[
  {
    "path": ".JuliaFormatter.toml",
    "content": "# Configuration file for JuliaFormatter.jl\n # For more information, see: https://domluna.github.io/JuliaFormatter.jl/stable/config/\n\n always_for_in = true\n always_use_return = true\n margin = 90\n remove_extra_newlines = true\n short_to_long_function_def = true"
  },
  {
    "path": ".codecov.yml",
    "content": "status:\n    project:                 # measuring the overall project coverage\n      default:               # context, you can create multiple ones with custom titles\n        enabled: yes         # must be yes|true to enable this status\n        target: 80%\n        threshold: 5%        # allowed to drop X% and still result in a \"success\" PR status\n      branches:\n        threshold: 5%        # allowed to drop X% and still result in a \"success\" commit status"
  },
  {
    "path": ".github/ISSUE_TEMPLATE/bug_report.md",
    "content": "---\nname: Bug report\nabout: Help us track down bugs in Alpine.\ntitle: ''\nlabels: 'bug'\nassignees: ''\n\n---\n\n**Describe the bug**\nA clear and concise description of what the bug is. Simple examples which reproduce the bug will be helpful.\n"
  },
  {
    "path": ".github/ISSUE_TEMPLATE/feature_request.md",
    "content": "---\nname: Feature request\nabout: 'Suggest an idea for Alpine. '\ntitle: ''\nlabels: 'enhancement'\nassignees: ''\n\n---\n\nWelcome to Alpine! You can use this Github issue to suggest a new feature for Alpine.\n\n**Is your feature request related to a problem? Please describe.**\nA clear and concise description of what the problem is. \n\n**Describe the solution you'd like**\nA clear and concise description of what you want to happen.\n\n**Describe alternatives you've considered**\nA clear and concise description of any alternative solutions or features you've considered.\n"
  },
  {
    "path": ".github/workflows/CompatHelper.yml",
    "content": "name: CompatHelper\non:\n  schedule:\n    - cron: 0 0 * * *\n  workflow_dispatch:\njobs:\n  CompatHelper:\n    runs-on: ubuntu-latest\n    steps:\n      - name: Pkg.add(\"CompatHelper\")\n        run: julia -e 'using Pkg; Pkg.add(\"CompatHelper\")'\n      - name: CompatHelper.main()\n        env:\n          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }}\n        run: julia -e 'using CompatHelper; CompatHelper.main()'"
  },
  {
    "path": ".github/workflows/TagBot.yml",
    "content": "name: TagBot\non:\n  issue_comment:\n    types:\n      - created\n  workflow_dispatch:\njobs:\n  TagBot:\n    if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'\n    runs-on: ubuntu-latest\n    steps:\n      - uses: JuliaRegistries/TagBot@v1\n        with:\n          token: ${{ secrets.GITHUB_TOKEN }}\n          ssh: ${{ secrets.DOCUMENTER_KEY }}"
  },
  {
    "path": ".github/workflows/ci.yml",
    "content": "name: CI\non:\n  push:\n    branches:\n      - master\n      - release-*\n  pull_request:\n    types: [opened, synchronize, reopened]\n# needed to allow julia-actions/cache to delete old caches that it has created\npermissions:\n  actions: write\n  contents: read\njobs:\n  test:\n    name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}\n    runs-on: ${{ matrix.os }}\n    strategy:\n      fail-fast: false\n      matrix:\n        version: ['1']\n        os: [ubuntu-latest, macOS-latest, windows-latest]\n        arch: [x64]\n    steps:\n      - uses: actions/checkout@v4\n      - uses: julia-actions/setup-julia@v2\n        with:\n          version: ${{ matrix.version }}\n          arch: ${{ matrix.arch }}\n      - uses: julia-actions/cache@v2\n      - uses: julia-actions/julia-buildpkg@v1\n      - uses: julia-actions/julia-runtest@v1\n        with:\n          depwarn: error\n      - uses: julia-actions/julia-processcoverage@v1\n      - uses: codecov/codecov-action@v4\n        with:\n          file: lcov.info\n"
  },
  {
    "path": ".github/workflows/documentation.yml",
    "content": "name: Documentation\non:\n  push:\n    branches: [master]\n    tags: '*'\n  pull_request:\n    types: [opened, synchronize, reopened]\njobs:\n  docs:\n    if: \"!contains(github.event.head_commit.message, 'skip ci')\"\n    name: Documentation\n    runs-on: ubuntu-latest\n    steps:\n      - uses: actions/checkout@v4\n      - uses: julia-actions/setup-julia@latest\n        with:\n          version: '1'\n      - name: Install Dependencies\n        run: julia --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'\n      - name: Build and Deploy\n        env:\n          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}\n          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} \n        run: julia --project=docs docs/make.jl\n"
  },
  {
    "path": ".github/workflows/format_check.yml",
    "content": "name: format-check\non:\n  push:\n    branches:\n      - master\n      - release-*\n  pull_request:\n    types: [opened, synchronize, reopened]\njobs:\n  build:\n    runs-on: ubuntu-latest\n    steps:\n      - uses: julia-actions/setup-julia@latest\n        with:\n          version: '1'\n      - uses: actions/checkout@v4\n      - name: Format check\n        shell: julia --color=yes {0}\n        run: |\n          using Pkg\n          Pkg.add(PackageSpec(name=\"JuliaFormatter\", version=\"1\"))\n          using JuliaFormatter\n          format(\"src/MOI_wrapper\", verbose=true)\n          format(\"test\", verbose=true)\n          format(\"docs\", verbose=true)\n          out = String(read(Cmd(`git diff`)))\n          if isempty(out)\n              exit(0)\n          end\n          @error \"Some files have not been formatted !!!\"\n          write(stdout, out)\n          exit(1)\n"
  },
  {
    "path": ".gitignore",
    "content": "# Files generated by invoking Julia with --code-coverage\n*.jl.cov\n*.jl.*.cov\n\n# Files generated by invoking Julia with --track-allocation\n*.jl.mem\n\n.DS_Store\n\n# Build artifacts for creating documentation generated by the Documenter package\ndocs/build/\ndocs/site/\n\n# File generated by Pkg, the package manager, based on a corresponding Project.toml\n# It records a fixed state of all packages used by the project. As such, it should not be\n# committed for packages, but should be committed for applications that require a static\n# environment.\nManifest.toml\ntest/examples/Manifest.toml\ndocs/Manifest.toml\n\n.vscode\n"
  },
  {
    "path": "CHANGELOG.md",
    "content": "# Alpine.jl Change Log\n\n## v0.5.8\n- Relax tests for upcoming MOI release (#257)\n- Add support for `MOI.ScalarNonlinearFunction` (#258)\n- Relax tests that are flakey on Windows (#259)\n\n## v0.5.7\n- Fix failing tests (#241), (#250)\n- Update `Project.toml` (#239), (#246), (#249)\n- Remove unnecessary Alp module reference (#247)\n- Remove unnecessary `Base.eval` calls (#251)\n- Fix empty summations (#252), (#253)\n- Fix support for `MOI.Integer` variables (#245)\n- Loosen tolerances in tests (#254)\n- Update versions in GitHub actions (#255)\n\n## v0.5.6\n- Minor Readme updates (#235)\n- Implemented RawStatusString for solution summary (#238)\n- Dependency update for docs\n- Bug fix in LB exceeding UB outside relative tolerance bounds\n\n## v0.5.5\n- Removed use of e.g. for JuMP documentation in README (#230)\n- Dropped support for integer variable MINLPs in `examples` (#233)\n- Updated README in `examples` folder to clarify `minlp_solver` dependency (#232)\n\n## v0.5.4\n- Added `random_QCQPs` folder with python generator files for all the instances appearing in this paper: https://arxiv.org/pdf/2301.00306.pdf\n- Minor tweaks in docs and main README file\n\n## v0.5.3\n- Removed compatability on Pkg #225\n- Added raw NL expression interface example for a dense multilinear problem\n\n## v0.5.2\n- Fixed issue with `@NLconstraint` created from a quadratic `@expression` (#221)\n- Fixed error message in nlexpr parsing of constraints with non-integer exponents (#223)\n- Clean up in `expr_is_fractional_exponent` (related to #223)\n- Added dependency on `Pkg` package\n- Added unit tests for testing multilinear binary products (`hmittelman`)\n\n## v0.5.1\n- Re-org and clean-up in partition additions within bounding MIP model\n- Updated to cheaper `AffExpr` evaluation within linking constraints\n- Minor update in gap evaluataion after OBBT termination with fixed iterations\n- Added solver option `use_start_as_incumbent` to use warm start value as also an intial incumbent solution  in presolve without invoking a local solver. (#218)\n- Added unit tests for testing warm start point\n\n## v0.5.0\n- New feature: Linking constraints for multilinear terms with uniform and adaptive partitions (significant speed up in run times for multilinear problems: http://www.optimization-online.org/DB_HTML/2022/07/8974.html) (@jongeunkim)\n- Added dependency on Combinatorics package for linking constraints\n- Added unit tests for linking constraints feature\n- Changed Cbc test dependency to HiGHS solver\n- Dropped a few redundant unit tests\n- Dropped support for (slower) piecewise McCormick formulations\n- Changed `disc_ratio` to `partition_scaling_factor`\n- Added JuliaFormatter.toml and formatting workfow\n\n## v0.4.3\n- Dropped support for checking solver availability. User can choose to use any MILP, MINLP and/or NLP solver with Alpine\n- `GRB_ENV` now works with Gurobi solver to avoid printing License info multiple times during iterations\n- Updates tests to reflect above changes\n- Default `convhull_warmstart` set to `true` for a MIP solver in bounding-MIP iterations\n\n## v0.4.2\n- Fix support for JuMP v1.2 (@odow)\n\n## v0.4.1\n- Added MOI attribute for tightened bounds post-OBBT (@blegat)\n\n## v0.4.0\n- Fixed OBBT convergence issue due to average bound reduction\n- Added new termination criteria to OBBT: max_reduction, max_width, rel_gap at every iteration of OBBT\n- Fixed the issue to tighten only original nonlinear variables (aux vars were counted before)\n- `presolve_bt_bound_tol` changed to `1E-4` (numerically stable)\n- `presolve_bt_obj_bound_tol` added to avoid infeasibility in OBBT iterations when bounds are tights\n- Parameter tuning (tolerances) for stable OBBT convergence\n- Fixed bug in `best_rel_gap` evaluation\n- Bug fixed to check any user-defined operators, and disable hessians based on availabe features. Unit test added for this\n- Now, Alpine terminates (w/o invoking `global_solve`) when presolve finds the global optimum due to `rel_gap` eval at every OBBT iteration. Unit test added for this.\n- Post-OBBT optimality gap (`presolve_best_rel_gap`) user-option added to be able to extract best opt gap after OBBT when Alpine terminates\n- `apply_partitioning` feature added to be able to terminate Alpine without applying the MIP-based paritioning algorithm (mainly to run only OBBT)\n- Revised unit test (in `test_algorithm`) for reduced run times\n\n## v0.3.0\n- JuMP v1.0+ in examples\n- Pavito v0.3.5 support\n- Dropped support for redundant `run_bounding_iteration` function\n- Clean-up and re-org of optimizer structs and `MOI_wrapper` functions\n- Bug fix in `relax_integrality` under presolve\n- Added Rosenbrock function\n- Added user-definable `presolve_bt_improv_tol` for variable range reductions in OBBT\n- Minor update on finite values for obj-bound in `create_obbt_model`\n- NLP solution rounding issue resolved (now compatible with default tol, 1e-6), to avoid the variable solution outside discretization (#190)\n- `circleN` instance updated to `circle_MINLPLib` to eliminate Pavito's mixed-integer cycling in unit tests (#190)\n- Clean-up in printing variable solutions (`variable_values`)\n\n## v0.2.10\n- Add support for the HiGHS solver\n\n## v0.2.9\n- Update to JuMP v1.0\n\n## v0.2.8\n- Update to JuMP v0.22, v0.23\n- Update to MOI v1.0\n- Simplify test dependencies\n\n## v0.2.7\n- Support for module shortcut `Alp` in function calls\n- Solver options clean up in `examples` folder\n- Dropped support for unsued functions:\n     `_bound_sense`\n     `update_boundstop_options`\n     `amp_post_inequalities_int`\n     `amp_pick_ratevec`\n     `amp_collect_tight_regions`\n- Improved code coverage\n- Docs cleanup\n\n## v0.2.6\n- Bug fix in `algorithm.jl` to handle Gurobi as the MIP solver with updated MOI\n- Deactivated redundant functions `collect_lb_pool`, `merge_solution_pool` and `track_new_partition_idx`\n- Moved `examples` out of `test` folder\n- Updated `run_examples` to handle Gurobi as the MIP solver\n- Removed dependency on the `Distributed` package\n- Improved code coverage\n- Typos fixed in docs\n\n## v0.2.5\n- Cleaning up of solver logs\n- Time correction for local solve\n- Removed unused `Alpine.Optimizer` options in solver.jl\n\n## v0.2.4\n- Added unit tests for utility functions\n- Removed un-used functions from utility functions which aren't part of Alpine's algorithm\n- Dropped support for heuristic rounding algorithm (`heu_basic_rounding`) - `minlp_solver` input is a must\n- Dropped support for adjusting branching priority in MIP solvers (`adjust_branch_priority`)\n\n\n## v0.2.3\n- Migrating from Travis to Github-actions\n- Major documentation clean-up\n- Dependency packages clean-up\n- runtests.jl clean-up\n- Solver options update: `presolve_max_iter` => `presolve_bt_max_iter` and others\n- Added `test/examples/run_example.jl`\n\n## v0.2.2\n- README clean up\n\nClosed issues:\n- Constraints are not supported and cannot be bridged into supported constrained variables and constraints (#164)\n\n## v0.2.1\n- Logging clean up\n- Removal of redundant tests\n\nClosed issues:\n- Juniper's ALMOST_LOCALLY SOLVED error (#157)\n- unncessary eval usages (#153)\n- Logging issue with constants in objective (#159)\n\n## v0.2.0\n- MOI wrapper and JuMP v0.21 support\n- expression.jl clean up\n- eval() removal where unnecessary (#153)\n- Drop support for all trigonometric related functions (both in src and testing)\n- Drop support of expression parsing for generic integer variables in MINLPs (both in src and testing)\n\nClosed issues:\n- arc consistency partitioning pruning scheme as an example extension for POD (#37)\n- Generate convex relaxations for nonconvex MINLPs (#86)\n- Error in convexification of monomials (#104)\n- On variables chosen for partitioning (#121)\n- Travis and Documeter Maintenance (#144)\n- Compilation error (#146)\n- bound propagation buggy (#147)\n- Reenable test: Validation Test || PBT-AMP-TMC || basic solve || examples/nlp3.jl (#150)\n- Reenable test: Validation Test || AMP-CONV-FACET || basic solve || examples/nlp1.jl (#151)\n\n## v0.1.16\n- Fixed CBC version to make it compatible\n- Removed support for \"Mini\" Formulation for convex hulls\n- Updated tests and removed a few\n\n## v0.1.15\n- Bug fixes for issues 134 and 135 (fractional exponents, constants within integer exponents)\n- Added function 'expr_isolate_const' to nlexpr.jl\n- Meaningful optimality gaps for zero upper bound values (issue 103)\n- Typos in comments\n- Dropped support for colorful_alpine\n- Ole Kroger's updates to docs/make.jl\n\n## v0.1.10\n- Multiple bug fixes in expression parsing\n- Added support for feasibility problems with constant objectives\n- Typos in comments\n\n## v0.1.9\n- Drop support for Julia < v1.0.\n- Move to the new Registrator system.\n- The last supported version for Julia v0.6 is v0.1.8\n- The last supported version for Julia v0.7 is v0.1.7 (the bugs fixed in v0.1.8 is not ported to Julia v0.7)\n\n\n## v0.1.8\n- Bug fixes in solver recognition\n- Updated Issue template and Readme.\n- Rounding bug fixed for binaries.\n- This version is only available for Julia v0.6\n\n## v0.1.7\n- Bug fixes for bounds on lifted variables representing nonlinear terms\n- Inf bound warning issue fixed\n\n## v0.1.6\n- Bug fix in operators.jl for accounting all extreme points in the bound evaluation\n\n## v0.1.5\n- Unit exponent bug-fix\n- Meaningful error messages for unsupported functions\n- Pinned tests to JuMP 0.18.5\n- Cleaner & meaningful logs\n\n## v0.1.3\n- Finite large bounds on unbounded variables\n\n## Staged\n- typo fix\n- set Big-M values for unbounded variables\n\n## v0.1.2\n- Bug fix in bound tightening tolerance corner case\n\n## v0.1.1\n- Bug fix in Cplex solver recognition\n\n## v0.1.0\n- Alpine.jl first release\n\n## Merged Features\n- `partition_scaling_factor` selection algorithm\n- logarithm embedding formulation\n- bounding model warm starting and no-good-cuts using solution pool\n- `disc_vars` selection algorithm based on weighted minimum vertex cover\n- more support for binary problem\n- rounding heuristic and multi-start heuristic for feasible solutions\n- recursive linear lifting\n- some attempts to reason bounds for variables with infinite bounds\n\n## New Operators\n- `BINPROD`: product of binary vars\n- `BINLIN`: product of a binary var and continuous var\n\n## Data Structure\n- Some refactoring to shorten the attribute names\n- Eliminated unnecessary/obsolete user options\n- Strengthen the checks to problems\n\n## Code Structure\n- `Alpine.jl`: \"header\" file\n- `solver.jl`: data structure and problem loading\n- `algorithm.jl`: high-level algorithms and major utilities (`presolve()`, `local_solve()`, `bounding_solve()`)\n- `amp.jl`: algorithms for bounding formulation constructions\n- `presolve.jl`: algorithms for presolves\n- `heuristics.jl`: algorithms for heuristics\n- `bounds.jl`: algorithms and utilities for handling bounds including bounds propagation and reasoning with lifting\n- `mpb2moi.jl`: preparation for migration to `MOI` interface, a collection of all solver & modeling interface warpping functions\n- `multi.jl`: high-level piecewise convex relaxation formulation construction and utilities for multilinear/monomial terms\n- `tmc.jl`: old McCormick-based methods\n- `const.jl`: (experimental) tries to categorize operators for cleaner and safer operations\n- `embedding.jl`: logarithm embedding formulations and utilities\n- `nlexpr.jl`: algorithms for expression handling\n- `operators.jl`: operator detection algorithm and associated utilities for bounds, discretization variable selection, etc.\n- `log.jl`: logging utilities\n- `utility.jl`: general utility functions\n\n\n## Debugs\n- Fixed multiple bugs in recursive expression handling\n- Fixed duplicates in constructing convex relaxations\n- Fixed bound reasoning steps for complex terms\n- Fixed many other things\n\n## Tests & Coverage\n- Most new features are covered (embedding, `partition_scaling_factor` algorithm, etc.)\n- Stronger expression parsing tests with new operators covered\n- Coverage should be more than `~90%`\n"
  },
  {
    "path": "CITATION.bib",
    "content": "@article{alpine_JOGO2019,\n  author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell and Sundar, Kaarthik},\n  title = {An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs},\n  journal = {Journal of Global Optimization},\n  year = {2019},\n  issn = {1573-2916},\n  doi = {10.1007/s10898-018-00734-1},\n}"
  },
  {
    "path": "LICENSE.md",
    "content": "Copyright (c) 2017, Triad National Security, LLC\nAll rights reserved.\nCopyright 2017. Triad National Security, LLC. All rights reserved. This software was produced under U.S. Government contract 89233218CNA000001 for Los Alamos National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. Department of Energy/National Nuclear Security Administration. All rights in the program are reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear Security Administration. The Government is granted for itself and others acting on its behalf a nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare derivative works, distribute copies to the public, perform publicly and display publicly, and to permit others to do so. NEITHER THE GOVERNMENT NOR TRIAD NATIONAL SECURITY, LLC MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LIABILITY FOR THE USE OF THIS SOFTWARE. If software is modified to produce derivative works, such modified software should be clearly marked, so as not to confuse it with the version available from LANL.\n\nAdditionally, redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:\n1.\tRedistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.\n2.\tRedistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.\n3.\tNeither the name of Triad National Security, LLC, Los Alamos National Laboratory, LANL, the U.S. Government, nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission THIS SOFTWARE IS PROVIDED BY  TRIAD NATIONAL SECURITY, LLC AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL TRIAD NATIONAL SECURITY, LLC OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE."
  },
  {
    "path": "Project.toml",
    "content": "name = \"Alpine\"\nuuid = \"07493b3f-dabb-5b16-a503-4139292d7dd4\"\nauthors = [\"Harsha Nagarajan, Site Wang, Kaarthik Sundar and contributors\"]\nrepo = \"https://github.com/lanl-ansi/Alpine.jl.git\"\nversion = \"0.5.8\"\n\n[deps]\nCombinatorics = \"861a8166-3701-5b0c-9a16-15d98fcdc6aa\"\nJuMP = \"4076af6c-e467-56ae-b986-b466b2749572\"\nMathOptInterface = \"b8f27783-ece8-5eb3-8dc8-9495eed66fee\"\nStatistics = \"10745b16-79ce-11e8-11f9-7d13ad32a3b2\"\n\n[compat]\nCombinatorics = \"1\"\nHiGHS = \"1\"\nIpopt = \"0.8, 0.9, 1\"\nJuMP = \"0.22, 0.23, 1\"\nJuniper = \"0.8, 0.9\"\nMathOptInterface = \"0.10, 1\"\nPavito = \"0.3.4, 0.3.5\"\nStatistics = \"1\"\njulia = \"1\"\n\n[extras]\nHiGHS = \"87dc4568-4c63-4d18-b0c0-bb2238e4078b\"\nIpopt = \"b6b21f68-93f8-5de0-b562-5493be1d77c9\"\nJuniper = \"2ddba703-00a4-53a7-87a5-e8b9971dde84\"\nPavito = \"cd433a01-47d1-575d-afb7-6db927ee8d8f\"\nRandom = \"9a3f8284-a2c9-5f02-9a11-845980a1fd5c\"\nTest = \"8dfed614-e22c-5e08-85e1-65c5234f0b40\"\n\n[targets]\ntest = [\"HiGHS\", \"Ipopt\", \"Juniper\", \"Pavito\", \"Random\", \"Test\"]\n"
  },
  {
    "path": "README.md",
    "content": "# Alpine, a global solver for non-convex MINLPs\n\n[![CI](https://github.com/lanl-ansi/Alpine.jl/actions/workflows/ci.yml/badge.svg)](https://github.com/lanl-ansi/Alpine.jl/actions/workflows/ci.yml)\n[![codecov](https://codecov.io/gh/lanl-ansi/Alpine.jl/branch/master/badge.svg)](https://codecov.io/gh/lanl-ansi/Alpine.jl)\n[![Documentation](https://github.com/lanl-ansi/Alpine.jl/actions/workflows/documentation.yml/badge.svg)](https://lanl-ansi.github.io/Alpine.jl/latest/) \n[![version](https://juliahub.com/docs/Alpine/version.svg)](https://juliahub.com/ui/Packages/Alpine/TRSJF)\n\nALPINE (glob(AL) o(P)timization for mixed-(I)nteger programs with (N)onlinear (E)quations), is a novel global optimization solver that uses an adaptive, piecewise convexification scheme and constraint programming methods to solve non-convex Mixed-Integer Non-Linear Programs (MINLPs) efficiently. MINLPs are typically \"hard\" optimization problems which appear in numerous applications (see [MINLPLib.jl](https://github.com/lanl-ansi/MINLPLib.jl)). \n\nAlpine is entirely built upon [JuMP](https://github.com/jump-dev/JuMP.jl) and [MathOptInterface](https://github.com/jump-dev/MathOptInterface.jl) in Julia, which provides incredible flexibility for usage and further development.\n\nAlpine globally solves a given MINLP by:\n\n* Analyzing the problem's expressions (objective & constraints) and applies appropriate convex relaxations and polyhedral outer-approximations\n\n* Performing sequential optimization-based bound tightening (OBBT) and an iterative MIP-based adaptive partitioning scheme via piecewise polyhedral relaxations with a guarantee of global convergence\n\nUpon Alpine's convergence, for a given relative gap tolerance `ε`, the user is guaranteed that the global optimal solution is in the `ε`-neighborhood of the solution found by the solver.\n\n## Installation\n\nInstall Alpine using the Julia package manager:\n\n```julia\nimport Pkg\nPkg.add(\"Alpine\")\n```\n\n## Usage with JuMP\n\nUse Alpine with [JuMP](https://github.com/jump-dev/JuMP.jl) as follows:\n\n```julia\nusing JuMP, Alpine, Ipopt, HiGHS\nipopt = optimizer_with_attributes(Ipopt.Optimizer, \"print_level\" => 0)\nhighs = optimizer_with_attributes(HiGHS.Optimizer, \"output_flag\" => false)\nmodel = Model(\n    optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => ipopt,\n        \"mip_solver\" => highs,\n    ),\n)\n```\n\n## Documentation\n\nFor more details, see the [online documentation](https://lanl-ansi.github.io/Alpine.jl/latest/).\n\n## Support problem types\n\nAlpine can currently handle MINLPs with polynomials in constraints and/or in the objective. Currently, there is no support for exponential cones and Positive Semi-Definite (PSD) cones in MINLPs. Alpine is also a good fit for subsets of the MINLP family, for example, Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs), Non-Linear Programs (NLPs), etc.\n\nFor more details, check out this [video](https://www.youtube.com/watch?v=mwkhiEIS5JA) on Alpine.jl at [JuMP-dev 2018](http://www.juliaopt.org/meetings/bordeaux2018/).\n\n## Underlying solvers\n\nThough an MIP-based bounding algorithm implemented in Alpine is quite involved, most of the computational bottleneck arises in the underlying MIP solvers. Since every iteration of Alpine solves an MIP sub-problem, which is typically a convex MILP/MIQCQP, Alpine's run time heavily depends on the run-time of these solvers. For the best performance of Alpine, we recommend using the commercial solver [Gurobi](https://www.gurobi.com), which is available [free](https://www.gurobi.com/academia/academic-program-and-licenses/) for academic purposes. However, due to the flexibility offered by [JuMP](https://github.com/jump-dev/JuMP.jl), the following MIP and NLP solvers are supported in Alpine: \n\n\n| Solver                                                                         | Julia Package                                                |\n|--------------------------------------------------------------------------------|--------------------------------------------------------------|\n| [Gurobi](http://gurobi.com/)                                                   | [Gurobi.jl](https://github.com/jump-dev/Gurobi.jl)           |\n| [CPLEX](https://www.ibm.com/analytics/cplex-optimizer) | [CPLEX.jl](https://github.com/jump-dev/CPLEX.jl)             |\n| [HiGHS](https://highs.dev/)            | [HiGHS.jl](https://github.com/jump-dev/HiGHS.jl)\n| [Cbc](https://projects.coin-or.org/Cbc)                                        | [Cbc.jl](https://github.com/jump-dev/Cbc.jl)                 |\n| [Ipopt](https://projects.coin-or.org/Ipopt)                                    | [Ipopt.jl](https://github.com/jump-dev/Ipopt.jl)             |\n| [Bonmin](https://projects.coin-or.org/Bonmin)                                  | [Bonmin.jl](https://github.com/jump-dev/AmplNLWriter.jl)   |\n| [Artelys KNITRO](http://artelys.com/en/optimization-tools/knitro)              | [KNITRO.jl](https://github.com/jump-dev/KNITRO.jl)           |\n| [Xpress](https://www.fico.com/en/products/fico-xpress-optimization)            | [Xpress.jl](https://github.com/jump-dev/Xpress.jl)\n\n## Bug reports and support\n\nPlease report any issues via the GitHub [issue tracker](https://github.com/lanl-ansi/Alpine.jl/issues).\nAll types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc. \n\n## Challenging Problems\n\nWe are seeking out hard benchmark instances for MINLPs. Please get in touch either by opening an issue or [privately](https://harshangrjn.github.io/#contact) if you would like to share any hard instances.\n\n## Citing Alpine\n\nIf you find Alpine useful in your work, we kindly request that you cite the following papers ([PDF](http://harshangrjn.github.io/pdf/JOGO_2018.pdf), [PDF](http://harshangrjn.github.io/pdf/CP_2016.pdf))\n```bibtex\n@article{alpine_JOGO2019,\n  title = {An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs},\n  author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell and Sundar, Kaarthik},\n  journal = {Journal of Global Optimization},\n  year = {2019},\n  issn = {1573-2916},\n  doi = {10.1007/s10898-018-00734-1},\n}\n\n@inproceedings{alpine_CP2016,\n  title = {Tightening {McCormick} relaxations for nonlinear programs via dynamic multivariate partitioning},\n  author = {Nagarajan, Harsha and Lu, Mowen and Yamangil, Emre and Bent, Russell},\n  booktitle = {International Conference on Principles and Practice of Constraint Programming},\n  pages = {369--387},\n  year = {2016},\n  organization = {Springer},\n  doi = {10.1007/978-3-319-44953-1_24},\n}\n```\n\nIf you find the underlying piecewise polyhedral formulations implemented in Alpine useful in your work, we kindly request that you cite the following papers ([link-1](https://doi.org/10.1016/j.orl.2020.12.002), [link-2](http://www.optimization-online.org/DB_HTML/2022/07/8974.html)): \n```bibtex\n@article{alpine_ORL2021,\n  title = {Piecewise polyhedral formulations for a multilinear term},\n  author = {Sundar, Kaarthik and Nagarajan, Harsha and Linderoth, Jeff and Wang, Site and Bent, Russell},\n  journal = {Operations Research Letters},\n  volume = {49},\n  number = {1},\n  pages = {144--149},\n  year = {2021},\n  publisher = {Elsevier}\n}\n\n@article{alpine_OptOnline2022,\n  title={Piecewise Polyhedral Relaxations of Multilinear Optimization},\n  author={Kim, Jongeun and Richard, Jean-Philippe P. and Tawarmalani, Mohit},\n  eprinttype={Optimization Online},\n  date={2022}\n}\n```\n"
  },
  {
    "path": "docs/Project.toml",
    "content": "[deps]\nDocumenter = \"e30172f5-a6a5-5a46-863b-614d45cd2de4\"\nDocumenterTools = \"35a29f4d-8980-5a13-9543-d66fff28ecb8\"\n"
  },
  {
    "path": "docs/README.md",
    "content": "# Documentation for Alpine\n\n## Installation\nAlpine's documentation is generated using [Documenter.jl](https://github.com/JuliaDocs/Documenter.jl). To install it, run the following command in a Julia session:\n\n```julia\nPkg.add(\"Documenter\")\nPkg.add(\"DocumenterTools\")\n```\n\n## Building the Docs\nTo preview the `html` output of the documents, run the following command:\n\n```julia\njulia --color=yes make.jl\n```\n\nYou can then view the documents in `build/index.html`."
  },
  {
    "path": "docs/make.jl",
    "content": "using Documenter, Alpine\nusing DocumenterTools: Themes\n\nfor w in (\"light\", \"dark\")\n    header = read(joinpath(@__DIR__, \"src/assets/themes/style.scss\"), String)\n    theme = read(joinpath(@__DIR__, \"src/assets/themes/$(w)defs.scss\"), String)\n    write(joinpath(@__DIR__, \"src/assets/themes/$(w).scss\"), header * \"\\n\" * theme)\nend\n\nThemes.compile(\n    joinpath(@__DIR__, \"src/assets/themes/documenter-light.css\"),\n    joinpath(@__DIR__, \"src/assets/themes/light.scss\"),\n)\nThemes.compile(\n    joinpath(@__DIR__, \"src/assets/themes/documenter-dark.css\"),\n    joinpath(@__DIR__, \"src/assets/themes/dark.scss\"),\n)\n\nmakedocs(\n    sitename = \"Alpine\",\n    authors = \"Harsha Nagarajan, Site Wang, Kaarthik Sundar and contributors\",\n    format = Documenter.HTML(\n        mathengine = Documenter.MathJax(),\n        prettyurls = get(ENV, \"CI\", nothing) == \"true\",\n    ),\n    # strict = true,\n    pages = [\n        \"Introduction\" => \"index.md\",\n        \"Choosing Sub-solvers\" => \"choosingsolver.md\",\n        # \"Algorithm\" => \"algorithm.md\",\n        \"Solver Options\" => \"parameters.md\",\n        \"Methods\" => \"functions.md\",\n    ],\n)\n\ndeploydocs(repo = \"github.com/lanl-ansi/Alpine.jl.git\", push_preview = true)\n"
  },
  {
    "path": "docs/src/algorithm.md",
    "content": "# Demo\n\n```@meta\nCurrentModule = Alpine\n```\n\nConsider the following [problem](https://link.springer.com/article/10.1007/s10898-012-0022-1) as an example.\n\n```math\n\\min_{x}\\, &c^Tx\\\\\ns.t.     &a_i^Tx \\text{ sense}_i \\, b_i \\forall\\,\\, i\\\\\n         &l \\leq x \\leq u\\\\\n```\n"
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#documenter .docs-sidebar form.docs-search>input.icon,html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search>input.icon,html.theme--documenter-dark .button .icon.is-medium,html.theme--documenter-dark .button .icon.is-large{height:1.5em;width:1.5em}html.theme--documenter-dark .button .icon:first-child:not(:last-child){margin-left:calc(-0.375em - 1px);margin-right:0.1875em}html.theme--documenter-dark .button .icon:last-child:not(:first-child){margin-left:0.1875em;margin-right:calc(-0.375em - 1px)}html.theme--documenter-dark .button .icon:first-child:last-child{margin-left:calc(-0.375em - 1px);margin-right:calc(-0.375em - 1px)}html.theme--documenter-dark .button:hover,html.theme--documenter-dark .button.is-hovered{border-color:#b5b5b5;color:#f2be9e}html.theme--documenter-dark .button:focus,html.theme--documenter-dark .button.is-focused{border-color:#2e63b8;color:#363636}html.theme--documenter-dark .button:focus:not(:active),html.theme--documenter-dark 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.button.is-white{background-color:white;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:hover,html.theme--documenter-dark .button.is-white.is-hovered{background-color:#f9f9f9;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:focus,html.theme--documenter-dark .button.is-white.is-focused{border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:focus:not(:active),html.theme--documenter-dark .button.is-white.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:white;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;color:white}html.theme--documenter-dark .button.is-white.is-inverted:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-hovered{background-color:black}html.theme--documenter-dark .button.is-white.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted{background-color:#0a0a0a;border-color:transparent;box-shadow:none;color:white}html.theme--documenter-dark .button.is-white.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:white;color:white}html.theme--documenter-dark .button.is-white.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-outlined.is-focused{background-color:white;border-color:white;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after{border-color:transparent transparent white white !important}html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-white.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined{background-color:transparent;border-color:white;box-shadow:none;color:white}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused{background-color:#0a0a0a;color:white}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent white white !important}html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:white}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:white}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:white}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:black;border-color:transparent;color:white}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-black.is-inverted{background-color:white;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:white;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent white white !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:white}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent white white !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:white;color:white}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused{background-color:white;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:white;box-shadow:none;color:white}html.theme--documenter-dark .button.is-light{background-color:whitesmoke;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#eeeeee;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light{background-color:whitesmoke;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;color:whitesmoke}html.theme--documenter-dark .button.is-light.is-inverted:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-hovered{background-color:#292929}html.theme--documenter-dark .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted{background-color:#363636;border-color:transparent;box-shadow:none;color:whitesmoke}html.theme--documenter-dark .button.is-light.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:whitesmoke;color:whitesmoke}html.theme--documenter-dark .button.is-light.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-outlined.is-focused{background-color:whitesmoke;border-color:whitesmoke;color:#363636}html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent whitesmoke whitesmoke !important}html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined{background-color:transparent;border-color:whitesmoke;box-shadow:none;color:whitesmoke}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused{background-color:#363636;color:whitesmoke}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent whitesmoke whitesmoke !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;color:whitesmoke}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#2f2f2f;border-color:transparent;color:whitesmoke}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:whitesmoke}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,54,54,0.25)}html.theme--documenter-dark .button.is-dark:active,html.theme--documenter-dark .content kbd.button:active,html.theme--documenter-dark .button.is-dark.is-active,html.theme--documenter-dark .content kbd.button.is-active{background-color:#292929;border-color:transparent;color:whitesmoke}html.theme--documenter-dark .button.is-dark[disabled],html.theme--documenter-dark .content kbd.button[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark,fieldset[disabled] html.theme--documenter-dark .content kbd.button{background-color:#363636;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-dark.is-inverted,html.theme--documenter-dark .content kbd.button.is-inverted{background-color:whitesmoke;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted:hover,html.theme--documenter-dark .content kbd.button.is-inverted:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered{background-color:#e8e8e8}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:whitesmoke;border-color:transparent;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent whitesmoke whitesmoke !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;color:#363636}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#363636;border-color:#363636;color:whitesmoke}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent whitesmoke whitesmoke !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#363636;box-shadow:none;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:whitesmoke;color:whitesmoke}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:whitesmoke;color:#363636}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:whitesmoke;box-shadow:none;color:whitesmoke}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#4eb5de;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#43b1dc;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus:not(:active),html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus:not(:active),html.theme--documenter-dark .button.is-primary.is-focused:not(:active),html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink:not(:active){box-shadow:0 0 0 0.125em rgba(78,181,222,0.25)}html.theme--documenter-dark .button.is-primary:active,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:active,html.theme--documenter-dark .button.is-primary.is-active,html.theme--documenter-dark .docstring>section>a.button.is-active.docs-sourcelink{background-color:#39acda;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary[disabled],html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#4eb5de;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-primary.is-inverted,html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-inverted:hover,html.theme--documenter-dark .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered,html.theme--documenter-dark 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rgba(218,11,0,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#c10a00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#da0b00;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#da0b00;box-shadow:none;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark 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.button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:whitesmoke;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:0.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#97b3e2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:whitesmoke;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0.7rem 0.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#97b3e2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#97b3e2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#97b3e2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:0.75rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar 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  {
    "path": "docs/src/assets/themes/darkdefs.scss",
    "content": "// This template file overrides some of the Documenter theme variables to customize the theme:\n$themename: \"documenter-dark\"; // CSS file must be called `$(themename).css`\n// Instruct documenter/*.scss files that this is a dark theme\n$documenter-is-dark-theme: true;\n\n$boldcolor: lighten-color($maincolor, 4.5);\n\n$body-background-color: $darkbg; // main page background\n\n// this is the color the links get, and also when they are hovered\n$link: lighten-color($secondcolor, 2);\n$link-hover: lighten-color($link, 3);\n\n// Main text color:\n$text: darken-color($mainwhite, 0.2);\n// Bold text color, also affects headers\n$text-strong: $boldcolor;\n\n// Code text color:\n$code: #fff;\n//$code-background: rgba(0.5,0,0, 0.05);\n$codebg: darken-color($maincolor, 3);\n$code-background: $codebg; // for inline code\n$pre-background: $codebg;  // for code blocks\n$documenter-docstring-header-background: lighten-color($body-background-color, 0.5);\n\n// Sidebar\n$documenter-sidebar-background: darken-color($maincolor, 1.5); //background color for sidebar\n$documenter-sidebar-color: $text; //font color for sidebar\n$documenter-sidebar-menu-hover-color: $documenter-sidebar-color;\n$documenter-sidebar-menu-hover-background: darken-color($documenter-sidebar-background, 1.2);\n\n$documenter-sidebar-menu-active-background: $darkbg;\n$documenter-sidebar-menu-active-color: $mainwhite;\n$documenter-sidebar-menu-active-hover-background: darken-color($documenter-sidebar-background, 1);\n$documenter-sidebar-menu-active-hover-color: $documenter-sidebar-menu-active-color;\n// these two change what happens with input boxes (the search box):\n$input-hover-border-color: $secondcolor;\n$input-focus-border-color: $mainwhite;\n\n$documenter-docstring-shadow: 3px 3px 4px invert($shadow-color);\n\n// Admonition stuff\n$admbg: lighten-color($body-background-color, 0.5);\n$admonition-background: (\n  'default': $admbg, 'info': $admbg, 'success': $admbg, 'warning': $admbg,\n  'danger': $admbg, 'compat': $admbg\n);\n$admonition-header-background: (\n  'default': #ba3f1f, 'warning': #a88b17, 'danger': #c7524c,\n  'success': #42ac68, 'info': #28c);\n\n// All secondary themes have to be nested in a theme--$(themename) class. When Documenter\n// switches themes, it applies this class to <html> and then disables the primary\n// stylesheet.\n@import \"documenter/utilities\";\n@import \"documenter/variables\";\n@import \"bulma/utilities/all\";\n@import \"bulma/base/minireset.sass\";\n@import \"bulma/base/helpers.sass\";\n\nhtml.theme--#{$themename} {\n  @import \"bulma/base/generic.sass\";\n\n  @import \"documenter/overrides\";\n\n  @import \"bulma/elements/all\";\n  @import \"bulma/form/all\";\n  @import \"bulma/components/all\";\n  @import \"bulma/grid/all\";\n  @import \"bulma/layout/all\";\n\n  // Additional overrides, if need be\n\n  @import \"documenter/elements\";\n  @import \"documenter/components/all\";\n  @import \"documenter/patches\";\n  @import \"documenter/layout/all\";\n\n  @import \"documenter/theme_overrides\";\n\n  // $shadow-color: #202224;\n\n  #documenter .docs-sidebar { // This makes sidebar have shadow at all displays\n    border-right: none;\n    box-shadow: 1.2*$shadow-size 0rem 1*$shadow-blur invert($shadow-color);\n\n    form.docs-search > input { // these controls are for the searchbar\n      color: $mainwhite;\n      background-color: darken-color($documenter-sidebar-background, 1);\n      border-color: darken-color($documenter-sidebar-background, 2);\n      margin-top: 1.0rem;\n      margin-bottom: 1.0rem; // adjust the margings between search and other elements\n      &::placeholder {\n        color: $mainwhite; // placeholder text color (\"Search here...\")\n      }\n    }\n  }\n  // FIXME: Hack to get a proper theme for highlight.js in the dark theme\n  @import \"highlightjs/a11y-dark\";\n  // Also, a11y-dark does not highlight string interpolation properly.\n  .hljs-subst {\n    color: #f8f8f2;\n  }\n}\n"
  },
  {
    "path": "docs/src/assets/themes/documenter-dark.css",
    "content": "@charset \"UTF-8\";\n/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */\n@keyframes spinAround {\n  from {\n    transform: rotate(0deg); }\n  to {\n    transform: rotate(359deg); } }\n\nhtml.theme--documenter-dark .delete, html.theme--documenter-dark .modal-close, .is-unselectable, html.theme--documenter-dark .button, html.theme--documenter-dark .file, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .pagination-previous,\nhtml.theme--documenter-dark .pagination-next,\nhtml.theme--documenter-dark .pagination-link,\nhtml.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .tabs {\n  -webkit-touch-callout: none;\n  -webkit-user-select: none;\n  -moz-user-select: none;\n  -ms-user-select: none;\n  user-select: none; }\n\nhtml.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after, html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after {\n  border: 3px solid transparent;\n  border-radius: 2px;\n  border-right: 0;\n  border-top: 0;\n  content: \" \";\n  display: block;\n  height: 0.625em;\n  margin-top: -0.4375em;\n  pointer-events: none;\n  position: absolute;\n  top: 50%;\n  transform: rotate(-45deg);\n  transform-origin: center;\n  width: 0.625em; }\n\nhtml.theme--documenter-dark .box:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .title:not(:last-child),\nhtml.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .admonition:not(:last-child) {\n  margin-bottom: 1.5rem; }\n\nhtml.theme--documenter-dark .delete, html.theme--documenter-dark .modal-close {\n  -moz-appearance: none;\n  -webkit-appearance: none;\n  background-color: rgba(10, 10, 10, 0.2);\n  border: none;\n  border-radius: 290486px;\n  cursor: pointer;\n  pointer-events: auto;\n  display: inline-block;\n  flex-grow: 0;\n  flex-shrink: 0;\n  font-size: 0;\n  height: 20px;\n  max-height: 20px;\n  max-width: 20px;\n  min-height: 20px;\n  min-width: 20px;\n  outline: none;\n  position: relative;\n  vertical-align: top;\n  width: 20px; }\n  html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::after, html.theme--documenter-dark .modal-close::after {\n    background-color: white;\n    content: \"\";\n    display: block;\n    left: 50%;\n    position: absolute;\n    top: 50%;\n    transform: translateX(-50%) translateY(-50%) rotate(45deg);\n    transform-origin: center center; }\n  html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::before {\n    height: 2px;\n    width: 50%; }\n  html.theme--documenter-dark .delete::after, html.theme--documenter-dark .modal-close::after {\n    height: 50%;\n    width: 2px; }\n  html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:focus, html.theme--documenter-dark .modal-close:focus {\n    background-color: rgba(10, 10, 10, 0.3); }\n  html.theme--documenter-dark .delete:active, html.theme--documenter-dark .modal-close:active {\n    background-color: rgba(10, 10, 10, 0.4); }\n  html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete, html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close {\n    height: 16px;\n    max-height: 16px;\n    max-width: 16px;\n    min-height: 16px;\n    min-width: 16px;\n    width: 16px; }\n  html.theme--documenter-dark .is-medium.delete, html.theme--documenter-dark .is-medium.modal-close {\n    height: 24px;\n    max-height: 24px;\n    max-width: 24px;\n    min-height: 24px;\n    min-width: 24px;\n    width: 24px; }\n  html.theme--documenter-dark .is-large.delete, html.theme--documenter-dark .is-large.modal-close {\n    height: 32px;\n    max-height: 32px;\n    max-width: 32px;\n    min-height: 32px;\n    min-width: 32px;\n    width: 32px; }\n\nhtml.theme--documenter-dark .button.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .control.is-loading::after {\n  animation: spinAround 500ms infinite linear;\n  border: 2px solid #dbdbdb;\n  border-radius: 290486px;\n  border-right-color: transparent;\n  border-top-color: transparent;\n  content: \"\";\n  display: block;\n  height: 1em;\n  position: relative;\n  width: 1em; }\n\n.is-overlay, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img,\nhtml.theme--documenter-dark .image.is-square .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img,\nhtml.theme--documenter-dark .image.is-1by1 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img,\nhtml.theme--documenter-dark .image.is-5by4 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img,\nhtml.theme--documenter-dark .image.is-4by3 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img,\nhtml.theme--documenter-dark .image.is-3by2 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img,\nhtml.theme--documenter-dark .image.is-5by3 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img,\nhtml.theme--documenter-dark .image.is-16by9 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img,\nhtml.theme--documenter-dark .image.is-2by1 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img,\nhtml.theme--documenter-dark .image.is-3by1 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img,\nhtml.theme--documenter-dark .image.is-4by5 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img,\nhtml.theme--documenter-dark .image.is-3by4 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img,\nhtml.theme--documenter-dark .image.is-2by3 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img,\nhtml.theme--documenter-dark .image.is-3by5 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img,\nhtml.theme--documenter-dark .image.is-9by16 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img,\nhtml.theme--documenter-dark .image.is-1by2 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img,\nhtml.theme--documenter-dark .image.is-1by3 .has-ratio,\nhtml.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, html.theme--documenter-dark .modal, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .hero-video {\n  bottom: 0;\n  left: 0;\n  position: absolute;\n  right: 0;\n  top: 0; }\n\nhtml.theme--documenter-dark .button, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea, html.theme--documenter-dark .select select, html.theme--documenter-dark .file-cta,\nhtml.theme--documenter-dark .file-name, html.theme--documenter-dark .pagination-previous,\nhtml.theme--documenter-dark .pagination-next,\nhtml.theme--documenter-dark .pagination-link,\nhtml.theme--documenter-dark .pagination-ellipsis {\n  -moz-appearance: none;\n  -webkit-appearance: none;\n  align-items: center;\n  border: 1px solid transparent;\n  border-radius: 4px;\n  box-shadow: none;\n  display: inline-flex;\n  font-size: 1rem;\n  height: 2.25em;\n  justify-content: flex-start;\n  line-height: 1.5;\n  padding-bottom: calc(0.375em - 1px);\n  padding-left: calc(0.625em - 1px);\n  padding-right: calc(0.625em - 1px);\n  padding-top: calc(0.375em - 1px);\n  position: relative;\n  vertical-align: top; }\n  html.theme--documenter-dark .button:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .file-cta:focus,\n  html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .pagination-previous:focus,\n  html.theme--documenter-dark .pagination-next:focus,\n  html.theme--documenter-dark .pagination-link:focus,\n  html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.file-cta,\n  html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .is-focused.pagination-previous,\n  html.theme--documenter-dark .is-focused.pagination-next,\n  html.theme--documenter-dark .is-focused.pagination-link,\n  html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .button:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .file-cta:active,\n  html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .pagination-previous:active,\n  html.theme--documenter-dark .pagination-next:active,\n  html.theme--documenter-dark .pagination-link:active,\n  html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .is-active.button, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.file-cta,\n  html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .is-active.pagination-previous,\n  html.theme--documenter-dark .is-active.pagination-next,\n  html.theme--documenter-dark .is-active.pagination-link,\n  html.theme--documenter-dark .is-active.pagination-ellipsis {\n    outline: none; }\n  html.theme--documenter-dark .button[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .file-cta[disabled],\n  html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .pagination-previous[disabled],\n  html.theme--documenter-dark .pagination-next[disabled],\n  html.theme--documenter-dark .pagination-link[disabled],\n  html.theme--documenter-dark .pagination-ellipsis[disabled],\n  fieldset[disabled] html.theme--documenter-dark .button,\n  html.theme--documenter-dark fieldset[disabled] .button,\n  fieldset[disabled] html.theme--documenter-dark .input,\n  html.theme--documenter-dark fieldset[disabled] .input,\n  fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,\n  html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search > input,\n  fieldset[disabled] html.theme--documenter-dark .textarea,\n  html.theme--documenter-dark fieldset[disabled] .textarea,\n  fieldset[disabled] html.theme--documenter-dark .select select,\n  html.theme--documenter-dark .select fieldset[disabled] select,\n  fieldset[disabled] html.theme--documenter-dark .file-cta,\n  html.theme--documenter-dark fieldset[disabled] .file-cta,\n  fieldset[disabled] html.theme--documenter-dark .file-name,\n  html.theme--documenter-dark fieldset[disabled] .file-name,\n  fieldset[disabled] html.theme--documenter-dark .pagination-previous,\n  html.theme--documenter-dark fieldset[disabled] .pagination-previous,\n  fieldset[disabled] html.theme--documenter-dark .pagination-next,\n  html.theme--documenter-dark fieldset[disabled] .pagination-next,\n  fieldset[disabled] html.theme--documenter-dark .pagination-link,\n  html.theme--documenter-dark fieldset[disabled] .pagination-link,\n  fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,\n  html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis {\n    cursor: not-allowed; }\n\n/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */\nhtml,\nbody,\np,\nol,\nul,\nli,\ndl,\ndt,\ndd,\nblockquote,\nfigure,\nfieldset,\nlegend,\ntextarea,\npre,\niframe,\nhr,\nh1,\nh2,\nh3,\nh4,\nh5,\nh6 {\n  margin: 0;\n  padding: 0; }\n\nh1,\nh2,\nh3,\nh4,\nh5,\nh6 {\n  font-size: 100%;\n  font-weight: normal; }\n\nul {\n  list-style: none; }\n\nbutton,\ninput,\nselect,\ntextarea {\n  margin: 0; }\n\nhtml {\n  box-sizing: border-box; }\n\n*, *::before, *::after {\n  box-sizing: inherit; }\n\nimg,\nembed,\niframe,\nobject,\nvideo {\n  height: auto;\n  max-width: 100%; }\n\naudio {\n  max-width: 100%; }\n\niframe {\n  border: 0; }\n\ntable {\n  border-collapse: collapse;\n  border-spacing: 0; }\n\ntd,\nth {\n  padding: 0; }\n  td:not([align]),\n  th:not([align]) {\n    text-align: left; }\n\n.is-clearfix::after {\n  clear: both;\n  content: \" \";\n  display: table; }\n\n.is-pulled-left {\n  float: left !important; }\n\n.is-pulled-right {\n  float: right !important; }\n\n.is-clipped {\n  overflow: hidden !important; }\n\n.is-size-1 {\n  font-size: 3rem !important; }\n\n.is-size-2 {\n  font-size: 2.5rem !important; }\n\n.is-size-3 {\n  font-size: 2rem !important; }\n\n.is-size-4 {\n  font-size: 1.5rem !important; }\n\n.is-size-5 {\n  font-size: 1.25rem !important; }\n\n.is-size-6 {\n  font-size: 1rem !important; }\n\n.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink {\n  font-size: 0.75rem !important; }\n\n@media screen and (max-width: 768px) {\n  .is-size-1-mobile {\n    font-size: 3rem !important; }\n  .is-size-2-mobile {\n    font-size: 2.5rem !important; }\n  .is-size-3-mobile {\n    font-size: 2rem !important; }\n  .is-size-4-mobile {\n    font-size: 1.5rem !important; }\n  .is-size-5-mobile {\n    font-size: 1.25rem !important; }\n  .is-size-6-mobile {\n    font-size: 1rem !important; }\n  .is-size-7-mobile {\n    font-size: 0.75rem !important; } }\n\n@media screen and (min-width: 769px), print {\n  .is-size-1-tablet {\n    font-size: 3rem !important; }\n  .is-size-2-tablet {\n    font-size: 2.5rem !important; }\n  .is-size-3-tablet {\n    font-size: 2rem !important; }\n  .is-size-4-tablet {\n    font-size: 1.5rem !important; }\n  .is-size-5-tablet {\n    font-size: 1.25rem !important; }\n  .is-size-6-tablet {\n    font-size: 1rem !important; }\n  .is-size-7-tablet {\n    font-size: 0.75rem !important; } }\n\n@media screen and (max-width: 1055px) {\n  .is-size-1-touch {\n    font-size: 3rem !important; }\n  .is-size-2-touch {\n    font-size: 2.5rem !important; }\n  .is-size-3-touch {\n    font-size: 2rem !important; }\n  .is-size-4-touch {\n    font-size: 1.5rem !important; }\n  .is-size-5-touch {\n    font-size: 1.25rem !important; }\n  .is-size-6-touch {\n    font-size: 1rem !important; }\n  .is-size-7-touch {\n    font-size: 0.75rem !important; } }\n\n@media screen and (min-width: 1056px) {\n  .is-size-1-desktop {\n    font-size: 3rem !important; }\n  .is-size-2-desktop {\n    font-size: 2.5rem !important; }\n  .is-size-3-desktop {\n    font-size: 2rem !important; 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} }\n\n@media screen and (min-width: 1216px) {\n  .is-invisible-widescreen {\n    visibility: hidden !important; } }\n\n@media screen and (min-width: 1216px) and (max-width: 1407px) {\n  .is-invisible-widescreen-only {\n    visibility: hidden !important; } }\n\n@media screen and (min-width: 1408px) {\n  .is-invisible-fullhd {\n    visibility: hidden !important; } }\n\n.is-marginless {\n  margin: 0 !important; }\n\n.is-paddingless {\n  padding: 0 !important; }\n\n.is-radiusless {\n  border-radius: 0 !important; }\n\n.is-shadowless {\n  box-shadow: none !important; }\n\n.is-relative {\n  position: relative !important; }\n\nhtml.theme--documenter-dark {\n  /* This file contain the overall layout.\n *\n * The main container is <div> that is identified by id #documenter.\n */\n  /* a11y-dark theme */\n  /* Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css */\n  /* @author: ericwbailey */\n  /* Comment */\n  /* Red */\n  /* Orange */\n  /* Yellow */\n  /* Green */\n  /* Blue */\n  /* Purple */ }\n  html.theme--documenter-dark html {\n    background-color: #1b1f28;\n    font-size: 16px;\n    -moz-osx-font-smoothing: grayscale;\n    -webkit-font-smoothing: antialiased;\n    min-width: 300px;\n    overflow-x: auto;\n    overflow-y: scroll;\n    text-rendering: optimizeLegibility;\n    text-size-adjust: 100%; }\n  html.theme--documenter-dark article,\n  html.theme--documenter-dark aside,\n  html.theme--documenter-dark figure,\n  html.theme--documenter-dark footer,\n  html.theme--documenter-dark header,\n  html.theme--documenter-dark hgroup,\n  html.theme--documenter-dark section {\n    display: block; }\n  html.theme--documenter-dark body,\n  html.theme--documenter-dark button,\n  html.theme--documenter-dark input,\n  html.theme--documenter-dark select,\n  html.theme--documenter-dark textarea {\n    font-family: \"Montserrat\", sans-serif; }\n  html.theme--documenter-dark code,\n  html.theme--documenter-dark pre {\n    -moz-osx-font-smoothing: auto;\n    -webkit-font-smoothing: auto;\n    font-family: \"Source Code Pro\", monospace; }\n  html.theme--documenter-dark body {\n    color: #ececec;\n    font-size: 1em;\n    font-weight: 400;\n    line-height: 1.5; }\n  html.theme--documenter-dark a {\n    color: #e37733;\n    cursor: pointer;\n    text-decoration: none; }\n    html.theme--documenter-dark a strong {\n      color: currentColor; }\n    html.theme--documenter-dark a:hover {\n      color: #f2be9e; }\n  html.theme--documenter-dark code {\n    background-color: #101f38;\n    color: #fff;\n    font-size: 0.875em;\n    font-weight: normal;\n    padding: 0.1em; }\n  html.theme--documenter-dark hr {\n    background-color: whitesmoke;\n    border: none;\n    display: block;\n    height: 2px;\n    margin: 1.5rem 0; }\n  html.theme--documenter-dark img {\n    height: auto;\n    max-width: 100%; }\n  html.theme--documenter-dark input[type=\"checkbox\"],\n  html.theme--documenter-dark input[type=\"radio\"] {\n    vertical-align: baseline; }\n  html.theme--documenter-dark small {\n    font-size: 0.875em; }\n  html.theme--documenter-dark span {\n    font-style: inherit;\n    font-weight: inherit; }\n  html.theme--documenter-dark strong {\n    color: #97b3e2;\n    font-weight: 700; }\n  html.theme--documenter-dark fieldset {\n    border: none; }\n  html.theme--documenter-dark pre {\n    -webkit-overflow-scrolling: touch;\n    background-color: #101f38;\n    color: #ececec;\n    font-size: 0.875em;\n    overflow-x: auto;\n    padding: 1.25rem 1.5rem;\n    white-space: pre;\n    word-wrap: normal; }\n    html.theme--documenter-dark pre code {\n      background-color: transparent;\n      color: currentColor;\n      font-size: 1em;\n      padding: 0; }\n  html.theme--documenter-dark table td,\n  html.theme--documenter-dark table th {\n    vertical-align: top; }\n    html.theme--documenter-dark table td:not([align]),\n    html.theme--documenter-dark table th:not([align]) {\n      text-align: left; }\n  html.theme--documenter-dark table th {\n    color: #97b3e2; }\n  html.theme--documenter-dark .box {\n    background-color: white;\n    border-radius: 6px;\n    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);\n    color: #ececec;\n    display: block;\n    padding: 1.25rem; }\n  html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus {\n    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #e37733; }\n  html.theme--documenter-dark a.box:active {\n    box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #e37733; }\n  html.theme--documenter-dark .button {\n    background-color: white;\n    border-color: #dbdbdb;\n    border-width: 1px;\n    color: #363636;\n    cursor: pointer;\n    justify-content: center;\n    padding-bottom: calc(0.375em - 1px);\n    padding-left: 0.75em;\n    padding-right: 0.75em;\n    padding-top: calc(0.375em - 1px);\n    text-align: center;\n    white-space: nowrap; }\n    html.theme--documenter-dark .button strong {\n      color: inherit; }\n    html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large {\n      height: 1.5em;\n      width: 1.5em; }\n    html.theme--documenter-dark .button .icon:first-child:not(:last-child) {\n      margin-left: calc(-0.375em - 1px);\n      margin-right: 0.1875em; }\n    html.theme--documenter-dark .button .icon:last-child:not(:first-child) {\n      margin-left: 0.1875em;\n      margin-right: calc(-0.375em - 1px); }\n    html.theme--documenter-dark .button .icon:first-child:last-child {\n      margin-left: calc(-0.375em - 1px);\n      margin-right: calc(-0.375em - 1px); }\n    html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered {\n      border-color: #b5b5b5;\n      color: #f2be9e; }\n    html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused {\n      border-color: #2e63b8;\n      color: #363636; }\n      html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) {\n        box-shadow: 0 0 0 0.125em rgba(227, 119, 51, 0.25); }\n    html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active {\n      border-color: #4a4a4a;\n      color: #363636; }\n    html.theme--documenter-dark .button.is-text {\n      background-color: transparent;\n      border-color: transparent;\n      color: #ececec;\n      text-decoration: underline; }\n      html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused {\n        background-color: whitesmoke;\n        color: #97b3e2; }\n      html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active {\n        background-color: #e8e8e8;\n        color: #97b3e2; }\n      html.theme--documenter-dark .button.is-text[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-text {\n        background-color: transparent;\n        border-color: transparent;\n        box-shadow: none; }\n    html.theme--documenter-dark .button.is-white {\n      background-color: white;\n      border-color: transparent;\n      color: #0a0a0a; }\n      html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered {\n        background-color: #f9f9f9;\n        border-color: transparent;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused {\n        border-color: transparent;\n        color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }\n      html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active {\n        background-color: #f2f2f2;\n        border-color: transparent;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .button.is-white[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-white {\n        background-color: white;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-white.is-inverted {\n        background-color: #0a0a0a;\n        color: white; }\n        html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered {\n          background-color: black; }\n        html.theme--documenter-dark .button.is-white.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted {\n          background-color: #0a0a0a;\n          border-color: transparent;\n          box-shadow: none;\n          color: white; }\n      html.theme--documenter-dark .button.is-white.is-loading::after {\n        border-color: transparent transparent #0a0a0a #0a0a0a !important; }\n      html.theme--documenter-dark .button.is-white.is-outlined {\n        background-color: transparent;\n        border-color: white;\n        color: white; }\n        html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused {\n          background-color: white;\n          border-color: white;\n          color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after {\n          border-color: transparent transparent white white !important; }\n        html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #0a0a0a #0a0a0a !important; }\n        html.theme--documenter-dark .button.is-white.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined {\n          background-color: transparent;\n          border-color: white;\n          box-shadow: none;\n          color: white; }\n      html.theme--documenter-dark .button.is-white.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #0a0a0a;\n        color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused {\n          background-color: #0a0a0a;\n          color: white; }\n        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent white white !important; }\n        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #0a0a0a;\n          box-shadow: none;\n          color: #0a0a0a; }\n    html.theme--documenter-dark .button.is-black {\n      background-color: #0a0a0a;\n      border-color: transparent;\n      color: white; }\n      html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered {\n        background-color: #040404;\n        border-color: transparent;\n        color: white; }\n      html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused {\n        border-color: transparent;\n        color: white; }\n        html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }\n      html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active {\n        background-color: black;\n        border-color: transparent;\n        color: white; }\n      html.theme--documenter-dark .button.is-black[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-black {\n        background-color: #0a0a0a;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-black.is-inverted {\n        background-color: white;\n        color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-black.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted {\n          background-color: white;\n          border-color: transparent;\n          box-shadow: none;\n          color: #0a0a0a; }\n      html.theme--documenter-dark .button.is-black.is-loading::after {\n        border-color: transparent transparent white white !important; }\n      html.theme--documenter-dark .button.is-black.is-outlined {\n        background-color: transparent;\n        border-color: #0a0a0a;\n        color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused {\n          background-color: #0a0a0a;\n          border-color: #0a0a0a;\n          color: white; }\n        html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after {\n          border-color: transparent transparent #0a0a0a #0a0a0a !important; }\n        html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent white white !important; }\n        html.theme--documenter-dark .button.is-black.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined {\n          background-color: transparent;\n          border-color: #0a0a0a;\n          box-shadow: none;\n          color: #0a0a0a; }\n      html.theme--documenter-dark .button.is-black.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: white;\n        color: white; }\n        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused {\n          background-color: white;\n          color: #0a0a0a; }\n        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #0a0a0a #0a0a0a !important; }\n        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: white;\n          box-shadow: none;\n          color: white; }\n    html.theme--documenter-dark .button.is-light {\n      background-color: whitesmoke;\n      border-color: transparent;\n      color: #363636; }\n      html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered {\n        background-color: #eeeeee;\n        border-color: transparent;\n        color: #363636; }\n      html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused {\n        border-color: transparent;\n        color: #363636; }\n        html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }\n      html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active {\n        background-color: #e8e8e8;\n        border-color: transparent;\n        color: #363636; }\n      html.theme--documenter-dark .button.is-light[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-light {\n        background-color: whitesmoke;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-light.is-inverted {\n        background-color: #363636;\n        color: whitesmoke; }\n        html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered {\n          background-color: #292929; }\n        html.theme--documenter-dark .button.is-light.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted {\n          background-color: #363636;\n          border-color: transparent;\n          box-shadow: none;\n          color: whitesmoke; }\n      html.theme--documenter-dark .button.is-light.is-loading::after {\n        border-color: transparent transparent #363636 #363636 !important; }\n      html.theme--documenter-dark .button.is-light.is-outlined {\n        background-color: transparent;\n        border-color: whitesmoke;\n        color: whitesmoke; }\n        html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused {\n          background-color: whitesmoke;\n          border-color: whitesmoke;\n          color: #363636; }\n        html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after {\n          border-color: transparent transparent whitesmoke whitesmoke !important; }\n        html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #363636 #363636 !important; }\n        html.theme--documenter-dark .button.is-light.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined {\n          background-color: transparent;\n          border-color: whitesmoke;\n          box-shadow: none;\n          color: whitesmoke; }\n      html.theme--documenter-dark .button.is-light.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #363636;\n        color: #363636; }\n        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused {\n          background-color: #363636;\n          color: whitesmoke; }\n        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent whitesmoke whitesmoke !important; }\n        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #363636;\n          box-shadow: none;\n          color: #363636; }\n    html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button {\n      background-color: #363636;\n      border-color: transparent;\n      color: whitesmoke; }\n      html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered {\n        background-color: #2f2f2f;\n        border-color: transparent;\n        color: whitesmoke; }\n      html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused {\n        border-color: transparent;\n        color: whitesmoke; }\n        html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }\n      html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active {\n        background-color: #292929;\n        border-color: transparent;\n        color: whitesmoke; }\n      html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-dark,\n      fieldset[disabled] html.theme--documenter-dark .content kbd.button {\n        background-color: #363636;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted {\n        background-color: whitesmoke;\n        color: #363636; }\n        html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered {\n          background-color: #e8e8e8; }\n        html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,\n        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted {\n          background-color: whitesmoke;\n          border-color: transparent;\n          box-shadow: none;\n          color: #363636; }\n      html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after {\n        border-color: transparent transparent whitesmoke whitesmoke !important; }\n      html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined {\n        background-color: transparent;\n        border-color: #363636;\n        color: #363636; }\n        html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused {\n          background-color: #363636;\n          border-color: #363636;\n          color: whitesmoke; }\n        html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after {\n          border-color: transparent transparent #363636 #363636 !important; }\n        html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent whitesmoke whitesmoke !important; }\n        html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,\n        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined {\n          background-color: transparent;\n          border-color: #363636;\n          box-shadow: none;\n          color: #363636; }\n      html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: whitesmoke;\n        color: whitesmoke; }\n        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused {\n          background-color: whitesmoke;\n          color: #363636; }\n        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #363636 #363636 !important; }\n        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,\n        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: whitesmoke;\n          box-shadow: none;\n          color: whitesmoke; }\n    html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink {\n      background-color: #4eb5de;\n      border-color: transparent;\n      color: #fff; }\n      html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink {\n        background-color: #43b1dc;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink {\n        border-color: transparent;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }\n      html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink {\n        background-color: #39acda;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-primary,\n      fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink {\n        background-color: #4eb5de;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink {\n        background-color: #fff;\n        color: #4eb5de; }\n        html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,\n        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink {\n          background-color: #fff;\n          border-color: transparent;\n          box-shadow: none;\n          color: #4eb5de; }\n      html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after {\n        border-color: transparent transparent #fff #fff !important; }\n      html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink {\n        background-color: transparent;\n        border-color: #4eb5de;\n        color: #4eb5de; }\n        html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink {\n          background-color: #4eb5de;\n          border-color: #4eb5de;\n          color: #fff; }\n        html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after {\n          border-color: transparent transparent #4eb5de #4eb5de !important; }\n        html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after {\n          border-color: transparent transparent #fff #fff !important; }\n        html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,\n        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink {\n          background-color: transparent;\n          border-color: #4eb5de;\n          box-shadow: none;\n          color: #4eb5de; }\n      html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {\n        background-color: transparent;\n        border-color: #fff;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink {\n          background-color: #fff;\n          color: #4eb5de; }\n        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after {\n          border-color: transparent transparent #4eb5de #4eb5de !important; }\n        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined,\n        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {\n          background-color: transparent;\n          border-color: #fff;\n          box-shadow: none;\n          color: #fff; }\n    html.theme--documenter-dark .button.is-link {\n      background-color: #e37733;\n      border-color: transparent;\n      color: #fff; }\n      html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered {\n        background-color: #e16f28;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused {\n        border-color: transparent;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(227, 119, 51, 0.25); }\n      html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active {\n        background-color: #dd681f;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-link[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-link {\n        background-color: #e37733;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-link.is-inverted {\n        background-color: #fff;\n        color: #e37733; }\n        html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-link.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted {\n          background-color: #fff;\n          border-color: transparent;\n          box-shadow: none;\n          color: #e37733; }\n      html.theme--documenter-dark .button.is-link.is-loading::after {\n        border-color: transparent transparent #fff #fff !important; }\n      html.theme--documenter-dark .button.is-link.is-outlined {\n        background-color: transparent;\n        border-color: #e37733;\n        color: #e37733; }\n        html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused {\n          background-color: #e37733;\n          border-color: #e37733;\n          color: #fff; }\n        html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after {\n          border-color: transparent transparent #e37733 #e37733 !important; }\n        html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #fff #fff !important; }\n        html.theme--documenter-dark .button.is-link.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined {\n          background-color: transparent;\n          border-color: #e37733;\n          box-shadow: none;\n          color: #e37733; }\n      html.theme--documenter-dark .button.is-link.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #fff;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused {\n          background-color: #fff;\n          color: #e37733; }\n        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #e37733 #e37733 !important; }\n        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #fff;\n          box-shadow: none;\n          color: #fff; }\n    html.theme--documenter-dark .button.is-info {\n      background-color: #209cee;\n      border-color: transparent;\n      color: #fff; }\n      html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered {\n        background-color: #1496ed;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused {\n        border-color: transparent;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }\n      html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active {\n        background-color: #118fe4;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-info[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-info {\n        background-color: #209cee;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-info.is-inverted {\n        background-color: #fff;\n        color: #209cee; }\n        html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-info.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted {\n          background-color: #fff;\n          border-color: transparent;\n          box-shadow: none;\n          color: #209cee; }\n      html.theme--documenter-dark .button.is-info.is-loading::after {\n        border-color: transparent transparent #fff #fff !important; }\n      html.theme--documenter-dark .button.is-info.is-outlined {\n        background-color: transparent;\n        border-color: #209cee;\n        color: #209cee; }\n        html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused {\n          background-color: #209cee;\n          border-color: #209cee;\n          color: #fff; }\n        html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after {\n          border-color: transparent transparent #209cee #209cee !important; }\n        html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #fff #fff !important; }\n        html.theme--documenter-dark .button.is-info.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined {\n          background-color: transparent;\n          border-color: #209cee;\n          box-shadow: none;\n          color: #209cee; }\n      html.theme--documenter-dark .button.is-info.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #fff;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused {\n          background-color: #fff;\n          color: #209cee; }\n        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #209cee #209cee !important; }\n        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #fff;\n          box-shadow: none;\n          color: #fff; }\n    html.theme--documenter-dark .button.is-success {\n      background-color: #22c35b;\n      border-color: transparent;\n      color: #fff; }\n      html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered {\n        background-color: #20b856;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused {\n        border-color: transparent;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }\n      html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active {\n        background-color: #1ead51;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-success[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-success {\n        background-color: #22c35b;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-success.is-inverted {\n        background-color: #fff;\n        color: #22c35b; }\n        html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-success.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted {\n          background-color: #fff;\n          border-color: transparent;\n          box-shadow: none;\n          color: #22c35b; }\n      html.theme--documenter-dark .button.is-success.is-loading::after {\n        border-color: transparent transparent #fff #fff !important; }\n      html.theme--documenter-dark .button.is-success.is-outlined {\n        background-color: transparent;\n        border-color: #22c35b;\n        color: #22c35b; }\n        html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused {\n          background-color: #22c35b;\n          border-color: #22c35b;\n          color: #fff; }\n        html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after {\n          border-color: transparent transparent #22c35b #22c35b !important; }\n        html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #fff #fff !important; }\n        html.theme--documenter-dark .button.is-success.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined {\n          background-color: transparent;\n          border-color: #22c35b;\n          box-shadow: none;\n          color: #22c35b; }\n      html.theme--documenter-dark .button.is-success.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #fff;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused {\n          background-color: #fff;\n          color: #22c35b; }\n        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #22c35b #22c35b !important; }\n        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #fff;\n          box-shadow: none;\n          color: #fff; }\n    html.theme--documenter-dark .button.is-warning {\n      background-color: #ffdd57;\n      border-color: transparent;\n      color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered {\n        background-color: #ffdb4a;\n        border-color: transparent;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused {\n        border-color: transparent;\n        color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }\n      html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active {\n        background-color: #ffd83d;\n        border-color: transparent;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .button.is-warning[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-warning {\n        background-color: #ffdd57;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-warning.is-inverted {\n        background-color: rgba(0, 0, 0, 0.7);\n        color: #ffdd57; }\n        html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered {\n          background-color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .button.is-warning.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted {\n          background-color: rgba(0, 0, 0, 0.7);\n          border-color: transparent;\n          box-shadow: none;\n          color: #ffdd57; }\n      html.theme--documenter-dark .button.is-warning.is-loading::after {\n        border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; }\n      html.theme--documenter-dark .button.is-warning.is-outlined {\n        background-color: transparent;\n        border-color: #ffdd57;\n        color: #ffdd57; }\n        html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused {\n          background-color: #ffdd57;\n          border-color: #ffdd57;\n          color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after {\n          border-color: transparent transparent #ffdd57 #ffdd57 !important; }\n        html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; }\n        html.theme--documenter-dark .button.is-warning.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined {\n          background-color: transparent;\n          border-color: #ffdd57;\n          box-shadow: none;\n          color: #ffdd57; }\n      html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: rgba(0, 0, 0, 0.7);\n        color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused {\n          background-color: rgba(0, 0, 0, 0.7);\n          color: #ffdd57; }\n        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #ffdd57 #ffdd57 !important; }\n        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: rgba(0, 0, 0, 0.7);\n          box-shadow: none;\n          color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .button.is-danger {\n      background-color: #da0b00;\n      border-color: transparent;\n      color: #fff; }\n      html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered {\n        background-color: #cd0a00;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused {\n        border-color: transparent;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) {\n          box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }\n      html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active {\n        background-color: #c10a00;\n        border-color: transparent;\n        color: #fff; }\n      html.theme--documenter-dark .button.is-danger[disabled],\n      fieldset[disabled] html.theme--documenter-dark .button.is-danger {\n        background-color: #da0b00;\n        border-color: transparent;\n        box-shadow: none; }\n      html.theme--documenter-dark .button.is-danger.is-inverted {\n        background-color: #fff;\n        color: #da0b00; }\n        html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered {\n          background-color: #f2f2f2; }\n        html.theme--documenter-dark .button.is-danger.is-inverted[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted {\n          background-color: #fff;\n          border-color: transparent;\n          box-shadow: none;\n          color: #da0b00; }\n      html.theme--documenter-dark .button.is-danger.is-loading::after {\n        border-color: transparent transparent #fff #fff !important; }\n      html.theme--documenter-dark .button.is-danger.is-outlined {\n        background-color: transparent;\n        border-color: #da0b00;\n        color: #da0b00; }\n        html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused {\n          background-color: #da0b00;\n          border-color: #da0b00;\n          color: #fff; }\n        html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after {\n          border-color: transparent transparent #da0b00 #da0b00 !important; }\n        html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #fff #fff !important; }\n        html.theme--documenter-dark .button.is-danger.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined {\n          background-color: transparent;\n          border-color: #da0b00;\n          box-shadow: none;\n          color: #da0b00; }\n      html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined {\n        background-color: transparent;\n        border-color: #fff;\n        color: #fff; }\n        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused {\n          background-color: #fff;\n          color: #da0b00; }\n        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after {\n          border-color: transparent transparent #da0b00 #da0b00 !important; }\n        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],\n        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined {\n          background-color: transparent;\n          border-color: #fff;\n          box-shadow: none;\n          color: #fff; }\n    html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button {\n      border-radius: 2px;\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .button.is-normal {\n      font-size: 1rem; }\n    html.theme--documenter-dark .button.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .button.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .button[disabled],\n    fieldset[disabled] html.theme--documenter-dark .button {\n      background-color: white;\n      border-color: #dbdbdb;\n      box-shadow: none;\n      opacity: 0.5; }\n    html.theme--documenter-dark .button.is-fullwidth {\n      display: flex;\n      width: 100%; }\n    html.theme--documenter-dark .button.is-loading {\n      color: transparent !important;\n      pointer-events: none; }\n      html.theme--documenter-dark .button.is-loading::after {\n        position: absolute;\n        left: calc(50% - (1em / 2));\n        top: calc(50% - (1em / 2));\n        position: absolute !important; }\n    html.theme--documenter-dark .button.is-static {\n      background-color: whitesmoke;\n      border-color: #dbdbdb;\n      color: #7a7a7a;\n      box-shadow: none;\n      pointer-events: none; }\n    html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button {\n      border-radius: 290486px;\n      padding-left: 1em;\n      padding-right: 1em; }\n  html.theme--documenter-dark .buttons {\n    align-items: center;\n    display: flex;\n    flex-wrap: wrap;\n    justify-content: flex-start; }\n    html.theme--documenter-dark .buttons .button {\n      margin-bottom: 0.5rem; }\n      html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) {\n        margin-right: 0.5rem; }\n    html.theme--documenter-dark .buttons:last-child {\n      margin-bottom: -0.5rem; }\n    html.theme--documenter-dark .buttons:not(:last-child) {\n      margin-bottom: 1rem; }\n    html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) {\n      border-radius: 2px;\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) {\n      border-bottom-left-radius: 0;\n      border-top-left-radius: 0; }\n    html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) {\n      border-bottom-right-radius: 0;\n      border-top-right-radius: 0;\n      margin-right: -1px; }\n    html.theme--documenter-dark .buttons.has-addons .button:last-child {\n      margin-right: 0; }\n    html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered {\n      z-index: 2; }\n    html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected {\n      z-index: 3; }\n      html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover {\n        z-index: 4; }\n    html.theme--documenter-dark .buttons.has-addons .button.is-expanded {\n      flex-grow: 1;\n      flex-shrink: 1; }\n    html.theme--documenter-dark .buttons.is-centered {\n      justify-content: center; }\n      html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) {\n        margin-left: 0.25rem;\n        margin-right: 0.25rem; }\n    html.theme--documenter-dark .buttons.is-right {\n      justify-content: flex-end; }\n      html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) {\n        margin-left: 0.25rem;\n        margin-right: 0.25rem; }\n  html.theme--documenter-dark .container {\n    flex-grow: 1;\n    margin: 0 auto;\n    position: relative;\n    width: auto; }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .container {\n        max-width: 992px; }\n        html.theme--documenter-dark .container.is-fluid {\n          margin-left: 32px;\n          margin-right: 32px;\n          max-width: none; } }\n    @media screen and (max-width: 1215px) {\n      html.theme--documenter-dark .container.is-widescreen {\n        max-width: 1152px; } }\n    @media screen and (max-width: 1407px) {\n      html.theme--documenter-dark .container.is-fullhd {\n        max-width: 1344px; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .container {\n        max-width: 1152px; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .container {\n        max-width: 1344px; } }\n  html.theme--documenter-dark .content li + li {\n    margin-top: 0.25em; }\n  html.theme--documenter-dark .content p:not(:last-child),\n  html.theme--documenter-dark .content dl:not(:last-child),\n  html.theme--documenter-dark .content ol:not(:last-child),\n  html.theme--documenter-dark .content ul:not(:last-child),\n  html.theme--documenter-dark .content blockquote:not(:last-child),\n  html.theme--documenter-dark .content pre:not(:last-child),\n  html.theme--documenter-dark .content table:not(:last-child) {\n    margin-bottom: 1em; }\n  html.theme--documenter-dark .content h1,\n  html.theme--documenter-dark .content h2,\n  html.theme--documenter-dark .content h3,\n  html.theme--documenter-dark .content h4,\n  html.theme--documenter-dark .content h5,\n  html.theme--documenter-dark .content h6 {\n    color: #97b3e2;\n    font-weight: 600;\n    line-height: 1.125; }\n  html.theme--documenter-dark .content h1 {\n    font-size: 2em;\n    margin-bottom: 0.5em; }\n    html.theme--documenter-dark .content h1:not(:first-child) {\n      margin-top: 1em; }\n  html.theme--documenter-dark .content h2 {\n    font-size: 1.75em;\n    margin-bottom: 0.5714em; }\n    html.theme--documenter-dark .content h2:not(:first-child) {\n      margin-top: 1.1428em; }\n  html.theme--documenter-dark .content h3 {\n    font-size: 1.5em;\n    margin-bottom: 0.6666em; }\n    html.theme--documenter-dark .content h3:not(:first-child) {\n      margin-top: 1.3333em; }\n  html.theme--documenter-dark .content h4 {\n    font-size: 1.25em;\n    margin-bottom: 0.8em; }\n  html.theme--documenter-dark .content h5 {\n    font-size: 1.125em;\n    margin-bottom: 0.8888em; }\n  html.theme--documenter-dark .content h6 {\n    font-size: 1em;\n    margin-bottom: 1em; }\n  html.theme--documenter-dark .content blockquote {\n    background-color: whitesmoke;\n    border-left: 5px solid #dbdbdb;\n    padding: 1.25em 1.5em; }\n  html.theme--documenter-dark .content ol {\n    list-style-position: outside;\n    margin-left: 2em;\n    margin-top: 1em; }\n    html.theme--documenter-dark .content ol:not([type]) {\n      list-style-type: decimal; }\n      html.theme--documenter-dark .content ol:not([type]).is-lower-alpha {\n        list-style-type: lower-alpha; }\n      html.theme--documenter-dark .content ol:not([type]).is-lower-roman {\n        list-style-type: lower-roman; }\n      html.theme--documenter-dark .content ol:not([type]).is-upper-alpha {\n        list-style-type: upper-alpha; }\n      html.theme--documenter-dark .content ol:not([type]).is-upper-roman {\n        list-style-type: upper-roman; }\n  html.theme--documenter-dark .content ul {\n    list-style: disc outside;\n    margin-left: 2em;\n    margin-top: 1em; }\n    html.theme--documenter-dark .content ul ul {\n      list-style-type: circle;\n      margin-top: 0.5em; }\n      html.theme--documenter-dark .content ul ul ul {\n        list-style-type: square; }\n  html.theme--documenter-dark .content dd {\n    margin-left: 2em; }\n  html.theme--documenter-dark .content figure {\n    margin-left: 2em;\n    margin-right: 2em;\n    text-align: center; }\n    html.theme--documenter-dark .content figure:not(:first-child) {\n      margin-top: 2em; }\n    html.theme--documenter-dark .content figure:not(:last-child) {\n      margin-bottom: 2em; }\n    html.theme--documenter-dark .content figure img {\n      display: inline-block; }\n    html.theme--documenter-dark .content figure figcaption {\n      font-style: italic; }\n  html.theme--documenter-dark .content pre {\n    -webkit-overflow-scrolling: touch;\n    overflow-x: auto;\n    padding: 0.7rem 0.5rem;\n    white-space: pre;\n    word-wrap: normal; }\n  html.theme--documenter-dark .content sup,\n  html.theme--documenter-dark .content sub {\n    font-size: 75%; }\n  html.theme--documenter-dark .content table {\n    width: 100%; }\n    html.theme--documenter-dark .content table td,\n    html.theme--documenter-dark .content table th {\n      border: 1px solid #dbdbdb;\n      border-width: 0 0 1px;\n      padding: 0.5em 0.75em;\n      vertical-align: top; }\n    html.theme--documenter-dark .content table th {\n      color: #97b3e2; }\n      html.theme--documenter-dark .content table th:not([align]) {\n        text-align: left; }\n    html.theme--documenter-dark .content table thead td,\n    html.theme--documenter-dark .content table thead th {\n      border-width: 0 0 2px;\n      color: #97b3e2; }\n    html.theme--documenter-dark .content table tfoot td,\n    html.theme--documenter-dark .content table tfoot th {\n      border-width: 2px 0 0;\n      color: #97b3e2; }\n    html.theme--documenter-dark .content table tbody tr:last-child td,\n    html.theme--documenter-dark .content table tbody tr:last-child th {\n      border-bottom-width: 0; }\n  html.theme--documenter-dark .content .tabs li + li {\n    margin-top: 0; }\n  html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content {\n    font-size: 0.75rem; }\n  html.theme--documenter-dark .content.is-medium {\n    font-size: 1.25rem; }\n  html.theme--documenter-dark .content.is-large {\n    font-size: 1.5rem; }\n  html.theme--documenter-dark .icon {\n    align-items: center;\n    display: inline-flex;\n    justify-content: center;\n    height: 1.5rem;\n    width: 1.5rem; }\n    html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon {\n      height: 1rem;\n      width: 1rem; }\n    html.theme--documenter-dark .icon.is-medium {\n      height: 2rem;\n      width: 2rem; }\n    html.theme--documenter-dark .icon.is-large {\n      height: 3rem;\n      width: 3rem; }\n  html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img {\n    display: block;\n    position: relative; }\n    html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img {\n      display: block;\n      height: auto;\n      width: 100%; }\n      html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded {\n        border-radius: 290486px; }\n    html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img,\n    html.theme--documenter-dark .image.is-square .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img,\n    html.theme--documenter-dark .image.is-1by1 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img,\n    html.theme--documenter-dark .image.is-5by4 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img,\n    html.theme--documenter-dark .image.is-4by3 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img,\n    html.theme--documenter-dark .image.is-3by2 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img,\n    html.theme--documenter-dark .image.is-5by3 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img,\n    html.theme--documenter-dark .image.is-16by9 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img,\n    html.theme--documenter-dark .image.is-2by1 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img,\n    html.theme--documenter-dark .image.is-3by1 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img,\n    html.theme--documenter-dark .image.is-4by5 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img,\n    html.theme--documenter-dark .image.is-3by4 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img,\n    html.theme--documenter-dark .image.is-2by3 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img,\n    html.theme--documenter-dark .image.is-3by5 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img,\n    html.theme--documenter-dark .image.is-9by16 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img,\n    html.theme--documenter-dark .image.is-1by2 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img,\n    html.theme--documenter-dark .image.is-1by3 .has-ratio,\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio {\n      height: 100%;\n      width: 100%; }\n    html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 {\n      padding-top: 100%; }\n    html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 {\n      padding-top: 80%; }\n    html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 {\n      padding-top: 75%; }\n    html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 {\n      padding-top: 66.6666%; }\n    html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 {\n      padding-top: 60%; }\n    html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 {\n      padding-top: 56.25%; }\n    html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 {\n      padding-top: 50%; }\n    html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 {\n      padding-top: 33.3333%; }\n    html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 {\n      padding-top: 125%; }\n    html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 {\n      padding-top: 133.3333%; }\n    html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 {\n      padding-top: 150%; }\n    html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 {\n      padding-top: 166.6666%; }\n    html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 {\n      padding-top: 177.7777%; }\n    html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 {\n      padding-top: 200%; }\n    html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 {\n      padding-top: 300%; }\n    html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 {\n      height: 16px;\n      width: 16px; }\n    html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 {\n      height: 24px;\n      width: 24px; }\n    html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 {\n      height: 32px;\n      width: 32px; }\n    html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 {\n      height: 48px;\n      width: 48px; }\n    html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 {\n      height: 64px;\n      width: 64px; }\n    html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 {\n      height: 96px;\n      width: 96px; }\n    html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 {\n      height: 128px;\n      width: 128px; }\n  html.theme--documenter-dark .notification {\n    background-color: whitesmoke;\n    border-radius: 4px;\n    padding: 1.25rem 2.5rem 1.25rem 1.5rem;\n    position: relative; }\n    html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) {\n      color: currentColor;\n      text-decoration: underline; }\n    html.theme--documenter-dark .notification strong {\n      color: currentColor; }\n    html.theme--documenter-dark .notification code,\n    html.theme--documenter-dark .notification pre {\n      background: white; }\n    html.theme--documenter-dark .notification pre code {\n      background: transparent; }\n    html.theme--documenter-dark .notification > .delete {\n      position: absolute;\n      right: 0.5rem;\n      top: 0.5rem; }\n    html.theme--documenter-dark .notification .title,\n    html.theme--documenter-dark .notification .subtitle,\n    html.theme--documenter-dark .notification .content {\n      color: currentColor; }\n    html.theme--documenter-dark .notification.is-white {\n      background-color: white;\n      color: #0a0a0a; }\n    html.theme--documenter-dark .notification.is-black {\n      background-color: #0a0a0a;\n      color: white; }\n    html.theme--documenter-dark .notification.is-light {\n      background-color: whitesmoke;\n      color: #363636; }\n    html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification {\n      background-color: #363636;\n      color: whitesmoke; }\n    html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink {\n      background-color: #4eb5de;\n      color: #fff; }\n    html.theme--documenter-dark .notification.is-link {\n      background-color: #e37733;\n      color: #fff; }\n    html.theme--documenter-dark .notification.is-info {\n      background-color: #209cee;\n      color: #fff; }\n    html.theme--documenter-dark .notification.is-success {\n      background-color: #22c35b;\n      color: #fff; }\n    html.theme--documenter-dark .notification.is-warning {\n      background-color: #ffdd57;\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .notification.is-danger {\n      background-color: #da0b00;\n      color: #fff; }\n  html.theme--documenter-dark .progress {\n    -moz-appearance: none;\n    -webkit-appearance: none;\n    border: none;\n    border-radius: 290486px;\n    display: block;\n    height: 1rem;\n    overflow: hidden;\n    padding: 0;\n    width: 100%; }\n    html.theme--documenter-dark .progress::-webkit-progress-bar {\n      background-color: #dbdbdb; }\n    html.theme--documenter-dark .progress::-webkit-progress-value {\n      background-color: #ececec; }\n    html.theme--documenter-dark .progress::-moz-progress-bar {\n      background-color: #ececec; }\n    html.theme--documenter-dark .progress::-ms-fill {\n      background-color: #ececec;\n      border: none; }\n    html.theme--documenter-dark .progress.is-white::-webkit-progress-value {\n      background-color: white; }\n    html.theme--documenter-dark .progress.is-white::-moz-progress-bar {\n      background-color: white; }\n    html.theme--documenter-dark .progress.is-white::-ms-fill {\n      background-color: white; }\n    html.theme--documenter-dark .progress.is-white:indeterminate {\n      background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-black::-webkit-progress-value {\n      background-color: #0a0a0a; }\n    html.theme--documenter-dark .progress.is-black::-moz-progress-bar {\n      background-color: #0a0a0a; }\n    html.theme--documenter-dark .progress.is-black::-ms-fill {\n      background-color: #0a0a0a; }\n    html.theme--documenter-dark .progress.is-black:indeterminate {\n      background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-light::-webkit-progress-value {\n      background-color: whitesmoke; }\n    html.theme--documenter-dark .progress.is-light::-moz-progress-bar {\n      background-color: whitesmoke; }\n    html.theme--documenter-dark .progress.is-light::-ms-fill {\n      background-color: whitesmoke; }\n    html.theme--documenter-dark .progress.is-light:indeterminate {\n      background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value {\n      background-color: #363636; }\n    html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar {\n      background-color: #363636; }\n    html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill {\n      background-color: #363636; }\n    html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate {\n      background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value {\n      background-color: #4eb5de; }\n    html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar {\n      background-color: #4eb5de; }\n    html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill {\n      background-color: #4eb5de; }\n    html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate {\n      background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-link::-webkit-progress-value {\n      background-color: #e37733; }\n    html.theme--documenter-dark .progress.is-link::-moz-progress-bar {\n      background-color: #e37733; }\n    html.theme--documenter-dark .progress.is-link::-ms-fill {\n      background-color: #e37733; }\n    html.theme--documenter-dark .progress.is-link:indeterminate {\n      background-image: linear-gradient(to right, #e37733 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-info::-webkit-progress-value {\n      background-color: #209cee; }\n    html.theme--documenter-dark .progress.is-info::-moz-progress-bar {\n      background-color: #209cee; }\n    html.theme--documenter-dark .progress.is-info::-ms-fill {\n      background-color: #209cee; }\n    html.theme--documenter-dark .progress.is-info:indeterminate {\n      background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-success::-webkit-progress-value {\n      background-color: #22c35b; }\n    html.theme--documenter-dark .progress.is-success::-moz-progress-bar {\n      background-color: #22c35b; }\n    html.theme--documenter-dark .progress.is-success::-ms-fill {\n      background-color: #22c35b; }\n    html.theme--documenter-dark .progress.is-success:indeterminate {\n      background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-warning::-webkit-progress-value {\n      background-color: #ffdd57; }\n    html.theme--documenter-dark .progress.is-warning::-moz-progress-bar {\n      background-color: #ffdd57; }\n    html.theme--documenter-dark .progress.is-warning::-ms-fill {\n      background-color: #ffdd57; }\n    html.theme--documenter-dark .progress.is-warning:indeterminate {\n      background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress.is-danger::-webkit-progress-value {\n      background-color: #da0b00; }\n    html.theme--documenter-dark .progress.is-danger::-moz-progress-bar {\n      background-color: #da0b00; }\n    html.theme--documenter-dark .progress.is-danger::-ms-fill {\n      background-color: #da0b00; }\n    html.theme--documenter-dark .progress.is-danger:indeterminate {\n      background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); }\n    html.theme--documenter-dark .progress:indeterminate {\n      animation-duration: 1.5s;\n      animation-iteration-count: infinite;\n      animation-name: moveIndeterminate;\n      animation-timing-function: linear;\n      background-color: #dbdbdb;\n      background-image: linear-gradient(to right, #ececec 30%, #dbdbdb 30%);\n      background-position: top left;\n      background-repeat: no-repeat;\n      background-size: 150% 150%; }\n      html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar {\n        background-color: transparent; }\n      html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar {\n        background-color: transparent; }\n    html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress {\n      height: 0.75rem; }\n    html.theme--documenter-dark .progress.is-medium {\n      height: 1.25rem; }\n    html.theme--documenter-dark .progress.is-large {\n      height: 1.5rem; }\n\n@keyframes moveIndeterminate {\n  from {\n    background-position: 200% 0; }\n  to {\n    background-position: -200% 0; } }\n  html.theme--documenter-dark .table {\n    background-color: white;\n    color: #363636; }\n    html.theme--documenter-dark .table td,\n    html.theme--documenter-dark .table th {\n      border: 1px solid #dbdbdb;\n      border-width: 0 0 1px;\n      padding: 0.5em 0.75em;\n      vertical-align: top; }\n      html.theme--documenter-dark .table td.is-white,\n      html.theme--documenter-dark .table th.is-white {\n        background-color: white;\n        border-color: white;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .table td.is-black,\n      html.theme--documenter-dark .table th.is-black {\n        background-color: #0a0a0a;\n        border-color: #0a0a0a;\n        color: white; }\n      html.theme--documenter-dark .table td.is-light,\n      html.theme--documenter-dark .table th.is-light {\n        background-color: whitesmoke;\n        border-color: whitesmoke;\n        color: #363636; }\n      html.theme--documenter-dark .table td.is-dark,\n      html.theme--documenter-dark .table th.is-dark {\n        background-color: #363636;\n        border-color: #363636;\n        color: whitesmoke; }\n      html.theme--documenter-dark .table td.is-primary,\n      html.theme--documenter-dark .table th.is-primary {\n        background-color: #4eb5de;\n        border-color: #4eb5de;\n        color: #fff; }\n      html.theme--documenter-dark .table td.is-link,\n      html.theme--documenter-dark .table th.is-link {\n        background-color: #e37733;\n        border-color: #e37733;\n        color: #fff; }\n      html.theme--documenter-dark .table td.is-info,\n      html.theme--documenter-dark .table th.is-info {\n        background-color: #209cee;\n        border-color: #209cee;\n        color: #fff; }\n      html.theme--documenter-dark .table td.is-success,\n      html.theme--documenter-dark .table th.is-success {\n        background-color: #22c35b;\n        border-color: #22c35b;\n        color: #fff; }\n      html.theme--documenter-dark .table td.is-warning,\n      html.theme--documenter-dark .table th.is-warning {\n        background-color: #ffdd57;\n        border-color: #ffdd57;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .table td.is-danger,\n      html.theme--documenter-dark .table th.is-danger {\n        background-color: #da0b00;\n        border-color: #da0b00;\n        color: #fff; }\n      html.theme--documenter-dark .table td.is-narrow,\n      html.theme--documenter-dark .table th.is-narrow {\n        white-space: nowrap;\n        width: 1%; }\n      html.theme--documenter-dark .table td.is-selected,\n      html.theme--documenter-dark .table th.is-selected {\n        background-color: #4eb5de;\n        color: #fff; }\n        html.theme--documenter-dark .table td.is-selected a,\n        html.theme--documenter-dark .table td.is-selected strong,\n        html.theme--documenter-dark .table th.is-selected a,\n        html.theme--documenter-dark .table th.is-selected strong {\n          color: currentColor; }\n    html.theme--documenter-dark .table th {\n      color: #97b3e2; }\n      html.theme--documenter-dark .table th:not([align]) {\n        text-align: left; }\n    html.theme--documenter-dark .table tr.is-selected {\n      background-color: #4eb5de;\n      color: #fff; }\n      html.theme--documenter-dark .table tr.is-selected a,\n      html.theme--documenter-dark .table tr.is-selected strong {\n        color: currentColor; }\n      html.theme--documenter-dark .table tr.is-selected td,\n      html.theme--documenter-dark .table tr.is-selected th {\n        border-color: #fff;\n        color: currentColor; }\n    html.theme--documenter-dark .table thead {\n      background-color: transparent; }\n      html.theme--documenter-dark .table thead td,\n      html.theme--documenter-dark .table thead th {\n        border-width: 0 0 2px;\n        color: #97b3e2; }\n    html.theme--documenter-dark .table tfoot {\n      background-color: transparent; }\n      html.theme--documenter-dark .table tfoot td,\n      html.theme--documenter-dark .table tfoot th {\n        border-width: 2px 0 0;\n        color: #97b3e2; }\n    html.theme--documenter-dark .table tbody {\n      background-color: transparent; }\n      html.theme--documenter-dark .table tbody tr:last-child td,\n      html.theme--documenter-dark .table tbody tr:last-child th {\n        border-bottom-width: 0; }\n    html.theme--documenter-dark .table.is-bordered td,\n    html.theme--documenter-dark .table.is-bordered th {\n      border-width: 1px; }\n    html.theme--documenter-dark .table.is-bordered tr:last-child td,\n    html.theme--documenter-dark .table.is-bordered tr:last-child th {\n      border-bottom-width: 1px; }\n    html.theme--documenter-dark .table.is-fullwidth {\n      width: 100%; }\n    html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover {\n      background-color: #fafafa; }\n    html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover {\n      background-color: #fafafa; }\n      html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) {\n        background-color: whitesmoke; }\n    html.theme--documenter-dark .table.is-narrow td,\n    html.theme--documenter-dark .table.is-narrow th {\n      padding: 0.25em 0.5em; }\n    html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) {\n      background-color: #fafafa; }\n  html.theme--documenter-dark .table-container {\n    -webkit-overflow-scrolling: touch;\n    overflow: auto;\n    overflow-y: hidden;\n    max-width: 100%; }\n  html.theme--documenter-dark .tags {\n    align-items: center;\n    display: flex;\n    flex-wrap: wrap;\n    justify-content: flex-start; }\n    html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd {\n      margin-bottom: 0.5rem; }\n      html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child) {\n        margin-right: 0.5rem; }\n    html.theme--documenter-dark .tags:last-child {\n      margin-bottom: -0.5rem; }\n    html.theme--documenter-dark .tags:not(:last-child) {\n      margin-bottom: 1rem; }\n    html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large) {\n      font-size: 1rem; }\n    html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium) {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .tags.is-centered {\n      justify-content: center; }\n      html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd {\n        margin-right: 0.25rem;\n        margin-left: 0.25rem; }\n    html.theme--documenter-dark .tags.is-right {\n      justify-content: flex-end; }\n      html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child) {\n        margin-left: 0.5rem; }\n      html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child) {\n        margin-right: 0; }\n    html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd {\n      margin-right: 0; }\n      html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child) {\n        margin-left: 0;\n        border-bottom-left-radius: 0;\n        border-top-left-radius: 0; }\n      html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child) {\n        border-bottom-right-radius: 0;\n        border-top-right-radius: 0; }\n  html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body), html.theme--documenter-dark .content kbd:not(body) {\n    align-items: center;\n    background-color: whitesmoke;\n    border-radius: 4px;\n    color: #ececec;\n    display: inline-flex;\n    font-size: 0.75rem;\n    height: 2em;\n    justify-content: center;\n    line-height: 1.5;\n    padding-left: 0.75em;\n    padding-right: 0.75em;\n    white-space: nowrap; }\n    html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete {\n      margin-left: 0.25rem;\n      margin-right: -0.375rem; }\n    html.theme--documenter-dark .tag:not(body).is-white, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-white, html.theme--documenter-dark .content kbd:not(body).is-white {\n      background-color: white;\n      color: #0a0a0a; }\n    html.theme--documenter-dark .tag:not(body).is-black, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-black, html.theme--documenter-dark .content kbd:not(body).is-black {\n      background-color: #0a0a0a;\n      color: white; }\n    html.theme--documenter-dark .tag:not(body).is-light, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-light, html.theme--documenter-dark .content kbd:not(body).is-light {\n      background-color: whitesmoke;\n      color: #363636; }\n    html.theme--documenter-dark .tag:not(body).is-dark, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-dark, html.theme--documenter-dark .content kbd:not(body) {\n      background-color: #363636;\n      color: whitesmoke; }\n    html.theme--documenter-dark .tag:not(body).is-primary, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body), html.theme--documenter-dark .content kbd:not(body).is-primary {\n      background-color: #4eb5de;\n      color: #fff; }\n    html.theme--documenter-dark .tag:not(body).is-link, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-link, html.theme--documenter-dark .content kbd:not(body).is-link {\n      background-color: #e37733;\n      color: #fff; }\n    html.theme--documenter-dark .tag:not(body).is-info, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-info, html.theme--documenter-dark .content kbd:not(body).is-info {\n      background-color: #209cee;\n      color: #fff; }\n    html.theme--documenter-dark .tag:not(body).is-success, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-success, html.theme--documenter-dark .content kbd:not(body).is-success {\n      background-color: #22c35b;\n      color: #fff; }\n    html.theme--documenter-dark .tag:not(body).is-warning, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-warning, html.theme--documenter-dark .content kbd:not(body).is-warning {\n      background-color: #ffdd57;\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .tag:not(body).is-danger, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-danger, html.theme--documenter-dark .content kbd:not(body).is-danger {\n      background-color: #da0b00;\n      color: #fff; }\n    html.theme--documenter-dark .tag:not(body).is-normal, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-normal, html.theme--documenter-dark .content kbd:not(body).is-normal {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .tag:not(body).is-medium, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-medium, html.theme--documenter-dark .content kbd:not(body).is-medium {\n      font-size: 1rem; }\n    html.theme--documenter-dark .tag:not(body).is-large, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-large, html.theme--documenter-dark .content kbd:not(body).is-large {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child) {\n      margin-left: -0.375em;\n      margin-right: 0.1875em; }\n    html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child) {\n      margin-left: 0.1875em;\n      margin-right: -0.375em; }\n    html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child {\n      margin-left: -0.375em;\n      margin-right: -0.375em; }\n    html.theme--documenter-dark .tag:not(body).is-delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete, html.theme--documenter-dark .content kbd:not(body).is-delete {\n      margin-left: 1px;\n      padding: 0;\n      position: relative;\n      width: 2em; }\n      html.theme--documenter-dark .tag:not(body).is-delete::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::before, html.theme--documenter-dark .content kbd:not(body).is-delete::before, html.theme--documenter-dark .tag:not(body).is-delete::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::after, html.theme--documenter-dark .content kbd:not(body).is-delete::after {\n        background-color: currentColor;\n        content: \"\";\n        display: block;\n        left: 50%;\n        position: absolute;\n        top: 50%;\n        transform: translateX(-50%) translateY(-50%) rotate(45deg);\n        transform-origin: center center; }\n      html.theme--documenter-dark .tag:not(body).is-delete::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::before, html.theme--documenter-dark .content kbd:not(body).is-delete::before {\n        height: 1px;\n        width: 50%; }\n      html.theme--documenter-dark .tag:not(body).is-delete::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::after, html.theme--documenter-dark .content kbd:not(body).is-delete::after {\n        height: 50%;\n        width: 1px; }\n      html.theme--documenter-dark .tag:not(body).is-delete:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:hover, html.theme--documenter-dark .content kbd:not(body).is-delete:hover, html.theme--documenter-dark .tag:not(body).is-delete:focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:focus, html.theme--documenter-dark .content kbd:not(body).is-delete:focus {\n        background-color: #e8e8e8; }\n      html.theme--documenter-dark .tag:not(body).is-delete:active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:active, html.theme--documenter-dark .content kbd:not(body).is-delete:active {\n        background-color: #dbdbdb; }\n    html.theme--documenter-dark .tag:not(body).is-rounded, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-rounded, html.theme--documenter-dark .content kbd:not(body).is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tag:not(body) {\n      border-radius: 290486px; }\n  html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover {\n    text-decoration: underline; }\n  html.theme--documenter-dark .title,\n  html.theme--documenter-dark .subtitle {\n    word-break: break-word; }\n    html.theme--documenter-dark .title em,\n    html.theme--documenter-dark .title span,\n    html.theme--documenter-dark .subtitle em,\n    html.theme--documenter-dark .subtitle span {\n      font-weight: inherit; }\n    html.theme--documenter-dark .title sub,\n    html.theme--documenter-dark .subtitle sub {\n      font-size: 0.75em; }\n    html.theme--documenter-dark .title sup,\n    html.theme--documenter-dark .subtitle sup {\n      font-size: 0.75em; }\n    html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd,\n    html.theme--documenter-dark .subtitle .tag,\n    html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink,\n    html.theme--documenter-dark .subtitle .content kbd,\n    html.theme--documenter-dark .content .subtitle kbd {\n      vertical-align: middle; }\n  html.theme--documenter-dark .title {\n    color: #363636;\n    font-size: 2rem;\n    font-weight: 600;\n    line-height: 1.125; }\n    html.theme--documenter-dark .title strong {\n      color: inherit;\n      font-weight: inherit; }\n    html.theme--documenter-dark .title + .highlight {\n      margin-top: -0.75rem; }\n    html.theme--documenter-dark .title:not(.is-spaced) + .subtitle {\n      margin-top: -1.25rem; }\n    html.theme--documenter-dark .title.is-1 {\n      font-size: 3rem; }\n    html.theme--documenter-dark .title.is-2 {\n      font-size: 2.5rem; }\n    html.theme--documenter-dark .title.is-3 {\n      font-size: 2rem; }\n    html.theme--documenter-dark .title.is-4 {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .title.is-5 {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .title.is-6 {\n      font-size: 1rem; }\n    html.theme--documenter-dark .title.is-7 {\n      font-size: 0.75rem; }\n  html.theme--documenter-dark .subtitle {\n    color: #4a4a4a;\n    font-size: 1.25rem;\n    font-weight: 400;\n    line-height: 1.25; }\n    html.theme--documenter-dark .subtitle strong {\n      color: #363636;\n      font-weight: 600; }\n    html.theme--documenter-dark .subtitle:not(.is-spaced) + .title {\n      margin-top: -1.25rem; }\n    html.theme--documenter-dark .subtitle.is-1 {\n      font-size: 3rem; }\n    html.theme--documenter-dark .subtitle.is-2 {\n      font-size: 2.5rem; }\n    html.theme--documenter-dark .subtitle.is-3 {\n      font-size: 2rem; }\n    html.theme--documenter-dark .subtitle.is-4 {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .subtitle.is-5 {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .subtitle.is-6 {\n      font-size: 1rem; }\n    html.theme--documenter-dark .subtitle.is-7 {\n      font-size: 0.75rem; }\n  html.theme--documenter-dark .heading {\n    display: block;\n    font-size: 11px;\n    letter-spacing: 1px;\n    margin-bottom: 5px;\n    text-transform: uppercase; }\n  html.theme--documenter-dark .highlight {\n    font-weight: 400;\n    max-width: 100%;\n    overflow: hidden;\n    padding: 0; }\n    html.theme--documenter-dark .highlight pre {\n      overflow: auto;\n      max-width: 100%; }\n  html.theme--documenter-dark .number {\n    align-items: center;\n    background-color: whitesmoke;\n    border-radius: 290486px;\n    display: inline-flex;\n    font-size: 1.25rem;\n    height: 2em;\n    justify-content: center;\n    margin-right: 1.5rem;\n    min-width: 2.5em;\n    padding: 0.25rem 0.5rem;\n    text-align: center;\n    vertical-align: top; }\n  html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea, html.theme--documenter-dark .select select {\n    background-color: white;\n    border-color: #dbdbdb;\n    border-radius: 4px;\n    color: #363636; }\n    html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .select select::-moz-placeholder {\n      color: rgba(54, 54, 54, 0.3); }\n    html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .select select::-webkit-input-placeholder {\n      color: rgba(54, 54, 54, 0.3); }\n    html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .select select:-moz-placeholder {\n      color: rgba(54, 54, 54, 0.3); }\n    html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .select select:-ms-input-placeholder {\n      color: rgba(54, 54, 54, 0.3); }\n    html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .select select.is-hovered {\n      border-color: #ac5118; }\n    html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .select select.is-active {\n      border-color: #f0f0f0;\n      box-shadow: 0 0 0 0.125em rgba(227, 119, 51, 0.25); }\n    html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .select select[disabled],\n    fieldset[disabled] html.theme--documenter-dark .input,\n    fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,\n    fieldset[disabled] html.theme--documenter-dark .textarea,\n    fieldset[disabled] html.theme--documenter-dark .select select {\n      background-color: whitesmoke;\n      border-color: whitesmoke;\n      box-shadow: none;\n      color: #7a7a7a; }\n      html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .select select[disabled]::-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder {\n        color: rgba(122, 122, 122, 0.3); }\n      html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder {\n        color: rgba(122, 122, 122, 0.3); }\n      html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .select select[disabled]:-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder {\n        color: rgba(122, 122, 122, 0.3); }\n      html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder,\n      fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder {\n        color: rgba(122, 122, 122, 0.3); }\n  html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea {\n    box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1);\n    max-width: 100%;\n    width: 100%; }\n    html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly], html.theme--documenter-dark .textarea[readonly] {\n      box-shadow: none; }\n    html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white, html.theme--documenter-dark .is-white.textarea {\n      border-color: white; }\n      html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white.is-focused, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white.is-active, html.theme--documenter-dark .is-white.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }\n    html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black, html.theme--documenter-dark .is-black.textarea {\n      border-color: #0a0a0a; }\n      html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black.is-focused, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black.is-active, html.theme--documenter-dark .is-black.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }\n    html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light, html.theme--documenter-dark .is-light.textarea {\n      border-color: whitesmoke; }\n      html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light.is-focused, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light.is-active, html.theme--documenter-dark .is-light.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }\n    html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark .content kbd.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea {\n      border-color: #363636; }\n      html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark.is-focused, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark.is-active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }\n    html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink {\n      border-color: #4eb5de; }\n      html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary.is-focused, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary.is-active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink {\n        box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }\n    html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link, html.theme--documenter-dark .is-link.textarea {\n      border-color: #e37733; }\n      html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link.is-focused, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link.is-active, html.theme--documenter-dark .is-link.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(227, 119, 51, 0.25); }\n    html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info, html.theme--documenter-dark .is-info.textarea {\n      border-color: #209cee; }\n      html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info.is-focused, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info.is-active, html.theme--documenter-dark .is-info.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }\n    html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success, html.theme--documenter-dark .is-success.textarea {\n      border-color: #22c35b; }\n      html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success.is-focused, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success.is-active, html.theme--documenter-dark .is-success.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }\n    html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning, html.theme--documenter-dark .is-warning.textarea {\n      border-color: #ffdd57; }\n      html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning.is-focused, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning.is-active, html.theme--documenter-dark .is-warning.