADcDwAcgISAihFBFBEBBASEJA0AgCCgCwAcgCUEBa0YEQCAIQcAHakHc98AAEKUDCyAIKALEByAKaiAiPgIAICJC/////w9WICFCAFIgIVAgIUIghiAiQiCIhCEiIApBBGohCiAhQiCIISEgCCAJNgLIByAJQQFqIQkbDQALCyAIQfQGaiAIQcgHaigCADYCACAIIAgpA8AHNwLsBiAIQaAHaiINIAhB6AZqKQMANwMAIAhBqAdqIg4gCEHwBmopAwA3AwAgCCAIKQPgBjcDmAcgCCgCBCAIKAIMIglrQQFNBEAgCEEEaiAJQQJBBEEMEIgDIAgoAgwhCQsgCCgCCCAJQQxsaiIKIAgpA5gHNwIAIApBCGogDSkDADcCACAKQRBqIA4pAwA3AgAgCCAJQQJqIgk2AgwgCEHIAGpBjKHEACgCADYCACAIQYShxAApAgA3A0AgC0H/AXEiCwRAIAhBQGtB6KLEABClAyAIKAJEIAs2AgAgCEEBNgJIIAgoAgwhCQsgCEEYaiILIAhByABqKAIANgIAIAggCCkDQDcDECAIKAIEIAlGBEAgCEEEakHcq8QAEJ8DCyAIKAIIIAlBDGxqIgogCCkDEDcCACAKQQhqIAsoAgA2AgAgCCAJQQFqNgIMIAhBQGsgDBDiASAIKQNYISEgCCkDUCEiIAgpA0ghICAIKQNAISNBACEKIAhBoAdqQeD2wAAoAgA2AgAgCEHY9sAAKQIANwOYByAgICOEUEUEQEEBIQkDQCAIKAKYByAJQQFrRgRAIAhBmAdqQdz3wAAQpQMLIAgoApwHIApqICM+AgAgI0L/////D1YgIEIAUiAgUCAgQiCGICNCIIiEISMgCkEEaiEKICBCIIghICAIIAk2AqAHIAlBAWohCRsNAAsLIAhBuAdqIAhBoAdqIgsoAgAiCjYCACAIQegGaiINIAo2AgAgCCAIKQOYByIgNwOwByAIICA3A+AGQQAhCiAIQcgHaiIOQeD2wAAoAgA2AgAgCEHY9sAAKQIANwPAByAhICKEUEUEQEEBIQkDQCAIKALAByAJQQFrRgRAIAhBwAdqQdz3wAAQpQMLIAgoAsQHIApqICI+AgAgIkL/////D1YgIUIAUiAhUCAhQiCGICJCIIiEISIgCkEEaiEKICFCIIghISAIIAk2AsgHIAlBAWohCRsNAAsLIAhB9AZqIA4oAgA2AgAgCCAIKQPABzcC7AYgCyANKQMANwMAIAhBqAdqIgogCEHwBmopAwA3AwAgCCAIKQPgBjcDmAcgCCgCBCAIKAIMIglrQQFNBEAgCEEEaiAJQQJBBEEMEIgDIAgoAgwhCQsgCCgCCCAJQQxsaiILIAgpA5gHNwIAIAtBCGogCEGgB2opAwA3AgAgC0EQaiAKKQMANwIAIAggCUECajYCDCAIIAc2AsAHQQAhCgJAAkACQAJAAkACQAJAAkACQAJAAkAgBw4GBgABAgMEBQtBASEKDAULQQIhCgwEC0EDIQoMAwtBBCEKDAILQQUhCiAIQQU6AOQGDAELIAhBATYCRCAIQciawQA2AkAgCEIBNwJMIAggCEHAB2qtQoCAgIDgAYQ3A5gHIAggCEGYB2o2AkggCEHgBmogCEFAaxDSAiAILQDkBiEKIAgoAuAGIgdBgICAgHhGDQAgEiAIKADlBjYACSASQQxqIAhB6AZqKAAANgAAIBIgCjoACCASIAc2AgQgEkEBNgIAIAgoAgwiCgRAIAgoAgghCQNAIAkoAgAiBwRAIAlBBGooAgAgB0ECdBDfBAsgCUEMaiEJIApBAWsiCg0ACwsgCCgCBCIHBEAgCCgCCCAHQQxsEN8ECyAMKAIAIgcEQCAMKAIEIAdBAnQQ3wQLIBQoAgAiBwRAIBQoAgQgB0ECdBDfBAsgEygCACIHBEAgEygCBCAHQQJ0EN8ECyACKAIAIgdFBEAgBiECDAILIAIoAgQgB0ECdBDfBCAGIQIMAQsgCEEcaiAKEIECIAgoAiQiCUECdCELQQAhBwJAAkACQAJAIAlB/////wNLIAtB/P///wdLcg0AIAgoAiAhDgJ/IAtFBEBBBCENQQAMAQtB0c7FAC0AABpBBCEHIAtBBBDWBCINRQ0BIAkLIQcgCwRAIA0gDiAL/AoAAAsgCCAJNgKgByAIIA02ApwHIAggBzYCmAcgCEHIAGpBjKHEACgCADYCACAIQYShxAApAgA3A0AgCEFAayIHQeiixAAQpQMgCCgCREECNgIAIAhB6AZqQQE2AgAgCCAIKQNANwPgBiAHIAhBmAdqIAhB4AZqEIcCIAgoAuAGIgcEQCAIKALkBiAHQQJ0EN8ECyAIQbAHaiACIAhBQGsgCEEcahDjBCAIKAJAIgcEQCAIKAJEIAdBAnQQ3wQLIAwoAgQhDiAMKAIAIREgCCgCtAchCSAMKAIIIgdBACAIKAK4ByILGw0BIAhB6AZqQYyhxAAoAgA2AgAgCEGEocQAKQIANwPgBgwCCyAHIAtB+IHAABDIBAALIAtBAUYEQCAJKAIAIQcgCEHIAGoiDSAMQQhqKAIANgIAIAggDCkCADcDQCAIQUBrIAcQswIgCEHoBmogDSgCADYCACAIIAgpA0A3A+AGDAILIAdBAUYEQEEAIQcgC0H/////A0sgC0ECdCINQfz///8HS3INBCAOKAIAIRYCfyANRQRAQQQhD0EADAELQdHOxQAtAAAaQQQhByANQQQQ1gQiD0UNBSALCyEHIA0EQCAPIAkgDfwKAAALIAhByABqIg0gCzYCACAIIA82AkQgCCAHNgJAIAhBQGsgFhCzAiAIQegGaiANKAIANgIAIAggCCkCQDcD4AYMAQsgCEHgBmogDiAHIAkgCxDtAgsgEUUNACAOIBFBAnQQ3wQLIAhBKGogCEHgBmogCEEcahCKAiAIKALgBiIHBEAgCCgC5AYgB0ECdBDfBAsgBigCBCENIAYoAgAhDwJAAkACQCALBEAgBigCCCIHDQELIAhB6AZqQYyhxAAoAgA2AgAgCEGEocQAKQIANwPgBgwBCyALQQFGBEAgCSgCACEHIAhByABqIgsgBkEIaigCADYCACAIIAYpAgA3A0AgCEFAayAHELMCIAhB6AZqIAsoAgA2AgAgCCAIKQNANwPgBgwCCyAHQQFGBEBBACEHIAtB/////wNLIAtBAnQiBkH8////B0tyDQUgDSgCACERAn8gBkUEQEEEIQ5BAAwBC0HRzsUALQAAGkEEIQcgBkEEENYEIg5FDQYgCwshByAGBEAgDiAJIAb8CgAACyAIQcgAaiIGIAs2AgAgCCAONgJEIAggBzYCQCAIQUBrIBEQswIgCEHoBmogBigCADYCACAIIAgpAkA3A+AGDAELIAhB4AZqIA0gByAJIAsQ7QILIA9FDQAgDSAPQQJ0EN8ECyAIQTRqIAhB4AZqIAhBHGoQigIgCCgC4AYiBgRAIAgoAuQGIAZBAnQQ3wQLAkACQAJAAkACQAJAAkAgCkH/AXEiB0EBaw4FAQIDBAUACyAIQUBrECEgCEHAB2ogCEHAAWoQ2gIgCCgC7AQiBgRAIAgoAvAEIAZBAnQQ3wQLAkAgCCgCpAIiBkUNACAGIAZBDGxBE2pBeHEiC2pBCWoiBkUNACAIKAKgAiALayAGEN8ECyAIKALQAiIGQYCAgIB4RiAGRXJFBEAgCCgC1AIgBkECdBDfBAsgCEFAaxAhIAhBmAdqIAhB4AFqENoCIAgoAuwEIgYEQCAIKALwBCAGQQJ0EN8ECwJAIAgoAqQCIgZFDQAgBiAGQQxsQRNqQXhxIgtqQQlqIgZFDQAgCCgCoAIgC2sgBhDfBAsgCCgC0AIiBkGAgICAeEYgBkVyDQUgCCgC1AIgBkECdBDfBAwFCyAIQUBrECYgCEHAB2ogCEGgAmoQ2AIgCCgCzAYiBgRAIAgoAtAGIAZBAnQQ3wQLAkAgCCgCRCIGRQ0AIAYgBkEMbEETakF4cSILakEJaiIGRQ0AIAgoAkAgC2sgBhDfBAsgCCgCwAMiBkGAgICAeEYgBkVyRQRAIAgoAsQDIAZBAnQQ3wQLIAhBQGsQJiAIQZgHaiAIQdACahDYAiAIKALMBiIGBEAgCCgC0AYgBkECdBDfBAsCQCAIKAJEIgZFDQAgBiAGQQxsQRNqQXhxIgtqQQlqIgZFDQAgCCgCQCALayAGEN8ECyAIKALAAyIGQYCAgIB4RiAGRXINBCAIKALEAyAGQQJ0EN8EDAQLIAhBQGsQVSAIQcAHaiAIQcABahDXAiAIKALsBCIGBEAgCCgC8AQgBkECdBDfBAsCQCAIKAKkAiIGRQ0AIAYgBkEMbEETakF4cSILakEJaiIGRQ0AIAgoAqACIAtrIAYQ3wQLIAgoAtACIgZBgICAgHhGIAZFckUEQCAIKALUAiAGQQJ0EN8ECyAIQUBrEFUgCEGYB2ogCEHgAWoQ1wIgCCgC7AQiBgRAIAgoAvAEIAZBAnQQ3wQLAkAgCCgCpAIiBkUNACAGIAZBDGxBE2pBeHEiC2pBCWoiBkUNACAIKAKgAiALayAGEN8ECyAIKALQAiIGQYCAgIB4RiAGRXINAyAIKALUAiAGQQJ0EN8EDAMLIAhBQGsQPiAIQcAHaiAIQcABahDbAiAIKALsBCIGBEAgCCgC8AQgBkECdBDfBAsCQCAIKAKkAiIGRQ0AIAYgBkEMbEETakF4cSILakEJaiIGRQ0AIAgoAqACIAtrIAYQ3wQLIAgoAtACIgZBgICAgHhGIAZFckUEQCAIKALUAiAGQQJ0EN8ECyAIQUBrED4gCEGYB2ogCEHgAWoQ2wIgCCgC7AQiBgRAIAgoAvAEIAZBAnQQ3wQLAkAgCCgCpAIiBkUNACAGIAZBDGxBE2pBeHEiC2pBCWoiBkUNACAIKAKgAiALayAGEN8ECyAIKALQAiIGQYCAgIB4RiAGRXINAiAIKALUAiAGQQJ0EN8EDAILIAhBQGsQSSAIQcAHaiAIQcABahDZAiAIKALsBCIGBEAgCCgC8AQgBkECdBDfBAsCQCAIKAKkAiIGRQ0AIAYgBkEMbEETakF4cSILakEJaiIGRQ0AIAgoAqACIAtrIAYQ3wQLIAgoAtACIgZBgICAgHhGIAZFckUEQCAIKALUAiAGQQJ0EN8ECyAIQUBrEEkgCEGYB2ogCEHgAWoQ2QIgCCgC7AQiBgRAIAgoAvAEIAZBAnQQ3wQLAkAgCCgCpAIiBkUNACAGIAZBDGxBE2pBeHEiC2pBCWoiBkUNACAIKAKgAiALayAGEN8ECyAIKALQAiIGQYCAgIB4RiAGRXINASAIKALUAiAGQQJ0EN8EDAELIAhBQGsQOiAIQcAHaiAIQcABahDcAiAIKALsBCIGBEAgCCgC8AQgBkECdBDfBAsCQCAIKAKkAiIGRQ0AIAYgBkEMbEETakF4cSILakEJaiIGRQ0AIAgoAqACIAtrIAYQ3wQLIAgoAtACIgZBgICAgHhGIAZFckUEQCAIKALUAiAGQQJ0EN8ECyAIQUBrEDogCEGYB2ogCEHgAWoQ3AIgCCgC7AQiBgRAIAgoAvAEIAZBAnQQ3wQLAkAgCCgCpAIiBkUNACAGIAZBDGxBE2pBeHEiC2pBCWoiBkUNACAIKAKgAiALayAGEN8ECyAIKALQAiIGQYCAgIB4RiAGRXINACAIKALUAiAGQQJ0EN8ECyAIQYAHaiATQQhqKAIANgIAIAhBjAdqIBRBCGooAgA2AgAgCEHoBmogCEHIB2ooAgA2AgAgCEH0BmogCEGgB2ooAgA2AgAgCCAIKQLABzcD4AYgCCAIKQKYBzcC7AYgCCATKQIANwP4BiAIIBQpAgA3AoQHIAhByABqIAhBMGooAgA2AgAgCCAIKQIoNwNAIAhB1ABqIAhBPGooAgA2AgAgCCAIKQI0NwJMIAhBmAdqIAhB4AZqQQQgCEFAa0ECIAdBAEEBEBwgCCgCpAchBiAIKAKgByELIAgoApwHIQogCCgCmAdBAUYEQCASIAY2AgwgEiALNgIIIBIgCjYCBCASQQE2AgAgCCgCQCIGBEAgCCgCRCAGQQJ0EN8ECyAIKAJMIgYEQCAIKAJQIAZBAnQQ3wQLIAgoAuAGIgYEQCAIKALkBiAGQQJ0EN8ECyAIKALsBiIGBEAgCCgC8AYgBkECdBDfBAsgCCgC+AYiBgRAIAgoAvwGIAZBAnQQ3wQLIAgoAoQHIgYEQCAIKAKIByAGQQJ0EN8ECyAIKAKwByIGBEAgCSAGQQJ0EN8ECyAIKAIcIgYEQCAIKAIgIAZBAnQQ3wQLIAgoAgwiCgRAIAgoAgghCQNAIAkoAgAiBgRAIAlBBGooAgAgBkECdBDfBAsgCUEMaiEJIApBAWsiCg0ACwsgCCgCBCIGRQ0BIAgoAgggBkEMbBDfBAwBCyAIKAJAIgcEQCAIKAJEIAdBAnQQ3wQLIAgoAkwiBwRAIAgoAlAgB0ECdBDfBAsgCCgC4AYiBwRAIAgoAuQGIAdBAnQQ3wQLIAgoAuwGIgcEQCAIKALwBiAHQQJ0EN8ECyAIKAL4BiIHBEAgCCgC/AYgB0ECdBDfBAsgCCgChAciBwRAIAgoAogHIAdBAnQQ3wQLIAgoAgQgCCgCDCIHayAGSQRAIAhBBGogByAGQQRBDBCIAyAIKAIMIQcLIAZBDGwiEwRAIAgoAgggB0EMbGogCyAT/AoAAAsgCCAGIAdqNgIMIAoEQCALIApBDGwQ3wQLIBIgCCkCBDcCBCASQQA2AgAgEkEMaiAIQQxqKAIANgIAIAgoArAHIgYEQCAJIAZBAnQQ3wQLIAgoAhwiBkUNACAIKAIgIAZBAnQQ3wQLIAIoAgAiBgRAIAIoAgQgBkECdBDfBAsgCEHQB2okAAwCCyAHIA1B+IHAABDIBAALIAcgBkH4gcAAEMgEAAsCQCAMKAIMQQFGBEAgDEHYAGogDEEQaiICQQhqKAIANgIAIAwgAikCADcDUCAUEN4DIQIMAQsgDCgCFCECIAwoAhAiBkGAgICAeEYNACAMKAIYIQcgDCAGNgJIIAwgAjYCRCAMIAI2AkAgDCACIAdBDGxqNgJMIBAgDEFAaxCPAwwKCyAQQYCAgIB4NgIAIBAgAjYCBAwJCyAQQYCAgIB4NgIAIBAgGTYCBCACRQ0AIAYgAkECdBDfBAsgAkGAgICAeEYhAkEAIQYgFkUNACARIBZBAnQQ3wQLIAtB/wFLIQcgD0UNACAOIA9BAnQQ3wQLIAkEQCANIAlBAnQQ3wQLIAINACAGDQEMAgsgCkGEAU8EQCAKEKsDCyAGRQ0BCyATQYQBTwRAIBMQqwMLIAdFDQIMAQsgBw0ADAELIBRBhAFPBEAgFBCrAwsLIAlBgICAgHhHIAhBhAFJcg0AIAgQqwMLIAxB4ABqJAACQAJAAn8gFygCBCIHQYCAgIB4RgRAQQEhBkEAIQIgFygCCAwBCyAXKAIIIQYCQCAXKAIMIgIgB08EQCAGIRgMAQsgB0ECdCEHIAJFBEBBBCEYIAYgBxDfBAwBCyAGIAdBBCACQQJ0IgYQzgQiGEUNAgtBACEGQQALIQcgFSAGNgIMIBUgBzYCCCAVIAI2AgQgFSAYNgIAIBdBEGokAAwBC0EEIAZB6PHAABDIBAALIBUoAgAgFSgCBCAVKAIIIBUoAgwgFUEQaiQACzIBAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECyAAKAIMIgEEQCAAKAIQIAFBAnQQ3wQLC5IEAgV/A34gACgCACEAIAEoAggiA0GAgIAQcUUEQCADQYCAgCBxRQRAIAApAwAhCSMAQSBrIgMkAEEUIQAgCSIHQugHWgRAIAchCANAIANBDGogAGoiAkEDayAIIAhCkM4AgCIHQpDOAH59pyIEQf//A3FB5ABuIgVBAXQiBkH+t8UAai0AADoAACACQQRrIAZB/bfFAGotAAA6AAAgAkEBayAEIAVB5ABsa0H//wNxQQF0IgRB/rfFAGotAAA6AAAgAkECayAEQf23xQBqLQAAOgAAIABBBGshACAIQv+s4gRWIAchCA0ACwsgB0IJVgRAIAAgA2pBC2ogB6ciAiACQf//A3FB5ABuIgJB5ABsa0H//wNxQQF0IgRB/rfFAGotAAA6AAAgAEECayIAIANBDGpqIARB/bfFAGotAAA6AAAgAq0hBwsgCVBFIAdQcUUEQCAAQQFrIgAgA0EMamogB6dBAXRBHnFB/rfFAGotAAA6AAALIAFBAUEBQQAgA0EMaiAAakEUIABrEIkCIANBIGokAA8LIwBBgAFrIgMkACAAKQMAIQdBACEAA0AgACADakH/AGogB6dBD3EiAkEwciACQTdqIAJBCkkbOgAAIABBAWshACAHQg9WIAdCBIghBw0ACyABQQFB+7fFAEECIAAgA2pBgAFqQQAgAGsQiQIgA0GAAWokAA8LIAAgARDDAwvKAgEDfyAAKAIAIQIgASgCCCIAQYCAgBBxRQRAIABBgICAIHFFBEAjAEEQayIAJABBAyEDIAItAAAiAiEEIAJBCk8EQCAAIAIgAkHkAG4iBEHkAGxrQf8BcUEBdCIDQf63xQBqLQAAOgAPIAAgA0H9t8UAai0AADoADkEBIQMLQQAgAiAEG0UEQCADQQFrIgMgAEENamogBEEBdEH+AXFB/rfFAGotAAA6AAALIAFBAUEBQQAgAEENaiADakEDIANrEIkCIABBEGokAA8LIAIgARDCAw8LIwBBgAFrIgQkACACLQAAIQBBACECA0AgAiAEakH/AGogAEEPcSIDQTByIANB1wBqIANBCkkbOgAAIAJBAWshAiAAIgNBBHYhACADQQ9LDQALIAFBAUH7t8UAQQIgAiAEakGAAWpBACACaxCJAiAEQYABaiQACz8BAX8gACgCACEAIAEoAggiAkGAgIAQcUUEQCACQYCAgCBxRQRAIAAgARCsBA8LIAAgARDFAw8LIAAgARDEAwsyAQJ/IwBBQGoiAiQAIAIgARD3AiACQSBqIgMgAUEMahD3AiAAIAIgAxBDIAJBQGskAAs/AQF/IAAoAgAhACABKAIIIgJBgICAEHFFBEAgAkGAgIAgcUUEQCAAIAEQ5wQPCyAAIAEQxQMPCyAAIAEQxAMLqAsBCn8jAEEQayIKJAAjAEEwayIIJAAgCCABNgIUIAggADYCECAIIAE2AgwgCCADNgIgIAggAjYCHCAIIAM2AhggCEEkaiELIAhBGGohDCAFQQBHIQUgBkEARyEDIwBBMGsiByQAIAhBDGoiACgCACEBIAAoAgQhAiAAKAIIIQAgB0EANgIAIAcgAiAAQQJ0ajYCJCAHIAE2AiAgByACNgIcIAcgAjYCGCAHIAc2AiggB0EMaiAHQRhqEJYCAkACQAJAIAcoAgBBAUYEQCAHKAIQIQEgBygCBCECIAcoAhQiCQRAIAEhAANAIAAoAgAiAwRAIABBBGooAgAgA0ECdBDfBAsgAEEMaiEAIAlBAWsiCQ0ACwsgBygCDCIARQ0BIAEgAEEMbBDfBAwBCyAHKAIQIQIgBygCDCIOQYCAgIB4Rw0BCyALQYCAgIB4NgIAIAsgAjYCBCAMKAIEIQEgDCgCCCIJBEAgASEAA0AgACgCACICQYQBTwRAIAIQqwMLIABBBGohACAJQQFrIgkNAAsLIAwoAgAiAEUNASABIABBAnQQ3wQMAQsgBygCFCEJIAwoAgAhASAMKAIEIQYgDCgCCCEAIAdBADYCACAHIAYgAEECdGo2AiQgByABNgIgIAcgBjYCHCAHIAY2AhggByAHNgIoIAdBDGogB0EYahCWAgJAAkACQAJAIAcoAgBBAUYEQCAHKAIQIQQgBygCBCEBIAcoAhQiAwRAIAQhAANAIAAoAgAiBQRAIABBBGooAgAgBUECdBDfBAsgAEEMaiEAIANBAWsiAw0ACwsgBygCDCIARQ0BIAQgAEEMbBDfBAwBCyAHKAIQIQEgBygCDCIPQYCAgIB4Rw0BCyALQYCAgIB4NgIAIAsgATYCBAwBCyAHQRhqIAIgCSABIAcoAhQiACAEIAUgAxAcIAcoAhhBAUcNASAHQQhqIAdBHGoiA0EIaigCADYCACAHIAMpAgA3AwAgB0EMaiAHENQDIAcoAhAiBSAHKAIUEM0EIQQgBygCDCIDBEAgBSADEN8ECyAHKAIAIgMEQCAHKAIEIAMQ3wQLIAtBgICAgHg2AgAgCyAENgIEIAAEQCABIQMDQCADKAIAIgQEQCADQQRqKAIAIARBAnQQ3wQLIANBDGohAyAAQQFrIgANAAsLIA9FDQAgASAPQQxsEN8ECyAJBEAgAiEAA0AgACgCACIBBEAgAEEEaigCACABQQJ0EN8ECyAAQQxqIQAgCUEBayIJDQALCyAORQ0BIAIgDkEMbBDfBAwBCyAHKAIcIQYgBygCICIFIRAgBygCJCIDBEAgA0EMbCEMIAUiBCEDA0AgB0EgaiADQQhqKAIANgIAIAcgAykCADcDGCAEIAdBGGoQuwM2AgAgEEEEaiEQIARBBGohBCADQQxqIQMgDEEMayIMDQALCyALIAU2AgQgCyAGQQNsNgIAIAsgECAFa0ECdjYCCCAABEAgASEDA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgAEEBayIADQALCyAPBEAgASAPQQxsEN8ECyAJBEAgAiEAA0AgACgCACIBBEAgAEEEaigCACABQQJ0EN8ECyAAQQxqIQAgCUEBayIJDQALCyAORQ0AIAIgDkEMbBDfBAsgB0EwaiQAAkACQCAKAn8gCCgCJCIBQYCAgIB4RgRAIAgoAighAUEAIQJBAQwBCyAIKAIoIQACQCAIKAIsIgIgAU8EQCAAIQ0MAQsgAUECdCEBIAJFBEBBBCENIAAgARDfBAwBCyAAIAFBBCACQQJ0IgAQzgQiDUUNAgtBACEBQQALNgIMIAogATYCCCAKIAI2AgQgCiANNgIAIAhBMGokAAwBC0EEIABB6PHAABDIBAALIAooAgAgCigCBCAKKAIIIAooAgwgCkEQaiQAC6UtAhd/BH4jAEEQayITJAAQrQMiByAAJgEQrQMiCiABJgEQrQMiDCACJgEQrQMiEiADJgEQrQMiDSAEJgEjAEEQayIWJAAgFkEEaiEPIAVBAEchGCAGIQsjAEHgAGsiCCQAIAhBDGogBxDsAiAIKAIQIQ4CQAJAAkACQAJAAkAgCCgCDCIFQYCAgIB4RgRAIA9BgICAgHg2AgAgDyAONgIEQQEhBkEBIQsMAQsgCCgCFCEZIAhBDGogChDsAiAIKAIQIRQCQAJAIAgoAgwiB0GAgICAeEYEQCAPQYCAgIB4NgIAIA8gFDYCBEEBIQlBASEGDAELIAgoAhQhGiAIQQxqIAwQ7AIgCCgCECEQAkAgCCgCDCIGQYCAgIB4RgRAIA9BgICAgHg2AgAgDyAQNgIEQQEhCQwBCyAIKAIUIRsgCEEMaiASEOwCIAgoAhAhEQJAIAgoAgwiCUGAgICAeEYEQCAPQYCAgIB4NgIAIA8gETYCBAwBCyAIKAIUIRwgCEEMaiANEOwCIAgoAhAhFSAIKAIMIh1BgICAgHhHDQMgD0GAgICAeDYCACAPIBU2AgQgCUUNACARIAlBAnQQ3wQLIAlBgICAgHhGIQkgBkUNACAQIAZBAnQQ3wQLIAZBgICAgHhGIQYgB0UNACAUIAdBAnQQ3wQLIAUEQCAOIAVBAnQQ3wQLIAdBgICAgHhGIQsgCQ0BIAYNAgwDCyAIIAgoAhQ2AgggCCAVNgIEIAggHTYCACAIIBk2AiQgCCAONgIgIAggBTYCHCAIIBo2AjAgCCAUNgIsIAggBzYCKCAIIBs2AjwgCCAQNgI4IAggBjYCNCAIIBw2AlggCCARNgJUIAggCTYCUCAIQdAAaiESQQAhBUEAIQkjAEHAB2siByQAIAdBADYCFCAHQoCAgIDAADcCDEEEIQYgGARAIAdBMGoiCSASEK0BIAdB0AZqIgwgCRDUASAHQoCAgIDAADcCgAcgB0EMaiINQQBBBEEEQQwQiAMgBygCECIGIAcoAhQiCkEMbGoiBSAHKQLQBjcCACAFQQhqIAdB2AZqIg4pAgA3AgAgBUEQaiAHQeAGaiIUKQIANwIAIAVBGGogB0HoBmoiECkCADcCACAFQSBqIAdB8AZqIhEpAgA3AgAgBUEoaiAHQfgGaiIVKQIANwIAIAcgCkEEaiIKNgIUIAkgCBCtASAMIAkQ1AEgBygCDCIFIAprQQNNBEAgDSAKQQRBBEEMEIgDIAcoAhAhBiAHKAIUIQogBygCDCEFCyAGIApBDGxqIgkgBykC0AY3AgAgCUEoaiAVKQIANwIAIAlBIGogESkCADcCACAJQRhqIBApAgA3AgAgCUEQaiAUKQIANwIAIAlBCGogDikCADcCACAHIApBBGoiCTYCFAsgB0EwaiIKIAhBHGoiFBCtASAHQdAGaiAKENQBIAUgCWtBA00EQCAHQQxqIAlBBEEEQQwQiAMgBygCFCEJIAcoAhAhBgsgBiAJQQxsaiIFIAcpAtAGNwIAIAVBKGogB0H4BmopAgA3AgAgBUEgaiAHQfAGaikCADcCACAFQRhqIAdB6AZqKQIANwIAIAVBEGogB0HgBmopAgA3AgAgBUEIaiAHQdgGaiIMKQIANwIAIAcgCUEEaiIKNgIUIAdBMGogCEEoaiINEOIBIAcpA0ghHyAHKQNAISAgBykDOCEeIAcpAzAhIUEAIQkgB0GQB2oiDkHg9sAAKAIANgIAIAdB2PbAACkCADcDiAcgHiAhhFBFBEBBASEFA0AgBygCiAcgBUEBa0YEQCAHQYgHakHc98AAEKUDCyAHKAKMByAJaiAhPgIAICFC/////w9WIB5CAFIgHlAgHkIghiAhQiCIhCEhIAlBBGohCSAeQiCIIR4gByAFNgKQByAFQQFqIQUbDQALCyAHQagHaiAOKAIAIgU2AgAgDCAFNgIAIAcgBykDiAciHjcDoAcgByAeNwPQBkEAIQkgB0G4B2pB4PbAACgCADYCACAHQdj2wAApAgA3A7AHIB8gIIRQRQRAQQEhBQNAIAcoArAHIAVBAWtGBEAgB0GwB2pB3PfAABClAwsgBygCtAcgCWogID4CACAgQv////8PViAfQgBSIB9QIB9CIIYgIEIgiIQhICAJQQRqIQkgH0IgiCEfIAcgBTYCuAcgBUEBaiEFGw0ACwsgB0HkBmogB0G4B2ooAgA2AgAgByAHKQOwBzcC3AYgB0GQB2oiBSAHQdgGaikDADcDACAHQZgHaiIMIAdB4AZqKQMANwMAIAcgBykD0AY3A4gHIAcoAgwgCmtBAU0EQCAHQQxqIApBAkEEQQwQiAMgBygCFCEKIAcoAhAhBgsgBiAKQQxsaiIJIAcpA4gHNwIAIAlBEGogDCkDADcCACAJQQhqIAUpAwA3AgAgByAKQQJqIgo2AhQgB0EwaiAIQTRqIg4Q4gEgBykDSCEfIAcpA0AhICAHKQM4IR4gBykDMCEhQQAhCSAFQeD2wAAoAgA2AgAgB0HY9sAAKQIANwOIByAeICGEUEUEQEEBIQUDQCAHKAKIByAFQQFrRgRAIAdBiAdqQdz3wAAQpQMLIAcoAowHIAlqICE+AgAgIUL/////D1YgHkIAUiAeUCAeQiCGICFCIIiEISEgCUEEaiEJIB5CIIghHiAHIAU2ApAHIAVBAWohBRsNAAsLIAdBqAdqIAdBkAdqIgwoAgAiBTYCACAHQdgGaiIQIAU2AgAgByAHKQOIByIeNwOgByAHIB43A9AGQQAhCSAHQbgHaiIRQeD2wAAoAgA2AgAgB0HY9sAAKQIANwOwByAfICCEUEUEQEEBIQUDQCAHKAKwByAFQQFrRgRAIAdBsAdqQdz3wAAQpQMLIAcoArQHIAlqICA+AgAgIEL/////D1YgH0IAUiAfUCAfQiCGICBCIIiEISAgCUEEaiEJIB9CIIghHyAHIAU2ArgHIAVBAWohBRsNAAsLIAdB5AZqIBEoAgA2AgAgByAHKQOwBzcC3AYgDCAQKQMANwMAIAdBmAdqIgkgB0HgBmopAwA3AwAgByAHKQPQBjcDiAcgBygCDCAKa0EBTQRAIAdBDGogCkECQQRBDBCIAyAHKAIUIQogBygCECEGCyAIQQxqIQwgBiAKQQxsaiIFIAcpA4gHNwIAIAVBEGogCSkDADcCACAFQQhqIAdBkAdqKQMANwIAIAcgCkECaiIJNgIUIAcgCzYCsAdBACEFAkACQAJAAkACQAJAAkACQCALDgYGAAECAwQFC0EBIQUMBQtBAiEFDAQLQQMhBQwDC0EEIQUMAgtBBSEFIAdBBToA1AYMAQsgB0EBNgI0IAdByJrBADYCMCAHQgE3AjwgByAHQbAHaq1CgICAgOABhDcDiAcgByAHQYgHajYCOCAHQdAGaiAHQTBqENICIActANQGIQUgBygC0AYiC0GAgICAeEYNACAMIAcoANUGNgAJIAxBDGogB0HYBmooAAA2AAAgDCAFOgAIIAwgCzYCBCAMQQE2AgAgCQRAIAYhBQNAIAUoAgAiCwRAIAVBBGooAgAgC0ECdBDfBAsgBUEMaiEFIAlBAWsiCQ0ACwsgBygCDCIFBEAgBiAFQQxsEN8ECyAIKAIAIgUEQCAIKAIEIAVBAnQQ3wQLIBIoAgAiBQRAIBIoAgQgBUECdBDfBAsgDigCACIFBEAgDigCBCAFQQJ0EN8ECyANKAIAIgVFDQEgDSgCBCAFQQJ0EN8EDAELIAdBGGoiCyAFEIECIAdBOGogDkEIaigCADYCACAHIA4pAgA3AzAgB0EkaiALIAdBMGoQhwIgBygCMCILBEAgBygCNCALQQJ0EN8ECwJAAkACQAJAAkACQAJAIAVB/wFxIgtBAWsOBQECAwQFAAsgB0EwahAhIAdBsAdqIAdBsAFqENoCIAcoAtwEIgUEQCAHKALgBCAFQQJ0EN8ECwJAIAcoApQCIgVFDQAgBSAFQQxsQRNqQXhxIgpqQQlqIgVFDQAgBygCkAIgCmsgBRDfBAsgBygCwAIiBUGAgICAeEYgBUVyRQRAIAcoAsQCIAVBAnQQ3wQLIAdBMGoQISAHQYgHaiAHQdABahDaAiAHKALcBCIFBEAgBygC4AQgBUECdBDfBAsCQCAHKAKUAiIFRQ0AIAUgBUEMbEETakF4cSIKakEJaiIFRQ0AIAcoApACIAprIAUQ3wQLIAcoAsACIgVBgICAgHhGIAVFcg0FIAcoAsQCIAVBAnQQ3wQMBQsgB0EwahAmIAdBsAdqIAdBkAJqENgCIAcoArwGIgUEQCAHKALABiAFQQJ0EN8ECwJAIAcoAjQiBUUNACAFIAVBDGxBE2pBeHEiCmpBCWoiBUUNACAHKAIwIAprIAUQ3wQLIAcoArADIgVBgICAgHhGIAVFckUEQCAHKAK0AyAFQQJ0EN8ECyAHQTBqECYgB0GIB2ogB0HAAmoQ2AIgBygCvAYiBQRAIAcoAsAGIAVBAnQQ3wQLAkAgBygCNCIFRQ0AIAUgBUEMbEETakF4cSIKakEJaiIFRQ0AIAcoAjAgCmsgBRDfBAsgBygCsAMiBUGAgICAeEYgBUVyDQQgBygCtAMgBUECdBDfBAwECyAHQTBqEFUgB0GwB2ogB0GwAWoQ1wIgBygC3AQiBQRAIAcoAuAEIAVBAnQQ3wQLAkAgBygClAIiBUUNACAFIAVBDGxBE2pBeHEiCmpBCWoiBUUNACAHKAKQAiAKayAFEN8ECyAHKALAAiIFQYCAgIB4RiAFRXJFBEAgBygCxAIgBUECdBDfBAsgB0EwahBVIAdBiAdqIAdB0AFqENcCIAcoAtwEIgUEQCAHKALgBCAFQQJ0EN8ECwJAIAcoApQCIgVFDQAgBSAFQQxsQRNqQXhxIgpqQQlqIgVFDQAgBygCkAIgCmsgBRDfBAsgBygCwAIiBUGAgICAeEYgBUVyDQMgBygCxAIgBUECdBDfBAwDCyAHQTBqED4gB0GwB2ogB0GwAWoQ2wIgBygC3AQiBQRAIAcoAuAEIAVBAnQQ3wQLAkAgBygClAIiBUUNACAFIAVBDGxBE2pBeHEiCmpBCWoiBUUNACAHKAKQAiAKayAFEN8ECyAHKALAAiIFQYCAgIB4RiAFRXJFBEAgBygCxAIgBUECdBDfBAsgB0EwahA+IAdBiAdqIAdB0AFqENsCIAcoAtwEIgUEQCAHKALgBCAFQQJ0EN8ECwJAIAcoApQCIgVFDQAgBSAFQQxsQRNqQXhxIgpqQQlqIgVFDQAgBygCkAIgCmsgBRDfBAsgBygCwAIiBUGAgICAeEYgBUVyDQIgBygCxAIgBUECdBDfBAwCCyAHQTBqEEkgB0GwB2ogB0GwAWoQ2QIgBygC3AQiBQRAIAcoAuAEIAVBAnQQ3wQLAkAgBygClAIiBUUNACAFIAVBDGxBE2pBeHEiCmpBCWoiBUUNACAHKAKQAiAKayAFEN8ECyAHKALAAiIFQYCAgIB4RiAFRXJFBEAgBygCxAIgBUECdBDfBAsgB0EwahBJIAdBiAdqIAdB0AFqENkCIAcoAtwEIgUEQCAHKALgBCAFQQJ0EN8ECwJAIAcoApQCIgVFDQAgBSAFQQxsQRNqQXhxIgpqQQlqIgVFDQAgBygCkAIgCmsgBRDfBAsgBygCwAIiBUGAgICAeEYgBUVyDQEgBygCxAIgBUECdBDfBAwBCyAHQTBqEDogB0GwB2ogB0GwAWoQ3AIgBygC3AQiBQRAIAcoAuAEIAVBAnQQ3wQLAkAgBygClAIiBUUNACAFIAVBDGxBE2pBeHEiCmpBCWoiBUUNACAHKAKQAiAKayAFEN8ECyAHKALAAiIFQYCAgIB4RiAFRXJFBEAgBygCxAIgBUECdBDfBAsgB0EwahA6IAdBiAdqIAdB0AFqENwCIAcoAtwEIgUEQCAHKALgBCAFQQJ0EN8ECwJAIAcoApQCIgVFDQAgBSAFQQxsQRNqQXhxIgpqQQlqIgVFDQAgBygCkAIgCmsgBRDfBAsgBygCwAIiBUGAgICAeEYgBUVyDQAgBygCxAIgBUECdBDfBAsgB0HwBmogEkEIaigCADYCACAHQfwGaiAIQQhqKAIANgIAIAdB2AZqIAdBuAdqKAIANgIAIAdB5AZqIAdBkAdqKAIANgIAIAcgBykCsAc3A9AGIAcgBykCiAc3AtwGIAcgEikCADcD6AYgByAIKQIANwL0BiAHQThqIA1BCGooAgA2AgAgByANKQIANwMwIAdBxABqIAdBLGooAgA2AgAgByAHKQIkNwI8IAdBiAdqIAdB0AZqQQQgB0EwakECIAtBAEEBEBwgBygClAchBSAHKAKQByELIAcoAowHIQogBygCiAdBAUYEQCAMIAU2AgwgDCALNgIIIAwgCjYCBCAMQQE2AgAgBygCMCIFBEAgBygCNCAFQQJ0EN8ECyAHKAI8IgUEQCAHKAJAIAVBAnQQ3wQLIAcoAtAGIgUEQCAHKALUBiAFQQJ0EN8ECyAHKALcBiIFBEAgBygC4AYgBUECdBDfBAsgBygC6AYiBQRAIAcoAuwGIAVBAnQQ3wQLIAcoAvQGIgUEQCAHKAL4BiAFQQJ0EN8ECyAJBEAgBiEFA0AgBSgCACILBEAgBUEEaigCACALQQJ0EN8ECyAFQQxqIQUgCUEBayIJDQALCyAHKAIMIgVFDQEgBiAFQQxsEN8EDAELIAcoAjAiDQRAIAcoAjQgDUECdBDfBAsgBygCPCINBEAgBygCQCANQQJ0EN8ECyAHKALQBiINBEAgBygC1AYgDUECdBDfBAsgBygC3AYiDQRAIAcoAuAGIA1BAnQQ3wQLIAcoAugGIg0EQCAHKALsBiANQQJ0EN8ECyAHKAL0BiINBEAgBygC+AYgDUECdBDfBAsgBygCDCAJayAFSQRAIAdBDGogCSAFQQRBDBCIAyAHKAIUIQkgBygCECEGCyAFQQxsIg0EQCAGIAlBDGxqIAsgDfwKAAALIAcgBSAJajYCFCAKBEAgCyAKQQxsEN8ECyAMIAcpAgw3AgQgDEEANgIAIAxBDGogB0EUaigCADYCAAsgFCgCACIFBEAgFCgCBCAFQQJ0EN8ECyAHQcAHaiQAAkAgCCgCDEEBRgRAIAhB2ABqIAhBEGoiBUEIaigCADYCACAIIAUpAgA3A1AgEhDeAyEGDAELIAgoAhQhBiAIKAIQIgVBgICAgHhGDQAgCCgCGCELIAggBTYCSCAIIAY2AkQgCCAGNgJAIAggBiALQQxsajYCTCAPIAhBQGsQjwMMBgsgD0GAgICAeDYCACAPIAY2AgQMBQsgDUGEAU8EQCANEKsDCyAGRQ0BCyASQYQBTwRAIBIQqwMLIAtFDQIMAQsgCw0ADAELIAxBhAFPBEAgDBCrAwsLIAVBgICAgHhHIApBhAFJcg0AIAoQqwMLIAhB4ABqJAACQAJAAn8gFigCBCILQYCAgIB4RgRAQQEhBUEAIQYgFigCCAwBCyAWKAIIIQUCQCAWKAIMIgYgC08EQCAFIRcMAQsgC0ECdCELIAZFBEBBBCEXIAUgCxDfBAwBCyAFIAtBBCAGQQJ0IgUQzgQiF0UNAgtBACEFQQALIQsgEyAFNgIMIBMgCzYCCCATIAY2AgQgEyAXNgIAIBZBEGokAAwBC0EEIAVB6PHAABDIBAALIBMoAgAgEygCBCATKAIIIBMoAgwgE0EQaiQACzsBAX8jAEEQayICJAAgAiAAKAIANgIMIAFBhM/BAEEPQZPPwQBBBSACQQxqQfTOwQAQsAMgAkEQaiQACzsBAX8jAEEQayICJAAgAiAAKAIANgIMIAFBhM/BAEEPQZPPwQBBBSACQQxqQZjPwQAQsAMgAkEQaiQACzsBAX8jAEEQayICJAAgAiAAKAIANgIMIAFBvKrEAEEMQciqxABBBSACQQxqQdCqxAAQsAMgAkEQaiQACzsBAX8jAEEQayICJAAgAiAAKAIANgIMIAFBvKrEAEEMQciqxABBBSACQQxqQeCqxAAQsAMgAkEQaiQACzgAAkAgAkGAgMQARg0AIAAgAiABKAIQEQIARQ0AQQEPCyADRQRAQQAPCyAAIAMgBCABKAIMEQMAC50LAQp/IwBBEGsiCSQAIwBBMGsiByQAIAcgAjYCFCAHIAE2AhAgByACNgIMIAcgBTYCICAHIAQ2AhwgByAFNgIYIAdBJGohCiAHQRhqIQsjAEEwayIGJAAgB0EMaiIBKAIAIQIgASgCBCEEIAEoAgghASAGQQA2AgAgBiAEIAFBAnRqNgIkIAYgAjYCICAGIAQ2AhwgBiAENgIYIAYgBjYCKCAGQQxqIAZBGGoQlgICQAJAAkAgBigCAEEBRgRAIAYoAhAhASAGKAIEIQIgBigCFCIIBEAgASEAA0AgACgCACIDBEAgAEEEaigCACADQQJ0EN8ECyAAQQxqIQAgCEEBayIIDQALCyAGKAIMIgBFDQEgASAAQQxsEN8EDAELIAYoAhAhAiAGKAIMIgxBgICAgHhHDQELIApBgICAgHg2AgAgCiACNgIEIAsoAgQhASALKAIIIggEQCABIQADQCAAKAIAIgJBhAFPBEAgAhCrAwsgAEEEaiEAIAhBAWsiCA0ACwsgCygCACIARQ0BIAEgAEECdBDfBAwBCyAGKAIUIQggCygCACEEIAsoAgQhBSALKAIIIQEgBkEANgIAIAYgBSABQQJ0ajYCJCAGIAQ2AiAgBiAFNgIcIAYgBTYCGCAGIAY2AiggBkEMaiAGQRhqEJYCAkACQAJAAkAgBigCAEEBRgRAIAYoAhAhBCAGKAIEIQEgBigCFCIDBEAgBCEAA0AgACgCACIFBEAgAEEEaigCACAFQQJ0EN8ECyAAQQxqIQAgA0EBayIDDQALCyAGKAIMIgBFDQEgBCAAQQxsEN8EDAELIAYoAhAhASAGKAIMIg1BgICAgHhHDQELIApBgICAgHg2AgAgCiABNgIEDAELIAZBGGogACACIAggAyABIAYoAhQiABCEAiAGKAIYQQFHDQEgBkEIaiAGQRxqIgNBCGooAgA2AgAgBiADKQIANwMAIAZBDGogBhDUAyAGKAIQIgUgBigCFBDNBCEEIAYoAgwiAwRAIAUgAxDfBAsgBigCACIDBEAgBigCBCADEN8ECyAKQYCAgIB4NgIAIAogBDYCBCAABEAgASEDA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgAEEBayIADQALCyANRQ0AIAEgDUEMbBDfBAsgCARAIAIhAANAIAAoAgAiAQRAIABBBGooAgAgAUECdBDfBAsgAEEMaiEAIAhBAWsiCA0ACwsgDEUNASACIAxBDGwQ3wQMAQsgBigCHCELIAYoAiAiBCEOIAYoAiQiAwRAIANBDGwhDyAEIgUhAwNAIAZBIGogA0EIaigCADYCACAGIAMpAgA3AxggBSAGQRhqELsDNgIAIA5BBGohDiAFQQRqIQUgA0EMaiEDIA9BDGsiDw0ACwsgCiAENgIEIAogC0EDbDYCACAKIA4gBGtBAnY2AgggAARAIAEhAwNAIAMoAgAiBARAIANBBGooAgAgBEECdBDfBAsgA0EMaiEDIABBAWsiAA0ACwsgDQRAIAEgDUEMbBDfBAsgCARAIAIhAANAIAAoAgAiAQRAIABBBGooAgAgAUECdBDfBAsgAEEMaiEAIAhBAWsiCA0ACwsgDEUNACACIAxBDGwQ3wQLIAZBMGokAAJAAkAgCQJ/IAcoAiQiAUGAgICAeEYEQEEAIQEgBygCKCEFQQAhAkEBDAELIAcoAighAAJAIAcoAiwiAiABTwRAIAAhAQwBCyABQQJ0IQMgAkUEQEEEIQEgACADEN8EDAELIAAgA0EEIAJBAnQiABDOBCIBRQ0CC0EAIQVBAAs2AgwgCSAFNgIIIAkgAjYCBCAJIAE2AgAgB0EwaiQADAELQQQgAEHo8cAAEMgEAAsgCSgCACAJKAIEIAkoAgggCSgCDCAJQRBqJAALOAEBfyMAQRBrIgIkACACIAA2AgwgAUGoosAAQRBBuKLAAEEEIAJBDGpBmKLAABCwAyACQRBqJAALOAEBfyMAQRBrIgIkACACIAA2AgwgAUHMosAAQQ1BuKLAAEEEIAJBDGpBvKLAABCwAyACQRBqJAALOAEBfyMAQRBrIgIkACACIAA2AgwgAUGkpMAAQQxBsKTAAEEFIAJBDGpBlKTAABCwAyACQRBqJAALPQEBfyMAQRBrIgIkACACQdCGwQA2AgwgAiAANgIIIAJBCGpB+JbBACACQQxqQfiWwQAgAUGUj8EAEOYCAAs3AQF/IwBBEGsiBCQAIAQgATYCDCAEIAA2AgggBEEIakGIlsEAIARBDGpBiJbBACACIAMQ5gIACzcBAX8jAEEQayIEJAAgBCABNgIMIAQgADYCCCAEQQhqQfiVwQAgBEEMakH4lcEAIAIgAxDmAgALOAEBfyMAQRBrIgIkACACIAA2AgwgAUGU2cEAQRBBpNnBAEEEIAJBDGpBhNnBABCwAyACQRBqJAALNwEBfyMAQRBrIgQkACAEIAE2AgwgBCAANgIIIARBCGpBmLbFACAEQQxqQZi2xQAgAiADEOYCAAuCUAIafwR+IwBBEGsiFCQAEK0DIgsgACYBEK0DIgkgASYBEK0DIgcgAiYBIAkhBRCtAyIJIAMmASAHIQYjAEEQayIXJAAgF0EEaiETIARBAEchFiMAQdAAayIKJAAgCkEMaiALEOwCIAooAhAhBwJAAkACQCAKKAIMIgtBgICAgHhGBEAgE0GAgICAeDYCACATIAc2AgRBASEEDAELIAooAhQhECAKQQxqIAUQ7AIgCigCECEIIAooAgwiDUGAgICAeEYEQCATQYCAgIB4NgIAIBMgCDYCBEEBIQQgC0UNASAHIAtBAnQQ3wQMAQsgCigCFCERIApBDGogBhDsAiAKKAIQIQ4CQCAKKAIMIgxBgICAgHhGBEAgE0GAgICAeDYCACATIA42AgQMAQsgCigCFCEPIAogCTYCDCAJIQQCQCAKQQxqIhIQ4gRFDQAgCiAENgJEIBIgCkHEAGoQugMgBEGEAU8EQCAEEKsDCyAKKAIQIQQgCigCDCISQYCAgIB4Rg0AIAogCigCFDYCCCAKIAQ2AgQgCiASNgIAIAogEDYCJCAKIAc2AiAgCiALNgIcIAogETYCQCAKIAg2AjwgCiANNgI4IAogDzYCTCAKIA42AkggCiAMNgJEIApBDGohECAKQRxqIQ8gCkE4aiESIApBxABqIRFBACEIIwBBkAxrIgUkACAFQoCAgIDAADcCCCAFQQA2AhAgBUGYB2pBjKHEACgCADYCACAFQYShxAApAgA3A5AHIAVBkAdqQeiixAAQpQMgBSgClAdBATYCACAFKAKUByEEAn8CQCAFKAKQByIJQYCAgIB4Rw0AIAQoAggNACAFQQA2AhwgBUKAgICAwAA3AhRBAAwBCyAFQQE2ApgHIAUgBDYClAcgBSAJNgKQByAFQRRqIAVBkAdqQQhBABDPASAFKAIcCyEEAkACQAJAAkACQAJAAkACQAJAAkACQAJAIAQgDygCCCIJRgRAIAUoAhhBBGshCSAEQQJ0IQYgDygCBEEEayELAkADQCAGRQ0BIAYgCWohByAGIAtqIAZBBGshBigCACIMIAcoAgAiB0YNAAsgByAMSw0CDAMLIAYNAQwCCyAEIAlNDQELIBEoAggiCSAERw0BIAUoAhhBBGshCSAEQQJ0IQYgESgCBEEEayELA0AgBkUNAyAGIAlqIQcgBiALaiAGQQRrIQYoAgAiDCAHKAIAIgdGDQALIAcgDEsNBgwDC0HRzsUALQAAGkEQIQhBEEEBENYEIgZFDQMgBkEIakHnrcQAKQAANwAAIAZB363EACkAADcAAAwGCyAEIAlNDQEMBAsgBg0DC0HRzsUALQAAGkEQIQhBEEEBENYEIgZFDQEgBkEIakHXrcQAKQAANwAAIAZBz63EACkAADcAAAwDC0EBQRBBrKrEABDIBAALQQFBEEGsqsQAEMgEAAsCQAJAIAQgEigCCCIJRgRAIAUoAhhBBGshCSAEQQJ0IQYgEigCBEEEayEEA0AgBkUNAiAGIAlqIQsgBCAGaiAGQQRrIQYoAgAiByALKAIAIgtGDQALIAcgC0kNBQwCCyAEIAlNDQEMBAsgBg0DC0HRzsUALQAAGkEPIQhBD0EBENYEIgZFDQEgBkEHakHHrcQAKQAANwAAIAZBwK3EACkAADcAAAsgECAINgIMIBAgBjYCCCAQIAg2AgQgEEEBNgIAIAUoAhQiBARAIAUoAhggBEECdBDfBAsgBSgCECIIBEAgBSgCDCEGA0AgBigCACIEBEAgBkEEaigCACAEQQJ0EN8ECyAGQQxqIQYgCEEBayIIDQALCyAFKAIIIgQEQCAFKAIMIARBDGwQ3wQLIAooAgAiBARAIAooAgQgBBDfBAsgESgCACIEBEAgESgCBCAEQQJ0EN8ECyASKAIAIgQEQCASKAIEIARBAnQQ3wQLIA8oAgAiBEUNAiAPKAIEIARBAnQQ3wQMAgtBAUEPQayqxAAQyAQACyAWBEAgBUGQB2ogERDiASAFKQOoByEfIAUpA6AHISEgBSkDmAchICAFKQOQByEiIAVBmAZqIgRB4PbAACgCADYCACAFQdj2wAApAgA3A5AGICAgIoRQRQRAQQEhBgNAIAUoApAGIAZBAWtGBEAgBUGQBmpB3PfAABClAwsgBSgClAYgCGogIj4CACAiQv////8PViAgQgBSICBQICBCIIYgIkIgiIQhIiAIQQRqIQggIEIgiCEgIAUgBjYCmAYgBkEBaiEGGw0ACwsgBUH4BWogBCgCACIENgIAIAVByABqIAQ2AgAgBSAFKQOQBiIgNwPwBSAFICA3A0BBACEIIAVBwAJqQeD2wAAoAgA2AgAgBUHY9sAAKQIANwO4AiAfICGEUEUEQEEBIQYDQCAFKAK4AiAGQQFrRgRAIAVBuAJqQdz3wAAQpQMLIAUoArwCIAhqICE+AgAgIUL/////D1YgH0IAUiAfUCAfQiCGICFCIIiEISEgCEEEaiEIIB9CIIghHyAFIAY2AsACIAZBAWohBhsNAAsLIAVB1ABqIAVBwAJqKAIANgIAIAUgBSkDuAI3AkwgBUGYBmoiCSAFQcgAaikDADcDACAFQaAGaiILIAVB0ABqKQMANwMAIAUgBSkDQDcDkAYgBSgCCCAFKAIQIgZrQQFNBEAgBUEIaiAGQQJBBEEMEIgDIAUoAhAhBgsgBSgCDCAGQQxsaiIEIAUpA5AGNwIAIARBCGogCSkDADcCACAEQRBqIAspAwA3AgAgBSAGQQJqNgIQCyAFQZAHaiAPEOIBIAUpA6gHIR8gBSkDoAchISAFKQOYByEgIAUpA5AHISJBACEIIAVBmAZqIgRB4PbAACgCADYCACAFQdj2wAApAgA3A5AGICAgIoRQRQRAQQEhBgNAIAUoApAGIAZBAWtGBEAgBUGQBmpB3PfAABClAwsgBSgClAYgCGogIj4CACAiQv////8PViAgQgBSICBQICBCIIYgIkIgiIQhIiAIQQRqIQggIEIgiCEgIAUgBjYCmAYgBkEBaiEGGw0ACwsgBUH4BWogBCgCACIENgIAIAVByABqIAQ2AgAgBSAFKQOQBiIgNwPwBSAFICA3A0BBACEIIAVBwAJqQeD2wAAoAgA2AgAgBUHY9sAAKQIANwO4AiAfICGEUEUEQEEBIQYDQCAFKAK4AiAGQQFrRgRAIAVBuAJqQdz3wAAQpQMLIAUoArwCIAhqICE+AgAgIUL/////D1YgH0IAUiAfUCAfQiCGICFCIIiEISEgCEEEaiEIIB9CIIghHyAFIAY2AsACIAZBAWohBhsNAAsLIAVB1ABqIAVBwAJqKAIANgIAIAUgBSkDuAI3AkwgBUGYBmoiBCAFQcgAaikDADcDACAFQaAGaiILIAVB0ABqKQMANwMAIAUgBSkDQDcDkAYgBSgCCCAFKAIQIgZrQQFNBEAgBUEIaiAGQQJBBEEMEIgDIAUoAhAhBgsgBSgCDCAGQQxsaiIJIAUpA5AGNwIAIAlBCGogBCkDADcCACAJQRBqIAspAwA3AgAgBSAGQQJqNgIQIAVBkAdqIBIQ4gEgBSkDqAchHyAFKQOgByEhIAUpA5gHISAgBSkDkAchIkEAIQggBEHg9sAAKAIANgIAIAVB2PbAACkCADcDkAYgICAihFBFBEBBASEGA0AgBSgCkAYgBkEBa0YEQCAFQZAGakHc98AAEKUDCyAFKAKUBiAIaiAiPgIAICJC/////w9WICBCAFIgIFAgIEIghiAiQiCIhCEiIAhBBGohCCAgQiCIISAgBSAGNgKYBiAGQQFqIQYbDQALCyAFQfgFaiAFQZgGaiIEKAIAIgk2AgAgBUHIAGoiCyAJNgIAIAUgBSkDkAYiIDcD8AUgBSAgNwNAQQAhCCAFQcACaiIJQeD2wAAoAgA2AgAgBUHY9sAAKQIANwO4AiAfICGEUEUEQEEBIQYDQCAFKAK4AiAGQQFrRgRAIAVBuAJqQdz3wAAQpQMLIAUoArwCIAhqICE+AgAgIUL/////D1YgH0IAUiAfUCAfQiCGICFCIIiEISEgCEEEaiEIIB9CIIghHyAFIAY2AsACIAZBAWohBhsNAAsLIAVB1ABqIAkoAgA2AgAgBSAFKQO4AjcCTCAEIAspAwA3AwAgBUGgBmoiCSAFQdAAaikDADcDACAFIAUpA0A3A5AGIAUoAgggBSgCECIGa0EBTQRAIAVBCGogBkECQQRBDBCIAyAFKAIQIQYLIAUoAgwgBkEMbGoiBCAFKQOQBjcCACAEQQhqIAVBmAZqKQMANwIAIARBEGogCSkDADcCACAFIAZBAmoiBjYCECAKKAIIIQ0gBUGYB2oiBEGMocQAKAIANgIAIAVBhKHEACkCADcDkAcgDQRAIAVBkAdqQeiixAAQpQMgBSgClAcgDTYCACAFQQE2ApgHIAUoAhAhBgsgBUEoaiAEKAIANgIAIAUgBSkDkAc3AyAgBSgCCCAGRgRAIAVBCGpB7KvEABCfAwsgBSgCDCAGQQxsaiIEIAUpAyA3AgAgBEEIaiAFQShqKAIANgIAIAUgBkEBajYCECAKKAIEIQwCQAJAAkACQCANBEBB0c7FAC0AABogDUEBENYEIgRFDQEgDQRAIAQgDCAN/AoAAAtBACEGQYyhxAAoAgAhByAFQZgHaiEJQYShxAApAgAhHwNAIAQgBmotAAAhCyAJIAc2AgAgBSAfNwOQByALBEAgBUGQB2pB6KLEABClAyAFKAKUByALNgIAIAVBATYCmAcLIAVBOGoiCCAJKAIANgIAIAUgBSkDkAc3AzAgBSgCECILIAUoAghGBEAgBUEIakGwrcQAEJ8DCyAFKAIMIAtBDGxqIg4gBSkDMDcCACAOQQhqIAgoAgA2AgAgBSALQQFqNgIQIA0gBkEBaiIGRw0ACyAEIA0Q3wQLIAVBkAFqIg5BAEGBAfwLACAFQfgAakG4rMQAKQMANwMAIAVB8ABqQbCsxAApAwA3AwAgBUHoAGpBqKzEACkDADcDACAFQeAAakGgrMQAKQMANwMAIAVB2ABqQZisxAApAwA3AwAgBUHQAGpBkKzEACkDADcDACAFQgA3A4gBIAVCADcDgAEgBUGIrMQAKQMANwNIIAVBgKzEACkDADcDQCAPKAIIDQFB0c7FAC0AABpBAUEBENYEIgRFDQIgBEEAOgAAIAVBATYCqAIgBSAENgKkAiAFQQE2AqACDAMLQQEgDUH4gcAAEMgEAAsgBUGgAmogD0EIELACDAELQQFBARD/BAALAkACQCARKAIIRQRAQdHOxQAtAAAaQQFBARDWBCIERQ0BIARBADoAACAFQQE2ArQCIAUgBDYCsAIgBUEBNgKsAgwCCyAFQawCaiARQQgQsAIMAQtBAUEBEP8EAAsCQAJAAkACQAJ/IAUoAqgCIhZBIE8EQCAFKAKgAiEYIAUoAqQCIhwhCSAWDAELQdHOxQAtAAAaQSBBARDXBCIJRQ0BIAUoAqQCIRwgFgRAIAkgHCAW/AoAAAtBICEYQSALIQYCfyAFKAK0AiIZQSBPBEAgBSgCrAIhGiAFKAKwAiIdIQsgGQwBC0HRzsUALQAAGkEgQQEQ1wQiC0UNAiAFKAKwAiEdIBkEQCALIB0gGfwKAAALQSAhGkEgCyEIQYABIAUtAJACIgRrIhUgBk0EQCAERQRAIAkhBwwECyAVBEAgBCAOaiAJIBX8CgAACyAFIAUpA4ABQgF8Ih83A4ABIAUgBSkDiAEgH1CtfDcDiAEgBUFAayAOQQEQ+QQgCSAVaiEHIAYgFWshBgwDCyAGBEAgBCAOaiAJIAb8CgAACyAEIAZqIQQMAwtBAUEgQcCsxAAQyAQAC0EBQSBB0KzEABDIBAALIAZB/wBxIQQgBkGAAU8EQCAFIAUpA4ABIh8gBkEHdiIVrXwiIDcDgAEgBSAFKQOIASAfICBWrXw3A4gBIAVBQGsgByAVEPkECyAERQ0AIA4gByAGQYB/cWogBPwKAAALIAUgBDoAkAICQAJAQYABIARB/wBxIgZrIgcgCE0EQCAEQf8BcUUEQCALIQQMAgsgBwRAIAYgDmogCyAH/AoAAAsgBSAFKQOAAUIBfCIfNwOAASAFIAUpA4gBIB9QrXw3A4gBIAVBQGsgDkEBEPkEIAcgC2ohBCAIIAdrIQgMAQsgCARAIAYgDmogCyAI/AoAAAsgBiAIaiEGDAELIAhB/wBxIQYgCEGAAU8EQCAFIAUpA4ABIh8gCEEHdiIHrXwiIDcDgAEgBSAFKQOIASAfICBWrXw3A4gBIAVBQGsgBCAHEPkECyAGRQ0AIA4gBCAIQYB/cWogBvwKAAALIAUgBjoAkAIgCigCACEIAkACQEGAASAGQf8AcSIEayIHIA1NBEAgBkUEQCAMIQQMAgsgBwRAIAQgDmogDCAH/AoAAAsgBSAFKQOAAUIBfCIfNwOAASAFIAUpA4gBIB9QrXw3A4gBIAVBQGsgDkEBEPkEIAcgDGohBCANIAdrIQ0MAQsgDQRAIAQgDmogDCAN/AoAAAsgBCANaiEGDAELIA1B/wBxIQYgDUGAAU8EQCAFIAUpA4ABIh8gDUEHdiIHrXwiIDcDgAEgBSAFKQOIASAfICBWrXw3A4gBIAVBQGsgBCAHEPkECyAGRQ0AIA4gBCANQYB/cWogBvwKAAALIAUgBjoAkAIgCARAIAwgCBDfBAsgBUGQB2ogBUFAa0HgAfwKAAAgBUHgB2oiByAFLQDgCCIEaiIMQYABOgAAIAUpA9AHIh9CNogiIUI4hiAhIAUpA9gHIiBCCoYiIoQiIUKA/gODQiiGhCAhQoCA/AeDQhiGICFCgICA+A+DQgiGhIQgIEIChkKAgID4D4MgIEIOiEKAgPwHg4QgIEIeiEKA/gODICJCOIiEhIQhICAErSIhQjuGIB9CCoYiIiAhQgOGhCIhQoD+A4NCKIaEICFCgID8B4NCGIYgIUKAgID4D4NCCIaEhCAfQgKGQoCAgPgPgyAfQg6IQoCA/AeDhCAfQh6IQoD+A4MgIkI4iISEhCEfAkACQCAEQf8ARwRAIARB/wBzIgYEQCAMQQFqQQAgBvwLAAsgBEHwAHNBD0sNAQsgBUGQB2oiBCAHQQEQ+QQgBUGQBmoiB0EAQfAA/AsAIAUgHzcAiAcgBSAgNwCAByAEIAdBARD5BAwBCyAFICA3A9AIIAUgHzcD2AggBUGQB2ogB0EBEPkECyAFIAUpA8gHIh9COIYgH0KA/gODQiiGhCAfQoCA/AeDQhiGIB9CgICA+A+DQgiGhIQgH0IIiEKAgID4D4MgH0IYiEKAgPwHg4QgH0IoiEKA/gODIB9COIiEhIQ3A/ACIAUgBSkDwAciH0I4hiAfQoD+A4NCKIaEIB9CgID8B4NCGIYgH0KAgID4D4NCCIaEhCAfQgiIQoCAgPgPgyAfQhiIQoCA/AeDhCAfQiiIQoD+A4MgH0I4iISEhDcD6AIgBSAFKQO4ByIfQjiGIB9CgP4Dg0IohoQgH0KAgPwHg0IYhiAfQoCAgPgPg0IIhoSEIB9CCIhCgICA+A+DIB9CGIhCgID8B4OEIB9CKIhCgP4DgyAfQjiIhISENwPgAiAFIAUpA7AHIh9COIYgH0KA/gODQiiGhCAfQoCA/AeDQhiGIB9CgICA+A+DQgiGhIQgH0IIiEKAgID4D4MgH0IYiEKAgPwHg4QgH0IoiEKA/gODIB9COIiEhIQ3A9gCIAUgBSkDqAciH0I4hiAfQoD+A4NCKIaEIB9CgID8B4NCGIYgH0KAgID4D4NCCIaEhCAfQgiIQoCAgPgPgyAfQhiIQoCA/AeDhCAfQiiIQoD+A4MgH0I4iISEhDcD0AIgBSAFKQOgByIfQjiGIB9CgP4Dg0IohoQgH0KAgPwHg0IYhiAfQoCAgPgPg0IIhoSEIB9CCIhCgICA+A+DIB9CGIhCgID8B4OEIB9CKIhCgP4DgyAfQjiIhISENwPIAiAFIAUpA5gHIh9COIYgH0KA/gODQiiGhCAfQoCA/AeDQhiGIB9CgICA+A+DQgiGhIQgH0IIiEKAgID4D4MgH0IYiEKAgPwHg4QgH0IoiEKA/gODIB9COIiEhIQ3A8ACIAUgBSkDkAciH0I4hiAfQoD+A4NCKIaEIB9CgID8B4NCGIYgH0KAgID4D4NCCIaEhCAfQgiIQoCAgPgPgyAfQhiIQoCA/AeDhCAfQiiIQoD+A4MgH0I4iISEhDcDuAIgBUH8AmogBUG4AmpBwABBCBDPAiAFQZgGaiIMIA9BCGooAgA2AgAgBSAPKQIANwOQBiAFQZAHaiIEIAVBkAZqIhUQMCAFQZADaiAFQZgHaiIHKQMANwMAIAVBmANqIAVBoAdqIgYpAwA3AwAgBUGgA2ogBUGoB2oiCCkDADcDACAFQbADaiAFQbgHaiINKQMANwMAIAVBuANqIAVBwAdqIg4pAwA3AwAgBUHAA2ogBUHIB2oiDykDADcDACAFIAUpA5AHNwOIAyAFIAUpA7AHNwOoAyAMIBFBCGooAgA2AgAgBSARKQIANwOQBiAEIBUQMCAFQdADaiAHKQMANwMAIAVB2ANqIAYpAwA3AwAgBUHgA2ogCCkDADcDACAFQfADaiANKQMANwMAIAVB+ANqIA4pAwA3AwAgBUGABGogDykDADcDACAFIAUpA5AHNwPIAyAFIAUpA7AHNwPoAyAEIAVBiANqIAVBqANqEBcgBUGgBGogCCkDADcDACAFQZgEaiAGKQMANwMAIAVBkARqIAcpAwA3AwAgBUGwBGogDSkDADcDACAFQbgEaiAOKQMANwMAIAVBwARqIA8pAwA3AwAgBSAFKQOQBzcDiAQgBSAFKQOwBzcDqAQgBCAFQcgDaiAFQegDahAXIAVB4ARqIh4gCCkDADcDACAFQdgEaiAGKQMAIh83AwAgBUHQBGogBykDACIgNwMAIAVB8ARqIgYgDSkDADcDACAFQfgEaiIIIA4pAwA3AwAgBUGABWoiDSAPKQMANwMAIAUgBSkDkAciITcDyAQgBSAFKQOwBzcD6AQgBUGABmogHzcDACAFQfgFaiAgNwMAIAVBiAZqIB4pAwA3AwAgBSAhNwPwBSAFQagGaiANKQMANwMAIAVBoAZqIAgpAwA3AwAgDCAGKQMANwMAIAUgBSkD6AQ3A5AGIAQgBUHwBWogFRBFAkACQAJAIAUtANAHQQJHBEAgBCAFQYgEaiAFQagEahBFIAUtANAHQQJGDQEgBBBJIAVBjAVqIAVBkAhqENkCIAUoArwLIgQEQCAFKALACyAEQQJ0EN8ECwJAIAUoAvQIIgRFDQAgBCAEQQxsQRNqQXhxIgdqQQlqIgRFDQAgBSgC8AggB2sgBBDfBAsgBSgCoAkiBEGAgICAeEYgBEVyRQRAIAUoAqQJIARBAnQQ3wQLIAVBmAVqIgRBwJ3BAEHCABCVAyAFQZAHahBJIAVBkAZqIgcgBUGwCGoQ2QIgBUGkBWogBCAHEIcCIAUoApAGIgQEQCAFKAKUBiAEQQJ0EN8ECyAFKAK8CyIEBEAgBSgCwAsgBEECdBDfBAsCQCAFKAL0CCIERQ0AIAQgBEEMbEETakF4cSIHakEJaiIERQ0AIAUoAvAIIAdrIAQQ3wQLIAUoAqAJIgRBgICAgHhGIARFckUEQCAFKAKkCSAEQQJ0EN8ECyAFQZAHahBJIAVBmAZqIAVBxAtqKAIANgIAIAUgBSkCvAs3A5AGAkAgBSgC9AgiBEUNACAEIARBDGxBE2pBeHEiB2pBCWoiBEUNACAFKALwCCAHayAEEN8ECyAFKAKgCSIEQYCAgIB4RiAERXJFBEAgBSgCpAkgBEECdBDfBAsgBUG8BWogBUH8AmogBUGQBmoiBBDwASAFQagHaiAFQcgEahDZAiAFQbQHaiAFQegEahDZAiAFQZgHaiAFQZQFaigCADYCACAFQaQHaiAFQawFaigCADYCACAFQbgFaiASQQhqKAIANgIAIAUgBSkCjAU3A5AHIAUgBSkCpAU3ApwHIAUgEikCADcDsAUgBCAFQZAHakEEIAVBsAVqQQJBBEEAQQEQHCAFKAKcBiEHIAUoApgGIQwgBSgClAYhBgJAIAUoApAGQQFGBEAgECAHNgIMIBAgDDYCCCAQIAY2AgQgEEEBNgIAIAUoArAFIgQEQCAFKAK0BSAEQQJ0EN8ECyAFKAK8BSIEBEAgBSgCwAUgBEECdBDfBAsgBSgCkAciBARAIAUoApQHIARBAnQQ3wQLIAUoApwHIgQEQCAFKAKgByAEQQJ0EN8ECyAFKAKoByIEBEAgBSgCrAcgBEECdBDfBAsgBSgCtAciBARAIAUoArgHIARBAnQQ3wQLIBoEQCALIBoQ3wQLIBgEQCAJIBgQ3wQLIBlBIEkNAQwFCyAFKAIIIAUoAhAiBGsgB0kEQCAFQQhqIAQgB0EEQQwQiAMgBSgCECEECyAHQQxsIggEQCAFKAIMIARBDGxqIAwgCPwKAAALIAUgBCAHajYCECAGBEAgDCAGQQxsEN8ECyAFQcwFaiIEIAVBiANqENkCIAVBkAZqIAQQ4gEgBSkDqAYhHyAFKQOgBiEhIAUpA5gGISAgBSkDkAYhIkEAIQggBUHgBWoiBEHg9sAAKAIANgIAIAVB2PbAACkCADcD2AUgICAihFBFBEBBASEGA0AgBSgC2AUgBkEBa0YEQCAFQdgFakHc98AAEKUDCyAFKALcBSAIaiAiPgIAICJC/////w9WICBCAFIgIFAgIEIghiAiQiCIhCEiIAhBBGohCCAgQiCIISAgBSAGNgLgBSAGQQFqIQYbDQALCyAFQeALaiAEKAIAIgQ2AgAgBUH4BWogBDYCACAFIAUpA9gFIiA3A9gLIAUgIDcD8AVBACEIIAVB8AtqQeD2wAAoAgA2AgAgBUHY9sAAKQIANwPoCyAfICGEUEUEQEEBIQYDQCAFKALoCyAGQQFrRgRAIAVB6AtqQdz3wAAQpQMLIAUoAuwLIAhqICE+AgAgIUL/////D1YgH0IAUiAfUCAfQiCGICFCIIiEISEgCEEEaiEIIB9CIIghHyAFIAY2AvALIAZBAWohBhsNAAsLIAVBhAZqIAVB8AtqKAIANgIAIAUgBSkD6As3AvwFIAVB4AVqIgcgBUH4BWopAwA3AwAgBUHoBWoiDCAFQYAGaikDADcDACAFIAUpA/AFNwPYBSAFKAIIIAUoAhAiBmtBAU0EQCAFQQhqIAZBAkEEQQwQiAMgBSgCECEGCyAFKAIMIAZBDGxqIgQgBSkD2AU3AgAgBEEIaiAHKQMANwIAIARBEGogDCkDADcCACAFIAZBAmo2AhAgBSgCzAUiBARAIAUoAtAFIARBAnQQ3wQLIAVB6AtqIgQgBUHIA2oQ2QIgBUGQBmogBBDiASAFKQOoBiEfIAUpA6AGISEgBSkDmAYhICAFKQOQBiEiQQAhCCAFQfgFaiIEQeD2wAAoAgA2AgAgBUHY9sAAKQIANwPwBSAgICKEUEUEQEEBIQYDQCAFKALwBSAGQQFrRgRAIAVB8AVqQdz3wAAQpQMLIAUoAvQFIAhqICI+AgAgIkL/////D1YgIEIAUiAgUCAgQiCGICJCIIiEISIgCEEEaiEIICBCIIghICAFIAY2AvgFIAZBAWohBhsNAAsLIAVB4AVqIAQoAgAiBzYCACAFQYAMaiAHNgIAIAUgBSkD8AUiIDcD2AUgBSAgNwP4C0EAIQggBEHg9sAAKAIANgIAIAVB2PbAACkCADcD8AUgHyAhhFBFBEBBASEGA0AgBSgC8AUgBkEBa0YEQCAFQfAFakHc98AAEKUDCyAFKAL0BSAIaiAhPgIAICFC/////w9WIB9CAFIgH1AgH0IghiAhQiCIhCEhIAhBBGohCCAfQiCIIR8gBSAGNgL4BSAGQQFqIQYbDQALCyAFQYwMaiAFQfgFaigCADYCACAFIAUpA/AFNwKEDCAFKAIIIAUoAhAiBmtBAU0EQCAFQQhqIAZBAkEEQQwQiAMgBSgCECEGCyAFKAIMIAZBDGxqIgQgBSkD+As3AgAgBEEIaiAFQYAMaikDADcCACAEQRBqIAVBiAxqKQMANwIAIAUgBkECajYCECAFKALoCyIEBEAgBSgC7AsgBEECdBDfBAsgECAFKQIINwIEIBBBADYCACAQQQxqIAVBEGooAgA2AgAgBSgCsAUiBARAIAUoArQFIARBAnQQ3wQLIAUoArwFIgQEQCAFKALABSAEQQJ0EN8ECyAFKAKQByIEBEAgBSgClAcgBEECdBDfBAsgBSgCnAciBARAIAUoAqAHIARBAnQQ3wQLIAUoAqgHIgQEQCAFKAKsByAEQQJ0EN8ECyAFKAK0ByIEBEAgBSgCuAcgBEECdBDfBAsgGgRAIAsgGhDfBAsgGARAIAkgGBDfBAsgGUEgTw0DIAUoAqwCIgRFDQMgHSAEEN8EDAMLIAUoAqwCIgRFDQMgHSAEEN8EDAMLIAwgBygCADYCACAFIAUpA5AHNwOQBkGQrcQAQQ8gBUGQBmpB4KzEAEGgrcQAEMoDAAsgBUGYBmogBUGYB2ooAgA2AgAgBSAFKQOQBzcDkAZB8KzEAEEPIAVBkAZqQeCsxABBgK3EABDKAwALAkAgFkEgTw0AIAUoAqACIgRFDQAgHCAEEN8ECyAFKAIUIgRFDQEgBSgCGCAEQQJ0EN8EDAELAkAgFkEgTw0AIAUoAqACIgRFDQAgHCAEEN8ECyAFKAIUIgQEQCAFKAIYIARBAnQQ3wQLIAUoAhAiCARAIAUoAgwhBgNAIAYoAgAiBARAIAZBBGooAgAgBEECdBDfBAsgBkEMaiEGIAhBAWsiCA0ACwsgBSgCCCIERQ0AIAUoAgwgBEEMbBDfBAsgBUGQDGokACAKKAIMQQFGBEAgCkFAayAKQRBqIgRBCGooAgA2AgAgCiAEKQIANwM4IBEgEhDUAyAKKAJIIgQgCigCTBDNBCEJIAooAkQiCwRAIAQgCxDfBAsgCigCOCIERQ0EIAooAjwgBBDfBAwECyAKKAIUIQkgCigCECIEQYCAgIB4Rg0DIAooAhghCyAKIAQ2AjAgCiAJNgIsIAogCTYCKCAKIAkgC0EMbGo2AjQgEyAKQShqEI8DDAQLIBNBgICAgHg2AgAgEyAENgIEIAxFDQAgDiAMQQJ0EN8ECyANBEAgCCANQQJ0EN8ECyALBEAgByALQQJ0EN8EC0EAIQQgDEGAgICAeEcNAgsgCUGEAU8EQCAJEKsDCyAEIAZBhAFPcQRAIAYQqwMLIAtBgICAgHhHIAVBhAFJcg0BIAUQqwMMAQsgE0GAgICAeDYCACATIAk2AgQLIApB0ABqJAACQAJAAn8gFygCBCIJQYCAgIB4RgRAQQEhBEEAIQcgFygCCAwBCyAXKAIIIQQCQCAXKAIMIgcgCU8EQCAEIRsMAQsgCUECdCEJIAdFBEBBBCEbIAQgCRDfBAwBCyAEIAlBBCAHQQJ0IgQQzgQiG0UNAgtBACEEQQALIQkgFCAENgIMIBQgCTYCCCAUIAc2AgQgFCAbNgIAIBdBEGokAAwBC0EEIARB6PHAABDIBAALIBQoAgAgFCgCBCAUKAIIIBQoAgwgFEEQaiQACy0AAkAgACABEMkERQ0AIAAEQEHRzsUALQAAGiAAIAEQ1gQiAUUNAQsgAQ8LAAs3AQF/IwBBIGsiASQAIAFBADYCGCABQQE2AgwgAUHwysUANgIIIAFCBDcCECABQQhqIAAQqAQACzcBAX8jAEEgayIBJAAgAUEANgIYIAFBATYCDCABQbTLxQA2AgggAUIENwIQIAFBCGogABCoBAALjwcBDX8jAEEQayIJJAAQrQMiBiAAJgEQrQMiCiABJgEQrQMiBSACJgEgCiEHQQAhCiMAQRBrIgskACALQQRqIQggA0EARyENIwBBQGoiBCQAIARBGGogBhDsAiAEKAIcIQYCQCAEKAIYIgNBgICAgHhGBEAgCEGAgICAeDYCACAIIAY2AgQgBUGEAU8EQCAFEKsDCyAHQYQBSQ0BIAcQqwMMAQsgBCgCICEOIARBGGogBxDsAiAEKAIcIQcgBCgCGCIMQYCAgIB4RgRAIAhBgICAgHg2AgAgCCAHNgIEIAMEQCAGIANBAnQQ3wQLIAVBhAFJDQEgBRCrAwwBCyAEKAIgIQ8gBEEYaiAFEOwCIAQoAhwhBSAEKAIYIhBBgICAgHhGBEAgCEGAgICAeDYCACAIIAU2AgQgDARAIAcgDEECdBDfBAsgA0UNASAGIANBAnQQ3wQMAQsgBCAEKAIgNgIUIAQgBTYCECAEIBA2AgwgBCAONgIwIAQgBjYCLCAEIAM2AiggBCAPNgI8IAQgBzYCOCAEIAw2AjQgBEEYaiAEQShqIgMgBEE0aiIFIARBDGogDRBQIAQoAhhBAUYEQCAEQTBqIARBHGoiBkEIaigCADYCACAEIAYpAgA3AyggBSADENQDIAQoAjgiAyAEKAI8EM0EIQUgBCgCNCIGBEAgAyAGEN8ECyAEKAIoIgMEQCAEKAIsIAMQ3wQLIAhBgICAgHg2AgAgCCAFNgIEDAELIAQoAhwhDSAEKAIgIgMhByAEKAIkIgUEQCAFQQxsIQwgAyIFIQYDQCAEQSBqIAZBCGooAgA2AgAgBCAGKQIANwMYIAUgBEEYahC7AzYCACAHQQRqIQcgBUEEaiEFIAZBDGohBiAMQQxrIgwNAAsLIAggAzYCBCAIIA1BA2w2AgAgCCAHIANrQQJ2NgIICyAEQUBrJAACQAJAAn8gCygCBCIEQYCAgIB4RgRAQQEhBkEAIQUgCygCCAwBCyALKAIIIQMCQCALKAIMIgUgBE8EQCADIQoMAQsgBEECdCEEIAVFBEBBBCEKIAMgBBDfBAwBCyADIARBBCAFQQJ0IgMQzgQiCkUNAgtBACEGQQALIQMgCSAGNgIMIAkgAzYCCCAJIAU2AgQgCSAKNgIAIAtBEGokAAwBC0EEIANB6PHAABDIBAALIAkoAgAgCSgCBCAJKAIIIAkoAgwgCUEQaiQAC/0iAhh/A34jAEEQayIRJAAQrQMiByAAJgEQrQMiBiABJgEQrQMiBSACJgEjAEEQayITJAAgE0EEaiESIANBAEchGiMAQdAAayIIJAAgCEEYaiAHEOwCIAgoAhwhBwJAIAgoAhgiA0GAgICAeEYEQCASQYCAgIB4NgIAIBIgBzYCBCAFQYQBTwRAIAUQqwMLIAZBhAFJDQEgBhCrAwwBCyAIKAIgIQogCCAGNgIYAkACQCAIQRhqEOIERQRAQZXywABBHBDNBCEPIAZBhAFJDQEgBhCrAwwBCyAIIAY2AkQgCEEYaiAIQcQAahC6AyAGQYQBTwRAIAYQqwMLIAgoAhwhDyAIKAIYIhRBgICAgHhHDQELIBJBgICAgHg2AgAgEiAPNgIEIAMEQCAHIANBAnQQ3wQLIAVBgwFNDQEgBRCrAwwBCyAIKAIgIQYgCEEYaiAFEOwCIAgoAhgiBUGAgICAeEYEQCAIKAIcIQUgEkGAgICAeDYCACASIAU2AgQgFARAIA8gFBDfBAsgA0UNASAHIANBAnQQ3wQMAQsgCCAIKQIcNwIQIAggBTYCDCAIIAo2AkwgCCAHNgJIIAggAzYCRCAIQRhqIRUgCEHEAGohGSAIQQxqIRsjAEHwAmsiBCQAIARB0ABqIgVBAEHBAPwLACAEQUBrQdipxAApAwA3AwAgBEE4akHQqcQAKQMANwMAIARBMGpByKnEACkDADcDACAEQgA3A0ggBEHAqcQAKQMANwMoAkAgBkHAAE8EQCAEIAZBBnYiA603A0ggBEEoaiAPIAMQLSAGQT9xIgNFDQEgBSAPIAZBQHFqIAP8CgAADAELIAYEQCAFIA8gBvwKAAALIAYhAwsgBCADOgCQASAEQZgBaiAEQShqQfAA/AoAACAEQcABaiIFIAQtAIACIgNqIgdBgAE6AAAgA60iHUI7hiAEKQO4ASIcQgmGIh4gHUIDhoQiHUKA/gODQiiGhCAdQoCA/AeDQhiGIB1CgICA+A+DQgiGhIQgHEIBhkKAgID4D4MgHEIPiEKAgPwHg4QgHEIfiEKA/gODIB5COIiEhIQhHAJAAkAgA0E/RwRAIANBP3MiCgRAIAdBAWpBACAK/AsACyADQThzQQdLDQELIARBmAFqIgMgBUEBEC0gBEG4AmpCADcDACAEQbACakIANwMAIARBqAJqQgA3AwAgBEGgAmpCADcDACAEQZgCakIANwMAIARBkAJqQgA3AwAgBEIANwOIAiAEIBw3A8ACIAMgBEGIAmpBARAtDAELIAQgHDcD+AEgBEGYAWogBUEBEC0LQdHOxQAtAAAaIAQoArQBIQwgBCgCsAEhECAEKAKsASEJIAQoAqgBIQ0gBCgCpAEhDiAEKAKgASELIAQoApwBIRcgBCgCmAEhGAJAAkACQAJAAkBBAkEBENYEIgMEQCADQYACOwAAIARBAjYCoAEgBCADNgKcASAEQQI2ApgBIARBmAFqIgdBAkHKAUEBQQEQiAMgBCgCoAEiAyAEKAKcAWpB/wFBygH8CwAgBCADQcoBaiIFNgKgASAEKAKYASAFRgRAIAdBgLDEABC2AwsgBCgCnAEgBWpBADoAACAEIANBywFqIgM2AqABIAQoApgBIgcgA2tBEk0EQCAEQZgBaiADQRNBAUEBEIgDIAQoApgBIQcgBCgCoAEhAwsgBCgCnAEiBSADaiIKQZCwxAApAAA3AAAgCkEIakGYsMQAKQAANwAAIApBD2pBn7DEACgAADYAACAEIANBE2oiCjYCoAEgByAKa0EfTQRAIARBmAFqIApBIEEBQQEQiAMgBCgCoAEhCiAEKAKcASEFCyAFIApqIgMgDEEIdkGA/gNxIAxBGHZyIAxBGHQgDEGA/gNxQQh0cnI2ABwgAyAQQQh2QYD+A3EgEEEYdnIgEEEYdCAQQYD+A3FBCHRycjYAGCADIAlBCHZBgP4DcSAJQRh2ciAJQRh0IAlBgP4DcUEIdHJyNgAUIAMgDUEIdkGA/gNxIA1BGHZyIA1BGHQgDUGA/gNxQQh0cnI2ABAgAyAOQQh2QYD+A3EgDkEYdnIgDkEYdCAOQYD+A3FBCHRycjYADCADIAtBCHZBgP4DcSALQRh2ciALQRh0IAtBgP4DcUEIdHJyNgAIIAMgF0EIdkGA/gNxIBdBGHZyIBdBGHQgF0GA/gNxQQh0cnI2AAQgAyAYQQh2QYD+A3EgGEEYdnIgGEEYdCAYQYD+A3FBCHRycjYAACAEIApBIGoiBzYCoAFBACEDIAdBAEgNAUHRzsUALQAAGkEBIQMgB0EBENYEIgxFDQEgBwRAIAwgBSAH/AoAAAsgByAMaiEQQQAhAyAHQQF2IglBAUcEQCAKQR9qIQUgCUH+////A3EhDQNAIAUgDGoiCS0AACEOIAkgAyAMaiIJLQAAOgAAIAkgDjoAACAQIANBfnNqIg4tAAAhCyAOIAlBAWoiCS0AADoAACAJIAs6AAAgBUECayEFIA0gA0ECaiIDRw0ACwsgCkECcQRAIAMgDGoiBS0AACEKIAUgECADQX9zaiIDLQAAOgAAIAMgCjoAAAsgBEEMaiAMIAdBCBDPAiAMIAcQ3wQgBCgCmAEiAwRAIAQoApwBIAMQ3wQLIARBMGogGUEIaigCADYCACAEIBkpAgA3AyggBEGYAWogBEEoaiAEQQxqIBsgGhBQIARBkAJqIgMgBEGkAWooAgA2AgAgBCAEKQKcATcDiAIgBCgCmAFBAUYEQCAVIAQpA4gCNwIEIBVBATYCACAVQQxqIAMoAgA2AgAMBgsgBEEgaiAEQZACaigCADYCACAEIAQpA4gCNwMYIARCgICAgMAANwLMAkEAIQMgBEEANgLUAiAEQaABakGMocQAKAIAIgU2AgAgBEGEocQAKQIAIhw3A5gBIAZBH3AhECAGQR9uIQogBkEeTQRAIARB4AJqIAU2AgAgBCAcNwPYAgwDCyAEQZgBakHoosQAEKUDIAQoApwBIAo2AgAgBEHgAmoiBUEBNgIAIAQgBCkDmAE3A9gCIAQoAtQCIgMgBCgCzAJGDQIgBCgC0AIgA0EMbGoiByAEKQPYAjcCACAHQQhqIAUoAgA2AgAgBCADQQFqNgLUAgwDC0EBQQIQ/wQACyADIAdBrKrEABDIBAALIARBzAJqQaSwxAAQnwMgBCgC0AIgA0EMbGoiBSAEKQPYAjcCACAFQQhqIARB4AJqKAIANgIAIAQgA0EBaiIDNgLUAiAGQR5NDQELIAohB0EAIQUCQANAIAYgBUEfaiIMTwRAQdHOxQAtAAAaQR9BARDWBCIDRQ0CIANBF2oiCSAFIA9qIgVBF2opAAA3AAAgAyAFKQAAIhw3AAAgA0EQaiINIAVBEGopAAA3AAAgA0EIaiIOIAVBCGopAAA3AAAgAyADQR5qIgUtAAA6AAAgBSAcPAAAIAMtAAEhBSADIANBHWoiCy0AADoAASALIAU6AAAgA0EcaiIFLQAAIQsgBSADLQACOgAAIAMgCzoAAiADQRtqIgUtAAAhCyAFIAMtAAM6AAAgAyALOgADIANBGmoiBS0AACELIAUgAy0ABDoAACADIAs6AAQgA0EZaiIFLQAAIQsgBSADLQAFOgAAIAMgCzoABSADQRhqIgUtAAAhCyAFIAMtAAY6AAAgAyALOgAGIAktAAAhBSAJIAMtAAc6AAAgAyAFOgAHIANBFmoiBS0AACEJIAUgDi0AADoAACAOIAk6AAAgA0EVaiIFLQAAIQkgBSADLQAJOgAAIAMgCToACSADQRRqIgUtAAAhCSAFIAMtAAo6AAAgAyAJOgAKIANBE2oiBS0AACEJIAUgAy0ACzoAACADIAk6AAsgA0ESaiIFLQAAIQkgBSADLQAMOgAAIAMgCToADCADQRFqIgUtAAAhCSAFIAMtAA06AAAgAyAJOgANIA0tAAAhBSANIAMtAA46AAAgAyAFOgAOIARB5AJqIANBH0EIEM8CIANBHxDfBCAEKALUAiIDIAQoAswCRgRAIARBzAJqQYSxxAAQnwMLIAQoAtACIANBDGxqIgUgBCkC5AI3AgAgBUEIaiAEQewCaigCADYCACAEIANBAWoiAzYC1AIgDCEFIAdBAWsiBw0BDAMLCyAFQR9qIAZB9LDEABDlBAALQQFBH0GsqsQAEMgEAAsCQCAQRQRAIAQoAswCIANGBEAgBEHMAmpBtLDEABCfAwsgBCgC0AIgA0EMbGoiBUGEocQAKQIAIhw3AgAgBUEIakGMocQAKAIAIgU2AgAgBCADQQFqIgM2AtQCIARBoAFqIAU2AgAgBCAcNwOYAQwBCwJAAkACQCAKQR9sIgUgBk0EQAJAIAUgBkYEQCAEQZACakGMocQAKAIANgIAIARBhKHEACkCADcDiAIMAQtBACEDIAYgBWsiB0EASA0DQdHOxQAtAAAaQQEhAyAHQQEQ1gQiCkUNAyAHBEAgCiAFIA9qIAf8CgAACyAEQYgCaiAKAn9BASAHQQFGDQAaIAcgCmohDEEAIQMgB0EBdiIJQQFHBEAgCUH+////A3EhCSAFQX9zIAZqIQUDQCAFIApqIgYtAAAhDSAGIAMgCmoiBi0AADoAACAGIA06AAAgDCADQX5zaiINLQAAIQ4gDSAGQQFqIgYtAAA6AAAgBiAOOgAAIAVBAmshBSAJIANBAmoiA0cNAAsLIAcgB0ECcUUNABogAyAKaiIFLQAAIQYgBSAMIANBf3NqIgMtAAA6AAAgAyAGOgAAIAcLQQgQzwIgCiAHEN8EIAQoAtQCIQMLIAMgBCgCzAJGDQEMAwsgBSAGQeSwxAAQ5AQACyAEQcwCakHEsMQAEJ8DDAELIAMgB0GsqsQAEMgEAAsgBCgC0AIgA0EMbGoiBSAEKQOIAjcCACAFQQhqIARBkAJqKAIANgIAIAQgA0EBajYC1AIgBEGgAWoiA0GMocQAKAIANgIAIARBhKHEACkCADcDmAEgBEGYAWpB6KLEABClAyAEKAKcASAQNgIAIANBATYCACAEKALUAiEDCyAEQTBqIgUgBEGgAWooAgA2AgAgBCAEKQOYATcDKCAEKALMAiADRgRAIARBzAJqQdSwxAAQnwMLIANBDGwiByAEKALQAmoiAyAEKQMoNwIAIANBCGogBSgCADYCACAEKALMAiEDIAQoAtACIQYgB0EMaiIHQQxuIgogBCgCGCAEKAIgIgVrSwRAIARBGGogBSAKQQRBDBCIAyAEKAIgIQULIAcEQCAEKAIcIAVBDGxqIAYgB/wKAAALIAQgBSAKajYCICADBEAgBiADQQxsEN8ECyAVIAQpAxg3AgQgFUEANgIAIBVBDGogBEEgaigCADYCAAsgBEHwAmokAAJAAkAgCCgCGEEBRgRAIAhBQGsgCEEcaiIDQQhqKAIANgIAIAggAykCADcDOCAZIAhBOGoQ1AMgCCgCSCIFIAgoAkwQzQQhAyAIKAJEIgYEQCAFIAYQ3wQLIAgoAjgiBUUNASAIKAI8IAUQ3wQMAQsgCCgCICEDIAgoAhwiBUGAgICAeEcNAQsgEkGAgICAeDYCACASIAM2AgQgFEUNASAPIBQQ3wQMAQsgCCgCJCEGIAggBTYCMCAIIAM2AiwgCCADNgIoIAggAyAGQQxsajYCNCASIAhBKGoQjwMgFEUNACAPIBQQ3wQLIAhB0ABqJAACQAJAAn8gEygCBCIGQYCAgIB4RgRAQQEhA0EAIQUgEygCCAwBCyATKAIIIQMCQCATKAIMIgUgBk8EQCADIRYMAQsgBkECdCEGIAVFBEBBBCEWIAMgBhDfBAwBCyADIAZBBCAFQQJ0IgMQzgQiFkUNAgtBACEDQQALIQYgESADNgIMIBEgBjYCCCARIAU2AgQgESAWNgIAIBNBEGokAAwBC0EEIANB6PHAABDIBAALIBEoAgAgESgCBCARKAIIIBEoAgwgEUEQaiQAC7MBAQJ/IwBBEGsiACQAIAEoAgBBhKnFAEELIAEoAgQoAgwRAwAhAyAAQQhqIgJBADoABSACIAM6AAQgAiABNgIAIAIiAS0ABCECIAEtAAUEQCABAn9BASACQQFxDQAaIAEoAgAiAS0ACkGAAXFFBEAgASgCAEHzt8UAQQIgASgCBCgCDBEDAAwBCyABKAIAQfK3xQBBASABKAIEKAIMEQMACyICOgAECyACQQFxIABBEGokAAv7rwECIn8QfiMAQRBrIhwkABCtAyIDIAAmARCtAyIEIAEmARCtAyIeIAImASMAQRBrIiAkACAgQQRqIREjAEHwBWsiByQAIAcgAzYCkAQCQAJAAkACQAJAAkAgB0GQBGoQ4QRFBEBBhPPAAEEZEM0EIQYgA0GEAU8EQCADEKsDCyARQYCAgIB4NgIAIBEgBjYCBCAeQYQBTw0BDAQLIAcgAzYCiAEgB0Gd88AAQQEQzQQiAzYCkAQgB0GAAWogB0GIAWogB0GQBGoQgAQgBygChAEhCSAHKAKAASADQYQBTwRAIAMQqwMLQQFxBEAgEUGAgICAeDYCACARIAk2AgQgBygCiAEiA0GEAU8EQCADEKsDCyAeQYQBSQ0EDAELIAdBkARqIAkQxwIgBygClAQhCwJAIAcoApAEIhNBgICAgHhGBEAgEUGAgICAeDYCACARIAs2AgQMAQsgBygCpAQhGSAHKAKgBCEaIAcoApwEIQ0gBygCmAQhGyAHQZ7zwABBARDNBCIDNgLIASAHQfgAaiAHQYgBaiAHQcgBahCABCAHKAJ8IQkgBygCeCEMIANBhAFPBEAgAxCrAwsCQCAMQQFxBEAgEUGAgICAeDYCACARIAk2AgQMAQsgB0GQBGogCRDyASAHKAKUBCESIAcoApAEIhhBgICAgHhGBEAgEUGAgICAeDYCACARIBI2AgQMAQsgBygCvAQhHyAHKAK4BCEUIAcoArQEIRcgBygCsAQhISAHKAKsBCEWIAcoAqgEIRUgBygCpAQhIiAHKAKgBCEdIAcoApwEIQ4gBygCmAQhIyAHQZSiwABBARDNBCIDNgLIASAHQfAAaiAHQYgBaiAHQcgBahCABCAHKAJ0IQkgBygCcCEMIANBhAFPBEAgAxCrAwsCQCAMQQFxBEAgEUGAgICAeDYCACARIAk2AgQMAQsgB0GQBGogCRDHAiAHKAKUBCEDIAcoApAEIglBgICAgHhGBEAgEUGAgICAeDYCACARIAM2AgQMAQsgB0GcAWogB0GgBGopAgA3AgAgByAHKQKYBDcClAEgByADNgKQASAHIAk2AowBIAdB6ABqIAdBiAFqQZ/zwABBDBDqAyAHKAJsIQMCQCAHKAJoQQFxBEAgEUGAgICAeDYCACARIAM2AgQMAQsgB0GQBGohDyMAQTBrIgwkACAMIAM2AiACQCAMQSBqEOAERQRAQcfwwABBHRDNBCEJIANBhAFPBEAgAxCrAwsgD0GAgICAeDYCACAPIAk2AgQMAQsgDCADNgIIIAxBIGoiAyAMQQhqIgkoAgAQhgU2AgggA0EANgIEIAMgCTYCACAMQQA2AgwgDCAMQQxqNgIsIAxBFGohCCMAQUBqIgkkACADKAIMIQoCQANAIAlBCGogAxD8AyAJKAIMIQUCQAJAIAkoAggiEEEBcQRAIAlBIGogBRDsAiAJKQIkISUgCSgCICIFQYCAgIB4Rw0CICWnIQMCQCAKKAIARQ0AIAooAgQiBUGEAUkNACAFEKsDCyAKIAM2AgQgCkEBNgIADAELIBBFIAVBhAFJcg0AIAUQqwMLIAhBADYCCCAIQoCAgIDAADcCAAwCCyAFQYGAgIB4Rg0AC0HRzsUALQAAGkEwQQQQ1gQiCgRAIAogJTcCBCAKIAU2AgAgCUEBNgIcIAkgCjYCGCAJQQQ2AhQgCUEoaiADQQhqKQIANwMAIAkgAykCADcDIEEBIQMDQCAJKAIsIQUDQCAJIAlBIGoQ/AMgCSgCBCEQAkACQCAJKAIAIiRBAXEEQCAJQTRqIBAQ7AIgCSkCOCElIAkoAjQiEEGAgICAeEcNAiAlpyEDAkAgBSgCAEUNACAFKAIEIgpBhAFJDQAgChCrAwsgBSADNgIEIAVBATYCAAwBCyAkRSAQQYQBSXINACAQEKsDCyAIIAkpAhQ3AgAgCEEIaiAJQRxqKAIANgIADAQLIBBBgYCAgHhGDQALIAkoAhQgA0YEQCAJQRRqIANBAUEEQQwQiAMgCSgCGCEKCyAKIANBDGxqIgUgJTcCBCAFIBA2AgAgCSADQQFqIgM2AhwMAAsAC0EEQTBBkJbCABDIBAALIAlBQGskAAJAIAwoAgxBAUYEQCAPIAwoAhA2AgQgD0GAgICAeDYCACAMKAIYIQkgDCgCHCIPBEAgCSEDA0AgAygCACIKBEAgA0EEaigCACAKQQJ0EN8ECyADQQxqIQMgD0EBayIPDQALCyAMKAIUIgNFDQEgCSADQQxsEN8EDAELIA8gDCkCFDcCACAPQQhqIAxBHGooAgA2AgALIAwoAggiA0GEAUkNACADEKsDCyAMQTBqJAAgBygClAQhDyAHKAKQBCIIQYCAgIB4RgRAIBFBgICAgHg2AgAgESAPNgIEDAELIAcgBygCmAQ2AqwBIAcgDzYCqAEgByAINgKkASAHQeAAaiAHQYgBakGr88AAQRMQ6gMgBygCZCEDAkACQCAHKAJgQQFxRQRAAkAgAxCEBUEBRg0AIAMQhQVBAUYNACAHIAM2ApAEIAdBkARqEOEERQRAQb7zwABBJBDNBCEGIANBhAFPBEAgAxCrAwsgEUGAgICAeDYCACARIAY2AgQMBAsgByADNgLgAyAHQdgAaiAHQeADakHi88AAQQcQ6gMgBygCXCEJAkACQAJAAkAgBygCWEEBcQRAIAkhAwwBCyAHIAk2ApAEIAdBkARqIgMQ4gQEQCAHIAk2AsgBIAMgB0HIAWoQugMgBygCyAEiA0GEAU8EQCADEKsDCyAHKAKUBCEJIAcoApAEIgxBgICAgHhHDQILQenzwABBGxDNBCEDIAlBhAFJDQAgCRCrAwsgEUGAgICAeDYCACARIAM2AgQMAQsgBygCmAQhAyAHQdAAaiAHQeADakGE9MAAQQcQ6gMgBygCVCEGAkAgBygCUEEBcQRAIAYhAwwBCyAHIAY2ApAEIAdBkARqIgoQ4gQEQCAHIAY2AsgBIAogB0HIAWoQugMgBygCyAEiBkGEAU8EQCAGEKsDCyAHKAKUBCEGIAcoApAEIgpBgICAgHhHDQMLQYv0wABBGxDNBCEDIAZBhAFJDQAgBhCrAwsgEUGAgICAeDYCACARIAM2AgQgDEUNACAJIAwQ3wQLIAcoAuADIgNBhAFJDQQgAxCrAwwECyAHIAcoApgENgLEASAHIAY2AsABIAcgCjYCvAEgByADNgK4ASAHIAk2ArQBIAcgDDYCsAEgBygC4AMiA0GEAUkNAiADEKsDDAILCyAHQYCAgIB4NgKwASADQYQBSQ0AIAMQqwMLIAdByABqIAdBiAFqQab0wABBExDqAyAHKAJMIQkCQCAHKAJIQQFxRQRAAkAgCRCEBUEBRwRAIAkQhQVBAUcNAQtBgICAgHghCiAJQYQBSQ0KDAkLIAcgCTYCkAQgB0GQBGoQ4QRFBEBBufTAAEEkEM0EIQMgCUGEAU8EQCAJEKsDCyARQYCAgIB4NgIAIBEgAzYCBAwCCyAHIAk2AuADIAdBQGsgB0HgA2pB3fTAAEEEEOoDIAcoAkQhDAJAAkACQAJAIAcoAkBBAXEEQCAMIQMMAQsgByAMNgKQBCAHQZAEaiIDEOIEBEAgByAMNgLIASADIAdByAFqELoDIAcoAsgBIgNBhAFPBEAgAxCrAwsgBykClAQiJqchDCAHKAKQBCIKQYCAgIB4Rw0CC0Hh9MAAQRgQzQQhAyAMQYQBSQ0AIAwQqwMLIBFBgICAgHg2AgAgESADNgIEDAELIAdBOGogB0HgA2pB+fTAAEEMEOoDIAcoAjwhCQJAIAcoAjhBAXEEQCAJIQMMAQsgByAJNgKQBCAHQZAEaiIDEOIEBEAgByAJNgLIASADIAdByAFqELoDIAcoAsgBIgNBhAFPBEAgAxCrAwsgBygClAQhCSAHKAKQBCIGQYCAgIB4Rw0DC0GF9cAAQSAQzQQhAyAJQYQBSQ0AIAkQqwMLIBFBgICAgHg2AgAgESADNgIEIApFDQAgDCAKEN8ECyAHKALgAyIDQYQBSQ0CIAMQqwMMAgsgBygCmAQhDyAHKALgAyIDQYQBSQ0JIAMQqwMMCQtBgICAgHghCiAJQYQBTw0HDAgLAkAgB0GwAWoiAygCACIGQYCAgIB4Rg0AIAYEQCADKAIEIAYQ3wQLIAMoAgwiBkUNACADKAIQIAYQ3wQLCyAHQaQBahDzAyAIRQ0AIA8gCEEMbBDfBAsgB0GMAWoQggQLIBgEQCASIBhBAnQQ3wQLIA4EQCAdIA5BAnQQ3wQLIBUEQCAWIBVBAnQQ3wQLIBdFDQAgFCAXQQJ0EN8ECyATBEAgCyATQQJ0EN8ECyANRQ0AIBogDUECdBDfBAsgBygCiAEiA0GEAU8EQCADEKsDCyAeQYQBSQ0DCyAeEKsDDAILIAkQqwMLIAcgHzYCjAIgByAUNgKIAiAHIBc2AoQCIAcgITYCgAIgByAWNgL8ASAHIBU2AvgBIAcgIjYC9AEgByAdNgLwASAHIA42AuwBIAcgIzYC6AEgByASNgLkASAHIBg2AuABIAcgGTYC3AEgByAaNgLYASAHIA02AtQBIAcgGzYC0AEgByALNgLMASAHIBM2AsgBIAdBmAJqIAdBlAFqKQIANwIAIAdBoAJqIAdBnAFqKQIANwIAIAdBsAJqIAdBrAFqKAIANgIAIAdBvAJqIAdBuAFqKQIANwIAIAdBxAJqIAdBwAFqKQIANwIAIAcgCjYCzAIgByAmNwLQAiAHIAY2AtgCIAcgCTYC3AIgByAPNgLgAiAHIAcpAowBNwKQAiAHIAcpAqQBNwKoAiAHIAcpArABNwK0AiAHIAQ2ApAEAkAgB0GQBGoQ4QRFBEBBpfXAAEEWEM0EIQMgBEGEAU8EQCAEEKsDCyARQYCAgIB4NgIAIBEgAzYCBAwBCyAHIAQ2AuQCIAdBMGogB0HkAmpBu/XAAEEFEOoDIAcoAjQhAwJAAkAgBygCMEEBcQRAIBFBgICAgHg2AgAgESADNgIEDAELIAdBkARqIAMQxwIgBygClAQhAyAHKAKQBCIEQYCAgIB4RgRAIBFBgICAgHg2AgAgESADNgIEDAELIAdB+AJqIAdBoARqKQIANwIAIAcgBykCmAQ3AvACIAcgAzYC7AIgByAENgLoAiAHQShqIAdB5AJqQcD1wABBBBDqAyAHKAIsIQMCQAJAIAcoAihBAXEEQCARQYCAgIB4NgIAIBEgAzYCBAwBCyAHQZAEaiADEPIBIAcoApQEIQMgBygCkAQiBEGAgICAeEYEQCARQYCAgIB4NgIAIBEgAzYCBAwBCyAHQagDaiAHQbgEaikCADcCACAHQaADaiAHQbAEaikCADcCACAHQZgDaiAHQagEaikCADcCACAHQZADaiAHQaAEaikCADcCACAHIAcpApgENwKIAyAHIAM2AoQDIAcgBDYCgAMgB0EgaiAHQeQCakHE9cAAQQUQ6gMgBygCJCEDAkAgBygCIEEBcQRAIBFBgICAgHg2AgAgESADNgIEDAELIAdBkARqIAMQ8gEgBygClAQhAyAHKAKQBCIEQYCAgIB4RgRAIBFBgICAgHg2AgAgESADNgIEDAELIAdB2ANqIAdBuARqKQIANwIAIAdB0ANqIAdBsARqKQIANwIAIAdByANqIAdBqARqKQIANwIAIAdBwANqIAdBoARqKQIANwIAIAcgBykCmAQ3ArgDIAcgAzYCtAMgByAENgKwAyAHQRhqIAdB5AJqQcn1wABBBRDqAyAHKAIcIQMCQCAHKAIYQQFxBEAgEUGAgICAeDYCACARIAM2AgQMAQsgB0GQBGogAxDyASAHKAKUBCEDIAcoApAEIgRBgICAgHhGBEAgEUGAgICAeDYCACARIAM2AgQMAQsgB0GIBGogB0G4BGopAgA3AgAgB0GABGogB0GwBGopAgA3AgAgB0H4A2ogB0GoBGopAgA3AgAgB0HwA2ogB0GgBGopAgA3AgAgByAHKQKYBDcC6AMgByADNgLkAyAHIAQ2AuADIAdBEGogB0HkAmpBzvXAAEECEOoDIAcoAhQhAyAHKAIQQQFxRQRAIAdBkARqIQlBACEGIwBBQGoiBCQAIAQgAzYCGAJAIARBGGoQ4ARFBEBB9PDAAEESEM0EIQYgA0GEAU8EQCADEKsDCyAJQYCAgIB4NgIAIAkgBjYCBAwBCyAEIAM2AgggBEEANgIUIARCgICAgMAANwIMIARBCGooAgAQhgUiCARAIARBIGohDANAIARBGGogBEEIaiAGEPcEEMcCIAQoAhwhCiAEKAIYIgVBgICAgHhGBEAgCUGAgICAeDYCACAJIAo2AgQgBCgCFCIGBEAgBCgCECEDA0AgAygCACIJBEAgA0EEaigCACAJQQJ0EN8ECyADQQxqKAIAIgkEQCADQRBqKAIAIAlBAnQQ3wQLIANBGGohAyAGQQFrIgYNAAsLIAQoAgwiAwRAIAQoAhAgA0EYbBDfBAsgBCgCCCIDQYQBSQ0DIAMQqwMMAwsgBEE4aiILIAxBCGopAgA3AwAgBCAMKQIANwMwIAQoAhQiDyAEKAIMRgRAIARBDGpB5PDAABCZAwsgBCgCECAPQRhsaiIDIAo2AgQgAyAFNgIAIAMgBCkDMDcCCCADQRBqIAspAwA3AgAgBCAPQQFqNgIUIAggBkEBaiIGRw0ACyAEKAIIIQMLIAkgBCkCDDcCACAJQQhqIARBFGooAgA2AgAgA0GEAUkNACADEKsDCyAEQUBrJAAgBygClAQhAyAHKAKQBCIEQYCAgIB4Rw0ECyARQYCAgIB4NgIAIBEgAzYCBCAHQeADahDWAwsgB0GwA2oQ1gMLIAdBgANqENYDCyAHQegCahCCBAwBCyAHKAKYBCEGIAdBoARqIAdB+AJqKQIANwMAIAdBmARqIAdB8AJqKQIANwMAIAdBsARqIAdBiANqKQIANwMAIAdBuARqIAdBkANqKQIANwMAIAdBwARqIAdBmANqKQIANwMAIAdByARqIAdBoANqKQIANwMAIAdB0ARqIAdBqANqKQIANwMAIAcgBykC6AI3A5AEIAcgBykCgAM3A6gEIAdBgAVqIAdB2ANqKQIANwMAIAdB+ARqIAdB0ANqKQIANwMAIAdB8ARqIAdByANqKQIANwMAIAdB6ARqIAdBwANqKQIANwMAIAdB4ARqIAdBuANqKQIANwMAIAdBkAVqIAdB6ANqKQIANwMAIAdBmAVqIAdB8ANqKQIANwMAIAdBoAVqIAdB+ANqKQIANwMAIAdBqAVqIAdBgARqKQIANwMAIAdBsAVqIAdBiARqKQIANwMAIAcgBykCsAM3A9gEIAcgBykC4AM3A4gFIAcgBjYCwAUgByADNgK8BSAHIAQ2ArgFIAcgHiUBEAYCQCAHKAIARQRAQdD1wABBGxDNBCEDDAELIAdBxAVqIQMgBysDCPwDIQYjAEEwayIEJAAgBCAGNgIMAkACQAJAAkACQAJAAkACQCAGDgYBAgMEBQYACyAEQQE2AhQgBEHImsEANgIQIARCATcCHCAEIARBDGqtQoCAgIDgAYQ3AyggBCAEQShqNgIYIAMgBEEQahDSAgwGCyADQYCAgIB4NgIAIANBADoABAwFCyADQYCAgIB4NgIAIANBAToABAwECyADQYCAgIB4NgIAIANBAjoABAwDCyADQYCAgIB4NgIAIANBAzoABAwCCyADQYCAgIB4NgIAIANBBDoABAwBCyADQYCAgIB4NgIAIANBBToABAsgBEEwaiQAIAcoAsQFIgRBgICAgHhHBEAgBygCyAUiBiAHKALMBRDNBCEDIARFDQEgBiAEEN8EDAELIAdB0AVqIRggBy0AyAUhEEEAIQxBACENQQAhCSMAQcADayIFJAAgBUEANgIIIAVCgICAgMAANwIAIAdByAFqIhMoAmwhHSAHQZAEaiIXKAKwASELIBcoAqwBIQggEygCaCEOIBMoAmQhCgJAAkACfwJAAn8CQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQCAQDgIBAgALIAVBADYC6AIgBUEBNgLcAiAFQaTuwAA2AtgCIAVCBDcC4AIgBUHYAmpBrO7AABCoBAALIAVBADYCYCAFQQA2AlAgBSAINgJwIAUgCCALQRhsajYCdCAFQfABaiAFQdAAahDDASAFKAL4ASIEQQV0IQMgBEH///8/SyADQfj///8HS3INAiAFKAL0ASEPAn8gA0UEQEEIIQZBAAwBC0HRzsUALQAAGkEIIQwgA0EIENYEIgZFDQMgBAshFCAEBEAgDyEJIAYhAyAEIQwDQCAFQdgCaiAJEPcCIANBGGogBUHwAmopAwA3AwAgA0EQaiAFQegCaikDADcDACADQQhqIAVB4AJqKQMANwMAIAMgBSkD2AI3AwAgA0EgaiEDIAlBDGohCSAMQQFrIgwNAAsgDyEDIAQhCQNAIAMoAgAiDARAIANBBGooAgAgDEECdBDfBAsgA0EMaiEDIAlBAWsiCQ0ACyAEIQkLIAUoAvABIgMEQCAPIANBDGwQ3wQLIAVBgICAgHg2AnggBUECNgLgAiAFIAk2AtwCIAUgBjYC2AIgBSAFQfgAajYC5AIgBUHwAWogBUHYAmoQjwEgBSgCeCIDQYCAgIB4RwRAIAUoAoABIQQgBSgCfCEGIAUoAvABIgkEQCAFKAL0ASAJQcgAbBDfBAsMGwsgBSgC+AEiGkUNAyAFKALwASEWIAVBkAFqIAUoAvQBIgxBGGopAwA3AwAgBUGIAWogDEEQaikDADcDACAFQYABaiAMQQhqKQMANwMAIAwpAwAhJSAFQaABaiAMQShqKQMANwMAIAVBqAFqIAxBMGopAwA3AwAgBUGwAWogDEE4aikDADcDACAFICU3A3ggDCkDICElIAUgDC0AQDoAuAEgBSAlNwOYASAOBEAgCiAOQQxsaiEZIAxByABqIQ8gGkEBayEbIApBDGohAyAOQQFrQf////8DcUEBaiEfIAohBANAIAQoAggiFUECdCESIBVB/////wNLIBJB/P///wdLcg0aIAMhCSAEKAIEIQMCfyASRQRAQQQhBEEADAELQdHOxQAtAAAaQQQgEkEEENYEIgRFDRwaIBULISEgEgRAIAQgAyAS/AoAAAsgBSAENgLkASAFICE2AuABIAUgFTYC6AEgBUECQQEgFRs6AOwBIA0gG0YNBiAFQfABaiIDIA8gBUHgAWoQqAEgBUHYAmoiBCAFQfgAaiISIAMQNiASIARByAD8CgAAQQxBACAJIBlHGyAJaiEDIA9ByABqIQ8gCSEEIB8gDUEBaiINRw0ACwsgBUEMaiAFQfgAahDaAiAFQRhqIAVBmAFqENoCIBYEQCAMIBZByABsEN8ECyAURQ0BIAYgFEEFdBDfBAwBCyAFQQA2AmAgBUEANgJQIAUgCDYCcCAFIAggC0EYbGo2AnQgBUHwAWogBUHQAGoQwwEgBSgC+AEiBK1CMH4iJachAyAlQiCIpyADQfj///8HS3INBCAFKAL0ASEPAn8gA0UEQEEIIQZBAAwBC0HRzsUALQAAGkEIIQkgA0EIENYEIgZFDQUgBAshFCAEBEAgDyEJIAYhAyAEIQwDQCAFQdgCaiAJEPYCIANBKGogBUGAA2opAwA3AwAgA0EgaiAFQfgCaikDADcDACADQRhqIAVB8AJqKQMANwMAIANBEGogBUHoAmopAwA3AwAgA0EIaiAFQeACaikDADcDACADIAUpA9gCNwMAIANBMGohAyAJQQxqIQkgDEEBayIMDQALIA8hAyAEIQkDQCADKAIAIgwEQCADQQRqKAIAIAxBAnQQ3wQLIANBDGohAyAJQQFrIgkNAAsgBCEMCyAFKALwASIDBEAgDyADQQxsEN8ECyAFQYCAgIB4NgJ4IAVBAjYC4AIgBSAMNgLcAiAFIAY2AtgCIAUgBUH4AGo2AuQCIAVB8AFqIAVB2AJqEI8CIAUoAngiA0GAgICAeEcEQCAFKAKAASEEIAUoAnwhBiAFKALwASIJBEAgBSgC9AEgCUHoAGwQ3wQLDBoLIAUoAvgBIhpFDQUgBSgC8AEhFiAFQaABaiAFKAL0ASIMQShqKQMANwMAIAVBmAFqIAxBIGopAwA3AwAgBUGQAWogDEEYaikDADcDACAFQYgBaiAMQRBqKQMANwMAIAVBgAFqIAxBCGopAwA3AwAgDCkDACElIAVBsAFqIAxBOGopAwA3AwAgBUG4AWogDEFAaykDADcDACAFQcABaiAMQcgAaikDADcDACAFQcgBaiAMQdAAaikDADcDACAFQdABaiAMQdgAaikDADcDACAFICU3A3ggBSAMKQMwNwOoASAFIAwtAGA6ANgBIA4EQCAKIA5BDGxqIRkgDEHoAGohDyAaQQFrIRsgCkEMaiEDIA5BAWtB/////wNxQQFqIR8gCiEEA0AgBCgCCCIVQQJ0IRIgFUH/////A0sgEkH8////B0tyDRcgAyEJIAQoAgQhAwJ/IBJFBEBBBCEEQQAMAQtB0c7FAC0AABpBBCASQQQQ1gQiBEUNGRogFQshISASBEAgBCADIBL8CgAACyAFIAQ2AuQBIAUgITYC4AEgBSAVNgLoASAFQQJBASAVGzoA7AEgDSAbRg0IIAVB8AFqIgMgDyAFQeABahCnASAFQdgCaiIEIAVB+ABqIhIgAxAnIBIgBEHoAPwKAABBDEEAIAkgGUcbIAlqIQMgD0HoAGohDyAJIQQgHyANQQFqIg1HDQALCyAFQQxqIAVB+ABqENgCIAVBGGogBUGoAWoQ2AIgFgRAIAwgFkHoAGwQ3wQLIBRFDQAgBiAUQTBsEN8EC0EAIQwgBUEANgLoASAFQoCAgIDAADcC4AEgBUHYAmogBUEMahD9AiAFKALgAiIDQQxsIQQgBSgC3AIhBiAFKALYAiEJIAMEfyAFQeABakEAIANBBEEMEIgDIAUoAugBIQwgBSgC5AEFQQQLIQ8gBARAIA8gDEEMbGogBiAE/AoAAAsgBSADIAxqIgM2AugBIAkEQCAGIAlBDGwQ3wQLIAVB2AJqIBdByABqEKgCIAUoAuACIgRBDGwhBiAFKALcAiEJIAUoAtgCIQwgBSgC4AEgA2sgBEkEQCAFQeABaiADIARBBEEMEIgDIAUoAuQBIQ8gBSgC6AEhAwsgBgRAIA8gA0EMbGogCSAG/AoAAAsgBSADIARqIgM2AugBIAwEQCAJIAxBDGwQ3wQLIAVB2AJqIBNByABqEP0CIAUoAuACIgZBDGwhCSAFKALcAiEMIAUoAtgCIQ8gBSgC4AEgA2sgBkkEQCAFQeABaiADIAZBBEEMEIgDIAUoAugBIQMLIAUoAuQBIQQgCQRAIAQgA0EMbGogDCAJ/AoAAAsgBSADIAZqIgM2AugBIA8EQCAMIA9BDGwQ3wQLIAVB2AJqIBdB+ABqEKgCIAUoAuACIgZBDGwhCSAFKALcAiEMIAUoAtgCIQ8gBSgC4AEgA2sgBkkEQCAFQeABaiADIAZBBEEMEIgDIAUoAuQBIQQgBSgC6AEhAwsgCQRAIAQgA0EMbGogDCAJ/AoAAAsgBSADIAZqIgM2AugBIA8EQCAMIA9BDGwQ3wQLIAVB2AJqIQ0jAEEgayIGJAAgBkEIaiEJAkACQAJAAkACQAJAAkAgEEEBaw4FAQIDBAUACyAJQZibwQBBwgAQlQMMBQsgCUHam8EAQeIAEJUDDAQLIAlBvJzBAEHCABCVAwwDCyAJQf6cwQBBwgAQlQMMAgsgCUHAncEAQcIAEJUDDAELIAlBgp7BAEHCABCVAwsgEygCCCISQQJ0IQlBACEPAkACQAJAIBJB/////wNLIAlB/P///wdLcg0AIBMoAgQhFQJ/IAlFBEBBBCEMQQAMAQtB0c7FAC0AABpBBCEPIAlBBBDWBCIMRQ0BIBILIQ8gCQRAIAwgFSAJ/AoAAAsgDSASNgIIIA0gDDYCBCANIA82AgAgBigCECISQQJ0IQlBACEPIBJB/////wNLIAlB/P///wdLcg0BIAYoAgwhFQJ/IAlFBEBBBCEMQQAMAQtB0c7FAC0AABpBBCEPIAlBBBDWBCIMRQ0CIBILIQ8gCQRAIAwgFSAJ/AoAAAsgBiASNgIcIAYgDDYCGCAGIA82AhQgDUEMaiAGQRRqIBNBDGoQhwIgBigCCCIJBEAgFSAJQQJ0EN8ECyAGQSBqJAAMAgsgDyAJQfiBwAAQyAQACyAPIAlB+IHAABDIBAALIAVB8AFqIA0Q/QIgBSgC+AEiBkEMbCEJIAUoAvQBIQwgBSgC8AEhDyAFKALgASADayAGSQRAIAVB4AFqIAMgBkEEQQwQiAMgBSgC5AEhBCAFKALoASEDCyAJBEAgBCADQQxsaiAMIAn8CgAACyAFIAMgBmoiAzYC6AEgDwRAIAwgD0EMbBDfBAsgBSgC2AIiBARAIAUoAtwCIARBAnQQ3wQLIAUoAuQCIgQEQCAFKALoAiAEQQJ0EN8ECyAFQdgCaiATQRhqEKgCIAUoAuACIgRBDGwhBiAFKALcAiEJIAUoAtgCIQwgBSgC4AEgA2sgBEkEQCAFQeABaiADIARBBEEMEIgDIAUoAugBIQMLIAUoAuQBIQ8gBgRAIA8gA0EMbGogCSAG/AoAAAsgBSADIARqIhU2AugBIAwEQCAJIAxBDGwQ3wQLQQAhBCAFQQA2AlggBUKAgICAwAA3AlAgBUHYAmogFxD9AiAFKALgAiIDQQxsIQYgBSgC3AIhCSAFKALYAiENIAMEfyAFQdAAakEAIANBBEEMEIgDIAUoAlghBCAFKAJUBUEECyEMIAYEQCAMIARBDGxqIAkgBvwKAAALIAUgAyAEaiIDNgJYIA0EQCAJIA1BDGwQ3wQLIAVB2AJqIBdBGGoQqAIgBSgC4AIiBEEMbCEGIAUoAtwCIQ0gBSgC2AIhEiAFKAJQIANrIARJBEAgBUHQAGogAyAEQQRBDBCIAyAFKAJUIQwgBSgCWCEDCyAGBEAgDCADQQxsaiANIAb8CgAACyAFIAMgBGoiCTYCWCASBEAgDSASQQxsEN8ECyAFQdgCaiAQIA8gFUECIAwgCRCEAiAFKALkAiEMIAUoAuACIQ8gBSgC3AIhGiAFKALYAkEBRgRAIBggDDYCDCAYIA82AgggGCAaNgIEIBhBATYCAAwTCwJAIB1BgICAgHhGBEAgBUEBNgJMIAVBADYCNCAFQQA2AiQgBSAINgJEIAUgCCALQRhsajYCSCAFQfABaiENQQAhBkEAIRIjAEHgAGsiCyQAIAtBFGogBUEkaiIIEPgBAkACQAJAIAsoAhRBgICAgHhHBEAgCCgCAARAIAgoAgwgCCgCBGtBDG4hBgsgCCgCEAR/IAgoAhwgCCgCFGtBDG4FQQALIAZqIQQCfwJAIAgoAiAiA0UNACAIKAIoIAgoAiQgA2tBGG5PDQAgC0EgaiEDQQAMAQsgC0HMAGohAyAECyEGIAMgBjYCAEEDIAQgBEEDTRtBAWoiBq1CDH4iJachBCAlQiCIpyAEQfz///8HS3INAQJAIARFBEBBBCEDQQAhBgwBC0HRzsUALQAAGkEEIRIgBEEEENYEIgNFDQILIAMgCykCFDcCACADQQhqIAtBHGooAgA2AgAgC0EBNgIQIAsgAzYCDCALIAY2AgggC0HIAGogCEEoaigCADYCACALQUBrIAhBIGopAgA3AwAgC0E4aiAIQRhqKQIANwMAIAtBMGogCEEQaikCADcDACALQShqIAhBCGopAgA3AwAgCyAIKQIANwMgIAtBzABqIAtBIGoQ+AEgCygCTEGAgICAeEYNAkEMIQZBASEEA0AgCygCCCAERgRAQQAhAyALKAIgBEAgCygCLCALKAIka0EMbiEDCyALKAIwBH8gCygCPCALKAI0a0EMbgVBAAsgA2ohCAJ/AkAgCygCQCIDRQ0AIAsoAkggCygCRCADa0EYbk8NAEEAIQMgC0HcAGoMAQsgCCEDIAtB2ABqCyADNgIAIAtBCGogBCAIQQFqQQRBDBCIAyALKAIMIQMLIAMgBmoiCCALKQJMNwIAIAhBCGogC0HUAGooAgA2AgAgCyAEQQFqIgQ2AhAgBkEMaiEGIAtBzABqIAtBIGoQ+AEgCygCTEGAgICAeEcNAAsMAgsgDUEANgIIIA1CgICAgMAANwIAAkAgCCgCACIDRQ0AIAgoAgwiDSAIKAIEIgRrQQxuIQYgBCANRwRAA0AgBCgCACINBEAgBEEEaigCACANQQJ0EN8ECyAEQQxqIQQgBkEBayIGDQALCyAIKAIIIgRFDQAgAyAEQQxsEN8ECyAIKAIQIgNFDQIgCCgCHCINIAgoAhQiBGtBDG4hBiAEIA1HBEADQCAEKAIAIg0EQCAEQQRqKAIAIA1BAnQQ3wQLIARBDGohBCAGQQFrIgYNAAsLIAgoAhgiBEUNAiADIARBDGwQ3wQMAgsgEiAEQaStwAAQyAQACwJAIAsoAiAiA0UNACALKAIsIgggCygCJCIEa0EMbiEGIAQgCEcEQANAIAQoAgAiCARAIARBBGooAgAgCEECdBDfBAsgBEEMaiEEIAZBAWsiBg0ACwsgCygCKCIERQ0AIAMgBEEMbBDfBAsCQCALKAIwIgNFDQAgCygCPCIIIAsoAjQiBGtBDG4hBiAEIAhHBEADQCAEKAIAIggEQCAEQQRqKAIAIAhBAnQQ3wQLIARBDGohBCAGQQFrIgYNAAsLIAsoAjgiBEUNACADIARBDGwQ3wQLIA0gCykCCDcCACANQQhqIAtBEGooAgA2AgALIAtB4ABqJAAgBUHYAmogBSgC9AEiBiAFKAL4ASIDIAogDiAQQQBBARAcIAUoAuQCIRcgBSgC4AIhEiAFKALcAiEVIAUoAtgCBEAgGCAXNgIMIBggEjYCCCAYIBU2AgQgGEEBNgIAIAMEQCAGIQQDQCAEKAIAIgoEQCAEQQRqKAIAIApBAnQQ3wQLIARBDGohBCADQQFrIgMNAAsLIAUoAvABIgNFDRQgBiADQQxsEN8EDBQLIAMEQCAGIQQDQCAEKAIAIgoEQCAEQQRqKAIAIApBAnQQ3wQLIARBDGohBCADQQFrIgMNAAsLIAUoAvABIgNFDQEgBiADQQxsEN8EDAELIAtBA00NByAIKAJQIg1BAnQhA0EAIRcgDUH/////A0sgA0H8////B0tyDQggCCgCTCEEAn8gA0UEQEEEIRJBAAwBC0HRzsUALQAAGkEEIRcgA0EEENYEIhJFDQkgDQshFCADBEAgEiAEIAP8CgAACyAIKAJcIhdBAnQhA0EAIRUgF0H/////A0sgA0H8////B0tyDQkgCCgCWCEEAn8gA0UEQEEEIQZBAAwBC0HRzsUALQAAGkEEIRUgA0EEENYEIgZFDQogFwshFiADBEAgBiAEIAP8CgAACyALQQRGDQogCCgCaCIVQQJ0IQtBACEEIBVB/////wNLIAtB/P///wdLcg0LIAgoAmQhHQJ/IAtFBEBBBCEDQQAMAQtB0c7FAC0AABpBBCEEIAtBBBDWBCIDRQ0MIBULIQQgCwRAIAMgHSAL/AoAAAsgBSAVNgL4AiAFIAM2AvQCIAUgBDYC8AIgCCgCdCIVQQJ0IQtBACEEIBVB/////wNLIAtB/P///wdLcg0MIAgoAnAhCAJ/IAtFBEBBBCEDQQAMAQtB0c7FAC0AABpBBCEEIAtBBBDWBCIDRQ0NIBULIQQgCwRAIAMgCCAL/AoAAAsgBSAVNgKEAyAFIAM2AoADIAUgBDYC/AIgBSAXNgLsAiAFIAY2AugCIAUgFjYC5AIgBSANNgLgAiAFIBI2AtwCIAUgFDYC2AIgDkEDSQ0OIAooAiAiBkECdCEDQQAhFyAGQf////8DSyADQfz///8HS3INDSAKKAIcIQQCfyADRQRAQQQhFUEADAELQdHOxQAtAAAaQQQhFyADQQQQ1gQiFUUNDiAGCyELIAMEQCAVIAQgA/wKAAALIA5BA0YNECAKKAIsIghBAnQhBEEAIQMgCEH/////A0sgBEH8////B0tyDQ8gCigCKCEKAn8gBEUEQEEEIRJBAAwBC0HRzsUALQAAGkEEIQMgBEEEENYEIhJFDRAgCAshAyAEBEAgEiAKIAT8CgAACyAFIAg2AoQCIAUgEjYCgAIgBSADNgL8ASAFIAY2AvgBIAUgFTYC9AEgBSALNgLwASAFQfgAaiAFQdgCakEEIAVB8AFqQQIgEEEAQQEQHCAFKAKEASEXIAUoAoABIRIgBSgCfCEVIAUoAngEQCAYIBc2AgwgGCASNgIIIBggFTYCBCAYQQE2AgAgBSgC8AEiAwRAIAUoAvQBIANBAnQQ3wQLIAUoAvwBIgMEQCAFKAKAAiADQQJ0EN8ECyAFKALYAiIDBEAgBSgC3AIgA0ECdBDfBAsgBSgC5AIiAwRAIAUoAugCIANBAnQQ3wQLIAUoAvACIgMEQCAFKAL0AiADQQJ0EN8ECyAFKAL8AiIDRQ0TIAUoAoADIANBAnQQ3wQMEwsgBSgC8AEiAwRAIAUoAvQBIANBAnQQ3wQLIAUoAvwBIgMEQCAFKAKAAiADQQJ0EN8ECyAFKALYAiIDBEAgBSgC3AIgA0ECdBDfBAsgBSgC5AIiAwRAIAUoAugCIANBAnQQ3wQLIAUoAvACIgMEQCAFKAL0AiADQQJ0EN8ECyAFKAL8AiIDRQ0AIAUoAoADIANBAnQQ3wQLIAUoAggiAyAFKAIARgRAIAVB5O3AABCfAwsgBSgCBCADQQxsaiIEQdSawAApAgA3AgAgBEEIakHcmsAAKAIANgIAIAUgA0EBajYCCCAFQdgCaiEdQQAhDSMAQfACayIIJAAgCEEANgIMIAhCgICAgMAANwIEIAhCgICAgIABNwIwIAggE0HUAGo2AiwgCCATQcgAajYCKCAIIBNBPGo2AiQgCCATQTBqNgIgIAggE0EkajYCHCAIIBNBGGo2AhggCCATQQxqNgIUIAggEzYCEEHg9sAAKAIAIQsgCEHoAmohBEHY9sAAKQIAISgDQCAIQfAAaiAIQRBqIA1BAnRqKAIAEK0BIAgoAgQgCCgCDCIOa0EDTQRAIAhBBGogDkEEQQRBDBCIAyAIKAIMIQ4LIAgoAgggCCkDeCElIAgpA3AhJiAEIAs2AgAgCCAoNwPgAiAlICaEUEUEQEEBIQZBACEDA0AgCCgC4AIgBkEBa0YEQCAIQeACakHc98AAEKUDCyAIKALkAiADaiAmPgIAICZC/////w9WICVCAFIgJVAgJUIghiAmQiCIhCEmIANBBGohAyAlQiCIISUgCCAGNgLoAiAGQQFqIQYbDQALCyAIQdgCaiIQIAQoAgAiAzYCACAIIAgpA+ACIiU3A9ACIA5BDGxqIgpBCGogAzYCACAKICU3AgAgCCkDiAEhJSAIKQOAASEmIAQgCzYCACAIICg3A+ACICUgJoRQRQRAQQEhBkEAIQMDQCAIKALgAiAGQQFrRgRAIAhB4AJqQdz3wAAQpQMLIAgoAuQCIANqICY+AgAgJkL/////D1YgJUIAUiAlUCAlQiCGICZCIIiEISYgA0EEaiEDICVCIIghJSAIIAY2AugCIAZBAWohBhsNAAsLIBAgBCgCACIDNgIAIAggCCkD4AIiJTcD0AIgCkEUaiADNgIAIApBDGogJTcCACAIKQOYASElIAgpA5ABISYgBCALNgIAIAggKDcD4AIgJSAmhFBFBEBBASEGQQAhAwNAIAgoAuACIAZBAWtGBEAgCEHgAmpB3PfAABClAwsgCCgC5AIgA2ogJj4CACAmQv////8PViAlQgBSICVQICVCIIYgJkIgiIQhJiADQQRqIQMgJUIgiCElIAggBjYC6AIgBkEBaiEGGw0ACwsgECAEKAIAIgM2AgAgCCAIKQPgAiIlNwPQAiAKQSBqIAM2AgAgCkEYaiAlNwIAIAgpA6gBISUgCCkDoAEhJiAEIAs2AgAgCCAoNwPgAiAlICaEUEUEQEEBIQZBACEDA0AgCCgC4AIgBkEBa0YEQCAIQeACakHc98AAEKUDCyAIKALkAiADaiAmPgIAICZC/////w9WICVCAFIgJVAgJUIghiAmQiCIhCEmIANBBGohAyAlQiCIISUgCCAGNgLoAiAGQQFqIQYbDQALCyAQIAQoAgAiAzYCACAIIAgpA+ACIiU3A9ACIApBLGogAzYCACAKQSRqICU3AgAgCCAOQQRqIgY2AgwgDUEBaiINQQhHDQALAkACQAJAAkACQAJAAkACQAJAIBMoAoQBIgNBgICAgHhGIBMoAmwiBEGAgICAeEdxRQRAIANBgICAgHhHDQEgEygCaCEDIAhB+ABqIgRB3JrAACgCADYCACAIQdSawAApAgA3A3AgAwRAIAhB8ABqQcibwAAQpQMgCCgCdCADNgIAIAhBATYCeCAIKAIMIQYLIAhByAJqIAQoAgA2AgAgCCAIKQNwNwPAAiAIKAIEIAZGBEAgCEEEakHQ7MAAEJ8DCyAIKAIIIAZBDGxqIgQgCCkDwAI3AgAgBEEIaiAIQcgCaigCADYCACAIIAZBAWo2AgwgA0UNCSATKAJkIgogA0EMbGohDkHg9sAAKAIAIQ0gCEEYaiELQdj2wAApAgAhJwNAIAhB8ABqIAoQ4gEgCCgCBCAIKAIMIgRrQQFNBEAgCEEEaiAEQQJBBEEMEIgDIAgoAgwhBAsgCCgCCCAIKQN4ISUgCCkDcCEmIAsgDTYCACAIICc3AxAgJSAmhFBFBEBBASEGQQAhAwNAIAgoAhAgBkEBa0YEQCAIQRBqQdz3wAAQpQMLIAgoAhQgA2ogJj4CACAmQv////8PViAlQgBSICVQICVCIIYgJkIgiIQhJiADQQRqIQMgJUIgiCElIAggBjYCGCAGQQFqIQYbDQALCyAIQegCaiIQIAsoAgAiAzYCACAIIAgpAxAiJTcD4AIgBEEMbGoiE0EIaiADNgIAIBMgJTcCACAIKQOIASElIAgpA4ABISYgCyANNgIAIAggJzcDECAlICaEUEUEQEEBIQZBACEDA0AgCCgCECAGQQFrRgRAIAhBEGpB3PfAABClAwsgCCgCFCADaiAmPgIAICZC/////w9WICVCAFIgJVAgJUIghiAmQiCIhCEmIANBBGohAyAlQiCIISUgCCAGNgIYIAZBAWohBhsNAAsLIBAgCygCACIDNgIAIAggCCkDECIlNwPgAiATQRRqIAM2AgAgE0EMaiAlNwIAIAggBEECajYCDCAKQQxqIgogDkcNAAsMCQsCQCATKAJ0IgRFBEAgCEHYAmpB3JrAACgCADYCACAIQdSawAApAgA3A9ACDAELQQAhBiAEQQBIDQIgEygCcCEDQdHOxQAtAAAaQQEhBiAEQQEQ1gQiCkUNAiAEBEAgCiADIAT8CgAAC0EBIQMCQCAEQQFGDQAgBCAKaiELQQAhBiAEQQF2Ig1BAUcEQCAEQQFrIQMgDUH+////A3EhDgNAIAMgCmoiDS0AACEQIA0gBiAKaiINLQAAOgAAIA0gEDoAACALIAZBfnNqIhAtAAAhFCAQIA1BAWoiDS0AADoAACANIBQ6AAAgA0ECayEDIA4gBkECaiIGRw0ACwsgBCIDQQJxRQ0AIAYgCmoiDS0AACEOIA0gCyAGQX9zaiIGLQAAOgAAIAYgDjoAAAsgCEHQAmogCiADQQgQzwIgCiAEEN8ECyAIQfAAaiELQgAhJUIAISZCACEoIwBBEGsiDSQAAkACQAJAAkAgCEHQAmoiAygCCEUEQEHRzsUALQAAGkEBIQRBAUEBENYEIgNFDQIgA0EAOgAAIA1BATYCBAwBCyANQQRqIANBCBCwAiANKAIIIQMgDSgCDCIEQQJJDQAgAyAEaiEOQQAhBiAEQQF2IhBBAUcEQCAEQQFrIQogEEH+////B3EhFANAIAMgCmoiEC0AACEWIBAgAyAGaiIQLQAAOgAAIBAgFjoAACAOIAZBfnNqIhYtAAAhGSAWIBBBAWoiEC0AADoAACAQIBk6AAAgCkECayEKIBQgBkECaiIGRw0ACwsgBEECcQRAIAMgBmoiCi0AACEQIAogDiAGQX9zaiIGLQAAOgAAIAYgEDoAAAsgBEEhTw0CCwJAIAQgBEEEayIGQQAgBCAGTxsiEEYNACADIBBqIQZBBCAEIARBBE8bIg5BA3EhCiAOQQFrQQNPBEAgDkEEcSEOA0AgJUIgiEKAgPz/D4MgKEIghoQgJUIQhiIlQjCIhCEoIAZBA2oxAAAgBkEBajEAACAlIAYxAABCCIaEhEIQhiAGQQJqMQAAQgiGhIQhJSAGQQRqIQYgDkEEayIODQALCyAKRQ0AA0AgKEIIhiAlQjiIhCEoIAYxAAAgJUIIhoQhJSAGQQFqIQYgCkEBayIKDQALCyAQIARBCGsiBkEAIAQgBk8bIg5HBEAgAyAOaiEGQQggBCAEQQhPG0EEIAQgBEEETxtrIQoDQCAvQgiGIClCOIiEIS8gBjEAACApQgiGhCEpIAZBAWohBiAKQQFrIgoNAAsLIA4gBEEMayIGQQAgBCAGTxsiEEcEQCADIBBqIQZBDCAEIARBDE8bQQggBCAEQQhPG2shCgNAIDBCCIYgK0I4iIQhMCAGMQAAICtCCIaEISsgBkEBaiEGIApBAWsiCg0ACwsgECAEQRBrIgZBACAEIAZPGyIORwRAIAMgDmohBkEQIAQgBEEQTxtBDCAEIARBDE8bayEKA0AgMUIIhiAqQjiIhCExIAYxAAAgKkIIhoQhKiAGQQFqIQYgCkEBayIKDQALCyAOIARBFGsiBkEAIAQgBk8bIhBHBEAgAyAQaiEGQRQgBCAEQRRPG0EQIAQgBEEQTxtrIQoDQCAyQgiGIC1COIiEITIgBjEAACAtQgiGhCEtIAZBAWohBiAKQQFrIgoNAAsLIBAgBEEYayIGQQAgBCAGTxsiFEcEQCADIBRqIQZBGCAEIARBGE8bQRQgBCAEQRRPG2shCgNAIDNCCIYgLEI4iIQhMyAGMQAAICxCCIaEISwgBkEBaiEGIApBAWsiCg0ACwsgFCAEQRxrIgZBACAEIAZPGyIORwRAQRwgBCAEQRxPG0EYIAQgBEEYTxtrIQogAyAOaiEGA0AgNEIIhiAuQjiIhCE0IAYxAAAgLkIIhoQhLiAGQQFqIQYgCkEBayIKDQALCwJAIARBHUkNACAOQQNxIQoCQCAEQR1rQQNJBEAgAyEGDAELIA5BPHEhBCADIQYDQCAmQiCIQoCA/P8PgyAnQiCGhCAmQhCGIiZCMIiEIScgBkEDajEAACAGQQFqMQAAICYgBjEAAEIIhoSEQhCGIAZBAmoxAABCCIaEhCEmIAZBBGohBiAEQQRrIgQNAAsLIApFDQADQCAnQgiGICZCOIiEIScgBjEAACAmQgiGhCEmIAZBAWohBiAKQQFrIgoNAAsLIAsgJjcDcCALIC43A2AgCyAsNwNQIAsgLTcDQCALICo3AzAgCyArNwMgIAsgKTcDECALICU3AwAgCyAnNwN4IAsgNDcDaCALIDM3A1ggCyAyNwNIIAsgMTcDOCALIDA3AyggCyAvNwMYIAsgKDcDCCANKAIEIgQEQCADIAQQ3wQLIA1BEGokAAwCC0EBQQEQ/wQAC0HU2sIAQS1BhNvCABD+AwALQQAhCiMAQYABayIEJAAgCykDeCElIAspA3AhLSALKQNoISYgCykDYCEuIAspA1ghKCALKQNQIS8gCykDSCEnIAspA0AhMCALKQM4ISkgCykDMCExIAspAyghKiALKQMgITIgCykDGCErIAspAxAhMyALKQMIISwgCykDACE0IARB+ABqIgZB4PbAACgCADYCACAEQdj2wAApAgA3A3AgLCA0hFBFBEBBASEDA0AgBCgCcCADQQFrRgRAIARB8ABqQdz3wAAQpQMLIAQoAnQgCmogND4CACA0Qv////8PViAsQgBSICxQICxCIIYgNEIgiIQhNCAKQQRqIQogLEIgiCEsIAQgAzYCeCADQQFqIQMbDQALCyAEQegAaiAGKAIAIgM2AgAgBEEIaiADNgIAIAQgBCkDcCIsNwNgIAQgLDcDAEEAIQogBkHg9sAAKAIANgIAIARB2PbAACkCADcDcCArIDOEUEUEQEEBIQMDQCAEKAJwIANBAWtGBEAgBEHwAGpB3PfAABClAwsgBCgCdCAKaiAzPgIAIDNC/////w9WICtCAFIgK1AgK0IghiAzQiCIhCEzIApBBGohCiArQiCIISsgBCADNgJ4IANBAWohAxsNAAsLIARB6ABqIg0gBEH4AGoiBigCACIDNgIAIARBFGogAzYCACAEIAQpA3AiKzcDYCAEICs3AgxBACEKIAZB4PbAACgCADYCACAEQdj2wAApAgA3A3AgKiAyhFBFBEBBASEDA0AgBCgCcCADQQFrRgRAIARB8ABqQdz3wAAQpQMLIAQoAnQgCmogMj4CACAyQv////8PViAqQgBSICpQICpCIIYgMkIgiIQhMiAKQQRqIQogKkIgiCEqIAQgAzYCeCADQQFqIQMbDQALCyANIAYoAgAiAzYCACAEQSBqIAM2AgAgBCAEKQNwIio3A2AgBCAqNwMYQQAhCiAGQeD2wAAoAgA2AgAgBEHY9sAAKQIANwNwICkgMYRQRQRAQQEhAwNAIAQoAnAgA0EBa0YEQCAEQfAAakHc98AAEKUDCyAEKAJ0IApqIDE+AgAgMUL/////D1YgKUIAUiApUCApQiCGIDFCIIiEITEgCkEEaiEKIClCIIghKSAEIAM2AnggA0EBaiEDGw0ACwsgBEHoAGoiDSAEQfgAaiIGKAIAIgM2AgAgBEEsaiADNgIAIAQgBCkDcCIpNwNgIAQgKTcCJEEAIQogBkHg9sAAKAIANgIAIARB2PbAACkCADcDcCAnIDCEUEUEQEEBIQMDQCAEKAJwIANBAWtGBEAgBEHwAGpB3PfAABClAwsgBCgCdCAKaiAwPgIAIDBC/////w9WICdCAFIgJ1AgJ0IghiAwQiCIhCEwIApBBGohCiAnQiCIIScgBCADNgJ4IANBAWohAxsNAAsLIA0gBigCACIDNgIAIARBOGogAzYCACAEIAQpA3AiJzcDYCAEICc3AzBBACEKIAZB4PbAACgCADYCACAEQdj2wAApAgA3A3AgKCAvhFBFBEBBASEDA0AgBCgCcCADQQFrRgRAIARB8ABqQdz3wAAQpQMLIAQoAnQgCmogLz4CACAvQv////8PViAoQgBSIChQIChCIIYgL0IgiIQhLyAKQQRqIQogKEIgiCEoIAQgAzYCeCADQQFqIQMbDQALCyAEQegAaiINIARB+ABqIgYoAgAiAzYCACAEQcQAaiADNgIAIAQgBCkDcCInNwNgIAQgJzcCPEEAIQogBkHg9sAAKAIANgIAIARB2PbAACkCADcDcCAmIC6EUEUEQEEBIQMDQCAEKAJwIANBAWtGBEAgBEHwAGpB3PfAABClAwsgBCgCdCAKaiAuPgIAIC5C/////w9WICZCAFIgJlAgJkIghiAuQiCIhCEuIApBBGohCiAmQiCIISYgBCADNgJ4IANBAWohAxsNAAsLIA0gBigCACIDNgIAIARB0ABqIAM2AgAgBCAEKQNwIiY3A2AgBCAmNwNIQQAhCiAGQeD2wAAoAgA2AgAgBEHY9sAAKQIANwNwICUgLYRQRQRAQQEhAwNAIAQoAnAgA0EBa0YEQCAEQfAAakHc98AAEKUDCyAEKAJ0IApqIC0+AgAgLUL/////D1YgJUIAUiAlUCAlQiCGIC1CIIiEIS0gCkEEaiEKICVCIIghJSAEIAM2AnggA0EBaiEDGw0ACwsgBEHcAGogBEH4AGooAgA2AgAgBCAEKQNwNwJUIAhBEGoiECAEQeAA/AoAACAEQYABaiQAIAhB9AFqIRRBACEKQQAhDiALIBBrIgRBDG4hGQJAAkAgBEH8////B0sNAAJAAkAgCyAQRgRAQQAhGUEEIQMMAQtB0c7FAC0AABpBBCEKIARBBBDWBCIDRQ0CIAtBCGshDSADIQYDQCANQQRqKAIAIgpBAnQhBEEAIRsgCkH/////A0sgBEH8////B0tyDQIgDSgCACEfAn8gBEUEQEEEIRZBAAwBC0HRzsUALQAAGkEEIRsgBEEEENYEIhZFDQMgCgshGyAEBEAgFiAfIAT8CgAACyAGQQhqIAo2AgAgBkEEaiAWNgIAIAYgGzYCACAGQQxqIQYgDkEBaiEOIA1BBGsgDUEMayENIBBHDQALCyAUIA42AgggFCADNgIEIBQgGTYCAAwCCyAbIARB+IHAABDIBAALIAogBEGkrcAAEMgEAAsgCEH4AGpB3JrAACgCADYCACAIQdSawAApAgA3A3AgC0HIm8AAEKUDIAgoAnRBCDYCACAIQYgCaiIEQQE2AgAgCCAIKQNwNwOAAiAIKAIMIgMgCCgCBEYEQCAIQQRqQfTqwAAQnwMLIAgoAgggA0EMbGoiBiAIKQOAAjcCACAGQQhqIAQoAgA2AgAgCCADQQFqIgY2AgwgCCgC/AEiA0EMbCEEIAgoAvgBIQogCCgC9AEhCyAIKAIEIAZrIANJBEAgCEEEaiAGIANBBEEMEIgDIAgoAgwhBgsgBARAIAgoAgggBkEMbGogCiAE/AoAAAsgCCADIAZqNgIMIAsEQCAKIAtBDGwQ3wQLIBMoAoABIQQgCEH4AGoiA0HcmsAAKAIANgIAIAhB1JrAACkCADcDcCAEBEAgCEHwAGpByJvAABClAyAIKAJ0IAQ2AgAgCEEBNgJ4CyAIQZgCaiADKAIANgIAIAggCCkDcDcDkAIgCCgCDCIDIAgoAgRGBEAgCEEEakGE68AAEJ8DCyAIKAIIIANBDGxqIgYgCCkDkAI3AgAgBkEIaiAIQZgCaigCADYCACAIIANBAWoiBjYCDCATKAJ8IQMCQAJ/IAgoAgQgBmsgBEkEQCAIQQRqIAYgBEEEQQwQiAMgCCgCDCEGIAgoAggMAQsgBEUNASAIKAIICyAEIAZqIQogBkEMbGohBkHg9sAAKAIAIQ0gCEH4AGohC0HY9sAAKQIAISUDQCADLQAAIRMgCyANNgIAIAggJTcDcCATBEAgCEHwAGpBzPfAABClAyAIKAJ0IBM2AgAgCEEBNgJ4CyAIQegCaiALKAIAIhM2AgAgCCAIKQNwIiY3A+ACIAZBCGogEzYCACAGICY3AgAgA0EBaiEDIAZBDGohBiAEQQFrIgQNAAsgCiEGCyAIIAY2AgwgCCgCECIDBEAgCCgCFCADQQJ0EN8ECyAIKAIcIgMEQCAIKAIgIANBAnQQ3wQLIAgoAigiAwRAIAgoAiwgA0ECdBDfBAsgCCgCNCIDBEAgCCgCOCADQQJ0EN8ECyAIKAJAIgMEQCAIKAJEIANBAnQQ3wQLIAgoAkwiAwRAIAgoAlAgA0ECdBDfBAsgCCgCWCIDBEAgCCgCXCADQQJ0EN8ECyAIKAJkIgMEQCAIKAJoIANBAnQQ3wQLIAgoAtACIgNFDQggCCgC1AIgA0ECdBDfBAwICyAEQYCAgIB4RgRAIBMoAmhFDQIgCEHwAGogEygCZBDiASAIKAIEIAgoAgwiBGtBAU0EQCAIQQRqIARBAkEEQQwQiAMgCCgCDCEECyAIKAIIIAgpA3ghJSAIKQNwISZBACEDIAhBGGoiC0Hg9sAAKAIANgIAIAhB2PbAACkCADcDECAlICaEUEUEQEEBIQYDQCAIKAIQIAZBAWtGBEAgCEEQakHc98AAEKUDCyAIKAIUIANqICY+AgAgJkL/////D1YgJUIAUiAlUCAlQiCGICZCIIiEISYgA0EEaiEDICVCIIghJSAIIAY2AhggBkEBaiEGGw0ACwsgCEHoAmogCygCACIDNgIAIAggCCkDECIlNwPgAiAEQQxsaiIKQQhqIAM2AgAgCiAlNwIAIAgpA4gBISUgCCkDgAEhJkEAIQMgC0Hg9sAAKAIANgIAIAhB2PbAACkCADcDECAlICaEUEUEQEEBIQYDQCAIKAIQIAZBAWtGBEAgCEEQakHc98AAEKUDCyAIKAIUIANqICY+AgAgJkL/////D1YgJUIAUiAlUCAlQiCGICZCIIiEISYgA0EEaiEDICVCIIghJSAIIAY2AhggBkEBaiEGGw0ACwsgCEHoAmogCEEYaiIDKAIAIgY2AgAgCCAIKQMQIiU3A+ACIApBFGogBjYCACAKQQxqICU3AgAgCCAEQQJqIgY2AgwgCCATKAKYASIEQR9xIgo2AuACIAoNAyADQdyawAAoAgA2AgAgCEHUmsAAKQIANwMQIAQEQCAIQRBqQcibwAAQpQMgCCgCFCAEQQV2NgIAIAhBATYCGCAIKAIMIQYLIAhBqAJqIgMgCEEYaigCADYCACAIIAgpAxA3A6ACIAgoAgQgBkYEQCAIQQRqQfDrwAAQnwMLIAgoAgggBkEMbGoiCiAIKQOgAjcCACAKQQhqIAMoAgA2AgAgCCAGQQFqIgM2AgwgBEUNCCAEQQJ2IgZBf3NBASAGIAYbaiEKIBMoApQBIRNBACEGA0AgBCAGTQ0FIAZBAWogBE8NBiAGQQJqIARPDQcgBkEDaiAETw0IIAYgE2oiCy0AACALQQFqLQAAIAtBA2otAAAhECALQQJqLQAAIQsgCEEYaiIUQdyawAAoAgA2AgAgCEHUmsAAKQIANwMQQQh0ciALQRB0ciAQQRh0ciILBEAgCEEQakHIm8AAEKUDIAgoAhQgC0EYdCALQYD+A3FBCHRyIAtBCHZBgP4DcSALQRh2cnI2AgAgCEEBNgIYIAgoAgwhAwsgCEG4AmoiCyAUKAIANgIAIAggCCkDEDcDsAIgCCgCBCADRgRAIAhBBGpBwOzAABCfAwsgCCgCCCADQQxsaiINIAgpA7ACNwIAIA1BCGogCygCADYCACAIIANBAWoiAzYCDCAGQQRqIQYgCkEBaiIKDQALDAgLIAhBADYCgAEgCEEBNgJ0IAhBjO3AADYCcCAIQgQ3AnggCEHwAGpBlO3AABCoBAALIAYgBEGEpMAAEMgEAAtBAEEAQZTrwAAQ2QMACyAIQgA3AhwgCEKBgICAwAA3AhQgCEHY68AANgIQIAhB4AJqQaTrwAAgCEEQakHg68AAEJcEAAsgBiAEQYDswAAQ2QMACyAGQQFqIARBkOzAABDZAwALIAZBAmogBEGg7MAAENkDAAsgBkEDaiAEQbDswAAQ2QMACyAdIAgpAgQ3AgAgHUEIaiAIQQxqKAIANgIAIAhB8AJqJAAgBSgC4AIiA0EMbCEEIAUoAtwCIQYgBSgC2AIhCiAFKAIAIAUoAggiDWsgA0kEQCAFIA0gA0EEQQwQiAMgBSgCCCENCyAEBEAgBSgCBCANQQxsaiAGIAT8CgAACyAFIAMgDWoiAzYCCCAKBEAgBiAKQQxsEN8EIAUoAgghAwsgBSgCACADayAMSQRAIAUgAyAMQQRBDBCIAyAFKAIIIQMLIAxBDGwiBARAIAUoAgQgA0EMbGogDyAE/AoAAAsgBSADIAxqIgM2AgggGgRAIA8gGkEMbBDfBCAFKAIIIQMLIAUoAgAgA2sgF0kEQCAFIAMgF0EEQQwQiAMgBSgCCCEDCyAXQQxsIgQEQCAFKAIEIANBDGxqIBIgBPwKAAALIAUgAyAXaiIDNgIIIBUEQCASIBVBDGwQ3wQgBSgCCCEDCyAFQeACakHcmsAAKAIAIgQ2AgAgBUHUmsAAKQIAIiU3A9gCAkAgA0EBayIDRQRAIAVB+AFqIAQ2AgAgBSAlNwPwAQwBCyAFQdgCakHIm8AAEKUDIAUoAtwCIAM2AgAgBUH4AWpBATYCACAFIAUpA9gCNwPwASAFKAIIRQ0RCyAFKAIEIgMoAgAiBARAIAMoAgQgBEECdBDfBAsgAyAFKQPwATcCACADQQhqIAVB+AFqKAIANgIAIBhBDGogBUEIaigCADYCACAYIAUpAgA3AgQgGEEANgIAIAUoAlQhBCAJBEAgBCEDA0AgAygCACIGBEAgA0EEaigCACAGQQJ0EN8ECyADQQxqIQMgCUEBayIJDQALCyAFKAJQIgMEQCAEIANBDGwQ3wQLIAUoAuQBIQQgBSgC6AEiCQRAIAQhAwNAIAMoAgAiBgRAIANBBGooAgAgBkECdBDfBAsgA0EMaiEDIAlBAWsiCQ0ACwsgBSgC4AEiAwRAIAQgA0EMbBDfBAsgBSgCDCIDBEAgBSgCECADQQJ0EN8ECyAFKAIYIgNFDRMgBSgCHCADQQJ0EN8EDBMLIAwgA0GkrcAAEMgEAAtBAEEAQbzuwAAQ2QMACyAaIBpBzO7AABDZAwALIAkgA0GkrcAAEMgEAAtBAEEAQbzuwAAQ2QMACyAaIBpBzO7AABDZAwALQQMgC0Gk7cAAENkDAAsgFyADQfiBwAAQyAQACyAVIANB+IHAABDIBAALQQRBBEG07cAAENkDAAsgBCALQfiBwAAQyAQACyAEIAtB+IHAABDIBAALIBcgA0H4gcAAEMgEAAtBAiAOQcTtwAAQ2QMACyADIARB+IHAABDIBAALQQNBA0HU7cAAENkDAAtBAEEAQfTtwAAQ2QMACyAMBEAgDyEDA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgDEEBayIMDQALCyAaRQ0AIA8gGkEMbBDfBAsgBSgCVCEEIAkEQCAEIQMDQCADKAIAIgYEQCADQQRqKAIAIAZBAnQQ3wQLIANBDGohAyAJQQFrIgkNAAsLIAUoAlAiAwRAIAQgA0EMbBDfBAsgBSgC5AEhBCAFKALoASIJBEAgBCEDA0AgAygCACIGBEAgA0EEaigCACAGQQJ0EN8ECyADQQxqIQMgCUEBayIJDQALCyAFKALgASIDBEAgBCADQQxsEN8ECyAFKAIMIgMEQCAFKAIQIANBAnQQ3wQLIAUoAhgiAwRAIAUoAhwgA0ECdBDfBAsgBSgCCCIJBEAgBSgCBCEDA0AgAygCACIEBEAgA0EEaigCACAEQQJ0EN8ECyADQQxqIQMgCUEBayIJDQALCyAFKAIAIgNFDQAgBSgCBCADQQxsEN8ECyAFQcADaiQADAULQQALIBJB+IHAABDIBAALQQALIBJB+IHAABDIBAALIAUgBDYC4AIgBSAGNgLcAiAFIAM2AtgCQYSdwABBKyAFQdgCakHYq8AAQdzuwAAQygMACyAHKALcBSEDIAcoAtgFIQQgBygC1AUhBiAHKALQBUEBRw0CIAQgAxDNBCEDIAZFDQAgBCAGEN8ECyARQYCAgIB4NgIAIBEgAzYCBCAHQZAEahC6AgsgBygC5AIiA0GEAUkNASADEKsDDAELIAcgBjYC6AUgByAENgLkBSAHIAQ2AuAFIAcgBCADQQxsajYC7AUgESAHQeAFahCPAyAHQZAEahC6AiAHKALkAiIDQYQBTwRAIAMQqwMLIAdByAFqENACIAcoAogBIgNBhAFPBEAgAxCrAwsgHiIEQYQBSQ0DDAILIAdByAFqENACIAcoAogBIgNBhAFPBEAgAxCrAwsgHiIEQYMBSw0BDAILIARBgwFNDQELIAQQqwMLIAdB8AVqJAACQAJAIBwCfyAgKAIEIgNBgICAgHhGBEBBACEDICAoAgghBEEAIQZBAQwBCyAgKAIIIQQCQCAgKAIMIgYgA08EQCAEIQMMAQsgA0ECdCEJIAZFBEBBBCEDIAQgCRDfBAwBCyAEIAlBBCAGQQJ0IgQQzgQiA0UNAgtBACEEQQALNgIMIBwgBDYCCCAcIAY2AgQgHCADNgIAICBBEGokAAwBC0EEIARB6PHAABDIBAALIBwoAgAgHCgCBCAcKAIIIBwoAgwgHEEQaiQAC8m9DgLHAX84fiMAQRBrIjEkABCtAyIoIAAmARCtAyIFIAEmARCtAyIeIAImASMAQRBrIjckACA3QQRqISojAEHg1QBrIhUkACAVICg2ArwtAkACQAJAAkACQAJAIBVBvC1qIgoQ4gQEQCAVICg2ArgFIAogFUG4BWoQugMgKEGEAU8EQCAoEKsDCyAVKALALSEoIBUoArwtIjhBgICAgHhHDQELICpBgICAgHg2AgAgKiAoNgIEQQEhCgwBCyAVKALELSEWIBUgBTYCvC0gBSEyIBVBvC1qIgoQ4gQEQCAVIAU2ArgFIAogFUG4BWoQugMgBUGEAU8EQCAFEKsDCyAVKALALSEyIBUoArwtIjtBgICAgHhHDQILICpBgICAgHg2AgAgKiAyNgIEQQAhCiA4RQ0AICggOBDfBAsgHkGEAU8EQCAeEKsDCyAFQYMBSyAKcUUNASAFEKsDDAELIBUoAsQtIRggFSAeNgK8LQJAAkACQCAVQbwtaiIFEOIEBEAgFSAeNgK4BSAFIBVBuAVqELoDIB5BhAFPBEAgHhCrAwsgFSgCwC0hHiAVKAK8LSI8QYCAgIB4Rw0BCyAqQYCAgIB4NgIAICogHjYCBAwBCyAVQbwtaiEJIBUoAsQtIQUjAEGgDmsiCyQAIAtB4A42AgwCQAJAAkACQAJAIAVB4A5GBEAgC0HgCGoiBUEAQcgB/AsAIAtBsApqQQBBiQH8CwAgC0EYNgKoCiAFIB5B4A4Q+wEgC0HAC2ogBUHgAvwKAAAgCy0AmA4iCiALQZANamohBUGIASAKayIKBEAgBUEAIAr8CwALIAtBADoAmA4gBUEBOgAAIAtByAtqIgUgBSkDACALKQOYDYU3AwAgC0HQC2oiCiAKKQMAIAspA6ANhTcDACALQdgLaiIHIAcpAwAgCykDqA2FNwMAIAsgCy0Alw5BgAFyOgCXDiALIAspA8ALIAspA5ANhTcDwAsgCyALKQPgCyALKQOwDYU3A+ALIAsgCykD6AsgCykDuA2FNwPoCyALIAspA/ALIAspA8ANhTcD8AsgCyALKQP4CyALKQPIDYU3A/gLIAsgCykDgAwgCykD0A2FNwOADCALIAspA4gMIAspA9gNhTcDiAwgCyALKQOQDCALKQPgDYU3A5AMIAsgCykDmAwgCykD6A2FNwOYDCALIAspA6AMIAspA/ANhTcDoAwgCyALKQOoDCALKQP4DYU3A6gMIAsgCykDsAwgCykDgA6FNwOwDCALIAspA7gMIAspA4gOhTcDuAwgCyALKQPADCALKQOQDoU3A8AMIAtBwAtqIgggCygCiA0QggUgC0EoaiIMIAcpAwA3AwAgC0EgaiIPIAopAwA3AwAgC0EYaiINIAUpAwA3AwAgCyALKQPACzcDEEHRzsUALQAAGkEgQQEQ1gQiBQRAIAVBGGoiCiAMKQMANwAAIAUgCykDECLKATcAACAFQRBqIgcgDykDADcAACAFQQhqIgwgDSkDADcAACAFIAVBH2oiDy0AADoAACAPIMoBPAAAIAUtAAEhDyAFIAVBHmoiDS0AADoAASANIA86AAAgBUEdaiIPLQAAIQ0gDyAFLQACOgAAIAUgDToAAiAFQRxqIg8tAAAhDSAPIAUtAAM6AAAgBSANOgADIAVBG2oiDy0AACENIA8gBS0ABDoAACAFIA06AAQgBUEaaiIPLQAAIQ0gDyAFLQAFOgAAIAUgDToABSAFQRlqIg8tAAAhDSAPIAUtAAY6AAAgBSANOgAGIAotAAAhDyAKIAUtAAc6AAAgBSAPOgAHIAVBF2oiCi0AACEPIAogDC0AADoAACAMIA86AAAgBUEWaiIKLQAAIQwgCiAFLQAJOgAAIAUgDDoACSAFQRVqIgotAAAhDCAKIAUtAAo6AAAgBSAMOgAKIAVBFGoiCi0AACEMIAogBS0ACzoAACAFIAw6AAsgBUETaiIKLQAAIQwgCiAFLQAMOgAAIAUgDDoADCAFQRJqIgotAAAhDCAKIAUtAA06AAAgBSAMOgANIAVBEWoiCi0AACEMIAogBS0ADjoAACAFIAw6AA4gBy0AACEKIAcgBS0ADzoAACAFIAo6AA8gC0E0aiIKIAVBIEEIEM8CIAVBIBDfBCAIQcSbwgBBwAAQkgICQAJAAkACQAJAAkACQCALKALACw0AIAggCygCxAsgCygCyAtBEBDxASALKALACyIFQYCAgIB4Rg0AIAsgCykCxAs3AkQgCyAFNgJAIAtBzABqIAogC0FAaxDuAUHRzsUALQAAGkEgQQEQ1gQiBUUNESAFQRhqIgogHkEYaikAADcAACAFIB4pAAAiygE3AAAgBUEQaiIHIB5BEGopAAA3AAAgBUEIaiIIIB5BCGopAAA3AAAgBSAFQR9qIgwtAAA6AAAgDCDKATwAACAFLQABIQwgBSAFQR5qIg8tAAA6AAEgDyAMOgAAIAVBHWoiDC0AACEPIAwgBS0AAjoAACAFIA86AAIgBUEcaiIMLQAAIQ8gDCAFLQADOgAAIAUgDzoAAyAFQRtqIgwtAAAhDyAMIAUtAAQ6AAAgBSAPOgAEIAVBGmoiDC0AACEPIAwgBS0ABToAACAFIA86AAUgBUEZaiIMLQAAIQ8gDCAFLQAGOgAAIAUgDzoABiAKLQAAIQwgCiAFLQAHOgAAIAUgDDoAByAFQRdqIgotAAAhDCAKIAgtAAA6AAAgCCAMOgAAIAVBFmoiCi0AACEIIAogBS0ACToAACAFIAg6AAkgBUEVaiIKLQAAIQggCiAFLQAKOgAAIAUgCDoACiAFQRRqIgotAAAhCCAKIAUtAAs6AAAgBSAIOgALIAVBE2oiCi0AACEIIAogBS0ADDoAACAFIAg6AAwgBUESaiIKLQAAIQggCiAFLQANOgAAIAUgCDoADSAFQRFqIgotAAAhCCAKIAUtAA46AAAgBSAIOgAOIActAAAhCiAHIAUtAA86AAAgBSAKOgAPIAtB2ABqIAVBIEEIEM8CIAVBIBDfBEHRzsUALQAAGkEgQQEQ1gQiBUUNESAFQRhqIgogHkE4aikAADcAACAFIB4pACAiygE3AAAgBUEQaiIHIB5BMGopAAA3AAAgBUEIaiIIIB5BKGopAAA3AAAgBSAFQR9qIgwtAAA6AAAgDCDKATwAACAFLQABIQwgBSAFQR5qIg8tAAA6AAEgDyAMOgAAIAVBHWoiDC0AACEPIAwgBS0AAjoAACAFIA86AAIgBUEcaiIMLQAAIQ8gDCAFLQADOgAAIAUgDzoAAyAFQRtqIgwtAAAhDyAMIAUtAAQ6AAAgBSAPOgAEIAVBGmoiDC0AACEPIAwgBS0ABToAACAFIA86AAUgBUEZaiIMLQAAIQ8gDCAFLQAGOgAAIAUgDzoABiAKLQAAIQwgCiAFLQAHOgAAIAUgDDoAByAFQRdqIgotAAAhDCAKIAgtAAA6AAAgCCAMOgAAIAVBFmoiCi0AACEIIAogBS0ACToAACAFIAg6AAkgBUEVaiIKLQAAIQggCiAFLQAKOgAAIAUgCDoACiAFQRRqIgotAAAhCCAKIAUtAAs6AAAgBSAIOgALIAVBE2oiCi0AACEIIAogBS0ADDoAACAFIAg6AAwgBUESaiIKLQAAIQggCiAFLQANOgAAIAUgCDoADSAFQRFqIgotAAAhCCAKIAUtAA46AAAgBSAIOgAOIActAAAhCiAHIAUtAA86AAAgBSAKOgAPIAtB5ABqIAVBIEEIEM8CIAVBIBDfBEHRzsUALQAAGkEgQQEQ1gQiBUUNESAFQRhqIgogHkHYAGopAAA3AAAgBSAeKQBAIsoBNwAAIAVBEGoiByAeQdAAaikAADcAACAFQQhqIgggHkHIAGopAAA3AAAgBSAFQR9qIgwtAAA6AAAgDCDKATwAACAFLQABIQwgBSAFQR5qIg8tAAA6AAEgDyAMOgAAIAVBHWoiDC0AACEPIAwgBS0AAjoAACAFIA86AAIgBUEcaiIMLQAAIQ8gDCAFLQADOgAAIAUgDzoAAyAFQRtqIgwtAAAhDyAMIAUtAAQ6AAAgBSAPOgAEIAVBGmoiDC0AACEPIAwgBS0ABToAACAFIA86AAUgBUEZaiIMLQAAIQ8gDCAFLQAGOgAAIAUgDzoABiAKLQAAIQwgCiAFLQAHOgAAIAUgDDoAByAFQRdqIgotAAAhDCAKIAgtAAA6AAAgCCAMOgAAIAVBFmoiCi0AACEIIAogBS0ACToAACAFIAg6AAkgBUEVaiIKLQAAIQggCiAFLQAKOgAAIAUgCDoACiAFQRRqIgotAAAhCCAKIAUtAAs6AAAgBSAIOgALIAVBE2oiCi0AACEIIAogBS0ADDoAACAFIAg6AAwgBUESaiIKLQAAIQggCiAFLQANOgAAIAUgCDoADSAFQRFqIgotAAAhCCAKIAUtAA46AAAgBSAIOgAOIActAAAhCiAHIAUtAA86AAAgBSAKOgAPIAtB8ABqIAVBIEEIEM8CIAVBIBDfBCALKAJcIQcgCygCYCIFBEAgBUEBayIFQf7///8DcQ0CIAVB/////wNxIgpBAWoiDEEDcSEIQgAhygEgByEFIApBA08EQCAMQfz///8HcSEPA0AgygFCgAF8IcoBIAVBEGohBSAPQQRrIg8NAAsLIAgEQANAIAU1AgAgygGGIMsBfCHLASDKAUIgfCHKASAFQQRqIQUgCEEBayIIDQALCyDLAUL/////D1YNAgsgCygCWCIFBEAgByAFQQJ0EN8ECyDLAachBwwCC0HEnMIAEOgEAAsgCygCWCIKQYCAgIB4Rg0AIAtBADYC6AggC0KAgICAEDcC4AggC0HAl8IANgLECyALQqCAgIAONwLICyALIAtB4AhqNgLAC0GA18IAQTcgC0HAC2oQgQUNCiALKALoCCEMIAsoAuQIIQUgCygC4AghCCAKBEAgByAKQQJ0EN8ECyAIQYCAgIB4Rw0BIAUhBwsgCyAHNgJ8IAsoAmghCiALKAJkIQ0gCygCbCIFDQFCACHLAQwCCyAJIAw2AgwgCSAFNgIIIAkgCDYCBCAJQYCAgIB4NgIAIAsoAnAiBQRAIAsoAnQgBUECdBDfBAsgCygCZCIFRQ0GIAsoAmggBUECdBDfBAwGCyAFQQFrIgVB/v///wNxDQEgBUH/////A3EiBUEBaiIMQQNxIQgCQCAFQQNJBEBCACHKASAKIQUMAQsgDEH8////B3EhD0IAIcoBIAohBQNAIMoBQoABfCHKASAFQRBqIQUgD0EEayIPDQALCyAIBEBCACHLAQNAIAU1AgAgygGGIMsBfCHLASDKAUIgfCHKASAFQQRqIQUgCEEBayIIDQALCyDLAUL/////D1YNAQsgywGnIQwgDUUNAyAKIA1BAnQQ3wQMAwsgDUGAgICAeEYEQCAKIQwMAwsgC0EANgLoCCALQoCAgIAQNwLgCCALQcCXwgA2AsQLIAtCoICAgA43AsgLIAsgC0HgCGo2AsALQYDXwgBBNyALQcALahCBBQ0FIAsoAugIIQggCygC5AghDCALKALgCCEFIA0EQCAKIA1BAnQQ3wQLIAVBgICAgHhGDQIgCSAINgIMIAkgDDYCCCAJIAU2AgQgCUGAgICAeDYCACALKAJwIgVFDQMgCygCdCAFQQJ0EN8EDAMLDAkLIAtBAzYCxAsgC0GYnsIANgLACyALQgI3AswLIAsgBTYCECALIAtBDGqtQoCAgIDgAYQ3A+gIIAsgC0EQaq1CgICAgOABhDcD4AggCyALQeAIajYCyAsgCUEEaiALQcALahDSAiAJQYCAgIB4NgIADAILIAsgDDYCgAEgCygCdCEKIAsoAnAhDQJAAkACQAJAIAsoAngiBUUEQEIAIcsBDAELIAVBAWsiBUH+////A3ENASAFQf////8DcSIFQQFqIg9BA3EhCAJAIAVBA0kEQEIAIcoBIAohBQwBCyAPQfz///8HcSEPQgAhygEgCiEFA0AgygFCgAF8IcoBIAVBEGohBSAPQQRrIg8NAAsLIAgEQEIAIcsBA0AgBTUCACDKAYYgywF8IcsBIMoBQiB8IcoBIAVBBGohBSAIQQFrIggNAAsLIMsBQv////8PVg0BCyDLAachBSANRQ0BIAogDUECdBDfBAwBCyANQYCAgIB4RgRAIAohBQwBCyALQQA2AugIIAtCgICAgBA3AuAIIAtBwJfCADYCxAsgC0KggICADjcCyAsgCyALQeAIajYCwAtBgNfCAEE3IAtBwAtqEIEFRQRAIAsoAugIIQ8gCygC5AghBSALKALgCCEIIA0EQCAKIA1BAnQQ3wQLIAhBgICAgHhGDQEgCSAPNgIMIAkgBTYCCCAJIAg2AgQMAgsMBAsgCyAFNgKEAQJAAkACQCAFQQFGBEAgB0EcSw0BIAxBEEkNAiALQQA2ApABIAtCgICAgMAANwKIASAeQYABaiEKIAtBrAFqIQNBASEPA0BB0c7FAC0AABpBIEEBENYEIgVFDQ0gBUEYaiIIIApBIGsiB0EYaikAADcAACAFIAcpAAAiygE3AAAgBUEQaiIMIAdBEGopAAA3AAAgBUEIaiINIAdBCGopAAA3AAAgBSAFQR9qIgctAAA6AAAgByDKATwAACAFLQABIQcgBSAFQR5qIgQtAAA6AAEgBCAHOgAAIAVBHWoiBy0AACEEIAcgBS0AAjoAACAFIAQ6AAIgBUEcaiIHLQAAIQQgByAFLQADOgAAIAUgBDoAAyAFQRtqIgctAAAhBCAHIAUtAAQ6AAAgBSAEOgAEIAVBGmoiBy0AACEEIAcgBS0ABToAACAFIAQ6AAUgBUEZaiIHLQAAIQQgByAFLQAGOgAAIAUgBDoABiAILQAAIQcgCCAFLQAHOgAAIAUgBzoAByAFQRdqIgctAAAhCCAHIA0tAAA6AAAgDSAIOgAAIAVBFmoiBy0AACEIIAcgBS0ACToAACAFIAg6AAkgBUEVaiIHLQAAIQggByAFLQAKOgAAIAUgCDoACiAFQRRqIgctAAAhCCAHIAUtAAs6AAAgBSAIOgALIAVBE2oiBy0AACEIIAcgBS0ADDoAACAFIAg6AAwgBUESaiIHLQAAIQggByAFLQANOgAAIAUgCDoADSAFQRFqIgctAAAhCCAHIAUtAA46AAAgBSAIOgAOIAwtAAAhByAMIAUtAA86AAAgBSAHOgAPIAtBlAFqIAVBIEEIEM8CIAVBIBDfBEHRzsUALQAAGkEgQQEQ1gQiBUUNBCAFQRhqIgcgCkEYaikAADcAACAFIAopAAAiygE3AAAgBUEQaiIIIApBEGopAAA3AAAgBUEIaiIMIApBCGopAAA3AAAgBSAFQR9qIg0tAAA6AAAgDSDKATwAACAFLQABIQ0gBSAFQR5qIgQtAAA6AAEgBCANOgAAIAVBHWoiDS0AACEEIA0gBS0AAjoAACAFIAQ6AAIgBUEcaiINLQAAIQQgDSAFLQADOgAAIAUgBDoAAyAFQRtqIg0tAAAhBCANIAUtAAQ6AAAgBSAEOgAEIAVBGmoiDS0AACEEIA0gBS0ABToAACAFIAQ6AAUgBUEZaiINLQAAIQQgDSAFLQAGOgAAIAUgBDoABiAHLQAAIQ0gByAFLQAHOgAAIAUgDToAByAFQRdqIgctAAAhDSAHIAwtAAA6AAAgDCANOgAAIAVBFmoiBy0AACEMIAcgBS0ACToAACAFIAw6AAkgBUEVaiIHLQAAIQwgByAFLQAKOgAAIAUgDDoACiAFQRRqIgctAAAhDCAHIAUtAAs6AAAgBSAMOgALIAVBE2oiBy0AACEMIAcgBS0ADDoAACAFIAw6AAwgBUESaiIHLQAAIQwgByAFLQANOgAAIAUgDDoADSAFQRFqIgctAAAhDCAHIAUtAA46AAAgBSAMOgAOIAgtAAAhByAIIAUtAA86AAAgBSAHOgAPIAMgBUEgQQgQzwIgBUEgEN8EIAtBqAFqIgwgC0GcAWooAgA2AgAgCyALKQKUATcDoAEgCygCkAEiByALKAKIAUYEQCALQYgBakH0nMIAEJkDCyALKAKMASIFIAdBGGxqIgggCykDoAE3AgAgCEEIaiAMKQMANwIAIAhBEGogC0GwAWopAwA3AgAgCyAHQQFqIgc2ApABIApBQGshCiAPIA9BHEkiCGohDyAIDQALIAsoAogBIQgCQCAHQRxGBEAgC0GwBmogBUEgaikCADcDACALQbgGaiAFQShqKQIANwMAIAtBmAZqIAVBOGopAgA3AwAgC0GgBmogBUFAaykCADcDACALIAUpAhg3A6gGIAsgBSkCMDcDkAYgBSkCECHKASAFKAIMIQcgBSgCCCEKIAUoAgQhDCAFKAIAIQ8gC0GIBmogBUHYAGopAgA3AwAgC0GABmogBUHQAGopAgA3AwAgC0HoBWogBUHoAGopAgA3AwAgC0HwBWogBUHwAGopAgA3AwAgC0HQBWogBUGAAWopAgA3AwAgC0HYBWogBUGIAWopAgA3AwAgCyAFKQJINwP4BSALIAUpAmA3A+AFIAsgBSkCeDcDyAUgC0HABWogBUGgAWopAgA3AwAgC0G4BWogBUGYAWopAgA3AwAgC0GoBWogBUG4AWopAgA3AwAgC0GgBWogBUGwAWopAgA3AwAgC0GQBWogBUHQAWopAgA3AwAgC0GIBWogBUHIAWopAgA3AwAgCyAFKQKQATcDsAUgCyAFKQKoATcDmAUgCyAFKQLAATcDgAUgC0H4BGogBUHoAWopAgA3AwAgC0HwBGogBUHgAWopAgA3AwAgCyAFKQLYATcD6AQgC0HgBGogBUGAAmopAgA3AwAgC0HYBGogBUH4AWopAgA3AwAgCyAFKQLwATcD0AQgC0HIBGogBUGYAmopAgA3AwAgC0HABGogBUGQAmopAgA3AwAgCyAFKQKIAjcDuAQgC0GwBGogBUGwAmopAgA3AwAgC0GoBGogBUGoAmopAgA3AwAgCyAFKQKgAjcDoAQgC0GYBGogBUHIAmopAgA3AwAgC0GQBGogBUHAAmopAgA3AwAgCyAFKQK4AjcDiAQgC0GABGogBUHgAmopAgA3AwAgC0H4A2ogBUHYAmopAgA3AwAgCyAFKQLQAjcD8AMgC0HoA2ogBUH4AmopAgA3AwAgC0HgA2ogBUHwAmopAgA3AwAgCyAFKQLoAjcD2AMgC0HQA2ogBUGQA2opAgA3AwAgC0HIA2ogBUGIA2opAgA3AwAgCyAFKQKAAzcDwAMgC0G4A2ogBUGoA2opAgA3AwAgC0GwA2ogBUGgA2opAgA3AwAgCyAFKQKYAzcDqAMgC0GgA2ogBUHAA2opAgA3AwAgC0GYA2ogBUG4A2opAgA3AwAgCyAFKQKwAzcDkAMgC0GIA2ogBUHYA2opAgA3AwAgC0GAA2ogBUHQA2opAgA3AwAgCyAFKQLIAzcD+AIgC0HwAmogBUHwA2opAgA3AwAgC0HoAmogBUHoA2opAgA3AwAgCyAFKQLgAzcD4AIgC0HYAmogBUGIBGopAgA3AwAgC0HQAmogBUGABGopAgA3AwAgCyAFKQL4AzcDyAIgC0HAAmogBUGgBGopAgA3AwAgC0G4AmogBUGYBGopAgA3AwAgCyAFKQKQBDcDsAIgC0GoAmogBUG4BGopAgA3AwAgC0GgAmogBUGwBGopAgA3AwAgCyAFKQKoBDcDmAIgC0GQAmogBUHQBGopAgA3AwAgC0GIAmogBUHIBGopAgA3AwAgCyAFKQLABDcDgAIgC0H4AWogBUHoBGopAgA3AwAgC0HwAWogBUHgBGopAgA3AwAgCyAFKQLYBDcD6AEgC0HgAWogBUGABWopAgA3AwAgC0HYAWogBUH4BGopAgA3AwAgCyAFKQLwBDcD0AEgC0HIAWogBUGYBWopAgA3AwAgC0HAAWogBUGQBWopAgA3AwAgCyAFKQKIBTcDuAEgCARAIAUgCEEYbBDfBAsgD0GAgICAeEcNASAMIQggCiEFCyALIAc2AsgLIAsgBTYCxAsgCyAINgLAC0HKmcIAQSsgC0HAC2pB1JzCAEHknMIAEMoDAAsgC0HQC2oiBSALQbgGaikDADcDACALQcgLaiIIIAtBsAZqKQMANwMAIAsgCykDqAY3A8ALIAtB8AhqIg0gC0GgBmopAwA3AwAgC0HoCGoiAyALQZgGaikDADcDACALIAspA5AGNwPgCCALQdgIaiIEIAtBiAZqKQMANwMAIAtB0AhqIgYgC0GABmopAwA3AwAgCyALKQP4BTcDyAggC0HACGoiEiALQfAFaikDADcDACALQbgIaiIOIAtB6AVqKQMANwMAIAsgCykD4AU3A7AIIAtBqAhqIhAgC0HYBWopAwA3AwAgC0GgCGoiESALQdAFaikDADcDACALIAspA8gFNwOYCCALQZAIaiITIAtBwAVqKQMANwMAIAtBiAhqIhQgC0G4BWopAwA3AwAgCyALKQOwBTcDgAggC0H4B2oiGSALQagFaikDADcDACALQfAHaiIXIAtBoAVqKQMANwMAIAsgCykDmAU3A+gHIAtB4AdqIhogC0GQBWopAwA3AwAgC0HYB2oiICALQYgFaikDADcDACALIAspA4AFNwPQByALQcgHaiIdIAtB+ARqKQMANwMAIAtBwAdqIicgC0HwBGopAwA3AwAgCyALKQPoBDcDuAcgC0GwB2oiHyALQeAEaikDADcDACALQagHaiIkIAtB2ARqKQMANwMAIAsgCykD0AQ3A6AHIAtBmAdqIiEgC0HIBGopAwA3AwAgC0GQB2oiKyALQcAEaikDADcDACALIAspA7gENwOIByALQYAHaiIiIAtBsARqKQMANwMAIAtB+AZqIiwgC0GoBGopAwA3AwAgCyALKQOgBDcD8AYgC0HoBmoiGyALQZgEaikDADcDACALQeAGaiItIAtBkARqKQMANwMAIAsgCykDiAQ3A9gGIAtB0AZqIiUgC0GABGopAwA3AwAgC0HIBmoiLiALQfgDaikDADcDACALIAspA/ADNwPABiAJIAspA9gDNwLoAiAJQfACaiALQeADaikDADcCACAJQfgCaiALQegDaikDADcCACAJIAspA8ADNwKAAyAJQYgDaiALQcgDaikDADcCACAJQZADaiALQdADaikDADcCACAJQagDaiALQbgDaikDADcCACAJQaADaiALQbADaikDADcCACAJIAspA6gDNwKYAyAJQcADaiALQaADaikDADcCACAJQbgDaiALQZgDaikDADcCACAJIAspA5ADNwKwAyAJQdgDaiALQYgDaikDADcCACAJQdADaiALQYADaikDADcCACAJIAspA/gCNwLIAyAJQfADaiALQfACaikDADcCACAJQegDaiALQegCaikDADcCACAJIAspA+ACNwLgAyAJQYgEaiALQdgCaikDADcCACAJQYAEaiALQdACaikDADcCACAJIAspA8gCNwL4AyAJQaAEaiALQcACaikDADcCACAJQZgEaiALQbgCaikDADcCACAJIAspA7ACNwKQBCAJQbgEaiALQagCaikDADcCACAJQbAEaiALQaACaikDADcCACAJIAspA5gCNwKoBCAJQdAEaiALQZACaikDADcCACAJQcgEaiALQYgCaikDADcCACAJIAspA4ACNwLABCAJQegEaiALQfgBaikDADcCACAJQeAEaiALQfABaikDADcCACAJIAspA+gBNwLYBCAJQYAFaiALQeABaikDADcCACAJQfgEaiALQdgBaikDADcCACAJIAspA9ABNwLwBCAJQZgFaiALQcgBaikDADcCACAJQZAFaiALQcABaikDADcCACAJIAspA7gBNwKIBSAJIMoBNwIQIAkgBzYCDCAJIAo2AgggCSAMNgIEIAkgDzYCACALKAJ8IQogCygCgAEhByALKAKEASEMIAkgCykCTDcCoAUgCUGoBWogC0HUAGooAgA2AgAgCSALKQPACzcCGCAJQSBqIAgpAwA3AgAgCUEoaiAFKQMANwIAIAlBQGsgDSkDADcCACAJQThqIAMpAwA3AgAgCSALKQPgCDcCMCAJQdgAaiAEKQMANwIAIAlB0ABqIAYpAwA3AgAgCSALKQPICDcCSCAJQfAAaiASKQMANwIAIAlB6ABqIA4pAwA3AgAgCSALKQOwCDcCYCAJQYgBaiAQKQMANwIAIAlBgAFqIBEpAwA3AgAgCSALKQOYCDcCeCAJQaABaiATKQMANwIAIAlBmAFqIBQpAwA3AgAgCSALKQOACDcCkAEgCUG4AWogGSkDADcCACAJQbABaiAXKQMANwIAIAkgCykD6Ac3AqgBIAlB0AFqIBopAwA3AgAgCUHIAWogICkDADcCACAJIAspA9AHNwLAASAJQegBaiAdKQMANwIAIAlB4AFqICcpAwA3AgAgCSALKQO4BzcC2AEgCUGAAmogHykDADcCACAJQfgBaiAkKQMANwIAIAkgCykDoAc3AvABIAlBmAJqICEpAwA3AgAgCUGQAmogKykDADcCACAJIAspA4gHNwKIAiAJQbACaiAiKQMANwIAIAlBqAJqICwpAwA3AgAgCSALKQPwBjcCoAIgCUHIAmogGykDADcCACAJQcACaiAtKQMANwIAIAkgCykD2AY3ArgCIAlB4AJqICUpAwA3AgAgCUHYAmogLikDADcCACAJIAspA8AGNwLQAiAJIAw2ArQFIAkgBzYCsAUgCSAKNgKsBQwGCyALQQE2AsQLIAtB7J3CADYCwAsgC0IBNwLMCyALIAtBhAFqrUKAgICA4AGENwPgCCALIAtB4AhqNgLICyAJQQRqIAtBwAtqENICDAMLIAtBATYCxAsgC0HEncIANgLACyALQgE3AswLIAsgC0H8AGqtQoCAgIDgAYQ3A+AIIAsgC0HgCGo2AsgLIAlBBGogC0HAC2oQ0gIMAgsgC0EBNgLECyALQaCdwgA2AsALIAtCATcCzAsgCyALQYABaq1CgICAgOABhDcD4AggCyALQeAIajYCyAsgCUEEaiALQcALahDSAgwBCwwICyAJQYCAgIB4NgIACyALKAJMIgVFDQAgCygCUCAFQQJ0EN8ECyALQaAOaiQADAELQeiXwgBBNyALQcgIakHYl8IAQeyYwgAQygMACyAVKALALSEFAkAgFSgCvC0iCkGAgICAeEYEQCAVKALELSIKIBUoAsgtEM0EIQcgBQRAIAogBRDfBAsgKkGAgICAeDYCACAqIAc2AgQMAQsgFUEIaiAVQcQtaiJBQbAF/AoAACAVIAU2AgQgFSAKNgIAIBVBvC1qIRAgFSgCrAUhByMAQeAAayIRJAACQAJAAkACQCAHQQxsQdoAaiIIQQV0IgUgFkYEQCARQQA2AiAgEUKAgICAwAA3AhgCQAJAAkACQCAIRQ0AQSAhCiAWQSBJDQdB0c7FAC0AABpBIEEBENYEIgVFDQ0gBUEYaiIKIChBGGopAAA3AAAgBSAoKQAAIsoBNwAAIAVBEGoiDCAoQRBqKQAANwAAIAVBCGoiDyAoQQhqKQAANwAAIAUgBUEfaiILLQAAOgAAIAsgygE8AAAgBS0AASELIAUgBUEeaiIJLQAAOgABIAkgCzoAACAFQR1qIgstAAAhCSALIAUtAAI6AAAgBSAJOgACIAVBHGoiCy0AACEJIAsgBS0AAzoAACAFIAk6AAMgBUEbaiILLQAAIQkgCyAFLQAEOgAAIAUgCToABCAFQRpqIgstAAAhCSALIAUtAAU6AAAgBSAJOgAFIAVBGWoiCy0AACEJIAsgBS0ABjoAACAFIAk6AAYgCi0AACELIAogBS0ABzoAACAFIAs6AAcgBUEXaiIKLQAAIQsgCiAPLQAAOgAAIA8gCzoAACAFQRZqIgotAAAhDyAKIAUtAAk6AAAgBSAPOgAJIAVBFWoiCi0AACEPIAogBS0ACjoAACAFIA86AAogBUEUaiIKLQAAIQ8gCiAFLQALOgAAIAUgDzoACyAFQRNqIgotAAAhDyAKIAUtAAw6AAAgBSAPOgAMIAVBEmoiCi0AACEPIAogBS0ADToAACAFIA86AA0gBUERaiIKLQAAIQ8gCiAFLQAOOgAAIAUgDzoADiAMLQAAIQogDCAFLQAPOgAAIAUgCjoADyARQSRqIAVBIEEIEM8CIAVBIBDfBCARKAIgIgUgESgCGEYEQCARQRhqQbyfwgAQnwMLIBEoAhwgBUEMbGoiCiARKQIkNwIAIApBCGogEUEsaigCADYCACARIAVBAWo2AiAgCEEBRg0AQad/IAdBDGxrIQxBICEFA0AgBUEfa0FASw0CIBYgBUEgaiIKSQ0IQdHOxQAtAAAaQSBBARDWBCIIRQ0OIAhBGGoiDyAFIChqIgVBGGopAAA3AAAgCCAFKQAAIsoBNwAAIAhBEGoiCyAFQRBqKQAANwAAIAhBCGoiCSAFQQhqKQAANwAAIAggCEEfaiIFLQAAOgAAIAUgygE8AAAgCC0AASEFIAggCEEeaiINLQAAOgABIA0gBToAACAIQR1qIgUtAAAhDSAFIAgtAAI6AAAgCCANOgACIAhBHGoiBS0AACENIAUgCC0AAzoAACAIIA06AAMgCEEbaiIFLQAAIQ0gBSAILQAEOgAAIAggDToABCAIQRpqIgUtAAAhDSAFIAgtAAU6AAAgCCANOgAFIAhBGWoiBS0AACENIAUgCC0ABjoAACAIIA06AAYgDy0AACEFIA8gCC0ABzoAACAIIAU6AAcgCEEXaiIFLQAAIQ8gBSAJLQAAOgAAIAkgDzoAACAIQRZqIgUtAAAhDyAFIAgtAAk6AAAgCCAPOgAJIAhBFWoiBS0AACEPIAUgCC0ACjoAACAIIA86AAogCEEUaiIFLQAAIQ8gBSAILQALOgAAIAggDzoACyAIQRNqIgUtAAAhDyAFIAgtAAw6AAAgCCAPOgAMIAhBEmoiBS0AACEPIAUgCC0ADToAACAIIA86AA0gCEERaiIFLQAAIQ8gBSAILQAOOgAAIAggDzoADiALLQAAIQUgCyAILQAPOgAAIAggBToADyARQSRqIAhBIEEIEM8CIAhBIBDfBCARKAIgIgUgESgCGEYEQCARQRhqQbyfwgAQnwMLIBEoAhwgBUEMbGoiCCARKQIkNwIAIAhBCGogEUEsaigCADYCACARIAVBAWo2AiAgCiEFIAxBAWoiDA0ACwsgGEEfcQRAIBFBATYCNCARQYSfwgA2AjAgEUIBNwI8IBEgGDYCSCARIBFByABqrUKAgICA4AGENwMIIBEgEUEIajYCOCAQQQRqIBFBMGoQ0gIgEEGAgICAeDYCACARKAIgIgUEQCARKAIcIQoDQCAKKAIAIgcEQCAKQQRqKAIAIAdBAnQQ3wQLIApBDGohCiAFQQFrIgUNAAsLIBEoAhgiBUUNBSARKAIcIAVBDGwQ3wQMBQsgEUEANgJQIBFCgICAgMAANwJIAkAgGEUNAEEgIQogGEEgSQ0GQdHOxQAtAAAaQSBBARDWBCIFRQ0DIBhBBXZBAWshDCAFQRhqIgogMkEYaikAADcAACAFIDIpAAAiygE3AAAgBUEQaiIIIDJBEGopAAA3AAAgBUEIaiIPIDJBCGopAAA3AAAgBSAFQR9qIgstAAA6AAAgCyDKATwAACAFLQABIQsgBSAFQR5qIgktAAA6AAEgCSALOgAAIAVBHWoiCy0AACEJIAsgBS0AAjoAACAFIAk6AAIgBUEcaiILLQAAIQkgCyAFLQADOgAAIAUgCToAAyAFQRtqIgstAAAhCSALIAUtAAQ6AAAgBSAJOgAEIAVBGmoiCy0AACEJIAsgBS0ABToAACAFIAk6AAUgBUEZaiILLQAAIQkgCyAFLQAGOgAAIAUgCToABiAKLQAAIQsgCiAFLQAHOgAAIAUgCzoAByAFQRdqIgotAAAhCyAKIA8tAAA6AAAgDyALOgAAIAVBFmoiCi0AACEPIAogBS0ACToAACAFIA86AAkgBUEVaiIKLQAAIQ8gCiAFLQAKOgAAIAUgDzoACiAFQRRqIgotAAAhDyAKIAUtAAs6AAAgBSAPOgALIAVBE2oiCi0AACEPIAogBS0ADDoAACAFIA86AAwgBUESaiIKLQAAIQ8gCiAFLQANOgAAIAUgDzoADSAFQRFqIgotAAAhDyAKIAUtAA46AAAgBSAPOgAOIAgtAAAhCiAIIAUtAA86AAAgBSAKOgAPIBFB1ABqIAVBIEEIEM8CIAVBIBDfBCARKAJQIgUgESgCSEYEQCARQcgAakGcn8IAEJ8DCyARKAJMIAVBDGxqIgogESkCVDcCACAKQQhqIBFB3ABqKAIANgIAIBEgBUEBajYCUCAMRQ0AQSAhBQNAIAVBH2tBQEsNAyAYIAVBIGoiCkkNB0HRzsUALQAAGkEgQQEQ1gQiCEUNBCAIQRhqIg8gBSAyaiIFQRhqKQAANwAAIAggBSkAACLKATcAACAIQRBqIgsgBUEQaikAADcAACAIQQhqIgkgBUEIaikAADcAACAIIAhBH2oiBS0AADoAACAFIMoBPAAAIAgtAAEhBSAIIAhBHmoiFi0AADoAASAWIAU6AAAgCEEdaiIFLQAAIRYgBSAILQACOgAAIAggFjoAAiAIQRxqIgUtAAAhFiAFIAgtAAM6AAAgCCAWOgADIAhBG2oiBS0AACEWIAUgCC0ABDoAACAIIBY6AAQgCEEaaiIFLQAAIRYgBSAILQAFOgAAIAggFjoABSAIQRlqIgUtAAAhFiAFIAgtAAY6AAAgCCAWOgAGIA8tAAAhBSAPIAgtAAc6AAAgCCAFOgAHIAhBF2oiBS0AACEPIAUgCS0AADoAACAJIA86AAAgCEEWaiIFLQAAIQ8gBSAILQAJOgAAIAggDzoACSAIQRVqIgUtAAAhDyAFIAgtAAo6AAAgCCAPOgAKIAhBFGoiBS0AACEPIAUgCC0ACzoAACAIIA86AAsgCEETaiIFLQAAIQ8gBSAILQAMOgAAIAggDzoADCAIQRJqIgUtAAAhDyAFIAgtAA06AAAgCCAPOgANIAhBEWoiBS0AACEPIAUgCC0ADjoAACAIIA86AA4gCy0AACEFIAsgCC0ADzoAACAIIAU6AA8gEUHUAGogCEEgQQgQzwIgCEEgEN8EIBEoAlAiBSARKAJIRgRAIBFByABqQZyfwgAQnwMLIBEoAkwgBUEMbGoiCCARKQJUNwIAIAhBCGogEUHcAGooAgA2AgAgESAFQQFqNgJQIAohBSAMQQFrIgwNAAsLIBFBEGogEUEgaigCADYCACARIBEpAhg3AwggEUE4aiARQdAAaigCADYCACARIBEpAkg3AzAgEUEwaiEaQQAhCSMAQdDBAGsiDiQAIA4gByIKQQFrIhdBAXQiGyAHIAdBCWwiBGpqQdwAaiIUNgIMAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAAkACQAJAIBQgEUEIaiInKAIIIhlGBEAgDkEANgIQIBRBD00NAiAnKAIEIRNB0c7FAC0AABpBwAFBBBDWBCIFRQ0DIBMoAggiB0ECdCEGIAdB/////wNLIAZB/P///wdLcg0PIBMoAgQhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgIIIAUgCDYCBCAFIA82AgAgEygCFCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAhAhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgIUIAUgCDYCECAFIA82AgwgEygCICIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAhwhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgIgIAUgCDYCHCAFIA82AhggEygCLCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAighDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgIsIAUgCDYCKCAFIA82AiQgEygCOCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAjQhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgI4IAUgCDYCNCAFIA82AjAgEygCRCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAkAhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgJEIAUgCDYCQCAFIA82AjwgEygCUCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAkwhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgJQIAUgCDYCTCAFIA82AkggEygCXCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAlghDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgJcIAUgCDYCWCAFIA82AlQgEygCaCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAmQhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgJoIAUgCDYCZCAFIA82AmAgEygCdCIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAnAhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgJ0IAUgCDYCcCAFIA82AmwgEygCgAEiB0ECdCEGQQAhCSAHQf////8DSyAGQfz///8HS3INDyATKAJ8IQwCfyAGRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhCSAGQQQQ1gQiCEUNECAHCyEPIAYEQCAIIAwgBvwKAAALIAUgBzYCgAEgBSAINgJ8IAUgDzYCeCATKAKMASIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAogBIQwCfyAGRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhCSAGQQQQ1gQiCEUNECAHCyEPIAYEQCAIIAwgBvwKAAALIAUgBzYCjAEgBSAINgKIASAFIA82AoQBIBMoApgBIgdBAnQhBkEAIQkgB0H/////A0sgBkH8////B0tyDQ8gEygClAEhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgKYASAFIAg2ApQBIAUgDzYCkAEgEygCpAEiB0ECdCEGQQAhCSAHQf////8DSyAGQfz///8HS3INDyATKAKgASEMAn8gBkUEQEEEIQhBAAwBC0HRzsUALQAAGkEEIQkgBkEEENYEIghFDRAgBwshDyAGBEAgCCAMIAb8CgAACyAFIAc2AqQBIAUgCDYCoAEgBSAPNgKcASATKAKwASIHQQJ0IQZBACEJIAdB/////wNLIAZB/P///wdLcg0PIBMoAqwBIQwCfyAGRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhCSAGQQQQ1gQiCEUNECAHCyEPIAYEQCAIIAwgBvwKAAALIAUgBzYCsAEgBSAINgKsASAFIA82AqgBIBMoArwBIgdBAnQhBkEAIQkgB0H/////A0sgBkH8////B0tyDQ8gEygCuAEhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0QIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgK8ASAFIAg2ArgBIAUgDzYCtAEgBSgCBCEtIAUoAgghJSAFKAIMIS4gBSgCACEmIA5BuB1qIAVBEGpBsAH8CgAAIAVBwAEQ3wQgJkGAgICAeEcNASAOIC42Avg4IA4gJTYC9DggDiAtNgLwOEHKmcIAQSsgDkHwOGpBsKHCAEHApMIAEMoDAAsgDkEDNgK8HSAOQeikwgA2ArgdIA5CAjcCxB0gDiAZNgKIBCAOIA5BDGqtQoCAgIDgAYQ3A/g4IA4gDkGIBGqtQoCAgIDgAYQ3A/A4IA4gDkHwOGo2AsAdIBBBBGogDkG4HWoQ0gIgEEGAgICAeDYCACAaKAIEIQUgGigCCCIMBEAgBSEHA0AgBygCACIKBEAgB0EEaigCACAKQQJ0EN8ECyAHQQxqIQcgDEEBayIMDQALCyAaKAIAIgpFDQcgBSAKQQxsEN8EDAcLIA5BFGogDkG4HWpBsAH8CgAAIA5BEDYCECAOQQA2AswBIA5CgICAgMAANwLEAUESIQYgFEESSQ0CQdHOxQAtAAAaQRhBBBDWBCIFRQ0OIBMoAsgBIgdBAnQhBkEAIQkgB0H/////A0sgBkH8////B0tyDQ0gEygCxAEhDAJ/IAZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEJIAZBBBDWBCIIRQ0OIAcLIQ8gBgRAIAggDCAG/AoAAAsgBSAHNgIIIAUgCDYCBCAFIA82AgAgEygC1AEiB0ECdCEGQQAhCSAHQf////8DSyAGQfz///8HS3INDSATKALQASEMAn8gBkUEQEEEIQhBAAwBC0HRzsUALQAAGkEEIQkgBkEEENYEIghFDQ4gBwshCSAGBEAgCCAMIAb8CgAACyAFIAc2AhQgBSAINgIQIAUgCTYCDCAFKQIEIcoBIAUpAhAhywEgBSgCACEHIAVBGBDfBCAHQYCAgIB4Rg0MIA5BxAFqQaCkwgAQmQMgDigCyAEiBSDKATcCBCAFIAc2AgAgBSDLATcCECAFIAk2AgwgDkEBNgLMASATQewBaiEMQRQhBgNAIAYgFEsNA0HRzsUALQAAGkEYQQQQ1gQiB0UNDyAMQQxrKAIAIg9BAnQhCEEAIQUgD0H/////A0sgCEH8////B0tyDQQgDEEQaygCACELAn8gCEUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQUgCEEEENYEIglFDQUgDwshBSAIBEAgCSALIAj8CgAACyAHIA82AgggByAJNgIEIAcgBTYCACAMKAIAIg9BAnQhCEEAIQkgD0H/////A0sgCEH8////B0tyDQUgDEEEaygCACELAn8gCEUEQEEEIQVBAAwBC0HRzsUALQAAGkEEIQkgCEEEENYEIgVFDQYgDwshCSAIBEAgBSALIAj8CgAACyAHIA82AhQgByAFNgIQIAcgCTYCDCAHKQIEIcoBIAcpAhAhywEgBygCACEIIAdBGBDfBCAIQYCAgIB4Rg0NIA4oAswBIgcgDigCxAFGBEAgDkHEAWpBoKTCABCZAwsgDigCyAEgB0EYbGoiBSDLATcCECAFIAk2AgwgBSDKATcCBCAFIAg2AgAgDiAHQQFqIiA2AswBIAxBGGohDCAGQQJqIgZBJEcNAAsMBQtBECAUQYCgwgAQ5QQAC0EEQcABQZSbwgAQyAQACyAGIBRBkKTCABDlBAALIAUgCEH4gcAAEMgEAAsgCSAIQfiBwAAQyAQACyAOQSI2AhAgDigCyAEhByAOKALEASEMAkAgIEEJRgRAIA5BwB1qIAdBIGopAgA3AwAgDkHIHWogB0EoaikCADcDACAOQfg4aiAHQThqKQIANwMAIA5BgDlqIAdBQGspAgA3AwAgDiAHKQIYNwO4HSAOIAcpAjA3A/A4IAcpAhAhywEgBygCDCEgIAcoAgghGCAHKAIEIRYgBygCACEpIA5BmARqIAdB2ABqKQIANwMAIA5BkARqIAdB0ABqKQIANwMAIA5B+ANqIAdB6ABqKQIANwMAIA5BgARqIAdB8ABqKQIANwMAIA5B4ANqIAdBgAFqKQIANwMAIA5B6ANqIAdBiAFqKQIANwMAIA4gBykCSDcDiAQgDiAHKQJgNwPwAyAOIAcpAng3A9gDIA5B0ANqIAdBoAFqKQIANwMAIA5ByANqIAdBmAFqKQIANwMAIA5BuANqIAdBuAFqKQIANwMAIA5BsANqIAdBsAFqKQIANwMAIA5BoANqIAdB0AFqKQIANwMAIA5BmANqIAdByAFqKQIANwMAIA4gBykCkAE3A8ADIA4gBykCqAE3A6gDIA4gBykCwAE3A5ADIAwEQCAHIAxBGGwQ3wQLIClBgICAgHhHDQEgFiEMIBghBwsgDiAgNgLMQSAOIAc2AshBIA4gDDYCxEFBypnCAEErIA5BxMEAakHUnMIAQYCkwgAQygMACyAOQeABaiAOQcgdaikDADcDACAOQdgBaiAOQcAdaikDADcDACAOQfABaiAOQfg4aikDADcDACAOQfgBaiAOQYA5aikDADcDACAOQYgCaiAOQZAEaikDADcDACAOQZACaiAOQZgEaikDADcDACAOIA4pA7gdNwPQASAOIA4pA/A4NwPoASAOIA4pA4gENwOAAiAOQagCaiAOQYAEaikDADcDACAOQaACaiAOQfgDaikDADcDACAOQbgCaiAOQeADaikDADcDACAOQcACaiAOQegDaikDADcDACAOQdACaiAOQcgDaikDADcDACAOQdgCaiAOQdADaikDADcDACAOIA4pA/ADNwOYAiAOIA4pA9gDNwOwAiAOIA4pA8ADNwPIAiAOQfACaiAOQbgDaikDADcDACAOQegCaiAOQbADaikDADcDACAOQYgDaiAOQaADaikDADcDACAOQYADaiAOQZgDaikDADcDACAOIA4pA6gDNwPgAiAOIA4pA5ADNwP4AgJAAkACQAJAAkACQAJAIBRBI08EQCATKAKgAyIfQQJ0IQVBACEMAkAgH0H/////A0sgBUH8////B0tyDQAgEygCnAMhBwJ/IAVFBEBBBCEkQQAMAQtB0c7FAC0AABpBBCEMIAVBBBDWBCIkRQ0BIB8LIUIgBQRAICQgByAF/AoAAAtBIyEHIA5BIzYCECAOQQA2ArADIA5CgICAgMAANwKoAyAKRQ0HIAohBUEAIQwDQCAHIAxqIglBCWohByAJQXZLDQMgByAUSw0EQdHOxQAtAAAaQewAQQQQ1gQiB0UNBSATIAlBDGxqIggoAggiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAIEIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCCCAHIAY2AgQgByALNgIAIAgoAhQiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAIQIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCFCAHIAY2AhAgByALNgIMIAgoAiAiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAIcIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCICAHIAY2AhwgByALNgIYIAgoAiwiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAIoIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCLCAHIAY2AiggByALNgIkIAgoAjgiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAI0IQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCOCAHIAY2AjQgByALNgIwIAgoAkQiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAJAIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCRCAHIAY2AkAgByALNgI8IAgoAlAiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAJMIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCUCAHIAY2AkwgByALNgJIIAgoAlwiDEECdCEPQQAhCyAMQf////8DSyAPQfz///8HS3INEyAIKAJYIQ0CfyAPRQRAQQQhBkEADAELQdHOxQAtAAAaQQQhCyAPQQQQ1gQiBkUNFCAMCyELIA8EQCAGIA0gD/wKAAALIAcgDDYCXCAHIAY2AlggByALNgJUIAgoAmgiC0ECdCEPQQAhBiALQf////8DSyAPQfz///8HS3INBiAIKAJkIQgCfyAPRQRAQQQhDEEADAELQdHOxQAtAAAaQQQhBiAPQQQQ1gQiDEUNByALCyENIA8EQCAMIAggD/wKAAALIAcgCzYCaCAHIAw2AmQgByANNgJgIAcoAgQhCCAHKAIIIQwgBygCDCEPIAcoAgAhCyAOQbgdaiAHQRBqQdwA/AoAACAHQewAEN8EIAtBgICAgHhGBEAgDiAPNgL4OCAOIAw2AvQ4IA4gCDYC8DhBypnCAEErIA5B8DhqQbChwgBB8KPCABDKAwALIA5BoARqIA5BuB1qQdwA/AoAACAOKAKwAyINIA4oAqgDRgRAIA5BqANqQeCjwgAQmwMLIA4oAqwDIA1B7ABsaiIHIA82AgwgByAMNgIIIAcgCDYCBCAHIAs2AgAgB0EQaiAOQaAEakHcAPwKAAAgCUEBaiEHIA4gDUEBaiIINgKwA0EIIQwgBUEBayIFDQALDAYLIAwgBUH4gcAAEMgEAAtBIiAUQZCgwgAQ2QMACyAJIAdB0KPCABDmBAALIAcgFEHQo8IAEOUEAAtBBEHsAEGUm8IAEMgEAAsgBiAPQfiBwAAQyAQACyAIQRxPDQELA0AgDkHAHWpBADoAACAOQgA3A7gdIwBBkAFrIgUkACAOQbgdaiIHLQAIIQggBy0AByEMIActAAYhDyAHLQAFIQsgBy0ABCEJIActAAMhDSAHLQACIQMgBy0AASEGIActAAAhByAFQYgBaiISQeD2wAAoAgAiHTYCACAFQdj2wAApAgAiygE3A4ABIAcEQCAFQYABakHM98AAEKUDIAUoAoQBIAc2AgAgBUEBNgKIAQsgBUH4AGogEigCACIHNgIAIAVBCGogBzYCACAFIAUpA4ABIswBNwNwIAUgzAE3AwAgEiAdNgIAIAUgygE3A4ABIAYEQCAFQYABakHM98AAEKUDIAUoAoQBIAY2AgAgBUEBNgKIAQsgBUH4AGoiBiAFQYgBaiIHKAIAIhI2AgAgBUEUaiASNgIAIAUgBSkDgAEiygE3A3AgBSDKATcCDCAHQeD2wAAoAgAiEjYCACAFQdj2wAApAgAiygE3A4ABIAMEQCAFQYABakHM98AAEKUDIAUoAoQBIAM2AgAgBUEBNgKIAQsgBiAHKAIAIgM2AgAgBUEgaiADNgIAIAUgBSkDgAEizAE3A3AgBSDMATcDGCAHIBI2AgAgBSDKATcDgAEgDQRAIAVBgAFqQcz3wAAQpQMgBSgChAEgDTYCACAFQQE2AogBCyAFQfgAaiINIAVBiAFqIgcoAgAiAzYCACAFQSxqIAM2AgAgBSAFKQOAASLKATcDcCAFIMoBNwIkIAdB4PbAACgCACIDNgIAIAVB2PbAACkCACLKATcDgAEgCQRAIAVBgAFqQcz3wAAQpQMgBSgChAEgCTYCACAFQQE2AogBCyANIAcoAgAiCTYCACAFQThqIAk2AgAgBSAFKQOAASLMATcDcCAFIMwBNwMwIAcgAzYCACAFIMoBNwOAASALBEAgBUGAAWpBzPfAABClAyAFKAKEASALNgIAIAVBATYCiAELIAVB+ABqIgsgBUGIAWoiBygCACIJNgIAIAVBxABqIAk2AgAgBSAFKQOAASLKATcDcCAFIMoBNwI8IAdB4PbAACgCACIJNgIAIAVB2PbAACkCACLKATcDgAEgDwRAIAVBgAFqQcz3wAAQpQMgBSgChAEgDzYCACAFQQE2AogBCyALIAcoAgAiDzYCACAFQdAAaiAPNgIAIAUgBSkDgAEizAE3A3AgBSDMATcDSCAHIAk2AgAgBSDKATcDgAEgDARAIAVBgAFqQcz3wAAQpQMgBSgChAEgDDYCACAFQQE2AogBCyAFQfgAaiAFQYgBaiIHKAIAIgw2AgAgBUHcAGogDDYCACAFIAUpA4ABIsoBNwNwIAUgygE3AlQgB0Hg9sAAKAIANgIAIAVB2PbAACkCADcDgAEgCARAIAVBgAFqQcz3wAAQpQMgBSgChAEgCDYCACAFQQE2AogBCyAFQegAaiAHKAIANgIAIAUgBSkDgAE3A2AgDkH8BGogBUHsAPwKAAAgBUGQAWokACAOKAKwAyIFIA4oAqgDRgRAIA5BqANqQcCjwgAQmwMLIA4oAqwDIAVB7ABsaiAOQfwEakHsAPwKAAAgDiAFQQFqIgU2ArADIAVBHEkNAAsLIA5B+DhqIA5BsANqIgUoAgAiBzYCACAOIA4pAqgDNwPwOCAHQRxHDQQgDkGQBGogDigC9DgiBUEMaigCADYCACAOQQA2Avg4IA4gBSkCBDcDiAQgBSgCACEcIA5BuB1qIAVBEGpBwBf8CgAAIA5B8DhqEOsCIA4oAvA4IgcEQCAFIAdB7ABsEN8ECyAcQYCAgIB4Rg0FIA5BsB1qIA5BkARqKAIANgIAIA4gDikDiAQ3A6gdIA5B6AVqIA5BuB1qQcAX/AoAACAOIARBI2oiBTYCECAEQcwAaiEHAkACQAJAAkACQAJAAkACQAJAAkAgBUFWTQRAIAcgFEsNAUHRzsUALQAAGkHsA0EEENYEIgVFDQIgEyAKQewAbGohDUGUfCEMA0AgDCANaiIIQZgHaigCACILQQJ0IQ9BACEJIAtB/////wNLIA9B/P///wdLcg0EIAhBlAdqKAIAIQMCfyAPRQRAQQQhCEEADAELQdHOxQAtAAAaQQQhCSAPQQQQ1gQiCEUNBSALCyEJIA8EQCAIIAMgD/wKAAALIAUgDGoiD0HsA2ogCTYCACAPQfQDaiALNgIAIA9B8ANqIAg2AgAgDEEMaiIMDQALIAUoAgwhIyAFKAIIITAgBSgCBCEzIAUoAgAhNCAOQbgdaiIIIAVBEGpB3AP8CgAAIAVB7AMQ3wQgNEGAgICAeEYNBCAOQfw0aiAIQdwD/AoAACAHIBRPDQYgEyAHQQxsaiIHKAIIIiFBAnQhBUEAIQ8gIUH/////A0sgBUH8////B0tyDQUgBygCBCEHAn8gBUUEQEEEIStBAAwBC0HRzsUALQAAGkEEIQ8gBUEEENYEIitFDQYgIQshQyAFBEAgKyAHIAX8CgAACyAOIARBzQBqIgc2AhAgDkEANgLIAyAOQoCAgIDAADcCwAMgBEHPAGoiBSAUSw0OQdHOxQAtAAAaQRhBBBDWBCIIRQ0TIBMgB0EMbGoiDCgCCCIPQQJ0IQdBACEGIA9B/////wNLIAdB/P///wdLcg0VIAwoAgQhCwJ/IAdFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEGIAdBBBDWBCIJRQ0WIA8LIQ0gBwRAIAkgCyAH/AoAAAsgCCAPNgIIIAggCTYCBCAIIA02AgAgDCgCFCILQQJ0IQdBACEGIAtB/////wNLIAdB/P///wdLcg0VIAwoAhAhDAJ/IAdFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEGIAdBBBDWBCIJRQ0WIAsLIQ8gBwRAIAkgDCAH/AoAAAsgCCALNgIUIAggCTYCECAIIA82AgwgCCkCBCHKASAIKQIQIcwBIAgoAgAhDCAIQRgQ3wQgDEGAgICAeEYNByAOKALIAyIIIA4oAsADRgRAIA5BwANqQfCiwgAQmQMLIA4oAsQDIAhBGGxqIgcgzAE3AhAgByAPNgIMIAcgygE3AgQgByAMNgIAIA4gCEEBajYCyAMgBEHRAGohCAJAIAVBfU0EQCAIIBRLBEAgCCEFDBELQQAhBkHRzsUALQAAGkEYQQQQ1gQiB0UNFSATIAVBDGxqIg8oAggiC0ECdCEMIAtB/////wNLIAxB/P///wdLcg0ZIA8oAgQhCQJ/IAxFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIAxBBBDWBCIFRQ0aIAsLIQ0gDARAIAUgCSAM/AoAAAsgByALNgIIIAcgBTYCBCAHIA02AgAgDygCFCILQQJ0IQxBACEGIAtB/////wNLIAxB/P///wdLcg0ZIA8oAhAhCQJ/IAxFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIAxBBBDWBCIFRQ0aIAsLIQ8gDARAIAUgCSAM/AoAAAsgByALNgIUIAcgBTYCECAHIA82AgwgBykCBCHKASAHKQIQIcwBIAcoAgAhDCAHQRgQ3wQgDEGAgICAeEYNCSAOKALIAyIHIA4oAsADRgRAIA5BwANqQfCiwgAQmQMLIA4oAsQDIAdBGGxqIgUgzAE3AhAgBSAPNgIMIAUgygE3AgQgBSAMNgIAIA4gB0EBajYCyAMgBEHTAGohCyAIQX1NDQEgCCEFIAshCAsgBSAIQeCiwgAQ5gQACyALIBRLBEAgCyEFDA8LQQAhBkHRzsUALQAAGkEYQQQQ1gQiB0UNEyATIAhBDGxqIggoAggiD0ECdCEMIA9B/////wNLIAxB/P///wdLcg0XIAgoAgQhCQJ/IAxFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIAxBBBDWBCIFRQ0YIA8LIQ0gDARAIAUgCSAM/AoAAAsgByAPNgIIIAcgBTYCBCAHIA02AgAgCCgCFCIJQQJ0IQxBACEGIAlB/////wNLIAxB/P///wdLcg0XIAgoAhAhCAJ/IAxFBEBBBCEFQQAMAQtB0c7FAC0AABpBBCEGIAxBBBDWBCIFRQ0YIAkLIQ8gDARAIAUgCCAM/AoAAAsgByAJNgIUIAcgBTYCECAHIA82AgwgBykCBCHKASAHKQIQIcwBIAcoAgAhCCAHQRgQ3wQgCEGAgICAeEYNByAOKALIAyIHIA4oAsADRgRAIA5BwANqQfCiwgAQmQMLIA4oAsQDIAdBGGxqIgUgzAE3AhAgBSAPNgIMIAUgygE3AgQgBSAINgIAIA4gB0EBaiIdNgLIAyAOKALEAyEHIA4oAsADIQwgHUEDRg0IDAkLIAUgB0GgoMIAEOYEAAsgByAUQaCgwgAQ5QQAC0EEQewDQZSbwgAQyAQACyAJIA9B+IHAABDIBAALIA4gIzYC+DggDiAwNgL0OCAOIDM2AvA4QcqZwgBBKyAOQfA4akGwocIAQZCjwgAQygMACyAPIAVB+IHAABDIBAALIAcgFEGwoMIAENkDAAsgDiAPNgLAHSAOIMoBNwO4HUHKmcIAQSsgDkG4HWpBsKHCAEGAo8IAEMoDAAsgDkHAHWogB0EgaikCADcDACAOQcgdaiAHQShqKQIANwMAIA5B+DhqIAdBOGopAgA3AwAgDkGAOWogB0FAaykCADcDACAOIAcpAhg3A7gdIA4gBykCMDcD8DggBykCECHMASAHKAIMIR0gBygCCCENIAcoAgQhAyAHKAIAITUgDARAIAcgDEEYbBDfBAsgNUGAgICAeEcNASADIQwgDSEHCyAOIB02ApAEIA4gBzYCjAQgDiAMNgKIBEHKmcIAQSsgDkGIBGpB1JzCAEHQosIAEMoDAAsgDkGYOWogDkHIHWopAwA3AwAgDkGQOWogDkHAHWopAwA3AwAgDkHgOGogDkH4OGopAwA3AwAgDkHoOGogDkGAOWopAwA3AwAgDkGoOWogDkGAA2opAwA3AwAgDkGwOWogDkGIA2opAwA3AwAgDiAOKQO4HTcDiDkgDiAOKQPwODcD2DggDiAOKQP4AjcDoDkCQAJ/AkACQAJAAkACQAJAAkAgCyAUSQRAIBMgC0EMbGoiBygCCCIiQQJ0IQVBACEPAkACQCAiQf////8DSyAFQfz///8HS3INACAHKAIEIQcCfyAFRQRAQQQhLEEADAELQdHOxQAtAAAaQQQhDyAFQQQQ1gQiLEUNASAiCyFEIAUEQCAsIAcgBfwKAAALIA4gBEHUAGoiEjYCECAOQQA2AuADIA5CgICAgMAANwLYAyAXRQRAQQQhCUEAIQcMCAsgBEHWAGoiCCAUSw0EQQAhBkHRzsUALQAAGkEYQQQQ1gQiBUUNFCATIBJBDGxqIggoAggiB0ECdCEMIAdB/////wNLIAxB/P///wdLcg0YIAgoAgQhDwJ/IAxFBEBBBCEJQQAMAQtB0c7FAC0AABpBBCEGIAxBBBDWBCIJRQ0ZIAcLIQsgDARAIAkgDyAM/AoAAAsgBSAHNgIIIAUgCTYCBCAFIAs2AgAgCCgCFCIMQQJ0IQdBACEJIAxB/////wNLIAdB/P///wdLcg0BIAgoAhAhCAJ/IAdFBEBBBCEPQQAMAQtB0c7FAC0AABpBBCEJIAdBBBDWBCIPRQ0CIAwLIQYgBwRAIA8gCCAH/AoAAAsgBSAMNgIUIAUgDzYCECAFIAY2AgwgBSkCBCHKASAFKQIQIc8BIAUoAgAhByAFQRgQ3wQgB0GAgICAeEYNDiAKQQJrIQsgDigC4AMiCCAOKALYA0YEQCAOQdgDakGwosIAEJkDCyAOKALcAyIJIAhBGGxqIgUgzwE3AhAgBSAGNgIMIAUgygE3AgQgBSAHNgIAIA4gCEEBaiIHNgLgAyALRQ0GIARB2ABqIQggEyAKQewAbGohDANAIAhBAmtBfUsNBCAIIBRLDQVB0c7FAC0AABpBGEEEENYEIg9FDRUgDEGQCGooAgAiCUECdCEHQQAhBSAJQf////8DSyAHQfz///8HS3INBiAMQYwIaigCACEEAn8gB0UEQEEEIQZBAAwBC0HRzsUALQAAGkEEIQUgB0EEENYEIgZFDQcgCQshBSAHBEAgBiAEIAf8CgAACyAPIAk2AgggDyAGNgIEIA8gBTYCACAMQZwIaigCACIJQQJ0IQdBACEGIAlB/////wNLIAdB/P///wdLcg0XIAxBmAhqKAIAIQQCfyAHRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhBiAHQQQQ1gQiBUUNGCAJCyEGIAcEQCAFIAQgB/wKAAALIA8gCTYCFCAPIAU2AhAgDyAGNgIMIA8pAgQhygEgDykCECHPASAPKAIAIQcgD0EYEN8EIAdBgICAgHhGDQ8gDigC4AMiDyAOKALYA0YEQCAOQdgDakGwosIAEJkDCyAOKALcAyIJIA9BGGxqIgUgzwE3AhAgBSAGNgIMIAUgygE3AgQgBSAHNgIAIA4gD0EBaiIHNgLgAyAMQRhqIQwgCEECaiEIIAtBAWsiCw0ACwwGCyAPIAVB+IHAABDIBAALIAkgB0H4gcAAEMgEAAsgCyAUQcCgwgAQ2QMACyAIQQJrIAhBoKLCABDmBAALIAggFEGgosIAEOUEAAsgBSAHQfiBwAAQyAQACyAHQRpLDQELIAdBGGwhDCAOQcQ5aiEFQZCSwgAoAgAhCEGIksIAKQIAIcoBA0AgDkHAOWoiCyAINgIAIAUgygE3AgAgBUEIaiAINgIAIA4gygE3A7g5IA4oAtgDIAdGBEAgDkHYA2pBkKLCABCZAyAOKALcAyEJCyAJIAxqIg8gDikDuDk3AgAgD0EQaiAOQcg5aikDADcCACAPQQhqIAspAwA3AgAgDiAHQQFqIgc2AuADIAxBGGohDCAHQRtHDQALIA4oAtwDIQwgDigC2AMhDwwBCyAOKALYAyEPIA4oAtwDIgwgB0EbRw0BGgsgDCgCDCEHIAwoAgghNiAMKAIEIQQgDCgCACE9IA5BuB1qIAxBEGpB+AT8CgAAIA8EQCAMIA9BGGwQ3wQLID1BgICAgHhHDQEgBCEPIDYLIQUgDiAHNgL4OCAOIAU2AvQ4IA4gDzYC8DhBypnCAEErIA5B8DhqQdScwgBBgKLCABDKAwALIA5B0DlqIA5BuB1qQfgE/AoAACAOIBIgG2oiCDYCEAJAAkACQAJAAkACQAJAAkAgCCAIIApqIhdNBEAgFCAXSQ0BIAqtQgx+IsoBpyESQQAhDyDKAUIgiKcgEkH8////B0tyDQIgEkUEQEEEIQUMBQtB0c7FAC0AABpBBCEPIBJBBBDWBCIFRQ0CIApFDQQgEyAIQQxsaiEIQQAhDyAKIQsDQCAPIBJHBEAgCCgCCCIbQQJ0IQlBACEMIBtB/////wNLIAlB/P///wdLcg0FIAgoAgQhOQJ/IAlFBEBBBCEGQQAMAQtB0c7FAC0AABpBBCEMIAlBBBDWBCIGRQ0GIBsLIS8gCQRAIAYgOSAJ/AoAAAsgCEEMaiEIIAUgD2oiDCAvNgIAIAxBCGogGzYCACAMQQRqIAY2AgAgD0EMaiEPIAtBAWsiCw0BCwsgDiAKNgL4AyAOIAU2AvQDIA4gCjYC8AMgCkEbTQ0FIAoiC0EcRw0HDAYLIAggF0HQoMIAEOYEAAsgFyAUQdCgwgAQ5QQACyAPIBJBlJvCABDIBAALIAwgCUH4gcAAEMgEAAsgDiAKNgL4AyAOIAU2AvQDIA5BADYC8AMLIApBDGwhDEGIksIAKQIAIcoBQZCSwgAoAgAhBQNAIA4oAvADIApGBEAgDkHwA2pB8KHCABCfAwsgDigC9AMgDGoiCCDKATcCACAIQQhqIAU2AgAgDiAKQQFqIgo2AvgDIAxBDGohDCAKQRxHDQALIA4oAvQDIQUgDigC8AMhCgsgBSgCDCELIAUoAgghBiAFKAIEIRIgBSgCACE5IA5BuB1qIAVBEGpBwAL8CgAAIAoEQCAFIApBDGwQ3wQLIDlBgICAgHhHDQEgEiEKIAYhBQsgDiALNgL4OCAOIAU2AvQ4IA4gCjYC8DhBypnCAEErIA5B8DhqQbChwgBB4KHCABDKAwALIA5ByD5qIA5BuB1qQcAC/AoAACAOIBc2AhACQAJAAkACQAJAAkACQCAUIBdBBGoiCU8EQEEAIQxB0c7FAC0AABpBMEEEENYEIghFDQEgEyAXQQxsaiIPKAIIIhtBAnQhCiAbQf////8DSyAKQfz///8HS3INEyAPKAIEIS8CfyAKRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhDCAKQQQQ1gQiBUUNFCAbCyEMIAoEQCAFIC8gCvwKAAALIAggGzYCCCAIIAU2AgQgCCAMNgIAIA8oAhQiG0ECdCEKQQAhDCAbQf////8DSyAKQfz///8HS3INEyAPKAIQIS8CfyAKRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhDCAKQQQQ1gQiBUUNFCAbCyEMIAoEQCAFIC8gCvwKAAALIAggGzYCFCAIIAU2AhAgCCAMNgIMIA8oAiAiG0ECdCEKQQAhDCAbQf////8DSyAKQfz///8HS3INEyAPKAIcIS8CfyAKRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhDCAKQQQQ1gQiBUUNFCAbCyEMIAoEQCAFIC8gCvwKAAALIAggGzYCICAIIAU2AhwgCCAMNgIYIA8oAiwiG0ECdCEKQQAhDCAbQf////8DSyAKQfz///8HS3INEyAPKAIoIQ8CfyAKRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhDCAKQQQQ1gQiBUUNFCAbCyEMIAoEQCAFIA8gCvwKAAALIAggDDYCJCAIIBs2AiwgCCAFNgIoIA5BwB1qIgogCEEQaiIFQQhqKQIANwMAIA5ByB1qIgwgBUEQaikCADcDACAOQdAdaiIPIAVBGGopAgA3AwAgDiAFKQIANwO4HSAIKAIEIRsgCCgCCCEvIAgoAgwhPiAIKAIAIT8gCEEwEN8EID9BgICAgHhGDQIgDkGgwQBqIA8pAwA3AwAgDkGYwQBqIAwpAwA3AwAgDkGQwQBqIAopAwA3AwAgDiAOKQO4HTcDiEEgDiAJNgIQIA5BADYCkAQgDkKAgICAwAA3AogEAkAgFCAXQQZqIkBPBH9B0c7FAC0AABpBGEEEENYEIgVFDRIgEyAJQQxsaiIIKAIIIgxBAnQhCkEAIQ8gDEH/////A0sgCkH8////B0tyDQUgCCgCBCE6An8gCkUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQ8gCkEEENYEIglFDQYgDAshDyAKBEAgCSA6IAr8CgAACyAFIAw2AgggBSAJNgIEIAUgDzYCACAIKAIUIgxBAnQhCkEAIQ8gDEH/////A0sgCkH8////B0tyDQYgCCgCECE6An8gCkUEQEEEIQlBAAwBC0HRzsUALQAAGkEEIQ8gCkEEENYEIglFDQcgDAshCCAKBEAgCSA6IAr8CgAACyAFIAw2AhQgBSAJNgIQIAUgCDYCDCAFKQIEIcoBIAUpAhAhzwEgBSgCACEKIAVBGBDfBCAKQYCAgIB4RgRAIA4gCDYCwB0gDiDKATcDuB1BypnCAEErIA5BuB1qQbChwgBBwKHCABDKAwALIA5BiARqQaChwgAQmQMgDigCjAQiBSDKATcCBCAFIAo2AgAgBSDPATcCECAFIAg2AgwgDkEBNgKQBCAXQQhqIhcgFE0NASAXBSBACyAUQZChwgAQ5QQAC0EAIQlB0c7FAC0AABpBGEEEENYEIgpFDRAgEyBAQQxsaiIPKAIIIgxBAnQhCCAMQf////8DSyAIQfz///8HS3INBSAPKAIEIRQCfyAIRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhCSAIQQQQ1gQiBUUNBiAMCyETIAgEQCAFIBQgCPwKAAALIAogDDYCCCAKIAU2AgQgCiATNgIAIA8oAhQiCUECdCEIQQAhDCAJQf////8DSyAIQfz///8HS3INBiAPKAIQIQ8CfyAIRQRAQQQhBUEADAELQdHOxQAtAAAaQQQhDCAIQQQQ1gQiBUUNByAJCyEMIAgEQCAFIA8gCPwKAAALIAogCTYCFCAKIAU2AhAgCiAMNgIMIAopAgQhygEgCikCECHPASAKQRgQ3wQgDigCkAQiCiAOKAKIBEYEQCAOQYgEakGgocIAEJkDCyAOKAKMBCAKQRhsaiIFIM8BNwIQIAUgDDYCDCAFIMoBNwIEIAUgEzYCACAOIApBAWoiDzYCkAQgDigCjAQhCiAOKAKIBCEIAkAgD0ECRwRAIAohCSAIIQUMAQsgDkHAHWogCkEgaikCADcDACAOQcgdaiAKQShqKQIANwMAIA4gCikCGDcDuB0gCikCECHKASAKKAIMIQ8gCigCCCEJIAooAgQhBSAKKAIAIQwgCARAIAogCEEYbBDfBAsgDEGAgICAeEcNCAsgDiAPNgL4OCAOIAk2AvQ4IA4gBTYC8DhBypnCAEErIA5B8DhqQdScwgBBgKHCABDKAwALIAkgFEHgoMIAEOUEAAtBBEEwQZSbwgAQyAQACyAOID42Avg4IA4gLzYC9DggDiAbNgLwOEHKmcIAQSsgDkHwOGpBsKHCAEHQocIAEMoDAAsgDyAKQfiBwAAQyAQACyAPIApB+IHAABDIBAALIAkgCEH4gcAAEMgEAAsgDCAIQfiBwAAQyAQACyAOQbjBAGoiCiAOQcgdaikDADcDACAOQbDBAGoiCCAOQcAdaikDADcDACAOIA4pA7gdNwOoQSAOIBc2AhAgFyAOKAIMRw0BIBBBHGogDkEUakGwAfwKAAAgEEH0AWogDkHgAWopAwA3AgAgEEHsAWogDkHYAWopAwA3AgAgECAOKQPQATcC5AEgECAOKQPoATcC/AEgEEGEAmogDkHwAWopAwA3AgAgEEGMAmogDkH4AWopAwA3AgAgECAOKQOwAjcClAIgEEGcAmogDkG4AmopAwA3AgAgEEGkAmogDkHAAmopAwA3AgAgEEG8AmogDkHwAmopAwA3AgAgEEG0AmogDkHoAmopAwA3AgAgECAOKQPgAjcCrAIgEEHUAmogDkGQAmopAwA3AgAgEEHMAmogDkGIAmopAwA3AgAgECAOKQOAAjcCxAIgEEHsAmogDkGoAmopAwA3AgAgEEHkAmogDkGgAmopAwA3AgAgECAOKQOYAjcC3AIgEEGEA2ogDkHYAmopAwA3AgAgEEH8AmogDkHQAmopAwA3AgAgECAOKQPIAjcC9AIgEEGcA2ogDkGwOWopAwA3AgAgEEGUA2ogDkGoOWopAwA3AgAgECAOKQOgOTcCjAMgEEHMA2ogDkGYOWopAwA3AgAgEEHEA2ogDkGQOWopAwA3AgAgECAOKQOIOTcCvAMgEEHsA2ogDkGwHWooAgA2AgAgECAOKQOoHTcC5AMgEEHwA2ogDkHoBWpBwBf8CgAAIBBBwBtqIA5B/DRqQdwD/AoAACAQQbgfaiAOQeg4aikDADcCACAQQbAfaiAOQeA4aikDADcCACAQIA4pA9g4NwKoHyAQQdwfaiAOQdA5akH4BPwKAAAgEEHkJGogDkHIPmpBwAL8CgAAIBBBzCdqIA5BoMEAaikDADcCACAQQcQnaiAOQZjBAGopAwA3AgAgEEG8J2ogDkGQwQBqKQMANwIAIBAgDikDiEE3ArQnIBAgDikDqEE3AuwnIBBB9CdqIAgpAwA3AgAgEEH8J2ogCikDADcCACAQIBopAgA3AgAgEEEIaiAaQQhqKAIANgIAIBAgygE3AuQnIBAgDzYC4CcgECAJNgLcJyAQIAU2AtgnIBAgDDYC1CcgECA+NgKwJyAQIC82AqwnIBAgGzYCqCcgECA/NgKkJyAQIAs2AuAkIBAgBjYC3CQgECASNgLYJCAQIDk2AtQkIBAgBzYC2B8gECA2NgLUHyAQIAQ2AtAfIBAgPTYCzB8gECAiNgLIHyAQICw2AsQfIBAgRDYCwB8gECAhNgKkHyAQICs2AqAfIBAgQzYCnB8gECAjNgK8GyAQIDA2ArgbIBAgMzYCtBsgECA0NgKwGyAQIBw2AuADIBAgHzYC3AMgECAkNgLYAyAQIEI2AtQDIBAgzAE3ArQDIBAgHTYCsAMgECANNgKsAyAQIAM2AqgDIBAgNTYCpAMgECDLATcC3AEgECAgNgLYASAQIBg2AtQBIBAgFjYC0AEgECApNgLMASAQIC42AhggECAlNgIUIBAgLTYCECAQICY2AgwLICcoAgQhBSAZBEAgBSEHA0AgBygCACIKBEAgB0EEaigCACAKQQJ0EN8ECyAHQQxqIQcgGUEBayIZDQALCyAnKAIAIgoEQCAFIApBDGwQ3wQLIA5B0MEAaiQADAwLIA5BADYCuB0gDkEQaiAOQQxqIA5BuB1qQfCgwgAQlwQACyAOIAY2AsAdIA4gygE3A7gdQcqZwgBBKyAOQbgdakGwocIAQcCiwgAQygMACyAFIBRB4KLCABDlBAALIA5BkARqIAUoAgA2AgAgDiAOKQKoAzcDiAQLIA5B+DhqIA5BkARqKAIANgIAIA4gDikDiAQ3A/A4QcqZwgBBKyAOQfA4akGgo8IAQbCjwgAQygMACyAOIAk2AsAdIA4gygE3A7gdQcqZwgBBKyAOQbgdakGwocIAQbCkwgAQygMACyAJIAZB+IHAABDIBAALQQRBGEGUm8IAEMgEAAsgCyAPQfiBwAAQyAQACyAGIAdB+IHAABDIBAALIAwgCkH4gcAAEMgEAAsgBiAMQfiBwAAQyAQACwwEC0FgQQBBrJ/CABDmBAALQWBBAEGMn8IAEOYEAAsMCQsgESAWNgIYIBFBAzYCNCARQeifwgA2AjAgEUICNwI8IBEgEUHIAGqtQoCAgIDgAYQ3AxAgESARQRhqrUKAgICA4AGENwMIIBEgBTYCSCARIBFBCGo2AjggEEEEaiARQTBqENICIBBBgICAgHg2AgALIBFB4ABqJAAMAgsgCiAYQYyfwgAQ5QQACyAKIBZBrJ/CABDlBAALIBUoAsAtIQUCQCAVKAK8LSIKQYCAgIB4RgRAIBUoAsQtIgogFSgCyC0QzQQhByAFBEAgCiAFEN8ECyAqQYCAgIB4NgIAICogBzYCBAwBCyAVQcAFaiBBQfwn/AoAACAVIAU2ArwFIBUgCjYCuAUgFUHA1QBqIRJBACEIQQAhDCMAQaDlAGsiBCQAIARBsCdqIRYjAEHwDWsiCSQAAkACQCAVQbgFaiINKAIIIgUgFSgCsAVBEGsiCkYEQCAJQQA2AqgEIAlCgICAgBA3AqAEIAlBoARqIBVBoAVqELYCIAUEQCANKAIEIQcgBUEMbCEFA0AgCUGgBGogBxC2AiAHQQxqIQcgBUEMayIFDQALCyAJQaAEaiIFIA1BDGoQtgIgBSANQRhqELYCIAUgDUEkahC2AiAFIA1BMGoQtgIgBSANQTxqELYCIAUgDUHIAGoQtgIgBSANQdQAahC2AiAFIA1B4ABqELYCIAUgDUHsAGoQtgIgBSANQfgAahC2AiAFIA1BhAFqELYCIAUgDUGQAWoQtgIgBSANQZwBahC2AiAFIA1BqAFqELYCIAUgDUG0AWoQtgIgBSANQcABahC2AiAFIA1BzAFqELYCIAUgDUHYAWoQtgIgBSANQeQBahC2AiAFIA1B8AFqELYCIAUgDUH8AWoQtgIgBSANQYgCahC2AiAJQawEaiAFEIgBIAkoAqAEIgUEQCAJKAKkBCAFEN8ECyAJQQA2AqgEIAlCgICAgBA3AqAEIAkgCSgCsAQiByAJKAK0BCIKEH8gCUHABGogCUEIaigCADYCACAJQdAEaiAJQRRqKAIANgIAIAkgCSkCADcDuAQgCSAJKQIMNwPIBCAJKAKgBCAJKAKoBCIFayAKSQRAIAlBoARqIAUgCkEBQQEQiAMgCSgCqAQhBQsgCgRAIAkoAqQEIAVqIAcgCvwKAAALIAkgBSAKajYCqAQgCUHUBGogCUGgBGoQiAEgCSgCoAQiBQRAIAkoAqQEIAUQ3wQLIAlBADYCqAQgCUKAgICAEDcCoAQgCSAJKALYBCIHIAkoAtwEIgoQfyAJQegEaiAJQQhqKAIANgIAIAkgCSkCADcD4AQgCSgCDCIFBEAgCSgCECAFQQJ0EN8ECyAJKAKgBCAJKAKoBCIFayAKSQRAIAlBoARqIAUgCkEBQQEQiAMgCSgCqAQhBQsgCgRAIAkoAqQEIAVqIAcgCvwKAAALIAkgBSAKajYCqAQgCUGgBGoiBSANQcQCahC2AiAFIA1B0AJqELYCIAUgDUHcAmoQtgIgBSANQegCahC2AiAFIA1BlAJqELYCIAUgDUGgAmoQtgIgCUHsBGogBRCIASAJKAKgBCIFBEAgCSgCpAQgBRDfBAsgCUEANgKoBCAJQoCAgIAQNwKgBCAJIAkoAvAEIgcgCSgC9AQiChB/IAlBgAVqIAlBCGooAgA2AgAgCUGQBWogCUEUaigCADYCACAJIAkpAgA3A/gEIAkgCSkCDDcDiAUgCSgCoAQgCSgCqAQiBWsgCkkEQCAJQaAEaiAFIApBAUEBEIgDIAkoAqgEIQULIAoEQCAJKAKkBCAFaiAHIAr8CgAACyAJIAUgCmo2AqgEIAlBoARqIgUgDUH0AmoQtgIgBSANQYADahC2AiAFIA1BrAJqELYCIAUgDUG4AmoQtgIgCUGUBWogBRCIASAJKAKgBCIFBEAgCSgCpAQgBRDfBAsgCUEANgKoBCAJQoCAgIAQNwKgBCAJIAkoApgFIgcgCSgCnAUiChB/IAlBqAVqIAlBCGooAgA2AgAgCSAJKQIANwOgBSAJKAIMIgUEQCAJKAIQIAVBAnQQ3wQLIAkoAqAEIAkoAqgEIgVrIApJBEAgCUGgBGogBSAKQQFBARCIAyAJKAKoBCEFCyAKBEAgCSgCpAQgBWogByAK/AoAAAsgCSAFIApqNgKoBCAJQawFaiAJQaAEahCIASAJKAKgBCIFBEAgCSgCpAQgBRDfBAsgCUEANgKoBCAJQoCAgIAQNwKgBCAJIAkoArAFIgcgCSgCtAUiChB/IAlBwAVqIAlBCGooAgA2AgAgCSAJKQIANwO4BSAJKAIMIgUEQCAJKAIQIAVBAnQQ3wQLIAkoAqAEIAkoAqgEIgVrIApJBEAgCUGgBGogBSAKQQFBARCIAyAJKAKoBCEFCyAKBEAgCSgCpAQgBWogByAK/AoAAAsgCSAFIApqNgKoBCAJQaAEaiIFIA1BjANqELYCIAUgDUGYA2oQtgIgBSANQdQDahC2AiAJQcQFaiAFEIgBIAkoAqAEIgUEQCAJKAKkBCAFEN8ECyAJQQA2AqgEIAlCgICAgBA3AqAEIAkgCSgCyAUiDyAJKALMBSIHEH8gCUHYBWogCUEIaiIFKAIANgIAIAkgCSkCADcD0AUgCSgCDCIKBEAgCSgCECAKQQJ0EN8ECyAJQRhqQQA2AgAgCUEQakIANwMAIAVCADcDACAJQgA3AwAjAEHwAmsiBSQAIAktABshCyAJLQAaIRggCS0AGSEDIAktABghBiAJLQAXIQ4gCS0AFiEQIAktABUhESAJLQAUIRMgCS0AEyEUIAktABIhGSAJLQARIRcgCS0AECEaIAktAA8hICAJLQAOIR0gCS0ADSEnIAktAAwhHyAJLQALISQgCS0ACiEhIAktAAkhKyAJLQAIISIgCS0AByEsIAktAAYhGyAJLQAFIS0gCS0ABCElIAktAAMhLiAJLQACISYgCS0AASEKIAktAAAhKSAFQegCaiIcQeD2wAAoAgAiIzYCACAFQdj2wAApAgAiygE3A+ACICkEQCAFQeACakHM98AAEKUDIAUoAuQCICk2AgAgBUEBNgLoAgsgBUHYAmogHCgCACIpNgIAIAVBCGogKTYCACAFIAUpA+ACIssBNwPQAiAFIMsBNwMAIBwgIzYCACAFIMoBNwPgAiAKBEAgBUHgAmpBzPfAABClAyAFKALkAiAKNgIAIAVBATYC6AILIAVB2AJqIikgBUHoAmoiCigCACIcNgIAIAVBFGogHDYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwIMIApB4PbAACgCACIcNgIAIAVB2PbAACkCACLKATcD4AIgJgRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgJjYCACAFQQE2AugCCyApIAooAgAiJjYCACAFQSBqICY2AgAgBSAFKQPgAiLLATcD0AIgBSDLATcDGCAKIBw2AgAgBSDKATcD4AIgLgRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgLjYCACAFQQE2AugCCyAFQdgCaiIuIAVB6AJqIgooAgAiJjYCACAFQSxqICY2AgAgBSAFKQPgAiLKATcD0AIgBSDKATcCJCAKQeD2wAAoAgAiJjYCACAFQdj2wAApAgAiygE3A+ACICUEQCAFQeACakHM98AAEKUDIAUoAuQCICU2AgAgBUEBNgLoAgsgLiAKKAIAIiU2AgAgBUE4aiAlNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3AzAgCiAmNgIAIAUgygE3A+ACIC0EQCAFQeACakHM98AAEKUDIAUoAuQCIC02AgAgBUEBNgLoAgsgBUHYAmoiLSAFQegCaiIKKAIAIiU2AgAgBUHEAGogJTYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwI8IApB4PbAACgCACIlNgIAIAVB2PbAACkCACLKATcD4AIgGwRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgGzYCACAFQQE2AugCCyAtIAooAgAiGzYCACAFQdAAaiAbNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A0ggCiAlNgIAIAUgygE3A+ACICwEQCAFQeACakHM98AAEKUDIAUoAuQCICw2AgAgBUEBNgLoAgsgBUHYAmoiLCAFQegCaiIKKAIAIhs2AgAgBUHcAGogGzYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwJUIApB4PbAACgCACIbNgIAIAVB2PbAACkCACLKATcD4AIgIgRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgIjYCACAFQQE2AugCCyAsIAooAgAiIjYCACAFQegAaiAiNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A2AgCiAbNgIAIAUgygE3A+ACICsEQCAFQeACakHM98AAEKUDIAUoAuQCICs2AgAgBUEBNgLoAgsgBUHYAmoiKyAFQegCaiIKKAIAIiI2AgAgBUH0AGogIjYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwJsIApB4PbAACgCACIiNgIAIAVB2PbAACkCACLKATcD4AIgIQRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgITYCACAFQQE2AugCCyArIAooAgAiITYCACAFQYABaiAhNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A3ggCiAiNgIAIAUgygE3A+ACICQEQCAFQeACakHM98AAEKUDIAUoAuQCICQ2AgAgBUEBNgLoAgsgBUHYAmoiJCAFQegCaiIKKAIAIiE2AgAgBUGMAWogITYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwKEASAKQeD2wAAoAgAiITYCACAFQdj2wAApAgAiygE3A+ACIB8EQCAFQeACakHM98AAEKUDIAUoAuQCIB82AgAgBUEBNgLoAgsgJCAKKAIAIh82AgAgBUGYAWogHzYCACAFIAUpA+ACIssBNwPQAiAFIMsBNwOQASAKICE2AgAgBSDKATcD4AIgJwRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgJzYCACAFQQE2AugCCyAFQdgCaiInIAVB6AJqIgooAgAiHzYCACAFQaQBaiAfNgIAIAUgBSkD4AIiygE3A9ACIAUgygE3ApwBIApB4PbAACgCACIfNgIAIAVB2PbAACkCACLKATcD4AIgHQRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgHTYCACAFQQE2AugCCyAnIAooAgAiHTYCACAFQbABaiAdNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A6gBIAogHzYCACAFIMoBNwPgAiAgBEAgBUHgAmpBzPfAABClAyAFKALkAiAgNgIAIAVBATYC6AILIAVB2AJqIiAgBUHoAmoiCigCACIdNgIAIAVBvAFqIB02AgAgBSAFKQPgAiLKATcD0AIgBSDKATcCtAEgCkHg9sAAKAIAIh02AgAgBUHY9sAAKQIAIsoBNwPgAiAaBEAgBUHgAmpBzPfAABClAyAFKALkAiAaNgIAIAVBATYC6AILICAgCigCACIaNgIAIAVByAFqIBo2AgAgBSAFKQPgAiLLATcD0AIgBSDLATcDwAEgCiAdNgIAIAUgygE3A+ACIBcEQCAFQeACakHM98AAEKUDIAUoAuQCIBc2AgAgBUEBNgLoAgsgBUHYAmoiFyAFQegCaiIKKAIAIho2AgAgBUHUAWogGjYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwLMASAKQeD2wAAoAgAiGjYCACAFQdj2wAApAgAiygE3A+ACIBkEQCAFQeACakHM98AAEKUDIAUoAuQCIBk2AgAgBUEBNgLoAgsgFyAKKAIAIhk2AgAgBUHgAWogGTYCACAFIAUpA+ACIssBNwPQAiAFIMsBNwPYASAKIBo2AgAgBSDKATcD4AIgFARAIAVB4AJqQcz3wAAQpQMgBSgC5AIgFDYCACAFQQE2AugCCyAFQdgCaiIUIAVB6AJqIgooAgAiGTYCACAFQewBaiAZNgIAIAUgBSkD4AIiygE3A9ACIAUgygE3AuQBIApB4PbAACgCACIZNgIAIAVB2PbAACkCACLKATcD4AIgEwRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgEzYCACAFQQE2AugCCyAUIAooAgAiEzYCACAFQfgBaiATNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A/ABIAogGTYCACAFIMoBNwPgAiARBEAgBUHgAmpBzPfAABClAyAFKALkAiARNgIAIAVBATYC6AILIAVB2AJqIhEgBUHoAmoiCigCACITNgIAIAVBhAJqIBM2AgAgBSAFKQPgAiLKATcD0AIgBSDKATcC/AEgCkHg9sAAKAIAIhM2AgAgBUHY9sAAKQIAIsoBNwPgAiAQBEAgBUHgAmpBzPfAABClAyAFKALkAiAQNgIAIAVBATYC6AILIBEgCigCACIQNgIAIAVBkAJqIBA2AgAgBSAFKQPgAiLLATcD0AIgBSDLATcDiAIgCiATNgIAIAUgygE3A+ACIA4EQCAFQeACakHM98AAEKUDIAUoAuQCIA42AgAgBUEBNgLoAgsgBUHYAmoiDiAFQegCaiIKKAIAIhA2AgAgBUGcAmogEDYCACAFIAUpA+ACIsoBNwPQAiAFIMoBNwKUAiAKQeD2wAAoAgAiEDYCACAFQdj2wAApAgAiygE3A+ACIAYEQCAFQeACakHM98AAEKUDIAUoAuQCIAY2AgAgBUEBNgLoAgsgDiAKKAIAIgY2AgAgBUGoAmogBjYCACAFIAUpA+ACIssBNwPQAiAFIMsBNwOgAiAKIBA2AgAgBSDKATcD4AIgAwRAIAVB4AJqQcz3wAAQpQMgBSgC5AIgAzYCACAFQQE2AugCCyAFQdgCaiIDIAVB6AJqIgooAgAiBjYCACAFQbQCaiAGNgIAIAUgBSkD4AIiygE3A9ACIAUgygE3AqwCIApB4PbAACgCACIGNgIAIAVB2PbAACkCACLKATcD4AIgGARAIAVB4AJqQcz3wAAQpQMgBSgC5AIgGDYCACAFQQE2AugCCyADIAooAgAiGDYCACAFQcACaiAYNgIAIAUgBSkD4AIiywE3A9ACIAUgywE3A7gCIAogBjYCACAFIMoBNwPgAiALBEAgBUHgAmpBzPfAABClAyAFKALkAiALNgIAIAVBATYC6AILIAVBzAJqIAVB6AJqKAIANgIAIAUgBSkD4AI3AsQCIAlB4AVqIAVB0AL8CgAAIAVB8AJqJAAgCSgCxAUhBiAVKAKsBSIYRQ0BIA1B4ANqIRNBASEFA0AgBSEKIAkoAqAEIAkoAqgEIgVrIAdJBEAgCUGgBGogBSAHQQFBARCIAyAJKAKoBCEFCyAHBEAgCSgCpAQgBWogDyAH/AoAAAsgCSAFIAdqNgKoBAJAIAhBG00EQCATIAhB7ABsaiEUQQAhB0EBIQUDQAJAIAUhCwJAAkAgFCAHQQxsaiIFKAIIBEAgCSAFQQgQsAIgCSgCCCIFQQJJDQEgCSgCBCIOIAVqIRBBACEHIAVBAXYiEUEBRwRAIAVBAWshAyARQf7///8HcSEZA0AgAyAOaiIRLQAAIRcgESAHIA5qIhEtAAA6AAAgESAXOgAAIBAgB0F+c2oiFy0AACEaIBcgEUEBaiIRLQAAOgAAIBEgGjoAACADQQJrIQMgGSAHQQJqIgdHDQALCyAFQQJxBEAgByAOaiIFLQAAIQMgBSAQIAdBf3NqIgUtAAA6AAAgBSADOgAACyAJKAIIIgVBH00NAQwCC0HRzsUALQAAGkEBQQEQ1gQiB0UNAiAHQQA6AABBASEFIAlBATYCCCAJIAc2AgQgCUEBNgIACyAFIQcDQCAJKAIAIAdGBEAgCUGwnsIAELYDCyAJKAIEIQUgBwRAIAVBAWogBSAH/AoAAAsgBUEAOgAAIAkgB0EBaiIFNgIIIAdBH0kgBSEHDQALCyAJKAIEIQMgCSgCoAQgCSgCqAQiB2sgBUkEQCAJQaAEaiAHIAVBAUEBEIgDIAkoAqgEIQcLIAUEQCAJKAKkBCAHaiADIAX8CgAACyAJIAUgB2o2AqgEIAkoAgAiBQRAIAkoAgQgBRDfBAsgCyALQQlJIgNqIQUgCyEHIAMNAQwDCwtBAUEBEP8EAAsgCEEcQYiswgAQ2QMACyAJIAlBoARqEIgBIAkoAqAEIgUEQCAJKAKkBCAFEN8ECyAJQQA2AqgEIAlCgICAgBA3AqAEIAYEQCAPIAYQ3wQLIAkoAgAhBiAJIAkoAgQiDyAJKAIIIgcQfyAJQbgIaiILIAlBCGooAgA2AgAgCSAJKQIANwOwCCAJKAIMIgUEQCAJKAIQIAVBAnQQ3wQLIAlB4AVqIAhBDGxqIgUoAgAiCARAIAUoAgQgCEECdBDfBAsgBSAJKQOwCDcCACAFQQhqIAsoAgA2AgAgCiAKIBhJIgtqIQUgCiEIIAsNAAsMAQsgCSAFNgKwCSAJQQI2AgQgCUGspcIANgIAIAlCAjcCDCAJIAlB4AVqrUKAgICA4AGENwOYCiAJIAlBsAlqrUKAgICA4AGENwOQCiAJIAo2AuAFIAkgCUGQCmo2AgggFkEEaiAJENICIBZBgICAgHg2AgAMAQsgCSgCoAQgCSgCqAQiBWsgB0kEQCAJQaAEaiAFIAdBAUEBEIgDIAkoAqgEIQULIAcEQCAJKAKkBCAFaiAPIAf8CgAACyAJIAUgB2o2AqgEIAlBoARqIgUgDUGwG2oQtgIgBSANQbwbahC2AiAFIA1ByBtqELYCIAUgDUHUG2oQtgIgBSANQeAbahC2AiAFIA1B7BtqELYCIAUgDUH4G2oQtgIgBSANQYQcahC2AiAFIA1BkBxqELYCIAUgDUGcHGoQtgIgBSANQagcahC2AiAFIA1BtBxqELYCIAUgDUHAHGoQtgIgBSANQcwcahC2AiAFIA1B2BxqELYCIAUgDUHkHGoQtgIgBSANQfAcahC2AiAFIA1B/BxqELYCIAUgDUGIHWoQtgIgBSANQZQdahC2AiAFIA1BoB1qELYCIAUgDUGsHWoQtgIgBSANQbgdahC2AiAFIA1BxB1qELYCIAUgDUHQHWoQtgIgBSANQdwdahC2AiAFIA1B6B1qELYCIAUgDUH0HWoQtgIgBSANQYAeahC2AiAFIA1BjB5qELYCIAUgDUGYHmoQtgIgBSANQaQeahC2AiAFIA1BsB5qELYCIAUgDUG8HmoQtgIgBSANQcgeahC2AiAFIA1B1B5qELYCIAUgDUHgHmoQtgIgBSANQeweahC2AiAFIA1B+B5qELYCIAUgDUGEH2oQtgIgBSANQZAfahC2AiAFIA1BnB9qELYCIAUgDUGkA2oQtgIgBSANQbADahC2AiAFIA1BvANqELYCIAUgDUHIA2oQtgIgBSANQagfahC2AiAFIA1BtB9qELYCIAUgDUHAH2oQtgIgCUG8CGogBRCIASAJKAKgBCIFBEAgCSgCpAQgBRDfBAsgCUEANgKoBCAJQoCAgIAQNwKgBCAJIAkoAsAIIgcgCSgCxAgiChB/IAlB0AhqIAlBCGooAgA2AgAgCSAJKQIANwPICCAJKAIMIgUEQCAJKAIQIAVBAnQQ3wQLIAkoAqAEIAkoAqgEIgVrIApJBEAgCUGgBGogBSAKQQFBARCIAyAJKAKoBCEFCyAKBEAgCSgCpAQgBWogByAK/AoAAAsgCSAFIApqNgKoBAJAIBhBAUYNACAJQaAEaiIFIA1BzB9qELYCIAUgDUHYH2oQtgIgGEECRg0AIAUgDUHkH2oQtgIgBSANQfAfahC2AiAYQQNGDQAgBSANQfwfahC2AiAFIA1BiCBqELYCIBhBBEYNACAFIA1BlCBqELYCIAUgDUGgIGoQtgIgGEEFRg0AIAUgDUGsIGoQtgIgBSANQbggahC2AiAYQQZGDQAgBSANQcQgahC2AiAFIA1B0CBqELYCIBhBB0YNACAFIA1B3CBqELYCIAUgDUHoIGoQtgIgGEEIRg0AIAUgDUH0IGoQtgIgBSANQYAhahC2AiAYQQlGDQAgBSANQYwhahC2AiAFIA1BmCFqELYCIBhBCkYNACAFIA1BpCFqELYCIAUgDUGwIWoQtgIgGEELRg0AIAUgDUG8IWoQtgIgBSANQcghahC2AiAYQQxGDQAgBSANQdQhahC2AiAFIA1B4CFqELYCIBhBDUYNACAFIA1B7CFqELYCIAUgDUH4IWoQtgIgGEEORg0AIAUgDUGEImoQtgIgBSANQZAiahC2AiAYQQ9GDQAgBSANQZwiahC2AiAFIA1BqCJqELYCIBhBEEYNACAFIA1BtCJqELYCIAUgDUHAImoQtgIgGEERRg0AIAUgDUHMImoQtgIgBSANQdgiahC2AiAYQRJGDQAgBSANQeQiahC2AiAFIA1B8CJqELYCIBhBE0YNACAFIA1B/CJqELYCIAUgDUGII2oQtgIgGEEURg0AIAUgDUGUI2oQtgIgBSANQaAjahC2AiAYQRVGDQAgBSANQawjahC2AiAFIA1BuCNqELYCIBhBFkYNACAFIA1BxCNqELYCIAUgDUHQI2oQtgIgGEEXRg0AIAUgDUHcI2oQtgIgBSANQegjahC2AiAYQRhGDQAgBSANQfQjahC2AiAFIA1BgCRqELYCIBhBGUYNACAFIA1BjCRqELYCIAUgDUGYJGoQtgIgGEEaRg0AIAUgDUGkJGoQtgIgBSANQbAkahC2AiAYQRtGDQAgBSANQbwkahC2AiAFIA1ByCRqELYCIBhBHEYNAEEbQRtB+KvCABDZAwALIAlB1AhqIAlBoARqEIgBIAkoAqAEIgUEQCAJKAKkBCAFEN8ECyAJQQA2AqgEIAlCgICAgBA3AqAEIAkgCSgC2AgiCCAJKALcCCIKEH8gCUHoCGogCUEIaigCADYCACAJIAkpAgA3A+AIIAkoAgwiBQRAIAkoAhAgBUECdBDfBAsgCSgCoAQgCSgCqAQiBWsgCkkEQCAJQaAEaiAFIApBAUEBEIgDIAkoAqgEIQULIAoEQCAJKAKkBCAFaiAIIAr8CgAACyAJIAUgCmo2AqgEIAlBoARqIgUgDUHUJGoQtgICQCAYQQFqIgpBAkYNACAFIA1B4CRqELYCIApBA0YNACAFIA1B7CRqELYCIApBBEYNACAFIA1B+CRqELYCIApBBUYNACAFIA1BhCVqELYCIApBBkYNACAFIA1BkCVqELYCIApBB0YNACAFIA1BnCVqELYCIApBCEYNACAFIA1BqCVqELYCIApBCUYNACAFIA1BtCVqELYCIApBCkYNACAFIA1BwCVqELYCIApBC0YNACAFIA1BzCVqELYCIApBDEYNACAFIA1B2CVqELYCIApBDUYNACAFIA1B5CVqELYCIApBDkYNACAFIA1B8CVqELYCIApBD0YNACAFIA1B/CVqELYCIApBEEYNACAFIA1BiCZqELYCIApBEUYNACAFIA1BlCZqELYCIApBEkYNACAFIA1BoCZqELYCIApBE0YNACAFIA1BrCZqELYCIApBFEYNACAFIA1BuCZqELYCIApBFUYNACAFIA1BxCZqELYCIApBFkYNACAFIA1B0CZqELYCIApBF0YNACAFIA1B3CZqELYCIApBGEYNACAFIA1B6CZqELYCIApBGUYNACAFIA1B9CZqELYCIApBGkYNACAFIA1BgCdqELYCIApBG0YNACAFIA1BjCdqELYCIApBHEYNACAFIA1BmCdqELYCCyAJQaAEaiIFIA1BpCdqELYCIAUgDUGwJ2oQtgIgBSANQbwnahC2AiAFIA1ByCdqELYCIAlB7AhqIAUQiAEgCSgCoAQiBQRAIAkoAqQEIAUQ3wQLIAlBADYCqAQgCUKAgICAEDcCoAQgCSAJKALwCCILIAkoAvQIIgoQfyAJQYAJaiAJQQhqKAIANgIAIAkgCSkCADcD+AggCSgCDCIFBEAgCSgCECAFQQJ0EN8ECyAJKAKgBCAJKAKoBCIFayAKSQRAIAlBoARqIAUgCkEBQQEQiAMgCSgCqAQhBQsgCgRAIAkoAqQEIAVqIAsgCvwKAAALIAkgBSAKajYCqAQgCUGgBGoiBSANQdQnahC2AiAFIA1B4CdqELYCIAlBhAlqIAUQiAEgCSgCoAQiBQRAIAkoAqQEIAUQ3wQLIAlBADYCqAQgCUKAgICAEDcCoAQgCSAJKAKICSIFIAkoAowJEH8gCUGYCWoiCiAJQQhqKAIANgIAIAkgCSkCADcDkAkgCUGoCWogCUEUaigCADYCACAJIAkpAgw3A6AJIAlBsAlqIhggCUGQCWoQ+AIgCUHQCWogCUGgCWoQ+AIgCUGACmpCfzcDACAJQn83A/gJIAlC0Pf///////8HNwPwCSAJQkE3A4gKIBgQRiAJQfgDaiAJQcgJaikDADcDACAJQfADaiAJQcAJaikDADcDACAJQegDaiAJQbgJaikDADcDACAJQYgEaiAJQdgJaikDADcDACAJQZAEaiAJQeAJaikDADcDACAJQZgEaiAJQegJaikDADcDACAJIAkpA7AJNwPgAyAJIAkpA9AJNwOABCAJQfAKaiAJQeAFakHQAvwKAAAgCUGYCmogCUHABGooAgA2AgAgCUGkCmogCUHQBGooAgA2AgAgCUGwCmogCUHoBGooAgA2AgAgCUG8CmogCUGABWooAgA2AgAgCUHICmogCUGQBWooAgA2AgAgCSAJKQO4BDcDkAogCSAJKQPIBDcCnAogCSAJKQPgBDcDqAogCSAJKQP4BDcCtAogCSAJKQOIBTcDwAogCUHUCmogCUGoBWooAgA2AgAgCUHgCmogCUHABWooAgA2AgAgCUHsCmogCUHYBWooAgA2AgAgCUHIDWogCUHQCGooAgA2AgAgCUHUDWogCUHoCGooAgA2AgAgCSAJKQOgBTcCzAogCSAJKQO4BTcD2AogCSAJKQPQBTcC5AogCSAJKQPICDcDwA0gCSAJKQPgCDcCzA0gCUHgDWogCUGACWooAgA2AgAgCUHsDWogCigCADYCACAJIAkpA/gINwPYDSAJIAkpA5AJNwLkDSAJIAlBkApqQeAD/AoAACAJKAKgCSIKBEAgCSgCpAkgCkECdBDfBAsgCSgChAkiCgRAIAUgChDfBAsgCSgC7AgiBQRAIAsgBRDfBAsgCSgC1AgiBQRAIAggBRDfBAsgCSgCvAgiBQRAIAcgBRDfBAsgBgRAIA8gBhDfBAsgCSgCrAUiBQRAIAkoArAFIAUQ3wQLIAkoApQFIgUEQCAJKAKYBSAFEN8ECyAJKALsBCIFBEAgCSgC8AQgBRDfBAsgCSgC1AQiBQRAIAkoAtgEIAUQ3wQLIAkoAqwEIgUEQCAJKAKwBCAFEN8ECyAJKAKgBCIFBEAgCSgCpAQgBRDfBAsgFiAJQaAE/AoAAAsgCUHwDWokACAEQeDMAGoiBSAEQbwnaigCADYCACAEIAQpArQnNwPYTAJAIAQoArAnIgpBgICAgHhGBEAgEiAEKQPYTDcCBCASQQE2AgAgEkEMaiAFKAIANgIADAELIARBkB1qIgUgBEHAJ2pB8AP8CgAAIARBjBBqIARB4MwAaigCADYCACAEIAQpA9hMNwKEECAEQZAQaiAFQdAD/AoAACAEQejkAGogBEH4IGopAwA3AwAgBEHg5ABqIARB8CBqKQMANwMAIARB2OQAaiAEQeggaikDADcDACAEIAo2AoAQIAQgBCkD4CA3A9BkIA0oAggiFkEFdCEFAkACQAJAAkACQAJAAkACQAJAAkACQCAWQf///z9LIAVB+P///wdLcg0AIA0oAgQhBwJ/IAVFBEBBCCEPQQAMAQtB0c7FAC0AABpBCCEMIAVBCBDWBCIPRQ0BIBYLIScgFgRAIA8hBSAWIQwDQCAEQbAnaiAHEPQCIAVBGGogBEHIJ2opAwA3AwAgBUEQaiAEQcAnaikDADcDACAFQQhqIARBuCdqKQMANwMAIAUgBCkDsCc3AwAgBUEgaiEFIAdBDGohByAMQQFrIgwNAAsLQdHOxQAtAAAaQYAEQQgQ1gQiDkUNASAEQbAnaiIFIA1BDGoQ9AIgDkEYaiAEQcgnaiIKKQMANwMAIA5BEGogBEHAJ2oiBykDADcDACAOQQhqIARBuCdqIggpAwA3AwAgDiAEKQOwJzcDACAFIA1BGGoQ9AIgDkE4aiAKKQMANwMAIA5BMGogBykDADcDACAOQShqIAgpAwA3AwAgDiAEKQOwJzcDICAFIA1BJGoQ9AIgDkHYAGogCikDADcDACAOQdAAaiAHKQMANwMAIA5ByABqIAgpAwA3AwAgDiAEKQOwJzcDQCAFIA1BMGoQ9AIgDkH4AGogCikDADcDACAOQfAAaiAHKQMANwMAIA5B6ABqIAgpAwA3AwAgDiAEKQOwJzcDYCAFIA1BPGoQ9AIgDkGYAWogCikDADcDACAOQZABaiAHKQMANwMAIA5BiAFqIAgpAwA3AwAgDiAEKQOwJzcDgAEgBSANQcgAahD0AiAOQbgBaiAKKQMANwMAIA5BsAFqIAcpAwA3AwAgDkGoAWogCCkDADcDACAOIAQpA7AnNwOgASAFIA1B1ABqEPQCIA5B2AFqIAopAwA3AwAgDkHQAWogBykDADcDACAOQcgBaiAIKQMANwMAIA4gBCkDsCc3A8ABIAUgDUHgAGoQ9AIgDkH4AWogCikDADcDACAOQfABaiAHKQMANwMAIA5B6AFqIAgpAwA3AwAgDiAEKQOwJzcD4AEgBSANQewAahD0AiAOQZgCaiAKKQMANwMAIA5BkAJqIAcpAwA3AwAgDkGIAmogCCkDADcDACAOIAQpA7AnNwOAAiAFIA1B+ABqEPQCIA5BuAJqIAopAwA3AwAgDkGwAmogBykDADcDACAOQagCaiAIKQMANwMAIA4gBCkDsCc3A6ACIAUgDUGEAWoQ9AIgDkHYAmogCikDADcDACAOQdACaiAHKQMANwMAIA5ByAJqIAgpAwA3AwAgDiAEKQOwJzcDwAIgBSANQZABahD0AiAOQfgCaiAKKQMANwMAIA5B8AJqIAcpAwA3AwAgDkHoAmogCCkDADcDACAOIAQpA7AnNwPgAiAFIA1BnAFqEPQCIA5BmANqIAopAwA3AwAgDkGQA2ogBykDADcDACAOQYgDaiAIKQMANwMAIA4gBCkDsCc3A4ADIAUgDUGoAWoQ9AIgDkG4A2ogCikDADcDACAOQbADaiAHKQMANwMAIA5BqANqIAgpAwA3AwAgDiAEKQOwJzcDoAMgBSANQbQBahD0AiAOQdgDaiAKKQMANwMAIA5B0ANqIAcpAwA3AwAgDkHIA2ogCCkDADcDACAOIAQpA7AnNwPAAyAFIA1BwAFqEPQCIA5B+ANqIAopAwA3AwAgDkHwA2ogBykDADcDACAOQegDaiAIKQMANwMAIA4gBCkDsCc3A+ADIARBqDNqIgwgDUHMAWoQ9wIgBEHYzABqIgsgDUHYAWoQ9wIgBSAMIAsQQyAELQDwJyIhQQJGBEAgBEGYHWogCCgCACIFNgIAIAQgBCkDsCciygE3A5AdIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwLCyAEQcgdaiIMIARB6CdqKQMANwMAIARBwB1qIgsgBEHgJ2opAwA3AwAgBEG4HWoiCSAEQdgnaikDADcDACAEQbAdaiIIIARB0CdqIgMpAwA3AwAgBEGoHWoiBiAKKQMANwMAIARBoB1qIgogBykDADcDACAEQZgdaiIFIARBuCdqIhgpAwA3AwAgBCAEKQOwJzcDkB0gBCAEKADxJzYCqBQgBCAEQfQnaiIQKAAANgCrFCAEQbgUaiAFKQMAIsoBNwMAIARBwBRqIAopAwAiywE3AwAgBEHIFGogBikDACLMATcDACAEQdAUaiAIKQMAIs8BNwMAIARB2BRqIAkpAwAizQE3AwAgBEHgFGogCykDACLOATcDACAEQegUaiAMKQMAItIBNwMAIARB6BNqIMoBNwMAIARB8BNqIMsBNwMAIARB+BNqIMwBNwMAIARBgBRqIM8BNwMAIARBiBRqIM0BNwMAIARBkBRqIM4BNwMAIARBmBRqINIBNwMAIAQgBCkDkB0iygE3A7AUIAQgygE3A+ATIARBpBRqIAQoAKsUNgAAIAQgIToAoBQgBCAEKAKoFDYAoRQgBEGoM2oiCiANQeQBahD3AiAEQdjMAGoiByANQfABahD3AiAEQbAnaiAKIAcQQyAELQDwJyIrQQJGBEAgBSAYKAIAIgU2AgAgBCAEKQOwJyLKATcDkB0gEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAsLIARByB1qIgogBEHoJ2oiBikDADcDACAEQcAdaiIHIARB4CdqIhEpAwA3AwAgBEG4HWoiDCAEQdgnaiITKQMANwMAIAggAykDADcDACAEQagdaiILIARByCdqIgMpAwA3AwAgBEGgHWoiCSAEQcAnaiIUKQMANwMAIAUgGCkDADcDACAEIAQpA7AnNwOQHSAEIAQoAPEnNgK4FSAEIBAoAAA2ALsVIARByBVqIAUpAwAiygE3AwAgBEHQFWogCSkDACLLATcDACAEQdgVaiALKQMAIswBNwMAIARB4BVqIAgpAwAizwE3AwAgBEHoFWogDCkDACLNATcDACAEQfAVaiAHKQMAIs4BNwMAIARB+BVqIAopAwAi0gE3AwAgBEH4FGogygE3AwAgBEGAFWogywE3AwAgBEGIFWogzAE3AwAgBEGQFWogzwE3AwAgBEGYFWogzQE3AwAgBEGgFWogzgE3AwAgBEGoFWog0gE3AwAgBCAEKQOQHSLKATcDwBUgBCDKATcD8BQgBEG0FWogBCgAuxU2AAAgBCArOgCwFSAEIAQoArgVNgCxFSAEQagzaiIFIA1B/AFqEPcCIARB2MwAaiIIIA1BiAJqEPcCIARBsCdqIAUgCBBDIAQtAPAnIiJBAkYEQCAEQZgdaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A5AdIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwLCyAKIAYpAwA3AwAgByARKQMANwMAIAwgEykDADcDACAEQbAdaiIIIARB0CdqIgYpAwA3AwAgCyADKQMANwMAIAkgFCkDADcDACAEQZgdaiIFIARBuCdqIhgpAwA3AwAgBCAEKQOwJzcDkB0gBCAEKADxJzYCyBYgBCAEQfQnaiIDKAAANgDLFiAEQdgWaiAFKQMAIsoBNwMAIARB4BZqIAkpAwAiywE3AwAgBEHoFmogCykDACLMATcDACAEQfAWaiAIKQMAIs8BNwMAIARB+BZqIAwpAwAizQE3AwAgBEGAF2ogBykDACLOATcDACAEQYgXaiAKKQMAItIBNwMAIARBiBZqIMoBNwMAIARBkBZqIMsBNwMAIARBmBZqIMwBNwMAIARBoBZqIM8BNwMAIARBqBZqIM0BNwMAIARBsBZqIM4BNwMAIARBuBZqINIBNwMAIAQgBCkDkB0iygE3A9AWIAQgygE3A4AWIARBxBZqIAQoAMsWNgAAIAQgIjoAwBYgBCAEKALIFjYAwRYgBEGoM2oiCiANQZQCahD3AiAEQdjMAGoiByANQaACahD3AiAEQbAnaiAKIAcQQyAELQDwJyIsQQJGBEAgBSAYKAIAIgU2AgAgBCAEKQOwJyLKATcDkB0gEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAsLIARByB1qIgogBEHoJ2oiECkDADcDACAEQcAdaiIHIARB4CdqIhEpAwA3AwAgBEG4HWoiDCAEQdgnaiITKQMANwMAIAggBikDADcDACAEQagdaiILIARByCdqIgYpAwA3AwAgBEGgHWoiCSAEQcAnaiIUKQMANwMAIAUgGCkDADcDACAEIAQpA7AnNwOQHSAEIAQoAPEnNgLYFyAEIAMoAAA2ANsXIARB6BdqIAUpAwAiygE3AwAgBEHwF2ogCSkDACLLATcDACAEQfgXaiALKQMAIswBNwMAIARBgBhqIAgpAwAizwE3AwAgBEGIGGogDCkDACLNATcDACAEQZAYaiAHKQMAIs4BNwMAIARBmBhqIAopAwAi0gE3AwAgBEGYF2ogygE3AwAgBEGgF2ogywE3AwAgBEGoF2ogzAE3AwAgBEGwF2ogzwE3AwAgBEG4F2ogzQE3AwAgBEHAF2ogzgE3AwAgBEHIF2og0gE3AwAgBCAEKQOQHSLKATcD4BcgBCDKATcDkBcgBEHUF2ogBCgA2xc2AAAgBCAsOgDQFyAEIAQoAtgXNgDRFyAEQagzaiIFIA1BrAJqEPcCIARB2MwAaiIIIA1BuAJqEPcCIARBsCdqIAUgCBBDIAQtAPAnIhtBAkYEQCAEQZgdaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A5AdIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwLCyAKIBApAwA3AwAgByARKQMANwMAIAwgEykDADcDACAEQbAdaiIIIARB0CdqIgMpAwA3AwAgCyAGKQMANwMAIAkgFCkDADcDACAEQZgdaiIFIARBuCdqIhgpAwA3AwAgBCAEKQOwJzcDkB0gBCAEKADxJzYC6BggBCAEQfQnaiIGKAAANgDrGCAEQfgYaiAFKQMAIsoBNwMAIARBgBlqIAkpAwAiywE3AwAgBEGIGWogCykDACLMATcDACAEQZAZaiAIKQMAIs8BNwMAIARBmBlqIAwpAwAizQE3AwAgBEGgGWogBykDACLOATcDACAEQagZaiAKKQMAItIBNwMAIARBqBhqIMoBNwMAIARBsBhqIMsBNwMAIARBuBhqIMwBNwMAIARBwBhqIM8BNwMAIARByBhqIM0BNwMAIARB0BhqIM4BNwMAIARB2BhqINIBNwMAIAQgBCkDkB0iygE3A/AYIAQgygE3A6AYIARB5BhqIAQoAOsYNgAAIAQgGzoA4BggBCAEKALoGDYA4RggBEGwJ2ogDUHEAmoQhgQgBC0A8CciLUECRgRAIAUgGCgCACIFNgIAIAQgBCkDsCciygE3A5AdIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwLCyAEQcgdaiIKIARB6CdqIhApAwA3AwAgBEHAHWoiByAEQeAnaiIRKQMANwMAIARBuB1qIgwgBEHYJ2oiEykDADcDACAIIAMpAwA3AwAgBEGoHWoiCyAEQcgnaiIDKQMANwMAIARBoB1qIgkgBEHAJ2oiFCkDADcDACAFIBgpAwA3AwAgBCAEKQOwJzcDkB0gBCAEKADxJzYC+BkgBCAGKAAANgD7GSAEQYgaaiAFKQMAIsoBNwMAIARBkBpqIAkpAwAiywE3AwAgBEGYGmogCykDACLMATcDACAEQaAaaiAIKQMAIs8BNwMAIARBqBpqIAwpAwAizQE3AwAgBEGwGmogBykDACLOATcDACAEQbgaaiAKKQMAItIBNwMAIARBuBlqIMoBNwMAIARBwBlqIMsBNwMAIARByBlqIMwBNwMAIARB0BlqIM8BNwMAIARB2BlqIM0BNwMAIARB4BlqIM4BNwMAIARB6BlqINIBNwMAIAQgBCkDkB0iygE3A4AaIAQgygE3A7AZIARB9BlqIAQoAPsZNgAAIAQgLToA8BkgBCAEKAL4GTYA8RkgBEGwJ2ogDUHcAmoQhgQgBC0A8CciJUECRgRAIARBmB1qIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcDkB0gEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAsLIAogECkDADcDACAHIBEpAwA3AwAgDCATKQMANwMAIARBsB1qIgggBEHQJ2oiBikDADcDACALIAMpAwA3AwAgCSAUKQMANwMAIARBmB1qIgUgBEG4J2oiGCkDADcDACAEIAQpA7AnNwOQHSAEIAQoAPEnNgKIGyAEIARB9CdqIgMoAAA2AIsbIARBmBtqIAUpAwAiygE3AwAgBEGgG2ogCSkDACLLATcDACAEQagbaiALKQMAIswBNwMAIARBsBtqIAgpAwAizwE3AwAgBEG4G2ogDCkDACLNATcDACAEQcAbaiAHKQMAIs4BNwMAIARByBtqIAopAwAi0gE3AwAgBEHIGmogygE3AwAgBEHQGmogywE3AwAgBEHYGmogzAE3AwAgBEHgGmogzwE3AwAgBEHoGmogzQE3AwAgBEHwGmogzgE3AwAgBEH4Gmog0gE3AwAgBCAEKQOQHSLKATcDkBsgBCDKATcDwBogBEGEG2ogBCgAixs2AAAgBCAlOgCAGyAEIAQoAogbNgCBGyAEQbAnaiANQfQCahCGBCAELQDwJyIuQQJGBEAgBSAYKAIAIgU2AgAgBCAEKQOwJyLKATcDkB0gEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAsLIARByB1qIgogBEHoJ2opAwA3AwAgBEHAHWoiByAEQeAnaikDADcDACAEQbgdaiIMIARB2CdqKQMANwMAIAggBikDADcDACAEQagdaiILIARByCdqKQMANwMAIARBoB1qIgkgBEHAJ2opAwA3AwAgBSAYKQMANwMAIAQgBCkDsCc3A5AdIAQgBCgA8Sc2ApgcIAQgAygAADYAmxwgBEGoHGogBSkDACLKATcDACAEQbAcaiAJKQMAIssBNwMAIARBuBxqIAspAwAizAE3AwAgBEHAHGogCCkDACLPATcDACAEQcgcaiAMKQMAIs0BNwMAIARB0BxqIAcpAwAizgE3AwAgBEHYHGogCikDACLSATcDACAEQdgbaiDKATcDACAEQeAbaiDLATcDACAEQegbaiDMATcDACAEQfAbaiDPATcDACAEQfgbaiDNATcDACAEQYAcaiDOATcDACAEQYgcaiDSATcDACAEIAQpA5AdIsoBNwOgHCAEIMoBNwPQGyAEQZQcaiAEKACbHDYAACAEIC46AJAcIAQgBCgCmBw2AJEcIARBsCdqIA1BjANqIA1B1ANqIgUQpwMgBCgCvCchHyAEKAK4JyEYIAQoArQnISAgBCgCsCdBAUYEQCASIB82AgwgEiAYNgIIIBIgIDYCBCASQQE2AgAMCwsgBEHgHGogBRD0AiAEQYQdaiETIwBBIGsiCiQAIA1BsBtqIgsgDUHgA2oiCWtB7ABuIQcCQCAJIAtGBEBBBCEIQQAhBwwBC0HRzsUALQAAGiAHQQxsIgVBBBDWBCIIDQBBBCAFQZCWwgAQyAQACyAKQRBqIhRBADYCACAKIAg2AgwgCiAHNgIIIAogCDYCHCAKQQA2AhggCiAUNgIUQQAhECMAQTBrIgUkACAKQRRqIgcoAgQhAyAHKAIAIR0CQAJAAkAgCSALRwRAIAcoAgghJCALIAlrQewAbiEmA0BB0c7FAC0AABpBoAJBCBDWBCIZRQ0CIAkgEEHsAGxqISlBACEGA0ACQAJAICkgBkEMbGoiBygCCEUEQEHRzsUALQAAGkEBQQEQ1gQiB0UNByAHQQA6AABBASEIIAUgB0EBEIsBDAELIAVBJGogB0EIELACIAUoAighBwJAIAUoAiwiDEECSQ0AIAcgDGohF0EAIQggDEEBdiIaQQFHBEAgDEEBayERIBpB/v///wdxIRwDQCAHIBFqIhotAAAhIyAaIAcgCGoiGi0AADoAACAaICM6AAAgFyAIQX5zaiIjLQAAITAgIyAaQQFqIhotAAA6AAAgGiAwOgAAIBFBAmshESAcIAhBAmoiCEcNAAsLIAxBAnFFDQAgByAIaiIRLQAAIRogESAXIAhBf3NqIggtAAA6AAAgCCAaOgAACyAFKAIkIQggBSAHIAwQiwEgCEUNAQsgByAIEN8ECyAZIAZBBXRqIgcgBSkDADcDACAHQRhqIAVBGGopAwA3AwAgB0EQaiAFQRBqKQMANwMAIAdBCGogBUEIaikDADcDACAGQQFqIgZBCUcNAAsgJCADQQxsaiIHQQk2AgggByAZNgIEIAdBCTYCACADQQFqIQMgEEEBaiIQICZHDQALCyAdIAM2AgAgBUEwaiQADAILQQhBoAJBmPnAABDIBAALQQFBARD/BAALIBNBCGogFCgCADYCACATIAopAgg3AgAgCkEgaiQAIARB2MwAaiALIA1BnB9qIgUQjAMgBCgC4ExBKUcNAiAEQQA2AuBMIARBsCdqQQRyIgogBCgC3EwiB0GgCvwKAAAgBCgC2EwiCARAIAcgCEEFdBDfBAsgBEGQHWogCkGgCvwKAAAgBEHYMWogBRD0AiAEQbAnaiANQagfahCGBAJAAkAgBC0A8CciJkECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEDAELIARBkM0AaiIFIARB6CdqKQMANwMAIARBiM0AaiIKIARB4CdqKQMANwMAIARBgM0AaiIHIARB2CdqKQMANwMAIARB+MwAaiIIIARB0CdqKQMANwMAIARB8MwAaiIMIARByCdqKQMANwMAIARB6MwAaiILIARBwCdqKQMANwMAIARB4MwAaiIJIARBuCdqKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AsAyIAQgBEH0J2ooAAA2AMMyIARB0DJqIAkpAwAiygE3AwAgBEHYMmogCykDACLLATcDACAEQeAyaiAMKQMAIswBNwMAIARB6DJqIAgpAwAizwE3AwAgBEHwMmogBykDACLNATcDACAEQfgyaiAKKQMAIs4BNwMAIARBgDNqIAUpAwAi0gE3AwAgBEGAMmogygE3AwAgBEGIMmogywE3AwAgBEGQMmogzAE3AwAgBEGYMmogzwE3AwAgBEGgMmogzQE3AwAgBEGoMmogzgE3AwAgBEGwMmog0gE3AwAgBCAEKQPYTCLKATcDyDIgBCDKATcD+DEgBEG8MmogBCgAwzI2AAAgBCAmOgC4MiAEIAQoAsAyNgC5MiAEQYgzaiANQcAfahD0AiAEQbAnaiANQcwfaiANQdQkaiIFEKcDIAQoArwnISQgBCgCuCchCyAEKAK0JyEdIAQoArAnQQFHDQEgEiAkNgIMIBIgCzYCCCASIB02AgQLIBJBATYCACAEQYQdahDyAyAEKAKEHSIFBEAgBCgCiB0gBUEMbBDfBAsgIEUNCwwKCyAEQdjMAGogBSANQaQnaiIFEIwDIAQoAuBMQRxHDQMgBEEANgLgTCAEQbAnakEEciIKIAQoAtxMIgdBgAf8CgAAIAQoAthMIggEQCAHIAhBBXQQ3wQLIARBqDNqIApBgAf8CgAAIARB2MwAaiAFIA1B1CdqIgUQjAMgBCgC4ExBBEcNBCAEQQA2AuBMIARBsCdqQQRyIgogBCgC3EwiB0GAAfwKAAAgBCgC2EwiCARAIAcgCEEFdBDfBAsgBEGoOmogCkGAAfwKAAAgBEGwJ2ogBRCGBCAELQDwJyIQQQJGBEAgBEHgzABqIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIARBkM0AaiIKIARB6CdqIhEpAwA3AwAgBEGIzQBqIgcgBEHgJ2oiEykDADcDACAEQYDNAGoiCCAEQdgnaiIUKQMANwMAIARB+MwAaiIMIARB0CdqIhkpAwA3AwAgBEHwzABqIgkgBEHIJ2oiFykDADcDACAEQejMAGoiAyAEQcAnaiIaKQMANwMAIARB4MwAaiIFIARBuCdqIgYpAwA3AwAgBEHsO2ogBEH0J2oiHCgAADYAACAEIAQpA7AnNwPYTCAEIAQoAPEnNgDpOyAEQbA7aiAFKQMANwMAIARBuDtqIAMpAwA3AwAgBEHAO2ogCSkDADcDACAEQcg7aiAMKQMANwMAIARB0DtqIAgpAwA3AwAgBEHYO2ogBykDADcDACAEQeA7aiAKKQMANwMAIAQgEDoA6DsgBCAEKQPYTDcDqDsgBEGwJ2ogDUHsJ2oQhgQgBC0A8CciKUECRgRAIAUgBigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIBEpAwA3AwAgByATKQMANwMAIAggFCkDADcDACAMIBkpAwA3AwAgCSAXKQMANwMAIAMgGikDADcDACAFIAYpAwA3AwAgBEG0PGogHCgAADYAACAEIAQpA7AnNwPYTCAEIAQoAPEnNgCxPCAEQcA8aiAFKQMAIsoBNwMAIARByDxqIAMpAwAiywE3AwAgBEHQPGogCSkDACLMATcDACAEQdg8aiAMKQMAIs8BNwMAIARB4DxqIAgpAwAizQE3AwAgBEHoPGogBykDACLOATcDACAEQfA8aiAKKQMAItIBNwMAIARB+DtqIMoBNwMAIARBgDxqIMsBNwMAIARBiDxqIMwBNwMAIARBkDxqIM8BNwMAIARBmDxqIM0BNwMAIARBoDxqIM4BNwMAIARBqDxqINIBNwMAIAQgBCkD2EwiygE3A7g8IAQgygE3A/A7IAQgKToAsDwgBEGwJ2ogFRCGBCAELQDwJyI9QQJGBEAgBEHgzABqIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIARBkM0AaiIKIARB6CdqIgYpAwA3AwAgBEGIzQBqIgcgBEHgJ2oiECkDADcDACAEQYDNAGoiCCAEQdgnaiIRKQMANwMAIARB+MwAaiIMIARB0CdqIhMpAwA3AwAgBEHwzABqIgkgBEHIJ2oiFCkDADcDACAEQejMAGoiDSAEQcAnaiIZKQMANwMAIARB4MwAaiIFIARBuCdqIgMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYC+DwgBCAEQfQnaiIXKAAANgD7PCAEQYg9aiAFKQMANwMAIARBkD1qIA0pAwA3AwAgBEGYPWogCSkDADcDACAEQaA9aiAMKQMANwMAIARBqD1qIAgpAwA3AwAgBEGwPWogBykDADcDACAEQbg9aiAKKQMANwMAIAQgBCkD2Ew3A4A9IARBsCdqIBVBGGoQhgQgBC0A8CciOUECRgRAIAUgAygCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIAYpAwA3AwAgByAQKQMANwMAIAggESkDADcDACAMIBMpAwA3AwAgCSAUKQMANwMAIA0gGSkDADcDACAFIAMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCwD0gBCAXKAAANgDDPSAEQdA9aiAFKQMANwMAIARB2D1qIA0pAwA3AwAgBEHgPWogCSkDADcDACAEQeg9aiAMKQMANwMAIARB8D1qIAgpAwA3AwAgBEH4PWogBykDADcDACAEQYA+aiAKKQMANwMAIAQgBCkD2Ew3A8g9IARBsCdqIBVBMGoQhgQgBC0A8CciL0ECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2Aog+IAQgBEH0J2oiFygAADYAiz4gBEGYPmogBSkDADcDACAEQaA+aiANKQMANwMAIARBqD5qIAkpAwA3AwAgBEGwPmogDCkDADcDACAEQbg+aiAIKQMANwMAIARBwD5qIAcpAwA3AwAgBEHIPmogCikDADcDACAEIAQpA9hMNwOQPiAEQbAnaiAVQcgAahCGBCAELQDwJyI+QQJGBEAgBSADKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIAogBikDADcDACAHIBApAwA3AwAgCCARKQMANwMAIAwgEykDADcDACAJIBQpAwA3AwAgDSAZKQMANwMAIAUgAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgLQPiAEIBcoAAA2ANM+IARB4D5qIAUpAwA3AwAgBEHoPmogDSkDADcDACAEQfA+aiAJKQMANwMAIARB+D5qIAwpAwA3AwAgBEGAP2ogCCkDADcDACAEQYg/aiAHKQMANwMAIARBkD9qIAopAwA3AwAgBCAEKQPYTDcD2D4gBEGwJ2ogFUHgAGoQhgQgBC0A8CciP0ECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2Apg/IAQgBEH0J2oiFygAADYAmz8gBEGoP2ogBSkDADcDACAEQbA/aiANKQMANwMAIARBuD9qIAkpAwA3AwAgBEHAP2ogDCkDADcDACAEQcg/aiAIKQMANwMAIARB0D9qIAcpAwA3AwAgBEHYP2ogCikDADcDACAEIAQpA9hMNwOgPyAEQbAnaiAVQfgAahCGBCAELQDwJyJAQQJGBEAgBSADKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIAogBikDADcDACAHIBApAwA3AwAgCCARKQMANwMAIAwgEykDADcDACAJIBQpAwA3AwAgDSAZKQMANwMAIAUgAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgLgPyAEIBcoAAA2AOM/IARB8D9qIAUpAwA3AwAgBEH4P2ogDSkDADcDACAEQYBAayAJKQMANwMAIARBiMAAaiAMKQMANwMAIARBkMAAaiAIKQMANwMAIARBmMAAaiAHKQMANwMAIARBoMAAaiAKKQMANwMAIAQgBCkD2Ew3A+g/IARBsCdqIBVBkAFqEIYEIAQtAPAnIkFBAkYEQCAEQeDMAGogBEG4J2ooAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgBEGQzQBqIgogBEHoJ2oiBikDADcDACAEQYjNAGoiByAEQeAnaiIQKQMANwMAIARBgM0AaiIIIARB2CdqIhEpAwA3AwAgBEH4zABqIgwgBEHQJ2oiEykDADcDACAEQfDMAGoiCSAEQcgnaiIUKQMANwMAIARB6MwAaiINIARBwCdqIhkpAwA3AwAgBEHgzABqIgUgBEG4J2oiAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgKoQCAEIARB9CdqIhcoAAA2AKtAIARBuMAAaiAFKQMANwMAIARBwMAAaiANKQMANwMAIARByMAAaiAJKQMANwMAIARB0MAAaiAMKQMANwMAIARB2MAAaiAIKQMANwMAIARB4MAAaiAHKQMANwMAIARB6MAAaiAKKQMANwMAIAQgBCkD2Ew3A7BAIARBsCdqIBVBqAFqEIYEIAQtAPAnIkJBAkYEQCAFIAMoAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgCiAGKQMANwMAIAcgECkDADcDACAIIBEpAwA3AwAgDCATKQMANwMAIAkgFCkDADcDACANIBkpAwA3AwAgBSADKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AvBAIAQgFygAADYA80AgBEGAwQBqIAUpAwA3AwAgBEGIwQBqIA0pAwA3AwAgBEGQwQBqIAkpAwA3AwAgBEGYwQBqIAwpAwA3AwAgBEGgwQBqIAgpAwA3AwAgBEGowQBqIAcpAwA3AwAgBEGwwQBqIAopAwA3AwAgBCAEKQPYTDcD+EAgBEGwJ2ogFUHAAWoQhgQgBC0A8CciQ0ECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2ArhBIAQgBEH0J2oiFygAADYAu0EgBEHIwQBqIAUpAwA3AwAgBEHQwQBqIA0pAwA3AwAgBEHYwQBqIAkpAwA3AwAgBEHgwQBqIAwpAwA3AwAgBEHowQBqIAgpAwA3AwAgBEHwwQBqIAcpAwA3AwAgBEH4wQBqIAopAwA3AwAgBCAEKQPYTDcDwEEgBEGwJ2ogFUHYAWoQhgQgBC0A8CciREECRgRAIAUgAygCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIAYpAwA3AwAgByAQKQMANwMAIAggESkDADcDACAMIBMpAwA3AwAgCSAUKQMANwMAIA0gGSkDADcDACAFIAMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCgEIgBCAXKAAANgCDQiAEQZDCAGogBSkDADcDACAEQZjCAGogDSkDADcDACAEQaDCAGogCSkDADcDACAEQajCAGogDCkDADcDACAEQbDCAGogCCkDADcDACAEQbjCAGogBykDADcDACAEQcDCAGogCikDADcDACAEIAQpA9hMNwOIQiAEQbAnaiAVQfABahCGBCAELQDwJyI6QQJGBEAgBEHgzABqIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIARBkM0AaiIKIARB6CdqIgYpAwA3AwAgBEGIzQBqIgcgBEHgJ2oiECkDADcDACAEQYDNAGoiCCAEQdgnaiIRKQMANwMAIARB+MwAaiIMIARB0CdqIhMpAwA3AwAgBEHwzABqIgkgBEHIJ2oiFCkDADcDACAEQejMAGoiDSAEQcAnaiIZKQMANwMAIARB4MwAaiIFIARBuCdqIgMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCyEIgBCAEQfQnaiIXKAAANgDLQiAEQdjCAGogBSkDADcDACAEQeDCAGogDSkDADcDACAEQejCAGogCSkDADcDACAEQfDCAGogDCkDADcDACAEQfjCAGogCCkDADcDACAEQYDDAGogBykDADcDACAEQYjDAGogCikDADcDACAEIAQpA9hMNwPQQiAEQbAnaiAVQYgCahCGBCAELQDwJyJJQQJGBEAgBSADKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIAogBikDADcDACAHIBApAwA3AwAgCCARKQMANwMAIAwgEykDADcDACAJIBQpAwA3AwAgDSAZKQMANwMAIAUgAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgKQQyAEIBcoAAA2AJNDIARBoMMAaiAFKQMANwMAIARBqMMAaiANKQMANwMAIARBsMMAaiAJKQMANwMAIARBuMMAaiAMKQMANwMAIARBwMMAaiAIKQMANwMAIARByMMAaiAHKQMANwMAIARB0MMAaiAKKQMANwMAIAQgBCkD2Ew3A5hDIARBsCdqIBVBoAJqEIYEIAQtAPAnIkpBAkYEQCAEQeDMAGogBEG4J2ooAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgBEGQzQBqIgogBEHoJ2oiBikDADcDACAEQYjNAGoiByAEQeAnaiIQKQMANwMAIARBgM0AaiIIIARB2CdqIhEpAwA3AwAgBEH4zABqIgwgBEHQJ2oiEykDADcDACAEQfDMAGoiCSAEQcgnaiIUKQMANwMAIARB6MwAaiINIARBwCdqIhkpAwA3AwAgBEHgzABqIgUgBEG4J2oiAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgLYQyAEIARB9CdqIhcoAAA2ANtDIARB6MMAaiAFKQMANwMAIARB8MMAaiANKQMANwMAIARB+MMAaiAJKQMANwMAIARBgMQAaiAMKQMANwMAIARBiMQAaiAIKQMANwMAIARBkMQAaiAHKQMANwMAIARBmMQAaiAKKQMANwMAIAQgBCkD2Ew3A+BDIARBsCdqIBVBuAJqEIYEIAQtAPAnIktBAkYEQCAFIAMoAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgCiAGKQMANwMAIAcgECkDADcDACAIIBEpAwA3AwAgDCATKQMANwMAIAkgFCkDADcDACANIBkpAwA3AwAgBSADKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AqBEIAQgFygAADYAo0QgBEGwxABqIAUpAwA3AwAgBEG4xABqIA0pAwA3AwAgBEHAxABqIAkpAwA3AwAgBEHIxABqIAwpAwA3AwAgBEHQxABqIAgpAwA3AwAgBEHYxABqIAcpAwA3AwAgBEHgxABqIAopAwA3AwAgBCAEKQPYTDcDqEQgBEGwJ2ogFUHQAmoQhgQgBC0A8CciTEECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AuhEIAQgBEH0J2oiFygAADYA60QgBEH4xABqIAUpAwA3AwAgBEGAxQBqIA0pAwA3AwAgBEGIxQBqIAkpAwA3AwAgBEGQxQBqIAwpAwA3AwAgBEGYxQBqIAgpAwA3AwAgBEGgxQBqIAcpAwA3AwAgBEGoxQBqIAopAwA3AwAgBCAEKQPYTDcD8EQgBEGwJ2ogFUHoAmoQhgQgBC0A8CciTUECRgRAIAUgAygCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIAYpAwA3AwAgByAQKQMANwMAIAggESkDADcDACAMIBMpAwA3AwAgCSAUKQMANwMAIA0gGSkDADcDACAFIAMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCsEUgBCAXKAAANgCzRSAEQcDFAGogBSkDADcDACAEQcjFAGogDSkDADcDACAEQdDFAGogCSkDADcDACAEQdjFAGogDCkDADcDACAEQeDFAGogCCkDADcDACAEQejFAGogBykDADcDACAEQfDFAGogCikDADcDACAEIAQpA9hMNwO4RSAEQbAnaiAVQYADahCGBCAELQDwJyJOQQJGBEAgBEHgzABqIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIARBkM0AaiIKIARB6CdqIgYpAwA3AwAgBEGIzQBqIgcgBEHgJ2oiECkDADcDACAEQYDNAGoiCCAEQdgnaiIRKQMANwMAIARB+MwAaiIMIARB0CdqIhMpAwA3AwAgBEHwzABqIgkgBEHIJ2oiFCkDADcDACAEQejMAGoiDSAEQcAnaiIZKQMANwMAIARB4MwAaiIFIARBuCdqIgMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYC+EUgBCAEQfQnaiIXKAAANgD7RSAEQYjGAGogBSkDADcDACAEQZDGAGogDSkDADcDACAEQZjGAGogCSkDADcDACAEQaDGAGogDCkDADcDACAEQajGAGogCCkDADcDACAEQbDGAGogBykDADcDACAEQbjGAGogCikDADcDACAEIAQpA9hMNwOARiAEQbAnaiAVQZgDahCGBCAELQDwJyJPQQJGBEAgBSADKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIAogBikDADcDACAHIBApAwA3AwAgCCARKQMANwMAIAwgEykDADcDACAJIBQpAwA3AwAgDSAZKQMANwMAIAUgAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgLARiAEIBcoAAA2AMNGIARB0MYAaiAFKQMANwMAIARB2MYAaiANKQMANwMAIARB4MYAaiAJKQMANwMAIARB6MYAaiAMKQMANwMAIARB8MYAaiAIKQMANwMAIARB+MYAaiAHKQMANwMAIARBgMcAaiAKKQMANwMAIAQgBCkD2Ew3A8hGIARBsCdqIBVBsANqEIYEIAQtAPAnIlBBAkYEQCAEQeDMAGogBEG4J2ooAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgBEGQzQBqIgogBEHoJ2oiBikDADcDACAEQYjNAGoiByAEQeAnaiIQKQMANwMAIARBgM0AaiIIIARB2CdqIhEpAwA3AwAgBEH4zABqIgwgBEHQJ2oiEykDADcDACAEQfDMAGoiCSAEQcgnaiIUKQMANwMAIARB6MwAaiINIARBwCdqIhkpAwA3AwAgBEHgzABqIgUgBEG4J2oiAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgKIRyAEIARB9CdqIhcoAAA2AItHIARBmMcAaiAFKQMANwMAIARBoMcAaiANKQMANwMAIARBqMcAaiAJKQMANwMAIARBsMcAaiAMKQMANwMAIARBuMcAaiAIKQMANwMAIARBwMcAaiAHKQMANwMAIARByMcAaiAKKQMANwMAIAQgBCkD2Ew3A5BHIARBsCdqIBVByANqEIYEIAQtAPAnIlFBAkYEQCAFIAMoAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgCiAGKQMANwMAIAcgECkDADcDACAIIBEpAwA3AwAgDCATKQMANwMAIAkgFCkDADcDACANIBkpAwA3AwAgBSADKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AtBHIAQgFygAADYA00cgBEHgxwBqIAUpAwA3AwAgBEHoxwBqIA0pAwA3AwAgBEHwxwBqIAkpAwA3AwAgBEH4xwBqIAwpAwA3AwAgBEGAyABqIAgpAwA3AwAgBEGIyABqIAcpAwA3AwAgBEGQyABqIAopAwA3AwAgBCAEKQPYTDcD2EcgBEGwJ2ogFUHgA2oQhgQgBC0A8CciUkECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AphIIAQgBEH0J2oiFygAADYAm0ggBEGoyABqIAUpAwA3AwAgBEGwyABqIA0pAwA3AwAgBEG4yABqIAkpAwA3AwAgBEHAyABqIAwpAwA3AwAgBEHIyABqIAgpAwA3AwAgBEHQyABqIAcpAwA3AwAgBEHYyABqIAopAwA3AwAgBCAEKQPYTDcDoEggBEGwJ2ogFUH4A2oQhgQgBC0A8CciU0ECRgRAIAUgAygCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIAYpAwA3AwAgByAQKQMANwMAIAggESkDADcDACAMIBMpAwA3AwAgCSAUKQMANwMAIA0gGSkDADcDACAFIAMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYC4EggBCAXKAAANgDjSCAEQfDIAGogBSkDADcDACAEQfjIAGogDSkDADcDACAEQYDJAGogCSkDADcDACAEQYjJAGogDCkDADcDACAEQZDJAGogCCkDADcDACAEQZjJAGogBykDADcDACAEQaDJAGogCikDADcDACAEIAQpA9hMNwPoSCAEQbAnaiAVQZAEahCGBCAELQDwJyJUQQJGBEAgBEHgzABqIARBuCdqKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIARBkM0AaiIKIARB6CdqIgYpAwA3AwAgBEGIzQBqIgcgBEHgJ2oiECkDADcDACAEQYDNAGoiCCAEQdgnaiIRKQMANwMAIARB+MwAaiIMIARB0CdqIhMpAwA3AwAgBEHwzABqIgkgBEHIJ2oiFCkDADcDACAEQejMAGoiDSAEQcAnaiIZKQMANwMAIARB4MwAaiIFIARBuCdqIgMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCqEkgBCAEQfQnaiIXKAAANgCrSSAEQbjJAGogBSkDADcDACAEQcDJAGogDSkDADcDACAEQcjJAGogCSkDADcDACAEQdDJAGogDCkDADcDACAEQdjJAGogCCkDADcDACAEQeDJAGogBykDADcDACAEQejJAGogCikDADcDACAEIAQpA9hMNwOwSSAEQbAnaiAVQagEahCGBCAELQDwJyJVQQJGBEAgBSADKAIAIgU2AgAgBCAEKQOwJyLKATcD2EwgEkEMaiAFNgIAIBIgygE3AgQgEkEBNgIADAgLIAogBikDADcDACAHIBApAwA3AwAgCCARKQMANwMAIAwgEykDADcDACAJIBQpAwA3AwAgDSAZKQMANwMAIAUgAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgLwSSAEIBcoAAA2APNJIARBgMoAaiAFKQMANwMAIARBiMoAaiANKQMANwMAIARBkMoAaiAJKQMANwMAIARBmMoAaiAMKQMANwMAIARBoMoAaiAIKQMANwMAIARBqMoAaiAHKQMANwMAIARBsMoAaiAKKQMANwMAIAQgBCkD2Ew3A/hJIARBsCdqIBVBwARqEIYEIAQtAPAnIlZBAkYEQCAEQeDMAGogBEG4J2ooAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgBEGQzQBqIgogBEHoJ2oiBikDADcDACAEQYjNAGoiByAEQeAnaiIQKQMANwMAIARBgM0AaiIIIARB2CdqIhEpAwA3AwAgBEH4zABqIgwgBEHQJ2oiEykDADcDACAEQfDMAGoiCSAEQcgnaiIUKQMANwMAIARB6MwAaiINIARBwCdqIhkpAwA3AwAgBEHgzABqIgUgBEG4J2oiAykDADcDACAEIAQpA7AnNwPYTCAEIAQoAPEnNgK4SiAEIARB9CdqIhcoAAA2ALtKIARByMoAaiAFKQMANwMAIARB0MoAaiANKQMANwMAIARB2MoAaiAJKQMANwMAIARB4MoAaiAMKQMANwMAIARB6MoAaiAIKQMANwMAIARB8MoAaiAHKQMANwMAIARB+MoAaiAKKQMANwMAIAQgBCkD2Ew3A8BKIARBsCdqIBVB2ARqEIYEIAQtAPAnIldBAkYEQCAFIAMoAgAiBTYCACAEIAQpA7AnIsoBNwPYTCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMCAsgCiAGKQMANwMAIAcgECkDADcDACAIIBEpAwA3AwAgDCATKQMANwMAIAkgFCkDADcDACANIBkpAwA3AwAgBSADKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AoBLIAQgFygAADYAg0sgBEGQywBqIAUpAwA3AwAgBEGYywBqIA0pAwA3AwAgBEGgywBqIAkpAwA3AwAgBEGoywBqIAwpAwA3AwAgBEGwywBqIAgpAwA3AwAgBEG4ywBqIAcpAwA3AwAgBEHAywBqIAopAwA3AwAgBCAEKQPYTDcDiEsgBEGwJ2ogFUHwBGoQhgQgBC0A8CciWEECRgRAIARB4MwAaiAEQbgnaigCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAEQZDNAGoiCiAEQegnaiIGKQMANwMAIARBiM0AaiIHIARB4CdqIhApAwA3AwAgBEGAzQBqIgggBEHYJ2oiESkDADcDACAEQfjMAGoiDCAEQdAnaiITKQMANwMAIARB8MwAaiIJIARByCdqIhQpAwA3AwAgBEHozABqIg0gBEHAJ2oiGSkDADcDACAEQeDMAGoiBSAEQbgnaiIDKQMANwMAIAQgBCkDsCc3A9hMIAQgBCgA8Sc2AshLIAQgBEH0J2oiFygAADYAy0sgBEHYywBqIAUpAwA3AwAgBEHgywBqIA0pAwA3AwAgBEHoywBqIAkpAwA3AwAgBEHwywBqIAwpAwA3AwAgBEH4ywBqIAgpAwA3AwAgBEGAzABqIAcpAwA3AwAgBEGIzABqIAopAwA3AwAgBCAEKQPYTDcD0EsgBEGwJ2ogFUGIBWoQhgQgBC0A8CciWUECRgRAIAUgAygCACIFNgIAIAQgBCkDsCciygE3A9hMIBJBDGogBTYCACASIMoBNwIEIBJBATYCAAwICyAKIAYpAwA3AwAgByAQKQMANwMAIAggESkDADcDACAMIBMpAwA3AwAgCSAUKQMANwMAIA0gGSkDADcDACAFIAMpAwA3AwAgBCAEKQOwJzcD2EwgBCAEKADxJzYCkEwgBCAXKAAANgCTTCAEQaDMAGogBSkDADcDACAEQajMAGogDSkDADcDACAEQbDMAGogCSkDADcDACAEQbjMAGogDCkDADcDACAEQcDMAGogCCkDADcDACAEQcjMAGogBykDADcDACAEQdDMAGogCikDADcDACAEIAQpA9hMNwOYTCAEQejiAGogBEHgEGogBEGwE2oiChCMAyAEKALwYkEcRw0FIARBADYC8GIgBEGwJ2pBBHIiByAEKALsYiIFQYAH/AoAACAEKALoYiIIBEAgBSAIQQV0EN8ECyAEQdjMAGoiBSAHQYAH/AoAACAEQdjTAGogChD0AiAEQfjTAGoiGiAEQbwTahD0AiAEQZjUAGogBEHIE2oQ9AIgBEG41ABqIARB1BNqEPQCIARBoOEAaiEUIARB2DFqIRcgBEGoOmohECAFIQ0gFSgCrAUiCSEZQQAhBSMAQZDAAGsiBiQAIAZB8D9qIRFBgAIhCiMAQcAKayIIJAAgGikDGCHRASAaKQMQIcoBIBopAwghzAEgGikDACHQAQNAIAhB4AlqIMoBQgAg0QFCABDJAyAIQcAJaiDMAUIAINEBQgAQyQMgCEGQCWog0AFCACDRAUIAEMkDIAhBsAlqIMwBQgAgygFCABDJAyAIQYAJaiDQAUIAIMoBQgAQyQMgCEHwCGog0AFCACDMAUIAEMkDIAhBsApqINEBQgAg0QFCABDJAyAIQdAJaiDKAUIAIMoBQgAQyQMgCEGgCWogzAFCACDMAUIAEMkDIAhB4AhqINABQgAg0AFCABDJAyAIQaAKaiAIKQOwCiLQAUL/////vrL98EJ+IsoBQgBCgYCAgL+y/fDDAEIAEMkDIAhBkApqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgCEGACmogygFCAELdsIWM6LaRqLh/QgAQyQMgCEHwCWogygFCAEKpwMaJrs6TsjBCABDJAyAIKQP4CCAIKQOICSAIKQOYCSAIKQPICSAIKQPoCSLLASAIKQPACXwiygEgywFUrXwizAEgCCkDkAl8IssBIMwBVK18Is8BIAgpA4AJfCLMASDPAVStfCDMASDMASAIKQO4CSDLASDLASAIKQOwCXwizwFWrXx8IssBVq18Is0BIAgpA/AIfCLMASDNAVStfCLNAUI/iCAIKQPoCCAIKQPgCCLOASDNAUIBhiDMAUI/iIR8Is0BIM4BVK18IM0BIAgpA6gJIAgpA9gJIAgpA9AJItIBIMoBQgGGIAgpA+AJItEBQj+IhHwizgEg0gFUrXwgzgEgzgEgCCkDuAoi0gEg0QFCAYZ8ItQBINIBVK18ItUBVq18Is4BIM8BQgGGIMoBQj+IhHwi1wEgzgFUrSLOASAIKQOgCXwiygEgzgFUrXwgygEgywFCAYYgzwFCP4iEfCLPASDKAVStfCLKASDMAUIBhiDLAUI/iIR8ItEBIMoBVK18ItMBIM0BVK18fCHSAUEAIQwCfwJAIAgpA/gJIAgpA4gKIAgpA5gKIAgpA6gKIAgpA6AKIsoBINABQn2DfCDKAVStfCLLASAIKQOQCnwiygEgywFUrXwgygEg1AF8IssBIMoBVK18IswBIAgpA4AKfCLKASDMAVStfCDKASDVAXwizAEgygFUrXwizQEgCCkD8Al8IsoBIM0BVK18IMoBINcBfCLNASDKAVStfCLKAVANACDKASDPAXwizwEgygFUIgdFDQAgB60iygEg0QF8ItEBIMoBWg0AIMoBINEBVq0iygEg0wF8ItMBIMoBWg0AIMoBINMBVq0iygEg0gF8ItIBIMoBVAwBC0EACyETIAhB0AhqIMsBQv////++sv3wQn4iygFCAEKBgICAv7L98MMAQgAQyQMgCEHACGogygFCAEKR4eXNh4n6mShCABDJAyAIQbAIaiDKAUIAQt2whYzotpGouH9CABDJAyAIQaAIaiDKAUIAQqnAxomuzpOyMEIAEMkDAkAgCCkDqAggCCkDuAggCCkDyAggCCkD2AggCCkD0AgiygEgywF8IMoBVK18IssBIAgpA8AIfCLKASDLAVStfCDKASDMAXwiywEgygFUrXwizAEgCCkDsAh8IsoBIMwBVK18IMoBIM0BfCLMASDKAVStfCLNASAIKQOgCHwiygEgzQFUrXwgygEgzwF8Is8BIMoBVK18IsoBUA0AIMoBINEBfCLRASDKAVoNACDKASDRAVatIsoBINMBfCLTASDKAVoNACDKASDTAVatIsoBINIBfCLSASDKAVQhDAsgCEGQCGogywFC/////76y/fBCfiLKAUIAQoGAgIC/sv3wwwBCABDJAyAIQYAIaiDKAUIAQpHh5c2HifqZKEIAEMkDIAhB8AdqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAhB4AdqIMoBQgBCqcDGia7Ok7IwQgAQyQNBACEDIAgpA+gHIAgpA/gHIAgpA4gIIAgpA5gIIAgpA5AIIsoBIMsBfCDKAVStfCLLASAIKQOACHwiygEgywFUrXwgygEgzAF8IssBIMoBVK18IswBIAgpA/AHfCLKASDMAVStfCDKASDPAXwizAEgygFUrXwizwEgCCkD4Ad8IsoBIM8BVK18IMoBINEBfCLPASDKAVStfCLKAVBFBEAgygEg0wF8ItMBIMoBVCIHrSLKASDSAXwizQEg0gEgBxsh0gEgByDKASDNAVZxIQMLIAohByAIQdAHaiDLAUL/////vrL98EJ+IsoBQgBCgYCAgL+y/fDDAEIAEMkDIAhBwAdqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgCEGwB2ogygFCAELdsIWM6LaRqLh/QgAQyQMgCEGgB2ogygFCAEKpwMaJrs6TsjBCABDJAyAIKQOoByAIKQO4ByAIKQPIByAIKQPYByAIKQPQByLKASDLAXwgygFUrXwiywEgCCkDwAd8IsoBIMsBVK18IMoBIMwBfCLRASDKAVStfCLLASAIKQOwB3wiygEgywFUrXwgygEgzwF8IswBIMoBVK18IssBIAgpA6AHfCLKASDLAVStfCDKASDTAXwiywEgygFUrXwiygEg0gF8Is8BINIBIMoBQgBSIgobIdABAkACQAJAIAwgE3IgA3IgygEgzwFWIgytIMoBIAobQgBSciAKIAxxINABQqnAxomuzpOyMFZycg0AINABQqnAxomuzpOyMFIEQCDMASHKASDLASHMAQwDCyDLAULdsIWM6LaRqLh/Vg0AIMsBQt2whYzotpGouH9SBEAgzAEhygEgywEhzAFCqcDGia7Ok7IwIdABDAMLQt2whYzotpGouH8hywEgzAFCkeHlzYeJ+pkoVg0AIMwBQpHh5c2HifqZKFIg0QFCgICAgL+y/fDDAFhyDQELIMwBQpHh5c2HifqZKH0izwEg0QFCgYCAgL+y/fDDAFStIs0BfSHKASDLAUKjz/rzl8nu18cAfCLOASDMAUKR4eXNh4n6mShUIM0BIM8BVnKtIs8BfSHMASDQASDLAULdsIWM6LaRqLh/VCDOASDPAVRyrX1CqcDGia7Ok7IwfSHQASDRAUKBgICAv7L98MMAfSHRAQwBCyDMASHKAULdsIWM6LaRqLh/IcwBQqnAxomuzpOyMCHQAQsgB0EBdiEKIAdBAnFFDQALAkACQCAKDgIBAQALINEBIdMBIMoBIcsBIMwBIc8BINABIdIBA0AgCEHABmogywFCACDTAUIAEMkDIAhBoAZqIM8BQgAg0wFCABDJAyAIQfAFaiDSAUIAINMBQgAQyQMgCEGQBmogzwFCACDLAUIAEMkDIAhB4AVqINIBQgAgywFCABDJAyAIQdAFaiDSAUIAIM8BQgAQyQMgCEGQB2og0wFCACDTAUIAEMkDIAhBsAZqIMsBQgAgywFCABDJAyAIQYAGaiDPAUIAIM8BQgAQyQMgCEHABWog0gFCACDSAUIAEMkDIAhBgAdqIAgpA5AHItQBQv////++sv3wQn4iywFCAEKBgICAv7L98MMAQgAQyQMgCEHwBmogywFCAEKR4eXNh4n6mShCABDJAyAIQeAGaiDLAUIAQt2whYzotpGouH9CABDJAyAIQdAGaiDLAUIAQqnAxomuzpOyMEIAEMkDIAgpA9gFIAgpA+gFIAgpA/gFIAgpA6gGIAgpA8gGIs8BIAgpA6AGfCLLASDPAVStfCLNASAIKQPwBXwizwEgzQFUrXwizgEgCCkD4AV8Is0BIM4BVK18IM0BIAgpA5gGIM8BIM8BIAgpA5AGfCLOAVatfHwizwEgzQFUrXwizQEgCCkD0AV8ItIBIM0BVK18Is0BQj+IIAgpA8gFIAgpA8AFItUBIM0BQgGGINIBQj+IhHwi0wEg1QFUrXwg0wEgCCkDiAYgCCkDuAYgCCkDsAYi1QEgywFCAYYgCCkDwAYi1wFCP4iEfCLNASDVAVStfCDNASAIKQOYByLVASDXAUIBhnwi1wEg1QFUrXwi1QEgzQFUrXwizQEgzgFCAYYgywFCP4iEfCLYASDNAVStIs0BIAgpA4AGfCLLASDNAVStfCDLASDPAUIBhiDOAUI/iIR8Is0BIMsBVK18IssBINIBQgGGIM8BQj+IhHwizwEgywFUrXwiywEg0wFUrXx8IdIBQQAhDAJ/AkAgCCkD2AYgCCkD6AYgCCkD+AYgCCkDiAcgCCkDgAcizgEg1AFCfYN8IM4BVK18ItMBIAgpA/AGfCLOASDTAVStfCDOASDXAXwi0wEgzgFUrXwi1AEgCCkD4AZ8Is4BINQBVK18IM4BINUBfCLUASDOAVStfCLVASAIKQPQBnwizgEg1QFUrXwgzgEg2AF8ItUBIM4BVK18Is4BUA0AIM0BIM4BfCLNASDOAVQiB0UNACAHrSLOASDPAXwizwEgzgFaDQAgzgEgzwFWrSLOASDLAXwiywEgzgFaDQAgywEgzgFUrSLOASDSAXwi0gEgzgFUDAELQQALIRMgCEGwBWog0wFC/////76y/fBCfiLOAUIAQoGAgIC/sv3wwwBCABDJAyAIQaAFaiDOAUIAQpHh5c2HifqZKEIAEMkDIAhBkAVqIM4BQgBC3bCFjOi2kai4f0IAEMkDIAhBgAVqIM4BQgBCqcDGia7Ok7IwQgAQyQMCQCAIKQOIBSAIKQOYBSAIKQOoBSAIKQO4BSAIKQOwBSLOASDTAXwgzgFUrXwi0wEgCCkDoAV8Is4BINMBVK18IM4BIM4BINQBfCLTAVatfCLUASAIKQOQBXwizgEg1AFUrXwgzgEg1QF8ItQBIM4BVK18ItUBIAgpA4AFfCLOASDVAVStfCDOASDNASDOAXwi1QFWrXwizQFQDQAgzQEgzwF8Is8BIM0BWg0AIM0BIM8BVq0izQEgywF8IssBIM0BWg0AIMsBIM0BVK0izQEg0gF8ItIBIM0BVCEMCyAIQfAEaiDTAUL/////vrL98EJ+Is0BQgBCgYCAgL+y/fDDAEIAEMkDIAhB4ARqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgCEHQBGogzQFCAELdsIWM6LaRqLh/QgAQyQMgCEHABGogzQFCAEKpwMaJrs6TsjBCABDJA0EAIQMgCCkDyAQgCCkD2AQgCCkD6AQgCCkD+AQgCCkD8AQizQEg0wF8IM0BVK18Is4BIAgpA+AEfCLNASDOAVStfCDNASDNASDUAXwizgFWrXwi0wEgCCkD0AR8Is0BINMBVK18IM0BINUBfCLTASDNAVStfCLUASAIKQPABHwizQEg1AFUrXwgzQEgzQEgzwF8ItQBVq18Is8BUEUEQCDLASDPAXwiywEgzwFUIgetIs8BINIBfCLNASDSASAHGyHSASAHIM0BIM8BVHEhAwsgCiEHIAhBsARqIM4BQv////++sv3wQn4izwFCAEKBgICAv7L98MMAQgAQyQMgCEGgBGogzwFCAEKR4eXNh4n6mShCABDJAyAIQZAEaiDPAUIAQt2whYzotpGouH9CABDJAyAIQYAEaiDPAUIAQqnAxomuzpOyMEIAEMkDIAgpA4gEIAgpA5gEIAgpA6gEIAgpA7gEIAgpA7AEIs8BIM4BfCDPAVStfCLNASAIKQOgBHwizwEgzQFUrXwgzwEg0wF8ItMBIM8BVK18Is8BIAgpA5AEfCLNASDPAVStfCDNASDNASDUAXwizwFWrXwizQEgCCkDgAR8Is4BIM0BVK18IM4BIMsBIM4BfCLNAVatfCLLASDSAXwizgEg0gEgywFCAFIiChsh0gECQAJAAkACQCAMIBNyIANyIMsBIM4BViIMrSDLASAKG0IAUnIgCiAMcSDSAUKpwMaJrs6TsjBWcnINACDSAUKpwMaJrs6TsjBSDQEgzQFC3bCFjOi2kai4f1YNACDNAULdsIWM6LaRqLh/UgRAIM8BIcsBIM0BIc8BQqnAxomuzpOyMCHSAQwEC0LdsIWM6LaRqLh/Ic0BIM8BQpHh5c2HifqZKFYNACDPAUKR4eXNh4n6mShSINMBQoCAgIC/sv3wwwBYcg0CCyDPAUKR4eXNh4n6mSh9Is4BINMBQoGAgIC/sv3wwwBUrSLUAX0hywEgzQFCo8/685fJ7tfHAHwi1QEgzwFCkeHlzYeJ+pkoVCDOASDUAVRyrSLOAX0hzwEg0gEgzQFC3bCFjOi2kai4f1QgzgEg1QFWcq19QqnAxomuzpOyMH0h0gEg0wFCgYCAgL+y/fDDAH0h0wEMAgsgzwEhywEgzQEhzwEMAQsgzwEhywFC3bCFjOi2kai4fyHPAUKpwMaJrs6TsjAh0gELAkAgB0ECcUUNACAIQfADaiDTAUIAINEBQgAQyQMgCEGgA2og0wFCACDKAUIAEMkDIAhBkANqINMBQgAgzAFCABDJAyAIQYADaiDTAUIAINABQgAQyQMgCEHgA2ogCCkD8AMi1AFC/////76y/fBCfiLNAUIAQoGAgIC/sv3wwwBCABDJAyAIQdADaiDNAUIAQpHh5c2HifqZKEIAEMkDIAhBwANqIM0BQgBC3bCFjOi2kai4f0IAEMkDIAhBsANqIM0BQgBCqcDGia7Ok7IwQgAQyQMgCEHwAmogywFCACDRAUIAEMkDIAhBoAJqIMsBQgAgygFCABDJAyAIQZACaiDLAUIAIMwBQgAQyQMgCEGAAmogywFCACDQAUIAEMkDIAhB4AJqIAgpA9ADItoBIAgpA/gDItgBIAgpA6ADfCLWAXwizgEgCCkD6AMg1AEgCCkD4AMizQF8IM0BVK18fCLUASAIKQPwAnwi1QFC/////76y/fBCfiLNAUIAQoGAgIC/sv3wwwBCABDJAyAIQdACaiDNAUIAQpHh5c2HifqZKEIAEMkDIAhBwAJqIM0BQgBC3bCFjOi2kai4f0IAEMkDIAhBsAJqIM0BQgBCqcDGia7Ok7IwQgAQyQMgCEHwAWogzwFCACDRAUIAEMkDIAhBoAFqIM8BQgAgygFCABDJAyAIQZABaiDPAUIAIMwBQgAQyQMgCEGAAWogzwFCACDQAUIAEMkDIAhB4AFqIAgpA/gCINQBINUBVq18ItkBIAgpA6ACfCLXASAIKQOoAyDWASDYAVStfCLbASAIKQOQA3wi2AEgCCkDwAN8ItYBIM4BINQBVq0gCCkD2AMgzgEg2gFUrXx8fCLcAXwizgEgCCkD0AJ8ItQBIAgpA+gCIAgpA+ACIs0BINUBfCDNAVStfHwi1QEgCCkD8AF8ItoBQv////++sv3wQn4izQFCAEKBgICAv7L98MMAQgAQyQMgCEHQAWogzQFCAEKR4eXNh4n6mShCABDJAyAIQcABaiDNAUIAQt2whYzotpGouH9CABDJAyAIQbABaiDNAUIAQqnAxomuzpOyMEIAEMkDIAhB8ABqINIBQgAg0QFCABDJAyAIQSBqINIBQgAgygFCABDJAyAIQRBqINIBQgAgzAFCABDJAyAIINIBQgAg0AFCABDJAyAIQeAAaiAIKQP4ASDVASDaAVatfCLeASAIKQOgAXwizAEgCCkDmAMg2AEg2wFUrXwi2wEgCCkDgAN8Is0BIAgpA7ADfCLRASDWASDcAVatIAgpA8gDINYBINgBVK18fHwi0AEgCCkDkAJ8ItgBIM4BINcBVK0gCCkDqAIg1wEg2QFUrXx8fCLXASAIKQPAAnwi1gEg1AEg1QFWrSAIKQPYAiDOASDUAVatfHx8ItkBfCLOASAIKQPQAXwi1AEgCCkD6AEgCCkD4AEiygEg2gF8IMoBVK18fCLVASAIKQNwfCLaAUL/////vrL98EJ+IsoBQgBCgYCAgL+y/fDDAEIAEMkDIAhB0ABqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgCEFAayDKAUIAQt2whYzotpGouH9CABDJAyAIQTBqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAgpAzggCCkDuAEgCCkDuAIg0AEg0QFUrSAIKQO4AyDNASDRAVatfHwgCCkDiAMgzQEg2wFUrXx8ItsBIAgpA4ACfCLKASDXASDYAVStIAgpA5gCINABINgBVq18fHwizQEgCCkDsAJ8ItEBIM0BVK18INEBINEBINYBINkBVq0gCCkDyAIg1gEg1wFUrXx8fCLQAVatfCDKASDNAVatIAgpA4gCIMoBINsBVK18fHwi1wEgCCkDgAF8IsoBIAgpA5gBINABIAgpA5ABfCLNASDQAVStfCDNASDMASDOAVatIAgpA6gBIMwBIN4BVK18fHwizAEgzQFUrXx8Is0BIAgpA7ABfCLRASDNAVStfCDRASAIKQPIASDMASDMASAIKQPAAXwi0AFWrXwg0AEg1AEg1QFWrSAIKQPYASDOASDUAVatfHx8Is4BINABVK18fCLMASDRAVStfCDKASDNAVatIAgpA4gBIMoBINcBVK18fHwi1wEgCCkDAHwiygEgCCkDGCDMASDMASAIKQMQfCLNAVatfCDNASDNASAIKQMoIAgpA3gg1QEg2gFWrXwi0QEgCCkDIHwizAEg0QFUrXwgzAEgzAEgzgF8Is4BVq18fCLMAVatfHwi0AEgCCkDMHwi1AEg0AFUrXwg1AEg1AEgCCkDSCDMASDMASAIKQNAfCLVAVatfCDVASDVASAIKQNYIM4BIM4BIAgpA1B8IswBVq18IMwBIAgpA2ggCCkDYCLNASDaAXwgzQFUrXx8ItEBIMwBVK18fCLNAVatfHwizgFWrXwgygEg0AFWrSAIKQMIIMoBINcBVK18fHwi0AFCqcDGia7Ok7IwVg0AINABQqnAxomuzpOyMFIEQCDNASHKASDOASHMAQwDCyDOAULdsIWM6LaRqLh/Vg0AIM4BQt2whYzotpGouH9SBEAgzQEhygEgzgEhzAFCqcDGia7Ok7IwIdABDAMLIM0BQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcwBIM0BQpHh5c2HifqZKFIg0QFCgYCAgL+y/fDDAFRyDQELIM0BQpHh5c2HifqZKH0izAEg0QFCgYCAgL+y/fDDAFStItQBfSHKASDOAUKjz/rzl8nu18cAfCLVASDNAUKR4eXNh4n6mShUIMwBINQBVHKtIs0BfSHMASDQASDOAULdsIWM6LaRqLh/VCDNASDVAVZyrX1CqcDGia7Ok7IwfSHQASDRAUKBgICAv7L98MMAfSHRAQwBCyDNASHKAUKpwMaJrs6TsjAh0AELIAdBAXYhCiAHQQRPDQALCyARINEBNwMYIBEgygE3AxAgESDMATcDCCARINABNwMAIAhBwApqJABCr76f0Jn4nYUOIdoBIAYpA/A/IsoBIc4BAn4CQAJ+AkAgygFCr76f0Jn4nYUOUg0AQq6M5cP37ai35gAh2gEgBikD+D8izgFCrozlw/ftqLfmAFINAEKpmoP72dKd/jYh2gEgBikDgEAizgFCqZqD+9nSnf42Ug0AQvv////Eg43LrH8h2gEgBikDiEAizgFC+////8SDjcusf1INAEKpmoP72dKd/jYhzwFCrozlw/ftqLfmAAwBCyDOASDaAVQgBikDiEAh2gENASAGKQOAQCHPASAGKQP4PwshywEgzwFCqZqD+9nSnf42fSLMASDaAUL7////xIONy6x/VK0izQF9Ic4BIMsBQq6M5cP37ai35gB9ItIBIM8BQqmag/vZ0p3+NlQgzAEgzQFUcq0izAF9Ic8BIMsBQq6M5cP37ai35gBUIMwBINIBVnIhCiDaAUKFgICAu/zytNMAfCHaASDKAUKvvp/QmfidhQ59DAELQt2whYzotpGouH9Crozlw/ftqLfmACAGKQP4PyLLAX0izAEgBikDgEAizwFCqZqD+9nSnf42VkKpmoP72dKd/jYgzwF9Is8BINoBQvv////Eg43LrH9WrSLNAVRyrSLSAX0izgF9ItEBIM8BIM0BfSLPAUKR4eXNh4n6mShWQpHh5c2HifqZKCDPAX0izQEg2gFChICAgLv88rTTAHxC/v///8DNgo+8f1StItABVHKtItMBfSHPASDRASDTAVQgzgFC3bCFjOi2kai4f1ZyIQogzQEg0AF9Ic4BINoBQvr///+F0Y/a6AB9IdoBIMoBIMwBINIBVCDLAUKujOXD9+2ot+YAVnKtfEL6gae5lNb1rCJ8CyHKASAGINoBNwPYPiAGIM4BNwPQPiAGIM8BNwPIPiAGIMoBIAqtfTcDwD4gBkGIwABqQgA3AwAgBkGAQGtCADcDACAGQfg/akIANwMAIAZCADcD8D8CQAJAAkACQCAGQcA+aiAGQfA/akEgEPEDBEBB0c7FAC0AABoCQAJAQYDAAEEIENYEIhMEQCATQSBqQQBB4D/8CwAgE0L7////xIONy6x/NwMYIBNCqZqD+9nSnf42NwMQIBNCrozlw/ftqLfmADcDCCATQq++n9CZ+J2FDjcDACAZRQ0CQQMhCEEAIQoMAQtBCEGAwABB6K/CABDIBAALA0AgBUEcRg0BQYAHIApBIGogCkGAB0YiERsgGUEBayEZIBMgBUEJbCIDQQV0aiIMQvv////Eg43LrH83AzggDEKpmoP72dKd/jY3AzAgDEKujOXD9+2ot+YANwMoIAxCr76f0Jn4nYUONwMgQQAgCiANaiARGyIKKQMAIc4BIAopAwgh0gEgCikDECHQASAKKQMYIdMBIAVBAWohBSADQQJqIQwgA0EKaiERIAghCgJAA0AgBkHAPGog0wFCACATIAxBBXRqIgNBCGspAwAiygFCABDJAyAGQYA9aiDTAUIAIANBEGspAwAiywFCABDJAyAGQcA9aiDTAUIAIANBGGspAwAizAFCABDJAyAGQYA+aiDTAUIAIANBIGspAwAizwFCABDJAyAGQbA8aiAGKQPAPCLUAUIAQgBC/////76y/fBCEMkDIAZBoDxqIAYpA7g8Is0BQgBCgYCAgL+y/fDDAEIAEMkDIAZBkDxqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgBkGwO2ogzQFCAELdsIWM6LaRqLh/QgAQyQMgBkHQOmogzQFCAEKpwMaJrs6TsjBCABDJAyAGQdA8aiDQAUIAIMoBQgAQyQMgBkGQPWog0AFCACDLAUIAEMkDIAZB0D1qINABQgAgzAFCABDJAyAGQZA+aiDQAUIAIM8BQgAQyQMgBkGAPGogBikDkDwi2gEgBikDyDwi2AEgBikDgD18ItYBfCLRASAGKQOoPCDUASAGKQOgPCLNAXwgzQFUrXx8ItQBIAYpA9A8fCLVAUIAQgBC/////76y/fBCEMkDIAZB8DtqIAYpA4g8Is0BQgBCgYCAgL+y/fDDAEIAEMkDIAZB4DtqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgBkHQO2ogzQFCAELdsIWM6LaRqLh/QgAQyQMgBkHAO2ogzQFCAEKpwMaJrs6TsjBCABDJAyAGQeA8aiDSAUIAIMoBQgAQyQMgBkGgPWog0gFCACDLAUIAEMkDIAZB4D1qINIBQgAgzAFCABDJAyAGQaA+aiDSAUIAIM8BQgAQyQMgBkGgO2ogBikD2Dwg1AEg1QFWrXwi2QEgBikDkD18ItcBIAYpA4g9INYBINgBVK18ItsBIAYpA8A9fCLYASAGKQOwO3wi1gEg0QEg1AFWrSAGKQOYPCDRASDaAVStfHx8ItwBfCLRASAGKQPgO3wi1AEgBikD+DsgBikD8DsizQEg1QF8IM0BVK18fCLVASAGKQPgPHwi2gFCAEIAQv////++sv3wQhDJAyAGQZA7aiAGKQOoOyLNAUIAQoGAgIC/sv3wwwBCABDJAyAGQYA7aiDNAUIAQpHh5c2HifqZKEIAEMkDIAZB8DpqIM0BQgBC3bCFjOi2kai4f0IAEMkDIAZB4DpqIM0BQgBCqcDGia7Ok7IwQgAQyQMgBkHwPGogzgFCACDKAUIAEMkDIAZBsD1qIM4BQgAgywFCABDJAyAGQfA9aiDOAUIAIMwBQgAQyQMgBkGwPmogzgFCACDPAUIAEMkDIAZBwDpqIAYpA+g8INUBINoBVq18It4BIAYpA6A9fCLLASAGKQPIPSDYASDbAVStfCLbASAGKQOAPnwizAEgBikD0Dp8Is8BINYBINwBVq0gBikDuDsg1gEg2AFUrXx8fCLNASAGKQPQPXwi2AEg0QEg1wFUrSAGKQOYPSDXASDZAVStfHx8ItcBIAYpA9A7fCLWASDUASDVAVatIAYpA+g7INEBINQBVq18fHwi2QF8ItEBIAYpA4A7fCLUASAGKQOYOyAGKQOQOyLKASDaAXwgygFUrXx8ItUBIAYpA/A8fCLaAUIAQgBC/////76y/fBCEMkDIAZBsDpqIAYpA8g6IsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZBoDpqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkGQOmogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGAOmogygFCAEKpwMaJrs6TsjBCABDJAwJAAkACQCAGKQOIOiAGKQPoOiAGKQPIOyDNASDPAVStIAYpA9g6IMwBIM8BVq18fCAGKQOIPiDMASDbAVStfHwi2wEgBikDkD58IsoBINcBINgBVK0gBikD2D0gzQEg2AFWrXx8fCLMASAGKQPAO3wizwEgzAFUrXwgzwEgzwEg1gEg2QFWrSAGKQPYOyDWASDXAVStfHx8Is0BVq18IMoBIMwBVq0gBikDmD4gygEg2wFUrXx8fCLXASAGKQOgPnwiygEgBikD6D0gzQEgBikD4D18IswBIM0BVK18IMwBIMsBINEBVq0gBikDqD0gywEg3gFUrXx8fCLLASDMAVStfHwizAEgBikD4Dp8Is8BIMwBVK18IM8BIAYpA/g6IMsBIMsBIAYpA/A6fCLNAVatfCDNASDNASDUASDVAVatIAYpA4g7INEBINQBVq18fHwi0QFWrXx8IssBIM8BVK18IMoBIMwBVq0gBikDqD4gygEg1wFUrXx8fCLXASAGKQOwPnwiygEgBikD+D0gywEgywEgBikD8D18IswBVq18IMwBIMwBIAYpA7g9IAYpA/g8INUBINoBVq18Is8BIAYpA7A9fCLLASDPAVStfCDLASDLASDRAXwizwFWrXx8IssBVq18fCLMASAGKQOAOnwi0QEgzAFUrXwg0QEg0QEgBikDmDogywEgywEgBikDkDp8Is0BVq18IM0BIM0BIAYpA6g6IM8BIM8BIAYpA6A6fCLUAVatfCDUASDUASAGKQO4OiAGKQOwOiLLASDaAXwgywFUrXx8IssBVq18fCLPAVatfHwizQFWrXwgygEgzAFWrSAGKQO4PiDKASDXAVStfHx8IsoBQqnAxomuzpOyMFYNACDKAUKpwMaJrs6TsjBSDQEgzQFC3bCFjOi2kai4f1YNACDNAULdsIWM6LaRqLh/UgRAQqnAxomuzpOyMCHKAQwCCyDPAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHMASDPAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIcoBIM8BIdEBDAMLQpHh5c2HifqZKCHRASDLAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHKAQwCCyDPAUKR4eXNh4n6mSh9IswBIMsBQoGAgIC/sv3wwwBUrSLUAX0h0QEgzQFCo8/685fJ7tfHAHwi1QEgzwFCkeHlzYeJ+pkoVCDMASDUAVRyrSLPAX0hzAEgygEgzQFC3bCFjOi2kai4f1QgzwEg1QFWcq19QqnAxomuzpOyMH0hygEgywFCgYCAgL+y/fDDAH0hywEMAQsgzQEhzAEgzwEh0QELIAxB/wFNBEAgAyDLATcDGCADINEBNwMQIAMgzAE3AwggAyDKATcDACAKIgxBAWohCiAMIBFPDQIMAQsLIAxBgAJByLDCABDZAwALIAhBCWohCCEKIBkNAAsLIAZB8D9qQfivwgBBwAAQtwIgBkGAOGogBikDiEAiygFCAEKn24Xx2si53BtCABDJAyAGQcA4aiAGKQOAQCLLAUIAQqfbhfHayLncG0IAEMkDIAZBgDlqIAYpA/g/IswBQgBCp9uF8drIudwbQgAQyQMgBkHAOWogBikD8D8izwFCAEKn24Xx2si53BtCABDJAyAGQfA3aiAGKQOAOCLSAUL/////vrL98EJ+Is0BQgBCgYCAgL+y/fDDAEIAEMkDIAZB4DdqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgBkGQN2ogzQFCAELdsIWM6LaRqLh/QgAQyQMgBkHANmogzQFCAEKpwMaJrs6TsjBCABDJAyAGQZA4aiDKAUIAQuOz8Zqe1o7/0wBCABDJAyAGQdA4aiDLAUIAQuOz8Zqe1o7/0wBCABDJAyAGQZA5aiDMAUIAQuOz8Zqe1o7/0wBCABDJAyAGQdA5aiDPAUIAQuOz8Zqe1o7/0wBCABDJAyAGQdA3aiAGKQPgNyLVASAGKQOIOCLTASAGKQPAOHwi1AF8Is4BIAYpA/g3INIBIAYpA/A3Is0BfCDNAVStfHwi0gEgBikDkDh8ItEBQv////++sv3wQn4izQFCAEKBgICAv7L98MMAQgAQyQMgBkHAN2ogzQFCAEKR4eXNh4n6mShCABDJAyAGQbA3aiDNAUIAQt2whYzotpGouH9CABDJAyAGQaA3aiDNAUIAQqnAxomuzpOyMEIAEMkDIAZBoDhqIMoBQgBChYHundXn4KSMf0IAEMkDIAZB4DhqIMsBQgBChYHundXn4KSMf0IAEMkDIAZBoDlqIMwBQgBChYHundXn4KSMf0IAEMkDIAZB4DlqIM8BQgBChYHundXn4KSMf0IAEMkDIAZBgDdqIAYpA5g4INEBINIBVK18ItcBIAYpA9A4fCLQASAGKQPIOCDTASDUAVatfCLYASAGKQOAOXwi0wEgBikDkDd8ItQBIM4BINIBVq0gBikD6DcgzgEg1QFUrXx8fCLWAXwizgEgBikDwDd8ItIBIAYpA9g3IAYpA9A3Is0BINEBfCDNAVStfHwi0QEgBikDoDh8ItUBQv////++sv3wQn4izQFCAEKBgICAv7L98MMAQgAQyQMgBkHwNmogzQFCAEKR4eXNh4n6mShCABDJAyAGQeA2aiDNAUIAQt2whYzotpGouH9CABDJAyAGQdA2aiDNAUIAQqnAxomuzpOyMEIAEMkDIAZBsDhqIMoBQgBCpYm5+peWtIsCQgAQyQMgBkHwOGogywFCAEKlibn6l5a0iwJCABDJAyAGQbA5aiDMAUIAQqWJufqXlrSLAkIAEMkDIAZB8DlqIM8BQgBCpYm5+peWtIsCQgAQyQMgBkGwNmogBikDqDgg0QEg1QFWrXwi2gEgBikD4Dh8IssBIAYpA4g5INMBINgBVK18ItgBIAYpA8A5fCLMASAGKQPANnwizwEg1AEg1gFWrSAGKQOYNyDTASDUAVatfHx8Is0BIAYpA5A5fCLTASDOASDQAVStIAYpA9g4INABINcBVK18fHwi0AEgBikDsDd8ItQBINEBINIBVK0gBikDyDcgzgEg0gFWrXx8fCLXAXwizgEgBikD8DZ8ItIBIAYpA4g3IAYpA4A3IsoBINUBfCDKAVStfHwi0QEgBikDsDh8ItUBQv////++sv3wQn4iygFCAEKBgICAv7L98MMAQgAQyQMgBkGgNmogygFCAEKR4eXNh4n6mShCABDJAyAGQZA2aiDKAUIAQt2whYzotpGouH9CABDJAyAGQYA2aiDKAUIAQqnAxomuzpOyMEIAEMkDIAYpA4g2IAYpA+g5IAYpA9g5IAYpA8g5IMwBINgBVK18ItgBIAYpA9A5fCLKASDYAVStfCDKASDKASDNASDPAVStIAYpA8g2IMwBIM8BVq18fHwizAFWrXwgzAEgzAEg0AEg0wFUrSAGKQOYOSDNASDTAVatfHx8IsoBVq18Is8BIAYpA+A5fCLMASDPAVStfCDMASDMASAGKQOoNyDKASDKASAGKQOgN3wizwFWrXwgzwEgzwEg1AEg1wFWrSAGKQO4NyDQASDUAVatfHx8IsoBVq18fCLPAVatfCDPASAGKQOoOSDKASDKASAGKQOgOXwizAFWrXwgzAEgzAEgywEgzgFWrSAGKQPoOCDLASDaAVStfHx8IsoBVq18fCLLASDPAVStfCLQASAGKQPwOXwizAEgBikD2DYgywEgywEgBikD0DZ8Is8BVq18IM8BIAYpA+g2IMoBIMoBIAYpA+A2fCLLAVatfCDLASDRASDSAVStIAYpA/g2IM4BINIBVq18fHwizQEgywFUrXx8IsoBIM8BVK18fCLPASAGKQO4OSDKASDKASAGKQOwOXwiywFWrXwgywEgywEgBikD+DggBikDuDgg0QEg1QFWrXwizgEgBikD8Dh8IsoBIM4BVK18IMoBIMoBIM0BfCLNAVatfHwiygFWrXx8Is4BIAYpA4A2fCLSASDOAVStfCDSASDSASAGKQOYNiDKASDKASAGKQOQNnwiywFWrXwgywEgywEgBikDqDYgzQEgzQEgBikDoDZ8IsoBVq18IMoBIAYpA7g2IAYpA7A2Is0BINUBfCDNAVStfHwi4QEgygFUrXx8IsoBVq18fCLLAVatfCDOASDPAVStIMwBIM8BVq0gBikD+DkgzAEg0AFUrXx8fHwi6AFCqcDGia7Ok7IwWA0BDAILIBRCAzcDACAUQQA6AAgMAwsg6AFCqcDGia7Ok7IwUgRAIMoBId4BIMsBId0BDAILIMsBQt2whYzotpGouH9WDQAgywFC3bCFjOi2kai4f1IEQCDKASHeASDLASHdAUKpwMaJrs6TsjAh6AEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h3QEgygFCkeHlzYeJ+pkoUgRAIMoBId4BQqnAxomuzpOyMCHoAQwCC0KR4eXNh4n6mSgh3gEg4QFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh6AEMAQsgygFCkeHlzYeJ+pkofSLMASDhAUKBgICAv7L98MMAVK0izwF9Id4BIMsBQqPP+vOXye7XxwB8Is0BIMoBQpHh5c2HifqZKFQgzAEgzwFUcq0iygF9Id0BIOgBIMsBQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IegBIOEBQoGAgIC/sv3wwwB9IeEBC0EAIQdB0c7FAC0AABoCQAJAQYDAAEEIENYEIhEEQCARQQBBgMAA/AsAIAZB4D9qIQggBkGAQGshAyAaKQMAIe8BIBopAwgh5QEgGikDECHnASAaKQMYIe4BQq++n9CZ+J2FDiHrAUL7////xIONy6x/IewBQqmag/vZ0p3+NiHgAUKujOXD9+2ot+YAId8BQQEhCgNAIAchDSAKIQcgBkHwNWog7AFCACDuAUIAEMkDIAZB4DRqIOABQgAg7gFCABDJAyAGQdAzaiDfAUIAIO4BQgAQyQMgBkHAMmog6wFCACDuAUIAEMkDIAZB4DVqIAYpA/A1IswBQgBCAEL/////vrL98EIQyQMgBkHQNWogBikD6DUiygFCAEKBgICAv7L98MMAQgAQyQMgBkHANWogygFCAEKR4eXNh4n6mShCABDJAyAGQbA1aiDKAUIAQt2whYzotpGouH9CABDJAyAGQaA1aiDKAUIAQqnAxomuzpOyMEIAEMkDIAZBkDVqIOwBQgAg5wFCABDJAyAGQYA0aiDgAUIAIOcBQgAQyQMgBkHwMmog3wFCACDnAUIAEMkDIAZB4DFqIOsBQgAg5wFCABDJAyAGQdA0aiAGKQPANSLRASAGKQP4NSLOASAGKQPgNHwi0gF8IssBIAYpA9g1IMwBIAYpA9A1IsoBfCDKAVStfHwizAEgBikDkDV8Is8BQgBCAEL/////vrL98EIQyQMgBkHANGogBikD2DQiygFCAEKBgICAv7L98MMAQgAQyQMgBkGwNGogygFCAEKR4eXNh4n6mShCABDJAyAGQaA0aiDKAUIAQt2whYzotpGouH9CABDJAyAGQZA0aiDKAUIAQqnAxomuzpOyMEIAEMkDIAZBgDVqIOwBQgAg5QFCABDJAyAGQfAzaiDgAUIAIOUBQgAQyQMgBkHgMmog3wFCACDlAUIAEMkDIAZB0DFqIOsBQgAg5QFCABDJAyAGQcAzaiAGKQOYNSDMASDPAVatfCLVASAGKQOANHwizQEgBikD6DQgzgEg0gFWrXwi0wEgBikD0DN8Is4BIAYpA7A1fCLSASDLASDMAVatIAYpA8g1IMsBINEBVK18fHwi1wF8IssBIAYpA7A0fCLMASAGKQPINCAGKQPANCLKASDPAXwgygFUrXx8Is8BIAYpA4A1fCLRAUIAQgBC/////76y/fBCEMkDIAZBsDNqIAYpA8gzIsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZBoDNqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkGQM2ogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGAM2ogygFCAEKpwMaJrs6TsjBCABDJAyAGQfA0aiDsAUIAIO8BQgAQyQMgBkHgM2og4AFCACDvAUIAEMkDIAZB0DJqIN8BQgAg7wFCABDJAyAGQcAxaiDrAUIAIO8BQgAQyQMgBkGwMmogBikDiDUgzwEg0QFWrXwi2AEgBikD8DN8ItABIAYpA9gzIM4BINMBVK18ItoBIAYpA8AyfCLTASAGKQOgNXwi1AEg0gEg1wFWrSAGKQO4NSDOASDSAVatfHx8Is4BIAYpA/AyfCLSASDLASDNAVStIAYpA4g0IM0BINUBVK18fHwizQEgBikDoDR8ItUBIMwBIM8BVq0gBikDuDQgywEgzAFWrXx8fCLXAXwiywEgBikDoDN8IswBIAYpA7gzIAYpA7AzIsoBINEBfCDKAVStfHwizwEgBikD8DR8ItEBQgBCAEL/////vrL98EIQyQMgBkGgMmogBikDuDIiygFCAEKBgICAv7L98MMAQgAQyQMgBkGQMmogygFCAEKR4eXNh4n6mShCABDJAyAGQYAyaiDKAUIAQt2whYzotpGouH9CABDJAyAGQfAxaiDKAUIAQqnAxomuzpOyMEIAEMkDIBEgDUEFdCIaaiIKAn4CQAJ+AkACQCAGKQP4MSAGKQOIMyAGKQOYNCDOASDUAVStIAYpA6g1INMBINQBVq18fCAGKQPIMiDTASDaAVStfHwi0wEgBikD4DF8IsoBIM0BINIBVK0gBikD+DIgzgEg0gFWrXx8fCLOASAGKQOQNHwi0gEgzgFUrXwg0gEg1QEg1wFWrSAGKQOoNCDNASDVAVatfHx8Is0BINIBVK18IMoBIM4BVq0gBikD6DEgygEg0wFUrXx8fCLTASAGKQPQMXwiygEgBikD6DIgzQEgzQEgBikD4DJ8Is4BVq18IM4BIM4BIMsBINABVK0gBikD+DMg0AEg2AFUrXx8fCLNAVatfHwizgEgBikDgDN8ItIBIM4BVK18INIBIAYpA5gzIM0BIM0BIAYpA5AzfCLQAVatfCDQASDQASDMASDPAVatIAYpA6gzIMsBIMwBVq18fHwizAFWrXx8IssBINIBVK18IMoBIM4BVq0gBikD2DEgygEg0wFUrXx8fCLQASAGKQPAMXwizQEgBikD2DIgywEgywEgBikD0DJ8IsoBVq18IMoBIMoBIAYpA+gzIAYpA/g0IM8BINEBVq18Is8BIAYpA+AzfCLLASDPAVStfCDLASDLASDMAXwizAFWrXx8IssBVq18fCLPASAGKQPwMXwizgEgzwFUrXwgzgEgzgEgBikDiDIgywEgywEgBikDgDJ8ItIBVq18INIBINIBIAYpA5gyIMwBIMwBIAYpA5AyfCLKAVatfCDKASAGKQOoMiAGKQOgMiLLASDRAXwgywFUrXx8ItgBIMoBVK18fCLKAVatfHwizAFWrXwgzQEgzwFWrSAGKQPIMSDNASDQAVStfHx8ItoBQqnAxomuzpOyMFYNAAJAINoBQqnAxomuzpOyMFEEQCDMAULdsIWM6LaRqLh/Vg0CIMwBQt2whYzotpGouH9SBEAgygEhywEgzAEhzwFCqcDGia7Ok7IwIdoBINgBDAULIMoBQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/Ic8BIMoBQpHh5c2HifqZKFENASDKASHLAUKpwMaJrs6TsjAh2gEg2AEMBAsgzAEhzwEgygEhywEMAgtCkeHlzYeJ+pkoIcsBINgBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdoBINgBDAILIMoBQpHh5c2HifqZKH0izwEg2AFCgYCAgL+y/fDDAFStIs0BfSHLASDMAUKjz/rzl8nu18cAfCLOASDKAUKR4eXNh4n6mShUIM0BIM8BVnKtIsoBfSHPASDaASDMAULdsIWM6LaRqLh/VCDKASDOAVZyrX1CqcDGia7Ok7IwfSHaASDYAUKBgICAv7L98MMAfSHYAQtCr76f0Jn4nYUOIc4BAkAg2gFCr76f0Jn4nYUOUgRAINoBIcoBDAELQq6M5cP37ai35gAhzgFCr76f0Jn4nYUOIdoBIM8BQq6M5cP37ai35gBSBEAgzwEhygEMAQtCqZqD+9nSnf42Ic4BQq6M5cP37ai35gAhzwEgywEiygFCqZqD+9nSnf42Ug0AQqmag/vZ0p3+NiHLAUL7////xIONy6x/Is4BINgBIsoBQvv////Eg43LrH9RDQEaCyDKASDOAVQNASDYAQshzAEgywFCqZqD+9nSnf42fSLNASDMAUL7////xIONy6x/VK0izgF9IcoBIM8BQq6M5cP37ai35gB9ItIBIMsBQqmag/vZ0p3+NlQgzQEgzgFUcq0izQF9IcsBIM8BQq6M5cP37ai35gBUIM0BINIBVnIhDCDaAUKvvp/QmfidhQ59IdoBIMwBQoWAgIC7/PK00wB8DAELQt2whYzotpGouH9Crozlw/ftqLfmACDPAX0izAFCqZqD+9nSnf42IMsBfSLKASDYAUL7////xIONy6x/Vq0izQFUIMsBQqmag/vZ0p3+NlZyrSLOAX0i0gF9ItEBIMoBIM0BfSLKAUKR4eXNh4n6mShWQpHh5c2HifqZKCDKAX0iygEg2AFChICAgLv88rTTAHxC/v///8DNgo+8f1StIs0BVHKtItABfSHLASDQASDRAVYg0gFC3bCFjOi2kai4f1ZyIQwgygEgzQF9IcoBINoBIMwBIM4BVCDPAUKujOXD9+2ot+YAVnKtfEL6gae5lNb1rCJ8IdoBINgBQvr///+F0Y/a6AB9CzcDGCAKIMoBNwMQIAogywE3AwggCiDaASAMrX03AwACQCAKQcCWwgBBIBDxAwRAQgAh2gEgBkGAP2pCADcDACAGQfg+akIANwMAIAZCADcD8D4gBkIBNwOIPyAGQag/aiAKQRhqKQMANwMAIAZBoD9qIApBEGoiDCkDADcDACAGQZg/aiAKQQhqKQMANwMAIAYgCikDADcDkD8gBkHIP2pBuJbCACkDADcDACAGQcA/akGwlsIAKQMANwMAIAZBuD9qQaiWwgApAwA3AwAgBkGglsIAKQMANwOwPyAGQdA/aiEZIAZBkD9qIAZB8D5qQSAQ8QNFBEBCp9uF8drIudwbIc4BQuOz8Zqe1o7/0wAh2wFChYHundXn4KSMfyHWAUKlibn6l5a0iwIh2AFCACHXAUIAIc8BIAghBQwCC0Kn24Xx2si53BshzgFC47Pxmp7Wjv/TACHbAUKFge6d1efgpIx/IdABQqWJufqXlrSLAiHYAUKR4eXNh4n6mSgh1AFC3bCFjOi2kai4fyHRAUKpwMaJrs6TsjAhzQFCgYCAgL+y/fDDACHKASAGKQOoPyHLASAGKQOQPyHZASAGKQOYPyHMASAGKQOgPyHTAUIAIdYBQgAh1wFCACHPAQNAIAZBsD9qIAZB8D5qQSAQ8QNFBEAgBkHwP2ohGSADIQUMAwsgywGnQQFxRQRAA0Ag0wFCP4YgywFCAYiEIcsBAkAgzgFCAYNQBEAg0AEh0gEg2wEh1QEgzgEh3AEMAQsg2AEg0AEg0AFCo8/685fJ7tfHAH0i6gFWIOoBIOoBINsBQpHh5c2HifqZKHwi0gEg2wFUINIBIM4BQoGAgIC/sv3wwwB8ItwBIM4BVK18ItUBINIBVHKtfCLSAVZyrXxCqcDGia7Ok7IwfCHYAQsg2QFCP4YgzAFCP4Yg0wFCAYiEIdMBINkBQgGIIdkBINgBQj+GINIBQgGIhCHQASDSAUI/hiDVAUIBiIQh2wEg1QFCP4Yg3AFCAYiEIc4BINgBQgGIIdgBIMwBQgGIhCHMASDLAUIBg1ANAAsgBiDTATcDoD8gBiDLATcDqD8gBiDMATcDmD8gBiDZATcDkD8LIMoBp0EBcUUEQANAINQBQj+GIMoBQgGIhCHKAQJAIM8BQgGDUARAINYBIdIBINcBIdUBIM8BIdwBDAELINoBINYBINYBQqPP+vOXye7XxwB9IuoBViDqASDqASDXAUKR4eXNh4n6mSh8ItIBINcBVCDSASDSASDPAUKBgICAv7L98MMAfCLcASDPAVStfCLVAVZyrXwi0gFWcq18QqnAxomuzpOyMHwh2gELIM0BQj+GINEBQj+GINQBQgGIhCHUASDNAUIBiCHNASDaAUI/hiDSAUIBiIQh1gEg0gFCP4Yg1QFCAYiEIdcBINUBQj+GINwBQgGIhCHPASDaAUIBiCHaASDRAUIBiIQh0QEgygFCAYNQDQALIAYg1AE3A8A/IAYgygE3A8g/IAYg0QE3A7g/IAYgzQE3A7A/CyDNASHSAQJAAkACQAJAAkACQAJAIM0BINkBItUBUg0AINEBIdIBIMwBIdUBIMwBINEBUg0AINMBItUBINQBItIBUg0AIMoBIdIBIMsBIdUBIMoBIMsBUQ0BCyDSASDVAVgNACAGIMoBIMsBfSLSATcDyD8gBiDUASDTAX0i3AEgygEgywFUrSLKAX0i1QE3A8A/IAYg0QEgzAF9IuoBIMoBINwBViDTASDUAVZyrSLKAX0i3AE3A7g/IAYgzQEg2QF9IMoBIOoBViDMASDRAVZyrX0izQE3A7A/AkACQCDaASLKASDYASLRAVINACDQASLRASDWASLKAVINACDbASLRASDXASLKAVINACDOASHRASDPASLKASDOAVENAQsgygEg0QFUDQILINoBINgBfSDWASDQAX0iygEg1wEg2wF9ItEBIM4BIM8BVq0i1AFUINcBINsBVHKtIuoBVCDQASDWAVZyrX0h2gEgzwEgzgF9Ic8BINEBINQBfSHXASDKASDqAX0h1gEMAgsgBiDLASDKAX0i0gE3A6g/IAYg0wEg1AF9ItwBIMoBIMsBVq0iywF9ItUBNwOgPyAGIMwBINEBfSLqASDTASDUAVQgywEg3AFWcq0iywF9ItwBNwOYPyAGINkBIM0BfSDMASDRAVQgywEg6gFWcq19ItkBNwOQPwJAAkAg2gEizAEg2AEiywFSDQAg0AEiywEg1gEizAFSDQAg2wEiywEg1wEizAFSDQAgzgEiywEgzwEizAFRDQELIMsBIMwBVA0DCyDYASDaAX0g0AEg1gFUINABINYBfSLLASDbASDXAX0izAEgzgEgzwFUrSLQAVQg1wEg2wFWcq0i0wFUcq19IdgBIM4BIM8BfSHOASDMASDQAX0h2wEgywEg0wF9IdABDAMLINoBINgBfULdsIWM6LaRqLh/INABfSLKAUKR4eXNh4n6mSgg2wF9ItEBIM4BQoGAgIC/sv3wwwBWrSLUAVQg2wFCkeHlzYeJ+pkoVnKtItoBVCDQAULdsIWM6LaRqLh/VnKtfSDWASDKASDaAX0i2gF8IsoBINoBVCDKASDRASDUAX0i1AEg1wF8ItEBINQBVCDRAUKBgICAv7L98MMAIM4BfSLUASDPAXwizwEg1AFUrXwi1wEg0QFUcq18ItYBIMoBVHKtfEKpwMaJrs6TsjB8IdoBCyDVASHUASDcASHRASDSASHKAQwCCyDYASDaAX1C3bCFjOi2kai4fyDWAX0iywFCkeHlzYeJ+pkoINcBfSLMASDPAUKBgICAv7L98MMAVq0i0wFUINcBQpHh5c2HifqZKFZyrSLYAVQg1gFC3bCFjOi2kai4f1ZyrX0g0AEgywEg2AF9ItgBfCLLASDYAVQgywEgzAEg0wF9ItABINsBfCLMASDQAVQgzAFCgYCAgL+y/fDDACDPAX0i0AEgzgF8Is4BINABVK18ItsBIMwBVHKtfCLQASDLAVRyrXxCqcDGia7Ok7IwfCHYAQsg1QEh0wEg3AEhzAEg0gEhywELIAZBkD9qIAZB8D5qQSAQ8QMNAAsgCCEFINABIdYBDAELIBQg1gE3AwggFEICNwMADAQLIAYgzwE3A4hAIAYg1wE3A4BAIAYg2wE3A+A/IAYgzgE3A+g/IAZB6D5qIhwgBUEIaikDADcDACAGINgBNwPQPyAGINoBNwPwPyAGIAUpAwA3A+A+IBkpAwAhygEgCiDWATcDCCAKIMoBNwMAIAxBCGogHCkDADcDACAMIAYpA+A+NwMAIAZBsDFqIAopAxgiywFCACATIBpqIgUpAxgizAFCABDJAyAGQaAwaiDLAUIAIAUpAxAizwFCABDJAyAGQZAvaiDLAUIAIAUpAwgizQFCABDJAyAGQYAuaiDLAUIAIAUpAwAiywFCABDJAyAGQaAxaiAGKQOwMSLRAUIAQgBC/////76y/fBCEMkDIAZBkDFqIAYpA6gxIs4BQgBCgYCAgL+y/fDDAEIAEMkDIAZBgDFqIM4BQgBCkeHlzYeJ+pkoQgAQyQMgBkHwMGogzgFCAELdsIWM6LaRqLh/QgAQyQMgBkHgMGogzgFCAEKpwMaJrs6TsjBCABDJAyAGQdAwaiAKKQMQIs4BQgAgzAFCABDJAyAGQcAvaiDOAUIAIM8BQgAQyQMgBkGwLmogzgFCACDNAUIAEMkDIAZBoC1qIM4BQgAgywFCABDJAyAGQZAwaiAGKQOAMSLXASAGKQO4MSLUASAGKQOgMHwi1QF8ItIBIAYpA5gxINEBIAYpA5AxIs4BfCDOAVStfHwi0QEgBikD0DB8ItABQgBCAEL/////vrL98EIQyQMgBkGAMGogBikDmDAizgFCAEKBgICAv7L98MMAQgAQyQMgBkHwL2ogzgFCAEKR4eXNh4n6mShCABDJAyAGQeAvaiDOAUIAQt2whYzotpGouH9CABDJAyAGQdAvaiDOAUIAQqnAxomuzpOyMEIAEMkDIAZBwDBqIMwBQgAg1gFCABDJAyAGQbAvaiDPAUIAINYBQgAQyQMgBkGgLmogzQFCACDWAUIAEMkDIAZBkC1qIMsBQgAg1gFCABDJAyAGQYAvaiAGKQPYMCDQASDRAVStfCLYASAGKQPAL3wi0wEgBikDqDAg1AEg1QFWrXwi2gEgBikDkC98ItQBIAYpA/AwfCLVASDRASDSAVStIAYpA4gxINIBINcBVK18fHwi2QF8ItIBIAYpA/AvfCLRASAGKQOIMCAGKQOAMCLOASDQAXwgzgFUrXx8ItABIAYpA8AwfCLXAUIAQgBC/////76y/fBCEMkDIAZB8C5qIAYpA4gvIs4BQgBCgYCAgL+y/fDDAEIAEMkDIAZB4C5qIM4BQgBCkeHlzYeJ+pkoQgAQyQMgBkHQLmogzgFCAELdsIWM6LaRqLh/QgAQyQMgBkHALmogzgFCAEKpwMaJrs6TsjBCABDJAyAGQbAwaiDMAUIAIMoBQgAQyQMgBkGgL2ogzwFCACDKAUIAEMkDIAZBkC5qIM0BQgAgygFCABDJAyAGQYAtaiDLAUIAIMoBQgAQyQMgBkHwLWogBikDyDAg0AEg1wFWrXwi2wEgBikDsC98IssBIAYpA5gvINQBINoBVK18ItoBIAYpA4AufCLMASAGKQPgMHwizwEg1QEg2QFWrSAGKQP4MCDUASDVAVatfHx8Is0BIAYpA7AufCLOASDSASDTAVStIAYpA8gvINMBINgBVK18fHwi0wEgBikD4C98ItQBINABINEBVK0gBikD+C8g0QEg0gFUrXx8fCLYAXwi0gEgBikD4C58ItEBIAYpA/guIAYpA/AuIsoBINcBfCDKAVStfHwi0AEgBikDsDB8ItUBQgBCAEL/////vrL98EIQyQMgBkHgLWogBikD+C0iygFCAEKBgICAv7L98MMAQgAQyQMgBkHQLWogygFCAEKR4eXNh4n6mShCABDJAyAGQcAtaiDKAUIAQt2whYzotpGouH9CABDJAyAGQbAtaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQAJAIAYpA7gtIAYpA8guIAYpA9gvIM0BIM8BVK0gBikD6DAgzAEgzwFWrXx8IAYpA4guIMwBINoBVK18fCLXASAGKQOgLXwiygEgzgEg0wFWrSAGKQO4LiDNASDOAVatfHx8IswBIAYpA9AvfCLPASDMAVStfCDPASDPASDUASDYAVatIAYpA+gvINMBINQBVq18fHwizQFWrXwgygEgzAFWrSAGKQOoLSDKASDXAVStfHx8Is4BIAYpA5AtfCLKASAGKQOoLiDNASAGKQOgLnwizAEgzQFUrXwgzAEgywEg0gFWrSAGKQO4LyDLASDbAVStfHx8IssBIMwBVK18fCLMASAGKQPALnwizwEgzAFUrXwgzwEgBikD2C4gywEgywEgBikD0C58Is0BVq18IM0BIM0BINABINEBVK0gBikD6C4g0QEg0gFUrXx8fCLSAVatfHwiywEgzwFUrXwgygEgzAFWrSAGKQOYLSDKASDOAVStfHx8ItEBIAYpA4AtfCLPASAGKQOYLiDLASDLASAGKQOQLnwiygFWrXwgygEgygEgBikDqC8gBikDuDAg0AEg1QFWrXwizAEgBikDoC98IssBIMwBVK18IMsBIMsBINIBfCLMAVatfHwiywFWrXx8Is0BIAYpA7AtfCLOASDNAVStfCDOASAGKQPILSDLASDLASAGKQPALXwi0gFWrXwg0gEg0gEgBikD2C0gzAEgzAEgBikD0C18IsoBVq18IMoBIAYpA+gtIAYpA+AtIssBINUBfCDLAVStfHwi2gEgygFUrXx8IsoBVq18fCLMASDOAVStfCDNASDPAVStIAYpA4gtIM8BINEBVK18fHwi2AFCqcDGia7Ok7IwVg0AINgBQqnAxomuzpOyMFINASDMAULdsIWM6LaRqLh/Vg0AIMwBQt2whYzotpGouH9SBEBCqcDGia7Ok7IwIdgBDAILIMoBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/Ic8BIMoBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh2AEgygEhywEMAwtCkeHlzYeJ+pkoIcsBINoBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdgBDAILIMoBQpHh5c2HifqZKH0izwEg2gFCgYCAgL+y/fDDAFStIs0BfSHLASDMAUKjz/rzl8nu18cAfCLOASDKAUKR4eXNh4n6mShUIM0BIM8BVnKtIsoBfSHPASDYASDMAULdsIWM6LaRqLh/VCDKASDOAVZyrX1CqcDGia7Ok7IwfSHYASDaAUKBgICAv7L98MMAfSHaAQwBCyDMASHPASDKASHLAQtCqcDGia7Ok7IwIcoBIM8BIM8BIOYBfCLNAVYgzQEgzQEgywEgywEg4wF8IswBViDMASDMASDaASDiAXwi4gEg2gFUrXwiywFWcq18IswBVnKtINgBIOQBfHwi5AEhzgECQAJAAkAg5AFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hygEgzAEizgFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghygEgywEizgFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhygEg4gEizgFCgYCAgL+y/fDDAFENAQsgygEgzgFYDQAgzAEh5gEgywEh4wEMAQsgywFCkeHlzYeJ+pkofSLKASDiAUKBgICAv7L98MMAVK0izwF9IeMBIMwBQqPP+vOXye7XxwB8Is0BIMsBQpHh5c2HifqZKFQgygEgzwFUcq0iygF9IeYBIOQBIMwBQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IeQBIOIBQoGAgIC/sv3wwwB9IeIBCwJAIA1B/wFGDQAgBkGwK2og7AFCACDhAUIAEMkDIAZB8CtqIOwBQgAg3gFCABDJAyAGQbAsaiDsAUIAIN0BQgAQyQMgBkHwLGog7AFCACDoAUIAEMkDIAZBoCtqIAYpA7ArIswBQgBCAEL/////vrL98EIQyQMgBkGQK2ogBikDqCsiygFCAEKBgICAv7L98MMAQgAQyQMgBkGAK2ogygFCAEKR4eXNh4n6mShCABDJAyAGQfAqaiDKAUIAQt2whYzotpGouH9CABDJAyAGQeAqaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZB0CpqIOABQgAg4QFCABDJAyAGQeAraiDgAUIAIN4BQgAQyQMgBkGgLGog4AFCACDdAUIAEMkDIAZB4CxqIOABQgAg6AFCABDJAyAGQcAqaiAGKQOAKyLRASAGKQO4KyLOASAGKQPwK3wi0gF8IssBIAYpA5grIMwBIAYpA5ArIsoBfCDKAVStfHwizAEgBikD0Cp8Is8BQgBCAEL/////vrL98EIQyQMgBkGwKmogBikDyCoiygFCAEKBgICAv7L98MMAQgAQyQMgBkGgKmogygFCAEKR4eXNh4n6mShCABDJAyAGQZAqaiDKAUIAQt2whYzotpGouH9CABDJAyAGQYAqaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZB8ClqIN8BQgAg4QFCABDJAyAGQdAraiDfAUIAIN4BQgAQyQMgBkGQLGog3wFCACDdAUIAEMkDIAZB0CxqIN8BQgAg6AFCABDJAyAGQeApaiAGKQPYKiDMASDPAVatfCLVASAGKQPgK3wizQEgBikD+CsgzgEg0gFWrXwi0wEgBikDsCx8Is4BIAYpA/AqfCLSASDLASDMAVatIAYpA4grIMsBINEBVK18fHwi1wF8IssBIAYpA6AqfCLMASAGKQO4KiAGKQOwKiLKASDPAXwgygFUrXx8Is8BIAYpA/ApfCLRAUIAQgBC/////76y/fBCEMkDIAZB0ClqIAYpA+gpIsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZBwClqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkGwKWogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGgKWogygFCAEKpwMaJrs6TsjBCABDJAyAGQZApaiDrAUIAIOEBQgAQyQMgBkHAK2og6wFCACDeAUIAEMkDIAZBgCxqIOsBQgAg3QFCABDJAyAGQcAsaiDrAUIAIOgBQgAQyQMgBkGAKWogBikD+CkgzwEg0QFWrXwi2AEgBikD0Ct8ItABIAYpA7gsIM4BINMBVK18ItoBIAYpA/AsfCLTASAGKQPgKnwi1AEg0gEg1wFWrSAGKQP4KiDOASDSAVatfHx8Is4BIAYpA6AsfCLSASDLASDNAVStIAYpA+grIM0BINUBVK18fHwizQEgBikDkCp8ItUBIMwBIM8BVq0gBikDqCogywEgzAFWrXx8fCLXAXwiywEgBikDwCl8IswBIAYpA9gpIAYpA9ApIsoBINEBfCDKAVStfHwizwEgBikDkCl8ItEBQgBCAEL/////vrL98EIQyQMgBkHwKGogBikDiCkiygFCAEKBgICAv7L98MMAQgAQyQMgBkHgKGogygFCAEKR4eXNh4n6mShCABDJAyAGQdAoaiDKAUIAQt2whYzotpGouH9CABDJAyAGQcAoaiDKAUIAQqnAxomuzpOyMEIAEMkDAkAgBikDyCggBikDqCkgBikDiCogzgEg1AFUrSAGKQPoKiDTASDUAVatfHwgBikD+Cwg0wEg2gFUrXx8ItMBIAYpA+AsfCLKASDNASDSAVStIAYpA6gsIM4BINIBVq18fHwizgEgBikDgCp8ItIBIM4BVK18INIBINUBINcBVq0gBikDmCogzQEg1QFWrXx8fCLNASDSAVStfCDKASDOAVatIAYpA+gsIMoBINMBVK18fHwi0wEgBikD0Cx8IsoBIAYpA5gsIM0BIM0BIAYpA5AsfCLOAVatfCDOASDOASDLASDQAVStIAYpA9grINABINgBVK18fHwizQFWrXx8Is4BIAYpA6ApfCLSASDOAVStfCDSASAGKQO4KSDNASDNASAGKQOwKXwi0AFWrXwg0AEg0AEgzAEgzwFWrSAGKQPIKSDLASDMAVatfHx8Is0BVq18fCLLASDSAVStfCDKASDOAVatIAYpA9gsIMoBINMBVK18fHwi0AEgBikDwCx8IswBIAYpA4gsIMsBIAYpA4AsfCLKASDLAVStfCDKASDKASAGKQPIKyAGKQOYKSDPASDRAVatfCLPASAGKQPAK3wiywEgzwFUrXwgywEgywEgzQF8Is8BVq18fCLLAVatfHwizQEgBikDwCh8Is4BIM0BVK18IM4BIAYpA9goIMsBIMsBIAYpA9AofCLSAVatfCDSASDSASAGKQPoKCDPASDPASAGKQPgKHwiygFWrXwgygEgBikD+CggBikD8CgiywEg0QF8IMsBVK18fCLsASDKAVStfHwiygFWrXx8IssBIM4BVK18IMwBIM0BVq0gBikDyCwgzAEg0AFUrXx8fCLrAUKpwMaJrs6TsjBWDQAg6wFCqcDGia7Ok7IwUgRAIMoBIeABIMsBId8BDAILIMsBQt2whYzotpGouH9WDQAgywFC3bCFjOi2kai4f1IEQCDKASHgASDLASHfAUKpwMaJrs6TsjAh6wEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h3wEgygFCkeHlzYeJ+pkoUgRAIMoBIeABQqnAxomuzpOyMCHrAQwCC0KR4eXNh4n6mSgh4AEg7AFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh6wEMAQsgygFCkeHlzYeJ+pkofSLMASDsAUKBgICAv7L98MMAVK0izwF9IeABIMsBQqPP+vOXye7XxwB8Is0BIMoBQpHh5c2HifqZKFQgzAEgzwFUcq0iygF9Id8BIOsBIMsBQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IesBIOwBQoGAgIC/sv3wwwB9IewBCyAHIAdBgAJJIgVqIQogBQ0ACwwBC0EIQYDAAEG4sMIAEMgEAAsgBikD2D4h3wEgBikD0D4h6wEgBikDyD4h7AEgBikDwD4h6gEgBkK29f//yfHH8XY3A6g/IAZCrr/KicOV3LrdADcDoD8gBkLJxorP8JbStyc3A5g/IAZC18ab/M6MxbwNNwOQPwJAIAZBkD9qQcCWwgBBIBDxAwRAQgAh2AEgBkHAP2pCADcDACAGQbg/akIANwMAIAZCADcDsD8gBkIBNwPIPyAGQeg/aiAGQag/aikDADcDACAGQeA/aiAGQaA/aikDADcDACAGQdg/aiAGQZg/aikDADcDACAGIAYpA5A/NwPQPyAGQYjAAGpBuJbCACkDADcDACAGQYBAa0GwlsIAKQMANwMAIAZB+D9qQaiWwgApAwA3AwAgBkGglsIAKQMANwPwPwJAIAZB0D9qIAZBsD9qQSAQ8QNFBEBCpYm5+peWtIsCIdoBQqfbhfHayLncGyHOAULjs/GantaO/9MAIdABQoWB7p3V5+CkjH8h1QEMAQtCp9uF8drIudwbIc4BQuOz8Zqe1o7/0wAh0AFChYHundXn4KSMfyHVAUKlibn6l5a0iwIh2gEgBikD6D8hywEgBikD0D8h2QEgBikD2D8hzAEgBikD4D8h0wFCACHWAUIAIdsBQgAhzwFCgYCAgL+y/fDDACHKAUKpwMaJrs6TsjAh0QFC3bCFjOi2kai4fyHNAUKR4eXNh4n6mSgh1AEDQCAGQfA/aiAGQbA/akEgEPEDRQRAINYBIdUBINsBIdABIM8BIc4BINgBIdoBDAILIMsBp0EBcUUEQANAINMBQj+GIMsBQgGIhCHLAQJAIM4BQgGDUARAIM4BIdcBINABIc4BINUBIdIBDAELINoBINUBINUBQqPP+vOXye7XxwB9ItwBViDcASDcASDQASDQAUKR4eXNh4n6mSh8ItIBViDSASDOAUKBgICAv7L98MMAfCLXASDOAVStfCLOASDSAVRyrXwi0gFWcq18QqnAxomuzpOyMHwh2gELINkBQj+GIMwBQj+GINMBQgGIhCHTASDZAUIBiCHZASDaAUI/hiDSAUIBiIQh1QEg0gFCP4YgzgFCAYiEIdABIM4BQj+GINcBQgGIhCHOASDaAUIBiCHaASDMAUIBiIQhzAEgywFCAYNQDQALIAYg0wE3A+A/IAYgywE3A+g/IAYgzAE3A9g/IAYg2QE3A9A/CyDKAadBAXFFBEADQCDUAUI/hiDKAUIBiIQhygECQCDPAUIBg1AEQCDPASHXASDbASHPASDWASHSAQwBCyDYASDWASDWAUKjz/rzl8nu18cAfSLcAVYg3AEg3AEg2wFCkeHlzYeJ+pkofCLSASDbAVQg0gEgzwFCgYCAgL+y/fDDAHwi1wEgzwFUrXwizwEg0gFUcq18ItIBVnKtfEKpwMaJrs6TsjB8IdgBCyDRAUI/hiDNAUI/hiDUAUIBiIQh1AEg0QFCAYgh0QEg2AFCP4Yg0gFCAYiEIdYBINIBQj+GIM8BQgGIhCHbASDPAUI/hiDXAUIBiIQhzwEg2AFCAYgh2AEgzQFCAYiEIc0BIMoBQgGDUA0ACyAGINQBNwOAQCAGIMoBNwOIQCAGIM0BNwP4PyAGINEBNwPwPwsg0QEh0gECQAJAAkACQAJAINEBINkBItcBUg0AIM0BIdIBIMwBIdcBIMwBIM0BUg0AINMBIdcBINQBItIBINMBUg0AIMoBIdIBIMsBIdcBIMoBIMsBUQ0BCyDSASDXAVgNACAGIMoBIMsBfSLSATcDiEAgBiDUASDTAX0i3AEgygEgywFUrSLKAX0i1wE3A4BAIAYgzQEgzAF9IuABIMoBINwBViDTASDUAVZyrSLKAX0i3AE3A/g/IAYg0QEg2QF9IMoBIOABViDMASDNAVZyrX0i0QE3A/A/AkACQCDaASLNASDYASLKAVINACDVASLNASDWASLKAVINACDQASLNASDbASLKAVINACDOASHNASDPASLKASDOAVENAQsgygEgzQFUDQILINgBINoBfSDWASDVAX0i4AEg2wEg0AF9IvABIM4BIM8BVq0i+AFUINABINsBVnKtIu0BVCDVASDWAVZyrX0h2AEgzwEgzgF9Ic8BINcBIdQBINwBIc0BINIBIcoBIPABIPgBfSHbASDgASDtAX0h1gEMAwsgBiDLASDKAX0i0gE3A+g/IAYg0wEg1AF9ItwBIMoBIMsBVq0iywF9ItcBNwPgPyAGIMwBIM0BfSLgASDTASDUAVQgywEg3AFWcq0iywF9ItwBNwPYPyAGINkBINEBfSDMASDNAVQgywEg4AFWcq19ItkBNwPQPwJAAkAg2gEiywEg2AEizAFSDQAg1QEiywEg1gEizAFSDQAg0AEiywEg2wEizAFSDQAgzgEiywEgzwEizAFRDQELIMsBIMwBVA0CCyDaASDYAX0g1QEg1gFUINUBINYBfSLVASDQASDbAVQg0AEg2wF9ItABIM4BIM8BVK0i4AFUcq0i8AFUcq19IdoBIM4BIM8BfSHOASDXASHTASDcASHMASDSASHLASDQASDgAX0h0AEg1QEg8AF9IdUBDAILINgBQt2whYzotpGouH8g1QF9IsoBQpHh5c2HifqZKCDQAX0izQEgzgFCgYCAgL+y/fDDAFatItQBVCDQAUKR4eXNh4n6mShWcq0i2AFUINUBQt2whYzotpGouH9Wcq0g2gF8fSDKASDYAX0i2AEg1gF8IsoBINgBVCDKASDNASDUAX0i1AEg2wF8Is0BINQBVCDNAUKBgICAv7L98MMAIM4BfSLUASDPAXwizwEg1AFUrXwi2wEgzQFUcq18ItYBIMoBVHKtfEKpwMaJrs6TsjB8IdgBINcBIdQBINwBIc0BINIBIcoBDAELINoBINgBfULdsIWM6LaRqLh/INYBfSLLAUKR4eXNh4n6mSgg2wF9IswBIM8BQoGAgIC/sv3wwwBWrSLTAVQg2wFCkeHlzYeJ+pkoVnKtItoBVCDWAULdsIWM6LaRqLh/VnKtfSDVASDLASDaAX0i2gF8IssBINoBVCDLASDQASDMASDTAX0i0wF8IswBINMBVCDMAUKBgICAv7L98MMAIM8BfSLQASDOAXwizgEg0AFUrXwi0AEgzAFUcq18ItUBIMsBVHKtfEKpwMaJrs6TsjB8IdoBINcBIdMBINwBIcwBINIBIcsBCyAGQdA/aiAGQbA/akEgEPEDDQALCyAGQbAoaiDOAUIAIN8BQgAQyQMgBkHQJ2ogzgFCACDrAUIAEMkDIAZBwCdqIM4BQgAg7AFCABDJAyAGQbAnaiDOAUIAIOoBQgAQyQMgBkGgKGogBikDsCgizAFCAEIAQv////++sv3wQhDJAyAGQZAoaiAGKQOoKCLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQYAoaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZB8CdqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZB4CdqIMoBQgBCqcDGia7Ok7IwQgAQyQMgBkGgJ2og0AFCACDfAUIAEMkDIAZBwCZqINABQgAg6wFCABDJAyAGQbAmaiDQAUIAIOwBQgAQyQMgBkGgJmog0AFCACDqAUIAEMkDIAZBkCdqIAYpA4AoItEBIAYpA7goIs4BIAYpA9AnfCLSAXwiywEgBikDmCggzAEgBikDkCgiygF8IMoBVK18fCLMASAGKQOgJ3wizwFCAEIAQv////++sv3wQhDJAyAGQYAnaiAGKQOYJyLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQfAmaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZB4CZqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZB0CZqIMoBQgBCqcDGia7Ok7IwQgAQyQMgBkGQJmog1QFCACDfAUIAEMkDIAZBsCVqINUBQgAg6wFCABDJAyAGQaAlaiDVAUIAIOwBQgAQyQMgBkGQJWog1QFCACDqAUIAEMkDIAZBgCZqIAYpA6gnIMwBIM8BVq18ItUBIAYpA8AmfCLNASAGKQPYJyDOASDSAVatfCLTASAGKQPAJ3wizgEgBikD8Cd8ItIBIMsBIMwBVq0gBikDiCggywEg0QFUrXx8fCLXAXwiywEgBikD8CZ8IswBIAYpA4gnIAYpA4AnIsoBIM8BfCDKAVStfHwizwEgBikDkCZ8ItEBQgBCAEL/////vrL98EIQyQMgBkHwJWogBikDiCYiygFCAEKBgICAv7L98MMAQgAQyQMgBkHgJWogygFCAEKR4eXNh4n6mShCABDJAyAGQdAlaiDKAUIAQt2whYzotpGouH9CABDJAyAGQcAlaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZBgCVqINoBQgAg3wFCABDJAyAGQaAkaiDaAUIAIOsBQgAQyQMgBkGQJGog2gFCACDsAUIAEMkDIAZBgCRqINoBQgAg6gFCABDJAyAGQfAkaiAGKQOYJiDPASDRAVatfCLYASAGKQOwJXwi0AEgBikDyCcgzgEg0wFUrXwi1gEgBikDsCd8ItMBIAYpA+AnfCLUASDSASDXAVatIAYpA/gnIM4BINIBVq18fHwizgEgBikDsCZ8ItIBIMsBIM0BVK0gBikDyCYgzQEg1QFUrXx8fCLNASAGKQPgJnwi1QEgzAEgzwFWrSAGKQP4JiDLASDMAVatfHx8ItcBfCLLASAGKQPgJXwizAEgBikD+CUgBikD8CUiygEg0QF8IMoBVK18fCLPASAGKQOAJXwi0QFCAEIAQv////++sv3wQhDJAyAGQeAkaiAGKQP4JCLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQdAkaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZBwCRqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZBsCRqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA7gkIAYpA8glIAYpA9gmIM4BINQBVK0gBikD6Ccg0wEg1AFWrXx8IAYpA7gnINMBINYBVK18fCLTASAGKQOgJnwiygEgzQEg0gFUrSAGKQO4JiDOASDSAVatfHx8Is4BIAYpA9AmfCLSASDOAVStfCDSASDVASDXAVatIAYpA+gmIM0BINUBVq18fHwizQEg0gFUrXwgygEgzgFWrSAGKQOoJiDKASDTAVStfHx8ItMBIAYpA5AlfCLKASAGKQOoJSDNASDNASAGKQOgJXwizgFWrXwgzgEgzgEgywEg0AFUrSAGKQO4JSDQASDYAVStfHx8Is0BVq18fCLOASAGKQPAJXwi0gEgzgFUrXwg0gEgBikD2CUgzQEgzQEgBikD0CV8ItABVq18INABINABIMwBIM8BVq0gBikD6CUgywEgzAFWrXx8fCLNAVatfHwiywEg0gFUrXwgygEgzgFWrSAGKQOYJSDKASDTAVStfHx8ItABIAYpA4AkfCLMASAGKQOYJCDLASAGKQOQJHwiygEgywFUrXwgygEgygEgBikDqCQgBikDiCUgzwEg0QFWrXwizwEgBikDoCR8IssBIM8BVK18IMsBIMsBIM0BfCLPAVatfHwiywFWrXx8Is0BIAYpA7AkfCLOASDNAVStfCDOASAGKQPIJCDLASDLASAGKQPAJHwi0gFWrXwg0gEg0gEgBikD2CQgzwEgzwEgBikD0CR8IsoBVq18IMoBIAYpA+gkIAYpA+AkIssBINEBfCDLAVStfHwi2gEgygFUrXx8IsoBVq18fCLLASDOAVStfCDMASDNAVatIAYpA4gkIMwBINABVK18fHwi2AFCqcDGia7Ok7IwVg0AAkAg2AFCqcDGia7Ok7IwUQRAIMsBQt2whYzotpGouH9WDQIgywFC3bCFjOi2kai4f1IEQCDKASHOASDLASHPAUKpwMaJrs6TsjAh2AEMBAsgygFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8hzwEgygFCkeHlzYeJ+pkoUQ0BIMoBIc4BQqnAxomuzpOyMCHYAQwDCyDKASHOASDLASHPAQwCC0KR4eXNh4n6mSghzgEg2gFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh2AEMAQsgygFCkeHlzYeJ+pkofSLMASDaAUKBgICAv7L98MMAVK0izwF9Ic4BIMsBQqPP+vOXye7XxwB8Is0BIMoBQpHh5c2HifqZKFQgzAEgzwFUcq0iygF9Ic8BINgBIMsBQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IdgBINoBQoGAgIC/sv3wwwB9IdoBCyAGQfAjaiDaAUIAIOIBQgAQyQMgBkGQI2ogzgFCACDiAUIAEMkDIAZBgCNqIM8BQgAg4gFCABDJAyAGQfAiaiDYAUIAIOIBQgAQyQMgBkHgI2ogBikD8CMizAFCAEIAQv////++sv3wQhDJAyAGQdAjaiAGKQPoIyLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQcAjaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZBsCNqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZBoCNqIMoBQgBCqcDGia7Ok7IwQgAQyQMgBkHgImog2gFCACDjAUIAEMkDIAZBgCJqIM4BQgAg4wFCABDJAyAGQfAhaiDPAUIAIOMBQgAQyQMgBkHgIWog2AFCACDjAUIAEMkDIAZB0CJqIAYpA8AjItMBIAYpA/gjItEBIAYpA5AjfCLQAXwiywEgBikD2CMgzAEgBikD0CMiygF8IMoBVK18fCLMASAGKQPgInwizQFCAEIAQv////++sv3wQhDJAyAGQcAiaiAGKQPYIiLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQbAiaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZBoCJqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZBkCJqIMoBQgBCqcDGia7Ok7IwQgAQyQMgBkHQIWog2gFCACDmAUIAEMkDIAZB8CBqIM4BQgAg5gFCABDJAyAGQeAgaiDPAUIAIOYBQgAQyQMgBkHQIGog2AFCACDmAUIAEMkDIAZBwCFqIAYpA+giIMwBIM0BVq18ItYBIAYpA4AifCLSASAGKQOYIyDQASDRAVStfCLVASAGKQOAI3wi0QEgBikDsCN8ItABIMsBIMwBVq0gBikDyCMgywEg0wFUrXx8fCLZAXwiywEgBikDsCJ8IswBIAYpA8giIAYpA8AiIsoBIM0BfCDKAVStfHwizQEgBikD0CF8ItMBQgBCAEL/////vrL98EIQyQMgBkGwIWogBikDyCEiygFCAEKBgICAv7L98MMAQgAQyQMgBkGgIWogygFCAEKR4eXNh4n6mShCABDJAyAGQZAhaiDKAUIAQt2whYzotpGouH9CABDJAyAGQYAhaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZBwCBqINoBQgAg5AFCABDJAyAGQeAfaiDOAUIAIOQBQgAQyQMgBkHQH2ogzwFCACDkAUIAEMkDIAZBwB9qINgBQgAg5AFCABDJAyAGQbAgaiAGKQPYISDNASDTAVatfCLbASAGKQPwIHwi1AEgBikDiCMg0QEg1QFUrXwi3AEgBikD8CJ8ItUBIAYpA6AjfCLXASDQASDZAVatIAYpA7gjINABINEBVK18fHwi0QEgBikD8CF8ItABIMsBINIBVK0gBikDiCIg0gEg1gFUrXx8fCLSASAGKQOgInwi1gEgzAEgzQFWrSAGKQO4IiDLASDMAVatfHx8ItkBfCLLASAGKQOgIXwizAEgBikDuCEgBikDsCEiygEg0wF8IMoBVK18fCLNASAGKQPAIHwi0wFCAEIAQv////++sv3wQhDJAyAGQaAgaiAGKQO4ICLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQZAgaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZBgCBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZB8B9qIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA/gfIAYpA4ghIAYpA5giINEBINcBVK0gBikDqCMg1QEg1wFWrXx8IAYpA/giINUBINwBVK18fCLVASAGKQPgIXwiygEg0AEg0gFWrSAGKQP4ISDQASDRAVStfHx8ItEBIAYpA5AifCLQASDRAVStfCDQASDWASDZAVatIAYpA6giINIBINYBVq18fHwi0gEg0AFUrXwgygEg0QFWrSAGKQPoISDKASDVAVStfHx8ItUBIAYpA9AgfCLKASAGKQPoICDSASDSASAGKQPgIHwi0QFWrXwg0QEg0QEgywEg1AFUrSAGKQP4ICDUASDbAVStfHx8ItIBVq18fCLRASAGKQOAIXwi0AEg0QFUrXwg0AEgBikDmCEg0gEg0gEgBikDkCF8ItQBVq18INQBINQBIMwBIM0BVq0gBikDqCEgywEgzAFWrXx8fCLMAVatfHwiywEg0AFUrXwgygEg0QFWrSAGKQPYICDKASDVAVStfHx8ItQBIAYpA8AffCLSASAGKQPYHyDLASAGKQPQH3wiygEgywFUrXwgygEgygEgBikD6B8gBikDyCAgzQEg0wFWrXwizQEgBikD4B98IssBIM0BVK18IMsBIMsBIMwBfCLMAVatfHwiywFWrXx8Is0BIAYpA/AffCLRASDNAVStfCDRASDRASAGKQOIICDLASAGKQOAIHwi0AEgywFUrXwg0AEg0AEgBikDmCAgzAEgzAEgBikDkCB8IsoBVq18IMoBIMoBIAYpA6ggIAYpA6AgIssBINMBfCDLAVStfHwiywFWrXx8IsoBVq18fCLMAVatfCDNASDSAVStIAYpA8gfINIBINQBVK18fHwi2QFCqcDGia7Ok7IwVg0AAkAg2QFCqcDGia7Ok7IwUQRAIMwBQt2whYzotpGouH9WDQIgzAFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh2QELIMwBIdEBIMoBIc0BDAILIMoBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IdEBIMoBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh2QEgygEhzQEMAgtCkeHlzYeJ+pkoIc0BIMsBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdkBDAELIMoBQpHh5c2HifqZKH0i0gEgywFCgYCAgL+y/fDDAFStItEBfSHNASDMAUKjz/rzl8nu18cAfCLQASDKAUKR4eXNh4n6mShUINEBINIBVnKtIsoBfSHRASDZASDMAULdsIWM6LaRqLh/VCDKASDQAVZyrX1CqcDGia7Ok7IwfSHZASDLAUKBgICAv7L98MMAfSHLAQsgBkGAHmogESkDGCLKAUIAINoBQgAQyQMgBkHAHmogESkDECLMAUIAINoBQgAQyQMgBkGAH2ogESkDCCLSAUIAINoBQgAQyQMgBkHQG2ogESkDACLQAUIAINoBQgAQyQMgBkHwHWogBikDgB4i1QFCAEIAQv////++sv3wQhDJAyAGQeAdaiAGKQP4HSLTAUIAQoGAgIC/sv3wwwBCABDJAyAGQdAdaiDTAUIAQpHh5c2HifqZKEIAEMkDIAZB8BxqINMBQgBC3bCFjOi2kai4f0IAEMkDIAZBkBxqINMBQgBCqcDGia7Ok7IwQgAQyQMgBkGQHmogygFCACDOAUIAEMkDIAZB0B5qIMwBQgAgzgFCABDJAyAGQZAfaiDSAUIAIM4BQgAQyQMgBkHgG2og0AFCACDOAUIAEMkDIAZBwB1qIAYpA9AdIuABIAYpA4geItsBIAYpA8AefCLcAXwi1AEgBikD6B0g1QEgBikD4B0i0wF8INMBVK18fCLVASAGKQOQHnwi1wFCAEIAQv////++sv3wQhDJAyAGQbAdaiAGKQPIHSLTAUIAQoGAgIC/sv3wwwBCABDJAyAGQaAdaiDTAUIAQpHh5c2HifqZKEIAEMkDIAZBkB1qINMBQgBC3bCFjOi2kai4f0IAEMkDIAZBgB1qINMBQgBCqcDGia7Ok7IwQgAQyQMgBkGgHmogygFCACDPAUIAEMkDIAZB4B5qIMwBQgAgzwFCABDJAyAGQaAfaiDSAUIAIM8BQgAQyQMgBkHwG2og0AFCACDPAUIAEMkDIAZB4BxqIAYpA5geINUBINcBVq18IuYBIAYpA9AefCLWASAGKQPIHiDbASDcAVatfCLjASAGKQOAH3wi2wEgBikD8Bx8ItwBINQBINUBVq0gBikD2B0g1AEg4AFUrXx8fCLiAXwi1AEgBikDoB18ItUBIAYpA7gdIAYpA7AdItMBINcBfCDTAVStfHwi1wEgBikDoB58IuABQgBCAEL/////vrL98EIQyQMgBkHQHGogBikD6Bwi0wFCAEKBgICAv7L98MMAQgAQyQMgBkHAHGog0wFCAEKR4eXNh4n6mShCABDJAyAGQbAcaiDTAUIAQt2whYzotpGouH9CABDJAyAGQaAcaiDTAUIAQqnAxomuzpOyMEIAEMkDIAZBsB5qIMoBQgAg2AFCABDJAyAGQfAeaiDMAUIAINgBQgAQyQMgBkGwH2og0gFCACDYAUIAEMkDIAZBgBxqINABQgAg2AFCABDJAyAGQcAbaiAGKQOoHiDXASDgAVatfCLkASAGKQPgHnwizAEgBikDiB8g2wEg4wFUrXwi4wEgBikD0Bt8ItIBIAYpA5AcfCLQASDcASDiAVatIAYpA/gcINsBINwBVq18fHwi0wEgBikDkB98ItsBINQBINYBVK0gBikD2B4g1gEg5gFUrXx8fCLWASAGKQOQHXwi3AEg1QEg1wFWrSAGKQOoHSDUASDVAVatfHx8IuYBfCLUASAGKQPAHHwi1QEgBikD2BwgBikD0BwiygEg4AF8IMoBVK18fCLXASAGKQOwHnwi4AFCAEIAQv////++sv3wQhDJAyAGQbAbaiAGKQPIGyLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQaAbaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZBkBtqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZBgBtqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA4gbIAYpA6gcIAYpA4gdINABINMBVq0gBikDmBwg0AEg0gFUrXx8IAYpA9gbINIBIOMBVK18fCLjASAGKQPgG3wiygEg1gEg2wFUrSAGKQOYHyDTASDbAVatfHx8ItIBIAYpA4AdfCLQASDSAVStfCDQASDQASDcASDmAVatIAYpA5gdINYBINwBVq18fHwi0wFWrXwgygEg0gFWrSAGKQPoGyDKASDjAVStfHx8ItYBIAYpA/AbfCLKASAGKQOoHyDTASAGKQOgH3wi0gEg0wFUrXwg0gEgzAEg1AFWrSAGKQPoHiDMASDkAVStfHx8IswBINIBVK18fCLSASAGKQOgHHwi0AEg0gFUrXwg0AEgBikDuBwgzAEgzAEgBikDsBx8ItMBVq18INMBINUBINcBVq0gBikDyBwg1AEg1QFWrXx8fCLUASDTAVStfHwizAEg0AFUrXwgygEg0gFWrSAGKQP4GyDKASDWAVStfHx8ItYBIAYpA4AcfCLTASAGKQO4HyDMASAGKQOwH3wiygEgzAFUrXwgygEgygEgBikD+B4gBikDuB4g1wEg4AFWrXwi0gEgBikD8B58IswBINIBVK18IMwBIMwBINQBfCLSAVatfHwizAFWrXx8ItQBIAYpA4AbfCLVASDUAVStfCDVASDVASAGKQOYGyDMASDMASAGKQOQG3wi0AFWrXwg0AEg0AEgBikDqBsg0gEg0gEgBikDoBt8IswBVq18IMwBIMwBIAYpA7gbIAYpA7AbIsoBIOABfCDKAVStfHwiygFWrXx8ItIBVq18fCLQAVatfCDTASDUAVatIAYpA4gcINMBINYBVK18fHwizAFCqcDGia7Ok7IwVg0AAkAgzAFCqcDGia7Ok7IwUQRAINABQt2whYzotpGouH9WDQIg0AFC3bCFjOi2kai4f1IEQCDSASHTASDQASHUAUKpwMaJrs6TsjAhzAEMBAsg0gFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8h1AEg0gFCkeHlzYeJ+pkoUQ0BINIBIdMBQqnAxomuzpOyMCHMAQwDCyDSASHTASDQASHUAQwCC0KR4eXNh4n6mSgh0wEgygFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhzAEMAQsg0gFCkeHlzYeJ+pkofSLUASDKAUKBgICAv7L98MMAVK0i1QF9IdMBINABQqPP+vOXye7XxwB8ItcBINIBQpHh5c2HifqZKFQg1AEg1QFUcq0i0gF9IdQBIMwBINABQt2whYzotpGouH9UINIBINcBVnKtfUKpwMaJrs6TsjB9IcwBIMoBQoGAgIC/sv3wwwB9IcoBCyAGQYAZaiARKQP4PyLSAUIAINoBQgAQyQMgBkHAGWogESkD8D8i0AFCACDaAUIAEMkDIAZBgBpqIBEpA+g/ItUBQgAg2gFCABDJAyAGQcAaaiARQeA/aikDACLXAUIAINoBQgAQyQMgBkHwGGogBikDgBki2gFCAEIAQv////++sv3wQhDJAyAGQeAYaiAGKQP4GCLWAUIAQoGAgIC/sv3wwwBCABDJAyAGQdAYaiDWAUIAQpHh5c2HifqZKEIAEMkDIAZB8BdqINYBQgBC3bCFjOi2kai4f0IAEMkDIAZBkBdqINYBQgBCqcDGia7Ok7IwQgAQyQMgBkGQGWog0gFCACDOAUIAEMkDIAZB0BlqINABQgAgzgFCABDJAyAGQZAaaiDVAUIAIM4BQgAQyQMgBkHQGmog1wFCACDOAUIAEMkDIAZBwBhqIAYpA9AYIuYBIAYpA4gZItwBIAYpA8AZfCLgAXwi1gEgBikD6Bgg2gEgBikD4BgizgF8IM4BVK18fCLaASAGKQOQGXwi2wFCAEIAQv////++sv3wQhDJAyAGQbAYaiAGKQPIGCLOAUIAQoGAgIC/sv3wwwBCABDJAyAGQaAYaiDOAUIAQpHh5c2HifqZKEIAEMkDIAZBkBhqIM4BQgBC3bCFjOi2kai4f0IAEMkDIAZBgBhqIM4BQgBCqcDGia7Ok7IwQgAQyQMgBkGgGWog0gFCACDPAUIAEMkDIAZB4BlqINABQgAgzwFCABDJAyAGQaAaaiDVAUIAIM8BQgAQyQMgBkHgGmog1wFCACDPAUIAEMkDIAZB4BdqIAYpA5gZINoBINsBVq18IuMBIAYpA9AZfCLOASAGKQPIGSDcASDgAVatfCLiASAGKQOAGnwi3AEgBikD8Bd8IuABINYBINoBVq0gBikD2Bgg1gEg5gFUrXx8fCLkAXwi1gEgBikDoBh8ItoBIAYpA7gYIAYpA7AYIs8BINsBfCDPAVStfHwi2wEgBikDoBl8IuYBQgBCAEL/////vrL98EIQyQMgBkHQF2ogBikD6BcizwFCAEKBgICAv7L98MMAQgAQyQMgBkHAF2ogzwFCAEKR4eXNh4n6mShCABDJAyAGQbAXaiDPAUIAQt2whYzotpGouH9CABDJAyAGQaAXaiDPAUIAQqnAxomuzpOyMEIAEMkDIAZBsBlqINIBQgAg2AFCABDJAyAGQfAZaiDQAUIAINgBQgAQyQMgBkGwGmog1QFCACDYAUIAEMkDIAZB8BpqINcBQgAg2AFCABDJAyAGQYAXaiAGKQOoGSDbASDmAVatfCLwASAGKQPgGXwi0gEgBikDiBog3AEg4gFUrXwi4gEgBikDwBp8ItABIAYpA5AXfCLVASDgASDkAVatIAYpA/gXINwBIOABVq18fHwi1wEgBikDkBp8ItgBIM4BINYBVq0gBikD2BkgzgEg4wFUrXx8fCLOASAGKQOQGHwi3AEg2gEg2wFWrSAGKQOoGCDWASDaAVatfHx8IuMBfCLWASAGKQPAF3wi2gEgBikD2BcgBikD0BcizwEg5gF8IM8BVK18fCLbASAGKQOwGXwi4AFCAEIAQv////++sv3wQhDJAyAGQfAWaiAGKQOIFyLPAUIAQoGAgIC/sv3wwwBCABDJAyAGQeAWaiDPAUIAQpHh5c2HifqZKEIAEMkDIAZB0BZqIM8BQgBC3bCFjOi2kai4f0IAEMkDIAZBwBZqIM8BQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA8gWIAYpA6gXIAYpA4gYINUBINcBVq0gBikDmBcg0AEg1QFWrXx8IAYpA8gaINABIOIBVK18fCLmASAGKQPQGnwizwEgzgEg2AFUrSAGKQOYGiDXASDYAVatfHx8ItABIAYpA4AYfCLVASDQAVStfCDVASDcASDjAVatIAYpA5gYIM4BINwBVq18fHwizgEg1QFUrXwgzwEg0AFWrSAGKQPYGiDPASDmAVStfHx8ItcBIAYpA+AafCLPASAGKQOoGiDOASDOASAGKQOgGnwi0AFWrXwg0AEg0AEg0gEg1gFWrSAGKQPoGSDSASDwAVStfHx8Is4BVq18fCLSASAGKQOgF3wi0AEg0gFUrXwg0AEgBikDuBcgzgEgzgEgBikDsBd8ItUBVq18INUBINUBINoBINsBVq0gBikDyBcg1gEg2gFWrXx8fCLYAVatfHwizgEg0AFUrXwgzwEg0gFWrSAGKQPoGiDPASDXAVStfHx8ItYBIAYpA/AafCLPASAGKQO4GiDOASDOASAGKQOwGnwi0gFWrXwg0gEg0gEgBikD+BkgBikDuBkg2wEg4AFWrXwi0AEgBikD8Bl8Is4BINABVK18IM4BIM4BINgBfCLQAVatfHwizgFWrXx8ItIBIAYpA8AWfCLVASDSAVStfCDVASDVASAGKQPYFiDOASDOASAGKQPQFnwi1wFWrXwg1wEg1wEgBikD6BYg0AEg0AEgBikD4BZ8ItgBVq18INgBINgBIAYpA/gWIAYpA/AWIs4BIOABfCDOAVStfHwizgFWrXx8ItABVq18fCLXAVatfCDPASDSAVatIAYpA/gaIM8BINYBVK18fHwizwFCqcDGia7Ok7IwVg0AAkAgzwFCqcDGia7Ok7IwUQRAINcBQt2whYzotpGouH9WDQIg1wFC3bCFjOi2kai4f1IEQCDQASHSASDXASHVAUKpwMaJrs6TsjAhzwEMBAsg0AFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8h1QEg0AFCkeHlzYeJ+pkoUQ0BINABIdIBQqnAxomuzpOyMCHPAQwDCyDQASHSASDXASHVAQwCC0KR4eXNh4n6mSgh0gEgzgFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhzwEMAQsg0AFCkeHlzYeJ+pkofSLVASDOAUKBgICAv7L98MMAVK0i2AF9IdIBINcBQqPP+vOXye7XxwB8ItYBINABQpHh5c2HifqZKFQg1QEg2AFUcq0i0AF9IdUBIM8BINcBQt2whYzotpGouH9UINABINYBVnKtfUKpwMaJrs6TsjB9Ic8BIM4BQoGAgIC/sv3wwwB9Ic4BCyAGQbAWaiAQKQNYItABQgAgygFCABDJAyAGQaAVaiDQAUIAINMBQgAQyQMgBkGQFGog0AFCACDUAUIAEMkDIAZBgBNqINABQgAgzAFCABDJAyAGQaAWaiAGKQOwFiLYAUIAQgBC/////76y/fBCEMkDIAZBkBZqIAYpA6gWItABQgBCgYCAgL+y/fDDAEIAEMkDIAZBgBZqINABQgBCkeHlzYeJ+pkoQgAQyQMgBkHwFWog0AFCAELdsIWM6LaRqLh/QgAQyQMgBkHgFWog0AFCAEKpwMaJrs6TsjBCABDJAyAGQdAVaiAQKQNQItABQgAgygFCABDJAyAGQcAUaiDQAUIAINMBQgAQyQMgBkGwE2og0AFCACDUAUIAEMkDIAZBoBJqINABQgAgzAFCABDJAyAGQZAVaiAGKQOAFiLgASAGKQO4FiLbASAGKQOgFXwi3AF8ItcBIAYpA5gWINgBIAYpA5AWItABfCDQAVStfHwi2AEgBikD0BV8ItYBQgBCAEL/////vrL98EIQyQMgBkGAFWogBikDmBUi0AFCAEKBgICAv7L98MMAQgAQyQMgBkHwFGog0AFCAEKR4eXNh4n6mShCABDJAyAGQeAUaiDQAUIAQt2whYzotpGouH9CABDJAyAGQdAUaiDQAUIAQqnAxomuzpOyMEIAEMkDIAZBwBVqIBApA0gi0AFCACDKAUIAEMkDIAZBsBRqINABQgAg0wFCABDJAyAGQaATaiDQAUIAINQBQgAQyQMgBkGQEmog0AFCACDMAUIAEMkDIAZBgBRqIAYpA9gVINYBINgBVK18IuMBIAYpA8AUfCLaASAGKQOoFSDbASDcAVatfCLiASAGKQOQFHwi2wEgBikD8BV8ItwBINcBINgBVq0gBikDiBYg1wEg4AFUrXx8fCLkAXwi1wEgBikD8BR8ItgBIAYpA4gVIAYpA4AVItABINYBfCDQAVStfHwi1gEgBikDwBV8IuYBQgBCAEL/////vrL98EIQyQMgBkHwE2ogBikDiBQi0AFCAEKBgICAv7L98MMAQgAQyQMgBkHgE2og0AFCAEKR4eXNh4n6mShCABDJAyAGQdATaiDQAUIAQt2whYzotpGouH9CABDJAyAGQcATaiDQAUIAQqnAxomuzpOyMEIAEMkDIAZBsBVqIBApA0Ai4AFCACDKAUIAEMkDIAZBoBRqIOABQgAg0wFCABDJAyAGQZATaiDgAUIAINQBQgAQyQMgBkGAEmog4AFCACDMAUIAEMkDIAZB8BJqIAYpA8gVINYBIOYBVq18IvABIAYpA7AUfCLMASAGKQOYFCDbASDiAVStfCLiASAGKQOAE3wi0AEgBikD4BV8ItMBINwBIOQBVq0gBikD+BUg2wEg3AFWrXx8fCLUASAGKQOwE3wi2wEg1wEg2gFUrSAGKQPIFCDaASDjAVStfHx8ItoBIAYpA+AUfCLcASDWASDYAVStIAYpA/gUINcBINgBVq18fHwi4wF8ItcBIAYpA+ATfCLYASAGKQP4EyAGKQPwEyLKASDmAXwgygFUrXx8ItYBIAYpA7AVfCLmAUIAQgBC/////76y/fBCEMkDIAZB4BJqIAYpA/gSIsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZB0BJqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkHAEmogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGwEmogygFCAEKpwMaJrs6TsjBCABDJAwJAAkAgBikDuBIgBikDyBMgBikD2BQg0wEg1AFWrSAGKQPoFSDQASDTAVatfHwgBikDiBMg0AEg4gFUrXx8IuIBIAYpA6ASfCLKASDaASDbAVStIAYpA7gTINQBINsBVq18fHwi0AEgBikD0BR8ItMBINABVK18INMBINMBINwBIOMBVq0gBikD6BQg2gEg3AFWrXx8fCLUAVatfCDKASDQAVatIAYpA6gSIMoBIOIBVK18fHwi2gEgBikDkBJ8IsoBIAYpA6gTINQBIAYpA6ATfCLQASDUAVStfCDQASDMASDXAVatIAYpA7gUIMwBIPABVK18fHwizAEg0AFUrXx8ItABIAYpA8ATfCLTASDQAVStfCDTASAGKQPYEyDMASDMASAGKQPQE3wi1AFWrXwg1AEg1AEg1gEg2AFUrSAGKQPoEyDXASDYAVatfHx8ItcBVq18fCLMASDTAVStfCDKASDQAVatIAYpA5gSIMoBINoBVK18fHwi2gEgBikDgBJ8ItABIAYpA5gTIMwBIAYpA5ATfCLKASDMAVStfCDKASDKASAGKQOoFCAGKQO4FSDWASDmAVatfCLTASAGKQOgFHwizAEg0wFUrXwgzAEgzAEg1wF8ItMBVq18fCLMAVatfHwi1AEgBikDsBJ8ItcBINQBVK18INcBIAYpA8gSIMwBIMwBIAYpA8ASfCLYAVatfCDYASDYASAGKQPYEiDTASDTASAGKQPQEnwiygFWrXwgygEgBikD6BIgBikD4BIizAEg5gF8IMwBVK18fCLbASDKAVStfHwiygFWrXx8IswBINcBVK18INABINQBVq0gBikDiBIg0AEg2gFUrXx8fCLkAUKpwMaJrs6TsjBWDQACQCDkAUKpwMaJrs6TsjBRBEAgzAFC3bCFjOi2kai4f1YNAiDMAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHkAQsgzAEh4wEgygEh5gEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h4wEgygFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHkASDKASHmAQwCC0KR4eXNh4n6mSgh5gEg2wFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh5AEMAQsgygFCkeHlzYeJ+pkofSLQASDbAUKBgICAv7L98MMAVK0i0wF9IeYBIMwBQqPP+vOXye7XxwB8ItQBIMoBQpHh5c2HifqZKFQg0AEg0wFUcq0iygF9IeMBIOQBIMwBQt2whYzotpGouH9UIMoBINQBVnKtfUKpwMaJrs6TsjB9IeQBINsBQoGAgIC/sv3wwwB9IdsBCwJ+AkACQCDoASLYASDvASLKAVINACDdASLYASDlASLKAVINACDeASLYASDnASLKAVINACDhASLYASDuASLKAVENAQsgygEg2AFaDQBC3bCFjOi2kai4fyDdASDlAX0iygEg3gEg5wFUIN4BIOcBfSLMASDhASDuAVStItABVHKtItcBfSLUAX0i2AEgzAEg0AF9IswBQpHh5c2HifqZKFZCkeHlzYeJ+pkoIMwBfSLMASDhASDuAX0i0AFCgYCAgL+y/fDDAFatItYBVHKtItoBfSHTASDYASDaAVQg1AFC3bCFjOi2kai4f1ZyIQogzAEg1gF9IdQBIN0BIOUBVCDKASDXAVRyrSDvASDoAX18QqnAxomuzpOyMHwh6AFCgYCAgL+y/fDDACDQAX0MAQsg5wEg3gF9IsoBIOEBIO4BVq0izAF9IdQBIOUBIN0BfSLQASDKASDMAVQg3gEg5wFWcq0iygF9IdMBIMoBINABViDdASDlAVZyIQog7wEg6AF9IegBIO4BIOEBfQsh5QEgECkDWCHaASAQKQNQId4BIBApA0gh2AEgECkDOCHMASAQKQMwIdABIBApAygh1wEgECkDICLWASHKAQJ+AkACQCDWASDgASLcAVINACDYASLcASDXASLKAVINACDeASLcASDQASLKAVINACDaASLcASDMASLKAVENAQsgygEg3AFaDQBC3bCFjOi2kai4fyDYASDXAX0i3QEg0AEg3gFWIN4BINABfSLKASDMASDaAVatItABVHKtIuEBfSLiAX0i5wEgygEg0AF9IsoBQpHh5c2HifqZKFZCkeHlzYeJ+pkoIMoBfSLKASDaASDMAX0izAFCgYCAgL+y/fDDAFatItABVHKtIu4BfSHcASDnASDuAVQg4gFC3bCFjOi2kai4f1ZyIQcgygEg0AF9IcoBIN0BIOEBVCDXASDYAVZyrSDWASDgAX18QqnAxomuzpOyMHwh4QFCgYCAgL+y/fDDACDMAX0MAQsg0AEg3gF9ItwBIMwBINoBVK0i3QF9IcoBINcBINgBfSLhASDcASDdAVQg0AEg3gFUcq0i0AF9IdwBINcBINgBVCDQASDhAVZyIQcg1gEg4AF9IeEBIMwBINoBfQsh1gEgCq0h+AEgBkHwEWogECkDGCLMAUIAIMsBQgAQyQMgBkGQEWogECkDECLQAUIAIMsBQgAQyQMgBkGAEWogECkDCCLXAUIAIMsBQgAQyQMgBkHwEGogECkDACLdAUIAIMsBQgAQyQMgBkHgEWogBikD8BEi4gFCAEIAQv////++sv3wQhDJAyAGQdARaiAGKQPoESLLAUIAQoGAgIC/sv3wwwBCABDJAyAGQcARaiDLAUIAQpHh5c2HifqZKEIAEMkDIAZBsBFqIMsBQgBC3bCFjOi2kai4f0IAEMkDIAZBoBFqIMsBQgBCqcDGia7Ok7IwQgAQyQMgBkHgEGogzAFCACDNAUIAEMkDIAZBgBBqINABQgAgzQFCABDJAyAGQfAPaiDXAUIAIM0BQgAQyQMgBkHgD2og3QFCACDNAUIAEMkDIAZB0BBqIAYpA8ARIvABIAYpA/gRIu4BIAYpA5ARfCLvAXwizQEgBikD2BEg4gEgBikD0BEiywF8IMsBVK18fCLiASAGKQPgEHwi5wFCAEIAQv////++sv3wQhDJAyAGQcAQaiAGKQPYECLLAUIAQoGAgIC/sv3wwwBCABDJAyAGQbAQaiDLAUIAQpHh5c2HifqZKEIAEMkDIAZBoBBqIMsBQgBC3bCFjOi2kai4f0IAEMkDIAZBkBBqIMsBQgBCqcDGia7Ok7IwQgAQyQMgBkHQD2ogzAFCACDRAUIAEMkDIAZB8A5qINABQgAg0QFCABDJAyAGQeAOaiDXAUIAINEBQgAQyQMgBkHQDmog3QFCACDRAUIAEMkDIAZBwA9qIAYpA+gQIOIBIOcBVq18Iu0BIAYpA4AQfCLRASAGKQOYESDuASDvAVatfCLpASAGKQOAEXwi7gEgBikDsBF8Iu8BIM0BIOIBVq0gBikDyBEgzQEg8AFUrXx8fCLxAXwizQEgBikDsBB8IuIBIAYpA8gQIAYpA8AQIssBIOcBfCDLAVStfHwi5wEgBikD0A98IvABQgBCAEL/////vrL98EIQyQMgBkGwD2ogBikDyA8iywFCAEKBgICAv7L98MMAQgAQyQMgBkGgD2ogywFCAEKR4eXNh4n6mShCABDJAyAGQZAPaiDLAUIAQt2whYzotpGouH9CABDJAyAGQYAPaiDLAUIAQqnAxomuzpOyMEIAEMkDIAZBwA5qIMwBQgAg2QFCABDJAyAGQeANaiDQAUIAINkBQgAQyQMgBkHQDWog1wFCACDZAUIAEMkDIAZBwA1qIN0BQgAg2QFCABDJAyAGQbAOaiAGKQPYDyDnASDwAVatfCLyASAGKQPwDnwizAEgBikDiBEg6QEg7gFWrXwi6QEgBikD8BB8ItABIAYpA6ARfCLXASDvASDxAVatIAYpA7gRIO4BIO8BVq18fHwi2QEgBikD8A98Iu4BIM0BINEBVK0gBikDiBAg0QEg7QFUrXx8fCLRASAGKQOgEHwi7wEg4gEg5wFWrSAGKQO4ECDNASDiAVatfHx8Iu0BfCLNASAGKQOgD3wi4gEgBikDuA8gBikDsA8iywEg8AF8IMsBVK18fCLnASAGKQPADnwi8AFCAEIAQv////++sv3wQhDJAyAGQaAOaiAGKQO4DiLLAUIAQoGAgIC/sv3wwwBCABDJAyAGQZAOaiDLAUIAQpHh5c2HifqZKEIAEMkDIAZBgA5qIMsBQgBC3bCFjOi2kai4f0IAEMkDIAZB8A1qIMsBQgBCqcDGia7Ok7IwQgAQyQMg4QEgB619Id0BAkACQCAGKQP4DSAGKQOIDyAGKQOYECDXASDZAVatIAYpA6gRINABINcBVq18fCAGKQP4ECDQASDpAVStfHwi4QEgBikD4A98IssBINEBIO4BVK0gBikD+A8g2QEg7gFWrXx8fCLQASAGKQOQEHwi1wEg0AFUrXwg1wEg7QEg7wFUrSAGKQOoECDRASDvAVatfHx8ItEBINcBVK18IMsBINABVq0gBikD6A8gywEg4QFUrXx8fCLZASAGKQPQDnwiywEgBikD6A4g0QEg0QEgBikD4A58ItABVq18INABIMwBIM0BVq0gBikD+A4gzAEg8gFUrXx8fCLMASDQAVStfHwi0QEgBikDgA98ItABINEBVK18INABIAYpA5gPIMwBIMwBIAYpA5APfCLXAVatfCDXASDXASDiASDnAVatIAYpA6gPIM0BIOIBVq18fHwi4QFWrXx8IswBINABVK18IMsBINEBVq0gBikD2A4gywEg2QFUrXx8fCLiASAGKQPADXwiywEgBikD2A0gzAEgzAEgBikD0A18Is0BVq18IM0BIM0BIAYpA+gNIAYpA8gOIOcBIPABVq18ItEBIAYpA+ANfCLMASDRAVStfCDMASDMASDhAXwi0QFWrXx8IswBVq18fCLNASAGKQPwDXwi0AEgzQFUrXwg0AEg0AEgBikDiA4gzAEgzAEgBikDgA58ItcBVq18INcBIAYpA5gOINEBINEBIAYpA5AOfCLMAVatfCDMASAGKQOoDiAGKQOgDiLRASDwAXwg0QFUrXx8ItkBIMwBVK18fCLMASDXAVStfHwi0QFWrXwgywEgzQFWrSAGKQPIDSDLASDiAVStfHx8IssBQqnAxomuzpOyMFYNAAJAIMsBQqnAxomuzpOyMFEEQCDRAULdsIWM6LaRqLh/Vg0CINEBQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIcsBCyDRASHXASDMASHNAQwCCyDMAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHXASDMAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIcsBIMwBIc0BDAILQpHh5c2HifqZKCHNASDZAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHLAQwBCyDMAUKR4eXNh4n6mSh9ItABINkBQoGAgIC/sv3wwwBUrSLXAX0hzQEg0QFCo8/685fJ7tfHAHwi4QEgzAFCkeHlzYeJ+pkoVCDQASDXAVRyrSLMAX0h1wEgywEg0QFC3bCFjOi2kai4f1QgzAEg4QFWcq19QqnAxomuzpOyMH0hywEg2QFCgYCAgL+y/fDDAH0h2QELIOgBIPgBfSHRASDLASHQASAGQbANagJ+AkACQCDdASLMASDLAVINACDXASLQASDcASLMAVINACDKASHMASDKASDNASLQAVINACDZASLQASDWASLMAVENAQsgzAEg0AFaDQBC3bCFjOi2kai4fyDXASDcAX0izAEgzQEgygF9ItABINYBINkBVq0i4QFUIMoBIM0BVnKtIsoBfSLoAX0i4gEg0AEg4QF9Is0BQpHh5c2HifqZKFZCkeHlzYeJ+pkoIM0BfSLQASDZASDWAX0i1gFCgYCAgL+y/fDDAFatItkBVHKtIuEBfSHNASDhASDiAVYg6AFC3bCFjOi2kai4f1ZyIQog0AEg2QF9IdABINcBINwBVCDKASDMAVZyrSDdASDLAX18QqnAxomuzpOyMHwh4gFCgYCAgL+y/fDDACDWAX0MAQsgygEgzQF9IswBINYBINkBVK0i4QF9IdABINwBINcBfSLoASDMASDhAVQgygEgzQFUcq0iygF9Ic0BIMoBIOgBViDXASDcAVZyIQog3QEgywF9IeIBINYBINkBfQsiygFCACDlAUIAEMkDIAZBwAxqIMoBQgAg1AFCABDJAyAGQaAMaiDKAUIAINMBQgAQyQMgBkGADGogygFCACDRAUIAEMkDIAZBoA1qIAYpA7ANIswBQgBCAEL/////vrL98EIQyQMgBkGQDWogBikDqA0iygFCAEKBgICAv7L98MMAQgAQyQMgBkGADWogygFCAEKR4eXNh4n6mShCABDJAyAGQfAMaiDKAUIAQt2whYzotpGouH9CABDJAyAGQeAMaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZB4AtqINABQgAg5QFCABDJAyAGQYALaiDQAUIAINQBQgAQyQMgBkHwCmog0AFCACDTAUIAEMkDIAZB4ApqINABQgAg0QFCABDJAyAGQdALaiAGKQOADSLZASAGKQO4DSLXASAGKQPADHwi1gF8IssBIAYpA5gNIMwBIAYpA5ANIsoBfCDKAVStfHwizAEgBikD4At8ItABQgBCAEL/////vrL98EIQyQMgBkHAC2ogBikD2AsiygFCAEKBgICAv7L98MMAQgAQyQMgBkGwC2ogygFCAEKR4eXNh4n6mShCABDJAyAGQaALaiDKAUIAQt2whYzotpGouH9CABDJAyAGQZALaiDKAUIAQqnAxomuzpOyMEIAEMkDIAZB0ApqIM0BQgAg5QFCABDJAyAGQfAJaiDNAUIAINQBQgAQyQMgBkGQCWogzQFCACDTAUIAEMkDIAZBgAlqIM0BQgAg0QFCABDJAyAGQcAKaiAGKQPoCyDMASDQAVatfCLcASAGKQOAC3wizQEgBikDyAwg1gEg1wFUrXwi3QEgBikDoAx8ItcBIAYpA/AMfCLWASDLASDMAVatIAYpA4gNIMsBINkBVK18fHwi4QF8IssBIAYpA7ALfCLMASAGKQPICyAGKQPACyLKASDQAXwgygFUrXx8ItABIAYpA9AKfCLZAUIAQgBC/////76y/fBCEMkDIAZBsApqIAYpA8gKIsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZBoApqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkGQCmogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGACmogygFCAEKpwMaJrs6TsjBCABDJAyAGQdAMaiDiASAKrX0iygFCACDlAUIAEMkDIAZBsAxqIMoBQgAg1AFCABDJAyAGQZAMaiDKAUIAINMBQgAQyQMgBkHwC2ogygFCACDRAUIAEMkDIAZB4AlqIAYpA9gKINABINkBVq18IugBIAYpA/AJfCLRASAGKQOoDCDXASDdAVStfCLdASAGKQOADHwi0wEgBikD4Ax8ItQBINYBIOEBVq0gBikD+Awg1gEg1wFUrXx8fCLXASAGKQPwCnwi1gEgywEgzQFUrSAGKQOICyDNASDcAVStfHx8Is0BIAYpA6ALfCLcASDMASDQAVatIAYpA7gLIMsBIMwBVq18fHwi4QF8IssBIAYpA6AKfCLMASAGKQO4CiAGKQOwCiLKASDZAXwgygFUrXx8ItABIAYpA9AMfCLZAUIAQgBC/////76y/fBCEMkDIAZB0AlqIAYpA+gJIsoBQgBCgYCAgL+y/fDDAEIAEMkDIAZBwAlqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgBkGwCWogygFCAELdsIWM6LaRqLh/QgAQyQMgBkGgCWogygFCAEKpwMaJrs6TsjBCABDJAwJAAkAgBikDqAkgBikDiAogBikDmAsg1AEg1wFWrSAGKQPoDCDTASDUAVatfHwgBikDiAwg0wEg3QFUrXx8It0BIAYpA+AKfCLKASDNASDWAVStIAYpA/gKINYBINcBVK18fHwi0wEgBikDkAt8ItQBINMBVK18INQBINwBIOEBVq0gBikDqAsgzQEg3AFWrXx8fCLNASDUAVStfCDKASDTAVatIAYpA+gKIMoBIN0BVK18fHwi1wEgBikDgAl8IsoBIAYpA5gJIM0BIM0BIAYpA5AJfCLTAVatfCDTASDTASDLASDRAVStIAYpA/gJINEBIOgBVK18fHwizQFWrXx8ItEBIAYpA4AKfCLTASDRAVStfCDTASAGKQOYCiDNASDNASAGKQOQCnwi1AFWrXwg1AEgzAEg0AFWrSAGKQOoCiDLASDMAVatfHx8IswBINQBVK18fCLLASDTAVStfCDKASDRAVatIAYpA4gJIMoBINcBVK18fHwi1AEgBikD8At8Is0BIAYpA5gMIMsBIAYpA5AMfCLKASDLAVStfCDKASDKASAGKQO4DCAGKQPYDCDQASDZAVatfCLRASAGKQOwDHwiywEg0QFUrXwgywEgywEgzAF8IswBVq18fCLLAVatfHwi0QEgBikDoAl8ItABINEBVK18INABINABIAYpA7gJIMsBIAYpA7AJfCLTASDLAVStfCDTASDTASAGKQPICSDMASDMASAGKQPACXwiygFWrXwgygEgygEgBikD2AkgBikD0AkiywEg2QF8IMsBVK18fCLLAVatfHwiygFWrXx8IswBVq18IM0BINEBVq0gBikD+AsgzQEg1AFUrXx8fCLZAUKpwMaJrs6TsjBWDQACQCDZAUKpwMaJrs6TsjBRBEAgzAFC3bCFjOi2kai4f1YNAiDMAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHZAQsgzAEhzQEgygEh0wEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8hzQEgygFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHZASDKASHTAQwCC0KR4eXNh4n6mSgh0wEgywFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh2QEMAQsgygFCkeHlzYeJ+pkofSLNASDLAUKBgICAv7L98MMAVK0i0QF9IdMBIMwBQqPP+vOXye7XxwB8ItABIMoBQpHh5c2HifqZKFQgzQEg0QFUcq0iygF9Ic0BINkBIMwBQt2whYzotpGouH9UIMoBINABVnKtfUKpwMaJrs6TsjB9IdkBIMsBQoGAgIC/sv3wwwB9IcsBC0KpwMaJrs6TsjAh1gEg2QEg5AF8IM0BIOMBfCLMASDNAVQgzAEgzAEg0wEg5gF8Is0BINMBVCDNASDNASDLASDbAXwi2QEgywFUrXwiygFWcq18IssBVnKtfCLRASHTAQJAAkACQCDRAUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyHWASDLASLTAULdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCHWASDKASLTAUKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACHWASDZASLTAUKBgICAv7L98MMAUQ0BCyDTASDWAVoNACDLASHWASDKASHQAQwBCyDKAUKR4eXNh4n6mSh9IswBINkBQoGAgIC/sv3wwwBUrSLNAX0h0AEgywFCo8/685fJ7tfHAHwi0wEgygFCkeHlzYeJ+pkoVCDMASDNAVRyrSLKAX0h1gEg0QEgywFC3bCFjOi2kai4f1QgygEg0wFWcq19QqnAxomuzpOyMH0h0QEg2QFCgYCAgL+y/fDDAH0h2QELIBcpAwAizAEhywECQAJ+AkAgzAEg4AEi1AFSDQAg2AEi1AEgFykDCCLLAVINACDeASLUASAXKQMQIssBUg0AINQBIdcBINgBINoBItQBIs0BIBcpAxgiywFRDQEaCyAXKQMYIc0BIMsBINQBVg0BIBcpAxAh1wEgFykDCAsh0wEg3gEg1wF9IsoBIM0BINoBVq0i1AF9IcsBINgBINMBfSLbASDKASDUAVQg1wEg3gFWcq0i1AF9IcoBINMBINgBViDUASDbAVZyIQog4AEgzAF9IcwBINoBIM0BfSHaAQwCC0LdsIWM6LaRqLh/IBcpAwgi0wEg2AF9ItQBIBcpAxAiygEg3gFUIMoBIN4BfSLKASDNASDaAVStIssBVHKtItcBfSLbAX0i3AEgygEgywF9IsoBQpHh5c2HifqZKFZCkeHlzYeJ+pkoIMoBfSLLASDNASDaAX0izQFCgYCAgL+y/fDDAFatItoBVHKtIt4BfSHKASDcASDeAVQg2wFC3bCFjOi2kai4f1ZyIQogywEg2gF9IcsBINQBINcBVCDTASDYAVRyrSDgASDMAX18QqnAxomuzpOyMHwhzAFCgYCAgL+y/fDDACDNAX0h2gEMAQsgFEICNwMADAELIAZB8AhqINoBQgAgzgFCABDJAyAGQYAIaiDaAUIAINIBQgAQyQMgBkHgB2og2gFCACDVAUIAEMkDIAZBwAdqINoBQgAgzwFCABDJAyAGQeAIaiAGKQPwCCLTAUIAQgBC/////76y/fBCEMkDIAZB0AhqIAYpA+gIIs0BQgBCgYCAgL+y/fDDAEIAEMkDIAZBwAhqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgBkGwCGogzQFCAELdsIWM6LaRqLh/QgAQyQMgBkGgCGogzQFCAEKpwMaJrs6TsjBCABDJAyAGQaAHaiDLAUIAIM4BQgAQyQMgBkHABmogywFCACDSAUIAEMkDIAZBsAZqIMsBQgAg1QFCABDJAyAGQaAGaiDLAUIAIM8BQgAQyQMgBkGQB2ogBikDwAgi2gEgBikD+Agi1wEgBikDgAh8ItgBfCLNASAGKQPYCCDTASAGKQPQCCLLAXwgywFUrXx8ItMBIAYpA6AHfCLUAUIAQgBC/////76y/fBCEMkDIAZBgAdqIAYpA5gHIssBQgBCgYCAgL+y/fDDAEIAEMkDIAZB8AZqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgBkHgBmogywFCAELdsIWM6LaRqLh/QgAQyQMgBkHQBmogywFCAEKpwMaJrs6TsjBCABDJAyAGQZAGaiDKAUIAIM4BQgAQyQMgBkGwBWogygFCACDSAUIAEMkDIAZB0ARqIMoBQgAg1QFCABDJAyAGQcAEaiDKAUIAIM8BQgAQyQMgBkGABmogBikDqAcg0wEg1AFWrXwi2wEgBikDwAZ8IssBIAYpA4gIINcBINgBVq18ItwBIAYpA+AHfCLXASAGKQOwCHwi2AEgzQEg0wFWrSAGKQPICCDNASDaAVStfHx8It4BfCLNASAGKQPwBnwi0wEgBikDiAcgBikDgAciygEg1AF8IMoBVK18fCLUASAGKQOQBnwi2gFCAEIAQv////++sv3wQhDJAyAGQfAFaiAGKQOIBiLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQeAFaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZB0AVqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZBwAVqIMoBQgBCqcDGia7Ok7IwQgAQyQMgBkGQCGogzAEgCq19IsoBQgAgzgFCABDJAyAGQfAHaiDKAUIAINIBQgAQyQMgBkHQB2ogygFCACDVAUIAEMkDIAZBsAdqIMoBQgAgzwFCABDJAyAGQaAFaiAGKQOYBiDUASDaAVatfCLgASAGKQOwBXwizAEgBikD6Acg1wEg3AFUrXwi3AEgBikDwAd8Is8BIAYpA6AIfCLOASDYASDeAVatIAYpA7gIINcBINgBVq18fHwi0gEgBikDsAZ8ItUBIMsBIM0BVq0gBikDyAYgywEg2wFUrXx8fCLLASAGKQPgBnwi1wEg0wEg1AFWrSAGKQP4BiDNASDTAVatfHx8ItsBfCLNASAGKQPgBXwi0wEgBikD+AUgBikD8AUiygEg2gF8IMoBVK18fCLUASAGKQOQCHwi2AFCAEIAQv////++sv3wQhDJAyAGQZAFaiAGKQOoBSLKAUIAQoGAgIC/sv3wwwBCABDJAyAGQYAFaiDKAUIAQpHh5c2HifqZKEIAEMkDIAZB8ARqIMoBQgBC3bCFjOi2kai4f0IAEMkDIAZB4ARqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAYpA+gEIAYpA8gFIAYpA9gGIM4BINIBVq0gBikDqAggzgEgzwFUrXx8IAYpA8gHIM8BINwBVK18fCLaASAGKQOgBnwiygEgywEg1QFUrSAGKQO4BiDSASDVAVatfHx8Is8BIAYpA9AGfCLOASDPAVStfCDOASDXASDbAVatIAYpA+gGIMsBINcBVq18fHwiywEgzgFUrXwgygEgzwFWrSAGKQOoBiDKASDaAVStfHx8ItIBIAYpA8AEfCLKASAGKQPYBCDLASDLASAGKQPQBHwizwFWrXwgzwEgzwEgzAEgzQFWrSAGKQO4BSDMASDgAVStfHx8IssBVq18fCLMASAGKQPABXwizwEgzAFUrXwgzwEgBikD2AUgywEgywEgBikD0AV8Is4BVq18IM4BINMBINQBVq0gBikD6AUgzQEg0wFWrXx8fCLNASDOAVStfHwiywEgzwFUrXwgygEgzAFWrSAGKQPIBCDKASDSAVStfHx8ItMBIAYpA7AHfCLPASAGKQPYByDLASDLASAGKQPQB3wiygFWrXwgygEgygEgBikD+AcgBikDmAgg1AEg2AFWrXwizAEgBikD8Ad8IssBIMwBVK18IMsBIMsBIM0BfCLMAVatfHwiywFWrXx8Is0BIAYpA+AEfCLOASDNAVStfCDOASAGKQP4BCDLASDLASAGKQPwBHwi0gFWrXwg0gEg0gEgBikDiAUgzAEgzAEgBikDgAV8IsoBVq18IMoBIAYpA5gFIAYpA5AFIssBINgBfCDLAVStfHwi2gEgygFUrXx8IsoBVq18fCLMASDOAVStfCDNASDPAVStIAYpA7gHIM8BINMBVK18fHwi2AFCqcDGia7Ok7IwVg0AAkAg2AFCqcDGia7Ok7IwUQRAIMwBQt2whYzotpGouH9WDQIgzAFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh2AELIMwBIcsBIMoBIc8BDAILIMoBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcsBIMoBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh2AEgygEhzwEMAgtCkeHlzYeJ+pkoIc8BINoBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdgBDAELIMoBQpHh5c2HifqZKH0iywEg2gFCgYCAgL+y/fDDAFStIs0BfSHPASDMAUKjz/rzl8nu18cAfCLOASDKAUKR4eXNh4n6mShUIMsBIM0BVHKtIsoBfSHLASDYASDMAULdsIWM6LaRqLh/VCDKASDOAVZyrX1CqcDGia7Ok7IwfSHYASDaAUKBgICAv7L98MMAfSHaAQtCqcDGia7Ok7IwIcoBIMsBINYBfCLLASDWAVQgywEgzwEg0AF8IswBINABVCDMASDMASDZASDaAXwizwEg2QFUrXwizQFWcq18Is4BIMsBVHKtINEBINgBfHwi2gEhywECQAJAAkAg2gFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hygEgzgEiywFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghygEgzQEiywFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhygEgzwEiywFCgYCAgL+y/fDDAFENAQsgygEgywFYDQAgzgEhygEgzQEhzAEMAQsgzQFCkeHlzYeJ+pkofSLKASDPAUKBgICAv7L98MMAVK0iywF9IcwBIM4BQqPP+vOXye7XxwB8ItIBIM0BQpHh5c2HifqZKFQgygEgywFUcq0iywF9IcoBINoBIM4BQt2whYzotpGouH9UIMsBINIBVnKtfUKpwMaJrs6TsjB9IdoBIM8BQoGAgIC/sv3wwwB9Ic8BCyAGQcACaiAQKQN4IssBQgAg3wFCABDJAyAGQdACaiDLAUIAIOsBQgAQyQMgBkHgAmogywFCACDsAUIAEMkDIAZB8AJqIMsBQgAg6gFCABDJAyAGQbACaiAGKQPAAiLOAUIAQgBC/////76y/fBCEMkDIAZBoAJqIAYpA7gCIssBQgBCgYCAgL+y/fDDAEIAEMkDIAZBkAJqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgBkGwAWogywFCAELdsIWM6LaRqLh/QgAQyQMgBkHQAGogywFCAEKpwMaJrs6TsjBCABDJAyAGQYADaiAQKQNwIssBQgAg3wFCABDJAyAGQZADaiDLAUIAIOsBQgAQyQMgBkGgA2ogywFCACDsAUIAEMkDIAZBsANqIMsBQgAg6gFCABDJAyAGQYACaiAGKQOQAiLUASAGKQPIAiLQASAGKQPQAnwi0wF8Is0BIAYpA6gCIM4BIAYpA6ACIssBfCDLAVStfHwizgEgBikDgAN8ItIBQgBCAEL/////vrL98EIQyQMgBkHwAWogBikDiAIiywFCAEKBgICAv7L98MMAQgAQyQMgBkHgAWogywFCAEKR4eXNh4n6mShCABDJAyAGQdABaiDLAUIAQt2whYzotpGouH9CABDJAyAGQcABaiDLAUIAQqnAxomuzpOyMEIAEMkDIAZBwANqIBApA2giywFCACDfAUIAEMkDIAZB0ANqIMsBQgAg6wFCABDJAyAGQeADaiDLAUIAIOwBQgAQyQMgBkHwA2ogywFCACDqAUIAEMkDIAZBoAFqIAYpA4gDIM4BINIBVq18ItYBIAYpA5ADfCLRASAGKQPYAiDQASDTAVatfCLXASAGKQPgAnwi0AEgBikDsAF8ItMBIM0BIM4BVq0gBikDmAIgzQEg1AFUrXx8fCLZAXwizQEgBikD4AF8Is4BIAYpA/gBIAYpA/ABIssBINIBfCDLAVStfHwi0gEgBikDwAN8ItQBQgBCAEL/////vrL98EIQyQMgBkGQAWogBikDqAEiywFCAEKBgICAv7L98MMAQgAQyQMgBkGAAWogywFCAEKR4eXNh4n6mShCABDJAyAGQfAAaiDLAUIAQt2whYzotpGouH9CABDJAyAGQeAAaiDLAUIAQqnAxomuzpOyMEIAEMkDIAZBgARqIBApA2AiywFCACDfAUIAEMkDIAZBkARqIMsBQgAg6wFCABDJAyAGQaAEaiDLAUIAIOwBQgAQyQMgBkGwBGogywFCACDqAUIAEMkDIAZBQGsgBikDyAMg0gEg1AFWrXwi2wEgBikD0AN8ItUBIAYpA+gCINABINcBVK18ItwBIAYpA/ACfCLXASAGKQNQfCLYASDTASDZAVatIAYpA7gBINABINMBVq18fHwi0AEgBikDoAN8ItMBIM0BINEBVK0gBikDmAMg0QEg1gFUrXx8fCLRASAGKQPQAXwi1gEgzgEg0gFWrSAGKQPoASDNASDOAVatfHx8ItkBfCLNASAGKQOAAXwizgEgBikDmAEgBikDkAEiywEg1AF8IMsBVK18fCLSASAGKQOABHwi1AFCAEIAQv////++sv3wQhDJAyAGQTBqIAYpA0giywFCAEKBgICAv7L98MMAQgAQyQMgBkEgaiDLAUIAQpHh5c2HifqZKEIAEMkDIAZBEGogywFCAELdsIWM6LaRqLh/QgAQyQMgBiDLAUIAQqnAxomuzpOyMEIAEMkDAkACQCAGKQMIIAYpA2ggBikDyAEg0AEg2AFUrSAGKQNYINcBINgBVq18fCAGKQP4AiDXASDcAVStfHwi1wEgBikDsAN8IssBINEBINMBVK0gBikDqAMg0AEg0wFWrXx8fCLQASAGKQPAAXwi0wEg0AFUrXwg0wEg1gEg2QFWrSAGKQPYASDRASDWAVatfHx8ItEBINMBVK18IMsBINABVq0gBikDuAMgywEg1wFUrXx8fCLXASAGKQPwA3wiywEgBikD6AMg0QEg0QEgBikD4AN8ItABVq18INABINABIM0BINUBVK0gBikD2AMg1QEg2wFUrXx8fCLRAVatfHwi0AEgBikDYHwi0wEg0AFUrXwg0wEgBikDeCDRASDRASAGKQNwfCLVAVatfCDVASDVASDOASDSAVatIAYpA4gBIM0BIM4BVq18fHwi0QFWrXx8Is0BINMBVK18IMsBINABVq0gBikD+AMgywEg1wFUrXx8fCLVASAGKQOwBHwiywEgBikDqAQgzQEgzQEgBikDoAR8Is4BVq18IM4BIM4BIAYpA5gEIAYpA4gEINIBINQBVq18ItIBIAYpA5AEfCLNASDSAVStfCDNASDNASDRAXwi0gFWrXx8Is0BVq18fCLRASAGKQMAfCLQASDRAVStfCDQASDQASAGKQMYIM0BIM0BIAYpAxB8ItMBVq18INMBINMBIAYpAygg0gEg0gEgBikDIHwizQFWrXwgzQEgzQEgBikDOCAGKQMwIs4BINQBfCDOAVStfHwizgFWrXx8Is0BVq18fCLSAVatfCDLASDRAVatIAYpA7gEIMsBINUBVK18fHwi2AFCqcDGia7Ok7IwVg0AAkAg2AFCqcDGia7Ok7IwUQRAINIBQt2whYzotpGouH9WDQIg0gFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh2AELINIBIcsBIM0BIdkBDAILIM0BQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcsBIM0BQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh2AEgzQEh2QEMAgtCkeHlzYeJ+pkoIdkBIM4BQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdgBDAELIM0BQpHh5c2HifqZKH0iywEgzgFCgYCAgL+y/fDDAFStItEBfSHZASDSAUKjz/rzl8nu18cAfCLQASDNAUKR4eXNh4n6mShUIMsBINEBVHKtIs0BfSHLASDYASDSAULdsIWM6LaRqLh/VCDNASDQAVZyrX1CqcDGia7Ok7IwfSHYASDOAUKBgICAv7L98MMAfSHOAQsgBgJ+AkACQCDaASLNASDYASLRAVINACDLASHRASDKASHNASDKASDLAVINACDZASLRASDMASLNAVINACDOASHRASDPASLNASDOAVENAQsgzQEg0QFaDQBC3bCFjOi2kai4fyDLASDKAX0izQEg2QEgzAF9ItIBIM4BIM8BVK0i0QFUIMwBINkBVnKtIswBfSLQAX0i0wEg0gEg0QF9ItIBQpHh5c2HifqZKFZCkeHlzYeJ+pkoINIBfSLSASDOASDPAX0izwFCgYCAgL+y/fDDAFatIs4BVHKtItEBfSHZASDRASDTAVYg0AFC3bCFjOi2kai4f1ZyIQog0gEgzgF9IdEBIMwBIM0BViDKASDLAVZyrSDaASDYAX18QqnAxomuzpOyMHwh2gFCgYCAgL+y/fDDACDPAX0MAQsgzAEg2QF9Is0BIM4BIM8BVq0i0gF9IdEBIMoBIMsBfSLQASDNASDSAVQgzAEg2QFUcq0izAF9IdkBIMoBIMsBVCDMASDQAVZyIQog2gEg2AF9IdoBIM8BIM4BfQs3A+g/IAYg0QE3A+A/IAYg2QE3A9g/IAYg2gEgCq19NwPQPyAGQYjAAGpCADcDACAGQYBAa0IANwMAIAZB+D9qQgA3AwAgBkIANwPwPyAGQdA/aiAGQfA/akEgEPEDRQRAIBRCAzcDACAUQQE6AAggEUGAwAAQ3wQgE0GAwAAQ3wQMAgsgFEIDNwMAIBRBADoACAsgEUGAwAAQ3wQgE0GAwAAQ3wQLIAZBkMAAaiQAAkAgBCkDoGEiygFCA1EEQCAELQCoYUUNAQwICyAEIAQpA6hhNwPwYiAEIMoBNwPoYiAEQQE2ArQnIARBzKXCADYCsCcgBEIBNwK8JyAEIARB6OIAaq1CgICAgNAIhDcDwGAgBCAEQcDgAGo2ArgnIARBwN0AaiAEQbAnahCuAyAEIAQoAMVdNgLwZCAEIARByN0AaigAADYA82QgBC0AxF0hBSAEKALAXSIKQYCAgIB4RwRAIBIgBCgC8GQ2AAkgEkEMaiAEKADzZDYAACASIAU6AAggEiAKNgIEIBJBATYCAAwJCyAFQQFxDQcLQdHOxQAtAAAaQRhBARDWBCIFRQRAQQFBGEGkm8IAEMgEAAsgBEGwJ2oiCkEYNgIIIAogBTYCBCAKQRg2AgAgBUEQakHkpcIAKQAANwAAIAVBCGpB3KXCACkAADcAACAFQdSlwgApAAA3AAAgEkEBNgIAIBJBDGogBEG4J2ooAgA2AgAgEiAEKQKwJzcCBAwHCyAMIAVBkJbCABDIBAALQQhBgARBkJbCABDIBAALIARBuCdqIARB4MwAaiIFKAIAIgo2AgAgBCAEKQLYTCLKATcDsCcgBSAKNgIAIAQgygE3A9hMQcqZwgBBKyAEQdjMAGpBmKvCAEHYq8IAEMoDAAsgBEG4J2ogBEHgzABqIgUoAgAiCjYCACAEIAQpAthMIsoBNwOwJyAFIAo2AgAgBCDKATcD2ExBypnCAEErIARB2MwAakGYq8IAQcirwgAQygMACyAEQbgnaiAEQeDMAGoiBSgCACIKNgIAIAQgBCkC2EwiygE3A7AnIAUgCjYCACAEIMoBNwPYTEHKmcIAQSsgBEHYzABqQZirwgBBuKvCABDKAwALIARBuCdqIARB8OIAaiIFKAIAIgo2AgAgBCAEKQLoYiLKATcDsCcgBSAKNgIAIAQgygE3A+hiQcqZwgBBKyAEQejiAGpBmKvCAEGoq8IAEMoDAAsgBEGwJ2ohBiAEQZAdaiEMIARBiDNqIQ0gBEGoM2ohEyAEQag6aiFaIARB+NMAaiEQIARB2NMAaiEXIARBuNQAaiERIARBmNQAaiEHIARB2MwAaiFFIwBBgMIBayIDJAAgA0EANgKIhQEgA0KAgICAgAE3AoCFAQJ+AkACQCAJIghFDQAgECkDACHOASAQKQMIIcsBIBApAxAhzwEgECkDGCHRAUEBIQoDQCADKAKIhQEiFCADKAKAhQFGBEAgA0GAhQFqQdivwgAQogMLIAohBSADKAKEhQEgFEEFdGoiCiDRATcDGCAKIM8BNwMQIAogywE3AwggCiDOATcDACADIBRBAWo2AoiFASADQZCEAWog0QFCACDRAUIAEMkDIANBsIMBaiDPAUIAINEBQgAQyQMgA0HQggFqIMsBQgAg0QFCABDJAyADQfCBAWogzgFCACDRAUIAEMkDIANBgIQBaiADKQOQhAFCfYMizQFCAEIAQv////++sv3wQhDJAyADQfCDAWogAykDiIQBIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB4IMBaiDKAUIAQpHh5c2HifqZKEIAEMkDIANB0IMBaiDKAUIAQt2whYzotpGouH9CABDJAyADQcCDAWogygFCAEKpwMaJrs6TsjBCABDJAyADQcCEAWogzwFCACDPAUIAEMkDIANBsIQBaiDLAUIAIM8BQgAQyQMgA0GghAFqIM4BQgAgzwFCABDJAyADQaCDAWogAykD4IMBItABIAMpA5iEASLSASADKQOwgwEiygF8ItEBfCLMASADKQP4gwEgzQEgAykD8IMBIs8BfCDPAVStfHwizwEgygF8Is0BQgBCAEL/////vrL98EIQyQMgA0GQgwFqIAMpA6iDASLKAUIAQoGAgIC/sv3wwwBCABDJAyADQYCDAWogygFCAEKR4eXNh4n6mShCABDJAyADQfCCAWogygFCAELdsIWM6LaRqLh/QgAQyQMgA0HgggFqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HghAFqIMsBQgAgywFCABDJAyADQdCEAWogzgFCACDLAUIAEMkDIANBwIIBaiADKQO4gwEiygEgzQEgzwFUrXwi1QEgAykDwIQBfCLLASDKASDRASDSAVStfCLTASADKQPQggEiygF8ItIBIAMpA9CDAXwi0QEgzAEgzwFWrSADKQPogwEgzAEg0AFUrXx8fCLXAXwizAEgAykDgIMBfCLPASADKQOYgwEgzQEgAykDkIMBItABfCDQAVStfHwizQEgygF8ItABQgBCAEL/////vrL98EIQyQMgA0GwggFqIAMpA8iCASLKAUIAQoGAgIC/sv3wwwBCABDJAyADQaCCAWogygFCAEKR4eXNh4n6mShCABDJAyADQZCCAWogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GAggFqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HwhAFqIM4BQgAgzgFCABDJAyADQeCBAWogAykD2IIBIsoBIM0BINABVq18ItgBIAMpA7CEASLWAXwizgEg1gEgygEg0gEg0wFUrXwi2gEgAykD8IEBIsoBfCLTASADKQPAgwF8ItQBINEBINcBVq0gAykD2IMBINEBINIBVK18fHwi0gF8ItEBIMsBIMwBVq0gAykDyIQBIMsBINUBVK18fHwiywEgAykD8IIBfCLVASDNASDPAVStIAMpA4iDASDMASDPAVatfHx8ItcBfCLMASADKQOgggF8Is8BIAMpA7iCASADKQOwggEizQEg0AF8IM0BVK18fCLNASDKAXwi0AFCAEIAQv////++sv3wQhDJAyADQdCBAWogAykD6IEBIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBwIEBaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBsIEBaiDKAUIAQt2whYzotpGouH9CABDJAyADQaCBAWogygFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDqIEBIAMpA4iCASADKQPoggEg0gEg1AFUrSADKQPIgwEg0wEg1AFWrXx8IAMpA/iBASLUASDTASDaAVStfHwi0wEgAykDoIQBItYBfCLKASDLASDRAVStIAMpA7iEASLaASDRASDSAVStfHx8ItIBIAMpA+CCAXwi0QEg0gFUrXwg0QEg1QEg1wFWrSADKQP4ggEgywEg1QFWrXx8fCLLASDRAVStfCDKASDSAVatIAMpA6iEASLVASDKASDTAVStfHx8ItMBIAMpA9CEASLXAXwiygEgAykD6IQBIMsBIMsBIAMpA+CEAXwi0gFWrXwg0gEg0gEgzAEgzgFUrSDaASDOASDYAVStfHx8IssBVq18fCLOASADKQOAggF8ItIBIM4BVK18INIBINIBIAMpA5iCASDLASDLASADKQOQggF8ItEBVq18INEBIM0BIM8BVK0gAykDqIIBIMwBIM8BVq18fHwizAEg0QFUrXx8IssBVq18IMoBIM4BVq0gAykD2IQBIs4BIMoBINMBVK18fHwi0wEgAykD8IQBfCLPASDOASDLASDLASDXAXwiygFWrXwgygEgygEg1QEg1AEgzQEg0AFWrXwizQEg1gF8IssBIM0BVK18IMsBIMsBIMwBfCLMAVatfHwiywFWrXx8Is0BIAMpA6CBAXwizgEgzQFUrXwgzgEgzgEgAykDuIEBIMsBIMsBIAMpA7CBAXwi0gFWrXwg0gEg0gEgAykDyIEBIMwBIMwBIAMpA8CBAXwiygFWrXwgygEgAykD2IEBIAMpA9CBASLLASDQAXwgywFUrXx8ItEBIMoBVK18fCLKAVatfHwizAFWrXwgzQEgzwFUrSADKQP4hAEgzwEg0wFUrXx8fCLOAUKpwMaJrs6TsjBWDQAgzgFCqcDGia7Ok7IwUgRAIMoBIc8BIMwBIcsBDAILIMwBQt2whYzotpGouH9WDQAgzAFC3bCFjOi2kai4f1IEQCDKASHPASDMASHLAUKpwMaJrs6TsjAhzgEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8hywEgygFCkeHlzYeJ+pkoUgRAIMoBIc8BQqnAxomuzpOyMCHOAQwCC0KR4eXNh4n6mSghzwEg0QFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhzgEMAQsgygFCkeHlzYeJ+pkofSLLASDRAUKBgICAv7L98MMAVK0izQF9Ic8BIMwBQqPP+vOXye7XxwB8ItIBIMoBQpHh5c2HifqZKFQgywEgzQFUcq0iygF9IcsBIM4BIMwBQt2whYzotpGouH9UIMoBINIBVnKtfUKpwMaJrs6TsjB9Ic4BINEBQoGAgIC/sv3wwwB9IdEBCyAFQQFqIQogBSAISQ0ACyADKAKIhQEiGUUNACADKAKEhQEiFCkDGCHbASAUKQMQIdwBIBQpAwgh2QEgFCkDACLmASHRASARKQMAIvgBIc4BAn4CQCDmASD4AVINACARKQMIIs4BINkBItEBUg0AIBEpAxAizgEg3AEi0QFSDQAg0QEh7wEg2wEi0QEh8AEg2QEg0QEgESkDGCLOAVENARoLIBEpAxgh8AEgzgEg0QFUDQIgESkDECHvASARKQMICyHuASDvASDcAX0iygEg2wEg8AFWrSLLAX0h0QEg7gEg2QF9IswBIMoBIMsBVCDcASDvAVZyrSLKAX0hzgEg2QEg7gFWIMoBIMwBVnIhCiDwASDbAX0hzwEg+AEg5gF9DAILQQBBAEGYrMIAENkDAAtC3bCFjOi2kai4fyDZASARKQMIIu4BfSLKASDcASARKQMQIu8BVCDcASDvAX0iywEg2wEg8AFUrSLMAVRyrSLNAX0izwF9ItIBIMsBIMwBfSLLAUKR4eXNh4n6mShWQpHh5c2HifqZKCDLAX0iywEg2wEg8AF9IswBQoGAgIC/sv3wwwBWrSLRAVRyrSLQAX0hzgEg0AEg0gFWIM8BQt2whYzotpGouH9WciEKIMsBINEBfSHRAUKBgICAv7L98MMAIMwBfSHPASDKASDNAVQg2QEg7gFUcq0g+AEg5gF9fEKpwMaJrs6TsjB8CyHKASADKAKAhQEhGiADIM8BNwP4wQEgAyDRATcD8MEBIAMgzgE3A+jBASADIMoBIAqtfTcD4MEBAkAgA0HgwQFqQcCWwgBBIBDxAwRAQgAh0QEgA0HApAFqQgA3AwAgA0G4pAFqQgA3AwAgA0IANwOwpAEgA0IBNwPIpAEgA0HIpQFqIANB+MEBaikDADcDACADQcClAWogA0HwwQFqKQMANwMAIANBuKUBaiADQejBAWopAwA3AwAgAyADKQPgwQE3A7ClASADQZiFAWpBuJbCACkDADcDACADQZCFAWpBsJbCACkDADcDACADQYiFAWpBqJbCACkDADcDACADQaCWwgApAwA3A4CFAQJAIANBsKUBaiADQbCkAWpBIBDxA0UEQEKlibn6l5a0iwIh4AFCp9uF8drIudwbId4BQuOz8Zqe1o7/0wAh4gFChYHundXn4KSMfyHjAQwBC0Kn24Xx2si53Bsh3gFC47Pxmp7Wjv/TACHiAUKFge6d1efgpIx/IeMBQqWJufqXlrSLAiHgASADKQPIpQEhywEgAykDsKUBIc0BIAMpA7ilASHKASADKQPApQEh2AFCACHUAUIAIdUBQgAhzgFCgYCAgL+y/fDDACHPAUKpwMaJrs6TsjAh0gFC3bCFjOi2kai4fyHMAUKR4eXNh4n6mSgh0AEDQCADQYCFAWogA0GwpAFqQSAQ8QNFBEAg1AEh4wEg1QEh4gEgzgEh3gEg0QEh4AEMAgsgywGnQQFxRQRAA0Ag2AFCP4YgywFCAYiEIcsBAkAg3gFCAYNQBEAg3gEh2gEg4gEh0wEg4wEh1wEMAQsg4AEg4wFCo8/685fJ7tfHAH0i1gEg4wFUINYBINYBIOIBQpHh5c2HifqZKHwi1wEg4gFUINcBINcBIN4BQoGAgIC/sv3wwwB8ItoBIN4BVK18ItMBVnKtfCLXAVZyrXxCqcDGia7Ok7IwfCHgAQsgzQFCP4YgygFCP4Yg2AFCAYiEIdgBIM0BQgGIIc0BIOABQj+GINcBQgGIhCHjASDXAUI/hiDTAUIBiIQh4gEg0wFCP4Yg2gFCAYiEId4BIOABQgGIIeABIMoBQgGIhCHKASDLAUIBg1ANAAsgAyDYATcDwKUBIAMgywE3A8ilASADIMoBNwO4pQEgAyDNATcDsKUBCyDPAadBAXFFBEADQCDQAUI/hiDPAUIBiIQhzwECQCDOAUIBg1AEQCDOASHXASDVASHOASDUASHTAQwBCyDRASDUASDUAUKjz/rzl8nu18cAfSLWAVYg1gEg1gEg1QFCkeHlzYeJ+pkofCLTASDVAVQg0wEgzgFCgYCAgL+y/fDDAHwi1wEgzgFUrXwizgEg0wFUcq18ItMBVnKtfEKpwMaJrs6TsjB8IdEBCyDSAUI/hiDMAUI/hiDQAUIBiIQh0AEg0gFCAYgh0gEg0QFCP4Yg0wFCAYiEIdQBINMBQj+GIM4BQgGIhCHVASDOAUI/hiDXAUIBiIQhzgEg0QFCAYgh0QEgzAFCAYiEIcwBIM8BQgGDUA0ACyADINABNwOQhQEgAyDPATcDmIUBIAMgzAE3A4iFASADINIBNwOAhQELIM0BIdcBAkACQAJAAkACQCDSASLTASDNAVINACDMASHTASDKASHXASDKASDMAVINACDYASLXASDQASLTAVINACDPASHTASDLASHXASDLASDPAVENAQsg0wEg1wFYDQAgAyDPASDLAX0i0wE3A5iFASADINABINgBfSLWASDLASDPAVatIs8BfSLXATcDkIUBIAMgzAEgygF9ItoBINABINgBVCDPASDWAVZyrSLPAX0i1gE3A4iFASADINIBIM0BfSDPASDaAVYgygEgzAFWcq19ItIBNwOAhQECQAJAINEBIs8BIOABIswBUg0AINQBIs8BIOMBIswBUg0AINUBIs8BIOIBIswBUg0AIM4BIs8BIN4BIswBUQ0BCyDMASDPAVYNAgsg0QEg4AF9INQBIOMBVCDUASDjAX0i1AEg1QEg4gFUINUBIOIBfSLVASDOASDeAVStItoBVHKtIt0BVHKtfSHRASDOASDeAX0hzgEg1wEh0AEg1gEhzAEg0wEhzwEg1QEg2gF9IdUBINQBIN0BfSHUAQwDCyADIMsBIM8BfSLTATcDyKUBIAMg2AEg0AF9ItYBIMsBIM8BVK0iywF9ItcBNwPApQEgAyDKASDMAX0i2gEgywEg1gFWINABINgBVnKtIssBfSLWATcDuKUBIAMgzQEg0gF9IMoBIMwBVCDLASDaAVZyrX0izQE3A7ClAQJAAkAg0QEiygEg4AEiywFSDQAg1AEiygEg4wEiywFSDQAg1QEiygEg4gEiywFSDQAgzgEiygEg3gEiywFRDQELIMoBIMsBVg0CCyDgASDRAX0g4wEg1AF9ItoBIOIBINUBfSLdASDOASDeAVatIt8BVCDVASDiAVZyrSLhAVQg1AEg4wFWcq19IeABIN4BIM4BfSHeASDXASHYASDWASHKASDTASHLASDdASDfAX0h4gEg2gEg4QF9IeMBDAILINEBQt2whYzotpGouH8g4wF9IswBQpHh5c2HifqZKCDiAX0izwEg3gFCgYCAgL+y/fDDAFatItEBVCDiAUKR4eXNh4n6mShWcq0i0AFUIOMBQt2whYzotpGouH9Wcq0g4AF8fSDMASDQAX0i0AEg1AF8IswBINABVCDMASDPASDRAX0i0QEg1QF8Is8BINEBVCDPAUKBgICAv7L98MMAIN4BfSLRASDOAXwizgEg0QFUrXwi1QEgzwFUcq18ItQBIMwBVHKtfEKpwMaJrs6TsjB8IdEBINcBIdABINYBIcwBINMBIc8BDAELIOABINEBfULdsIWM6LaRqLh/INQBfSLKAUKR4eXNh4n6mSgg1QF9IssBIM4BQoGAgIC/sv3wwwBWrSLYAVQg1QFCkeHlzYeJ+pkoVnKtItoBVCDUAULdsIWM6LaRqLh/VnKtfSDKASDaAX0i2gEg4wF8IsoBINoBVCDKASDLASDYAX0i2AEg4gF8IssBINgBVCDLAUKBgICAv7L98MMAIM4BfSLYASDeAXwi3gEg2AFUrXwi4gEgywFUcq18IuMBIMoBVHKtfEKpwMaJrs6TsjB8IeABINcBIdgBINYBIcoBINMBIcsBCyADQbClAWogA0GwpAFqQSAQ8QMNAAsLQqnAxomuzpOyMCHNASDZASDuAXwiygEg7gFUIMoBIMoBINwBIO8BfCLMASDvAVQgzAEgzAEg2wEg8AF8Is4BIPABVK18IssBVnKtfCLMAVZyrSDmASD4AXx8ItEBIcoBAkACQAJAINEBQqnAxomuzpOyMFINAELdsIWM6LaRqLh/Ic0BIMwBIsoBQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIc0BIMsBIsoBQpHh5c2HifqZKFINAEKBgICAv7L98MMAIc0BIM4BIsoBQoGAgIC/sv3wwwBRDQELIMoBIM0BWg0AIMwBIc0BIMsBIcoBDAELIMsBQpHh5c2HifqZKH0izwEgzgFCgYCAgL+y/fDDAFStIs0BfSHKASDMAUKjz/rzl8nu18cAfCLSASDLAUKR4eXNh4n6mShUIM0BIM8BVnKtIssBfSHNASDRASDMAULdsIWM6LaRqLh/VCDLASDSAVZyrX1CqcDGia7Ok7IwfSHRASDOAUKBgICAv7L98MMAfSHOAQsgAyDOATcD+MEBIAMgygE3A/DBASADIM0BNwPowQEgAyDRATcD4MEBAkACQCADQeDBAWpBwJbCAEEgEPEDBEBCACHRASADQcCkAWoiBUIANwMAIANBuKQBaiIcQgA3AwAgA0IANwOwpAEgA0IBNwPIpAEgA0HIpQFqIiMgA0H4wQFqIjApAwA3AwAgA0HApQFqIjMgA0HwwQFqIjQpAwA3AwAgA0G4pQFqIjUgA0HowQFqIjYpAwA3AwAgAyADKQPgwQE3A7ClASADQZiFAWoiRkG4lsIAKQMANwMAIANBkIUBaiJHQbCWwgApAwA3AwAgA0GIhQFqIgpBqJbCACkDADcDACADQaCWwgApAwA3A4CFAQJAIANBsKUBaiADQbCkAWpBIBDxA0UEQEKlibn6l5a0iwIh6gFCp9uF8drIudwbIegBQuOz8Zqe1o7/0wAh5gFChYHundXn4KSMfyHhAQwBC0Kn24Xx2si53Bsh6AFC47Pxmp7Wjv/TACHmAUKFge6d1efgpIx/IeEBQqWJufqXlrSLAiHqASADKQPIpQEhywEgAykDsKUBIc0BIAMpA7ilASHKASADKQPApQEh2AFCACHUAUIAIdUBQgAhzgFCgYCAgL+y/fDDACHPAUKpwMaJrs6TsjAh0gFC3bCFjOi2kai4fyHMAUKR4eXNh4n6mSgh0AEDQCADQYCFAWogA0GwpAFqQSAQ8QNFBEAg1AEh4QEg1QEh5gEgzgEh6AEg0QEh6gEMAgsgywGnQQFxRQRAA0Ag2AFCP4YgywFCAYiEIcsBAkAg6AFCAYNQBEAg6AEh2gEg5gEh0wEg4QEh1wEMAQsg6gEg4QFCo8/685fJ7tfHAH0i1gEg4QFUINYBINYBIOYBQpHh5c2HifqZKHwi1wEg5gFUINcBINcBIOgBQoGAgIC/sv3wwwB8ItoBIOgBVK18ItMBVnKtfCLXAVZyrXxCqcDGia7Ok7IwfCHqAQsgzQFCP4YgygFCP4Yg2AFCAYiEIdgBIM0BQgGIIc0BIOoBQj+GINcBQgGIhCHhASDXAUI/hiDTAUIBiIQh5gEg0wFCP4Yg2gFCAYiEIegBIOoBQgGIIeoBIMoBQgGIhCHKASDLAUIBg1ANAAsgAyDYATcDwKUBIAMgywE3A8ilASADIMoBNwO4pQEgAyDNATcDsKUBCyDPAadBAXFFBEADQCDQAUI/hiDPAUIBiIQhzwECQCDOAUIBg1AEQCDOASHXASDVASHOASDUASHTAQwBCyDRASDUASDUAUKjz/rzl8nu18cAfSLWAVYg1gEg1gEg1QFCkeHlzYeJ+pkofCLTASDVAVQg0wEgzgFCgYCAgL+y/fDDAHwi1wEgzgFUrXwizgEg0wFUcq18ItMBVnKtfEKpwMaJrs6TsjB8IdEBCyDSAUI/hiDMAUI/hiDQAUIBiIQh0AEg0gFCAYgh0gEg0QFCP4Yg0wFCAYiEIdQBINMBQj+GIM4BQgGIhCHVASDOAUI/hiDXAUIBiIQhzgEg0QFCAYgh0QEgzAFCAYiEIcwBIM8BQgGDUA0ACyADINABNwOQhQEgAyDPATcDmIUBIAMgzAE3A4iFASADINIBNwOAhQELIM0BIdcBAkACQAJAAkACQCDSASLTASDNAVINACDMASHTASDKASHXASDKASDMAVINACDYASLXASDQASLTAVINACDPASHTASDLASHXASDLASDPAVENAQsg0wEg1wFYDQAgAyDPASDLAX0i0wE3A5iFASADINABINgBfSLWASDLASDPAVatIs8BfSLXATcDkIUBIAMgzAEgygF9ItoBINABINgBVCDPASDWAVZyrSLPAX0i1gE3A4iFASADINIBIM0BfSDPASDaAVYgygEgzAFWcq19ItIBNwOAhQECQAJAINEBIs8BIOoBIswBUg0AINQBIs8BIOEBIswBUg0AINUBIs8BIOYBIswBUg0AIM4BIs8BIOgBIswBUQ0BCyDMASDPAVYNAgsg0QEg6gF9INQBIOEBVCDUASDhAX0i1AEg1QEg5gFUINUBIOYBfSLVASDOASDoAVStItoBVHKtItkBVHKtfSHRASDOASDoAX0hzgEg1wEh0AEg1gEhzAEg0wEhzwEg1QEg2gF9IdUBINQBINkBfSHUAQwDCyADIMsBIM8BfSLTATcDyKUBIAMg2AEg0AF9ItYBIMsBIM8BVK0iywF9ItcBNwPApQEgAyDKASDMAX0i2gEgywEg1gFWINABINgBVnKtIssBfSLWATcDuKUBIAMgzQEg0gF9IMoBIMwBVCDLASDaAVZyrX0izQE3A7ClAQJAAkAg0QEiygEg6gEiywFSDQAg1AEiygEg4QEiywFSDQAg1QEiygEg5gEiywFSDQAgzgEiygEg6AEiywFRDQELIMoBIMsBVg0CCyDqASDRAX0g4QEg1AF9ItoBIOYBINUBfSLZASDOASDoAVatItsBVCDVASDmAVZyrSLcAVQg1AEg4QFWcq19IeoBIOgBIM4BfSHoASDXASHYASDWASHKASDTASHLASDZASDbAX0h5gEg2gEg3AF9IeEBDAILINEBQt2whYzotpGouH8g4QF9IswBQpHh5c2HifqZKCDmAX0izwEg6AFCgYCAgL+y/fDDAFatItEBVCDmAUKR4eXNh4n6mShWcq0i0AFUIOEBQt2whYzotpGouH9Wcq0g6gF8fSDMASDQAX0i0AEg1AF8IswBINABVCDMASDPASDRAX0i0QEg1QF8Is8BINEBVCDPAUKBgICAv7L98MMAIOgBfSLRASDOAXwizgEg0QFUrXwi1QEgzwFUcq18ItQBIMwBVHKtfEKpwMaJrs6TsjB8IdEBINcBIdABINYBIcwBINMBIc8BDAELIOoBINEBfULdsIWM6LaRqLh/INQBfSLKAUKR4eXNh4n6mSgg1QF9IssBIM4BQoGAgIC/sv3wwwBWrSLYAVQg1QFCkeHlzYeJ+pkoVnKtItoBVCDUAULdsIWM6LaRqLh/VnKtfSDKASDaAX0i2gEg4QF8IsoBINoBVCDKASDLASDYAX0i2AEg5gF8IssBINgBVCDLAUKBgICAv7L98MMAIM4BfSLYASDoAXwi6AEg2AFUrXwi5gEgywFUcq18IuEBIMoBVHKtfEKpwMaJrs6TsjB8IeoBINcBIdgBINYBIcoBINMBIcsBCyADQbClAWogA0GwpAFqQSAQ8QMNAAsLICNCADcDACAzQgA3AwAgNUIANwMAIANCADcDsKUBIANByKQBaiJIQgA3AwAgBUIANwMAIBxCADcDACADQgA3A7CkASAwQgA3AwAgNEIANwMAIDZCADcDACADQgA3A+DBASADQYikAWoiW0IANwMAIANBgKQBaiJcQgA3AwAgA0H4owFqIl1CADcDACADQgA3A/CjASADQeijAWoiXkIANwMAIANB4KMBaiJfQgA3AwAgA0HYowFqImBCADcDACADQgA3A9CjASADQcijAWoiYUIANwMAIANBwKMBaiJiQgA3AwAgA0G4owFqImNCADcDACADQgA3A7CjASADQaijAWoiZEIANwMAIANBoKMBaiJlQgA3AwAgA0GYowFqImZCADcDACADQgA3A5CjASADQYijAWoiZ0IANwMAIANBgKMBaiJoQgA3AwAgA0H4ogFqImlCADcDACADQgA3A/CiASADQeiiAWoiakIANwMAIANB4KIBaiJrQgA3AwAgA0HYogFqImxCADcDACADQgA3A9CiASADQciiAWoibUIANwMAIANBwKIBaiJuQgA3AwAgA0G4ogFqIm9CADcDACADQgA3A7CiASADQaiiAWoicEIANwMAIANBoKIBaiJxQgA3AwAgA0GYogFqInJCADcDACADQgA3A5CiASADQYiiAWoic0IANwMAIANBgKIBaiJ0QgA3AwAgA0H4oQFqInVCADcDACADQgA3A/ChASADQeihAWoidkIANwMAIANB4KEBaiJ3QgA3AwAgA0HYoQFqInhCADcDACADQgA3A9ChASADQcihAWoieUIANwMAIANBwKEBaiJ6QgA3AwAgA0G4oQFqIntCADcDACADQgA3A7ChASADQaihAWoifEIANwMAIANBoKEBaiJ9QgA3AwAgA0GYoQFqIn5CADcDACADQgA3A5ChASADQYihAWoif0IANwMAIANBgKEBaiKAAUIANwMAIANB+KABaiKBAUIANwMAIANCADcD8KABIANB6KABaiKCAUIANwMAIANB4KABaiKDAUIANwMAIANB2KABaiKEAUIANwMAIANCADcD0KABIANByKABaiKFAUIANwMAIANBwKABaiKGAUIANwMAIANBuKABaiKHAUIANwMAIANCADcDsKABIANBqKABaiKIAUIANwMAIANBoKABaiKJAUIANwMAIANBmKABaiKKAUIANwMAIANCADcDkKABIANBiKABaiKLAUIANwMAIANBgKABaiKMAUIANwMAIANB+J8BaiKNAUIANwMAIANCADcD8J8BIANB6J8BaiKOAUIANwMAIANB4J8BaiKPAUIANwMAIANB2J8BaiKQAUIANwMAIANCADcD0J8BIANByJ8BaiKRAUIANwMAIANBwJ8BaiKSAUIANwMAIANBuJ8BaiKTAUIANwMAIANCADcDsJ8BIANBqJ8BaiKUAUIANwMAIANBoJ8BaiKVAUIANwMAIANBmJ8BaiKWAUIANwMAIANCADcDkJ8BIANBiJ8BaiKXAUIANwMAIANBgJ8BaiKYAUIANwMAIANB+J4BaiKZAUIANwMAIANCADcD8J4BIANB6J4BaiKaAUIANwMAIANB4J4BaiKbAUIANwMAIANB2J4BaiKcAUIANwMAIANCADcD0J4BIANByJ4BaiKdAUIANwMAIANBwJ4BaiKeAUIANwMAIANBuJ4BaiKfAUIANwMAIANCADcDsJ4BIANBqJ4BaiKgAUIANwMAIANBoJ4BaiKhAUIANwMAIANBmJ4BaiKiAUIANwMAIANCADcDkJ4BIANBiJ4BaiKjAUIANwMAIANBgJ4BaiKkAUIANwMAIANB+J0BaiKlAUIANwMAIANCADcD8J0BIANB6J0BaiKmAUIANwMAIANB4J0BaiKnAUIANwMAIANB2J0BaiKoAUIANwMAIANCADcD0J0BIANByJ0BaiKpAUIANwMAIANBwJ0BaiKqAUIANwMAIANBuJ0BaiKrAUIANwMAIANCADcDsJ0BIANBqJ0BaiKsAUIANwMAIANBoJ0BaiKtAUIANwMAIANBmJ0BaiKuAUIANwMAIANCADcDkJ0BIANBiJ0BaiKvAUIANwMAIANBgJ0BaiKwAUIANwMAIANB+JwBaiKxAUIANwMAIANCADcD8JwBIANB6JwBaiKyAUIANwMAIANB4JwBaiKzAUIANwMAIANB2JwBaiK0AUIANwMAIANCADcD0JwBIANByJwBaiK1AUIANwMAIANBwJwBaiK2AUIANwMAIANBuJwBaiK3AUIANwMAIANCADcDsJwBIANBqJwBaiK4AUIANwMAIANBoJwBaiK5AUIANwMAIANBmJwBaiK6AUIANwMAIANCADcDkJwBIANBiJwBaiK7AUIANwMAIANBgJwBaiK8AUIANwMAIANB+JsBaiK9AUIANwMAIANCADcD8JsBIANB6JsBaiK+AUIANwMAIANB4JsBaiK/AUIANwMAIANB2JsBaiLAAUIANwMAIANCADcD0JsBIANByJsBaiLBAUIANwMAIANBwJsBaiLCAUIANwMAIANBuJsBaiLDAUIANwMAIANCADcDsJsBIANBqJsBaiLEAUIANwMAIANBoJsBaiLFAUIANwMAIANBmJsBaiLGAUIANwMAIANCADcDkJsBIANBiJsBaiLHAUIANwMAIANBgJsBaiLIAUIANwMAIANB+JoBaiLJAUIANwMAIANCADcD8JoBIANCATcDgIUBIANBoIUBakIANwMAIEZCADcDACBHQgA3AwAgA0IANwOIhQEgA0IBNwOohQEgA0HIhQFqQgA3AwAgA0HAhQFqQgA3AwAgA0G4hQFqQgA3AwAgA0IANwOwhQEgA0IBNwPQhQEgA0HwhQFqQgA3AwAgA0HohQFqQgA3AwAgA0HghQFqQgA3AwAgA0IANwPYhQEgA0IBNwP4hQEgA0GYhgFqQgA3AwAgA0GQhgFqQgA3AwAgA0GIhgFqQgA3AwAgA0IANwOAhgEgA0IBNwOghgEgA0HAhgFqQgA3AwAgA0G4hgFqQgA3AwAgA0GwhgFqQgA3AwAgA0IANwOohgEgA0IBNwPIhgEgA0HohgFqQgA3AwAgA0HghgFqQgA3AwAgA0HYhgFqQgA3AwAgA0IANwPQhgEgA0IBNwPwhgEgA0GQhwFqQgA3AwAgA0GIhwFqQgA3AwAgA0GAhwFqQgA3AwAgA0IANwP4hgEgA0IBNwOYhwEgA0G4hwFqQgA3AwAgA0GwhwFqQgA3AwAgA0GohwFqQgA3AwAgA0IANwOghwEgA0IBNwPAhwEgA0HghwFqQgA3AwAgA0HYhwFqQgA3AwAgA0HQhwFqQgA3AwAgA0IANwPIhwEgA0IBNwPohwEgA0GIiAFqQgA3AwAgA0GAiAFqQgA3AwAgA0H4hwFqQgA3AwAgA0IANwPwhwEgA0IBNwOQiAEgA0GwiAFqQgA3AwAgA0GoiAFqQgA3AwAgA0GgiAFqQgA3AwAgA0IANwOYiAEgA0IBNwO4iAEgA0HYiAFqQgA3AwAgA0HQiAFqQgA3AwAgA0HIiAFqQgA3AwAgA0IANwPAiAEgA0IBNwPgiAEgA0GAiQFqQgA3AwAgA0H4iAFqQgA3AwAgA0HwiAFqQgA3AwAgA0IANwPoiAEgA0IBNwOIiQEgA0GoiQFqQgA3AwAgA0GgiQFqQgA3AwAgA0GYiQFqQgA3AwAgA0IANwOQiQEgA0IBNwOwiQEgA0HQiQFqQgA3AwAgA0HIiQFqQgA3AwAgA0HAiQFqQgA3AwAgA0IANwO4iQEgA0IBNwPYiQEgA0H4iQFqQgA3AwAgA0HwiQFqQgA3AwAgA0HoiQFqQgA3AwAgA0IANwPgiQEgA0IBNwOAigEgA0GgigFqQgA3AwAgA0GYigFqQgA3AwAgA0GQigFqQgA3AwAgA0IANwOIigEgA0IBNwOoigEgA0HIigFqQgA3AwAgA0HAigFqQgA3AwAgA0G4igFqQgA3AwAgA0IANwOwigEgA0IBNwPQigEgA0HwigFqQgA3AwAgA0HoigFqQgA3AwAgA0HgigFqQgA3AwAgA0IANwPYigEgA0IBNwP4igEgA0GYiwFqQgA3AwAgA0GQiwFqQgA3AwAgA0GIiwFqQgA3AwAgA0IANwOAiwEgA0IBNwOgiwEgA0HAiwFqQgA3AwAgA0G4iwFqQgA3AwAgA0GwiwFqQgA3AwAgA0IANwOoiwEgA0IBNwPIiwEgA0HoiwFqQgA3AwAgA0HgiwFqQgA3AwAgA0HYiwFqQgA3AwAgA0IANwPQiwEgA0IBNwPwiwEgA0GQjAFqQgA3AwAgA0GIjAFqQgA3AwAgA0GAjAFqQgA3AwAgA0IANwP4iwEgA0IBNwOYjAEgA0G4jAFqQgA3AwAgA0GwjAFqQgA3AwAgA0GojAFqQgA3AwAgA0IANwOgjAEgA0IBNwPAjAEgA0HgjAFqQgA3AwAgA0HYjAFqQgA3AwAgA0HQjAFqQgA3AwAgA0IANwPIjAEgA0IBNwPojAEgA0GIjQFqQgA3AwAgA0GAjQFqQgA3AwAgA0H4jAFqQgA3AwAgA0IANwPwjAEgA0IBNwOQjQEgA0GwjQFqQgA3AwAgA0GojQFqQgA3AwAgA0GgjQFqQgA3AwAgA0IANwOYjQEgA0IBNwO4jQEgA0HYjQFqQgA3AwAgA0HQjQFqQgA3AwAgA0HIjQFqQgA3AwAgA0IANwPAjQEgA0IBNwPgjQEgA0GAjgFqQgA3AwAgA0H4jQFqQgA3AwAgA0HwjQFqQgA3AwAgA0IANwPojQEgA0IBNwOIjgEgA0GojgFqQgA3AwAgA0GgjgFqQgA3AwAgA0GYjgFqQgA3AwAgA0IANwOQjgEgA0IBNwOwjgEgA0HQjgFqICMpAwA3AwAgA0HIjgFqIDMpAwA3AwAgA0HAjgFqIDUpAwA3AwAgAyADKQOwpQE3A7iOASADQgE3A9iOASADQfiOAWogSCkDADcDACADQfCOAWogBSkDADcDACADQeiOAWogHCkDADcDACADIAMpA7CkATcD4I4BIANCATcDgI8BIANBoI8BaiAwKQMANwMAIANBmI8BaiA0KQMANwMAIANBkI8BaiA2KQMANwMAIAMgAykD4MEBNwOIjwEgA0IBNwOojwEgA0HIjwFqIFspAwA3AwAgA0HAjwFqIFwpAwA3AwAgA0G4jwFqIF0pAwA3AwAgAyADKQPwowE3A7CPASADQgE3A9CPASADQfCPAWogXikDADcDACADQeiPAWogXykDADcDACADQeCPAWogYCkDADcDACADIAMpA9CjATcD2I8BIANCATcD+I8BIANBmJABaiBhKQMANwMAIANBkJABaiBiKQMANwMAIANBiJABaiBjKQMANwMAIAMgAykDsKMBNwOAkAEgA0IBNwOgkAEgA0HAkAFqIGQpAwA3AwAgA0G4kAFqIGUpAwA3AwAgA0GwkAFqIGYpAwA3AwAgAyADKQOQowE3A6iQASADQgE3A8iQASADQeiQAWogZykDADcDACADQeCQAWogaCkDADcDACADQdiQAWogaSkDADcDACADIAMpA/CiATcD0JABIANCATcD8JABIANBkJEBaiBqKQMANwMAIANBiJEBaiBrKQMANwMAIANBgJEBaiBsKQMANwMAIAMgAykD0KIBNwP4kAEgA0IBNwOYkQEgA0G4kQFqIG0pAwA3AwAgA0GwkQFqIG4pAwA3AwAgA0GokQFqIG8pAwA3AwAgAyADKQOwogE3A6CRASADQgE3A8CRASADQeCRAWogcCkDADcDACADQdiRAWogcSkDADcDACADQdCRAWogcikDADcDACADIAMpA5CiATcDyJEBIANCATcD6JEBIANBiJIBaiBzKQMANwMAIANBgJIBaiB0KQMANwMAIANB+JEBaiB1KQMANwMAIAMgAykD8KEBNwPwkQEgA0IBNwOQkgEgA0GwkgFqIHYpAwA3AwAgA0GokgFqIHcpAwA3AwAgA0GgkgFqIHgpAwA3AwAgAyADKQPQoQE3A5iSASADQgE3A7iSASADQdiSAWogeSkDADcDACADQdCSAWogeikDADcDACADQciSAWogeykDADcDACADIAMpA7ChATcDwJIBIANCATcD4JIBIANBgJMBaiB8KQMANwMAIANB+JIBaiB9KQMANwMAIANB8JIBaiB+KQMANwMAIAMgAykDkKEBNwPokgEgA0IBNwOIkwEgA0GokwFqIH8pAwA3AwAgA0GgkwFqIIABKQMANwMAIANBmJMBaiCBASkDADcDACADIAMpA/CgATcDkJMBIANCATcDsJMBIANB0JMBaiCCASkDADcDACADQciTAWoggwEpAwA3AwAgA0HAkwFqIIQBKQMANwMAIAMgAykD0KABNwO4kwEgA0IBNwPYkwEgA0H4kwFqIIUBKQMANwMAIANB8JMBaiCGASkDADcDACADQeiTAWoghwEpAwA3AwAgAyADKQOwoAE3A+CTASADQgE3A4CUASADQaCUAWogiAEpAwA3AwAgA0GYlAFqIIkBKQMANwMAIANBkJQBaiCKASkDADcDACADIAMpA5CgATcDiJQBIANCATcDqJQBIANByJQBaiCLASkDADcDACADQcCUAWogjAEpAwA3AwAgA0G4lAFqII0BKQMANwMAIAMgAykD8J8BNwOwlAEgA0IBNwPQlAEgA0HwlAFqII4BKQMANwMAIANB6JQBaiCPASkDADcDACADQeCUAWogkAEpAwA3AwAgAyADKQPQnwE3A9iUASADQgE3A/iUASADQZiVAWogkQEpAwA3AwAgA0GQlQFqIJIBKQMANwMAIANBiJUBaiCTASkDADcDACADIAMpA7CfATcDgJUBIANCATcDoJUBIANBwJUBaiCUASkDADcDACADQbiVAWoglQEpAwA3AwAgA0GwlQFqIJYBKQMANwMAIAMgAykDkJ8BNwOolQEgA0IBNwPIlQEgA0HolQFqIJcBKQMANwMAIANB4JUBaiCYASkDADcDACADQdiVAWogmQEpAwA3AwAgAyADKQPwngE3A9CVASADQgE3A/CVASADQZCWAWogmgEpAwA3AwAgA0GIlgFqIJsBKQMANwMAIANBgJYBaiCcASkDADcDACADIAMpA9CeATcD+JUBIANCATcDmJYBIANBuJYBaiCdASkDADcDACADQbCWAWogngEpAwA3AwAgA0GolgFqIJ8BKQMANwMAIAMgAykDsJ4BNwOglgEgA0IBNwPAlgEgA0HglgFqIKABKQMANwMAIANB2JYBaiChASkDADcDACADQdCWAWogogEpAwA3AwAgAyADKQOQngE3A8iWASADQgE3A+iWASADQYiXAWogowEpAwA3AwAgA0GAlwFqIKQBKQMANwMAIANB+JYBaiClASkDADcDACADIAMpA/CdATcD8JYBIANCATcDkJcBIANBsJcBaiCmASkDADcDACADQaiXAWogpwEpAwA3AwAgA0GglwFqIKgBKQMANwMAIAMgAykD0J0BNwOYlwEgA0IBNwO4lwEgA0HYlwFqIKkBKQMANwMAIANB0JcBaiCqASkDADcDACADQciXAWogqwEpAwA3AwAgAyADKQOwnQE3A8CXASADQgE3A+CXASADQYCYAWogrAEpAwA3AwAgA0H4lwFqIK0BKQMANwMAIANB8JcBaiCuASkDADcDACADIAMpA5CdATcD6JcBIANCATcDiJgBIANBqJgBaiCvASkDADcDACADQaCYAWogsAEpAwA3AwAgA0GYmAFqILEBKQMANwMAIAMgAykD8JwBNwOQmAEgA0IBNwOwmAEgA0HQmAFqILIBKQMANwMAIANByJgBaiCzASkDADcDACADQcCYAWogtAEpAwA3AwAgAyADKQPQnAE3A7iYASADQgE3A9iYASADQfiYAWogtQEpAwA3AwAgA0HwmAFqILYBKQMANwMAIANB6JgBaiC3ASkDADcDACADIAMpA7CcATcD4JgBIANCATcDgJkBIANBoJkBaiC4ASkDADcDACADQZiZAWoguQEpAwA3AwAgA0GQmQFqILoBKQMANwMAIAMgAykDkJwBNwOImQEgA0IBNwOomQEgA0HImQFqILsBKQMANwMAIANBwJkBaiC8ASkDADcDACADQbiZAWogvQEpAwA3AwAgAyADKQPwmwE3A7CZASADQgE3A9CZASADQfCZAWogvgEpAwA3AwAgA0HomQFqIL8BKQMANwMAIANB4JkBaiDAASkDADcDACADIAMpA9CbATcD2JkBIANCATcD+JkBIANBmJoBaiDBASkDADcDACADQZCaAWogwgEpAwA3AwAgA0GImgFqIMMBKQMANwMAIAMgAykDsJsBNwOAmgEgA0IBNwOgmgEgA0HAmgFqIMQBKQMANwMAIANBuJoBaiDFASkDADcDACADQbCaAWogxgEpAwA3AwAgAyADKQOQmwE3A6iaASADQgE3A8iaASADQeiaAWogxwEpAwA3AwAgA0HgmgFqIMgBKQMANwMAIANB2JoBaiDJASkDADcDACADIAMpA/CaATcD0JoBIANBkIEBaiAHKQMYIvQBQgAg6AFCABDJAyADQbCAAWogBykDECL1AUIAIOgBQgAQyQMgA0GggAFqIAcpAwgi9gFCACDoAUIAEMkDIANBkIABaiAHKQMAIvcBQgAg6AFCABDJAyADQYCBAWogAykDkIEBIswBQgBCAEL/////vrL98EIQyQMgA0HwgAFqIAMpA4iBASLKAUIAQoGAgIC/sv3wwwBCABDJAyADQeCAAWogygFCAEKR4eXNh4n6mShCABDJAyADQdCAAWogygFCAELdsIWM6LaRqLh/QgAQyQMgA0HAgAFqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0GAgAFqIPQBQgAg5gFCABDJAyADQaD/AGog9QFCACDmAUIAEMkDIANBkP8AaiD2AUIAIOYBQgAQyQMgA0GA/wBqIPcBQgAg5gFCABDJAyADQfD/AGogAykD4IABItEBIAMpA5iBASLOASADKQOwgAF8ItIBfCLLASADKQP4gAEgzAEgAykD8IABIsoBfCDKAVStfHwizAEgAykDgIABfCLPAUIAQgBC/////76y/fBCEMkDIANB4P8AaiADKQP4fyLKAUIAQoGAgIC/sv3wwwBCABDJAyADQdD/AGogygFCAEKR4eXNh4n6mShCABDJAyADQcD/AGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0Gw/wBqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0Hw/gBqIPQBQgAg4QFCABDJAyADQZD+AGog9QFCACDhAUIAEMkDIANBgP4AaiD2AUIAIOEBQgAQyQMgA0Hw/QBqIPcBQgAg4QFCABDJAyADQeD+AGogAykDiIABIMwBIM8BVq18ItUBIAMpA6B/fCLNASADKQO4gAEgzgEg0gFWrXwi0wEgAykDoIABfCLOASADKQPQgAF8ItIBIMsBIMwBVq0gAykD6IABIMsBINEBVK18fHwi1wF8IssBIAMpA9B/fCLMASADKQPofyDPASADKQPgfyLKAXwgygFUrXx8Is8BIAMpA/B+fCLRAUIAQgBC/////76y/fBCEMkDIANB0P4AaiADKQPofiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQcD+AGogygFCAEKR4eXNh4n6mShCABDJAyADQbD+AGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0Gg/gBqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0Hg/QBqIPQBQgAg6gFCABDJAyADQYD9AGog9QFCACDqAUIAEMkDIANB8PwAaiD2AUIAIOoBQgAQyQMgA0Hg/ABqIPcBQgAg6gFCABDJAyADQdD9AGogAykD+H4gzwEg0QFWrXwi2AEgAykDkH58ItABIAMpA6iAASDOASDTAVStfCLWASADKQOQgAF8ItMBIAMpA8CAAXwi1AEg0gEg1wFWrSADKQPYgAEgzgEg0gFWrXx8fCLOASADKQOQf3wi0gEgywEgzQFUrSADKQOofyDNASDVAVStfHx8Is0BIAMpA8B/fCLVASDMASDPAVatIAMpA9h/IMsBIMwBVq18fHwi1wF8IssBIAMpA8B+fCLMASADKQPYfiDRASADKQPQfiLKAXwgygFUrXx8Is8BIAMpA+B9fCLRAUIAQgBC/////76y/fBCEMkDIANBwP0AaiADKQPYfSLKAUIAQoGAgIC/sv3wwwBCABDJAyADQbD9AGogygFCAEKR4eXNh4n6mShCABDJAyADQaD9AGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GQ/QBqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA5h9IAMpA6h+IAMpA7h/IM4BINQBVK0gAykDyIABINMBINQBVq18fCADKQOYgAEg0wEg1gFUrXx8ItMBIAMpA4B/fCLKASDNASDSAVStIAMpA5h/IM4BINIBVq18fHwizgEgAykDsH98ItIBIM4BVK18INIBINUBINcBVq0gAykDyH8gzQEg1QFWrXx8fCLNASDSAVStfCDKASDOAVatIAMpA4h/IMoBINMBVK18fHwi0wEgAykD8H18IsoBIAMpA4h+IM0BIM0BIAMpA4B+fCLOAVatfCDOASDOASDLASDQAVStIAMpA5h+INABINgBVK18fHwizQFWrXx8Is4BIAMpA6B+fCLSASDOAVStfCDSASDSASADKQO4fiDNASDNASADKQOwfnwi0AFWrXwg0AEgzAEgzwFWrSADKQPIfiDLASDMAVatfHx8Is0BINABVK18fCLLAVatfCDKASDOAVatIAMpA/h9IMoBINMBVK18fHwi0gEgAykD4Hx8IsoBIAMpA/h8IMsBIMsBIAMpA/B8fCLMAVatfCDMASDMASADKQOIfSADKQPofSDPASDRAVatfCLPASADKQOAfXwiywEgzwFUrXwgywEgywEgzQF8Is8BVq18fCLLAVatfHwizAEgAykDkH18Is0BIMwBVK18IM0BIAMpA6h9IMsBIMsBIAMpA6B9fCLOAVatfCDOASADKQO4fSDPASDPASADKQOwfXwiywFWrXwgywEgAykDyH0gAykDwH0izwEg0QF8IM8BVK18fCLnASDLAVStfHwi3AEgzgFUrXx8IusBIM0BVK18IMoBIMwBVq0gAykD6HwgygEg0gFUrXx8fCLsAUKpwMaJrs6TsjBWDQAg6wEhzgEg3AEhywEg5wEhzQEg7AEi0QFCqcDGia7Ok7IwUg0BIM4BQt2whYzotpGouH9WDQBCqcDGia7Ok7IwIdEBAkAgzgFC3bCFjOi2kai4f1EEQCDLAUKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyHOASDLAUKR4eXNh4n6mShRDQELDAILQpHh5c2HifqZKCHLASDnAUKBgICAv7L98MMAVA0BCyDcAUKR4eXNh4n6mSh9IsoBIOcBQoGAgIC/sv3wwwBUrSLMAX0hywEg6wFCo8/685fJ7tfHAHwizwEg3AFCkeHlzYeJ+pkoVCDKASDMAVRyrSLKAX0hzgEg7AEg6wFC3bCFjOi2kai4f1QgygEgzwFWcq19QqnAxomuzpOyMH0h0QEg5wFCgYCAgL+y/fDDAH0hzQELQqnAxomuzpOyMCHPASDOASDjAXwizAEg4wFUIMwBIMsBIOIBfCLLASDiAVQgywEgywEgzQEg3gF8It0BIN4BVK18IsoBVnKtfCLLASDMAVRyrSDRASDgAXx8It8BIdEBAkACQAJAIN8BQqnAxomuzpOyMFINAELdsIWM6LaRqLh/Ic8BIMsBItEBQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIc8BIMoBItEBQpHh5c2HifqZKFINAEKBgICAv7L98MMAIc8BIN0BItEBQoGAgIC/sv3wwwBRDQELIM8BINEBWA0AIMoBIdEBIMsBIc4BDAELIMoBQpHh5c2HifqZKH0izAEg3QFCgYCAgL+y/fDDAFStIs8BfSHRASDLAUKjz/rzl8nu18cAfCLNASDKAUKR4eXNh4n6mShUIMwBIM8BVHKtIsoBfSHOASDfASDLAULdsIWM6LaRqLh/VCDKASDNAVZyrX1CqcDGia7Ok7IwfSHfASDdAUKBgICAv7L98MMAfSHdAQsgAyDdATcDyKUBIAMg0QE3A8ClASADIM4BNwO4pQEgAyDfATcDsKUBAkAgA0GwpQFqQcCWwgBBIBDxA0UEQCDRASHlASDOASHkAQwBC0KR4eXNh4n6mSgg0QF9IsoBIN0BQoGAgIC/sv3wwwBWrSLLAX0h5QFC3bCFjOi2kai4fyDOAX0izAEgygEgywFUINEBQpHh5c2HifqZKFZyrSLKAX0h5AFCqcDGia7Ok7IwIMoBIMwBViDOAULdsIWM6LaRqLh/VnKtIN8BfH0h3wFCgYCAgL+y/fDDACDdAX0h3QELIBBBwJbCAEEgEPEDRQ0CQgAhzgEgA0HwwQFqQgA3AwAgA0HowQFqQgA3AwAgA0IANwPgwQEgA0IBNwP4wQEgA0HIpAFqIBBBGGopAwA3AwAgA0HApAFqIBBBEGopAwA3AwAgA0G4pAFqIBBBCGopAwA3AwAgAyAQKQMANwOwpAEgA0HIpQFqQbiWwgApAwA3AwAgA0HApQFqQbCWwgApAwA3AwAgA0G4pQFqQaiWwgApAwA3AwAgA0GglsIAKQMANwOwpQECQCADQbCkAWogA0HgwQFqQSAQ8QNFBEBCpYm5+peWtIsCIdEBQqfbhfHayLncGyHLAULjs/GantaO/9MAIdYBQoWB7p3V5+CkjH8h1QEMAQtCp9uF8drIudwbIcsBQuOz8Zqe1o7/0wAh1gFChYHundXn4KSMfyHVAUKlibn6l5a0iwIh0QEgAykDyKQBIc0BIAMpA7CkASHMASADKQO4pAEh0gEgAykDwKQBIdMBQgAh2gFCACHbAUIAIc8BQoGAgIC/sv3wwwAhygFCqcDGia7Ok7IwIdgBQt2whYzotpGouH8h0AFCkeHlzYeJ+pkoIdcBA0AgA0GwpQFqIANB4MEBakEgEPEDRQRAINoBIdUBINsBIdYBIM8BIcsBIM4BIdEBDAILIM0Bp0EBcUUEQANAINMBQj+GIM0BQgGIhCHNAQJAIMsBQgGDUARAIMsBIdkBINYBIcsBINUBIdQBDAELINEBINUBINUBQqPP+vOXye7XxwB9Iu0BViDtASDtASDWAUKR4eXNh4n6mSh8ItQBINYBVCDUASDLAUKBgICAv7L98MMAfCLZASDLAVStfCLLASDUAVRyrXwi1AFWcq18QqnAxomuzpOyMHwh0QELIMwBQj+GINIBQj+GINMBQgGIhCHTASDMAUIBiCHMASDRAUI/hiDUAUIBiIQh1QEg1AFCP4YgywFCAYiEIdYBIMsBQj+GINkBQgGIhCHLASDRAUIBiCHRASDSAUIBiIQh0gEgzQFCAYNQDQALIAMg0wE3A8CkASADIM0BNwPIpAEgAyDSATcDuKQBIAMgzAE3A7CkAQsgygGnQQFxRQRAA0Ag1wFCP4YgygFCAYiEIcoBAkAgzwFCAYNQBEAgzwEh2QEg2wEhzwEg2gEh1AEMAQsgzgEg2gEg2gFCo8/685fJ7tfHAH0i7QFWIO0BIO0BINsBQpHh5c2HifqZKHwi1AEg2wFUINQBIM8BQoGAgIC/sv3wwwB8ItkBIM8BVK18Is8BINQBVHKtfCLUAVZyrXxCqcDGia7Ok7IwfCHOAQsg2AFCP4Yg0AFCP4Yg1wFCAYiEIdcBINgBQgGIIdgBIM4BQj+GINQBQgGIhCHaASDUAUI/hiDPAUIBiIQh2wEgzwFCP4Yg2QFCAYiEIc8BIM4BQgGIIc4BINABQgGIhCHQASDKAUIBg1ANAAsgAyDXATcDwKUBIAMgygE3A8ilASADINABNwO4pQEgAyDYATcDsKUBCyDMASHZAQJAAkACQAJAAkAgzAEg2AEi1AFSDQAg0gEh2QEg0AEi1AEg0gFSDQAg0wEh2QEg0wEg1wEi1AFSDQAgygEh1AEgzQEh2QEgygEgzQFRDQELINQBINkBWA0AIAMgygEgzQF9ItQBNwPIpQEgAyDXASDTAX0i7QEgygEgzQFUrSLKAX0i2QE3A8ClASADINABINIBfSLpASDKASDtAVYg0wEg1wFWcq0iygF9Iu0BNwO4pQEgAyDYASDMAX0g0AEg0gFUIMoBIOkBVnKtfSLYATcDsKUBAkACQCDOASLKASDRASLQAVINACDVASLQASDaASLKAVINACDWASLQASDbASLKAVINACDLASHQASDPASLKASDLAVENAQsgygEg0AFUDQILIM4BINEBfSDaASDVAX0i6QEg2wEg1gF9IvEBIMsBIM8BVq0i8gFUINYBINsBVnKtIvMBVCDVASDaAVZyrX0hzgEgzwEgywF9Ic8BINkBIdcBIO0BIdABINQBIcoBIPEBIPIBfSHbASDpASDzAX0h2gEMAwsgAyDNASDKAX0i1AE3A8ikASADINMBINcBfSLtASDKASDNAVatIs0BfSLZATcDwKQBIAMg0gEg0AF9IukBINMBINcBVCDNASDtAVZyrSLNAX0i7QE3A7ikASADIMwBINgBfSDNASDpAVYg0AEg0gFWcq19IswBNwOwpAEgzgEh0gECQAJAINEBIs0BIM4BUg0AINUBIs0BINoBItIBUg0AINYBIs0BINsBItIBUg0AIMsBIc0BIM8BIdIBIMsBIM8BUQ0BCyDNASDSAVQNAgsg0QEgzgF9INUBINoBVCDVASDaAX0i1QEg1gEg2wFUINYBINsBfSLWASDLASDPAVStIukBVHKtIvEBVHKtfSHRASDLASDPAX0hywEg2QEh0wEg7QEh0gEg1AEhzQEg1gEg6QF9IdYBINUBIPEBfSHVAQwCCyDOAULdsIWM6LaRqLh/INUBfSLKAUKR4eXNh4n6mSgg1gF9Is4BIMsBQoGAgIC/sv3wwwBWrSLQAVQg1gFCkeHlzYeJ+pkoVnKtItcBVCDVAULdsIWM6LaRqLh/VnKtINEBfH0gygEg1wF9ItcBINoBfCLKASDXAVQgygEgzgEg0AF9ItABINsBfCLOASDQAVQgzgFCgYCAgL+y/fDDACDLAX0i0AEgzwF8Is8BINABVK18ItsBIM4BVHKtfCLaASDKAVRyrXxCqcDGia7Ok7IwfCHOASDZASHXASDtASHQASDUASHKAQwBCyDRASDOAX1C3bCFjOi2kai4fyDaAX0izQFCkeHlzYeJ+pkoINsBfSLSASDPAUKBgICAv7L98MMAVq0i0QFUINsBQpHh5c2HifqZKFZyrSLTAVQg2gFC3bCFjOi2kai4f1ZyrX0gzQEg0wF9ItMBINUBfCLNASDTAVQgzQEg0gEg0QF9ItEBINYBfCLSASDRAVQg0gFCgYCAgL+y/fDDACDPAX0i0QEgywF8IssBINEBVK18ItYBINIBVHKtfCLVASDNAVRyrXxCqcDGia7Ok7IwfCHRASDZASHTASDtASHSASDUASHNAQsgA0GwpAFqIANB4MEBakEgEPEDDQALCwJAAkAg7AFCqcDGia7Ok7IwVg0AAkAg7AFCqcDGia7Ok7IwUQRAIOsBQt2whYzotpGouH9WDQIg6wFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh7AELIOsBIc0BINwBIc4BDAILINwBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/Ic0BINwBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh7AEg3AEhzgEMAgtCkeHlzYeJ+pkoIc4BIOcBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIewBDAELINwBQpHh5c2HifqZKH0iygEg5wFCgYCAgL+y/fDDAFStIswBfSHOASDrAUKjz/rzl8nu18cAfCLPASDcAUKR4eXNh4n6mShUIMoBIMwBVHKtIsoBfSHNASDsASDrAULdsIWM6LaRqLh/VCDKASDPAVZyrX1CqcDGia7Ok7IwfSHsASDnAUKBgICAv7L98MMAfSHnAQsgA0HQ/ABqAn4CQAJAIOABIsoBIOwBIs8BUg0AIM0BIs8BIOMBIsoBUg0AIM4BIs8BIOIBIsoBUg0AIN4BIsoBIOcBIs8BUQ0BCyDKASDPAVoNAELdsIWM6LaRqLh/IM0BIOMBfSLKASDOASDiAVQgzgEg4gF9IswBIN4BIOcBVq0izwFUcq0i0gF9ItABfSLTASDMASDPAX0izAFCkeHlzYeJ+pkoVkKR4eXNh4n6mSggzAF9IswBIOcBIN4BfSLUAUKBgICAv7L98MMAVq0izwFUcq0i1wF9Ic4BINMBINcBVCDQAULdsIWM6LaRqLh/VnIhBSDMASDPAX0hzwEgzQEg4wFUIMoBINIBVHKtIOABIOwBfXxCqcDGia7Ok7IwfCHaAUKBgICAv7L98MMAINQBfQwBCyDiASDOAX0iygEg3gEg5wFUrSLMAX0hzwEg4wEgzQF9ItIBIMoBIMwBVCDOASDiAVZyrSLKAX0hzgEgygEg0gFWIM0BIOMBVnIhBSDgASDsAX0h2gEg3gEg5wF9CyLKAUIAIMsBQgAQyQMgA0Hg+wBqIMoBQgAg1gFCABDJAyADQcD7AGogygFCACDVAUIAEMkDIANBoPsAaiDKAUIAINEBQgAQyQMgA0HA/ABqIAMpA9B8Is0BQgBCAEL/////vrL98EIQyQMgA0Gw/ABqIAMpA8h8IsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBoPwAaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBkPwAaiDKAUIAQt2whYzotpGouH9CABDJAyADQYD8AGogygFCAEKpwMaJrs6TsjBCABDJAyADQYD7AGogzwFCACDLAUIAEMkDIANBoPoAaiDPAUIAINYBQgAQyQMgA0GQ+gBqIM8BQgAg1QFCABDJAyADQYD6AGogzwFCACDRAUIAEMkDIANB8PoAaiADKQOgfCLTASADKQPYfCLSASADKQPge3wi0AF8IswBIAMpA7h8IM0BIAMpA7B8IsoBfCDKAVStfHwizwEgAykDgHt8Is0BQgBCAEL/////vrL98EIQyQMgA0Hg+gBqIAMpA/h6IsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB0PoAaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBwPoAaiDKAUIAQt2whYzotpGouH9CABDJAyADQbD6AGogygFCAEKpwMaJrs6TsjBCABDJAyADQfD5AGogzgFCACDLAUIAEMkDIANBkPkAaiDOAUIAINYBQgAQyQMgA0Gw+ABqIM4BQgAg1QFCABDJAyADQaD4AGogzgFCACDRAUIAEMkDIANB4PkAaiADKQOIeyDNASDPAVStfCLXASADKQOgenwizgEgAykD6Hsg0AEg0gFUrXwi1AEgAykDwHt8ItIBIAMpA5B8fCLQASDMASDPAVatIAMpA6h8IMwBINMBVK18fHwi2AF8IswBIAMpA9B6fCLPASADKQPoeiDNASADKQPgeiLKAXwgygFUrXx8Is0BIAMpA/B5fCLTAUIAQgBC/////76y/fBCEMkDIANB0PkAaiADKQPoeSLKAUIAQoGAgIC/sv3wwwBCABDJAyADQcD5AGogygFCAEKR4eXNh4n6mShCABDJAyADQbD5AGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0Gg+QBqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0Hw+wBqINoBIAWtfSLKAUIAIMsBQgAQyQMgA0HQ+wBqIMoBQgAg1gFCABDJAyADQbD7AGogygFCACDVAUIAEMkDIANBkPsAaiDKAUIAINEBQgAQyQMgA0GA+QBqIAMpA/h5IM0BINMBVq18ItYBIAMpA5B5fCLLASADKQPIeyDSASDUAVStfCLaASADKQOge3wi0QEgAykDgHx8ItQBINABINgBVq0gAykDmHwg0AEg0gFUrXx8fCLSASADKQOQenwi0AEgzAEgzgFUrSADKQOoeiDOASDXAVStfHx8Is4BIAMpA8B6fCLVASDNASDPAVStIAMpA9h6IMwBIM8BVq18fHwi1wF8IswBIAMpA8B5fCLPASADKQPYeSDTASADKQPQeSLKAXwgygFUrXx8Is0BIAMpA/B7fCLTAUIAQgBC/////76y/fBCEMkDIANB8PgAaiADKQOIeSLKAUIAQoGAgIC/sv3wwwBCABDJAyADQeD4AGogygFCAEKR4eXNh4n6mShCABDJAyADQdD4AGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0HA+ABqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA8h4IAMpA6h5IAMpA7h6INIBINQBVK0gAykDiHwg0QEg1AFWrXx8IAMpA6h7INEBINoBVK18fCLUASADKQOAenwiygEgzgEg0AFUrSADKQOYeiDQASDSAVStfHx8ItIBIAMpA7B6fCLRASDSAVStfCDRASDVASDXAVatIAMpA8h6IM4BINUBVq18fHwizgEg0QFUrXwgygEg0gFWrSADKQOIeiDKASDUAVStfHx8ItABIAMpA6B4fCLKASADKQO4eCDOASDOASADKQOweHwi0gFWrXwg0gEg0gEgywEgzAFWrSADKQOYeSDLASDWAVStfHx8IssBVq18fCLOASADKQOgeXwi0gEgzgFUrXwg0gEgAykDuHkgywEgywEgAykDsHl8ItEBVq18INEBINEBIM0BIM8BVK0gAykDyHkgzAEgzwFWrXx8fCLPAVatfHwiywEg0gFUrXwgygEgzgFWrSADKQOoeCDKASDQAVStfHx8ItEBIAMpA5B7fCLMASADKQO4eyDLASADKQOwe3wiygEgywFUrXwgygEgygEgAykD2HsgAykD+HsgzQEg0wFWrXwizQEgAykD0Ht8IssBIM0BVK18IMsBIMsBIM8BfCLPAVatfHwiywFWrXx8Is0BIAMpA8B4fCLOASDNAVStfCDOASADKQPYeCDLASDLASADKQPQeHwi0gFWrXwg0gEg0gEgAykD6HggzwEgzwEgAykD4Hh8IsoBVq18IMoBIAMpA/h4IAMpA/B4IssBINMBfCDLAVStfHwi1QEgygFUrXx8IsoBVq18fCLLASDOAVStfCDMASDNAVatIAMpA5h7IMwBINEBVK18fHwi2gFCqcDGia7Ok7IwVg0AAkAg2gFCqcDGia7Ok7IwUQRAIMsBQt2whYzotpGouH9WDQIgywFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh2gELIMsBIdEBIMoBIc4BDAILIMoBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IdEBIMoBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh2gEgygEhzgEMAgtCkeHlzYeJ+pkoIc4BINUBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdoBDAELIMoBQpHh5c2HifqZKH0izAEg1QFCgYCAgL+y/fDDAFStIs8BfSHOASDLAUKjz/rzl8nu18cAfCLNASDKAUKR4eXNh4n6mShUIMwBIM8BVHKtIsoBfSHRASDaASDLAULdsIWM6LaRqLh/VCDKASDNAVZyrX1CqcDGia7Ok7IwfSHaASDVAUKBgICAv7L98MMAfSHVAQsgAyDVATcDiKQBIAMgzgE3A4CkASADINEBNwP4owEgAyDaATcD8KMBAkAgA0HwowFqQcCWwgBBIBDxA0UEQCDOASHrASDRASHsAQwBC0KR4eXNh4n6mSggzgF9IsoBINUBQoGAgIC/sv3wwwBWrSLLAX0h6wFC3bCFjOi2kai4fyDRAX0izAEgygEgywFUIM4BQpHh5c2HifqZKFZyrSLKAX0h7AFCqcDGia7Ok7IwIMoBIMwBViDRAULdsIWM6LaRqLh/VnKtINoBfH0h2gFCgYCAgL+y/fDDACDVAX0h1QELQQAhByAKQaiswgApAwA3AwAgCkEIakGwrMIAKQMANwMAIApBEGpBuKzCACkDADcDACAKQRhqQcCswgApAwA3AwAgA0IBNwOAhQEgDSkDACHNASANKQMIIdIBIA0pAxAhzAEgDSkDGCHKASAXKQMAIdcBIBcpAwgh2AEgFykDECHnASAXKQMYIe0BIAMg3QE3A8iFASADIOUBNwPAhQEgAyDkATcDuIUBIAMg3wE3A7CFASADQgE3A6iFAUEBIQUgDCEKIO0BIdEBIOcBIcsBINgBIc8BINcBIc4BA0AgBSENIANBkPgAaiDRAUIAIN0BQgAQyQMgA0Gw9wBqINEBQgAg5QFCABDJAyADQaD3AGog0QFCACDkAUIAEMkDIANBkPcAaiDRAUIAIN8BQgAQyQMgA0GA+ABqIAMpA5B4ItQBQgBCAEL/////vrL98EIQyQMgA0Hw9wBqIAMpA4h4ItABQgBCgYCAgL+y/fDDAEIAEMkDIANB4PcAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB0PcAaiDQAUIAQt2whYzotpGouH9CABDJAyADQcD3AGog0AFCAEKpwMaJrs6TsjBCABDJAyADQYD3AGogywFCACDdAUIAEMkDIANBoPYAaiDLAUIAIOUBQgAQyQMgA0GQ9gBqIMsBQgAg5AFCABDJAyADQYD2AGogywFCACDfAUIAEMkDIANB8PYAaiADKQPgdyLpASADKQOYeCLbASADKQOwd3wi3AF8ItMBIAMpA/h3INQBIAMpA/B3ItABfCDQAVStfHwi1AEgAykDgHd8ItYBQgBCAEL/////vrL98EIQyQMgA0Hg9gBqIAMpA/h2ItABQgBCgYCAgL+y/fDDAEIAEMkDIANB0PYAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANBwPYAaiDQAUIAQt2whYzotpGouH9CABDJAyADQbD2AGog0AFCAEKpwMaJrs6TsjBCABDJAyADQfD1AGogzwFCACDdAUIAEMkDIANBkPUAaiDPAUIAIOUBQgAQyQMgA0GA9QBqIM8BQgAg5AFCABDJAyADQfD0AGogzwFCACDfAUIAEMkDIANB4PUAaiADKQOIdyDUASDWAVatfCL5ASADKQOgdnwi2QEgAykDuHcg2wEg3AFWrXwi8gEgAykDoHd8ItsBIAMpA9B3fCLcASDTASDUAVatIAMpA+h3INMBIOkBVK18fHwi+gF8ItMBIAMpA9B2fCLUASADKQPodiDWASADKQPgdiLQAXwg0AFUrXx8ItYBIAMpA/B1fCLpAUIAQgBC/////76y/fBCEMkDIANB0PUAaiADKQPodSLQAUIAQoGAgIC/sv3wwwBCABDJAyADQcD1AGog0AFCAEKR4eXNh4n6mShCABDJAyADQbD1AGog0AFCAELdsIWM6LaRqLh/QgAQyQMgA0Gg9QBqINABQgBCqcDGia7Ok7IwQgAQyQMgA0Hg9ABqIM4BQgAg3QFCABDJAyADQYD0AGogzgFCACDlAUIAEMkDIANB8PMAaiDOAUIAIOQBQgAQyQMgA0Hg8wBqIM4BQgAg3wFCABDJAyADQdD0AGogAykD+HUg1gEg6QFWrXwi+wEgAykDkHV8IvEBIAMpA6h3INsBIPIBVK18IvwBIAMpA5B3fCLyASADKQPAd3wi8wEg3AEg+gFWrSADKQPYdyDbASDcAVatfHx8ItsBIAMpA5B2fCLcASDTASDZAVStIAMpA6h2INkBIPkBVK18fHwi2QEgAykDwHZ8IvkBINQBINYBVq0gAykD2HYg0wEg1AFWrXx8fCL6AXwi0wEgAykDwHV8ItQBIAMpA9h1IOkBIAMpA9B1ItABfCDQAVStfHwi1gEgAykD4HR8IukBQgBCAEL/////vrL98EIQyQMgA0HA9ABqIAMpA9h0ItABQgBCgYCAgL+y/fDDAEIAEMkDIANBsPQAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANBoPQAaiDQAUIAQt2whYzotpGouH9CABDJAyADQZD0AGog0AFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDmHQgAykDqHUgAykDuHYg2wEg8wFUrSADKQPIdyDyASDzAVatfHwgAykDmHcg8gEg/AFUrXx8IvIBIAMpA4B2fCLQASDZASDcAVStIAMpA5h2INsBINwBVq18fHwi2wEgAykDsHZ8ItwBINsBVK18INwBIPkBIPoBVq0gAykDyHYg2QEg+QFWrXx8fCLZASDcAVStfCDQASDbAVatIAMpA4h2INABIPIBVK18fHwi8gEgAykD8HR8ItABIAMpA4h1INkBINkBIAMpA4B1fCLbAVatfCDbASDbASDTASDxAVStIAMpA5h1IPEBIPsBVK18fHwi2QFWrXx8ItsBIAMpA6B1fCLcASDbAVStfCDcASDcASADKQO4dSDZASDZASADKQOwdXwi8QFWrXwg8QEg8QEg1AEg1gFWrSADKQPIdSDTASDUAVatfHx8ItQBVq18fCLTAVatfCDQASDbAVatIAMpA/h0INABIPIBVK18fHwi8QEgAykD4HN8ItkBIAMpA/hzINMBIAMpA/BzfCLQASDTAVStfCDQASDQASADKQOIdCADKQPodCDWASDpAVatfCLWASADKQOAdHwi0wEg1gFUrXwg0wEg0wEg1AF8ItQBVq18fCLTAVatfHwi1gEgAykDkHR8ItsBINYBVK18INsBIAMpA6h0INMBINMBIAMpA6B0fCLcAVatfCDcASDcASADKQO4dCDUASDUASADKQOwdHwi0AFWrXwg0AEg0AEgAykDyHQgAykDwHQi0wEg6QF8INMBVK18fCLUAVatfHwi0AFWrXx8ItMBINsBVK18INYBINkBVK0gAykD6HMg2QEg8QFUrXx8fCLWAUKpwMaJrs6TsjBWDQACQCDWAUKpwMaJrs6TsjBRBEAg0wFC3bCFjOi2kai4f1YNAiDTAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHWAQsg0wEh2QEg0AEh3AEMAgsg0AFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h2QEg0AFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHWASDQASHcAQwCC0KR4eXNh4n6mSgh3AEg1AFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh1gEMAQsg0AFCkeHlzYeJ+pkofSLZASDUAUKBgICAv7L98MMAVK0i2wF9IdwBINMBQqPP+vOXye7XxwB8IukBINABQpHh5c2HifqZKFQg2QEg2wFUcq0i0AF9IdkBINYBINMBQt2whYzotpGouH9UINABIOkBVnKtfUKpwMaJrs6TsjB9IdYBINQBQoGAgIC/sv3wwwB9IdQBCyADQYCFAWogB2oiBUHwAGog1AE3AwAgBUHoAGog3AE3AwAgBUHgAGog2QE3AwAgBUHYAGog1gE3AwAgBUHQAGpCATcDACADQdDyAGogCkEYaikDACLQAUIAINEBQgAQyQMgA0GQ8wBqIApBEGopAwAi0wFCACDRAUIAEMkDIANB0PMAaiAKQQhqKQMAItQBQgAg0QFCABDJAyADQaDwAGogCikDACLWAUIAINEBQgAQyQMgA0HA8gBqIAMpA9ByItwBQgBCAEL/////vrL98EIQyQMgA0Gw8gBqIAMpA8hyItkBQgBCgYCAgL+y/fDDAEIAEMkDIANBoPIAaiDZAUIAQpHh5c2HifqZKEIAEMkDIANBkPIAaiDZAUIAQt2whYzotpGouH9CABDJAyADQYDyAGog2QFCAEKpwMaJrs6TsjBCABDJAyADQfDxAGog0AFCACDLAUIAEMkDIANBgPMAaiDTAUIAIMsBQgAQyQMgA0HA8wBqINQBQgAgywFCABDJAyADQcDvAGog1gFCACDLAUIAEMkDIANB4PEAaiADKQOgciL5ASADKQPYciLyASADKQOQc3wi8wF8ItsBIAMpA7hyINwBIAMpA7ByItkBfCDZAVStfHwi3AEgAykD8HF8IukBQgBCAEL/////vrL98EIQyQMgA0HQ8QBqIAMpA+hxItkBQgBCgYCAgL+y/fDDAEIAEMkDIANBwPEAaiDZAUIAQpHh5c2HifqZKEIAEMkDIANBsPEAaiDZAUIAQt2whYzotpGouH9CABDJAyADQaDxAGog2QFCAEKpwMaJrs6TsjBCABDJAyADQZDxAGog0AFCACDPAUIAEMkDIANB8PIAaiDTAUIAIM8BQgAQyQMgA0Gw8wBqINQBQgAgzwFCABDJAyADQbDvAGog1gFCACDPAUIAEMkDIANBgPEAaiADKQP4cSDcASDpAVatfCL6ASADKQOAc3wi8QEgAykDmHMg8gEg8wFWrXwi+wEgAykD0HN8IvIBIAMpA5ByfCLzASDbASDcAVatIAMpA6hyINsBIPkBVK18fHwi/AF8ItsBIAMpA8BxfCLcASADKQPYcSDpASADKQPQcSLZAXwg2QFUrXx8IukBIAMpA5BxfCL5AUIAQgBC/////76y/fBCEMkDIANB8PAAaiADKQOIcSLZAUIAQoGAgIC/sv3wwwBCABDJAyADQeDwAGog2QFCAEKR4eXNh4n6mShCABDJAyADQdDwAGog2QFCAELdsIWM6LaRqLh/QgAQyQMgA0HA8ABqINkBQgBCqcDGia7Ok7IwQgAQyQMgA0Gw8ABqINABQgAgzgFCABDJAyADQeDyAGog0wFCACDOAUIAEMkDIANBoPMAaiDUAUIAIM4BQgAQyQMgA0Gg7wBqINYBQgAgzgFCABDJAyADQZDwAGogAykDmHEg6QEg+QFWrXwi/QEgAykD8HJ8ItMBIAMpA9hzIPIBIPsBVK18IvsBIAMpA6BwfCLUASADKQOAcnwi1gEg8wEg/AFWrSADKQOYciDyASDzAVatfHx8ItkBIAMpA8BzfCLyASDbASDxAVStIAMpA4hzIPEBIPoBVK18fHwi8QEgAykDsHF8IvMBINwBIOkBVq0gAykDyHEg2wEg3AFWrXx8fCL6AXwi2wEgAykD4HB8ItwBIAMpA/hwIPkBIAMpA/BwItABfCDQAVStfHwi6QEgAykDsHB8IvkBQgBCAEL/////vrL98EIQyQMgA0GA8ABqIAMpA5hwItABQgBCgYCAgL+y/fDDAEIAEMkDIANB8O8AaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB4O8AaiDQAUIAQt2whYzotpGouH9CABDJAyADQdDvAGog0AFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD2G8gAykDyHAgAykDqHEg1gEg2QFWrSADKQOIciDUASDWAVatfHwgAykDqHAg1AEg+wFUrXx8IvsBIAMpA8BvfCLQASDxASDyAVStIAMpA8hzINkBIPIBVq18fHwi1AEgAykDoHF8ItYBINQBVK18INYBINYBIPMBIPoBVq0gAykDuHEg8QEg8wFWrXx8fCLZAVatfCDQASDUAVatIAMpA8hvINABIPsBVK18fHwi8QEgAykDsG98ItABIAMpA7hzINkBINkBIAMpA7BzfCLUAVatfCDUASDUASDTASDbAVatIAMpA/hyINMBIP0BVK18fHwi0wFWrXx8ItQBIAMpA8BwfCLWASDUAVStfCDWASDWASADKQPYcCDTASDTASADKQPQcHwi2QFWrXwg2QEg2QEg3AEg6QFWrSADKQPocCDbASDcAVatfHx8ItsBVq18fCLTAVatfCDQASDUAVatIAMpA7hvINABIPEBVK18fHwi8QEgAykDoG98ItYBIAMpA6hzINMBIAMpA6BzfCLQASDTAVStfCDQASDQASADKQPociADKQO4cCDpASD5AVatfCLUASADKQPgcnwi0wEg1AFUrXwg0wEg0wEg2wF8ItQBVq18fCLTAVatfHwi2QEgAykD0G98ItsBINkBVK18INsBIAMpA+hvINMBINMBIAMpA+BvfCLcAVatfCDcASDcASADKQP4byDUASDUASADKQPwb3wi0AFWrXwg0AEg0AEgAykDiHAgAykDgHAi0wEg+QF8INMBVK18fCLUAVatfHwi0AFWrXx8ItMBINsBVK18INYBINkBVq0gAykDqG8g1gEg8QFUrXx8fCLWAUKpwMaJrs6TsjBWDQACQCDWAUKpwMaJrs6TsjBRBEAg0wFC3bCFjOi2kai4f1YNAiDTAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHWAQsg0wEh2QEg0AEh3AEMAgsg0AFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h2QEg0AFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHWASDQASHcAQwCC0KR4eXNh4n6mSgh3AEg1AFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh1gEMAQsg0AFCkeHlzYeJ+pkofSLZASDUAUKBgICAv7L98MMAVK0i2wF9IdwBINMBQqPP+vOXye7XxwB8IukBINABQpHh5c2HifqZKFQg2QEg2wFUcq0i0AF9IdkBINYBINMBQt2whYzotpGouH9UINABIOkBVnKtfUKpwMaJrs6TsjB9IdYBINQBQoGAgIC/sv3wwwB9IdQBC0KpwMaJrs6TsjAh2wEg0gEg2QF8ItIBINkBVCDSASDMASDcAXwizAEg3AFUIMwBIMoBINQBfCLKASDUAVStfCLQASDMAVRyrXwi0wEg0gFUcq0gzQEg1gF8fCLNASHSAQJAAkACQCDNAUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyHbASDTASLSAULdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCHbASDQASLSAUKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACHbASDKASHSASDKAUKBgICAv7L98MMAUQ0BCyDSASDbAVoNACDTASHSASDQASHMAQwBCyDQAUKR4eXNh4n6mSh9ItIBIMoBQoGAgIC/sv3wwwBUrSLUAX0hzAEg0wFCo8/685fJ7tfHAHwi1gEg0AFCkeHlzYeJ+pkoVCDSASDUAVRyrSLQAX0h0gEgzQEg0wFC3bCFjOi2kai4f1Qg0AEg1gFWcq19QqnAxomuzpOyMH0hzQEgygFCgYCAgL+y/fDDAH0hygELIANB0O0AaiDRAUIAIO0BQgAQyQMgA0GQ7gBqINEBQgAg5wFCABDJAyADQdDuAGog0QFCACDYAUIAEMkDIANBkO8AaiDRAUIAINcBQgAQyQMgA0HA7QBqIAMpA9BtItABQgBCAEL/////vrL98EIQyQMgA0Gw7QBqIAMpA8htItEBQgBCgYCAgL+y/fDDAEIAEMkDIANBoO0AaiDRAUIAQpHh5c2HifqZKEIAEMkDIANBkO0AaiDRAUIAQt2whYzotpGouH9CABDJAyADQYDtAGog0QFCAEKpwMaJrs6TsjBCABDJAyADQfDsAGogywFCACDtAUIAEMkDIANBgO4AaiDLAUIAIOcBQgAQyQMgA0HA7gBqIMsBQgAg2AFCABDJAyADQYDvAGogywFCACDXAUIAEMkDIANB4OwAaiADKQOgbSLZASADKQPYbSLUASADKQOQbnwi1gF8ItEBIAMpA7htINABIAMpA7BtIssBfCDLAVStfHwi0AEgAykD8Gx8ItMBQgBCAEL/////vrL98EIQyQMgA0HQ7ABqIAMpA+hsIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBwOwAaiDLAUIAQpHh5c2HifqZKEIAEMkDIANBsOwAaiDLAUIAQt2whYzotpGouH9CABDJAyADQaDsAGogywFCAEKpwMaJrs6TsjBCABDJAyADQZDsAGogzwFCACDtAUIAEMkDIANB8O0AaiDPAUIAIOcBQgAQyQMgA0Gw7gBqIM8BQgAg2AFCABDJAyADQfDuAGogzwFCACDXAUIAEMkDIANBgOwAaiADKQP4bCDQASDTAVatfCLpASADKQOAbnwizwEgAykDmG4g1AEg1gFWrXwi2wEgAykD0G58ItQBIAMpA5BtfCLWASDQASDRAVStIAMpA6htINEBINkBVK18fHwi8QF8ItEBIAMpA8BsfCLQASADKQPYbCDTASADKQPQbCLLAXwgywFUrXx8ItMBIAMpA5BsfCLZAUIAQgBC/////76y/fBCEMkDIANB8OsAaiADKQOIbCLLAUIAQoGAgIC/sv3wwwBCABDJAyADQeDrAGogywFCAEKR4eXNh4n6mShCABDJAyADQdDrAGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0HA6wBqIMsBQgBCqcDGia7Ok7IwQgAQyQMgA0Gw6wBqIM4BQgAg7QFCABDJAyADQeDtAGogzgFCACDnAUIAEMkDIANBoO4AaiDOAUIAINgBQgAQyQMgA0Hg7gBqIM4BQgAg1wFCABDJAyADQaDrAGogAykDmGwg0wEg2QFWrXwi8gEgAykD8G18Is4BIAMpA9huINQBINsBVK18IvMBIAMpA5BvfCLbASADKQOAbXwi3AEg1gEg8QFWrSADKQOYbSDUASDWAVatfHx8ItQBIAMpA8BufCLWASDPASDRAVatIAMpA4huIM8BIOkBVK18fHwizwEgAykDsGx8IukBINABINMBVq0gAykDyGwg0AEg0QFUrXx8fCLxAXwi0QEgAykD4Gt8ItABIAMpA/hrINkBIAMpA/BrIssBfCDLAVStfHwi0wEgAykDsGt8ItkBQgBCAEL/////vrL98EIQyQMgA0GQ6wBqIAMpA6hrIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBgOsAaiDLAUIAQpHh5c2HifqZKEIAEMkDIANB8OoAaiDLAUIAQt2whYzotpGouH9CABDJAyADQeDqAGogywFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD6GogAykDyGsgAykDqGwg1AEg3AFUrSADKQOIbSDbASDcAVatfHwgAykDmG8g2wEg8wFUrXx8ItsBIAMpA4BvfCLLASDPASDWAVStIAMpA8huINQBINYBVq18fHwi1AEgAykDoGx8ItYBINQBVK18INYBIOkBIPEBVq0gAykDuGwgzwEg6QFWrXx8fCLPASDWAVStfCDLASDUAVatIAMpA4hvIMsBINsBVK18fHwi2wEgAykD8G58IssBIAMpA7huIM8BIM8BIAMpA7BufCLUAVatfCDUASDUASDOASDRAVatIAMpA/htIM4BIPIBVK18fHwizwFWrXx8Is4BIAMpA8BrfCLUASDOAVStfCDUASDUASADKQPYayDPASDPASADKQPQa3wi1gFWrXwg1gEg0AEg0wFWrSADKQPoayDQASDRAVStfHx8ItEBINYBVK18fCLPAVatfCDLASDOAVatIAMpA/huIMsBINsBVK18fHwi1gEgAykD4G58IssBIAMpA6huIM8BIM8BIAMpA6BufCLOAVatfCDOASDOASADKQPobSADKQO4ayDTASDZAVatfCLQASADKQPgbXwizwEg0AFUrXwgzwEgzwEg0QF8ItEBVq18fCLPAVatfHwizgEgAykD4Gp8ItQBIM4BVK18INQBINQBIAMpA/hqIM8BIM8BIAMpA/BqfCLTAVatfCDTASDTASADKQOIayDRASDRASADKQOAa3wizwFWrXwgzwEgzwEgAykDmGsgAykDkGsi0QEg2QF8INEBVK18fCLRAVatfHwi0AFWrXx8ItMBVq18IMsBIM4BVq0gAykD6G4gywEg1gFUrXx8fCLOAUKpwMaJrs6TsjBWDQACQCDOAUKpwMaJrs6TsjBRBEAg0wFC3bCFjOi2kai4f1YNAiDTAULdsIWM6LaRqLh/UgRAINABIcsBINMBIc8BQqnAxomuzpOyMCHOAQwECyDQAUKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyHPASDQAUKR4eXNh4n6mShRDQEg0AEhywFCqcDGia7Ok7IwIc4BDAMLINABIcsBINMBIc8BDAILQpHh5c2HifqZKCHLASDRAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHOAQwBCyDQAUKR4eXNh4n6mSh9Is8BINEBQoGAgIC/sv3wwwBUrSLUAX0hywEg0wFCo8/685fJ7tfHAHwi1gEg0AFCkeHlzYeJ+pkoVCDPASDUAVRyrSLQAX0hzwEgzgEg0wFC3bCFjOi2kai4f1Qg0AEg1gFWcq19QqnAxomuzpOyMH0hzgEg0QFCgYCAgL+y/fDDAH0h0QELIA1BAWohBSAHQShqIQcgCkEgaiEKIA1BJEkNAAsgDEGYCWohCkEAIQdBASEFA0AgBSEMAkACQCADQYCFAWogB2oiBUGwCWoiDSgCAEEBcQRAIANB0OoAaiDRAUIAINUBQgAQyQMgA0Hw6QBqINEBQgAg6wFCABDJAyADQeDpAGog0QFCACDsAUIAEMkDIANB0OkAaiDRAUIAINoBQgAQyQMgA0HA6gBqIAMpA9BqItQBQgBCAEL/////vrL98EIQyQMgA0Gw6gBqIAMpA8hqItABQgBCgYCAgL+y/fDDAEIAEMkDIANBoOoAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANBkOoAaiDQAUIAQt2whYzotpGouH9CABDJAyADQYDqAGog0AFCAEKpwMaJrs6TsjBCABDJAyADQcDpAGogywFCACDVAUIAEMkDIANB4OgAaiDLAUIAIOsBQgAQyQMgA0HQ6ABqIMsBQgAg7AFCABDJAyADQcDoAGogywFCACDaAUIAEMkDIANBsOkAaiADKQOgaiLdASADKQPYaiLbASADKQPwaXwi3AF8ItMBIAMpA7hqINQBIAMpA7BqItABfCDQAVStfHwi1AEgAykDwGl8ItYBQgBCAEL/////vrL98EIQyQMgA0Gg6QBqIAMpA7hpItABQgBCgYCAgL+y/fDDAEIAEMkDIANBkOkAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANBgOkAaiDQAUIAQt2whYzotpGouH9CABDJAyADQfDoAGog0AFCAEKpwMaJrs6TsjBCABDJAyADQbDoAGogzwFCACDVAUIAEMkDIANB0OcAaiDPAUIAIOsBQgAQyQMgA0HA5wBqIM8BQgAg7AFCABDJAyADQbDnAGogzwFCACDaAUIAEMkDIANBoOgAaiADKQPIaSDUASDWAVatfCLpASADKQPgaHwi2QEgAykD+Gkg2wEg3AFWrXwi5AEgAykD4Gl8ItsBIAMpA5BqfCLcASDTASDUAVatIAMpA6hqINMBIN0BVK18fHwi8QF8ItMBIAMpA5BpfCLUASADKQOoaSDWASADKQOgaSLQAXwg0AFUrXx8ItYBIAMpA7BofCLdAUIAQgBC/////76y/fBCEMkDIANBkOgAaiADKQOoaCLQAUIAQoGAgIC/sv3wwwBCABDJAyADQYDoAGog0AFCAEKR4eXNh4n6mShCABDJAyADQfDnAGog0AFCAELdsIWM6LaRqLh/QgAQyQMgA0Hg5wBqINABQgBCqcDGia7Ok7IwQgAQyQMgA0Gg5wBqIM4BQgAg1QFCABDJAyADQcDmAGogzgFCACDrAUIAEMkDIANBsOYAaiDOAUIAIOwBQgAQyQMgA0Gg5gBqIM4BQgAg2gFCABDJAyADQZDnAGogAykDuGgg1gEg3QFWrXwi+QEgAykD0Gd8It8BIAMpA+hpINsBIOQBVK18IvoBIAMpA9BpfCLkASADKQOAanwi5QEg3AEg8QFWrSADKQOYaiDbASDcAVatfHx8ItsBIAMpA9BofCLcASDTASDZAVStIAMpA+hoINkBIOkBVK18fHwi2QEgAykDgGl8IukBINQBINYBVq0gAykDmGkg0wEg1AFWrXx8fCL7AXwi0wEgAykDgGh8ItQBIAMpA5hoIN0BIAMpA5BoItABfCDQAVStfHwi1gEgAykDoGd8It0BQgBCAEL/////vrL98EIQyQMgA0GA5wBqIAMpA5hnItABQgBCgYCAgL+y/fDDAEIAEMkDIANB8OYAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB4OYAaiDQAUIAQt2whYzotpGouH9CABDJAyADQdDmAGog0AFCAEKpwMaJrs6TsjBCABDJAyAFQbgJaiIXKQMAIfwBIAVB0AlqIhwpAwAh8QEgBUHICWoiIykDACHyASAFQcAJaiIFKQMAIfMBAkAgAykD2GYgAykD6GcgAykD+Ggg2wEg5QFUrSADKQOIaiDkASDlAVatfHwgAykD2Gkg5AEg+gFUrXx8IuQBIAMpA8BofCLQASDZASDcAVStIAMpA9hoINsBINwBVq18fHwi2wEgAykD8Gh8ItwBINsBVK18INwBIOkBIPsBVq0gAykDiGkg2QEg6QFWrXx8fCLZASDcAVStfCDQASDbAVatIAMpA8hoINABIOQBVK18fHwi5AEgAykDsGd8ItABIAMpA8hnINkBINkBIAMpA8BnfCLbAVatfCDbASDbASDTASDfAVStIAMpA9hnIN8BIPkBVK18fHwi2QFWrXx8ItsBIAMpA+BnfCLcASDbAVStfCDcASDcASADKQP4ZyDZASDZASADKQPwZ3wi3wFWrXwg3wEg3wEg1AEg1gFWrSADKQOIaCDTASDUAVatfHx8ItQBVq18fCLTAVatfCDQASDbAVatIAMpA7hnINABIOQBVK18fHwi3wEgAykDoGZ8ItkBIAMpA7hmINMBIAMpA7BmfCLQASDTAVStfCDQASDQASADKQPIZiADKQOoZyDWASDdAVatfCLWASADKQPAZnwi0wEg1gFUrXwg0wEg0wEg1AF8ItQBVq18fCLTAVatfHwi1gEgAykD0GZ8ItsBINYBVK18INsBIAMpA+hmINMBINMBIAMpA+BmfCLcAVatfCDcASDcASADKQP4ZiDUASDUASADKQPwZnwi0AFWrXwg0AEg0AEgAykDiGcgAykDgGci0wEg3QF8INMBVK18fCLUAVatfHwi0AFWrXx8ItMBINsBVK18INYBINkBVK0gAykDqGYg2QEg3wFUrXx8fCLWAUKpwMaJrs6TsjBWDQAg1gFCqcDGia7Ok7IwUg0CINMBQt2whYzotpGouH9WDQAg0wFC3bCFjOi2kai4f1IEQEKpwMaJrs6TsjAh1gEMAwsg0AFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h2QEg0AFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHWASDQASHfAQwEC0KR4eXNh4n6mSgh3wEg1AFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh1gEMAwsg0AFCkeHlzYeJ+pkofSLZASDUAUKBgICAv7L98MMAVK0i2wF9Id8BINMBQqPP+vOXye7XxwB8ItwBINABQpHh5c2HifqZKFQg2QEg2wFUcq0i0AF9IdkBINYBINMBQt2whYzotpGouH9UINABINwBVnKtfUKpwMaJrs6TsjB9IdYBINQBQoGAgIC/sv3wwwB9IdQBDAILQcivwgAQ6AQACyDTASHZASDQASHfAQtCqcDGia7Ok7IwId0BINYBIPwBfCDZASDzAXwi2QEg8wFUINkBINkBIN8BIPIBfCLTASDyAVQg0wEg0wEg1AEg8QF8ItYBIPEBVK18ItABVnKtfCLTAVZyrXwi1AEh3AECQAJAAkAg1AFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8h3QEg0wEi3AFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSgh3QEg0AEi3AFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAh3QEg1gEh3AEg1gFCgYCAgL+y/fDDAFENAQsg3AEg3QFaDQAg0wEh3AEg0AEh3QEMAQsg0AFCkeHlzYeJ+pkofSLZASDWAUKBgICAv7L98MMAVK0i2wF9Id0BINMBQqPP+vOXye7XxwB8It8BINABQpHh5c2HifqZKFQg2QEg2wFUcq0i0AF9IdwBINQBINMBQt2whYzotpGouH9UINABIN8BVnKtfUKpwMaJrs6TsjB9IdQBINYBQoGAgIC/sv3wwwB9IdYBCyAXINQBNwMAIA1CATcDACAFINwBNwMAICMg3QE3AwAgHCDWATcDACADQdDkAGogCikDACLQAUIAINEBQgAQyQMgA0GQ5QBqIApBCGspAwAi0wFCACDRAUIAEMkDIANB0OUAaiAKQRBrKQMAItQBQgAg0QFCABDJAyADQZDmAGogCkEYaykDACLWAUIAINEBQgAQyQMgA0HA5ABqIAMpA9BkItwBQgBCAEL/////vrL98EIQyQMgA0Gw5ABqIAMpA8hkItkBQgBCgYCAgL+y/fDDAEIAEMkDIANBoOQAaiDZAUIAQpHh5c2HifqZKEIAEMkDIANBkOQAaiDZAUIAQt2whYzotpGouH9CABDJAyADQYDkAGog2QFCAEKpwMaJrs6TsjBCABDJAyADQfDjAGog0AFCACDLAUIAEMkDIANBgOUAaiDTAUIAIMsBQgAQyQMgA0HA5QBqINQBQgAgywFCABDJAyADQYDmAGog1gFCACDLAUIAEMkDIANB4OMAaiADKQOgZCLpASADKQPYZCLkASADKQOQZXwi5QF8ItsBIAMpA7hkINwBIAMpA7BkItkBfCDZAVStfHwi3AEgAykD8GN8It0BQgBCAEL/////vrL98EIQyQMgA0HQ4wBqIAMpA+hjItkBQgBCgYCAgL+y/fDDAEIAEMkDIANBwOMAaiDZAUIAQpHh5c2HifqZKEIAEMkDIANBsOMAaiDZAUIAQt2whYzotpGouH9CABDJAyADQaDjAGog2QFCAEKpwMaJrs6TsjBCABDJAyADQZDjAGog0AFCACDPAUIAEMkDIANB8OQAaiDTAUIAIM8BQgAQyQMgA0Gw5QBqINQBQgAgzwFCABDJAyADQfDlAGog1gFCACDPAUIAEMkDIANBgOMAaiADKQP4YyDcASDdAVatfCLxASADKQOAZXwi3wEgAykDmGUg5AEg5QFWrXwi8gEgAykD0GV8IuQBIAMpA5BkfCLlASDbASDcAVatIAMpA6hkINsBIOkBVK18fHwi8wF8ItsBIAMpA8BjfCLcASADKQPYYyDdASADKQPQYyLZAXwg2QFUrXx8It0BIAMpA5BjfCLpAUIAQgBC/////76y/fBCEMkDIANB8OIAaiADKQOIYyLZAUIAQoGAgIC/sv3wwwBCABDJAyADQeDiAGog2QFCAEKR4eXNh4n6mShCABDJAyADQdDiAGog2QFCAELdsIWM6LaRqLh/QgAQyQMgA0HA4gBqINkBQgBCqcDGia7Ok7IwQgAQyQMgA0Gw4gBqINABQgAgzgFCABDJAyADQeDkAGog0wFCACDOAUIAEMkDIANBoOUAaiDUAUIAIM4BQgAQyQMgA0Hg5QBqINYBQgAgzgFCABDJAyADQaDiAGogAykDmGMg3QEg6QFWrXwi+QEgAykD8GR8ItMBIAMpA9hlIOQBIPIBVK18IvIBIAMpA5BmfCLUASADKQOAZHwi1gEg5QEg8wFWrSADKQOYZCDkASDlAVatfHx8ItkBIAMpA8BlfCLkASDbASDfAVStIAMpA4hlIN8BIPEBVK18fHwi3wEgAykDsGN8IuUBINwBIN0BVq0gAykDyGMg2wEg3AFWrXx8fCLxAXwi2wEgAykD4GJ8ItwBIAMpA/hiIOkBIAMpA/BiItABfCDQAVStfHwi3QEgAykDsGJ8IukBQgBCAEL/////vrL98EIQyQMgA0GQ4gBqIAMpA6hiItABQgBCgYCAgL+y/fDDAEIAEMkDIANBgOIAaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB8OEAaiDQAUIAQt2whYzotpGouH9CABDJAyADQeDhAGog0AFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykD6GEgAykDyGIgAykDqGMg1gEg2QFWrSADKQOIZCDUASDWAVatfHwgAykDmGYg1AEg8gFUrXx8IvIBIAMpA4BmfCLQASDfASDkAVStIAMpA8hlINkBIOQBVq18fHwi1AEgAykDoGN8ItYBINQBVK18INYBINYBIOUBIPEBVq0gAykDuGMg3wEg5QFWrXx8fCLZAVatfCDQASDUAVatIAMpA4hmINABIPIBVK18fHwi3wEgAykD8GV8ItABIAMpA7hlINkBINkBIAMpA7BlfCLUAVatfCDUASDUASDTASDbAVatIAMpA/hkINMBIPkBVK18fHwi0wFWrXx8ItQBIAMpA8BifCLWASDUAVStfCDWASDWASADKQPYYiDTASDTASADKQPQYnwi2QFWrXwg2QEg2QEg3AEg3QFWrSADKQPoYiDbASDcAVatfHx8ItsBVq18fCLTAVatfCDQASDUAVatIAMpA/hlINABIN8BVK18fHwi3wEgAykD4GV8ItYBIAMpA6hlINMBIAMpA6BlfCLQASDTAVStfCDQASDQASADKQPoZCADKQO4YiDdASDpAVatfCLUASADKQPgZHwi0wEg1AFUrXwg0wEg0wEg2wF8ItQBVq18fCLTAVatfHwi2QEgAykD4GF8ItsBINkBVK18INsBIAMpA/hhINMBINMBIAMpA/BhfCLcAVatfCDcASDcASADKQOIYiDUASDUASADKQOAYnwi0AFWrXwg0AEg0AEgAykDmGIgAykDkGIi0wEg6QF8INMBVK18fCLUAVatfHwi0AFWrXx8ItMBINsBVK18INYBINkBVq0gAykD6GUg1gEg3wFUrXx8fCLWAUKpwMaJrs6TsjBWDQACQCDWAUKpwMaJrs6TsjBRBEAg0wFC3bCFjOi2kai4f1YNAiDTAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHWAQsg0wEh2QEg0AEh3AEMAgsg0AFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8h2QEg0AFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHWASDQASHcAQwCC0KR4eXNh4n6mSgh3AEg1AFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh1gEMAQsg0AFCkeHlzYeJ+pkofSLZASDUAUKBgICAv7L98MMAVK0i2wF9IdwBINMBQqPP+vOXye7XxwB8It0BINABQpHh5c2HifqZKFQg2QEg2wFUcq0i0AF9IdkBINYBINMBQt2whYzotpGouH9UINABIN0BVnKtfUKpwMaJrs6TsjB9IdYBINQBQoGAgIC/sv3wwwB9IdQBC0KpwMaJrs6TsjAh2wEg0gEg2QF8ItIBINkBVCDSASDMASDcAXwizAEg3AFUIMwBIMoBINQBfCLKASDUAVStfCLQASDMAVRyrXwi0wEg0gFUcq0gzQEg1gF8fCLNASHSAQJAAkACQCDNAUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyHbASDTASLSAULdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCHbASDQASLSAUKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACHbASDKASHSASDKAUKBgICAv7L98MMAUQ0BCyDSASDbAVoNACDTASHSASDQASHMAQwBCyDQAUKR4eXNh4n6mSh9ItIBIMoBQoGAgIC/sv3wwwBUrSLUAX0hzAEg0wFCo8/685fJ7tfHAHwi1gEg0AFCkeHlzYeJ+pkoVCDSASDUAVRyrSLQAX0h0gEgzQEg0wFC3bCFjOi2kai4f1Qg0AEg1gFWcq19QqnAxomuzpOyMH0hzQEgygFCgYCAgL+y/fDDAH0hygELAkAgB0GgAUYNACADQZDgAGog0QFCACDtAUIAEMkDIANB0OAAaiDRAUIAIOcBQgAQyQMgA0GQ4QBqINEBQgAg2AFCABDJAyADQdDhAGog0QFCACDXAUIAEMkDIANBgOAAaiADKQOQYCLQAUIAQgBC/////76y/fBCEMkDIANB8N8AaiADKQOIYCLRAUIAQoGAgIC/sv3wwwBCABDJAyADQeDfAGog0QFCAEKR4eXNh4n6mShCABDJAyADQdDfAGog0QFCAELdsIWM6LaRqLh/QgAQyQMgA0HA3wBqINEBQgBCqcDGia7Ok7IwQgAQyQMgA0Gw3wBqIMsBQgAg7QFCABDJAyADQcDgAGogywFCACDnAUIAEMkDIANBgOEAaiDLAUIAINgBQgAQyQMgA0HA4QBqIMsBQgAg1wFCABDJAyADQaDfAGogAykD4F8i2QEgAykDmGAi1AEgAykD0GB8ItYBfCLRASADKQP4XyDQASADKQPwXyLLAXwgywFUrXx8ItABIAMpA7BffCLTAUIAQgBC/////76y/fBCEMkDIANBkN8AaiADKQOoXyLLAUIAQoGAgIC/sv3wwwBCABDJAyADQYDfAGogywFCAEKR4eXNh4n6mShCABDJAyADQfDeAGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0Hg3gBqIMsBQgBCqcDGia7Ok7IwQgAQyQMgA0HQ3gBqIM8BQgAg7QFCABDJAyADQbDgAGogzwFCACDnAUIAEMkDIANB8OAAaiDPAUIAINgBQgAQyQMgA0Gw4QBqIM8BQgAg1wFCABDJAyADQcDeAGogAykDuF8g0AEg0wFWrXwi3QEgAykDwGB8Is8BIAMpA9hgINQBINYBVq18ItsBIAMpA5BhfCLUASADKQPQX3wi1gEg0AEg0QFUrSADKQPoXyDRASDZAVStfHx8It8BfCLRASADKQOAX3wi0AEgAykDmF8g0wEgAykDkF8iywF8IMsBVK18fCLTASADKQPQXnwi2QFCAEIAQv////++sv3wQhDJAyADQbDeAGogAykDyF4iywFCAEKBgICAv7L98MMAQgAQyQMgA0Gg3gBqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0GQ3gBqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANBgN4AaiDLAUIAQqnAxomuzpOyMEIAEMkDIANB8N0AaiDOAUIAIO0BQgAQyQMgA0Gg4ABqIM4BQgAg5wFCABDJAyADQeDgAGogzgFCACDYAUIAEMkDIANBoOEAaiDOAUIAINcBQgAQyQMgA0Hg3QBqIAMpA9heINMBINkBVq18IuQBIAMpA7BgfCLOASADKQOYYSDUASDbAVStfCLlASADKQPQYXwi2wEgAykDwF98ItwBINYBIN8BVq0gAykD2F8g1AEg1gFWrXx8fCLUASADKQOAYXwi1gEgzwEg0QFWrSADKQPIYCDPASDdAVStfHx8Is8BIAMpA/BefCLdASDQASDTAVatIAMpA4hfINABINEBVK18fHwi3wF8ItEBIAMpA6BefCLQASADKQO4XiDZASADKQOwXiLLAXwgywFUrXx8ItMBIAMpA/BdfCLZAUIAQgBC/////76y/fBCEMkDIANB0N0AaiADKQPoXSLLAUIAQoGAgIC/sv3wwwBCABDJAyADQcDdAGogywFCAEKR4eXNh4n6mShCABDJAyADQbDdAGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0Gg3QBqIMsBQgBCqcDGia7Ok7IwQgAQyQMCQCADKQOoXSADKQOIXiADKQPoXiDUASDcAVStIAMpA8hfINsBINwBVq18fCADKQPYYSDbASDlAVStfHwi2wEgAykDwGF8IssBIM8BINYBVK0gAykDiGEg1AEg1gFWrXx8fCLUASADKQPgXnwi1gEg1AFUrXwg1gEg3QEg3wFWrSADKQP4XiDPASDdAVatfHx8Is8BINYBVK18IMsBINQBVq0gAykDyGEgywEg2wFUrXx8fCLbASADKQOwYXwiywEgAykD+GAgzwEgzwEgAykD8GB8ItQBVq18INQBINQBIM4BINEBVq0gAykDuGAgzgEg5AFUrXx8fCLPAVatfHwizgEgAykDgF58ItQBIM4BVK18INQBINQBIAMpA5heIM8BIM8BIAMpA5BefCLWAVatfCDWASDQASDTAVatIAMpA6heINABINEBVK18fHwi0QEg1gFUrXx8Is8BVq18IMsBIM4BVq0gAykDuGEgywEg2wFUrXx8fCLWASADKQOgYXwiywEgAykD6GAgzwEgzwEgAykD4GB8Is4BVq18IM4BIM4BIAMpA6hgIAMpA/hdINMBINkBVq18ItABIAMpA6BgfCLPASDQAVStfCDPASDPASDRAXwi0QFWrXx8Is8BVq18fCLOASADKQOgXXwi1AEgzgFUrXwg1AEg1AEgAykDuF0gzwEgzwEgAykDsF18ItMBVq18INMBINMBIAMpA8hdINEBINEBIAMpA8BdfCLPAVatfCDPASDPASADKQPYXSADKQPQXSLRASDZAXwg0QFUrXx8ItEBVq18fCLQAVatfHwi0wFWrXwgywEgzgFWrSADKQOoYSDLASDWAVStfHx8Is4BQqnAxomuzpOyMFYNACDOAUKpwMaJrs6TsjBSBEAg0AEhywEg0wEhzwEMAgsg0wFC3bCFjOi2kai4f1YNACDTAULdsIWM6LaRqLh/UgRAINABIcsBINMBIc8BQqnAxomuzpOyMCHOAQwCCyDQAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHPASDQAUKR4eXNh4n6mShSBEAg0AEhywFCqcDGia7Ok7IwIc4BDAILQpHh5c2HifqZKCHLASDRAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHOAQwBCyDQAUKR4eXNh4n6mSh9Is8BINEBQoGAgIC/sv3wwwBUrSLUAX0hywEg0wFCo8/685fJ7tfHAHwi1gEg0AFCkeHlzYeJ+pkoVCDPASDUAVRyrSLQAX0hzwEgzgEg0wFC3bCFjOi2kai4f1Qg0AEg1gFWcq19QqnAxomuzpOyMH0hzgEg0QFCgYCAgL+y/fDDAH0h0QELIAxBAWohBSAKQSBqIQogB0EoaiEHIAxBBUkNAAsMAQsgBkGBgICAeDYCACAGQgI3AwgMAwtB0c7FAC0AABoCQAJAAkACQAJAQYAHQQgQ1gQiDARAIAxBAEGAB/wLACAIQQFrIRcgCCEHA0AgByIFQQFrIQcCfwJAAkACfgJAIBcgGUkEQCAFQR1PDQMgFCAHQQV0Ig1qIQpCr76f0Jn4nYUOIdEBIA0gRWoiBSkDACLWASHOASDWAUKvvp/QmfidhQ5SDQFCrozlw/ftqLfmACHRASAFKQMIIs4BQq6M5cP37ai35gBSDQFCqZqD+9nSnf42IdEBIAUpAxAizgFCqZqD+9nSnf42Ug0BQvv////Eg43LrH8h0QEgBSkDGCLOAUL7////xIONy6x/Ug0BQqmag/vZ0p3+NiHOAUKujOXD9+2ot+YADAILIAcgGUGor8IAENkDAAsgzgEg0QFWIAUpAxgh0QENAiAFKQMQIc4BIAUpAwgLIcsBQqmag/vZ0p3+NiDOAX0izwEg0QFC+////8SDjcusf1atItABfSHYAUKujOXD9+2ot+YAIMsBfSLUASDPASDQAVQgzgFCqZqD+9nSnf42VnKtIs8BfSHTAUKvvp/QmfidhQ4g1gF9IdwBQvv////Eg43LrH8g0QF9IdcBIM8BINQBViDLAUKujOXD9+2ot+YAVnIMAgsgB0EcQbivwgAQ2QMAC0LdsIWM6LaRqLh/IAUpAwgiywFCrozlw/ftqLfmAH0izwEgBSkDECLOAUKpmoP72dKd/jZUIM4BQqmag/vZ0p3+Nn0izgEg0QFC+////8SDjcusf1StItABVHKtItQBfSLVAX0i2QEgzgEg0AF9Is4BQpHh5c2HifqZKFZCkeHlzYeJ+pkoIM4BfSLOASDRAUKDgICA/Mn1ww98Qv7////AzYKPvH9UrSLQAVRyrSLbAX0h0wEgzgEg0AF9IdgBIMsBQq6M5cP37ai35gBUIM8BINQBVHKtINYBfULY/uXZx8axtz58IdwBQvz///+Dtoq8cCDRAX0h1wEg2QEg2wFUINUBQt2whYzotpGouH9WcgshHCADQZDdAGogCikDGCLOAUIAINcBQgAQyQMgA0Gg3ABqIAopAxAi0QFCACDXAUIAEMkDIANBgNwAaiAKKQMIItABQgAg1wFCABDJAyADQeDbAGogCikDACLVAUIAINcBQgAQyQMgA0GA3QBqIAMpA5BdItQBQgBCAEL/////vrL98EIQyQMgA0Hw3ABqIAMpA4hdIssBQgBCgYCAgL+y/fDDAEIAEMkDIANB4NwAaiDLAUIAQpHh5c2HifqZKEIAEMkDIANB0NwAaiDLAUIAQt2whYzotpGouH9CABDJAyADQcDcAGogywFCAEKpwMaJrs6TsjBCABDJAyADQcDbAGogzgFCACDYAUIAEMkDIANB4NoAaiDRAUIAINgBQgAQyQMgA0HQ2gBqINABQgAg2AFCABDJAyADQcDaAGog1QFCACDYAUIAEMkDIANBsNsAaiADKQPgXCLbASADKQOYXSLYASADKQOgXHwi2QF8Is8BIAMpA/hcINQBIAMpA/BcIssBfCDLAVStfHwi1AEgAykDwFt8ItcBQgBCAEL/////vrL98EIQyQMgA0Gg2wBqIAMpA7hbIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBkNsAaiDLAUIAQpHh5c2HifqZKEIAEMkDIANBgNsAaiDLAUIAQt2whYzotpGouH9CABDJAyADQfDaAGogywFCAEKpwMaJrs6TsjBCABDJAyADQbDaAGogzgFCACDTAUIAEMkDIANB0NkAaiDRAUIAINMBQgAQyQMgA0Hw2ABqINABQgAg0wFCABDJAyADQeDYAGog1QFCACDTAUIAEMkDIANBoNoAaiADKQPIWyDUASDXAVatfCLkASADKQPgWnwi0wEgAykDqFwg2AEg2QFWrXwi3QEgAykDgFx8ItgBIAMpA9BcfCLZASDPASDUAVatIAMpA+hcIM8BINsBVK18fHwi5QF8Is8BIAMpA5BbfCLUASADKQOoWyDXASADKQOgWyLLAXwgywFUrXx8ItcBIAMpA7BafCLbAUIAQgBC/////76y/fBCEMkDIANBkNoAaiADKQOoWiLLAUIAQoGAgIC/sv3wwwBCABDJAyADQYDaAGogywFCAEKR4eXNh4n6mShCABDJAyADQfDZAGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0Hg2QBqIMsBQgBCqcDGia7Ok7IwQgAQyQMgA0Gw3ABqIM4BQgAg3AEgHK19IssBQgAQyQMgA0GQ3ABqINEBQgAgywFCABDJAyADQfDbAGog0AFCACDLAUIAEMkDIANB0NsAaiDVAUIAIMsBQgAQyQMgA0HA2QBqIAMpA7haINcBINsBVq18IusBIAMpA9BZfCLcASADKQOIXCDYASDdAVStfCLnASADKQPgW3wi3QEgAykDwFx8It8BINkBIOUBVq0gAykD2Fwg2AEg2QFWrXx8fCLYASADKQPQWnwi2QEgzwEg0wFUrSADKQPoWiDTASDkAVStfHx8ItMBIAMpA4BbfCLkASDUASDXAVatIAMpA5hbIM8BINQBVq18fHwi5QF8Is8BIAMpA4BafCLUASADKQOYWiDbASADKQOQWiLLAXwgywFUrXx8ItcBIAMpA7BcfCLbAUIAQgBC/////76y/fBCEMkDIANBsNkAaiADKQPIWSLLAUIAQoGAgIC/sv3wwwBCABDJAyADQaDZAGogywFCAEKR4eXNh4n6mShCABDJAyADQZDZAGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0GA2QBqIMsBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA4hZIAMpA+hZIAMpA/haINgBIN8BVK0gAykDyFwg3QEg3wFWrXx8IAMpA+hbIN0BIOcBVK18fCLdASADKQPAWnwiywEg0wEg2QFUrSADKQPYWiDYASDZAVatfHx8ItgBIAMpA/BafCLZASDYAVStfCDZASDkASDlAVatIAMpA4hbINMBIOQBVq18fHwi0wEg2QFUrXwgywEg2AFWrSADKQPIWiDLASDdAVStfHx8It0BIAMpA+BYfCLLASADKQP4WCDTASDTASADKQPwWHwi2AFWrXwg2AEg2AEgzwEg3AFUrSADKQPYWSDcASDrAVStfHx8ItMBVq18fCLYASADKQPgWXwi2QEg2AFUrXwg2QEgAykD+Fkg0wEg0wEgAykD8Fl8ItwBVq18INwBINwBINQBINcBVq0gAykDiFogzwEg1AFWrXx8fCLUAVatfHwizwEg2QFUrXwgywEg2AFWrSADKQPoWCDLASDdAVStfHx8It0BIAMpA9BbfCLTASADKQP4WyDPASADKQPwW3wiywEgzwFUrXwgywEgywEgAykDmFwgAykDuFwg1wEg2wFWrXwi1wEgAykDkFx8Is8BINcBVK18IM8BIM8BINQBfCLUAVatfHwizwFWrXx8ItcBIAMpA4BZfCLZASDXAVStfCDZASADKQOYWSDPASDPASADKQOQWXwi3AFWrXwg3AEg3AEgAykDqFkg1AEg1AEgAykDoFl8IssBVq18IMsBIMsBIAMpA7hZIAMpA7BZIs8BINsBfCDPAVStfHwi2AFWrXx8IssBVq18fCLPASDZAVStfCDTASDXAVatIAMpA9hbINMBIN0BVK18fHwi0wFCqcDGia7Ok7IwVg0AAkAg0wFCqcDGia7Ok7IwUQRAIM8BQt2whYzotpGouH9WDQIgzwFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAh0wELIM8BIdcBIMsBIdQBDAILIMsBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IdcBIMsBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAh0wEgywEh1AEMAgtCkeHlzYeJ+pkoIdQBINgBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIdMBDAELIMsBQpHh5c2HifqZKH0i1wEg2AFCgYCAgL+y/fDDAFStItkBfSHUASDPAUKjz/rzl8nu18cAfCLbASDLAUKR4eXNh4n6mShUINcBINkBVHKtIssBfSHXASDTASDPAULdsIWM6LaRqLh/VCDLASDbAVZyrX1CqcDGia7Ok7IwfSHTASDYAUKBgICAv7L98MMAfSHYAQsgA0GQ1wBqIM4BQgBC9v///4mHmpbZAEIAEMkDIANBsNYAaiDOAUIAQtO0hvazpbv87QBCABDJAyADQdDVAGogzgFCAELcmMqH79vR7kxCABDJAyADQfDUAGogzgFCAELe/L6gs/C7ihxCABDJAyADQYDXAGogAykDkFdCfoMizgFCAEIAQv////++sv3wQhDJAyADQfDWAGogAykDiFciywFCAEKBgICAv7L98MMAQgAQyQMgA0Hg1gBqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQ1gBqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANBwNYAaiDLAUIAQqnAxomuzpOyMEIAEMkDIANB0NcAaiDRAUIAQvb///+Jh5qW2QBCABDJAyADQcDXAGog0QFCAELTtIb2s6W7/O0AQgAQyQMgA0Gw1wBqINEBQgBC3JjKh+/b0e5MQgAQyQMgA0Gg1wBqINEBQgBC3vy+oLPwu4ocQgAQyQMgA0Gg1gBqIAMpA+BWItwBIAMpA5hXItkBIAMpA7BWfCLbAXwizwEgAykD+FYgzgEgAykD8FYiywF8IMsBVK18fCLOASADKQPQV3wi0QFCAEIAQv////++sv3wQhDJAyADQZDWAGogAykDqFYiywFCAEKBgICAv7L98MMAQgAQyQMgA0GA1gBqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0Hw1QBqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANB4NUAaiDLAUIAQqnAxomuzpOyMEIAEMkDIANBkNgAaiDQAUIAQvb///+Jh5qW2QBCABDJAyADQYDYAGog0AFCAELTtIb2s6W7/O0AQgAQyQMgA0Hw1wBqINABQgBC3JjKh+/b0e5MQgAQyQMgA0Hg1wBqINABQgBC3vy+oLPwu4ocQgAQyQMgA0HA1QBqIAMpA9hXIM4BINEBVq18IuQBIAMpA8BXfCLQASADKQO4ViDZASDbAVatfCLdASADKQPQVXwi2QEgAykD0FZ8ItsBIM4BIM8BVK0gAykD6FYgzwEg3AFUrXx8fCLlAXwizwEgAykDgFZ8Is4BIAMpA5hWINEBIAMpA5BWIssBfCDLAVStfHwi0QEgAykDkFh8ItwBQgBCAEL/////vrL98EIQyQMgA0Gw1QBqIAMpA8hVIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBoNUAaiDLAUIAQpHh5c2HifqZKEIAEMkDIANBkNUAaiDLAUIAQt2whYzotpGouH9CABDJAyADQYDVAGogywFCAEKpwMaJrs6TsjBCABDJAyADQdDYAGog1QFCAEL2////iYealtkAQgAQyQMgA0HA2ABqINUBQgBC07SG9rOlu/ztAEIAEMkDIANBsNgAaiDVAUIAQtyYyofv29HuTEIAEMkDIANBoNgAaiDVAUIAQt78vqCz8LuKHEIAEMkDIANB4NQAaiADKQOYWCDRASDcAVatfCLrASADKQOAWHwi1QEgAykD2FUg2QEg3QFUrXwi5wEgAykD8FR8It0BIAMpA8BWfCLfASDbASDlAVatIAMpA9hWINkBINsBVq18fHwi2QEgAykDsFd8ItsBIM8BINABVK0gAykDyFcg0AEg5AFUrXx8fCLQASADKQPwVXwi5AEgzgEg0QFWrSADKQOIViDOASDPAVStfHx8IuUBfCLPASADKQOgVXwizgEgAykDuFUg3AEgAykDsFUiywF8IMsBVK18fCLRASADKQPQWHwi3AFCAEIAQv////++sv3wQhDJAyADQdDUAGogAykD6FQiywFCAEKBgICAv7L98MMAQgAQyQMgA0HA1ABqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0Gw1ABqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANBoNQAaiDLAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQOoVCADKQPoVyADKQOoVyADKQP4VCDdASDnAVStfCLnASADKQOgV3wiywEg5wFUrXwgywEgywEg2QEg3wFUrSADKQPIViDdASDfAVatfHx8It0BVq18IN0BIN0BINABINsBVK0gAykDuFcg2QEg2wFWrXx8fCLLAVatfCLbASADKQPgV3wi2QEg2wFUrXwg2QEg2QEgAykD6FUgywEgywEgAykD4FV8ItsBVq18INsBINsBIOQBIOUBVq0gAykD+FUg0AEg5AFWrXx8fCLLAVatfHwi0AFWrXwg0AEg0AEgAykD+FcgywEgywEgAykD8Fd8ItkBVq18INkBIM8BINUBVK0gAykDiFgg1QEg6wFUrXx8fCLLASDZAVStfHwi1QFWrXwi3QEgAykDoFh8ItkBIAMpA4hVINUBINUBIAMpA4BVfCLQAVatfCDQASDQASADKQOYVSDLASDLASADKQOQVXwi1QFWrXwg1QEg1QEgzgEg0QFWrSADKQOoVSDOASDPAVStfHx8ItsBVq18fCLLAVatfHwizwEgAykDuFggywEgywEgAykDsFh8Is4BVq18IM4BIM4BIAMpA8hYIAMpA9hYINEBINwBVq18ItEBIAMpA8BYfCLLASDRAVStfCDLASDLASDbAXwi0QFWrXx8IssBVq18fCLOASADKQOgVHwi2wEgzgFUrXwg2wEg2wEgAykDuFQgywEgywEgAykDsFR8ItUBVq18INUBINUBIAMpA8hUINEBINEBIAMpA8BUfCLLAVatfCDLASDLASADKQPYVCADKQPQVCLRASDcAXwg0QFUrXx8ItEBVq18fCLQAVatfHwi1QFWrXwgzgEgzwFUrSDPASDZAVStIAMpA6hYINkBIN0BVK18fHx8Is4BQqnAxomuzpOyMFYNAAJAIM4BQqnAxomuzpOyMFEEQCDVAULdsIWM6LaRqLh/Vg0CINUBQt2whYzotpGouH9SBEAg0AEhywEg1QEhzwFCqcDGia7Ok7IwIc4BDAQLINABQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/Ic8BINABQpHh5c2HifqZKFENASDQASHLAUKpwMaJrs6TsjAhzgEMAwsg0AEhywEg1QEhzwEMAgtCkeHlzYeJ+pkoIcsBINEBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc4BDAELINABQpHh5c2HifqZKH0izwEg0QFCgYCAgL+y/fDDAFStItkBfSHLASDVAUKjz/rzl8nu18cAfCLbASDQAUKR4eXNh4n6mShUIM8BINkBVHKtItABfSHPASDOASDVAULdsIWM6LaRqLh/VCDQASDbAVZyrX1CqcDGia7Ok7IwfSHOASDRAUKBgICAv7L98MMAfSHRAQsgA0GQ1ABqINEBQgAgygFCABDJAyADQbDTAGogywFCACDKAUIAEMkDIANBoNMAaiDPAUIAIMoBQgAQyQMgA0GQ0wBqIM4BQgAgygFCABDJAyADQYDUAGogAykDkFQi0AFCAEIAQv////++sv3wQhDJAyADQfDTAGogAykDiFQiygFCAEKBgICAv7L98MMAQgAQyQMgA0Hg0wBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQ0wBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBwNMAaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBgNMAaiDRAUIAIMwBQgAQyQMgA0Gg0gBqIMsBQgAgzAFCABDJAyADQZDSAGogzwFCACDMAUIAEMkDIANBgNIAaiDOAUIAIMwBQgAQyQMgA0Hw0gBqIAMpA+BTItwBIAMpA5hUItkBIAMpA7BTfCLbAXwizAEgAykD+FMg0AEgAykD8FMiygF8IMoBVK18fCLQASADKQOAU3wi1QFCAEIAQv////++sv3wQhDJAyADQeDSAGogAykD+FIiygFCAEKBgICAv7L98MMAQgAQyQMgA0HQ0gBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HA0gBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBsNIAaiDKAUIAQqnAxomuzpOyMEIAEMkDIANB8NEAaiDRAUIAINIBQgAQyQMgA0GQ0QBqIMsBQgAg0gFCABDJAyADQYDRAGogzwFCACDSAUIAEMkDIANB8NAAaiDOAUIAINIBQgAQyQMgA0Hg0QBqIAMpA4hTINABINUBVq18It0BIAMpA6BSfCLSASADKQO4UyDZASDbAVatfCLfASADKQOgU3wi2QEgAykD0FN8ItsBIMwBINABVq0gAykD6FMgzAEg3AFUrXx8fCLkAXwizAEgAykD0FJ8ItABIAMpA+hSINUBIAMpA+BSIsoBfCDKAVStfHwi1QEgAykD8FF8ItwBQgBCAEL/////vrL98EIQyQMgA0HQ0QBqIAMpA+hRIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBwNEAaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBsNEAaiDKAUIAQt2whYzotpGouH9CABDJAyADQaDRAGogygFCAEKpwMaJrs6TsjBCABDJAyADQeDQAGog0QFCACDNAUIAEMkDIANBgNAAaiDLAUIAIM0BQgAQyQMgA0HwzwBqIM8BQgAgzQFCABDJAyADQeDPAGogzgFCACDNAUIAEMkDIANB0NAAaiADKQP4USDVASDcAVatfCLlASADKQOQUXwiywEgAykDqFMg2QEg3wFUrXwi3wEgAykDkFN8Is8BIAMpA8BTfCLNASDbASDkAVatIAMpA9hTINkBINsBVq18fHwizgEgAykDkFJ8ItEBIMwBINIBVK0gAykDqFIg0gEg3QFUrXx8fCLSASADKQPAUnwi2QEg0AEg1QFWrSADKQPYUiDMASDQAVatfHx8It0BfCLMASADKQPAUXwi0AEgAykD2FEg3AEgAykD0FEiygF8IMoBVK18fCLVASADKQPgUHwi2wFCAEIAQv////++sv3wQhDJAyADQcDQAGogAykD2FAiygFCAEKBgICAv7L98MMAQgAQyQMgA0Gw0ABqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0Gg0ABqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBkNAAaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQOYUCADKQOoUSADKQO4UiDNASDOAVatIAMpA8hTIM0BIM8BVK18fCADKQOYUyDPASDfAVStfHwi3AEgAykDgFJ8IsoBINEBINIBVq0gAykDmFIgzgEg0QFWrXx8fCLPASADKQOwUnwizQEgzwFUrXwgzQEgzQEg2QEg3QFWrSADKQPIUiDSASDZAVatfHx8Is4BVq18IMoBIM8BVq0gAykDiFIgygEg3AFUrXx8fCLSASADKQPwUHwiygEgAykDiFEgzgEgzgEgAykDgFF8Is8BVq18IM8BIM8BIMsBIMwBVq0gAykDmFEgywEg5QFUrXx8fCLLAVatfHwizwEgAykDoFF8Is0BIM8BVK18IM0BIM0BIAMpA7hRIMsBIMsBIAMpA7BRfCLOAVatfCDOASDOASDQASDVAVatIAMpA8hRIMwBINABVq18fHwi0QFWrXx8IssBVq18IMoBIM8BVq0gAykD+FAgygEg0gFUrXx8fCLQASADKQPgT3wiygEgAykD+E8gywEgywEgAykD8E98IswBVq18IMwBIMwBIAMpA4hQIAMpA+hQINUBINsBVq18Is8BIAMpA4BQfCLLASDPAVStfCDLASDLASDRAXwizwFWrXx8IssBVq18fCLNASADKQOQUHwizgEgzQFUrXwgzgEgzgEgAykDqFAgywEgAykDoFB8ItIBIMsBVK18INIBINIBIAMpA7hQIM8BIM8BIAMpA7BQfCLMAVatfCDMASDMASADKQPIUCADKQPAUCLLASDbAXwgywFUrXx8IssBVq18fCLMAVatfHwizwFWrXwgygEgzQFWrSADKQPoTyDKASDQAVStfHx8ItEBQqnAxomuzpOyMFYNAAJAINEBQqnAxomuzpOyMFEEQCDPAULdsIWM6LaRqLh/Vg0CIM8BQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIdEBCyDPASHKASDMASHbAQwCCyDMAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHKASDMAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIdEBIMwBIdsBDAILQpHh5c2HifqZKCHbASDLAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHRAQwBCyDMAUKR4eXNh4n6mSh9IsoBIMsBQoGAgIC/sv3wwwBUrSLNAX0h2wEgzwFCo8/685fJ7tfHAHwizgEgzAFCkeHlzYeJ+pkoVCDKASDNAVRyrSLMAX0hygEg0QEgzwFC3bCFjOi2kai4f1QgzAEgzgFWcq19QqnAxomuzpOyMH0h0QEgywFCgYCAgL+y/fDDAH0hywELIA0gE2ohCgJ/AkACfgJAINMBIs8BINYBIs4BUg0AINcBIs8BIAUpAwgizgFSDQAg1AEizwEgBSkDECLOAVINACDPASHMASDXASDYASLPASLNASAFKQMYIs4BUQ0BGgsgBSkDGCHNASDOASDPAVYNASAFKQMQIcwBIAUpAwgLIdIBINQBIMwBfSLPASDNASDYAVatItABfSHOASDXASDSAX0i1QEgzwEg0AFUIMwBINQBVnKtIswBfSHPASDTASDWAX0h5AEg2AEgzQF9Ic0BIMwBINUBViDSASDXAVZyDAELQt2whYzotpGouH8gBSkDCCLMASDXAX0i0gEgBSkDECLPASDUAVQgzwEg1AF9Is8BIM0BINgBVK0izgFUcq0i0AF9ItUBfSLZASDPASDOAX0izwFCkeHlzYeJ+pkoVkKR4eXNh4n6mSggzwF9Is4BIM0BINgBfSLNAUKBgICAv7L98MMAVq0i3AFUcq0i3QF9Ic8BIM4BINwBfSHOASDMASDXAVQg0AEg0gFWcq0g0wEg1gF9fEKpwMaJrs6TsjB8IeQBQoGAgIC/sv3wwwAgzQF9Ic0BINkBIN0BVCDVAULdsIWM6LaRqLh/VnILIRwgA0HAzwBqIAopAxgizAFCACDNAUIAEMkDIANB0M4AaiAKKQMQItIBQgAgzQFCABDJAyADQbDOAGogCikDCCLQAUIAIM0BQgAQyQMgA0GQzgBqIAopAwAi1QFCACDNAUIAEMkDIANBsM8AaiADKQPATyLZAUIAQgBC/////76y/fBCEMkDIANBoM8AaiADKQO4TyLNAUIAQoGAgIC/sv3wwwBCABDJAyADQZDPAGogzQFCAEKR4eXNh4n6mShCABDJAyADQYDPAGogzQFCAELdsIWM6LaRqLh/QgAQyQMgA0HwzgBqIM0BQgBCqcDGia7Ok7IwQgAQyQMgA0GAzgBqIMwBQgAgzgFCABDJAyADQaDNAGog0gFCACDOAUIAEMkDIANBkM0AaiDQAUIAIM4BQgAQyQMgA0GAzQBqINUBQgAgzgFCABDJAyADQfDNAGogAykDkE8i5QEgAykDyE8i3QEgAykD0E58It8BfCLOASADKQOoTyDZASADKQOgTyLNAXwgzQFUrXx8ItkBIAMpA4BOfCLcAUIAQgBC/////76y/fBCEMkDIANB4M0AaiADKQP4TSLNAUIAQoGAgIC/sv3wwwBCABDJAyADQdDNAGogzQFCAEKR4eXNh4n6mShCABDJAyADQcDNAGogzQFCAELdsIWM6LaRqLh/QgAQyQMgA0GwzQBqIM0BQgBCqcDGia7Ok7IwQgAQyQMgA0HwzABqIMwBQgAgzwFCABDJAyADQZDMAGog0gFCACDPAUIAEMkDIANBsMsAaiDQAUIAIM8BQgAQyQMgA0GgywBqINUBQgAgzwFCABDJAyADQeDMAGogAykDiE4g2QEg3AFWrXwi6wEgAykDoE18Is0BIAMpA9hOIN0BIN8BVq18IucBIAMpA7BOfCLdASADKQOAT3wi3wEgzgEg2QFWrSADKQOYTyDOASDlAVStfHx8IuwBfCLOASADKQPQTXwi2QEgAykD6E0g3AEgAykD4E0izwF8IM8BVK18fCLcASADKQPwTHwi5QFCAEIAQv////++sv3wQhDJAyADQdDMAGogAykD6EwizwFCAEKBgICAv7L98MMAQgAQyQMgA0HAzABqIM8BQgBCkeHlzYeJ+pkoQgAQyQMgA0GwzABqIM8BQgBC3bCFjOi2kai4f0IAEMkDIANBoMwAaiDPAUIAQqnAxomuzpOyMEIAEMkDIANB0M8AaiDMAUIAIOQBIBytfSLMAUIAEMkDIANB4M4AaiDSAUIAIMwBQgAQyQMgA0HAzgBqINABQgAgzAFCABDJAyADQaDOAGog1QFCACDMAUIAEMkDIANBgMwAaiADKQP4TCDcASDlAVatfCLtASADKQOQTHwizwEgAykDuE4g3QEg5wFUrXwi5wEgAykDkE58ItIBIAMpA/BOfCLQASDfASDsAVatIAMpA4hPIN0BIN8BVq18fHwi1QEgAykDkE18It0BIM0BIM4BVq0gAykDqE0gzQEg6wFUrXx8fCLNASADKQPATXwi3wEg2QEg3AFWrSADKQPYTSDOASDZAVatfHx8IusBfCLOASADKQPATHwi2QEgAykD2Ewg5QEgAykD0EwizAF8IMwBVK18fCLcASADKQPQT3wi5AFCAEIAQv////++sv3wQhDJAyADQfDLAGogAykDiEwizAFCAEKBgICAv7L98MMAQgAQyQMgA0HgywBqIMwBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQywBqIMwBQgBC3bCFjOi2kai4f0IAEMkDIANBwMsAaiDMAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQPISyADKQOoTCADKQO4TSDQASDVAVatIAMpA/hOINABINIBVK18fCADKQOYTiDSASDnAVStfHwi5QEgAykDgE18IswBIM0BIN0BVK0gAykDmE0g1QEg3QFWrXx8fCLSASADKQOwTXwi0AEg0gFUrXwg0AEg3wEg6wFWrSADKQPITSDNASDfAVatfHx8Is0BINABVK18IMwBINIBVq0gAykDiE0gzAEg5QFUrXx8fCLVASADKQOgS3wizAEgAykDuEsgzQEgzQEgAykDsEt8ItIBVq18INIBINIBIM4BIM8BVK0gAykDmEwgzwEg7QFUrXx8fCLPAVatfHwizQEgAykDoEx8ItIBIM0BVK18INIBIAMpA7hMIM8BIM8BIAMpA7BMfCLQAVatfCDQASDQASDZASDcAVatIAMpA8hMIM4BINkBVq18fHwizgFWrXx8Is8BINIBVK18IMwBIM0BVq0gAykDqEsgzAEg1QFUrXx8fCLZASADKQOgTnwizQEgAykDyE4gzwEgAykDwE58IswBIM8BVK18IMwBIMwBIAMpA+hOIAMpA9hPINwBIOQBVq18ItIBIAMpA+BOfCLPASDSAVStfCDPASDOASDPAXwizgFWrXx8Is8BVq18fCLSASADKQPAS3wi1QEg0gFUrXwg1QEg1QEgAykD2EsgzwEgzwEgAykD0Et8ItABVq18INABINABIAMpA+hLIM4BIM4BIAMpA+BLfCLMAVatfCDMASDMASADKQP4SyADKQPwSyLPASDkAXwgzwFUrXx8Is8BVq18fCLMAVatfHwi0AFWrXwgzQEg0gFWrSADKQOoTiDNASDZAVStfHx8Is4BQqnAxomuzpOyMFYNAAJAIM4BQqnAxomuzpOyMFEEQCDQAULdsIWM6LaRqLh/Vg0CINABQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIc4BCyDQASHNASDMASHSAQwCCyDMAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHNASDMAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIc4BIMwBIdIBDAILQpHh5c2HifqZKCHSASDPAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHOAQwBCyDMAUKR4eXNh4n6mSh9Is0BIM8BQoGAgIC/sv3wwwBUrSLVAX0h0gEg0AFCo8/685fJ7tfHAHwi2QEgzAFCkeHlzYeJ+pkoVCDNASDVAVRyrSLMAX0hzQEgzgEg0AFC3bCFjOi2kai4f1QgzAEg2QFWcq19QqnAxomuzpOyMH0hzgEgzwFCgYCAgL+y/fDDAH0hzwELINEBIdUBAn8CQAJAINEBIM4BIswBUg0AIMoBIdUBIMoBIM0BIswBUg0AINIBIswBINsBItUBUg0AIMsBIdUBIM8BIswBIMsBUQ0BCyDMASDVAVgNAELdsIWM6LaRqLh/IM0BIMoBfSLMASDSASDbAVQg0gEg2wF9ItIBIMsBIM8BVq0i0AFUcq0i1QF9ItkBfSLbASDSASDQAX0i0gFCkeHlzYeJ+pkoVkKR4eXNh4n6mSgg0gF9ItIBIM8BIMsBfSLLAUKBgICAv7L98MMAVq0izwFUcq0i0AF9IeUBINIBIM8BfSHkASDMASDVAVQgygEgzQFWcq0g0QEgzgF9fEKpwMaJrs6TsjB8IdIBQoGAgIC/sv3wwwAgywF9IesBINABINsBViDZAULdsIWM6LaRqLh/VnIMAQsg2wEg0gF9IswBIMsBIM8BVK0i0AF9IeQBIMoBIM0BfSLVASDMASDQAVQg0gEg2wFWcq0izAF9IeUBINEBIM4BfSHSASDLASDPAX0h6wEgygEgzQFUIMwBINUBVnILIQpCqcDGia7Ok7IwIc0BINcBIAUpAwh8IsoBINcBVCDKASDKASDUASAFKQMQfCLMASDUAVQgzAEgzAEg2AEgBSkDGHwizgEg2AFUrXwiywFWcq18IswBVnKtINMBINYBfHwi0QEhygECQAJAAkAg0QFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hzQEgzAEiygFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghzQEgywEiygFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhzQEgzgEiygFCgYCAgL+y/fDDAFENAQsgygEgzQFaDQAgzAEhzQEgywEhygEMAQsgywFCkeHlzYeJ+pkofSLPASDOAUKBgICAv7L98MMAVK0izQF9IcoBIMwBQqPP+vOXye7XxwB8ItABIMsBQpHh5c2HifqZKFQgzQEgzwFWcq0iywF9Ic0BINEBIMwBQt2whYzotpGouH9UIMsBINABVnKtfUKpwMaJrs6TsjB9IdEBIM4BQoGAgIC/sv3wwwB9Ic4BCyADIM4BNwOIpAEgAyDKATcDgKQBIAMgzQE3A/ijASADINEBNwPwowEgA0HwowFqQcCWwgBBIBDxA0UNAiDSASAKrX0h3QEgA0HwwQFqQgA3AwAgA0HowQFqQgA3AwAgA0IANwPgwQEgA0IBNwP4wQEgA0HIpAFqIANBiKQBaikDADcDACADQcCkAWogA0GApAFqKQMANwMAIANBuKQBaiADQfijAWopAwA3AwAgAyADKQPwowE3A7CkASADQcilAWpBuJbCACkDADcDACADQcClAWpBsJbCACkDADcDACADQbilAWpBqJbCACkDADcDACADQaCWwgApAwA3A7ClAQJAIANBsKQBaiADQeDBAWpBIBDxA0UEQEKlibn6l5a0iwIh0QFChYHundXn4KSMfyHaAULjs/GantaO/9MAIdsBQqfbhfHayLncGyHLAQwBC0KR4eXNh4n6mSgh1wFC3bCFjOi2kai4fyHYAUKpwMaJrs6TsjAh0AFCgYCAgL+y/fDDACHKAUKFge6d1efgpIx/IdoBQuOz8Zqe1o7/0wAh2wFCp9uF8drIudwbIcsBQqWJufqXlrSLAiHRAUIAIc4BIAMpA8ikASHNASADKQOwpAEh0gEgAykDuKQBIcwBIAMpA8CkASHTAUIAIdYBQgAh2QFCACHPAQNAIANBsKUBaiADQeDBAWpBIBDxA0UEQCDPASHLASDZASHbASDWASHaASDOASHRAQwCCyDNAadBAXFFBEADQCDTAUI/hiDNAUIBiIQhzQECQCDLAUIBg1AEQCDaASHUASDbASHVASDLASHcAQwBCyDRASDaASDaAUKjz/rzl8nu18cAfSLfAVYg3wEg3wEg2wFCkeHlzYeJ+pkofCLUASDbAVQg1AEg1AEgywFCgYCAgL+y/fDDAHwi3AEgywFUrXwi1QFWcq18ItQBVnKtfEKpwMaJrs6TsjB8IdEBCyDSAUI/hiDMAUI/hiDTAUIBiIQh0wEg0gFCAYgh0gEg0QFCP4Yg1AFCAYiEIdoBINQBQj+GINUBQgGIhCHbASDVAUI/hiDcAUIBiIQhywEg0QFCAYgh0QEgzAFCAYiEIcwBIM0BQgGDUA0ACyADINMBNwPApAEgAyDNATcDyKQBIAMgzAE3A7ikASADINIBNwOwpAELIMoBp0EBcUUEQANAINcBQj+GIMoBQgGIhCHKAQJAIM8BQgGDUARAIM8BIdUBINkBIc8BINYBIdQBDAELIM4BINYBINYBQqPP+vOXye7XxwB9ItwBViDcASDcASDZAUKR4eXNh4n6mSh8ItQBINkBVCDUASDPAUKBgICAv7L98MMAfCLVASDPAVStfCLPASDUAVRyrXwi1AFWcq18QqnAxomuzpOyMHwhzgELINABQj+GINgBQj+GINcBQgGIhCHXASDQAUIBiCHQASDOAUI/hiDUAUIBiIQh1gEg1AFCP4YgzwFCAYiEIdkBIM8BQj+GINUBQgGIhCHPASDOAUIBiCHOASDYAUIBiIQh2AEgygFCAYNQDQALIAMg1wE3A8ClASADIMoBNwPIpQEgAyDYATcDuKUBIAMg0AE3A7ClAQsg0gEh1QECQAJAAkACQAJAINABItQBINIBUg0AIMwBIdUBIMwBINgBItQBUg0AINcBItQBINMBItUBUg0AIMoBIdQBIM0BIdUBIMoBIM0BUQ0BCyDUASDVAVgNACADIMoBIM0BfSLUATcDyKUBIAMg1wEg0wF9ItwBIMoBIM0BVK0iygF9ItUBNwPApQEgAyDYASDMAX0i3wEgygEg3AFWINMBINcBVnKtIsoBfSLcATcDuKUBIAMg0AEg0gF9IMoBIN8BViDMASDYAVZyrX0i0AE3A7ClASDRASHYAQJAAkAg0QEgzgEiygFSDQAg2gEi2AEg1gEiygFSDQAg2QEiygEg2wEi2AFSDQAgywEh2AEgzwEiygEgywFRDQELIMoBINgBVA0CCyDOASDRAX0g1gEg2gF9It8BINkBINsBVCDZASDbAX0i2QEgywEgzwFWrSLnAVRyrSLsAVQg1gEg2gFUcq19Ic4BIM8BIMsBfSHPASDVASHXASDcASHYASDUASHKASDZASDnAX0h2QEg3wEg7AF9IdYBDAMLIAMgzQEgygF9ItQBNwPIpAEgAyDTASDXAX0i3AEgygEgzQFWrSLNAX0i1QE3A8CkASADIMwBINgBfSLfASDTASDXAVQgzQEg3AFWcq0izQF9ItwBNwO4pAEgAyDSASDQAX0gzAEg2AFUIM0BIN8BVnKtfSLSATcDsKQBAkACQCDOASLMASDRASLNAVINACDaASLNASDWASLMAVINACDZASLMASDbASLNAVINACDLASHNASDPASLMASDLAVENAQsgzAEgzQFWDQILINEBIM4BfSDaASDWAX0i3wEg2wEg2QF9IucBIMsBIM8BVK0i7AFUINkBINsBVnKtItsBVCDWASDaAVZyrX0h0QEgywEgzwF9IcsBINUBIdMBINwBIcwBINQBIc0BIN8BINsBfSHaASDnASDsAX0h2wEMAgsgzgFC3bCFjOi2kai4fyDaAX0iygFCkeHlzYeJ+pkoINsBfSLOASDLAUKBgICAv7L98MMAVq0i1wFUINsBQpHh5c2HifqZKFZyrSLYAVQg2gFC3bCFjOi2kai4f1ZyrSDRAXx9IMoBINgBfSLYASDWAXwiygEg2AFUIMoBIM4BINcBfSLXASDZAXwizgEg1wFUIM4BQoGAgIC/sv3wwwAgywF9ItcBIM8BfCLPASDXAVStfCLZASDOAVRyrXwi1gEgygFUcq18QqnAxomuzpOyMHwhzgEg1QEh1wEg3AEh2AEg1AEhygEMAQsg0QEgzgF9Qt2whYzotpGouH8g1gF9IswBQpHh5c2HifqZKCDZAX0izQEgzwFCgYCAgL+y/fDDAFatItEBVCDZAUKR4eXNh4n6mShWcq0i0wFUINYBQt2whYzotpGouH9Wcq19IMwBINMBfSLTASDaAXwizAEg0wFUIMwBIM0BINEBfSLRASDbAXwizQEg0QFUIM0BQoGAgIC/sv3wwwAgzwF9ItEBIMsBfCLLASDRAVStfCLbASDNAVRyrXwi2gEgzAFUcq18QqnAxomuzpOyMHwh0QEg1QEh0wEg3AEhzAEg1AEhzQELIANBsKQBaiADQeDBAWpBIBDxAw0ACwsgA0GQywBqIMsBQgAg6wFCABDJAyADQbDKAGogywFCACDkAUIAEMkDIANBoMoAaiDLAUIAIOUBQgAQyQMgA0GQygBqIMsBQgAg3QFCABDJAyADQYDLAGogAykDkEsizAFCAEIAQv////++sv3wQhDJAyADQfDKAGogAykDiEsiygFCAEKBgICAv7L98MMAQgAQyQMgA0HgygBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQygBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBwMoAaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBgMoAaiDbAUIAIOsBQgAQyQMgA0GgyQBqINsBQgAg5AFCABDJAyADQZDJAGog2wFCACDlAUIAEMkDIANBgMkAaiDbAUIAIN0BQgAQyQMgA0HwyQBqIAMpA+BKItABIAMpA5hLIs4BIAMpA7BKfCLSAXwiywEgAykD+EogzAEgAykD8EoiygF8IMoBVK18fCLMASADKQOASnwizwFCAEIAQv////++sv3wQhDJAyADQeDJAGogAykD+EkiygFCAEKBgICAv7L98MMAQgAQyQMgA0HQyQBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HAyQBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBsMkAaiDKAUIAQqnAxomuzpOyMEIAEMkDIANB8MgAaiDaAUIAIOsBQgAQyQMgA0GQyABqINoBQgAg5AFCABDJAyADQYDIAGog2gFCACDlAUIAEMkDIANB8McAaiDaAUIAIN0BQgAQyQMgA0HgyABqIAMpA4hKIMwBIM8BVq18ItUBIAMpA6BJfCLNASADKQO4SiDOASDSAVatfCLTASADKQOgSnwizgEgAykD0Ep8ItIBIMsBIMwBVq0gAykD6EogywEg0AFUrXx8fCLXAXwiywEgAykD0El8IswBIAMpA+hJIM8BIAMpA+BJIsoBfCDKAVStfHwizwEgAykD8Eh8ItABQgBCAEL/////vrL98EIQyQMgA0HQyABqIAMpA+hIIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBwMgAaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBsMgAaiDKAUIAQt2whYzotpGouH9CABDJAyADQaDIAGogygFCAEKpwMaJrs6TsjBCABDJAyADQeDHAGog0QFCACDrAUIAEMkDIANBgMcAaiDRAUIAIOQBQgAQyQMgA0HwxgBqINEBQgAg5QFCABDJAyADQeDGAGog0QFCACDdAUIAEMkDIANB0McAaiADKQP4SCDPASDQAVatfCLYASADKQOQSHwi0QEgAykDqEogzgEg0wFUrXwi1gEgAykDkEp8ItMBIAMpA8BKfCLUASDSASDXAVatIAMpA9hKIM4BINIBVq18fHwizgEgAykDkEl8ItIBIMsBIM0BVK0gAykDqEkgzQEg1QFUrXx8fCLNASADKQPASXwi1QEgzAEgzwFWrSADKQPYSSDLASDMAVatfHx8ItcBfCLLASADKQPASHwizAEgAykD2Egg0AEgAykD0EgiygF8IMoBVK18fCLPASADKQPgR3wi0AFCAEIAQv////++sv3wQhDJAyADQcDHAGogAykD2EciygFCAEKBgICAv7L98MMAQgAQyQMgA0GwxwBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0GgxwBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBkMcAaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQOYRyADKQOoSCADKQO4SSDOASDUAVStIAMpA8hKINMBINQBVq18fCADKQOYSiDTASDWAVStfHwi0wEgAykDgEl8IsoBIM0BINIBVK0gAykDmEkgzgEg0gFWrXx8fCLOASADKQOwSXwi0gEgzgFUrXwg0gEg1QEg1wFWrSADKQPISSDNASDVAVatfHx8Is0BINIBVK18IMoBIM4BVq0gAykDiEkgygEg0wFUrXx8fCLTASADKQPwR3wiygEgAykDiEggzQEgzQEgAykDgEh8Is4BVq18IM4BIM4BIMsBINEBVK0gAykDmEgg0QEg2AFUrXx8fCLNAVatfHwizgEgAykDoEh8ItIBIM4BVK18INIBINIBIAMpA7hIIM0BIM0BIAMpA7BIfCLRAVatfCDRASDMASDPAVatIAMpA8hIIMsBIMwBVq18fHwizQEg0QFUrXx8IssBVq18IMoBIM4BVq0gAykD+EcgygEg0wFUrXx8fCLRASADKQPgRnwizAEgAykD+EYgywEgAykD8EZ8IsoBIMsBVK18IMoBIMoBIAMpA4hHIAMpA+hHIM8BINABVq18Is8BIAMpA4BHfCLLASDPAVStfCDLASDLASDNAXwizwFWrXx8IssBVq18fCLNASADKQOQR3wizgEgzQFUrXwgzgEgzgEgAykDqEcgywEgywEgAykDoEd8ItIBVq18INIBINIBIAMpA7hHIM8BIM8BIAMpA7BHfCLLAVatfCDLASDLASADKQPIRyADKQPARyLKASDQAXwgygFUrXx8IsoBVq18fCLLAVatfHwizwFWrXwgzAEgzQFWrSADKQPoRiDMASDRAVStfHx8Is0BQqnAxomuzpOyMFYNACDNAUKpwMaJrs6TsjBSBEAgywEhzAEgzwEh0gEMAgsgzwFC3bCFjOi2kai4f1YNACDPAULdsIWM6LaRqLh/UgRAIMsBIcwBIM8BIdIBQqnAxomuzpOyMCHNAQwCCyDLAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHSASDLAUKR4eXNh4n6mShSBEAgywEhzAFCqcDGia7Ok7IwIc0BDAILQpHh5c2HifqZKCHMASDKAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHNAQwBCyDLAUKR4eXNh4n6mSh9Is4BIMoBQoGAgIC/sv3wwwBUrSLSAX0hzAEgzwFCo8/685fJ7tfHAHwi0QEgywFCkeHlzYeJ+pkoVCDOASDSAVRyrSLLAX0h0gEgzQEgzwFC3bCFjOi2kai4f1QgywEg0QFWcq19QqnAxomuzpOyMH0hzQEgygFCgYCAgL+y/fDDAH0hygELIAwgDWoiBSDKATcDGCAFIMwBNwMQIAUg0gE3AwggBSDNATcDACAHDQALIANB0MYAaiAMKQMYIsoBQgAg3gFCABDJAyADQfDFAGogDCkDECLLAUIAIN4BQgAQyQMgA0HgxQBqIAwpAwgizAFCACDeAUIAEMkDIANB0MUAaiAMKQMAIs8BQgAg3gFCABDJAyADQcDGAGogAykD0EYi0gFCAEIAQv////++sv3wQhDJAyADQbDGAGogAykDyEYizQFCAEKBgICAv7L98MMAQgAQyQMgA0GgxgBqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgA0GQxgBqIM0BQgBC3bCFjOi2kai4f0IAEMkDIANBgMYAaiDNAUIAQqnAxomuzpOyMEIAEMkDIANBwMUAaiDKAUIAIOIBQgAQyQMgA0HgxABqIMsBQgAg4gFCABDJAyADQdDEAGogzAFCACDiAUIAEMkDIANBwMQAaiDPAUIAIOIBQgAQyQMgA0GwxQBqIAMpA6BGItUBIAMpA9hGItMBIAMpA/BFfCLUAXwizgEgAykDuEYg0gEgAykDsEYizQF8IM0BVK18fCLSASADKQPARXwi0QFCAEIAQv////++sv3wQhDJAyADQaDFAGogAykDuEUizQFCAEKBgICAv7L98MMAQgAQyQMgA0GQxQBqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgA0GAxQBqIM0BQgBC3bCFjOi2kai4f0IAEMkDIANB8MQAaiDNAUIAQqnAxomuzpOyMEIAEMkDIANBsMQAaiDKAUIAIOMBQgAQyQMgA0HQwwBqIMsBQgAg4wFCABDJAyADQcDDAGogzAFCACDjAUIAEMkDIANBsMMAaiDPAUIAIOMBQgAQyQMgA0GgxABqIAMpA8hFINEBINIBVK18ItcBIAMpA+BEfCLQASADKQP4RSDTASDUAVatfCLYASADKQPgRXwi0wEgAykDkEZ8ItQBIM4BINIBVq0gAykDqEYgzgEg1QFUrXx8fCLWAXwizgEgAykDkEV8ItIBIAMpA6hFINEBIAMpA6BFIs0BfCDNAVStfHwi0QEgAykDsER8ItUBQgBCAEL/////vrL98EIQyQMgA0GQxABqIAMpA6hEIs0BQgBCgYCAgL+y/fDDAEIAEMkDIANBgMQAaiDNAUIAQpHh5c2HifqZKEIAEMkDIANB8MMAaiDNAUIAQt2whYzotpGouH9CABDJAyADQeDDAGogzQFCAEKpwMaJrs6TsjBCABDJAyADQaDDAGogygFCACDgAUIAEMkDIANBwMIAaiDLAUIAIOABQgAQyQMgA0GwwgBqIMwBQgAg4AFCABDJAyADQaDCAGogzwFCACDgAUIAEMkDIANBkMMAaiADKQO4RCDRASDVAVatfCLaASADKQPQQ3wiywEgAykD6EUg0wEg2AFUrXwi2AEgAykD0EV8IswBIAMpA4BGfCLPASDUASDWAVatIAMpA5hGINMBINQBVq18fHwizQEgAykD0ER8ItMBIM4BINABVK0gAykD6EQg0AEg1wFUrXx8fCLQASADKQOARXwi1AEg0QEg0gFUrSADKQOYRSDOASDSAVatfHx8ItcBfCLOASADKQOARHwi0gEgAykDmEQg1QEgAykDkEQiygF8IMoBVK18fCLRASADKQOgQ3wi1QFCAEIAQv////++sv3wQhDJAyADQYDDAGogAykDmEMiygFCAEKBgICAv7L98MMAQgAQyQMgA0HwwgBqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HgwgBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB0MIAaiDKAUIAQqnAxomuzpOyMEIAEMkDIAMpA9hCIAMpA+hDIAMpA/hEIM0BIM8BVK0gAykDiEYgzAEgzwFWrXx8IAMpA9hFIMwBINgBVK18fCLYASADKQPARHwiygEg0AEg0wFUrSADKQPYRCDNASDTAVatfHx8IswBIAMpA/BEfCLPASDMAVStfCDPASDPASDUASDXAVatIAMpA4hFINABINQBVq18fHwizQFWrXwgygEgzAFWrSADKQPIRCDKASDYAVStfHx8ItABIAMpA7BDfCLKASADKQPIQyDNASDNASADKQPAQ3wizAFWrXwgzAEgzAEgywEgzgFWrSADKQPYQyDLASDaAVStfHx8IssBVq18fCLMASADKQPgQ3wizwEgzAFUrXwgzwEgAykD+EMgywEgywEgAykD8EN8Is0BVq18IM0BIM0BINEBINIBVK0gAykDiEQgzgEg0gFWrXx8fCLOAVatfHwiywEgzwFUrXwgygEgzAFWrSADKQO4QyDKASDQAVStfHx8ItABIAMpA6BCfCLMASADKQO4QiDLASADKQOwQnwiygEgywFUrXwgygEgygEgAykDyEIgAykDqEMg0QEg1QFWrXwizwEgAykDwEJ8IssBIM8BVK18IMsBIMsBIM4BfCLPAVatfHwiywFWrXx8Is4BIAMpA9BCfCLSASDOAVStfCDSASADKQPoQiDLASDLASADKQPgQnwi0QFWrXwg0QEg0QEgAykD+EIgzwEgzwEgAykD8EJ8IsoBVq18IMoBIMoBIAMpA4hDIAMpA4BDIssBINUBfCDLAVStfHwizQFWrXx8IsoBVq18fCLLASDSAVStfCDMASDOAVatIAMpA6hCIMwBINABVK18fHwi0gFCqcDGia7Ok7IwVg0DINIBQqnAxomuzpOyMFENAgwEC0EIQYAHQciswgAQyAQACyAGINoBNwMQIAZCAjcDCCAGQYGAgIB4NgIAIAxBgAcQ3wQMBgsgywFC3bCFjOi2kai4f1YNACDLAULdsIWM6LaRqLh/UgRAQqnAxomuzpOyMCHSAQwCCyDKAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHaASDKAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIdIBIMoBIdYBDAMLQpHh5c2HifqZKCHWASDNAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHSAQwCCyDKAUKR4eXNh4n6mSh9IswBIM0BQoGAgIC/sv3wwwBUrSLPAX0h1gEgywFCo8/685fJ7tfHAHwizgEgygFCkeHlzYeJ+pkoVCDMASDPAVRyrSLKAX0h2gEg0gEgywFC3bCFjOi2kai4f1QgygEgzgFWcq19QqnAxomuzpOyMH0h0gEgzQFCgYCAgL+y/fDDAH0hzQEMAQsgywEh2gEgygEh1gELIANB4MEAaiATKQMYIsoBQgAg9AFCABDJAyADQdDAAGogEykDECLLAUIAIPQBQgAQyQMgA0HAP2ogEykDCCLMAUIAIPQBQgAQyQMgA0GwPmogEykDACLPAUIAIPQBQgAQyQMgA0HQwQBqIAMpA+BBItABQgBCAEL/////vrL98EIQyQMgA0HAwQBqIAMpA9hBIs4BQgBCgYCAgL+y/fDDAEIAEMkDIANBsMEAaiDOAUIAQpHh5c2HifqZKEIAEMkDIANBoMEAaiDOAUIAQt2whYzotpGouH9CABDJAyADQZDBAGogzgFCAEKpwMaJrs6TsjBCABDJAyADQfDBAGogygFCACD1AUIAEMkDIANB4MAAaiDLAUIAIPUBQgAQyQMgA0HQP2ogzAFCACD1AUIAEMkDIANBwD5qIM8BQgAg9QFCABDJAyADQcDAAGogAykDsEEi2AEgAykD6EEi1QEgAykD0EB8ItcBfCLRASADKQPIQSDQASADKQPAQSLOAXwgzgFUrXx8ItABIAMpA/BBfCLTAUIAQgBC/////76y/fBCEMkDIANBsMAAaiADKQPIQCLOAUIAQoGAgIC/sv3wwwBCABDJAyADQaDAAGogzgFCAEKR4eXNh4n6mShCABDJAyADQZDAAGogzgFCAELdsIWM6LaRqLh/QgAQyQMgA0GAQGsgzgFCAEKpwMaJrs6TsjBCABDJAyADQYDCAGogygFCACD2AUIAEMkDIANB8MAAaiDLAUIAIPYBQgAQyQMgA0HgP2ogzAFCACD2AUIAEMkDIANB0D5qIM8BQgAg9gFCABDJAyADQbA/aiADKQP4QSDQASDTAVatfCLZASADKQPgQHwi1AEgAykD2EAg1QEg1wFWrXwi2wEgAykDwD98ItUBIAMpA6BBfCLXASDQASDRAVStIAMpA7hBINEBINgBVK18fHwi3AF8ItEBIAMpA6BAfCLQASADKQO4QCDTASADKQOwQCLOAXwgzgFUrXx8ItMBIAMpA4BCfCLYAUIAQgBC/////76y/fBCEMkDIANBoD9qIAMpA7g/Is4BQgBCgYCAgL+y/fDDAEIAEMkDIANBkD9qIM4BQgBCkeHlzYeJ+pkoQgAQyQMgA0GAP2ogzgFCAELdsIWM6LaRqLh/QgAQyQMgA0HwPmogzgFCAEKpwMaJrs6TsjBCABDJAyADQZDCAGogygFCACD3AUIAEMkDIANBgMEAaiDLAUIAIPcBQgAQyQMgA0HwP2ogzAFCACD3AUIAEMkDIANB4D5qIM8BQgAg9wFCABDJAyADQaA+aiADKQOIQiDTASDYAVatfCLeASADKQPwQHwiywEgAykDyD8g1QEg2wFUrXwi2wEgAykDsD58IswBIAMpA5BBfCLPASDXASDcAVatIAMpA6hBINUBINcBVq18fHwizgEgAykD0D98ItUBINEBINQBVK0gAykD6EAg1AEg2QFUrXx8fCLUASADKQOQQHwi1wEg0AEg0wFWrSADKQOoQCDQASDRAVStfHx8ItkBfCLRASADKQOQP3wi0AEgAykDqD8g2AEgAykDoD8iygF8IMoBVK18fCLTASADKQOQQnwi2AFCAEIAQv////++sv3wQhDJAyADQZA+aiADKQOoPiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQYA+aiDKAUIAQpHh5c2HifqZKEIAEMkDIANB8D1qIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB4D1qIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA+g9IAMpA/g+IAMpA4hAIM4BIM8BVK0gAykDmEEgzAEgzwFWrXx8IAMpA7g+IMwBINsBVK18fCLbASADKQPAPnwiygEg1AEg1QFUrSADKQPYPyDOASDVAVatfHx8IswBIAMpA4BAfCLPASDMAVStfCDPASDPASDXASDZAVatIAMpA5hAINQBINcBVq18fHwizgFWrXwgygEgzAFWrSADKQPIPiDKASDbAVStfHx8ItQBIAMpA9A+fCLKASADKQPoPyDOASDOASADKQPgP3wizAFWrXwgzAEgzAEgywEg0QFWrSADKQP4QCDLASDeAVStfHx8IssBVq18fCLMASADKQPwPnwizwEgzAFUrXwgzwEgAykDiD8gywEgywEgAykDgD98Is4BVq18IM4BIM4BINABINMBVq0gAykDmD8g0AEg0QFUrXx8fCLRAVatfHwiywEgzwFUrXwgygEgzAFWrSADKQPYPiDKASDUAVStfHx8ItQBIAMpA+A+fCLPASADKQP4PyDLASADKQPwP3wiygEgywFUrXwgygEgygEgAykDiEEgAykDmEIg0wEg2AFWrXwizAEgAykDgEF8IssBIMwBVK18IMsBIMsBINEBfCLMAVatfHwiywFWrXx8Is4BIAMpA+A9fCLQASDOAVStfCDQASDQASADKQP4PSDLASDLASADKQPwPXwi0wFWrXwg0wEg0wEgAykDiD4gzAEgzAEgAykDgD58IsoBVq18IMoBIMoBIAMpA5g+IAMpA5A+IssBINgBfCDLAVStfHwi0QFWrXx8IsoBVq18fCLMAVatfCDOASDPAVStIAMpA+g+IM8BINQBVK18fHwizgFCqcDGia7Ok7IwVg0AAkAgzgFCqcDGia7Ok7IwUQRAIMwBQt2whYzotpGouH9WDQIgzAFC3bCFjOi2kai4f1IEQCDKASHLASDMASHPAUKpwMaJrs6TsjAhzgEMBAsgygFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8hzwEgygFCkeHlzYeJ+pkoUQ0BIMoBIcsBQqnAxomuzpOyMCHOAQwDCyDKASHLASDMASHPAQwCC0KR4eXNh4n6mSghywEg0QFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhzgEMAQsgygFCkeHlzYeJ+pkofSLPASDRAUKBgICAv7L98MMAVK0i0AF9IcsBIMwBQqPP+vOXye7XxwB8ItMBIMoBQpHh5c2HifqZKFQgzwEg0AFUcq0iygF9Ic8BIM4BIMwBQt2whYzotpGouH9UIMoBINMBVnKtfUKpwMaJrs6TsjB9Ic4BINEBQoGAgIC/sv3wwwB9IdEBCyADQdA9aiDRAUIAIOgBQgAQyQMgA0HAPGogywFCACDoAUIAEMkDIANBsDtqIM8BQgAg6AFCABDJAyADQaA6aiDOAUIAIOgBQgAQyQMgA0HAPWogAykD0D0i0AFCAEIAQv////++sv3wQhDJAyADQbA9aiADKQPIPSLKAUIAQoGAgIC/sv3wwwBCABDJAyADQaA9aiDKAUIAQpHh5c2HifqZKEIAEMkDIANBkD1qIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBgD1qIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HwPGog0QFCACDmAUIAEMkDIANB4DtqIMsBQgAg5gFCABDJAyADQdA6aiDPAUIAIOYBQgAQyQMgA0HAOWogzgFCACDmAUIAEMkDIANBsDxqIAMpA6A9ItgBIAMpA9g9ItUBIAMpA8A8fCLXAXwizAEgAykDuD0g0AEgAykDsD0iygF8IMoBVK18fCLQASADKQPwPHwi0wFCAEIAQv////++sv3wQhDJAyADQaA8aiADKQO4PCLKAUIAQoGAgIC/sv3wwwBCABDJAyADQZA8aiDKAUIAQpHh5c2HifqZKEIAEMkDIANBgDxqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB8DtqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HgPGog0QFCACDhAUIAEMkDIANB0DtqIMsBQgAg4QFCABDJAyADQcA6aiDPAUIAIOEBQgAQyQMgA0GwOWogzgFCACDhAUIAEMkDIANBoDtqIAMpA/g8INABINMBVq18ItkBIAMpA+A7fCLUASADKQPIPCDVASDXAVatfCLbASADKQOwO3wi1QEgAykDkD18ItcBIMwBINABVq0gAykDqD0gzAEg2AFUrXx8fCLcAXwizAEgAykDkDx8ItABIAMpA6g8INMBIAMpA6A8IsoBfCDKAVStfHwi0wEgAykD4Dx8ItgBQgBCAEL/////vrL98EIQyQMgA0GQO2ogAykDqDsiygFCAEKBgICAv7L98MMAQgAQyQMgA0GAO2ogygFCAEKR4eXNh4n6mShCABDJAyADQfA6aiDKAUIAQt2whYzotpGouH9CABDJAyADQeA6aiDKAUIAQqnAxomuzpOyMEIAEMkDIANB0DxqINEBQgAg6gFCABDJAyADQcA7aiDLAUIAIOoBQgAQyQMgA0GwOmogzwFCACDqAUIAEMkDIANBoDlqIM4BQgAg6gFCABDJAyADQZA6aiADKQPoPCDTASDYAVatfCLeASADKQPQO3wiywEgAykDuDsg1QEg2wFUrXwi4AEgAykDoDp8Is8BIAMpA4A9fCLOASDXASDcAVatIAMpA5g9INUBINcBVq18fHwi0QEgAykD0Dp8ItUBIMwBINQBVK0gAykD6Dsg1AEg2QFUrXx8fCLUASADKQOAPHwi1wEg0AEg0wFWrSADKQOYPCDMASDQAVatfHx8ItsBfCLMASADKQOAO3wi0AEgAykDmDsg2AEgAykDkDsiygF8IMoBVK18fCLTASADKQPQPHwi2AFCAEIAQv////++sv3wQhDJAyADQYA6aiADKQOYOiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQfA5aiDKAUIAQpHh5c2HifqZKEIAEMkDIANB4DlqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB0DlqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA9g5IAMpA+g6IAMpA/g7IM4BINEBVq0gAykDiD0gzgEgzwFUrXx8IAMpA6g6IM8BIOABVK18fCLZASADKQPAOXwiygEg1AEg1QFUrSADKQPYOiDRASDVAVatfHx8Is8BIAMpA/A7fCLOASDPAVStfCDOASDOASDXASDbAVatIAMpA4g8INQBINcBVq18fHwi0QFWrXwgygEgzwFWrSADKQPIOSDKASDZAVStfHx8ItQBIAMpA7A5fCLKASADKQPIOiDRASDRASADKQPAOnwizwFWrXwgzwEgzwEgywEgzAFWrSADKQPYOyDLASDeAVStfHx8IssBVq18fCLPASADKQPgOnwizgEgzwFUrXwgzgEgzgEgAykD+DogywEgywEgAykD8Dp8ItEBVq18INEBINEBINABINMBVq0gAykDiDsgzAEg0AFWrXx8fCLQAVatfHwiywFWrXwgygEgzwFWrSADKQO4OSDKASDUAVStfHx8ItQBIAMpA6A5fCLKASADKQO4OiDLASDLASADKQOwOnwizAFWrXwgzAEgzAEgAykDyDsgAykD2Dwg0wEg2AFWrXwizwEgAykDwDt8IssBIM8BVK18IMsBIMsBINABfCLPAVatfHwiywFWrXx8Is4BIAMpA9A5fCLQASDOAVStfCDQASDQASADKQPoOSDLASDLASADKQPgOXwizAFWrXwgzAEgzAEgAykD+DkgzwEgzwEgAykD8Dl8IssBVq18IMsBIMsBIAMpA4g6IAMpA4A6Is8BINgBfCDPAVStfHwi0QFWrXx8IssBVq18fCLMAVatfCDKASDOAVatIAMpA6g5IMoBINQBVK18fHwizgFCqcDGia7Ok7IwVg0AAkAgzgFCqcDGia7Ok7IwUQRAIMwBQt2whYzotpGouH9WDQIgzAFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhzgELIMwBIc8BIMsBIcoBDAILIMsBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/Ic8BIMsBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAhzgEgywEhygEMAgtCkeHlzYeJ+pkoIcoBINEBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc4BDAELIMsBQpHh5c2HifqZKH0izwEg0QFCgYCAgL+y/fDDAFStItABfSHKASDMAUKjz/rzl8nu18cAfCLTASDLAUKR4eXNh4n6mShUIM8BINABVHKtIssBfSHPASDOASDMAULdsIWM6LaRqLh/VCDLASDTAVZyrX1CqcDGia7Ok7IwfSHOASDRAUKBgICAv7L98MMAfSHRAQtCqcDGia7Ok7IwIcwBIM8BINoBfCLLASDPAVQgywEgygEgygEg1gF8Is8BViDPASDNASDRAXwi5gEg0QFUrXwiygEgzwFUcq18Is8BIMsBVHKtIM4BINIBfHwi6gEhywECQAJAAkAg6gFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hzAEgzwEiywFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghzAEgygEiywFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhzAEg5gEiywFCgYCAgL+y/fDDAFENAQsgywEgzAFaDQAgzwEh5AEgygEh6wEMAQsgygFCkeHlzYeJ+pkofSLLASDmAUKBgICAv7L98MMAVK0izAF9IesBIM8BQqPP+vOXye7XxwB8Is0BIMoBQpHh5c2HifqZKFQgywEgzAFUcq0iygF9IeQBIOoBIM8BQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IeoBIOYBQoGAgIC/sv3wwwB9IeYBCyADQbA4aiD0AUIAIPQBQgAQyQMgA0HQN2og9QFCACD0AUIAEMkDIANB8DZqIPYBQgAg9AFCABDJAyADQZA2aiD3AUIAIPQBQgAQyQMgA0GgOGogAykDsDhCfYMizAFCAEIAQv////++sv3wQhDJAyADQZA4aiADKQOoOCLKAUIAQoGAgIC/sv3wwwBCABDJAyADQYA4aiDKAUIAQpHh5c2HifqZKEIAEMkDIANB8DdqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB4DdqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HgOGog9QFCACD1AUIAEMkDIANB0DhqIPYBQgAg9QFCABDJAyADQcA4aiD3AUIAIPUBQgAQyQMgA0HAN2ogAykDgDgi0QEgAykDuDgizgEgAykD0DciygF8ItIBfCLLASADKQOYOCDMASADKQOQOCLPAXwgzwFUrXx8IswBIMoBfCLPAUIAQgBC/////76y/fBCEMkDIANBsDdqIAMpA8g3IsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBoDdqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0GQN2ogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GAN2ogygFCAEKpwMaJrs6TsjBCABDJAyADQYA5aiD2AUIAIPYBQgAQyQMgA0HwOGog9wFCACD2AUIAEMkDIANB4DZqIAMpA9g3IsoBIMwBIM8BVq18ItUBIAMpA+A4fCLNASDKASDOASDSAVatfCLTASADKQPwNiLKAXwizgEgAykD8Dd8ItIBIMsBIMwBVq0gAykDiDggywEg0QFUrXx8fCLXAXwiywEgAykDoDd8IswBIAMpA7g3IM8BIAMpA7A3ItEBfCDRAVStfHwizwEgygF8ItEBQgBCAEL/////vrL98EIQyQMgA0HQNmogAykD6DYiygFCAEKBgICAv7L98MMAQgAQyQMgA0HANmogygFCAEKR4eXNh4n6mShCABDJAyADQbA2aiDKAUIAQt2whYzotpGouH9CABDJAyADQaA2aiDKAUIAQqnAxomuzpOyMEIAEMkDIANBkDlqIPcBQgAg9wFCABDJAyADQYA2aiADKQP4NiLKASDPASDRAVatfCLYASADKQPQOCLWAXwi0AEg1gEgygEgzgEg0wFUrXwi2gEgAykDkDYiygF8ItMBIAMpA+A3fCLUASDSASDXAVatIAMpA/g3IM4BINIBVq18fHwizgF8ItIBIMsBIM0BVK0gAykD6DggzQEg1QFUrXx8fCLNASADKQOQN3wi1QEgzAEgzwFWrSADKQOoNyDLASDMAVatfHx8ItcBfCLLASADKQPANnwizAEgAykD2DYgAykD0DYizwEg0QF8IM8BVK18fCLPASDKAXwi0QFCAEIAQv////++sv3wQhDJAyADQfA1aiADKQOINiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQeA1aiDKAUIAQpHh5c2HifqZKEIAEMkDIANB0DVqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBwDVqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA8g1IAMpA6g2IAMpA4g3IM4BINQBVK0gAykD6Dcg0wEg1AFWrXx8IAMpA5g2ItQBINMBINoBVK18fCLTASADKQPAOCLWAXwiygEgzQEg0gFUrSADKQPYOCLaASDOASDSAVatfHx8Is4BIAMpA4A3fCLSASDOAVStfCDSASDVASDXAVatIAMpA5g3IM0BINUBVq18fHwizQEg0gFUrXwgygEgzgFWrSADKQPIOCLVASDKASDTAVStfHx8ItMBIAMpA/A4ItcBfCLKASADKQOIOSDNASDNASADKQOAOXwizgFWrXwgzgEgywEg0AFUrSDaASDQASDYAVStfHx8Is0BIM4BVK18fCLOASADKQOgNnwi0gEgzgFUrXwg0gEg0gEgAykDuDYgzQEgzQEgAykDsDZ8ItABVq18INABIMwBIM8BVq0gAykDyDYgywEgzAFWrXx8fCLNASDQAVStfHwiywFWrXwgygEgzgFWrSADKQP4OCLOASDKASDTAVStfHx8ItIBIAMpA5A5fCLKASDOASDLASDLASDXAXwizAFWrXwgzAEgzAEg1QEg1AEgzwEg0QFWrXwizwEg1gF8IssBIM8BVK18IMsBIMsBIM0BfCLPAVatfHwiywFWrXx8IswBIAMpA8A1fCLNASDMAVStfCDNASADKQPYNSDLASDLASADKQPQNXwizgFWrXwgzgEgAykD6DUgzwEgzwEgAykD4DV8IssBVq18IMsBIAMpA/g1IAMpA/A1Is8BINEBfCDPAVStfHwi5wEgywFUrXx8IuIBIM4BVK18fCLsASDNAVStfCDKASDMAVatIAMpA5g5IMoBINIBVK18fHwi7QFCqcDGia7Ok7IwVg0AIOcBIegBIOIBId8BIOwBIeUBIO0BIuEBQqnAxomuzpOyMFINASDlAULdsIWM6LaRqLh/Vg0AQqnAxomuzpOyMCHhASDlAULdsIWM6LaRqLh/Ug0BIN8BQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IeUBIN8BQpHh5c2HifqZKFINAUKR4eXNh4n6mSgh3wEg5wFCgYCAgL+y/fDDAFQNAQsg4gFCkeHlzYeJ+pkofSLKASDnAUKBgICAv7L98MMAVK0iywF9Id8BIOwBQqPP+vOXye7XxwB8IswBIOIBQpHh5c2HifqZKFQgygEgywFUcq0iygF9IeUBIO0BIOwBQt2whYzotpGouH9UIMoBIMwBVnKtfUKpwMaJrs6TsjB9IeEBIOcBQoGAgIC/sv3wwwB9IegBCwJAAkACQAJAAkACQAJAIBcEQCDiAUKR4eXNh4n6mSh9IsoBIOcBQoGAgIC/sv3wwwBUIhytIssBfSHxASDsAUKjz/rzl8nu18cAfCLMASDiAUKR4eXNh4n6mShUIMoBIMsBVHKtIsoBfSHyASDtASDsAULdsIWM6LaRqLh/VCDKASDMAVZyrX1CqcDGia7Ok7IwfSHzAUEBIBkgGUEBTRshDSDnAUKBgICAv7L98MMAfSH5ASD4AUKpwMaJrs6TsjB8IfsBQQEhBUEAIQoDQCAKIQcgBSIKIA1GDQUgFCAFQQV0IhdqIgUpAxgh4AEgBSkDECHjASAFKQMIIekBIAUpAwAi+gEh0QECfgJAAkAg+gEg+AEizgFSDQAg7gEizgEg6QEi0QFSDQAg7wEizgEg4wEi0QFSDQAg8AEizgEg4AEi0QFRDQELIM4BINEBWg0AQt2whYzotpGouH8g6QEg7gF9IsoBIOMBIO8BfSLLASDgASDwAVStIswBVCDjASDvAVRyrSLNAX0izwF9Is4BIMsBIMwBfSLLAUKR4eXNh4n6mShWQpHh5c2HifqZKCDLAX0iywEg4AEg8AF9IswBQoGAgIC/sv3wwwBWrSLSAVRyrSLQAX0h0QEgzgEg0AFUIM8BQt2whYzotpGouH9WciEFIMsBINIBfSHOAUKBgICAv7L98MMAIMwBfSHPASDKASDNAVQg6QEg7gFUcq0g+wEg+gF9fAwBCyDvASDjAX0iygEg4AEg8AFWrSLLAX0hzgEg7gEg6QF9IswBIMoBIMsBVCDjASDvAVZyrSLKAX0h0QEg6QEg7gFWIMoBIMwBVnIhBSDwASDgAX0hzwEg+AEg+gF9CyHKASADIM8BNwOIpAEgAyDOATcDgKQBIAMg0QE3A/ijASADIMoBIAWtfTcD8KMBIANB8KMBakHAlsIAQSAQ8QNFDQIgA0HwwQFqIgVCADcDACADQejBAWoiI0IANwMAIANCADcD4MEBIANCATcD+MEBIANByKQBaiIwIANBiKQBaiIzKQMANwMAIANBwKQBaiI0IANBgKQBaiI1KQMANwMAIANBuKQBaiI2IANB+KMBaiJFKQMANwMAIAMgAykD8KMBNwOwpAEgA0HIpQFqIkZBuJbCACkDACL8ATcDACADQcClAWoiR0GwlsIAKQMAIv0BNwMAIANBuKUBaiJIQaiWwgApAwAi/wE3AwAgA0GglsIAKQMAIoACNwOwpQECQCADQbCkAWogA0HgwQFqQSAQ8QNFBEBChYHundXn4KSMfyHbAUKlibn6l5a0iwIh0QFC47Pxmp7Wjv/TACHZAUKn24Xx2si53BshzwEMAQtCkeHlzYeJ+pkoIdcBQt2whYzotpGouH8h0AFCqcDGia7Ok7IwIdgBQoGAgIC/sv3wwwAhygFChYHundXn4KSMfyHbAULjs/GantaO/9MAIdkBQqfbhfHayLncGyHPAUKlibn6l5a0iwIh0QFCACHOASADKQPIpAEhzQEgAykDsKQBIdIBIAMpA7ikASHMASADKQPApAEh0wFCACHaAUIAIdYBQgAhywEDQCADQbClAWogA0HgwQFqQSAQ8QNFBEAgywEhzwEg1gEh2QEgzgEh0QEg2gEh2wEMAgsgzQGnQQFxRQRAA0Ag0wFCP4YgzQFCAYiEIc0BAkAgzwFCAYNQBEAg2wEh1AEg2QEh1QEgzwEh3QEMAQsg0QEg2wEg2wFCo8/685fJ7tfHAH0i3gFWIN4BIN4BINkBQpHh5c2HifqZKHwi1AEg2QFUINQBINQBIM8BQoGAgIC/sv3wwwB8It0BIM8BVK18ItUBVnKtfCLUAVZyrXxCqcDGia7Ok7IwfCHRAQsg0gFCP4YgzAFCP4Yg0wFCAYiEIdMBINIBQgGIIdIBINEBQj+GINQBQgGIhCHbASDUAUI/hiDVAUIBiIQh2QEg1QFCP4Yg3QFCAYiEIc8BINEBQgGIIdEBIMwBQgGIhCHMASDNAUIBg1ANAAsgAyDTATcDwKQBIAMgzQE3A8ikASADIMwBNwO4pAEgAyDSATcDsKQBCyDKAadBAXFFBEADQCDXAUI/hiDKAUIBiIQhygECQCDLAUIBg1AEQCDLASHVASDWASHLASDaASHUAQwBCyDOASDaASDaAUKjz/rzl8nu18cAfSLeAVYg3gEg3gEg1gEg1gFCkeHlzYeJ+pkofCLUAVYg1AEgywFCgYCAgL+y/fDDAHwi1QEgywFUrXwiywEg1AFUcq18ItQBVnKtfEKpwMaJrs6TsjB8Ic4BCyDYAUI/hiDQAUI/hiDXAUIBiIQh1wEg2AFCAYgh2AEgzgFCP4Yg1AFCAYiEIdoBINQBQj+GIMsBQgGIhCHWASDLAUI/hiDVAUIBiIQhywEgzgFCAYghzgEg0AFCAYiEIdABIMoBQgGDUA0ACyADINcBNwPApQEgAyDKATcDyKUBIAMg0AE3A7ilASADINgBNwOwpQELINIBIdUBAkACQAJAAkACQCDSASDYASLUAVINACDMASHVASDQASLUASDMAVINACDXASLUASDTASLVAVINACDKASHUASDNASHVASDKASDNAVENAQsg1AEg1QFYDQAgAyDKASDNAX0i1AE3A8ilASADINcBINMBfSLeASDKASDNAVStIsoBfSLVATcDwKUBIAMg0AEgzAF9It0BIMoBIN4BViDTASDXAVZyrSLKAX0i3gE3A7ilASADINgBINIBfSDKASDdAVYgzAEg0AFWcq19ItgBNwOwpQECQAJAIM4BIsoBINEBItABUg0AINoBIsoBINsBItABUg0AINYBIsoBINkBItABUg0AIM8BIdABIM8BIMsBIsoBUQ0BCyDKASDQAVQNAgsgzgEg0QF9INoBINsBVCDaASDbAX0i2gEg1gEg2QFUINYBINkBfSLWASDLASDPAVStIt0BVHKtIv4BVHKtfSHOASDLASDPAX0hywEg1QEh1wEg3gEh0AEg1AEhygEg1gEg3QF9IdYBINoBIP4BfSHaAQwDCyADIM0BIMoBfSLUATcDyKQBIAMg0wEg1wF9It4BIMoBIM0BVq0izQF9ItUBNwPApAEgAyDMASDQAX0i3QEg0wEg1wFUIM0BIN4BVnKtIs0BfSLeATcDuKQBIAMg0gEg2AF9IMwBINABVCDNASDdAVZyrX0i0gE3A7CkAQJAAkAgzgEizAEg0QEizQFSDQAg2gEizAEg2wEizQFSDQAg1gEizAEg2QEizQFSDQAgywEizAEgzwEizQFRDQELIMwBIM0BVg0CCyDRASDOAX0g2wEg2gF9It0BINkBINYBfSL+ASDLASDPAVatIoECVCDWASDZAVZyrSLZAVQg2gEg2wFWcq19IdEBIM8BIMsBfSHPASDVASHTASDeASHMASDUASHNASDdASDZAX0h2wEg/gEggQJ9IdkBDAILIM4BQt2whYzotpGouH8g2wF9IsoBQpHh5c2HifqZKCDZAX0izgEgzwFCgYCAgL+y/fDDAFatItABVCDZAUKR4eXNh4n6mShWcq0i1wFUINsBQt2whYzotpGouH9Wcq0g0QF8fSDKASDXAX0i1wEg2gF8IsoBINcBVCDKASDOASDQAX0i0AEg1gF8Is4BINABVCDOAUKBgICAv7L98MMAIM8BfSLQASDLAXwiywEg0AFUrXwi1gEgzgFUcq18ItoBIMoBVHKtfEKpwMaJrs6TsjB8Ic4BINUBIdcBIN4BIdABINQBIcoBDAELINEBIM4BfULdsIWM6LaRqLh/INoBfSLMAUKR4eXNh4n6mSgg1gF9Is0BIMsBQoGAgIC/sv3wwwBWrSLRAVQg1gFCkeHlzYeJ+pkoVnKtItMBVCDaAULdsIWM6LaRqLh/VnKtfSDMASDTAX0i0wEg2wF8IswBINMBVCDMASDNASDRAX0i0QEg2QF8Is0BINEBVCDNAUKBgICAv7L98MMAIMsBfSLRASDPAXwizwEg0QFUrXwi2QEgzQFUcq18ItsBIMwBVHKtfEKpwMaJrs6TsjB8IdEBINUBIdMBIN4BIcwBINQBIc0BCyADQbCkAWogA0HgwQFqQSAQ8QMNAAsLQqnAxomuzpOyMCHSASDpASDuAXwizAEg7gFUIMwBIOMBIO8BfCLNASDvAVQgzQEgzQEg4AEg8AF8IssBIPABVK18IsoBVnKtfCLNASDMAVRyrSD4ASD6AXx8Is4BIcwBAkACQAJAIM4BQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IdIBIM0BIswBQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIdIBIMoBIswBQpHh5c2HifqZKFINAEKBgICAv7L98MMAIdIBIMsBIswBQoGAgIC/sv3wwwBRDQELIMwBINIBWg0AIM0BIdIBIMoBIcwBDAELIMoBQpHh5c2HifqZKH0i0gEgywFCgYCAgL+y/fDDAFStItABfSHMASDNAUKjz/rzl8nu18cAfCLTASDKAUKR4eXNh4n6mShUINABINIBVnKtIsoBfSHSASDOASDNAULdsIWM6LaRqLh/VCDKASDTAVZyrX1CqcDGia7Ok7IwfSHOASDLAUKBgICAv7L98MMAfSHLAQsgAyDLATcDiKQBIAMgzAE3A4CkASADINIBNwP4owEgAyDOATcD8KMBIANB8KMBakHAlsIAQSAQ8QNFDQMgBUIANwMAICNCADcDACADQgA3A+DBASADQgE3A/jBASAwIDMpAwA3AwAgNCA1KQMANwMAIDYgRSkDADcDACADIAMpA/CjATcDsKQBIEYg/AE3AwAgRyD9ATcDACBIIP8BNwMAIAMggAI3A7ClAQJAIANBsKQBaiADQeDBAWpBIBDxA0UEQEKFge6d1efgpIx/IdwBQqWJufqXlrSLAiHOAULjs/GantaO/9MAIeABQqfbhfHayLncGyHNAQwBC0KR4eXNh4n6mSgh1QFC3bCFjOi2kai4fyHTAUKpwMaJrs6TsjAh1wFCgYCAgL+y/fDDACHMAUKFge6d1efgpIx/IdwBQuOz8Zqe1o7/0wAh4AFCp9uF8drIudwbIc0BQqWJufqXlrSLAiHOAUIAIcsBIAMpA8ikASHSASADKQOwpAEh2AEgAykDuKQBIdABIAMpA8CkASHUAUIAId0BQgAh3gFCACHKAQNAIANBsKUBaiADQeDBAWpBIBDxA0UEQCDKASHNASDeASHgASDLASHOASDdASHcAQwCCyDSAadBAXFFBEADQCDUAUI/hiDSAUIBiIQh0gECQCDNAUIBg1AEQCDcASHaASDgASHWASDNASHjAQwBCyDOASDcASDcAUKjz/rzl8nu18cAfSLpAVYg6QEg6QEg4AFCkeHlzYeJ+pkofCLaASDgAVQg2gEg2gEgzQFCgYCAgL+y/fDDAHwi4wEgzQFUrXwi1gFWcq18ItoBVnKtfEKpwMaJrs6TsjB8Ic4BCyDYAUI/hiDQAUI/hiDUAUIBiIQh1AEg2AFCAYgh2AEgzgFCP4Yg2gFCAYiEIdwBINoBQj+GINYBQgGIhCHgASDWAUI/hiDjAUIBiIQhzQEgzgFCAYghzgEg0AFCAYiEIdABINIBQgGDUA0ACyADINQBNwPApAEgAyDSATcDyKQBIAMg0AE3A7ikASADINgBNwOwpAELIMwBp0EBcUUEQANAINUBQj+GIMwBQgGIhCHMAQJAIMoBQgGDUARAIMoBIdYBIN4BIcoBIN0BIdoBDAELIMsBIN0BIN0BQqPP+vOXye7XxwB9IuMBViDjASDjASDeASDeAUKR4eXNh4n6mSh8ItoBViDaASDKAUKBgICAv7L98MMAfCLWASDKAVStfCLKASDaAVRyrXwi2gFWcq18QqnAxomuzpOyMHwhywELINcBQj+GINMBQj+GINUBQgGIhCHVASDXAUIBiCHXASDLAUI/hiDaAUIBiIQh3QEg2gFCP4YgygFCAYiEId4BIMoBQj+GINYBQgGIhCHKASDLAUIBiCHLASDTAUIBiIQh0wEgzAFCAYNQDQALIAMg1QE3A8ClASADIMwBNwPIpQEgAyDTATcDuKUBIAMg1wE3A7ClAQsCQAJAAkACQAJAINgBItYBINcBItoBUg0AINABItYBINMBItoBUg0AINQBIdYBINUBItoBINQBUg0AINIBIdYBINIBIMwBItoBUQ0BCyDWASDaAVoNACADIMwBINIBfSLWATcDyKUBIAMg1QEg1AF9IuMBIMwBINIBVK0izAF9ItoBNwPApQEgAyDTASDQAX0i6QEgzAEg4wFWINQBINUBVnKtIswBfSLjATcDuKUBIAMg1wEg2AF9IMwBIOkBViDQASDTAVZyrX0i1wE3A7ClASDOASHTAQJAAkAgywEizAEgzgFSDQAg3AEi0wEg3QEizAFSDQAg4AEi0wEg3gEizAFSDQAgygEhzAEgygEgzQEi0wFRDQELIMwBINMBVA0CCyDLASDOAX0g3QEg3AF9IukBIN4BIOABfSL6ASDKASDNAVStIvwBVCDeASDgAVRyrSL9AVQg3AEg3QFWcq19IcsBIMoBIM0BfSHKASDaASHVASDjASHTASDWASHMASD6ASD8AX0h3gEg6QEg/QF9Id0BDAMLIAMg0gEgzAF9ItYBNwPIpAEgAyDUASDVAX0i4wEgzAEg0gFWrSLSAX0i2gE3A8CkASADINABINMBfSLpASDUASDVAVQg0gEg4wFWcq0i0gF9IuMBNwO4pAEgAyDYASDXAX0g0AEg0wFUINIBIOkBVnKtfSLYATcDsKQBIM4BIdIBIMsBIdABAkACQCDLASDOAVINACDcASLSASDdASLQAVINACDgASLSASDeASLQAVINACDNASHSASDKASHQASDKASDNAVENAQsg0AEg0gFWDQILIM4BIMsBfSDcASDdAVQg3AEg3QF9ItwBIOABIN4BfSLpASDKASDNAVatIvoBVCDeASDgAVZyrSLgAVRyrX0hzgEgzQEgygF9Ic0BINoBIdQBIOMBIdABINYBIdIBINwBIOABfSHcASDpASD6AX0h4AEMAgsgywFC3bCFjOi2kai4fyDcAX0iywFCkeHlzYeJ+pkoIOABfSLMASDNAUKBgICAv7L98MMAVq0i0wFUIOABQpHh5c2HifqZKFZyrSLVAVQg3AFC3bCFjOi2kai4f1ZyrSDOAXx9IMsBINUBfSLVASDdAXwiywEg1QFUIMsBIMwBINMBfSLTASDeAXwizAEg0wFUIMwBQoGAgIC/sv3wwwAgzQF9ItMBIMoBfCLKASDTAVStfCLeASDMAVRyrXwi3QEgywFUcq18QqnAxomuzpOyMHwhywEg2gEh1QEg4wEh0wEg1gEhzAEMAQsgzgEgywF9Qt2whYzotpGouH8g3QF9Is4BQpHh5c2HifqZKCDeAX0i0gEgygFCgYCAgL+y/fDDAFatItABVCDeAUKR4eXNh4n6mShWcq0i1AFUIN0BQt2whYzotpGouH9Wcq19IM4BINQBfSLUASDcAXwizgEg1AFUIM4BINIBINABfSLQASDgAXwi0gEg0AFUINIBQoGAgIC/sv3wwwAgygF9ItABIM0BfCLNASDQAVStfCLgASDSAVRyrXwi3AEgzgFUcq18QqnAxomuzpOyMHwhzgEg2gEh1AEg4wEh0AEg1gEh0gELIANBsKQBaiADQeDBAWpBIBDxAw0ACwsgA0GwNWogzwFCACDoAUIAEMkDIANB0DRqIM8BQgAg3wFCABDJAyADQcA0aiDPAUIAIOUBQgAQyQMgA0GwNGogzwFCACDhAUIAEMkDIANBoDVqIAMpA7A1IswBQgBCAEL/////vrL98EIQyQMgA0GQNWogAykDqDUiygFCAEKBgICAv7L98MMAQgAQyQMgA0GANWogygFCAEKR4eXNh4n6mShCABDJAyADQfA0aiDKAUIAQt2whYzotpGouH9CABDJAyADQeA0aiDKAUIAQqnAxomuzpOyMEIAEMkDIANBoDRqINkBQgAg6AFCABDJAyADQcAzaiDZAUIAIN8BQgAQyQMgA0GwM2og2QFCACDlAUIAEMkDIANBoDNqINkBQgAg4QFCABDJAyADQZA0aiADKQOANSLUASADKQO4NSLQASADKQPQNHwi0wF8IssBIAMpA5g1IMwBIAMpA5A1IsoBfCDKAVStfHwizAEgAykDoDR8Is8BQgBCAEL/////vrL98EIQyQMgA0GANGogAykDmDQiygFCAEKBgICAv7L98MMAQgAQyQMgA0HwM2ogygFCAEKR4eXNh4n6mShCABDJAyADQeAzaiDKAUIAQt2whYzotpGouH9CABDJAyADQdAzaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBkDNqINsBQgAg6AFCABDJAyADQbAyaiDbAUIAIN8BQgAQyQMgA0GgMmog2wFCACDlAUIAEMkDIANBkDJqINsBQgAg4QFCABDJAyADQYAzaiADKQOoNCDMASDPAVatfCLYASADKQPAM3wi0gEgAykD2DQg0AEg0wFWrXwi1QEgAykDwDR8ItABIAMpA/A0fCLTASDLASDMAVatIAMpA4g1IMsBINQBVK18fHwi1gF8IssBIAMpA/AzfCLMASADKQOINCDPASADKQOANCLKAXwgygFUrXx8Is8BIAMpA5AzfCLUAUIAQgBC/////76y/fBCEMkDIANB8DJqIAMpA4gzIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB4DJqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQMmogygFCAELdsIWM6LaRqLh/QgAQyQMgA0HAMmogygFCAEKpwMaJrs6TsjBCABDJAyADQYAyaiDRAUIAIOgBQgAQyQMgA0GgMWog0QFCACDfAUIAEMkDIANBkDFqINEBQgAg5QFCABDJAyADQYAxaiDRAUIAIOEBQgAQyQMgA0HwMWogAykDmDMgzwEg1AFWrXwi2gEgAykDsDJ8ItEBIAMpA8g0INABINUBVK18ItkBIAMpA7A0fCLVASADKQPgNHwi1wEg0wEg1gFWrSADKQP4NCDQASDTAVatfHx8ItABIAMpA7AzfCLTASDLASDSAVStIAMpA8gzINIBINgBVK18fHwi0gEgAykD4DN8ItgBIMwBIM8BVq0gAykD+DMgywEgzAFWrXx8fCLWAXwiywEgAykD4DJ8IswBIAMpA/gyINQBIAMpA/AyIsoBfCDKAVStfHwizwEgAykDgDJ8ItQBQgBCAEL/////vrL98EIQyQMgA0HgMWogAykD+DEiygFCAEKBgICAv7L98MMAQgAQyQMgA0HQMWogygFCAEKR4eXNh4n6mShCABDJAyADQcAxaiDKAUIAQt2whYzotpGouH9CABDJAyADQbAxaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQO4MSADKQPIMiADKQPYMyDQASDXAVStIAMpA+g0INUBINcBVq18fCADKQO4NCDVASDZAVStfHwi1QEgAykDoDN8IsoBINIBINMBVK0gAykDuDMg0AEg0wFWrXx8fCLQASADKQPQM3wi0wEg0AFUrXwg0wEg1gEg2AFUrSADKQPoMyDSASDYAVatfHx8ItIBINMBVK18IMoBINABVq0gAykDqDMgygEg1QFUrXx8fCLVASADKQOQMnwiygEgAykDqDIg0gEg0gEgAykDoDJ8ItABVq18INABINABIMsBINEBVK0gAykDuDIg0QEg2gFUrXx8fCLSAVatfHwi0QEgAykDwDJ8ItABINEBVK18INABINABIAMpA9gyINIBINIBIAMpA9AyfCLTAVatfCDTASDTASDMASDPAVatIAMpA+gyIMsBIMwBVq18fHwizAFWrXx8IssBVq18IMoBINEBVq0gAykDmDIgygEg1QFUrXx8fCLTASADKQOAMXwi0gEgAykDmDEgywEgAykDkDF8IsoBIMsBVK18IMoBIMoBIAMpA6gxIAMpA4gyIM8BINQBVq18Is8BIAMpA6AxfCLLASDPAVStfCDLASDLASDMAXwizAFWrXx8IssBVq18fCLPASADKQOwMXwi0QEgzwFUrXwg0QEg0QEgAykDyDEgywEgywEgAykDwDF8ItABVq18INABINABIAMpA9gxIMwBIMwBIAMpA9AxfCLKAVatfCDKASADKQPoMSADKQPgMSLLASDUAXwgywFUrXx8IssBIMoBVK18fCLKAVatfHwizAFWrXwgzwEg0gFUrSADKQOIMSDSASDTAVStfHx8Is8BQqnAxomuzpOyMFYNAAJAIM8BQqnAxomuzpOyMFEEQCDMAULdsIWM6LaRqLh/Vg0CIMwBQt2whYzotpGouH9SBEAgygEh2AEgzAEh0AFCqcDGia7Ok7IwIc8BDAQLIMoBQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IdABIMoBQpHh5c2HifqZKFENASDKASHYAUKpwMaJrs6TsjAhzwEMAwsgygEh2AEgzAEh0AEMAgtCkeHlzYeJ+pkoIdgBIMsBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc8BDAELIMoBQpHh5c2HifqZKH0i0gEgywFCgYCAgL+y/fDDAFStItEBfSHYASDMAUKjz/rzl8nu18cAfCLTASDKAUKR4eXNh4n6mShUINEBINIBVnKtIsoBfSHQASDPASDMAULdsIWM6LaRqLh/VCDKASDTAVZyrX1CqcDGia7Ok7IwfSHPASDLAUKBgICAv7L98MMAfSHLAQsgA0GwL2og6AFCACD0AUIAEMkDIANB0C5qIN8BQgAg9AFCABDJAyADQfAtaiDlAUIAIPQBQgAQyQMgA0GQLWog4QFCACD0AUIAEMkDIANBoC9qIAMpA7AvItIBQgBCAEL/////vrL98EIQyQMgA0GQL2ogAykDqC8iygFCAEKBgICAv7L98MMAQgAQyQMgA0GAL2ogygFCAEKR4eXNh4n6mShCABDJAyADQfAuaiDKAUIAQt2whYzotpGouH9CABDJAyADQeAuaiDKAUIAQqnAxomuzpOyMEIAEMkDIANB8C9qIOgBQgAg9QFCABDJAyADQeAvaiDfAUIAIPUBQgAQyQMgA0HQL2og5QFCACD1AUIAEMkDIANBwC9qIOEBQgAg9QFCABDJAyADQcAuaiADKQOALyLXASADKQO4LyLUASADKQPQLnwi1QF8IswBIAMpA5gvINIBIAMpA5AvIsoBfCDKAVStfHwi0gEgAykD8C98ItEBQgBCAEL/////vrL98EIQyQMgA0GwLmogAykDyC4iygFCAEKBgICAv7L98MMAQgAQyQMgA0GgLmogygFCAEKR4eXNh4n6mShCABDJAyADQZAuaiDKAUIAQt2whYzotpGouH9CABDJAyADQYAuaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBsDBqIOgBQgAg9gFCABDJAyADQaAwaiDfAUIAIPYBQgAQyQMgA0GQMGog5QFCACD2AUIAEMkDIANBgDBqIOEBQgAg9gFCABDJAyADQeAtaiADKQP4LyDRASDSAVStfCLeASADKQPgL3wi0wEgAykD2C4g1AEg1QFWrXwi2gEgAykD8C18ItQBIAMpA/AufCLVASDMASDSAVatIAMpA4gvIMwBINcBVK18fHwi3QF8IswBIAMpA6AufCLSASADKQO4LiDRASADKQOwLiLKAXwgygFUrXx8ItEBIAMpA7AwfCLXAUIAQgBC/////76y/fBCEMkDIANB0C1qIAMpA+gtIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBwC1qIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0GwLWogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GgLWogygFCAEKpwMaJrs6TsjBCABDJAyADQfAwaiDoAUIAIPcBQgAQyQMgA0HgMGog3wFCACD3AUIAEMkDIANB0DBqIOUBQgAg9wFCABDJAyADQcAwaiDhAUIAIPcBQgAQyQMgA0GALWogAykDuDAg0QEg1wFWrXwi4wEgAykDoDB8ItYBIAMpA/gtINQBINoBVK18IukBIAMpA5AtfCLaASADKQPgLnwi2QEg1QEg3QFWrSADKQP4LiDUASDVAVatfHx8ItQBIAMpA9AvfCLVASDMASDTAVStIAMpA+gvINMBIN4BVK18fHwi0wEgAykDkC58It4BINEBINIBVK0gAykDqC4gzAEg0gFWrXx8fCLdAXwizAEgAykDwC18ItIBIAMpA9gtINcBIAMpA9AtIsoBfCDKAVStfHwi0QEgAykD8DB8ItcBQgBCAEL/////vrL98EIQyQMgA0HwLGogAykDiC0iygFCAEKBgICAv7L98MMAQgAQyQMgA0HgLGogygFCAEKR4eXNh4n6mShCABDJAyADQdAsaiDKAUIAQt2whYzotpGouH9CABDJAyADQcAsaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQPILCADKQOoLSADKQOILiDUASDZAVStIAMpA+guINkBINoBVK18fCADKQOYLSDaASDpAVStfHwi2gEgAykDwC98IsoBINMBINUBVK0gAykD2C8g1AEg1QFWrXx8fCLUASADKQOALnwi1QEg1AFUrXwg1QEg3QEg3gFUrSADKQOYLiDTASDeAVatfHx8ItMBINUBVK18IMoBINQBVq0gAykDyC8gygEg2gFUrXx8fCLaASADKQOAMHwiygEgAykDmDAg0wEg0wEgAykDkDB8ItQBVq18INQBINQBIMwBINYBVK0gAykDqDAg1gEg4wFUrXx8fCLTAVatfHwi1AEgAykDoC18ItUBINQBVK18INUBINUBIAMpA7gtINMBINMBIAMpA7AtfCLWAVatfCDWASDRASDSAVStIAMpA8gtIMwBINIBVq18fHwi0wEg1gFUrXx8IswBVq18IMoBINQBVq0gAykDiDAgygEg2gFUrXx8fCLWASADKQPAMHwiygEgAykD2DAgzAEgzAEgAykD0DB8ItIBVq18INIBINIBIAMpA+gwIAMpA/gwINEBINcBVq18ItEBIAMpA+AwfCLMASDRAVStfCDMASDMASDTAXwi0QFWrXx8IswBVq18fCLSASADKQPALHwi1QEg0gFUrXwg1QEg1QEgAykD2CwgzAEgzAEgAykD0Cx8ItQBVq18INQBINQBIAMpA+gsINEBINEBIAMpA+AsfCLMAVatfCDMASDMASADKQP4LCADKQPwLCLRASDXAXwg0QFUrXx8ItEBVq18fCLTAVatfHwi1AFWrXwgygEg0gFWrSADKQPIMCDKASDWAVStfHx8IsoBQqnAxomuzpOyMFYNAAJAIMoBQqnAxomuzpOyMFEEQCDUAULdsIWM6LaRqLh/Vg0CINQBQt2whYzotpGouH9SBEAg0wEh0gEg1AEhzAFCqcDGia7Ok7IwIcoBDAQLINMBQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IcwBINMBQpHh5c2HifqZKFENASDTASHSAUKpwMaJrs6TsjAhygEMAwsg0wEh0gEg1AEhzAEMAgtCkeHlzYeJ+pkoIdIBINEBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIcoBDAELINMBQpHh5c2HifqZKH0izAEg0QFCgYCAgL+y/fDDAFStItUBfSHSASDUAUKjz/rzl8nu18cAfCLXASDTAUKR4eXNh4n6mShUIMwBINUBVHKtItMBfSHMASDKASDUAULdsIWM6LaRqLh/VCDTASDXAVZyrX1CqcDGia7Ok7IwfSHKASDRAUKBgICAv7L98MMAfSHRAQsgA0GwLGog0QFCACDNAUIAEMkDIANB0CtqINIBQgAgzQFCABDJAyADQcAraiDMAUIAIM0BQgAQyQMgA0GwK2ogygFCACDNAUIAEMkDIANBoCxqIAMpA7AsItQBQgBCAEL/////vrL98EIQyQMgA0GQLGogAykDqCwizQFCAEKBgICAv7L98MMAQgAQyQMgA0GALGogzQFCAEKR4eXNh4n6mShCABDJAyADQfAraiDNAUIAQt2whYzotpGouH9CABDJAyADQeAraiDNAUIAQqnAxomuzpOyMEIAEMkDIANBoCtqINEBQgAg4AFCABDJAyADQcAqaiDSAUIAIOABQgAQyQMgA0GwKmogzAFCACDgAUIAEMkDIANBoCpqIMoBQgAg4AFCABDJAyADQZAraiADKQOALCLZASADKQO4LCLWASADKQPQK3wi2gF8ItMBIAMpA5gsINQBIAMpA5AsIs0BfCDNAVStfHwi1AEgAykDoCt8ItUBQgBCAEL/////vrL98EIQyQMgA0GAK2ogAykDmCsizQFCAEKBgICAv7L98MMAQgAQyQMgA0HwKmogzQFCAEKR4eXNh4n6mShCABDJAyADQeAqaiDNAUIAQt2whYzotpGouH9CABDJAyADQdAqaiDNAUIAQqnAxomuzpOyMEIAEMkDIANBkCpqINEBQgAg3AFCABDJAyADQbApaiDSAUIAINwBQgAQyQMgA0GgKWogzAFCACDcAUIAEMkDIANBkClqIMoBQgAg3AFCABDJAyADQYAqaiADKQOoKyDUASDVAVatfCLeASADKQPAKnwi1wEgAykD2Csg1gEg2gFWrXwi4AEgAykDwCt8ItYBIAMpA/ArfCLaASDTASDUAVatIAMpA4gsINMBINkBVK18fHwi3QF8ItMBIAMpA/AqfCLUASADKQOIKyDVASADKQOAKyLNAXwgzQFUrXx8ItUBIAMpA5AqfCLZAUIAQgBC/////76y/fBCEMkDIANB8ClqIAMpA4gqIs0BQgBCgYCAgL+y/fDDAEIAEMkDIANB4ClqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgA0HQKWogzQFCAELdsIWM6LaRqLh/QgAQyQMgA0HAKWogzQFCAEKpwMaJrs6TsjBCABDJAyADQYApaiDRAUIAIM4BQgAQyQMgA0GgKGog0gFCACDOAUIAEMkDIANBkChqIMwBQgAgzgFCABDJAyADQYAoaiDKAUIAIM4BQgAQyQMgA0HwKGogAykDmCog1QEg2QFWrXwi4wEgAykDsCl8IswBIAMpA8grINYBIOABVK18IuABIAMpA7ArfCLNASADKQPgK3wizgEg2gEg3QFWrSADKQP4KyDWASDaAVatfHx8ItIBIAMpA7AqfCLRASDTASDXAVStIAMpA8gqINcBIN4BVK18fHwi1wEgAykD4Cp8ItYBINQBINUBVq0gAykD+Cog0wEg1AFWrXx8fCLeAXwi0wEgAykD4Cl8ItQBIAMpA/gpIAMpA/ApIsoBINkBfCDKAVStfHwi1QEgAykDgCl8ItoBQgBCAEL/////vrL98EIQyQMgA0HgKGogAykD+CgiygFCAEKBgICAv7L98MMAQgAQyQMgA0HQKGogygFCAEKR4eXNh4n6mShCABDJAyADQcAoaiDKAUIAQt2whYzotpGouH9CABDJAyADQbAoaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQO4KCADKQPIKSADKQPYKiDOASDSAVatIAMpA+grIM0BIM4BVq18fCADKQO4KyDNASDgAVStfHwi2QEgAykDoCp8IsoBINEBINcBVq0gAykDuCog0QEg0gFUrXx8fCLNASADKQPQKnwizgEgzQFUrXwgzgEgzgEg1gEg3gFWrSADKQPoKiDWASDXAVStfHx8ItIBVq18IMoBIM0BVq0gAykDqCogygEg2QFUrXx8fCLRASADKQOQKXwiygEgAykDqCkg0gEg0gEgAykDoCl8Is0BVq18IM0BIM0BIMwBINMBVq0gAykDuCkgzAEg4wFUrXx8fCLMAVatfHwizQEgAykDwCl8Is4BIM0BVK18IM4BIAMpA9gpIMwBIMwBIAMpA9ApfCLSAVatfCDSASDSASDUASDVAVatIAMpA+gpINMBINQBVq18fHwi0wFWrXx8IswBIM4BVK18IMoBIM0BVq0gAykDmCkgygEg0QFUrXx8fCLUASADKQOAKHwiygEgAykDmCggzAEgzAEgAykDkCh8Is0BVq18IM0BIM0BIAMpA6goIAMpA4gpINUBINoBVq18Is4BIAMpA6AofCLMASDOAVStfCDMASDMASDTAXwizgFWrXx8IswBVq18fCLNASADKQOwKHwi0wEgzQFUrXwg0wEg0wEgAykDyCggzAEgzAEgAykDwCh8ItIBVq18INIBINIBIAMpA9goIM4BIM4BIAMpA9AofCLMAVatfCDMASADKQPoKCADKQPgKCLOASDaAXwgzgFUrXx8ItEBIMwBVK18fCLMAVatfHwi0gFWrXwgygEgzQFWrSADKQOIKCDKASDUAVStfHx8Is4BQqnAxomuzpOyMFYNAAJAIM4BQqnAxomuzpOyMFEEQCDSAULdsIWM6LaRqLh/Vg0CINIBQt2whYzotpGouH9SBEAgzAEhzQEg0gEhygFCqcDGia7Ok7IwIc4BDAQLIMwBQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IcoBIMwBQpHh5c2HifqZKFENASDMASHNAUKpwMaJrs6TsjAhzgEMAwsgzAEhzQEg0gEhygEMAgtCkeHlzYeJ+pkoIc0BINEBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc4BDAELIMwBQpHh5c2HifqZKH0iygEg0QFCgYCAgL+y/fDDAFStItMBfSHNASDSAUKjz/rzl8nu18cAfCLUASDMAUKR4eXNh4n6mShUIMoBINMBVHKtIswBfSHKASDOASDSAULdsIWM6LaRqLh/VCDMASDUAVZyrX1CqcDGia7Ok7IwfSHOASDRAUKBgICAv7L98MMAfSHRAQtCqcDGia7Ok7IwIdcBIMoBINABfCLMASDKAVQgzAEgzQEg2AF8ItMBIM0BVCDTASDLASDRAXwi0gEg0QFUrXwi1AEg0wFUcq18ItUBIMwBVHKtIM4BIM8BfHwizAEh0wECQAJAAkAgzAFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8h1wEg1QEi0wFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSgh1wEg1AEi0wFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAh1wEg0gEi0wFCgYCAgL+y/fDDAFENAQsg0wEg1wFaDQAg1QEh0wEg1AEh1wEMAQsg1AFCkeHlzYeJ+pkofSLTASDSAUKBgICAv7L98MMAVK0i1gF9IdcBINUBQqPP+vOXye7XxwB8ItoBINQBQpHh5c2HifqZKFQg0wEg1gFUcq0i1AF9IdMBIMwBINUBQt2whYzotpGouH9UINQBINoBVnKtfUKpwMaJrs6TsjB9IcwBINIBQoGAgIC/sv3wwwB9IdIBCyADINIBNwPIpQEgAyDXATcDwKUBIAMg0wE3A7ilASADIMwBNwOwpQECQCADQbClAWpBwJbCAEEgEPEDRQRAINMBIdQBINcBIdUBDAELQpHh5c2HifqZKCDXAX0i1AEg0gFCgYCAgL+y/fDDAFatItYBfSHVAULdsIWM6LaRqLh/INMBfSLaASDUASDWAVQg1wFCkeHlzYeJ+pkoVnKtItcBfSHUAUKpwMaJrs6TsjAg1wEg2gFWINMBQt2whYzotpGouH9Wcq0gzAF8fSHMAUKBgICAv7L98MMAINIBfSHSAQsgA0GAhQFqIAdBKGxqIgUg0gE3A5AMIAUg1QE3A4gMIAUg1AE3A4AMIAUgzAE3A/gLIAVCATcD8AsCQAJAIApBHEcEQCADQfAnaiATIBdqIgUpAxgizAFCACDRAUIAEMkDIANB4CZqIMwBQgAgzQFCABDJAyADQdAlaiDMAUIAIMoBQgAQyQMgA0HAJGogzAFCACDOAUIAEMkDIANB4CdqIAMpA/AnItMBQgBCAEL/////vrL98EIQyQMgA0HQJ2ogAykD6CcizAFCAEKBgICAv7L98MMAQgAQyQMgA0HAJ2ogzAFCAEKR4eXNh4n6mShCABDJAyADQbAnaiDMAUIAQt2whYzotpGouH9CABDJAyADQaAnaiDMAUIAQqnAxomuzpOyMEIAEMkDIANBkCdqIAUpAxAizAFCACDRAUIAEMkDIANBgCZqIMwBQgAgzQFCABDJAyADQfAkaiDMAUIAIMoBQgAQyQMgA0HgI2ogzAFCACDOAUIAEMkDIANB0CZqIAMpA8AnItoBIAMpA/gnItcBIAMpA+AmfCLWAXwi0gEgAykD2Ccg0wEgAykD0CcizAF8IMwBVK18fCLTASADKQOQJ3wi1AFCAEIAQv////++sv3wQhDJAyADQcAmaiADKQPYJiLMAUIAQoGAgIC/sv3wwwBCABDJAyADQbAmaiDMAUIAQpHh5c2HifqZKEIAEMkDIANBoCZqIMwBQgBC3bCFjOi2kai4f0IAEMkDIANBkCZqIMwBQgBCqcDGia7Ok7IwQgAQyQMgA0GAJ2ogBSkDCCLMAUIAINEBQgAQyQMgA0HwJWogzAFCACDNAUIAEMkDIANB4CRqIMwBQgAgygFCABDJAyADQdAjaiDMAUIAIM4BQgAQyQMgA0HAJWogAykDmCcg0wEg1AFWrXwi2QEgAykDgCZ8ItUBIAMpA+gmINYBINcBVK18It4BIAMpA9AlfCLXASADKQOwJ3wi1gEg0gEg0wFWrSADKQPIJyDSASDaAVStfHx8IuABfCLSASADKQOwJnwi0wEgAykDyCYg1AEgAykDwCYizAF8IMwBVK18fCLUASADKQOAJ3wi2gFCAEIAQv////++sv3wQhDJAyADQbAlaiADKQPIJSLMAUIAQoGAgIC/sv3wwwBCABDJAyADQaAlaiDMAUIAQpHh5c2HifqZKEIAEMkDIANBkCVqIMwBQgBC3bCFjOi2kai4f0IAEMkDIANBgCVqIMwBQgBCqcDGia7Ok7IwQgAQyQMgA0HwJmogBSkDACLMAUIAINEBQgAQyQMgA0HgJWogzAFCACDNAUIAEMkDIANB0CRqIMwBQgAgygFCABDJAyADQcAjaiDMAUIAIM4BQgAQyQMgA0GwJGogAykDiCcg1AEg2gFWrXwi3QEgAykD8CV8IswBIAMpA9glINcBIN4BVK18It4BIAMpA8AkfCLNASADKQOgJ3wizgEg1gEg4AFWrSADKQO4JyDWASDXAVStfHx8ItEBIAMpA/AkfCLXASDSASDVAVStIAMpA4gmINUBINkBVK18fHwi1QEgAykDoCZ8ItYBINMBINQBVq0gAykDuCYg0gEg0wFWrXx8fCLZAXwi0gEgAykDoCV8ItMBIAMpA7glIAMpA7AlIsoBINoBfCDKAVStfHwi1AEgAykD8CZ8ItoBQgBCAEL/////vrL98EIQyQMgA0GgJGogAykDuCQiygFCAEKBgICAv7L98MMAQgAQyQMgA0GQJGogygFCAEKR4eXNh4n6mShCABDJAyADQYAkaiDKAUIAQt2whYzotpGouH9CABDJAyADQfAjaiDKAUIAQqnAxomuzpOyMEIAEMkDIAMpA/gjIAMpA4glIAMpA5gmIM4BINEBVq0gAykDqCcgzQEgzgFWrXx8IAMpA8gkIM0BIN4BVK18fCLeASADKQPgI3wiygEg1QEg1wFUrSADKQP4JCDRASDXAVatfHx8Is0BIAMpA5AmfCLOASDNAVStfCDOASDOASDWASDZAVatIAMpA6gmINUBINYBVq18fHwi0QFWrXwgygEgzQFWrSADKQPoIyDKASDeAVStfHx8ItUBIAMpA9AjfCLKASADKQPoJCDRASDRASADKQPgJHwizQFWrXwgzQEgzQEgzAEg0gFWrSADKQP4JSDMASDdAVStfHx8IswBVq18fCLNASADKQOAJXwizgEgzQFUrXwgzgEgAykDmCUgzAEgzAEgAykDkCV8ItEBVq18INEBINEBINMBINQBVq0gAykDqCUg0gEg0wFWrXx8fCLSAVatfHwizAEgzgFUrXwgygEgzQFWrSADKQPYIyDKASDVAVStfHx8ItUBIAMpA8AjfCLNASADKQPYJCDMASADKQPQJHwiygEgzAFUrXwgygEgygEgAykD6CUgAykD+CYg1AEg2gFWrXwizgEgAykD4CV8IswBIM4BVK18IMwBIMwBINIBfCLOAVatfHwizAFWrXx8ItIBIAMpA/AjfCLRASDSAVStfCDRASADKQOIJCDMASDMASADKQOAJHwi0wFWrXwg0wEg0wEgAykDmCQgzgEgzgEgAykDkCR8IsoBVq18IMoBIMoBIAMpA6gkIAMpA6AkIswBINoBfCDMAVStfHwizgFWrXx8IsoBVq18fCLMASDRAVStfCDNASDSAVatIAMpA8gjIM0BINUBVK18fHwizQFCqcDGia7Ok7IwVg0BAkAgzQFCqcDGia7Ok7IwUQRAIMwBQt2whYzotpGouH9WDQMgzAFC3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhzQELIMwBIdoBIMoBIdYBDAMLIMoBQpHh5c2HifqZKFYNAULdsIWM6LaRqLh/IdoBIMoBQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAhzQEgygEh1gEMAwtCkeHlzYeJ+pkoIdYBIM4BQoGAgIC/sv3wwwBaDQFCqcDGia7Ok7IwIc0BDAILQRxBHEGYr8IAENkDAAsgygFCkeHlzYeJ+pkofSLSASDOAUKBgICAv7L98MMAVK0i0QF9IdYBIMwBQqPP+vOXye7XxwB8ItMBIMoBQpHh5c2HifqZKFQg0QEg0gFWcq0iygF9IdoBIM0BIMwBQt2whYzotpGouH9UIMoBINMBVnKtfUKpwMaJrs6TsjB9Ic0BIM4BQoGAgIC/sv3wwwB9Ic4BCyADQbAjaiAMIBdqIgUpAxgiygFCACDLAUIAEMkDIANBoCJqIMoBQgAg2AFCABDJAyADQZAhaiDKAUIAINABQgAQyQMgA0GAIGogygFCACDPAUIAEMkDIANBoCNqIAMpA7AjItIBQgBCAEL/////vrL98EIQyQMgA0GQI2ogAykDqCMiygFCAEKBgICAv7L98MMAQgAQyQMgA0GAI2ogygFCAEKR4eXNh4n6mShCABDJAyADQfAiaiDKAUIAQt2whYzotpGouH9CABDJAyADQeAiaiDKAUIAQqnAxomuzpOyMEIAEMkDIANB0CJqIAUpAxAiygFCACDLAUIAEMkDIANBwCFqIMoBQgAg2AFCABDJAyADQbAgaiDKAUIAINABQgAQyQMgA0GgH2ogygFCACDPAUIAEMkDIANBkCJqIAMpA4AjItcBIAMpA7gjItQBIAMpA6AifCLVAXwizAEgAykDmCMg0gEgAykDkCMiygF8IMoBVK18fCLSASADKQPQInwi0QFCAEIAQv////++sv3wQhDJAyADQYAiaiADKQOYIiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQfAhaiDKAUIAQpHh5c2HifqZKEIAEMkDIANB4CFqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB0CFqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HAImogBSkDCCLKAUIAIMsBQgAQyQMgA0GwIWogygFCACDYAUIAEMkDIANBoCBqIMoBQgAg0AFCABDJAyADQZAfaiDKAUIAIM8BQgAQyQMgA0GAIWogAykD2CIg0QEg0gFUrXwi2QEgAykDwCF8ItMBIAMpA6giINQBINUBVq18It4BIAMpA5AhfCLUASADKQPwInwi1QEgzAEg0gFWrSADKQOIIyDMASDXAVStfHx8IuABfCLMASADKQPwIXwi0gEgAykDiCIg0QEgAykDgCIiygF8IMoBVK18fCLRASADKQPAInwi1wFCAEIAQv////++sv3wQhDJAyADQfAgaiADKQOIISLKAUIAQoGAgIC/sv3wwwBCABDJAyADQeAgaiDKAUIAQpHh5c2HifqZKEIAEMkDIANB0CBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBwCBqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0GwImogBSkDACLKAUIAIMsBQgAQyQMgA0GgIWogygFCACDYAUIAEMkDIANBkCBqIMoBQgAg0AFCABDJAyADQYAfaiDKAUIAIM8BQgAQyQMgA0HwH2ogAykDyCIg0QEg1wFWrXwi3QEgAykDsCF8IssBIAMpA5ghINQBIN4BVK18It4BIAMpA4AgfCLPASADKQPgInwi0AEg1QEg4AFWrSADKQP4IiDUASDVAVatfHx8ItQBIAMpA7AgfCLVASDMASDTAVStIAMpA8ghINMBINkBVK18fHwi0wEgAykD4CF8ItgBINEBINIBVK0gAykD+CEgzAEg0gFWrXx8fCLZAXwizAEgAykD4CB8ItIBIAMpA/ggINcBIAMpA/AgIsoBfCDKAVStfHwi0QEgAykDsCJ8ItcBQgBCAEL/////vrL98EIQyQMgA0HgH2ogAykD+B8iygFCAEKBgICAv7L98MMAQgAQyQMgA0HQH2ogygFCAEKR4eXNh4n6mShCABDJAyADQcAfaiDKAUIAQt2whYzotpGouH9CABDJAyADQbAfaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQO4HyADKQPIICADKQPYISDQASDUAVatIAMpA+giIM8BINABVq18fCADKQOIICDPASDeAVStfHwi3gEgAykDoB98IsoBINMBINUBVK0gAykDuCAg1AEg1QFWrXx8fCLPASADKQPQIXwi0AEgzwFUrXwg0AEg0AEg2AEg2QFWrSADKQPoISDTASDYAVatfHx8ItMBVq18IMoBIM8BVq0gAykDqB8gygEg3gFUrXx8fCLUASADKQOQH3wiygEgAykDqCAg0wEg0wEgAykDoCB8Is8BVq18IM8BIM8BIMsBIMwBVq0gAykDuCEgywEg3QFUrXx8fCLLAVatfHwizwEgAykDwCB8ItABIM8BVK18INABIAMpA9ggIMsBIMsBIAMpA9AgfCLTAVatfCDTASDTASDRASDSAVStIAMpA+ggIMwBINIBVq18fHwi0gFWrXx8IssBINABVK18IMoBIM8BVq0gAykDmB8gygEg1AFUrXx8fCLUASADKQOAH3wiygEgAykDmCAgywEgywEgAykDkCB8IswBVq18IMwBIMwBIAMpA6ghIAMpA7giINEBINcBVq18Is8BIAMpA6AhfCLLASDPAVStfCDLASDLASDSAXwizwFWrXx8IssBVq18fCLSASADKQOwH3wi0AEg0gFUrXwg0AEg0AEgAykDyB8gywEgywEgAykDwB98ItMBVq18INMBINMBIAMpA9gfIM8BIM8BIAMpA9AffCLLAVatfCDLASDLASADKQPoHyADKQPgHyLMASDXAXwgzAFUrXx8ItEBVq18fCLMAVatfHwizwFWrXwgygEg0gFWrSADKQOIHyDKASDUAVStfHx8IssBQqnAxomuzpOyMFYNAAJAIMsBQqnAxomuzpOyMFEEQCDPAULdsIWM6LaRqLh/Vg0CIM8BQt2whYzotpGouH9RDQFCqcDGia7Ok7IwIcsBCyDPASHKASDMASHSAQwCCyDMAUKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyHKASDMAUKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIcsBIMwBIdIBDAILQpHh5c2HifqZKCHSASDRAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHLAQwBCyDMAUKR4eXNh4n6mSh9IsoBINEBQoGAgIC/sv3wwwBUrSLQAX0h0gEgzwFCo8/685fJ7tfHAHwi0wEgzAFCkeHlzYeJ+pkoVCDKASDQAVRyrSLMAX0hygEgywEgzwFC3bCFjOi2kai4f1QgzAEg0wFWcq19QqnAxomuzpOyMH0hywEg0QFCgYCAgL+y/fDDAH0h0QELQqnAxomuzpOyMCHMASDKASDKASDaAXwi0AFWINABINABINIBINYBfCLKASDSAVQgygEgygEgzgEg0QF8Is4BINEBVK18Is8BVnKtfCLSAVZyrSDLASDNAXx8ItEBIc0BAkACQAJAINEBQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IcwBINIBIs0BQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIcwBIM8BIs0BQpHh5c2HifqZKFINAEKBgICAv7L98MMAIcwBIM4BIc0BIM4BQoGAgIC/sv3wwwBRDQELIMwBIM0BWA0AINIBIc0BIM8BIcoBDAELIM8BQpHh5c2HifqZKH0iywEgzgFCgYCAgL+y/fDDAFStIswBfSHKASDSAUKjz/rzl8nu18cAfCLQASDPAUKR4eXNh4n6mShUIMsBIMwBVHKtIssBfSHNASDRASDSAULdsIWM6LaRqLh/VCDLASDQAVZyrX1CqcDGia7Ok7IwfSHRASDOAUKBgICAv7L98MMAfSHOAQtCqcDGia7Ok7IwIc8BIM0BIOQBfCLLASDNAVQgywEgygEgygEg6wF8IswBViDMASDOASDmAXwi5gEgzgFUrXwiygEgzAFUcq18IswBIMsBVHKtINEBIOoBfHwi6gEhywECQAJAAkAg6gFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hzwEgzAEiywFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghzwEgygEiywFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhzwEg5gEiywFCgYCAgL+y/fDDAFENAQsgywEgzwFaDQAgzAEh5AEgygEh6wEMAQsgygFCkeHlzYeJ+pkofSLLASDmAUKBgICAv7L98MMAVK0izwF9IesBIMwBQqPP+vOXye7XxwB8Is0BIMoBQpHh5c2HifqZKFQgywEgzwFUcq0iygF9IeQBIOoBIMwBQt2whYzotpGouH9UIMoBIM0BVnKtfUKpwMaJrs6TsjB9IeoBIOYBQoGAgIC/sv3wwwB9IeYBCwJAAkAg7QFCqcDGia7Ok7IwVg0AIOcBIc4BIOIBIcsBIOwBIc8BIO0BItEBQqnAxomuzpOyMFINASDPAULdsIWM6LaRqLh/Vg0AQqnAxomuzpOyMCHRASDPAULdsIWM6LaRqLh/Ug0BIMsBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/Ic8BIMsBQpHh5c2HifqZKFINAUKR4eXNh4n6mSghywEgHA0BCyD5ASHOASDxASHLASDyASHPASDzASHRAQsgA0HwHmogzgFCACDoAUIAEMkDIANB4B1qIMsBQgAg6AFCABDJAyADQdAcaiDPAUIAIOgBQgAQyQMgA0HAG2og0QFCACDoAUIAEMkDIANB4B5qIAMpA/AeIs0BQgBCAEL/////vrL98EIQyQMgA0HQHmogAykD6B4iygFCAEKBgICAv7L98MMAQgAQyQMgA0HAHmogygFCAEKR4eXNh4n6mShCABDJAyADQbAeaiDKAUIAQt2whYzotpGouH9CABDJAyADQaAeaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBkB5qIM4BQgAg3wFCABDJAyADQYAdaiDLAUIAIN8BQgAQyQMgA0HwG2ogzwFCACDfAUIAEMkDIANB4BpqINEBQgAg3wFCABDJAyADQdAdaiADKQPAHiLVASADKQP4HiLTASADKQPgHXwi1AF8IswBIAMpA9geIM0BIAMpA9AeIsoBfCDKAVStfHwizQEgAykDkB58ItIBQgBCAEL/////vrL98EIQyQMgA0HAHWogAykD2B0iygFCAEKBgICAv7L98MMAQgAQyQMgA0GwHWogygFCAEKR4eXNh4n6mShCABDJAyADQaAdaiDKAUIAQt2whYzotpGouH9CABDJAyADQZAdaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBgB5qIM4BQgAg5QFCABDJAyADQfAcaiDLAUIAIOUBQgAQyQMgA0HgG2ogzwFCACDlAUIAEMkDIANB0BpqINEBQgAg5QFCABDJAyADQcAcaiADKQOYHiDNASDSAVatfCLXASADKQOAHXwi0AEgAykD6B0g0wEg1AFWrXwi2AEgAykD0Bx8ItMBIAMpA7AefCLUASDMASDNAVatIAMpA8geIMwBINUBVK18fHwi1gF8IswBIAMpA7AdfCLNASADKQPIHSDSASADKQPAHSLKAXwgygFUrXx8ItIBIAMpA4AefCLVAUIAQgBC/////76y/fBCEMkDIANBsBxqIAMpA8gcIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANBoBxqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0GQHGogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GAHGogygFCAEKpwMaJrs6TsjBCABDJAyADQfAdaiDOAUIAIOEBQgAQyQMgA0HgHGogywFCACDhAUIAEMkDIANB0BtqIM8BQgAg4QFCABDJAyADQcAaaiDRAUIAIOEBQgAQyQMgA0GwG2ogAykDiB4g0gEg1QFWrXwi2gEgAykD8Bx8IssBIAMpA9gcINMBINgBVK18ItgBIAMpA8AbfCLPASADKQOgHnwizgEg1AEg1gFWrSADKQO4HiDTASDUAVatfHx8ItEBIAMpA/AbfCLTASDMASDQAVStIAMpA4gdINABINcBVK18fHwi0AEgAykDoB18ItQBIM0BINIBVq0gAykDuB0gzAEgzQFWrXx8fCLXAXwizAEgAykDoBx8Is0BIAMpA7gcINUBIAMpA7AcIsoBfCDKAVStfHwi0gEgAykD8B18ItUBQgBCAEL/////vrL98EIQyQMgA0GgG2ogAykDuBsiygFCAEKBgICAv7L98MMAQgAQyQMgA0GQG2ogygFCAEKR4eXNh4n6mShCABDJAyADQYAbaiDKAUIAQt2whYzotpGouH9CABDJAyADQfAaaiDKAUIAQqnAxomuzpOyMEIAEMkDAkACQCADKQP4GiADKQOIHCADKQOYHSDOASDRAVatIAMpA6geIM4BIM8BVK18fCADKQPIGyDPASDYAVStfHwi2AEgAykD4Bp8IsoBINABINMBVK0gAykD+Bsg0QEg0wFWrXx8fCLPASADKQOQHXwizgEgzwFUrXwgzgEgzgEg1AEg1wFWrSADKQOoHSDQASDUAVatfHx8ItEBVq18IMoBIM8BVq0gAykD6BogygEg2AFUrXx8fCLQASADKQPQGnwiygEgAykD6Bsg0QEg0QEgAykD4Bt8Is8BVq18IM8BIM8BIMsBIMwBVq0gAykD+BwgywEg2gFUrXx8fCLLAVatfHwizwEgAykDgBx8Is4BIM8BVK18IM4BIAMpA5gcIMsBIMsBIAMpA5AcfCLRAVatfCDRASDRASDNASDSAVatIAMpA6gcIMwBIM0BVq18fHwizQFWrXx8IssBIM4BVK18IMoBIM8BVq0gAykD2BogygEg0AFUrXx8fCLRASADKQPAGnwizAEgAykD2BsgywEgAykD0Bt8IsoBIMsBVK18IMoBIMoBIAMpA+gcIAMpA/gdINIBINUBVq18Is8BIAMpA+AcfCLLASDPAVStfCDLASDLASDNAXwizwFWrXx8IssBVq18fCLNASADKQPwGnwizgEgzQFUrXwgzgEgAykDiBsgywEgywEgAykDgBt8ItIBVq18INIBINIBIAMpA5gbIM8BIM8BIAMpA5AbfCLKAVatfCDKASADKQOoGyADKQOgGyLLASDVAXwgywFUrXx8IugBIMoBVK18fCLKAVatfHwiywEgzgFUrXwgzAEgzQFWrSADKQPIGiDMASDRAVStfHx8IuEBQqnAxomuzpOyMFYNAAJAIOEBQqnAxomuzpOyMFEEQCDLAULdsIWM6LaRqLh/Vg0CIMsBQt2whYzotpGouH9SBEAgygEh3wEgywEh5QFCqcDGia7Ok7IwIeEBDAQLIMoBQpHh5c2HifqZKFYNAkLdsIWM6LaRqLh/IeUBIMoBQpHh5c2HifqZKFENASDKASHfAUKpwMaJrs6TsjAh4QEMAwsgygEh3wEgywEh5QEMAgtCkeHlzYeJ+pkoId8BIOgBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIeEBDAELIMoBQpHh5c2HifqZKH0izAEg6AFCgYCAgL+y/fDDAFStIs8BfSHfASDLAUKjz/rzl8nu18cAfCLNASDKAUKR4eXNh4n6mShUIMwBIM8BVHKtIsoBfSHlASDhASDLAULdsIWM6LaRqLh/VCDKASDNAVZyrX1CqcDGia7Ok7IwfSHhASDoAUKBgICAv7L98MMAfSHoAQsgCkEBaiIFIAhHDQALCyADQbClAWpB2KzCAEHAABC3AiADQcAYaiADKQPIpQEiygFCAEKn24Xx2si53BtCABDJAyADQYAZaiADKQPApQEiywFCAEKn24Xx2si53BtCABDJAyADQcAZaiADKQO4pQEizAFCAEKn24Xx2si53BtCABDJAyADQYAaaiADKQOwpQEizwFCAEKn24Xx2si53BtCABDJAyADQbAYaiADKQPAGCLSAUL/////vrL98EJ+Is0BQgBCgYCAgL+y/fDDAEIAEMkDIANBoBhqIM0BQgBCkeHlzYeJ+pkoQgAQyQMgA0HQF2ogzQFCAELdsIWM6LaRqLh/QgAQyQMgA0GAF2ogzQFCAEKpwMaJrs6TsjBCABDJAyADQdAYaiDKAUIAQuOz8Zqe1o7/0wBCABDJAyADQZAZaiDLAUIAQuOz8Zqe1o7/0wBCABDJAyADQdAZaiDMAUIAQuOz8Zqe1o7/0wBCABDJAyADQZAaaiDPAUIAQuOz8Zqe1o7/0wBCABDJAyADQZAYaiADKQOgGCLVASADKQPIGCLTASADKQOAGXwi1AF8Is4BIAMpA7gYINIBIAMpA7AYIs0BfCDNAVStfHwi0gEgAykD0Bh8ItEBQv////++sv3wQn4izQFCAEKBgICAv7L98MMAQgAQyQMgA0GAGGogzQFCAEKR4eXNh4n6mShCABDJAyADQfAXaiDNAUIAQt2whYzotpGouH9CABDJAyADQeAXaiDNAUIAQqnAxomuzpOyMEIAEMkDIANB4BhqIMoBQgBChYHundXn4KSMf0IAEMkDIANBoBlqIMsBQgBChYHundXn4KSMf0IAEMkDIANB4BlqIMwBQgBChYHundXn4KSMf0IAEMkDIANBoBpqIM8BQgBChYHundXn4KSMf0IAEMkDIANBwBdqIAMpA9gYINEBINIBVK18ItcBIAMpA5AZfCLQASADKQOIGSDTASDUAVatfCLYASADKQPAGXwi0wEgAykD0Bd8ItQBIM4BINIBVq0gAykDqBggzgEg1QFUrXx8fCLWAXwizgEgAykDgBh8ItIBIAMpA5gYINEBIAMpA5AYIs0BfCDNAVStfHwi0QEgAykD4Bh8ItUBQv////++sv3wQn4izQFCAEKBgICAv7L98MMAQgAQyQMgA0GwF2ogzQFCAEKR4eXNh4n6mShCABDJAyADQaAXaiDNAUIAQt2whYzotpGouH9CABDJAyADQZAXaiDNAUIAQqnAxomuzpOyMEIAEMkDIANB8BhqIMoBQgBCpYm5+peWtIsCQgAQyQMgA0GwGWogywFCAEKlibn6l5a0iwJCABDJAyADQfAZaiDMAUIAQqWJufqXlrSLAkIAEMkDIANBsBpqIM8BQgBCpYm5+peWtIsCQgAQyQMgA0HwFmogAykD6Bgg0QEg1QFWrXwi2gEgAykDoBl8IssBIAMpA8gZINMBINgBVK18ItgBIAMpA4AafCLMASADKQOAF3wizwEg1AEg1gFWrSADKQPYFyDTASDUAVatfHx8Is0BIAMpA9AZfCLTASDOASDQAVStIAMpA5gZINABINcBVK18fHwi0AEgAykD8Bd8ItQBINEBINIBVK0gAykDiBggzgEg0gFWrXx8fCLXAXwizgEgAykDsBd8ItIBIAMpA8gXINUBIAMpA8AXIsoBfCDKAVStfHwi0QEgAykD8Bh8ItUBQv////++sv3wQn4iygFCAEKBgICAv7L98MMAQgAQyQMgA0HgFmogygFCAEKR4eXNh4n6mShCABDJAyADQdAWaiDKAUIAQt2whYzotpGouH9CABDJAyADQcAWaiDKAUIAQqnAxomuzpOyMEIAEMkDIAMpA8gWIAMpA6gaIAMpA5gaIAMpA4gaIMwBINgBVK18ItgBIAMpA5AafCLKASDYAVStfCDKASDKASDNASDPAVStIAMpA4gXIMwBIM8BVq18fHwizAFWrXwgzAEgzAEg0AEg0wFUrSADKQPYGSDNASDTAVatfHx8IsoBVq18Is8BIAMpA6AafCLMASDPAVStfCDMASDMASADKQPoFyDKASDKASADKQPgF3wizwFWrXwgzwEgzwEg1AEg1wFWrSADKQP4FyDQASDUAVatfHx8IsoBVq18fCLPAVatfCDPASDPASADKQPoGSDKASDKASADKQPgGXwizAFWrXwgzAEgywEgzgFWrSADKQOoGSDLASDaAVStfHx8IsoBIMwBVK18fCLLAVatfCLQASADKQOwGnwizAEgAykDmBcgywEgywEgAykDkBd8Is8BVq18IM8BIM8BIAMpA6gXIMoBIMoBIAMpA6AXfCLLAVatfCDLASDRASDSAVStIAMpA7gXIM4BINIBVq18fHwizgEgywFUrXx8IsoBVq18fCLNASADKQP4GSDKASDKASADKQPwGXwiywFWrXwgywEgywEgAykDuBkgAykD+Bgg0QEg1QFWrXwizwEgAykDsBl8IsoBIM8BVK18IMoBIMoBIM4BfCLPAVatfHwiygFWrXx8Is4BIAMpA8AWfCLSASDOAVStfCDSASDSASADKQPYFiDKASDKASADKQPQFnwiywFWrXwgywEgywEgAykD6BYgzwEgzwEgAykD4BZ8IsoBVq18IMoBIMoBIAMpA/gWIAMpA/AWIs8BINUBfCDPAVStfHwizwFWrXx8IsoBVq18fCLLAVatfCDNASDOAVatIMwBIM0BVq0gAykDuBogzAEg0AFUrXx8fHwizQFCqcDGia7Ok7IwVg0FIM0BQqnAxomuzpOyMFENBCDKASHSASDLASHMAQwGCyAGINsBNwMQDAELIAYg3AE3AxALIAZCAjcDCCAGQYGAgIB4NgIAIAxBgAcQ3wQMBgsgDSAZQYivwgAQ2QMACyDLAULdsIWM6LaRqLh/Vg0AIMsBQt2whYzotpGouH9SBEAgygEh0gEgywEhzAFCqcDGia7Ok7IwIc0BDAILIMoBQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcwBIMoBQpHh5c2HifqZKFIEQCDKASHSAUKpwMaJrs6TsjAhzQEMAgtCkeHlzYeJ+pkoIdIBIM8BQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc0BDAELIMoBQpHh5c2HifqZKH0izAEgzwFCgYCAgL+y/fDDAFStIs4BfSHSASDLAUKjz/rzl8nu18cAfCLRASDKAUKR4eXNh4n6mShUIMwBIM4BVHKtIsoBfSHMASDNASDLAULdsIWM6LaRqLh/VCDKASDRAVZyrX1CqcDGia7Ok7IwfSHNASDPAUKBgICAv7L98MMAfSHPAQsgA0L7////xIONy6x/NwP4wQEgA0KpmoP72dKd/jY3A/DBASADQq6M5cP37ai35gA3A+jBASADQq++n9CZ+J2FDjcD4MEBAn4CQAJAIBApAwAiygEg+AFSBEAgECkDCCHRASAQKQMQIc4BIMoBIdgBIPgBIdABDAELIBApAxAhzgEg7gEgECkDCCLRAVIEQCDRASHYASDuASHQAQwBCyDuASHRASDOASHYASDvASLQASDOAVINACDQASHOASDwASLQASLLASAQKQMYItgBUQ0BCyAQKQMYIcsBINABINgBWg0AQt2whYzotpGouH8g0QEg7gF9ItMBIM4BIO8BVCDOASDvAX0i0AEgywEg8AFUrSLUAVRyrSLVAX0i1wF9ItYBINABINQBfSLQAUKR4eXNh4n6mShWQpHh5c2HifqZKCDQAX0i0AEgywEg8AF9ItQBQoGAgIC/sv3wwwBWrSLaAVRyrSLZAX0h2AEg1gEg2QFUINcBQt2whYzotpGouH9WciEKINABINoBfSHQAUKBgICAv7L98MMAINQBfSHXASDRASDuAVQg0wEg1QFUcq0g+AEgygF9fEKpwMaJrs6TsjB8DAELIO8BIM4BfSLTASDLASDwAVatItQBfSHQASDuASDRAX0i1QEg0wEg1AFUIM4BIO8BVnKtItMBfSHYASDTASDVAVYg0QEg7gFWciEKIPABIMsBfSHXASD4ASDKAX0LIdMBIAMg1wE3A8ikASADINABNwPApAEgAyDYATcDuKQBIAMg0wEgCq19NwOwpAEgA0GwpQFqIANB4MEBaiADQbCkAWoQWgJAIAMoArClAUEBRwRAIANBqKQBaiADQdClAWopAwA3AwAgA0GgpAFqIANByKUBaikDADcDACADQZikAWogA0HApQFqKQMANwMAIAMgAykDuKUBNwOQpAEgA0L7////xIONy6x/NwP4wQEgA0KpmoP72dKd/jY3A/DBASADQq6M5cP37ai35gA3A+jBASADQq++n9CZ+J2FDjcD4MEBIANBsBZqIMsBQgAgzwFCABDJAyADQdAVaiDLAUIAINIBQgAQyQMgA0HAFWogywFCACDMAUIAEMkDIANBsBVqIMsBQgAgzQFCABDJAyADQaAWaiADKQOwFiLQAUIAQgBC/////76y/fBCEMkDIANBkBZqIAMpA6gWIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBgBZqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0HwFWogywFCAELdsIWM6LaRqLh/QgAQyQMgA0HgFWogywFCAEKpwMaJrs6TsjBCABDJAyADQaAVaiDOAUIAIM8BQgAQyQMgA0HAFGogzgFCACDSAUIAEMkDIANBsBRqIM4BQgAgzAFCABDJAyADQaAUaiDOAUIAIM0BQgAQyQMgA0GQFWogAykDgBYi1wEgAykDuBYi1AEgAykD0BV8ItUBfCLOASADKQOYFiDQASADKQOQFiLLAXwgywFUrXx8ItABIAMpA6AVfCLTAUIAQgBC/////76y/fBCEMkDIANBgBVqIAMpA5gVIssBQgBCgYCAgL+y/fDDAEIAEMkDIANB8BRqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0HgFGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0HQFGogywFCAEKpwMaJrs6TsjBCABDJAyADQZAUaiDRAUIAIM8BQgAQyQMgA0GwE2og0QFCACDSAUIAEMkDIANBoBNqINEBQgAgzAFCABDJAyADQZATaiDRAUIAIM0BQgAQyQMgA0GAFGogAykDkBQi2AEgAykDqBUg0AEg0wFWrXwi1gEgAykDwBR8ItEBIAMpA9gVINQBINUBVq18ItoBIAMpA8AVfCLUASADKQPwFXwi1QEgzgEg0AFWrSADKQOIFiDOASDXAVStfHx8ItcBfCLOASADKQPwFHwi0AEgAykDiBUg0wEgAykDgBUiywF8IMsBVK18fCLZAXwi0wFCAEIAQv////++sv3wQhDJAyADQfATaiADKQOIFCLLAUIAQoGAgIC/sv3wwwBCABDJAyADQeATaiDLAUIAQpHh5c2HifqZKEIAEMkDIANB0BNqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANBwBNqIMsBQgBCqcDGia7Ok7IwQgAQyQMgA0GAE2ogygFCACDPAUIAEMkDIANBoBJqIMoBQgAg0gFCABDJAyADQZASaiDKAUIAIMwBQgAQyQMgA0GAEmogygFCACDNAUIAEMkDIANB8BJqIAMpA+ATItsBIAMpA7ATItwBIAMpA8gVINQBINoBVK18ItoBIAMpA7AVfCLLASADKQPgFXwizAEg1QEg1wFWrSADKQP4FSDUASDVAVatfHx8Is8BIAMpA7AUfCLNASDOASDRAVStIAMpA8gUINEBINYBVK18fHwi0gEgAykD4BR8ItEBINABINkBVq0gAykD+BQgzgEg0AFWrXx8fCLVAXwizgEgAykDmBQg0wEg2AFUrXx8ItcBfCLQASADKQP4EyADKQPwEyLKASDTAXwgygFUrXx8ItMBIAMpA4ATfCLUAUIAQgBC/////76y/fBCEMkDIANB4BJqIAMpA/gSIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB0BJqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HAEmogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GwEmogygFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDuBIgAykDyBMgAykDkBMi2AEgAykD2BQgzAEgzwFWrSADKQPoFSDLASDMAVatfHwgAykDuBUgywEg2gFUrXx8ItYBIAMpA6AUfCLKASDNASDSAVatIAMpA7gUIM0BIM8BVK18fHwiywEgAykD0BR8IswBIMsBVK18IMwBIMwBINEBINUBVq0gAykD6BQg0QEg0gFUrXx8fCLPAVatfCDKASDLAVatIAMpA6gUIMoBINYBVK18fHx8IsoBIAMpA6gTIM8BIAMpA6ATIswBfCLLASDMAVStfCDLASDLASDOASDXAVatIAMpA7gTIM4BINwBVK18fHwizAFWrXx8IssBIAMpA8ATfCLPASDLAVStfCDPASADKQPYEyDMASDMASADKQPQE3wizQFWrXwgzQEgzQEg0AEg0wFWrSADKQPoEyDQASDbAVStfHx8Is4BVq18fCLMASDPAVStfCDKASDLAVatIAMpA5gTIMoBINgBVK18fHwi0AEgAykDgBJ8IssBIAMpA5gSIMwBIAMpA5ASfCLKASDMAVStfCDKASDKASADKQOoEiADKQOIEyDTASDUAVatfCLPASADKQOgEnwizAEgzwFUrXwgzAEgzAEgzgF8Is8BVq18fCLMAVatfHwizQEgAykDsBJ8ItIBIM0BVK18INIBINIBIAMpA8gSIMwBIMwBIAMpA8ASfCLRAVatfCDRASDRASADKQPYEiDPASDPASADKQPQEnwiygFWrXwgygEgygEgAykD6BIgAykD4BIizAEg1AF8IMwBVK18fCLOAVatfHwiygFWrXx8IswBVq18IMsBIM0BVq0gAykDiBIgywEg0AFUrXx8fCLRAUKpwMaJrs6TsjBWDQACQCDRAUKpwMaJrs6TsjBRBEAgzAFC3bCFjOi2kai4f1YNAiDMAULdsIWM6LaRqLh/UQ0BQqnAxomuzpOyMCHRAQsgzAEhywEgygEhzwEMAgsgygFCkeHlzYeJ+pkoVg0AQt2whYzotpGouH8hywEgygFCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCHRASDKASHPAQwCC0KR4eXNh4n6mSghzwEgzgFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh0QEMAQsgygFCkeHlzYeJ+pkofSLLASDOAUKBgICAv7L98MMAVK0izQF9Ic8BIMwBQqPP+vOXye7XxwB8ItIBIMoBQpHh5c2HifqZKFQgywEgzQFUcq0iygF9IcsBINEBIMwBQt2whYzotpGouH9UIMoBINIBVnKtfUKpwMaJrs6TsjB9IdEBIM4BQoGAgIC/sv3wwwB9Ic4BCyADAn4CQAJAINEBIs0BIPgBIsoBUg0AIMsBIc0BIO4BIsoBIMsBUg0AIM8BIs0BIO8BIsoBUg0AIM4BIc0BIPABIsoBIM4BUQ0BCyDKASDNAVoNAELdsIWM6LaRqLh/IMsBIO4BfSLKASDPASDvAVQgzwEg7wF9IswBIM4BIPABVK0izwFUcq0i0gF9Is0BfSLQASDMASDPAX0izAFCkeHlzYeJ+pkoVkKR4eXNh4n6mSggzAF9IswBIM4BIPABfSLOAUKBgICAv7L98MMAVq0i0wFUcq0i1AF9Ic8BINABINQBVCDNAULdsIWM6LaRqLh/VnIhCiDMASDTAX0hzQEgywEg7gFUIMoBINIBVHKtIPgBINEBfXxCqcDGia7Ok7IwfCHRAUKBgICAv7L98MMAIM4BfQwBCyDvASDPAX0iygEgzgEg8AFWrSLMAX0hzQEg7gEgywF9ItIBIMoBIMwBVCDPASDvAVZyrSLKAX0hzwEgygEg0gFWIMsBIO4BVnIhCiD4ASDRAX0h0QEg8AEgzgF9CzcDyKQBIAMgzQE3A8CkASADIM8BNwO4pAEgAyDRASAKrX03A7CkASADQbClAWogA0HgwQFqIANBsKQBahBaIAMoArClAUEBRwRAIANB6KQBaiADQdClAWopAwA3AwAgA0HgpAFqIANByKUBaikDADcDACADQdikAWogA0HApQFqKQMANwMAIANBuKQBaiADQZikAWoiBSkDADcDACADQcCkAWogA0GgpAFqIgopAwA3AwAgA0HIpAFqIANBqKQBaiIHKQMANwMAIAMgAykDuKUBNwPQpAEgAyADKQOQpAE3A7CkASADQfikAWogBSkDADcDACADQYClAWogCikDADcDACADQYilAWogBykDADcDACADIAMpA5CkATcD8KQBIANBqKUBaiAHKQMANwMAIANBoKUBaiAKKQMANwMAIANBmKUBaiAFKQMANwMAIAMgAykDkKQBNwOQpQEgA0EANgL4owEgA0KAgICAgAE3AvCjAQJAAkAg7QFCqcDGia7Ok7IwVg0AAkAg7QFCqcDGia7Ok7IwUQRAIOwBQt2whYzotpGouH9WDQIg7AFC3bCFjOi2kai4f1IEQCDiASHRASDsASHOAUKpwMaJrs6TsjAh7QEMBAsg4gFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8hzgEg4gFCkeHlzYeJ+pkoUQ0BIOIBIdEBQqnAxomuzpOyMCHtAQwDCyDiASHRASDsASHOAQwCC0KR4eXNh4n6mSgh0QEg5wFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAh7QEMAQsg4gFCkeHlzYeJ+pkofSLKASDnAUKBgICAv7L98MMAVK0iywF9IdEBIOwBQqPP+vOXye7XxwB8IswBIOIBQpHh5c2HifqZKFQgygEgywFUcq0iygF9Ic4BIO0BIOwBQt2whYzotpGouH9UIMoBIMwBVnKtfUKpwMaJrs6TsjB9Ie0BIOcBQoGAgIC/sv3wwwB9IecBCyADQfARaiDnAUIAIOgBQgAQyQMgA0GQEWog0QFCACDoAUIAEMkDIANBgBFqIM4BQgAg6AFCABDJAyADQfAQaiDtAUIAIOgBQgAQyQMgA0HgEWogAykD8BEizAFCAEIAQv////++sv3wQhDJAyADQdARaiADKQPoESLKAUIAQoGAgIC/sv3wwwBCABDJAyADQcARaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBsBFqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBoBFqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HgEGog5wFCACDfAUIAEMkDIANBgBBqINEBQgAg3wFCABDJAyADQfAPaiDOAUIAIN8BQgAQyQMgA0HgD2og7QFCACDfAUIAEMkDIANB0BBqIAMpA8ARItMBIAMpA/gRItIBIAMpA5ARfCLQAXwiywEgAykD2BEgzAEgAykD0BEiygF8IMoBVK18fCLMASADKQPgEHwizwFCAEIAQv////++sv3wQhDJAyADQcAQaiADKQPYECLKAUIAQoGAgIC/sv3wwwBCABDJAyADQbAQaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBoBBqIMoBQgBC3bCFjOi2kai4f0IAEMkDIANBkBBqIMoBQgBCqcDGia7Ok7IwQgAQyQMgA0HQD2og5wFCACDlAUIAEMkDIANB8A5qINEBQgAg5QFCABDJAyADQeAOaiDOAUIAIOUBQgAQyQMgA0HQDmog7QFCACDlAUIAEMkDIANBwA9qIAMpA+gQIMwBIM8BVq18ItUBIAMpA4AQfCLNASADKQOYESDQASDSAVStfCLUASADKQOAEXwi0gEgAykDsBF8ItABIMsBIMwBVq0gAykDyBEgywEg0wFUrXx8fCLXAXwiywEgAykDsBB8IswBIAMpA8gQIM8BIAMpA8AQIsoBfCDKAVStfHwizwEgAykD0A98ItMBQgBCAEL/////vrL98EIQyQMgA0GwD2ogAykDyA8iygFCAEKBgICAv7L98MMAQgAQyQMgA0GgD2ogygFCAEKR4eXNh4n6mShCABDJAyADQZAPaiDKAUIAQt2whYzotpGouH9CABDJAyADQYAPaiDKAUIAQqnAxomuzpOyMEIAEMkDIANBwA5qIOcBQgAg4QFCABDJAyADQeANaiDRAUIAIOEBQgAQyQMgA0HQDWogzgFCACDhAUIAEMkDIANBwA1qIO0BQgAg4QFCABDJAyADQbAOaiADKQPYDyDPASDTAVatfCLYASADKQPwDnwizgEgAykDiBEg0gEg1AFUrXwi1gEgAykD8BB8ItEBIAMpA6ARfCLUASDQASDXAVatIAMpA7gRINABINIBVK18fHwi0gEgAykD8A98ItABIMsBIM0BVK0gAykDiBAgzQEg1QFUrXx8fCLNASADKQOgEHwi1QEgzAEgzwFWrSADKQO4ECDLASDMAVatfHx8ItcBfCLLASADKQOgD3wizAEgAykDuA8g0wEgAykDsA8iygF8IMoBVK18fCLPASADKQPADnwi0wFCAEIAQv////++sv3wQhDJAyADQaAOaiADKQO4DiLKAUIAQoGAgIC/sv3wwwBCABDJAyADQZAOaiDKAUIAQpHh5c2HifqZKEIAEMkDIANBgA5qIMoBQgBC3bCFjOi2kai4f0IAEMkDIANB8A1qIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAMpA/gNIAMpA4gPIAMpA5gQINIBINQBVK0gAykDqBEg0QEg1AFWrXx8IAMpA/gQINEBINYBVK18fCLUASADKQPgD3wiygEgzQEg0AFUrSADKQP4DyDQASDSAVStfHx8ItIBIAMpA5AQfCLRASDSAVStfCDRASDVASDXAVatIAMpA6gQIM0BINUBVq18fHwizQEg0QFUrXwgygEg0gFWrSADKQPoDyDKASDUAVStfHx8ItABIAMpA9AOfCLKASADKQPoDiDNASDNASADKQPgDnwi0gFWrXwg0gEg0gEgywEgzgFUrSADKQP4DiDOASDYAVStfHx8Is0BVq18fCLOASADKQOAD3wi0gEgzgFUrXwg0gEg0gEgAykDmA8gzQEgzQEgAykDkA98ItEBVq18INEBIMwBIM8BVq0gAykDqA8gywEgzAFWrXx8fCLNASDRAVStfHwiywFWrXwgygEgzgFWrSADKQPYDiDKASDQAVStfHx8ItEBIAMpA8ANfCLMASADKQPYDSDLASADKQPQDXwiygEgywFUrXwgygEgygEgAykD6A0gAykDyA4gzwEg0wFWrXwizwEgAykD4A18IssBIM8BVK18IMsBIMsBIM0BfCLPAVatfHwiywFWrXx8Is4BIAMpA/ANfCLSASDOAVStfCDSASDSASADKQOIDiDLASDLASADKQOADnwizQFWrXwgzQEgzQEgAykDmA4gzwEgzwEgAykDkA58IsoBVq18IMoBIMoBIAMpA6gOIAMpA6AOIssBINMBfCDLAVStfHwiywFWrXx8IsoBVq18fCLNAVatfCDMASDOAVatIAMpA8gNIMwBINEBVK18fHwizwFCqcDGia7Ok7IwVg0AAkAgzwFCqcDGia7Ok7IwUQRAIM0BQt2whYzotpGouH9WDQIgzQFC3bCFjOi2kai4f1IEQCDKASHSASDNASHMAUKpwMaJrs6TsjAhzwEMBAsgygFCkeHlzYeJ+pkoVg0CQt2whYzotpGouH8hzAEgygFCkeHlzYeJ+pkoUQ0BIMoBIdIBQqnAxomuzpOyMCHPAQwDCyDKASHSASDNASHMAQwCC0KR4eXNh4n6mSgh0gEgywFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhzwEMAQsgygFCkeHlzYeJ+pkofSLMASDLAUKBgICAv7L98MMAVK0izgF9IdIBIM0BQqPP+vOXye7XxwB8ItEBIMoBQpHh5c2HifqZKFQgzAEgzgFUcq0iygF9IcwBIM8BIM0BQt2whYzotpGouH9UIMoBINEBVnKtfUKpwMaJrs6TsjB9Ic8BIMsBQoGAgIC/sv3wwwB9IcsBCyAIQSVqIRMgCEEmaiEZQaB/IQpBASEHA0AgA0GwDWogA0GwpAFqIApqIgVB+ABqKQMAIsoBQgAgywFCABDJAyADQdAMaiAFQfAAaikDACLNAUIAIMsBQgAQyQMgA0HADGogBUHoAGopAwAizgFCACDLAUIAEMkDIANBsAxqIAVB4ABqKQMAItEBQgAgywFCABDJAyADQaANaiADKQOwDSLUAUIAQgBC/////76y/fBCEMkDIANBkA1qIAMpA6gNItABQgBCgYCAgL+y/fDDAEIAEMkDIANBgA1qINABQgBCkeHlzYeJ+pkoQgAQyQMgA0HwDGog0AFCAELdsIWM6LaRqLh/QgAQyQMgA0HgDGog0AFCAEKpwMaJrs6TsjBCABDJAyADQaAMaiDKAUIAINIBQgAQyQMgA0HAC2ogzQFCACDSAUIAEMkDIANBsAtqIM4BQgAg0gFCABDJAyADQaALaiDRAUIAINIBQgAQyQMgA0GQDGogAykDgA0i2gEgAykDuA0i2AEgAykD0Ax8ItYBfCLTASADKQOYDSDUASADKQOQDSLQAXwg0AFUrXx8ItQBIAMpA6AMfCLVAUIAQgBC/////76y/fBCEMkDIANBgAxqIAMpA5gMItABQgBCgYCAgL+y/fDDAEIAEMkDIANB8AtqINABQgBCkeHlzYeJ+pkoQgAQyQMgA0HgC2og0AFCAELdsIWM6LaRqLh/QgAQyQMgA0HQC2og0AFCAEKpwMaJrs6TsjBCABDJAyADQZALaiDKAUIAIMwBQgAQyQMgA0GwCmogzQFCACDMAUIAEMkDIANBoApqIM4BQgAgzAFCABDJAyADQZAKaiDRAUIAIMwBQgAQyQMgA0GAC2ogAykDqAwg1AEg1QFWrXwi2QEgAykDwAt8ItcBIAMpA9gMINYBINgBVK18ItsBIAMpA8AMfCLYASADKQPwDHwi1gEg0wEg1AFWrSADKQOIDSDTASDaAVStfHx8ItwBfCLTASADKQPwC3wi1AEgAykDiAwg1QEgAykDgAwi0AF8INABVK18fCLVASADKQOQC3wi2gFCAEIAQv////++sv3wQhDJAyADQfAKaiADKQOICyLQAUIAQoGAgIC/sv3wwwBCABDJAyADQeAKaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB0ApqINABQgBC3bCFjOi2kai4f0IAEMkDIANBwApqINABQgBCqcDGia7Ok7IwQgAQyQMgA0GACmogygFCACDPAUIAEMkDIANBoAlqIM0BQgAgzwFCABDJAyADQZAJaiDOAUIAIM8BQgAQyQMgA0GACWog0QFCACDPAUIAEMkDIANB8AlqIAMpA5gLINUBINoBVq18It4BIAMpA7AKfCLNASADKQPIDCDYASDbAVStfCLbASADKQOwDHwizgEgAykD4Ax8ItEBINYBINwBVq0gAykD+Awg1gEg2AFUrXx8fCLQASADKQOwC3wi2AEg0wEg1wFUrSADKQPICyDXASDZAVStfHx8ItcBIAMpA+ALfCLWASDUASDVAVatIAMpA/gLINMBINQBVq18fHwi2QF8ItMBIAMpA+AKfCLUASADKQP4CiDaASADKQPwCiLKAXwgygFUrXx8ItUBIAMpA4AKfCLaAUIAQgBC/////76y/fBCEMkDIANB4AlqIAMpA/gJIsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB0AlqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0HACWogygFCAELdsIWM6LaRqLh/QgAQyQMgA0GwCWogygFCAEKpwMaJrs6TsjBCABDJAwJAAkAgAykDuAkgAykDyAogAykD2Asg0AEg0QFUrSADKQPoDCDOASDRAVatfHwgAykDuAwgzgEg2wFUrXx8ItsBIAMpA6ALfCLKASDXASDYAVStIAMpA7gLINABINgBVq18fHwizgEgAykD0At8ItEBIM4BVK18INEBINEBINYBINkBVq0gAykD6Asg1gEg1wFUrXx8fCLQAVatfCDKASDOAVatIAMpA6gLIMoBINsBVK18fHwi1wEgAykDkAp8IsoBIAMpA6gKINABINABIAMpA6AKfCLOAVatfCDOASDOASDNASDTAVatIAMpA7gKIM0BIN4BVK18fHwizQFWrXx8Is4BIAMpA8AKfCLRASDOAVStfCDRASDRASADKQPYCiDNASDNASADKQPQCnwi0AFWrXwg0AEg0AEg1AEg1QFWrSADKQPoCiDTASDUAVatfHx8ItMBVq18fCLNAVatfCDKASDOAVatIAMpA5gKIMoBINcBVK18fHwi1wEgAykDgAl8IsoBIAMpA5gJIM0BIM0BIAMpA5AJfCLOAVatfCDOASDOASADKQOoCSADKQOICiDVASDaAVatfCLRASADKQOgCXwizQEg0QFUrXwgzQEgzQEg0wF8ItEBVq18fCLNAVatfHwizgEgAykDsAl8ItQBIM4BVK18INQBINQBIAMpA8gJIM0BIM0BIAMpA8AJfCLTAVatfCDTASDTASADKQPYCSDRASDRASADKQPQCXwizQFWrXwgzQEgzQEgAykD6AkgAykD4Aki0QEg2gF8INEBVK18fCLRAVatfHwi0AFWrXx8ItMBVq18IMoBIM4BVq0gAykDiAkgygEg1wFUrXx8fCLOAUKpwMaJrs6TsjBWDQACQCDOAUKpwMaJrs6TsjBRBEAg0wFC3bCFjOi2kai4f1YNAiDTAULdsIWM6LaRqLh/UgRAINABIcoBINMBIc0BQqnAxomuzpOyMCHOAQwECyDQAUKR4eXNh4n6mShWDQJC3bCFjOi2kai4fyHNASDQAUKR4eXNh4n6mShRDQEg0AEhygFCqcDGia7Ok7IwIc4BDAMLINABIcoBINMBIc0BDAILQpHh5c2HifqZKCHKASDRAUKBgICAv7L98MMAWg0AQqnAxomuzpOyMCHOAQwBCyDQAUKR4eXNh4n6mSh9Is0BINEBQoGAgIC/sv3wwwBUrSLUAX0hygEg0wFCo8/685fJ7tfHAHwi1QEg0AFCkeHlzYeJ+pkoVCDNASDUAVRyrSLQAX0hzQEgzgEg0wFC3bCFjOi2kai4f1Qg0AEg1QFWcq19QqnAxomuzpOyMH0hzgEg0QFCgYCAgL+y/fDDAH0h0QELIAMg0QE3A8ilASADIMoBNwPApQEgAyDNATcDuKUBIAMgzgE3A7ClASDRASHYASDKASHQASDNASHTASDOASHXASADQbClAWpBwJbCAEEgEPEDBEBCkeHlzYeJ+pkoIMoBfSLTASDRAUKBgICAv7L98MMAVq0i1AF9IdABQt2whYzotpGouH8gzQF9ItUBINMBINQBVCDKAUKR4eXNh4n6mShWcq0i1AF9IdMBQoGAgIC/sv3wwwAg0QF9IdgBQqnAxomuzpOyMCDUASDVAVYgzQFC3bCFjOi2kai4f1ZyrSDOAXx9IdcBCyADKAL4owEiDSADKALwowFGBEAgA0HwowFqQciuwgAQogMLIAMoAvSjASANQQV0aiIFINgBNwMYIAUg0AE3AxAgBSDTATcDCCAFINcBNwMAIAMgDUEBaiIQNgL4owECQCAKRQ0AIANBsAdqIMsBQgAg9AFCABDJAyADQfAHaiDLAUIAIPUBQgAQyQMgA0GwCGogywFCACD2AUIAEMkDIANB8AhqIMsBQgAg9wFCABDJAyADQaAHaiADKQOwByLQAUIAQgBC/////76y/fBCEMkDIANBkAdqIAMpA6gHIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBgAdqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0HwBmogywFCAELdsIWM6LaRqLh/QgAQyQMgA0HgBmogywFCAEKpwMaJrs6TsjBCABDJAyADQdAGaiDSAUIAIPQBQgAQyQMgA0HgB2og0gFCACD1AUIAEMkDIANBoAhqINIBQgAg9gFCABDJAyADQeAIaiDSAUIAIPcBQgAQyQMgA0HABmogAykDgAci1wEgAykDuAci1AEgAykD8Ad8ItUBfCLSASADKQOYByDQASADKQOQByLLAXwgywFUrXx8ItABIAMpA9AGfCLTAUIAQgBC/////76y/fBCEMkDIANBsAZqIAMpA8gGIssBQgBCgYCAgL+y/fDDAEIAEMkDIANBoAZqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0GQBmogywFCAELdsIWM6LaRqLh/QgAQyQMgA0GABmogywFCAEKpwMaJrs6TsjBCABDJAyADQfAFaiDMAUIAIPQBQgAQyQMgA0HQB2ogzAFCACD1AUIAEMkDIANBkAhqIMwBQgAg9gFCABDJAyADQdAIaiDMAUIAIPcBQgAQyQMgA0HgBWogAykD2AYg0AEg0wFWrXwi2gEgAykD4Ad8IswBIAMpA/gHINQBINUBVq18ItgBIAMpA7AIfCLUASADKQPwBnwi1QEg0AEg0gFUrSADKQOIByDSASDXAVStfHx8ItkBfCLSASADKQOgBnwi0AEgAykDuAYgAykDsAYiywEg0wF8IMsBVK18fCLTASADKQPwBXwi1wFCAEIAQv////++sv3wQhDJAyADQdAFaiADKQPoBSLLAUIAQoGAgIC/sv3wwwBCABDJAyADQcAFaiDLAUIAQpHh5c2HifqZKEIAEMkDIANBsAVqIMsBQgBC3bCFjOi2kai4f0IAEMkDIANBoAVqIMsBQgBCqcDGia7Ok7IwQgAQyQMgA0GQBWogzwFCACD0AUIAEMkDIANBwAdqIM8BQgAg9QFCABDJAyADQYAIaiDPAUIAIPYBQgAQyQMgA0HACGogzwFCACD3AUIAEMkDIANBgAVqIAMpA/gFINMBINcBVq18ItsBIAMpA9AHfCLPASADKQO4CCDUASDYAVStfCLcASADKQPwCHwi2AEgAykD4AZ8ItYBINUBINkBVq0gAykD+AYg1AEg1QFWrXx8fCLUASADKQOgCHwi1QEgzAEg0gFWrSADKQPoByDMASDaAVStfHx8IswBIAMpA5AGfCLaASDQASDTAVatIAMpA6gGINABINIBVK18fHwi2QF8ItIBIAMpA8AFfCLQASADKQPYBSDXASADKQPQBSLLAXwgywFUrXx8ItMBIAMpA5AFfCLXAUIAQgBC/////76y/fBCEMkDIANB8ARqIAMpA4gFIssBQgBCgYCAgL+y/fDDAEIAEMkDIANB4ARqIMsBQgBCkeHlzYeJ+pkoQgAQyQMgA0HQBGogywFCAELdsIWM6LaRqLh/QgAQyQMgA0HABGogywFCAEKpwMaJrs6TsjBCABDJAwJAIAMpA8gEIAMpA6gFIAMpA4gGINQBINYBVK0gAykD6AYg1gEg2AFUrXx8IAMpA/gIINgBINwBVK18fCLYASADKQPgCHwiywEgzAEg1QFUrSADKQOoCCDUASDVAVatfHx8ItQBIAMpA4AGfCLVASDUAVStfCDVASDZASDaAVStIAMpA5gGIMwBINoBVq18fHwizAEg1QFUrXwgywEg1AFWrSADKQPoCCDLASDYAVStfHx8ItgBIAMpA9AIfCLLASADKQOYCCDMASDMASADKQOQCHwi1AFWrXwg1AEg1AEgzwEg0gFWrSADKQPYByDPASDbAVStfHx8IswBVq18fCLPASADKQOgBXwi1AEgzwFUrXwg1AEgAykDuAUgzAEgzAEgAykDsAV8ItUBVq18INUBINUBINABINMBVq0gAykDyAUg0AEg0gFUrXx8fCLSAVatfHwizAEg1AFUrXwgywEgzwFWrSADKQPYCCDLASDYAVStfHx8ItgBIAMpA8AIfCLPASADKQOICCDMASADKQOACHwiywEgzAFUrXwgywEgywEgAykDyAcgAykDmAUg0wEg1wFWrXwi0AEgAykDwAd8IswBINABVK18IMwBIMwBINIBfCLSAVatfHwizAFWrXx8ItQBIAMpA8AEfCLVASDUAVStfCDVASDVASADKQPYBCDMASDMASADKQPQBHwi0wFWrXwg0wEg0wEgAykD6AQg0gEg0gEgAykD4AR8IswBVq18IMwBIMwBIAMpA/gEIAMpA/AEIssBINcBfCDLAVStfHwiywFWrXx8ItABVq18fCLTAVatfCDPASDUAVatIAMpA8gIIM8BINgBVK18fHwizwFCqcDGia7Ok7IwVg0AIM8BQqnAxomuzpOyMFIEQCDQASHSASDTASHMAQwCCyDTAULdsIWM6LaRqLh/Vg0AINMBQt2whYzotpGouH9SBEAg0AEh0gEg0wEhzAFCqcDGia7Ok7IwIc8BDAILINABQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcwBINABQpHh5c2HifqZKFIEQCDQASHSAUKpwMaJrs6TsjAhzwEMAgtCkeHlzYeJ+pkoIdIBIMsBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc8BDAELINABQpHh5c2HifqZKH0izAEgywFCgYCAgL+y/fDDAFStItQBfSHSASDTAUKjz/rzl8nu18cAfCLVASDQAUKR4eXNh4n6mShUIMwBINQBVHKtItABfSHMASDPASDTAULdsIWM6LaRqLh/VCDQASDVAVZyrX1CqcDGia7Ok7IwfSHPASDLAUKBgICAv7L98MMAfSHLAQsgA0GwBGogCiBaaiIFQfgAaikDACLQAUIAINEBQgAQyQMgA0GgA2og0AFCACDKAUIAEMkDIANBkAJqINABQgAgzQFCABDJAyADQYABaiDQAUIAIM4BQgAQyQMgA0GgBGogAykDsAQi1AFCAEIAQv////++sv3wQhDJAyADQZAEaiADKQOoBCLQAUIAQoGAgIC/sv3wwwBCABDJAyADQYAEaiDQAUIAQpHh5c2HifqZKEIAEMkDIANB8ANqINABQgBC3bCFjOi2kai4f0IAEMkDIANB4ANqINABQgBCqcDGia7Ok7IwQgAQyQMgA0HQA2ogBUHwAGopAwAi0AFCACDRAUIAEMkDIANBwAJqINABQgAgygFCABDJAyADQbABaiDQAUIAIM0BQgAQyQMgA0EgaiDQAUIAIM4BQgAQyQMgA0GQA2ogAykDgAQi2gEgAykDuAQi2AEgAykDoAN8ItYBfCLTASADKQOYBCDUASADKQOQBCLQAXwg0AFUrXx8ItQBIAMpA9ADfCLVAUIAQgBC/////76y/fBCEMkDIANBgANqIAMpA5gDItABQgBCgYCAgL+y/fDDAEIAEMkDIANB8AJqINABQgBCkeHlzYeJ+pkoQgAQyQMgA0HgAmog0AFCAELdsIWM6LaRqLh/QgAQyQMgA0HQAmog0AFCAEKpwMaJrs6TsjBCABDJAyADQcADaiAFQegAaikDACLQAUIAINEBQgAQyQMgA0GwAmog0AFCACDKAUIAEMkDIANBoAFqINABQgAgzQFCABDJAyADQRBqINABQgAgzgFCABDJAyADQYACaiADKQPYAyDUASDVAVatfCLZASADKQPAAnwi1wEgAykDqAMg1gEg2AFUrXwi2wEgAykDkAJ8ItgBIAMpA/ADfCLWASDTASDUAVatIAMpA4gEINMBINoBVK18fHwi3AF8ItMBIAMpA/ACfCLUASADKQOIAyDVASADKQOAAyLQAXwg0AFUrXx8ItUBIAMpA8ADfCLaAUIAQgBC/////76y/fBCEMkDIANB8AFqIAMpA4gCItABQgBCgYCAgL+y/fDDAEIAEMkDIANB4AFqINABQgBCkeHlzYeJ+pkoQgAQyQMgA0HQAWog0AFCAELdsIWM6LaRqLh/QgAQyQMgA0HAAWog0AFCAEKpwMaJrs6TsjBCABDJAyADQbADaiAFQeAAaikDACLQAUIAINEBQgAQyQMgA0GgAmog0AFCACDKAUIAEMkDIANBkAFqINABQgAgzQFCABDJAyADINABQgAgzgFCABDJAyADQfAAaiADKQPIAyDVASDaAVatfCLeASADKQOwAnwizQEgAykDmAIg2AEg2wFUrXwi2wEgAykDgAF8Is4BIAMpA+ADfCLRASDWASDcAVatIAMpA/gDINYBINgBVK18fHwi0AEgAykDsAF8ItgBINMBINcBVK0gAykDyAIg1wEg2QFUrXx8fCLXASADKQPgAnwi1gEg1AEg1QFWrSADKQP4AiDTASDUAVatfHx8ItkBfCLTASADKQPgAXwi1AEgAykD+AEgAykD8AEiygEg2gF8IMoBVK18fCLVASADKQOwA3wi2gFCAEIAQv////++sv3wQhDJAyADQeAAaiADKQN4IsoBQgBCgYCAgL+y/fDDAEIAEMkDIANB0ABqIMoBQgBCkeHlzYeJ+pkoQgAQyQMgA0FAayDKAUIAQt2whYzotpGouH9CABDJAyADQTBqIMoBQgBCqcDGia7Ok7IwQgAQyQMCQAJAAkAgAykDOCADKQPIASADKQPYAiDQASDRAVStIAMpA+gDIM4BINEBVq18fCADKQOIASDOASDbAVStfHwi2wEgAykDIHwiygEg1wEg2AFUrSADKQO4ASDQASDYAVatfHx8Is4BIAMpA9ACfCLRASDOAVStfCDRASDRASDWASDZAVatIAMpA+gCINYBINcBVK18fHwi0AFWrXwgygEgzgFWrSADKQMoIMoBINsBVK18fHwi1wEgAykDEHwiygEgAykDqAEg0AEg0AEgAykDoAF8Is4BVq18IM4BIM4BIM0BINMBVq0gAykDuAIgzQEg3gFUrXx8fCLNAVatfHwizgEgAykDwAF8ItEBIM4BVK18INEBIAMpA9gBIM0BIM0BIAMpA9ABfCLQAVatfCDQASDQASDUASDVAVatIAMpA+gBINMBINQBVq18fHwi0wFWrXx8Is0BINEBVK18IMoBIM4BVq0gAykDGCDKASDXAVStfHx8ItQBIAMpAwB8IsoBIAMpA5gBIM0BIM0BIAMpA5ABfCLOAVatfCDOASDOASADKQOoAiADKQO4AyDVASDaAVatfCLRASADKQOgAnwizQEg0QFUrXwgzQEgzQEg0wF8ItEBVq18fCLNAVatfHwizgEgAykDMHwi0wEgzgFUrXwg0wEg0wEgAykDSCDNASDNASADKQNAfCLQAVatfCDQASDQASADKQNYINEBINEBIAMpA1B8Is0BVq18IM0BIM0BIAMpA2ggAykDYCLRASDaAXwg0QFUrXx8ItEBVq18fCLNAVatfHwi0AFWrXwgygEgzgFWrSADKQMIIMoBINQBVK18fHwizgFCqcDGia7Ok7IwVg0AIM4BQqnAxomuzpOyMFINASDQAULdsIWM6LaRqLh/Vg0AINABQt2whYzotpGouH9SBEBCqcDGia7Ok7IwIc4BDAILIM0BQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IcoBIM0BQpHh5c2HifqZKFIEQEKpwMaJrs6TsjAhzgEgzQEh2AEMAwtCkeHlzYeJ+pkoIdgBINEBQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwIc4BDAILIM0BQpHh5c2HifqZKH0iygEg0QFCgYCAgL+y/fDDAFStItMBfSHYASDQAUKjz/rzl8nu18cAfCLUASDNAUKR4eXNh4n6mShUIMoBINMBVHKtIs0BfSHKASDOASDQAULdsIWM6LaRqLh/VCDNASDUAVZyrX1CqcDGia7Ok7IwfSHOASDRAUKBgICAv7L98MMAfSHRAQwBCyDQASHKASDNASHYAQtCqcDGia7Ok7IwIdABIMoBIOQBfCLNASDKAVQgzQEg2AEg6wF8ItMBINgBVCDTASDTASDRASDmAXwi5gEg0QFUrXwiygFWcq18ItEBIM0BVHKtIM4BIOoBfHwi6gEhzQECQAJAAkAg6gFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8h0AEg0QEizQFC3bCFjOi2kai4f1INAEKR4eXNh4n6mSgh0AEgygEizQFCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAh0AEg5gEizQFCgYCAgL+y/fDDAFENAQsgzQEg0AFaDQAg0QEh5AEgygEh6wEMAQsgygFCkeHlzYeJ+pkofSLNASDmAUKBgICAv7L98MMAVK0izgF9IesBINEBQqPP+vOXye7XxwB8ItABIMoBQpHh5c2HifqZKFQgzQEgzgFUcq0iygF9IeQBIOoBINEBQt2whYzotpGouH9UIMoBINABVnKtfUKpwMaJrs6TsjB9IeoBIOYBQoGAgIC/sv3wwwB9IeYBCyAKQSBqIQogB0EESSAHQQFqIQcNAAsMAgsgAyADKQPApQE3A7ikASADIAMpA7ilATcDsKQBQcqZwgBBKyADQbCkAWpB2K7CAEHorsIAEMoDAAsgAyADKQPApQE3A7ikASADIAMpA7ilATcDsKQBQcqZwgBBKyADQbCkAWpB2K7CAEH4rsIAEMoDAAsCQAJAAkACQAJAAkACQAJAAkACQCAQBEAgCEEhTw0BIAMoAvSjASEFIANBgIUBaiATQShsaiIKQgE3AwAgCiAFKQMANwMIIApBEGogBUEIaikDADcDACAKQRhqIAVBEGopAwA3AwAgCkEgaiAFQRhqKQMANwMAIA1FDQIgEEECTQ0DQqnAxomuzpOyMCHNASAFKQMoIssBIAUpA0h8IsoBIMsBVCDKASAFKQMwIssBIAUpA1B8IswBIMsBVCDMASDMASAFKQM4IssBIAUpA1h8Is4BIMsBVK18IssBVnKtfCLMASDKAVRyrSAFKQNAIAUpAyB8fCLRASHKAQJAAkACQCDRAUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyHNASDMASLKAULdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCHNASDLASLKAUKR4eXNh4n6mShSDQBCgYCAgL+y/fDDACHNASDOASLKAUKBgICAv7L98MMAUQ0BCyDKASDNAVoNACDMASHNASDLASHKAQwBCyDLAUKR4eXNh4n6mSh9Is8BIM4BQoGAgIC/sv3wwwBUrSLNAX0hygEgzAFCo8/685fJ7tfHAHwi0gEgywFCkeHlzYeJ+pkoVCDNASDPAVZyrSLLAX0hzQEg0QEgzAFC3bCFjOi2kai4f1QgywEg0gFWcq19QqnAxomuzpOyMH0h0QEgzgFCgYCAgL+y/fDDAH0hzgELIAhBIEYNBCADQYCFAWoiByAZQShsaiIKIM4BNwMgIAogygE3AxggCiDNATcDECAKINEBNwMIIApCATcDACAQQQNGDQUgCEEnaiEKIAhBH08NBiAKQShsIAdqIgpCATcDACAKIAUpA2A3AwggCkEQaiAFQegAaikDADcDACAKQRhqIAVB8ABqKQMANwMAIApBIGogBUH4AGopAwA3AwAgCEEoaiEFIAhBHkYNByAFQShsIAdqIgUg5gE3AyAgBSDrATcDGCAFIOQBNwMQIAUg6gE3AwggBUIBNwMAIAhBKWohBSAIQR1PDQkgBUEobCAHaiIFQgE3AwAgBSARKQMANwMIIAVBEGogEUEIaikDADcDACAFQRhqIBFBEGopAwA3AwAgBUEgaiARQRhqKQMANwMAIANB6KsBaiIKIAdB8BX8CgAAQQAhBUHRzsUALQAAGiADQoCAgIDgCDcD2MEBQcgGQQQQ1gQiB0UNCANAAkAgCigCAEEBcQRAIANByKUBaiAKQSBqKQMANwMAIANBwKUBaiAKQRhqKQMANwMAIANBuKUBaiAKQRBqKQMANwMAIAMgCkEIaikDADcDsKUBIANB4MEBaiADQbClAWoQ3AIMAQsgA0GAgICAeDYC4MEBCyAFIAdqIgggAykC4MEBNwIAIAhBCGogA0HowQFqKAIANgIAIApBKGohCiAFQQxqIgVByAZHDQALIAcoAgwhBSAHKAIIIQogBygCBCEIIAcoAgAhDSADQbClAWoiECAHQRBqQbgG/AoAACAHQcgGEN8EIA1BgYCAgHhGDQogBiAFNgIMIAYgCjYCCCAGIAg2AgQgBiANNgIAIAZBEGogEEG4BvwKAAAgAygC8KMBIgUEQCADKAL0owEgBUEFdBDfBAsgDEGABxDfBAwNC0EAQQBBmK3CABDZAwALIBNBxgBBqK3CABDZAwALQQFBAUG4rcIAENkDAAtBAkECQcitwgAQ2QMACyAZQcYAQditwgAQ2QMAC0EDQQNB6K3CABDZAwALIApBxgBB+K3CABDZAwALIAVBxgBBiK7CABDZAwALQQRByAZBkJbCABDIBAALIAVBxgBBmK7CABDZAwALIAMgBTYC6MEBIAMgCjYC5MEBIAMgCDYC4MEBQcqZwgBBKyADQeDBAWpBqK7CAEG4rsIAEMoDAAsgBkGBgICAeDYCACAGQgI3AwgMAQsgBkGBgICAeDYCACAGQgI3AwgLIBoEQCAUIBpBBXQQ3wQLIANBgMIBaiQAIAQoArAnIgVBgYCAgHhHIgpFBEAgBCkDuCchygEgBCAEKQPAJzcDqGEgBCDKATcDoGEgBEEBNgLsYiAEQcylwgA2AuhiIARCATcC9GIgBCAEQaDhAGqtQoCAgIDQCIQ3A/BkIAQgBEHw5ABqNgLwYiAEQcDdAGogBEHo4gBqEK4DIARByOAAaiAEQcjdAGooAgAiBTYCACAEIAQpAsBdIsoBNwPAYCASQQxqIAU2AgAgEiDKATcCBCASQQE2AgAMAgsgBEHI3QBqIgcgBEG8J2ooAgA2AgAgBCAEKQK0JzcDwF0gBEH41ABqIARBwCdqQbgG/AoAACAEQcjgAGogBygCACIHNgIAIARB9NQAaiAHNgIAIAQgBCkDwF0iygE3A8BgIAQgBTYC6FQgBCDKATcC7FQgBEHc1ABqIREgBEHo1ABqIRQjAEFAaiIIJAACQAJAAkACQAJAIAlBJWoiBQRAIAVBxgBLDQEgCUEqaiIHIAVJDQIgB0HGAEsNA0EAIQxB0c7FAC0AABogCUEpaiIHQQxsIg1BBBDWBCIDRQ0EIAhBADYCPCAIIAM2AjggCCAHNgI0IAhBNGoiByAUQQxqIg0gDSAJQQxsakGwA2oQhQMgByAUIAVBDGxqIgUgBUE8ahCFAyAIQYGAgIB4NgIYIAhBgYCAgHg2AgwgCCAIKAI0NgIsIAggCCgCOCIFNgIoIAggBTYCJCAIIAUgCCgCPEEMbGo2AjAjAEEQayIDJAACQAJAAkACQCAIQQxqIg0oAhgiF0UEQCARQQA2AgggEUKAgICAwAA3AgAMAQsgDSgCHCIFIA0oAiQiEEcEQANAAkAgBSIHKAIAIgZBgICAgHhHBEAgBkGBgICAeEYNASANIAVBDGoiBTYCHCAHQQRqKQIAIcoBQdHOxQAtAAAaQTBBBBDWBCITRQ0GIBMgygE3AgQgEyAGNgIAIANBATYCDCADIBM2AgggA0EENgIEIA0oAiAhGiANKAIQISMgDSgCDCEZIA0oAgQhMCANKAIAIQ0CQCAFIBBGDQBBASEGA0ACQCAFIgcoAgAiHEGAgICAeEcEQCAcQYGAgIB4Rg0BIAVBBGopAgAhygEgAygCBCAGRgRAIANBBGogBkEBQQRBDBCIAyADKAIIIRMLIBMgBkEMbGoiBSDKATcCBCAFIBw2AgAgAyAGQQFqIgY2AgwgB0EMaiIFIBBHDQIMAwsgB0EMaiIFIBBHDQELCyAHQQxqIQULIBAgBWtBDG4hBiAFIBBHBEADQCAFKAIAIgdBgICAgHhGIAdFckUEQCAFQQRqKAIAIAdBAnQQ3wQLIAVBDGohBSAGQQFrIgYNAAsLIBoEQCAXIBpBDGwQ3wQLIA1FIA1BgoCAgHhIckUEQCAwIA1BAnQQ3wQLIBlFIBlBgoCAgHhIckUEQCAjIBlBAnQQ3wQLIBEgAykCBDcCACARQQhqIANBDGooAgA2AgAMBQsgB0EMaiIFIBBHDQELCyANIAdBDGoiBTYCHAsgEUEANgIIIBFCgICAgMAANwIAIBAgBWtBDG4hBiAFIBBHBEADQCAFKAIAIgdBgICAgHhGIAdFckUEQCAFQQRqKAIAIAdBAnQQ3wQLIAVBDGohBSAGQQFrIgYNAAsLIA0oAiAiBUUNACAXIAVBDGwQ3wQLIA0oAgAiBUGCgICAeEggBUVyRQRAIA0oAgQgBUECdBDfBAsgDSgCDCIFQYKAgIB4SCAFRXINACANKAIQIAVBAnQQ3wQLIANBEGokAAwBC0EEQTBBkJbCABDIBAALA0AgDCAUaiIHKAIAIgVBgICAgHhGIAVFckUEQCAHQQRqKAIAIAVBAnQQ3wQLIAxBDGoiDEHIBkcNAAsgCEFAayQADAULQQFBAEHYsMIAEOYEAAsgBUHGAEHYsMIAEOUEAAsgBSAHQeiwwgAQ5gQACyAHQcYAQeiwwgAQ5QQAC0EEIA1BxITAABDIBAALIARBuNsAaiAEQeTUAGooAgAiBzYCACAEIAQpAtxUNwOwWyAHQQFLBEAgBCgCtFsgB0EMbGoiB0EYayIFKQIAIcoBIAUgB0EMayIHKQIANwIAIAcgygE3AgAgBUEIaiIFKAIAIQggBSAHQQhqIgUoAgA2AgAgBSAINgIAIAQoArhbIQcLIAcEQCAEQcjbAGogBCgCtFsiBUEIaigCADYCACAEIAUpAgA3A8BbIAdBAWsiB0EMbCIIBEAgBSAFQQxqIAj8CgAACyAEIAc2ArhbIARBwNsAaiEMAkAgBEGw2wBqIgUoAggiB0EcTwRAIAUoAgAgB0YEQCAFQeylwgAQnwMLIAUoAgRB0AJqIQgCQCAHQRxNDQAgB0Eca0EMbCINRQ0AIAhBDGogCCAN/AoAAAsgCCAMKQIANwIAIAhBCGogDEEIaigCADYCACAFIAdBAWo2AggMAQsjAEEwayIFJAAgBSAHNgIEIAVBHDYCACAFQQM2AgwgBUGEr8UANgIIIAVCAjcCFCAFIAVBBGqtQoCAgIDgAYQ3AyggBSAFrUKAgICA4AGENwMgIAUgBUEgajYCECAFQQhqQeylwgAQqAQACwsgBEEANgLwYiAEQoCAgIDAADcC6GIgBEHo4gBqIgUgDyAWEJYDIAUgDkEQEJYDIAUgBEHgE2oQuQEgBSAEQYAUahC5ASAFIARB8BRqELkBIAUgBEGQFWoQuQEgBSAEQYAWahC5ASAFIARBoBZqELkBIAUgBEGQF2oQuQEgBSAEQbAXahC5ASAFIARBoBhqELkBIAUgBEHAGGoQuQEgBSAEQbAZahC5ASAFIARB0BlqELkBIAUgBEHAGmoQuQEgBSAEQeAaahC5ASAFIARB0BtqELkBIAUgBEHwG2oQuQEgBSAfELEDIBggH0HIAGxqIREgHwRAIBghBQNAIARB6OIAaiIHIAUQuQEgByAFQSBqELkBIAVByABqIgUgEUcNAAsLIARB6OIAaiIDIARB4BxqELoBIAQgCTYCiFwgBEEANgKEXCAEQQA2AvBbIARBADYC4FsgBCAEQYQdajYCgFwgBEGwJ2ohDUEAIQdBACEGIwBB8ABrIgwkACAMQRBqIARB4NsAaiIWEJgCAkACQAJAAkAgDCgCEEEBRgRAIBYoAhwgFigCFGtBBXZBACAWKAIQGyAWKAIMIBYoAgRrQQV2QQAgFigCABtqIQgCfyAWKAIgBEAgDEFAayAWKAIoIBYoAiRLDQEaCyAIIQcgDEHsAGoLIAc2AgAgCEH+//8/Sw0DQQMgCCAIQQNNG0EBaiIHQQV0IghB+P///wdLDQMCQCAIRQRAQQAhB0EIIQUMAQtB0c7FAC0AABpBCCEGIAhBCBDWBCIFRQ0ECyAFIAxBGGoiCCkDADcDACAFQRhqIAhBGGopAwA3AwAgBUEQaiAIQRBqKQMANwMAIAVBCGogCEEIaikDADcDACAMIAU2AgggDCAHNgIEIAxBATYCDCAMQThqIBZBKGooAgA2AgAgDEEwaiAWQSBqKQIANwMAIAxBKGogFkEYaikCADcDACAMQSBqIBZBEGopAgA3AwAgCCAWQQhqKQIANwMAIAwgFikCADcDECAMQUBrIAxBEGoQmAIgDCgCQEEBRw0BIAxByABqIRZBICEGQQEhBwNAIAwoAgQgB0YEQCAMKAIsIAwoAiRrQQV2QQAgDCgCIBsgDCgCHCAMKAIUa0EFdkEAIAwoAhAbaiEIAn8CQCAMKAIwRQ0AIAwoAjggDCgCNE0NAEEAIQUgDEHsAGoMAQsgCCEFIAxB6ABqCyAFNgIAIAxBBGogByAIQQFqQQhBIBCIAyAMKAIIIQULIAUgBmoiCCAWKQMANwMAIAhBGGogFkEYaikDADcDACAIQRBqIBZBEGopAwA3AwAgCEEIaiAWQQhqKQMANwMAIAwgB0EBaiIHNgIMIAZBIGohBiAMQUBrIAxBEGoQmAIgDCgCQA0ACwwBCyANQQA2AgggDUKAgICAgAE3AgACQCAWKAIAIgVFDQAgFigCCCIHRQ0AIAUgB0EFdBDfBAsgFigCECIFRQ0BIBYoAhgiB0UNASAFIAdBBXQQ3wQMAQsCQCAMKAIQIgVFDQAgDCgCGCIHRQ0AIAUgB0EFdBDfBAsCQCAMKAIgIgVFDQAgDCgCKCIHRQ0AIAUgB0EFdBDfBAsgDSAMKQIENwIAIA1BCGogDEEMaigCADYCAAsgDEHwAGokAAwBCyAGIAhBkJbCABDIBAALIAMgBCgCtCciBSAEKAK4JxCWAyAEKAKwJyIHBEAgBSAHQQV0EN8ECyAEQejiAGoiBSAEQZAdakEpEJYDIAUgBEHYMWoQugEgBSAEQfgxahC5ASAFIARBmDJqELkBIAUgBEGIM2oQugEgBSAJQQFrIgwQsQMCQAJAAkAgDCAkTQRAIAwEQCALIAxByABsaiEHIAshBQNAIARB6OIAaiIIIAUQuQEgCCAFQSBqELkBIAVByABqIgUgB0cNAAsgCUEdTw0CCyAEQejiAGoiBSAEQagzaiAJEJYDIAUgBEGoOmpBBBCWAyAFIARBqDtqELkBIAUgBEHIO2oQuQEgBSAEQfA7ahC5ASAFIARBkDxqELkBIARB2NsAaiAEQfDiAGooAgA2AgAgBCAEKQLoYjcD0FtB0c7FAC0AABpB6BRBCBDWBCIHRQ0CIAcgBCkDgD03AwAgByA9OgBAIAcgBCgC+Dw2AEEgB0HEAGogBCgA+zw2AAAgB0E4aiAEQbg9aikDADcDACAHQTBqIARBsD1qKQMANwMAIAdBKGogBEGoPWopAwA3AwAgB0EgaiAEQaA9aikDADcDACAHQRhqIARBmD1qKQMANwMAIAdBEGogBEGQPWopAwA3AwAgB0EIaiAEQYg9aikDADcDACAHIDk6AIgBIAdBgAFqIARBgD5qKQMANwMAIAdB+ABqIARB+D1qKQMANwMAIAdB8ABqIARB8D1qKQMANwMAIAdB6ABqIARB6D1qKQMANwMAIAdB4ABqIARB4D1qKQMANwMAIAdB2ABqIARB2D1qKQMANwMAIAdB0ABqIARB0D1qKQMANwMAIAcgBCkDyD03A0ggB0GMAWogBCgAwz02AAAgByAEKALAPTYAiQEgByAEKQOQPjcDkAEgB0GYAWogBEGYPmopAwA3AwAgB0GgAWogBEGgPmopAwA3AwAgB0GoAWogBEGoPmopAwA3AwAgB0GwAWogBEGwPmopAwA3AwAgB0G4AWogBEG4PmopAwA3AwAgB0HAAWogBEHAPmopAwA3AwAgB0HIAWogBEHIPmopAwA3AwAgByAvOgDQASAHIAQoAog+NgDRASAHQdQBaiAEKACLPjYAACAHQZACaiAEQZA/aikDADcDACAHQYgCaiAEQYg/aikDADcDACAHQYACaiAEQYA/aikDADcDACAHQfgBaiAEQfg+aikDADcDACAHQfABaiAEQfA+aikDADcDACAHQegBaiAEQeg+aikDADcDACAHQeABaiAEQeA+aikDADcDACAHIAQpA9g+NwPYASAHID46AJgCIAdBnAJqIAQoANM+NgAAIAcgBCgC0D42AJkCIAdB2AJqIARB2D9qKQMANwMAIAdB0AJqIARB0D9qKQMANwMAIAdByAJqIARByD9qKQMANwMAIAdBwAJqIARBwD9qKQMANwMAIAdBuAJqIARBuD9qKQMANwMAIAdBsAJqIARBsD9qKQMANwMAIAdBqAJqIARBqD9qKQMANwMAIAcgBCkDoD83A6ACIAcgPzoA4AIgB0HkAmogBCgAmz82AAAgByAEKAKYPzYA4QIgB0GgA2ogBEGgwABqKQMANwMAIAdBmANqIARBmMAAaikDADcDACAHQZADaiAEQZDAAGopAwA3AwAgB0GIA2ogBEGIwABqKQMANwMAIAdBgANqIARBgEBrKQMANwMAIAdB+AJqIARB+D9qKQMANwMAIAdB8AJqIARB8D9qKQMANwMAIAcgBCkD6D83A+gCIAcgQDoAqAMgB0GsA2ogBCgA4z82AAAgByAEKALgPzYAqQMgB0HoA2ogBEHowABqKQMANwMAIAdB4ANqIARB4MAAaikDADcDACAHQdgDaiAEQdjAAGopAwA3AwAgB0HQA2ogBEHQwABqKQMANwMAIAdByANqIARByMAAaikDADcDACAHQcADaiAEQcDAAGopAwA3AwAgB0G4A2ogBEG4wABqKQMANwMAIAcgBCkDsEA3A7ADIAcgQToA8AMgB0H0A2ogBCgAq0A2AAAgByAEKAKoQDYA8QMgB0GwBGogBEGwwQBqKQMANwMAIAdBqARqIARBqMEAaikDADcDACAHQaAEaiAEQaDBAGopAwA3AwAgB0GYBGogBEGYwQBqKQMANwMAIAdBkARqIARBkMEAaikDADcDACAHQYgEaiAEQYjBAGopAwA3AwAgB0GABGogBEGAwQBqKQMANwMAIAcgBCkD+EA3A/gDIAcgQjoAuAQgB0G8BGogBCgA80A2AAAgByAEKALwQDYAuQQgB0H4BGogBEH4wQBqKQMANwMAIAdB8ARqIARB8MEAaikDADcDACAHQegEaiAEQejBAGopAwA3AwAgB0HgBGogBEHgwQBqKQMANwMAIAdB2ARqIARB2MEAaikDADcDACAHQdAEaiAEQdDBAGopAwA3AwAgB0HIBGogBEHIwQBqKQMANwMAIAcgBCkDwEE3A8AEIAcgQzoAgAUgB0GEBWogBCgAu0E2AAAgByAEKAK4QTYAgQUgB0HABWogBEHAwgBqKQMANwMAIAdBuAVqIARBuMIAaikDADcDACAHQbAFaiAEQbDCAGopAwA3AwAgB0GoBWogBEGowgBqKQMANwMAIAdBoAVqIARBoMIAaikDADcDACAHQZgFaiAEQZjCAGopAwA3AwAgB0GQBWogBEGQwgBqKQMANwMAIAcgBCkDiEI3A4gFIAcgRDoAyAUgB0HMBWogBCgAg0I2AAAgByAEKAKAQjYAyQUgB0GIBmogBEGIwwBqKQMANwMAIAdBgAZqIARBgMMAaikDADcDACAHQfgFaiAEQfjCAGopAwA3AwAgB0HwBWogBEHwwgBqKQMANwMAIAdB6AVqIARB6MIAaikDADcDACAHQeAFaiAEQeDCAGopAwA3AwAgB0HYBWogBEHYwgBqKQMANwMAIAcgBCkD0EI3A9AFIAcgOjoAkAYgB0GUBmogBCgAy0I2AAAgByAEKALIQjYAkQYgB0HQBmogBEHQwwBqKQMANwMAIAdByAZqIARByMMAaikDADcDACAHQcAGaiAEQcDDAGopAwA3AwAgB0G4BmogBEG4wwBqKQMANwMAIAdBsAZqIARBsMMAaikDADcDACAHQagGaiAEQajDAGopAwA3AwAgB0GgBmogBEGgwwBqKQMANwMAIAcgBCkDmEM3A5gGIAcgSToA2AYgB0HcBmogBCgAk0M2AAAgByAEKAKQQzYA2QYgB0GYB2ogBEGYxABqKQMANwMAIAdBkAdqIARBkMQAaikDADcDACAHQYgHaiAEQYjEAGopAwA3AwAgB0GAB2ogBEGAxABqKQMANwMAIAdB+AZqIARB+MMAaikDADcDACAHQfAGaiAEQfDDAGopAwA3AwAgB0HoBmogBEHowwBqKQMANwMAIAcgBCkD4EM3A+AGIAcgSjoAoAcgB0GkB2ogBCgA20M2AAAgByAEKALYQzYAoQcgB0HgB2ogBEHgxABqKQMANwMAIAdB2AdqIARB2MQAaikDADcDACAHQdAHaiAEQdDEAGopAwA3AwAgB0HIB2ogBEHIxABqKQMANwMAIAdBwAdqIARBwMQAaikDADcDACAHQbgHaiAEQbjEAGopAwA3AwAgB0GwB2ogBEGwxABqKQMANwMAIAcgBCkDqEQ3A6gHIAcgSzoA6AcgB0HsB2ogBCgAo0Q2AAAgByAEKAKgRDYA6QcgB0GoCGogBEGoxQBqKQMANwMAIAdBoAhqIARBoMUAaikDADcDACAHQZgIaiAEQZjFAGopAwA3AwAgB0GQCGogBEGQxQBqKQMANwMAIAdBiAhqIARBiMUAaikDADcDACAHQYAIaiAEQYDFAGopAwA3AwAgB0H4B2ogBEH4xABqKQMANwMAIAcgBCkD8EQ3A/AHIAcgTDoAsAggB0G0CGogBCgA60Q2AAAgByAEKALoRDYAsQggB0HwCGogBEHwxQBqKQMANwMAIAdB6AhqIARB6MUAaikDADcDACAHQeAIaiAEQeDFAGopAwA3AwAgB0HYCGogBEHYxQBqKQMANwMAIAdB0AhqIARB0MUAaikDADcDACAHQcgIaiAEQcjFAGopAwA3AwAgB0HACGogBEHAxQBqKQMANwMAIAcgBCkDuEU3A7gIIAcgTToA+AggB0H8CGogBCgAs0U2AAAgByAEKAKwRTYA+QggB0G4CWogBEG4xgBqKQMANwMAIAdBsAlqIARBsMYAaikDADcDACAHQagJaiAEQajGAGopAwA3AwAgB0GgCWogBEGgxgBqKQMANwMAIAdBmAlqIARBmMYAaikDADcDACAHQZAJaiAEQZDGAGopAwA3AwAgB0GICWogBEGIxgBqKQMANwMAIAcgBCkDgEY3A4AJIAcgTjoAwAkgB0HECWogBCgA+0U2AAAgByAEKAL4RTYAwQkgB0GACmogBEGAxwBqKQMANwMAIAdB+AlqIARB+MYAaikDADcDACAHQfAJaiAEQfDGAGopAwA3AwAgB0HoCWogBEHoxgBqKQMANwMAIAdB4AlqIARB4MYAaikDADcDACAHQdgJaiAEQdjGAGopAwA3AwAgB0HQCWogBEHQxgBqKQMANwMAIAcgBCkDyEY3A8gJIAcgTzoAiAogB0GMCmogBCgAw0Y2AAAgByAEKALARjYAiQogB0HICmogBEHIxwBqKQMANwMAIAdBwApqIARBwMcAaikDADcDACAHQbgKaiAEQbjHAGopAwA3AwAgB0GwCmogBEGwxwBqKQMANwMAIAdBqApqIARBqMcAaikDADcDACAHQaAKaiAEQaDHAGopAwA3AwAgB0GYCmogBEGYxwBqKQMANwMAIAcgBCkDkEc3A5AKIAcgUDoA0AogB0HUCmogBCgAi0c2AAAgByAEKAKIRzYA0QogB0GQC2ogBEGQyABqKQMANwMAIAdBiAtqIARBiMgAaikDADcDACAHQYALaiAEQYDIAGopAwA3AwAgB0H4CmogBEH4xwBqKQMANwMAIAdB8ApqIARB8McAaikDADcDACAHQegKaiAEQejHAGopAwA3AwAgB0HgCmogBEHgxwBqKQMANwMAIAcgBCkD2Ec3A9gKIAcgUToAmAsgB0GcC2ogBCgA00c2AAAgByAEKALQRzYAmQsgB0HYC2ogBEHYyABqKQMANwMAIAdB0AtqIARB0MgAaikDADcDACAHQcgLaiAEQcjIAGopAwA3AwAgB0HAC2ogBEHAyABqKQMANwMAIAdBuAtqIARBuMgAaikDADcDACAHQbALaiAEQbDIAGopAwA3AwAgB0GoC2ogBEGoyABqKQMANwMAIAcgBCkDoEg3A6ALIAcgUjoA4AsgB0HkC2ogBCgAm0g2AAAgByAEKAKYSDYA4QsgB0GgDGogBEGgyQBqKQMANwMAIAdBmAxqIARBmMkAaikDADcDACAHQZAMaiAEQZDJAGopAwA3AwAgB0GIDGogBEGIyQBqKQMANwMAIAdBgAxqIARBgMkAaikDADcDACAHQfgLaiAEQfjIAGopAwA3AwAgB0HwC2ogBEHwyABqKQMANwMAIAcgBCkD6Eg3A+gLIAcgUzoAqAwgB0GsDGogBCgA40g2AAAgByAEKALgSDYAqQwgB0HoDGogBEHoyQBqKQMANwMAIAdB4AxqIARB4MkAaikDADcDACAHQdgMaiAEQdjJAGopAwA3AwAgB0HQDGogBEHQyQBqKQMANwMAIAdByAxqIARByMkAaikDADcDACAHQcAMaiAEQcDJAGopAwA3AwAgB0G4DGogBEG4yQBqKQMANwMAIAcgBCkDsEk3A7AMIAcgVDoA8AwgB0H0DGogBCgAq0k2AAAgByAEKAKoSTYA8QwgB0GwDWogBEGwygBqKQMANwMAIAdBqA1qIARBqMoAaikDADcDACAHQaANaiAEQaDKAGopAwA3AwAgB0GYDWogBEGYygBqKQMANwMAIAdBkA1qIARBkMoAaikDADcDACAHQYgNaiAEQYjKAGopAwA3AwAgB0GADWogBEGAygBqKQMANwMAIAcgBCkD+Ek3A/gMIAcgVToAuA0gB0G8DWogBCgA80k2AAAgByAEKALwSTYAuQ0gB0H4DWogBEH4ygBqKQMANwMAIAdB8A1qIARB8MoAaikDADcDACAHQegNaiAEQejKAGopAwA3AwAgB0HgDWogBEHgygBqKQMANwMAIAdB2A1qIARB2MoAaikDADcDACAHQdANaiAEQdDKAGopAwA3AwAgB0HIDWogBEHIygBqKQMANwMAIAcgBCkDwEo3A8ANIAcgVjoAgA4gB0GEDmogBCgAu0o2AAAgByAEKAK4SjYAgQ4gB0HADmogBEHAywBqKQMANwMAIAdBuA5qIARBuMsAaikDADcDACAHQbAOaiAEQbDLAGopAwA3AwAgB0GoDmogBEGoywBqKQMANwMAIAdBoA5qIARBoMsAaikDADcDACAHQZgOaiAEQZjLAGopAwA3AwAgB0GQDmogBEGQywBqKQMANwMAIAcgBCkDiEs3A4gOIAcgVzoAyA4gB0HMDmogBCgAg0s2AAAgByAEKAKASzYAyQ4gB0GID2ogBEGIzABqKQMANwMAIAdBgA9qIARBgMwAaikDADcDACAHQfgOaiAEQfjLAGopAwA3AwAgB0HwDmogBEHwywBqKQMANwMAIAdB6A5qIARB6MsAaikDADcDACAHQeAOaiAEQeDLAGopAwA3AwAgB0HYDmogBEHYywBqKQMANwMAIAcgBCkD0Es3A9AOIAcgWDoAkA8gB0GUD2ogBCgAy0s2AAAgByAEKALISzYAkQ8gB0HQD2ogBEHQzABqKQMANwMAIAdByA9qIARByMwAaikDADcDACAHQcAPaiAEQcDMAGopAwA3AwAgB0G4D2ogBEG4zABqKQMANwMAIAdBsA9qIARBsMwAaikDADcDACAHQagPaiAEQajMAGopAwA3AwAgB0GgD2ogBEGgzABqKQMANwMAIAcgBCkDmEw3A5gPIAcgWToA2A8gB0HcD2ogBCgAk0w2AAAgByAEKAKQTDYA2Q8gB0GYEGogBEGAM2opAwA3AwAgB0GQEGogBEH4MmopAwA3AwAgB0GIEGogBEHwMmopAwA3AwAgB0GAEGogBEHoMmopAwA3AwAgB0H4D2ogBEHgMmopAwA3AwAgB0HwD2ogBEHYMmopAwA3AwAgB0HoD2ogBEHQMmopAwA3AwAgByAEKQPIMjcD4A8gByAmOgCgECAHQaQQaiAEKADDMjYAACAHIAQoAsAyNgChECAHQeAQaiAEQegUaikDADcDACAHQdgQaiAEQeAUaikDADcDACAHQdAQaiAEQdgUaikDADcDACAHQcgQaiAEQdAUaikDADcDACAHQcAQaiAEQcgUaikDADcDACAHQbgQaiAEQcAUaikDADcDACAHQbAQaiAEQbgUaikDADcDACAHIAQpA7AUNwOoECAHICE6AOgQIAdB7BBqIAQoAKsUNgAAIAcgBCgCqBQ2AOkQIAdBqBFqIARB+BVqKQMANwMAIAdBoBFqIARB8BVqKQMANwMAIAdBmBFqIARB6BVqKQMANwMAIAdBkBFqIARB4BVqKQMANwMAIAdBiBFqIARB2BVqKQMANwMAIAdBgBFqIARB0BVqKQMANwMAIAdB+BBqIARByBVqKQMANwMAIAcgBCkDwBU3A/AQIAcgKzoAsBEgB0G0EWogBCgAuxU2AAAgByAEKAK4FTYAsREgB0HwEWogBEGIF2opAwA3AwAgB0HoEWogBEGAF2opAwA3AwAgB0HgEWogBEH4FmopAwA3AwAgB0HYEWogBEHwFmopAwA3AwAgB0HQEWogBEHoFmopAwA3AwAgB0HIEWogBEHgFmopAwA3AwAgB0HAEWogBEHYFmopAwA3AwAgByAEKQPQFjcDuBEgByAiOgD4ESAHQfwRaiAEKADLFjYAACAHIAQoAsgWNgD5ESAHQbgSaiAEQZgYaikDADcDACAHQbASaiAEQZAYaikDADcDACAHQagSaiAEQYgYaikDADcDACAHQaASaiAEQYAYaikDADcDACAHQZgSaiAEQfgXaikDADcDACAHQZASaiAEQfAXaikDADcDACAHQYgSaiAEQegXaikDADcDACAHIAQpA+AXNwOAEiAHICw6AMASIAdBxBJqIAQoANsXNgAAIAcgBCgC2Bc2AMESIAdBgBNqIARBqBlqKQMANwMAIAdB+BJqIARBoBlqKQMANwMAIAdB8BJqIARBmBlqKQMANwMAIAdB6BJqIARBkBlqKQMANwMAIAdB4BJqIARBiBlqKQMANwMAIAdB2BJqIARBgBlqKQMANwMAIAdB0BJqIARB+BhqKQMANwMAIAcgBCkD8Bg3A8gSIAcgGzoAiBMgB0GME2ogBCgA6xg2AAAgByAEKALoGDYAiRMgB0HIE2ogBEHYHGopAwA3AwAgB0HAE2ogBEHQHGopAwA3AwAgB0G4E2ogBEHIHGopAwA3AwAgB0GwE2ogBEHAHGopAwA3AwAgB0GoE2ogBEG4HGopAwA3AwAgB0GgE2ogBEGwHGopAwA3AwAgB0GYE2ogBEGoHGopAwA3AwAgByAEKQOgHDcDkBMgByAuOgDQEyAHQdQTaiAEKACbHDYAACAHIAQoApgcNgDREyAHQZAUaiAEQbgaaikDADcDACAHQYgUaiAEQbAaaikDADcDACAHQYAUaiAEQagaaikDADcDACAHQfgTaiAEQaAaaikDADcDACAHQfATaiAEQZgaaikDADcDACAHQegTaiAEQZAaaikDADcDACAHQeATaiAEQYgaaikDADcDACAHIAQpA4AaNwPYEyAHIC06AJgUIAdBnBRqIAQoAPsZNgAAIAcgBCgC+Bk2AJkUIAdB2BRqIARByBtqKQMANwMAIAdB0BRqIARBwBtqKQMANwMAIAdByBRqIARBuBtqKQMANwMAIAdBwBRqIARBsBtqKQMANwMAIAdBuBRqIARBqBtqKQMANwMAIAdBsBRqIARBoBtqKQMANwMAIAdBqBRqIARBmBtqKQMANwMAIAcgBCkDkBs3A6AUIAcgJToA4BQgB0HkFGogBCgAixs2AAAgByAEKAKIGzYA4RQgBEElNgKUXCAEIAc2ApBcIARBJTYCjFwgBSEJIAshB0EAIQhBACEQIwBBQGoiFiQAIAwiBa1CyAB+IsoBpyENAkACQCDKAUIgiKcgDUH4////B0tyDQACQCANRQRAQQghAwwBC0HRzsUALQAAGkEIIQggDUEIENYEIgNFDQEgBUUNACAWQSBqIQYgBSEIA0AgDSAQRg0BIAYgBykDIDcDACAGQRhqIAdBOGopAwA3AwAgBkEQaiAHQTBqKQMANwMAIAZBCGogB0EoaikDADcDACAWQQhqIAdBCGopAwAiygE3AwAgFkEQaiAHQRBqKQMAIssBNwMAIBZBGGogB0EYaikDACLMATcDACAWIAcpAwAizwE3AwAgBy0AQCETIAMgEGoiDEEgaiAGKQMANwMAIAxBGGogzAE3AwAgDEEQaiDLATcDACAMQQhqIMoBNwMAIAwgzwE3AwAgDEE4aiAWQThqKQMANwMAIAxBMGogFkEwaikDADcDACAMQShqIBZBKGopAwA3AwAgDEFAayATOgAAIBBByABqIRAgB0HIAGohByAIQQFrIggNAAsLIAkgBTYCCCAJIAM2AgQgCSAFNgIAIBZBQGskAAwBCyAIIA1BlJvCABDIBAALIAQgBCgC6GI2ArgnIAQgBCgC7GIiBTYCsCcgBCAFNgK0JyAEIAUgBCgC8GJByABsajYCvCcgBEGM3ABqIgUgBEGwJ2oiBxDGAyAEICA2ArgnIAQgGDYCsCcgBCARNgK8JyAEIBg2ArQnIAUgBxDGAyAEQaDcAGogBEHAPGopAwA3AwAgBEGo3ABqIgggBEHIPGopAwA3AwAgBEGw3ABqIgwgBEHQPGopAwA3AwAgBEHA3ABqIgkgBEHgPGopAwA3AwAgBEHI3ABqIhYgBEHoPGopAwA3AwAgBEHQ3ABqIg0gBEHwPGopAwA3AwAgBCAEKQO4PDcDmFwgBCAEKQPYPDcDuFwgBCgClFwiByAEKAKMXEYEQCAFQbymwgAQmgMLIAQoApBcIAdByABsaiIFIAQpA5hcNwMAIAUgKUEBcToAQCAFQQhqIARBoNwAaikDADcDACAFQRBqIAgpAwA3AwAgBUEYaiAMKQMANwMAIAVBIGogBEG43ABqKQMANwMAIAVBKGogCSkDADcDACAFQTBqIBYpAwA3AwAgBUE4aiANKQMANwMAIAQgB0EBajYClFwgBEHY3ABqIQcjAEGgBWsiBSQAIAUQISAFQcgEaiIIIAVBgAFqIAVBoAFqEEMCQCAFLQCIBUECRwRAIAcgCEHIAPwKAAAgBSgCrAQiBwRAIAUoArAEIAdBAnQQ3wQLAkAgBSgC5AEiB0UNACAHIAdBDGxBE2pBeHEiCGpBCWoiB0UNACAFKALgASAIayAHEN8ECyAFKAKQAiIHQYCAgIB4RiAHRXJFBEAgBSgClAIgB0ECdBDfBAsgBUGgBWokAAwBCyAFQZgFaiAFQdAEaigCADYCACAFIAUpA8gENwOQBUGM98EAQSsgBUGQBWpB7PjBAEH8+MEAEMoDAAsgBCgClFwiBSAEKAKMXEYEQCAEQYzcAGpBzKbCABCaAwsgBCgCkFwgBUHIAGxqIARB2NwAakHIAPwKAAAgBCAFQQFqNgKUXCAEQbAnaiIFQfimwgApAwAiywFB+KbCACkDAHwizAE3AxggBUHwpsIAKQMAIs8BQfCmwgApAwB8IsoBIMsBIMwBVq18IswBNwMQIAVB6KbCACkDACLNAUHopsIAKQMAfCLLASDKASDPAVQgygEgzAFWcq18IswBNwMIIAVB4KbCACkDACLPAUHgpsIAKQMAfCLKASDLASDNAVQgywEgzAFWcq18IssBNwMAIAUgygEgzwFUIMoBIMsBVnI6ACBCkYCAgICAgIAIIcwBIAQpA8gnIcsBIAQpA8AnIc8BIAQpA7gnIc0BIAQpA7AnItIBIcoBAkACQCDSAUKRgICAgICAgAhRBEAgzQEgzwGEQgBSDQFCASHMASDLASLKAUIBUQ0BCyDKASDMAVoNACDNASHMASDPASHKASDLASHOAQwBCyDLAUIBfSHOASDPASDLAVCtIssBfSHKASDNASDLASDPAVatIssBfSHMASDSASDLASDNAVatfUKRgICAgICAgAh9IdIBCyAEQaDdAGogFUGgBWoQ+AIgBEHY3QBqIARBuN0AaikDADcDACAEQdDdAGogBEGw3QBqKQMANwMAIARByN0AaiAEQajdAGopAwA3AwAgBEHo3QBqIARB2OQAaikDADcDACAEQfDdAGogBEHg5ABqKQMANwMAIARB+N0AaiAEQejkAGopAwA3AwAgBCAEKQOgXTcDwF0gBCAEKQPQZDcD4F0gBCDOATcDmF4gBCDKATcDkF4gBCDMATcDiF4gBCDSATcDgF4gBEHA3QBqEEYgBEGk3gBqIAQoApBcIAQoApRcIAQoArRbIAQoArhbQQBBARBgIARBsCdqIRAgBCgCkFwhAyAEKAKUXCEJIAQoArRbIQ0gBCgCuFshByMAQeABayIFJAACQAJAAkACQAJAIAkEQCAFIAk2AlAgBSAHNgIEIAcgCUcNASANKAIIIhZBAnQhDEEAIQggFkH/////A0sgDEH8////B0tyDQIgDSgCBCEGAn8gDEUEQEEEIQdBAAwBC0HRzsUALQAAGkEEIQggDEEEENYEIgdFDQMgFgshCCAMBEAgByAGIAz8CgAACwJAIBZFBEAgBUGgAWpB0PfBACkCADcDACAFQcj3wQApAgA3A5gBIAhFDQEgByAIQQJ0EN8EDAELIAVBAjoApAEgBSAWNgKgASAFIAc2ApwBIAUgCDYCmAELIAVBCGogAyAFQZgBahCoASAJQQFGDQUgA0HIAGohByANQRBqIQwgBUHYAGohEUEBIQYDQCAGIAlGDQUgDEEEaigCACINQQJ0IRZBACEDIA1B/////wNLIBZB/P///wdLcg0EIAwoAgAhEwJ/IBZFBEBBBCEIQQAMAQtB0c7FAC0AABpBBCEDIBZBBBDWBCIIRQ0FIA0LIQMgFgRAIAggEyAW/AoAAAsCQCANRQRAIBFB0PfBACkCADcDACAFQcj3wQApAgA3A1AgA0UNASAIIANBAnQQ3wQMAQsgBUECOgBcIAUgDTYCWCAFIAg2AlQgBSADNgJQCyAFQZgBaiIWIAcgBUHQAGoiCBCoASAIIAVBCGoiDSAWEDYgDSAIQcgA/AoAACAMQQxqIQwgB0HIAGohByAJIAZBAWoiBkcNAAsMBQtBjPnBAEEkQbD5wQAQ/gMACyAFQQA2ApgBIAVB0ABqIAVBBGogBUGYAWpBwPnBABCXBAALIAggDEH4gcAAEMgEAAsgAyAWQfiBwAAQyAQACyAJIAlB0PnBABDZAwALIBAgBUEIakHIAPwKAAAgBUHgAWokACAEQbDeAGogECAEQag7ahA2IARB+N4AaiAEQfA7ahDdAiAEQcDfAGohByMAQeAFayIFJAAgBRAhAkACQAJAIAUoApgDQQFxBEAgBSgC4ANBAXFFDQEgBUHIBGogBUGgA2ogBUHoA2oQYiAFKALIBA0CIAcgBUHQBGpBgAH8CgAAIAUoAqwEIgcEQCAFKAKwBCAHQQJ0EN8ECwJAIAUoAuQBIgdFDQAgByAHQQxsQRNqQXhxIghqQQlqIgdFDQAgBSgC4AEgCGsgBxDfBAsgBSgCkAIiB0GAgICAeEYgB0VyRQRAIAUoApQCIAdBAnQQ3wQLIAVB4AVqJAAMAwtBlITBAEEzQfCEwQAQ6AMAC0GUhMEAQTNBgIXBABDoAwALIAVB2AVqIAVB1ARqKAIANgIAIAUgBSkCzAQ3A9AFQdT+wABBKyAFQdAFakGQhcEAQaCFwQAQygMACyAEQcDgAGpBgKfCAEHAABC3AiAEQYAOaiAEKQPYYCLKAUIAQon1q5y1i7+Wc0IAEMkDIARBwA5qIAQpA9BgIssBQgBCifWrnLWLv5ZzQgAQyQMgBEGAD2ogBCkDyGAizAFCAEKJ9auctYu/lnNCABDJAyAEQcAPaiAEKQPAYCLPAUIAQon1q5y1i7+Wc0IAEMkDIARB8A1qIAQpA4AOItIBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHgDWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGQDWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEHADGogzQFCAEKpwMaJrs6TsjBCABDJAyAEQZAOaiDKAUIAQvuDlKKdosbztX9CABDJAyAEQdAOaiDLAUIAQvuDlKKdosbztX9CABDJAyAEQZAPaiDMAUIAQvuDlKKdosbztX9CABDJAyAEQdAPaiDPAUIAQvuDlKKdosbztX9CABDJAyAEQdANaiAEKQPgDSLVASAEKQOIDiLTASAEKQPADnwi1AF8Is4BIAQpA/gNINIBIAQpA/ANIs0BfCDNAVStfHwi0gEgBCkDkA58ItEBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHADWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGwDWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEGgDWogzQFCAEKpwMaJrs6TsjBCABDJAyAEQaAOaiDKAUIAQvb/hdLw38fVxwBCABDJAyAEQeAOaiDLAUIAQvb/hdLw38fVxwBCABDJAyAEQaAPaiDMAUIAQvb/hdLw38fVxwBCABDJAyAEQeAPaiDPAUIAQvb/hdLw38fVxwBCABDJAyAEQYANaiAEKQOYDiDRASDSAVStfCLXASAEKQPQDnwi0AEgBCkDyA4g0wEg1AFWrXwi2AEgBCkDgA98ItMBIAQpA5ANfCLUASDOASDSAVatIAQpA+gNIM4BINUBVK18fHwi1gF8Is4BIAQpA8ANfCLSASAEKQPYDSDRASAEKQPQDSLNAXwgzQFUrXx8ItEBIAQpA6AOfCLVAUKJx5mkrvCB6Yd/fiLNAUIAQsf688PtgqOQPEIAEMkDIARB8AxqIM0BQgBCjZXHw5bS2sCXf0IAEMkDIARB4AxqIM0BQgBC3bCFjOi2kai4f0IAEMkDIARB0AxqIM0BQgBCqcDGia7Ok7IwQgAQyQMgBEGwDmogygFCAEKf6uDVnO6n7AZCABDJAyAEQfAOaiDLAUIAQp/q4NWc7qfsBkIAEMkDIARBsA9qIMwBQgBCn+rg1Zzup+wGQgAQyQMgBEHwD2ogzwFCAEKf6uDVnO6n7AZCABDJAyAEQbAMaiAEKQOoDiDRASDVAVatfCLaASAEKQPgDnwiywEgBCkDiA8g0wEg2AFUrXwi2AEgBCkDwA98IswBIAQpA8AMfCLPASDUASDWAVatIAQpA5gNINMBINQBVq18fHwizQEgBCkDkA98ItMBIM4BINABVK0gBCkD2A4g0AEg1wFUrXx8fCLQASAEKQOwDXwi1AEg0QEg0gFUrSAEKQPIDSDOASDSAVatfHx8ItYBfCLOASAEKQPwDHwi0gEgBCkDiA0g1QEgBCkDgA0iygF8IMoBVK18fCLRASAEKQOwDnwi1QFCiceZpK7wgemHf34iygFCAELH+vPD7YKjkDxCABDJAyAEQaAMaiDKAUIAQo2Vx8OW0trAl39CABDJAyAEQZAMaiDKAUIAQt2whYzotpGouH9CABDJAyAEQYAMaiDKAUIAQqnAxomuzpOyMEIAEMkDIAQgBCkDuA4g0QEg1QFWrXwi2QEgBCkD8A58ItcBIM0BIM8BVK0gBCkDyAwgzAEgzwFWrXx8ItsBIAQpA8gPIMwBINgBVK18fCLMASAEKQPQD3wizwEg0AEg0wFUrSAEKQOYDyDNASDTAVatfHx8Is0BIAQpA6ANfCLTASDUASDWAVatIAQpA7gNINABINQBVq18fHwi0AEgBCkDoA98ItQBIMsBIM4BVq0gBCkD6A4gywEg2gFUrXx8fCLLASAEKQPgDHwi2AEg0QEg0gFUrSAEKQP4DCDOASDSAVatfHx8ItYBfCLOASAEKQOgDHwi0gEgBCkDuAwg1QEgBCkDsAwiygF8IMoBVK18fCLKATcDgGMgBCAEKQPgDyDMASDbAVSthCLaASDNASDPAVStIAQpA9gPIMwBIM8BVq18fHwizAEg0AEg0wFUrSAEKQOoDSDNASDTAVatfHx8Is8BIMsBINQBVK0gBCkDqA8g0AEg1AFWrXx8fCLNASAEKQPQDHwi0QEg1gEg2AFUrSAEKQPoDCDLASDYAVatfHx8ItABIAQpA7APfCLTASDOASDXAVStIAQpA/gOINcBINkBVK18fHwi1AEgBCkDkAx8ItUBIMoBINIBVK0gBCkDqAwgzgEg0gFWrXx8fCLLATcD+GIgBCDNASDPAVStIMwBIM8BVq0gBCkD6A8gzAEg2gFUrXx8fCLXASAEKQPwD3wizwEg0AEg0QFUrSAEKQPYDCDNASDRAVatfHx8Is0BINMBINQBVq0gBCkDuA8g0AEg0wFWrXx8fCLOASAEKQOADHwi0gEgywEg1QFUrSAEKQOYDCDUASDVAVatfHx8IswBNwPwYiAEIMwBINIBVK0gBCkDiAwgzgEg0gFWrXx8IM0BIM4BVq0gzQEgzwFUrSAEKQP4DyDPASDXAVStfHx8fCLPATcD6GIgBEHo4gBqENIDBEAgBCDKAULH+vPD7YKjkDx9NwOAYyAEIMsBQvPquLzpraW/6AB8Is0BIMoBQsf688PtgqOQPFStIsoBfTcD+GIgBCDMAUKjz/rzl8nu18cAfCLOASDLAUKNlcfDltLawJd/VCDKASDNAVZyrSLKAX03A/BiIAQgzwEgzAFC3bCFjOi2kai4f1QgygEgzgFWcq19QqnAxomuzpOyMH03A+hiCyAEQcjkAGogBEGA4wBqKQMANwMAIARBwOQAaiAEQfjiAGopAwA3AwAgBEG45ABqIARB8OIAaikDADcDACAEIAQpA+hiNwOwZCAEQfDkAGpB4KfCAEHAABC3AiAEQYAKaiAEKQOIZSLKAUIAQon1q5y1i7+Wc0IAEMkDIARBwApqIAQpA4BlIssBQgBCifWrnLWLv5ZzQgAQyQMgBEGAC2ogBCkD+GQizAFCAEKJ9auctYu/lnNCABDJAyAEQcALaiAEKQPwZCLPAUIAQon1q5y1i7+Wc0IAEMkDIARB8AlqIAQpA4AKItIBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHgCWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGQCWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEHACGogzQFCAEKpwMaJrs6TsjBCABDJAyAEQZAKaiDKAUIAQvuDlKKdosbztX9CABDJAyAEQdAKaiDLAUIAQvuDlKKdosbztX9CABDJAyAEQZALaiDMAUIAQvuDlKKdosbztX9CABDJAyAEQdALaiDPAUIAQvuDlKKdosbztX9CABDJAyAEQdAJaiAEKQPgCSLVASAEKQOICiLTASAEKQPACnwi1AF8Is4BIAQpA/gJINIBIAQpA/AJIs0BfCDNAVStfHwi0gEgBCkDkAp8ItEBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHACWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGwCWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEGgCWogzQFCAEKpwMaJrs6TsjBCABDJAyAEQaAKaiDKAUIAQvb/hdLw38fVxwBCABDJAyAEQeAKaiDLAUIAQvb/hdLw38fVxwBCABDJAyAEQaALaiDMAUIAQvb/hdLw38fVxwBCABDJAyAEQeALaiDPAUIAQvb/hdLw38fVxwBCABDJAyAEQYAJaiAEKQOYCiDRASDSAVStfCLXASAEKQPQCnwi0AEgBCkDyAog0wEg1AFWrXwi2AEgBCkDgAt8ItMBIAQpA5AJfCLUASDOASDSAVatIAQpA+gJIM4BINUBVK18fHwi1gF8Is4BIAQpA8AJfCLSASAEKQPYCSDRASAEKQPQCSLNAXwgzQFUrXx8ItEBIAQpA6AKfCLVAUKJx5mkrvCB6Yd/fiLNAUIAQsf688PtgqOQPEIAEMkDIARB8AhqIM0BQgBCjZXHw5bS2sCXf0IAEMkDIARB4AhqIM0BQgBC3bCFjOi2kai4f0IAEMkDIARB0AhqIM0BQgBCqcDGia7Ok7IwQgAQyQMgBEGwCmogygFCAEKf6uDVnO6n7AZCABDJAyAEQfAKaiDLAUIAQp/q4NWc7qfsBkIAEMkDIARBsAtqIMwBQgBCn+rg1Zzup+wGQgAQyQMgBEHwC2ogzwFCAEKf6uDVnO6n7AZCABDJAyAEQbAIaiAEKQOoCiDRASDVAVatfCLaASAEKQPgCnwiywEgBCkDiAsg0wEg2AFUrXwi2AEgBCkDwAt8IswBIAQpA8AIfCLPASDUASDWAVatIAQpA5gJINMBINQBVq18fHwizQEgBCkDkAt8ItMBIM4BINABVK0gBCkD2Aog0AEg1wFUrXx8fCLQASAEKQOwCXwi1AEg0QEg0gFUrSAEKQPICSDOASDSAVatfHx8ItYBfCLOASAEKQPwCHwi0gEgBCkDiAkg1QEgBCkDgAkiygF8IMoBVK18fCLRASAEKQOwCnwi1QFCiceZpK7wgemHf34iygFCAELH+vPD7YKjkDxCABDJAyAEQaAIaiDKAUIAQo2Vx8OW0trAl39CABDJAyAEQZAIaiDKAUIAQt2whYzotpGouH9CABDJAyAEQYAIaiDKAUIAQqnAxomuzpOyMEIAEMkDIAQgBCkDuAog0QEg1QFWrXwi2QEgBCkD8Ap8ItcBIM0BIM8BVK0gBCkDyAggzAEgzwFWrXx8ItsBIAQpA8gLIMwBINgBVK18fCLMASAEKQPQC3wizwEg0AEg0wFUrSAEKQOYCyDNASDTAVatfHx8Is0BIAQpA6AJfCLTASDUASDWAVatIAQpA7gJINABINQBVq18fHwi0AEgBCkDoAt8ItQBIMsBIM4BVq0gBCkD6AogywEg2gFUrXx8fCLLASAEKQPgCHwi2AEg0QEg0gFUrSAEKQP4CCDOASDSAVatfHx8ItYBfCLOASAEKQOgCHwi0gEgBCkDuAgg1QEgBCkDsAgiygF8IMoBVK18fCLKATcDgGMgBCAEKQPgCyDMASDbAVSthCLaASDNASDPAVStIAQpA9gLIMwBIM8BVq18fHwizAEg0AEg0wFUrSAEKQOoCSDNASDTAVatfHx8Is8BIMsBINQBVK0gBCkDqAsg0AEg1AFWrXx8fCLNASAEKQPQCHwi0QEg1gEg2AFUrSAEKQPoCCDLASDYAVatfHx8ItABIAQpA7ALfCLTASDOASDXAVStIAQpA/gKINcBINkBVK18fHwi1AEgBCkDkAh8ItUBIMoBINIBVK0gBCkDqAggzgEg0gFWrXx8fCLLATcD+GIgBCDNASDPAVStIMwBIM8BVq0gBCkD6AsgzAEg2gFUrXx8fCLXASAEKQPwC3wizwEg0AEg0QFUrSAEKQPYCCDNASDRAVatfHx8Is0BINMBINQBVq0gBCkDuAsg0AEg0wFWrXx8fCLOASAEKQOACHwi0gEgywEg1QFUrSAEKQOYCCDUASDVAVatfHx8IswBNwPwYiAEIMwBINIBVK0gBCkDiAggzgEg0gFWrXx8IM0BIM4BVq0gzQEgzwFUrSAEKQP4CyDPASDXAVStfHx8fCLPATcD6GIgBEHo4gBqENIDBEAgBCDKAULH+vPD7YKjkDx9NwOAYyAEIMsBQvPquLzpraW/6AB8Is0BIMoBQsf688PtgqOQPFStIsoBfTcD+GIgBCDMAUKjz/rzl8nu18cAfCLOASDLAUKNlcfDltLawJd/VCDKASDNAVZyrSLKAX03A/BiIAQgzwEgzAFC3bCFjOi2kai4f1QgygEgzgFWcq19QqnAxomuzpOyMH03A+hiCyAEQfjgAGogBEGA4wBqIgUpAwA3AwAgBEHw4ABqIARB+OIAaiIHKQMANwMAIARB6OAAaiAEQfDiAGoiCCkDADcDACAEQcjgAGogBEG45ABqKQMANwMAIARB0OAAaiAEQcDkAGopAwA3AwAgBEHY4ABqIARByOQAaikDADcDACAEIAQpA+hiNwPgYCAEIAQpA7BkNwPAYCAEQfDkAGpBoKjCAEHAABC3AiAEQYAGaiAEKQOIZSLKAUIAQon1q5y1i7+Wc0IAEMkDIARBwAZqIAQpA4BlIssBQgBCifWrnLWLv5ZzQgAQyQMgBEGAB2ogBCkD+GQizAFCAEKJ9auctYu/lnNCABDJAyAEQcAHaiAEKQPwZCLPAUIAQon1q5y1i7+Wc0IAEMkDIARB8AVqIAQpA4AGItIBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHgBWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGQBWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEHABGogzQFCAEKpwMaJrs6TsjBCABDJAyAEQZAGaiDKAUIAQvuDlKKdosbztX9CABDJAyAEQdAGaiDLAUIAQvuDlKKdosbztX9CABDJAyAEQZAHaiDMAUIAQvuDlKKdosbztX9CABDJAyAEQdAHaiDPAUIAQvuDlKKdosbztX9CABDJAyAEQdAFaiAEKQPgBSLVASAEKQOIBiLTASAEKQPABnwi1AF8Is4BIAQpA/gFINIBIAQpA/AFIs0BfCDNAVStfHwi0gEgBCkDkAZ8ItEBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHABWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGwBWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEGgBWogzQFCAEKpwMaJrs6TsjBCABDJAyAEQaAGaiDKAUIAQvb/hdLw38fVxwBCABDJAyAEQeAGaiDLAUIAQvb/hdLw38fVxwBCABDJAyAEQaAHaiDMAUIAQvb/hdLw38fVxwBCABDJAyAEQeAHaiDPAUIAQvb/hdLw38fVxwBCABDJAyAEQYAFaiAEKQOYBiDRASDSAVStfCLXASAEKQPQBnwi0AEgBCkDyAYg0wEg1AFWrXwi2AEgBCkDgAd8ItMBIAQpA5AFfCLUASDOASDSAVatIAQpA+gFIM4BINUBVK18fHwi1gF8Is4BIAQpA8AFfCLSASAEKQPYBSDRASAEKQPQBSLNAXwgzQFUrXx8ItEBIAQpA6AGfCLVAUKJx5mkrvCB6Yd/fiLNAUIAQsf688PtgqOQPEIAEMkDIARB8ARqIM0BQgBCjZXHw5bS2sCXf0IAEMkDIARB4ARqIM0BQgBC3bCFjOi2kai4f0IAEMkDIARB0ARqIM0BQgBCqcDGia7Ok7IwQgAQyQMgBEGwBmogygFCAEKf6uDVnO6n7AZCABDJAyAEQfAGaiDLAUIAQp/q4NWc7qfsBkIAEMkDIARBsAdqIMwBQgBCn+rg1Zzup+wGQgAQyQMgBEHwB2ogzwFCAEKf6uDVnO6n7AZCABDJAyAEQbAEaiAEKQOoBiDRASDVAVatfCLaASAEKQPgBnwiywEgBCkDiAcg0wEg2AFUrXwi2AEgBCkDwAd8IswBIAQpA8AEfCLPASDUASDWAVatIAQpA5gFINMBINQBVq18fHwizQEgBCkDkAd8ItMBIM4BINABVK0gBCkD2AYg0AEg1wFUrXx8fCLQASAEKQOwBXwi1AEg0QEg0gFUrSAEKQPIBSDOASDSAVatfHx8ItYBfCLOASAEKQPwBHwi0gEgBCkDiAUg1QEgBCkDgAUiygF8IMoBVK18fCLRASAEKQOwBnwi1QFCiceZpK7wgemHf34iygFCAELH+vPD7YKjkDxCABDJAyAEQaAEaiDKAUIAQo2Vx8OW0trAl39CABDJAyAEQZAEaiDKAUIAQt2whYzotpGouH9CABDJAyAEQYAEaiDKAUIAQqnAxomuzpOyMEIAEMkDIAQgBCkDuAYg0QEg1QFWrXwi2QEgBCkD8AZ8ItcBIM0BIM8BVK0gBCkDyAQgzAEgzwFWrXx8ItsBIAQpA8gHIMwBINgBVK18fCLMASAEKQPQB3wizwEg0AEg0wFUrSAEKQOYByDNASDTAVatfHx8Is0BIAQpA6AFfCLTASDUASDWAVatIAQpA7gFINABINQBVq18fHwi0AEgBCkDoAd8ItQBIMsBIM4BVq0gBCkD6AYgywEg2gFUrXx8fCLLASAEKQPgBHwi2AEg0QEg0gFUrSAEKQP4BCDOASDSAVatfHx8ItYBfCLOASAEKQOgBHwi0gEgBCkDuAQg1QEgBCkDsAQiygF8IMoBVK18fCLKATcDgGMgBCAEKQPgByDMASDbAVSthCLaASDNASDPAVStIAQpA9gHIMwBIM8BVq18fHwizAEg0AEg0wFUrSAEKQOoBSDNASDTAVatfHx8Is8BIMsBINQBVK0gBCkDqAcg0AEg1AFWrXx8fCLNASAEKQPQBHwi0QEg1gEg2AFUrSAEKQPoBCDLASDYAVatfHx8ItABIAQpA7AHfCLTASDOASDXAVStIAQpA/gGINcBINkBVK18fHwi1AEgBCkDkAR8ItUBIMoBINIBVK0gBCkDqAQgzgEg0gFWrXx8fCLLATcD+GIgBCDNASDPAVStIMwBIM8BVq0gBCkD6AcgzAEg2gFUrXx8fCLXASAEKQPwB3wizwEg0AEg0QFUrSAEKQPYBCDNASDRAVatfHx8Is0BINMBINQBVq0gBCkDuAcg0AEg0wFWrXx8fCLOASAEKQOABHwi0gEgywEg1QFUrSAEKQOYBCDUASDVAVatfHx8IswBNwPwYiAEIMwBINIBVK0gBCkDiAQgzgEg0gFWrXx8IM0BIM4BVq0gzQEgzwFUrSAEKQP4ByDPASDXAVStfHx8fCLPATcD6GIgBEHo4gBqENIDBEAgBCDKAULH+vPD7YKjkDx9NwOAYyAEIMsBQvPquLzpraW/6AB8Is0BIMoBQsf688PtgqOQPFStIsoBfTcD+GIgBCDMAUKjz/rzl8nu18cAfCLOASDLAUKNlcfDltLawJd/VCDKASDNAVZyrSLKAX03A/BiIAQgzwEgzAFC3bCFjOi2kai4f1QgygEgzgFWcq19QqnAxomuzpOyMH03A+hiCyAEQZjhAGogBSkDADcDACAEQZDhAGogBykDADcDACAEQYjhAGogCCkDADcDACAEIAQpA+hiNwOAYSAEQbDkAGpB4KjCAEHAABC3AiAEQYACaiAEKQPIZCLKAUIAQon1q5y1i7+Wc0IAEMkDIARBwAJqIAQpA8BkIssBQgBCifWrnLWLv5ZzQgAQyQMgBEGAA2ogBCkDuGQizAFCAEKJ9auctYu/lnNCABDJAyAEQcADaiAEKQOwZCLPAUIAQon1q5y1i7+Wc0IAEMkDIARB8AFqIAQpA4ACItIBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHgAWogzQFCAEKNlcfDltLawJd/QgAQyQMgBEGQAWogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEFAayDNAUIAQqnAxomuzpOyMEIAEMkDIARBkAJqIMoBQgBC+4OUop2ixvO1f0IAEMkDIARB0AJqIMsBQgBC+4OUop2ixvO1f0IAEMkDIARBkANqIMwBQgBC+4OUop2ixvO1f0IAEMkDIARB0ANqIM8BQgBC+4OUop2ixvO1f0IAEMkDIARB0AFqIAQpA+ABItUBIAQpA4gCItMBIAQpA8ACfCLUAXwizgEgBCkD+AEg0gEgBCkD8AEizQF8IM0BVK18fCLSASAEKQOQAnwi0QFCiceZpK7wgemHf34izQFCAELH+vPD7YKjkDxCABDJAyAEQcABaiDNAUIAQo2Vx8OW0trAl39CABDJAyAEQbABaiDNAUIAQt2whYzotpGouH9CABDJAyAEQaABaiDNAUIAQqnAxomuzpOyMEIAEMkDIARBoAJqIMoBQgBC9v+F0vDfx9XHAEIAEMkDIARB4AJqIMsBQgBC9v+F0vDfx9XHAEIAEMkDIARBoANqIMwBQgBC9v+F0vDfx9XHAEIAEMkDIARB4ANqIM8BQgBC9v+F0vDfx9XHAEIAEMkDIARBgAFqIAQpA5gCINEBINIBVK18ItcBIAQpA9ACfCLQASAEKQPIAiDTASDUAVatfCLYASAEKQOAA3wi0wEgBCkDkAF8ItQBIM4BINIBVq0gBCkD6AEgzgEg1QFUrXx8fCLWAXwizgEgBCkDwAF8ItIBIAQpA9gBINEBIAQpA9ABIs0BfCDNAVStfHwi0QEgBCkDoAJ8ItUBQonHmaSu8IHph39+Is0BQgBCx/rzw+2Co5A8QgAQyQMgBEHwAGogzQFCAEKNlcfDltLawJd/QgAQyQMgBEHgAGogzQFCAELdsIWM6LaRqLh/QgAQyQMgBEHQAGogzQFCAEKpwMaJrs6TsjBCABDJAyAEQbACaiDKAUIAQp/q4NWc7qfsBkIAEMkDIARB8AJqIMsBQgBCn+rg1Zzup+wGQgAQyQMgBEGwA2ogzAFCAEKf6uDVnO6n7AZCABDJAyAEQfADaiDPAUIAQp/q4NWc7qfsBkIAEMkDIARBMGogBCkDqAIg0QEg1QFWrXwi2gEgBCkD4AJ8IssBIAQpA4gDINMBINgBVK18ItgBIAQpA8ADfCLMASAEKQNAfCLPASDUASDWAVatIAQpA5gBINMBINQBVq18fHwizQEgBCkDkAN8ItMBIM4BINABVK0gBCkD2AIg0AEg1wFUrXx8fCLQASAEKQOwAXwi1AEg0QEg0gFUrSAEKQPIASDOASDSAVatfHx8ItYBfCLOASAEKQNwfCLSASAEKQOIASDVASAEKQOAASLKAXwgygFUrXx8ItEBIAQpA7ACfCLVAUKJx5mkrvCB6Yd/fiLKAUIAQsf688PtgqOQPEIAEMkDIARBIGogygFCAEKNlcfDltLawJd/QgAQyQMgBEEQaiDKAUIAQt2whYzotpGouH9CABDJAyAEIMoBQgBCqcDGia7Ok7IwQgAQyQMgBCAEKQO4AiDRASDVAVatfCLZASAEKQPwAnwi1wEgzQEgzwFUrSAEKQNIIMwBIM8BVq18fCLbASAEKQPIAyDMASDYAVStfHwizAEgBCkD0AN8Is8BINABINMBVK0gBCkDmAMgzQEg0wFWrXx8fCLNASAEKQOgAXwi0wEg1AEg1gFWrSAEKQO4ASDQASDUAVatfHx8ItABIAQpA6ADfCLUASDLASDOAVatIAQpA+gCIMsBINoBVK18fHwiywEgBCkDYHwi2AEg0QEg0gFUrSAEKQN4IM4BINIBVq18fHwi1gF8Is4BIAQpAyB8ItIBIAQpAzgg1QEgBCkDMCLKAXwgygFUrXx8IsoBNwOIZSAEIAQpA+ADIMwBINsBVK2EItoBIM0BIM8BVK0gBCkD2AMgzAEgzwFWrXx8fCLMASDQASDTAVStIAQpA6gBIM0BINMBVq18fHwizwEgywEg1AFUrSAEKQOoAyDQASDUAVatfHx8Is0BIAQpA1B8ItEBINYBINgBVK0gBCkDaCDLASDYAVatfHx8ItABIAQpA7ADfCLTASDOASDXAVStIAQpA/gCINcBINkBVK18fHwi1AEgBCkDEHwi1QEgygEg0gFUrSAEKQMoIM4BINIBVq18fHwiywE3A4BlIAQgzQEgzwFUrSDMASDPAVatIAQpA+gDIMwBINoBVK18fHwi1wEgBCkD8AN8Is8BINABINEBVK0gBCkDWCDNASDRAVatfHx8Is0BINMBINQBVq0gBCkDuAMg0AEg0wFWrXx8fCLOASAEKQMAfCLSASDLASDVAVStIAQpAxgg1AEg1QFWrXx8fCLMATcD+GQgBCDMASDSAVStIAQpAwggzgEg0gFWrXx8IM0BIM4BVq0gzQEgzwFUrSAEKQP4AyDPASDXAVStfHx8fCLPATcD8GQgBEHw5ABqENIDBEAgBCDKAULH+vPD7YKjkDx9NwOIZSAEIMsBQvPquLzpraW/6AB8Is0BIMoBQsf688PtgqOQPFStIsoBfTcDgGUgBCDMAUKjz/rzl8nu18cAfCLOASDLAUKNlcfDltLawJd/VCDKASDNAVZyrSLKAX03A/hkIAQgzwEgzAFC3bCFjOi2kai4f1QgygEgzgFWcq19QqnAxomuzpOyMH03A/BkCyAEQaDjAGogBEGI5QBqKQMANwMAIARBmOMAaiAEQYDlAGopAwA3AwAgBEGQ4wBqIARB+OQAaikDADcDACAEQfDiAGogBEGI4QBqKQMANwMAIARB+OIAaiAEQZDhAGopAwA3AwAgBEGA4wBqIARBmOEAaikDADcDACAEIAQpA/BkNwOIYyAEIAQpA4BhNwPoYiAEQbAnaiAEQcDgAGogBEHo4gBqEGICQAJAIAQoArAnQQFGBEAgBEGo4QBqIARBvCdqKAIAIgU2AgAgBCAEKQK0JyLKATcDoGEgEkEMaiAFNgIAIBIgygE3AgQMAQsgBEGk4QBqIgcgBEG4J2pBgAH8CgAAIARB6OIAaiIFIAdBgAH8CgAAIARBoOIAaiAEQbDeAGpByAD8CgAAIARBoOEAaiIHIARBwN8AakGAAfwKAAAgBEHo4wBqIARB+N4AakHIAPwKAAAgBEGwJ2oiCCAHQcgB/AoAACAEQfgoaiAFQcgB/AoAACAFIAhBAkECQaCpwgAQNyAEKAL0YiEHIAQoAvBiIQUgBCgC7GIhCCAEKALoYkEBRw0BIBIgBzYCDCASIAU2AgggEiAINgIECyASQQE2AgAgBEGk3gBqEPMDIAQoAqReIgUEQCAEKAKoXiAFQQxsEN8ECyAEKAKMXCIFBEAgBCgCkFwgBUHIAGwQ3wQLIARB0NsAahDzAyAEKALQWyIFBEAgBCgC1FsgBUEMbBDfBAsgBEGw2wBqEPMDIAQoArBbIgVFDQYgBCgCtFsgBUEMbBDfBAwGC0HRzsUALQAAGiAEKAKsXiEMIAQoAthbIQlBDEEEENYEIgpFDQMgBEHw4gBqIhhBkJLCACgCADYCACAEQYiSwgApAgA3A+hiIAcgCWogDGoiFgRAIARB6OIAakGMk8IAEKUDIAQoAuxiIBY2AgAgBEEBNgLwYgsgCiAEKQPoYjcCACAKQQhqIBgoAgA2AgAgBEGo4QBqIhZBATYCACAEIAo2AqRhIARBATYCoGEgBCgC1FshCiAEIAQoAtBbNgLwYiAEIAo2AuhiIAQgCiAJQQxsajYC9GIgBCAKNgLsYiAEQaDhAGoiCSAEQejiAGoiGBDHAyAEKAKoXiEKIAQgBCgCpF42AvBiIAQgCjYC6GIgBCAKIAxBDGxqNgL0YiAEIAo2AuxiIAkgGBDHAyAEIAg2AvBiIAQgBTYC6GIgBCAFIAdBDGxqNgL0YiAEIAU2AuxiIAkgGBDHAyASQQxqIBYoAgA2AgAgEiAEKQKgYTcCBCASQQA2AgAgBCgCjFwiBQRAIAQoApBcIAVByABsEN8ECyAEQbDbAGoQ8wMgBCgCsFsiBQRAIAQoArRbIAVBDGwQ3wQLIB0EQCALIB1ByABsEN8ECyAEQYQdahDyAyAEKAKEHSIFBEAgBCgCiB0gBUEMbBDfBAsgDkGABBDfBCAnBEAgDyAnQQV0EN8ECyAEQYAQahDFAQwICyAMICRB/KXCABDlBAALIAlBHEGMpsIAEOUEAAtBCEHoFBD/BAALQQRBDBD/BAALQQAhCgsgHQRAIAsgHUHIAGwQ3wQLIARBhB1qEPIDIAQoAoQdIgUEQCAEKAKIHSAFQQxsEN8ECyAKICBFcg0BCyAYICBByABsEN8ECyAOQYAEEN8EICcEQCAPICdBBXQQ3wQLIARBgBBqEMUBCyAEQaDlAGokACAVKALMVSEHIBUoAshVIQUgFSgCxFUhCiAVKALAVUEBRw0DIAUgBxDNBCEHIAoEQCAFIAoQ3wQLICpBgICAgHg2AgAgKiAHNgIEIBVBuAVqEEoLIBUQjAELIDxFDQAgHiA8EN8ECyA7BEAgMiA7EN8ECyA4RQ0BICggOBDfBAwBCyAVIAo2AthVIBUgBTYC1FUgFSAFNgLQVSAVIAUgB0EMbGo2AtxVICogFUHQ1QBqEI8DIBVBuAVqEEogFRCMASA8BEAgHiA8EN8ECyA7BEAgMiA7EN8ECyA4RQ0AICggOBDfBAsgFUHg1QBqJAAMAQtBAUEgQaSbwgAQyAQACwJAAkAgMQJ/IDcoAgQiBUGAgICAeEYEQEEAIQUgNygCCCEKQQAhB0EBDAELIDcoAgghCgJAIDcoAgwiByAFTwRAIAohBQwBCyAFQQJ0IQggB0UEQEEEIQUgCiAIEN8EDAELIAogCEEEIAdBAnQiChDOBCIFRQ0CC0EAIQpBAAs2AgwgMSAKNgIIIDEgBzYCBCAxIAU2AgAgN0EQaiQADAELQQQgCkHo8cAAEMgEAAsgMSgCACAxKAIEIDEoAgggMSgCDCAxQRBqJAALOAEBf0EBIQEgAC0ABEUEQCAAKAIAIgEoAgBB+rfFAEEBIAEoAgQoAgwRAwAhAQsgACABOgAEIAELy1YCG38TfiMAQRBrIhYkACMAQSBrIhUkACAVIAE2AhAgFSAANgIMIBUgATYCCCAVQRRqIRkjAEEwayILJAAgFUEIaiIAKAIAIQEgACgCBCEEIAAoAgghACALQQA2AgAgCyAEIABBAnRqNgIkIAsgATYCICALIAQ2AhwgCyAENgIYIAsgCzYCKCALQQxqIAtBGGoQlgICQAJAAkAgCygCAEEBRgRAIAsoAhAhBCALKAIEIQEgCygCFCIABEAgBCEUA0AgFCgCACIFBEAgFEEEaigCACAFQQJ0EN8ECyAUQQxqIRQgAEEBayIADQALCyALKAIMIgBFDQEgBCAAQQxsEN8EDAELIAsoAhAhASALKAIMIhtBgICAgHhHDQELIBlBgICAgHg2AgAgGSABNgIEDAELIAtBGGohACALKAIUIhQhBCMAQYAGayIGJAACQAJAIARBA0YEQAJAIAFBCGooAgAiBARAIARBAWsiBUH+////A3ENASABQQRqKAIAIQQgBUH/////A3EiB0EBaiIFQQNxIQogB0EDTwRAIAVB/P///wdxIQgDQCAdQoABfCEdIARBEGohBCAIQQRrIggNAAsLIAoEQANAIAQ1AgAgHYYgHnwhHiAdQiB8IR0gBEEEaiEEIApBAWsiCg0ACwsgHkL/////D1YNAQsgHqchHAwCCyAGQQE2AnwgBkH8pMAANgJ4IAZCATcChAEgBiAGQf8Faq1CgICAgNABhDcDaCAGIAZB6ABqNgKAASAGQThqIAZB+ABqENICIAYoAjwhHCAGKAI4IgRBgICAgHhGDQEgACAGKAJANgIMIAAgHDYCCCAAIAQ2AgQgAEEBNgIADAILIAZBATYCfCAGQfSlwAA2AnggBkIBNwKEASAGIAQ2AmggBiAGQegAaq1CgICAgOABhDcDOCAGIAZBOGo2AoABIABBBGogBkH4AGoQ0gIgAEEBNgIADAELAkACQCABKAIURQRAQdHOxQAtAAAaQQEhDUEBQQEQ1gQiCEUNASAIQQA6AAAgBkEBNgI4DAILIAZBOGogAUEMakEIELACIAYoAjwhCCAGKAJAIg1BAkkNASAIIA1qIQ9BACEEIA1BAXYiBUEBRwRAIA1BAWshCiAFQf7///8HcSEMA0AgCCAKaiIHLQAAIQUgByAEIAhqIhAtAAA6AAAgECAFOgAAIA8gBEF+c2oiBS0AACEHIAUgEEEBaiIFLQAAOgAAIAUgBzoAACAKQQJrIQogDCAEQQJqIgRHDQALCyANQQJxBEAgBCAIaiIHLQAAIQUgByAPIARBf3NqIgQtAAA6AAAgBCAFOgAACyANQSFJDQEgBkEBNgJ8IAZB0KXAADYCeCAGQgE3AoQBIAYgDTYCLCAGIAZBLGqtQoCAgIDgAYQ3A2ggBiAGQegAajYCgAEgAEEEaiAGQfgAahDSAiAAQQE2AgAgBigCOCIARQ0CIAggABDfBAwCC0EBQQEQ/wQACyAGQSBqQgA3AwAgBkEYakIANwMAIAZBEGpCADcDACAGQgA3AwggDQRAIAYgDWtBKGogCCAN/AoAAAsgBigCOCIEBEAgCCAEEN8ECwJAAkAgASgCIEUEQEHRzsUALQAAGkEBIQ5BAUEBENYEIghFDQEgCEEAOgAAIAZBATYCLAwCCyAGQSxqIAFBGGpBCBCwAiAGKAIwIQggBigCNCIOQQJJDQEgCCAOaiEPQQAhBCAOQQF2IgVBAUcEQCAOQQFrIQogBUH+////B3EhDANAIAggCmoiBy0AACEFIAcgBCAIaiIQLQAAOgAAIBAgBToAACAPIARBfnNqIgUtAAAhByAFIBBBAWoiBS0AADoAACAFIAc6AAAgCkECayEKIAwgBEECaiIERw0ACwsgDkECcQRAIAQgCGoiBy0AACEFIAcgDyAEQX9zaiIELQAAOgAAIAQgBToAAAsgDkExSQ0BIAZBATYCfCAGQaSlwAA2AnggBkIBNwKEASAGIA42AmggBiAGQegAaq1CgICAgOABhDcDOCAGIAZBOGo2AoABIABBBGogBkH4AGoQ0gIgAEEBNgIAIAYoAiwiAEUNAiAIIAAQ3wQMAgtBAUEBEP8EAAsgBkHgAGpCADcDACAGQdgAakIANwMAIAZB0ABqQgA3AwAgBkHIAGpCADcDACAGQUBrQgA3AwAgBkIANwM4IA4EQCAGIA5rQegAaiAIIA78CgAACyAGQfgAaiESQgAhHUIAIR4jAEHAC2siAyQAAkACQAJAAkACQAJAAkACQAJAIAZBOGoiBS0AACIEQeABcSIHQSBGIAdB4ABGckUgB0HgAUdxRQRAQdHOxQAtAAAaQRBBARDWBCIERQ0BIBJBEDYCECASIAQ2AgwgEkEQNgIIIBJCAjcDACAEQQhqQfThwAApAAA3AAAgBEHs4cAAKQAANwAADAkLQdHOxQAtAAAaQTBBARDWBCIaRQ0CIBogBUEw/AoAACAaIBotAABBH3E6AAAgBMAiBEHAAHEEQEEAIQoCQANAIApBMEYNASAKIBpqIApBAWohCi0AAEUNAAtB0c7FAC0AABpBJkEBENYEIgRFDQMgEkEmNgIQIBIgBDYCDCASQSY2AgggEkICNwMAIARBHmpBmuLAACkAADcAACAEQRhqQZTiwAApAAA3AAAgBEEQakGM4sAAKQAANwAAIARBCGpBhOLAACkAADcAACAEQfzhwAApAAA3AAAMCQsgA0GgA2oiBEEAQeEA/AsAIBJCADcDACASQQhqIARBwAH8CgAADAgLIARBAE4NBiADQcAKaiAaQTAQjgFBKCEKIAMpA8AKISogAykDyAohLSADKQPQCiEpIAMpA9gKISMgAykD4AohJCADKQPoCiElA0AgA0HAAmogA0HACmogCmopAwAiIEIAICVCABDJAyADQdACaiAgQgAgJEIAEMkDIANB4AJqICBCACAjQgAQyQMgA0HwAmogIEIAIClCABDJAyADQYADaiAgQgAgLUIAEMkDIANBkANqICBCACAqQgAQyQMgA0GwAmogKCADKQPAAiImfCIrQgBCAEL9//P/z///+Yl/EMkDIANBoAJqIAMpA7gCIiBCAEKr1f7///+//7l/QgAQyQMgA0GQAmogIEIAQv//z4rr///VHkIAEMkDIANBgAJqICBCAEKk7MO1j9S0mOcAQgAQyQMgA0HwAWogIEIAQr+llJzP8NK75ABCABDJAyADQeABaiAgQgBC19mumuT26Y3LAEIAEMkDIANB0AFqICBCAEKazf/Lo73EgBpCABDJAyADKQPYASAiIAMpA5ADIid8IiwgAykDiAMgAykDgAMiICAhfCIhICBUrXwgISADKQP4AiAdIAMpA/ACIh18IiAgHVStfCAgICAgAykD6AIgAykD4AIiHSAefCIeIB1UrXwgHiAeIAMpA9gCIAMpA9ACIh0gH3wiHyAdVK18IB8gHyADKQPIAiAmICtWrXx8Ih9WrXx8IihWrXx8Ih5WrXx8Ih0gIVStfHwiIiADKQPQAXwiISAiVK18ICEgISADKQPoASAdIB0gAykD4AF8IiZWrXwgJiAmIAMpA/gBIB4gHiADKQPwAXwiIFatfCAgIAMpA4gCICggKCADKQOAAnwiHlatfCAeIAMpA5gCIB8gAykDkAIiHXwiHyAdVK18IB8gAykDqAIgKyADKQOgAiIdfCAdVK18fCIoIB9UrXx8Ih8gHlStfHwiHiAgVK18fCIdVq18fCIhVq18ICIgLFStIAMpA5gDICcgLFatfHx8ISIgCkEIayIKQXhHDQALICJCms3/y6O9xIAaWA0DDAQLQQFBEEGEpMAAEMgEAAtBAUEmQYSkwAAQyAQAC0EBQTBBhKTAABDIBAALICJCms3/y6O9xIAaUgRAIB8hICAeIScgHSEmICEhJQwCCyAhQtfZrprk9umNywBWDQAgIULX2a6a5PbpjcsAUgRAIB8hICAeIScgHSEmICEhJUKazf/Lo73EgBohIgwCCyAdQr+llJzP8NK75ABWDQBC19mumuT26Y3LACElIB1Cv6WUnM/w0rvkAFIEQCAfISAgHiEnIB0hJkKazf/Lo73EgBohIgwCCyAeQqTsw7WP1LSY5wBWDQBCv6WUnM/w0rvkACEmIB5CpOzDtY/UtJjnAFIEQCAfISAgHiEnQprN/8ujvcSAGiEiDAILIB9C///Piuv//9UeVg0AQqTsw7WP1LSY5wAhJyAfQv//z4rr///VHlIEQCAfISBCms3/y6O9xIAaISIMAgtC///Piuv//9UeISAgKEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiEiDAELIB9C///Piuv//9UefSIlIChCq9X+////v/+5f1StIid9ISAgHkKk7MO1j9S0mOcAfSImIB9C///Piuv//9UeVCAlICdUcq0iH30hJyAdQr+llJzP8NK75AB9IiUgHkKk7MO1j9S0mOcAVCAfICZWcq0iHn0hJiAhQtfZrprk9umNywB9Ih8gHUK/pZScz/DSu+QAVCAeICVWcq0iHX0hJSAiICFC19mumuT26Y3LAFQgHSAfVnKtfUKazf/Lo73EgBp9ISIgKELVqoGAgIDAgMYAfCEoC0EoIQpCACEdQgAhHkIAISNCACEpQgAhJEIAISEDQCADQfAAaiADQcAKaiAKaikDACIfQgAgKEIAEMkDIANBgAFqIB9CACAgQgAQyQMgA0GQAWogH0IAICdCABDJAyADQaABaiAfQgAgJkIAEMkDIANBsAFqIB9CACAlQgAQyQMgA0HAAWogH0IAICJCABDJAyADQeAAaiADKQNwIh8gIXwiLkIAQgBC/f/z/8////mJfxDJAyADQdAAaiADKQNoIiFCAEKr1f7///+//7l/QgAQyQMgA0FAayAhQgBC///Piuv//9UeQgAQyQMgA0EwaiAhQgBCpOzDtY/UtJjnAEIAEMkDIANBIGogIUIAQr+llJzP8NK75ABCABDJAyADQRBqICFCAELX2a6a5PbpjcsAQgAQyQMgAyAhQgBCms3/y6O9xIAaQgAQyQMgAykDCCADKQPAASItIB18Ii8gAykDuAEgAykDsAEiHSAefCIqIB1UrXwgKiAqIAMpA6gBICMgAykDoAEiHXwiISAdVK18ICEgISADKQOYASApIAMpA5ABIh18IiMgHVStfCAjICMgAykDiAEgAykDgAEiHSAkfCIeIB1UrXwgHiAeIAMpA3ggHyAuVq18fCIfVq18fCIkVq18fCIeVq18fCIdVq18fCIrIAMpAwB8IiwgK1StfCAsICwgAykDGCAdIB0gAykDEHwiKlatfCAqIAMpAyggHiAeIAMpAyB8IiNWrXwgIyADKQM4ICQgJCADKQMwfCIeVq18IB4gAykDSCAfIAMpA0AiHXwiHyAdVK18IB8gAykDWCAuIAMpA1AiHXwgHVStfHwiISAfVK18fCIkIB5UrXx8IikgI1StfHwiIyAqVK18fCIeVq18ICsgL1StIAMpA8gBIC0gL1atfHx8IR0gCkEIayIKQXhHDQALAkACQCAdQprN/8ujvcSAGlYNAAJAAkACQAJAIB1Cms3/y6O9xIAaUg0AIB5C19mumuT26Y3LAFYNBCAeQtfZrprk9umNywBSBEBCms3/y6O9xIAaIR0MAQsgI0K/pZScz/DSu+QAVg0EQtfZrprk9umNywAhJSAjQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIR0MAgsgKUKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhIiApQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIR0MAwsgJEL//8+K6///1R5WDQRCpOzDtY/UtJjnACEfICRC///Piuv//9UeUQ0DQprN/8ujvcSAGiEdICQhKAwFCyAeISULICMhIgsgKSEfICQhKAwCC0L//8+K6///1R4hKCAhQqrV/v///7//uX9WDQBCms3/y6O9xIAaIR0MAQsgJEL//8+K6///1R59IiAgIUKr1f7///+//7l/VK0iH30hKCApQqTsw7WP1LSY5wB9IicgJEL//8+K6///1R5UIB8gIFZyrSIgfSEfICNCv6WUnM/w0rvkAH0iJiApQqTsw7WP1LSY5wBUICAgJ1ZyrSIgfSEiIB5C19mumuT26Y3LAH0iJyAjQr+llJzP8NK75ABUICAgJlZyrSIgfSElIB0gHkLX2a6a5PbpjcsAVCAgICdWcq19QprN/8ujvcSAGn0hHSAhQtWqgYCAgMCAxgB8ISELQprN/8ujvcSAGiEkIB0gJULRqZ2ExJijm/EAfSIjICVUICMgIkKptpfKkaigls4AfSIlICJUICUgJSAfQv+Aqtimr/rHxwB8Ih4gH1QgHiAeIChCioDQ4a+GgObTAHwiHyAoVCAfIB8gIUKNgMz///+/7NUAfSIiICFUrXwiJlZyrXwiJ1ZyrXwiIFZyrXwiHyAjVHKtfEL+vI/sk6qR6wl8IiUhHQJAAkACQCAlQprN/8ujvcSAGlINAELX2a6a5PbpjcsAISQgHyIdQtfZrprk9umNywBSDQBCv6WUnM/w0rvkACEkICAiHUK/pZScz/DSu+QAUg0AQqTsw7WP1LSY5wAhJCAnIh1CpOzDtY/UtJjnAFINAEL//8+K6///1R4hJCAmIh1C///Piuv//9UeUg0AQqvV/v///7//uX8hJCAiIh1Cq9X+////v/+5f1ENAQsgHSAkWg0AIB8hHSAgIR4gJyEjICYhJAwBCyAmQv//z4rr///VHn0iIyAiQqvV/v///7//uX9UrSIdfSEkICdCpOzDtY/UtJjnAH0iHiAmQv//z4rr///VHlQgHSAjVnKtIh19ISMgIEK/pZScz/DSu+QAfSImICdCpOzDtY/UtJjnAFQgHSAeVnKtIh19IR4gH0LX2a6a5PbpjcsAfSInICBCv6WUnM/w0rvkAFQgHSAmVnKtIiB9IR0gJSAfQtfZrprk9umNywBUICAgJ1ZyrX1Cms3/y6O9xIAafSElICJC1aqBgICAwIDGAHwhIgsgAyAiNwOoCSADICQ3A6AJIAMgIzcDmAkgAyAeNwOQCSADIB03A4gJIAMgJTcDgAkCQCAEQSBxBEAgA0HwCmogA0GACWoQoQIMAQsgA0G4B2oiAiADQYAJahAqAn8CQCADKAK4B0EBRgRAIANBmAZqIhggA0HoB2opAwA3AwAgA0GQBmoiDSADQeAHaiIJKQMANwMAIANBiAZqIhEgA0HYB2oiEykDADcDACADQYAGaiIXIANB0AdqIgopAwA3AwAgA0H4BWoiDiADQcgHaiIPKQMANwMAIANBqAZqIhAgA0H4B2opAwA3AwAgA0GwBmoiDCADQYAIaikDADcDACADQbgGaiIHIANBiAhqKQMANwMAIANBwAZqIgUgA0GQCGopAwA3AwAgA0HIBmoiBCADQZgIaikDADcDACADIAMpA8AHNwPwBSADIAMpA/AHNwOgBiADQYgKaiAYKQMANwMAIANBgApqIA0pAwA3AwAgA0H4CWogESkDADcDACADQfAJaiAXKQMANwMAIANB6AlqIA4pAwA3AwAgAyADKQPwBTcD4AkgCSAEKQMANwMAIBMgBSkDADcDACAKIAcpAwA3AwAgDyAMKQMANwMAIANBwAdqIBApAwA3AwAgAyADKQOgBjcDuAcgA0GkC2ogA0HgCWoQ2AIgA0GwC2ogAhDYAiADKAKsCyIFIAMoArgLIgRGBEAgAygCqAtBBGshECADKAK0C0EEayEMIAVBAnQhCgJAA0AgCkUNASAKIAxqIQcgCiAQaiAKQQRrIQooAgAiBSAHKAIAIgRGDQALIAQgBUsNAyADQbgHagwECyAKDQIgA0G4B2oMAwsgBCAFSw0BIANBuAdqDAILQdiuwAAQ6AQACyADQeAJagshBSADKAKwCyIEBEAgAygCtAsgBEECdBDfBAsgAygCpAsiBARAIAMoAqgLIARBAnQQ3wQLIANB+ApqIAVBCGopAwA3AwAgA0GAC2ogBUEQaikDADcDACADQYgLaiAFQRhqKQMANwMAIANBkAtqIAVBIGopAwA3AwAgA0GYC2ogBUEoaikDADcDACADIAUpAwA3A/AKCyADQYgKaiADQegKaikDADcDACADQYAKaiADQeAKaikDADcDACADQfgJaiADQdgKaikDADcDACADQfAJaiADQdAKaikDADcDACADQegJaiADQcgKaikDADcDACADIAMpA8AKNwPgCSADQbgHaiADQeAJaiADQfAKakEAEDEgAy0AmAgiBUECRgRAIANB+AVqIANBwAdqKAIAIgQ2AgAgAyADKQO4ByIdNwPwBSASQRBqIAQ2AgAgEiAdNwMIIBJCAjcDAAwCCyADQfAFaiIEIANBuAdqQeAA/AoAACASQewAaiADQZwIaigAADYAACASIAMoAJkINgBpIBJBCGogBEHgAPwKAAAgEiAFOgBoIBJCADcDAAwBCyADQQE2ArwHIANBzOLAADYCuAcgA0IBNwLEByADQTA2AuAJIAMgA0HgCWqtQoCAgIDgAYQ3A/AFIAMgA0HwBWo2AsAHIBJBCGogA0G4B2oQ0gIgEkICNwMAIBpBMBDfBAwBCyAaQTAQ3wQLIANBwAtqJAAgBkHwAGoiBCAGQYgBaigCADYCACAGIAYpA4ABNwNoIAYpA3giHUICUQRAIAAgBikDaDcCBCAAQQE2AgAgAEEMaiAEKAIANgIAIAYoAiwiAEUNASAIIAAQ3wQMAQsgBkHUAmogBkGMAWpBtAH8CgAAIAZB0AJqIAZB8ABqKAIANgIAIAYgBikDaDcDyAIgBigCLCIEBEAgCCAEEN8ECyAGQdgFaiAGQRBqKQMANwMAIAZB4AVqIAZBGGopAwA3AwAgBkHoBWogBkEgaikDADcDACAGIBw2AvAFIAYgBikDCDcD0AUgBkICNwOIBCAGIB03A8ACIAZBwAJqIREjAEGQD2siAiQAIAJB8AhqIgRBnOHAABCuAiACQaAEaiAEEDQgAkGgC2oiBCACQbAEaigCADYCACACIAIpA6gENwOYCwJAIAIpA6AEIh1CAlEEQCAAIAIpA5gLNwIEIABBATYCACAAQQxqIAQoAgA2AgAMAQsgAkEcaiACQbQEakGMAvwKAAAgAkEYaiACQaALaigCADYCACACIB03AwggAiACKQOYCzcDECARKAKwAyIKrSEdIwBB8AFrIgkkACAJQRBqIg9CADcDACAJQRhqIhBCADcDACAJQSBqIgxCADcDACAJQShqIgdCADcDACAJQTBqIgVCADcDACAJQThqIgRCADcDACAJQgA3AwggCUHYAGpBsKPAACkDADcDACAJQdAAakGoo8AAKQMANwMAIAlByABqQaCjwAApAwA3AwAgCUGYo8AAKQMANwNAIAlCADcDYCAJIB1COIYgHUKA/gODQiiGhCAdQoCA/AeDQhiGIB1CgICA+A+DQgiGhIQgHUIIiEKAgID4D4MgHUIYiEKAgPwHg4QgHUIoiEKA/gODIB1COIiEhIQ3A2ggCUH4AGogDykDADcDACAJQYABaiAQKQMANwMAIAlBiAFqIAwpAwA3AwAgCUGQAWogBykDADcDACAJQZgBaiAFKQMANwMAIAlBoAFqIAQpAwA3AwAgCSAJKQMINwNwIAlBCDoAqAEgCUGsAWogCUEEaigAADYAACAJIAkoAAE2AKkBIAlBgAE6AHAgCSkDYCIeQgmGIh1CwACEIh9CgPwDg0IohiAfQoCA/AeDQhiGIB9CgICA+A+DQgiGhIQgHkIBhkKAgID4D4MgHkIPiEKAgPwHg4QgHkIfiEKA/gODIB1COIiEhIRCgICAgICAgIDAAIQhHSAJQfEAakEAQTf8CwAgCSAdNwOgASAJQUBrIAlB6ABqQQEQLSAJKAJAIRcgCSgCRCEOIAkoAkghDyAJKAJMIRAgCSgCUCEMIAkoAlQhByAJKAJYIQUgAkGoAmoiEyAJKAJcIgRBGHQgBEGA/gNxQQh0ciAEQQh2QYD+A3EgBEEYdnJyNgAcIBMgBUEYdCAFQYD+A3FBCHRyIAVBCHZBgP4DcSAFQRh2cnI2ABggEyAHQRh0IAdBgP4DcUEIdHIgB0EIdkGA/gNxIAdBGHZycjYAFCATIAxBGHQgDEGA/gNxQQh0ciAMQQh2QYD+A3EgDEEYdnJyNgAQIBMgEEEYdCAQQYD+A3FBCHRyIBBBCHZBgP4DcSAQQRh2cnI2AAwgEyAPQRh0IA9BgP4DcUEIdHIgD0EIdkGA/gNxIA9BGHZycjYACCATIA5BGHQgDkGA/gNxQQh0ciAOQQh2QYD+A3EgDkEYdnJyNgAEIBMgF0EYdCAXQYD+A3FBCHRyIBdBCHZBgP4DcSAXQRh2cnI2AAAgCUHwAWokACACQaAEaiATQfylwAAQHQJAAkACQAJAAkACQCACLQCABSIQQQJGBEAgAkH4CGogAkGoBGooAgAiBDYCACACIAIpA6AEIh03A/AIIABBDGogBDYCACAAIB03AgQgAEEBNgIADAELIAJB8AhqIgQgAkGgBGoiDEHgAPwKAAAgAiACQYQFaigAADYAywIgAiACKACBBTYCyAIgAkHQAmogBEHgAPwKAAAgESgCAA0CIAJB2ANqIBFBMGopAwA3AwAgAkHQA2ogEUEoaikDADcDACACQcgDaiARQSBqKQMANwMAIAJBwANqIBFBGGopAwA3AwAgAkG4A2ogEUEQaikDADcDACACQegDaiARQUBrKQMANwMAIAJB8ANqIBFByABqKQMANwMAIAJB+ANqIBFB0ABqKQMANwMAIAJBgARqIBFB2ABqKQMANwMAIAJBiARqIBFB4ABqKQMANwMAIAIgESkDCDcDsAMgAiARKQM4NwPgAyACIBEtAGg6AJAEIAJBgA9qIAJBqAJqQfylwAAQViACKAKMDyENIAIoAogPIQUgAigChA8hCAJAIAIoAoAPQQFGDQAgDUECRw0CIAUoAgQhByAFKAIAIQQgDCAFQQhqQdgA/AoAACAIBEAgBSAIQTBsEN8ECyACQagOaiACQaAEaiIOQdgA/AoAACACQdgNaiACQbAOaikDADcDACACQeANaiACQbgOaikDADcDACACQegNaiACQcAOaikDADcDACACQfANaiACQcgOaikDADcDACACQYAOaiACQdgOaikDADcDACACQYgOaiACQeAOaikDADcDACACQZAOaiACQegOaikDADcDACACQZgOaiACQfAOaikDADcDACACQaAOaiACQfgOaikDADcDACACIAc2AswNIAIgBDYCyA0gAiACKQOoDjcD0A0gAiACKQPQDjcD+A0gDiACQcgNahAWIAJB2ARqIAJB+A1qEBYgAigCqAQhDSACKAKkBCEFIAIoAqAEIQggAkGYC2oiDyACQawEakHdAPwKAAAgAkGcBGoiDCACQY4Fai8BADsBACACIAIoAYoFNgKYBCACLQCJBSIHQQJGDQAgAkH8CGogD0HdAPwKAABBBCEEIAJB3glqIAwvAQA7AQAgAiACKAKYBDYB2gkgAiAHOgDZCSACIA02AvgIIAIgBTYC9AggAiAINgLwCEEAIQ0gAkEANgKgCyACQoCAgIDAADcCmAsgDiACQfAIahDVAiACKAKoBCIOQQxsIQUgAigCpAQhDCACKAKgBCEHIA4EQCAPQQAgDkEEQQwQiAMgAigCoAshDSACKAKcCyEECyAFBEAgBCANQQxsaiAMIAX8CgAACyACIA0gDmoiBTYCoAsgBwRAIAwgB0EMbBDfBAsgAkGgBGogAkGoCWoQ1QIgAigCqAQiDkEMbCEPIAIoAqQEIQwgAigCoAQhByACKAKYCyAFayAOSQRAIAJBmAtqIAUgDkEEQQwQiAMgAigCoAshBSACKAKcCyEECyAPBEAgBCAFQQxsaiAMIA/8CgAACyAHBEAgDCAHQQxsEN8ECyACKAKYCyEJIAJB8AhqIg8QhwMgAkGwCmogAkGwA2pB6AD8CgAAIAIoAghBAUcNBCACQZgLaiIMIAJBEGoQyAEgAkHYDGogAkHQAmpB4AD8CgAAIAJB7AhqIAIoAMsCNgAAIAIgAigCyAI2AOkIIAJBoARqIgcgD0GoAvwKAAAgAkHIBmogDEGgAvwKAAAgBSAOaiEIIAIgEDoA6AggDyAHQQJBAkGopsAAEDIgAigC/AghGCACKAL4CCERIAIoAvQIIRMgAigC8AgEQCAAIBg2AgwgACARNgIIIAAgEzYCBCAAQQE2AgAgCARAIAQhBQNAIAUoAgAiAARAIAVBBGooAgAgAEECdBDfBAsgBUEMaiEFIAhBAWsiCA0ACwsgCUUNAiAEIAlBDGwQ3wQMAgtB0c7FAC0AABpBDEEEENYEIgxFDQUgAkH4CGoiB0HcmsAAKAIAIgU2AgAgAkHUmsAAKQIAIh03A/AIIAJB8AhqQcibwAAQpQMgAigC9AggCCAYakEJaiIONgIAIAxBCGpBATYCACAMIAIpA/AINwIAIAJBATYCsA4gAiAMNgKsDiACQQE2AqgOIAcgBTYCACACIB03A/AIAkAgCkUEQCACQcANakHcmsAAKAIANgIAIAJB1JrAACkCADcDuA0MAQsgAkHwCGpByJvAABClAyACKAL0CCAKNgIAIAJBwA1qQQE2AgAgB0EBNgIAIAIgAikD8Ag3A7gNCyACQagOaiIHQdCowAAQnwMgAigCrA4iBSACKQO4DTcCDCAFQRRqIAJBwA1qKAIANgIAIAJBAjYCsA4gAkHwCGoiBSACQbADahDfASACQZgLaiAFENQBIAIoAqgOIAIoArAOIgVrQQNNBEAgByAFQQRBBEEMEIgDIAIoArAOIQULIAIoAqwOIAVBDGxqIgcgAikCmAs3AgAgB0EIaiACQaALaikCADcCACAHQRBqIAJBqAtqIg8pAgA3AgAgB0EYaiACQbALaiIQKQIANwIAIAdBIGogAkG4C2oiDCkCADcCACAHQShqIAJBwAtqIgcpAgA3AgAgAiAFQQRqNgKwDiACQfAIaiIFIAJB4ANqEN8BIAJBmAtqIAUQ1AEgAigCqA4iFyACKAKwDiIFa0EDTQRAIAJBqA5qIAVBBEEEQQwQiAMgAigCqA4hFyACKAKwDiEFCyACKAKsDiIKIAVBDGxqIg0gAikCmAs3AgAgDUEIaiACQaALaikCADcCACANQRBqIA8pAgA3AgAgDUEYaiAQKQIANwIAIA1BIGogDCkCADcCACANQShqIAcpAgA3AgAgAiAFQQRqIg02ArAOIBcgDWsgCEkEQCACQagOaiANIAhBBEEMEIgDIAIoArAOIQ0gAigCrA4hCgsgCEEMbCIFBEAgCiANQQxsaiAEIAX8CgAACyACIAggDWoiCDYCsA4gCQRAIAQgCUEMbBDfBCACKAKwDiEICyACKAKoDiAIayAYSQRAIAJBqA5qIAggGEEEQQwQiAMgAigCsA4hCAsgGEEMbCIEBEAgAigCrA4gCEEMbGogESAE/AoAAAsgAiAIIBhqIgQ2ArAOIBMEfyARIBNBDGwQ3wQgAigCsA4FIAQLIA5BAWpHDQYgACACKQKoDjcCBCAAQQA2AgAgAEEMaiACQbAOaigCADYCACACKAKQAiIARQ0HIAIoApQCIAAQ3wQMBwsgACANNgIMIAAgBTYCCCAAIAg2AgQgAEEBNgIACyACKAKQAiIARQ0FIAIoApQCIAAQ3wQMBQsgAiANNgKIDyACIAU2AoQPIAIgCDYCgA9BhJ3AAEErIAJBgA9qQfypwABB/N/AABDKAwALQYSmwAAQ6AQAC0GUpsAAEOgEAAtBBEEMEP8EAAtB4KjAAEEtQZCpwAAQ/gMACyACQZAPaiQACyAGQYAGaiQAIAsoAhhBAUYEQCALQQhqIAtBHGoiAEEIaigCADYCACALIAApAgA3AwAgC0EMaiALENQDIAsoAhAiBSALKAIUEM0EIQQgCygCDCIABEAgBSAAEN8ECyALKAIAIgAEQCALKAIEIAAQ3wQLIBlBgICAgHg2AgAgGSAENgIEIBQEQCABIQADQCAAKAIAIgQEQCAAQQRqKAIAIARBAnQQ3wQLIABBDGohACAUQQFrIhQNAAsLIBtFDQEgASAbQQxsEN8EDAELIAsoAhwhByALKAIgIgQhECALKAIkIgAEQCAAQQxsIQwgBCEFIAQhAANAIAtBIGogAEEIaigCADYCACALIAApAgA3AxggBSALQRhqELsDNgIAIBBBBGohECAFQQRqIQUgAEEMaiEAIAxBDGsiDA0ACwsgGSAENgIEIBkgB0EDbDYCACAZIBAgBGtBAnY2AgggFARAIAEhAANAIAAoAgAiBARAIABBBGooAgAgBEECdBDfBAsgAEEMaiEAIBRBAWsiFA0ACwsgG0UNACABIBtBDGwQ3wQLIAtBMGokAAJAAkAgFgJ/IBUoAhQiAEGAgICAeEYEQEEAIQAgFSgCGCEEQQAhAUEBDAELIBUoAhghBAJAIBUoAhwiASAATwRAIAQhAAwBCyAAQQJ0IQUgAUUEQEEEIQAgBCAFEN8EDAELIAQgBUEEIAFBAnQiBBDOBCIARQ0CC0EAIQRBAAs2AgwgFiAENgIIIBYgATYCBCAWIAA2AgAgFUEgaiQADAELQQQgBEHo8cAAEMgEAAsgFigCACAWKAIEIBYoAgggFigCDCAWQRBqJAAL2rAFAh5+Sn8jAEEQayJUJAAjAEEgayJSJAAgUiABNgIQIFIgADYCDCBSIAE2AgggUkEUaiFfIwBBMGsiOyQAIFJBCGoiACgCACEBIAAoAgQhJiAAKAIIIQAgO0EANgIAIDsgJiAAQQJ0ajYCJCA7IAE2AiAgOyAmNgIcIDsgJjYCGCA7IDs2AiggO0EMaiA7QRhqEJYCAkACQAJAAkAgOygCAEEBRgRAIDsoAhAhJiA7KAIEIQEgOygCFCIABEAgJiFRA0AgUSgCACInBEAgUUEEaigCACAnQQJ0EN8ECyBRQQxqIVEgAEEBayIADQALCyA7KAIMIgBFDQEgJiAAQQxsEN8EDAELIDsoAhAhASA7KAIMImZBgICAgHhHDQELIF9BgICAgHg2AgAgXyABNgIEDAELIDtBGGohQSA7KAIUIlEhACMAQbALayIsJAACQAJAAkACQAJAAkAgAEEDRgRAAkAgAUEIaigCACIABEAgAEEBayIAQf7///8DcQ0BIAFBBGooAgAhJyAAQf////8DcSImQQFqIgBBA3EhLyAmQQNPBEAgAEH8////B3EhLgNAIARCgAF8IQQgJ0EQaiEnIC5BBGsiLg0ACwsgLwRAA0AgJzUCACAEhiACfCECIARCIHwhBCAnQQRqIScgL0EBayIvDQALCyACQv////8PVg0BCyACpyFlDAILICxBATYCrAIgLEHQh8EANgKoAiAsQgE3ArQCICwgLEGvC2qtQoCAgIDQAYQ3A+gHICwgLEHoB2o2ArACICxBKGogLEGoAmoQ0gIgLCgCLCFlICwoAigiAEGAgICAeEYNASBBICwoAjA2AgwgQSBlNgIIIEEgADYCBCBBQQE2AgAMAgsgLEEBNgKsAiAsQaiJwQA2AqgCICxCATcCtAIgLCAANgLoByAsICxB6AdqrUKAgICA4AGENwMoICwgLEEoajYCsAIgQUEEaiAsQagCahDSAiBBQQE2AgAMAQsCQCABKAIURQRAQdHOxQAtAAAaQQEhMEEBQQEQ1gQiLkUNCCAuQQA6AAAgLEEBNgIoDAELICxBKGogAUEMakEIELACICwoAiwhLiAsKAIwIjBBAkkNACAuIDBqISVBACEnIDBBAXYiAEEBRwRAIDBBAWshLyAAQf7///8HcSEqA0AgLiAvaiImLQAAIQAgJiAnIC5qIigtAAA6AAAgKCAAOgAAICUgJ0F+c2oiAC0AACEmIAAgKEEBaiIALQAAOgAAIAAgJjoAACAvQQJrIS8gKiAnQQJqIidHDQALCyAwQQJxBEAgJyAuaiIALQAAISYgACAlICdBf3NqIgAtAAA6AAAgACAmOgAACyAwQRFJDQAgLEEBNgKsAiAsQYSJwQA2AqgCICxCATcCtAIgLCAwNgKIBiAsICxBiAZqrUKAgICA4AGENwPoByAsICxB6AdqNgKwAiBBQQRqICxBqAJqENICIEFBATYCACAsKAIoIgBFDQEgLiAAEN8EDAELICxBEGpCADcDACAsQgA3AwggMARAICwgMGtBGGogLiAw/AoAAAsgLCgCKCIABEAgLiAAEN8ECwJAIAEoAiBFBEBB0c7FAC0AABpBASEkQQFBARDWBCIuRQ0IIC5BADoAACAsQQE2AigMAQsgLEEoaiABQRhqQQgQsAIgLCgCLCEuICwoAjAiJEECSQ0AICQgLmohJUEAIScgJEEBdiIAQQFHBEAgJEEBayEvIABB/v///wdxISoDQCAuIC9qIiYtAAAhACAmICcgLmoiKC0AADoAACAoIAA6AAAgJSAnQX5zaiIALQAAISYgACAoQQFqIgAtAAA6AAAgACAmOgAAIC9BAmshLyAqICdBAmoiJ0cNAAsLICRBAnEEQCAnIC5qIgAtAAAhJiAAICUgJ0F/c2oiAC0AADoAACAAICY6AAALICRBEUkNACAsQQE2AqwCICxB3IjBADYCqAIgLEIBNwK0AiAsICQ2AogGICwgLEGIBmqtQoCAgIDgAYQ3A+gHICwgLEHoB2o2ArACIEFBBGogLEGoAmoQ0gIgQUEBNgIAICwoAigiAEUNASAuIAAQ3wQMAQsgLEEgakIANwMAICxCADcDGCAkBEAgLCAka0EoaiAuICT8CgAACyAsKAIoIgAEQCAuIAAQ3wQLICxB6AdqIgBBnOHAABCuAiAsQagCaiAAEDQgLEGQBmoiACAsQbgCaigCADYCACAsICwpA7ACNwOIBiAsKQOoAiICQgJRBEAgQSAsKQOIBjcCBCBBQQE2AgAgQUEMaiAAKAIANgIADAELICxBNGogLEG8AmpB9AH8CgAAICxBMGoiACAsQZAGaigCADYCACAsICwpA4gGNwMoIAKnQQFxRQ0BICwoArQEIWkgLCgCsAQhZyAsQZAKaiAsQdAAaikDADcDACAsQYgKaiAsQcgAaikDADcDACAsQYAKaiAsQUBrKQMANwMAICxB+AlqICxBOGopAwA3AwAgLEHwCWogACkDADcDACAsQaAKaiAsQeAAaikDADcDACAsQagKaiAsQegAaikDADcDACAsQbAKaiAsQfAAaikDADcDACAsQbgKaiAsQfgAaikDADcDACAsQcAKaiAsQYABaikDADcDACAsICwpAyg3A+gJICwgLCkDWDcDmAogLEHwCmogLEGwAWopAwA3AwAgLEHoCmogLEGoAWopAwA3AwAgLEHgCmogLEGgAWopAwA3AwAgLEHYCmogLEGYAWopAwA3AwAgLEHQCmogLEGQAWopAwA3AwAgLEGAC2ogLEHAAWopAwA3AwAgLEGIC2ogLEHIAWopAwA3AwAgLEGQC2ogLEHQAWopAwA3AwAgLEGYC2ogLEHYAWopAwA3AwAgLEGgC2ogLEHgAWopAwA3AwAgLCAsKQOIATcDyAogLCAsKQO4ATcD+AogLEHIBGoiACAsQegJakHgAPwKAAAgLEGoBWogLEHICmpB4AD8CgAAICxBqAJqIUUgLEEIaiFDICxBGGohaCMAQbAsayIhJAAgIUGAJGpCADcDACAhQfgjakIANwMAICFB8CNqQgA3AwAgIUHoI2pCADcDACAhQeAjakIANwMAICFB2CNqQgA3AwAgIUGwI2pBqKPAACkDADcDACAhQbgjakGwo8AAKQMANwMAICFBCDoAiCQgIUGoI2oiKEGgo8AAKQMANwMAICFCADcD0CMgIUIANwPAIyAhQZijwAApAwA3A6AjICEgZa0iAkI4hiACQoD+A4NCKIaEIAJCgID8B4NCGIYgAkKAgID4D4NCCIaEhDcDyCMgIUGgLGpCADcDACAhQZgsakIANwMAICFBkCxqQgA3AwAgIUIANwOILCAhQYgsaiEvIwBBQGoiMiQAICFByCNqIiQtAEAiJSAkaiIqQYABOgAAICWtIgRCO4YgIUGgI2oiJykDICIDQgmGIgIgBEIDhoQiBEKA/gODQiiGhCAEQoCA/AeDQhiGIARCgICA+A+DQgiGhIQgA0IBhkKAgID4D4MgA0IPiEKAgPwHg4QgA0IfiEKA/gODIAJCOIiEhIQhAgJAAkAgJUE/RwRAICVBP3MiJgRAICpBAWpBACAm/AsACyAlQThzQQdLDQELICcgJEEBEC0gMkEwakIANwMAIDJBKGpCADcDACAyQSBqQgA3AwAgMkEYakIANwMAIDJBEGpCADcDACAyQQhqQgA3AwAgMkIANwMAIDIgAjcDOCAnIDJBARAtDAELICQgAjcAOCAnICRBARAtCyAkQQA6AEAgLyAnKAIcIiZBGHQgJkGA/gNxQQh0ciAmQQh2QYD+A3EgJkEYdnJyNgAcIC8gJygCGCImQRh0ICZBgP4DcUEIdHIgJkEIdkGA/gNxICZBGHZycjYAGCAvICcoAhQiJkEYdCAmQYD+A3FBCHRyICZBCHZBgP4DcSAmQRh2cnI2ABQgLyAnKAIQIiZBGHQgJkGA/gNxQQh0ciAmQQh2QYD+A3EgJkEYdnJyNgAQIC8gJygCDCImQRh0ICZBgP4DcUEIdHIgJkEIdkGA/gNxICZBGHZycjYADCAvICcoAggiJkEYdCAmQYD+A3FBCHRyICZBCHZBgP4DcSAmQRh2cnI2AAggLyAnKAIEIiZBGHQgJkGA/gNxQQh0ciAmQQh2QYD+A3EgJkEYdnJyNgAEIC8gJygCACImQRh0ICZBgP4DcUEIdHIgJkEIdkGA/gNxICZBGHZycjYAACAyQUBrJAAgJyAvQdCJwQAQHQJAAkACQAJAAkACQAJAICEtAIAkQQJGBEAgIUHgG2ogKCgCACIANgIAICEgISkDoCMiAjcD2BsgRUEMaiAANgIAIEUgAjcCBCBFQQE2AgAMAQsgIUHYG2oiJiAhQaAjaiIlQeAA/AoAACAhQQhqICZB4AD8CgAAICFB+CBqICFB4ABqKQMANwMAICFB8CBqICFB2ABqKQMANwMAICFB6CBqICFB0ABqKQMANwMAICFB4CBqICFByABqKQMANwMAICFB2CBqICFBQGspAwA3AwAgISAhKQM4NwPQICAhQaggaiAhQRBqKQMANwMAICFBsCBqICFBGGopAwA3AwAgIUG4IGogIUEgaikDADcDACAhQcAgaiAhQShqKQMANwMAICFByCBqICFBMGopAwA3AwAgISAhKQMINwOgICAhQaghakHI/8AAKQMANwMAICFBoCFqQcD/wAApAwA3AwAgIUGYIWpBuP/AACkDADcDACAhQZAhakGw/8AAKQMANwMAICFBiCFqQaj/wAApAwA3AwAgIUGg/8AAKQMANwOAISMAQcABayIxJAACQAJAICFBoCBqIi9B4ABqIjJB2LPCAEEwEPEDBEBBACEwQQAhJCMAQdAdayIgJAAgIEGQGWogL0EwaiImKQMgIgdCACAmKQMoIgZCABDJAyAgQaAZaiAmKQMYIgVCACAGQgAQyQMgIEGwGWogJikDECIDQgAgBkIAEMkDICBBwBlqICYpAwgiBEIAIAZCABDJAyAgQdAZaiAmKQMAIgJCACAGQgAQyQMgIEHwGWogBUIAIAdCABDJAyAgQYAaaiADQgAgB0IAEMkDICBBkBpqIARCACAHQgAQyQMgIEGgGmogAkIAIAdCABDJAyAgQcAaaiADQgAgBUIAEMkDICBB0BpqIARCACAFQgAQyQMgIEHgGmogAkIAIAVCABDJAyAgQYAbaiAEQgAgA0IAEMkDICBBkBtqIAJCACADQgAQyQMgIEGwG2ogAkIAIARCABDJAyAgQeAZaiAGQgAgBkIAEMkDICBBsBpqIAdCACAHQgAQyQMgIEHwGmogBUIAIAVCABDJAyAgQaAbaiADQgAgA0IAEMkDICBBwBtqIARCACAEQgAQyQMgIEHQG2ogAkIAIAJCABDJAyAgQYAZaiAgKQPgGSIPQv3/8//P///5iX9+IgJCAEKr1f7///+//7l/QgAQyQMgIEHwGGogAkIAQv//z4rr///VHkIAEMkDICBB4BhqIAJCAEKk7MO1j9S0mOcAQgAQyQMgIEHQGGogAkIAQr+llJzP8NK75ABCABDJAyAgQcAYaiACQgBC19mumuT26Y3LAEIAEMkDICBBsBhqIAJCAEKazf/Lo73EgBpCABDJAyAgKQO4GyAgKQOYGyAgKQOIGyAgKQPYGiAgKQPIGiAgKQOIGiAgKQP4GSAgKQOoGSAgKQOYGSICICApA6AZfCIMIAJUrXwiAiAgKQOwGXwiBCAgKQPwGXwiCiAEVK18IgMgICkDuBkgAiAEVq18IgQgICkDwBl8IgJ8IgUgA1StfCAFIAUgICkDgBp8IhdWrXwiAyAgKQPIGSACIARUrXwiBSAgKQPQGXwiAnwiByAgKQOQGnwiBiAgKQPAGnwiCSAGVK18IgQgBiAHVK0gICkDmBogAyAHVq18fCIDICApA9gZIAIgBVStfHwiBiAgKQOgGnwiAnwiBSAEVK18IAUgICkD0Bp8IhUgBVStfCIEIAIgBlStICApA6gaIAMgBlatfHx8IgUgICkD4Bp8IgMgICkDgBt8IhYgA1StfCICIAMgBVStICApA+gaIAQgBVatfHx8IgQgAlStfCAEIAQgICkDkBt8IhBWrXwiAiAgKQOwG3wiEiACVK18IgRCP4ggICkD2BsgICkD0BsiAiAEQgGGIBJCP4iEfCIRIAJUrXwgESAgKQPIGyAgKQPAGyICIBBCAYYgFkI/iIR8IgsgAlStfCALICApA6gbICApA6AbIgIgFUIBhiAJQj+IhHwiByACVK18IAcgByAgKQP4GiAgKQPwGiICIBdCAYYgCkI/iIR8IgUgAlStfCAFIAUgICkDuBogICkDsBoiAiAMQgGGICApA5AZIgRCP4iEfCIDIAJUrXwgAyADICApA+gZIgIgBEIBhnwiDSACVK18Ig5WrXwiAiAKQgGGIAxCP4iEfCIMIAJUrXwiClatfCICIAlCAYYgF0I/iIR8IgkgAlStfCIGVq18IgIgFkIBhiAVQj+IhHwiBSACVK18IgMgC1StfCICIBJCAYYgEEI/iIR8IgsgAlStfCICIBFUrXx8IQQCfwJAICApA7gYICApA8gYICApA9gYICApA+gYICApA/gYICApA4gZICApA4AZIgcgD0J9g3wgB1StfCIHICApA/AYfCIPIAdUrXwgDyANIA98Ig9WrXwiByAgKQPgGHwiDSAHVK18IA0gDnwiDiANVK18IgcgICkD0Bh8Ig0gB1StfCAMIA18IgwgDVStfCIHICApA8AYfCINIAdUrXwgCiANfCIKIA1UrXwiByAgKQOwGHwiDSAHVK18IAkgDXwiCSANVK18IgdQDQAgBiAHfCIGIAdUIiZFDQAgJq0iByAFfCIFIAdaDQAgBSAHVK0iByADfCIDIAdaDQAgAyAHVK0iByALfCILIAdaDQAgByALVq0iByACfCICIAdaDQAgAiAHVK0iByAEfCIEIAdUDAELQQALISogIEGgGGogD0L9//P/z///+Yl/fiIHQgBCq9X+////v/+5f0IAEMkDICBBkBhqIAdCAEL//8+K6///1R5CABDJAyAgQYAYaiAHQgBCpOzDtY/UtJjnAEIAEMkDICBB8BdqIAdCAEK/pZScz/DSu+QAQgAQyQMgIEHgF2ogB0IAQtfZrprk9umNywBCABDJAyAgQdAXaiAHQgBCms3/y6O9xIAaQgAQyQMCQCAgKQPYFyAgKQPoFyAgKQP4FyAgKQOIGCAgKQOYGCAgKQOoGCAgKQOgGCIHIA98IAdUrXwiByAgKQOQGHwiDyAHVK18IA8gDiAPfCINVq18IgcgICkDgBh8Ig4gB1StfCAMIA58IgwgDlStfCIHICApA/AXfCIOIAdUrXwgCiAOfCIKIA5UrXwiByAgKQPgF3wiDiAHVK18IAkgDnwiCSAOVK18IgcgICkD0Bd8Ig4gB1StfCAOIAYgDnwiB1atfCIGUA0AIAUgBnwiBSAGWg0AIAUgBlStIgYgA3wiAyAGWg0AIAMgBlStIgYgC3wiCyAGWg0AIAYgC1atIgYgAnwiAiAGWg0AIAIgBlStIgYgBHwiBCAGVCEkCyAgQcAXaiANQv3/8//P///5iX9+IgZCAEKr1f7///+//7l/QgAQyQMgIEGwF2ogBkIAQv//z4rr///VHkIAEMkDICBBoBdqIAZCAEKk7MO1j9S0mOcAQgAQyQMgIEGQF2ogBkIAQr+llJzP8NK75ABCABDJAyAgQYAXaiAGQgBC19mumuT26Y3LAEIAEMkDICBB8BZqIAZCAEKazf/Lo73EgBpCABDJAwJ/QQAgICkD+BYgICkDiBcgICkDmBcgICkDqBcgICkDuBcgICkDyBcgICkDwBciBiANfCAGVK18IgYgICkDsBd8Ig0gBlStfCANIAwgDXwiDlatfCIGICApA6AXfCIMIAZUrXwgCiAMfCIKIAxUrXwiBiAgKQOQF3wiDCAGVK18IAkgDHwiCSAMVK18IgYgICkDgBd8IgwgBlStfCAHIAx8IgcgDFStfCIGICApA/AWfCIMIAZUrXwgDCAFIAx8IgZWrXwiBVANABpBACAFIAMgBXwiA1gNABpBACADIAVUrSIFIAt8IgsgBVoNABpBACAFIAtWrSIFIAJ8IgIgBVoNABogAiAFVK0iBSAEfCIEIAVUCyEnICBB4BZqIA5C/f/z/8////mJf34iBUIAQqvV/v///7//uX9CABDJAyAgQdAWaiAFQgBC///Piuv//9UeQgAQyQMgIEHAFmogBUIAQqTsw7WP1LSY5wBCABDJAyAgQbAWaiAFQgBCv6WUnM/w0rvkAEIAEMkDICBBoBZqIAVCAELX2a6a5PbpjcsAQgAQyQMgIEGQFmogBUIAQprN/8ujvcSAGkIAEMkDAkAgICkDmBYgICkDqBYgICkDuBYgICkDyBYgICkD2BYgICkD6BYgICkD4BYiBSAOfCAFVK18IgUgICkD0BZ8Ig4gBVStfCAOIAogDnwiDFatfCIFICApA8AWfCIKIAVUrXwgCSAKfCIJIApUrXwiBSAgKQOwFnwiCiAFVK18IAcgCnwiByAKVK18IgUgICkDoBZ8IgogBVStfCAGIAp8IgYgClStfCIFICApA5AWfCIKIAVUrXwgCiADIAp8IgVWrXwiA1ANACADIAt8IgsgA1oNACADIAtWrSIDIAJ8IgIgA1oNACACIANUrSIDIAR8IgQgA1QhMAsgIEGAFmogDEL9//P/z///+Yl/fiIDQgBCq9X+////v/+5f0IAEMkDICBB8BVqIANCAEL//8+K6///1R5CABDJAyAgQeAVaiADQgBCpOzDtY/UtJjnAEIAEMkDICBB0BVqIANCAEK/pZScz/DSu+QAQgAQyQMgIEHAFWogA0IAQtfZrprk9umNywBCABDJAyAgQbAVaiADQgBCms3/y6O9xIAaQgAQyQMgICkDuBUgICkDyBUgICkD2BUgICkD6BUgICkD+BUgICkDiBYgICkDgBYiAyAMfCADVK18IgMgICkD8BV8IgogA1StfCAJIAp8IgwgClStfCIDICApA+AVfCIJIANUrXwgByAJfCIKIAlUrXwiAyAgKQPQFXwiByADVK18IAYgB3wiCSAHVK18IgMgICkDwBV8IgYgA1StfCAGIAUgBnwiBlatfCIDICApA7AVfCIFIANUrXwgBSALfCIHIAVUrXwiA1BFBEAgAiADfCICIANUIiatIgUgBHwiAyAEICYbIQQgJiADIAVUcSErCyAgQaAVaiAMQv3/8//P///5iX9+IgNCAEKr1f7///+//7l/QgAQyQMgIEGQFWogA0IAQv//z4rr///VHkIAEMkDICBBgBVqIANCAEKk7MO1j9S0mOcAQgAQyQMgIEHwFGogA0IAQr+llJzP8NK75ABCABDJAyAgQeAUaiADQgBC19mumuT26Y3LAEIAEMkDICBB0BRqIANCAEKazf/Lo73EgBpCABDJAyAgKQPYFCAgKQPoFCAgKQP4FCAgKQOIFSAgKQOYFSAgKQOoFSAgKQOgFSIDIAx8IANUrXwiAyAgKQOQFXwiBSADVK18IAUgCnwiCyAFVK18IgMgICkDgBV8IgUgA1StfCAFIAUgCXwiBVatfCIDICApA/AUfCIJIANUrXwgBiAJfCIGIAlUrXwiAyAgKQPgFHwiCSADVK18IAcgCXwiByAJVK18IgMgICkD0BR8IgkgA1StfCACIAl8IgIgCVStfCIKIAR8IgMgBCAKQgBSIigbIQkCQAJAAkAgAyAKVCImrSAKICgbUEUEQCACIQQMAQsgKyAkICpyICdyIDBycgRAIAIhBAwBCyAmIChxBEAgAiEEDAELIAlCms3/y6O9xIAaVgRAIAIhBAwBCyAJQprN/8ujvcSAGlINASACQtfZrprk9umNywBWBEAgAiEEDAELIAJC19mumuT26Y3LAFINAULX2a6a5PbpjcsAIQQgB0K/pZScz/DSu+QAVg0AIAdCv6WUnM/w0rvkAFINASAGQqTsw7WP1LSY5wBWDQAgBkKk7MO1j9S0mOcAUg0BIAVC///Piuv//9UeVg0AIAVC///Piuv//9UeUiALQqrV/v///7//uX9Ycg0BCyAFQv//z4rr///VHn0iDCALQqvV/v///7//uX9UrSICfSEDIAZCpOzDtY/UtJjnAH0iCiAFQv//z4rr///VHlQgAiAMVnKtIgJ9IQUgB0K/pZScz/DSu+QAfSIMIAZCpOzDtY/UtJjnAFQgAiAKVnKtIgJ9IQYgBELX2a6a5PbpjcsAfSIKIAdCv6WUnM/w0rvkAFQgAiAMVnKtIgd9IQIgCSAEQtfZrprk9umNywBUIAcgClZyrX1Cms3/y6O9xIAafSEJIAtC1aqBgICAwIDGAHwhCwwBCyAFIQMgBiEFIAchBgsgICALNwPIHSAgIAM3A8AdICAgBTcDuB0gICAGNwOwHSAgIAI3A6gdICAgCTcDoB0gIEHgG2ogIEGgHWogMhCyASAgQcATaiAvKQMgIgdCACAvKQMoIgZCABDJAyAgQZATaiAvKQMYIgVCACAGQgAQyQMgIEHQEmogLykDECIDQgAgBkIAEMkDICBBgBJqIC8pAwgiBEIAIAZCABDJAyAgQaARaiAvKQMAIgJCACAGQgAQyQMgIEGgE2ogBUIAIAdCABDJAyAgQeASaiADQgAgB0IAEMkDICBBkBJqIARCACAHQgAQyQMgIEGwEWogAkIAIAdCABDJAyAgQfASaiADQgAgBUIAEMkDICBBoBJqIARCACAFQgAQyQMgIEHAEWogAkIAIAVCABDJAyAgQbASaiAEQgAgA0IAEMkDICBB0BFqIAJCACADQgAQyQMgIEHgEWogAkIAIARCABDJAyAgQcAUaiAGQgAgBkIAEMkDICBB0BNqIAdCACAHQgAQyQMgIEGwE2ogBUIAIAVCABDJAyAgQYATaiADQgAgA0IAEMkDICBBwBJqIARCACAEQgAQyQMgIEHwEWogAkIAIAJCABDJAyAgQbAUaiAgKQPAFCIPQv3/8//P///5iX9+IgJCAEKr1f7///+//7l/QgAQyQMgIEGgFGogAkIAQv//z4rr///VHkIAEMkDICBBkBRqIAJCAEKk7MO1j9S0mOcAQgAQyQMgIEGAFGogAkIAQr+llJzP8NK75ABCABDJAyAgQfATaiACQgBC19mumuT26Y3LAEIAEMkDICBB4BNqIAJCAEKazf/Lo73EgBpCABDJAyAgKQPoESAgKQPYESAgKQO4EiAgKQOoEiAgKQP4EiAgKQPoEiAgKQOoEyAgKQOYEyAgKQPIEyICICApA5ATfCIMIAJUrXwiAiAgKQPQEnwiBCAgKQOgE3wiCiAEVK18IgMgICkD2BIgAiAEVq18IgQgICkDgBJ8IgJ8IgUgA1StfCAFIAUgICkD4BJ8IhdWrXwiAyAgKQOIEiACIARUrXwiBSAgKQOgEXwiAnwiByAgKQOQEnwiBiAgKQPwEnwiCSAGVK18IgQgBiAHVK0gICkDmBIgAyAHVq18fCIDICApA6gRIAIgBVStfHwiBiAgKQOwEXwiAnwiBSAEVK18IAUgICkDoBJ8IhUgBVStfCIEIAIgBlStICApA7gRIAMgBlatfHx8IgUgICkDwBF8IgMgICkDsBJ8IhYgA1StfCICIAMgBVStICApA8gRIAQgBVatfHx8IgQgAlStfCAEIAQgICkD0BF8IhBWrXwiAiAgKQPgEXwiEiACVK18IgRCP4ggICkD+BEgICkD8BEiAiAEQgGGIBJCP4iEfCIRIAJUrXwgESAgKQPIEiAgKQPAEiICIBBCAYYgFkI/iIR8IgsgAlStfCALICApA4gTICApA4ATIgIgFUIBhiAJQj+IhHwiByACVK18IAcgByAgKQO4EyAgKQOwEyICIBdCAYYgCkI/iIR8IgUgAlStfCAFIAUgICkD2BMgICkD0BMiAiAMQgGGICApA8ATIgRCP4iEfCIDIAJUrXwgAyADICApA8gUIgIgBEIBhnwiDSACVK18Ig5WrXwiAiAKQgGGIAxCP4iEfCIMIAJUrXwiClatfCICIAlCAYYgF0I/iIR8IgkgAlStfCIGVq18IgIgFkIBhiAVQj+IhHwiBSACVK18IgMgC1StfCICIBJCAYYgEEI/iIR8IgsgAlStfCICIBFUrXx8IQRBACEkAn8CQCAgKQPoEyAgKQP4EyAgKQOIFCAgKQOYFCAgKQOoFCAgKQO4FCAgKQOwFCIHIA9CfYN8IAdUrXwiByAgKQOgFHwiDyAHVK18IA8gDSAPfCIPVq18IgcgICkDkBR8Ig0gB1StfCANIA58Ig4gDVStfCIHICApA4AUfCINIAdUrXwgDCANfCIMIA1UrXwiByAgKQPwE3wiDSAHVK18IAogDXwiCiANVK18IgcgICkD4BN8Ig0gB1StfCAJIA18IgkgDVStfCIHUA0AIAYgB3wiBiAHVCImRQ0AICatIgcgBXwiBSAHWg0AIAUgB1StIgcgA3wiAyAHWg0AIAMgB1StIgcgC3wiCyAHWg0AIAcgC1atIgcgAnwiAiAHWg0AIAIgB1StIgcgBHwiBCAHVAwBC0EACyEqICBBkBFqIA9C/f/z/8////mJf34iB0IAQqvV/v///7//uX9CABDJAyAgQYARaiAHQgBC///Piuv//9UeQgAQyQMgIEHwEGogB0IAQqTsw7WP1LSY5wBCABDJAyAgQeAQaiAHQgBCv6WUnM/w0rvkAEIAEMkDICBB0BBqIAdCAELX2a6a5PbpjcsAQgAQyQMgIEHAEGogB0IAQprN/8ujvcSAGkIAEMkDAkAgICkDyBAgICkD2BAgICkD6BAgICkD+BAgICkDiBEgICkDmBEgICkDkBEiByAPfCAHVK18IgcgICkDgBF8Ig8gB1StfCAPIA4gD3wiDVatfCIHICApA/AQfCIOIAdUrXwgDCAOfCIMIA5UrXwiByAgKQPgEHwiDiAHVK18IAogDnwiCiAOVK18IgcgICkD0BB8Ig4gB1StfCAJIA58IgkgDlStfCIHICApA8AQfCIOIAdUrXwgDiAGIA58IgdWrXwiBlANACAFIAZ8IgUgBloNACAFIAZUrSIGIAN8IgMgBloNACADIAZUrSIGIAt8IgsgBloNACAGIAtWrSIGIAJ8IgIgBloNACACIAZUrSIGIAR8IgQgBlQhJAsgIEGwEGogDUL9//P/z///+Yl/fiIGQgBCq9X+////v/+5f0IAEMkDICBBoBBqIAZCAEL//8+K6///1R5CABDJAyAgQZAQaiAGQgBCpOzDtY/UtJjnAEIAEMkDICBBgBBqIAZCAEK/pZScz/DSu+QAQgAQyQMgIEHwD2ogBkIAQtfZrprk9umNywBCABDJAyAgQeAPaiAGQgBCms3/y6O9xIAaQgAQyQNBACEwAn9BACAgKQPoDyAgKQP4DyAgKQOIECAgKQOYECAgKQOoECAgKQO4ECAgKQOwECIGIA18IAZUrXwiBiAgKQOgEHwiDSAGVK18IA0gDCANfCIOVq18IgYgICkDkBB8IgwgBlStfCAKIAx8IgogDFStfCIGICApA4AQfCIMIAZUrXwgCSAMfCIJIAxUrXwiBiAgKQPwD3wiDCAGVK18IAcgDHwiByAMVK18IgYgICkD4A98IgwgBlStfCAMIAUgDHwiBlatfCIFUA0AGkEAIAUgAyAFfCIDWA0AGkEAIAMgBVStIgUgC3wiCyAFWg0AGkEAIAUgC1atIgUgAnwiAiAFWg0AGiACIAVUrSIFIAR8IgQgBVQLIScgIEHQD2ogDkL9//P/z///+Yl/fiIFQgBCq9X+////v/+5f0IAEMkDICBBwA9qIAVCAEL//8+K6///1R5CABDJAyAgQbAPaiAFQgBCpOzDtY/UtJjnAEIAEMkDICBBoA9qIAVCAEK/pZScz/DSu+QAQgAQyQMgIEGQD2ogBUIAQtfZrprk9umNywBCABDJAyAgQYAPaiAFQgBCms3/y6O9xIAaQgAQyQMCQCAgKQOIDyAgKQOYDyAgKQOoDyAgKQO4DyAgKQPIDyAgKQPYDyAgKQPQDyIFIA58IAVUrXwiBSAgKQPAD3wiDiAFVK18IA4gCiAOfCIMVq18IgUgICkDsA98IgogBVStfCAJIAp8IgkgClStfCIFICApA6APfCIKIAVUrXwgByAKfCIHIApUrXwiBSAgKQOQD3wiCiAFVK18IAYgCnwiBiAKVK18IgUgICkDgA98IgogBVStfCAKIAMgCnwiBVatfCIDUA0AIAMgC3wiCyADWg0AIAMgC1atIgMgAnwiAiADWg0AIAIgA1StIgMgBHwiBCADVCEwCyAgQfAOaiAMQv3/8//P///5iX9+IgNCAEKr1f7///+//7l/QgAQyQMgIEHgDmogA0IAQv//z4rr///VHkIAEMkDICBB0A5qIANCAEKk7MO1j9S0mOcAQgAQyQMgIEHADmogA0IAQr+llJzP8NK75ABCABDJAyAgQbAOaiADQgBC19mumuT26Y3LAEIAEMkDICBBoA5qIANCAEKazf/Lo73EgBpCABDJA0EAISsgICkDqA4gICkDuA4gICkDyA4gICkD2A4gICkD6A4gICkD+A4gICkD8A4iAyAMfCADVK18IgMgICkD4A58IgogA1StfCAJIAp8IgwgClStfCIDICApA9AOfCIJIANUrXwgByAJfCIKIAlUrXwiAyAgKQPADnwiByADVK18IAYgB3wiCSAHVK18IgMgICkDsA58IgYgA1StfCAGIAUgBnwiBlatfCIDICApA6AOfCIFIANUrXwgBSALfCIHIAVUrXwiA1BFBEAgAiADfCICIANUIiatIgUgBHwiAyAEICYbIQQgJiADIAVUcSErCyAgQZAOaiAMQv3/8//P///5iX9+IgNCAEKr1f7///+//7l/QgAQyQMgIEGADmogA0IAQv//z4rr///VHkIAEMkDICBB8A1qIANCAEKk7MO1j9S0mOcAQgAQyQMgIEHgDWogA0IAQr+llJzP8NK75ABCABDJAyAgQdANaiADQgBC19mumuT26Y3LAEIAEMkDICBBwA1qIANCAEKazf/Lo73EgBpCABDJAyAgKQPIDSAgKQPYDSAgKQPoDSAgKQP4DSAgKQOIDiAgKQOYDiAgKQOQDiIDIAx8IANUrXwiAyAgKQOADnwiBSADVK18IAUgCnwiCyAFVK18IgMgICkD8A18IgUgA1StfCAFIAUgCXwiBVatfCIDICApA+ANfCIJIANUrXwgBiAJfCIGIAlUrXwiAyAgKQPQDXwiCSADVK18IAcgCXwiByAJVK18IgMgICkDwA18IgkgA1StfCACIAl8IgIgCVStfCIKIAR8IgMgBCAKQgBSIigbIQkCQAJAAkAgAyAKVCImrSAKICgbUEUEQCACIQQMAQsgKyAkICpyICdyIDBycgRAIAIhBAwBCyAmIChxBEAgAiEEDAELIAlCms3/y6O9xIAaVgRAIAIhBAwBCyAJQprN/8ujvcSAGlINASACQtfZrprk9umNywBWBEAgAiEEDAELIAJC19mumuT26Y3LAFINAULX2a6a5PbpjcsAIQQgB0K/pZScz/DSu+QAVg0AIAdCv6WUnM/w0rvkAFINASAGQqTsw7WP1LSY5wBWDQAgBkKk7MO1j9S0mOcAUg0BIAVC///Piuv//9UeVg0AIAVC///Piuv//9UeUiALQqrV/v///7//uX9Ycg0BCyAFQv//z4rr///VHn0iDCALQqvV/v///7//uX9UrSICfSEDIAZCpOzDtY/UtJjnAH0iCiAFQv//z4rr///VHlQgAiAMVnKtIgJ9IQUgB0K/pZScz/DSu+QAfSIMIAZCpOzDtY/UtJjnAFQgAiAKVnKtIgJ9IQYgBELX2a6a5PbpjcsAfSIKIAdCv6WUnM/w0rvkAFQgAiAMVnKtIgd9IQIgCSAEQtfZrprk9umNywBUIAcgClZyrX1Cms3/y6O9xIAafSEJIAtC1aqBgICAwIDGAHwhCwwBCyAFIQMgBiEFIAchBgsgICALNwO4HCAgIAM3A7AcICAgBTcDqBwgICAGNwOgHCAgIAI3A5gcICAgCTcDkBwgIEHwHGoiJkIANwMAICZBKGpCADcDACAmQSBqQgA3AwAgJkEYakIANwMAICZBEGpCADcDACAmQQhqQgA3AwAgIEGwDGogMikDICIHQgAgMikDKCIGQgAQyQMgIEGADGogMikDGCIFQgAgBkIAEMkDICBBwAtqIDIpAxAiA0IAIAZCABDJAyAgQfAKaiAyKQMIIgRCACAGQgAQyQMgIEGQCmogMikDACICQgAgBkIAEMkDICBBkAxqIAVCACAHQgAQyQMgIEHQC2ogA0IAIAdCABDJAyAgQYALaiAEQgAgB0IAEMkDICBBoApqIAJCACAHQgAQyQMgIEHgC2ogA0IAIAVCABDJAyAgQZALaiAEQgAgBUIAEMkDICBBsApqIAJCACAFQgAQyQMgIEGgC2ogBEIAIANCABDJAyAgQcAKaiACQgAgA0IAEMkDICBB0ApqIAJCACAEQgAQyQMgIEGwDWogBkIAIAZCABDJAyAgQcAMaiAHQgAgB0IAEMkDICBBoAxqIAVCACAFQgAQyQMgIEHwC2ogA0IAIANCABDJAyAgQbALaiAEQgAgBEIAEMkDICBB4ApqIAJCACACQgAQyQMgIEGgDWogICkDsA0iH0L9//P/z///+Yl/fiICQgBCq9X+////v/+5f0IAEMkDICBBkA1qIAJCAEL//8+K6///1R5CABDJAyAgQYANaiACQgBCpOzDtY/UtJjnAEIAEMkDICBB8AxqIAJCAEK/pZScz/DSu+QAQgAQyQMgIEHgDGogAkIAQtfZrprk9umNywBCABDJAyAgQdAMaiACQgBCms3/y6O9xIAaQgAQyQMgICkD2AogICkDyAogICkDqAsgICkDmAsgICkD6AsgICkD2AsgICkDmAwgICkDiAwgICkDuAwiAiAgKQOADHwiDCACVK18IgIgICkDwAt8IgQgICkDkAx8IgogBFStfCIDICApA8gLIAIgBFatfCIEICApA/AKfCICfCIFIANUrXwgBSAFICApA9ALfCITVq18IgMgICkD+AogAiAEVK18IgUgICkDkAp8IgJ8IgcgICkDgAt8IgYgICkD4At8IgkgBlStfCIEIAYgB1StICApA4gLIAMgB1atfHwiAyAgKQOYCiACIAVUrXx8IgYgICkDoAp8IgJ8IgUgBFStfCAFIAUgICkDkAt8IhhWrXwiBCACIAZUrSAgKQOoCiADIAZWrXx8fCIFICApA7AKfCIDICApA6ALfCIZIANUrXwiAiADIAVUrSAgKQO4CiAEIAVWrXx8fCIEIAJUrXwgBCAEICApA8AKfCIXVq18IgIgICkD0Ap8IgsgAlStfCICQj+IICApA+gKIhYgICkD4AoiGiACQgGGIAtCP4iEfCIVIBpUrXwgFSAgKQO4CyIQICApA7ALIhsgF0IBhiAZQj+IhHwiByAbVK18IAcgICkD+AsiEiAgKQPwCyIcIBhCAYYgCUI/iIR8IgUgHFStfCAFIAUgICkDqAwiESAgKQOgDCIdIBNCAYYgCkI/iIR8IgMgHVStfCADIAMgICkDyAwiDyAgKQPADCIeIAxCAYYgICkDsAwiAkI/iIR8IgQgHlStfCAEIAQgICkDuA0iFCACQgGGfCINIBRUrXwiDlatfCICIApCAYYgDEI/iIR8IgwgAlStfCIKVq18IgIgCUIBhiATQj+IhHwiCSACVK18IgZWrXwiAiAZQgGGIBhCP4iEfCIFIAJUrXwiAyAHVK18IgIgC0IBhiAXQj+IhHwiCyACVK18IgIgFVStfHwhBEEAISQCfwJAICApA9gMICApA+gMICApA/gMICApA4gNICApA5gNICApA6gNICApA6ANIgcgH0J9g3wgB1StfCIHICApA5ANfCIVIAdUrXwgFSANIBV8IhVWrXwiByAgKQOADXwiDSAHVK18IA0gDnwiDiANVK18IgcgICkD8Ax8Ig0gB1StfCAMIA18IgwgDVStfCIHICApA+AMfCINIAdUrXwgCiANfCIKIA1UrXwiByAgKQPQDHwiDSAHVK18IAkgDXwiCSANVK18IgdQDQAgBiAHfCIGIAdUIiZFDQAgJq0iByAFfCIFIAdaDQAgBSAHVK0iByADfCIDIAdaDQAgAyAHVK0iByALfCILIAdaDQAgByALVq0iByACfCICIAdaDQAgAiAHVK0iByAEfCIEIAdUDAELQQALISogIEGACmogFUL9//P/z///+Yl/fiIHQgBCq9X+////v/+5f0IAEMkDICBB8AlqIAdCAEL//8+K6///1R5CABDJAyAgQeAJaiAHQgBCpOzDtY/UtJjnAEIAEMkDICBB0AlqIAdCAEK/pZScz/DSu+QAQgAQyQMgIEHACWogB0IAQtfZrprk9umNywBCABDJAyAgQbAJaiAHQgBCms3/y6O9xIAaQgAQyQMCQCAgKQO4CSAgKQPICSAgKQPYCSAgKQPoCSAgKQP4CSAgKQOICiAgKQOACiIHIBV8IAdUrXwiByAgKQPwCXwiFSAHVK18IBUgDiAVfCINVq18IgcgICkD4Al8Ig4gB1StfCAMIA58IgwgDlStfCIHICApA9AJfCIOIAdUrXwgCiAOfCIKIA5UrXwiByAgKQPACXwiDiAHVK18IAkgDnwiCSAOVK18IgcgICkDsAl8Ig4gB1StfCAOIAYgDnwiB1atfCIGUA0AIAUgBnwiBSAGWg0AIAUgBlStIgYgA3wiAyAGWg0AIAMgBlStIgYgC3wiCyAGWg0AIAYgC1atIgYgAnwiAiAGWg0AIAIgBlStIgYgBHwiBCAGVCEkCyAgQaAJaiANQv3/8//P///5iX9+IgZCAEKr1f7///+//7l/QgAQyQMgIEGQCWogBkIAQv//z4rr///VHkIAEMkDICBBgAlqIAZCAEKk7MO1j9S0mOcAQgAQyQMgIEHwCGogBkIAQr+llJzP8NK75ABCABDJAyAgQeAIaiAGQgBC19mumuT26Y3LAEIAEMkDICBB0AhqIAZCAEKazf/Lo73EgBpCABDJA0EAITACf0EAICApA9gIICApA+gIICApA/gIICApA4gJICApA5gJICApA6gJICApA6AJIgYgDXwgBlStfCIGICApA5AJfCINIAZUrXwgDSAMIA18Ig5WrXwiBiAgKQOACXwiDCAGVK18IAogDHwiCiAMVK18IgYgICkD8Ah8IgwgBlStfCAJIAx8IgkgDFStfCIGICApA+AIfCIMIAZUrXwgByAMfCIHIAxUrXwiBiAgKQPQCHwiDCAGVK18IAwgBSAMfCIGVq18IgVQDQAaQQAgBSADIAV8IgNYDQAaQQAgAyAFVK0iBSALfCILIAVaDQAaQQAgBSALVq0iBSACfCICIAVaDQAaIAIgBVStIgUgBHwiBCAFVAshJyAgQcAIaiAOQv3/8//P///5iX9+IgVCAEKr1f7///+//7l/QgAQyQMgIEGwCGogBUIAQv//z4rr///VHkIAEMkDICBBoAhqIAVCAEKk7MO1j9S0mOcAQgAQyQMgIEGQCGogBUIAQr+llJzP8NK75ABCABDJAyAgQYAIaiAFQgBC19mumuT26Y3LAEIAEMkDICBB8AdqIAVCAEKazf/Lo73EgBpCABDJAwJAICApA/gHICApA4gIICApA5gIICApA6gIICApA7gIICApA8gIICApA8AIIgUgDnwgBVStfCIFICApA7AIfCIOIAVUrXwgDiAKIA58IgxWrXwiBSAgKQOgCHwiCiAFVK18IAkgCnwiCSAKVK18IgUgICkDkAh8IgogBVStfCAHIAp8IgcgClStfCIFICApA4AIfCIKIAVUrXwgBiAKfCIGIApUrXwiBSAgKQPwB3wiCiAFVK18IAogAyAKfCIFVq18IgNQDQAgAyALfCILIANaDQAgAyALVq0iAyACfCICIANaDQAgAiADVK0iAyAEfCIEIANUITALICBB4AdqIAxC/f/z/8////mJf34iA0IAQqvV/v///7//uX9CABDJAyAgQdAHaiADQgBC///Piuv//9UeQgAQyQMgIEHAB2ogA0IAQqTsw7WP1LSY5wBCABDJAyAgQbAHaiADQgBCv6WUnM/w0rvkAEIAEMkDICBBoAdqIANCAELX2a6a5PbpjcsAQgAQyQMgIEGQB2ogA0IAQprN/8ujvcSAGkIAEMkDQQAhKyAgKQOYByAgKQOoByAgKQO4ByAgKQPIByAgKQPYByAgKQPoByAgKQPgByIDIAx8IANUrXwiAyAgKQPQB3wiCiADVK18IAkgCnwiDCAKVK18IgMgICkDwAd8IgkgA1StfCAHIAl8IgogCVStfCIDICApA7AHfCIHIANUrXwgBiAHfCIJIAdUrXwiAyAgKQOgB3wiBiADVK18IAYgBSAGfCIGVq18IgMgICkDkAd8IgUgA1StfCAFIAt8IgcgBVStfCIDUEUEQCACIAN8IgIgA1QiJq0iBSAEfCIDIAQgJhshBCAmIAMgBVRxISsLICBBgAdqIAxC/f/z/8////mJf34iA0IAQqvV/v///7//uX9CABDJAyAgQfAGaiADQgBC///Piuv//9UeQgAQyQMgIEHgBmogA0IAQqTsw7WP1LSY5wBCABDJAyAgQdAGaiADQgBCv6WUnM/w0rvkAEIAEMkDICBBwAZqIANCAELX2a6a5PbpjcsAQgAQyQMgIEGwBmogA0IAQprN/8ujvcSAGkIAEMkDICApA7gGICApA8gGICApA9gGICApA+gGICApA/gGICApA4gHICApA4AHIgMgDHwgA1StfCIDICApA/AGfCIFIANUrXwgBSAKfCILIAVUrXwiAyAgKQPgBnwiBSADVK18IAUgBSAJfCIFVq18IgMgICkD0AZ8IgkgA1StfCAGIAl8IgYgCVStfCIDICApA8AGfCIJIANUrXwgByAJfCIHIAlUrXwiAyAgKQOwBnwiCSADVK18IAIgCXwiAiAJVK18IgogBHwiAyAEIApCAFIiKBshCQJAAkACQCADIApUIiatIAogKBtQRQRAIAIhBAwBCyArICQgKnIgJ3IgMHJyBEAgAiEEDAELICYgKHEEQCACIQQMAQsgCUKazf/Lo73EgBpWBEAgAiEEDAELIAlCms3/y6O9xIAaUg0BIAJC19mumuT26Y3LAFYEQCACIQQMAQsgAkLX2a6a5PbpjcsAUg0BQtfZrprk9umNywAhBCAHQr+llJzP8NK75ABWDQAgB0K/pZScz/DSu+QAUg0BIAZCpOzDtY/UtJjnAFYNACAGQqTsw7WP1LSY5wBSDQEgBUL//8+K6///1R5WDQAgBUL//8+K6///1R5SIAtCqtX+////v/+5f1hyDQELIAVC///Piuv//9UefSIMIAtCq9X+////v/+5f1StIgJ9IQMgBkKk7MO1j9S0mOcAfSIKIAVC///Piuv//9UeVCACIAxWcq0iAn0hBSAHQr+llJzP8NK75AB9IgwgBkKk7MO1j9S0mOcAVCACIApWcq0iAn0hBiAEQtfZrprk9umNywB9IgogB0K/pZScz/DSu+QAVCACIAxWcq0iB30hAiAJIARC19mumuT26Y3LAFQgByAKVnKtfUKazf/Lo73EgBp9IQkgC0LVqoGAgIDAgMYAfCELDAELIAUhAyAGIQUgByEGCyAgIAs3A8gdICAgAzcDwB0gICAFNwO4HSAgIAY3A7AdICAgAjcDqB0gICAJNwOgHSAgQcAcaiInICBB8BxqIiggIEGgHWoiKhCyASAqICBBkBxqIiYgJxC9AiAmICogLxCyASAoQvP/s4CAgMCTqn83AyggKEKKgNDhr4aA5tMANwMgIChC/4Cq2Kav+sfHADcDGCAoQtfJ6LXu19/psX83AxAgKEKv1uL7u+fc5I5/NwMIIChC/ryP7JOqkesJNwMAICBBoAZqIDIpAyAiB0IAIDIpAygiBkIAEMkDICBBgAZqIDIpAxgiBUIAIAZCABDJAyAgQdAFaiAyKQMQIgNCACAGQgAQyQMgIEGQBWogMikDCCIEQgAgBkIAEMkDICBBwARqIDIpAwAiAkIAIAZCABDJAyAgQZAGaiAFQgAgB0IAEMkDICBB4AVqIANCACAHQgAQyQMgIEGgBWogBEIAIAdCABDJAyAgQdAEaiACQgAgB0IAEMkDICBB8AVqIANCACAFQgAQyQMgIEGwBWogBEIAIAVCABDJAyAgQeAEaiACQgAgBUIAEMkDICBBwAVqIARCACADQgAQyQMgIEHwBGogAkIAIANCABDJAyAgQYAFaiACQgAgBEIAEMkDICBBsARqIB9C/f/z/8////mJf34iAkIAQqvV/v///7//uX9CABDJAyAgQaAEaiACQgBC///Piuv//9UeQgAQyQMgIEGQBGogAkIAQqTsw7WP1LSY5wBCABDJAyAgQYAEaiACQgBCv6WUnM/w0rvkAEIAEMkDICBB8ANqIAJCAELX2a6a5PbpjcsAQgAQyQMgIEHgA2ogAkIAQprN/8ujvcSAGkIAEMkDICApA4gFICApA/gEICApA8gFICApA7gFICApA/gFICApA+gFICApA5gGICApA4gGICApA6gGIgIgICkDgAZ8IgwgAlStfCICICApA9AFfCIEICApA5AGfCIKIARUrXwiAyAgKQPYBSACIARWrXwiBCAgKQOQBXwiAnwiBSADVK18IAUgBSAgKQPgBXwiE1atfCIDICApA5gFIAIgBFStfCIFICApA8AEfCICfCIHICApA6AFfCIGICApA/AFfCIJIAZUrXwiBCAGIAdUrSAgKQOoBSADIAdWrXx8IgMgICkDyAQgAiAFVK18fCIGICApA9AEfCICfCIFIARUrXwgBSAFICApA7AFfCIYVq18IgQgAiAGVK0gICkD2AQgAyAGVq18fHwiBSAgKQPgBHwiAyAgKQPABXwiGSADVK18IgIgAyAFVK0gICkD6AQgBCAFVq18fHwiBCACVK18IAQgBCAgKQPwBHwiF1atfCICICApA4AFfCILIAJUrXwiAkI/iCAWIBogGiACQgGGIAtCP4iEfCIVVq18IBUgECAbIBsgF0IBhiAZQj+IhHwiB1atfCAHIBIgHCAYQgGGIAlCP4iEfCIFIBxUrXwgBSAFIBEgHSATQgGGIApCP4iEfCIDIB1UrXwgAyADIA8gHiAMQgGGICApA6AGIgJCP4iEfCIEIB5UrXwgBCAEIBQgAkIBhnwiDSAUVK18Ig5WrXwiAiAKQgGGIAxCP4iEfCIMIAJUrXwiClatfCICIAlCAYYgE0I/iIR8IgkgAlStfCIGVq18IgIgGUIBhiAYQj+IhHwiBSACVK18IgMgB1StfCICIAtCAYYgF0I/iIR8IgsgAlStfCICIBVUrXx8IQRBACEwAn8CQCAgKQPoAyAgKQP4AyAgKQOIBCAgKQOYBCAgKQOoBCAgKQO4BCAgKQOwBCIHIB9CfYN8IAdUrXwiByAgKQOgBHwiDyAHVK18IA8gDSAPfCIPVq18IgcgICkDkAR8Ig0gB1StfCANIA58Ig4gDVStfCIHICApA4AEfCINIAdUrXwgDCANfCIMIA1UrXwiByAgKQPwA3wiDSAHVK18IAogDXwiCiANVK18IgcgICkD4AN8Ig0gB1StfCAJIA18IgkgDVStfCIHUA0AIAYgB3wiBiAHVCImRQ0AICatIgcgBXwiBSAHWg0AIAUgB1StIgcgA3wiAyAHWg0AIAMgB1StIgcgC3wiCyAHWg0AIAcgC1atIgcgAnwiAiAHWg0AIAIgB1StIgcgBHwiBCAHVAwBC0EACyEqICBB0ANqIA9C/f/z/8////mJf34iB0IAQqvV/v///7//uX9CABDJAyAgQcADaiAHQgBC///Piuv//9UeQgAQyQMgIEGwA2ogB0IAQqTsw7WP1LSY5wBCABDJAyAgQaADaiAHQgBCv6WUnM/w0rvkAEIAEMkDICBBkANqIAdCAELX2a6a5PbpjcsAQgAQyQMgIEGAA2ogB0IAQprN/8ujvcSAGkIAEMkDAkAgICkDiAMgICkDmAMgICkDqAMgICkDuAMgICkDyAMgICkD2AMgICkD0AMiByAPfCAHVK18IgcgICkDwAN8Ig8gB1StfCAPIA4gD3wiDVatfCIHICApA7ADfCIOIAdUrXwgDCAOfCIMIA5UrXwiByAgKQOgA3wiDiAHVK18IAogDnwiCiAOVK18IgcgICkDkAN8Ig4gB1StfCAJIA58IgkgDlStfCIHICApA4ADfCIOIAdUrXwgDiAGIA58IgdWrXwiBlANACAFIAZ8IgUgBloNACAFIAZUrSIGIAN8IgMgBloNACADIAZUrSIGIAt8IgsgBloNACAGIAtWrSIGIAJ8IgIgBloNACACIAZUrSIGIAR8IgQgBlQhMAsgIEHwAmogDUL9//P/z///+Yl/fiIGQgBCq9X+////v/+5f0IAEMkDICBB4AJqIAZCAEL//8+K6///1R5CABDJAyAgQdACaiAGQgBCpOzDtY/UtJjnAEIAEMkDICBBwAJqIAZCAEK/pZScz/DSu+QAQgAQyQMgIEGwAmogBkIAQtfZrprk9umNywBCABDJAyAgQaACaiAGQgBCms3/y6O9xIAaQgAQyQNBACErAn9BACAgKQOoAiAgKQO4AiAgKQPIAiAgKQPYAiAgKQPoAiAgKQP4AiAgKQPwAiIGIA18IAZUrXwiBiAgKQPgAnwiDSAGVK18IA0gDCANfCIOVq18IgYgICkD0AJ8IgwgBlStfCAKIAx8IgogDFStfCIGICApA8ACfCIMIAZUrXwgCSAMfCIJIAxUrXwiBiAgKQOwAnwiDCAGVK18IAcgDHwiByAMVK18IgYgICkDoAJ8IgwgBlStfCAMIAUgDHwiBlatfCIFUA0AGkEAIAUgAyAFfCIDWA0AGkEAIAMgBVStIgUgC3wiCyAFWg0AGkEAIAUgC1atIgUgAnwiAiAFWg0AGiACIAVUrSIFIAR8IgQgBVQLIScgIEGQAmogDkL9//P/z///+Yl/fiIFQgBCq9X+////v/+5f0IAEMkDICBBgAJqIAVCAEL//8+K6///1R5CABDJAyAgQfABaiAFQgBCpOzDtY/UtJjnAEIAEMkDICBB4AFqIAVCAEK/pZScz/DSu+QAQgAQyQMgIEHQAWogBUIAQtfZrprk9umNywBCABDJAyAgQcABaiAFQgBCms3/y6O9xIAaQgAQyQMCQCAgKQPIASAgKQPYASAgKQPoASAgKQP4ASAgKQOIAiAgKQOYAiAgKQOQAiIFIA58IAVUrXwiBSAgKQOAAnwiDiAFVK18IA4gCiAOfCIMVq18IgUgICkD8AF8IgogBVStfCAJIAp8IgkgClStfCIFICApA+ABfCIKIAVUrXwgByAKfCIHIApUrXwiBSAgKQPQAXwiCiAFVK18IAYgCnwiBiAKVK18IgUgICkDwAF8IgogBVStfCAKIAMgCnwiBVatfCIDUA0AIAMgC3wiCyADWg0AIAMgC1atIgMgAnwiAiADWg0AIAIgA1StIgMgBHwiBCADVCErCyAgQbABaiAMQv3/8//P///5iX9+IgNCAEKr1f7///+//7l/QgAQyQMgIEGgAWogA0IAQv//z4rr///VHkIAEMkDICBBkAFqIANCAEKk7MO1j9S0mOcAQgAQyQMgIEGAAWogA0IAQr+llJzP8NK75ABCABDJAyAgQfAAaiADQgBC19mumuT26Y3LAEIAEMkDICBB4ABqIANCAEKazf/Lo73EgBpCABDJA0EAISQgICkDaCAgKQN4ICApA4gBICApA5gBICApA6gBICApA7gBICApA7ABIgMgDHwgA1StfCIDICApA6ABfCIKIANUrXwgCSAKfCIMIApUrXwiAyAgKQOQAXwiCSADVK18IAcgCXwiCiAJVK18IgMgICkDgAF8IgcgA1StfCAGIAd8IgkgB1StfCIDICApA3B8IgYgA1StfCAGIAUgBnwiBlatfCIDICApA2B8IgUgA1StfCAFIAt8IgcgBVStfCIDUEUEQCACIAN8IgIgA1QiJq0iBSAEfCIDIAQgJhshBCAmIAMgBVRxISQLICBB0ABqIAxC/f/z/8////mJf34iA0IAQqvV/v///7//uX9CABDJAyAgQUBrIANCAEL//8+K6///1R5CABDJAyAgQTBqIANCAEKk7MO1j9S0mOcAQgAQyQMgIEEgaiADQgBCv6WUnM/w0rvkAEIAEMkDICBBEGogA0IAQtfZrprk9umNywBCABDJAyAgIANCAEKazf/Lo73EgBpCABDJAyAgKQMIICApAxggICkDKCAgKQM4ICApA0ggICkDWCAgKQNQIgMgDHwgA1StfCIDICApA0B8IgUgA1StfCAFIAp8IgsgBVStfCIDICApAzB8IgUgA1StfCAFIAUgCXwiBVatfCIDICApAyB8IgkgA1StfCAGIAl8IgYgCVStfCIDICApAxB8IgkgA1StfCAHIAl8IgcgCVStfCIDICApAwB8IgkgA1StfCACIAl8IgIgCVStfCIKIAR8IgMgBCAKQgBSIigbIQkCQAJAAkAgAyAKVCImrSAKICgbUEUEQCACIQQMAQsgKiAwciAnciArciAkcgRAIAIhBAwBCyAmIChxBEAgAiEEDAELIAlCms3/y6O9xIAaVgRAIAIhBAwBCyAJQprN/8ujvcSAGlINASACQtfZrprk9umNywBWBEAgAiEEDAELIAJC19mumuT26Y3LAFINAULX2a6a5PbpjcsAIQQgB0K/pZScz/DSu+QAVg0AIAdCv6WUnM/w0rvkAFINASAGQqTsw7WP1LSY5wBWDQAgBkKk7MO1j9S0mOcAUg0BIAVC///Piuv//9UeVg0AIAVC///Piuv//9UeUiALQqrV/v///7//uX9Ycg0BCyAFQv//z4rr///VHn0iDCALQqvV/v///7//uX9UrSICfSEDIAZCpOzDtY/UtJjnAH0iCiAFQv//z4rr///VHlQgAiAMVnKtIgJ9IQUgB0K/pZScz/DSu+QAfSIMIAZCpOzDtY/UtJjnAFQgAiAKVnKtIgJ9IQYgBELX2a6a5PbpjcsAfSIKIAdCv6WUnM/w0rvkAFQgAiAMVnKtIgd9IQIgCSAEQtfZrprk9umNywBUIAcgClZyrX1Cms3/y6O9xIAafSEJIAtC1aqBgICAwIDGAHwhCwwBCyAFIQMgBiEFIAchBgsgICALNwPIHSAgIAM3A8AdICAgBTcDuB0gICAGNwOwHSAgIAI3A6gdICAgCTcDoB0gIEHAHGoiJiAgQfAcaiIqICBBoB1qIicQsgEgJyAmIDIQsgEgKiAgQZAcaiAnEL0CIDEgIEHgG2ogKhCDAiAgQdAdaiQAIDFB2LPCAEEwEPEDRQ0BC0IBIQggL0HYs8IAQTAQ8QMNASAyQdizwgBBMBDxAw0BQgAhCCAxQdgAakIANwMAIDFB0ABqQgA3AwAgMUHIAGpCADcDACAxQUBrQgA3AwAgMUE4akIANwMAIDFB6ABqQcC0wgApAwA3AwAgMUHwAGpByLTCACkDADcDACAxQfgAakHQtMIAKQMANwMAIDFBgAFqQdi0wgApAwA3AwAgMUGIAWpB4LTCACkDADcDACAxQgA3AzAgMUG4tMIAKQMANwNgIDFBuAFqQgA3AwAgMUGwAWpCADcDACAxQagBakIANwMAIDFBoAFqQgA3AwAgMUGYAWpCADcDACAxQgA3A5ABICVBCGogMUEwakGQAfwKAAAMAQsgJUEIaiAvQZAB/AoAAAsgJSAINwMAIDFBwAFqJAACQAJAICEoAqAjQQFGBEAgIUEBNgKkICAhQaCLwQA2AqAgICFCATcCrCAgISAhQa8saq1CgICAgNAEhDcD8BQgISAhQfAUajYCqCAgIUHYG2ogLxDSAiAhQfgJaiAhQeAbaigCADYCACAhICEpAtgbIgI3A5AXICEgAjcD8AkMAQsgIUHcG2oiJyAhQagjakGQAfwKAAAgIUGUF2oiJiAnQZAB/AoAACAhQeATaiAmQZAB/AoAACAhQYAhaiAAQeAAakHgAPwKAAAgIUH4ImpCADcDACAhQYAjakIANwMAICFBiCNqQgA3AwAgIUGQI2pCADcDACAhQZgjakIANwMAICFB6CJqQcj/wAApAwA3AwAgIUHgImpBwP/AACkDADcDACAhQdgiakG4/8AAKQMANwMAICFB0CJqQbD/wAApAwA3AwAgIUHIImpBqP/AACkDADcDACAhQgA3A/AiICFBoP/AACkDADcDwCIgIUGgIGoiJiAAQeAA/AoAACAhQeAhaiAhQcAiakHgAPwKAAAgIUGgI2ogJhCZAiAhKAKgI0EBRgRAICFBATYCpCAgIUGgi8EANgKgICAhQgE3AqwgICEgIUGvLGqtQoCAgIDQBIQ3A/grICEgIUH4K2o2AqggICFB2BtqICYQ0gIgIUH4CWogIUHgG2ooAgA2AgAgISAhKQLYGyICNwOQFyAhIAI3A/AJDAELICFB3BtqIgAgIUGoI2pBoAL8CgAAICFBlBdqIiYgAEGgAvwKAAAgIUHwFGoiACAmQaAC/AoAACAhIAA2AswpICEgIUHgE2o2AsgpIwBB8BBrIiokACAqQdgMakHwocUAKQMANwMAICpB0AxqQeihxQApAwA3AwAgKkHIDGpB4KHFACkDADcDACAqQcAMakHYocUAKQMANwMAICpBuAxqQdChxQApAwA3AwAgKkHoDGpCADcDACAqQfAMakIANwMAICpB+AxqQgA3AwAgKkGADWpCADcDACAqQYgNakIANwMAICpByKHFACkDADcDsAwgKkIANwPgDCAqQeAAakEAQcAB/AsAICogKkGwDGpB4AD8CgAAICpBoAJqQQBBoAL8CwAgIUGgI2oiXQJ/ICFByClqIidBCGohRiAqQeAMaiFHAkADQCAnKAIAIjUhJkEAITAjAEGQBmsiJSQAICVB2AJqIgAgJhD6ASAlQcgBaiAAEPoBAn4gJUH4AWpBwI3FAEEwEPEDBEBC///Piuv//9UeICUpA5gCIgZ9IgUgJSkDoAIiCEKr1f7///+//7l/Vq0iAn0hC0Kk7MO1j9S0mOcAICUpA5ACIgN9IgQgAiAFViAGQv//z4rr///VHlZyrSICfSEKQr+llJzP8NK75AAgJSkDiAIiBn0iBSACIARWIANCpOzDtY/UtJjnAFZyrSICfSEJQtfZrprk9umNywAgJSkDgAIiA30iBCACIAVWIAZCv6WUnM/w0rvkAFZyrSICfSEHQprN/8ujvcSAGiAlKQP4ASACIARWIANC19mumuT26Y3LAFZyrXx9IQZCq9X+////v/+5fyAIfQwBCyAlKQOYAiELICUpA5ACIQogJSkDiAIhCSAlKQOAAiEHICUpA/gBIQYgJSkDoAILIQIgJUGIBmogJUHQAmopAwA3AwAgJUGABmogJUHIAmopAwA3AwAgJUH4BWogJUHAAmopAwA3AwAgJUHwBWogJUG4AmopAwA3AwAgJUHoBWogJUGwAmopAwA3AwAgJUGIBWogJUHQAWopAwA3AwAgJUGQBWogJUHYAWopAwA3AwAgJUGYBWogJUHgAWopAwA3AwAgJUGgBWogJUHoAWopAwA3AwAgJUGoBWogJUHwAWopAwA3AwAgJSAlKQOoAjcD4AUgJSAlKQPIATcDgAUgJSACNwPYBSAlIAs3A9AFICUgCjcDyAUgJSAJNwPABSAlIAc3A7gFICUgBjcDsAUgJUHoA2ogJUGABWoiABDyAgJAAkACQCAlKALoA0EBRwRAIAAgJUHwA2pBkAH8CgAAICYpA4gBIRwgJikDgAEhHSAmKQN4IR4gJikDcCEUICYpA2ghEyAmKQNgIRggJikDWCEZICYpA1AhFyAmKQNIIRUgJikDQCEWICYpAzghECAmKQMwIRIgJikDKCERICYpAyAhDyAmKQMYIQ0gJikDECEOICYpAwghDCAmKQMAIQtBKCEAQgAhCkIAIQJCACEDQgAhBkIAIQdCACEJA0AgJUHgAGogAEHwjcUAaikDACIEQgAgEUIAEMkDICVB8ABqIARCACAPQgAQyQMgJUGAAWogBEIAIA1CABDJAyAlQZABaiAEQgAgDkIAEMkDICVBoAFqIARCACAMQgAQyQMgJUGwAWogBEIAIAtCABDJAyAlQdAAaiAlKQNgIgggCnwiCkL9//P/z///+Yl/fiIEQgBCq9X+////v/+5f0IAEMkDICVBQGsgBEIAQv//z4rr///VHkIAEMkDICVBMGogBEIAQqTsw7WP1LSY5wBCABDJAyAlQSBqIARCAEK/pZScz/DSu+QAQgAQyQMgJUEQaiAEQgBC19mumuT26Y3LAEIAEMkDICUgBEIAQprN/8ujvcSAGkIAEMkDICUpAwggCSAlKQOwASIFfCIaICUpA6gBIAcgJSkDoAEiBHwiCSAEVK18IAkgJSkDmAEgJSkDkAEiBCAGfCIGIARUrXwgBiAlKQOIASAlKQOAASIEIAN8IgMgBFStfCADICUpA3ggAiAlKQNwIgJ8IgQgAlStfCAEIAQgJSkDaCAIIApWrXx8IgRWrXx8IgcgA1StfHwiAyAGVK18fCICIAlUrXx8IhsgJSkDAHwiCSAbVK18IAkgCSAlKQMYIAIgJSkDEHwiCCACVK18IAggCCAlKQMoIAMgAyAlKQMgfCIGVq18IAYgBiAlKQM4IAcgByAlKQMwfCIDVq18IAMgAyAlKQNIIAQgJSkDQCICfCIEIAJUrXwgBCAlKQNYIAogJSkDUCICfCACVK18fCIKIARUrXx8IgJWrXx8IgNWrXx8IgZWrXx8IgdWrXwgGiAbVq0gJSkDuAEgBSAaVq18fHwhCSAAQQhrIgBBeEcNAAsgCUKazf/Lo73EgBpWDQIgCUKazf/Lo73EgBpRDQEgAiEEIAMhBSAGIQggByELDAMLQZCNxQBBKyAlQYAFakGAjcUAQdCSxQAQygMACyAHQtfZrprk9umNywBWDQACQCAHQtfZrprk9umNywBSBEAgAiEEIAMhBSAGIQggByELDAELIAZCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIQsgBkK/pZScz/DSu+QAUgRAIAIhBCADIQUgBiEIDAELIANCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQggA0Kk7MO1j9S0mOcAUgRAIAIhBCADIQUMAQsgAkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEFIAJC///Piuv//9UeUgRAIAIhBAwBC0L//8+K6///1R4hBCAKQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEJDAELIAJC///Piuv//9UefSILIApCq9X+////v/+5f1StIgV9IQQgA0Kk7MO1j9S0mOcAfSIIIAJC///Piuv//9UeVCAFIAtWcq0iAn0hBSAGQr+llJzP8NK75AB9IgsgA0Kk7MO1j9S0mOcAVCACIAhWcq0iAn0hCCAHQtfZrprk9umNywB9IgMgBkK/pZScz/DSu+QAVCACIAtWcq0iAn0hCyAJIAdC19mumuT26Y3LAFQgAiADVnKtfUKazf/Lo73EgBp9IQkgCkLVqoGAgIDAgMYAfCEKCyAlIBw3A/AEICUgHTcD6AQgJSAeNwPgBCAlIBQ3A9gEICUgEzcD0AQgJSAYNwPIBCAlIBk3A8AEICUgFzcDuAQgJSAVNwOwBCAlIBY3A6gEICUgEDcDoAQgJSASNwOYBCAlIAo3A5AEICUgBDcDiAQgJSAFNwOABCAlIAg3A/gDICUgCzcD8AMgJSAJNwPoA0IAIQJCACEDQgAhB0IAIQZCACEJQgAhCiMAQeAGayIkJAAgJUHoA2oiJkGIAWohACAlQYAFaiIoKQMAIREgKCkDCCEPICgpAxAhDSAoKQMYIQ4gKCkDICEMICgpAyghCwNAICRBoAVqIAAgMGopAwAiBEIAIAtCABDJAyAkQbAFaiAEQgAgDEIAEMkDICRBwAVqIARCACAOQgAQyQMgJEHQBWogBEIAIA1CABDJAyAkQeAFaiAEQgAgD0IAEMkDICRB8AVqIARCACARQgAQyQMgJEGQBWogJCkDoAUiCCAKfCIKQv3/8//P///5iX9+IgRCAEKr1f7///+//7l/QgAQyQMgJEGABWogBEIAQv//z4rr///VHkIAEMkDICRB8ARqIARCAEKk7MO1j9S0mOcAQgAQyQMgJEHgBGogBEIAQr+llJzP8NK75ABCABDJAyAkQdAEaiAEQgBC19mumuT26Y3LAEIAEMkDICRBwARqIARCAEKazf/Lo73EgBpCABDJAyAkKQPIBCAJICQpA/AFIgV8IhAgJCkD6AUgByAkKQPgBSIEfCIJIARUrXwgCSAkKQPYBSAkKQPQBSIEIAZ8IgYgBFStfCAGICQpA8gFICQpA8AFIgQgA3wiAyAEVK18IAMgJCkDuAUgAiAkKQOwBSICfCIEIAJUrXwgBCAEICQpA6gFIAggClatfHwiBFatfHwiByADVK18fCIDIAZUrXx8IgIgCVStfHwiEiAkKQPABHwiCSASVK18IAkgCSAkKQPYBCACIAIgJCkD0AR8IghWrXwgCCAIICQpA+gEIAMgAyAkKQPgBHwiBlatfCAGIAYgJCkD+AQgByAHICQpA/AEfCIDVq18IAMgAyAkKQOIBSAEICQpA4AFIgJ8IgQgAlStfCAEICQpA5gFIAogJCkDkAUiAnwgAlStfHwiCiAEVK18fCICVq18fCIDVq18fCIGVq18fCIHVq18IBAgElatICQpA/gFIAUgEFatfHx8IQkgMEEIayIwQVBHDQALAkACQCAJQprN/8ujvcSAGlYNACAJQprN/8ujvcSAGlIEQCACIQQgAyEFIAYhCCAHIQsMAgsgB0LX2a6a5PbpjcsAVg0AAkAgB0LX2a6a5PbpjcsAUgRAIAIhBCADIQUgBiEIIAchCwwBCyAGQr+llJzP8NK75ABWDQFC19mumuT26Y3LACELIAZCv6WUnM/w0rvkAFIEQCACIQQgAyEFIAYhCAwBCyADQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEIIANCpOzDtY/UtJjnAFIEQCACIQQgAyEFDAELIAJC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhBSACQv//z4rr///VHlIEQCACIQQMAQtC///Piuv//9UeIQQgCkKq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohCQwBCyACQv//z4rr///VHn0iCyAKQqvV/v///7//uX9UrSIFfSEEIANCpOzDtY/UtJjnAH0iCCACQv//z4rr///VHlQgBSALVnKtIgJ9IQUgBkK/pZScz/DSu+QAfSILIANCpOzDtY/UtJjnAFQgAiAIVnKtIgJ9IQggB0LX2a6a5PbpjcsAfSIDIAZCv6WUnM/w0rvkAFQgAiALVnKtIgJ9IQsgCSAHQtfZrprk9umNywBUIAIgA1ZyrX1Cms3/y6O9xIAafSEJIApC1aqBgICAwIDGAHwhCgsgJCAKNwOoBiAkIAQ3A6AGICQgBTcDmAYgJCAINwOQBiAkIAs3A4gGICQgCTcDgAYgKCkDYCERICgpA2ghDyAoKQNwIQ0gKCkDeCEOICgpA4ABIQwgKCkDiAEhC0EoITBCACEJQgAhB0IAIQZCACEDQgAhAkIAIQoDQCAkQeADaiAmIDBqKQMAIgRCACALQgAQyQMgJEHwA2ogBEIAIAxCABDJAyAkQYAEaiAEQgAgDkIAEMkDICRBkARqIARCACANQgAQyQMgJEGgBGogBEIAIA9CABDJAyAkQbAEaiAEQgAgEUIAEMkDICRB0ANqICQpA+ADIgggCnwiCkL9//P/z///+Yl/fiIEQgBCq9X+////v/+5f0IAEMkDICRBwANqIARCAEL//8+K6///1R5CABDJAyAkQbADaiAEQgBCpOzDtY/UtJjnAEIAEMkDICRBoANqIARCAEK/pZScz/DSu+QAQgAQyQMgJEGQA2ogBEIAQtfZrprk9umNywBCABDJAyAkQYADaiAEQgBCms3/y6O9xIAaQgAQyQMgJCkDiAMgCSAkKQOwBCIFfCIQICQpA6gEIAcgJCkDoAQiBHwiCSAEVK18IAkgJCkDmAQgJCkDkAQiBCAGfCIGIARUrXwgBiAkKQOIBCAkKQOABCIEIAN8IgMgBFStfCADICQpA/gDIAIgJCkD8AMiAnwiBCACVK18IAQgBCAkKQPoAyAIIApWrXx8IgRWrXx8IgcgA1StfHwiAyAGVK18fCICIAlUrXx8IhIgJCkDgAN8IgkgElStfCAJIAkgJCkDmAMgAiACICQpA5ADfCIIVq18IAggCCAkKQOoAyADIAMgJCkDoAN8IgZWrXwgBiAGICQpA7gDIAcgByAkKQOwA3wiA1atfCADIAMgJCkDyAMgBCAkKQPAAyICfCIEIAJUrXwgBCAkKQPYAyAKICQpA9ADIgJ8IAJUrXx8IgogBFStfHwiAlatfHwiA1atfHwiBlatfHwiB1atfCAQIBJWrSAkKQO4BCAFIBBWrXx8fCEJIDBBCGsiMEF4Rw0ACwJAAkAgCUKazf/Lo73EgBpWDQAgCUKazf/Lo73EgBpSBEAgAiEEIAMhBSAGIQggByELDAILIAdC19mumuT26Y3LAFYNAAJAIAdC19mumuT26Y3LAFIEQCACIQQgAyEFIAYhCCAHIQsMAQsgBkK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhCyAGQr+llJzP8NK75ABSBEAgAiEEIAMhBSAGIQgMAQsgA0Kk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhCCADQqTsw7WP1LSY5wBSBEAgAiEEIAMhBQwBCyACQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIQUgAkL//8+K6///1R5SBEAgAiEEDAELQv//z4rr///VHiEEIApCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQkMAQsgAkL//8+K6///1R59IgsgCkKr1f7///+//7l/VK0iBX0hBCADQqTsw7WP1LSY5wB9IgggAkL//8+K6///1R5UIAUgC1ZyrSICfSEFIAZCv6WUnM/w0rvkAH0iCyADQqTsw7WP1LSY5wBUIAIgCFZyrSICfSEIIAdC19mumuT26Y3LAH0iAyAGQr+llJzP8NK75ABUIAIgC1ZyrSICfSELIAkgB0LX2a6a5PbpjcsAVCACIANWcq19QprN/8ujvcSAGn0hCSAKQtWqgYCAgMCAxgB8IQoLICQgCjcD2AYgJCAENwPQBiAkIAU3A8gGICQgCDcDwAYgJCALNwO4BiAkIAk3A7AGQQAhMCAkQYAGaiAkQbAGakEwEPEDRQRAICZBiAFqIQAgKCkDMCERICgpAzghDyAoKQNAIQ0gKCkDSCEOICgpA1AhDCAoKQNYIQtCACEKQgAhAkIAIQNCACEGQgAhB0IAIQkDQCAkQaACaiAAIDBqKQMAIgRCACALQgAQyQMgJEGwAmogBEIAIAxCABDJAyAkQcACaiAEQgAgDkIAEMkDICRB0AJqIARCACANQgAQyQMgJEHgAmogBEIAIA9CABDJAyAkQfACaiAEQgAgEUIAEMkDICRBkAJqICQpA6ACIgggCnwiCkL9//P/z///+Yl/fiIEQgBCq9X+////v/+5f0IAEMkDICRBgAJqIARCAEL//8+K6///1R5CABDJAyAkQfABaiAEQgBCpOzDtY/UtJjnAEIAEMkDICRB4AFqIARCAEK/pZScz/DSu+QAQgAQyQMgJEHQAWogBEIAQtfZrprk9umNywBCABDJAyAkQcABaiAEQgBCms3/y6O9xIAaQgAQyQMgJCkDyAEgCSAkKQPwAiIFfCIQICQpA+gCIAcgJCkD4AIiBHwiCSAEVK18IAkgJCkD2AIgJCkD0AIiBCAGfCIGIARUrXwgBiAkKQPIAiAkKQPAAiIEIAN8IgMgBFStfCADICQpA7gCIAIgJCkDsAIiAnwiBCACVK18IAQgBCAkKQOoAiAIIApWrXx8IgRWrXx8IgcgA1StfHwiAyAGVK18fCICIAlUrXx8IhIgJCkDwAF8IgkgElStfCAJIAkgJCkD2AEgAiACICQpA9ABfCIIVq18IAggCCAkKQPoASADIAMgJCkD4AF8IgZWrXwgBiAGICQpA/gBIAcgByAkKQPwAXwiA1atfCADIAMgJCkDiAIgBCAkKQOAAiICfCIEIAJUrXwgBCAkKQOYAiAKICQpA5ACIgJ8IAJUrXx8IgogBFStfHwiAlatfHwiA1atfHwiBlatfHwiB1atfCAQIBJWrSAkKQP4AiAFIBBWrXx8fCEJIDBBCGsiMEFQRw0ACwJAAkAgCUKazf/Lo73EgBpWDQAgCUKazf/Lo73EgBpSBEAgAiEEIAMhBSAGIQggByELDAILIAdC19mumuT26Y3LAFYNAAJAIAdC19mumuT26Y3LAFIEQCACIQQgAyEFIAYhCCAHIQsMAQsgBkK/pZScz/DSu+QAVg0BQtfZrprk9umNywAhCyAGQr+llJzP8NK75ABSBEAgAiEEIAMhBSAGIQgMAQsgA0Kk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhCCADQqTsw7WP1LSY5wBSBEAgAiEEIAMhBQwBCyACQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIQUgAkL//8+K6///1R5SBEAgAiEEDAELQv//z4rr///VHiEEIApCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQkMAQsgAkL//8+K6///1R59IgsgCkKr1f7///+//7l/VK0iBX0hBCADQqTsw7WP1LSY5wB9IgggAkL//8+K6///1R5UIAUgC1ZyrSICfSEFIAZCv6WUnM/w0rvkAH0iCyADQqTsw7WP1LSY5wBUIAIgCFZyrSICfSEIIAdC19mumuT26Y3LAH0iAyAGQr+llJzP8NK75ABUIAIgC1ZyrSICfSELIAkgB0LX2a6a5PbpjcsAVCACIANWcq19QprN/8ujvcSAGn0hCSAKQtWqgYCAgMCAxgB8IQoLICQgCjcDqAYgJCAENwOgBiAkIAU3A5gGICQgCDcDkAYgJCALNwOIBiAkIAk3A4AGIChBiAFqIQAgJikDMCERICYpAzghDyAmKQNAIQ0gJikDSCEOICYpA1AhDCAmKQNYIQtBACEwQgAhCkIAIQJCACEDQgAhBkIAIQdCACEJA0AgJEHgAGogACAwaikDACIEQgAgC0IAEMkDICRB8ABqIARCACAMQgAQyQMgJEGAAWogBEIAIA5CABDJAyAkQZABaiAEQgAgDUIAEMkDICRBoAFqIARCACAPQgAQyQMgJEGwAWogBEIAIBFCABDJAyAkQdAAaiAkKQNgIgggCnwiCkL9//P/z///+Yl/fiIEQgBCq9X+////v/+5f0IAEMkDICRBQGsgBEIAQv//z4rr///VHkIAEMkDICRBMGogBEIAQqTsw7WP1LSY5wBCABDJAyAkQSBqIARCAEK/pZScz/DSu+QAQgAQyQMgJEEQaiAEQgBC19mumuT26Y3LAEIAEMkDICQgBEIAQprN/8ujvcSAGkIAEMkDICQpAwggCSAkKQOwASIFfCIQICQpA6gBIAcgJCkDoAEiBHwiCSAEVK18IAkgJCkDmAEgJCkDkAEiBCAGfCIGIARUrXwgBiAkKQOIASAkKQOAASIEIAN8IgMgBFStfCADICQpA3ggAiAkKQNwIgJ8IgQgAlStfCAEIAQgJCkDaCAIIApWrXx8IgRWrXx8IgcgA1StfHwiAyAGVK18fCICIAlUrXx8IhIgJCkDAHwiCSASVK18IAkgCSAkKQMYIAIgAiAkKQMQfCIIVq18IAggCCAkKQMoIAMgAyAkKQMgfCIGVq18IAYgBiAkKQM4IAcgByAkKQMwfCIDVq18IAMgAyAkKQNIIAQgJCkDQCICfCIEIAJUrXwgBCAkKQNYIAogJCkDUCICfCACVK18fCIKIARUrXx8IgJWrXx8IgNWrXx8IgZWrXx8IgdWrXwgECASVq0gJCkDuAEgBSAQVq18fHwhCSAwQQhrIjBBUEcNAAsCQAJAIAlCms3/y6O9xIAaVg0AIAlCms3/y6O9xIAaUgRAIAIhBCADIQUgBiEIIAchCwwCCyAHQtfZrprk9umNywBWDQACQCAHQtfZrprk9umNywBSBEAgAiEEIAMhBSAGIQggByELDAELIAZCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIQsgBkK/pZScz/DSu+QAUgRAIAIhBCADIQUgBiEIDAELIANCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQggA0Kk7MO1j9S0mOcAUgRAIAIhBCADIQUMAQsgAkL//8+K6///1R5WDQFCpOzDtY/UtJjnACEFIAJC///Piuv//9UeUgRAIAIhBAwBC0L//8+K6///1R4hBCAKQqrV/v///7//uX9WDQELQprN/8ujvcSAGiEJDAELIAJC///Piuv//9UefSILIApCq9X+////v/+5f1StIgV9IQQgA0Kk7MO1j9S0mOcAfSIIIAJC///Piuv//9UeVCAFIAtWcq0iAn0hBSAGQr+llJzP8NK75AB9IgsgA0Kk7MO1j9S0mOcAVCACIAhWcq0iAn0hCCAHQtfZrprk9umNywB9IgMgBkK/pZScz/DSu+QAVCACIAtWcq0iAn0hCyAJIAdC19mumuT26Y3LAFQgAiADVnKtfUKazf/Lo73EgBp9IQkgCkLVqoGAgIDAgMYAfCEKCyAkIAo3A9gGICQgBDcD0AYgJCAFNwPIBiAkIAg3A8AGICQgCzcDuAYgJCAJNwOwBiAkQYAGaiAkQbAGakEwEPEDRSEwCyAkQeAGaiQAICVBkAZqJAAgMEUNAQJ/ICdBBGooAgAiOSEoIwBB8AxrIi0kAAJ+IChBMGoiJkGgjMUAQTAQ8QMEQEL//8+K6///1R4gKCkDUCIGfSIDICgpA1giCUKr1f7///+//7l/Vq0iBH0hAkKk7MO1j9S0mOcAICgpA0giB30iBSADIARUIAZC///Piuv//9UeVnKtIgN9IQRCv6WUnM/w0rvkACAoKQNAIgh9IgYgAyAFViAHQqTsw7WP1LSY5wBWcq0iBX0hA0LX2a6a5PbpjcsAICgpAzgiC30iByAFIAZWIAhCv6WUnM/w0rvkAFZyrSIIfSEFQqvV/v///7//uX8gCX0hBkKazf/Lo73EgBogKCkDMCAHIAhUIAtC19mumuT26Y3LAFZyrXx9DAELICgpA1ghBiAoKQNQIQIgKCkDSCEEICgpA0AhAyAoKQM4IQUgKCkDMAshCCAtQegEaiAoQShqKQMANwMAIC1B4ARqIChBIGopAwA3AwAgLUHYBGogKEEYaikDADcDACAtQdAEaiAoQRBqKQMANwMAIC1ByARqIChBCGopAwA3AwAgLSAGNwOYBSAtIAI3A5AFIC0gBDcDiAUgLSADNwOABSAtIAU3A/gEIC0gCDcD8AQgLSAoKQMANwPABCAtQeAGaiIAQaCOxQBB4AD8CgAAIChB4ABqITcgLUGICWogLUHABGogABA/An4gKEGQAWoiNEGgjMUAQTAQ8QMEQEL//8+K6///1R4gKCkDsAEiBn0iAyAoKQO4ASIJQqvV/v///7//uX9WrSIEfSECQqTsw7WP1LSY5wAgKCkDqAEiB30iBSADIARUIAZC///Piuv//9UeVnKtIgN9IQRCv6WUnM/w0rvkACAoKQOgASIIfSIGIAMgBVYgB0Kk7MO1j9S0mOcAVnKtIgV9IQNC19mumuT26Y3LACAoKQOYASILfSIHIAUgBlYgCEK/pZScz/DSu+QAVnKtIgh9IQVCq9X+////v/+5fyAJfSEGQprN/8ujvcSAGiAoKQOQASAHIAhUIAtC19mumuT26Y3LAFZyrXx9DAELICgpA7gBIQYgKCkDsAEhAiAoKQOoASEEICgpA6ABIQMgKCkDmAEhBSAoKQOQAQshCCAtQegEaiA3QShqKQMANwMAIC1B4ARqIDdBIGopAwA3AwAgLUHYBGogN0EYaikDADcDACAtQdAEaiA3QRBqKQMANwMAIC1ByARqIDdBCGopAwA3AwAgLSAGNwOYBSAtIAI3A5AFIC0gBDcDiAUgLSADNwOABSAtIAU3A/gEIC0gCDcD8AQgLSA3KQMANwPABCAtQeAGaiIAQYCPxQBB4AD8CgAAIChBwAFqITMgLUHoCWogLUHABGogABA/IC1ByApqIQACfiAoQfABaiI2QaCMxQBBMBDxAwRAQv//z4rr///VHiAoKQOQAiIGfSIDICgpA5gCIglCq9X+////v/+5f1atIgR9IQJCpOzDtY/UtJjnACAoKQOIAiIHfSIFIAMgBFQgBkL//8+K6///1R5Wcq0iA30hBEK/pZScz/DSu+QAICgpA4ACIgh9IgYgAyAFViAHQqTsw7WP1LSY5wBWcq0iBX0hA0LX2a6a5PbpjcsAICgpA/gBIgt9IgcgBSAGViAIQr+llJzP8NK75ABWcq0iCH0hBUKr1f7///+//7l/IAl9IQZCms3/y6O9xIAaICgpA/ABIAcgCFQgC0LX2a6a5PbpjcsAVnKtfH0MAQsgKCkDmAIhBiAoKQOQAiECICgpA4gCIQQgKCkDgAIhAyAoKQP4ASEFICgpA/ABCyEIIAAgMykDADcDACAAQShqIDNBKGopAwA3AwAgAEEgaiAzQSBqKQMANwMAIABBGGogM0EYaikDADcDACAAQRBqIDNBEGopAwA3AwAgAEEIaiAzQQhqKQMANwMAIC0gBjcDoAsgLSACNwOYCyAtIAQ3A5ALIC0gAzcDiAsgLSAFNwOACyAtIAg3A/gKIC1B4AZqIi4gLUGICWoiKxCvAgJAAkAgLSgC4AZBAUcEQCAtIC1B6AZqIgBBoAL8CgAAICtBAEHgAPwLACAtQdgCakIANwMAIC1B4AJqQgA3AwAgLUHoAmpCADcDACAtQfACakIANwMAIC1B+AJqQgA3AwAgLUHIAmpBoJHFACkDADcDACAtQcACakGYkcUAKQMANwMAIC1BuAJqQZCRxQApAwA3AwAgLUGwAmpBiJHFACkDADcDACAtQagCakGAkcUAKQMANwMAIC1CADcD0AIgLUH4kMUAKQMANwOgAiAtQcgKakEAQeAA/AsAIC1B6AlqIC1BoAJqQeAA/AoAACAuICsQrwIgLSgC4AZBAUYNASAtQcAEaiAAQaAC/AoAACAtQZAMaiAoQQhqKQMANwMAIC1BmAxqIChBEGopAwA3AwAgLUGgDGogKEEYaikDADcDACAtQagMaiAoQSBqKQMANwMAIC1BsAxqIChBKGopAwA3AwAgLUHADGogJkEIaikDADcDACAtQcgMaiAmQRBqKQMANwMAIC1B0AxqICZBGGopAwA3AwAgLUHYDGogJkEgaikDADcDACAtQeAMaiAmQShqKQMANwMAIC0gKCkDADcDiAwgLSAmKQMANwO4DCAuIC1BiAxqIilB4AD8CgAAIC1BsAlqIiAgN0EoaikDADcDACAtQagJaiIwIDdBIGopAwA3AwAgLUGgCWoiMSA3QRhqKQMANwMAIC1BmAlqIjIgN0EQaikDADcDACAtQZAJaiIvIDdBCGopAwA3AwAgLUHACWoiJCA0QQhqKQMANwMAIC1ByAlqIiUgNEEQaikDADcDACAtQdAJaiIoIDRBGGopAwA3AwAgLUHYCWoiJiA0QSBqKQMANwMAIC1B4AlqIgAgNEEoaikDADcDACAtIDcpAwA3A4gJIC0gNCkDADcDuAkgKSArQeAA/AoAACAtQcAHaiApQeAA/AoAACAgIDNBKGopAwA3AwAgMCAzQSBqKQMANwMAIDEgM0EYaikDADcDACAyIDNBEGopAwA3AwAgLyAzQQhqKQMANwMAICQgNkEIaikDADcDACAlIDZBEGopAwA3AwAgKCA2QRhqKQMANwMAICYgNkEgaikDADcDACAAIDZBKGopAwA3AwAgLSAzKQMANwOICSAtIDYpAwA3A7gJICkgK0HgAPwKAAAgLUGgCGogKUHgAPwKAAAgKyAuQaAC/AoAAEKAgISAgIDAgFIhAgNAIAJCAYNQRQRAIC1B4AZqIiYgLUHABGoiACAtQYgJahBRIAAgJkGgAvwKAAALIC1B4AZqIiYgLUGICWoiJSAlEFEgJSAmQaAC/AoAACACQgFWIAJCAYghAg0ACyAtQaACaiAtQcAEaiIAQaAC/AoAACAtQbALaiAtQagCaikDADcDACAtQbgLaiAtQbACaikDADcDACAtQcALaiAtQbgCaikDADcDACAtQcgLaiAtQcACaikDADcDACAtQdALaiAtQcgCaikDADcDACAtIC0pA6ACNwOoCyAtQeALaiAtQdgCaikDADcDACAtQegLaiAtQeACaikDADcDACAtQfALaiAtQegCaikDADcDACAtQfgLaiAtQfACaikDADcDACAtQYAMaiAtQfgCaikDADcDACAtIC0pA9ACNwPYCyAtQegJaiAtQYADahC0AiAtQegEaiAtQYgEaikDADcDACAtQeAEaiAtQYAEaikDADcDACAtQdgEaiAtQfgDaikDADcDACAtQdAEaiAtQfADaikDADcDACAtQcgEaiAtQegDaikDADcDACAtQfgEaiAtQZgEaikDADcDACAtQYAFaiAtQaAEaikDADcDACAtQYgFaiAtQagEaikDADcDACAtQZAFaiAtQbAEaikDADcDACAtQZgFaiAtQbgEaikDADcDACAtIC0pA+ADNwPABCAtIC0pA5AENwPwBCAlIC1BqAtqQeAA/AoAACAtQcgKaiAAQeAA/AoAACAmICUQrwIgLSgC4AZBAUYNAiAlIC1B6AZqQaAC/AoAACMAQcABayIkJAAgJCAtICVBwAFqIiYQPyAkQeAAaiIoIC1BwAFqIgAgJRA/An9BACAkIChBMBDxAw0AGkEAICRBMGogJEGQAWpBMBDxAw0AGiAkIC1B4ABqICYQPyAoICVB4ABqIAAQP0EAICQgKEEwEPEDDQAaICRBMGogJEGQAWpBMBDxA0ULICRBwAFqJAAgLUHwDGokAAwDC0GQjcUAQSsgLUHvDGpBgI3FAEHokMUAEMoDAAtBkI3FAEErIC1B7wxqQYCNxQBBsJLFABDKAwALQZCNxQBBKyAtQe8MakGAjcUAQdCSxQAQygMAC0UNAQJAIDVB4ABqQcCNxQBBMBDxA0UNACAqQbAMaiIAQQBB4AD8CwAgOUHAAWogAEEwEPEDRQRAIDlB8AFqIEdBMBDxA0UNAQsgKkHABGohVUIAIQJCACEOIwBB4ARrIiQkAAJAAkAgNUHgAGoiAEGoo8UAQTAQ8QMEQCAkQcADakIANwMAICRBuANqQgA3AwAgJEGwA2pCADcDACAkQagDakIANwMAICRCADcDoAMgJEIBNwPIA0EoISUgJEH4A2ogAEEoaikDADcDACAkQfADaiAAQSBqKQMANwMAICRB6ANqIABBGGopAwA3AwAgJEHgA2ogAEEQaikDADcDACAkQdgDaiAAQQhqKQMANwMAICQgACkDADcD0AMgJEGoBGpBsKTFACkDADcDACAkQaAEakGopMUAKQMANwMAICRBmARqQaCkxQApAwA3AwAgJEGQBGpBmKTFACkDADcDACAkQYgEakGQpMUAKQMANwMAICRBiKTFACkDADcDgAQgJEHYBGpB4KTFACkDADcDACAkQdAEakHYpMUAKQMANwMAICRByARqQdCkxQApAwA3AwAgJEHABGoiAEHIpMUAKQMANwMAICRBuARqQcCkxQApAwA3AwAgJEG4pMUAKQMANwOwBCAkQZgCakIANwMAICRBkAJqQgA3AwAgJEGIAmpCADcDACAkQYACaiImQgA3AwAgJEH4AWpCADcDACAkQgA3A/ABICRB0ANqICRBoANqQTAQ8QNFBEBCqserltn8o8wRIQ5CrarmqNvQz7yafyECDAILICRBgARqICRBoANqQTAQ8QNFBEAgJiEADAILQqvV/v///7//uX8hBgNAICQtAPgDQQFxRQRAA0AgJEHQA2oQvwIgJCkD2AQiBEIBg1BFBEAgJCkD0AQhBiAkIARC1aqBgICAwIDGAH0iAjcD2AQgJCAGQv//z4rr///VHnwiAyACIARUrXwiAjcD0AQgJCAkKQPIBCIEQqTsw7WP1LSY5wB8IgUgAyAGVCACIANUcq18IgI3A8gEICQgJCkDwAQiA0K/pZScz/DSu+QAfCIGIAIgBVQgBCAFVnKtfCICNwPABCAkICQpA7gEIgRC19mumuT26Y3LAHwiBSACIAZUIAMgBlZyrXwiAjcDuAQgJCAkKQOwBCACIAVUIAQgBVZyrXxCms3/y6O9xIAafDcDsAQLICRBsARqEL8CICQtAPgDQQFxRQ0ACyAkKQOoBCEGCyAGp0EBcUUEQANAICRBgARqEL8CICQpA5gCIgRCAYNQRQRAICQpA5ACIQYgJCAEQtWqgYCAgMCAxgB9IgI3A5gCICQgBkL//8+K6///1R58IgMgAiAEVK18IgI3A5ACICQgJCkDiAIiBEKk7MO1j9S0mOcAfCIFIAMgBlQgAiADVHKtfCICNwOIAiAkICQpA4ACIgNCv6WUnM/w0rvkAHwiBiACIAVUIAQgBVZyrXwiAjcDgAIgJCAkKQP4ASIEQtfZrprk9umNywB8IgUgAiAGVCADIAZWcq18IgI3A/gBICQgJCkD8AEgAiAFVCAEIAVWcq18QprN/8ujvcSAGnw3A/ABCyAkQfABahC/AiAkKQOoBCIGQgGDUA0ACwsgJCkD2AMhBAJAAkAgJAJ+AkACQAJAAn4gJCkDgAQiEiAkKQPQAyIRUgRAICQpA5AEIQggJCkDiAQhCSASIQIgESEKICQpA+ADDAELICQpA5AEIQggJCkD4AMhByAEICQpA4gEIglSBEAgCSECIAQhCiAHDAELIAcgCFIEQCAEIQkgCCECIAchCiAHDAELICQpA5gEIgIgJCkD6AMiClIEQCAEIQkgByIIDAELICQpA6AEIgUgJCkD8AMiClIEQCAEIQkgBSECIAciCAwBCyAGICQpA/gDIgpRDQEgBCEJIAYhAiAHIggLIQsgAiAKViAkKQPwASEKICQpA7AEIQ4gJCkDoAQhBSAkKQOYBCECICQpA/gDIQMgJCkD8AMhDCAkKQPoAyEPRQRAIAghBwwCCyAkIAYgA30iDTcDqAQgJCAFIAx9IgcgAyAGVq0iA303A6AEICQgAiAPfSIGIAUgDFQgAyAHVnKtIgN9NwOYBCAkIAggC30iBSACIA9UIAMgBlZyrSICfTcDkAQgJCAJIAR9IgMgCCALVCACIAVWcq0iAn03A4gEICQgEiARfSAEIAlWIAIgA1ZyrX03A4AEICQpA/gBIQkCQAJAIAogDlIEQCAkKQPABCEEICQpA7gEIQIgJCkDgAIhAyAKIQYgDiEIDAELICQpA8AEIQQgJCkDgAIhAyAkKQO4BCICIAlSBEAgCSEGIAIhCAwBCyADIARSBEAgCSECIAMhBiAEIQgMAQsgJCkDiAIiBSAkKQPIBCIIUgRAIAMhBCAJIQIgBSEGDAELICQpA5ACIgsgJCkD0AQiCFIEQCADIQQgCSECIAshBgwBCyADIQQgCSECICQpA5gCIgYhDCALIQ8gBSEHIAYgJCkD2AQiCFENAQsgBiAIVCAkKQPYBCEGICQpA9AEIQsgJCkDyAQhBSAkKQOYAiEMICQpA5ACIQ8gJCkDiAIhBw0DCyAkIAwgBn03A5gCICQgDyALfSIIIAYgDFatIgZ9NwOQAiAkIAcgBX0iDCAGIAhWIAsgD1ZyrSIGfTcDiAIgJCADIAR9IgggBiAMViAFIAdWcq0iBn03A4ACICQgCSACfSIFIAMgBFQgBiAIVnKtIgN9IgQ3A/gBIAogDn0gAyAFViACIAlWcq19DAMLICQpA/ABIQogJCkDsAQhDiAEIQkgBiEDIAUhDCACIQ8gByELCyAkIAMgBn03A/gDICQgDCAFfSINIAMgBlStIgN9NwPwAyAkIA8gAn0iCCADIA1WIAUgDFZyrSIDfTcD6AMgJCALIAd9IgUgAyAIViACIA9Wcq0iAn03A+ADICQgBCAJfSIDIAIgBVYgByALVnKtIgJ9NwPYAyAkIBEgEn0gBCAJVCACIANWcq19NwPQAyAkKQO4BCEJAkACQCAKIA5SBEAgJCkDgAIhBSAkKQP4ASEEICQpA8AEIQwgDiECIAohDQwBCyAkKQOAAiEFICQpA8AEIQwgJCkD+AEiBCAJUgRAIAkhAiAEIQ0MAQsgBSAMUgRAIAkhBCAMIQIgBSENDAELICQpA8gEIgsgJCkDiAIiDVIEQCAMIQUgCSEEIAshAgwBCyAkKQPQBCIDICQpA5ACIg1SBEAgDCEFIAkhBCADIQIMAQsgDCEFIAkhBCAkKQPYBCICIQ8gAyEHIAshCCACICQpA5gCIg1RDQELIAIgDVQgJCkDmAIhAiAkKQOQAiEDICQpA4gCIQsgJCkD2AQhDyAkKQPQBCEHICQpA8gEIQgNAwsgJCAPIAJ9NwPYBCAkIAcgA30iESACIA9WrSICfTcD0AQgJCAIIAt9Ig0gAiARViADIAdWcq0iAn03A8gEICQgDCAFfSIDIAggC1QgAiANVnKtIgJ9NwPABCAkIAkgBH0iCCACIANWIAUgDFZyrSIDfSICNwO4BCAkIA4gCn0gAyAIViAEIAlWcq19Ig43A7AEDAMLICQgDEKr1f7///+//7l/IAZ9IhB8IhI3A5gCICQgD0L//8+K6///1R4gC30iDCAGQqvV/v///7//uX9WrSIIfSIRfCIWIBAgElatfCIGNwOQAiAkIAdCpOzDtY/UtJjnACAFfSIPIAggDFYgC0L//8+K6///1R5Wcq0iDH0iCHwiEiAGIBZUIBEgFlZyrXwiBjcDiAIgJCADQr+llJzP8NK75AAgBH0iCyAMIA9WIAVCpOzDtY/UtJjnAFZyrSIDfSIHfCIMIAYgElQgCCASVnKtfCIINwOAAiAkIAlC19mumuT26Y3LACACfSIGIAMgC1YgBEK/pZScz/DSu+QAVnKtIgV9IgN8IgsgCCAMVCAHIAxWcq18IgQ3A/gBIAQgC1QgAyALVnKtIAogDn0gBSAGViACQtfZrprk9umNywBWcq19fEKazf/Lo73EgBp8CyIKNwPwASANIQYMAQsgJEKr1f7///+//7l/IAJ9IhAgD3wiEjcD2AQgJCAHQv//z4rr///VHiADfSIRIAJCq9X+////v/+5f1atIg99Ig18IhYgECASVq18IgI3A9AEICQgCEKk7MO1j9S0mOcAIAt9IgcgDyARViADQv//z4rr///VHlZyrSIDfSIPfCIIIAIgFlQgDSAWVnKtfCICNwPIBCAkIAxCv6WUnM/w0rvkACAFfSINIAMgB1YgC0Kk7MO1j9S0mOcAVnKtIgN9Igd8IgwgCCAPVCACIAhUcq18IgI3A8AEICQgCULX2a6a5PbpjcsAIAR9IgggAyANViAFQr+llJzP8NK75ABWcq0iBX0iA3wiCyACIAxUIAcgDFZyrXwiAjcDuAQgJCACIAtUIAMgC1ZyrSAOIAp9IAUgCFYgBELX2a6a5PbpjcsAVnKtfXxCms3/y6O9xIAafCIONwOwBAsgJEHQA2ogJEGgA2oiKEEwEPEDRQ0CICRBgARqIChBMBDxAw0ACyAmIQAgBCECIAohDgwBCyAkQZgCakIANwMAICRBkAJqQgA3AwAgJEGIAmpCADcDACAkQYACakIANwMAICRB+AFqQgA3AwAgJEGoAmpB4KPFACkDADcDACAkQbACakHoo8UAKQMANwMAICRBuAJqQfCjxQApAwA3AwAgJEHAAmpB+KPFACkDADcDACAkQcgCakGApMUAKQMANwMAICRCADcD8AEgJEHYo8UAKQMANwOgAiAkQfgCakIANwMAICRB8AJqQgA3AwAgJEHoAmpCADcDACAkQeACakIANwMAICRB2AJqQgA3AwAgJEIANwPQAgwBCyA1QTBqISYgJEGYA2ogAEEYaikDACIFNwMAICRBkANqIABBEGopAwAiAzcDACAkQYgDaiAAQQhqKQMAIgQ3AwAgJEHYAWogBDcDACAkQeABaiADNwMAICRB6AFqIAU3AwAgJCAAKQMAIgQ3A4ADICQgAjcDyAEgJCAONwPAASAkIAQ3A9ABIDUpAwAhDyA1KQMIIQ0gNSkDECEMIDUpAxghCyA1KQMgIQcgNSkDKCEIQgAhAkIAIQNCACEJQgAhBEIAIQ5CACEKA0AgJEHgAGogJEHAAWogJWopAwAiBUIAIAhCABDJAyAkQfAAaiAFQgAgB0IAEMkDICRBgAFqIAVCACALQgAQyQMgJEGQAWogBUIAIAxCABDJAyAkQaABaiAFQgAgDUIAEMkDICRBsAFqIAVCACAPQgAQyQMgJEHQAGogJCkDYCIGIAJ8IhZC/f/z/8////mJf34iAkIAQqvV/v///7//uX9CABDJAyAkQUBrIAJCAEL//8+K6///1R5CABDJAyAkQTBqIAJCAEKk7MO1j9S0mOcAQgAQyQMgJEEgaiACQgBCv6WUnM/w0rvkAEIAEMkDICRBEGogAkIAQtfZrprk9umNywBCABDJAyAkIAJCAEKazf/Lo73EgBpCABDJAyAkKQMIIAogJCkDsAEiBXwiECAkKQOoASAkKQOgASICIA58Ig4gAlStfCAOIA4gJCkDmAEgJCkDkAEiAiAEfCIKIAJUrXwgCiAKICQpA4gBICQpA4ABIgIgCXwiCSACVK18IAkgCSAkKQN4ICQpA3AiAiADfCIEIAJUrXwgBCAEICQpA2ggBiAWVq18fCIEVq18fCIJVq18fCIDVq18fCICVq18fCISICQpAwB8IhEgElStfCARIBEgJCkDGCACIAIgJCkDEHwiDlatfCAOIA4gJCkDKCADIAMgJCkDIHwiClatfCAKIAogJCkDOCAJIAkgJCkDMHwiBlatfCAGIAYgJCkDSCAEICQpA0AiAnwiBCACVK18IAQgBCAkKQNYIBYgJCkDUCICfCACVK18fCICVq18fCIDVq18fCIJVq18fCIEVq18fCIOVq18IBAgElatICQpA7gBIAUgEFatfHx8IQogJUEIayIlQXhHDQALAkACQCAKQprN/8ujvcSAGlYNAAJAAkACQAJAIApCms3/y6O9xIAaUg0AIA5C19mumuT26Y3LAFYNBCAOQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQoMAQsgBEK/pZScz/DSu+QAVg0EQtfZrprk9umNywAhBiAEQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQoMAgsgCUKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhBSAJQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQoMAwsgA0L//8+K6///1R5WDQRCpOzDtY/UtJjnACEMIANC///Piuv//9UeUQ0DQprN/8ujvcSAGiEKIAMhCwwFCyAOIQYLIAQhBQsgCSEMIAMhCwwCC0L//8+K6///1R4hCyACQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQoMAQsgA0L//8+K6///1R59IgggAkKr1f7///+//7l/VK0iBn0hCyAJQqTsw7WP1LSY5wB9IgUgA0L//8+K6///1R5UIAYgCFZyrSIDfSEMIARCv6WUnM/w0rvkAH0iCCAJQqTsw7WP1LSY5wBUIAMgBVZyrSIGfSEFIA5C19mumuT26Y3LAH0iAyAEQr+llJzP8NK75ABUIAYgCFZyrSIEfSEGIAogDkLX2a6a5PbpjcsAVCADIARUcq19QprN/8ujvcSAGn0hCiACQtWqgYCAgMCAxgB8IQILICQgAjcDmAIgJCALNwOQAiAkIAw3A4gCICQgBTcDgAIgJCAGNwP4ASAkIAo3A/ABICRBoAJqICYgJEHAAWoQuwEgJEH4AmpBgKTFACkDADcDACAkQfACakH4o8UAKQMANwMAICRB6AJqQfCjxQApAwA3AwAgJEHgAmpB6KPFACkDADcDACAkQdgCakHgo8UAKQMANwMAICRB2KPFACkDADcD0AILIFUgJEHwAWpBkAH8CgAAICRB4ARqJAAgKkGwDGoiViMAQaAFayIlJAAgJUHgAGoiAEEAQeAA/AsAAkACQAJAIDlBwAFqIiYgAEEwEPEDRQRAIDlB8AFqICVBkAFqQTAQ8QNFDQELICVB4ABqIgAgJhA9ICUpA3AhBCAlKQNoIQIgJSgCYEUNASAlIAQ3A2ggJSACNwNgQYiixQBBKyAAQfihxQBBmKPFABDKAwALICVB4ABqQQBB4AD8CwAgJUGYBGpCADcDACAlQaAEakIANwMAICVBqARqQgA3AwAgJUGwBGpCADcDACAlQbgEakIANwMAICVBiARqQYCkxQApAwA3AwAgJUGABGpB+KPFACkDADcDACAlQfgDakHwo8UAKQMANwMAICVB8ANqQeijxQApAwA3AwAgJUHoA2pB4KPFACkDADcDACAlQgA3A5AEICVB2KPFACkDADcD4AMgJUGgAmpBAEHgAPwLACAlQcABaiAlQeADakHgAPwKAAAMAQsgJUEQaiAlQfgAakHQAPwKAAAgJSAENwMIICUgAjcDACAlQeAAaiA5ICUQPyAlQYADaiIAICVB4AD8CgAAICVBwAFqIDlB4ABqIAAQPyAlQfgEakIANwMAICVBgAVqQgA3AwAgJUGIBWpCADcDACAlQZAFakIANwMAICVBmAVqQgA3AwAgJUHIBGpB4KPFACkDADcDACAlQdAEakHoo8UAKQMANwMAICVB2ARqQfCjxQApAwA3AwAgJUHgBGpB+KPFACkDADcDACAlQegEakGApMUAKQMANwMAICVCADcD8AQgJUHYo8UAKQMANwPABCAlQaACaiAlQcAEakHgAPwKAAALICVB4ABqQaAC/AoAACAlQaAFaiQAICpB0AVqIjggVkGgAvwKAAAgKkHwB2ohQkEAIVcjAEGwMWsiIyQAICNBmCxqIDhBCGopAwA3AwAgI0GgLGogOEEQaikDADcDACAjQagsaiA4QRhqKQMANwMAICNBsCxqIDhBIGopAwA3AwAgI0G4LGogOEEoaikDADcDACAjQcgsaiA4QThqKQMANwMAICNB0CxqIDhBQGspAwA3AwAgI0HYLGogOEHIAGopAwA3AwAgI0HgLGogOEHQAGopAwA3AwAgI0HoLGogOEHYAGopAwA3AwAgIyA4KQMANwOQLCAjIDgpAzA3A8AsICNB8CxqIisgI0GQLGoiNkHgAPwKAAAgI0GYFWoiKSA4QYgBaikDADcDACAjQZAVaiIuIDhBgAFqKQMANwMAICNBiBVqIiAgOEH4AGopAwA3AwAgI0GAFWoiMCA4QfAAaikDADcDACAjQfgUaiIxIDhB6ABqKQMANwMAICNBqBVqIjIgOEGYAWopAwA3AwAgI0GwFWoiLyA4QaABaikDADcDACAjQbgVaiIkIDhBqAFqKQMANwMAICNBwBVqIiUgOEGwAWopAwA3AwAgI0HIFWoiKCA4QbgBaikDADcDACAjIDgpA2A3A/AUICMgOCkDkAE3A6AVIDYgI0HwFGoiJkHgAPwKAAAgI0HQLWoiACA2QeAA/AoAACApIDhB6AFqKQMANwMAIC4gOEHgAWopAwA3AwAgICA4QdgBaikDADcDACAwIDhB0AFqKQMANwMAIDEgOEHIAWopAwA3AwAgMiA4QfgBaikDADcDACAvIDhBgAJqKQMANwMAICQgOEGIAmopAwA3AwAgJSA4QZACaikDADcDACAoIDhBmAJqKQMANwMAICMgOCkDwAE3A/AUICMgOCkD8AE3A6AVIDYgJkHgAPwKAAAgI0GwLmogNkHgAPwKAAAgI0GADWogK0GgAvwKAAAgKUHwocUAKQMANwMAIC5B6KHFACkDADcDACAgQeChxQApAwA3AwAgMEHYocUAKQMANwMAIDFB0KHFACkDADcDACAyQgA3AwAgL0IANwMAICRCADcDACAlQgA3AwAgKEIANwMAICNByKHFACkDADcD8BQgI0IANwOgFSAAQQBBwAH8CwAgKyAmQeAA/AoAACAjQZAvaiJIQQBBoAL8CwAgI0GgD2ogK0HABPwKAAAgOEHgAGohPCAjQbAWaiFKICNB0BVqIUsgI0HwJmohTCAjQZAmaiFOICNBgBNqIU0gI0GAEGohWCAjQeAQaiFZICNBoBJqIU8gI0HAEWohUyAjQcAdaiFkICNB4BxqIWAgI0HgGWohPSAjQeAraiEiICNB8BpqITMgI0GQGmohNSAjQdAYaiFaICNB8BdqIVsgI0GQF2ohXCAjQaAhaiE5ICNBwA5qIV4gI0HgDWohYQNAICNB4BNqEHUgI0HQG2ohJUIAIQJCACEJQgAhA0IAIQZCACEHQgAhBUIAIQojAEHwAWsiACQAIABBwAFqQayTxQBB3wAQpwJBKCErIAApA8ABIRIgACkDyAEhESAAKQPQASEPIAApA9gBIQ0gACkD4AEhDiAAKQPoASEMA0AgAEHgAGogK0HQjMUAaikDACIEQgAgDEIAEMkDIABB8ABqIARCACAOQgAQyQMgAEGAAWogBEIAIA1CABDJAyAAQZABaiAEQgAgD0IAEMkDIABBoAFqIARCACARQgAQyQMgAEGwAWogBEIAIBJCABDJAyAAQdAAaiAAKQNgIgggCnwiCkL9//P/z///+Yl/fiIEQgBCq9X+////v/+5f0IAEMkDIABBQGsgBEIAQv//z4rr///VHkIAEMkDIABBMGogBEIAQqTsw7WP1LSY5wBCABDJAyAAQSBqIARCAEK/pZScz/DSu+QAQgAQyQMgAEEQaiAEQgBC19mumuT26Y3LAEIAEMkDIAAgBEIAQprN/8ujvcSAGkIAEMkDIAApAwggACkDsAEiCyAJfCIWIAApA6gBIAApA6ABIgQgB3wiCSAEVK18IAkgACkDmAEgACkDkAEiBCAGfCIGIARUrXwgBiAAKQOIASAAKQOAASIEIAN8IgMgBFStfCADIAApA3ggAiAAKQNwIgJ8IgQgAlStfCAEIAQgACkDaCAIIApWrXx8IgRWrXx8IgcgA1StfHwiAyAGVK18fCICIAlUrXx8IhAgACkDAHwiCSAQVK18IAkgCSAAKQMYIAIgAiAAKQMQfCIIVq18IAggCCAAKQMoIAMgAyAAKQMgfCIGVq18IAYgBiAAKQM4IAcgByAAKQMwfCIDVq18IAMgAyAAKQNIIAQgACkDQCICfCIEIAJUrXwgBCAAKQNYIAogACkDUCICfCACVK18fCIKIARUrXx8IgJWrXx8IgNWrXx8IgZWrXx8IgdWrXwiCCAFIBAgFlStIAApA7gBIAsgFlatfHwiBXwiBHwiCSAIVK0gBCAFVK18IQUgK0EIayIrQXhHDQALAkACQCAFQgBSIAlCms3/y6O9xIAaVnINAAJAIAlCms3/y6O9xIAaUQRAIAdC19mumuT26Y3LAFYNAiAHQtfZrprk9umNywBSBEAgAiEEIAMhBSAGIQggByELQprN/8ujvcSAGiEJDAQLIAZCv6WUnM/w0rvkAFYNAkLX2a6a5PbpjcsAIQsgBkK/pZScz/DSu+QAUgRAIAIhBCADIQUgBiEIQprN/8ujvcSAGiEJDAQLIANCpOzDtY/UtJjnAFYNAkK/pZScz/DSu+QAIQggA0Kk7MO1j9S0mOcAUgRAIAIhBCADIQVCms3/y6O9xIAaIQkMBAsgAkL//8+K6///1R5WDQJCpOzDtY/UtJjnACEFIAJC///Piuv//9UeUQ0BIAIhBEKazf/Lo73EgBohCQwDCyACIQQgAyEFIAYhCCAHIQsMAgtC///Piuv//9UeIQQgCkKr1f7///+//7l/Wg0AQprN/8ujvcSAGiEJDAELIAJC///Piuv//9UefSILIApCq9X+////v/+5f1StIgV9IQQgA0Kk7MO1j9S0mOcAfSIIIAJC///Piuv//9UeVCAFIAtWcq0iAn0hBSAGQr+llJzP8NK75AB9IgsgA0Kk7MO1j9S0mOcAVCACIAhWcq0iAn0hCCAHQtfZrprk9umNywB9IgMgBkK/pZScz/DSu+QAVCACIAtWcq0iAn0hCyAJIAdC19mumuT26Y3LAFQgAiADVnKtfUKazf/Lo73EgBp9IQkgCkLVqoGAgIDAgMYAfCEKCyAlQgA3AzAgJSAKNwMoICUgBDcDICAlIAU3AxggJSAINwMQICUgCzcDCCAlIAk3AwAgJUHYAGpCADcDACAlQdAAakIANwMAICVByABqQgA3AwAgJUFAa0IANwMAICVBOGpCADcDACAAQfABaiQAICNB6BRqIiBCodWmgICAwI5uNwMAICNB4BRqIjBCh4Dwy96EgMKGfzcDACAjQdgUaiIxQui70O/A+Ii8zwA3AwAgI0HQFGoiMkLRwLPPhr6cvp5/NwMAICNByBRqIi9Cmde1g6aLgO/9ADcDACAjQoXBi+T3jr7wDTcDwBQgI0HwFGoiRCAlICNBgA1qIikQPyAjQbAcaiIkIEQgYRA/ICNBkB1qIkkgYRBeICNB8B1qIigiACBeEF4gRCAjQcAUaiImIAAQdyAjQbAraiIrEO4DICNB0B5qIlAiACArIEQQPyAjQbAfaiIuICYgABB3ICsgJUHgAPwKAAAgRCBJIC4Q1QEgI0GQIGoiACArIEQQPyAjQdAqaiJiIGEgXhDVASAjQfApaiI/IGIQXiBEIEkgKBDVASArID8gRBCNASAjQfAgaiIlICtB4AD8CgAAIEQgSSAuEI0BICNB0CFqIiggJCBEED8gPyAAEF4gRCBQEF4gYiAmIEQQdyAjQbAiaiImID8gYhCNASAjQZAjaiIAIEkgJRA/ICNBmCpqICApAwA3AwAgI0GQKmogMCkDADcDACAjQYgqaiAxKQMANwMAICNBgCpqIDIpAwA3AwAgI0H4KWogLykDADcDACAjICMpA8AUNwPwKSBiICkQXiBEID8gYhB3ICMpA8gVIRcgIykDwBUhFSAjKQO4FSEWICMpA7AVIRAgIykDqBUhEiAjKQOgFSERICMpA5gVIQ8gIykDkBUhDiAjKQOIFSEMICMpA4AVIQogIykD+BQhCSAjKQPwFCELICkgKEHgAPwKAAAgYSAmQeAA/AoAACBeIABB4AD8CgAAIwBBwA1rIjokACA6ICNBoA9qIjcgN0GgAmoiJhC5AiA6QaACaiI0IDcgJhDVASA6QYADaiA3QeAAaiI2IDdBgANqENUBIDpB4ANqIDdBwAFqIisgN0HgA2oQ1QEgOkGIB2oiKUHQnMUAKQMAIgg3AwAgOkGAB2oiLkHInMUAKQMAIgY3AwAgOkH4BmoiIEHAnMUAKQMAIgU3AwAgOkHwBmoiMEG4nMUAKQMAIgM3AwAgOkHoBmoiMUGwnMUAKQMAIgQ3AwAgOkGYB2oiMkIANwMAIDpBoAdqIi9CADcDACA6QagHaiIkQgA3AwAgOkGwB2oiJUIANwMAIDpBuAdqIihCADcDACA6QaicxQApAwAiAjcD4AYgOkIANwOQByA6QYAJaiIAQQBB4AD8CwAgOkHgCWogOkHgBmoiY0HgAPwKAAAgOkHACmpBAEHgAPwLACBjIAAgJhC5AiA6QcAEaiImIgAgNyBjENUBIDpBoAVqIj4gNiA6QcAHaiJAENUBIDpBgAZqIi0gKyA6QaAIaiI3ENUBIGMgNCAAELkCIAAgYyA6EI0BID4gQCA6QeAAaiI2EI0BIC0gNyA6QcABaiIrEI0BICkgCDcDACAuIAY3AwAgICAFNwMAIDAgAzcDACAxIAQ3AwAgMkIANwMAIC9CADcDACAkQgA3AwAgJUIANwMAIChCADcDACA6IAI3A+AGIDpCADcDkAcgOkGgC2oiAEEAQeAA/AsAIDpBgAxqIGNB4AD8CgAAIDpB4AxqQQBB4AD8CwAgYyAAIDoQuQIgRCAmIGMQjQEgREHgAGogPiBAEI0BIERBwAFqIC0gNxCNASBEQaACaiA6IDoQ1QEgREGAA2ogNiA2ENUBIERB4ANqICsgKxDVASA6QcANaiQAID8gUEHgAPwKAAAgYiBJQeAA/AoAACBXQe2SxQBqLQAAICNB8CNqID8gYhCNAUIAIRRBKCErQgAhAkIAIQRCACEDQgAhCEIAIQ0DQCAjQaAMaiArIFVqKQMAIgVCACAPQgAQyQMgI0GwDGogBUIAIA5CABDJAyAjQcAMaiAFQgAgDEIAEMkDICNB0AxqIAVCACAKQgAQyQMgI0HgDGogBUIAIAlCABDJAyAjQfAMaiAFQgAgC0IAEMkDICNBkAxqICMpA6AMIgcgFHwiE0IAQgBC/f/z/8////mJfxDJAyAjQYAMaiAjKQOYDCIFQgBCq9X+////v/+5f0IAEMkDICNB8AtqIAVCAEL//8+K6///1R5CABDJAyAjQeALaiAFQgBCpOzDtY/UtJjnAEIAEMkDICNB0AtqIAVCAEK/pZScz/DSu+QAQgAQyQMgI0HAC2ogBUIAQtfZrprk9umNywBCABDJAyAjQbALaiAFQgBCms3/y6O9xIAaQgAQyQMgIykDuAsgDSAjKQPwDCIGfCIYICMpA+gMICMpA+AMIgUgCHwiCCAFVK18IAggIykD2AwgAyAjKQPQDCIDfCIFIANUrXwgBSAjKQPIDCAEICMpA8AMIgR8IgMgBFStfCADICMpA7gMIAIgIykDsAwiAnwiBCACVK18IAQgBCAjKQOoDCAHIBNWrXx8IgRWrXx8IhkgA1StfHwiAyAFVK18fCICIAhUrXx8Ig0gIykDsAt8IgcgDVStfCAHIAcgIykDyAsgAiACICMpA8ALfCIIVq18IAggCCAjKQPYCyADIAMgIykD0At8IgVWrXwgBSAFICMpA+gLIBkgGSAjKQPgC3wiA1atfCADIAMgIykD+AsgBCAjKQPwCyICfCIEIAJUrXwgBCAjKQOIDCATICMpA4AMIgJ8IAJUrXx8IhQgBFStfHwiAlatfHwiBFatfHwiA1atfHwiCFatfCANIBhUrSAjKQP4DCAGIBhWrXx8fCENICtBCGsiK0F4Rw0ACwJAAkAgDUKazf/Lo73EgBpWDQAgDUKazf/Lo73EgBpSBEAgAiEGIAQhCyADIQogCCEODAILIAhC19mumuT26Y3LAFYNAAJAIAhC19mumuT26Y3LAFIEQCACIQYgBCELIAMhCiAIIQ4MAQsgA0K/pZScz/DSu+QAVg0BQtfZrprk9umNywAhDiADQr+llJzP8NK75ABSBEAgAiEGIAQhCyADIQoMAQsgBEKk7MO1j9S0mOcAVg0BQr+llJzP8NK75AAhCiAEQqTsw7WP1LSY5wBSBEAgAiEGIAQhCwwBCyACQv//z4rr///VHlYNAUKk7MO1j9S0mOcAIQsgAkL//8+K6///1R5SBEAgAiEGDAELQv//z4rr///VHiEGIBRCqtX+////v/+5f1YNAQtCms3/y6O9xIAaIQ0MAQsgAkL//8+K6///1R59IgsgFEKr1f7///+//7l/VK0iBX0hBiAEQqTsw7WP1LSY5wB9IgcgAkL//8+K6///1R5UIAUgC1ZyrSICfSELIANCv6WUnM/w0rvkAH0iBSAEQqTsw7WP1LSY5wBUIAIgB1ZyrSICfSEKIAhC19mumuT26Y3LAH0iBCADQr+llJzP8NK75ABUIAIgBVZyrSICfSEOIA0gCELX2a6a5PbpjcsAVCACIARWcq19QprN/8ujvcSAGn0hDSAUQtWqgYCAgMCAxgB8IRQLQgAhE0EoIStCACECQgAhBEIAIQNCACEIQgAhDwNAICNB0ApqICsgVWopAwAiBUIAIBdCABDJAyAjQeAKaiAFQgAgFUIAEMkDICNB8ApqIAVCACAWQgAQyQMgI0GAC2ogBUIAIBBCABDJAyAjQZALaiAFQgAgEkIAEMkDICNBoAtqIAVCACARQgAQyQMgI0HACmogIykD0AoiCSATfCIYQgBCAEL9//P/z///+Yl/EMkDICNBsApqICMpA8gKIgVCAEKr1f7///+//7l/QgAQyQMgI0GgCmogBUIAQv//z4rr///VHkIAEMkDICNBkApqIAVCAEKk7MO1j9S0mOcAQgAQyQMgI0GACmogBUIAQr+llJzP8NK75ABCABDJAyAjQfAJaiAFQgBC19mumuT26Y3LAEIAEMkDICNB4AlqIAVCAEKazf/Lo73EgBpCABDJAyAjKQPoCSAPICMpA6ALIgd8IhkgIykDmAsgIykDkAsiBSAIfCIIIAVUrXwgCCAjKQOICyADICMpA4ALIgN8IgUgA1StfCAFICMpA/gKIAQgIykD8AoiBHwiAyAEVK18IAMgIykD6AogAiAjKQPgCiICfCIEIAJUrXwgBCAEICMpA9gKIAkgGFatfHwiBFatfHwiDyADVK18fCIDIAVUrXx8IgIgCFStfHwiDCAjKQPgCXwiCSAMVK18IAkgCSAjKQP4CSACIAIgIykD8Al8IghWrXwgCCAIICMpA4gKIAMgAyAjKQOACnwiBVatfCAFIAUgIykDmAogDyAPICMpA5AKfCIDVq18IAMgAyAjKQOoCiAEICMpA6AKIgJ8IgQgAlStfCAEICMpA7gKIBggIykDsAoiAnwgAlStfHwiEyAEVK18fCICVq18fCIEVq18fCIDVq18fCIIVq18IAwgGVStICMpA6gLIAcgGVatfHx8IQ8gK0EIayIrQXhHDQALAkACQCAPQprN/8ujvcSAGlYNACAPQprN/8ujvcSAGlIEQCACIQUgBCEHIAMhCSAIIQwMAgsgCELX2a6a5PbpjcsAVg0AAkAgCELX2a6a5PbpjcsAUgRAIAIhBSAEIQcgAyEJIAghDAwBCyADQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEMIANCv6WUnM/w0rvkAFIEQCACIQUgBCEHIAMhCQwBCyAEQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEJIARCpOzDtY/UtJjnAFIEQCACIQUgBCEHDAELIAJC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhByACQv//z4rr///VHlIEQCACIQUMAQtC///Piuv//9UeIQUgE0Kq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDwwBCyACQv//z4rr///VHn0iDCATQqvV/v///7//uX9UrSIHfSEFIARCpOzDtY/UtJjnAH0iCSACQv//z4rr///VHlQgByAMVnKtIgJ9IQcgA0K/pZScz/DSu+QAfSIMIARCpOzDtY/UtJjnAFQgAiAJVnKtIgJ9IQkgCELX2a6a5PbpjcsAfSIEIANCv6WUnM/w0rvkAFQgAiAMVnKtIgJ9IQwgDyAIQtfZrprk9umNywBUIAIgBFZyrX1Cms3/y6O9xIAafSEPIBNC1aqBgICAwIDGAHwhEwsgIyATNwOoJSAjIAU3A6AlICMgBzcDmCUgIyAJNwOQJSAjIAw3A4glICMgDzcDgCUgIyAUNwP4JCAjIAY3A/AkICMgCzcD6CQgIyAKNwPgJCAjIA43A9gkICMgDTcD0CQCfiAjQfAgakGQlMUAQTAQ8QMEQEL//8+K6///1R4gIykDkCEiCH0iBSAjKQOYISIKQqvV/v///7//uX9WrSICfSEGQqTsw7WP1LSY5wAgIykDiCEiA30iBCACIAVWIAhC///Piuv//9UeVnKtIgJ9IQVCv6WUnM/w0rvkACAjKQOAISILfSIIIAIgBFYgA0Kk7MO1j9S0mOcAVnKtIgJ9IQdC19mumuT26Y3LACAjKQP4ICIDfSIEIAIgCFYgC0K/pZScz/DSu+QAVnKtIgJ9IQlCq9X+////v/+5fyAKfSELQprN/8ujvcSAGiAjKQPwICACIARWIANC19mumuT26Y3LAFZyrXx9DAELICMpA9grIQsgIykD0CshBiAjKQPIKyEFICMpA8ArIQcgIykDuCshCSAjKQOwKwshDkIAIRRB2AAhK0IAIQJCACEEQgAhA0IAIQhCACENA0AgI0GACWogKyBVaikDACIKQgAgC0IAEMkDICNBkAlqIApCACAGQgAQyQMgI0GgCWogCkIAIAVCABDJAyAjQbAJaiAKQgAgB0IAEMkDICNBwAlqIApCACAJQgAQyQMgI0HQCWogCkIAIA5CABDJAyAjQfAIaiAjKQOACSIMIBR8IhBCAEIAQv3/8//P///5iX8QyQMgI0HgCGogIykD+AgiCkIAQqvV/v///7//uX9CABDJAyAjQdAIaiAKQgBC///Piuv//9UeQgAQyQMgI0HACGogCkIAQqTsw7WP1LSY5wBCABDJAyAjQbAIaiAKQgBCv6WUnM/w0rvkAEIAEMkDICNBoAhqIApCAELX2a6a5PbpjcsAQgAQyQMgI0GQCGogCkIAQprN/8ujvcSAGkIAEMkDICMpA5gIICMpA9AJIgogDXwiEiAjKQPICSAIICMpA8AJIgh8Ig0gCFStfCANICMpA7gJIAMgIykDsAkiA3wiCCADVK18IAggIykDqAkgBCAjKQOgCSIEfCIDIARUrXwgAyAjKQOYCSACICMpA5AJIgJ8IgQgAlStfCAEIAQgIykDiAkgDCAQVq18fCIEVq18fCIRIANUrXx8IgMgCFStfHwiAiANVK18fCIPICMpA5AIfCINIA9UrXwgDSANICMpA6gIIAIgAiAjKQOgCHwiDFatfCAMIAwgIykDuAggAyADICMpA7AIfCIIVq18IAggCCAjKQPICCARIBEgIykDwAh8IgNWrXwgAyADICMpA9gIIAQgIykD0AgiAnwiBCACVK18IAQgIykD6AggECAjKQPgCCICfCACVK18fCIUIARUrXx8IgJWrXx8IgRWrXx8IgNWrXx8IghWrXwgDyASVK0gIykD2AkgCiASVq18fHwhDSArQQhrIitBKEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AIA1Cms3/y6O9xIAaUgRAIAIhBiAEIQsgAyEKIAghDgwCCyAIQtfZrprk9umNywBWDQACQCAIQtfZrprk9umNywBSBEAgAiEGIAQhCyADIQogCCEODAELIANCv6WUnM/w0rvkAFYNAULX2a6a5PbpjcsAIQ4gA0K/pZScz/DSu+QAUgRAIAIhBiAEIQsgAyEKDAELIARCpOzDtY/UtJjnAFYNAUK/pZScz/DSu+QAIQogBEKk7MO1j9S0mOcAUgRAIAIhBiAEIQsMAQsgAkL//8+K6///1R5WDQFCpOzDtY/UtJjnACELIAJC///Piuv//9UeUgRAIAIhBgwBC0L//8+K6///1R4hBiAUQqrV/v///7//uX9WDQELQprN/8ujvcSAGiENDAELIAJC///Piuv//9UefSILIBRCq9X+////v/+5f1StIgV9IQYgBEKk7MO1j9S0mOcAfSIHIAJC///Piuv//9UeVCAFIAtWcq0iAn0hCyADQr+llJzP8NK75AB9IgUgBEKk7MO1j9S0mOcAVCACIAdWcq0iAn0hCiAIQtfZrprk9umNywB9IgQgA0K/pZScz/DSu+QAVCACIAVWcq0iAn0hDiANIAhC19mumuT26Y3LAFQgAiAEVnKtfUKazf/Lo73EgBp9IQ0gFELVqoGAgIDAgMYAfCEUCwJ+IDlBkJTFAEEwEPEDBEBC///Piuv//9UeICMpA8AhIgd9IgggIykDyCEiD0Kr1f7///+//7l/Vq0iAn0hBUKk7MO1j9S0mOcAICMpA7ghIgN9IgQgAiAIViAHQv//z4rr///VHlZyrSICfSEHQr+llJzP8NK75AAgIykDsCEiDH0iCCACIARWIANCpOzDtY/UtJjnAFZyrSICfSEJQtfZrprk9umNywAgIykDqCEiA30iBCACIAhWIAxCv6WUnM/w0rvkAFZyrSICfSEMQqvV/v///7//uX8gD30hGEKazf/Lo73EgBogIykDoCEgAiAEViADQtfZrprk9umNywBWcq18fQwBCyAjKQOILCEYICMpA4AsIQUgIykD+CshByAjKQPwKyEJICMpA+grIQwgIykD4CsLIRJCACETQdgAIStCACECQgAhBEIAIQNCACEIQgAhDwNAICNBsAdqICsgVWopAwAiEUIAIBhCABDJAyAjQcAHaiARQgAgBUIAEMkDICNB0AdqIBFCACAHQgAQyQMgI0HgB2ogEUIAIAlCABDJAyAjQfAHaiARQgAgDEIAEMkDICNBgAhqIBFCACASQgAQyQMgI0GgB2ogIykDsAciESATfCIZQgBCAEL9//P/z///+Yl/EMkDICNBkAdqICMpA6gHIhBCAEKr1f7///+//7l/QgAQyQMgI0GAB2ogEEIAQv//z4rr///VHkIAEMkDICNB8AZqIBBCAEKk7MO1j9S0mOcAQgAQyQMgI0HgBmogEEIAQr+llJzP8NK75ABCABDJAyAjQdAGaiAQQgBC19mumuT26Y3LAEIAEMkDICNBwAZqIBBCAEKazf/Lo73EgBpCABDJAyAjKQPIBiAPICMpA4AIIg98IhcgIykD+AcgCCAjKQPwByIIfCIQIAhUrXwgECAjKQPoByADICMpA+AHIgN8IgggA1StfCAIICMpA9gHIAQgIykD0AciBHwiAyAEVK18IAMgIykDyAcgAiAjKQPAByICfCIEIAJUrXwgBCAEICMpA7gHIBEgGVatfHwiBFatfHwiFSADVK18fCIDIAhUrXx8IgIgEFStfHwiFiAjKQPABnwiECAWVK18IBAgECAjKQPYBiACIAIgIykD0AZ8IhFWrXwgESARICMpA+gGIAMgAyAjKQPgBnwiCFatfCAIIAggIykD+AYgFSAVICMpA/AGfCIDVq18IAMgAyAjKQOIByAEICMpA4AHIgJ8IgQgAlStfCAEIAQgIykDmAcgGSAjKQOQByICfCACVK18fCITVq18fCICVq18fCIEVq18fCIDVq18fCIIVq18IBYgF1StICMpA4gIIA8gF1atfHx8IQ8gK0EIayIrQShHDQALAkACQCAPQprN/8ujvcSAGlYNACAPQprN/8ujvcSAGlIEQCACIQUgBCEHIAMhCSAIIQwMAgsgCELX2a6a5PbpjcsAVg0AAkAgCELX2a6a5PbpjcsAUgRAIAIhBSAEIQcgAyEJIAghDAwBCyADQr+llJzP8NK75ABWDQFC19mumuT26Y3LACEMIANCv6WUnM/w0rvkAFIEQCACIQUgBCEHIAMhCQwBCyAEQqTsw7WP1LSY5wBWDQFCv6WUnM/w0rvkACEJIARCpOzDtY/UtJjnAFIEQCACIQUgBCEHDAELIAJC///Piuv//9UeVg0BQqTsw7WP1LSY5wAhByACQv//z4rr///VHlIEQCACIQUMAQtC///Piuv//9UeIQUgE0Kq1f7///+//7l/Vg0BC0Kazf/Lo73EgBohDwwBCyACQv//z4rr///VHn0iDCATQqvV/v///7//uX9UrSIHfSEFIARCpOzDtY/UtJjnAH0iCSACQv//z4rr///VHlQgByAMVnKtIgJ9IQcgA0K/pZScz/DSu+QAfSIMIARCpOzDtY/UtJjnAFQgAiAJVnKtIgJ9IQkgCELX2a6a5PbpjcsAfSIEIANCv6WUnM/w0rvkAFQgAiAMVnKtIgJ9IQwgDyAIQtfZrprk9umNywBUIAIgBFZyrX1Cms3/y6O9xIAafSEPIBNC1aqBgICAwIDGAHwhEwsgIyATNwOoKCAjIAU3A6AoICMgBzcDmCggIyAJNwOQKCAjIAw3A4goICMgDzcDgCggIyAUNwP4JyAjIAY3A/AnICMgCzcD6CcgIyAKNwPgJyAjIA43A9gnICMgDTcD0CcgI0GwKGoiICAjQfAUaiIkICNB8CNqIjEQPyAjQfApaiIuIFsgI0HQJ2oiMBA/ICNB0CpqIiUgSiAjQdAkaiIyED8gI0GQKWoiKSAuICUQ1QEgJSAjQeATaiIAICkQPyAjQbAZaiIvICAgJRDVASApIEsgMRA/ICUgACBaED8gLiAlIDAQPyAgICkgLhDVASAlICQgMhA/IDUgICAlENUBIC4gSiAxED8gJSBcIDAQPyApIC4gJRDVASAlIEsgMhA/IDMgKSAlENUBICAgXCAxED8gLiBKIDAQPyAlIFogMhA/ICkgLiAlENUBICUgACApED8gI0GwJWoiJiAgICUQ1QEgLiBbIDEQPyAlICQgMBA/ICkgLiAlENUBICUgXCAyED8gTiApICUQ1QEgLiBaIDEQPyAlIEsgMBA/ICkgLiAlENUBICUgWyAyED8gTCApICUQ1QEgI0HwLGoiACAvQaAC/AoAACBIICZBoAL8CgAAICNBoA9qIABBwAT8CgAAQQFxBEAgI0HQG2oQdSApIDwgXhA/IC4gOCBeED8gJSBhICkQjQEgI0GwHGoiMSAlQeAA/AoAACAjQZAdaiIAICNBgA1qIiQgLhCNASApIDEQXiAjQfAdaiImIAAQXiAjQdAeaiIyIAAgJhA/IC4gXiApED8gKSAmQeAA/AoAACAjQbAfaiIlICQgKRA/ICkgMiAuENUBICNCz6qZgICAwIkyNwPYKCAjQoWAkLaNg4CeuX83A9AoICNC0fb2htvBl7DXADcDyCggI0LLt/7onqTZkot/NwPAKCAjQoPYiIuQr6P57AA3A7goICNCjMWH3Nvz6vURNwOwKCAuICAgJRB3ICNBkCBqIiYgKSAuEI0BIC4gYSAyED8gI0HwIGoiKCAAICYQPyAgICVB4AD8CgAAICkgJkHgAPwKAAAgMCAgICkQjQEgKSAxIDAQPyAjQdAhaiImICkgLhCNASAuIDJB4AD8CgAAICNBsCJqIgAgXiAuED8gJCAoQeAA/AoAACBhICZB4AD8CgAAIF4gAEHgAPwKAAAgI0G4K2ogI0GYHWopAwA3AwAgI0HAK2ogI0GgHWopAwA3AwAgI0HIK2ogI0GoHWopAwA3AwAgI0HQK2ogI0GwHWopAwA3AwAgI0HYK2ogI0G4HWopAwA3AwAgIiBkKQMANwMAICJBCGogZEEIaikDADcDACAiQRBqIGRBEGopAwA3AwAgIkEYaiBkQRhqKQMANwMAICJBIGogZEEgaikDADcDACAiQShqIGRBKGopAwA3AwAgIyAjKQOQHTcDsCsgLiAjQbArakHgAPwKAAAgKSAuELQCICAgKSA8ED8gI0G4GWogI0G4HGopAwA3AwAgI0HAGWogI0HAHGopAwA3AwAgI0HIGWogI0HIHGopAwA3AwAgI0HQGWogI0HQHGopAwA3AwAgI0HYGWogI0HYHGopAwA3AwAgPSBgKQMANwMAID1BCGogYEEIaikDADcDACA9QRBqIGBBEGopAwA3AwAgPUEYaiBgQRhqKQMANwMAID1BIGogYEEgaikDADcDACA9QShqIGBBKGopAwA3AwAgIyAjKQOwHDcDsBkgLiAvQeAA/AoAACApIC4gOBA/ICNBkCNqICAgKRDVAQJ+IDFBkJTFAEEwEPEDBEBC///Piuv//9UeICMpA9AcIgh9IgUgIykD2BwiCkKr1f7///+//7l/Vq0iAn0hBkKk7MO1j9S0mOcAICMpA8gcIgN9IgQgAiAFViAIQv//z4rr///VHlZyrSICfSEFQr+llJzP8NK75AAgIykDwBwiC30iCCACIARWIANCpOzDtY/UtJjnAFZyrSICfSEHQtfZrprk9umNywAgIykDuBwiA30iBCACIAhWIAtCv6WUnM/w0rvkAFZyrSICfSEJQqvV/v///7//uX8gCn0hC0Kazf/Lo73EgBogIykDsBwgAiAEViADQtfZrprk9umNywBWcq18fQwBCyAjKQP4KiELICMpA/AqIQYgIykD6CohBSAjKQPgKiEHICMpA9gqIQkgIykD0CoLIQ5CACEUQSghK0IAIQJCACEEQgAhA0IAIQhCACENA0AgI0HgBWogKyBVaikDACIKQgAgC0IAEMkDICNB8AVqIApCACAGQgAQyQMgI0GABmogCkIAIAVCABDJAyAjQZAGaiAKQgAgB0IAEMkDICNBoAZqIApCACAJQgAQyQMgI0GwBmogCkIAIA5CABDJAyAjQdAFaiAjKQPgBSIMIBR8IhBCAEIAQv3/8//P///5iX8QyQMgI0HABWogIykD2AUiCkIAQqvV/v///7//uX9CABDJAyAjQbAFaiAKQgBC///Piuv//9UeQgAQyQMgI0GgBWogCkIAQqTsw7WP1LSY5wBCABDJAyAjQZAFaiAKQgBCv6WUnM/w0rvkAEIAEMkDICNBgAVqIApCAELX2a6a5PbpjcsAQgAQyQMgI0HwBGogCkIAQprN/8ujvcSAGkIAEMkDICMpA/gEICMpA7AGIgogDXwiEiAjKQOoBiAIICMpA6AGIgh8Ig0gCFStfCANICMpA5gGIAMgIykDkAYiA3wiCCADVK18IAggIykDiAYgBCAjKQOABiIEfCIDIARUrXwgAyAjKQP4BSACICMpA/AFIgJ8IgQgAlStfCAEIAQgIykD6AUgDCAQVq18fCIEVq18fCIRIANUrXx8IgMgCFStfHwiAiANVK18fCIPICMpA/AEfCINIA9UrXwgDSANICMpA4gFIAIgAiAjKQOABXwiDFatfCAMIAwgIykDmAUgAyADICMpA5AFfCIIVq18IAggCCAjKQOoBSARIBEgIykDoAV8IgNWrXwgAyADICMpA7gFIAQgIykDsAUiAnwiBCACVK18IAQgIykDyAUgECAjKQPABSICfCACVK18fCIUIARUrXx8IgJWrXx8IgRWrXx8IgNWrXx8IghWrXwgDyASVK0gIykDuAYgCiASVq18fHwhDSArQQhrIitBeEcNAAsCQAJAIA1Cms3/y6O9xIAaVg0AAkACQAJAAkAgDUKazf/Lo73EgBpSDQAgCELX2a6a5PbpjcsAVg0EIAhC19mumuT26Y3LAFIEQEKazf/Lo73EgBohDQwBCyADQr+llJzP8NK75ABWDQRC19mumuT26Y3LACEOIANCv6WUnM/w0rvkAFIEQEKazf/Lo73EgBohDQwCCyAEQqTsw7WP1LSY5wBWDQRCv6WUnM/w0rvkACEKIARCpOzDtY/UtJjnAFIEQEKazf/Lo73EgBohDQwDCyACQv//z4rr///VHlYNBEKk7MO1j9S0mOcAIQsgAkL//8+K6///1R5RDQNCms3/y6O9xIAaIQ0gAiEGDAULIAghDgsgAyEKCyAEIQsgAiEGDAILQv//z4rr///VHiEGIBRCqtX+////v/+5f1YNAEKazf/Lo73EgBohDQwBCyACQv//z4rr///VHn0iCyAUQqvV/v///7//uX9UrSIFfSEGIARCpOzDtY/UtJjnAH0iByACQv//z4rr///VHlQgBSALVnKtIgJ9IQsgA0K/pZScz/DSu+QAfSIFIARCpOzDtY/UtJjnAFQgAiAHVnKtIgJ9IQogCELX2a6a5PbpjcsAfSIEIANCv6WUnM/w0rvkAFQgAiAFVnKtIgJ9IQ4gDSAIQtfZrprk9umNywBUIAIgBFZyrX1Cms3/y6O9xIAafSENIBRC1aqBgICAwIDGAHwhFAsCfiBgQZCUxQBBMBDxAwRAQv//z4rr///VHiAjKQOAHSIHfSIIICMpA4gdIg9Cq9X+////v/+5f1atIgJ9IQVCpOzDtY/UtJjnACAjKQP4HCIDfSIEIAIgCFYgB0L//8+K6///1R5Wcq0iAn0hB0K/pZScz/DSu+QAICMpA/AcIgx9IgggAiAEViADQqTsw7WP1LSY5wBWcq0iAn0hCULX2a6a5PbpjcsAICMpA+gcIgN9IgQgAiAIViAMQr+llJzP8NK75ABWcq0iAn0hDEKr1f7///+//7l/IA99IRhCms3/y6O9xIAaICMpA+AcIAIgBFYgA0LX2a6a5PbpjcsAVnKtfH0MAQsgIykDqCshGCAjKQOgKyEFICMpA5grIQcgIykDkCshCSAjKQOIKyEMICMpA4ArCyESQgAhE0EoIStCACECQgAhBEIAIQNCACEIQgAhDwNAICNBkARqICsgVWopAwAiEUIAIBhCABDJAyAjQaAEaiARQgAgBUIAEMkDICNBsARqIBFCACAHQgAQyQMgI0HABGogEUIAIAlCABDJAyAjQdAEaiARQgAgDEIAEMkDICNB4ARqIBFCACASQgAQyQMgI0GABGogIykDkAQiESATfCIZQgBCAEL9//P/z///+Yl/EMkDICNB8ANqICMpA4gEIhBCAEKr1f7///+//7l/QgAQyQMgI0HgA2ogEEIAQv//z4rr///VHkIAEMkDICNB0ANqIBBCAEKk7MO1j9S0mOcAQgAQyQMgI0HAA2ogEEIAQr+llJzP8NK75ABCABDJAyAjQbADaiAQQgBC19mumuT26Y3LAEIAEMkDICNBoANqIBBCAEKazf/Lo73EgBpCABDJAyAjKQOoAyAPICMpA+AEIg98IhcgIykD2AQgCCAjKQPQBCIIfCIQIAhUrXwgECAjKQPIBCADICMpA8AEIgN8IgggA1StfCAIICMpA7gEIAQgIykDsAQiBHwiAyAEVK18IAMgIykDqAQgAiAjKQOgBCICfCIEIAJUrXwgBCAEICMpA5gEIBEgGVatfHwiBFatfHwiFSADVK18fCIDIAhUrXx8IgIgEFStfHwiFiAjKQOgA3wiECAWVK18IBAgECAjKQO4AyACIAIgIykDsAN8IhFWrXwgESARICMpA8gDIAMgAyAjKQPAA3wiCFatfCAIIAggIykD2AMgFSAVICMpA9ADfCIDVq18IAMgAyAjKQPoAyAEICMpA+ADIgJ8IgQgAlStfCAEIAQgIykD+AMgGSAjKQPwAyICfCACVK18fCITVq18fCICVq18fCIEVq18fCIDVq18fCIIVq18IBYgF1StICMpA+gEIA8gF1atfHx8IQ8gK0EIayIrQXhHDQALAkACQCAPQprN/8ujvcSAGlYNAAJAAkACQAJAIA9Cms3/y6O9xIAaUg0AIAhC19mumuT26Y3LAFYNBCAIQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ8MAQsgA0K/pZScz/DSu+QAVg0EQtfZrprk9umNywAhDCADQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ8MAgsgBEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhCSAEQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ8MAwsgAkL//8+K6///1R5WDQRCpOzDtY/UtJjnACEHIAJC///Piuv//9UeUQ0DQprN/8ujvcSAGiEPIAIhBQwFCyAIIQwLIAMhCQsgBCEHIAIhBQwCC0L//8+K6///1R4hBSATQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ8MAQsgAkL//8+K6///1R59IgwgE0Kr1f7///+//7l/VK0iB30hBSAEQqTsw7WP1LSY5wB9IgkgAkL//8+K6///1R5UIAcgDFZyrSICfSEHIANCv6WUnM/w0rvkAH0iDCAEQqTsw7WP1LSY5wBUIAIgCVZyrSICfSEJIAhC19mumuT26Y3LAH0iBCADQr+llJzP8NK75ABUIAIgDFZyrSICfSEMIA8gCELX2a6a5PbpjcsAVCACIARWcq19QprN/8ujvcSAGn0hDyATQtWqgYCAgMCAxgB8IRMLICMgEzcDyCQgIyAFNwPAJCAjIAc3A7gkICMgCTcDsCQgIyAMNwOoJCAjIA83A6AkICMgFDcDmCQgIyAGNwOQJCAjIAs3A4gkICMgCjcDgCQgIyAONwP4IyAjIA03A/AjQgAhFEHYACErICMpA5AdIQ8gIykDmB0hDiAjKQOgHSEMICMpA6gdIQogIykDsB0hCSAjKQO4HSELQgAhAkIAIQRCACEDQgAhCEIAIQ0DQCAjQcACaiArIFVqKQMAIgVCACALQgAQyQMgI0HQAmogBUIAIAlCABDJAyAjQeACaiAFQgAgCkIAEMkDICNB8AJqIAVCACAMQgAQyQMgI0GAA2ogBUIAIA5CABDJAyAjQZADaiAFQgAgD0IAEMkDICNBsAJqICMpA8ACIgcgFHwiEEIAQgBC/f/z/8////mJfxDJAyAjQaACaiAjKQO4AiIFQgBCq9X+////v/+5f0IAEMkDICNBkAJqIAVCAEL//8+K6///1R5CABDJAyAjQYACaiAFQgBCpOzDtY/UtJjnAEIAEMkDICNB8AFqIAVCAEK/pZScz/DSu+QAQgAQyQMgI0HgAWogBUIAQtfZrprk9umNywBCABDJAyAjQdABaiAFQgBCms3/y6O9xIAaQgAQyQMgIykD2AEgDSAjKQOQAyIGfCISICMpA4gDICMpA4ADIgUgCHwiCCAFVK18IAggIykD+AIgAyAjKQPwAiIDfCIFIANUrXwgBSAjKQPoAiAEICMpA+ACIgR8IgMgBFStfCADICMpA9gCIAIgIykD0AIiAnwiBCACVK18IAQgBCAjKQPIAiAHIBBWrXx8IgRWrXx8IhEgA1StfHwiAyAFVK18fCICIAhUrXx8Ig0gIykD0AF8IgcgDVStfCAHIAcgIykD6AEgAiACICMpA+ABfCIIVq18IAggCCAjKQP4ASADIAMgIykD8AF8IgVWrXwgBSAFICMpA4gCIBEgESAjKQOAAnwiA1atfCADIAMgIykDmAIgBCAjKQOQAiICfCIEIAJUrXwgBCAjKQOoAiAQICMpA6ACIgJ8IAJUrXx8IhQgBFStfHwiAlatfHwiBFatfHwiA1atfHwiCFatfCANIBJUrSAjKQOYAyAGIBJWrXx8fCENICtBCGsiK0EoRw0ACwJAAkAgDUKazf/Lo73EgBpWDQACQAJAAkACQCANQprN/8ujvcSAGlINACAIQtfZrprk9umNywBWDQQgCELX2a6a5PbpjcsAUgRAQprN/8ujvcSAGiENDAELIANCv6WUnM/w0rvkAFYNBELX2a6a5PbpjcsAIQ4gA0K/pZScz/DSu+QAUgRAQprN/8ujvcSAGiENDAILIARCpOzDtY/UtJjnAFYNBEK/pZScz/DSu+QAIQogBEKk7MO1j9S0mOcAUgRAQprN/8ujvcSAGiENDAMLIAJC///Piuv//9UeVg0EQqTsw7WP1LSY5wAhCyACQv//z4rr///VHlENA0Kazf/Lo73EgBohDSACIQYMBQsgCCEOCyADIQoLIAQhCyACIQYMAgtC///Piuv//9UeIQYgFEKq1f7///+//7l/Vg0AQprN/8ujvcSAGiENDAELIAJC///Piuv//9UefSILIBRCq9X+////v/+5f1StIgV9IQYgBEKk7MO1j9S0mOcAfSIHIAJC///Piuv//9UeVCAFIAtWcq0iAn0hCyADQr+llJzP8NK75AB9IgUgBEKk7MO1j9S0mOcAVCACIAdWcq0iAn0hCiAIQtfZrprk9umNywB9IgQgA0K/pZScz/DSu+QAVCACIAVWcq0iAn0hDiANIAhC19mumuT26Y3LAFQgAiAEVnKtfUKazf/Lo73EgBp9IQ0gFELVqoGAgIDAgMYAfCEUC0IAIRNB2AAhKyAjKQPAHSEVICMpA8gdIRYgIykD0B0hECAjKQPYHSESICMpA+AdIREgIykD6B0hDEIAIQJCACEEQgAhA0IAIQhCACEPA0AgI0HwAGogKyBVaikDACIFQgAgDEIAEMkDICNBgAFqIAVCACARQgAQyQMgI0GQAWogBUIAIBJCABDJAyAjQaABaiAFQgAgEEIAEMkDICNBsAFqIAVCACAWQgAQyQMgI0HAAWogBUIAIBVCABDJAyAjQeAAaiAjKQNwIgkgE3wiGEIAQgBC/f/z/8////mJfxDJAyAjQdAAaiAjKQNoIgVCAEKr1f7///+//7l/QgAQyQMgI0FAayAFQgBC///Piuv//9UeQgAQyQMgI0EwaiAFQgBCpOzDtY/UtJjnAEIAEMkDICNBIGogBUIAQr+llJzP8NK75ABCABDJAyAjQRBqIAVCAELX2a6a5PbpjcsAQgAQyQMgIyAFQgBCms3/y6O9xIAaQgAQyQMgIykDCCAPICMpA8ABIgd8IhkgIykDuAEgIykDsAEiBSAIfCIIIAVUrXwgCCAjKQOoASADICMpA6ABIgN8IgUgA1StfCAFICMpA5gBIAQgIykDkAEiBHwiAyAEVK18IAMgIykDiAEgAiAjKQOAASICfCIEIAJUrXwgBCAEICMpA3ggCSAYVq18fCIEVq18fCIXIANUrXx8IgMgBVStfHwiAiAIVK18fCIPICMpAwB8IgkgD1StfCAJIAkgIykDGCACIAIgIykDEHwiCFatfCAIIAggIykDKCADIAMgIykDIHwiBVatfCAFIAUgIykDOCAXIBcgIykDMHwiA1atfCADIAMgIykDSCAEICMpA0AiAnwiBCACVK18IAQgIykDWCAYICMpA1AiAnwgAlStfHwiEyAEVK18fCICVq18fCIEVq18fCIDVq18fCIIVq18IA8gGVStICMpA8gBIAcgGVatfHx8IQ8gK0EIayIrQShHDQALAkACQCAPQprN/8ujvcSAGlYNAAJAAkACQAJAIA9Cms3/y6O9xIAaUg0AIAhC19mumuT26Y3LAFYNBCAIQtfZrprk9umNywBSBEBCms3/y6O9xIAaIQ8MAQsgA0K/pZScz/DSu+QAVg0EQtfZrprk9umNywAhDCADQr+llJzP8NK75ABSBEBCms3/y6O9xIAaIQ8MAgsgBEKk7MO1j9S0mOcAVg0EQr+llJzP8NK75AAhCSAEQqTsw7WP1LSY5wBSBEBCms3/y6O9xIAaIQ8MAwsgAkL//8+K6///1R5WDQRCpOzDtY/UtJjnACEHIAJC///Piuv//9UeUQ0DQprN/8ujvcSAGiEPIAIhBQwFCyAIIQwLIAMhCQsgBCEHIAIhBQwCC0L//8+K6///1R4hBSATQqrV/v///7//uX9WDQBCms3/y6O9xIAaIQ8MAQsgAkL//8+K6///1R59IgwgE0Kr1f7///+//7l/VK0iB30hBSAEQqTsw7WP1LSY5wB9IgkgAkL//8+K6///1R5UIAcgDFZyrSICfSEHIANCv6WUnM/w0rvkAH0iDCAEQqTsw7WP1LSY5wBUIAIgCVZyrSICfSEJIAhC19mumuT26Y3LAH0iBCADQr+llJzP8NK75ABUIAIgDFZyrSICfSEMIA8gCELX2a6a5PbpjcsAVCACIARWcq19QprN/8ujvcSAGn0hDyATQtWqgYCAgMCAxgB8IRMLICMgEzcDqCUgIyAFNwOgJSAjIAc3A5glICMgCTcDkCUgIyAMNwOIJSAjIA83A4AlICMgFDcD+CQgIyAGNwPwJCAjIAs3A+gkICMgCjcD4CQgIyAONwPYJCAjIA03A9AkICNB0CdqIjEgI0GgD2oiJSAjQZAjaiIyED8gI0GQKWoiICBPICNB0CRqIi8QPyAjQfApaiIuIFkgI0HwI2oiJBA/ICNBsChqIjAgICAuENUBIC4gI0HQG2oiACAwED8gI0GwJWoiKCAxIC4Q1QEgMCBYIDIQPyAuIAAgTRA/ICAgLiAvED8gMSAwICAQ1QEgLiAlICQQPyBOIDEgLhDVASAgIFkgMhA/IC4gUyAvED8gMCAgIC4Q1QEgLiBYICQQPyBMIDAgLhDVASAxIFMgMhA/ICAgWSAvED8gLiBNICQQPyAwICAgLhDVASAuIAAgMBA/ICNB8BRqIiYgMSAuENUBICAgTyAyED8gLiAlIC8QPyAwICAgLhDVASAuIFMgJBA/IEsgMCAuENUBICAgTSAyED8gLiBYIC8QPyAwICAgLhDVASAuIE8gJBA/IEogMCAuENUBICNB8CxqIgAgKEGgAvwKAAAgSCAmQaAC/AoAACAlIABBwAT8CgAACyBXQQFqIldBP0cNAAsgI0G4JWogI0GoD2opAwA3AwAgI0HAJWogI0GwD2opAwA3AwAgI0HIJWogI0G4D2opAwA3AwAgI0HQJWogI0HAD2opAwA3AwAgI0HYJWogI0HID2opAwA3AwAgI0HoJWogI0HYD2opAwA3AwAgI0HwJWogI0HgD2opAwA3AwAgI0H4JWogI0HoD2opAwA3AwAgI0GAJmogI0HwD2opAwA3AwAgI0GIJmogI0H4D2opAwA3AwAgIyAjKQOgDzcDsCUgIyAjKQPQDzcD4CUgI0HwFGoiLiAjQbAlaiIrQeAA/AoAACAjQagtaiIgICNBuBBqKQMANwMAICNBsC1qIjAgI0HAEGopAwA3AwAgI0G4LWoiMSAjQcgQaikDADcDACAjQcAtaiIyICNB0BBqKQMANwMAICNByC1qIi8gI0HYEGopAwA3AwAgI0GYLWoiJCBYQShqKQMANwMAICNBkC1qIiUgWEEgaikDADcDACAjQYgtaiIoIFhBGGopAwA3AwAgI0GALWoiJiBYQRBqKQMANwMAICNB+CxqIgAgWEEIaikDADcDACAjICMpA7AQNwOgLSAjIFgpAwA3A/AsICsgI0HwLGoiKUHgAPwKAAAgI0HQFWogK0HgAPwKAAAgICAjQZgRaikDADcDACAwICNBoBFqKQMANwMAIDEgI0GoEWopAwA3AwAgMiAjQbARaikDADcDACAvICNBuBFqKQMANwMAICQgWUEoaikDADcDACAlIFlBIGopAwA3AwAgKCBZQRhqKQMANwMAICYgWUEQaikDADcDACAAIFlBCGopAwA3AwAgIyAjKQOQETcDoC0gIyBZKQMANwPwLCArIClB4AD8CgAAICNBsBZqICtB4AD8CgAAICNBkC9qIFMQtAIgI0HwL2ogTxC0AiAjQdAwaiBNELQCICkgLkGgAvwKAAAgQiApQcAE/AoAACAjQbAxaiQAIFYgQiAqEJ4CICogVkHABPwKAAALICdBCGoiJyBGRw0ACyBdQQhqIS0jAEGwO2siIiQAICJBkBJqICpBCGopAwA3AwAgIkGYEmogKkEQaikDADcDACAiQaASaiAqQRhqKQMANwMAICJBqBJqICpBIGopAwA3AwAgIkGwEmogKkEoaikDADcDACAiQcASaiAqQThqKQMANwMAICJByBJqICpBQGspAwA3AwAgIkHQEmogKkHIAGopAwA3AwAgIkHYEmogKkHQAGopAwA3AwAgIkHgEmogKkHYAGopAwA3AwAgIiAqKQMANwOIEiAiICopAzA3A7gSICJB0B9qIiAgIkGIEmoiLkHgAPwKAAAgIkGwG2oiMCAqQYgBaikDADcDACAiQagbaiIxICpBgAFqKQMANwMAICJBoBtqIjIgKkH4AGopAwA3AwAgIkGYG2oiLyAqQfAAaikDADcDACAiQZAbaiIkICpB6ABqKQMANwMAICJBwBtqIiUgKkGYAWopAwA3AwAgIkHIG2oiKCAqQaABaikDADcDACAiQdAbaiInICpBqAFqKQMANwMAICJB2BtqIiYgKkGwAWopAwA3AwAgIkHgG2oiACAqQbgBaikDADcDACAiICopA2A3A4gbICIgKikDkAE3A7gbIC4gIkGIG2oiKUHgAPwKAAAgIkGwIGogLkHgAPwKAAAgMCAqQegBaikDADcDACAxICpB4AFqKQMANwMAIDIgKkHYAWopAwA3AwAgLyAqQdABaikDADcDACAkICpByAFqKQMANwMAICUgKkH4AWopAwA3AwAgKCAqQYACaikDADcDACAnICpBiAJqKQMANwMAICYgKkGQAmopAwA3AwAgACAqQZgCaikDADcDACAiICopA8ABNwOIGyAiICopA/ABNwO4GyAuIClB4AD8CgAAICJBkCFqIC5B4AD8CgAAICJBqB1qICpBoAJqIiUQtAIgIkGIHmogKkGAA2oQtAIgIkHoHmogKkHgA2oQtAIgKSAgQaAC/AoAACAiQcgWaiIoIClBwAT8CgAAIwBB4A9rIjQkACA0QYAJaiInICoQcSA0QegEakHQnMUAKQMANwMAIDRB4ARqQcicxQApAwA3AwAgNEHYBGpBwJzFACkDADcDACA0QdAEakG4nMUAKQMANwMAIDRByARqQbCcxQApAwA3AwAgNEH4BGpCADcDACA0QYAFakIANwMAIDRBiAVqQgA3AwAgNEGQBWpCADcDACA0QZgFakIANwMAIDRBqJzFACkDADcDwAQgNEIANwPwBCA0QcANaiImQQBB4AD8CwAgNEGgDmogNEHABGoiMEHgAPwKAAAgNEGAD2pBAEHgAPwLACAwICUQcSA0QaALaiIAICYgMBC5AiA0QaACaiIuICcgABCNASA0QYADaiA0QeAJaiA0QYAMahCNASA0QeADaiA0QcAKaiA0QeAMahCNASMAQcAHayI2JAAgNhBtIDZBoAVqIiYgLkIDEM4BIDZB4AZqIjIgLkHgAGoiL0IDEM4BIDZBoAJqIjEQdSA2QYAGaiInIDIgMRA/IDZBwARqIgAgJiAnENUBIDIgLkHAAWoiJEIDEM4BICYQdSAxICZCAhDOASAnIDIgMRA/IDZBwAFqIiYgACAnENUBIDEgNiAuED8gMiAxIC8QPyAnIDIgJBA/IDEQdSAyICcgMRA/IDZB4ABqIgAgJiAyEI0BIDEgABA9IDYpA7ACIQQgNikDqAIhAiAwAn4gNigCoAJBAUYEQCAwIAQ3AxAgMCACNwMIQgEMAQsgNkHQAWogNkG4AmpB0AD8CgAAIDYgBDcDyAEgNiACNwPAASA2QaAFaiIxIC5CAhDOASA2QeAGaiIrIC8gJBA/IDZBoAJqIicQdSA2QYAGaiIyICsgJxA/ICsgMSAyEI0BICcgKyA2QcABaiImED8gKyAuELQCIDZBwARqIgAgKyAvED8gMiAkQgIQzgEgKxB1IDEgMiArED8gKyAAIDEQ1QEgNkGAA2ogKyAmED8gKyAuELQCIDIgKyAkED8gKyAvQgIQzgEgMSAyICsQ1QEgNkHgA2ogMSAmED8gMEEIaiAnQaAC/AoAAEIACzcDACA2QcAHaiQAIDQpA9AEIQQgNCkDyAQhAiApAn4gNCgCwARBAUYEQCApIAQ3AxAgKSACNwMIQgEMAQsgNEEQaiA0QdgEakGQAvwKAAAgNCAENwMIIDQgAjcDACA0QcAEaiInICogNBC5AiA0QYAJaiImICUQtAIgNEHgCWogKkGAA2oQtAIgNEHACmogKkHgA2oQtAIgNEGgC2oiACA0QaAC/AoAACA0QeAGaiAmIAAQuQIgKUEIaiAnQcAE/AoAAEIACzcDACA0QeAPaiQAICIpA5gbIQQgIikDkBshAgJAICIoAogbQQFHBEAgIkHgH2ogIkGgG2oiMUGwBPwKAAAgIiAENwPYHyAiIAI3A9AfICJBCGoiJyAoICAQngIgIkHQDWogIkEQaikDADcDACAiQdgNaiAiQRhqKQMANwMAICJB4A1qICJBIGopAwA3AwAgIkHoDWogIkEoaikDADcDACAiQfANaiAiQTBqKQMANwMAICIgIikDCDcDyA0gIkGADmogIkFAaykDADcDACAiQYgOaiAiQcgAaikDADcDACAiQZAOaiAiQdAAaikDADcDACAiQZgOaiAiQdgAaikDADcDACAiQaAOaiAiQeAAaikDADcDACAiICIpAzg3A/gNICJBsBtqIjJBoJrFACkDADcDACAiQagbaiIvQZiaxQApAwA3AwAgMUGQmsUAKQMANwMAICJBmBtqIiRBiJrFACkDADcDACAiQZAbaiIlQYCaxQApAwA3AwAgIkH4mcUAKQMANwOIGyAiQegSaiApICJB6ABqEHcgMkHQmsUAKQMANwMAIC9ByJrFACkDADcDACAxQcCaxQApAwA3AwAgJEG4msUAKQMANwMAICVBsJrFACkDADcDACAiQaiaxQApAwA3A4gbICJByBNqICkgIkHIAWoQdyAiQYgSaiImICJByA1qQeAA/AoAACAyQYCbxQApAwA3AwAgL0H4msUAKQMANwMAIDFB8JrFACkDADcDACAkQeiaxQApAwA3AwAgJUHgmsUAKQMANwMAICJB2JrFACkDADcDiBsgIkHIFmoiACAiQYgbaiIoICJBqAJqEHcgMkGwm8UAKQMANwMAIC9BqJvFACkDADcDACAxQaCbxQApAwA3AwAgJEGYm8UAKQMANwMAICVBkJvFACkDADcDACAiQYibxQApAwA3A4gbICJBqBdqICggIkGIA2oQdyAyQeCbxQApAwA3AwAgL0HYm8UAKQMANwMAIDFB0JvFACkDADcDACAkQcibxQApAwA3AwAgJUHAm8UAKQMANwMAICJBuJvFACkDADcDiBsgIkGIGGogKCAiQegDahB3ICggJkGgAvwKAAAgIkGoHWogAEGgAvwKAAAgIkHQH2oiJiAoQcAE/AoAACAiQcgEaiIAICYgJxCeAiAiQYgJaiAAEFcgMkHwocUAKQMANwMAIC9B6KHFACkDADcDACAxQeChxQApAwA3AwAgJEHYocUAKQMANwMAICVB0KHFACkDADcDACAiQcAbakIANwMAICJByBtqQgA3AwAgIkHQG2pCADcDACAiQdgbakIANwMAICJB4BtqQgA3AwAgIkHIocUAKQMANwOIGyAiQgA3A7gbICJBsCBqQQBBwAH8CwAgJiAoQeAA/AoAACAiQfAhakEAQaAC/AsAQUAhAANAICJBiBtqIicgIkHQH2oiJhBXICYgJ0HABPwKAAAgAEGsk8UAai0AAEEBRgRAICcgJiAiQcgEahCeAiAmICdBwAT8CgAACyAAQQFqIgANAAsgIkHIFmoiTCAiQdAfaiJIIgBBwAT8CgAAICJBkBJqICJB0BZqIispAwA3AwAgIkGYEmogIkHYFmoiKSkDADcDACAiQaASaiAiQeAWaiIuKQMANwMAICJBqBJqICJB6BZqIiApAwA3AwAgIkGwEmogIkHwFmoiMCkDADcDACAiQcASaiAiQYAXaiIxKQMANwMAICJByBJqICJBiBdqIjIpAwA3AwAgIkHQEmogIkGQF2oiLykDADcDACAiQdgSaiAiQZgXaiIkKQMANwMAICJB4BJqICJBoBdqIiUpAwA3AwAgIiAiKQPIFjcDiBIgIiAiKQP4FjcDuBIgACAiQYgSaiI8QeAA/AoAACAiQbAbaiJOICJB0BdqKQMANwMAICJBqBtqIlAgIkHIF2opAwA3AwAgIkGgG2oiPiAiQcAXaikDADcDACAiQZgbaiJAICJBuBdqKQMANwMAICJBkBtqIjcgIkGwF2opAwA3AwAgIkHAG2oiRiAiQeAXaikDADcDACAiQcgbaiJHICJB6BdqKQMANwMAICJB0BtqIjMgIkHwF2opAwA3AwAgIkHYG2oiNSAiQfgXaikDADcDACAiQeAbaiI5ICJBgBhqKQMANwMAICIgIikDqBc3A4gbICIgIikD2Bc3A7gbIDwgIkGIG2oiQkHgAPwKAAAgIkGwIGoiNCA8QeAA/AoAACBOICJBsBhqKQMANwMAIFAgIkGoGGopAwA3AwAgPiAiQaAYaikDADcDACBAICJBmBhqKQMANwMAIDcgIkGQGGopAwA3AwAgRiAiQcAYaikDADcDACBHICJByBhqKQMANwMAIDMgIkHQGGopAwA3AwAgNSAiQdgYaikDADcDACA5ICJB4BhqKQMANwMAICIgIikDiBg3A4gbICIgIikDuBg3A7gbIDwgQkHgAPwKAAAgIkGQIWoiKCA8QeAA/AoAACAiQagdaiInICJB6BhqELQCICJBiB5qIiYgIkHIGWoQtAIgIkHoHmoiACAiQagaahC0AiBCIEhBoAL8CgAAICJByA1qIjYgQkHABPwKAAAgKyAiQdAEaikDADcDACApICJB2ARqKQMANwMAIC4gIkHgBGopAwA3AwAgICAiQegEaikDADcDACAwICJB8ARqKQMANwMAICIgIikDyAQ3A8gWIDEgIkGABWopAwA3AwAgMiAiQYgFaikDADcDACAvICJBkAVqKQMANwMAICQgIkGYBWopAwA3AwAgJSAiQaAFaikDADcDACAiICIpA/gENwP4FiBIIExB4AD8CgAAIE4gIkHQBWopAwA3AwAgUCAiQcgFaikDADcDACA+ICJBwAVqKQMANwMAIEAgIkG4BWopAwA3AwAgNyAiQbAFaikDADcDACBGICJB4AVqKQMANwMAIEcgIkHoBWopAwA3AwAgMyAiQfAFaikDADcDACA1ICJB+AVqKQMANwMAIDkgIkGABmopAwA3AwAgIiAiKQOoBTcDiBsgIiAiKQPYBTcDuBsgTCBCQeAA/AoAACA0IExB4AD8CgAAIE4gIkGwBmopAwA3AwAgUCAiQagGaikDADcDACA+ICJBoAZqKQMANwMAIEAgIkGYBmopAwA3AwAgNyAiQZAGaikDADcDACBGICJBwAZqKQMANwMAIEcgIkHIBmopAwA3AwAgMyAiQdAGaikDADcDACA1ICJB2AZqKQMANwMAIDkgIkHgBmopAwA3AwAgIiAiKQOIBjcDiBsgIiAiKQO4BjcDuBsgTCBCQeAA/AoAACAoIExB4AD8CgAAICcgIkHoBmoQtAIgJiAiQcgHahC0AiAAICJBqAhqELQCIEIgSEGgAvwKAAAgPCBCQcAE/AoAACBIIDxBwAT8CgAAIEIgSCA2EJ4CIDYgQkHABPwKAAAgTkHwocUAKQMANwMAIFBB6KHFACkDADcDACA+QeChxQApAwA3AwAgQEHYocUAKQMANwMAIDdB0KHFACkDADcDACBGQgA3AwAgR0IANwMAIDNCADcDACA1QgA3AwAgOUIANwMAICJByKHFACkDADcDiBsgIkIANwO4GyA0QQBBwAH8CwAgSCBCQeAA/AoAACAiQfAhakEAQaAC/AsAQUAhAANAICJBiBtqIicgIkHQH2oiJhBXICYgJ0HABPwKAAAgAEGsk8UAai0AAEEBRgRAICcgJiAiQcgNahCeAiAmICdBwAT8CgAACyAAQQFqIgANAAsgIkHIFmoiPiAiQdAfaiJAIiBBwAT8CgAAICJB2DFqICJB0BZqIjApAwA3AwAgIkHgMWogIkHYFmoiMSkDADcDACAiQegxaiAiQeAWaiIyKQMANwMAICJB8DFqICJB6BZqIi8pAwA3AwAgIkH4MWogIkHwFmoiJCkDADcDACAiQYgyaiAiQYAXaiIlKQMANwMAICJBkDJqICJBiBdqIigpAwA3AwAgIkGYMmogIkGQF2oiJykDADcDACAiQaAyaiAiQZgXaiImKQMANwMAICJBqDJqICJBoBdqIgApAwA3AwAgIiAiKQPIFjcD0DEgIiAiKQP4FjcDgDIgICAiQdAxaiIgQeAA/AoAACAiQbAbaiI3ICJB0BdqKQMANwMAICJBqBtqIkYgIkHIF2opAwA3AwAgIkGgG2oiRyAiQcAXaikDADcDACAiQZgbaiIzICJBuBdqKQMANwMAICJBkBtqIjUgIkGwF2opAwA3AwAgIkHAG2oiOSAiQeAXaikDADcDACAiQcgbaiI0ICJB6BdqKQMANwMAICJB0BtqIjYgIkHwF2opAwA3AwAgIkHYG2oiKyAiQfgXaikDADcDACAiQeAbaiIpICJBgBhqKQMANwMAICIgIikDqBc3A4gbICIgIikD2Bc3A7gbICAgIkGIG2oiPEHgAPwKAAAgIkGwIGoiLiAgQeAA/AoAACA3ICJBsBhqKQMANwMAIEYgIkGoGGopAwA3AwAgRyAiQaAYaikDADcDACAzICJBmBhqKQMANwMAIDUgIkGQGGopAwA3AwAgOSAiQcAYaikDADcDACA0ICJByBhqKQMANwMAIDYgIkHQGGopAwA3AwAgKyAiQdgYaikDADcDACApICJB4BhqKQMANwMAICIgIikDiBg3A4gbICIgIikDuBg3A7gbICAgPEHgAPwKAAAgIkGQIWogIEHgAPwKAAAgIkGoHWogIkHoGGoQtAIgIkGIHmogIkHIGWoQtAIgIkHoHmogIkGoGmoQtAIgPCBAQaAC/AoAACAiQYgSaiIgIDxBwAT8CgAAIDAgIkHQDWopAwA3AwAgMSAiQdgNaikDADcDACAyICJB4A1qKQMANwMAIC8gIkHoDWopAwA3AwAgJCAiQfANaikDADcDACAlICJBgA5qKQMANwMAICggIkGIDmopAwA3AwAgJyAiQZAOaikDADcDACAmICJBmA5qKQMANwMAIAAgIkGgDmopAwA3AwAgIiAiKQPIDTcDyBYgIiAiKQP4DTcD+BYgPCA+QeAA/AoAACAiQfgfaiIwICJB0A5qKQMANwMAICJB8B9qIjEgIkHIDmopAwA3AwAgIkHoH2oiMiAiQcAOaikDADcDACAiQeAfaiIvICJBuA5qKQMANwMAICJB2B9qIiQgIkGwDmopAwA3AwAgIkGIIGoiJSAiQeAOaikDADcDACAiQZAgaiIoICJB6A5qKQMANwMAICJBmCBqIicgIkHwDmopAwA3AwAgIkGgIGoiJiAiQfgOaikDADcDACAiQaggaiIAICJBgA9qKQMANwMAICIgIikDqA43A9AfICIgIikD2A43A4AgID4gQEHgAPwKAAAgIkHoG2ogPkHgAPwKAAAgMCAiQbAPaikDADcDACAxICJBqA9qKQMANwMAIDIgIkGgD2opAwA3AwAgLyAiQZgPaikDADcDACAkICJBkA9qKQMANwMAICUgIkHAD2opAwA3AwAgKCAiQcgPaikDADcDACAnICJB0A9qKQMANwMAICYgIkHYD2opAwA3AwAgACAiQeAPaikDADcDACAiICIpA4gPNwPQHyAiICIpA7gPNwOAICA+IEBB4AD8CgAAICJByBxqID5B4AD8CgAAICJBsCZqICJB6A9qIkwQtAIgIkGQJ2ogIkHIEGoiThC0AiAiQfAnaiAiQagRaiJQELQCICJBkCRqIgAgPEGgAvwKAAAgIkHIDWoiJiAAQcAE/AoAACA8ICAgJhCeAiAmIDxBwAT8CgAAIDdB8KHFACkDADcDACBGQeihxQApAwA3AwAgR0HgocUAKQMANwMAIDNB2KHFACkDADcDACA1QdChxQApAwA3AwAgOUIANwMAIDRCADcDACA2QgA3AwAgK0IANwMAIClCADcDACAiQcihxQApAwA3A4gbICJCADcDuBsgLkEAQcAB/AsAIEAgPEHgAPwKAAAgIkHwIWpBAEGgAvwLAEFAIQADQCAiQYgbaiInICJB0B9qIiYQVyAmICdBwAT8CgAAIABBrJPFAGotAABBAUYEQCAnICYgIkHIDWoQngIgJiAnQcAE/AoAAAsgAEEBaiIADQALICJBiBtqIj4gIkHQH2oiQEHABPwKAAAgIkHYMWogIkGQG2oiNykDADcDACAiQeAxaiAiQZgbaiJGKQMANwMAICJB6DFqICJBoBtqIkcpAwA3AwAgIkHwMWogIkGoG2oiMykDADcDACAiQfgxaiAiQbAbaiI1KQMANwMAICJBiDJqICJBwBtqIjkpAwA3AwAgIkGQMmogIkHIG2oiNCkDADcDACAiQZgyaiAiQdAbaiI2KQMANwMAICJBoDJqICJB2BtqIispAwA3AwAgIkGoMmogIkHgG2oiKSkDADcDACAiICIpA4gbNwPQMSAiICIpA7gbNwOAMiBAICJB0DFqIjxB4AD8CgAAICJB8BZqIi4gIkGQHGopAwA3AwAgIkHoFmoiICAiQYgcaikDADcDACAiQeAWaiIwICJBgBxqKQMANwMAICJB2BZqIjEgIkH4G2opAwA3AwAgIkHQFmoiMiAiQfAbaikDADcDACAiQYAXaiIvICJBoBxqKQMANwMAICJBiBdqIiQgIkGoHGopAwA3AwAgIkGQF2oiJSAiQbAcaikDADcDACAiQZgXaiIoICJBuBxqKQMANwMAICJBoBdqIicgIkHAHGopAwA3AwAgIiAiKQPoGzcDyBYgIiAiKQOYHDcD+BYgPCAiQcgWaiIAQeAA/AoAACAiQbAgaiImIDxB4AD8CgAAIC4gIkHwHGopAwA3AwAgICAiQegcaikDADcDACAwICJB4BxqKQMANwMAIDEgIkHYHGopAwA3AwAgMiAiQdAcaikDADcDACAvICJBgB1qKQMANwMAICQgIkGIHWopAwA3AwAgJSAiQZAdaikDADcDACAoICJBmB1qKQMANwMAICcgIkGgHWopAwA3AwAgIiAiKQPIHDcDyBYgIiAiKQP4HDcD+BYgPCAAQeAA/AoAACAiQZAhaiA8QeAA/AoAACAiQfAqaiAiQagdahC0AiAiQdAraiAiQYgeahC0AiAiQbAsaiAiQegeahC0AiAiQdAoaiIAIEBBoAL8CgAAICJBiBJqIABBwAT8CgAAIwBBwAprIigkAAJ+ICJByA1qIiVBMGpBoIzFAEEwEPEDBEBC///Piuv//9UeICUpA1AiBn0iAyAlKQNYIglCq9X+////v/+5f1atIgR9IQJCpOzDtY/UtJjnACAlKQNIIgd9IgUgAyAEVCAGQv//z4rr///VHlZyrSIDfSEEQr+llJzP8NK75AAgJSkDQCIIfSIGIAMgBVYgB0Kk7MO1j9S0mOcAVnKtIgV9IQNC19mumuT26Y3LACAlKQM4Igt9IgcgBSAGViAIQr+llJzP8NK75ABWcq0iCH0hBUKr1f7///+//7l/IAl9IQZCms3/y6O9xIAaICUpAzAgByAIVCALQtfZrprk9umNywBWcq18fQwBCyAlKQNYIQYgJSkDUCECICUpA0ghBCAlKQNAIQMgJSkDOCEFICUpAzALIQggJUHgAGohACAoQShqICVBKGopAwA3AwAgKEEgaiAlQSBqKQMANwMAIChBGGogJUEYaikDADcDACAoQRBqICVBEGopAwA3AwAgKEEIaiAlQQhqKQMANwMAICggBjcDWCAoIAI3A1AgKCAENwNIICggAzcDQCAoIAU3AzggKCAINwMwICggJSkDADcDAAJ+ICVBkAFqQaCMxQBBMBDxAwRAQv//z4rr///VHiAlKQOwASIGfSIDICUpA7gBIglCq9X+////v/+5f1atIgR9IQJCpOzDtY/UtJjnACAlKQOoASIHfSIFIAMgBFQgBkL//8+K6///1R5Wcq0iA30hBEK/pZScz/DSu+QAICUpA6ABIgh9IgYgAyAFViAHQqTsw7WP1LSY5wBWcq0iBX0hA0LX2a6a5PbpjcsAICUpA5gBIgt9IgcgBSAGViAIQr+llJzP8NK75ABWcq0iCH0hBUKr1f7///+//7l/IAl9IQZCms3/y6O9xIAaICUpA5ABIAcgCFQgC0LX2a6a5PbpjcsAVnKtfH0MAQsgJSkDuAEhBiAlKQOwASECICUpA6gBIQQgJSkDoAEhAyAlKQOYASEFICUpA5ABCyEIIChB6ARqIABBKGopAwA3AwAgKEHgBGogAEEgaikDADcDACAoQdgEaiAAQRhqKQMANwMAIChB0ARqIABBEGopAwA3AwAgKEHIBGogAEEIaikDADcDACAoIAY3A5gFICggAjcDkAUgKCAENwOIBSAoIAM3A4AFICggBTcD+AQgKCAINwPwBCAoIAApAwA3A8AEIChB4AlqIgBBmJbFAEHgAPwKAAAgJUHAAWohJyAoQeAAaiAoQcAEaiAAED8CfiAlQfABakGgjMUAQTAQ8QMEQEL//8+K6///1R4gJSkDkAIiBn0iAyAlKQOYAiIJQqvV/v///7//uX9WrSIEfSECQqTsw7WP1LSY5wAgJSkDiAIiB30iBSADIARUIAZC///Piuv//9UeVnKtIgN9IQRCv6WUnM/w0rvkACAlKQOAAiIIfSIGIAMgBVYgB0Kk7MO1j9S0mOcAVnKtIgV9IQNC19mumuT26Y3LACAlKQP4ASILfSIHIAUgBlYgCEK/pZScz/DSu+QAVnKtIgh9IQVCq9X+////v/+5fyAJfSEGQprN/8ujvcSAGiAlKQPwASAHIAhUIAtC19mumuT26Y3LAFZyrXx9DAELICUpA5gCIQYgJSkDkAIhAiAlKQOIAiEEICUpA4ACIQMgJSkD+AEhBSAlKQPwAQshCCAoQegEaiAnQShqKQMANwMAIChB4ARqICdBIGopAwA3AwAgKEHYBGogJ0EYaikDADcDACAoQdAEaiAnQRBqKQMANwMAIChByARqICdBCGopAwA3AwAgKCAGNwOYBSAoIAI3A5AFICggBDcDiAUgKCADNwOABSAoIAU3A/gEICggCDcD8AQgKCAnKQMANwPABCAoQeAJaiIAQfiWxQBB4AD8CgAAICVBoAJqIScgKEHAAWogKEHABGogABA/An4gJUHQAmpBoIzFAEEwEPEDBEBC///Piuv//9UeICUpA/ACIgZ9IgMgJSkD+AIiCUKr1f7///+//7l/Vq0iBH0hAkKk7MO1j9S0mOcAICUpA+gCIgd9IgUgAyAEVCAGQv//z4rr///VHlZyrSIDfSEEQr+llJzP8NK75AAgJSkD4AIiCH0iBiADIAVWIAdCpOzDtY/UtJjnAFZyrSIFfSEDQtfZrprk9umNywAgJSkD2AIiC30iByAFIAZWIAhCv6WUnM/w0rvkAFZyrSIIfSEFQqvV/v///7//uX8gCX0hBkKazf/Lo73EgBogJSkD0AIgByAIVCALQtfZrprk9umNywBWcq18fQwBCyAlKQP4AiEGICUpA/ACIQIgJSkD6AIhBCAlKQPgAiEDICUpA9gCIQUgJSkD0AILIQggKEHoBGogJ0EoaikDADcDACAoQeAEaiAnQSBqKQMANwMAIChB2ARqICdBGGopAwA3AwAgKEHQBGogJ0EQaikDADcDACAoQcgEaiAnQQhqKQMANwMAICggBjcDmAUgKCACNwOQBSAoIAQ3A4gFICggAzcDgAUgKCAFNwP4BCAoIAg3A/AEICggJykDADcDwAQgKEHgCWoiAEHYl8UAQeAA/AoAACAlQYADaiEnIChBoAJqIChBwARqIAAQPwJ+ICVBsANqQaCMxQBBMBDxAwRAQv//z4rr///VHiAlKQPQAyIGfSIDICUpA9gDIglCq9X+////v/+5f1atIgR9IQJCpOzDtY/UtJjnACAlKQPIAyIHfSIFIAMgBFQgBkL//8+K6///1R5Wcq0iA30hBEK/pZScz/DSu+QAICUpA8ADIgh9IgYgAyAFViAHQqTsw7WP1LSY5wBWcq0iBX0hA0LX2a6a5PbpjcsAICUpA7gDIgt9IgcgBSAGViAIQr+llJzP8NK75ABWcq0iCH0hBUKr1f7///+//7l/IAl9IQZCms3/y6O9xIAaICUpA7ADIAcgCFQgC0LX2a6a5PbpjcsAVnKtfH0MAQsgJSkD2AMhBiAlKQPQAyECICUpA8gDIQQgJSkDwAMhAyAlKQO4AyEFICUpA7ADCyEIIChB6ARqICdBKGopAwA3AwAgKEHgBGogJ0EgaikDADcDACAoQdgEaiAnQRhqKQMANwMAIChB0ARqICdBEGopAwA3AwAgKEHIBGogJ0EIaikDADcDACAoIAY3A5gFICggAjcDkAUgKCAENwOIBSAoIAM3A4AFICggBTcD+AQgKCAINwPwBCAoICcpAwA3A8AEIChB4AlqIgBBuJjFAEHgAPwKAAAgKEGAA2ogKEHABGogABA/An4gJUGQBGpBoIzFAEEwEPEDBEBC///Piuv//9UeICUpA7AEIgZ9IgMgJSkDuAQiCUKr1f7///+//7l/Vq0iBH0hAkKk7MO1j9S0mOcAICUpA6gEIgd9IgUgAyAEVCAGQv//z4rr///VHlZyrSIDfSEEQr+llJzP8NK75AAgJSkDoAQiCH0iBiADIAVWIAdCpOzDtY/UtJjnAFZyrSIFfSEDQtfZrprk9umNywAgJSkDmAQiC30iByAFIAZWIAhCv6WUnM/w0rvkAFZyrSIIfSEFQqvV/v///7//uX8gCX0hBkKazf/Lo73EgBogJSkDkAQgByAIVCALQtfZrprk9umNywBWcq18fQwBCyAlKQO4BCEGICUpA7AEIQIgJSkDqAQhBCAlKQOgBCEDICUpA5gEIQUgJSkDkAQLIQggKEHoBGogJUGIBGopAwA3AwAgKEHgBGogJUGABGopAwA3AwAgKEHYBGogJUH4A2opAwA3AwAgKEHQBGogJUHwA2opAwA3AwAgKEHIBGogJUHoA2opAwA3AwAgKCAGNwOYBSAoIAI3A5AFICggBDcDiAUgKCADNwOABSAoIAU3A/gEICggCDcD8AQgKCAlKQPgAzcDwAQgKEHgCWoiAEGYmcUAQeAA/AoAACAoQeADaiAoQcAEaiAAED8gKEGgBWoiACAoQaAC/AoAACAoQcAHaiAoQaACakGgAvwKAAAgPiAAQcAE/AoAACAoQcAKaiQAICUgPkHABPwKAAAgIkGIG2oiKCAiQYgSaiAiQcgNaiIAEJ4CIAAgKEHABPwKAAAgIkHQH2oiJyAiQYgJakHABPwKAAAgKCAnICJByARqIgAQngIgACAoQcAE/AoAACA1QfChxQApAwA3AwAgM0HoocUAKQMANwMAIEdB4KHFACkDADcDACBGQdihxQApAwA3AwAgN0HQocUAKQMANwMAIDlCADcDACA0QgA3AwAgNkIANwMAICtCADcDACApQgA3AwAgIkHIocUAKQMANwOIGyAiQgA3A7gbICZBAEHAAfwLACAnIChB4AD8CgAAICJB8CFqQQBBoAL8CwBBQCEAA0AgIkGIG2oiJyAiQdAfaiImEFcgJiAnQcAE/AoAACAAQayTxQBqLQAAQQFGBEAgJyAmICJByA1qEJ4CICYgJ0HABPwKAAALIABBAWoiAA0ACyAiQcgWaiAiQdAfaiIuQcAE/AoAACAiQdgxaiAiQdAWaikDADcDACAiQeAxaiAiQdgWaikDADcDACAiQegxaiAiQeAWaikDADcDACAiQfAxaiAiQegWaikDADcDACAiQfgxaiAiQfAWaikDADcDACAiQYgyaiAiQYAXaikDADcDACAiQZAyaiAiQYgXaikDADcDACAiQZgyaiAiQZAXaikDADcDACAiQaAyaiAiQZgXaikDADcDACAiQagyaiAiQaAXaikDADcDACAiICIpA8gWNwPQMSAiICIpA/gWNwOAMiAuICJB0DFqIitB4AD8CgAAICJBsBtqIiAgIkHQF2opAwA3AwAgIkGoG2oiMCAiQcgXaikDADcDACAiQaAbaiIxICJBwBdqKQMANwMAICJBmBtqIjIgIkG4F2opAwA3AwAgIkGQG2oiLyAiQbAXaikDADcDACAiQcAbaiIkICJB4BdqKQMANwMAICJByBtqIiUgIkHoF2opAwA3AwAgIkHQG2oiKCAiQfAXaikDADcDACAiQdgbaiInICJB+BdqKQMANwMAICJB4BtqIiYgIkGAGGopAwA3AwAgIiAiKQOoFzcDiBsgIiAiKQPYFzcDuBsgKyAiQYgbaiIpQeAA/AoAACAiQbAgaiIAICtB4AD8CgAAICAgIkGwGGopAwA3AwAgMCAiQagYaikDADcDACAxICJBoBhqKQMANwMAIDIgIkGYGGopAwA3AwAgLyAiQZAYaikDADcDACAkICJBwBhqKQMANwMAICUgIkHIGGopAwA3AwAgKCAiQdAYaikDADcDACAnICJB2BhqKQMANwMAICYgIkHgGGopAwA3AwAgIiAiKQOIGDcDiBsgIiAiKQO4GDcDuBsgKyApQeAA/AoAACAiQZAhaiArQeAA/AoAACAiQagdaiAiQegYahC0AiAiQYgeaiAiQcgZahC0AiAiQegeaiAiQagaahC0AiApIC5BoAL8CgAAICJBiAlqIClBwAT8CgAAICBB8KHFACkDADcDACAwQeihxQApAwA3AwAgMUHgocUAKQMANwMAIDJB2KHFACkDADcDACAvQdChxQApAwA3AwAgJEIANwMAICVCADcDACAoQgA3AwAgJ0IANwMAICZCADcDACAiQcihxQApAwA3A4gbICJCADcDuBsgAEEAQcAB/AsAIC4gKUHgAPwKAAAgIkHwIWpBAEGgAvwLAEFAIQADQCAiQYgbaiInICJB0B9qIiYQVyAmICdBwAT8CgAAIABBrJPFAGotAABBAUYEQCAnICYgIkGICWoQngIgJiAnQcAE/AoAAAsgAEEBaiIADQALICJBiBtqIj8gIkHQH2oiTyIAQcAE/AoAACAiQdgxaiJTICJBkBtqIjMpAwA3AwAgIkHgMWoiViAiQZgbaiI1KQMANwMAICJB6DFqIlcgIkGgG2oiOSkDADcDACAiQfAxaiJaICJBqBtqIjQpAwA3AwAgIkH4MWoiWyAiQbAbaiIpKQMANwMAICJBiDJqICJBwBtqKQMANwMAICJBkDJqICJByBtqKQMANwMAICJBmDJqICJB0BtqKQMANwMAICJBoDJqICJB2BtqKQMANwMAICJBqDJqICJB4BtqKQMANwMAICIgIikDiBs3A9AxICIgIikDuBs3A4AyIAAgIkHQMWoiSUHgAPwKAAAgIkHwFmoiXCAiQZAcaikDADcDACAiQegWaiJdICJBiBxqKQMANwMAICJB4BZqIkIgIkGAHGopAwA3AwAgIkHYFmoiSCAiQfgbaikDADcDACAiQdAWaiI8ICJB8BtqKQMANwMAICJBgBdqIj4gIkGgHGopAwA3AwAgIkGIF2oiQCAiQagcaikDADcDACAiQZAXaiI3ICJBsBxqKQMANwMAICJBmBdqIkYgIkG4HGopAwA3AwAgIkGgF2oiRyAiQcAcaikDADcDACAiICIpA+gbNwPIFiAiICIpA5gcNwP4FiBJICJByBZqIkpB4AD8CgAAICJBsCBqIi4gSUHgAPwKAAAgXCAiQfAcaikDADcDACBdICJB6BxqKQMANwMAIEIgIkHgHGopAwA3AwAgSCAiQdgcaikDADcDACA8ICJB0BxqKQMANwMAID4gIkGAHWopAwA3AwAgQCAiQYgdaikDADcDACA3ICJBkB1qKQMANwMAIEYgIkGYHWopAwA3AwAgRyAiQaAdaikDADcDACAiICIpA8gcNwPIFiAiICIpA/gcNwP4FiBJIEpB4AD8CgAAICJBkCFqIiAgSUHgAPwKAAAgIkGwL2ogIkGoHWoQtAIgIkGQMGogIkGIHmoQtAIgIkHwMGogIkHoHmoQtAIgIkGQLWoiACBPQaAC/AoAACAiQYgSaiI2IABBwAT8CgAAIDwgIkHQDWoiKykDADcDACBIICJB2A1qIjApAwA3AwAgQiAiQeANaiIxKQMANwMAIF0gIkHoDWoiMikDADcDACBcICJB8A1qIi8pAwA3AwAgPiAiQfgNaiJLQQhqIiQpAwA3AwAgQCBLQRBqIiUpAwA3AwAgNyBLQRhqIigpAwA3AwAgRiBLQSBqIicpAwA3AwAgRyBLQShqIiYpAwA3AwAgIiAiKQPIDTcDyBYgIiBLKQMANwP4FiApQaCaxQApAwA3AwAgNEGYmsUAKQMANwMAIDlBkJrFACkDADcDACA1QYiaxQApAwA3AwAgM0GAmsUAKQMANwMAICJB+JnFACkDADcDiBsgLiA/ICJBqA5qIk0QdyApQdCaxQApAwA3AwAgNEHImsUAKQMANwMAIDlBwJrFACkDADcDACA1QbiaxQApAwA3AwAgM0GwmsUAKQMANwMAICJBqJrFACkDADcDiBsgICA/ICJBiA9qIjQQdyBPIEpB4AD8CgAAIFtBgJvFACkDADcDACBaQfiaxQApAwA3AwAgV0HwmsUAKQMANwMAIFZB6JrFACkDADcDACBTQeCaxQApAwA3AwAgIkHYmsUAKQMANwPQMSA/IEkgTBB3IFtBsJvFACkDADcDACBaQaibxQApAwA3AwAgV0Ggm8UAKQMANwMAIFZBmJvFACkDADcDACBTQZCbxQApAwA3AwAgIkGIm8UAKQMANwPQMSAiQegbaiIpIEkgThB3IFtB4JvFACkDADcDACBaQdibxQApAwA3AwAgV0HQm8UAKQMANwMAIFZByJvFACkDADcDACBTQcCbxQApAwA3AwAgIkG4m8UAKQMANwPQMSAiQcgcaiIuIEkgUBB3ICJBsDJqIgAgT0GgAvwKAAAgIkHQNGogP0GgAvwKAAAgIkGICWoiICAAQcAE/AoAACA8ICspAwA3AwAgSCAwKQMANwMAIEIgMSkDADcDACBdIDIpAwA3AwAgXCAvKQMANwMAID4gJCkDADcDACBAICUpAwA3AwAgNyAoKQMANwMAIEYgJykDADcDACBHICYpAwA3AwAgIiAiKQPIDTcDyBYgIiBLKQMANwP4FiA/IEpB4AD8CgAAICJB+B9qIjAgTUEoaikDADcDACAiQfAfaiIxIE1BIGopAwA3AwAgIkHoH2oiMiBNQRhqKQMANwMAICJB4B9qIi8gTUEQaikDADcDACAiQdgfaiIkIE1BCGopAwA3AwAgIkGIIGoiJSAiQdgOaiIrQQhqKQMANwMAICJBkCBqIiggK0EQaikDADcDACAiQZggaiInICtBGGopAwA3AwAgIkGgIGoiJiArQSBqKQMANwMAICJBqCBqIgAgK0EoaikDADcDACAiIE0pAwA3A9AfICIgKykDADcDgCAgSiBPQeAA/AoAACApIEpB4AD8CgAAIDAgNEEoaikDADcDACAxIDRBIGopAwA3AwAgMiA0QRhqKQMANwMAIC8gNEEQaikDADcDACAkIDRBCGopAwA3AwAgJSAiQbgPaiIlQQhqKQMANwMAICggJUEQaikDADcDACAnICVBGGopAwA3AwAgJiAlQSBqKQMANwMAIAAgJUEoaikDADcDACAiIDQpAwA3A9AfICIgJSkDADcDgCAgSiBPQeAA/AoAACAuIEpB4AD8CgAAICJBkDlqIEwQtAIgIkHwOWogThC0AiAiQdA6aiBQELQCICJB8DZqIgAgP0GgAvwKAAAgIkHIDWoiJiAAQcAE/AoAACA/IDYgJhCeAiAmID9BwAT8CgAAID8gICAmEJ4CICYgP0HABPwKAAAgPyAmICJByARqIgAQngIgACA/QcAE/AoAACAtIABBwAT8CgAAICJBsDtqJAAMAQsgIiAENwOQGyAiIAI3A4gbQdCUxQBBKyAiQYgbakHAlMUAQYSWxQAQygMAC0EADAELIF1BADoAAUEBCzoAACAqQfAQaiQAICEtAKAjQQFHDQEgISAhLQChIzoAwA4gIUEBNgKkICAhQaCLwQA2AqAgICFCATcCrCAgISAhQcAOaq1CgICAgOAEhDcD+CsgISAhQfgrajYCqCAgIUHYG2ogIUGgIGoQ0gIgIUGYF2ogIUHgG2ooAgAiADYCACAhQfgJaiAANgIAICEgISkC2Bs3A/AJCyAhQbAFaiAhQfgJaigCACIANgIAICEgISkD8AkiAjcDqAUgRUEMaiAANgIAIEUgAjcCBCBFQQE2AgAMAQsgIUHcG2oiJiAhQagjaiIoQcAE/AoAACAhQZQXaiIAICZBwAT8CgAAICFB9AlqIiYgAEHABPwKAAAgIUGsBWoiACAmQcAE/AoAACAhQegAaiAAQcAE/AoAACAhQQA2AugTICFCgICAgBA3AuATICFB4BNqIipBAEEGQQFBARCIAyAhQdgTakKAgICAgAI3AwAgIUHQE2ogaEEIaikAACICNwMAICEoAugTIiYgISgC5BNqIgBB1onBACgAADYAACAAQQRqQdqJwQAvAAA7AAAgISBoKQAAIgg3A8gTICEgJkEGaiInNgLoEyAhQbAjakKAgICAgAI3AwAgKCACNwMAICEgCDcDoCMgISgCtCMiACAhKALgEyAna0sEQCAqICcgAEEBQQEQiAMgISgC6BMhJwsgAARAIAAEQCAhKALkEyAnaiAhQaAjaiAA/AoAAAsgACAnaiEnCyAhICc2AugTIEMtAA8hIiBDLQAOIT8gQy0ADSFJIEMtAAwhSiBDLQALIUsgQy0ACiFNIEMtAAkhTyBDLQAIIVMgQy0AByFWIEMtAAYhVyBDLQAFIVogQy0ABCFbIEMtAAMhXCBDLQACIWggQy0AASFdIEMtAAAhQiAhKALgEyAna0EPTQRAICFB4BNqICdBEEEBQQEQiAMgISgC6BMhJwsgISgC5BMiJiAnaiIAIEMpAAA3AAAgAEEIaiBDQQhqKQAANwAAICEgJ0EQaiIANgLoEyAhQfAJaiAmIAAQ3QEgIUGgI2oQJiAhQfgUaiAhQbQpaigCADYCACAhICEpAqwpNwPwFEEBIT0CQANAICFBADYC4BsgIUKAgICAEDcC2BsgIUHYG2oiKEEAQQJBAUEBEIgDICEoAtwbIgAgISgC4BsiJmogPTsAACAhICZBAmoiJzYC4BsgISgC2BsiKiAna0EfTQRAICggJ0EgQQFBARCIAyAhKALYGyEqICEoAuAbIScgISgC3BshAAsgACAnaiImICEpAPAJNwAAICZBGGogIUGICmopAAA3AAAgJkEQaiAhQYAKaikAADcAACAmQQhqICFB+AlqKQAANwAAICFBkBdqIAAgJ0EgahDdASAqBEAgACAqEN8ECyAhLQCvFyFIICEtAK4XITwgIS0ArRchTCAhLQCsFyFOICEtAKsXIVAgIS0AqhchPiAhLQCpFyFAICEtAKgXIS0gIS0ApxchNyAhLQCmFyFGICEtAKUXIUcgIS0ApBchMyAhLQCjFyE1ICEtAKIXITkgIS0AoRchNCAhLQCgFyE2ICEtAJ8XISsgIS0AnhchKSAhLQCdFyEuICEtAJwXISAgIS0AmxchMCAhLQCaFyExICEtAJkXITIgIS0AmBchLyAhLQCXFyEkICEtAJYXISUgIS0AlRchKCAhLQCUFyEqICEtAJMXIScgIS0AkhchJiAhLQCRFyEAICEgIS0AkBdBAXY6APcbICEgADoA9hsgISAmOgD1GyAhICc6APQbICEgKjoA8xsgISAoOgDyGyAhICU6APEbICEgJDoA8BsgISAvOgDvGyAhIDI6AO4bICEgMToA7RsgISAwOgDsGyAhICA6AOsbICEgLjoA6hsgISApOgDpGyAhICs6AOgbICEgNjoA5xsgISA0OgDmGyAhIDk6AOUbICEgNToA5BsgISAzOgDjGyAhIEc6AOIbICEgRjoA4RsgISA3OgDgGyAhIC06AN8bICEgQDoA3hsgISA+OgDdGyAhIFA6ANwbICEgTjoA2xsgISBMOgDaGyAhIDw6ANkbICEgSDoA2BsgIUGgIGogIUHYG2pBIEEIEM8CAkACQAJ/AkACQCAhKAL4FCIARQ0AAkAgAEEBayIAQf7///8DcUUEQCAhKAL0FCEnIABB/////wNxIiZBAWoiAEEDcSErQgAhAiAmQQNPBEAgAEH8////B3EhAANAIAJCgAF8IQIgJ0EQaiEnIABBBGsiAA0ACwsgKwRAQgAhCANAICc1AgAgAoYgCHwhCCACQiB8IQIgJ0EEaiEnICtBAWsiKw0ACwsgCEKAgICAEFQNAQsgIUGoBWogIUGgIGogIUHwFGoQoQEgISgCvAUhACAhKAK4BSEqICEoArQFIScgISgCqAUiJkUNBSAhKAKsBSAmQQJ0EN8EDAULIAhQDQAgISgCqCAhKCAhKAKkICEnAkACQCAIQoCABFoEQCAoRQ0CIChB/////wNqISYgKEECdCEAIChB/////wNxQQFHDQFCACEEIAAgJ2oMBQsgKEUNASAIpyEqICdBBGshJiAoQQJ0ISdBACErA0AgK0EQdCAmICdqKAIAIgBBEHZyICpwQRB0IABB//8DcXIgKnAhKyAnQQRrIicNAAsMBQsgACAnakEIayEnICZB/////wNxQQFqQf7///8HcSErQgAhAgNAICc1AgAgJ0EEajUCACACQiCGhCAIgkIghoQgCIIhAiAnQQhrIScgK0ECayIrDQALDAILQQQhKkEAIQBBACEnDAQLICFBADYCuAUgIUEBNgKsBSAhQdT9wAA2AqgFICFCBDcCsAUgIUGoBWpBxP7AABCoBAALIAJCIIYhBCAnQQhqCyEAICZBAXEEfiACBSAEIABBBGs1AgCEIAiCC6chKwtBACEAICFBsAVqQaz8wAAoAgA2AgAgIUGk/MAAKQIANwOoBSArRQRAQQQhKkEAIScMAQsgIUGoBWpBmP3AABClAyAhKAKsBSArNgIAQQEhACAhKAKsBSEqICEoAqgFIScLICEoAqAgIiYEQCAhKAKkICAmQQJ0EN8ECyAADQEgJwRAICogJ0ECdBDfBAsgPUEBaiI9QYCABEcNAAsgIUEANgLoGyAhQQE2AtwbICFB8IvBADYC2BsgIUIENwLgGyAhQdgbakH4i8EAEKgEAAtB0c7FAC0AABoCQAJAAkACfwJAAkBBIEEBENYEIigEQCAoICEpANgbNwAAIChBGGogIUHwG2opAAA3AAAgKEEQaiAhQegbaikAADcAACAoQQhqICFB4BtqKQAANwAAICcEQCAqICdBAnQQ3wQLICEoAvAUIgAEQCAhKAL0FCAAQQJ0EN8ECwJAICEoAqQjIgBFDQAgACAAQQxsQRNqQXhxIiZqQQlqIgBFDQAgISgCoCMgJmsgABDfBAsgISgCoCYiAEGAgICAeEYgAEVyRQRAICEoAqQmIABBAnQQ3wQLICFBtA5qIChBIEEIEM8CICEoAuATIgAEQCAhKALkEyAAEN8ECyAoQSAQ3wQgIUGgI2oQJiAhKAK0KSIARQ0BAkAgAEEBayIAQf7///8DcUUEQCAAQf////8DcSImQQFqIgBBA3EhK0IAIQIgISgCsCkiKiEnICZBA08EQCAAQfz///8HcSEAA0AgAkKAAXwhAiAnQRBqIScgAEEEayIADQALCyArBEBCACEIA0AgJzUCACAChiAIfCEIIAJCIHwhAiAnQQRqIScgK0EBayIrDQALCyAIQoCAgIAQVA0BCyAhQfgJaiAhQbwOaigCADYCACAhICEpArQONwPwCSAhQZgXaiAhQawpaiIAQQhqKAIANgIAICEgACkCADcDkBcgIUHYG2ogIUHwCWogIUGQF2oQnAEgIUHIDmogIUHsG2ooAgA2AgAgISAhKQLkGzcDwA4gISgC2BsiAEUNByAhKALcGyAAQQJ0EN8EDAcLIAhQDQEgISgCrCkhJCAhKAK8DiEnICEoArgOIS8gISgCtA4hJQJAAkAgCEKAgARaBEAgJ0UNAiAnQf////8DaiEmICdBAnQhACAnQf////8DcUEBRw0BQgAhBCAAIC9qDAYLICdFDQEgCKchKCAvQQRrISYgJ0ECdCEnQQAhKwNAICtBEHQgJiAnaigCACIAQRB2ciAocEEQdCAAQf//A3FyIChwISsgJ0EEayInDQALDAYLIAAgL2pBCGshJyAmQf////8DcUEBakH+////B3EhK0IAIQIDQCAnNQIAICdBBGo1AgAgAkIghoQgCIJCIIaEIAiCIQIgJ0EIayEnICtBAmsiKw0ACwwDCyAhQeAbakGs/MAAKAIANgIAICFBpPzAACkCADcD2BsMBQtBAUEgQayDwQAQyAQACyAhQQA2AugbICFBATYC3BsgIUHU/cAANgLYGyAhQgQ3AuAbICFB2BtqQcT+wAAQqAQACyACQiCGIQQgJ0EIagshACAmQQFxBH4gAgUgBCAAQQRrNQIAhCAIggunISsLICFB4BtqQaz8wAAoAgA2AgAgIUGk/MAAKQIANwPYGyArRQ0AICFB2BtqQZj9wAAQpQMgISgC3BsgKzYCACAhQQE2AuAbCyAhQcgOaiAhQeAbaigCADYCACAhICEpA9gbNwPADiAkBEAgKiAkQQJ0EN8ECyAlRQ0AIC8gJUECdBDfBAsCQCAhKAKkIyIARQ0AIAAgAEEMbEETakF4cSImakEJaiIARQ0AICEoAqAjICZrIAAQ3wQLICEoAqAmIgBBgICAgHhGIABFckUEQCAhKAKkJiAAQQJ0EN8ECyAhQfAJahCHAyAhKALIDiImQQJ0ISpBACEAAkACQAJAICZB/////wNLICpB/P///wdLcg0AICEoAsQOIScCfwJ/AkAgKgRAQdHOxQAtAAAaQQQhACAqQQQQ1gQiOUUNBCAqBEAgOSAnICr8CgAACyAmRQ0BQQIhPSAmISpBAAwDC0EEITkgKgRAQQQgJyAq/AoAAAtBAAwBC0EEITlBAAshKkEBIT1BAQshACAhQaAjaiInQQBB4AD8CwACQAJAAkAgIUHwCWogJxCmBARAICFB0ApqIiggJxCmBA0BCyAADQEgIUHAK2ogIUGYCmopAwA3AwAgIUG4K2ogIUGQCmopAwA3AwAgIUGwK2ogIUGICmopAwA3AwAgIUGoK2ogIUGACmopAwA3AwAgIUGgK2ogIUH4CWopAwA3AwAgIUHQK2ogIUGoCmopAwA3AwAgIUHYK2ogIUGwCmopAwA3AwAgIUHgK2ogIUG4CmopAwA3AwAgIUHoK2ogIUHACmopAwA3AwAgIUHwK2ogIUHICmopAwA3AwAgISAhKQPwCTcDmCsgISAhKQOgCjcDyCsgIUGIFGogIUH4CmopAwA3AwAgIUGAFGogIUHwCmopAwA3AwAgIUH4E2ogIUHoCmopAwA3AwAgIUHwE2ogIUHgCmopAwA3AwAgIUHoE2ogIUHYCmopAwA3AwAgIUGYFGogIUGIC2opAwA3AwAgIUGgFGogIUGQC2opAwA3AwAgIUGoFGogIUGYC2opAwA3AwAgIUGwFGogIUGgC2opAwA3AwAgIUG4FGogIUGoC2opAwA3AwAgISAhKQPQCjcD4BMgISAhKQOACzcDkBQgIUHPImpBADoAACAhQQA7AM0iICEgPToAzCIgISAmNgLIIiAhIDk2AsQiICEgKjYCwCIgIUGgI2oiJiAhQcAiahC+AyAhQdApaiAhQagjaigCADYCACAhICEpAqAjNwPIKSAhQbgcaiAhQeATakHgAPwKAAAgIUGoFWpCADcDACAhQbAVakIANwMAICFBuBVqQgA3AwAgIUHAFWpCADcDACAhQcgVakIANwMAICFBmBVqQcj/wAApAwA3AwAgIUGQFWpBwP/AACkDADcDACAhQYgVakG4/8AAKQMANwMAICFBgBVqQbD/wAApAwA3AwAgIUH4FGpBqP/AACkDADcDACAhQgA3A6AVICFBoP/AACkDADcD8BQgIUHYG2oiACAhQZgrakHgAPwKAAAgIUGYHWogIUHwFGpB4AD8CgAAICYgABCZAiAhKAKgI0UNAkHU/sAAQSsgIUGvLGpB5IbBAEH0hsEAEMoDAAsgIUGAHGogIUGYCmopAwA3AwAgIUH4G2ogIUGQCmopAwA3AwAgIUHwG2ogIUGICmopAwA3AwAgIUHoG2ogIUGACmopAwA3AwAgIUHgG2ogIUH4CWopAwA3AwAgIUGQHGogIUGoCmopAwA3AwAgIUGYHGogIUGwCmopAwA3AwAgIUGgHGogIUG4CmopAwA3AwAgIUGoHGogIUHACmopAwA3AwAgIUGwHGogIUHICmopAwA3AwAgISAhKQPwCTcD2BsgISAhKQOgCjcDiBwgIUHII2ogKEEoaikDADcDACAhQcAjaiAoQSBqKQMANwMAICFBuCNqIChBGGopAwA3AwAgIUGwI2ogKEEQaikDADcDACAhQagjaiAoQQhqKQMANwMAICFB+CNqICFBqAtqKQMANwMAICFB8CNqICFBoAtqKQMANwMAICFB6CNqICFBmAtqKQMANwMAICFB4CNqICFBkAtqKQMANwMAICFB2CNqICFBiAtqKQMANwMAICEgKCkDADcDoCMgISAhKQOACzcD0CMgIUHYKWogIUHYG2pB4AD8CgAAICFBuCpqICFBoCNqQeAA/AoAAAwDCyAhQdgbakEAQeAA/AsAICFByCNqQgA3AwAgIUHAI2pCADcDACAhQbgjakIANwMAICFBsCNqQgA3AwAgIUGoI2pCADcDACAhQdgjaiAhQZAcaikDADcDACAhQeAjaiAhQZgcaikDADcDACAhQegjaiAhQaAcaikDADcDACAhQfAjaiAhQagcaikDADcDACAhQfgjaiAhQbAcaikDADcDACAhQgA3A6AjICEgISkDiBw3A9AjICFBuCpqQQBB4AD8CwAgIUHYKWogIUGgI2pB4AD8CgAADAILICFBkBdqICFBqCNqQaAC/AoAACAhQaAjaiElIwBBIGsiJCQAAkACQCAhQcgpaiIAKAIIRQRAQdHOxQAtAAAaQQFBARDWBCIADQEMEwsgJEEIaiAAQRAQQAJAICQoAhAiKEUNACAkKAIMIiYhACAoQQNxIikEQANAIAAgAC0AACInQTByICdB1wBqICdBCkkbOgAAIABBAWohACApQQFrIikNAAsLIChBBEkNACAmIChqIScDQCAAIAAtAAAiJkEwciAmQdcAaiAmQQpJGzoAACAAQQFqIiYgJi0AACImQTByICZB1wBqICZBCkkbOgAAIABBAmoiJiAmLQAAIiZBMHIgJkHXAGogJkEKSRs6AAAgAEEDaiImICYtAAAiJkEwciAmQdcAaiAmQQpJGzoAACAAQQRqIgAgJ0cNAAsLICUgJCkCCDcCACAlQQhqICRBEGooAgA2AgAMAQsgJUEBNgIIICUgADYCBCAlQQE2AgAgAEEwOgAACyAkQSBqJAAgISgCpCMhMgJAICEoAqgjIi9BAkkNACAvIDJqISRBACEnIC9BAXYiAEEBRwRAIC9BAWshKyAAQf7///8HcSEoA0AgKyAyaiImLQAAIQAgJiAnIDJqIiUtAAA6AAAgJSAAOgAAICQgJ0F+c2oiAC0AACEmIAAgJUEBaiIALQAAOgAAIAAgJjoAACArQQJrISsgKCAnQQJqIidHDQALCyAvQQJxRQ0AICcgMmoiAC0AACEmIAAgJCAnQX9zaiIALQAAOgAAIAAgJjoAAAsgISgCoCMhACAhQdgbaiAyIC8QtwIgAARAIDIgABDfBAsgIUGgI2ohNiAhQZAXaiE1ICFB2BtqITQjAEGwCGsiMyQAIDNB0ARqIitBAEHgAPwLACAzQagHakIANwMAIDNBsAdqQgA3AwAgM0G4B2pCADcDACAzQcAHakIANwMAIDNByAdqQgA3AwAgM0GYB2pB4LTCACkDADcDACAzQZAHakHYtMIAKQMANwMAIDNBiAdqQdC0wgApAwA3AwAgM0GAB2pByLTCACkDADcDACAzQfgGakHAtMIAKQMANwMAIDNCADcDoAcgM0G4tMIAKQMANwPwBiAzQZAGakEAQeAA/AsAIDNBsAVqIDNB8AZqQeAA/AoAACAzQagCaiIuICsQmQICQCAzKAKoAkEBRwRAIDNBCGogM0GwAmoiIEGgAvwKAAAgM0HYB2ogNUEIaikDADcDACAzQeAHaiA1QRBqKQMANwMAIDNB6AdqIDVBGGopAwA3AwAgM0HwB2ogNUEgaikDADcDACAzQfgHaiA1QShqKQMANwMAIDNBiAhqIDVBOGopAwA3AwAgM0GQCGogNUFAaykDADcDACAzQZgIaiA1QcgAaikDADcDACAzQaAIaiA1QdAAaikDADcDACAzQagIaiA1QdgAaikDADcDACAzIDUpAwA3A9AHIDMgNSkDMDcDgAggLiAzQdAHaiIpQeAA/AoAACAzQfgEaiIwIDVBiAFqKQMANwMAIDNB8ARqIjEgNUGAAWopAwA3AwAgM0HoBGoiMiA1QfgAaikDADcDACAzQeAEaiIvIDVB8ABqKQMANwMAIDNB2ARqIiQgNUHoAGopAwA3AwAgM0GIBWoiJSA1QZgBaikDADcDACAzQZAFaiIoIDVBoAFqKQMANwMAIDNBmAVqIicgNUGoAWopAwA3AwAgM0GgBWoiJiA1QbABaikDADcDACAzQagFaiIAIDVBuAFqKQMANwMAIDMgNSkDYDcD0AQgMyA1KQOQATcDgAUgKSArQeAA/AoAACAzQYgDaiApQeAA/AoAACAwIDVB6AFqKQMANwMAIDEgNUHgAWopAwA3AwAgMiA1QdgBaikDADcDACAvIDVB0AFqKQMANwMAICQgNUHIAWopAwA3AwAgJSA1QfgBaikDADcDACAoIDVBgAJqKQMANwMAICcgNUGIAmopAwA3AwAgJiA1QZACaikDADcDACAAIDVBmAJqKQMANwMAIDMgNSkDwAE3A9AEIDMgNSkD8AE3A4AFICkgK0HgAPwKAAAgM0HoA2ogKUHgAPwKAAAgKyAuQaAC/AoAACA0KQMAIQggM0HAAmoiKEIANwMAIDNBuAJqQgA3AwAgIEIANwMAIDNCADcDqAIgNCAuQSAQ8QMEQCA0KQMYIQUgNCkDECECIDQpAwghBgNAIDNBgAdqQgA3AwAgM0H4BmpCADcDACAzQgA3A/AGIDMgBUIBgzcDiAcgM0G4AmoiJ0IANwMAIDNBsAJqIiZCADcDACAzQgA3A6gCIDNCATcDwAIgM0HwBmogM0GoAmoiJUEgEPEDRQRAICUgM0EIaiIAIDNB0ARqEFQgACAlQaAC/AoAAAsgNCAIQgGIIgM3AwAgNCAGQj+GIAJCAYiEIgQ3AxAgNCACQj+GIAVCAYiEIgU3AxggNCAIQj+GIAZCAYiEIgY3AwggM0GoAmoiJSAzQdAEaiIAIAAQVCAAICVBoAL8CgAAIChCADcDACAnQgA3AwAgJkIANwMAIDNCADcDqAIgBCECIAMhCCA0ICVBIBDxAw0ACwsgNiAzQQhqQaAC/AoAACAzQbAIaiQADAELQaCxwgBBKyAzQdAEakGQscIAQdSywgAQygMACyMAQaAFayInJAAgJ0HgAGoiJkEAQeAA/AsAAkACQCA2QcABaiIAICYQpgRFBEAgJiAAED0gJykDcCEEICcpA2ghAiAnKAJgRQ0BICcgBDcDaCAnIAI3A2BBlKTEAEErICZBkKfEAEGEqMQAEMoDAAsgJ0HgAGpBAEHgAPwLACAnQZgEakIANwMAICdBoARqQgA3AwAgJ0GoBGpCADcDACAnQbAEakIANwMAICdBuARqQgA3AwAgJ0GIBGpBwKjEACkDADcDACAnQYAEakG4qMQAKQMANwMAICdB+ANqQbCoxAApAwA3AwAgJ0HwA2pBqKjEACkDADcDACAnQegDakGgqMQAKQMANwMAICdCADcDkAQgJ0GYqMQAKQMANwPgAyAnQaACakEAQeAA/AsAICdBwAFqICdB4ANqQeAA/AoAAAwBCyAnQRBqICdB+ABqQdAA/AoAACAnIAQ3AwggJyACNwMAICdB4ABqIDYgJxA/ICdBgANqIgAgJ0HgAPwKAAAgJ0HAAWogNkHgAGogABA/ICdB+ARqQgA3AwAgJ0GABWpCADcDACAnQYgFakIANwMAICdBkAVqQgA3AwAgJ0GYBWpCADcDACAnQcgEakGgqMQAKQMANwMAICdB0ARqQaioxAApAwA3AwAgJ0HYBGpBsKjEACkDADcDACAnQeAEakG4qMQAKQMANwMAICdB6ARqQcCoxAApAwA3AwAgJ0IANwPwBCAnQZioxAApAwA3A8AEICdBoAJqICdBwARqQeAA/AoAAAsgNCAnQeAAakGgAvwKAAAgJ0GgBWokACA2QQBB4AD8CwACQAJAICFBmB1qIDYQpgRFBEAgIUHIIGogIUGAHGopAwA3AwAgIUHAIGogIUH4G2opAwA3AwAgIUG4IGogIUHwG2opAwA3AwAgIUGwIGogIUHoG2opAwA3AwAgIUGoIGogIUHgG2opAwA3AwAgIUHYIGogIUGQHGopAwA3AwAgIUHgIGogIUGYHGopAwA3AwAgIUHoIGogIUGgHGopAwA3AwAgIUHwIGogIUGoHGopAwA3AwAgIUH4IGogIUGwHGopAwA3AwAgISAhKQPYGzcDoCAgISAhKQOIHDcD0CAgIUHQBWogIUHgHGopAwA3AwAgIUHIBWogIUHYHGopAwA3AwAgIUHABWogIUHQHGopAwA3AwAgIUG4BWogIUHIHGopAwA3AwAgIUGwBWogIUHAHGopAwA3AwAgIUHgBWogIUHwHGopAwA3AwAgIUHoBWogIUH4HGopAwA3AwAgIUHwBWogIUGAHWopAwA3AwAgIUH4BWogIUGIHWopAwA3AwAgIUGABmogIUGQHWopAwA3AwAgISAhKQO4HDcDqAUgISAhKQPoHDcD2AUgNiAhQaAgaiAhQagFahBsICEoAqAjRQ0BICFBgCxqICFBrCNqKAIANgIAICEgISkCpCM3A/grQdT+wABBKyAhQfgrakGQhcEAQdSGwQAQygMACyAhQagFakEAQeAA/AsAICFByCNqQgA3AwAgIUHAI2pCADcDACAhQbgjakIANwMAICFBsCNqQgA3AwAgIUGoI2pCADcDACAhQdgjaiAhQeAFaikDADcDACAhQeAjaiAhQegFaikDADcDACAhQegjaiAhQfAFaikDADcDACAhQfAjaiAhQfgFaikDADcDACAhQfgjaiAhQYAGaikDADcDACAhQgA3A6AjICEgISkD2AU3A9AjICFBuCpqQQBB4AD8CwAgIUHYKWogIUGgI2pB4AD8CgAADAELICFB2ClqICFBqCNqQcAB/AoAAAsgISgCyCkiAARAICEoAswpIABBAnQQ3wQLICpFDQIgOSAqQQJ0EN8EDAILIAAgKkH4gcAAEMgEAAsgKkUNACA5ICpBAnQQ3wQLICFB0A5qITIgIUHoAGohJSMAQaAhayIgJAACQCAhQcAOaiInKAIIIiZFBEAgIEGADmpB4LTCACkDADcDACAgQfgNakHYtMIAKQMANwMAICBB8A1qQdC0wgApAwA3AwAgIEHoDWpByLTCACkDADcDACAgQeANakHAtMIAKQMANwMAICBBkA5qQgA3AwAgIEGYDmpCADcDACAgQaAOakIANwMAICBBqA5qQgA3AwAgIEGwDmpCADcDACAgQgA3A4gOICBBuLTCACkDADcD2A0gMkHgAGpBAEHAAfwLACAyICBB2A1qQeAA/AoAACAyQaACakEAQaAC/AsADAELICcoAgQhACAgQeANakGQksIAKAIANgIAICBBiJLCACkCADcD2A0gIEHYDWpBjJPCABClAyAgKALcDUEBNgIAICAoAtwNISogICgC2A0hKAJAICZBAUcNACAAKAAAICooAABHDQAgKARAICogKEECdBDfBAsgICAlNgLAICAgICVBoAJqIiY2AsQgICBBmAlqIiQiACAgQcAgaiIoEJADICBByARqIjEgAEHgAPwKAAAgIEEIaiIvIDFB4AD8CgAAICBB2A1qIiogL0HgAPwKAAAgIEGgHmoiJyAqQeAA/AoAACAkICgQkAMgMSAkQeAA/AoAACAvIDFB4AD8CgAAICogL0HgAPwKAAAgIEGAH2ogKkHgAPwKAAAgJCAoEJADIDEgJEHgAPwKAAAgLyAxQeAA/AoAACAqIC9B4AD8CgAAICBB4B9qICpB4AD8CgAAICBB2BZqIgAgJ0GgAvwKAAAgICAlQcAEajYCxB0gICAmNgLAHSAxICBBwB1qIiYQkAMgLyAxQeAA/AoAACAoIC9B4AD8CgAAICQgKEHgAPwKAAAgKiAkQeAA/AoAACAxICYQkAMgLyAxQeAA/AoAACAoIC9B4AD8CgAAICQgKEHgAPwKAAAgIEG4DmogJEHgAPwKAAAgMSAmEJADIC8gMUHgAPwKAAAgKCAvQeAA/AoAACAkIChB4AD8CgAAICBBmA9qICRB4AD8CgAAICcgKkGgAvwKAAAgIEH4GGogJ0GgAvwKAAAgMiAAQcAE/AoAAAwBCyAoBEAgKiAoQQJ0EN8ECyAgQYAOakHgtMIAKQMANwMAICBB+A1qQdi0wgApAwA3AwAgIEHwDWpB0LTCACkDADcDACAgQegNakHItMIAKQMANwMAICBB4A1qQcC0wgApAwA3AwAgIEGQDmpCADcDACAgQZgOakIANwMAICBBoA5qQgA3AwAgIEGoDmpCADcDACAgQbAOakIANwMAICBBuLTCACkDADcD2A0gIEIANwOIDiAgQegAakEAQcAB/AsAICBBCGogIEHYDWoiJEHgAPwKAAAgIEGoAmpBAEGgAvwLACAgICU2AsAdICAgJUGgAmoiJjYCxB0gIEGYCWoiMSAgQcAdaiIoEJADICBByARqIjAgMUHgAPwKAAAgIEHAIGoiLyAwQeAA/AoAACAkIC9B4AD8CgAAICBBmBtqIiogJEHgAPwKAAAgMSAoEJADIDAgMUHgAPwKAAAgLyAwQeAA/AoAACAkIC9B4AD8CgAAICBB+BtqICRB4AD8CgAAIDEgKBCQAyAwIDFB4AD8CgAAIC8gMEHgAPwKAAAgJCAvQeAA/AoAACAgQdgcaiAkQeAA/AoAACAgQZgSaiIAICpBoAL8CgAAICAgJUHABGo2ArwdICAgJjYCuB0gMCAgQbgdaiImEJADIC8gMEHgAPwKAAAgKCAvQeAA/AoAACAxIChB4AD8CgAAICQgMUHgAPwKAAAgMCAmEJADIC8gMEHgAPwKAAAgKCAvQeAA/AoAACAxIChB4AD8CgAAICBBuA5qIDFB4AD8CgAAIDAgJhCQAyAvIDBB4AD8CgAAICggL0HgAPwKAAAgMSAoQeAA/AoAACAgQZgPaiAxQeAA/AoAACAqICRBoAL8CgAAICBBuBRqICpBoAL8CgAAIDAgAEHABPwKAAAgIEGMCWogJ0EIELACICAoApAJISYCQCAgKAKUCSIrQQJJDQAgJiAraiEvQQAhACArQQF2IidBAUcEQCArQQFrISogJ0H+////B3EhJQNAICYgKmoiKC0AACEnICggACAmaiIkLQAAOgAAICQgJzoAACAvIABBfnNqIictAAAhKCAnICRBAWoiJy0AADoAACAnICg6AAAgKkECayEqICUgAEECaiIARw0ACwsgK0ECcUUNACAAICZqIiotAAAhJyAqIC8gAEF/c2oiAC0AADoAACAAICc6AAALICAoAowJIScgKwRAICYhAANAIAAsAAAhJCAgQdgNaiIlICBBCGoiKBCNAiAgQZgJaiIqICVBwAT8CgAAICggKkHABPwKAAAgJEEASARAICUgKCAgQcgEahCbAiAqICVBwAT8CgAAICggKkHABPwKAAALICBB2A1qIiUgIEEIaiIoEI0CICBBmAlqIiogJUHABPwKAAAgKCAqQcAE/AoAACAkQcAAcQRAICUgKCAgQcgEahCbAiAqICVBwAT8CgAAICggKkHABPwKAAALICBB2A1qIiUgIEEIaiIoEI0CICBBmAlqIiogJUHABPwKAAAgKCAqQcAE/AoAACAkQSBxBEAgJSAoICBByARqEJsCICogJUHABPwKAAAgKCAqQcAE/AoAAAsgIEHYDWoiJSAgQQhqIigQjQIgIEGYCWoiKiAlQcAE/AoAACAoICpBwAT8CgAAICRBEHEEQCAlICggIEHIBGoQmwIgKiAlQcAE/AoAACAoICpBwAT8CgAACyAgQdgNaiIlICBBCGoiKBCNAiAgQZgJaiIqICVBwAT8CgAAICggKkHABPwKAAAgJEEIcQRAICUgKCAgQcgEahCbAiAqICVBwAT8CgAAICggKkHABPwKAAALICBB2A1qIiUgIEEIaiIoEI0CICBBmAlqIiogJUHABPwKAAAgKCAqQcAE/AoAACAkQQRxBEAgJSAoICBByARqEJsCICogJUHABPwKAAAgKCAqQcAE/AoAAAsgIEHYDWoiJSAgQQhqIigQjQIgIEGYCWoiKiAlQcAE/AoAACAoICpBwAT8CgAAICRBAnEEQCAlICggIEHIBGoQmwIgKiAlQcAE/AoAACAoICpBwAT8CgAACyAgQdgNaiIlICBBCGoiKBCNAiAgQZgJaiIqICVBwAT8CgAAICggKkHABPwKAAAgJEEBcQRAICUgKCAgQcgEahCbAiAqICVBwAT8CgAAICggKkHABPwKAAALIABBAWohACArQQFrIisNAAsLICcEQCAmICcQ3wQLIDIgIEEIakHABPwKAAALICBBoCFqJABBACEnICFBADYCsAUgIUKAgICAEDcCqAUgIUHYG2oiJiAyELUDICEoAtwcIQAgISAhKALYGzYC3BwgISAANgLYGyAhKQLcGyECICEgISkC4Bw3AtwbICEgAjcC4BwgISkC5BshAiAhICEpAtAcNwLkGyAhIAI3AtAcICEoAtgcIQAgISAhKALsGzYC2BwgISAANgLsGyAhKALEHCEAICEgISgC8Bs2AsQcICEgADYC8BsgISgCyBwhACAhICEoAvQbNgLIHCAhIAA2AvQbICEoAswcIQAgISAhKAL4GzYCzBwgISAANgL4GyAhKAK4HCEAICEgISgC/Bs2ArgcICEgADYC/BsgISgCvBwhACAhICEoAoAcNgK8HCAhIAA2AoAcICEoAsAcIQAgISAhKAKEHDYCwBwgISAANgKEHCAhKAKsHCEAICEgISgCiBw2AqwcICEgADYCiBwgISgCsBwhACAhICEoAowcNgKwHCAhIAA2AowcICEoArQcIQAgISAhKAKQHDYCtBwgISAANgKQHCAhKAKgHCEAICEgISgClBw2AqAcICEgADYClBwgISgCpBwhACAhICEoApgcNgKkHCAhIAA2ApgcICEoAqgcIQAgISAhKAKcHDYCqBwgISAANgKcHCAhQaAjaiAmQZAB/AoAACAhQoCAgIDAATcCsCQgIUGwI2ohOUELISkgIUGYE2ohLiAhQagTaiEgICFBsBNqITAgIUG4E2ohMQNAAkAgJ0EBaiEAAkAgIUGgI2ogJ0EMbGoiJygCACImQYCAgIB4RwRAIC5CADcDACAhQaATaiIkQgA3AwAgIEIANwMAIDBCADcDACAxQgA3AwAgIUIANwOQEyAhICcpAgQiAjcC9AkgISAmNgLwCSACQv////8PWARAQdHOxQAtAAAaQQFBARDWBCI9RQ0SID1BADoAAEEBISogIUEBNgKQFwwCCyAhQZAXaiAhQfAJakEIELACICEoApQXIT0gISgCmBciKkECSQ0BICogPWohMkEAIScgKkEBdiImQQFHBEAgKkEBayErICZB/v///wdxISUDQCArID1qIigtAAAhJiAoICcgPWoiLy0AADoAACAvICY6AAAgMiAnQX5zaiImLQAAISggJiAvQQFqIiYtAAA6AAAgJiAoOgAAICtBAmshKyAlICdBAmoiJ0cNAAsLICpBAnEEQCAnID1qIiYtAAAhKCAmIDIgJ0F/c2oiJi0AADoAACAmICg6AAALICpBMUkNAUH0isEAQRtBkIvBABD+AwALICEgADYCsCQgAEEMRg0BA0AgOUEEaygCACIABEAgOSgCACAAQQJ0EN8ECyA5QQxqITkgKUEBayIpDQALDAELICoEQCAhICprQcATaiA9ICr8CgAACyAhKAKoBSAhKAKwBSIra0EvTQRAICFBqAVqICtBMEEBQQEQiAMgISgCsAUhKwsgISgCrAUgK2oiJiAhKQOQEzcAACAmQQhqIC4pAwA3AAAgJkEQaiAkKQMANwAAICZBGGogICkDADcAACAmQSBqIDApAwA3AAAgJkEoaiAxKQMANwAAICEgK0EwajYCsAUgISgCkBciJgRAID0gJhDfBAsgISgC8AkiJgRAICEoAvQJICZBAnQQ3wQLIDlBDGohOSApQQFrISkgACInQQxHDQELCyAhKAKoBSElICEoAqwFISggISgCsAUhJCAhQQA2AuAbICFCgICAgBA3AtgbICFB2BtqIipBAEEGQQFBARCIAyAhKALcGyIAICEoAuAbIidqIiZB3InBACgAADYAACAmQQRqQeCJwQAvAAA7AAAgISAnQQZqIis2AuAbICEoAtgbICtrICRJBEAgKiArICRBAUEBEIgDICEoAuAbISsgISgC3BshAAsgJARAIAAgK2ogKCAk/AoAAAsgJQRAICggJRDfBAsgIUGgI2ogACAkICtqEN0BQdHOxQAtAAAaQRBBARDWBCImRQ0BICYgISkAoCM3AAAgJkEIaiAhQagjaikAADcAACAhICEvAKAjOwHEEyAhICFBoiNqLQAAOgDGEyAmKAADIS8gJigAByEkICYoAAshJSAmLQAPISggJkEQEN8EICEoAtgbIiYEQCAAICYQ3wQLQRAgISgC3BMiJiAhKALYEyIxayIwIDBBEE8bIQBBASEqICYgMUcEQEHRzsUALQAAGiAAQQEQ1gQiKkUNAwsgIUG6I2ogIS0AxhM6AAAgIUGoI2ogIUHQE2opAwA3AwAgISAhKQPIEzcDoCMgISAhLwHEEzsBuCNBACEnICFBADYC2CMgIUIANwPQIyAhICg6AMcjICEgJTYAwyMgISAkNgC/IyAhIC82ALsjICFCgICAgIACNwPIIyAhIDE2ArAjICEgJjYCtCMgJiAxRg0FICFBoCNqIDFqIS8gMEEBRwRAIABBHnEhJANAICcgKmoiJSAhQaAjaiAnaiIoQRhqLQAAICcgL2oiJi0AAHM6AAAgJUEBaiAoQRlqLQAAICZBAWotAABzOgAAICQgJ0ECaiInRw0ACwsgAEEBcQRAICcgKmogIUG4I2ogJ2otAAAgJyAvai0AAHM6AAALIAAhJyAwQQ9NDQUgIUHCE2ogKkECai0AADoAACAhICovAAA7AcATICooAAMhMiAqKAAHIS8gKigACyEkICotAA8hJSAqQRAQ3wQgIUEANgLgGyAhQoCAgIAQNwLYGyAhQdgbaiIoQQBBBkEBQQEQiAMgISgC3BsiKiAhKALgGyImaiIAQcyKwQAoAAA2AAAgAEEEakHQisEALwAAOwAAICEgJkEGaiInNgLgGyAhKALYGyAnayAwSQRAICggJyAwQQFBARCIAyAhKALcGyEqICEoAuAbIScLIDAEQCAnICpqICFByBNqIDFqIDD8CgAACyAhQaAjaiAqICcgMGoQ3QFB0c7FAC0AABpBEEEBENYEIgBFDQMgACAhKQCgIyICNwAAIABBCGogIUGoI2opAAA3AAAgAC0AASEoIAAtAAIhJiAAKAADISAgACgAByEwIAAoAAshMSAALQAPIScgAEEQEN8EICEoAtgbIgAEQCAqIAAQ3wQLQdHOxQAtAAAaQRBBARDWBCIqRQ0EICogKCBdczoAASAqIAKnIEJzOgAAICogMCBWczoAByAqICAgXHM6AAMgKiBNIDBBGHZzOgAKICogTyAwQRB2czoACSAqIFMgMEEIdnM6AAggKiBXICBBGHZzOgAGICogWiAgQRB2czoABSAqIFsgIEEIdnM6AAQgKiAxIEtzOgALICogPyAxQRh2czoADiAqIEkgMUEQdnM6AA0gKiBKIDFBCHZzOgAMICpBAmogJiBocyIAOgAAIEVB2gFqIAA6AAAgRSAqLwAAOwDYASAqKQADIQIgKigACyEmICpBEBDfBCAhQaAjaiIAICFB2ClqQcAB/AoAACAhQeIkaiAhQcITai0AADoAACAhICEvAcATOwHgJCBFQQhqIABBwwH8CgAAIEUgIiAnczoA5wEgRSAmNgDjASBFIAI3ANsBIEUgJToA1wEgRSAkNgDTASBFIC82AM8BIEUgMjYAywEgRUEANgIAICEoAsAOIgBFDQAgISgCxA4gAEECdBDfBAsgIUGwLGokAAwFC0EBQRBBrIPBABDIBAALQQEgAEG8isEAEMgEAAtBAUEQQayDwQAQyAQAC0EBQRBBvIrBABDIBAALICEgJzYCqCMgISAqNgKkIyAhIAA2AqAjQdT+wABBKyAhQaAjakHUisEAQeSKwQAQygMACyAsKAKoAgRAICxB8AdqICxBtAJqKAIAIgA2AgAgLCAsKQKsAiICNwPoByBBQQxqIAA2AgAgQSACNwIEIEFBATYCACBnRQ0BIGkgZxDfBAwBCyAsQewHaiIAICxBsAJqQeAB/AoAACAsQYgGaiIgIABB4AH8CgAAICxBzAlqITIjAEHQBGsiKSQAIClBuAJqICBBCGopAwA3AwAgKUHAAmogIEEQaikDADcDACApQcgCaiAgQRhqKQMANwMAIClB0AJqICBBIGopAwA3AwAgKUHYAmogIEEoaikDADcDACApQegCaiAgQThqKQMANwMAIClB8AJqICBBQGspAwA3AwAgKUH4AmogIEHIAGopAwA3AwAgKUGAA2ogIEHQAGopAwA3AwAgKUGIA2ogIEHYAGopAwA3AwAgKSAgKQMANwOwAiApICApAzA3A+ACIClB6ABqIiogKUGwAmoQ9wMgKSgCbCEuICkoAmghJwJAICkoAnAiMEECRgRAAkAgLigCBCEmIC4oAgAhACAqIC5BCGpB2AD8CgAAICcEQCAuICdBMGwQ3wQLIClBGGogKUHwAGopAwA3AwAgKUEgaiApQfgAaikDADcDACApQShqIClBgAFqKQMANwMAIClBMGogKUGIAWopAwA3AwAgKUFAayApQZgBaikDADcDACApQcgAaiApQaABaikDADcDACApQdAAaiApQagBaikDADcDACApQdgAaiApQbABaikDADcDACApQeAAaiApQbgBaikDADcDACApICY2AgwgKSAANgIIICkgKSkDaDcDECApICkpA5ABNwM4IClBmANqICBB4ABqIgBBCGopAwA3AwAgKUGgA2ogAEEQaikDADcDACApQagDaiAAQRhqKQMANwMAIClBsANqIABBIGopAwA3AwAgKUG4A2ogAEEoaikDADcDACApQcgDaiAgQZgBaikDADcDACApQdADaiAgQaABaikDADcDACApQdgDaiAgQagBaikDADcDACApQeADaiAgQbABaikDADcDACApQegDaiAgQbgBaikDADcDACApIAApAwA3A5ADICkgICkDkAE3A8ADIClB6ABqIClBkANqEPcDICkoAmwhLiApKAJoIScgKSgCcCIwQQJHDQAgLigCBCEmIC4oAgAhACApQfADaiAuQQhqQdgA/AoAACAnBEAgLiAnQTBsEN8ECyApQfgAaiApQfgDaikDADcDACApQYABaiApQYAEaikDADcDACApQYgBaiApQYgEaikDADcDACApQZABaiApQZAEaikDADcDACApQaABaiApQaAEaikDADcDACApQagBaiApQagEaikDADcDACApQbABaiApQbAEaikDADcDACApQbgBaiApQbgEaikDADcDACApQcABaiApQcAEaikDADcDACApICY2AmwgKSAANgJoICkgKSkD8AM3A3AgKSApKQOYBDcDmAEgKUEANgLUASApQoCAgIDAADcCzAEgKUHwA2oiMSApQQhqEN8BIClB+AFqIi8gMRDUASApQcwBaiIkQQBBBEEEQQwQiAMgKSgCzAEhMCApKALQASIuICkoAtQBIidBDGxqIgAgKSkC+AE3AgAgAEEIaiApQYACaiIlKQIANwIAIABBEGogKUGIAmoiKCkCADcCACAAQRhqIClBkAJqIiopAgA3AgAgAEEgaiApQZgCaiImKQIANwIAIABBKGogKUGgAmoiACkCADcCACApICdBBGoiJzYC1AEgMSApQThqEN8BIC8gMRDUASAwICdrQQNNBEAgJCAnQQRBBEEMEIgDICkoAswBITAgKSgC0AEhLiApKALUASEnCyAuICdBDGxqIiQgKSkC+AE3AgAgJEEoaiAAKQIANwIAICRBIGogJikCADcCACAkQRhqICopAgA3AgAgJEEQaiAoKQIANwIAICRBCGogJSkCADcCACApICdBBGoiJzYC1AEgKUHwA2oiACApQegAahDfASApQfgBaiAAENQBIDAgJ2tBA00EQCApQcwBaiAnQQRBBEEMEIgDICkoAswBITAgKSgC0AEhLiApKALUASEnCyAuICdBDGxqIgAgKSkC+AE3AgAgAEEoaiApQaACaiIlKQIANwIAIABBIGogKUGYAmoiKCkCADcCACAAQRhqIClBkAJqIiopAgA3AgAgAEEQaiApQYgCaiImKQIANwIAIABBCGogKUGAAmoiJCkCADcCACApICdBBGoiJzYC1AEgKUHwA2oiACApQZgBahDfASApQfgBaiAAENQBIDAgJ2tBA00EQCApQcwBaiAnQQRBBEEMEIgDICkoAtABIS4gKSgC1AEhJwsgLiAnQQxsaiIAICkpAvgBNwIAIABBKGogJSkCADcCACAAQSBqICgpAgA3AgAgAEEYaiAqKQIANwIAIABBEGogJikCADcCACAAQQhqICQpAgA3AgAgKSAnQQRqIic2AtQBIClB+ANqICBBwAFqIgBBCGopAgA3AwAgKUKAgICAgAI3A4AEICkgACkCADcD8ANBACEuQaz8wAAoAgAhKkGk/MAAKQIAIQIDQCApQfADaiAuai0AACEAICQgKjYCACApIAI3A/gBIAAEQCApQfgBakGY/cAAEKUDICkoAvwBIAA2AgAgKUEBNgKAAiApKALUASEnCyApQeABaiImICQoAgA2AgAgKSApKQP4ATcD2AEgKSgCzAEgJ0YEQCApQcwBakHAicEAEJ8DCyApKALQASAnQQxsaiIAICkpA9gBNwIAIABBCGogJigCADYCACApICdBAWoiJzYC1AEgLkEBaiIuQRBHDQALIClB+ANqICBB2AFqKQIANwMAIClCgICAgIACNwOABCApICApAtABNwPwA0EAIS5BrPzAACgCACEqQaT8wAApAgAhAgNAIClB8ANqIC5qLQAAISYgKUGAAmoiACAqNgIAICkgAjcD+AEgJgRAIClB+AFqQZj9wAAQpQMgKSgC/AEgJjYCACApQQE2AoACICkoAtQBIScLIClB8AFqIiYgACgCADYCACApICkpA/gBNwPoASApKALMASAnRgRAIClBzAFqQbCJwQAQnwMLICkoAtABICdBDGxqIgAgKSkD6AE3AgAgAEEIaiAmKAIANgIAICkgJ0EBaiInNgLUASAuQQFqIi5BEEcNAAsgMiApKQLMATcCACAyQQhqIClB1AFqKAIANgIAIClB0ARqJAAMAgsLICkgMDYCcCApIC42AmwgKSAnNgJoQYCLwABBKyApQegAakGsi8AAQaSNwAAQygMAC0HRzsUALQAAGiAsKALUCSEoQQxBBBDWBCInRQ0CICxBsAJqIiZBrPzAACgCACIANgIAICxBpPzAACkCACICNwOoAiAsQagCakGY/cAAEKUDICwoAqwCIChBAWo2AgAgJ0EIakEBNgIAICcgLCkDqAI3AgAgLEEBNgLwByAsICc2AuwHICxBATYC6AcgJiAANgIAICwgAjcDqAICQCBlRQRAICxB4AlqQaz8wAAoAgA2AgAgLEGk/MAAKQIANwPYCQwBCyAsQagCakGY/cAAEKUDICwoAqwCIGU2AgAgLEHgCWpBATYCACAmQQE2AgAgLCAsKQOoAjcD2AkLICxB6AdqIgBB6IfBABCfAyAsKALsByIvICwpA9gJNwIMIC9BFGogLEHgCWooAgA2AgBBAiEnICxBAjYC8AcgLCgC0AkhKiAsKALMCSEmICwoAugHQQJrIChJBEAgAEECIChBBEEMEIgDICwoAuwHIS8gLCgC8AchJwsgKEEMbCIABEAgLyAnQQxsaiAqIAD8CgAACyAsICcgKGoiADYC8AcgJgR/ICogJkEMbBDfBCAsKALwBwUgAAsgKEECakcNAyBBICwpAugHNwIEIEFBADYCACBBQQxqICxB8AdqKAIANgIAIGdFDQAgaSBnEN8ECyAsQbALaiQADAMLQdiHwQAQ6AQAC0EEQQwQ/wQAC0H4h8EAQS1BqIjBABD+AwALIDsoAhhBAUYEQCA7QQhqIDtBHGoiAEEIaigCADYCACA7IAApAgA3AwAgO0EMaiA7ENQDIDsoAhAiJyA7KAIUEM0EISYgOygCDCIABEAgJyAAEN8ECyA7KAIAIgAEQCA7KAIEIAAQ3wQLIF9BgICAgHg2AgAgXyAmNgIEIFEEQCABIQADQCAAKAIAIiYEQCAAQQRqKAIAICZBAnQQ3wQLIABBDGohACBRQQFrIlENAAsLIGZFDQEgASBmQQxsEN8EDAELIDsoAhwhKiA7KAIgIiYhLiA7KAIkIgAEQCAAQQxsISQgJiInIQADQCA7QSBqIABBCGooAgA2AgAgOyAAKQIANwMYICcgO0EYahC7AzYCACAuQQRqIS4gJ0EEaiEnIABBDGohACAkQQxrIiQNAAsLIF8gJjYCBCBfICpBA2w2AgAgXyAuICZrQQJ2NgIIIFEEQCABIQADQCAAKAIAIiYEQCAAQQRqKAIAICZBAnQQ3wQLIABBDGohACBRQQFrIlENAAsLIGZFDQAgASBmQQxsEN8ECyA7QTBqJAACQAJAIFQCfyBSKAIUIgBBgICAgHhGBEBBACEAIFIoAhghL0EAIQFBAQwBCyBSKAIYISYCQCBSKAIcIgEgAE8EQCAmIQAMAQsgAEECdCEnIAFFBEBBBCEAICYgJxDfBAwBCyAmICdBBCABQQJ0IiYQzgQiAEUNAgtBACEvQQALNgIMIFQgLzYCCCBUIAE2AgQgVCAANgIAIFJBIGokAAwBC0EEICZB6PHAABDIBAALIFQoAgAgVCgCBCBUKAIIIFQoAgwgVEEQaiQADwtBAUEBEP8EAAuABQEIfyMAQRBrIgYkABCtAyIEIAAmARCtAyIIIAEmASMAQRBrIgckACAHQQRqIQMjAEHAAWsiAiQAIAJB6ABqIgUgBBDsAgJAAkACQCACKAJoQYCAgIB4RwRAIAJBEGogAkHwAGoiBCgCADYCACACIAIpAmg3AwggAkEYaiIJIAJBCGoQ9QIgBSAIEOwCIAIoAmhBgICAgHhGDQEgAkFAayAEKAIANgIAIAIgAikCaDcDOCACQcgAaiIEIAJBOGoQ9QIgBSAJIAQQFyACQagBaiIEIAUQ2QIgAkG0AWoiCCACQYgBahDZAkHRzsUALQAAGkEIQQQQ1gQiBUUNAiAEELsDIQQgBSAIELsDNgIEIAUgBDYCACADQQI2AgggAyAFNgIEIANBAjYCACACKAI4IgMEQCACKAI8IANBAnQQ3wQLIAIoAggiAwRAIAIoAgwgA0ECdBDfBAsgAkHAAWokAAwDCyACIAIoAmw2AjhBhJ3AAEErIAJBOGpBtPLAAEHU8sAAEMoDAAsgAiACKAJsNgI4QYSdwABBKyACQThqQbTywABBxPLAABDKAwALQQRBCBD/BAALAkACQCAGAn8gBygCBCICQYCAgIB4RgRAQQAhAiAHKAIIIQNBACEFQQEMAQsgBygCCCEDAkAgBygCDCIFIAJPBEAgAyECDAELIAJBAnQhBCAFRQRAQQQhAiADIAQQ3wQMAQsgAyAEQQQgBUECdCIDEM4EIgJFDQILQQAhA0EACzYCDCAGIAM2AgggBiAFNgIEIAYgAjYCACAHQRBqJAAMAQtBBCADQejxwAAQyAQACyAGKAIAIAYoAgQgBigCCCAGKAIMIAZBEGokAAuFpQECCX8ifiMAQRBrIggkABCtAyIFIAAmARCtAyIHIAEmASMAQRBrIgkkACAJQQRqIQojAEHAAWsiAyQAIANB6ABqIgQgBRDsAgJAAkACQCADKAJoQYCAgIB4RwRAIANBEGogA0HwAGoiAigCADYCACADIAMpAmg3AwggA0EYaiIFIANBCGoQ9QIgBCAHEOwCIAMoAmhBgICAgHhGDQEgA0FAayACKAIANgIAIAMgAykCaDcDOCADQcgAaiIHIANBOGoQ9QIjAEGAHmsiAiQAIAJB4B1qIgZB5I/CAEHCABCVAyACQcAcaiAGEPUCIAIoAuAdIgYEQCACKALkHSAGQQJ0EN8ECyACQeAdaiIGQaaQwgBBwgAQlQMgAkHgHGogBhD1AiACKALgHSIGBEAgAigC5B0gBkECdBDfBAsgAkGwHGogAikD2BwiJEIAQr4BQgAQyQMgAkGgHGogAikDsBwiDEKblK/D8rWo3oZ/fiILQgBCbUIAEMkDIAJBkBxqIAtCAEJ/QgAQyQMgAkGAHGogC0IAQv///////////wBCABDJAyACQfAbaiACKQPQHCImQgBCvgFCABDJAyACQeAbaiACKQOQHCILIAIpA7gcfCIPIAIpA6gcIAIpA6AcIg4gDEJ+g3wgDlStfHwiDCACKQPwG3wiDkKblK/D8rWo3oZ/fiINQgBCbUIAEMkDIAJB0BtqIA1CAEJ/QgAQyQMgAkHAG2ogDUIAQv///////////wBCABDJAyACQbAbaiACKQPIHCIgQgBCvgFCABDJAyACQaAbaiACKQPQGyINIAIpA/gbIAwgDlatfCISIAsgDCAPVK0gAikDmBwiESALIA9WrXx8IhR8IhB8IhV8IgsgAikD6BsgAikD4BsiDyAOfCAPVK18fCIPIAIpA7AbfCIMQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkGQG2ogDkIAQn9CABDJAyACQYAbaiAOQgBC////////////AEIAEMkDIAJB8BpqIAIpA8AcIihCAEK+AUIAEMkDIAJB4BpqIAIpA5AbIg4gDSASIBVWrSIVIBEgECAUVK18IhAgAikDgBx8IhN8IhJ8IhEgCyAPVq0gAikD2BsiFiALIA1UrXx8fCILIAIpA7gbIAwgD1StfHwiF3wiDyACKQOoGyAMIAIpA6AbIg18IA1UrXx8IgwgAikD8Bp8Ig1Cm5Svw/K1qN6Gf34iFEIAQm1CABDJAyACQdAaaiAUQgBCf0IAEMkDIAJBwBpqIBRCAEL///////////8AQgAQyQMCQAJAIAIpA8gaIAIpA4gbIAIpA8gbIAIpA8AbIhkgAikDiBwgECATVq18fCIUIBlUrXwgFCAUIBIgFVStfCIQVq18IBAgCyARVK0gFiARIBJUrXx8fCISIBBUrXwiFCACKQOAG3wiESAUVK18IBEgESASIAsgF1atfCILIBJUrXwiElatfCASIBIgAikDmBsiFCALIAsgDnwiEVatfCARIBEgDCAPVK0gFCAOIA9WrXx8fCILVq18fCIPVq18IhIgAikDwBp8Ig4gElStfCAOIA8gDyALIAsgAikD+BogDCANVq18fCISVq18IgtWrXwiDyAOVK18IA8gAikD2BoiESALIAsgAikD0BoiDHwiDlatfCAOIA4gESAMIBJ8IgsgDFStfCALIAIpA+gaIAIpA+AaIgwgDXwgDFStfHwiESALVK18fCILVq18fCIMIA9UrXwiEkIAWQRAIBJC////////////AFIgEUJtVHIgCyAMg0J/UnINAQsgC0IBfCIPIBFCbVStIg59IRYgDEIBfCINIAtCf1IgDiAPVnKtIgt9IQ8gEiAMQn9SIAsgDVZyrX1C////////////AH0hEiARQhN8IREMAQsgDCEPIAshFgsgAkGwGmogBSkDGCIUQgBCyANCABDJAyACQaAaaiACKQOwGiIOQpuUr8Pytajehn9+IgtCAEJtQgAQyQMgAkGQGmogC0IAQn9CABDJAyACQYAaaiALQgBC////////////AEIAEMkDIAJB8BlqIAUpAxAiGUIAQsgDQgAQyQMgAkHgGWogAikDkBoiCyACKQO4GnwiDCACKQOoGiACKQOgGiINIA5CeIN8IA1UrXx8Ig4gAikD8Bl8Ig1Cm5Svw/K1qN6Gf34iEEIAQm1CABDJAyACQdAZaiAQQgBCf0IAEMkDIAJBwBlqIBBCAEL///////////8AQgAQyQMgAkGwGWogBSkDCCIYQgBCyANCABDJAyACQaAZaiACKQPQGSIQIAIpA/gZIA0gDlStfCIVIAsgDCAOVq0gAikDmBoiEyALIAxWrXx8Ihd8Ihp8Ihx8IgsgAikD6BkgAikD4BkiDCANfCAMVK18fCIMIAIpA7AZfCIOQpuUr8Pytajehn9+Ig1CAEJtQgAQyQMgAkGQGWogDUIAQn9CABDJAyACQYAZaiANQgBC////////////AEIAEMkDIAJB8BhqIAUpAwAiG0IAQsgDQgAQyQMgAkHgGGogAikDkBkiDSAQIBUgHFatIhwgEyAXIBpWrXwiGiACKQOAGnwiHXwiFXwiEyALIAxWrSACKQPYGSIhIAsgEFStfHx8IgsgAikDuBkgDCAOVq18fCIffCIMIAIpA6gZIA4gAikDoBkiEHwgEFStfHwiDiACKQPwGHwiEEKblK/D8rWo3oZ/fiIXQgBCbUIAEMkDIAJB0BhqIBdCAEJ/QgAQyQMgAkHAGGogF0IAQv///////////wBCABDJAwJAAkAgAikDyBggAikDiBkgAikDyBkgAikDwBkiHiACKQOIGiAaIB1WrXx8IhcgHlStfCAXIBcgFSAcVK18IhpWrXwgGiALIBNUrSAhIBMgFVStfHx8IhUgGlStfCIXIAIpA4AZfCITIBdUrXwgEyATIBUgCyAfVq18IgsgFVStfCIVVq18IBUgFSACKQOYGSIXIAsgCyANfCITVq18IBMgEyAMIA5WrSAXIAwgDVStfHx8IgtWrXx8IgxWrXwiFSACKQPAGHwiDSAVVK18IA0gDCAMIAsgCyACKQP4GCAOIBBWrXx8IhVWrXwiC1atfCIMIA1UrXwgDCACKQPYGCITIAsgCyACKQPQGCIOfCINVq18IA0gEyAOIBV8IgsgDlStfCALIAIpA+gYIAIpA+AYIg4gEHwgDlStfHwiECALVK18fCILIA1UrXx8Ig4gDFStfCIMQgBZBEAgDEL///////////8AUiAQQm1UciALIA6DQn9Scg0BCyALQgF8Ig0gEEJtVK0iFX0hFyAOQgF8IhMgC0J/UiANIBVUcq0iC30hDSAMIA5Cf1IgCyATVnKtfUL///////////8AfSEMIBBCE3whEAwBCyAOIQ0gCyEXCyAMIRUgEiETAn4CQAJAIAwgElINACANIRUgDyETIA0gD1INACAWIhMgFyIVUg0AIBAhFSARIRMgECARUQ0BCyATIBVaDQAgFyAWfSILIBAgEVStIg5UIBYgF1ZyrSITIA0gD30iF0J/hXwiFSAOIAtCf4V8IgsgECARfSIOQm1WrSIRVK0iEH0hFiAQIBVWIQYgCyARfSEVQm0gDn0hESANIA9UIBMgF1ZyrSASIAx9fEL///////////8AfAwBCyAWIBd9IgsgECARVq0iDn0hFSAPIA19IhMgFiAXVCALIA5Ucq0iC30hFiALIBNWIA0gD1ZyIQYgESAQfSERIBIgDH0LIAIpA/gcIR0gAikD8BwhISACKQPoHCEfIAIpA+AcIichEiAGrX0iCyEMAn4CQAJAIAsgJ1INACAWIgwgHyISUg0AIBUiDCAhIhJSDQAgESIMIB0iElENAQsgDCASWg0AICEgFX0iDyARIB1WrSIMVCAVICFWcq0iDiAfIBZ9Ig1Cf4V8IhIgDCAPQn+FfCIPIB0gEX0iDEJtVq0iEVStIhB9ISIgECASViEFIA8gEX0hJSANIA5UIBYgH1ZyrSALICd9fEL///////////8AfCEVQm0gDH0MAQsgFSAhfSIPIBEgHVStIgx9ISUgFiAffSIOIBUgIVQgDCAPVnKtIg99ISIgFiAfVCAOIA9UciEFIAsgJ30hFSARIB19CyEjIAJB8B1qQgA3AwAgAkHoHWpCADcDACACQgA3A+AdIAJCyAM3A/gdIAJBsBhqQqV8QsgDIAJB4B1qQejRwQBBIBDxAyIGGyILQgAgFEIAEMkDIAJBgBdqQn9CACAGGyIPQgAgFEIAEMkDIAJB8BdqQv///////////wBCACAGGyIMQgAgFEIAEMkDIAJB8BZqIAIpA7AYIhJCm5Svw/K1qN6Gf34iDkIAQm1CABDJAyACQeAWaiAOQgBCf0IAEMkDIAJB0BZqIA5CAEL///////////8AQgAQyQMgAkGgGGogC0IAIBlCABDJAyACQZAXaiAPQgAgGUIAEMkDIAJB4BdqIAxCACAZQgAQyQMgAkHAFmogAikD4BYiDiACKQO4GCIQIAIpA4AXIhN8IhZ8Ig0gAikD+BYgEiACKQPwFiIRfCARVK18fCISIAIpA6AYfCIRQpuUr8Pytajehn9+IhRCAEJtQgAQyQMgAkGwFmogFEIAQn9CABDJAyACQaAWaiAUQgBC////////////AEIAEMkDIAJBkBhqIAtCACAYQgAQyQMgAkGgF2ogD0IAIBhCABDJAyACQdAXaiAMQgAgGEIAEMkDIAJBkBZqIAIpA6gYIBEgElStfCIXIAIpA5AXIhl8IhQgDiATIAIpA4gXIhggECAWVq18Ihp8IhB8IhMgDSASVq0gAikD6BYiHCANIA5UrXx8fCIefCIOIAIpA7AWIip8Ig0gAikDyBYgAikDwBYiEiARfCASVK18fCISIAIpA5AYfCIRQpuUr8Pytajehn9+IhZCAEJtQgAQyQMgAkGAFmogFkIAQn9CABDJAyACQfAVaiAWQgBC////////////AEIAEMkDIAJBgBhqIAtCACAbQgAQyQMgAkGwF2ogD0IAIBtCABDJAyACQcAXaiAMQgAgG0IAEMkDIAJB4BVqIAIpA5gYIBEgElStfCIbIAIpA6AXIil8IgsgKiAZIBggECAaVK18IhggAikD8Bd8Ig8gAikD0BZ8IgwgEyAeVq0gHCAQIBNWrXx8fCIQfCITIA4gFFStIAIpA5gXIhkgFCAXVK18fHwiFHwiFiANIBJWrSACKQO4FiIaIA0gDlStfHx8Ihx8Ig4gAikDgBYiHnwiDSACKQOYFiACKQOQFiISIBF8IBJUrXx8IhIgAikDgBh8IhFCm5Svw/K1qN6Gf34iF0IAQm1CABDJAyACQdAVaiAXQgBCf0IAEMkDIAJBwBVqIBdCAEL///////////8AQgAQyQMCQAJAIAIpA8gXIAIpA9gXIAIpA6gWIAIpA/gXIA8gGFStfCIYIAIpA+AXfCIXIAwgEFatIAIpA9gWIAwgD1StfHx8Ig8gEyAUVq0gGSAQIBNWrXx8fCIMIAIpA6AWfCIQIAxUrXwgECAWIBxWrSAaIBQgFlatfHx8IhQgEFStfCITIAwgD1StIA8gF1StIAIpA+gXIBcgGFStfHx8fCIPIAIpA9AXfCIMIA9UrXwgDCAMIAIpA6gXIhYgFCAUICl8IhBWrXwgECALIA5WrSAWIAsgG1StfHx8IgsgEFStfHwiFFatfCIQIA8gE1StfCIPIAIpA/gVIBQgFCACKQPwFXwiDFatfCAMIAwgAikDiBYiEyALIAsgHnwiFFatfCAUIBQgDSASVq0gEyANIA5UrXx8fCITVq18fCILVq18fCIMIAIpA8AXfCIOIAxUrXwgDiAOIAIpA7gXIhQgCyALIAIpA7AXIhZ8Ig1WrXwgDSANIBQgFiACKQOIGCARIBJUrXwiEnwiCyASVK18IAsgCyATfCISVq18fCILVq18fCINVq18IhQgDyAQVK0gDCAPVK18fCIMIAIpA8gVIA0gAikDwBV8Ig4gDVStfCAOIA4gAikD2BUiDSALIAsgAikD0BUiEHwiD1atfCAPIA0gECASfCILIBJUrXwgCyACKQPoFSACKQPgFSINIBF8IA1UrXx8IhAgC1StfHwiCyAPVK18fCIPVq18fCIRQgBTIAwgFFStIAwgEVatfCIMQgBSIAxQG0UEQCALIA+DQn9SIBBCbVRyIBFC////////////AFJyDQELIAtCAXwiDiAQQm1UrSINfSEMIA9CAXwiFCALQn9SIA0gDlZyrSILfSESIBEgD0J/UiALIBRWcq19Qv///////////wB9IREgEEITfCEQDAELIA8hEiALIQwLAn4CQAJAIBEiCyAoIg9SDQAgEiILICAiD1INACAMIgsgJiIPUg0AICQiDyAQIgtRDQELIAsgD1oNACAmIAx9IgsgECAkVq0iD1QgDCAmVnKtIgwgICASfSIOQn+FfCINIA8gC0J/hXwiCyAkIBB9IhRCbVatIhBUrSITfSEPIA0gE1QhBiALIBB9IQsgDCAOViASICBWcq0gESAofXxC////////////AHwhF0JtIBR9DAELIAwgJn0iDyAQICRUrSIOfSELIBIgIH0iDSAMICZUIA4gD1ZyrSIMfSEPIBIgIFQgDCANVnIhBiARICh9IRcgECAkfQshEiACQbAVaiAdQgBCvgFCABDJAyACQaAVaiACKQOwFSINQpuUr8Pytajehn9+IgxCAEJtQgAQyQMgAkGQFWogDEIAQn9CABDJAyACQYAVaiAMQgBC////////////AEIAEMkDIAJB8BRqICFCAEK+AUIAEMkDIAJB4BRqIAIpA5AVIgwgAikDuBV8Ig4gAikDqBUgAikDoBUiESANQn6DfCARVK18fCINIAIpA/AUfCIRQpuUr8Pytajehn9+IhRCAEJtQgAQyQMgAkHQFGogFEIAQn9CABDJAyACQcAUaiAUQgBC////////////AEIAEMkDIAJBsBRqIB9CAEK+AUIAEMkDIAJBoBRqIAIpA9AUIhQgAikD+BQgDSARVq18IhAgDCANIA5UrSACKQOYFSITIAwgDlatfHwiFnwiGXwiGHwiDCACKQPoFCACKQPgFCIOIBF8IA5UrXx8Ig4gAikDsBR8Ig1Cm5Svw/K1qN6Gf34iEUIAQm1CABDJAyACQZAUaiARQgBCf0IAEMkDIAJBgBRqIBFCAEL///////////8AQgAQyQMgAkHwE2ogJ0IAQr4BQgAQyQMgAkHgE2ogAikDkBQiESAUIBAgGFatIhggEyAWIBlWrXwiGSACKQOAFXwiG3wiEHwiEyAMIA5WrSACKQPYFCIaIAwgFFStfHx8IgwgAikDuBQgDSAOVK18fCIcfCIOIAIpA6gUIA0gAikDoBQiFHwgFFStfHwiDSACKQPwE3wiFEKblK/D8rWo3oZ/fiIWQgBCbUIAEMkDIAJB0BNqIBZCAEJ/QgAQyQMgAkHAE2ogFkIAQv///////////wBCABDJAyAXIAatfSEWAkACQCACKQPIEyACKQOIFCACKQPIFCACKQPAFCIeIAIpA4gVIBkgG1atfHwiFyAeVK18IBcgFyAQIBhUrXwiGVatfCAZIAwgE1StIBogECATVq18fHwiECAZVK18IhcgAikDgBR8IhMgF1StfCATIBMgECAMIBxWrXwiDCAQVK18IhBWrXwgECAQIAIpA5gUIhcgDCAMIBF8IhNWrXwgEyATIA0gDlStIBcgDiARVK18fHwiDFatfHwiDlatfCIQIAIpA8ATfCIRIBBUrXwgESAOIA4gDCAMIAIpA/gTIA0gFFatfHwiE1atfCIMVq18Ig4gEVStfCAOIAIpA9gTIhEgDCAMIAIpA9ATIg18IhBWrXwgECAQIBEgDSATfCIMIA1UrXwgDCACKQPoEyACKQPgEyINIBR8IA1UrXx8IhEgDFStfHwiDFatfHwiDSAOVK18IhBCAFkEQCAQQv///////////wBSIBFCbVRyIAwgDYNCf1JyDQELIAxCAXwiFCARQm1UrSITfSEOIA1CAXwiFyAMQn9SIBMgFFZyrSIMfSEZIBAgDUJ/UiAMIBdWcq19Qv///////////wB9IRAgEUITfCERDAELIA0hGSAMIQ4LIBAgFnwiDCAPIBl8Ig0gD1QgDSANIAsgCyAOfCIOViAOIA4gESASfCIRIBJUrXwiD1ZyrXwiDlZyrXwhDQJAAkAgDCAWVCAMIA1Wcg0AQv///////////wAhDCANIgtC////////////AFEEQEJ/IQxC////////////ACELIA5Cf1IEQCAPIRQgDiEMDAMLIA9Cf1IEQCAPIRQMAwtCbSEMIBEiC0JtUQ0BCyALIAxaDQAgDyEUIA4hDCANIQsMAQsgD0IBfCILIBFCbVStIgx9IRQgDkIBfCISIA9Cf1IgCyAMVHKtIgt9IQwgDSAOQn9SIAsgElZyrX1C////////////AH0hCyARQhN8IRELIAIgETcDmB0gAiAUNwOQHSACIAw3A4gdIAIgCzcDgB0CQAJAIAJBgB1qQejRwQBBIBDxAwRAIBUgBa19ISogAkGwHWpCADcDACACQagdakIANwMAIAJCADcDoB0gAkIBNwO4HSACQdgdaiACQZgdaikDADcDACACQdAdaiACQZAdaikDADcDACACQcgdaiACQYgdaikDADcDACACIAIpA4AdNwPAHSACQfgdakHg0cEAKQMANwMAIAJB8B1qQdjRwQApAwA3AwAgAkHoHWpB0NHBACkDADcDACACQcjRwQApAwA3A+AdAkAgAkHAHWogAkGgHWpBIBDxA0UEQEKkCyESQgAhFkIAIRFCACETDAELQqQLIRIgAikD2B0hDyACKQPAHSEUIAIpA9AdIRcgAikDyB0hDkIAIQxCACEaQgAhHEIAIRBCACETQgAhFkIAIRFCbSELQv///////////wAhGUJ/IQ1CfyEVA0AgAkHgHWogAkGgHWpBIBDxA0UEQCAcIRYgECERIBohEyAMIRIMAgsgD6dBAXFFBEADQCAXQj+GIA9CAYiEIQ8CfiASp0EBcUUEQCATQj+GIBJCAYiEIRIgFkI/hiATQgGIhCETIBFCP4YgFkIBiIQMAQsgFkIBfSIbIBNCAFIgE0IBfSITIBIgEkITfSIeVq18IhIgE1RyrXwiGEI/hiASQgGIhCETIBJCP4YgHkIBiIQhEiARIBZCAFIgGCAbVHKtfEL///////////8AfCIRQj+GIBhCAYiECyEWIBRCP4YgDkI/hiAXQgGIhCEXIBRCAYghFCARQgGIIREgDkIBiIQhDiAPQgGDUA0ACyACIA43A8gdIAIgFzcD0B0LIAIgFDcDwB0gAiAPNwPYHSALp0EBcUUEQANAIBVCP4YgC0IBiIQhCwJ+IAxCAYNQRQRAIBxCAX0iGyAaQgBSIBpCAX0iGCAMIAxCE30iHlatfCIMIBhUcq18IhhCP4YgDEIBiIQhGiAMQj+GIB5CAYiEIQwgECAcQgBSIBggG1RyrXxC////////////AHwiEEI/hiAYQgGIhAwBCyAaQj+GIAxCAYiEIQwgHEI/hiAaQgGIhCEaIBBCP4YgHEIBiIQLIRwgGUI/hiANQj+GIBVCAYiEIRUgGUIBiCEZIBBCAYghECANQgGIhCENIAtCAYNQDQALIAIgDTcD6B0gAiAVNwPwHQsgAiALNwP4HSACIBk3A+AdIBQhGAJAAkACQAJAAkAgGSIbIBRSDQAgDSEbIA4hGCANIA5SDQAgFSEbIBUgFyIYUg0AIAshGyAPIRggCyAPUQ0BCyAYIBtaDQAgAiALIA99Ihg3A/gdIAIgFSAXfSIeIAsgD1StIgt9Ihs3A/AdIAIgDSAOfSIpIBUgF1QgCyAeVnKtIgt9Ih43A+gdIAIgGSAUfSANIA5UIAsgKVZyrX0iGTcD4B0CQAJAIBEiDSAQIgtSDQAgFiINIBwiC1INACATIg0gGiILUg0AIBIiDSAMIgtRDQELIAsgDVQNAgsgECARfSAcIBZ9IikgGiATfSIrIAwgElStIixUIBMgGlZyrSIaVCAWIBxWcq19IRAgDCASfSEMIBshFSAeIQ0gGCELICkgGn0hHCArICx9IRoMAwsgAiAPIAt9Ihg3A9gdIAIgFyAVfSIeIAsgD1atIg99Ihs3A9AdIAIgDiANfSIpIA8gHlYgFSAXVnKtIg99Ihc3A8gdIAIgFCAZfSAPIClWIA0gDlZyrX0iFDcDwB0CQAJAIBEiDyAQIg5SDQAgFiIPIBwiDlINACATIg8gGiIOUg0AIBIiDyAMIg5RDQELIA4gD1YNAgsgESAQfSAWIBxUIBYgHH0iFiATIBpUIBMgGn0iEyAMIBJWrSIeVHKtIilUcq19IREgEiAMfSESIBchDiAbIRcgGCEPIBYgKX0hFiATIB59IRMMAgsgEEJ/QgAgFkJ/hSILIBNCf4UiDSASQm1WrSIVVK0iKVQbIBF9fCALICl9IhAgHHwiCyAQVCALIA0gFX0iECAafCINIBBUIA1CbSASfSIQIAx8IgwgEFStfCIaIA1Ucq18IhwgC1RyrXxC////////////AHwhECAbIRUgHiENIBghCwwBCyARIBB9IBxCf4UiDyAaQn+FIg4gDEJtVq0iEVStIh5UrX0gFiAPIB59Ih58Ig8gHlQgDyAPIA4gEX0iESATfCIOIBFUIA5CbSAMfSIRIBJ8IhIgEVStfCITIA5Ucq18IhZWcq18Qv///////////wB8IREgFyEOIBshFyAYIQ8LIAJBwB1qIAJBoB1qQSAQ8QMNAAsLIAJBsBNqIBJCACAjQgAQyQMgAkHwEmogEkIAICVCABDJAyACQeASaiASQgAgIkIAEMkDIAJB0BJqIBJCACAqQgAQyQMgAkGgE2ogAikDsBMiDEKblK/D8rWo3oZ/fiILQgBCbUIAEMkDIAJBkBNqIAtCAEJ/QgAQyQMgAkGAE2ogC0IAQv///////////wBCABDJAyACQcASaiATQgAgI0IAEMkDIAJBgBJqIBNCACAlQgAQyQMgAkHwEWogE0IAICJCABDJAyACQeARaiATQgAgKkIAEMkDIAJBsBJqIAIpA5ATIgsgAikDuBMiEiACKQPwEnwiFHwiDyACKQOoEyAMIAIpA6ATIg58IA5UrXx8IgwgAikDwBJ8Ig5Cm5Svw/K1qN6Gf34iDUIAQm1CABDJAyACQaASaiANQgBCf0IAEMkDIAJBkBJqIA1CAEL///////////8AQgAQyQMgAkHQEWogFkIAICNCABDJAyACQZARaiAWQgAgJUIAEMkDIAJBgBFqIBZCACAiQgAQyQMgAkHwEGogFkIAICpCABDJAyACQcARaiACKQPIEiAMIA5WrXwiEyACKQOAEnwiDSALIAIpA/gSIBIgFFatfCIVIAIpA+ASfCISfCIUIAwgD1StIAIpA5gTIhYgCyAPVq18fHwiF3wiCyACKQOgEiIZfCIPIAIpA7gSIAIpA7ASIgwgDnwgDFStfHwiDCACKQPQEXwiDkKblK/D8rWo3oZ/fiIQQgBCbUIAEMkDIAJBsBFqIBBCAEJ/QgAQyQMgAkGgEWogEEIAQv///////////wBCABDJAyACQeAQaiARQgAgI0IAEMkDIAJBoBBqIBFCACAlQgAQyQMgAkGQEGogEUIAICJCABDJAyACQYAQaiARQgAgKkIAEMkDIAJB0BBqIAIpA9gRIAwgDlatfCIYIAIpA5ARfCIRIBkgAikD6BIgEiAVVK18IhsgAikD0BJ8IhAgAikDgBN8IhUgFCAXVq0gFiASIBRWrXx8fCISIAIpA/ARfCIUIAsgDVStIAIpA4gSIA0gE1StfHx8Ig18IhMgDCAPVK0gAikDqBIiFyALIA9WrXx8fCIZfCILIAIpA7ARIhp8Ig8gAikDyBEgAikDwBEiDCAOfCAMVK18fCIMIAIpA+AQfCIOQpuUr8Pytajehn9+IhZCAEJtQgAQyQMgAkHAEGogFkIAQn9CABDJAyACQbAQaiAWQgBC////////////AEIAEMkDIAIpA7gQIAIpA6gRIAIpA5gSIBIgFVStIAIpA4gTIBAgFVatfHwiFiACKQPYEiAQIBtUrXx8IhAgAikD4BF8IhUgDSAUVK0gAikD+BEgEiAUVq18fHwiEiACKQOQEnwiFCASVK18IBQgEyAZVq0gFyANIBNWrXx8fCINIBRUrXwiEyASIBVUrSACKQPoESAQIBVWrXx8IhcgECAWVK18IhZ8IhIgAikD8BB8IhQgAikDiBEgDSANIAIpA4ARfCIQVq18IBAgECALIBFUrSACKQOYESARIBhUrXx8fCINVq18fCIRIAIpA6ARfCIQIBFUrXwgECACKQO4ESIZIA0gDSAafCIVVq18IBUgFSAMIA9UrSAZIAsgD1atfHx8IhlWrXx8IgsgEFStfCIQIBEgFFStIAIpA/gQIBIgFFatfHwiFSASIBNUrSAWIBdUrXx8IhN8Ig0gAikDgBB8IhIgAikDmBAgCyALIAIpA5AQfCIPVq18IA8gDyACKQOoECACKQPoECAMIA5WrXwiDCACKQOgEHwiCyAMVK18IAsgCyAZfCIMVq18fCILVq18fCIRIAIpA7AQfCIUIBFUrXwgFCAUIAIpA8gQIhYgCyALIAIpA8AQIhd8Ig9WrXwgDyAPIBYgDCAMIBd8IgtWrXwgCyACKQPYECAOIAIpA9AQIgx8IAxUrXx8IiMgC1StfHwiC1atfHwiD1atfCIMIBEgElStIAIpA4gQIA0gElatfHwiDiANIBBUrSATIBVUrXx8Ig18IiIgDFQgDSAOVHIgIkIAU3JFBEAgCyAPg0J/UiAjQm1UciAiQv///////////wBScg0CCyALQgF8IgwgI0JtVK0iDn0hHiAPQgF8Ig0gC0J/UiAMIA5Ucq0iC30hJSAiIA9Cf1IgCyANVnKtfUL///////////8AfSEiICNCE3whIwwCCyACQgI3A+AdQYz3wQBBKyACQeAdakH89sEAQZiRwgAQygMACyAPISUgCyEeCyACQfAPaiAjQgAgJEIAEMkDIAJBsA9qICNCACAmQgAQyQMgAkGgD2ogI0IAICBCABDJAyACQZAPaiAjQgAgKEIAEMkDIAJB4A9qIAIpA/APIgxCm5Svw/K1qN6Gf34iC0IAQm1CABDJAyACQdAPaiALQgBCf0IAEMkDIAJBwA9qIAtCAEL///////////8AQgAQyQMgAkGAD2ogHkIAICRCABDJAyACQcAOaiAeQgAgJkIAEMkDIAJBsA5qIB5CACAgQgAQyQMgAkGgDmogHkIAIChCABDJAyACQfAOaiACKQPQDyILIAIpA/gPIhIgAikDsA98IhF8Ig8gAikD6A8gDCACKQPgDyIOfCAOVK18fCIMIAIpA4APfCIOQpuUr8Pytajehn9+Ig1CAEJtQgAQyQMgAkHgDmogDUIAQn9CABDJAyACQdAOaiANQgBC////////////AEIAEMkDIAJBkA5qICVCACAkQgAQyQMgAkHQDWogJUIAICZCABDJAyACQcANaiAlQgAgIEIAEMkDIAJBsA1qICVCACAoQgAQyQMgAkGADmogAikDiA8gDCAOVq18IhMgAikDwA58Ig0gCyACKQO4DyARIBJUrXwiECACKQOgD3wiEnwiESAMIA9UrSACKQPYDyIWIAsgD1atfHx8Ihd8IgsgAikD4A4iGXwiDyACKQP4DiACKQPwDiIMIA58IAxUrXx8IgwgAikDkA58Ig5Cm5Svw/K1qN6Gf34iFEIAQm1CABDJAyACQfANaiAUQgBCf0IAEMkDIAJB4A1qIBRCAEL///////////8AQgAQyQMgAkGgDWogIkIAICRCABDJAyACQeAMaiAiQgAgJkIAEMkDIAJB0AxqICJCACAgQgAQyQMgAkHADGogIkIAIChCABDJAyACQZANaiACKQOYDiAMIA5WrXwiGCACKQPQDXwiFCAZIAIpA6gPIBAgElatfCIbIAIpA5APfCIQIAIpA8APfCIVIBEgF1atIBYgESASVK18fHwiEiACKQOwDnwiESALIA1UrSACKQPIDiANIBNUrXx8fCINfCITIAwgD1StIAIpA+gOIhcgCyAPVq18fHwiGXwiCyACKQPwDSIafCIPIAIpA4gOIAIpA4AOIgwgDnwgDFStfHwiDCACKQOgDXwiDkKblK/D8rWo3oZ/fiIWQgBCbUIAEMkDIAJBgA1qIBZCAEJ/QgAQyQMgAkHwDGogFkIAQv///////////wBCABDJAwJAAkAgAikD+AwgAikD6A0gAikD2A4gEiAVVK0gAikDyA8gECAVVq18fCIWIAIpA5gPIBAgG1StfHwiECACKQOgDnwiFSANIBFUrSACKQO4DiARIBJUrXx8fCISIAIpA9AOfCIRIBJUrXwgESATIBlWrSAXIA0gE1atfHx8Ig0gEVStfCITIBIgFVStIAIpA6gOIBAgFVatfHwiFyAQIBZUrXwiFnwiEiACKQOwDXwiESACKQPIDSANIA0gAikDwA18IhBWrXwgECAQIAsgFFStIAIpA9gNIBQgGFStfHx8Ig1WrXx8IhQgAikD4A18IhAgFFStfCAQIAIpA/gNIhkgDSANIBp8IhVWrXwgFSAVIAwgD1StIBkgCyAPVq18fHwiGVatfHwiCyAQVK18IhggESAUVq0gAikDuA0gESASVK18fCIbIBIgE1StIBYgF1StfHwiE3wiDSACKQPADHwiEiACKQPYDCALIAsgAikD0Ax8Ig9WrXwgDyAPIAIpA+gMIAIpA6gNIAwgDlatfCIMIAIpA+AMfCILIAxUrXwgCyALIBl8IgxWrXx8IgtWrXx8IhQgAikD8Ax8IhAgFFStfCAQIBAgAikDiA0iDyALIAsgAikDgA0iEXwiFVatfCAVIBUgDyAMIAwgEXwiC1atfCALIAIpA5gNIA4gAikDkA0iD3wgD1StfHwiESALVK18fCIPVq18fCIMVq18IgsgEiAUVq0gAikDyAwgDSASVq18fCIOIA0gGFStIBMgG1StfHwiDXwiECALVCANIA5UciAQQgBTckUEQCAMIA+DQn9SIBFCbVRyIBBC////////////AFJyDQELIA9CAXwiCyARQm1UrSIOfSEUIAxCAXwiDSAPQn9SIAsgDlRyrSIPfSELIBAgDEJ/UiANIA9Ucq19Qv///////////wB9IRAgEUITfCERDAELIAwhCyAPIRQLIBAgKHwiDyALICB8IgwgIFQgDCAUICZ8Ig4gJlQgDiAOIBEgJHwiEiAkVK18IgtWcq18Ig4gDFRyrXwhDQJAAkAgDyAoVCANIA9Ucg0AQv///////////wAhECANIgxC////////////AFEEQEJ/IQxC////////////ACEPIA5Cf1IEQCALIRQgDiEMDAMLIAtCf1IEQCALIRQMAwtCbSEQIBIiDEJtUQ0BCyAMIBBaDQAgCyEUIA4hDCANIQ8MAQsgC0IBfCIPIBJCbVStIgx9IRQgDkIBfCIRIAtCf1IgDCAPVnKtIgt9IQwgDSAOQn9SIAsgEVZyrX1C////////////AH0hDyASQhN8IRILIAJB8ApqICNCACAdQgAQyQMgAkGwC2ogI0IAICFCABDJAyACQfALaiAjQgAgH0IAEMkDIAJBsAxqICNCACAnQgAQyQMgAkHgCmogAikD8AoiDUKblK/D8rWo3oZ/fiILQgBCbUIAEMkDIAJB0ApqIAtCAEJ/QgAQyQMgAkHACmogC0IAQv///////////wBCABDJAyACQbAKaiAeQgAgHUIAEMkDIAJBoAtqIB5CACAhQgAQyQMgAkHgC2ogHkIAIB9CABDJAyACQaAMaiAeQgAgJ0IAEMkDIAJBoApqIAIpA9AKIgsgAikD+AoiFSACKQOwC3wiE3wiDiACKQPoCiANIAIpA+AKIhF8IBFUrXx8Ig0gAikDsAp8IhFCm5Svw/K1qN6Gf34iEEIAQm1CABDJAyACQZAKaiAQQgBCf0IAEMkDIAJBgApqIBBCAEL///////////8AQgAQyQMgAkHwCWogJUIAIB1CABDJAyACQZALaiAlQgAgIUIAEMkDIAJB0AtqICVCACAfQgAQyQMgAkGQDGogJUIAICdCABDJAyACQeAJaiACKQO4CiANIBFWrXwiGCACKQOgC3wiECALIAIpA7gLIBMgFVStfCIXIAIpA/ALfCIVfCITIA0gDlStIAIpA9gKIhsgCyAOVq18fHwiGnwiCyACKQOQCiIcfCIOIAIpA6gKIAIpA6AKIg0gEXwgDVStfHwiDSACKQPwCXwiEUKblK/D8rWo3oZ/fiIWQgBCbUIAEMkDIAJB0AlqIBZCAEJ/QgAQyQMgAkHACWogFkIAQv///////////wBCABDJAyACQbAJaiAiQgAgHUIAEMkDIAJBgAtqICJCACAhQgAQyQMgAkHAC2ogIkIAIB9CABDJAyACQYAMaiAiQgAgJ0IAEMkDIAJBoAlqIAIpA/gJIA0gEVatfCIkIAIpA5ALfCIWIBwgAikD+AsgFSAXVK18IiYgAikDsAx8IhcgAikDwAp8IhkgEyAaVq0gGyATIBVUrXx8fCIVIAIpA+ALfCITIAsgEFStIAIpA6gLIBAgGFStfHx8IhB8IhggDSAOVK0gAikDmAoiGiALIA5WrXx8fCIcfCILIAIpA9AJIiB8Ig4gAikD6AkgAikD4AkiDSARfCANVK18fCINIAIpA7AJfCIRQpuUr8Pytajehn9+IhtCAEJtQgAQyQMgAkGQCWogG0IAQn9CABDJAyACQYAJaiAbQgBC////////////AEIAEMkDAkACQCACKQOICSACKQPICSACKQOICiAVIBlUrSACKQPICiAXIBlWrXx8IhsgAikDuAwgFyAmVK18fCIXIAIpA6AMfCIZIBAgE1StIAIpA+gLIBMgFVStfHx8IhUgAikDgAp8IhMgFVStfCATIBggHFatIBogECAYVq18fHwiECATVK18IhggFSAZVK0gAikDqAwgFyAZVq18fCIaIBcgG1StfCIbfCIVIAIpA5AMfCITIAIpA9gLIBAgECACKQPQC3wiF1atfCAXIBcgCyAWVK0gAikDmAsgFiAkVK18fHwiEFatfHwiFiACKQPACXwiFyAWVK18IBcgAikD2AkiHCAQIBAgIHwiGVatfCAZIBkgDSAOVK0gHCALIA5WrXx8fCIQVq18fCILIBdUrXwiHCATIBZWrSACKQOYDCATIBVUrXx8IiQgFSAYVK0gGiAbVq18fCIYfCIVIAIpA4AMfCITIAIpA8gLIAsgCyACKQPAC3wiDlatfCAOIA4gAikDiAsgAikDuAkgDSARVq18Ig0gAikDgAt8IgsgDVStfCALIAsgEHwiDVatfHwiC1atfHwiFiACKQOACXwiFyAWVK18IBcgFyACKQOYCSIOIAsgCyACKQOQCSIQfCIZVq18IBkgGSAOIA0gDSAQfCILVq18IAsgAikDqAkgESACKQOgCSIOfCAOVK18fCIQIAtUrXx8Ig5WrXx8Ig1WrXwiCyATIBZWrSACKQOIDCATIBVUrXx8IhMgFSAcVK0gGCAkVK18fCIVfCIRIAtUIBMgFVZyIBFCAFNyRQRAIA0gDoNCf1IgEEJtVHIgEUL///////////8AUnINAQsgDkIBfCILIBBCbVStIhV9IRkgDUIBfCITIA5Cf1IgCyAVVHKtIg59IQsgESANQn9SIA4gE1ZyrX1C////////////AH0hESAQQhN8IRAMAQsgDSELIA4hGQsCfgJAAkAgESIOIA8iDVINACALIQ4gCyAMIg1SDQAgFCINIBkiDlINACASIg0gECIOUQ0BCyANIA5aDQAgGSAUfSIOIBAgElStIg1UIBQgGVZyrSIVIAsgDH0iE0J/hXwiFiANIA5Cf4V8Ig4gECASfSINQm1WrSISVK0iEH0hFCAQIBZWIQYgDiASfSEOIAsgDFQgEyAVVHKtIA8gEX18Qv///////////wB8IQxCbSANfQwBCyAUIBl9Ig0gECASVq0iFX0hDiAMIAt9IhMgFCAZVCANIBVUcq0iDX0hFCANIBNWIAsgDFZyIQYgDyARfSEMIBIgEH0LIQsgDCAGrX0iDyEMAn4CQAJAIA8gJyISUg0AIBQiDCAfIhJSDQAgDiIMICEiElINACALIgwgHSISUQ0BCyAMIBJaDQAgISAOfSIMIAsgHVatIg1UIA4gIVZyrSIOIB8gFH0iEkJ/hXwiESAMQn+FIA18IgwgHSALfSILQm1WrSINVK0iEH0hISAQIBFWIQUgDCANfSEkQm0gC30hJiAOIBJWIBQgH1ZyrSAPICd9fEL///////////8AfAwBCyAOICF9IgwgCyAdVK0iDX0hJCAUIB99IhIgDiAhVCAMIA1Ucq0iDH0hISAUIB9UIAwgElZyIQUgCyAdfSEmIA8gJ30LIRogAkHwCGogBykDGEIAQpgBQgAQyQMgAkHgCGogAikD8AgiDEKblK/D8rWo3oZ/fiILQgBCbUIAEMkDIAJB0AhqIAtCAEJ/QgAQyQMgAkHACGogC0IAQv///////////wBCABDJAyACQbAIaiAHKQMQQgBCmAFCABDJAyACQaAIaiACKQPQCCILIAIpA/gIfCIPIAIpA+gIIAIpA+AIIg4gDEJ4g3wgDlStfHwiDCACKQOwCHwiDkKblK/D8rWo3oZ/fiINQgBCbUIAEMkDIAJBkAhqIA1CAEJ/QgAQyQMgAkGACGogDUIAQv///////////wBCABDJAyACQfAHaiAHKQMIQgBCmAFCABDJAyACQeAHaiACKQOQCCINIAIpA7gIIAwgDlatfCISIAsgDCAPVK0gAikD2AgiESALIA9WrXx8IhR8IhB8IhV8IgsgAikDqAggAikDoAgiDyAOfCAPVK18fCIPIAIpA/AHfCIMQpuUr8Pytajehn9+Ig5CAEJtQgAQyQMgAkHQB2ogDkIAQn9CABDJAyACQcAHaiAOQgBC////////////AEIAEMkDIAJBsAdqIAcpAwBCAEKYAUIAEMkDIAJBoAdqIAIpA9AHIg4gDSASIBVWrSIVIBEgECAUVK18IhAgAikDwAh8IhN8IhJ8IhEgCyAPVq0gAikDmAgiFiALIA1UrXx8fCILIAIpA/gHIAwgD1StfHwiF3wiDyACKQPoByAMIAIpA+AHIg18IA1UrXx8IgwgAikDsAd8Ig1Cm5Svw/K1qN6Gf34iFEIAQm1CABDJAyACQZAHaiAUQgBCf0IAEMkDIAJBgAdqIBRCAEL///////////8AQgAQyQMCQAJAAn4CQAJAIAIpA4gHIAIpA8gHIAIpA4gIIAIpA4AIIhkgAikDyAggECATVq18fCIUIBlUrXwgFCAUIBIgFVStfCIQVq18IBAgCyARVK0gFiARIBJUrXx8fCISIBBUrXwiFCACKQPAB3wiESAUVK18IBEgESASIAsgF1atfCILIBJUrXwiElatfCASIBIgAikD2AciFCALIAsgDnwiEVatfCARIBEgDCAPVK0gFCAOIA9WrXx8fCILVq18fCIPVq18IhIgAikDgAd8Ig4gElStfCAOIA8gDyALIAsgAikDuAcgDCANVq18fCISVq18IgtWrXwiDyAOVK18IA8gDyACKQOYByIRIAsgCyACKQOQByIMfCIOVq18IA4gESAMIBJ8IgsgDFStfCALIAIpA6gHIAIpA6AHIgwgDXwgDFStfHwiDCALVK18fCIRIA5UrXx8IhJWrXwiEEIAUyIHRQRAIBEgEoMhDyAQQv///////////wBSIAxCbVRyDQEgDCEOIBEhDSASIRQgECEZIA9Cf1INAgsgEUIBfCIWIAxCbVStIgt9IQ0gEkIBfCIXIBFCf1IgCyAWVnKtIgt9IRQgEEL///////////8AfSIVIBJCf1IgCyAXVnKtfSEZIAxCE3wiDiAHDQIaIBEgEoMhDwwBCyAMIQ4gESENIBIhFCAQIRkLIBBC////////////AFIgDEJtVHIgD0J/UnINASASQgF8IRcgEUIBfCEWQgAhFSAMQhN8CyEPIBcgEUJ/UiAWIAxCbVStIgxUcq0iEX0hCyAVIBJCf1IgESAXVnKtfSEQIBYgDH0hEQwBCyASIQsgDCEPCyACQfAGaiAPQgAgI0IAEMkDIAJBgAZqIBFCACAjQgAQyQMgAkGQBWogC0IAICNCABDJAyACQaAEaiAQQgAgI0IAEMkDIAJB4AZqIAIpA/AGIhVCm5Svw/K1qN6Gf34iDEIAQm1CABDJAyACQdAGaiAMQgBCf0IAEMkDIAJBwAZqIAxCAEL///////////8AQgAQyQMgAkGwBmogD0IAIB5CABDJAyACQcAFaiARQgAgHkIAEMkDIAJB0ARqIAtCACAeQgAQyQMgAkHgA2ogEEIAIB5CABDJAyACQfAFaiACKQPQBiIMIAIpA/gGIhcgAikDgAZ8Ihh8IhIgAikD6AYgFSACKQPgBiITfCATVK18fCIVIAIpA7AGfCITQpuUr8Pytajehn9+IhZCAEJtQgAQyQMgAkHgBWogFkIAQn9CABDJAyACQdAFaiAWQgBC////////////AEIAEMkDIAJBoAZqIA9CACAlQgAQyQMgAkGwBWogEUIAICVCABDJAyACQcAEaiALQgAgJUIAEMkDIAJB0ANqIBBCACAlQgAQyQMgAkGABWogAikDuAYgEyAVVK18IhwgAikDwAV8IhYgDCACKQOIBiAXIBhWrXwiHSACKQOQBXwiF3wiGCASIBVWrSACKQPYBiIfIAwgElatfHx8IiB8IgwgAikD4AUiJ3wiEiACKQP4BSACKQPwBSIVIBN8IBVUrXx8IhUgAikDoAZ8IhNCm5Svw/K1qN6Gf34iG0IAQm1CABDJAyACQfAEaiAbQgBCf0IAEMkDIAJB4ARqIBtCAEL///////////8AQgAQyQMgAkGQBmogD0IAICJCABDJAyACQaAFaiARQgAgIkIAEMkDIAJBsARqIAtCACAiQgAQyQMgAkHAA2ogEEIAICJCABDJAyACQZAEaiACKQOoBiATIBVUrXwiKCACKQOwBXwiCyAnIAIpA5gFIBcgHVStfCIdIAIpA6AEfCIPIAIpA8AGfCIRIBggIFatIB8gFyAYVq18fHwiECACKQPQBHwiFyAMIBZUrSACKQPIBSAWIBxUrXx8fCIWfCIYIBIgFVatIAIpA+gFIhwgDCASVq18fHwiH3wiDCACKQPwBCIgfCISIAIpA4gFIAIpA4AFIhUgE3wgFVStfHwiFSACKQOQBnwiE0KblK/D8rWo3oZ/fiIbQgBCbUIAEMkDIAJBgARqIBtCAEJ/QgAQyQMgAkHwA2ogG0IAQv///////////wBCABDJAwJAAkAgAikD+AMgAikD6AQgAikD2AUgECARVK0gAikDyAYgDyARVq18fCIbIAIpA6gEIA8gHVStfHwiDyACKQPgA3wiESAWIBdUrSACKQPYBCAQIBdWrXx8fCIQIAIpA9AFfCIXIBBUrXwgFyAXIBggH1atIBwgFiAYVq18fHwiFlatfCIYIBAgEVStIAIpA+gDIA8gEVatfHwiHCAPIBtUrXwiG3wiDyACKQPQA3wiESACKQPIBCAWIAIpA8AEfCIQIBZUrXwgECALIAxWrSACKQO4BSALIChUrXx8fCILIBBUrXx8IhAgAikD4AR8IhYgEFStfCAWIAIpA/gEIh0gCyALICB8IhdWrXwgFyAXIBIgFVatIB0gDCASVq18fHwiHVatfHwiCyAWVK18IhcgECARVK0gAikD2AMgDyARVq18fCIfIA8gGFStIBsgHFStfHwiGHwiDCACKQPAA3wiEiACKQO4BCALIAsgAikDsAR8Ig9WrXwgDyAPIAIpA6gFIAIpA5gGIBMgFVStfCIRIAIpA6AFfCILIBFUrXwgCyALIB18IhFWrXx8IgtWrXx8IhUgAikD8AN8IhYgFVStfCAWIBYgAikDiAQiECALIAsgAikDgAQiG3wiD1atfCAPIA8gECARIBEgG3wiC1atfCALIAIpA5gEIAIpA5AEIhEgE3wgEVStfHwiECALVK18fCILVq18fCIPVq18IhMgEiAVVq0gAikDyAMgDCASVq18fCISIAwgF1StIBggH1StfHwiDHwiESATVCAMIBJUciARQgBTckUEQCALIA+DQn9SIBBCbVRyIBFC////////////AFJyDQELIAtCAXwiEiAQQm1UrSIVfSEMIA9CAXwiEyALQn9SIBIgFVRyrSILfSESIBEgD0J/UiALIBNWcq19Qv///////////wB9IREgEEITfCEQDAELIA8hEiALIQwLAn8CQAJAIBEiDyAZIgtSDQAgEiIPIBQiC1INACAMIQ8gDSILIAxSDQAgECIPIA4iC1ENAQsgCyAPWg0AIAwgDX0iCyAOIBBWrSIPVCAMIA1Ucq0iDSASIBR9IhVCf4V8IhMgDyALQn+FfCILIBAgDn0iDkJtVq0iD1StIhZ9IQwgCyAPfSEPIBIgFFQgDSAVVnKtIBkgEX18Qv///////////wB8IRFCbSAOfSEQIBMgFlQMAQsgDSAMfSILIA4gEFStIhV9IQ8gFCASfSITIAsgFVQgDCANVnKtIgt9IQwgGSARfSERIA4gEH0hECALIBNWIBIgFFZyCyEHIAIgEDcDmB0gAiAPNwOQHSACIAw3A4gdIAIgESAHrX03A4AdAkACQCACQYAdakHo0cEAQSAQ8QMEQCAaIAWtfSEfIAJBsB1qQgA3AwAgAkGoHWpCADcDACACQgA3A6AdIAJCATcDuB0gAkHYHWogAkGYHWopAwA3AwAgAkHQHWogAkGQHWopAwA3AwAgAkHIHWogAkGIHWopAwA3AwAgAiACKQOAHTcDwB0gAkH4HWpB4NHBACkDADcDACACQfAdakHY0cEAKQMANwMAIAJB6B1qQdDRwQApAwA3AwAgAkHI0cEAKQMANwPgHQJAIAJBwB1qIAJBoB1qQSAQ8QNFBEBCpAshEkIAIRFCACEWQgAhEwwBC0KkCyESIAIpA9gdIQ8gAikDwB0hFCACKQPQHSEXIAIpA8gdIQ5CACEMQgAhGkIAIRxCACEQQgAhE0IAIRZCACERQm0hC0L///////////8AIRlCfyENQn8hFQNAIAJB4B1qIAJBoB1qQSAQ8QNFBEAgECERIBwhFiAaIRMgDCESDAILIA+nQQFxRQRAA0AgF0I/hiAPQgGIhCEPAn4gEqdBAXFFBEAgE0I/hiASQgGIhCESIBZCP4YgE0IBiIQhEyARQj+GIBZCAYiEDAELIBZCAX0iGyATQgBSIBNCAX0iEyASIBJCE30iHVatfCISIBNUcq18IhhCP4YgEkIBiIQhEyASQj+GIB1CAYiEIRIgESAWQgBSIBggG1RyrXxC////////////AHwiEUI/hiAYQgGIhAshFiAUQj+GIA5CP4YgF0IBiIQhFyAUQgGIIRQgEUIBiCERIA5CAYiEIQ4gD0IBg1ANAAsgAiAONwPIHSACIBc3A9AdCyACIBQ3A8AdIAIgDzcD2B0gC6dBAXFFBEADQCAVQj+GIAtCAYiEIQsCfiAMQgGDUEUEQCAcQgF9IhsgGkIAUiAaQgF9IhggDCAMQhN9Ih1WrXwiDCAYVHKtfCIYQj+GIAxCAYiEIRogDEI/hiAdQgGIhCEMIBAgHEIAUiAYIBtUcq18Qv///////////wB8IhBCP4YgGEIBiIQMAQsgGkI/hiAMQgGIhCEMIBxCP4YgGkIBiIQhGiAQQj+GIBxCAYiECyEcIBlCP4YgDUI/hiAVQgGIhCEVIBlCAYghGSAQQgGIIRAgDUIBiIQhDSALQgGDUA0ACyACIA03A+gdIAIgFTcD8B0LIAIgCzcD+B0gAiAZNwPgHSAUIRgCQAJAAkACQAJAIBkiGyAUUg0AIA0hGyAOIRggDSAOUg0AIBUhGyAVIBciGFINACALIRsgDyEYIAsgD1ENAQsgGCAbWg0AIAIgCyAPfSIYNwP4HSACIBUgF30iHSALIA9UrSILfSIbNwPwHSACIA0gDn0iICAVIBdUIAsgHVZyrSILfSIdNwPoHSACIBkgFH0gDSAOVCALICBWcq19Ihk3A+AdAkACQCARIg0gECILUg0AIBYiDSAcIgtSDQAgEyINIBoiC1INACASIg0gDCILUQ0BCyALIA1UDQILIBAgEX0gHCAWfSIgIBogE30iJyAMIBJUrSIoVCATIBpWcq0iGlQgFiAcVnKtfSEQIAwgEn0hDCAbIRUgHSENIBghCyAgIBp9IRwgJyAofSEaDAMLIAIgDyALfSIYNwPYHSACIBcgFX0iHSALIA9WrSIPfSIbNwPQHSACIA4gDX0iICAPIB1WIBUgF1ZyrSIPfSIXNwPIHSACIBQgGX0gDyAgViANIA5Wcq19IhQ3A8AdAkACQCARIg8gECIOUg0AIBYiDyAcIg5SDQAgEyIPIBoiDlINACASIg8gDCIOUQ0BCyAOIA9WDQILIBEgEH0gFiAcVCAWIBx9IhYgEyAaVCATIBp9IhMgDCASVq0iHVRyrSIgVHKtfSERIBIgDH0hEiAXIQ4gGyEXIBghDyAWICB9IRYgEyAdfSETDAILIBBCf0IAIBZCf4UiCyATQn+FIg0gEkJtVq0iFVStIiBUGyARfXwgCyAgfSIQIBx8IgsgEFQgCyANIBV9IhAgGnwiDSAQVCANQm0gEn0iECAMfCIMIBBUrXwiGiANVHKtfCIcIAtUcq18Qv///////////wB8IRAgGyEVIB0hDSAYIQsMAQsgESAQfSAcQn+FIg8gGkJ/hSIOIAxCbVatIhFUrSIdVK19IBYgDyAdfSIdfCIPIB1UIA8gDyAOIBF9IhEgE3wiDiARVCAOQm0gDH0iESASfCISIBFUrXwiEyAOVHKtfCIWVnKtfEL///////////8AfCERIBchDiAbIRcgGCEPCyACQcAdaiACQaAdakEgEPEDDQALCyACQbADaiASQgAgJkIAEMkDIAJB8AJqIBJCACAkQgAQyQMgAkHgAmogEkIAICFCABDJAyACQdACaiASQgAgH0IAEMkDIAJBoANqIAIpA7ADIgxCm5Svw/K1qN6Gf34iC0IAQm1CABDJAyACQZADaiALQgBCf0IAEMkDIAJBgANqIAtCAEL///////////8AQgAQyQMgAkHAAmogE0IAICZCABDJAyACQYACaiATQgAgJEIAEMkDIAJB8AFqIBNCACAhQgAQyQMgAkHgAWogE0IAIB9CABDJAyACQbACaiACKQOQAyILIAIpA7gDIhIgAikD8AJ8IhR8Ig8gAikDqAMgDCACKQOgAyIOfCAOVK18fCIMIAIpA8ACfCIOQpuUr8Pytajehn9+Ig1CAEJtQgAQyQMgAkGgAmogDUIAQn9CABDJAyACQZACaiANQgBC////////////AEIAEMkDIAJB0AFqIBZCACAmQgAQyQMgAkGQAWogFkIAICRCABDJAyACQYABaiAWQgAgIUIAEMkDIAJB8ABqIBZCACAfQgAQyQMgAkHAAWogAikDyAIgDCAOVq18IhMgAikDgAJ8Ig0gCyACKQP4AiASIBRWrXwiFSACKQPgAnwiEnwiFCAMIA9UrSACKQOYAyIWIAsgD1atfHx8Ihd8IgsgAikDoAIiGXwiDyACKQO4AiACKQOwAiIMIA58IAxUrXx8IgwgAikD0AF8Ig5Cm5Svw/K1qN6Gf34iEEIAQm1CABDJAyACQbABaiAQQgBCf0IAEMkDIAJBoAFqIBBCAEL///////////8AQgAQyQMgAkHgAGogEUIAICZCABDJAyACQSBqIBFCACAkQgAQyQMgAkEQaiARQgAgIUIAEMkDIAIgEUIAIB9CABDJAyACQdAAaiACKQPYASAMIA5WrXwiGCACKQOQAXwiESAZIAIpA+gCIBIgFVStfCIbIAIpA9ACfCIQIAIpA4ADfCIVIBQgF1atIBYgEiAUVq18fHwiEiACKQPwAXwiFCALIA1UrSACKQOIAiANIBNUrXx8fCINfCITIAwgD1StIAIpA6gCIhcgCyAPVq18fHwiGXwiCyACKQOwASIafCIPIAIpA8gBIAIpA8ABIgwgDnwgDFStfHwiDCACKQNgfCIOQpuUr8Pytajehn9+IhZCAEJtQgAQyQMgAkFAayAWQgBCf0IAEMkDIAJBMGogFkIAQv///////////wBCABDJAyACKQM4IAIpA6gBIAIpA5gCIBIgFVStIAIpA4gDIBAgFVatfHwiFiACKQPYAiAQIBtUrXx8IhAgAikD4AF8IhUgDSAUVK0gAikD+AEgEiAUVq18fHwiEiACKQOQAnwiFCASVK18IBQgEyAZVq0gFyANIBNWrXx8fCINIBRUrXwiEyASIBVUrSACKQPoASAQIBVWrXx8IhcgECAWVK18IhZ8IhIgAikDcHwiFCACKQOIASANIA0gAikDgAF8IhBWrXwgECAQIAsgEVStIAIpA5gBIBEgGFStfHx8Ig1WrXx8IhEgAikDoAF8IhAgEVStfCAQIAIpA7gBIhkgDSANIBp8IhVWrXwgFSAVIAwgD1StIBkgCyAPVq18fHwiGVatfHwiCyAQVK18IhUgESAUVK0gAikDeCASIBRWrXx8IhggEiATVK0gFiAXVK18fCITfCIPIAIpAwB8Ig0gAikDGCALIAsgAikDEHwiElatfCASIBIgAikDKCACKQNoIAwgDlatfCIMIAIpAyB8IgsgDFStfCALIAsgGXwiDFatfHwiC1atfHwiEiACKQMwfCIUIBJUrXwgFCACKQNIIhEgCyALIAIpA0AiFnwiEFatfCAQIBAgESAMIAwgFnwiC1atfCALIAIpA1ggDiACKQNQIgx8IAxUrXx8IhEgC1StfHwiDFatfHwiDiAUVK18IgsgDSASVq0gAikDCCANIA9UrXx8Ig0gDyAVVK0gEyAYVK18fCIPfCIQIAtUIA0gD1ZyIBBCAFNyRQRAIAwgDoNCf1IgEUJtVHIgEEL///////////8AUnINAgsgDEIBfCIPIBFCbVStIg19IQsgDkIBfCISIAxCf1IgDSAPVnKtIgx9IQ8gECAOQn9SIAwgElZyrX1C////////////AH0hECARQhN8IREMAgsgAkICNwPgHUGM98EAQSsgAkHgHWpB/PbBAEGIkcIAEMoDAAsgDiEPIAwhCwsgBCAjNwM4IAQgHjcDMCAEICU3AyggBCAiNwMgIAQgETcDGCAEIAs3AxAgBCAPNwMIIAQgEDcDACACQYAeaiQAIANBqAFqIgUgBBDZAiADQbQBaiIHIANBiAFqENkCQdHOxQAtAAAaQQhBBBDWBCIERQ0CIAUQuwMhBSAEIAcQuwM2AgQgBCAFNgIAIApBAjYCCCAKIAQ2AgQgCkECNgIAIAMoAjgiBARAIAMoAjwgBEECdBDfBAsgAygCCCIEBEAgAygCDCAEQQJ0EN8ECyADQcABaiQADAMLIAMgAygCbDYCOEGEncAAQSsgA0E4akG08sAAQfTywAAQygMACyADIAMoAmw2AjhBhJ3AAEErIANBOGpBtPLAAEHk8sAAEMoDAAtBBEEIEP8EAAsCQAJAIAgCfyAJKAIEIgRBgICAgHhGBEBBACEEIAkoAgghBUEAIQZBAQwBCyAJKAIIIQUCQCAJKAIMIgYgBE8EQCAFIQQMAQsgBEECdCEHIAZFBEBBBCEEIAUgBxDfBAwBCyAFIAdBBCAGQQJ0IgUQzgQiBEUNAgtBACEFQQALNgIMIAggBTYCCCAIIAY2AgQgCCAENgIAIAlBEGokAAwBC0EEIAVB6PHAABDIBAALIAgoAgAgCCgCBCAIKAIIIAgoAgwgCEEQaiQACyMBAX8gACABQTAQ8QMEfyACBSAAQTBqIAFBMGpBMBDxA0ULCyMBAX8gACABQSAQ8QMEfyACBSAAQSBqIAFBIGpBIBDxA0ULC/wBAgJ/AX4jAEEQayICJAAgAkEBOwEMIAIgATYCCCACIAA2AgQjAEEQayIBJAAgAkEEaiIAKQIAIQQgASAANgIMIAEgBDcCBCMAQRBrIgAkACABQQRqIgEoAgAiAigCDCEDAkACQAJAAkAgAigCBA4CAAECCyADDQFBASECQQAhAwwCCyADDQAgAigCACICKAIEIQMgAigCACECDAELIABBgICAgHg2AgAgACABNgIMIABB+KrFACABKAIEIAEoAggiAC0ACCAALQAJEJgDAAsgACADNgIEIAAgAjYCACAAQdyqxQAgASgCBCABKAIIIgAtAAggAC0ACRCYAwALrnkCGH8UfiMAQRBrIhAkABCtAyIEIAAmARCtAyIFIAEmASMAQRBrIhQkACAUQQhqIRcjAEGQAWsiCiQAIApB4ABqIAQQ7AIgCigCZCEEAkAgCigCYCIDQYCAgIB4RgRAQYn2wABBHhDNBCEDIARBhAFPBEAgBBCrAwtBASEEIAVBhAFJDQEgBRCrAwwBCyAKIAooAmg2AgwgCiAENgIIIAogAzYCBCAKQRBqIApBBGoQ9AIgCkHgAGogBRDsAiAKKAJkIQQgCigCYCIFQYCAgIB4RgRAQev1wABBHhDNBCEDIARBhAFPBEAgBBCrAwsgCigCBCIEBEAgCigCCCAEQQJ0EN8EC0EBIQQMAQsgCiAKKAJoNgI8IAogBDYCOCAKIAU2AjQgCkFAayIFIApBNGoQ9AIgCkHgAGohDyAKQRBqIQMjAEHADGsiAiQAQdHOxQAtAAAaAkACQAJAAkACQAJAAkACQEHgAEEIENYEIgQEQCAEQgA3AwAgBEEYakIANwMAIARBEGpCADcDACAEQQhqQgA3AwAgBCADKQMANwMgIAQgBSkDADcDQCAEQShqIANBCGopAwA3AwAgBEEwaiADQRBqKQMANwMAIARBOGogA0EYaikDADcDACAEQcgAaiAFQQhqKQMANwMAIARB0ABqIAVBEGopAwA3AwAgBEHYAGogBUEYaikDADcDAEGQzsUAIQsgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhCwsgCygCCCEDIAsoAgQhBiACQQA2AoQMQdHOxQAtAAAaQQghCEHgAEEIENYEIgVFDQYgAkEANgKQDCACIAU2AowMIAJBAzYCiAwgAiADNgKwDCACIAY2AqwMIAJBADYCqAwgAiAEQeAAajYCpAwgAiAENgKgDCACIAJBhAxqNgK0DCACIAU2ApwMIAJBADYCmAwgAiACQZAMajYClAwgAkGgDGogAkGUDGoQuwIgAigCiAwhByACKAKMDCEJIAIoApAMIQUgBEHgABDfBCAFBEBBACEDQdHOxQAtAAAaIAVBBXQiBEEIENYEIghFDQggBSEEA0AgAkGgDGogAyAJahBHIAMgCGoiBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDACADQSBqIQMgBEEBayIEDQALCyAHBEAgCSAHQQV0EN8EC0GQzsUAIQMgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhAwsgAygCCCEGIAMoAgQhByACQQM2AoQMIAVBBXQhBEEIIQMgBQRAQdHOxQAtAAAaIARBCBDWBCIDRQ0ICyACQQA2ApAMIAIgAzYCjAwgAiAFNgKIDCACIAY2ArAMIAIgBzYCrAwgAkEANgKoDCACIAQgCGo2AqQMIAIgCDYCoAwgAiACQYQMajYCtAwgAiADNgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqELsCIAIoAogMIQYgAigCjAwhByACKAKQDCEJIAUEQCAIIAQQ3wQLQaDOxQAhAyACQaDOxQA2AogMQazOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMahD6AiACKAKIDCEDC0HRzsUALQAAGiADKAIIIQUgAygCBCEDQeAAQQgQ1gQiBEUNBiACQQA2ApAMIAIgBDYCjAwgAkEDNgKIDCACQoCAgIAwNwKwDCACIAU2AqwMIAIgAzYCqAwgAiAJNgKkDCACIAc2AqAMIAIgBDYCnAwgAkEANgKYDCACIAJBkAxqNgKUDCACQaAMaiACQZQMahBzIAIoAogMIQkgAigCjAwhDSACKAKQDCEFIAYEQCAHIAZBBXQQ3wQLAkAgBUUEQEEIIQgMAQtBACEDQdHOxQAtAAAaIAVBBXQiBEEIENYEIghFDQggBSEEA0AgAkGgDGogAyANahBHIAMgCGoiBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDACADQSBqIQMgBEEBayIEDQALCyAJBEAgDSAJQQV0EN8EC0GQzsUAIQMgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhAwsgAygCCCEGIAMoAgQhByACQQY2AoQMIAVBBXQhBEEIIQMgBQRAQdHOxQAtAAAaIARBCBDWBCIDRQ0ICyACQQA2ApAMIAIgAzYCjAwgAiAFNgKIDCACIAY2ArAMIAIgBzYCrAwgAkEANgKoDCACIAQgCGo2AqQMIAIgCDYCoAwgAiACQYQMajYCtAwgAiADNgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqELsCIAIoAogMIQYgAigCjAwhByACKAKQDCEJIAUEQCAIIAQQ3wQLQaDOxQAhAyACQaDOxQA2AogMQazOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMahD6AiACKAKIDCEDC0HRzsUALQAAGiADKAIIIQUgAygCBCEDQeAAQQgQ1gQiBEUNBiACQQA2ApAMIAIgBDYCjAwgAkEDNgKIDCACQoCAgIAwNwKwDCACIAU2AqwMIAIgAzYCqAwgAiAJNgKkDCACIAc2AqAMIAIgBDYCnAwgAkEANgKYDCACIAJBkAxqNgKUDCACQaAMaiACQZQMahBzIAIoAogMIQkgAigCjAwhDSACKAKQDCEFIAYEQCAHIAZBBXQQ3wQLAkAgBUUEQEEIIQgMAQtBACEDQdHOxQAtAAAaIAVBBXQiBEEIENYEIghFDQggBSEEA0AgAkGgDGogAyANahBHIAMgCGoiBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDACADQSBqIQMgBEEBayIEDQALCyAJBEAgDSAJQQV0EN8EC0GQzsUAIQMgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhAwsgAygCCCEGIAMoAgQhByACQQk2AoQMIAVBBXQhBEEIIQMgBQRAQdHOxQAtAAAaIARBCBDWBCIDRQ0ICyACQQA2ApAMIAIgAzYCjAwgAiAFNgKIDCACIAY2ArAMIAIgBzYCrAwgAkEANgKoDCACIAQgCGo2AqQMIAIgCDYCoAwgAiACQYQMajYCtAwgAiADNgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqELsCIAIoAogMIQYgAigCjAwhByACKAKQDCEJIAUEQCAIIAQQ3wQLQaDOxQAhAyACQaDOxQA2AogMQazOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMahD6AiACKAKIDCEDC0HRzsUALQAAGiADKAIIIQUgAygCBCEDQeAAQQgQ1gQiBEUNBiACQQA2ApAMIAIgBDYCjAwgAkEDNgKIDCACQoCAgIAwNwKwDCACIAU2AqwMIAIgAzYCqAwgAiAJNgKkDCACIAc2AqAMIAIgBDYCnAwgAkEANgKYDCACIAJBkAxqNgKUDCACQaAMaiACQZQMahBzIAIoAogMIQkgAigCjAwhDSACKAKQDCEFIAYEQCAHIAZBBXQQ3wQLAkAgBUUEQEEIIQgMAQtBACEDQdHOxQAtAAAaIAVBBXQiBEEIENYEIghFDQggBSEEA0AgAkGgDGogAyANahBHIAMgCGoiBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDACADQSBqIQMgBEEBayIEDQALCyAJBEAgDSAJQQV0EN8EC0GQzsUAIQMgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhAwsgAygCCCEGIAMoAgQhByACQQw2AoQMIAVBBXQhBEEIIQMgBQRAQdHOxQAtAAAaIARBCBDWBCIDRQ0ICyACQQA2ApAMIAIgAzYCjAwgAiAFNgKIDCACIAY2ArAMIAIgBzYCrAwgAkEANgKoDCACIAQgCGo2AqQMIAIgCDYCoAwgAiACQYQMajYCtAwgAiADNgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqELsCIAIoAogMIQkgAigCjAwhDCACKAKQDCEHIAUEQCAIIAQQ3wQLQbDOxQAhAyACQbDOxQA2AogMQbzOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMaiEFIwBBIGsiBCQAAkACQAJAAkACQAJAAkACQEG8zsUALQAAQQFrDgMEAwEAC0G8zsUAQQI6AAAgBSgCACIDKAIAIQUgA0EANgIAIAVFDQQgBSgCACEDQdHOxQAtAAAaQSRBBBDWBCIFRQ0BIARBCGoiCEG4mcMAQdCZwwBBmPnAABChAyAFQQhqIARBEGoiBigCADYCACAFIAQpAgg3AgAgCEHQmcMAQeiZwwBBmPnAABChAyAFQRRqIAYoAgA2AgAgBSAEKQIINwIMIAhB6JnDAEGAmsMAQZj5wAAQoQMgBUEgaiAGKAIANgIAIAUgBCkCCDcCGCADQQM2AgggAyAFNgIEIANBAzYCAEG8zsUAQQM6AAALIARBIGokAAwFC0EEQSRB6NnCABDIBAALIARBADYCGCAEQQE2AgwgBEHw0sIANgIIDAILIARBADYCGCAEQQE2AgwgBEGw0sIANgIIDAELQczTwgAQ6AQACyAEQgQ3AhAgBEEIakH0zMEAEKgEAAsgAigCiAwhAwtB0c7FAC0AABogAygCCCEFIAMoAgQhA0HgAEEIENYEIgRFDQYgAkEANgKQDCACIAQ2AowMIAJBAzYCiAwgAkKAgICAMDcCsAwgAiAFNgKsDCACIAM2AqgMIAIgBzYCpAwgAiAMNgKgDCACIAQ2ApwMIAJBADYCmAwgAiACQZAMajYClAwgAkGgDGogAkGUDGoQcyACKAKIDCENIAIoAowMIQYgAigCkAwhByAJBEAgDCAJQQV0EN8EC0EAIQlBASEDQQAhCANAIAdFBEBBAEEAQcSZwQAQ2QMACyADIQUgAkGgDGoiBCAGEEcgBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDAEHRzsUALQAAGkEgQQgQ1gQiA0UNAiAGKQMYIRogBikDECEcIAYpAwghHSAGKQMAIR9BkM7FACELIAJBkM7FADYCiAxBnM7FAC0AAEEDRwRAIAIgAkGIDGo2ApQMIAIgAkGUDGo2AqAMIAQQlwMgAigCiAwhCwsCQAJAIAhBD2oiBCALKAIIIgxJBEBCqcDGia7Ok7IwIRsgCygCBCAEQQV0aiIEKQMAIB98IB0gBCkDCHwiJCAdVCAkICQgHCAcIAQpAxB8Ih9WIB8gHyAaIAQpAxh8Ih0gGlStfCIcVnKtfCIfVnKtfCIhIRoCQCAhQqnAxomuzpOyMFINAELdsIWM6LaRqLh/IRsgHyIaQt2whYzotpGouH9SDQBCkeHlzYeJ+pkoIRsgHCIaQpHh5c2HifqZKFINAEKBgICAv7L98MMAIRsgHSIaQoGAgIC/sv3wwwBRDQILIBogG1oNASAfIRogHCEbDAILIAQgDEHUmcEAENkDAAsgHEKR4eXNh4n6mSh9IhogHUKBgICAv7L98MMAVK0iJH0hGyAfQqPP+vOXye7XxwB8IiggHEKR4eXNh4n6mShUIBogJFRyrSIcfSEaICEgH0LdsIWM6LaRqLh/VCAcIChWcq19QqnAxomuzpOyMH0hISAdQoGAgIC/sv3wwwB9IR0LIAMgHTcDGCADIBs3AxAgAyAaNwMIIAMgITcDAEEBIQQgAkEBNgKcDCACIAM2ApgMIAJBATYClAwgB0EFdEEgayIHQQV2IQwgBwRAIAJBlAxqQQEgDEEIQSAQiAMgAigCmAwhAyACKAKcDCEECyAHBEAgAyAEQQV0aiAGQSBqIAf8CgAACyACIAQgDGoiBDYCnAxBwM7FACELIAJBwM7FADYChAxBzM7FAC0AAEEDRwRAIAIgAkGEDGo2AogMIAIgAkGIDGo2AqAMIAJBoAxqIQwjAEEgayIHJAACQAJAAkACQAJAAkACQEHMzsUALQAAQQFrDgMCBAEAC0HMzsUAQQI6AAAgDCgCACILKAIAIQwgC0EANgIAIAxFDQIgDCgCACEMIAdBCGpB7I3EAEHUn8QAQejZwgAQoQMgDEEIaiAHQRBqKAIANgIAIAwgBykCCDcCAEHMzsUAQQM6AAALIAdBIGokAAwECyAHQQA2AhggB0EBNgIMIAdBsNLCADYCCAwCC0HM08IAEOgEAAsgB0EANgIYIAdBATYCDCAHQfDSwgA2AggLIAdCBDcCECAHQQhqQfTMwQAQqAQACyACKAKEDCELC0HRzsUALQAAGiALKAIIIRIgCygCBCEYQSBBCBDWBCIRRQ0DAkAgBEUEQEIAISRCACEoQgAhH0IAISEMAQsgEiAJIAkgEksbIQ4gFSAYaiEZQgAhIUEAIQsgCSEHIAQhDEIAIR9CACEoQgAhJANAAkACQCAOIBJHBEAgAkHACmogAyALaiITQRhqKQMAIhtCACALIBlqIhZBGGopAwAiGkIAEMkDIAJBgAtqIBtCACAWQRBqKQMAIhxCABDJAyACQcALaiAbQgAgFkEIaikDACIdQgAQyQMgAkHACGogG0IAIBYpAwAiG0IAEMkDIAJBsApqIAIpA8AKIiJC/////76y/fBCfiIeQgBCgYCAgL+y/fDDAEIAEMkDIAJBoApqIB5CAEKR4eXNh4n6mShCABDJAyACQdAJaiAeQgBC3bCFjOi2kai4f0IAEMkDIAJBgAlqIB5CAEKpwMaJrs6TsjBCABDJAyACQdAKaiATQRBqKQMAIh5CACAaQgAQyQMgAkGQC2ogHkIAIBxCABDJAyACQdALaiAeQgAgHUIAEMkDIAJB0AhqIB5CACAbQgAQyQMgAkGQCmogAikDoAoiKSACKQPICiIlIAIpA4ALfCImfCIgIAIpA7gKICIgAikDsAoiHnwgHlStfHwiIiACKQPQCnwiI0L/////vrL98EJ+Ih5CAEKBgICAv7L98MMAQgAQyQMgAkGACmogHkIAQpHh5c2HifqZKEIAEMkDIAJB8AlqIB5CAELdsIWM6LaRqLh/QgAQyQMgAkHgCWogHkIAQqnAxomuzpOyMEIAEMkDIAJB4ApqIBNBCGopAwAiHkIAIBpCABDJAyACQaALaiAeQgAgHEIAEMkDIAJB4AtqIB5CACAdQgAQyQMgAkHgCGogHkIAIBtCABDJAyACQcAJaiACKQPYCiAiICNWrXwiKyACKQOQC3wiJyACKQOICyAlICZWrXwiKiACKQPAC3wiJSACKQPQCXwiJiAgICJWrSACKQOoCiAgIClUrXx8fCIsfCIgIAIpA4AKfCIiIAIpA5gKIAIpA5AKIh4gI3wgHlStfHwiIyACKQPgCnwiKUL/////vrL98EJ+Ih5CAEKBgICAv7L98MMAQgAQyQMgAkGwCWogHkIAQpHh5c2HifqZKEIAEMkDIAJBoAlqIB5CAELdsIWM6LaRqLh/QgAQyQMgAkGQCWogHkIAQqnAxomuzpOyMEIAEMkDIAJB8ApqIBMpAwAiHkIAIBpCABDJAyACQbALaiAeQgAgHEIAEMkDIAJB8AtqIB5CACAdQgAQyQMgAkHwCGogHkIAIBtCABDJAyACQbAIaiACKQPoCiAjIClWrXwiLSACKQOgC3wiGiACKQPICyAlICpUrXwiKiACKQPACHwiHCACKQOACXwiHSAmICxWrSACKQPYCSAlICZWrXx8fCIeIAIpA9ALfCIlICAgJ1StIAIpA5gLICcgK1StfHx8IicgAikD8Al8IiYgIiAjVq0gAikDiAogICAiVq18fHwiK3wiICACKQOwCXwiIiACKQPICSACKQPACSIbICl8IBtUrXx8IiMgAikD8Ap8IilC/////76y/fBCfiIbQgBCgYCAgL+y/fDDAEIAEMkDIAJBoAhqIBtCAEKR4eXNh4n6mShCABDJAyACQZAIaiAbQgBC3bCFjOi2kai4f0IAEMkDIAJBgAhqIBtCAEKpwMaJrs6TsjBCABDJAwJAAkAgAikDiAggAikDmAkgAikD6AkgHSAeVq0gAikDiAkgHCAdVq18fCACKQPICCAcICpUrXx8IiogAikD0Ah8IhsgJSAnVq0gAikD2AsgHiAlVq18fHwiHCACKQPgCXwiHSAcVK18IB0gHSAmICtWrSACKQP4CSAmICdUrXx8fCIeVq18IBsgHFatIAIpA9gIIBsgKlStfHx8IicgAikD4Ah8IhsgAikD6AsgHiACKQPgC3wiHCAeVK18IBwgGiAgVq0gAikDqAsgGiAtVK18fHwiGiAcVK18fCIcIAIpA5AJfCIdIBxUrXwgHSACKQOoCSAaIBogAikDoAl8Ih5WrXwgHiAeICIgI1atIAIpA7gJICAgIlatfHx8IiBWrXx8IhogHVStfCAbIBxWrSACKQPoCCAbICdUrXx8fCIiIAIpA/AIfCIbIAIpA/gLIBogGiACKQPwC3wiHFatfCAcIBwgAikDuAsgAikD+AogIyApVq18Ih0gAikDsAt8IhogHVStfCAaIBogIHwiHVatfHwiGlatfHwiHCACKQOACHwiICAcVK18ICAgICACKQOYCCAaIBogAikDkAh8Ih5WrXwgHiAeIAIpA6gIIB0gHSACKQOgCHwiGlatfCAaIAIpA7gIIAIpA7AIIh0gKXwgHVStfHwiHSAaVK18fCIaVq18fCIeVq18IBsgHFatIAIpA/gIIBsgIlStfHx8IiBCqcDGia7Ok7IwVg0AAkAgIEKpwMaJrs6TsjBRBEAgHkLdsIWM6LaRqLh/Vg0CIB5C3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhIAsgHiEbIBohHAwCCyAaQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IRsgGkKR4eXNh4n6mShSBEBCqcDGia7Ok7IwISAgGiEcDAILQpHh5c2HifqZKCEcIB1CgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhIAwBCyAaQpHh5c2HifqZKH0iGyAdQoGAgIC/sv3wwwBUrSIifSEcIB5Co8/685fJ7tfHAHwiIyAaQpHh5c2HifqZKFQgGyAiVHKtIhp9IRsgICAeQt2whYzotpGouH9UIBogI1ZyrX1CqcDGia7Ok7IwfSEgIB1CgYCAgL+y/fDDAH0hHQtCqcDGia7Ok7IwIRogGyAffCIbIB9UIBsgHCAofCIfIChUIB8gHyAkIB0gJHwiJFatfCIcVnKtfCIdIBtUcq0gICAhfHwiISEbAkAgIUKpwMaJrs6TsjBSDQBC3bCFjOi2kai4fyEaIB0iG0LdsIWM6LaRqLh/Ug0AQpHh5c2HifqZKCEaIBwiG0KR4eXNh4n6mShSDQBCgYCAgL+y/fDDACEaICQiG0KBgICAv7L98MMAUQ0CCyAaIBtYDQEgHSEfIBwhKAwCCyAHIBJBhM3BABDZAwALIBxCkeHlzYeJ+pkofSIbICRCgYCAgL+y/fDDAFStIhp9ISggHUKjz/rzl8nu18cAfCIeIBxCkeHlzYeJ+pkoVCAaIBtWcq0iG30hHyAhIB1C3bCFjOi2kai4f1QgGyAeVnKtfUKpwMaJrs6TsjB9ISEgJEKBgICAv7L98MMAfSEkCyAHQQFqIQcgDkEBaiEOIAtBIGohCyAMQQFrIgwNAAsLIBEgJDcDGCARICg3AxAgESAfNwMIIBEgITcDAEEBIQsgAkEBNgKoDCACIBE2AqQMIAJBATYCoAxBASAEIARBAU0bIQwgCEEFbEECaiERQQAhCANAIAsgDEYNBSALIBFqIg4gEk8NBiADIAtBBXRqIgcpAxghJCAHKQMQISggBykDCCEeIAcpAwAhKSACQcAGaiAYIA5BBXRqIgcpAxgiG0IAIAMpAxgiGkIAEMkDIAJB0AZqIBtCACADKQMQIhxCABDJAyACQeAGaiAbQgAgAykDCCIdQgAQyQMgAkHwBmogG0IAIAMpAwAiG0IAEMkDIAJBsAZqIAIpA8AGIiBC/////76y/fBCfiIfQgBCgYCAgL+y/fDDAEIAEMkDIAJBoAZqIB9CAEKR4eXNh4n6mShCABDJAyACQdAFaiAfQgBC3bCFjOi2kai4f0IAEMkDIAJBgAVqIB9CAEKpwMaJrs6TsjBCABDJAyACQYAHaiAHKQMQIh9CACAaQgAQyQMgAkGQB2ogH0IAIBxCABDJAyACQaAHaiAfQgAgHUIAEMkDIAJBsAdqIB9CACAbQgAQyQMgAkGQBmogAikDoAYiJiACKQPIBiInIAIpA9AGfCIlfCIhIAIpA7gGICAgAikDsAYiH3wgH1StfHwiICACKQOAB3wiIkL/////vrL98EJ+Ih9CAEKBgICAv7L98MMAQgAQyQMgAkGABmogH0IAQpHh5c2HifqZKEIAEMkDIAJB8AVqIB9CAELdsIWM6LaRqLh/QgAQyQMgAkHgBWogH0IAQqnAxomuzpOyMEIAEMkDIAJBwAdqIAcpAwgiH0IAIBpCABDJAyACQdAHaiAfQgAgHEIAEMkDIAJB4AdqIB9CACAdQgAQyQMgAkHwB2ogH0IAIBtCABDJAyACQcAFaiACKQOIByAgICJWrXwiKyACKQOQB3wiIyACKQPYBiAlICdUrXwiKiACKQPgBnwiJyACKQPQBXwiJSAgICFUrSACKQOoBiAhICZUrXx8fCIsfCIhIAIpA4AGfCIgIAIpA5gGIAIpA5AGIh8gInwgH1StfHwiIiACKQPAB3wiJkL/////vrL98EJ+Ih9CAEKBgICAv7L98MMAQgAQyQMgAkGwBWogH0IAQpHh5c2HifqZKEIAEMkDIAJBoAVqIB9CAELdsIWM6LaRqLh/QgAQyQMgAkGQBWogH0IAQqnAxomuzpOyMEIAEMkDIAJBwARqIAcpAwAiH0IAIBpCABDJAyACQdAEaiAfQgAgHEIAEMkDIAJB4ARqIB9CACAdQgAQyQMgAkHwBGogH0IAIBtCABDJAyACQbAEaiACKQPIByAiICZWrXwiLSACKQPQB3wiGiACKQPoBiAnICpUrXwiKiACKQPwBnwiHCACKQOABXwiHSAlICxWrSACKQPYBSAlICdUrXx8fCIfIAIpA6AHfCInICEgI1StIAIpA5gHICMgK1StfHx8IiMgAikD8AV8IiUgICAiVq0gAikDiAYgICAhVK18fHwiK3wiISACKQOwBXwiICACKQPIBSACKQPABSIbICZ8IBtUrXx8IiIgAikDwAR8IiZC/////76y/fBCfiIbQgBCgYCAgL+y/fDDAEIAEMkDIAJBoARqIBtCAEKR4eXNh4n6mShCABDJAyACQZAEaiAbQgBC3bCFjOi2kai4f0IAEMkDIAJBgARqIBtCAEKpwMaJrs6TsjBCABDJAwJAAkAgAikDiAQgAikDmAUgAikD6AUgHSAfVq0gAikDiAUgHCAdVq18fCACKQP4BiAcICpUrXx8IiogAikDsAd8IhsgIyAnVK0gAikDqAcgHyAnVq18fHwiHCACKQPgBXwiHSAcVK18IB0gHSAlICtWrSACKQP4BSAjICVWrXx8fCIfVq18IBsgHFatIAIpA7gHIBsgKlStfHx8IiMgAikD8Ad8IhsgAikD6AcgHyACKQPgB3wiHCAfVK18IBwgGiAhVq0gAikD2AcgGiAtVK18fHwiGiAcVK18fCIcIAIpA5AFfCIdIBxUrXwgHSACKQOoBSAaIBogAikDoAV8Ih9WrXwgHyAfICAgIlatIAIpA7gFICAgIVStfHx8IiFWrXx8IhogHVStfCAbIBxWrSACKQP4ByAbICNUrXx8fCIjIAIpA/AEfCIbIAIpA+gEIBogGiACKQPgBHwiHFatfCAcIBwgAikD2AQgAikDyAQgIiAmVq18Ih0gAikD0AR8IhogHVStfCAaIBogIXwiHVatfHwiGlatfHwiHCACKQOABHwiICAcVK18ICAgICACKQOYBCAaIBogAikDkAR8Ih9WrXwgHyAfIAIpA6gEIB0gHSACKQOgBHwiGlatfCAaIAIpA7gEIAIpA7AEIh0gJnwgHVStfHwiISAaVK18fCIaVq18fCIfVq18IBsgHFatIAIpA/gEIBsgI1StfHx8Ih1CqcDGia7Ok7IwVg0AAkAgHUKpwMaJrs6TsjBRBEAgH0LdsIWM6LaRqLh/Vg0CIB9C3bCFjOi2kai4f1ENAUKpwMaJrs6TsjAhHQsgHyEbIBohHAwCCyAaQpHh5c2HifqZKFYNAELdsIWM6LaRqLh/IRsgGkKR4eXNh4n6mShSBEBCqcDGia7Ok7IwIR0gGiEcDAILQpHh5c2HifqZKCEcICFCgYCAgL+y/fDDAFoNAEKpwMaJrs6TsjAhHQwBCyAaQpHh5c2HifqZKH0iGyAhQoGAgIC/sv3wwwBUrSIgfSEcIB9Co8/685fJ7tfHAHwiIiAaQpHh5c2HifqZKFQgGyAgVHKtIhp9IRsgHSAfQt2whYzotpGouH9UIBogIlZyrX1CqcDGia7Ok7IwfSEdICFCgYCAgL+y/fDDAH0hIQtCqcDGia7Ok7IwIR8gHSApfCAbIB58IhsgHlQgGyAcICh8IhogKFQgGiAhICR8Ih0gJFStfCIcIBpUcq18IiQgG1RyrXwiISEaAkACQAJAICFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hHyAkIhpC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghHyAcIhpCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhHyAdIhpCgYCAgL+y/fDDAFENAQsgGiAfWg0AICQhGiAcIRsMAQsgHEKR4eXNh4n6mSh9IhogHUKBgICAv7L98MMAVK0iH30hGyAkQqPP+vOXye7XxwB8IiggHEKR4eXNh4n6mShUIBogH1RyrSIcfSEaICEgJELdsIWM6LaRqLh/VCAcIChWcq19QqnAxomuzpOyMH0hISAdQoGAgIC/sv3wwwB9IR0LIAIoAqgMIg4gAigCoAxGBEAgAkGgDGpBpJrBABCiAwsgAigCpAwgDkEFdGoiByAdNwMYIAcgGzcDECAHIBo3AwggByAhNwMAIAIgDkEBaiIHNgKoDCAIQQFxQQIhC0EBIQhFDQALIAIoAqQMIQQgAigCoAwhDCANBEAgBiANQQV0EN8ECyACKAKUDCIIBEAgAyAIQQV0EN8ECyAVQaABaiEVIAlBBWohCSAFIAVBOUkiC2ohAyAEIQYgDCENIAUhCCALDQALDAULQQhB4AAQ/wQAC0EIQSAQ/wQAC0EIQSAQ/wQACyAMIARBhJrBABDZAwALIA4gEkGUmsEAENkDAAsCQAJAAkACQAJAIAdFBEBBCCEGDAELQQAhA0HRzsUALQAAGiAHQQV0IgVBCBDWBCIGRQ0BIA5BAWohDgNAIAJBoAxqIAMgBGoQRyADIAZqIgVBGGogAkG4DGopAwA3AwAgBUEQaiACQbAMaikDADcDACAFQQhqIAJBqAxqKQMANwMAIAUgAikDoAw3AwAgA0EgaiEDIA5BAWsiDg0ACwsgDARAIAQgDEEFdBDfBAtBkM7FACEDIAJBkM7FADYCiAxBnM7FAC0AAEEDRwRAIAIgAkGIDGo2ApQMIAIgAkGUDGo2AqAMIAJBoAxqEJcDIAIoAogMIQMLIAMoAgghBSADKAIEIQggAkHIADYChAwgB0EFdCEEQQghAyAHBEBB0c7FAC0AABogBEEIENYEIgNFDQYLIAJBADYCkAwgAiADNgKMDCACIAc2AogMIAIgBTYCsAwgAiAINgKsDCACQQA2AqgMIAIgBCAGajYCpAwgAiAGNgKgDCACIAJBhAxqNgK0DCACIAM2ApwMIAJBADYCmAwgAiACQZAMajYClAwgAkGgDGogAkGUDGoQuwIgAigCiAwhCCACKAKMDCEJIAIoApAMIQUgBwRAIAYgBBDfBAtBoM7FACEDIAJBoM7FADYCiAxBrM7FAC0AAEEDRwRAIAIgAkGIDGo2ApQMIAIgAkGUDGo2AqAMIAJBoAxqEPoCIAIoAogMIQMLQdHOxQAtAAAaIAMoAgghBiADKAIEIQNB4ABBCBDWBCIERQ0EIAJBADYCkAwgAiAENgKMDCACQQM2AogMIAJCgICAgDA3ArAMIAIgBjYCrAwgAiADNgKoDCACIAU2AqQMIAIgCTYCoAwgAiAENgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqEHMgAigCiAwhByACKAKMDCENIAIoApAMIQUgCARAIAkgCEEFdBDfBAsCQCAFRQRAQQghCAwBC0EAIQNB0c7FAC0AABogBUEFdCIEQQgQ1gQiCEUNBiAFIQQDQCACQaAMaiADIA1qEEcgAyAIaiIGQRhqIAJBuAxqKQMANwMAIAZBEGogAkGwDGopAwA3AwAgBkEIaiACQagMaikDADcDACAGIAIpA6AMNwMAIANBIGohAyAEQQFrIgQNAAsLIAcEQCANIAdBBXQQ3wQLQZDOxQAhAyACQZDOxQA2AogMQZzOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMahCXAyACKAKIDCEDCyADKAIIIQYgAygCBCEHIAJBywA2AoQMIAVBBXQhBEEIIQMgBQRAQdHOxQAtAAAaIARBCBDWBCIDRQ0GCyACQQA2ApAMIAIgAzYCjAwgAiAFNgKIDCACIAY2ArAMIAIgBzYCrAwgAkEANgKoDCACIAQgCGo2AqQMIAIgCDYCoAwgAiACQYQMajYCtAwgAiADNgKcDCACQQA2ApgMIAIgAkGQDGo2ApQMIAJBoAxqIAJBlAxqELsCIAIoAogMIQYgAigCjAwhByACKAKQDCEJIAUEQCAIIAQQ3wQLQaDOxQAhAyACQaDOxQA2AogMQazOxQAtAABBA0cEQCACIAJBiAxqNgKUDCACIAJBlAxqNgKgDCACQaAMahD6AiACKAKIDCEDC0HRzsUALQAAGiADKAIIIQUgAygCBCEDQeAAQQgQ1gQiBEUNBCACQQA2ApAMIAIgBDYCjAwgAkEDNgKIDCACQoCAgIAwNwKwDCACIAU2AqwMIAIgAzYCqAwgAiAJNgKkDCACIAc2AqAMIAIgBDYCnAwgAkEANgKYDCACIAJBkAxqNgKUDCACQaAMaiACQZQMahBzIAIoAogMIQkgAigCjAwhDSACKAKQDCEFIAYEQCAHIAZBBXQQ3wQLAkAgBUUEQEEIIQgMAQtBACEDQdHOxQAtAAAaIAVBBXQiBEEIENYEIghFDQYgBSEEA0AgAkGgDGogAyANahBHIAMgCGoiBkEYaiACQbgMaikDADcDACAGQRBqIAJBsAxqKQMANwMAIAZBCGogAkGoDGopAwA3AwAgBiACKQOgDDcDACADQSBqIQMgBEEBayIEDQALCyAJBEAgDSAJQQV0EN8EC0GQzsUAIQMgAkGQzsUANgKIDEGczsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQlwMgAigCiAwhAwsgAygCCCEGIAMoAgQhByACQc4ANgKEDCAFQQV0IQRBCCEDIAUEQEHRzsUALQAAGiAEQQgQ1gQiA0UNBgsgAkEANgKQDCACIAM2AowMIAIgBTYCiAwgAiAGNgKwDCACIAc2AqwMIAJBADYCqAwgAiAEIAhqNgKkDCACIAg2AqAMIAIgAkGEDGo2ArQMIAIgAzYCnAwgAkEANgKYDCACIAJBkAxqNgKUDCACQaAMaiACQZQMahC7AiACKAKIDCEGIAIoAowMIQcgAigCkAwhCSAFBEAgCCAEEN8EC0GgzsUAIQMgAkGgzsUANgKIDEGszsUALQAAQQNHBEAgAiACQYgMajYClAwgAiACQZQMajYCoAwgAkGgDGoQ+gIgAigCiAwhAwtB0c7FAC0AABogAygCCCEFIAMoAgQhA0HgAEEIENYEIgRFDQQgAkEANgKQDCACIAQ2AowMIAJBAzYCiAwgAkKAgICAMDcCsAwgAiAFNgKsDCACIAM2AqgMIAIgCTYCpAwgAiAHNgKgDCACIAQ2ApwMIAJBADYCmAwgAiACQZAMajYClAwgAkGgDGogAkGUDGoQcyACKAKIDCEJIAIoAowMIQ0gAigCkAwhBSAGBEAgByAGQQV0EN8ECwJAIAVFBEBBCCEGDAELQQAhA0HRzsUALQAAGiAFQQV0IgRBCBDWBCIGRQ0GIAUhBANAIAJBoAxqIAMgDWoQRyADIAZqIghBGGogAkG4DGopAwA3AwAgCEEQaiACQbAMaikDADcDACAIQQhqIAJBqAxqKQMANwMAIAggAikDoAw3AwAgA0EgaiEDIARBAWsiBA0ACwsgCQRAIA0gCUEFdBDfBAtBoM7FACEDIAJBoM7FADYCiAxBrM7FAC0AAEEDRwRAIAIgAkGIDGo2ApQMIAIgAkGUDGo2AqAMIAJBoAxqEPoCIAIoAogMIQMLIAVFDQEgAygCCCEEIAMoAgRBBGohA0EAIQ5BACEIQgAhIUIAISRCACEoQgAhHwNAIAQgCEYNAwJAAkAgA0EEaigCAARAIAJBwANqIAYgDmoiB0EYaikDACIbQgAgAygCACIJKQMYIhpCABDJAyACQdADaiAbQgAgCSkDECIcQgAQyQMgAkHgA2ogG0IAIAkpAwgiHUIAEMkDIAJB8ANqIBtCACAJKQMAIhtCABDJAyACQbADaiACKQPAAyIiQv////++sv3wQn4iHkIAQoGAgIC/sv3wwwBCABDJAyACQaADaiAeQgBCkeHlzYeJ+pkoQgAQyQMgAkGQA2ogHkIAQt2whYzotpGouH9CABDJAyACQYADaiAeQgBCqcDGia7Ok7IwQgAQyQMgAkHAAmogB0EQaikDACIeQgAgGkIAEMkDIAJB0AJqIB5CACAcQgAQyQMgAkHgAmogHkIAIB1CABDJAyACQfACaiAeQgAgG0IAEMkDIAJBsAJqIAIpA6ADIikgAikDyAMiJSACKQPQA3wiJnwiICACKQO4AyAiIAIpA7ADIh58IB5UrXx8IiIgAikDwAJ8IiNC/////76y/fBCfiIeQgBCgYCAgL+y/fDDAEIAEMkDIAJBoAJqIB5CAEKR4eXNh4n6mShCABDJAyACQZACaiAeQgBC3bCFjOi2kai4f0IAEMkDIAJBgAJqIB5CAEKpwMaJrs6TsjBCABDJAyACQcABaiAHQQhqKQMAIh5CACAaQgAQyQMgAkHQAWogHkIAIBxCABDJAyACQeABaiAeQgAgHUIAEMkDIAJB8AFqIB5CACAbQgAQyQMgAkGwAWogAikDyAIgIiAjVq18IisgAikD0AJ8IicgAikD2AMgJSAmVq18IiogAikD4AN8IiUgAikDkAN8IiYgICAiVq0gAikDqAMgICApVK18fHwiLHwiICACKQOgAnwiIiACKQO4AiACKQOwAiIeICN8IB5UrXx8IiMgAikDwAF8IilC/////76y/fBCfiIeQgBCgYCAgL+y/fDDAEIAEMkDIAJBoAFqIB5CAEKR4eXNh4n6mShCABDJAyACQZABaiAeQgBC3bCFjOi2kai4f0IAEMkDIAJBgAFqIB5CAEKpwMaJrs6TsjBCABDJAyACQUBrIAcpAwAiHkIAIBpCABDJAyACQdAAaiAeQgAgHEIAEMkDIAJB4ABqIB5CACAdQgAQyQMgAkHwAGogHkIAIBtCABDJAyACQTBqIAIpA8gBICMgKVatfCItIAIpA9ABfCIaIAIpA+gDICUgKlStfCIqIAIpA/ADfCIcIAIpA4ADfCIdICYgLFatIAIpA5gDICUgJlatfHx8Ih4gAikD4AJ8IiUgICAnVK0gAikD2AIgJyArVK18fHwiJyACKQOQAnwiJiAiICNWrSACKQOoAiAgICJWrXx8fCIrfCIgIAIpA6ABfCIiIAIpA7gBIAIpA7ABIhsgKXwgG1StfHwiIyACKQNAfCIpQv////++sv3wQn4iG0IAQoGAgIC/sv3wwwBCABDJAyACQSBqIBtCAEKR4eXNh4n6mShCABDJAyACQRBqIBtCAELdsIWM6LaRqLh/QgAQyQMgAiAbQgBCqcDGia7Ok7IwQgAQyQMCQAJAIAIpAwggAikDiAEgAikDiAIgHSAeVq0gAikDiAMgHCAdVq18fCACKQP4AyAcICpUrXx8IiogAikD8AJ8IhsgJSAnVq0gAikD6AIgHiAlVq18fHwiHCACKQOAAnwiHSAcVK18IB0gHSAmICtWrSACKQOYAiAmICdUrXx8fCIeVq18IBsgHFatIAIpA/gCIBsgKlStfHx8IicgAikD8AF8IhsgAikD6AEgHiACKQPgAXwiHCAeVK18IBwgGiAgVq0gAikD2AEgGiAtVK18fHwiGiAcVK18fCIcIAIpA4ABfCIdIBxUrXwgHSACKQOYASAaIBogAikDkAF8Ih5WrXwgHiAeICIgI1atIAIpA6gBICAgIlatfHx8IiBWrXx8IhogHVStfCAbIBxWrSACKQP4ASAbICdUrXx8fCIiIAIpA3B8IhsgAikDaCAaIBogAikDYHwiHFatfCAcIBwgAikDWCACKQNIICMgKVatfCIdIAIpA1B8IhogHVStfCAaIBogIHwiHVatfHwiGlatfHwiHCACKQMAfCIgIBxUrXwgICAgIAIpAxggGiAaIAIpAxB8Ih5WrXwgHiAeIAIpAyggHSAdIAIpAyB8IhpWrXwgGiACKQM4IAIpAzAiHSApfCAdVK18fCIdIBpUrXx8IhpWrXx8Ih5WrXwgGyAcVq0gAikDeCAbICJUrXx8fCIgQqnAxomuzpOyMFYNAAJAICBCqcDGia7Ok7IwUQRAIB5C3bCFjOi2kai4f1YNAiAeQt2whYzotpGouH9RDQFCqcDGia7Ok7IwISALIB4hHCAaIRsMAgsgGkKR4eXNh4n6mShWDQBC3bCFjOi2kai4fyEcIBpCkeHlzYeJ+pkoUgRAQqnAxomuzpOyMCEgIBohGwwCC0KR4eXNh4n6mSghGyAdQoGAgIC/sv3wwwBaDQBCqcDGia7Ok7IwISAMAQsgGkKR4eXNh4n6mSh9IhwgHUKBgICAv7L98MMAVK0iIn0hGyAeQqPP+vOXye7XxwB8IiMgGkKR4eXNh4n6mShUIBwgIlRyrSIafSEcICAgHkLdsIWM6LaRqLh/VCAaICNWcq19QqnAxomuzpOyMH0hICAdQoGAgIC/sv3wwwB9IR0LQqnAxomuzpOyMCEaICQgHCAkfCIeViAeIBsgKHwiGyAoVCAbIB8gHSAffCIfVq18IhwgG1RyrXwiHSAeVHKtICAgIXx8IiEhGwJAICFCqcDGia7Ok7IwUg0AQt2whYzotpGouH8hGiAdIhtC3bCFjOi2kai4f1INAEKR4eXNh4n6mSghGiAcIhtCkeHlzYeJ+pkoUg0AQoGAgIC/sv3wwwAhGiAfIhtCgYCAgL+y/fDDAFENAgsgGiAbWA0BIB0hJCAcISgMAgtBAEEAQfSZwQAQ2QMACyAcQpHh5c2HifqZKH0iGyAfQoGAgIC/sv3wwwBUrSIafSEoIB1Co8/685fJ7tfHAHwiHiAcQpHh5c2HifqZKFQgGiAbVnKtIht9ISQgISAdQt2whYzotpGouH9UIBsgHlZyrX1CqcDGia7Ok7IwfSEhIB9CgYCAgL+y/fDDAH0hHwsgDkEgaiEOIANBDGohAyAFIAhBAWoiCEcNAAsgDyAfNwMYIA8gKDcDECAPICQ3AwggDyAhNwMAIAYgBUEFdBDfBAwDC0EIIAVBiJnBABDIBAALIA9CADcDACAPQRhqQgA3AwAgD0EQakIANwMAIA9BCGpCADcDAAwBCyAEIARB5JnBABDZAwALIAJBwAxqJAAMAgtBCEHgAEGImcEAEMgEAAtBCCAEQYiZwQAQyAQACyAKQYQBaiIEIA8Q3AIgBBC7AyEDIAooAjQiBARAIAooAjggBEECdBDfBAsgCigCBCIEBEAgCigCCCAEQQJ0EN8EC0EAIQQLIBcgAzYCBCAXIAQ2AgAgCkGQAWokACAUKAIMIQQgECAUKAIIQQFxIgU2AgggEEEAIAQgBRs2AgAgECAEQQAgBRs2AgQgFEEQaiQAIBAoAgAgECgCBCAQKAIIIBBBEGokAAsyAQF/IAEoAgBBqLXFAEEBIAEoAgQoAgwRAwAhAiAAQQA6AAUgACACOgAEIAAgATYCAAshAAJAIAEgAxDJBARAIAAgASADIAIQzgQiAA0BCwALIAALIwEBfyAAKAIAIgAgAEEfdSICcyACayAAQX9zQR92IAEQ3gILKAAgASAAKAIALQAAQQJ0IgBB3M3BAGooAgAgAEHEzcEAaigCABDQBAshAQF/IAAQ6wIgACgCACIBBEAgACgCBCABQewAbBDfBAsLKAAgASAAKAIALQAAQQJ0IgBBmKDEAGooAgAgAEGEoMQAaigCABDQBAseACAARQRAEPgEAAsgACACIAMgBCAFIAEoAhARCgALJQAgASAALQAAQQJ0IgBBwPbAAGooAgAgAEGo9sAAaigCABDQBAslACABIAAtAABBAnQiAEHclMEAaigCACAAQcyUwQBqKAIAENAECyUAIAEgAC0AAEECdCIAQYTOwQBqKAIAIABB9M3BAGooAgAQ0AQLJQAgASAALQAAQQJ0IgBB9MLCAGooAgAgAEHkwsIAaigCABDQBAslACABIAAtAABBAnQiAEHAoMQAaigCACAAQaygxABqKAIAENAECyUAIAEgAC0AAEECdCIAQeygxABqKAIAIABB1KDEAGooAgAQ0AQLJQAgASAALQAAQQJ0IgBBjLTEAGooAgAgAEH8s8QAaigCABDQBAscACAARQRAEPgEAAsgACACIAMgBCABKAIQEREACxwAIABFBEAQ+AQACyAAIAIgAyAEIAEoAhARLwALHAAgAEUEQBD4BAALIAAgAiADIAQgASgCEBEFAAscACAARQRAEPgEAAsgACACIAMgBCABKAIQETEACxwAIABFBEAQ+AQACyAAIAIgAyAEIAEoAhARMwALJgEBfyAAKAIAIgFBgICAgHhyQYCAgIB4RwRAIAAoAgQgARDfBAsLCgBBCCAAEP8EAAsbAQF/IAAoAgAiAQRAIAAoAgQgAUEFdBDfBAsLGwEBfyAAKAIAIgEEQCAAKAIEIAFBMGwQ3wQLCxsBAX8gACgCACIBBEAgACgCBCABQQJ0EN8ECwsjACABQbXVwgBBsNXCACAAKAIALQAAIgAbQQxBBSAAGxDQBAsaACAARQRAEPgEAAsgACACIAMgASgCEBEBAAsgACABQbaBwQBBpIHBACAALQAAIgAbQQ5BEiAAGxDQBAsYACAARQRAEPgEAAsgACACIAEoAhARAgALGAEBfyAAKAIAIgEEQCAAKAIEIAEQ3wQLC54BAgN/AX5BwNLFACgCAEUEQCMAQRBrIgAkACMAQRBrIgEkAEHRzsUALQAAGiABQQA6AA9BAUEBENYEIgJFBEBBAUEBEP8EAAsgACABQQ9qrTcDACAAIAKtNwMIIAJBARDfBCABQRBqJAAgACkDACEDQdDSxQAgACkDCDcDAEHI0sUAIAM3AwBBwNLFAEIBNwMAIABBEGokAAtByNLFAAtCACAABEAgACABEP8EAAsjAEEgayIAJAAgAEEANgIYIABBATYCDCAAQaisxQA2AgggAEIENwIQIABBCGogAhCoBAALFQAgAWlBAUYgAEGAgICAeCABa01xCxkBAW8gACUBIAEQByECEK0DIgAgAiYBIAALFQAgACgCACIAQYQBTwRAIAAQqwMLCxwAIABBADYCECAAQgA3AgggAEKAgICAwAA3AgALFwEBbyAAIAEQACECEK0DIgAgAiYBIAAL8wYBBn8CfwJAAkACQAJAAkAgAEEEayIFKAIAIgZBeHEiBEEEQQggBkEDcSIHGyABak8EQCAHQQAgAUEnaiIJIARJGw0BAkACQCACQQlPBEAgAiADENQCIggNAUEADAkLIANBzP97Sw0BQRAgA0ELakF4cSADQQtJGyEBAkAgB0UEQCABQYACSSAEIAFBBHJJciAEIAFrQYGACE9yDQEMCQsgAEEIayICIARqIQcCQAJAAkACQCABIARLBEAgB0Gc0sUAKAIARg0EIAdBmNLFACgCAEYNAiAHKAIEIgZBAnENBSAGQXhxIgYgBGoiBCABSQ0FIAcgBhDgAiAEIAFrIgNBEEkNASAFIAEgBSgCAEEBcXJBAnI2AgAgASACaiIBIANBA3I2AgQgAiAEaiICIAIoAgRBAXI2AgQgASADEMQCDA0LIAQgAWsiA0EPSw0CDAwLIAUgBCAFKAIAQQFxckECcjYCACACIARqIgEgASgCBEEBcjYCBAwLC0GQ0sUAKAIAIARqIgQgAUkNAgJAIAQgAWsiA0EPTQRAIAUgBkEBcSAEckECcjYCACACIARqIgEgASgCBEEBcjYCBEEAIQNBACEBDAELIAUgASAGQQFxckECcjYCACABIAJqIgEgA0EBcjYCBCACIARqIgIgAzYCACACIAIoAgRBfnE2AgQLQZjSxQAgATYCAEGQ0sUAIAM2AgAMCgsgBSABIAZBAXFyQQJyNgIAIAEgAmoiASADQQNyNgIEIAcgBygCBEEBcjYCBCABIAMQxAIMCQtBlNLFACgCACAEaiIEIAFLDQcLIAMQUyIBRQ0BIANBfEF4IAUoAgAiAkEDcRsgAkF4cWoiAiACIANLGyICBEAgASAAIAL8CgAACyAAEJMCIAEMCAsgAyABIAEgA0sbIgIEQCAIIAAgAvwKAAALIAUoAgAiAkF4cSIDIAFBBEEIIAJBA3EiAhtqSQ0DIAJBACADIAlLGw0EIAAQkwILIAgMBgtBhajFAEEuQbSoxQAQ/gMAC0HEqMUAQS5B9KjFABD+AwALQYWoxQBBLkG0qMUAEP4DAAtBxKjFAEEuQfSoxQAQ/gMACyAFIAEgBkEBcXJBAnI2AgAgASACaiICIAQgAWsiAUEBcjYCBEGU0sUAIAE2AgBBnNLFACACNgIAIAAMAQsgAAsLDgAgAQRAIAAgARDfBAsLFgAgACgCACABIAIgACgCBCgCDBEDAAsUACAAKAIAIAEgACgCBCgCDBECAAuDCAEEfyMAQfAAayIFJAAgBSADNgIMIAUgAjYCCAJ/IAFBgQJPBEACf0GAAiAALACAAkG/f0oNABpB/wEgACwA/wFBv39KDQAaQf4BQf0BIAAsAP4BQb9/ShsLIgYgAGosAABBv39KBEBBp7zFACEHQQUMAgsgACABQQAgBiAEENIEAAtBASEHIAEhBkEACyEIIAUgBjYCFCAFIAA2AhAgBSAINgIcIAUgBzYCGAJAAkACQAJAIAEgAkkiBiABIANJckUEQCACIANLDQEgAkUgASACTXJFBEAgBUEMaiAFQQhqIAAgAmosAABBv39KGygCACEDCyAFIAM2AiAgAyABIgJJBEAgA0EBaiICIANBA2siBkEAIAMgBk8bIgZJDQMCfyACIAZrIgdBAWsgACADaiwAAEG/f0oNABogB0ECayAAIAJqIgJBAmssAABBv39KDQAaIAdBA2sgAkEDaywAAEG/f0oNABogB0F8QXsgAkEEaywAAEG/f0obagsgBmohAgsCQCACRQ0AIAEgAk0EQCABIAJGDQEMBQsgACACaiwAAEG/f0wNBAsCfwJAAkAgASACRg0AAkACQCAAIAJqIgEsAAAiAEEASARAIAEtAAFBP3EhBiAAQR9xIQMgAEFfSw0BIANBBnQgBnIhAAwCCyAFIABB/wFxNgIkQQEMBAsgAS0AAkE/cSAGQQZ0ciEGIABBcEkEQCAGIANBDHRyIQAMAQsgA0ESdEGAgPAAcSABLQADQT9xIAZBBnRyciIAQYCAxABGDQELIAUgADYCJCAAQYABTw0BQQEMAgsgBBDoBAALQQIgAEGAEEkNABpBA0EEIABBgIAESRsLIQAgBSACNgIoIAUgACACajYCLCAFQQU2AjQgBUGwvcUANgIwIAVCBTcCPCAFIAVBGGqtQoCAgIDAEoQ3A2ggBSAFQRBqrUKAgICAwBKENwNgIAUgBUEoaq1CgICAgOAShDcDWCAFIAVBJGqtQoCAgIDwEoQ3A1AgBSAFQSBqrUKAgICA4AGENwNIDAQLIAUgAiADIAYbNgIoIAVBAzYCNCAFQfC9xQA2AjAgBUIDNwI8IAUgBUEYaq1CgICAgMAShDcDWCAFIAVBEGqtQoCAgIDAEoQ3A1AgBSAFQShqrUKAgICA4AGENwNIDAMLIAVBBDYCNCAFQdC8xQA2AjAgBUIENwI8IAUgBUEYaq1CgICAgMAShDcDYCAFIAVBEGqtQoCAgIDAEoQ3A1ggBSAFQQxqrUKAgICA4AGENwNQIAUgBUEIaq1CgICAgOABhDcDSAwCCyAGIAJBiL7FABDmBAALIAAgASACIAEgBBDSBAALIAUgBUHIAGo2AjggBUEwaiAEEKgEAAvhBgEPfyAAKAIEIQcgACgCCCEFQQAhACMAQRBrIgYkAEEBIQwCQCABKAIAIgpBIiABKAIEIg0oAhAiDhECAA0AAkAgBUUEQAwBC0EAIAVrIQ8gByEBIAUhAAJAAn8CQANAIAAgAWohEEEAIQMCQANAIAEgA2oiBC0AACIJQf8Aa0H/AXFBoQFJIAlBIkZyIAlB3ABGcg0BIAAgA0EBaiIDRw0ACyAAIAhqDAMLIARBAWohAQJAIAQsAAAiAEEATgRAIABB/wFxIQAMAQsgAS0AAEE/cSELIABBH3EhCSAEQQJqIQEgAEFfTQRAIAlBBnQgC3IhAAwBCyABLQAAQT9xIAtBBnRyIQsgBEEDaiEBIABBcEkEQCALIAlBDHRyIQAMAQsgCUESdEGAgPAAcSABLQAAQT9xIAtBBnRyciEAIARBBGohAQsgBkEEaiAAQYGABBCIAgJAAkAgBi0ABEGAAUYNACAGLQAPIAYtAA5rQf8BcUEBRg0AAkACQCACIAMgCGoiBEsNAAJAIAJFDQAgAiAFTwRAIAIgBUcNAgwBCyACIAdqLAAAQb9/TA0BCwJAIARFDQAgBCAFTwRAIAQgD2pFDQEMAgsgByAIaiADaiwAAEFASA0BCyAKIAIgB2ogCCACayADaiANKAIMIgIRAwBFDQEMAwsgByAFIAIgBEHsucUAENIEAAsCQCAGLQAEQYABRgRAIAogBigCCCAOEQIADQMMAQsgCiAGLQAOIgQgBkEEamogBi0ADyAEayACEQMADQILAn9BASAAQYABSQ0AGkECIABBgBBJDQAaQQNBBCAAQYCABEkbCyAIaiADaiECCwJ/QQEgAEGAAUkNABpBAiAAQYAQSQ0AGkEDQQQgAEGAgARJGwsgCGoiBCADaiEIIBAgAWsiAEUNAgwBCwsMBAsgAyAEagsiAyACSQ0AQQAhAAJAIAJFDQAgAiAFTwRAIAIiACAFRw0CDAELIAIiACAHaiwAAEG/f0wNAQsgA0UEQEEAIQMMAgsgAyAFTwRAIAMgBUYNAiAAIQIMAQsgAyAHaiwAAEG/f0oNASAAIQILIAcgBSACIANB/LnFABDSBAALIAogACAHaiADIABrIA0oAgwRAwANACAKQSIgDhECACEMCyAGQRBqJAAgDAsRACAAKAIAIAAoAgQgARCBBQsRACAAKAIEIAAoAgggARCBBQsaAAJ/IAFBCU8EQCABIAAQ1AIMAQsgABBTCws/AAJAAn8gAUEJTwRAIAEgABDUAgwBCyAAEFMLIgFFDQAgAUEEay0AAEEDcUUgAEVyDQAgAUEAIAD8CwALIAELFgBB2M7FACAANgIAQdTOxQBBATYCAAsiACAAQu26rbbNhdT14wA3AwggAEL4gpm9le7Gxbl/NwMACyEAIABCgLzfhaul+JsnNwMIIABCn/WWlNbu7cOhfzcDAAsTACAAQcyqxQA2AgQgACABNgIACxEAIAEgACgCACAAKAIEENAECxEAIAEgACgCACAAKAIEEJUCCxEAIAEoAgAgASgCBCAAEKsCC2IBAn8CQAJAIABBBGsoAgAiAkF4cSIDQQRBCCACQQNxIgIbIAFqTwRAIAJBACADIAFBJ2pLGw0BIAAQkwIMAgtBhajFAEEuQbSoxQAQ/gMAC0HEqMUAQS5B9KjFABD+AwALCw4AIAAoAgAlARAKQQBHCw4AIAAoAgAlARALQQBHCw4AIAAoAgAlARAQQQBHC7w3AhV/A34gACEGIwBB0ABrIgUkAAJAAkACfwJAAkAgAygCCCIABEAgAygCBCIHLQAAQQFxDQEgAigCCCEMIAIoAgQhECAFIAM2AgQCQAJAIAwEQCAMQQJ0IRIDQCAIIBBqIhMoAgANAiANQQFqIQ0gEiAIQQRqIghHDQALC0HRzsUALQAAGkEEQQQQ1gQiAEUNASAGQQE2AgggBiAANgIEIAZBATYCACAAQQE2AgAMBgsgBUEIaiABIAMQjAIgDQRAIABB/////wNqIgBB/v///wNxIRYgAEH/////A3EiFEEBaiIAQfz///8HcSEOIABBA3EhAiAFQcQAaiEVIAVBQGshCUEBIQADQCAAIQpBASEEA0AgBSgCDCELAkACQAJAAn8CQAJAAkACQAJAAkACQCAFKAIQIgAOAgABAgsgBUEwakG4gMUAKAIANgIAIAVBsIDFACkCADcDKAwCCyALKAIAIQFB0c7FAC0AABpBBEEEENYEIgBFDQIgCUEBNgIAIAAgCygCADYCACAFIAA2AjwgBUEBNgI4IAVBOGogARCzAiAFQTBqIAkoAgA2AgAgBSAFKQI4NwMoDAELIAVBKGogCyAAIAsgABDtAgsCQCAWRQRAQgAhGSAHIQAgFEEDTwRAIA4hAQNAIBlCgAF8IRkgAEEQaiEAIAFBBGsiAQ0ACwsgAgRAQgAhGiACIQEDQCAANQIAIBmGIBp8IRogGUIgfCEZIABBBGohACABQQFrIgENAAsLIBpCgICAgBBUDQELIAVBOGogBUEoaiADEKEBIAVBIGogFUEIaigCADYCACAFIBUpAgA3AxggBSgCOCIARQ0HIAUoAjwgAEECdBDfBAwHCyAaUA0BIAUoAjAhACAFKAIsIQECQAJAIBpCgIAEWgRAIABFDQIgAEH/////A2ohDyAAQQJ0IREgAEH/////A3FBAUcNAUIAIRsgASARagwGCyAARQ0BIBqnIQ8gAUEEayERIABBAnQhAEEAIQEDQCABQRB0IAAgEWooAgAiAUEQdnIgD3BBEHQgAUH//wNxciAPcCEBIABBBGsiAA0ACwwGCyABIBFqQQhrIQAgD0H/////A3FBAWpB/v///wdxIQFCACEZA0AgADUCACAAQQRqNQIAIBlCIIaEIBqCQiCGhCAagiEZIABBCGshACABQQJrIgENAAsMAwsgCUG4gMUAKAIANgIAIAVBsIDFACkCADcDOAwFC0EEQQRBpIPFABDIBAALIAVBADYCSCAFQQE2AjwgBUGw/8QANgI4IAVCBDcCQCAFQThqQaCAxQAQqAQACyAZQiCGIRsgAEEIagshACAPQQFxBH4gGQUgGyAAQQRrNQIAhCAaggunIQELIAlBuIDFACgCADYCACAFQbCAxQApAgA3AzggAUUNACAFQThqQaSBxQAQpQMgBSgCPCABNgIAIAVBATYCQAsgBUEgaiAJKAIANgIAIAUgBSkDODcDGAsgBSgCKCIABEAgBSgCLCAAQQJ0EN8ECyAFKAIIIgAEQCALIABBAnQQ3wQLIAVBEGogBUEgaigCADYCACAFIAUpAxg3AwggBCAEQf8BcUEgSSIAaiEEIAANAAsgCiAKIA1JIgFqIQAgAQ0ACwtBASEBAkACQAJAIBMoAgAiAEEBcQRAIAAhAgwBC0EAIQEDQCABIQogBSgCDCEBAkACQAJAAkAgBSgCECICDgIAAQILIAVBMGpBuIDFACgCADYCACAFQbCAxQApAgA3AygMAgsgASgCACEHQdHOxQAtAAAaQQRBBBDWBCICRQ0EIAVBQGsiDkEBNgIAIAIgASgCADYCACAFIAI2AjwgBUEBNgI4IAVBOGogBxCzAiAFQTBqIA4oAgA2AgAgBSAFKQI4NwMoDAELIAVBKGogASACIAEgAhDtAgsgBUE4aiAFQShqIAMQjAIgBSgCKCICBEAgBSgCLCACQQJ0EN8ECyAFKAIIIgIEQCABIAJBAnQQ3wQLIAVBEGogBUFAaygCADYCACAFIAUpAjg3AwggCkEBaiEBIABBAnEgAEEBdiICIQBFDQALIApBAmohAQsgDEEBayANRyACQQFHckUEQCAGIAUpAwg3AgAgBkEIaiAFQRBqKAIANgIADAgLIAUoAhAiCkECdCEDQQAhACAKQf////8DSyADQfz///8HS3INASAFKAIMIQ4CfyADRQRAQQQhBEEADAELQdHOxQAtAAAaQQQhACADQQQQ1gQiBEUNAiAKCyEAIAxBAnQiB0EEayEJIAMEQCAEIA4gA/wKAAALIAUgCjYCMCAFIAQ2AiwgBSAANgIoIAUgBUEoajYCQCAFIAVBBGo2AjwgBSAFQQhqNgI4IAJBAXYiACAIIAlGDQYaIAcgEGpBBGsoAgAhCiABQf8BcUEfTQRAA0AgBUE4aiAAQQFxEIYCIABBAXYhACABQf8BcSABQQFqIQFBH0kNAAsLIAdBCGsgCEYNBSASIAhrQQxrIQIgE0EEaiEBA0AgBUE4aiIAIAEoAgAiA0EBcRCGAiAAIANBAnFBAXYQhgIgACADQQRxQQJ2EIYCIAAgA0EIcUEDdhCGAiAAIANBEHFBBHYQhgIgACADQSBxQQV2EIYCIAAgA0HAAHFBBnYQhgIgACADQYABcUEHdhCGAiAAIANBgAJxQQh2EIYCIAAgA0GABHFBCXYQhgIgACADQYAIcUEKdhCGAiAAIANBgBBxQQt2EIYCIAAgA0GAIHFBDHYQhgIgACADQYDAAHFBDXYQhgIgACADQYCAAXFBDnYQhgIgACADQYCAAnFBD3YQhgIgACADQYCABHFBEHYQhgIgACADQYCACHFBEXYQhgIgACADQYCAEHFBEnYQhgIgACADQYCAIHFBE3YQhgIgACADQYCAwABxQRR2EIYCIAAgA0GAgIABcUEVdhCGAiAAIANBgICAAnFBFnYQhgIgACADQYCAgARxQRd2EIYCIAAgA0GAgIAIcUEYdhCGAiAAIANBgICAEHFBGXYQhgIgACADQYCAgCBxQRp2EIYCIAAgA0GAgIDAAHFBG3YQhgIgACADQYCAgIABcUEcdhCGAiAAIANBgICAgAJxQR12EIYCIAAgA0GAgICABHFBHnYQhgIgACADQR92EIYCIAFBBGohASACQQRrIgJBfEcNAAsMBQtBBEEEQaSDxQAQyAQACyAAIANBpIPFABDIBAALDAULIAVBADYCSCAFQQE2AjwgBUHcgcUANgI4IAVCBDcCQCAFQThqQciCxQAQqAQACyAGIQ4gAiEGIwBBgAFrIgQkAAJAAkACQAJAIAMiCigCCCICBEAgAygCBCISKAIAIglBAXFFDQIgASgCCCIDQQJ0IQAgA0H/////A0sgAEH8////B0tyDQEgASgCBCEHAn8gAEUEQEEEIQFBAAwBC0HRzsUALQAAGkEEIQggAEEEENYEIgFFDQIgAwshCCAABEAgASAHIAD8CgAACyAEIAE2AgQgBCAINgIAIAQgAzYCCCACIANJBEAgBEH0AGogBCAKEIsCIAQoAgAiAARAIAQoAgQgAEECdBDfBAsgBEEIaiAEQfwAaigCACIDNgIAIAQgBCkCdDcDAAsgAiADSwRAIAIgAyIAayIHIAQoAgAgAGtLBEAgBCAAIAcQiQMgBCgCCCEACyAEKAIEIgggAEECdGohASAHQQJPBEAgAiADQX9zakECdCILBEAgAUEAIAv8CwALIAAgAmpBAnQgA0ECdGsgCGpBBGshASAAIAdqQQFrIQALIAFBADYCACAEIABBAWo2AggLQdHOxQAtAAAaQQRBBBDWBCIARQ0IIABBATYCACAEQQE2AhggBCAANgIUIARBATYCECAEQQE2AnwgBCAANgJ4IARBATYCdCAEQegAaiIAIARB9ABqIgEgAkEBdEEAEM8BIAEgACAKEIsCIAQoAmgiAARAIAQoAmwgAEECdBDfBAsgBEEYaiAEQfwAaigCACIDNgIAIAQgBCkCdDcDECACIANLBEAgAiADIgBrIgcgBCgCECAAa0sEQCAEQRBqIAAgBxCJAyAEKAIYIQALIAQoAhQiCCAAQQJ0aiEBIAdBAk8EQCACIANBf3NqQQJ0IgsEQCABQQAgC/wLAAsgACACakECdCADQQJ0ayAIakEEayEBIAAgB2pBAWshAAsgAUEANgIAIAQgAEEBajYCGAtB0c7FAC0AABpBBEEEENYEIgBFDQggAEEBNgIAIARBATYCJCAEIAA2AiAgBEEBNgIcIAQgAkEBRwR/IARBHGpBASACQQFrIgEQiQMgBCgCICIHIAQoAiQiA0ECdGohACABQQJPBH8gAkECdEEIayIBBEAgAEEAIAH8CwALIAIgA2oiAEECayEDIAcgAEECdGpBCGsFIAALQQA2AgAgA0EBagVBAQs2AiRB0c7FAC0AABpBwAFBBBDWBCIARQ0DIARBADYCMCAEIAA2AiwgBEEQNgIoIARBNGogBEEcaiAEQRBqIAogCUECayAJQQFrIgAgAGwiAEEBcmwgACAAbCIAQQFybCAAIABsIgBBAXJsIAAgAGwiAEEBcmwgACAAbEEBamwiCSACEJABIAQoAjAiACAEKAIoRgRAIARBKGpB8P3EABCfAwsgBCgCLCAAQQxsaiIBIAQpAjQ3AgAgAUEIaiAEQTxqKAIANgIAIAQgAEEBajYCMCAEQUBrIAQgBEEQaiAKIAkgAhCQASAEKAIwIgAgBCgCKEYEQCAEQShqQYD+xAAQnwMLIAQoAiwgAEEMbGoiASAEKQJANwIAIAFBCGogBEHIAGooAgA2AgAgBCAAQQFqIgM2AjBBASEAQQwhAQNAIAAgA08EQCAAIANBsP7EABDZAwALIARBzABqIAQoAiwiAyABaiADQQxqIAogCSACEJABIAQoAjAiAyAEKAIoRgRAIARBKGpBwP7EABCfAwsgBCgCLCADQQxsaiIHIAQpAkw3AgAgB0EIaiAEQdQAaigCADYCACAEIANBAWoiAzYCMCAAQQFqIQAgAUEMaiIBQbQBRw0ACwwEC0EAQQBB8PzEABDZAwALIAggAEGkg8UAEMgEAAtB0P7EAEEkQfT+xAAQ/gMAC0EEQcABQeD9xAAQyAQACwJAIAMEQCAEKAIsIgEoAggiAEECdCEHQQAhCAJAIABB/////wNLIAdB/P///wdLcg0AIAEoAgQhAQJ/IAdFBEBBBCEDQQAMAQtB0c7FAC0AABpBBCEIIAdBBBDWBCIDRQ0BIAALIQggBwRAIAMgASAH/AoAAAsgBCADNgJcIAQgCDYCWCAEIAA2AmAgBCAAIAJJBH8gAiAAIgFrIgsgCCAAa0sEQCAEQdgAaiAAIAsQiQMgBCgCXCEDIAQoAmAhAQsgAyABQQJ0aiEIIAtBAk8EQCACIABBf3NqQQJ0IgAEQCAIQQAgAPwLAAsgASACakECdCAHayADakEEayEIIAEgC2pBAWshAQsgCEEANgIAIAFBAWoFIAILNgJgIARB8ABqIgBBiPrEACgCADYCACAEQYD6xAApAgA3A2ggBEHoAGpBACACEIkDIAQoAmwiAyAAKAIAIgFBAnRqIQAgAkEBRwRAIAJBAWsiB0ECdCIIBEAgAEEAIAj8CwALIAMgASACakECdGpBBGshACABIAdqIQELIABBADYCACAEIAFBAWo2AnACQCAGKAIIIgcEQCAGKAIEIQ0gByEAA0AgACAHRiANIABBAWsiAEECdGooAgAhCEUEQCAEQfQAaiAEQdgAaiIBIAEgCiAJIAIQkAEgBCgCaCIBBEAgBCgCbCABQQJ0EN8ECyAEQfAAaiIDIARB/ABqIgEoAgA2AgAgBCAEKQJ0NwNoIARB9ABqIARB6ABqIgYgBiAKIAkgAhCQASAEKAJYIgYEQCAEKAJcIAZBAnQQ3wQLIARB4ABqIgYgASgCADYCACAEIAQpAnQ3A1ggBEH0AGogBEHYAGoiCyALIAogCSACEJABIAQoAmgiCwRAIAQoAmwgC0ECdBDfBAsgAyABKAIANgIAIAQgBCkCdDcDaCAEQfQAaiAEQegAaiIDIAMgCiAJIAIQkAEgBCgCWCIDBEAgBCgCXCADQQJ0EN8ECyAGIAEoAgA2AgAgBCAEKQJ0NwNYCyAIQRx2IgYgBCgCMCIBTw0CIARB9ABqIARB2ABqIAQoAiwgBkEMbGogCiAJIAIQkAEgBCgCaCIBBEAgBCgCbCABQQJ0EN8ECyAEQfAAaiILIARB/ABqIgwoAgAiATYCACALIAQoAmA2AgAgBCAEKQJ0Ihk3A2ggBCkDWCEaIAQgGT4CWCAEIAQoAmw2AlwgBCAaNwNoIAQgATYCYEEEIQMDQCAEQfQAaiAEQdgAaiIBIAEgCiAJIAIQkAEgBCgCaCIBBEAgBCgCbCABQQJ0EN8ECyALIAwoAgA2AgAgBCAEKQJ0NwNoIARB9ABqIARB6ABqIgEgASAKIAkgAhCQASAEKAJYIgEEQCAEKAJcIAFBAnQQ3wQLIARB4ABqIgEgDCgCADYCACAEIAQpAnQ3A1ggBEH0AGogBEHYAGoiBiAGIAogCSACEJABIAQoAmgiBgRAIAQoAmwgBkECdBDfBAsgCyAMKAIANgIAIAQgBCkCdDcDaCAEQfQAaiAEQegAaiIGIAYgCiAJIAIQkAEgBCgCWCIGBEAgBCgCXCAGQQJ0EN8ECyABIAwoAgA2AgAgBCAEKQJ0NwNYIAhBBHQiCEEcdiIGIAQoAjAiAU8NAyAEQfQAaiAEQdgAaiAEKAIsIAZBDGxqIAogCSACEJABIAQoAmgiAQRAIAQoAmwgAUECdBDfBAsgCyAMKAIAIgE2AgAgCyAEKAJgNgIAIAQgBCkCdCIZNwNoIAQpA1ghGiAEIBk+AlggBCAEKAJsNgJcIAQgGjcDaCAEIAE2AmAgA0H/AXEgA0EEaiEDQRxJDQALIAANAAsLIARB9ABqIARB2ABqIARBHGogCiAJIAIQkAEgBCgCaCIABEAgBCgCbCAAQQJ0EN8ECyAEQfAAaiAEQfwAaigCACIANgIAIAQgBCkCdDcDaCAARQRAQQAhAAwECyAEKAJsIgEgAEECdCIDakEEaygCAA0DIAFBBGshBiAAQf////8DcSEBAkADQCADRQRAQQAhAwwCCyABQQFrIQEgAyAGaiADQQRrIQMoAgBFDQALIAFBAWoiAyAASw0ECyAEIAM2AnAgAyEADAMLIAYgAUGg/sQAENkDAAsgCCAHQaSDxQAQyAQAC0EAQQBBkP7EABDZAwALAkACQAJAAkAgACAEKAJoIgFBAnZPIAFFckUEQCAEKAJsIQYgAUECdCEBAkAgAEUEQEEEIQMgBiABEN8EDAELIAYgAUEEIABBAnQiARDOBCIDRQ0CCyAEIAA2AmggBCADNgJsIAQoAnAhAAsCQCAAIAJGBEAgBCgCbEEEayEAIBJBBGshASACQQJ0IQMCQANAIANFDQEgASADaiEGIAAgA2ogA0EEayEDKAIAIgcgBigCACIGRg0ACyAGIAdNDQIgAiEADAYLIANFDQEgAiEADAULIAAgAkkNBAtBACEIQQAhDSMAQSBrIgkkACAKKAIIIhMgBEHoAGoiCygCCCIAIAAgE0sbIgxBAnQhECAKKAIEIQcgCygCBCEDAkACQAJAIAxFDQAgDEEBRwRAIAxBfnEhFSAHIQYgAyEBA0AgASABKAIAIg8gBigCACIRayIWIAhrNgIAIAFBBGoiFCAUKAIAIhQgBkEEaigCACIXayIYIA8gEUkgCCAWS3IiCGs2AgAgFCAXSSAIIBhLciEIIAZBCGohBiABQQhqIQEgFSANQQJqIg1HDQALCyAMQQFxBH8gAyANQQJ0IgFqIgYgBigCACIGIAEgB2ooAgAiAWsiDSAIazYCACABIAZLIAggDUtyBSAIC0UNACADIBBqIQEgAEECdCAMQQJ0ayEGA0AgBkUNAiABIAEoAgAiCEEBazYCACAGQQRrIQYgAUEEaiEBIAhFDQALCyAHIBBqIQYgE0ECdCAQayEBA0AgAUUNAiABQQRrIQEgBigCACAGQQRqIQZFDQALCyAJQQA2AhggCUEBNgIMIAlBxIrFADYCCCAJQgQ3AhAgCUEIakHMisUAEKgEAAsCQCAARQRAQQAhAAwBCyADIABBAnQiAWpBBGsoAgANACADQQRrIQcgAEH/////A3EhBgJAA0AgAUUEQEEAIQEMAgsgBkEBayEGIAEgB2ogAUEEayEBKAIARQ0ACyAGQQFqIgEgAEsNAQsgCyABNgIIIAEhAAsCQAJAIAAgCygCACIBQQJ2TyABRXJFBEAgAUECdCEBAkAgAEUEQEEEIQYgAyABEN8EDAELIAMgAUEEIABBAnQiARDOBCIGRQ0CCyALIAA2AgAgCyAGNgIECyAJQSBqJAAMAQtBBCABQYzBxAAQyAQACyACIAQoAnAiAEYEQCAEKAJsQQRrIQAgEkEEayEBIAJBAnQhAwNAIANFDQMgASADaiEGIAAgA2ogA0EEayEDKAIAIgcgBigCACIGRg0ACyACIQAgBiAHSw0EDAMLIAAgAkkNAwwCC0EEIAFBhP/EABDIBAALIAIhACADDQELIARB9ABqIARB6ABqIAoQiwIgBCgCaCIABEAgBCgCbCAAQQJ0EN8ECyAEQfAAaiAEQfwAaigCACIANgIAIAQgBCkCdDcDaAsCQCAARQRAQQAhAAwBCyAEKAJsIgIgAEECdCIBakEEaygCAA0AIAJBBGshAyAAQf////8DcSECAkADQCABRQRAQQAhAQwCCyACQQFrIQIgASADaiABQQRrIQEoAgBFDQALIAJBAWoiASAASw0BCyAEIAE2AnAgASEACwJAAkAgACAEKAJoIgFBAnZPIAFFckUEQCAEKAJsIQIgAUECdCEBAkAgAEUEQEEEIQMgAiABEN8EDAELIAIgAUEEIABBAnQiARDOBCIDRQ0CCyAEIAA2AmggBCADNgJsCyAOIAQpA2g3AgAgDkEIaiAEQfAAaigCADYCACAEKAJYIgAEQCAEKAJcIABBAnQQ3wQLIAQoAjAiAgRAIAQoAiwhAQNAIAEoAgAiAARAIAFBBGooAgAgAEECdBDfBAsgAUEMaiEBIAJBAWsiAg0ACwsgBCgCKCIABEAgBCgCLCAAQQxsEN8ECyAEKAIcIgAEQCAEKAIgIABBAnQQ3wQLIAQoAhAiAARAIAQoAhQgAEECdBDfBAsgBCgCACIABEAgBCgCBCAAQQJ0EN8ECyAEQYABaiQADAELQQQgAUGE/8QAEMgEAAsMAgsgCgsiAARAA0AgBUE4aiAAQQFxEIYCIABBAkkgAEEBdiEARQ0ACwsgBiAFKQIoNwIAIAZBCGogBUEwaigCADYCACAFKAIIIgBFDQAgBSgCDCAAQQJ0EN8ECyAFQdAAaiQADwtBBEEEEP8EAAtrAQF/IwBBMGsiAyQAIAMgATYCBCADIAA2AgAgA0ECNgIMIANB8MvFADYCCCADQgI3AhQgAyADQQRqrUKAgICA4AGENwMoIAMgA61CgICAgOABhDcDICADIANBIGo2AhAgA0EIaiACEKgEAAtrAQF/IwBBMGsiAyQAIAMgATYCBCADIAA2AgAgA0ECNgIMIANBkMzFADYCCCADQgI3AhQgAyADQQRqrUKAgICA4AGENwMoIAMgA61CgICAgOABhDcDICADIANBIGo2AhAgA0EIaiACEKgEAAtrAQF/IwBBMGsiAyQAIAMgATYCBCADIAA2AgAgA0ECNgIMIANBxMzFADYCCCADQgI3AhQgAyADQQRqrUKAgICA4AGENwMoIAMgA61CgICAgOABhDcDICADIANBIGo2AhAgA0EIaiACEKgEAAsOACAAKAIAQQEgARDeAgsPAEGptcUAQSsgABD+AwALDgAgAUGUocAAQQUQ0AQLDgAgAUGMgcEAQQUQ0AQLDgAgAUG8g8EAQQwQ0AQLDgAgAEGw18EAIAEQqwILDgAgAUHs2MEAQQUQ0AQLKwACfyAAKAIALQAARQRAIAFB4LnFAEEFEJUCDAELIAFB5bnFAEEEEJUCCwsMACAAKAIAIAEQwwMLDAAgACgCACABEMIDCw4AIAFB9ZnCAEEFENAECw4AIAFB+LbCAEEMENAECwwAIAAoAgAgARCiAguyDgEJfwJ/IAAoAgAhBiMAQfAAayICJAACQAJAAkACfwJAAkACQAJAAkAgBi0AHCIJQQFHBEACQCAGLQAMQQFHBEAgAkEBNgJcIAJB/NzCADYCWCACQgE3AmQgAiAGrUKAgICAoAuENwNAIAIgAkFAazYCYCACQQxqIAJB2ABqENICDAELIAJBADYCFCACQoCAgIAQNwIMC0HRzsUALQAAGkEEQQQQ1gQiA0UNASADQQE2AgAgCUECRyAGKAIYIgBBAUdyDQIgBigCFCIIKAAAIAMoAABHDQIgA0EEEN8EQdHOxQAtAAAaQQJBARDWBCIDRQRAQQFBAkHU2MIAEMgEAAsgA0HPkwI7AAAgAkECNgIgIAIgAzYCHCACQQI2AhggAigCFA0EDAMLIAJBATYCXCACQfzcwgA2AlggAkIBNwJkIAIgBq1CgICAgKALhDcDQCACIAJBQGs2AmAgASgCACABKAIEIAJB2ABqEKsCIQMMBwtBBEEEEP8EAAsgA0EEEN8EIAJB4ABqQbjMwgAoAgA2AgAgAkGwzMIAKQIANwNYIAJB2ABqQaTNwgAQpQMgAigCXEEBNgIAIAIoAlwhAyACKAJYIQQCQAJAIAkgAEEBR3INACAGKAIUIggoAAAgAygAAEcNACAEBEAgAyAEQQJ0EN8EC0HRzsUALQAAGkEDQQEQ1gQiAw0BQQFBA0HU2MIAEMgEAAsgBARAIAMgBEECdBDfBAsgAkECNgJcIAJBiN3CADYCWCACQgE3AmQgAiAGQRBqrUKAgICAoAuENwNAIAIgAkFAazYCYCACQRhqIAJB2ABqENICIAIoAhRFDQEgBigCFCEIIAkNAgwDCyADQQJqQZrdwgAtAAA6AAAgA0GY3cIALwAAOwAAIAJBAzYCICACIAM2AhwgAkEDNgIYIAIoAhQNAgsgAkEBNgJcIAJB/NzCADYCWCACQgE3AmQgAiACQRhqrUKAgICAsAuENwNAIAIgAkFAazYCYCABKAIAIAEoAgQgAkHYAGoQqwIhAwwDCyACQQM2AiggAkGe3cIANgIkQQAhAwJAIABB/////wNLIABBAnQiBEH8////B0tyDQACfyAERQRAQQQhBUEADAELQdHOxQAtAAAaQQQhAyAEQQQQ1gQiBUUNASAACyEDIAQEQCAFIAggBPwKAAALIAlBAkYhCiAADAILDAQLIAJBAzYCKCACQZvdwgA2AiRBACEDIABB/////wNLIABBAnQiBEH8////B0tyDQMCfwJAIAQEQEHRzsUALQAAGkEEIQMgBEEEENYEIgVFDQYgBARAIAUgCCAE/AoAAAtBASEHIABFDQFBASEKIAAiAwwDC0EEIQUgBARAQQQgCCAE/AoAAAtBASEHQQAMAQtBBCEFQQALIQNBAAshBEHRzsUALQAAGgJAAkACQAJAAkBBBEEEENYEIgYEQCAGQQE2AgAgCkUgBEEBR3INAiAFKAAAIAYoAABHDQIgBkEEEN8EIAMEQCAFIANBAnQQ3wQLQdHOxQAtAAAaQQJBARDWBCIARQ0BIABBz5MCOwAAIAJBAjYCNCACIAA2AjAgAkECNgIsDAMLQQRBBBD/BAALQQFBAkHU2MIAEMgEAAsgBkEEEN8EIAMEQCAFIANBAnQQ3wQLAkACQCAHBEAgAEECdCEEIABB/////wFLBEBBACEDDAYLAn8gAEUEQEEEIQVBAAwBC0HRzsUALQAAGkEEIQMgBEEEENYEIgVFDQYgAAshAyAEBEAgBSAIIAT8CgAACyAADQEgAkHIAGpBqMzCACkCADcDACACQaDMwgApAgA3A0AgA0UNAiAFIANBAnQQ3wQMAgsgAEECdCEHIABB/////wFLBEBBACEFDAQLAn8gAEUEQEEEIQNBAAwBC0HRzsUALQAAGkEEIQUgB0EEENYEIgNFDQQgAAshBCAHBEAgAyAIIAf8CgAACyACIAk6AEwgAiAANgJIIAIgAzYCRCACIAQ2AkAMAQsgAkECOgBMIAIgADYCSCACIAU2AkQgAiADNgJACyACQQI2AlwgAkGI3cIANgJYIAJCATcCZCACIAJBQGutQoCAgICgC4Q3AzggAiACQThqNgJgIAJBLGogAkHYAGoQ0gIgAigCQCIARQ0AIAIoAkQgAEECdBDfBAsgAkEDNgJEIAJBpN3CADYCQCACQgM3AkwgAiACQSxqrUKAgICAsAuENwNoIAIgAkEkaq1CgICAgKAChDcDYCACIAJBDGqtQoCAgICwC4Q3A1ggAiACQdgAajYCSCABKAIAIAEoAgQgAkFAaxCrAiEDIAIoAiwiAEUNAiACKAIwIAAQ3wQMAgsgBSAHQfiBwAAQyAQACwwCCyACKAIYIgAEQCACKAIcIAAQ3wQLIAIoAgwiAEUNACACKAIQIAAQ3wQLIAJB8ABqJAAgAwwBCyADIARB+IHAABDIBAALCw4AIAFBmNXCAEEFENAECw4AQYDXwgBBNyABEIEFCwwAIAAoAgAgARDKBAsMAEGAtsQAQTIQEgALv1cBIn4gACkDOCEjIAApAzAhICAAKQMoIR8gACkDICEdIAApAxghJCAAKQMQISEgACkDCCEeIAApAwAhHCACBEAgASACQQd0aiECA0AgHCABKQAAIgRCOIYgBEKA/gODQiiGhCAEQoCA/AeDQhiGIARCgICA+A+DQgiGhIQgBEIIiEKAgID4D4MgBEIYiEKAgPwHg4QgBEIoiEKA/gODIARCOIiEhIQiESAjIB1CMokgHUIuiYUgHUIXiYV8IB8gIIUgHYMgIIV8fEKi3KK5jfOLxcIAfCIDIB4gIYUgHIMgHiAhg4UgHEIkiSAcQh6JhSAcQhmJhXx8IgRCJIkgBEIeiYUgBEIZiYUgBCAcIB6FgyAcIB6DhXwgICABQQhqKQAAIgVCOIYgBUKA/gODQiiGhCAFQoCA/AeDQhiGIAVCgICA+A+DQgiGhIQgBUIIiEKAgID4D4MgBUIYiEKAgPwHg4QgBUIoiEKA/gODIAVCOIiEhIQiEnwgAyAkfCIIIB0gH4WDIB+FfCAIQjKJIAhCLomFIAhCF4mFfELNy72fkpLRm/EAfCIGfCIFQiSJIAVCHomFIAVCGYmFIAUgBCAchYMgBCAcg4V8IB8gAUEQaikAACIDQjiGIANCgP4Dg0IohoQgA0KAgPwHg0IYhiADQoCAgPgPg0IIhoSEIANCCIhCgICA+A+DIANCGIhCgID8B4OEIANCKIhCgP4DgyADQjiIhISEIhN8IAYgIXwiDiAIIB2FgyAdhXwgDkIyiSAOQi6JhSAOQheJhXxC0YnLnYGGwZ/KAH0iD3wiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAdIAFBGGopAAAiBkI4hiAGQoD+A4NCKIaEIAZCgID8B4NCGIYgBkKAgID4D4NCCIaEhCAGQgiIQoCAgPgPgyAGQhiIQoCA/AeDhCAGQiiIQoD+A4MgBkI4iISEhCIVfCAPIB58Ig8gCCAOhYMgCIV8IA9CMokgD0IuiYUgD0IXiYV8QsTI2POni4mlFn0iB3wiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCAIIAFBIGopAAAiEEI4hiAQQoD+A4NCKIaEIBBCgID8B4NCGIYgEEKAgID4D4NCCIaEhCAQQgiIQoCAgPgPgyAQQhiIQoCA/AeDhCAQQiiIQoD+A4MgEEI4iISEhCIWfCAHIBx8IhAgDiAPhYMgDoV8IBBCMokgEEIuiYUgEEIXiYV8Qrjqopq/y7CrOXwiDXwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCAOIAFBKGopAAAiB0I4hiAHQoD+A4NCKIaEIAdCgID8B4NCGIYgB0KAgID4D4NCCIaEhCAHQgiIQoCAgPgPgyAHQhiIQoCA/AeDhCAHQiiIQoD+A4MgB0I4iISEhCIXfCAEIA18Ig4gDyAQhYMgD4V8IA5CMokgDkIuiYUgDkIXiYV8Qpmgl7CbvsT42QB8Ig18IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgDyABQTBqKQAAIgdCOIYgB0KA/gODQiiGhCAHQoCA/AeDQhiGIAdCgICA+A+DQgiGhIQgB0IIiEKAgID4D4MgB0IYiEKAgPwHg4QgB0IoiEKA/gODIAdCOIiEhIQiFHwgBSANfCIPIA4gEIWDIBCFfCAPQjKJIA9CLomFIA9CF4mFfELl4JqHtauf4O0AfSINfCIFQiSJIAVCHomFIAVCGYmFIAUgBCAIhYMgBCAIg4V8IBAgAUE4aikAACIHQjiGIAdCgP4Dg0IohoQgB0KAgPwHg0IYhiAHQoCAgPgPg0IIhoSEIAdCCIhCgICA+A+DIAdCGIhCgID8B4OEIAdCKIhCgP4DgyAHQjiIhISEIhh8IAMgDXwiECAOIA+FgyAOhXwgEEIyiSAQQi6JhSAQQheJhXxC6P3JrKKl6PHUAH0iDXwiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAOIAFBQGspAAAiB0I4hiAHQoD+A4NCKIaEIAdCgID8B4NCGIYgB0KAgID4D4NCCIaEhCAHQgiIQoCAgPgPgyAHQhiIQoCA/AeDhCAHQiiIQoD+A4MgB0I4iISEhCIbfCAGIA18Ig4gDyAQhYMgD4V8IA5CMokgDkIuiYUgDkIXiYV8Qr778+f1rJX8J30iDXwiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCAPIAFByABqKQAAIgdCOIYgB0KA/gODQiiGhCAHQoCA/AeDQhiGIAdCgICA+A+DQgiGhIQgB0IIiEKAgID4D4MgB0IYiEKAgPwHg4QgB0IoiEKA/gODIAdCOIiEhIQiGXwgCCANfCIPIA4gEIWDIBCFfCAPQjKJIA9CLomFIA9CF4mFfEK+38GrlODWwRJ8Ig18IghCJIkgCEIeiYUgCEIZiYUgCCADIAaFgyADIAaDhXwgECABQdAAaikAACIHQjiGIAdCgP4Dg0IohoQgB0KAgPwHg0IYhiAHQoCAgPgPg0IIhoSEIAdCCIhCgICA+A+DIAdCGIhCgID8B4OEIAdCKIhCgP4DgyAHQjiIhISEIhp8IAQgDXwiECAOIA+FgyAOhXwgEEIyiSAQQi6JhSAQQheJhXxCjOWS9+S34ZgkfCINfCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IA4gAUHYAGopAAAiB0I4hiAHQoD+A4NCKIaEIAdCgID8B4NCGIYgB0KAgID4D4NCCIaEhCAHQgiIQoCAgPgPgyAHQhiIQoCA/AeDhCAHQiiIQoD+A4MgB0I4iISEhCIKfCAFIA18Ig4gDyAQhYMgD4V8IA5CMokgDkIuiYUgDkIXiYV8QuLp/q+9uJ+G1QB8Ig18IgVCJIkgBUIeiYUgBUIZiYUgBSAEIAiFgyAEIAiDhXwgDyABQeAAaikAACIHQjiGIAdCgP4Dg0IohoQgB0KAgPwHg0IYhiAHQoCAgPgPg0IIhoSEIAdCCIhCgICA+A+DIAdCGIhCgID8B4OEIAdCKIhCgP4DgyAHQjiIhISEIgl8IAMgDXwiDyAOIBCFgyAQhXwgD0IyiSAPQi6JhSAPQheJhXxC75Luk8+ul9/yAHwiDXwiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAQIAFB6ABqKQAAIgdCOIYgB0KA/gODQiiGhCAHQoCA/AeDQhiGIAdCgICA+A+DQgiGhIQgB0IIiEKAgID4D4MgB0IYiEKAgPwHg4QgB0IoiEKA/gODIAdCOIiEhIQiC3wgBiANfCIQIA4gD4WDIA6FfCAQQjKJIBBCLomFIBBCF4mFfELP0qWnnMDTkP8AfSIHfCIGQiSJIAZCHomFIAZCGYmFIAYgAyAFhYMgAyAFg4V8IA4gAUHwAGopAAAiDkI4hiAOQoD+A4NCKIaEIA5CgID8B4NCGIYgDkKAgID4D4NCCIaEhCAOQgiIQoCAgPgPgyAOQhiIQoCA/AeDhCAOQiiIQoD+A4MgDkI4iISEhCIOfCAHIAh8IgcgDyAQhYMgD4V8IAdCMokgB0IuiYUgB0IXiYV8Qsvb49GNq/6R5AB9Ig18IghCJIkgCEIeiYUgCEIZiYUgCCADIAaFgyADIAaDhXwgDyABQfgAaikAACIPQjiGIA9CgP4Dg0IohoQgD0KAgPwHg0IYhiAPQoCAgPgPg0IIhoSEIA9CCIhCgICA+A+DIA9CGIhCgID8B4OEIA9CKIhCgP4DgyAPQjiIhISEIg98IAQgDXwiDSAHIBCFgyAQhXwgDUIyiSANQi6JhSANQheJhXxC7LLbhLPRg7I+fSIMfCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IBAgEkI/iSASQjiJhSASQgeIhSARfCAZfCAOQi2JIA5CA4mFIA5CBoiFfCIQfCAFIAx8IhEgByANhYMgB4V8IBFCMokgEUIuiYUgEUIXiYV8Qq7quojmx6WyG30iDHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAHIBNCP4kgE0I4iYUgE0IHiIUgEnwgGnwgD0ItiSAPQgOJhSAPQgaIhXwiB3wgAyAMfCISIA0gEYWDIA2FfCASQjKJIBJCLomFIBJCF4mFfEKdtMO9nI/uoBB9Igx8IgNCJIkgA0IeiYUgA0IZiYUgAyAEIAWFgyAEIAWDhXwgDSAVQj+JIBVCOImFIBVCB4iFIBN8IAp8IBBCLYkgEEIDiYUgEEIGiIV8Ig18IAYgDHwiEyARIBKFgyARhXwgE0IyiSATQi6JhSATQheJhXxCtauz3Oi45+APfCIMfCIGQiSJIAZCHomFIAZCGYmFIAYgAyAFhYMgAyAFg4V8IBEgFkI/iSAWQjiJhSAWQgeIhSAVfCAJfCAHQi2JIAdCA4mFIAdCBoiFfCIRfCAIIAx8IhUgEiAThYMgEoV8IBVCMokgFUIuiYUgFUIXiYV8QuW4sr3HuaiGJHwiDHwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCASIBdCP4kgF0I4iYUgF0IHiIUgFnwgC3wgDUItiSANQgOJhSANQgaIhXwiEnwgBCAMfCIWIBMgFYWDIBOFfCAWQjKJIBZCLomFIBZCF4mFfEL1hKzJ9Y3L9C18Igx8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgEyAUQj+JIBRCOImFIBRCB4iFIBd8IA58IBFCLYkgEUIDiYUgEUIGiIV8IhN8IAUgDHwiFyAVIBaFgyAVhXwgF0IyiSAXQi6JhSAXQheJhXxCg8mb9aaVobrKAHwiDHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAVIBhCP4kgGEI4iYUgGEIHiIUgFHwgD3wgEkItiSASQgOJhSASQgaIhXwiFXwgAyAMfCIUIBYgF4WDIBaFfCAUQjKJIBRCLomFIBRCF4mFfELU94fqy7uq2NwAfCIMfCIDQiSJIANCHomFIANCGYmFIAMgBCAFhYMgBCAFg4V8IBYgG0I/iSAbQjiJhSAbQgeIhSAYfCAQfCATQi2JIBNCA4mFIBNCBoiFfCIWfCAGIAx8IhggFCAXhYMgF4V8IBhCMokgGEIuiYUgGEIXiYV8QrWnxZiom+L89gB8Igx8IgZCJIkgBkIeiYUgBkIZiYUgBiADIAWFgyADIAWDhXwgFyAZQj+JIBlCOImFIBlCB4iFIBt8IAd8IBVCLYkgFUIDiYUgFUIGiIV8Ihd8IAggDHwiGyAUIBiFgyAUhXwgG0IyiSAbQi6JhSAbQheJhXxC1cDkjNHV6+DnAH0iDHwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCAUIBpCP4kgGkI4iYUgGkIHiIUgGXwgDXwgFkItiSAWQgOJhSAWQgaIhXwiFHwgBCAMfCIZIBggG4WDIBiFfCAZQjKJIBlCLomFIBlCF4mFfELwm6+SrbKO59cAfSIMfCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IBggCkI/iSAKQjiJhSAKQgeIhSAafCARfCAXQi2JIBdCA4mFIBdCBoiFfCIYfCAFIAx8IhogGSAbhYMgG4V8IBpCMokgGkIuiYUgGkIXiYV8QsG9k7j2hrb+zwB9Igx8IgVCJIkgBUIeiYUgBUIZiYUgBSAEIAiFgyAEIAiDhXwgGyAJQj+JIAlCOImFIAlCB4iFIAp8IBJ8IBRCLYkgFEIDiYUgFEIGiIV8Iht8IAMgDHwiCiAZIBqFgyAZhXwgCkIyiSAKQi6JhSAKQheJhXxCnOLDiISHoNPAAH0iDHwiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAZIAtCP4kgC0I4iYUgC0IHiIUgCXwgE3wgGEItiSAYQgOJhSAYQgaIhXwiGXwgBiAMfCIJIAogGoWDIBqFfCAJQjKJIAlCLomFIAlCF4mFfEK+4N2SzIH9jzl9Igx8IgZCJIkgBkIeiYUgBkIZiYUgBiADIAWFgyADIAWDhXwgGiAOQj+JIA5COImFIA5CB4iFIAt8IBV8IBtCLYkgG0IDiYUgG0IGiIV8Ihp8IAggDHwiCyAJIAqFgyAKhXwgC0IyiSALQi6JhSALQheJhXxC27HV54bXm6wqfSIMfCIIQiSJIAhCHomFIAhCGYmFIAggAyAGhYMgAyAGg4V8IA9CP4kgD0I4iYUgD0IHiIUgDnwgFnwgGUItiSAZQgOJhSAZQgaIhXwiDiAKfCAEIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8Qu+EjoCe6pjlBnwiDHwiBEIkiSAEQh6JhSAEQhmJhSAEIAYgCIWDIAYgCIOFfCAQQj+JIBBCOImFIBBCB4iFIA98IBd8IBpCLYkgGkIDiYUgGkIGiIV8Ig8gCXwgBSAMfCIJIAogC4WDIAuFfCAJQjKJIAlCLomFIAlCF4mFfELw3LnQ8KzKlBR8Igx8IgVCJIkgBUIeiYUgBUIZiYUgBSAEIAiFgyAEIAiDhXwgB0I/iSAHQjiJhSAHQgeIhSAQfCAUfCAOQi2JIA5CA4mFIA5CBoiFfCIQIAt8IAMgDHwiCyAJIAqFgyAKhXwgC0IyiSALQi6JhSALQheJhXxC/N/IttTQwtsnfCIMfCIDQiSJIANCHomFIANCGYmFIAMgBCAFhYMgBCAFg4V8IA1CP4kgDUI4iYUgDUIHiIUgB3wgGHwgD0ItiSAPQgOJhSAPQgaIhXwiByAKfCAGIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8QqaSm+GFp8iNLnwiDHwiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCARQj+JIBFCOImFIBFCB4iFIA18IBt8IBBCLYkgEEIDiYUgEEIGiIV8Ig0gCXwgCCAMfCIJIAogC4WDIAuFfCAJQjKJIAlCLomFIAlCF4mFfELt1ZDWxb+bls0AfCIMfCIIQiSJIAhCHomFIAhCGYmFIAggAyAGhYMgAyAGg4V8IBJCP4kgEkI4iYUgEkIHiIUgEXwgGXwgB0ItiSAHQgOJhSAHQgaIhXwiESALfCAEIAx8IgsgCSAKhYMgCoV8IAtCMokgC0IuiYUgC0IXiYV8Qt/n1uy5ooOc0wB8Igx8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgE0I/iSATQjiJhSATQgeIhSASfCAafCANQi2JIA1CA4mFIA1CBoiFfCISIAp8IAUgDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxC3se93cjqnIXlAHwiDHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAVQj+JIBVCOImFIBVCB4iFIBN8IA58IBFCLYkgEUIDiYUgEUIGiIV8IhMgCXwgAyAMfCIJIAogC4WDIAuFfCAJQjKJIAlCLomFIAlCF4mFfEKo5d7js9eCtfYAfCIMfCIDQiSJIANCHomFIANCGYmFIAMgBCAFhYMgBCAFg4V8IBZCP4kgFkI4iYUgFkIHiIUgFXwgD3wgEkItiSASQgOJhSASQgaIhXwiFSALfCAGIAx8IgsgCSAKhYMgCoV8IAtCMokgC0IuiYUgC0IXiYV8QpqiycCb2s2e/gB9Igx8IgZCJIkgBkIeiYUgBkIZiYUgBiADIAWFgyADIAWDhXwgF0I/iSAXQjiJhSAXQgeIhSAWfCAQfCATQi2JIBNCA4mFIBNCBoiFfCIWIAp8IAggDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxCxZX3267v9MbtAH0iDHwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCAUQj+JIBRCOImFIBRCB4iFIBd8IAd8IBVCLYkgFUIDiYUgFUIGiIV8IhcgCXwgBCAMfCIJIAogC4WDIAuFfCAJQjKJIAlCLomFIAlCF4mFfEKc+buY6+uFoN0AfSIMfCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IBhCP4kgGEI4iYUgGEIHiIUgFHwgDXwgFkItiSAWQgOJhSAWQgaIhXwiFCALfCAFIAx8IgsgCSAKhYMgCoV8IAtCMokgC0IuiYUgC0IXiYV8Qv+f953Etuby1wB9Igx8IgVCJIkgBUIeiYUgBUIZiYUgBSAEIAiFgyAEIAiDhXwgG0I/iSAbQjiJhSAbQgeIhSAYfCARfCAXQi2JIBdCA4mFIBdCBoiFfCIYIAp8IAMgDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxC79Cd+PKRndo9fSIMfCIDQiSJIANCHomFIANCGYmFIAMgBCAFhYMgBCAFg4V8IBlCP4kgGUI4iYUgGUIHiIUgG3wgEnwgFEItiSAUQgOJhSAUQgaIhXwiGyAJfCAGIAx8IgkgCiALhYMgC4V8IAlCMokgCUIuiYUgCUIXiYV8QtCDrc3Py+vJOH0iDHwiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCAaQj+JIBpCOImFIBpCB4iFIBl8IBN8IBhCLYkgGEIDiYUgGEIGiIV8IhkgC3wgCCAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfELo28LI4vzFti59Igx8IghCJIkgCEIeiYUgCEIZiYUgCCADIAaFgyADIAaDhXwgDkI/iSAOQjiJhSAOQgeIhSAafCAVfCAbQi2JIBtCA4mFIBtCBoiFfCIaIAp8IAQgDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxC8K3p1Lq7vrMpfSIMfCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IA9CP4kgD0I4iYUgD0IHiIUgDnwgFnwgGUItiSAZQgOJhSAZQgaIhXwiDiAJfCAFIAx8IgkgCiALhYMgC4V8IAlCMokgCUIuiYUgCUIXiYV8Qta/u8Sqz/L4C30iDHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAQQj+JIBBCOImFIBBCB4iFIA98IBd8IBpCLYkgGkIDiYUgGkIGiIV8Ig8gC3wgAyAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfEK4o++Vg46otRB8Igx8IgNCJIkgA0IeiYUgA0IZiYUgAyAEIAWFgyAEIAWDhXwgB0I/iSAHQjiJhSAHQgeIhSAQfCAUfCAOQi2JIA5CA4mFIA5CBoiFfCIQIAp8IAYgDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxCyKHLxuuisNIZfCIMfCIGQiSJIAZCHomFIAZCGYmFIAYgAyAFhYMgAyAFg4V8IA1CP4kgDUI4iYUgDUIHiIUgB3wgGHwgD0ItiSAPQgOJhSAPQgaIhXwiByAJfCAIIAx8IgkgCiALhYMgC4V8IAlCMokgCUIuiYUgCUIXiYV8QtPWhoqFgdubHnwiDHwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCARQj+JIBFCOImFIBFCB4iFIA18IBt8IBBCLYkgEEIDiYUgEEIGiIV8Ig0gC3wgBCAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfEKZ17v8zemdpCd8Igx8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgEkI/iSASQjiJhSASQgeIhSARfCAZfCAHQi2JIAdCA4mFIAdCBoiFfCIRIAp8IAUgDHwiCiAJIAuFgyAJhXwgCkIyiSAKQi6JhSAKQheJhXxCqJHtjN6Wr9g0fCIMfCIFQiSJIAVCHomFIAVCGYmFIAUgBCAIhYMgBCAIg4V8IBNCP4kgE0I4iYUgE0IHiIUgEnwgGnwgDUItiSANQgOJhSANQgaIhXwiEiAJfCADIAx8IgkgCiALhYMgC4V8IAlCMokgCUIuiYUgCUIXiYV8QuO0pa68loOOOXwiDHwiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAVQj+JIBVCOImFIBVCB4iFIBN8IA58IBFCLYkgEUIDiYUgEUIGiIV8IhMgC3wgBiAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfELLlYaarsmq7M4AfCIMfCIGQiSJIAZCHomFIAZCGYmFIAYgAyAFhYMgAyAFg4V8IBZCP4kgFkI4iYUgFkIHiIUgFXwgD3wgEkItiSASQgOJhSASQgaIhXwiFSAKfCAIIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8QvPGj7v3ybLO2wB8Igx8IghCJIkgCEIeiYUgCEIZiYUgCCADIAaFgyADIAaDhXwgF0I/iSAXQjiJhSAXQgeIhSAWfCAQfCATQi2JIBNCA4mFIBNCBoiFfCIWIAl8IAQgDHwiCSAKIAuFgyALhXwgCUIyiSAJQi6JhSAJQheJhXxCo/HKtb3+m5foAHwiDHwiBEIkiSAEQh6JhSAEQhmJhSAEIAYgCIWDIAYgCIOFfCAUQj+JIBRCOImFIBRCB4iFIBd8IAd8IBVCLYkgFUIDiYUgFUIGiIV8IhcgC3wgBSAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfEL85b7v5d3gx/QAfCIMfCIFQiSJIAVCHomFIAVCGYmFIAUgBCAIhYMgBCAIg4V8IBhCP4kgGEI4iYUgGEIHiIUgFHwgDXwgFkItiSAWQgOJhSAWQgaIhXwiFCAKfCADIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8QuDe3Jj07djS+AB8Igx8IgNCJIkgA0IeiYUgA0IZiYUgAyAEIAWFgyAEIAWDhXwgG0I/iSAbQjiJhSAbQgeIhSAYfCARfCAXQi2JIBdCA4mFIBdCBoiFfCIYIAl8IAYgDHwiCSAKIAuFgyALhXwgCUIyiSAJQi6JhSAJQheJhXxCjqm98LX94Zv7AH0iDHwiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCAZQj+JIBlCOImFIBlCB4iFIBt8IBJ8IBRCLYkgFEIDiYUgFEIGiIV8IhsgC3wgCCAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfEKUjO+s/r6/nPMAfSIMfCIIQiSJIAhCHomFIAhCGYmFIAggAyAGhYMgAyAGg4V8IBpCP4kgGkI4iYUgGkIHiIUgGXwgE3wgGEItiSAYQgOJhSAYQgaIhXwiGSAKfCAEIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8QtjD8+TdgMCg7wB9Igx8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgDkI/iSAOQjiJhSAOQgeIhSAafCAVfCAbQi2JIBtCA4mFIBtCBoiFfCIaIAl8IAUgDHwiCSAKIAuFgyALhXwgCUIyiSAJQi6JhSAJQheJhXxCl4T1i8Li5NfbAH0iDHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAPQj+JIA9COImFIA9CB4iFIA58IBZ8IBlCLYkgGUIDiYUgGUIGiIV8Ig4gC3wgAyAMfCILIAkgCoWDIAqFfCALQjKJIAtCLomFIAtCF4mFfELrjebphIGXg8EAfSIMfCIDQiSJIANCHomFIANCGYmFIAMgBCAFhYMgBCAFg4V8IBBCP4kgEEI4iYUgEEIHiIUgD3wgF3wgGkItiSAaQgOJhSAaQgaIhXwiDyAKfCAGIAx8IgogCSALhYMgCYV8IApCMokgCkIuiYUgCkIXiYV8QtXZtuTR4aHHOX0iDHwiBkIkiSAGQh6JhSAGQhmJhSAGIAMgBYWDIAMgBYOFfCAHQj+JIAdCOImFIAdCB4iFIBB8IBR8IA5CLYkgDkIDiYUgDkIGiIV8IhAgCXwgCCAMfCIJIAogC4WDIAuFfCAJQjKJIAlCLomFIAlCF4mFfELkvOaukaaw7DV9IiJ8IghCJIkgCEIeiYUgCEIZiYUgCCADIAaFgyADIAaDhXwgCyANQj+JIA1COImFIA1CB4iFIAd8IBh8IA9CLYkgD0IDiYUgD0IGiIV8Igx8IAQgInwiByAJIAqFgyAKhXwgB0IyiSAHQi6JhSAHQheJhXxC+fv88Y3n0bwufSIifCIEQiSJIARCHomFIARCGYmFIAQgBiAIhYMgBiAIg4V8IAogEUI/iSARQjiJhSARQgeIhSANfCAbfCAQQi2JIBBCA4mFIBBCBoiFfCILfCAFICJ8Ig0gByAJhYMgCYV8IA1CMokgDUIuiYUgDUIXiYV8QuKp/JCTxeCSFX0iInwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAJIBJCP4kgEkI4iYUgEkIHiIUgEXwgGXwgDEItiSAMQgOJhSAMQgaIhXwiCnwgAyAifCIRIAcgDYWDIAeFfCARQjKJIBFCLomFIBFCF4mFfEKI3cSMgZCswQp9Igl8IgNCJIkgA0IeiYUgA0IZiYUgAyAEIAWFgyAEIAWDhXwgE0I/iSATQjiJhSATQgeIhSASfCAafCALQi2JIAtCA4mFIAtCBoiFfCISIAd8IAYgCXwiByANIBGFgyANhXwgB0IyiSAHQi6JhSAHQheJhXxCut/dkKf1mfgGfCIJfCIGQiSJIAZCHomFIAZCGYmFIAYgAyAFhYMgAyAFg4V8IBVCP4kgFUI4iYUgFUIHiIUgE3wgDnwgCkItiSAKQgOJhSAKQgaIhXwiEyANfCAIIAl8Ig0gByARhYMgEYV8IA1CMokgDUIuiYUgDUIXiYV8QqaxopbauN+xCnwiCXwiCEIkiSAIQh6JhSAIQhmJhSAIIAMgBoWDIAMgBoOFfCAWQj+JIBZCOImFIBZCB4iFIBV8IA98IBJCLYkgEkIDiYUgEkIGiIV8IhUgEXwgBCAJfCIRIAcgDYWDIAeFfCARQjKJIBFCLomFIBFCF4mFfEKum+T3y4DmnxF8Igl8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgF0I/iSAXQjiJhSAXQgeIhSAWfCAQfCATQi2JIBNCA4mFIBNCBoiFfCIWIAd8IAUgCXwiByANIBGFgyANhXwgB0IyiSAHQi6JhSAHQheJhXxCm47xmNHmwrgbfCIJfCIFQiSJIAVCHomFIAVCGYmFIAUgBCAIhYMgBCAIg4V8IBRCP4kgFEI4iYUgFEIHiIUgF3wgDHwgFUItiSAVQgOJhSAVQgaIhXwiFyANfCADIAl8Ig0gByARhYMgEYV8IA1CMokgDUIuiYUgDUIXiYV8QoT7kZjS/t3tKHwiCXwiA0IkiSADQh6JhSADQhmJhSADIAQgBYWDIAQgBYOFfCAYQj+JIBhCOImFIBhCB4iFIBR8IAt8IBZCLYkgFkIDiYUgFkIGiIV8IhQgEXwgBiAJfCIRIAcgDYWDIAeFfCARQjKJIBFCLomFIBFCF4mFfEKTyZyGtO+q5TJ8Igl8IgZCJIkgBkIeiYUgBkIZiYUgBiADIAWFgyADIAWDhXwgG0I/iSAbQjiJhSAbQgeIhSAYfCAKfCAXQi2JIBdCA4mFIBdCBoiFfCIYIAd8IAggCXwiByANIBGFgyANhXwgB0IyiSAHQi6JhSAHQheJhXxCvP2mrqHBr888fCIKfCIIQiSJIAhCHomFIAhCGYmFIAggAyAGhYMgAyAGg4V8IBlCP4kgGUI4iYUgGUIHiIUgG3wgEnwgFEItiSAUQgOJhSAUQgaIhXwiEiANfCAEIAp8Ig0gByARhYMgEYV8IA1CMokgDUIuiYUgDUIXiYV8QsyawODJ+NmOwwB8IhR8IgRCJIkgBEIeiYUgBEIZiYUgBCAGIAiFgyAGIAiDhXwgGkI/iSAaQjiJhSAaQgeIhSAZfCATfCAYQi2JIBhCA4mFIBhCBoiFfCITIBF8IAUgFHwiESAHIA2FgyAHhXwgEUIyiSARQi6JhSARQheJhXxCtoX52eyX9eLMAHwiFHwiBUIkiSAFQh6JhSAFQhmJhSAFIAQgCIWDIAQgCIOFfCAOQj+JIA5COImFIA5CB4iFIBp8IBV8IBJCLYkgEkIDiYUgEkIGiIV8IhIgB3wgAyAUfCIDIA0gEYWDIA2FfCADQjKJIANCLomFIANCF4mFfEKq/JXjz7PKv9kAfCIVfCIHQiSJIAdCHomFIAdCGYmFIAcgBCAFhYMgBCAFg4V8IA4gD0I/iSAPQjiJhSAPQgeIhXwgFnwgE0ItiSATQgOJhSATQgaIhXwgDXwgBiAVfCIGIAMgEYWDIBGFfCAGQjKJIAZCLomFIAZCF4mFfELs9dvWs/Xb5d8AfCINfCIOIAUgB4WDIAUgB4OFfCAOQiSJIA5CHomFIA5CGYmFfCAPIBBCP4kgEEI4iYUgEEIHiIV8IBd8IBJCLYkgEkIDiYUgEkIGiIV8IBF8IAggDXwiCCADIAaFgyADhXwgCEIyiSAIQi6JhSAIQheJhXxCl7Cd0sSxhqLsAHwiD3whHCAOIB58IR4gBCAdfCAPfCEdIAcgIXwhISAIIB98IR8gBSAkfCEkIAYgIHwhICADICN8ISMgAUGAAWoiASACRw0ACwsgACAjNwM4IAAgIDcDMCAAIB83AyggACAdNwMgIAAgJDcDGCAAICE3AxAgACAeNwMIIAAgHDcDAAsOACABQeCSxQBBDBDQBAsOACAAQcSnxQAgARCrAgsMACAAIAEpAgA3AwALDgAgAEH8q8UAIAEQqwILDgAgAUH0q8UAQQUQ0AQLGgAgACABQdzOxQAoAgAiAEH+ACAAGxEAAAALDgAgAEHMt8UAIAEQqwILCwAgAiAAIAEQlQILvQgBLX4CQCABQRhNBEAgAQRAQQAgAUEDdGshASAAKQPAASEQIAApA5gBIRwgACkDcCERIAApA0ghEiAAKQMgIR0gACkDuAEhHiAAKQOQASEfIAApA2ghAiAAKQNAIQ4gACkDGCEJIAApA7ABIQMgACkDiAEhEyAAKQNgIQogACkDOCEUIAApAxAhBSAAKQOoASEVIAApA4ABIQQgACkDWCEWIAApAzAhFyAAKQMIIQsgACkDoAEhDCAAKQN4IRggACkDUCENIAApAyghGSAAKQMAIRoDQCAMIBiFIA2FIBmFIBqFIgYgAyAThSAKhSAUhSAFhSIHQgGJhSIPIBeFIB4gH4UgAoUgDoUgCYUiCCAGQgGJhSIGIBCFIS4gDyAVhUICiSIgIA4gByAQIByFIBGFIBKFIB2FIhtCAYmFIgeFQjeJIiEgBSAEIBWFIBaFIBeFIAuFIg4gCEIBiYUiCIVCPokiIkJ/hYOFIRAgDkIBiSAbhSIFIBiFQimJIhsgBiARhUIniSIjQn+FgyAhhSEVIA8gFoVCCokiJCAHIB6FQjiJIiUgCCAThUIPiSImQn+Fg4UhEyAGIB2FQhuJIicgJCAFIBmFQiSJIihCf4WDhSEYIAUgDIVCEokiDCAIIBSFQgaJIikgCyAPhUIBiSIqQn+Fg4UhESAGIByFQgiJIisgAiAHhUIZiSIsQn+FgyAphSEWIAMgCIVCPYkiAiAGIBKFQhSJIgMgByAJhUIciSIJQn+Fg4UhEiAEIA+FQi2JIgQgCSACQn+Fg4UhDiAFIA2FQgOJIgsgAiAEQn+Fg4UhFCAEIAtCf4WDIAOFIRcgCyADQn+FgyAJhSEZIAcgH4VCFYkiAiAFIBqFIgMgLkIOiSIEQn+Fg4UhCSAIIAqFQiuJIgogBCACQn+Fg4UhBUIsiSINIAIgCkJ/hYOFIQsgAUHYucQAaikDACAKIA1Cf4WDhSADhSEaICggJ0J/hYMgJYUiDyEcIA0gA0J/hYMgBIUiBiEdICIgIEJ/hYMgG4UiByEeICcgJUJ/hYMgJoUiCCEfICogDEJ/hYMgK4UhAiAgIBtCf4WDICOFIQMgDCArQn+FgyAshSEKICYgJEJ/hYMgKIUhBCAjICFCf4WDICKFIQwgKiAsIClCf4WDhSENIAFBCGoiAQ0ACyAAIAw3A6ABIAAgGDcDeCAAIA03A1AgACAZNwMoIAAgFTcDqAEgACAENwOAASAAIBY3A1ggACAXNwMwIAAgCzcDCCAAIAM3A7ABIAAgEzcDiAEgACAKNwNgIAAgFDcDOCAAIAU3AxAgACAHNwO4ASAAIAg3A5ABIAAgAjcDaCAAIA43A0AgACAJNwMYIAAgEDcDwAEgACAPNwOYASAAIBE3A3AgACASNwNIIAAgBjcDICAAIBo3AwALDAELQa66xABBwQBB8LrEABD+AwALCwkAIABBADYCAAsIACAAJQEQBAsIACAAJQEQBQsIACAAJQEQCAsIACAAJQEQDwsL7MAFNgBBgIDAAAvVAi9ydXN0Yy8xNzA2N2U5YWM2ZDdlY2I3MGU1MGY5MmMxOTQ0ZTU0NTE4OGQyMzU5L2xpYnJhcnkvYWxsb2Mvc3JjL3ZlYy9zcGVjX2Zyb21faXRlcl9uZXN0ZWQucnMAAAAAEABeAAAANAAAAAUAAAAAABAAXgAAABMAAAAFAAAAY2FwYWNpdHkgb3ZlcmZsb3cAAACAABAAEQAAAC9ydXN0Yy8xNzA2N2U5YWM2ZDdlY2I3MGU1MGY5MmMxOTQ0ZTU0NTE4OGQyMzU5L2xpYnJhcnkvYWxsb2Mvc3JjL3NsaWNlLnJzAACcABAASgAAAKgBAAAfAAAAnAAQAEoAAAC+AQAAHQAAAHRvb2xzL2dhcmFnYV9ycy9zcmMvY2FsbGRhdGEvZnVsbF9wcm9vZl93aXRoX2hpbnRzL3prX2hvbmsucnMAAAAIARAAPQAAAPYCAAAzAEGog8AAC8kbL98HmsF3Cg4sRnl4b6NuZj0Lx/Uo63gKnQ2PxY1DXdOT5ID6w172FW3sVqKXGgdcRVdScFNYzne6WMdTV5hIXwIADMQLAPTr/f8CAAAACXYvcnVzdGMvMTcwNjdlOWFjNmQ3ZWNiNzBlNTBmOTJjMTk0NGU1NDUxODhkMjM1OS9saWJyYXJ5L2FsbG9jL3NyYy9zbGljZS5ycwAA+AEQAE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================================================ FILE: tools/npm/garaga_ts/tests/starknet/drandCalldata.test.ts ================================================ import * as garaga from "../../src/node/index"; describe('Drand Getting calldata', () => { const roundNumbers = [1, 2, 3, 'latest']; test.each(roundNumbers)("should get Drand calldata for round %s", async (roundNumber) => { await garaga.init(); console.log("roundNumber", roundNumber); const drandCalldata = await garaga.fetchAndGetDrandCallData(roundNumber as number | 'latest'); console.log("drandCalldata", drandCalldata); }); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/drandTlockCalldata.test.ts ================================================ import * as garaga from "../../src/node/index"; describe('Drand Tlock Encrypting and Getting calldata', () => { const roundNumbers = [1, 2, 3]; test.each(roundNumbers)("should encrypt message and get Drand tlock calldata for round %s", async (roundNumber) => { await garaga.init(); const text = 'Hello, world!'; const message = new Uint8Array(16); message.set(new TextEncoder().encode(text)); const randomness = new Uint8Array(16); randomness.set(new TextEncoder().encode('fixed_randomness')); console.log("roundNumber", roundNumber); console.log("message", message); const drandCalldata = garaga.encryptToDrandRoundAndGetCallData(roundNumber as number, message, randomness); console.log("drandCalldata", drandCalldata); expect(drandCalldata).toBeDefined(); expect(drandCalldata.length).toBeGreaterThan(0); }); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/groth16Calldata.test.ts ================================================ import { Groth16Proof, parseGroth16ProofFromJson, parseGroth16VerifyingKeyFromJson } from "../../src/node/starknet/groth16ContractGenerator/parsingUtils"; import * as garaga from "../../src/node/index"; const PATH = '../../../hydra/garaga/starknet/groth16_contract_generator/examples'; describe('Groth16 Getting calldata', () => { const proofAndVkWithPublicInputs = [ [`${PATH}/proof_bn254.json`, `${PATH}/vk_bn254.json`, null], [`${PATH}/proof_bls.json`, `${PATH}/vk_bls.json`, null], [`${PATH}/gnark_proof_bn254.json`, `${PATH}/gnark_vk_bn254.json`, `${PATH}/gnark_public_bn254.json`], [`${PATH}/snarkjs_proof_bn254.json`, `${PATH}/snarkjs_vk_bn254.json`, `${PATH}/snarkjs_public_bn254.json`], [`${PATH}/proof_risc0.json`, `${PATH}/vk_risc0.json`, null], [`${PATH}/proof_sp1.json`, `${PATH}/vk_sp1.json`, null], ] test.each(proofAndVkWithPublicInputs)("should get groth16 calldata from proof %s, vk %s and pub inputs %s", async (proofPath, vkPath, pubInputsPath) => { await garaga.init(); const vk = parseGroth16VerifyingKeyFromJson(vkPath as string); let proof: Groth16Proof; if (pubInputsPath == null) { proof = parseGroth16ProofFromJson(proofPath as string); } else { proof = parseGroth16ProofFromJson(proofPath as string, pubInputsPath); } const curveId: garaga.CurveId = proof.a.curveId; console.log("proof", proof); console.log("vk", vk); console.log("curveId", curveId); const groth16Calldata = garaga.getGroth16CallData(proof, vk, curveId); console.log("groth16Calldata", groth16Calldata); }); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/groth16VkProofParsing.test.ts ================================================ import { parseGroth16ProofFromJson, parseGroth16VerifyingKeyFromJson } from "../../src/node/starknet/groth16ContractGenerator/parsingUtils"; const PATH = '../../../hydra/garaga/starknet/groth16_contract_generator/examples'; describe('Groth16 Parsing Tests', () => { const vkPaths = [ `${PATH}/snarkjs_vk_bn254.json`, `${PATH}/snarkjs_vk_bls12381.json`, `${PATH}/vk_bn254.json`, `${PATH}/vk_bls.json`, `${PATH}/gnark_vk_bn254.json`, `${PATH}/vk_risc0.json`, `${PATH}/vk_sp1.json`, ]; test.each(vkPaths)('should parse vk from %s', (vkPath) => { const vk = parseGroth16VerifyingKeyFromJson(vkPath); console.log(vk); }); const proofPaths = [ `${PATH}/proof_bn254.json`, `${PATH}/proof_bls.json`, `${PATH}/proof_risc0.json`, `${PATH}/proof_sp1.json`, ]; test.each(proofPaths)('should parse proof from %s', (proofPath) => { const proof = parseGroth16ProofFromJson(proofPath); console.log(proof); }); const proofWithPublicInput = [ [`${PATH}/snarkjs_proof_bn254.json`, `${PATH}/snarkjs_public_bn254.json`], [`${PATH}/snarkjs_proof_bls12381.json`, `${PATH}/snarkjs_public_bls12381.json`], [`${PATH}/gnark_proof_bn254.json`, `${PATH}/gnark_public_bn254.json`], ]; test.each(proofWithPublicInput)( 'should parse proof with public inputs from %s and %s', (proofPath, pubInputsPath) => { const proof = parseGroth16ProofFromJson(proofPath, pubInputsPath); console.log(proof); } ); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/poseidonHash.test.ts ================================================ import * as garaga from "../../src/node/index"; describe('Poseidon Hash Tests', () => { test("should compute Poseidon hash for BN254", async () => { await garaga.init(); // Test vectors from the Rust implementation const x = 1n; const y = 2n; const hash = garaga.poseidonHashBN254(x, y); // Expected hash value from Rust test const expectedHash = BigInt("0x115cc0f5e7d690413df64c6b9662e9cf2a3617f2743245519e19607a4417189a"); expect(hash).toBe(expectedHash); }); test("should compute different hashes for different inputs", async () => { await garaga.init(); const hash1 = garaga.poseidonHashBN254(1n, 2n); const hash2 = garaga.poseidonHashBN254(2n, 1n); expect(hash1).not.toBe(hash2); }); test("should handle large numbers", async () => { await garaga.init(); const x = BigInt("0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"); const y = BigInt("0xeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee"); const hash = garaga.poseidonHashBN254(x, y); expect(typeof hash).toBe('bigint'); expect(hash.toString(16).length).toBeLessThanOrEqual(64); // Should be within field size }); test("should handle invalid inputs gracefully", async () => { await garaga.init(); expect(() => { // Try to hash an invalid number garaga.poseidonHashBN254(-1n, 1n); }).toThrow(); }); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/signaturesCalldata.test.ts ================================================ import * as garaga from "../../src/node/index"; import { CurveId } from "../../src/node/definitions"; describe('Signatures Getting calldata', () => { test("should get calldata from Schnorr signature", async () => { await garaga.init(); const rx = 2035568083744286872562076170424183686789303771874924387134332885848716527973n; const s = 16951964772773949134099030503529813788531799557122970289125566478359203530341n; const e = 12379944220159143227935478555737246072763864785692867509458453554537054077909n; const px = 1460015317007179873453105936321786126342173668635633375793615328879270166120n; const py = 11788876621134198315085358602693659440838178818373737092676489706543309378340n; const curveId = CurveId.BN254; const schnorrCalldata = garaga.schnorrCalldataBuilder(rx, s, e, px, py, true, curveId); console.log("schnorrCalldata", schnorrCalldata); }); test("should get calldata from ECDSA signature", async () => { await garaga.init(); const r = 17830031845148496611971159596372798561444562703217806657239186935632770088766n; const s = 15775553683756501243755332794094542682114105716241054629352056498655356866971n; const v = 0; const px = 11329275913325725487970330398927775211322605183390088341941803765401909426169n; const py = 8682249405907851087539181920418463468320177419465741864050204044014651446009n; const z = 7590902656267229106356493910512635750747848737569325419577764035270226305644n; const curveId = CurveId.BN254; const ecdsaCalldata = garaga.ecdsaCalldataBuilder(r, s, v, px, py, z, true, curveId); console.log("ecdsaCalldata", ecdsaCalldata); }); }); ================================================ FILE: tools/npm/garaga_ts/tests/starknet/zkHonkCalldata.test.ts ================================================ import { HonkFlavor } from "../../src/node/starknet/honkContractGenerator/parsingUtils"; import * as fs from 'fs'; import * as garaga from "../../src/node/index"; const PATH = '../../../hydra/garaga/starknet/honk_contract_generator/examples'; describe('ZK Honk Getting calldata', () => { const proofAndVkWithFlavors = [ [`${PATH}/proof_ultra_keccak_zk.bin`, `${PATH}/public_inputs_ultra_keccak.bin`, `${PATH}/vk_ultra_keccak.bin`, HonkFlavor.KECCAK], // [`${PATH}/proof_ultra_starknet_zk.bin`, `${PATH}/public_inputs_ultra_keccak.bin`, `${PATH}/vk_ultra_keccak.bin`, HonkFlavor.STARKNET], ] test.each(proofAndVkWithFlavors)("should get zk honk calldata from proof %s, public inputs %s, vk %s and pub inputs %s", async (proofPath, publicInputsPath, vkPath, flavor) => { await garaga.init(); const vkBytes = new Uint8Array(fs.readFileSync(vkPath as string)); const publicInputsBytes = new Uint8Array(fs.readFileSync(publicInputsPath as string)); const proofBytes = new Uint8Array(fs.readFileSync(proofPath as string)); console.log("proof", proofBytes); console.log("publicInputs", publicInputsBytes); console.log("vk", vkBytes); console.log("flavor", flavor); const honkCalldata = garaga.getZKHonkCallData(proofBytes, publicInputsBytes, vkBytes); console.log("honkCalldata", honkCalldata); }); }); ================================================ FILE: tools/npm/integration-test-suite/.gitignore ================================================ /node_modules/ /*.tgz .turbo package-lock.json .output.txt ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-cjs-tsc/.gitignore ================================================ /node_modules/ /dist/ ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-cjs-tsc/output.txt ================================================ Output of msm_calldata_builder: [ "1n", "1n", "0n", "0n", "0n", "2n", "0n", "0n", "0n", "1n", "10n", "0n", "0n", "75759116906411131289250842036n", "1443316740970346987535705368n", "708088064087366360n", "0n", "31894839170900604627010243180n", "26562388390640533846098233871n", "1678682860455561629n", "0n", "340282366920938463463374607431768211466n", "0n", "1n", "0n" ] Output of get_groth16_calldata: [ "1935n", "561151868347580495583090954n", "76095163897123765080010407949n", "3078964875882710626n", "0n", "68760071548346057889257256130n", "33987009017980255890281589641n", "10169520226989098n", "0n", "27526525353537266686222475850n", "14475456397330869216192753448n", "2537199318039088506n", "0n", "21536768652854740401912377472n", "61033740543581523820282161323n", "2466548432040548587n", "0n", "49356715888972701601325049347n", "69887821523610458575318250963n", "1742488265497548861n", "0n", "68106177540828336088045306219n", "961134836681944563222599448n", "1065964868903753173n", "0n", "1800806384039658546158952406n", "44097612892395787951554989634n", "2954998394940821894n", "0n", "57407696252580182379957914390n", "68043785987214905719851221030n", "1575697798130653691n", "0n", "1n", "64622861075918021861446670503650833524n", "40000715384012656934033607729992139113n", "65343516826393976703500119419n", "64215924997604874724268545467n", "988361220710881918n", "30419768492628197858619568261n", "27248300164153194572764431995n", "2977039154666701832n", "65685384868591218376868464427n", "70847639348750339988496276918n", "477777041053646529n", "29991939756641252358878134746n", "39295947558852310211017126572n", "2815628384676858047n", "41723516601424502403187247204n", "17017221925427596342628818049n", "440483370607139100n", "10413180469465695361837522183n", "19423959337400646488247227266n", "1196856567711091031n", "14918739433528640782272739139n", "2386255189434407583576372032n", "2110030772171629820n", "66403863065153192042460667734n", "26490228722781507311620127895n", "1376925612093868452n", "16095686441528704658448370761n", "51022389018232154188872438326n", "1610491282614910455n", "37997039872158612927722452114n", "76461913933066610895201145075n", "951074374291802403n", "71303405408633411813876113602n", "65378028046199379258519780162n", "2796976393851271662n", "66043194162972766020432949924n", "72668519642029141849369643840n", "1767421250104456939n", "34724757470958269778491338738n", "67907574914053181941994051296n", "1074861315591297211n", "57811416502141401297494384261n", "66717953782642686044297384228n", "619071555217927229n", "11747815192199388258706152779n", "39655522309044272057593243434n", "2667518659266923661n", "74545987263802105943401974456n", "25100780504941704736052597181n", "1614091262172996678n", "61496830641585942728225636367n", "47520662928915336127912320093n", "1483128622047069223n", "60688370891239308805053347678n", "6154252422157238786881911133n", "1595810747040934713n", "4083087877564984515505707949n", "8098795933662806280871012387n", "392529588828430050n", "14388273410011291023320103380n", "59643003630595652724715495246n", "2978244255961784640n", "73005708620970672578538518429n", "64274822400727474231693975117n", "824761225328685267n", "58979395441344004425345087397n", "50034285490796369376342018474n", "1071577406066675668n", "37552244383550540565443579029n", "66651519402295869947385119697n", "1816081760201573675n", "48020280081371249748563352979n", "19387797072717949389382225132n", "1075380445499260082n", "0n", "0n", "0n", "0n", "0n", "0n", "35717919122505863182793101258n", "38321232967395819819318928199n", "33653293845735846n", "0n", "0n", "0n", "0n", "0n", "0n", "60126610212574038899502857656n", "7521540037295293717633716927n", "2853604986499631260n", "34n", "21051189327279847889561754607n", "15679397574132606210591767826n", "2165541175263187167n", "11461504713279098434997837844n", "29843864593792422920685859506n", "1460931496621397613n", "31444402670555100638844582863n", "41564870089383627374040254466n", "3317275169749288672n", "72559701040108110454251376272n", "22887416934578586124987839996n", "233686850646424299n", "51667851121405518271474152545n", "8297160697759020633045233343n", "2193876459774314419n", "50048470992987075597478354517n", "7622325433377464914372402739n", "2354852892440837544n", "51371930649223862037533589505n", "79037515700470610379424985426n", "3103776711054728122n", "62017664743365054011497714498n", "18400895627048394641412939651n", "1348549913115407530n", "68135824164391051249850625519n", "66467776056179325801077769907n", "21934170737946721n", "43733194692565917370190335652n", "20871497235942649279957719973n", "668366294714005293n", "69461224576101086641240237729n", "66163212446743341874016516713n", "2187872754580648643n", "17220145241406859216639481755n", "16637691490800642336304328427n", "699908274655976347n", "63497807423928467541336180608n", "5826616601935275548523889948n", "1995878641893268059n", "45351336804917798268705814434n", "32809386436253774870015191481n", "2479634507910679085n", "29902151727900563245652302915n", "70978449320724687288838934154n", "2324927884830925807n", "70956000718854853515484101425n", "18794223695576985859644098754n", "851712710373510834n", "10098225054790962506843798879n", "23663666343921865703011477995n", "2539135702270490911n", "13745949463631524266514217644n", "70097334773007528061348260208n", "1449740726324507950n", "77747255839650031066990598333n", "33186206179829484467075523327n", "3072781249488320507n", "73980383885811324159893986758n", "1765445723258696625718806089n", "2271055079390534326n", "65413433113844994807777190576n", "48033870016967321544035758027n", "486427727733872709n", "26974899297726311987406093631n", "5590641036960446176988521755n", "827510576486023036n", "29009837304935242599458620885n", "20410410399336048506493809410n", "1954580703151327584n", "64135814011222089868428198367n", "56261294792918650387740643327n", "1226348411176360117n", "71834179960057214052393522783n", "46252419010406289556729694820n", "1393685374555389118n", "71368042768790547323904986882n", "66161706759499128280107017373n", "2031846388120562115n", "21220965229609488481377288540n", "63634474338013450603335409627n", "821621475859559449n", "18432973800914453913616171088n", "8237366564750917100218776918n", "3448970319177548904n", "51266071561401723888120442902n", "33637427514172279767467204013n", "3304964589143840434n", "38819453582756888614388081676n", "38995523514738195349996597496n", "2323381859757397191n", "60884424754479179074928199128n", "3834764671648885586861880739n", "864611594127789300n", "9851774469429652901432809299n", "37101389540039872112071709899n", "2559626381308197564n", "406646090122284731360238690n", "44652954714826373590985929530n", "683398595921263332n", "20271182213679030346920227775n", "37600328594433178897257972399n", "432396126057182521n", "4187404064813213379278146332n", "44537571235199588707429377798n", "3148695479824963911n", "25801656964836714839982503508n", "51572074862943493111482365520n", "1230107506438930488n", "51625253538057090130489675612n", "11815326077763625426679125713n", "521507079758837629n", "9648925458348520397354094791n", "31712274845777377436963587786n", "1997027570431487029n", "67411860089204789431616372347n", "66528411456550554620624110152n", "186478859944874837n", "61267275259145597446660035124n", "8554664316600082912178209665n", "2375445434845419873n", "1589782365755830876261985911n", "14834270454057237025174127570n", "963005115183332390n", "23249702285165109375700438720n", "20760791667651963569657008881n", "2149068190029611973n", "74674158355316816901821060837n", "13278131002009659818927519878n", "992778641153509292n", "8743794935416188942200722720n", "51445266496970909016857135378n", "438732749332832318n", "64511635865187456937539832569n", "68455428209776466334096458368n", "1196547129512189429n", "16652864649326843859619189651n", "47031229552259361752165531n", "1977848333533964373n", "32230433718106499209616712783n", "50152042404552913889735459326n", "2647553318887157906n", "15558003702184603194095500825n", "75789384763919593972512743955n", "3199452366147221980n", "23639206276595496029173201731n", "49198122874004051169498469698n", "3017499313473475023n", "14633623354742611699704494011n", "13838793228838994907197164815n", "1865567661799564691n", "63554437295278917743885851002n", "43774994641723817700539915508n", "2096263880799998644n", "39241367224191359271532780985n", "11996031360599781980224407856n", "669587303349757211n", "70309465524306380398946854940n", "69691793870844727391235380992n", "1097884931999290463n", "4880550284873697839328338960n", "8683184578595981266384193421n", "1704353262400573542n", "43209925421984317108056960491n", "71838424302727061831479195619n", "1719485935656079288n", "20281500369447070817728689103n", "7827101470501627130702651299n", "1802787150264131673n", "46990609747636025825158033861n", "44506561326339289883265865893n", "168363193009253293n", "72644600526598920979602995563n", "23734595505295435652505772841n", "3066825941193215846n", "35922864395887621958431954121n", "36164080296393340386782836739n", "2806406594668460083n", "9559608083309233656821926408n", "21435397197883361901646100159n", "1173438743001539534n", "45502332725513884072895701183n", "21110593816020485943815437920n", "2156839344197406156n", "14935455230205682855615996549n", "3176509029633635649806564693n", "2744065159326778800n", "50144289937074876149408247339n", "73476828119785067069284584679n", "1137921320963525519n", "7764782370318985672713086089n", "35186333034809438599544173388n", "2599319187054853443n", "71090896326220687050059751719n", "7138127862158940765217036726n", "2525413991973636711n", "74465662641034900763924596241n", 