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }\n    html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger, html.theme--documenter-dark .is-danger.textarea {\n      border-color: #da0b00; }\n      html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger.is-focused, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger.is-active, html.theme--documenter-dark .is-danger.is-active.textarea {\n        box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }\n    html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .is-small.textarea {\n      border-radius: 2px;\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium, html.theme--documenter-dark .is-medium.textarea {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large, html.theme--documenter-dark .is-large.textarea {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth, html.theme--documenter-dark .is-fullwidth.textarea {\n      display: block;\n      width: 100%; }\n    html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline, html.theme--documenter-dark .is-inline.textarea {\n      display: inline;\n      width: auto; }\n  html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input {\n    border-radius: 290486px;\n    padding-left: 1em;\n    padding-right: 1em; }\n  html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static {\n    background-color: transparent;\n    border-color: transparent;\n    box-shadow: none;\n    padding-left: 0;\n    padding-right: 0; }\n  html.theme--documenter-dark .textarea {\n    display: block;\n    max-width: 100%;\n    min-width: 100%;\n    padding: 0.625em;\n    resize: vertical; }\n    html.theme--documenter-dark .textarea:not([rows]) {\n      max-height: 600px;\n      min-height: 120px; }\n    html.theme--documenter-dark .textarea[rows] {\n      height: initial; }\n    html.theme--documenter-dark .textarea.has-fixed-size {\n      resize: none; }\n  html.theme--documenter-dark .checkbox, html.theme--documenter-dark .radio {\n    cursor: pointer;\n    display: inline-block;\n    line-height: 1.25;\n    position: relative; }\n    html.theme--documenter-dark .checkbox input, html.theme--documenter-dark .radio input {\n      cursor: pointer; }\n    html.theme--documenter-dark .checkbox:hover, html.theme--documenter-dark .radio:hover {\n      color: #363636; }\n    html.theme--documenter-dark .checkbox[disabled], html.theme--documenter-dark .radio[disabled],\n    fieldset[disabled] html.theme--documenter-dark .checkbox,\n    fieldset[disabled] html.theme--documenter-dark .radio {\n      color: #7a7a7a;\n      cursor: not-allowed; }\n  html.theme--documenter-dark .radio + .radio {\n    margin-left: 0.5em; }\n  html.theme--documenter-dark .select {\n    display: inline-block;\n    max-width: 100%;\n    position: relative;\n    vertical-align: top; }\n    html.theme--documenter-dark .select:not(.is-multiple) {\n      height: 2.25em; }\n    html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after {\n      border-color: #e37733;\n      right: 1.125em;\n      z-index: 4; }\n    html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select {\n      border-radius: 290486px;\n      padding-left: 1em; }\n    html.theme--documenter-dark .select select {\n      cursor: pointer;\n      display: block;\n      font-size: 1em;\n      max-width: 100%;\n      outline: none; }\n      html.theme--documenter-dark .select select::-ms-expand {\n        display: none; }\n      html.theme--documenter-dark .select select[disabled]:hover,\n      fieldset[disabled] html.theme--documenter-dark .select select:hover {\n        border-color: whitesmoke; }\n      html.theme--documenter-dark .select select:not([multiple]) {\n        padding-right: 2.5em; }\n      html.theme--documenter-dark .select select[multiple] {\n        height: auto;\n        padding: 0; }\n        html.theme--documenter-dark .select select[multiple] option {\n          padding: 0.5em 1em; }\n    html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after {\n      border-color: #363636; }\n    html.theme--documenter-dark .select.is-white:not(:hover)::after {\n      border-color: white; }\n    html.theme--documenter-dark .select.is-white select {\n      border-color: white; }\n      html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered {\n        border-color: #f2f2f2; }\n      html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }\n    html.theme--documenter-dark .select.is-black:not(:hover)::after {\n      border-color: #0a0a0a; }\n    html.theme--documenter-dark .select.is-black select {\n      border-color: #0a0a0a; }\n      html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered {\n        border-color: black; }\n      html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }\n    html.theme--documenter-dark .select.is-light:not(:hover)::after {\n      border-color: whitesmoke; }\n    html.theme--documenter-dark .select.is-light select {\n      border-color: whitesmoke; }\n      html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered {\n        border-color: #e8e8e8; }\n      html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }\n    html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after {\n      border-color: #363636; }\n    html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select {\n      border-color: #363636; }\n      html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered {\n        border-color: #292929; }\n      html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }\n    html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after {\n      border-color: #4eb5de; }\n    html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select {\n      border-color: #4eb5de; }\n      html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered {\n        border-color: #39acda; }\n      html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }\n    html.theme--documenter-dark .select.is-link:not(:hover)::after {\n      border-color: #e37733; }\n    html.theme--documenter-dark .select.is-link select {\n      border-color: #e37733; }\n      html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered {\n        border-color: #dd681f; }\n      html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(227, 119, 51, 0.25); }\n    html.theme--documenter-dark .select.is-info:not(:hover)::after {\n      border-color: #209cee; }\n    html.theme--documenter-dark .select.is-info select {\n      border-color: #209cee; }\n      html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered {\n        border-color: #118fe4; }\n      html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }\n    html.theme--documenter-dark .select.is-success:not(:hover)::after {\n      border-color: #22c35b; }\n    html.theme--documenter-dark .select.is-success select {\n      border-color: #22c35b; }\n      html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered {\n        border-color: #1ead51; }\n      html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }\n    html.theme--documenter-dark .select.is-warning:not(:hover)::after {\n      border-color: #ffdd57; }\n    html.theme--documenter-dark .select.is-warning select {\n      border-color: #ffdd57; }\n      html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered {\n        border-color: #ffd83d; }\n      html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }\n    html.theme--documenter-dark .select.is-danger:not(:hover)::after {\n      border-color: #da0b00; }\n    html.theme--documenter-dark .select.is-danger select {\n      border-color: #da0b00; }\n      html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered {\n        border-color: #c10a00; }\n      html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active {\n        box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }\n    html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select {\n      border-radius: 2px;\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .select.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .select.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .select.is-disabled::after {\n      border-color: #7a7a7a; }\n    html.theme--documenter-dark .select.is-fullwidth {\n      width: 100%; }\n      html.theme--documenter-dark .select.is-fullwidth select {\n        width: 100%; }\n    html.theme--documenter-dark .select.is-loading::after {\n      margin-top: 0;\n      position: absolute;\n      right: 0.625em;\n      top: 0.625em;\n      transform: none; }\n    html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select.is-loading:after {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .select.is-loading.is-medium:after {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .select.is-loading.is-large:after {\n      font-size: 1.5rem; }\n  html.theme--documenter-dark .file {\n    align-items: stretch;\n    display: flex;\n    justify-content: flex-start;\n    position: relative; }\n    html.theme--documenter-dark .file.is-white .file-cta {\n      background-color: white;\n      border-color: transparent;\n      color: #0a0a0a; }\n    html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta {\n      background-color: #f9f9f9;\n      border-color: transparent;\n      color: #0a0a0a; }\n    html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25);\n      color: #0a0a0a; }\n    html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta {\n      background-color: #f2f2f2;\n      border-color: transparent;\n      color: #0a0a0a; }\n    html.theme--documenter-dark .file.is-black .file-cta {\n      background-color: #0a0a0a;\n      border-color: transparent;\n      color: white; }\n    html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta {\n      background-color: #040404;\n      border-color: transparent;\n      color: white; }\n    html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25);\n      color: white; }\n    html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta {\n      background-color: black;\n      border-color: transparent;\n      color: white; }\n    html.theme--documenter-dark .file.is-light .file-cta {\n      background-color: whitesmoke;\n      border-color: transparent;\n      color: #363636; }\n    html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta {\n      background-color: #eeeeee;\n      border-color: transparent;\n      color: #363636; }\n    html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25);\n      color: #363636; }\n    html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta {\n      background-color: #e8e8e8;\n      border-color: transparent;\n      color: #363636; }\n    html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta {\n      background-color: #363636;\n      border-color: transparent;\n      color: whitesmoke; }\n    html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta {\n      background-color: #2f2f2f;\n      border-color: transparent;\n      color: whitesmoke; }\n    html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25);\n      color: whitesmoke; }\n    html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta {\n      background-color: #292929;\n      border-color: transparent;\n      color: whitesmoke; }\n    html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta {\n      background-color: #4eb5de;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta {\n      background-color: #43b1dc;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25);\n      color: #fff; }\n    html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta {\n      background-color: #39acda;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-link .file-cta {\n      background-color: #e37733;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta {\n      background-color: #e16f28;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(227, 119, 51, 0.25);\n      color: #fff; }\n    html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta {\n      background-color: #dd681f;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-info .file-cta {\n      background-color: #209cee;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta {\n      background-color: #1496ed;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25);\n      color: #fff; }\n    html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta {\n      background-color: #118fe4;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-success .file-cta {\n      background-color: #22c35b;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta {\n      background-color: #20b856;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25);\n      color: #fff; }\n    html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta {\n      background-color: #1ead51;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-warning .file-cta {\n      background-color: #ffdd57;\n      border-color: transparent;\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta {\n      background-color: #ffdb4a;\n      border-color: transparent;\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25);\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta {\n      background-color: #ffd83d;\n      border-color: transparent;\n      color: rgba(0, 0, 0, 0.7); }\n    html.theme--documenter-dark .file.is-danger .file-cta {\n      background-color: #da0b00;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta {\n      background-color: #cd0a00;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta {\n      border-color: transparent;\n      box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25);\n      color: #fff; }\n    html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta {\n      background-color: #c10a00;\n      border-color: transparent;\n      color: #fff; }\n    html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .file.is-medium {\n      font-size: 1.25rem; }\n      html.theme--documenter-dark .file.is-medium .file-icon .fa {\n        font-size: 21px; }\n    html.theme--documenter-dark .file.is-large {\n      font-size: 1.5rem; }\n      html.theme--documenter-dark .file.is-large .file-icon .fa {\n        font-size: 28px; }\n    html.theme--documenter-dark .file.has-name .file-cta {\n      border-bottom-right-radius: 0;\n      border-top-right-radius: 0; }\n    html.theme--documenter-dark .file.has-name .file-name {\n      border-bottom-left-radius: 0;\n      border-top-left-radius: 0; }\n    html.theme--documenter-dark .file.has-name.is-empty .file-cta {\n      border-radius: 4px; }\n    html.theme--documenter-dark .file.has-name.is-empty .file-name {\n      display: none; }\n    html.theme--documenter-dark .file.is-boxed .file-label {\n      flex-direction: column; }\n    html.theme--documenter-dark .file.is-boxed .file-cta {\n      flex-direction: column;\n      height: auto;\n      padding: 1em 3em; }\n    html.theme--documenter-dark .file.is-boxed .file-name {\n      border-width: 0 1px 1px; }\n    html.theme--documenter-dark .file.is-boxed .file-icon {\n      height: 1.5em;\n      width: 1.5em; }\n      html.theme--documenter-dark .file.is-boxed .file-icon .fa {\n        font-size: 21px; }\n    html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file.is-boxed .file-icon .fa {\n      font-size: 14px; }\n    html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa {\n      font-size: 28px; }\n    html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa {\n      font-size: 35px; }\n    html.theme--documenter-dark .file.is-boxed.has-name .file-cta {\n      border-radius: 4px 4px 0 0; }\n    html.theme--documenter-dark .file.is-boxed.has-name .file-name {\n      border-radius: 0 0 4px 4px;\n      border-width: 0 1px 1px; }\n    html.theme--documenter-dark .file.is-centered {\n      justify-content: center; }\n    html.theme--documenter-dark .file.is-fullwidth .file-label {\n      width: 100%; }\n    html.theme--documenter-dark .file.is-fullwidth .file-name {\n      flex-grow: 1;\n      max-width: none; }\n    html.theme--documenter-dark .file.is-right {\n      justify-content: flex-end; }\n      html.theme--documenter-dark .file.is-right .file-cta {\n        border-radius: 0 4px 4px 0; }\n      html.theme--documenter-dark .file.is-right .file-name {\n        border-radius: 4px 0 0 4px;\n        border-width: 1px 0 1px 1px;\n        order: -1; }\n  html.theme--documenter-dark .file-label {\n    align-items: stretch;\n    display: flex;\n    cursor: pointer;\n    justify-content: flex-start;\n    overflow: hidden;\n    position: relative; }\n    html.theme--documenter-dark .file-label:hover .file-cta {\n      background-color: #eeeeee;\n      color: #363636; }\n    html.theme--documenter-dark .file-label:hover .file-name {\n      border-color: #d5d5d5; }\n    html.theme--documenter-dark .file-label:active .file-cta {\n      background-color: #e8e8e8;\n      color: #363636; }\n    html.theme--documenter-dark .file-label:active .file-name {\n      border-color: #cfcfcf; }\n  html.theme--documenter-dark .file-input {\n    height: 100%;\n    left: 0;\n    opacity: 0;\n    outline: none;\n    position: absolute;\n    top: 0;\n    width: 100%; }\n  html.theme--documenter-dark .file-cta,\n  html.theme--documenter-dark .file-name {\n    border-color: #dbdbdb;\n    border-radius: 4px;\n    font-size: 1em;\n    padding-left: 1em;\n    padding-right: 1em;\n    white-space: nowrap; }\n  html.theme--documenter-dark .file-cta {\n    background-color: whitesmoke;\n    color: #4a4a4a; }\n  html.theme--documenter-dark .file-name {\n    border-color: #dbdbdb;\n    border-style: solid;\n    border-width: 1px 1px 1px 0;\n    display: block;\n    max-width: 16em;\n    overflow: hidden;\n    text-align: left;\n    text-overflow: ellipsis; }\n  html.theme--documenter-dark .file-icon {\n    align-items: center;\n    display: flex;\n    height: 1em;\n    justify-content: center;\n    margin-right: 0.5em;\n    width: 1em; }\n    html.theme--documenter-dark .file-icon .fa {\n      font-size: 14px; }\n  html.theme--documenter-dark .label {\n    color: #363636;\n    display: block;\n    font-size: 1rem;\n    font-weight: 700; }\n    html.theme--documenter-dark .label:not(:last-child) {\n      margin-bottom: 0.5em; }\n    html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .label.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .label.is-large {\n      font-size: 1.5rem; }\n  html.theme--documenter-dark .help {\n    display: block;\n    font-size: 0.75rem;\n    margin-top: 0.25rem; }\n    html.theme--documenter-dark .help.is-white {\n      color: white; }\n    html.theme--documenter-dark .help.is-black {\n      color: #0a0a0a; }\n    html.theme--documenter-dark .help.is-light {\n      color: whitesmoke; }\n    html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help {\n      color: #363636; }\n    html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink {\n      color: #4eb5de; }\n    html.theme--documenter-dark .help.is-link {\n      color: #e37733; }\n    html.theme--documenter-dark .help.is-info {\n      color: #209cee; }\n    html.theme--documenter-dark .help.is-success {\n      color: #22c35b; }\n    html.theme--documenter-dark .help.is-warning {\n      color: #ffdd57; }\n    html.theme--documenter-dark .help.is-danger {\n      color: #da0b00; }\n  html.theme--documenter-dark .field:not(:last-child) {\n    margin-bottom: 0.75rem; }\n  html.theme--documenter-dark .field.has-addons {\n    display: flex;\n    justify-content: flex-start; }\n    html.theme--documenter-dark .field.has-addons .control:not(:last-child) {\n      margin-right: -1px; }\n    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button,\n    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input,\n    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input,\n    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select {\n      border-radius: 0; }\n    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button,\n    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input,\n    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input,\n    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select {\n      border-bottom-right-radius: 0;\n      border-top-right-radius: 0; }\n    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button,\n    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input,\n    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input,\n    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select {\n      border-bottom-left-radius: 0;\n      border-top-left-radius: 0; }\n    html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-hovered,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-hovered,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-hovered,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-hovered,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-hovered {\n      z-index: 2; }\n    html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-focused, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-active,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-focused,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active,\n    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-active,\n    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active,\n    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-focused,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active,\n    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-active {\n      z-index: 3; }\n      html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-focused:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-active:hover,\n      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover,\n      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover,\n      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover,\n      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-focused:hover,\n      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused:hover,\n      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused:hover,\n      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover,\n      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover,\n      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover,\n      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-active:hover,\n      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active:hover,\n      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active:hover,\n      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover,\n      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-focused:hover,\n      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover,\n      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-active:hover {\n        z-index: 4; }\n    html.theme--documenter-dark .field.has-addons .control.is-expanded {\n      flex-grow: 1;\n      flex-shrink: 1; }\n    html.theme--documenter-dark .field.has-addons.has-addons-centered {\n      justify-content: center; }\n    html.theme--documenter-dark .field.has-addons.has-addons-right {\n      justify-content: flex-end; }\n    html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control {\n      flex-grow: 1;\n      flex-shrink: 0; }\n  html.theme--documenter-dark .field.is-grouped {\n    display: flex;\n    justify-content: flex-start; }\n    html.theme--documenter-dark .field.is-grouped > .control {\n      flex-shrink: 0; }\n      html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) {\n        margin-bottom: 0;\n        margin-right: 0.75rem; }\n      html.theme--documenter-dark .field.is-grouped > .control.is-expanded {\n        flex-grow: 1;\n        flex-shrink: 1; }\n    html.theme--documenter-dark .field.is-grouped.is-grouped-centered {\n      justify-content: center; }\n    html.theme--documenter-dark .field.is-grouped.is-grouped-right {\n      justify-content: flex-end; }\n    html.theme--documenter-dark .field.is-grouped.is-grouped-multiline {\n      flex-wrap: wrap; }\n      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) {\n        margin-bottom: 0.75rem; }\n      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child {\n        margin-bottom: -0.75rem; }\n      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) {\n        margin-bottom: 0; }\n  @media screen and (min-width: 769px), print {\n    html.theme--documenter-dark .field.is-horizontal {\n      display: flex; } }\n  html.theme--documenter-dark .field-label .label {\n    font-size: inherit; }\n  @media screen and (max-width: 768px) {\n    html.theme--documenter-dark .field-label {\n      margin-bottom: 0.5rem; } }\n  @media screen and (min-width: 769px), print {\n    html.theme--documenter-dark .field-label {\n      flex-basis: 0;\n      flex-grow: 1;\n      flex-shrink: 0;\n      margin-right: 1.5rem;\n      text-align: right; }\n      html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label {\n        font-size: 0.75rem;\n        padding-top: 0.375em; }\n      html.theme--documenter-dark .field-label.is-normal {\n        padding-top: 0.375em; }\n      html.theme--documenter-dark .field-label.is-medium {\n        font-size: 1.25rem;\n        padding-top: 0.375em; }\n      html.theme--documenter-dark .field-label.is-large {\n        font-size: 1.5rem;\n        padding-top: 0.375em; } }\n  html.theme--documenter-dark .field-body .field .field {\n    margin-bottom: 0; }\n  @media screen and (min-width: 769px), print {\n    html.theme--documenter-dark .field-body {\n      display: flex;\n      flex-basis: 0;\n      flex-grow: 5;\n      flex-shrink: 1; }\n      html.theme--documenter-dark .field-body .field {\n        margin-bottom: 0; }\n      html.theme--documenter-dark .field-body > .field {\n        flex-shrink: 1; }\n        html.theme--documenter-dark .field-body > .field:not(.is-narrow) {\n          flex-grow: 1; }\n        html.theme--documenter-dark .field-body > .field:not(:last-child) {\n          margin-right: 0.75rem; } }\n  html.theme--documenter-dark .control {\n    box-sizing: border-box;\n    clear: both;\n    font-size: 1rem;\n    position: relative;\n    text-align: left; }\n    html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon,\n    html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon,\n    html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon {\n      color: #7a7a7a; }\n    html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon,\n    html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon,\n    html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.select ~ .icon,\n    html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.select ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon,\n    html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon,\n    html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.select ~ .icon,\n    html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.select ~ .icon {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon,\n    html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon,\n    html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon,\n    html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon,\n    html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon {\n      color: #dbdbdb;\n      height: 2.25em;\n      pointer-events: none;\n      position: absolute;\n      top: 0;\n      width: 2.25em;\n      z-index: 4; }\n    html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input,\n    html.theme--documenter-dark .control.has-icons-left .select select {\n      padding-left: 2.25em; }\n    html.theme--documenter-dark .control.has-icons-left .icon.is-left {\n      left: 0; }\n    html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input,\n    html.theme--documenter-dark .control.has-icons-right .select select {\n      padding-right: 2.25em; }\n    html.theme--documenter-dark .control.has-icons-right .icon.is-right {\n      right: 0; }\n    html.theme--documenter-dark .control.is-loading::after {\n      position: absolute !important;\n      right: 0.625em;\n      top: 0.625em;\n      z-index: 4; }\n    html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.control.is-loading:after {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .control.is-loading.is-medium:after {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .control.is-loading.is-large:after {\n      font-size: 1.5rem; }\n  html.theme--documenter-dark .breadcrumb {\n    font-size: 1rem;\n    white-space: nowrap; }\n    html.theme--documenter-dark .breadcrumb a {\n      align-items: center;\n      color: #e37733;\n      display: flex;\n      justify-content: center;\n      padding: 0 0.75em; }\n      html.theme--documenter-dark .breadcrumb a:hover {\n        color: #f2be9e; }\n    html.theme--documenter-dark .breadcrumb li {\n      align-items: center;\n      display: flex; }\n      html.theme--documenter-dark .breadcrumb li:first-child a {\n        padding-left: 0; }\n      html.theme--documenter-dark .breadcrumb li.is-active a {\n        color: #97b3e2;\n        cursor: default;\n        pointer-events: none; }\n      html.theme--documenter-dark .breadcrumb li + li::before {\n        color: #b5b5b5;\n        content: \"\\0002f\"; }\n    html.theme--documenter-dark .breadcrumb ul,\n    html.theme--documenter-dark .breadcrumb ol {\n      align-items: flex-start;\n      display: flex;\n      flex-wrap: wrap;\n      justify-content: flex-start; }\n    html.theme--documenter-dark .breadcrumb .icon:first-child {\n      margin-right: 0.5em; }\n    html.theme--documenter-dark .breadcrumb .icon:last-child {\n      margin-left: 0.5em; }\n    html.theme--documenter-dark .breadcrumb.is-centered ol,\n    html.theme--documenter-dark .breadcrumb.is-centered ul {\n      justify-content: center; }\n    html.theme--documenter-dark .breadcrumb.is-right ol,\n    html.theme--documenter-dark .breadcrumb.is-right ul {\n      justify-content: flex-end; }\n    html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .breadcrumb.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .breadcrumb.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before {\n      content: \"\\02192\"; }\n    html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before {\n      content: \"\\02022\"; }\n    html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before {\n      content: \"\\000b7\"; }\n    html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before {\n      content: \"\\0227B\"; }\n  html.theme--documenter-dark .card {\n    background-color: white;\n    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);\n    color: #ececec;\n    max-width: 100%;\n    position: relative; }\n  html.theme--documenter-dark .card-header {\n    background-color: transparent;\n    align-items: stretch;\n    box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);\n    display: flex; }\n  html.theme--documenter-dark .card-header-title {\n    align-items: center;\n    color: #97b3e2;\n    display: flex;\n    flex-grow: 1;\n    font-weight: 700;\n    padding: 0.75rem; }\n    html.theme--documenter-dark .card-header-title.is-centered {\n      justify-content: center; }\n  html.theme--documenter-dark .card-header-icon {\n    align-items: center;\n    cursor: pointer;\n    display: flex;\n    justify-content: center;\n    padding: 0.75rem; }\n  html.theme--documenter-dark .card-image {\n    display: block;\n    position: relative; }\n  html.theme--documenter-dark .card-content {\n    background-color: transparent;\n    padding: 1rem 1.25rem; }\n  html.theme--documenter-dark .card-footer {\n    background-color: transparent;\n    border-top: 1px solid #dbdbdb;\n    align-items: stretch;\n    display: flex; }\n  html.theme--documenter-dark .card-footer-item {\n    align-items: center;\n    display: flex;\n    flex-basis: 0;\n    flex-grow: 1;\n    flex-shrink: 0;\n    justify-content: center;\n    padding: 0.75rem; }\n    html.theme--documenter-dark .card-footer-item:not(:last-child) {\n      border-right: 1px solid #dbdbdb; }\n  html.theme--documenter-dark .card .media:not(:last-child) {\n    margin-bottom: 1.5rem; }\n  html.theme--documenter-dark .dropdown {\n    display: inline-flex;\n    position: relative;\n    vertical-align: top; }\n    html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu {\n      display: block; }\n    html.theme--documenter-dark .dropdown.is-right .dropdown-menu {\n      left: auto;\n      right: 0; }\n    html.theme--documenter-dark .dropdown.is-up .dropdown-menu {\n      bottom: 100%;\n      padding-bottom: 4px;\n      padding-top: initial;\n      top: auto; }\n  html.theme--documenter-dark .dropdown-menu {\n    display: none;\n    left: 0;\n    min-width: 12rem;\n    padding-top: 4px;\n    position: absolute;\n    top: 100%;\n    z-index: 20; }\n  html.theme--documenter-dark .dropdown-content {\n    background-color: white;\n    border-radius: 4px;\n    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);\n    padding-bottom: 0.5rem;\n    padding-top: 0.5rem; }\n  html.theme--documenter-dark .dropdown-item {\n    color: #4a4a4a;\n    display: block;\n    font-size: 0.875rem;\n    line-height: 1.5;\n    padding: 0.375rem 1rem;\n    position: relative; }\n  html.theme--documenter-dark a.dropdown-item,\n  html.theme--documenter-dark button.dropdown-item {\n    padding-right: 3rem;\n    text-align: left;\n    white-space: nowrap;\n    width: 100%; }\n    html.theme--documenter-dark a.dropdown-item:hover,\n    html.theme--documenter-dark button.dropdown-item:hover {\n      background-color: whitesmoke;\n      color: #0a0a0a; }\n    html.theme--documenter-dark a.dropdown-item.is-active,\n    html.theme--documenter-dark button.dropdown-item.is-active {\n      background-color: #e37733;\n      color: #fff; }\n  html.theme--documenter-dark .dropdown-divider {\n    background-color: #dbdbdb;\n    border: none;\n    display: block;\n    height: 1px;\n    margin: 0.5rem 0; }\n  html.theme--documenter-dark .level {\n    align-items: center;\n    justify-content: space-between; }\n    html.theme--documenter-dark .level code {\n      border-radius: 4px; }\n    html.theme--documenter-dark .level img {\n      display: inline-block;\n      vertical-align: top; }\n    html.theme--documenter-dark .level.is-mobile {\n      display: flex; }\n      html.theme--documenter-dark .level.is-mobile .level-left,\n      html.theme--documenter-dark .level.is-mobile .level-right {\n        display: flex; }\n      html.theme--documenter-dark .level.is-mobile .level-left + .level-right {\n        margin-top: 0; }\n      html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) {\n        margin-bottom: 0;\n        margin-right: 0.75rem; }\n      html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) {\n        flex-grow: 1; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .level {\n        display: flex; }\n        html.theme--documenter-dark .level > .level-item:not(.is-narrow) {\n          flex-grow: 1; } }\n  html.theme--documenter-dark .level-item {\n    align-items: center;\n    display: flex;\n    flex-basis: auto;\n    flex-grow: 0;\n    flex-shrink: 0;\n    justify-content: center; }\n    html.theme--documenter-dark .level-item .title,\n    html.theme--documenter-dark .level-item .subtitle {\n      margin-bottom: 0; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .level-item:not(:last-child) {\n        margin-bottom: 0.75rem; } }\n  html.theme--documenter-dark .level-left,\n  html.theme--documenter-dark .level-right {\n    flex-basis: auto;\n    flex-grow: 0;\n    flex-shrink: 0; }\n    html.theme--documenter-dark .level-left .level-item.is-flexible,\n    html.theme--documenter-dark .level-right .level-item.is-flexible {\n      flex-grow: 1; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .level-left .level-item:not(:last-child),\n      html.theme--documenter-dark .level-right .level-item:not(:last-child) {\n        margin-right: 0.75rem; } }\n  html.theme--documenter-dark .level-left {\n    align-items: center;\n    justify-content: flex-start; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .level-left + .level-right {\n        margin-top: 1.5rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .level-left {\n        display: flex; } }\n  html.theme--documenter-dark .level-right {\n    align-items: center;\n    justify-content: flex-end; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .level-right {\n        display: flex; } }\n  html.theme--documenter-dark .list {\n    background-color: white;\n    border-radius: 4px;\n    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); }\n  html.theme--documenter-dark .list-item {\n    display: block;\n    padding: 0.5em 1em; }\n    html.theme--documenter-dark .list-item:not(a) {\n      color: #ececec; }\n    html.theme--documenter-dark .list-item:first-child {\n      border-top-left-radius: 4px;\n      border-top-right-radius: 4px; }\n    html.theme--documenter-dark .list-item:last-child {\n      border-bottom-left-radius: 4px;\n      border-bottom-right-radius: 4px; }\n    html.theme--documenter-dark .list-item:not(:last-child) {\n      border-bottom: 1px solid #dbdbdb; }\n    html.theme--documenter-dark .list-item.is-active {\n      background-color: #e37733;\n      color: #fff; }\n  html.theme--documenter-dark a.list-item {\n    background-color: whitesmoke;\n    cursor: pointer; }\n  html.theme--documenter-dark .media {\n    align-items: flex-start;\n    display: flex;\n    text-align: left; }\n    html.theme--documenter-dark .media .content:not(:last-child) {\n      margin-bottom: 0.75rem; }\n    html.theme--documenter-dark .media .media {\n      border-top: 1px solid rgba(219, 219, 219, 0.5);\n      display: flex;\n      padding-top: 0.75rem; }\n      html.theme--documenter-dark .media .media .content:not(:last-child),\n      html.theme--documenter-dark .media .media .control:not(:last-child) {\n        margin-bottom: 0.5rem; }\n      html.theme--documenter-dark .media .media .media {\n        padding-top: 0.5rem; }\n        html.theme--documenter-dark .media .media .media + .media {\n          margin-top: 0.5rem; }\n    html.theme--documenter-dark .media + .media {\n      border-top: 1px solid rgba(219, 219, 219, 0.5);\n      margin-top: 1rem;\n      padding-top: 1rem; }\n    html.theme--documenter-dark .media.is-large + .media {\n      margin-top: 1.5rem;\n      padding-top: 1.5rem; }\n  html.theme--documenter-dark .media-left,\n  html.theme--documenter-dark .media-right {\n    flex-basis: auto;\n    flex-grow: 0;\n    flex-shrink: 0; }\n  html.theme--documenter-dark .media-left {\n    margin-right: 1rem; }\n  html.theme--documenter-dark .media-right {\n    margin-left: 1rem; }\n  html.theme--documenter-dark .media-content {\n    flex-basis: auto;\n    flex-grow: 1;\n    flex-shrink: 1;\n    text-align: left; }\n  @media screen and (max-width: 768px) {\n    html.theme--documenter-dark .media-content {\n      overflow-x: auto; } }\n  html.theme--documenter-dark .menu {\n    font-size: 1rem; }\n    html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .menu.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .menu.is-large {\n      font-size: 1.5rem; }\n  html.theme--documenter-dark .menu-list {\n    line-height: 1.25; }\n    html.theme--documenter-dark .menu-list a {\n      border-radius: 2px;\n      color: #ececec;\n      display: block;\n      padding: 0.5em 0.75em; }\n      html.theme--documenter-dark .menu-list a:hover {\n        background-color: whitesmoke;\n        color: #97b3e2; }\n      html.theme--documenter-dark .menu-list a.is-active {\n        background-color: #e37733;\n        color: #fff; }\n    html.theme--documenter-dark .menu-list li ul {\n      border-left: 1px solid #dbdbdb;\n      margin: 0.75em;\n      padding-left: 0.75em; }\n  html.theme--documenter-dark .menu-label {\n    color: #7a7a7a;\n    font-size: 0.75em;\n    letter-spacing: 0.1em;\n    text-transform: uppercase; }\n    html.theme--documenter-dark .menu-label:not(:first-child) {\n      margin-top: 1em; }\n    html.theme--documenter-dark .menu-label:not(:last-child) {\n      margin-bottom: 1em; }\n  html.theme--documenter-dark .message {\n    background-color: whitesmoke;\n    border-radius: 4px;\n    font-size: 1rem; }\n    html.theme--documenter-dark .message strong {\n      color: currentColor; }\n    html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) {\n      color: currentColor;\n      text-decoration: underline; }\n    html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .message.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .message.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .message.is-white {\n      background-color: white; }\n      html.theme--documenter-dark .message.is-white .message-header {\n        background-color: white;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .message.is-white .message-body {\n        border-color: white;\n        color: #4d4d4d; }\n    html.theme--documenter-dark .message.is-black {\n      background-color: #fafafa; }\n      html.theme--documenter-dark .message.is-black .message-header {\n        background-color: #0a0a0a;\n        color: white; }\n      html.theme--documenter-dark .message.is-black .message-body {\n        border-color: #0a0a0a;\n        color: #090909; }\n    html.theme--documenter-dark .message.is-light {\n      background-color: #fafafa; }\n      html.theme--documenter-dark .message.is-light .message-header {\n        background-color: whitesmoke;\n        color: #363636; }\n      html.theme--documenter-dark .message.is-light .message-body {\n        border-color: whitesmoke;\n        color: #505050; }\n    html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message {\n      background-color: #fafafa; }\n      html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header {\n        background-color: #363636;\n        color: whitesmoke; }\n      html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body {\n        border-color: #363636;\n        color: #2a2a2a; }\n    html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink {\n      background-color: #f6fbfd; }\n      html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header {\n        background-color: #4eb5de;\n        color: #fff; }\n      html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body {\n        border-color: #4eb5de;\n        color: #1f556a; }\n    html.theme--documenter-dark .message.is-link {\n      background-color: #fef9f6; }\n      html.theme--documenter-dark .message.is-link .message-header {\n        background-color: #e37733;\n        color: #fff; }\n      html.theme--documenter-dark .message.is-link .message-body {\n        border-color: #e37733;\n        color: #7f411b; }\n    html.theme--documenter-dark .message.is-info {\n      background-color: #f6fbfe; }\n      html.theme--documenter-dark .message.is-info .message-header {\n        background-color: #209cee;\n        color: #fff; }\n      html.theme--documenter-dark .message.is-info .message-body {\n        border-color: #209cee;\n        color: #12537e; }\n    html.theme--documenter-dark .message.is-success {\n      background-color: #f6fdf9; }\n      html.theme--documenter-dark .message.is-success .message-header {\n        background-color: #22c35b;\n        color: #fff; }\n      html.theme--documenter-dark .message.is-success .message-body {\n        border-color: #22c35b;\n        color: #0f361d; }\n    html.theme--documenter-dark .message.is-warning {\n      background-color: #fffdf5; }\n      html.theme--documenter-dark .message.is-warning .message-header {\n        background-color: #ffdd57;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .message.is-warning .message-body {\n        border-color: #ffdd57;\n        color: #3b3108; }\n    html.theme--documenter-dark .message.is-danger {\n      background-color: #fff5f5; }\n      html.theme--documenter-dark .message.is-danger .message-header {\n        background-color: #da0b00;\n        color: #fff; }\n      html.theme--documenter-dark .message.is-danger .message-body {\n        border-color: #da0b00;\n        color: #9b0c04; }\n  html.theme--documenter-dark .message-header {\n    align-items: center;\n    background-color: #ececec;\n    border-radius: 4px 4px 0 0;\n    color: rgba(0, 0, 0, 0.7);\n    display: flex;\n    font-weight: 700;\n    justify-content: space-between;\n    line-height: 1.25;\n    padding: 0.75em;\n    position: relative; }\n    html.theme--documenter-dark .message-header .delete {\n      flex-grow: 0;\n      flex-shrink: 0;\n      margin-left: 0.75em; }\n    html.theme--documenter-dark .message-header + .message-body {\n      border-width: 0;\n      border-top-left-radius: 0;\n      border-top-right-radius: 0; }\n  html.theme--documenter-dark .message-body {\n    border-color: #dbdbdb;\n    border-radius: 4px;\n    border-style: solid;\n    border-width: 0 0 0 4px;\n    color: #ececec;\n    padding: 1em 1.25em; }\n    html.theme--documenter-dark .message-body code,\n    html.theme--documenter-dark .message-body pre {\n      background-color: white; }\n    html.theme--documenter-dark .message-body pre code {\n      background-color: transparent; }\n  html.theme--documenter-dark .modal {\n    align-items: center;\n    display: none;\n    flex-direction: column;\n    justify-content: center;\n    overflow: hidden;\n    position: fixed;\n    z-index: 40; }\n    html.theme--documenter-dark .modal.is-active {\n      display: flex; }\n  html.theme--documenter-dark .modal-background {\n    background-color: rgba(10, 10, 10, 0.86); }\n  html.theme--documenter-dark .modal-content,\n  html.theme--documenter-dark .modal-card {\n    margin: 0 20px;\n    max-height: calc(100vh - 160px);\n    overflow: auto;\n    position: relative;\n    width: 100%; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .modal-content,\n      html.theme--documenter-dark .modal-card {\n        margin: 0 auto;\n        max-height: calc(100vh - 40px);\n        width: 640px; } }\n  html.theme--documenter-dark .modal-close {\n    background: none;\n    height: 40px;\n    position: fixed;\n    right: 20px;\n    top: 20px;\n    width: 40px; }\n  html.theme--documenter-dark .modal-card {\n    display: flex;\n    flex-direction: column;\n    max-height: calc(100vh - 40px);\n    overflow: hidden;\n    -ms-overflow-y: visible; }\n  html.theme--documenter-dark .modal-card-head,\n  html.theme--documenter-dark .modal-card-foot {\n    align-items: center;\n    background-color: whitesmoke;\n    display: flex;\n    flex-shrink: 0;\n    justify-content: flex-start;\n    padding: 20px;\n    position: relative; }\n  html.theme--documenter-dark .modal-card-head {\n    border-bottom: 1px solid #dbdbdb;\n    border-top-left-radius: 6px;\n    border-top-right-radius: 6px; }\n  html.theme--documenter-dark .modal-card-title {\n    color: #97b3e2;\n    flex-grow: 1;\n    flex-shrink: 0;\n    font-size: 1.5rem;\n    line-height: 1; }\n  html.theme--documenter-dark .modal-card-foot {\n    border-bottom-left-radius: 6px;\n    border-bottom-right-radius: 6px;\n    border-top: 1px solid #dbdbdb; }\n    html.theme--documenter-dark .modal-card-foot .button:not(:last-child) {\n      margin-right: 0.5em; }\n  html.theme--documenter-dark .modal-card-body {\n    -webkit-overflow-scrolling: touch;\n    background-color: white;\n    flex-grow: 1;\n    flex-shrink: 1;\n    overflow: auto;\n    padding: 20px; }\n  html.theme--documenter-dark .navbar {\n    background-color: white;\n    min-height: 3.25rem;\n    position: relative;\n    z-index: 30; }\n    html.theme--documenter-dark .navbar.is-white {\n      background-color: white;\n      color: #0a0a0a; }\n      html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link {\n        color: #0a0a0a; }\n      html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active {\n        background-color: #f2f2f2;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after {\n        border-color: #0a0a0a; }\n      html.theme--documenter-dark .navbar.is-white .navbar-burger {\n        color: #0a0a0a; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link {\n          color: #0a0a0a; }\n        html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active {\n          background-color: #f2f2f2;\n          color: #0a0a0a; }\n        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after {\n          border-color: #0a0a0a; }\n        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #f2f2f2;\n          color: #0a0a0a; }\n        html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active {\n          background-color: white;\n          color: #0a0a0a; } }\n    html.theme--documenter-dark .navbar.is-black {\n      background-color: #0a0a0a;\n      color: white; }\n      html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link {\n        color: white; }\n      html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active {\n        background-color: black;\n        color: white; }\n      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after {\n        border-color: white; }\n      html.theme--documenter-dark .navbar.is-black .navbar-burger {\n        color: white; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link {\n          color: white; }\n        html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active {\n          background-color: black;\n          color: white; }\n        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after {\n          border-color: white; }\n        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: black;\n          color: white; }\n        html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active {\n          background-color: #0a0a0a;\n          color: white; } }\n    html.theme--documenter-dark .navbar.is-light {\n      background-color: whitesmoke;\n      color: #363636; }\n      html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link {\n        color: #363636; }\n      html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active {\n        background-color: #e8e8e8;\n        color: #363636; }\n      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after {\n        border-color: #363636; }\n      html.theme--documenter-dark .navbar.is-light .navbar-burger {\n        color: #363636; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link {\n          color: #363636; }\n        html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active {\n          background-color: #e8e8e8;\n          color: #363636; }\n        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after {\n          border-color: #363636; }\n        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #e8e8e8;\n          color: #363636; }\n        html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active {\n          background-color: whitesmoke;\n          color: #363636; } }\n    html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar {\n      background-color: #363636;\n      color: whitesmoke; }\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link,\n      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link {\n        color: whitesmoke; }\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active,\n      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active {\n        background-color: #292929;\n        color: whitesmoke; }\n      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after {\n        border-color: whitesmoke; }\n      html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger {\n        color: whitesmoke; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link,\n        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link {\n          color: whitesmoke; }\n        html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active {\n          background-color: #292929;\n          color: whitesmoke; }\n        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after,\n        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after {\n          border-color: whitesmoke; }\n        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link,\n        html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #292929;\n          color: whitesmoke; }\n        html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active {\n          background-color: #363636;\n          color: whitesmoke; } }\n    html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink {\n      background-color: #4eb5de;\n      color: #fff; }\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link,\n      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link {\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active,\n      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active {\n        background-color: #39acda;\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after {\n        border-color: #fff; }\n      html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger {\n        color: #fff; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link {\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active {\n          background-color: #39acda;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after {\n          border-color: #fff; }\n        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link,\n        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #39acda;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active {\n          background-color: #4eb5de;\n          color: #fff; } }\n    html.theme--documenter-dark .navbar.is-link {\n      background-color: #e37733;\n      color: #fff; }\n      html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link {\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active {\n        background-color: #dd681f;\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after {\n        border-color: #fff; }\n      html.theme--documenter-dark .navbar.is-link .navbar-burger {\n        color: #fff; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link {\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active {\n          background-color: #dd681f;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after {\n          border-color: #fff; }\n        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #dd681f;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active {\n          background-color: #e37733;\n          color: #fff; } }\n    html.theme--documenter-dark .navbar.is-info {\n      background-color: #209cee;\n      color: #fff; }\n      html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link {\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active {\n        background-color: #118fe4;\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after {\n        border-color: #fff; }\n      html.theme--documenter-dark .navbar.is-info .navbar-burger {\n        color: #fff; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link {\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active {\n          background-color: #118fe4;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after {\n          border-color: #fff; }\n        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #118fe4;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active {\n          background-color: #209cee;\n          color: #fff; } }\n    html.theme--documenter-dark .navbar.is-success {\n      background-color: #22c35b;\n      color: #fff; }\n      html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link {\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active {\n        background-color: #1ead51;\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after {\n        border-color: #fff; }\n      html.theme--documenter-dark .navbar.is-success .navbar-burger {\n        color: #fff; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link {\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active {\n          background-color: #1ead51;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after {\n          border-color: #fff; }\n        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #1ead51;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active {\n          background-color: #22c35b;\n          color: #fff; } }\n    html.theme--documenter-dark .navbar.is-warning {\n      background-color: #ffdd57;\n      color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link {\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active {\n        background-color: #ffd83d;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after {\n        border-color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .navbar.is-warning .navbar-burger {\n        color: rgba(0, 0, 0, 0.7); }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link {\n          color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active {\n          background-color: #ffd83d;\n          color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after {\n          border-color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #ffd83d;\n          color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active {\n          background-color: #ffdd57;\n          color: rgba(0, 0, 0, 0.7); } }\n    html.theme--documenter-dark .navbar.is-danger {\n      background-color: #da0b00;\n      color: #fff; }\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item,\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link {\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active {\n        background-color: #c10a00;\n        color: #fff; }\n      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after {\n        border-color: #fff; }\n      html.theme--documenter-dark .navbar.is-danger .navbar-burger {\n        color: #fff; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item,\n        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link {\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active {\n          background-color: #c10a00;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after,\n        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after {\n          border-color: #fff; }\n        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link,\n        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link,\n        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link {\n          background-color: #c10a00;\n          color: #fff; }\n        html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active {\n          background-color: #da0b00;\n          color: #fff; } }\n    html.theme--documenter-dark .navbar > .container {\n      align-items: stretch;\n      display: flex;\n      min-height: 3.25rem;\n      width: 100%; }\n    html.theme--documenter-dark .navbar.has-shadow {\n      box-shadow: 0 2px 0 0 whitesmoke; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top {\n      left: 0;\n      position: fixed;\n      right: 0;\n      z-index: 30; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom {\n      bottom: 0; }\n      html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow {\n        box-shadow: 0 -2px 0 0 whitesmoke; }\n    html.theme--documenter-dark .navbar.is-fixed-top {\n      top: 0; }\n  html.theme--documenter-dark html.has-navbar-fixed-top,\n  html.theme--documenter-dark body.has-navbar-fixed-top {\n    padding-top: 3.25rem; }\n  html.theme--documenter-dark html.has-navbar-fixed-bottom,\n  html.theme--documenter-dark body.has-navbar-fixed-bottom {\n    padding-bottom: 3.25rem; }\n  html.theme--documenter-dark .navbar-brand,\n  html.theme--documenter-dark .navbar-tabs {\n    align-items: stretch;\n    display: flex;\n    flex-shrink: 0;\n    min-height: 3.25rem; }\n  html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover {\n    background-color: transparent; }\n  html.theme--documenter-dark .navbar-tabs {\n    -webkit-overflow-scrolling: touch;\n    max-width: 100vw;\n    overflow-x: auto;\n    overflow-y: hidden; }\n  html.theme--documenter-dark .navbar-burger {\n    color: #4a4a4a;\n    cursor: pointer;\n    display: block;\n    height: 3.25rem;\n    position: relative;\n    width: 3.25rem;\n    margin-left: auto; }\n    html.theme--documenter-dark .navbar-burger span {\n      background-color: currentColor;\n      display: block;\n      height: 1px;\n      left: calc(50% - 8px);\n      position: absolute;\n      transform-origin: center;\n      transition-duration: 86ms;\n      transition-property: background-color, opacity, transform;\n      transition-timing-function: ease-out;\n      width: 16px; }\n      html.theme--documenter-dark .navbar-burger span:nth-child(1) {\n        top: calc(50% - 6px); }\n      html.theme--documenter-dark .navbar-burger span:nth-child(2) {\n        top: calc(50% - 1px); }\n      html.theme--documenter-dark .navbar-burger span:nth-child(3) {\n        top: calc(50% + 4px); }\n    html.theme--documenter-dark .navbar-burger:hover {\n      background-color: rgba(0, 0, 0, 0.05); }\n    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) {\n      transform: translateY(5px) rotate(45deg); }\n    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) {\n      opacity: 0; }\n    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) {\n      transform: translateY(-5px) rotate(-45deg); }\n  html.theme--documenter-dark .navbar-menu {\n    display: none; }\n  html.theme--documenter-dark .navbar-item,\n  html.theme--documenter-dark .navbar-link {\n    color: #4a4a4a;\n    display: block;\n    line-height: 1.5;\n    padding: 0.5rem 0.75rem;\n    position: relative; }\n    html.theme--documenter-dark .navbar-item .icon:only-child,\n    html.theme--documenter-dark .navbar-link .icon:only-child {\n      margin-left: -0.25rem;\n      margin-right: -0.25rem; }\n  html.theme--documenter-dark a.navbar-item,\n  html.theme--documenter-dark .navbar-link {\n    cursor: pointer; }\n    html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active,\n    html.theme--documenter-dark .navbar-link:focus,\n    html.theme--documenter-dark .navbar-link:focus-within,\n    html.theme--documenter-dark .navbar-link:hover,\n    html.theme--documenter-dark .navbar-link.is-active {\n      background-color: #fafafa;\n      color: #e37733; }\n  html.theme--documenter-dark .navbar-item {\n    display: block;\n    flex-grow: 0;\n    flex-shrink: 0; }\n    html.theme--documenter-dark .navbar-item img {\n      max-height: 1.75rem; }\n    html.theme--documenter-dark .navbar-item.has-dropdown {\n      padding: 0; }\n    html.theme--documenter-dark .navbar-item.is-expanded {\n      flex-grow: 1;\n      flex-shrink: 1; }\n    html.theme--documenter-dark .navbar-item.is-tab {\n      border-bottom: 1px solid transparent;\n      min-height: 3.25rem;\n      padding-bottom: calc(0.5rem - 1px); }\n      html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover {\n        background-color: transparent;\n        border-bottom-color: #e37733; }\n      html.theme--documenter-dark .navbar-item.is-tab.is-active {\n        background-color: transparent;\n        border-bottom-color: #e37733;\n        border-bottom-style: solid;\n        border-bottom-width: 3px;\n        color: #e37733;\n        padding-bottom: calc(0.5rem - 3px); }\n  html.theme--documenter-dark .navbar-content {\n    flex-grow: 1;\n    flex-shrink: 1; }\n  html.theme--documenter-dark .navbar-link:not(.is-arrowless) {\n    padding-right: 2.5em; }\n    html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after {\n      border-color: #e37733;\n      margin-top: -0.375em;\n      right: 1.125em; }\n  html.theme--documenter-dark .navbar-dropdown {\n    font-size: 0.875rem;\n    padding-bottom: 0.5rem;\n    padding-top: 0.5rem; }\n    html.theme--documenter-dark .navbar-dropdown .navbar-item {\n      padding-left: 1.5rem;\n      padding-right: 1.5rem; }\n  html.theme--documenter-dark .navbar-divider {\n    background-color: whitesmoke;\n    border: none;\n    display: none;\n    height: 2px;\n    margin: 0.5rem 0; }\n  @media screen and (max-width: 1055px) {\n    html.theme--documenter-dark .navbar > .container {\n      display: block; }\n    html.theme--documenter-dark .navbar-brand .navbar-item,\n    html.theme--documenter-dark .navbar-tabs .navbar-item {\n      align-items: center;\n      display: flex; }\n    html.theme--documenter-dark .navbar-link::after {\n      display: none; }\n    html.theme--documenter-dark .navbar-menu {\n      background-color: white;\n      box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1);\n      padding: 0.5rem 0; }\n      html.theme--documenter-dark .navbar-menu.is-active {\n        display: block; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch {\n      left: 0;\n      position: fixed;\n      right: 0;\n      z-index: 30; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom-touch {\n      bottom: 0; }\n      html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow {\n        box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }\n    html.theme--documenter-dark .navbar.is-fixed-top-touch {\n      top: 0; }\n    html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu {\n      -webkit-overflow-scrolling: touch;\n      max-height: calc(100vh - 3.25rem);\n      overflow: auto; }\n    html.theme--documenter-dark html.has-navbar-fixed-top-touch,\n    html.theme--documenter-dark body.has-navbar-fixed-top-touch {\n      padding-top: 3.25rem; }\n    html.theme--documenter-dark html.has-navbar-fixed-bottom-touch,\n    html.theme--documenter-dark body.has-navbar-fixed-bottom-touch {\n      padding-bottom: 3.25rem; } }\n  @media screen and (min-width: 1056px) {\n    html.theme--documenter-dark .navbar,\n    html.theme--documenter-dark .navbar-menu,\n    html.theme--documenter-dark .navbar-start,\n    html.theme--documenter-dark .navbar-end {\n      align-items: stretch;\n      display: flex; }\n    html.theme--documenter-dark .navbar {\n      min-height: 3.25rem; }\n      html.theme--documenter-dark .navbar.is-spaced {\n        padding: 1rem 2rem; }\n        html.theme--documenter-dark .navbar.is-spaced .navbar-start,\n        html.theme--documenter-dark .navbar.is-spaced .navbar-end {\n          align-items: center; }\n        html.theme--documenter-dark .navbar.is-spaced a.navbar-item,\n        html.theme--documenter-dark .navbar.is-spaced .navbar-link {\n          border-radius: 4px; }\n      html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active,\n      html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus,\n      html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover,\n      html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active {\n        background-color: transparent !important; }\n      html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link {\n        background-color: transparent !important; }\n      html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover {\n        background-color: whitesmoke;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active {\n        background-color: whitesmoke;\n        color: #e37733; }\n    html.theme--documenter-dark .navbar-burger {\n      display: none; }\n    html.theme--documenter-dark .navbar-item,\n    html.theme--documenter-dark .navbar-link {\n      align-items: center;\n      display: flex; }\n    html.theme--documenter-dark .navbar-item {\n      display: flex; }\n      html.theme--documenter-dark .navbar-item.has-dropdown {\n        align-items: stretch; }\n      html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after {\n        transform: rotate(135deg) translate(0.25em, -0.25em); }\n      html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown {\n        border-bottom: 2px solid #dbdbdb;\n        border-radius: 6px 6px 0 0;\n        border-top: none;\n        bottom: 100%;\n        box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1);\n        top: auto; }\n      html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown {\n        display: block; }\n        .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed {\n          opacity: 1;\n          pointer-events: auto;\n          transform: translateY(0); }\n    html.theme--documenter-dark .navbar-menu {\n      flex-grow: 1;\n      flex-shrink: 0; }\n    html.theme--documenter-dark .navbar-start {\n      justify-content: flex-start;\n      margin-right: auto; }\n    html.theme--documenter-dark .navbar-end {\n      justify-content: flex-end;\n      margin-left: auto; }\n    html.theme--documenter-dark .navbar-dropdown {\n      background-color: white;\n      border-bottom-left-radius: 6px;\n      border-bottom-right-radius: 6px;\n      border-top: 2px solid #dbdbdb;\n      box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1);\n      display: none;\n      font-size: 0.875rem;\n      left: 0;\n      min-width: 100%;\n      position: absolute;\n      top: 100%;\n      z-index: 20; }\n      html.theme--documenter-dark .navbar-dropdown .navbar-item {\n        padding: 0.375rem 1rem;\n        white-space: nowrap; }\n      html.theme--documenter-dark .navbar-dropdown a.navbar-item {\n        padding-right: 3rem; }\n        html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover {\n          background-color: whitesmoke;\n          color: #0a0a0a; }\n        html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active {\n          background-color: whitesmoke;\n          color: #e37733; }\n      .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed {\n        border-radius: 6px;\n        border-top: none;\n        box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);\n        display: block;\n        opacity: 0;\n        pointer-events: none;\n        top: calc(100% + (-4px));\n        transform: translateY(-5px);\n        transition-duration: 86ms;\n        transition-property: opacity, transform; }\n      html.theme--documenter-dark .navbar-dropdown.is-right {\n        left: auto;\n        right: 0; }\n    html.theme--documenter-dark .navbar-divider {\n      display: block; }\n    html.theme--documenter-dark .navbar > .container .navbar-brand,\n    html.theme--documenter-dark .container > .navbar .navbar-brand {\n      margin-left: -.75rem; }\n    html.theme--documenter-dark .navbar > .container .navbar-menu,\n    html.theme--documenter-dark .container > .navbar .navbar-menu {\n      margin-right: -.75rem; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop {\n      left: 0;\n      position: fixed;\n      right: 0;\n      z-index: 30; }\n    html.theme--documenter-dark .navbar.is-fixed-bottom-desktop {\n      bottom: 0; }\n      html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow {\n        box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }\n    html.theme--documenter-dark .navbar.is-fixed-top-desktop {\n      top: 0; }\n    html.theme--documenter-dark html.has-navbar-fixed-top-desktop,\n    html.theme--documenter-dark body.has-navbar-fixed-top-desktop {\n      padding-top: 3.25rem; }\n    html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,\n    html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop {\n      padding-bottom: 3.25rem; }\n    html.theme--documenter-dark html.has-spaced-navbar-fixed-top,\n    html.theme--documenter-dark body.has-spaced-navbar-fixed-top {\n      padding-top: 5.25rem; }\n    html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,\n    html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom {\n      padding-bottom: 5.25rem; }\n    html.theme--documenter-dark a.navbar-item.is-active,\n    html.theme--documenter-dark .navbar-link.is-active {\n      color: #0a0a0a; }\n    html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),\n    html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) {\n      background-color: transparent; }\n    html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link {\n      background-color: #fafafa; } }\n  html.theme--documenter-dark .hero.is-fullheight-with-navbar {\n    min-height: calc(100vh - 3.25rem); }\n  html.theme--documenter-dark .pagination {\n    font-size: 1rem;\n    margin: -0.25rem; }\n    html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .pagination.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .pagination.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous,\n    html.theme--documenter-dark .pagination.is-rounded .pagination-next,\n    html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next {\n      padding-left: 1em;\n      padding-right: 1em;\n      border-radius: 290486px; }\n    html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link {\n      border-radius: 290486px; }\n  html.theme--documenter-dark .pagination,\n  html.theme--documenter-dark .pagination-list {\n    align-items: center;\n    display: flex;\n    justify-content: center;\n    text-align: center; }\n  html.theme--documenter-dark .pagination-previous,\n  html.theme--documenter-dark .pagination-next,\n  html.theme--documenter-dark .pagination-link,\n  html.theme--documenter-dark .pagination-ellipsis {\n    font-size: 1em;\n    justify-content: center;\n    margin: 0.25rem;\n    padding-left: 0.5em;\n    padding-right: 0.5em;\n    text-align: center; }\n  html.theme--documenter-dark .pagination-previous,\n  html.theme--documenter-dark .pagination-next,\n  html.theme--documenter-dark .pagination-link {\n    border-color: #dbdbdb;\n    color: #363636;\n    min-width: 2.25em; }\n    html.theme--documenter-dark .pagination-previous:hover,\n    html.theme--documenter-dark .pagination-next:hover,\n    html.theme--documenter-dark .pagination-link:hover {\n      border-color: #b5b5b5;\n      color: #f2be9e; }\n    html.theme--documenter-dark .pagination-previous:focus,\n    html.theme--documenter-dark .pagination-next:focus,\n    html.theme--documenter-dark .pagination-link:focus {\n      border-color: #2e63b8; }\n    html.theme--documenter-dark .pagination-previous:active,\n    html.theme--documenter-dark .pagination-next:active,\n    html.theme--documenter-dark .pagination-link:active {\n      box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); }\n    html.theme--documenter-dark .pagination-previous[disabled],\n    html.theme--documenter-dark .pagination-next[disabled],\n    html.theme--documenter-dark .pagination-link[disabled] {\n      background-color: #dbdbdb;\n      border-color: #dbdbdb;\n      box-shadow: none;\n      color: #7a7a7a;\n      opacity: 0.5; }\n  html.theme--documenter-dark .pagination-previous,\n  html.theme--documenter-dark .pagination-next {\n    padding-left: 0.75em;\n    padding-right: 0.75em;\n    white-space: nowrap; }\n  html.theme--documenter-dark .pagination-link.is-current {\n    background-color: #e37733;\n    border-color: #e37733;\n    color: #fff; }\n  html.theme--documenter-dark .pagination-ellipsis {\n    color: #b5b5b5;\n    pointer-events: none; }\n  html.theme--documenter-dark .pagination-list {\n    flex-wrap: wrap; }\n  @media screen and (max-width: 768px) {\n    html.theme--documenter-dark .pagination {\n      flex-wrap: wrap; }\n    html.theme--documenter-dark .pagination-previous,\n    html.theme--documenter-dark .pagination-next {\n      flex-grow: 1;\n      flex-shrink: 1; }\n    html.theme--documenter-dark .pagination-list li {\n      flex-grow: 1;\n      flex-shrink: 1; } }\n  @media screen and (min-width: 769px), print {\n    html.theme--documenter-dark .pagination-list {\n      flex-grow: 1;\n      flex-shrink: 1;\n      justify-content: flex-start;\n      order: 1; }\n    html.theme--documenter-dark .pagination-previous {\n      order: 2; }\n    html.theme--documenter-dark .pagination-next {\n      order: 3; }\n    html.theme--documenter-dark .pagination {\n      justify-content: space-between; }\n      html.theme--documenter-dark .pagination.is-centered .pagination-previous {\n        order: 1; }\n      html.theme--documenter-dark .pagination.is-centered .pagination-list {\n        justify-content: center;\n        order: 2; }\n      html.theme--documenter-dark .pagination.is-centered .pagination-next {\n        order: 3; }\n      html.theme--documenter-dark .pagination.is-right .pagination-previous {\n        order: 1; }\n      html.theme--documenter-dark .pagination.is-right .pagination-next {\n        order: 2; }\n      html.theme--documenter-dark .pagination.is-right .pagination-list {\n        justify-content: flex-end;\n        order: 3; } }\n  html.theme--documenter-dark .panel {\n    font-size: 1rem; }\n    html.theme--documenter-dark .panel:not(:last-child) {\n      margin-bottom: 1.5rem; }\n  html.theme--documenter-dark .panel-heading,\n  html.theme--documenter-dark .panel-tabs,\n  html.theme--documenter-dark .panel-block {\n    border-bottom: 1px solid #dbdbdb;\n    border-left: 1px solid #dbdbdb;\n    border-right: 1px solid #dbdbdb; }\n    html.theme--documenter-dark .panel-heading:first-child,\n    html.theme--documenter-dark .panel-tabs:first-child,\n    html.theme--documenter-dark .panel-block:first-child {\n      border-top: 1px solid #dbdbdb; }\n  html.theme--documenter-dark .panel-heading {\n    background-color: whitesmoke;\n    border-radius: 4px 4px 0 0;\n    color: #97b3e2;\n    font-size: 1.25em;\n    font-weight: 300;\n    line-height: 1.25;\n    padding: 0.5em 0.75em; }\n  html.theme--documenter-dark .panel-tabs {\n    align-items: flex-end;\n    display: flex;\n    font-size: 0.875em;\n    justify-content: center; }\n    html.theme--documenter-dark .panel-tabs a {\n      border-bottom: 1px solid #dbdbdb;\n      margin-bottom: -1px;\n      padding: 0.5em; }\n      html.theme--documenter-dark .panel-tabs a.is-active {\n        border-bottom-color: #4a4a4a;\n        color: #363636; }\n  html.theme--documenter-dark .panel-list a {\n    color: #ececec; }\n    html.theme--documenter-dark .panel-list a:hover {\n      color: #e37733; }\n  html.theme--documenter-dark .panel-block {\n    align-items: center;\n    color: #97b3e2;\n    display: flex;\n    justify-content: flex-start;\n    padding: 0.5em 0.75em; }\n    html.theme--documenter-dark .panel-block input[type=\"checkbox\"] {\n      margin-right: 0.75em; }\n    html.theme--documenter-dark .panel-block > .control {\n      flex-grow: 1;\n      flex-shrink: 1;\n      width: 100%; }\n    html.theme--documenter-dark .panel-block.is-wrapped {\n      flex-wrap: wrap; }\n    html.theme--documenter-dark .panel-block.is-active {\n      border-left-color: #e37733;\n      color: #363636; }\n      html.theme--documenter-dark .panel-block.is-active .panel-icon {\n        color: #e37733; }\n  html.theme--documenter-dark a.panel-block,\n  html.theme--documenter-dark label.panel-block {\n    cursor: pointer; }\n    html.theme--documenter-dark a.panel-block:hover,\n    html.theme--documenter-dark label.panel-block:hover {\n      background-color: whitesmoke; }\n  html.theme--documenter-dark .panel-icon {\n    display: inline-block;\n    font-size: 14px;\n    height: 1em;\n    line-height: 1em;\n    text-align: center;\n    vertical-align: top;\n    width: 1em;\n    color: #7a7a7a;\n    margin-right: 0.75em; }\n    html.theme--documenter-dark .panel-icon .fa {\n      font-size: inherit;\n      line-height: inherit; }\n  html.theme--documenter-dark .tabs {\n    -webkit-overflow-scrolling: touch;\n    align-items: stretch;\n    display: flex;\n    font-size: 1rem;\n    justify-content: space-between;\n    overflow: hidden;\n    overflow-x: auto;\n    white-space: nowrap; }\n    html.theme--documenter-dark .tabs a {\n      align-items: center;\n      border-bottom-color: #dbdbdb;\n      border-bottom-style: solid;\n      border-bottom-width: 1px;\n      color: #ececec;\n      display: flex;\n      justify-content: center;\n      margin-bottom: -1px;\n      padding: 0.5em 1em;\n      vertical-align: top; }\n      html.theme--documenter-dark .tabs a:hover {\n        border-bottom-color: #97b3e2;\n        color: #97b3e2; }\n    html.theme--documenter-dark .tabs li {\n      display: block; }\n      html.theme--documenter-dark .tabs li.is-active a {\n        border-bottom-color: #e37733;\n        color: #e37733; }\n    html.theme--documenter-dark .tabs ul {\n      align-items: center;\n      border-bottom-color: #dbdbdb;\n      border-bottom-style: solid;\n      border-bottom-width: 1px;\n      display: flex;\n      flex-grow: 1;\n      flex-shrink: 0;\n      justify-content: flex-start; }\n      html.theme--documenter-dark .tabs ul.is-left {\n        padding-right: 0.75em; }\n      html.theme--documenter-dark .tabs ul.is-center {\n        flex: none;\n        justify-content: center;\n        padding-left: 0.75em;\n        padding-right: 0.75em; }\n      html.theme--documenter-dark .tabs ul.is-right {\n        justify-content: flex-end;\n        padding-left: 0.75em; }\n    html.theme--documenter-dark .tabs .icon:first-child {\n      margin-right: 0.5em; }\n    html.theme--documenter-dark .tabs .icon:last-child {\n      margin-left: 0.5em; }\n    html.theme--documenter-dark .tabs.is-centered ul {\n      justify-content: center; }\n    html.theme--documenter-dark .tabs.is-right ul {\n      justify-content: flex-end; }\n    html.theme--documenter-dark .tabs.is-boxed a {\n      border: 1px solid transparent;\n      border-radius: 4px 4px 0 0; }\n      html.theme--documenter-dark .tabs.is-boxed a:hover {\n        background-color: whitesmoke;\n        border-bottom-color: #dbdbdb; }\n    html.theme--documenter-dark .tabs.is-boxed li.is-active a {\n      background-color: white;\n      border-color: #dbdbdb;\n      border-bottom-color: transparent !important; }\n    html.theme--documenter-dark .tabs.is-fullwidth li {\n      flex-grow: 1;\n      flex-shrink: 0; }\n    html.theme--documenter-dark .tabs.is-toggle a {\n      border-color: #dbdbdb;\n      border-style: solid;\n      border-width: 1px;\n      margin-bottom: 0;\n      position: relative; }\n      html.theme--documenter-dark .tabs.is-toggle a:hover {\n        background-color: whitesmoke;\n        border-color: #b5b5b5;\n        z-index: 2; }\n    html.theme--documenter-dark .tabs.is-toggle li + li {\n      margin-left: -1px; }\n    html.theme--documenter-dark .tabs.is-toggle li:first-child a {\n      border-radius: 4px 0 0 4px; }\n    html.theme--documenter-dark .tabs.is-toggle li:last-child a {\n      border-radius: 0 4px 4px 0; }\n    html.theme--documenter-dark .tabs.is-toggle li.is-active a {\n      background-color: #e37733;\n      border-color: #e37733;\n      color: #fff;\n      z-index: 1; }\n    html.theme--documenter-dark .tabs.is-toggle ul {\n      border-bottom: none; }\n    html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a {\n      border-bottom-left-radius: 290486px;\n      border-top-left-radius: 290486px;\n      padding-left: 1.25em; }\n    html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a {\n      border-bottom-right-radius: 290486px;\n      border-top-right-radius: 290486px;\n      padding-right: 1.25em; }\n    html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .tabs.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .tabs.is-large {\n      font-size: 1.5rem; }\n  html.theme--documenter-dark .column {\n    display: block;\n    flex-basis: 0;\n    flex-grow: 1;\n    flex-shrink: 1;\n    padding: 0.75rem; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-narrow {\n      flex: none; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-full {\n      flex: none;\n      width: 100%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters {\n      flex: none;\n      width: 75%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds {\n      flex: none;\n      width: 66.6666%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-half {\n      flex: none;\n      width: 50%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-one-third {\n      flex: none;\n      width: 33.3333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter {\n      flex: none;\n      width: 25%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth {\n      flex: none;\n      width: 20%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths {\n      flex: none;\n      width: 40%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths {\n      flex: none;\n      width: 60%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths {\n      flex: none;\n      width: 80%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters {\n      margin-left: 75%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds {\n      margin-left: 66.6666%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half {\n      margin-left: 50%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third {\n      margin-left: 33.3333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter {\n      margin-left: 25%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth {\n      margin-left: 20%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths {\n      margin-left: 40%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths {\n      margin-left: 60%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths {\n      margin-left: 80%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-0 {\n      flex: none;\n      width: 0%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 {\n      margin-left: 0%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-1 {\n      flex: none;\n      width: 8.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 {\n      margin-left: 8.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-2 {\n      flex: none;\n      width: 16.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 {\n      margin-left: 16.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-3 {\n      flex: none;\n      width: 25%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 {\n      margin-left: 25%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-4 {\n      flex: none;\n      width: 33.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 {\n      margin-left: 33.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-5 {\n      flex: none;\n      width: 41.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 {\n      margin-left: 41.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-6 {\n      flex: none;\n      width: 50%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 {\n      margin-left: 50%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-7 {\n      flex: none;\n      width: 58.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 {\n      margin-left: 58.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-8 {\n      flex: none;\n      width: 66.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 {\n      margin-left: 66.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-9 {\n      flex: none;\n      width: 75%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 {\n      margin-left: 75%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-10 {\n      flex: none;\n      width: 83.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 {\n      margin-left: 83.33333%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-11 {\n      flex: none;\n      width: 91.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 {\n      margin-left: 91.66667%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-12 {\n      flex: none;\n      width: 100%; }\n    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 {\n      margin-left: 100%; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .column.is-narrow-mobile {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full-mobile {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters-mobile {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds-mobile {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half-mobile {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third-mobile {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter-mobile {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth-mobile {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths-mobile {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths-mobile {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths-mobile {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters-mobile {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds-mobile {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half-mobile {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third-mobile {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter-mobile {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth-mobile {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths-mobile {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths-mobile {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths-mobile {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0-mobile {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0-mobile {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1-mobile {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1-mobile {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2-mobile {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2-mobile {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3-mobile {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3-mobile {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4-mobile {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4-mobile {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5-mobile {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5-mobile {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6-mobile {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6-mobile {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7-mobile {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7-mobile {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8-mobile {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8-mobile {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9-mobile {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9-mobile {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10-mobile {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10-mobile {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11-mobile {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11-mobile {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12-mobile {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12-mobile {\n        margin-left: 100%; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet {\n        margin-left: 100%; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .column.is-narrow-touch {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full-touch {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters-touch {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds-touch {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half-touch {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third-touch {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter-touch {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth-touch {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths-touch {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths-touch {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths-touch {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters-touch {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds-touch {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half-touch {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third-touch {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter-touch {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth-touch {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths-touch {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths-touch {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths-touch {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0-touch {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0-touch {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1-touch {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1-touch {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2-touch {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2-touch {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3-touch {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3-touch {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4-touch {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4-touch {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5-touch {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5-touch {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6-touch {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6-touch {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7-touch {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7-touch {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8-touch {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8-touch {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9-touch {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9-touch {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10-touch {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10-touch {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11-touch {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11-touch {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12-touch {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12-touch {\n        margin-left: 100%; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .column.is-narrow-desktop {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full-desktop {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters-desktop {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds-desktop {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half-desktop {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third-desktop {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter-desktop {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth-desktop {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths-desktop {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths-desktop {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths-desktop {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters-desktop {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds-desktop {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half-desktop {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third-desktop {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter-desktop {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth-desktop {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths-desktop {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths-desktop {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths-desktop {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0-desktop {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0-desktop {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1-desktop {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1-desktop {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2-desktop {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2-desktop {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3-desktop {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3-desktop {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4-desktop {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4-desktop {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5-desktop {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5-desktop {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6-desktop {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6-desktop {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7-desktop {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7-desktop {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8-desktop {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8-desktop {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9-desktop {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9-desktop {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10-desktop {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10-desktop {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11-desktop {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11-desktop {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12-desktop {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12-desktop {\n        margin-left: 100%; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .column.is-narrow-widescreen {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full-widescreen {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters-widescreen {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds-widescreen {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half-widescreen {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third-widescreen {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter-widescreen {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth-widescreen {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths-widescreen {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths-widescreen {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths-widescreen {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters-widescreen {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds-widescreen {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half-widescreen {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third-widescreen {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter-widescreen {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth-widescreen {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths-widescreen {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths-widescreen {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths-widescreen {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0-widescreen {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0-widescreen {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1-widescreen {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1-widescreen {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2-widescreen {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2-widescreen {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3-widescreen {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3-widescreen {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4-widescreen {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4-widescreen {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5-widescreen {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5-widescreen {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6-widescreen {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6-widescreen {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7-widescreen {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7-widescreen {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8-widescreen {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8-widescreen {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9-widescreen {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9-widescreen {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10-widescreen {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10-widescreen {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11-widescreen {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11-widescreen {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12-widescreen {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12-widescreen {\n        margin-left: 100%; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .column.is-narrow-fullhd {\n        flex: none; }\n      html.theme--documenter-dark .column.is-full-fullhd {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-three-quarters-fullhd {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-two-thirds-fullhd {\n        flex: none;\n        width: 66.6666%; }\n      html.theme--documenter-dark .column.is-half-fullhd {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-one-third-fullhd {\n        flex: none;\n        width: 33.3333%; }\n      html.theme--documenter-dark .column.is-one-quarter-fullhd {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-one-fifth-fullhd {\n        flex: none;\n        width: 20%; }\n      html.theme--documenter-dark .column.is-two-fifths-fullhd {\n        flex: none;\n        width: 40%; }\n      html.theme--documenter-dark .column.is-three-fifths-fullhd {\n        flex: none;\n        width: 60%; }\n      html.theme--documenter-dark .column.is-four-fifths-fullhd {\n        flex: none;\n        width: 80%; }\n      html.theme--documenter-dark .column.is-offset-three-quarters-fullhd {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-offset-two-thirds-fullhd {\n        margin-left: 66.6666%; }\n      html.theme--documenter-dark .column.is-offset-half-fullhd {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-offset-one-third-fullhd {\n        margin-left: 33.3333%; }\n      html.theme--documenter-dark .column.is-offset-one-quarter-fullhd {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-offset-one-fifth-fullhd {\n        margin-left: 20%; }\n      html.theme--documenter-dark .column.is-offset-two-fifths-fullhd {\n        margin-left: 40%; }\n      html.theme--documenter-dark .column.is-offset-three-fifths-fullhd {\n        margin-left: 60%; }\n      html.theme--documenter-dark .column.is-offset-four-fifths-fullhd {\n        margin-left: 80%; }\n      html.theme--documenter-dark .column.is-0-fullhd {\n        flex: none;\n        width: 0%; }\n      html.theme--documenter-dark .column.is-offset-0-fullhd {\n        margin-left: 0%; }\n      html.theme--documenter-dark .column.is-1-fullhd {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .column.is-offset-1-fullhd {\n        margin-left: 8.33333%; }\n      html.theme--documenter-dark .column.is-2-fullhd {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .column.is-offset-2-fullhd {\n        margin-left: 16.66667%; }\n      html.theme--documenter-dark .column.is-3-fullhd {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .column.is-offset-3-fullhd {\n        margin-left: 25%; }\n      html.theme--documenter-dark .column.is-4-fullhd {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .column.is-offset-4-fullhd {\n        margin-left: 33.33333%; }\n      html.theme--documenter-dark .column.is-5-fullhd {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .column.is-offset-5-fullhd {\n        margin-left: 41.66667%; }\n      html.theme--documenter-dark .column.is-6-fullhd {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .column.is-offset-6-fullhd {\n        margin-left: 50%; }\n      html.theme--documenter-dark .column.is-7-fullhd {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .column.is-offset-7-fullhd {\n        margin-left: 58.33333%; }\n      html.theme--documenter-dark .column.is-8-fullhd {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .column.is-offset-8-fullhd {\n        margin-left: 66.66667%; }\n      html.theme--documenter-dark .column.is-9-fullhd {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .column.is-offset-9-fullhd {\n        margin-left: 75%; }\n      html.theme--documenter-dark .column.is-10-fullhd {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .column.is-offset-10-fullhd {\n        margin-left: 83.33333%; }\n      html.theme--documenter-dark .column.is-11-fullhd {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .column.is-offset-11-fullhd {\n        margin-left: 91.66667%; }\n      html.theme--documenter-dark .column.is-12-fullhd {\n        flex: none;\n        width: 100%; }\n      html.theme--documenter-dark .column.is-offset-12-fullhd {\n        margin-left: 100%; } }\n  html.theme--documenter-dark .columns {\n    margin-left: -0.75rem;\n    margin-right: -0.75rem;\n    margin-top: -0.75rem; }\n    html.theme--documenter-dark .columns:last-child {\n      margin-bottom: -0.75rem; }\n    html.theme--documenter-dark .columns:not(:last-child) {\n      margin-bottom: calc(1.5rem - 0.75rem); }\n    html.theme--documenter-dark .columns.is-centered {\n      justify-content: center; }\n    html.theme--documenter-dark .columns.is-gapless {\n      margin-left: 0;\n      margin-right: 0;\n      margin-top: 0; }\n      html.theme--documenter-dark .columns.is-gapless > .column {\n        margin: 0;\n        padding: 0 !important; }\n      html.theme--documenter-dark .columns.is-gapless:not(:last-child) {\n        margin-bottom: 1.5rem; }\n      html.theme--documenter-dark .columns.is-gapless:last-child {\n        margin-bottom: 0; }\n    html.theme--documenter-dark .columns.is-mobile {\n      display: flex; }\n    html.theme--documenter-dark .columns.is-multiline {\n      flex-wrap: wrap; }\n    html.theme--documenter-dark .columns.is-vcentered {\n      align-items: center; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns:not(.is-desktop) {\n        display: flex; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-desktop {\n        display: flex; } }\n  html.theme--documenter-dark .columns.is-variable {\n    --columnGap: 0.75rem;\n    margin-left: calc(-1 * var(--columnGap));\n    margin-right: calc(-1 * var(--columnGap)); }\n    html.theme--documenter-dark .columns.is-variable .column {\n      padding-left: var(--columnGap);\n      padding-right: var(--columnGap); }\n    html.theme--documenter-dark .columns.is-variable.is-0 {\n      --columnGap: 0rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-mobile {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-0-tablet {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-tablet-only {\n        --columnGap: 0rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-touch {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-desktop {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-desktop-only {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-widescreen {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only {\n        --columnGap: 0rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-0-fullhd {\n        --columnGap: 0rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-1 {\n      --columnGap: 0.25rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-mobile {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-1-tablet {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-tablet-only {\n        --columnGap: 0.25rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-touch {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-desktop {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-desktop-only {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-widescreen {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only {\n        --columnGap: 0.25rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-1-fullhd {\n        --columnGap: 0.25rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-2 {\n      --columnGap: 0.5rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-mobile {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-2-tablet {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-tablet-only {\n        --columnGap: 0.5rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-touch {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-desktop {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-desktop-only {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-widescreen {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only {\n        --columnGap: 0.5rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-2-fullhd {\n        --columnGap: 0.5rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-3 {\n      --columnGap: 0.75rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-mobile {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-3-tablet {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-tablet-only {\n        --columnGap: 0.75rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-touch {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-desktop {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-desktop-only {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-widescreen {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only {\n        --columnGap: 0.75rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-3-fullhd {\n        --columnGap: 0.75rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-4 {\n      --columnGap: 1rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-mobile {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-4-tablet {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-tablet-only {\n        --columnGap: 1rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-touch {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-desktop {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-desktop-only {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-widescreen {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only {\n        --columnGap: 1rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-4-fullhd {\n        --columnGap: 1rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-5 {\n      --columnGap: 1.25rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-mobile {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-5-tablet {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-tablet-only {\n        --columnGap: 1.25rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-touch {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-desktop {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-desktop-only {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-widescreen {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only {\n        --columnGap: 1.25rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-5-fullhd {\n        --columnGap: 1.25rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-6 {\n      --columnGap: 1.5rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-mobile {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-6-tablet {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-tablet-only {\n        --columnGap: 1.5rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-touch {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-desktop {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-desktop-only {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-widescreen {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only {\n        --columnGap: 1.5rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-6-fullhd {\n        --columnGap: 1.5rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-7 {\n      --columnGap: 1.75rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-mobile {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-7-tablet {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-tablet-only {\n        --columnGap: 1.75rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-touch {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-desktop {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-desktop-only {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-widescreen {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only {\n        --columnGap: 1.75rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-7-fullhd {\n        --columnGap: 1.75rem; } }\n    html.theme--documenter-dark .columns.is-variable.is-8 {\n      --columnGap: 2rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-mobile {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .columns.is-variable.is-8-tablet {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 769px) and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-tablet-only {\n        --columnGap: 2rem; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-touch {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-desktop {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 1056px) and (max-width: 1215px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-desktop-only {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 1216px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-widescreen {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 1216px) and (max-width: 1407px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only {\n        --columnGap: 2rem; } }\n    @media screen and (min-width: 1408px) {\n      html.theme--documenter-dark .columns.is-variable.is-8-fullhd {\n        --columnGap: 2rem; } }\n  html.theme--documenter-dark .tile {\n    align-items: stretch;\n    display: block;\n    flex-basis: 0;\n    flex-grow: 1;\n    flex-shrink: 1;\n    min-height: min-content; }\n    html.theme--documenter-dark .tile.is-ancestor {\n      margin-left: -0.75rem;\n      margin-right: -0.75rem;\n      margin-top: -0.75rem; }\n      html.theme--documenter-dark .tile.is-ancestor:last-child {\n        margin-bottom: -0.75rem; }\n      html.theme--documenter-dark .tile.is-ancestor:not(:last-child) {\n        margin-bottom: 0.75rem; }\n    html.theme--documenter-dark .tile.is-child {\n      margin: 0 !important; }\n    html.theme--documenter-dark .tile.is-parent {\n      padding: 0.75rem; }\n    html.theme--documenter-dark .tile.is-vertical {\n      flex-direction: column; }\n      html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) {\n        margin-bottom: 1.5rem !important; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .tile:not(.is-child) {\n        display: flex; }\n      html.theme--documenter-dark .tile.is-1 {\n        flex: none;\n        width: 8.33333%; }\n      html.theme--documenter-dark .tile.is-2 {\n        flex: none;\n        width: 16.66667%; }\n      html.theme--documenter-dark .tile.is-3 {\n        flex: none;\n        width: 25%; }\n      html.theme--documenter-dark .tile.is-4 {\n        flex: none;\n        width: 33.33333%; }\n      html.theme--documenter-dark .tile.is-5 {\n        flex: none;\n        width: 41.66667%; }\n      html.theme--documenter-dark .tile.is-6 {\n        flex: none;\n        width: 50%; }\n      html.theme--documenter-dark .tile.is-7 {\n        flex: none;\n        width: 58.33333%; }\n      html.theme--documenter-dark .tile.is-8 {\n        flex: none;\n        width: 66.66667%; }\n      html.theme--documenter-dark .tile.is-9 {\n        flex: none;\n        width: 75%; }\n      html.theme--documenter-dark .tile.is-10 {\n        flex: none;\n        width: 83.33333%; }\n      html.theme--documenter-dark .tile.is-11 {\n        flex: none;\n        width: 91.66667%; }\n      html.theme--documenter-dark .tile.is-12 {\n        flex: none;\n        width: 100%; } }\n  html.theme--documenter-dark .hero {\n    align-items: stretch;\n    display: flex;\n    flex-direction: column;\n    justify-content: space-between; }\n    html.theme--documenter-dark .hero .navbar {\n      background: none; }\n    html.theme--documenter-dark .hero .tabs ul {\n      border-bottom: none; }\n    html.theme--documenter-dark .hero.is-white {\n      background-color: white;\n      color: #0a0a0a; }\n      html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-white strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-white .title {\n        color: #0a0a0a; }\n      html.theme--documenter-dark .hero.is-white .subtitle {\n        color: rgba(10, 10, 10, 0.9); }\n        html.theme--documenter-dark .hero.is-white .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-white .subtitle strong {\n          color: #0a0a0a; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-white .navbar-menu {\n          background-color: white; } }\n      html.theme--documenter-dark .hero.is-white .navbar-item,\n      html.theme--documenter-dark .hero.is-white .navbar-link {\n        color: rgba(10, 10, 10, 0.7); }\n      html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-white .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-white .navbar-link.is-active {\n        background-color: #f2f2f2;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .hero.is-white .tabs a {\n        color: #0a0a0a;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-white .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-white .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a {\n        color: #0a0a0a; }\n        html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover {\n        background-color: #0a0a0a;\n        border-color: #0a0a0a;\n        color: white; }\n      html.theme--documenter-dark .hero.is-white.is-bold {\n        background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); } }\n    html.theme--documenter-dark .hero.is-black {\n      background-color: #0a0a0a;\n      color: white; }\n      html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-black strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-black .title {\n        color: white; }\n      html.theme--documenter-dark .hero.is-black .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-black .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-black .subtitle strong {\n          color: white; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-black .navbar-menu {\n          background-color: #0a0a0a; } }\n      html.theme--documenter-dark .hero.is-black .navbar-item,\n      html.theme--documenter-dark .hero.is-black .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-black .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-black .navbar-link.is-active {\n        background-color: black;\n        color: white; }\n      html.theme--documenter-dark .hero.is-black .tabs a {\n        color: white;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-black .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-black .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a {\n        color: white; }\n        html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover {\n        background-color: white;\n        border-color: white;\n        color: #0a0a0a; }\n      html.theme--documenter-dark .hero.is-black.is-bold {\n        background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } }\n    html.theme--documenter-dark .hero.is-light {\n      background-color: whitesmoke;\n      color: #363636; }\n      html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-light strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-light .title {\n        color: #363636; }\n      html.theme--documenter-dark .hero.is-light .subtitle {\n        color: rgba(54, 54, 54, 0.9); }\n        html.theme--documenter-dark .hero.is-light .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-light .subtitle strong {\n          color: #363636; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-light .navbar-menu {\n          background-color: whitesmoke; } }\n      html.theme--documenter-dark .hero.is-light .navbar-item,\n      html.theme--documenter-dark .hero.is-light .navbar-link {\n        color: rgba(54, 54, 54, 0.7); }\n      html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-light .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-light .navbar-link.is-active {\n        background-color: #e8e8e8;\n        color: #363636; }\n      html.theme--documenter-dark .hero.is-light .tabs a {\n        color: #363636;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-light .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-light .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a {\n        color: #363636; }\n        html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover {\n        background-color: #363636;\n        border-color: #363636;\n        color: whitesmoke; }\n      html.theme--documenter-dark .hero.is-light.is-bold {\n        background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } }\n    html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero {\n      background-color: #363636;\n      color: whitesmoke; }\n      html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-dark strong,\n      html.theme--documenter-dark .content kbd.hero strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title {\n        color: whitesmoke; }\n      html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle {\n        color: rgba(245, 245, 245, 0.9); }\n        html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-dark .subtitle strong,\n        html.theme--documenter-dark .content kbd.hero .subtitle strong {\n          color: whitesmoke; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu {\n          background-color: #363636; } }\n      html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item,\n      html.theme--documenter-dark .hero.is-dark .navbar-link,\n      html.theme--documenter-dark .content kbd.hero .navbar-link {\n        color: rgba(245, 245, 245, 0.7); }\n      html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-dark .navbar-link:hover,\n      html.theme--documenter-dark .content kbd.hero .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-dark .navbar-link.is-active,\n      html.theme--documenter-dark .content kbd.hero .navbar-link.is-active {\n        background-color: #292929;\n        color: whitesmoke; }\n      html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a {\n        color: whitesmoke;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a {\n        color: whitesmoke; }\n        html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a:hover {\n        background-color: whitesmoke;\n        border-color: whitesmoke;\n        color: #363636; }\n      html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold {\n        background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } }\n    html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink {\n      background-color: #4eb5de;\n      color: #fff; }\n      html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-primary strong,\n      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title {\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-primary .subtitle strong,\n        html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong {\n          color: #fff; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu {\n          background-color: #4eb5de; } }\n      html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item,\n      html.theme--documenter-dark .hero.is-primary .navbar-link,\n      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-primary .navbar-link:hover,\n      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-primary .navbar-link.is-active,\n      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active {\n        background-color: #39acda;\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a {\n        color: #fff;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a {\n        color: #fff; }\n        html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a:hover {\n        background-color: #fff;\n        border-color: #fff;\n        color: #4eb5de; }\n      html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink {\n        background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu {\n            background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } }\n    html.theme--documenter-dark .hero.is-link {\n      background-color: #e37733;\n      color: #fff; }\n      html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-link strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-link .title {\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-link .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-link .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-link .subtitle strong {\n          color: #fff; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-link .navbar-menu {\n          background-color: #e37733; } }\n      html.theme--documenter-dark .hero.is-link .navbar-item,\n      html.theme--documenter-dark .hero.is-link .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-link .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-link .navbar-link.is-active {\n        background-color: #dd681f;\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-link .tabs a {\n        color: #fff;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-link .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-link .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a {\n        color: #fff; }\n        html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover {\n        background-color: #fff;\n        border-color: #fff;\n        color: #e37733; }\n      html.theme--documenter-dark .hero.is-link.is-bold {\n        background-image: linear-gradient(141deg, #d23b10 0%, #e37733 71%, #eba044 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #d23b10 0%, #e37733 71%, #eba044 100%); } }\n    html.theme--documenter-dark .hero.is-info {\n      background-color: #209cee;\n      color: #fff; }\n      html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-info strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-info .title {\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-info .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-info .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-info .subtitle strong {\n          color: #fff; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-info .navbar-menu {\n          background-color: #209cee; } }\n      html.theme--documenter-dark .hero.is-info .navbar-item,\n      html.theme--documenter-dark .hero.is-info .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-info .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-info .navbar-link.is-active {\n        background-color: #118fe4;\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-info .tabs a {\n        color: #fff;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-info .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-info .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a {\n        color: #fff; }\n        html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover {\n        background-color: #fff;\n        border-color: #fff;\n        color: #209cee; }\n      html.theme--documenter-dark .hero.is-info.is-bold {\n        background-image: linear-gradient(141deg, #04a6d7 0%, #209cee 71%, #3287f5 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #04a6d7 0%, #209cee 71%, #3287f5 100%); } }\n    html.theme--documenter-dark .hero.is-success {\n      background-color: #22c35b;\n      color: #fff; }\n      html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-success strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-success .title {\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-success .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-success .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-success .subtitle strong {\n          color: #fff; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-success .navbar-menu {\n          background-color: #22c35b; } }\n      html.theme--documenter-dark .hero.is-success .navbar-item,\n      html.theme--documenter-dark .hero.is-success .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-success .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-success .navbar-link.is-active {\n        background-color: #1ead51;\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-success .tabs a {\n        color: #fff;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-success .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-success .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a {\n        color: #fff; }\n        html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover {\n        background-color: #fff;\n        border-color: #fff;\n        color: #22c35b; }\n      html.theme--documenter-dark .hero.is-success.is-bold {\n        background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } }\n    html.theme--documenter-dark .hero.is-warning {\n      background-color: #ffdd57;\n      color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-warning strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-warning .title {\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .hero.is-warning .subtitle {\n        color: rgba(0, 0, 0, 0.9); }\n        html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-warning .subtitle strong {\n          color: rgba(0, 0, 0, 0.7); }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-warning .navbar-menu {\n          background-color: #ffdd57; } }\n      html.theme--documenter-dark .hero.is-warning .navbar-item,\n      html.theme--documenter-dark .hero.is-warning .navbar-link {\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-warning .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-warning .navbar-link.is-active {\n        background-color: #ffd83d;\n        color: rgba(0, 0, 0, 0.7); }\n      html.theme--documenter-dark .hero.is-warning .tabs a {\n        color: rgba(0, 0, 0, 0.7);\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-warning .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-warning .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a {\n        color: rgba(0, 0, 0, 0.7); }\n        html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover {\n        background-color: rgba(0, 0, 0, 0.7);\n        border-color: rgba(0, 0, 0, 0.7);\n        color: #ffdd57; }\n      html.theme--documenter-dark .hero.is-warning.is-bold {\n        background-image: linear-gradient(141deg, #ffaf24 0%, #ffdd57 71%, #fffa70 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #ffaf24 0%, #ffdd57 71%, #fffa70 100%); } }\n    html.theme--documenter-dark .hero.is-danger {\n      background-color: #da0b00;\n      color: #fff; }\n      html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),\n      html.theme--documenter-dark .hero.is-danger strong {\n        color: inherit; }\n      html.theme--documenter-dark .hero.is-danger .title {\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-danger .subtitle {\n        color: rgba(255, 255, 255, 0.9); }\n        html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button),\n        html.theme--documenter-dark .hero.is-danger .subtitle strong {\n          color: #fff; }\n      @media screen and (max-width: 1055px) {\n        html.theme--documenter-dark .hero.is-danger .navbar-menu {\n          background-color: #da0b00; } }\n      html.theme--documenter-dark .hero.is-danger .navbar-item,\n      html.theme--documenter-dark .hero.is-danger .navbar-link {\n        color: rgba(255, 255, 255, 0.7); }\n      html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active,\n      html.theme--documenter-dark .hero.is-danger .navbar-link:hover,\n      html.theme--documenter-dark .hero.is-danger .navbar-link.is-active {\n        background-color: #c10a00;\n        color: #fff; }\n      html.theme--documenter-dark .hero.is-danger .tabs a {\n        color: #fff;\n        opacity: 0.9; }\n        html.theme--documenter-dark .hero.is-danger .tabs a:hover {\n          opacity: 1; }\n      html.theme--documenter-dark .hero.is-danger .tabs li.is-active a {\n        opacity: 1; }\n      html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a {\n        color: #fff; }\n        html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover {\n          background-color: rgba(10, 10, 10, 0.1); }\n      html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover {\n        background-color: #fff;\n        border-color: #fff;\n        color: #da0b00; }\n      html.theme--documenter-dark .hero.is-danger.is-bold {\n        background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); }\n        @media screen and (max-width: 768px) {\n          html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu {\n            background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } }\n    html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body {\n      padding-bottom: 1.5rem;\n      padding-top: 1.5rem; }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .hero.is-medium .hero-body {\n        padding-bottom: 9rem;\n        padding-top: 9rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .hero.is-large .hero-body {\n        padding-bottom: 18rem;\n        padding-top: 18rem; } }\n    html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body {\n      align-items: center;\n      display: flex; }\n      html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container {\n        flex-grow: 1;\n        flex-shrink: 1; }\n    html.theme--documenter-dark .hero.is-halfheight {\n      min-height: 50vh; }\n    html.theme--documenter-dark .hero.is-fullheight {\n      min-height: 100vh; }\n  html.theme--documenter-dark .hero-video {\n    overflow: hidden; }\n    html.theme--documenter-dark .hero-video video {\n      left: 50%;\n      min-height: 100%;\n      min-width: 100%;\n      position: absolute;\n      top: 50%;\n      transform: translate3d(-50%, -50%, 0); }\n    html.theme--documenter-dark .hero-video.is-transparent {\n      opacity: 0.3; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .hero-video {\n        display: none; } }\n  html.theme--documenter-dark .hero-buttons {\n    margin-top: 1.5rem; }\n    @media screen and (max-width: 768px) {\n      html.theme--documenter-dark .hero-buttons .button {\n        display: flex; }\n        html.theme--documenter-dark .hero-buttons .button:not(:last-child) {\n          margin-bottom: 0.75rem; } }\n    @media screen and (min-width: 769px), print {\n      html.theme--documenter-dark .hero-buttons {\n        display: flex;\n        justify-content: center; }\n        html.theme--documenter-dark .hero-buttons .button:not(:last-child) {\n          margin-right: 1.5rem; } }\n  html.theme--documenter-dark .hero-head,\n  html.theme--documenter-dark .hero-foot {\n    flex-grow: 0;\n    flex-shrink: 0; }\n  html.theme--documenter-dark .hero-body {\n    flex-grow: 1;\n    flex-shrink: 0;\n    padding: 3rem 1.5rem; }\n  html.theme--documenter-dark .section {\n    padding: 3rem 1.5rem; }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark .section.is-medium {\n        padding: 9rem 1.5rem; }\n      html.theme--documenter-dark .section.is-large {\n        padding: 18rem 1.5rem; } }\n  html.theme--documenter-dark .footer {\n    background-color: #fafafa;\n    padding: 3rem 1.5rem 6rem; }\n  html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited {\n    color: #97b3e2; }\n  html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink {\n    visibility: hidden;\n    vertical-align: middle;\n    margin-left: 0.5em;\n    font-size: 0.7rem; }\n    html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before {\n      font-family: \"Font Awesome 5 Free\";\n      font-weight: 900;\n      content: \"\\f0c1\"; }\n  html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink {\n    visibility: visible; }\n  html.theme--documenter-dark .docs-light-only {\n    display: none !important; }\n  html.theme--documenter-dark .admonition {\n    background-color: #232834;\n    border-style: solid;\n    border-width: 1px;\n    border-color: #ba3f1f;\n    border-radius: 4px;\n    font-size: 1rem; }\n    html.theme--documenter-dark .admonition strong {\n      color: currentColor; }\n    html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition {\n      font-size: 0.75rem; }\n    html.theme--documenter-dark .admonition.is-medium {\n      font-size: 1.25rem; }\n    html.theme--documenter-dark .admonition.is-large {\n      font-size: 1.5rem; }\n    html.theme--documenter-dark .admonition.is-default {\n      background-color: #232834;\n      border-color: #ba3f1f; }\n      html.theme--documenter-dark .admonition.is-default > .admonition-header {\n        background-color: #ba3f1f; }\n    html.theme--documenter-dark .admonition.is-info {\n      background-color: #232834;\n      border-color: #28c; }\n      html.theme--documenter-dark .admonition.is-info > .admonition-header {\n        background-color: #28c; }\n    html.theme--documenter-dark .admonition.is-success {\n      background-color: #232834;\n      border-color: #42ac68; }\n      html.theme--documenter-dark .admonition.is-success > .admonition-header {\n        background-color: #42ac68; }\n    html.theme--documenter-dark .admonition.is-warning {\n      background-color: #232834;\n      border-color: #a88b17; }\n      html.theme--documenter-dark .admonition.is-warning > .admonition-header {\n        background-color: #a88b17; }\n    html.theme--documenter-dark .admonition.is-danger {\n      background-color: #232834;\n      border-color: #c7524c; }\n      html.theme--documenter-dark .admonition.is-danger > .admonition-header {\n        background-color: #c7524c; }\n    html.theme--documenter-dark .admonition.is-compat {\n      background-color: #232834;\n      border-color: #1db5c9; }\n      html.theme--documenter-dark .admonition.is-compat > .admonition-header {\n        background-color: #1db5c9; }\n  html.theme--documenter-dark .admonition-header {\n    background-color: #ba3f1f;\n    align-items: center;\n    font-weight: 700;\n    justify-content: space-between;\n    line-height: 1.25;\n    padding: 0.75em;\n    position: relative; }\n    html.theme--documenter-dark .admonition-header:before {\n      font-family: \"Font Awesome 5 Free\";\n      font-weight: 900;\n      margin-right: 0.75em;\n      content: \"\\f06a\"; }\n  html.theme--documenter-dark .admonition-body {\n    color: #ececec;\n    padding: 1em 1.25em; }\n    html.theme--documenter-dark .admonition-body pre {\n      background-color: #101f38; }\n    html.theme--documenter-dark .admonition-body code {\n      background-color: #101f38; }\n  html.theme--documenter-dark .docstring {\n    margin-bottom: 1em;\n    background-color: transparent;\n    border: 1px solid #dbdbdb;\n    box-shadow: 3px 3px 4px #444444;\n    max-width: 100%; }\n    html.theme--documenter-dark .docstring > header {\n      display: flex;\n      flex-grow: 1;\n      align-items: stretch;\n      padding: 0.75rem;\n      background-color: #232834;\n      box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);\n      box-shadow: none;\n      border-bottom: 1px solid #dbdbdb; }\n      html.theme--documenter-dark .docstring > header code {\n        background-color: transparent; }\n      html.theme--documenter-dark .docstring > header .docstring-binding {\n        margin-right: 0.3em; }\n      html.theme--documenter-dark .docstring > header .docstring-category {\n        margin-left: 0.3em; }\n    html.theme--documenter-dark .docstring > section {\n      position: relative;\n      padding: 1rem 1.25rem;\n      border-bottom: 1px solid #dbdbdb; }\n      html.theme--documenter-dark .docstring > section:last-child {\n        border-bottom: none; }\n      html.theme--documenter-dark .docstring > section > a.docs-sourcelink {\n        transition: opacity 0.3s;\n        opacity: 0;\n        position: absolute;\n        right: 0.625rem;\n        bottom: 0.5rem; }\n    html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink {\n      opacity: 0.2; }\n    html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink {\n      opacity: 1; }\n  html.theme--documenter-dark .documenter-example-output {\n    background-color: #1b1f28; }\n  html.theme--documenter-dark .content pre {\n    border: 1px solid #dbdbdb; }\n  html.theme--documenter-dark .content code {\n    font-weight: inherit; }\n  html.theme--documenter-dark .content a code {\n    color: #e37733; }\n  html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code {\n    color: #97b3e2; }\n  html.theme--documenter-dark .content table {\n    display: block;\n    width: initial;\n    max-width: 100%;\n    overflow-x: auto; }\n  html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child {\n    margin-top: 0; }\n  html.theme--documenter-dark .breadcrumb a.is-disabled {\n    cursor: default;\n    pointer-events: none; }\n    html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover {\n      color: #97b3e2; }\n  html.theme--documenter-dark .hljs {\n    background: initial !important;\n    padding: initial !important; }\n  html.theme--documenter-dark .katex .katex-mathml {\n    top: 0;\n    right: 0; }\n  html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display {\n    margin: 0.5em 0 !important; }\n  html.theme--documenter-dark html {\n    -moz-osx-font-smoothing: auto;\n    -webkit-font-smoothing: auto; }\n  html.theme--documenter-dark #documenter .docs-main > article {\n    overflow-wrap: break-word; }\n    html.theme--documenter-dark #documenter .docs-main > article .math-container {\n      overflow-x: auto; }\n  @media screen and (min-width: 1056px) {\n    html.theme--documenter-dark #documenter .docs-main {\n      max-width: 52rem;\n      margin-left: 20rem;\n      padding-right: 1rem; } }\n  @media screen and (max-width: 1055px) {\n    html.theme--documenter-dark #documenter .docs-main {\n      width: 100%; }\n      html.theme--documenter-dark #documenter .docs-main > article {\n        max-width: 52rem;\n        margin-left: auto;\n        margin-right: auto;\n        margin-bottom: 1rem;\n        padding: 0 1rem; }\n      html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav {\n        max-width: 100%;\n        width: 100%;\n        margin: 0; } }\n  html.theme--documenter-dark #documenter .docs-main header.docs-navbar {\n    background-color: #1b1f28;\n    border-bottom: 1px solid #dbdbdb;\n    z-index: 2;\n    min-height: 4rem;\n    margin-bottom: 1rem;\n    display: flex; }\n    html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb {\n      flex-grow: 1; }\n    html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right {\n      display: flex;\n      white-space: nowrap; }\n      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button {\n        display: inline-block; }\n      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label {\n        padding: 0;\n        margin-left: 0.3em; }\n      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button {\n        margin: auto 0 auto 1rem; }\n      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button {\n        font-size: 1.5rem;\n        margin: auto 0 auto 1rem; }\n    html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * {\n      margin: auto 0; }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark #documenter .docs-main header.docs-navbar {\n        position: sticky;\n        top: 0;\n        padding: 0 1rem;\n        /* For Headroom.js */\n        transition-property: top, box-shadow;\n        -webkit-transition-property: top, box-shadow;\n        /* Safari */\n        transition-duration: 0.3s;\n        -webkit-transition-duration: 0.3s;\n        /* Safari */ }\n        html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top {\n          box-shadow: 0.2rem 0rem 0.4rem #bbb;\n          transition-duration: 0.7s;\n          -webkit-transition-duration: 0.7s;\n          /* Safari */ }\n        html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {\n          top: -4.5rem;\n          transition-duration: 0.7s;\n          -webkit-transition-duration: 0.7s;\n          /* Safari */ } }\n  html.theme--documenter-dark #documenter .docs-main section.footnotes {\n    border-top: 1px solid #dbdbdb; }\n    html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child {\n      margin-right: 1em;\n      margin-bottom: 0.4em; }\n  html.theme--documenter-dark #documenter .docs-main .docs-footer {\n    display: flex;\n    flex-wrap: wrap;\n    margin-left: 0;\n    margin-right: 0;\n    border-top: 1px solid #dbdbdb;\n    padding-top: 1rem;\n    padding-bottom: 1rem; }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark #documenter .docs-main .docs-footer {\n        padding-left: 1rem;\n        padding-right: 1rem; } }\n    html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage {\n      flex-grow: 1; }\n    html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage {\n      text-align: right; }\n    html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break {\n      flex-basis: 100%;\n      height: 0; }\n    html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message {\n      font-size: 0.8em;\n      margin: 0.5em auto 0 auto;\n      text-align: center; }\n  html.theme--documenter-dark #documenter .docs-sidebar {\n    display: flex;\n    flex-direction: column;\n    color: #ececec;\n    background-color: #1d3968;\n    border-right: 1px solid #dbdbdb;\n    padding: 0;\n    flex: 0 0 18rem;\n    z-index: 5;\n    font-size: 1rem;\n    position: fixed;\n    left: -18rem;\n    width: 18rem;\n    height: 100%;\n    transition: left 0.3s;\n    /* Setting up a nicer theme style for the scrollbar */ }\n    html.theme--documenter-dark #documenter .docs-sidebar.visible {\n      left: 0;\n      box-shadow: 0.4rem 0rem 0.8rem #bbb; }\n      @media screen and (min-width: 1056px) {\n        html.theme--documenter-dark #documenter .docs-sidebar.visible {\n          box-shadow: none; } }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark #documenter .docs-sidebar {\n        left: 0;\n        top: 0; } }\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo {\n      margin-top: 1rem;\n      padding: 0 1rem; }\n      html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img {\n        max-height: 6rem;\n        margin: auto; }\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name {\n      flex-shrink: 0;\n      font-size: 1.5rem;\n      font-weight: 700;\n      text-align: center;\n      white-space: nowrap;\n      overflow: hidden;\n      padding: 0.5rem 0; }\n      html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit {\n        max-width: 16.2rem; }\n    html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector {\n      border-top: 1px solid #dbdbdb;\n      display: none;\n      padding: 0.5rem; }\n      html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible {\n        display: flex; }\n    html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu {\n      flex-grow: 1;\n      user-select: none;\n      border-top: 1px solid #dbdbdb;\n      padding-bottom: 1.5rem;\n      /* Managing collapsible submenus */ }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem {\n        font-weight: bold; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li {\n        font-size: 0.95rem;\n        margin-left: 1em;\n        border-left: 1px solid #dbdbdb; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle {\n        display: none; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed {\n        display: none; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed {\n        display: block; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem {\n        display: flex; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label {\n          flex-grow: 2; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron {\n          display: inline-block;\n          font-style: normal;\n          font-variant: normal;\n          text-rendering: auto;\n          line-height: 1;\n          font-size: 0.75rem;\n          margin-left: 1rem;\n          margin-top: auto;\n          margin-bottom: auto; }\n          html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before {\n            font-family: \"Font Awesome 5 Free\";\n            font-weight: 900;\n            content: \"\\f054\"; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before {\n        content: \"\\f078\"; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem {\n        display: block;\n        padding: 0.5rem 0.5rem; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover {\n          color: #ececec;\n          background: #1d3968; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover {\n        color: #ececec;\n        background-color: #122442; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active {\n        border-top: 1px solid #dbdbdb;\n        border-bottom: 1px solid #dbdbdb;\n        background-color: #1b1f28; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover {\n          background-color: #1b1f28;\n          color: #f0f0f0; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover {\n          background-color: #142748;\n          color: #f0f0f0; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child {\n        border-top: none; }\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal {\n        margin: 0 0.5rem 0.5rem;\n        border-top: 1px solid #dbdbdb; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li {\n          font-size: 0.85rem;\n          border-left: none;\n          margin-left: 0;\n          margin-top: 0.5rem; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem {\n          width: 100%;\n          padding: 0; }\n          html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before {\n            content: \"⚬\";\n            margin-right: 0.4em; }\n    html.theme--documenter-dark #documenter .docs-sidebar form.docs-search {\n      margin: auto;\n      margin-top: 0.5rem;\n      margin-bottom: 0.5rem; }\n      html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input {\n        width: 14.4rem; }\n    @media screen and (min-width: 1056px) {\n      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu {\n        overflow-y: auto;\n        -webkit-overflow-scroll: touch; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar {\n          width: .3rem;\n          background: none; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb {\n          border-radius: 5px 0px 0px 5px;\n          background: #142748; }\n        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover {\n          background: #0b1628; } }\n    @media screen and (max-width: 1055px) {\n      html.theme--documenter-dark #documenter .docs-sidebar {\n        overflow-y: auto;\n        -webkit-overflow-scroll: touch; }\n        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar {\n          width: .3rem;\n          background: none; }\n        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb {\n          border-radius: 5px 0px 0px 5px;\n          background: #142748; }\n        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover {\n          background: #0b1628; } }\n  html.theme--documenter-dark #documenter .docs-main #documenter-search-info {\n    margin-bottom: 1rem; }\n  html.theme--documenter-dark #documenter .docs-main #documenter-search-results {\n    list-style-type: circle;\n    list-style-position: outside; }\n    html.theme--documenter-dark #documenter .docs-main #documenter-search-results li {\n      margin-left: 2rem; }\n    html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight {\n      background-color: yellow; }\n  html.theme--documenter-dark {\n    background-color: #1b1f28;\n    font-size: 16px;\n    min-width: 300px;\n    overflow-x: auto;\n    overflow-y: scroll;\n    text-rendering: optimizeLegibility;\n    text-size-adjust: 100%; }\n  html.theme--documenter-dark #documenter .docs-sidebar {\n    border-right: none;\n    box-shadow: 0.24rem 0rem 0.4rem #444444; }\n    html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input {\n      color: #f0f0f0;\n      background-color: #142748;\n      border-color: #0b1628;\n      margin-top: 1.0rem;\n      margin-bottom: 1.0rem; }\n      html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::placeholder {\n        color: #f0f0f0; }\n  html.theme--documenter-dark .hljs-comment,\n  html.theme--documenter-dark .hljs-quote {\n    color: #d4d0ab; }\n  html.theme--documenter-dark .hljs-variable,\n  html.theme--documenter-dark .hljs-template-variable,\n  html.theme--documenter-dark .hljs-tag,\n  html.theme--documenter-dark .hljs-name,\n  html.theme--documenter-dark .hljs-selector-id,\n  html.theme--documenter-dark .hljs-selector-class,\n  html.theme--documenter-dark .hljs-regexp,\n  html.theme--documenter-dark .hljs-deletion {\n    color: #ffa07a; }\n  html.theme--documenter-dark .hljs-number,\n  html.theme--documenter-dark .hljs-built_in,\n  html.theme--documenter-dark .hljs-builtin-name,\n  html.theme--documenter-dark .hljs-literal,\n  html.theme--documenter-dark .hljs-type,\n  html.theme--documenter-dark .hljs-params,\n  html.theme--documenter-dark .hljs-meta,\n  html.theme--documenter-dark .hljs-link {\n    color: #f5ab35; }\n  html.theme--documenter-dark .hljs-attribute {\n    color: #ffd700; }\n  html.theme--documenter-dark .hljs-string,\n  html.theme--documenter-dark .hljs-symbol,\n  html.theme--documenter-dark .hljs-bullet,\n  html.theme--documenter-dark .hljs-addition {\n    color: #abe338; }\n  html.theme--documenter-dark .hljs-title,\n  html.theme--documenter-dark .hljs-section {\n    color: #00e0e0; }\n  html.theme--documenter-dark .hljs-keyword,\n  html.theme--documenter-dark .hljs-selector-tag {\n    color: #dcc6e0; }\n  html.theme--documenter-dark .hljs {\n    display: block;\n    overflow-x: auto;\n    background: #2b2b2b;\n    color: #f8f8f2;\n    padding: 0.5em; }\n  html.theme--documenter-dark .hljs-emphasis {\n    font-style: italic; }\n  html.theme--documenter-dark .hljs-strong {\n    font-weight: bold; }\n  @media screen and (-ms-high-contrast: active) {\n    html.theme--documenter-dark .hljs-addition,\n    html.theme--documenter-dark .hljs-attribute,\n    html.theme--documenter-dark .hljs-built_in,\n    html.theme--documenter-dark .hljs-builtin-name,\n    html.theme--documenter-dark .hljs-bullet,\n    html.theme--documenter-dark .hljs-comment,\n    html.theme--documenter-dark .hljs-link,\n    html.theme--documenter-dark .hljs-literal,\n    html.theme--documenter-dark .hljs-meta,\n    html.theme--documenter-dark .hljs-number,\n    html.theme--documenter-dark .hljs-params,\n    html.theme--documenter-dark .hljs-string,\n    html.theme--documenter-dark .hljs-symbol,\n    html.theme--documenter-dark .hljs-type,\n    html.theme--documenter-dark .hljs-quote {\n      color: highlight; }\n    html.theme--documenter-dark .hljs-keyword,\n    html.theme--documenter-dark .hljs-selector-tag {\n      font-weight: bold; } }\n  html.theme--documenter-dark .hljs-subst {\n    color: #f8f8f2; }\n"
  },
  {
    "path": "docs/src/assets/themes/documenter-dark.css.css",
    "content": "@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .delete,html.theme--documenter-dark .modal-close,.is-unselectable,html.theme--documenter-dark .button,html.theme--documenter-dark .file,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .tabs{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after,html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after{border:3px solid transparent;border-radius:2px;border-right:0;border-top:0;content:\" \";display:block;height:0.625em;margin-top:-0.4375em;pointer-events:none;position:absolute;top:50%;transform:rotate(-45deg);transform-origin:center;width:0.625em}html.theme--documenter-dark .box:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .title:not(:last-child),html.theme--documenter-dark .subtitle:not(:last-child),html.theme--documenter-dark .block:not(:last-child),html.theme--documenter-dark .highlight:not(:last-child),html.theme--documenter-dark .breadcrumb:not(:last-child),html.theme--documenter-dark .level:not(:last-child),html.theme--documenter-dark .list:not(:last-child),html.theme--documenter-dark .message:not(:last-child),html.theme--documenter-dark .tabs:not(:last-child),html.theme--documenter-dark .admonition:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .delete,html.theme--documenter-dark .modal-close{-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:290486px;cursor:pointer;pointer-events:auto;display:inline-block;flex-grow:0;flex-shrink:0;font-size:0;height:20px;max-height:20px;max-width:20px;min-height:20px;min-width:20px;outline:none;position:relative;vertical-align:top;width:20px}html.theme--documenter-dark .delete::before,html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::after,html.theme--documenter-dark .modal-close::after{background-color:white;content:\"\";display:block;left:50%;position:absolute;top:50%;transform:translateX(-50%) translateY(-50%) rotate(45deg);transform-origin:center center}html.theme--documenter-dark .delete::before,html.theme--documenter-dark .modal-close::before{height:2px;width:50%}html.theme--documenter-dark .delete::after,html.theme--documenter-dark .modal-close::after{height:50%;width:2px}html.theme--documenter-dark .delete:hover,html.theme--documenter-dark .modal-close:hover,html.theme--documenter-dark .delete:focus,html.theme--documenter-dark .modal-close:focus{background-color:rgba(10,10,10,0.3)}html.theme--documenter-dark .delete:active,html.theme--documenter-dark .modal-close:active{background-color:rgba(10,10,10,0.4)}html.theme--documenter-dark .is-small.delete,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.delete,html.theme--documenter-dark .is-small.modal-close,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.modal-close{height:16px;max-height:16px;max-width:16px;min-height:16px;min-width:16px;width:16px}html.theme--documenter-dark .is-medium.delete,html.theme--documenter-dark .is-medium.modal-close{height:24px;max-height:24px;max-width:24px;min-height:24px;min-width:24px;width:24px}html.theme--documenter-dark .is-large.delete,html.theme--documenter-dark .is-large.modal-close{height:32px;max-height:32px;max-width:32px;min-height:32px;min-width:32px;width:32px}html.theme--documenter-dark .button.is-loading::after,html.theme--documenter-dark .loader,html.theme--documenter-dark .select.is-loading::after,html.theme--documenter-dark .control.is-loading::after{animation:spinAround 500ms infinite linear;border:2px solid #dbdbdb;border-radius:290486px;border-right-color:transparent;border-top-color:transparent;content:\"\";display:block;height:1em;position:relative;width:1em}.is-overlay,html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--documenter-dark .image.is-16by9 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--documenter-dark .image.is-2by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--documenter-dark .image.is-2by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--documenter-dark .image.is-3by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--documenter-dark .image.is-3by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--documenter-dark .image.is-4by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--documenter-dark .image.is-4by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--documenter-dark .image.is-3by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--documenter-dark .image.is-3by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--documenter-dark .image.is-2by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--documenter-dark .image.is-2by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--documenter-dark .image.is-3by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--documenter-dark .image.is-3by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--documenter-dark .image.is-9by16 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--documenter-dark .image.is-9by16 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--documenter-dark .image.is-1by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--documenter-dark .image.is-1by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--documenter-dark .image.is-1by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--documenter-dark .image.is-1by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio,html.theme--documenter-dark .modal,html.theme--documenter-dark .modal-background,html.theme--documenter-dark .hero-video{bottom:0;left:0;position:absolute;right:0;top:0}html.theme--documenter-dark .button,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .textarea,html.theme--documenter-dark .select select,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:4px;box-shadow:none;display:inline-flex;font-size:1rem;height:2.25em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.375em - 1px);padding-left:calc(0.625em - 1px);padding-right:calc(0.625em - 1px);padding-top:calc(0.375em - 1px);position:relative;vertical-align:top}html.theme--documenter-dark .button:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus,html.theme--documenter-dark .pagination-ellipsis:focus,html.theme--documenter-dark .is-focused.button,html.theme--documenter-dark .is-focused.input,html.theme--documenter-dark 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th:not([align]){text-align:left}html.theme--documenter-dark table th{color:#97b3e2}html.theme--documenter-dark .box{background-color:white;border-radius:6px;box-shadow:0 2px 3px rgba(10,10,10,0.1),0 0 0 1px rgba(10,10,10,0.1);color:#ececec;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 2px 3px rgba(10,10,10,0.1),0 0 0 1px #e37733}html.theme--documenter-dark a.box:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2),0 0 0 1px #e37733}html.theme--documenter-dark .button{background-color:white;border-color:#dbdbdb;border-width:1px;color:#363636;cursor:pointer;justify-content:center;padding-bottom:calc(0.375em - 1px);padding-left:0.75em;padding-right:0.75em;padding-top:calc(0.375em - 1px);text-align:center;white-space:nowrap}html.theme--documenter-dark .button strong{color:inherit}html.theme--documenter-dark .button .icon,html.theme--documenter-dark .button .icon.is-small,html.theme--documenter-dark .button 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html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:white;box-shadow:none;color:white}html.theme--documenter-dark .button.is-light{background-color:whitesmoke;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:hover,html.theme--documenter-dark .button.is-light.is-hovered{background-color:#eeeeee;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:focus,html.theme--documenter-dark .button.is-light.is-focused{border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light:focus:not(:active),html.theme--documenter-dark .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--documenter-dark .button.is-light:active,html.theme--documenter-dark .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:#363636}html.theme--documenter-dark .button.is-light[disabled],fieldset[disabled] 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kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363636 #363636 !important}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent whitesmoke whitesmoke !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content 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!important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:whitesmoke;box-shadow:none;color:whitesmoke}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#4eb5de;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#43b1dc;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-primary.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #4eb5de #4eb5de !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-primary.is-outlined[disabled],html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,fieldset[disabled] html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink{background-color:transparent;border-color:#4eb5de;box-shadow:none;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-focused.docs-sourcelink{background-color:#fff;color:#4eb5de}html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after,html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--documenter-dark 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.button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e37733}html.theme--documenter-dark .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#e37733;color:#e37733}html.theme--documenter-dark .button.is-link.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-outlined.is-focused{background-color:#e37733;border-color:#e37733;color:#fff}html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #e37733 #e37733 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.button.is-warning{background-color:#ffdd57;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:hover,html.theme--documenter-dark .button.is-warning.is-hovered{background-color:#ffdb4a;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus,html.theme--documenter-dark .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning:focus:not(:active),html.theme--documenter-dark .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,221,87,0.25)}html.theme--documenter-dark .button.is-warning:active,html.theme--documenter-dark .button.is-warning.is-active{background-color:#ffd83d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ffdd57;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#ffdd57}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ffdd57}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ffdd57;color:#ffdd57}html.theme--documenter-dark .button.is-warning.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-outlined.is-focused{background-color:#ffdd57;border-color:#ffdd57;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #ffdd57 #ffdd57 !important}html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ffdd57 #ffdd57 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-danger{background-color:#da0b00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#cd0a00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(218,11,0,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#c10a00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#da0b00;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#da0b00;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#da0b00;border-color:#da0b00;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #da0b00 #da0b00 !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#da0b00;box-shadow:none;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#da0b00}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #da0b00 #da0b00 !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:2px;font-size:0.75rem}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:white;border-color:#dbdbdb;box-shadow:none;opacity:0.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:whitesmoke;border-color:#dbdbdb;color:#7a7a7a;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:2px;font-size:0.75rem}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#97b3e2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:whitesmoke;border-left:5px solid #dbdbdb;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0.7rem 0.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #dbdbdb;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#97b3e2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#97b3e2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#97b3e2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:0.75rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--documenter-dark .image.is-16by9 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--documenter-dark .image.is-2by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--documenter-dark .image.is-2by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--documenter-dark .image.is-3by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--documenter-dark .image.is-3by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--documenter-dark .image.is-4by5 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--documenter-dark .image.is-4by5 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--documenter-dark .image.is-3by4 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th.is-light{background-color:whitesmoke;border-color:whitesmoke;color:#363636}html.theme--documenter-dark .table td.is-dark,html.theme--documenter-dark .table th.is-dark{background-color:#363636;border-color:#363636;color:whitesmoke}html.theme--documenter-dark .table td.is-primary,html.theme--documenter-dark .table th.is-primary{background-color:#4eb5de;border-color:#4eb5de;color:#fff}html.theme--documenter-dark .table td.is-link,html.theme--documenter-dark .table th.is-link{background-color:#e37733;border-color:#e37733;color:#fff}html.theme--documenter-dark .table td.is-info,html.theme--documenter-dark .table th.is-info{background-color:#209cee;border-color:#209cee;color:#fff}html.theme--documenter-dark .table td.is-success,html.theme--documenter-dark .table th.is-success{background-color:#22c35b;border-color:#22c35b;color:#fff}html.theme--documenter-dark .table td.is-warning,html.theme--documenter-dark .table 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a,html.theme--documenter-dark .table tr.is-selected strong{color:currentColor}html.theme--documenter-dark .table tr.is-selected td,html.theme--documenter-dark .table tr.is-selected th{border-color:#fff;color:currentColor}html.theme--documenter-dark .table thead{background-color:transparent}html.theme--documenter-dark .table thead td,html.theme--documenter-dark .table thead th{border-width:0 0 2px;color:#97b3e2}html.theme--documenter-dark .table tfoot{background-color:transparent}html.theme--documenter-dark .table tfoot td,html.theme--documenter-dark .table tfoot th{border-width:2px 0 0;color:#97b3e2}html.theme--documenter-dark .table tbody{background-color:transparent}html.theme--documenter-dark .table tbody tr:last-child td,html.theme--documenter-dark .table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .table.is-bordered td,html.theme--documenter-dark .table.is-bordered th{border-width:1px}html.theme--documenter-dark .table.is-bordered tr:last-child 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.columns.is-variable.is-0-tablet-only{--columnGap: 0rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-0-touch{--columnGap: 0rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-0-desktop{--columnGap: 0rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-0-desktop-only{--columnGap: 0rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-0-widescreen{--columnGap: 0rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only{--columnGap: 0rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-0-fullhd{--columnGap: 0rem}}html.theme--documenter-dark .columns.is-variable.is-1{--columnGap: 0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-1-mobile{--columnGap: 0.25rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-1-tablet{--columnGap: 0.25rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-1-tablet-only{--columnGap: 0.25rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-1-touch{--columnGap: 0.25rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-1-desktop{--columnGap: 0.25rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-1-desktop-only{--columnGap: 0.25rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-1-widescreen{--columnGap: 0.25rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only{--columnGap: 0.25rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-1-fullhd{--columnGap: 0.25rem}}html.theme--documenter-dark .columns.is-variable.is-2{--columnGap: 0.5rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-2-mobile{--columnGap: 0.5rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-2-tablet{--columnGap: 0.5rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-2-tablet-only{--columnGap: 0.5rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-2-touch{--columnGap: 0.5rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-2-desktop{--columnGap: 0.5rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-2-desktop-only{--columnGap: 0.5rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-2-widescreen{--columnGap: 0.5rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only{--columnGap: 0.5rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-2-fullhd{--columnGap: 0.5rem}}html.theme--documenter-dark .columns.is-variable.is-3{--columnGap: 0.75rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-3-mobile{--columnGap: 0.75rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-3-tablet{--columnGap: 0.75rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-3-tablet-only{--columnGap: 0.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-3-touch{--columnGap: 0.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-3-desktop{--columnGap: 0.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-3-desktop-only{--columnGap: 0.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-3-widescreen{--columnGap: 0.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only{--columnGap: 0.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-3-fullhd{--columnGap: 0.75rem}}html.theme--documenter-dark .columns.is-variable.is-4{--columnGap: 1rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-4-mobile{--columnGap: 1rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-4-tablet{--columnGap: 1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-4-tablet-only{--columnGap: 1rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-4-touch{--columnGap: 1rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-4-desktop{--columnGap: 1rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-4-desktop-only{--columnGap: 1rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-4-widescreen{--columnGap: 1rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only{--columnGap: 1rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-4-fullhd{--columnGap: 1rem}}html.theme--documenter-dark .columns.is-variable.is-5{--columnGap: 1.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-5-mobile{--columnGap: 1.25rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-5-tablet{--columnGap: 1.25rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-5-tablet-only{--columnGap: 1.25rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-5-touch{--columnGap: 1.25rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-5-desktop{--columnGap: 1.25rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-5-desktop-only{--columnGap: 1.25rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-5-widescreen{--columnGap: 1.25rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only{--columnGap: 1.25rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-5-fullhd{--columnGap: 1.25rem}}html.theme--documenter-dark .columns.is-variable.is-6{--columnGap: 1.5rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-6-mobile{--columnGap: 1.5rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-6-tablet{--columnGap: 1.5rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-6-tablet-only{--columnGap: 1.5rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-6-touch{--columnGap: 1.5rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-6-desktop{--columnGap: 1.5rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-6-desktop-only{--columnGap: 1.5rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-6-widescreen{--columnGap: 1.5rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only{--columnGap: 1.5rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-6-fullhd{--columnGap: 1.5rem}}html.theme--documenter-dark .columns.is-variable.is-7{--columnGap: 1.75rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-7-mobile{--columnGap: 1.75rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-7-tablet{--columnGap: 1.75rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-tablet-only{--columnGap: 1.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-touch{--columnGap: 1.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-7-desktop{--columnGap: 1.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-7-desktop-only{--columnGap: 1.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen{--columnGap: 1.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only{--columnGap: 1.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-7-fullhd{--columnGap: 1.75rem}}html.theme--documenter-dark .columns.is-variable.is-8{--columnGap: 2rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-8-mobile{--columnGap: 2rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-8-tablet{--columnGap: 2rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-tablet-only{--columnGap: 2rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-touch{--columnGap: 2rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-8-desktop{--columnGap: 2rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-8-desktop-only{--columnGap: 2rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-8-widescreen{--columnGap: 2rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only{--columnGap: 2rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-8-fullhd{--columnGap: 2rem}}html.theme--documenter-dark .tile{align-items:stretch;display:block;flex-basis:0;flex-grow:1;flex-shrink:1;min-height:min-content}html.theme--documenter-dark .tile.is-ancestor{margin-left:-0.75rem;margin-right:-0.75rem;margin-top:-0.75rem}html.theme--documenter-dark .tile.is-ancestor:last-child{margin-bottom:-0.75rem}html.theme--documenter-dark .tile.is-ancestor:not(:last-child){margin-bottom:0.75rem}html.theme--documenter-dark .tile.is-child{margin:0 !important}html.theme--documenter-dark .tile.is-parent{padding:0.75rem}html.theme--documenter-dark .tile.is-vertical{flex-direction:column}html.theme--documenter-dark .tile.is-vertical>.tile.is-child:not(:last-child){margin-bottom:1.5rem !important}@media screen and (min-width: 769px),print{html.theme--documenter-dark .tile:not(.is-child){display:flex}html.theme--documenter-dark .tile.is-1{flex:none;width:8.33333%}html.theme--documenter-dark .tile.is-2{flex:none;width:16.66667%}html.theme--documenter-dark .tile.is-3{flex:none;width:25%}html.theme--documenter-dark .tile.is-4{flex:none;width:33.33333%}html.theme--documenter-dark .tile.is-5{flex:none;width:41.66667%}html.theme--documenter-dark .tile.is-6{flex:none;width:50%}html.theme--documenter-dark .tile.is-7{flex:none;width:58.33333%}html.theme--documenter-dark .tile.is-8{flex:none;width:66.66667%}html.theme--documenter-dark .tile.is-9{flex:none;width:75%}html.theme--documenter-dark .tile.is-10{flex:none;width:83.33333%}html.theme--documenter-dark .tile.is-11{flex:none;width:91.66667%}html.theme--documenter-dark .tile.is-12{flex:none;width:100%}}html.theme--documenter-dark .hero{align-items:stretch;display:flex;flex-direction:column;justify-content:space-between}html.theme--documenter-dark .hero .navbar{background:none}html.theme--documenter-dark .hero .tabs ul{border-bottom:none}html.theme--documenter-dark .hero.is-white{background-color:white;color:#0a0a0a}html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),html.theme--documenter-dark .hero.is-white strong{color:inherit}html.theme--documenter-dark .hero.is-white .title{color:#0a0a0a}html.theme--documenter-dark .hero.is-white .subtitle{color:rgba(10,10,10,0.9)}html.theme--documenter-dark .hero.is-white .subtitle a:not(.button),html.theme--documenter-dark .hero.is-white .subtitle strong{color:#0a0a0a}@media screen and (max-width: 1055px){html.theme--documenter-dark .hero.is-white .navbar-menu{background-color:white}}html.theme--documenter-dark .hero.is-white .navbar-item,html.theme--documenter-dark .hero.is-white .navbar-link{color:rgba(10,10,10,0.7)}html.theme--documenter-dark .hero.is-white a.navbar-item:hover,html.theme--documenter-dark .hero.is-white a.navbar-item.is-active,html.theme--documenter-dark .hero.is-white .navbar-link:hover,html.theme--documenter-dark .hero.is-white 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.hero.is-white.is-bold{background-image:linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%)}@media screen and (max-width: 768px){html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu{background-image:linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%)}}html.theme--documenter-dark .hero.is-black{background-color:#0a0a0a;color:white}html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),html.theme--documenter-dark .hero.is-black strong{color:inherit}html.theme--documenter-dark .hero.is-black .title{color:white}html.theme--documenter-dark .hero.is-black .subtitle{color:rgba(255,255,255,0.9)}html.theme--documenter-dark .hero.is-black .subtitle a:not(.button),html.theme--documenter-dark .hero.is-black .subtitle strong{color:white}@media screen and (max-width: 1055px){html.theme--documenter-dark .hero.is-black .navbar-menu{background-color:#0a0a0a}}html.theme--documenter-dark .hero.is-black .navbar-item,html.theme--documenter-dark .hero.is-black .navbar-link{color:rgba(255,255,255,0.7)}html.theme--documenter-dark .hero.is-black a.navbar-item:hover,html.theme--documenter-dark .hero.is-black a.navbar-item.is-active,html.theme--documenter-dark .hero.is-black .navbar-link:hover,html.theme--documenter-dark .hero.is-black .navbar-link.is-active{background-color:black;color:white}html.theme--documenter-dark .hero.is-black .tabs a{color:white;opacity:0.9}html.theme--documenter-dark .hero.is-black .tabs a:hover{opacity:1}html.theme--documenter-dark .hero.is-black .tabs li.is-active a{opacity:1}html.theme--documenter-dark .hero.is-black .tabs.is-boxed a,html.theme--documenter-dark .hero.is-black .tabs.is-toggle a{color:white}html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover,html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover{background-color:rgba(10,10,10,0.1)}html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active 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    "content": "// This template file overrides some of the Documenter theme variables to customize the theme:\n$themename: \"documenter-light\"; // CSS file must be called `$(themename).css`\n\n$boldcolor: $maincolor; // darken-color($maincolor, 1);\n\n$body-background-color: $mainwhite; // main page background\n\n// Sidebar\n$documenter-sidebar-background: $maincolor; //background color for sidebar\n$documenter-sidebar-color: $mainwhite; //font color all sidebar\n$documenter-sidebar-menu-hover-color: $documenter-sidebar-color; // text color\n$documenter-sidebar-menu-hover-background: darken-color($documenter-sidebar-background, 1.5);\n\n$documenter-sidebar-menu-active-background: $mainwhite;\n$documenter-sidebar-menu-active-color: $mainblack;\n$documenter-sidebar-menu-active-hover-background: lighten-color($documenter-sidebar-background, 5.2);\n$documenter-sidebar-menu-active-hover-color: $documenter-sidebar-menu-active-color;\n\n// this is the color the links get, and also when they are hovered\n$link: $secondcolor;\n$link-hover: darken-color($link, 1);\n\n// Main text color:\n$text: $mainblack;\n// Bold text color, also affects headers\n$text-strong: $boldcolor;\n\n// Section headers (markdown ###) text color:\n// TODO\n\n// Code text color:\n$code: #000000;\n//$code-background: rgba(0.5,0,0, 0.05);\n$codebg: lighten-color($maincolor, 7);\n// $codebg: lighten-color($secondcolor, 8);\n$code-background: $codebg; // for inline code\n$pre-background: $codebg;  // for code blocks\n$documenter-docstring-header-background: darken-color($body-background-color, 0.4);\n\n// main text font size\n$body-font-size: 1.0em; // the default is 1.0\n// Sidebar text font size\n$documenter-sidebar-size: 1.0em; // the default is 1.0 as well\n\n// these two change what happens with input boxes (the search box):\n$input-hover-border-color: $secondcolor;\n$input-focus-border-color: $mainwhite;\n\n// Include the original theme which will now use the updated variables.\n// This should be the last thing in the SCSS file.\n@import \"documenter-light\";\n\n#documenter .docs-sidebar { // This makes sidebar have shadow at all displays\n  border-right: none;\n  box-shadow: 1.2*$shadow-size 0rem 1*$shadow-blur $shadow-color;\n\n  form.docs-search > input { // these controls are for the searchbar\n    color: $mainwhite;\n    background-color: darken-color($documenter-sidebar-background, 1);\n    border-color: darken-color($documenter-sidebar-background, 2);\n    margin-top: 1.0rem;\n    margin-bottom: 1.0rem; // adjust the margings between search and other elements\n    &::placeholder {\n      color: $mainwhite; // placeholder text color (\"Search here...\")\n    }\n  }\n}\n"
  },
  {
    "path": "docs/src/assets/themes/style.scss",
    "content": "@charset \"UTF-8\";\r\n// The customizable varibles can be found here:\r\n// https://github.com/JuliaDocs/Documenter.jl/tree/master/assets/html/scss\r\n// under documenter/_variables or documenter/_overrides. But some stuff are Bulma defaults\r\n// as well, so you may need to look them up too: https://bulma.io/documentation/customize/variables/\r\n\r\n\r\n////////////////////////////////////////////////////////////////////////\r\n////////////////////////////////////////////////////////////////////////\r\n$maincolor: #2a5398;   // main color of the org theme\r\n$secondcolor: #ac5118; // secondary color that serves as accents\r\n                       // it is used as-is for links in light theme\r\n$mainwhite: #f0f0f0;      // color representing white\r\n$mainblack: #202020;   // color representing black\r\n$darkbg: #1b1f28;      // dark theme main page background\r\n\r\n// These commands set up the fonts for the main text and code blocks.\r\n// the fonds must be included into the assets of the `makdocs` command, with e.g.\r\n// format = Documenter.HTML(\r\n//     prettyurls = CI,\r\n//     assets = [\r\n//         \"assets/logo.ico\",\r\n//         asset(\"https://fonts.googleapis.com/css?family=Montserrat|Source+Code+Pro&display=swap\", class=:css),\r\n//         ],\r\n//     ),\r\n$family-sans-serif: 'Montserrat', sans-serif;\r\n$family-monospace: 'Source Code Pro', monospace;\r\n////////////////////////////////////////////////////////////////////////\r\n////////////////////////////////////////////////////////////////////////\r\n\r\n// variables controlling the siderbar's shadow\r\n$shadow-color: #bbb !default;\r\n$shadow-size: 0.2rem !default;\r\n$shadow-blur: 0.4rem !default;\r\n\r\n// Two cool helper functions:\r\n$lightness-unit: 8% !default;\r\n// Uses adjust-color to create a darker version of $color\r\n@function darken-color($color, $factor) {\r\n  @return adjust-color($color, $lightness: -$factor*$lightness-unit);\r\n}\r\n// Uses adjust-color to create a lighter version of $color\r\n@function lighten-color($color, $factor) {\r\n  @return adjust-color($color, $lightness: $factor*$lightness-unit);\r\n}\r\n"
  },
  {
    "path": "docs/src/choosingsolver.md",
    "content": "# Choosing Sub-Solvers\n\n```@meta\nCurrentModule = Alpine\n```\n\nAlpine's global optimization algorithm requires a few types of optimization problems to be solved efficiently. For its best performance, it is recommended that a dedicated solver is used for these purposes. The design of Alpine takes advantage of [MathOptInterface](https://github.com/jump-dev/MathOptInterface.jl) to seemlessly interface with a majority of optimization software. Currently, the following sub-solvers with Julia Interface are supported by Alpine:\n\n| Solver                                                                         | Julia Package                                                |\n|--------------------------------------------------------------------------------|--------------------------------------------------------------|\n| [CPLEX](http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/) | [CPLEX.jl](https://github.com/JuliaOpt/CPLEX.jl)             |\n| [Cbc](https://projects.coin-or.org/Cbc)                                        | [Cbc.jl](https://github.com/JuliaOpt/Clp.jl)                 |\n| [Gurobi](http://gurobi.com/)                                                   | [Gurobi.jl](https://github.com/JuliaOpt/Gurobi.jl)           |\n| [Ipopt](https://projects.coin-or.org/Ipopt)                                    | [Ipopt.jl](https://github.com/JuliaOpt/Ipopt.jl)             |\n| [Bonmin](https://projects.coin-or.org/Bonmin)                                  | [Bonmin.jl](https://github.com/JackDunnNZ/AmplNLWriter.jl)   |\n| [Artelys KNITRO](http://artelys.com/en/optimization-tools/knitro)              | [KNITRO.jl](https://github.com/JuliaOpt/KNITRO.jl)           |\n\nAs the development of Alpine continues, supports for solvers such as [Mosek](http://www.mosek.com/), [GLPK](http://www.gnu.org/software/glpk/), [NLopt](http://ab-initio.mit.edu/wiki/index.php/NLopt) and [Xpress](http://www.fico.com/en/products/fico-xpress-optimization-suite) are in the development roadmap.\n\n!!! tip\n    Performance of Alpine is significantly faster and robust while using [Gurobi](https://www.gurobi.com) as the underlying convex mixed-integer programming (MIP) solver. Note that Gurobi's individual-usage license is available [free](https://www.gurobi.com/academia/academic-program-and-licenses/) for academic purposes. \n\nTo solve any continuous nonlinear program to global optimality, here is an example to utilize different sub-solvers with default options set for Alpine:\n\n```julia\nusing Alpine\nusing JuMP \nusing Gurobi \nusing Ipopt\n\n# MIP optimizer\nconst gurobi = optimizer_with_attributes(Gurobi.Optimizer, \n                                         MOI.Silent() => true,\n                                         \"Presolve\"   => 1) \n\n# NLP optimizer\nconst ipopt = optimizer_with_attributes(Ipopt.Optimizer, \n                                        MOI.Silent() => true, \n                                        \"sb\" => \"yes\", \n                                        \"max_iter\"   => 9999)\n\n# Global optimizer\nconst alpine = optimizer_with_attributes(Alpine.Optimizer, \n                                         \"nlp_solver\" => ipopt,\n                                         \"mip_solver\" => gurobi)\nm = Model(alpine)\n```\nSimilarly, many such optimizer options and nonconvex problems (both NLPs and MINLPs) can be found in the [examples](https://github.com/lanl-ansi/Alpine.jl/tree/master/examples) folder. "
  },
  {
    "path": "docs/src/functions.md",
    "content": "# Functions\n\n```@meta\nCurrentModule = Alpine\n```\n\n## High-level Algorithmic Functions\nThese are the high-level algorithmic functions:\n```@docs\npresolve\nglobal_solve\nlocal_solve\nbounding_solve\n```\n\n## Adapative Partitioning Methods\n```@docs\ncreate_bounding_mip\npick_disc_vars\nfix_domains\nmin_vertex_cover\n```\n\n## Presolve Methods\n```@docs\nbound_tightening_wrapper\noptimization_based_bound_tightening\ncreate_obbt_model\nsolve_obbt_model\nresolve_var_bounds\npost_objective_bound\n```\n\n## Utility Methods\n```@docs\nupdate_var_bounds\ndiscretization_to_bounds\ninit_disc\n_get_discretization_dict\nflatten_discretization\nadd_adaptive_partition\n```\n"
  },
  {
    "path": "docs/src/index.md",
    "content": "# Alpine's Documentation\n\n```@meta\nCurrentModule = Alpine\n```\n## Overview\n**[Alpine](https://github.com/lanl-ansi/Alpine.jl)** is a Julia/JuMP-based global optimization solver for non-convex programs. Alpine applies a two-stage approach to strengthen piecewise convex relaxations for mixed-integer nonlinear programs (MINLP) with multi-linear terms. In the first stage, Alpine exploits Constraint Programing techniques to contract the variable bounds. Further, it applies optimality-based bound tightening (OBBT) methods iteratively until a fixed point with respect to the bounds are achieved. In the second stage, Alpine partitions the variable domains using an adaptive multivariate partitioning scheme (a parametrized partition at the current solution of sequentially solved MILPs), leading to sparser but tighter relaxations. This approach decouples the number of partitions from the size of the variable domains, leading to a significant reduction in computation time, and limits the number of binary variables that are introduced by the partitioning. Alpine also applies polyhedral cutting plane methods to handle convex relaxations of higher-order monomial terms.\n\n**Allowable nonlinearities**: Alpine can currently handle MINLPs with polynomials in constraints and/or in the objective. Currently, there is no support for exponential cones and Positive Semi-Definite (PSD) cones in MINLPs. Alpine is also a good fit for subsets of the MINLP family, e.g., Mixed-Integer Quadratically Constrainted Quadradic Programs (MIQCQPs), Non-Linear Programs (NLPs), etc.\n\nFor more details, check out this [video](https://www.youtube.com/watch?v=mwkhiEIS5JA) on Alpine at the [2nd Annual JuMP-dev Workshop](http://www.juliaopt.org/meetings/bordeaux2018/), held at the Institut de Mathématiques de Bordeaux, June 2018.\n\n## Installation\nTo use Alpine, first [download and install](https://julialang.org/downloads/) Julia. Note that the current version of Alpine is compatible with Julia 1.0 and later. \n\nThe latest stable release of Alpine can be installed using the Julia package manager with\n\n```julia\nimport Pkg\nPkg.add(\"Alpine\")\n```\n\nAt least one local nonlinear-programming (NLP) solver and a convex mixed-integer programming (MIP) solver are required for running Alpine. If your problem is an NLP, we recommend [Ipopt](https://github.com/jump-dev/Ipopt.jl), and else if your problem is a mixed-integer NLP (MINLP), we recommend [Juniper](https://github.com/lanl-ansi/Juniper.jl). For the underlying MIP solver, [Gurobi](https://github.com/jump-dev/Gurobi.jl) is highly recommended, as it is fast, scaleable and can be used to solve on fairly large-scale non-convex programs. However, the open-source [HiGHS](https://github.com/jump-dev/HiGHS.jl) or [GLPK](https://github.com/jump-dev/GLPK.jl) solver is also compatible with Alpine. For example, Ipopt and Gurobi can be installed via the package manager with\n\n```julia\nimport Pkg\nPkg.add(\"Ipopt\")\nPkg.add(\"Gurobi\")\n```\nFor more details on choosing sub-solvers for Alpine, check out [here](https://lanl-ansi.github.io/Alpine.jl/latest/choosingsolver/). \n\n## Unit Tests\nTo run the tests in the package, run the following command after installing the Alpine package.\n\n```julia\nimport Pkg\nPkg.test(\"Alpine\")\n```\n\n## Citing Alpine\nIf you find Alpine useful in your work, we request you to cite the following paper [\\[pdf\\]](https://harshangrjn.github.io/pdf/JOGO_2018.pdf) [\\[pdf\\]](http://harshangrjn.github.io/pdf/CP_2016.pdf): \n```bibtex\n@article{alpine_JOGO2019,\n  title = {An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs},\n  author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell and Sundar, Kaarthik},\n  journal = {Journal of Global Optimization},\n  year = {2019},\n  issn = {1573-2916},\n  doi = {10.1007/s10898-018-00734-1},\n}\n\n@inproceedings{alpine_CP2016,\n  title = {Tightening {McCormick} relaxations for nonlinear programs via dynamic multivariate partitioning},\n  author = {Nagarajan, Harsha and Lu, Mowen and Yamangil, Emre and Bent, Russell},\n  booktitle = {International Conference on Principles and Practice of Constraint Programming},\n  pages = {369--387},\n  year = {2016},\n  organization = {Springer},\n  doi = {10.1007/978-3-319-44953-1_24},\n}\n```\nIf you find the underlying piecewise polyhedral formulations implemented in Alpine useful in your work, we kindly request that you cite the following papers ([link-1](https://doi.org/10.1016/j.orl.2020.12.002), [link-2](http://www.optimization-online.org/DB_HTML/2022/07/8974.html)): \n```bibtex\n@article{alpine_ORL2021,\n  title = {Piecewise polyhedral formulations for a multilinear term},\n  author = {Sundar, Kaarthik and Nagarajan, Harsha and Linderoth, Jeff and Wang, Site and Bent, Russell},\n  journal = {Operations Research Letters},\n  volume = {49},\n  number = {1},\n  pages = {144--149},\n  year = {2021},\n  publisher = {Elsevier}\n}\n\n@article{alpine_OptOnline2022,\n  title={Piecewise Polyhedral Relaxations of Multilinear Optimization},\n  author={Kim, Jongeun and Richard, Jean-Philippe P. and Tawarmalani, Mohit},\n  eprinttype={Optimization Online},\n  date={2022}\n}\n```\n\nIf you find the random families of non-convex QCQP instances (using generator files within this [folder](https://github.com/lanl-ansi/Alpine.jl/tree/master/examples/random_QCQPs)) useful for your research, we kindly request that you cite the following paper [arXiv link](https://arxiv.org/abs/2301.00306):\n```bibtex\n@article{alpine_learning_2022,\n  title={Learning to Accelerate the Global Optimization of Quadratically-Constrained Quadratic Programs},\n  author={Kannan, Rohit and Nagarajan, Harsha and Deka, Deepjyoti},\n  journal={arXiv preprint:2301.00306},\n  url={https://arxiv.org/abs/2301.00306},\n  year={2022}\n}\n```"
  },
  {
    "path": "docs/src/parameters.md",
    "content": "# Solver options for Alpine\n\n```@meta\nCurrentModule = Alpine\n```\n\n## General Options\n\nHere are a few general solver options which control the performance of Alpine:\n\n* `log_level (default = 0)`: verbosity level of Alpine; choose `1` for turning on logging, else `100` for detailed debugging mode.\n\n* `time_limit (default = Inf)`: total limit on run time for Alpine in seconds.\n\n* `max_iter (default = 999)`: total number of iterations allowed in the [`global_solve`](@ref).\n\n* `rel_gap (default = 1e-4)`: relative gap considered for global convergence during [`global_solve`](@ref). Bounds are evaluated using ``\\frac{UB-LB}{UB} \\cdot 100 \\%``.\n\n* `tol (default = 1e-6)`: numerical tolerance used during the process of [`global_solve`](@ref).\n\n## Adaptive Partitioning Options\n* `apply_partitioning (default = true)`: applies Alpine's built-in MIP-based partitioning algorithm only when activated; else terminates with the presolve solution.\n\n* `partition_scaling_factor (default = 10)`: used during [`add_adaptive_partition`](@ref) for scaling the width of new partitions relative to the active partition chosen in the sequentially-solved lower-bounding MIP models. This value can substantially affect the run time for global convergence; this value can be set to different integer values (>= 4) for various classes of problems.\n\n* `disc_var_pick (default = 0)`: controls Alpine's algorithm used for selecting variables for partitioning; `0` is for max-cover, `1` is for minimum-vertex-cover. This parameter allows functional inputs.\n\n* `disc_add_partition_method`: allows functional input on how new partitions could be constructed.\n\n## Presolve Options\n\n* `presolve_track_time (default = true)`: includes/excludes presolve run time in the total Alpine's run time.\n\n* `presolve_bt (default = false)`: performs sequential, optimization-based bound tightening (OBBT) at the presolve step.\n\n* `presolve_bt_max_iter (default = 9999)`: maximum number of iterations allowed using the sequential OBBT step.\n\n* `presolve_bt_width_tol (default = 1e-3)`: numerical tolerance value used in the OBBT step. Note that smaller values of this tolerance can lead to inaccurate solutions.\n\n* `presolve_bt_algo (default = 1)`: method chosen to perform the presolve step; choose `1` for the built-in OBBT, else `2` for user-input functions for presolve.\n\n* `presolve_bt_relax_integrality (default = false)`: relaxes the integrality of the existing integer variables in the OBBT step, if the input problem is an MINLP.\n\n* `presolve_bt_mip_time_limit (default = Inf)`: time limit for individual MILPs solved during the sequential OBBT procedure.\n\n* `use_start_as_incumbent (default = false)`: if `true`, Alpine does not perform any local optimization during the presolve and uses the starting value instead (*warning*: Alpine assumes the feasibility of the starting value and does not check it).\n\nNote that the above-mentioned list of solver options is not comprehensive, but can be found in [solver.jl](https://github.com/lanl-ansi/Alpine.jl/blob/master/src/solver.jl).\n"
  },
  {
    "path": "examples/JuMP_models.jl",
    "content": "include(\"MINLPs/nlp.jl\")\ninclude(\"MINLPs/bnlp.jl\")\ninclude(\"MINLPs/blend.jl\")\ninclude(\"MINLPs/brainpc3.jl\")\ninclude(\"MINLPs/castro.jl\")\ninclude(\"MINLPs/circle.jl\")\ninclude(\"MINLPs/convex.jl\")\ninclude(\"MINLPs/discretemulti.jl\")\ninclude(\"MINLPs/div.jl\")\ninclude(\"MINLPs/exprstest.jl\")\ninclude(\"MINLPs/linearlift.jl\")\ninclude(\"MINLPs/multi.jl\")\ninclude(\"MINLPs/mult3.jl\")\ninclude(\"MINLPs/mult4.jl\")\ninclude(\"MINLPs/rosenbrock.jl\")\n"
  },
  {
    "path": "examples/MINLPs/blend.jl",
    "content": "function blend029(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[1:102])\n    for i in 67:102\n        set_binary(x[i])\n    end\n\n    for i in 1:48\n        set_lower_bound(x[i], 0)\n        set_upper_bound(x[i], 1)\n    end\n    for i in 49:66\n        set_lower_bound(x[i], 0)\n        set_upper_bound(x[i], 2)\n    end\n\n    @objective(\n        m,\n        Max,\n        -1.74 * x[1] - 1.74 * x[2] - 1.74 * x[3] - 1.45 * x[4] - 1.45 * x[5] -\n        1.45 * x[6] +\n        7.38 * x[7] +\n        7.38 * x[8] +\n        7.38 * x[9] +\n        5.6 * x[10] +\n        5.6 * x[11] +\n        5.6 * x[12] - 1.7 * x[13] - 1.7 * x[14] - 1.7 * x[15] - 1.18 * x[16] -\n        1.18 * x[17] - 1.18 * x[18] +\n        7.21 * x[19] +\n        7.21 * x[20] +\n        7.21 * x[21] +\n        5.45 * x[22] +\n        5.45 * x[23] +\n        5.45 * x[24] - 0.3 * x[25] - 0.3 * x[26] - 0.3 * x[27] +\n        7.71 * x[28] +\n        7.71 * x[29] +\n        7.71 * x[30] +\n        6.28 * x[31] +\n        6.28 * x[32] +\n        6.28 * x[33] +\n        7.74 * x[34] +\n        7.74 * x[35] +\n        7.74 * x[36] - 0.84 * x[67] - 0.84 * x[68] - 0.84 * x[69] - 0.05 * x[70] -\n        0.05 * x[71] - 0.05 * x[72] - 0.94 * x[73] - 0.94 * x[74] - 0.94 * x[75] -\n        0.81 * x[76] - 0.81 * x[77] - 0.81 * x[78] - 0.79 * x[79] - 0.79 * x[80] -\n        0.79 * x[81] - 0.05 * x[82] - 0.05 * x[83] - 0.05 * x[84] - 0.65 * x[85] -\n        0.65 * x[86] - 0.65 * x[87] - 0.97 * x[88] - 0.97 * x[89] - 0.97 * x[90] -\n        0.57 * x[91] - 0.57 * x[92] - 0.57 * x[93] - 0.26 * x[94] - 0.26 * x[95] -\n        0.26 * x[96] - 0.45 * x[97] - 0.45 * x[98] - 0.45 * x[99] - 0.1 * x[100] -\n        0.1 * x[101] - 0.1 * x[102]\n    )\n\n    @NLconstraint(\n        m,\n        x[37] * x[55] - 0.6 * x[1] - 0.2 * x[13] +\n        0.2 * x[25] +\n        0.2 * x[28] +\n        0.2 * x[31] == 0.04\n    )  #= e8: =#\n    @NLconstraint(\n        m,\n        x[40] * x[58] - 0.6 * x[4] - 0.2 * x[16] - 0.2 * x[25] + 0.7 * x[34] == 0.07\n    )  #= e9: =#\n    @NLconstraint(\n        m,\n        x[43] * x[55] - 0.4 * x[1] - 0.4 * x[13] +\n        0.5 * x[25] +\n        0.5 * x[28] +\n        0.5 * x[31] == 0.1\n    )  #= e10: =#\n    @NLconstraint(\n        m,\n        x[46] * x[58] - 0.4 * x[4] - 0.4 * x[16] - 0.5 * x[25] + 0.6 * x[34] == 0.06\n    )  #= e11: =#\n    @NLconstraint(\n        m,\n        x[38] * x[56] -\n        (x[37] * x[55] - (x[37] * x[26] + x[37] * x[29] + x[37] * x[32])) - 0.6 * x[2] -\n        0.2 * x[14] == 0\n    )  #= e24: =#\n    @NLconstraint(\n        m,\n        x[39] * x[57] -\n        (x[38] * x[56] - (x[38] * x[27] + x[38] * x[30] + x[38] * x[33])) - 0.6 * x[3] -\n        0.2 * x[15] == 0\n    )  #= e25: =#\n    @NLconstraint(\n        m,\n        x[41] * x[59] - (x[40] * x[58] + x[37] * x[26] - x[40] * x[35]) - 0.6 * x[5] -\n        0.2 * x[17] == 0\n    )  #= e26: =#\n    @NLconstraint(\n        m,\n        x[42] * x[60] - (x[41] * x[59] + x[38] * x[27] - x[41] * x[36]) - 0.6 * x[6] -\n        0.2 * x[18] == 0\n    )  #= e27: =#\n    @NLconstraint(\n        m,\n        x[44] * x[56] -\n        (x[43] * x[55] - (x[43] * x[26] + x[43] * x[29] + x[43] * x[32])) - 0.4 * x[2] -\n        0.4 * x[14] == 0\n    )  #= e28: =#\n    @NLconstraint(\n        m,\n        x[45] * x[57] -\n        (x[44] * x[56] - (x[44] * x[27] + x[44] * x[30] + x[44] * x[33])) - 0.4 * x[3] -\n        0.4 * x[15] == 0\n    )  #= e29: =#\n    @NLconstraint(\n        m,\n        x[47] * x[59] - (x[46] * x[58] + x[43] * x[26] - x[46] * x[35]) - 0.4 * x[5] -\n        0.4 * x[17] == 0\n    )  #= e30: =#\n    @NLconstraint(\n        m,\n        x[48] * x[60] - (x[47] * x[59] + x[44] * x[27] - x[47] * x[36]) - 0.4 * x[6] -\n        0.4 * x[18] == 0\n    )  #= e31: =#\n\n    @constraint(m, x[1] + x[4] + x[7] + x[10] + x[49] == 1)  #= e2: =#\n    @constraint(m, x[13] + x[16] + x[19] + x[22] + x[52] == 1.1)  #= e3: =#\n    @constraint(m, -x[1] - x[13] + x[25] + x[28] + x[31] + x[55] == 0.2)  #= e4: =#\n    @constraint(m, -x[4] - x[16] - x[25] + x[34] + x[58] == 0.1)  #= e5: =#\n    @constraint(m, -x[7] - x[19] - x[28] - x[34] + x[61] == 1.55)  #= e6: =#\n    @constraint(m, -x[10] - x[22] - x[31] + x[64] == 0.49)  #= e7: =#\n    @constraint(m, x[2] + x[5] + x[8] + x[11] - x[49] + x[50] == 1)  #= e12: =#\n    @constraint(m, x[3] + x[6] + x[9] + x[12] - x[50] + x[51] == 0)  #= e13: =#\n    @constraint(m, x[14] + x[17] + x[20] + x[23] - x[52] + x[53] == 0.1)  #= e14: =#\n    @constraint(m, x[15] + x[18] + x[21] + x[24] - x[53] + x[54] == 0.9)  #= e15: =#\n    @constraint(m, -x[2] - x[14] + x[26] + x[29] + x[32] - x[55] + x[56] == 0)  #= e16: =#\n    @constraint(m, -x[3] - x[15] + x[27] + x[30] + x[33] - x[56] + x[57] == 0)  #= e17: =#\n    @constraint(m, -x[5] - x[17] - x[26] + x[35] - x[58] + x[59] == 0)  #= e18: =#\n    @constraint(m, -x[6] - x[18] - x[27] + x[36] - x[59] + x[60] == 0)  #= e19: =#\n    @constraint(m, -x[8] - x[20] - x[29] - x[35] - x[61] + x[62] == -0.81)  #= e20: =#\n    @constraint(m, -x[9] - x[21] - x[30] - x[36] - x[62] + x[63] == -0.88)  #= e21: =#\n    @constraint(m, -x[11] - x[23] - x[32] - x[64] + x[65] == -0.14)  #= e22: =#\n    @constraint(m, -x[12] - x[24] - x[33] - x[65] + x[66] == -0.1)  #= e23: =#\n    @constraint(m, x[1] - x[67] <= 0)  #= e32: =#\n    @constraint(m, x[2] - x[68] <= 0)  #= e33: =#\n    @constraint(m, x[3] - x[69] <= 0)  #= e34: =#\n    @constraint(m, x[4] - x[70] <= 0)  #= e35: =#\n    @constraint(m, x[5] - x[71] <= 0)  #= e36: =#\n    @constraint(m, x[6] - x[72] <= 0)  #= e37: =#\n    @constraint(m, x[7] - x[73] <= 0)  #= e38: =#\n    @constraint(m, x[8] - x[74] <= 0)  #= e39: =#\n    @constraint(m, x[9] - x[75] <= 0)  #= e40: =#\n    @constraint(m, x[10] - x[76] <= 0)  #= e41: =#\n    @constraint(m, x[11] - x[77] <= 0)  #= e42: =#\n    @constraint(m, x[12] - x[78] <= 0)  #= e43: =#\n    @constraint(m, x[13] - x[79] <= 0)  #= e44: =#\n    @constraint(m, x[14] - x[80] <= 0)  #= e45: =#\n    @constraint(m, x[15] - x[81] <= 0)  #= e46: =#\n    @constraint(m, x[16] - x[82] <= 0)  #= e47: =#\n    @constraint(m, x[17] - x[83] <= 0)  #= e48: =#\n    @constraint(m, x[18] - x[84] <= 0)  #= e49: =#\n    @constraint(m, x[19] - x[85] <= 0)  #= e50: =#\n    @constraint(m, x[20] - x[86] <= 0)  #= e51: =#\n    @constraint(m, x[21] - x[87] <= 0)  #= e52: =#\n    @constraint(m, x[22] - x[88] <= 0)  #= e53: =#\n    @constraint(m, x[23] - x[89] <= 0)  #= e54: =#\n    @constraint(m, x[24] - x[90] <= 0)  #= e55: =#\n    @constraint(m, x[25] - x[91] <= 0)  #= e56: =#\n    @constraint(m, x[26] - x[92] <= 0)  #= e57: =#\n    @constraint(m, x[27] - x[93] <= 0)  #= e58: =#\n    @constraint(m, x[28] - x[94] <= 0)  #= e59: =#\n    @constraint(m, x[29] - x[95] <= 0)  #= e60: =#\n    @constraint(m, x[30] - x[96] <= 0)  #= e61: =#\n    @constraint(m, x[31] - x[97] <= 0)  #= e62: =#\n    @constraint(m, x[32] - x[98] <= 0)  #= e63: =#\n    @constraint(m, x[33] - x[99] <= 0)  #= e64: =#\n    @constraint(m, x[34] - x[100] <= 0)  #= e65: =#\n    @constraint(m, x[35] - x[101] <= 0)  #= e66: =#\n    @constraint(m, x[36] - x[102] <= 0)  #= e67: =#\n    @constraint(m, x[1] >= 0)  #= e68: =#\n    @constraint(m, x[2] >= 0)  #= e69: =#\n    @constraint(m, x[3] >= 0)  #= e70: =#\n    @constraint(m, x[4] >= 0)  #= e71: =#\n    @constraint(m, x[5] >= 0)  #= e72: =#\n    @constraint(m, x[6] >= 0)  #= e73: =#\n    @constraint(m, x[7] >= 0)  #= e74: =#\n    @constraint(m, x[8] >= 0)  #= e75: =#\n    @constraint(m, x[9] >= 0)  #= e76: =#\n    @constraint(m, x[10] >= 0)  #= e77: =#\n    @constraint(m, x[11] >= 0)  #= e78: =#\n    @constraint(m, x[12] >= 0)  #= e79: =#\n    @constraint(m, x[13] >= 0)  #= e80: =#\n    @constraint(m, x[14] >= 0)  #= e81: =#\n    @constraint(m, x[15] >= 0)  #= e82: =#\n    @constraint(m, x[16] >= 0)  #= e83: =#\n    @constraint(m, x[17] >= 0)  #= e84: =#\n    @constraint(m, x[18] >= 0)  #= e85: =#\n    @constraint(m, x[19] >= 0)  #= e86: =#\n    @constraint(m, x[20] >= 0)  #= e87: =#\n    @constraint(m, x[21] >= 0)  #= e88: =#\n    @constraint(m, x[22] >= 0)  #= e89: =#\n    @constraint(m, x[23] >= 0)  #= e90: =#\n    @constraint(m, x[24] >= 0)  #= e91: =#\n    @constraint(m, x[25] >= 0)  #= e92: =#\n    @constraint(m, x[26] >= 0)  #= e93: =#\n    @constraint(m, x[27] >= 0)  #= e94: =#\n    @constraint(m, x[28] >= 0)  #= e95: =#\n    @constraint(m, x[29] >= 0)  #= e96: =#\n    @constraint(m, x[30] >= 0)  #= e97: =#\n    @constraint(m, x[31] >= 0)  #= e98: =#\n    @constraint(m, x[32] >= 0)  #= e99: =#\n    @constraint(m, x[33] >= 0)  #= e100: =#\n    @constraint(m, x[34] >= 0)  #= e101: =#\n    @constraint(m, x[35] >= 0)  #= e102: =#\n    @constraint(m, x[36] >= 0)  #= e103: =#\n    @constraint(m, x[73] <= 1.5)  #= e104: =#\n    @constraint(m, x[74] <= 1.5)  #= e105: =#\n    @constraint(m, x[75] <= 1.5)  #= e106: =#\n    @constraint(m, x[76] <= 0.6)  #= e107: =#\n    @constraint(m, x[77] <= 0.6)  #= e108: =#\n    @constraint(m, x[78] <= 0.6)  #= e109: =#\n    @constraint(m, x[85] <= 1.1)  #= e110: =#\n    @constraint(m, x[86] <= 1.1)  #= e111: =#\n    @constraint(m, x[87] <= 1.1)  #= e112: =#\n    @constraint(m, x[88] <= 0.2)  #= e113: =#\n    @constraint(m, x[89] <= 0.2)  #= e114: =#\n    @constraint(m, x[90] <= 0.2)  #= e115: =#\n    @constraint(m, x[73] <= 1)  #= e116: =#\n    @constraint(m, x[74] <= 1)  #= e117: =#\n    @constraint(m, x[75] <= 1)  #= e118: =#\n    @constraint(m, x[76] <= 0.8)  #= e119: =#\n    @constraint(m, x[77] <= 0.8)  #= e120: =#\n    @constraint(m, x[78] <= 0.8)  #= e121: =#\n    @constraint(m, x[85] <= 1)  #= e122: =#\n    @constraint(m, x[86] <= 1)  #= e123: =#\n    @constraint(m, x[87] <= 1)  #= e124: =#\n    @constraint(m, x[88] <= 0.8)  #= e125: =#\n    @constraint(m, x[89] <= 0.8)  #= e126: =#\n    @constraint(m, x[90] <= 0.8)  #= e127: =#\n    @constraint(m, -x[73] >= -1.3)  #= e128: =#\n    @constraint(m, -x[74] >= -1.3)  #= e129: =#\n    @constraint(m, -x[75] >= -1.3)  #= e130: =#\n    @constraint(m, -x[76] >= -1.4)  #= e131: =#\n    @constraint(m, -x[77] >= -1.4)  #= e132: =#\n    @constraint(m, -x[78] >= -1.4)  #= e133: =#\n    @constraint(m, -x[85] >= -1.7)  #= e134: =#\n    @constraint(m, -x[86] >= -1.7)  #= e135: =#\n    @constraint(m, -x[87] >= -1.7)  #= e136: =#\n    @constraint(m, -x[88] >= -1.8)  #= e137: =#\n    @constraint(m, -x[89] >= -1.8)  #= e138: =#\n    @constraint(m, -x[90] >= -1.8)  #= e139: =#\n    @constraint(m, -x[73] >= -1)  #= e140: =#\n    @constraint(m, -x[74] >= -1)  #= e141: =#\n    @constraint(m, -x[75] >= -1)  #= e142: =#\n    @constraint(m, -x[76] >= -1.4)  #= e143: =#\n    @constraint(m, -x[77] >= -1.4)  #= e144: =#\n    @constraint(m, -x[78] >= -1.4)  #= e145: =#\n    @constraint(m, -x[85] >= -1)  #= e146: =#\n    @constraint(m, -x[86] >= -1)  #= e147: =#\n    @constraint(m, -x[87] >= -1)  #= e148: =#\n    @constraint(m, -x[88] >= -1.4)  #= e149: =#\n    @constraint(m, -x[89] >= -1.4)  #= e150: =#\n    @constraint(m, -x[90] >= -1.4)  #= e151: =#\n    @constraint(m, -x[37] + x[95] <= 0.9)  #= e152: =#\n    @constraint(m, -x[38] + x[96] <= 0.9)  #= e153: =#\n    @constraint(m, -x[37] + x[98] <= 0)  #= e154: =#\n    @constraint(m, -x[38] + x[99] <= 0)  #= e155: =#\n    @constraint(m, -x[40] + x[101] <= 0.9)  #= e156: =#\n    @constraint(m, -x[41] + x[102] <= 0.9)  #= e157: =#\n    @constraint(m, -x[43] + x[95] <= 0.6)  #= e158: =#\n    @constraint(m, -x[44] + x[96] <= 0.6)  #= e159: =#\n    @constraint(m, -x[43] + x[98] <= 0.4)  #= e160: =#\n    @constraint(m, -x[44] + x[99] <= 0.4)  #= e161: =#\n    @constraint(m, -x[46] + x[101] <= 0.6)  #= e162: =#\n    @constraint(m, -x[47] + x[102] <= 0.6)  #= e163: =#\n    @constraint(m, -x[37] - x[95] >= -1.9)  #= e164: =#\n    @constraint(m, -x[38] - x[96] >= -1.9)  #= e165: =#\n    @constraint(m, -x[37] - x[98] >= -2)  #= e166: =#\n    @constraint(m, -x[38] - x[99] >= -2)  #= e167: =#\n    @constraint(m, -x[40] - x[101] >= -1.9)  #= e168: =#\n    @constraint(m, -x[41] - x[102] >= -1.9)  #= e169: =#\n    @constraint(m, -x[43] - x[95] >= -1.4)  #= e170: =#\n    @constraint(m, -x[44] - x[96] >= -1.4)  #= e171: =#\n    @constraint(m, -x[43] - x[98] >= -1.8)  #= e172: =#\n    @constraint(m, -x[44] - x[99] >= -1.8)  #= e173: =#\n    @constraint(m, -x[46] - x[101] >= -1.4)  #= e174: =#\n    @constraint(m, -x[47] - x[102] >= -1.4)  #= e175: =#\n    @constraint(m, x[94] <= 1.1)  #= e176: =#\n    @constraint(m, x[97] <= 0.2)  #= e177: =#\n    @constraint(m, x[100] <= 1.6)  #= e178: =#\n    @constraint(m, x[94] <= 1.1)  #= e179: =#\n    @constraint(m, x[97] <= 0.9)  #= e180: =#\n    @constraint(m, x[100] <= 1.2)  #= e181: =#\n    @constraint(m, -x[94] >= -1.7)  #= e182: =#\n    @constraint(m, -x[97] >= -1.8)  #= e183: =#\n    @constraint(m, -x[100] >= -1.2)  #= e184: =#\n    @constraint(m, -x[94] >= -0.9)  #= e185: =#\n    @constraint(m, -x[97] >= -1.3)  #= e186: =#\n    @constraint(m, -x[100] >= -0.8)  #= e187: =#\n    @constraint(m, x[67] + x[91] <= 1)  #= e188: =#\n    @constraint(m, x[68] + x[92] <= 1)  #= e189: =#\n    @constraint(m, x[69] + x[93] <= 1)  #= e190: =#\n    @constraint(m, x[67] + x[94] <= 1)  #= e191: =#\n    @constraint(m, x[68] + x[95] <= 1)  #= e192: =#\n    @constraint(m, x[69] + x[96] <= 1)  #= e193: =#\n    @constraint(m, x[67] + x[97] <= 1)  #= e194: =#\n    @constraint(m, x[68] + x[98] <= 1)  #= e195: =#\n    @constraint(m, x[69] + x[99] <= 1)  #= e196: =#\n    @constraint(m, x[79] + x[91] <= 1)  #= e197: =#\n    @constraint(m, x[80] + x[92] <= 1)  #= e198: =#\n    @constraint(m, x[81] + x[93] <= 1)  #= e199: =#\n    @constraint(m, x[79] + x[94] <= 1)  #= e200: =#\n    @constraint(m, x[80] + x[95] <= 1)  #= e201: =#\n    @constraint(m, x[81] + x[96] <= 1)  #= e202: =#\n    @constraint(m, x[79] + x[97] <= 1)  #= e203: =#\n    @constraint(m, x[80] + x[98] <= 1)  #= e204: =#\n    @constraint(m, x[81] + x[99] <= 1)  #= e205: =#\n    @constraint(m, x[70] + x[100] <= 1)  #= e206: =#\n    @constraint(m, x[71] + x[101] <= 1)  #= e207: =#\n    @constraint(m, x[72] + x[102] <= 1)  #= e208: =#\n    @constraint(m, x[82] + x[100] <= 1)  #= e209: =#\n    @constraint(m, x[83] + x[101] <= 1)  #= e210: =#\n    @constraint(m, x[84] + x[102] <= 1)  #= e211: =#\n    @constraint(m, x[91] + x[100] <= 1)  #= e212: =#\n    @constraint(m, x[92] + x[101] <= 1)  #= e213: =#\n    @constraint(m, x[93] + x[102] <= 1)  #= e214: =#\n\n    return m\nend\n\nfunction blend029_gl(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[1:102])\n    for i in 67:102\n        JuMP.set_binary(x[i])\n    end\n\n    for i in 1:48\n        set_lower_bound(x[i], 0)\n        set_upper_bound(x[i], 1)\n    end\n\n    for i in 49:66\n        set_lower_bound(x[i], 0)\n        set_upper_bound(x[i], 2)\n    end\n\n    @objective(\n        m,\n        Max,\n        -1.74 * x[1] - 1.74 * x[2] - 1.74 * x[3] - 1.45 * x[4] - 1.45 * x[5] -\n        1.45 * x[6] +\n        7.38 * x[7] +\n        7.38 * x[8] +\n        7.38 * x[9] +\n        5.6 * x[10] +\n        5.6 * x[11] +\n        5.6 * x[12] - 1.7 * x[13] - 1.7 * x[14] - 1.7 * x[15] - 1.18 * x[16] -\n        1.18 * x[17] - 1.18 * x[18] +\n        7.21 * x[19] +\n        7.21 * x[20] +\n        7.21 * x[21] +\n        5.45 * x[22] +\n        5.45 * x[23] +\n        5.45 * x[24] - 0.3 * x[25] - 0.3 * x[26] - 0.3 * x[27] +\n        7.71 * x[28] +\n        7.71 * x[29] +\n        7.71 * x[30] +\n        6.28 * x[31] +\n        6.28 * x[32] +\n        6.28 * x[33] +\n        7.74 * x[34] +\n        7.74 * x[35] +\n        7.74 * x[36] - 0.84 * x[67] - 0.84 * x[68] - 0.84 * x[69] - 0.05 * x[70] -\n        0.05 * x[71] - 0.05 * x[72] - 0.94 * x[73] - 0.94 * x[74] - 0.94 * x[75] -\n        0.81 * x[76] - 0.81 * x[77] - 0.81 * x[78] - 0.79 * x[79] - 0.79 * x[80] -\n        0.79 * x[81] - 0.05 * x[82] - 0.05 * x[83] - 0.05 * x[84] - 0.65 * x[85] -\n        0.65 * x[86] - 0.65 * x[87] - 0.97 * x[88] - 0.97 * x[89] - 0.97 * x[90] -\n        0.57 * x[91] - 0.57 * x[92] - 0.57 * x[93] - 0.26 * x[94] - 0.26 * x[95] -\n        0.26 * x[96] - 0.45 * x[97] - 0.45 * x[98] - 0.45 * x[99] - 0.1 * x[100] -\n        0.1 * x[101] - 0.1 * x[102]\n    )\n\n    @NLconstraint(\n        m,\n        x[37] * x[55] - 0.6 * x[1] - 0.2 * x[13] +\n        0.2 * x[25] +\n        0.2 * x[28] +\n        0.2 * x[31] >= 0.04\n    )  #= e8: =#\n    @NLconstraint(\n        m,\n        x[40] * x[58] - 0.6 * x[4] - 0.2 * x[16] - 0.2 * x[25] + 0.7 * x[34] >= 0.07\n    )  #= e9: =#\n    @NLconstraint(\n        m,\n        x[43] * x[55] - 0.4 * x[1] - 0.4 * x[13] +\n        0.5 * x[25] +\n        0.5 * x[28] +\n        0.5 * x[31] >= 0.1\n    )  #= e10: =#\n    @NLconstraint(\n        m,\n        x[46] * x[58] - 0.4 * x[4] - 0.4 * x[16] - 0.5 * x[25] + 0.6 * x[34] >= 0.06\n    )  #= e11: =#\n    @NLconstraint(\n        m,\n        x[38] * x[56] -\n        (x[37] * x[55] - (x[37] * x[26] + x[37] * x[29] + x[37] * x[32])) - 0.6 * x[2] -\n        0.2 * x[14] >= 0\n    )  #= e24: =#\n    @NLconstraint(\n        m,\n        x[39] * x[57] -\n        (x[38] * x[56] - (x[38] * x[27] + x[38] * x[30] + x[38] * x[33])) - 0.6 * x[3] -\n        0.2 * x[15] >= 0\n    )  #= e25: =#\n    @NLconstraint(\n        m,\n        x[41] * x[59] - (x[40] * x[58] + x[37] * x[26] - x[40] * x[35]) - 0.6 * x[5] -\n        0.2 * x[17] >= 0\n    )  #= e26: =#\n    @NLconstraint(\n        m,\n        x[42] * x[60] - (x[41] * x[59] + x[38] * x[27] - x[41] * x[36]) - 0.6 * x[6] -\n        0.2 * x[18] >= 0\n    )  #= e27: =#\n    @NLconstraint(\n        m,\n        x[44] * x[56] -\n        (x[43] * x[55] - (x[43] * x[26] + x[43] * x[29] + x[43] * x[32])) - 0.4 * x[2] -\n        0.4 * x[14] >= 0\n    )  #= e28: =#\n    @NLconstraint(\n        m,\n        x[45] * x[57] -\n        (x[44] * x[56] - (x[44] * x[27] + x[44] * x[30] + x[44] * x[33])) - 0.4 * x[3] -\n        0.4 * x[15] >= 0\n    )  #= e29: =#\n    @NLconstraint(\n        m,\n        x[47] * x[59] - (x[46] * x[58] + x[43] * x[26] - x[46] * x[35]) - 0.4 * x[5] -\n        0.4 * x[17] >= 0\n    )  #= e30: =#\n    @NLconstraint(\n        m,\n        x[48] * x[60] - (x[47] * x[59] + x[44] * x[27] - x[47] * x[36]) - 0.4 * x[6] -\n        0.4 * x[18] >= 0\n    )  #= e31: =#\n\n    @NLconstraint(\n        m,\n        x[37] * x[55] - 0.6 * x[1] - 0.2 * x[13] +\n        0.2 * x[25] +\n        0.2 * x[28] +\n        0.2 * x[31] <= 0.04\n    )  #= e8: =#\n    @NLconstraint(\n        m,\n        x[40] * x[58] - 0.6 * x[4] - 0.2 * x[16] - 0.2 * x[25] + 0.7 * x[34] <= 0.07\n    )  #= e9: =#\n    @NLconstraint(\n        m,\n        x[43] * x[55] - 0.4 * x[1] - 0.4 * x[13] +\n        0.5 * x[25] +\n        0.5 * x[28] +\n        0.5 * x[31] <= 0.1\n    )  #= e10: =#\n    @NLconstraint(\n        m,\n        x[46] * x[58] - 0.4 * x[4] - 0.4 * x[16] - 0.5 * x[25] + 0.6 * x[34] <= 0.06\n    )  #= e11: =#\n    @NLconstraint(\n        m,\n        x[38] * x[56] -\n        (x[37] * x[55] - (x[37] * x[26] + x[37] * x[29] + x[37] * x[32])) - 0.6 * x[2] -\n        0.2 * x[14] <= 0\n    )  #= e24: =#\n    @NLconstraint(\n        m,\n        x[39] * x[57] -\n        (x[38] * x[56] - (x[38] * x[27] + x[38] * x[30] + x[38] * x[33])) - 0.6 * x[3] -\n        0.2 * x[15] <= 0\n    )  #= e25: =#\n    @NLconstraint(\n        m,\n        x[41] * x[59] - (x[40] * x[58] + x[37] * x[26] - x[40] * x[35]) - 0.6 * x[5] -\n        0.2 * x[17] <= 0\n    )  #= e26: =#\n    @NLconstraint(\n        m,\n        x[42] * x[60] - (x[41] * x[59] + x[38] * x[27] - x[41] * x[36]) - 0.6 * x[6] -\n        0.2 * x[18] <= 0\n    )  #= e27: =#\n    @NLconstraint(\n        m,\n        x[44] * x[56] -\n        (x[43] * x[55] - (x[43] * x[26] + x[43] * x[29] + x[43] * x[32])) - 0.4 * x[2] -\n        0.4 * x[14] <= 0\n    )  #= e28: =#\n    @NLconstraint(\n        m,\n        x[45] * x[57] -\n        (x[44] * x[56] - (x[44] * x[27] + x[44] * x[30] + x[44] * x[33])) - 0.4 * x[3] -\n        0.4 * x[15] <= 0\n    )  #= e29: =#\n    @NLconstraint(\n        m,\n        x[47] * x[59] - (x[46] * x[58] + x[43] * x[26] - x[46] * x[35]) - 0.4 * x[5] -\n        0.4 * x[17] <= 0\n    )  #= e30: =#\n    @NLconstraint(\n        m,\n        x[48] * x[60] - (x[47] * x[59] + x[44] * x[27] - x[47] * x[36]) - 0.4 * x[6] -\n        0.4 * x[18] <= 0\n    )  #= e31: =#\n\n    warmstarter = [\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        1.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.53351,\n        0.60649,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.2,\n        0.2,\n        0.2,\n        0.7,\n        0.7,\n        0.7,\n        0.5,\n        0.5,\n        0.5,\n        0.6,\n        0.6,\n        0.6,\n        1.0,\n        2.0,\n        1.0,\n        1.1,\n        0.66649,\n        0.96,\n        0.2,\n        0.2,\n        0.2,\n        0.1,\n        0.1,\n        0.1,\n        1.55,\n        1.27351,\n        2.0,\n        0.49,\n        0.35,\n        0.25,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        1.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        1.0,\n        1.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n        0.0,\n    ]\n    for i in 1:102\n        JuMP.set_start_value(x[i], warmstarter[i])\n    end\n\n    @constraint(m, x[1] + x[4] + x[7] + x[10] + x[49] == 1)  #= e2: =#\n    @constraint(m, x[13] + x[16] + x[19] + x[22] + x[52] == 1.1)  #= e3: =#\n    @constraint(m, -x[1] - x[13] + x[25] + x[28] + x[31] + x[55] == 0.2)  #= e4: =#\n    @constraint(m, -x[4] - x[16] - x[25] + x[34] + x[58] == 0.1)  #= e5: =#\n    @constraint(m, -x[7] - x[19] - x[28] - x[34] + x[61] == 1.55)  #= e6: =#\n    @constraint(m, -x[10] - x[22] - x[31] + x[64] == 0.49)  #= e7: =#\n    @constraint(m, x[2] + x[5] + x[8] + x[11] - x[49] + x[50] == 1)  #= e12: =#\n    @constraint(m, x[3] + x[6] + x[9] + x[12] - x[50] + x[51] == 0)  #= e13: =#\n    @constraint(m, x[14] + x[17] + x[20] + x[23] - x[52] + x[53] == 0.1)  #= e14: =#\n    @constraint(m, x[15] + x[18] + x[21] + x[24] - x[53] + x[54] == 0.9)  #= e15: =#\n    @constraint(m, -x[2] - x[14] + x[26] + x[29] + x[32] - x[55] + x[56] == 0)  #= e16: =#\n    @constraint(m, -x[3] - x[15] + x[27] + x[30] + x[33] - x[56] + x[57] == 0)  #= e17: =#\n    @constraint(m, -x[5] - x[17] - x[26] + x[35] - x[58] + x[59] == 0)  #= e18: =#\n    @constraint(m, -x[6] - x[18] - x[27] + x[36] - x[59] + x[60] == 0)  #= e19: =#\n    @constraint(m, -x[8] - x[20] - x[29] - x[35] - x[61] + x[62] == -0.81)  #= e20: =#\n    @constraint(m, -x[9] - x[21] - x[30] - x[36] - x[62] + x[63] == -0.88)  #= e21: =#\n    @constraint(m, -x[11] - x[23] - x[32] - x[64] + x[65] == -0.14)  #= e22: =#\n    @constraint(m, -x[12] - x[24] - x[33] - x[65] + x[66] == -0.1)  #= e23: =#\n    @constraint(m, x[1] - x[67] <= 0)  #= e32: =#\n    @constraint(m, x[2] - x[68] <= 0)  #= e33: =#\n    @constraint(m, x[3] - x[69] <= 0)  #= e34: =#\n    @constraint(m, x[4] - x[70] <= 0)  #= e35: =#\n    @constraint(m, x[5] - x[71] <= 0)  #= e36: =#\n    @constraint(m, x[6] - x[72] <= 0)  #= e37: =#\n    @constraint(m, x[7] - x[73] <= 0)  #= e38: =#\n    @constraint(m, x[8] - x[74] <= 0)  #= e39: =#\n    @constraint(m, x[9] - x[75] <= 0)  #= e40: =#\n    @constraint(m, x[10] - x[76] <= 0)  #= e41: =#\n    @constraint(m, x[11] - x[77] <= 0)  #= e42: =#\n    @constraint(m, x[12] - x[78] <= 0)  #= e43: =#\n    @constraint(m, x[13] - x[79] <= 0)  #= e44: =#\n    @constraint(m, x[14] - x[80] <= 0)  #= e45: =#\n    @constraint(m, x[15] - x[81] <= 0)  #= e46: =#\n    @constraint(m, x[16] - x[82] <= 0)  #= e47: =#\n    @constraint(m, x[17] - x[83] <= 0)  #= e48: =#\n    @constraint(m, x[18] - x[84] <= 0)  #= e49: =#\n    @constraint(m, x[19] - x[85] <= 0)  #= e50: =#\n    @constraint(m, x[20] - x[86] <= 0)  #= e51: =#\n    @constraint(m, x[21] - x[87] <= 0)  #= e52: =#\n    @constraint(m, x[22] - x[88] <= 0)  #= e53: =#\n    @constraint(m, x[23] - x[89] <= 0)  #= e54: =#\n    @constraint(m, x[24] - x[90] <= 0)  #= e55: =#\n    @constraint(m, x[25] - x[91] <= 0)  #= e56: =#\n    @constraint(m, x[26] - x[92] <= 0)  #= e57: =#\n    @constraint(m, x[27] - x[93] <= 0)  #= e58: =#\n    @constraint(m, x[28] - x[94] <= 0)  #= e59: =#\n    @constraint(m, x[29] - x[95] <= 0)  #= e60: =#\n    @constraint(m, x[30] - x[96] <= 0)  #= e61: =#\n    @constraint(m, x[31] - x[97] <= 0)  #= e62: =#\n    @constraint(m, x[32] - x[98] <= 0)  #= e63: =#\n    @constraint(m, x[33] - x[99] <= 0)  #= e64: =#\n    @constraint(m, x[34] - x[100] <= 0)  #= e65: =#\n    @constraint(m, x[35] - x[101] <= 0)  #= e66: =#\n    @constraint(m, x[36] - x[102] <= 0)  #= e67: =#\n    @constraint(m, x[1] >= 0)  #= e68: =#\n    @constraint(m, x[2] >= 0)  #= e69: =#\n    @constraint(m, x[3] >= 0)  #= e70: =#\n    @constraint(m, x[4] >= 0)  #= e71: =#\n    @constraint(m, x[5] >= 0)  #= e72: =#\n    @constraint(m, x[6] >= 0)  #= e73: =#\n    @constraint(m, x[7] >= 0)  #= e74: =#\n    @constraint(m, x[8] >= 0)  #= e75: =#\n    @constraint(m, x[9] >= 0)  #= e76: =#\n    @constraint(m, x[10] >= 0)  #= e77: =#\n    @constraint(m, x[11] >= 0)  #= e78: =#\n    @constraint(m, x[12] >= 0)  #= e79: =#\n    @constraint(m, x[13] >= 0)  #= e80: =#\n    @constraint(m, x[14] >= 0)  #= e81: =#\n    @constraint(m, x[15] >= 0)  #= e82: =#\n    @constraint(m, x[16] >= 0)  #= e83: =#\n    @constraint(m, x[17] >= 0)  #= e84: =#\n    @constraint(m, x[18] >= 0)  #= e85: =#\n    @constraint(m, x[19] >= 0)  #= e86: =#\n    @constraint(m, x[20] >= 0)  #= e87: =#\n    @constraint(m, x[21] >= 0)  #= e88: =#\n    @constraint(m, x[22] >= 0)  #= e89: =#\n    @constraint(m, x[23] >= 0)  #= e90: =#\n    @constraint(m, x[24] >= 0)  #= e91: =#\n    @constraint(m, x[25] >= 0)  #= e92: =#\n    @constraint(m, x[26] >= 0)  #= e93: =#\n    @constraint(m, x[27] >= 0)  #= e94: =#\n    @constraint(m, x[28] >= 0)  #= e95: =#\n    @constraint(m, x[29] >= 0)  #= e96: =#\n    @constraint(m, x[30] >= 0)  #= e97: =#\n    @constraint(m, x[31] >= 0)  #= e98: =#\n    @constraint(m, x[32] >= 0)  #= e99: =#\n    @constraint(m, x[33] >= 0)  #= e100: =#\n    @constraint(m, x[34] >= 0)  #= e101: =#\n    @constraint(m, x[35] >= 0)  #= e102: =#\n    @constraint(m, x[36] >= 0)  #= e103: =#\n    @constraint(m, x[73] <= 1.5)  #= e104: =#\n    @constraint(m, x[74] <= 1.5)  #= e105: =#\n    @constraint(m, x[75] <= 1.5)  #= e106: =#\n    @constraint(m, x[76] <= 0.6)  #= e107: =#\n    @constraint(m, x[77] <= 0.6)  #= e108: =#\n    @constraint(m, x[78] <= 0.6)  #= e109: =#\n    @constraint(m, x[85] <= 1.1)  #= e110: =#\n    @constraint(m, x[86] <= 1.1)  #= e111: =#\n    @constraint(m, x[87] <= 1.1)  #= e112: =#\n    @constraint(m, x[88] <= 0.2)  #= e113: =#\n    @constraint(m, x[89] <= 0.2)  #= e114: =#\n    @constraint(m, x[90] <= 0.2)  #= e115: =#\n    @constraint(m, x[73] <= 1)  #= e116: =#\n    @constraint(m, x[74] <= 1)  #= e117: =#\n    @constraint(m, x[75] <= 1)  #= e118: =#\n    @constraint(m, x[76] <= 0.8)  #= e119: =#\n    @constraint(m, x[77] <= 0.8)  #= e120: =#\n    @constraint(m, x[78] <= 0.8)  #= e121: =#\n    @constraint(m, x[85] <= 1)  #= e122: =#\n    @constraint(m, x[86] <= 1)  #= e123: =#\n    @constraint(m, x[87] <= 1)  #= e124: =#\n    @constraint(m, x[88] <= 0.8)  #= e125: =#\n    @constraint(m, x[89] <= 0.8)  #= e126: =#\n    @constraint(m, x[90] <= 0.8)  #= e127: =#\n    @constraint(m, -x[73] >= -1.3)  #= e128: =#\n    @constraint(m, -x[74] >= -1.3)  #= e129: =#\n    @constraint(m, -x[75] >= -1.3)  #= e130: =#\n    @constraint(m, -x[76] >= -1.4)  #= e131: =#\n    @constraint(m, -x[77] >= -1.4)  #= e132: =#\n    @constraint(m, -x[78] >= -1.4)  #= e133: =#\n    @constraint(m, -x[85] >= -1.7)  #= e134: =#\n    @constraint(m, -x[86] >= -1.7)  #= e135: =#\n    @constraint(m, -x[87] >= -1.7)  #= e136: =#\n    @constraint(m, -x[88] >= -1.8)  #= e137: =#\n    @constraint(m, -x[89] >= -1.8)  #= e138: =#\n    @constraint(m, -x[90] >= -1.8)  #= e139: =#\n    @constraint(m, -x[73] >= -1)  #= e140: =#\n    @constraint(m, -x[74] >= -1)  #= e141: =#\n    @constraint(m, -x[75] >= -1)  #= e142: =#\n    @constraint(m, -x[76] >= -1.4)  #= e143: =#\n    @constraint(m, -x[77] >= -1.4)  #= e144: =#\n    @constraint(m, -x[78] >= -1.4)  #= e145: =#\n    @constraint(m, -x[85] >= -1)  #= e146: =#\n    @constraint(m, -x[86] >= -1)  #= e147: =#\n    @constraint(m, -x[87] >= -1)  #= e148: =#\n    @constraint(m, -x[88] >= -1.4)  #= e149: =#\n    @constraint(m, -x[89] >= -1.4)  #= e150: =#\n    @constraint(m, -x[90] >= -1.4)  #= e151: =#\n    @constraint(m, -x[37] + x[95] <= 0.9)  #= e152: =#\n    @constraint(m, -x[38] + x[96] <= 0.9)  #= e153: =#\n    @constraint(m, -x[37] + x[98] <= 0)  #= e154: =#\n    @constraint(m, -x[38] + x[99] <= 0)  #= e155: =#\n    @constraint(m, -x[40] + x[101] <= 0.9)  #= e156: =#\n    @constraint(m, -x[41] + x[102] <= 0.9)  #= e157: =#\n    @constraint(m, -x[43] + x[95] <= 0.6)  #= e158: =#\n    @constraint(m, -x[44] + x[96] <= 0.6)  #= e159: =#\n    @constraint(m, -x[43] + x[98] <= 0.4)  #= e160: =#\n    @constraint(m, -x[44] + x[99] <= 0.4)  #= e161: =#\n    @constraint(m, -x[46] + x[101] <= 0.6)  #= e162: =#\n    @constraint(m, -x[47] + x[102] <= 0.6)  #= e163: =#\n    @constraint(m, -x[37] - x[95] >= -1.9)  #= e164: =#\n    @constraint(m, -x[38] - x[96] >= -1.9)  #= e165: =#\n    @constraint(m, -x[37] - x[98] >= -2)  #= e166: =#\n    @constraint(m, -x[38] - x[99] >= -2)  #= e167: =#\n    @constraint(m, -x[40] - x[101] >= -1.9)  #= e168: =#\n    @constraint(m, -x[41] - x[102] >= -1.9)  #= e169: =#\n    @constraint(m, -x[43] - x[95] >= -1.4)  #= e170: =#\n    @constraint(m, -x[44] - x[96] >= -1.4)  #= e171: =#\n    @constraint(m, -x[43] - x[98] >= -1.8)  #= e172: =#\n    @constraint(m, -x[44] - x[99] >= -1.8)  #= e173: =#\n    @constraint(m, -x[46] - x[101] >= -1.4)  #= e174: =#\n    @constraint(m, -x[47] - x[102] >= -1.4)  #= e175: =#\n    @constraint(m, x[94] <= 1.1)  #= e176: =#\n    @constraint(m, x[97] <= 0.2)  #= e177: =#\n    @constraint(m, x[100] <= 1.6)  #= e178: =#\n    @constraint(m, x[94] <= 1.1)  #= e179: =#\n    @constraint(m, x[97] <= 0.9)  #= e180: =#\n    @constraint(m, x[100] <= 1.2)  #= e181: =#\n    @constraint(m, -x[94] >= -1.7)  #= e182: =#\n    @constraint(m, -x[97] >= -1.8)  #= e183: =#\n    @constraint(m, -x[100] >= -1.2)  #= e184: =#\n    @constraint(m, -x[94] >= -0.9)  #= e185: =#\n    @constraint(m, -x[97] >= -1.3)  #= e186: =#\n    @constraint(m, -x[100] >= -0.8)  #= e187: =#\n    @constraint(m, x[67] + x[91] <= 1)  #= e188: =#\n    @constraint(m, x[68] + x[92] <= 1)  #= e189: =#\n    @constraint(m, x[69] + x[93] <= 1)  #= e190: =#\n    @constraint(m, x[67] + x[94] <= 1)  #= e191: =#\n    @constraint(m, x[68] + x[95] <= 1)  #= e192: =#\n    @constraint(m, x[69] + x[96] <= 1)  #= e193: =#\n    @constraint(m, x[67] + x[97] <= 1)  #= e194: =#\n    @constraint(m, x[68] + x[98] <= 1)  #= e195: =#\n    @constraint(m, x[69] + x[99] <= 1)  #= e196: =#\n    @constraint(m, x[79] + x[91] <= 1)  #= e197: =#\n    @constraint(m, x[80] + x[92] <= 1)  #= e198: =#\n    @constraint(m, x[81] + x[93] <= 1)  #= e199: =#\n    @constraint(m, x[79] + x[94] <= 1)  #= e200: =#\n    @constraint(m, x[80] + x[95] <= 1)  #= e201: =#\n    @constraint(m, x[81] + x[96] <= 1)  #= e202: =#\n    @constraint(m, x[79] + x[97] <= 1)  #= e203: =#\n    @constraint(m, x[80] + x[98] <= 1)  #= e204: =#\n    @constraint(m, x[81] + x[99] <= 1)  #= e205: =#\n    @constraint(m, x[70] + x[100] <= 1)  #= e206: =#\n    @constraint(m, x[71] + x[101] <= 1)  #= e207: =#\n    @constraint(m, x[72] + x[102] <= 1)  #= e208: =#\n    @constraint(m, x[82] + x[100] <= 1)  #= e209: =#\n    @constraint(m, x[83] + x[101] <= 1)  #= e210: =#\n    @constraint(m, x[84] + x[102] <= 1)  #= e211: =#\n    @constraint(m, x[91] + x[100] <= 1)  #= e212: =#\n    @constraint(m, x[92] + x[101] <= 1)  #= e213: =#\n    @constraint(m, x[93] + x[102] <= 1)  #= e214: =#\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/bnlp.jl",
    "content": "function hmittelman(; solver = nothing)\n    # Source: https://www.minlplib.org/hmittelman.html\n    # Global solution: 13.0\n\n    m = JuMP.Model(solver)\n\n    # ----- Variables ----- #\n    @variable(m, 0 <= objvar <= 20)\n    b_Idx = Any[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n    @variable(m, b[b_Idx], Bin)\n\n    # ----- Constraints ----- #\n    @NLconstraint(\n        m,\n        e1,\n        -(\n            10 * b[5] * b[7] * b[9] * b[10] * b[14] * b[15] * b[16] +\n            7 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] +\n            b[3] * b[4] * b[6] * b[7] * b[8] +\n            12 * b[3] * b[4] * b[8] * b[11] +\n            8 * b[6] * b[7] * b[8] * b[12] +\n            3 * b[6] * b[7] * b[9] * b[14] * b[16] +\n            b[9] * b[10] * b[14] * b[16] +\n            5 * b[5] * b[10] * b[14] * b[15] * b[16] +\n            3 * b[1] * b[2] * b[11] * b[12]\n        ) + objvar == 0.0\n    )\n    @NLconstraint(\n        m,\n        e2,\n        3 * b[5] * b[7] * b[9] * b[10] * b[14] * b[15] * b[16] -\n        12 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] -\n        8 * b[3] * b[4] * b[6] * b[7] * b[8] + b[3] * b[4] * b[8] * b[11] -\n        7 * b[1] * b[2] * b[11] * b[12] + 2 * b[13] * b[14] * b[15] * b[16] <= -2.0\n    )\n    @NLconstraint(\n        m,\n        e3,\n        b[1] * b[2] * b[3] * b[4] * b[8] * b[11] - 10 * b[3] * b[4] * b[6] * b[7] * b[8] -\n        5 * b[6] * b[7] * b[8] * b[12] +\n        b[6] * b[7] * b[9] * b[14] * b[16] +\n        7 * b[9] * b[10] * b[14] * b[16] +\n        b[5] * b[10] * b[14] * b[15] * b[16] <= -1.0\n    )\n    @NLconstraint(\n        m,\n        e4,\n        5 * b[5] * b[7] * b[9] * b[10] * b[14] * b[15] * b[16] -\n        3 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] - b[3] * b[4] * b[6] * b[7] * b[8] -\n        2 * b[5] * b[10] * b[14] * b[15] * b[16] + b[13] * b[14] * b[15] * b[16] <= -1.0\n    )\n    @NLconstraint(\n        m,\n        e5,\n        3 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] -\n        5 * b[5] * b[7] * b[9] * b[10] * b[14] * b[15] * b[16] +\n        b[3] * b[4] * b[6] * b[7] * b[8] +\n        2 * b[5] * b[10] * b[14] * b[15] * b[16] - b[13] * b[14] * b[15] * b[16] <= 1.0\n    )\n    @NLconstraint(\n        m,\n        e6,\n        (-4 * b[3] * b[4] * b[6] * b[7] * b[8]) - 2 * b[3] * b[4] * b[8] * b[11] -\n        5 * b[6] * b[7] * b[9] * b[14] * b[16] + b[9] * b[10] * b[14] * b[16] -\n        9 * b[5] * b[10] * b[14] * b[15] * b[16] - 2 * b[1] * b[2] * b[11] * b[12] <=\n        -3.0\n    )\n    @NLconstraint(\n        m,\n        e7,\n        9 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] - 12 * b[3] * b[4] * b[8] * b[11] -\n        7 * b[6] * b[7] * b[8] * b[12] +\n        6 * b[6] * b[7] * b[9] * b[14] * b[16] +\n        2 * b[5] * b[10] * b[14] * b[15] * b[16] - 15 * b[1] * b[2] * b[11] * b[12] +\n        3 * b[13] * b[14] * b[15] * b[16] <= -7.0\n    )\n    @NLconstraint(\n        m,\n        e8,\n        5 * b[1] * b[2] * b[3] * b[4] * b[8] * b[11] -\n        8 * b[5] * b[7] * b[9] * b[10] * b[14] * b[15] * b[16] +\n        2 * b[3] * b[4] * b[6] * b[7] * b[8] - 7 * b[3] * b[4] * b[8] * b[11] -\n        b[6] * b[7] * b[8] * b[12] - 5 * b[9] * b[10] * b[14] * b[16] -\n        10 * b[1] * b[2] * b[11] * b[12] <= -1.0\n    )\n\n    # ----- Objective ----- #\n    @objective(m, Min, objvar)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/brainpc3.jl",
    "content": "function brainpc3(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    # ----- Variables ----- #\n    @variable(m, x[1:6907])\n\n    @NLobjective(\n        m,\n        Min,\n        (\n            (-0.003214) + x[16] - (x[16] + x[3467]) * x[6903] +\n            x[3467] +\n            6.34e-6 * x[6903]\n        )^2 +\n        (x[46] - (x[46] + x[3497]) * x[6903] + x[3497] + 0.01551 * x[6903])^2 +\n        (x[76] - (x[76] + x[3527]) * x[6903] + x[3527] + 0.008919 * x[6903])^2 +\n        (x[106] - (x[106] + x[3557]) * x[6903] + x[3557] + 0.005968 * x[6903])^2 +\n        (x[136] - (x[136] + x[3587]) * x[6903] + x[3587] + 0.005773 * x[6903])^2 +\n        (x[166] - (x[166] + x[3617]) * x[6903] + x[3617] + 0.004985 * x[6903])^2 +\n        (x[196] - (x[196] + x[3647]) * x[6903] + x[3647] + 0.004795 * x[6903])^2 +\n        (x[226] - (x[226] + x[3677]) * x[6903] + x[3677] + 0.004409 * x[6903])^2 +\n        (x[271] - (x[271] + x[3722]) * x[6903] + x[3722] + 0.003829 * x[6903])^2 +\n        (x[331] - (x[331] + x[3782]) * x[6903] + x[3782] + 0.003269 * x[6903])^2 +\n        (x[391] - (x[391] + x[3842]) * x[6903] + x[3842] + 0.00317 * x[6903])^2 +\n        (x[451] - (x[451] + x[3902]) * x[6903] + x[3902] + 0.00307 * x[6903])^2 +\n        (x[511] - (x[511] + x[3962]) * x[6903] + x[3962] + 0.002971 * x[6903])^2 +\n        (x[631] - (x[631] + x[4082]) * x[6903] + x[4082] + 0.002765 * x[6903])^2 +\n        (x[811] - (x[811] + x[4262]) * x[6903] + x[4262] + 0.00247 * x[6903])^2 +\n        (x[991] - (x[991] + x[4442]) * x[6903] + x[4442] + 0.002252 * x[6903])^2 +\n        (x[1171] - (x[1171] + x[4622]) * x[6903] + x[4622] + 0.002066 * x[6903])^2 +\n        (x[1351] - (x[1351] + x[4802]) * x[6903] + x[4802] + 0.001891 * x[6903])^2 +\n        (x[1531] - (x[1531] + x[4982]) * x[6903] + x[4982] + 0.00173 * x[6903])^2 +\n        (x[1711] - (x[1711] + x[5162]) * x[6903] + x[5162] + 0.001713 * x[6903])^2 +\n        (x[1951] - (x[1951] + x[5402]) * x[6903] + x[5402] + 0.00166 * x[6903])^2 +\n        (x[2251] - (x[2251] + x[5702]) * x[6903] + x[5702] + 0.001548 * x[6903])^2 +\n        (x[2551] - (x[2551] + x[6002]) * x[6903] + x[6002] + 0.001435 * x[6903])^2 +\n        (x[2851] - (x[2851] + x[6302]) * x[6903] + x[6302] + 0.001323 * x[6903])^2 +\n        (x[3151] - (x[3151] + x[6602]) * x[6903] + x[6602] + 0.00121 * x[6903])^2 +\n        (x[3451] - (x[3451] + x[6902]) * x[6903] + x[6902] + 0.001098 * x[6903])^2\n    )\n\n    return m  # model get returned when including this script.\nend\n"
  },
  {
    "path": "examples/MINLPs/castro.jl",
    "content": "function castro2m2(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:41] <= 1E5)\n    @variable(m, 0 <= obj <= 1E3)\n    @objective(m, Min, obj)\n\n    @NLconstraint(m, e31, x[28] * x[30] - x[16] == 0.0)\n    @NLconstraint(m, e32, x[28] * x[31] - x[17] == 0.0)\n    @NLconstraint(m, e33, x[29] * x[32] - x[18] == 0.0)\n    @NLconstraint(m, e34, x[29] * x[33] - x[19] == 0.0)\n    @NLconstraint(m, e35, x[28] * x[36] - x[22] == 0.0)\n    @NLconstraint(m, e36, x[29] * x[37] - x[23] == 0.0)\n    @NLconstraint(m, e37, x[14] * x[30] - x[1] == 0.0)\n    @NLconstraint(m, e38, x[14] * x[31] - x[2] == 0.0)\n    @NLconstraint(m, e39, x[15] * x[32] - x[3] == 0.0)\n    @NLconstraint(m, e40, x[15] * x[33] - x[4] == 0.0)\n    @NLconstraint(m, e41, x[14] * x[36] - x[7] == 0.0)\n    @NLconstraint(m, e42, x[15] * x[37] - x[8] == 0.0)\n\n    @constraint(m, e1, -x[14] - x[15] + obj == 0.0)\n    @constraint(m, e2, -x[5] - x[9] - x[10] == -60.0)\n    @constraint(m, e3, -x[6] - x[11] - x[12] == -20.0)\n    @constraint(m, e4, -x[1] - x[3] - x[9] - x[11] + x[14] == 0.0)\n    @constraint(m, e5, -x[2] - x[4] - x[10] - x[12] + x[15] == 0.0)\n    @constraint(m, e6, -x[1] - x[2] - x[7] + x[14] == 0.0)\n    @constraint(m, e7, -x[3] - x[4] - x[8] + x[15] == 0.0)\n    @constraint(m, e8, -x[5] - x[6] - x[7] - x[8] + x[13] == 0.0)\n    @constraint(m, e9, -x[20] - x[24] - x[25] == -24000.0)\n    @constraint(m, e10, -x[21] - x[26] - x[27] == -16000.0)\n    @constraint(m, e11, -x[24] + 24000 * x[38] == 0.0)\n    @constraint(m, e12, -x[25] + 24000 * x[39] == 0.0)\n    @constraint(m, e13, -x[26] + 16000 * x[40] == 0.0)\n    @constraint(m, e14, -x[27] + 16000 * x[41] == 0.0)\n    @constraint(m, e15, -x[20] + 24000 * x[34] == 0.0)\n    @constraint(m, e16, -x[21] + 16000 * x[35] == 0.0)\n    @constraint(m, e17, -x[9] + 60 * x[38] == 0.0)\n    @constraint(m, e18, -x[10] + 60 * x[39] == 0.0)\n    @constraint(m, e19, -x[11] + 20 * x[40] == 0.0)\n    @constraint(m, e20, -x[12] + 20 * x[41] == 0.0)\n    @constraint(m, e21, -x[5] + 60 * x[34] == 0.0)\n    @constraint(m, e22, -x[6] + 20 * x[35] == 0.0)\n    @constraint(m, e23, x[34] + x[38] + x[39] == 1.0)\n    @constraint(m, e24, x[35] + x[40] + x[41] == 1.0)\n    @constraint(m, e25, -200 * x[14] + x[16] + x[18] + x[24] + x[26] <= 0.0)\n    @constraint(m, e26, -1000 * x[15] + x[17] + x[19] + x[25] + x[27] <= 0.0)\n    @constraint(\n        m,\n        e27,\n        0.01 * x[16] + 0.01 * x[18] + 0.01 * x[24] + 0.01 * x[26] - x[28] == 0.0\n    )\n    @constraint(\n        m,\n        e28,\n        0.2 * x[17] + 0.2 * x[19] + 0.2 * x[25] + 0.2 * x[27] - x[29] == 0.0\n    )\n    @constraint(m, e29, -x[16] - x[17] - x[22] + x[28] == 0.0)\n    @constraint(m, e30, -x[18] - x[19] - x[23] + x[29] == 0.0)\n    @constraint(m, e43, x[30] + x[31] + x[36] == 1.0)\n    @constraint(m, e44, x[32] + x[33] + x[37] == 1.0)\n    @constraint(m, e45, -10 * x[13] + x[20] + x[21] + x[22] + x[23] <= 0.0)\n\n    return m\nend\n\nfunction castro6m2(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:133] <= 1E6)\n    @variable(m, obj)\n    @variable(m, b[1:40])   #Additional variables to increase degree of freedom and Ipopt's convergence\n    @objective(m, Min, obj)\n\n    # Non-Linear Constraints\n    @NLconstraint(m, e99, x[101] * x[110] - x[29] == 0.0)\n    @NLconstraint(m, e100, x[102] * x[110] - x[30] == 0.0)\n    @NLconstraint(m, e101, x[103] * x[110] - x[31] == 0.0)\n    @NLconstraint(m, e102, x[101] * x[111] - x[32] == 0.0)\n    @NLconstraint(m, e103, x[102] * x[111] - x[33] == 0.0)\n    @NLconstraint(m, e104, x[103] * x[111] - x[34] == 0.0)\n    @NLconstraint(m, e105, x[101] * x[112] - x[35] == 0.0)\n    @NLconstraint(m, e106, x[102] * x[112] - x[36] == 0.0)\n    @NLconstraint(m, e107, x[103] * x[112] - x[37] == 0.0)\n    @NLconstraint(m, e108, x[104] * x[113] - x[38] == 0.0)\n    @NLconstraint(m, e109, x[105] * x[113] - x[39] == 0.0)\n    @NLconstraint(m, e110, x[106] * x[113] - x[40] == 0.0)\n    @NLconstraint(m, e111, x[104] * x[114] - x[41] == 0.0)\n    @NLconstraint(m, e112, x[105] * x[114] - x[42] == 0.0)\n    @NLconstraint(m, e113, x[106] * x[114] - x[43] == 0.0)\n    @NLconstraint(m, e114, x[104] * x[115] - x[44] == 0.0)\n    @NLconstraint(m, e115, x[105] * x[115] - x[45] == 0.0)\n    @NLconstraint(m, e116, x[106] * x[115] - x[46] == 0.0)\n    @NLconstraint(m, e117, x[107] * x[116] - x[47] == 0.0)\n    @NLconstraint(m, e118, x[108] * x[116] - x[48] == 0.0)\n    @NLconstraint(m, e119, x[109] * x[116] - x[49] == 0.0)\n    @NLconstraint(m, e120, x[107] * x[117] - x[50] == 0.0)\n    @NLconstraint(m, e121, x[108] * x[117] - x[51] == 0.0)\n    @NLconstraint(m, e122, x[109] * x[117] - x[52] == 0.0)\n    @NLconstraint(m, e123, x[107] * x[118] - x[53] == 0.0)\n    @NLconstraint(m, e124, x[108] * x[118] - x[54] == 0.0)\n    @NLconstraint(m, e125, x[109] * x[118] - x[55] == 0.0)\n    @NLconstraint(m, e126, x[101] * x[122] - x[65] == 0.0)\n    @NLconstraint(m, e127, x[102] * x[122] - x[66] == 0.0)\n    @NLconstraint(m, e128, x[103] * x[122] - x[67] == 0.0)\n    @NLconstraint(m, e129, x[104] * x[123] - x[68] == 0.0)\n    @NLconstraint(m, e130, x[105] * x[123] - x[69] == 0.0)\n    @NLconstraint(m, e131, x[106] * x[123] - x[70] == 0.0)\n    @NLconstraint(m, e132, x[107] * x[124] - x[71] == 0.0)\n    @NLconstraint(m, e133, x[108] * x[124] - x[72] == 0.0)\n    @NLconstraint(m, e134, x[109] * x[124] - x[73] == 0.0)\n    @NLconstraint(m, e135, x[26] * x[110] - x[1] == 0.0)\n    @NLconstraint(m, e136, x[26] * x[111] - x[2] == 0.0)\n    @NLconstraint(m, e137, x[26] * x[112] - x[3] == 0.0)\n    @NLconstraint(m, e138, x[27] * x[113] - x[4] == 0.0)\n    @NLconstraint(m, e139, x[27] * x[114] - x[5] == 0.0)\n    @NLconstraint(m, e140, x[27] * x[115] - x[6] == 0.0)\n    @NLconstraint(m, e141, x[28] * x[116] - x[7] == 0.0)\n    @NLconstraint(m, e142, x[28] * x[117] - x[8] == 0.0)\n    @NLconstraint(m, e143, x[28] * x[118] - x[9] == 0.0)\n    @NLconstraint(m, e144, x[26] * x[122] - x[13] == 0.0)\n    @NLconstraint(m, e145, x[27] * x[123] - x[14] == 0.0)\n    @NLconstraint(m, e146, x[28] * x[124] - x[15] == 0.0)\n\n    @constraint(m, e1, -x[26] - x[27] - x[28] + obj == 0.0)\n    @constraint(m, e2, -x[10] - x[16] - x[17] - x[18] == -13.1)\n    @constraint(m, e3, -x[11] - x[19] - x[20] - x[21] == -32.7)\n    @constraint(m, e4, -x[12] - x[22] - x[23] - x[24] == -56.5)\n    @constraint(m, e5, -x[1] - x[4] - x[7] - x[16] - x[19] - x[22] + x[26] == 0.0)\n    @constraint(m, e6, -x[2] - x[5] - x[8] - x[17] - x[20] - x[23] + x[27] == 0.0)\n    @constraint(m, e7, -x[3] - x[6] - x[9] - x[18] - x[21] - x[24] + x[28] == 0.0)\n    @constraint(m, e8, -x[1] - x[2] - x[3] - x[13] + x[26] == 0.0)\n    @constraint(m, e9, -x[4] - x[5] - x[6] - x[14] + x[27] == 0.0)\n    @constraint(m, e10, -x[7] - x[8] - x[9] - x[15] + x[28] == 0.0)\n    @constraint(m, e11, -x[10] - x[11] - x[12] - x[13] - x[14] - x[15] + x[25] == 0.0)\n    @constraint(m, e12, -x[56] - x[74] - x[77] - x[80] == -131.0)\n    @constraint(m, e13, -x[57] - x[75] - x[78] - x[81] == -5109.0)\n    @constraint(m, e14, -x[58] - x[76] - x[79] - x[82] == -3275.0)\n    @constraint(m, e15, -x[59] - x[83] - x[86] - x[89] == -3597.0)\n    @constraint(m, e16, -x[60] - x[84] - x[87] - x[90] == -548706.0)\n    @constraint(m, e17, -x[61] - x[85] - x[88] - x[91] == -13080.0)\n    @constraint(m, e18, -x[62] - x[92] - x[95] - x[98] == -5650.0)\n    @constraint(m, e19, -x[63] - x[93] - x[96] - x[99] == -1412.5)\n    @constraint(m, e20, -x[64] - x[94] - x[97] - x[100] == -19775.0)\n    @constraint(m, e21, -x[74] + 131 * x[125] == 0.0)\n    @constraint(m, e22, -x[75] + 5109 * x[125] == 0.0)\n    @constraint(m, e23, -x[76] + 3275 * x[125] == 0.0)\n    @constraint(m, e24, -x[77] + 131 * x[126] == 0.0)\n    @constraint(m, e25, -x[78] + 5109 * x[126] == 0.0)\n    @constraint(m, e26, -x[79] + 3275 * x[126] == 0.0)\n    @constraint(m, e27, -x[80] + 131 * x[127] == 0.0)\n    @constraint(m, e28, -x[81] + 5109 * x[127] == 0.0)\n    @constraint(m, e29, -x[82] + 3275 * x[127] == 0.0)\n    @constraint(m, e30, -x[83] + 3597 * x[128] == 0.0)\n    @constraint(m, e31, -x[84] + 548706 * x[128] == 0.0)\n    @constraint(m, e32, -x[85] + 13080 * x[128] == 0.0)\n    @constraint(m, e33, -x[86] + 3597 * x[129] == 0.0)\n    @constraint(m, e34, -x[87] + 548706 * x[129] == 0.0)\n    @constraint(m, e35, -x[88] + 13080 * x[129] == 0.0)\n    @constraint(m, e36, -x[89] + 3597 * x[130] == 0.0)\n    @constraint(m, e37, -x[90] + 548706 * x[130] == 0.0)\n    @constraint(m, e38, -x[91] + 13080 * x[130] == 0.0)\n    @constraint(m, e39, -x[92] + 5650 * x[131] == 0.0)\n    @constraint(m, e40, -x[93] + 1412.5 * x[131] == 0.0)\n    @constraint(m, e41, -x[94] + 19775 * x[131] == 0.0)\n    @constraint(m, e42, -x[95] + 5650 * x[132] == 0.0)\n    @constraint(m, e43, -x[96] + 1412.5 * x[132] == 0.0)\n    @constraint(m, e44, -x[97] + 19775 * x[132] == 0.0)\n    @constraint(m, e45, -x[98] + 5650 * x[133] == 0.0)\n    @constraint(m, e46, -x[99] + 1412.5 * x[133] == 0.0)\n    @constraint(m, e47, -x[100] + 19775 * x[133] == 0.0)\n    @constraint(m, e48, -x[56] + 131 * x[119] == 0.0)\n    @constraint(m, e49, -x[57] + 5109 * x[119] == 0.0)\n    @constraint(m, e50, -x[58] + 3275 * x[119] == 0.0)\n    @constraint(m, e51, -x[59] + 3597 * x[120] == 0.0)\n    @constraint(m, e52, -x[60] + 548706 * x[120] == 0.0)\n    @constraint(m, e53, -x[61] + 13080 * x[120] == 0.0)\n    @constraint(m, e54, -x[62] + 5650 * x[121] == 0.0)\n    @constraint(m, e55, -x[63] + 1412.5 * x[121] == 0.0)\n    @constraint(m, e56, -x[64] + 19775 * x[121] == 0.0)\n    @constraint(m, e57, -x[16] + 13.1 * x[125] == 0.0)\n    @constraint(m, e58, -x[17] + 13.1 * x[126] == 0.0)\n    @constraint(m, e59, -x[18] + 13.1 * x[127] == 0.0)\n    @constraint(m, e60, -x[19] + 32.7 * x[128] == 0.0)\n    @constraint(m, e61, -x[20] + 32.7 * x[129] == 0.0)\n    @constraint(m, e62, -x[21] + 32.7 * x[130] == 0.0)\n    @constraint(m, e63, -x[22] + 56.5 * x[131] == 0.0)\n    @constraint(m, e64, -x[23] + 56.5 * x[132] == 0.0)\n    @constraint(m, e65, -x[24] + 56.5 * x[133] == 0.0)\n    @constraint(m, e66, -x[10] + 13.1 * x[119] == 0.0)\n    @constraint(m, e67, -x[11] + 32.7 * x[120] == 0.0)\n    @constraint(m, e68, -x[12] + 56.5 * x[121] == 0.0)\n    @constraint(m, e69, x[119] + x[125] + x[126] + x[127] == 1.0)\n    @constraint(m, e70, x[120] + x[128] + x[129] + x[130] == 1.0)\n    @constraint(m, e71, x[121] + x[131] + x[132] + x[133] == 1.0)\n    @constraint(\n        m,\n        e72,\n        -110 * x[26] + x[29] + x[38] + x[47] + x[74] + x[83] + x[92] <= 0.0\n    )\n    @constraint(\n        m,\n        e73,\n        -16780 * x[26] + x[30] + x[39] + x[48] + x[75] + x[84] + x[93] <= 0.0\n    )\n    @constraint(\n        m,\n        e74,\n        -400 * x[26] + x[31] + x[40] + x[49] + x[76] + x[85] + x[94] <= 0.0\n    )\n    @constraint(\n        m,\n        e75,\n        -110 * x[27] + x[32] + x[41] + x[50] + x[77] + x[86] + x[95] <= 0.0\n    )\n    @constraint(\n        m,\n        e76,\n        -16780 * x[27] + x[33] + x[42] + x[51] + x[78] + x[87] + x[96] <= 0.0\n    )\n    @constraint(\n        m,\n        e77,\n        -400 * x[27] + x[34] + x[43] + x[52] + x[79] + x[88] + x[97] <= 0.0\n    )\n    @constraint(\n        m,\n        e78,\n        -110 * x[28] + x[35] + x[44] + x[53] + x[80] + x[89] + x[98] <= 0.0\n    )\n    @constraint(\n        m,\n        e79,\n        -16780 * x[28] + x[36] + x[45] + x[54] + x[81] + x[90] + x[99] <= 0.0\n    )\n    @constraint(\n        m,\n        e80,\n        -400 * x[28] + x[37] + x[46] + x[55] + x[82] + x[91] + x[100] <= 0.0\n    )\n    @constraint(m, e81, x[29] + x[38] + x[47] + x[74] + x[83] + x[92] - x[101] == 0.0)\n    @constraint(\n        m,\n        e82,\n        0.001 * x[30] +\n        0.001 * x[39] +\n        0.001 * x[48] +\n        0.001 * x[75] +\n        0.001 * x[84] +\n        0.001 * x[93] - x[102] == 0.0\n    )\n    @constraint(m, e83, x[31] + x[40] + x[49] + x[76] + x[85] + x[94] - x[103] == 0.0)\n    @constraint(\n        m,\n        e84,\n        0.3 * x[32] +\n        0.3 * x[41] +\n        0.3 * x[50] +\n        0.3 * x[77] +\n        0.3 * x[86] +\n        0.3 * x[95] - x[104] == 0.0\n    )\n    @constraint(\n        m,\n        e85,\n        0.1 * x[33] +\n        0.1 * x[42] +\n        0.1 * x[51] +\n        0.1 * x[78] +\n        0.1 * x[87] +\n        0.1 * x[96] - x[105] == 0.0\n    )\n    @constraint(\n        m,\n        e86,\n        0.02 * x[34] +\n        0.02 * x[43] +\n        0.02 * x[52] +\n        0.02 * x[79] +\n        0.02 * x[88] +\n        0.02 * x[97] - x[106] == 0.0\n    )\n    @constraint(\n        m,\n        e87,\n        0.3 * x[35] +\n        0.3 * x[44] +\n        0.3 * x[53] +\n        0.3 * x[80] +\n        0.3 * x[89] +\n        0.3 * x[98] - x[107] == 0.0\n    )\n    @constraint(m, e88, x[36] + x[45] + x[54] + x[81] + x[90] + x[99] - x[108] == 0.0)\n    @constraint(\n        m,\n        e89,\n        0.5 * x[37] +\n        0.5 * x[46] +\n        0.5 * x[55] +\n        0.5 * x[82] +\n        0.5 * x[91] +\n        0.5 * x[100] - x[109] == 0.0\n    )\n    @constraint(m, e90, -x[29] - x[32] - x[35] - x[65] + x[101] == 0.0)\n    @constraint(m, e91, -x[30] - x[33] - x[36] - x[66] + x[102] == 0.0)\n    @constraint(m, e92, -x[31] - x[34] - x[37] - x[67] + x[103] == 0.0)\n    @constraint(m, e93, -x[38] - x[41] - x[44] - x[68] + x[104] == 0.0)\n    @constraint(m, e94, -x[39] - x[42] - x[45] - x[69] + x[105] == 0.0)\n    @constraint(m, e95, -x[40] - x[43] - x[46] - x[70] + x[106] == 0.0)\n    @constraint(m, e96, -x[47] - x[50] - x[53] - x[71] + x[107] == 0.0)\n    @constraint(m, e97, -x[48] - x[51] - x[54] - x[72] + x[108] == 0.0)\n    @constraint(m, e98, -x[49] - x[52] - x[55] - x[73] + x[109] == 0.0)\n    @constraint(m, e147, x[110] + x[111] + x[112] + x[122] == 1.0)\n    @constraint(m, e148, x[113] + x[114] + x[115] + x[123] == 1.0)\n    @constraint(m, e149, x[116] + x[117] + x[118] + x[124] == 1.0)\n    @constraint(\n        m,\n        e150,\n        -20 * x[25] + x[56] + x[59] + x[62] + x[65] + x[68] + x[71] <= 0.0\n    )\n    @constraint(\n        m,\n        e151,\n        -5 * x[25] + x[57] + x[60] + x[63] + x[66] + x[69] + x[72] <= 0.0\n    )\n    @constraint(\n        m,\n        e152,\n        -100 * x[25] + x[58] + x[61] + x[64] + x[67] + x[70] + x[73] <= 0.0\n    )\n\n    return m\nend\n\nfunction castro4m2(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    # ----- Variables ----- #\n    @variable(m, 0 <= x[1:55] <= 1E6)\n    @variable(m, obj)\n    @variable(m, b[1:20]) #Additional variables to increase degree of freedom and Ipopt's convergence\n    @objective(m, Min, obj)\n\n    @NLconstraint(m, e45, x[40] * x[44] - x[16] == 0.0)\n    @NLconstraint(m, e46, x[41] * x[44] - x[17] == 0.0)\n    @NLconstraint(m, e47, x[40] * x[45] - x[18] == 0.0)\n    @NLconstraint(m, e48, x[41] * x[45] - x[19] == 0.0)\n    @NLconstraint(m, e49, x[42] * x[46] - x[20] == 0.0)\n    @NLconstraint(m, e50, x[43] * x[46] - x[21] == 0.0)\n    @NLconstraint(m, e51, x[42] * x[47] - x[22] == 0.0)\n    @NLconstraint(m, e52, x[43] * x[47] - x[23] == 0.0)\n    @NLconstraint(m, e53, x[40] * x[50] - x[28] == 0.0)\n    @NLconstraint(m, e54, x[41] * x[50] - x[29] == 0.0)\n    @NLconstraint(m, e55, x[42] * x[51] - x[30] == 0.0)\n    @NLconstraint(m, e56, x[43] * x[51] - x[31] == 0.0)\n    @NLconstraint(m, e57, x[14] * x[44] - x[1] == 0.0)\n    @NLconstraint(m, e58, x[14] * x[45] - x[2] == 0.0)\n    @NLconstraint(m, e59, x[15] * x[46] - x[3] == 0.0)\n    @NLconstraint(m, e60, x[15] * x[47] - x[4] == 0.0)\n    @NLconstraint(m, e61, x[14] * x[50] - x[7] == 0.0)\n    @NLconstraint(m, e62, x[15] * x[51] - x[8] == 0.0)\n\n    @constraint(m, e1, -x[14] - x[15] + obj == 0.0)\n    @constraint(m, e2, -x[5] - x[9] - x[10] == -40.0)\n    @constraint(m, e3, -x[6] - x[11] - x[12] == -40.0)\n    @constraint(m, e4, -x[1] - x[3] - x[9] - x[11] + x[14] == 0.0)\n    @constraint(m, e5, -x[2] - x[4] - x[10] - x[12] + x[15] == 0.0)\n    @constraint(m, e6, -x[1] - x[2] - x[7] + x[14] == 0.0)\n    @constraint(m, e7, -x[3] - x[4] - x[8] + x[15] == 0.0)\n    @constraint(m, e8, -x[5] - x[6] - x[7] - x[8] + x[13] == 0.0)\n    @constraint(m, e9, -x[24] - x[32] - x[34] == -4000.0)\n    @constraint(m, e10, -x[25] - x[33] - x[35] == -800.0)\n    @constraint(m, e11, -x[26] - x[36] - x[38] == -600.0)\n    @constraint(m, e12, -x[27] - x[37] - x[39] == -8000.0)\n    @constraint(m, e13, -x[32] + 4000 * x[52] == 0.0)\n    @constraint(m, e14, -x[33] + 800 * x[52] == 0.0)\n    @constraint(m, e15, -x[34] + 4000 * x[53] == 0.0)\n    @constraint(m, e16, -x[35] + 800 * x[53] == 0.0)\n    @constraint(m, e17, -x[36] + 600 * x[54] == 0.0)\n    @constraint(m, e18, -x[37] + 8000 * x[54] == 0.0)\n    @constraint(m, e19, -x[38] + 600 * x[55] == 0.0)\n    @constraint(m, e20, -x[39] + 8000 * x[55] == 0.0)\n    @constraint(m, e21, -x[24] + 4000 * x[48] == 0.0)\n    @constraint(m, e22, -x[25] + 800 * x[48] == 0.0)\n    @constraint(m, e23, -x[26] + 600 * x[49] == 0.0)\n    @constraint(m, e24, -x[27] + 8000 * x[49] == 0.0)\n    @constraint(m, e25, -x[9] + 40 * x[52] == 0.0)\n    @constraint(m, e26, -x[10] + 40 * x[53] == 0.0)\n    @constraint(m, e27, -x[11] + 40 * x[54] == 0.0)\n    @constraint(m, e28, -x[12] + 40 * x[55] == 0.0)\n    @constraint(m, e29, -x[5] + 40 * x[48] == 0.0)\n    @constraint(m, e30, -x[6] + 40 * x[49] == 0.0)\n    @constraint(m, e31, x[48] + x[52] + x[53] == 1.0)\n    @constraint(m, e32, x[49] + x[54] + x[55] == 1.0)\n    @constraint(m, e33, -200 * x[14] + x[16] + x[20] + x[32] + x[36] <= 0.0)\n    @constraint(m, e34, -200 * x[14] + x[17] + x[21] + x[33] + x[37] <= 0.0)\n    @constraint(m, e35, -200 * x[15] + x[18] + x[22] + x[34] + x[38] <= 0.0)\n    @constraint(m, e36, -200 * x[15] + x[19] + x[23] + x[35] + x[39] <= 0.0)\n    @constraint(\n        m,\n        e37,\n        0.05 * x[16] + 0.05 * x[20] + 0.05 * x[32] + 0.05 * x[36] - x[40] == 0.0\n    )\n    @constraint(m, e38, x[17] + x[21] + x[33] + x[37] - x[41] == 0.0)\n    @constraint(m, e39, x[18] + x[22] + x[34] + x[38] - x[42] == 0.0)\n    @constraint(\n        m,\n        e40,\n        0.024 * x[19] + 0.024 * x[23] + 0.024 * x[35] + 0.024 * x[39] - x[43] == 0.0\n    )\n    @constraint(m, e41, -x[16] - x[18] - x[28] + x[40] == 0.0)\n    @constraint(m, e42, -x[17] - x[19] - x[29] + x[41] == 0.0)\n    @constraint(m, e43, -x[20] - x[22] - x[30] + x[42] == 0.0)\n    @constraint(m, e44, -x[21] - x[23] - x[31] + x[43] == 0.0)\n    @constraint(m, e63, x[44] + x[45] + x[50] == 1.0)\n    @constraint(m, e64, x[46] + x[47] + x[51] == 1.0)\n    @constraint(m, e65, -10 * x[13] + x[24] + x[26] + x[28] + x[30] <= 0.0)\n    @constraint(m, e66, -10 * x[13] + x[25] + x[27] + x[29] + x[31] <= 0.0)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/circle.jl",
    "content": "function circle(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:2] <= 2)\n    @NLconstraint(m, x[1]^2 + x[2]^2 >= 2)\n    @objective(m, Min, x[1] + x[2])\n\n    return m\nend\n\nfunction circle_MINLPLib(; solver = nothing)\n    # Source: https://www.minlplib.org/circle.html \n    # Above instance has been mofified to convert the problem into a non-convex NLP\n    # Global solution: 4.45670663096, arg min =  [4.2536125, 3.4367961]\n\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= objvar <= 5)\n    @variable(m, 1 <= x[1:2] <= 5)\n\n    @NLconstraint(\n        m,\n        e1,\n        (2.545724188 - x[1])^2 + (9.983058643 - x[2])^2 - (objvar)^2 >= 0.0\n    )\n    @NLconstraint(\n        m,\n        e2,\n        (8.589400372 - x[1])^2 + (6.208600402 - x[2])^2 - (objvar)^2 >= 0.0\n    )\n    @NLconstraint(\n        m,\n        e3,\n        (5.953378204 - x[1])^2 + (9.920197351 - x[2])^2 - (objvar)^2 >= 0.0\n    )\n    @NLconstraint(\n        m,\n        e4,\n        (3.710241136 - x[1])^2 + (7.860254203 - x[2])^2 - (objvar)^2 >= 0.0\n    )\n    @NLconstraint(\n        m,\n        e5,\n        (3.629909053 - x[1])^2 + (2.176232347 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n    @NLconstraint(\n        m,\n        e6,\n        (3.016475803 - x[1])^2 + (6.757468831 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n    @NLconstraint(\n        m,\n        e7,\n        (4.148474536 - x[1])^2 + (2.435660776 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n    @NLconstraint(\n        m,\n        e8,\n        (8.706433123 - x[1])^2 + (3.250724797 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n    @NLconstraint(\n        m,\n        e9,\n        (1.604023507 - x[1])^2 + (7.020357481 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n    @NLconstraint(\n        m,\n        e10,\n        (5.501896021 - x[1])^2 + (4.918207429 - x[2])^2 - (objvar)^2 <= 0.0\n    )\n\n    @objective(m, Min, objvar)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/convex.jl",
    "content": "function convex_test(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:5] <= 2)\n\n    @constraint(m, 3 * x[1] * x[1] + 4 * x[2] * x[2] <= 25)                             # 1: true\n    @constraint(m, 3 * x[1] * x[1] - 25 + 4 * x[2] * x[2] <= 0)                         # 2: true\n    @constraint(m, 3(x[1]x[1]) + 4 * x[2] * x[2] <= -5)                             # 3: false\n    @constraint(m, 3(x[1]x[1]) + 4 * x[2]^2 <= 10)                                # 4: true\n    @constraint(m, 3x[1]^2 + 4x[2]^2 + 6x[3]^2 <= 10)                           # 5: true\n\n    # @NLconstraint(m, 3x[1]^0.5 + 4x[2]^0.5 + 5x[5]^0.5 <= 100)# 6: true | type-C\n    # @NLconstraint(m, -3x[1]^0.5 - 4x[2]^0.5 >= -100)# 7: true | type-C\n    @NLconstraint(m, x[1]^2 <= 2) # convex - dummy\n    @NLconstraint(m, x[2]^2 <= 2) # convex - dummy\n\n    @NLconstraint(m, 3x[1]^3 + x[2]^3 + 5x[3]^3 <= 200)                         # 8: true | type-a\n    @NLconstraint(\n        m,\n        x[1] * x[1] * x[1] +\n        x[2] * x[2] * x[2] +\n        x[3] * x[3] * x[3] +\n        5 * x[4] * 20 * x[4] * x[4] <= 200\n    ) # 9: true\n    @NLconstraint(m, 3 * x[1] * x[1] + 4 * x[2] * x[2] <= 25)                           # 10: true\n\n    @NLconstraint(m, (3 * x[1] * x[1] + 4 * x[2] * x[2]) <= 25)                         # 11: true\n    @NLconstraint(m, 3 * x[1] * x[1] + 4 * x[2] * x[2] - 25 <= 0)                       # 12: true\n    @NLconstraint(m, -3 * x[1] * x[1] - 4 * x[2] * x[2] >= -25)                          # 13: true\n    @NLconstraint(m, 3 * x[1] * x[1] + 5x[2] * x[2] <= 25)                            # 14: true\n    @NLconstraint(m, x[1] * 3 * x[1] + x[2] * x[2] * 5 + x[4]^(3 - 1) <= 25)              # 15: true\n\n    @NLconstraint(m, 4 * x[1]^2 + 5x[2]^2 <= 25)                                  # 16: true\n    @NLconstraint(m, 3 * x[1] * x[1] - 25 + 4 * x[2] * x[2] <= 0)                       # 17: false (unsupported when with @NLconstraint)\n    @NLconstraint(m, 3 * x[1] * x[1] + 4 * x[2] * x[1] <= 25)                           # 18: false\n    @NLconstraint(m, 3 * x[1] * x[1] + 16 * x[2]^2 <= 40)                             # 19: true\n    @NLconstraint(m, 3 * x[1]^2 + 16 * x[2]^2 + 17 <= 16)                           # 20: false\n\n    @NLconstraint(m, 3 * x[1]^3 + 16 * x[2]^2 <= 20 - 20)                           # 21: false\n    @NLconstraint(\n        m,\n        3 * x[1] * x[1] + 4 * x[2] * x[2] + 5 * x[3] * x[3] + 6x[4]x[4] <= 15\n    ) # 22: true\n    @NLconstraint(m, 3x[1]x[1] + 4x[2]x[2] + 5x[3]^2 <= -15)                    # 23: false\n    @NLconstraint(m, 3x[1]^2 + 4x[2]^2 >= 15)                                   # 24: false\n    @NLconstraint(m, sum(x[i]^2 for i in 1:5) <= 99999)                         # 25: true\n\n    @NLconstraint(m, 3x[1]^4 + 4x[2]^4 <= 200)                                  # 26: true\n    @NLconstraint(m, 3x[1]^4 + 4x[2]x[2]x[2]x[2] - 200 <= 0)                    # 27: true\n    @NLconstraint(m, 3x[1]^4 + 4x[2]^2 * x[2] * x[2] <= 200)                        # 28: true\n    @NLconstraint(m, 3x[1]^4 + 4x[2]^3 <= 200)                                  # 29: false\n    @NLconstraint(m, 3x[1]^8 + 16 * 25 * x[2]^8 - 30x[3]^8 <= 50)                   # 30: false\n\n    @objective(m, Max, x[1]^2 + x[3]^2)                                           # true\n\n    return m\nend\n\nfunction convex_solve(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:5] <= 100)\n\n    @NLconstraint(m, 3 * x[1] * x[1] + 4 * x[2] * x[2] <= 25)                             # 1: true\n    @NLconstraint(m, 3(x[1]x[1]) + 4 * x[2]^2 <= 10)                                # 4: true\n    @NLconstraint(m, 3x[1]^2 + 4x[2]^2 + 6x[3]^2 <= 10)                           # 5: true\n    @NLconstraint(m, (x[1] + x[2])^2 <= 100)\n    @NLconstraint(m, -3 * x[1] * x[1] - 4 * x[2] * x[2] >= -25)                            # 13: true\n\n    @objective(m, Max, x[1]^2 + x[3]^2)                                             # true\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/discretemulti.jl",
    "content": "function binprod_nlp3(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    LB = [100, 1000, 1000, 10, 10, 10, 10, 10]\n    UB = [10000, 10000, 10000, 1000, 1000, 1000, 1000, 1000]\n\n    @variable(m, LB[i] <= x[i = 1:8] <= UB[i])\n    @variable(m, 0 <= y[1:5] <= 1, Bin)\n\n    @constraint(m, 0.0025 * (x[4] * y[1] + x[6] * y[2]) <= 1)\n    @constraint(m, 0.0025 * (x[5] - x[4] * y[1] + x[7]) <= 1)\n    @constraint(m, 0.01(x[8] - x[5] * y[3]) <= 1)\n    @NLconstraint(\n        m,\n        100 * x[1] - x[1] * x[6] * y[1] + 833.33252 * x[4] * y[1] <= 83333.333\n    )\n    @NLconstraint(m, x[2] * x[4] * y[4] - x[2] * x[7] - 1250 * x[4] + 1250 * x[5] <= 0)\n    @NLconstraint(\n        m,\n        x[3] * x[5] * y[2] * y[5] - x[3] * x[8] * y[5] - 2500 * x[5] * y[1] * y[4] +\n        1250000 <= 0\n    )\n\n    @NLconstraint(m, y[1] * y[2] * y[3] <= 0)\n    @NLconstraint(m, y[2] * y[3] >= y[4] * y[5])\n    @NLconstraint(m, y[1] * y[5] <= y[2] * y[4])\n\n    @objective(m, Min, x[1] + x[2] + x[3])\n\n    return m\nend\n\nfunction circlebin(; verbose = false, solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:5] <= 1, Bin)\n    @NLconstraint(m, x[1]^2 + x[2]^2 >= 2)\n    @objective(m, Min, x[1] + x[2])\n\n    return m\nend\n\nfunction bpml(; verbose = false, solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:5] <= 1, Bin)\n    @variable(m, y[1:5] >= 0)\n\n    @NLconstraint(m, x[1] * y[1] >= 10)\n    @NLconstraint(m, x[1] * x[2] * y[1] >= 10)\n    @NLconstraint(m, x[1] * x[2] * x[3] * y[1] >= 10)\n    @NLconstraint(m, x[1] * y[1] * y[2] >= 10)\n    @NLconstraint(m, x[1] * y[1] * y[2] * y[3] >= 10)\n    @NLconstraint(m, x[1] * x[2] * x[3] * y[1] * y[2] * y[3] >= 10)\n    @NLconstraint(m, x[1] * x[2] * x[3] * x[4] * x[5] >= 1)\n    @NLconstraint(m, y[1] * y[2] * y[4] * y[5] * y[1] >= 99)\n\n    @objective(m, Min, x[1] + x[2] + x[3])\n\n    return m\nend\n\nfunction bmpl_linearlifting(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0 <= x[1:5] <= 1, Bin)\n    @variable(m, y[1:5] >= 0)\n\n    @NLconstraint(m, 15 * x[1] * (2 * y[1] + y[2]) >= 10)\n    @NLconstraint(m, 15 * (x[1] + x[2] * y[1]) * (y[1] + y[2] * x[1] * x[2]) + 10 >= 10)\n    @NLconstraint(m, 15 * x[2] * (y[1] + y[2] * x[3] * y[5] * x[4]) + 50 >= 10)\n\n    @NLobjective(m, Min, x[1] * (y[1] * y[2] * y[3] + x[2] * x[3]))\n\n    return m\nend\n\nfunction bpml_lnl(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    Random.seed!(10)\n    @variable(m, 0 <= X[1:5] <= 1, Bin)\n    @variable(m, 0.1 <= Y[1:5] <= 0.1 + 10 * rand())\n    @constraint(m, sum(X) >= 3)\n    @NLobjective(m, Min, sum(X[i] * Y[i] for i in 1:5))\n\n    return m\nend\n\nfunction bpml_binl(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    Random.seed!(10)\n    @variable(m, 0 <= X[1:5] <= 1, Bin)\n    @variable(m, 50 <= Y[1:5] <= 50 + 100 * rand() * rand())\n    @constraint(m, sum(X) >= 3)\n    @NLobjective(m, Max, sum(X[i] * Y[i] * Y[i+1] for i in 1:4) - X[5] * Y[5] * Y[1])\n\n    return m\nend\n\nfunction bpml_monl(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    Random.seed!(10)\n    @variable(m, 0 <= X[1:5] <= 1, Bin)\n    @variable(m, 50 <= Y[1:5] <= 50 + 100 * rand() * rand())\n    @constraint(m, sum(X) >= 3)\n    @NLobjective(m, Max, sum(X[i] * Y[i] * Y[i] for i in 1:5))\n\n    return m\nend\n\nfunction bpml_negative(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    Random.seed!(10)\n    @variable(m, 0 <= X[1:5] <= 1, Bin)\n    @variable(m, 50 <= Y[1:5] <= 50 + 100 * rand() * rand())\n    JuMP.set_lower_bound(Y[1], -10)\n    JuMP.set_upper_bound(Y[1], -1)\n    JuMP.set_lower_bound(Y[2], -40)\n    JuMP.set_lower_bound(Y[3], -30)\n    JuMP.set_lower_bound(Y[4], -50)\n    @constraint(m, sum(X) >= 3)\n    @NLobjective(m, Max, sum(X[i] * Y[i] * Y[i+1] for i in 1:4) - X[5] * Y[5] * Y[1])\n\n    return m\nend\n\nfunction intprod_basic(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 1 <= Z[1:10] <= 10, Int)\n    @NLconstraint(m, (Z[1] + Z[2]) * (Z[3] + Z[4]) >= 25)\n    @NLconstraint(m, Z[1] * (Z[2] + Z[3]) * Z[4] >= 25)\n    @NLconstraint(m, Z[1] - Z[2] * Z[3] * Z[4] + 15 >= 25)\n    @NLconstraint(m, Z[5] * (Z[2] - Z[3]) * Z[5]^2 >= 40)\n    @NLobjective(m, Min, sum(Z[i] for i in 1:5) * Z[2])\n\n    return m\nend\n\nfunction discretemulti_basic(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    Random.seed!(10)\n    @variable(m, 0 <= X[1:5] <= 1, Bin)\n    @variable(m, 0.1 <= Y[1:5] <= 0.1 + 10 * rand())\n    @variable(m, 1 <= Z[1:5] <= 10, Int)\n    @constraint(m, sum(X) >= 3)\n    @constraint(m, sum(Z) >= 10)\n    @NLobjective(m, Min, sum(X[i] * Y[i] for i in 1:5))\n    @NLconstraint(m, sum(X[i] * Z[i] for i in 1:5) >= 8)\n    @NLconstraint(m, [i in 1:5], Y[i] * Z[i] >= 17.1)\n    @NLconstraint(m, [i in 1:4], Y[i] * Z[i] * Z[i+1] >= 18.6)\n    @NLconstraint(m, [i in 1:5], X[i] * Y[i] * Z[i] <= 28.1)\n    @NLconstraint(m, [i in 1:4], X[i] * X[i+1] * Y[i] * Y[i+1] * Z[i] * Z[i+1] <= 33.2)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/div.jl",
    "content": "function div(; verbose = false, solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 1 <= x[1:2] <= 10)\n\n    @NLobjective(m, Min, 6 * x[1]^2 + 4 * x[2]^2 - 2.5 / 5 * x[1] * x[2])\n\n    @constraint(m, x[1] * (-1 * 3 / 5 * 5) >= 0)\n    @constraint(m, x[2] * 5 / 20 >= 0)\n    @constraint(m, x[2] * (5 * 15 / 15) >= 0)\n    @constraint(m, x[2] * (120 * 2 / -2) >= 0)\n    @constraint(m, 1 * 2 * 3 * 4 * 5 * 6 * x[2] / 0.01 >= 0)\n    @constraint(m, x[1] * 1 * 2 * 3 * 4 * 5 * 6 / 0.01 >= 0)\n    @NLconstraint(m, (3 / 5) * x[1] * (60 / 60) * x[2] >= 8)\n    @NLconstraint(\n        m,\n        (1 * 2 * 3 * 4 / 5 / 6 * 7) * x[2] - x[1] * 1 * 2 * 3 * 4 * 5 * 6 * x[2] / 0.01 >=\n        0\n    )\n    @NLconstraint(\n        m,\n        (1 * 2 * 3 * 4 / 5 / 6 * 7) * x[2] -\n        0.5(x[1] * 1 * 2 * 3 * 4 * 5 * 6 * x[2] / 0.01) >= 0\n    )\n    @NLconstraint(\n        m,\n        (1 * 2 * 3 * 4 / 5 / 6 * 7) * x[2] -\n        0.5(x[1] * 2 * 3 * x[2] / 0.01 + 5 * 7 / 10 * x[2]) >= 0\n    )\n    @NLconstraint(m, (1 * 2 * 3 * 4 / 5 / 6 * 7) * x[2] - 0.5 * (x[1] - x[2]x[1]) >= 0)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/exprstest.jl",
    "content": "function exprstest(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, px[i = 1:6] >= 1) # At some point if an initial value is given, keep them\n\n    @NLconstraint(m, sum(3 * px[i]^2 for i in 1:4) >= 111)\n    @NLconstraint(m, -px[1] * px[2] + 4 * 5 * px[3] * px[4] >= 222)\n    @NLconstraint(m, -px[1] * px[2] <= 115)\n    @NLconstraint(m, -px[1] * -px[2] >= 115)\n    @NLconstraint(m, px[1] * -px[2] <= 115)\n    @constraint(m, -px[1] + (-5) - 4 <= 100)\n    @NLconstraint(m, px[1] + px[2] * px[3] >= 555) # => px[1] + x23 >= 555 && x23 == px[2]*px[3]\n    @NLconstraint(m, px[1]^2 - 7 * px[2]^2 + px[3]^2 + px[4] <= 6666)\n    @NLconstraint(m, 13 * px[1] - px[2] + 5 * px[3] * 6 + px[4] >= 77)\n\n    @NLobjective(\n        m,\n        Min,\n        7 * px[1] * 6 * px[4] * 2 +\n        5 +\n        17 +\n        px[1] +\n        px[2] +\n        px[3] +\n        8 +\n        3 * 5 * px[1]^2 * 4\n    )\n\n    return m\nend\n\nfunction operator_b(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[1:4] >= 0)\n    @variable(m, y[1:3] <= 0)\n    # PARSING TARGETS #\n    @constraint(m, x[1] + x[2] + -y[1] >= 1)# None\n    @constraint(m, 5x[1] + 8x[2] + 9y[2] <= 2)# None\n    @constraint(m, 4 * x[1] + 5 * x[2] + -3 * y[1] >= 3)# None\n    # @constraint(m, 3 <= x[1] + x[2] <= 4)\t\t\t\t\t\t# None\n\n    @NLconstraint(m, x[1] * x[2] + 3 * x[2] * x[3] >= 5)# x[1]*x[2] and 3*x[2]*x[3]\n    @NLconstraint(m, x[1] * (x[2] + 4) + 10 * 44 * x[2] * 5 * x[3] <= 6)# x[2]*x[3]\n    @NLconstraint(m, x[1] * 4 + x[2] * (x[2] + x[3]) >= 7)# None\n    @NLconstraint(m, 3 * x[1] * x[2] + x[2] - x[3] <= 8)# x[1]*x[2]\n\n    @NLconstraint(m, -1 * x[1]^2 - x[2]^2 >= 9)# x[1]^2 and x[2]^2\n    @NLconstraint(m, x[1]^(1 + 1) + 5 * x[2]^2 + 3 * x[3]^3 <= 10)# x[1]^2 and x[2]^2\n    @NLconstraint(m, (x[1] + 5)^2 >= 11)# None\n    @NLconstraint(m, x[1]^3 + x[3]^99 >= 12)# None\n\n    @NLconstraint(m, x[1] * x[2] * x[3] <= 13)# x[1]*x[2]*x[3]\n    @NLconstraint(m, (x[1] * x[2]) * x[3] >= 14)# x[1]*x[2]  ******\n    @NLconstraint(m, x[1] * (x[2] * x[3]) <= 15)# x[2]*x[3]  ******\n    @NLconstraint(m, x[1] * x[2] * x[3] * x[4] >= 16)# x[1]*x[2]*x[3]*x[4]\n    @NLconstraint(m, (x[1] * x[2]) * (x[3] * x[4]) <= 17)# x[1]*x[2] and x[3]*x[4]\n    @NLconstraint(m, x[1] * (x[2] * x[3]) * x[4] >= 18)# x[2]*x[3]  ******\n    @NLconstraint(m, (x[1] * x[2]) * x[3] * x[4] <= 19)# x[1]*x[2]  ******\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]) * x[4] >= 20)# x[1]*x[2]\t ******\n    @NLconstraint(m, (x[1] * (x[2] * x[3]) * x[4]) <= 21)# x[2]*x[3]\t ******\n\n    @NLconstraint(m, 4 * 5 * 6 * x[1] * x[2] * x[3] * x[4] >= 22)# x[1]*x[2]*x[3]*x[4]\n    @NLconstraint(m, x[1]^2 * x[2]^2 * x[3]^2 * x[4] <= 23)# None\n    @NLconstraint(m, x[1] * x[1] * x[2] * x[2] * x[3] * x[3] >= 24)# x[1]*x[1]*x[2]*x[2]*x[3]*x[3]\n    @NLconstraint(m, (x[1] + 1) * (x[2] + 2) * (x[3] + 3) * (x[4] + 4) <= 25)# None\n\n    @NLconstraint(m, 50sin(x[1]) - 32 * cos(x[2]) >= 26)# sin(x[1]), cos(x[2])\n    @NLconstraint(m, sin(x[1] + x[2]) - cos(x[2] - x[3]) + sin(-x[2] + x[3]) <= 27)\n    @NLconstraint(m, sin(4 * x[1] * x[2]) + cos(x[2] * -1 * x[3]) >= 28)# x[1]*x[2] and x[2]*-1*x[3]  ******\n    @NLconstraint(m, sin(x[1] * x[2] * x[3]) <= 29)# x[1]*x[2]*x[3]\n\n    return m\nend\n\nfunction operator_basic(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[1:4] >= 0)\n\n    @NLconstraint(m, x[1]^2 >= 1)\n    @NLconstraint(m, x[1] * x[2] <= 1)\n    @NLconstraint(m, x[1]^2 + x[2] * x[3] <= 1)\n\n    @NLconstraint(m, x[1] * (x[2] * x[3]) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2]^2 * x[3]^2) <= 1)\n\n    @NLconstraint(m, (x[1] * x[2]) * x[3] >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]^2) * x[3]^2 <= 1)\n\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3]^2) >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * x[3]^2 <= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3]) >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2) * x[3] <= 1)\n\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]) * x[4] >= 1)\n    @NLconstraint(m, ((x[1]^2 * x[2]) * x[3]) * x[4] <= 1)\n    @NLconstraint(m, ((x[1] * x[2]^2) * x[3]) * x[4] >= 1)\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]^2) * x[4] <= 1)\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]) * x[4]^2 >= 1)\n    @NLconstraint(m, ((x[1]^2 * x[2]^2) * x[3]^2) * x[4]^2 <= 1)\n\n    @NLconstraint(m, x[1] * (x[2] * (x[3] * x[4])) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * (x[3] * x[4])) <= 1)\n    @NLconstraint(m, x[1] * (x[2]^2 * (x[3] * x[4])) >= 1)\n    @NLconstraint(m, x[1] * (x[2] * (x[3]^2 * x[4])) <= 1)\n    @NLconstraint(m, x[1] * (x[2] * (x[3] * x[4]^2)) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2]^2 * (x[3]^2 * x[4]^2)) <= 1)\n\n    @NLconstraint(m, x[1] * x[2] * x[3] >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3] >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3] >= 1)\n    @NLconstraint(m, x[1] * x[2] * x[3]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * x[2]^2 * x[3] >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * x[2]^2 * x[3]^2 >= 1)\n\n    @NLconstraint(m, (x[1] * x[2]) * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2) * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * (x[3]^2 * x[4]) >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * (x[3]^2 * x[4]^2) >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * (x[3] * x[4]^2) >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * (x[3]^2 * x[4]) >= 1)\n\n    @NLconstraint(m, x[1] * x[2] * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1] * x[2] * x[3]^2 * x[4]^2 >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3]^2 * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3] * x[4]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * x[2]^2 * x[3]^2 * x[4]^2 >= 1)\n\n    @NLconstraint(m, (x[1] * x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2 * x[3]) * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2] * x[3]^2) * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2] * x[3]) * x[4]^2 >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]^2 * x[3]^2) * x[4]^2 >= 1)\n\n    @NLconstraint(m, x[1] * (x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3]^2) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3]) * x[4]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3]) * x[4]^2 >= 1)\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3]^2) * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2]^2 * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3]^2) * x[4]^2 >= 1)\n\n    @NLconstraint(m, x[1] * (x[2] * x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3]^2 * x[4]) >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3] * x[4]^2) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3]^2 * x[4]) >= 1)\n    @NLconstraint(m, x[1]^2 * (x[2]^2 * x[3]^2 * x[4]^2) >= 1)\n\n    @NLconstraint(m, x[1] * x[2] * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * (x[3] * x[4]) >= 1)\n    @NLconstraint(m, x[1] * x[2] * (x[3]^2 * x[4]) >= 1)\n    @NLconstraint(m, x[1] * x[2] * (x[3] * x[4]^2) >= 1)\n    @NLconstraint(m, x[1]^2 * x[2]^2 * (x[3]^2 * x[4]^2) >= 1)\n\n    @NLconstraint(m, (x[1] * x[2]) * x[3] * x[4] >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * x[3] * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2) * x[3] * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3]^2 * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3] * x[4]^2 >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3]^2 * x[4]^2 >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]^2) * x[3]^2 * x[4]^2 >= 1)\n\n    return m\nend\n\nfunction operator_c(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, px[i = 1:6] >= 1) # At some point if an initial value is given, keep them\n\n    @NLconstraint(m, sum(3 * px[i]^2 for i in 1:4) >= 111)\n    @NLconstraint(m, -1 * px[1] * px[2] + 4 * 5 * px[3] * px[4] >= 222)\n    @NLconstraint(m, px[1] + px[2] * px[3] >= 555) # => px[1] + x23 >= 555 && x23 == px[2]*px[3]\n    @NLconstraint(m, px[1]^2 - 7 * px[2]^2 + px[3]^2 + px[4] <= 6666)\n    @NLconstraint(m, 13 * px[1] - px[2] + 5 * px[3] * 6 + px[4] >= 77)\n\n    @NLobjective(\n        m,\n        Min,\n        7 * px[1] * 6 * px[4] * 2 +\n        5 +\n        17 +\n        px[1] +\n        px[2] +\n        px[3] +\n        8 +\n        3 * 5 * px[1]^2 * 4\n    )\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/linearlift.jl",
    "content": "function basic_linear_lift(; verbose = false, solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[i = 1:3] >= 1) # At some point if an initial value is given, keep them\n    @constraint(m, (x[1] - x[2]) * (3 * x[2] - x[3]) >= 111)\n    @NLconstraint(m, (x[1] - x[2]) * (3 * x[2] - x[3]) >= 111)\n    @NLconstraint(m, (x[1] - x[2])^2 >= 100)\n    @NLconstraint(m, (x[1] - x[2]) * (3 * x[2] - x[3]) * (x[1] + x[3]) >= 111)\n    @NLconstraint(m, (3 + x[1] + x[2] + x[3]) * (x[1] + x[2])^2 >= 111)\n\n    # Next level goal\n    # @NLconstraint(m, (9-x[1]-x[2]-x[3])^2 >= 111)\n\n    @objective(m, Min, x[1] + x[2] + x[3])\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/mult3.jl",