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"0n", "31709724516548461033720090826n", "30157355094312078251107514164n", "2598882554441689462n", "0n", "340282366920938463467229529119593204504n", "2783209552014905048n", "340282366920938463475639663367112901035n", "340282366920938463466510485605024151680n" ] Output of encryptToDrandRoundAndGetCallData: 50 elements ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-cjs-tsc/src/examples.ts ================================================ import * as garaga from 'garaga'; export const proofBn254: { a: { x: bigint; y: bigint; curveId: number; }; b: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; c: { x: bigint; y: bigint; curveId: number; }; publicInputs: bigint[]; } = { a: { x: 19326975765597999023026309242851464618295625967876195641207265702903971944714n, y: 63835113064883221423828958902442994957834669122245713027012799265225733314n, curveId: garaga.CurveId.BN254 }, b: { x: [ 15926258242285065430281020483827261910589109953358642697562602626998569607754n, 15482775443177023962384497625528997151098293635727021527127534892096530509952n ], y: [ 10937776115245591292644949547008094885240742374542777857501160790374675834371n, 6691169928456984700056024515478772626466687376966760922939239504103847739755n ], curveId: garaga.CurveId.BN254 }, c: { x: 18548825552947889373136407684636046437705490810597995577018381312170231914454n, y: 9890815383090898074006770716054740281870916546141552254207684185588486179606n, curveId: garaga.CurveId.BN254 }, publicInputs: [ BigInt('0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474') ] } export const vkBn254: { alpha: { x: bigint; y: bigint; curveId: number; }; beta: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; gamma: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; delta: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; ic: { x: bigint; y: bigint; curveId: number; }[]; } = { alpha: { x: 6763126530687886999315782887200758703366235230289874831627658839515656330867n, y: 12297948670392550312636836114470404429657568989657927437959695771502446445179n, curveId: garaga.CurveId.BN254 }, beta: { x: [ 15362786867599176251482538547160991918100063526460909721657878971551583339657n, 3804423004921008809819632629079723167970572551072432396497601916259815496626n ], y: [ 21885719103633717693283841528133243510750001708857084897139570082577218850374n, 2076817281717432063622727433912740683541778328445173073030513609350245776784n ], curveId: garaga.CurveId.BN254 }, gamma: { x: [ 1505558511994093266228972967760414664043255115544025409518939393775943607863n, 21131173266568468249589649137903719095480044620502529067534622738225157042304n ], y: [ 4008759115482693545406793535591568078300615151288108694080317738431649117177n, 18835856718271757625037377080288624550370480296914695806777038708085497610013n ], curveId: garaga.CurveId.BN254 }, delta: { x: [ 1497911744463986566314308077983046202449361313910668647770797503379177516252n, 10829154948357654897792444316512827659620136273388886760324770466776134105520n ], y: [ 10850392992008761830625471778404650447428083833210258292805429019728339148884n, 12593805385728178657844996215584371401133999503150901444097670307277076679963n ], curveId: garaga.CurveId.BN254 }, ic: [ { x: 8279781786940010385190155571855963988492685408361021424114669994156938727612n, y: 14410809027374663415870055712464930833085570569392210261413081131467855918386n, curveId: garaga.CurveId.BN254 }, { x: 10075286447651977124250383403562829564641026794366918560412684031493085120161n, y: 13393494704849149158598989372790154670517815409968589728896053397011959461594n, curveId: garaga.CurveId.BN254 } ] } ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-cjs-tsc/src/index.ts ================================================ import * as garaga from 'garaga'; import { proofBn254, vkBn254 } from './examples'; async function main(): Promise { await garaga.init(); const result = garaga.msmCalldataBuilder([[1n, 2n]], [10n], garaga.CurveId.BN254); const json = JSON.stringify(result, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const message = 'Output of msm_calldata_builder: ' + json; console.log(message); const groth16Calldata = garaga.getGroth16CallData(proofBn254, vkBn254,garaga.CurveId.BN254); const jsonCalldata = JSON.stringify(groth16Calldata, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const messageCalldata = 'Output of get_groth16_calldata: ' + jsonCalldata; console.log(messageCalldata); // Tlock encrypt const message2 = new Uint8Array(16); message2.set(new TextEncoder().encode('Hello, world!')); const randomness = new Uint8Array(16); randomness.set(new TextEncoder().encode('fixed_random_val')); const tlockCalldata = garaga.encryptToDrandRoundAndGetCallData(1, message2, randomness); console.log('Output of encryptToDrandRoundAndGetCallData:', tlockCalldata.length, 'elements'); } main() .catch(console.error); ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-esm-tsc/.gitignore ================================================ /node_modules/ /dist/ ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-esm-tsc/output.txt ================================================ Output of msm_calldata_builder: [ "1n", "1n", "0n", "0n", "0n", "2n", "0n", "0n", "0n", "1n", "10n", "0n", "0n", "75759116906411131289250842036n", "1443316740970346987535705368n", "708088064087366360n", "0n", "31894839170900604627010243180n", "26562388390640533846098233871n", "1678682860455561629n", "0n", "340282366920938463463374607431768211466n", "0n", "1n", "0n" ] Output of get_groth16_calldata: [ "1935n", "561151868347580495583090954n", "76095163897123765080010407949n", "3078964875882710626n", "0n", "68760071548346057889257256130n", "33987009017980255890281589641n", "10169520226989098n", "0n", "27526525353537266686222475850n", "14475456397330869216192753448n", "2537199318039088506n", "0n", "21536768652854740401912377472n", "61033740543581523820282161323n", "2466548432040548587n", "0n", "49356715888972701601325049347n", "69887821523610458575318250963n", "1742488265497548861n", "0n", "68106177540828336088045306219n", "961134836681944563222599448n", "1065964868903753173n", "0n", "1800806384039658546158952406n", "44097612892395787951554989634n", "2954998394940821894n", "0n", "57407696252580182379957914390n", "68043785987214905719851221030n", "1575697798130653691n", "0n", "1n", "64622861075918021861446670503650833524n", "40000715384012656934033607729992139113n", "65343516826393976703500119419n", "64215924997604874724268545467n", "988361220710881918n", "30419768492628197858619568261n", "27248300164153194572764431995n", "2977039154666701832n", "65685384868591218376868464427n", "70847639348750339988496276918n", "477777041053646529n", "29991939756641252358878134746n", "39295947558852310211017126572n", "2815628384676858047n", "41723516601424502403187247204n", "17017221925427596342628818049n", "440483370607139100n", "10413180469465695361837522183n", "19423959337400646488247227266n", "1196856567711091031n", "14918739433528640782272739139n", "2386255189434407583576372032n", "2110030772171629820n", "66403863065153192042460667734n", "26490228722781507311620127895n", "1376925612093868452n", "16095686441528704658448370761n", "51022389018232154188872438326n", "1610491282614910455n", "37997039872158612927722452114n", "76461913933066610895201145075n", "951074374291802403n", "71303405408633411813876113602n", "65378028046199379258519780162n", "2796976393851271662n", "66043194162972766020432949924n", "72668519642029141849369643840n", "1767421250104456939n", "34724757470958269778491338738n", "67907574914053181941994051296n", "1074861315591297211n", "57811416502141401297494384261n", "66717953782642686044297384228n", "619071555217927229n", "11747815192199388258706152779n", "39655522309044272057593243434n", "2667518659266923661n", "74545987263802105943401974456n", "25100780504941704736052597181n", "1614091262172996678n", "61496830641585942728225636367n", "47520662928915336127912320093n", "1483128622047069223n", "60688370891239308805053347678n", "6154252422157238786881911133n", "1595810747040934713n", "4083087877564984515505707949n", "8098795933662806280871012387n", "392529588828430050n", "14388273410011291023320103380n", "59643003630595652724715495246n", "2978244255961784640n", "73005708620970672578538518429n", "64274822400727474231693975117n", "824761225328685267n", "58979395441344004425345087397n", "50034285490796369376342018474n", "1071577406066675668n", "37552244383550540565443579029n", "66651519402295869947385119697n", "1816081760201573675n", "48020280081371249748563352979n", "19387797072717949389382225132n", "1075380445499260082n", "0n", "0n", "0n", "0n", "0n", "0n", "35717919122505863182793101258n", "38321232967395819819318928199n", "33653293845735846n", "0n", "0n", "0n", "0n", "0n", "0n", "60126610212574038899502857656n", "7521540037295293717633716927n", "2853604986499631260n", "34n", "21051189327279847889561754607n", "15679397574132606210591767826n", "2165541175263187167n", "11461504713279098434997837844n", "29843864593792422920685859506n", "1460931496621397613n", "31444402670555100638844582863n", "41564870089383627374040254466n", "3317275169749288672n", "72559701040108110454251376272n", "22887416934578586124987839996n", "233686850646424299n", "51667851121405518271474152545n", "8297160697759020633045233343n", "2193876459774314419n", "50048470992987075597478354517n", "7622325433377464914372402739n", "2354852892440837544n", "51371930649223862037533589505n", "79037515700470610379424985426n", "3103776711054728122n", "62017664743365054011497714498n", "18400895627048394641412939651n", "1348549913115407530n", "68135824164391051249850625519n", "66467776056179325801077769907n", "21934170737946721n", "43733194692565917370190335652n", "20871497235942649279957719973n", "668366294714005293n", "69461224576101086641240237729n", "66163212446743341874016516713n", "2187872754580648643n", "17220145241406859216639481755n", "16637691490800642336304328427n", "699908274655976347n", "63497807423928467541336180608n", "5826616601935275548523889948n", "1995878641893268059n", "45351336804917798268705814434n", "32809386436253774870015191481n", "2479634507910679085n", "29902151727900563245652302915n", "70978449320724687288838934154n", "2324927884830925807n", "70956000718854853515484101425n", "18794223695576985859644098754n", "851712710373510834n", "10098225054790962506843798879n", "23663666343921865703011477995n", "2539135702270490911n", "13745949463631524266514217644n", "70097334773007528061348260208n", "1449740726324507950n", "77747255839650031066990598333n", "33186206179829484467075523327n", "3072781249488320507n", "73980383885811324159893986758n", "1765445723258696625718806089n", "2271055079390534326n", "65413433113844994807777190576n", "48033870016967321544035758027n", "486427727733872709n", "26974899297726311987406093631n", "5590641036960446176988521755n", "827510576486023036n", "29009837304935242599458620885n", "20410410399336048506493809410n", "1954580703151327584n", "64135814011222089868428198367n", "56261294792918650387740643327n", "1226348411176360117n", "71834179960057214052393522783n", "46252419010406289556729694820n", "1393685374555389118n", "71368042768790547323904986882n", "66161706759499128280107017373n", "2031846388120562115n", "21220965229609488481377288540n", "63634474338013450603335409627n", "821621475859559449n", "18432973800914453913616171088n", "8237366564750917100218776918n", "3448970319177548904n", "51266071561401723888120442902n", "33637427514172279767467204013n", "3304964589143840434n", "38819453582756888614388081676n", "38995523514738195349996597496n", "2323381859757397191n", "60884424754479179074928199128n", "3834764671648885586861880739n", "864611594127789300n", "9851774469429652901432809299n", "37101389540039872112071709899n", "2559626381308197564n", "406646090122284731360238690n", "44652954714826373590985929530n", "683398595921263332n", "20271182213679030346920227775n", "37600328594433178897257972399n", "432396126057182521n", "4187404064813213379278146332n", "44537571235199588707429377798n", "3148695479824963911n", "25801656964836714839982503508n", "51572074862943493111482365520n", "1230107506438930488n", "51625253538057090130489675612n", "11815326077763625426679125713n", "521507079758837629n", "9648925458348520397354094791n", "31712274845777377436963587786n", "1997027570431487029n", "67411860089204789431616372347n", "66528411456550554620624110152n", "186478859944874837n", "61267275259145597446660035124n", "8554664316600082912178209665n", "2375445434845419873n", "1589782365755830876261985911n", "14834270454057237025174127570n", "963005115183332390n", "23249702285165109375700438720n", "20760791667651963569657008881n", "2149068190029611973n", "74674158355316816901821060837n", "13278131002009659818927519878n", "992778641153509292n", "8743794935416188942200722720n", "51445266496970909016857135378n", "438732749332832318n", "64511635865187456937539832569n", "68455428209776466334096458368n", "1196547129512189429n", "16652864649326843859619189651n", "47031229552259361752165531n", "1977848333533964373n", "32230433718106499209616712783n", "50152042404552913889735459326n", "2647553318887157906n", "15558003702184603194095500825n", "75789384763919593972512743955n", "3199452366147221980n", "23639206276595496029173201731n", "49198122874004051169498469698n", "3017499313473475023n", "14633623354742611699704494011n", "13838793228838994907197164815n", "1865567661799564691n", "63554437295278917743885851002n", "43774994641723817700539915508n", "2096263880799998644n", "39241367224191359271532780985n", "11996031360599781980224407856n", "669587303349757211n", "70309465524306380398946854940n", "69691793870844727391235380992n", "1097884931999290463n", "4880550284873697839328338960n", "8683184578595981266384193421n", "1704353262400573542n", "43209925421984317108056960491n", "71838424302727061831479195619n", "1719485935656079288n", "20281500369447070817728689103n", "7827101470501627130702651299n", "1802787150264131673n", "46990609747636025825158033861n", "44506561326339289883265865893n", "168363193009253293n", "72644600526598920979602995563n", "23734595505295435652505772841n", "3066825941193215846n", "35922864395887621958431954121n", "36164080296393340386782836739n", "2806406594668460083n", "9559608083309233656821926408n", "21435397197883361901646100159n", "1173438743001539534n", "45502332725513884072895701183n", "21110593816020485943815437920n", "2156839344197406156n", 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"35486247734767358887659775332n", "63676560163395574209410974039n", "1346859065344137509n", "42626666034641293807810059734n", "78692725054674081196434522843n", "2899402626497036759n", "4466386979191688634974299793n", "73590084746022202502283403859n", "859759454707498102n", "49530047850904057997975767021157383838285524079350821991880424926644689941n", "12n", "73833755054290735615493473493n", "59827914949558952876927624612n", "1842769298355464193n", "0n", "31709724516548461033720090826n", "30157355094312078251107514164n", "2598882554441689462n", "0n", "340282366920938463467229529119593204504n", "2783209552014905048n", "340282366920938463475639663367112901035n", "340282366920938463466510485605024151680n" ] Output of encryptToDrandRoundAndGetCallData: 50 elements ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-esm-tsc/src/examples.ts ================================================ import * as garaga from 'garaga'; export const proofBn254: { a: { x: bigint; y: bigint; curveId: number; }; b: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; c: { x: bigint; y: bigint; curveId: number; }; publicInputs: bigint[]; } = { a: { x: 19326975765597999023026309242851464618295625967876195641207265702903971944714n, y: 63835113064883221423828958902442994957834669122245713027012799265225733314n, curveId: garaga.CurveId.BN254 }, b: { x: [ 15926258242285065430281020483827261910589109953358642697562602626998569607754n, 15482775443177023962384497625528997151098293635727021527127534892096530509952n ], y: [ 10937776115245591292644949547008094885240742374542777857501160790374675834371n, 6691169928456984700056024515478772626466687376966760922939239504103847739755n ], curveId: garaga.CurveId.BN254 }, c: { x: 18548825552947889373136407684636046437705490810597995577018381312170231914454n, y: 9890815383090898074006770716054740281870916546141552254207684185588486179606n, curveId: garaga.CurveId.BN254 }, publicInputs: [ BigInt('0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474') ] } export const vkBn254: { alpha: { x: bigint; y: bigint; curveId: number; }; beta: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; gamma: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; delta: { x: [bigint, bigint]; y: [bigint, bigint]; curveId: number; }; ic: { x: bigint; y: bigint; curveId: number; }[]; } = { alpha: { x: 6763126530687886999315782887200758703366235230289874831627658839515656330867n, y: 12297948670392550312636836114470404429657568989657927437959695771502446445179n, curveId: garaga.CurveId.BN254 }, beta: { x: [ 15362786867599176251482538547160991918100063526460909721657878971551583339657n, 3804423004921008809819632629079723167970572551072432396497601916259815496626n ], y: [ 21885719103633717693283841528133243510750001708857084897139570082577218850374n, 2076817281717432063622727433912740683541778328445173073030513609350245776784n ], curveId: garaga.CurveId.BN254 }, gamma: { x: [ 1505558511994093266228972967760414664043255115544025409518939393775943607863n, 21131173266568468249589649137903719095480044620502529067534622738225157042304n ], y: [ 4008759115482693545406793535591568078300615151288108694080317738431649117177n, 18835856718271757625037377080288624550370480296914695806777038708085497610013n ], curveId: garaga.CurveId.BN254 }, delta: { x: [ 1497911744463986566314308077983046202449361313910668647770797503379177516252n, 10829154948357654897792444316512827659620136273388886760324770466776134105520n ], y: [ 10850392992008761830625471778404650447428083833210258292805429019728339148884n, 12593805385728178657844996215584371401133999503150901444097670307277076679963n ], curveId: garaga.CurveId.BN254 }, ic: [ { x: 8279781786940010385190155571855963988492685408361021424114669994156938727612n, y: 14410809027374663415870055712464930833085570569392210261413081131467855918386n, curveId: garaga.CurveId.BN254 }, { x: 10075286447651977124250383403562829564641026794366918560412684031493085120161n, y: 13393494704849149158598989372790154670517815409968589728896053397011959461594n, curveId: garaga.CurveId.BN254 } ] } ================================================ FILE: tools/npm/integration-test-suite/packages/nodejs-ts-esm-tsc/src/index.ts ================================================ import * as garaga from 'garaga'; import { proofBn254, vkBn254 } from './examples.js'; async function main(): Promise { await garaga.init(); const result = garaga.msmCalldataBuilder([[1n, 2n]], [10n], garaga.CurveId.BN254); const json = JSON.stringify(result, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const message = 'Output of msm_calldata_builder: ' + json; console.log(message); const groth16Calldata = garaga.getGroth16CallData(proofBn254, vkBn254,garaga.CurveId.BN254); const jsonCalldata = JSON.stringify(groth16Calldata, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const messageCalldata = 'Output of get_groth16_calldata: ' + jsonCalldata; console.log(messageCalldata); // Tlock encrypt const message2 = new Uint8Array(16); message2.set(new TextEncoder().encode('Hello, world!')); const randomness = new Uint8Array(16); randomness.set(new TextEncoder().encode('fixed_random_val')); const tlockCalldata = garaga.encryptToDrandRoundAndGetCallData(1, message2, randomness); console.log('Output of encryptToDrandRoundAndGetCallData:', tlockCalldata.length, 'elements'); } main() .catch(console.error); ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/.gitignore ================================================ /node_modules/ /.next/ ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/next.config.mjs ================================================ /** @type {import('next').NextConfig} */ const nextConfig = {}; export default nextConfig; ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/output.txt ================================================ Output of msm_calldata_builder: [ "1n", "1n", "0n", "0n", "0n", "2n", "0n", "0n", "0n", "1n", "10n", "0n", "0n", "75759116906411131289250842036n", "1443316740970346987535705368n", "708088064087366360n", "0n", "31894839170900604627010243180n", "26562388390640533846098233871n", "1678682860455561629n", "0n", "340282366920938463463374607431768211466n", "0n", "1n", "0n" ] Output of get_groth16_calldata: [ "1935n", "561151868347580495583090954n", "76095163897123765080010407949n", "3078964875882710626n", "0n", "68760071548346057889257256130n", "33987009017980255890281589641n", "10169520226989098n", "0n", "27526525353537266686222475850n", "14475456397330869216192753448n", "2537199318039088506n", "0n", "21536768652854740401912377472n", "61033740543581523820282161323n", "2466548432040548587n", "0n", "49356715888972701601325049347n", "69887821523610458575318250963n", "1742488265497548861n", "0n", "68106177540828336088045306219n", "961134836681944563222599448n", "1065964868903753173n", "0n", "1800806384039658546158952406n", "44097612892395787951554989634n", "2954998394940821894n", "0n", "57407696252580182379957914390n", "68043785987214905719851221030n", "1575697798130653691n", "0n", "1n", "64622861075918021861446670503650833524n", "40000715384012656934033607729992139113n", "65343516826393976703500119419n", "64215924997604874724268545467n", "988361220710881918n", "30419768492628197858619568261n", "27248300164153194572764431995n", "2977039154666701832n", "65685384868591218376868464427n", "70847639348750339988496276918n", "477777041053646529n", "29991939756641252358878134746n", "39295947558852310211017126572n", "2815628384676858047n", "41723516601424502403187247204n", "17017221925427596342628818049n", "440483370607139100n", "10413180469465695361837522183n", "19423959337400646488247227266n", "1196856567711091031n", "14918739433528640782272739139n", "2386255189434407583576372032n", "2110030772171629820n", "66403863065153192042460667734n", "26490228722781507311620127895n", "1376925612093868452n", "16095686441528704658448370761n", "51022389018232154188872438326n", "1610491282614910455n", "37997039872158612927722452114n", "76461913933066610895201145075n", "951074374291802403n", "71303405408633411813876113602n", "65378028046199379258519780162n", "2796976393851271662n", "66043194162972766020432949924n", "72668519642029141849369643840n", "1767421250104456939n", "34724757470958269778491338738n", "67907574914053181941994051296n", "1074861315591297211n", "57811416502141401297494384261n", "66717953782642686044297384228n", "619071555217927229n", "11747815192199388258706152779n", "39655522309044272057593243434n", "2667518659266923661n", "74545987263802105943401974456n", "25100780504941704736052597181n", "1614091262172996678n", "61496830641585942728225636367n", "47520662928915336127912320093n", "1483128622047069223n", "60688370891239308805053347678n", "6154252422157238786881911133n", "1595810747040934713n", "4083087877564984515505707949n", "8098795933662806280871012387n", "392529588828430050n", "14388273410011291023320103380n", "59643003630595652724715495246n", "2978244255961784640n", "73005708620970672578538518429n", "64274822400727474231693975117n", "824761225328685267n", "58979395441344004425345087397n", "50034285490796369376342018474n", "1071577406066675668n", "37552244383550540565443579029n", "66651519402295869947385119697n", "1816081760201573675n", "48020280081371249748563352979n", "19387797072717949389382225132n", "1075380445499260082n", "0n", "0n", "0n", "0n", "0n", "0n", "35717919122505863182793101258n", "38321232967395819819318928199n", "33653293845735846n", "0n", "0n", "0n", "0n", "0n", "0n", "60126610212574038899502857656n", "7521540037295293717633716927n", "2853604986499631260n", "34n", "21051189327279847889561754607n", "15679397574132606210591767826n", "2165541175263187167n", "11461504713279098434997837844n", "29843864593792422920685859506n", "1460931496621397613n", "31444402670555100638844582863n", "41564870089383627374040254466n", "3317275169749288672n", "72559701040108110454251376272n", "22887416934578586124987839996n", "233686850646424299n", "51667851121405518271474152545n", "8297160697759020633045233343n", "2193876459774314419n", "50048470992987075597478354517n", "7622325433377464914372402739n", "2354852892440837544n", "51371930649223862037533589505n", "79037515700470610379424985426n", "3103776711054728122n", "62017664743365054011497714498n", "18400895627048394641412939651n", "1348549913115407530n", "68135824164391051249850625519n", "66467776056179325801077769907n", "21934170737946721n", "43733194692565917370190335652n", "20871497235942649279957719973n", "668366294714005293n", "69461224576101086641240237729n", "66163212446743341874016516713n", "2187872754580648643n", "17220145241406859216639481755n", "16637691490800642336304328427n", "699908274655976347n", "63497807423928467541336180608n", "5826616601935275548523889948n", "1995878641893268059n", "45351336804917798268705814434n", "32809386436253774870015191481n", "2479634507910679085n", "29902151727900563245652302915n", "70978449320724687288838934154n", "2324927884830925807n", "70956000718854853515484101425n", "18794223695576985859644098754n", "851712710373510834n", "10098225054790962506843798879n", "23663666343921865703011477995n", "2539135702270490911n", "13745949463631524266514217644n", "70097334773007528061348260208n", "1449740726324507950n", "77747255839650031066990598333n", "33186206179829484467075523327n", "3072781249488320507n", "73980383885811324159893986758n", "1765445723258696625718806089n", "2271055079390534326n", "65413433113844994807777190576n", "48033870016967321544035758027n", "486427727733872709n", "26974899297726311987406093631n", "5590641036960446176988521755n", "827510576486023036n", "29009837304935242599458620885n", "20410410399336048506493809410n", "1954580703151327584n", "64135814011222089868428198367n", "56261294792918650387740643327n", "1226348411176360117n", "71834179960057214052393522783n", "46252419010406289556729694820n", "1393685374555389118n", "71368042768790547323904986882n", "66161706759499128280107017373n", "2031846388120562115n", "21220965229609488481377288540n", "63634474338013450603335409627n", "821621475859559449n", "18432973800914453913616171088n", "8237366564750917100218776918n", "3448970319177548904n", "51266071561401723888120442902n", "33637427514172279767467204013n", "3304964589143840434n", "38819453582756888614388081676n", "38995523514738195349996597496n", "2323381859757397191n", "60884424754479179074928199128n", "3834764671648885586861880739n", "864611594127789300n", "9851774469429652901432809299n", "37101389540039872112071709899n", "2559626381308197564n", "406646090122284731360238690n", "44652954714826373590985929530n", "683398595921263332n", "20271182213679030346920227775n", "37600328594433178897257972399n", "432396126057182521n", "4187404064813213379278146332n", "44537571235199588707429377798n", "3148695479824963911n", "25801656964836714839982503508n", "51572074862943493111482365520n", "1230107506438930488n", "51625253538057090130489675612n", "11815326077763625426679125713n", "521507079758837629n", "9648925458348520397354094791n", "31712274845777377436963587786n", "1997027570431487029n", "67411860089204789431616372347n", "66528411456550554620624110152n", "186478859944874837n", "61267275259145597446660035124n", "8554664316600082912178209665n", "2375445434845419873n", "1589782365755830876261985911n", "14834270454057237025174127570n", "963005115183332390n", "23249702285165109375700438720n", "20760791667651963569657008881n", "2149068190029611973n", "74674158355316816901821060837n", "13278131002009659818927519878n", "992778641153509292n", "8743794935416188942200722720n", "51445266496970909016857135378n", "438732749332832318n", "64511635865187456937539832569n", "68455428209776466334096458368n", "1196547129512189429n", "16652864649326843859619189651n", "47031229552259361752165531n", "1977848333533964373n", "32230433718106499209616712783n", "50152042404552913889735459326n", "2647553318887157906n", "15558003702184603194095500825n", "75789384763919593972512743955n", "3199452366147221980n", "23639206276595496029173201731n", "49198122874004051169498469698n", "3017499313473475023n", "14633623354742611699704494011n", "13838793228838994907197164815n", "1865567661799564691n", "63554437295278917743885851002n", "43774994641723817700539915508n", "2096263880799998644n", "39241367224191359271532780985n", "11996031360599781980224407856n", "669587303349757211n", "70309465524306380398946854940n", "69691793870844727391235380992n", "1097884931999290463n", "4880550284873697839328338960n", "8683184578595981266384193421n", 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"40673401721781629455927974763n", "816921835574909421n", "41466998290124345097221160853n", "77602619970761915549134486486n", "2270380655319303423n", "37278580144182814004827303266n", "22631466550317400025567159166n", "1256554869446519681n", "44512857141401466618198683938n", "75645231533450873900978589761n", "2839895442152180859n", "31711543132209616307103122831n", "78955556053482715721582593706n", "626995298916699271n", "50496746606014163961365206592n", "62746915431247250243776212132n", "2682171950447987392n", "8649064541355918845604157106n", "3642459701627177804195047993n", "304942239933523054n", "52349349447437650280979204973n", "38235331305898406894352347179n", "574973155769907953n", "35486247734767358887659775332n", "63676560163395574209410974039n", "1346859065344137509n", "42626666034641293807810059734n", "78692725054674081196434522843n", "2899402626497036759n", "4466386979191688634974299793n", "73590084746022202502283403859n", "859759454707498102n", "49530047850904057997975767021157383838285524079350821991880424926644689941n", "12n", "73833755054290735615493473493n", "59827914949558952876927624612n", "1842769298355464193n", "0n", "31709724516548461033720090826n", "30157355094312078251107514164n", "2598882554441689462n", "0n", "340282366920938463467229529119593204504n", "2783209552014905048n", "340282366920938463475639663367112901035n", "340282366920938463466510485605024151680n" ] Output of encryptToDrandRoundAndGetCallData: 50 elements ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/scrape.cjs ================================================ const puppeteer = require('puppeteer'); async function loadWebContent(url) { const browser = await puppeteer.launch({ args: ['--no-sandbox'] }); const page = await browser.newPage(); await page.goto(url); await page.waitForSelector('body pre', { visible: true, timeout: 90000 }); const content = await page.evaluate(() => document.querySelector('body pre').innerHTML); await browser.close(); return content; } async function scrape() { const content = await loadWebContent('http://localhost:8080'); console.log(content); } scrape() .then(() => process.exit(0)) .catch((e) => process.exit((console.error(e), 1))); ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/src/app/examples.js ================================================ import * as garaga from 'garaga'; export const proofBn254 = { a: { x: 19326975765597999023026309242851464618295625967876195641207265702903971944714n, y: 63835113064883221423828958902442994957834669122245713027012799265225733314n, curveId: garaga.CurveId.BN254 }, b: { x: [ 15926258242285065430281020483827261910589109953358642697562602626998569607754n, 15482775443177023962384497625528997151098293635727021527127534892096530509952n ], y: [ 10937776115245591292644949547008094885240742374542777857501160790374675834371n, 6691169928456984700056024515478772626466687376966760922939239504103847739755n ], curveId: garaga.CurveId.BN254 }, c: { x: 18548825552947889373136407684636046437705490810597995577018381312170231914454n, y: 9890815383090898074006770716054740281870916546141552254207684185588486179606n, curveId: garaga.CurveId.BN254 }, publicInputs: [ BigInt('0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474') ] } export const vkBn254 = { alpha: { x: 6763126530687886999315782887200758703366235230289874831627658839515656330867n, y: 12297948670392550312636836114470404429657568989657927437959695771502446445179n, curveId: garaga.CurveId.BN254 }, beta: { x: [ 15362786867599176251482538547160991918100063526460909721657878971551583339657n, 3804423004921008809819632629079723167970572551072432396497601916259815496626n ], y: [ 21885719103633717693283841528133243510750001708857084897139570082577218850374n, 2076817281717432063622727433912740683541778328445173073030513609350245776784n ], curveId: garaga.CurveId.BN254 }, gamma: { x: [ 1505558511994093266228972967760414664043255115544025409518939393775943607863n, 21131173266568468249589649137903719095480044620502529067534622738225157042304n ], y: [ 4008759115482693545406793535591568078300615151288108694080317738431649117177n, 18835856718271757625037377080288624550370480296914695806777038708085497610013n ], curveId: garaga.CurveId.BN254 }, delta: { x: [ 1497911744463986566314308077983046202449361313910668647770797503379177516252n, 10829154948357654897792444316512827659620136273388886760324770466776134105520n ], y: [ 10850392992008761830625471778404650447428083833210258292805429019728339148884n, 12593805385728178657844996215584371401133999503150901444097670307277076679963n ], curveId: garaga.CurveId.BN254 }, ic: [ { x: 8279781786940010385190155571855963988492685408361021424114669994156938727612n, y: 14410809027374663415870055712464930833085570569392210261413081131467855918386n, curveId: garaga.CurveId.BN254 }, { x: 10075286447651977124250383403562829564641026794366918560412684031493085120161n, y: 13393494704849149158598989372790154670517815409968589728896053397011959461594n, curveId: garaga.CurveId.BN254 } ] } ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/src/app/layout.js ================================================ export const metadata = { title: "Create Next App", description: "Generated by create next app", }; export default function RootLayout({ children }) { return ( {children} ); } ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-react/src/app/page.js ================================================ 'use client'; import { useState, useEffect } from 'react'; import * as garaga from 'garaga'; import { proofBn254, vkBn254 } from './examples'; export default function Home() { const [loading, setLoading] = useState(true); const [data, setData] = useState(null); const [error, setError] = useState(null); useEffect(async () => { try { await garaga.init(); const result = garaga.msmCalldataBuilder([[1n, 2n]], [10n], garaga.CurveId.BN254); const json = JSON.stringify(result, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const message = 'Output of msm_calldata_builder: ' + json; let tmpData = message; const groth16Calldata = garaga.getGroth16CallData(proofBn254, vkBn254,garaga.CurveId.BN254); const jsonCalldata = JSON.stringify(groth16Calldata, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const messageCalldata = 'Output of get_groth16_calldata: ' + jsonCalldata; // Tlock encrypt const message2 = new Uint8Array(16); message2.set(new TextEncoder().encode('Hello, world!')); const randomness = new Uint8Array(16); randomness.set(new TextEncoder().encode('fixed_random_val')); const tlockCalldata = garaga.encryptToDrandRoundAndGetCallData(1, message2, randomness); const messageTlock = 'Output of encryptToDrandRoundAndGetCallData: ' + tlockCalldata.length + ' elements'; setData(tmpData + "\n" + messageCalldata + "\n" + messageTlock); } catch (e) { setError(String(e)); } finally { setLoading(false); } }, []); if (loading) { return
Loading...
; } if (error) { return
Error: {error}
; } return ( 
      {data}
); } ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/.gitignore ================================================ /node_modules/ /dist/ ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/output.txt ================================================ Output of msm_calldata_builder: [ "1n", "1n", "0n", "0n", "0n", "2n", "0n", "0n", "0n", "1n", "10n", "0n", "0n", "75759116906411131289250842036n", "1443316740970346987535705368n", "708088064087366360n", "0n", "31894839170900604627010243180n", "26562388390640533846098233871n", "1678682860455561629n", "0n", "340282366920938463463374607431768211466n", "0n", "1n", "0n" ] Output of get_groth16_calldata: [ "1935n", "561151868347580495583090954n", "76095163897123765080010407949n", "3078964875882710626n", "0n", "68760071548346057889257256130n", "33987009017980255890281589641n", "10169520226989098n", "0n", "27526525353537266686222475850n", "14475456397330869216192753448n", "2537199318039088506n", "0n", "21536768652854740401912377472n", "61033740543581523820282161323n", "2466548432040548587n", "0n", "49356715888972701601325049347n", "69887821523610458575318250963n", "1742488265497548861n", "0n", "68106177540828336088045306219n", "961134836681944563222599448n", "1065964868903753173n", "0n", "1800806384039658546158952406n", "44097612892395787951554989634n", "2954998394940821894n", "0n", "57407696252580182379957914390n", "68043785987214905719851221030n", "1575697798130653691n", "0n", "1n", "64622861075918021861446670503650833524n", "40000715384012656934033607729992139113n", "65343516826393976703500119419n", "64215924997604874724268545467n", "988361220710881918n", "30419768492628197858619568261n", "27248300164153194572764431995n", "2977039154666701832n", "65685384868591218376868464427n", "70847639348750339988496276918n", "477777041053646529n", "29991939756641252358878134746n", "39295947558852310211017126572n", "2815628384676858047n", "41723516601424502403187247204n", "17017221925427596342628818049n", "440483370607139100n", "10413180469465695361837522183n", "19423959337400646488247227266n", "1196856567711091031n", "14918739433528640782272739139n", "2386255189434407583576372032n", "2110030772171629820n", "66403863065153192042460667734n", "26490228722781507311620127895n", "1376925612093868452n", "16095686441528704658448370761n", "51022389018232154188872438326n", "1610491282614910455n", "37997039872158612927722452114n", "76461913933066610895201145075n", "951074374291802403n", "71303405408633411813876113602n", "65378028046199379258519780162n", "2796976393851271662n", "66043194162972766020432949924n", "72668519642029141849369643840n", "1767421250104456939n", "34724757470958269778491338738n", "67907574914053181941994051296n", "1074861315591297211n", "57811416502141401297494384261n", "66717953782642686044297384228n", "619071555217927229n", "11747815192199388258706152779n", "39655522309044272057593243434n", "2667518659266923661n", "74545987263802105943401974456n", "25100780504941704736052597181n", "1614091262172996678n", "61496830641585942728225636367n", "47520662928915336127912320093n", "1483128622047069223n", "60688370891239308805053347678n", "6154252422157238786881911133n", "1595810747040934713n", "4083087877564984515505707949n", "8098795933662806280871012387n", "392529588828430050n", "14388273410011291023320103380n", "59643003630595652724715495246n", "2978244255961784640n", "73005708620970672578538518429n", "64274822400727474231693975117n", "824761225328685267n", "58979395441344004425345087397n", "50034285490796369376342018474n", "1071577406066675668n", "37552244383550540565443579029n", "66651519402295869947385119697n", "1816081760201573675n", "48020280081371249748563352979n", "19387797072717949389382225132n", "1075380445499260082n", "0n", "0n", "0n", "0n", "0n", "0n", "35717919122505863182793101258n", "38321232967395819819318928199n", "33653293845735846n", "0n", "0n", "0n", "0n", "0n", "0n", "60126610212574038899502857656n", "7521540037295293717633716927n", "2853604986499631260n", "34n", "21051189327279847889561754607n", "15679397574132606210591767826n", "2165541175263187167n", "11461504713279098434997837844n", "29843864593792422920685859506n", "1460931496621397613n", "31444402670555100638844582863n", "41564870089383627374040254466n", "3317275169749288672n", "72559701040108110454251376272n", "22887416934578586124987839996n", "233686850646424299n", "51667851121405518271474152545n", "8297160697759020633045233343n", "2193876459774314419n", "50048470992987075597478354517n", "7622325433377464914372402739n", "2354852892440837544n", "51371930649223862037533589505n", "79037515700470610379424985426n", "3103776711054728122n", "62017664743365054011497714498n", "18400895627048394641412939651n", "1348549913115407530n", "68135824164391051249850625519n", "66467776056179325801077769907n", "21934170737946721n", "43733194692565917370190335652n", "20871497235942649279957719973n", "668366294714005293n", "69461224576101086641240237729n", "66163212446743341874016516713n", "2187872754580648643n", "17220145241406859216639481755n", "16637691490800642336304328427n", "699908274655976347n", "63497807423928467541336180608n", "5826616601935275548523889948n", "1995878641893268059n", "45351336804917798268705814434n", "32809386436253774870015191481n", "2479634507910679085n", "29902151727900563245652302915n", "70978449320724687288838934154n", "2324927884830925807n", "70956000718854853515484101425n", "18794223695576985859644098754n", "851712710373510834n", "10098225054790962506843798879n", "23663666343921865703011477995n", "2539135702270490911n", "13745949463631524266514217644n", "70097334773007528061348260208n", "1449740726324507950n", "77747255839650031066990598333n", "33186206179829484467075523327n", "3072781249488320507n", "73980383885811324159893986758n", "1765445723258696625718806089n", "2271055079390534326n", "65413433113844994807777190576n", "48033870016967321544035758027n", "486427727733872709n", "26974899297726311987406093631n", "5590641036960446176988521755n", "827510576486023036n", "29009837304935242599458620885n", "20410410399336048506493809410n", "1954580703151327584n", "64135814011222089868428198367n", "56261294792918650387740643327n", "1226348411176360117n", "71834179960057214052393522783n", "46252419010406289556729694820n", "1393685374555389118n", "71368042768790547323904986882n", "66161706759499128280107017373n", "2031846388120562115n", "21220965229609488481377288540n", "63634474338013450603335409627n", "821621475859559449n", "18432973800914453913616171088n", "8237366564750917100218776918n", "3448970319177548904n", "51266071561401723888120442902n", "33637427514172279767467204013n", "3304964589143840434n", "38819453582756888614388081676n", "38995523514738195349996597496n", "2323381859757397191n", "60884424754479179074928199128n", "3834764671648885586861880739n", "864611594127789300n", "9851774469429652901432809299n", "37101389540039872112071709899n", "2559626381308197564n", "406646090122284731360238690n", "44652954714826373590985929530n", "683398595921263332n", "20271182213679030346920227775n", "37600328594433178897257972399n", "432396126057182521n", "4187404064813213379278146332n", "44537571235199588707429377798n", "3148695479824963911n", "25801656964836714839982503508n", "51572074862943493111482365520n", "1230107506438930488n", "51625253538057090130489675612n", "11815326077763625426679125713n", "521507079758837629n", "9648925458348520397354094791n", "31712274845777377436963587786n", "1997027570431487029n", "67411860089204789431616372347n", "66528411456550554620624110152n", "186478859944874837n", "61267275259145597446660035124n", "8554664316600082912178209665n", "2375445434845419873n", "1589782365755830876261985911n", "14834270454057237025174127570n", "963005115183332390n", 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"23895248556901354081433241434n", "16615401776547671346915841714n", "3136707560354543978n", "21834987311199156124647763244n", "70345068331037455105782146634n", "3216348569578182800n", "14552026033494402774981149080n", "46810169065384954077118190274n", "1911480149318741295n", "30149592931357591699950156644n", "14166482924045038689605819053n", "2327000634007357378n", "38247650175016523126038806200n", "57691234003597921786155373117n", "859973345968241198n", "71714837789763600565992214961n", "73412375228179646879012079459n", "1974246974270865632n", "52446930245349056255719340345n", "970285520444299081223312008n", "1628797543941019300n", "50919498183802806944452291286n", "37490783833480294299979274400n", "2991807516764641990n", "32377691154331801475818794360n", "39750977600721907402675106371n", "2263832844069227231n", "17627606237803241511589218465n", "3828538907962341287451709925n", "1651077712155795619n", "65746494371320988039239195368n", "40429923959132850189737190904n", "1761591307449813117n", "62030904653045818611809336637n", "31416196507873606617755041492n", "1626933121429044990n", "56278396859095728868031718464n", "40673401721781629455927974763n", "816921835574909421n", "41466998290124345097221160853n", "77602619970761915549134486486n", "2270380655319303423n", "37278580144182814004827303266n", "22631466550317400025567159166n", "1256554869446519681n", "44512857141401466618198683938n", "75645231533450873900978589761n", "2839895442152180859n", "31711543132209616307103122831n", "78955556053482715721582593706n", "626995298916699271n", "50496746606014163961365206592n", "62746915431247250243776212132n", "2682171950447987392n", "8649064541355918845604157106n", "3642459701627177804195047993n", "304942239933523054n", "52349349447437650280979204973n", "38235331305898406894352347179n", "574973155769907953n", "35486247734767358887659775332n", "63676560163395574209410974039n", "1346859065344137509n", "42626666034641293807810059734n", "78692725054674081196434522843n", "2899402626497036759n", "4466386979191688634974299793n", "73590084746022202502283403859n", "859759454707498102n", "49530047850904057997975767021157383838285524079350821991880424926644689941n", "12n", "73833755054290735615493473493n", "59827914949558952876927624612n", "1842769298355464193n", "0n", "31709724516548461033720090826n", "30157355094312078251107514164n", "2598882554441689462n", "0n", "340282366920938463467229529119593204504n", "2783209552014905048n", "340282366920938463475639663367112901035n", "340282366920938463466510485605024151680n" ] Output of encryptToDrandRoundAndGetCallData: 50 elements ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/scrape.cjs ================================================ const puppeteer = require('puppeteer'); async function loadWebContent(url) { const browser = await puppeteer.launch({ args: ['--no-sandbox'] }); const page = await browser.newPage(); await page.goto(url); await page.waitForSelector('body pre', { visible: true, timeout: 90000 }); const content = await page.evaluate(() => document.querySelector('body pre').innerHTML); await browser.close(); return content; } async function scrape() { const content = await loadWebContent('http://localhost:8080'); console.log(content); } scrape() .then(() => process.exit(0)) .catch((e) => process.exit((console.error(e), 1))); ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/src/bootstrap.js ================================================ // A dependency graph that contains any wasm must all be imported // asynchronously. This `bootstrap.js` file does the single async import, so // that no one else needs to worry about it again. import('./index.js') .catch((e) => console.error('Error importing "index.js":', e)); ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/src/examples.js ================================================ import * as garaga from 'garaga'; export const proofBn254 = { a: { x: 19326975765597999023026309242851464618295625967876195641207265702903971944714n, y: 63835113064883221423828958902442994957834669122245713027012799265225733314n, curveId: garaga.CurveId.BN254 }, b: { x: [ 15926258242285065430281020483827261910589109953358642697562602626998569607754n, 15482775443177023962384497625528997151098293635727021527127534892096530509952n ], y: [ 10937776115245591292644949547008094885240742374542777857501160790374675834371n, 6691169928456984700056024515478772626466687376966760922939239504103847739755n ], curveId: garaga.CurveId.BN254 }, c: { x: 18548825552947889373136407684636046437705490810597995577018381312170231914454n, y: 9890815383090898074006770716054740281870916546141552254207684185588486179606n, curveId: garaga.CurveId.BN254 }, publicInputs: [ BigInt('0x1e17db88c1d2e83e49f692cce4bb8169309de90afb2b141156243106aa34b474') ] } export const vkBn254 = { alpha: { x: 6763126530687886999315782887200758703366235230289874831627658839515656330867n, y: 12297948670392550312636836114470404429657568989657927437959695771502446445179n, curveId: garaga.CurveId.BN254 }, beta: { x: [ 15362786867599176251482538547160991918100063526460909721657878971551583339657n, 3804423004921008809819632629079723167970572551072432396497601916259815496626n ], y: [ 21885719103633717693283841528133243510750001708857084897139570082577218850374n, 2076817281717432063622727433912740683541778328445173073030513609350245776784n ], curveId: garaga.CurveId.BN254 }, gamma: { x: [ 1505558511994093266228972967760414664043255115544025409518939393775943607863n, 21131173266568468249589649137903719095480044620502529067534622738225157042304n ], y: [ 4008759115482693545406793535591568078300615151288108694080317738431649117177n, 18835856718271757625037377080288624550370480296914695806777038708085497610013n ], curveId: garaga.CurveId.BN254 }, delta: { x: [ 1497911744463986566314308077983046202449361313910668647770797503379177516252n, 10829154948357654897792444316512827659620136273388886760324770466776134105520n ], y: [ 10850392992008761830625471778404650447428083833210258292805429019728339148884n, 12593805385728178657844996215584371401133999503150901444097670307277076679963n ], curveId: garaga.CurveId.BN254 }, ic: [ { x: 8279781786940010385190155571855963988492685408361021424114669994156938727612n, y: 14410809027374663415870055712464930833085570569392210261413081131467855918386n, curveId: garaga.CurveId.BN254 }, { x: 10075286447651977124250383403562829564641026794366918560412684031493085120161n, y: 13393494704849149158598989372790154670517815409968589728896053397011959461594n, curveId: garaga.CurveId.BN254 } ] } ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/src/index.js ================================================ import * as garaga from 'garaga'; import { proofBn254, vkBn254 } from './examples'; async function main() { await garaga.init(); const result = garaga.msmCalldataBuilder([[1n, 2n]], [10n], garaga.CurveId.BN254); const json = JSON.stringify(result, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const message = 'Output of msm_calldata_builder: ' + json; const element = document.createElement('pre'); element.textContent = message; const groth16Calldata = garaga.getGroth16CallData(proofBn254, vkBn254,garaga.CurveId.BN254); const jsonCalldata = JSON.stringify(groth16Calldata, (key, value) => typeof value === 'bigint' ? value + 'n' : value, 2); const messageCalldata = 'Output of get_groth16_calldata: ' + jsonCalldata; element.textContent += "\n" + messageCalldata; // Tlock encrypt const message2 = new Uint8Array(16); message2.set(new TextEncoder().encode('Hello, world!')); const randomness = new Uint8Array(16); randomness.set(new TextEncoder().encode('fixed_random_val')); const tlockCalldata = garaga.encryptToDrandRoundAndGetCallData(1, message2, randomness); element.textContent += "\n" + 'Output of encryptToDrandRoundAndGetCallData: ' + tlockCalldata.length + ' elements'; document.body.appendChild(element); } main() .catch(console.error); ================================================ FILE: tools/npm/integration-test-suite/packages/web-js-esm-webpack/webpack.config.js ================================================ const path = require('path'); const CopyPlugin = require('copy-webpack-plugin'); module.exports = { entry: './src/bootstrap.js', output: { path: path.resolve(__dirname, 'dist'), filename: 'bootstrap.js', }, mode: 'production', resolve: { fallback: { "crypto": require.resolve("crypto-browserify"), "stream": require.resolve("stream-browserify"), "vm": require.resolve("vm-browserify"), "fs": false } }, performance: { maxAssetSize: 4 * 1024 * 1024, // 4MB to avoid warning }, plugins: [ new CopyPlugin({ patterns: ['./public/index.html'] }), ], }; ================================================ FILE: tools/process_manager.py ================================================ import os import signal import subprocess import threading from contextlib import contextmanager from typing import List class ProcessManager: """Smart process manager with interrupt handling and cleanup.""" def __init__(self): self.processes: List[subprocess.Popen] = [] self.shutdown_event = threading.Event() self.original_signal_handler = None self.main_process_group = None self.is_main_thread = threading.current_thread() is threading.main_thread() def __enter__(self): # Store the main process group (don't change it) self.main_process_group = os.getpgrp() # Only install signal handler in main thread if self.is_main_thread: try: self.original_signal_handler = signal.signal( signal.SIGINT, self._signal_handler ) except ValueError: # Signal operations not supported in this context, continue without signal handling self.is_main_thread = False return self def __exit__(self, exc_type, exc_val, exc_tb): self.cleanup() def _signal_handler(self, signum, frame): """Enhanced signal handler that kills all processes.""" from rich.console import Console console = Console() console.print( "\n🛑 [bold red]Interrupt received - terminating all processes[/bold red]" ) self.shutdown_event.set() self.cleanup() # Re-raise KeyboardInterrupt to properly exit raise KeyboardInterrupt("Process terminated by user") def cleanup(self): """Kill all tracked processes (but not the main process group).""" # Kill individual tracked processes more aggressively for proc in self.processes: try: if proc.poll() is None: # Still running proc.terminate() try: proc.wait(timeout=0.5) # Reduced timeout except subprocess.TimeoutExpired: proc.kill() try: proc.wait(timeout=0.5) # Reduced timeout for kill except subprocess.TimeoutExpired: pass # Process is stuck, move on except Exception: try: proc.kill() except Exception: pass # Clear the process list self.processes.clear() # Restore original handler only if we set it up in main thread if self.is_main_thread and self.original_signal_handler: try: signal.signal(signal.SIGINT, self.original_signal_handler) except ValueError: # Signal operations not supported, ignore pass def run_subprocess( self, cmd: List[str], timeout: int = 900, check: bool = False, capture_output: bool = False, text: bool = False, **kwargs, ) -> subprocess.CompletedProcess: """Run subprocess with timeout and interrupt handling.""" if self.shutdown_event.is_set(): raise KeyboardInterrupt("Shutdown requested") # Handle capture_output parameter (convert to stdout/stderr settings) if capture_output: if "stdout" in kwargs or "stderr" in kwargs: raise ValueError( "capture_output cannot be used with stdout or stderr arguments" ) kwargs["stdout"] = subprocess.PIPE kwargs["stderr"] = subprocess.PIPE # Handle text parameter if text: kwargs["text"] = True # Only set up process groups on Unix-like systems and when not already specified import sys if sys.platform != "win32" and "preexec_fn" not in kwargs: try: kwargs["start_new_session"] = True except Exception: # If start_new_session fails, don't use it pass proc = subprocess.Popen(cmd, **kwargs) self.processes.append(proc) try: stdout, stderr = proc.communicate(timeout=timeout) completed_process = subprocess.CompletedProcess( cmd, proc.returncode, stdout, stderr ) # Handle 'check' parameter like subprocess.run if check and proc.returncode != 0: raise subprocess.CalledProcessError( proc.returncode, cmd, stdout, stderr ) return completed_process except subprocess.TimeoutExpired: proc.kill() proc.wait() # Clean up zombie raise except KeyboardInterrupt: proc.kill() proc.wait() # Clean up zombie raise finally: # Remove from tracking list when done if proc in self.processes: self.processes.remove(proc) @contextmanager def managed_subprocess(): """Context manager for subprocess calls with interrupt handling.""" with ProcessManager() as pm: def run_cmd(cmd, **kwargs): return pm.run_subprocess(cmd, **kwargs) yield run_cmd, pm ================================================ FILE: tools/profile_tests.py ================================================ #!/usr/bin/env python3 """ Garaga Test Profiling Tool This script automates the process of running snforge tests with trace data collection, generating individual profile data using cairo-profiler, creating performance visualizations using pprof, and organizing the results. Usage: python tools/profile_tests.py [test_name_filter] python tools/profile_tests.py --all Examples: python tools/profile_tests.py msm_BN254_1P # Run specific test python tools/profile_tests.py --all # Run all tests python tools/profile_tests.py # Run all tests (same as --all) """ import argparse import json import os import re import subprocess import sys from abc import ABC, abstractmethod from collections import defaultdict from concurrent.futures import ThreadPoolExecutor from dataclasses import dataclass, field from datetime import datetime from functools import wraps from pathlib import Path from typing import Dict, List, Optional, Tuple import pandas as pd from rich.align import Align from rich.console import Console from rich.panel import Panel from rich.progress import ( BarColumn, Progress, SpinnerColumn, TaskProgressColumn, TextColumn, TimeElapsedColumn, TimeRemainingColumn, ) from rich.text import Text from tabulate import tabulate from tools.process_manager import ProcessManager, managed_subprocess # Global state console = Console() # Configuration & Constants @dataclass class Config: """Consolidated configuration for the profiling tool.""" contracts: List[str] = field( default_factory=lambda: [ "autogenerated/groth16_example_bn254", "autogenerated/groth16_example_bls12_381", "autogenerated/risc0_verifier_bn254", "autogenerated/sp1_verifier_bn254", "autogenerated/noir_ultra_keccak_honk_example", "autogenerated/noir_ultra_keccak_zk_honk_example", "autogenerated/noir_ultra_starknet_honk_example", "autogenerated/noir_ultra_starknet_zk_honk_example", ] ) excluded_profile_samples: set = field( default_factory=lambda: {"memory holes", "casm size", "calls"} ) sierra_gas_weights: Dict[str, int] = field( default_factory=lambda: { "steps": 100, "range_check": 70, "range_check96": 56, "keccak": 136189, "pedersen": 4050, "bitwise": 583, "ecop": 4085, "poseidon": 491, "add_mod": 230, "mul_mod": 604, } ) @dataclass class Paths: """Path management with validation.""" workspace_root: Path def __post_init__(self): self.src_dir = self.workspace_root / "src" self.trace_dir = self.src_dir / "snfoundry_trace" self.docs_benchmarks = self.workspace_root / "docs" / "benchmarks" self.readme = self.workspace_root / "README.md" def ensure_dirs(self): """Ensure necessary directories exist.""" self.docs_benchmarks.mkdir(parents=True, exist_ok=True) # Logging & UI class Logger: """Centralized logging with decorators and context management.""" STYLES = { "info": ("ℹ️", "[dim]{message}[/dim]"), "success": ("✅", "[green]{message}[/green]"), "warning": ("⚠️", "[yellow]{message}[/yellow]"), "error": ("❌", "[bold red]{message}[/bold red]"), "debug": ("🔍", "[dim cyan]{message}[/dim cyan]"), } @staticmethod def log(message: str, level: str = "info", emoji: str = None): """Consolidated logging function.""" if level == "debug" and not console.is_terminal: return emoji_char, style_template = Logger.STYLES.get(level, Logger.STYLES["info"]) if emoji: emoji_char = emoji formatted_message = style_template.format(message=message) console.print(f"{emoji_char} {formatted_message}") @staticmethod def header(title: str): """Print formatted header.""" console.print( Panel( Align.center(Text(title, style="bold cyan")), border_style="cyan", padding=(0, 1), width=80, ) ) @staticmethod def exit_panel(message: str, status: str, border_style: str = "green"): """Show standardized exit panel.""" console.print( Panel( Align.center(message), border_style=border_style, title=f"[{border_style}]{status}[/{border_style}]", ) ) def handle_errors(func): """Decorator for centralized error handling - only for non-critical functions.""" @wraps(func) def wrapper(*args, **kwargs): try: return func(*args, **kwargs) except Exception as e: Logger.log(f"Error in {func.__name__}: {e}", level="error") return False return wrapper def fail_on_error(func): """Decorator that prints errors and exits immediately.""" @wraps(func) def wrapper(*args, **kwargs): try: return func(*args, **kwargs) except Exception as e: import traceback Logger.log(f"FATAL ERROR in {func.__name__}: {e}", level="error") Logger.log(f"Full traceback:\n{traceback.format_exc()}", level="error") Logger.exit_panel(f"💥 Fatal error in {func.__name__}: {e}", "Error", "red") sys.exit(1) return wrapper def log_step(description: str): """Decorator for logging method execution steps.""" def decorator(func): @wraps(func) def wrapper(*args, **kwargs): Logger.log(f"Starting: {description}", level="info") result = func(*args, **kwargs) Logger.log(f"Completed: {description}", level="success") return result return wrapper return decorator class UIBuilder: """Builder for console UI elements.""" @staticmethod def progress(advanced: bool = False) -> Progress: """Create progress bar.""" base_elements = [ SpinnerColumn(), TextColumn("[progress.description]{task.description}"), ] if advanced: return Progress( *base_elements, BarColumn(bar_width=40, style="cyan", complete_style="green"), "[progress.percentage]{task.percentage:>3.0f}%", "•", TextColumn("({task.completed}/{task.total} files)"), "•", TimeElapsedColumn(), "•", TimeRemainingColumn(), console=console, transient=False, ) return Progress( *base_elements, BarColumn(bar_width=30, style="cyan", complete_style="green"), TaskProgressColumn(), "•", TimeElapsedColumn(), "•", TimeRemainingColumn(), console=console, transient=False, ) # Enhanced TestResourceInfo @dataclass class TestResourceInfo: """Container for test resource information with enhanced methods.""" test_name_hierarchical: str test_name_simple: str steps: int builtins: dict = field(default_factory=dict) image_path: str = "" category: str = "garaga" sierra_gas: int = field(init=False) def __post_init__(self): self.sierra_gas = self._calculate_sierra_gas() if self.category == "garaga" and "::" in self.test_name_hierarchical: if not self.test_name_hierarchical.startswith("garaga::"): self.category = "contracts" @classmethod def from_trace_file( cls, test_name: str, trace_path: Path, profile_path: Path, resources: dict, image_path: str = "", ): """Create instance from trace file data.""" steps = resources.get("steps", 0) builtins = {k: v for k, v in resources.items() if k != "steps"} test_name_simple = test_name.split("::")[-1] return cls( test_name_hierarchical=test_name, test_name_simple=test_name_simple, steps=steps, builtins=builtins, image_path=image_path, category="contracts" if not test_name.startswith("garaga::") else "garaga", ) @staticmethod def predict_trace_path(test_name: str, base_dir: Path) -> Path: """Predict trace file path from hierarchical test name.""" return base_dir / f"{test_name.replace('::', '_')}.json" @staticmethod def extract_hierarchy_parts(test_name: str) -> List[str]: """Extract module hierarchy parts.""" parts = test_name.split("::") if parts and parts[-1].startswith("test_"): parts = parts[:-1] if parts and parts[0] == "garaga": parts = parts[1:] return parts if parts else ["tests"] def _calculate_sierra_gas(self) -> int: """Calculate Sierra gas using weight table.""" config = Config() total = self.steps * config.sierra_gas_weights["steps"] for builtin, count in self.builtins.items(): if builtin in config.sierra_gas_weights: total += count * config.sierra_gas_weights[builtin] return total def to_benchmark_row(self) -> dict: """Convert to benchmark row format.""" result = { "test_name_hierarchical": self.test_name_hierarchical, "test_name": self.test_name_simple, "steps": self.steps, "sierra_gas": self.sierra_gas, "image_path": self.image_path, "category": self.category, } # Add builtin columns config = Config() for builtin in config.sierra_gas_weights.keys(): if builtin != "steps": result[builtin] = self.builtins.get(builtin, 0) return result # Data Processing class JsonManager: """Utility class for JSON operations with context management.""" @staticmethod @handle_errors def read(file_path: Path, default=None): """Read JSON file with error handling.""" if not file_path.exists(): return default if default is not None else {} with open(file_path, "r") as f: return json.load(f) @staticmethod @handle_errors def write(file_path: Path, data, indent: int = 2) -> bool: """Write JSON file with error handling.""" with open(file_path, "w") as f: json.dump(data, f, indent=indent) return True class TraceProcessor: """Strategy for processing trace files.""" def __init__(self, config: Config): self.config = config self.sample_mapping = { "steps": "steps", "range check builtin": "range_check", "range check96 builtin": "range_check96", "keccak builtin": "keccak", "pedersen builtin": "pedersen", "bitwise builtin": "bitwise", "ecop builtin": "ecop", "poseidon builtin": "poseidon", "add mod builtin": "add_mod", "mul mod builtin": "mul_mod", } def process( self, test_name: str, trace_path: Path ) -> Tuple[bool, str, str, Optional[TestResourceInfo]]: """Process a single trace file.""" try: with managed_subprocess() as (run_cmd, pm): profile_file = self._generate_profile(trace_path, run_cmd) if not profile_file or not profile_file.exists(): Logger.log( f"Profile file not generated for {test_name}: {trace_path}", level="warning", ) return False, test_name, "", None resources = self._extract_resources(profile_file, run_cmd) test_name_simple = test_name.split("::")[-1] docs_image_path = ( Paths(Path.cwd()).docs_benchmarks / f"{test_name_simple}.png" ) image_success = self._generate_image( profile_file, docs_image_path, run_cmd ) test_info = TestResourceInfo.from_trace_file( test_name, trace_path, profile_file, resources, f"docs/benchmarks/{test_name_simple}.png", ) return image_success, test_name, test_info.image_path, test_info except Exception as e: import traceback # Re-raise with more context including full traceback full_tb = traceback.format_exc() raise Exception( f"Failed to process {test_name}:\nTrace path: {trace_path}\nError: {str(e)}\nTraceback:\n{full_tb}" ) from e def _generate_profile(self, trace_file: Path, run_cmd) -> Optional[Path]: """Generate profile from trace file.""" profile_file = trace_file.parent / f"{trace_file.stem}.pb.gz" cmd = [ "cairo-profiler", "build-profile", str(trace_file), "--output-path", str(profile_file), ] result = run_cmd( cmd, check=False, # Don't raise, we'll handle the error ourselves capture_output=True, text=True, ) if result.returncode != 0: error_msg = f"cairo-profiler build-profile failed:\nCommand: {' '.join(cmd)}\nReturn code: {result.returncode}" if result.stdout: error_msg += f"\nSTDOUT:\n{result.stdout}" if result.stderr: error_msg += f"\nSTDERR:\n{result.stderr}" raise Exception(error_msg) return profile_file def _extract_resources(self, profile_file: Path, run_cmd) -> dict: """Extract resources from profile file.""" cmd = ["cairo-profiler", "view", str(profile_file), "--list-samples"] result = run_cmd( cmd, check=False, # Don't raise, we'll handle the error ourselves capture_output=True, text=True, ) if result.returncode != 0: error_msg = f"cairo-profiler view --list-samples failed:\nCommand: {' '.join(cmd)}\nReturn code: {result.returncode}" if result.stdout: error_msg += f"\nSTDOUT:\n{result.stdout}" if result.stderr: error_msg += f"\nSTDERR:\n{result.stderr}" raise Exception(error_msg) samples = [ line.strip() for line in result.stdout.strip().split("\n") if line.strip() and line.strip() not in self.config.excluded_profile_samples ] resources = {} for sample in samples: try: sample_result = run_cmd( ["cairo-profiler", "view", str(profile_file), "--sample", sample], check=True, capture_output=True, text=True, ) # Updated regex to handle the new cairo-profiler output format # Example: "Showing nodes accounting for 11582 steps, 94.63% of 12239 steps total" pattern = rf"(\d+) {re.escape(sample)} total" match = re.search(pattern, sample_result.stdout, re.IGNORECASE) if match: count = int(match.group(1)) normalized = self.sample_mapping.get(sample.lower().strip()) if normalized: resources[normalized] = count except subprocess.CalledProcessError as e: # Log individual sample errors but continue Logger.log(f"Failed to extract sample '{sample}': {e}", level="warning") continue return resources def _generate_image(self, profile_file: Path, output_path: Path, run_cmd) -> bool: """Generate PNG image using pprof.""" cmd = [ "go", "tool", "pprof", "-png", "-sample_index=steps", "-output", str(output_path), str(profile_file), ] result = run_cmd( cmd, check=False, # Don't raise, we'll handle the error ourselves capture_output=True, text=True, ) if result.returncode != 0: error_msg = f"pprof failed:\nCommand: {' '.join(cmd)}\nReturn code: {result.returncode}" if result.stdout: error_msg += f"\nSTDOUT:\n{result.stdout}" if result.stderr: error_msg += f"\nSTDERR:\n{result.stderr}" raise Exception(error_msg) return True # Command Pattern Implementation class Command(ABC): """Abstract base class for commands.""" @abstractmethod def execute(self) -> bool: """Execute the command.""" @abstractmethod def can_execute(self) -> bool: """Check if command can be executed.""" class CheckDependenciesCommand(Command): """Command to check tool dependencies.""" def __init__(self, config: Config): self.config = config self.tools = [ ("snforge", "Starknet Foundry", ["snforge", "--version"]), ("cairo-profiler", "cairo-profiler", ["cairo-profiler", "--version"]), ("go", "Go to use pprof", ["go", "version"]), ] @log_step("Checking Dependencies") @handle_errors def execute(self) -> bool: Logger.header("🔍 Checking Dependencies") with managed_subprocess() as (run_cmd, pm): for tool, desc, cmd in self.tools: try: result = run_cmd(cmd, check=True, capture_output=True, text=True) Logger.log(f"{tool}: {result.stdout.strip()}", level="success") except subprocess.CalledProcessError: Logger.log( f"{tool} not found. Please install {desc}.", level="error" ) return False Logger.log("All dependencies satisfied!", level="success") return True def can_execute(self) -> bool: return True class RunTestsCommand(Command): """Command to run tests with trace collection.""" def __init__(self, paths: Paths, test_filter: Optional[str] = None): self.paths = paths self.test_filter = test_filter self.passed_tests = [] @log_step("Running Tests & Collecting Traces") @handle_errors def execute(self) -> bool: Logger.header("🧪 Running Tests & Collecting Traces") original_cwd = os.getcwd() cmd = ["snforge", "test"] if self.test_filter: cmd.append(self.test_filter) cmd.append("--save-trace-data") test_dirs = [self.paths.src_dir] + self._get_contract_paths() success_count = 0 with managed_subprocess() as (run_cmd, pm): with UIBuilder.progress() as progress: # Create a single task outside the loop base_desc = ( f"Running tests matching: {self.test_filter}" if self.test_filter else "Running all tests" ) task = progress.add_task(base_desc, total=len(test_dirs)) for i, test_dir in enumerate(test_dirs): # Update the description for the current directory current_desc = f"{base_desc} from {test_dir.relative_to(self.paths.workspace_root)}" progress.update(task, description=current_desc) if not test_dir.exists() or not (test_dir / "Scarb.toml").exists(): Logger.log( f"Skipping {test_dir}: directory or Scarb.toml not found", level="debug", ) continue os.chdir(test_dir) Logger.log( f"Running command: {' '.join(cmd)} in {test_dir}", level="debug" ) result = run_cmd(cmd, capture_output=True, text=True) if result.returncode == 0: success_count += 1 passed = re.findall( r"\[PASS\]\s+([^\s]+)\s+\(l1_gas:", result.stdout ) self.passed_tests.extend(passed) Logger.log( f"Found {len(passed)} passed tests in {test_dir.name}", level="debug", ) else: error_details = [] error_details.append(f"Directory: {test_dir}") error_details.append(f"Command: {' '.join(cmd)}") error_details.append(f"Return code: {result.returncode}") if result.stdout: error_details.append(f"STDOUT:\n{result.stdout}") if result.stderr: error_details.append(f"STDERR:\n{result.stderr}") full_error = "\n".join(error_details) raise Exception(f"Failed to run tests:\n{full_error}") # Advance the progress by 1 for each directory processed progress.advance(task, 1) os.chdir(original_cwd) if success_count > 0: Logger.log(f"Found {len(self.passed_tests)} passed tests", level="success") return True else: Logger.log("No tests executed successfully", level="error") return False def can_execute(self) -> bool: return self.paths.src_dir.exists() def _get_contract_paths(self) -> List[Path]: """Get contract paths from config.""" config = Config() return [ self.paths.workspace_root / "src" / "contracts" / contract for contract in config.contracts ] class ProcessTracesCommand(Command): """Command to process trace files and generate profiles.""" def __init__(self, paths: Paths, passed_tests: List[str], parallel_jobs: int = 4): self.paths = paths self.passed_tests = passed_tests self.parallel_jobs = parallel_jobs self.test_resources = [] @log_step("Processing Traces & Extracting Resources") def execute(self) -> bool: if not self.passed_tests: Logger.log("No passed tests to process", level="warning") return False Logger.header( f"🚀 Processing {len(self.passed_tests)} tests with {self.parallel_jobs} parallel jobs" ) trace_files = self._find_trace_files() if not trace_files: Logger.log("No trace files found", level="warning") return False processor = TraceProcessor(Config()) try: with ( ProcessManager() as pm, ThreadPoolExecutor(max_workers=self.parallel_jobs) as executor, ): futures = { executor.submit(processor.process, test_name, trace_path): test_name for test_name, trace_path, _ in trace_files } success_count = self._process_futures_interruptible(futures, pm) if self.test_resources: self._update_summary() Logger.log( f"Successfully processed {success_count}/{len(trace_files)} tests", level="success", ) return success_count > 0 except KeyboardInterrupt: Logger.log("Processing interrupted by user", level="warning") raise def can_execute(self) -> bool: return len(self.passed_tests) > 0 def _find_trace_files(self) -> List[Tuple[str, Path, Path]]: """Find trace files for passed tests.""" found = [] trace_dirs = self._get_trace_directories() for test_name in self.passed_tests: for trace_dir in trace_dirs: if not trace_dir.exists(): continue predicted_path = TestResourceInfo.predict_trace_path( test_name, trace_dir ) if predicted_path.exists(): found.append((test_name, predicted_path, trace_dir.parent)) break return found def _get_trace_directories(self) -> List[Path]: """Get all potential trace directories.""" dirs = [self.paths.trace_dir] config = Config() for contract in config.contracts: dirs.append( self.paths.workspace_root / "src" / "contracts" / contract / "snfoundry_trace" ) return dirs def _process_futures_interruptible(self, futures, pm) -> int: """Process completed futures with progress tracking and interruptibility.""" success_count = 0 with UIBuilder.progress(True) as progress: task = progress.add_task("Processing tests", total=len(futures)) try: for future in futures: if pm.shutdown_event.is_set(): future.cancel() continue try: success, test_name, _, test_info = future.result( timeout=60 * 20 ) # Increased timeout if success and test_info: self.test_resources.append(test_info) console.print(f"✨ [green]{test_name}[/green]") success_count += 1 else: console.print( f"💥 [red]{test_name}[/red]: Processing failed" ) except Exception as e: test_name = futures[future] error_msg = str(e) console.print(f"💥 [red]{test_name}[/red]: {error_msg}") # Print full error details and exit import traceback Logger.log( f"FATAL ERROR processing {test_name}: {error_msg}", level="error", ) Logger.log( f"Full traceback:\n{traceback.format_exc()}", level="error" ) Logger.exit_panel( f"💥 Fatal error processing {test_name}: {error_msg}", "Error", "red", ) sys.exit(1) progress.advance(task, 1) except KeyboardInterrupt: # Cancel all remaining futures immediately for future in futures: future.cancel() # Re-raise to propagate the interrupt raise return success_count def _update_summary(self): """Update global summary JSON.""" summary_file = self.paths.docs_benchmarks / "test_summary.json" summary_data = JsonManager.read(summary_file, {}) timestamp_iso = datetime.now().isoformat() for test_info in self.test_resources: summary_data[test_info.test_name_simple] = { "last_updated": timestamp_iso, "latest_metrics": test_info.to_benchmark_row(), } if JsonManager.write(summary_file, summary_data): Logger.log("Performance data saved", level="success") class GenerateBenchmarksCommand(Command): """Command to generate Cairo benchmarks.""" def __init__(self, paths: Paths): self.paths = paths @log_step("Generating Cairo Benchmarks") def execute(self) -> bool: Logger.log("Generating Cairo benchmarks...", level="info") summary_file = self.paths.docs_benchmarks / "test_summary.json" test_data = JsonManager.read(summary_file, {}) if not test_data: Logger.log("No test data available", level="warning") return False success = self._update_readme(test_data) if success: Logger.log( f"Generated benchmarks for {len(test_data)} tests", level="success" ) return success def can_execute(self) -> bool: return self.paths.readme.exists() @handle_errors def _update_readme(self, test_data: dict) -> bool: """Update README with benchmarks.""" with open(self.paths.readme, "r", encoding="utf-8") as f: content = f.read() start_idx, end_idx = self._find_benchmarks_section(content) lines = content.split("\n") new_content = self._generate_benchmarks_content(test_data) new_lines = new_content.rstrip().split("\n") if start_idx is not None: if end_idx < len(lines) and lines[end_idx - 1].strip() == "": updated_lines = lines[:start_idx] + new_lines + lines[end_idx:] else: updated_lines = lines[:start_idx] + new_lines + [""] + lines[end_idx:] else: support_idx = next( ( i for i, line in enumerate(lines) if "Support & How to Contribute" in line ), None, ) if support_idx: updated_lines = ( lines[:support_idx] + new_lines + [""] + lines[support_idx:] ) else: updated_lines = lines + [""] + new_lines with open(self.paths.readme, "w", encoding="utf-8") as f: f.write("\n".join(updated_lines)) Logger.log("Updated README.md with benchmarks", level="success") return True def _find_benchmarks_section( self, content: str ) -> Tuple[Optional[int], Optional[int]]: """Find Cairo Benchmarks section.""" lines = content.split("\n") start_idx = end_idx = None for i, line in enumerate(lines): if line.strip() == "## Cairo Benchmarks": start_idx = i elif ( start_idx is not None and line.startswith("## ") and line.strip() != "## Cairo Benchmarks" ): end_idx = i break if start_idx is not None and end_idx is None: end_idx = len(lines) return start_idx, end_idx def _generate_benchmarks_content(self, test_data: dict) -> str: """Generate complete benchmarks content.""" if not test_data: return "## Cairo Benchmarks\n\n*No benchmark data available.*\n\n" report_builder = ReportBuilder(test_data) content = report_builder.build() return f"""## Cairo Benchmarks 📊 **Click on any section below to expand and view detailed benchmark tables with test performance metrics.** **Note:** Click on the test name to view the profiling image. Resources shown in the table for contracts include extra costs due to the foundry logic. Check the profile file for more details. {content.rstrip()} --- 🔄 **To regenerate these benchmarks:** Run `make profile-test` from the project root. """ # Report Generation with Builder Pattern class ReportBuilder: """Builder for generating benchmark reports with fluent interface.""" def __init__(self, test_data: dict): self.test_data = test_data self.grouped_data = None def build(self) -> str: """Build the final report.""" if not self.grouped_data: self._group_by_module() return self._generate_nested_hierarchy(self.grouped_data) def _group_by_module(self): """Group tests by module hierarchy.""" main_grouped = { "garaga": defaultdict(lambda: defaultdict(list)), "contracts": defaultdict(lambda: defaultdict(list)), } for test_name, test_info in self.test_data.items(): latest_metrics = test_info.get("latest_metrics", {}) if not latest_metrics: continue hierarchical_name = latest_metrics.get("test_name_hierarchical", "") category = latest_metrics.get("category", "garaga") hierarchy_parts = TestResourceInfo.extract_hierarchy_parts( hierarchical_name ) current = main_grouped[category] for module in hierarchy_parts[:-1]: if module not in current: current[module] = defaultdict(list) current = current[module] final_module = hierarchy_parts[-1] if hierarchy_parts else "tests" if not isinstance(current[final_module], list): current[final_module] = [] current[final_module].append(latest_metrics) self.grouped_data = {k: dict(v) for k, v in main_grouped.items() if v} def _generate_nested_hierarchy( self, grouped_data: dict, current_path: List[str] = None ) -> str: """Generate nested collapsible hierarchy.""" if current_path is None: current_path = [] content = "" # Sort sections alphabetically by module name for module_name, module_data in sorted(grouped_data.items()): if isinstance(module_data, list): df = self._create_dataframe(module_data) table_content = self._generate_table(df) content += self._collapsible_section( module_name, table_content, False, len(current_path) ) elif isinstance(module_data, dict): merged_name, current_data = self._merge_single_children( module_name, module_data ) if isinstance(current_data, list): df = self._create_dataframe(current_data) table_content = self._generate_table(df) content += self._collapsible_section( merged_name, table_content, False, len(current_path) ) else: inner_content = self._generate_nested_hierarchy( current_data, current_path + [module_name] ) is_open = len(current_path) > 0 content += self._collapsible_section( merged_name, inner_content, is_open, len(current_path) ) return content def _merge_single_children(self, name: str, data: dict) -> Tuple[str, any]: """Merge chains of single children.""" merged_name = name current_data = data while len(current_data) == 1: child_name = list(current_data.keys())[0] child_data = list(current_data.values())[0] if isinstance(child_data, list): merged_name += "::" + child_name return merged_name, child_data elif isinstance(child_data, dict): merged_name += "::" + child_name current_data = child_data else: break return merged_name, current_data def _create_dataframe(self, tests: List[dict]) -> pd.DataFrame: """Create DataFrame from test data.""" if not tests: return pd.DataFrame() columns = [ "test_name", "steps", "range_check", "range_check96", "bitwise", "poseidon", "add_mod", "mul_mod", "keccak", "pedersen", "ecop", "syscalls_count", "sierra_gas", "image_path", ] df = pd.DataFrame(tests) available_columns = [col for col in columns if col in df.columns] df = df[available_columns] # Remove zero columns except essentials essential = ["test_name", "steps", "sierra_gas", "image_path"] for col in df.columns: if col not in essential and (df[col] == 0).all(): df = df.drop(columns=[col]) if "sierra_gas" in df.columns: df = df.sort_values("sierra_gas", ascending=False) return df def _generate_table(self, df: pd.DataFrame) -> str: """Generate markdown table.""" if df.empty: return "*No tests found.*\n" df = df.copy() if "test_name" in df.columns: df["test_name"] = df.apply( lambda row: f"[{row['test_name']}]({row.get('image_path', 'docs/benchmarks/' + row['test_name'] + '.png')})", axis=1, ) # Format numbers numeric_cols = [ "steps", "range_check", "range_check96", "bitwise", "poseidon", "add_mod", "mul_mod", "keccak", "pedersen", "ecop", "syscalls_count", "sierra_gas", ] for col in numeric_cols: if col in df.columns: df[col] = df[col].apply(lambda x: f"{x:,}" if pd.notna(x) else "0") # Rename columns column_mapping = { "test_name": "Test Name", "steps": "Steps", "range_check": "Range Check", "range_check96": "Range Check 96", "bitwise": "Bitwise", "poseidon": "Poseidon", "add_mod": "Add Mod", "mul_mod": "Mul Mod", "keccak": "Keccak", "pedersen": "Pedersen", "ecop": "ECOP", "syscalls_count": "Syscalls", "sierra_gas": "Sierra Gas", } display_df = df.drop(columns=["image_path"], errors="ignore") df_display = display_df.rename(columns=column_mapping) return ( tabulate(df_display, headers="keys", tablefmt="github", showindex=False) + "\n" ) def _collapsible_section( self, title: str, content: str, is_open: bool, indent_level: int ) -> str: """Generate collapsible section.""" open_attr = " open" if is_open else "" if indent_level > 0: base_indent = "│ " * (indent_level - 1) branch = "└── " title = f"{base_indent}{branch}{title}" return f""" {title} {content} """ # Workflow Executor class WorkflowExecutor: """Executes command chains with automatic rollback.""" def __init__(self, config: Config, paths: Paths): self.config = config self.paths = paths self.executed_commands = [] def execute_workflow( self, test_filter: Optional[str] = None, parallel_jobs: int = 2, generate_benchmarks: bool = False, ) -> bool: """Execute the complete workflow.""" try: self.paths.ensure_dirs() commands = [ CheckDependenciesCommand(self.config), RunTestsCommand(self.paths, test_filter), ] for cmd in commands: if not cmd.can_execute(): raise Exception(f"Cannot execute {cmd.__class__.__name__}") if not cmd.execute(): raise Exception(f"Command {cmd.__class__.__name__} failed") self.executed_commands.append(cmd) # Get passed tests from RunTestsCommand run_tests_cmd = next( cmd for cmd in self.executed_commands if isinstance(cmd, RunTestsCommand) ) # Process traces process_cmd = ProcessTracesCommand( self.paths, run_tests_cmd.passed_tests, parallel_jobs ) if not process_cmd.can_execute(): raise Exception("Cannot execute ProcessTracesCommand") if not process_cmd.execute(): raise Exception("ProcessTracesCommand failed") self.executed_commands.append(process_cmd) # Generate benchmarks if requested if generate_benchmarks: benchmark_cmd = GenerateBenchmarksCommand(self.paths) if benchmark_cmd.can_execute(): if not benchmark_cmd.execute(): raise Exception("GenerateBenchmarksCommand failed") Logger.header("🎯 Workflow Complete") Logger.log("Profiling workflow completed successfully!", level="success") return True except KeyboardInterrupt: # Re-raise KeyboardInterrupt to be handled by main() raise except Exception as e: import traceback Logger.log(f"FATAL ERROR in execute_workflow: {e}", level="error") Logger.log(f"Full traceback:\n{traceback.format_exc()}", level="error") Logger.exit_panel( f"💥 Fatal error in execute_workflow: {e}", "Error", "red" ) sys.exit(1) # Simplified Main Function & CLI @dataclass class CLIConfig: """CLI configuration.""" test_filter: Optional[str] = None workspace: Optional[str] = None parallel_jobs: int = 2 generate_benchmarks: bool = False benchmarks_only: bool = False def main(): """Simplified main entry point.""" Logger.header("🐺 Garaga Test Profiler") # Parse arguments parser = argparse.ArgumentParser(description="Run snforge tests with profiling") parser.add_argument("test_filter", nargs="?", help="Test name filter") parser.add_argument("--all", action="store_true", help="Run all tests") parser.add_argument("--workspace", help="Workspace root path") parser.add_argument("--parallel-jobs", type=int, default=2, help="Parallel jobs") parser.add_argument( "--generate-benchmarks", action="store_true", help="Generate benchmarks" ) parser.add_argument( "--benchmarks-only", action="store_true", help="Only generate benchmarks" ) args = parser.parse_args() # Create CLI config cli_config = CLIConfig( test_filter=None if args.all else args.test_filter, workspace=args.workspace, parallel_jobs=max(1, min(8, args.parallel_jobs)), generate_benchmarks=args.generate_benchmarks, benchmarks_only=args.benchmarks_only, ) # Setup paths and config workspace_root = Path(cli_config.workspace or os.getcwd()) paths = Paths(workspace_root) config = Config() # Handle benchmarks-only mode if cli_config.benchmarks_only: Logger.log("Running in benchmarks-only mode", level="info") cmd = GenerateBenchmarksCommand(paths) success = cmd.execute() if cmd.can_execute() else False if success: Logger.exit_panel( "📊 Cairo benchmarks generated successfully!", "Success", "green" ) sys.exit(0) else: Logger.exit_panel("💥 Failed to generate Cairo benchmarks!", "Error", "red") sys.exit(1) # Log configuration if cli_config.test_filter: Logger.log(f"Running tests matching: {cli_config.test_filter}", level="info") else: Logger.log("Running all tests", level="info") Logger.log(f"Using {cli_config.parallel_jobs} parallel jobs", level="info") # Execute workflow executor = WorkflowExecutor(config, paths) try: success = executor.execute_workflow( cli_config.test_filter, cli_config.parallel_jobs, cli_config.generate_benchmarks, ) except KeyboardInterrupt: Logger.exit_panel( "👋 Process interrupted by user\nPartial results may be available", "Interrupted", "yellow", ) sys.exit(130) # Handle results if success: Logger.exit_panel( "🎉 All operations completed successfully!", "Success", "green" ) sys.exit(0) else: Logger.exit_panel("💥 Workflow failed!", "Error", "red") sys.exit(1) if __name__ == "__main__": main()