    "content": "function linking_constraints_testing(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    x_Idx = Any[1, 2, 3, 4]\n    @variable(m, 0 <= x[x_Idx] <= 1)\n    @variable(m, obj)\n    @objective(m, Min, obj)\n    @NLconstraint(\n        m,\n        e1,\n        -(\n            0.4931 * x[1] * x[2] + 0.6864 * x[1] * x[3] - 0.0577 * x[1] * x[4] +\n            0.3468 * x[1] * x[2] * x[3] - 0.6988 * x[1] * x[3] * x[4] -\n            0.9648 * x[1] * x[2] * x[4]\n        ) + obj == 0.0\n    )\n\n    return m\nend\n\nfunction m_10_3_0_100_1(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    x_Idx = Any[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n    @variable(m, 0 <= x[x_Idx] <= 1)\n    @variable(m, obj)\n    @objective(m, Min, obj)\n    @NLconstraint(\n        m,\n        e1,\n        -(\n            0.4931 * x[1] * x[2] +\n            0.6864 * x[1] * x[3] +\n            0.0577 * x[1] * x[4] +\n            0.331 * x[1] * x[5] +\n            0.4615 * x[1] * x[6] - 0.1788 * x[1] * x[7] - 0.2886 * x[1] * x[8] +\n            0.4708 * x[1] * x[9] - 0.0574 * x[1] * x[10] - 0.0747 * x[2] * x[3] +\n            0.5194 * x[2] * x[4] +\n            0.4049 * x[2] * x[5] - 0.4841 * x[2] * x[6] + 0.8754 * x[2] * x[7] -\n            0.0878 * x[2] * x[8] +\n            0.617 * x[2] * x[9] +\n            0.8177 * x[2] * x[10] +\n            0.3898 * x[3] * x[4] - 0.561 * x[3] * x[5] +\n            0.7099 * x[3] * x[6] +\n            0.4888 * x[3] * x[7] - 0.3978 * x[3] * x[8] +\n            0.3439 * x[3] * x[9] +\n            0.2374 * x[3] * x[10] +\n            0.9351 * x[4] * x[5] +\n            0.9805 * x[4] * x[6] - 0.324 * x[4] * x[7] + 0.8415 * x[4] * x[8] -\n            0.3219 * x[4] * x[9] +\n            0.8619 * x[4] * x[10] +\n            0.0931 * x[5] * x[6] - 0.069 * x[5] * x[7] - 0.6462 * x[5] * x[8] -\n            0.244 * x[5] * x[9] - 0.6496 * x[5] * x[10] - 0.2863 * x[6] * x[7] +\n            0.3314 * x[6] * x[8] +\n            0.2371 * x[6] * x[9] - 0.0621 * x[6] * x[10] - 0.3675 * x[7] * x[8] -\n            0.4622 * x[7] * x[9] - 0.6002 * x[7] * x[10] - 0.1691 * x[8] * x[9] +\n            0.9586 * x[8] * x[10] +\n            0.0864 * x[9] * x[10] - 0.741 * x[1] +\n            0.6095 * x[2] +\n            0.6916 * x[3] +\n            0.4181 * x[4] +\n            0.0579 * x[5] +\n            0.3277 * x[6] +\n            0.8015 * x[7] +\n            0.8823 * x[8] - 0.7712 * x[9] +\n            0.7333 * x[10] +\n            0.9951 * x[1] * x[2] * x[3] +\n            0.1336 * x[1] * x[2] * x[4] +\n            0.9318 * x[1] * x[2] * x[5] +\n            0.4959 * x[1] * x[2] * x[6] - 0.2652 * x[1] * x[2] * x[7] -\n            0.0387 * x[1] * x[2] * x[8] - 0.8525 * x[1] * x[2] * x[9] -\n            0.9893 * x[1] * x[2] * x[10] - 0.3058 * x[1] * x[3] * x[4] -\n            0.3155 * x[1] * x[3] * x[5] - 0.5641 * x[1] * x[3] * x[6] -\n            0.7337 * x[1] * x[3] * x[7] + 0.801 * x[1] * x[3] * x[8] -\n            0.2265 * x[1] * x[3] * x[9] - 0.109 * x[1] * x[3] * x[10] +\n            0.3239 * x[1] * x[4] * x[5] - 0.9678 * x[1] * x[4] * x[6] +\n            0.3017 * x[1] * x[4] * x[7] +\n            0.2928 * x[1] * x[4] * x[8] - 0.354 * x[1] * x[4] * x[9] +\n            0.7114 * x[1] * x[4] * x[10] - 0.1974 * x[1] * x[5] * x[6] -\n            0.5863 * x[1] * x[5] * x[7] +\n            0.9371 * x[1] * x[5] * x[8] +\n            0.1968 * x[1] * x[5] * x[9] +\n            0.346 * x[1] * x[5] * x[10] - 0.0862 * x[1] * x[6] * x[7] -\n            0.34 * x[1] * x[6] * x[8] - 0.7992 * x[1] * x[6] * x[9] +\n            0.5109 * x[1] * x[6] * x[10] +\n            0.2114 * x[1] * x[7] * x[8] +\n            0.4381 * x[1] * x[7] * x[9] +\n            0.7947 * x[1] * x[7] * x[10] +\n            0.3165 * x[1] * x[8] * x[9] - 0.6986 * x[1] * x[8] * x[10] +\n            0.2246 * x[1] * x[9] * x[10] +\n            0.9573 * x[2] * x[3] * x[4] +\n            0.9983 * x[2] * x[3] * x[5] - 0.4864 * x[2] * x[3] * x[6] +\n            0.1017 * x[2] * x[3] * x[7] +\n            0.3181 * x[2] * x[3] * x[8] +\n            0.108 * x[2] * x[3] * x[9] +\n            0.9555 * x[2] * x[3] * x[10] +\n            0.8038 * x[2] * x[4] * x[5] +\n            0.3158 * x[2] * x[4] * x[6] +\n            0.4577 * x[2] * x[4] * x[7] - 0.1951 * x[2] * x[4] * x[8] +\n            0.8573 * x[2] * x[4] * x[9] - 0.7043 * x[2] * x[4] * x[10] +\n            0.3491 * x[2] * x[5] * x[6] +\n            0.5392 * x[2] * x[5] * x[7] - 0.3214 * x[2] * x[5] * x[8] -\n            0.7684 * x[2] * x[5] * x[9] +\n            0.2287 * x[2] * x[5] * x[10] +\n            0.6412 * x[2] * x[6] * x[7] +\n            0.8942 * x[2] * x[6] * x[8] +\n            0.4623 * x[2] * x[6] * x[9] - 0.0048 * x[2] * x[6] * x[10] -\n            0.2504 * x[2] * x[7] * x[8] - 0.157 * x[2] * x[7] * x[9] +\n            0.1058 * x[2] * x[7] * x[10] +\n            0.9958 * x[2] * x[8] * x[9] +\n            0.9808 * x[2] * x[8] * x[10] +\n            0.4926 * x[2] * x[9] * x[10] +\n            0.9075 * x[3] * x[4] * x[5] - 0.8135 * x[3] * x[4] * x[6] +\n            0.468 * x[3] * x[4] * x[7] +\n            0.5035 * x[3] * x[4] * x[8] +\n            0.8937 * x[3] * x[4] * x[9] +\n            0.4124 * x[3] * x[4] * x[10] +\n            0.6276 * x[3] * x[5] * x[6] +\n            0.1172 * x[3] * x[5] * x[7] - 0.8766 * x[3] * x[5] * x[8] -\n            0.0392 * x[3] * x[5] * x[9] + 0.1954 * x[3] * x[5] * x[10] -\n            0.7249 * x[3] * x[6] * x[7] +\n            0.1748 * x[3] * x[6] * x[8] +\n            0.0399 * x[3] * x[6] * x[9] +\n            0.7718 * x[3] * x[6] * x[10] - 0.3924 * x[3] * x[7] * x[8] +\n            0.3393 * x[3] * x[7] * x[9] +\n            0.3299 * x[3] * x[7] * x[10] +\n            0.0074 * x[3] * x[8] * x[9] - 0.4768 * x[3] * x[8] * x[10] -\n            0.8469 * x[3] * x[9] * x[10] - 0.7975 * x[4] * x[5] * x[6] +\n            0.0985 * x[4] * x[5] * x[7] - 0.2488 * x[4] * x[5] * x[8] -\n            0.9697 * x[4] * x[5] * x[9] +\n            0.5858 * x[4] * x[5] * x[10] +\n            0.2418 * x[4] * x[6] * x[7] +\n            0.5472 * x[4] * x[6] * x[8] +\n            0.9072 * x[4] * x[6] * x[9] - 0.7715 * x[4] * x[6] * x[10] -\n            0.3631 * x[4] * x[7] * x[8] + 0.1936 * x[4] * x[7] * x[9] -\n            0.9037 * x[4] * x[7] * x[10] - 0.7716 * x[4] * x[8] * x[9] -\n            0.5681 * x[4] * x[8] * x[10] - 0.7989 * x[4] * x[9] * x[10] -\n            0.8533 * x[5] * x[6] * x[7] - 0.5063 * x[5] * x[6] * x[8] -\n            0.1132 * x[5] * x[6] * x[9] - 0.5833 * x[5] * x[6] * x[10] +\n            0.134 * x[5] * x[7] * x[8] - 0.9514 * x[5] * x[7] * x[9] -\n            0.1594 * x[5] * x[7] * x[10] - 0.2043 * x[5] * x[8] * x[9] +\n            0.9532 * x[5] * x[8] * x[10] +\n            0.3852 * x[5] * x[9] * x[10] - 0.9901 * x[6] * x[7] * x[8] -\n            0.7402 * x[6] * x[7] * x[9] - 0.9064 * x[6] * x[7] * x[10] +\n            0.6796 * x[6] * x[8] * x[9] +\n            0.357 * x[6] * x[8] * x[10] +\n            0.1639 * x[6] * x[9] * x[10] +\n            0.4671 * x[7] * x[8] * x[9] - 0.7679 * x[7] * x[8] * x[10] +\n            0.6806 * x[7] * x[9] * x[10] +\n            0.67 * x[8] * x[9] * x[10]\n        ) + obj == 0.0\n    )\n\n    return m\nend\n\nfunction m_10_3_0_100_2(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    x_Idx = Any[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n    @variable(m, 0 <= x[x_Idx] <= 1)\n    @variable(m, obj)\n    @objective(m, Min, obj)\n    @NLconstraint(\n        m,\n        e1,\n        -(\n            0.9844 * x[1] * x[2] - 0.5504 * x[1] * x[3] +\n            0.8946 * x[1] * x[4] +\n            0.6956 * x[1] * x[5] +\n            0.4003 * x[1] * x[6] +\n            0.1089 * x[1] * x[7] - 0.1168 * x[1] * x[8] - 0.5016 * x[1] * x[9] +\n            0.7953 * x[1] * x[10] - 0.7085 * x[2] * x[3] - 0.1308 * x[2] * x[4] -\n            0.0852 * x[2] * x[5] - 0.3812 * x[2] * x[6] - 0.0382 * x[2] * x[7] +\n            0.3795 * x[2] * x[8] +\n            0.6216 * x[2] * x[9] - 0.2157 * x[2] * x[10] - 0.4137 * x[3] * x[4] +\n            0.152 * x[3] * x[5] +\n            0.4507 * x[3] * x[6] - 0.7145 * x[3] * x[7] - 0.3329 * x[3] * x[8] -\n            0.6792 * x[3] * x[9] +\n            0.0692 * x[3] * x[10] +\n            0.4467 * x[4] * x[5] - 0.5436 * x[4] * x[6] - 0.602 * x[4] * x[7] +\n            0.9452 * x[4] * x[8] +\n            0.9871 * x[4] * x[9] - 0.8361 * x[4] * x[10] - 0.4982 * x[5] * x[6] -\n            0.5683 * x[5] * x[7] - 0.6084 * x[5] * x[8] + 0.7005 * x[5] * x[9] -\n            0.9106 * x[5] * x[10] + 0.7278 * x[6] * x[7] - 0.8657 * x[6] * x[8] -\n            0.1454 * x[6] * x[9] - 0.7254 * x[6] * x[10] - 0.7618 * x[7] * x[8] -\n            0.3881 * x[7] * x[9] +\n            0.2265 * x[7] * x[10] +\n            0.3273 * x[8] * x[9] +\n            0.7918 * x[8] * x[10] +\n            0.5074 * x[9] * x[10] +\n            0.2597 * x[1] - 0.558 * x[2] - 0.0323 * x[3] +\n            0.23 * x[4] +\n            0.9753 * x[5] +\n            0.1184 * x[6] - 0.2582 * x[7] - 0.3248 * x[8] +\n            0.4909 * x[9] +\n            0.1395 * x[10] +\n            0.2647 * x[1] * x[2] * x[3] - 0.5144 * x[1] * x[2] * x[4] -\n            0.6792 * x[1] * x[2] * x[5] - 0.9575 * x[1] * x[2] * x[6] -\n            0.6195 * x[1] * x[2] * x[7] - 0.3753 * x[1] * x[2] * x[8] +\n            0.6193 * x[1] * x[2] * x[9] +\n            0.1474 * x[1] * x[2] * x[10] +\n            0.6525 * x[1] * x[3] * x[4] - 0.4271 * x[1] * x[3] * x[5] -\n            0.679 * x[1] * x[3] * x[6] - 0.3382 * x[1] * x[3] * x[7] -\n            0.4683 * x[1] * x[3] * x[8] +\n            0.0896 * x[1] * x[3] * x[9] +\n            0.107 * x[1] * x[3] * x[10] - 0.9568 * x[1] * x[4] * x[5] -\n            0.7025 * x[1] * x[4] * x[6] - 0.7902 * x[1] * x[4] * x[7] +\n            0.2284 * x[1] * x[4] * x[8] - 0.1874 * x[1] * x[4] * x[9] +\n            0.8031 * x[1] * x[4] * x[10] +\n            0.8857 * x[1] * x[5] * x[6] - 0.6868 * x[1] * x[5] * x[7] +\n            0.8739 * x[1] * x[5] * x[8] - 0.7291 * x[1] * x[5] * x[9] -\n            0.2574 * x[1] * x[5] * x[10] - 0.357 * x[1] * x[6] * x[7] +\n            0.4299 * x[1] * x[6] * x[8] +\n            0.4594 * x[1] * x[6] * x[9] - 0.2428 * x[1] * x[6] * x[10] +\n            0.6579 * x[1] * x[7] * x[8] +\n            0.9073 * x[1] * x[7] * x[9] - 0.3832 * x[1] * x[7] * x[10] +\n            0.1595 * x[1] * x[8] * x[9] - 0.5331 * x[1] * x[8] * x[10] +\n            0.6888 * x[1] * x[9] * x[10] - 0.4837 * x[2] * x[3] * x[4] +\n            0.6795 * x[2] * x[3] * x[5] +\n            0.0753 * x[2] * x[3] * x[6] +\n            0.2431 * x[2] * x[3] * x[7] - 0.0184 * x[2] * x[3] * x[8] -\n            0.4303 * x[2] * x[3] * x[9] - 0.5289 * x[2] * x[3] * x[10] +\n            0.3028 * x[2] * x[4] * x[5] +\n            0.2143 * x[2] * x[4] * x[6] - 0.2037 * x[2] * x[4] * x[7] +\n            0.6976 * x[2] * x[4] * x[8] +\n            0.2752 * x[2] * x[4] * x[9] - 0.4824 * x[2] * x[4] * x[10] -\n            0.2823 * x[2] * x[5] * x[6] + 0.1237 * x[2] * x[5] * x[7] -\n            0.7571 * x[2] * x[5] * x[8] + 0.9569 * x[2] * x[5] * x[9] -\n            0.2336 * x[2] * x[5] * x[10] + 0.4414 * x[2] * x[6] * x[7] -\n            0.2835 * x[2] * x[6] * x[8] +\n            0.8198 * x[2] * x[6] * x[9] +\n            0.0874 * x[2] * x[6] * x[10] +\n            0.9194 * x[2] * x[7] * x[8] +\n            0.8589 * x[2] * x[7] * x[9] +\n            0.2666 * x[2] * x[7] * x[10] - 0.4088 * x[2] * x[8] * x[9] -\n            0.6505 * x[2] * x[8] * x[10] +\n            0.6852 * x[2] * x[9] * x[10] +\n            0.2372 * x[3] * x[4] * x[5] +\n            0.4118 * x[3] * x[4] * x[6] - 0.5151 * x[3] * x[4] * x[7] +\n            0.5959 * x[3] * x[4] * x[8] - 0.218 * x[3] * x[4] * x[9] -\n            0.7801 * x[3] * x[4] * x[10] + 0.5074 * x[3] * x[5] * x[6] -\n            0.9404 * x[3] * x[5] * x[7] +\n            0.4013 * x[3] * x[5] * x[8] +\n            0.0504 * x[3] * x[5] * x[9] +\n            0.5051 * x[3] * x[5] * x[10] +\n            0.2954 * x[3] * x[6] * x[7] +\n            0.7422 * x[3] * x[6] * x[8] +\n            0.6614 * x[3] * x[6] * x[9] +\n            0.9144 * x[3] * x[6] * x[10] - 0.5555 * x[3] * x[7] * x[8] +\n            0.159 * x[3] * x[7] * x[9] +\n            0.9815 * x[3] * x[7] * x[10] +\n            0.6799 * x[3] * x[8] * x[9] - 0.6504 * x[3] * x[8] * x[10] +\n            0.4191 * x[3] * x[9] * x[10] - 0.3969 * x[4] * x[5] * x[6] -\n            0.9499 * x[4] * x[5] * x[7] +\n            0.8335 * x[4] * x[5] * x[8] +\n            0.3776 * x[4] * x[5] * x[9] +\n            0.5135 * x[4] * x[5] * x[10] +\n            0.8655 * x[4] * x[6] * x[7] - 0.89 * x[4] * x[6] * x[8] -\n            0.0021 * x[4] * x[6] * x[9] - 0.881 * x[4] * x[6] * x[10] -\n            0.6563 * x[4] * x[7] * x[8] + 0.3767 * x[4] * x[7] * x[9] -\n            0.3868 * x[4] * x[7] * x[10] +\n            0.4704 * x[4] * x[8] * x[9] +\n            0.5043 * x[4] * x[8] * x[10] - 0.2086 * x[4] * x[9] * x[10] -\n            0.8244 * x[5] * x[6] * x[7] - 0.9021 * x[5] * x[6] * x[8] +\n            0.5587 * x[5] * x[6] * x[9] +\n            0.3616 * x[5] * x[6] * x[10] - 0.3769 * x[5] * x[7] * x[8] +\n            0.0455 * x[5] * x[7] * x[9] +\n            0.0116 * x[5] * x[7] * x[10] - 0.1229 * x[5] * x[8] * x[9] +\n            0.1753 * x[5] * x[8] * x[10] - 0.4053 * x[5] * x[9] * x[10] -\n            0.4102 * x[6] * x[7] * x[8] - 0.8524 * x[6] * x[7] * x[9] +\n            0.9499 * x[6] * x[7] * x[10] +\n            0.4563 * x[6] * x[8] * x[9] +\n            0.5162 * x[6] * x[8] * x[10] - 0.3816 * x[6] * x[9] * x[10] -\n            0.507 * x[7] * x[8] * x[9] - 0.4862 * x[7] * x[8] * x[10] +\n            0.2361 * x[7] * x[9] * x[10] +\n            0.8756 * x[8] * x[9] * x[10]\n        ) + obj == 0.0\n    )\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/mult4.jl",
    "content": "#= \n    1. Using the below raw expression interface for dense nonlinear problems significantly \n      reduces JuMP's building time\n    2. `linking_constraints = true` is necessary to be able to solve this dense quadrilinear instance\n=#\n\nreplace_expr(expr::Any, x) = expr\nfunction replace_expr(expr::Expr, x)\n    if Base.Meta.isexpr(expr, :ref)\n        return x[expr.args[2]]\n    end\n    for i in 1:length(expr.args)\n        expr.args[i] = replace_expr(expr.args[i], x)\n    end\n    return expr\nend\n\nfunction m_10_4_10_100_1(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    # ----- Variables ----- #\n    x_Idx = Any[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n    @variable(m, 0 <= x[x_Idx] <= 1)\n\n    # ----- Objective ----- #\n    obj = :((\n        0.7278 * x[1] * x[2] - 0.8657 * x[1] * x[3] - 0.1454 * x[1] * x[4] -\n        0.7254 * x[1] * x[5] - 0.7618 * x[1] * x[6] - 0.3881 * x[1] * x[7] +\n        0.2265 * x[1] * x[8] +\n        0.3273 * x[1] * x[9] +\n        0.7918 * x[1] * x[10] +\n        0.5074 * x[2] * x[3] +\n        0.2597 * x[2] * x[4] - 0.558 * x[2] * x[5] - 0.0323 * x[2] * x[6] +\n        0.23 * x[2] * x[7] +\n        0.9753 * x[2] * x[8] +\n        0.1184 * x[2] * x[9] - 0.2582 * x[2] * x[10] - 0.3248 * x[3] * x[4] +\n        0.4909 * x[3] * x[5] +\n        0.1395 * x[3] * x[6] - 0.0877 * x[3] * x[7] +\n        0.2964 * x[3] * x[8] +\n        0.3672 * x[3] * x[9] - 0.6592 * x[3] * x[10] - 0.4539 * x[4] * x[5] -\n        0.1185 * x[4] * x[6] - 0.0846 * x[4] * x[7] - 0.2095 * x[4] * x[8] +\n        0.3767 * x[4] * x[9] - 0.4022 * x[4] * x[10] - 0.5895 * x[5] * x[6] -\n        0.6154 * x[5] * x[7] - 0.162 * x[5] * x[8] + 0.3813 * x[5] * x[9] -\n        0.7189 * x[5] * x[10] - 0.7125 * x[6] * x[7] +\n        0.3249 * x[6] * x[8] +\n        0.1514 * x[6] * x[9] +\n        0.5499 * x[6] * x[10] +\n        0.5506 * x[7] * x[8] +\n        0.5307 * x[7] * x[9] +\n        0.753 * x[7] * x[10] - 0.8016 * x[8] * x[9] - 0.331 * x[8] * x[10] +\n        0.2902 * x[9] * x[10] - 0.7368 * x[1] +\n        0.6151 * x[2] +\n        0.0837 * x[3] - 0.4685 * x[4] - 0.0823 * x[5] +\n        0.0219 * x[6] +\n        0.0097 * x[7] +\n        0.9235 * x[8] +\n        0.1005 * x[9] - 0.6207 * x[10] + 0.6888 * x[1] * x[2] * x[3] -\n        0.4837 * x[1] * x[2] * x[4] +\n        0.6795 * x[1] * x[2] * x[5] +\n        0.0753 * x[1] * x[2] * x[6] +\n        0.2431 * x[1] * x[2] * x[7] - 0.0184 * x[1] * x[2] * x[8] -\n        0.4303 * x[1] * x[2] * x[9] - 0.5289 * x[1] * x[2] * x[10] +\n        0.3028 * x[1] * x[3] * x[4] +\n        0.2143 * x[1] * x[3] * x[5] - 0.2037 * x[1] * x[3] * x[6] +\n        0.6976 * x[1] * x[3] * x[7] +\n        0.2752 * x[1] * x[3] * x[8] - 0.4824 * x[1] * x[3] * x[9] -\n        0.2823 * x[1] * x[3] * x[10] + 0.1237 * x[1] * x[4] * x[5] -\n        0.7571 * x[1] * x[4] * x[6] + 0.9569 * x[1] * x[4] * x[7] -\n        0.2336 * x[1] * x[4] * x[8] + 0.4414 * x[1] * x[4] * x[9] -\n        0.2835 * x[1] * x[4] * x[10] +\n        0.8198 * x[1] * x[5] * x[6] +\n        0.0874 * x[1] * x[5] * x[7] +\n        0.9194 * x[1] * x[5] * x[8] +\n        0.8589 * x[1] * x[5] * x[9] +\n        0.2666 * x[1] * x[5] * x[10] - 0.4088 * x[1] * x[6] * x[7] -\n        0.6505 * x[1] * x[6] * x[8] +\n        0.6852 * x[1] * x[6] * x[9] +\n        0.2372 * x[1] * x[6] * x[10] +\n        0.4118 * x[1] * x[7] * x[8] - 0.5151 * x[1] * x[7] * x[9] +\n        0.5959 * x[1] * x[7] * x[10] - 0.218 * x[1] * x[8] * x[9] -\n        0.7801 * x[1] * x[8] * x[10] + 0.5074 * x[1] * x[9] * x[10] -\n        0.9404 * x[2] * x[3] * x[4] +\n        0.4013 * x[2] * x[3] * x[5] +\n        0.0504 * x[2] * x[3] * x[6] +\n        0.5051 * x[2] * x[3] * x[7] +\n        0.2954 * x[2] * x[3] * x[8] +\n        0.7422 * x[2] * x[3] * x[9] +\n        0.6614 * x[2] * x[3] * x[10] +\n        0.9144 * x[2] * x[4] * x[5] - 0.5555 * x[2] * x[4] * x[6] +\n        0.159 * x[2] * x[4] * x[7] +\n        0.9815 * x[2] * x[4] * x[8] +\n        0.6799 * x[2] * x[4] * x[9] - 0.6504 * x[2] * x[4] * x[10] +\n        0.4191 * x[2] * x[5] * x[6] - 0.3969 * x[2] * x[5] * x[7] -\n        0.9499 * x[2] * x[5] * x[8] +\n        0.8335 * x[2] * x[5] * x[9] +\n        0.3776 * x[2] * x[5] * x[10] +\n        0.5135 * x[2] * x[6] * x[7] +\n        0.8655 * x[2] * x[6] * x[8] - 0.89 * x[2] * x[6] * x[9] -\n        0.0021 * x[2] * x[6] * x[10] - 0.881 * x[2] * x[7] * x[8] -\n        0.6563 * x[2] * x[7] * x[9] + 0.3767 * x[2] * x[7] * x[10] -\n        0.3868 * x[2] * x[8] * x[9] +\n        0.4704 * x[2] * x[8] * x[10] +\n        0.5043 * x[2] * x[9] * x[10] - 0.2086 * x[3] * x[4] * x[5] -\n        0.8244 * x[3] * x[4] * x[6] - 0.9021 * x[3] * x[4] * x[7] +\n        0.5587 * x[3] * x[4] * x[8] +\n        0.3616 * x[3] * x[4] * x[9] - 0.3769 * x[3] * x[4] * x[10] +\n        0.0455 * x[3] * x[5] * x[6] +\n        0.0116 * x[3] * x[5] * x[7] - 0.1229 * x[3] * x[5] * x[8] +\n        0.1753 * x[3] * x[5] * x[9] - 0.4053 * x[3] * x[5] * x[10] -\n        0.4102 * x[3] * x[6] * x[7] - 0.8524 * x[3] * x[6] * x[8] +\n        0.9499 * x[3] * x[6] * x[9] +\n        0.4563 * x[3] * x[6] * x[10] +\n        0.5162 * x[3] * x[7] * x[8] - 0.3816 * x[3] * x[7] * x[9] -\n        0.507 * x[3] * x[7] * x[10] - 0.4862 * x[3] * x[8] * x[9] +\n        0.2361 * x[3] * x[8] * x[10] +\n        0.8756 * x[3] * x[9] * x[10] +\n        0.9844 * x[4] * x[5] * x[6] - 0.5504 * x[4] * x[5] * x[7] +\n        0.8946 * x[4] * x[5] * x[8] +\n        0.6956 * x[4] * x[5] * x[9] +\n        0.4003 * x[4] * x[5] * x[10] +\n        0.1089 * x[4] * x[6] * x[7] - 0.1168 * x[4] * x[6] * x[8] -\n        0.5016 * x[4] * x[6] * x[9] + 0.7953 * x[4] * x[6] * x[10] -\n        0.7085 * x[4] * x[7] * x[8] - 0.1308 * x[4] * x[7] * x[9] -\n        0.0852 * x[4] * x[7] * x[10] - 0.3812 * x[4] * x[8] * x[9] -\n        0.0382 * x[4] * x[8] * x[10] +\n        0.3795 * x[4] * x[9] * x[10] +\n        0.6216 * x[5] * x[6] * x[7] - 0.2157 * x[5] * x[6] * x[8] -\n        0.4137 * x[5] * x[6] * x[9] +\n        0.152 * x[5] * x[6] * x[10] +\n        0.4507 * x[5] * x[7] * x[8] - 0.7145 * x[5] * x[7] * x[9] -\n        0.3329 * x[5] * x[7] * x[10] - 0.6792 * x[5] * x[8] * x[9] +\n        0.0692 * x[5] * x[8] * x[10] +\n        0.4467 * x[5] * x[9] * x[10] - 0.5436 * x[6] * x[7] * x[8] -\n        0.602 * x[6] * x[7] * x[9] +\n        0.9452 * x[6] * x[7] * x[10] +\n        0.9871 * x[6] * x[8] * x[9] - 0.8361 * x[6] * x[8] * x[10] -\n        0.4982 * x[6] * x[9] * x[10] - 0.5683 * x[7] * x[8] * x[9] -\n        0.6084 * x[7] * x[8] * x[10] + 0.7005 * x[7] * x[9] * x[10] -\n        0.9106 * x[8] * x[9] * x[10] +\n        0.9951 * x[1] * x[2] * x[3] * x[4] +\n        0.1336 * x[1] * x[2] * x[3] * x[5] +\n        0.9318 * x[1] * x[2] * x[3] * x[6] +\n        0.4959 * x[1] * x[2] * x[3] * x[7] - 0.2652 * x[1] * x[2] * x[3] * x[8] -\n        0.0387 * x[1] * x[2] * x[3] * x[9] - 0.8525 * x[1] * x[2] * x[3] * x[10] -\n        0.9893 * x[1] * x[2] * x[4] * x[5] - 0.3058 * x[1] * x[2] * x[4] * x[6] -\n        0.3155 * x[1] * x[2] * x[4] * x[7] - 0.5641 * x[1] * x[2] * x[4] * x[8] -\n        0.7337 * x[1] * x[2] * x[4] * x[9] + 0.801 * x[1] * x[2] * x[4] * x[10] -\n        0.2265 * x[1] * x[2] * x[5] * x[6] - 0.109 * x[1] * x[2] * x[5] * x[7] +\n        0.3239 * x[1] * x[2] * x[5] * x[8] - 0.9678 * x[1] * x[2] * x[5] * x[9] +\n        0.3017 * x[1] * x[2] * x[5] * x[10] +\n        0.2928 * x[1] * x[2] * x[6] * x[7] - 0.354 * x[1] * x[2] * x[6] * x[8] +\n        0.7114 * x[1] * x[2] * x[6] * x[9] - 0.1974 * x[1] * x[2] * x[6] * x[10] -\n        0.5863 * x[1] * x[2] * x[7] * x[8] +\n        0.9371 * x[1] * x[2] * x[7] * x[9] +\n        0.1968 * x[1] * x[2] * x[7] * x[10] +\n        0.346 * x[1] * x[2] * x[8] * x[9] - 0.0862 * x[1] * x[2] * x[8] * x[10] -\n        0.34 * x[1] * x[2] * x[9] * x[10] - 0.7992 * x[1] * x[3] * x[4] * x[5] +\n        0.5109 * x[1] * x[3] * x[4] * x[6] +\n        0.2114 * x[1] * x[3] * x[4] * x[7] +\n        0.4381 * x[1] * x[3] * x[4] * x[8] +\n        0.7947 * x[1] * x[3] * x[4] * x[9] +\n        0.3165 * x[1] * x[3] * x[4] * x[10] - 0.6986 * x[1] * x[3] * x[5] * x[6] +\n        0.2246 * x[1] * x[3] * x[5] * x[7] +\n        0.9573 * x[1] * x[3] * x[5] * x[8] +\n        0.9983 * x[1] * x[3] * x[5] * x[9] - 0.4864 * x[1] * x[3] * x[5] * x[10] +\n        0.1017 * x[1] * x[3] * x[6] * x[7] +\n        0.3181 * x[1] * x[3] * x[6] * x[8] +\n        0.108 * x[1] * x[3] * x[6] * x[9] +\n        0.9555 * x[1] * x[3] * x[6] * x[10] +\n        0.8038 * x[1] * x[3] * x[7] * x[8] +\n        0.3158 * x[1] * x[3] * x[7] * x[9] +\n        0.4577 * x[1] * x[3] * x[7] * x[10] - 0.1951 * x[1] * x[3] * x[8] * x[9] +\n        0.8573 * x[1] * x[3] * x[8] * x[10] - 0.7043 * x[1] * x[3] * x[9] * x[10] +\n        0.3491 * x[1] * x[4] * x[5] * x[6] +\n        0.5392 * x[1] * x[4] * x[5] * x[7] - 0.3214 * x[1] * x[4] * x[5] * x[8] -\n        0.7684 * x[1] * x[4] * x[5] * x[9] +\n        0.2287 * x[1] * x[4] * x[5] * x[10] +\n        0.6412 * x[1] * x[4] * x[6] * x[7] +\n        0.8942 * x[1] * x[4] * x[6] * x[8] +\n        0.4623 * x[1] * x[4] * x[6] * x[9] - 0.0048 * x[1] * x[4] * x[6] * x[10] -\n        0.2504 * x[1] * x[4] * x[7] * x[8] - 0.157 * x[1] * x[4] * x[7] * x[9] +\n        0.1058 * x[1] * x[4] * x[7] * x[10] +\n        0.9958 * x[1] * x[4] * x[8] * x[9] +\n        0.9808 * x[1] * x[4] * x[8] * x[10] +\n        0.4926 * x[1] * x[4] * x[9] * x[10] +\n        0.9075 * x[1] * x[5] * x[6] * x[7] - 0.8135 * x[1] * x[5] * x[6] * x[8] +\n        0.468 * x[1] * x[5] * x[6] * x[9] +\n        0.5035 * x[1] * x[5] * x[6] * x[10] +\n        0.8937 * x[1] * x[5] * x[7] * x[8] +\n        0.4124 * x[1] * x[5] * x[7] * x[9] +\n        0.6276 * x[1] * x[5] * x[7] * x[10] +\n        0.1172 * x[1] * x[5] * x[8] * x[9] - 0.8766 * x[1] * x[5] * x[8] * x[10] -\n        0.0392 * x[1] * x[5] * x[9] * x[10] + 0.1954 * x[1] * x[6] * x[7] * x[8] -\n        0.7249 * x[1] * x[6] * x[7] * x[9] +\n        0.1748 * x[1] * x[6] * x[7] * x[10] +\n        0.0399 * x[1] * x[6] * x[8] * x[9] +\n        0.7718 * x[1] * x[6] * x[8] * x[10] - 0.3924 * x[1] * x[6] * x[9] * x[10] +\n        0.3393 * x[1] * x[7] * x[8] * x[9] +\n        0.3299 * x[1] * x[7] * x[8] * x[10] +\n        0.0074 * x[1] * x[7] * x[9] * x[10] - 0.4768 * x[1] * x[8] * x[9] * x[10] -\n        0.8469 * x[2] * x[3] * x[4] * x[5] - 0.7975 * x[2] * x[3] * x[4] * x[6] +\n        0.0985 * x[2] * x[3] * x[4] * x[7] - 0.2488 * x[2] * x[3] * x[4] * x[8] -\n        0.9697 * x[2] * x[3] * x[4] * x[9] +\n        0.5858 * x[2] * x[3] * x[4] * x[10] +\n        0.2418 * x[2] * x[3] * x[5] * x[6] +\n        0.5472 * x[2] * x[3] * x[5] * x[7] +\n        0.9072 * x[2] * x[3] * x[5] * x[8] - 0.7715 * x[2] * x[3] * x[5] * x[9] -\n        0.3631 * x[2] * x[3] * x[5] * x[10] + 0.1936 * x[2] * x[3] * x[6] * x[7] -\n        0.9037 * x[2] * x[3] * x[6] * x[8] - 0.7716 * x[2] * x[3] * x[6] * x[9] -\n        0.5681 * x[2] * x[3] * x[6] * x[10] - 0.7989 * x[2] * x[3] * x[7] * x[8] -\n        0.8533 * x[2] * x[3] * x[7] * x[9] - 0.5063 * x[2] * x[3] * x[7] * x[10] -\n        0.1132 * x[2] * x[3] * x[8] * x[9] - 0.5833 * x[2] * x[3] * x[8] * x[10] +\n        0.134 * x[2] * x[3] * x[9] * x[10] - 0.9514 * x[2] * x[4] * x[5] * x[6] -\n        0.1594 * x[2] * x[4] * x[5] * x[7] - 0.2043 * x[2] * x[4] * x[5] * x[8] +\n        0.9532 * x[2] * x[4] * x[5] * x[9] +\n        0.3852 * x[2] * x[4] * x[5] * x[10] - 0.9901 * x[2] * x[4] * x[6] * x[7] -\n        0.7402 * x[2] * x[4] * x[6] * x[8] - 0.9064 * x[2] * x[4] * x[6] * x[9] +\n        0.6796 * x[2] * x[4] * x[6] * x[10] +\n        0.357 * x[2] * x[4] * x[7] * x[8] +\n        0.1639 * x[2] * x[4] * x[7] * x[9] +\n        0.4671 * x[2] * x[4] * x[7] * x[10] - 0.7679 * x[2] * x[4] * x[8] * x[9] +\n        0.6806 * x[2] * x[4] * x[8] * x[10] +\n        0.67 * x[2] * x[4] * x[9] * x[10] +\n        0.4931 * x[2] * x[5] * x[6] * x[7] +\n        0.6864 * x[2] * x[5] * x[6] * x[8] +\n        0.0577 * x[2] * x[5] * x[6] * x[9] +\n        0.331 * x[2] * x[5] * x[6] * x[10] +\n        0.4615 * x[2] * x[5] * x[7] * x[8] - 0.1788 * x[2] * x[5] * x[7] * x[9] -\n        0.2886 * x[2] * x[5] * x[7] * x[10] + 0.4708 * x[2] * x[5] * x[8] * x[9] -\n        0.0574 * x[2] * x[5] * x[8] * x[10] - 0.0747 * x[2] * x[5] * x[9] * x[10] +\n        0.5194 * x[2] * x[6] * x[7] * x[8] +\n        0.4049 * x[2] * x[6] * x[7] * x[9] - 0.4841 * x[2] * x[6] * x[7] * x[10] +\n        0.8754 * x[2] * x[6] * x[8] * x[9] - 0.0878 * x[2] * x[6] * x[8] * x[10] +\n        0.617 * x[2] * x[6] * x[9] * x[10] +\n        0.8177 * x[2] * x[7] * x[8] * x[9] +\n        0.3898 * x[2] * x[7] * x[8] * x[10] - 0.561 * x[2] * x[7] * x[9] * x[10] +\n        0.7099 * x[2] * x[8] * x[9] * x[10] +\n        0.4888 * x[3] * x[4] * x[5] * x[6] - 0.3978 * x[3] * x[4] * x[5] * x[7] +\n        0.3439 * x[3] * x[4] * x[5] * x[8] +\n        0.2374 * x[3] * x[4] * x[5] * x[9] +\n        0.9351 * x[3] * x[4] * x[5] * x[10] +\n        0.9805 * x[3] * x[4] * x[6] * x[7] - 0.324 * x[3] * x[4] * x[6] * x[8] +\n        0.8415 * x[3] * x[4] * x[6] * x[9] - 0.3219 * x[3] * x[4] * x[6] * x[10] +\n        0.8619 * x[3] * x[4] * x[7] * x[8] +\n        0.0931 * x[3] * x[4] * x[7] * x[9] - 0.069 * x[3] * x[4] * x[7] * x[10] -\n        0.6462 * x[3] * x[4] * x[8] * x[9] - 0.244 * x[3] * x[4] * x[8] * x[10] -\n        0.6496 * x[3] * x[4] * x[9] * x[10] - 0.2863 * x[3] * x[5] * x[6] * x[7] +\n        0.3314 * x[3] * x[5] * x[6] * x[8] +\n        0.2371 * x[3] * x[5] * x[6] * x[9] - 0.0621 * x[3] * x[5] * x[6] * x[10] -\n        0.3675 * x[3] * x[5] * x[7] * x[8] - 0.4622 * x[3] * x[5] * x[7] * x[9] -\n        0.6002 * x[3] * x[5] * x[7] * x[10] - 0.1691 * x[3] * x[5] * x[8] * x[9] +\n        0.9586 * x[3] * x[5] * x[8] * x[10] +\n        0.0864 * x[3] * x[5] * x[9] * x[10] - 0.741 * x[3] * x[6] * x[7] * x[8] +\n        0.6095 * x[3] * x[6] * x[7] * x[9] +\n        0.6916 * x[3] * x[6] * x[7] * x[10] +\n        0.4181 * x[3] * x[6] * x[8] * x[9] +\n        0.0579 * x[3] * x[6] * x[8] * x[10] +\n        0.3277 * x[3] * x[6] * x[9] * x[10] +\n        0.8015 * x[3] * x[7] * x[8] * x[9] +\n        0.8823 * x[3] * x[7] * x[8] * x[10] - 0.7712 * x[3] * x[7] * x[9] * x[10] +\n        0.7333 * x[3] * x[8] * x[9] * x[10] +\n        0.2647 * x[4] * x[5] * x[6] * x[7] - 0.5144 * x[4] * x[5] * x[6] * x[8] -\n        0.6792 * x[4] * x[5] * x[6] * x[9] - 0.9575 * x[4] * x[5] * x[6] * x[10] -\n        0.6195 * x[4] * x[5] * x[7] * x[8] - 0.3753 * x[4] * x[5] * x[7] * x[9] +\n        0.6193 * x[4] * x[5] * x[7] * x[10] +\n        0.1474 * x[4] * x[5] * x[8] * x[9] +\n        0.6525 * x[4] * x[5] * x[8] * x[10] - 0.4271 * x[4] * x[5] * x[9] * x[10] -\n        0.679 * x[4] * x[6] * x[7] * x[8] - 0.3382 * x[4] * x[6] * x[7] * x[9] -\n        0.4683 * x[4] * x[6] * x[7] * x[10] +\n        0.0896 * x[4] * x[6] * x[8] * x[9] +\n        0.107 * x[4] * x[6] * x[8] * x[10] - 0.9568 * x[4] * x[6] * x[9] * x[10] -\n        0.7025 * x[4] * x[7] * x[8] * x[9] - 0.7902 * x[4] * x[7] * x[8] * x[10] +\n        0.2284 * x[4] * x[7] * x[9] * x[10] - 0.1874 * x[4] * x[8] * x[9] * x[10] +\n        0.8031 * x[5] * x[6] * x[7] * x[8] +\n        0.8857 * x[5] * x[6] * x[7] * x[9] - 0.6868 * x[5] * x[6] * x[7] * x[10] +\n        0.8739 * x[5] * x[6] * x[8] * x[9] - 0.7291 * x[5] * x[6] * x[8] * x[10] -\n        0.2574 * x[5] * x[6] * x[9] * x[10] - 0.357 * x[5] * x[7] * x[8] * x[9] +\n        0.4299 * x[5] * x[7] * x[8] * x[10] +\n        0.4594 * x[5] * x[7] * x[9] * x[10] - 0.2428 * x[5] * x[8] * x[9] * x[10] +\n        0.6579 * x[6] * x[7] * x[8] * x[9] +\n        0.9073 * x[6] * x[7] * x[8] * x[10] - 0.3832 * x[6] * x[7] * x[9] * x[10] +\n        0.1595 * x[6] * x[8] * x[9] * x[10] - 0.5331 * x[7] * x[8] * x[9] * x[10]\n    ))\n    obj = replace_expr(obj, x)\n    JuMP.set_nonlinear_objective(m, MOI.MIN_SENSE, obj)\n\n    # ----- Constraints ----- #\n    e2 = :(\n        0.4626 * x[1] * x[2] + 0.0198 * x[1] * x[3] - 0.4397 * x[1] * x[4] +\n        0.9861 * x[1] * x[5] +\n        0.5225 * x[1] * x[6] - 0.9346 * x[1] * x[7] +\n        0.4133 * x[1] * x[8] +\n        0.3442 * x[1] * x[9] - 0.8199 * x[1] * x[10] - 0.0776 * x[2] * x[3] -\n        0.4723 * x[2] * x[4] - 0.289 * x[2] * x[5] + 0.4463 * x[2] * x[6] -\n        0.9454 * x[2] * x[7] +\n        0.1697 * x[2] * x[8] +\n        0.3885 * x[2] * x[9] - 0.7786 * x[2] * x[10] +\n        0.0525 * x[3] * x[4] +\n        0.9874 * x[3] * x[5] +\n        0.4525 * x[3] * x[6] +\n        0.521 * x[3] * x[7] - 0.5928 * x[3] * x[8] + 0.7265 * x[3] * x[9] -\n        0.615 * x[3] * x[10] - 0.8237 * x[4] * x[5] - 0.5174 * x[4] * x[6] +\n        0.821 * x[4] * x[7] +\n        0.6597 * x[4] * x[8] - 0.8449 * x[4] * x[9] +\n        0.743 * x[4] * x[10] +\n        0.1144 * x[5] * x[6] - 0.2056 * x[5] * x[7] +\n        0.9986 * x[5] * x[8] +\n        0.54 * x[5] * x[9] +\n        0.5713 * x[5] * x[10] +\n        0.5068 * x[6] * x[7] +\n        0.1204 * x[6] * x[8] +\n        0.3888 * x[6] * x[9] +\n        0.7512 * x[6] * x[10] - 0.9713 * x[7] * x[8] - 0.4285 * x[7] * x[9] -\n        0.6373 * x[7] * x[10] +\n        0.6154 * x[8] * x[9] +\n        0.1051 * x[8] * x[10] - 0.0283 * x[9] * x[10] + 0.0735 * x[1] -\n        0.9093 * x[2] - 0.7123 * x[3] +\n        0.5603 * x[4] +\n        0.5412 * x[5] - 0.6809 * x[6] - 0.0621 * x[7] - 0.674 * x[8] + 0.0977 * x[9] -\n        0.3899 * x[10] + (-0.6347 * x[1] * x[2] * x[3]) -\n        0.9763 * x[1] * x[2] * x[4] + 0.8874 * x[1] * x[2] * x[5] -\n        0.0161 * x[1] * x[2] * x[6] +\n        0.9611 * x[1] * x[2] * x[7] +\n        0.2266 * x[1] * x[2] * x[8] - 0.2746 * x[1] * x[2] * x[9] +\n        0.0648 * x[1] * x[2] * x[10] - 0.7084 * x[1] * x[3] * x[4] -\n        0.7343 * x[1] * x[3] * x[5] - 0.2376 * x[1] * x[3] * x[6] +\n        0.4007 * x[1] * x[3] * x[7] +\n        0.0995 * x[1] * x[3] * x[8] +\n        0.6511 * x[1] * x[3] * x[9] +\n        0.0747 * x[1] * x[3] * x[10] +\n        0.3247 * x[1] * x[4] * x[5] - 0.8937 * x[1] * x[4] * x[6] -\n        0.6571 * x[1] * x[4] * x[7] +\n        0.2373 * x[1] * x[4] * x[8] +\n        0.5175 * x[1] * x[4] * x[9] +\n        0.8201 * x[1] * x[4] * x[10] +\n        0.428 * x[1] * x[5] * x[6] +\n        0.48 * x[1] * x[5] * x[7] - 0.2866 * x[1] * x[5] * x[8] +\n        0.6437 * x[1] * x[5] * x[9] +\n        0.1041 * x[1] * x[5] * x[10] +\n        0.3016 * x[1] * x[6] * x[7] - 0.6249 * x[1] * x[6] * x[8] +\n        0.6366 * x[1] * x[6] * x[9] - 0.9552 * x[1] * x[6] * x[10] +\n        0.3144 * x[1] * x[7] * x[8] - 0.7607 * x[1] * x[7] * x[9] -\n        0.2293 * x[1] * x[7] * x[10] - 0.5147 * x[1] * x[8] * x[9] +\n        0.9307 * x[1] * x[8] * x[10] - 0.0294 * x[1] * x[9] * x[10] +\n        0.9847 * x[2] * x[3] * x[4] - 0.4374 * x[2] * x[3] * x[5] +\n        0.9569 * x[2] * x[3] * x[6] +\n        0.9057 * x[2] * x[3] * x[7] - 0.5138 * x[2] * x[3] * x[8] -\n        0.1668 * x[2] * x[3] * x[9] + 0.4716 * x[2] * x[3] * x[10] -\n        0.6094 * x[2] * x[4] * x[5] +\n        0.2787 * x[2] * x[4] * x[6] +\n        0.2594 * x[2] * x[4] * x[7] - 0.7943 * x[2] * x[4] * x[8] -\n        0.7225 * x[2] * x[4] * x[9] - 0.0902 * x[2] * x[4] * x[10] +\n        0.9687 * x[2] * x[5] * x[6] - 0.1502 * x[2] * x[5] * x[7] +\n        0.4096 * x[2] * x[5] * x[8] - 0.2692 * x[2] * x[5] * x[9] -\n        0.5992 * x[2] * x[5] * x[10] - 0.1808 * x[2] * x[6] * x[7] -\n        0.5216 * x[2] * x[6] * x[8] + 0.41 * x[2] * x[6] * x[9] -\n        0.8418 * x[2] * x[6] * x[10] - 0.5924 * x[2] * x[7] * x[8] -\n        0.9653 * x[2] * x[7] * x[9] - 0.3314 * x[2] * x[7] * x[10] -\n        0.4303 * x[2] * x[8] * x[9] + 0.6908 * x[2] * x[8] * x[10] -\n        0.0111 * x[2] * x[9] * x[10] + 0.4202 * x[3] * x[4] * x[5] -\n        0.4907 * x[3] * x[4] * x[6] + 0.6454 * x[3] * x[4] * x[7] -\n        0.4368 * x[3] * x[4] * x[8] +\n        0.2496 * x[3] * x[4] * x[9] +\n        0.4916 * x[3] * x[4] * x[10] +\n        0.7479 * x[3] * x[5] * x[6] - 0.7442 * x[3] * x[5] * x[7] -\n        0.4416 * x[3] * x[5] * x[8] +\n        0.847 * x[3] * x[5] * x[9] +\n        0.9726 * x[3] * x[5] * x[10] +\n        0.5786 * x[3] * x[6] * x[7] - 0.3041 * x[3] * x[6] * x[8] +\n        0.5286 * x[3] * x[6] * x[9] - 0.6138 * x[3] * x[6] * x[10] -\n        0.8712 * x[3] * x[7] * x[8] - 0.9096 * x[3] * x[7] * x[9] -\n        0.707 * x[3] * x[7] * x[10] +\n        0.6138 * x[3] * x[8] * x[9] +\n        0.312 * x[3] * x[8] * x[10] - 0.5107 * x[3] * x[9] * x[10] -\n        0.3513 * x[4] * x[5] * x[6] +\n        0.9673 * x[4] * x[5] * x[7] +\n        0.2275 * x[4] * x[5] * x[8] - 0.415 * x[4] * x[5] * x[9] -\n        0.0089 * x[4] * x[5] * x[10] + 0.4723 * x[4] * x[6] * x[7] -\n        0.9209 * x[4] * x[6] * x[8] - 0.9687 * x[4] * x[6] * x[9] -\n        0.043 * x[4] * x[6] * x[10] +\n        0.5532 * x[4] * x[7] * x[8] +\n        0.8139 * x[4] * x[7] * x[9] +\n        0.8304 * x[4] * x[7] * x[10] - 0.3323 * x[4] * x[8] * x[9] -\n        0.4014 * x[4] * x[8] * x[10] + 0.6574 * x[4] * x[9] * x[10] -\n        0.0813 * x[5] * x[6] * x[7] - 0.9703 * x[5] * x[6] * x[8] -\n        0.3218 * x[5] * x[6] * x[9] - 0.8836 * x[5] * x[6] * x[10] -\n        0.8145 * x[5] * x[7] * x[8] + 0.3035 * x[5] * x[7] * x[9] -\n        0.2096 * x[5] * x[7] * x[10] +\n        0.2399 * x[5] * x[8] * x[9] +\n        0.6504 * x[5] * x[8] * x[10] - 0.3218 * x[5] * x[9] * x[10] -\n        0.3831 * x[6] * x[7] * x[8] - 0.2782 * x[6] * x[7] * x[9] -\n        0.1766 * x[6] * x[7] * x[10] - 0.0781 * x[6] * x[8] * x[9] -\n        0.2352 * x[6] * x[8] * x[10] + 0.2862 * x[6] * x[9] * x[10] -\n        0.5167 * x[7] * x[8] * x[9] +\n        0.4314 * x[7] * x[8] * x[10] +\n        0.7136 * x[7] * x[9] * x[10] - 0.6721 * x[8] * x[9] * x[10] +\n        (-0.5978 * x[1] * x[2] * x[3] * x[4]) - 0.5025 * x[1] * x[2] * x[3] * x[5] +\n        0.9402 * x[1] * x[2] * x[3] * x[6] +\n        0.5528 * x[1] * x[2] * x[3] * x[7] - 0.4546 * x[1] * x[2] * x[3] * x[8] -\n        0.0061 * x[1] * x[2] * x[3] * x[9] - 0.2025 * x[1] * x[2] * x[3] * x[10] +\n        0.2266 * x[1] * x[2] * x[4] * x[5] - 0.8295 * x[1] * x[2] * x[4] * x[6] +\n        0.474 * x[1] * x[2] * x[4] * x[7] +\n        0.7257 * x[1] * x[2] * x[4] * x[8] - 0.3179 * x[1] * x[2] * x[4] * x[9] +\n        0.3889 * x[1] * x[2] * x[4] * x[10] +\n        0.2838 * x[1] * x[2] * x[5] * x[6] - 0.829 * x[1] * x[2] * x[5] * x[7] +\n        0.416 * x[1] * x[2] * x[5] * x[8] +\n        0.1849 * x[1] * x[2] * x[5] * x[9] - 0.5344 * x[1] * x[2] * x[5] * x[10] -\n        0.8496 * x[1] * x[2] * x[6] * x[7] - 0.3513 * x[1] * x[2] * x[6] * x[8] +\n        0.8262 * x[1] * x[2] * x[6] * x[9] - 0.5914 * x[1] * x[2] * x[6] * x[10] -\n        0.0945 * x[1] * x[2] * x[7] * x[8] + 0.4543 * x[1] * x[2] * x[7] * x[9] -\n        0.9433 * x[1] * x[2] * x[7] * x[10] +\n        0.0341 * x[1] * x[2] * x[8] * x[9] +\n        0.5353 * x[1] * x[2] * x[8] * x[10] +\n        0.7887 * x[1] * x[2] * x[9] * x[10] +\n        0.889 * x[1] * x[3] * x[4] * x[5] - 0.4204 * x[1] * x[3] * x[4] * x[6] +\n        0.0629 * x[1] * x[3] * x[4] * x[7] - 0.5343 * x[1] * x[3] * x[4] * x[8] -\n        0.3744 * x[1] * x[3] * x[4] * x[9] - 0.717 * x[1] * x[3] * x[4] * x[10] -\n        0.3148 * x[1] * x[3] * x[5] * x[6] - 0.6929 * x[1] * x[3] * x[5] * x[7] +\n        0.6984 * x[1] * x[3] * x[5] * x[8] +\n        0.9441 * x[1] * x[3] * x[5] * x[9] - 0.1182 * x[1] * x[3] * x[5] * x[10] +\n        0.5489 * x[1] * x[3] * x[6] * x[7] - 0.0876 * x[1] * x[3] * x[6] * x[8] +\n        0.729 * x[1] * x[3] * x[6] * x[9] +\n        0.456 * x[1] * x[3] * x[6] * x[10] +\n        0.2747 * x[1] * x[3] * x[7] * x[8] +\n        0.4481 * x[1] * x[3] * x[7] * x[9] +\n        0.2084 * x[1] * x[3] * x[7] * x[10] - 0.9474 * x[1] * x[3] * x[8] * x[9] -\n        0.4145 * x[1] * x[3] * x[8] * x[10] - 0.6056 * x[1] * x[3] * x[9] * x[10] +\n        0.8973 * x[1] * x[4] * x[5] * x[6] +\n        0.0637 * x[1] * x[4] * x[5] * x[7] - 0.9793 * x[1] * x[4] * x[5] * x[8] -\n        0.0957 * x[1] * x[4] * x[5] * x[9] +\n        0.9272 * x[1] * x[4] * x[5] * x[10] +\n        0.9722 * x[1] * x[4] * x[6] * x[7] - 0.3182 * x[1] * x[4] * x[6] * x[8] +\n        0.9186 * x[1] * x[4] * x[6] * x[9] - 0.3466 * x[1] * x[4] * x[6] * x[10] +\n        0.4085 * x[1] * x[4] * x[7] * x[8] +\n        0.5809 * x[1] * x[4] * x[7] * x[9] +\n        0.4471 * x[1] * x[4] * x[7] * x[10] +\n        0.4579 * x[1] * x[4] * x[8] * x[9] - 0.1092 * x[1] * x[4] * x[8] * x[10] -\n        0.2364 * x[1] * x[4] * x[9] * x[10] +\n        0.8444 * x[1] * x[5] * x[6] * x[7] +\n        0.4968 * x[1] * x[5] * x[6] * x[8] - 0.1465 * x[1] * x[5] * x[6] * x[9] -\n        0.5651 * x[1] * x[5] * x[6] * x[10] +\n        0.4588 * x[1] * x[5] * x[7] * x[8] +\n        0.5938 * x[1] * x[5] * x[7] * x[9] +\n        0.1168 * x[1] * x[5] * x[7] * x[10] +\n        0.7708 * x[1] * x[5] * x[8] * x[9] - 0.2337 * x[1] * x[5] * x[8] * x[10] -\n        0.5184 * x[1] * x[5] * x[9] * x[10] - 0.3698 * x[1] * x[6] * x[7] * x[8] -\n        0.1342 * x[1] * x[6] * x[7] * x[9] - 0.904 * x[1] * x[6] * x[7] * x[10] -\n        0.1518 * x[1] * x[6] * x[8] * x[9] +\n        0.4747 * x[1] * x[6] * x[8] * x[10] +\n        0.7456 * x[1] * x[6] * x[9] * x[10] - 0.384 * x[1] * x[7] * x[8] * x[9] +\n        0.6866 * x[1] * x[7] * x[8] * x[10] +\n        0.6322 * x[1] * x[7] * x[9] * x[10] - 0.1864 * x[1] * x[8] * x[9] * x[10] +\n        0.73 * x[2] * x[3] * x[4] * x[5] +\n        0.7045 * x[2] * x[3] * x[4] * x[6] +\n        0.0242 * x[2] * x[3] * x[4] * x[7] +\n        0.5528 * x[2] * x[3] * x[4] * x[8] - 0.0143 * x[2] * x[3] * x[4] * x[9] -\n        0.5903 * x[2] * x[3] * x[4] * x[10] - 0.1097 * x[2] * x[3] * x[5] * x[6] -\n        0.1329 * x[2] * x[3] * x[5] * x[7] - 0.8906 * x[2] * x[3] * x[5] * x[8] +\n        0.401 * x[2] * x[3] * x[5] * x[9] +\n        0.8385 * x[2] * x[3] * x[5] * x[10] - 0.222 * x[2] * x[3] * x[6] * x[7] -\n        0.5022 * x[2] * x[3] * x[6] * x[8] - 0.2673 * x[2] * x[3] * x[6] * x[9] +\n        0.9973 * x[2] * x[3] * x[6] * x[10] +\n        0.3242 * x[2] * x[3] * x[7] * x[8] - 0.6405 * x[2] * x[3] * x[7] * x[9] +\n        0.7448 * x[2] * x[3] * x[7] * x[10] - 0.5121 * x[2] * x[3] * x[8] * x[9] -\n        0.7672 * x[2] * x[3] * x[8] * x[10] +\n        0.6364 * x[2] * x[3] * x[9] * x[10] +\n        0.0713 * x[2] * x[4] * x[5] * x[6] +\n        0.9761 * x[2] * x[4] * x[5] * x[7] - 0.1674 * x[2] * x[4] * x[5] * x[8] +\n        0.6164 * x[2] * x[4] * x[5] * x[9] - 0.5201 * x[2] * x[4] * x[5] * x[10] +\n        0.9405 * x[2] * x[4] * x[6] * x[7] - 0.2474 * x[2] * x[4] * x[6] * x[8] +\n        0.2668 * x[2] * x[4] * x[6] * x[9] - 0.7262 * x[2] * x[4] * x[6] * x[10] +\n        0.5369 * x[2] * x[4] * x[7] * x[8] - 0.7976 * x[2] * x[4] * x[7] * x[9] +\n        0.1039 * x[2] * x[4] * x[7] * x[10] +\n        0.6633 * x[2] * x[4] * x[8] * x[9] - 0.2455 * x[2] * x[4] * x[8] * x[10] +\n        0.7355 * x[2] * x[4] * x[9] * x[10] +\n        0.2493 * x[2] * x[5] * x[6] * x[7] +\n        0.1046 * x[2] * x[5] * x[6] * x[8] - 0.5768 * x[2] * x[5] * x[6] * x[9] +\n        0.6454 * x[2] * x[5] * x[6] * x[10] - 0.2728 * x[2] * x[5] * x[7] * x[8] -\n        0.539 * x[2] * x[5] * x[7] * x[9] - 0.3418 * x[2] * x[5] * x[7] * x[10] +\n        0.3602 * x[2] * x[5] * x[8] * x[9] - 0.1419 * x[2] * x[5] * x[8] * x[10] -\n        0.0954 * x[2] * x[5] * x[9] * x[10] + 0.8552 * x[2] * x[6] * x[7] * x[8] -\n        0.1075 * x[2] * x[6] * x[7] * x[9] +\n        0.3345 * x[2] * x[6] * x[7] * x[10] +\n        0.5617 * x[2] * x[6] * x[8] * x[9] +\n        0.5817 * x[2] * x[6] * x[8] * x[10] - 0.6045 * x[2] * x[6] * x[9] * x[10] -\n        0.4872 * x[2] * x[7] * x[8] * x[9] +\n        0.3536 * x[2] * x[7] * x[8] * x[10] +\n        0.7971 * x[2] * x[7] * x[9] * x[10] - 0.25 * x[2] * x[8] * x[9] * x[10] -\n        0.9599 * x[3] * x[4] * x[5] * x[6] - 0.196 * x[3] * x[4] * x[5] * x[7] +\n        0.9819 * x[3] * x[4] * x[5] * x[8] +\n        0.9495 * x[3] * x[4] * x[5] * x[9] +\n        0.9406 * x[3] * x[4] * x[5] * x[10] +\n        0.9377 * x[3] * x[4] * x[6] * x[7] - 0.2505 * x[3] * x[4] * x[6] * x[8] -\n        0.8054 * x[3] * x[4] * x[6] * x[9] +\n        0.5014 * x[3] * x[4] * x[6] * x[10] +\n        0.649 * x[3] * x[4] * x[7] * x[8] +\n        0.4489 * x[3] * x[4] * x[7] * x[9] - 0.2659 * x[3] * x[4] * x[7] * x[10] +\n        0.2441 * x[3] * x[4] * x[8] * x[9] - 0.3874 * x[3] * x[4] * x[8] * x[10] -\n        0.3974 * x[3] * x[4] * x[9] * x[10] +\n        0.3528 * x[3] * x[5] * x[6] * x[7] +\n        0.6601 * x[3] * x[5] * x[6] * x[8] +\n        0.1126 * x[3] * x[5] * x[6] * x[9] +\n        0.1189 * x[3] * x[5] * x[6] * x[10] - 0.3444 * x[3] * x[5] * x[7] * x[8] +\n        0.4614 * x[3] * x[5] * x[7] * x[9] - 0.6835 * x[3] * x[5] * x[7] * x[10] +\n        0.0658 * x[3] * x[5] * x[8] * x[9] +\n        0.5684 * x[3] * x[5] * x[8] * x[10] - 0.5684 * x[3] * x[5] * x[9] * x[10] -\n        0.3494 * x[3] * x[6] * x[7] * x[8] + 0.0029 * x[3] * x[6] * x[7] * x[9] -\n        0.5542 * x[3] * x[6] * x[7] * x[10] - 0.067 * x[3] * x[6] * x[8] * x[9] -\n        0.6264 * x[3] * x[6] * x[8] * x[10] - 0.6098 * x[3] * x[6] * x[9] * x[10] -\n        0.5862 * x[3] * x[7] * x[8] * x[9] +\n        0.8116 * x[3] * x[7] * x[8] * x[10] +\n        0.5998 * x[3] * x[7] * x[9] * x[10] +\n        0.4699 * x[3] * x[8] * x[9] * x[10] - 0.1693 * x[4] * x[5] * x[6] * x[7] +\n        0.622 * x[4] * x[5] * x[6] * x[8] +\n        0.9767 * x[4] * x[5] * x[6] * x[9] - 0.0178 * x[4] * x[5] * x[6] * x[10] -\n        0.5614 * x[4] * x[5] * x[7] * x[8] +\n        0.5238 * x[4] * x[5] * x[7] * x[9] +\n        0.8146 * x[4] * x[5] * x[7] * x[10] +\n        0.1793 * x[4] * x[5] * x[8] * x[9] +\n        0.7412 * x[4] * x[5] * x[8] * x[10] - 0.9228 * x[4] * x[5] * x[9] * x[10] +\n        0.8761 * x[4] * x[6] * x[7] * x[8] - 0.9062 * x[4] * x[6] * x[7] * x[9] +\n        0.7942 * x[4] * x[6] * x[7] * x[10] - 0.9605 * x[4] * x[6] * x[8] * x[9] +\n        0.9985 * x[4] * x[6] * x[8] * x[10] +\n        0.9604 * x[4] * x[6] * x[9] * x[10] +\n        0.2233 * x[4] * x[7] * x[8] * x[9] +\n        0.1751 * x[4] * x[7] * x[8] * x[10] +\n        0.9245 * x[4] * x[7] * x[9] * x[10] +\n        0.7868 * x[4] * x[8] * x[9] * x[10] - 0.5956 * x[5] * x[6] * x[7] * x[8] -\n        0.9745 * x[5] * x[6] * x[7] * x[9] - 0.49 * x[5] * x[6] * x[7] * x[10] +\n        0.7809 * x[5] * x[6] * x[8] * x[9] - 0.4609 * x[5] * x[6] * x[8] * x[10] +\n        0.778 * x[5] * x[6] * x[9] * x[10] +\n        0.0383 * x[5] * x[7] * x[8] * x[9] - 0.2656 * x[5] * x[7] * x[8] * x[10] +\n        0.9676 * x[5] * x[7] * x[9] * x[10] +\n        0.7539 * x[5] * x[8] * x[9] * x[10] +\n        0.3629 * x[6] * x[7] * x[8] * x[9] - 0.2751 * x[6] * x[7] * x[8] * x[10] -\n        0.6036 * x[6] * x[7] * x[9] * x[10] - 0.6255 * x[6] * x[8] * x[9] * x[10] +\n        0.9753 * x[7] * x[8] * x[9] * x[10] <= 15.442\n    )\n    e2 = replace_expr(e2, x)\n    JuMP.add_nonlinear_constraint(m, e2)\n    e3 = :(\n        (-0.4919 * x[1] * x[2]) - 0.0339 * x[1] * x[3] +\n        0.2248 * x[1] * x[4] +\n        0.366 * x[1] * x[5] - 0.1987 * x[1] * x[6] - 0.5784 * x[1] * x[7] +\n        0.8198 * x[1] * x[8] - 0.0486 * x[1] * x[9] +\n        0.7126 * x[1] * x[10] +\n        0.8337 * x[2] * x[3] +\n        0.0308 * x[2] * x[4] +\n        0.4378 * x[2] * x[5] - 0.4249 * x[2] * x[6] - 0.876 * x[2] * x[7] -\n        0.247 * x[2] * x[8] - 0.482 * x[2] * x[9] +\n        0.0808 * x[2] * x[10] +\n        0.0687 * x[3] * x[4] - 0.9379 * x[3] * x[5] - 0.1556 * x[3] * x[6] -\n        0.1534 * x[3] * x[7] + 0.2972 * x[3] * x[8] - 0.682 * x[3] * x[9] -\n        0.2246 * x[3] * x[10] +\n        0.2078 * x[4] * x[5] +\n        0.0801 * x[4] * x[6] +\n        0.412 * x[4] * x[7] - 0.7653 * x[4] * x[8] +\n        0.7097 * x[4] * x[9] +\n        0.1609 * x[4] * x[10] +\n        0.0463 * x[5] * x[6] - 0.049 * x[5] * x[7] - 0.9321 * x[5] * x[8] +\n        0.5337 * x[5] * x[9] +\n        0.6369 * x[5] * x[10] - 0.8873 * x[6] * x[7] - 0.5746 * x[6] * x[8] +\n        0.4865 * x[6] * x[9] - 0.3803 * x[6] * x[10] - 0.7699 * x[7] * x[8] +\n        0.7363 * x[7] * x[9] - 0.2812 * x[7] * x[10] + 0.8172 * x[8] * x[9] -\n        0.5754 * x[8] * x[10] - 0.2821 * x[9] * x[10] - 0.8113 * x[1] +\n        0.3038 * x[2] +\n        0.8093 * x[3] +\n        0.5277 * x[4] +\n        0.7849 * x[5] +\n        0.6706 * x[6] +\n        0.0152 * x[7] - 0.009 * x[8] +\n        0.0082 * x[9] +\n        0.5372 * x[10] +\n        (-0.0925 * x[1] * x[2] * x[3]) - 0.4232 * x[1] * x[2] * x[4] +\n        0.4301 * x[1] * x[2] * x[5] - 0.1282 * x[1] * x[2] * x[6] +\n        0.2232 * x[1] * x[2] * x[7] +\n        0.124 * x[1] * x[2] * x[8] - 0.3137 * x[1] * x[2] * x[9] +\n        0.5432 * x[1] * x[2] * x[10] - 0.0037 * x[1] * x[3] * x[4] -\n        0.0924 * x[1] * x[3] * x[5] + 0.3913 * x[1] * x[3] * x[6] -\n        0.6371 * x[1] * x[3] * x[7] - 0.1172 * x[1] * x[3] * x[8] -\n        0.1265 * x[1] * x[3] * x[9] - 0.8825 * x[1] * x[3] * x[10] -\n        0.2623 * x[1] * x[4] * x[5] - 0.1383 * x[1] * x[4] * x[6] -\n        0.6027 * x[1] * x[4] * x[7] - 0.21 * x[1] * x[4] * x[8] -\n        0.5062 * x[1] * x[4] * x[9] - 0.8757 * x[1] * x[4] * x[10] +\n        0.8153 * x[1] * x[5] * x[6] +\n        0.0395 * x[1] * x[5] * x[7] - 0.8308 * x[1] * x[5] * x[8] -\n        0.2081 * x[1] * x[5] * x[9] - 0.797 * x[1] * x[5] * x[10] -\n        0.9042 * x[1] * x[6] * x[7] - 0.5208 * x[1] * x[6] * x[8] +\n        0.2869 * x[1] * x[6] * x[9] +\n        0.0977 * x[1] * x[6] * x[10] - 0.6313 * x[1] * x[7] * x[8] -\n        0.1462 * x[1] * x[7] * x[9] + 0.2552 * x[1] * x[7] * x[10] -\n        0.8255 * x[1] * x[8] * x[9] +\n        0.0742 * x[1] * x[8] * x[10] +\n        0.6895 * x[1] * x[9] * x[10] - 0.181 * x[2] * x[3] * x[4] -\n        0.5937 * x[2] * x[3] * x[5] +\n        0.6543 * x[2] * x[3] * x[6] +\n        0.9317 * x[2] * x[3] * x[7] - 0.2445 * x[2] * x[3] * x[8] +\n        0.2943 * x[2] * x[3] * x[9] +\n        0.3555 * x[2] * x[3] * x[10] - 0.1086 * x[2] * x[4] * x[5] -\n        0.6558 * x[2] * x[4] * x[6] - 0.296 * x[2] * x[4] * x[7] -\n        0.3417 * x[2] * x[4] * x[8] + 0.4937 * x[2] * x[4] * x[9] -\n        0.457 * x[2] * x[4] * x[10] + 0.1226 * x[2] * x[5] * x[6] -\n        0.7351 * x[2] * x[5] * x[7] + 0.5968 * x[2] * x[5] * x[8] -\n        0.5881 * x[2] * x[5] * x[9] - 0.9469 * x[2] * x[5] * x[10] -\n        0.6075 * x[2] * x[6] * x[7] - 0.9843 * x[2] * x[6] * x[8] +\n        0.6435 * x[2] * x[6] * x[9] +\n        0.8889 * x[2] * x[6] * x[10] - 0.064 * x[2] * x[7] * x[8] -\n        0.7728 * x[2] * x[7] * x[9] - 0.679 * x[2] * x[7] * x[10] +\n        0.6905 * x[2] * x[8] * x[9] +\n        0.7074 * x[2] * x[8] * x[10] - 0.3972 * x[2] * x[9] * x[10] -\n        0.4977 * x[3] * x[4] * x[5] - 0.5983 * x[3] * x[4] * x[6] -\n        0.4784 * x[3] * x[4] * x[7] - 0.4858 * x[3] * x[4] * x[8] +\n        0.2572 * x[3] * x[4] * x[9] - 0.0521 * x[3] * x[4] * x[10] +\n        0.7398 * x[3] * x[5] * x[6] +\n        0.2972 * x[3] * x[5] * x[7] +\n        0.7789 * x[3] * x[5] * x[8] +\n        0.5905 * x[3] * x[5] * x[9] +\n        0.7603 * x[3] * x[5] * x[10] - 0.5705 * x[3] * x[6] * x[7] +\n        0.9037 * x[3] * x[6] * x[8] +\n        0.4382 * x[3] * x[6] * x[9] - 0.7787 * x[3] * x[6] * x[10] +\n        0.9149 * x[3] * x[7] * x[8] +\n        0.2939 * x[3] * x[7] * x[9] +\n        0.1637 * x[3] * x[7] * x[10] - 0.9742 * x[3] * x[8] * x[9] -\n        0.4477 * x[3] * x[8] * x[10] + 0.6009 * x[3] * x[9] * x[10] -\n        0.3442 * x[4] * x[5] * x[6] + 0.1588 * x[4] * x[5] * x[7] -\n        0.9521 * x[4] * x[5] * x[8] + 0.3398 * x[4] * x[5] * x[9] -\n        0.6371 * x[4] * x[5] * x[10] - 0.4268 * x[4] * x[6] * x[7] +\n        0.3169 * x[4] * x[6] * x[8] +\n        0.1779 * x[4] * x[6] * x[9] - 0.8726 * x[4] * x[6] * x[10] -\n        0.7344 * x[4] * x[7] * x[8] +\n        0.4833 * x[4] * x[7] * x[9] +\n        0.0007 * x[4] * x[7] * x[10] - 0.9371 * x[4] * x[8] * x[9] +\n        0.9815 * x[4] * x[8] * x[10] - 0.9932 * x[4] * x[9] * x[10] +\n        0.3986 * x[5] * x[6] * x[7] +\n        0.5181 * x[5] * x[6] * x[8] - 0.4916 * x[5] * x[6] * x[9] -\n        0.3371 * x[5] * x[6] * x[10] +\n        0.1457 * x[5] * x[7] * x[8] +\n        0.9832 * x[5] * x[7] * x[9] - 0.0207 * x[5] * x[7] * x[10] +\n        0.1223 * x[5] * x[8] * x[9] +\n        0.2128 * x[5] * x[8] * x[10] - 0.8286 * x[5] * x[9] * x[10] -\n        0.4837 * x[6] * x[7] * x[8] - 0.0592 * x[6] * x[7] * x[9] +\n        0.6266 * x[6] * x[7] * x[10] +\n        0.4492 * x[6] * x[8] * x[9] +\n        0.9861 * x[6] * x[8] * x[10] - 0.8687 * x[6] * x[9] * x[10] -\n        0.8504 * x[7] * x[8] * x[9] + 0.6624 * x[7] * x[8] * x[10] -\n        0.1745 * x[7] * x[9] * x[10] +\n        0.3241 * x[8] * x[9] * x[10] +\n        0.15 * x[1] * x[2] * x[3] * x[4] - 0.7118 * x[1] * x[2] * x[3] * x[5] -\n        0.6134 * x[1] * x[2] * x[3] * x[6] +\n        0.3822 * x[1] * x[2] * x[3] * x[7] +\n        0.9004 * x[1] * x[2] * x[3] * x[8] - 0.7372 * x[1] * x[2] * x[3] * x[9] +\n        0.42 * x[1] * x[2] * x[3] * x[10] - 0.2405 * x[1] * x[2] * x[4] * x[5] -\n        0.204 * x[1] * x[2] * x[4] * x[6] - 0.998 * x[1] * x[2] * x[4] * x[7] -\n        0.1736 * x[1] * x[2] * x[4] * x[8] +\n        0.6076 * x[1] * x[2] * x[4] * x[9] +\n        0.7557 * x[1] * x[2] * x[4] * x[10] - 0.7184 * x[1] * x[2] * x[5] * x[6] -\n        0.9139 * x[1] * x[2] * x[5] * x[7] + 0.1313 * x[1] * x[2] * x[5] * x[8] -\n        0.8836 * x[1] * x[2] * x[5] * x[9] + 0.7427 * x[1] * x[2] * x[5] * x[10] -\n        0.3114 * x[1] * x[2] * x[6] * x[7] - 0.0203 * x[1] * x[2] * x[6] * x[8] -\n        0.4356 * x[1] * x[2] * x[6] * x[9] - 0.5229 * x[1] * x[2] * x[6] * x[10] +\n        0.0993 * x[1] * x[2] * x[7] * x[8] +\n        0.4277 * x[1] * x[2] * x[7] * x[9] +\n        0.8057 * x[1] * x[2] * x[7] * x[10] +\n        0.5147 * x[1] * x[2] * x[8] * x[9] +\n        0.0785 * x[1] * x[2] * x[8] * x[10] +\n        0.2918 * x[1] * x[2] * x[9] * x[10] +\n        0.5539 * x[1] * x[3] * x[4] * x[5] +\n        0.758 * x[1] * x[3] * x[4] * x[6] +\n        0.2055 * x[1] * x[3] * x[4] * x[7] - 0.877 * x[1] * x[3] * x[4] * x[8] -\n        0.1218 * x[1] * x[3] * x[4] * x[9] - 0.9826 * x[1] * x[3] * x[4] * x[10] -\n        0.4008 * x[1] * x[3] * x[5] * x[6] +\n        0.947 * x[1] * x[3] * x[5] * x[7] +\n        0.9103 * x[1] * x[3] * x[5] * x[8] - 0.5734 * x[1] * x[3] * x[5] * x[9] +\n        0.3479 * x[1] * x[3] * x[5] * x[10] +\n        0.0723 * x[1] * x[3] * x[6] * x[7] - 0.2806 * x[1] * x[3] * x[6] * x[8] -\n        0.9973 * x[1] * x[3] * x[6] * x[9] + 0.6989 * x[1] * x[3] * x[6] * x[10] -\n        0.1571 * x[1] * x[3] * x[7] * x[8] + 0.4957 * x[1] * x[3] * x[7] * x[9] -\n        0.9767 * x[1] * x[3] * x[7] * x[10] + 0.2287 * x[1] * x[3] * x[8] * x[9] -\n        0.1111 * x[1] * x[3] * x[8] * x[10] +\n        0.3253 * x[1] * x[3] * x[9] * x[10] +\n        0.3775 * x[1] * x[4] * x[5] * x[6] +\n        0.8783 * x[1] * x[4] * x[5] * x[7] +\n        0.4335 * x[1] * x[4] * x[5] * x[8] - 0.0967 * x[1] * x[4] * x[5] * x[9] +\n        0.269 * x[1] * x[4] * x[5] * x[10] - 0.5516 * x[1] * x[4] * x[6] * x[7] -\n        0.2037 * x[1] * x[4] * x[6] * x[8] + 0.6602 * x[1] * x[4] * x[6] * x[9] -\n        0.722 * x[1] * x[4] * x[6] * x[10] +\n        0.5119 * x[1] * x[4] * x[7] * x[8] +\n        0.586 * x[1] * x[4] * x[7] * x[9] - 0.5442 * x[1] * x[4] * x[7] * x[10] +\n        0.0562 * x[1] * x[4] * x[8] * x[9] - 0.7251 * x[1] * x[4] * x[8] * x[10] -\n        0.6521 * x[1] * x[4] * x[9] * x[10] - 0.7049 * x[1] * x[5] * x[6] * x[7] +\n        0.62 * x[1] * x[5] * x[6] * x[8] - 0.497 * x[1] * x[5] * x[6] * x[9] -\n        0.1799 * x[1] * x[5] * x[6] * x[10] +\n        0.9132 * x[1] * x[5] * x[7] * x[8] +\n        0.4395 * x[1] * x[5] * x[7] * x[9] +\n        0.6708 * x[1] * x[5] * x[7] * x[10] +\n        0.5537 * x[1] * x[5] * x[8] * x[9] +\n        0.0758 * x[1] * x[5] * x[8] * x[10] +\n        0.2226 * x[1] * x[5] * x[9] * x[10] +\n        0.3882 * x[1] * x[6] * x[7] * x[8] +\n        0.2014 * x[1] * x[6] * x[7] * x[9] - 0.8073 * x[1] * x[6] * x[7] * x[10] +\n        0.0984 * x[1] * x[6] * x[8] * x[9] - 0.4142 * x[1] * x[6] * x[8] * x[10] -\n        0.5883 * x[1] * x[6] * x[9] * x[10] +\n        0.6861 * x[1] * x[7] * x[8] * x[9] +\n        0.303 * x[1] * x[7] * x[8] * x[10] +\n        0.9262 * x[1] * x[7] * x[9] * x[10] +\n        0.2199 * x[1] * x[8] * x[9] * x[10] - 0.1922 * x[2] * x[3] * x[4] * x[5] -\n        0.7428 * x[2] * x[3] * x[4] * x[6] - 0.7244 * x[2] * x[3] * x[4] * x[7] -\n        0.5698 * x[2] * x[3] * x[4] * x[8] +\n        0.046 * x[2] * x[3] * x[4] * x[9] +\n        0.4195 * x[2] * x[3] * x[4] * x[10] +\n        0.0448 * x[2] * x[3] * x[5] * x[6] - 0.6311 * x[2] * x[3] * x[5] * x[7] +\n        0.7262 * x[2] * x[3] * x[5] * x[8] - 0.3714 * x[2] * x[3] * x[5] * x[9] -\n        0.9939 * x[2] * x[3] * x[5] * x[10] +\n        0.9992 * x[2] * x[3] * x[6] * x[7] +\n        0.7608 * x[2] * x[3] * x[6] * x[8] - 0.5125 * x[2] * x[3] * x[6] * x[9] +\n        0.0878 * x[2] * x[3] * x[6] * x[10] +\n        0.522 * x[2] * x[3] * x[7] * x[8] +\n        0.3632 * x[2] * x[3] * x[7] * x[9] - 0.1574 * x[2] * x[3] * x[7] * x[10] +\n        0.1895 * x[2] * x[3] * x[8] * x[9] - 0.1071 * x[2] * x[3] * x[8] * x[10] +\n        0.889 * x[2] * x[3] * x[9] * x[10] - 0.6673 * x[2] * x[4] * x[5] * x[6] +\n        0.9491 * x[2] * x[4] * x[5] * x[7] - 0.8262 * x[2] * x[4] * x[5] * x[8] -\n        0.6978 * x[2] * x[4] * x[5] * x[9] + 0.8198 * x[2] * x[4] * x[5] * x[10] -\n        0.5889 * x[2] * x[4] * x[6] * x[7] - 0.5569 * x[2] * x[4] * x[6] * x[8] -\n        0.7317 * x[2] * x[4] * x[6] * x[9] +\n        0.3949 * x[2] * x[4] * x[6] * x[10] +\n        0.9541 * x[2] * x[4] * x[7] * x[8] - 0.9943 * x[2] * x[4] * x[7] * x[9] -\n        0.0116 * x[2] * x[4] * x[7] * x[10] - 0.5047 * x[2] * x[4] * x[8] * x[9] +\n        0.8051 * x[2] * x[4] * x[8] * x[10] - 0.7914 * x[2] * x[4] * x[9] * x[10] +\n        0.5505 * x[2] * x[5] * x[6] * x[7] - 0.7908 * x[2] * x[5] * x[6] * x[8] +\n        0.2414 * x[2] * x[5] * x[6] * x[9] - 0.3313 * x[2] * x[5] * x[6] * x[10] +\n        0.9555 * x[2] * x[5] * x[7] * x[8] +\n        0.3839 * x[2] * x[5] * x[7] * x[9] +\n        0.6554 * x[2] * x[5] * x[7] * x[10] +\n        0.9363 * x[2] * x[5] * x[8] * x[9] - 0.4451 * x[2] * x[5] * x[8] * x[10] -\n        0.2679 * x[2] * x[5] * x[9] * x[10] - 0.6916 * x[2] * x[6] * x[7] * x[8] +\n        0.9618 * x[2] * x[6] * x[7] * x[9] +\n        0.8635 * x[2] * x[6] * x[7] * x[10] - 0.5314 * x[2] * x[6] * x[8] * x[9] -\n        0.7532 * x[2] * x[6] * x[8] * x[10] - 0.2676 * x[2] * x[6] * x[9] * x[10] +\n        0.6789 * x[2] * x[7] * x[8] * x[9] - 0.7484 * x[2] * x[7] * x[8] * x[10] +\n        0.9799 * x[2] * x[7] * x[9] * x[10] - 0.04 * x[2] * x[8] * x[9] * x[10] +\n        0.9229 * x[3] * x[4] * x[5] * x[6] +\n        0.9211 * x[3] * x[4] * x[5] * x[7] +\n        0.5065 * x[3] * x[4] * x[5] * x[8] +\n        0.2912 * x[3] * x[4] * x[5] * x[9] +\n        0.3298 * x[3] * x[4] * x[5] * x[10] +\n        0.7586 * x[3] * x[4] * x[6] * x[7] +\n        0.4593 * x[3] * x[4] * x[6] * x[8] +\n        0.3926 * x[3] * x[4] * x[6] * x[9] +\n        0.0687 * x[3] * x[4] * x[6] * x[10] +\n        0.4976 * x[3] * x[4] * x[7] * x[8] +\n        0.6535 * x[3] * x[4] * x[7] * x[9] - 0.9917 * x[3] * x[4] * x[7] * x[10] -\n        0.5502 * x[3] * x[4] * x[8] * x[9] - 0.1718 * x[3] * x[4] * x[8] * x[10] +\n        0.2573 * x[3] * x[4] * x[9] * x[10] - 0.9025 * x[3] * x[5] * x[6] * x[7] +\n        0.3264 * x[3] * x[5] * x[6] * x[8] - 0.6443 * x[3] * x[5] * x[6] * x[9] +\n        0.1642 * x[3] * x[5] * x[6] * x[10] +\n        0.9221 * x[3] * x[5] * x[7] * x[8] - 0.428 * x[3] * x[5] * x[7] * x[9] -\n        0.4399 * x[3] * x[5] * x[7] * x[10] +\n        0.7566 * x[3] * x[5] * x[8] * x[9] +\n        0.354 * x[3] * x[5] * x[8] * x[10] - 0.5276 * x[3] * x[5] * x[9] * x[10] -\n        0.6272 * x[3] * x[6] * x[7] * x[8] - 0.8758 * x[3] * x[6] * x[7] * x[9] -\n        0.6662 * x[3] * x[6] * x[7] * x[10] - 0.5727 * x[3] * x[6] * x[8] * x[9] -\n        0.1467 * x[3] * x[6] * x[8] * x[10] - 0.8066 * x[3] * x[6] * x[9] * x[10] -\n        0.53 * x[3] * x[7] * x[8] * x[9] - 0.7406 * x[3] * x[7] * x[8] * x[10] +\n        0.8858 * x[3] * x[7] * x[9] * x[10] - 0.3289 * x[3] * x[8] * x[9] * x[10] -\n        0.8604 * x[4] * x[5] * x[6] * x[7] - 0.0148 * x[4] * x[5] * x[6] * x[8] +\n        0.3933 * x[4] * x[5] * x[6] * x[9] +\n        0.4846 * x[4] * x[5] * x[6] * x[10] - 0.7567 * x[4] * x[5] * x[7] * x[8] +\n        0.083 * x[4] * x[5] * x[7] * x[9] - 0.0985 * x[4] * x[5] * x[7] * x[10] +\n        0.3703 * x[4] * x[5] * x[8] * x[9] +\n        0.6679 * x[4] * x[5] * x[8] * x[10] +\n        0.8643 * x[4] * x[5] * x[9] * x[10] +\n        0.533 * x[4] * x[6] * x[7] * x[8] +\n        0.1871 * x[4] * x[6] * x[7] * x[9] - 0.1905 * x[4] * x[6] * x[7] * x[10] +\n        0.9994 * x[4] * x[6] * x[8] * x[9] - 0.7306 * x[4] * x[6] * x[8] * x[10] -\n        0.2797 * x[4] * x[6] * x[9] * x[10] - 0.7742 * x[4] * x[7] * x[8] * x[9] +\n        0.2634 * x[4] * x[7] * x[8] * x[10] - 0.6882 * x[4] * x[7] * x[9] * x[10] -\n        0.1916 * x[4] * x[8] * x[9] * x[10] - 0.6292 * x[5] * x[6] * x[7] * x[8] +\n        0.3706 * x[5] * x[6] * x[7] * x[9] +\n        0.2252 * x[5] * x[6] * x[7] * x[10] - 0.5111 * x[5] * x[6] * x[8] * x[9] -\n        0.7106 * x[5] * x[6] * x[8] * x[10] +\n        0.436 * x[5] * x[6] * x[9] * x[10] +\n        0.6397 * x[5] * x[7] * x[8] * x[9] - 0.7626 * x[5] * x[7] * x[8] * x[10] -\n        0.7465 * x[5] * x[7] * x[9] * x[10] - 0.4273 * x[5] * x[8] * x[9] * x[10] +\n        0.9735 * x[6] * x[7] * x[8] * x[9] - 0.5091 * x[6] * x[7] * x[8] * x[10] -\n        0.0217 * x[6] * x[7] * x[9] * x[10] - 0.9406 * x[6] * x[8] * x[9] * x[10] -\n        0.5301 * x[7] * x[8] * x[9] * x[10] <= 38.337\n    )\n    e3 = replace_expr(e3, x)\n    JuMP.add_nonlinear_constraint(m, e3)\n    e4 = :(\n        0.802 * x[1] * x[2] - 0.8383 * x[1] * x[3] +\n        0.3569 * x[1] * x[4] +\n        0.0003 * x[1] * x[5] +\n        0.8089 * x[1] * x[6] - 0.875 * x[1] * x[7] + 0.4462 * x[1] * x[8] -\n        0.3338 * x[1] * x[9] + 0.1814 * x[1] * x[10] - 0.8771 * x[2] * x[3] -\n        0.9101 * x[2] * x[4] + 0.1635 * x[2] * x[5] - 0.1352 * x[2] * x[6] -\n        0.8026 * x[2] * x[7] +\n        0.9155 * x[2] * x[8] +\n        0.5442 * x[2] * x[9] - 0.7053 * x[2] * x[10] +\n        0.4455 * x[3] * x[4] +\n        0.9929 * x[3] * x[5] - 0.3529 * x[3] * x[6] - 0.8803 * x[3] * x[7] -\n        0.9694 * x[3] * x[8] +\n        0.7938 * x[3] * x[9] +\n        0.664 * x[3] * x[10] +\n        0.5083 * x[4] * x[5] - 0.3124 * x[4] * x[6] - 0.4061 * x[4] * x[7] +\n        0.0858 * x[4] * x[8] - 0.2714 * x[4] * x[9] - 0.8232 * x[4] * x[10] -\n        0.1146 * x[5] * x[6] +\n        0.9703 * x[5] * x[7] +\n        0.9858 * x[5] * x[8] +\n        0.859 * x[5] * x[9] +\n        0.0264 * x[5] * x[10] - 0.8325 * x[6] * x[7] - 0.2402 * x[6] * x[8] +\n        0.9962 * x[6] * x[9] - 0.612 * x[6] * x[10] - 0.7468 * x[7] * x[8] +\n        0.5066 * x[7] * x[9] +\n        0.5209 * x[7] * x[10] - 0.8096 * x[8] * x[9] + 0.2097 * x[8] * x[10] -\n        0.8223 * x[9] * x[10] +\n        0.8219 * x[1] +\n        0.8915 * x[2] +\n        0.4384 * x[3] +\n        0.0104 * x[4] - 0.6145 * x[5] + 0.3569 * x[6] - 0.0835 * x[7] -\n        0.1778 * x[8] + 0.1688 * x[9] - 0.6302 * x[10] +\n        (-0.9893 * x[1] * x[2] * x[3]) - 0.5615 * x[1] * x[2] * x[4] +\n        0.7985 * x[1] * x[2] * x[5] +\n        0.1976 * x[1] * x[2] * x[6] - 0.1837 * x[1] * x[2] * x[7] -\n        0.7994 * x[1] * x[2] * x[8] - 0.7895 * x[1] * x[2] * x[9] +\n        0.146 * x[1] * x[2] * x[10] - 0.5227 * x[1] * x[3] * x[4] +\n        0.3006 * x[1] * x[3] * x[5] +\n        0.8038 * x[1] * x[3] * x[6] - 0.0596 * x[1] * x[3] * x[7] +\n        0.152 * x[1] * x[3] * x[8] +\n        0.5178 * x[1] * x[3] * x[9] - 0.1747 * x[1] * x[3] * x[10] +\n        0.9976 * x[1] * x[4] * x[5] +\n        0.1196 * x[1] * x[4] * x[6] - 0.5697 * x[1] * x[4] * x[7] -\n        0.8498 * x[1] * x[4] * x[8] - 0.6921 * x[1] * x[4] * x[9] -\n        0.0832 * x[1] * x[4] * x[10] +\n        0.7875 * x[1] * x[5] * x[6] +\n        0.2374 * x[1] * x[5] * x[7] +\n        0.2773 * x[1] * x[5] * x[8] +\n        0.8304 * x[1] * x[5] * x[9] - 0.2771 * x[1] * x[5] * x[10] +\n        0.8288 * x[1] * x[6] * x[7] - 0.6953 * x[1] * x[6] * x[8] +\n        0.9491 * x[1] * x[6] * x[9] - 0.1701 * x[1] * x[6] * x[10] +\n        0.4837 * x[1] * x[7] * x[8] - 0.9392 * x[1] * x[7] * x[9] -\n        0.0295 * x[1] * x[7] * x[10] +\n        0.8232 * x[1] * x[8] * x[9] +\n        0.8049 * x[1] * x[8] * x[10] +\n        0.8403 * x[1] * x[9] * x[10] +\n        0.0402 * x[2] * x[3] * x[4] +\n        0.4708 * x[2] * x[3] * x[5] +\n        0.653 * x[2] * x[3] * x[6] +\n        0.4072 * x[2] * x[3] * x[7] +\n        0.3477 * x[2] * x[3] * x[8] - 0.8469 * x[2] * x[3] * x[9] -\n        0.0643 * x[2] * x[3] * x[10] +\n        0.9855 * x[2] * x[4] * x[5] +\n        0.169 * x[2] * x[4] * x[6] +\n        0.1277 * x[2] * x[4] * x[7] +\n        0.1701 * x[2] * x[4] * x[8] - 0.2288 * x[2] * x[4] * x[9] +\n        0.6269 * x[2] * x[4] * x[10] - 0.165 * x[2] * x[5] * x[6] -\n        0.3328 * x[2] * x[5] * x[7] +\n        0.0711 * x[2] * x[5] * x[8] +\n        0.8548 * x[2] * x[5] * x[9] +\n        0.4886 * x[2] * x[5] * x[10] - 0.4103 * x[2] * x[6] * x[7] +\n        0.1394 * x[2] * x[6] * x[8] - 0.3792 * x[2] * x[6] * x[9] -\n        0.061 * x[2] * x[6] * x[10] - 0.6923 * x[2] * x[7] * x[8] +\n        0.194 * x[2] * x[7] * x[9] - 0.2253 * x[2] * x[7] * x[10] -\n        0.6197 * x[2] * x[8] * x[9] - 0.799 * x[2] * x[8] * x[10] -\n        0.9851 * x[2] * x[9] * x[10] - 0.164 * x[3] * x[4] * x[5] +\n        0.1448 * x[3] * x[4] * x[6] +\n        0.0185 * x[3] * x[4] * x[7] +\n        0.3829 * x[3] * x[4] * x[8] +\n        0.2687 * x[3] * x[4] * x[9] +\n        0.9428 * x[3] * x[4] * x[10] +\n        0.9418 * x[3] * x[5] * x[6] +\n        0.4694 * x[3] * x[5] * x[7] +\n        0.8523 * x[3] * x[5] * x[8] - 0.87 * x[3] * x[5] * x[9] -\n        0.5796 * x[3] * x[5] * x[10] - 0.486 * x[3] * x[6] * x[7] +\n        0.3746 * x[3] * x[6] * x[8] +\n        0.4788 * x[3] * x[6] * x[9] +\n        0.0586 * x[3] * x[6] * x[10] +\n        0.1473 * x[3] * x[7] * x[8] +\n        0.2498 * x[3] * x[7] * x[9] - 0.6388 * x[3] * x[7] * x[10] +\n        0.2472 * x[3] * x[8] * x[9] - 0.3687 * x[3] * x[8] * x[10] +\n        0.3536 * x[3] * x[9] * x[10] +\n        0.0072 * x[4] * x[5] * x[6] - 0.5806 * x[4] * x[5] * x[7] -\n        0.5058 * x[4] * x[5] * x[8] - 0.116 * x[4] * x[5] * x[9] +\n        0.191 * x[4] * x[5] * x[10] +\n        0.3699 * x[4] * x[6] * x[7] +\n        0.3731 * x[4] * x[6] * x[8] +\n        0.0031 * x[4] * x[6] * x[9] +\n        0.9294 * x[4] * x[6] * x[10] - 0.6047 * x[4] * x[7] * x[8] +\n        0.2348 * x[4] * x[7] * x[9] +\n        0.8324 * x[4] * x[7] * x[10] +\n        0.6608 * x[4] * x[8] * x[9] - 0.1673 * x[4] * x[8] * x[10] -\n        0.9519 * x[4] * x[9] * x[10] + 0.8066 * x[5] * x[6] * x[7] -\n        0.9313 * x[5] * x[6] * x[8] - 0.0297 * x[5] * x[6] * x[9] -\n        0.7382 * x[5] * x[6] * x[10] - 0.672 * x[5] * x[7] * x[8] +\n        0.3061 * x[5] * x[7] * x[9] - 0.1984 * x[5] * x[7] * x[10] -\n        0.8696 * x[5] * x[8] * x[9] - 0.5035 * x[5] * x[8] * x[10] +\n        0.2835 * x[5] * x[9] * x[10] +\n        0.2576 * x[6] * x[7] * x[8] - 0.5016 * x[6] * x[7] * x[9] -\n        0.738 * x[6] * x[7] * x[10] - 0.6402 * x[6] * x[8] * x[9] +\n        0.2333 * x[6] * x[8] * x[10] - 0.1863 * x[6] * x[9] * x[10] +\n        0.6045 * x[7] * x[8] * x[9] - 0.5819 * x[7] * x[8] * x[10] -\n        0.809 * x[7] * x[9] * x[10] - 0.3189 * x[8] * x[9] * x[10] +\n        0.8521 * x[1] * x[2] * x[3] * x[5] - 0.8164 * x[1] * x[2] * x[3] * x[4] +\n        0.4163 * x[1] * x[2] * x[3] * x[6] +\n        0.6625 * x[1] * x[2] * x[3] * x[7] +\n        0.6022 * x[1] * x[2] * x[3] * x[8] +\n        0.1782 * x[1] * x[2] * x[3] * x[9] +\n        0.63 * x[1] * x[2] * x[3] * x[10] +\n        0.4385 * x[1] * x[2] * x[4] * x[5] +\n        0.9963 * x[1] * x[2] * x[4] * x[6] +\n        0.8737 * x[1] * x[2] * x[4] * x[7] +\n        0.382 * x[1] * x[2] * x[4] * x[8] +\n        0.4417 * x[1] * x[2] * x[4] * x[9] +\n        0.2669 * x[1] * x[2] * x[4] * x[10] +\n        0.7712 * x[1] * x[2] * x[5] * x[6] +\n        0.5226 * x[1] * x[2] * x[5] * x[7] +\n        0.3681 * x[1] * x[2] * x[5] * x[8] +\n        0.7255 * x[1] * x[2] * x[5] * x[9] - 0.4059 * x[1] * x[2] * x[5] * x[10] +\n        0.9658 * x[1] * x[2] * x[6] * x[7] - 0.8057 * x[1] * x[2] * x[6] * x[8] +\n        0.2716 * x[1] * x[2] * x[6] * x[9] - 0.8667 * x[1] * x[2] * x[6] * x[10] -\n        0.6541 * x[1] * x[2] * x[7] * x[8] - 0.0723 * x[1] * x[2] * x[7] * x[9] -\n        0.1218 * x[1] * x[2] * x[7] * x[10] + 0.6082 * x[1] * x[2] * x[8] * x[9] -\n        0.1423 * x[1] * x[2] * x[8] * x[10] +\n        0.5249 * x[1] * x[2] * x[9] * x[10] +\n        0.4167 * x[1] * x[3] * x[4] * x[5] - 0.507 * x[1] * x[3] * x[4] * x[6] +\n        0.8024 * x[1] * x[3] * x[4] * x[7] - 0.8732 * x[1] * x[3] * x[4] * x[8] -\n        0.9641 * x[1] * x[3] * x[4] * x[9] + 0.8948 * x[1] * x[3] * x[4] * x[10] -\n        0.0228 * x[1] * x[3] * x[5] * x[6] - 0.2308 * x[1] * x[3] * x[5] * x[7] -\n        0.8365 * x[1] * x[3] * x[5] * x[8] - 0.0407 * x[1] * x[3] * x[5] * x[9] -\n        0.6009 * x[1] * x[3] * x[5] * x[10] - 0.2916 * x[1] * x[3] * x[6] * x[7] -\n        0.1374 * x[1] * x[3] * x[6] * x[8] +\n        0.8125 * x[1] * x[3] * x[6] * x[9] +\n        0.8725 * x[1] * x[3] * x[6] * x[10] +\n        0.4909 * x[1] * x[3] * x[7] * x[8] +\n        0.9356 * x[1] * x[3] * x[7] * x[9] +\n        0.7571 * x[1] * x[3] * x[7] * x[10] - 0.4834 * x[1] * x[3] * x[8] * x[9] +\n        0.5875 * x[1] * x[3] * x[8] * x[10] - 0.8418 * x[1] * x[3] * x[9] * x[10] -\n        0.9637 * x[1] * x[4] * x[5] * x[6] - 0.3318 * x[1] * x[4] * x[5] * x[7] -\n        0.3304 * x[1] * x[4] * x[5] * x[8] + 0.0086 * x[1] * x[4] * x[5] * x[9] -\n        0.2382 * x[1] * x[4] * x[5] * x[10] + 0.7865 * x[1] * x[4] * x[6] * x[7] -\n        0.4775 * x[1] * x[4] * x[6] * x[8] - 0.0112 * x[1] * x[4] * x[6] * x[9] +\n        0.4793 * x[1] * x[4] * x[6] * x[10] +\n        0.2361 * x[1] * x[4] * x[7] * x[8] +\n        0.3537 * x[1] * x[4] * x[7] * x[9] +\n        0.4693 * x[1] * x[4] * x[7] * x[10] +\n        0.7316 * x[1] * x[4] * x[8] * x[9] +\n        0.3182 * x[1] * x[4] * x[8] * x[10] +\n        0.8041 * x[1] * x[4] * x[9] * x[10] - 0.4561 * x[1] * x[5] * x[6] * x[7] +\n        0.8676 * x[1] * x[5] * x[6] * x[8] - 0.7196 * x[1] * x[5] * x[6] * x[9] -\n        0.3273 * x[1] * x[5] * x[6] * x[10] - 0.0517 * x[1] * x[5] * x[7] * x[8] -\n        0.9975 * x[1] * x[5] * x[7] * x[9] - 0.5365 * x[1] * x[5] * x[7] * x[10] +\n        0.9168 * x[1] * x[5] * x[8] * x[9] +\n        0.7715 * x[1] * x[5] * x[8] * x[10] +\n        0.1129 * x[1] * x[5] * x[9] * x[10] - 0.3254 * x[1] * x[6] * x[7] * x[8] -\n        0.6267 * x[1] * x[6] * x[7] * x[9] - 0.2341 * x[1] * x[6] * x[7] * x[10] +\n        0.332 * x[1] * x[6] * x[8] * x[9] +\n        0.8281 * x[1] * x[6] * x[8] * x[10] - 0.1747 * x[1] * x[6] * x[9] * x[10] +\n        0.9767 * x[1] * x[7] * x[8] * x[9] - 0.6643 * x[1] * x[7] * x[8] * x[10] -\n        0.7506 * x[1] * x[7] * x[9] * x[10] + 0.0168 * x[1] * x[8] * x[9] * x[10] -\n        0.0513 * x[2] * x[3] * x[4] * x[5] - 0.6878 * x[2] * x[3] * x[4] * x[6] -\n        0.0265 * x[2] * x[3] * x[4] * x[7] +\n        0.6138 * x[2] * x[3] * x[4] * x[8] +\n        0.9757 * x[2] * x[3] * x[4] * x[9] - 0.8293 * x[2] * x[3] * x[4] * x[10] +\n        0.9219 * x[2] * x[3] * x[5] * x[6] +\n        0.403 * x[2] * x[3] * x[5] * x[7] - 0.0383 * x[2] * x[3] * x[5] * x[8] -\n        0.1156 * x[2] * x[3] * x[5] * x[9] - 0.9505 * x[2] * x[3] * x[5] * x[10] -\n        0.5166 * x[2] * x[3] * x[6] * x[7] - 0.7652 * x[2] * x[3] * x[6] * x[8] -\n        0.9915 * x[2] * x[3] * x[6] * x[9] - 0.477 * x[2] * x[3] * x[6] * x[10] +\n        0.1948 * x[2] * x[3] * x[7] * x[8] - 0.9361 * x[2] * x[3] * x[7] * x[9] -\n        0.0442 * x[2] * x[3] * x[7] * x[10] - 0.4517 * x[2] * x[3] * x[8] * x[9] -\n        0.8448 * x[2] * x[3] * x[8] * x[10] - 0.8462 * x[2] * x[3] * x[9] * x[10] +\n        0.7179 * x[2] * x[4] * x[5] * x[6] +\n        0.1438 * x[2] * x[4] * x[5] * x[7] - 0.831 * x[2] * x[4] * x[5] * x[8] +\n        0.1377 * x[2] * x[4] * x[5] * x[9] +\n        0.2404 * x[2] * x[4] * x[5] * x[10] +\n        0.4776 * x[2] * x[4] * x[6] * x[7] +\n        0.9781 * x[2] * x[4] * x[6] * x[8] - 0.4061 * x[2] * x[4] * x[6] * x[9] -\n        0.8912 * x[2] * x[4] * x[6] * x[10] +\n        0.9125 * x[2] * x[4] * x[7] * x[8] +\n        0.706 * x[2] * x[4] * x[7] * x[9] - 0.8906 * x[2] * x[4] * x[7] * x[10] +\n        0.942 * x[2] * x[4] * x[8] * x[9] - 0.0261 * x[2] * x[4] * x[8] * x[10] -\n        0.068 * x[2] * x[4] * x[9] * x[10] - 0.847 * x[2] * x[5] * x[6] * x[7] +\n        0.5746 * x[2] * x[5] * x[6] * x[8] - 0.3526 * x[2] * x[5] * x[6] * x[9] +\n        0.4389 * x[2] * x[5] * x[6] * x[10] +\n        0.4542 * x[2] * x[5] * x[7] * x[8] +\n        0.0367 * x[2] * x[5] * x[7] * x[9] - 0.3709 * x[2] * x[5] * x[7] * x[10] +\n        0.8193 * x[2] * x[5] * x[8] * x[9] +\n        0.5633 * x[2] * x[5] * x[8] * x[10] - 0.0382 * x[2] * x[5] * x[9] * x[10] -\n        0.959 * x[2] * x[6] * x[7] * x[8] - 0.7036 * x[2] * x[6] * x[7] * x[9] +\n        0.7485 * x[2] * x[6] * x[7] * x[10] - 0.0868 * x[2] * x[6] * x[8] * x[9] -\n        0.6044 * x[2] * x[6] * x[8] * x[10] +\n        0.3054 * x[2] * x[6] * x[9] * x[10] +\n        0.6064 * x[2] * x[7] * x[8] * x[9] - 0.5288 * x[2] * x[7] * x[8] * x[10] -\n        0.0285 * x[2] * x[7] * x[9] * x[10] - 0.5481 * x[2] * x[8] * x[9] * x[10] -\n        0.7647 * x[3] * x[4] * x[5] * x[6] + 0.6671 * x[3] * x[4] * x[5] * x[7] -\n        0.0921 * x[3] * x[4] * x[5] * x[8] + 0.7822 * x[3] * x[4] * x[5] * x[9] -\n        0.688 * x[3] * x[4] * x[5] * x[10] - 0.623 * x[3] * x[4] * x[6] * x[7] -\n        0.6958 * x[3] * x[4] * x[6] * x[8] +\n        0.2072 * x[3] * x[4] * x[6] * x[9] +\n        0.8573 * x[3] * x[4] * x[6] * x[10] +\n        0.9353 * x[3] * x[4] * x[7] * x[8] - 0.7581 * x[3] * x[4] * x[7] * x[9] -\n        0.6678 * x[3] * x[4] * x[7] * x[10] +\n        0.7244 * x[3] * x[4] * x[8] * x[9] +\n        0.497 * x[3] * x[4] * x[8] * x[10] +\n        0.8841 * x[3] * x[4] * x[9] * x[10] - 0.419 * x[3] * x[5] * x[6] * x[7] -\n        0.5639 * x[3] * x[5] * x[6] * x[8] +\n        0.3384 * x[3] * x[5] * x[6] * x[9] +\n        0.8517 * x[3] * x[5] * x[6] * x[10] +\n        0.2487 * x[3] * x[5] * x[7] * x[8] +\n        0.352 * x[3] * x[5] * x[7] * x[9] - 0.9956 * x[3] * x[5] * x[7] * x[10] +\n        0.1963 * x[3] * x[5] * x[8] * x[9] +\n        0.6505 * x[3] * x[5] * x[8] * x[10] +\n        0.8868 * x[3] * x[5] * x[9] * x[10] +\n        0.064 * x[3] * x[6] * x[7] * x[8] - 0.2306 * x[3] * x[6] * x[7] * x[9] +\n        0.3456 * x[3] * x[6] * x[7] * x[10] - 0.0124 * x[3] * x[6] * x[8] * x[9] -\n        0.7644 * x[3] * x[6] * x[8] * x[10] - 0.9407 * x[3] * x[6] * x[9] * x[10] -\n        0.5041 * x[3] * x[7] * x[8] * x[9] - 0.4612 * x[3] * x[7] * x[8] * x[10] +\n        0.6372 * x[3] * x[7] * x[9] * x[10] - 0.9423 * x[3] * x[8] * x[9] * x[10] +\n        0.4769 * x[4] * x[5] * x[6] * x[7] +\n        0.6691 * x[4] * x[5] * x[6] * x[8] - 0.6518 * x[4] * x[5] * x[6] * x[9] +\n        0.5892 * x[4] * x[5] * x[6] * x[10] +\n        0.1282 * x[4] * x[5] * x[7] * x[8] - 0.0097 * x[4] * x[5] * x[7] * x[9] -\n        0.0037 * x[4] * x[5] * x[7] * x[10] - 0.4974 * x[4] * x[5] * x[8] * x[9] -\n        0.1368 * x[4] * x[5] * x[8] * x[10] - 0.663 * x[4] * x[5] * x[9] * x[10] -\n        0.3471 * x[4] * x[6] * x[7] * x[8] - 0.9665 * x[4] * x[6] * x[7] * x[9] -\n        0.6331 * x[4] * x[6] * x[7] * x[10] - 0.0998 * x[4] * x[6] * x[8] * x[9] +\n        0.9348 * x[4] * x[6] * x[8] * x[10] - 0.5585 * x[4] * x[6] * x[9] * x[10] -\n        0.1588 * x[4] * x[7] * x[8] * x[9] + 0.3535 * x[4] * x[7] * x[8] * x[10] -\n        0.5013 * x[4] * x[7] * x[9] * x[10] +\n        0.5619 * x[4] * x[8] * x[9] * x[10] +\n        0.6594 * x[5] * x[6] * x[7] * x[8] - 0.6765 * x[5] * x[6] * x[7] * x[9] +\n        0.8412 * x[5] * x[6] * x[7] * x[10] - 0.6171 * x[5] * x[6] * x[8] * x[9] +\n        0.5953 * x[5] * x[6] * x[8] * x[10] +\n        0.9679 * x[5] * x[6] * x[9] * x[10] +\n        0.7684 * x[5] * x[7] * x[8] * x[9] +\n        0.3959 * x[5] * x[7] * x[8] * x[10] +\n        0.61 * x[5] * x[7] * x[9] * x[10] +\n        0.6235 * x[5] * x[8] * x[9] * x[10] - 0.2316 * x[6] * x[7] * x[8] * x[9] +\n        0.2738 * x[6] * x[7] * x[8] * x[10] - 0.5261 * x[6] * x[7] * x[9] * x[10] +\n        0.6011 * x[6] * x[8] * x[9] * x[10] +\n        0.421 * x[7] * x[8] * x[9] * x[10] <= 52.864\n    )\n    e4 = replace_expr(e4, x)\n    JuMP.add_nonlinear_constraint(m, e4)\n    e5 = :(\n        (-0.1375 * x[1] * x[2]) - 0.0134 * x[1] * x[3] - 0.7802 * x[1] * x[4] +\n        0.1529 * x[1] * x[5] - 0.7427 * x[1] * x[6] + 0.034 * x[1] * x[7] -\n        0.1986 * x[1] * x[8] + 0.1794 * x[1] * x[9] - 0.2451 * x[1] * x[10] -\n        0.1578 * x[2] * x[3] +\n        0.2522 * x[2] * x[4] +\n        0.562 * x[2] * x[5] +\n        0.9868 * x[2] * x[6] +\n        0.0232 * x[2] * x[7] +\n        0.5897 * x[2] * x[8] +\n        0.1998 * x[2] * x[9] - 0.9026 * x[2] * x[10] + 0.5954 * x[3] * x[4] -\n        0.0184 * x[3] * x[5] - 0.9132 * x[3] * x[6] - 0.0269 * x[3] * x[7] +\n        0.5776 * x[3] * x[8] +\n        0.2437 * x[3] * x[9] - 0.9638 * x[3] * x[10] + 0.4683 * x[4] * x[5] -\n        0.0524 * x[4] * x[6] + 0.865 * x[4] * x[7] - 0.0714 * x[4] * x[8] -\n        0.5196 * x[4] * x[9] +\n        0.2146 * x[4] * x[10] +\n        0.2514 * x[5] * x[6] - 0.9667 * x[5] * x[7] - 0.328 * x[5] * x[8] +\n        0.185 * x[5] * x[9] - 0.1588 * x[5] * x[10] - 0.6343 * x[6] * x[7] +\n        0.7847 * x[6] * x[8] +\n        0.2423 * x[6] * x[9] - 0.357 * x[6] * x[10] - 0.2066 * x[7] * x[8] -\n        0.1247 * x[7] * x[9] - 0.9086 * x[7] * x[10] - 0.4053 * x[8] * x[9] -\n        0.6526 * x[8] * x[10] - 0.7753 * x[9] * x[10] +\n        0.6139 * x[1] +\n        0.0606 * x[2] - 0.4917 * x[3] + 0.82 * x[4] - 0.8487 * x[5] - 0.4958 * x[6] -\n        0.4949 * x[7] +\n        0.7862 * x[8] +\n        0.7091 * x[9] - 0.6288 * x[10] + 0.496 * x[1] * x[2] * x[3] -\n        0.6663 * x[1] * x[2] * x[4] + 0.2055 * x[1] * x[2] * x[5] -\n        0.1878 * x[1] * x[2] * x[6] +\n        0.5555 * x[1] * x[2] * x[7] +\n        0.0953 * x[1] * x[2] * x[8] - 0.3364 * x[1] * x[2] * x[9] -\n        0.0269 * x[1] * x[2] * x[10] + 0.958 * x[1] * x[3] * x[4] -\n        0.871 * x[1] * x[3] * x[5] - 0.3226 * x[1] * x[3] * x[6] -\n        0.8197 * x[1] * x[3] * x[7] - 0.1814 * x[1] * x[3] * x[8] -\n        0.8487 * x[1] * x[3] * x[9] + 0.2095 * x[1] * x[3] * x[10] -\n        0.2767 * x[1] * x[4] * x[5] - 0.3641 * x[1] * x[4] * x[6] -\n        0.0245 * x[1] * x[4] * x[7] +\n        0.4568 * x[1] * x[4] * x[8] +\n        0.3128 * x[1] * x[4] * x[9] +\n        0.4853 * x[1] * x[4] * x[10] +\n        0.9152 * x[1] * x[5] * x[6] - 0.5344 * x[1] * x[5] * x[7] +\n        0.9609 * x[1] * x[5] * x[8] +\n        0.1761 * x[1] * x[5] * x[9] +\n        0.344 * x[1] * x[5] * x[10] - 0.3941 * x[1] * x[6] * x[7] +\n        0.8352 * x[1] * x[6] * x[8] - 0.8145 * x[1] * x[6] * x[9] +\n        0.4713 * x[1] * x[6] * x[10] - 0.2967 * x[1] * x[7] * x[8] +\n        0.1227 * x[1] * x[7] * x[9] +\n        0.6128 * x[1] * x[7] * x[10] - 0.5156 * x[1] * x[8] * x[9] -\n        0.1357 * x[1] * x[8] * x[10] + 0.4391 * x[1] * x[9] * x[10] -\n        0.916 * x[2] * x[3] * x[4] - 0.9986 * x[2] * x[3] * x[5] +\n        0.3863 * x[2] * x[3] * x[6] - 0.0975 * x[2] * x[3] * x[7] +\n        0.8211 * x[2] * x[3] * x[8] +\n        0.6467 * x[2] * x[3] * x[9] +\n        0.054 * x[2] * x[3] * x[10] +\n        0.0186 * x[2] * x[4] * x[5] +\n        0.3056 * x[2] * x[4] * x[6] +\n        0.6154 * x[2] * x[4] * x[7] +\n        0.0074 * x[2] * x[4] * x[8] +\n        0.4949 * x[2] * x[4] * x[9] +\n        0.6723 * x[2] * x[4] * x[10] +\n        0.3352 * x[2] * x[5] * x[6] +\n        0.0008 * x[2] * x[5] * x[7] +\n        0.5953 * x[2] * x[5] * x[8] - 0.6033 * x[2] * x[5] * x[9] +\n        0.5045 * x[2] * x[5] * x[10] - 0.269 * x[2] * x[6] * x[7] +\n        0.6495 * x[2] * x[6] * x[8] +\n        0.8248 * x[2] * x[6] * x[9] - 0.6363 * x[2] * x[6] * x[10] +\n        0.6394 * x[2] * x[7] * x[8] +\n        0.1078 * x[2] * x[7] * x[9] +\n        0.8161 * x[2] * x[7] * x[10] - 0.4037 * x[2] * x[8] * x[9] +\n        0.2088 * x[2] * x[8] * x[10] - 0.6234 * x[2] * x[9] * x[10] -\n        0.5131 * x[3] * x[4] * x[5] - 0.3159 * x[3] * x[4] * x[6] -\n        0.3376 * x[3] * x[4] * x[7] - 0.8348 * x[3] * x[4] * x[8] -\n        0.4805 * x[3] * x[4] * x[9] +\n        0.8075 * x[3] * x[4] * x[10] +\n        0.1383 * x[3] * x[5] * x[6] - 0.8913 * x[3] * x[5] * x[7] -\n        0.4103 * x[3] * x[5] * x[8] + 0.4252 * x[3] * x[5] * x[9] -\n        0.7663 * x[3] * x[5] * x[10] - 0.9546 * x[3] * x[6] * x[7] +\n        0.1664 * x[3] * x[6] * x[8] - 0.1357 * x[3] * x[6] * x[9] +\n        0.843 * x[3] * x[6] * x[10] - 0.4141 * x[3] * x[7] * x[8] +\n        0.9824 * x[3] * x[7] * x[9] +\n        0.8706 * x[3] * x[7] * x[10] +\n        0.3098 * x[3] * x[8] * x[9] - 0.8453 * x[3] * x[8] * x[10] +\n        0.4691 * x[3] * x[9] * x[10] - 0.4006 * x[4] * x[5] * x[6] +\n        0.3848 * x[4] * x[5] * x[7] +\n        0.9792 * x[4] * x[5] * x[8] - 0.4612 * x[4] * x[5] * x[9] -\n        0.9516 * x[4] * x[5] * x[10] - 0.4543 * x[4] * x[6] * x[7] +\n        0.5378 * x[4] * x[6] * x[8] - 0.8641 * x[4] * x[6] * x[9] +\n        0.6423 * x[4] * x[6] * x[10] - 0.8484 * x[4] * x[7] * x[8] -\n        0.3092 * x[4] * x[7] * x[9] +\n        0.6513 * x[4] * x[7] * x[10] +\n        0.0055 * x[4] * x[8] * x[9] +\n        0.0029 * x[4] * x[8] * x[10] +\n        0.9821 * x[4] * x[9] * x[10] +\n        0.477 * x[5] * x[6] * x[7] +\n        0.9873 * x[5] * x[6] * x[8] +\n        0.2413 * x[5] * x[6] * x[9] +\n        0.3671 * x[5] * x[6] * x[10] - 0.2025 * x[5] * x[7] * x[8] -\n        0.5689 * x[5] * x[7] * x[9] +\n        0.6425 * x[5] * x[7] * x[10] +\n        0.4043 * x[5] * x[8] * x[9] - 0.2493 * x[5] * x[8] * x[10] -\n        0.4849 * x[5] * x[9] * x[10] + 0.3103 * x[6] * x[7] * x[8] -\n        0.2523 * x[6] * x[7] * x[9] +\n        0.7611 * x[6] * x[7] * x[10] +\n        0.3698 * x[6] * x[8] * x[9] - 0.8896 * x[6] * x[8] * x[10] +\n        0.7634 * x[6] * x[9] * x[10] - 0.3524 * x[7] * x[8] * x[9] -\n        0.7996 * x[7] * x[8] * x[10] +\n        0.4739 * x[7] * x[9] * x[10] +\n        0.5203 * x[8] * x[9] * x[10] +\n        0.8851 * x[1] * x[2] * x[3] * x[4] +\n        0.9515 * x[1] * x[2] * x[3] * x[5] - 0.0604 * x[1] * x[2] * x[3] * x[6] -\n        0.8915 * x[1] * x[2] * x[3] * x[7] - 0.0968 * x[1] * x[2] * x[3] * x[8] -\n        0.5954 * x[1] * x[2] * x[3] * x[9] - 0.902 * x[1] * x[2] * x[3] * x[10] +\n        0.9315 * x[1] * x[2] * x[4] * x[5] +\n        0.4294 * x[1] * x[2] * x[4] * x[6] +\n        0.7398 * x[1] * x[2] * x[4] * x[7] - 0.6759 * x[1] * x[2] * x[4] * x[8] -\n        0.0166 * x[1] * x[2] * x[4] * x[9] + 0.3176 * x[1] * x[2] * x[4] * x[10] -\n        0.434 * x[1] * x[2] * x[5] * x[6] - 0.8219 * x[1] * x[2] * x[5] * x[7] -\n        0.9323 * x[1] * x[2] * x[5] * x[8] - 0.2384 * x[1] * x[2] * x[5] * x[9] +\n        0.2604 * x[1] * x[2] * x[5] * x[10] +\n        0.4567 * x[1] * x[2] * x[6] * x[7] +\n        0.7508 * x[1] * x[2] * x[6] * x[8] +\n        0.1384 * x[1] * x[2] * x[6] * x[9] - 0.5557 * x[1] * x[2] * x[6] * x[10] -\n        0.2385 * x[1] * x[2] * x[7] * x[8] +\n        0.0199 * x[1] * x[2] * x[7] * x[9] +\n        0.7632 * x[1] * x[2] * x[7] * x[10] - 0.9947 * x[1] * x[2] * x[8] * x[9] -\n        0.3877 * x[1] * x[2] * x[8] * x[10] + 0.8177 * x[1] * x[2] * x[9] * x[10] -\n        0.3725 * x[1] * x[3] * x[4] * x[5] - 0.3487 * x[1] * x[3] * x[4] * x[6] -\n        0.8521 * x[1] * x[3] * x[4] * x[7] + 0.7201 * x[1] * x[3] * x[4] * x[8] -\n        0.9411 * x[1] * x[3] * x[4] * x[9] - 0.6075 * x[1] * x[3] * x[4] * x[10] +\n        0.4446 * x[1] * x[3] * x[5] * x[6] - 0.6889 * x[1] * x[3] * x[5] * x[7] +\n        0.5368 * x[1] * x[3] * x[5] * x[8] +\n        0.9675 * x[1] * x[3] * x[5] * x[9] - 0.1386 * x[1] * x[3] * x[5] * x[10] -\n        0.4474 * x[1] * x[3] * x[6] * x[7] - 0.8875 * x[1] * x[3] * x[6] * x[8] -\n        0.7171 * x[1] * x[3] * x[6] * x[9] - 0.2179 * x[1] * x[3] * x[6] * x[10] -\n        0.317 * x[1] * x[3] * x[7] * x[8] - 0.0332 * x[1] * x[3] * x[7] * x[9] -\n        0.625 * x[1] * x[3] * x[7] * x[10] +\n        0.2913 * x[1] * x[3] * x[8] * x[9] +\n        0.0755 * x[1] * x[3] * x[8] * x[10] - 0.0178 * x[1] * x[3] * x[9] * x[10] -\n        0.215 * x[1] * x[4] * x[5] * x[6] - 0.7588 * x[1] * x[4] * x[5] * x[7] +\n        0.2416 * x[1] * x[4] * x[5] * x[8] - 0.1383 * x[1] * x[4] * x[5] * x[9] +\n        0.2175 * x[1] * x[4] * x[5] * x[10] - 0.5311 * x[1] * x[4] * x[6] * x[7] -\n        0.6322 * x[1] * x[4] * x[6] * x[8] - 0.8211 * x[1] * x[4] * x[6] * x[9] -\n        0.2421 * x[1] * x[4] * x[6] * x[10] - 0.9794 * x[1] * x[4] * x[7] * x[8] +\n        0.6866 * x[1] * x[4] * x[7] * x[9] +\n        0.144 * x[1] * x[4] * x[7] * x[10] +\n        0.935 * x[1] * x[4] * x[8] * x[9] - 0.7224 * x[1] * x[4] * x[8] * x[10] -\n        0.79 * x[1] * x[4] * x[9] * x[10] - 0.6261 * x[1] * x[5] * x[6] * x[7] -\n        0.59 * x[1] * x[5] * x[6] * x[8] +\n        0.8708 * x[1] * x[5] * x[6] * x[9] +\n        0.5423 * x[1] * x[5] * x[6] * x[10] +\n        0.3356 * x[1] * x[5] * x[7] * x[8] +\n        0.142 * x[1] * x[5] * x[7] * x[9] +\n        0.5119 * x[1] * x[5] * x[7] * x[10] +\n        0.7599 * x[1] * x[5] * x[8] * x[9] - 0.4022 * x[1] * x[5] * x[8] * x[10] +\n        0.4446 * x[1] * x[5] * x[9] * x[10] - 0.8166 * x[1] * x[6] * x[7] * x[8] +\n        0.6446 * x[1] * x[6] * x[7] * x[9] - 0.1284 * x[1] * x[6] * x[7] * x[10] -\n        0.3651 * x[1] * x[6] * x[8] * x[9] - 0.2567 * x[1] * x[6] * x[8] * x[10] +\n        0.1421 * x[1] * x[6] * x[9] * x[10] - 0.8825 * x[1] * x[7] * x[8] * x[9] -\n        0.6058 * x[1] * x[7] * x[8] * x[10] + 0.503 * x[1] * x[7] * x[9] * x[10] -\n        0.0462 * x[1] * x[8] * x[9] * x[10] - 0.717 * x[2] * x[3] * x[4] * x[5] +\n        0.0253 * x[2] * x[3] * x[4] * x[6] - 0.9476 * x[2] * x[3] * x[4] * x[7] -\n        0.3171 * x[2] * x[3] * x[4] * x[8] + 0.5691 * x[2] * x[3] * x[4] * x[9] -\n        0.3612 * x[2] * x[3] * x[4] * x[10] +\n        0.0488 * x[2] * x[3] * x[5] * x[6] +\n        0.423 * x[2] * x[3] * x[5] * x[7] +\n        0.2762 * x[2] * x[3] * x[5] * x[8] +\n        0.0221 * x[2] * x[3] * x[5] * x[9] +\n        0.3975 * x[2] * x[3] * x[5] * x[10] - 0.5281 * x[2] * x[3] * x[6] * x[7] -\n        0.722 * x[2] * x[3] * x[6] * x[8] - 0.1433 * x[2] * x[3] * x[6] * x[9] +\n        0.1957 * x[2] * x[3] * x[6] * x[10] +\n        0.7882 * x[2] * x[3] * x[7] * x[8] +\n        0.9988 * x[2] * x[3] * x[7] * x[9] +\n        0.8552 * x[2] * x[3] * x[7] * x[10] +\n        0.3681 * x[2] * x[3] * x[8] * x[9] - 0.6187 * x[2] * x[3] * x[8] * x[10] -\n        0.2208 * x[2] * x[3] * x[9] * x[10] - 0.8222 * x[2] * x[4] * x[5] * x[6] +\n        0.3944 * x[2] * x[4] * x[5] * x[7] +\n        0.4808 * x[2] * x[4] * x[5] * x[8] - 0.8075 * x[2] * x[4] * x[5] * x[9] -\n        0.8579 * x[2] * x[4] * x[5] * x[10] - 0.5665 * x[2] * x[4] * x[6] * x[7] -\n        0.895 * x[2] * x[4] * x[6] * x[8] - 0.3975 * x[2] * x[4] * x[6] * x[9] +\n        0.4934 * x[2] * x[4] * x[6] * x[10] +\n        0.2624 * x[2] * x[4] * x[7] * x[8] +\n        0.2931 * x[2] * x[4] * x[7] * x[9] - 0.8108 * x[2] * x[4] * x[7] * x[10] -\n        0.6769 * x[2] * x[4] * x[8] * x[9] - 0.2571 * x[2] * x[4] * x[8] * x[10] +\n        0.1818 * x[2] * x[4] * x[9] * x[10] - 0.5706 * x[2] * x[5] * x[6] * x[7] +\n        0.6166 * x[2] * x[5] * x[6] * x[8] - 0.7727 * x[2] * x[5] * x[6] * x[9] -\n        0.2887 * x[2] * x[5] * x[6] * x[10] - 0.6625 * x[2] * x[5] * x[7] * x[8] -\n        0.4673 * x[2] * x[5] * x[7] * x[9] + 0.9985 * x[2] * x[5] * x[7] * x[10] -\n        0.0513 * x[2] * x[5] * x[8] * x[9] - 0.243 * x[2] * x[5] * x[8] * x[10] +\n        0.9283 * x[2] * x[5] * x[9] * x[10] - 0.9095 * x[2] * x[6] * x[7] * x[8] +\n        0.0583 * x[2] * x[6] * x[7] * x[9] +\n        0.823 * x[2] * x[6] * x[7] * x[10] - 0.5969 * x[2] * x[6] * x[8] * x[9] +\n        0.8222 * x[2] * x[6] * x[8] * x[10] - 0.0405 * x[2] * x[6] * x[9] * x[10] -\n        0.131 * x[2] * x[7] * x[8] * x[9] - 0.3485 * x[2] * x[7] * x[8] * x[10] +\n        0.8998 * x[2] * x[7] * x[9] * x[10] - 0.2805 * x[2] * x[8] * x[9] * x[10] +\n        0.5217 * x[3] * x[4] * x[5] * x[6] - 0.933 * x[3] * x[4] * x[5] * x[7] +\n        0.9836 * x[3] * x[4] * x[5] * x[8] - 0.9513 * x[3] * x[4] * x[5] * x[9] -\n        0.9415 * x[3] * x[4] * x[5] * x[10] - 0.4551 * x[3] * x[4] * x[6] * x[7] +\n        0.4972 * x[3] * x[4] * x[6] * x[8] - 0.429 * x[3] * x[4] * x[6] * x[9] -\n        0.5465 * x[3] * x[4] * x[6] * x[10] - 0.1411 * x[3] * x[4] * x[7] * x[8] +\n        0.5444 * x[3] * x[4] * x[7] * x[9] +\n        0.1779 * x[3] * x[4] * x[7] * x[10] +\n        0.0402 * x[3] * x[4] * x[8] * x[9] - 0.9732 * x[3] * x[4] * x[8] * x[10] -\n        0.3496 * x[3] * x[4] * x[9] * x[10] - 0.2575 * x[3] * x[5] * x[6] * x[7] +\n        0.6694 * x[3] * x[5] * x[6] * x[8] - 0.4773 * x[3] * x[5] * x[6] * x[9] +\n        0.4754 * x[3] * x[5] * x[6] * x[10] - 0.9142 * x[3] * x[5] * x[7] * x[8] +\n        0.6845 * x[3] * x[5] * x[7] * x[9] - 0.7219 * x[3] * x[5] * x[7] * x[10] +\n        0.7798 * x[3] * x[5] * x[8] * x[9] +\n        0.0733 * x[3] * x[5] * x[8] * x[10] - 0.7376 * x[3] * x[5] * x[9] * x[10] +\n        0.0256 * x[3] * x[6] * x[7] * x[8] - 0.2386 * x[3] * x[6] * x[7] * x[9] +\n        0.8016 * x[3] * x[6] * x[7] * x[10] +\n        0.6794 * x[3] * x[6] * x[8] * x[9] +\n        0.6011 * x[3] * x[6] * x[8] * x[10] - 0.1622 * x[3] * x[6] * x[9] * x[10] -\n        0.0369 * x[3] * x[7] * x[8] * x[9] - 0.5992 * x[3] * x[7] * x[8] * x[10] +\n        0.9241 * x[3] * x[7] * x[9] * x[10] +\n        0.9873 * x[3] * x[8] * x[9] * x[10] +\n        0.5992 * x[4] * x[5] * x[6] * x[7] +\n        0.8133 * x[4] * x[5] * x[6] * x[8] +\n        0.4239 * x[4] * x[5] * x[6] * x[9] - 0.1981 * x[4] * x[5] * x[6] * x[10] +\n        0.5006 * x[4] * x[5] * x[7] * x[8] - 0.5385 * x[4] * x[5] * x[7] * x[9] +\n        0.1593 * x[4] * x[5] * x[7] * x[10] - 0.0871 * x[4] * x[5] * x[8] * x[9] -\n        0.9382 * x[4] * x[5] * x[8] * x[10] - 0.0148 * x[4] * x[5] * x[9] * x[10] -\n        0.4904 * x[4] * x[6] * x[7] * x[8] + 0.5096 * x[4] * x[6] * x[7] * x[9] -\n        0.4809 * x[4] * x[6] * x[7] * x[10] - 0.4848 * x[4] * x[6] * x[8] * x[9] +\n        0.3062 * x[4] * x[6] * x[8] * x[10] +\n        0.9318 * x[4] * x[6] * x[9] * x[10] - 0.1853 * x[4] * x[7] * x[8] * x[9] +\n        0.5946 * x[4] * x[7] * x[8] * x[10] - 0.9998 * x[4] * x[7] * x[9] * x[10] +\n        0.054 * x[4] * x[8] * x[9] * x[10] +\n        0.9006 * x[5] * x[6] * x[7] * x[8] - 0.322 * x[5] * x[6] * x[7] * x[9] -\n        0.4127 * x[5] * x[6] * x[7] * x[10] - 0.6934 * x[5] * x[6] * x[8] * x[9] +\n        0.408 * x[5] * x[6] * x[8] * x[10] - 0.6923 * x[5] * x[6] * x[9] * x[10] -\n        0.0869 * x[5] * x[7] * x[8] * x[9] - 0.0219 * x[5] * x[7] * x[8] * x[10] +\n        0.4814 * x[5] * x[7] * x[9] * x[10] - 0.0782 * x[5] * x[8] * x[9] * x[10] -\n        0.3978 * x[6] * x[7] * x[8] * x[9] - 0.0586 * x[6] * x[7] * x[8] * x[10] +\n        0.8491 * x[6] * x[7] * x[9] * x[10] - 0.9975 * x[6] * x[8] * x[9] * x[10] +\n        0.5027 * x[7] * x[8] * x[9] * x[10] <= 85.414\n    )\n    e5 = replace_expr(e5, x)\n    JuMP.add_nonlinear_constraint(m, e5)\n    e6 = :(\n        (-0.4481 * x[1] * x[2]) - 0.0269 * x[1] * x[3] - 0.1364 * x[1] * x[4] -\n        0.9192 * x[1] * x[5] +\n        0.5189 * x[1] * x[6] +\n        0.3404 * x[1] * x[7] +\n        0.1516 * x[1] * x[8] +\n        0.4074 * x[1] * x[9] - 0.3842 * x[1] * x[10] + 0.4361 * x[2] * x[3] -\n        0.6147 * x[2] * x[4] - 0.8 * x[2] * x[5] + 0.1892 * x[2] * x[6] -\n        0.8637 * x[2] * x[7] +\n        0.3065 * x[2] * x[8] +\n        0.2325 * x[2] * x[9] +\n        0.2648 * x[2] * x[10] +\n        0.3826 * x[3] * x[4] +\n        0.6438 * x[3] * x[5] - 0.5217 * x[3] * x[6] +\n        0.3787 * x[3] * x[7] +\n        0.7293 * x[3] * x[8] - 0.1202 * x[3] * x[9] +\n        0.5314 * x[3] * x[10] +\n        0.2886 * x[4] * x[5] - 0.4004 * x[4] * x[6] - 0.3376 * x[4] * x[7] -\n        0.9079 * x[4] * x[8] - 0.4125 * x[4] * x[9] +\n        0.8876 * x[4] * x[10] +\n        0.3379 * x[5] * x[6] - 0.2619 * x[5] * x[7] - 0.7405 * x[5] * x[8] +\n        0.1524 * x[5] * x[9] +\n        0.8941 * x[5] * x[10] +\n        0.2131 * x[6] * x[7] - 0.3442 * x[6] * x[8] + 0.5042 * x[6] * x[9] -\n        0.931 * x[6] * x[10] + 0.6521 * x[7] * x[8] - 0.3237 * x[7] * x[9] +\n        0.27 * x[7] * x[10] +\n        0.2362 * x[8] * x[9] +\n        0.5923 * x[8] * x[10] +\n        0.986 * x[9] * x[10] - 0.0644 * x[1] + 0.6635 * x[2] - 0.7397 * x[3] +\n        0.942 * x[4] - 0.6956 * x[5] +\n        0.7189 * x[6] +\n        0.2027 * x[7] +\n        0.7485 * x[8] +\n        0.4619 * x[9] +\n        0.0043 * x[10] +\n        (-0.4047 * x[1] * x[2] * x[3]) - 0.8727 * x[1] * x[2] * x[4] -\n        0.014 * x[1] * x[2] * x[5] - 0.9627 * x[1] * x[2] * x[6] -\n        0.15 * x[1] * x[2] * x[7] - 0.7809 * x[1] * x[2] * x[8] -\n        0.4473 * x[1] * x[2] * x[9] +\n        0.4151 * x[1] * x[2] * x[10] +\n        0.0728 * x[1] * x[3] * x[4] - 0.2027 * x[1] * x[3] * x[5] -\n        0.4616 * x[1] * x[3] * x[6] +\n        0.1176 * x[1] * x[3] * x[7] +\n        0.108 * x[1] * x[3] * x[8] +\n        0.3765 * x[1] * x[3] * x[9] +\n        0.305 * x[1] * x[3] * x[10] - 0.5298 * x[1] * x[4] * x[5] -\n        0.0275 * x[1] * x[4] * x[6] - 0.8101 * x[1] * x[4] * x[7] -\n        0.4449 * x[1] * x[4] * x[8] - 0.8782 * x[1] * x[4] * x[9] -\n        0.6795 * x[1] * x[4] * x[10] - 0.8655 * x[1] * x[5] * x[6] -\n        0.6457 * x[1] * x[5] * x[7] + 0.8807 * x[1] * x[5] * x[8] -\n        0.7634 * x[1] * x[5] * x[9] + 0.217 * x[1] * x[5] * x[10] -\n        0.0549 * x[1] * x[6] * x[7] - 0.9422 * x[1] * x[6] * x[8] -\n        0.9389 * x[1] * x[6] * x[9] - 0.2805 * x[1] * x[6] * x[10] -\n        0.3906 * x[1] * x[7] * x[8] +\n        0.8925 * x[1] * x[7] * x[9] +\n        0.359 * x[1] * x[7] * x[10] - 0.3714 * x[1] * x[8] * x[9] -\n        0.5488 * x[1] * x[8] * x[10] +\n        0.1483 * x[1] * x[9] * x[10] +\n        0.225 * x[2] * x[3] * x[4] +\n        0.7272 * x[2] * x[3] * x[5] - 0.8881 * x[2] * x[3] * x[6] -\n        0.0211 * x[2] * x[3] * x[7] - 0.4108 * x[2] * x[3] * x[8] -\n        0.0434 * x[2] * x[3] * x[9] - 0.7799 * x[2] * x[3] * x[10] -\n        0.4614 * x[2] * x[4] * x[5] - 0.0865 * x[2] * x[4] * x[6] +\n        0.3207 * x[2] * x[4] * x[7] +\n        0.0431 * x[2] * x[4] * x[8] +\n        0.8559 * x[2] * x[4] * x[9] - 0.2257 * x[2] * x[4] * x[10] -\n        0.1022 * x[2] * x[5] * x[6] - 0.5768 * x[2] * x[5] * x[7] -\n        0.8797 * x[2] * x[5] * x[8] +\n        0.3955 * x[2] * x[5] * x[9] +\n        0.7964 * x[2] * x[5] * x[10] +\n        0.2734 * x[2] * x[6] * x[7] +\n        0.0895 * x[2] * x[6] * x[8] - 0.4146 * x[2] * x[6] * x[9] +\n        0.9077 * x[2] * x[6] * x[10] - 0.1895 * x[2] * x[7] * x[8] +\n        0.994 * x[2] * x[7] * x[9] - 0.6899 * x[2] * x[7] * x[10] +\n        0.9394 * x[2] * x[8] * x[9] - 0.2503 * x[2] * x[8] * x[10] -\n        0.2187 * x[2] * x[9] * x[10] - 0.1793 * x[3] * x[4] * x[5] +\n        0.9029 * x[3] * x[4] * x[6] +\n        0.1218 * x[3] * x[4] * x[7] +\n        0.2453 * x[3] * x[4] * x[8] +\n        0.7306 * x[3] * x[4] * x[9] - 0.2001 * x[3] * x[4] * x[10] +\n        0.7936 * x[3] * x[5] * x[6] - 0.7984 * x[3] * x[5] * x[7] -\n        0.589 * x[3] * x[5] * x[8] + 0.6958 * x[3] * x[5] * x[9] -\n        0.0455 * x[3] * x[5] * x[10] - 0.267 * x[3] * x[6] * x[7] +\n        0.8622 * x[3] * x[6] * x[8] - 0.5897 * x[3] * x[6] * x[9] +\n        0.1178 * x[3] * x[6] * x[10] +\n        0.8772 * x[3] * x[7] * x[8] - 0.7239 * x[3] * x[7] * x[9] +\n        0.8153 * x[3] * x[7] * x[10] +\n        0.9875 * x[3] * x[8] * x[9] +\n        0.0661 * x[3] * x[8] * x[10] +\n        0.0747 * x[3] * x[9] * x[10] - 0.9466 * x[4] * x[5] * x[6] +\n        0.9993 * x[4] * x[5] * x[7] +\n        0.4921 * x[4] * x[5] * x[8] +\n        0.1736 * x[4] * x[5] * x[9] - 0.5295 * x[4] * x[5] * x[10] -\n        0.5874 * x[4] * x[6] * x[7] - 0.9963 * x[4] * x[6] * x[8] -\n        0.6875 * x[4] * x[6] * x[9] - 0.6238 * x[4] * x[6] * x[10] +\n        0.0738 * x[4] * x[7] * x[8] +\n        0.3122 * x[4] * x[7] * x[9] +\n        0.9116 * x[4] * x[7] * x[10] - 0.7073 * x[4] * x[8] * x[9] +\n        0.3956 * x[4] * x[8] * x[10] +\n        0.6408 * x[4] * x[9] * x[10] +\n        0.906 * x[5] * x[6] * x[7] +\n        0.4384 * x[5] * x[6] * x[8] - 0.0051 * x[5] * x[6] * x[9] +\n        0.689 * x[5] * x[6] * x[10] +\n        0.8015 * x[5] * x[7] * x[8] - 0.1671 * x[5] * x[7] * x[9] +\n        0.1501 * x[5] * x[7] * x[10] - 0.6129 * x[5] * x[8] * x[9] -\n        0.4673 * x[5] * x[8] * x[10] - 0.2172 * x[5] * x[9] * x[10] +\n        0.5448 * x[6] * x[7] * x[8] +\n        0.5743 * x[6] * x[7] * x[9] - 0.2467 * x[6] * x[7] * x[10] +\n        0.8448 * x[6] * x[8] * x[9] - 0.784 * x[6] * x[8] * x[10] -\n        0.2975 * x[6] * x[9] * x[10] - 0.9803 * x[7] * x[8] * x[9] +\n        0.9786 * x[7] * x[8] * x[10] +\n        0.1967 * x[7] * x[9] * x[10] - 0.9423 * x[8] * x[9] * x[10] +\n        0.4814 * x[1] * x[2] * x[3] * x[4] +\n        0.1703 * x[1] * x[2] * x[3] * x[5] +\n        0.511 * x[1] * x[2] * x[3] * x[6] +\n        0.9122 * x[1] * x[2] * x[3] * x[7] +\n        0.1772 * x[1] * x[2] * x[3] * x[8] +\n        0.6143 * x[1] * x[2] * x[3] * x[9] +\n        0.0351 * x[1] * x[2] * x[3] * x[10] - 0.6117 * x[1] * x[2] * x[4] * x[5] +\n        0.6903 * x[1] * x[2] * x[4] * x[6] +\n        0.8105 * x[1] * x[2] * x[4] * x[7] +\n        0.3583 * x[1] * x[2] * x[4] * x[8] +\n        0.296 * x[1] * x[2] * x[4] * x[9] +\n        0.6876 * x[1] * x[2] * x[4] * x[10] - 0.393 * x[1] * x[2] * x[5] * x[6] -\n        0.3819 * x[1] * x[2] * x[5] * x[7] - 0.3434 * x[1] * x[2] * x[5] * x[8] +\n        0.498 * x[1] * x[2] * x[5] * x[9] +\n        0.3344 * x[1] * x[2] * x[5] * x[10] - 0.6604 * x[1] * x[2] * x[6] * x[7] +\n        0.1448 * x[1] * x[2] * x[6] * x[8] - 0.2679 * x[1] * x[2] * x[6] * x[9] -\n        0.9699 * x[1] * x[2] * x[6] * x[10] + 0.4874 * x[1] * x[2] * x[7] * x[8] -\n        0.2642 * x[1] * x[2] * x[7] * x[9] +\n        0.0611 * x[1] * x[2] * x[7] * x[10] +\n        0.1584 * x[1] * x[2] * x[8] * x[9] - 0.3937 * x[1] * x[2] * x[8] * x[10] +\n        0.9029 * x[1] * x[2] * x[9] * x[10] - 0.3443 * x[1] * x[3] * x[4] * x[5] +\n        0.1484 * x[1] * x[3] * x[4] * x[6] +\n        0.4433 * x[1] * x[3] * x[4] * x[7] +\n        0.3218 * x[1] * x[3] * x[4] * x[8] - 0.2226 * x[1] * x[3] * x[4] * x[9] +\n        0.3904 * x[1] * x[3] * x[4] * x[10] +\n        0.6146 * x[1] * x[3] * x[5] * x[6] - 0.8245 * x[1] * x[3] * x[5] * x[7] +\n        0.8728 * x[1] * x[3] * x[5] * x[8] - 0.3059 * x[1] * x[3] * x[5] * x[9] +\n        0.8877 * x[1] * x[3] * x[5] * x[10] +\n        0.1024 * x[1] * x[3] * x[6] * x[7] +\n        0.1653 * x[1] * x[3] * x[6] * x[8] - 0.3166 * x[1] * x[3] * x[6] * x[9] +\n        0.13 * x[1] * x[3] * x[6] * x[10] - 0.4146 * x[1] * x[3] * x[7] * x[8] -\n        0.0127 * x[1] * x[3] * x[7] * x[9] +\n        0.4993 * x[1] * x[3] * x[7] * x[10] +\n        0.6925 * x[1] * x[3] * x[8] * x[9] - 0.0677 * x[1] * x[3] * x[8] * x[10] -\n        0.2175 * x[1] * x[3] * x[9] * x[10] + 0.828 * x[1] * x[4] * x[5] * x[6] -\n        0.1967 * x[1] * x[4] * x[5] * x[7] + 0.4211 * x[1] * x[4] * x[5] * x[8] -\n        0.2497 * x[1] * x[4] * x[5] * x[9] + 0.462 * x[1] * x[4] * x[5] * x[10] -\n        0.7244 * x[1] * x[4] * x[6] * x[7] + 0.5054 * x[1] * x[4] * x[6] * x[8] -\n        0.6719 * x[1] * x[4] * x[6] * x[9] +\n        0.2062 * x[1] * x[4] * x[6] * x[10] +\n        0.4854 * x[1] * x[4] * x[7] * x[8] - 0.8001 * x[1] * x[4] * x[7] * x[9] +\n        0.4813 * x[1] * x[4] * x[7] * x[10] - 0.2475 * x[1] * x[4] * x[8] * x[9] +\n        0.659 * x[1] * x[4] * x[8] * x[10] - 0.8335 * x[1] * x[4] * x[9] * x[10] +\n        0.2203 * x[1] * x[5] * x[6] * x[7] +\n        0.8903 * x[1] * x[5] * x[6] * x[8] - 0.7647 * x[1] * x[5] * x[6] * x[9] +\n        0.5881 * x[1] * x[5] * x[6] * x[10] - 0.3864 * x[1] * x[5] * x[7] * x[8] -\n        0.5257 * x[1] * x[5] * x[7] * x[9] - 0.5672 * x[1] * x[5] * x[7] * x[10] -\n        0.0589 * x[1] * x[5] * x[8] * x[9] - 0.1993 * x[1] * x[5] * x[8] * x[10] -\n        0.4537 * x[1] * x[5] * x[9] * x[10] +\n        0.7725 * x[1] * x[6] * x[7] * x[8] +\n        0.1709 * x[1] * x[6] * x[7] * x[9] - 0.0676 * x[1] * x[6] * x[7] * x[10] -\n        0.6013 * x[1] * x[6] * x[8] * x[9] + 0.8428 * x[1] * x[6] * x[8] * x[10] -\n        0.6915 * x[1] * x[6] * x[9] * x[10] +\n        0.8838 * x[1] * x[7] * x[8] * x[9] +\n        0.9223 * x[1] * x[7] * x[8] * x[10] +\n        0.5193 * x[1] * x[7] * x[9] * x[10] +\n        0.3182 * x[1] * x[8] * x[9] * x[10] - 0.221 * x[2] * x[3] * x[4] * x[5] +\n        0.6815 * x[2] * x[3] * x[4] * x[6] - 0.0966 * x[2] * x[3] * x[4] * x[7] -\n        0.1797 * x[2] * x[3] * x[4] * x[8] - 0.7994 * x[2] * x[3] * x[4] * x[9] +\n        0.6868 * x[2] * x[3] * x[4] * x[10] +\n        0.4518 * x[2] * x[3] * x[5] * x[6] +\n        0.8514 * x[2] * x[3] * x[5] * x[7] +\n        0.6759 * x[2] * x[3] * x[5] * x[8] - 0.6871 * x[2] * x[3] * x[5] * x[9] +\n        0.6584 * x[2] * x[3] * x[5] * x[10] - 0.2458 * x[2] * x[3] * x[6] * x[7] +\n        0.6472 * x[2] * x[3] * x[6] * x[8] - 0.3359 * x[2] * x[3] * x[6] * x[9] -\n        0.863 * x[2] * x[3] * x[6] * x[10] +\n        0.1233 * x[2] * x[3] * x[7] * x[8] +\n        0.6612 * x[2] * x[3] * x[7] * x[9] +\n        0.2013 * x[2] * x[3] * x[7] * x[10] +\n        0.6938 * x[2] * x[3] * x[8] * x[9] - 0.7642 * x[2] * x[3] * x[8] * x[10] +\n        0.3951 * x[2] * x[3] * x[9] * x[10] - 0.3524 * x[2] * x[4] * x[5] * x[6] -\n        0.9741 * x[2] * x[4] * x[5] * x[7] + 0.6833 * x[2] * x[4] * x[5] * x[8] -\n        0.4752 * x[2] * x[4] * x[5] * x[9] - 0.3353 * x[2] * x[4] * x[5] * x[10] +\n        0.9698 * x[2] * x[4] * x[6] * x[7] - 0.9741 * x[2] * x[4] * x[6] * x[8] -\n        0.1607 * x[2] * x[4] * x[6] * x[9] +\n        0.7583 * x[2] * x[4] * x[6] * x[10] +\n        0.803 * x[2] * x[4] * x[7] * x[8] - 0.4884 * x[2] * x[4] * x[7] * x[9] +\n        0.459 * x[2] * x[4] * x[7] * x[10] +\n        0.7593 * x[2] * x[4] * x[8] * x[9] +\n        0.3966 * x[2] * x[4] * x[8] * x[10] +\n        0.2922 * x[2] * x[4] * x[9] * x[10] - 0.8999 * x[2] * x[5] * x[6] * x[7] -\n        0.3177 * x[2] * x[5] * x[6] * x[8] + 0.2054 * x[2] * x[5] * x[6] * x[9] -\n        0.0702 * x[2] * x[5] * x[6] * x[10] - 0.1661 * x[2] * x[5] * x[7] * x[8] +\n        0.949 * x[2] * x[5] * x[7] * x[9] +\n        0.8319 * x[2] * x[5] * x[7] * x[10] - 0.2402 * x[2] * x[5] * x[8] * x[9] +\n        0.3515 * x[2] * x[5] * x[8] * x[10] - 0.6997 * x[2] * x[5] * x[9] * x[10] +\n        0.7683 * x[2] * x[6] * x[7] * x[8] - 0.6599 * x[2] * x[6] * x[7] * x[9] +\n        0.1491 * x[2] * x[6] * x[7] * x[10] +\n        0.4292 * x[2] * x[6] * x[8] * x[9] +\n        0.5753 * x[2] * x[6] * x[8] * x[10] - 0.2752 * x[2] * x[6] * x[9] * x[10] -\n        0.7367 * x[2] * x[7] * x[8] * x[9] +\n        0.2302 * x[2] * x[7] * x[8] * x[10] +\n        0.9897 * x[2] * x[7] * x[9] * x[10] - 0.5626 * x[2] * x[8] * x[9] * x[10] -\n        0.3133 * x[3] * x[4] * x[5] * x[6] - 0.113 * x[3] * x[4] * x[5] * x[7] +\n        0.3194 * x[3] * x[4] * x[5] * x[8] +\n        0.4135 * x[3] * x[4] * x[5] * x[9] - 0.4578 * x[3] * x[4] * x[5] * x[10] -\n        0.4937 * x[3] * x[4] * x[6] * x[7] +\n        0.2359 * x[3] * x[4] * x[6] * x[8] +\n        0.2791 * x[3] * x[4] * x[6] * x[9] - 0.8753 * x[3] * x[4] * x[6] * x[10] -\n        0.8146 * x[3] * x[4] * x[7] * x[8] +\n        0.3627 * x[3] * x[4] * x[7] * x[9] +\n        0.6978 * x[3] * x[4] * x[7] * x[10] - 0.1502 * x[3] * x[4] * x[8] * x[9] +\n        0.8516 * x[3] * x[4] * x[8] * x[10] - 0.8482 * x[3] * x[4] * x[9] * x[10] -\n        0.7326 * x[3] * x[5] * x[6] * x[7] + 0.3347 * x[3] * x[5] * x[6] * x[8] -\n        0.3677 * x[3] * x[5] * x[6] * x[9] +\n        0.8576 * x[3] * x[5] * x[6] * x[10] +\n        0.8423 * x[3] * x[5] * x[7] * x[8] +\n        0.4222 * x[3] * x[5] * x[7] * x[9] +\n        0.3568 * x[3] * x[5] * x[7] * x[10] +\n        0.1597 * x[3] * x[5] * x[8] * x[9] +\n        0.2008 * x[3] * x[5] * x[8] * x[10] +\n        0.6678 * x[3] * x[5] * x[9] * x[10] - 0.7699 * x[3] * x[6] * x[7] * x[8] +\n        0.6536 * x[3] * x[6] * x[7] * x[9] - 0.4263 * x[3] * x[6] * x[7] * x[10] +\n        0.5469 * x[3] * x[6] * x[8] * x[9] +\n        0.6991 * x[3] * x[6] * x[8] * x[10] +\n        0.4764 * x[3] * x[6] * x[9] * x[10] - 0.6822 * x[3] * x[7] * x[8] * x[9] -\n        0.709 * x[3] * x[7] * x[8] * x[10] - 0.6123 * x[3] * x[7] * x[9] * x[10] -\n        0.6075 * x[3] * x[8] * x[9] * x[10] - 0.6624 * x[4] * x[5] * x[6] * x[7] +\n        0.3302 * x[4] * x[5] * x[6] * x[8] +\n        0.6541 * x[4] * x[5] * x[6] * x[9] - 0.6579 * x[4] * x[5] * x[6] * x[10] -\n        0.5587 * x[4] * x[5] * x[7] * x[8] - 0.1261 * x[4] * x[5] * x[7] * x[9] +\n        0.8603 * x[4] * x[5] * x[7] * x[10] +\n        0.1445 * x[4] * x[5] * x[8] * x[9] - 0.773 * x[4] * x[5] * x[8] * x[10] +\n        0.1692 * x[4] * x[5] * x[9] * x[10] +\n        0.8432 * x[4] * x[6] * x[7] * x[8] +\n        0.8133 * x[4] * x[6] * x[7] * x[9] +\n        0.1169 * x[4] * x[6] * x[7] * x[10] - 0.1312 * x[4] * x[6] * x[8] * x[9] +\n        0.9717 * x[4] * x[6] * x[8] * x[10] +\n        0.3126 * x[4] * x[6] * x[9] * x[10] +\n        0.4154 * x[4] * x[7] * x[8] * x[9] - 0.0105 * x[4] * x[7] * x[8] * x[10] +\n        0.4772 * x[4] * x[7] * x[9] * x[10] +\n        0.1875 * x[4] * x[8] * x[9] * x[10] +\n        0.9525 * x[5] * x[6] * x[7] * x[8] - 0.3099 * x[5] * x[6] * x[7] * x[9] -\n        0.239 * x[5] * x[6] * x[7] * x[10] +\n        0.5059 * x[5] * x[6] * x[8] * x[9] +\n        0.466 * x[5] * x[6] * x[8] * x[10] - 0.334 * x[5] * x[6] * x[9] * x[10] +\n        0.8077 * x[5] * x[7] * x[8] * x[9] +\n        0.3148 * x[5] * x[7] * x[8] * x[10] - 0.4982 * x[5] * x[7] * x[9] * x[10] +\n        0.2499 * x[5] * x[8] * x[9] * x[10] - 0.4484 * x[6] * x[7] * x[8] * x[9] +\n        0.0002 * x[6] * x[7] * x[8] * x[10] +\n        0.9242 * x[6] * x[7] * x[9] * x[10] - 0.3877 * x[6] * x[8] * x[9] * x[10] -\n        0.776 * x[7] * x[8] * x[9] * x[10] <= 91.904\n    )\n    e6 = replace_expr(e6, x)\n    JuMP.add_nonlinear_constraint(m, e6)\n    e7 = :(\n        0.1493 * x[1] * x[2] - 0.0821 * x[1] * x[3] + 0.497 * x[1] * x[4] -\n        0.9345 * x[1] * x[5] +\n        0.4136 * x[1] * x[6] +\n        0.7518 * x[1] * x[7] - 0.343 * x[1] * x[8] - 0.4928 * x[1] * x[9] +\n        0.7599 * x[1] * x[10] +\n        0.6319 * x[2] * x[3] - 0.8854 * x[2] * x[4] +\n        0.7768 * x[2] * x[5] +\n        0.0498 * x[2] * x[6] - 0.87 * x[2] * x[7] + 0.2151 * x[2] * x[8] -\n        0.5144 * x[2] * x[9] - 0.4663 * x[2] * x[10] - 0.7141 * x[3] * x[4] +\n        0.3885 * x[3] * x[5] +\n        0.8542 * x[3] * x[6] +\n        0.7864 * x[3] * x[7] +\n        0.2841 * x[3] * x[8] - 0.2428 * x[3] * x[9] - 0.8116 * x[3] * x[10] +\n        0.8953 * x[4] * x[5] +\n        0.2995 * x[4] * x[6] - 0.2316 * x[4] * x[7] - 0.7342 * x[4] * x[8] +\n        0.3091 * x[4] * x[9] - 0.114 * x[4] * x[10] - 0.6494 * x[5] * x[6] -\n        0.5173 * x[5] * x[7] - 0.7047 * x[5] * x[8] - 0.764 * x[5] * x[9] -\n        0.2591 * x[5] * x[10] - 0.6065 * x[6] * x[7] - 0.5798 * x[6] * x[8] +\n        0.1489 * x[6] * x[9] - 0.7814 * x[6] * x[10] + 0.0265 * x[7] * x[8] -\n        0.0071 * x[7] * x[9] - 0.985 * x[7] * x[10] +\n        0.9441 * x[8] * x[9] +\n        0.4356 * x[8] * x[10] +\n        0.9238 * x[9] * x[10] - 0.8049 * x[1] - 0.4609 * x[2] + 0.0185 * x[3] -\n        0.5567 * x[4] +\n        0.5428 * x[5] +\n        0.8039 * x[6] - 0.7982 * x[7] +\n        0.433 * x[8] +\n        0.3945 * x[9] - 0.8879 * x[10] + 0.7921 * x[1] * x[2] * x[4] -\n        0.9752 * x[1] * x[2] * x[3] - 0.6234 * x[1] * x[2] * x[5] -\n        0.2596 * x[1] * x[2] * x[6] +\n        0.038 * x[1] * x[2] * x[7] +\n        0.7493 * x[1] * x[2] * x[8] +\n        0.0256 * x[1] * x[2] * x[9] - 0.457 * x[1] * x[2] * x[10] -\n        0.3738 * x[1] * x[3] * x[4] + 0.2854 * x[1] * x[3] * x[5] -\n        0.4543 * x[1] * x[3] * x[6] - 0.03 * x[1] * x[3] * x[7] -\n        0.9105 * x[1] * x[3] * x[8] - 0.7535 * x[1] * x[3] * x[9] -\n        0.1891 * x[1] * x[3] * x[10] +\n        0.6336 * x[1] * x[4] * x[5] +\n        0.1559 * x[1] * x[4] * x[6] - 0.3327 * x[1] * x[4] * x[7] -\n        0.0413 * x[1] * x[4] * x[8] - 0.3352 * x[1] * x[4] * x[9] -\n        0.9197 * x[1] * x[4] * x[10] - 0.3498 * x[1] * x[5] * x[6] -\n        0.3321 * x[1] * x[5] * x[7] + 0.3069 * x[1] * x[5] * x[8] -\n        0.6815 * x[1] * x[5] * x[9] - 0.9023 * x[1] * x[5] * x[10] -\n        0.3243 * x[1] * x[6] * x[7] - 0.7002 * x[1] * x[6] * x[8] +\n        0.8733 * x[1] * x[6] * x[9] +\n        0.7257 * x[1] * x[6] * x[10] +\n        0.807 * x[1] * x[7] * x[8] - 0.3247 * x[1] * x[7] * x[9] +\n        0.751 * x[1] * x[7] * x[10] - 0.1371 * x[1] * x[8] * x[9] +\n        0.3378 * x[1] * x[8] * x[10] +\n        0.4854 * x[1] * x[9] * x[10] +\n        0.6818 * x[2] * x[3] * x[4] - 0.2154 * x[2] * x[3] * x[5] +\n        0.9713 * x[2] * x[3] * x[6] +\n        0.0508 * x[2] * x[3] * x[7] - 0.0821 * x[2] * x[3] * x[8] -\n        0.2744 * x[2] * x[3] * x[9] +\n        0.3301 * x[2] * x[3] * x[10] +\n        0.0977 * x[2] * x[4] * x[5] +\n        0.7447 * x[2] * x[4] * x[6] +\n        0.152 * x[2] * x[4] * x[7] +\n        0.6629 * x[2] * x[4] * x[8] - 0.8393 * x[2] * x[4] * x[9] +\n        0.1067 * x[2] * x[4] * x[10] - 0.9084 * x[2] * x[5] * x[6] +\n        0.761 * x[2] * x[5] * x[7] +\n        0.5597 * x[2] * x[5] * x[8] - 0.2003 * x[2] * x[5] * x[9] -\n        0.9542 * x[2] * x[5] * x[10] - 0.1824 * x[2] * x[6] * x[7] -\n        0.8383 * x[2] * x[6] * x[8] - 0.6698 * x[2] * x[6] * x[9] +\n        0.0278 * x[2] * x[6] * x[10] - 0.6996 * x[2] * x[7] * x[8] -\n        0.3721 * x[2] * x[7] * x[9] - 0.0097 * x[2] * x[7] * x[10] -\n        0.1389 * x[2] * x[8] * x[9] - 0.1557 * x[2] * x[8] * x[10] +\n        0.3259 * x[2] * x[9] * x[10] +\n        0.2066 * x[3] * x[4] * x[5] +\n        0.4973 * x[3] * x[4] * x[6] - 0.0794 * x[3] * x[4] * x[7] +\n        0.9822 * x[3] * x[4] * x[8] +\n        0.9661 * x[3] * x[4] * x[9] - 0.7344 * x[3] * x[4] * x[10] +\n        0.5813 * x[3] * x[5] * x[6] - 0.0259 * x[3] * x[5] * x[7] -\n        0.8178 * x[3] * x[5] * x[8] +\n        0.1696 * x[3] * x[5] * x[9] +\n        0.0474 * x[3] * x[5] * x[10] - 0.6102 * x[3] * x[6] * x[7] +\n        0.3413 * x[3] * x[6] * x[8] - 0.0321 * x[3] * x[6] * x[9] +\n        0.3867 * x[3] * x[6] * x[10] - 0.9594 * x[3] * x[7] * x[8] -\n        0.0941 * x[3] * x[7] * x[9] +\n        0.2824 * x[3] * x[7] * x[10] +\n        0.2279 * x[3] * x[8] * x[9] - 0.2678 * x[3] * x[8] * x[10] +\n        0.8357 * x[3] * x[9] * x[10] - 0.1385 * x[4] * x[5] * x[6] -\n        0.0028 * x[4] * x[5] * x[7] +\n        0.6343 * x[4] * x[5] * x[8] +\n        0.6558 * x[4] * x[5] * x[9] - 0.3929 * x[4] * x[5] * x[10] +\n        0.5754 * x[4] * x[6] * x[7] +\n        0.5376 * x[4] * x[6] * x[8] - 0.9033 * x[4] * x[6] * x[9] -\n        0.3758 * x[4] * x[6] * x[10] +\n        0.0538 * x[4] * x[7] * x[8] +\n        0.5201 * x[4] * x[7] * x[9] +\n        0.0502 * x[4] * x[7] * x[10] +\n        0.6526 * x[4] * x[8] * x[9] +\n        0.3788 * x[4] * x[8] * x[10] - 0.2957 * x[4] * x[9] * x[10] +\n        0.2894 * x[5] * x[6] * x[7] - 0.7789 * x[5] * x[6] * x[8] -\n        0.7901 * x[5] * x[6] * x[9] +\n        0.4762 * x[5] * x[6] * x[10] +\n        0.4641 * x[5] * x[7] * x[8] +\n        0.4006 * x[5] * x[7] * x[9] +\n        0.9277 * x[5] * x[7] * x[10] +\n        0.1455 * x[5] * x[8] * x[9] - 0.2138 * x[5] * x[8] * x[10] +\n        0.5281 * x[5] * x[9] * x[10] - 0.3557 * x[6] * x[7] * x[8] +\n        0.9451 * x[6] * x[7] * x[9] +\n        0.3845 * x[6] * x[7] * x[10] - 0.931 * x[6] * x[8] * x[9] -\n        0.7231 * x[6] * x[8] * x[10] - 0.1203 * x[6] * x[9] * x[10] +\n        0.6813 * x[7] * x[8] * x[9] - 0.1748 * x[7] * x[8] * x[10] -\n        0.893 * x[7] * x[9] * x[10] +\n        0.3339 * x[8] * x[9] * x[10] +\n        (-0.8394 * x[1] * x[2] * x[3] * x[4]) - 0.7701 * x[1] * x[2] * x[3] * x[5] -\n        0.3017 * x[1] * x[2] * x[3] * x[6] - 0.2722 * x[1] * x[2] * x[3] * x[7] +\n        0.4795 * x[1] * x[2] * x[3] * x[8] +\n        0.3531 * x[1] * x[2] * x[3] * x[9] +\n        0.2825 * x[1] * x[2] * x[3] * x[10] +\n        0.3274 * x[1] * x[2] * x[4] * x[5] - 0.4461 * x[1] * x[2] * x[4] * x[6] +\n        0.2588 * x[1] * x[2] * x[4] * x[7] +\n        0.5324 * x[1] * x[2] * x[4] * x[8] - 0.6424 * x[1] * x[2] * x[4] * x[9] -\n        0.573 * x[1] * x[2] * x[4] * x[10] +\n        0.6427 * x[1] * x[2] * x[5] * x[6] +\n        0.1464 * x[1] * x[2] * x[5] * x[7] +\n        0.7913 * x[1] * x[2] * x[5] * x[8] +\n        0.0191 * x[1] * x[2] * x[5] * x[9] +\n        0.6857 * x[1] * x[2] * x[5] * x[10] +\n        0.3674 * x[1] * x[2] * x[6] * x[7] - 0.7488 * x[1] * x[2] * x[6] * x[8] -\n        0.9634 * x[1] * x[2] * x[6] * x[9] - 0.2154 * x[1] * x[2] * x[6] * x[10] +\n        0.9814 * x[1] * x[2] * x[7] * x[8] +\n        0.3058 * x[1] * x[2] * x[7] * x[9] - 0.5648 * x[1] * x[2] * x[7] * x[10] +\n        0.043 * x[1] * x[2] * x[8] * x[9] +\n        0.3748 * x[1] * x[2] * x[8] * x[10] - 0.1711 * x[1] * x[2] * x[9] * x[10] +\n        0.1803 * x[1] * x[3] * x[4] * x[5] - 0.3642 * x[1] * x[3] * x[4] * x[6] +\n        0.4124 * x[1] * x[3] * x[4] * x[7] +\n        0.2058 * x[1] * x[3] * x[4] * x[8] +\n        0.2026 * x[1] * x[3] * x[4] * x[9] +\n        0.3626 * x[1] * x[3] * x[4] * x[10] +\n        0.5458 * x[1] * x[3] * x[5] * x[6] - 0.0222 * x[1] * x[3] * x[5] * x[7] -\n        0.7975 * x[1] * x[3] * x[5] * x[8] - 0.5112 * x[1] * x[3] * x[5] * x[9] +\n        0.0613 * x[1] * x[3] * x[5] * x[10] +\n        0.769 * x[1] * x[3] * x[6] * x[7] +\n        0.701 * x[1] * x[3] * x[6] * x[8] - 0.7641 * x[1] * x[3] * x[6] * x[9] +\n        0.3574 * x[1] * x[3] * x[6] * x[10] - 0.0437 * x[1] * x[3] * x[7] * x[8] +\n        0.7193 * x[1] * x[3] * x[7] * x[9] +\n        0.4535 * x[1] * x[3] * x[7] * x[10] +\n        0.5978 * x[1] * x[3] * x[8] * x[9] +\n        0.0133 * x[1] * x[3] * x[8] * x[10] +\n        0.8512 * x[1] * x[3] * x[9] * x[10] - 0.6772 * x[1] * x[4] * x[5] * x[6] +\n        0.5878 * x[1] * x[4] * x[5] * x[7] - 0.3585 * x[1] * x[4] * x[5] * x[8] +\n        0.1872 * x[1] * x[4] * x[5] * x[9] +\n        0.0589 * x[1] * x[4] * x[5] * x[10] - 0.3317 * x[1] * x[4] * x[6] * x[7] +\n        0.7479 * x[1] * x[4] * x[6] * x[8] - 0.9671 * x[1] * x[4] * x[6] * x[9] +\n        0.9391 * x[1] * x[4] * x[6] * x[10] +\n        0.9018 * x[1] * x[4] * x[7] * x[8] +\n        0.32 * x[1] * x[4] * x[7] * x[9] +\n        0.6027 * x[1] * x[4] * x[7] * x[10] - 0.6141 * x[1] * x[4] * x[8] * x[9] +\n        0.531 * x[1] * x[4] * x[8] * x[10] +\n        0.2639 * x[1] * x[4] * x[9] * x[10] +\n        0.3663 * x[1] * x[5] * x[6] * x[7] - 0.233 * x[1] * x[5] * x[6] * x[8] +\n        0.4189 * x[1] * x[5] * x[6] * x[9] +\n        0.4041 * x[1] * x[5] * x[6] * x[10] +\n        0.304 * x[1] * x[5] * x[7] * x[8] +\n        0.3126 * x[1] * x[5] * x[7] * x[9] +\n        0.0481 * x[1] * x[5] * x[7] * x[10] - 0.5275 * x[1] * x[5] * x[8] * x[9] -\n        0.1305 * x[1] * x[5] * x[8] * x[10] - 0.6678 * x[1] * x[5] * x[9] * x[10] -\n        0.5155 * x[1] * x[6] * x[7] * x[8] +\n        0.5784 * x[1] * x[6] * x[7] * x[9] +\n        0.0016 * x[1] * x[6] * x[7] * x[10] - 0.1111 * x[1] * x[6] * x[8] * x[9] -\n        0.3946 * x[1] * x[6] * x[8] * x[10] - 0.98 * x[1] * x[6] * x[9] * x[10] -\n        0.1806 * x[1] * x[7] * x[8] * x[9] + 0.988 * x[1] * x[7] * x[8] * x[10] -\n        0.6747 * x[1] * x[7] * x[9] * x[10] - 0.3078 * x[1] * x[8] * x[9] * x[10] +\n        0.2953 * x[2] * x[3] * x[4] * x[5] - 0.8559 * x[2] * x[3] * x[4] * x[6] +\n        0.3771 * x[2] * x[3] * x[4] * x[7] - 0.6117 * x[2] * x[3] * x[4] * x[8] +\n        0.1766 * x[2] * x[3] * x[4] * x[9] +\n        0.472 * x[2] * x[3] * x[4] * x[10] - 0.1445 * x[2] * x[3] * x[5] * x[6] -\n        0.1965 * x[2] * x[3] * x[5] * x[7] +\n        0.5678 * x[2] * x[3] * x[5] * x[8] +\n        0.8256 * x[2] * x[3] * x[5] * x[9] - 0.0288 * x[2] * x[3] * x[5] * x[10] -\n        0.0473 * x[2] * x[3] * x[6] * x[7] +\n        0.1173 * x[2] * x[3] * x[6] * x[8] +\n        0.6063 * x[2] * x[3] * x[6] * x[9] - 0.8786 * x[2] * x[3] * x[6] * x[10] +\n        0.8495 * x[2] * x[3] * x[7] * x[8] +\n        0.1714 * x[2] * x[3] * x[7] * x[9] +\n        0.4934 * x[2] * x[3] * x[7] * x[10] - 0.7093 * x[2] * x[3] * x[8] * x[9] -\n        0.5405 * x[2] * x[3] * x[8] * x[10] + 0.7902 * x[2] * x[3] * x[9] * x[10] -\n        0.333 * x[2] * x[4] * x[5] * x[6] +\n        0.9342 * x[2] * x[4] * x[5] * x[7] +\n        0.6046 * x[2] * x[4] * x[5] * x[8] - 0.7882 * x[2] * x[4] * x[5] * x[9] +\n        0.4245 * x[2] * x[4] * x[5] * x[10] - 0.3577 * x[2] * x[4] * x[6] * x[7] -\n        0.6746 * x[2] * x[4] * x[6] * x[8] - 0.1915 * x[2] * x[4] * x[6] * x[9] -\n        0.0401 * x[2] * x[4] * x[6] * x[10] - 0.9931 * x[2] * x[4] * x[7] * x[8] +\n        0.0294 * x[2] * x[4] * x[7] * x[9] +\n        0.5066 * x[2] * x[4] * x[7] * x[10] +\n        0.9387 * x[2] * x[4] * x[8] * x[9] +\n        0.4504 * x[2] * x[4] * x[8] * x[10] - 0.8174 * x[2] * x[4] * x[9] * x[10] -\n        0.1996 * x[2] * x[5] * x[6] * x[7] +\n        0.3514 * x[2] * x[5] * x[6] * x[8] +\n        0.316 * x[2] * x[5] * x[6] * x[9] +\n        0.6336 * x[2] * x[5] * x[6] * x[10] - 0.5032 * x[2] * x[5] * x[7] * x[8] -\n        0.4267 * x[2] * x[5] * x[7] * x[9] - 0.9986 * x[2] * x[5] * x[7] * x[10] -\n        0.5176 * x[2] * x[5] * x[8] * x[9] - 0.9889 * x[2] * x[5] * x[8] * x[10] -\n        0.2244 * x[2] * x[5] * x[9] * x[10] - 0.1486 * x[2] * x[6] * x[7] * x[8] +\n        0.4237 * x[2] * x[6] * x[7] * x[9] +\n        0.7526 * x[2] * x[6] * x[7] * x[10] +\n        0.3702 * x[2] * x[6] * x[8] * x[9] - 0.0792 * x[2] * x[6] * x[8] * x[10] +\n        0.3093 * x[2] * x[6] * x[9] * x[10] - 0.3792 * x[2] * x[7] * x[8] * x[9] +\n        0.5826 * x[2] * x[7] * x[8] * x[10] - 0.027 * x[2] * x[7] * x[9] * x[10] +\n        0.2429 * x[2] * x[8] * x[9] * x[10] +\n        0.4158 * x[3] * x[4] * x[5] * x[6] - 0.5107 * x[3] * x[4] * x[5] * x[7] -\n        0.3875 * x[3] * x[4] * x[5] * x[8] - 0.8247 * x[3] * x[4] * x[5] * x[9] -\n        0.1237 * x[3] * x[4] * x[5] * x[10] - 0.9108 * x[3] * x[4] * x[6] * x[7] +\n        0.8865 * x[3] * x[4] * x[6] * x[8] - 0.2339 * x[3] * x[4] * x[6] * x[9] -\n        0.3238 * x[3] * x[4] * x[6] * x[10] + 0.3171 * x[3] * x[4] * x[7] * x[8] -\n        0.7991 * x[3] * x[4] * x[7] * x[9] + 0.8642 * x[3] * x[4] * x[7] * x[10] -\n        0.3354 * x[3] * x[4] * x[8] * x[9] - 0.9854 * x[3] * x[4] * x[8] * x[10] +\n        0.6736 * x[3] * x[4] * x[9] * x[10] +\n        0.9472 * x[3] * x[5] * x[6] * x[7] - 0.6774 * x[3] * x[5] * x[6] * x[8] +\n        0.2819 * x[3] * x[5] * x[6] * x[9] - 0.8312 * x[3] * x[5] * x[6] * x[10] +\n        0.9588 * x[3] * x[5] * x[7] * x[8] +\n        0.6607 * x[3] * x[5] * x[7] * x[9] - 0.7955 * x[3] * x[5] * x[7] * x[10] -\n        0.3957 * x[3] * x[5] * x[8] * x[9] - 0.7523 * x[3] * x[5] * x[8] * x[10] -\n        0.232 * x[3] * x[5] * x[9] * x[10] + 0.7743 * x[3] * x[6] * x[7] * x[8] -\n        0.4182 * x[3] * x[6] * x[7] * x[9] - 0.8409 * x[3] * x[6] * x[7] * x[10] +\n        0.2953 * x[3] * x[6] * x[8] * x[9] - 0.6522 * x[3] * x[6] * x[8] * x[10] +\n        0.2996 * x[3] * x[6] * x[9] * x[10] - 0.319 * x[3] * x[7] * x[8] * x[9] +\n        0.092 * x[3] * x[7] * x[8] * x[10] - 0.9485 * x[3] * x[7] * x[9] * x[10] +\n        0.7382 * x[3] * x[8] * x[9] * x[10] - 0.1359 * x[4] * x[5] * x[6] * x[7] +\n        0.3935 * x[4] * x[5] * x[6] * x[8] +\n        0.8373 * x[4] * x[5] * x[6] * x[9] +\n        0.8982 * x[4] * x[5] * x[6] * x[10] - 0.5906 * x[4] * x[5] * x[7] * x[8] -\n        0.1772 * x[4] * x[5] * x[7] * x[9] + 0.834 * x[4] * x[5] * x[7] * x[10] -\n        0.6971 * x[4] * x[5] * x[8] * x[9] - 0.5593 * x[4] * x[5] * x[8] * x[10] +\n        0.5782 * x[4] * x[5] * x[9] * x[10] - 0.0524 * x[4] * x[6] * x[7] * x[8] +\n        0.3458 * x[4] * x[6] * x[7] * x[9] - 0.5235 * x[4] * x[6] * x[7] * x[10] -\n        0.1639 * x[4] * x[6] * x[8] * x[9] +\n        0.8372 * x[4] * x[6] * x[8] * x[10] +\n        0.6061 * x[4] * x[6] * x[9] * x[10] - 0.0421 * x[4] * x[7] * x[8] * x[9] +\n        0.0078 * x[4] * x[7] * x[8] * x[10] +\n        0.992 * x[4] * x[7] * x[9] * x[10] - 0.9383 * x[4] * x[8] * x[9] * x[10] +\n        0.3232 * x[5] * x[6] * x[7] * x[8] - 0.1077 * x[5] * x[6] * x[7] * x[9] -\n        0.6034 * x[5] * x[6] * x[7] * x[10] +\n        0.5167 * x[5] * x[6] * x[8] * x[9] +\n        0.5893 * x[5] * x[6] * x[8] * x[10] +\n        0.3498 * x[5] * x[6] * x[9] * x[10] +\n        0.9897 * x[5] * x[7] * x[8] * x[9] - 0.4292 * x[5] * x[7] * x[8] * x[10] +\n        0.6811 * x[5] * x[7] * x[9] * x[10] - 0.9318 * x[5] * x[8] * x[9] * x[10] -\n        0.628 * x[6] * x[7] * x[8] * x[9] - 0.7347 * x[6] * x[7] * x[8] * x[10] -\n        0.6338 * x[6] * x[7] * x[9] * x[10] - 0.0089 * x[6] * x[8] * x[9] * x[10] +\n        0.435 * x[7] * x[8] * x[9] * x[10] <= 46.589\n    )\n    e7 = replace_expr(e7, x)\n    JuMP.add_nonlinear_constraint(m, e7)\n    e8 = :(\n        0.0457 * x[1] * x[2] + 0.9914 * x[1] * x[3] - 0.2043 * x[1] * x[4] -\n        0.8175 * x[1] * x[5] - 0.3506 * x[1] * x[6] +\n        0.8449 * x[1] * x[7] +\n        0.9969 * x[1] * x[8] +\n        0.7066 * x[1] * x[9] +\n        0.7814 * x[1] * x[10] - 0.2681 * x[2] * x[3] +\n        0.1122 * x[2] * x[4] +\n        0.5142 * x[2] * x[5] +\n        0.5563 * x[2] * x[6] +\n        0.7168 * x[2] * x[7] +\n        0.1767 * x[2] * x[8] - 0.4082 * x[2] * x[9] +\n        0.6883 * x[2] * x[10] +\n        0.4342 * x[3] * x[4] +\n        0.2648 * x[3] * x[5] +\n        0.3778 * x[3] * x[6] - 0.8064 * x[3] * x[7] +\n        0.6143 * x[3] * x[8] +\n        0.0073 * x[3] * x[9] - 0.385 * x[3] * x[10] - 0.1292 * x[4] * x[5] +\n        0.0795 * x[4] * x[6] - 0.3467 * x[4] * x[7] +\n        0.4255 * x[4] * x[8] +\n        0.5645 * x[4] * x[9] - 0.6424 * x[4] * x[10] + 0.0119 * x[5] * x[6] -\n        0.6729 * x[5] * x[7] +\n        0.5847 * x[5] * x[8] +\n        0.7055 * x[5] * x[9] +\n        0.325 * x[5] * x[10] +\n        0.2792 * x[6] * x[7] +\n        0.0091 * x[6] * x[8] - 0.8959 * x[6] * x[9] - 0.2254 * x[6] * x[10] +\n        0.718 * x[7] * x[8] +\n        0.7289 * x[7] * x[9] +\n        0.0895 * x[7] * x[10] - 0.3158 * x[8] * x[9] - 0.6424 * x[8] * x[10] -\n        0.4076 * x[9] * x[10] - 0.7606 * x[1] - 0.4835 * x[2] + 0.7128 * x[3] -\n        0.7993 * x[4] + 0.1586 * x[5] - 0.2892 * x[6] - 0.297 * x[7] +\n        0.4053 * x[8] +\n        0.5703 * x[9] +\n        0.8903 * x[10] +\n        (-0.9557 * x[1] * x[2] * x[3]) - 0.0043 * x[1] * x[2] * x[4] -\n        0.3711 * x[1] * x[2] * x[5] - 0.3175 * x[1] * x[2] * x[6] -\n        0.3467 * x[1] * x[2] * x[7] - 0.0837 * x[1] * x[2] * x[8] +\n        0.397 * x[1] * x[2] * x[9] - 0.8681 * x[1] * x[2] * x[10] -\n        0.2124 * x[1] * x[3] * x[4] + 0.9815 * x[1] * x[3] * x[5] -\n        0.5043 * x[1] * x[3] * x[6] - 0.2869 * x[1] * x[3] * x[7] +\n        0.6841 * x[1] * x[3] * x[8] - 0.4616 * x[1] * x[3] * x[9] +\n        0.4655 * x[1] * x[3] * x[10] - 0.6494 * x[1] * x[4] * x[5] -\n        0.2862 * x[1] * x[4] * x[6] - 0.5755 * x[1] * x[4] * x[7] -\n        0.5887 * x[1] * x[4] * x[8] +\n        0.3282 * x[1] * x[4] * x[9] +\n        0.0774 * x[1] * x[4] * x[10] +\n        0.6841 * x[1] * x[5] * x[6] - 0.2826 * x[1] * x[5] * x[7] +\n        0.9124 * x[1] * x[5] * x[8] +\n        0.8253 * x[1] * x[5] * x[9] +\n        0.1537 * x[1] * x[5] * x[10] - 0.6056 * x[1] * x[6] * x[7] +\n        0.1527 * x[1] * x[6] * x[8] +\n        0.8957 * x[1] * x[6] * x[9] - 0.5742 * x[1] * x[6] * x[10] +\n        0.235 * x[1] * x[7] * x[8] - 0.5581 * x[1] * x[7] * x[9] -\n        0.6459 * x[1] * x[7] * x[10] +\n        0.6936 * x[1] * x[8] * x[9] +\n        0.5801 * x[1] * x[8] * x[10] +\n        0.6639 * x[1] * x[9] * x[10] +\n        0.6154 * x[2] * x[3] * x[4] +\n        0.593 * x[2] * x[3] * x[5] - 0.5041 * x[2] * x[3] * x[6] -\n        0.8966 * x[2] * x[3] * x[7] +\n        0.2624 * x[2] * x[3] * x[8] +\n        0.1377 * x[2] * x[3] * x[9] - 0.3901 * x[2] * x[3] * x[10] -\n        0.244 * x[2] * x[4] * x[5] - 0.0898 * x[2] * x[4] * x[6] +\n        0.7614 * x[2] * x[4] * x[7] - 0.7333 * x[2] * x[4] * x[8] +\n        0.3803 * x[2] * x[4] * x[9] +\n        0.6721 * x[2] * x[4] * x[10] - 0.1619 * x[2] * x[5] * x[6] +\n        0.8134 * x[2] * x[5] * x[7] +\n        0.9525 * x[2] * x[5] * x[8] +\n        0.992 * x[2] * x[5] * x[9] +\n        0.7007 * x[2] * x[5] * x[10] +\n        0.3342 * x[2] * x[6] * x[7] +\n        0.7684 * x[2] * x[6] * x[8] +\n        0.3835 * x[2] * x[6] * x[9] - 0.3171 * x[2] * x[6] * x[10] -\n        0.5577 * x[2] * x[7] * x[8] + 0.6115 * x[2] * x[7] * x[9] -\n        0.1189 * x[2] * x[7] * x[10] +\n        0.8643 * x[2] * x[8] * x[9] +\n        0.3953 * x[2] * x[8] * x[10] - 0.3491 * x[2] * x[9] * x[10] -\n        0.7712 * x[3] * x[4] * x[5] - 0.8291 * x[3] * x[4] * x[6] -\n        0.3737 * x[3] * x[4] * x[7] + 0.388 * x[3] * x[4] * x[8] -\n        0.5345 * x[3] * x[4] * x[9] - 0.2952 * x[3] * x[4] * x[10] +\n        0.2886 * x[3] * x[5] * x[6] +\n        0.0765 * x[3] * x[5] * x[7] +\n        0.8758 * x[3] * x[5] * x[8] +\n        0.4549 * x[3] * x[5] * x[9] - 0.0236 * x[3] * x[5] * x[10] -\n        0.1005 * x[3] * x[6] * x[7] + 0.7607 * x[3] * x[6] * x[8] -\n        0.7844 * x[3] * x[6] * x[9] - 0.0479 * x[3] * x[6] * x[10] +\n        0.9452 * x[3] * x[7] * x[8] - 0.1973 * x[3] * x[7] * x[9] +\n        0.6377 * x[3] * x[7] * x[10] +\n        0.5098 * x[3] * x[8] * x[9] - 0.3909 * x[3] * x[8] * x[10] +\n        0.9553 * x[3] * x[9] * x[10] +\n        0.1032 * x[4] * x[5] * x[6] +\n        0.6899 * x[4] * x[5] * x[7] +\n        0.8619 * x[4] * x[5] * x[8] +\n        0.3971 * x[4] * x[5] * x[9] - 0.3458 * x[4] * x[5] * x[10] -\n        0.5388 * x[4] * x[6] * x[7] + 0.8271 * x[4] * x[6] * x[8] -\n        0.4226 * x[4] * x[6] * x[9] +\n        0.3216 * x[4] * x[6] * x[10] +\n        0.5984 * x[4] * x[7] * x[8] +\n        0.8383 * x[4] * x[7] * x[9] +\n        0.9912 * x[4] * x[7] * x[10] - 0.6707 * x[4] * x[8] * x[9] +\n        0.623 * x[4] * x[8] * x[10] +\n        0.93 * x[4] * x[9] * x[10] - 0.9724 * x[5] * x[6] * x[7] +\n        0.693 * x[5] * x[6] * x[8] - 0.4268 * x[5] * x[6] * x[9] -\n        0.9103 * x[5] * x[6] * x[10] + 0.0769 * x[5] * x[7] * x[8] -\n        0.9401 * x[5] * x[7] * x[9] +\n        0.4041 * x[5] * x[7] * x[10] +\n        0.256 * x[5] * x[8] * x[9] - 0.4499 * x[5] * x[8] * x[10] -\n        0.967 * x[5] * x[9] * x[10] +\n        0.7441 * x[6] * x[7] * x[8] +\n        0.9925 * x[6] * x[7] * x[9] - 0.8395 * x[6] * x[7] * x[10] +\n        0.0652 * x[6] * x[8] * x[9] +\n        0.6151 * x[6] * x[8] * x[10] - 0.5872 * x[6] * x[9] * x[10] -\n        0.021 * x[7] * x[8] * x[9] - 0.355 * x[7] * x[8] * x[10] -\n        0.0804 * x[7] * x[9] * x[10] - 0.8904 * x[8] * x[9] * x[10] +\n        0.8792 * x[1] * x[2] * x[3] * x[5] - 0.0645 * x[1] * x[2] * x[3] * x[4] -\n        0.8687 * x[1] * x[2] * x[3] * x[6] + 0.3423 * x[1] * x[2] * x[3] * x[7] -\n        0.9285 * x[1] * x[2] * x[3] * x[8] - 0.8432 * x[1] * x[2] * x[3] * x[9] -\n        0.5799 * x[1] * x[2] * x[3] * x[10] - 0.6942 * x[1] * x[2] * x[4] * x[5] -\n        0.4111 * x[1] * x[2] * x[4] * x[6] +\n        0.386 * x[1] * x[2] * x[4] * x[7] +\n        0.1187 * x[1] * x[2] * x[4] * x[8] +\n        0.12 * x[1] * x[2] * x[4] * x[9] +\n        0.3772 * x[1] * x[2] * x[4] * x[10] - 0.7117 * x[1] * x[2] * x[5] * x[6] -\n        0.5063 * x[1] * x[2] * x[5] * x[7] - 0.5562 * x[1] * x[2] * x[5] * x[8] +\n        0.5658 * x[1] * x[2] * x[5] * x[9] - 0.9644 * x[1] * x[2] * x[5] * x[10] +\n        0.9425 * x[1] * x[2] * x[6] * x[7] - 0.7938 * x[1] * x[2] * x[6] * x[8] +\n        0.0856 * x[1] * x[2] * x[6] * x[9] +\n        0.9841 * x[1] * x[2] * x[6] * x[10] - 0.5537 * x[1] * x[2] * x[7] * x[8] -\n        0.6452 * x[1] * x[2] * x[7] * x[9] - 0.6664 * x[1] * x[2] * x[7] * x[10] -\n        0.5412 * x[1] * x[2] * x[8] * x[9] + 0.6908 * x[1] * x[2] * x[8] * x[10] -\n        0.5576 * x[1] * x[2] * x[9] * x[10] + 0.1221 * x[1] * x[3] * x[4] * x[5] -\n        0.925 * x[1] * x[3] * x[4] * x[6] + 0.4836 * x[1] * x[3] * x[4] * x[7] -\n        0.4814 * x[1] * x[3] * x[4] * x[8] - 0.8928 * x[1] * x[3] * x[4] * x[9] +\n        0.8237 * x[1] * x[3] * x[4] * x[10] +\n        0.2967 * x[1] * x[3] * x[5] * x[6] +\n        0.519 * x[1] * x[3] * x[5] * x[7] - 0.4036 * x[1] * x[3] * x[5] * x[8] +\n        0.2184 * x[1] * x[3] * x[5] * x[9] +\n        0.5597 * x[1] * x[3] * x[5] * x[10] - 0.6636 * x[1] * x[3] * x[6] * x[7] -\n        0.2396 * x[1] * x[3] * x[6] * x[8] + 0.2761 * x[1] * x[3] * x[6] * x[9] -\n        0.8421 * x[1] * x[3] * x[6] * x[10] + 0.5215 * x[1] * x[3] * x[7] * x[8] -\n        0.3457 * x[1] * x[3] * x[7] * x[9] +\n        0.54 * x[1] * x[3] * x[7] * x[10] +\n        0.1788 * x[1] * x[3] * x[8] * x[9] +\n        0.2414 * x[1] * x[3] * x[8] * x[10] - 0.055 * x[1] * x[3] * x[9] * x[10] -\n        0.2767 * x[1] * x[4] * x[5] * x[6] +\n        0.3488 * x[1] * x[4] * x[5] * x[7] +\n        0.0979 * x[1] * x[4] * x[5] * x[8] - 0.6934 * x[1] * x[4] * x[5] * x[9] -\n        0.6615 * x[1] * x[4] * x[5] * x[10] + 0.503 * x[1] * x[4] * x[6] * x[7] -\n        0.7626 * x[1] * x[4] * x[6] * x[8] - 0.7943 * x[1] * x[4] * x[6] * x[9] -\n        0.3063 * x[1] * x[4] * x[6] * x[10] + 0.0558 * x[1] * x[4] * x[7] * x[8] -\n        0.2301 * x[1] * x[4] * x[7] * x[9] + 0.5779 * x[1] * x[4] * x[7] * x[10] -\n        0.0523 * x[1] * x[4] * x[8] * x[9] +\n        0.4117 * x[1] * x[4] * x[8] * x[10] +\n        0.7896 * x[1] * x[4] * x[9] * x[10] - 0.3012 * x[1] * x[5] * x[6] * x[7] -\n        0.0166 * x[1] * x[5] * x[6] * x[8] - 0.6013 * x[1] * x[5] * x[6] * x[9] -\n        0.27 * x[1] * x[5] * x[6] * x[10] - 0.5193 * x[1] * x[5] * x[7] * x[8] +\n        0.0948 * x[1] * x[5] * x[7] * x[9] +\n        0.2315 * x[1] * x[5] * x[7] * x[10] - 0.8466 * x[1] * x[5] * x[8] * x[9] -\n        0.4082 * x[1] * x[5] * x[8] * x[10] + 0.7234 * x[1] * x[5] * x[9] * x[10] -\n        0.2451 * x[1] * x[6] * x[7] * x[8] + 0.486 * x[1] * x[6] * x[7] * x[9] -\n        0.9333 * x[1] * x[6] * x[7] * x[10] - 0.577 * x[1] * x[6] * x[8] * x[9] +\n        0.6391 * x[1] * x[6] * x[8] * x[10] - 0.078 * x[1] * x[6] * x[9] * x[10] -\n        0.7901 * x[1] * x[7] * x[8] * x[9] + 0.3108 * x[1] * x[7] * x[8] * x[10] -\n        0.5911 * x[1] * x[7] * x[9] * x[10] - 0.7161 * x[1] * x[8] * x[9] * x[10] +\n        0.6677 * x[2] * x[3] * x[4] * x[5] +\n        0.9834 * x[2] * x[3] * x[4] * x[6] - 0.2604 * x[2] * x[3] * x[4] * x[7] +\n        0.1312 * x[2] * x[3] * x[4] * x[8] +\n        0.1699 * x[2] * x[3] * x[4] * x[9] +\n        0.8036 * x[2] * x[3] * x[4] * x[10] +\n        0.4179 * x[2] * x[3] * x[5] * x[6] - 0.4876 * x[2] * x[3] * x[5] * x[7] -\n        0.9695 * x[2] * x[3] * x[5] * x[8] + 0.8412 * x[2] * x[3] * x[5] * x[9] -\n        0.6245 * x[2] * x[3] * x[5] * x[10] - 0.2725 * x[2] * x[3] * x[6] * x[7] +\n        0.9959 * x[2] * x[3] * x[6] * x[8] +\n        0.7839 * x[2] * x[3] * x[6] * x[9] - 0.2566 * x[2] * x[3] * x[6] * x[10] -\n        0.3715 * x[2] * x[3] * x[7] * x[8] - 0.1659 * x[2] * x[3] * x[7] * x[9] -\n        0.3605 * x[2] * x[3] * x[7] * x[10] +\n        0.4571 * x[2] * x[3] * x[8] * x[9] +\n        0.157 * x[2] * x[3] * x[8] * x[10] +\n        0.3664 * x[2] * x[3] * x[9] * x[10] +\n        0.2114 * x[2] * x[4] * x[5] * x[6] - 0.8717 * x[2] * x[4] * x[5] * x[7] +\n        0.7656 * x[2] * x[4] * x[5] * x[8] - 0.1614 * x[2] * x[4] * x[5] * x[9] +\n        0.208 * x[2] * x[4] * x[5] * x[10] +\n        0.2939 * x[2] * x[4] * x[6] * x[7] +\n        0.4719 * x[2] * x[4] * x[6] * x[8] +\n        0.1079 * x[2] * x[4] * x[6] * x[9] - 0.1952 * x[2] * x[4] * x[6] * x[10] +\n        0.9831 * x[2] * x[4] * x[7] * x[8] - 0.3912 * x[2] * x[4] * x[7] * x[9] -\n        0.0164 * x[2] * x[4] * x[7] * x[10] - 0.7641 * x[2] * x[4] * x[8] * x[9] +\n        0.825 * x[2] * x[4] * x[8] * x[10] +\n        0.7573 * x[2] * x[4] * x[9] * x[10] - 0.0731 * x[2] * x[5] * x[6] * x[7] -\n        0.7839 * x[2] * x[5] * x[6] * x[8] +\n        0.2375 * x[2] * x[5] * x[6] * x[9] +\n        0.342 * x[2] * x[5] * x[6] * x[10] - 0.2362 * x[2] * x[5] * x[7] * x[8] +\n        0.7813 * x[2] * x[5] * x[7] * x[9] +\n        0.6021 * x[2] * x[5] * x[7] * x[10] +\n        0.3864 * x[2] * x[5] * x[8] * x[9] +\n        0.7828 * x[2] * x[5] * x[8] * x[10] - 0.2355 * x[2] * x[5] * x[9] * x[10] +\n        0.1796 * x[2] * x[6] * x[7] * x[8] - 0.7816 * x[2] * x[6] * x[7] * x[9] +\n        0.6992 * x[2] * x[6] * x[7] * x[10] - 0.5391 * x[2] * x[6] * x[8] * x[9] +\n        0.1898 * x[2] * x[6] * x[8] * x[10] - 0.3419 * x[2] * x[6] * x[9] * x[10] -\n        0.6057 * x[2] * x[7] * x[8] * x[9] + 0.4886 * x[2] * x[7] * x[8] * x[10] -\n        0.0693 * x[2] * x[7] * x[9] * x[10] + 0.6415 * x[2] * x[8] * x[9] * x[10] -\n        0.1695 * x[3] * x[4] * x[5] * x[6] - 0.662 * x[3] * x[4] * x[5] * x[7] -\n        0.6558 * x[3] * x[4] * x[5] * x[8] - 0.2137 * x[3] * x[4] * x[5] * x[9] +\n        0.0807 * x[3] * x[4] * x[5] * x[10] +\n        0.2775 * x[3] * x[4] * x[6] * x[7] - 0.639 * x[3] * x[4] * x[6] * x[8] +\n        0.1566 * x[3] * x[4] * x[6] * x[9] +\n        0.4792 * x[3] * x[4] * x[6] * x[10] +\n        0.1403 * x[3] * x[4] * x[7] * x[8] - 0.6095 * x[3] * x[4] * x[7] * x[9] +\n        0.9322 * x[3] * x[4] * x[7] * x[10] - 0.0214 * x[3] * x[4] * x[8] * x[9] +\n        0.3126 * x[3] * x[4] * x[8] * x[10] - 0.6241 * x[3] * x[4] * x[9] * x[10] +\n        0.1136 * x[3] * x[5] * x[6] * x[7] +\n        0.4677 * x[3] * x[5] * x[6] * x[8] - 0.6577 * x[3] * x[5] * x[6] * x[9] +\n        0.3394 * x[3] * x[5] * x[6] * x[10] - 0.7785 * x[3] * x[5] * x[7] * x[8] -\n        0.7024 * x[3] * x[5] * x[7] * x[9] + 0.2443 * x[3] * x[5] * x[7] * x[10] -\n        0.2521 * x[3] * x[5] * x[8] * x[9] + 0.2286 * x[3] * x[5] * x[8] * x[10] -\n        0.0991 * x[3] * x[5] * x[9] * x[10] - 0.7218 * x[3] * x[6] * x[7] * x[8] +\n        0.9204 * x[3] * x[6] * x[7] * x[9] - 0.1743 * x[3] * x[6] * x[7] * x[10] +\n        0.2405 * x[3] * x[6] * x[8] * x[9] +\n        0.1433 * x[3] * x[6] * x[8] * x[10] +\n        0.402 * x[3] * x[6] * x[9] * x[10] +\n        0.7113 * x[3] * x[7] * x[8] * x[9] - 0.14 * x[3] * x[7] * x[8] * x[10] +\n        0.1251 * x[3] * x[7] * x[9] * x[10] +\n        0.0473 * x[3] * x[8] * x[9] * x[10] - 0.5929 * x[4] * x[5] * x[6] * x[7] +\n        0.0649 * x[4] * x[5] * x[6] * x[8] +\n        0.9708 * x[4] * x[5] * x[6] * x[9] +\n        0.6177 * x[4] * x[5] * x[6] * x[10] +\n        0.5806 * x[4] * x[5] * x[7] * x[8] - 0.1607 * x[4] * x[5] * x[7] * x[9] +\n        0.059 * x[4] * x[5] * x[7] * x[10] - 0.8811 * x[4] * x[5] * x[8] * x[9] -\n        0.4492 * x[4] * x[5] * x[8] * x[10] +\n        0.7614 * x[4] * x[5] * x[9] * x[10] +\n        0.2033 * x[4] * x[6] * x[7] * x[8] - 0.9171 * x[4] * x[6] * x[7] * x[9] -\n        0.0382 * x[4] * x[6] * x[7] * x[10] - 0.8299 * x[4] * x[6] * x[8] * x[9] -\n        0.5709 * x[4] * x[6] * x[8] * x[10] - 0.396 * x[4] * x[6] * x[9] * x[10] +\n        0.7934 * x[4] * x[7] * x[8] * x[9] +\n        0.0689 * x[4] * x[7] * x[8] * x[10] - 0.4928 * x[4] * x[7] * x[9] * x[10] -\n        0.4895 * x[4] * x[8] * x[9] * x[10] +\n        0.8422 * x[5] * x[6] * x[7] * x[8] +\n        0.8058 * x[5] * x[6] * x[7] * x[9] - 0.3989 * x[5] * x[6] * x[7] * x[10] -\n        0.7604 * x[5] * x[6] * x[8] * x[9] - 0.2455 * x[5] * x[6] * x[8] * x[10] -\n        0.1685 * x[5] * x[6] * x[9] * x[10] - 0.5593 * x[5] * x[7] * x[8] * x[9] -\n        0.7832 * x[5] * x[7] * x[8] * x[10] +\n        0.0926 * x[5] * x[7] * x[9] * x[10] +\n        0.6215 * x[5] * x[8] * x[9] * x[10] +\n        0.3352 * x[6] * x[7] * x[8] * x[9] +\n        0.3423 * x[6] * x[7] * x[8] * x[10] - 0.8728 * x[6] * x[7] * x[9] * x[10] +\n        0.6484 * x[6] * x[8] * x[9] * x[10] - 0.2626 * x[7] * x[8] * x[9] * x[10] <=\n        14.826\n    )\n    e8 = replace_expr(e8, x)\n    JuMP.add_nonlinear_constraint(m, e8)\n    e9 = :(\n        0.1204 * x[1] * x[3] - 0.6331 * x[1] * x[2] + 0.2074 * x[1] * x[4] -\n        0.0007 * x[1] * x[5] + 0.1524 * x[1] * x[6] - 0.1373 * x[1] * x[7] -\n        0.5286 * x[1] * x[8] + 0.0533 * x[1] * x[9] - 0.0113 * x[1] * x[10] +\n        0.039 * x[2] * x[3] +\n        0.746 * x[2] * x[4] - 0.7493 * x[2] * x[5] - 0.3501 * x[2] * x[6] -\n        0.7046 * x[2] * x[7] + 0.623 * x[2] * x[8] - 0.3282 * x[2] * x[9] +\n        0.2535 * x[2] * x[10] +\n        0.7369 * x[3] * x[4] - 0.3179 * x[3] * x[5] - 0.7554 * x[3] * x[6] +\n        0.3384 * x[3] * x[7] +\n        0.7428 * x[3] * x[8] +\n        0.6871 * x[3] * x[9] - 0.2774 * x[3] * x[10] + 0.1942 * x[4] * x[5] -\n        0.0372 * x[4] * x[6] +\n        0.9036 * x[4] * x[7] +\n        0.9891 * x[4] * x[8] +\n        0.2623 * x[4] * x[9] +\n        0.4058 * x[4] * x[10] +\n        0.2905 * x[5] * x[6] +\n        0.8707 * x[5] * x[7] - 0.6906 * x[5] * x[8] +\n        0.0175 * x[5] * x[9] +\n        0.7644 * x[5] * x[10] +\n        0.1747 * x[6] * x[7] - 0.3217 * x[6] * x[8] - 0.3756 * x[6] * x[9] -\n        0.4446 * x[6] * x[10] - 0.5191 * x[7] * x[8] + 0.8229 * x[7] * x[9] -\n        0.0585 * x[7] * x[10] +\n        0.7931 * x[8] * x[9] +\n        0.2165 * x[8] * x[10] +\n        0.3018 * x[9] * x[10] - 0.6853 * x[1] + 0.4834 * x[2] - 0.9677 * x[3] +\n        0.9793 * x[4] - 0.3145 * x[5] + 0.9356 * x[6] - 0.651 * x[7] - 0.7873 * x[8] +\n        0.5914 * x[9] - 0.82 * x[10] + 0.6907 * x[1] * x[2] * x[4] -\n        0.4133 * x[1] * x[2] * x[3] + 0.0963 * x[1] * x[2] * x[5] -\n        0.2825 * x[1] * x[2] * x[6] +\n        0.0354 * x[1] * x[2] * x[7] +\n        0.5125 * x[1] * x[2] * x[8] +\n        0.9351 * x[1] * x[2] * x[9] +\n        0.7973 * x[1] * x[2] * x[10] - 0.8916 * x[1] * x[3] * x[4] -\n        0.7597 * x[1] * x[3] * x[5] +\n        0.2381 * x[1] * x[3] * x[6] +\n        0.0077 * x[1] * x[3] * x[7] +\n        0.3442 * x[1] * x[3] * x[8] +\n        0.1405 * x[1] * x[3] * x[9] +\n        0.8568 * x[1] * x[3] * x[10] - 0.261 * x[1] * x[4] * x[5] -\n        0.8792 * x[1] * x[4] * x[6] - 0.0695 * x[1] * x[4] * x[7] -\n        0.827 * x[1] * x[4] * x[8] +\n        0.5092 * x[1] * x[4] * x[9] +\n        0.4796 * x[1] * x[4] * x[10] - 0.7576 * x[1] * x[5] * x[6] -\n        0.2986 * x[1] * x[5] * x[7] - 0.6192 * x[1] * x[5] * x[8] -\n        0.8556 * x[1] * x[5] * x[9] - 0.0737 * x[1] * x[5] * x[10] -\n        0.0614 * x[1] * x[6] * x[7] - 0.0832 * x[1] * x[6] * x[8] -\n        0.6275 * x[1] * x[6] * x[9] - 0.4122 * x[1] * x[6] * x[10] +\n        0.1479 * x[1] * x[7] * x[8] - 0.4795 * x[1] * x[7] * x[9] +\n        0.4531 * x[1] * x[7] * x[10] - 0.564 * x[1] * x[8] * x[9] -\n        0.7735 * x[1] * x[8] * x[10] +\n        0.5994 * x[1] * x[9] * x[10] +\n        0.5007 * x[2] * x[3] * x[4] +\n        0.5843 * x[2] * x[3] * x[5] - 0.436 * x[2] * x[3] * x[6] -\n        0.2484 * x[2] * x[3] * x[7] +\n        0.5402 * x[2] * x[3] * x[8] +\n        0.4467 * x[2] * x[3] * x[9] - 0.7388 * x[2] * x[3] * x[10] +\n        0.449 * x[2] * x[4] * x[5] +\n        0.2 * x[2] * x[4] * x[6] - 0.2227 * x[2] * x[4] * x[7] +\n        0.1216 * x[2] * x[4] * x[8] - 0.1403 * x[2] * x[4] * x[9] +\n        0.2873 * x[2] * x[4] * x[10] - 0.9251 * x[2] * x[5] * x[6] -\n        0.9097 * x[2] * x[5] * x[7] - 0.299 * x[2] * x[5] * x[8] -\n        0.037 * x[2] * x[5] * x[9] +\n        0.1356 * x[2] * x[5] * x[10] +\n        0.1424 * x[2] * x[6] * x[7] +\n        0.9099 * x[2] * x[6] * x[8] - 0.8295 * x[2] * x[6] * x[9] -\n        0.9163 * x[2] * x[6] * x[10] - 0.886 * x[2] * x[7] * x[8] -\n        0.5395 * x[2] * x[7] * x[9] +\n        0.4885 * x[2] * x[7] * x[10] +\n        0.0733 * x[2] * x[8] * x[9] +\n        0.6171 * x[2] * x[8] * x[10] +\n        0.9443 * x[2] * x[9] * x[10] +\n        0.8452 * x[3] * x[4] * x[5] +\n        0.2589 * x[3] * x[4] * x[6] - 0.3954 * x[3] * x[4] * x[7] +\n        0.2099 * x[3] * x[4] * x[8] - 0.4274 * x[3] * x[4] * x[9] +\n        0.7638 * x[3] * x[4] * x[10] +\n        0.0518 * x[3] * x[5] * x[6] - 0.7951 * x[3] * x[5] * x[7] -\n        0.0508 * x[3] * x[5] * x[8] - 0.2861 * x[3] * x[5] * x[9] +\n        0.0163 * x[3] * x[5] * x[10] +\n        0.3989 * x[3] * x[6] * x[7] - 0.3631 * x[3] * x[6] * x[8] -\n        0.1875 * x[3] * x[6] * x[9] +\n        0.6995 * x[3] * x[6] * x[10] +\n        0.5373 * x[3] * x[7] * x[8] +\n        0.7748 * x[3] * x[7] * x[9] +\n        0.0892 * x[3] * x[7] * x[10] +\n        0.093 * x[3] * x[8] * x[9] - 0.4689 * x[3] * x[8] * x[10] +\n        0.4298 * x[3] * x[9] * x[10] - 0.4441 * x[4] * x[5] * x[6] -\n        0.9731 * x[4] * x[5] * x[7] - 0.0911 * x[4] * x[5] * x[8] -\n        0.8933 * x[4] * x[5] * x[9] - 0.3553 * x[4] * x[5] * x[10] -\n        0.1372 * x[4] * x[6] * x[7] +\n        0.239 * x[4] * x[6] * x[8] +\n        0.9347 * x[4] * x[6] * x[9] - 0.8911 * x[4] * x[6] * x[10] -\n        0.528 * x[4] * x[7] * x[8] - 0.13 * x[4] * x[7] * x[9] -\n        0.2034 * x[4] * x[7] * x[10] - 0.69 * x[4] * x[8] * x[9] +\n        0.2966 * x[4] * x[8] * x[10] +\n        0.9593 * x[4] * x[9] * x[10] - 0.9582 * x[5] * x[6] * x[7] +\n        0.4532 * x[5] * x[6] * x[8] +\n        0.5574 * x[5] * x[6] * x[9] - 0.4571 * x[5] * x[6] * x[10] -\n        0.9344 * x[5] * x[7] * x[8] - 0.1114 * x[5] * x[7] * x[9] +\n        0.477 * x[5] * x[7] * x[10] - 0.0515 * x[5] * x[8] * x[9] -\n        0.456 * x[5] * x[8] * x[10] +\n        0.1071 * x[5] * x[9] * x[10] +\n        0.3639 * x[6] * x[7] * x[8] +\n        0.1604 * x[6] * x[7] * x[9] +\n        0.7412 * x[6] * x[7] * x[10] - 0.842 * x[6] * x[8] * x[9] +\n        0.2298 * x[6] * x[8] * x[10] - 0.7632 * x[6] * x[9] * x[10] +\n        0.467 * x[7] * x[8] * x[9] - 0.3678 * x[7] * x[8] * x[10] -\n        0.0498 * x[7] * x[9] * x[10] +\n        0.2148 * x[8] * x[9] * x[10] +\n        0.607 * x[1] * x[2] * x[3] * x[4] - 0.984 * x[1] * x[2] * x[3] * x[5] +\n        0.1984 * x[1] * x[2] * x[3] * x[6] - 0.3261 * x[1] * x[2] * x[3] * x[7] +\n        0.9942 * x[1] * x[2] * x[3] * x[8] +\n        0.4899 * x[1] * x[2] * x[3] * x[9] +\n        0.1859 * x[1] * x[2] * x[3] * x[10] +\n        0.7152 * x[1] * x[2] * x[4] * x[5] +\n        0.6231 * x[1] * x[2] * x[4] * x[6] - 0.3239 * x[1] * x[2] * x[4] * x[7] +\n        0.6656 * x[1] * x[2] * x[4] * x[8] +\n        0.6511 * x[1] * x[2] * x[4] * x[9] +\n        0.4798 * x[1] * x[2] * x[4] * x[10] - 0.6549 * x[1] * x[2] * x[5] * x[6] +\n        0.3657 * x[1] * x[2] * x[5] * x[7] +\n        0.2469 * x[1] * x[2] * x[5] * x[8] +\n        0.1256 * x[1] * x[2] * x[5] * x[9] - 0.83 * x[1] * x[2] * x[5] * x[10] +\n        0.8632 * x[1] * x[2] * x[6] * x[7] - 0.6316 * x[1] * x[2] * x[6] * x[8] +\n        0.901 * x[1] * x[2] * x[6] * x[9] +\n        0.2282 * x[1] * x[2] * x[6] * x[10] - 0.3158 * x[1] * x[2] * x[7] * x[8] -\n        0.9495 * x[1] * x[2] * x[7] * x[9] + 0.379 * x[1] * x[2] * x[7] * x[10] -\n        0.7787 * x[1] * x[2] * x[8] * x[9] - 0.3534 * x[1] * x[2] * x[8] * x[10] +\n        0.0053 * x[1] * x[2] * x[9] * x[10] - 0.1876 * x[1] * x[3] * x[4] * x[5] -\n        0.502 * x[1] * x[3] * x[4] * x[6] +\n        0.1311 * x[1] * x[3] * x[4] * x[7] +\n        0.6431 * x[1] * x[3] * x[4] * x[8] +\n        0.3694 * x[1] * x[3] * x[4] * x[9] - 0.7882 * x[1] * x[3] * x[4] * x[10] -\n        0.3699 * x[1] * x[3] * x[5] * x[6] - 0.874 * x[1] * x[3] * x[5] * x[7] -\n        0.4416 * x[1] * x[3] * x[5] * x[8] +\n        0.2313 * x[1] * x[3] * x[5] * x[9] +\n        0.357 * x[1] * x[3] * x[5] * x[10] +\n        0.1096 * x[1] * x[3] * x[6] * x[7] +\n        0.9751 * x[1] * x[3] * x[6] * x[8] +\n        0.4229 * x[1] * x[3] * x[6] * x[9] - 0.0638 * x[1] * x[3] * x[6] * x[10] +\n        0.9879 * x[1] * x[3] * x[7] * x[8] +\n        0.8635 * x[1] * x[3] * x[7] * x[9] +\n        0.4333 * x[1] * x[3] * x[7] * x[10] +\n        0.8267 * x[1] * x[3] * x[8] * x[9] +\n        0.3304 * x[1] * x[3] * x[8] * x[10] +\n        0.7375 * x[1] * x[3] * x[9] * x[10] +\n        0.1234 * x[1] * x[4] * x[5] * x[6] - 0.2028 * x[1] * x[4] * x[5] * x[7] +\n        0.4864 * x[1] * x[4] * x[5] * x[8] +\n        0.4254 * x[1] * x[4] * x[5] * x[9] - 0.7986 * x[1] * x[4] * x[5] * x[10] -\n        0.3318 * x[1] * x[4] * x[6] * x[7] +\n        0.7505 * x[1] * x[4] * x[6] * x[8] +\n        0.8088 * x[1] * x[4] * x[6] * x[9] - 0.4503 * x[1] * x[4] * x[6] * x[10] +\n        0.8307 * x[1] * x[4] * x[7] * x[8] - 0.9624 * x[1] * x[4] * x[7] * x[9] -\n        0.172 * x[1] * x[4] * x[7] * x[10] + 0.2328 * x[1] * x[4] * x[8] * x[9] -\n        0.0483 * x[1] * x[4] * x[8] * x[10] - 0.8543 * x[1] * x[4] * x[9] * x[10] -\n        0.1414 * x[1] * x[5] * x[6] * x[7] - 0.6745 * x[1] * x[5] * x[6] * x[8] +\n        0.2956 * x[1] * x[5] * x[6] * x[9] - 0.9646 * x[1] * x[5] * x[6] * x[10] +\n        0.6631 * x[1] * x[5] * x[7] * x[8] - 0.921 * x[1] * x[5] * x[7] * x[9] +\n        0.7216 * x[1] * x[5] * x[7] * x[10] - 0.0916 * x[1] * x[5] * x[8] * x[9] +\n        0.5066 * x[1] * x[5] * x[8] * x[10] - 0.2279 * x[1] * x[5] * x[9] * x[10] +\n        0.4388 * x[1] * x[6] * x[7] * x[8] +\n        0.1251 * x[1] * x[6] * x[7] * x[9] - 0.4666 * x[1] * x[6] * x[7] * x[10] -\n        0.6096 * x[1] * x[6] * x[8] * x[9] - 0.1296 * x[1] * x[6] * x[8] * x[10] +\n        0.147 * x[1] * x[6] * x[9] * x[10] - 0.8773 * x[1] * x[7] * x[8] * x[9] +\n        0.3256 * x[1] * x[7] * x[8] * x[10] +\n        0.1917 * x[1] * x[7] * x[9] * x[10] - 0.7454 * x[1] * x[8] * x[9] * x[10] +\n        0.953 * x[2] * x[3] * x[4] * x[5] - 0.2524 * x[2] * x[3] * x[4] * x[6] +\n        0.6998 * x[2] * x[3] * x[4] * x[7] +\n        0.9019 * x[2] * x[3] * x[4] * x[8] +\n        0.0886 * x[2] * x[3] * x[4] * x[9] - 0.745 * x[2] * x[3] * x[4] * x[10] +\n        0.7499 * x[2] * x[3] * x[5] * x[6] +\n        0.064 * x[2] * x[3] * x[5] * x[7] - 0.919 * x[2] * x[3] * x[5] * x[8] -\n        0.9064 * x[2] * x[3] * x[5] * x[9] + 0.2797 * x[2] * x[3] * x[5] * x[10] -\n        0.6761 * x[2] * x[3] * x[6] * x[7] - 0.9433 * x[2] * x[3] * x[6] * x[8] +\n        0.4738 * x[2] * x[3] * x[6] * x[9] - 0.469 * x[2] * x[3] * x[6] * x[10] -\n        0.6195 * x[2] * x[3] * x[7] * x[8] +\n        0.4109 * x[2] * x[3] * x[7] * x[9] +\n        0.774 * x[2] * x[3] * x[7] * x[10] - 0.6599 * x[2] * x[3] * x[8] * x[9] +\n        0.5277 * x[2] * x[3] * x[8] * x[10] - 0.207 * x[2] * x[3] * x[9] * x[10] +\n        0.7556 * x[2] * x[4] * x[5] * x[6] - 0.0444 * x[2] * x[4] * x[5] * x[7] -\n        0.6359 * x[2] * x[4] * x[5] * x[8] +\n        0.5783 * x[2] * x[4] * x[5] * x[9] +\n        0.4262 * x[2] * x[4] * x[5] * x[10] - 0.5666 * x[2] * x[4] * x[6] * x[7] +\n        0.4188 * x[2] * x[4] * x[6] * x[8] +\n        0.3495 * x[2] * x[4] * x[6] * x[9] - 0.6488 * x[2] * x[4] * x[6] * x[10] -\n        0.9492 * x[2] * x[4] * x[7] * x[8] - 0.2321 * x[2] * x[4] * x[7] * x[9] -\n        0.0055 * x[2] * x[4] * x[7] * x[10] - 0.556 * x[2] * x[4] * x[8] * x[9] +\n        0.3175 * x[2] * x[4] * x[8] * x[10] +\n        0.392 * x[2] * x[4] * x[9] * x[10] +\n        0.7571 * x[2] * x[5] * x[6] * x[7] - 0.123 * x[2] * x[5] * x[6] * x[8] -\n        0.9402 * x[2] * x[5] * x[6] * x[9] + 0.9707 * x[2] * x[5] * x[6] * x[10] -\n        0.9632 * x[2] * x[5] * x[7] * x[8] +\n        0.5879 * x[2] * x[5] * x[7] * x[9] +\n        0.7006 * x[2] * x[5] * x[7] * x[10] +\n        0.3368 * x[2] * x[5] * x[8] * x[9] +\n        0.7005 * x[2] * x[5] * x[8] * x[10] - 0.9946 * x[2] * x[5] * x[9] * x[10] -\n        0.5453 * x[2] * x[6] * x[7] * x[8] - 0.6007 * x[2] * x[6] * x[7] * x[9] +\n        0.1658 * x[2] * x[6] * x[7] * x[10] +\n        0.5857 * x[2] * x[6] * x[8] * x[9] - 0.6648 * x[2] * x[6] * x[8] * x[10] -\n        0.3842 * x[2] * x[6] * x[9] * x[10] - 0.8785 * x[2] * x[7] * x[8] * x[9] -\n        0.3002 * x[2] * x[7] * x[8] * x[10] - 0.1467 * x[2] * x[7] * x[9] * x[10] +\n        0.5581 * x[2] * x[8] * x[9] * x[10] +\n        0.255 * x[3] * x[4] * x[5] * x[6] - 0.3062 * x[3] * x[4] * x[5] * x[7] -\n        0.1995 * x[3] * x[4] * x[5] * x[8] +\n        0.7855 * x[3] * x[4] * x[5] * x[9] +\n        0.076 * x[3] * x[4] * x[5] * x[10] +\n        0.9889 * x[3] * x[4] * x[6] * x[7] +\n        0.6766 * x[3] * x[4] * x[6] * x[8] +\n        0.3158 * x[3] * x[4] * x[6] * x[9] - 0.8643 * x[3] * x[4] * x[6] * x[10] -\n        0.8024 * x[3] * x[4] * x[7] * x[8] - 0.6817 * x[3] * x[4] * x[7] * x[9] -\n        0.9275 * x[3] * x[4] * x[7] * x[10] + 0.5669 * x[3] * x[4] * x[8] * x[9] -\n        0.8213 * x[3] * x[4] * x[8] * x[10] +\n        0.3068 * x[3] * x[4] * x[9] * x[10] +\n        0.9216 * x[3] * x[5] * x[6] * x[7] +\n        0.8245 * x[3] * x[5] * x[6] * x[8] - 0.387 * x[3] * x[5] * x[6] * x[9] +\n        0.2332 * x[3] * x[5] * x[6] * x[10] - 0.2114 * x[3] * x[5] * x[7] * x[8] -\n        0.5222 * x[3] * x[5] * x[7] * x[9] - 0.1285 * x[3] * x[5] * x[7] * x[10] +\n        0.2733 * x[3] * x[5] * x[8] * x[9] - 0.5025 * x[3] * x[5] * x[8] * x[10] -\n        0.3684 * x[3] * x[5] * x[9] * x[10] - 0.1281 * x[3] * x[6] * x[7] * x[8] +\n        0.7043 * x[3] * x[6] * x[7] * x[9] +\n        0.4752 * x[3] * x[6] * x[7] * x[10] +\n        0.4398 * x[3] * x[6] * x[8] * x[9] - 0.2425 * x[3] * x[6] * x[8] * x[10] +\n        0.0265 * x[3] * x[6] * x[9] * x[10] +\n        0.1761 * x[3] * x[7] * x[8] * x[9] +\n        0.6789 * x[3] * x[7] * x[8] * x[10] - 0.2652 * x[3] * x[7] * x[9] * x[10] -\n        0.7416 * x[3] * x[8] * x[9] * x[10] +\n        0.3104 * x[4] * x[5] * x[6] * x[7] +\n        0.5838 * x[4] * x[5] * x[6] * x[8] - 0.2481 * x[4] * x[5] * x[6] * x[9] -\n        0.5737 * x[4] * x[5] * x[6] * x[10] +\n        0.1995 * x[4] * x[5] * x[7] * x[8] +\n        0.7254 * x[4] * x[5] * x[7] * x[9] - 0.6076 * x[4] * x[5] * x[7] * x[10] +\n        0.2583 * x[4] * x[5] * x[8] * x[9] +\n        0.3748 * x[4] * x[5] * x[8] * x[10] - 0.821 * x[4] * x[5] * x[9] * x[10] -\n        0.7231 * x[4] * x[6] * x[7] * x[8] +\n        0.792 * x[4] * x[6] * x[7] * x[9] +\n        0.1935 * x[4] * x[6] * x[7] * x[10] +\n        0.3677 * x[4] * x[6] * x[8] * x[9] - 0.3893 * x[4] * x[6] * x[8] * x[10] -\n        0.5531 * x[4] * x[6] * x[9] * x[10] + 0.3063 * x[4] * x[7] * x[8] * x[9] -\n        0.3756 * x[4] * x[7] * x[8] * x[10] + 0.9983 * x[4] * x[7] * x[9] * x[10] -\n        0.4544 * x[4] * x[8] * x[9] * x[10] +\n        0.8651 * x[5] * x[6] * x[7] * x[8] +\n        0.8738 * x[5] * x[6] * x[7] * x[9] +\n        0.7123 * x[5] * x[6] * x[7] * x[10] - 0.789 * x[5] * x[6] * x[8] * x[9] -\n        0.9015 * x[5] * x[6] * x[8] * x[10] + 0.8536 * x[5] * x[6] * x[9] * x[10] -\n        0.6222 * x[5] * x[7] * x[8] * x[9] + 0.531 * x[5] * x[7] * x[8] * x[10] -\n        0.7534 * x[5] * x[7] * x[9] * x[10] +\n        0.1807 * x[5] * x[8] * x[9] * x[10] +\n        0.8496 * x[6] * x[7] * x[8] * x[9] +\n        0.0791 * x[6] * x[7] * x[8] * x[10] +\n        0.8057 * x[6] * x[7] * x[9] * x[10] - 0.81 * x[6] * x[8] * x[9] * x[10] +\n        0.7906 * x[7] * x[8] * x[9] * x[10] <= 9.957\n    )\n    e9 = replace_expr(e9, x)\n    JuMP.add_nonlinear_constraint(m, e9)\n    e10 = :(\n        (-0.6891 * x[1] * x[2]) - 0.416 * x[1] * x[3] - 0.4715 * x[1] * x[4] +\n        0.6858 * x[1] * x[5] - 0.4223 * x[1] * x[6] +\n        0.7652 * x[1] * x[7] +\n        0.7955 * x[1] * x[8] +\n        0.5377 * x[1] * x[9] +\n        0.9667 * x[1] * x[10] - 0.8157 * x[2] * x[3] - 0.9023 * x[2] * x[4] -\n        0.5467 * x[2] * x[5] - 0.3177 * x[2] * x[6] - 0.9398 * x[2] * x[7] +\n        0.2349 * x[2] * x[8] +\n        0.001 * x[2] * x[9] +\n        0.3641 * x[2] * x[10] - 0.9461 * x[3] * x[4] +\n        0.1124 * x[3] * x[5] +\n        0.0992 * x[3] * x[6] +\n        0.0372 * x[3] * x[7] - 0.6933 * x[3] * x[8] + 0.9793 * x[3] * x[9] -\n        0.2495 * x[3] * x[10] - 0.865 * x[4] * x[5] - 0.5344 * x[4] * x[6] +\n        0.3443 * x[4] * x[7] +\n        0.0946 * x[4] * x[8] +\n        0.99 * x[4] * x[9] +\n        0.1293 * x[4] * x[10] - 0.1439 * x[5] * x[6] - 0.1023 * x[5] * x[7] +\n        0.4527 * x[5] * x[8] - 0.9526 * x[5] * x[9] - 0.9404 * x[5] * x[10] -\n        0.4876 * x[6] * x[7] - 0.4892 * x[6] * x[8] - 0.8809 * x[6] * x[9] +\n        0.5844 * x[6] * x[10] - 0.5909 * x[7] * x[8] +\n        0.8432 * x[7] * x[9] +\n        0.4261 * x[7] * x[10] - 0.7159 * x[8] * x[9] +\n        0.6584 * x[8] * x[10] +\n        0.0654 * x[9] * x[10] +\n        0.9716 * x[1] +\n        0.3374 * x[2] - 0.6073 * x[3] - 0.4237 * x[4] +\n        0.4155 * x[5] +\n        0.8152 * x[6] - 0.6799 * x[7] - 0.7925 * x[8] - 0.3313 * x[9] -\n        0.8543 * x[10] + (-0.1007 * x[1] * x[2] * x[3]) -\n        0.5326 * x[1] * x[2] * x[4] +\n        0.6566 * x[1] * x[2] * x[5] +\n        0.1937 * x[1] * x[2] * x[6] - 0.9996 * x[1] * x[2] * x[7] -\n        0.5367 * x[1] * x[2] * x[8] - 0.1918 * x[1] * x[2] * x[9] -\n        0.8802 * x[1] * x[2] * x[10] - 0.6497 * x[1] * x[3] * x[4] -\n        0.3399 * x[1] * x[3] * x[5] +\n        0.0515 * x[1] * x[3] * x[6] +\n        0.8846 * x[1] * x[3] * x[7] +\n        0.022 * x[1] * x[3] * x[8] +\n        0.9133 * x[1] * x[3] * x[9] - 0.7262 * x[1] * x[3] * x[10] -\n        0.7918 * x[1] * x[4] * x[5] - 0.6313 * x[1] * x[4] * x[6] +\n        0.9966 * x[1] * x[4] * x[7] - 0.6426 * x[1] * x[4] * x[8] -\n        0.3197 * x[1] * x[4] * x[9] - 0.2285 * x[1] * x[4] * x[10] +\n        0.0003 * x[1] * x[5] * x[6] +\n        0.8027 * x[1] * x[5] * x[7] +\n        0.8966 * x[1] * x[5] * x[8] +\n        0.6134 * x[1] * x[5] * x[9] +\n        0.0598 * x[1] * x[5] * x[10] - 0.9651 * x[1] * x[6] * x[7] +\n        0.9353 * x[1] * x[6] * x[8] +\n        0.8902 * x[1] * x[6] * x[9] - 0.007 * x[1] * x[6] * x[10] +\n        0.5675 * x[1] * x[7] * x[8] +\n        0.8712 * x[1] * x[7] * x[9] +\n        0.2321 * x[1] * x[7] * x[10] - 0.3199 * x[1] * x[8] * x[9] +\n        0.0664 * x[1] * x[8] * x[10] - 0.3827 * x[1] * x[9] * x[10] +\n        0.4324 * x[2] * x[3] * x[4] +\n        0.9173 * x[2] * x[3] * x[5] +\n        0.0144 * x[2] * x[3] * x[6] +\n        0.0691 * x[2] * x[3] * x[7] - 0.2872 * x[2] * x[3] * x[8] -\n        0.8985 * x[2] * x[3] * x[9] +\n        0.0914 * x[2] * x[3] * x[10] +\n        0.1849 * x[2] * x[4] * x[5] - 0.0897 * x[2] * x[4] * x[6] -\n        0.7576 * x[2] * x[4] * x[7] - 0.1726 * x[2] * x[4] * x[8] +\n        0.9337 * x[2] * x[4] * x[9] +\n        0.0318 * x[2] * x[4] * x[10] - 0.2369 * x[2] * x[5] * x[6] +\n        0.9287 * x[2] * x[5] * x[7] - 0.9551 * x[2] * x[5] * x[8] -\n        0.6268 * x[2] * x[5] * x[9] +\n        0.4162 * x[2] * x[5] * x[10] +\n        0.7695 * x[2] * x[6] * x[7] +\n        0.615 * x[2] * x[6] * x[8] +\n        0.4118 * x[2] * x[6] * x[9] - 0.8214 * x[2] * x[6] * x[10] +\n        0.1937 * x[2] * x[7] * x[8] +\n        0.2846 * x[2] * x[7] * x[9] - 0.1472 * x[2] * x[7] * x[10] +\n        0.307 * x[2] * x[8] * x[9] +\n        0.7698 * x[2] * x[8] * x[10] - 0.6545 * x[2] * x[9] * x[10] -\n        0.5534 * x[3] * x[4] * x[5] +\n        0.0359 * x[3] * x[4] * x[6] +\n        0.7667 * x[3] * x[4] * x[7] +\n        0.0927 * x[3] * x[4] * x[8] - 0.5321 * x[3] * x[4] * x[9] -\n        0.4937 * x[3] * x[4] * x[10] +\n        0.7388 * x[3] * x[5] * x[6] +\n        0.9809 * x[3] * x[5] * x[7] +\n        0.0004 * x[3] * x[5] * x[8] +\n        0.695 * x[3] * x[5] * x[9] +\n        0.5494 * x[3] * x[5] * x[10] +\n        0.6195 * x[3] * x[6] * x[7] +\n        0.2356 * x[3] * x[6] * x[8] - 0.1412 * x[3] * x[6] * x[9] +\n        0.7508 * x[3] * x[6] * x[10] - 0.769 * x[3] * x[7] * x[8] -\n        0.1995 * x[3] * x[7] * x[9] + 0.7897 * x[3] * x[7] * x[10] -\n        0.9464 * x[3] * x[8] * x[9] - 0.0035 * x[3] * x[8] * x[10] +\n        0.7893 * x[3] * x[9] * x[10] +\n        0.2009 * x[4] * x[5] * x[6] +\n        0.573 * x[4] * x[5] * x[7] +\n        0.0687 * x[4] * x[5] * x[8] +\n        0.3609 * x[4] * x[5] * x[9] +\n        0.7069 * x[4] * x[5] * x[10] +\n        0.3176 * x[4] * x[6] * x[7] - 0.2025 * x[4] * x[6] * x[8] +\n        0.9283 * x[4] * x[6] * x[9] +\n        0.6098 * x[4] * x[6] * x[10] +\n        0.6859 * x[4] * x[7] * x[8] - 0.3653 * x[4] * x[7] * x[9] -\n        0.406 * x[4] * x[7] * x[10] + 0.6706 * x[4] * x[8] * x[9] -\n        0.4475 * x[4] * x[8] * x[10] - 0.1989 * x[4] * x[9] * x[10] -\n        0.5974 * x[5] * x[6] * x[7] +\n        0.4318 * x[5] * x[6] * x[8] +\n        0.3654 * x[5] * x[6] * x[9] - 0.2119 * x[5] * x[6] * x[10] -\n        0.0018 * x[5] * x[7] * x[8] - 0.9865 * x[5] * x[7] * x[9] -\n        0.8902 * x[5] * x[7] * x[10] - 0.6653 * x[5] * x[8] * x[9] +\n        0.3769 * x[5] * x[8] * x[10] - 0.2194 * x[5] * x[9] * x[10] +\n        0.8789 * x[6] * x[7] * x[8] - 0.7093 * x[6] * x[7] * x[9] +\n        0.3827 * x[6] * x[7] * x[10] - 0.0405 * x[6] * x[8] * x[9] +\n        0.7626 * x[6] * x[8] * x[10] +\n        0.4358 * x[6] * x[9] * x[10] +\n        0.7368 * x[7] * x[8] * x[9] - 0.0174 * x[7] * x[8] * x[10] -\n        0.4531 * x[7] * x[9] * x[10] +\n        0.3375 * x[8] * x[9] * x[10] +\n        (-0.4826 * x[1] * x[2] * x[3] * x[4]) - 0.2493 * x[1] * x[2] * x[3] * x[5] +\n        0.5075 * x[1] * x[2] * x[3] * x[6] - 0.6548 * x[1] * x[2] * x[3] * x[7] -\n        0.7159 * x[1] * x[2] * x[3] * x[8] - 0.7049 * x[1] * x[2] * x[3] * x[9] -\n        0.3438 * x[1] * x[2] * x[3] * x[10] - 0.1976 * x[1] * x[2] * x[4] * x[5] +\n        0.0079 * x[1] * x[2] * x[4] * x[6] - 0.8311 * x[1] * x[2] * x[4] * x[7] +\n        0.3371 * x[1] * x[2] * x[4] * x[8] +\n        0.6852 * x[1] * x[2] * x[4] * x[9] +\n        0.2669 * x[1] * x[2] * x[4] * x[10] +\n        0.3508 * x[1] * x[2] * x[5] * x[6] - 0.281 * x[1] * x[2] * x[5] * x[7] -\n        0.1383 * x[1] * x[2] * x[5] * x[8] - 0.5659 * x[1] * x[2] * x[5] * x[9] +\n        0.008 * x[1] * x[2] * x[5] * x[10] - 0.2438 * x[1] * x[2] * x[6] * x[7] +\n        0.8352 * x[1] * x[2] * x[6] * x[8] - 0.6792 * x[1] * x[2] * x[6] * x[9] -\n        0.505 * x[1] * x[2] * x[6] * x[10] - 0.117 * x[1] * x[2] * x[7] * x[8] -\n        0.3067 * x[1] * x[2] * x[7] * x[9] - 0.3803 * x[1] * x[2] * x[7] * x[10] +\n        0.7882 * x[1] * x[2] * x[8] * x[9] +\n        0.3372 * x[1] * x[2] * x[8] * x[10] - 0.919 * x[1] * x[2] * x[9] * x[10] -\n        0.7383 * x[1] * x[3] * x[4] * x[5] +\n        0.7541 * x[1] * x[3] * x[4] * x[6] +\n        0.5834 * x[1] * x[3] * x[4] * x[7] +\n        0.1474 * x[1] * x[3] * x[4] * x[8] +\n        0.0948 * x[1] * x[3] * x[4] * x[9] - 0.3359 * x[1] * x[3] * x[4] * x[10] +\n        0.165 * x[1] * x[3] * x[5] * x[6] +\n        0.3496 * x[1] * x[3] * x[5] * x[7] +\n        0.6279 * x[1] * x[3] * x[5] * x[8] - 0.6031 * x[1] * x[3] * x[5] * x[9] +\n        0.1115 * x[1] * x[3] * x[5] * x[10] - 0.7796 * x[1] * x[3] * x[6] * x[7] -\n        0.5661 * x[1] * x[3] * x[6] * x[8] +\n        0.1693 * x[1] * x[3] * x[6] * x[9] +\n        0.957 * x[1] * x[3] * x[6] * x[10] +\n        0.7301 * x[1] * x[3] * x[7] * x[8] - 0.1917 * x[1] * x[3] * x[7] * x[9] +\n        0.9096 * x[1] * x[3] * x[7] * x[10] - 0.2321 * x[1] * x[3] * x[8] * x[9] -\n        0.1408 * x[1] * x[3] * x[8] * x[10] + 0.9235 * x[1] * x[3] * x[9] * x[10] -\n        0.5794 * x[1] * x[4] * x[5] * x[6] + 0.227 * x[1] * x[4] * x[5] * x[7] -\n        0.3337 * x[1] * x[4] * x[5] * x[8] - 0.3646 * x[1] * x[4] * x[5] * x[9] -\n        0.4327 * x[1] * x[4] * x[5] * x[10] - 0.1094 * x[1] * x[4] * x[6] * x[7] +\n        0.3825 * x[1] * x[4] * x[6] * x[8] +\n        0.5071 * x[1] * x[4] * x[6] * x[9] +\n        0.8944 * x[1] * x[4] * x[6] * x[10] - 0.3627 * x[1] * x[4] * x[7] * x[8] +\n        0.065 * x[1] * x[4] * x[7] * x[9] +\n        0.7137 * x[1] * x[4] * x[7] * x[10] +\n        0.5367 * x[1] * x[4] * x[8] * x[9] +\n        0.1169 * x[1] * x[4] * x[8] * x[10] +\n        0.1142 * x[1] * x[4] * x[9] * x[10] - 0.814 * x[1] * x[5] * x[6] * x[7] +\n        0.7162 * x[1] * x[5] * x[6] * x[8] +\n        0.4038 * x[1] * x[5] * x[6] * x[9] +\n        0.3275 * x[1] * x[5] * x[6] * x[10] - 0.7578 * x[1] * x[5] * x[7] * x[8] +\n        0.2681 * x[1] * x[5] * x[7] * x[9] +\n        0.618 * x[1] * x[5] * x[7] * x[10] +\n        0.8112 * x[1] * x[5] * x[8] * x[9] +\n        0.652 * x[1] * x[5] * x[8] * x[10] +\n        0.5574 * x[1] * x[5] * x[9] * x[10] +\n        0.1105 * x[1] * x[6] * x[7] * x[8] - 0.685 * x[1] * x[6] * x[7] * x[9] +\n        0.2517 * x[1] * x[6] * x[7] * x[10] - 0.2113 * x[1] * x[6] * x[8] * x[9] -\n        0.9952 * x[1] * x[6] * x[8] * x[10] - 0.9702 * x[1] * x[6] * x[9] * x[10] -\n        0.3537 * x[1] * x[7] * x[8] * x[9] + 0.326 * x[1] * x[7] * x[8] * x[10] -\n        0.2615 * x[1] * x[7] * x[9] * x[10] - 0.1564 * x[1] * x[8] * x[9] * x[10] +\n        0.9175 * x[2] * x[3] * x[4] * x[5] - 0.5903 * x[2] * x[3] * x[4] * x[6] +\n        0.9029 * x[2] * x[3] * x[4] * x[7] +\n        0.3648 * x[2] * x[3] * x[4] * x[8] - 0.9126 * x[2] * x[3] * x[4] * x[9] -\n        0.644 * x[2] * x[3] * x[4] * x[10] +\n        0.7789 * x[2] * x[3] * x[5] * x[6] +\n        0.0203 * x[2] * x[3] * x[5] * x[7] +\n        0.8897 * x[2] * x[3] * x[5] * x[8] - 0.5469 * x[2] * x[3] * x[5] * x[9] -\n        0.2008 * x[2] * x[3] * x[5] * x[10] +\n        0.6762 * x[2] * x[3] * x[6] * x[7] +\n        0.3243 * x[2] * x[3] * x[6] * x[8] - 0.6903 * x[2] * x[3] * x[6] * x[9] +\n        0.2058 * x[2] * x[3] * x[6] * x[10] +\n        0.3876 * x[2] * x[3] * x[7] * x[8] +\n        0.3695 * x[2] * x[3] * x[7] * x[9] +\n        0.0322 * x[2] * x[3] * x[7] * x[10] - 0.502 * x[2] * x[3] * x[8] * x[9] -\n        0.9679 * x[2] * x[3] * x[8] * x[10] + 0.6939 * x[2] * x[3] * x[9] * x[10] -\n        0.7335 * x[2] * x[4] * x[5] * x[6] - 0.0071 * x[2] * x[4] * x[5] * x[7] +\n        0.7911 * x[2] * x[4] * x[5] * x[8] - 0.8217 * x[2] * x[4] * x[5] * x[9] -\n        0.6734 * x[2] * x[4] * x[5] * x[10] + 0.5343 * x[2] * x[4] * x[6] * x[7] -\n        0.6164 * x[2] * x[4] * x[6] * x[8] - 0.0679 * x[2] * x[4] * x[6] * x[9] -\n        0.3156 * x[2] * x[4] * x[6] * x[10] - 0.9986 * x[2] * x[4] * x[7] * x[8] -\n        0.0287 * x[2] * x[4] * x[7] * x[9] + 0.3193 * x[2] * x[4] * x[7] * x[10] -\n        0.92 * x[2] * x[4] * x[8] * x[9] - 0.147 * x[2] * x[4] * x[8] * x[10] -\n        0.9656 * x[2] * x[4] * x[9] * x[10] - 0.9044 * x[2] * x[5] * x[6] * x[7] +\n        0.9256 * x[2] * x[5] * x[6] * x[8] - 0.0849 * x[2] * x[5] * x[6] * x[9] -\n        0.2946 * x[2] * x[5] * x[6] * x[10] + 0.4543 * x[2] * x[5] * x[7] * x[8] -\n        0.6516 * x[2] * x[5] * x[7] * x[9] - 0.2951 * x[2] * x[5] * x[7] * x[10] -\n        0.5713 * x[2] * x[5] * x[8] * x[9] +\n        0.9107 * x[2] * x[5] * x[8] * x[10] +\n        0.5607 * x[2] * x[5] * x[9] * x[10] +\n        0.5813 * x[2] * x[6] * x[7] * x[8] +\n        0.1879 * x[2] * x[6] * x[7] * x[9] +\n        0.0879 * x[2] * x[6] * x[7] * x[10] - 0.1947 * x[2] * x[6] * x[8] * x[9] -\n        0.5199 * x[2] * x[6] * x[8] * x[10] - 0.661 * x[2] * x[6] * x[9] * x[10] +\n        0.7548 * x[2] * x[7] * x[8] * x[9] - 0.8094 * x[2] * x[7] * x[8] * x[10] -\n        0.8729 * x[2] * x[7] * x[9] * x[10] + 0.703 * x[2] * x[8] * x[9] * x[10] -\n        0.6193 * x[3] * x[4] * x[5] * x[6] +\n        0.863 * x[3] * x[4] * x[5] * x[7] +\n        0.3731 * x[3] * x[4] * x[5] * x[8] +\n        0.975 * x[3] * x[4] * x[5] * x[9] - 0.9151 * x[3] * x[4] * x[5] * x[10] -\n        0.1013 * x[3] * x[4] * x[6] * x[7] - 0.7563 * x[3] * x[4] * x[6] * x[8] -\n        0.9394 * x[3] * x[4] * x[6] * x[9] - 0.1056 * x[3] * x[4] * x[6] * x[10] +\n        0.5528 * x[3] * x[4] * x[7] * x[8] - 0.4469 * x[3] * x[4] * x[7] * x[9] -\n        0.6919 * x[3] * x[4] * x[7] * x[10] + 0.6454 * x[3] * x[4] * x[8] * x[9] -\n        0.7436 * x[3] * x[4] * x[8] * x[10] - 0.4406 * x[3] * x[4] * x[9] * x[10] -\n        0.6553 * x[3] * x[5] * x[6] * x[7] + 0.0815 * x[3] * x[5] * x[6] * x[8] -\n        0.2592 * x[3] * x[5] * x[6] * x[9] - 0.3449 * x[3] * x[5] * x[6] * x[10] -\n        0.723 * x[3] * x[5] * x[7] * x[8] + 0.7367 * x[3] * x[5] * x[7] * x[9] -\n        0.5166 * x[3] * x[5] * x[7] * x[10] - 0.6852 * x[3] * x[5] * x[8] * x[9] +\n        0.5099 * x[3] * x[5] * x[8] * x[10] - 0.1606 * x[3] * x[5] * x[9] * x[10] -\n        0.8887 * x[3] * x[6] * x[7] * x[8] +\n        0.499 * x[3] * x[6] * x[7] * x[9] +\n        0.6686 * x[3] * x[6] * x[7] * x[10] +\n        0.4415 * x[3] * x[6] * x[8] * x[9] - 0.2126 * x[3] * x[6] * x[8] * x[10] -\n        0.8338 * x[3] * x[6] * x[9] * x[10] - 0.8861 * x[3] * x[7] * x[8] * x[9] -\n        0.9484 * x[3] * x[7] * x[8] * x[10] - 0.2048 * x[3] * x[7] * x[9] * x[10] -\n        0.1835 * x[3] * x[8] * x[9] * x[10] - 0.2758 * x[4] * x[5] * x[6] * x[7] -\n        0.5844 * x[4] * x[5] * x[6] * x[8] +\n        0.3621 * x[4] * x[5] * x[6] * x[9] +\n        0.6829 * x[4] * x[5] * x[6] * x[10] - 0.5893 * x[4] * x[5] * x[7] * x[8] +\n        0.5491 * x[4] * x[5] * x[7] * x[9] - 0.8351 * x[4] * x[5] * x[7] * x[10] +\n        0.5027 * x[4] * x[5] * x[8] * x[9] +\n        0.7318 * x[4] * x[5] * x[8] * x[10] - 0.8597 * x[4] * x[5] * x[9] * x[10] +\n        0.7574 * x[4] * x[6] * x[7] * x[8] - 0.9517 * x[4] * x[6] * x[7] * x[9] -\n        0.6703 * x[4] * x[6] * x[7] * x[10] +\n        0.1705 * x[4] * x[6] * x[8] * x[9] +\n        0.3118 * x[4] * x[6] * x[8] * x[10] - 0.299 * x[4] * x[6] * x[9] * x[10] +\n        0.1919 * x[4] * x[7] * x[8] * x[9] +\n        0.2 * x[4] * x[7] * x[8] * x[10] +\n        0.0314 * x[4] * x[7] * x[9] * x[10] - 0.9798 * x[4] * x[8] * x[9] * x[10] -\n        0.4391 * x[5] * x[6] * x[7] * x[8] + 0.4177 * x[5] * x[6] * x[7] * x[9] -\n        0.3681 * x[5] * x[6] * x[7] * x[10] - 0.7607 * x[5] * x[6] * x[8] * x[9] +\n        0.6108 * x[5] * x[6] * x[8] * x[10] +\n        0.9076 * x[5] * x[6] * x[9] * x[10] +\n        0.3781 * x[5] * x[7] * x[8] * x[9] +\n        0.4656 * x[5] * x[7] * x[8] * x[10] - 0.965 * x[5] * x[7] * x[9] * x[10] -\n        0.7647 * x[5] * x[8] * x[9] * x[10] - 0.7166 * x[6] * x[7] * x[8] * x[9] -\n        0.7744 * x[6] * x[7] * x[8] * x[10] - 0.1137 * x[6] * x[7] * x[9] * x[10] +\n        0.2768 * x[6] * x[8] * x[9] * x[10] - 0.1211 * x[7] * x[8] * x[9] * x[10] <=\n        84.029\n    )\n    e10 = replace_expr(e10, x)\n    JuMP.add_nonlinear_constraint(m, e10)\n    e11 = :(\n        0.591 * x[1] * x[3] - 0.6987 * x[1] * x[2] + 0.7248 * x[1] * x[4] -\n        0.3342 * x[1] * x[5] +\n        0.2565 * x[1] * x[6] +\n        0.0506 * x[1] * x[7] +\n        0.1018 * x[1] * x[8] +\n        0.6964 * x[1] * x[9] - 0.3124 * x[1] * x[10] - 0.0906 * x[2] * x[3] -\n        0.4594 * x[2] * x[4] - 0.7137 * x[2] * x[5] + 0.6835 * x[2] * x[6] -\n        0.9256 * x[2] * x[7] + 0.8048 * x[2] * x[8] - 0.8525 * x[2] * x[9] +\n        0.6184 * x[2] * x[10] +\n        0.6039 * x[3] * x[4] - 0.1299 * x[3] * x[5] +\n        0.7409 * x[3] * x[6] +\n        0.7098 * x[3] * x[7] - 0.7156 * x[3] * x[8] + 0.7937 * x[3] * x[9] -\n        0.9671 * x[3] * x[10] - 0.8201 * x[4] * x[5] - 0.9828 * x[4] * x[6] -\n        0.2199 * x[4] * x[7] - 0.1975 * x[4] * x[8] +\n        0.6526 * x[4] * x[9] +\n        0.8052 * x[4] * x[10] +\n        0.2971 * x[5] * x[6] +\n        0.1198 * x[5] * x[7] +\n        0.217 * x[5] * x[8] +\n        0.0079 * x[5] * x[9] - 0.3018 * x[5] * x[10] + 0.9843 * x[6] * x[7] -\n        0.9696 * x[6] * x[8] + 0.8791 * x[6] * x[9] - 0.9214 * x[6] * x[10] -\n        0.6654 * x[7] * x[8] +\n        0.8961 * x[7] * x[9] +\n        0.7488 * x[7] * x[10] - 0.816 * x[8] * x[9] +\n        0.7283 * x[8] * x[10] +\n        0.7735 * x[9] * x[10] +\n        0.4313 * x[1] - 0.8995 * x[2] - 0.0242 * x[3] + 0.1137 * x[4] -\n        0.0807 * x[5] + 0.3716 * x[6] - 0.9041 * x[7] - 0.0494 * x[8] +\n        0.8577 * x[9] +\n        0.4838 * x[10] +\n        0.4225 * x[1] * x[2] * x[4] - 0.2484 * x[1] * x[2] * x[3] +\n        0.9204 * x[1] * x[2] * x[5] +\n        0.4425 * x[1] * x[2] * x[6] +\n        0.8533 * x[1] * x[2] * x[7] - 0.8434 * x[1] * x[2] * x[8] +\n        0.3368 * x[1] * x[2] * x[9] - 0.2922 * x[1] * x[2] * x[10] -\n        0.674 * x[1] * x[3] * x[4] - 0.506 * x[1] * x[3] * x[5] +\n        0.45 * x[1] * x[3] * x[6] +\n        0.9451 * x[1] * x[3] * x[7] - 0.6033 * x[1] * x[3] * x[8] -\n        0.5666 * x[1] * x[3] * x[9] - 0.5187 * x[1] * x[3] * x[10] -\n        0.2378 * x[1] * x[4] * x[5] - 0.8728 * x[1] * x[4] * x[6] +\n        0.2078 * x[1] * x[4] * x[7] - 0.4754 * x[1] * x[4] * x[8] -\n        0.0257 * x[1] * x[4] * x[9] - 0.6292 * x[1] * x[4] * x[10] -\n        0.3056 * x[1] * x[5] * x[6] +\n        0.9041 * x[1] * x[5] * x[7] +\n        0.9193 * x[1] * x[5] * x[8] +\n        0.1786 * x[1] * x[5] * x[9] - 0.8288 * x[1] * x[5] * x[10] +\n        0.8871 * x[1] * x[6] * x[7] - 0.5883 * x[1] * x[6] * x[8] -\n        0.4245 * x[1] * x[6] * x[9] + 0.2509 * x[1] * x[6] * x[10] -\n        0.8896 * x[1] * x[7] * x[8] - 0.7735 * x[1] * x[7] * x[9] +\n        0.6383 * x[1] * x[7] * x[10] - 0.7938 * x[1] * x[8] * x[9] -\n        0.6181 * x[1] * x[8] * x[10] + 0.0857 * x[1] * x[9] * x[10] -\n        0.4053 * x[2] * x[3] * x[4] + 0.2158 * x[2] * x[3] * x[5] -\n        0.7104 * x[2] * x[3] * x[6] + 0.1614 * x[2] * x[3] * x[7] -\n        0.5585 * x[2] * x[3] * x[8] - 0.0765 * x[2] * x[3] * x[9] -\n        0.9573 * x[2] * x[3] * x[10] + 0.744 * x[2] * x[4] * x[5] -\n        0.1551 * x[2] * x[4] * x[6] +\n        0.4025 * x[2] * x[4] * x[7] +\n        0.9942 * x[2] * x[4] * x[8] - 0.2869 * x[2] * x[4] * x[9] -\n        0.6106 * x[2] * x[4] * x[10] + 0.5482 * x[2] * x[5] * x[6] -\n        0.5155 * x[2] * x[5] * x[7] +\n        0.2689 * x[2] * x[5] * x[8] +\n        0.291 * x[2] * x[5] * x[9] - 0.6436 * x[2] * x[5] * x[10] -\n        0.6477 * x[2] * x[6] * x[7] - 0.0194 * x[2] * x[6] * x[8] -\n        0.2997 * x[2] * x[6] * x[9] + 0.7213 * x[2] * x[6] * x[10] -\n        0.9991 * x[2] * x[7] * x[8] +\n        0.8354 * x[2] * x[7] * x[9] +\n        0.9739 * x[2] * x[7] * x[10] +\n        0.9231 * x[2] * x[8] * x[9] - 0.5433 * x[2] * x[8] * x[10] -\n        0.5059 * x[2] * x[9] * x[10] +\n        0.1579 * x[3] * x[4] * x[5] +\n        0.9595 * x[3] * x[4] * x[6] - 0.4744 * x[3] * x[4] * x[7] -\n        0.7872 * x[3] * x[4] * x[8] +\n        0.8894 * x[3] * x[4] * x[9] +\n        0.6219 * x[3] * x[4] * x[10] - 0.9093 * x[3] * x[5] * x[6] +\n        0.9121 * x[3] * x[5] * x[7] +\n        0.4676 * x[3] * x[5] * x[8] - 0.056 * x[3] * x[5] * x[9] +\n        0.7962 * x[3] * x[5] * x[10] +\n        0.2177 * x[3] * x[6] * x[7] - 0.1877 * x[3] * x[6] * x[8] +\n        0.2283 * x[3] * x[6] * x[9] +\n        0.5367 * x[3] * x[6] * x[10] - 0.594 * x[3] * x[7] * x[8] +\n        0.022 * x[3] * x[7] * x[9] - 0.9741 * x[3] * x[7] * x[10] -\n        0.7372 * x[3] * x[8] * x[9] - 0.0799 * x[3] * x[8] * x[10] +\n        0.6106 * x[3] * x[9] * x[10] +\n        0.4631 * x[4] * x[5] * x[6] - 0.7378 * x[4] * x[5] * x[7] -\n        0.8125 * x[4] * x[5] * x[8] - 0.4392 * x[4] * x[5] * x[9] -\n        0.7147 * x[4] * x[5] * x[10] - 0.974 * x[4] * x[6] * x[7] +\n        0.9874 * x[4] * x[6] * x[8] +\n        0.422 * x[4] * x[6] * x[9] +\n        0.6878 * x[4] * x[6] * x[10] +\n        0.12 * x[4] * x[7] * x[8] - 0.8755 * x[4] * x[7] * x[9] -\n        0.2555 * x[4] * x[7] * x[10] - 0.5743 * x[4] * x[8] * x[9] -\n        0.5735 * x[4] * x[8] * x[10] - 0.6477 * x[4] * x[9] * x[10] +\n        0.0007 * x[5] * x[6] * x[7] +\n        0.0896 * x[5] * x[6] * x[8] +\n        0.1403 * x[5] * x[6] * x[9] +\n        0.0392 * x[5] * x[6] * x[10] - 0.9063 * x[5] * x[7] * x[8] -\n        0.3817 * x[5] * x[7] * x[9] +\n        0.8622 * x[5] * x[7] * x[10] +\n        0.0331 * x[5] * x[8] * x[9] - 0.1539 * x[5] * x[8] * x[10] -\n        0.684 * x[5] * x[9] * x[10] +\n        0.8427 * x[6] * x[7] * x[8] +\n        0.679 * x[6] * x[7] * x[9] - 0.8744 * x[6] * x[7] * x[10] -\n        0.5763 * x[6] * x[8] * x[9] +\n        0.131 * x[6] * x[8] * x[10] +\n        0.7207 * x[6] * x[9] * x[10] +\n        0.2711 * x[7] * x[8] * x[9] +\n        0.901 * x[7] * x[8] * x[10] - 0.0142 * x[7] * x[9] * x[10] +\n        0.7093 * x[8] * x[9] * x[10] +\n        0.7493 * x[1] * x[2] * x[3] * x[5] - 0.7313 * x[1] * x[2] * x[3] * x[4] -\n        0.1795 * x[1] * x[2] * x[3] * x[6] - 0.6154 * x[1] * x[2] * x[3] * x[7] +\n        0.4774 * x[1] * x[2] * x[3] * x[8] +\n        0.2237 * x[1] * x[2] * x[3] * x[9] +\n        0.819 * x[1] * x[2] * x[3] * x[10] - 0.2799 * x[1] * x[2] * x[4] * x[5] -\n        0.4367 * x[1] * x[2] * x[4] * x[6] - 0.7202 * x[1] * x[2] * x[4] * x[7] +\n        0.7141 * x[1] * x[2] * x[4] * x[8] +\n        0.2112 * x[1] * x[2] * x[4] * x[9] +\n        0.7705 * x[1] * x[2] * x[4] * x[10] +\n        0.0843 * x[1] * x[2] * x[5] * x[6] +\n        0.3562 * x[1] * x[2] * x[5] * x[7] +\n        0.7516 * x[1] * x[2] * x[5] * x[8] +\n        0.6577 * x[1] * x[2] * x[5] * x[9] +\n        0.288 * x[1] * x[2] * x[5] * x[10] +\n        0.179 * x[1] * x[2] * x[6] * x[7] +\n        0.1567 * x[1] * x[2] * x[6] * x[8] - 0.3688 * x[1] * x[2] * x[6] * x[9] +\n        0.7408 * x[1] * x[2] * x[6] * x[10] - 0.4765 * x[1] * x[2] * x[7] * x[8] +\n        0.6741 * x[1] * x[2] * x[7] * x[9] +\n        0.112 * x[1] * x[2] * x[7] * x[10] - 0.8509 * x[1] * x[2] * x[8] * x[9] +\n        0.4165 * x[1] * x[2] * x[8] * x[10] - 0.9974 * x[1] * x[2] * x[9] * x[10] -\n        0.3871 * x[1] * x[3] * x[4] * x[5] +\n        0.6783 * x[1] * x[3] * x[4] * x[6] +\n        0.8508 * x[1] * x[3] * x[4] * x[7] - 0.7738 * x[1] * x[3] * x[4] * x[8] +\n        0.6638 * x[1] * x[3] * x[4] * x[9] +\n        0.5599 * x[1] * x[3] * x[4] * x[10] +\n        0.7158 * x[1] * x[3] * x[5] * x[6] +\n        0.1086 * x[1] * x[3] * x[5] * x[7] - 0.69 * x[1] * x[3] * x[5] * x[8] -\n        0.4714 * x[1] * x[3] * x[5] * x[9] +\n        0.6628 * x[1] * x[3] * x[5] * x[10] +\n        0.1565 * x[1] * x[3] * x[6] * x[7] +\n        0.2639 * x[1] * x[3] * x[6] * x[8] - 0.0214 * x[1] * x[3] * x[6] * x[9] -\n        0.6831 * x[1] * x[3] * x[6] * x[10] - 0.7759 * x[1] * x[3] * x[7] * x[8] +\n        0.3236 * x[1] * x[3] * x[7] * x[9] - 0.768 * x[1] * x[3] * x[7] * x[10] -\n        0.4247 * x[1] * x[3] * x[8] * x[9] +\n        0.4122 * x[1] * x[3] * x[8] * x[10] +\n        0.4506 * x[1] * x[3] * x[9] * x[10] +\n        0.3552 * x[1] * x[4] * x[5] * x[6] +\n        0.446 * x[1] * x[4] * x[5] * x[7] +\n        0.3144 * x[1] * x[4] * x[5] * x[8] +\n        0.4965 * x[1] * x[4] * x[5] * x[9] - 0.8063 * x[1] * x[4] * x[5] * x[10] -\n        0.612 * x[1] * x[4] * x[6] * x[7] +\n        0.7794 * x[1] * x[4] * x[6] * x[8] +\n        0.834 * x[1] * x[4] * x[6] * x[9] +\n        0.6108 * x[1] * x[4] * x[6] * x[10] +\n        0.8644 * x[1] * x[4] * x[7] * x[8] - 0.8542 * x[1] * x[4] * x[7] * x[9] -\n        0.2302 * x[1] * x[4] * x[7] * x[10] - 0.1178 * x[1] * x[4] * x[8] * x[9] -\n        0.9046 * x[1] * x[4] * x[8] * x[10] - 0.262 * x[1] * x[4] * x[9] * x[10] -\n        0.6183 * x[1] * x[5] * x[6] * x[7] + 0.6188 * x[1] * x[5] * x[6] * x[8] -\n        0.0381 * x[1] * x[5] * x[6] * x[9] - 0.7188 * x[1] * x[5] * x[6] * x[10] -\n        0.1034 * x[1] * x[5] * x[7] * x[8] +\n        0.4047 * x[1] * x[5] * x[7] * x[9] +\n        0.0084 * x[1] * x[5] * x[7] * x[10] - 0.4031 * x[1] * x[5] * x[8] * x[9] +\n        0.702 * x[1] * x[5] * x[8] * x[10] - 0.8478 * x[1] * x[5] * x[9] * x[10] +\n        0.7782 * x[1] * x[6] * x[7] * x[8] +\n        0.7223 * x[1] * x[6] * x[7] * x[9] +\n        0.5405 * x[1] * x[6] * x[7] * x[10] +\n        0.7626 * x[1] * x[6] * x[8] * x[9] - 0.2324 * x[1] * x[6] * x[8] * x[10] -\n        0.6926 * x[1] * x[6] * x[9] * x[10] - 0.4473 * x[1] * x[7] * x[8] * x[9] +\n        0.5227 * x[1] * x[7] * x[8] * x[10] - 0.1544 * x[1] * x[7] * x[9] * x[10] +\n        0.1788 * x[1] * x[8] * x[9] * x[10] - 0.8851 * x[2] * x[3] * x[4] * x[5] -\n        0.397 * x[2] * x[3] * x[4] * x[6] - 0.8556 * x[2] * x[3] * x[4] * x[7] +\n        0.5239 * x[2] * x[3] * x[4] * x[8] +\n        0.0308 * x[2] * x[3] * x[4] * x[9] - 0.7734 * x[2] * x[3] * x[4] * x[10] +\n        0.3039 * x[2] * x[3] * x[5] * x[6] - 0.7162 * x[2] * x[3] * x[5] * x[7] +\n        0.3885 * x[2] * x[3] * x[5] * x[8] - 0.999 * x[2] * x[3] * x[5] * x[9] -\n        0.1183 * x[2] * x[3] * x[5] * x[10] - 0.1821 * x[2] * x[3] * x[6] * x[7] +\n        0.6174 * x[2] * x[3] * x[6] * x[8] - 0.854 * x[2] * x[3] * x[6] * x[9] +\n        0.5544 * x[2] * x[3] * x[6] * x[10] +\n        0.232 * x[2] * x[3] * x[7] * x[8] - 0.6641 * x[2] * x[3] * x[7] * x[9] -\n        0.3447 * x[2] * x[3] * x[7] * x[10] +\n        0.6963 * x[2] * x[3] * x[8] * x[9] +\n        0.1228 * x[2] * x[3] * x[8] * x[10] +\n        0.1779 * x[2] * x[3] * x[9] * x[10] +\n        0.973 * x[2] * x[4] * x[5] * x[6] +\n        0.1374 * x[2] * x[4] * x[5] * x[7] - 0.5653 * x[2] * x[4] * x[5] * x[8] +\n        0.3235 * x[2] * x[4] * x[5] * x[9] - 0.7351 * x[2] * x[4] * x[5] * x[10] +\n        0.1866 * x[2] * x[4] * x[6] * x[7] - 0.1166 * x[2] * x[4] * x[6] * x[8] +\n        0.6616 * x[2] * x[4] * x[6] * x[9] +\n        0.3928 * x[2] * x[4] * x[6] * x[10] +\n        0.4047 * x[2] * x[4] * x[7] * x[8] - 0.492 * x[2] * x[4] * x[7] * x[9] +\n        0.0233 * x[2] * x[4] * x[7] * x[10] - 0.0839 * x[2] * x[4] * x[8] * x[9] +\n        0.9802 * x[2] * x[4] * x[8] * x[10] +\n        0.2466 * x[2] * x[4] * x[9] * x[10] +\n        0.0186 * x[2] * x[5] * x[6] * x[7] +\n        0.761 * x[2] * x[5] * x[6] * x[8] +\n        0.1837 * x[2] * x[5] * x[6] * x[9] +\n        0.6049 * x[2] * x[5] * x[6] * x[10] - 0.782 * x[2] * x[5] * x[7] * x[8] +\n        0.8772 * x[2] * x[5] * x[7] * x[9] +\n        0.9354 * x[2] * x[5] * x[7] * x[10] +\n        0.5135 * x[2] * x[5] * x[8] * x[9] +\n        0.5527 * x[2] * x[5] * x[8] * x[10] +\n        0.5089 * x[2] * x[5] * x[9] * x[10] - 0.9858 * x[2] * x[6] * x[7] * x[8] +\n        0.7245 * x[2] * x[6] * x[7] * x[9] - 0.7463 * x[2] * x[6] * x[7] * x[10] -\n        0.5182 * x[2] * x[6] * x[8] * x[9] - 0.6181 * x[2] * x[6] * x[8] * x[10] -\n        0.815 * x[2] * x[6] * x[9] * x[10] - 0.1105 * x[2] * x[7] * x[8] * x[9] -\n        0.6992 * x[2] * x[7] * x[8] * x[10] +\n        0.2491 * x[2] * x[7] * x[9] * x[10] +\n        0.6866 * x[2] * x[8] * x[9] * x[10] - 0.7184 * x[3] * x[4] * x[5] * x[6] +\n        0.7077 * x[3] * x[4] * x[5] * x[7] - 0.8608 * x[3] * x[4] * x[5] * x[8] -\n        0.851 * x[3] * x[4] * x[5] * x[9] + 0.6374 * x[3] * x[4] * x[5] * x[10] -\n        0.0365 * x[3] * x[4] * x[6] * x[7] +\n        0.7884 * x[3] * x[4] * x[6] * x[8] +\n        0.6555 * x[3] * x[4] * x[6] * x[9] - 0.3754 * x[3] * x[4] * x[6] * x[10] -\n        0.0738 * x[3] * x[4] * x[7] * x[8] +\n        0.9879 * x[3] * x[4] * x[7] * x[9] +\n        0.0135 * x[3] * x[4] * x[7] * x[10] - 0.3498 * x[3] * x[4] * x[8] * x[9] -\n        0.0971 * x[3] * x[4] * x[8] * x[10] + 0.904 * x[3] * x[4] * x[9] * x[10] -\n        0.2376 * x[3] * x[5] * x[6] * x[7] + 0.2933 * x[3] * x[5] * x[6] * x[8] -\n        0.9793 * x[3] * x[5] * x[6] * x[9] - 0.2463 * x[3] * x[5] * x[6] * x[10] +\n        0.4602 * x[3] * x[5] * x[7] * x[8] +\n        0.2682 * x[3] * x[5] * x[7] * x[9] - 0.5987 * x[3] * x[5] * x[7] * x[10] +\n        0.5991 * x[3] * x[5] * x[8] * x[9] - 0.2997 * x[3] * x[5] * x[8] * x[10] +\n        0.4424 * x[3] * x[5] * x[9] * x[10] - 0.2551 * x[3] * x[6] * x[7] * x[8] -\n        0.4591 * x[3] * x[6] * x[7] * x[9] +\n        0.191 * x[3] * x[6] * x[7] * x[10] +\n        0.7592 * x[3] * x[6] * x[8] * x[9] - 0.4934 * x[3] * x[6] * x[8] * x[10] -\n        0.5187 * x[3] * x[6] * x[9] * x[10] - 0.1522 * x[3] * x[7] * x[8] * x[9] -\n        0.7995 * x[3] * x[7] * x[8] * x[10] +\n        0.2015 * x[3] * x[7] * x[9] * x[10] +\n        0.7515 * x[3] * x[8] * x[9] * x[10] - 0.3003 * x[4] * x[5] * x[6] * x[7] -\n        0.0052 * x[4] * x[5] * x[6] * x[8] - 0.2116 * x[4] * x[5] * x[6] * x[9] -\n        0.069 * x[4] * x[5] * x[6] * x[10] +\n        0.4125 * x[4] * x[5] * x[7] * x[8] +\n        0.1911 * x[4] * x[5] * x[7] * x[9] +\n        0.141 * x[4] * x[5] * x[7] * x[10] - 0.4838 * x[4] * x[5] * x[8] * x[9] +\n        0.0428 * x[4] * x[5] * x[8] * x[10] - 0.3545 * x[4] * x[5] * x[9] * x[10] -\n        0.836 * x[4] * x[6] * x[7] * x[8] +\n        0.9044 * x[4] * x[6] * x[7] * x[9] +\n        0.9537 * x[4] * x[6] * x[7] * x[10] +\n        0.0803 * x[4] * x[6] * x[8] * x[9] - 0.4248 * x[4] * x[6] * x[8] * x[10] +\n        0.9858 * x[4] * x[6] * x[9] * x[10] +\n        0.8136 * x[4] * x[7] * x[8] * x[9] +\n        0.6273 * x[4] * x[7] * x[8] * x[10] +\n        0.3116 * x[4] * x[7] * x[9] * x[10] +\n        0.5186 * x[4] * x[8] * x[9] * x[10] +\n        0.4613 * x[5] * x[6] * x[7] * x[8] +\n        0.5744 * x[5] * x[6] * x[7] * x[9] - 0.5661 * x[5] * x[6] * x[7] * x[10] -\n        0.7528 * x[5] * x[6] * x[8] * x[9] - 0.1247 * x[5] * x[6] * x[8] * x[10] -\n        0.5048 * x[5] * x[6] * x[9] * x[10] +\n        0.1487 * x[5] * x[7] * x[8] * x[9] +\n        0.6904 * x[5] * x[7] * x[8] * x[10] - 0.4091 * x[5] * x[7] * x[9] * x[10] +\n        0.8667 * x[5] * x[8] * x[9] * x[10] +\n        0.4524 * x[6] * x[7] * x[8] * x[9] - 0.4188 * x[6] * x[7] * x[8] * x[10] -\n        0.3955 * x[6] * x[7] * x[9] * x[10] + 0.3814 * x[6] * x[8] * x[9] * x[10] -\n        0.4766 * x[7] * x[8] * x[9] * x[10] <= 99.878\n    )\n    e11 = replace_expr(e11, x)\n    JuMP.add_nonlinear_constraint(m, e11)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/multi.jl",
    "content": "# println(\"--------------------------------------------------------------------------\")\n# println(\"Multi4/N - exprmode 1 -> X1 * X2 * X3 * X4\")\n# println(\"Multi4/N - exprmode 2 -> (X1*X2) * (X3*X4)\")\n# println(\"Multi4/N - exprmode 3 -> (X1*X2) * X3 * X4\")\n# println(\"Multi4/N - exprmode 4 -> X1 * X2 * (X3*X4)\")\n# println(\"Multi4/N - exprmode 5 -> ((X1*X2) * X3) * X4\")\n# println(\"Multi4/N - exprmode 6 -> (X1*X2*X3) *X4\")\n# println(\"Multi4/N - exprmode 7 -> X1 * (X2 * (X3*X4))\")\n# println(\"Multi4/N - exprmode 8 -> X1 * (X2*X3) * X4\")\n# println(\"Multi4/N - exprmode 9 -> X1 * (X2*X3*X4)\")\n# println(\"Multi4/N - exprmode 10 -> X1 * ((X2*X3) * X4)\")\n# println(\"Multi4/N - exprmode 11 -> (X1 * (X2*X3)) * X4\")\n# println(\"--------------------------------------------------------------------------\")\n# println(\"Multi3/N - exprmode 1 -> X1 * X2 * X3\")\n# println(\"Multi3/N - exprmode 2 -> (X1*X2) * X3\")\n# println(\"Multi3/N - exprmode 3 -> X1 * (X2*X3)\")\n# println(\"--------------------------------------------------------------------------\")\n# println(\"                                Options\")\n# println(\"N | K | convhull | exprmode | unifrom | randomub | sos2 | presolve | delta\")\n# println(\"--------------------------------------------------------------------------\")\n\nfunction multi4(; verbose = false, solver = nothing, exprmode = 1)\n    m = JuMP.Model(solver)\n\n    Random.seed!(1)\n    @variable(m, 0.1 <= x[1:4] <= rand() * 100)\n    if exprmode == 1\n        @NLobjective(m, Max, x[1] * x[2] * x[3] * x[4])\n    elseif exprmode == 2\n        @NLobjective(m, Max, (x[1] * x[2]) * (x[3] * x[4]))\n    elseif exprmode == 3\n        @NLobjective(m, Max, (x[1] * x[2]) * x[3] * x[4])\n    elseif exprmode == 4\n        @NLobjective(m, Max, x[1] * x[2] * (x[3] * x[4]))\n    elseif exprmode == 5\n        @NLobjective(m, Max, (((x[1] * x[2]) * x[3]) * x[4]))\n    elseif exprmode == 6\n        @NLobjective(m, Max, (x[1] * x[2] * x[3]) * x[4])\n    elseif exprmode == 7\n        @NLobjective(m, Max, x[1] * (x[2] * (x[3] * x[4])))\n    elseif exprmode == 8\n        @NLobjective(m, Max, x[1] * (x[2] * x[3]) * x[4])\n    elseif exprmode == 9\n        @NLobjective(m, Max, x[1] * (x[2] * x[3] * x[4]))\n    elseif exprmode == 10\n        @NLobjective(m, Max, x[1] * ((x[2] * x[3]) * x[4]))\n    elseif exprmode == 11\n        @NLobjective(m, Max, (x[1] * (x[2] * x[3])) * x[4])\n    else\n        error(\"exprmode argument only taks from 1-7\")\n    end\n    @constraint(m, sum(x[i] for i in 1:4) <= 4)\n\n    if verbose\n        print(m)\n    end\n\n    return m\nend\n\nfunction multi3(; verbose = false, solver = nothing, exprmode = 1)\n    m = JuMP.Model(solver)\n\n    Random.seed!(1)\n    ub = rand()\n    @variable(m, 0.1 <= x[1:3] <= ub * 1000)\n    if exprmode == 1\n        @NLobjective(m, Max, x[1] * x[2] * x[3])\n    elseif exprmode == 2\n        @NLobjective(m, Max, (x[1] * x[2]) * x[3])\n    elseif exprmode == 3\n        @NLobjective(m, Max, x[1] * (x[2] * x[3]))\n    else\n        error(\"exprmode argument only taks from 1-7\")\n    end\n\n    @constraint(m, sum(x[i] for i in 1:3) <= 3)\n\n    if verbose\n        print(m)\n    end\n\n    return m\nend\n\nfunction multi2(; verbose = false, solver = nothing)\n    # Global solution: 0.92906489 (arg min: [0.7336635, 1.266336])\n\n    m = JuMP.Model(solver)\n\n    Random.seed!(1)\n    @variable(m, 0.1 <= x[1:2] <= rand() * 10)\n    @NLobjective(m, Max, x[1] * x[2])\n    @constraint(m, sum(x[i] for i in 1:2) <= 2)\n\n    if verbose\n        print(m)\n    end\n\n    return m\nend\n\nfunction multi4N(;\n    verbose = false,\n    exprmode = 1,\n    solver = nothing,\n    N = 1,\n    randomub = true,\n)\n    m = JuMP.Model(solver)\n\n    M = 1 + 3 * N\n    Random.seed!(100)\n    isa(randomub, Bool) ? @variable(m, 0.1 <= x[1:M] <= 100 * rand()) :\n    @variable(m, 0.1 <= x[1:M] <= randomub)\n\n    if exprmode == 1\n        @NLobjective(m, Max, sum(x[i] * x[i+1] * x[i+2] * x[i+3] for i in 1:3:(M-1)))\n    elseif exprmode == 2\n        @NLobjective(m, Max, sum((x[i] * x[i+1]) * (x[i+2] * x[i+3]) for i in 1:3:(M-1)))\n    elseif exprmode == 3\n        @NLobjective(m, Max, sum((x[i] * x[i+1]) * x[i+2] * x[i+3] for i in 1:3:(M-1)))\n    elseif exprmode == 4\n        @NLobjective(m, Max, sum(x[i] * x[i+1] * (x[i+2] * x[i+3]) for i in 1:3:(M-1)))\n    elseif exprmode == 5\n        @NLobjective(\n            m,\n            Max,\n            sum((((x[i] * x[i+1]) * x[i+2]) * x[i+3]) for i in 1:3:(M-1))\n        )\n    elseif exprmode == 6\n        @NLobjective(m, Max, sum((x[i] * x[i+1] * x[i+2]) * x[i+3] for i in 1:3:(M-1)))\n    elseif exprmode == 7\n        @NLobjective(m, Max, sum(x[i] * (x[i+1] * (x[i+2] * x[i+3])) for i in 1:3:(M-1)))\n    elseif exprmode == 8\n        @NLobjective(m, Max, sum(x[i] * (x[i+1] * x[i+2]) * x[i+3] for i in 1:3:(M-1)))\n    elseif exprmode == 9\n        @NLobjective(m, Max, sum(x[i] * (x[i+1] * x[i+2] * x[i+3]) for i in 1:3:(M-1)))\n    elseif exprmode == 10\n        @NLobjective(m, Max, sum(x[i] * ((x[i+1] * x[i+2]) * x[i+3]) for i in 1:3:(M-1)))\n    elseif exprmode == 11\n        @NLobjective(m, Max, sum((x[i] * (x[i+1] * x[i+2])) * x[i+3] for i in 1:3:(M-1)))\n    else\n        error(\"exprmode argument only taks from 1-7\")\n    end\n\n    @constraint(m, [i in 1:3:(M-1)], x[i] + x[i+1] + x[i+2] + x[i+3] <= 4)\n\n    if verbose\n        print(m)\n    end\n\n    return m\nend\n\nfunction multi3N(;\n    verbose = false,\n    randomub = nothing,\n    solver = nothing,\n    exprmode = 1,\n    N = 1,\n    delta = 4,\n)\n    m = JuMP.Model(solver)\n\n    M = 1 + 2 * N\n    Random.seed!(100)\n    isa(randomub, Int) ? @variable(m, 0.1 <= x[1:M] <= randomub) :\n    @variable(m, 0.1 <= x[1:M] <= rand() * 100)\n    if exprmode == 1\n        @NLobjective(m, Max, sum(x[i] * x[i+1] * x[i+2] for i in 1:2:(M-1)))\n    elseif exprmode == 2\n        @NLobjective(m, Max, sum((x[i] * x[i+1]) * x[i+2] for i in 1:2:(M-1)))\n    elseif exprmode == 3\n        @NLobjective(m, Max, sum(x[i] * (x[i+1] * x[i+2]) for i in 1:2:(M-1)))\n    else\n        error(\"exprmode argument only taks from 1-7\")\n    end\n\n    @constraint(m, [i in 1:2:(M-1)], x[i] + x[i+1] + x[i+2] <= 3)\n\n    if verbose\n        print(m)\n    end\n\n    return m\nend\n\nfunction multiKND(;\n    verbose = false,\n    solver = nothing,\n    exprmode = 1,\n    randomub = true,\n    N = 1,\n    K = 2,\n    D = 1,\n)\n    m = JuMP.Model(solver)\n\n    M = K + (K - D) * (N - 1)\n    Random.seed!(100)\n    isa(randomub, Int) ? @variable(m, 0.1 <= x[1:M] <= randomub) :\n    @variable(m, 0.1 <= x[1:M] <= rand() * 100)\n    @NLobjective(m, Max, sum(prod(x[i+k] for k in 0:(K-1)) for i in 1:(K-D):(M-D)))\n    @constraint(m, [i in 1:(K-D):(M-D)], sum(x[i+k] for k in 0:(K-1)) <= K)\n\n    verbose && print(m)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/nlp.jl",
    "content": "function nlp1(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 1 <= x[1:2] <= 4)\n    @NLconstraint(m, x[1] * x[2] >= 8)\n    @NLobjective(m, Min, 6 * x[1]^2 + 4 * x[2]^2 - 2.5 * x[1] * x[2])\n\n    return m\nend\n\nfunction nlp2(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, -500 <= x[1:2] <= 500)\n    @NLobjective(m, Min, sum((x[i]^2 - i)^2 for i in 1:2))\n\n    return m\nend\n\nfunction max_cover_var_picker(m::Alpine.Optimizer)\n    nodes = Set()\n    for pair in keys(m.nonconvex_terms)\n        for i in pair\n            @assert isa(i.args[2], Int)\n            push!(nodes, i.args[2])\n        end\n    end\n    nodes = collect(nodes)\n    m.num_var_disc_mip = length(nodes)\n    m.disc_vars = nodes\n    return\nend\n\nfunction mathopt(; solver = nothing)\n    # Modified based on `mathopt` instances from MINLPLib\n    # Global solution: -1004.73094034, arg min: [ -10.0, 15.2543377, -3.2034701]\n\n    m = JuMP.Model(solver)\n\n    LB = [-10, -15, -10]\n    UB = [20, 20, 20]\n    x0 = [-10.0, 15.3, -3.2]\n    @variable(\n        m,\n        LB[i] <= x[i = 1:3] <= UB[i],\n        start = x0[i],\n    )\n    @NLobjective(m, Min, 10 * (x[1] * x[2] - x[2] * x[3]) + x[1] * x[3])\n    @NLconstraint(m, x[1] * x[2] + x[2] * x[3]^2 >= 4)\n    @constraint(m, 3 * x[1] + 4 * x[2] + 5 * x[3] <= 15)\n\n    return m\nend\n\nfunction nlp3(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    LB = [100, 1000, 1000, 10, 10, 10, 10, 10]\n    UB = [10000, 10000, 10000, 1000, 1000, 1000, 1000, 1000]\n\n    @variable(m, LB[i] <= x[i = 1:8] <= UB[i])\n\n    @constraint(m, 0.0025 * (x[4] + x[6]) <= 1)\n    @constraint(m, 0.0025 * (x[5] - x[4] + x[7]) <= 1)\n    @constraint(m, 0.01(x[8] - x[5]) <= 1)\n    @NLconstraint(m, 100 * x[1] - x[1] * x[6] + 833.33252 * x[4] <= 83333.333)\n    @NLconstraint(m, x[2] * x[4] - x[2] * x[7] - 1250 * x[4] + 1250 * x[5] <= 0)\n    @NLconstraint(m, x[3] * x[5] - x[3] * x[8] - 2500 * x[5] + 1250000 <= 0)\n\n    @objective(m, Min, x[1] + x[2] + x[3])\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/rosenbrock.jl",
    "content": "# Reference: https://direct.mit.edu/evco/article/14/1/119/1232/A-Note-on-the-Extended-Rosenbrock-Function\n# Global optimum = 0.0, arg min = (1,1)\n\nfunction rosenbrock(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, -10 <= x <= 10)\n    @variable(m, -10 <= y <= 10)\n\n    @NLobjective(m, Min, 100 * (y - x^2)^2 + (1 - x)^2)\n\n    return m\nend\n"
  },
  {
    "path": "examples/MINLPs/sincos.jl",
    "content": "# Functions in this file are not tested until support for trigonometric functions is added. \n\nfunction sincos_p1(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, 0.1 <= x[1:10] <= 10)\n    @NLconstraint(m, [i in 1:9], x[i] * x[i+1] * sin(x[i]) >= 0.32)\n    @NLconstraint(m, [i in 1:9], x[i] * x[i+1] * sin(x[i]) <= 0.42)\n    @NLobjective(m, Min, sum(cos(x[i]) + sin(x[i]) for i in 1:10))\n\n    return m\nend\n\nfunction trig(; solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, objvar)\n    x_Idx = Any[1]\n    @variable(m, x[x_Idx])\n    JuMP.set_lower_bound(x[1], -2.0)\n    JuMP.set_upper_bound(x[1], 5.0)\n\n    @NLconstraint(\n        m,\n        e1,\n        -(sin(11 * x[1]) + cos(13 * x[1]) - sin(17 * x[1]) - cos(19 * x[1])) + objvar ==\n        0.0\n    )\n    @NLconstraint(m, e2, 5 * sin(x[1]) - x[1] <= 0.0)\n\n    @objective(m, Min, objvar)\n\n    return m\nend\n\nfunction specialopts(; verbose = false, solver = nothing)\n    m = JuMP.Model(solver)\n\n    @variable(m, x[i = 1:6])\n\n    @NLconstraint(m, sin(x[1]) + cos(x[2]) >= 1)\n    @NLconstraint(m, sin(x[1]) * x[2] >= 1)\n    @NLconstraint(m, sin(x[1]) * cos(x[2]) >= 1)\n    #\n    @NLconstraint(m, sin(x[1] * x[2]) >= 0.5)\n    @NLconstraint(m, cos(x[1] + x[2]) >= 0.5)\n    @NLconstraint(m, cos(x[1] / 2) >= 0.5)\n    @NLconstraint(m, cos(x[1] * x[2] / 5) >= 0.5)\n    @NLconstraint(m, sin(x[1] / 5 + x[2] / 5) >= 0.5)\n\n    return m\nend\n"
  },
  {
    "path": "examples/Project.toml",
    "content": "[deps]\nAlpine = \"07493b3f-dabb-5b16-a503-4139292d7dd4\"\nCPLEX = \"a076750e-1247-5638-91d2-ce28b192dca0\"\nGurobi = \"2e9cd046-0924-5485-92f1-d5272153d98b\"\nHiGHS = \"87dc4568-4c63-4d18-b0c0-bb2238e4078b\"\nIpopt = \"b6b21f68-93f8-5de0-b562-5493be1d77c9\"\nJuMP = \"4076af6c-e467-56ae-b986-b466b2749572\"\nJuniper = \"2ddba703-00a4-53a7-87a5-e8b9971dde84\"\nPavito = \"cd433a01-47d1-575d-afb7-6db927ee8d8f\"\nRevise = \"295af30f-e4ad-537b-8983-00126c2a3abe\"\n\n[compat]\nJuMP = \"1\"\njulia = \"1\"\n"
  },
  {
    "path": "examples/README.md",
    "content": "# Examples for Alpine\n`run_examples.jl` file contains the main driver file which can be executed to compute global optimality for a non-convex MINLP of your choice. Multiple such JuMP models of MINLPs can be found inside the `examples/MINLPs` folder.\n\nA few useful **hints** to explore within Alpine: \n* Try different integer values (>= 4) for `partition_scaling_factor` to potentially observe \n    better Alpine run times, which can be instance specific.\n* Choose `presolve_bt` to `false` if you prefer the optimization-based bound tightening (OBBT) presolve to be turned off. \n* If you prefer to use Alpine for only OBBT presolve, without any paritioning applied to the \n    nonlinear terms, include option `\"apply_partitioning\"` and set it to `false` while initializing the \n    Alpine solver. \n* If the nonconvex instance you want to solve has binary variables (i.e., a MINLP like in [here](https://github.com/lanl-ansi/Alpine.jl/blob/32757b2568acfe71257e41ed4122a120717a6460/examples/MINLPs/blend.jl#LL1C1-L1C1), then include a local MINLP solver as an additional attribute while initializing `Alpine.Optimizer` in `run_examples.jl`. \n\n# Random families of non-convex QCQPs\nScripts for generating homogeneous families of nonconvex QCQP instances, useful for benchmarking ML-based models for tuning certain algorithmic parameters of global optimization, can be found [here](https://github.com/lanl-ansi/Alpine.jl/tree/master/examples/random_QCQPs). "
  },
  {
    "path": "examples/optimizers.jl",
    "content": "#---------------------------;\n# MIP solvers - commercial  ;\n#---------------------------;\n# https://github.com/jump-dev/Gurobi.jl\nfunction get_gurobi()\n    GRB_ENV = Gurobi.Env()\n    return optimizer_with_attributes(\n        () -> Gurobi.Optimizer(GRB_ENV), # To avoid printing License info multiple times\n        MOI.Silent() => true,\n        \"Presolve\" => 1,\n    )\nend\n\n# https://github.com/jump-dev/CPLEX.jl\nfunction get_cplex()\n    return optimizer_with_attributes(\n        CPLEX.Optimizer,\n        MOI.Silent() => true,\n        \"CPX_PARAM_PREIND\" => 1,\n    )\nend\n\n#---------------------------;\n# MIP solvers - open-source\n#---------------------------;\n# https://github.com/jump-dev/HiGHS.jl\nfunction get_highs()\n    return JuMP.optimizer_with_attributes(\n        HiGHS.Optimizer,\n        \"presolve\" => \"on\",\n        \"log_to_console\" => false,\n    )\nend\n\n# https://github.com/jump-dev/Cbc.jl\nfunction get_cbc()\n    return optimizer_with_attributes(Cbc.Optimizer, MOI.Silent() => true)\nend\n\n#---------------------------;\n# Continuous local solver   ; \n#---------------------------;\n# https://github.com/jump-dev/Ipopt.jl\nfunction get_ipopt()\n    return optimizer_with_attributes(\n        Ipopt.Optimizer,\n        MOI.Silent() => true,\n        \"sb\" => \"yes\",\n        \"max_iter\" => Int(1E4),\n    )\nend\n\n#----------------------;\n# Convex MINLP solver  ;\n#----------------------;\n# https://github.com/jump-dev/Pavito.jl\nfunction get_pavito(mip_solver, cont_solver)\n    return optimizer_with_attributes(\n        Pavito.Optimizer,\n        MOI.Silent() => true,\n        \"mip_solver\" => mip_solver,\n        \"cont_solver\" => cont_solver,\n        \"mip_solver_drives\" => false,\n    )\nend\n\n#-------------------------------;\n# Non-convex Local MINLP solver ;\n#-------------------------------;\n# https://github.com/lanl-ansi/Juniper.jl\nfunction get_juniper(mip_solver, nl_solver)\n    return optimizer_with_attributes(\n        Juniper.Optimizer,\n        MOI.Silent() => true,\n        \"mip_solver\" => mip_solver,\n        \"nl_solver\" => nl_solver,\n    )\nend\n"
  },
  {
    "path": "examples/random_QCQPs/README.md",
    "content": "# Random families of non-convex QCQPs \nScripts for generating a family of random non-convex quadratically-constrained quadratic programs (QCQPs) instances in Section 5 of the paper \"Learning to Accelerate the Global Optimization of Quadratically-Constrained Quadratic Programs\" by R. Kannan, H. Nagarajan, and D. Deka ([arXiv](https://arxiv.org/abs/2301.00306)). As discussed in the aforementioned paper, these homogeneous families of instances can be very useful for benchmarking machine learning-based models for tuning certain algorithmic parameters of global optimization.\n\nInstances in the above paper were generated using Python 3.8.5 and NumPy 1.19.2.\n\nTo generate 1000 random bilinear instances with `N` variables (`N = 10, 20, 50`), run\n```\npython3 generate_bilinear_instances.py --numVariables N --numInstances 1000\n```\n\nTo generate 1000 random QCQP instances (including both bilinear and univariate quadratic terms) with `N` variables (`N = 10, 20, 50`), run\n```\npython3 generate_qcqp_instances.py --numVariables N --numInstances 1000\n```\n\nTo generate 1000 random pooling instances, run\n```\npython3 generate_pooling_instances.py --numInstances 1000\n```\nAdditional data files for generating the pooling instances can be found within the `pooling` folder. These data files were generated using the scripts [here](https://github.com/poolinginstances/poolinginstances).\n\n\nIf you find these instances useful in your work, we kindly request that you cite the following paper [arXiv link](https://arxiv.org/abs/2301.00306):\n```bibtex\n@article{alpine_learning_2022,\n  title={Learning to Accelerate the Global Optimization of Quadratically-Constrained Quadratic Programs},\n  author={Kannan, Rohit and Nagarajan, Harsha and Deka, Deepjyoti},\n  journal={arXiv preprint:2301.00306},\n  url={https://arxiv.org/abs/2301.00306},\n  year={2022}\n}\n```"
  },
  {
    "path": "examples/random_QCQPs/bilinear/generate_bilinear_instances.py",
    "content": "\"\"\"\n// @brief  Script to generate the nonconvex instances with only bilinear terms\n//\t\t   Input arguments: numVariables, numInstances\n// Reference: \"Learning to Accelerate the Global Optimization of Quadratically-Constrained \n\t\t\t   Quadratic Programs\" by R. Kannan, H. Nagarajan, and D. Deka \n\t\t\t   (Link: https://arxiv.org/abs/2301.00306)\n// Contributor: @rohitkannan \n\"\"\"\n\nimport random\nimport json\nimport numpy as np\nimport argparse\nimport os\n\n\nparser = argparse.ArgumentParser()\nparser.add_argument('--numVariables', type=int, required=True)\nparser.add_argument('--numInstances', type=int, required=True)\nargs = parser.parse_args()\n\nnumVariables = int(args.numVariables)\nnumInstances = int(args.numInstances)\n\ninstances_path = \"./N_\" + str(numVariables) + \"/\"\nos.makedirs(instances_path)\n\n# random seed for instances\nif numVariables == 10:\n\trandom.seed(4898)\nelif numVariables == 20:\n\trandom.seed(6736) \nelif numVariables == 50:\n\trandom.seed(8197) \n\nnp.random.seed(round(random.random()*10000)) \n\n\nstart = 1  # starting instance number\n\nnumQuadraticConstraints = numVariables  # number of constraints with bilinear and linear terms\nnumLinearConstraints = round(numVariables/5)  # number of linear equality constraints\n\nconstraint_sparsity = 1.0  # (actually opposite of sparsity) fraction of possible bilinear and linear terms occurring in each constraint\nmaxNumBilinearTerms = round(numVariables*(numVariables-1)/2)\nnumBilinearTerms = min(5*numVariables,maxNumBilinearTerms)  # number of bilinear terms in the formulation\n\nfrac_quad_con_pert = 0.2  # fraction of quadratic constraints perturbed\nnumPertFactors = 3  # number of perturbation factors per perturbed quadratic constraint\npert_frac = 0.5  # perturbation fraction around nominal instance\n\n\n# to sort list of lists\ndef Sort(sub_li):\n    return(sorted(sub_li, key = lambda x: (x[0],x[1])))    \n\n\n# GENERATE COMMON BILINEAR TERMS FOR ALL INSTANCES\npossible_bilinear_terms = [[i,j] for i in range(numVariables) for j in range(i+1,numVariables)]\nrandom.shuffle(possible_bilinear_terms)\nbilinear_terms = Sort(possible_bilinear_terms[:numBilinearTerms])\n\n\n# GENERATE BASE COEFFICIENTS\nq_bilinear = []  # bilinear coefficients\nq_bilinear_ind = []  # bilinear coefficient indices\n\n# OBJECTIVE COEFFICIENTS\nq_bilinear.append([2*random.random()-1 for j in range(numBilinearTerms)])  # all bilinear terms participate in the objective (sparsity not applied here)\nq_bilinear_ind.append(list(np.arange(numBilinearTerms)))\n\n# CONSTRAINT COEFFICIENTS\nnumQuadNonZero = round(numBilinearTerms*constraint_sparsity)\nfor i in range(numQuadraticConstraints):\n\tq_bilinear.append([2*random.random()-1 for j in range(numQuadNonZero)])\n\ttmp_ind = list(np.random.choice(numBilinearTerms, numQuadNonZero, replace=False))\n\ttmp_ind.sort()\n\tq_bilinear_ind.append(tmp_ind)\n\n\nq_linear = []  # linear coefficients\nq_linear_ind = []  # linear coefficient indices\n\n# OBJECTIVE COEFFICIENTS\nq_linear.append([2*random.random()-1 for j in range(numVariables)])  # all linear terms participate in the objective (sparsity not applied here)\nq_linear_ind.append(list(np.arange(numVariables)))\n\n# CONSTRAINT COEFFICIENTS\nnumLinNonZero = round(numVariables*constraint_sparsity)\nfor i in range(numQuadraticConstraints+numLinearConstraints):\n\tif i < numQuadraticConstraints:  # only a fraction of linear terms appear in quadratic constraints\n\t\tq_linear.append([2*random.random()-1 for j in range(numLinNonZero)])\n\t\ttmp_ind = list(np.random.choice(numVariables, numLinNonZero, replace=False))\n\telse:  # all linear terms appear in linear equality constraints\n\t\tq_linear.append([2*random.random()-1 for j in range(numVariables)])\n\t\ttmp_ind = list(np.arange(numVariables))\n\ttmp_ind.sort()\n\tq_linear_ind.append(tmp_ind)\n\n\n# GENERATE BASE RHS COEFFICIENTS\nquadratic_scaling = 100\nrhs_quadratic = [quadratic_scaling*random.random() for i in range(numQuadraticConstraints)]\n\nlinear_scaling = 1\nrhs_linear = [linear_scaling*(2*random.random()-1) for i in range(numLinearConstraints)]\n\n\n# RE-SCALE PROBLEM SO THAT CONSTRAINTS RHS ARE EQUAL TO ONE\nfor i in range(numQuadraticConstraints):\n\tfor j in range(numQuadNonZero):\n\t\tq_bilinear[i+1][j] /= rhs_quadratic[i]\n\tfor j in range(numLinNonZero):\n\t\tq_linear[i+1][j] /= rhs_quadratic[i]\n\n\nfor i in range(numLinearConstraints):\n\tfor j in range(numVariables):\n\t\tq_linear[i+1+numQuadraticConstraints][j] /= rhs_linear[i]\n\n\n# CONSTRUCT PERTURBATION FACTORS FOR THE OBJECTIVE AND QUADRATIC CONSTRAINT COEFFICIENTS\nq_bilinear_obj_factors = np.zeros((numPertFactors,numBilinearTerms))\nq_linear_obj_factors = np.zeros((numPertFactors,numVariables))\nfor j in range(numBilinearTerms):\n\tfor k in range(numPertFactors):\n\t\tq_bilinear_obj_factors[k,j] = pert_frac*random.random()*q_bilinear[0][j]\nfor j in range(numVariables):\n\tfor k in range(numPertFactors):\n\t\tq_linear_obj_factors[k,j] = pert_frac*random.random()*q_linear[0][j]\n\nnumQuadConPert = round(numQuadraticConstraints*frac_quad_con_pert)\nq_bilinear_con_factors = np.zeros((numPertFactors,numQuadConPert,numQuadNonZero))\nq_linear_con_factors = np.zeros((numPertFactors,numQuadConPert,numLinNonZero))\nfor i in range(numQuadConPert):\n\tfor j in range(numQuadNonZero):\n\t\tfor k in range(numPertFactors):\n\t\t\tq_bilinear_con_factors[k,i,j] = pert_frac*random.random()*q_bilinear[i+1][j]\n\tfor j in range(numLinNonZero):\n\t\tfor k in range(numPertFactors):\n\t\t\tq_linear_con_factors[k,i,j] = pert_frac*random.random()*q_linear[i+1][j]\n\n\n\n# GENERATE PERTURBED INSTANCES\nfor inst in range(start,numInstances+start):\n\toutput_file = instances_path + \"bilinear_v\" + str(numVariables) + \"_b\" + str(numBilinearTerms) + \"_s\" + str(round(constraint_sparsity*100)) + \"_\" + str(inst) + \".jl\"\n\tjson_file = instances_path + \"bilinear_v\" + str(numVariables) + \"_b\" + str(numBilinearTerms) + \"_s\" + str(round(constraint_sparsity*100)) + \"_\" + str(inst) + \".json\"\n\n\tjson_dict = {}\n\tjson_dict[\"numVariables\"] = numVariables\n\tjson_dict[\"numQuadraticConstraints\"] = numQuadraticConstraints\n\tjson_dict[\"numLinearConstraints\"] = numLinearConstraints\n\tjson_dict[\"constraint_sparsity\"] = constraint_sparsity\n\n\tjson_dict[\"numBilinearTerms\"] = numBilinearTerms\n\tjson_dict[\"bilinear_terms\"] = bilinear_terms\n\n\tjson_dict[\"pert_frac\"] = pert_frac\n\tjson_dict[\"numPertFactors\"] = numPertFactors\n\tjson_dict[\"numQuadConPert\"] = numQuadConPert\n\tjson_dict[\"bilinear_obj_factors\"] = q_bilinear_obj_factors.tolist()\n\tjson_dict[\"linear_obj_factors\"] = q_linear_obj_factors.tolist()\n\tjson_dict[\"bilinear_con_factors\"] = q_bilinear_con_factors.tolist()\n\tjson_dict[\"linear_con_factors\"] = q_linear_con_factors.tolist()\n\n\n# GENERATE PERTURBATION FACTORS\n\ttheta = 2*(np.random.rand(numPertFactors,numQuadConPert+1) - 0.5)\n\n\tjson_dict[\"theta\"] = theta.tolist()\n\n# STORE SPARSITY PATTERN AND INITIALIZE DATA\n\tf = open(output_file, \"w\")\n\n\tf.write(\"# ----- Bilinear Terms ----- #\\n\")\n\tf.write(\"numBilinearTerms = \" + str(numBilinearTerms) + \"\\n\")\n\tf.write(\"bilinear_terms = [\")\n\tcount_bilinear = 0\n\tfor term in bilinear_terms:\n\t\tf.write(\"[\" + str(term[0]+1) + \",\" + str(term[1]+1) + \"]\")\n\t\tcount_bilinear += 1\n\t\tif count_bilinear < numBilinearTerms:\n\t\t\tf.write(\", \")\n\t\telse:\n\t\t\tf.write(\"] \\n\\n\")\n\t\n\tf.write(\"numQuadNonZero = \" + str(numQuadNonZero) + \"\\n\")\n\tf.write(\"numLinNonZero = \" + str(numLinNonZero) + \"\\n\\n\")\n\n\tf.write(\"# ----- Data Matrices ----- #\\n\")\n\tf.write(\"bilinear_obj_coeffs = zeros(Float64,\" + str(numBilinearTerms) + \") \\n\")\n\tf.write(\"bilinear_con_coeffs = zeros(Float64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero) + \") \\n\")\n\tf.write(\"bilinear_con_coeff_indices = zeros(Int64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero) + \") \\n\")\n\tf.write(\"linear_obj_coeffs = zeros(Float64,\" + str(numVariables) + \") \\n\")\n\tf.write(\"linear_con_coeffs_1 = zeros(Float64,\" + str(numQuadraticConstraints) + \",\" + str(numLinNonZero) + \") \\n\")\n\tf.write(\"linear_con_coeff_indices_1 = zeros(Int64,\" + str(numQuadraticConstraints) + \",\" + str(numLinNonZero) + \") \\n\")\n\tf.write(\"linear_con_coeffs_2 = zeros(Float64,\" + str(numLinearConstraints) + \",\" + str(numVariables) + \") \\n\")\n\tf.write(\"linear_con_coeff_indices_2 = zeros(Int64,\" + str(numLinearConstraints) + \",\" + str(numVariables) + \") \\n\\n\")\n\n\tf.write(\"# ----- Variables ----- #\\n\")\n\tf.write(\"@variable(m, 0 <= x[1:\" + str(numVariables) + \"] <= 1)\\n\")\n\tf.write(\"@variable(m, 0 <= w[1:\" + str(numBilinearTerms) + \"] <= 1)\\n\\n\")\n\n\tf.write(\"# ----- Bilinear Equations ----- #\\n\")\n\tf.write(\"@NLconstraint(m, [i=1:\" + str(numBilinearTerms) + \"], w[i] == x[bilinear_terms[i][1]]*x[bilinear_terms[i][2]])\\n\\n\\n\")\n\n\tjson_dict[\"x_lower\"] = [0 for i in range(numVariables)]\n\tjson_dict[\"x_upper\"] = [1 for i in range(numVariables)]\n\n\n# OBJECTIVE\n\t# tmp variables for storing generated data\n\tQ = [0.]*numBilinearTerms\n\tq = [0.]*numVariables\n\n\tcount_quad_con = 0\n\tcount_lin_con = 0\n\tfor i in range(numVariables):\n\t\tq[i] = q_linear[0][i]\n\t\tfor k in range(numPertFactors):\n\t\t\tq[i] += q_linear_obj_factors[k,i]*theta[k,0]\n\tfor i in range(numBilinearTerms):\n\t\tQ[i] = q_bilinear[0][i]\n\t\tfor k in range(numPertFactors):\n\t\t\tQ[i] += q_bilinear_obj_factors[k,i]*theta[k,0]\n\n\tjson_dict[\"obj_bilinear_coeffs\"] = Q\n\tjson_dict[\"obj_linear_coeffs\"] = q\n\n\tf.write(\"# ----- Objective ----- #\\n\")\n\tf.write(\"bilinear_obj_coeffs = \" + str(Q) + \"\\n\")\n\tf.write(\"linear_obj_coeffs = \" + str(q) + \"\\n\")\n\n\tf.write(\"\\n\")\n\tf.write(\"@objective(m, Min, sum(bilinear_obj_coeffs[i]*w[i] for i = 1:\" + str(numBilinearTerms) + \") + sum(linear_obj_coeffs[i]*x[i] for i = 1:\" + str(numVariables) + \")) \\n\\n\\n\")\n\n\n\tbilinear_obj_matrix = np.zeros((numVariables, numVariables))\n\tfor i in range(numBilinearTerms):\n\t\tbilinear_obj_matrix[bilinear_terms[i][0]][bilinear_terms[i][1]] = Q[i]/2.0\n\t\tbilinear_obj_matrix[bilinear_terms[i][1]][bilinear_terms[i][0]] = Q[i]/2.0\n\n\tjson_dict[\"obj_bilinear_eigvals\"] = np.linalg.eigvals(bilinear_obj_matrix).tolist()\n\n\n# QUADRATIC CONSTRAINTS\n\tf.write(\"# ----- Constraints ----- #\\n\")\n\n\tjson_dict[\"quadratic_con_rhs\"] = [1.0 for i in range(numQuadraticConstraints)]\n\n\tbilinear_con_coeffs = []\n\tbilinear_con_coeff_indices = []\n\tlinear_con_coeffs = []\n\tlinear_con_coeff_indices = []\n\tcon_bilinear_eigvals = np.empty([numQuadraticConstraints, numVariables], dtype=float)\n\n\tfor k in range(numQuadraticConstraints):\n\t\tQ = [0.]*numQuadNonZero\n\t\tQ_ind = [i+1 for i in q_bilinear_ind[count_quad_con+1]]\n\t\tq = [0.]*numLinNonZero\n\t\tq_ind = [i+1 for i in q_linear_ind[count_lin_con+1]]\n\n\t\tcount_quad_con += 1\n\t\tcount_lin_con += 1\n\t\tfor i in range(numLinNonZero):\n\t\t\tq[i] = q_linear[count_lin_con][i]\n\t\t\tif k < numQuadConPert:\n\t\t\t\tfor j in range(numPertFactors):\n\t\t\t\t\tq[i] += q_linear_con_factors[j,count_lin_con-1,i]*theta[j,count_lin_con]\n\t\tfor i in range(numQuadNonZero):\n\t\t\tQ[i] = q_bilinear[count_quad_con][i]\n\t\t\tif k < numQuadConPert:\n\t\t\t\tfor j in range(numPertFactors):\n\t\t\t\t\tQ[i] += q_bilinear_con_factors[j,count_quad_con-1,i]*theta[j,count_quad_con]\n\n\t\tbilinear_con_coeffs.append(Q)\n\t\tbilinear_con_coeff_indices.append([float(i) for i in q_bilinear_ind[count_quad_con]])\n\t\tlinear_con_coeffs.append(q)\n\t\tlinear_con_coeff_indices.append([float(i) for i in q_linear_ind[count_lin_con]])\n\n\t\tf.write(\"bilinear_con_coeffs[\" + str(count_quad_con) + \",:] = \" + str(Q) + \"\\n\")\n\t\tf.write(\"bilinear_con_coeff_indices[\" + str(count_quad_con) + \",:] = \" + str(Q_ind) + \"\\n\")\n\t\tf.write(\"linear_con_coeffs_1[\" + str(count_lin_con) + \",:] = \" + str(q) + \"\\n\")\n\t\tf.write(\"linear_con_coeff_indices_1[\" + str(count_lin_con) + \",:] = \" + str(q_ind) + \"\\n\")\n\t\tf.write(\"\\n\")\n\n\t\tf.write(\"@constraint(m, sum(bilinear_con_coeffs[\" + str(count_quad_con) + \",i]*w[bilinear_con_coeff_indices[\" + str(count_quad_con) + \",i]] for i = 1:\" + str(numQuadNonZero) + \") + sum(linear_con_coeffs_1[\" + str(count_lin_con) + \",i]*x[linear_con_coeff_indices_1[\" + str(count_lin_con) + \",i]] for i = 1:\" + str(numLinNonZero) + \") <= 1) \\n\\n\\n\")\n\n\n\t\tbilinear_con_matrix = np.zeros((numVariables, numVariables))\n\t\tfor i in range(numQuadNonZero):\n\t\t\tind = q_bilinear_ind[count_quad_con][i]\n\t\t\tind1 = bilinear_terms[ind][0]\n\t\t\tind2 = bilinear_terms[ind][1]\n\t\t\tbilinear_con_matrix[ind1][ind2] = Q[i]/2.0\n\t\t\tbilinear_con_matrix[ind2][ind1] = Q[i]/2.0\n\n\t\tcon_bilinear_eigvals[k] = np.linalg.eigvals(bilinear_con_matrix)\n\n\t\n\tjson_dict[\"con_bilinear_eigvals\"] = con_bilinear_eigvals.tolist()\n\n\n# LINEAR CONSTRAINTS\n\tjson_dict[\"linear_con_rhs\"] = [1.0 for i in range(numLinearConstraints)]\n\n\tfor k in range(numLinearConstraints):\n\t\tq = [0.]*numVariables\n\t\tq_ind = [i+1 for i in q_linear_ind[count_lin_con+1]]\n\n\t\tcount_lin_con += 1\n\t\tfor i in range(numVariables):\n\t\t\tq[i] = q_linear[count_lin_con][i]\n\n\t\tlinear_con_coeffs.append(q)\n\t\tlinear_con_coeff_indices.append([float(i) for i in q_linear_ind[count_lin_con]])\n\n\t\tf.write(\"linear_con_coeffs_2[\" + str(count_lin_con - numQuadraticConstraints) + \",:] = \" + str(q) + \"\\n\")\n\t\tf.write(\"linear_con_coeff_indices_2[\" + str(count_lin_con - numQuadraticConstraints) + \",:] = \" + str(q_ind) + \"\\n\")\n\t\tf.write(\"\\n\")\n\n\t\tf.write(\"@constraint(m, sum(linear_con_coeffs_2[\" + str(count_lin_con - numQuadraticConstraints) + \",i]*x[linear_con_coeff_indices_2[\" + str(count_lin_con - numQuadraticConstraints) + \",i]] for i = 1:\" + str(numVariables) + \") == 1) \\n\\n\\n\")\n\t\t\n\tf.close()\n\n\n\tjson_dict[\"con_bilinear_coeffs\"] = bilinear_con_coeffs\n\tjson_dict[\"con_bilinear_coeff_indices\"] = bilinear_con_coeff_indices\n\tjson_dict[\"con_linear_coeffs\"] = linear_con_coeffs\n\tjson_dict[\"con_linear_coeff_indices\"] = linear_con_coeff_indices\n\n\twith open(json_file, 'w', encoding='utf-8') as outF:\n\t\tjson.dump(json_dict, outF, ensure_ascii=False, indent=4)\n"
  },
  {
    "path": "examples/random_QCQPs/pooling/generate_pooling_instances.py",
    "content": "\"\"\"\n// @brief  Script to generate the nonconvex pooling instances based on Luedtke et al. (SIOPT vol. 30 (2020), pp. 1582–1609)\n//\t\t   Input arguments: numInstances\n// Reference: \"Learning to Accelerate the Global Optimization of Quadratically-Constrained \n\t\t\t   Quadratic Programs\" by R. Kannan, H. Nagarajan, and D. Deka \n\t\t\t   (Link: https://arxiv.org/abs/2301.00306)\n// Contributor: @rohitkannan \n\"\"\"\n\nimport numpy as np\nimport random\nimport json\nimport argparse\nimport os\n\nparser = argparse.ArgumentParser()\nparser.add_argument('--numInstances', type=int, required=True)\nargs = parser.parse_args()\n\nnumInstances = int(args.numInstances)\n\ninstances_path = \"./pooling_instances/\"\nos.mkdir(instances_path)\n\n# random seed for instances\nrandom.seed(8446) \nnp.random.seed(round(random.random()*10000)) \n\n\ndef flatten(t):\n\treturn [item for sublist in t for item in sublist]\n\n\n# parameters defining the instance\nnum_copies = 15\nnum_added_edges = 150\nnum_specs = 1\n\n\nnum_orig_inputs = 3\nnum_orig_pools = 1\nnum_orig_outputs = 2\n\n\n# fraction by which to perturb the nominal input qualities\npert_frac = 0.2\n\n\n# scaling factors for parameters\ncapacities_scaling = 100.0\ncosts_scaling = 2.0\n\n\n\ninput_file = \"haverly_\" + str(num_copies) + \"_addedges_\" + str(num_added_edges) + \"_attr_\" + str(num_specs-1) + \"_1.dat\"\n\n\n\n# first map the vertex labels to integers\ninputs_dict = dict()\noutputs_dict = dict()\npools_dict = dict()\n\nfor c in range(num_copies):\n\tfor i in range(num_orig_inputs):\n\t\tif c < 10 and num_copies > 10:\n\t\t\ttmp = \"h0\" + str(c) + \"_i\" + str(i+1)\n\t\telse:\n\t\t\ttmp = \"h\" + str(c) + \"_i\" + str(i+1)\n\t\tinputs_dict[tmp] = c*num_orig_inputs + i\n\n\tfor j in range(num_orig_outputs):\n\t\tif c < 10 and num_copies > 10:\n\t\t\ttmp = \"h0\" + str(c) + \"_j\" + str(j+1)\n\t\telse:\n\t\t\ttmp = \"h\" + str(c) + \"_j\" + str(j+1)\n\t\toutputs_dict[tmp] = c*num_orig_outputs + j\n\n\tfor l in range(num_orig_pools):\n\t\tif c < 10 and num_copies > 10:\n\t\t\ttmp = \"h0\" + str(c) + \"_l\" + str(l+1)\n\t\telse:\n\t\t\ttmp = \"h\" + str(c) + \"_l\" + str(l+1)\n\t\tpools_dict[tmp] = c*num_orig_pools + l\n\n\n# compute actual number of inputs, pools, and outputs\nnum_inputs = num_orig_inputs*num_copies\nnum_pools = num_orig_pools*num_copies\nnum_outputs = num_orig_outputs*num_copies\n\n\n# extract the relevant lines for each input parameter\nfile1 = open(input_file, 'r')\nLines = file1.readlines()\n\nstart_edges = False\nstart_costs = False\nstart_capacities = False\nstart_specs = False\nstart_limits = False\n\nlines_edges = []\nlines_costs = []\nlines_capacities = []\nlines_specs = []\nlines_limits = []\n\nfor line in Lines:\n\tif start_edges and line.startswith('/;'):\n\t\tstart_edges = False\n\tif start_costs and line.startswith('/;'):\n\t\tstart_costs = False\n\tif start_capacities and line.startswith('/;'):\n\t\tstart_capacities = False\n\tif start_specs and line.startswith('/;'):\n\t\tstart_specs = False\n\tif start_limits and line.startswith('/;'):\n\t\tstart_limits = False\n\n\tif start_edges:\n\t\tlines_edges.append(line)\n\tif start_costs:\n\t\tlines_costs.append(line)\n\tif start_capacities:\n\t\tlines_capacities.append(line)\n\tif start_specs:\n\t\tlines_specs.append(line)\n\tif start_limits:\n\t\tlines_limits.append(line)\n\n\tif line.startswith('set A /'):\n\t\tstart_edges = True\n\tif line.startswith('parameter cost(V,V) /'):\n\t\tstart_costs = True\n\tif line.startswith('parameter C(V) /'):\n\t\tstart_capacities = True\n\tif line.startswith('parameter lambda(K,V) /'):\n\t\tstart_specs = True\n\tif line.startswith('parameter overbeta(K,V) /'):\n\t\tstart_limits = True\n\n\n# first, extract capacities\ncap_i = [0.0 for i in range(num_inputs)]\ncap_j = [0.0 for j in range(num_outputs)]\ncap_l = [0.0 for l in range(num_pools)]\n\nfor line in lines_capacities:\n\tif num_copies > 10:\n\t\tid = line[4:10]\n\t\tval = float(line[11:])\n\telse:\n\t\tid = line[4:9]\n\t\tval = float(line[10:])\n\n\tif id in inputs_dict:\n\t\tcap_i[inputs_dict[id]] = val/capacities_scaling\n\tif id in outputs_dict:\n\t\tcap_j[outputs_dict[id]] = val/capacities_scaling\n\tif id in pools_dict:\n\t\tcap_l[pools_dict[id]] = val/capacities_scaling\n\n\n# next, extract costs\ncost_ij_rows = []\ncost_ij_cols = []\ncost_ij_vals = []\n\ncost_il_rows = []\ncost_il_cols = []\ncost_il_vals = []\n\ncost_lj_rows = []\ncost_lj_cols = []\ncost_lj_vals = []\n\nfor line in lines_costs:\n\tids = line.rstrip().split('.')\n\tif num_copies > 10:\n\t\tid1 = ids[0][-6:]\n\t\tid2 = ids[1][:6]\n\t\tval = float(line[18:])\n\telse:\n\t\tid1 = ids[0][-5:]\n\t\tid2 = ids[1][:5]\n\t\tval = float(line[16:])\n\n\tif id1 in inputs_dict and id2 in outputs_dict:\n\t\tcost_ij_rows.append(inputs_dict[id1])\n\t\tcost_ij_cols.append(outputs_dict[id2])\n\t\tcost_ij_vals.append(val/costs_scaling)\n\n\tif id1 in inputs_dict and id2 in pools_dict:\n\t\tcost_il_rows.append(inputs_dict[id1])\n\t\tcost_il_cols.append(pools_dict[id2])\n\t\tcost_il_vals.append(val/costs_scaling)\n\n\tif id1 in pools_dict and id2 in outputs_dict:\n\t\tcost_lj_rows.append(pools_dict[id1])\n\t\tcost_lj_cols.append(outputs_dict[id2])\n\t\tcost_lj_vals.append(val/costs_scaling)\n\n\n# next, extract the edges\narcs_ij = []\narcs_il = []\narcs_lj = []\n\nfor line in lines_edges:\n\tids = line.rstrip().split('.')\n\tif num_copies > 10:\n\t\tid1 = ids[0][-6:]\n\t\tid2 = ids[1][:6]\n\telse:\n\t\tid1 = ids[0][-5:]\n\t\tid2 = ids[1][:5]\n\n\tif id1 in inputs_dict and id2 in outputs_dict:\n\t\tarcs_ij.append((inputs_dict[id1],outputs_dict[id2]))\n\n\tif id1 in inputs_dict and id2 in pools_dict:\n\t\tarcs_il.append((inputs_dict[id1],pools_dict[id2]))\n\n\tif id1 in pools_dict and id2 in outputs_dict:\n\t\tarcs_lj.append((pools_dict[id1],outputs_dict[id2]))\n\t\t\n\n# next, extract the nominal input qualities\n# ignore limits on output qualities\nspecs_in_nominal = [[0.0 for k in range(num_specs)] for i in range(num_inputs)]\n\nfor line in lines_specs:\n\tif num_specs > 1:\n\t\tattr = int(line.rstrip().split('.')[0][-1])\n\telse:\n\t\tattr = 0\n\n\tif (num_specs == 1) or (attr > 0):\n\t\tif num_copies > 10:\n\t\t\tid = line.rstrip().split('.')[1][:6]\n\t\t\tval = float(line[14:])\n\t\telse:\n\t\t\tid = line.rstrip().split('.')[1][:5]\n\t\t\tval = float(line[13:])\n\telse:\n\t\tif num_copies > 10:\n\t\t\tid = line.rstrip().split('.')[1][:6]\n\t\t\tval = float(line[16:])\n\t\telse:\n\t\t\tid = line.rstrip().split('.')[1][:5]\n\t\t\tval = float(line[15:])\n\n\tspecs_in_nominal[inputs_dict[id]][attr] = val\n\n\n# define aliases for problem dimensions\nnum_i = num_inputs\nnum_l = num_pools\nnum_j = num_outputs\nnum_k = num_specs\n\n\n# generate auxiliary sets for the model\ninputs_to_pool = [[t[0] for t in arcs_il if t[1] == l] for l in range(num_l)]  # which inputs are connected to each pool?\ninputs_to_output = [[t[0] for t in arcs_ij if t[1] == j] for j in range(num_j)]  # which inputs are directly connected to each output?\noutputs_from_input = [[t[1] for t in arcs_ij if t[0] == i] for i in range(num_i)]  # which outputs are directly connected to each input?\noutputs_from_pool = [[t[1] for t in arcs_lj if t[0] == l] for l in range(num_l)]  # which outputs are connected to each pool?\npools_from_input = [[t[1] for t in arcs_il if t[0] == i] for i in range(num_i)] # which pools are connected to each input?\npools_to_output = [[t[0] for t in arcs_lj if t[1] == j] for j in range(num_j)]  # which pools are directly connected to each output?\ninputs_pools_to_output = [[(i,t[0]) for t in arcs_lj if t[1] == j for i in inputs_to_pool[t[0]]] for j in range(num_j)]  # which input-pool pairs connected to each output?\narcs_ilj = [(i,l,j) for l in range(num_l) for i in inputs_to_pool[l] for j in outputs_from_pool[l]]  # list of arcs from inputs to pools to outputs\n\noutputs_reachable_from_input = [list(set([t[1] for t in arcs_ij if t[0] == i] + flatten([[t[1] for t in arcs_lj if t[0] == l if i in inputs_to_pool[l]] for l in range(num_l)]))) for i in range(num_i)]  # which outputs are reachable starting from each input?\ninputs_reachable_from_output = [[i for i in range(num_i) if j in outputs_reachable_from_input[i]] for j in range(num_j)]  # which inputs are reachable starting from each output reversing arc directions?\n\n\n# randomly generate target qualities at outputs\nspecs_out_min = [[0.0 for k in range(num_specs)] for j in range(num_outputs)]\nspecs_out_max = [[0.0 for k in range(num_specs)] for j in range(num_outputs)]\n\nfor j in range(num_j):\n\tfor k in range(num_k):\n\t\tspec_out_min = np.amin([specs_in_nominal[i][k] for i in inputs_reachable_from_output[j]])\n\t\tspec_out_max = np.amax([specs_in_nominal[i][k] for i in inputs_reachable_from_output[j]])\n\n\t\tstart_frac = 0.2 + 0.2*random.random()\n\t\tstop_frac = 0.6 + 0.2*random.random()\n\n\t\tspecs_out_min[j][k] = spec_out_min + start_frac*(spec_out_max - spec_out_min)\n\t\tspecs_out_max[j][k] = spec_out_min + stop_frac*(spec_out_max - spec_out_min)\n\n\n\nfor inst in range(numInstances):\n\n\toutput_file = instances_path + \"pooling_c15_e150_q1_\" + str(inst+1) + \".jl\"\n\tjson_file = instances_path + \"pooling_c15_e150_q1_\" + str(inst+1) + \".json\"\n\n\ttheta_specs = np.random.rand(num_inputs, num_specs)\n\tspecs_in = [[0.0 for k in range(num_specs)] for i in range(num_inputs)]\n\tfor i in range(num_inputs):\n\t\tfor k in range(num_specs):\n\t\t\tspecs_in[i][k] = (1 - pert_frac + 2*pert_frac*theta_specs[i,k])*specs_in_nominal[i][k]\n\n\n\t# define auxiliary parameters for the quality constraints\n\tgamma_low = [[[specs_in[i][k]-specs_out_min[j][k] for k in range(num_specs)] for j in range(num_outputs)] for i in range(num_inputs)]\n\tgamma_up = [[[specs_in[i][k]-specs_out_max[j][k] for k in range(num_specs)] for j in range(num_outputs)] for i in range(num_inputs)]\n\n\n\t# Write to file. Convert to one indexing before creating Julia input\n\tf = open(output_file, \"w\")\n\tf.write(\"using SparseArrays \\n\\n\")\n\n\tf.write(\"num_i = \" + str(num_i) + \"\\n\")\n\tf.write(\"num_l = \" + str(num_l) + \"\\n\")\n\tf.write(\"num_j = \" + str(num_j) + \"\\n\")\n\tf.write(\"num_k = \" + str(num_k) + \"\\n\\n\")\n\n\tf.write(\"arcs_ij = \" + str([(i+1,j+1) for (i,j) in arcs_ij]) + \"\\n\")\n\tf.write(\"arcs_il = \" + str([(i+1,l+1) for (i,l) in arcs_il]) + \"\\n\")\n\tf.write(\"arcs_lj = \" + str([(l+1,j+1) for (l,j) in arcs_lj]) + \"\\n\")\n\tf.write(\"arcs_ilj = \" + str([(i+1,l+1,j+1) for (i,l,j) in arcs_ilj]) + \"\\n\\n\")\n\n\tf.write(\"inputs_to_pool = [Int64[] for l=1:num_l] \\n\")\n\tfor l in range(num_l):\n\t\tf.write(\"inputs_to_pool[\" + str(l+1) + \"] = \" + str([i+1 for i in inputs_to_pool[l]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"inputs_to_output = [Int64[] for j=1:num_j] \\n\")\n\tfor j in range(num_j):\n\t\tf.write(\"inputs_to_output[\" + str(j+1) + \"] = \" + str([i+1 for i in inputs_to_output[j]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"pools_to_output = [Int64[] for j=1:num_j] \\n\")\n\tfor j in range(num_j):\n\t\tf.write(\"pools_to_output[\" + str(j+1) + \"] = \" + str([l+1 for l in pools_to_output[j]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"pools_from_input = [Int64[] for i=1:num_i] \\n\")\n\tfor i in range(num_i):\n\t\tf.write(\"pools_from_input[\" + str(i+1) + \"] = \" + str([l+1 for l in pools_from_input[i]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"outputs_from_pool = [Int64[] for l=1:num_l] \\n\")\n\tfor l in range(num_l):\n\t\tf.write(\"outputs_from_pool[\" + str(l+1) + \"] = \" + str([j+1 for j in outputs_from_pool[l]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"outputs_from_input = [Int64[] for i=1:num_i] \\n\")\n\tfor i in range(num_i):\n\t\tf.write(\"outputs_from_input[\" + str(i+1) + \"] = \" + str([j+1 for j in outputs_from_input[i]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\tf.write(\"inputs_pools_to_output = [Tuple{Int64, Int64}[] for j=1:num_j] \\n\")\n\tfor j in range(num_j):\n\t\tf.write(\"inputs_pools_to_output[\" + str(j+1) + \"] = \" + str([(i+1,l+1) for (i,l) in inputs_pools_to_output[j]]) + \"\\n\")\n\tf.write(\"\\n\")\n\n\n\tf.write(\"cap_i = \" + str(cap_i) + \"\\n\")\n\tf.write(\"cap_l = \" + str(cap_l) + \"\\n\")\n\tf.write(\"cap_j = \" + str(cap_j) + \"\\n\\n\")\n\n\tf.write(\"cost_ij_rows = \" + str([i+1 for i in cost_ij_rows]) + \"\\n\")\n\tf.write(\"cost_ij_cols = \" + str([j+1 for j in cost_ij_cols]) + \"\\n\")\n\tf.write(\"cost_ij_vals = \" + str(cost_ij_vals) + \"\\n\")\n\tf.write(\"cost_ij = sparse(cost_ij_rows, cost_ij_cols, cost_ij_vals) \\n\\n\")\n\n\tf.write(\"cost_il_rows = \" + str([i+1 for i in cost_il_rows]) + \"\\n\")\n\tf.write(\"cost_il_cols = \" + str([l+1 for l in cost_il_cols]) + \"\\n\")\n\tf.write(\"cost_il_vals = \" + str(cost_il_vals) + \"\\n\")\n\tf.write(\"cost_il = sparse(cost_il_rows, cost_il_cols, cost_il_vals) \\n\\n\")\n\n\tf.write(\"cost_lj_rows = \" + str([l+1 for l in cost_lj_rows]) + \"\\n\")\n\tf.write(\"cost_lj_cols = \" + str([j+1 for j in cost_lj_cols]) + \"\\n\")\n\tf.write(\"cost_lj_vals = \" + str(cost_lj_vals) + \"\\n\")\n\tf.write(\"cost_lj = sparse(cost_lj_rows, cost_lj_cols, cost_lj_vals) \\n\\n\")\n\n\tf.write(\"gamma_low = \" + str(gamma_low) + \"\\n\\n\")\n\tf.write(\"gamma_up = \" + str(gamma_up) + \"\\n\\n\\n\\n\")\n\n\n\tf.write(\"# ----- Variables ----- #\\n\")\n\tf.write(\"@variables(m, begin \\n\")\n\tf.write(\"\t0 <= w[(i,l,j) in arcs_ilj] <= min(cap_i[i],cap_l[l],cap_j[j]) \\n\")\n\tf.write(\"\t0 <= x_il[(i,l) in arcs_il] <= min(cap_i[i],cap_l[l]) \\n\")\n\tf.write(\"\t0 <= x_lj[(l,j) in arcs_lj] <= min(cap_l[l],cap_j[j]) \\n\")\n\tf.write(\"\t0 <= x_ij[(i,j) in arcs_ij] <= min(cap_i[i],cap_j[j]) \\n\")\n\tf.write(\"\t0 <= q[arcs_il] <= 1 \\n\")\n\tf.write(\"end) \\n\\n\\n\")\n\n\n\tf.write(\"# ----- Constraints ----- #\\n\")\n\tf.write(\"@constraints(m, begin \\n\")\n\tf.write(\"\tcapi[i=1:num_i], sum(x_ij[(i,j)] for j in outputs_from_input[i]) + sum(x_il[(i,l)] for l in pools_from_input[i]) <= cap_i[i] \\n\\n\")\n\tf.write(\"\tcapl[l=1:num_l], sum(x_lj[(l,j)] for j in outputs_from_pool[l]) <= cap_l[l] \\n\\n\")\n\tf.write(\"\tcapj[j=1:num_j], sum(x_ij[(i,j)] for i in inputs_to_output[j]) + sum(x_lj[(l,j)] for l in pools_to_output[j]) <= cap_j[j] \\n\\n\")\n\tf.write(\"\tsumfrac[l=1:num_l], sum(q[(i,l)] for i in inputs_to_pool[l]) == 1 \\n\\n\")\n\tf.write(\"\teq1[(i,l) in arcs_il], x_il[(i,l)] == sum(w[(i,l,j)] for j in outputs_from_pool[l]) \\n\\n\")\n\tf.write(\"    specdown[k=1:num_k, j=1:num_j], sum(gamma_low[i][j][k]*w[(i,l,j)] for (i,l) in inputs_pools_to_output[j]) + sum(gamma_low[i][j][k]*x_ij[(i,j)] for i in inputs_to_output[j]) >= 0 \\n\\n\")\n\tf.write(\"\tspecup[k=1:num_k, j=1:num_j], sum(gamma_up[i][j][k]*w[(i,l,j)] for (i,l) in inputs_pools_to_output[j]) + sum(gamma_up[i][j][k]*x_ij[(i,j)] for i in inputs_to_output[j]) <= 0 \\n\\n\")\n\tf.write(\"\trlt1[(l,j) in arcs_lj], sum(w[(i,l,j)] for i in inputs_to_pool[l]) == x_lj[(l,j)] \\n\\n\")\n\tf.write(\"\trlt2[(i,l) in arcs_il], sum(w[(i,l,j)] for j in outputs_from_pool[l]) <= cap_l[l]*q[(i,l)] \\n\\n\")\n\tf.write(\"end) \\n\\n\\n\")\n\n\tf.write(\"@NLconstraint(m, blin[(i,l,j) in arcs_ilj], w[(i,l,j)] == q[(i,l)]*x_lj[(l,j)]) \\n\\n\\n\")\n\n\n\tf.write(\"# ----- Objective ----- #\\n\")\n\tf.write(\"@objective(m, Min, sum(cost_ij[i,j]*x_ij[(i,j)] for (i,j) in arcs_ij) + sum(cost_il[i,l]*x_il[(i,l)] for (i,l) in arcs_il) + sum(cost_lj[l,j]*x_lj[(l,j)] for (l,j) in arcs_lj) ) \\n\")\n\t\n\t\t\n\tf.close()\n\n\n\tjson_dict = {}\n\tjson_dict[\"num_inputs\"] = num_i\n\tjson_dict[\"num_pools\"] = num_l\n\tjson_dict[\"num_outputs\"] = num_j\n\tjson_dict[\"num_qualities\"] = num_k\n\n\tjson_dict[\"num_copies\"] = num_copies\n\tjson_dict[\"num_added_edges\"] = num_added_edges\n\tjson_dict[\"pert_frac\"] = pert_frac\n\tjson_dict[\"capacities_scaling\"] = capacities_scaling\n\tjson_dict[\"costs_scaling\"] = costs_scaling\n\n\tjson_dict[\"arcs_inputs_outputs\"] = [(i+1,j+1) for (i,j) in arcs_ij]\n\tjson_dict[\"arcs_inputs_pools\"] = [(i+1,l+1) for (i,l) in arcs_il]\n\tjson_dict[\"arcs_pools_outputs\"] = [(l+1,j+1) for (l,j) in arcs_lj]\n\tjson_dict[\"arcs_inputs_pools_outputs\"] = [(i+1,l+1,j+1) for (i,l,j) in arcs_ilj]\n\n\tjson_dict[\"capacities_inputs\"] = cap_i\n\tjson_dict[\"capacities_pools\"] = cap_l\n\tjson_dict[\"capacities_outputs\"] = cap_j\n\n\tjson_dict[\"cost_ij_rows\"] = [i+1 for i in cost_ij_rows]\n\tjson_dict[\"cost_ij_cols\"] = [i+1 for i in cost_ij_rows]\n\tjson_dict[\"cost_ij_vals\"] = cost_ij_vals\n\tjson_dict[\"cost_il_rows\"] = [i+1 for i in cost_il_rows]\n\tjson_dict[\"cost_il_cols\"] = [i+1 for i in cost_il_rows]\n\tjson_dict[\"cost_il_vals\"] = cost_il_vals\n\tjson_dict[\"cost_lj_rows\"] = [i+1 for i in cost_lj_rows]\n\tjson_dict[\"cost_lj_cols\"] = [i+1 for i in cost_lj_rows]\n\tjson_dict[\"cost_lj_vals\"] = cost_lj_vals\n\n\tjson_dict[\"specs_inputs_nominal\"] = specs_in_nominal\n\tjson_dict[\"theta_specs_inputs\"] = theta_specs.tolist()\n\tjson_dict[\"specs_inputs\"] = specs_in\n\tjson_dict[\"specs_outputs_min\"] = spec_out_min\n\tjson_dict[\"specs_outputs_max\"] = spec_out_max\n\tjson_dict[\"gamma_low\"] = gamma_low\n\tjson_dict[\"gamma_up\"] = gamma_up\n\n\n\twith open(json_file, 'w', encoding='utf-8') as outF:\n\t\tjson.dump(json_dict, outF, ensure_ascii=False, indent=4)\n"
  },
  {
    "path": "examples/random_QCQPs/pooling/haverly_15_addedges_150_attr_0_1.json",
    "content": "{\n    \"out\": \"test_instances/haverly_15_addedges_150_attr_0_1\",\n    \"seed\": 0,\n    \"haverly\": 15,\n    \"scalehaverlys\": \"random\",\n    \"scalequalities\": null,\n    \"density\": null,\n    \"addedges\": 150,\n    \"attributes\": 0,\n    \"nodes\": 90,\n    \"edges\": 240,\n    \"inputs\": 45,\n    \"pools\": 15,\n    \"outputs\": 30,\n    \"components\": 1,\n    \"density_real\": 0.09696969696969697,\n    \"input->pool\": 71,\n    \"pool->output\": 53,\n    \"input->output\": 116,\n    \"min_cost\": -15,\n    \"max_cost\": 16,\n    \"graph\": {\n        \"directed\": true,\n        \"multigraph\": false,\n        \"graph\": {\n            \"name\": \"compose( ,  )\",\n            \"attributes\": [\n                \"k1\"\n            ]\n        },\n        \"nodes\": [\n            {\n                \"type\": \"output\",\n                \"C\": 200,\n                \"overbeta\": {\n                    \"k1\": 0.8407370060109167\n                },\n                \"id\": \"h14_j2\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 800,\n                \"lambda\": {\n                    \"k1\": 1.6814740120218334\n                },\n                \"id\": \"h14_i1\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 800,\n                \"lambda\": {\n                    \"k1\": 0.5604913373406112\n                },\n                \"id\": \"h14_i2\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 800,\n                \"lambda\": {\n                    \"k1\": 1.1209826746812224\n                },\n                \"id\": \"h14_i3\"\n            },\n            {\n                \"type\": \"output\",\n                \"C\": 600,\n                \"overbeta\": {\n                    \"k1\": 1.401228343351528\n                },\n                \"id\": \"h14_j1\"\n            },\n            {\n                \"type\": \"pool\",\n                \"C\": 800,\n                \"id\": \"h14_l1\"\n            },\n            {\n                \"type\": \"output\",\n                \"C\": 200,\n                \"overbeta\": {\n                    \"k1\": 1.1611932187032805\n                },\n                \"id\": \"h13_j2\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 300,\n                \"lambda\": {\n                    \"k1\": 2.322386437406561\n                },\n                \"id\": \"h13_i1\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 300,\n                \"lambda\": {\n                    \"k1\": 0.7741288124688537\n                },\n                \"id\": \"h13_i2\"\n            },\n            {\n                \"type\": \"input\",\n                \"C\": 300,\n                \"lambda\": {\n                    \"k1\": 1.5482576249377074\n                },\n     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12.90303962411355,\n                \"source\": 80,\n                \"target\": 70\n            },\n            {\n                \"cost\": 11.237157569998345,\n                \"source\": 80,\n                \"target\": 41\n            },\n            {\n                \"cost\": -6.0155549354488205,\n                \"source\": 80,\n                \"target\": 48\n            },\n            {\n                \"cost\": -5,\n                \"source\": 81,\n                \"target\": 78\n            },\n            {\n                \"cost\": 1,\n                \"source\": 81,\n                \"target\": 82\n            },\n            {\n                \"cost\": 6.188449949996006,\n                \"source\": 81,\n                \"target\": 29\n            },\n            {\n                \"cost\": -15,\n                \"source\": 83,\n                \"target\": 78\n            },\n            {\n                \"cost\": -9,\n                \"source\": 83,\n                \"target\": 82\n            },\n            {\n                \"cost\": -4.6847341042125805,\n                \"source\": 83,\n                \"target\": 88\n            },\n            {\n                \"cost\": -13.597743896166017,\n                \"source\": 83,\n                \"target\": 76\n            },\n            {\n                \"cost\": 6,\n                \"source\": 85,\n                \"target\": 89\n            },\n            {\n                \"cost\": -6.924738377849259,\n                \"source\": 85,\n                \"target\": 48\n            },\n            {\n                \"cost\": -12.172305431262998,\n                \"source\": 85,\n                \"target\": 59\n            },\n            {\n                \"cost\": -8.700742573447567,\n                \"source\": 85,\n                \"target\": 60\n            },\n            {\n                \"cost\": 11.116266917345655,\n                \"source\": 85,\n                \"target\": 22\n            },\n            {\n                \"cost\": 15.387583922629606,\n                \"source\": 85,\n                \"target\": 77\n            },\n            {\n                \"cost\": -11.959628178119313,\n                \"source\": 85,\n                \"target\": 88\n            },\n            {\n                \"cost\": 16,\n                \"source\": 86,\n                \"target\": 89\n            },\n            {\n                \"cost\": -9.432807679711775,\n                \"source\": 86,\n                \"target\": 5\n            },\n            {\n                \"cost\": -5,\n                \"source\": 87,\n                \"target\": 84\n            },\n            {\n                \"cost\": 1,\n                \"source\": 87,\n                \"target\": 88\n            },\n            {\n                \"cost\": -15,\n                \"source\": 89,\n                \"target\": 84\n            },\n            {\n                \"cost\": -9,\n                \"source\": 89,\n                \"target\": 88\n            },\n            {\n                \"cost\": -3.8118950483310883,\n                \"source\": 89,\n                \"target\": 48\n            }\n        ]\n    }\n}"
  },
  {
    "path": "examples/random_QCQPs/qcqp/generate_qcqp_instances.py",
    "content": "\"\"\"\n// @brief  Script to generate the nonconvex QCQP instances with both bilinear and univariate quadratics\n//\t\t   Input arguments: numVariables, numInstances\n// Reference: \"Learning to Accelerate the Global Optimization of Quadratically-Constrained \n\t\t\t   Quadratic Programs\" by R. Kannan, H. Nagarajan, and D. Deka \n\t\t\t   (Link: https://arxiv.org/abs/2301.00306)\n// Contributor: @rohitkannan \n\"\"\"\n\nimport random\nimport json\nimport numpy as np\nimport argparse\nimport os\n\nparser = argparse.ArgumentParser()\nparser.add_argument('--numVariables', type=int, required=True)\nparser.add_argument('--numInstances', type=int, required=True)\nargs = parser.parse_args()\n\nnumVariables = int(args.numVariables)\nnumInstances = int(args.numInstances)\n\ninstances_path = \"./N_\" + str(numVariables) + \"/\"\nos.makedirs(instances_path)\n\n# random seed for instances\nif numVariables == 10:\n\trandom.seed(3090)\nelif numVariables == 20:\n\trandom.seed(1168) \nelif numVariables == 50:\n\trandom.seed(9119) \n\nnp.random.seed(round(random.random()*10000)) \n\n\nstart = 1  # starting instance number\n\nnumQuadraticConstraints = numVariables  # number of constraints with bilinear, quadratic and linear terms\nnumLinearConstraints = round(numVariables/5)  # number of linear equality constraints\n\nconstraint_sparsity = 1.0  # (actually opposite of sparsity) fraction of possible bilinear, quadratic and linear terms occurring in each constraint\nmaxNumBilinearTerms = round(numVariables*(numVariables-1)/2)\nnumBilinearTerms = min(5*numVariables,maxNumBilinearTerms)  # number of bilinear terms in the formulation\n\nfrac_quad_terms = 0.25  # anticipated fraction of possible quadratic terms in the formulation\nnumQuadraticTerms = round(frac_quad_terms*numVariables)\n\nfrac_quad_con_pert = 0.2  # fraction of quadratic constraints perturbed\nnumPertFactors = 3  # number of perturbation factors per perturbed quadratic constraint\npert_frac = 0.5  # perturbation fraction around nominal instance\n\n\n# to sort list of lists\ndef Sort(sub_li):\n    return(sorted(sub_li, key = lambda x: (x[0],x[1])))    \n\n\n# GENERATE COMMON BILINEAR TERMS FOR ALL INSTANCES\npossible_bilinear_terms = [[i,j] for i in range(numVariables) for j in range(i+1,numVariables)]\nrandom.shuffle(possible_bilinear_terms)\nbilinear_terms = Sort(possible_bilinear_terms[:numBilinearTerms])\n\n\n# GENERATE COMMON QUADRATIC TERMS FOR ALL INSTANCES\npossible_quadratic_terms = list(range(numVariables))\nrandom.shuffle(possible_quadratic_terms)\nquadratic_terms = possible_quadratic_terms[:numQuadraticTerms]\n\n\n# GENERATE BASE COEFFICIENTS\nq_bilinear = []  # bilinear coefficients\nq_bilinear_ind = []  # bilinear coefficient indices\nq_quadratic = []  # quadratic coefficients\nq_quadratic_ind = []  # quadratic coefficient indices\n\n# OBJECTIVE COEFFICIENTS\nq_bilinear.append([2*random.random()-1 for j in range(numBilinearTerms)])  # all bilinear terms participate in the objective (sparsity not applied here)\nq_bilinear_ind.append(list(np.arange(numBilinearTerms)))\nq_quadratic.append([2*random.random()-1 for j in range(numQuadraticTerms)])  # all quadratic terms participate in the objective (sparsity not applied here)\nq_quadratic_ind.append(list(np.arange(numQuadraticTerms)))\n\n# CONSTRAINT COEFFICIENTS\nnumQuadNonZero = round(numBilinearTerms*constraint_sparsity)\nfor i in range(numQuadraticConstraints):\n\tq_bilinear.append([2*random.random()-1 for j in range(numQuadNonZero)])\n\ttmp_ind = list(np.random.choice(numBilinearTerms, numQuadNonZero, replace=False))\n\ttmp_ind.sort()\n\tq_bilinear_ind.append(tmp_ind)\n\nnumQuadNonZero2 = round(numQuadraticTerms*constraint_sparsity)\nfor i in range(numQuadraticConstraints):\n\tq_quadratic.append([2*random.random()-1 for j in range(numQuadNonZero2)])\n\ttmp_ind = list(np.random.choice(numQuadraticTerms, numQuadNonZero2, replace=False))\n\ttmp_ind.sort()\n\tq_quadratic_ind.append(tmp_ind)\n\n\nq_linear = []  # linear coefficients\nq_linear_ind = []  # linear coefficient indices\n\n# OBJECTIVE COEFFICIENTS\nq_linear.append([2*random.random()-1 for j in range(numVariables)])  # all linear terms participate in the objective (sparsity not applied here)\nq_linear_ind.append(list(np.arange(numVariables)))\n\n# CONSTRAINT COEFFICIENTS\nnumLinNonZero = round(numVariables*constraint_sparsity)\nfor i in range(numQuadraticConstraints+numLinearConstraints):\n\tif i < numQuadraticConstraints:  # only a fraction of linear terms appear in quadratic constraints\n\t\tq_linear.append([2*random.random()-1 for j in range(numLinNonZero)])\n\t\ttmp_ind = list(np.random.choice(numVariables, numLinNonZero, replace=False))\n\telse:  # all linear terms appear in linear equality constraints\n\t\tq_linear.append([2*random.random()-1 for j in range(numVariables)])\n\t\ttmp_ind = list(np.arange(numVariables))\n\ttmp_ind.sort()\n\tq_linear_ind.append(tmp_ind)\n\n\n# GENERATE BASE RHS COEFFICIENTS\nquadratic_scaling = 100\nrhs_quadratic = [quadratic_scaling*random.random() for i in range(numQuadraticConstraints)]\n\nlinear_scaling = 1\nrhs_linear = [linear_scaling*(2*random.random()-1) for i in range(numLinearConstraints)]\n\n\n# RE-SCALE PROBLEM SO THAT CONSTRAINTS RHS ARE EQUAL TO ONE\nfor i in range(numQuadraticConstraints):\n\tfor j in range(numQuadNonZero):\n\t\tq_bilinear[i+1][j] /= rhs_quadratic[i]\n\tfor j in range(numQuadNonZero2):\n\t\tq_quadratic[i+1][j] /= rhs_quadratic[i]\n\tfor j in range(numLinNonZero):\n\t\tq_linear[i+1][j] /= rhs_quadratic[i]\n\n\nfor i in range(numLinearConstraints):\n\tfor j in range(numVariables):\n\t\tq_linear[i+1+numQuadraticConstraints][j] /= rhs_linear[i]\n\n\n# CONSTRUCT PERTURBATION FACTORS FOR THE OBJECTIVE AND QUADRATIC CONSTRAINT COEFFICIENTS\nq_bilinear_obj_factors = np.zeros((numPertFactors,numBilinearTerms))\nq_quadratic_obj_factors = np.zeros((numPertFactors,numQuadraticTerms))\nq_linear_obj_factors = np.zeros((numPertFactors,numVariables))\nfor j in range(numBilinearTerms):\n\tfor k in range(numPertFactors):\n\t\tq_bilinear_obj_factors[k,j] = pert_frac*random.random()*q_bilinear[0][j]\nfor j in range(numQuadraticTerms):\n\tfor k in range(numPertFactors):\n\t\tq_quadratic_obj_factors[k,j] = pert_frac*random.random()*q_quadratic[0][j]\nfor j in range(numVariables):\n\tfor k in range(numPertFactors):\n\t\tq_linear_obj_factors[k,j] = pert_frac*random.random()*q_linear[0][j]\n\nnumQuadConPert = round(numQuadraticConstraints*frac_quad_con_pert)\nq_bilinear_con_factors = np.zeros((numPertFactors,numQuadConPert,numQuadNonZero))\nq_quadratic_con_factors = np.zeros((numPertFactors,numQuadConPert,numQuadNonZero2))\nq_linear_con_factors = np.zeros((numPertFactors,numQuadConPert,numLinNonZero))\nfor i in range(numQuadConPert):\n\tfor j in range(numQuadNonZero):\n\t\tfor k in range(numPertFactors):\n\t\t\tq_bilinear_con_factors[k,i,j] = pert_frac*random.random()*q_bilinear[i+1][j]\n\tfor j in range(numQuadNonZero2):\n\t\tfor k in range(numPertFactors):\n\t\t\tq_quadratic_con_factors[k,i,j] = pert_frac*random.random()*q_quadratic[i+1][j]\n\tfor j in range(numLinNonZero):\n\t\tfor k in range(numPertFactors):\n\t\t\tq_linear_con_factors[k,i,j] = pert_frac*random.random()*q_linear[i+1][j]\n\n\n\n# GENERATE PERTURBED INSTANCES\nfor inst in range(start,numInstances+start):\n\toutput_file = instances_path + \"qcqp_v\" + str(numVariables) + \"_b\" + str(numBilinearTerms) + \"_q\" + str(numQuadraticTerms) + \"_s\" + str(round(constraint_sparsity*100)) + \"_\" + str(inst) + \".jl\"\n\tjson_file = instances_path + \"qcqp_v\" + str(numVariables) + \"_b\" + str(numBilinearTerms) + \"_q\" + str(numQuadraticTerms) + \"_s\" + str(round(constraint_sparsity*100)) + \"_\" + str(inst) + \".json\"\n\n\tjson_dict = {}\n\tjson_dict[\"numVariables\"] = numVariables\n\tjson_dict[\"numQuadraticConstraints\"] = numQuadraticConstraints\n\tjson_dict[\"numLinearConstraints\"] = numLinearConstraints\n\tjson_dict[\"constraint_sparsity\"] = constraint_sparsity\n\n\tjson_dict[\"numBilinearTerms\"] = numBilinearTerms\n\tjson_dict[\"bilinear_terms\"] = bilinear_terms\n\n\tjson_dict[\"numQuadraticTerms\"] = numQuadraticTerms\n\tjson_dict[\"quadratic_terms\"] = quadratic_terms\n\n\tjson_dict[\"pert_frac\"] = pert_frac\n\tjson_dict[\"numPertFactors\"] = numPertFactors\n\tjson_dict[\"numQuadConPert\"] = numQuadConPert\n\tjson_dict[\"bilinear_obj_factors\"] = q_bilinear_obj_factors.tolist()\n\tjson_dict[\"quadratic_obj_factors\"] = q_quadratic_obj_factors.tolist()\n\tjson_dict[\"linear_obj_factors\"] = q_linear_obj_factors.tolist()\n\tjson_dict[\"bilinear_con_factors\"] = q_bilinear_con_factors.tolist()\n\tjson_dict[\"quadratic_con_factors\"] = q_quadratic_con_factors.tolist()\n\tjson_dict[\"linear_con_factors\"] = q_linear_con_factors.tolist()\n\n\n# GENERATE PERTURBATION FACTORS\n\ttheta = 2*(np.random.rand(numPertFactors,numQuadConPert+1) - 0.5)\n\n\tjson_dict[\"theta\"] = theta.tolist()\n\n# STORE SPARSITY PATTERN AND INITIALIZE DATA\n\tf = open(output_file, \"w\")\n\n\tf.write(\"# ----- Bilinear Terms ----- #\\n\")\n\tf.write(\"numBilinearTerms = \" + str(numBilinearTerms) + \"\\n\")\n\tf.write(\"bilinear_terms = [\")\n\tcount_bilinear = 0\n\tfor term in bilinear_terms:\n\t\tf.write(\"[\" + str(term[0]+1) + \",\" + str(term[1]+1) + \"]\")\n\t\tcount_bilinear += 1\n\t\tif count_bilinear < numBilinearTerms:\n\t\t\tf.write(\", \")\n\t\telse:\n\t\t\tf.write(\"] \\n\\n\")\n\n\t\n\tf.write(\"# ----- Quadratic Terms ----- #\\n\")\n\tf.write(\"numQuadraticTerms = \" + str(numQuadraticTerms) + \"\\n\")\n\tf.write(\"quadratic_terms = \" + str([term+1 for term in quadratic_terms]) + \"\\n\\n\")\n\t\n\tf.write(\"numQuadNonZero = \" + str(numQuadNonZero) + \"\\n\")\n\tf.write(\"numQuadNonZero2 = \" + str(numQuadNonZero2) + \"\\n\")\n\tf.write(\"numLinNonZero = \" + str(numLinNonZero) + \"\\n\\n\")\n\n\tf.write(\"# ----- Data Matrices ----- #\\n\")\n\tf.write(\"bilinear_obj_coeffs = zeros(Float64,\" + str(numBilinearTerms) + \") \\n\")\n\tf.write(\"bilinear_con_coeffs = zeros(Float64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero) + \") \\n\")\n\tf.write(\"bilinear_con_coeff_indices = zeros(Int64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero) + \") \\n\")\n\tf.write(\"quadratic_obj_coeffs = zeros(Float64,\" + str(numQuadraticTerms) + \") \\n\")\n\tf.write(\"quadratic_con_coeffs = zeros(Float64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero2) + \") \\n\")\n\tf.write(\"quadratic_con_coeff_indices = zeros(Int64,\" + str(numQuadraticConstraints) + \",\" + str(numQuadNonZero2) + \") \\n\")\n\tf.write(\"linear_obj_coeffs = zeros(Float64,\" + str(numVariables) + \") \\n\")\n\tf.write(\"linear_con_coeffs_1 = zeros(Float64,\" + str(numQuadraticConstraints) + \",\" + str(numLinNonZero) + \") \\n\")\n\tf.write(\"linear_con_coeff_indices_1 = zeros(Int64,\" + str(numQuadraticConstraints) + \",\" + str(numLinNonZero) + \") \\n\")\n\tf.write(\"linear_con_coeffs_2 = zeros(Float64,\" + str(numLinearConstraints) + \",\" + str(numVariables) + \") \\n\")\n\tf.write(\"linear_con_coeff_indices_2 = zeros(Int64,\" + str(numLinearConstraints) + \",\" + str(numVariables) + \") \\n\\n\")\n\n\tf.write(\"# ----- Variables ----- #\\n\")\n\tf.write(\"@variable(m, 0 <= x[1:\" + str(numVariables) + \"] <= 1)\\n\")\n\tf.write(\"@variable(m, 0 <= w[1:\" + str(numBilinearTerms) + \"] <= 1)\\n\")\n\tf.write(\"@variable(m, 0 <= v[1:\" + str(numQuadraticTerms) + \"] <= 1)\\n\\n\")\n\n\tf.write(\"# ----- Bilinear Equations ----- #\\n\")\n\tf.write(\"@NLconstraint(m, [i=1:\" + str(numBilinearTerms) + \"], w[i] == x[bilinear_terms[i][1]]*x[bilinear_terms[i][2]])\\n\\n\\n\")\n\n\tf.write(\"# ----- Quadratic Equations ----- #\\n\")\n\tf.write(\"@NLconstraint(m, [i=1:\" + str(numQuadraticTerms) + \"], v[i] == (x[quadratic_terms[i]])^2)\\n\\n\\n\")\n\n\tjson_dict[\"x_lower\"] = [0 for i in range(numVariables)]\n\tjson_dict[\"x_upper\"] = [1 for i in range(numVariables)]\n\n\n# OBJECTIVE\n\t# tmp variables for storing generated data\n\tQ = [0.]*numBilinearTerms\n\tR = [0.]*numQuadraticTerms\n\tq = [0.]*numVariables\n\n\tcount_quad_con = 0\n\tcount_lin_con = 0\n\tfor i in range(numVariables):\n\t\tq[i] = q_linear[0][i]\n\t\tfor k in range(numPertFactors):\n\t\t\tq[i] += q_linear_obj_factors[k,i]*theta[k,0]\n\tfor i in range(numBilinearTerms):\n\t\tQ[i] = q_bilinear[0][i]\n\t\tfor k in range(numPertFactors):\n\t\t\tQ[i] += q_bilinear_obj_factors[k,i]*theta[k,0]\n\tfor i in range(numQuadraticTerms):\n\t\tR[i] = q_quadratic[0][i]\n\t\tfor k in range(numPertFactors):\n\t\t\tR[i] += q_quadratic_obj_factors[k,i]*theta[k,0]\n\n\tjson_dict[\"obj_bilinear_coeffs\"] = Q\n\tjson_dict[\"obj_quadratic_coeffs\"] = R\n\tjson_dict[\"obj_linear_coeffs\"] = q\n\n\tf.write(\"# ----- Objective ----- #\\n\")\n\tf.write(\"bilinear_obj_coeffs = \" + str(Q) + \"\\n\")\n\tf.write(\"quadratic_obj_coeffs = \" + str(R) + \"\\n\")\n\tf.write(\"linear_obj_coeffs = \" + str(q) + \"\\n\")\n\n\tf.write(\"\\n\")\n\tf.write(\"@objective(m, Min, sum(bilinear_obj_coeffs[i]*w[i] for i = 1:\" + str(numBilinearTerms) + \") + sum(quadratic_obj_coeffs[i]*v[i] for i = 1:\" + str(numQuadraticTerms) + \") + sum(linear_obj_coeffs[i]*x[i] for i = 1:\" + str(numVariables) + \")) \\n\\n\\n\")\n\n\n\tbilinear_obj_matrix = np.zeros((numVariables, numVariables))\n\tfor i in range(numBilinearTerms):\n\t\tbilinear_obj_matrix[bilinear_terms[i][0]][bilinear_terms[i][1]] = Q[i]/2.0\n\t\tbilinear_obj_matrix[bilinear_terms[i][1]][bilinear_terms[i][0]] = Q[i]/2.0\n\tfor i in range(numQuadraticTerms):\n\t\tbilinear_obj_matrix[quadratic_terms[i]][quadratic_terms[i]] = R[i]\n\n\tjson_dict[\"obj_bilinear_eigvals\"] = np.linalg.eigvals(bilinear_obj_matrix).tolist()\n\n\n# QUADRATIC CONSTRAINTS\n\tf.write(\"# ----- Constraints ----- #\\n\")\n\n\tjson_dict[\"quadratic_con_rhs\"] = [1.0 for i in range(numQuadraticConstraints)]\n\n\tbilinear_con_coeffs = []\n\tbilinear_con_coeff_indices = []\n\tquadratic_con_coeffs = []\n\tquadratic_con_coeff_indices = []\n\tlinear_con_coeffs = []\n\tlinear_con_coeff_indices = []\n\tcon_bilinear_eigvals = np.empty([numQuadraticConstraints, numVariables], dtype=float)\n\n\tfor k in range(numQuadraticConstraints):\n\t\tQ = [0.]*numQuadNonZero\n\t\tQ_ind = [i+1 for i in q_bilinear_ind[count_quad_con+1]]\n\t\tR = [0.]*numQuadNonZero2\n\t\tR_ind = [i+1 for i in q_quadratic_ind[count_quad_con+1]]\n\t\tq = [0.]*numLinNonZero\n\t\tq_ind = [i+1 for i in q_linear_ind[count_lin_con+1]]\n\n\t\tcount_quad_con += 1\n\t\tcount_lin_con += 1\n\t\tfor i in range(numLinNonZero):\n\t\t\tq[i] = q_linear[count_lin_con][i]\n\t\t\tif k < numQuadConPert:\n\t\t\t\tfor j in range(numPertFactors):\n\t\t\t\t\tq[i] += q_linear_con_factors[j,count_lin_con-1,i]*theta[j,count_lin_con]\n\t\tfor i in range(numQuadNonZero):\n\t\t\tQ[i] = q_bilinear[count_quad_con][i]\n\t\t\tif k < numQuadConPert:\n\t\t\t\tfor j in range(numPertFactors):\n\t\t\t\t\tQ[i] += q_bilinear_con_factors[j,count_quad_con-1,i]*theta[j,count_quad_con]\n\t\tfor i in range(numQuadNonZero2):\n\t\t\tR[i] = q_quadratic[count_quad_con][i]\n\t\t\tif k < numQuadConPert:\n\t\t\t\tfor j in range(numPertFactors):\n\t\t\t\t\tR[i] += q_quadratic_con_factors[j,count_quad_con-1,i]*theta[j,count_quad_con]\n\n\t\tbilinear_con_coeffs.append(Q)\n\t\tbilinear_con_coeff_indices.append([float(i) for i in q_bilinear_ind[count_quad_con]])\n\t\tquadratic_con_coeffs.append(R)\n\t\tquadratic_con_coeff_indices.append([float(i) for i in q_quadratic_ind[count_quad_con]])\n\t\tlinear_con_coeffs.append(q)\n\t\tlinear_con_coeff_indices.append([float(i) for i in q_linear_ind[count_lin_con]])\n\n\t\tf.write(\"bilinear_con_coeffs[\" + str(count_quad_con) + \",:] = \" + str(Q) + \"\\n\")\n\t\tf.write(\"bilinear_con_coeff_indices[\" + str(count_quad_con) + \",:] = \" + str(Q_ind) + \"\\n\")\n\t\tf.write(\"quadratic_con_coeffs[\" + str(count_quad_con) + \",:] = \" + str(R) + \"\\n\")\n\t\tf.write(\"quadratic_con_coeff_indices[\" + str(count_quad_con) + \",:] = \" + str(R_ind) + \"\\n\")\n\t\tf.write(\"linear_con_coeffs_1[\" + str(count_lin_con) + \",:] = \" + str(q) + \"\\n\")\n\t\tf.write(\"linear_con_coeff_indices_1[\" + str(count_lin_con) + \",:] = \" + str(q_ind) + \"\\n\")\n\t\tf.write(\"\\n\")\n\n\t\tf.write(\"@constraint(m, sum(bilinear_con_coeffs[\" + str(count_quad_con) + \",i]*w[bilinear_con_coeff_indices[\" + str(count_quad_con) + \",i]] for i = 1:\" + str(numQuadNonZero) + \") + sum(quadratic_con_coeffs[\" + str(count_quad_con) + \",i]*v[quadratic_con_coeff_indices[\" + str(count_quad_con) + \",i]] for i = 1:\" + str(numQuadNonZero2) + \") + sum(linear_con_coeffs_1[\" + str(count_lin_con) + \",i]*x[linear_con_coeff_indices_1[\" + str(count_lin_con) + \",i]] for i = 1:\" + str(numLinNonZero) + \") <= 1) \\n\\n\\n\")\n\n\n\t\tbilinear_con_matrix = np.zeros((numVariables, numVariables))\n\t\tfor i in range(numQuadNonZero):\n\t\t\tind = q_bilinear_ind[count_quad_con][i]\n\t\t\tind1 = bilinear_terms[ind][0]\n\t\t\tind2 = bilinear_terms[ind][1]\n\t\t\tbilinear_con_matrix[ind1][ind2] = Q[i]/2.0\n\t\t\tbilinear_con_matrix[ind2][ind1] = Q[i]/2.0\n\t\tfor i in range(numQuadNonZero2):\n\t\t\tbilinear_con_matrix[quadratic_terms[i]][quadratic_terms[i]] = R[i]\n\n\t\tcon_bilinear_eigvals[k] = np.linalg.eigvals(bilinear_con_matrix)\n\n\t\n\tjson_dict[\"con_bilinear_eigvals\"] = con_bilinear_eigvals.tolist()\n\n\n# LINEAR CONSTRAINTS\n\tjson_dict[\"linear_con_rhs\"] = [1.0 for i in range(numLinearConstraints)]\n\n\tfor k in range(numLinearConstraints):\n\t\tq = [0.]*numVariables\n\t\tq_ind = [i+1 for i in q_linear_ind[count_lin_con+1]]\n\n\t\tcount_lin_con += 1\n\t\tfor i in range(numVariables):\n\t\t\tq[i] = q_linear[count_lin_con][i]\n\n\t\tlinear_con_coeffs.append(q)\n\t\tlinear_con_coeff_indices.append([float(i) for i in q_linear_ind[count_lin_con]])\n\n\t\tf.write(\"linear_con_coeffs_2[\" + str(count_lin_con - numQuadraticConstraints) + \",:] = \" + str(q) + \"\\n\")\n\t\tf.write(\"linear_con_coeff_indices_2[\" + str(count_lin_con - numQuadraticConstraints) + \",:] = \" + str(q_ind) + \"\\n\")\n\t\tf.write(\"\\n\")\n\n\t\tf.write(\"@constraint(m, sum(linear_con_coeffs_2[\" + str(count_lin_con - numQuadraticConstraints) + \",i]*x[linear_con_coeff_indices_2[\" + str(count_lin_con - numQuadraticConstraints) + \",i]] for i = 1:\" + str(numVariables) + \") == 1) \\n\\n\\n\")\n\t\t\n\tf.close()\n\n\n\tjson_dict[\"con_bilinear_coeffs\"] = bilinear_con_coeffs\n\tjson_dict[\"con_bilinear_coeff_indices\"] = bilinear_con_coeff_indices\n\tjson_dict[\"con_quadratic_coeffs\"] = quadratic_con_coeffs\n\tjson_dict[\"con_quadratic_coeff_indices\"] = quadratic_con_coeff_indices\n\tjson_dict[\"con_linear_coeffs\"] = linear_con_coeffs\n\tjson_dict[\"con_linear_coeff_indices\"] = linear_con_coeff_indices\n\n\twith open(json_file, 'w', encoding='utf-8') as outF:\n\t\tjson.dump(json_dict, outF, ensure_ascii=False, indent=4)\n"
  },
  {
    "path": "examples/run_examples.jl",
    "content": "# - Necessary - #\nusing Alpine\nusing JuMP\nusing Gurobi\nusing Ipopt\nusing Juniper\n\n# - Additional - #\n# using CPLEX\n# using HiGHS\n# using Pavito\n\ninclude(\"JuMP_models.jl\")\ninclude(\"optimizers.jl\")\n\n# Choose underlying solvers for Alpine\nnlp_solver = get_ipopt() # local continuous solver\nmip_solver = get_gurobi() # convex mip solver\nminlp_solver = get_juniper(mip_solver, nlp_solver) # local mixed-intger solver\n\n#= Global solver\n Hints: \n => Try different integer values (>=4) for `partition_scaling_factor` to potentially observe \n    better Alpine run times (can be instance specific).\n => Choose `presolve_bt` to `false` if you prefer the bound tightening (OBBT) presolve to be turned off. \n => If you prefer to use Alpine for only OBBT presolve, without any paritioning applied to the \n    nonlinear terms, include option \"apply_partitioning\" below and set it to false. \n=#\n\nconst alpine = JuMP.optimizer_with_attributes(\n    Alpine.Optimizer,\n    # \"minlp_solver\" => minlp_solver,\n    \"nlp_solver\" => nlp_solver,\n    \"mip_solver\" => mip_solver,\n    \"presolve_bt\" => true,\n    \"apply_partitioning\" => true,\n    \"partition_scaling_factor\" => 10,\n)\n\nm = nlp3(solver = alpine)\n\nJuMP.optimize!(m)\n# Alpine.variable_values(m)\n"
  },
  {
    "path": "src/Alpine.jl",
    "content": "module Alpine\n\nusing JuMP\n\nimport Combinatorics\nimport Statistics\n\nconst ALPINE_DEBUG = false\n\ninclude(\"const.jl\")\n\n# Engine for high-level algorithmic control and user-interface\n\ninclude(\"solver_options.jl\")\ninclude(\"MOI_wrapper/MOI_wrapper.jl\")\ninclude(\"MOI_wrapper/MOI_function2expr.jl\")\n\n# Engine for expression handling\ninclude(\"nlexpr.jl\")\ninclude(\"operators.jl\")\n\n# Main algorithm\ninclude(\"main_algorithm.jl\")\ninclude(\"presolve.jl\")\ninclude(\"bounding_model.jl\")\ninclude(\"embedding.jl\")\ninclude(\"heuristics.jl\")\n\n# Convexification\ninclude(\"relaxations.jl\")\ninclude(\"multilinear.jl\")\n\n# Model manipulation and utilities\ninclude(\"variable_bounds.jl\")\ninclude(\"utility.jl\")\n\n# Logging\ninclude(\"log.jl\")\n\nend # module\n"
  },
  {
    "path": "src/MOI_wrapper/MOI_function2expr.jl",
    "content": "function _constraint_expr(expr, set::MOI.Interval)\n    return Expr(:comparison, set.lower, :(<=), expr, :(<=), set.upper)\nend\n\n_sense(::MOI.EqualTo) = :(==)\n_sense(::MOI.LessThan) = :(<=)\n_sense(::MOI.GreaterThan) = :(>=)\nfunction _constraint_expr(expr, set)\n    return Expr(:call, _sense(set), expr, MOI.constant(set))\nend\n\n_moi_function_to_expr(f::Number) = f\n\n_moi_function_to_expr(v::MOI.VariableIndex) = Expr(:ref, :x, v.value)\n\nfunction _moi_function_to_expr(t::MOI.ScalarAffineTerm)\n    return Expr(:call, :*, t.coefficient, _moi_function_to_expr(t.variable))\nend\n\nfunction _moi_function_to_expr(t::MOI.ScalarQuadraticTerm)\n    coef = t.coefficient\n    if t.variable_1 == t.variable_2\n        coef /= 2\n    end\n    return Expr(\n        :call,\n        :*,\n        coef,\n        _moi_function_to_expr(t.variable_1),\n        _moi_function_to_expr(t.variable_2),\n    )\nend\n\nfunction _add_constant(expr::Expr, constant)\n    if !iszero(constant)\n        push!(expr.args, constant)\n    end\n    return\nend\n\nfunction _add_terms(expr::Expr, terms::Vector)\n    for term in terms\n        push!(expr.args, _moi_function_to_expr(term))\n    end\n    return\nend\n\nfunction _moi_function_to_expr(f::MOI.ScalarAffineFunction)\n    if iszero(f)\n        return 0 # Similar to `JuMP.affToExpr` in JuMP v0.18 and earlier\n    end\n    expr = Expr(:call, :+)\n    _add_terms(expr, f.terms)\n    _add_constant(expr, f.constant)\n    return expr\nend\n\nfunction _moi_function_to_expr(f::MOI.ScalarQuadraticFunction)\n    if iszero(f)\n        return 0 # Similar to `JuMP.quadToExpr` in JuMP v0.18 and earlier\n    end\n    expr = Expr(:call, :+)\n    _add_terms(expr, f.quadratic_terms)\n    _add_terms(expr, f.affine_terms)\n    _add_constant(expr, f.constant)\n    return expr\nend\n\nfunction _moi_function_to_expr(f::MOI.ScalarNonlinearFunction)\n    return Expr(:call, f.head, _moi_function_to_expr.(f.args)...)\nend\n"
  },
  {
    "path": "src/MOI_wrapper/MOI_wrapper.jl",
    "content": "\"\"\"\n MOI_wrapper.jl defines the Alpine.Optimizer struct\n with all mandatory MOI functions overloaded\n\"\"\"\n\n\"\"\"\n Alpine.Optimizer struct\n\"\"\"\nmutable struct Optimizer <: MOI.AbstractOptimizer\n    options::OptimizerOptions                                # Options set by user\n\n    # Sub-solver identifier for customized solver option\n    nlp_solver_id::String                                     # NLP Solver identifier string\n    minlp_solver_id::String                                   # MINLP local solver identifier string\n    mip_solver_id::String                                     # MIP solver identifier string\n\n    # User inputs\n    num_var_orig::Int                                        # Initial number of variables\n    num_cont_var_orig::Int                                   # Initial number of continuous variables\n    num_int_var_orig::Int                                    # Initial number of binary/integer variables\n    num_constr_orig::Int                                     # Initial number of constraints\n    num_lconstr_orig::Int                                    # Initial number of linear constraints\n    num_nlconstr_orig::Int                                   # Initial number of non-linear constraints\n    var_type_orig::Vector{Symbol}                            # Variable type vector on original variables (only :Bin, :Cont, :Int)\n    var_start_orig::Vector{Float64}                          # Variable warm start vector on original variables\n    constr_type_orig::Vector{Symbol}                         # Constraint type vector on original variables (only :(==), :(>=), :(<=))\n    scalar_constraints::Vector{Any}                        # Constraint `func`-in-`set` values\n    constr_expr_orig::Vector{Expr}                           # Constraint expressions\n    obj_expr_orig::Union{Expr,Number}                        # Objective expression\n\n    # Additional user inputs concerning local solves\n    l_var_orig::Vector{Float64}                              # Variable lower bounds\n    u_var_orig::Vector{Float64}                              # Variable upper bounds\n    constraint_bounds_orig::Vector{MOI.NLPBoundsPair}        # Constraint lower bounds\n    nl_constraint_bounds_orig::Vector{MOI.NLPBoundsPair}     # Constraint lower bounds\n    sense_orig::MOI.OptimizationSense                        # Problem type (:Min, :Max)\n    d_orig::Union{Nothing,MOI.AbstractNLPEvaluator}          # Instance of AbstractNLPEvaluator for evaluating gradient, Hessian-vector products, and Hessians of the Lagrangian\n    disable_hessian::Bool                                    # Check if there are any user-defined operators, and disable hessians if necessary.\n    has_nl_objective::Bool\n    objective_function::Union{\n        Nothing,\n        MOI.ScalarAffineFunction{Float64},\n        MOI.ScalarQuadraticFunction{Float64},\n        MOI.ScalarNonlinearFunction,\n    }\n\n    # Additional initial data\n    is_obj_linear_orig::Bool                             # Boolean parameter for type of objective\n\n    # Local solution model (extra data for each iteration)\n    l_var::Vector{Float64}                               # Updated variable lower bounds for local solve\n    u_var::Vector{Float64}                               # Updated variable upper bounds for local solve\n\n    # MIP bounding model\n    model_mip::JuMP.Model                                # JuMP's convex-MIP model for bounding\n\n    num_var_linear_mip::Int                              # Number of linear lifted variables required\n    num_var_nonlinear_mip::Int                           # Number of lifted variables\n    num_var_disc_mip::Int                                # Number of variables which are discretized\n    num_constr_convex::Int                               # Number of convex constraints\n\n    # Expression-related and structural property placeholder\n    linear_terms::Dict{Any,Any}                          # Dictionary containing details of lifted linear terms\n    nonconvex_terms::Dict{Any,Any}                       # Dictionary containing details of lifted non-linear terms\n    term_seq::Dict{Int,Any}                              # Vector-Dictionary for NL terms detection\n    nonlinear_constrs::Dict{Any,Any}                     # Dictionary containing details of special constraints\n    obj_structure::Symbol                                # A symbolic indicator of the expression type of objective function\n    constr_structure::Vector{Symbol}                     # A vector indicating whether a constraint is with the special structure\n    bounding_obj_expr_mip::Union{Expr,Number}            # Lifted objective expression; if linear, same as obj_expr_orig\n    bounding_constr_expr_mip::Vector{Expr}               # Lifted constraints; if linear, same as corresponding constr_expr_orig\n    bounding_obj_mip::Dict{Any,Any}                      # Lifted objective expression in affine form\n    bounding_constr_mip::Vector{Dict{Any,Any}}           # Lifted constraint expressions in affine form\n\n    # Discretization Related options\n    candidate_disc_vars::Vector{Int}                  # A vector of all original variable indices that is involved in the nonlinear terms\n    discretization::Dict{Any,Any}                     # Discretization points with variable keys\n    disc_vars::Vector{Int}                            # Variables chosen for discretization\n    int_vars::Vector{Int}                             # Index vector of integer variables\n    bin_vars::Vector{Int}                             # Index vector of binary variables\n\n    # Reformulated problem options\n    l_var_tight::Vector{Float64}                        # Post-presolve variable upper bounds\n    u_var_tight::Vector{Float64}                        # Post-presolve variable lower bounds\n    var_type::Vector{Symbol}                            # Updated variable type for local solve\n\n    # Solution information\n    presolve_infeasible::Bool                            # Presolve infeasibility detection flag\n    best_bound::Float64                                  # Best bound from MIP\n    best_obj::Float64                                    # Best feasible objective value\n    warm_start_value::Vector{Float64}                    # Warmstart values set to Alpine\n    best_sol::Vector{Float64}                            # Best feasible solution\n    best_bound_sol::Vector{Float64}                      # Best bound solution (arg-min)\n    presolve_best_rel_gap::Float64                       # Post-OBBT relative optimality gap = |best_obj - best_bound|/|best_obj|*100\n    best_rel_gap::Float64                                # Relative optimality gap = |best_obj - best_bound|/|best_obj|*100\n    best_abs_gap::Float64                                # Absolute gap = |best_obj - best_bound|\n    bound_sol_history::Vector{Vector{Float64}}           # History of bounding solutions limited by \"parameter disc_consecutive_forbid\"\n    bound_sol_pool::Dict{Any,Any}                        # A pool of solutions from solving model_mip\n\n    # Linking constraints info for Multilinear terms\n    linking_constraints_info::Union{Nothing,Dict{Any,Any}}     # Stored multilinear linking constraints info\n\n    # Logging information and status\n    logs::Dict{Symbol,Any}                          # Logging information\n    detected_incumbent::Bool\n    detected_bound::Bool\n    status::Dict{Symbol,MOI.TerminationStatusCode}   # Detailed status of every iteration in the algorithm\n    alpine_status::MOI.TerminationStatusCode         # Current Alpine's status\n\n    # Constructor for Alpine.Optimizer\n    function Optimizer()\n        m = new()\n        m.options = get_default_options()\n        MOI.empty!(m)\n        return m\n    end\nend\n\nstruct NumberOfIterations <: MOI.AbstractModelAttribute end\nMOI.is_set_by_optimize(::NumberOfIterations) = true\nMOI.get(m::Optimizer, ::NumberOfIterations) = m.logs[:n_iter]\n\nstruct NumberOfPresolveIterations <: MOI.AbstractModelAttribute end\nMOI.is_set_by_optimize(::NumberOfPresolveIterations) = true\nMOI.get(m::Optimizer, ::NumberOfPresolveIterations) = m.logs[:bt_iter]\n\nstruct TightenedLowerBound <: MOI.AbstractVariableAttribute end\nMOI.is_set_by_optimize(::TightenedLowerBound) = true\nfunction MOI.get(m::Optimizer, ::TightenedLowerBound, vi::MOI.VariableIndex)\n    return m.l_var_tight[vi.value]\nend\n\nstruct TightenedUpperBound <: MOI.AbstractVariableAttribute end\nMOI.is_set_by_optimize(::TightenedUpperBound) = true\nfunction MOI.get(m::Optimizer, ::TightenedUpperBound, vi::MOI.VariableIndex)\n    return m.u_var_tight[vi.value]\nend\n\nfunction MOI.get(m::Optimizer, ::MOI.RawStatusString)\n    return \"Alpine ended with status $(m.alpine_status)\"\nend\n\nMOI.get(m::Optimizer, ::MOI.TerminationStatus) = m.alpine_status\n\nfunction MOI.get(m::Optimizer, attr::MOI.PrimalStatus)\n    if attr.result_index != 1\n        return MOI.NO_SOLUTION\n    end\n\n    status = m.alpine_status\n    if status == MOI.OPTIMAL\n        return MOI.FEASIBLE_POINT\n    elseif status == MOI.NEARLY_FEASIBLE_POINT\n        return MOI.NEARLY_FEASIBLE_POINT\n    elseif status == MOI.INFEASIBLE_POINT\n        return MOI.INFEASIBLE_POINT\n    elseif status == MOI.LOCALLY_SOLVED\n        return MOI.FEASIBLE_POINT\n    end\n\n    return MOI.NO_SOLUTION\nend\n\nMOI.get(::Optimizer, ::MOI.DualStatus) = MOI.NO_SOLUTION\n\nMOI.get(m::Optimizer, ::MOI.ObjectiveValue) = m.best_obj\nMOI.get(m::Optimizer, ::MOI.ObjectiveBound) = m.best_bound\nMOI.get(m::Optimizer, ::MOI.SolveTimeSec) = m.logs[:total_time]\n\nfunction get_option(m::Optimizer, s::Symbol)\n    return getproperty(m.options, s)\nend\n\nfunction set_option(m::Optimizer, s::Symbol, val)\n    return setproperty!(m.options, s, val)\nend\n\nfunction MOI.is_empty(model::Optimizer)\n    return iszero(model.num_var_orig)\nend\n\nfunction MOI.empty!(m::Optimizer)\n    m.nlp_solver_id = \"\"\n    m.minlp_solver_id = \"\"\n    m.mip_solver_id = \"\"\n\n    m.num_var_orig = 0\n    m.num_cont_var_orig = 0\n    m.num_int_var_orig = 0\n    m.num_constr_orig = 0\n    m.num_lconstr_orig = 0\n    m.num_nlconstr_orig = 0\n    m.var_type_orig = Symbol[]\n    m.var_start_orig = Float64[]\n    m.constr_type_orig = Symbol[]\n    m.scalar_constraints = Any[]\n    m.constr_expr_orig = Expr[]\n    # m.num_lconstr_updated = 0\n    # m.num_nlconstr_updated = 0\n    # m.indices_lconstr_updated = Int[]\n\n    m.l_var_orig = Float64[]\n    m.u_var_orig = Float64[]\n    m.constraint_bounds_orig = MOI.NLPBoundsPair[]\n    m.nl_constraint_bounds_orig = MOI.NLPBoundsPair[]\n    m.sense_orig = MOI.FEASIBILITY_SENSE\n\n    m.d_orig = nothing\n    m.has_nl_objective = false\n    m.objective_function = nothing\n\n    m.linear_terms = Dict()\n    m.nonconvex_terms = Dict()\n    m.term_seq = Dict()\n    m.nonlinear_constrs = Dict()\n    m.candidate_disc_vars = Int[]\n    m.bounding_constr_expr_mip = []\n    m.bounding_constr_mip = []\n    m.disc_vars = []\n    m.int_vars = []\n    m.bin_vars = []\n    m.discretization = Dict()\n    m.num_var_linear_mip = 0\n    m.num_var_nonlinear_mip = 0\n    m.num_var_disc_mip = 0\n    m.num_constr_convex = 0\n    m.constr_structure = Symbol[]\n    m.best_bound_sol = []\n    m.bound_sol_history = []\n    m.presolve_infeasible = false\n    m.bound_sol_history =\n        Vector{Vector{Float64}}(undef, m.options.disc_consecutive_forbid)\n\n    m.best_obj = Inf\n    m.warm_start_value = Float64[]\n    m.best_sol = Float64[]\n    m.best_bound = -Inf\n    m.presolve_best_rel_gap = Inf\n    m.best_rel_gap = Inf\n    m.best_abs_gap = Inf\n    m.alpine_status = MOI.OPTIMIZE_NOT_CALLED\n\n    m.linking_constraints_info = nothing\n\n    create_status!(m)\n    return create_logs!(m)\nend\n\nMOI.supports_incremental_interface(::Optimizer) = true\n\nfunction MOI.copy_to(model::Optimizer, src::MOI.ModelLike)\n    return MOIU.default_copy_to(model, src)\nend\n\nMOI.get(::Optimizer, ::MOI.SolverName) = \"Alpine\"\nMOI.get(::Optimizer, ::MOI.SolverVersion) = _ALPINE_VERSION\n\nfunction MOI.set(model::Optimizer, param::MOI.RawOptimizerAttribute, value)\n    return set_option(model, Symbol(param.name), value)\nend\nfunction MOI.get(model::Optimizer, param::MOI.RawOptimizerAttribute)\n    return get_option(model, Symbol(param.name))\nend\n\nfunction MOI.add_variables(model::Optimizer, n::Int)\n    return [MOI.add_variable(model) for i in 1:n]\nend\nfunction MOI.add_variable(model::Optimizer)\n    model.num_var_orig += 1\n    push!(model.l_var_orig, -Inf)\n    push!(model.u_var_orig, Inf)\n    push!(model.var_type_orig, :Cont)\n    push!(model.warm_start_value, 0.0)\n    push!(model.best_sol, 0.0)\n    return MOI.VariableIndex(model.num_var_orig)\nend\n\nfunction MOI.supports(::Optimizer, ::MOI.VariablePrimalStart, ::Type{MOI.VariableIndex})\n    return true\nend\nfunction MOI.set(\n    model::Optimizer,\n    ::MOI.VariablePrimalStart,\n    vi::MOI.VariableIndex,\n    value::Union{Real,Nothing},\n)\n    model.best_sol[vi.value] = model.warm_start_value[vi.value] = something(value, 0.0)\n    return\nend\n\nconst SCALAR_SET = Union{\n    MOI.EqualTo{Float64},\n    MOI.LessThan{Float64},\n    MOI.GreaterThan{Float64},\n    MOI.Interval{Float64},\n}\n\nfunction MOI.supports_constraint(\n    ::Optimizer,\n    ::Type{MOI.VariableIndex},\n    ::Type{<:SCALAR_SET},\n)\n    return true\nend\n\n_lower(set::MOI.EqualTo) = set.value\n_upper(set::MOI.EqualTo) = set.value\n_lower(set::MOI.LessThan) = nothing\n_upper(set::MOI.LessThan) = set.upper\n_lower(set::MOI.GreaterThan) = set.lower\n_upper(set::MOI.GreaterThan) = nothing\n_lower(set::MOI.Interval) = set.lower\n_upper(set::MOI.Interval) = set.upper\n\nfunction MOI.add_constraint(model::Optimizer, vi::MOI.VariableIndex, set::SCALAR_SET)\n    l = _lower(set)\n    if l !== nothing\n        model.l_var_orig[vi.value] = l\n    end\n    u = _upper(set)\n    if u !== nothing\n        model.u_var_orig[vi.value] = u\n    end\n    return MOI.ConstraintIndex{typeof(vi),typeof(set)}(vi.value)\nend\n\nfunction MOI.supports_constraint(\n    ::Optimizer,\n    ::Type{MOI.VariableIndex},\n    ::Type{MOI.ZeroOne},\n)\n    return true\nend\n\nfunction MOI.add_constraint(model::Optimizer, f::MOI.VariableIndex, set::MOI.ZeroOne)\n    model.var_type_orig[f.value] = :Bin\n    return MOI.ConstraintIndex{typeof(f),typeof(set)}(f.value)\nend\n\nfunction MOI.supports_constraint(\n    model::Optimizer,\n    ::Type{\n        <:Union{MOI.ScalarAffineFunction{Float64},MOI.ScalarQuadraticFunction{Float64}},\n    },\n    ::Type{<:SCALAR_SET},\n)\n    return true\nend\n\nfunction MOI.add_constraint(\n    model::Optimizer,\n    f::Union{MOI.ScalarAffineFunction{Float64},MOI.ScalarQuadraticFunction{Float64}},\n    set::SCALAR_SET,\n)\n    model.num_constr_orig += 1\n    push!(\n        model.constraint_bounds_orig,\n        MOI.NLPBoundsPair(something(_lower(set), -Inf), something(_upper(set), Inf)),\n    )\n    iszero(f.constant) || throw(\n        MOI.ScalarFunctionConstantNotZero{Float64,typeof(f),typeof(set)}(f.constant),\n    )\n    push!(model.scalar_constraints, (copy(f), copy(set)))\n    push!(model.constr_expr_orig, _constraint_expr(_moi_function_to_expr(f), set))\n    if f isa MOI.ScalarAffineFunction\n        model.num_lconstr_orig += 1\n        push!(model.constr_structure, :generic_linear)\n    else\n        model.num_nlconstr_orig += 1\n        push!(model.constr_structure, :generic_nonlinear)\n    end\n\n    return MOI.ConstraintIndex{typeof(f),typeof(set)}(model.num_constr_orig)\nend\n\nfunction MOI.supports_constraint(\n    ::Optimizer,\n    ::Type{<:MOI.ScalarNonlinearFunction},\n    ::Type{<:SCALAR_SET},\n)\n    return true\nend\n\nfunction MOI.add_constraint(\n    model::Optimizer,\n    f::MOI.ScalarNonlinearFunction,\n    set::SCALAR_SET,\n)\n    model.num_constr_orig += 1\n    push!(\n        model.constraint_bounds_orig,\n        MOI.NLPBoundsPair(something(_lower(set), -Inf), something(_upper(set), Inf)),\n    )\n    push!(model.scalar_constraints, (copy(f), copy(set)))\n    push!(model.constr_expr_orig, _constraint_expr(_moi_function_to_expr(f), set))\n    model.num_nlconstr_orig += 1\n    push!(model.constr_structure, :generic_nonlinear)\n    return MOI.ConstraintIndex{typeof(f),typeof(set)}(model.num_constr_orig)\nend\n\nfunction MOI.supports(\n    model::Optimizer,\n    ::Union{MOI.ObjectiveSense,MOI.ObjectiveFunction{F}},\n) where {\n    F<:Union{\n        MOI.ScalarAffineFunction{Float64},\n        MOI.ScalarQuadraticFunction{Float64},\n        MOI.ScalarNonlinearFunction,\n    },\n}\n    return true\nend\n\nis_min_sense(model::Optimizer) = model.sense_orig == MOI.MIN_SENSE\nis_max_sense(model::Optimizer) = model.sense_orig == MOI.MAX_SENSE\n\nfunction MOI.set(model::Optimizer, ::MOI.ObjectiveSense, sense)\n    model.sense_orig = sense\n    if is_max_sense(model)\n        model.best_obj = -Inf\n        model.best_bound = Inf\n    elseif is_min_sense(model)\n        model.best_obj = Inf\n        model.best_bound = -Inf\n    else\n        error(\"Feasibility sense is not supported by Alpine.\")\n    end\nend\n\nfunction MOI.set(model::Optimizer, ::MOI.ObjectiveFunction{F}, func::F) where {F}\n    model.objective_function = func\n    return\nend\n\nfunction MOI.set(m::Optimizer, ::MOI.NLPBlock, block)\n    m.d_orig = block.evaluator\n    m.disable_hessian = !(\n        (:Hess in MOI.features_available(block.evaluator)) &&\n        (:HessVec in MOI.features_available(block.evaluator))\n    )\n    m.has_nl_objective = block.has_objective\n\n    # We cache it to add it in `load!` as we cannot call `MOI.constraint_expr` yet\n    # so we will add the nonlinear `constr_expr_orig` at the end so we need\n    # to add the bounds at the end too.\n    # So we can consider that the nonlinear constraints are the\n    # `length(m.nl_constraint_bounds_orig)` last ones.\n    m.nl_constraint_bounds_orig = block.constraint_bounds\n    return\nend\n\n# In JuMP v0.18/MathProgBase, the 5th decision variable would be `:(x[5])`.\n# In JuMP v0.19/MathOptInterface, it is now `:(x[MOI.VariableIndex(5)])`.\n# To ease the transition, we simply transform it back to what it used to be.\n_variable_index_to_index(expr::Union{Number,Symbol}) = expr\n_variable_index_to_index(expr::MOI.VariableIndex) = expr.value\nfunction _variable_index_to_index(expr::Expr)\n    for i in eachindex(expr.args)\n        expr.args[i] = _variable_index_to_index(expr.args[i])\n    end\n    return expr\nend\n\nfunction _index_to_variable_ref(m::JuMP.Model, idx::Int64)\n    return JuMP.VariableRef(m, MOI.VariableIndex(idx))\nend\n\nfunction MOI.get(model::Optimizer, attr::MOI.VariablePrimal, vi::MOI.VariableIndex)\n    MOI.check_result_index_bounds(model, attr)\n    MOI.throw_if_not_valid(model, vi)\n\n    return model.best_sol[vi.value]\nend\n\nfunction MOI.get(model::Optimizer, ::MOI.ResultCount)\n    return model.alpine_status == MOI.OPTIMIZE_NOT_CALLED ? 0 : 1\nend\n\nfunction MOI.is_valid(model::Alpine.Optimizer, vi::MOI.VariableIndex)\n    return 1 <= vi.value <= model.num_var_orig\nend\n\nfunction _get_bound_set(model::Alpine.Optimizer, vi::MOI.VariableIndex)\n    if !MOI.is_valid(model, vi)\n        throw(MOI.InvalidIndex(vi))\n    end\n    return _bound_set(model.l_var_orig[vi.value], model.u_var_orig[vi.value])\nend\n\nfunction MOI.is_valid(\n    model::Alpine.Optimizer,\n    ci::MOI.ConstraintIndex{MOI.VariableIndex,S},\n) where {S<:SCALAR_SET}\n    set = _get_bound_set(model, MOI.VariableIndex(ci.value))\n    return set isa S\nend\n\nfunction MOI.get(\n    model::Alpine.Optimizer,\n    ::MOI.ConstraintSet,\n    ci::MOI.ConstraintIndex{MOI.VariableIndex,S},\n) where {S<:SCALAR_SET}\n    if !MOI.is_valid(model, ci)\n        throw(MOI.InvalidIndex(ci))\n    end\n    return _get_bound_set(model, MOI.VariableIndex(ci.value))\nend\n\n# Taken from MatrixOptInterface.jl\n@enum ConstraintSense EQUAL_TO GREATER_THAN LESS_THAN INTERVAL\n_sense(::Type{<:MOI.EqualTo}) = EQUAL_TO\n_sense(::Type{<:MOI.LessThan}) = LESS_THAN\n_sense(::Type{<:MOI.GreaterThan}) = GREATER_THAN\n_sense(::Type{<:MOI.Interval}) = INTERVAL\n\n_no_upper(bound) = bound != typemax(bound)\n_no_lower(bound) = bound != typemin(bound)\n\nfunction _bound_set(lb::T, ub::T) where {T}\n    if _no_upper(ub)\n        if _no_lower(lb)\n            if ub == lb\n                return MOI.EqualTo(lb)\n            else\n                return MOI.Interval(lb, ub)\n            end\n        else\n            return MOI.LessThan(ub)\n        end\n    else\n        if _no_lower(lb)\n            return MOI.GreaterThan(lb)\n        else\n            return\n        end\n    end\nend\n\n#=\nfunction _bound_sense(lb::T, ub::T) where T\n    if _no_upper(ub)\n        if _no_lower(lb)\n            if lb == ub\n                return EQUAL_TO\n            else\n                return INTERVAL\n            end\n        else\n            return LESS_THAN\n        end\n    else\n        if _no_lower(lb)\n            return GREATER_THAN\n        else\n            return\n        end\n    end\nend\n=#\n"
  },
  {
    "path": "src/bounding_model.jl",
    "content": "\"\"\"\n    create_bounding_mip(m::Optimizer; use_disc = nothing)\n\nSet up a MILP bounding model base on variable domain partitioning information stored in `use_disc`.\nBy default, if `use_disc` is not provided, it will use `m.discretizations` store in the Alpine model.\nThe basic idea of this MILP bounding model is to use piecewise polyhedral/convex relaxations to tighten the\nbasic relaxations of the original non-convex region. Among all presented partitions, the bounding model\nwill choose one specific partition as the lower bound solution. The more partitions there are, the\nbetter or finer bounding model relax the original MINLP while the more efforts required to solve\nthis MILP is required.\n\"\"\"\nfunction create_bounding_mip(m::Optimizer; use_disc = nothing)\n    if (use_disc === nothing)\n        if (m.logs[:n_iter] == 1) &&\n           (m.status[:local_solve] in union(STATUS_OPT, STATUS_LIMIT, STATUS_WARM_START))\n            # Setting up an initial partition\n            add_partition(m, use_solution = m.best_sol)\n        elseif m.logs[:n_iter] >= 2\n            # Add subsequent iteration partitions\n            add_partition(m)\n        end\n        discretization = m.discretization\n    else\n        discretization = use_disc\n    end\n\n    m.model_mip = JuMP.Model(get_option(m, :mip_solver)) # Construct JuMP Model\n    start_build = time()\n    # ------- Model Construction ------ #\n    amp_post_vars(m)                                                # Post original and lifted variables\n    amp_post_lifted_constraints(m)                                  # Post original and lifted constraints\n    amp_post_lifted_objective(m)                                    # Post original and/or objective\n    amp_post_convexification(m, use_disc = discretization)          # Post convexification constraints\n    # --------------------------------- #\n    cputime_build = time() - start_build\n    m.logs[:total_time] += cputime_build\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n\n    return\nend\n\n\"\"\"\n    amp_post_convexification(m::Optimizer; use_disc = nothing)\n\nWrapper function to apply piecewise convexification of the problem for the bounding MIP model. This function talks to nonconvex_terms and convexification methods\nto finish the last step required during the construction of bounding model.\n\"\"\"\nfunction amp_post_convexification(m::Optimizer; use_disc = nothing)\n    use_disc === nothing ? discretization = m.discretization : discretization = use_disc\n\n    amp_post_convhull(m, use_disc = discretization)  # convex hull representation\n    _is_fully_convexified(m) # Ensure if all the non-linear terms are convexified\n\n    return\nend\n\nfunction amp_post_vars(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n\n    if haskey(options, :use_disc)\n        l_var = [\n            options[:use_disc][i][1] for\n            i in 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)\n        ]\n        u_var = [\n            options[:use_disc][i][end] for\n            i in 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)\n        ]\n    else\n        l_var = m.l_var_tight\n        u_var = m.u_var_tight\n    end\n\n    JuMP.@variable(\n        m.model_mip,\n        x[i = 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)]\n    )\n\n    for i in 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)\n        # Interestingly, not enforcing category of lifted variables is able to improve performance\n        if i <= m.num_var_orig\n            if m.var_type_orig[i] == :Bin\n                set_binary(x[i])\n            elseif m.var_type_orig[i] == :Int\n                set_integer(x[i])\n            end\n        end\n        # Changed to tight bound, if no bound tightening is performed, will be just .l_var_orig\n        l_var[i] > -Inf && JuMP.set_lower_bound(x[i], l_var[i])\n        # Changed to tight bound, if no bound tightening is performed, will be just .u_var_orig\n        u_var[i] < Inf && JuMP.set_upper_bound(x[i], u_var[i])\n\n        m.var_type[i] == :Int && error(\n            \"Alpine does not support MINLPs with generic integer (non-binary) variables yet! Try Juniper.jl for finding a local feasible solution\",\n        )\n    end\n\n    return\nend\n\nfunction amp_post_lifted_constraints(m::Optimizer)\n    for i in 1:m.num_constr_orig\n        if m.constr_structure[i] == :affine\n            amp_post_affine_constraint(m.model_mip, m.bounding_constr_mip[i])\n        elseif m.constr_structure[i] == :convex\n            amp_post_convex_constraint(m.model_mip, m.bounding_constr_mip[i])\n        else\n            error(\"Unknown constr_structure type $(m.constr_structure[i])\")\n        end\n    end\n\n    for i in keys(m.linear_terms)\n        amp_post_linear_lift_constraints(m.model_mip, m.linear_terms[i])\n    end\n\n    return\nend\n\nfunction amp_post_affine_constraint(model_mip::JuMP.Model, affine::Dict)\n    if affine[:sense] == :(>=)\n        JuMP.@constraint(\n            model_mip,\n            sum(\n                affine[:coefs][j] *\n                _index_to_variable_ref(model_mip, affine[:vars][j].args[2]) for\n                j in 1:affine[:cnt]\n            ) >= affine[:rhs]\n        )\n    elseif affine[:sense] == :(<=)\n        JuMP.@constraint(\n            model_mip,\n            sum(\n                affine[:coefs][j] *\n                _index_to_variable_ref(model_mip, affine[:vars][j].args[2]) for\n                j in 1:affine[:cnt]\n            ) <= affine[:rhs]\n        )\n    elseif affine[:sense] == :(==)\n        JuMP.@constraint(\n            model_mip,\n            sum(\n                affine[:coefs][j] *\n                _index_to_variable_ref(model_mip, affine[:vars][j].args[2]) for\n                j in 1:affine[:cnt]\n            ) == affine[:rhs]\n        )\n    else\n        error(\"Unkown sense.\")\n    end\n\n    return\nend\n\nfunction amp_post_convex_constraint(model_mip::JuMP.Model, convex::Dict)\n    !prod([i == 2 for i in convex[:powers]]) && error(\"No relaxation implementation for convex constraints $(convex[:expr])\")\n\n    if convex[:sense] == :(<=)\n        JuMP.@constraint(\n            model_mip,\n            sum(\n                convex[:coefs][j] *\n                _index_to_variable_ref(model_mip, convex[:vars][j].args[2])^2 for\n                j in 1:convex[:cnt]\n            ) <= convex[:rhs]\n        )\n    elseif convex[:sense] == :(>=)\n        JuMP.@constraint(\n            model_mip,\n            sum(\n                convex[:coefs][j] *\n                _index_to_variable_ref(model_mip, convex[:vars][j].args[2])^2 for\n                j in 1:convex[:cnt]\n            ) >= convex[:rhs]\n        )\n    else\n        error(\n            \"No equality constraints should be recognized as supported convex constriants\",\n        )\n    end\n\n    return\nend\n\nfunction amp_post_linear_lift_constraints(model_mip::JuMP.Model, l::Dict)\n    @assert l[:ref][:sign] == :+\n    JuMP.@constraint(\n        model_mip,\n        _index_to_variable_ref(model_mip, l[:y_idx]) ==\n        sum(i[1] * _index_to_variable_ref(model_mip, i[2]) for i in l[:ref][:coef_var]) +\n        l[:ref][:scalar]\n    )\n    return\nend\n\nfunction amp_post_lifted_objective(m::Optimizer)\n\n    #if isa(m.obj_expr_orig, Number)\n    if m.obj_expr_orig == :(+())\n        JuMP.@objective(m.model_mip, m.sense_orig, 0.0)\n    elseif expr_isconst(m.obj_expr_orig)\n        # This eval is okay because expr_isconst is true\n        JuMP.@objective(m.model_mip, m.sense_orig, eval(m.obj_expr_orig))\n    elseif m.obj_structure == :affine\n        JuMP.@objective(\n            m.model_mip,\n            m.sense_orig,\n            m.bounding_obj_mip[:rhs] + sum(\n                m.bounding_obj_mip[:coefs][i] *\n                _index_to_variable_ref(m.model_mip, m.bounding_obj_mip[:vars][i].args[2])\n                for i in 1:m.bounding_obj_mip[:cnt]\n            )\n        )\n    elseif m.obj_structure == :convex\n        # This works only when the original objective is convex quadratic.\n        # Higher-order convex monomials need implementation of outer-approximation (check resolve_convex_constr in operators.jl)\n        JuMP.@objective(\n            m.model_mip,\n            m.sense_orig,\n            m.bounding_obj_mip[:rhs] + sum(\n                m.bounding_obj_mip[:coefs][i] *\n                _index_to_variable_ref(\n                    m.model_mip,\n                    m.bounding_obj_mip[:vars][i].args[2],\n                )^2 for i in 1:m.bounding_obj_mip[:cnt]\n            )\n        )\n    else\n        error(\"Unknown structural obj type $(m.obj_structure)\")\n    end\n    return\nend\n\nfunction add_partition(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n    haskey(options, :use_disc) ? discretization = options[:use_disc] :\n    discretization = m.discretization\n    haskey(options, :use_solution) ? point_vec = options[:use_solution] :\n    point_vec = m.best_bound_sol\n\n    if isa(get_option(m, :disc_add_partition_method), Function)\n        m.discretization = get_option(m, :disc_add_partition_method)(\n            m,\n            use_disc = discretization,\n            use_solution = point_vec,\n        )\n    elseif get_option(m, :disc_add_partition_method) == \"adaptive\"\n        m.discretization =\n            add_adaptive_partition(m, use_disc = discretization, use_solution = point_vec)\n    elseif get_option(m, :disc_add_partition_method) == \"uniform\"\n        m.discretization = add_uniform_partition(m, use_disc = discretization)\n    else\n        error(\"Unknown input on how to add partitions.\")\n    end\n\n    return\nend\n\n# TODO: also need to document the special diverted cases when new partition touches both corners\n\"\"\"\n\n    add_adaptive_partition(m::Optimizer; use_disc::Dict, use_solution::Vector)\n\nA built-in method used to add a new partition on feasible domains of variables chosen for partitioning.\n\nThis can be illustrated by the following example. Let the previous iteration's partition vector on\nvariable \"x\" be given by [0, 3, 7, 9]. And say, the lower bounding solution has a value of 4 for variable \"x\".\nIn the case when `partition_scaling_factor = 4`, this function creates the new partition vector as follows: [0, 3, 3.5, 4, 4.5, 7, 9]\n\nThere are two options for this function,\n\n    * `use_disc(default=m.discretization)`:: to regulate which is the base to add new partitions on\n    * `use_solution(default=m.best_bound_sol)`:: to regulate which solution to use when adding new partitions on\n\nThis function can be accordingly modified by the user to change the behavior of the solver, and thus the convergence.\n\n\"\"\"\nfunction add_adaptive_partition(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n\n    haskey(options, :use_disc) ? discretization = options[:use_disc] :\n    discretization = m.discretization\n    haskey(options, :use_solution) ? point_vec = copy(options[:use_solution]) :\n    point_vec = copy(m.best_bound_sol)\n    haskey(options, :use_ratio) ? ratio = options[:use_ratio] :\n    ratio = get_option(m, :partition_scaling_factor)\n    haskey(options, :branching) ? branching = options[:branching] : branching = false\n\n    if length(point_vec) < m.num_var_orig + m.num_var_linear_mip + m.num_var_nonlinear_mip\n        point_vec = resolve_lifted_var_value(m, point_vec)  # Update the solution vector for lifted variable\n    end\n\n    if branching\n        discretization = deepcopy(discretization)\n    end\n\n    processed = Set{Int}()\n\n    # Perform discretization based on type of nonlinear terms #\n    for i in m.disc_vars\n        point = point_vec[i]                # Original Variable\n        λCnt = length(discretization[i])\n\n        # Built-in method based-on variable type\n        if m.var_type[i] == :Cont\n            i in processed && continue\n            point = correct_point(m, discretization[i], point, i)\n            for j in 1:λCnt\n                if point >= discretization[i][j] && point <= discretization[i][j+1]  # Locating the right location\n                    radius = calculate_radius(discretization[i], j, ratio)\n                    insert_partition_helper(m, i, j, point, radius, discretization[i])\n                    push!(processed, i)\n                    break\n                end\n            end\n        elseif m.var_type[i] == :Bin # This should never happen\n            @warn \"  Warning: Binary variable in m.disc_vars. Check out what is wrong...\"\n            continue  # No partition should be added to binary variable unless user specified\n        elseif m.var_type[i] == :Int\n            error(\n                \"Alpine does not support MINLPs with generic integer (non-binary) variables yet!\",\n            )\n        else\n            error(\"Unexpected variable types while inserting partitions\")\n        end\n    end\n\n    return discretization\nend\n\n\"\"\"\n    This function targets to address unexpected numerical issues when adding partitions in tight regions.\n\"\"\"\nfunction correct_point(m::Optimizer, partvec::Vector, point::Float64, var::Int)\n    tol = get_option(m, :tol)\n\n    if point < partvec[1] - tol || point > partvec[end] + tol\n        @warn \"  Warning: VAR$(var) SOL=$(point) out of discretization [$(partvec[1]),$(partvec[end])]. Hence, taking the middle point.\"\n        return 0.5 * (partvec[1] + partvec[end]) # Should choose the longest range\n    end\n\n    isapprox(point, partvec[1]; atol = tol) && return partvec[1]\n    isapprox(point, partvec[end]; atol = tol) && return partvec[end]\n\n    return point\nend\n\nfunction calculate_radius(partvec::Vector, part::Int, ratio::Any)\n    lb_local = partvec[part]\n    ub_local = partvec[part+1]\n\n    distance = ub_local - lb_local\n    if isa(ratio, Float64) || isa(ratio, Int)\n        radius = distance / ratio\n    elseif isa(ratio, Function)\n        radius = distance / ratio(m)\n    else\n        error(\"Undetermined partition scaling factor\")\n    end\n\n    return radius\nend\n\nfunction insert_partition_helper(\n    m::Optimizer,\n    var::Int,\n    partidx::Int,\n    point::Number,\n    radius::Float64,\n    partvec::Vector,\n)\n    abstol, reltol =\n        get_option(m, :disc_abs_width_tol), get_option(m, :disc_rel_width_tol)\n\n    lb_local, ub_local = partvec[partidx], partvec[partidx+1]\n    ub_touch, lb_touch = true, true\n    lb_new, ub_new = max(point - radius, lb_local), min(point + radius, ub_local)\n\n    if ub_new < ub_local &&\n       !isapprox(ub_new, ub_local; atol = abstol) &&\n       abs(ub_new - ub_local) / (1e-8 + abs(ub_local)) > reltol # Insert new UB-based partition\n        insert!(partvec, partidx + 1, ub_new)\n        ub_touch = false\n    end\n\n    if lb_new > lb_local &&\n       !isapprox(lb_new, lb_local; atol = abstol) &&\n       abs(lb_new - lb_local) / (1e-8 + abs(lb_local)) > reltol # Insert new LB-based partition\n        insert!(partvec, partidx + 1, lb_new)\n        lb_touch = false\n    end\n\n    if (ub_touch && lb_touch) || check_solution_history(m, var)\n        distvec = [(j, partvec[j+1] - partvec[j]) for j in 1:length(partvec)-1]\n        sort!(distvec, by = x -> x[2])\n        point_orig = point\n        pos = distvec[end][1]\n        lb_local = partvec[pos]\n        ub_local = partvec[pos+1]\n        isapprox(lb_local, ub_local; atol = get_option(m, :tol)) && return\n        chunk = (ub_local - lb_local) / get_option(m, :disc_divert_chunks)\n        point = lb_local + (ub_local - lb_local) / get_option(m, :disc_divert_chunks)\n        for i in 2:get_option(m, :disc_divert_chunks)\n            insert!(\n                partvec,\n                pos + 1,\n                lb_local + chunk * (get_option(m, :disc_divert_chunks) - (i - 1)),\n            )\n        end\n        (get_option(m, :log_level) > 199) && println(\n            \"[DEBUG] !D! VAR$(var): SOL=$(round(point_orig; digits = 4))=>$(point) |$(round(lb_local; digits = 4)) | $(get_option(m, :disc_divert_chunks)) SEGMENTS | $(round(ub_local; digits = 4))|\",\n        )\n    else\n        (get_option(m, :log_level) > 199) && println(\n            \"[DEBUG] VAR$(var): SOL=$(round(point; digits = 4)) RADIUS=$(radius), PARTITIONS=$(length(partvec)-1) |$(round(lb_local; digits = 4)) |$(round(lb_new; digits = 6)) <- * -> $(round(ub_new; digits = 6))| $(round(ub_local; digits = 4))|\",\n        )\n    end\n\n    return\nend\n\nfunction add_uniform_partition(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n    haskey(options, :use_disc) ? discretization = options[:use_disc] :\n    discretization = m.discretization\n\n    for i in m.disc_vars  # Only construct when discretized\n        lb_local = discretization[i][1]\n        ub_local = discretization[i][end]\n        distance = ub_local - lb_local\n        # chunk = distance / ((m.logs[:n_iter] + 1) * get_option(m, :disc_uniform_rate))\n        chunk = distance / (m.logs[:n_iter] * get_option(m, :disc_uniform_rate))\n        discretization[i] = [\n            lb_local + chunk * (j - 1) for\n            j in 1:(m.logs[:n_iter])*get_option(m, :disc_uniform_rate)\n        ]\n        push!(discretization[i], ub_local)   # Safety Scheme\n    end\n\n    return discretization\nend\n\nfunction update_partition_scaling_factor(m::Optimizer, presolve = false)\n    m.logs[:n_iter] > 2 && return get_option(m, :partition_scaling_factor) # Stop branching after the second iterations\n\n    ratio_pool = [8:2:20;]  # Built-in try range\n    incumb_ratio = ratio_pool[1]\n    is_min_sense(m) ? incumb_res = -Inf : incumb_res = Inf\n    res_collector = Float64[]\n\n    for r in ratio_pool\n        st = time()\n        if !isempty(m.best_sol)\n            branch_disc = add_adaptive_partition(\n                m,\n                use_disc = m.discretization,\n                branching = true,\n                use_ratio = r,\n                use_solution = m.best_sol,\n            )\n        else\n            branch_disc = add_adaptive_partition(\n                m,\n                use_disc = m.discretization,\n                branching = true,\n                use_ratio = r,\n            )\n        end\n        create_bounding_mip(m, use_disc = branch_disc)\n        res = disc_branch_solve(m)\n        push!(res_collector, res)\n        if m.sense_orig == MOI.MAX_SENSE ? res < incumb_res : res > incumb_res\n            incumb_res = res\n            incumb_ratio = r\n        end\n        et = time() - st\n        if et > 300  # 5 minutes limitation\n            println(\"Expensive disc branching pass... Fixed at 8\")\n            return 8\n        end\n        get_option(m, :log_level) > 0 &&\n            println(\"BRANCH RATIO = $(r), METRIC = $(res) || TIME = $(time()-st)\")\n    end\n\n    if Statistics.std(res_collector) >= 1e-2    # Detect if all solutions are similar to each other\n        get_option(m, :log_level) > 0 &&\n            println(\"RATIO BRANCHING OFF due to solution variance test passed.\")\n        set_option(m, :partition_scaling_factor_branch, false) # If an incumbent ratio is selected, then stop the branching scheme\n    end\n\n    if !isempty(m.best_sol)\n        m.discretization = add_adaptive_partition(\n            m,\n            use_disc = m.discretization,\n            branching = true,\n            use_ratio = incumb_ratio,\n            use_solution = m.best_sol,\n        )\n    else\n        m.discretization = add_adaptive_partition(\n            m,\n            use_disc = m.discretization,\n            branching = true,\n            use_ratio = incumb_ratio,\n        )\n    end\n\n    get_option(m, :log_level) > 0 && println(\"INCUMB_RATIO = $(incumb_ratio)\")\n\n    return incumb_ratio\nend\n\nfunction disc_branch_solve(m::Optimizer)\n\n    # ================= Solve Start ================ #\n    set_mip_time_limit(m)\n    start_bounding_solve = time()\n    JuMP.optimize!(m.model_mip)\n    status = MOI.get(m.model_mip, MOI.TerminationStatus())\n    cputime_branch_bounding_solve = time() - start_bounding_solve\n    m.logs[:total_time] += cputime_branch_bounding_solve\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n    # ================= Solve End ================ #\n\n    if status in STATUS_OPT || status in STATUS_LIMIT\n        return MOI.get(m.model_mip, MOI.ObjectiveBound())\n    else\n        @warn \"  Warning: Unexpected solving condition $(status) during disc branching.\"\n    end\n\n    # Safety scheme\n    if is_min_sense(m)\n        return -Inf\n    elseif is_max_sense(m)\n        return Inf\n    end\nend\n"
  },
  {
    "path": "src/const.jl",
    "content": "const ALPINE_C_NLTERMS = [\n    :BILINEAR,\n    :MONOMIAL,\n    :MULTILINEAR,\n    :BININT,\n    :BINLIN,\n    :INTLIN,\n    :BINPROD,\n    :INTPROD,\n    :cos,\n    :sin,\n]\nconst ALPINE_C_MONOMIAL = [:BILINEAR, :MONOMIAL, :MULTILINEAR]\nconst ALPINE_C_TRIGONOMETRIC = [:sin, :cos]\n"
  },
  {
    "path": "src/embedding.jl",
    "content": "\"\"\"\n\tThis function creates a mapping dictionary to link the right λ to the right bineary variables\n\tbased on how many partitions are required and a given encoding method.\n\"\"\"\nfunction embedding_map(λCnt::Int, encoding::Any = ebd_gray, ibs::Bool = false)\n    map = Dict()\n\n    encoding = resolve_encoding_key(encoding)\n    L = Int(ceil(log(2, λCnt - 1)))\n    for i in 1:L*2\n        map[i] = Set()\n    end\n    H = [encoding(i, L) for i in 0:max(1, (2^L - 1))]\n    map[:H_orig] = H\n    map[:H] = [ebd_support_binary_vec(H[i]) for i in 1:length(H)] # Store the map\n    map[:L] = L\n\n    !is_compatible_encoding(H) && error(\"Encodign method is not SOS-2 compatible...\")\n\n    # Mapping SOS-2 :: Aλ <= x  &&  A'λ <=  1-x\n    # |x| = L : Flip  1 -> bCnt : bCnt + 1 -> bCnt + bCnt\n    J = Set(collect(1:(2^L+1)))\n    J_s = Set(collect(1:λCnt))\n    for l in 1:L\n        if ibs\n            L_constr = Set()\n            R_constr = Set()\n            for j in 0:2^L\n                prod([(l in ebd_σ(H[i])) for i in ebd_I(j, 2^L + 1)]) && push!(L_constr, j + 1)\n                prod([!(l in ebd_σ(H[i])) for i in ebd_I(j, 2^L + 1)]) && push!(R_constr, j + 1)\n            end\n            L_branch = intersect(J_s, setdiff(J, L_constr))\n            R_branch = intersect(J_s, setdiff(J, R_constr))\n            map[l] = setdiff(J_s, L_branch)\n            map[l+L] = setdiff(J_s, R_branch)\n        else\n            for j in 0:(λCnt-1)\n                prod([(l in ebd_σ(H[i])) for i in ebd_I(j, λCnt)]) && push!(map[l], j + 1)\n                prod([!(l in ebd_σ(H[i])) for i in ebd_I(j, λCnt)]) && push!(map[l+L], j + 1)\n            end\n        end\n    end\n\n    return map\nend\n\n\"\"\"\n\tThis function parse the encoding key string and return the built-in encoding function.\n\"\"\"\nfunction resolve_encoding_key(encoding::Any)\n    isa(encoding, Function) && return encoding\n    encoding == \"default\" && return ebd_gray\n    return error(\"Must specify a encoding method when using convhull_ebd formulation\")\nend\n\n\"\"\"\n\tThis function is the same σ() function described in Vielma and Nemhauser 2011.\n\"\"\"\nfunction ebd_σ(b::String)\n    sv = ebd_support_bool_vec(b)\n    return [i for i in 1:length(sv) if sv[i]]\nend\n\n\"\"\"\n\tThis function is the same I() function described in Vielma and Nemhauser 2011.\n\"\"\"\nfunction ebd_I(j, λCnt)\n    return [i for i in collect(1:Int((λCnt - 1))) if j in [i - 1, i]] #Page 52\nend\n\n\"\"\"\n\tThis function is the same S() function described in Vielma and Nemhauser 2011.\n\"\"\"\nfunction ebd_S(i)\n    (i <= 0) && error(\"Embedding utility S_[i] doesn't take i<=0\")\n    return [i, i - 1]\nend\n\n\"\"\"\n\tThis function checks whether the encoding method is compatible or not to obtain a valid mapping.\n\"\"\"\nfunction is_compatible_encoding(code_seq::Vector)\n    for i in 1:(length(code_seq)-1)\n        sum(\n            abs.(ebd_support_bool_vec(code_seq[i]) - ebd_support_bool_vec(code_seq[i+1])),\n        ) != 1 && return false\n    end\n    return true\nend\n\n\"\"\"\n\tThis is a utility function that convert the binary string into bool vector\n\"\"\"\nfunction ebd_support_bool_vec(s::String)\n    v = Vector{Bool}(undef, length(s))\n    for i in 1:length(s)\n        s[i] == '1' ? v[i] = true : v[i] = false\n    end\n    return v\nend\n\n\"\"\"\n\tThis is a utility function that convert the binary string into 0/1 vector\n\"\"\"\nfunction ebd_support_binary_vec(s::String)\n    v = Vector{Int}(undef, length(s))\n    for i in 1:length(s)\n        s[i] == '1' ? v[i] = 1 : v[i] = 0\n    end\n    return v\nend\n\n\"\"\"\n\tThis is the function that translate the bounding constraints (α¹b⁰+α²b¹ <= x <= α¹b¹+α²b²)\n\twith log # of binary variables, i.e., generate these constraints using log # of binary variables.\n\"\"\"\nfunction ebd_link_xα(\n    m::Optimizer,\n    α::Vector,\n    λCnt::Int,\n    disc_vec::Vector,\n    code_seq::Vector,\n    var_idx::Int,\n)\n    lifters = Dict()\n    exprs = Dict()\n    L = Int(ceil(log(2, λCnt - 1)))\n    P = length(disc_vec) - 1\n\n    # Expression expansion\n    for i in 1:P\n        code_vec = ebd_support_bool_vec(code_seq[i])\n        lifters, exprs = ebd_link_expression(code_vec, lifters, exprs, i)\n    end\n\n    # Construct Variable Vector\n    α_A = JuMP.@variable(\n        m.model_mip,\n        [1:length(keys(lifters))],\n        lower_bound = 0.0,\n        upper_bound = 1.0,\n        base_name = \"αA$(var_idx)\"\n    )\n    for i in keys(lifters) # Build first-level evaluation\n        relaxation_multilinear_binary(m.model_mip, α_A[lifters[i]-L], [α[j] for j in i])\n    end\n\n    α_R = [α; α_A] # Initialize/re-arrgange the variable sequence\n\n    for i in 1:P # Start populating sub-expressions\n        exprs[i][:expr] = JuMP.@expression(\n            m.model_mip,\n            sum(\n                exprs[i][:coefs][j] * α_R[exprs[i][:vars][j]] for\n                j in 1:exprs[i][:length] if exprs[i][:vars][j] != 0\n            ) + exprs[i][:vals]\n        )\n    end\n\n    # Contructing final constraints\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, var_idx) >=\n        sum(exprs[j][:expr] * disc_vec[j] for j in 1:P)\n    )\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, var_idx) <=\n        sum(exprs[j-1][:expr] * disc_vec[j] for j in 2:(P+1))\n    )\n\n    return\nend\n\n\"\"\"\n\tThis is a utility function used in ebd_link_xα() that constructing the mapping that links partitions with\n\tcombinations of binary variables.\n\"\"\"\nfunction ebd_link_expression(code::Vector, lift_dict::Dict, link_dict::Dict, p_idx::Int)\n    L = length(code)\n\n    # Strickly mapping p_idx -> x\n    code[1] ? coefs = Any[1] : coefs = Any[1, -1]\n    code[1] ? vars = Any[1] : vars = Any[0, 1]\n    prod(.!code) ? vals = 1.0 : vals = 0.0  # Marks the eventual expression is going have 1 or not\n\n    for i in 2:L\n        if code[i]\n            for j in 1:length(coefs)\n                (vars[j] == 0) ? vars[j] = i : vars[j] = [vars[j]; i] # Update vars\n                @assert length(vars) == length(coefs)\n            end\n        else\n            for j in 1:length(coefs)\n                (vars[j] == 0) ? push!(vars, i) : push!(vars, [vars[j]; i]) # Update vars with variable multiplier (ADDING)\n                (vars[j] == 0) ? push!(coefs, -1) : push!(coefs, coefs[j] * -1) # Update the coeffs with -1 (ADDING)\n            end\n        end\n    end\n    @assert length(coefs) == length(vars)\n\n    # Maintaining the dictionary of lifted variables and swp\n    for i in 1:length(vars)\n        if isa(vars[i], Vector)\n            !haskey(lift_dict, vars[i]) &&\n                (lift_dict[vars[i]] = L + length(keys(lift_dict)) + 1)\n            vars[i] = lift_dict[vars[i]]\n        end\n    end\n\n    # Maintain the expression dictionary\n    link_dict[p_idx] = Dict(\n        :p_idx => p_idx,\n        :coefs => coefs,\n        :vars => vars,\n        :vals => vals,\n        :length => length(coefs),\n    )\n\n    return lift_dict, link_dict\nend\n\n\"\"\"\n\tBuilt-in Encoding methods: binary encoding\n\tThis is a compatible encoding\n\"\"\"\nebd_binary(n, idx) = string(n, base = 2, pad = idx)\n\n\"\"\"\n\tBuilt-in Encoding methods: gray encoding\n\tThis is a compatible encoding\n\"\"\"\nfunction ebd_gray(n, idx)\n    code_decimal = xor(n, n >> 1)\n    return string(code_decimal, base = 2, pad = idx)\nend\n"
  },
  {
    "path": "src/heuristics.jl",
    "content": "\"\"\"\n    Ranking of variables involved in nonlinear terms for piecewise adaptive partitioning:\n    Ranked based on the absolute gap between each variable's solution from the lower-bounding MIP and the best feasible solution to the MINLP.\n    Currently doesn't support recursive convexification\n\"\"\"\nfunction update_disc_cont_var(m::Optimizer)\n    length(m.candidate_disc_vars) <= 15 && return   # Algorithm Separation Point\n\n    var_idxs = copy(m.candidate_disc_vars)\n    var_diffs = Vector{Float64}(\n        undef,\n        m.num_var_orig + length(keys(m.linear_terms)) + length(keys(m.nonconvex_terms)),\n    )\n\n    for i in 1:m.num_var_orig       # Original Variables\n        var_diffs[i] = abs(m.best_sol[i] - m.best_bound_sol[i])\n    end\n\n    !isempty(m.linear_terms) && (var_diffs = _eval_var_diffs!(m.linear_terms, var_diffs))\n    !isempty(m.nonconvex_terms) &&\n        (var_diffs = _eval_var_diffs!(m.nonconvex_terms, var_diffs))\n\n    distance = Dict(zip(var_idxs, var_diffs))\n    weighted_min_vertex_cover(m, distance)\n\n    (get_option(m, :log_level) > 100) &&\n        println(\"updated partition var selection => $(m.disc_vars)\")\n    return\nend\n\n# Helper function for sequential evaluation to avoid dependency issue\nfunction _eval_var_diffs!(terms::Dict{Any,Any}, var_diffs::Vector{Float64})\n    for i in 1:length(keys(terms))\n        for j in keys(terms)\n            if terms[j][:id] == i\n                var_diffs[terms[j][:lifted_var_ref].args[2]] =\n                    terms[j][:evaluator](terms[j], var_diffs)\n            end\n        end\n    end\n\n    return var_diffs\nend\n"
  },
  {
    "path": "src/log.jl",
    "content": "# Create dictionary of logs for timing and iteration counts\nfunction create_logs!(m)\n    logs = Dict{Symbol,Any}()\n\n    # Timers\n    logs[:presolve_time] = 0.0                           # Total presolve-time of the algorithm\n    logs[:total_time] = 0.0                              # Total run-time of the algorithm\n    logs[:time_left] = get_option(m, :time_limit)    # Total remaining time of the algorithm if time-out is specified\n\n    # Values\n    logs[:obj] = []                 # Iteration-based objective\n    logs[:bound] = []               # Iteration-based objective bound\n\n    # Counters\n    logs[:n_iter] = 0               # Number of iterations\n    logs[:n_feas] = 0               # Number of times a new feasible solution is obtained\n    logs[:ub_incumb_cnt] = 0        # Number of incumbents detected in the upper bound\n    logs[:lb_incumb_cnt] = 0        # Number of incumebnts detected in the lower bound\n    logs[:bt_iter] = 0\n\n    return m.logs = logs\nend\n\nfunction reset_timer(m::Optimizer)\n    m.logs[:total_time] = 0.0\n    m.logs[:time_left] = get_option(m, :time_limit)\n    return m\nend\n\nfunction logging_summary(m::Optimizer)\n    if get_option(m, :log_level) > 0\n        printstyled(\"\\nPROBLEM STATISTICS\\n\", color = :cyan, bold = true)\n        is_min_sense(m) && (println(\"  Objective sense = Min\"))\n        is_max_sense(m) && (println(\"  Objective sense = Max\"))\n        println(\n            \"  # Variables = \",\n            length([i for i in 1:m.num_var_orig if m.var_type[i] == :Cont]) +\n            length([i for i in 1:m.num_var_orig if m.var_type[i] == :Bin]) +\n            length([i for i in 1:m.num_var_orig if m.var_type[i] == :Int]),\n        )\n        println(\n            \"  # Bin-Int Variables = \",\n            length([i for i in 1:m.num_var_orig if m.var_type[i] == :Bin]) + length([i for i in 1:m.num_var_orig if m.var_type[i] == :Int]),\n        )\n        println(\"  # Constraints = \", m.num_constr_orig)\n        println(\"  # NL Constraints = \", m.num_nlconstr_orig)\n        println(\"  # Linear Constraints = \", m.num_lconstr_orig)\n        get_option(m, :recognize_convex) && println(\n            \"  # Detected convex constraints = $(length([i for i in m.constr_structure if i == :convex]))\",\n        )\n        println(\"  # Detected nonlinear terms = \", length(m.nonconvex_terms))\n        println(\n            \"  # Variables involved in nonlinear terms = \",\n            length(m.candidate_disc_vars),\n        )\n        println(\"  # Potential variables for partitioning = \", length(m.disc_vars))\n\n        printstyled(\"SUB-SOLVERS USED BY ALPINE\\n\", color = :cyan, bold = true)\n        if get_option(m, :minlp_solver) === nothing\n            println(\"  NLP local solver = \", m.nlp_solver_id)\n        else\n            println(\"  MINLP local solver = \", m.minlp_solver_id)\n        end\n        println(\"  MIP solver = \", m.mip_solver_id)\n\n        printstyled(\"ALPINE CONFIGURATION\\n\", color = :cyan, bold = true)\n        project = read(joinpath(dirname(@__DIR__), \"Project.toml\"), String)\n        m_version = match(r\"version \\= \\\"(.+?)\\\"\", project)\n        println(\"  Alpine version = \", m_version[1])\n        if is_min_sense(m)\n            println(\n                \"  Maximum iterations (lower-bounding MIPs) = \",\n                get_option(m, :max_iter),\n            )\n        elseif is_max_sense(m)\n            println(\n                \"  Maximum iterations (upper-bounding MIPs) = \",\n                get_option(m, :max_iter),\n            )\n        else\n            println(\"  Maximum iterations (bounding MIPs) =  \", get_option(m, :max_iter))\n        end\n\n        println(\"  Relative global optimality gap = \", get_option(m, :rel_gap) * 100, \"%\")\n\n        if get_option(m, :disc_var_pick) == 0\n            println(\"  Potential variables chosen for partitioning = All\")\n        elseif get_option(m, :disc_var_pick) == 1\n            println(\n                \"  Potential variables chosen for partitioning = Minimum vertex cover\",\n            )\n        end\n\n        if get_option(m, :partition_scaling_factor_branch)\n            println(\"  Partition scaling factor branch activated\")\n        else\n            println(\n                \"  Partition scaling factor = \",\n                get_option(m, :partition_scaling_factor),\n            )\n        end\n        (get_option(m, :convhull_ebd)) && println(\"  Using convhull_ebd formulation\")\n        (get_option(m, :convhull_ebd)) &&\n            println(\"  Encoding method = $(get_option(m, :convhull_ebd_encode))\")\n        (get_option(m, :convhull_ebd)) && println(\n            \"  Independent branching scheme = $(get_option(m, :convhull_ebd_ibs))\",\n        )\n        println(\"  Bound-tightening presolve = \", get_option(m, :presolve_bt))\n        get_option(m, :presolve_bt) && println(\n            \"  Maximum iterations (OBBT) = \",\n            get_option(m, :presolve_bt_max_iter),\n        )\n    end\nend\n\nfunction logging_head(m::Optimizer)\n    if !is_max_sense(m)\n        printstyled(\"LOWER-BOUNDING ITERATIONS\", color = :cyan, bold = true)\n        UB_iter = \"Incumbent\"\n        UB = \"Best Incumbent\"\n        LB = \"Lower Bound\"\n    else\n        printstyled(\"UPPER-BOUNDING ITERATIONS\", color = :cyan, bold = true)\n        UB_iter = \"Incumbent\"\n        UB = \"Best Incumbent\"\n        LB = \"Upper Bound\"\n    end\n    println(\n        \"\\n====================================================================================================\",\n    )\n    if m.logs[:time_left] < Inf\n        printstyled(\n            bold = true,\n            \"| Iter   | $UB_iter       | $UB      | $LB        | Gap (%)         | Time      \\n\",\n        )\n    end\nend\n\nfunction logging_row_entry(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n\n    b_len = 16\n    if !isempty(m.logs[:obj]) && isa(m.logs[:obj][end], Float64)\n        objstr = string(round(m.logs[:obj][end]; digits = 4))\n        spc = max(0, b_len - length(objstr))\n    else\n        objstr = string(\"-\")\n        spc = max(0, b_len - length(objstr))\n    end\n    UB_block = string(\" \", objstr, \" \"^spc)\n    if m.obj_expr_orig == :(+())\n        bdstr = 0.0\n        spc = b_len - 1\n    elseif expr_isconst(m.obj_expr_orig)\n        # This eval is okay because expr_isconst is true\n        bdstr = eval(m.obj_expr_orig)\n        spc = b_len - length(bdstr)\n    elseif isa(m.logs[:bound][end], Float64)\n        bdstr = string(round(m.logs[:bound][end]; digits = 4))\n        spc = max(0, b_len - length(bdstr))\n    else\n        bdstr = string(m.logs[:bound][end])\n        spc = b_len - length(bdstr)\n    end\n    LB_block = string(\" \", bdstr, \" \"^spc)\n\n    bobjstr = string(round(m.best_obj; digits = 4))\n    spc = max(0, b_len + 4 - length(bobjstr))\n    incumb_UB_block = string(\" \", bobjstr, \" \"^spc)\n\n    bbdstr = string(round(m.best_bound; digits = 4))\n    spc = max(0, b_len + 3 - length(bbdstr))\n    incumb_LB_block = string(\" \", bbdstr, \" \"^spc)\n\n    rel_gap = round(m.best_rel_gap * 100, digits = 3)\n    rel_gap > 999 ? rel_gap = \"LARGE\" : rel_gap = string(rel_gap)\n    GAP_block = string(\" \", rel_gap, \" \"^(b_len - length(rel_gap)))\n\n    UTIME_block = string(\n        \" \",\n        round(m.logs[:total_time]; digits = 2),\n        \"s\",\n        \" \"^(b_len - 1 - length(string(round(m.logs[:total_time]; digits = 2)))),\n    )\n\n    if m.logs[:time_left] < Inf\n        LTIME_block = \" \"\n    end\n\n    haskey(options, :finish_entry) ? (ITER_block = string(\" \", \"finish \")) :\n    (ITER_block = string(\" \", m.logs[:n_iter], \" \"^(7 - length(string(m.logs[:n_iter])))))\n\n    println(\n        \"|\",\n        ITER_block,\n        \"|\",\n        UB_block,\n        \"|\",\n        incumb_UB_block,\n        \"|\",\n        incumb_LB_block,\n        \"|\",\n        GAP_block,\n        \"|\",\n        UTIME_block,\n        LTIME_block,\n    )\n    return\nend\n\n#Logging and printing functions\n\n# Create dictionary of statuses for Alpine algorithm\nfunction create_status!(m)\n    status = Dict{Symbol,MOI.TerminationStatusCode}()\n\n    status[:local_solve] = MOI.OPTIMIZE_NOT_CALLED # Status of local solve\n    status[:bounding_solve] = MOI.OPTIMIZE_NOT_CALLED # Status of bounding solve\n    m.detected_incumbent = false\n    m.detected_bound = false\n\n    return m.status = status\nend\n\n\"\"\"\nThis function summarizes the eventual solver status based on all available information\nrecorded in the solver. The output status is self-defined which requires users to\nread our documentation to understand the details behind every status symbols.\n\"\"\"\nfunction summary_status(m::Optimizer)\n\n    # Alpine Solver Status Definition\n    # :Optimal : normal termination with optimality gap closed within time limits\n    # :UserLimits : any non-optimal termination related to user-defined parameters\n    # :Infeasible : termination with relaxation proven infeasible or detection of\n    #               variable bound conflicts\n    # :Heuristic : termination with feasible solution found but not bounds detected\n    #               happens when lower bound problem is extremely hard to solve\n    # :Unknown : termination with no exception recorded\n\n    if m.detected_bound && m.detected_incumbent\n        m.alpine_status =\n            m.best_rel_gap > get_option(m, :rel_gap) ? MOI.OTHER_LIMIT : MOI.OPTIMAL\n    elseif m.status[:bounding_solve] == MOI.INFEASIBLE\n        m.alpine_status = MOI.INFEASIBLE\n    elseif m.detected_bound && !m.detected_incumbent\n        m.alpine_status = MOI.OTHER_LIMIT\n    elseif !m.detected_bound && m.detected_incumbent\n        m.alpine_status = MOI.LOCALLY_SOLVED\n    else\n        @warn \"  [EXCEPTION] Indefinite Alpine status. Please report your instance (& solver configuration) as an issue (https://github.com/lanl-ansi/Alpine.jl/issues) to help us make Alpine better.\"\n    end\n\n    raw = MOI.get(m, MOI.RawStatusString())\n    printstyled(\"\\n*** $raw ***\\n\")\n\n    return\nend\n\n# Some useful logging details:\n\n# for i in ALPINE_C_NLTERMS\n#     cnt = length([1 for j in keys(m.nonconvex_terms) if m.nonconvex_terms[j][:nonlinear_type] == i])\n#     cnt > 0 && println(\"\\tTerm $(i) Count = $(cnt) \")\n# end\n# println(\"  Maximum solution time = \", get_option(m, :time_limit))\n# println(\"  Basic bound propagation = \", get_option(m, :presolve_bp))\n# println(\"  Conseuctive solution rejection = after \", get_option(m, :disc_consecutive_forbid), \" times\")\n# get_option(m, :presolve_bt) && println(\"bound tightening presolve algorithm = \", get_option(m, :presolve_bt)_algo)\n# get_option(m, :presolve_bt) && println(\"bound tightening presolve width tolerance = \", get_option(m, :presolve_bt)_width_tol)\n# get_option(m, :presolve_bt) && println(\"bound tightening presolve output tolerance = \", get_option(m, :presolve_bt)_output_tol)\n# get_option(m, :presolve_bt) && println(\"bound tightening presolve relaxation = \", get_option(m, :presolve_bt)_relax)\n# get_option(m, :presolve_bt) && println(\"bound tightening presolve mip regulation time = \", get_option(m, :presolve_bt)_mip_time_limit)\n"
  },
  {
    "path": "src/main_algorithm.jl",
    "content": "const STATUS_LIMIT = [\n    MOI.ITERATION_LIMIT,\n    MOI.TIME_LIMIT,\n    MOI.NODE_LIMIT,\n    MOI.SOLUTION_LIMIT,\n    MOI.MEMORY_LIMIT,\n    MOI.OBJECTIVE_LIMIT,\n    MOI.NORM_LIMIT,\n    MOI.OTHER_LIMIT,\n]\nconst STATUS_OPT =\n    [MOI.OPTIMAL, MOI.LOCALLY_SOLVED, MOI.ALMOST_OPTIMAL, MOI.ALMOST_LOCALLY_SOLVED]\n\nconst STATUS_WARM_START = [MOI.OPTIMIZE_NOT_CALLED]\n\nconst STATUS_INF = [MOI.INFEASIBLE, MOI.LOCALLY_INFEASIBLE]\n\nfunction features_available(m::Optimizer)\n    features = [:Grad, :Jac, :JacVec, :ExprGraph]\n    if !m.disable_hessian\n        push!(features, :Hess)\n        push!(features, :HessVec)\n    end\n\n    return features\nend\n\nfunction load!(m::Optimizer)\n\n    # Initialize NLP interface\n    requested_features = features_available(m)\n    if m.d_orig !== nothing\n        MOI.initialize(m.d_orig, requested_features::Vector{Symbol})\n    end\n    for feat in requested_features\n        if !(feat in features_available(m))\n            error(\"Unsupported feature $feat\")\n        end\n    end\n\n    # Collect objective & constraint expressions\n    if m.has_nl_objective\n        m.obj_expr_orig =\n            expr_isolate_const(_variable_index_to_index(MOI.objective_expr(m.d_orig))) # see in nlexpr.jl if this expr isolation has any issue\n    elseif m.objective_function isa Nothing\n        m.obj_expr_orig = Expr(:call, :+)\n    else\n        m.obj_expr_orig = _moi_function_to_expr(m.objective_function)\n    end\n\n    # Collect original variable type and build dynamic variable type space\n    m.var_type = copy(m.var_type_orig)\n    m.int_vars = [i for i in 1:m.num_var_orig if m.var_type[i] == :Int]\n    m.bin_vars = [i for i in 1:m.num_var_orig if m.var_type[i] == :Bin]\n\n    if !isempty(m.int_vars) || !isempty(m.bin_vars)\n        (get_option(m, :minlp_solver) === nothing) && (error(\n            \"No MINLP local solver specified; use option 'minlp_solver' to specify a MINLP local solver\",\n        ))\n    end\n\n    m.num_constr_orig += length(m.nl_constraint_bounds_orig)\n    m.num_nlconstr_orig += length(m.nl_constraint_bounds_orig)\n    append!(m.constraint_bounds_orig, m.nl_constraint_bounds_orig)\n    for i in eachindex(m.nl_constraint_bounds_orig)\n        push!(\n            m.constr_expr_orig,\n            _variable_index_to_index(MOI.constraint_expr(m.d_orig, i)),\n        )\n        push!(m.constr_structure, :generic_nonlinear)\n    end\n\n    # Summarize constraints information in original model\n    m.constr_type_orig = Array{Symbol}(undef, m.num_constr_orig)\n\n    for i in 1:m.num_constr_orig\n        if m.constraint_bounds_orig[i].lower > -Inf &&\n           m.constraint_bounds_orig[i].upper < Inf\n            m.constr_type_orig[i] = :(==)\n        elseif m.constraint_bounds_orig[i].lower > -Inf\n            m.constr_type_orig[i] = :(>=)\n        else\n            m.constr_type_orig[i] = :(<=)\n        end\n    end\n\n    # Initialize recognizable structure properties with :none\n    m.obj_structure = :none\n\n    @assert m.num_constr_orig == m.num_nlconstr_orig + m.num_lconstr_orig\n    m.is_obj_linear_orig =\n        !m.has_nl_objective && m.objective_function isa MOI.ScalarAffineFunction{Float64}\n    m.is_obj_linear_orig ? (m.obj_structure = :generic_linear) :\n    (m.obj_structure = :generic_nonlinear)\n    isa(m.obj_expr_orig, Number) && (m.obj_structure = :constant)\n\n    # Populate data to create the bounding MIP model\n    recategorize_var(m)             # Initial round of variable re-categorization\n\n    # Solver-dependent detection\n    _fetch_mip_solver_identifier(m)\n    _fetch_nlp_solver_identifier(m)\n    _fetch_minlp_solver_identifier(m)\n\n    # Main Algorithmic Initialization\n    process_expr(m)                         # Compact process of every expression\n    init_tight_bound(m)                     # Initialize bounds for algorithmic processes\n    resolve_var_bounds(m)                   # resolve lifted var bounds\n    pick_disc_vars(m)                       # Picking variables to be discretized\n    init_disc(m)                            # Initialize discretization dictionaries\n\n    # Turn-on bt presolve if variables are not discrete\n    if isempty(m.int_vars) &&\n       length(m.bin_vars) <= 50 &&\n       m.num_var_orig <= 10000 &&\n       length(m.candidate_disc_vars) <= 300 &&\n       get_option(m, :presolve_bt) == nothing\n        set_option(m, :presolve_bt, true)\n        println(\"Automatically turning on bound-tightening presolve\")\n    elseif get_option(m, :presolve_bt) == nothing  # If no use indication\n        set_option(m, :presolve_bt, false)\n    end\n\n    if length(m.bin_vars) > 200 || m.num_var_orig > 2000\n        println(\n            \"Automatically turning OFF 'partition_scaling_factor_branch' due to the size of the problem\",\n        )\n        set_option(m, :partition_scaling_factor_branch, false)\n    end\n\n    # Initialize the solution pool\n    m.bound_sol_pool = initialize_solution_pool(m, 0)  # Initialize the solution pool\n\n    # Check if any illegal term exist in the warm-solution\n    any(isnan, m.best_sol) && (m.best_sol = zeros(length(m.best_sol)))\n\n    # Initialize log\n    logging_summary(m)\n\n    return\nend\n\n\"\"\"\n   High-level Function\n\"\"\"\nfunction MOI.optimize!(m::Optimizer)\n    load!(m)\n    if getproperty(m, :presolve_infeasible)\n        summary_status(m)\n        return\n    end\n\n    presolve(m)\n\n    if !check_exit(m) && get_option(m, :apply_partitioning)\n        global_solve(m)\n        get_option(m, :log_level) > 0 && logging_row_entry(m, finish_entry = true)\n        println(\n            \"====================================================================================================\",\n        )\n    end\n\n    summary_status(m)\n\n    return\nend\n\n\"\"\"\n   global_solve(m::Optimizer)\n\nPerform global optimization algorithm that is based on the adaptive piecewise convexification.\nThis iterative algorithm loops over [`bounding_solve`](@ref) and [`local_solve`](@ref) until the optimality gap between the lower bound (relaxed problem with min. objective) and the upper bound (feasible problem) is within the user prescribed limits.\nEach [`bounding_solve`](@ref) provides a lower bound that serves as the partitioning point for the next iteration (this feature can be modified given a different `add_adaptive_partition`).\nEach [`local_solve`](@ref) provides an incumbent feasible solution. The algorithm terminates when atleast one of these conditions are satisfied: time limit, optimality condition, or iteration limit.\n\n\"\"\"\nfunction global_solve(m::Optimizer)\n    get_option(m, :log_level) > 0 && logging_head(m)\n    get_option(m, :presolve_track_time) || reset_timer(m)\n    while !check_exit(m)\n        m.logs[:n_iter] += 1\n        create_bounding_mip(m)                  # Build the relaxation model\n        bounding_solve(m)                       # Solve the relaxation model\n        update_opt_gap(m)                       # Update optimality gap\n        check_exit(m) && break                  # Feasibility check\n        get_option(m, :log_level) > 0 && logging_row_entry(m)  # Logging\n        local_solve(m)                          # Solve local model for feasible solution\n        update_opt_gap(m)                       # Update optimality gap\n        check_exit(m) && break                  # Detect optimality termination\n        algorithm_automation(m)                 # Automated adjustments\n    end\n\n    return\nend\n\n\"\"\"\n   presolve(m::Optimizer)\n\"\"\"\nfunction presolve(m::Optimizer)\n    start_presolve = time()\n    get_option(m, :log_level) > 0 &&\n        printstyled(\"PRESOLVE \\n\", color = :cyan, bold = true)\n    get_option(m, :log_level) > 0 && println(\"  Doing local search\")\n\n    if get_option(m, :use_start_as_incumbent)\n        # Check for bound feasibility of the warm start value\n        if !(m.l_var_orig <= m.warm_start_value <= m.u_var_orig)\n            error(\n                \"Provide a valid, feasible, warm starting point. Else, set use_start_as_incumbent to false\",\n            )\n        end\n\n        obj_warmval = if m.has_nl_objective\n            MOI.eval_objective(m.d_orig, m.warm_start_value)\n        else\n            MOI.Utilities.eval_variables(\n                vi -> m.warm_start_value[vi.value],\n                m.objective_function,\n            )\n        end\n        update_incumbent(m, obj_warmval, m.warm_start_value)\n        m.status[:local_solve] = MOI.OPTIMIZE_NOT_CALLED\n        get_option(m, :log_level) > 0 && println(\n            \"  Using warm starting point as a local incumbent solution with value $(round(m.best_obj, digits=4))\",\n        )\n    else\n        local_solve(m, presolve = true)\n    end\n\n    # Solver status\n    if m.status[:local_solve] in union(STATUS_OPT, STATUS_LIMIT, STATUS_WARM_START)\n        if !get_option(m, :use_start_as_incumbent)\n            get_option(m, :log_level) > 0 && println(\n                \"  Local solver returns a feasible point with value $(round(m.best_obj, digits=4))\",\n            )\n        end\n        bound_tightening_wrapper(m, use_bound = true)    # performs bound-tightening with the local solve objective value\n        get_option(m, :presolve_bt) && init_disc(m)            # Re-initialize discretization dictionary on tight bounds\n        get_option(m, :partition_scaling_factor_branch) && (set_option(\n            m,\n            :partition_scaling_factor,\n            update_partition_scaling_factor(m, true),\n        ))\n\n    elseif m.status[:local_solve] in STATUS_INF\n        (get_option(m, :log_level) > 0) &&\n            println(\"  Bound tightening without objective bounds (OBBT)\")\n        bound_tightening_wrapper(m, use_bound = false)                      # do bound tightening without objective value\n        (get_option(m, :partition_scaling_factor_branch)) && (set_option(\n            m,\n            :partition_scaling_factor,\n            update_partition_scaling_factor(m, true),\n        ))\n        get_option(m, :presolve_bt) && init_disc(m)\n\n    elseif m.status[:local_solve] == MOI.INVALID_MODEL\n        @warn \" Warning: Presolve ends with local solver yielding $(m.status[:local_solve]). \\n This may come from Ipopt's `:Not_Enough_Degrees_Of_Freedom`.\"\n    elseif !get_option(m, :use_start_as_incumbent)\n        @warn \" Warning: Presolve ends with local solver yielding $(m.status[:local_solve]).\"\n    end\n\n    cputime_presolve = time() - start_presolve\n    m.logs[:presolve_time] += cputime_presolve\n    m.logs[:total_time] = m.logs[:presolve_time]\n    m.logs[:time_left] -= m.logs[:presolve_time]\n\n    if get_option(m, :presolve_bt)\n        (get_option(m, :log_level) > 0) && println(\n            \"  Post-presolve optimality gap: $(round(m.presolve_best_rel_gap; digits = 3))%\",\n        )\n    end\n    (get_option(m, :log_level) > 0) &&\n        println(\"  Completed presolve in $(round.(m.logs[:total_time]; digits = 2))s\")\n\n    return\nend\n\n\"\"\"\n   A wrapper function that collects automated solver adjustments within the main while loop.\n\"\"\"\nfunction algorithm_automation(m::Optimizer)\n\n    # Only if a feasible solution is detected\n    if (get_option(m, :disc_var_pick) == 3) && m.detected_incumbent\n        update_disc_cont_var(m)\n    end\n\n    if get_option(m, :partition_scaling_factor_branch)\n        set_option(m, :partition_scaling_factor, update_partition_scaling_factor(m, true))    # Only perform for a maximum three times\n    end\n\n    return\nend\n\n\"\"\"\n   Summarized function to determine whether to interrupt the main while loop.\n\"\"\"\nfunction check_exit(m::Optimizer)\n\n    # constant objective with feasible local solve check\n    if expr_isconst(m.obj_expr_orig) &&\n       (m.status[:local_solve] == MOI.OPTIMAL || m.status == MOI.LOCALLY_SOLVED)\n        m.best_bound = m.obj_expr_orig\n        m.best_rel_gap = 0.0\n        m.best_abs_gap = 0.0\n        m.status[:bounding_solve] = MOI.OPTIMAL\n        m.alpine_status = :Optimal\n        m.detected_bound = true\n        return true\n    end\n\n    # Infeasibility check\n    m.status[:bounding_solve] == MOI.INFEASIBLE && return true\n\n    # Unbounded check\n    m.status[:bounding_solve] == MOI.DUAL_INFEASIBLE && return true\n\n    # Optimality check\n    if m.best_rel_gap <= get_option(m, :rel_gap)\n        m.detected_bound = true\n        return true\n    end\n    m.logs[:n_iter] >= get_option(m, :max_iter) && return true\n    m.best_abs_gap <= get_option(m, :abs_gap) && return true\n\n    # User-limits check\n    m.logs[:time_left] < get_option(m, :tol) && return true\n\n    return false\nend\n\nfunction load_nonlinear_model(m::Optimizer, model::MOI.ModelLike, l_var, u_var)\n    x = MOI.add_variables(model, m.num_var_orig)\n    for i in eachindex(x)\n        set = _bound_set(l_var[i], u_var[i])\n        if set !== nothing\n            MOI.add_constraint(model, x[i], set)\n        end\n    end\n    for (func, set) in m.scalar_constraints\n        MOI.add_constraint(model, func, set)\n    end\n    MOI.set(model, MOI.ObjectiveSense(), m.sense_orig)\n    if m.objective_function !== nothing\n        MOI.set(\n            model,\n            MOI.ObjectiveFunction{typeof(m.objective_function)}(),\n            m.objective_function,\n        )\n    end\n\n    if m.d_orig !== nothing\n        block =\n            MOI.NLPBlockData(m.nl_constraint_bounds_orig, m.d_orig, m.has_nl_objective)\n        MOI.set(model, MOI.NLPBlock(), block)\n    end\n\n    return x\nend\n\nfunction set_variable_type(model::MOI.ModelLike, xs, variable_types)\n    for (x, variable_type) in zip(xs, variable_types)\n        if variable_type == :Int\n            MOI.add_constraint(model, x, MOI.Integer())\n        elseif variable_type == :Bin\n            MOI.add_constraint(model, x, MOI.ZeroOne())\n        else\n            @assert variable_type == :Cont\n        end\n    end\nend\n\n\"\"\"\n   local_solve(m::Optimizer, presolve::Bool=false)\n\nPerform a local NLP or MINLP solve to obtain a feasible solution.\nThe `presolve` option is set to `true` when the function is invoked in [`presolve`](@ref).\nOtherwise, the function is invoked from [`bounding_solve`](@ref).\n\n\"\"\"\nfunction local_solve(m::Optimizer; presolve = false)\n    local_nlp_status = :Unknown\n\n    var_type_screener = [i for i in m.var_type_orig if i in [:Bin, :Int]]\n\n    if presolve\n        if !isempty(var_type_screener) && get_option(m, :minlp_solver) !== nothing\n            local_solve_model =\n                MOI.instantiate(get_option(m, :minlp_solver), with_bridge_type = Float64)\n        elseif !isempty(var_type_screener)\n            local_solve_model =\n                MOI.instantiate(get_option(m, :nlp_solver), with_bridge_type = Float64)\n        else\n            local_solve_model =\n                MOI.instantiate(get_option(m, :nlp_solver), with_bridge_type = Float64)\n        end\n    else\n        local_solve_model =\n            MOI.instantiate(get_option(m, :nlp_solver), with_bridge_type = Float64)\n    end\n\n    if presolve == false\n        l_var, u_var = fix_domains(m)\n    else\n        l_var, u_var = m.l_var_tight[1:m.num_var_orig], m.u_var_tight[1:m.num_var_orig]\n    end\n\n    x = load_nonlinear_model(m, local_solve_model, l_var, u_var)\n    if m.d_orig !== nothing\n        MOI.initialize(m.d_orig, [:Grad, :Jac, :Hess, :HessVec, :ExprGraph]) # Safety scheme for sub-solvers re-initializing the NLPEvaluator\n    end\n\n    if !presolve\n        warmval = m.best_sol[1:m.num_var_orig]\n    else\n        warmval = m.warm_start_value[1:m.num_var_orig]\n    end\n    MOI.set(local_solve_model, MOI.VariablePrimalStart(), x, warmval)\n\n    # do_heuristic = false\n\n    # The only case when MINLP solver is actually used\n    if presolve && !isempty(var_type_screener)\n        if get_option(m, :minlp_solver) === nothing\n            error(\"Provide a valid MINLP solver\")\n            # do_heuristic = true\n        else\n            set_variable_type(local_solve_model, x, m.var_type_orig)\n        end\n    end\n\n    start_local_solve = time()\n    MOI.optimize!(local_solve_model)\n    local_nlp_status = MOI.get(local_solve_model, MOI.TerminationStatus())\n\n    # if !do_heuristic\n    #     local_nlp_status = MOI.get(local_solve_model, MOI.TerminationStatus())\n    # end\n\n    cputime_local_solve = time() - start_local_solve\n    m.logs[:total_time] += cputime_local_solve\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n\n    # if do_heuristic\n    # m.status[:local_solve] = heu_basic_rounding(m, MOI.get(local_solve_model, MOI.VariablePrimal(), x))\n    # return\n\n    if local_nlp_status in STATUS_OPT || local_nlp_status in STATUS_LIMIT\n        candidate_obj = MOI.get(local_solve_model, MOI.ObjectiveValue())\n        sol_temp = MOI.get(local_solve_model, MOI.VariablePrimal(), x)\n        candidate_sol = Vector{Float64}()\n\n        feas_tol = 1E-5\n\n        for i in 1:length(sol_temp)\n            if (sol_temp[i] >= m.l_var_orig[i] - feas_tol) &&\n               (sol_temp[i] <= m.l_var_orig[i] + feas_tol)\n                push!(candidate_sol, m.l_var_orig[i])\n            elseif (sol_temp[i] >= m.u_var_orig[i] - feas_tol) &&\n                   (sol_temp[i] <= m.u_var_orig[i] + feas_tol)\n                push!(candidate_sol, m.u_var_orig[i])\n            else\n                push!(candidate_sol, round(sol_temp[i], digits = 7))\n            end\n        end\n\n        @assert length(candidate_sol) == length(sol_temp)\n        update_incumbent(m, candidate_obj, candidate_sol)\n        m.status[:local_solve] = local_nlp_status\n        return\n\n        # elseif local_nlp_status in STATUS_INF\n        #     heu_pool_multistart(m) == MOI.LOCALLY_SOLVED && return\n        #     push!(m.logs[:obj], \"INF\")\n        #     m.status[:local_solve] = MOI.LOCALLY_INFEASIBLE\n        #     return\n\n    elseif local_nlp_status == MOI.DUAL_INFEASIBLE\n        push!(m.logs[:obj], \"U\")\n        m.status[:local_solve] = MOI.DUAL_INFEASIBLE\n        if presolve\n            @warn \"  Warning: NLP local solve is unbounded.\"\n        else\n            @warn \"  Warning: NLP local solve is unbounded.\"\n        end\n        return\n\n    else\n        push!(m.logs[:obj], \"E\")\n        m.status[:local_solve] = MOI.OTHER_ERROR\n        # if presolve\n        #     @warn \" Warning: NLP solve failure $(local_nlp_status).\"\n        # else\n        #     @warn \" Warning: NLP local solve failure.\"\n        # end\n        return\n    end\n\n    return\nend\n\n\"\"\"\n   bounding_solve(m::Optimizer; kwargs...)\n\nThis step usually solves a convex MILP/MIQCP/MIQCQP problem for lower bounding the given minimization problem.\nIt solves the problem built upon a piecewise convexification based on the discretization sictionary of some variables.\nSee `create_bounding_mip` for more details of the problem solved here.\n\"\"\"\nfunction bounding_solve(m::Optimizer)\n    convertor = Dict(MOI.MAX_SENSE => :<, MOI.MIN_SENSE => :>)\n\n    # Updates time metric and the termination bounds\n    set_mip_time_limit(m)\n    # update_boundstop_options(m)\n\n    # ================= Solve Start ================ #\n    start_bounding_solve = time()\n    JuMP.optimize!(m.model_mip)\n    status = JuMP.termination_status(m.model_mip)\n    m.logs[:total_time] += time() - start_bounding_solve\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n    # ================= Solve End ================ #\n\n    if status in STATUS_OPT || status in STATUS_LIMIT\n        candidate_bound =\n            (status == MOI.OPTIMAL) ? JuMP.objective_value(m.model_mip) :\n            JuMP.objective_bound(m.model_mip)\n        candidate_bound_sol = [\n            round.(JuMP.value(_index_to_variable_ref(m.model_mip, i)); digits = 7) for\n            i in 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)\n        ]\n\n        # Experimental code\n        measure_relaxed_deviation(m, sol = candidate_bound_sol)\n        if get_option(m, :disc_consecutive_forbid) > 0\n            m.bound_sol_history[mod(\n                m.logs[:n_iter] - 1,\n                get_option(m, :disc_consecutive_forbid),\n            )+1] = copy(candidate_bound_sol) # Requires proper offseting\n        end\n        push!(m.logs[:bound], candidate_bound)\n        is_tighter = ifelse(\n            m.sense_orig == MOI.MAX_SENSE,\n            candidate_bound < m.best_bound,\n            candidate_bound > m.best_bound,\n        )\n        if is_tighter\n            m.best_bound = candidate_bound\n            m.best_bound_sol = copy(candidate_bound_sol)\n            m.status[:bounding_solve] = status\n            m.detected_bound = true\n        end\n\n        # collect_lb_pool(m)    # Collect a pool of sub-optimal solutions - currently implemented for Gurobi only\n\n    elseif status in STATUS_INF || status == MOI.INFEASIBLE_OR_UNBOUNDED\n        push!(m.logs[:bound], \"-\")\n        m.status[:bounding_solve] = MOI.INFEASIBLE\n        @warn \"  Warning: Infeasibility detected in the MIP solver\"\n\n        if ALPINE_DEBUG\n            @warn \"Use Alpine.print_iis_gurobi(m.model_mip) function in src/utility.jl (commented out code) for further investigation, if your MIP solver is Gurobi\"\n        end\n\n    elseif status == :Unbounded\n        m.status[:bounding_solve] = MOI.DUAL_INFEASIBLE\n        @warn \"  Warning: MIP solver returns unbounded\"\n\n    else\n        error(\"  Warning: MIP solver failure $(status)\")\n    end\n\n    return\nend\n\n\"\"\"\n   pick_disc_vars(m::Optimizer)\n\nThis function helps pick the variables for discretization. The method chosen depends on user-inputs.\nIn case when `indices::Int` is provided, the method is chosen as built-in method. Currently,\nthere are two built-in options for users as follows:\n\n* `max_cover (get_option(m, :disc_var_pick)=0, default)`: pick all variables involved in the non-linear term for discretization\n* `min_vertex_cover (get_option(m, :disc_var_pick)=1)`: pick a minimum vertex cover for variables involved in non-linear terms so that each non-linear term is at least convexified\n\nFor advanced usage, `get_option(m, :disc_var_pick)` allows `::Function` inputs. User can provide his/her own function to choose the variables for discretization.\n\n\"\"\"\nfunction pick_disc_vars(m::Optimizer)\n    disc_var_pick = get_option(m, :disc_var_pick)\n\n    if isa(disc_var_pick, Function)\n        disc_var_pick(m)\n        length(m.disc_vars) == 0 &&\n            length(m.nonconvex_terms) > 0 &&\n            error(\n                \"[USER FUNCTION] must select at least one variable to perform discretization for convexificiation purpose\",\n            )\n    elseif isa(disc_var_pick, Int)\n        if disc_var_pick == 0\n            get_candidate_disc_vars(m)\n        elseif disc_var_pick == 1\n            min_vertex_cover(m)\n        elseif disc_var_pick == 2\n            (length(m.candidate_disc_vars) > 15) ? min_vertex_cover(m) :\n            get_candidate_disc_vars(m)\n        elseif disc_var_pick == 3 # Initial\n            (length(m.candidate_disc_vars) > 15) ? min_vertex_cover(m) :\n            get_candidate_disc_vars(m)\n        else\n            error(\n                \"Unsupported default indicator for picking variables for discretization\",\n            )\n        end\n    else\n        error(\n            \"Input for parameter :disc_var_pick is illegal. Should be either a Int for default methods indexes or functional inputs.\",\n        )\n    end\n\n    return\nend\n"
  },
  {
    "path": "src/multilinear.jl",
    "content": "function amp_post_convhull(m::Optimizer; kwargs...)\n    options = Dict(kwargs)\n    haskey(options, :use_disc) ? d = options[:use_disc] : d = m.discretization\n\n    # Variable holders\n    λ = Dict()  # Extreme points and multipliers\n    α = Dict()  # Partitioning Variables\n    β = Dict()  # Lifted variables for exact formulation\n\n    # Convexification for non-convex terms\n    contains_multilinear = false\n    for k in keys(m.nonconvex_terms)\n        nl_type = m.nonconvex_terms[k][:nonlinear_type]\n        if ((nl_type == :MULTILINEAR) || (nl_type == :BILINEAR)) &&\n           (m.nonconvex_terms[k][:convexified] == false)\n            λ, α = amp_convexify_multilinear(m, k, λ, α, d)\n            contains_multilinear = true\n        elseif nl_type == :MONOMIAL && !m.nonconvex_terms[k][:convexified]\n            λ, α = amp_convexify_quadratic_univariate(m, k, λ, α, d)\n        elseif nl_type == :BINLIN && !m.nonconvex_terms[k][:convexified]\n            β = amp_convexify_binlin(m, k, β)\n        elseif nl_type == :BINPROD && !m.nonconvex_terms[k][:convexified]\n            β = amp_convexify_multilinear_binary(m, k, β)\n        end\n    end\n\n    # Add lambda linking constraints\n    if m.options.linking_constraints && contains_multilinear\n        _add_multilinear_linking_constraints(m, λ)\n    end\n\n    # Code for warm starting bounding MIP iterations\n    get_option(m, :convhull_warmstart) &&\n        !isempty(m.best_bound_sol) &&\n        amp_warmstart_α(m, α)\n\n    return\nend\n\nfunction amp_convexify_multilinear(\n    m::Optimizer,\n    k::Any,\n    λ::Dict,\n    α::Dict,\n    discretization::Dict,\n)\n    m.nonconvex_terms[k][:convexified] = true  # Bookeeping the convexified terms\n\n    ml_indices, dim, extreme_point_cnt = amp_convhull_prepare(m, discretization, k)   # convert key to easy read mode\n    λ = amp_convhull_λ(m, k, ml_indices, λ, extreme_point_cnt, dim)\n    λ = populate_convhull_extreme_values(\n        m,\n        discretization,\n        ml_indices,\n        λ,\n        dim,\n        ones(Int, length(dim)),\n    )\n    α = amp_convhull_α(m, ml_indices, α, dim, discretization)\n    amp_post_convhull_constrs(m, λ, α, ml_indices, dim, extreme_point_cnt, discretization)\n\n    return λ, α\nend\n\nfunction amp_convexify_quadratic_univariate(\n    m::Optimizer,\n    k::Any,\n    λ::Dict,\n    α::Dict,\n    discretization::Dict,\n)\n    m.nonconvex_terms[k][:convexified] = true  # Bookeeping the convexified terms\n\n    monomial_index, dim, extreme_point_cnt =\n        amp_convhull_prepare(m, discretization, k, monomial = true)\n    λ = amp_convhull_λ(m, k, monomial_index, λ, extreme_point_cnt, dim)\n    λ = populate_convhull_extreme_values(m, discretization, monomial_index, λ, 2)\n    α = amp_convhull_α(m, [monomial_index], α, dim, discretization)\n    amp_post_convhull_constrs(m, λ, α, monomial_index, discretization)\n\n    return λ, α\nend\n\nfunction amp_convexify_binlin(m::Optimizer, k::Any, β::Dict)\n    m.nonconvex_terms[k][:convexified] = true  # Bookeeping the convexified terms\n\n    @assert length(m.nonconvex_terms[k][:var_idxs]) == 2\n\n    lift_idx = m.nonconvex_terms[k][:y_idx]\n\n    if haskey(β, lift_idx)\n        return β\n    else\n        β[lift_idx] = _index_to_variable_ref(m.model_mip, lift_idx)\n    end\n\n    bin_idx = [i for i in m.nonconvex_terms[k][:var_idxs] if m.var_type[i] == :Bin]\n    cont_idx = [i for i in m.nonconvex_terms[k][:var_idxs] if m.var_type[i] != :Bin]\n\n    @assert length(bin_idx) == length(cont_idx) == 1\n\n    bin_idx = bin_idx[1]\n    cont_idx = cont_idx[1]\n\n    relaxation_bilinear(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, lift_idx),\n        _index_to_variable_ref(m.model_mip, bin_idx),\n        _index_to_variable_ref(m.model_mip, cont_idx),\n        0,\n        1,\n        m.l_var_tight[cont_idx],\n        m.u_var_tight[cont_idx],\n    )\n\n    return β\nend\n\nfunction amp_convexify_multilinear_binary(m::Optimizer, k::Any, β::Dict)\n    m.nonconvex_terms[k][:convexified] = true  # Bookeeping the convexified terms\n\n    lift_idx = m.nonconvex_terms[k][:y_idx]\n    if haskey(β, lift_idx)\n        return β    # Already constructed\n    else\n        β[lift_idx] = _index_to_variable_ref(m.model_mip, lift_idx)\n    end\n\n    z = _index_to_variable_ref(m.model_mip, m.nonconvex_terms[k][:y_idx])\n    x = [_index_to_variable_ref(m.model_mip, i) for i in m.nonconvex_terms[k][:var_idxs]]\n\n    if length(x) >= 1\n        relaxation_multilinear_binary(m.model_mip, z, x)\n    end\n\n    return β\nend\n\n\"\"\"\n    Method for general nonlinear terms\n\"\"\"\nfunction amp_convhull_prepare(m::Optimizer, d::Dict, nonlinear_key::Any; monomial = false)\n    counted_var = []                # Keep both vector and set for collection sake\n    id = Set()                      # Coverting the nonlinear indices into a set\n\n    if isa(nonlinear_key, Vector)\n        for var in nonlinear_key        # This output regulates the sequence of how composing variable should be arranged\n            @assert isa(var, Expr)\n            m.var_type[var.args[2]] in [:Cont, :Int] && push!(id, var.args[2])\n            m.var_type[var.args[2]] in [:Cont, :Int] && push!(counted_var, var.args[2])\n        end\n    elseif isa(nonlinear_key, Dict)\n        for var in nonlinear_key[:vars]\n            @assert isa(var, Int)\n            m.var_type[var] in [:Cont, :Int] && push!(id, var)\n            m.var_type[var] in [:Cont, :Int] && push!(counted_var, var)\n        end\n    end\n\n    if length(id) < length(counted_var) # Got repeating terms, now the sequence matters\n        id = []\n        for var in nonlinear_key\n            m.var_type[var.args[2]] in [:Cont, :Int] && push!(id, var.args[2])\n        end\n    end\n\n    dim = [length(d[i]) for i in id]\n\n    monomial && return id[1], tuple(dim[1]), dim[1]   # One less dimension is required\n    return id, tuple([i for i in dim]...), prod(dim)\nend\n\n\"\"\"\n    Method for integers\n\"\"\"\nfunction amp_convhull_prepare(m::Optimizer, d::Dict, idx::Int)\n    return [idx], tuple(length(d[idx])), length(d[idx])\nend\n\n\"\"\"\n    Method for general nonlinear terms\n\"\"\"\nfunction amp_convhull_λ(\n    m::Optimizer,\n    nonlinear_key::Any,\n    indices::Any,\n    λ::Dict,\n    ext_cnt::Int,\n    dim::Tuple,\n)\n    y_idx = m.nonconvex_terms[nonlinear_key][:y_idx]\n\n    @assert !(y_idx in keys(λ))\n    λ[indices] = Dict(\n        :dim => dim,\n        :lifted_var_idx => y_idx,\n        :indices => reshape([1:ext_cnt;], dim),\n        :vars => JuMP.@variable(\n            m.model_mip,\n            [1:ext_cnt],\n            lower_bound = 0,\n            base_name = \"L$(y_idx)\"\n        ),\n        :vals => ones(dim),\n    )\n\n    return λ\nend\n\n\"\"\"\n    Method for power terms\n\"\"\"\nfunction populate_convhull_extreme_values(\n    m::Optimizer,\n    d::Dict,\n    mono_idx::Int,\n    λ::Dict,\n    p::Int,\n)\n    λ[mono_idx][:vals] = [d[mono_idx][i]^p for i in 1:length(d[mono_idx])]\n    return λ\nend\n\n\"\"\"\n    Method for regular multilinear terms\n\"\"\"\nfunction populate_convhull_extreme_values(\n    m::Optimizer,\n    discretization::Dict,\n    indices::Any,\n    λ::Dict,\n    dim::Tuple,\n    locator::Array,\n    level::Int = 1,\n)\n    if level > length(dim)\n        @assert length(indices) == length(dim)\n        @assert length(indices) == length(locator)\n        val = 1.0\n        k = 0\n        for i in indices\n            k += 1\n            val *= discretization[i][locator[k]]                      # Calculate extreme point z-value\n        end\n        λ[indices][:vals][CartesianIndex(tuple([i for i in locator]...))] = val  # Value assignment\n        return λ                                                         # finished with last dimension\n    else\n        for i in 1:dim[level]\n            locator[level] = i\n            λ = populate_convhull_extreme_values(\n                m,\n                discretization,\n                indices,\n                λ,\n                dim,\n                locator,\n                level + 1,\n            )\n        end\n    end\n\n    return λ\nend\n\n\"\"\"\n    General Method for all term\n\"\"\"\nfunction amp_convhull_α(\n    m::Optimizer,\n    indices::Any,\n    α::Dict,\n    dim::Tuple,\n    discretization::Dict,\n)\n    for i in indices\n        if !(i in keys(α))\n            lambda_cnt = length(discretization[i])\n            partition_cnt = length(discretization[i]) - 1\n            if get_option(m, :convhull_ebd) && partition_cnt > 2\n                αCnt = Int(ceil(log(2, partition_cnt)))\n                α[i] = JuMP.@variable(\n                    m.model_mip,\n                    [1:αCnt],\n                    Bin,\n                    base_name = string(\"YL\", i)\n                )\n            else\n                α[i] = JuMP.@variable(\n                    m.model_mip,\n                    [1:partition_cnt],\n                    Bin,\n                    base_name = \"A$(i)\"\n                )\n                JuMP.@constraint(m.model_mip, sum(α[i]) == 1)\n                JuMP.@constraint(\n                    m.model_mip,\n                    _index_to_variable_ref(m.model_mip, i) >=\n                    sum(α[i][j] * discretization[i][j] for j in 1:lambda_cnt-1)\n                ) # Add x = f(α) for regulating the domains\n                JuMP.@constraint(\n                    m.model_mip,\n                    _index_to_variable_ref(m.model_mip, i) <=\n                    sum(α[i][j-1] * discretization[i][j] for j in 2:lambda_cnt)\n                )\n            end\n        end\n    end\n\n    return α\nend\n\nfunction amp_convhull_α(m::Optimizer, idx::Int, α::Dict, dim, d::Dict)\n    return amp_convhull_α(m, [idx], α, dim, d)\nend\n\nfunction amp_warmstart_α(m::Optimizer, α::Dict)\n    d = m.discretization\n\n    if m.bound_sol_pool[:cnt] >= 2 # can only warm-start the problem when pool is large enough\n        ws_idx = -1\n        is_min_sense(m) ? ws_obj = Inf : ws_obj = -Inf\n        comp_opr = Dict(MOI.MIN_SENSE => :<, MOI.MAX_SENSE => :>)\n\n        # Search for the pool for incumbent warm starter\n        for i in 1:m.bound_sol_pool[:cnt]\n            m.bound_sol_pool[:stat][i] == :Warmstarter &&\n                (m.bound_sol_pool[:stat][i] = :Alive)   # reset the status if not dead\n            if m.bound_sol_pool[:stat][i] == :Dead\n                continue\n            end\n            is_better = ifelse(\n                m.sense_orig == MOI.MAX_SENSE,\n                m.bound_sol_pool[:obj][i] > ws_obj,\n                m.bound_sol_pool[:obj][i] < ws_obj,\n            )\n            if is_better\n                ws_idx = i\n                ws_obj = m.bound_sol_pool[:obj][i]\n            end\n        end\n\n        if ws_idx > 0 # If a warm starter is found\n            for v in m.bound_sol_pool[:vars]\n                partition_cnt = length(d[v]) - 1\n                active_j =\n                    get_active_partition_idx(d, m.bound_sol_pool[:sol][ws_idx][v], v)\n                for j in 1:partition_cnt\n                    j == active_j ? JuMP.set_start_value(α[v][j], 1.0) :\n                    JuMP.set_start_value(α[v][j], 0.0)\n                end\n            end\n            m.bound_sol_pool[:stat][ws_idx] = :Warmstarter\n            get_option(m, :log_level) > 0 && println(\n                \"!! WARM START bounding MIP using POOL SOL $(ws_idx) OBJ=$(m.bound_sol_pool[:obj][ws_idx])\",\n            )\n        end\n    end\n\n    return\nend\n\n\"\"\"\n    Method for general multilinear terms\n\"\"\"\nfunction amp_post_convhull_constrs(\n    m::Optimizer,\n    λ::Dict,\n    α::Dict,\n    indices::Any,\n    dim::Tuple,\n    ext_cnt::Int,\n    d::Dict,\n)\n\n    # Adding λ constraints\n    JuMP.@constraint(m.model_mip, sum(λ[indices][:vars]) == 1)\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, λ[indices][:lifted_var_idx]) ==\n        λ[indices][:vars]' * reshape(λ[indices][:vals], ext_cnt)\n    )\n\n    # Add links on each dimension\n    for (cnt, i) in enumerate(indices)\n        l_cnt = length(d[i])\n        if m.var_type[i] == :Cont\n            amp_post_inequalities_cont(m, d, λ, α, indices, dim, i, cnt)        # Add links between λ and α\n        else\n            error(\"EXCEPTION: unexpected variable type during integer related realxation\")\n        end\n        sliced_indices =\n            [collect_indices(λ[indices][:indices], cnt, [k], dim) for k in 1:l_cnt] # Add x = f(λ) for convex representation of x value\n        JuMP.@constraint(\n            m.model_mip,\n            _index_to_variable_ref(m.model_mip, i) == sum(\n                (repeat([d[i][k]], length(k_indices))' * λ[indices][:vars][k_indices]) for\n                (k, k_indices) in enumerate(sliced_indices)\n            )\n        )\n    end\n\n    return\nend\n\n\"\"\"\n    Constraints for univariate quadratic terms\n\"\"\"\nfunction amp_post_convhull_constrs(\n    m::Optimizer,\n    λ::Dict,\n    α::Dict,\n    monomial_idx::Int,\n    discretization::Dict,\n)\n    partition_cnt = length(discretization[monomial_idx]) - 1\n    lambda_cnt = length(discretization[monomial_idx])\n\n    # Adding λ constraints\n    JuMP.@constraint(m.model_mip, sum(λ[monomial_idx][:vars]) == 1)\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, λ[monomial_idx][:lifted_var_idx]) <=\n        λ[monomial_idx][:vars]' * λ[monomial_idx][:vals]\n    )\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, λ[monomial_idx][:lifted_var_idx]) >=\n        _index_to_variable_ref(m.model_mip, monomial_idx)^2\n    )\n\n    # Add SOS-2 Constraints with basic encoding\n    if get_option(m, :convhull_ebd) && partition_cnt > 2\n        ebd_map = embedding_map(\n            lambda_cnt,\n            get_option(m, :convhull_ebd_encode),\n            get_option(m, :convhull_ebd_ibs),\n        )\n        YCnt = Int(ebd_map[:L])\n        @assert YCnt == length(α[monomial_idx])\n        for i in 1:YCnt\n            JuMP.@constraint(\n                m.model_mip,\n                sum(λ[monomial_idx][:vars][collect(ebd_map[i])]) <= α[monomial_idx][i]\n            )\n            JuMP.@constraint(\n                m.model_mip,\n                sum(λ[monomial_idx][:vars][collect(ebd_map[i+YCnt])]) <=\n                1 - α[monomial_idx][i]\n            )\n        end\n    else\n        for i in 1:lambda_cnt\n            if i == 1\n                JuMP.@constraint(\n                    m.model_mip,\n                    λ[monomial_idx][:vars][i] <= α[monomial_idx][i]\n                )\n            elseif i == lambda_cnt\n                JuMP.@constraint(\n                    m.model_mip,\n                    λ[monomial_idx][:vars][i] <= α[monomial_idx][i-1]\n                )\n            else\n                JuMP.@constraint(\n                    m.model_mip,\n                    λ[monomial_idx][:vars][i] <=\n                    α[monomial_idx][i-1] + α[monomial_idx][i]\n                )\n            end\n        end\n        # Add x = f(α) for regulating the domains\n        JuMP.@constraint(\n            m.model_mip,\n            _index_to_variable_ref(m.model_mip, monomial_idx) >= sum(\n                α[monomial_idx][j] * discretization[monomial_idx][j] for\n                j in 1:lambda_cnt-1\n            )\n        )\n        JuMP.@constraint(\n            m.model_mip,\n            _index_to_variable_ref(m.model_mip, monomial_idx) <= sum(\n                α[monomial_idx][j-1] * discretization[monomial_idx][j] for\n                j in 2:lambda_cnt\n            )\n        )\n    end\n\n    # Add x = f(λ) for convex representation\n    JuMP.@constraint(\n        m.model_mip,\n        _index_to_variable_ref(m.model_mip, monomial_idx) ==\n        λ[monomial_idx][:vars]' * discretization[monomial_idx]\n    )\n\n    return\nend\n\n\"\"\"\n    Method for multilinear terms with only continuous variables\n\"\"\"\nfunction amp_post_inequalities_cont(\n    m::Optimizer,\n    discretization::Dict,\n    λ::Dict,\n    α::Dict,\n    ml_indices::Any,\n    dim::Tuple,\n    var_ind::Int,\n    cnt::Int,\n)\n    lambda_cnt = length(discretization[var_ind])\n    partition_cnt = lambda_cnt - 1\n\n    # Embedding formulation\n    if get_option(m, :convhull_formulation) == \"sos2\" &&\n       get_option(m, :convhull_ebd) &&\n       partition_cnt > 2\n        ebd_map = embedding_map(\n            lambda_cnt,\n            get_option(m, :convhull_ebd_encode),\n            get_option(m, :convhull_ebd_ibs),\n        )\n        YCnt = Int(ebd_map[:L])\n        @assert YCnt == length(α[var_ind])\n        for i in 1:YCnt\n            p_sliced_indices =\n                collect_indices(λ[ml_indices][:indices], cnt, collect(ebd_map[i]), dim)\n            n_sliced_indices = collect_indices(\n                λ[ml_indices][:indices],\n                cnt,\n                collect(ebd_map[i+YCnt]),\n                dim,\n            )\n            JuMP.@constraint(\n                m.model_mip,\n                sum(λ[ml_indices][:vars][p_sliced_indices]) <= α[var_ind][i]\n            )\n            JuMP.@constraint(\n                m.model_mip,\n                sum(λ[ml_indices][:vars][n_sliced_indices]) <= 1 - α[var_ind][i]\n            )\n        end\n        get_option(m, :convhull_ebd_link) && ebd_link_xα(\n            m,\n            α[var_ind],\n            lambda_cnt,\n            discretization[var_ind],\n            ebd_map[:H_orig],\n            var_ind,\n        )\n        return\n    end\n\n    # SOS-2 Formulation\n    if get_option(m, :convhull_formulation) == \"sos2\"\n        for j in 1:lambda_cnt\n            sliced_indices = collect_indices(λ[ml_indices][:indices], cnt, [j], dim)\n            if (j == 1)\n                JuMP.@constraint(\n                    m.model_mip,\n                    sum(λ[ml_indices][:vars][sliced_indices]) <= α[var_ind][j]\n                )\n            elseif (j == lambda_cnt)\n                JuMP.@constraint(\n                    m.model_mip,\n                    sum(λ[ml_indices][:vars][sliced_indices]) <=\n                    α[var_ind][partition_cnt]\n                )\n            else\n                JuMP.@constraint(\n                    m.model_mip,\n                    sum(λ[ml_indices][:vars][sliced_indices]) <= sum(α[var_ind][(j-1):j])\n                )\n            end\n        end\n        return\n    elseif get_option(m, :convhull_formulation) == \"facet\"\n        for j in 1:(partition_cnt-1) # Constraint cluster of α >= f(λ)\n            sliced_indices = collect_indices(λ[ml_indices][:indices], cnt, [1:j;], dim)\n            JuMP.@constraint(\n                m.model_mip,\n                sum(α[var_ind][1:j]) >= sum(λ[ml_indices][:vars][sliced_indices])\n            )\n        end\n        for j in 1:(partition_cnt-1) # Constraint cluster of α <= f(λ)\n            sliced_indices =\n                collect_indices(λ[ml_indices][:indices], cnt, [1:(j+1);], dim)\n            JuMP.@constraint(\n                m.model_mip,\n                sum(α[var_ind][1:j]) <= sum(λ[ml_indices][:vars][sliced_indices])\n            )\n        end\n        return\n    else\n        error(\"Must indicate a choice of convex hull formulation: sos2, facet\")\n    end\n\n    return\nend\n\nfunction collect_indices(l::Array, fixed_dim::Int, fixed_partition::Array, dim::Tuple)\n    k = 0\n    indices =\n        Vector{Int}(undef, Int(prod(dim) / dim[fixed_dim] * length(fixed_partition)))\n    for i in 1:prod(dim)\n        ind = Tuple(CartesianIndices(l)[i])\n        if ind[fixed_dim] in fixed_partition\n            k += 1\n            indices[k] = i\n        end\n    end\n\n    return indices\nend\n\n\"\"\"\n    _add_multilinear_linking_constraints(m::Optimizer, λ::Dict)\n\nThis internal function adds linking constraints between λ multipliers corresponding to multilinear terms\nthat share more than two variables and are partitioned. For example, suppose we have λ[i], λ[j], and\nλ[k] where i=(1,2,3), j=(1,2,4), and k=(1,2,5). λ[i] contains all multipliers for the extreme points\nin the space of (x1,x2,x3). λ[j] contains all multipliers for the extreme points in the space of (x1,x2,x4).\nλ[k] contains all multipliers for the extreme points in the space of (x1,x2,x5).\n\nUsing λ[i], λ[j], or λ[k], we can express multilinear function x1*x2.\nWe define a linking variable μ(1,2) that represents the value of x1*x2.\nLinking constraints are\n    μ(1,2) == convex combination expr for x1*x2 using λ[i],\n    μ(1,2) == convex combination expr for x1*x2 using λ[j], and\n    μ(1,2) == convex combination expr for x1*x2 using λ[k].\n\nThus, these constraints link between λ[i], λ[j], and λ[k] variables.\n\nReference: J. Kim, J.P. Richard, M. Tawarmalani, Piecewise Polyhedral Relaxations of Multilinear Optimization,\nhttp://www.optimization-online.org/DB_HTML/2022/07/8974.html\n\"\"\"\nfunction _add_multilinear_linking_constraints(m::Optimizer, λ::Dict)\n    if isnothing(m.linking_constraints_info)\n        m.linking_constraints_info = _get_shared_multilinear_terms_info(\n            λ,\n            m.options.linking_constraints_degree_limit,\n        )\n    end\n\n    if isnothing(m.linking_constraints_info)\n        return\n    end\n\n    # Additional linking variables (μ) to the MIP model to keep the constraints sparse\n    linking_variables =\n        JuMP.@variable(m.model_mip, [i in keys(m.linking_constraints_info)])\n\n    # Add linking constraints to the MIP model\n    for (shared_multilinear_idx, multilinear_terms_idx) in m.linking_constraints_info,\n        (i, multilinear_idx) in enumerate(multilinear_terms_idx)\n\n        var_location = [findfirst(multilinear_idx .== i) for i in shared_multilinear_idx]\n\n        lambda_expr = JuMP.AffExpr()\n        for idx in Iterators.product([1:d for d in λ[multilinear_idx][:dim]]...)\n            var = λ[multilinear_idx][:vars][λ[multilinear_idx][:indices][idx...]]\n            partitions_info = prod(\n                m.discretization[i][idx[j]] for\n                (i, j) in zip(shared_multilinear_idx, var_location)\n            )\n            JuMP.add_to_expression!(lambda_expr, partitions_info, var)\n        end\n\n        JuMP.@constraint(\n            m.model_mip,\n            linking_variables[shared_multilinear_idx] == lambda_expr\n        )\n    end\nend\n\n\"\"\"\n    _get_shared_multilinear_terms_info(λ, linking_constraints_degree_limit)\n\nThis function checks to see if linking constraints are\nnecessary for a given vector of each multilinear terms and returns the approapriate\nlinking constraints information.\n\"\"\"\nfunction _get_shared_multilinear_terms_info(\n    λ::Dict,\n    linking_constraints_degree_limit::Union{Nothing,T} where {T<:Int64} = nothing,\n)\n\n    # Compute maximum degree of multilinear terms and return if bilinear\n    max_degree = maximum([length(k) for k in keys(λ)])\n\n    if max_degree <= 2\n        return (linking_constraints_info = nothing)\n    end\n\n    # Limit the linking constraints to a prescribed multilinear degree\n    if !isnothing(linking_constraints_degree_limit) &&\n       (linking_constraints_degree_limit < max_degree)\n        max_degree = linking_constraints_degree_limit\n    end\n\n    # Collect all variable indices appearing in multilinear terms\n    all_variables_idx = collect(union((keys(λ) |> collect)...)) |> sort\n\n    linking_constraints_info = Dict(\n        shared_multilinear_idx =>\n            filter(r -> issubset(shared_multilinear_idx, r), keys(λ)) for\n        deg in 2:(max_degree-1) for\n        shared_multilinear_idx in Combinatorics.combinations(all_variables_idx, deg)\n    )\n\n    filter!(r -> length(r.second) >= 2, linking_constraints_info)\n    if isempty(linking_constraints_info)\n        return (linking_constraints_info = nothing)\n    end\n\n    return (linking_constraints_info = linking_constraints_info)\nend\n"
  },
  {
    "path": "src/nlexpr.jl",
    "content": "\"\"\"\nprocess_expr(expr; kwargs...)\n\nHigh-level wrapper for processing expression with sub-tree operators\n\"\"\"\nfunction process_expr(m::Optimizer)\n    expr_initialization(m)      # S0 : initialize the space for parsing and analyzing\n    expr_preprocess(m)          # S1 : pre-process the negative sign in expressions\n    expr_parsing(m)             # S2 : parsing the expressions for nonlinear information\n    expr_conversion(m)          # S3 : convert lifted(linear) expressions into affine function\n    expr_finalized(m)           # S4 : finalize process by extracting some measurements\n\n    return\nend\n\n\"\"\"\nSTEP 1: initialize the expression/ space\n\"\"\"\nfunction expr_initialization(m::Optimizer)\n\n    # 0 : deepcopy data into mip lifted expr place holders\n    m.bounding_obj_expr_mip = deepcopy(m.obj_expr_orig)\n    m.bounding_obj_mip = Dict()\n\n    for i in 1:m.num_constr_orig\n        push!(m.bounding_constr_expr_mip, deepcopy(m.constr_expr_orig[i]))\n        push!(m.bounding_constr_mip, Dict())\n    end\n\n    return\nend\n\n\"\"\"\nSTEP 2: preprocess expression for trivial sub-trees and nasty pieces for easier later process\n\"\"\"\nfunction expr_preprocess(m::Optimizer)\n    expr_resolve_const(m.bounding_obj_expr_mip)\n    expr_resolve_sign(m.bounding_obj_expr_mip)\n    expr_flatten(m.bounding_obj_expr_mip)\n    for i in 1:m.num_constr_orig\n        expr_resolve_const(m.bounding_constr_expr_mip[i])\n        expr_resolve_sign(m.bounding_constr_expr_mip[i])\n        expr_flatten(m.bounding_constr_expr_mip[i].args[2])\n    end\n\n    return\nend\n\n\"\"\"\nSTEP 3: parse expression for patterns on either the generic level or term level\n\"\"\"\nfunction expr_parsing(m::Optimizer)\n\n    # Throw an error if the objective expression has fractional exponents\n    expr_is_fractional_exponent(m.bounding_obj_expr_mip)\n    is_structural = expr_constr_parsing(m.bounding_obj_expr_mip, m)\n\n    if !is_structural\n        m.bounding_obj_expr_mip = expr_term_parsing(m.bounding_obj_expr_mip, 0, m)\n        m.obj_structure = :generic_linear\n    end\n    (get_option(m, :log_level) > 199) && println(\"[OBJ] $(m.obj_expr_orig)\")\n\n    for i in 1:m.num_constr_orig\n        expr = m.bounding_constr_expr_mip[i]\n\n        # Throw an error if the constraint expression has fractional exponents\n        if expr.args[1] in [:(<=), :(>=), :(==)]\n            expr_is_fractional_exponent(expr.args[2])\n        end\n\n        is_structural = expr_constr_parsing(expr, m, i)\n        if !is_structural\n            m.bounding_constr_expr_mip[i] = expr_term_parsing(expr, i, m)\n            m.constr_structure[i] = :generic_linear\n        end\n        (get_option(m, :log_level) > 199) && println(\"[CONSTR] $(m.constr_expr_orig[i])\")\n    end\n\n    return\nend\n\n\"\"\"\nSTEP 4: convert the parsed expressions into affine-based function that can be used for adding JuMP constraints\n\"\"\"\nfunction expr_conversion(m::Optimizer)\n    if m.obj_structure == :generic_linear\n        m.bounding_obj_mip = expr_linear_to_affine(m.bounding_obj_expr_mip)\n        m.obj_structure = :affine\n    end\n    get_option(m, :log_level) > 199 && println(\"type :: \", m.obj_structure)\n    get_option(m, :log_level) > 199 && println(\"lifted ::\", m.bounding_obj_expr_mip)\n    get_option(m, :log_level) > 199 && println(\"coeffs ::\", m.bounding_obj_mip[:coefs])\n    get_option(m, :log_level) > 199 && println(\"vars ::\", m.bounding_obj_mip[:vars])\n    get_option(m, :log_level) > 199 && println(\"sense ::\", m.bounding_obj_mip[:sense])\n    get_option(m, :log_level) > 199 && println(\"rhs ::\", m.bounding_obj_mip[:rhs])\n    get_option(m, :log_level) > 199 && println(\"----------------\")\n\n    for i in 1:m.num_constr_orig\n        if m.constr_structure[i] == :generic_linear\n            m.bounding_constr_mip[i] =\n                expr_linear_to_affine(m.bounding_constr_expr_mip[i])\n            m.constr_structure[i] = :affine\n        end\n        get_option(m, :log_level) > 199 && println(\"type :: \", m.constr_structure[i])\n        get_option(m, :log_level) > 199 &&\n            println(\"lifted ::\", m.bounding_constr_expr_mip[i])\n        get_option(m, :log_level) > 199 &&\n            println(\"coeffs ::\", m.bounding_constr_mip[i][:coefs])\n        get_option(m, :log_level) > 199 &&\n            println(\"vars ::\", m.bounding_constr_mip[i][:vars])\n        get_option(m, :log_level) > 199 &&\n            println(\"sense ::\", m.bounding_constr_mip[i][:sense])\n        get_option(m, :log_level) > 199 &&\n            println(\"rhs ::\", m.bounding_constr_mip[i][:rhs])\n        get_option(m, :log_level) > 199 && println(\"----------------\")\n    end\n\n    return\nend\n\n\"\"\"\nSTEP 5: collect information as needed for handy operations in the algorithm section\n\"\"\"\nfunction expr_finalized(m::Optimizer)\n    collect_nonconvex_vars(m)\n    m.candidate_disc_vars = sort(m.candidate_disc_vars)\n    m.num_var_linear_mip = length(m.linear_terms)\n    m.num_var_nonlinear_mip = length(m.nonconvex_terms)\n    m.num_constr_convex = length([i for i in m.constr_structure if i == :convex])\n\n    return m\nend\n\nfunction collect_nonconvex_vars(m::Optimizer)\n\n    # Walk through all nonconvex terms\n    for i in keys(m.nonconvex_terms)\n        m.nonconvex_terms[i][:discvar_collector](m, i)\n    end\n\n    # TODO : reconsider how to structure this\n    # NOTE : Walk through all integer variables that didn't appear in any nonconvex terms\n    for i in 1:m.num_var_orig\n        if !(i in m.candidate_disc_vars) && m.var_type[i] == :Int\n            push!(m.candidate_disc_vars, i)\n        end\n    end\n\n    return\nend\n\nfunction isa_variable_index(expr::Expr)\n    return length(expr.args == 2) && expr.args[2] == :(MathOptInterface.VariableIndex)\nend\nget_index(expr::Expr) = expr.args[2]\n\nfunction expr_strip_const(expr, subs = [], rhs = 0.0)\n    exhaust_const = [\n        !(expr.args[1] in [:+, :-]) ||\n        !(isa(expr.args[i], Float64) || isa(expr.args[i], Int)) for\n        i in 2:length(expr.args)\n    ]\n    if prod(exhaust_const)\n        push!(subs, expr)\n        return subs, rhs\n    end\n\n    for i in 2:length(expr.args)\n        if (\n            isa(expr.args[i], Float64) ||\n            isa(expr.args[i], Int) ||\n            isa(expr.args[i], Symbol)\n        )\n            (expr.args[1] == :+) && (rhs -= expr.args[i])\n            (expr.args[1] == :-) && ((i == 2) ? rhs -= expr.args[i] : rhs += expr.args[i])\n        elseif expr.args[i].head == :ref\n            continue\n        elseif expr.args[i].head == :call\n            subs, rhs = expr_strip_const(expr.args[i], subs, rhs)\n        end\n    end\n\n    return subs, rhs\nend\n\n\"\"\"\nThis utility function builds a constraint reference by repeating one\noperator with a vector variable references.\nFor example,\ninput => y, x[1,2,3], :+\noutput => (y = x[1] + x[2] + x[3])::Expr\n\"\"\"\nfunction build_constr_block(y_idx::Int, var_idxs::Vector, operator::Symbol)\n    expr_l_block = Expr(:call, :(==), Meta.parse(\"x[$(y_idx)]\"))\n    expr_r_block = Expr(:call, operator)\n    for j in 1:length(var_idxs)\n        push!(expr_r_block.args, Meta.parse(\"x[$(var_idxs[j])]\"))\n    end\n    push!(expr_l_block.args, expr_r_block)\n\n    return expr_l_block\nend\n\n\"\"\"\nexpr_constr_parsing(expr, m::Optimizer)\n\nRecognize structural constraints.\n\"\"\"\nfunction expr_constr_parsing(expr::Expr, m::Optimizer, idx::Int = 0)\n\n    # First process user-defined structures in-cases of over-ride\n    # for i in 1:length(get_option(m, :constr_patterns))\n    #    is_structural = get_option(m, :constr_patterns)[i](expr, m, idx)\n    #    return\n    # end\n\n    isa(expr, Number) && return false\n    # Recognize built-in special structural pattern\n    if get_option(m, :recognize_convex)\n        is_convex = resolve_convex_constr(expr, m, idx)\n        is_convex && return true\n    end\n\n    # More structural patterns go here\n    return false\nend\n\nfunction expr_is_axn(expr, scalar = 1.0, var_idxs = [], power = []; N = nothing)\n    expr.args[1] in [:*, :^] || return nothing, nothing, nothing         # Limited Area\n\n    if expr.args[1] == :*\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n            elseif (expr.args[i].head == :ref)\n                @assert isa(expr.args[i].args[2], Int)\n                push!(var_idxs, expr.args[i])\n                push!(power, 1)\n            elseif (expr.args[i].head == :call)\n                scalar, var_idxs, power =\n                    expr_is_axn(expr.args[i], scalar, var_idxs, power)\n                scalar === nothing && return nothing, nothing, nothing\n            end\n        end\n    elseif expr.args[1] == :^\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                push!(power, expr.args[i])\n                continue\n            elseif (expr.args[i].head == :ref)\n                push!(var_idxs, expr.args[i])\n                continue\n            elseif (expr.args[i].head == :call)\n                return nothing, nothing, nothing\n            end\n        end\n    end\n\n    # If the user wants a specific N\n    !(N === nothing) && !(length(var_idxs) == N) && return nothing, nothing, nothing\n    (var_idxs === nothing) &&\n        (scalar === nothing) &&\n        (power === nothing) &&\n        return nothing, nothing, nothing # Unrecognized sub-structure\n\n    @assert length(var_idxs) == length(power)\n    return scalar, var_idxs, power\nend\n\n\"\"\"\nThis function takes a constraint/objective expression and converts it into a affine expression data structure\nUse the function to traverse linear expressions traverse_expr_linear_to_affine()\n\"\"\"\nfunction expr_linear_to_affine(expr)\n\n    # The input should follow :(<=, LHS, RHS)\n    affdict = Dict()\n    isa(expr, Number) && return affdict\n\n    if expr.args[1] in [:(==), :(>=), :(<=)] # For a constraint expression\n        @assert isa(expr.args[3], Float64) || isa(expr.args[3], Int)\n        @assert isa(expr.args[2], Expr)\n        # non are buffer spaces, not used anywhere\n        lhscoeff, lhsvars, rhs, non, non = traverse_expr_linear_to_affine(expr.args[2])\n        rhs = -rhs + expr.args[3]\n        affdict[:sense] = expr.args[1]\n\n    elseif expr.head == :ref  # For single variable objective expression\n        lhscoeff = [1.0]\n        lhsvars = [expr]\n        rhs = 0\n        affdict[:sense] = nothing\n\n    else # For an objective expression\n        lhscoeff, lhsvars, rhs, non, non = traverse_expr_linear_to_affine(expr)\n        affdict[:sense] = nothing\n    end\n\n    affdict[:coefs] = lhscoeff\n    affdict[:vars] = lhsvars\n    affdict[:rhs] = rhs\n    @assert length(affdict[:coefs]) == length(affdict[:vars])\n    affdict[:cnt] = length(affdict[:coefs])\n\n    return affdict\nend\n\n\"\"\"\n\ntraverse_expr_linear_to_affine(expr, lhscoeffs=[], lhsvars=[], rhs=0.0, bufferVal=0.0, bufferVar=nothing, sign=1.0, level=0)\n\nThis function traverses the left hand side tree to collect affine terms.\nUpdated status : possible to handle (x-(x+y(t-z))) cases where signs are handled properly\n\"\"\"\nfunction traverse_expr_linear_to_affine(\n    expr,\n    lhscoeffs = [],\n    lhsvars = [],\n    rhs = 0.0,\n    bufferVal = nothing,\n    bufferVar = nothing,\n    sign = 1.0,\n    coef = 1.0,\n    level = 0,\n)\n\n    # reversor = Dict(true => -1.0, false => 1.0)\n    function sign_convertor(subexpr, pos)\n        if length(subexpr.args) == 2 && subexpr.args[1] == :-\n            return -1.0\n        elseif length(subexpr.args) > 2 && subexpr.args[1] == :- && pos > 2\n            return -1.0\n        end\n        return 1.0\n    end\n\n    if isa(expr, Number) # Capture any coefficients or right hand side\n        (bufferVal !== nothing) ? bufferVal *= expr : bufferVal = expr * coef\n        return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\n    elseif expr in [:+, :-]    # TODO: what is this condition?\n        if bufferVal !== nothing && bufferVar !== nothing\n            push!(lhscoeffs, bufferVal)\n            push!(lhsvars, bufferVar)\n            bufferVal = 0.0\n            bufferVar = nothing\n        end\n        return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\n    elseif expr in [:*]\n        return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\n    elseif expr in [:(<=), :(==), :(>=)]\n        return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\n    elseif expr.head == :ref\n        bufferVar = expr\n        return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\n    end\n\n    # PATCH : Special Structure Recognition\n    start_pos = 1\n    if (expr.args[1] == :*) && (length(expr.args) == 3)\n        if (isa(expr.args[2], Float64) || isa(expr.args[2], Int)) &&\n           (expr.args[3].head == :call)\n            (coef != 0.0) ? coef = expr.args[2] * coef : coef = expr.args[2]# Patch\n            # coef = expr.args[2]\n            start_pos = 3\n            # @warn \"Special expression structure detected [*, coef, :call, ...]. Currently using a beta fix...\"\n        end\n    end\n\n    for i in start_pos:length(expr.args)\n        lhscoeff, lhsvars, rhs, bufferVal, bufferVar = traverse_expr_linear_to_affine(\n            expr.args[i],\n            lhscoeffs,\n            lhsvars,\n            rhs,\n            bufferVal,\n            bufferVar,\n            sign * sign_convertor(expr, i),\n            coef,\n            level + 1,\n        )\n        if expr.args[1] in [:+, :-]  # Term segmentation [:-, :+], see this and wrap-up the current (linear) term\n            if bufferVal !== nothing && bufferVar !== nothing  # (sign) * (coef) * (var) => linear term\n                push!(lhscoeffs, sign * sign_convertor(expr, i) * bufferVal)\n                push!(lhsvars, bufferVar)\n                bufferVal = nothing\n                bufferVar = nothing\n            end\n            if bufferVal !== nothing && bufferVar === nothing  # (sign) * (coef) => right-hand-side term\n                rhs += sign * sign_convertor(expr, i) * bufferVal\n                bufferVal = nothing\n            end\n            if bufferVal === nothing && bufferVar !== nothing && expr.args[1] == :+\n                push!(lhscoeffs, sign * 1.0 * coef)\n                push!(lhsvars, bufferVar)\n                bufferVar = nothing\n            end\n            if bufferVal === nothing && bufferVar !== nothing && expr.args[1] == :-\n                push!(lhscoeffs, sign * sign_convertor(expr, i) * coef)\n                push!(lhsvars, bufferVar)\n                bufferVar = nothing\n            end\n        elseif expr.args[1] in [:(<=), :(==), :(>=)]\n            rhs = expr.args[end]\n        end\n    end\n\n    if level == 0\n        if bufferVal !== nothing && bufferVar !== nothing\n            push!(lhscoeffs, bufferVal)\n            push!(lhsvars, bufferVar)\n            bufferVal = nothing\n            bufferVar = nothing\n        end\n    end\n\n    return lhscoeffs, lhsvars, rhs, bufferVal, bufferVar\nend\n\n\"\"\"\nThis function is treats the sign in expression trees by cleaning the following structure:\nargs\n::+ || ::-\n::Call || ::ref\nBy separating the structure with some dummy treatments\n\"\"\"\nfunction expr_resolve_sign(expr::Expr, level = 0; kwargs...)\n    for (i, arg) in enumerate(expr.args)\n        if !(arg isa Expr)\n            continue  # Skip the coefficients\n        elseif arg.head == :call && length(arg.args) == 2\n            if arg.args[1] == :- # Treatment for :(-x), replace with :(x*-1)\n                if expr.args[1] == :* # Only perform the treatment when connected with *\n                    push!(expr.args, -1)\n                    expr.args[i] = arg.args[2]\n                elseif !(expr.args[1] in (:+, :-, :(==), :(<=), :(>=)))\n                    error(\"Unexpected operator $(arg) during resolving sign\")\n                end\n            elseif arg.args[1] == :+ # Treatment for :(+x) replace with :x\n                expr.args[i] = arg.args[2]\n            end\n        elseif arg.head == :call\n            expr_resolve_sign(arg, level + 1)\n        end\n    end\n    return\nend\n\nexpr_resolve_sign(expr, level = 0; kwargs...) = nothing\n\n\"\"\"\nRecursively pre-process the expression by treating the coefficients\nTODO: this function requires a lot of refining.\nMost issues can be caused by this function.\n\"\"\"\nfunction expr_flatten(expr::Expr, level = 0; kwargs...)\n    if level > 0  # No trivial constraint is allowed \"3>5\"\n        flat = expr_arrangeargs(expr.args)\n        if isa(flat, Number)\n            return flat\n        else\n            expr.args = flat\n        end\n    end\n    for i in 2:length(expr.args)\n        if isa(expr.args[i], Expr) && expr.args[i].head == :call\n            expr.args[i] = expr_flatten(expr.args[i], level + 1)\n        end\n    end\n    if level > 0  #Root level process, no additional processes\n        expr.args = expr_arrangeargs(expr.args)\n    end\n    return expr\nend\n\nexpr_flatten(expr, level = 0; kwargs...) = nothing\n\n\"\"\"\nRe-arrange children by their type.\nOnly consider 3 types: coefficients(Int64, Float64), :ref, :calls\nSequence arrangement is dependent on operator\n\"\"\"\nfunction expr_arrangeargs(args::Array; kwargs...)\n    # A mapping used for operator treatments\n    reverter = Dict(true => :-, false => :+)\n    operator_coefficient_base =\n        Dict{Symbol,Float64}(:+ => 0.0, :- => 0.0, :/ => 1.0, :* => 1.0, :^ => 1.0)\n\n    # Treatment => Flatten pure number sub-tree\n    allFloats = [i for i in 2:length(args) if isa(args[i], Float64)]\n    if length(allFloats) == length(args) - 1\n        val = args[2]\n        for i in 3:length(args)\n            val = eval(args[1])(val, args[i])\n        end\n        return val\n    end\n\n    if args[1] in [:^]\n        return args\n    elseif args[1] in [:/]\n        # error(\"Alpine does not currently support `$(args[1])` operator\")\n        if (typeof(args[3]) == Float64) || (typeof(args[3]) == Int64)\n            args = expr_resolve_const_denominator(args)\n        else\n            error(\n                \"Alpine does not currently support `$(args[1])` operator with a variable in the denominator\",\n            )\n        end\n    elseif args[1] in [:*, :+, :-]\n        # Such generic operators can be handled\n    else\n        error(\n            \"Alpine does not currently support `$(args[1])` operator acting on a variable\",\n        )\n    end\n\n    if args[1] in [:*, :+, :-]\n        val = operator_coefficient_base[args[1]] # initialize\n        exprs = []\n        refs = []\n\n        valinit = false  # what is first children : needs consideration with :(-)\n        refinit = false\n        callinit = false\n\n        for i in 2:length(args)\n            if isa(args[i], Float64) || isa(args[i], Int)\n                valinit += (i == 2)\n                val = eval(args[1])(val, eval(reverter[(i==2)&&(args[1]==:-)])(args[i])) # Revert the first sigh if (-)\n            elseif typeof(args[i]) == Expr\n                if args[i].head == :ref\n                    refinit += (i == 2)\n                    push!(refs, args[i])\n                elseif args[i].head == :call\n                    callinit += (i == 2)\n                    push!(exprs, args[i])\n                else\n                    error(\"Unkown expression head\")\n                end\n            else\n                error(\"Unkown argument type\")\n            end\n        end\n\n        # Treatment for 0.0 coefficients\n        if val == operator_coefficient_base[args[1]] && val == 0.0\n            val = []\n        end\n\n        # Re-arrange children :: without actually doing anything on them\n        if args[1] in [:*]\n            return [args[1]; val; refs; exprs]\n        elseif args[1] in [:+, :-]\n            if Bool(valinit)\n                return [args[1]; val; refs; exprs]\n            elseif Bool(refinit)\n                return [args[1]; refs; val; exprs]\n            elseif Bool(callinit)\n                return [args[1]; exprs; refs; val]\n            else\n                error(\"Unexpected condition encountered...\")\n            end\n        end\n    else\n        error(\"Unsupported expression arguments $args\")\n    end\n\n    return\nend\n\n\"\"\"\nCheck if it is a sample of `+()`\n\"\"\"\nexpr_is_emptysum(expr) = expr == :(+())\n\n\"\"\"\nCheck if a sub-tree is a constant or not\n\"\"\"\nfunction expr_resolve_const(expr)\n    isa(expr, Number) && return\n    for i in 1:length(expr.args)\n        if isa(expr.args[i], Number) || isa(expr.args[i], Symbol)\n            continue\n        elseif expr.args[i].head == :call\n            if expr_is_emptysum(expr.args[i])\n                expr.args[i] = :(0)\n            end\n            (expr_isconst(expr.args[i])) && (expr.args[i] = eval(expr.args[i]))\n            if isa(expr.args[i], Number) || isa(expr.args[i], Symbol)\n                continue\n            else\n                expr_resolve_const(expr.args[i])\n            end\n        end\n    end\n\n    return\nend\n\n\"\"\"\nIf the expression's fraction has a constant denominator, then replace the expression as product of a constant and the expression\n\"\"\"\nfunction expr_resolve_const_denominator(args)\n    @assert args[1] == :/\n    @assert length(args) == 3\n    resolvable = true\n\n    for i in 3:length(args)\n        resolvable *= expr_isconst(args[i])\n    end\n\n    if resolvable\n        for i in 3:length(args)\n            args[i] = 1 / eval(args[i])\n        end\n        args[1] = :*\n    end\n\n    return args\nend\n\n\"\"\"\nCheck if a sub-tree(:call) is totally composed of constant values\n\"\"\"\nfunction expr_isconst(expr)\n    (isa(expr, Number) || isa(expr, Symbol)) && return true\n\n    (expr.head == :ref) && return false\n    const_tree = true\n    for i in 1:length(expr.args)\n        if isa(expr.args[i], Number) || isa(expr.args[i], Symbol)\n            continue\n        elseif expr.args[i].head == :call\n            const_tree *= expr_isconst(expr.args[i])\n        elseif expr.args[i].head == :ref\n            return false\n        end\n    end\n\n    return const_tree\nend\n\n\"\"\"\nCheck if a sub-tree(:call) is contains any non-integer exponent values\n\"\"\"\nfunction expr_is_fractional_exponent(expr)\n    if expr.head == :call\n        if length(expr.args) == 3 && expr.args[1] == :^\n            if !(isinteger(expr.args[3])) || !(expr.args[3] >= 0)\n                error(\n                    \"Alpine currently supports `^` operator in constraints and/or objective with only positive integer exponents\",\n                )\n            end\n        end\n        for i in 1:length(expr.args)\n            if typeof(expr.args[i]) == Expr\n                expr_is_fractional_exponent(expr.args[i]) # Recursively search for fractional exponents\n            end\n        end\n    end\nend\n\n# Returns true if the expression is a constant, linear or affine\nfunction expr_isaffine(expr)\n    expr_isconst(expr) && return true\n    expr.head == :ref && return true\n\n    is_affine = false\n    if expr.head == :call\n        k = 0\n        for i in 1:length(expr.args)\n            if isa(expr.args[i], Number)\n                k += 1\n                continue\n            end\n            if isa(expr.args[i], Symbol)\n                (expr.args[i] in [:+, :-]) && (k += 1)\n                continue\n            end\n            if expr.args[i].head == :ref\n                k += 1\n            elseif expr.args[i].head == :call\n                status = expr_isaffine(expr.args[i])\n                status && (k += 1)\n            end\n        end\n        (k == length(expr.args)) && (is_affine = true)\n    end\n    return is_affine\nend\n\n\"\"\"\nConverts ((a_1*x[1])^2 + (a_2*x[2])^2 + ... + (a_n*x[n])^2) to (a_1^2*x[1]^2 + a_2^2*x[2]^2 + ... + a_n^2*x[n]^2)\nSigns in the summation can be +/-\nNote: This function does not support terms of type (a*(x[1] + x[2]))^2 yet.\n\"\"\"\nfunction expr_isolate_const(expr)\n    expr_isaffine(expr) && return expr\n\n    # Check nonlinear expressions\n    if (expr.head == :call && expr.args[1] in [:+, :-])\n        expr_array = Any[]\n        for i in 2:length(expr.args)\n            ind = 0\n\n            # Handle negative sign in the first term\n            if (!isa(expr.args[i], Number)) &&\n               (expr.args[i].args[1] == :-) &&\n               (length(expr.args[i].args) == 2)\n                expr_i = expr.args[i].args[2]\n                ind = 1\n            else\n                expr_i = expr.args[i]\n            end\n\n            # Handle constant and linear terms\n            if (isa(expr_i, Number)) || (expr_i.head == :ref)\n                if ((expr.args[1] == :-) && (i > 2)) || (ind == 1)\n                    push!(expr_array, :(-$(expr_i)))\n                else\n                    push!(expr_array, :($(expr_i)))\n                end\n\n                # Handle nonlinear terms with coefficients within the exponent\n            elseif (\n                expr.args[i].head == :call &&\n                expr_i.args[1] == :^ &&\n                expr_i.args[2].head == :call &&\n                isa(expr_i.args[2].args[2], Number) &&\n                isa(expr_i.args[3], Number)\n            )\n                expr_tmp = Expr(:call, :^, expr_i.args[2].args[3], expr_i.args[3])\n                if ((expr.args[1] == :-) && (i > 2)) || (ind == 1)\n                    push!(\n                        expr_array,\n                        Expr(:call, :*, -expr_i.args[2].args[2]^expr_i.args[3], expr_tmp),\n                    )\n                else\n                    push!(\n                        expr_array,\n                        Expr(:call, :*, expr_i.args[2].args[2]^expr_i.args[3], expr_tmp),\n                    )\n                end\n\n                # Handle no-coefficients case\n            elseif expr_i.args[1] == :^ && expr_i.args[2].head == :ref\n                if (expr.args[1] == :- && (i > 2)) || (ind == 1)\n                    push!(expr_array, Expr(:call, :*, -1, expr_i))\n                else\n                    push!(expr_array, expr_i)\n                end\n\n                # Handle coefficients which are not part of the exponent\n            elseif expr_i.args[1] == :* && isa(expr_i.args[2], Number)\n                if ((expr.args[1] == :-) && (i > 2)) || (ind == 1)\n                    #push!(expr_array, Expr(:call, :*, -expr_i.args[2], expr_i.args[3]))\n                    push!(expr_array, Expr(:call, :*, -1, expr_i))\n                else\n                    push!(expr_array, expr_i)\n                end\n\n                # Handle negative sign in the remaining terms\n            elseif (expr_i.args[1] in [:+, :-]) && (length(expr.args[i].args) > 2)\n                expr_rec = expr_isolate_const(expr_i) #recursion\n                push!(expr_array, expr_rec)\n\n                # For any other terms\n            else\n                if (expr.args[1] == :- && (i > 2)) || (ind == 1)\n                    push!(expr_array, Expr(:call, :*, -1, expr_i))\n                else\n                    push!(expr_array, expr_i)\n                end\n            end\n        end\n\n        # Construct the expression from the array\n        if length(expr_array) == 1\n            return expr_array[1]\n        else\n            expr_n = Expr(:call, :+, expr_array[1], expr_array[2])\n            if length(expr_array) >= 3\n                for i in 3:length(expr_array)\n                    expr_n = Expr(:call, :+, expr_n, expr_array[i])\n                end\n            end\n            return (expr_n)\n        end\n\n    elseif (\n        expr.head == :call &&\n        expr.args[1] == :^ &&\n        expr.args[2].head == :call &&\n        isa(expr.args[2].args[2], Number) &&\n        isa(expr.args[3], Number)\n    )\n        expr_tmp = Expr(:call, :^, expr.args[2].args[3], expr.args[3])\n        return (Expr(:call, :*, expr.args[2].args[2]^expr.args[3], expr_tmp))\n    else\n        return expr\n    end\nend\n"
  },
  {
    "path": "src/operators.jl",
    "content": "\"\"\"\n    expr_term_parsing(expr, m::Optimizer, level=0)\n\nRecognize and process nonlinear terms in an expression\n\"\"\"\nfunction expr_term_parsing(expr::Any, constr_id::Int, m::Optimizer, level = 0; options...)\n    isa(expr, Number) && return expr\n    cnt = 0\n    for node in expr.args\n        cnt += 1\n        if isa(node, Float64) || isa(node, Int64) || isa(node, Symbol)\n            continue\n        elseif node.head == :call\n            expr.args[cnt] = expr_term_parsing(node, constr_id, m, level + 1)\n        elseif node.head == :ref\n            continue\n        else\n            error(\"Type issue during expression parsing. \")\n        end\n    end\n\n    return detect_nonconvex_terms(expr, constr_id, m)\nend\n\n\"\"\"\n    detect_nonconvex_terms(expr, m::Optimizer)\n\nThis function recognizes, stores, and replaces a sub-tree `expr` with available\nuser-defined/built-in structures patterns. The procedure creates the required number\nof lifted variables based on the patterns that it is trying to recognize.\nThen, it goes through all built-in structures and performs operatins to convexify the problem.\n\nSpecific structure pattern information will be described formally.\n\"\"\"\nfunction detect_nonconvex_terms(expr::Any, constr_id::Int, m::Optimizer; kwargs...)\n\n    # First process user-defined structures in-cases of over-ride\n    # for i in 1:length(get_option(m, :term_patterns))\n    #     skip, expr = get_option(m, :term_patterns)[i](expr, constr_id, m)\n    #     skip && return expr\n    # end\n\n    # NOTE :: Sequence of which term to detect matters here\n    #         More specific term should be detected first to reduce the size of relaxation\n    #         model. For example, power-2 or bilinear term should be detected before\n    #         general multilinear terms to apply better outter approxiamtion.\n\n    # LEVEL 1 : : Recognize all built-in structural patterns\n    skip, expr = detect_discretemulti_term(expr, constr_id, m)     #L1 : General case : discrete variables * continous variables\n    skip && return expr\n\n    skip, expr = detect_binprod_term(expr, constr_id, m)           #L1 : binprod = binary products\n    skip && return expr\n\n    # LEVEL 2 : : Recognize all built-in structural patterns\n    skip, expr = detect_bilinear_term(expr, constr_id, m)          #L2\n    skip && return expr\n\n    skip, expr = detect_monomial_term(expr, constr_id, m)          #L2 : must go before multilinear\n    skip && return expr\n\n    skip, expr = detect_multilinear_term(expr, constr_id, m)       #L2\n    skip && return expr\n\n    return expr # if no structure is detected, simply return the original tree\nend\n\nfunction store_nonconvex_term(\n    m::Optimizer,\n    nl_key::Any,\n    var_idxs::Any,\n    term_type::Symbol,\n    operator::Symbol,\n    evaluator::Function,\n    bd_resolver::Function,\n    discvar_collector::Function,\n)\n    l_cnt = length(keys(m.linear_terms))\n    nl_cnt = length(keys(m.nonconvex_terms))\n\n    y_idx = m.num_var_orig + nl_cnt + l_cnt + 1   # y is always lifted var\n    lifted_var_ref = Expr(:ref, :x, y_idx)\n    lifted_constr_ref = build_constr_block(y_idx, var_idxs, operator)\n\n    m.nonconvex_terms[nl_key] = Dict(\n        :lifted_var_ref => lifted_var_ref,\n        :id => nl_cnt + 1,\n        :y_idx => y_idx,\n        :y_type =>\n            resolve_lifted_var_type([m.var_type[k] for k in var_idxs], operator),\n        :var_idxs => var_idxs,\n        :ref => nl_key,\n        :evaluator => evaluator,\n        :lifted_constr_ref => lifted_constr_ref,\n        :constr_id => Set(),\n        :nonlinear_type => term_type,\n        :convexified => false,\n        :bound_resolver => bd_resolver,\n        :discvar_collector => discvar_collector,\n    )\n\n    m.term_seq[nl_cnt+l_cnt+1] = nl_key                              # Assistive information\n\n    # push!(m.var_type, :Cont)  # TODO check if this replacement is good since additional constraints should be able to sufficiently constraint the type\n    push!(m.var_type, m.nonconvex_terms[nl_key][:y_type])            # Keep track of the lifted var type\n    get_option(m, :log_level) > 199 &&\n        println(\"found lifted $(term_type) term $(lifted_constr_ref)\")\n    return y_idx\nend\n\nfunction store_linear_term(m::Optimizer, term_key::Any, expr::Any)#, bound_resolver::Function)\n    l_cnt = length(keys(m.linear_terms))\n    nl_cnt = length(keys(m.nonconvex_terms))\n\n    y_idx = m.num_var_orig + nl_cnt + l_cnt + 1\n\n    lifted_var_ref = Expr(:ref, :x, y_idx)\n    lifted_constr_ref = Expr(:call, :(==), lifted_var_ref, expr)\n\n    m.linear_terms[term_key] = Dict(\n        :lifted_var_ref => lifted_var_ref,\n        :id => length(keys(m.linear_terms)) + 1,\n        :ref => term_key,\n        :y_idx => y_idx,\n        :y_type => resolve_lifted_var_type(\n            [m.var_type[k[2]] for k in term_key[:coef_var]],\n            :+,\n        ),\n        :evaluator => linear,\n        :lifted_constr_ref => lifted_constr_ref,\n        :constr_id => Set(),\n        :bound_resolver => nothing,\n    )\n\n    m.term_seq[l_cnt+nl_cnt+1] = term_key\n    push!(m.var_type, m.linear_terms[term_key][:y_type]) # Keep track of the lifted var type\n    get_option(m, :log_level) > 199 &&\n        println(\"found lifted linear term $(lifted_var_ref) = $expr\")\n\n    return y_idx\nend\n\nfunction lift_nonconvex_term(m::Optimizer, nl_key, constr_id::Int, scalar = 1.0)\n    push!(m.nonconvex_terms[nl_key][:constr_id], constr_id)\n\n    if scalar == 1.0\n        return m.nonconvex_terms[nl_key][:lifted_var_ref]\n    else\n        return Expr(:call, :*, m.nonconvex_terms[nl_key][:lifted_var_ref], scalar)\n    end\nend\n\nfunction lift_linear_term(m::Optimizer, term_key, constr_id::Int)\n    push!(m.linear_terms[term_key][:constr_id], constr_id)\n    return m.linear_terms[term_key][:lifted_var_ref]\n\n    return\nend\n\nfunction detect_linear_term(expr::Any, constr_id::Int, m::Optimizer)\n    @assert (expr.head == :call || expr.head == :ref)\n    coef_fetch = Dict(:+ => 1.0, :- => -1.0)\n\n    # Re-process the expression sub-tree [REQUIRED]\n    expr_resolve_const(expr)\n    expr_resolve_sign(expr)\n    expr_flatten(expr)\n\n    if expr.args[1] in [:+, :-]\n        scalar = 0.0\n        coef_var = Set()\n        for i in 2:length(expr.args)  # TODO: Consider recursive operation\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                (i == 2) ? scalar = expr.args[i] :\n                scalar += coef_fetch[expr.args[1]] * expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue #should never happen\n            if (expr.args[i].head == :ref) && isa(expr.args[i].args[2], Int)\n                (i == 2) ? push!(coef_var, (1.0, expr.args[i].args[2])) :\n                push!(coef_var, (coef_fetch[expr.args[1]], expr.args[i].args[2]))\n                continue\n            end\n\n            # Specical Check\n            if expr.args[i].head == :call &&\n               expr.args[i].args[1] == :* &&\n               length(expr.args[i].args) == 3\n                sub_coef =\n                    [j for j in expr.args[i].args if (isa(j, Int) || isa(j, Float64))]\n                sub_vars = [\n                    j.args[2] for j in expr.args[i].args if\n                    ((:head in fieldnames(typeof(j))) && j.head == :ref)\n                ]\n                (isempty(sub_coef) || isempty(sub_vars)) && return false, expr\n                (length(sub_coef) != 1 || length(sub_vars) != 1) && return false, expr\n                (i == 2) ? push!(coef_var, (1.0 * sub_coef[1], sub_vars[1])) :\n                push!(coef_var, (coef_fetch[expr.args[1]] * sub_coef[1], sub_vars[1]))\n                continue\n            end\n\n            # General Check\n            if expr.args[i].head == :call &&\n               expr.args[i].args[1] in [:-, :+] &&\n               length(expr.args[i].args) == 2 # resolve -(2) or -(x) terms\n                expr.args[i].args[1] == :+ ? sub_coef = [1.0] : sub_coef = [-1.0]\n                sub_vars = [\n                    j.args[2] for j in expr.args[i].args if\n                    ((:head in fieldnames(typeof(j))) && j.head == :ref)\n                ]\n                isempty(sub_vars) && return false, expr\n                length(sub_vars) != 1 && return false, expr\n                (i == 2) ? push!(coef_var, (1.0 * sub_coef[1], sub_vars[1])) :\n                push!(coef_var, (coef_fetch[expr.args[1]] * sub_coef[1], sub_vars[1]))\n            else\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)  # Recursive detection\n                down_check ? expr.args[i] = linear_lift_var : return false, expr\n                push!(coef_var, (1.0, expr.args[i].args[2]))\n            end\n        end\n        # By reaching here, it is already certain that we have found the term, always treat with :+\n        term_key = Dict(:scalar => scalar, :coef_var => coef_var, :sign => :+)\n        term_key in keys(m.linear_terms) || store_linear_term(m, term_key, expr)\n        return true, lift_linear_term(m, term_key, constr_id)\n    elseif expr.args[1] in [:*] && length(expr.args) == 3\n        # For terms like (3*x)*y\n        scalar = 0.0\n        coef_var = Set()\n\n        sub_coef = [i for i in expr.args if (isa(i, Int) || isa(i, Float64))]\n        sub_vars = [\n            i.args[2] for\n            i in expr.args if ((:head in fieldnames(typeof(i))) && i.head == :ref)\n        ]\n        (isempty(sub_coef) || isempty(sub_vars)) && return false, expr\n        (length(sub_coef) != 1 || length(sub_vars) != 1) && return false, expr\n        push!(coef_var, (1.0 * sub_coef[1], sub_vars[1]))\n\n        # By reaching here, it is already certain that we have found the term, always treat with :+\n        term_key = Dict(:scalar => scalar, :coef_var => coef_var, :sign => :+)\n        term_key in keys(m.linear_terms) || store_linear_term(m, term_key, expr)\n        return true, lift_linear_term(m, term_key, constr_id)\n    end\n\n    return false, expr\nend\n\nfunction basic_linear_bounds(m::Optimizer, k::Any, linear_terms = nothing)\n    linear_terms === nothing ? linear_terms = m.linear_terms : linear_term = linear_terms\n\n    lifted_idx = linear_terms[k][:y_idx]\n    ub = 0.0\n    lb = 0.0\n    for j in linear_terms[k][:ref][:coef_var]\n        (j[1] > 0.0) ? ub += abs(j[1]) * m.u_var_tight[j[2]] :\n        ub -= abs(j[1]) * m.l_var_tight[j[2]]\n        (j[1] > 0.0) ? lb += abs(j[1]) * m.l_var_tight[j[2]] :\n        lb -= abs(j[1]) * m.u_var_tight[j[2]]\n    end\n    lb += linear_terms[k][:ref][:scalar]\n    ub += linear_terms[k][:ref][:scalar]\n    if lb > m.l_var_tight[lifted_idx] + get_option(m, :tol)\n        m.l_var_tight[lifted_idx] = lb\n    end\n    if ub < m.u_var_tight[lifted_idx] - get_option(m, :tol)\n        m.u_var_tight[lifted_idx] = ub\n    end\n\n    return\nend\n\nfunction basic_linear_bounds(m::Optimizer, k::Any, d::Dict)\n    lifted_idx = m.linear_terms[k][:y_idx]\n    ub = 0.0\n    lb = 0.0\n    for j in m.linear_terms[k][:ref][:coef_var]\n        (j[1] > 0.0) ? ub += abs(j[1]) * d[j[2]][end] : ub -= abs(j[1]) * d[j[2]][1]\n        (j[1] > 0.0) ? lb += abs(j[1]) * d[j[2]][1] : lb -= abs(j[1]) * d[j[2]][end]\n    end\n    lb += m.linear_terms[k][:ref][:scalar]\n    ub += m.linear_terms[k][:ref][:scalar]\n\n    if lb > d[lifted_idx][1] + get_option(m, :tol)\n        d[lifted_idx][1] = lb\n    end\n    if ub < d[lifted_idx][end] - get_option(m, :tol)\n        d[lifted_idx][end] = ub\n    end\n\n    return d\nend\n\n## Evaluators ##\nbpml(k, vec) = prod([vec[i] for i in k[:var_idxs]])\ndiscretemulti(k, vec) = prod([vec[i] for i in k[:var_idxs]])\nbinprod(k, vec) = prod([vec[i] for i in k[:var_idxs]])\nbinlin(k, vec) = prod([vec[i] for i in k[:var_idxs]])\nbilinear(k, vec) = prod([vec[i] for i in k[:var_idxs]])\nmultilinear(k, vec) = prod([vec[i] for i in k[:var_idxs]])\nmonomial(k, vec) = vec[k[:var_idxs][1]]^2\nfunction linear(k, vec)\n    return k[:ref][:scalar] .+ sum([i[1] * vec[i[2]] for i in k[:ref][:coef_var]])\nend\n\n\"\"\"\n    Recognize prodcuts of binary variables and multilinear products\n\n        General Case : x1 * x2 .. * xN * y1 * y2 .. * yM\n            where x are binary variables, y are continous variables\n\n    Leads to BINLIN terms, with BINPROD, INTPROD, INTLIN if necessary\n\"\"\"\nfunction detect_discretemulti_term(expr::Any, constr_id::Int, m::Optimizer)\n    # Always construct the binlin term after lifting\n    if !(expr.head == :call || expr.head == :ref)\n        return false, expr\n    end\n\n    if (expr.args[1] == :*)\n        # Pattern: coefficients * x * y * z ..., where x, y, z are all binary variables\n        var_idxs = []\n        var_types = []\n        scalar = 1.0\n        for i in 1:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_types, m.var_type[expr.args[i].args[2]])\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                push!(var_types, m.var_type[linear_lift_var.args[2]])\n                continue\n            end\n        end\n\n        # term_key = [Expr(:ref, :x, idx) for idx in var_idxs]\n\n        cont_var_idxs = [idx for idx in var_idxs if m.var_type[idx] == :Cont]\n        bin_var_idxs = [idx for idx in var_idxs if m.var_type[idx] == :Bin]\n        int_var_idxs = [idx for idx in var_idxs if m.var_type[idx] == :Int]\n\n        # Must carry at both discrete and continous variables\n        isempty(int_var_idxs) && isempty(bin_var_idxs) && return false, expr\n        isempty(cont_var_idxs) && return false, expr\n\n        # Lift clusters of continous variables multiplication if necessary\n        if length(cont_var_idxs) > 1\n            # ml_term_key = [Expr(:ref, :x, idx) for idx in cont_var_idxs]\n            ml_term_expr = Expr(:call, :*)\n            for idx in cont_var_idxs\n                push!(ml_term_expr.args, Expr(:ref, :x, idx))\n            end\n            ml_lift_term = detect_nonconvex_terms(ml_term_expr, constr_id, m)\n            ml_idx = ml_lift_term.args[2]\n        else\n            ml_idx = cont_var_idxs[1]\n        end\n\n        # Lift clusters of binary vars multiplication if necessary\n        if length(bin_var_idxs) > 1\n            bp_term_key = [Expr(:ref, :x, idx) for idx in bin_var_idxs]\n            bp_term_expr = Expr(:call, :*)\n            for idx in bin_var_idxs\n                push!(bp_term_expr.args, Expr(:ref, :x, idx))\n            end\n            bp_lift_term = detect_nonconvex_terms(bp_term_expr, constr_id, m)\n            bp_idx = bp_lift_term.args[2]\n        else\n            isempty(bin_var_idxs) ? bp_idx = -1 : bp_idx = bin_var_idxs[1]\n        end\n\n        # lift clusters of integer variables multiplication if necessary\n        if length(int_var_idxs) > 1\n            ip_term_key = [Expr(:ref, :x, idx) for idx in int_var_idxs]\n            ip_term_expr = Expr(:call, :*)\n            for idx in int_var_idxs\n                push!(ip_term_expr.args, Expr(:ref, :x, idx))\n            end\n            ip_lift_term = detect_nonconvex_terms(ip_term_expr, constr_id, m)\n            ip_idx = ip_lift_term.args[2]\n        else\n            isempty(int_var_idxs) ? ip_idx = -1 : ip_idx = int_var_idxs[1]\n        end\n\n        if ip_idx < 0 # binlin term if no integer variable\n            binlin_key = [Expr(:ref, :x, bp_idx), Expr(:ref, :x, ml_idx)]\n            binlin_idxs = [bp_idx; ml_idx]\n            binlin_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                binlin_key,\n                binlin_idxs,\n                :BINLIN,\n                :*,\n                binlin,\n                basic_binlin_bounds,\n                collect_binlin_discvar,\n            )\n            return true, lift_nonconvex_term(m, binlin_key, constr_id, scalar)\n        end\n\n        # binlin_key = [Expr(:ref, :x, bp_idx), Expr(:ref, :x, intlin_idx)]\n        binlin_key = [Expr(:ref, :x, bp_idx)]\n        # binlin_idxs = [bp_idx; intlin_idx]\n        binlin_idxs = [bp_idx]\n        binlin_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n            m,\n            binlin_key,\n            binlin_idxs,\n            :BINLIN,\n            :*,\n            binlin,\n            basic_binlin_bounds,\n            collect_binlin_discvar,\n        )\n        return true, lift_nonconvex_term(m, binlin_key, constr_id, scalar)\n    end\n\n    return false, expr\nend\n\nfunction basic_binlin_bounds(m::Optimizer, k::Any)\n    lifted_idx = m.nonconvex_terms[k][:y_idx]\n\n    prod_idxs = [i for i in m.nonconvex_terms[k][:var_idxs] if m.var_type[i] == :Cont]\n    @assert length(prod_idxs) == 1\n    lin_idx = prod_idxs[1]\n\n    if m.l_var_tight[lin_idx] > 0.0\n        m.l_var_tight[lifted_idx] = 0.0\n        m.u_var_tight[lifted_idx] = m.u_var_tight[lin_idx]\n    elseif m.u_var_tight[lin_idx] < 0.0\n        m.u_var_tight[lifted_idx] = 0.0\n        m.l_var_tight[lifted_idx] = m.l_var_tight[lin_idx]\n    else\n        m.u_var_tight[lifted_idx] = m.u_var_tight[lin_idx]\n        m.l_var_tight[lifted_idx] = m.l_var_tight[lin_idx]\n    end\n\n    return\nend\n\nfunction basic_binlin_bounds(m::Optimizer, k::Any, d::Dict)\n    lifted_idx = m.nonconvex_terms[k][:y_idx]\n\n    prod_idxs = [i for i in m.nonconvex_terms[k][:var_idxs] if m.var_type[i] == :Cont]\n    @assert length(prod_idxs) == 1\n    lin_idx = prod_idxs[1]\n\n    if d[lin_idx][1] > 0.0\n        d[lifted_idx][1] = 0.0\n        d[lifted_idx][end] = d[lin_idx][end]\n    elseif d[lin_idx][end] < 0.0\n        d[lifted_idx][end] = 0.0\n        d[lifted_idx][1] = d[lin_idx][1]\n    else\n        d[lifted_idx][end] = d[lin_idx][end]\n        d[lifted_idx][1] = d[lin_idx][1]\n    end\n\n    return d\nend\n\nfunction collect_binlin_discvar(m::Optimizer, k::Any; var_bowl = nothing)\n    # Exact linearization exists\n    return\nend\n\n\"\"\"\n    Recognize products of binary variables : x1 * x2 * .. * xN\n\"\"\"\nfunction detect_binprod_term(expr::Any, constr_id::Int, m::Optimizer)\n    @assert (expr.head == :call || expr.head == :ref)\n    if (expr.args[1] == :*)\n        # Pattern: coefficients * x * y * z ..., where x, y, z are all binary variables\n        var_idxs = []\n        scalar = 1.0\n        for i in 1:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) && m.var_type[var_idxs[end]] != :Bin && return false, expr\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                m.var_type[linear_lift_var.args[2]] != :Bin && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                continue\n            end\n        end\n        if length(var_idxs) >= 2\n            term_key = [Expr(:ref, :x, idx) for idx in var_idxs]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :BINPROD,\n                :*,\n                binprod,\n                basic_binprod_bounds,\n                collect_binprod_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    elseif (expr.args[1] == :^) && length(expr.args) == 3\n        # Pattern: (x)^(>2), where x is binary variable\n        var_idxs = []\n        power_scalar = 0\n        scalar = 1.0\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                power_scalar += expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) && m.var_type[var_idxs[end]] != :Bin && return false, expr\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                m.var_type[linear_lift_var.args[2]] != :Bin && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                continue\n            end\n        end\n        if length(var_idxs) == 1 && power_scalar > 2.0 && mod(power_scalar, 1.0) == 0.0\n            term_key = [Expr(:ref, :x, var_idxs[1]) for i in 1:power_scalar]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :BINPROD,\n                :*,\n                binprod,\n                basic_binprod_bounds,\n                collect_binprod_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    end\n\n    return false, expr\nend\n\nfunction basic_binprod_bounds(m::Optimizer, k::Any)\n    lifted_idx = m.nonconvex_terms[k][:lifted_var_ref].args[2]\n    m.l_var_tight[lifted_idx] = 0\n    m.u_var_tight[lifted_idx] = 1\n\n    return\nend\n\nfunction basic_binprod_bounds(m::Optimizer, k::Any, d::Dict)\n    lifted_idx = m.nonconvex_terms[k][:lifted_var_ref].args[2]\n    d[lifted_idx][1] = 0\n    d[lifted_idx][end] = 1\n\n    return d\nend\n\nfunction collect_binprod_discvar(m::Optimizer, k::Any; var_bowl = nothing)\n    # Exact linearization exists\n    return\nend\n\n\"\"\"\n    Future MONOMIAL Cluster\n    Recognize bilinear terms: x * y, where x and y are continous variables\n    Recognize multilinear terms: x1 * x2 * .. * xN, where all x_i ∀ i are continous variables\n    Recognize monomial terms: x^2 or x * x, where x is continuous\n\"\"\"\nfunction detect_bilinear_term(expr::Any, constr_id::Int, m::Optimizer)\n    @assert (expr.head == :call || expr.head == :ref)\n    if (expr.args[1] == :*)  # confirm head (:*)\n        # ----- Pattern : coefficient * x * y  ------ #\n        # Collect children information for checking\n        scalar = 1.0\n        var_idxs = []\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) &&\n                m.var_type[var_idxs[end]] in [:Bin, :Int] &&\n                return false, expr    # Don't consider the discrete variable\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                m.var_type[var_idxs[end]] in [:Bin, :Int] && return false, expr  # Don't consider the discrete variable\n                continue\n            end\n        end\n\n        # Confirm detection of patter A and perform store & lifting procedures\n        if (length(var_idxs) == 2) && length(Set(var_idxs)) == 2\n            term_key = [Expr(:ref, :x, var_idxs[1]), Expr(:ref, :x, var_idxs[2])]\n            if term_key in keys(m.nonconvex_terms) ||\n               reverse(term_key) in keys(m.nonconvex_terms)\n                term_key in keys(m.nonconvex_terms) ? term_key = term_key :\n                term_key = reverse(term_key)\n                return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n            else\n                store_nonconvex_term(\n                    m,\n                    term_key,\n                    var_idxs,\n                    :BILINEAR,\n                    :*,\n                    bilinear,\n                    basic_monomial_bounds,\n                    collect_monomial_discvar,\n                )\n                return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n            end\n        end\n    end\n\n    return false, expr\nend\n\nfunction detect_multilinear_term(expr::Any, constr_id::Int, m::Optimizer)\n    @assert (expr.head == :call || expr.head == :ref)\n    if (expr.args[1] == :*) # Pattern: coefficients * x * y * z ...\n        var_idxs = []\n        scalar = 1.0\n        for i in 1:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) &&\n                m.var_type[var_idxs[end]] in [:Bin, :Int] &&\n                return false, expr\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                m.var_type[var_idxs[end]] in [:Bin, :Int] && return false, expr\n                continue\n            end\n        end\n        if length(var_idxs) > 2\n            term_key = [Expr(:ref, :x, idx) for idx in var_idxs]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :MULTILINEAR,\n                :*,\n                multilinear,\n                basic_monomial_bounds,\n                collect_monomial_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    elseif (expr.args[1] == :^) && length(expr.args) == 3 # Pattern: (x)^(>2)\n        var_idxs = []\n        power_scalar = 0\n        scalar = 1.0\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                power_scalar += expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) &&\n                m.var_type[var_idxs[end]] in [:Bin, :Int] &&\n                return false, expr # Avoid fetching terms with discrete variables\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                m.var_type[var_idxs[end]] in [:Bin, :Int] && return false, expr\n                continue\n            end\n        end\n        if length(var_idxs) == 1 && power_scalar > 2.0 && mod(power_scalar, 1.0) == 0.0\n            term_key = [Expr(:ref, :x, var_idxs[1]) for i in 1:power_scalar]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :MULTILINEAR,\n                :*,\n                multilinear,\n                basic_monomial_bounds,\n                collect_monomial_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    end\n\n    return false, expr\nend\n\nfunction detect_monomial_term(expr::Any, constr_id::Int, m::Optimizer)\n    if (expr.args[1] == :^) && length(expr.args) == 3\n        # Pattern: (x)^(2)\n        var_idxs = []\n        power_scalar = 0\n        scalar = 1.0\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                power_scalar += expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) &&\n                m.var_type[var_idxs[end]] in [:Bin, :Int] &&\n                return false, expr # Avoid fetching terms with discrete variables\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                m.var_type[var_idxs[end]] in [:Bin, :Int] && return false, expr # Avoid fetching terms with discrete variables\n                continue\n            end\n        end\n\n        # Detect 1.0 in the exponent and return only the variable\n        if length(var_idxs) == 1 && power_scalar == 1.0\n            return false, Expr(:call, expr.args[2])\n        end\n\n        if length(var_idxs) == 1 && power_scalar == 2.0\n            term_key = [Expr(:ref, :x, var_idxs[1]) for i in 1:2]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :MONOMIAL,\n                :*,\n                monomial,\n                basic_monomial_bounds,\n                collect_monomial_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    end\n\n    # Type 2 monomial term : x * x\n    if (expr.args[1] == :*)  # confirm head (:*)\n        # ----- Pattern : coefficient * x * y  ------ #\n        scalar = 1.0\n        var_idxs = []\n        for i in 2:length(expr.args)\n            if isa(expr.args[i], Float64) || isa(expr.args[i], Int)\n                scalar *= expr.args[i]\n                continue\n            end\n            (isa(expr.args[i], Symbol)) && continue\n            (expr.args[i].head == :ref) &&\n                isa(expr.args[i].args[2], Int) &&\n                push!(var_idxs, expr.args[i].args[2])\n            !isempty(var_idxs) &&\n                m.var_type[var_idxs[end]] in [:Bin, :Int] &&\n                return false, expr # Avoid fetching terms with discrete variables\n            if (expr.args[i].head == :call)\n                down_check, linear_lift_var =\n                    detect_linear_term(expr.args[i], constr_id, m)\n                !down_check && return false, expr\n                push!(var_idxs, linear_lift_var.args[2])\n                m.var_type[var_idxs[end]] in [:Bin, :Int] && return false, expr # Avoid fetching terms with discrete variables\n                continue\n            end\n        end\n        # Confirm detection of pattern A and perform store & lifting procedures\n        if (length(var_idxs) == 2) && (length(Set(var_idxs)) == 1)\n            term_key = [Expr(:ref, :x, var_idxs[1]) for i in 1:2]\n            term_key in keys(m.nonconvex_terms) || store_nonconvex_term(\n                m,\n                term_key,\n                var_idxs,\n                :MONOMIAL,\n                :*,\n                monomial,\n                basic_monomial_bounds,\n                collect_monomial_discvar,\n            )\n            return true, lift_nonconvex_term(m, term_key, constr_id, scalar)\n        end\n    end\n\n    return false, expr\nend\n\nfunction basic_monomial_bounds(m::Optimizer, k::Any)\n    lifted_idx = m.nonconvex_terms[k][:lifted_var_ref].args[2]\n    cnt = 0\n    bound = []\n    for var in k\n        cnt += 1\n        var_idx = var.args[2]\n        var_bounds = [m.l_var_tight[var_idx], m.u_var_tight[var_idx]]\n        if cnt == 1\n            bound = copy(var_bounds)\n        elseif cnt == 2\n            bound = bound * var_bounds'\n        else\n            bound = vec(bound) * var_bounds'\n        end\n    end\n    if minimum(bound) > m.l_var_tight[lifted_idx] + get_option(m, :tol)\n        m.l_var_tight[lifted_idx] = minimum(bound)\n        if m.nonconvex_terms[k][:nonlinear_type] == :MONOMIAL\n            m.l_var_tight[lifted_idx] = 0.0\n        end\n    end\n    if maximum(bound) < m.u_var_tight[lifted_idx] - get_option(m, :tol)\n        m.u_var_tight[lifted_idx] = maximum(bound)\n    end\n\n    return\nend\n\nfunction basic_monomial_bounds(m::Optimizer, nlk::Any, d::Dict)\n    lifted_idx = m.nonconvex_terms[nlk][:lifted_var_ref].args[2]\n    cnt = 0\n    bound = []\n    for var in nlk\n        cnt += 1\n        var_idx = var.args[2]\n        var_bounds = [d[var_idx][1], d[var_idx][end]]\n        if cnt == 1\n            bound = copy(var_bounds)\n        elseif cnt == 2\n            bound = bound * var_bounds'\n        else\n            bound = vec(bound) * var_bounds'\n        end\n    end\n\n    if minimum(bound) > d[lifted_idx][1] + get_option(m, :tol)\n        d[lifted_idx][1] = minimum(bound)\n    end\n\n    if maximum(bound) < d[lifted_idx][end] - get_option(m, :tol)\n        d[lifted_idx][end] = maximum(bound)\n    end\n\n    return d\nend\n\nfunction collect_monomial_discvar(m::Optimizer, k::Any; var_bowl = nothing)\n    for var in k\n        @assert isa(var.args[2], Int)\n        if var_bowl === nothing\n            var.args[2] in m.candidate_disc_vars ||\n                push!(m.candidate_disc_vars, var.args[2])\n        else\n            var.args[2] in var_bowl || push!(var_bowl, var.args[2])\n        end\n    end\n    return\nend\n\n\"\"\"\n    Recognize convex constraints\n    A catch for type-A convex constraint expression\n\"\"\"\nfunction resolve_convex_constr(\n    expr::Any,\n    m::Optimizer = nothing,\n    idx::Int = 0,\n    scalar_bin = [],\n    idxs_bin = [],\n    power_bin = [],\n    rhs = 0.0,\n)\n    expr_orig, subs = :empty, Any[]\n    if expr.args[1] in [:(<=), :(>=)] && idx > 0\n        expr_orig = :constr\n        sense = expr.args[1]\n        rhs = expr.args[3]\n        subs, rhs_strip = expr_strip_const(expr.args[2])  # Focus on the regularized subtree (stripped with constants)\n        rhs += rhs_strip                                      # TODO: check if sign is flipped\n    elseif expr.args[1] == :(==)\n        return false\n    elseif idx == 0\n        expr_orig = :obj\n        subs, rhs = expr_strip_const(expr)               # Focus on the regularized subtree (stripped with constants)\n    end\n\n    for sub in subs\n        (isa(sub, Float64) || isa(sub, Int) || isa(sub, Symbol)) && return false\n        !(sub.args[1] in [:+, :-, :*]) && return false\n        (sub.head == :ref) && return false\n        (sub.head == :call) && (length(sub.args) < 3) && return false\n        if sub.args[1] in [:-, :+]\n            for i in 2:length(sub.args)\n                if isa(sub.args[i], Float64) || isa(sub.args[i], Int)\n                    (sub.args[1] == [:-]) &&\n                        ((i == 1) ? rhs += sub.args[i] : rhs -= sub.args[i])\n                    (sub.args[1] == [:+]) && (rhs += sub.args[i])\n                elseif (sub.args[i].head == :ref)\n                    return false\n                elseif (sub.args[i].head == :call)\n                    scalar, idxs, powers = expr_is_axn(sub.args[i])\n                    (scalar === nothing) && return false\n                    if length(Set(idxs)) == 1\n                        push!(idxs_bin, idxs[1])\n                        push!(power_bin, sum(powers))\n                    else\n                        return false\n                    end\n                    (sub.args[1] == :-) && (\n                        (i == 2) ? push!(scalar_bin, scalar) : push!(scalar_bin, -scalar)\n                    )\n                    (sub.args[1] == :+) && (push!(scalar_bin, scalar))\n                end\n            end\n        elseif sub.args[1] in [:*]\n            scalar, idxs, powers = expr_is_axn(sub)\n            (scalar === nothing) && return false\n            if length(Set(idxs)) == 1\n                push!(idxs_bin, idxs[1])\n                push!(power_bin, sum(powers))\n            else\n                return false\n            end\n            push!(scalar_bin, scalar)\n        else\n            return false    # don't support other operators\n        end\n\n        scalar_sign = sign(scalar_bin[1])\n        if length(scalar_bin) > 1\n            for i in 2:length(scalar_bin)\n                !(scalar_sign == sign(scalar_bin[i])) && return false\n            end\n        end\n\n        !(length(Set(power_bin)) == 1) && return false\n        (expr.args[1] == :(<=)) && !(scalar_sign >= 0.0 && rhs >= 0.0) && return false\n        (expr.args[1] == :(>=)) && !(scalar_sign <= 0.0 && rhs <= 0.0) && return false\n        (expr.args[1] == :(<=)) && (scalar_sign <= 0.0) && return false\n        (expr.args[1] == :(>=)) && (scalar_sign >= 0.0) && return false\n    end\n\n    if expr_orig == :constr\n        # For anything reaches this point, we've detected most common attributes of a convex expression\n        # Now, we should use the differences to indicate different types of convex expression\n        convex_type = :Unknown\n\n        power_check = [(i > 1.0) && mod(i, 2) == 0 for i in power_bin]    # Special case for linear constraints within @NLconstraint\n        isempty(power_check) && return false\n\n        # Convex constraint Type-A\n        # sum_i (c_i*x_i^p) <= K (K > 0, p is an even positive integer and x_i \\in R)   => Convex\n        power_check = [(i > 1.0) && mod(i, 2) == 0 for i in power_bin]\n        (convex_type == :Unknown) && prod(power_check) && (convex_type = :convexA)\n\n        # Type-B: Convex constraint\n        # sum_i (c_i*x_i^p) <= K (K > 0, p >= 1 and x_i >= 0)                           => Convex\n        lb_check = [m.l_var_orig[i.args[2]] >= 0.0 for i in idxs_bin]\n        power_check = [i > 1.0 for i in power_bin]\n        (convex_type == :Unknown) &&\n            prod(lb_check) &&\n            prod(power_check) &&\n            (convex_type = :convexB)\n\n        # Convex constraint Type-C\n        # sum_i (c_i*x_i^p) >= K (K > 0, 0 < p < 1 and x_i >= 0)                        => Convex\n        power_check = [i < 1 && i > 0.0 for i in power_bin]\n        lb_check = [m.l_var_orig[i.args[2]] >= 0.0 for i in idxs_bin]\n        (convex_type == :Unknown) &&\n            prod(power_check) &&\n            prod(power_check) &&\n            (convex_type = :convexC)\n\n        # Convex constraint Type-D\n        # sum_i (c_i*x_i^p) <= K (K > 0, p <= 0 and x_i > 0)                            => Convex\n        power_check = [i <= 0.0 for i in power_bin]\n        lb_check = [m.l_var_orig[i.args[2]] >= 0.0 for i in idxs_bin]\n        (convex_type == :Unknown) &&\n            prod(power_check) &&\n            prod(power_check) &&\n            (convex_type = :convexD)\n\n        # If we really cannot figure out what is going on...\n        (convex_type == :Unknown) && return false\n\n        # Recording the nonlinear info\n        m.nonlinear_constrs[idx] = Dict(\n            :expr_idx => idx,\n            :convex_type => convex_type,\n            :nonlinear_type => :convex,\n            :expr_orig => :constraints,\n            :expr_ref => deepcopy(expr),\n            :convexified => false,\n        )\n\n        # Recording the un-changed expression\n        m.bounding_constr_expr_mip[idx] = expr\n\n        # Recording structural identifier\n        m.constr_structure[idx] = :convex\n\n        # Recording the function for adding constraints\n        m.bounding_constr_mip[idx] = Dict(\n            :idx => idx,\n            :expr => expr,\n            :sense => sense,\n            :coefs => scalar_bin,\n            :vars => idxs_bin,\n            :rhs => rhs,\n            :cnt => length(idxs_bin),\n            :powers => power_bin,\n        )\n\n        get_option(m, :log_level) > 99 && println(\"CONVEX Constraint $(idx): $(expr)\")\n\n        return true\n    elseif expr_orig == :obj\n        minimum\n        convex_type = :Unknown\n        (expr_isconst(m.obj_expr_orig)) && return true\n        # Follows the same mapping to convex constraints\n\n        # Important: This is a fix to return obj is non-convex if the exponents have value greater than 2.\n        # This is needs to be removed once outer-approximation for convex functions is implemented\n        (maximum(power_bin) > 2) && return false\n\n        # Type-A: Convex objective function\n        # sum_i (c_i*x_i^p) (p is an even positive integer and x_i \\in R)   => Convex\n        power_check = [i > 1.0 && mod(i, 2) == 0 for i in power_bin]\n        (convex_type == :Unknown) && prod(power_check) && (convex_type = :convexA)\n\n        # Type-B: Convex objective function\n        # sum_i (c_i*x_i^p) (p >= 1 and x_i >= 0)                           => Convex\n        lb_check = [m.l_var_orig[i.args[2]] >= 0.0 for i in idxs_bin]\n        power_check = [i > 1.0 for i in power_bin]\n        (convex_type == :Unknown) &&\n            prod(lb_check) &&\n            prod(power_check) &&\n            (convex_type = :convexB)\n\n        # Type-D: Convex objective function\n        # sum_i (c_i*x_i^p) (p <= 0 and x_i > 0) => Convex\n        power_check = [i <= 0.0 for i in power_bin]\n        lb_check = [m.l_var_orig[i.args[2]] >= 0.0 for i in idxs_bin]\n        (convex_type == :Unknown) &&\n            prod(power_check) &&\n            prod(power_check) &&\n            (convex_type = :convexD)\n\n        convex_type == :Unknown && return false\n\n        # Recording the nonlinear info\n        m.nonlinear_constrs[idx] = Dict(\n            :expr_orig => :objective,\n            :expr_idx => idx,\n            :convex_type => convex_type,\n            :nonlinear_type => :convex,\n            :expr_ref => deepcopy(expr),\n            :convexified => false,\n        )\n\n        # Recording the un-changed expression\n        m.bounding_obj_expr_mip = expr\n\n        # Recording structural identifier\n        m.obj_structure = :convex\n\n        # Record a function that can be used to add objective function\n        m.bounding_obj_mip = Dict(\n            :sense => nothing,\n            :coefs => scalar_bin,\n            :vars => idxs_bin,\n            :rhs => -rhs,\n            :cnt => length(idxs_bin),\n            :powers => power_bin,\n        )\n\n        get_option(m, :log_level) > 99 && println(\"CONVEX Objective: $(expr)\")\n        return true\n    end\n\n    return false\nend\n"
  },
  {
    "path": "src/presolve.jl",
    "content": "\"\"\"\n    bound_tightening_wrapper(m::Optimizer)\n\nEntry point to the optimization-based bound-tightening (OBBT) algorithm. The aim of the OBBT algorithm\nis to sequentially tighten the variable bounds until a fixed point is reached.\n\nCurrently, two OBBT methods are implemented in [`optimization_based_bound_tightening`](@ref).\n\n    * Bound-tightening with polyhedral relaxations (McCormick, Lambda for convex-hull)\n    * Bound-tightening with piecewise polyhedral relaxations: (with three partitions around the local feasible solution)\nIf no local feasible solution is obtained, the algorithm defaults to OBBT without partitions\n\"\"\"\nfunction bound_tightening_wrapper(m::Optimizer; use_bound = true, kwargs...)\n    get_option(m, :presolve_bt) || return\n\n    if get_option(m, :presolve_bt_algo) == 1\n        optimization_based_bound_tightening(m, use_bound = use_bound)\n    elseif get_option(m, :presolve_bt_algo) == 2\n        optimization_based_bound_tightening(m, use_bound = use_bound, use_tmc = true)\n    elseif isa(get_option(m, :presolve_bt_algo), Function)\n        get_option(m, :presolve_bt_algo)(m)\n    else\n        error(\"Unrecognized bound tightening algorithm\")\n    end\n\n    return\nend\n\n\"\"\"\n    optimization_based_bound_tightening(m:Optimizer; use_bound::Bool=true, use_tmc::Bool)\n\nThis function implements the OBBT algorithm to tighten the variable bounds.\nIt utilizes either the basic polyhedral relaxations or the piecewise polyhedral relaxations (TMC)\nto tighten the bounds. The TMC has additional binary variables while performing OBBT.\n\nThe algorithm as two main parameters. The first is the `use_tmc`, which when set to `true`\ninvokes the algorithm on the TMC relaxation. The second parameter `use_bound` takes in the\nobjective value of the local solve solution stored in `best_sol` for performing OBBT. The `use_bound` option is set\nto `true` when the local solve is successful in obtaining a feasible solution, else this parameter\nis set to `false`.\n\nFor details, refer to section 3.1.1 of\nNagarajan, Lu, Wang, Bent, Sundar, \"An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs\"\n[link](https://doi.org/10.1007/s10898-018-00734-1).\n\nSeveral other user-input options can be used to tune the OBBT algorithm.\nFor more details, see [Presolve Options](https://lanl-ansi.github.io/Alpine.jl/latest/parameters/#Presolve-Options).\n\n\"\"\"\nfunction optimization_based_bound_tightening(\n    m::Optimizer;\n    use_bound = true,\n    time_limit = Inf,\n    kwargs...,\n)\n\n    # Some functinal constants\n    both_senses = [MOI.MIN_SENSE, MOI.MAX_SENSE]             # Senses during bound tightening procedures\n    tell_side = Dict(MOI.MIN_SENSE => 1, MOI.MAX_SENSE => 2)     # Positional information\n    tell_round = Dict(MOI.MIN_SENSE => floor, MOI.MAX_SENSE => ceil)\n\n    options = Dict(kwargs)\n\n    st = time() # Track start time\n    if time_limit == Inf\n        time_limit = get_option(m, :presolve_bt_time_limit)\n    end\n\n    # Regulating special input conditions: default use best feasible solution objective value\n    (use_bound == true) ? bound = m.best_obj : bound = Inf\n    l_var_orig = copy(m.l_var_tight)\n    u_var_orig = copy(m.u_var_tight)\n\n    discretization = _get_discretization_dict(m, m.l_var_tight, m.u_var_tight)\n    if use_bound == false && haskey(options, :use_tmc)\n        (get_option(m, :log_level) > 0) &&\n            @warn \" Local solve infeasible; defaulting to doing bound-tightening without partitions.\"\n    end\n    if use_bound == true && haskey(options, :use_tmc)\n        discretization = add_adaptive_partition(\n            m,\n            use_solution = m.best_sol,\n            use_disc = discretization,\n        )\n    end\n    discretization = resolve_var_bounds(m, discretization) # recomputation of bounds for lifted_variables\n\n    (get_option(m, :log_level) > 0) && println(\"  Starting bound-tightening\")\n\n    width_tol = get_option(m, :presolve_bt_width_tol)\n    bound_tol = get_option(m, :presolve_bt_bound_tol)\n    improv_tol = get_option(m, :presolve_bt_improv_tol)\n\n    keep_tightening = true\n\n    # start of the solve\n    while keep_tightening &&\n              (m.logs[:time_left] > get_option(m, :tol)) &&\n              (m.logs[:bt_iter] < get_option(m, :presolve_bt_max_iter)) # Stopping criteria\n        keep_tightening = false\n        m.logs[:bt_iter] += 1\n        get_option(m, :log_level) > 199 && println(\"  Iteration - $(m.logs[:bt_iter])\")\n        temp_bounds = Dict()\n\n        avg_reduction = 0.0\n        max_reduction = 0.0\n        total_reduction = 0.0\n        max_width = 0.0\n        current_rel_gap = Inf\n\n        # Sequential optimization-based bound tightening (OBBT)\n        for var_idx in m.candidate_disc_vars\n            temp_bounds[var_idx] =\n                [discretization[var_idx][1], discretization[var_idx][end]]\n            if (discretization[var_idx][end] - discretization[var_idx][1]) > width_tol\n                create_obbt_model(m, discretization, bound)\n                for sense in both_senses\n                    JuMP.@objective(\n                        m.model_mip,\n                        sense,\n                        _index_to_variable_ref(m.model_mip, var_idx)\n                    )\n                    stats = solve_obbt_model(m)\n                    if stats[\"status\"] in STATUS_OPT\n                        temp_bounds[var_idx][tell_side[sense]] =\n                            tell_round[sense](\n                                JuMP.objective_value(m.model_mip) / bound_tol,\n                            ) * bound_tol  # Objective truncation for numerical issues\n                    elseif stats[\"status\"] in STATUS_LIMIT\n                        temp_bounds[var_idx][tell_side[sense]] =\n                            tell_round[sense](\n                                JuMP.objective_bound(m.model_mip) / bound_tol,\n                            ) * bound_tol\n                    elseif stats[\"status\"] in STATUS_INF\n                        @warn(\n                            \"Infeasible model detected within bound tightening - bounds not updated\"\n                        )\n                    else\n                        @warn(\"Unknown status within  bound tightening models\")\n                    end\n                end\n            end\n\n            if (\n                temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] >\n                temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]]\n            )\n                temp_bounds[var_idx] =\n                    [discretization[var_idx][1], discretization[var_idx][end]]\n            end\n            if (\n                temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] >\n                discretization[var_idx][end]\n            )\n                temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] =\n                    discretization[var_idx][1]\n            end\n            if (\n                temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] <\n                discretization[var_idx][1]\n            )\n                temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] =\n                    discretization[var_idx][end]\n            end\n\n            bound_reduction = 0.0\n            if (\n                temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] -\n                temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]]\n            ) <= width_tol\n                midpoint = (temp_bounds[var_idx][1] + temp_bounds[var_idx][end]) / 2\n                if (midpoint - discretization[var_idx][1] < width_tol / 2)\n                    temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] =\n                        discretization[var_idx][1]\n                    temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] =\n                        discretization[var_idx][1] + (width_tol)\n                elseif (discretization[var_idx][end] - midpoint < width_tol / 2)\n                    temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] =\n                        discretization[var_idx][end] - (width_tol)\n                    temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] =\n                        discretization[var_idx][end]\n                else\n                    temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]] =\n                        midpoint - (width_tol / 2)\n                    temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] =\n                        midpoint + (width_tol / 2)\n                end\n            end\n\n            new_range = round(\n                temp_bounds[var_idx][tell_side[MOI.MAX_SENSE]] -\n                temp_bounds[var_idx][tell_side[MOI.MIN_SENSE]],\n                digits = 4,\n            )\n            old_range = discretization[var_idx][end] - discretization[var_idx][1]\n            bound_reduction = old_range - new_range\n            total_reduction += bound_reduction\n            max_reduction = max(bound_reduction, max_reduction)\n            max_width = max(new_range, max_width)\n\n            (get_option(m, :log_level) > 99) && print(\"+\")\n            (get_option(m, :log_level) > 99) && println(\n                \"  VAR $(var_idx) LB contracted $(discretization[var_idx][1])=>$(temp_bounds[var_idx][1])\",\n            )\n            (get_option(m, :log_level) > 99) && print(\"+\")\n            (get_option(m, :log_level) > 99) && println(\n                \"  VAR $(var_idx) UB contracted $(discretization[var_idx][end])=>$(temp_bounds[var_idx][end])\",\n            )\n\n            discretization[var_idx][1] = temp_bounds[var_idx][1]\n            discretization[var_idx][end] = temp_bounds[var_idx][end]\n        end\n\n        avg_reduction = total_reduction / length(keys(temp_bounds))\n\n        bound_avg_reduction = (avg_reduction > improv_tol)\n        bound_max_reduction = (max_reduction > improv_tol)\n        bound_max_width = (max_width > width_tol)\n\n        # Deactivate this termination criterion if it slows down the OBBT convergence\n        stats = relaxation_model_obbt(m, discretization, bound)\n        if is_min_sense(m)\n            current_rel_gap = eval_opt_gap(m, stats[\"relaxed_obj\"], bound)\n        elseif is_max_sense(m)\n            current_rel_gap = eval_opt_gap(m, bound, stats[\"relaxed_obj\"])\n        end\n\n        keep_tightening =\n            (bound_avg_reduction) &&\n            (bound_max_reduction) &&\n            (bound_max_width) &&\n            (current_rel_gap > get_option(m, :rel_gap))\n\n        if !isinf(current_rel_gap)\n            m.presolve_best_rel_gap = current_rel_gap * 100\n        end\n\n        discretization = resolve_var_bounds(m, discretization)\n        if haskey(options, :use_tmc)\n            discretization = add_adaptive_partition(\n                m,\n                use_solution = m.best_sol,\n                use_disc = flatten_discretization(discretization),\n            )\n        end\n\n        time() - st > time_limit && break\n    end\n\n    (get_option(m, :log_level) > 1) && println(\"  Variables whose bounds were tightened:\")\n    (get_option(m, :log_level) > 0) &&\n        println(\"  Actual iterations (OBBT): \", (m.logs[:bt_iter]))\n\n    m.l_var_tight, m.u_var_tight = update_var_bounds(discretization)\n\n    if haskey(options, :use_tmc)\n        m.discretization = add_adaptive_partition(m, use_solution = m.best_sol)\n    end\n\n    for i in m.disc_vars\n        contract_ratio =\n            round(\n                1 -\n                abs(m.l_var_tight[i] - m.u_var_tight[i]) /\n                abs(l_var_orig[i] - u_var_orig[i]);\n                digits = 2,\n            ) * 100\n        if get_option(m, :log_level) > 0 && contract_ratio > 0.0001\n            (get_option(m, :log_level) > 1) && (println(\n                \"    VAR $(i): $(contract_ratio)% contraction |$(round(l_var_orig[i]; digits=4)) --> | $(round(m.l_var_tight[i]; digits=4)) - $(round(m.u_var_tight[i]; digits=4)) | <-- $(round(u_var_orig[i]; digits=4)) |\",\n            ))\n        end\n    end\n    return\nend\n\n\"\"\"\n    create_obbt_model(m::Optimizer, discretization::Dict, bound::Float64)\n\nThis function takes in the initial discretization information and builds the OBBT model.\nIt is an algorithm specific function called by [`optimization_based_bound_tightening`](@ref).\n\"\"\"\nfunction create_obbt_model(m::Optimizer, discretization, bound::Number; kwargs...)\n\n    # options = Dict(kwargs)\n    start_build = time()\n    m.model_mip = Model(get_option(m, :mip_solver)) # Construct JuMP model\n    amp_post_vars(m, use_disc = discretization)\n    amp_post_lifted_constraints(m)\n    amp_post_convexification(m, use_disc = discretization)  # Convexify problem\n\n    if !(isinf(bound))\n        post_objective_bound(m, bound)\n    else\n        @warn \"Dropping the objective bound constraint in presolve bound tightening\"\n    end\n\n    cputime_build = time() - start_build\n    m.logs[:total_time] += cputime_build\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n\n    return\nend\n\nfunction relaxation_model_obbt(m::Optimizer, discretization, bound::Number)\n    create_obbt_model(m, discretization, bound)\n\n    obj_expr = JuMP.@expression(\n        m.model_mip,\n        sum(\n            m.bounding_obj_mip[:coefs][j] *\n            _index_to_variable_ref(m.model_mip, m.bounding_obj_mip[:vars][j].args[2]) for\n            j in 1:m.bounding_obj_mip[:cnt]\n        ),\n    )\n\n    if is_min_sense(m)\n        JuMP.@objective(m.model_mip, Min, obj_expr)\n    elseif is_max_sense(m)\n        JuMP.@objective(m.model_mip, Max, obj_expr)\n    end\n\n    return solve_obbt_model(m)\nend\n\n\"\"\"\n    solve_obbt_model(m::Optimizer)\n\nA function that solves the min and max OBBT model.\n\"\"\"\nfunction solve_obbt_model(m::Optimizer; kwargs...)\n    stats = Dict()\n\n    # ========= MILP Solve ========= #\n    time_limit = max(\n        0.0,\n        if get_option(m, :presolve_bt_mip_time_limit) < Inf\n            min(\n                get_option(m, :presolve_bt_mip_time_limit),\n                get_option(m, :time_limit) - m.logs[:total_time],\n            )\n        else\n            get_option(m, :time_limit) - m.logs[:total_time]\n        end,\n    )\n    MOI.set(m.model_mip, MOI.TimeLimitSec(), time_limit)\n\n    start_solve = time()\n    if get_option(m, :presolve_bt_relax_integrality)\n        JuMP.relax_integrality(m.model_mip)\n    end\n\n    JuMP.optimize!(m.model_mip)\n    status = MOI.get(m.model_mip, MOI.TerminationStatus())\n\n    stats[\"status\"] = status\n    stats[\"relaxed_obj\"] = JuMP.objective_value(m.model_mip)\n\n    cputime_solve = time() - start_solve\n    m.logs[:total_time] += cputime_solve\n    m.logs[:time_left] = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n    # ========= MILP Solve ========= #\n\n    return stats\nend\n\n\"\"\"\n    post_objective_bound(m::Optimizer, bound::Float64; kwargs...)\n\nThis function adds the upper/lower bounding constraint on the objective function\nfor the optimization models solved within the OBBT algorithm.\n\"\"\"\nfunction post_objective_bound(m::Optimizer, bound::Number; kwargs...)\n    obj_expr = JuMP.@expression(\n        m.model_mip,\n        sum(\n            m.bounding_obj_mip[:coefs][j] *\n            _index_to_variable_ref(m.model_mip, m.bounding_obj_mip[:vars][j].args[2]) for\n            j in 1:m.bounding_obj_mip[:cnt]\n        ),\n    )\n\n    obj_bound_tol = get_option(m, :presolve_bt_obj_bound_tol)\n\n    if is_max_sense(m)\n        JuMP.@constraint(\n            m.model_mip,\n            obj_expr >= floor(bound / obj_bound_tol) * obj_bound_tol\n        )\n    elseif is_min_sense(m)\n        JuMP.@constraint(\n            m.model_mip,\n            obj_expr <= ceil(bound / obj_bound_tol) * obj_bound_tol\n        )\n    end\n\n    return\nend\n"
  },
  {
    "path": "src/relaxations.jl",
    "content": "\"\"\"\n    relaxation_bilinear(\n    m::JuMP.Model, \n    z::JuMP.VariableRef, \n    x::JuMP.VariableRef, \n    y::JuMP.VariableRef, \n    lb_x::Number,\n    ub_x::Number,\n    lb_y::Number,\n    ub_y::Number)\n\nGeneral relaxation of a binlinear term (McCormick relaxation). \n```\nz >= JuMP.lower_bound(x)*y + JuMP.lower_bound(y)*x - JuMP.lower_bound(x)*JuMP.lower_bound(y)\nz >= JuMP.upper_bound(x)*y + JuMP.upper_bound(y)*x - JuMP.upper_bound(x)*JuMP.upper_bound(y)\nz <= JuMP.lower_bound(x)*y + JuMP.upper_bound(y)*x - JuMP.lower_bound(x)*JuMP.upper_bound(y)\nz <= JuMP.upper_bound(x)*y + JuMP.lower_bound(y)*x - JuMP.upper_bound(x)*JuMP.lower_bound(y)\n```\n\"\"\"\nfunction relaxation_bilinear(\n    m::JuMP.Model,\n    z::JuMP.VariableRef,\n    x::JuMP.VariableRef,\n    y::JuMP.VariableRef,\n    lb_x::Number,\n    ub_x::Number,\n    lb_y::Number,\n    ub_y::Number,\n)\n    JuMP.@constraint(m, z >= lb_x * y + lb_y * x - lb_x * lb_y)\n    JuMP.@constraint(m, z >= ub_x * y + ub_y * x - ub_x * ub_y)\n    JuMP.@constraint(m, z <= lb_x * y + ub_y * x - lb_x * ub_y)\n    JuMP.@constraint(m, z <= ub_x * y + lb_y * x - ub_x * lb_y)\n\n    return\nend\n\n\"\"\"\n    relaxation_multilinear_binary(\n    m::JuMP.Model, \n    z::JuMP.VariableRef, \n    x::Vector{VariableRef})\n\nApplies Fortet linearization (see https://doi.org/10.1007/s10288-006-0015-3) for z = prod(x), \nwhere x is a vector of binary variables.\n\"\"\"\nfunction relaxation_multilinear_binary(\n    m::JuMP.Model,\n    z::JuMP.VariableRef,\n    x::Vector{VariableRef},\n)\n    for i in x\n        JuMP.@constraint(m, z <= i)\n    end\n    JuMP.@constraint(m, z >= sum(x) - (length(x) - 1))\n\n    return\nend\n\n#=\n\"\"\"\n    relaxation_quadratic_univariate(\n        m::JuMP.Model,\n        z::JuMP.VariableRef,\n        x::JuMP.VariableRef,\n        lb_x::Number,\n        ub_x::Number,\n    )\n\nApplies convex hull relaxation for z = x^2, where x is a variable.\n\"\"\"\nfunction relaxation_quadratic_univariate(\n    m::JuMP.Model,\n    z::JuMP.VariableRef,\n    x::JuMP.VariableRef,\n    lb_x::Number,\n    ub_x::Number,\n)\n    JuMP.@constraint(m, z >= x^2)\n    JuMP.@constraint(m, z <= (lb_x + ub_x) * x - (lb_x * ub_x))\n\n    return\nend\n=#\n"
  },
  {
    "path": "src/solver_options.jl",
    "content": "# Optimizer struct and user-defined options (with default settings) to tune Alpine solver\n\nmutable struct OptimizerOptions\n    # Parameters for tuning Alpine\n\n    # Basic solver parameters\n    log_level::Int                                              # Verbosity flag: 0 for quiet, 1 for basic solve info, 2 for iteration info\n    time_limit::Float64                                         # Time limit for algorithm (in seconds)\n    max_iter::Int                                               # Maximum bound on number of iterations for the partitioning algorithm\n    rel_gap::Float64                                            # Relative optimality gap for termination condition\n    abs_gap::Float64                                            # Absolute optimality gap for termination condition\n    tol::Float64                                                # Numerical tol used in algorithms\n    large_bound::Float64                                        # Large bounds for problems with unbounded variables\n\n    # All the solver options\n    nlp_solver::Union{MOI.OptimizerWithAttributes,Nothing}      # Local continuous NLP solver for solving NLPs at each iteration\n    minlp_solver::Union{MOI.OptimizerWithAttributes,Nothing}    # Local MINLP solver for solving MINLPs at each iteration\n    mip_solver::Union{MOI.OptimizerWithAttributes,Nothing}      # MIP solver for successive lower bound solves\n\n    # Convexification methods\n    recognize_convex::Bool                                      # Recognize convex expressions in parsing objective functions and constraints\n\n    # Expression-based user-inputs\n    # method_convexification :: Array{Function}                 # Array of functions that user can choose to convexify specific non-linear terms : no over-ride privilege\n\n    # Parameters used in Alpine's MIP-based partitioning algorithm\n    apply_partitioning::Bool                                    # Apply the partitioning algorithm only if thhis true, else terminate after presolve\n    disc_var_pick::Any                                          # Algorithm for choosing the variables for partitioning: 0 for all variables, 1 for minimum vertex cover, 3 for weighted minimum vertex cover\n    partition_scaling_factor::Int                               # Partition scaling parameter, which is critical for convergence (using a fixed value for now, later switch to a function)\n    disc_uniform_rate::Int                                      # Discretization rate parameter when using uniform partitions\n    disc_add_partition_method::Any                              # Additional methods to add discretization\n    disc_divert_chunks::Int                                     # How many uniform partitions to construct\n    disc_abs_width_tol::Float64                                 # Absolute tolerance used when setting up a partition\n    disc_rel_width_tol::Float64                                 # Relative width tolerance when setting up a partition\n    disc_consecutive_forbid::Int                                # Prevent bounding model to add partitions consecutively in the same region when bounds do not improve\n    partition_scaling_factor_branch::Bool                       # Branching tests for picking fixed discretization ratio\n\n    # MIP formulation parameters\n    convhull_formulation::String                                # MIP Formulation for the relaxation\n    convhull_ebd::Bool                                          # Enable embedding formulation\n    convhull_ebd_encode::Any                                    # Encoding method used for convhull_ebd\n    convhull_ebd_ibs::Bool                                      # Enable independent branching scheme\n    convhull_ebd_link::Bool                                     # Linking constraints between x and α, type 1 uses hierarchical and type 2 uses big-m\n    convhull_warmstart::Bool                                    # Warm start the bounding MIP\n    linking_constraints::Bool                                   # Multilinear linking constraint feature\n    linking_constraints_degree_limit::Int64                     # Degree of shared multilinear terms up to which the linking constraints are built and added\n\n    # Presolve and bound-tightening parameters\n    presolve_track_time::Bool                                   # Account presolve time for total time usage\n    presolve_bt::Bool                                           # Perform bound tightening procedure before the main algorithm (default: true)\n    presolve_bt_time_limit::Float64                             # Time limit for presolving (seconds)\n    presolve_bt_max_iter::Int                                   # Maximum iterations allowed to perform presolve\n    presolve_bt_width_tol::Float64                              # Width tolerance for bound-tightening\n    presolve_bt_improv_tol::Float64                             # Improvement tolerance for average reduction of variable ranges\n    presolve_bt_bound_tol::Float64                              # Variable bounds truncation precicision tol\n    presolve_bt_obj_bound_tol::Float64                          # Objective upper bound truncation tol\n    presolve_bt_algo::Any                                       # Method used for bound tightening procedures, can either be an index of default methods or functional inputs\n    presolve_bt_relax_integrality::Bool                         # Relax the MIP solved in built-in relaxation scheme for time performance\n    presolve_bt_mip_time_limit::Float64                         # Time limit for a single MIP solved in the built-in bound tightening algorithm (with partitions)\n    use_start_as_incumbent::Bool                           # Use starting value as a local incumbent solution for presolve without invoking a local solver\n\n    # Domain Reduction\n    presolve_bp::Bool                                           # Conduct basic bound propagation\nend\n\nfunction get_default_options()\n    log_level = 1\n    time_limit = 1E6\n    max_iter = 99\n    rel_gap = 1e-4\n    abs_gap = 1e-6\n    tol = 1e-6\n    large_bound = 1E6\n\n    nlp_solver = nothing\n    minlp_solver = nothing\n    mip_solver = nothing\n\n    recognize_convex = true\n\n    apply_partitioning = true\n    disc_var_pick = 2                # By default, uses the 15-variable selective rule\n    partition_scaling_factor = 10\n    disc_uniform_rate = 2\n    disc_add_partition_method = \"adaptive\"\n    disc_divert_chunks = 5\n    disc_abs_width_tol = 1e-4\n    disc_rel_width_tol = 1e-6\n    disc_consecutive_forbid = false\n    partition_scaling_factor_branch = false\n\n    convhull_formulation = \"sos2\"\n    convhull_ebd = false\n    convhull_ebd_encode = \"default\"\n    convhull_ebd_ibs = false\n    convhull_ebd_link = false\n    convhull_warmstart = true\n    linking_constraints = true\n    linking_constraints_degree_limit = 4 # check up to quadrilinear sharing across terms\n\n    presolve_track_time = true\n    presolve_bt = true\n    presolve_bt_time_limit = 900\n    presolve_bt_max_iter = 25\n    presolve_bt_width_tol = 1e-2\n    presolve_bt_improv_tol = 1e-3\n    presolve_bt_bound_tol = 1e-4\n    presolve_bt_obj_bound_tol = 1e-2\n    presolve_bt_algo = 1\n    presolve_bt_relax_integrality = false\n    presolve_bt_mip_time_limit = Inf\n    use_start_as_incumbent = false\n    presolve_bp = false\n\n    return OptimizerOptions(\n        log_level,\n        time_limit,\n        max_iter,\n        rel_gap,\n        abs_gap,\n        tol,\n        large_bound,\n        nlp_solver,\n        minlp_solver,\n        mip_solver,\n        recognize_convex,\n        apply_partitioning,\n        disc_var_pick,\n        partition_scaling_factor,\n        disc_uniform_rate,\n        disc_add_partition_method,\n        disc_divert_chunks,\n        disc_abs_width_tol,\n        disc_rel_width_tol,\n        disc_consecutive_forbid,\n        partition_scaling_factor_branch,\n        convhull_formulation,\n        convhull_ebd,\n        convhull_ebd_encode,\n        convhull_ebd_ibs,\n        convhull_ebd_link,\n        convhull_warmstart,\n        linking_constraints,\n        linking_constraints_degree_limit,\n        presolve_track_time,\n        presolve_bt,\n        presolve_bt_time_limit,\n        presolve_bt_max_iter,\n        presolve_bt_width_tol,\n        presolve_bt_improv_tol,\n        presolve_bt_bound_tol,\n        presolve_bt_obj_bound_tol,\n        presolve_bt_algo,\n        presolve_bt_relax_integrality,\n        presolve_bt_mip_time_limit,\n        use_start_as_incumbent,\n        presolve_bp,\n    )\nend\n"
  },
  {
    "path": "src/utility.jl",
    "content": "\"\"\"\n   update_opt_gap(m::Optimizer)\n\nUpdates Alpine model's relative & absolute optimality gaps.\n\nThe relative gap calculation is\n\n```math\n\\\\textbf{Gap} = \\\\frac{|UB-LB|}{ϵ+|UB|}\n```\n\nThe absolute gap calculation is\n```\n|UB-LB|\n```\n\"\"\"\nfunction update_opt_gap(m::Optimizer)\n    tol = get_option(m, :tol)\n\n    if m.best_obj in [Inf, -Inf]\n        m.best_rel_gap = Inf\n        return\n    else\n        p = convert(Int, round(abs(log(10, get_option(m, :rel_gap)))))\n        n = round(abs(m.best_obj - m.best_bound); digits = p)\n        # dn = round(abs(1e-12+abs(m.best_obj)); digits=p)\n        if isapprox(n, 0.0; atol = tol) && isapprox(m.best_obj, 0.0; atol = tol)\n            m.best_rel_gap = 0.0\n            return\n        end\n\n        if is_min_sense(m)\n            m.best_rel_gap = eval_opt_gap(m, m.best_bound, m.best_obj)\n        elseif is_max_sense(m)\n            m.best_rel_gap = eval_opt_gap(m, m.best_obj, m.best_bound)\n        end\n    end\n\n    m.best_abs_gap = abs(m.best_obj - m.best_bound)\n\n    return\nend\n\nfunction eval_opt_gap(m::Optimizer, lower_bound::Number, upper_bound::Number)\n    tol = get_option(m, :tol)\n\n    if isinf(lower_bound) || isinf(upper_bound)\n        error(\"Infinite bounds detected in optimality gap evalutation\")\n\n    else\n        m.best_rel_gap = _eval_best_rel_gap(lower_bound, upper_bound, tol)\n\n        # If LB > UB\n        if (m.best_rel_gap > get_option(m, :rel_gap)) &&\n           ((lower_bound - upper_bound) > 1E-1)\n            error(\n                \"Lower bound cannot exceed the upper bound in optimality gap evaluation\",\n            )\n        end\n    end\n\n    return m.best_rel_gap\nend\n\nfunction _eval_best_rel_gap(lower_bound::Number, upper_bound::Number, tol::Number)\n    if isapprox(lower_bound, upper_bound, atol = tol)\n        return 0.0\n\n    elseif isapprox(upper_bound, 0.0; atol = tol) # zero upper bound case\n        eps = 1 # shift factor\n        return abs((upper_bound + eps) - (lower_bound + eps)) /\n               (tol + abs(upper_bound) + eps)\n\n    else\n        return abs(upper_bound - lower_bound) / (tol + abs(upper_bound))\n    end\nend\n\nfunction measure_relaxed_deviation(m::Optimizer; sol = nothing)\n    sol = something(sol, m.best_bound_sol)\n\n    isempty(sol) && return\n\n    dev = []\n    for k in keys(m.nonconvex_terms)\n        y_idx = m.nonconvex_terms[k][:y_idx]\n        y_hat = sol[y_idx]\n        y_val = m.nonconvex_terms[k][:evaluator](m.nonconvex_terms[k], sol)\n        push!(\n            dev,\n            (y_idx, abs(y_hat - y_val), y_hat, y_val, m.nonconvex_terms[k][:var_idxs]),\n        )\n    end\n\n    sort!(dev, by = x -> x[1])\n\n    for i in dev\n        get_option(m, :log_level) > 199 && println(\n            \"Y-VAR$(i[1]): DIST=$(i[2]) || Y-hat = $(i[3]), Y-val = $(i[4]) || COMP $(i[5])\",\n        )\n    end\n\n    return\nend\n\n\"\"\"\n   discretization_to_bounds(d::Dict, l::Int)\n\nSame as [`update_var_bounds`](@ref)\n\"\"\"\ndiscretization_to_bounds(d::Dict, l::Int) = update_var_bounds(d, len = l)\n\n\"\"\"\nUpdate the data structure with feasible solution and its associated objective (if better)\n\"\"\"\nfunction update_incumbent(m::Optimizer, objval::Float64, sol::Vector)\n    push!(m.logs[:obj], objval)\n    if m.sense_orig == MOI.MAX_SENSE ? objval > m.best_obj : objval < m.best_obj\n        m.best_obj = objval\n        m.best_sol = sol\n        m.detected_incumbent = true\n    end\n    return\nend\n\n\"\"\"\n   variable_values(m::JuMP.Model)\n\nPrints values of all the variables after optimizing the original JuMP model.\n\"\"\"\nfunction variable_values(m::JuMP.Model)\n    for var in all_variables(m)\n        if isapprox(abs(JuMP.value(var)), 0, atol = 1E-6)\n            println(\"$var = 0.0\")\n        else\n            println(\"$var = $(round(JuMP.value(var), digits = 5))\")\n        end\n    end\n\n    return\nend\n\n\"\"\"\nMention the variable type of the lifted term.\nThis function is with limited functionality\n\n\"\"\"\nfunction resolve_lifted_var_type(var_types::Vector{Symbol}, operator::Symbol)\n    if operator == :+\n        detector = [i in [:Bin, :Int] ? true : false for i in var_types]\n        if length(detector) == 1 && detector[1] # Special case\n            if :Bin in var_types\n                return :Bin\n            else\n                return :Int\n            end\n        end\n        prod(detector) && return :Int\n        # o/w continous variables\n\n    elseif operator == :*\n        detector = [i == :Bin ? true : false for i in var_types]\n        prod(detector) && return :Bin\n        detector = [i in [:Bin, :Int] ? true : false for i in var_types]\n        prod(detector) && return :Int\n        # o/w continous variables\n\n    end\n\n    return :Cont\nend\n\n\"\"\"\n   check_solution_history(m::Optimizer, ind::Int)\n\nCheck if the solution is always the same within the last disc_consecutive_forbid iterations. Return `true` if solution has stalled.\n\"\"\"\nfunction check_solution_history(m::Optimizer, ind::Int)\n    get_option(m, :disc_consecutive_forbid) == 0 && return false\n    ((m.logs[:n_iter] - 1) < get_option(m, :disc_consecutive_forbid)) && return false\n\n    sol_val = m.bound_sol_history[mod(\n        m.logs[:n_iter] - 2,\n        get_option(m, :disc_consecutive_forbid),\n    )+1][ind]\n    for i in 1:(get_option(m, :disc_consecutive_forbid)-1)\n        search_pos =\n            mod(m.logs[:n_iter] - 2 - i, get_option(m, :disc_consecutive_forbid)) + 1\n        !isapprox(\n            sol_val,\n            m.bound_sol_history[search_pos][ind];\n            atol = get_option(m, :disc_rel_width_tol),\n        ) && return false\n    end\n\n    get_option(m, :log_level) > 99 &&\n        println(\"Consecutive bounding solution on VAR$(ind) obtained. Diverting...\")\n\n    return true\nend\n\n\"\"\"\n   fix_domains(m::Optimizer)\n\nThis function is used to fix variables to certain domains during the local solve process in the [`global_solve`](@ref).\nMore specifically, it is used in [`local_solve`](@ref) to fix binary and integer variables to lower bound solutions\nand discretizing variables to the active domain according to lower bound solution.\n\"\"\"\nfunction fix_domains(m::Optimizer; discrete_sol = nothing, use_orig = false)\n    discrete_sol !== nothing && @assert length(discrete_sol) >= m.num_var_orig\n\n    l_var = [m.l_var_tight[i] for i in 1:m.num_var_orig]\n    u_var = [m.u_var_tight[i] for i in 1:m.num_var_orig]\n\n    for i in 1:m.num_var_orig\n        if i in m.disc_vars && m.var_type[i] == :Cont\n            point = if discrete_sol === nothing\n                m.best_bound_sol[i]\n            else\n                discrete_sol[i]\n            end\n            PCnt = length(m.discretization[i]) - 1\n            for j in 1:PCnt\n                if point >= (m.discretization[i][j] - get_option(m, :tol)) &&\n                   (point <= m.discretization[i][j+1] + get_option(m, :tol))\n                    @assert j < length(m.discretization[i])\n                    use_orig ? l_var[i] = m.discretization[i][1] :\n                    l_var[i] = m.discretization[i][j]\n                    use_orig ? u_var[i] = m.discretization[i][end] :\n                    u_var[i] = m.discretization[i][j+1]\n                    break\n                end\n            end\n        elseif m.var_type[i] == :Bin || m.var_type[i] == :Int\n            if discrete_sol === nothing\n                l_var[i] = round(m.best_bound_sol[i])\n                u_var[i] = round(m.best_bound_sol[i])\n            else\n                l_var[i] = round(discrete_sol[i])\n                u_var[i] = round(discrete_sol[i])\n            end\n        end\n    end\n\n    return l_var, u_var\nend\n\n\"\"\"\n   _is_fully_convexified(m::Optimizer)\n\"\"\"\nfunction _is_fully_convexified(m::Optimizer)\n\n    # Other more advanced convexification check goes here\n    for term in keys(m.nonconvex_terms)\n        if !m.nonconvex_terms[term][:convexified]\n            @warn \"  Warning: Detected terms that is not convexified $(term[:lifted_constr_ref]), bounding model solver may report a error due to this\"\n            return\n        else\n            m.nonconvex_terms[term][:convexified] = false    # Reset status for next iteration\n        end\n    end\n\n    return\nend\n\n\"\"\"\nCollect active partition idx\nNeed to be careful with the diverted point\n\"\"\"\nfunction get_active_partition_idx(\n    discretization::Dict,\n    val::Float64,\n    idx::Int;\n    tol = 1e-6,\n)\n    for j in 1:length(discretization[idx])-1\n        if val > discretization[idx][j] - tol && val < discretization[idx][j+1] + tol\n            return j\n        end\n    end\n\n    @warn \"  Warning: Activate parition not found [VAR$(idx)]. Returning default partition 1.\"\n    return 1\nend\n\n\"\"\"\n   get_candidate_disc_vars(m:Optimizer)\n\n   A built-in method for selecting variables for discretization. This function selects all candidate variables in the nonlinear terms for discretization,\n   if under a threshold value of the number of nonlinear terms.\n\"\"\"\nfunction get_candidate_disc_vars(m::Optimizer; getoutput = false)\n\n    # Pick variables that is bound width more than tolerance length\n    if getoutput\n        return [i for i in m.candidate_disc_vars]\n    else\n        m.disc_vars = [i for i in m.candidate_disc_vars]\n        m.num_var_disc_mip = length(m.disc_vars)\n    end\n\n    return\nend\n\nfunction initialize_solution_pool(m::Optimizer, cnt::Int)\n    s = Dict()\n\n    s[:cnt] = cnt\n\n    # Column dimension changing variable\n    s[:len] = m.num_var_orig + m.num_var_linear_mip + m.num_var_nonlinear_mip\n\n    # !! Be careful with the :vars when utilizing the dynamic discretization variable selection !!\n    s[:vars] = [i for i in m.candidate_disc_vars if length(m.discretization[i]) > 2]\n\n    s[:sol] = Vector{Vector}(undef, cnt)                   # Solution value\n    s[:obj] = Vector{Float64}(undef, cnt)                  # Objecitve value\n    s[:disc] = Vector{Dict}(undef, cnt)                    # Discretization\n    s[:stat] = [:Alive for i in 1:cnt]              # Solution status\n    s[:iter] = [m.logs[:n_iter] for i in 1:cnt]     # Iteration collected\n    s[:ubstart] = [false for i in 1:cnt]            # Solution used for ub multistart\n\n    return s\nend\n\n\"\"\"\nReconsideration required\n\"\"\"\nfunction ncvar_collect_arcs(m::Optimizer, nodes::Vector)\n    arcs = Set()\n\n    for k in keys(m.nonconvex_terms)\n        if m.nonconvex_terms[k][:nonlinear_type] == :BILINEAR\n            arc = [i.args[2] for i in k]\n            length(arc) == 2 && push!(arcs, sort(arc))\n\n        elseif m.nonconvex_terms[k][:nonlinear_type] == :MONOMIAL\n            @assert isa(m.nonconvex_terms[k][:var_idxs][1], Int)\n            varidx = m.nonconvex_terms[k][:var_idxs][1]\n            push!(arcs, [varidx; varidx])\n\n        elseif m.nonconvex_terms[k][:nonlinear_type] == :MULTILINEAR\n            varidxs = m.nonconvex_terms[k][:var_idxs]\n            for i in 1:length(varidxs)\n                for j in 1:length(varidxs)\n                    if i != j\n                        push!(arcs, sort([varidxs[i]; varidxs[j]]))\n                    end\n                end\n            end\n            if length(varidxs) == 1\n                push!(arcs, sort([varidxs[1]; varidxs[1]]))\n            end\n\n            # elseif m.nonconvex_terms[k][:nonlinear_type] in [:cos, :sin]\n            #    @assert length(m.nonconvex_terms[k][:var_idxs]) == 1\n            #    var_idx = m.nonconvex_terms[k][:var_idxs][1]\n            #    push!(arcs, [var_idx; var_idx])\n\n        elseif m.nonconvex_terms[k][:nonlinear_type] in [:BININT, :BINLIN, :BINPROD]\n            continue\n        else\n            error(\n                \"[EXCEPTION] Unexpected nonlinear term when building interaction graphs for min. vertex cover.\",\n            )\n        end\n    end\n\n    return arcs\nend\n\n\"\"\"\n\"\"\"\nfunction build_discvar_graph(m::Optimizer)\n\n    # Collect the information of nonlinear terms in terms of arcs and nodes\n    nodes = get_candidate_disc_vars(m, getoutput = true)\n    arcs = ncvar_collect_arcs(m, nodes)\n\n    # Collect integer variables\n    for i in 1:m.num_var_orig\n        if !(i in nodes) && m.var_type[i] == :Int\n            push!(nodes, i)\n            push!(arcs, [i; i])\n        end\n    end\n\n    nodes = collect(nodes)\n    arcs = collect(arcs)\n\n    return nodes, arcs\nend\n\n\"\"\"\n   min_vertex_cover(m::Optimizer)\n\n`min_vertex_cover` chooses the variables based on the minimum vertex cover algorithm for the interaction graph of\nnonlinear terms which are adaptively partitioned for global optimization. This option can be activated by\nsetting `disc_var_pick = 1`.\n\"\"\"\nfunction min_vertex_cover(m::Optimizer)\n    nodes, arcs = build_discvar_graph(m)\n\n    # Set up minimum vertex cover problem\n    minvertex = Model(get_option(m, :mip_solver))\n    MOI.set(minvertex, MOI.TimeLimitSec(), 60.0) # Time limit for min vertex cover formulation\n    JuMP.@variable(minvertex, 0 <= x[nodes] <= 1, Bin)\n    JuMP.@constraint(minvertex, [a in arcs], x[a[1]] + x[a[2]] >= 1)\n    JuMP.@objective(minvertex, Min, sum(x))\n\n    JuMP.optimize!(minvertex)\n    # status = MOI.get(minvertex, MOI.TerminationStatus())\n    xVal = JuMP.value.(x)\n\n    # Collecting required information\n    m.num_var_disc_mip = Int(sum(xVal))\n    m.disc_vars = [\n        i for i in nodes if xVal[i] > get_option(m, :tol) &&\n        abs(m.u_var_tight[i] - m.l_var_tight[i]) >= get_option(m, :tol)\n    ]\n\n    return\nend\n\nfunction weighted_min_vertex_cover(m::Optimizer, distance::Dict)\n\n    # Collect the graph information\n    nodes, arcs = build_discvar_graph(m)\n\n    # A little bit redundancy before\n    disvec = [distance[i] for i in keys(distance) if i in m.candidate_disc_vars]\n    disvec = abs.(disvec[disvec.>0.0])\n    isempty(disvec) ? heavy = 1.0 : heavy = 1 / minimum(disvec)\n    weights = Dict()\n    for i in m.candidate_disc_vars\n        isapprox(distance[i], 0.0; atol = 1e-6) ? weights[i] = heavy :\n        (weights[i] = (1 / distance[i]))\n        (get_option(m, :log_level) > 100) &&\n            println(\"VAR$(i) WEIGHT -> $(weights[i]) ||| DISTANCE -> $(distance[i])\")\n    end\n\n    # Set up minimum vertex cover problem\n    minvertex = Model(get_option(m, :mip_solver))\n    MOI.set(minvertex, MOI.TimeLimitSec(), 60.0)  # Set a timer to avoid waste of time in proving optimality\n    JuMP.@variable(minvertex, 0 <= x[nodes] <= 1, Bin)\n    for arc in arcs\n        JuMP.@constraint(minvertex, x[arc[1]] + x[arc[2]] >= 1)\n    end\n    JuMP.@objective(minvertex, Min, sum(weights[i] * x[i] for i in nodes))\n\n    # Solve the minimum vertex cover\n    JuMP.optimize!(minvertex)\n\n    xVal = JuMP.value.(x)\n    m.num_var_disc_mip = Int(sum(xVal))\n    m.disc_vars = [\n        i for i in nodes if\n        xVal[i] > 0 && abs(m.u_var_tight[i] - m.l_var_tight[i]) >= get_option(m, :tol)\n    ]\n    get_option(m, :log_level) >= 99 &&\n        println(\"UPDATED DISC-VAR COUNT = $(length(m.disc_vars)) : $(m.disc_vars)\")\n\n    return\nend\n\nfunction _fetch_mip_solver_identifier(m::Optimizer; override = \"\")\n    (get_option(m, :mip_solver) === nothing) && return\n    m.mip_solver_id = _get_solver_name(m, :mip_solver, override)\n    return\nend\n\nfunction _fetch_nlp_solver_identifier(m::Optimizer; override = \"\")\n    (get_option(m, :nlp_solver) === nothing) && return\n    m.nlp_solver_id = _get_solver_name(m, :nlp_solver, override)\n    return\nend\n\nfunction _fetch_minlp_solver_identifier(m::Optimizer; override = \"\")\n    (get_option(m, :minlp_solver) === nothing) && return\n    m.minlp_solver_id = _get_solver_name(m, :minlp_solver, override)\n    return\nend\n\nfunction _get_solver_name(m::Optimizer, key::Symbol, override::String)\n    solver_string = override\n    if isempty(override)\n        solver = MOI.instantiate(get_option(m, key))\n        solver_string = try\n            MOI.get(solver, MOI.SolverName())\n        catch\n            \"$(typeof(solver))\"\n        end\n    end\n    for name in (\"Ipopt\", \"Gurobi\", \"CPLEX\", \"Juniper\")\n        if occursin(name, solver_string)\n            return name\n        end\n    end\n    return solver_string\nend\n\n\"\"\"\n    set_mip_time_limit(m::Optimizer)\n\nAn utility function used to dynamically regulate MILP solver time limits to fit Alpine solver's time limits.\n\"\"\"\nfunction set_mip_time_limit(m::Optimizer)\n    time_limit = max(0.0, get_option(m, :time_limit) - m.logs[:total_time])\n    return MOI.set(m.model_mip, MOI.TimeLimitSec(), time_limit)\nend\n\n\"\"\"\nFollow the definition of terms to calculate the value of lifted terms\n\"\"\"\nfunction resolve_lifted_var_value(m::Optimizer, sol_vec::Array)\n    @assert length(sol_vec) == m.num_var_orig\n    sol_vec = [sol_vec; fill(NaN, m.num_var_linear_mip + m.num_var_nonlinear_mip)]\n\n    for i in 1:length(m.term_seq)\n        k = m.term_seq[i]\n        if haskey(m.nonconvex_terms, k)\n            lvar_idx = m.nonconvex_terms[k][:y_idx]\n            sol_vec[lvar_idx] =\n                m.nonconvex_terms[k][:evaluator](m.nonconvex_terms[k], sol_vec)\n        elseif haskey(m.linear_terms, k)\n            lvar_idx = m.linear_terms[k][:y_idx]\n            sol_vec[lvar_idx] = m.linear_terms[k][:evaluator](m.linear_terms[k], sol_vec)\n        else\n            error(\"[RARE] Found homeless term key $(k) during bound resolution.\")\n        end\n    end\n\n    return sol_vec\nend\n\n# Unused functions\n# function amp_post_λ_upperbound(\n#     m::Optimizer,\n#     λ::Dict,\n#     indices::Any,\n#     dim::Tuple,\n#     d::Dict,\n#     tregions::Vector,\n#     reg = [],\n#     level = 0,\n# )\n#     if level == length(indices)\n#         isempty(tregions[level]) && return\n#         sliced_indices =\n#             Set(collect_indices(λ[indices][:indices], 1, [reg[1]; reg[1] + 1], dim))\n#         for i in 2:length(reg)\n#             sliced_indices = intersect(\n#                 sliced_indices,\n#                 Set(collect_indices(λ[indices][:indices], i, [reg[i], reg[i] + 1], dim)),\n#             )\n#         end\n#         for i in sliced_indices\n#             JuMP.set_upper_bound(λ[indices][:vars][i], (1 / 2)^level)\n#         end\n#         return\n#     end\n\n#     for i in 1:length(tregions[level+1])\n#         push!(reg, tregions[level+1][i])\n#         amp_post_λ_upperbound(m, λ, indices, dim, d, tregions, reg, level + 1)\n#         length(reg) < level && error(\"Something is wrong\")\n#         length(reg) > level && pop!(reg)\n#     end\n\n#     return\n# end\n\n# function amp_post_λ_upperbound(m::Optimizer, λ::Dict, indices::Any, ub::Float64)\n#     for i in λ[indices][:vars]\n#         JuMP.set_upper_bound(i, ub)\n#     end\n\n#     return\n# end\n\n# function amp_no_good_cut_α(m::Optimizer, α::Dict)\n#     println(\"Global Incumbent solution objective = $(m.best_obj)\")\n\n#     for i in 1:m.bound_sol_pool[:cnt]\n#         (m.bound_sol_pool[:stat][i] == :Cutoff) && (m.bound_sol_pool[:stat][i] = :Alive)\n#         if m.best_obj < m.bound_sol_pool[:obj][i] && m.bound_sol_pool[:stat][i] == :Alive\n#             no_good_idxs = keys(m.bound_sol_pool[:disc][i])\n#             no_good_size = length(no_good_idxs) - 1\n#             JuMP.@constraint(\n#                 m.model_mip,\n#                 sum(α[v][m.bound_sol_pool[:disc][i][v]] for v in no_good_idxs) <=\n#                 no_good_size\n#             )\n#             get_option(m, :log_level) > 0 && println(\n#                 \"!! GLOBAL cuts off POOL_SOL-$(i) POOL_OBJ=$(m.bound_sol_pool[:obj][i])!\",\n#             )\n#             m.bound_sol_pool[:stat][i] = :Cutoff\n#         end\n#     end\n\n#     return\n# end\n"
  },
  {
    "path": "src/variable_bounds.jl",
    "content": "\"\"\"\n    init_tight_bound(m::Optimizer)\n\nInitialize internal bound vectors (placeholders) to be used in other places.\nIn this case, we don't have to mess with the original bound information.\n\"\"\"\nfunction init_tight_bound(m::Optimizer)\n    m.l_var_tight = [\n        m.l_var_orig\n        fill(-Inf, m.num_var_linear_mip + m.num_var_nonlinear_mip)\n    ]\n    m.u_var_tight = [\n        m.u_var_orig\n        fill(Inf, m.num_var_linear_mip + m.num_var_nonlinear_mip)\n    ]\n    for i in 1:m.num_var_orig\n        if m.var_type_orig[i] == :Bin\n            m.l_var_tight[i] = 0.0\n            m.u_var_tight[i] = 1.0\n            # elseif m.var_type_orig[i] == :Int\n            #     m.l_var_tight[i] = floor(m.l_var_tight[i])\n            #     m.u_var_tight[i] = ceil(m.u_var_tight[i])\n        end\n    end\n\n    return\nend\n\n\"\"\"\n    init_disc(m::Optimizer)\n\nThis function initialize the dynamic discretization used for any bounding models. By default, it takes (.l_var_orig, .u_var_orig) as the base information. User is allowed to use alternative bounds for initializing the discretization dictionary.\nThe output is a dictionary with MathProgBase variable indices keys attached to the :Optimizer.discretization.\n\"\"\"\nfunction init_disc(m::Optimizer)\n    for var in 1:(m.num_var_orig+m.num_var_linear_mip+m.num_var_nonlinear_mip)\n        if m.var_type[var] in [:Bin, :Cont]\n            lb = m.l_var_tight[var]\n            ub = m.u_var_tight[var]\n            m.discretization[var] = [lb, ub]\n        else\n            error(\n                \"[EXCEPTION] Unexpected variable type when initializing discretization dictionary.\",\n            )\n        end\n    end\n\n    return\nend\n\n\"\"\"\n\n    _get_discretization_dict(m::Optimizer, lbs::Vector{Float64}, ubs::Vector{Float64})\n\nUtility functions to convert bounds vectors to Dictionary based structures that are more suitable for\npartition operations.\n\n\"\"\"\nfunction _get_discretization_dict(\n    m::Optimizer,\n    lbs::Vector{Float64},\n    ubs::Vector{Float64},\n)\n    @assert length(lbs) == length(ubs)\n\n    var_discretization = Dict()\n    total_var_cnt = m.num_var_orig + m.num_var_linear_mip + m.num_var_nonlinear_mip\n\n    for var in 1:total_var_cnt\n        if length(lbs) == total_var_cnt\n            lb = lbs[var]\n            ub = ubs[var]\n        else\n            lb = -Inf\n            ub = Inf\n        end\n        var_discretization[var] = [lb, ub]\n    end\n\n    return var_discretization\nend\n\n\"\"\"\n    flatten_discretization(discretization::Dict)\n\nUtility functions to eliminate all partition on discretizing variable and keep the loose bounds.\n\n\"\"\"\nfunction flatten_discretization(discretization::Dict; kwargs...)\n    flatten_discretization = Dict()\n    for var in keys(discretization)\n        flatten_discretization[var] = [discretization[var][1], discretization[var][end]]\n    end\n\n    return flatten_discretization\nend\n\n\"\"\"\n    detect_bound_from_aff(m::Optimizer)\n\nDetect bounds from parse affine constraint. This function examines the one variable constraints such as\nx >= 5, x <= 5 or x == 5 and fetch the information to m.l_var_tight and m.u_var_tight.\n\"\"\"\nfunction bound_propagation(m::Optimizer)\n    exhausted = false\n    infeasible = false\n    tol = get_option(m, :tol)\n\n    while !exhausted\n        exhausted = true\n        for aff in m.bounding_constr_mip\n            for i in 1:length(aff[:vars])\n                var_idx = aff[:vars][i].args[2]\n                var_coef = aff[:coefs][i]\n                @assert (isa(var_idx, Float64) || isa(var_idx, Int))\n\n                if aff[:sense] == :(==) && var_coef > 0.0\n                    eval_l_bound = aff[:rhs] / var_coef\n                    eval_u_bound = aff[:rhs] / var_coef\n                    for j in 1:length(aff[:vars])\n                        if j != i && aff[:coefs][j] * var_coef > 0.0     # same sign\n                            (eval_l_bound != -Inf) && (\n                                eval_l_bound -=\n                                    abs(aff[:coefs][j] / var_coef) *\n                                    m.u_var_tight[aff[:vars][j].args[2]]\n                            )\n                            (eval_u_bound != Inf) && (\n                                eval_u_bound -=\n                                    abs(aff[:coefs][j] / var_coef) *\n                                    m.l_var_tight[aff[:vars][j].args[2]]\n                            )\n                        elseif j != i && aff[:coefs][j] * var_coef < 0.0  # different sign\n                            (eval_l_bound != -Inf) && (\n                                eval_l_bound +=\n                                    abs(aff[:coefs][j] / var_coef) *\n                                    m.l_var_tight[aff[:vars][j].args[2]]\n                            )\n                            (eval_u_bound != Inf) && (\n                                eval_u_bound +=\n                                    abs(aff[:coefs][j] / var_coef) *\n                                    m.u_var_tight[aff[:vars][j].args[2]]\n                            )\n                        end\n                    end\n\n                    if eval_l_bound > m.l_var_tight[var_idx] + tol\n                        exhausted = false\n                        m.l_var_tight[var_idx] = eval_l_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] LB $(m.l_var_tight[var_idx]) evaluated from constraint\",\n                        )\n                    elseif eval_l_bound > m.u_var_tight[var_idx] + tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n\n                    if eval_u_bound < m.u_var_tight[var_idx] - tol\n                        exhausted = false\n                        m.u_var_tight[var_idx] = eval_u_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] UB $(m.u_var_tight[var_idx]) evaluated from constraints\",\n                        )\n                    elseif eval_u_bound < m.l_var_tight[var_idx] - tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n\n                elseif aff[:sense] == :(>=) && var_coef > 0.0  # a($) - by + cz >= 100, y∈[1,10], z∈[2,50], a,b,c > 0\n                    eval_bound = aff[:rhs] / var_coef\n                    for j in 1:length(aff[:vars])\n                        if j != i && aff[:coefs][j] > 0.0\n                            eval_bound -=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.u_var_tight[aff[:vars][j].args[2]]\n                        elseif j != i\n                            aff[:coefs][j] < 0.0\n                            eval_bound +=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.l_var_tight[aff[:vars][j].args[2]]\n                        end\n                        (eval_bound == -Inf) && break\n                    end\n\n                    if eval_bound > m.l_var_tight[var_idx] + tol\n                        exhausted = false\n                        m.l_var_tight[var_idx] = eval_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] LB $(m.l_var_tight[var_idx]) evaluated from constraints\",\n                        )\n                    elseif eval_bound > m.u_var_tight[var_idx] + tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n\n                elseif aff[:sense] == :(>=) && var_coef < 0.0  # -a($) - by + cz >= 100, y∈[1,10], z∈[2,50], a,b,c > 0\n                    eval_bound = aff[:rhs] / var_coef\n                    for j in 1:length(aff[:vars])\n                        if j != i && aff[:coefs][j] > 0.0\n                            eval_bound +=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.u_var_tight[aff[:vars][j].args[2]]\n                        elseif j != i && aff[:coefs][j] < 0.0\n                            eval_bound -=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.l_var_tight[aff[:vars][j].args[2]]\n                        end\n                        (eval_bound == Inf) && break\n                    end\n\n                    if eval_bound < m.u_var_tight[var_idx] - tol\n                        exhausted = false\n                        m.u_var_tight[var_idx] = eval_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] UB $(m.u_var_tight[var_idx]) evaluated from constraints\",\n                        )\n                    elseif eval_bound < m.l_var_tight[var_idx] - tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n\n                elseif (aff[:sense] == :(<=) && aff[:coefs][i] > 0.0) # a($) - by + cz <= 100, y∈[1,10], z∈[2,50], a,b,c > 0\n                    eval_bound = aff[:rhs] / var_coef\n                    for j in 1:length(aff[:vars])\n                        if j != i && aff[:coefs][j] > 0.0\n                            eval_bound -=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.l_var_tight[aff[:vars][j].args[2]]\n                        elseif j != i && aff[:coefs][j] < 0.0\n                            eval_bound +=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.u_var_tight[aff[:vars][j].args[2]]\n                        end\n                        (eval_bound == Inf) && break\n                    end\n\n                    if eval_bound < m.u_var_tight[var_idx] - tol\n                        exhausted = false\n                        m.u_var_tight[var_idx] = eval_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] UB $(m.u_var_tight[var_idx]) evaluated from constraints\",\n                        )\n                    elseif eval_bound < m.l_var_tight[var_idx] - tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n                elseif (aff[:sense] == :(<=) && aff[:coefs][i] < 0.0) # -a($) - by + cz <= 100, y∈[1,10], z∈[2,50], a,b,c > 0\n                    eval_bound = aff[:rhs] / var_coef\n                    for j in 1:length(aff[:vars])\n                        if j != i && aff[:coefs][j] > 0.0\n                            eval_bound +=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.l_var_tight[aff[:vars][j].args[2]]\n                        elseif j != i && aff[:coefs][j] < 0.0\n                            eval_bound -=\n                                abs(aff[:coefs][j] / var_coef) *\n                                m.u_var_tight[aff[:vars][j].args[2]]\n                        end\n                        (eval_bound == -Inf) && break\n                    end\n\n                    if eval_bound > m.l_var_tight[var_idx] + tol\n                        exhausted = false\n                        m.l_var_tight[var_idx] = eval_bound\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] LB $(m.l_var_tight[var_idx]) evaluated from constraints\",\n                        )\n                    elseif eval_bound > m.u_var_tight[var_idx] + tol\n                        (get_option(m, :log_level) > 199) && println(\n                            \"[VAR$(var_idx)] Infeasibility detection during bound propagation\",\n                        )\n                        infeasible = true\n                        break\n                    end\n                end\n            end\n        end\n        (exhausted == true && get_option(m, :log_level) > 99) &&\n            println(\"Initial constraint-based bound evaluation exhausted...\")\n    end\n\n    if infeasible\n        m.status[:bounding_solve] = MOI.INFEASIBLE\n        @warn \"[INFEASIBLE] Infeasibility detected via bound propagation\"\n    end\n\n    return infeasible\nend\n\n\"\"\"\n    Recategorize :Int variables to :Bin variables if variable bounds are [0,1]\n\"\"\"\nfunction recategorize_var(m::Optimizer)\n    for i in 1:m.num_var_orig\n        if m.var_type_orig[i] == :Int && m.l_var_orig[i] == 0.0 && m.u_var_orig[i] == 1.0\n            m.var_type_orig[i] = :Bin\n            m.var_type[i] = :Bin\n        end\n    end\n\n    return\nend\n\n\"\"\"\n    resolve_var_bounds(m::Optimizer)\n\nResolve the bounds of the lifted variable using the information in l_var_tight and u_var_tight. This method only takes\nin known or trivial bounds information to deduce lifted variable bounds and to potentially avoid the cases of infinity bounds.\n\"\"\"\nfunction resolve_var_bounds(m::Optimizer)\n\n    # Basic Bound propagation\n    if get_option(m, :presolve_bp)\n        setproperty!(m, :presolve_infeasible, bound_propagation(m)) # Fetch bounds from constraints\n    end\n\n    # Resolve unbounded variables in the original formulation\n    resolve_inf_bounds(m)\n\n    # Added sequential bound resolving process base on DFS process, which ensures all bounds are secured.\n    # Increased complexity from linear to square but a reasonable amount\n    # Potentially, additional mapping can be applied to reduce the complexity\n    for i in 1:length(m.term_seq)\n        k = m.term_seq[i]\n        if haskey(m.nonconvex_terms, k)\n            m.nonconvex_terms[k][:bound_resolver](m, k)\n        elseif haskey(m.linear_terms, k)\n            basic_linear_bounds(m, k)\n        else\n            error(\"Found homeless term key $(k) during bound resolution.\")\n        end\n    end\n\n    return\nend\n\n\"\"\"\n    Resolving Inf variable bounds since Alpine relies on finite bounds to construct relaxations\n\"\"\"\nfunction resolve_inf_bounds(m::Optimizer)\n    warnuser = false\n    infcount_l = 0\n    infcount_u = 0\n\n    # Only specify necessary bounds\n    for i in 1:length(m.l_var_orig)\n        if m.l_var_tight[i] == -Inf\n            warnuser = true\n            m.l_var_tight[i] = -get_option(m, :large_bound)\n            infcount_l += 1\n        end\n        if m.u_var_tight[i] == Inf\n            warnuser = true\n            m.u_var_tight[i] = get_option(m, :large_bound)\n            infcount_u += 1\n        end\n    end\n    infcount = min(infcount_l, infcount_u)\n    if infcount == 1\n        warnuser && println(\n            \"Warning: -/+Inf bounds detected on at least $infcount variable. Initializing with values -/+$(get_option(m, :large_bound)). This may affect global optimal values and run times.\",\n        )\n    elseif infcount > 1\n        warnuser && println(\n            \"Warning: -/+Inf bounds detected on at least $infcount variables. Initializing with values -/+$(get_option(m, :large_bound)). This may affect global optimal values and run times.\",\n        )\n    end\n\n    return\nend\n\n\"\"\"\n    resolve_var_bounds(nonconvex_terms::Dict, discretization::Dict)\n\n    For discretization to be performed, we do not allow a variable being discretized to have infinite bounds.\n    The lifted/auxiliary variables may have infinite bounds and the function infers bounds on these variables. This process\n    can help speed up the subsequent solve times.\n\n    Only used in presolve bound tightening\n\"\"\"\nfunction resolve_var_bounds(m::Optimizer, d::Dict; kwargs...)\n    # Added sequential bound resolving process base on DFS process, which ensures all bounds are accurate.\n    # Potentially, additional mapping can be applied to reduce the complexity\n    for i in 1:length(m.term_seq)\n        k = m.term_seq[i]\n        if haskey(m.nonconvex_terms, k)\n            nlk = k\n            if m.nonconvex_terms[nlk][:nonlinear_type] in ALPINE_C_MONOMIAL\n                d = basic_monomial_bounds(m, nlk, d)\n            elseif m.nonconvex_terms[nlk][:nonlinear_type] in [:BINPROD]\n                d = basic_binprod_bounds(m, nlk, d)\n            elseif m.nonconvex_terms[nlk][:nonlinear_type] in [:BINLIN]\n                d = basic_binlin_bounds(m, nlk, d)\n            else\n                error(\"EXPECTED ERROR : NEED IMPLEMENTATION\")\n            end\n        elseif haskey(m.linear_terms, k)\n            d = basic_linear_bounds(m, k, d)\n        else\n            error(\n                \"Found a homeless term key $(k) during bound resolution im resolve_var_bounds.\",\n            )\n        end\n    end\n\n    return d\nend\n\n\"\"\"\n    update_var_bounds(m::Optimizer, discretization::Dict; len::Float64=length(keys(discretization)))\n\nThis function takes in a dictionary-based discretization information and convert them into two bounds vectors (l_var, u_var) by picking the smallest and largest numbers. User can specify a certain length that may contains variables that is out of the scope of discretization.\n\nOutput::\n\n    l_var::Vector{Float64}, u_var::Vector{Float64}\n\"\"\"\nfunction update_var_bounds(discretization::Dict{Any,Any}; kwargs...)\n    options = Dict(kwargs)\n\n    haskey(options, :len) ? len = options[:len] : len = length(keys(discretization))\n\n    l_var = fill(-Inf, len)\n    u_var = fill(Inf, len)\n\n    for var_idx in keys(discretization)\n        l_var[var_idx] = discretization[var_idx][1]\n        u_var[var_idx] = discretization[var_idx][end]\n    end\n\n    return l_var, u_var\nend\n\n# ================================================================= unused, but needs testing\n# \"\"\"\n#     resolve_closed_var_bounds(m::Optimizer)\n\n# This function seeks variable with tight bounds (by presolve_bt_width_tol) by checking .l_var_tight and .u_var_tight.\n# If a variable is found to be within a sufficiently small interval then no discretization will be performed on this variable\n# and the .discretization will be cleared with the tight bounds for basic McCormick operation if necessary.\n\n# \"\"\"\n# function resolve_closed_var_bounds(m::Optimizer; kwargs...)\n#     for var in m.candidate_disc_vars\n#         if abs(m.l_var_tight[var] - m.u_var_tight[var]) <\n#            get_option(m, :presolve_bt_width_tol)         # Closed Bound Criteria\n#             deleteat!(m.disc_vars, findfirst(m.disc_vars, var)) # Clean nonconvex_terms by deleting the info\n#             m.discretization[var] = [m.l_var_tight[var], m.u_var_tight[var]]              # Clean up the discretization for basic McCormick if necessary\n#         end\n#     end\n\n#     return\n# end\n"
  },
  {
    "path": "test/runtests.jl",
    "content": "using JuMP\nusing Test\n\nimport Alpine\nimport HiGHS\nimport Ipopt\nimport Juniper\nimport Pavito\nimport Random\n\nconst _EXAMPLES_DIR = joinpath(@__DIR__, \"..\", \"examples\", \"MINLPs\")\nfor file in readdir(_EXAMPLES_DIR)\n    include(joinpath(_EXAMPLES_DIR, file))\nend\n\nconst IPOPT = MOI.OptimizerWithAttributes(\n    Ipopt.Optimizer,\n    MOI.Silent() => true,\n    \"sb\" => \"yes\",\n    \"max_iter\" => 9999,\n)\n\nconst HIGHS = MOI.OptimizerWithAttributes(\n    HiGHS.Optimizer,\n    \"presolve\" => \"on\",\n    \"log_to_console\" => false,\n    # \"small_matrix_value\" => 1e-12,\n    # \"allow_unbounded_or_infeasible\" => true,\n)\n\nconst JUNIPER = MOI.OptimizerWithAttributes(\n    Juniper.Optimizer,\n    MOI.Silent() => true,\n    \"mip_solver\" => HIGHS,\n    \"nl_solver\" => IPOPT,\n)\nconst PAVITO = MOI.OptimizerWithAttributes(\n    Pavito.Optimizer,\n    MOI.Silent() => true,\n    \"mip_solver\" => HIGHS,\n    \"cont_solver\" => IPOPT,\n    \"mip_solver_drives\" => false,\n)\n\nfunction _build(model::JuMP.Model)\n    JuMP.set_optimize_hook(model, MOI.Utilities.attach_optimizer)\n    JuMP.optimize!(model)\n    JuMP.JuMP.set_optimize_hook(model, nothing)\n    alpine = JuMP.backend(model).optimizer.model\n    Alpine.load!(alpine)\n    return alpine\nend\n\n# Perform Tests\n@testset \"Alpine tests\" begin\n    include(joinpath(@__DIR__, \"test_solver.jl\"))\n    include(joinpath(@__DIR__, \"test_expression.jl\"))\n    include(joinpath(@__DIR__, \"test_algorithm.jl\"))\n    include(joinpath(@__DIR__, \"test_utility.jl\"))\nend\n"
  },
  {
    "path": "test/test_algorithm.jl",
    "content": "@testset \" Validation Test || AMP-TMC || basic solve || examples/nlp3.jl (2 iterations)\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => false,\n        # \"monomial_convexhull\" => false,\n        \"presolve_bp\" => true,\n        \"max_iter\" => 2,\n        \"presolve_bt_width_tol\" => 1e-3,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 10,\n        \"disc_var_pick\" => 0,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n\n    @test isapprox(objective_value(m), 7049.247897696512; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 2\nend\n\n@testset \" Validation Test || AMP-TMC || minimum-vertex solving || examples/nlp3.jl (3 iterations)\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => false,\n        # \"monomial_convexhull\" => false,\n        \"presolve_bp\" => true,\n        \"disc_var_pick\" => 1,\n        \"max_iter\" => 2,\n        \"partition_scaling_factor\" => 10,\n        \"presolve_bt_width_tol\" => 1e-3,\n        \"presolve_bt\" => false,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.247897696512; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 2\nend\n\n@testset \" Validation Test || BT-AMP-TMC || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => false,\n        \"log_level\" => 100,\n        \"max_iter\" => 2,\n        \"partition_scaling_factor\" => 10,\n        \"presolve_bt_width_tol\" => 1e-3,\n        \"presolve_bt_bound_tol\" => 1e-1,\n        \"presolve_bt\" => true,\n        \"presolve_bt_algo\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt_max_iter\" => 2,\n        \"presolve_track_time\" => true,\n        \"disc_var_pick\" => max_cover_var_picker,\n    )\n    m = nlp3(solver = test_solver)\n\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 2\n    @test MOI.get(m, Alpine.NumberOfPresolveIterations()) == 2\n\n    vars = all_variables(m)\n    LB = [100, 1000, 1000, 10, 150.2, 10, 35.4, 168]\n    UB = [4573.6, 5547.8, 5913.3, 332.4, 551, 390, 571.1, 638.7]\n    @test isapprox(MOI.get.(m, Alpine.TightenedLowerBound(), vars), LB, atol = 1E-6)\n    @test isapprox(MOI.get.(m, Alpine.TightenedUpperBound(), vars), UB, atol = 1E-6)\nend\n\n# FIXME Pavito terminates with `NUMERICAL_ERROR` on Julia v1.0:\n@testset \" Validation Test || PBT-AMP-TMC || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => false,\n        \"log_level\" => 100,\n        \"max_iter\" => 2,\n        \"partition_scaling_factor\" => 10,\n        \"presolve_bt\" => true,\n        \"presolve_bt_width_tol\" => 1e-3,\n        \"presolve_bt_bound_tol\" => 1e-1,\n        \"presolve_bt_algo\" => 2,\n        \"presolve_bp\" => true,\n        \"presolve_bt_max_iter\" => 2,\n        \"disc_var_pick\" => max_cover_var_picker,\n    )\n\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 2\nend\n\n@testset \" Validation Test || AMP-CONV || basic solve || examples/nlp1.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => true,\n        \"partition_scaling_factor\" => 12,\n        \"max_iter\" => 1,\n    )\n    m = nlp1(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 58.38367169858795; atol = 1e-5)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\nend\n\n@testset \" Validation Test || AMP-CONV || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => false,\n        \"partition_scaling_factor\" => 14,\n        \"max_iter\" => 4,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.24789; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 4\nend\n\n@testset \" Validation Test || AMP || basic solve || examples/circle.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"disc_abs_width_tol\" => 1e-3,\n        \"partition_scaling_factor\" => 8,\n        \"max_iter\" => 6,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = circle(solver = test_solver)\n    # This is fixed in Alpine - TODO (odow): cycling detected in Pavito when disc_abs_width_tol = 1E-2\n    JuMP.optimize!(m)\n    @test isapprox(objective_value(m), 1.4142135534556992; atol = 1e-3)\nend\n\n@testset \" Validation Test || AMP-CONV-FACET || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => true,\n        \"convhull_formulation\" => \"facet\",\n        \"max_iter\" => 3,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test isapprox(objective_value(m), 7049.247897696188; atol = 1e-4)\n    @test 6650 <= objective_bound(m) <= 7049\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 3\nend\n\n@testset \" Validation Test || AMP || multi4N || N = 2 || exprmode=1:11\" begin\n    n_instances = 5\n    objValVec = 2.0 * ones(n_instances)\n\n    for i in 1:n_instances\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"disc_abs_width_tol\" => 1e-2,\n            \"max_iter\" => 4,\n            \"partition_scaling_factor\" => 4,\n            \"presolve_bp\" => false,\n            \"presolve_bt\" => false,\n            \"log_level\" => 1,\n        )\n\n        m = multi4N(solver = test_solver, N = 2, exprmode = i)\n        JuMP.optimize!(m)\n\n        @test termination_status(m) == MOI.OTHER_LIMIT\n        @test isapprox(objective_value(m), objValVec[i]; atol = 1e-3)\n    end\nend\n\n@testset \" Validation Test || AMP || multi2 || exprmode=1:11\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"max_iter\" => 5,\n        \"presolve_bt\" => false,\n        \"log_level\" => 1,\n    )\n\n    m = multi2(solver = test_solver)\n    JuMP.optimize!(m)\n    @test termination_status(m) == MOI.OPTIMAL\n    @test primal_status(m) == MOI.FEASIBLE_POINT\n    @test dual_status(m) == MOI.NO_SOLUTION\n    @test raw_status(m) isa String\n    @test isapprox(objective_value(m), 0.92906489; atol = 1e-3)\nend\n\n@testset \" Validation Test || AMP || multi3N || N = 2 || exprmode=1:11\" begin\n    n_instances = 3\n    objValVec = 2.0 * ones(n_instances)\n\n    objBoundVec = Any[2.97186, 3.85492, 4.23375]\n\n    for i in 1:n_instances\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"disc_abs_width_tol\" => 1e-2,\n            \"max_iter\" => 4,\n            \"partition_scaling_factor\" => 4,\n            \"presolve_bp\" => false,\n            \"presolve_bt\" => false,\n            \"log_level\" => 1,\n        )\n\n        m = multi3N(solver = test_solver, N = 2, exprmode = i)\n        JuMP.optimize!(m)\n\n        @test termination_status(m) == MOI.OTHER_LIMIT\n        @test isapprox(objective_value(m), objValVec[i]; atol = 1e-3)\n        @test objective_bound(m) <= objBoundVec[i] + 1e-3\n    end\nend\n\n@testset \" Validation Test || AMP || multiKND || K = 3, N = 3, D = 0 \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"max_iter\" => 3,\n        \"partition_scaling_factor\" => 4,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"log_level\" => 1,\n    )\n\n    m = multiKND(solver = test_solver, randomub = 50, K = 3, N = 3, D = 0)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 3.0000000824779454; atol = 1e-3)\n    @test isapprox(objective_bound(m), 12.054604248046875; atol = 1e-3)\nend\n\n@testset \" Validation Test || AMP-CONV-FACET || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => false,\n        \"max_iter\" => 3,\n        \"partition_scaling_factor\" => 4,\n        \"convhull_formulation\" => \"facet\",\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.247897696188; atol = 1e-4)\n    @test isapprox(objective_bound(m), 5871.530692199214; atol = 1E-5)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 3\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR || examples/nlp3.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => false,\n        \"partition_scaling_factor\" => 18,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 18\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/nlp3.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 14\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/castro2m2.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = castro2m2(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 8\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/multi3N.jl exprmode=2\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = multi3N(solver = test_solver, N = 3, exprmode = 1)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 16\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/multi3N.jl exprmode=2\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = multi3N(solver = test_solver, N = 3, exprmode = 1)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 20\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/multi4N.jl exprmode=1\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = multi4N(solver = test_solver, N = 2, exprmode = 1)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 12\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/multi4N.jl exprmode=2\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = multi4N(solver = test_solver, N = 2, exprmode = 1)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 20\nend\n\n@testset \" Validation Test || AMP || PARTITION-SCALING-FACTOR-BRANCH || examples/multi4N.jl exprmode=2\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_abs_width_tol\" => 1e-2,\n        \"partition_scaling_factor_branch\" => true,\n        \"max_iter\" => 1,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = multi4N(solver = test_solver, N = 2, exprmode = 2)\n    JuMP.optimize!(m)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"partition_scaling_factor\")) == 20\nend\n\n@testset \"Operator :: bmpl && binlin && binprod solve test I\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n\n    m = bpml_lnl(solver = test_solver)\n    JuMP.optimize!(m)\n    @test isapprox(objective_value(m), 0.3; atol = 1e-6)\n    alpine = JuMP.backend(m).optimizer.model\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[1]), :(x[6])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[2]), :(x[7])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[3]), :(x[8])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[4]), :(x[9])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[5]), :(x[10])])\n\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[7])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[8])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[9])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[10])]][:nonlinear_type] == :BINLIN\nend\n\n@testset \"Operator :: bmpl && binlin && binprod solve test II\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => JUNIPER,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 4,\n        \"log_level\" => 100,\n    )\n\n    m = bpml_binl(solver = test_solver)\n\n    # FIXME: Deactivating this until Juniper v0.9.0's numerical issues are fixed.\n    # JuMP.optimize!(m)\n    # @test isapprox(JuMP.objective_value(m), 22812.76415926; atol=1e-6)\n    # alpine = JuMP.backend(m).optimizer.model\n\n    alpine = _build(m)\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[6]), :(x[7])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[7]), :(x[8])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[8]), :(x[9])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[9]), :(x[10])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[10]), :(x[6])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[1]), :(x[11])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[2]), :(x[13])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[3]), :(x[15])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[4]), :(x[17])])\n    @test haskey(alpine.nonconvex_terms, Expr[:(x[5]), :(x[19])])\n\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[7])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[7]), :(x[8])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[8]), :(x[9])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[6])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[11])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[13])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[15])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[17])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[19])]][:nonlinear_type] == :BINLIN\nend\n\n@testset \"Embedding Test || AMP-CONV || basic solve || examples/nlp1.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => true,\n        \"convhull_ebd\" => true,\n        \"max_iter\" => 1,\n        \"partition_scaling_factor\" => 4,\n        \"log_level\" => 100,\n    )\n\n    m = nlp1(solver = test_solver)\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 58.38367169858795; atol = 1e-4)\n    @test isapprox(alp.best_bound, 52.9702, atol = 1E-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\nend\n\n@testset \"Embedding IBS Test || AMP-CONV || basic solve || examples/nlp1.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => true,\n        \"convhull_ebd\" => true,\n        \"convhull_ebd_ibs\" => true,\n        \"partition_scaling_factor\" => 8,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n    m = nlp1(solver = test_solver)\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 58.38367169858795; atol = 1e-5)\n    @test isapprox(alp.best_bound, 57.01, atol = 1E-2)\n\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\nend\n\n@testset \"Embedding IBS Test || AMP-CONV || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => false,\n        \"convhull_ebd\" => true,\n        \"convhull_ebd_ibs\" => true,\n        \"max_iter\" => 3,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.247897696188; atol = 1e-5)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 3\n    @test isapprox(alp.best_bound, 6893.2067, atol = 1E-4)\nend\n\n@testset \"Embedding IBS Test || AMP || special problem || ... \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"disc_abs_width_tol\" => 1e-3,\n        \"partition_scaling_factor\" => 8,\n        \"max_iter\" => 6,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => true,\n        \"presolve_bt_algo\" => 1,\n        \"presolve_bt_bound_tol\" => 1e-1,\n        \"convhull_ebd\" => true,\n        \"convhull_ebd_ibs\" => true,\n        \"log_level\" => 100,\n    )\n\n    m = circle(solver = test_solver)\n    # This is fixed in Alpine - TODO(odow): mixed-integer cycling detected, terminating Pavito\n    JuMP.optimize!(m)\n    @test isapprox(objective_value(m), 1.41421355; atol = 1e-3)\nend\n\n@testset \"Embedding LINK Test || AMP-CONV || basic solve || examples/nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bt\" => false,\n        \"presolve_bp\" => false,\n        \"convhull_ebd\" => true,\n        \"convhull_ebd_link\" => true,\n        \"partition_scaling_factor\" => 10,\n        \"max_iter\" => 3,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.247897696188; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 3\nend\n\n@testset \"Algorithm Logic Test || castro4m2 || 1 iteration || Error case\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"max_iter\" => 1,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 10,\n        \"log_level\" => 100,\n    )\n\n    m = castro4m2(solver = test_solver)\n    JuMP.optimize!(m)\n    @test termination_status(m) == MOI.OTHER_LIMIT\nend\n\n@testset \" Algorithm Logic Test || blend029_gl || 3 iterations || Infeasible Case\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bp\" => true,\n        \"disc_var_pick\" => 1,\n        \"log_level\" => 100,\n        \"max_iter\" => 3,\n        \"partition_scaling_factor\" => 10,\n        \"presolve_bt_width_tol\" => 1e-3,\n        \"presolve_bt\" => false,\n    )\n    m = blend029_gl(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 3\n    @test objective_bound(m) <= 14.0074\nend\n\n@testset \"Convex Model Solve\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"max_iter\" => 1,\n        \"presolve_bt\" => false,\n        \"log_level\" => 100,\n    )\n    m = convex_solve(solver = test_solver)\n    JuMP.optimize!(m)\n    @test termination_status(m) == MOI.OPTIMAL\nend\n\n@testset \"Uniform partitioning\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_add_partition_method\" => \"uniform\",\n        \"disc_uniform_rate\" => 10,\n        \"max_iter\" => 1,\n        \"presolve_bt\" => false,\n        \"time_limit\" => 100000,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    @test isapprox(objective_bound(m), 6561.7841; atol = 1e-3)\nend\n\n@testset \"Algorithm Test with binprod terms\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        # \"bilinear_convexhull\" => true,\n        # \"monomial_convexhull\" => true,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 10,\n        \"log_level\" => 100,\n    )\n    m = binprod_nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OPTIMAL\n    @test isapprox(objective_value(m), 3651.020370626844; rtol = 1e-4)\n    @test isapprox(objective_bound(m), 3650.786358471944; rtol = 1e-4)\n\n    alpine = JuMP.backend(m).optimizer.model\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4])]][:y_idx] == 19\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4])]][:id] == 6\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[19] == x[2] * x[4])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[8])]][:y_idx] == 25\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[8])]][:id] == 12\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[8])]][:lifted_constr_ref] ==\n          :(x[25] == x[3] * x[8])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[8])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5])]][:y_idx] == 22\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5])]][:id] == 9\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[22] == x[3] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[19])]][:y_idx] == 20\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[19])]][:id] == 7\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[19])]][:lifted_constr_ref] ==\n          :(x[20] == x[12] * x[19])\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[19])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[4])]][:y_idx] == 14\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[4])]][:id] == 1\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[14] == x[9] * x[4])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[4])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:y_idx] == 17\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:id] == 4\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:lifted_constr_ref] ==\n          :(x[17] == x[1] * x[6])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[11]), :(x[5])]][:y_idx] == 16\n    @test alpine.nonconvex_terms[Expr[:(x[11]), :(x[5])]][:id] == 3\n    @test alpine.nonconvex_terms[Expr[:(x[11]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[16] == x[11] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[11]), :(x[5])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[11])]][:y_idx] == 30\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[11])]][:id] == 17\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[11])]][:lifted_constr_ref] ==\n          :(x[30] == x[10] * x[11])\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[11])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[11])]][:y_idx] == 29\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[11])]][:id] == 16\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[11])]][:lifted_constr_ref] ==\n          :(x[29] == x[9] * x[10] * x[11])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[11])]][:nonlinear_type] ==\n          :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[7])]][:y_idx] == 21\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[7])]][:id] == 8\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[7])]][:lifted_constr_ref] ==\n          :(x[21] == x[2] * x[7])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[7])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[13])]][:y_idx] == 32\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[13])]][:id] == 19\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[13])]][:lifted_constr_ref] ==\n          :(x[32] == x[9] * x[13])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[13])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[6])]][:y_idx] == 15\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[6])]][:id] == 2\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[6])]][:lifted_constr_ref] ==\n          :(x[15] == x[10] * x[6])\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[6])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[12])]][:y_idx] == 33\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[12])]][:id] == 20\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[12])]][:lifted_constr_ref] ==\n          :(x[33] == x[10] * x[12])\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[12])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[27]), :(x[5])]][:y_idx] == 28\n    @test alpine.nonconvex_terms[Expr[:(x[27]), :(x[5])]][:id] == 15\n    @test alpine.nonconvex_terms[Expr[:(x[27]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[28] == x[27] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[27]), :(x[5])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[25])]][:y_idx] == 26\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[25])]][:id] == 13\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[25])]][:lifted_constr_ref] ==\n          :(x[26] == x[13] * x[25])\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[25])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[12])]][:y_idx] == 27\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[12])]][:id] == 14\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[12])]][:lifted_constr_ref] ==\n          :(x[27] == x[9] * x[12])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[12])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[13])]][:y_idx] == 23\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[13])]][:id] == 10\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[13])]][:lifted_constr_ref] ==\n          :(x[23] == x[10] * x[13])\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[13])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[23]), :(x[22])]][:y_idx] == 24\n    @test alpine.nonconvex_terms[Expr[:(x[23]), :(x[22])]][:id] == 11\n    @test alpine.nonconvex_terms[Expr[:(x[23]), :(x[22])]][:lifted_constr_ref] ==\n          :(x[24] == x[23] * x[22])\n    @test alpine.nonconvex_terms[Expr[:(x[23]), :(x[22])]][:nonlinear_type] == :BINLIN\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[13])]][:y_idx] == 31\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[13])]][:id] == 18\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[13])]][:lifted_constr_ref] ==\n          :(x[31] == x[12] * x[13])\n    @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[13])]][:nonlinear_type] == :BINPROD\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[17])]][:y_idx] == 18\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[17])]][:id] == 5\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[17])]][:lifted_constr_ref] ==\n          :(x[18] == x[9] * x[17])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[17])]][:nonlinear_type] == :BINLIN\n    @test alpine.bounding_constr_mip[1][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[14]), :(x[15])]\n    @test alpine.bounding_constr_mip[1][:coefs] == Any[0.0025, 0.0025]\n    @test alpine.bounding_constr_mip[1][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[1][:cnt] == 2\n    @test alpine.bounding_constr_mip[2][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[2][:vars] == Any[:(x[14]), :(x[5]), :(x[7])]\n    @test alpine.bounding_constr_mip[2][:coefs] == Any[-0.0025, 0.0025, 0.0025]\n    @test alpine.bounding_constr_mip[2][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[2][:cnt] == 3\n    @test alpine.bounding_constr_mip[3][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[3][:vars] == Any[:(x[16]), :(x[8])]\n    @test alpine.bounding_constr_mip[3][:coefs] == Any[-0.01, 0.01]\n    @test alpine.bounding_constr_mip[3][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[3][:cnt] == 2\n    @test alpine.bounding_constr_mip[4][:rhs] == 83333.333\n    @test alpine.bounding_constr_mip[4][:vars] == Any[:(x[1]), :(x[18]), :(x[14])]\n    @test alpine.bounding_constr_mip[4][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[4][:cnt] == 3\n    @test alpine.bounding_constr_mip[5][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[5][:vars] ==\n          Any[:(x[20]), :(x[21]), :(x[4]), :(x[5])]\n    @test alpine.bounding_constr_mip[5][:coefs] == Any[1.0, -1.0, -1250.0, 1250.0]\n    @test alpine.bounding_constr_mip[5][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[5][:cnt] == 4\n    @test alpine.bounding_constr_mip[6][:rhs] == -1.25e6\n    @test alpine.bounding_constr_mip[6][:vars] == Any[:(x[24]), :(x[26]), :(x[28])]\n    @test alpine.bounding_constr_mip[6][:coefs] == Any[1.0, -1.0, -2500.0]\n    @test alpine.bounding_constr_mip[6][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[6][:cnt] == 3\n    @test alpine.bounding_constr_mip[7][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[7][:vars] == Any[:(x[29])]\n    @test alpine.bounding_constr_mip[7][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[7][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[7][:cnt] == 1\n    @test alpine.bounding_constr_mip[8][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[8][:vars] == Any[:(x[30]), :(x[31])]\n    @test alpine.bounding_constr_mip[8][:coefs] == Any[1.0, -1.0]\n    @test alpine.bounding_constr_mip[8][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[8][:cnt] == 2\n    @test alpine.bounding_constr_mip[9][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[9][:vars] == Any[:(x[32]), :(x[33])]\n    @test alpine.bounding_constr_mip[9][:coefs] == Any[1.0, -1.0]\n    @test alpine.bounding_constr_mip[9][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[9][:cnt] == 2\nend\n\n@testset \"TESTS for closing the optimality gap in OBBT\" begin\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"presolve_bt\" => true,\n        \"presolve_bt_max_iter\" => 2,\n        \"log_level\" => 1,\n    )\n    m = JuMP.Model(test_solver)\n\n    # From issue #108\n    @variable(m, -2 <= x[1:2] <= 2)\n    @variable(m, -10 <= y[1:3] <= 10)\n    @NLobjective(m, Min, y[2] + y[1] * y[2] * y[3])\n    @constraint(m, y[1] == x[1])\n    @constraint(m, y[2] == x[2])\n    @NLconstraint(m, y[3] == x[2]^2)\n\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n    @test isapprox(JuMP.objective_value(m), -18, atol = 1E-6)\n    @test isapprox(value.(m[:x]), [2, -2], atol = 1E-6)\n    @test alp.logs[:n_iter] == 0\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 0\nend\n\n@testset \"Linking constraints for multilinear terms\" begin\n\n    # Without linking constraints\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => false,\n        \"apply_partitioning\" => true,\n        \"linking_constraints\" => false,\n    )\n    m = linking_constraints_testing(solver = test_solver)\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n    @test isapprox(JuMP.objective_value(m), -0.5294000135, atol = 1E-5)\n    @test isnothing(alp.linking_constraints_info)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 2\n\n    # With linking constraints\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => false,\n        \"apply_partitioning\" => true,\n        \"linking_constraints\" => true,\n    )\n    m = linking_constraints_testing(solver = test_solver)\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n    @test isapprox(JuMP.objective_value(m), -0.5294000135, atol = 1E-5)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n    @test in(Set{Any}([1, 2]), alp.linking_constraints_info[[1, 2]])\n    @test in(Set{Any}([1, 2, 3]), alp.linking_constraints_info[[1, 2]])\n    @test in(Set{Any}([1, 2, 4]), alp.linking_constraints_info[[1, 2]])\n    @test in(Set{Any}([1, 3]), alp.linking_constraints_info[[1, 3]])\n    @test in(Set{Any}([1, 2, 3]), alp.linking_constraints_info[[1, 3]])\n    @test in(Set{Any}([1, 3, 4]), alp.linking_constraints_info[[1, 3]])\n    @test in(Set{Any}([1, 4]), alp.linking_constraints_info[[1, 4]])\n    @test in(Set{Any}([1, 2, 4]), alp.linking_constraints_info[[1, 4]])\n    @test in(Set{Any}([1, 3, 4]), alp.linking_constraints_info[[1, 4]])\nend\n\n@testset \"Warm start value used as the incumbent solution\" begin\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"use_start_as_incumbent\" => false,\n    )\n    sol = [\n        579.30669,\n        1359.97066,\n        5109.97054,\n        182.0177,\n        295.60118,\n        217.9823,\n        286.41653,\n        395.60118,\n    ]\n\n    m = nlp3(solver = test_solver)\n    for i in 1:length(m[:x])\n        JuMP.set_start_value(m[:x][i], sol[i])\n    end\n\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(objective_value(m), 7049.247897696512, atol = 1e-6)\n    @test isapprox(alp.best_bound, 3834.978106740535, atol = 1E-6)\n    @test alp.options.use_start_as_incumbent == false\n\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => true,\n        \"max_iter\" => 1,\n        \"use_start_as_incumbent\" => true,\n    )\n\n    m = nlp3(solver = test_solver)\n    for i in 1:length(m[:x])\n        JuMP.set_start_value(m[:x][i], sol[i])\n    end\n\n    JuMP.optimize!(m)\n    alp = JuMP.backend(m).optimizer.model\n\n    @test termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(alp.best_bound, 4810.212866711817, atol = 1E-3)\n    @test alp.warm_start_value == sol\n    @test alp.options.use_start_as_incumbent == true\nend\n\n@testset \"Test binary multilinear product linearization\" begin\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n        \"presolve_bt\" => false,\n    )\n\n    m = hmittelman(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OPTIMAL\n    @test isapprox(objective_value(m), 13; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 1\n\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n        \"presolve_bt\" => true,\n    )\n\n    m = hmittelman(solver = test_solver)\n    JuMP.optimize!(m)\n\n    @test termination_status(m) == MOI.OPTIMAL\n    @test isapprox(objective_value(m), 13; atol = 1e-4)\n    @test MOI.get(m, Alpine.NumberOfIterations()) == 0\nend\n\n@testset \"Test integer variable support via IntegerToZeroOneBridge\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n    )\n    model = JuMP.Model(test_solver)\n    @variable(model, -10 <= x <= 20, Int)\n    @objective(model, Min, x)\n    JuMP.optimize!(model)\n    @test termination_status(model) == MOI.OPTIMAL\n    @test isapprox(objective_value(model), -10; atol = 1e-4)\n    @test isapprox(value(x), -10, atol = 1e-6)\n    @test MOI.get(model, Alpine.NumberOfIterations()) == 0\nend\n\n@testset \"Test integer variable support 0\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n    )\n    model = JuMP.Model(test_solver)\n    @variable(model, x, Int)\n    @objective(model, Min, x)\n    @test_throws Exception JuMP.optimize!(model)\nend\n\n@testset \"Test integer variable support 1\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n    )\n    model = JuMP.Model(test_solver)\n    @variable(model, -10 <= x, Int)\n    @objective(model, Min, x)\n    @test_throws Exception JuMP.optimize!(model)\nend\n\n@testset \"Test integer variable support 2\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"minlp_solver\" => JUNIPER,\n    )\n    model = JuMP.Model(test_solver)\n    @variable(model, x <= 20, Int)\n    @objective(model, Min, x)\n    @test_throws Exception JuMP.optimize!(model)\nend\n"
  },
  {
    "path": "test/test_expression.jl",
    "content": "@testset \"Expression Parsing || bilinear || Affine || exprs.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = exprstest(solver = test_solver)\n\n    alpine = _build(m)\n\n    ex = alpine.bounding_constr_expr_mip[1]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[1][:coefs]\n    @test affdict[:vars] == [:(x[1])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[1][:vars]\n    @test isapprox(affdict[:rhs], 109.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[1][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[1][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[2]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [3.0, 3.0, 3.0, 3.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[2][:coefs]\n    @test affdict[:vars] == [:(x[8]), :(x[9]), :(x[10]), :(x[11])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[2][:vars]\n    @test isapprox(affdict[:rhs], 111.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[2][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[2][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[3]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-1.0, 20.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[3][:coefs]\n    @test affdict[:vars] == [:(x[12]), :(x[13])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[3][:vars]\n    @test isapprox(affdict[:rhs], 222.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[3][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[3][:sense]\n\n    # 1.0 * x[12] - 115.0 >= 0.0\n    ex = alpine.bounding_constr_expr_mip[4]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[4][:coefs]\n    @test affdict[:vars] == [:(x[12])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[4][:vars]\n    @test isapprox(affdict[:rhs], 115.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[4][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[4][:sense]\n\n    # 1.0 * x[12] - 115.0 <= 0.0\n    ex = alpine.bounding_constr_expr_mip[5]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[5][:coefs]\n    @test affdict[:vars] == [:(x[12])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[5][:vars]\n    @test isapprox(affdict[:rhs], 115.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[5][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[5][:sense]\n\n    # -1.0 * x[12] - 115.0 >= 0.0\n    ex = alpine.bounding_constr_expr_mip[6]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[6][:coefs]\n    @test affdict[:vars] == [:(x[12])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[6][:vars]\n    @test isapprox(affdict[:rhs], 115.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[6][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[6][:sense]\n\n    # (x[1] + 1.0 * x[14]) - 555.0 >= 0.0\n    ex = alpine.bounding_constr_expr_mip[7]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0, 1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[7][:coefs]\n    @test affdict[:vars] == [:(x[1]), :(x[14])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[7][:vars]\n    @test isapprox(affdict[:rhs], 555.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[7][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[7][:sense]\n\n    # ((x[8] - 7.0 * x[9]) + x[10] + x[4]) - 6666.0 <= 0.0\n    ex = alpine.bounding_constr_expr_mip[8]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0, -7.0, 1.0, 1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[8][:coefs]\n    @test affdict[:vars] == [:(x[8]), :(x[9]), :(x[10]), :(x[4])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[8][:vars]\n    @test isapprox(affdict[:rhs], 6666.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[8][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[8][:sense]\n\n    # ((13.0 * x[1] - x[2]) + 30.0 * x[3] + x[4]) - 77.0 >= 0.0\n    ex = alpine.bounding_constr_expr_mip[9]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [13.0, -1.0, 30.0, 1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[9][:coefs]\n    @test affdict[:vars] == [:(x[1]), :(x[2]), :(x[3]), :(x[4])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[9][:vars]\n    @test isapprox(affdict[:rhs], 77.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[9][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[9][:sense]\nend\n\n@testset \"Expression Parsing || bilinear || Affine || nlp1.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n    m = nlp1(solver = test_solver)\n\n    alpine = _build(m)\n\n    ex = alpine.bounding_constr_expr_mip[1]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[1][:coefs]\n    @test affdict[:vars] == [:(x[5])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[1][:vars]\n    @test isapprox(affdict[:rhs], 8.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[1][:rhs]\n    @test affdict[:sense] == :(>=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[1][:sense]\nend\n\n@testset \"Expression Parsing || bilinear || Affine || nlp3.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = nlp3(solver = test_solver)\n\n    alpine = _build(m)\n\n    ex = alpine.bounding_constr_expr_mip[1]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [0.0025, 0.0025]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[1][:coefs]\n    @test affdict[:vars] == [:(x[4]), :(x[6])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[1][:vars]\n    @test isapprox(affdict[:rhs], 1.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[1][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[1][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[2]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-0.0025, 0.0025, 0.0025]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[2][:coefs]\n    @test affdict[:vars] == [:(x[4]), :(x[5]), :(x[7])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[2][:vars]\n    @test isapprox(affdict[:rhs], 1.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[2][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[2][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[3]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [-0.01, 0.01]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[3][:coefs]\n    @test affdict[:vars] == [:(x[5]), :(x[8])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[3][:vars]\n    @test isapprox(affdict[:rhs], 1.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[3][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[3][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[4]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test (affdict[:coefs] .== [100.0, -1.0, 833.33252]) == [true, true, true]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[4][:coefs]\n    @test affdict[:vars] == [:(x[1]), :(x[9]), :(x[4])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[4][:vars]\n    @test isapprox(affdict[:rhs], 83333.333; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[4][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[4][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[5]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0, -1.0, -1250.0, 1250.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[5][:coefs]\n    @test affdict[:vars] == [:(x[10]), :(x[11]), :(x[4]), :(x[5])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[5][:vars]\n    @test isapprox(affdict[:rhs], 0.0; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[5][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[5][:sense]\n\n    ex = alpine.bounding_constr_expr_mip[6]\n    affdict = Alpine.expr_linear_to_affine(ex)\n    @test affdict[:coefs] == [1.0, -1.0, -2500.0]\n    @test affdict[:coefs] == alpine.bounding_constr_mip[6][:coefs]\n    @test affdict[:vars] == [:(x[12]), :(x[13]), :(x[5])]\n    @test affdict[:vars] == alpine.bounding_constr_mip[6][:vars]\n    @test isapprox(affdict[:rhs], -1.25e6; atol = 1e-3)\n    @test affdict[:rhs] == alpine.bounding_constr_mip[6][:rhs]\n    @test affdict[:sense] == :(<=)\n    @test affdict[:sense] == alpine.bounding_constr_mip[6][:sense]\nend\n\n@testset \"Expression Parsing || bilinear || Simple || bi1.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = operator_c(solver = test_solver)\n\n    alpine = _build(m) # Setup internal model\n\n    @test length(keys(alpine.nonconvex_terms)) == 8\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 1), Expr(:ref, :x, 1)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 2), Expr(:ref, :x, 2)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 3), Expr(:ref, :x, 3)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 4), Expr(:ref, :x, 4)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 2), Expr(:ref, :x, 3)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 3), Expr(:ref, :x, 4)])\n\n    # TODO setup detailed check on this problem\nend\n@testset \"Expression Parsing || bilinear || Complex || blend029.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => JUNIPER,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = blend029(solver = test_solver)\n\n    alpine = _build(m) # Setup internal model\n\n    @test length(keys(alpine.nonconvex_terms)) == 28\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 37), Expr(:ref, :x, 55)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 38), Expr(:ref, :x, 56)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 37), Expr(:ref, :x, 26)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 43), Expr(:ref, :x, 26)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 47), Expr(:ref, :x, 59)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 48), Expr(:ref, :x, 60)])\n    @test haskey(alpine.nonconvex_terms, [Expr(:ref, :x, 47), Expr(:ref, :x, 36)])\n\n    @test alpine.bounding_constr_mip[1][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[1][:vars] ==\n          Any[:(x[1]), :(x[4]), :(x[7]), :(x[10]), :(x[49])]\n    @test alpine.bounding_constr_mip[1][:sense] == :(==)\n    @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, 1.0, 1.0, 1.0, 1.0]\n    @test alpine.bounding_constr_mip[1][:cnt] == 5\n\n    @test alpine.bounding_constr_mip[4][:rhs] == 0.1\n    @test alpine.bounding_constr_mip[4][:vars] ==\n          Any[:(x[4]), :(x[16]), :(x[25]), :(x[34]), :(x[58])]\n    @test alpine.bounding_constr_mip[4][:sense] == :(==)\n    @test alpine.bounding_constr_mip[4][:coefs] == Any[-1.0, -1.0, -1.0, 1.0, 1.0]\n    @test alpine.bounding_constr_mip[4][:cnt] == 5\n\n    @test alpine.bounding_constr_mip[17][:rhs] == -0.14\n    @test alpine.bounding_constr_mip[17][:vars] ==\n          Any[:(x[11]), :(x[23]), :(x[32]), :(x[64]), :(x[65])]\n    @test alpine.bounding_constr_mip[17][:sense] == :(==)\n    @test alpine.bounding_constr_mip[17][:coefs] == Any[-1.0, -1.0, -1.0, -1.0, 1.0]\n    @test alpine.bounding_constr_mip[17][:cnt] == 5\n\n    @test alpine.bounding_constr_mip[31][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[31][:vars] == Any[:(x[13])]\n    @test alpine.bounding_constr_mip[31][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[31][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[31][:cnt] == 1\n\n    @test alpine.bounding_constr_mip[145][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[145][:vars] == Any[:(x[73])]\n    @test alpine.bounding_constr_mip[145][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[145][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[145][:cnt] == 1\n\n    @test alpine.bounding_constr_mip[67][:rhs] == -1.0\n    @test alpine.bounding_constr_mip[67][:vars] == Any[:(x[73])]\n    @test alpine.bounding_constr_mip[67][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[67][:coefs] == Any[-1.0]\n    @test alpine.bounding_constr_mip[67][:cnt] == 1\n\n    @test alpine.bounding_constr_mip[187][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[187][:vars] == Any[:(x[79]), :(x[94])]\n    @test alpine.bounding_constr_mip[187][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[187][:coefs] == Any[1.0, 1.0]\n    @test alpine.bounding_constr_mip[187][:cnt] == 2\n\n    @test alpine.bounding_constr_mip[202][:rhs] == 0.04\n    @test alpine.bounding_constr_mip[202][:vars] ==\n          Any[:(x[103]), :(x[1]), :(x[13]), :(x[25]), :(x[28]), :(x[31])]\n    @test alpine.bounding_constr_mip[202][:sense] == :(==)\n    @test alpine.bounding_constr_mip[202][:coefs] == Any[1.0, -0.6, -0.2, 0.2, 0.2, 0.2]\n    @test alpine.bounding_constr_mip[202][:cnt] == 6\n\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[55])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[55])]][:lifted_var_ref] == :(x[103])\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[55])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[55])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.bounding_constr_mip[206][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[206][:vars] ==\n          Any[:(x[107]), :(x[103]), :(x[108]), :(x[109]), :(x[110]), :(x[2]), :(x[14])]\n    @test alpine.bounding_constr_mip[206][:sense] == :(==)\n    @test alpine.bounding_constr_mip[206][:coefs] ==\n          Any[1.0, -1.0, 1.0, 1.0, 1.0, -0.6, -0.2]\n    @test alpine.bounding_constr_mip[206][:cnt] == 7\n\n    @test alpine.nonconvex_terms[[:(x[38]), :(x[56])]][:id] == 5\n    @test alpine.nonconvex_terms[[:(x[38]), :(x[56])]][:lifted_var_ref] == :(x[107])\n    @test alpine.nonconvex_terms[[:(x[38]), :(x[56])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[38]), :(x[56])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[26])]][:id] == 6\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[26])]][:lifted_var_ref] == :(x[108])\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[26])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[26])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[32])]][:id] == 8\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[32])]][:lifted_var_ref] == :(x[110])\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[32])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[37]), :(x[32])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.bounding_constr_mip[213][:rhs] == 0.0\n    @test alpine.bounding_constr_mip[213][:vars] ==\n          Any[:(x[129]), :(x[127]), :(x[124]), :(x[130]), :(x[6]), :(x[18])]\n    @test alpine.bounding_constr_mip[213][:sense] == :(==)\n    @test alpine.bounding_constr_mip[213][:coefs] == Any[1.0, -1.0, -1.0, 1.0, -0.4, -0.4]\n    @test alpine.bounding_constr_mip[213][:cnt] == 6\n\n    @test alpine.nonconvex_terms[[:(x[48]), :(x[60])]][:id] == 27\n    @test alpine.nonconvex_terms[[:(x[48]), :(x[60])]][:lifted_var_ref] == :(x[129])\n    @test alpine.nonconvex_terms[[:(x[48]), :(x[60])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[48]), :(x[60])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[59])]][:id] == 25\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[59])]][:lifted_var_ref] == :(x[127])\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[59])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[59])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[36])]][:id] == 28\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[36])]][:lifted_var_ref] == :(x[130])\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[36])]][:convexified] == false\n    @test alpine.nonconvex_terms[[:(x[47]), :(x[36])]][:nonlinear_type] == :BILINEAR\nend\n\n@testset \"Expression Parsing || multilinear || Simple || multi.jl \" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = multi3(solver = test_solver, exprmode = 1)\n\n    alpine = _build(m) # Setup internal model\n\n    @test length(keys(alpine.nonconvex_terms)) == 1\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:lifted_var_ref] == :(x[4])\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:nonlinear_type] ==\n          :MULTILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[4])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    @test alpine.bounding_constr_mip[1][:rhs] == 3.0\n    @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[1]), :(x[2]), :(x[3])]\n    @test alpine.bounding_constr_mip[1][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, 1.0, 1.0]\n    @test alpine.bounding_constr_mip[1][:cnt] == 3\n\n    m = multi3(solver = test_solver, exprmode = 2)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[4])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 3)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 3)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 3)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[5])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi3(solver = test_solver, exprmode = 3)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:lifted_var_ref] ==\n          :(x[4])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 4)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[5])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 1)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 1\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[5])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n\n    @test alpine.bounding_constr_mip[1][:rhs] == 4.0\n    @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[1]), :(x[2]), :(x[3]), :(x[4])]\n    @test alpine.bounding_constr_mip[1][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, 1.0, 1.0, 1.0]\n    @test alpine.bounding_constr_mip[1][:cnt] == 4\n\n    m = multi4(solver = test_solver, exprmode = 2)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 3\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 6)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 6)]][:lifted_var_ref] ==\n          :(x[7])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 6)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 3)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[3]), :(x[4])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[3]), :(x[4])]][:lifted_var_ref] == :(x[6])\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[3]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 4)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[5])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[5])]][:lifted_var_ref] == :(x[6])\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[5])]][:nonlinear_type] ==\n          :MULTILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 5)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 3\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 5)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 5)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 5)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[7])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 6)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:lifted_var_ref] == :(x[5])\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 4)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 5), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 7)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 3\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 3), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 5)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 5)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 5)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:lifted_var_ref] ==\n          :(x[7])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 8)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[5]), :(x[4])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[5]), :(x[4])]][:lifted_var_ref] == :(x[6])\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[5]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 9)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 2\n\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3]), :(x[4])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3]), :(x[4])]][:lifted_var_ref] == :(x[5])\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[6])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 10)\n\n    alpine = _build(m)\n    @test length(keys(alpine.nonconvex_terms)) == 3\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 5)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 5)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 4), Expr(:ref, :x, 5)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:lifted_var_ref] ==\n          :(x[7])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 6)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\n\n    m = multi4(solver = test_solver, exprmode = 11)\n\n    alpine = _build(m)\n\n    @test length(keys(alpine.nonconvex_terms)) == 3\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 3)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:lifted_var_ref] ==\n          :(x[6])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 5)]][:nonlinear_type] ==\n          :BILINEAR\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:lifted_var_ref] ==\n          :(x[7])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 6), Expr(:ref, :x, 4)]][:nonlinear_type] ==\n          :BILINEAR\n\n    @test alpine.bounding_obj_mip[:rhs] == 0\n    @test alpine.bounding_obj_mip[:vars] == Expr[:(x[7])]\n    @test alpine.bounding_obj_mip[:coefs] == [1.0]\n    @test alpine.bounding_obj_mip[:cnt] == 1\n    @test alpine.bounding_obj_mip[:sense] === nothing\nend\n\n@testset \"Expression Parsing || bilinear || Complex-div || div.jl\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = div(solver = test_solver)\n\n    alpine = _build(m) # Setup internal model\n\n    @test length(keys(alpine.nonconvex_terms)) == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 1)]][:id] == 1\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 1)]][:lifted_var_ref] ==\n          :(x[3])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 1)]][:nonlinear_type] ==\n          :MONOMIAL\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 2)]][:id] == 2\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[4])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 2), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :MONOMIAL\n\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:id] == 3\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:lifted_var_ref] ==\n          :(x[5])\n    @test alpine.nonconvex_terms[[Expr(:ref, :x, 1), Expr(:ref, :x, 2)]][:nonlinear_type] ==\n          :BILINEAR\n\n    aff_mip = alpine.bounding_constr_mip\n\n    @test aff_mip[1][:rhs] == 0.0\n    @test aff_mip[1][:vars] == Any[:(x[1])]\n    @test aff_mip[1][:sense] == :(>=)\n    @test round(aff_mip[1][:coefs][1]; digits = 1) == -3.0\n    @test aff_mip[1][:cnt] == 1\n\n    @test aff_mip[2][:rhs] == 0.0\n    @test aff_mip[2][:vars] == Any[:(x[2])]\n    @test aff_mip[2][:sense] == :(>=)\n    @test aff_mip[2][:coefs] == Any[0.25]\n    @test aff_mip[2][:cnt] == 1\n\n    @test aff_mip[3][:rhs] == 0.0\n    @test aff_mip[3][:vars] == Any[:(x[2])]\n    @test aff_mip[3][:sense] == :(>=)\n    @test aff_mip[3][:coefs] == Any[5.0]\n    @test aff_mip[3][:cnt] == 1\n\n    @test aff_mip[4][:rhs] == 0.0\n    @test aff_mip[4][:vars] == Any[:(x[2])]\n    @test aff_mip[4][:sense] == :(>=)\n    @test aff_mip[4][:coefs] == Any[-120.0]\n    @test aff_mip[4][:cnt] == 1\n\n    @test aff_mip[5][:rhs] == 0.0\n    @test aff_mip[5][:vars] == Any[:(x[2])]\n    @test aff_mip[5][:sense] == :(>=)\n    @test aff_mip[5][:coefs] == Any[72000.0]\n    @test aff_mip[5][:cnt] == 1\n\n    @test aff_mip[6][:rhs] == 0.0\n    @test aff_mip[6][:vars] == Any[:(x[1])]\n    @test aff_mip[6][:sense] == :(>=)\n    @test aff_mip[6][:coefs] == Any[72000.0]\n    @test aff_mip[6][:cnt] == 1\n\n    @test aff_mip[7][:rhs] == 8.0\n    @test aff_mip[7][:vars] == Any[:(x[5])]\n    @test aff_mip[7][:sense] == :(>=)\n    @test aff_mip[7][:coefs] == Any[0.6]\n    @test aff_mip[7][:cnt] == 1\n\n    @test aff_mip[8][:rhs] == 0.0\n    @test aff_mip[8][:vars] == Any[:(x[2]), :(x[5])]\n    @test aff_mip[8][:sense] == :(>=)\n    @test aff_mip[8][:coefs] == Any[5.6, -72000.0]\n    @test aff_mip[8][:cnt] == 2\n\n    @test aff_mip[9][:rhs] == 0.0\n    @test aff_mip[9][:vars] == Any[:(x[2]), :(x[5])]\n    @test aff_mip[9][:sense] == :(>=)\n    @test aff_mip[9][:coefs] == Any[5.6, -36000.0]\n    @test aff_mip[9][:cnt] == 2\n\n    @test aff_mip[10][:rhs] == 0.0\n    @test aff_mip[10][:vars] == Any[:(x[2]), :(x[5]), :(x[2])]\n    @test aff_mip[10][:sense] == :(>=)\n    @test aff_mip[10][:coefs] == Any[5.6, -300.0, -1.75]\n    @test aff_mip[10][:cnt] == 3\n\n    @test aff_mip[11][:rhs] == 0.0\n    @test aff_mip[11][:vars] == Any[:(x[2]), :(x[1]), :(x[5])]\n    @test aff_mip[11][:sense] == :(>=)\n    @test aff_mip[11][:coefs] == Any[5.6, -0.5, 0.5]\n    @test aff_mip[11][:cnt] == 3\nend\n\n@testset \"Expression Parsing || part1 \" begin\n    m = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        ),\n    )\n    @variable(m, x[1:4] >= 0)\n    @NLconstraint(m, x[1]^2 >= 1)    # Basic monomial x[5]=x[1]^2\n    @NLconstraint(m, x[1] * x[2] <= 1)  # x[6] <= 1 : x[6] = x[1]*x[2]\n    @NLconstraint(m, x[1]^2 * x[2]^2 <= 1)          # x[5] + x[7] <= 1 : x[7] = x[2]^2\n    @NLconstraint(m, x[1] * (x[2] * x[3]) >= 1)         # x[9] >= 1 : x[8] = x[2] * x[3] && x[9] = x[1]*x[8]\n    @NLconstraint(m, x[1]^2 * (x[2]^2 * x[3]^2) <= 1) # x[12] <= 1 : x[10] = x[3] ^ 2 && x[11] = x[7] * x[10] && x[12] = x[11]*[5]\n\n    alpine = _build(m)\n\n    @test alpine.bounding_constr_expr_mip[1] == :(x[5] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[2] == :(x[6] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[3] == :(x[8] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[4] == :(x[10] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[5] == :(x[13] - 1.0 <= 0.0)\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])])\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2])])\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])])\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[3])])\n    @test haskey(alpine.nonconvex_terms, [:(x[5]), :(x[7])])\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[9])])\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[3])])\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2])])\n    @test haskey(alpine.nonconvex_terms, [:(x[5]), :(x[12])])\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:id] == 3\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[7])]][:id] == 4\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3])]][:id] == 5\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[9])]][:id] == 6\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[3])]][:id] == 7\n    @test alpine.nonconvex_terms[[:(x[7]), :(x[11])]][:id] == 8\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[12])]][:id] == 9\nend\n\n@testset \"Expression Parsing || part2\" begin\n    m = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        ),\n    )\n\n    @variable(m, x[1:4] >= 0)\n    @NLconstraint(m, (x[1] * x[2]) * x[3] >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]^2) * x[3]^2 <= 1)\n\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3]^2) >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]) * x[3]^2 <= 1)\n    @NLconstraint(m, x[1]^2 * (x[2] * x[3]) >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2) * x[3] <= 1)\n\n    alpine = _build(m)\n\n    @test alpine.bounding_constr_expr_mip[1] == :(x[6] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[2] == :(x[11] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[3] == :(x[13] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[4] == :(x[15] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[5] == :(x[17] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[6] == :(x[19] - 1.0 <= 0.0)\n\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2])]) #5\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[5])]) #6\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])]) #7\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])]) #8\n    @test haskey(alpine.nonconvex_terms, [:(x[7]), :(x[8])]) #9\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[3])]) #10\n    @test haskey(alpine.nonconvex_terms, [:(x[9]), :(x[10])]) #11\n    @test haskey(alpine.nonconvex_terms, [:(x[8]), :(x[10])]) #12\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[12])]) #13\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[7])])  #14\n    @test haskey(alpine.nonconvex_terms, [:(x[14]), :(x[10])]) #15\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[3])]) #16\n    @test haskey(alpine.nonconvex_terms, [:(x[7]), :(x[16])]) #17\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[8])]) #18\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[18])]) #19\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[5])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:id] == 3\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:id] == 4\n    @test alpine.nonconvex_terms[[:(x[7]), :(x[8])]][:id] == 5\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[3])]][:id] == 6\n    @test alpine.nonconvex_terms[[:(x[9]), :(x[10])]][:id] == 7\n    @test alpine.nonconvex_terms[[:(x[8]), :(x[10])]][:id] == 8\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[12])]][:id] == 9\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[7])]][:id] == 10\n    @test alpine.nonconvex_terms[[:(x[14]), :(x[10])]][:id] == 11\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3])]][:id] == 12\n    @test alpine.nonconvex_terms[[:(x[7]), :(x[16])]][:id] == 13\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[8])]][:id] == 14\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[18])]][:id] == 15\nend\n\n@testset \"Expression Parsing || part3\" begin\n    m = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        ),\n    )\n\n    @variable(m, x[1:4] >= 0)\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]) * x[4] >= 1)\n    @NLconstraint(m, ((x[1]^2 * x[2]) * x[3]) * x[4] <= 1)\n    @NLconstraint(m, ((x[1] * x[2]^2) * x[3]) * x[4] >= 1)\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]^2) * x[4] <= 1)\n    @NLconstraint(m, ((x[1] * x[2]) * x[3]) * x[4]^2 >= 1)\n    @NLconstraint(m, ((x[1]^2 * x[2]^2) * x[3]^2) * x[4]^2 <= 1)\n\n    alpine = _build(m)\n\n    @test alpine.bounding_constr_expr_mip[1] == :(x[7] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[2] == :(x[11] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[3] == :(x[15] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[4] == :(x[18] - 1.0 <= 0.0)\n    @test alpine.bounding_constr_expr_mip[5] == :(x[20] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[6] == :(x[23] - 1.0 <= 0.0)\n\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2])]) #5\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[5])]) #6\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[6])]) #7\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])]) #8\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[8])]) #9\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[9])]) #10\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[10])]) #11\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])]) #12\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[12])])  #13\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[13])]) #14\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[14])]) #15\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[3])]) #16\n    @test haskey(alpine.nonconvex_terms, [:(x[5]), :(x[16])]) #17\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[17])]) #18\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[4])]) #19\n    @test haskey(alpine.nonconvex_terms, [:(x[6]), :(x[19])]) #20\n    @test haskey(alpine.nonconvex_terms, [:(x[8]), :(x[12])]) #21\n    @test haskey(alpine.nonconvex_terms, [:(x[21]), :(x[16])]) #22\n    @test haskey(alpine.nonconvex_terms, [:(x[22]), :(x[19])]) #23\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2])]][:id] == 1\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[5])]][:id] == 2\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[6])]][:id] == 3\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:id] == 4\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[8])]][:id] == 5\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[9])]][:id] == 6\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[10])]][:id] == 7\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:id] == 8\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[12])]][:id] == 9\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[13])]][:id] == 10\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[14])]][:id] == 11\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[3])]][:id] == 12\n    @test alpine.nonconvex_terms[[:(x[5]), :(x[16])]][:id] == 13\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[17])]][:id] == 14\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[4])]][:id] == 15\n    @test alpine.nonconvex_terms[[:(x[6]), :(x[19])]][:id] == 16\n    @test alpine.nonconvex_terms[[:(x[8]), :(x[12])]][:id] == 17\n    @test alpine.nonconvex_terms[[:(x[21]), :(x[16])]][:id] == 18\n    @test alpine.nonconvex_terms[[:(x[22]), :(x[19])]][:id] == 19\nend\n\n@testset \"Expression Parsing || part7\" begin\n    m = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        ),\n    )\n    @variable(m, x[1:4] >= 0)\n\n    @NLconstraint(m, x[1] * x[2] * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3] * x[4] >= 1)\n    @NLconstraint(m, x[1] * x[2] * x[3]^2 * x[4]^2 >= 1)\n    @NLconstraint(m, x[1] * x[2]^2 * x[3]^2 * x[4] >= 1)\n    @NLconstraint(m, x[1]^2 * x[2] * x[3] * x[4]^2 >= 1)\n    @NLconstraint(m, x[1]^2 * x[2]^2 * x[3]^2 * x[4]^2 >= 1)\n\n    alpine = _build(m)\n\n    @test alpine.bounding_constr_expr_mip[1] == :(x[5] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[2] == :(x[7] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[3] == :(x[9] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[4] == :(x[12] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[5] == :(x[13] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[6] == :(x[14] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[7] == :(x[15] - 1.0 >= 0.0)\n\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2]), :(x[3]), :(x[4])]) #5\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])]) #6\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[3]), :(x[4]), :(x[6])]) #7\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])]) #8\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[3]), :(x[4]), :(x[8])]) #9\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[3])]) #10\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[4])]) #11\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2]), :(x[10]), :(x[11])]) #12\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[4]), :(x[8]), :(x[10])]) #13\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[3]), :(x[6]), :(x[11])]) #14\n    @test haskey(alpine.nonconvex_terms, [:(x[6]), :(x[8]), :(x[10]), :(x[11])]) #15\n\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:id] == 1 #5\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:id] == 2 #6\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3]), :(x[4]), :(x[6])]][:id] == 3 #7\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:id] == 4 #8\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[3]), :(x[4]), :(x[8])]][:id] == 5 #9\n    @test alpine.nonconvex_terms[[:(x[3]), :(x[3])]][:id] == 6 #10\n    @test alpine.nonconvex_terms[[:(x[4]), :(x[4])]][:id] == 7 #11\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[2]), :(x[10]), :(x[11])]][:id] == 8  #12\n    @test alpine.nonconvex_terms[[:(x[1]), :(x[4]), :(x[8]), :(x[10])]][:id] == 9 #13\n    @test alpine.nonconvex_terms[[:(x[2]), :(x[3]), :(x[6]), :(x[11])]][:id] == 10 #14\n    @test alpine.nonconvex_terms[[:(x[6]), :(x[8]), :(x[10]), :(x[11])]][:id] == 11 #15\nend\n\n@testset \"Expression Parsing || part8\" begin\n    m = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        ),\n    )\n    @variable(m, x[1:4] >= 0)\n\n    @NLconstraint(m, (x[1] * x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2] * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2]^2 * x[3]) * x[4] >= 1)\n    @NLconstraint(m, x[1] * (x[2] * x[3]^2) * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]^2) * x[3] * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3]^2 * x[4] >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3] * x[4]^2 >= 1)\n    @NLconstraint(m, (x[1] * x[2]) * x[3]^2 * x[4]^2 >= 1)\n    @NLconstraint(m, (x[1]^2 * x[2]^2 * x[3]^2) * x[4]^2 >= 1)\n\n    alpine = _build(m)\n\n    @test alpine.bounding_constr_expr_mip[1] == :(x[6] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[2] == :(x[9] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[3] == :(x[12] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[4] == :(x[15] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[5] == :(x[17] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[6] == :(x[19] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[7] == :(x[21] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[8] == :(x[22] - 1.0 >= 0.0)\n    @test alpine.bounding_constr_expr_mip[9] == :(x[24] - 1.0 >= 0.0)\n\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2]), :(x[3])]) #5\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[5])]) #6\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])]) #7\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[3]), :(x[7])]) #8\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[8])]) #9\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])]) #10\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[10])]) #11\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[4]), :(x[11])]) #12\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[3])]) #13\n    @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[13])]) #14\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[4]), :(x[14])]) #15\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[10])]) #16\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[4]), :(x[16])]) #17\n    @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[2])]) #18\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[18]), :(x[13])]) #19\n    @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[4])]) #20\n    @test haskey(alpine.nonconvex_terms, [:(x[3]), :(x[18]), :(x[20])]) #21\n    @test haskey(alpine.nonconvex_terms, [:(x[18]), :(x[13]), :(x[20])]) #22\n    @test haskey(alpine.nonconvex_terms, [:(x[7]), :(x[10]), :(x[13])]) #23\n    @test haskey(alpine.nonconvex_terms, [:(x[23]), :(x[20])]) #24\nend\n\n@testset \"Expression Parsing || Convex\" begin\n    @testset \"Convex Parsing :: PART I\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n        m = convex_test(solver = test_solver)\n\n        alpine = _build(m)\n\n        @test alpine.num_constr_convex == 19\n\n        # 0 : OBJ\n        @test alpine.obj_structure == :convex\n        @test alpine.nonlinear_constrs[0][:expr_orig] == :objective\n        @test alpine.nonlinear_constrs[0][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[0][:convexified] == false\n\n        @test alpine.bounding_obj_mip[:sense] === nothing\n        @test alpine.bounding_obj_mip[:coefs] == [1.0, 1.0]\n        @test alpine.bounding_obj_mip[:vars] == [:(x[1]), :(x[3])]\n        @test alpine.bounding_obj_mip[:rhs] == 0.0\n        @test alpine.bounding_obj_mip[:powers] == [2, 2]\n        @test alpine.bounding_obj_mip[:cnt] == 2\n\n        # 1\n        @test alpine.constr_structure[1] == :convex\n        @test alpine.nonlinear_constrs[1][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[1][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[1][:convexified] == false\n        @test alpine.bounding_constr_mip[1][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[1][:coefs] == [3.0, 4.0]\n        @test alpine.bounding_constr_mip[1][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[1][:rhs] == 25.0\n        @test alpine.bounding_constr_mip[1][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[1][:cnt] == 2\n\n        # 2\n        @test alpine.constr_structure[2] == :convex\n        @test alpine.nonlinear_constrs[2][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[2][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[2][:convexified] == false\n        @test alpine.bounding_constr_mip[2][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[2][:coefs] == [3.0, 4.0]\n        @test alpine.bounding_constr_mip[2][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[2][:rhs] == 25.0\n        @test alpine.bounding_constr_mip[2][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[2][:cnt] == 2\n\n        # 4\n        @test alpine.constr_structure[4] == :convex\n        @test alpine.nonlinear_constrs[4][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[4][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[4][:convexified] == false\n        @test alpine.bounding_constr_mip[4][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[4][:coefs] == [3.0, 4.0]\n        @test alpine.bounding_constr_mip[4][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[4][:rhs] == 10.0\n        @test alpine.bounding_constr_mip[4][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[4][:cnt] == 2\n\n        # 5\n        @test alpine.constr_structure[5] == :convex\n        @test alpine.nonlinear_constrs[5][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[5][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[5][:convexified] == :false\n        @test alpine.bounding_constr_mip[5][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[5][:coefs] == [3.0, 4.0, 6.0]\n        @test alpine.bounding_constr_mip[5][:vars] == [:(x[1]), :(x[2]), :(x[3])]\n        @test alpine.bounding_constr_mip[5][:rhs] == 10.0\n        @test alpine.bounding_constr_mip[5][:powers] == [2, 2, 2]\n        @test alpine.bounding_constr_mip[5][:cnt] == 3\n\n        #6,7 excluded \n\n        # 8\n        @test alpine.constr_structure[8] == :convex\n        @test alpine.nonlinear_constrs[8][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[8][:convex_type] == :convexB\n        @test alpine.nonlinear_constrs[8][:convexified] == :false\n        @test alpine.bounding_constr_mip[8][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[8][:coefs] == [3.0, 1.0, 5.0]\n        @test alpine.bounding_constr_mip[8][:vars] == [:(x[1]), :(x[2]), :(x[3])]\n        @test alpine.bounding_constr_mip[8][:rhs] == 200.0\n        @test alpine.bounding_constr_mip[8][:powers] == [3.0, 3.0, 3.0]\n        @test alpine.bounding_constr_mip[8][:cnt] == 3\n\n        # 9\n        @test alpine.constr_structure[9] == :convex\n        @test alpine.nonlinear_constrs[9][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[9][:convex_type] == :convexB\n        @test alpine.nonlinear_constrs[9][:convexified] == :false\n        @test alpine.bounding_constr_mip[9][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[9][:coefs] == [1.0, 1.0, 1.0, 100.0]\n        @test alpine.bounding_constr_mip[9][:vars] == [:(x[1]), :(x[2]), :(x[3]), :(x[4])]\n        @test alpine.bounding_constr_mip[9][:rhs] == 200.0\n        @test alpine.bounding_constr_mip[9][:powers] == [3, 3, 3, 3]\n        @test alpine.bounding_constr_mip[9][:cnt] == 4\n\n        # 11\n        @test alpine.constr_structure[11] == :convex\n        @test alpine.nonlinear_constrs[11][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[11][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[11][:convexified] == :false\n        @test alpine.bounding_constr_mip[11][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[11][:coefs] == [3.0, 4.0]\n        @test alpine.bounding_constr_mip[11][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[11][:rhs] == 25.0\n        @test alpine.bounding_constr_mip[11][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[11][:cnt] == 2\n\n        # 14\n        @test alpine.constr_structure[14] == :convex\n        @test alpine.nonlinear_constrs[14][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[14][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[14][:convexified] == :false\n        @test alpine.bounding_constr_mip[14][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[14][:coefs] == [3.0, 5.0]\n        @test alpine.bounding_constr_mip[14][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[14][:rhs] == 25.0\n        @test alpine.bounding_constr_mip[14][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[14][:cnt] == 2\n\n        # 15\n        @test alpine.constr_structure[15] == :convex\n        @test alpine.nonlinear_constrs[15][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[15][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[15][:convexified] == :false\n        @test alpine.bounding_constr_mip[15][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[15][:coefs] == [3.0, 5.0, 1.0]\n        @test alpine.bounding_constr_mip[15][:vars] == [:(x[1]), :(x[2]), :(x[4])]\n        @test alpine.bounding_constr_mip[15][:rhs] == 25.0\n        @test alpine.bounding_constr_mip[15][:powers] == [2, 2, 2]\n        @test alpine.bounding_constr_mip[15][:cnt] == 3\n\n        # 19\n        @test alpine.constr_structure[19] == :convex\n        @test alpine.nonlinear_constrs[19][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[19][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[19][:convexified] == :false\n        @test alpine.bounding_constr_mip[19][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[19][:coefs] == [3.0, 16.0]\n        @test alpine.bounding_constr_mip[19][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[19][:rhs] == 40.0\n        @test alpine.bounding_constr_mip[19][:powers] == [2, 2]\n        @test alpine.bounding_constr_mip[19][:cnt] == 2\n\n        # 22\n        @test alpine.constr_structure[22] == :convex\n        @test alpine.nonlinear_constrs[22][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[22][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[22][:convexified] == :false\n        @test alpine.bounding_constr_mip[22][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[22][:coefs] == [3.0, 4.0, 5.0, 6.0]\n        @test alpine.bounding_constr_mip[22][:vars] ==\n              [:(x[1]), :(x[2]), :(x[3]), :(x[4])]\n        @test alpine.bounding_constr_mip[22][:rhs] == 15.0\n        @test alpine.bounding_constr_mip[22][:powers] == [2, 2, 2, 2]\n        @test alpine.bounding_constr_mip[22][:cnt] == 4\n\n        # 25\n        @test alpine.constr_structure[25] == :convex\n        @test alpine.nonlinear_constrs[25][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[25][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[25][:convexified] == :false\n        @test alpine.bounding_constr_mip[25][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[25][:coefs] == [1.0, 1.0, 1.0, 1.0, 1.0]\n        @test alpine.bounding_constr_mip[25][:vars] ==\n              [:(x[1]), :(x[2]), :(x[3]), :(x[4]), :(x[5])]\n        @test alpine.bounding_constr_mip[25][:rhs] == 99999.0\n        @test alpine.bounding_constr_mip[25][:powers] == [2, 2, 2, 2, 2]\n        @test alpine.bounding_constr_mip[25][:cnt] == 5\n\n        # 26\n        @test alpine.constr_structure[26] == :convex\n        @test alpine.nonlinear_constrs[26][:expr_orig] == :constraints\n        @test alpine.nonlinear_constrs[26][:convex_type] == :convexA\n        @test alpine.nonlinear_constrs[26][:convexified] == :false\n        @test alpine.bounding_constr_mip[26][:sense] == :(<=)\n        @test alpine.bounding_constr_mip[26][:coefs] == [3.0, 4.0]\n        @test alpine.bounding_constr_mip[26][:vars] == [:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[26][:rhs] == 200.0\n        @test alpine.bounding_constr_mip[26][:powers] == [4, 4]\n        @test alpine.bounding_constr_mip[26][:cnt] == 2\n    end\nend\n\n@testset \"Expression Prasing || Linear Lifting\" begin\n    @testset \"Expression Parsing || Linear Lifting || nlp2\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"partition_scaling_factor\" => 8,\n            \"log_level\" => 100,\n        )\n\n        m = nlp2(solver = test_solver)\n\n        alpine = _build(m)\n\n        @test length(alpine.linear_terms) == 2\n        @test length(alpine.nonconvex_terms) == 4\n\n        lk = Vector{Any}(undef, 2)\n        lk[1] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, -1.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3)])),\n        )\n        lk[2] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, -2.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 6)])),\n        )\n\n        @test length(keys(alpine.linear_terms)) == 2\n        yids = [4, 7]\n        for i in 1:length(keys(alpine.linear_terms))\n            for j in keys(alpine.linear_terms)\n                if alpine.linear_terms[j][:id] == i\n                    @test j == lk[i]\n                    @test j[:sign] == :+\n                    @test j[:scalar] == lk[i][:scalar]\n                    @test j[:coef_var] == lk[i][:coef_var]\n                    @test alpine.linear_terms[j][:y_idx] == yids[i]\n                end\n            end\n        end\n\n        @test haskey(alpine.linear_terms, lk[1])\n        @test haskey(alpine.linear_terms, lk[2])\n\n        @test haskey(alpine.nonconvex_terms, [:(x[2]), :(x[2])])\n        @test haskey(alpine.nonconvex_terms, [:(x[4]), :(x[4])])\n        @test haskey(alpine.nonconvex_terms, [:(x[7]), :(x[7])])\n        @test haskey(alpine.nonconvex_terms, [:(x[1]), :(x[1])])\n        @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:id] == 1\n        @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:id] == 3\n        @test alpine.nonconvex_terms[[:(x[4]), :(x[4])]][:id] == 2\n        @test alpine.nonconvex_terms[[:(x[7]), :(x[7])]][:id] == 4\n        @test alpine.nonconvex_terms[[:(x[1]), :(x[1])]][:lifted_var_ref].args[2] == 3\n        @test alpine.nonconvex_terms[[:(x[2]), :(x[2])]][:lifted_var_ref].args[2] == 6\n        @test alpine.nonconvex_terms[[:(x[4]), :(x[4])]][:lifted_var_ref].args[2] == 5\n        @test alpine.nonconvex_terms[[:(x[7]), :(x[7])]][:lifted_var_ref].args[2] == 8\n    end\n\n    @testset \"Expression Parsing || Linear Lifting || general\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n\n        m = basic_linear_lift(solver = test_solver)\n\n        alpine = _build(m) # Setup internal model\n\n        lk = Vector{Any}(undef, 5)\n        lk[1] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1), (-1.0, 2)])),\n        )\n        lk[2] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(3.0, 2), (-1.0, 3)])),\n        )\n        lk[3] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1), (1.0, 3)])),\n        )\n        lk[4] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 2), (1.0, 1)])),\n        )\n        lk[5] = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 3.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 2), (1.0, 1), (1.0, 3)])),\n        )\n\n        @test length(keys(alpine.linear_terms)) == 5\n        yids = [8, 9, 12, 14, 16]\n        for i in 1:length(keys(alpine.linear_terms))\n            for j in keys(alpine.linear_terms)\n                if alpine.linear_terms[j][:id] == i\n                    @test j == lk[i]\n                    @test j[:sign] == :+\n                    @test j[:scalar] == lk[i][:scalar]\n                    @test j[:coef_var] == lk[i][:coef_var]\n                    @test alpine.linear_terms[j][:y_idx] == yids[i]\n                end\n            end\n        end\n\n        nlk1 = [:(x[8]), :(x[9]), :(x[12])]\n        nlk2 = [:(x[2]), :(x[2])]\n        nlk3 = [:(x[2]), :(x[3])]\n        nlk4 = [:(x[8]), :(x[8])]\n        nlk5 = [:(x[1]), :(x[3])]\n        nlk6 = [:(x[8]), :(x[9])]\n        nlk7 = [:(x[1]), :(x[2])]\n        nlk8 = [:(x[16]), :(x[15])]\n        nlk9 = [:(x[14]), :(x[14])]\n\n        @test alpine.nonconvex_terms[nlk1][:id] == 7\n        @test alpine.nonconvex_terms[nlk2][:id] == 3\n        @test alpine.nonconvex_terms[nlk3][:id] == 4\n        @test alpine.nonconvex_terms[nlk4][:id] == 6\n        @test alpine.nonconvex_terms[nlk5][:id] == 2\n        @test alpine.nonconvex_terms[nlk6][:id] == 5\n        @test alpine.nonconvex_terms[nlk7][:id] == 1\n        @test alpine.nonconvex_terms[nlk8][:id] == 9\n        @test alpine.nonconvex_terms[nlk9][:id] == 8\n\n        @test alpine.nonconvex_terms[nlk1][:lifted_var_ref].args[2] == 13\n        @test alpine.nonconvex_terms[nlk2][:lifted_var_ref].args[2] == 6\n        @test alpine.nonconvex_terms[nlk3][:lifted_var_ref].args[2] == 7\n        @test alpine.nonconvex_terms[nlk4][:lifted_var_ref].args[2] == 11\n        @test alpine.nonconvex_terms[nlk5][:lifted_var_ref].args[2] == 5\n        @test alpine.nonconvex_terms[nlk6][:lifted_var_ref].args[2] == 10\n        @test alpine.nonconvex_terms[nlk7][:lifted_var_ref].args[2] == 4\n        @test alpine.nonconvex_terms[nlk8][:lifted_var_ref].args[2] == 17\n        @test alpine.nonconvex_terms[nlk9][:lifted_var_ref].args[2] == 15\n\n        @test alpine.nonconvex_terms[nlk1][:nonlinear_type] == :MULTILINEAR\n        @test alpine.nonconvex_terms[nlk2][:nonlinear_type] == :MONOMIAL\n        @test alpine.nonconvex_terms[nlk3][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk4][:nonlinear_type] == :MONOMIAL\n        @test alpine.nonconvex_terms[nlk5][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk6][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk7][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk8][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk9][:nonlinear_type] == :MONOMIAL\n\n        @test alpine.nonconvex_terms[nlk1][:var_idxs] == [8, 9, 12]\n        @test alpine.nonconvex_terms[nlk2][:var_idxs] == [2, 2]\n        @test alpine.nonconvex_terms[nlk3][:var_idxs] == [2, 3]\n        @test alpine.nonconvex_terms[nlk4][:var_idxs] == [8]\n        @test alpine.nonconvex_terms[nlk5][:var_idxs] == [1, 3]\n        @test alpine.nonconvex_terms[nlk6][:var_idxs] == [8, 9]\n        @test alpine.nonconvex_terms[nlk7][:var_idxs] == [1, 2]\n        @test alpine.nonconvex_terms[nlk8][:var_idxs] == [16, 15]\n        @test alpine.nonconvex_terms[nlk9][:var_idxs] == [14]\n    end\n\n    @testset \"Expression Parsing || Linear Lifting || brainpc3\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"partition_scaling_factor\" => 8,\n            \"log_level\" => 100,\n        )\n\n        m = brainpc3(solver = test_solver)\n\n        alpine = _build(m)\n\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:y_idx] == 6913\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:id] == 2\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:lifted_constr_ref] ==\n              :(x[6913] == (*)(x[6912]))\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6912]), :(x[6912])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:y_idx] == 6970\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:id] == 25\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:lifted_constr_ref] ==\n              :(x[6970] == x[6903] * x[6969])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6969])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:y_idx] == 6915\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:id] == 3\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:lifted_constr_ref] ==\n              :(x[6915] == x[6903] * x[6914])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6914])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:y_idx] == 6920\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:id] == 5\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:lifted_constr_ref] ==\n              :(x[6920] == x[6903] * x[6919])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6919])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:y_idx] == 6928\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:id] == 8\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:lifted_constr_ref] ==\n              :(x[6928] == (*)(x[6927]))\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6927]), :(x[6927])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:y_idx] == 6953\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:id] == 18\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:lifted_constr_ref] ==\n              :(x[6953] == (*)(x[6952]))\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6952]), :(x[6952])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:y_idx] == 6963\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:id] == 22\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:lifted_constr_ref] ==\n              :(x[6963] == (*)(x[6962]))\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6962]), :(x[6962])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:y_idx] == 6975\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:id] == 27\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:lifted_constr_ref] ==\n              :(x[6975] == x[6903] * x[6974])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6974])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:y_idx] == 6935\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:id] == 11\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:lifted_constr_ref] ==\n              :(x[6935] == x[6903] * x[6934])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6934])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:y_idx] == 6960\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:id] == 21\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:lifted_constr_ref] ==\n              :(x[6960] == x[6903] * x[6959])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6959])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:y_idx] == 7015\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:id] == 43\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:lifted_constr_ref] ==\n              :(x[7015] == x[6903] * x[7014])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7014])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:y_idx] == 6940\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:id] == 13\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:lifted_constr_ref] ==\n              :(x[6940] == x[6903] * x[6939])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6939])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:y_idx] == 7018\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:id] == 44\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:lifted_constr_ref] ==\n              :(x[7018] == (*)(x[7017]))\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7017]), :(x[7017])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:y_idx] == 6930\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:id] == 9\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:lifted_constr_ref] ==\n              :(x[6930] == x[6903] * x[6929])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6929])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:y_idx] == 7013\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:id] == 42\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:lifted_constr_ref] ==\n              :(x[7013] == (*)(x[7012]))\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7012]), :(x[7012])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:y_idx] == 6948\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:id] == 16\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:lifted_constr_ref] ==\n              :(x[6948] == (*)(x[6947]))\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6947]), :(x[6947])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:y_idx] == 7033\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:id] == 50\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:lifted_constr_ref] ==\n              :(x[7033] == (*)(x[7032]))\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7032]), :(x[7032])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:y_idx] == 6998\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:id] == 36\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:lifted_constr_ref] ==\n              :(x[6998] == (*)(x[6997]))\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6997]), :(x[6997])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:y_idx] == 7028\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:id] == 48\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:lifted_constr_ref] ==\n              :(x[7028] == (*)(x[7027]))\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7027]), :(x[7027])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:y_idx] == 7038\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:id] == 52\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:lifted_constr_ref] ==\n              :(x[7038] == (*)(x[7037]))\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7037]), :(x[7037])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:y_idx] == 7008\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:id] == 40\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:lifted_constr_ref] ==\n              :(x[7008] == (*)(x[7007]))\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7007]), :(x[7007])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:y_idx] == 6965\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:id] == 23\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:lifted_constr_ref] ==\n              :(x[6965] == x[6903] * x[6964])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6964])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:y_idx] == 6925\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:id] == 7\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:lifted_constr_ref] ==\n              :(x[6925] == x[6903] * x[6924])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6924])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:y_idx] == 6980\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:id] == 29\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:lifted_constr_ref] ==\n              :(x[6980] == x[6903] * x[6979])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6979])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:y_idx] == 6995\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:id] == 35\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:lifted_constr_ref] ==\n              :(x[6995] == x[6903] * x[6994])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6994])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:y_idx] == 6973\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:id] == 26\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:lifted_constr_ref] ==\n              :(x[6973] == (*)(x[6972]))\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6972]), :(x[6972])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:y_idx] == 7020\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:id] == 45\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:lifted_constr_ref] ==\n              :(x[7020] == x[6903] * x[7019])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7019])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:y_idx] == 6993\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:id] == 34\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:lifted_constr_ref] ==\n              :(x[6993] == (*)(x[6992]))\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6992]), :(x[6992])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:y_idx] == 7003\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:id] == 38\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:lifted_constr_ref] ==\n              :(x[7003] == (*)(x[7002]))\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7002]), :(x[7002])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:y_idx] == 7023\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:id] == 46\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:lifted_constr_ref] ==\n              :(x[7023] == (*)(x[7022]))\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[7022]), :(x[7022])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:y_idx] == 6909\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:id] == 1\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:lifted_constr_ref] ==\n              :(x[6909] == x[6903] * x[6908])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6908])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:y_idx] == 6950\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:id] == 17\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:lifted_constr_ref] ==\n              :(x[6950] == x[6903] * x[6949])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6949])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:y_idx] == 7005\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:id] == 39\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:lifted_constr_ref] ==\n              :(x[7005] == x[6903] * x[7004])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7004])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:y_idx] == 6918\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:id] == 4\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:lifted_constr_ref] ==\n              :(x[6918] == (*)(x[6917]))\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6917]), :(x[6917])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:y_idx] == 6938\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:id] == 12\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:lifted_constr_ref] ==\n              :(x[6938] == (*)(x[6937]))\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6937]), :(x[6937])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:y_idx] == 6933\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:id] == 10\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:lifted_constr_ref] ==\n              :(x[6933] == (*)(x[6932]))\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6932]), :(x[6932])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:y_idx] == 6990\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:id] == 33\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:lifted_constr_ref] ==\n              :(x[6990] == x[6903] * x[6989])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6989])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:y_idx] == 6978\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:id] == 28\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:lifted_constr_ref] ==\n              :(x[6978] == (*)(x[6977]))\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6977]), :(x[6977])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:y_idx] == 6988\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:id] == 32\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:lifted_constr_ref] ==\n              :(x[6988] == (*)(x[6987]))\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6987]), :(x[6987])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:y_idx] == 7035\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:id] == 51\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:lifted_constr_ref] ==\n              :(x[7035] == x[6903] * x[7034])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7034])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:y_idx] == 6968\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:id] == 24\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:lifted_constr_ref] ==\n              :(x[6968] == (*)(x[6967]))\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6967]), :(x[6967])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:y_idx] == 6958\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:id] == 20\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:lifted_constr_ref] ==\n              :(x[6958] == (*)(x[6957]))\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6957]), :(x[6957])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:y_idx] == 7010\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:id] == 41\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:lifted_constr_ref] ==\n              :(x[7010] == x[6903] * x[7009])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7009])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:y_idx] == 6943\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:id] == 14\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:lifted_constr_ref] ==\n              :(x[6943] == (*)(x[6942]))\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6942]), :(x[6942])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:y_idx] == 6983\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:id] == 30\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:lifted_constr_ref] ==\n              :(x[6983] == (*)(x[6982]))\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6982]), :(x[6982])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:y_idx] == 7000\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:id] == 37\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:lifted_constr_ref] ==\n              :(x[7000] == x[6903] * x[6999])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6999])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:y_idx] == 6945\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:id] == 15\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:lifted_constr_ref] ==\n              :(x[6945] == x[6903] * x[6944])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6944])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:y_idx] == 7025\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:id] == 47\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:lifted_constr_ref] ==\n              :(x[7025] == x[6903] * x[7024])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7024])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:y_idx] == 6955\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:id] == 19\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:lifted_constr_ref] ==\n              :(x[6955] == x[6903] * x[6954])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6954])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:y_idx] == 6923\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:id] == 6\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:lifted_constr_ref] ==\n              :(x[6923] == (*)(x[6922]))\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:nonlinear_type] ==\n              :MONOMIAL\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6922]), :(x[6922])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:y_idx] == 6985\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:id] == 31\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:lifted_constr_ref] ==\n              :(x[6985] == x[6903] * x[6984])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[6984])]][:constr_id] ==\n              Set(Any[0])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:y_idx] == 7030\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:id] == 49\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:lifted_constr_ref] ==\n              :(x[7030] == x[6903] * x[7029])\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:nonlinear_type] ==\n              :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:y_type] == :Cont\n        @test alpine.nonconvex_terms[Expr[:(x[6903]), :(x[7029])]][:constr_id] ==\n              Set(Any[0])\n        lk1 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 6910), (-1.0, 6909)])),\n        )\n        @test alpine.linear_terms[lk1][:y_idx] == 6911\n        @test alpine.linear_terms[lk1][:id] == 3\n        @test alpine.linear_terms[lk1][:y_type] == :(Cont)\n        lk2 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3467), (1.0, 16)])),\n        )\n        @test alpine.linear_terms[lk2][:y_idx] == 6908\n        @test alpine.linear_terms[lk2][:id] == 1\n        @test alpine.linear_terms[lk2][:y_type] == :(Cont)\n        lk3 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.001548, 6903), (1.0, 7016), (1.0, 5702)]),\n            ),\n        )\n        @test alpine.linear_terms[lk3][:y_idx] == 7017\n        @test alpine.linear_terms[lk3][:id] == 67\n        @test alpine.linear_terms[lk3][:y_type] == :(Cont)\n        lk4 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 5162), (1.0, 1711)])),\n        )\n        @test alpine.linear_terms[lk4][:y_idx] == 7004\n        @test alpine.linear_terms[lk4][:id] == 59\n        @test alpine.linear_terms[lk4][:y_type] == :(Cont)\n        lk5 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7021), (0.001435, 6903), (1.0, 6002)]),\n            ),\n        )\n        @test alpine.linear_terms[lk5][:y_idx] == 7022\n        @test alpine.linear_terms[lk5][:id] == 70\n        @test alpine.linear_terms[lk5][:y_type] == :(Cont)\n        lk6 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6935), (1.0, 166)])),\n        )\n        @test alpine.linear_terms[lk6][:y_idx] == 6936\n        @test alpine.linear_terms[lk6][:id] == 18\n        @test alpine.linear_terms[lk6][:y_type] == :(Cont)\n        lk7 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 4262), (0.00247, 6903), (1.0, 6981)]),\n            ),\n        )\n        @test alpine.linear_terms[lk7][:y_idx] == 6982\n        @test alpine.linear_terms[lk7][:id] == 46\n        @test alpine.linear_terms[lk7][:y_type] == :(Cont)\n        lk8 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7005), (1.0, 1711)])),\n        )\n        @test alpine.linear_terms[lk8][:y_idx] == 7006\n        @test alpine.linear_terms[lk8][:id] == 60\n        @test alpine.linear_terms[lk8][:y_type] == :(Cont)\n        lk9 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1951), (1.0, 5402)])),\n        )\n        @test alpine.linear_terms[lk9][:y_idx] == 7009\n        @test alpine.linear_terms[lk9][:id] == 62\n        @test alpine.linear_terms[lk9][:y_type] == :(Cont)\n        lk10 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 226), (-1.0, 6945)])),\n        )\n        @test alpine.linear_terms[lk10][:y_idx] == 6946\n        @test alpine.linear_terms[lk10][:id] == 24\n        @test alpine.linear_terms[lk10][:y_type] == :(Cont)\n        lk11 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7030), (1.0, 3151)])),\n        )\n        @test alpine.linear_terms[lk11][:y_idx] == 7031\n        @test alpine.linear_terms[lk11][:id] == 75\n        @test alpine.linear_terms[lk11][:y_type] == :(Cont)\n        lk12 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6991), (1.0, 4622), (0.002066, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk12][:y_idx] == 6992\n        @test alpine.linear_terms[lk12][:id] == 52\n        @test alpine.linear_terms[lk12][:y_type] == :(Cont)\n        lk13 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7026), (1.0, 6302), (0.001323, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk13][:y_idx] == 7027\n        @test alpine.linear_terms[lk13][:id] == 73\n        @test alpine.linear_terms[lk13][:y_type] == :(Cont)\n        lk14 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 46), (1.0, 3497)])),\n        )\n        @test alpine.linear_terms[lk14][:y_idx] == 6914\n        @test alpine.linear_terms[lk14][:id] == 5\n        @test alpine.linear_terms[lk14][:y_type] == :(Cont)\n        lk15 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6960), (1.0, 391)])),\n        )\n        @test alpine.linear_terms[lk15][:y_idx] == 6961\n        @test alpine.linear_terms[lk15][:id] == 33\n        @test alpine.linear_terms[lk15][:y_type] == :(Cont)\n        lk16 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 631), (-1.0, 6975)])),\n        )\n        @test alpine.linear_terms[lk16][:y_idx] == 6976\n        @test alpine.linear_terms[lk16][:id] == 42\n        @test alpine.linear_terms[lk16][:y_type] == :(Cont)\n        lk17 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1351), (-1.0, 6995)])),\n        )\n        @test alpine.linear_terms[lk17][:y_idx] == 6996\n        @test alpine.linear_terms[lk17][:id] == 54\n        @test alpine.linear_terms[lk17][:y_type] == :(Cont)\n        lk18 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3557), (1.0, 106)])),\n        )\n        @test alpine.linear_terms[lk18][:y_idx] == 6924\n        @test alpine.linear_terms[lk18][:id] == 11\n        @test alpine.linear_terms[lk18][:y_type] == :(Cont)\n        lk19 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 3647), (1.0, 6941), (0.004795, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk19][:y_idx] == 6942\n        @test alpine.linear_terms[lk19][:id] == 22\n        @test alpine.linear_terms[lk19][:y_type] == :(Cont)\n        lk20 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3722), (1.0, 271)])),\n        )\n        @test alpine.linear_terms[lk20][:y_idx] == 6949\n        @test alpine.linear_terms[lk20][:id] == 26\n        @test alpine.linear_terms[lk20][:y_type] == :(Cont)\n        lk21 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3647), (1.0, 196)])),\n        )\n        @test alpine.linear_terms[lk21][:y_idx] == 6939\n        @test alpine.linear_terms[lk21][:id] == 20\n        @test alpine.linear_terms[lk21][:y_type] == :(Cont)\n        lk22 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 3467), (1.0, 6911), (6.34e-6, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk22][:y_idx] == 6912\n        @test alpine.linear_terms[lk22][:id] == 4\n        @test alpine.linear_terms[lk22][:y_type] == :(Cont)\n        lk23 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1531), (1.0, 4982)])),\n        )\n        @test alpine.linear_terms[lk23][:y_idx] == 6999\n        @test alpine.linear_terms[lk23][:id] == 56\n        @test alpine.linear_terms[lk23][:y_type] == :(Cont)\n        lk24 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 106), (-1.0, 6925)])),\n        )\n        @test alpine.linear_terms[lk24][:y_idx] == 6926\n        @test alpine.linear_terms[lk24][:id] == 12\n        @test alpine.linear_terms[lk24][:y_type] == :(Cont)\n        lk25 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 2251), (-1.0, 7015)])),\n        )\n        @test alpine.linear_terms[lk25][:y_idx] == 7016\n        @test alpine.linear_terms[lk25][:id] == 66\n        @test alpine.linear_terms[lk25][:y_type] == :(Cont)\n        lk26 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6936), (0.004985, 6903), (1.0, 3617)]),\n            ),\n        )\n        @test alpine.linear_terms[lk26][:y_idx] == 6937\n        @test alpine.linear_terms[lk26][:id] == 19\n        @test alpine.linear_terms[lk26][:y_type] == :(Cont)\n        lk27 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6915), (1.0, 46)])),\n        )\n        @test alpine.linear_terms[lk27][:y_idx] == 6916\n        @test alpine.linear_terms[lk27][:id] == 6\n        @test alpine.linear_terms[lk27][:y_type] == :(Cont)\n        lk28 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 3557), (0.005968, 6903), (1.0, 6926)]),\n            ),\n        )\n        @test alpine.linear_terms[lk28][:y_idx] == 6927\n        @test alpine.linear_terms[lk28][:id] == 13\n        @test alpine.linear_terms[lk28][:y_type] == :(Cont)\n        lk29 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 271), (-1.0, 6950)])),\n        )\n        @test alpine.linear_terms[lk29][:y_idx] == 6951\n        @test alpine.linear_terms[lk29][:id] == 27\n        @test alpine.linear_terms[lk29][:y_type] == :(Cont)\n        lk30 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.002971, 6903), (1.0, 6971), (1.0, 3962)]),\n            ),\n        )\n        @test alpine.linear_terms[lk30][:y_idx] == 6972\n        @test alpine.linear_terms[lk30][:id] == 40\n        @test alpine.linear_terms[lk30][:y_type] == :(Cont)\n        lk31 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 511), (-1.0, 6970)])),\n        )\n        @test alpine.linear_terms[lk31][:y_idx] == 6971\n        @test alpine.linear_terms[lk31][:id] == 39\n        @test alpine.linear_terms[lk31][:y_type] == :(Cont)\n        lk32 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7031), (1.0, 6602), (0.00121, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk32][:y_idx] == 7032\n        @test alpine.linear_terms[lk32][:id] == 76\n        @test alpine.linear_terms[lk32][:y_type] == :(Cont)\n        lk33 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.00166, 6903), (1.0, 7011), (1.0, 5402)]),\n            ),\n        )\n        @test alpine.linear_terms[lk33][:y_idx] == 7012\n        @test alpine.linear_terms[lk33][:id] == 64\n        @test alpine.linear_terms[lk33][:y_type] == :(Cont)\n        lk34 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, -0.003214),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 16)])),\n        )\n        @test alpine.linear_terms[lk34][:y_idx] == 6910\n        @test alpine.linear_terms[lk34][:id] == 2\n        @test alpine.linear_terms[lk34][:y_type] == :(Cont)\n        lk35 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7035), (1.0, 3451)])),\n        )\n        @test alpine.linear_terms[lk35][:y_idx] == 7036\n        @test alpine.linear_terms[lk35][:id] == 78\n        @test alpine.linear_terms[lk35][:y_type] == :(Cont)\n        lk36 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 2551), (1.0, 6002)])),\n        )\n        @test alpine.linear_terms[lk36][:y_idx] == 7019\n        @test alpine.linear_terms[lk36][:id] == 68\n        @test alpine.linear_terms[lk36][:y_type] == :(Cont)\n        lk37 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3842), (1.0, 391)])),\n        )\n        @test alpine.linear_terms[lk37][:y_idx] == 6959\n        @test alpine.linear_terms[lk37][:id] == 32\n        @test alpine.linear_terms[lk37][:y_type] == :(Cont)\n        lk38 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6966), (0.00307, 6903), (1.0, 3902)]),\n            ),\n        )\n        @test alpine.linear_terms[lk38][:y_idx] == 6967\n        @test alpine.linear_terms[lk38][:id] == 37\n        @test alpine.linear_terms[lk38][:y_type] == :(Cont)\n        lk39 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 3722), (0.003829, 6903), (1.0, 6951)]),\n            ),\n        )\n        @test alpine.linear_terms[lk39][:y_idx] == 6952\n        @test alpine.linear_terms[lk39][:id] == 28\n        @test alpine.linear_terms[lk39][:y_type] == :(Cont)\n        lk40 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 451), (1.0, 3902)])),\n        )\n        @test alpine.linear_terms[lk40][:y_idx] == 6964\n        @test alpine.linear_terms[lk40][:id] == 35\n        @test alpine.linear_terms[lk40][:y_type] == :(Cont)\n        lk41 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7006), (1.0, 5162), (0.001713, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk41][:y_idx] == 7007\n        @test alpine.linear_terms[lk41][:id] == 61\n        @test alpine.linear_terms[lk41][:y_type] == :(Cont)\n        lk42 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 811), (-1.0, 6980)])),\n        )\n        @test alpine.linear_terms[lk42][:y_idx] == 6981\n        @test alpine.linear_terms[lk42][:id] == 45\n        @test alpine.linear_terms[lk42][:y_type] == :(Cont)\n        lk43 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7001), (1.0, 4982), (0.00173, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk43][:y_idx] == 7002\n        @test alpine.linear_terms[lk43][:id] == 58\n        @test alpine.linear_terms[lk43][:y_type] == :(Cont)\n        lk44 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6920), (1.0, 76)])),\n        )\n        @test alpine.linear_terms[lk44][:y_idx] == 6921\n        @test alpine.linear_terms[lk44][:id] == 9\n        @test alpine.linear_terms[lk44][:y_type] == :(Cont)\n        lk45 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 4622), (1.0, 1171)])),\n        )\n        @test alpine.linear_terms[lk45][:y_idx] == 6989\n        @test alpine.linear_terms[lk45][:id] == 50\n        @test alpine.linear_terms[lk45][:y_type] == :(Cont)\n        lk46 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 991), (1.0, 4442)])),\n        )\n        @test alpine.linear_terms[lk46][:y_idx] == 6984\n        @test alpine.linear_terms[lk46][:id] == 47\n        @test alpine.linear_terms[lk46][:y_type] == :(Cont)\n        lk47 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6930), (1.0, 136)])),\n        )\n        @test alpine.linear_terms[lk47][:y_idx] == 6931\n        @test alpine.linear_terms[lk47][:id] == 15\n        @test alpine.linear_terms[lk47][:y_type] == :(Cont)\n        lk48 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 4802), (0.001891, 6903), (1.0, 6996)]),\n            ),\n        )\n        @test alpine.linear_terms[lk48][:y_idx] == 6997\n        @test alpine.linear_terms[lk48][:id] == 55\n        @test alpine.linear_terms[lk48][:y_type] == :(Cont)\n        lk49 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 511), (1.0, 3962)])),\n        )\n        @test alpine.linear_terms[lk49][:y_idx] == 6969\n        @test alpine.linear_terms[lk49][:id] == 38\n        @test alpine.linear_terms[lk49][:y_type] == :(Cont)\n        lk50 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 811), (1.0, 4262)])),\n        )\n        @test alpine.linear_terms[lk50][:y_idx] == 6979\n        @test alpine.linear_terms[lk50][:id] == 44\n        @test alpine.linear_terms[lk50][:y_type] == :(Cont)\n        lk51 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.01551, 6903), (1.0, 6916), (1.0, 3497)]),\n            ),\n        )\n        @test alpine.linear_terms[lk51][:y_idx] == 6917\n        @test alpine.linear_terms[lk51][:id] == 7\n        @test alpine.linear_terms[lk51][:y_type] == :(Cont)\n        lk52 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 451), (-1.0, 6965)])),\n        )\n        @test alpine.linear_terms[lk52][:y_idx] == 6966\n        @test alpine.linear_terms[lk52][:id] == 36\n        @test alpine.linear_terms[lk52][:y_type] == :(Cont)\n        lk53 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.005773, 6903), (1.0, 3587), (1.0, 6931)]),\n            ),\n        )\n        @test alpine.linear_terms[lk53][:y_idx] == 6932\n        @test alpine.linear_terms[lk53][:id] == 16\n        @test alpine.linear_terms[lk53][:y_type] == :(Cont)\n        lk54 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 631), (1.0, 4082)])),\n        )\n        @test alpine.linear_terms[lk54][:y_idx] == 6974\n        @test alpine.linear_terms[lk54][:id] == 41\n        @test alpine.linear_terms[lk54][:y_type] == :(Cont)\n        lk55 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 991), (-1.0, 6985)])),\n        )\n        @test alpine.linear_terms[lk55][:y_idx] == 6986\n        @test alpine.linear_terms[lk55][:id] == 48\n        @test alpine.linear_terms[lk55][:y_type] == :(Cont)\n        lk56 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 4802), (1.0, 1351)])),\n        )\n        @test alpine.linear_terms[lk56][:y_idx] == 6994\n        @test alpine.linear_terms[lk56][:id] == 53\n        @test alpine.linear_terms[lk56][:y_type] == :(Cont)\n        lk57 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6946), (0.004409, 6903), (1.0, 3677)]),\n            ),\n        )\n        @test alpine.linear_terms[lk57][:y_idx] == 6947\n        @test alpine.linear_terms[lk57][:id] == 25\n        @test alpine.linear_terms[lk57][:y_type] == :(Cont)\n        lk58 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 2251), (1.0, 5702)])),\n        )\n        @test alpine.linear_terms[lk58][:y_idx] == 7014\n        @test alpine.linear_terms[lk58][:id] == 65\n        @test alpine.linear_terms[lk58][:y_type] == :(Cont)\n        lk59 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7020), (1.0, 2551)])),\n        )\n        @test alpine.linear_terms[lk59][:y_idx] == 7021\n        @test alpine.linear_terms[lk59][:id] == 69\n        @test alpine.linear_terms[lk59][:y_type] == :(Cont)\n        lk60 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6940), (1.0, 196)])),\n        )\n        @test alpine.linear_terms[lk60][:y_idx] == 6941\n        @test alpine.linear_terms[lk60][:id] == 21\n        @test alpine.linear_terms[lk60][:y_type] == :(Cont)\n        lk61 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 3527), (1.0, 6921), (0.008919, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk61][:y_idx] == 6922\n        @test alpine.linear_terms[lk61][:id] == 10\n        @test alpine.linear_terms[lk61][:y_type] == :(Cont)\n        lk62 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7025), (1.0, 2851)])),\n        )\n        @test alpine.linear_terms[lk62][:y_idx] == 7026\n        @test alpine.linear_terms[lk62][:id] == 72\n        @test alpine.linear_terms[lk62][:y_type] == :(Cont)\n        lk63 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6986), (1.0, 4442), (0.002252, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk63][:y_idx] == 6987\n        @test alpine.linear_terms[lk63][:id] == 49\n        @test alpine.linear_terms[lk63][:y_type] == :(Cont)\n        lk64 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(0.002765, 6903), (1.0, 6976), (1.0, 4082)]),\n            ),\n        )\n        @test alpine.linear_terms[lk64][:y_idx] == 6977\n        @test alpine.linear_terms[lk64][:id] == 43\n        @test alpine.linear_terms[lk64][:y_type] == :(Cont)\n        lk65 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6956), (0.003269, 6903), (1.0, 3782)]),\n            ),\n        )\n        @test alpine.linear_terms[lk65][:y_idx] == 6957\n        @test alpine.linear_terms[lk65][:id] == 31\n        @test alpine.linear_terms[lk65][:y_type] == :(Cont)\n        lk66 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3587), (1.0, 136)])),\n        )\n        @test alpine.linear_terms[lk66][:y_idx] == 6929\n        @test alpine.linear_terms[lk66][:id] == 14\n        @test alpine.linear_terms[lk66][:y_type] == :(Cont)\n        lk67 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 166), (1.0, 3617)])),\n        )\n        @test alpine.linear_terms[lk67][:y_idx] == 6934\n        @test alpine.linear_terms[lk67][:id] == 17\n        @test alpine.linear_terms[lk67][:y_type] == :(Cont)\n        lk68 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 7010), (1.0, 1951)])),\n        )\n        @test alpine.linear_terms[lk68][:y_idx] == 7011\n        @test alpine.linear_terms[lk68][:id] == 63\n        @test alpine.linear_terms[lk68][:y_type] == :(Cont)\n        lk69 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 7036), (0.001098, 6903), (1.0, 6902)]),\n            ),\n        )\n        @test alpine.linear_terms[lk69][:y_idx] == 7037\n        @test alpine.linear_terms[lk69][:id] == 79\n        @test alpine.linear_terms[lk69][:y_type] == :(Cont)\n        lk70 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3527), (1.0, 76)])),\n        )\n        @test alpine.linear_terms[lk70][:y_idx] == 6919\n        @test alpine.linear_terms[lk70][:id] == 8\n        @test alpine.linear_terms[lk70][:y_type] == :(Cont)\n        lk71 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(\n                :coef_var,\n                Set(Any[(1.0, 6961), (1.0, 3842), (0.00317, 6903)]),\n            ),\n        )\n        @test alpine.linear_terms[lk71][:y_idx] == 6962\n        @test alpine.linear_terms[lk71][:id] == 34\n        @test alpine.linear_terms[lk71][:y_type] == :(Cont)\n        lk72 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6990), (1.0, 1171)])),\n        )\n        @test alpine.linear_terms[lk72][:y_idx] == 6991\n        @test alpine.linear_terms[lk72][:id] == 51\n        @test alpine.linear_terms[lk72][:y_type] == :(Cont)\n        lk73 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3451), (1.0, 6902)])),\n        )\n        @test alpine.linear_terms[lk73][:y_idx] == 7034\n        @test alpine.linear_terms[lk73][:id] == 77\n        @test alpine.linear_terms[lk73][:y_type] == :(Cont)\n        lk74 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 6302), (1.0, 2851)])),\n        )\n        @test alpine.linear_terms[lk74][:y_idx] == 7024\n        @test alpine.linear_terms[lk74][:id] == 71\n        @test alpine.linear_terms[lk74][:y_type] == :(Cont)\n        lk75 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1531), (-1.0, 7000)])),\n        )\n        @test alpine.linear_terms[lk75][:y_idx] == 7001\n        @test alpine.linear_terms[lk75][:id] == 57\n        @test alpine.linear_terms[lk75][:y_type] == :(Cont)\n        lk76 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3151), (1.0, 6602)])),\n        )\n        @test alpine.linear_terms[lk76][:y_idx] == 7029\n        @test alpine.linear_terms[lk76][:id] == 74\n        @test alpine.linear_terms[lk76][:y_type] == :(Cont)\n        lk77 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 3782), (1.0, 331)])),\n        )\n        @test alpine.linear_terms[lk77][:y_idx] == 6954\n        @test alpine.linear_terms[lk77][:id] == 29\n        @test alpine.linear_terms[lk77][:y_type] == :(Cont)\n        lk78 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(-1.0, 6955), (1.0, 331)])),\n        )\n        @test alpine.linear_terms[lk78][:y_idx] == 6956\n        @test alpine.linear_terms[lk78][:id] == 30\n        @test alpine.linear_terms[lk78][:y_type] == :(Cont)\n        lk79 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 226), (1.0, 3677)])),\n        )\n        @test alpine.linear_terms[lk79][:y_idx] == 6944\n        @test alpine.linear_terms[lk79][:id] == 23\n        @test alpine.linear_terms[lk79][:y_type] == :(Cont)\n    end\nend\n\n@testset \"Expression Parsing || Basic Multiplication Operators (Machine Generated for diffs)\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => JUNIPER,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n\n    m = operator_basic(solver = test_solver)\n    JuMP.set_optimize_hook(m, MOI.Utilities.attach_optimizer)\n    JuMP.optimize!(m)\n    JuMP.set_optimize_hook(m, nothing)\n    alpine = JuMP.backend(m).optimizer.model\n    Alpine.load!(alpine)\n\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4])]][:y_idx] == 31\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4])]][:id] == 27\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[31] == x[3] * x[4])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[76])]][:y_idx] == 83\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[76])]][:id] == 79\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[76])]][:lifted_constr_ref] ==\n          :(x[83] == x[4] * x[5] * x[76])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[76])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[2])]][:y_idx] == 9\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[2])]][:id] == 5\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[2])]][:lifted_constr_ref] ==\n          :(x[9] == (*)(x[2]))\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[2])]][:nonlinear_type] == :MONOMIAL\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7])]][:y_idx] == 19\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7])]][:id] == 15\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7])]][:lifted_constr_ref] ==\n          :(x[19] == x[5] * x[7])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[31])]][:y_idx] == 32\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[31])]][:id] == 28\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[32] == x[2] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[31])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10])]][:y_idx] == 49\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10])]][:id] == 45\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[49] == x[1] * x[2] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5]), :(x[9])]][:y_idx] == 50\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5]), :(x[9])]][:id] == 46\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[50] == x[3] * x[5] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[5]), :(x[9])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[47])]][:y_idx] == 69\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[47])]][:id] == 65\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[47])]][:lifted_constr_ref] ==\n          :(x[69] == x[4] * x[47])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[47])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[4])]][:y_idx] == 28\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[4])]][:id] == 24\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[28] == (*)(x[4]))\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[4])]][:nonlinear_type] == :MONOMIAL\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[10])]][:y_idx] == 37\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[10])]][:id] == 33\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[37] == x[4] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[1])]][:y_idx] == 5\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[1])]][:id] == 1\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[1])]][:lifted_constr_ref] ==\n          :(x[5] == (*)(x[1]))\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[1])]][:nonlinear_type] == :MONOMIAL\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[95])]][:y_idx] == 96\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[95])]][:id] == 92\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[95])]][:lifted_constr_ref] ==\n          :(x[96] == x[5] * x[95])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[95])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[40])]][:y_idx] == 41\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[40])]][:id] == 37\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[40])]][:lifted_constr_ref] ==\n          :(x[41] == x[2] * x[40])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[40])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10])]][:y_idx] == 26\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10])]][:id] == 22\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[26] == x[6] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[78]), :(x[28])]][:y_idx] == 84\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[78]), :(x[28])]][:id] == 80\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[78]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[84] == x[1] * x[78] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[78]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[43])]][:y_idx] == 58\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[43])]][:id] == 54\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[43])]][:lifted_constr_ref] ==\n          :(x[58] == x[6] * x[43])\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[43])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[6]), :(x[10])]][:y_idx] == 106\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[6]), :(x[10])]][:id] == 102\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[6]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[106] == x[4] * x[6] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[6]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4]), :(x[10])]][:y_idx] == 90\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4]), :(x[10])]][:id] == 86\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[90] == x[2] * x[4] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[4]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[41])]][:y_idx] == 42\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[41])]][:id] == 38\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[41])]][:lifted_constr_ref] ==\n          :(x[42] == x[1] * x[41])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[41])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[37])]][:y_idx] == 38\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[37])]][:id] == 34\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[37])]][:lifted_constr_ref] ==\n          :(x[38] == x[2] * x[37])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[37])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[85])]][:y_idx] == 87\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[85])]][:id] == 83\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[85])]][:lifted_constr_ref] ==\n          :(x[87] == x[5] * x[85])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[85])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5]), :(x[28])]][:y_idx] == 66\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5]), :(x[28])]][:id] == 62\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[66] == x[2] * x[3] * x[5] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10])]][:y_idx] == 53\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10])]][:id] == 49\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[53] == x[5] * x[9] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6]), :(x[28])]][:y_idx] == 107\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6]), :(x[28])]][:id] == 103\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[107] == x[3] * x[6] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5])]][:y_idx] == 17\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5])]][:id] == 13\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[17] == x[2] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[37])]][:y_idx] == 57\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[37])]][:id] == 53\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[37])]][:lifted_constr_ref] ==\n          :(x[57] == x[6] * x[37])\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[37])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7]), :(x[28])]][:y_idx] == 81\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7]), :(x[28])]][:id] == 77\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[81] == x[5] * x[7] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[7]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[38])]][:y_idx] == 39\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[38])]][:id] == 35\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[38])]][:lifted_constr_ref] ==\n          :(x[39] == x[1] * x[38])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[38])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[9])]][:y_idx] == 48\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[9])]][:id] == 44\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[48] == x[1] * x[3] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[9])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[23])]][:y_idx] == 24\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[23])]][:id] == 20\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[23])]][:lifted_constr_ref] ==\n          :(x[24] == x[4] * x[23])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[23])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[17])]][:y_idx] == 23\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[17])]][:id] == 19\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[17])]][:lifted_constr_ref] ==\n          :(x[23] == x[3] * x[17])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[17])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[10])]][:y_idx] == 51\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[10])]][:id] == 47\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[51] == x[1] * x[9] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[7])]][:y_idx] == 75\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[7])]][:id] == 71\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[7])]][:lifted_constr_ref] ==\n          :(x[75] == x[4] * x[5] * x[7])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[5]), :(x[7])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[28])]][:y_idx] == 95\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[28])]][:id] == 91\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[95] == x[9] * x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10])]][:y_idx] == 11\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10])]][:id] == 7\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[11] == x[9] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[37])]][:y_idx] == 100\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[37])]][:id] == 96\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[37])]][:lifted_constr_ref] ==\n          :(x[100] == x[1] * x[2] * x[37])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[37])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4]), :(x[5])]][:y_idx] == 62\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4]), :(x[5])]][:id] == 58\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[62] == x[2] * x[3] * x[4] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4]), :(x[5])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[9]), :(x[10])]][:y_idx] == 65\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[9]), :(x[10])]][:id] == 61\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[9]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[65] == x[1] * x[4] * x[9] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[9]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7]), :(x[28])]][:y_idx] == 80\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7]), :(x[28])]][:id] == 76\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[80] == x[1] * x[7] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:y_idx] == 46\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:id] == 42\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:lifted_constr_ref] ==\n          :(x[46] == x[1] * x[2] * x[3])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[40])]][:y_idx] == 59\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[40])]][:id] == 55\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[40])]][:lifted_constr_ref] ==\n          :(x[59] == x[17] * x[40])\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[40])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[85])]][:y_idx] == 86\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[85])]][:id] == 82\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[85])]][:lifted_constr_ref] ==\n          :(x[86] == x[1] * x[85])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[85])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[31])]][:y_idx] == 97\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[31])]][:id] == 93\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[97] == x[1] * x[2] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[31])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[28])]][:y_idx] == 29\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[28])]][:id] == 25\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[29] == x[13] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[13]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[28])]][:y_idx] == 92\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[28])]][:id] == 88\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[92] == x[2] * x[3] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9])]][:y_idx] == 20\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9])]][:id] == 16\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[20] == x[1] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10]), :(x[28])]][:y_idx] == 109\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10]), :(x[28])]][:id] == 105\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[109] == x[14] * x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[92])]][:y_idx] == 93\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[92])]][:id] == 89\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[92])]][:lifted_constr_ref] ==\n          :(x[93] == x[1] * x[92])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[92])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4])]][:y_idx] == 85\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4])]][:id] == 81\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[85] == x[2] * x[3] * x[4])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[11])]][:y_idx] == 16\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[11])]][:id] == 12\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[11])]][:lifted_constr_ref] ==\n          :(x[16] == x[1] * x[11])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[11])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[21])]][:y_idx] == 25\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[21])]][:id] == 21\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[21])]][:lifted_constr_ref] ==\n          :(x[25] == x[4] * x[21])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[21])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[53]), :(x[28])]][:y_idx] == 73\n    @test alpine.nonconvex_terms[Expr[:(x[53]), :(x[28])]][:id] == 69\n    @test alpine.nonconvex_terms[Expr[:(x[53]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[73] == x[53] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[53]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[32])]][:y_idx] == 34\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[32])]][:id] == 30\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[32])]][:lifted_constr_ref] ==\n          :(x[34] == x[5] * x[32])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[32])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[28])]][:y_idx] == 40\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[28])]][:id] == 36\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[40] == x[3] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10]), :(x[28])]][:y_idx] == 67\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10]), :(x[28])]][:id] == 63\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[67] == x[5] * x[9] * x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[10]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[43])]][:y_idx] == 102\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[43])]][:id] == 98\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[43])]][:lifted_constr_ref] ==\n          :(x[102] == x[5] * x[9] * x[43])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9]), :(x[43])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[26])]][:y_idx] == 27\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[26])]][:id] == 23\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[26])]][:lifted_constr_ref] ==\n          :(x[27] == x[4] * x[26])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[26])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[20]), :(x[31])]][:y_idx] == 56\n    @test alpine.nonconvex_terms[Expr[:(x[20]), :(x[31])]][:id] == 52\n    @test alpine.nonconvex_terms[Expr[:(x[20]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[56] == x[20] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[20]), :(x[31])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[4]), :(x[9])]][:y_idx] == 63\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[4]), :(x[9])]][:id] == 59\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[4]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[63] == x[1] * x[3] * x[4] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[3]), :(x[4]), :(x[9])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10])]][:y_idx] == 15\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10])]][:id] == 11\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[15] == x[14] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[76])]][:y_idx] == 77\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[76])]][:id] == 73\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[76])]][:lifted_constr_ref] ==\n          :(x[77] == x[1] * x[4] * x[76])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[76])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[88])]][:y_idx] == 89\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[88])]][:id] == 85\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[88])]][:lifted_constr_ref] ==\n          :(x[89] == x[1] * x[88])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[88])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[90])]][:y_idx] == 94\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[90])]][:id] == 90\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[90])]][:lifted_constr_ref] ==\n          :(x[94] == x[5] * x[90])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[90])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10]), :(x[28])]][:y_idx] == 108\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10]), :(x[28])]][:id] == 104\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[108] == x[6] * x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[10]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[48])]][:y_idx] == 70\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[48])]][:id] == 66\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[48])]][:lifted_constr_ref] ==\n          :(x[70] == x[4] * x[48])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[48])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[31])]][:y_idx] == 54\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[31])]][:id] == 50\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[54] == x[6] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[31])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[31])]][:y_idx] == 99\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[31])]][:id] == 95\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[99] == x[1] * x[9] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[9]), :(x[31])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[35])]][:y_idx] == 36\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[35])]][:id] == 32\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[35])]][:lifted_constr_ref] ==\n          :(x[36] == x[1] * x[35])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[35])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9])]][:y_idx] == 14\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9])]][:id] == 10\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[14] == x[5] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[9])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[13])]][:y_idx] == 22\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[13])]][:id] == 18\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[13])]][:lifted_constr_ref] ==\n          :(x[22] == x[4] * x[13])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[13])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10]), :(x[28])]][:y_idx] == 64\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10]), :(x[28])]][:id] == 60\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[64] == x[1] * x[2] * x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[10]), :(x[28])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[46]), :(x[28])]][:y_idx] == 72\n    @test alpine.nonconvex_terms[Expr[:(x[46]), :(x[28])]][:id] == 68\n    @test alpine.nonconvex_terms[Expr[:(x[46]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[72] == x[46] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[46]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[31])]][:y_idx] == 55\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[31])]][:id] == 51\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[55] == x[17] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[31])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[31])]][:y_idx] == 98\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[31])]][:id] == 94\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[98] == x[2] * x[5] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[31])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[28])]][:y_idx] == 43\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[28])]][:id] == 39\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[43] == x[10] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[10]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[10])]][:y_idx] == 78\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[10])]][:id] == 74\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[78] == x[2] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[10])]][:y_idx] == 52\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[10])]][:id] == 48\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[52] == x[2] * x[5] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[5]), :(x[10])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[90])]][:y_idx] == 91\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[90])]][:id] == 87\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[90])]][:lifted_constr_ref] ==\n          :(x[91] == x[1] * x[90])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[90])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[17])]][:y_idx] == 104\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[17])]][:id] == 100\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[17])]][:lifted_constr_ref] ==\n          :(x[104] == x[3] * x[4] * x[17])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[17])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[9])]][:y_idx] == 76\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[9])]][:id] == 72\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[76] == x[3] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[9])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[78])]][:y_idx] == 79\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[78])]][:id] == 75\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[78])]][:lifted_constr_ref] ==\n          :(x[79] == x[1] * x[4] * x[78])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[78])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[3])]][:y_idx] == 10\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[3])]][:id] == 6\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[3])]][:lifted_constr_ref] ==\n          :(x[10] == (*)(x[3]))\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[3])]][:nonlinear_type] == :MONOMIAL\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[49])]][:y_idx] == 71\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[49])]][:id] == 67\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[49])]][:lifted_constr_ref] ==\n          :(x[71] == x[4] * x[49])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[49])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[9])]][:y_idx] == 88\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[9])]][:id] == 84\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[9])]][:lifted_constr_ref] ==\n          :(x[88] == x[3] * x[4] * x[9])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[9])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[15]), :(x[28])]][:y_idx] == 30\n    @test alpine.nonconvex_terms[Expr[:(x[15]), :(x[28])]][:id] == 26\n    @test alpine.nonconvex_terms[Expr[:(x[15]), :(x[28])]][:lifted_constr_ref] ==\n          :(x[30] == x[15] * x[28])\n    @test alpine.nonconvex_terms[Expr[:(x[15]), :(x[28])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[46])]][:y_idx] == 68\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[46])]][:id] == 64\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[46])]][:lifted_constr_ref] ==\n          :(x[68] == x[4] * x[46])\n    @test alpine.nonconvex_terms[Expr[:(x[4]), :(x[46])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[11])]][:y_idx] == 12\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[11])]][:id] == 8\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[11])]][:lifted_constr_ref] ==\n          :(x[12] == x[5] * x[11])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[11])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[7])]][:y_idx] == 74\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[7])]][:id] == 70\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[7])]][:lifted_constr_ref] ==\n          :(x[74] == x[1] * x[4] * x[7])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[7])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[20])]][:y_idx] == 105\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[20])]][:id] == 101\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[20])]][:lifted_constr_ref] ==\n          :(x[105] == x[3] * x[4] * x[20])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[20])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[11])]][:y_idx] == 82\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[11])]][:id] == 78\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[11])]][:lifted_constr_ref] ==\n          :(x[82] == x[1] * x[4] * x[11])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[4]), :(x[11])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[43])]][:y_idx] == 44\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[43])]][:id] == 40\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[43])]][:lifted_constr_ref] ==\n          :(x[44] == x[9] * x[43])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[43])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:y_idx] == 61\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:id] == 57\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:lifted_constr_ref] ==\n          :(x[61] == x[1] * x[2] * x[3] * x[4])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3]), :(x[4])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[10])]][:y_idx] == 18\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[10])]][:id] == 14\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[10])]][:lifted_constr_ref] ==\n          :(x[18] == x[17] * x[10])\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[10])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7])]][:y_idx] == 8\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7])]][:id] == 4\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7])]][:lifted_constr_ref] ==\n          :(x[8] == x[1] * x[7])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[7])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:y_idx] == 6\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:id] == 2\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:lifted_constr_ref] ==\n          :(x[6] == x[1] * x[2])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[40])]][:y_idx] == 101\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[40])]][:id] == 97\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[40])]][:lifted_constr_ref] ==\n          :(x[101] == x[1] * x[2] * x[40])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[40])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[37])]][:y_idx] == 60\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[37])]][:id] == 56\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[37])]][:lifted_constr_ref] ==\n          :(x[60] == x[17] * x[37])\n    @test alpine.nonconvex_terms[Expr[:(x[17]), :(x[37])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[6])]][:y_idx] == 103\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[6])]][:id] == 99\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[6])]][:lifted_constr_ref] ==\n          :(x[103] == x[3] * x[4] * x[6])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[4]), :(x[6])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3])]][:y_idx] == 7\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3])]][:id] == 3\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3])]][:lifted_constr_ref] ==\n          :(x[7] == x[2] * x[3])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5])]][:y_idx] == 47\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5])]][:id] == 43\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5])]][:lifted_constr_ref] ==\n          :(x[47] == x[2] * x[3] * x[5])\n    @test alpine.nonconvex_terms[Expr[:(x[2]), :(x[3]), :(x[5])]][:nonlinear_type] ==\n          :MULTILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6])]][:y_idx] == 13\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6])]][:id] == 9\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6])]][:lifted_constr_ref] ==\n          :(x[13] == x[3] * x[6])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[6])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[31])]][:y_idx] == 35\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[31])]][:id] == 31\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[31])]][:lifted_constr_ref] ==\n          :(x[35] == x[9] * x[31])\n    @test alpine.nonconvex_terms[Expr[:(x[9]), :(x[31])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[32])]][:y_idx] == 33\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[32])]][:id] == 29\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[32])]][:lifted_constr_ref] ==\n          :(x[33] == x[1] * x[32])\n    @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[32])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[20])]][:y_idx] == 21\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[20])]][:id] == 17\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[20])]][:lifted_constr_ref] ==\n          :(x[21] == x[3] * x[20])\n    @test alpine.nonconvex_terms[Expr[:(x[3]), :(x[20])]][:nonlinear_type] == :BILINEAR\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[44])]][:y_idx] == 45\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[44])]][:id] == 41\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[44])]][:lifted_constr_ref] ==\n          :(x[45] == x[5] * x[44])\n    @test alpine.nonconvex_terms[Expr[:(x[5]), :(x[44])]][:nonlinear_type] == :BILINEAR\n\n    @test alpine.bounding_constr_mip[1][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[5])]\n    @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[1][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[1][:cnt] == 1\n    @test alpine.bounding_constr_mip[2][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[2][:vars] == Any[:(x[6])]\n    @test alpine.bounding_constr_mip[2][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[2][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[2][:cnt] == 1\n    @test alpine.bounding_constr_mip[3][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[3][:vars] == Any[:(x[5]), :(x[7])]\n    @test alpine.bounding_constr_mip[3][:coefs] == Any[1.0, 1.0]\n    @test alpine.bounding_constr_mip[3][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[3][:cnt] == 2\n    @test alpine.bounding_constr_mip[4][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[4][:vars] == Any[:(x[8])]\n    @test alpine.bounding_constr_mip[4][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[4][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[4][:cnt] == 1\n    @test alpine.bounding_constr_mip[5][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[5][:vars] == Any[:(x[12])]\n    @test alpine.bounding_constr_mip[5][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[5][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[5][:cnt] == 1\n    @test alpine.bounding_constr_mip[6][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[6][:vars] == Any[:(x[13])]\n    @test alpine.bounding_constr_mip[6][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[6][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[6][:cnt] == 1\n    @test alpine.bounding_constr_mip[7][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[7][:vars] == Any[:(x[15])]\n    @test alpine.bounding_constr_mip[7][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[7][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[7][:cnt] == 1\n    @test alpine.bounding_constr_mip[8][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[8][:vars] == Any[:(x[16])]\n    @test alpine.bounding_constr_mip[8][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[8][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[8][:cnt] == 1\n    @test alpine.bounding_constr_mip[9][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[9][:vars] == Any[:(x[18])]\n    @test alpine.bounding_constr_mip[9][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[9][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[9][:cnt] == 1\n    @test alpine.bounding_constr_mip[10][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[10][:vars] == Any[:(x[19])]\n    @test alpine.bounding_constr_mip[10][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[10][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[10][:cnt] == 1\n    @test alpine.bounding_constr_mip[11][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[11][:vars] == Any[:(x[21])]\n    @test alpine.bounding_constr_mip[11][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[11][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[11][:cnt] == 1\n    @test alpine.bounding_constr_mip[12][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[12][:vars] == Any[:(x[22])]\n    @test alpine.bounding_constr_mip[12][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[12][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[12][:cnt] == 1\n    @test alpine.bounding_constr_mip[13][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[13][:vars] == Any[:(x[24])]\n    @test alpine.bounding_constr_mip[13][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[13][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[13][:cnt] == 1\n    @test alpine.bounding_constr_mip[14][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[14][:vars] == Any[:(x[25])]\n    @test alpine.bounding_constr_mip[14][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[14][:sense] == :(>=)\n    @test alpine.bounding_constr_mip[14][:cnt] == 1\n    @test alpine.bounding_constr_mip[15][:rhs] == 1.0\n    @test alpine.bounding_constr_mip[15][:vars] == Any[:(x[27])]\n    @test alpine.bounding_constr_mip[15][:coefs] == Any[1.0]\n    @test alpine.bounding_constr_mip[15][:sense] == :(<=)\n    @test alpine.bounding_constr_mip[15][:cnt] == 1\nend\n\n@testset \"Expression Parsing || corner cases\" begin\n    @testset \"Corner Cases - 1 : sign convertor special case\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"minlp_solver\" => JUNIPER,\n            \"log_level\" => 100,\n        )\n\n        m = Model(test_solver)\n        @variable(m, 0 <= x[1:5] <= 1, Bin)\n        @NLconstraint(m, x[1] + -x[2] >= 2)\n        @objective(m, Min, x[1] + x[2])\n        alpine = _build(m)\n\n        @test alpine.bounding_constr_mip[1][:rhs] == 2.0\n        @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, -1.0]\n        @test alpine.bounding_constr_mip[1][:sense] == :(>=)\n        @test alpine.bounding_constr_mip[1][:cnt] == 2\n    end\n\n    @testset \"Corner Cases - 2 : full sub-expression\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n\n        m = Model(test_solver)\n        @variable(m, x[1:5] >= 0)\n        @NLconstraint(m, (x[1] + 10 + 4 * x[2] + 200) * 5 >= 2 * 5)\n        @constraint(m, x[1] + x[2] + 200 >= 2)\n        @objective(m, Min, x[1] + x[2])\n        alpine = _build(m)\n\n        @test alpine.bounding_constr_mip[1][:rhs] == -198.0\n        @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, 1.0]\n        @test alpine.bounding_constr_mip[1][:sense] == :(>=)\n        @test alpine.bounding_constr_mip[1][:cnt] == 2\n        @test alpine.bounding_constr_mip[2][:rhs] == -1040.0\n        @test alpine.bounding_constr_mip[2][:vars] == Any[:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[2][:coefs] == Any[5.0, 20.0]\n        @test alpine.bounding_constr_mip[2][:sense] == :(>=)\n        @test alpine.bounding_constr_mip[2][:cnt] == 2\n    end\n\n    @testset \"Corner Cases - 2 : full sub-expression\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n\n        m = Model(test_solver)\n        @variable(m, x[1:5] >= 0)\n        @NLconstraint(m, (x[1] + 10 + 4 * x[2] + 200) * 5 >= 2 * 5)\n        @constraint(m, x[1] + x[2] + 200 >= 2)\n        @objective(m, Min, x[1] + x[2])\n        alpine = _build(m)\n\n        @test alpine.bounding_constr_mip[1][:rhs] == -198.0\n        @test alpine.bounding_constr_mip[1][:vars] == Any[:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[1][:coefs] == Any[1.0, 1.0]\n        @test alpine.bounding_constr_mip[1][:sense] == :(>=)\n        @test alpine.bounding_constr_mip[1][:cnt] == 2\n        @test alpine.bounding_constr_mip[2][:rhs] == -1040.0\n        @test alpine.bounding_constr_mip[2][:vars] == Any[:(x[1]), :(x[2])]\n        @test alpine.bounding_constr_mip[2][:coefs] == Any[5.0, 20.0]\n        @test alpine.bounding_constr_mip[2][:sense] == :(>=)\n        @test alpine.bounding_constr_mip[2][:cnt] == 2\n    end\nend\n\n@testset \"Expression Parsing || Discrete Multilinear\" begin\n    @testset \"Expression Parsing || bmpl && binlin && binprod\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"minlp_solver\" => JUNIPER,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n\n        m = bpml(solver = test_solver)\n\n        alpine = _build(m) # Setup internal model\n\n        @test length(keys(alpine.nonconvex_terms)) == 12\n\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:y_idx] == 11\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:y_idx] == 12\n        @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[6])]][:y_idx] == 13\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:y_idx] == 14\n        @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[6])]][:y_idx] == 15\n        @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[7])]][:y_idx] == 16\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[16])]][:y_idx] == 17\n        @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[7]), :(x[8])]][:y_idx] == 18\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[18])]][:y_idx] == 19\n        @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[18])]][:y_idx] == 20\n        @test alpine.nonconvex_terms[Expr[\n            :(x[1]),\n            :(x[2]),\n            :(x[3]),\n            :(x[4]),\n            :(x[5]),\n        ]][:y_idx] == 21\n        @test alpine.nonconvex_terms[Expr[\n            :(x[6]),\n            :(x[7]),\n            :(x[9]),\n            :(x[10]),\n            :(x[6]),\n        ]][:y_idx] == 22\n\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[6])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2])]][:nonlinear_type] == :BINPROD\n        @test alpine.nonconvex_terms[Expr[:(x[12]), :(x[6])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[2]), :(x[3])]][:nonlinear_type] ==\n              :BINPROD\n        @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[6])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[7])]][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[16])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[:(x[6]), :(x[7]), :(x[8])]][:nonlinear_type] ==\n              :MULTILINEAR\n        @test alpine.nonconvex_terms[Expr[:(x[1]), :(x[18])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[:(x[14]), :(x[18])]][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[Expr[\n            :(x[1]),\n            :(x[2]),\n            :(x[3]),\n            :(x[4]),\n            :(x[5]),\n        ]][:nonlinear_type] == :BINPROD\n        @test alpine.nonconvex_terms[Expr[\n            :(x[6]),\n            :(x[7]),\n            :(x[9]),\n            :(x[10]),\n            :(x[6]),\n        ]][:nonlinear_type] == :MULTILINEAR\n\n        @test length(alpine.var_type) == 22\n        @test alpine.var_type[11] == :Cont\n        @test alpine.var_type[12] == :Bin\n        @test alpine.var_type[13] == :Cont\n        @test alpine.var_type[14] == :Bin\n        @test alpine.var_type[15] == :Cont\n        @test alpine.var_type[16] == :Cont\n        @test alpine.var_type[17] == :Cont\n        @test alpine.var_type[18] == :Cont\n        @test alpine.var_type[19] == :Cont\n        @test alpine.var_type[20] == :Cont\n        @test alpine.var_type[21] == :Bin\n        @test alpine.var_type[22] == :Cont\n    end\n\n    @testset \"Expression Parsing || bmpl && binlin && binprod with linear lifting and coefficients\" begin\n        test_solver = optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"minlp_solver\" => JUNIPER,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n            \"log_level\" => 100,\n        )\n\n        m = bmpl_linearlifting(solver = test_solver)\n\n        alpine = _build(m)\n\n        lk1 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 1), (1.0, 17)])),\n        )\n        lk2 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 11), (1.0, 12)])),\n        )\n        lk3 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 7), (2.0, 6)])),\n        )\n        lk4 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 6), (1.0, 19)])),\n        )\n        lk5 = Dict{Symbol,Any}(\n            Pair{Symbol,Any}(:sign, :+),\n            Pair{Symbol,Any}(:scalar, 0.0),\n            Pair{Symbol,Any}(:coef_var, Set(Any[(1.0, 6), (1.0, 25)])),\n        )\n\n        @test haskey(alpine.linear_terms, lk1)\n        @test haskey(alpine.linear_terms, lk2)\n        @test haskey(alpine.linear_terms, lk3)\n        @test haskey(alpine.linear_terms, lk4)\n        @test haskey(alpine.linear_terms, lk5)\n\n        @test alpine.linear_terms[lk1][:lifted_constr_ref] == :(x[20] == x[1] + x[17])\n        @test alpine.linear_terms[lk2][:lifted_constr_ref] == :(x[13] == x[11] + x[12])\n        @test alpine.linear_terms[lk3][:lifted_constr_ref] == :(x[15] == 2 * x[6] + x[7])\n        @test alpine.linear_terms[lk4][:lifted_constr_ref] == :(x[21] == x[6] + x[19])\n        @test alpine.linear_terms[lk5][:lifted_constr_ref] == :(x[26] == x[6] + x[25])\n\n        @test alpine.linear_terms[lk1][:y_idx] == 20\n        @test alpine.linear_terms[lk2][:y_idx] == 13\n        @test alpine.linear_terms[lk3][:y_idx] == 15\n        @test alpine.linear_terms[lk4][:y_idx] == 21\n        @test alpine.linear_terms[lk5][:y_idx] == 26\n\n        @test alpine.linear_terms[lk1][:y_type] == :Cont\n        @test alpine.linear_terms[lk2][:y_type] == :Cont\n        @test alpine.linear_terms[lk3][:y_type] == :Cont\n        @test alpine.linear_terms[lk4][:y_type] == :Cont\n        @test alpine.linear_terms[lk5][:y_type] == :Cont\n\n        nlk1 = Expr[:(x[18]), :(x[7])]\n        nlk2 = Expr[:(x[6]), :(x[7]), :(x[8])]\n        nlk3 = Expr[:(x[7]), :(x[10])]\n        nlk4 = Expr[:(x[2]), :(x[26])]\n        nlk5 = Expr[:(x[1]), :(x[13])]\n        nlk6 = Expr[:(x[1]), :(x[15])]\n        nlk7 = Expr[:(x[2]), :(x[6])]\n        nlk8 = Expr[:(x[24]), :(x[23])]\n        nlk9 = Expr[:(x[1]), :(x[2])]\n        nlk10 = Expr[:(x[2]), :(x[3])]\n        nlk11 = Expr[:(x[20]), :(x[21])]\n        nlk12 = Expr[:(x[3]), :(x[4])]\n\n        @test haskey(alpine.nonconvex_terms, nlk1)\n        @test haskey(alpine.nonconvex_terms, nlk2)\n        @test haskey(alpine.nonconvex_terms, nlk3)\n        @test haskey(alpine.nonconvex_terms, nlk4)\n        @test haskey(alpine.nonconvex_terms, nlk5)\n        @test haskey(alpine.nonconvex_terms, nlk6)\n        @test haskey(alpine.nonconvex_terms, nlk7)\n        @test haskey(alpine.nonconvex_terms, nlk8)\n        @test haskey(alpine.nonconvex_terms, nlk9)\n        @test haskey(alpine.nonconvex_terms, nlk10)\n        @test haskey(alpine.nonconvex_terms, nlk11)\n        @test haskey(alpine.nonconvex_terms, nlk12)\n\n        @test alpine.nonconvex_terms[nlk1][:id] == 7\n        @test alpine.nonconvex_terms[nlk2][:id] == 1\n        @test alpine.nonconvex_terms[nlk3][:id] == 9\n        @test alpine.nonconvex_terms[nlk4][:id] == 12\n        @test alpine.nonconvex_terms[nlk5][:id] == 3\n        @test alpine.nonconvex_terms[nlk6][:id] == 4\n        @test alpine.nonconvex_terms[nlk7][:id] == 5\n        @test alpine.nonconvex_terms[nlk8][:id] == 11\n        @test alpine.nonconvex_terms[nlk9][:id] == 6\n        @test alpine.nonconvex_terms[nlk10][:id] == 2\n        @test alpine.nonconvex_terms[nlk11][:id] == 8\n        @test alpine.nonconvex_terms[nlk12][:id] == 10\n\n        @test alpine.nonconvex_terms[nlk1][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk2][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk3][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk4][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk5][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk6][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk7][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk8][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk9][:y_type] == :Bin\n        @test alpine.nonconvex_terms[nlk10][:y_type] == :Bin\n        @test alpine.nonconvex_terms[nlk11][:y_type] == :Cont\n        @test alpine.nonconvex_terms[nlk12][:y_type] == :Bin\n\n        @test alpine.nonconvex_terms[nlk1][:y_idx] == 19\n        @test alpine.nonconvex_terms[nlk2][:y_idx] == 11\n        @test alpine.nonconvex_terms[nlk3][:y_idx] == 23\n        @test alpine.nonconvex_terms[nlk4][:y_idx] == 27\n        @test alpine.nonconvex_terms[nlk5][:y_idx] == 14\n        @test alpine.nonconvex_terms[nlk6][:y_idx] == 16\n        @test alpine.nonconvex_terms[nlk7][:y_idx] == 17\n        @test alpine.nonconvex_terms[nlk8][:y_idx] == 25\n        @test alpine.nonconvex_terms[nlk9][:y_idx] == 18\n        @test alpine.nonconvex_terms[nlk10][:y_idx] == 12\n        @test alpine.nonconvex_terms[nlk11][:y_idx] == 22\n        @test alpine.nonconvex_terms[nlk12][:y_idx] == 24\n\n        @test alpine.nonconvex_terms[nlk1][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk2][:nonlinear_type] == :MULTILINEAR\n        @test alpine.nonconvex_terms[nlk3][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk4][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk5][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk6][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk7][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk8][:nonlinear_type] == :BINLIN\n        @test alpine.nonconvex_terms[nlk9][:nonlinear_type] == :BINPROD\n        @test alpine.nonconvex_terms[nlk10][:nonlinear_type] == :BINPROD\n        @test alpine.nonconvex_terms[nlk11][:nonlinear_type] == :BILINEAR\n        @test alpine.nonconvex_terms[nlk12][:nonlinear_type] == :BINPROD\n    end\nend\n\n@testset \"Expr dereferencing for @NLexpression\" begin\n    # Taken from Juniper.jl\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => JUNIPER,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bt\" => true,\n    )\n\n    m = Model(test_solver)\n    @variable(m, 0 <= x <= 1)\n    @variable(m, 0 <= z <= 1, Bin)\n    b_expr = @NLexpression(m, z / 1)\n    @NLconstraint(m, 1.1 >= b_expr)\n    an_expr = @NLexpression(m, x / 1)\n    @NLobjective(m, Max, z + an_expr)\n    JuMP.optimize!(m)\n\n    @test isapprox(JuMP.objective_value(m), 2.0; atol = 1E-6)\n    @test isapprox(JuMP.value(z), 1; atol = 1e-6)\n    @test isapprox(JuMP.value(x), 1; atol = 1e-6)\nend\n\n@testset \"@NLexpression from quadratic @expression (Issue #221)\" begin\n    @testset \"Unit tests for `expr_is_emptysum`\" begin\n        # Empty sum\n        @test Alpine.expr_is_emptysum(:(+()))\n        # Not empty sum zero int\n        @test !Alpine.expr_is_emptysum(:(+(0, 0)))\n        # Not empty sum zero float\n        @test !Alpine.expr_is_emptysum(:(+(0.0, 0.0)))\n        # Not empty sum int with zero\n        @test !Alpine.expr_is_emptysum(:(+(1, 0)))\n        # Not empty sum int\n        @test !Alpine.expr_is_emptysum(:(+(1, 2)))\n        # Not empty sum float with zero\n        @test !Alpine.expr_is_emptysum(:(+(1.0, 0.0)))\n        # Not empty sum float\n        @test !Alpine.expr_is_emptysum(:(+(1.0, 3.0)))\n        # Not empty sum of variables\n        @test !Alpine.expr_is_emptysum(:(x + y))\n        # Not empty sum of variable with int\n        @test !Alpine.expr_is_emptysum(:(x + 1))\n        # Not empty sum of variable with float\n        @test !Alpine.expr_is_emptysum(:(x + 3.0))\n        # Not empty expression with non-linear function evaluation\n        @test !Alpine.expr_is_emptysum(:(sin(x)))\n        # Not empty expression with anonimus function\n        @test !Alpine.expr_is_emptysum(:(x -> log(x)))\n        # Not empty expression with anonimus function\n        @test !Alpine.expr_is_emptysum(:(x -> log(x)))\n        # Not empty expression with empty sum\n        @test !Alpine.expr_is_emptysum(:($(:(+())) + 1))\n    end\n\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"presolve_bt\" => true,\n        \"apply_partitioning\" => true,\n    )\n\n    m = JuMP.Model(test_solver)\n\n    @variable(m, -2 ≤ x ≤ 2, start = 1)\n    @expression(m, expr, x^2)\n    @NLconstraint(m, expr >= 1)\n    @NLconstraint(m, expr <= 2)\n    @NLobjective(m, Min, x^3)\n\n    JuMP.optimize!(m)\n    @test JuMP.termination_status(m) == JuMP.MOI.OPTIMAL\n    @test isapprox(JuMP.objective_value(m), -(sqrt(2))^3; atol = 1E-6)\n    @test isapprox(JuMP.value(m[:x]), -sqrt(2); atol = 1E-6)\nend\n"
  },
  {
    "path": "test/test_solver.jl",
    "content": "@testset \"Optimizer loading tests\" begin\n    # Random Model 1\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n    m = operator_c(solver = test_solver)\n\n    alpine = _build(m)\n    @test isa(alpine, Alpine.Optimizer)\n\n    # Expression Model 1\n    m = exprstest(solver = test_solver)\n    alpine = _build(m)\n    @test isa(alpine, Alpine.Optimizer)\nend\n\n@testset \"Partitioning variable selection tests :: nlp3\" begin\n    # Select all NL variable\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 0,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(JuMP.objective_value(m), 7049.2478976; atol = 1e-3)\n    @test length(alpine.candidate_disc_vars) == 8\n    @test length(alpine.disc_vars) == 8\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 0\n\n    # Select all NL variable\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 2,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(JuMP.objective_value(m), 7049.2478976; atol = 1e-3)\n    @test length(alpine.candidate_disc_vars) == 8\n    @test length(alpine.disc_vars) == 8\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 2\n\n    # Minimum vertex cover algorithm\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 1,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(JuMP.objective_value(m), 7049.2478976; atol = 1e-3)\n    @test length(alpine.candidate_disc_vars) == 8\n    @test length(alpine.disc_vars) == 3\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 1\n\n    # Adaptive variable selection scheme :: disc_var_pick = 3\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 3,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 2,\n        \"log_level\" => 100,\n    )\n    m = nlp3(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.OTHER_LIMIT\n    @test isapprox(JuMP.objective_value(m), 7049.2478976; atol = 1e-3)\n    @test length(alpine.candidate_disc_vars) == 8\n    @test length(alpine.disc_vars) == 8\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 3\nend\n\n@testset \"Partitioning variable selection tests :: castro2m2\" begin\n\n    # Select all NL variables\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 0,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 0,\n    )\n\n    m = castro2m2(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.LOCALLY_SOLVED\n\n    @test length(alpine.candidate_disc_vars) == 10\n    @test length(alpine.disc_vars) == 10\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 0\n\n    # Select minimum vertex cover\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 1,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 0,\n    )\n\n    m = castro2m2(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.LOCALLY_SOLVED\n    @test length(alpine.candidate_disc_vars) == 10\n    @test length(alpine.disc_vars) == 4\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 1\n\n    # Criteria 15 static selection\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 2,\n        \"disc_uniform_rate\" => 15,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 0,\n    )\n\n    m = castro2m2(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.LOCALLY_SOLVED\n\n    @test length(alpine.candidate_disc_vars) == 10\n    @test length(alpine.disc_vars) == 10\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 2\nend\n\n@testset \"Partitioning variable selection tests :: blend029\" begin\n\n    # Select all NL variable\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 0,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n\n    m = blend029_gl(solver = test_solver)\n    alpine = _build(m)\n\n    @test length(alpine.candidate_disc_vars) == 26\n    @test Set(alpine.candidate_disc_vars) == Set([\n        26,\n        27,\n        29,\n        30,\n        32,\n        33,\n        35,\n        36,\n        37,\n        38,\n        39,\n        40,\n        41,\n        42,\n        43,\n        44,\n        45,\n        46,\n        47,\n        48,\n        55,\n        56,\n        57,\n        58,\n        59,\n        60,\n    ])\n    @test length(alpine.disc_vars) == 26\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 0\n\n    # Minimum vertex cover\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 1,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n\n    m = blend029_gl(solver = test_solver)\n    alpine = _build(m)\n\n    @test length(alpine.candidate_disc_vars) == 26\n    @test Set(alpine.candidate_disc_vars) == Set([\n        26,\n        27,\n        29,\n        30,\n        32,\n        33,\n        35,\n        36,\n        37,\n        38,\n        39,\n        40,\n        41,\n        42,\n        43,\n        44,\n        45,\n        46,\n        47,\n        48,\n        55,\n        56,\n        57,\n        58,\n        59,\n        60,\n    ])\n    @test length(alpine.disc_vars) == 10\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 1\n\n    # Adaptive Scheme vertex cover\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"disc_var_pick\" => 2,\n        \"disc_uniform_rate\" => 10,\n        \"presolve_bp\" => false,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 1,\n        \"log_level\" => 100,\n    )\n\n    m = blend029_gl(solver = test_solver)\n    alpine = _build(m)\n\n    @test length(alpine.candidate_disc_vars) == 26\n    @test length(Set(alpine.candidate_disc_vars)) == 26\n    # TODO provide a check to see if candidate_disc_vars are all covered\n    @test length(alpine.disc_vars) == 10\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 2\nend\n\n@testset \"Partitioning variable selection tests :: castro6m2\" begin\n\n    # Dynamic Scheme step 1\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        # We don't use the default HiGHS because it struggles with the numerical\n        # scaling of this example.\n        # \"mip_solver\" => HIGHS,\n        \"mip_solver\" => optimizer_with_attributes(\n            HiGHS.Optimizer,\n            MOI.Silent() => true,\n            \"presolve\" => \"off\",\n        ),\n        \"disc_var_pick\" => 3,\n        \"presolve_bp\" => true,\n        \"presolve_bt\" => false,\n        \"max_iter\" => 2,\n        \"log_level\" => 100,\n    )\n\n    m = castro6m2(solver = test_solver)\n    JuMP.optimize!(m)\n    alpine = JuMP.backend(m).optimizer.model\n\n    @test JuMP.termination_status(m) == MOI.OTHER_LIMIT\n    @test JuMP.objective_value(m) <= 228.87\n\n    @test length(alpine.candidate_disc_vars) == 24\n    @test length(Set(alpine.candidate_disc_vars)) == 24\n    @test length(alpine.disc_vars) == 12\n    @test length(Set(alpine.disc_vars)) == 12\n    @test MOI.get(m, MOI.RawOptimizerAttribute(\"disc_var_pick\")) == 3\nend\n\n@testset \"Hessians disabled with user-defined multivariate functions\" begin\n    test_solver = JuMP.optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"log_level\" => 100,\n    )\n    m = Model(test_solver)\n    my_f(x, y) = (x - 1)^2 + (y - 2)^2\n    JuMP.register(m, :my_f, 2, my_f, autodiff = true)\n    @variable(m, x[1:2])\n    @NLobjective(m, Min, my_f(x[1], x[2]))\n\n    JuMP.set_optimize_hook(m, MOI.Utilities.attach_optimizer)\n    JuMP.optimize!(m)\n    JuMP.set_optimize_hook(m, nothing)\n    alpine = JuMP.backend(m).optimizer.model\n    @test !(:Hess in Alpine.features_available(alpine))\nend\n\n@testset \"test_scalar_nonlinear_function\" begin\n    model = Model(\n        optimizer_with_attributes(\n            Alpine.Optimizer,\n            \"nlp_solver\" => IPOPT,\n            \"mip_solver\" => HIGHS,\n        ),\n    )\n    @variable(model, -1 <= x[i in 1:3] <= 2)\n    @objective(model, Max, prod(x))\n    @constraint(model, x[1]^3 <= 1)\n    @constraint(model, x[2]^4 >= 1)\n    @constraint(model, x[3]^3 == 1)\n    optimize!(model)\n    @test isapprox(value.(x), [1, 2, 1]; atol = 1e-6)\n    @test isapprox(objective_value(model), 2; atol = 1e-6)\nend\n"
  },
  {
    "path": "test/test_utility.jl",
    "content": "@testset \"Utility Function Tests: Solver identifier fetch\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"minlp_solver\" => PAVITO,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => HIGHS,\n        \"presolve_bp\" => true,\n        \"disc_var_pick\" => 1,\n        \"log_level\" => 100,\n        \"max_iter\" => 2,\n    )\n\n    m = blend029_gl(solver = test_solver)\n    alpine = JuMP.backend(m).optimizer.model\n\n    Alpine._fetch_mip_solver_identifier(\n        alpine;\n        override = \"Gurobi.GurobiSolver(nothing, Any[])\",\n    )\n    @test alpine.mip_solver_id == \"Gurobi\"\n    Alpine._fetch_mip_solver_identifier(alpine; override = \"CPLEX.CplexSolver(Any[])\")\n    @test alpine.mip_solver_id == \"CPLEX\"\n    Alpine._fetch_nlp_solver_identifier(alpine; override = \"Ipopt.IpoptSolver(Any[])\")\n    @test alpine.nlp_solver_id == \"Ipopt\"\nend\n\n@testset \"Solver Funtion Tests :: Embedding\" begin\n    ebdmap = Alpine.embedding_map(5)\n    @test ebdmap[:L] == 2\n    @test ebdmap[:H] == [[0, 0], [0, 1], [1, 1], [1, 0]]\n    @test ebdmap[1] == Set([4, 5])\n    @test ebdmap[2] == Set([3])\n    @test ebdmap[3] == Set([2, 1])\n    @test ebdmap[4] == Set([5, 1])\n\n    ebdmap = Alpine.embedding_map(9)\n    @test ebdmap[:L] == 3\n    @test ebdmap[:H_orig] == [\"000\", \"001\", \"011\", \"010\", \"110\", \"111\", \"101\", \"100\"]\n    @test ebdmap[:H] == [\n        [0, 0, 0],\n        [0, 0, 1],\n        [0, 1, 1],\n        [0, 1, 0],\n        [1, 1, 0],\n        [1, 1, 1],\n        [1, 0, 1],\n        [1, 0, 0],\n    ]\n    @test ebdmap[1] == Set([7, 9, 8, 6])\n    @test ebdmap[2] == Set([4, 5, 6])\n    @test ebdmap[3] == Set([7, 3])\n    @test ebdmap[4] == Set([4, 3, 2, 1])\n    @test ebdmap[5] == Set([9, 2, 8, 1])\n    @test ebdmap[6] == Set([9, 5, 1])\n\n    ebdmap = Alpine.embedding_map(12)\n    @test ebdmap[:L] == 4\n    @test ebdmap[:H_orig] == [\n        \"0000\",\n        \"0001\",\n        \"0011\",\n        \"0010\",\n        \"0110\",\n        \"0111\",\n        \"0101\",\n        \"0100\",\n        \"1100\",\n        \"1101\",\n        \"1111\",\n        \"1110\",\n        \"1010\",\n        \"1011\",\n        \"1001\",\n        \"1000\",\n    ]\n    @test ebdmap[:H] == [\n        [0, 0, 0, 0],\n        [0, 0, 0, 1],\n        [0, 0, 1, 1],\n        [0, 0, 1, 0],\n        [0, 1, 1, 0],\n        [0, 1, 1, 1],\n        [0, 1, 0, 1],\n        [0, 1, 0, 0],\n        [1, 1, 0, 0],\n        [1, 1, 0, 1],\n        [1, 1, 1, 1],\n        [1, 1, 1, 0],\n        [1, 0, 1, 0],\n        [1, 0, 1, 1],\n        [1, 0, 0, 1],\n        [1, 0, 0, 0],\n    ]\n    @test ebdmap[1] == Set([10, 11, 12])\n    @test ebdmap[2] == Set([7, 9, 10, 11, 8, 6, 12])\n    @test ebdmap[3] == Set([4, 5, 6, 12])\n    @test ebdmap[4] == Set([7, 3, 11, 12])\n    @test ebdmap[5] == Set([7, 4, 2, 3, 5, 8, 6, 1])\n    @test ebdmap[6] == Set([4, 2, 3, 1])\n    @test ebdmap[7] == Set([9, 10, 2, 8, 1])\n    @test ebdmap[8] == Set([9, 5, 1])\nend\n\n@testset \"Utility Function Tests: check_solution_history test\" begin\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 10,\n        \"disc_consecutive_forbid\" => false,\n    )\n\n    m1 = mathopt(solver = test_solver)\n    JuMP.optimize!(m1)\n    alpine1 = JuMP.backend(m1).optimizer.model\n\n    Alpine.variable_values(m1)\n\n    test_solver = optimizer_with_attributes(\n        Alpine.Optimizer,\n        \"nlp_solver\" => IPOPT,\n        \"mip_solver\" => PAVITO,\n        \"presolve_bt\" => false,\n        \"partition_scaling_factor\" => 10,\n        \"disc_consecutive_forbid\" => true,\n    )\n\n    m2 = mathopt(solver = test_solver)\n    JuMP.optimize!(m2)\n    alpine2 = JuMP.backend(m2).optimizer.model\n\n    @test termination_status(m1) == MOI.OPTIMAL\n    @test termination_status(m2) == MOI.OPTIMAL\n    @test alpine1.logs[:n_iter] >= alpine2.logs[:n_iter]\n    @test isapprox(JuMP.objective_value(m1), JuMP.objective_value(m2), atol = 1E-5)\nend\n"
  }
]